{
 "sector": "S3",
 "note": "Left null vectors v of the response matrices A(eps) of Eq. (27) (v^T A = 0), i.e. the flow-free directions of Table 3, normalized to 1 on one support row.  The relation among master integrals is sum_row weight[row] * M[row] = 0 at each eps.  Rows are response-matrix rows (field response_matrix_row of the masters above).  Weights that are rational and independent of eps are given exactly; the others are given at the twelve eps values of the computation.",
 "eps_grid": [
  "0.0003114995735603784084585420144685587089594",
  "0.0003104656021947690595436839176405119643851",
  "0.0003084681229037284362826933778519755147468",
  "0.0003056432605996104618809126321647189760712",
  "0.0003021835249805230940456316082359488035615",
  "0.0002983246913110740122426265998887033945465",
  "0.0002943297327289927657206455203116304952699",
  "0.0002904708990595436839176405119643850862549",
  "0.0002870111634404563160823594880356149137451",
  "0.0002841863011363383416805787423483583750696",
  "0.0002821888218452977184195882025598219254313",
  "0.0002811548504796883695047301057317751808570"
 ],
 "left_null_vectors": [
  {
   "support": [
    "Itilde_1",
    "Itilde_5",
    "Itilde_7"
   ],
   "rows": [
    1,
    5,
    7
   ],
   "normalized_row": 7,
   "per_eps": [
    {
     "eps": "0.0003114995735603784084585420144685587089594",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740586753901385070360131144824258073831353392",
       "im": "-1.43697099413175941017773214061890407655712116e-80"
      },
      "Itilde_5": {
       "re": "0.0740509792486182111373602302460478136333058724",
       "im": "2.49315467566719596893285386217790408327607872e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "2.82e-79",
     "residual_vT_A": "3.01e-80"
    },
    {
     "eps": "0.0003104656021947690595436839176405119643851",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740587265564768124200629802872827592725682954",
       "im": "-1.46145877743139287304923602461823734475944308e-80"
      },
      "Itilde_5": {
       "re": "0.0740510559768944764161062160506772410302221706",
       "im": "2.51009411058082988186718085447022831288869361e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "2.86e-79",
     "residual_vT_A": "3.03e-80"
    },
    {
     "eps": "0.0003084681229037284362826933778519755147468",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740588254012521593331743134836677536191217898",
       "im": "-1.51015723951702144901811771082554448576116957e-80"
      },
      "Itilde_5": {
       "re": "0.0740512042032424480389399160142969988849087355",
       "im": "2.54328740664900994423079310048907579077567356e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 45,
     "max_off_support_weight": "2.93e-79",
     "residual_vT_A": "3.07e-80"
    },
    {
     "eps": "0.0003056432605996104618809126321647189760712",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740589651866247291922353437164076542262261546",
       "im": "-1.58229696589214939754654404331385668653045519e-80"
      },
      "Itilde_5": {
       "re": "0.0740514138240310779359155821577360820577782774",
       "im": "2.59130975059581536128959289573763445071547731e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.05e-79",
     "residual_vT_A": "3.14e-80"
    },
    {
     "eps": "0.0003021835249805230940456316082359488035615",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740591363844528099581620413775497737682999928",
       "im": "-1.67620156174178818461205451431321378604945917e-80"
      },
      "Itilde_5": {
       "re": "0.0740516705513515516586609456176968466909058053",
       "im": "2.65190758027071849264793120286090032118576261e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.20e-79",
     "residual_vT_A": "3.22e-80"
    },
    {
     "eps": "0.0002983246913110740122426265998887033945465",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740593273261558043548266760573784453858403025",
       "im": "-1.78872321432396422755780758430900452407647329e-80"
      },
      "Itilde_5": {
       "re": "0.074051956887411075019120478928119874452982707",
       "im": "2.72190945093239141741061945598065237916620085e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.37e-79",
     "residual_vT_A": "3.31e-80"
    },
    {
     "eps": "0.0002943297327289927657206455203116304952699",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740595249983726186402062084925509346364012001",
       "im": "-1.9146429132643549930351081625998408858280209e-80"
      },
      "Itilde_5": {
       "re": "0.0740522533175813795138933661033277651317001776",
       "im": "2.79719085520859967462396605350260275300148785e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.57e-79",
     "residual_vT_A": "3.40e-80"
    },
    {
     "eps": "0.0002904708990595436839176405119643850862549",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740597159300685473468253064893026037941119755",
       "im": "-2.04624126049052372761141883750619701345975114e-80"
      },
      "Itilde_5": {
       "re": "0.074052539640636464877367884048417802683501285",
       "im": "2.87275744626632935771187815539238478864251035e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.77e-79",
     "residual_vT_A": "3.50e-80"
    },
    {
     "eps": "0.0002870111634404563160823594880356149137451",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740598871105638818875877861999909661354463261",
       "im": "-2.17332662114844479726310280277665774409192378e-80"
      },
      "Itilde_5": {
       "re": "0.0740527963454325912501413845049073866105322076",
       "im": "2.94300603644033743960027684434208675840883953e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.97e-79",
     "residual_vT_A": "3.59e-80"
    },
    {
     "eps": "0.0002841863011363383416805787423483583750696",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740600268759223203220289514490332922853371298",
       "im": "-2.28400020852051057221028598629059345607287057e-80"
      },
      "Itilde_5": {
       "re": "0.0740530059402123451078536393997438483971946265",
       "im": "3.00219166085905903600779640683553490785367375e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.14e-79",
     "residual_vT_A": "3.67e-80"
    },
    {
     "eps": "0.0002821888218452977184195882025598219254313",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740601257033649209658635803227798431872802001",
       "im": "-2.36626135091479144628665457347640035741913779e-80"
      },
      "Itilde_5": {
       "re": "0.0740531541440359693359630951962986807351899302",
       "im": "3.04506957769381144935313258820666046859139971e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.26e-79",
     "residual_vT_A": "3.73e-80"
    },
    {
     "eps": "0.0002811548504796883695047301057317751808570",
     "weights": {
      "Itilde_1": {
       "re": "-0.0740601768596961606146268089021999174279765645",
       "im": "-2.41020775550161760794774791914540646281028418e-80"
      },
      "Itilde_5": {
       "re": "0.074053230859307796571505021472782702404432248",
       "im": "3.06760759400022099053225307659755693308816581e-83"
      },
      "Itilde_7": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.33e-79",
     "residual_vT_A": "3.76e-80"
    }
   ],
   "weight_digits": "two extractions at 60 and 120 digits agree to the number of digits listed per eps (at least 45)",
   "weights_at_eps_0": "(-2/27, 2/27, 1) (Table 5 of the paper)"
  },
  {
   "support": [
    "Itilde_1",
    "Itilde_5",
    "Itilde_6"
   ],
   "rows": [
    1,
    5,
    6
   ],
   "normalized_row": 6,
   "per_eps": [
    {
     "eps": "0.0003114995735603784084585420144685587089594",
     "weights": {
      "Itilde_1": {
       "re": "-0.129660426997500763705751548812926163011507099",
       "im": "-7.16727390963150073090545558036751751695731167e-81"
      },
      "Itilde_5": {
