-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1074445677687593496881827434507', 'a10': [-299.98662994715534, 0.0], 'a2': [-9.654269176669356, 0.0], 'a3': [0.0, 0.0], 'a4': [61.20491333558802, 0.0], 'a5': [31.072950676795635, 0.0], 'a6': [0.0, 0.0], 'a7': [-183.54667593282406, 0.0], 'a8': [-281.95209462306724, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 174.65797977633594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.1', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[[1.0, 0], [9.654269176669356, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-31.072950676795635, 0], [3125.0, 0]], [[1.0, 0], [183.54667593282406, 0], [16807.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [873.9813025009042, 0], [371293.0, 0]], [[1.0, 0], [-775.1190594493953, 0], [1419857.0, 0]], [[1.0, 0], [1497.8083051389456, 0], [2476099.0, 0]], [[1.0, 0], [1303.6778910290193, 0], [6436343.0, 0]], [[1.0, 0], [485.5557849575688, 0], [20511149.0, 0]], [[1.0, 0], [-7553.643164182062, 0], [28629151.0, 0]], [[1.0, 0], [-11690.114609398457, 0], [69343957.0, 0]], [[1.0, 0], [-8269.806796338084, 0], [115856201.0, 0]], [[1.0, 0], [-1748.0285911679111, 0], [147008443.0, 0]], [[1.0, 0], [-26640.89193289163, 0], [229345007.0, 0]], [[1.0, 0], [-24075.448297123665, 0], [418195493.0, 0]], [[1.0, 0], [34011.80088873643, 0], [714924299.0, 0]], [[1.0, 0], [-38822.38749146385, 0], [844596301.0, 0]], [[1.0, 0], [70517.08237347587, 0], [1350125107.0, 0]], [[1.0, 0], [-10974.688709553888, 0], [1804229351.0, 0]], [[1.0, 0], [-36006.003935348424, 0], [2073071593.0, 0]], [[1.0, 0], [-11860.090948485125, 0], [3077056399.0, 0]], [[1.0, 0], [9620.852435015693, 0], [3939040643.0, 0]], [[1.0, 0], [93324.60592439781, 0], [5584059449.0, 0]], [[1.0, 0], [-81958.97184652861, 0], [8587340257.0, 0]], [[1.0, 0], [3906.3268971895627, 0], [10510100501.0, 0]], [[1.0, 0], [12385.453819398028, 0], [11592740743.0, 0]], [[1.0, 0], [-128465.73739674043, 0], [14025517307.0, 0]], [[1.0, 0], [174532.0383065064, 0], [15386239549.0, 0]], [[1.0, 0], [-155496.84854335617, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 113, 'label': '2-33e2-1.1-c5-0-113', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1089/6/a/bl/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-5.894848456567683e-61, 0.09753164439107295, 0.19226543414883762, 0.2814590481674125, 0.36248038534227967, 0.4328605624756065, 0.49034439340764463, 0.5329375367032154, 0.5589495236283387, 0.5670319102336444, 0.5562108380306122, 0.5259133379677202, 0.4759867731376627, 0.40671088774442304, 0.31880201404883884, 0.21340908578966947, 0.09210121615018892, -0.04315327943844858, -0.19001640104982606, -0.3458183625575542, -0.5076035554516347, -0.6721841005324154, -0.8362003420944695, -0.996187469325088, -1.1486472810445343, -1.290123946445141, -1.4172824603160898, -1.526988350791492, -1.6163870754991108, -1.6829814427136056, -1.7247053222308144, -1.73999187044051, -1.7278344893651412, -1.6878387736036622, -1.6202637748510524, -1.5260510328201222, -1.4068399848940973, -1.2649685745500887, -1.1034581292263088, -0.9259818693482336, -0.7368167379038896, -0.5407785992134854, -0.3431412400703763, -0.14954000874719656, 0.03413866111551025, 0.20188018351481085, 0.34767515116301906, 0.46566062666265123, 0.5502666092334157, 0.5963645896114547, 0.5994148575093529, 0.5556090426552012, 0.4620042612406904, 0.31664521265380385, 0.11867063311431297, -0.13159933215636369, -0.4325980259011439, -0.7814722861909179, -1.1740699658710136, -1.6049568382581385, -2.067464155759469, -2.553767451283106, -3.0549964394757705, -3.561375101649348, -4.0623902425738, -4.5469860087369725, -5.003781077171782, -5.4213044833478, -5.7882453780234995, -6.093711408139019, -6.327489926611236, -6.480305869460816, -6.544069912961344, -6.5121104524481215, -6.3793830385554635, -6.142651172445099, -5.80063280107141, -5.354107463949092, -4.805979816506861, -4.161296179134746, -3.4272118176954387, -2.612907828065411, -1.7294577473456025, -0.7896453170814719, 0.19226385459684747, 1.2007926805878382, 2.2195597309453006, 3.2316166584905566, 4.219808426007752, 5.167147981961748, 6.057196361903687, 6.874438745753411, 7.604646799088002, 8.235217685306399, 8.755480463943405, 9.156961189701097, 9.433598890145205, 9.581905712468, 9.601065868115805, 9.492969537510357, 9.262179587482912, 8.915830757014396, 8.463462832871997, 7.916791212335875, 7.289420079664595, 6.5965051498281, 5.854374502005459, 5.080117383961261, 