-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '261195433679478962621842383458,423038992441214336543587752590,1049804838737308219162632650835,1245446351703697723220020222910,1629883758961203908077802383570,2661963224236883111088002092409', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3990424166.153653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '675.1', 'coefficient_field': '1.1.1.1', 'conductor': 94585080322265625, 'conductor_radical': 15, 'degree': 12, 'euler_factors': [[1, 0, -1, 0, -3, 0, -812, 0, -192, 0, -4096, 0, 262144], [1], [1], [1, 0, -1226, 0, 769535, 0, -316892876, 0, 90535023215, 0, -16969418108426, 0, 1628413597910449], [1, 76, 4206, 140708, 6941959, 323708584, 15228577508, 430856125304, 12298103827999, 331782103705228, 13200229752488526, 317470860875589476, 5559917313492231481], [1, 0, -3246, 0, 11631063, 0, -30956231140, 0, 56140919567967, 0, -75625584307573326, 0, 112455406951957393129], [1, 0, -6163, 0, 56646390, 0, -189472696871, 0, 1367306147225910, 0, -3590700848047017043, 0, 14063084452067724991009], [1, 374, 83297, 13116126, 1678114378, 178142128678, 16104727242289, 1221876860602402, 78948369331777018, 4232412502719284154, 184362492813454012817, 5677741509173174563826, 104127350297911241532841], [1, 0, -19839, 0, 507262974, 0, -5894416200139, 0, 75093125312873886, 0, -434764234106851148319, 0, 3244150909895248285300369], [1, -320, 76398, -7951120, 1855772023, -384085002800, 90944175951716, -9367449133289200, 1103856477739748383, -115348058511651523280, 27030741807331423794318, -2761340399231419021103680, 210457284365172120330305161], [1, -454, 194329, -59958470, 15604346290, -3335180728774, 637742673357065, -99358369090906234, 13848914771973693490, -1585279292131927333370, 153065721110845086505369, -10653228944297487412197754, 699053619999045038539170241], [1, 0, -97986, 0, 8873792007, 0, -470111365900348, 0, 22767722500333012863, 0, -645037135244241697044066, 0, 16890053810563300749953435929], [1, -676, 442146, -179778788, 72783658399, -22153724392024, 6633742695230108, -1526856838822686104, 345729964436585170159, -58856327378441823099268, 9976356982345707710969826, -1051246460934279627760694276, 107178930967531784356353269521], [1, 0, -156726, 0, 19336556583, 0, -1757584565934100, 0, 122233394278673901567, 0, -6262713096331774549023126, 0, 252599333573498060811820806649], [1, 0, -508570, 0, 117397962543, 0, -15651426994430252, 0, 1265457917436873421647, 0, -59091502564717978436025370, 0, 1252453015827223091648143056289], [1, 0, -744595, 0, 248680653006, 0, -47637358185692759, 0, 5511847799020523403774, 0, -365788923815037011114915395, 0, 10888439761782913818722623349689], [1, -280, 918978, -172662200, 393478450183, -58693055990080, 102589405915891196, -12054321146186640320, 16597131004952574106303, -1495771916639762808605800, 1635043285018929297093867618, -102314740236972757160884811720, 75047496554032956760519149093721], [1, -1190, 1710413, -1343700426, 1087127898034, -608446972507054, 340663988576853253, -138105902266623623974, 56009236284998715906274, -15713429086647470809044066, 4540032992175257233812296573, -716959273596698080524212092190, 136753052840548005895349735207881], [1, 0, -1185590, 0, 637803099863, 0, -223447532584291412, 0, 57694636555980125542847, 0, -9701349706143669102020075990, 0, 740195513856780056217081017732809], [1, -1204, 1342566, -890805452, 772040400799, -512811665615416, 379083129921051668, -183540936052079155976, 98898594540834535252879, -40842094406020313798917012, 22031082118371171241253402406, -7071339975100133998056265983404, 2102085018129621311776010144838961], [1, 0, -467850, 0, 420984954303, 0, -140390583242060428, 0, 63709432338754526271567, 0, -10714723178550467538185099850, 0, 3465863721549107204083472585375569], [1, 1258, 3547993, 3227336138, 4821357993874, 3244977887200810, 3268997100014035913, 1599900652527600161590, 1172011646886663765478354, 386801386911679720769512022, 209656267499802674478278997913, 36651099740492355879562619812342, 14364405059580771582276370834385761], [1, 0, -1042599, 0, 467625790374, 0, -106913777507688499, 0, 152885750501849286150006, 0, -111443415178320349648909448439, 0, 34946659039493167390823397237402409], [1, -4308, 10984674, -19889703636, 27941240181759, -31517105787288312, 29183298471007787932, -22218582549758854022328, 13886273616581954103780399, -6968485036716652441863519924, 2713109064292842335776439237154, -750111449209784923173122515317492, 122749609618842355502421774953773681], [1, 0, -4626246, 0, 9511067662287, 0, -11170340228400453268, 0, 7922453099670579471412623, 0, -3209885447185701067112932246086, 0, 577951262543040979328274795306257089], [1, -1368, 3173790, -1996459992, 4718037386247, -3556094828388336, 6957920172453606916, -3663848057783330969136, 5008291756790063846184447, -2183498890753936982935572792, 3576306012382544179737313121790, -1588205530946157996108395878453368, 1196147475686664860781049986817531801], [1, 0, -1510554, 0, 3764880930687, 0, -3294631050549092332, 0, 4495464721445051219685423, 0, -2153688810669042990762018013914, 0, 1702433061239903677780481956434843889], [1, 0, -5157858, 0, 13174963144935, 0, -20257924840907164540, 0, 19772067076095910132234815, 0, -11616484404654294339039619488258, 0, 3379932275732534791891466777752413049], [1, 5214, 16599765, 37260083218, 67231129389570, 99205084665041670, 123608927988955581117, 128473461588684248858430, 112753334551213459669328370, 80924924332635376464242733802, 46689574401372329482868718688965, 18991903544810729608257354737780886, 4717120417286669419611030657597553321], [1, 0, -7481434, 0, 24447791100015, 0, -45407402753853340844, 0, 50899121528094941256189135, 0, -32428448495559491681318201947354, 0, 9024267965168278308669913635234402529]], 'euler_factors_factorization': [[[[1, 0, -1, 0, -3, 0, -812, 0, -192, 0, -4096, 0, 262144], 1]], [1], [1], [[[1, 0, -1226, 0, 769535, 0, -316892876, 0, 90535023215, 0, -16969418108426, 0, 1628413597910449], 1]], [[[1, 38, 1381, 17876, 1838111, 67319318, 2357947691], 2]], [[[1, 0, -3246, 0, 11631063, 0, -30956231140, 0, 56140919567967, 0, -75625584307573326, 0, 112455406951957393129], 1]], [[[1, 0, -6163, 0, 56646390, 0, -189472696871, 0, 1367306147225910, 0, -3590700848047017043, 0, 14063084452067724991009], 1]], [[[1, 187, 24164, 2039395, 165740876, 8797579747, 322687697779], 2]], [[[1, 0, -19839, 0, 507262974, 0, -5894416200139, 0, 75093125312873886, 0, -434764234106851148319, 0, 3244150909895248285300369], 1]], [[[1, -160, 25399, 88280, 