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lfunc_lfunctions • Show schema
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{'Lhash': '1468213704193820250772809519195', 'a10': [35.00198520275212, 0.0], 'a2': [2.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [4.0, 0.0], 'a5': [17.50099260137606, 0.0], 'a6': [-6.0, 0.0], 'a7': [-7.0, 0.0], 'a8': [8.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.21504286313439, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [3, [[1.0, 0], [3.0, 0]]], [7, [[1.0, 0], [7.0, 0]]], [13, [[1.0, 0], [-13.0, 0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.1', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [-17.50099260137606, 0], [125.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [3.0805118642453646, 0], [1331.0, 0]], [[1.0, 0], [-13.0, 0]], [[1.0, 0], [-124.54022863655527, 0], [4913.0, 0]], [[1.0, 0], [78.96070937368597, 0], [6859.0, 0]], [[1.0, 0], 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'5.10262002890042975946948494122520', '5.69511202612237312662261677269197', '6.41058286286950942648420836216456', '7.34014146228772072466719811718097', '8.776572339520877250044150411411107', '9.838042566109044116423786882078653', '10.33821777560869723513486138236343'], 'prelabel': '2-546-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.675829707023846, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15821639174823189992608327213', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38667019151206458490095094702', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64249027771704366360354806105', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.21504286313439, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/4/a/p/1/3'], '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': '2-546-1.1-c3-0-16', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-546-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.675829707023846, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15821639174823189992608327213', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1468213704193820250772809519195', 'Lhash_array': ['1468213704193820250772809519195'], 'factors': ['2-546-1.1-c3-0-16'], 'label': '2-546-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/4/a/p/1/3'}