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lfunc_lfunctions • Show schema
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{'Lhash': '1238047406239858134193877243470', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.22474487139158905, 2.224744871391589], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.24460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.22474487139158905, -2.224744871391589]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '5040.1009', 'coefficient_field': 'CDF', 'conductor': 5040, 'conductor_radical': 210, 'conjugate': '1032046111800127828201719812455', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.22474487139158905, -2.224744871391589]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, 0.4494897427831781], [-13.0, 0]], [[1.0, 0], [0, -2.0], [-17.0, 0]], [[1.0, 0], 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[[1.0, 0], [0, 0.20204102886728761], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-5040-5.4-c1-0-57', 'leading_term': '2.3335920177111669070671192924977493641608786017646149414', '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/5040/2/t/t/1009/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.333592017711167, 2.3364905824495343, 2.3234419135417053, 2.294495519584399, 2.2496362378769494, 2.1888228869587536, 2.1120384623035724, 2.019348372669729, 1.9109628531049818, 1.787299626418149, 1.6490430662666995, 1.4971964724035398, 1.3331245324224563, 1.158583557146187, 0.9757375993823943, 0.7871590771994379, 0.5958130168806933, 0.4050245104522929, 0.21842945550098292, 0.03990911826940831, -0.12649046074343204, -0.27665271611663234, 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'4.49044459110839190857760679809896', '5.47099251331809770855341054473779', '5.80532248480771422934290188178315', '6.86209770778167519149121969280016', '7.51451823150925472458967499557089', '8.295674125336074724000199208397030'], 'prelabel': '2-5040-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.343863382728645, 'root_angle': -0.03204710842448747, 'root_number': '0.994936153005124052738804516547057381040868366920288399081 - 0.10050896200520817417513504905454688686462102307567810937*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.016023554212243735', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.976647197592900227250172239248', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.61381759945903315702740847014', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88607829786779263089333182912', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.24460261872533, 'bad_primes': [2, 3, 5, 7], 'central_character': '5.4', 'conductor': 5040, 'conductor_radical': 210, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5040/2/t/t/1009/4'], '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': '2-5040-5.4-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': '2-5040-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.343863382728645, 'root_angle': -0.016023554212243735, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.976647197592900227250172239248', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1238047406239858134193877243470', 'Lhash_array': ['1238047406239858134193877243470'], 'label': '2-5040-5.4-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5040/2/t/t/1009/4'}