       "re": "0.296296299496743783916673891855742435891936197",
       "im": "1.27991020564068962295899120765623016036854526e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "2.82e-79",
     "residual_vT_A": "3.01e-80"
    },
    {
     "eps": "0.0003104656021947690595436839176405119643851",
     "weights": {
      "Itilde_1": {
       "re": "-0.129660324664824152937651817203212259232641187",
       "im": "-7.2895387834420317935023275936307418938774991e-81"
      },
      "Itilde_5": {
       "re": "0.296296299475512591119345078953086435454703061",
       "im": "1.28866855024167131658093732969943547294584263e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "2.86e-79",
     "residual_vT_A": "3.03e-80"
    },
    {
     "eps": "0.0003084681229037284362826933778519755147468",
     "weights": {
      "Itilde_1": {
       "re": "-0.129660126975273459111429150810442270539534198",
       "im": "-7.53268914164654384608686711107213363608440162e-81"
      },
      "Itilde_5": {
       "re": "0.296296299434697542372511779122128701789559384",
       "im": "1.30583256995587939543775732327110178436878555e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 45,
     "max_off_support_weight": "2.93e-79",
     "residual_vT_A": "3.07e-80"
    },
    {
     "eps": "0.0003056432605996104618809126321647189760712",
     "weights": {
      "Itilde_1": {
       "re": "-0.129659847404528319393307090344962469325325469",
       "im": "-7.89289175987057411719604631543770938026946298e-81"
      },
      "Itilde_5": {
       "re": "0.296296299377427317480895899916457934051772379",
       "im": "1.33066879809984594434160522123124125512703842e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.05e-79",
     "residual_vT_A": "3.14e-80"
    },
    {
     "eps": "0.0003021835249805230940456316082359488035615",
     "weights": {
      "Itilde_1": {
       "re": "-0.129659505008872157861453695022678230241177792",
       "im": "-8.36178828165697350066935258492846338686988088e-81"
      },
      "Itilde_5": {
       "re": "0.296296299308005670054751216884705519371789149",
       "im": "1.36201591741171049270829124751429769989561258e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.20e-79",
     "residual_vT_A": "3.22e-80"
    },
    {
     "eps": "0.0002983246913110740122426265998887033945465",
     "weights": {
      "Itilde_1": {
       "re": "-0.129659123125466169068124425663020887006097173",
       "im": "-8.92367380294684331885643340057525774341846265e-81"
      },
      "Itilde_5": {
       "re": "0.296296299231510701820213798175385539707555587",
       "im": "1.39823753282983298752384628978984976054254318e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.37e-79",
     "residual_vT_A": "3.31e-80"
    },
    {
     "eps": "0.0002943297327289927657206455203116304952699",
     "weights": {
      "Itilde_1": {
       "re": "-0.129658727781032540497365360792675908504975378",
       "im": "-9.55249654113666926504478492164817711241261502e-81"
      },
      "Itilde_5": {
       "re": "0.296296299153355784886917386697834696510431711",
       "im": "1.43720262398744926876687030108748706280320731e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.57e-79",
     "residual_vT_A": "3.40e-80"
    },
    {
     "eps": "0.0002904708990595436839176405119643850862549",
     "weights": {
      "Itilde_1": {
       "re": "-0.129658345917640683084127164799172570189553827",
       "im": "-1.02097094228744750690084943809398148046159964e-80"
      },
      "Itilde_5": {
       "re": "0.296296299078866977190463257647797230325666655",
       "im": "1.47632734326469065159347265025073466979608541e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.77e-79",
     "residual_vT_A": "3.50e-80"
    },
    {
     "eps": "0.0002870111634404563160823594880356149137451",
     "weights": {
      "Itilde_1": {
       "re": "-0.129658003556650014002602205377795845506885126",
       "im": "-1.08444090976486023895542748751883445633008885e-80"
      },
      "Itilde_5": {
       "re": "0.296296299012920101752093038538254270740696052",
       "im": "1.51270934250329420557045911618091867086230932e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.97e-79",
     "residual_vT_A": "3.59e-80"
    },
    {
     "eps": "0.0002841863011363383416805787423483583750696",
     "weights": {
      "Itilde_1": {
       "re": "-0.129657724025933137133719874879711193207103518",
       "im": "-1.13971595990015248886475419678812410540064939e-80"
      },
      "Itilde_5": {
       "re": "0.296296298959662197958143545559527243302522265",
       "im": "1.54336970331143557116259439643406312823741622e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.14e-79",
     "residual_vT_A": "3.67e-80"
    },
    {
     "eps": "0.0002821888218452977184195882025598219254313",
     "weights": {
      "Itilde_1": {
       "re": "-0.129657526371047935846050617132218091403217378",
       "im": "-1.18080140185888231782927155190538717799828853e-80"
      },
      "Itilde_5": {
       "re": "0.296296298922321921220501058045462249287602963",
       "im": "1.56558654918013193320702739970803728797114363e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.26e-79",
     "residual_vT_A": "3.73e-80"
    },
    {
     "eps": "0.0002811548504796883695047301057317751808570",
     "weights": {
      "Itilde_1": {
       "re": "-0.129657424058385456548524159973377942921824649",
       "im": "-1.20275072055940072921285293880887038785305406e-80"
      },
      "Itilde_5": {
       "re": "0.296296298903096888982898141452816159595800735",
       "im": "1.57726594406179793266954761632567261043341151e-83"
      },
      "Itilde_6": {
       "re": "1.0",
       "im": "0.0"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.33e-79",
     "residual_vT_A": "3.76e-80"
    }
   ],
   "weight_digits": "two extractions at 60 and 120 digits agree to the number of digits listed per eps (at least 45)",
   "weights_at_eps_0": "(-7/54, 8/27, 1) (Table 5 of the paper)"
  },
  {
   "support": [
    "Itilde_3",
    "Itilde_4",
    "Itilde_9",
    "Itilde_10",
    "Itilde_19",
    "Itilde_20",
    "Itilde_23",
    "Itilde_24",
    "Itilde_31",
    "Itilde_32"
   ],
   "rows": [
    3,
    4,
    9,
    10,
    19,
    20,
    23,
    24,
    31,
    32
   ],
   "normalized_row": 24,
   "per_eps": [
    {
     "eps": "0.0003114995735603784084585420144685587089594",
     "weights": {
      "Itilde_3": {
       "re": "0.170378082179493954893174279270267366449729503",
       "im": "-1.44917931648010248253892274712838678326465601e-80"
      },
      "Itilde_4": {
       "re": "0.0284361604616928893593031369836660830953490651",
       "im": "-1.22259841561793132430066441687156774576544105e-78"
      },
      "Itilde_9": {
       "re": "0.49994803484303389878262030944987911066063155",
       "im": "-4.58592721199264937005877716842648055288407271e-80"
      },
      "Itilde_10": {
       "re": "0.416623362369194915652183591208232592217192958",
       "im": "-3.21908425600088313657847263006834240943994837e-80"
      },
      "Itilde_19": {
       "re": "-0.119892249896834464800967346624402334153303004",
       "im": "9.91987879731997131621840701236498371582835213e-81"
      },
      "Itilde_20": {
       "re": "0.0999102082473620540008061221870019451277525036",
       "im": "-8.74365714837795031956376979926198201898897304e-81"
      },
      "Itilde_23": {
       "re": "0.125038998186287037502953163734589397589470502",
       "im": "2.48099992998479076164688017913998704445218858e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.029935605301777611210635478857703656108237566",
       "im": "2.5424977099458954468420712083982807267668795e-81"
      },
      "Itilde_32": {
       "re": "-0.240008997687955291578067962382415904642287666",
       "im": "2.03851091350339124996582109275922084768287164e-80"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "2.82e-79",
     "residual_vT_A": "3.01e-80"
