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lfunc_lfunctions • Show schema
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{'Lhash': '3114114541502999616021009050518', 'a10': [-1.0, -3.0], 'a2': [0.0, -1.4142135623730951], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.1213203435596424, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.0, 3.0], 'a8': [0.0, -2.8284271247461903], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.1213203435596424, 0.7071067811865476]]]], 'bad_primes': [3, 5], 'central_character': '135.109', 'coefficient_field': 'CDF', 'conductor': 135, 'conductor_radical': 15, 'conjugate': '2459001646342101993443396543407', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1213203435596424, 0.7071067811865476]], [[1.0, 0], [0, -3.0], [-7.0, 0]], [[1.0, 0], [4.242640687119285, 0], [11.0, 0]], [[1.0, 0], [0, 3.0], [-13.0, 0]], [[1.0, 0], [0, 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'12.74279709354293528097188993694971', '13.85174070080401332303088791745461'], 'prelabel': '2-135-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0382583624933082, 'root_angle': 0.39758361765043326, 'root_number': '0.31622776601683794 + 0.9486832980505138*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.198791808825', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.45660321617197241438548096896', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.68698523821464655812134364779', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.95031934677130676969642251552', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/135/2/b/b/109/2'], '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': '2-135-5.4-c1-0-5', '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': '2-135-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0382583624933082, 'root_angle': 0.19879180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.45660321617197241438548096896', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3114114541502999616021009050518', 'Lhash_array': ['3114114541502999616021009050518'], 'label': '2-135-5.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/2/b/b/109/2'}