-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1266791270282290292212426724239,2423581698066462372841931936641', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2508.223967036574, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '6272.1', 'coefficient_field': '1.1.1.1', 'conductor': 39337984, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, -2, 4, -6, 9], [1, 2, 8, 10, 25], [1], [1, 4, 14, 44, 121], [1, 2, 24, 26, 169], [1, 8, 38, 136, 289], [1, -2, 12, -38, 361], [1, -4, 2, -92, 529], [1, 0, 46, 0, 841], [1, 12, 86, 372, 961], [1, -16, 126, -592, 1369], [1, 0, 70, 0, 1681], [1, 12, 110, 516, 1849], [1, 4, 86, 188, 2209], [1, -12, 142, -636, 2809], [1, -2, 92, -118, 3481], [1, 2, -24, 122, 3721], [1, 16, 150, 1072, 4489], [1, 0, -50, 0, 5041], [1, 4, 102, 292, 5329], [1, -16, 222, -1264, 6241], [1, 18, 244, 1494, 6889], [1, -4, 134, -356, 7921], [1, 8, 198, 776, 9409], [1, -18, 256, -1818, 10201], [1, -4, 102, -412, 10609], [1, -32, 470, -3424, 11449], [1, 0, 206, 0, 11881], [1, 20, 218, 2260, 12769]], 'euler_factors_factorization': [[1], [[[1, -2, 4, -6, 9], 1]], [[[1, 2, 8, 10, 25], 1]], [1], [[[1, 4, 14, 44, 121], 1]], [[[1, 2, 24, 26, 169], 1]], [[[1, 8, 38, 136, 289], 1]], [[[1, -2, 12, -38, 361], 1]], [[[1, -4, 2, -92, 529], 1]], [[[1, 0, 46, 0, 841], 1]], [[[1, 12, 86, 372, 961], 1]], [[[1, -16, 126, -592, 1369], 1]], [[[1, 0, 70, 0, 1681], 1]], [[[1, 12, 110, 516, 1849], 1]], [[[1, 4, 86, 188, 2209], 1]], [[[1, -6, 53], 2]], [[[1, -2, 92, -118, 3481], 1]], [[[1, 2, -24, 122, 3721], 1]], [[[1, 16, 150, 1072, 4489], 1]], [[[1, 0, -50, 0, 5041], 1]], [[[1, 4, 102, 292, 5329], 1]], [[[1, -8, 79], 2]], [[[1, 18, 244, 1494, 6889], 1]], [[[1, -4, 134, -356, 7921], 1]], [[[1, 8, 198, 776, 9409], 1]], [[[1, -18, 256, -1818, 10201], 1]], [[[1, -4, 102, -412, 10609], 1]], [[[1, -16, 107], 2]], [[[1, 0, 206, 0, 11881], 1]], [[[1, 20, 218, 2260, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 6, 'label': '4-6272e2-1.1-c1e2-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/6272/2/a/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [-9.556841962166082e-121, 0.009072012336078003, 0.03622538208141223, 0.08127178372563262, 0.14389497740832222, 0.22364930388761606, 0.3199539744753151, 0.4320920828699115, 0.5592012693328818, 0.7002750024664349, 0.8541502555663402, 1.0195126269656942, 1.194882496104316, 1.3786251534640992, 1.5689376585807613, 1.7638645806833448, 1.9612883692620848, 2.158950613572027, 2.3544490804457, 2.5452636378881963, 2.7287631578800595, 2.902234470548601, 3.062902041706795, 3.2079575838816825, 3.334594798681548, 3.440036623798091, 3.521586408354629, 3.576649275374405, 3.602799932026508, 3.597794328295013, 3.5596529771427585, 3.486659041662116, 3.377454657342068, 3.231021823049475, 3.046787898396684, 2.824586235912923, 2.564765897459871, 2.2681298534066383, 1.936043146928361, 1.5703476827328835, 1.17346267711475, 0.7482765156231037, 