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lfunc_lfunctions • Show schema
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{'Lhash': '1982424419297397491843768293895', 'a10': [0.5738777206930387, -0.9939853695721642], 'a2': [0.8660254037844386, 0.5], 'a3': [0, 0], 'a4': [0.5, 0.8660254037844386], 'a5': [0, -1.1477554413860773], 'a6': [0, 0], 'a7': [-0.8660254037844386, 0.5], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.079495851085733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [3.5434250479037908, -0.666437491358355]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.1135', 'coefficient_field': 'CDF', 'conductor': 1638, 'conductor_radical': 546, 'conjugate': '567558581294268715135146107888', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.1477554413860773], [-5.0, 0]], [[1.0, 0], [0.8660254037844386, -0.5]], 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'8.881760611411587958328129414420283', '9.848777662180376987647422672411864'], 'prelabel': '2-1638-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': 0.4367425396909743, 'root_number': '0.1974236752354217706905671745080115712265501267535333444 + 0.9803182607992869132195083775086838471623156698952015245*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21837126984548716', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56385712193918364956182058835', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86084337402300595353017255172', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33151598345395100137237007469', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.079495851085733, 'bad_primes': [2, 3, 7, 13], 'central_character': '13.4', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1638/2/bj/g/1135/5'], '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': '2-1638-13.4-c1-0-31', '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': '2-1638-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': 0.21837126984548716, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56385712193918364956182058835', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1982424419297397491843768293895', 'Lhash_array': ['1982424419297397491843768293895'], 'label': '2-1638-13.4-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/2/bj/g/1135/5'}