    },
    {
     "eps": "0.0003104656021947690595436839176405119643851",
     "weights": {
      "Itilde_3": {
       "re": "0.170378135462848288036051331435910063113697507",
       "im": "-1.45959753854471892802580812626469795273832392e-80"
      },
      "Itilde_4": {
       "re": "0.0284360371712456148129085068192572204357908925",
       "im": "-1.23515213272411043844339743718767398410264885e-78"
      },
      "Itilde_9": {
       "re": "0.499948207493592465515189271895577540377649786",
       "im": "-4.61898092828532758341408541536939445325668129e-80"
      },
      "Itilde_10": {
       "re": "0.416623506244660387929324393246314616981374822",
       "im": "-3.24228392917875045298652400295115780280609703e-80"
      },
      "Itilde_19": {
       "re": "-0.119891971922562509808322834153514319458251287",
       "im": "9.97474461053824550663018944465782521237926176e-81"
      },
      "Itilde_20": {
       "re": "0.0999099766021354248402690284612619328818760728",
       "im": "-8.79312462066004000221080536335864746445283909e-81"
      },
      "Itilde_23": {
       "re": "0.125038868536993066041977682173342552279608798",
       "im": "2.50612386366778961297911555537403849390936475e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299356605950761315123639698756406286328993181",
       "im": "2.55667662353643243108672102482169203131069986e-81"
      },
      "Itilde_32": {
       "re": "-0.240007694646255847765747538104354308721664469",
       "im": "2.04986423170266988232015995303569313935441198e-80"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "2.86e-79",
     "residual_vT_A": "3.03e-80"
    },
    {
     "eps": "0.0003084681229037284362826933778519755147468",
     "weights": {
      "Itilde_3": {
       "re": "0.170378238392214067733809652602948410568824005",
       "im": "-1.48010070825577499662960407165257198383885032e-80"
      },
      "Itilde_4": {
       "re": "0.0284357989916772310451595075547510130359424636",
       "im": "-1.25999799032137703079833331915049218719285304e-78"
      },
      "Itilde_9": {
       "re": "0.499948541025823199319866113567656849653470344",
       "im": "-4.68381274284389245589243375109088794938371009e-80"
      },
      "Itilde_10": {
       "re": "0.41662378418818599943322176130638070804455862",
       "im": "-3.28778787465942569257892537801412290045363613e-80"
      },
      "Itilde_19": {
       "re": "-0.119891434905004980947555788721037650988459585",
       "im": "1.00940900119909046082362404034924756442790969e-80"
      },
      "Itilde_20": {
       "re": "0.0999095290875041507896298239341980424903829874",
       "im": "-8.89929850105893630204566106627940118062644931e-81"
      },
      "Itilde_23": {
       "re": "0.125038618077592491586614830588585118722967587",
       "im": "2.54329886579330919113624476877206491011281276e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299357674018200057362637979924324834866143448",
       "im": "2.58739228562140630325887174915977658752933294e-81"
      },
      "Itilde_32": {
       "re": "-0.240005177374056182326324199136744294315277443",
       "im": "2.07446165943408612793848781732652372002155485e-80"
      }
     },
     "two_extraction_agreement_digits": 45,
     "max_off_support_weight": "2.93e-79",
     "residual_vT_A": "3.07e-80"
    },
    {
     "eps": "0.0003056432605996104618809126321647189760712",
     "weights": {
      "Itilde_3": {
       "re": "0.170378383942438234394332450536431415871975084",
       "im": "-1.50962331080506098240394291673324735929591633e-80"
      },
      "Itilde_4": {
       "re": "0.0284354621532950613153484527092481150984626378",
       "im": "-1.29606693051420360690206742925964576369587816e-78"
      },
      "Itilde_9": {
       "re": "0.499949012704797266834963218974166038984742784",
       "im": "-4.77775312099029003929695975048155812058634152e-80"
      },
      "Itilde_10": {
       "re": "0.416624177253997722362469349145138365820618986",
       "im": "-3.35372241603747174856618879678190003227092901e-80"
      },
      "Itilde_19": {
       "re": "-0.119890675419369732181608728868034443566696524",
       "im": "1.02357011378829333415508857055103415172013688e-80"
      },
      "Itilde_20": {
       "re": "0.0999088961828081101513406073900287029722471035",
       "im": "-9.02874623312319227979013147053739557357450207e-81"
      },
      "Itilde_23": {
       "re": "0.125038263883064867048639166757286922667246722",
       "im": "2.60999589047775513898276177275825915711503304e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299359184230314280851939251239374473063199641",
       "im": "2.62437635423285614606936367198583185245502305e-81"
      },
      "Itilde_32": {
       "re": "-0.240001617438453886206045771479148624645341822",
       "im": "2.10407195499802069390566868717304765343273691e-80"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.05e-79",
     "residual_vT_A": "3.14e-80"
    },
    {
     "eps": "0.0003021835249805230940456316082359488035615",
     "weights": {
      "Itilde_3": {
       "re": "0.17037856218217419619095548990199652913628224",
       "im": "-1.54705918190390239211309760161918591246240636e-80"
      },
      "Itilde_4": {
       "re": "0.0284350496096508498610901292479432661264974368",
       "im": "-1.34219696347750278078593774724464194128475048e-78"
      },
      "Itilde_9": {
       "re": "0.49994959038030019137028867289890647668385374",
       "im": "-4.89654468317180025958862853508030758700511803e-80"
      },
      "Itilde_10": {
       "re": "0.416624658650250159475240560749088730569878116",
       "im": "-3.43709926972616539174667701940006211606201349e-80"
      },
      "Itilde_19": {
       "re": "-0.119889745198349558484421597272867790614066357",
       "im": "1.04286664539092766921041420984474572671840474e-80"
      },
      "Itilde_20": {
       "re": "0.0999081209986246320703513310607231588450552974",
       "im": "-9.20305512466634321153693246930853121106060246e-81"
      },
      "Itilde_23": {
       "re": "0.125037830098785572314995761643807981730349979",
       "im": "2.69820824649143562244932883813602432033187574e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299361033434552398787085623435750394661704737",
       "im": "2.67431767933421851486351762876183178472806487e-81"
      },
      "Itilde_32": {
       "re": "-0.23999725746529992785421547335589515046895604",
       "im": "2.14405956470834487421813614254904790393040682e-80"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.20e-79",
     "residual_vT_A": "3.22e-80"
    },
    {
     "eps": "0.0002983246913110740122426265998887033945465",
     "weights": {
      "Itilde_3": {
       "re": "0.170378760953993496633671324112212942767042434",
       "im": "-1.59039380214922365378863738426462367238878459e-80"
      },
      "Itilde_4": {
       "re": "0.0284345894736766989706941375239809853491739695",
       "im": "-1.39624964422146215951440654573819063095732703e-78"
      },
      "Itilde_9": {
       "re": "0.499950234679443141633705587109540250150814898",
       "im": "-5.03412629891718426913237363633418859866061002e-80"
      },
      "Itilde_10": {
       "re": "0.416625195566202618028087989257950208459012415",
       "im": "-3.53366418903116446835668885807536443491387038e-80"
      },
      "Itilde_19": {
       "re": "-0.119888707613323712267573155715423482846611201",
       "im": "1.06484875340702455892469200129364940742383606e-80"
      },
      "Itilde_20": {
       "re": "0.0999072563444364268896442964295195690388426676",
       "im": "-9.40206035303005388961970290669556887855551238e-81"
      },
      "Itilde_23": {
       "re": "0.125037346293020569122537014791552674513041633",
       "im": "2.7864882757352818625392676210930639307292676e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299363095408001153307211478290970784787338578",
       "im": "2.73145186183898648755190045112747485959086827e-81"