0.2982334450387615, -0.17279538384795953, -0.6604443497723959, -1.1599993111917173, -1.6663532952780788, -2.174163981318821, -2.677835026081547, -3.171678204651018, -3.6499205971101265, -4.106863475573781, -4.536913171176603, -4.934728289243911, -5.2952696204035785, -5.6139274083824855, -5.886583394806541, -6.109710732472727, -6.280439399903839, -6.396622964361822, -6.456897395446057, -6.460711183634529, -6.408367208841931, -6.3010155836335064, -6.140668815451435, -5.9301599675184775, -5.673122930257231, -5.37392181349262, -5.037590652016343, -4.669743052750396, -4.2764689355814145, -3.8642360344942537, -3.439745053274934, -3.009836351386979, -2.5813088296555438, -2.1608457612338308, -1.754806417998669, -1.3691843601347642, -1.0093838596764095, -0.6802219784285942, -0.38570386247426575, -0.1290766905790722, 0.08738139800412886, 0.26225169916337787, 0.39515844110208215, 0.4866047356846193, 0.5381169154536598, 0.5520324913422976, 0.5315974918595564, 0.48071782906807126, 0.4040066234436223, 0.30651449536784725, 0.19372928545126683, 0.07130356166216444, -0.05498540267967419, -0.17949158842775237, -0.29676728463835567, -0.4017841570010983, -0.49001099046022023, -0.5575844942446174, -0.6013794862243637, -0.6191188827512376, -0.6094182510707319, -0.5718306700701694, -0.5068499478446492, -0.4158930784153175, -0.3012508496651033, -0.16601770214707987, -0.01398453084887505, 0.150467947332968, 0.3225323125096771, 0.49709673101545704, 0.6689548479432443, 0.8329204037206472, 0.9840682242099505, 1.1178180112662714, 1.2301858479447756, 1.3178169963621464, 1.37822480223084, 1.4097579314090412, 1.411803898690513, 1.3846838422475627, 1.3298012805636754, 1.2494664189138032, 1.1469769325732617, 1.0263828618959832, 0.8924946160237295, 0.7506075862513478, 0.606442207337111, 0.46585339207552967, 0.3347171797119719, 0.21865305326854567, 0.12288014823769304, 0.051979876114608484, 0.009750629818354, -0.0009662434707947043, 0.021598187428128118, 0.07804502540495802, 0.16775194955236514, 0.2888613365019563, 0.4383085586956066, 0.6118868784413316, 0.8043743513943804, 1.0096572282593743, 1.2209581131838831, 1.4309898740841691, 1.6322744578573822, 1.8172928145099783, 1.978871082368621, 2.110289901329174, 2.2057043513563706, 2.260178870235949, 2.2701009629816915, 2.2331157042445358, 2.1484920034343253, 2.016942622683239, 1.8409062140808485, 1.624253538718019, 1.3724583570291968, 1.092206213170642, 0.791441536061929, 0.4789098071859409, 0.16408519287734302, -0.14331199007124293, -0.43348537748012844, -0.6970219512628257, -0.9251227453103114, -1.1099916968968568, -1.24507878836942, -1.325358144839569, -1.3475306627489458, -1.3101645132694748, -1.2138068934330974, -1.0609781496196315, -0.8561523565709338, -0.6056167332405629, -0.3172973401832893, -0.000515531234225359, 0.3343438358126967, 0.6761304113891549, 1.0133974165516504, 1.3346948223709802, 1.6291341970811428, 1.8866148747941038, 2.0984266297711476, 2.2573526150976337, 2.3582430216022896, 2.397953049072744, 2.375821253511076, 2.2934222200673426, 2.154893849183025, 1.9665099975903915, 1.7368206160302562, 1.4760758714024456, 1.1961695133399135, 0.9099690128188404, 0.6310823070969398, 0.37316463932585325, 0.14955767664349742, -0.027349846193908765, -0.14653811005176323, -0.19886955409811452, -0.17747310694670324, -0.07807548864208214, 0.10073552317864341, 0.3573921191610446, 0.6872826143526151, 1.0828430865480991, 1.533748298202141, 2.0271784271068802, 2.5482872991716112, 3.0805781085852386, 3.6066333346821633, 4.108510845831222, 4.568681728433801, 4.9703476826589, 5.298500609535583, 5.540066090142386, 