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lfunc_lfunctions • Show schema
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{'Lhash': '842881262060360000300701017045', 'a10': [0, 0], 'a2': [0.8890272305900613, -3.8999526385931107], 'a3': [5.196152422706632, 0], 'a4': [-14.419261166538732, -6.934328187441671], 'a5': [0, 0], 'a6': [4.619520998082715, -20.264748351466714], 'a7': [44.099081745951715, 0], 'a8': [-39.862667333526474, 50.06962904852203], 'a9': [27.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.010988925153306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8890272305900613, 3.8999526385931107]]], [3, [[1.0, 0], [-5.196152422706632, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '300.199', 'coefficient_field': 'CDF', 'conductor': 300, 'conductor_radical': 30, 'conjugate': '1876531545116258553664522375942', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8890272305900613, 3.8999526385931107]], [[1.0, 0], [-5.196152422706632, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-44.099081745951715, 0], 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'data': '-0.002449470866887723', 'prec': 70}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66491607538276446393868775179', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72512389419101600145813731911', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02913450460899595064522755435', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.010988925153306, 'bad_primes': [2, 3, 5], 'central_character': '20.19', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/5/f/c/199/19'], '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': '2-300-20.19-c4-0-23', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-300-20.19-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.568751110002431, 'root_angle': -0.002449470866887723, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66491607538276446393868775179', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '842881262060360000300701017045', 'Lhash_array': ['842881262060360000300701017045'], 'label': '2-300-20.19-c4-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/5/f/c/199/19'}