-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2250491466445027268772278031338', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [0.3111078174659819, 2.2143197433775352], 'a6': [0, 0], 'a7': [0, -4.903211925911553], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.08050613361803, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [-0.3111078174659819, -2.2143197433775352]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '2640.529', 'coefficient_field': 'CDF', 'conductor': 2640, 'conductor_radical': 330, 'conjugate': '349613569207129918114842107871', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-0.3111078174659819, -2.2143197433775352]], [[1.0, 0], [0, 4.903211925911553], [-7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 4.147643195775481], [-13.0, 0]], [[1.0, 0], [0, 5.331851412666624], [-17.0, 0]], [[1.0, 0], [5.184208216891143, 0], [19.0, 0]], [[1.0, 0], [0, -4.0], [-23.0, 0]], [[1.0, 0], [1.8064238518231066, 0], [29.0, 0]], [[1.0, 0], [2.6222156349319636, 0], [31.0, 0]], [[1.0, 0], [0, -5.806423851823107], [-37.0, 0]], [[1.0, 0], [-1.8064238518231066, 0], [41.0, 0]], [[1.0, 0], [0, -4.903211925911553], [-43.0, 0]], [[1.0, 0], [0, 7.050855121687034], [-47.0, 0]], [[1.0, 0], [0, -7.184208216891143], [-53.0, 0]], [[1.0, 0], [-1.673070756618998, 0], [59.0, 0]], [[1.0, 0], [-0.7555687301360724, 0], [61.0, 0]], [[1.0, 0], [0, -4.857278973510141], [-67.0, 0]], [[1.0, 0], [0.42863948675507035, 0], [71.0, 0]], [[1.0, 0], [0, 12.70963577773466], [-73.0, 0]], [[1.0, 0], [6.4286394867550705, 0], [79.0, 0]], [[1.0, 0], [0, 2.9032119259115534], [-83.0, 0]], [[1.0, 0], [0.6222156349319637, 0], [89.0, 0]], [[1.0, 0], [0, 2.7555687301360723], [-97.0, 0]], [[1.0, 0], [17.806423851823105, 0], [101.0, 0]], [[1.0, 0], [0, -4.949144878312966], [-103.0, 0]], [[1.0, 0], [0, 11.198498317462516], [-107.0, 0]], [[1.0, 0], [15.714557947020282, 0], [109.0, 0]], [[1.0, 0], [0, -1.7649366614218231], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-2640-5.4-c1-0-57', 'leading_term': '0.8813955548215811080199431449723049013131611877063689917', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2640/2/d/i/529/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8813955548215812, 1.0726004158028524, 1.2639077747306553, 1.4545822379602482, 1.643656950132206, 1.8298710610624194, 2.0116287515136317, 2.186982487965647, 2.3536413945145775, 2.5090041133692815, 2.6502143736297996, 2.7742366983892395, 2.8779491819564984, 2.958249964363499, 3.0121738276003334, 3.0370151708468587, 3.030453455417635, 2.990677037902562, 2.916501147177208, 2.807475635926887, 2.6639780844176615, 2.4872878881412226, 2.279637152645873, 2.044234572880042, 1.7852590069919247, 1.507820172597593, 1.2178847937792967, 0.9221675957957586, 0.6279877575564031, 0.34309275518638477, 0.07545292009050977, -0.16696855965749716, -0.3764641029501194, -0.545841314792474, -0.668685242929002, -0.7396140183978478, -0.7545180238555974, -0.7107725168778518, -0.6074138078054886, -0.445269683082467, -0.22703578969722632, 0.04270884940104502, 0.3575521584823829, 0.7093679172731887, 1.0885034792082255, 1.4840337883123174, 1.884076333038218, 2.2761588262968657, 2.6476286783372127, 2.986090863581735, 3.279858704029886, 3.5184005237432157, 3.692764181414991, 3.7959612517441745, 3.823293166336896, 3.772602975309447, 3.6444385506662305, 3.442115982814405, 3.171675543870103, 2.841726788584507, 2.4631839824736534, 2.0488979021969094, 1.613194935503426, 1.17133909061199, 0.7389367744068541, 0.33130778629455426, -0.03715131307626393, -0.35358364703910167, -0.6072400254094434, -0.7899711054717342, -0.8966185129856474, -0.9252832427219128, -0.8774544017521636, -0.7579871690747649, -0.5749254993539353, -0.33917231709989515, -0.06401740487338235, 0.23545947307165915, 0.5430858261312587, 0.8423637075979162, 1.1172718730805313, 1.3530644622831687, 1.537026374157118, 1.6591459842802165, 1.7126683561152731, 1.69449660343734, 1.6054154423913796, 1.4501189951391276, 1.237034239811384, 0.9779417224388971, 0.6874057640459972, 0.38203687028880934, 0.0796188202121039, -0.20185857940803492, -0.4452133533712048, -0.6350795994954405, -0.7588559447118315, -0.8075409169640979, -0.7764056963667919, -0.6654613006980644, -0.47968645874637583, -0.2289938534893934, 0.07207444279041826, 0.40491730597448417, 0.7476910770894696, 1.076338547339187, 1.365783817061688, 1.591235552926522, 1.729532976630665, 1.7604639883881184, 1.6679835731828485, 1.4412632824137777, 1.0755091434834845, 