5.684977176665359, 5.72606730500767, 5.660044189306976, 5.487086831073701, 5.211615573261933, 4.841587946315418, 4.388987218363662, 3.8688550841090024, 3.2994603884975695, 2.7011467192210716, 2.0961901587599026, 1.507570400811486, 0.9585746945840593, 0.471616977112915, 0.06768737433280689, -0.23465820867156076, -0.4198742626956405, -0.4761638171602205, -0.39593999962093734, -0.17622716006631, 0.18112351993614492, 0.6693859901256914, 1.2770919706821007, 1.988298601831627, 2.783126003790995, 3.638252879616933, 4.52785964457915, 5.424224882122012, 6.299016323205816, 7.123839168442812, 7.871765238626262, 8.517683885922064, 9.039922208251367, 9.420271542383686, 9.645534938311217, 9.707144571664005, 9.602479947190636, 9.334048287966716, 8.910447834536507, 8.345146206476846, 7.657013681129768, 6.868794242653684, 6.007196697635063, 5.101200345809531, 4.181757916170823, 3.280104853923976, 2.427187294850905, 1.6521461002027704, 0.981626203973945, 0.4385827270567425, 0.041648107540772694, -0.19563908858595516, -0.26523927712878076, -0.16492264714267357, 0.10169114688959713, 0.5252506180770973, 1.0910823245452137, 1.7796392661686329, 2.567377898228973, 3.427388294624666, 4.330686467706231, 5.246848622824377, 6.145605555130222, 6.99730216558729, 7.774636908283326, 8.452794665321303, 9.011154844582395, 9.432996793531391, 9.707008091897102, 9.82652906271145, 9.790726525378954, 9.60341705669758, 9.273825215385436, 8.815092405307206, 8.244603327729758, 7.582337852963651, 6.850814405445904, 6.073468050861152, 5.274313924497191, 4.476531692813934, 3.7019871288149035, 2.9701718405814663, 2.2977312112956785, 1.6978540851149901, 1.1799394034831414, 0.7494624705115845, 0.40787415186859105, 0.15289974346676732, -0.021289086623529664, -0.12344825264670554, -0.16483529937858293, -0.15840388668096952, -0.11819585945367832, -0.05852044026921168, 0.006725706956085371, 0.06474184871546722, 0.10444944580269364, 0.11692196368955947, 0.0958410588840731, 0.037611310783342684, -0.058437720960064894, -0.19025097267066265, -0.35313478226478406, -0.5402109976598812, -0.7427709973671837, -0.9508804451282814, -1.1539252763921137, -1.3412408288948128, -1.5027349894496032, -1.629418885799659, -1.7139741140972535, -1.7510901106606234, -1.7378492071434255, -1.673822317117322, -1.5611764389229907, -1.4045359786435185, -1.2107665573925661, -0.9886630058461744, -0.7484216537950231, -0.5012570295239376, -0.25863107746133374, -0.03192061329974715, 0.16848473755827784, 0.3333474049927907, 0.4554814816700127, 0.5296624658384719, 0.5533945589055359, 0.52652603637199, 0.45178348337085833, 0.3341109952656314, 0.1809193650669155, 0.00122257600491004, -0.19439114556188503, -0.39471022066746075, -0.5881425331766184, -0.76361864544996, -0.9109399635779805, -1.02150607953051, -1.088637730977888, -1.108032731889938, -1.0779381471340923, -0.9992917291474063, -0.8756491247011686, -0.7130298456011118, -0.5195571515019699, -0.3050870108451044, -0.08058023595174417, 0.1423624649743329, 0.35231716273086344, 0.5384520153777164, 0.6914095387862101, 0.8035372170343794, 0.8696927495132741, 0.8871913051515693, 0.8564015564005774, 0.7803684632961978, 0.6651071182755162, 0.5189273344662902, 0.35239325588002185, 0.17743958283709774, 