      },
      "Itilde_32": {
       "re": "-0.23999239459871886373035858983291080653210011",
       "im": "2.18980548343393790840053230270699009054754407e-80"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.37e-79",
     "residual_vT_A": "3.31e-80"
    },
    {
     "eps": "0.0002943297327289927657206455203116304952699",
     "weights": {
      "Itilde_3": {
       "re": "0.170378966705757450869142323016149761215991383",
       "im": "-1.63728240393305738123551800575923957796956998e-80"
      },
      "Itilde_4": {
       "re": "0.0284341131021663935647720210217270279610210329",
       "im": "-1.45521384280951009499305452916000993539873346e-78"
      },
      "Itilde_9": {
       "re": "0.499950901691268909069683507108912954910230121",
       "im": "-5.18251377108969333655210376029685900307598587e-80"
      },
      "Itilde_10": {
       "re": "0.416625751409390757558069589257427462425191767",
       "im": "-3.63781324971948481680725505539008497079312039e-80"
      },
      "Itilde_19": {
       "re": "-0.119887633361503479774413599428515029127051537",
       "im": "1.08276810846350750224162950075563623046043955e-80"
      },
      "Itilde_20": {
       "re": "0.0999063611345862331453446661904291909392096145",
       "im": "-9.56934657787333397824047085736043215736019153e-81"
      },
      "Itilde_23": {
       "re": "0.125036845440133858499092436565420332250265871",
       "im": "2.8832482299226008516653351629151895897582227e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299365229513581334747795034262246393621413541",
       "im": "2.77883494143101292786308999282930393800291927e-81"
      },
      "Itilde_32": {
       "re": "-0.239987360246095561635511550671258571213848586",
       "im": "2.22772983898761993704155055741032131467896497e-80"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.57e-79",
     "residual_vT_A": "3.40e-80"
    },
    {
     "eps": "0.0002904708990595436839176405119643850862549",
     "weights": {
      "Itilde_3": {
       "re": "0.170379165415825246671731286297135310395939507",
       "im": "-1.68417951973988360737276860795913784433943033e-80"
      },
      "Itilde_4": {
       "re": "0.028433652959052267687433707893026836079066324",
       "im": "-1.51564455569434990248104074237224287715444044e-78"
      },
      "Itilde_9": {
       "re": "0.499951545960024411724090598939261675552279174",
       "im": "-5.33191486569236482703589420885552971318010836e-80"
      },
      "Itilde_10": {
       "re": "0.416626288300020343103408832449384729626899312",
       "im": "-3.74267344361318042000001372001808747032558715e-80"
      },
      "Itilde_19": {
       "re": "-0.11988659565138031226383424646002592149598619",
       "im": "1.11134511975133898472636594301901177876509527e-80"
      },
      "Itilde_20": {
       "re": "0.0999054963761502602198618720500216012466551582",
       "im": "-9.82384480294621212321118249123831169091518163e-81"
      },
      "Itilde_23": {
       "re": "0.125036361672420839910404903739601375697218615",
       "im": "2.97128534605314938306722401507219920564590293e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299367290315571271422437239895458901040963016",
       "im": "2.85250734181793743147477471448705919889601246e-81"
      },
      "Itilde_32": {
       "re": "-0.239982497490243632532841857853191121044554216",
       "im": "2.28672853352363466427595156422079542830563726e-80"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.77e-79",
     "residual_vT_A": "3.50e-80"
    },
    {
     "eps": "0.0002870111634404563160823594880356149137451",
     "weights": {
      "Itilde_3": {
       "re": "0.170379343548604464834610696588327498076680592",
       "im": "-1.7280662805855175619819032863227598653545798e-80"
      },
      "Itilde_4": {
       "re": "0.0284332404030412566158883911080831664508759614",
       "im": "-1.57242816863757054437145165668824225538403806e-78"
      },
      "Itilde_9": {
       "re": "0.499952123582894733050960616094379413926088954",
       "im": "-5.47120343203606362934943217726363092516427145e-80"
      },
      "Itilde_10": {
       "re": "0.416626769652412277542467180078649511605074128",
       "im": "-3.84043582888692490986049662193444257477703904e-80"
      },
      "Itilde_19": {
       "re": "-0.119885665213685221696547803144091844687088671",
       "im": "1.13271678110544901437261551279320717637346867e-80"
      },
      "Itilde_20": {
       "re": "0.0999047210114043514137898359534098705725738923",
       "im": "-1.00177968300263334200414378535697092086058725e-80"
      },
      "Itilde_23": {
       "re": "0.125035927954049515973677681610411445923467007",
       "im": "3.08018528127879848737671415682704785142750467e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.029936913749078319230436723960334457467142024",
       "im": "2.90788003412755682315194972117608173474997781e-81"
      },
      "Itilde_32": {
       "re": "-0.239978137708878161346352009583011638206044025",
       "im": "2.33106142271241536228442224326679969575708764e-80"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.97e-79",
     "residual_vT_A": "3.59e-80"
    },
    {
     "eps": "0.0002841863011363383416805787423483583750696",
     "weights": {
      "Itilde_3": {
       "re": "0.170379488975325621779881293228641018601842612",
       "im": "-1.7651086441520923532009772100376268418073718e-80"
      },
      "Itilde_4": {
       "re": "0.0284329035503791364318273341818714294368715616",
       "im": "-1.62089273256019336653834993818261685165829329e-78"
      },
      "Itilde_9": {
       "re": "0.499952595201093905238027944259497325250774389",
       "im": "-5.58885560605697601201971709898138287434817094e-80"
      },
      "Itilde_10": {
       "re": "0.416627162667578254365023286882914437708978658",
       "im": "-3.92301213175280404795259298386449847406587462e-80"
      },
      "Itilde_19": {
       "re": "-0.119884905477855328947749187346338138712816728",
       "im": "1.15048810606553456626967061786673848644435452e-80"
      },
      "Itilde_20": {
       "re": "0.0999040878982127741231243227886151155940139404",
       "im": "-1.0179448536680835505409745743571347492691407e-80"
      },
      "Itilde_23": {
       "re": "0.125035573835625861020415514432363926762485448",
       "im": "3.16078291901194955283565633794937161435695789e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.02993706453599797645733886216250918583149434",
       "im": "2.95412649983122938844506768557856046365742369e-81"
      },
      "Itilde_32": {
       "re": "-0.2399745779947341337419204043740484992214278",
       "im": "2.36808695594256715083146893094400286766038011e-80"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.14e-79",
     "residual_vT_A": "3.67e-80"
    },
    {
     "eps": "0.0002821888218452977184195882025598219254313",
     "weights": {
      "Itilde_3": {
       "re": "0.170379591797734657411466458752988219495955691",
       "im": "-1.79026685985138291665482285412224666936435883e-80"
      },
      "Itilde_4": {
       "re": "0.0284326653584439525667230126017790132722305858",
       "im": "-1.65596871470088015516276269360601722201076542e-78"
      },
      "Itilde_9": {
       "re": "0.499952928680692035725503368925834002852164964",
       "im": "-5.67425783024594273885320738114596384626423332e-80"
      },
      "Itilde_10": {
       "re": "0.41662744056724336310458614077152833571013747",
       "im": "-3.98295326201554327518494380395252533709976321e-80"
      },
      "Itilde_19": {
       "re": "-0.119884368243622881826697287644381019242931431",
       "im": "1.15372702119789179995842290826885707126111255e-80"
      },
      "Itilde_20": {
       "re": "0.0999036402030190681889144063703175160357761924",
       "im": "-1.02208882791711416183755663525801123151327546e-80"
      },
      "Itilde_23": {
       "re": "0.125035323442133257737556909930073108447035852",
