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lfunc_lfunctions • Show schema
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{'Lhash': '1249626865329189413365638718644', 'a10': [0.8660254037844386, 0.5], 'a2': [-0.9659258262890683, 0.25881904510252074], 'a3': [0.8887514204117087, 1.4866475415229294], 'a4': [0.8660254037844386, -0.5], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [-1.2432406472277375, -1.2059654609816801], 'a7': [0.4311030196288338, -1.6088983725511707], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [-1.4202418254323401, 2.6425202283601568], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, -0.25881904510252074]]], [3, [[1.0, 0], [-0.8887514204117087, -1.4866475415229294]]], [5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [13, [[1.0, 0], [-2.835545413733939, -2.2270343972764373]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.71', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 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['0.985781780172079773141440003328190', '2.65661612949843574928786934400582', '3.52301586551535938910392707155592', '5.62547834866833916827862492978434', '6.57278150353496017362681425880712', '7.56400885679579369299650999427122', '8.514677653005586851679799101876631', '8.861871550893787501441183285990212', '10.19791568634788407896700525651606', '11.21749822611031462309282944128011'], 'prelabel': '2-390-39.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.44729708333801804, 'root_number': '0.16481564356208567 - 0.9863243906733806*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.223648541669', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.985781780172079773141440003328', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.65661612949843574928786934401', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52301586551535938910392707156', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '39.32', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bh/c/71/4'], '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': '2-390-39.32-c1-0-4', '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': '2-390-39.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.22364854166900902, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.985781780172079773141440003328', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1249626865329189413365638718644', 'Lhash_array': ['1249626865329189413365638718644'], 'label': '2-390-39.32-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bh/c/71/4'}