-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1984248322136723752718232358919', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.465693822431187, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.0387109578734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '2760.1', 'coefficient_field': 'CDF', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.465693822431187, 0], [7.0, 0]], [[1.0, 0], [-3.394125634627469, 0], [11.0, 0]], [[1.0, 0], [4.705649410613527, 0], [13.0, 0]], [[1.0, 0], [6.548295681072598, 0], [17.0, 0]], [[1.0, 0], [6.225738234248847, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.4485206358316018, 0], [29.0, 0]], [[1.0, 0], [5.154170046445129, 0], [31.0, 0]], [[1.0, 0], [5.985782646066507, 0], [37.0, 0]], [[1.0, 0], [-3.071568187803718, 0], [41.0, 0]], [[1.0, 0], [4.47991117636468, 0], [43.0, 0]], [[1.0, 0], [-6.225738234248847, 0], [47.0, 0]], [[1.0, 0], [2.591657011439038, 0], [53.0, 0]], [[1.0, 0], [1.5514793641683982, 0], [59.0, 0]], [[1.0, 0], [4.914214458262789, 0], [61.0, 0]], [[1.0, 0], [-6.085557691307503, 0], [67.0, 0]], [[1.0, 0], [-1.071568187803718, 0], [71.0, 0]], [[1.0, 0], [8.705649410613526, 0], [73.0, 0]], [[1.0, 0], [13.139952692511637, 0], [79.0, 0]], [[1.0, 0], [13.028206857437278, 0], [83.0, 0]], [[1.0, 0], [-11.619863868876315, 0], [89.0, 0]], [[1.0, 0], [-4.308340092890258, 0], [97.0, 0]], [[1.0, 0], [-10.339730633423336, 0], [101.0, 0]], [[1.0, 0], [10.831612599621378, 0], [103.0, 0]], [[1.0, 0], [1.76004441181766, 0], [107.0, 0]], [[1.0, 0], [1.394125634627469, 0], [109.0, 0]], [[1.0, 0], [-1.1713432330447144, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 35, 'label': '2-2760-1.1-c1-0-35', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2760/2/a/v/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1370372641482613e-60, 0.1518719277607749, 0.3032948512967328, 0.4537772736027746, 0.6027454235373005, 0.7495086827460061, 0.8932323225798657, 1.0329191360534027, 1.1674009811781825, 1.295340695862707, 1.4152443492514992, 1.5254833865535844, 1.624325910075239, 1.7099761087745387, 1.7806206839375094, 1.8344809989523714, 1.869869588401623, 1.8852495825669968, 1.8792955305614854, 1.850954036736813, 1.7995025632258697, 1.7246047020090065, 1.626360190085085, 1.5053479392291327, 1.3626603852943069, 1.1999275380773962, 1.0193292370691296, 0.8235942948873204, 0.6159854407959722, 0.4002692612428358, 0.1806706703322871, -0.0381881741871534, -0.251364171564101, -0.4536840048270569, -0.6398480315378061, -0.8045455987172176, -0.9425795731847167, -1.0489974339930448, -1.119225869889979, -1.149205478372752, -1.135521890098511, -1.0755294583632622, -0.9674635716429139, -0.810537679161044, -0.6050212736517101, -0.3522953571035606, -0.05488232564893817, 0.2835522539736508, 0.6582278491565404, 1.0633082587593166, 1.4919922630354439, 1.9366349656136612, 2.3888982022836194, 2.8399274108198616, 3.2805513908903516, 3.7015004662215074, 4.093637726454013, 4.448197307046486, 4.757023094175214, 5.012800847070135, 5.209276537820443, 5.341453738337747, 5.405763149493508, 5.400197874757086, 5.324408788191813, 5.179755324076376, 4.969308203545524, 4.6978019845833074, 4.371536839217109, 3.998230582036074, 3.586823646891902, 3.1472413784629234, 2.690119613542684, 2.226501013315681, 1.767510913108892, 1.324022523765326, 0.9063220977879478, 0.5237851202220224, 0.1845746650275225, -0.10462724986005828, -0.33884518066468466, -0.5149836185326646, -0.6319406323819508, -0.6906560407641645, -0.6940904549411885, -0.6471338552855986, -0.5564448325877478, -0.43022416015866055, -0.27792887009594636, -0.10993539231999157, 0.0628375176506413, 0.229333478868622, 0.378776767242309, 0.5010891401848977, 0.5872896977400075, 0.6298623774352179, 0.623076373747765, 0.5632460562203954, 0.4489188086701705, 0.280981577798487, 0.0626797322538124, -0.2004549988540031, -0.5007673259413166, -0.8287282222175394, -1.1732645371788233, -1.5221578057414176, -1.8624985940925978, -2.1811800912626738, -2.465412578972398, -2.703238997496452, -2.8840311555484504, -2.9989462638897586, -3.0413244311570335, -3.00700953878892, -2.8945784680530315, -2.7054669100357707, -2.4439838406154184, -2.1172110491555163, -1.734788709463681, -1.3085926931056886, -0.8523139551321902, -0.3809546731591501, 