-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '317680642507658264862994385982,670058398231872044975930042134,1179602482693819901989854044017,1448969047484526790292787016299,1855844218452738897511394380121,2382010695612312197989202513031', 'a10': 30, 'a2': 6, 'a3': 0, 'a4': 12, 'a5': 5, 'a6': 0, 'a7': 8, 'a8': -16, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 123068589.72907074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -6, 24, -56, 96, -96, 64]], [3, [1]], [7, [1, -8, -154, 6811, -52822, -941192, 40353607]]], 'bad_primes': [2, 3, 7], 'central_character': '378.1', 'coefficient_field': '1.1.1.1', 'conductor': 2917096519063104, 'conductor_radical': 42, 'degree': 12, 'euler_factors': [[1, -6, 24, -56, 96, -96, 64], [1], [1, -5, -242, 1291, 31349, -94946, -3671531, -11868250, 489828125, 2521484375, -59082031250, -152587890625, 3814697265625], [1, -8, -154, 6811, -52822, -941192, 40353607], [1, 29, -2564, -60061, 4759283, 58883294, -5900798285, 78373664314, 8431360150763, -141620696269151, -8046930357912644, 121140196913053879, 5559917313492231481], [1, -20, 13116, -216834, 71816956, -946572092, 210156213331, -2079618886124, 346646729573404, -2299416017045082, 305577684466460796, -1023717860281815140, 112455406951957393129], [1, 38, -10148, -214318, 64981502, 384215870, -350665294625, 1887652569310, 1568495488248638, -25415516515084046, -5912450463407614628, 108772075957373000134, 14063084452067724991009], [1, -57, -14838, 254831, 166435821, -166961520, -1338012994557, -1145189065680, 7830119828903301, 82230828712720349, -32841166769103696918, -865324240702863503043, 104127350297911241532841], [1, 14, -24188, -1111042, 287732402, 11473339118, -3133578440789, 139596117048706, 42594721924175378, -2001156255297174446, -530070935761707524348, 3732893296501477438498, 3244150909895248285300369], [1, -362, 121531, -35449820, 7643263205, -1467483172382, 258002184349975, -35790447091224598, 4546391202875203805, -514275713558280393580, 42999464417743858021771, -3123766326630542767623538, 210457284365172120330305161], [1, 88, -19176, 2427606, -74706896, -63836425952, 24418143111607, -1901750965536032, -66302645196084176, 64184985394977883626, -15104221541929230216936, 2064943055282332361835688, 699053619999045038539170241], [1, -384, 6558, 23609678, -2205845910, -979004345454, 385902155257863, -49589507110281462, -5659597105471637190, 3068354828881553955206, 43170999254298951372798, -128043366893497077921981312, 16890053810563300749953435929], [1, 432, 426972, 142024050, 75304995504, 19099646219340, 6978658947274411, 1316366717083132140, 357706578512036332464, 46496108219464636762050, 9633978580527951203376732, 671802472076344377503875632, 107178930967531784356353269521], [1, 726, 369507, 188519864, 70137886437, 23601580221762, 7530228520363527, 1876490838691631334, 443367043657810066413, 94748690849738418949352, 14765363297004102818204307, 2306553085569315810549786882, 252599333573498060811820806649], [1, 183, -263418, -21765813, 50364860037, 1987643355060, -5827318049035865, 206363096052394380, 542893671353769907173, -24358784600156356304571, -30606928097593016583087738, 2207592748200127387684907769, 1252453015827223091648143056289], [1, 396, -171222, -33593058, 26399387130, -3085597337094, -6213949690744577, -459374474754543438, 585125549933594869770, -110849149725697378392714, -84114332104645165649941302, 28962312148055333410897310172, 10888439761782913818722623349689], [1, 427, -20846, -184632833, -58389254833, 9945164910982, 19570132793727955, 2042528024252572178, -2462889927756278336953, -1599473460265415637012187, -37089149380621299016101326, 156029978861383454670349337873, 75047496554032956760519149093721], [1, 427, -325797, -168225036, 60617986357, 21366910723417, -7516285932983282, 4849882762911914077, 3123061350122630592877, -1967248147456282711754076, -864778932779230677622506837, 257261856996462252423393750727, 136753052840548005895349735207881], [1, 32, -507154, 145892682, 107477835646, -39824972320442, -19149017206317005, -11977878150013097246, 9722271131562838996174, 3969234271000720680877854, -4149898623360172032292689394, 78753890749250944427827201376, 740195513856780056217081017732809], [1, -790, 1701451, -944166712, 1282031105045, -577556027544706, 586920380116026271, -206713655374553269166, 164228548551817875481445, -43288628173467659338856072, 27920271108746048745165483691, -4639832707914539749555191135290, 2102085018129621311776010144838961], [1, -373, -1002964, 125934813, 757146856945, -40185482983214, -334578208592440487, -15632836033680960638, 114582233782919741227105, 7413982263119005177555269, -22969929716900055838341948244, -3323163687288259862996052291661, 3465863721549107204083472585375569], [1, -1364, 318072, 576829470, -209637930452, -324379754397308, 410997275277132367, -159931869728294339012, -50960351094265041425492, 69133932589307854161060930, 18795355096866661314341701752, -39739348208292188727920042467436, 14364405059580771582276370834385761], [1, -154, 2175355, -688383220, 2457194857817, -711364910178034, 1791237335227803895, -406749207895967526758, 803356204255076848275473, -128686534868691424097237660, 232523712784335170291265782155, -9412220795649337564839360066878, 34946659039493167390823397237402409], [1, 1233, -175281, -162125424, 290804803809, -425032882464177, -812862837191430722, -299635006117888395513, 144524546814657150070449, -56801680502191211482853616, -43292724927322713214541464401, 214690672440962119376151360581817, 122749609618842355502421774953773681], [1, -1180, 5633882, -5136751260, 12999765882367, -9162903095428040, 15868409066087035660, -8362734256813595550920, 10828441050642850758186943, -3905117848434971783176923420, 3909025988449700231978226179162, -747236403181411475531065626419740, 577951262543040979328274795306257089], [1, -1391, -1223924, 778324159, 3126248736533, -591520249263866, -3458968634854021355, -609443904336810403666, 3318576029620696130606333, 851241670072740870723307259, -1379148198179240908390539772724, -1614907816919667962417235867637891, 1196147475686664860781049986817531801], [1, 747, -2155275, -1395827842, 3118671234423, 1105740393793551, -3172668509659723482, 1208272383288845603577, 3723856549581714468217767, -1821238737483843762779079886, -3072906795397398326650095511275, 1163801660200771141650220065448029, 1702433061239903677780481956434843889], [1, 783, -1201200, -2033885295, -283363871259, 828215102061684, 1707777940609562731, 1014599113274951552412, -425252762215813808607891, -3739215157598633613415274565, -2705332536659740993267823761200, 2160321696380106446917388603485869, 3379932275732534791891466777752413049], [1, -1780, -820867, 856683492, 3665789654266, -465960779599292, -5748589347507512627, -603432722443691519468, 6147896235489299668497706, 1860625118883969419912906388, -2308823701427779247815495972627, -6483618778243785712063308675345220, 4717120417286669419611030657597553321], [1, -3242, 7166029, -12475320110, 19994907355274, -28979767716698162, 