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lfunc_lfunctions • Show schema
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{'Lhash': '2456595316065748306351716007592', 'a10': [4.090917020079024, 0.0], 'a2': [1.0, 0.0], 'a3': [-0.36086998421864064, 0.0], 'a4': [1.0, 0.0], 'a5': [4.090917020079024, 0.0], 'a6': [-0.36086998421864064, 0.0], 'a7': [-3.96411746621377, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.869772854490038, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.383937661298898, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]], [103, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 13, 103], 'central_character': '2678.1', 'coefficient_field': 'CDF', 'conductor': 2678, 'conductor_radical': 2678, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.36086998421864064, 0], [3.0, 0]], [[1.0, 0], [-4.090917020079024, 0], [5.0, 0]], [[1.0, 0], [3.96411746621377, 0], [7.0, 0]], [[1.0, 0], [6.500672324439117, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0771934212672476, 0], [17.0, 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'5.89621512098332811996719038558225', '6.65642383774403088592281121975934', '7.43193546037779003299188739922837', '8.622779517013576062924270574522424'], 'prelabel': '2-2678-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.624276987951619, 'root_angle': 1.0, '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': '1.93791200479332381442051893488', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84644122407185267856831698901', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19201598386626682893451969174', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.383937661298898, 'bad_primes': [2, 13, 103], 'central_character': '1.1', 'conductor': 2678, 'conductor_radical': 2678, 'degree': 2, 'index': 94, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2678/2/a/s/1/6'], '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': '2-2678-1.1-c1-0-94', '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': '2-2678-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.624276987951619, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93791200479332381442051893488', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2456595316065748306351716007592', 'Lhash_array': ['2456595316065748306351716007592'], 'label': '2-2678-1.1-c1-0-94', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2678/2/a/s/1/6'}