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lfunc_lfunctions • Show schema
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{'Lhash': '2432347414465731826210354030877', 'a10': [-3558811116937509000000, 0], 'a2': [-4194304.0, 0], 'a3': [38093042574.16799, 0], 'a4': [17592186044416.0, 0], 'a5': [848486689791085.5, 0], 'a6': [-159773800841003100, 0], 'a7': [-4248842540412561000, 0], 'a8': [-73786976294838210000, 0], 'a9': [-1503232813993458700000, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.65114521485525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '22.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [4194304.0, 0]]]], 'bad_primes': [2], 'central_character': '2.1', 'coefficient_field': 'CDF', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[[1.0, 0], [4194304.0, 0]], [[1.0, 0], [-38093042574.16799, 0], [2954312706550833600000, 0]], [[1.0, 0], [-848486689791085.5, 0], [28421709430404005000000000000000, 0]], [[1.0, 0], [4248842540412561000, 0], [107006904423598030000000000000000000000, 0]], [[1.0, 0], [102236388209072130000000, 0], 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1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c45-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91878378318742479337122401395', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44388743437458894349875015741', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.08841909311783733854143528588', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.65114521485525, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2/46/a/a/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': '2-2-1.1-c45-0-2', 'motivic_weight': 45, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [45], 'order_of_vanishing': 1, 'prelabel': '2-2-1.1-c45-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.06469596470067, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c45-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91878378318742479337122401395', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2432347414465731826210354030877', 'Lhash_array': ['2432347414465731826210354030877'], 'label': '2-2-1.1-c45-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2/46/a/a/1/2'}