619456211, -95171731360, 14507145975869], 2]], [[[1, -227, 71400, -13771435, 2127077400, -201463335587, 26439622160671], 2]], [[[1, 0, -97986, 0, 8873792007, 0, -470111365900348, 0, 22767722500333012863, 0, -645037135244241697044066, 0, 16890053810563300749953435929], 1]], [[[1, -338, 163951, -34473956, 11299666871, -1605535233458, 327381934393961], 2]], [[[1, 0, -156726, 0, 19336556583, 0, -1757584565934100, 0, 122233394278673901567, 0, -6262713096331774549023126, 0, 252599333573498060811820806649], 1]], [[[1, 0, -508570, 0, 117397962543, 0, -15651426994430252, 0, 1265457917436873421647, 0, -59091502564717978436025370, 0, 1252453015827223091648143056289], 1]], [[[1, 0, -744595, 0, 248680653006, 0, -47637358185692759, 0, 5511847799020523403774, 0, -365788923815037011114915395, 0, 10888439761782913818722623349689], 1]], [[[1, -140, 449689, -23374640, 92356677131, -5905274709740, 8662995818654939], 2]], [[[1, -595, 678194, -268324783, 153937152314, -30654622744795, 11694146092834141], 2]], [[[1, 0, -1185590, 0, 637803099863, 0, -223447532584291412, 0, 57694636555980125542847, 0, -9701349706143669102020075990, 0, 740195513856780056217081017732809], 1]], [[[1, -602, 490081, -150373964, 175405380791, -77116370920442, 45848500718449031], 2]], [[[1, 0, -467850, 0, 420984954303, 0, -140390583242060428, 0, 63709432338754526271567, 0, -10714723178550467538185099850, 0, 3465863721549107204083472585375569], 1]], [[[1, 629, 1576176, 622253365, 777116238864, 152902009522709, 119851595982618319], 2]], [[[1, 0, -1042599, 0, 467625790374, 0, -106913777507688499, 0, 152885750501849286150006, 0, -111443415178320349648909448439, 0, 34946659039493167390823397237402409], 1]], [[[1, -2154, 3172479, -3111332052, 2236499348151, -1070497700729994, 350356403707485209], 2]], [[[1, 0, -4626246, 0, 9511067662287, 0, -11170340228400453268, 0, 7922453099670579471412623, 0, -3209885447185701067112932246086, 0, 577951262543040979328274795306257089], 1]], [[[1, -684, 1352967, -72800568, 1393963253067, -726079783011084, 1093685272684360901], 2]], [[[1, 0, -1510554, 0, 3764880930687, 0, -3294631050549092332, 0, 4495464721445051219685423, 0, -2153688810669042990762018013914, 0, 1702433061239903677780481956434843889], 1]], [[[1, 0, -5157858, 0, 13174963144935, 0, -20257924840907164540, 0, 19772067076095910132234815, 0, -11616484404654294339039619488258, 0, 3379932275732534791891466777752413049], 1]], [[[1, 2607, 4901658, 5851419203, 6347789258082, 4372199988962487, 2171893279442309389], 2]], [[[1, 0, -7481434, 0, 24447791100015, 0, -45407402753853340844, 0, 50899121528094941256189135, 0, -32428448495559491681318201947354, 0, 9024267965168278308669913635234402529], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '12-675e6-1.1-c3e6-0-2', 'leading_term': '2.6879265544341886135835582736323588870916064528725227103312768641700114985514123638171541', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/675/4/b/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.010416666666666666', 'prec': 67}, 'plot_values': [2.6879265544341884, 2.6764714802322294, 2.6431019066601897, 2.5882288445288184, 2.512514578055822, 2.4169365638542675, 2.302836344072249, 2.171822598136024, 2.025762582974827, 1.8667575068348201, 1.6970648437121318, 1.519057130403015, 1.3351945571157247, 1.148086424448113, 0.9604098686607369, 0.7748677356718296, 0.5941645259387447, 0.42097046852879566, 0.25786789054764464, 0.10728183012646496, -0.02852157734151644, -0.1474644888837209, -0.24768651371132058, -0.3275696494339426, -0.3857546982530243, -0.42115971320480744, -0.43300011625198576, -0.4208014790923986, -0.38440813815534436, -0.32398873855454663, -0.24004155006516223, -0.13338483923718708, -0.005145264516964701, 0.1432560889959098, 0.31012114242636185, 0.4934948500734874, 0.6911894484733118, 0.9008148208922909, 1.1198101726876393, 1.3454772695374895, 1.5750154872400137, 1.805558169047623, 2.0342121522916807, 2.2580979085867834, 2.474390591663828, 2.6803571237517043, 2.873392914066659, 3.05105885684458, 3.2111148949475607, 3.351551499179343, 3.4706208959520204, 3.566858968164303, 3.6391063921431686, 3.6865262093781985, 3.7086133894222004, 3.7052026616896305, 3.67647480511086, 3.6229502661074666, 3.545483126038896, 3.4452463910638484, 3.3237119908265944, 3.1826295178053985, 3.0240034879098956, 2.8500595809489075, 2.663211031558812, 2.466017171828053, 2.2611423702738445, 2.051314961393848, 1.8392868007159537, 1.6277871049446169, 1.4194761093474526, 1.2168988674479582, 1.022443043641341, 0.8382996406095393, 0.6664275302435723, 0.5085179048182664, 0.36596213095227315, 0.2398263820702131, 0.13083228456616958, 0.03934342305467488, -0.03464219810997061, -0.09149516607308664, -0.1319498868632939, -0.15709228389692795, -0.16834083113450837, -0.16742117255939257, -0.15633522302793196, -0.1373233065931001, -0.11281994997088782, -0.08540503083205415, -0.05775060694453412, -0.032564293118920104, -0.012529812317458065, -0.00024428228142219817, 0.0018448789712407524, -0.008497236476192447, -0.03323131214865817, -0.07398393844299433, -0.13199056103594847, -0.20804327452991211, -0.3024440391422488, -0.4149641959471299, -0.5448110470292092, -0.6906016180972303, -0.8503475181596364, -1.0214483664485312, -1.2006948182768165, -1.3842821237809697, -1.567833733797563, -1.7464358870801147, -1.9146871510457752, -2.066752659608042, -2.196428906345917, -2.2972185505600886, -2.362413430598407, -2.385186784311813, -2.358694173261677, -2.276172293757743, -2.1310440568222155, -1.9170275249452093, -1.6282462084119225, -1.2593377919496882, -0.8055571384025767, -0.262875692197357, 0.3719221020100361, 1.1011493292418015, 1.9261365586785912, 2.8471665959721437, 3.863437339655369, 4.973010844189514, 6.172778139978301, 7.458446468759133, 8.824539103825234, 10.264421638541736, 11.770385447127378, 13.33366775931344, 14.94450514442839, 16.59222421582759, 18.26532627931316, 19.951616462925376, 21.63841622305188, 23.312629194346226, 24.960869560262008, 26.569616830461378, 28.125344885733675, 29.614714295554606, 31.024864192320067, 32.3434587169519, 33.55883042709082, 34.66010416702615, 35.63730841787849, 36.48155297519023, 37.185312463927545, 37.74238612864136, 38.14795891665985, 38.398615249461244, 38.492372648169614, 38.42877085794059, 38.20906711959566, 37.836075668403986, 37.314065606626514, 36.64865911362755, 35.84675834303004, 34.916520660194564, 33.86744042690999, 32.71007626004116, 31.455806596643114, 30.116663794671073, 28.705186577713864, 27.2343207688698, 25.71742761911925, 