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lfunc_lfunctions • Show schema
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{'Lhash': '760556709988941055114707500077', 'a10': [1.8191639866285874, 0.0], 'a2': [-2.008524465257371, 0.0], 'a3': [-1.7590561113363243, 0.0], 'a4': [2.0341705275374076, 0.0], 'a5': [-0.9057215971703292, 0.0], 'a6': [3.533107235379501, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.068632340549634, 0.0], 'a9': [0.09427840282967079, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '760556709988941055114707500077', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.008524465257371, 0], [2.0, 0]], [[1.0, 0], [1.7590561113363243, 0], [3.0, 0]], [[1.0, 0], [0.9057215971703292, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7163611185415457, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'5.19146952663274279601492832562233', '6.45151260537239723045933174400428', '7.03542766398972229338840233413603', '8.227241499656225880955860428158240', '8.738217503189565302578205662200821', '9.793600687529902077373433257743661', '10.57323558578137676195984937418511'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, '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': '0.59997345471379059232210335297', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25130907375641470428688420174', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11950990912236128083857857925', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/k/1/1'], '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': '2-637-1.1-c1-0-0', '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': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59997345471379059232210335297', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '760556709988941055114707500077', 'Lhash_array': ['760556709988941055114707500077'], 'label': '2-637-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/k/1/1'}