       "im": "3.26136093586525914594165130014188637278427619e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299371711398392294278591924604686588977164756",
       "im": "2.96429078338534664949120349415829085708576091e-81"
      },
      "Itilde_32": {
       "re": "-0.239972060914322953936703493943917807054776897",
       "im": "2.3762020878709071777971738094604810928173332e-80"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.26e-79",
     "residual_vT_A": "3.73e-80"
    },
    {
     "eps": "0.0002811548504796883695047301057317751808570",
     "weights": {
      "Itilde_3": {
       "re": "0.170379645019337485474822671937150922645133187",
       "im": "-1.80614146673668543220888423899293591467190356e-80"
      },
      "Itilde_4": {
       "re": "0.0284325420608567025525124732449455341783268334",
       "im": "-1.67522807689875130685744574221246352676905188e-78"
      },
      "Itilde_9": {
       "re": "0.499953101300863154736889379879652351365659405",
       "im": "-5.71920843738175077990761729421362247528125788e-80"
      },
      "Itilde_10": {
       "re": "0.416627584417385962280741149899710292804716171",
       "im": "-4.01450243898250620564889623140334995820747156e-80"
      },
      "Itilde_19": {
       "re": "-0.119884090144253604136027628897216905200638633",
       "im": "1.16971977934906912868414438413466183650380858e-80"
      },
      "Itilde_20": {
       "re": "0.0999034084535446701133563574143474210005321944",
       "im": "-1.03548063464682792548951058882989327708468401e-80"
      },
      "Itilde_23": {
       "re": "0.12503519383089127126023227514019319188769758",
       "im": "3.24177643171031572489099056577876421078633384e-83"
      },
      "Itilde_24": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_31": {
       "re": "-0.0299372263159918663837695427341323453937885731",
       "im": "3.0043374019501050341343199739518753380312465e-81"
      },
      "Itilde_32": {
       "re": "-0.239970757983352643626924462022760693671052448",
       "im": "2.4082853624313714016154085327851005890567039e-80"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.33e-79",
     "residual_vT_A": "3.76e-80"
    }
   ],
   "weight_digits": "two extractions at 60 and 120 digits agree to the number of digits listed per eps (at least 45)"
  },
  {
   "support": [
    "Itilde_0",
    "Itilde_3",
    "Itilde_4",
    "Itilde_19",
    "Itilde_20",
    "Itilde_31",
    "Itilde_32"
   ],
   "rows": [
    0,
    3,
    4,
    19,
    20,
    31,
    32
   ],
   "normalized_row": 0,
   "per_eps": [
    {
     "eps": "0.0003114995735603784084585420144685587089594",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.40898197180517398336647489202431874609941437",
       "im": "-1.89094443060237403313808527006007655040168726e-83"
      },
      "Itilde_4": {
       "re": "0.0682592316301539597926490083760403336280936415",
       "im": "-5.7457682918208435909742559926828414508443009e-80"
      },
      "Itilde_19": {
       "re": "-0.287139456142102365470643753761521518718038471",
       "im": "-2.19609681400519936808619932714846174368441673e-82"
      },
      "Itilde_20": {
       "re": "0.239282880118418637892203128134601265598365393",
       "im": "2.26186821507628176461364302195089648996165812e-82"
      },
      "Itilde_31": {
       "re": "-0.0716951548831015221240090466292035334314870441",
       "im": "-6.06880207264037192335807810774181276538382512e-83"
      },
      "Itilde_32": {
       "re": "-0.574816580092807054737037543288260306421231593",
       "im": "-4.86015131226829060273357883948837459745581817e-82"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "2.82e-79",
     "residual_vT_A": "3.01e-80"
    },
    {
     "eps": "0.0003104656021947690595436839176405119643851",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408981851266132666941615274202943460063150272",
       "im": "-1.9155558327217295949036460331605963436439348e-83"
      },
      "Itilde_4": {
       "re": "0.0682588942141847109735149874317580880296195613",
       "im": "-5.80690205211694991956352483271118185684928472e-80"
      },
      "Itilde_19": {
       "re": "-0.28714078719551380433849432818879187340856001",
       "im": "-2.21230260851490257724291989693072222015270012e-82"
      },
      "Itilde_20": {
       "re": "0.239283989329594836948745273490659894507133342",
       "im": "2.27935140614619130894663665454290429793968167e-82"
      },
      "Itilde_31": {
       "re": "-0.0716957858866465665614938728146800122130810224",
       "im": "-6.12375918550807388696233453863824685567186902e-83"
      },
      "Itilde_32": {
       "re": "-0.574817456653551660183088150124824552922328863",
       "im": "-4.90415287568913789333680720710660913644232105e-82"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "2.86e-79",
     "residual_vT_A": "3.03e-80"
    },
    {
     "eps": "0.0003084681229037284362826933778519755147468",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408981618404429007906065714936626854698093544",
       "im": "-2.13128640913080998711156606826248623040262566e-83"
      },
      "Itilde_4": {
       "re": "0.0682582423787440598024142828187178242567189881",
       "im": "-5.95368889371117270861849823001215631548886589e-80"
      },
      "Itilde_19": {
       "re": "-0.287143358560661090894236668714764636617268142",
       "im": "-1.95014641855036760868335901583453914096854319e-82"
      },
      "Itilde_20": {
       "re": "0.239286132133884242411863890595637197181056785",
       "im": "2.08384894446934859780789678176106254802068478e-82"
      },
      "Itilde_31": {
       "re": "-0.0716970048749538289457458501740257884536262551",
       "im": "-5.50353221941328276531444819340386871459836288e-83"
      },
      "Itilde_32": {
       "re": "-0.574819149989643838574624557027390195925214937",
       "im": "-4.40679894853754976427348114860297996334795808e-82"
      }
     },
     "two_extraction_agreement_digits": 45,
     "max_off_support_weight": "2.93e-79",
     "residual_vT_A": "3.07e-80"
    },
    {
     "eps": "0.0003056432605996104618809126321647189760712",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408981289092394193786698297678742049569136308",
       "im": "-2.00230020466827147039124671712551782393149204e-83"
      },
      "Itilde_4": {
       "re": "0.0682573205490763033707841719851774821783100021",
       "im": "-6.12053803083784002698863294715401284138472768e-80"
      },
      "Itilde_19": {
       "re": "-0.287146994946821527694327203855436211233757854",
       "im": "-2.29020457731707769865315669731333922464686122e-82"
      },
      "Itilde_20": {
       "re": "0.239289162455684606411939336546196842694798212",
       "im": "2.3600045582736953078381913513346022805175305e-82"
      },
      "Itilde_31": {
       "re": "-0.0716987287466551529897667216708059495314273937",
       "im": "-6.33148871921450129570062080461038276399725344e-83"
      },
      "Itilde_32": {
       "re": "-0.574821544617760758168235480224323865130726467",
       "im": "-5.07043793544267355024367991341365926895073003e-82"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.05e-79",
     "residual_vT_A": "3.14e-80"
    },
    {
     "eps": "0.0003021835249805230940456316082359488035615",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408980885775783204361974027749855654254119578",
       "im": "-2.09548848819624283900938552223032318961355172e-83"
      },
      "Itilde_4": {
       "re": "0.0682561915506648435544323208410676931026783487",
       "im": "-6.35205604076950927451110449382097031684611157e-80"
      },
      "Itilde_19": {
       "re": "-0.287151448475120270028398622978883439042324421",
       "im": "-2.33682663338894002112228138846794949198517757e-82"
      },
      "Itilde_20": {
       "re": "0.239292873729266891690332185815736199201937017",
       "im": "2.41313203119935377656847403072159613900661308e-82"
