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lfunc_lfunctions • Show schema
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{'Lhash': '876575414613751420115847996004', 'a10': [-0.43704076642495576, 0.0], 'a2': [1.0, 0.0], 'a3': [-0.7710336320654001, 0.0], 'a4': [1.0, 0.0], 'a5': [-0.43704076642495576, 0.0], 'a6': [-0.7710336320654001, 0.0], 'a7': [-4.611282743892725, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.405507138224037, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.86304007342658, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [37, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 37], 'central_character': '2738.1', 'coefficient_field': 'CDF', 'conductor': 2738, 'conductor_radical': 74, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.7710336320654001, 0], [3.0, 0]], [[1.0, 0], [0.43704076642495576, 0], [5.0, 0]], [[1.0, 0], [4.611282743892725, 0], [7.0, 0]], [[1.0, 0], [1.8028301220776026, 0], [11.0, 0]], [[1.0, 0], [-6.122788180618002, 0], [13.0, 0]], [[1.0, 0], [2.2051886488478067, 0], [17.0, 0]], [[1.0, 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'3.88492172926377264681767876217266', '5.01220268393543167492852173559159', '6.01579724187601449994137720121077', '6.21093182574989105892561052021777', '6.95604846642844338892792011565628', '8.097113451002843524744468211708813', '8.755845246222323701934421960807311'], 'prelabel': '2-2738-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.675792988726787, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69149607506668768568094277197', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47048760289464139110962068932', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28841405870470454045920994450', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.86304007342658, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 2738, 'conductor_radical': 74, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2738/2/a/x/1/7'], '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': '2-2738-1.1-c1-0-14', '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': '2-2738-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.675792988726787, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69149607506668768568094277197', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '876575414613751420115847996004', 'Lhash_array': ['876575414613751420115847996004'], 'label': '2-2738-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2738/2/a/x/1/7'}