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lfunc_lfunctions • Show schema
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{'Lhash': '4572667010485746471357849476749', 'a10': -1084098960, 'a2': 456, 'a3': 50652, 'a4': -316352, 'a5': -2377410, 'a6': 23097312, 'a7': -16917544, 'a8': -383331840, 'a9': 1403363637, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.2881669655638075, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '9.5', 'prec': 10}, 'bad_lfactors': [], 'bad_primes': [], 'central_character': '1.1', 'coefficient_field': '1.1.1.1', 'conductor': 1, 'conductor_radical': 1, 'degree': 2, 'euler_factors': [[1, -456, 524288], [1, -50652, 1162261467], [1, 2377410, 19073486328125], [1, 16917544, 11398895185373143], [1, 16212108, 61159090448414546291], [1, -50421615062, 1461920290375446110677], [1, -225070099506, 239072435685151324847153], [1, 1710278572660, 1978419655660313589123979], [1, -14036534788872, 74615470927590710561908487], [1, -1137835269510, 6103261246589991489578849669], [1, 104626880141728, 21670662219970396194714277471], [1, 169392327370594, 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[[[1, -25742101939950990162, 1019742280064015448879700240781487485777], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1-1.1-c19-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 19, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [19], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1/20/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.9817354054335268, 1.9765030634083323, 1.960816851210307, 1.9347095423396081, 1.8982368620439505, 1.8514791291793362, 1.7945435299754406, 1.7275669981317765, 1.650719667339528, 1.5642088532676868, 1.4682835121586328, 1.3632391123656884, 1.2494228433882992, 1.1272390742173843, 0.9971549591421947, 0.8597060746956073, 0.7155019562955904, 0.5652313876148547, 0.4096672800922434, 0.2496709646821808, 0.08619570340000784, -0.07971078497632178, -0.2469050018975521, -0.414147774072676, -0.5801060168646702, 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'23.37831105449752633139466303809581', '25.59118621334058836769515346551408', '27.29445208791780927881588765642850', '30.55672605125458804006448947936114'], 'prelabel': '2-1-1.1-c19-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.512668822169548, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c19-0', 'trace_hash': 1309468426988552452, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.60719823716604384253001609923', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '8.677106764116385551617153434409', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '13.31064190731384332629695179807', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.2881669655638075, 'bad_primes': [], 'central_character': '1.1', 'conductor': 1, 'conductor_radical': 1, 'degree': 2, 'dirichlet_coefficients': [1, 456, 50652, -316352, -2377410, 23097312, -16917544, -383331840, 1403363637, -1084098960, -16212108, -16023861504, 50421615062, -7714400064, -120420571320, -8939761664, 225070099506, 639933818472, -1710278572660, 752098408320, -856907438688, -7392721248, 14036534788872, -19416524359680, -13421408020025, 22992256468272, 12212307114840, 5351898879488, 1137835269510, -54911780521920, -104626880141728, 196899752411136, -821175694416, 102631965374736, 40219938281040, -443956893292224, -169392327370594, -779887029132960, 2553955646120424, 911336949734400, -3309984750560838, -390749792041728, 1127913532193492, 5128732790016, -3336370744240170, 6400659863725632, 3498693987674256, -452816807804928, -11112691890381207, -6120162057131400, 11400250680177912, -15950978768093824, 29956294112980302, 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'ModularForm/GL2/Q/holomorphic/1/20/a/a'], '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': '2-1-1.1-c19-0-0', 'motivic_weight': 19, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [19], 'order_of_vanishing': 0, 'prelabel': '2-1-1.1-c19-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.512668822169548, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c19-0', 'trace_hash': 1309468426988552452, 'z1': {'__RealLiteral__': 0, 'data': '3.60719823716604384253001609923', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9964432
{'Lhash': '4572667010485746471357849476749', 'Lhash_array': ['4572667010485746471357849476749'], 'label': '2-1-1.1-c19-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1/20/a/a'}
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id: 24548877
{'Lhash': '4572667010485746471357849476749', 'Lhash_array': ['4572667010485746471357849476749'], 'label': '2-1-1.1-c19-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1/20/a/a/1/1'}