24.167954664244082, 22.599172137873943, 21.024017756016104, 19.454955899056667, 17.903886884133588, 16.38214730874371, 14.900233525183301, 13.467641941243565, 12.092795965635132, 10.782990895282355, 9.544385069895833, 8.382043049152069, 7.299810634217812, 6.300303096166523, 5.38494515806452, 4.554026811555745, 3.806789742478571, 3.1415278722503377, 2.5556198228686005, 2.045625301562731, 1.6074030830069321, 1.2362334789037914, 0.926947599894846, 0.6740521663686225, 0.4718311018987607, 0.3144635583535249, 0.19613993170596014, 0.11116874307892094, 0.05407295524415988, 0.01967330780620867, 0.0031566525520036305, 0.00013545724296512956, 0.006693449698035923, 0.01941631380985318, 0.035407669562173366, 0.052290499952577424, 0.06819685156375464, 0.08174536181969723, 0.0920076313840267, 0.09846546194546926, 0.10096002036196239, 0.09963530711395666, 0.09487889356328151, 0.08726049736140137, 0.07747090112187535, 0.06626312319650948, 0.05439732436502919, 0.04259182420956553, 0.03148153744687909, 0.02158459236788969, 0.01327821566729347, 0.006784322862893329, 0.0021652615821577876, -0.0006703384937272318, -0.0019521318488083816, -0.0020239553086300465, -0.0013120298861695103, -0.00028673687240071433, 0.0005804287429004646, 0.0008629168969467086, 0.00022616333694471257, -0.001526226847233159, -0.004409142783824814, -0.008217515725364442, -0.01249466196227882, -0.016509267107122104, -0.0192420281553041, -0.019383219571080863, -0.015342281863002228, -0.005269988235964862, 0.01290668311797464, 0.04143783549516239, 0.0826932542335123, 0.1390948528061046, 0.2130390793219336, 0.3068120463973096, 0.42250073833815355, 0.5619071438372499, 0.7264608110931017, 0.9171329050247439, 1.1343530501490238, 1.377935943856294, 1.647024470170671, 1.9400664046768616, 2.254789946007825, 2.588185376964711, 2.9365095296956962, 3.295313471562131, 3.6595045426373143, 4.023477676950716, 4.3811976519262, 4.7262821319727975, 5.052124503748243, 5.352033250721645, 5.61940880782345, 5.848010882994694, 6.032062003105487, 6.166365534568281, 6.246458538948502, 6.268757022611535, 6.230730135559473, 6.131141247418712, 5.970017398282807, 5.74866720568275, 5.469711896964325, 5.137087950822235, 4.756068613518576, 4.333287708978971, 3.8765004547434225, 3.3944101488180016, 2.896501228553904, 2.3928481417657013, 1.8939309570487322, 1.410428512693749, 0.9528577205913217, 0.5312831496539224, 0.155051660641405, -0.1674689635783455, -0.42913904965092714, -0.6242791542797114, -0.7489307235765347, -0.8010406870967384, -0.7805974471297146, -0.6897309517445736, -0.5327639406865805, -0.3162268294559224, -0.04880575216876239, 0.2587728805156837, 0.5939075403970165, 0.942346641761333, 1.2884527202465517, 1.6154821343488586, 1.9059547656954856, 2.142040352159842, 2.3059764615855536, 2.380517893144849, 2.3493346368606622, 2.1974112215543764, 1.9114679441762419, 1.4803430062028344, 0.8953920734214055, 0.15078809530922502, -0.756274555189483, -1.8253964445599011, -3.0528543797196535, -4.431535592452942, -5.9508897019369105, -7.597091173892741, -9.35324194525621, -11.199627427727137, -13.114039559598549, -15.072110836694373, -17.04772944940878, -19.01358208772089, -20.941683806797837, -22.803956198663098, -24.572759868782942, -26.221403279535384, -27.72470360662746, -29.059516084932024, -30.20522564161786, -31.144243922056816, -31.862318338576273, -32.34880896564678, -32.596900913548595, -32.60373439419898, -32.37048095094309, -31.90239441841211, -31.208627395809017, -30.30199016042593, -29.198633027545565, -27.9176875438452, -26.480872492845656, -24.912095337151683, -23.236888919175833, -21.481802853501133, -19.673830574859878, -17.839856270562898, -16.006125137348622, -14.197764071861585, -12.438256421956591, -10.748963272945781, -9.148754513935131, -7.653710691707936, -6.276896390861074, -5.028210565576807, -3.9143018743721743, -2.9385758398947637, -2.1012921644866664, -1.3997340847378847, -0.8284386411410206, -0.37947757434901896, -0.04282441379215608, 0.19324958105222714, 0.3417588656310704, 0.41657255223456857, 0.43198337634010736, 0.40228311861602795, 0.3413379708719373, 0.26221401760220847, 0.1768488656901034, 0.09577227295264507, 0.027881218149638936, -0.019726384263196423, -0.04184689847435075, -0.035198216839266806, 0.0016145370687039036, 0.06819258291830087, 0.16249494643872575, 0.2810441511655488, 0.41917030187801574, 0.5712799091948993, 0.7311438127967236, 0.8922012065994718, 1.0478668933918243, 1.1918413610824812, 1.3183636074304739, 1.422435931581144, 1.5000193250572316, 1.5481958911521296, 1.5652737175057196, 1.5508693373636573, 1.5058702557698318, 1.432365761065002, 1.333548922336573, 1.2135736862289583, 1.0773694189985503, 0.9304528857695681, 0.7786539317796556, 0.6278588413361951, 0.48376829846063124, 0.35165532365201696, 0.23614750464423737, 0.14104100170628886, 0.06911958418504946, 0.022036008855461756, 0.0002450499862159886, 0.0029859844844144093, 0.028316039959967322, 0.07318660991476653, 0.13357195732302812, 0.2046475157919725, 0.2810063327370987, 0.35690139516231684, 0.42650418893069586, 0.4841692090303099, 0.524712124659785, 0.5436797447781603, 0.5375880549072802, 0.5041238884988323, 0.4423077699686362, 0.35260953331987, 0.2370175258073774, 0.0990501870745743, -0.056309835160225974, -0.2227355708829641, -0.39273045678674123, -0.5578558669184007, -0.7090012871758812, -0.8366969052565048, -0.9314562925029123, -0.9841292695166415, -0.9862583950509839, -0.930429318561117, -0.8105939595862869, -0.6223573261545466, -0.36321866803508307, -0.032757455532338026, 0.36724436362178225, 0.8327545837338715, 1.357522071190821, 1.9331785340678584, 2.549410931662866, 3.194202695075129, 3.85414518241901, 4.514839605707682, 5.161296641687729, 5.778354835186651, 6.351127989198054, 6.865455085652849, 7.308362218118172, 7.6685518822711565, 7.936705530089893, 8.105765181374082, 8.171172170455446, 8.131033203494166, 7.986252872722369, 7.740572277550176, 7.400377857360958, 6.974502756227996, 6.473968618108015, 5.911663661153763, 5.301996086781822, 4.6604157250638885, 4.002882575385976, 3.345373733049823, 2.7033977953610147, 2.091534111584617, 1.5229905541916977, 1.0091524356200146, 0.5592621124048589, 0.18017937815655719, -0.12378099005524425, -0.35093025571972375, -0.5022140445953248, -0.5811249592681306, -0.5934673636639294, -0.547063708428652, -0.45140588974108986, -0.3172691036127083, -0.15625291348763493, 0.019714611464594627, 0.19888859549745833, 0.37018686225779407, 0.5236212290665555, 0.6506842635176742, 0.7447216970933354, 0.8012259265811892, 