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lfunc_lfunctions • Show schema
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{'Lhash': '2703522124500125695355508823412', 'a10': [-5.960569180742886, 0.0], 'a2': [2.7252503077255064, 0.0], 'a3': [1.346416008245993, 0.0], 'a4': [5.426989239757967, 0.0], 'a5': [-2.1871639327389256, 0.0], 'a6': [3.669320640798941, 0.0], 'a7': [0.0, 0.0], 'a8': [9.3394034802224, 0.0], 'a9': [-1.1871639327389258, 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': '2703522124500125695355508823412', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7252503077255064, 0], [2.0, 0]], [[1.0, 0], [-1.346416008245993, 0], [3.0, 0]], [[1.0, 0], [2.1871639327389256, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.048154940278454, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'4.97763389479724354941015833580009', '5.71622640375047307668373930776908', '6.98131857929503605017221182733154', '7.68430418621899595991319754355214', '8.460424822494051832029542626748627', '9.998667908267386675442593137963883', '10.99157091240352491817475414744013'], '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': '2.13270291041820213435822577536', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34211980293992660119808454250', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.70484676087682085648253846642', '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': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/k/1/5'], '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': '2-637-1.1-c1-0-30', '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': '2.13270291041820213435822577536', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2703522124500125695355508823412', 'Lhash_array': ['2703522124500125695355508823412'], 'label': '2-637-1.1-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/k/1/5'}