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lfunc_lfunctions • Show schema
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{'Lhash': '1470464841316756356735566103312', 'a10': [-0.5261260158436613, 0.30375899687500313], 'a2': [-0.25881904510252074, 0.9659258262890683], 'a3': [-1.3499592357642498, -1.085177433314388], 'a4': [-0.8660254037844386, -0.5], 'a5': [0.42958009307347605, 0.42958009307347605], 'a6': [1.3975960692722822, -1.0230959032049078], 'a7': [-0.9659258262890683, 0.25881904510252074], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.6447798764503943, 2.9298905970914024], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [1.3499592357642498, 1.085177433314388]]], [7, [[1.0, 0], [0.9659258262890683, -0.25881904510252074]]], [13, [[1.0, 0], [1.8227051393017488, 3.1109075806206445]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.197', 'coefficient_field': 'CDF', 'conductor': 546, 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['1.15999222581680790061280880050751', '2.99362884486956079261139225789303', '4.18572346557555800784368140015645', '4.98015254758219127224128306201600', '6.18943880524840956303834522406932', '7.04335375925348065974508675225018', '8.571816997590962262773917206466508', '9.302420985244657778577855388823384', '10.05896998277911436438284273782859', '10.77592217093493060944955457125968'], 'prelabel': '2-546-39.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.0550315518016344, 'root_number': '0.9850922792028517 + 0.172026746335943*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0275157759008', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15999222581680790061280880051', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99362884486956079261139225789', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18572346557555800784368140016', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '39.2', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bu/b/197/2'], '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': '2-546-39.2-c1-0-10', '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': '2-546-39.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.0275157759008172, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15999222581680790061280880051', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1470464841316756356735566103312', 'Lhash_array': ['1470464841316756356735566103312'], 'label': '2-546-39.2-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bu/b/197/2'}