0.5724956194826006, -0.059223204560838044, -0.8044478233538882, -1.6418174596513573, -2.544629762700884, -3.4819628433871257, -4.420048825860806, -5.323832743681144, -6.158638467405645, -6.891855226705927, -7.494554787333353, -7.942950818798229, -8.219618521857946, -8.31440396160988, -8.224968265476145, -7.956931115373981, -7.523599772223926, -6.945293015726626, -6.2482925403808975, -5.463476153152621, -4.624706239217959, -3.767062189242899, -2.925015801544067, -2.1306533383472677, -1.4120465017934043, -0.7918670355645798, -0.28632626016872054, 0.095497709465284, 0.35190502143107855, 0.48837692823961504, 0.5169488033119795, 0.4551922963098162, 0.32487018780314914, 0.1503485373477351, -0.04313321573559183, -0.23122357041114217, -0.39213796869056383, -0.5081458677279757, -0.5667674858386242, -0.5615996039172816, -0.49271312468720163, -0.36659256985951866, -0.19561763276247462, 0.0028826011995387005, 0.20794309118581328, 0.39655857689182333, 0.5454557300125726, 0.6329219504741194, 0.6405648704509072, 0.5548787800022357, 0.36850471344824254, 0.08108933402503378, -0.3003270169134085, -0.7614322108648369, -1.281279367046717, -1.8334091698282926, -2.387393724371369, -2.910707834222869, -3.370808876945518, -3.7372892357788654, -3.9839568801772307, -4.0907009707488635, -4.045010450206299, -3.8430339588143805, -3.4900979159959324, -3.000634484758036, -2.397510142646647, -1.7107861384105532, -0.9759814596609772, -0.2319443284001889, 0.48153286266981465, 1.1262000137451031, 1.6677720314323228, 2.0781238380697595, 2.337106277369255, 2.4338548114010257, 2.367495551092668, 2.1471930841523883, 1.7915291205791641, 1.3272471368891683, 0.7874427511802486, 0.20931932629146674, -0.3683396324012266, -0.9078077744072731, -1.3749793326640303, -1.7416779100295698, -1.9875455442937984, -2.101374703218706, -2.081783879873564, -1.937183236648772, -1.6850271402420556, -1.350401893788581, -0.9640458057165513, -0.5599413480930219, -0.1726523351060439, 0.1653998021463547, 0.42651923002468667, 0.5899842736347632, 0.6437888165595063, 0.5857387179884227, 0.4238108728454415, 0.1757356119533836, -0.13217992657123231, -0.4669131523183508, -0.7911455853401099, -1.066070295447773, -1.2543848848820032, -1.3232500896236736, -1.2469924747769163, -1.0093445142647592, -0.6050457825683712, -0.04067307298163676, 0.6653780391133278, 1.4837762332223523, 2.3759544218178195, 3.296517756585543, 4.196196570040365, 5.02513823071594, 5.7363036181583, 6.288722671511484, 6.650370352273822, 6.800449156061719, 6.730905418974957, 6.447061237231511, 5.967307931378312, 5.321875927735342, 4.550764547376523, 3.700978280166664, 2.8232688160150676, 1.9686202698686401, 1.184735588730189, 0.5127832965002793, -0.015354787085824766, -0.3791312108686702, -0.5705251073998396, -0.5942928339049672, -0.467262627342734, -0.21673208205849262, 0.12190369670685504, 0.5081059640208203, 0.899495817253325, 1.2552477518803662, 1.5393069042471388, 1.7231777212108088], 'positive_zeros': ['1.77532473541198652605608151931906', '2.39371914054203298518144493600972', '3.86091782906617814168235339384530', '4.46594944128980453040777266346274', '5.40661109872207471851989109025251', '5.96322073996326127071579241636508', '6.67463345187058765259299951919536', '8.186505105761158373685278597370693', '8.600327972004237773635333529808810', '9.139802904578349493196110997162985'], 'prelabel': '2-2640-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.591351231785478, 'root_angle': 0.9555688808365939, 'root_number': '-0.99027389402241168921319709201484307323652809395524592394 + 0.13913164563710637898751293080018099092129434591583018404*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.47778444041829693', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77532473541198652605608151932', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39371914054203298518144493601', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86091782906617814168235339385', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 21.08050613361803, 'bad_primes': [2, 3, 5, 11], 'central_character': '5.4', 'conductor': 2640, 'conductor_radical': 330, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2640/2/d/i/529/2'], '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': '2-2640-5.4-c1-0-57', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2640-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.591351231785478, 'root_angle': 0.47778444041829693, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77532473541198652605608151932', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2250491466445027268772278031338', 'Lhash_array': ['2250491466445027268772278031338'], 'label': '2-2640-5.4-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2640/2/d/i/529/2'}