-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1293614265802919771848722869136', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': 0, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1', 'coefficient_field': '1.1.1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1], [1, 0, 7], [1, -4, 11], [1, 1], [1, -6, 17], [1, -4, 19], [1, 8, 23], [1, -6, 29], [1, 8, 31], [1, -10, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -10, 53], [1, -4, 59], [1, 2, 61], [1, -12, 67], [1, -16, 71], [1, 2, 73], [1, 16, 79], [1, -12, 83], [1, -10, 89], [1, -6, 97], [1, 2, 101], [1, 0, 103], [1, -12, 107], [1, 10, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [1], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, 1], 1]], [[[1, -6, 17], 1]], [[[1, -4, 19], 1]], [[[1, 8, 23], 1]], [[[1, -6, 29], 1]], [[[1, 8, 31], 1]], [[[1, -10, 37], 1]], [[[1, 6, 41], 1]], [[[1, 4, 43], 1]], [[[1, 0, 47], 1]], [[[1, -10, 53], 1]], [[[1, -4, 59], 1]], [[[1, 2, 61], 1]], [[[1, -12, 67], 1]], [[[1, -16, 71], 1]], [[[1, 2, 73], 1]], [[[1, 16, 79], 1]], [[[1, -12, 83], 1]], [[[1, -10, 89], 1]], [[[1, -6, 97], 1]], [[[1, 2, 101], 1]], [[[1, 0, 103], 1]], [[[1, -12, 107], 1]], [[[1, 10, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-1950-1.1-c1-0-11', 'leading_term': '1.752923080621352821134545558110900000000000000000000000000000000000000000000000000000000000', '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/1950/2/a/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.7529230806213527, 1.7479193512457882, 1.7328049621153148, 1.7072806015059072, 1.6708808812644826, 1.6230217266769382, 1.5630615428352719, 1.4903718705932045, 1.4044130301890867, 1.3048104387858679, 1.1914277371106956, 1.06443342426995, 0.9243582650627723, 0.772141234520558, 0.6091621789666141, 0.43725971364299865, 0.2587331740720787, 0.07632772735263954, -0.1067979373639392, -0.2871215591062163, -0.46082469357070127, -0.6238768500656401, -0.7721351403642263, -0.9014576101292616, -1.0078278043845124, -1.0874874974622621, -1.1370739230305882, -1.1537573015101024, -1.1353740116620865, -1.08055042117942, -0.98881220674236, -0.8606739829947754, -0.6977042433965731, -0.5025610090497337, -0.27899419223496785, -0.03181150900774646, 0.23319418999163868, 0.5093570789584477, 0.7892895346497193, 1.065070361599962, 1.328466525195824, 1.5711832708581213, 1.785135975162384, 1.962735659345254, 2.0971788664509767, 2.182731628521181, 2.2149965937830993, 2.1911521024995526, 2.110152140237074, 1.9728766914252815, 1.782223080512983, 1.5431304204323821, 1.2625312658213377, 0.9492269476847752, 0.6136857818408327, 0.2677663102657584, -0.07562915130900548, -0.40296224343101605, -0.7005161134824225, -0.9548885272120156, -1.1535038555189039, -1.2851253333190256, -1.340347699461867, -1.3120497711517696, -1.195786761715435, -0.990103265633454, -0.6967498239346362, -0.3207888229964364, 0.12942089248360517, 0.6423669988886782, 1.20365571527551, 1.7964090916684696, 2.4017783990747987, 2.9995591285964798, 3.568888079920062, 4.088998534093867, 4.54000579440119, 4.903692654742138, 5.164262798207246, 5.309029878299024, 5.329011178873933, 5.219397314653735, 4.979873386206577, 4.614772239134384, 4.133046828420857, 3.5480559251437875, 2.8771652390113687, 2.1411741371801294, 1.3635861573357189, 0.5697490655581716, -0.21410307635865466, -0.9618678466634082, -1.6486103976165996, -2.25157312839856, -2.751114531552929, -3.1315343896942993, -3.381746294772764, -3.49576421635197, -3.4729773628914344, -3.3181965700241762, -3.0414655355963736, -2.657640955145905, -2.185756494237658, -1.6481960376527334, -1.0697112488151244, -0.47632664907816524, 0.10581827007987556, 0.6516363367918805, 1.138214302803322, 1.5458348403646316, 1.8588488923986177, 2.06635482068771, 2.162649631532787, 2.147428359379232, 2.0257199556137016, 1.8075611668530323, 1.5074232329398136, 1.1434190945673055, 0.7363304820044106, 0.30850410848979676, -0.11732635904048025, -0.5192312946562003, -0.8772264162841843, -1.1743036795824198, -1.3972963029192698, -1.5375308307620592, -1.5912302342420277, -1.5596453143245028, -1.4489064279337656, -1.2696030099506794, -1.0361136614272015, -0.7657238483294109, -0.4775806711090408, -0.1915439719059982, 0.0730003790639474, 0.2982962860089924, 0.46927463207744974, 0.5744492077294632, 0.6065974537069202, 0.5631842078479661, 0.44650143361063716, 0.2635135698966868, 0.025415725219558385, -0.253070588543052, -0.5546231816241375, -0.8604112441329199, -1.151287573722087, -1.409007613147909, -1.6173991120410183, -1.7634080546044164, -1.8379529781628194, -1.8365306617379915, -1.7595308252186406, -1.6122351311995746, -1.4044953957129125, -1.1501063103070026, -0.8659078915784855, -0.5706710332585669, -0.28383474071918086, -0.02417482937478065, 