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lfunc_lfunctions • Show schema
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{'Lhash': '1656756917827360900581230676900', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.4142135623730951, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.4823619097949585, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.7320508075688773, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.58538027081175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 23], 'central_character': '8464.1', 'coefficient_field': 'CDF', 'conductor': 8464, 'conductor_radical': 46, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [3.0, 0]], [[1.0, 0], [1.4823619097949585, 0], [5.0, 0]], [[1.0, 0], [0.7320508075688773, 0], [7.0, 0]], [[1.0, 0], [-0.7320508075688773, 0], [11.0, 0]], [[1.0, 0], [-2.8637033051562732, 0], [13.0, 0]], [[1.0, 0], [-1.550510257216822, 0], [17.0, 0]], [[1.0, 0], [-0.0963763171773128, 0], [19.0, 0]], [[1.0, 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'4.30029401118911711212395110552013', '5.54739625337777023522828719474567', '5.97346481766996957647476088510312', '6.89927527335498121364709746716585', '7.67034316452453692534272056571773'], 'prelabel': '2-92e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.221032798305318, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30695076192846539133152051762', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37985082259238084213132853844', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15196803262690178348692400100', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.58538027081175, 'bad_primes': [2, 23], 'central_character': '1.1', 'conductor': 8464, 'conductor_radical': 46, 'degree': 2, 'index': 183, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8464/2/a/bl/1/4'], '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': '2-92e2-1.1-c1-0-183', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-92e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.221032798305318, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30695076192846539133152051762', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1656756917827360900581230676900', 'Lhash_array': ['1656756917827360900581230676900'], 'factors': ['2-92e2-1.1-c1-0-183'], 'label': '2-92e2-1.1-c1-0-183', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8464/2/a/bl/1/4'}