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lfunc_lfunctions • Show schema
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{'Lhash': '1387672732037984968994428667015', 'a10': [-3.0, -1.0], 'a2': [-0.36602540378443865, -1.3660254037844386], 'a3': [-2.366025403784439, -0.6339745962155614], 'a4': [-1.7320508075688772, 1.0], 'a5': [1.2320508075688772, -1.8660254037844386], 'a6': [9.031111191672786e-62, 3.4641016151377544], 'a7': [3.4641016151377544, 3.4641016151377544], 'a8': [2.0, 2.0], 'a9': [2.598076211353316, 1.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.36602540378443865, 1.3660254037844386]]], [5, [[1.0, 0], [-1.2320508075688772, 1.8660254037844386]]], [19, [[1.0, 0], [2.598076211353316, 3.5]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.83', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '1462273819907616066706239034030', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.36602540378443865, 1.3660254037844386]], 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'10.58160449239254256355711432968114', '11.05826513834453006747734795060701'], 'prelabel': '2-380-380.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.3931179973997966, 'root_number': '0.32950543996149045 + 0.9441536765991989*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1965589987', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09468076754599937284568282782', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.95743138411987513109603953640', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99082182462089597280116828847', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '380.83', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/v/b/83/1'], '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': '2-380-380.83-c1-0-14', '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': '2-380-380.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.1965589986998983, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09468076754599937284568282782', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1387672732037984968994428667015', 'Lhash_array': ['1387672732037984968994428667015'], 'label': '2-380-380.83-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/v/b/83/1'}