      },
      "Itilde_31": {
       "re": "-0.071700839988876721722472179417772335526178429",
       "im": "-6.49241823184241448128415549189426199725782139e-83"
      },
      "Itilde_32": {
       "re": "-0.574824477249501736300671909225709402414278912",
       "im": "-5.19924956835985396266726620594635130821021123e-82"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.20e-79",
     "residual_vT_A": "3.22e-80"
    },
    {
     "eps": "0.0002983246913110740122426265998887033945465",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408980435943146107752984472766546215843502028",
       "im": "-2.1612976773529393334192626152304499241858093e-83"
      },
      "Itilde_4": {
       "re": "0.0682549323266229207753425085479998765588511642",
       "im": "-6.62683054570499048968719738506736222903229882e-80"
      },
      "Itilde_19": {
       "re": "-0.28715641558853019863095980426216624444775339",
       "im": "-2.40877832497971847971393706024263534097725702e-82"
      },
      "Itilde_20": {
       "re": "0.239297012990441832192466503551805203706461158",
       "im": "2.48583941945293379299295867270079867636894367e-82"
      },
      "Itilde_31": {
       "re": "-0.0717031946946229889586738559913655174371241421",
       "im": "-6.67425459719219064379405091179692824990484508e-83"
      },
      "Itilde_32": {
       "re": "-0.57482774794560721953885388526784544159987717",
       "im": "-5.34481173412433944519162674535245918709497659e-82"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.37e-79",
     "residual_vT_A": "3.31e-80"
    },
    {
     "eps": "0.0002943297327289927657206455203116304952699",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408979970251674302246961926390678882186458101",
       "im": "-2.60693125867411327925404903827550921071955632e-83"
      },
      "Itilde_4": {
       "re": "0.0682536286931465891809878262571643792420876313",
       "im": "-6.91228315703651001776968704169094215381755339e-80"
      },
      "Itilde_19": {
       "re": "-0.287161557753901428623790144539608068636840766",
       "im": "-3.79010466858020190588557663592853415873905686e-82"
      },
      "Itilde_20": {
       "re": "0.239301298128251190519825120449673390530700638",
       "im": "3.62984290919958239017516676966940072345775523e-82"
      },
      "Itilde_31": {
       "re": "-0.0717056323776580747935946737829632233112022691",
       "im": "-1.00744244632840263078561768639113851831901827e-82"
      },
      "Itilde_32": {
       "re": "-0.574831133764331332263014974826579823355220946",
       "im": "-8.07034473672866595343047927634147335310610294e-82"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.57e-79",
     "residual_vT_A": "3.40e-80"
    },
    {
     "eps": "0.0002904708990595436839176405119643850862549",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408979520437470623035182281022827479612008431",
       "im": "-2.32532257638117754888727598207219248190967005e-83"
      },
      "Itilde_4": {
       "re": "0.0682523694907038990916454026866790722075710212",
       "im": "-7.27785085321983523083962102632750606603241992e-80"
      },
      "Itilde_19": {
       "re": "-0.287166524541165815300022154287464970308448431",
       "im": "-2.57145621976747601097734419627611772660989827e-82"
      },
      "Itilde_20": {
       "re": "0.239305437117638179416685128572887475257040359",
       "im": "2.64899996499472263446021773161998267659499458e-82"
      },
      "Itilde_31": {
       "re": "-0.0717079869139140199523256540394203440937291905",
       "im": "-7.06441118291929680442332753881443320493064998e-83"
      },
      "Itilde_32": {
       "re": "-0.574834403967737162133373256479180167171943879",
       "im": "-5.65714063617857237267625241196258450113657049e-82"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.77e-79",
     "residual_vT_A": "3.50e-80"
    },
    {
     "eps": "0.0002870111634404563160823594880356149137451",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408979117152787249366601074628105355490970319",
       "im": "-2.46830418611369072220845798022934759428135545e-83"
      },
      "Itilde_4": {
       "re": "0.0682512405297034074840879879516755721055118513",
       "im": "-7.56649503195463155951300033737131130127441727e-80"
      },
      "Itilde_19": {
       "re": "-0.28717097750456390855054148351430098546955698",
       "im": "-2.62116037704786907106562384557841828500676742e-82"
      },
      "Itilde_20": {
       "re": "0.23930914792046992379211790292858415455796415",
       "im": "2.70872856877206592486107094149704509518343327e-82"
      },
      "Itilde_31": {
       "re": "-0.0717100978625697395468711764680132347735302972",
       "im": "-7.25600865073153906979327336145091329878256594e-83"
      },
      "Itilde_32": {
       "re": "-0.574837335746097306700592661006751588409087154",
       "im": "-5.81049315471559707335134777522835520547317273e-82"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.97e-79",
     "residual_vT_A": "3.59e-80"
    },
    {
     "eps": "0.0002841863011363383416805787423483583750696",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408978787877619270776146392793257874841753346",
       "im": "-2.53427357927821094460145226890498219512011167e-83"
      },
      "Itilde_4": {
       "re": "0.0682503187432341158520713030690275260101943202",
       "im": "-7.81251760953357696386287134163441525141633073e-80"
      },
      "Itilde_19": {
       "re": "-0.287174613238433261943942938801000662976082284",
       "im": "-2.67322340127128014647015590182386997202900803e-82"
      },
      "Itilde_20": {
       "re": "0.239312177698694384953285782334167219146735237",
       "im": "2.76395173991563840266865427458884745442634631e-82"
      },
      "Itilde_31": {
       "re": "-0.0717118213952904196401956298147213094068278397",
       "im": "-7.40131955145103264967942534617500220719070941e-83"
      },
      "Itilde_32": {
       "re": "-0.574839729388814916530188390910701566797107855",
       "im": "-5.92679552896377868162950451661532053286627538e-82"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.14e-79",
     "residual_vT_A": "3.67e-80"
    },
    {
     "eps": "0.0002821888218452977184195882025598219254313",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408978555047843228230465964722302893891859551",
       "im": "1.55853059706276469587807119399111843742726521e-83"
      },
      "Itilde_4": {
       "re": "0.0682496669452044323089851284274497444554057485",
       "im": "-7.89889517083605006204569977547743858199067981e-80"
      },
      "Itilde_19": {
       "re": "-0.287177184038679899875670484459658861471533386",
       "im": "-4.99284588756754384064931183933211264365690378e-82"
      },
      "Itilde_20": {
       "re": "0.239314320032233249896392070383049051226277822",
       "im": "4.59538355420210447258094299801130004428533405e-82"
      },
      "Itilde_31": {
       "re": "-0.0717130400900318330975836413725517823049934464",
       "im": "-1.30327065993697468868281820569181377725450533e-82"
      },
      "Itilde_32": {
       "re": "-0.574841421871526258348636836206880042049415385",
       "im": "-1.04406428758510981028285915821650518611808919e-81"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.26e-79",
     "residual_vT_A": "3.73e-80"
    },
    {
     "eps": "0.0002811548504796883695047301057317751808570",
     "weights": {
      "Itilde_0": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "0.408978434527235329938621276966843674337527925",
       "im": "-2.59886288777488853471881098502339153331620194e-83"
      },
      "Itilde_4": {
       "re": "0.0682493295508344156012545884660647789980027109",
       "im": "-8.11320005543392755847646957231565765777653131e-80"
      },
      "Itilde_19": {
       "re": "-0.287178514765945797239945924580034927529803088",
       "im": "-2.78008360047326923430586190607872939553098245e-82"
      },