38358976400320467829, -41814819899120627855314, 41628432411567289319409866, -37476384800218514849791870030, 31061318237143532725622520145549, -20276344564494595440081904671941194, 9024267965168278308669913635234402529]], 'euler_factors_factorization': [[[[1, -2, 4], 3]], [1], [[[1, -5, -242, 1291, 31349, -94946, -3671531, -11868250, 489828125, 2521484375, -59082031250, -152587890625, 3814697265625], 1]], [[[1, -8, -154, 6811, -52822, -941192, 40353607], 1]], [[[1, 29, -2564, -60061, 4759283, 58883294, -5900798285, 78373664314, 8431360150763, -141620696269151, -8046930357912644, 121140196913053879, 5559917313492231481], 1]], [[[1, -10, 6508, -43337, 14298076, -48268090, 10604499373], 2]], [[[1, 38, -10148, -214318, 64981502, 384215870, -350665294625, 1887652569310, 1568495488248638, -25415516515084046, -5912450463407614628, 108772075957373000134, 14063084452067724991009], 1]], [[[1, -57, -14838, 254831, 166435821, -166961520, -1338012994557, -1145189065680, 7830119828903301, 82230828712720349, -32841166769103696918, -865324240702863503043, 104127350297911241532841], 1]], [[[1, 14, -24188, -1111042, 287732402, 11473339118, -3133578440789, 139596117048706, 42594721924175378, -2001156255297174446, -530070935761707524348, 3732893296501477438498, 3244150909895248285300369], 1]], [[[1, -181, 44385, -9691225, 1082505765, -107663021101, 14507145975869], 2]], [[[1, 88, -19176, 2427606, -74706896, -63836425952, 24418143111607, -1901750965536032, -66302645196084176, 64184985394977883626, -15104221541929230216936, 2064943055282332361835688, 699053619999045038539170241], 1]], [[[1, -384, 6558, 23609678, -2205845910, -979004345454, 385902155257863, -49589507110281462, -5659597105471637190, 3068354828881553955206, 43170999254298951372798, -128043366893497077921981312, 16890053810563300749953435929], 1]], [[[1, 216, 190158, 29937897, 13105879518, 1026022516056, 327381934393961], 2]], [[[1, 363, 118869, 51110485, 9450917583, 2294654786787, 502592611936843], 2]], [[[1, 183, -263418, -21765813, 50364860037, 1987643355060, -5827318049035865, 206363096052394380, 542893671353769907173, -24358784600156356304571, -30606928097593016583087738, 2207592748200127387684907769, 1252453015827223091648143056289], 1]], [[[1, 396, -171222, -33593058, 26399387130, -3085597337094, -6213949690744577, -459374474754543438, 585125549933594869770, -110849149725697378392714, -84114332104645165649941302, 28962312148055333410897310172, 10888439761782913818722623349689], 1]], [[[1, 427, -20846, -184632833, -58389254833, 9945164910982, 19570132793727955, 2042528024252572178, -2462889927756278336953, -1599473460265415637012187, -37089149380621299016101326, 156029978861383454670349337873, 75047496554032956760519149093721], 1]], [[[1, 427, -325797, -168225036, 60617986357, 21366910723417, -7516285932983282, 4849882762911914077, 3123061350122630592877, -1967248147456282711754076, -864778932779230677622506837, 257261856996462252423393750727, 136753052840548005895349735207881], 1]], [[[1, 32, -507154, 145892682, 107477835646, -39824972320442, -19149017206317005, -11977878150013097246, 9722271131562838996174, 3969234271000720680877854, -4149898623360172032292689394, 78753890749250944427827201376, 740195513856780056217081017732809], 1]], [[[1, -395, 772713, -166861721, 276562482543, -50599612148795, 45848500718449031], 2]], [[[1, -373, -1002964, 125934813, 757146856945, -40185482983214, -334578208592440487, -15632836033680960638, 114582233782919741227105, 7413982263119005177555269, -22969929716900055838341948244, -3323163687288259862996052291661, 3465863721549107204083472585375569], 1]], [[[1, -1364, 318072, 576829470, -209637930452, -324379754397308, 410997275277132367, -159931869728294339012, -50960351094265041425492, 69133932589307854161060930, 18795355096866661314341701752, -39739348208292188727920042467436, 14364405059580771582276370834385761], 1]], [[[1, -77, 1084713, -260668709, 620224792131, -25174408749413, 186940255267540403], 2]], [[[1, 1233, -175281, -162125424, 290804803809, -425032882464177, -812862837191430722, -299635006117888395513, 144524546814657150070449, -56801680502191211482853616, -43292724927322713214541464401, 214690672440962119376151360581817, 122749609618842355502421774953773681], 1]], [[[1, -590, 2642891, -1009069940, 2412095257643, -491453482908110, 760231058654565217], 2]], [[[1, -1391, -1223924, 778324159, 3126248736533, -591520249263866, -3458968634854021355, -609443904336810403666, 3318576029620696130606333, 851241670072740870723307259, -1379148198179240908390539772724, -1614907816919667962417235867637891, 1196147475686664860781049986817531801], 1]], [[[1, 747, -2155275, -1395827842, 3118671234423, 1105740393793551, -3172668509659723482, 1208272383288845603577, 3723856549581714468217767, -1821238737483843762779079886, -3072906795397398326650095511275, 1163801660200771141650220065448029, 1702433061239903677780481956434843889], 1]], [[[1, 783, -1201200, -2033885295, -283363871259, 828215102061684, 1707777940609562731, 1014599113274951552412, -425252762215813808607891, -3739215157598633613415274565, -2705332536659740993267823761200, 2160321696380106446917388603485869, 3379932275732534791891466777752413049], 1]], [[[1, -1780, -820867, 856683492, 3665789654266, -465960779599292, -5748589347507512627, -603432722443691519468, 6147896235489299668497706, 1860625118883969419912906388, -2308823701427779247815495972627, -6483618778243785712063308675345220, 4717120417286669419611030657597553321], 1]], [[[1, -1621, 2269194, -2559296581, 3274213215018, -3374843790979189, 3004041937984268273], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '12-378e6-1.1-c3e6-0-0', 'leading_term': '12.6216213430476422137869767080846883157193207842313721591820807576759735528738299785225759', '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/378/4/g/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.01171875', 'prec': 34}, 'plot_values': [12.621621343047641, 12.551465643535783, 12.421972961484444, 12.228271546000329, 11.966088727613794, 11.63191225444683, 11.223374194507539, 10.7421058701208, 10.194019795201983, 9.586056194563835, 8.925575819544706, 8.220244345376974, 7.477535513838825, 6.704399420575443, 5.907676339331289, 5.094394403884069, 4.271786376203658, 3.447267932395575, 2.6284839623854577, 1.8230792904541113, 1.0385691543186828, 0.28222146702654866, -0.4390248802481905, -1.1186443376228545, -1.750572686763085, -2.329248690681218, -2.8496621895082495, -3.307403012872196, -3.6987005122706362, -4.020462733695481, -4.270319260290968, -4.446647890758082, -4.548595904290069, -4.576084464453576, -4.529806277221209, -4.411221402200791, -4.222542685619799, -3.966713100731259, -3.6473761887381264, -3.2688354369456873, -2.8360098571087398, -2.3543824602566414, -1.829941630387506, -1.2691172100780173, -0.6787111714213722, -0.06582175470713536, 0.5622343768070744, 1.1980026595563154, 1.8339730374805585, 2.462664166973842, 3.0767107852418545, 3.6689469818528395, 4.232487315120473, 4.760805686282508, 