0.818005189028211, 0.7952561274862688, 0.7355256557254338, 0.6436100299702467, 0.5263729381144494, 0.39246408343091965, 0.25191720963001774, 0.1156963139264102, -0.004790628224868644, -0.09818474021212334, -0.15369716128491565, -0.16162981632898668, -0.11387743741626681, -0.004340939051840494, 0.17075026332843696, 0.4125459947230297, 0.7193827821996327, 1.08669917971447, 1.5070758094031536, 1.9704996786831805, 2.4646134662818246, 2.975013536312005, 3.4856857070300715, 3.979540891225788, 4.4390585863260945, 4.8470738882288, 5.187244733737907, 5.444610673689496, 5.606169804927696, 5.6614475912364695, 5.603122946001368, 5.4273899131858645, 5.133977952190677, 4.726242711603252, 4.211157829480357, 3.599250792911001, 2.9045431974338367, 2.1439345617234133, 1.336577041575753, 0.503280419983577, -0.3341454565984883, -1.1534950016807637, -1.932838282244685, -2.651482104099601, -3.290694602092399, -3.834341113158281, -4.269436421578038, -4.586531115467085, -4.780112307755037, -4.848890656729387, -4.795851761509833, -4.628158795572189, -4.356901148532634, -3.996700952806161, -3.565259024600459, -3.082745015284779, -2.5710851496352585, -2.0531854462594477, -1.5521079849055501, -1.09023948442592, -0.688521656461328, -0.36570283975266155, -0.13765595386682877, -0.01679400206974995, -0.01160545123653566, -0.1263514482031762, -0.3609239749056394, -0.7108274303979921, -1.1673086613005952, -1.7176373046131819, -2.3455571034444946, -3.031944628419375, -3.755427191392652, -4.493083717964319, -5.221220403016921, -5.916188309588449, -6.55524688089825, -7.117489770612313, -7.584405650015138, -7.940434050961465, -8.17347542799652, -8.275307132567647, -8.241865261352917, -8.073449959294981, -7.774483635021639, -7.353262721660665, -6.821653926439796, -6.1946678803701944, -5.489901123047991, -4.726896567626827, -3.92635150958308, -3.109406413766865, -2.296966707841581, -1.5090209994727117, -0.7639823542438172, -0.07801826139437112, 0.5353629214195038, 1.0656124154961077, 1.5053577757441854, 1.8504959525262534, 2.1002084043661755, 2.2569507823236075, 2.326047306137667, 2.315283654266895, 2.234469656912485, 2.0949351695500478, 1.909038011280924, 1.6896994538982866, 1.4497375508737536, 1.20134277492138, 0.9556341745556626, 0.722291883454158, 0.5092885826953618, 0.32270880730788526, 0.16659688259306546, 0.0429597758433266, -0.04812358107895851, -0.10830704734877565, -0.14071461572827923, -0.14963208650113785, -0.14015052664786268, -0.11778161848096531, -0.08807683779982227, -0.05627201575669993, -0.026974864500420574, -0.003907925021606712, 0.010289354528821806, 0.014173684943343832, 0.007524582124230292, -0.008712475008540839, -0.03256097781415389, -0.061218061434175707, -0.09132158544421187, -0.11925966723871721, -0.14150284376790404, -0.15493924805487563, -0.15719379640267037, -0.1469154046463803, -0.12400099213623066, -0.08974491784632803, -0.046903595238472325, 0.0003344236856890324, 0.04647590524689286, 0.08494799614498542, 0.10842371977153505, 0.10922430570352662, 0.07978453682891457, 0.013162614757194099, -0.09642840037482855, -0.25309598111988246, -0.458778884326913, -0.7128162607061767, -1.0116011642246672, -1.3483421647427385, -1.7129599184472046, -2.092148480986077, -2.469557018182277, -2.826124924331688, -3.140572309702749, -3.3900271828616217, -3.55078184775715, -3.599204555846008, -3.5126063271074517, -3.2701705118694027, -2.8539035228716596, -2.2494921943274115, -1.447121414486922, -0.4422387181901403, 0.7639607336876851, 2.1641553399454048, 3.744724305506309, 5.485960010563692, 7.362244839278493, 9.342633487058404, 11.391514206823507, 13.469417636396978, 15.534204078920622, 17.542416718304132, 19.450324598169896, 21.215639235498415, 22.798533337096366, 24.162753075515155, 25.277136445234277, 26.11646255417203, 26.662135012611664, 26.903429362443347, 26.837306527583618, 26.468432103310725, 25.80936708666908, 24.879705718018176, 23.70551422614756, 22.319068187777273, 20.757150627159533, 19.059862704725482, 17.269332766669798, 15.428062016421487, 13.577753739426894, 11.758391355794517, 10.006563184982827, 8.354429466204055, 6.828748180787547, 5.4502094787310185, 4.233167541606361, 3.1856363232570155, 2.309190639753374, 1.5993179684074241, 1.046002807004228, 0.6345710588279272, 0.34669424364269646, 0.16148304821131454, 0.05659703539670198, 0.009429801874206186, -0.0017273410579235694, 0.003387406387621072, 0.007939989469529214, -0.0012347168933655116, -0.033062785592220444, -0.09189110909005001, -0.1773911045790921, -0.28470380008680274, -0.4048117048210534, -0.5251182151041451, -0.6302380989474351, -0.7029248305223321, -0.7250979427955713, -0.6789238417864432, -0.5479006829369082, -0.31791856390294565, 0.02178556842301571, 0.4778334277487088, 1.0520817308059962, 1.7412076680705393, 2.536528399265516, 3.4240801178819424, 4.384929418443012, 5.395710405488904, 6.4293743535259775, 7.456123209938752, 8.444549707768699, 9.36290600807488, 10.180238828700665, 10.867582554410172, 11.399121648884835, 11.753270349260024, 11.913725429486432, 11.870180782306049, 11.618655427970362, 11.16171344455899, 10.508469183478605, 9.674390355539096, 8.68086247179888, 7.554305671143521, 6.32516066009079, 5.026820727726524, 3.6944742783273252, 2.3639010930974322, 1.0701394313831538, -0.15389620406438775, -1.2784727703238794, -2.277962609619564, -3.1316343676856793, -3.8242967763961566, -4.346727285486192, -4.695938793328864, -4.874906074356135, -4.892169535679185, -4.761323779492646, -4.5003237853915445, -4.130605567151322, -3.6761862487433876, -3.162472890138165, -2.6151856950542207, -2.0593569801978098, -1.5183673287542174, -1.0131192083272387, -0.5613539288255169, -0.17707499072928543, 0.12979119128039415, 0.3535705759200568, 0.4927628135863804, 0.5497988879952062, 0.5306643780055351, 0.44435819647705477, 0.30228424148964383, 0.11755557086172434, -0.0957928739480936, -0.3235398737180288, -0.5519863391304817, -0.7685869737424786, -0.9624508100495944, -1.1247749073531126, -1.2491329264732767, -1.3316148897394622, -1.3708547116689114, -1.3678733972990371, -1.3258179219463455, -1.2496190944683043, -1.1455695973219981, -1.0208655771261703, -0.8831426404793941, -0.7399850082992023, -0.5984857899039352, -0.4648734867911302, -0.34422233427372817, -0.2402562788781347, -0.15525117153652104, -0.09003075231906978, -0.044060281144764867, -0.015627217852536898, -0.0020891844124316696, -0.0001683730225564504, -0.006271592360582881, -0.016812472618865922, -0.028509825518372018, -0.03864198988155254, -0.04523964587798962, -0.04720439096797163, -0.044345135157186265, -0.03732187112311962, -0.02750755317725951, -0.01677813805232611, -0.007244305847089476, -0.0009438195645348382, 