0.007035689497256455, -0.14577027983297805, -0.2683778006489916, -0.3495067609368158, -0.3797617542541343, -0.35227984227456033, -0.2631619965732158, -0.11179797910444438, 0.09898926611296431, 0.36297267028461633, 0.6707683342880449, 1.0101731071069757, 1.3668342310970276, 1.7247794755131638, 2.067455467392737, 2.3782848188626033, 2.6419416634900443, 2.844752912005014, 2.976024587548067, 3.0281244747500757, 2.9976533112106916, 2.8851012745812232, 2.695679836196827, 2.4385250013899187, 2.127066437237213, 1.7778406868903343, 1.4103637675724718, 1.0456994878798935, 0.705903451994783, 0.4125477330038607, 0.1858982220406047, 0.04361432244968267, -0.00011144262603168265, 0.06451304282653166, 0.24223544502706637, 0.5323159762155307, 0.9283301010486351, 1.4182424664589763, 1.9848165722809294, 2.6061237611522468, 3.256615139645535, 3.9078860248939975, 4.530344872185042, 5.093986826779244, 5.570481278453596, 5.933687547664303, 6.161899339966082, 6.23786767059171, 6.150904219867663, 5.896257645655337, 5.47679718979859, 4.901704835791487, 4.18753328340594, 3.3563066241423787, 2.4358601297879656, 1.4575612131288855, 0.45597110107067323, -0.5335180062954642, -1.4755330442330707, -2.336839434551777, -3.087441762586424, -3.7021617670118743, -4.161684209967437, -4.453382158063985, -4.572018823293766, -4.519737357487411, -4.30620358420023, -3.9478243792658376, -3.4672342741949036, -2.891943651222307, -2.253210932691824, -1.584422569962065, -0.9195240382554338, -0.29147787289446575, 0.2694760121697411, 0.7369594505192818, 1.090053286585686, 1.3137924332197324, 1.4003294756095495, 1.348674018349268, 1.1652143371958437, 0.862739514283606, 0.4602389140265142, -0.01861359684569621, -0.5463149785866163, -1.0933042684583638, -1.629268360197169, -2.1248417024288564, -2.5530603339217155, -2.890686148956179, -3.119469284395023, -3.2268792473897823, -3.206867087664149, -3.0599171643781804, -2.7930956637013233, -2.4194862788644533, -1.9574519175610408, -1.4296537829772749, -0.8616101640330578, -0.28059250901690524, 0.2862934188843044, 0.8130091616630895, 1.276658782743128, 1.6579008488204146, 1.9428289736126603, 2.122707137770647, 2.1953482208865585, 2.1641275207167827, 2.038661117995125, 1.8332059598962183, 1.5665926174570763, 1.2602525262002873, 0.9375244833337237, 0.621631521334421, 0.33462258979785275, 0.09563478956374762, -0.08017918087009908, -0.1828284637805483, -0.20820394431679365, -0.15854105701053367, -0.04248522528594528, 0.12515562280341277, 0.32419357726342624, 0.5298355794805869, 0.7142386933559406, 0.847623217835245, 0.9007967272851434, 0.8456794581219598, 0.6570014756939223, 0.31444850619681897, -0.1911815613029992, -0.8652873794831288, -1.7197229121028852, -2.747063698890753], 'positive_zeros': ['0.999322108200962951112315387171295', '1.91186885221378642424102552386392', '2.19294115135386060735377097562195', '2.53330423651033050960874388709372', '3.15306360203289288216961820493528', '3.16696771579471733991759654098436', '3.80926768636345113992586745861123', '4.14847408448494649388695057910452', '4.65992190911625580120420154320165', '4.76934367674532220389670324812570', '5.44208592528939446961605697304522', '5.56734612949879290319990936268394', '6.28441853973913646301673749066631', '6.36759962798243432206291716335072', '7.16835962094261489841952232758771', '7.31003724112895062071724493659565', '7.43998876743000581463994358104141', '7.948818919488398160726333560705645'], 