5.247810880108188, 5.6879216559418, 6.076138853239352, 6.408100626927383, 6.68013351464451, 6.889297458738425, 7.033425720433522, 7.111158183324084, 7.1219649162225425, 7.066147934011884, 6.944837739934577, 6.7599843983467185, 6.514342761743208, 6.211439630876346, 5.855539325457915, 5.451584378290584, 5.005134258868711, 4.5223043888121595, 4.009688839519764, 3.474276642219807, 2.923368392559018, 2.3644751451550654, 1.80522327129678, 1.253256790341691, 0.7161319849384211, 0.2012172559496023, -0.28440773333630515, -0.7340525373774122, -1.1415075418250533, -1.501134590192768, -1.8079485681740224, -2.0576924848589444, -2.2469101073921918, -2.3729995646508537, -2.4342564686752723, -2.4299062166967498, -2.3601242643171028, -2.2260474077322474, -2.029780627477609, -1.7743708293805656, -1.4637698962176233, -1.1027894807523986, -0.6970438629730745, -0.25288451244184795, 0.22267192359691215, 0.7220477523235355, 1.2372087175066242, 1.7597723363087514, 2.281122669279434, 2.7925315350022504, 3.285280685618743, 3.750794726381109, 4.180768177433155, 4.567288349028946, 4.90295901592118, 5.181018873091146, 5.395448034123436, 5.541066564143675, 5.613620157003199, 5.609856885094817, 5.527596002121774, 5.365767787825575, 5.124452981678619, 4.804890344026534, 4.409471025733002, 3.9417249806004375, 3.4062765077293164, 2.8087871389551196, 2.1558987399643685, 1.4551359815857339, 0.7148025494949696, -0.056137516967214446, -0.8481913906114407, -1.6514689354229024, -2.4558159174022416, -3.2509750812570046, -4.02675198453102, -4.77316758163287, -5.480606570495291, -6.139962350716272, -6.742778807812115, -7.281404692174159, -7.749114555787571, -8.140204724262874, -8.450083344265128, -8.67534731871822, -8.813865296535232, -8.864821217560198, -8.828705042248497, -8.707304452655084, -8.503678565886823, -8.22212414866473, -7.868145664986665, -7.448329409890225, -6.970224942975023, -6.442223534565686, -5.873424813604888, -5.273511426461479, -4.6525884067807555, -4.020986330939169, -3.3890867155708286, -2.7671515824736512, -2.16516041110717, -1.5926440030259692, -1.0585176011922464, -0.5709224284389071, -0.13709001776940372, 0.23677537439227014, 0.5456016036540899, 0.7855339371986503, 0.9539935782939851, 1.049715988810271, 1.0727637296935073, 1.024522350430289, 0.9076656989361495, 0.7260933916838058, 0.48484982771109236, 0.1900205275540812, -0.15138510068615588, -0.5315701544014784, -0.9421085965738977, -1.3741096275322646, -1.8183928702148104, -2.2656651258516067, -2.7067011271089965, -3.1325212816752566, -3.5345611639736023, -3.9048350381396766, -4.2360962459709, -4.52197736893047, -4.757103763324278, -4.937182422075945, -5.059075166981058, -5.120853854233207, -5.121852989119359, -5.062666063117797, -4.945099130667724, -4.772119544291743, -4.547783835967008, -4.2771546255661494, -3.9662147157241283, -3.621699905921473, -3.2509416062192154, -2.8617096064874246, -2.4620486847818763, -2.060123826851257, -1.6640435193948544, -1.281669286234313, -0.9204521450861309, -0.587282471678631, -0.2883562249717963, -0.02905170265466254, 0.18618354034906995, 0.35391791382532445, 0.4717937610220345, 0.5385614834049496, 0.554090855029578, 0.5193593223917105, 0.43641560108139327, 0.3083148804760739, 0.13903418692743633, -0.06663083431083432, -0.3031864800481607, -0.5645746831553442, -0.8443210133106354, -1.1356882888258861, -1.4318354620833906, -1.7259771244572766, -2.0115297576955515, -2.282256663753893, -2.532412509363491, -2.756862033658511, -2.9511931858666327, -3.111788893602128, -3.2358843887232362, -3.3216121340133578, -3.368038036427818, -3.375162723251235, -3.3438809871125335, -3.2759192800398584, -3.1737669393212458, -3.0405959193879863, -2.880186079319408, -2.6968000643728116, -2.495035613265714, -2.279696160252631, -2.0556618802654487, -1.8277692311651619, -1.600703281429147, -1.3788544422625, -1.1662079798851526, -0.9662557077055035, -0.781924422502864, -0.615526520568952, -0.46871930431079417, -0.34248043484910795, -0.23711318520691196, -0.15227241624074053, -0.08700919730408811, -0.03983035373594759, -0.008772988932246865, 0.008506490267849996, 0.014633243013324476, 0.012408706203188128, 0.004702310131688102, -0.005657399559898814, -0.01598807069644672, -0.023851290819171065, -0.02714010268658331, -0.02415465335804206, -0.013662574431110035, 0.005058450135427494, 0.03219676128321434, 0.0674023036299481, 0.10980005436042477, 0.15802241281338367, 0.21026102339420796, 0.2643343014074679, 0.3177708747254324, 0.36790098293899615, 0.4119565024313325, 0.4471769334511698, 0.4709161361367155, 0.4807481990217985, 0.4745706218041929, 0.4506921460549711, 0.4079087723278214, 0.3455653383690867, 0.2636009476917039, 0.16257646231287187, 0.0436817641451136, -0.0912840565854159, -0.23995068079667148, -0.3994315608980179, -0.5663965429453274, -0.737163253394552, -0.9078127015427555, -1.0743014340041057, -1.2325789268433853, -1.3787094440747807, -1.5089937358245613, -1.6200991328001684, -1.7091829280830746, -1.7739707646059506, -1.812829248518081, -1.8248245216766352, -1.8097680328759829, -1.7682432995092443, -1.7016015051310023, -1.6119079120134014, -1.501878428620234, -1.3748036441886922, -1.2344588361575006, -1.0849817555070835, -0.9307463784714581, -0.7762062956417328, -0.6257462910695242, -0.48354152545555384, -0.3534119795906788, -0.23868626373336657, -0.14208117170003173, -0.06559241724998038, -0.010413736399932016, 0.02312004580874261, 0.035564459849139064, 0.02836813171165186, 0.0038469734715941444, -0.03487273200964987, -0.08393882887224216, -0.13888235098189897, -0.19474790963157845, -0.24624365381760505, -0.2879119384255049, -0.3143058628605877, -0.32016577603615104, -0.300593641260178, -0.251221754328389, -0.16837360703298465, -0.04921838031154144, 0.10812017470768784, 0.30447935838779105, 0.5395960314223263, 0.8120751779237935, 1.1193890680684138, 1.4579132541635844, 1.8230074675536492, 2.2091174064433736, 2.609901084516019, 3.0183809233472036, 3.4271401596263367, 3.8285149344487337, 4.214783484148725, 4.578364857845487, 4.912014921308461, 5.209042983075737, 5.463513204457043, 5.670379663241488, 5.825603215611516, 5.9262477137852185, 5.970566325776789, 5.958087576033528, 5.889575695052377, 5.767003419792815, 5.593467449597703, 5.373091185712799, 5.110948559520441, 4.812890068075828, 4.485347052327662, 4.135168318282214, 3.769416861336875, 3.3952011959297783, 3.0194943943710166, 2.648919626424019, 2.289593215072996, 1.9469923583323376, 1.6258390829131215, 1.3300213861765786, 1.0625095968330445, 0.8253248692916575, 0.6195432695174627, 0.4453264967316695, 0.3019850245205205, 0.1880539312186439, 0.10139349404898522, 0.0393107033368685, -0.0013096589608858971, -0.02386900016225818, -0.03191276069079859, -0.028993831122270556, -0.018545099018931595, -0.003765247687309221, 0.012478996796961772, 0.02773309803798354, 0.04001364354612252, 0.04784230310701416, 0.05025683023031608, 0.04680038432671787, 0.03749238847449354, 0.022779474035657554, 