4.29115196892897, 3.504783847699281, 2.7377675068844285, 2.0058831558309196, 1.3235410059209558, 0.703424474921248, 0.1561827953273549, -0.3098178290173871, -0.6886770160389626, -0.9770713518889526, -1.1742904090266204, -1.2821964153461354, -1.3051086920864141, -1.2496163199822965, -1.1243247622767434, -0.9395442941701916, -0.7069299882909745, -0.4390846175603653, -0.14913710107907555, 0.14969001370117446, 0.4445101050709768, 0.7231851621761354, 0.9747081823359772, 1.1895428044226, 1.3599090770755162, 1.4800060280916907, 1.546163807288354, 1.5569205520991778, 1.5130216946610469, 1.4173421041332979, 1.2747341457510148, 1.0918073434729032, 0.8766477617987184, 0.6384873845553591, 0.3873355821458661, 0.1335861529129649, -0.11238565818167358, -0.34062136007763305, -0.5419579711486725, -0.7083733471207048, -0.8332853050216806, -0.9117934601940786, -0.9408548171626273, -0.9193866351293349, -0.8482928358906374, -0.7304131349146407, -0.5703970457244844, -0.37450781986178844, -0.15036412584282827, 0.09337026855763822, 0.3473364660045674, 0.6018561041104218, 0.847317683467088, 1.0745580426549342, 1.2752235952488824, 1.4420966960487887, 1.569373855524265, 1.6528844270529965, 1.6902407818323884, 1.6809137711044233, 1.6262303463346375, 1.5292934430422611, 1.394827501621784, 1.2289561631768222, 1.0389216059914184, 0.832757551728517, 0.6189300552394631, 0.40596170110875424, 0.20205568903275453, 0.01473645002072709, -0.1494771239754735, -0.2853510229967694, -0.38915515772189363, -0.4588117523050455, -0.4939657855665123, -0.49597358883173787, -0.4678093599793456, -0.41389308643989803, -0.3398470222137657, -0.2521912719690819, -0.1579920418427582, -0.06447857801967745, 0.021353393082913362, 0.09313288264190729, 0.14548048086095883, 0.17433245744928003, 0.17720528416794554, 0.15338608331139564, 0.1040375780631698, 0.032209806804875764, -0.05724498452536792, -0.15785341367428624, -0.26179259426361384, -0.36024248472631, -0.4438049756942265, -0.5029721084759464, -0.5286228745878121, -0.5125259465422232, -0.44782455711059915, -0.3294796626060152, -0.15464853548215177, 0.07702197491460977, 0.36320515395068226, 0.6988207032809735, 1.0760863748858671, 1.4846983427335227, 1.9121379405827554, 2.344096525370667, 2.7650045048159657, 3.1586452585645355, 3.5088300385132225, 3.800106189114059, 4.018468383676042, 4.152041186944274, 4.191701235751562, 4.1316087290949355, 3.9696207256889595, 3.707562886647723, 3.351341636997846, 2.910885057534093, 2.3999079118792497, 1.8355037740169236, 1.2375749297511727, 0.6281182446794453, 0.030392181437744917, -0.5320037176967531, -1.0361005910851249, -1.4605434104864583, -1.7865437392999983, -1.9987601344494104, -2.086065883038469, -2.042167232788036, -1.866040464267393, -1.5621628900288833, -1.140520903930702, -0.6163872309410174, -0.009869178024161871, 0.6547604437937594, 1.3499283931979695, 2.045791708070227, 2.711395712554671, 3.3159144334797657, 3.82992374198979, 4.226654752208037, 4.483174412405197, 4.581441899278722, 4.509193358174781, 4.260613606900411, 3.836761426097673], 'positive_zeros': ['0.847588189911438492264876310239739', '2.22464692528771889903345272551123', '2.76757903183241888279135359212536', '4.25581457702037421217542260945755', '5.80509002640716085421825245913932', '6.42383071257771229856981385006242', '7.28896429179541547653676532301953', '7.953560169250351855318936528787025', '8.992538617340413556165906699604393'], 'prelabel': '2-33e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.215823083574323, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.847588189911438492264876310240', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.22464692528771889903345272551', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.76757903183241888279135359213', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 174.65797977633594, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 113, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/6/a/bl/1/1'], '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': '2-33e2-1.1-c5-0-113', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-33e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.215823083574323, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.847588189911438492264876310240', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1074445677687593496881827434507', 'Lhash_array': ['1074445677687593496881827434507'], 'label': '2-33e2-1.1-c5-0-113', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/6/a/bl/1/1'}