0.19150975995764308, 0.34960587907619284, 0.4407077715135415, 0.46037886006869677, 0.40959626594932086, 0.2948397941637913, 0.12780935262682583, -0.07522129915574029, -0.2943824505010545, -0.5074632048614574, -0.6913684474363284, -0.823687742812155, -0.8842757014250708, -0.8567394223785227, -0.7297314031285344, -0.4979558371752679, -0.1628120927449076, 0.2673794562208437, 0.7775984136457613, 1.346792925440131, 1.9489672253974937, 2.5546311328866085, 3.1325288733248042, 3.6515436004692137, 4.082659144529534, 4.40085296742048, 4.586794807492852, 4.628234264769118, 4.520977298805605, 4.269375433277086, 3.8862810351720696, 3.392455588746872, 2.8154533215048323, 2.188037576525893, 1.5462196323201198, 0.9270370266164446, 0.36620888328284407, -0.10418228904918905, -0.4578304061533618, -0.6760228112330374, -0.7490073127219312, -0.6768082335661845, -0.46942397910719613, -0.14637753173965454, 0.26436688933565156, 0.7280657127133493, 1.2053416765712845, 1.6546843016593504, 2.0351497098420044, 2.3090874908370775, 2.4447165263062702, 2.41837758751639, 2.2163080205404753, 1.835812026036265, 1.2857372882123215, 0.5862127156507896, -0.23234998244158572, -1.1309393898530697, -2.0642143419180554, -2.9832222735484613, -3.8383953168739016, -4.582632199913096, -5.174265203861192, -5.579715996042461, -5.775662009524772, -5.750565216687185, -5.505455804338269, -5.053911806362125, -4.421228996809247, -3.642829718071977, -2.7620110982169614, -1.8271786947338982, -0.8887477521694944, 0.00408165739185298, 0.8064591676343098, 1.4807165112463982, 1.9987052674112078, 2.3434802877340504, 2.510213350985228, 2.506274259483281, 2.3504740895555942, 2.0715236523600677, 1.7058153006826262, 1.2946840990946353, 0.8813415860006729, 0.5076991398809303, 0.21130648723578502, 0.022623396750594688, -0.037180524088239866, 0.04225973735657975, 0.2597847857210373, 0.6028375126630139, 1.048427130228581, 1.564860617245687, 2.11411562399298, 2.654681704764234, 3.1446619505011335], 'positive_zeros': ['1.02048172072810586725444806437568', '2.05799963788222426145971930453915', '3.26819059787837421750330634065923', '3.96841057609218045594012616188157', '5.25724539674339433994151433277332', '6.20008378576346310195929413718240', '7.01490063638720124480711152469186', '7.83466570589962625459131201888910', '8.325976297604312961734027796654886', '9.322358641232610436784648285374063'], 'prelabel': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 635343229649930485, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02048172072810586725444806438', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05799963788222426145971930454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26819059787837421750330634066', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, 0, -1, 1, 0, 4, 1, -1, 0, 0, 1, 6, -1, 4, 0, 0, -4, -8, -1, 0, 1, 1, 0, 6, 0, -8, -1, 4, -6, 0, 1, 10, -4, -1, 0, -6, 0, -4, 4, 0, 8, 0, 1, -7, 0, 6, -1, 10, -1, 0, 0, 4, -6, 4, 0, -2, 8, 0, 1, 0, -4, 12, 6, -8, 0, 16, -1, -2, -10, 0, 4, 0, 1, -16, 0, 1, 6, 12, 0, 0, 4, 6, -4, 10, 0, 0, -8, -8, 0, 0, -1, 6, 7, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 1, 0], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 8, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 7], 'euler71': [1, -16, 71], 'euler73': [1, 2, 73], 'euler79': [1, 16, 79], 'euler83': [1, -12, 83], 'euler89': [1, -10, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 0], [1, 0, 7], [1, -4, 11], [1, 1, 0], [1, -6, 17], [1, -4, 19], [1, 8, 23], [1, -6, 29], [1, 8, 31], [1, -10, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -10, 53], [1, -4, 59], [1, 2, 61], [1, -12, 67], [1, -16, 71], [1, 2, 73], [1, 16, 79], [1, -12, 83], [1, -10, 89], [1, -6, 97]], 'index': 11, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1950/k', 'ModularForm/GL2/Q/holomorphic/1950/2/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/1950/2/a/k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1950-1.1-c1-0-11', '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': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 635343229649930485, 'z1': {'__RealLiteral__': 0, 'data': '1.02048172072810586725444806438', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20607904
{'Lhash': '1293614265802919771848722869136', 'Lhash_array': ['1293614265802919771848722869136'], 'label': '2-1950-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/k'}
-
id: 24555211
{'Lhash': '1293614265802919771848722869136', 'Lhash_array': ['1293614265802919771848722869136'], 'label': '2-1950-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/k/1/1'}
-
id: 41463
{'Lhash': '635343229649930485', 'Lhash_array': ['635343229649930485'], 'label': '2-1950-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1950/k'}