0.0034676770570742253, -0.019355177308614125, -0.0444041394865974, -0.07028420524488699, -0.09557815539859557, -0.11893440849689879, -0.13914273534239682, -0.1551977847063771, -0.16634867760035674, -0.17213258662900024, -0.17239487691852434, -0.1672928133430152, -0.1572762167594037, -0.14305444597926475, -0.12555039360310322, -0.1058457195134666, -0.0851192449145753, -0.06458031668419441, -0.04539812630695724, -0.028635803834375487, -0.015192669759569273, -0.005757113450248001, -0.0007698818109886572, -0.0004007654359297811, -0.004540895190777735, -0.012812457201435647, -0.024593032813303786, -0.03905241384185871, -0.05520140653913615, -0.07195188480144617, -0.08818510789361896, -0.10281893152487818, -0.11487156985205772, -0.12352199500213727, -0.1281632701629699, -0.12844975572549538, -0.12432240636929646, -0.11601221443355558, -0.10403086671540096, -0.0891443260773341, -0.07233098376509993, -0.05472521114466996, -0.0375365363279451, -0.021964649985128957, -0.009110829422542656, 0.00011196872104411144, 0.005066057337478418, 0.005468440226406752, 0.0014562613944078574, -0.0063672321142174415, -0.016908086235945325, -0.028581947730585762, -0.03934308258990212, -0.04673934458683921, -0.047993835244880226, -0.04011056160546512, -0.02000342163406573, 0.015349142839430209, 0.06874877816260488, 0.14261777210595927, 0.23884063782531112, 0.3586133919424069, 0.502295266382926, 0.6692996816965636, 0.8580256247929997, 1.0658241384134346, 1.288997017731439, 1.5228291349988745, 1.7616716655174078, 1.9990874681362567, 2.2280315057023627, 2.441083984992066, 2.630679905293174, 2.789368607242018, 2.91009829154767, 2.9864972106477117, 3.0131558558190497, 2.985913239252372, 2.902065435393171, 2.76053764789309, 2.562009806930011, 2.3089924432718747, 2.0058497643418356, 1.6587744512895832, 1.275638153976439, 0.8657823434086688, 0.43977258477622194, 0.009102594766013777, -0.41414771871352885, -0.8177099132584681, -1.1895402340856267, -1.5182174007969027, -1.793329442017312, -2.0058396538101104, -2.148449368995729, -2.215908456384352, -2.2051854351205966, -2.1155902943548415, -1.9488308865772626, -1.7090106285674818, -1.4025440959152715, -1.0379476029804457, -0.625529071876107, -0.1770471409040116, 0.29466457406854085, 0.7761042431803273, 1.2535785841945608, 1.7136980688142698, 2.1438295491420862, 2.532503660748268, 2.8697831780506964, 3.1475804331601, 3.3599152553999887, 3.5031338345888066, 3.5759401659285204, 3.5793653101955365, 3.5166637800501785, 3.3931110362764425, 3.215757473022481, 2.9931526931919374, 2.7349089356892606, 2.45127687982169, 2.152709416289642, 1.8494422024884805, 1.5511110324148225, 1.2664164466318764, 1.00277354288964, 0.7660648371567017, 0.5604877464996232, 0.38848537423605684, 0.2507625051889055, 0.14637864243343404, 0.07290714989895053, 0.026683239152865187, 0.003103502389477303, -0.003038110794986114, 0.002805662211297657, 0.015295553494810566, 0.029551636957920176, 0.04146048085486266, 0.04792950952697788, 0.04707596963664081, 0.03834136434908369, 0.022517380435244268, 0.0016827617242802999, -0.02094228639370301, -0.04121915042851029, -0.05438370195225572, -0.05539555424911176, -0.03931658001039406, -0.0017023366904228988, 0.061013752599586864, 0.15116338393304046, 0.2695381949352704, 0.4151684204452619, 0.585189819590906, 0.7748050394557823, 0.9773512022986246, 1.184502249715827, 1.386577423761742, 1.572933686098899, 1.7324590646529692, 1.854104769093991, 1.92750656010413, 1.943636570140525, 1.8953453043413715, 1.777895947679137, 1.5894356092485353, 1.3313571428655804, 1.0086209363000787, 0.629753330340192, 0.206725575318315, -0.24530388117608598, -0.7084111627560453, -1.1624067753979535, -1.5856052012369755, -1.9557334376695852, -2.2508543767689937, -2.450335086643806, -2.535786356713817, -2.4919892516238047, -2.307809066026585, -1.9769242611135864, -1.4983904346372015, -0.876988086718371, -0.12327700085682075, 0.7464637218503609, 1.7105612892809632, 2.742530194404082, 3.8118752796124156, 4.885168098059967, 5.927489193256646, 6.903581989788354, 7.779143353423444, 8.522189774071338, 9.104401873319812, 9.502489691414173, 9.699569483046066, 9.68567417674305, 9.458209682852546, 9.02225180360619, 8.39057399382329, 7.583371851201323, 6.6277752727775, 5.556515513311831, 4.406603438316259, 3.2179196556944496, 2.0316203385117, 0.8884678228958836, -0.17292019701995814, -1.1178862931624243, -1.9172459596403821, -2.5485547063377414, -2.9970756550467392, -3.2564884435433252, -3.329364762703307, -3.226993045187162, -2.9688141640854275, -2.58143982853503, -2.0973579211856888, -1.5533822737990923, -0.988874327377188, -0.44352332698829217, 0.04487558456161081, 0.4425592580398005, 0.7218073335526994, 0.8627686847901583, 0.8550960568450344, 0.6991559120935086, 0.4066992315694415, 0.0010431337482894798, -0.483262405023454, -1.0012584259847797, -1.4988631411884787, -1.9148630964390039, -2.183267008311631, -2.2359592856728474, -2.0055930898616605, -1.4286075795732618, -0.44818427989077564, 0.9827775249409616, 2.898978872686016, 5.320419332213344, 8.250617537521483, 11.675530524369659, 15.563068040078791, 19.863072548575555, 24.50802987773783, 29.4145848257841, 34.486072995933306, 39.615235345573, 44.6877064651946, 49.585209963982926, 54.1892103395566, 58.38546726022558, 62.06783872493283, 65.14172010001386, 67.52799507623045, 69.16500411334603, 70.0110120452579, 70.04611874151409, 69.27216708745898, 67.71288172569315, 65.4138116111016, 62.43989783491295, 58.87362076804787, 54.81133601742114, 50.35968436282307, 45.63217902045655, 40.74590680462626, 35.81715016242688, 30.95706294802487, 26.26784383681927, 21.83973538077391, 17.74865164723504, 14.054572063069807, 10.799812347047672, 8.00824804061928, 5.685668278954883, 3.8208289812430354, 2.3871448186321294, 1.3448876430842007, 0.6436678821454462, 0.22543949809252609, 0.027699650132134494, -0.013306235477350846, 0.040488845894842564, 0.1317946909391724, 0.21042569242298986, 0.23527903179374757, 0.17575252264283486, 0.012550195146811669, -0.2621426533411987, -0.6450864188656155, -1.122998249204943, -1.674049119424076, -2.269776779225967, -2.8773418108471884, -3.461865745395083, -3.988909646864523, -4.426762458528135, -4.748516119002009, -4.93391865098602, -4.970660971463, -4.855191850920738, -4.59318653286085, -4.199223485949649, -3.6960377264394633, -3.1132684814467524, -2.485713859693883, -1.8514084825252328, -1.2495324420398193, -0.7180443850637402, -0.2914143305587007, 0.0014731563095320061, 0.139081067397622, 0.10859834566841808, -0.09311395454135145, -0.45906295419974097, -0.9722716142020917, -1.606474942146604, -2.3273145692116057, -3.0939899397604496, -3.861353452750349, -4.5822619496548445, -5.209988044921064, -5.700678685229251, -6.015717842424721, -6.123930302323327, -6.0035555175453545, -5.643390824108621, -5.043528242824777, -4.21560424792687, -3.1824923363473996, -1.9774560512360886, -0.6425451143252325, 0.7734566529190277, 2.2172871110040218, 3.6336849618955815, 4.9680515161557715, 6.1692457982881574, 7.192267441543688, 8.00025840852111, 8.566151408352157, 8.873952154484481, 