'prelabel': '4-6272e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.0768758748297325, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 383812635316386362, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.999322108200962951112315387171', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.91186885221378642424102552386', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.19294115135386060735377097562', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2508.223967036574, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 39337984, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, -2, 0, 0, 0, 0, 0, -4, 0, -2, 0, -4, 0, -8, 0, 2, 0, 0, 0, 4, 0, -4, 0, -2, 0, 0, 0, -12, 0, -8, 0, 0, 0, 16, 0, -4, 0, 0, 0, -12, 0, 0, 0, -4, 0, 0, 0, -16, 0, 12, 0, 8, 0, 4, 0, 2, 0, -2, 0, 0, 0, 4, 0, -16, 0, 8, 0, 0, 0, -4, 0, -8, 0, 0, 0, 16, 0, -1, 0, -18, 0, 16, 0, 0, 0, 4, 0, 0, 0, -24, 0, -4, 0, -8, 0, 0, 0], 'euler11': [1, 4, 14, 44, 121], 'euler13': [1, 2, 24, 26, 169], 'euler17': [1, 8, 38, 136, 289], 'euler19': [1, -2, 12, -38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 2, -92, 529], 'euler29': [1, 0, 46, 0, 841], 'euler3': [1, -2, 4, -6, 9], 'euler31': [1, 12, 86, 372, 961], 'euler37': [1, -16, 126, -592, 1369], 'euler41': [1, 0, 70, 0, 1681], 'euler43': [1, 12, 110, 516, 1849], 'euler47': [1, 4, 86, 188, 2209], 'euler5': [1, 2, 8, 10, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, -2, 92, -118, 3481], 'euler61': [1, 2, -24, 122, 3721], 'euler67': [1, 16, 150, 1072, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -50, 0, 5041], 'euler73': [1, 4, 102, 292, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 18, 244, 1494, 6889], 'euler89': [1, -4, 134, -356, 7921], 'euler97': [1, 8, 198, 776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 4, -6, 9], [1, 2, 8, 10, 25], [1, 0, 0, 0, 0], [1, 4, 14, 44, 121], [1, 2, 24, 26, 169], [1, 8, 38, 136, 289], [1, -2, 12, -38, 361], [1, -4, 2, -92, 529], [1, 0, 46, 0, 841], [1, 12, 86, 372, 961], [1, -16, 126, -592, 1369], [1, 0, 70, 0, 1681], [1, 12, 110, 516, 1849], [1, 4, 86, 188, 2209], [1, -12, 142, -636, 2809], [1, -2, 92, -118, 3481], [1, 2, -24, 122, 3721], [1, 16, 150, 1072, 4489], [1, 0, -50, 0, 5041], [1, 4, 102, 292, 5329], [1, -16, 222, -1264, 6241], [1, 18, 244, 1494, 6889], [1, -4, 134, -356, 7921], [1, 8, 198, 776, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6272/2/a/s'], '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': '4-6272e2-1.1-c1e2-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-6272e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.0768758748297325, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 383812635316386362, 'z1': {'__RealLiteral__': 0, 'data': '0.999322108200962951112315387171', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1266791270282290292212426724239,2423581698066462372841931936641', 'Lhash_array': ['1266791270282290292212426724239', '2423581698066462372841931936641'], 'factors': ['2-6272-1.1-c1-0-79', '2-6272-1.1-c1-0-162'], 'label': '4-6272e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6272/2/a/s'}