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lfunc_lfunctions • Show schema
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{'Lhash': '2649678740465302096461736161560', 'a10': [3.753474187246929, -1.4560108662150975], 'a2': [1.040491247873474, -0.9577984981710405], 'a3': [-0.16738276424578835, -1.1105120803072395], 'a4': [0.16524407380259865, -1.9931619091466506], 'a5': [2.6500110309654836, 1.0400526881816952], 'a6': [-1.2378071039616838, -0.9951591400031139], 'a7': [2.564985563874447, 0.648728800898869], 'a8': [-1.7371124706378236, -2.232138047781668], 'a9': [1.6614983266166705, -0.5125043597723793], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.040491247873474, 0.9577984981710405]]], [7, [[1.0, 0], [-2.564985563874447, -0.648728800898869]]]], 'bad_primes': [2, 7], 'central_character': '392.109', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'conjugate': '2374614525842818752957419896717', 'degree': 2, 'euler_factors': [[[1.0, 0], 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.216796808776', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09022796974832861510451386876', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78599105118565999125549991727', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.93903306898490690990161792157', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'bad_primes': [2, 7], 'central_character': '392.109', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/2/z/a/109/43'], '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': '2-392-392.109-c1-0-40', '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': '2-392-392.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.769218968707433, 'root_angle': 0.21679680877618662, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09022796974832861510451386876', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2649678740465302096461736161560', 'Lhash_array': ['2649678740465302096461736161560'], 'factors': ['2-392-392.109-c1-0-40'], 'label': '2-392-392.109-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/2/z/a/109/43'}