0.000483261376540122, -0.0038901627517260898, -0.013999513745018028, -0.028568583566818455, -0.044969773805942755, -0.05918426627689984, -0.0658772721200849, -0.05858376277316909, -0.030006719328246757, 0.027578713353299037, 0.12182953984166632, 0.25976980693902935, 0.4472093992917212, 0.6881618962852947, 0.9842842280866159, 1.3343788070394298, 1.7339948485082868, 2.175195523932831, 2.646583117772526, 3.133375484539029, 3.6176636178094452, 4.07887251101474, 4.494427903440551, 4.84064707181451, 5.093959603064096, 5.231804552913807, 5.233634738777757, 5.081996044848862, 4.763591031664338, 4.270267869027334, 3.6001337261426274, 2.757776439396239, 1.754426058469526, 0.6079720813497573, -0.6573343833712598, -2.0113853865758875, -3.4188229030159025, -4.840511174397293, -6.2349811495897915, -7.560004853932438, -8.77423256961267, -9.83877153388543, -10.718810389820796, -11.385283524758995, -11.816245409676547, -11.998070358825945, -11.926092184017662, -11.605002854493918, -11.049049670498757, -10.281559471297104, -9.334205278332389, -8.24587173056219, -7.061033901230258, -5.828054116035978, -4.597354001522242, -3.419161428703995, -2.341397546753258, -1.4075548862445586, -0.6547750140680654, -0.11222616267800246, 0.20021937731297812, 0.2730038659108499, 0.10741700360729166, -0.2843731059294321, -0.8797741729329512, -1.646676010542898, -2.544802573863292, -3.5274354710839657, -4.543444919474069, -5.5395430117114035, -6.462632617532473, -7.262201413412692, -7.892740423625729, -8.31580176492675, -8.501726842133785, -8.431022879573561, -8.095311919444345, -7.497849244015994, -6.653640064264958, -5.588696553425493, -4.338837064908015, -2.9481439997312715, -1.4670558478612632, 0.04982503396165995, 1.5461785308935407, 2.9666285366144605, 4.259244134429257, 5.377860938907999, 6.284158732512642, 6.949463485317579, 7.356285779970104, 7.4990153156110395, 7.384122540249886, 7.029874935720392, 6.465532492730426, 5.7301300235016255, 4.870848936861713, 3.940631292415898, 2.995715034362041, 2.0930811041059814, 1.287861351324297, 0.6308357022566686, 0.16609405359069926, -0.07111452562923136, -0.05602768416950183, 0.22447107307200334, 0.7712010908512502, 1.5725964860034227, 2.605216408040954, 3.834734852952415, 5.21741877170083, 6.702018357431004, 8.232016461825765, 9.748155110290892, 11.191176355493187, 12.504291887791235, 13.635560084356124, 14.5400907674704, 15.181997143537053, 15.535924681320592, 15.58828750214691, 15.337483909452995, 14.79374038882559, 13.978566479857408, 12.923739864387894, 11.669855579265208, 10.26463301675026, 8.760508086123261, 7.212276401079131, 5.674801025537597, 4.200752231849686, 2.8384802703195686, 1.630108759564845, 0.6098203985517074, -0.19731589758114387, -0.7759602786519487, -1.120805267966647, -1.2364579306469423, -1.1369006974605507, -0.8444967828907509, -0.388506595608671, 0.19662931709918308, 0.8728868084634395, 1.6004618402290793, 2.3396389472354073, 3.0525982073689075, 3.7052825866118715, 4.268610407512468, 4.719347063352953, 5.040830344715684, 5.223425290879533, 5.264607976073698, 5.168776746491256, 4.946346867911978, 4.612813958432554, 4.1876975499830404, 3.693380752308798, 3.1538780387550576, 2.593478288111193, 2.035417959588696, 1.5008183454412705, 1.0078045254095473, 0.5708308273231962, 0.20025003431888566, -0.09791284051905241, -0.3218948008065122, -0.47388934412579525, -0.5595518771441588, -0.5873591423604295, -0.5678335062282458, -0.512699903118823, -0.43404554902397796, -0.34352312016192066, -0.2516391691910968, -0.16716514067317098, -0.09670419325669374, -0.04443183137351747, -0.01201495488859629, 0.0012964780482351721, -0.0015826619807657273, -0.015968813757259063, -0.03590777392865719, -0.054729981739727374, -0.06563419925696919, -0.06226336382006596, -0.03923617469371527, 0.007420453707506979, 0.07996171478026383, 0.17872774175182923, 0.3020758938607273, 0.44644807666279046, 0.6066034109036981, 0.7760131265332189, 0.9472450180793821, 1.1124055927268017, 1.2636202538010133, 1.3935317356325663, 1.4958233466872726, 1.5656713211323519, 1.5999268590353737, 1.5972461646512333, 1.558144361456138, 1.4849803536113697, 1.3818081962669484, 1.2541295923740643, 1.1084202607826712, 0.9516916671213815, 0.7910760339870191, 0.633432961948537, 0.4849377398050572, 0.35076171575877346, 0.23477005611677929, 0.13937490834406963, 0.06550901637288395, 0.012690410505834271, -0.020820238162935663, -0.03777671814352615, -0.041645083659791575, -0.036256817862870536, -0.02546011976036609, -0.012791194490154865, -0.0011953308951456979, 0.007177092552019331, 0.01109174174698049, 0.010250438188115042, 0.0052143140228486816, -0.002766459655372175, -0.011996969951438698, -0.020629090357191713, -0.02696985214008075, -0.02976940202248409, -0.02845425771380898, -0.02326938861140886, -0.015292322364248495, -0.00629550408603255, 0.001560690621947859, 0.006207441734663492, 0.006312221236523669, 0.0020677918056627846, -0.003910391537041167, -0.005627396765688593, 0.007248190703373346, 0.050275952856841784, 0.14499688413169337, 0.31947477087829956, 0.6085571427606346, 1.0538069735050228, 1.7030497045426582, 2.609496642583526, 3.8304231937335986, 5.425406669127249, 7.454200031253094, 9.97447285769857, 13.039170755746381, 16.693615996272687, 20.97253773632567, 25.897151913203704, 31.47266328521767, 37.687114700089836, 44.50959442383901, 51.88859292639149, 59.75130546538091, 68.00365492095351, 76.53180812073965, 85.20718056053333, 93.8877188208762, 102.4198476869256, 110.6420146400905, 118.38873354080494, 125.4966547309534, 131.81473098946427, 137.20477560815604, 141.54406717257484, 144.72912226056437, 146.67906179127868, 147.341237243143, 146.6981210728062, 144.76202242883443, 141.57323851513937, 137.19895680199826, 131.73164307418088, 125.28950760316114, 118.01509211849037, 110.06545317124267, 101.60620157212672, 92.80678535616134, 83.83639670801311, 74.86092443359966, 66.03867956612419, 57.513073542580436, 49.40870216578358, 41.82914791399972, 34.85607660036165, 28.548531700214884, 22.94296028701346, 18.052799804779358, 13.87009227440109, 10.3681312308958, 7.504612815402865, 5.224698252828517, 3.4645117713835902, 2.1543763848877324, 1.2222636928049628, 0.5970210724534388, 0.211122759761365, 0.0029060289216266467, -0.08171266336100387, -0.08812727477534503, -0.052506505238589254, -0.0018348049238388483, 0.045545787112369084, 0.07897690414086571, 