8.919622895994012, 8.71115254877312, 8.268225389610441, 7.620754924316719, 6.807138960007846, 5.872328045794795, 4.865357239746707, 3.8367021878745478, 2.8357029800691214, 1.9077224307555816, 1.09181970032465, 0.4188136291467516, -0.09024636529905805, -0.4249843208513426, -0.5860604052577582, -0.584849850709785, -0.44241205056973165, -0.18790141869541102, 0.1435205055757071, 0.5131207884041212, 0.8812293800246518, 1.210144876671231, 1.4669163941644827, 1.6258662183284143, 1.6707281870750978, 1.596263298848455, 1.4092281499205566, 1.1286935229042767, 0.7856311681803694, 0.42172606337835683, 0.087477240114467, -0.16035697501765592, -0.261844127745474, -0.1571770060813582, 0.20977005346579666, 0.8878301707465738, 1.915092997308466, 3.3159942766257, 5.099014093900188, 7.254878016252422, 9.755532230160767, 12.553973009832317, 15.585481476729884, 18.77000656132863, 22.014469151312685, 25.21594685859727, 28.265490791334997, 31.05285715109824, 33.47267178390753, 35.428094259848116, 36.83494798759207, 37.62536941578027, 37.75113826235656, 37.188105315017644, 35.93709785391522, 34.0231118478363, 31.494877609486807, 28.42297048225727, 24.898368164648392, 21.02941645981514, 16.935602697719442, 12.742672138105803, 8.57767250613165, 4.56412480383073, 0.8179237520285253, -2.5586729906229038, -5.481243650740517, -7.88615186987954, -9.73253905934876, -11.002981736980178, -11.703915015076205, -11.86475286435685, -11.535572631072073, -10.783903445351386, -9.69073787358288, -8.346222073002108, -6.8449613232337985, -5.281123592301894, -3.743722419799938, -2.3122640338573373, -1.0529152467854135, -0.01571075608631636, 0.767395245033928, 1.2835151002951193, 1.5387832368174734, 1.557357997784394, 1.379426721682855, 1.0581584134960442, 0.6561616483162183, 0.2415225746760819, -0.11639549996788082, -0.35121881525697185, -0.4036476379766554, -0.22501308855963906, 0.21979312852842153, 0.9501278670135509, 1.9682491775950202, 3.258979846788222, 4.7906513318975605, 6.516623534597243, 8.377555743530941, 10.304428739708241, 12.22205318457828, 14.05309242679589, 15.72282656684962, 17.162520521388785, 18.312742744025115, 19.126360978834736, 19.570707980652244, 19.629379789024615, 19.303766152947695, 18.611938608961875, 17.587299202259352, 16.276472204511737, 14.736681238263257, 13.032884149604818, 11.234805719648387, 9.412572137518689, 7.63288432017247, 5.955742350585759, 4.431698775897351, 3.0997561149222355, 1.985948239355825, 1.1023088696784866, 0.4470035311469582, 0.005365658976321065, -0.2483540556619796, -0.3486382170949315, -0.3359024032720949, -0.25334461474871134, -0.14365572544039162, -0.04583365047649458, 0.00771317288620616, -0.006402622540459131, -0.10073387373031972, -0.2759033884118696, -0.5203148638872649, -0.8106822901927833, -1.1133866339986893, -1.3865763900797698, -1.5828466112773796, -1.6523562250831783, -1.5462127612042869, -1.2199594190190248, -0.6369260652375921, 0.2288616242283969, 1.390142240474203, 2.844694113933801, 4.574363829091553, 6.545102567614412, 8.707901174794976, 11.00043441728057, 13.349559328853644, 15.674444857215924, 17.8904916381766, 19.913664609129764, 21.664283021038415, 23.071021780610636, 24.07484237688734, 24.63200409724635, 24.716965363370022, 24.32344913109722, 23.464854796862877, 22.174026840345615, 20.502285739809473, 18.51713153784708, 16.298810330934213, 13.93630717373756, 11.523250767238208, 9.15365914972008, 6.917757916707556, 4.897448286041514, 3.162341030244789, 1.7667253113680959, 0.747310262915779, 0.12182461831243264, -0.11147106878459367, 0.02672183550276861, 0.49827167697824726, 1.2499656460404545, 2.216541263190762, 3.324361448083551, 4.4954964294030955, 5.651781461639091, 6.718765572130845, 7.62937190010035, 8.327209536023986, 8.769284448111106, 8.927850455813697, 8.791172515205707, 8.363515708295534, 7.664395531613507, 6.727068361477138, 5.596205175141008, 4.325197610432437, 2.9728073988419443, 1.5997914384625787, 0.2654646403860951, -0.9754068300915854, -2.075241452133161, -2.9959512813355724, -3.7106029645601106, -4.204483415657841, -4.4753320765734035, -4.532527644380651, -4.395940521779824, -4.094370390261721, -3.663357990735666, -3.142784239674596, -2.574021502975993, -1.9973571953451013, -1.4496985786393533, -0.96260328662694, -0.5606119340598457, -0.26007159528619855, -0.06863307128194589, 0.014627445111089555, -0.0014451591043233931, -0.10120185277903926, -0.26373264192509593, -0.4647256075293802, -0.6784669515168824, -0.8798472186854076, -1.0462569594985562, -1.1592728394785152, -1.205930801809469, -1.1795556394220195, -1.0801149286992755, -0.9140799528291923, -0.6938188212562822, -0.43642514637400714, -0.1622319792014796, 0.10688978112271583, 0.3493746116173262, 0.5458417856318472, 0.6809162795453308, 0.7447728179867991, 0.7342050871541436, 0.6532943780260865, 0.5136284629077726, 0.33404406751983284, 0.13973191645573244, -0.03913434634065209, -0.16916534648267953, -0.21577233173487623, -0.14534835677310765, 0.07242932196989732, 0.4623890405341316, 1.0419459918883474, 1.8195687217154537, 2.793683454465155, 3.952083913963729, 5.271888987140262, 6.7201600163729225, 8.255323547243856, 9.828861189236092, 11.38748997592261, 12.875487674023534, 14.23723758686717, 15.420001117308972, 16.37699222243453, 17.069604267320734, 17.469076847942024, 17.557739665343544, 17.32988657980874, 16.79224186925359, 15.96423230709556, 14.876560616155261, 13.569291074905253, 12.089915765984554, 10.491129454314953, 8.82848939808471, 7.158000164596126, 5.533097758649643, 4.002266695775321, 2.607101455276165, 1.3807569403374034, 0.3467683956236532, -0.48155067333315, -1.1011307741948453, -1.5185982777004412, -1.749260044655796, -1.8157723576520484, -1.746445202859598, -1.5732373602964382, -1.3297180523849808, -1.049094712710788, -0.7624103587717623, -0.49696912140673866, -0.2750130446747053, -0.1128524728199807, -0.02041454515045767, -0.001199711260320564, -0.052624470902660474, -0.1667259161361183, -0.3311691328168699, -0.5304780754667474, -0.7473523538447923, -0.9640235009191174, -1.1635777918527357, -1.331091894511904, -1.4545836905095977, -1.525740582047293, -1.5402662499439523, -1.4980031923281207, -1.4026814342909244, -1.2614335113656423, -1.0841290456561945, -0.8825631496336093, -0.6694974927372871, -0.45767654643301675, -0.2589129397891363, -0.08331211747778122, 0.061343475690497994, 0.17002669384578376, 0.24067994308902574, 0.2741742539214711, 0.27405020727803814, 0.24607694820513762, 0.1976700718633762, 0.13720769097444901, 0.07327728938420883, 0.01395662139512766, -0.03382929228506666, -0.06483576936407162, -0.07588048363261375, -0.06604684928580598, -0.03667280764277166, 0.008841630634813842, 0.065389361718101, 0.12664715476770952, 0.18567088866924045, 0.23555302633529543, 0.27005966814229765, 0.28420629927011437, 0.27473681390789195, 0.24046803711687387, 0.1824615977005171, 0.10401579613551623, 0.010445123591030751, -0.09129954214196583, -0.19315916402828157, -0.2865973481642044, -0.36329108482346867, -0.41586374965245726, -0.4385511573494502, -0.4277798575831865, -0.38260033005233807, -0.3049245269549962, -0.1995982979547021, -0.07428438195067644, 