0.08974030085312669, 0.5438948916376757, 0.9661319579513267, 1.3421964918325542, 1.6595457672567757, 1.9078810114156428, 2.0795969404877157, 2.170128334753358, 2.178176638979044, 2.1058042310734817, 1.958389331206586, 1.744440315224058, 1.4752742127611915, 1.1645701560457655, 0.827814236371408, 0.4816573617913619, 0.1432120474559596, -0.17068260797423054, -0.4441963795504696, -0.6632116268143768, -0.8159636821725731, -0.8935883652059637, -0.890550468501314, -0.8049317199238145, -0.6385624759408083, -0.3969880137789988, -0.08926749326979302, 0.27238885713454086, 0.6731313436125976, 1.0961111727254402, 1.5232232376447388, 1.9359197026796684, 2.3160587909087282, 2.646750733828943, 2.91316207910082, 3.103240555181041, 3.208325462667325, 3.223613021868699, 3.148452093457631, 2.986452966711281, 2.7454001729122246, 2.4369691698254874, 2.076255856802505, 1.68113679690726, 1.27148631779161, 0.868283929691712, 0.49265136725903746, 0.16486271875862954, -0.09662668864361681, -0.2760868785189396, -0.3613115819816452, -0.34426883094735883, -0.22157040135441972, 0.005265416002694296, 0.32977399198282165, 0.7407335393571421, 1.222578633031706, 1.7560226901071414, 2.31886383483351, 2.886939404967171, 3.4351866803707924, 3.9387616364084996, 4.374163964541879, 4.720315479549101, 4.959540450807091, 5.07840033471945, 5.0683417019845285, 4.926124581223603, 4.654008603074304, 4.259685755312666, 3.7559607060555424, 3.1601919275499983, 2.4935186479919693, 1.77990937579742, 1.0450768250147862, 0.31531103923783443, -0.3837130203055677, -1.0280954536519398, -1.596782189805059, -2.0724938325128273, -2.4424666527280903, -2.6989689801992744, -2.839567398053053, -2.8671297168130874, -2.7895650683507403, -2.619314934004638, -2.3726218053227806, -2.0686137902949255, -1.7282531974082271, -1.3732044184641217, -1.0246808723015133, -0.7023320926853535, -0.42323013313894964, -0.2010093782393257, -0.04520582419999866, 0.039168687639619386, 0.05179439783921529, -0.003055207750283102, -0.11687333184302721, -0.27752079570301347, -0.4700343740797193, -0.677597149597382, -0.8826160740646691, -1.0678454181812223, -1.217491609482997, -1.3182353288069444, -1.3601106941434729, -1.337188746061813, -1.2480229069277675, -1.0958270859381212, -0.8883719614808966, -0.6376008930070849, -0.35898302356057676, -0.07063653108646961, 0.20773120638910356, 0.4560083559066308, 0.6549217827375183, 0.787267395541659, 0.8390557028561924, 0.8005039057070321, 0.6668131210877027, 0.43868023443779397, 0.12250787340457535, -0.26970764808665093, -0.7208127236100718, -1.209241143616889, -1.7100332074708722, -2.196079093214786, -2.6395225196692467, -3.0132502577089704, -3.2923865524022577, -3.455709452648649, -3.486908615292898, -3.375611302799967, -3.1181147126205135], 'positive_zeros': ['1.56529592758404973736493147686989', '2.34458977486626211746305060890797', '3.99224650779977918821725671012471', '4.55180035448100883605421666169235', '5.09098790663885614863503406183130', '6.18554474053802302852025575364515', '7.03033377115956082779424559305566', '7.52880888997681561854552068596749', '8.612287802091070089948138424636773'], 'prelabel': '2-2760-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.694540548112605, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56529592758404973736493147687', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34458977486626211746305060891', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99224650779977918821725671012', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 22.0387109578734, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2760/2/a/v/1/4'], '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': '2-2760-1.1-c1-0-35', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2760-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.694540548112605, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56529592758404973736493147687', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1984248322136723752718232358919', 'Lhash_array': ['1984248322136723752718232358919'], 'label': '2-2760-1.1-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2760/2/a/v/1/4'}