0.09420389507109855, 0.0918867920218761, 0.07602200699039101, 0.052393921233254, 0.02716061612437306, 0.00566262297476276, -0.008474391069969188, -0.013899442932624823, -0.011738047331247376, -0.005443704317684389, -0.00033040713776747636, -0.0028411079968739088, -0.01962838730007318, -0.05653517781266609, -0.11756267047970384, -0.20391858549024214, -0.3132339034916353, -0.4390324394247227, -0.5705298467719335, -0.6927431512665863, -0.7869564788882806, -0.8315310475357479, -0.8030364763323011, -0.6776544209448228, -0.4327368650515253, -0.04838821272815354, 0.4909432460331778, 1.1949663011585365, 2.0662318180105483, 3.0991747328052983, 4.279840663333864, 5.585796019187618, 6.9864038066654315, 8.443560797708436, 9.912869037101169, 11.345434497129895, 12.690743147106922, 13.89853541344355, 14.920729126530146, 15.713589119549765, 16.23980856084879, 16.470758552447755, 16.389353885618373, 15.99010937422623, 15.279144689437148, 14.274144785313785, 13.003829472052313, 11.507293996567498, 9.833409449551063, 8.03750455479189, 6.178658400514688, 4.317237791195405, 2.5124022537448827, 0.8198269640387837, -0.7103933531213882, -2.0365281242854243, -3.1269163336382673, -3.9609860057255974, -4.529756795041097, -4.83585995275812, -4.893079196600747, -4.7253623990208355, -4.365214159596828, -3.851724793373316, -3.2283817987840133, -2.5407922648148924, -1.834403505528871, -1.1521260573807808, -0.5322497842744689, -0.00673176937512682, 0.4001091507849527, 0.6724315435449975, 0.8031986916269723, 0.794107282025463, 0.654993632077358, 0.40280733510974626, 0.06024173901296257, -0.3459171370203589, -0.7866321888572233, -1.232402066863195, -1.6550099797876443, -2.0291319023709162, -2.333704332159177, -2.5530105697831833, -2.677461542223997, -2.7037734860911598, -2.6348274853653777, -2.4791819724297532, -2.250285904462645, -1.9654659939184642, -1.6447169951728775, -1.3092300771917298, -0.9799906069012023, -0.6764628806951947, -0.4154950183168682, -0.21039429309772897, -0.07023101762161701, 0.0005621814308847722, 0.002245464757002931, -0.06050766412394742, -0.17912839687320656, -0.34187140408982464, -0.5347414981354065, -0.7425216559838457, -0.9498957975163166, -1.142432488540183, -1.3074246649013286, -1.434639162916337, -1.5169464514616091, -1.5506066257326556, -1.5353612258368825, -1.4741277904118681, -1.37257755426393, -1.2385997651739309, -1.0816836873732725, -0.9120912172373498, -0.7400071768724986, -0.5747463068435493, -0.42413806176895275, -0.29407111856926477, -0.18821578893788934, -0.10787959713422796, -0.05208947274879199, -0.017906704282559593, -0.000909370626171827, 0.004209020742374127, 0.0029745126225674996, 0.0004502830292264362, 0.0005856669872793896, 0.005666553186283778, 0.01591662837187925, 0.0292849323152379, 0.041444026853978105, 0.04601197697101841, 0.03498886263822247, -0.0006207013651244283, -0.07003865407433113, -0.18184746134734914, -0.3430853961508207, -0.5583925324883341, -0.829261419438358, -1.1534520052808934, -1.5246250609558138, -1.9322548152042893, -2.3618675129103455, -2.795528502532115, -3.2126020257141383, -3.590754136260723, -3.907152199280472, -4.139869119100995, -4.269333623810841, -4.279554099106504, -4.159259723806985, -3.9028577036266, -3.5111382733287666, -2.99167258312398, -2.358760962145987, -1.6328483459873366, -0.839659342450953, -0.009035273227903498, 0.8265196190397143, 1.6335488633886461, 2.3794878341927226, 3.034464492849179, 3.572938235858873, 3.9751409215276334, 4.228282669309657, 4.327307214809464, 4.275281527452399, 4.083091676393587, 3.768732371379144, 3.3562367370271637, 2.8742099314842973, 2.354003936987295, 1.8277802379010335, 1.3263365465534434, 0.8771074182161094, 0.5023988942429027, 0.21791050055022956, 0.0316890276630694, -0.056428383943405665, -0.054794957335901236, 0.020670969271838095, 0.14766486752610514, 0.2991731039439557, 0.4455513617316634, 0.556897718969539, 0.6056200253495804, 0.5689573139122377, 0.4312935936731164, 0.18616531258143712, -0.16219961712560638, -0.5979414371368995, -1.0933472565662954, -1.6095508004401484, -2.0978277081461254, -2.5015148293332703, -2.7586443126330478, -2.8051498189170054, -2.5785062342603533, -2.0217169340994037, -1.0867041521169762, 0.26231232219183254, 2.0457625781277247, 4.266339266289865, 6.907259505192031, 9.931685922605476, 13.283202905688823, 16.88697147344476, 20.651895867015874, 24.47415190724262, 28.241360455606745, 31.836903209769932, 35.14442406458127, 38.052517829312904, 40.45957644735754, 42.27959801746949, 43.44628472346593, 43.91483278647718, 43.66370893532755, 42.69558873990198, 41.03763581243624, 38.742431923052756, 35.88460586061324, 32.55632741886415, 28.863345416820682, 24.920568049996835, 20.847817141481226, 16.766106786023556, 12.791067976347358, 9.028082280239863, 5.5685584189436135, 2.486986208530072, -0.16077615254443536, -2.3388346060432164, -4.032200846158653, -5.245980440921195, -6.003625346024802, -6.344429524573878, -6.320382219001686, -5.992866836841673, -5.429004173383235, -4.697892816580096, -3.867048692760703, -2.9992179471590945, -2.149679844280435, -1.3641314915892533, -0.6774382508877794, -0.1130427070720847, 0.31695068715265806, 0.6110499349482251, 0.7770933972753875, 0.8304624394823549, 0.7919654832723118, 0.6856664463373409, 0.536734124488044, 0.3694324344944635, 0.20533248011374897, 0.06188629474365716, -0.04843789607422126, -0.1185758554269199, -0.14685191393270994, -0.1365415288402401, -0.09504607024014709, -0.03273678679848368, 0.03835198633882777, 0.10584313179338979, 0.15829327204707158, 0.1863308530612308, 0.18356755632901792, 0.14720814798857157, 0.07819434194911021, -0.018954875829535093, -0.13659164893178333, -0.2647015001682355, -0.3918954556309717, -0.5066169641127514, -0.5982905311375029, -0.6583423950382427, -0.6810684631454271, -0.6642676132873505, -0.6095870011904069, -0.5225771176363773, -0.41212923853865885, -0.289622219755651, -0.16781810194550723, -0.05953474576853598, 0.023800546897421428, 0.07363379441090308, 0.08576037463890339, 0.06149711783531205, 0.008499479694321365, -0.058837417452167556, -0.11945272227936242, -0.14621852445948397, -0.10708733059766752, 0.03327099717502932, 0.31142685608586024, 0.7628471683568864, 1.4193636514108747, 2.306571400843799, 3.4414961827509023, 4.830567574094808, 6.4680072135224975, 8.33478532929951, 10.398249511688087, 12.612204832937573, 14.917310332003096, 17.243108734589534, 19.510609021768122, 21.635481286231126, 23.53220322591546, 25.12289867749392, 26.340824824699887, 27.13041808424843, 