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lfunc_lfunctions • Show schema
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{'Lhash': '2509015999723550122303942101986', 'a10': [0.0, 0.0], 'a2': [0.0, -0.41421356237309503], 'a3': [0.0, -1.0], 'a4': [1.82842712474619, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.41421356237309503, 0.0], 'a7': [0.0, -2.414213562373095], 'a8': [0.0, -1.5857864376269049], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.587658166755635, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.199', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'conjugate': '1059169645277370709860450446328', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.41421356237309503], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.414213562373095], [-7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-13.0, 0]], [[1.0, 0], [0, 0.41421356237309503], 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[[1.0, 0], [-17.31370849898476, 0], [109.0, 0]], [[1.0, 0], [0, -10.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-825-5.4-c1-0-23', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/825/2/c/d/199/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7468482837058046, 1.971434183377996, 2.1957219484130963, 2.416193609983151, 2.6241320475596397, 2.8061825840324706, 2.945660538559986, 3.024351715880754, 3.024614307155476, 2.9316390208316947, 2.7357227509885256, 2.4343725647225654, 2.0340099373590994, 1.5510154479523217, 1.011858934557462, 0.45210901133920317, -0.08578864898150947, -0.5559374969490156, -0.913426972887294, -1.1194090614626646, -1.1462814014932854, -0.9823252407300055, -0.6350992770262562, -0.13293682472407636, 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'8.031563125032195332069694299277390', '8.747122560134846947382452063048385', '9.666315561907652670363550433130734', '10.52838566225161487966085720359634'], 'prelabel': '2-825-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': 0.6475836176504333, 'root_number': '-0.4472135954999579 + 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.323791808825', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97926463275592165519936332302', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90379806582862881081652373243', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22333671755731136566954811878', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.587658166755635, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/c/d/199/2'], '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': '2-825-5.4-c1-0-23', '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': '2-825-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97926463275592165519936332302', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2509015999723550122303942101986', 'Lhash_array': ['2509015999723550122303942101986'], 'label': '2-825-5.4-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/c/d/199/2'}