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lfunc_lfunctions • Show schema
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{'Lhash': '2512607626461811250371760545230', 'a10': [-1.4142135623730951, 0.0], 'a2': [2.414213562373095, 0.0], 'a3': [0.0, 0.0], 'a4': [3.8284271247461903, 0.0], 'a5': [-0.585786437626905, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [4.414213562373095, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '2512607626461811250371760545230', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.414213562373095, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.585786437626905, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-5.414213562373095, 0], [13.0, 0]], [[1.0, 0], [6.242640687119285, 0], [17.0, 0]], [[1.0, 0], 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'6.93298289875662016544307328450127', '8.246147397636992144189467428597184', '9.307113614828823043519987160241434', '10.75716102976924003391464350568703', '11.42246573592320040955126608197131'], 'prelabel': '2-21e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98209792667588231872305161133', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.55027268374249635468919687494', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08922303615558275264143400460', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/a/i/1/2'], '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': '2-21e2-1.1-c1-0-8', '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': '2-21e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98209792667588231872305161133', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2512607626461811250371760545230', 'Lhash_array': ['2512607626461811250371760545230'], 'label': '2-21e2-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/a/i/1/2'}