0.06091328066349702, 0.19400939257006058, 0.31184418497803174, 0.4008804997941364, 0.4480605690250344, 0.4416863284660205, 0.37226729994137714, 0.23321909278362424, 0.02139674234730399, -0.26254490429837046, -0.6140015761004287, -1.0245321421073001, -1.4822249820265232, -1.9722284593924113, -2.477444320175813, -2.9793514146815783, -3.4589786244987195, -3.8980934328892194, -4.280011992848771, -4.590362522788437, -4.817770783530822, -4.954398219864438, -4.996480842968967, -4.944521838472416, -4.802913144981455, -4.579550143722586, -4.285327210642113, -3.933576625537534, -3.539374848392553, -3.118654574944433, -2.687241887614956, -2.2600664453189703, -1.8505165748025032, -1.4699271097830149, -1.1271353082520608, -0.8282590613035954, -0.5766103996584934, -0.3728256859970333, -0.21514486242176567, -0.09980728231993619, -0.021538455621502573, 0.025922002446101947, 0.04928606960594791, 0.05521410108205731, 0.04986939638497094, 0.03855814569249136, 0.025490228974801365, 0.013656620089319659, 0.004824261851532891, -0.0003642487002645521, -0.002203613694896861, -0.0016726782032629689, -0.00014680488092246244, 0.0008954700201974972, 0.000142589866464418, -0.0033298840874459294, -0.009907875289644473, -0.01936735278693489, -0.030887918515525165, -0.043153580692580705, -0.054524498451515226, -0.06325515121062414, -0.06774138072571846, -0.0667713677510686, -0.05975872317725115, -0.04693443821355709, -0.02944378950996895, -0.0093649642291498, 0.010358625226779038, 0.026076117149587883, 0.03367793351492561, 0.028919019737245814, 0.007777483797058451, -0.03317667737303013, -0.09642718469727371, -0.1831851126999684, -0.2931344079582205, -0.4243185737157608, -0.5731267903043471, -0.7343950657103178, -0.9016213113898126, -1.0672857325927834, -1.223308044052921, -1.3615888522137367, -1.474519392092612, -1.5554884299685425, -1.5993653951941549, -1.6029011294568627, -1.565019455483325, -1.4870034590338612, -1.3724517223391417, -1.2271178120747044, -1.0586051280538398, -0.8759035063280247, -0.6888487187066817, -0.5075206071775077, -0.3415926182011612, -0.19971090392111068, -0.08892103066061674, -0.014210760628191377, 0.021811076202480295, 0.019068406876740513, -0.019997472670370154, -0.09060749899441929, -0.1859828661838133, -0.29781456168394216, -0.4168486029196269, -0.5335861516884599, -0.6389264702503243, -0.7247616722854444, -0.784510005583891, -0.813540462714321, -0.8094873804027664, -0.7724522067426698, -0.704848085021603, -0.6111369559599988, -0.497456058603081, -0.3711343004799598, -0.24014845792307948, -0.11250246284356627, 0.004433006700391924, 0.10445583258745227, 0.18295329819678438, 0.2371900159624412, 0.2664519348293631, 0.2720430769969142, 0.2570654372891479, 0.22604755593581782, 0.1844615467784141, 0.13816050212908274, 0.09278794199601406, 0.05319928770472768, 0.02292090847005445, 0.0037397316274460453, -0.0045530574389928925, -0.004237854366345418, 0.0004403429037667822, 0.003561204969059608, -0.0020032177404846934, -0.02398169726262956, -0.07001171103007228, -0.14691416722272102, -0.25998037611540153, -0.4123178676166356, -0.6043487323758223, -0.8335352694331676, -1.0942779335182002, -1.3780285166271393, -1.6736366267809788, -1.967936280070823, -2.246630430615547, -2.4951968826994917, -2.6997765802119043, -2.8481206494600393, -2.9304980946568615, -2.940643477770171, -2.876361406610327, -2.7396277138934972, -2.5365817799822965, -2.277260887189209, -1.9751293248805186, -1.6464317609898727, -1.3089190157693842, -0.9806308882969317, -0.6787076140765655, -0.4182388791390705, -0.21124184447934988, -0.06569627789546395, 0.015118608501118822, 0.03289239956521674, -0.005786470955160735, -0.08981775204686859, -0.20428797770094145, -0.3315134569708684, -0.4522965695213301, -0.5473053405794317, -0.5984849853225549, -0.5904133554489942, -0.5115379595401988, -0.3550874797324842, -0.11970596147191066, 0.19026214483968518, 0.5648737133909595, 0.9890744488506995, 1.4436261306949754, 1.9065567345819563, 2.3544311989839923, 2.763803113081054, 3.11275679807066, 3.382341812044912, 3.557971306698822, 3.630815632642158, 3.59804964147278, 3.4629466040912704, 3.234623871286057, 2.9274325077256425, 2.5601241742284584, 2.154853134298982, 1.7352543780107714, 1.3247327343684248, 0.9449303883947232, 0.6143513375654772, 0.3472474554444048, 0.15278501631445873, 0.03436148897853605, -0.01042193756844399, 0.010672419419365769, 0.08532250896148452, 0.19776015529405097, 0.3301137725847323, 0.46392593730131604, 0.5817051721442826, 0.6683655239845555, 0.7124525000724335, 0.7070895965422589, 0.6504795010983752, 0.5460198203612289, 0.40198442873077567, 0.23078912173170946, 0.047908612938616965, -0.12950632903677378, -0.2841512743856377, -0.4000849847719786, -0.46416800204418684, -0.4673009255060548, -0.405357088219648, -0.2796407444270147, -0.09687547731433498, 0.13122080976623615, 0.3887835586883571, 0.6570613786230052, 0.915981492327076, 1.1458492041373844, 1.3290936940756348, 1.451748029326061, 1.5047553690938702, 1.4849124457796468, 1.3951961301938256, 1.2446180642959839, 1.0475460473727995, 0.8224008419742516, 0.5900067847208772, 0.37152263333066443, 0.18626628745702165, 0.0495723188002609, -0.02917032132968303, -0.04811635064988301, -0.014002009990078744, 0.05751285353244407, 0.14224709592296103, 0.20866832375117014, 0.2198241520984658, 0.1359181406767525, -0.08266276713023282, -0.47203814725100834, -1.0614495227972507, -1.8700136642218053, -2.9038679051378953, -4.154183623212001, -5.596051785667085, -7.188381051081712, -8.875018204044576, -10.588337591168996, -12.253217729430418, -13.79023103486919, -15.119927933611667, -16.167477611920248, -16.864296586977726, -17.151632999691625, -16.991570995417153, -16.371461772848786, -15.306748807958119, -13.84617791843737, -12.078023977329183, -10.105996297812263, -8.03956916279721, -5.989072913176278], 'positive_zeros': ['0.25060583921978394059552692693401', '0.52858287458013579756842990840338', '0.930542282298799680159045998668400', '1.14303503443587104245738110320331', '1.46400295011780878770269902689877', '1.87907511358686061399562601995173', '2.01060783014524403637409514505124', '2.40379140337805068954399009468428', '2.51593693752710297534547055889138', '2.98147374383528687196785681858254', '3.02894013184303166141345998998236', '3.10277078042029779704157686831673', '3.33206420274992405635196959696685', '3.70605692695588219538554065409244', '3.75136496311226683974630550936706', '3.89461580265313361246633090321971', '4.44091684015361031834302843912399', '4.50274045329319385299629358992759', '4.60735521975841952261691748678112', '4.86946700877978206789755968970598', '4.87066505132065839866633340472440', '5.13263028780337831471085681750892', '5.17060111296557596441528025177505', '5.26900638207473616054126684833779', '5.62524869189332348865029871611274', '5.81694842857669543468196394159887', '6.17888669273031702886815702138275', '6.19552520