27.449419617919595], 'positive_zeros': ['0.20604686625198852874512881353788', '0.33371892252096111230374058078294', '0.828149995391711281771873785558955', '0.969093584635709347704566490878805', '0.982483936409185624519269565669975', '1.28575157749916072699506230106633', '2.09991871873655084352031644836582', '2.10348371509837615737129583890142', '2.33022616579725847727764820505605', '2.37800815811876254332999011334093', '2.40809580187535808164944235330671', '2.50360962358946449610175176023255', '2.99436100914583143567323470228049', '3.09548739059331655859451273394412', '3.25187007387353048281582502363777', '3.78286239579947985653421401019863', '3.89088142332429302203860439398170', '3.92675635240559193458960460843450', '4.23986839540833921490792650258678', '4.24728976343177361405627388234510', '4.42341650003283301003544025171225', '4.56342519994204696079251652981873', '4.92251823871788678271149017095716', '5.01968882865059807055323890371844', '5.17662748439117658362962948428012', '5.22948159504429983294118847357003', '5.50624884525219354561002452777737', '5.75450931492486003774020820337204', '5.75684666730261384845037905507994', '6.08458722929550626111649704771305', '6.29613099818038788599820377925714', '6.39809765747283885470274749350510', '6.43261027455390484333895962931997', '6.56242698272141716308875421910537', '6.62651635333911371211059839357556', '6.83735562271273727985228382471393', '7.29758048640475857949668644318732', '7.30742308634950985235320591166323', '7.33264386419012854822471944413372', '7.46817422580999530575202340169693', '7.76948005825038946831702015513693', '7.974419144598456965370932301748069', '8.057951900375952081075878177928510', '8.317180492262126466353327027812394', '8.322191091759754522241541587699409', '8.450823095107822087322875618019781', '8.460753148221496131511489503825908', '8.547819293126021313861241693393043', '8.807196798815046496242127271612407', '9.075860399018865763306617892171037', '9.107669891487995054135097420324032', '9.322574327266213831475954344028388', '9.526827462673495767294920467715800', '9.544791872155365912946285047456365', '9.851334404736317357671774432569409', '9.923788457087067410563906709865386', '10.16294807774722505265696328435454', '10.32095619040348418012261483950779', '10.39449246800823800498689538623815', '10.69082772970058549305236857753190'], 'prelabel': '12-675e6-1.1-c3e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.310807337724305, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e6-0', 'trace_hash': 107372945884881176, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20604686625198852874512881354', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.33371892252096111230374058078', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.828149995391711281771873785559', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3990424166.153653, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 94585080322265625, 'conductor_radical': 15, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 4, 0, 0, -374, 0, 0, 0, 0, 0, 0, 0, 0, 0, 320, 0, 454, 0, 0, 0, 0, 0, 0, 0, 0, 0, 676, 0, 0, -76, 0, 0, 0, 0, 1226, 0, 0, 0, 0, 0, 0, 0, 0, 0, 280, 0, 1190, 0, 0, 819, 0, 0, 0, 0, 0, 0, 1204, 0, 0, 0, 0, -374, 0, 0, -1258, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4308, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 76, 4206, 140708, 6941959, 323708584, 15228577508, 430856125304, 12298103827999, 331782103705228, 13200229752488526, 317470860875589476, 5559917313492231481], 'euler13': [1, 0, -3246, 0, 11631063, 0, -30956231140, 0, 56140919567967, 0, -75625584307573326, 0, 112455406951957393129], 'euler17': [1, 0, -6163, 0, 56646390, 0, -189472696871, 0, 1367306147225910, 0, -3590700848047017043, 0, 14063084452067724991009], 'euler19': [1, 374, 83297, 13116126, 1678114378, 178142128678, 16104727242289, 1221876860602402, 78948369331777018, 4232412502719284154, 184362492813454012817, 5677741509173174563826, 104127350297911241532841], 'euler2': [1, 0, -1, 0, -3, 0, -812, 0, -192, 0, -4096, 0, 262144], 'euler23': [1, 0, -19839, 0, 507262974, 0, -5894416200139, 0, 75093125312873886, 0, -434764234106851148319, 0, 3244150909895248285300369], 'euler29': [1, -320, 76398, -7951120, 1855772023, -384085002800, 90944175951716, -9367449133289200, 1103856477739748383, -115348058511651523280, 27030741807331423794318, -2761340399231419021103680, 210457284365172120330305161], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -454, 194329, -59958470, 15604346290, -3335180728774, 637742673357065, -99358369090906234, 13848914771973693490, -1585279292131927333370, 153065721110845086505369, -10653228944297487412197754, 699053619999045038539170241], 'euler37': [1, 0, -97986, 0, 8873792007, 0, -470111365900348, 0, 22767722500333012863, 0, -645037135244241697044066, 0, 16890053810563300749953435929], 'euler41': [1, -676, 442146, -179778788, 72783658399, -22153724392024, 6633742695230108, -1526856838822686104, 345729964436585170159, -58856327378441823099268, 9976356982345707710969826, -1051246460934279627760694276, 107178930967531784356353269521], 'euler43': [1, 0, -156726, 0, 19336556583, 0, -1757584565934100, 0, 122233394278673901567, 0, -6262713096331774549023126, 0, 252599333573498060811820806649], 'euler47': [1, 0, -508570, 0, 117397962543, 0, -15651426994430252, 0, 1265457917436873421647, 0, -59091502564717978436025370, 0, 1252453015827223091648143056289], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -744595, 0, 248680653006, 0, -47637358185692759, 0, 5511847799020523403774, 0, -365788923815037011114915395, 0, 10888439761782913818722623349689], 'euler59': [1, -280, 918978, -172662200, 393478450183, -58693055990080, 102589405915891196, -12054321146186640320, 16597131004952574106303, -1495771916639762808605800, 1635043285018929297093867618, -102314740236972757160884811720, 75047496554032956760519149093721], 'euler61': [1, -1190, 1710413, -1343700426, 1087127898034, -608446972507054, 340663988576853253, -138105902266623623974, 56009236284998715906274, -15713429086647470809044066, 4540032992175257233812296573, -716959273596698080524212092190, 136753052840548005895349735207881], 'euler67': [1, 0, -1185590, 0, 637803099863, 0, -223447532584291412, 0, 57694636555980125542847, 0, -9701349706143669102020075990, 0, 740195513856780056217081017732809], 'euler7': [1, 0, -1226, 0, 769535, 0, -316892876, 0, 90535023215, 0, -16969418108426, 0, 1628413597910449], 'euler71': [1, -1204, 1342566, -890805452, 772040400799, -512811665615416, 