      "Itilde_20": {
       "re": "0.239315428971621497699954937150029106274835907",
       "im": "2.86472022896961768784688157512635234589034489e-82"
      },
      "Itilde_31": {
       "re": "-0.0717136709240865556497783293486904694981494474",
       "im": "-7.65774970852624944640267737021773315432456204e-83"
      },
      "Itilde_32": {
       "re": "-0.574842297939571207363425292630256469901511919",
       "im": "-6.13216231521347857506243311467368005666892657e-82"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.33e-79",
     "residual_vT_A": "3.76e-80"
    }
   ],
   "weight_digits": "two extractions at 60 and 120 digits agree to the number of digits listed per eps (at least 45)"
  },
  {
   "support": [
    "Itilde_2",
    "Itilde_3",
    "Itilde_4",
    "Itilde_19",
    "Itilde_20",
    "Itilde_31",
    "Itilde_32"
   ],
   "rows": [
    2,
    3,
    4,
    19,
    20,
    31,
    32
   ],
   "normalized_row": 2,
   "per_eps": [
    {
     "eps": "0.0003114995735603784084585420144685587089594",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.82072522692135989166114307355150243120565316",
       "im": "-4.38291891608629504167842258549595619736811673e-84"
      },
      "Itilde_4": {
       "re": "0.0113765386050256599654415013960067222713489403",
       "im": "-9.56052734680402565410818592608724766646273427e-81"
      },
      "Itilde_19": {
       "re": "-0.0478565760236837275784406256269202531196730785",
       "im": "-1.71789452164190792109318687983664799773749467e-83"
      },
      "Itilde_20": {
       "re": "0.0398804800197364396487005213557668775997275654",
       "im": "2.15063995929182895109638546750387292016598477e-83"
      },
      "Itilde_31": {
       "re": "-0.011949192480516920354001507771533922238581174",
       "im": "-5.26429107944235596888205387655096948788900631e-84"
      },
      "Itilde_32": {
       "re": "-0.0958027633488011757895062572147100510702052655",
       "im": "-4.21145576858632163757129959569233531249092605e-83"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "2.82e-79",
     "residual_vT_A": "3.01e-80"
    },
    {
     "eps": "0.0003104656021947690595436839176405119643851",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725247011200111065286343188398312211697177",
       "im": "-4.429012091008172220861217005777159674645907e-84"
      },
      "Itilde_4": {
       "re": "0.0113764823690307851622524979052930146716032602",
       "im": "-9.66230807590922264734146004607881347721459488e-81"
      },
      "Itilde_19": {
       "re": "-0.0478567978659189673897490546981319789014266684",
       "im": "-1.73165367438448573899646675908011289602975965e-83"
      },
      "Itilde_20": {
       "re": "0.0398806648882658061581242122484433157511888903",
       "im": "2.16873652588325294913131659232431302033380141e-83"
      },
      "Itilde_31": {
       "re": "-0.0119492976477744277602489788024466687021801704",
       "im": "-5.32278105937353994030488888960017733652509163e-84"
      },
      "Itilde_32": {
       "re": "-0.0958029094422586100305146916874707588203881439",
       "im": "-4.25827806603098389346360553645451412402055631e-83"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "2.86e-79",
     "residual_vT_A": "3.03e-80"
    },
    {
     "eps": "0.0003084681229037284362826933778519755147468",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725285821484054237877936399451079772539965",
       "im": "-4.79847917810588326601177170698008254630870967e-84"
      },
      "Itilde_4": {
       "re": "0.0113763737297906766337357138031196373761198313",
       "im": "-9.90673934475809696735696124962061409111985223e-81"
      },
      "Itilde_19": {
       "re": "-0.047857226426776848482372778119127439436211357",
       "im": "-1.26874743192726094553632599322609139432220283e-83"
      },
      "Itilde_20": {
       "re": "0.0398810220223140404019773150992728661968427975",
       "im": "1.8212497159807711973970677208553870222604577e-83"
      },
      "Itilde_31": {
       "re": "-0.0119495008124923048242909750290042980756043758",
       "im": "-4.22416238041215093206793751920271276593718122e-84"
      },
      "Itilde_32": {
       "re": "-0.0958031916649406397624374261712316993208691561",
       "im": "-3.3773716976089225004626254573804350625070437e-83"
      }
     },
     "two_extraction_agreement_digits": 45,
     "max_off_support_weight": "2.93e-79",
     "residual_vT_A": "3.07e-80"
    },
    {
     "eps": "0.0003056432605996104618809126321647189760712",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725340706823189924439172609098547294032838",
       "im": "-4.59778686640267493859191055816976843066986867e-84"
      },
      "Itilde_4": {
       "re": "0.0113762200915127172284640286641962470297183337",
       "im": "-1.01845120969944301147665434363243436094363108e-80"
      },
      "Itilde_19": {
       "re": "-0.0478578324911369212823878673092393685389596424",
       "im": "-1.79789103955007929441088693320208107786656051e-83"
      },
      "Itilde_20": {
       "re": "0.0398815270759474344019898894243661404491330353",
       "im": "2.25015910394667884841225409754735367125482236e-83"
      },
      "Itilde_31": {
       "re": "-0.0119497881244425254982944536118009915885712323",
       "im": "-5.51009893088156805320545369090009820403514933e-84"
      },
      "Itilde_32": {
       "re": "-0.0958035907696267930280392467040539775217877444",
       "im": "-4.40816131300585194653714304178397565193168156e-83"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.05e-79",
     "residual_vT_A": "3.14e-80"
    },
    {
     "eps": "0.0003021835249805230940456316082359488035615",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725407926258354828559884263912946513202293",
       "im": "-4.77102585988820448253105273666909523369518431e-84"
      },
      "Itilde_4": {
       "re": "0.0113760319251108072590720534735112821837797248",
       "im": "-1.05699848184288749264499331733040603227554339e-80"
      },
      "Itilde_19": {
       "re": "-0.0478585747458533783380664371631472398403874035",
       "im": "-1.82806359360329638126795408630202857376525997e-83"
      },
      "Itilde_20": {
       "re": "0.0398821456215444819483886976359560332003228362",
       "im": "2.29909587853190950708282095179982003185697184e-83"
      },
      "Itilde_31": {
       "re": "-0.0119501399981461202870786965696287225876964048",
       "im": "-5.65956142428399191310137354500920597537785832e-84"
      },
      "Itilde_32": {
       "re": "-0.0958040795415836227167786515376182337357131519",
       "im": "-4.52774140525641144972383533277401659062366486e-83"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.20e-79",
     "residual_vT_A": "3.22e-80"
    },
    {
     "eps": "0.0002983246913110740122426265998887033945465",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725482898364537596724810094464519581638551",
       "im": "-4.90128139520989280602846935835284296039125226e-84"
      },
      "Itilde_4": {
       "re": "0.011375822054437153462557084757999979426475194",
       "im": "-1.10274903265116244187722765939451031019832558e-80"
      },
      "Itilde_19": {
       "re": "-0.0478594025980883664384933007103610407412922317",
       "im": "-1.89299159454249760042900710219791476773326753e-83"
      },
      "Itilde_20": {
       "re": "0.0398828354984069720320777505919675339510768597",
       "im": "2.37444869831457347195411756875105645252923136e-83"
      },
      "Itilde_31": {
       "re": "-0.011950532449103831493112309331894252906187357",
       "im": "-5.82522770982172266208132716095899134874167901e-84"
      },
      "Itilde_32": {
       "re": "-0.0958046246576012032564756475446409069333128617",
       "im": "-4.66031154113582246599460184115911779877138857e-83"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.37e-79",
     "residual_vT_A": "3.31e-80"
    },
    {