776038482260812671920580', '6.29384872576902250271753530065945', '6.36367980437439484740786979079435', '6.61480174168559538342399617373572', '6.77519012067295202486172418109139', '7.05269755939054221436234277943551', '7.21758916172020907509569005415029', '7.30080930951396862377053571382093', '7.41035665099892632851253955043679', '7.937449645191948618886831626393145', '7.949958137175401666420175053176708', '8.016287700556914110804103256711990', '8.285077823944756761656596820508301', '8.316041467531257193234054054996495', '8.536624392107856017444763664720718', '8.786662810184262647819333123673751', '8.854543954144379077181969229489287', '9.003574034471747229632474288427213', '9.041325636205069199947416999784634', '9.401152454539939615885486666279215', '9.597856047343243649677561283111625', '9.698961376498069242029346267045908', '9.745103174434714571694097234252663', '10.11346582465373107374184307941689', '10.19240387506197688248694667848626', '10.20545630601726777544918467249504', '10.34491386395978496014923309517061', '10.70316961591729612228170402250028', '10.72160295636455464433351908941779', '10.95944884691580107973787369695789', '11.17605483848723931435934749839944', '11.19112428572580210989960954626998', '11.36244325772736814001473958100588'], 'prelabel': '12-378e6-1.1-c3e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.722575778340667, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e6-0', 'trace_hash': 777081736900640051, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25060583921978394059552692693', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.52858287458013579756842990840', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.930542282298799680159045998668', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 123068589.72907074, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 2917096519063104, 'conductor_radical': 42, 'degree': 12, 'dirichlet_coefficients': [1, 6, 0, 12, 5, 0, 8, -16, 0, 30, -29, 0, 20, 48, 0, -144, -38, 0, 57, 60, 0, -174, -14, 0, 267, 120, 0, 96, 362, 0, -88, -288, 0, -228, 40, 0, 384, 342, 0, -80, -432, 0, -726, -348, 0, -84, -183, 0, 218, 1602, 0, 240, -396, 0, -145, -128, 0, 2172, -427, 0, -427, -528, 0, 192, 100, 0, -32, -456, 0, 240, 790, 0, 373, 2304, 0, 684, -232, 0, 1364, -720, 0, -2592, 154, 0, -190, -4356, 0, 464, -1233, 0, 160, -168, 0, -1098, 285, 0, 1180, 1308, 0, 3204], 'euler11': [1, 29, -2564, -60061, 4759283, 58883294, -5900798285, 78373664314, 8431360150763, -141620696269151, -8046930357912644, 121140196913053879, 5559917313492231481], 'euler13': [1, -20, 13116, -216834, 71816956, -946572092, 210156213331, -2079618886124, 346646729573404, -2299416017045082, 305577684466460796, -1023717860281815140, 112455406951957393129], 'euler17': [1, 38, -10148, -214318, 64981502, 384215870, -350665294625, 1887652569310, 1568495488248638, -25415516515084046, -5912450463407614628, 108772075957373000134, 14063084452067724991009], 'euler19': [1, -57, -14838, 254831, 166435821, -166961520, -1338012994557, -1145189065680, 7830119828903301, 82230828712720349, -32841166769103696918, -865324240702863503043, 104127350297911241532841], 'euler2': [1, -6, 24, -56, 96, -96, 64, 0, 0, 0, 0, 0, 0], 'euler23': [1, 14, -24188, -1111042, 287732402, 11473339118, -3133578440789, 139596117048706, 42594721924175378, -2001156255297174446, -530070935761707524348, 3732893296501477438498, 3244150909895248285300369], 'euler29': [1, -362, 121531, -35449820, 7643263205, -1467483172382, 258002184349975, -35790447091224598, 4546391202875203805, -514275713558280393580, 42999464417743858021771, -3123766326630542767623538, 210457284365172120330305161], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 88, -19176, 2427606, -74706896, -63836425952, 24418143111607, -1901750965536032, -66302645196084176, 64184985394977883626, -15104221541929230216936, 2064943055282332361835688, 699053619999045038539170241], 'euler37': [1, -384, 6558, 23609678, -2205845910, -979004345454, 385902155257863, -49589507110281462, -5659597105471637190, 3068354828881553955206, 43170999254298951372798, -128043366893497077921981312, 16890053810563300749953435929], 'euler41': [1, 432, 426972, 142024050, 75304995504, 19099646219340, 6978658947274411, 1316366717083132140, 357706578512036332464, 46496108219464636762050, 9633978580527951203376732, 671802472076344377503875632, 107178930967531784356353269521], 'euler43': [1, 726, 369507, 188519864, 70137886437, 23601580221762, 7530228520363527, 1876490838691631334, 443367043657810066413, 94748690849738418949352, 14765363297004102818204307, 2306553085569315810549786882, 252599333573498060811820806649], 'euler47': [1, 183, -263418, -21765813, 50364860037, 1987643355060, -5827318049035865, 206363096052394380, 542893671353769907173, -24358784600156356304571, -30606928097593016583087738, 2207592748200127387684907769, 1252453015827223091648143056289], 'euler5': [1, -5, -242, 1291, 31349, -94946, -3671531, -11868250, 489828125, 2521484375, -59082031250, -152587890625, 3814697265625], 'euler53': [1, 396, -171222, -33593058, 26399387130, -3085597337094, -6213949690744577, -459374474754543438, 585125549933594869770, -110849149725697378392714, -84114332104645165649941302, 28962312148055333410897310172, 10888439761782913818722623349689], 'euler59': [1, 427, -20846, -184632833, -58389254833, 9945164910982, 19570132793727955, 2042528024252572178, -2462889927756278336953, -1599473460265415637012187, -37089149380621299016101326, 156029978861383454670349337873, 75047496554032956760519149093721], 'euler61': [1, 427, -325797, -168225036, 60617986357, 21366910723417, -7516285932983282, 4849882762911914077, 3123061350122630592877, -1967248147456282711754076, -864778932779230677622506837, 257261856996462252423393750727, 136753052840548005895349735207881], 'euler67': [1, 32, -507154, 145892682, 107477835646, -39824972320442, -19149017206317005, -11977878150013097246, 9722271131562838996174, 3969234271000720680877854, -4149898623360172032292689394, 78753890749250944427827201376, 740195513856780056217081017732809], 'euler7': [1, -8, -154, 6811, -52822, -941192, 40353607, 0, 0, 0, 0, 0, 0], 'euler71': [1, -790, 1701451, -944166712, 1282031105045, -577556027544706, 586920380116026271, -206713655374553269166, 164228548551817875481445, -43288628173467659338856072, 27920271108746048745165483691, -4639832707914539749555191135290, 2102085018129621311776010144838961], 'euler73': [1, -373, -1002964, 125934813, 757146856945, -40185482983214, -334578208592440487, -15632836033680960638, 114582233782919741227105, 7413982263119005177555269, -22969929716900055838341948244, -3323163687288259862996052291661, 3465863721549107204083472585375569], 'euler79': [1, -1364, 318072, 576829470, -209637930452, -324379754397308, 410997275277132367, -159931869728294339012, -50960351094265041425492, 69133932589307854161060930, 18795355096866661314341701752, -39739348208292188727920042467436, 14364405059580771582276370834385761], 'euler83': [1, -154, 2175355, -688383220, 