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lfunc_lfunctions • Show schema
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{'Lhash': '958061651176358279564129941981', 'a10': [-0.6333773721845972, -2.144489007760248], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [1.5327849776604279, 1.5327849776604279], 'a4': [0.0, -1.0], 'a5': [-1.0685172846454378, 1.9642481544891268], 'a6': [-2.1676853036091184, -9.538544333656891e-61], 'a7': [-1.647242509369749, 1.647242509369749], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 1.6988595754829563], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.433567286915058, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [1.0685172846454378, -1.9642481544891268]]], [43, [[1.0, 0], [6.1306246953014245, -2.327109977066042]]]], 'bad_primes': [2, 5, 43], 'central_character': '430.257', 'coefficient_field': 'CDF', 'conductor': 430, 'conductor_radical': 430, 'conjugate': '3101803596719737383474197594036', 'degree': 2, 'euler_factors': 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-0.8831010577511722, 'root_number': '-0.9333186713995475 - 0.359049101958191*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.441550528876', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75577738140451924224343121735', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17032280704782110768924115734', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52274206006880630000890147443', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.433567286915058, 'bad_primes': [2, 5, 43], 'central_character': '215.42', 'conductor': 430, 'conductor_radical': 430, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/430/2/g/b/257/8'], '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': '2-430-215.42-c1-0-3', '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': '2-430-215.42-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8529887444113249, 'root_angle': -0.4415505288755861, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75577738140451924224343121735', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '958061651176358279564129941981', 'Lhash_array': ['958061651176358279564129941981'], 'label': '2-430-215.42-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/430/2/g/b/257/8'}