     "eps": "0.0002943297327289927657206455203116304952699",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725560513609838514395234490442408524479205",
       "im": "-5.66597712628728884096090591848516681650612058e-84"
      },
      "Itilde_4": {
       "re": "0.0113756047821910981968313043761940632070146052",
       "im": "-1.1502757672914417478988797145478873082581333e-80"
      },
      "Itilde_19": {
       "re": "-0.0478602596256502381039650240899346781061401277",
       "im": "-4.13595983855744229640782059448217967767154695e-83"
      },
      "Itilde_20": {
       "re": "0.0398835496880418650866375200749455650884501064",
       "im": "4.23175268205812013568884847112411857196390178e-83"
      },
      "Itilde_31": {
       "re": "-0.0119509387296096791322657789638272038852003782",
       "im": "-1.13441613996912581391434053991172995116942731e-83"
      },
      "Itilde_32": {
       "re": "-0.095805188960721888710502495804429970559203491",
       "im": "-9.08432823506899568662362224943315655037524679e-83"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.57e-79",
     "residual_vT_A": "3.40e-80"
    },
    {
     "eps": "0.0002904708990595436839176405119643850862549",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725635482643785049691842051750975620220817",
       "im": "-5.21853498131152435756357659904735672030933607e-84"
      },
      "Itilde_4": {
       "re": "0.0113753949151173165152742337811131787012618369",
       "im": "-1.21115473419194884417726733959795771211260127e-80"
      },
      "Itilde_19": {
       "re": "-0.0478610874235276358833370257145774950514080718",
       "im": "-2.04530192153350064600567386961053892915304302e-83"
      },
      "Itilde_20": {
       "re": "0.0398842395196063632361141880954812458761733932",
       "im": "2.54736693399561560604262183709619570422707518e-83"
      },
      "Itilde_31": {
       "re": "-0.0119513311523190033253876090065700573489548651",
       "im": "-6.17861873394318406212265284513594785840002608e-84"
      },
      "Itilde_32": {
       "re": "-0.0958057339946228603555622094131966945286573131",
       "im": "-4.94311386352558644079887374726375423435277753e-83"
      }
     },
     "two_extraction_agreement_digits": 47,
     "max_off_support_weight": "3.77e-79",
     "residual_vT_A": "3.50e-80"
    },
    {
     "eps": "0.0002870111634404563160823594880356149137451",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725702696757680661122043117537996307060502",
       "im": "-5.47707298717325258038927094199611242387939649e-84"
      },
      "Itilde_4": {
       "re": "0.0113752067549505679140146646586125953509186419",
       "im": "-1.25921647268092271482066699788903833262784587e-80"
      },
      "Itilde_19": {
       "re": "-0.04786182958409398475842358058571683091159283",
       "im": "-2.07265610262723264637766084443214833221889618e-83"
      },
      "Itilde_20": {
       "re": "0.0398848579867449872986863171547640257596606916",
       "im": "2.60067635055876738116182050798762772394677e-83"
      },
      "Itilde_31": {
       "re": "-0.0119516829770949565911451960780022057955883829",
       "im": "-6.35931455831872946892908965898902228000050349e-84"
      },
      "Itilde_32": {
       "re": "-0.0958062226243495511167654435011252647348478591",
       "im": "-5.08768034180365727450459324759920287988663323e-83"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "3.97e-79",
     "residual_vT_A": "3.59e-80"
    },
    {
     "eps": "0.0002841863011363383416805787423483583750696",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725757575952343759531156756679243081929998",
       "im": "-5.60397870810491992899031797710588999645372615e-84"
      },
      "Itilde_4": {
       "re": "0.0113750531238723526420118838448379210016990534",
       "im": "-1.30018172797949147995052544693686077101763977e-80"
      },
      "Itilde_19": {
       "re": "-0.0478624355397388769906571564668334438293470474",
       "im": "-2.11260206208521320380542436984369267770530031e-83"
      },
      "Itilde_20": {
       "re": "0.0398853629497823974922142970556945365244558728",
       "im": "2.65369364911065486352142762562530905429175167e-83"
      },
      "Itilde_31": {
       "re": "-0.01195197023254840327336593830245355156780464",
       "im": "-6.48450340771166082135511793020579682764591083e-84"
      },
      "Itilde_32": {
       "re": "-0.0958066215648024860883647318184502611328513091",
       "im": "-5.18782535162059237759591673722806403245934477e-83"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.14e-79",
     "residual_vT_A": "3.67e-80"
    },
    {
     "eps": "0.0002821888218452977184195882025598219254313",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725796380915017517144561435171739906912297",
       "im": "1.20512748242607568120759051396288079205129863e-84"
      },
      "Itilde_4": {
       "re": "0.0113749444908674053848308547379082907425676247",
       "im": "-1.31455005119300284931652155385658415007945532e-80"
      },
      "Itilde_19": {
       "re": "-0.0478628640064466499792784140766098102452555643",
       "im": "-5.94467060340678056774499617024757724847456756e-83"
      },
      "Itilde_20": {
       "re": "0.0398857200053722083160653450638415085377129703",
       "im": "5.67777266638567052526730638823664271394804594e-83"
      },
      "Itilde_31": {
       "re": "-0.0119521733483386388495972735620919637174989077",
       "im": "-1.5785275341212758582677119272916925685320244e-83"
      },
      "Itilde_32": {
       "re": "-0.0958069036452543763914394727011466736749025642",
       "im": "-1.26429370678756137543489151247211887703387127e-82"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.26e-79",
     "residual_vT_A": "3.73e-80"
    },
    {
     "eps": "0.0002811548504796883695047301057317751808570",
     "weights": {
      "Itilde_2": {
       "re": "1.0",
       "im": "0.0"
      },
      "Itilde_3": {
       "re": "-0.820725816467683000565785342727748276499300901",
       "im": "-5.73027577741597362761518274724750740270752033e-84"
      },
      "Itilde_4": {
       "re": "0.0113748882584724026002090980776774631663337851",
       "im": "-1.35025283387023696313678149812732336646214434e-80"
      },
      "Itilde_19": {
       "re": "-0.0478630857943242995399909874300058212549671814",
       "im": "-2.2388628010730843105520497474718068989628034e-83"
      },
      "Itilde_20": {
       "re": "0.0398859048286035829499924895250048510458059845",
       "im": "2.77844163532481956310333427959772491250094151e-83"
      },
      "Itilde_31": {
       "re": "-0.0119522784873477592749630548914484115830249079",
       "im": "-6.78236295639563278074363220498012829158923852e-84"
      },
      "Itilde_32": {
       "re": "-0.0958070496565952012272375487717094116502519865",
       "im": "-5.42637947941506009099223710075099950718456325e-83"
      }
     },
     "two_extraction_agreement_digits": 46,
     "max_off_support_weight": "4.33e-79",
     "residual_vT_A": "3.76e-80"
    }
   ],
   "weight_digits": "two extractions at 60 and 120 digits agree to the number of digits listed per eps (at least 45)"
  }
 ],
 "check": "the combination (direction normalized on row 0) - 6 (direction normalized on row 2) has weight 5.3333333333333333333 on Itilde_3 (16/3 to 3.3e-45) and weights below 6.0e-46 on all other rows: the relation Itilde_0 - 6 Itilde_2 + (16/3) Itilde_3 = 0, the S_3 image of Eq. (36), lies in the span",
 "source_sha256": {
  "S3_nullvectors": {
   "description": "left null vectors of the S_3 response matrix at twelve values of epsilon (two extractions at 60 and 120 digits)",
   "sha256": "53de1b3fdf6260c5d3ac0e221f5506fdeefe865d335eeed8ffbcb1ae6b1f9653"
  },
  "S2_response_matrix": {
   "description": "response matrix A(epsilon) of S_2 (source of the epsilon grid, common to S_1, S_2, S_3)",
   "sha256": "c6255a2eca5bf90cd765e1657a128287c48aa2bf412d3446ceec23e99b8cccb5"
  }
 }
}