379083129921051668, -183540936052079155976, 98898594540834535252879, -40842094406020313798917012, 22031082118371171241253402406, -7071339975100133998056265983404, 2102085018129621311776010144838961], 'euler73': [1, 0, -467850, 0, 420984954303, 0, -140390583242060428, 0, 63709432338754526271567, 0, -10714723178550467538185099850, 0, 3465863721549107204083472585375569], 'euler79': [1, 1258, 3547993, 3227336138, 4821357993874, 3244977887200810, 3268997100014035913, 1599900652527600161590, 1172011646886663765478354, 386801386911679720769512022, 209656267499802674478278997913, 36651099740492355879562619812342, 14364405059580771582276370834385761], 'euler83': [1, 0, -1042599, 0, 467625790374, 0, -106913777507688499, 0, 152885750501849286150006, 0, -111443415178320349648909448439, 0, 34946659039493167390823397237402409], 'euler89': [1, -4308, 10984674, -19889703636, 27941240181759, -31517105787288312, 29183298471007787932, -22218582549758854022328, 13886273616581954103780399, -6968485036716652441863519924, 2713109064292842335776439237154, -750111449209784923173122515317492, 122749609618842355502421774953773681], 'euler97': [1, 0, -4626246, 0, 9511067662287, 0, -11170340228400453268, 0, 7922453099670579471412623, 0, -3209885447185701067112932246086, 0, 577951262543040979328274795306257089], 'euler_factors': [[1, 0, -1, 0, -3, 0, -812, 0, -192, 0, -4096, 0, 262144], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1226, 0, 769535, 0, -316892876, 0, 90535023215, 0, -16969418108426, 0, 1628413597910449], [1, 76, 4206, 140708, 6941959, 323708584, 15228577508, 430856125304, 12298103827999, 331782103705228, 13200229752488526, 317470860875589476, 5559917313492231481], [1, 0, -3246, 0, 11631063, 0, -30956231140, 0, 56140919567967, 0, -75625584307573326, 0, 112455406951957393129], [1, 0, -6163, 0, 56646390, 0, -189472696871, 0, 1367306147225910, 0, -3590700848047017043, 0, 14063084452067724991009], [1, 374, 83297, 13116126, 1678114378, 178142128678, 16104727242289, 1221876860602402, 78948369331777018, 4232412502719284154, 184362492813454012817, 5677741509173174563826, 104127350297911241532841], [1, 0, -19839, 0, 507262974, 0, -5894416200139, 0, 75093125312873886, 0, -434764234106851148319, 0, 3244150909895248285300369], [1, -320, 76398, -7951120, 1855772023, -384085002800, 90944175951716, -9367449133289200, 1103856477739748383, -115348058511651523280, 27030741807331423794318, -2761340399231419021103680, 210457284365172120330305161], [1, -454, 194329, -59958470, 15604346290, -3335180728774, 637742673357065, -99358369090906234, 13848914771973693490, -1585279292131927333370, 153065721110845086505369, -10653228944297487412197754, 699053619999045038539170241], [1, 0, -97986, 0, 8873792007, 0, -470111365900348, 0, 22767722500333012863, 0, -645037135244241697044066, 0, 16890053810563300749953435929], [1, -676, 442146, -179778788, 72783658399, -22153724392024, 6633742695230108, -1526856838822686104, 345729964436585170159, -58856327378441823099268, 9976356982345707710969826, -1051246460934279627760694276, 107178930967531784356353269521], [1, 0, -156726, 0, 19336556583, 0, -1757584565934100, 0, 122233394278673901567, 0, -6262713096331774549023126, 0, 252599333573498060811820806649], [1, 0, -508570, 0, 117397962543, 0, -15651426994430252, 0, 1265457917436873421647, 0, -59091502564717978436025370, 0, 1252453015827223091648143056289], [1, 0, -744595, 0, 248680653006, 0, -47637358185692759, 0, 5511847799020523403774, 0, -365788923815037011114915395, 0, 10888439761782913818722623349689], [1, -280, 918978, -172662200, 393478450183, -58693055990080, 102589405915891196, -12054321146186640320, 16597131004952574106303, -1495771916639762808605800, 1635043285018929297093867618, -102314740236972757160884811720, 75047496554032956760519149093721], [1, -1190, 1710413, -1343700426, 1087127898034, -608446972507054, 340663988576853253, -138105902266623623974, 56009236284998715906274, -15713429086647470809044066, 4540032992175257233812296573, -716959273596698080524212092190, 136753052840548005895349735207881], [1, 0, -1185590, 0, 637803099863, 0, -223447532584291412, 0, 57694636555980125542847, 0, -9701349706143669102020075990, 0, 740195513856780056217081017732809], [1, -1204, 1342566, -890805452, 772040400799, -512811665615416, 379083129921051668, -183540936052079155976, 98898594540834535252879, -40842094406020313798917012, 22031082118371171241253402406, -7071339975100133998056265983404, 2102085018129621311776010144838961], [1, 0, -467850, 0, 420984954303, 0, -140390583242060428, 0, 63709432338754526271567, 0, -10714723178550467538185099850, 0, 3465863721549107204083472585375569], [1, 1258, 3547993, 3227336138, 4821357993874, 3244977887200810, 3268997100014035913, 1599900652527600161590, 1172011646886663765478354, 386801386911679720769512022, 209656267499802674478278997913, 36651099740492355879562619812342, 14364405059580771582276370834385761], [1, 0, -1042599, 0, 467625790374, 0, -106913777507688499, 0, 152885750501849286150006, 0, -111443415178320349648909448439, 0, 34946659039493167390823397237402409], [1, -4308, 10984674, -19889703636, 27941240181759, -31517105787288312, 29183298471007787932, -22218582549758854022328, 13886273616581954103780399, -6968485036716652441863519924, 2713109064292842335776439237154, -750111449209784923173122515317492, 122749609618842355502421774953773681], [1, 0, -4626246, 0, 9511067662287, 0, -11170340228400453268, 0, 7922453099670579471412623, 0, -3209885447185701067112932246086, 0, 577951262543040979328274795306257089]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/4/b/k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-675e6-1.1-c3e6-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '12-675e6-1.1-c3e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.310807337724305, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e6-0', 'trace_hash': 107372945884881176, 'z1': {'__RealLiteral__': 0, 'data': '0.20604686625198852874512881354', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '261195433679478962621842383458,423038992441214336543587752590,1049804838737308219162632650835,1245446351703697723220020222910,1629883758961203908077802383570,2661963224236883111088002092409', 'Lhash_array': ['261195433679478962621842383458', '423038992441214336543587752590', '1049804838737308219162632650835', '1245446351703697723220020222910', '1629883758961203908077802383570', '2661963224236883111088002092409'], 'label': '12-675e6-1.1-c3e6-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/4/b/k'}