2457194857817, -711364910178034, 1791237335227803895, -406749207895967526758, 803356204255076848275473, -128686534868691424097237660, 232523712784335170291265782155, -9412220795649337564839360066878, 34946659039493167390823397237402409], 'euler89': [1, 1233, -175281, -162125424, 290804803809, -425032882464177, -812862837191430722, -299635006117888395513, 144524546814657150070449, -56801680502191211482853616, -43292724927322713214541464401, 214690672440962119376151360581817, 122749609618842355502421774953773681], 'euler97': [1, -1180, 5633882, -5136751260, 12999765882367, -9162903095428040, 15868409066087035660, -8362734256813595550920, 10828441050642850758186943, -3905117848434971783176923420, 3909025988449700231978226179162, -747236403181411475531065626419740, 577951262543040979328274795306257089], 'euler_factors': [[1, -6, 24, -56, 96, -96, 64, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -5, -242, 1291, 31349, -94946, -3671531, -11868250, 489828125, 2521484375, -59082031250, -152587890625, 3814697265625], [1, -8, -154, 6811, -52822, -941192, 40353607, 0, 0, 0, 0, 0, 0], [1, 29, -2564, -60061, 4759283, 58883294, -5900798285, 78373664314, 8431360150763, -141620696269151, -8046930357912644, 121140196913053879, 5559917313492231481], [1, -20, 13116, -216834, 71816956, -946572092, 210156213331, -2079618886124, 346646729573404, -2299416017045082, 305577684466460796, -1023717860281815140, 112455406951957393129], [1, 38, -10148, -214318, 64981502, 384215870, -350665294625, 1887652569310, 1568495488248638, -25415516515084046, -5912450463407614628, 108772075957373000134, 14063084452067724991009], [1, -57, -14838, 254831, 166435821, -166961520, -1338012994557, -1145189065680, 7830119828903301, 82230828712720349, -32841166769103696918, -865324240702863503043, 104127350297911241532841], [1, 14, -24188, -1111042, 287732402, 11473339118, -3133578440789, 139596117048706, 42594721924175378, -2001156255297174446, -530070935761707524348, 3732893296501477438498, 3244150909895248285300369], [1, -362, 121531, -35449820, 7643263205, -1467483172382, 258002184349975, -35790447091224598, 4546391202875203805, -514275713558280393580, 42999464417743858021771, -3123766326630542767623538, 210457284365172120330305161], [1, 88, -19176, 2427606, -74706896, -63836425952, 24418143111607, -1901750965536032, -66302645196084176, 64184985394977883626, -15104221541929230216936, 2064943055282332361835688, 699053619999045038539170241], [1, -384, 6558, 23609678, -2205845910, -979004345454, 385902155257863, -49589507110281462, -5659597105471637190, 3068354828881553955206, 43170999254298951372798, -128043366893497077921981312, 16890053810563300749953435929], [1, 432, 426972, 142024050, 75304995504, 19099646219340, 6978658947274411, 1316366717083132140, 357706578512036332464, 46496108219464636762050, 9633978580527951203376732, 671802472076344377503875632, 107178930967531784356353269521], [1, 726, 369507, 188519864, 70137886437, 23601580221762, 7530228520363527, 1876490838691631334, 443367043657810066413, 94748690849738418949352, 14765363297004102818204307, 2306553085569315810549786882, 252599333573498060811820806649], [1, 183, -263418, -21765813, 50364860037, 1987643355060, -5827318049035865, 206363096052394380, 542893671353769907173, -24358784600156356304571, -30606928097593016583087738, 2207592748200127387684907769, 1252453015827223091648143056289], [1, 396, -171222, -33593058, 26399387130, -3085597337094, -6213949690744577, -459374474754543438, 585125549933594869770, -110849149725697378392714, -84114332104645165649941302, 28962312148055333410897310172, 10888439761782913818722623349689], [1, 427, -20846, -184632833, -58389254833, 9945164910982, 19570132793727955, 2042528024252572178, -2462889927756278336953, -1599473460265415637012187, -37089149380621299016101326, 156029978861383454670349337873, 75047496554032956760519149093721], [1, 427, -325797, -168225036, 60617986357, 21366910723417, -7516285932983282, 4849882762911914077, 3123061350122630592877, -1967248147456282711754076, -864778932779230677622506837, 257261856996462252423393750727, 136753052840548005895349735207881], [1, 32, -507154, 145892682, 107477835646, -39824972320442, -19149017206317005, -11977878150013097246, 9722271131562838996174, 3969234271000720680877854, -4149898623360172032292689394, 78753890749250944427827201376, 740195513856780056217081017732809], [1, -790, 1701451, -944166712, 1282031105045, -577556027544706, 586920380116026271, -206713655374553269166, 164228548551817875481445, -43288628173467659338856072, 27920271108746048745165483691, -4639832707914539749555191135290, 2102085018129621311776010144838961], [1, -373, -1002964, 125934813, 757146856945, -40185482983214, -334578208592440487, -15632836033680960638, 114582233782919741227105, 7413982263119005177555269, -22969929716900055838341948244, -3323163687288259862996052291661, 3465863721549107204083472585375569], [1, -1364, 318072, 576829470, -209637930452, -324379754397308, 410997275277132367, -159931869728294339012, -50960351094265041425492, 69133932589307854161060930, 18795355096866661314341701752, -39739348208292188727920042467436, 14364405059580771582276370834385761], [1, -154, 2175355, -688383220, 2457194857817, -711364910178034, 1791237335227803895, -406749207895967526758, 803356204255076848275473, -128686534868691424097237660, 232523712784335170291265782155, -9412220795649337564839360066878, 34946659039493167390823397237402409], [1, 1233, -175281, -162125424, 290804803809, -425032882464177, -812862837191430722, -299635006117888395513, 144524546814657150070449, -56801680502191211482853616, -43292724927322713214541464401, 214690672440962119376151360581817, 122749609618842355502421774953773681], [1, -1180, 5633882, -5136751260, 12999765882367, -9162903095428040, 15868409066087035660, -8362734256813595550920, 10828441050642850758186943, -3905117848434971783176923420, 3909025988449700231978226179162, -747236403181411475531065626419740, 577951262543040979328274795306257089]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/4/g/b'], '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': '12-378e6-1.1-c3e6-0-0', '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': '12-378e6-1.1-c3e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.722575778340667, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e6-0', 'trace_hash': 777081736900640051, 'z1': {'__RealLiteral__': 0, 'data': '0.25060583921978394059552692693', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '317680642507658264862994385982,670058398231872044975930042134,1179602482693819901989854044017,1448969047484526790292787016299,1855844218452738897511394380121,2382010695612312197989202513031', 'Lhash_array': ['317680642507658264862994385982', '670058398231872044975930042134', '1179602482693819901989854044017', '1448969047484526790292787016299', '1855844218452738897511394380121', '2382010695612312197989202513031'], 'label': '12-378e6-1.1-c3e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/4/g/b'}