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  • lfunc_lfunctions • Show schema
    {'Lhash': '1905893685006131643563084810846', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8815235458175288, 0.0], 'a4': [0.0, 0.0], 'a5': [2.4684178195659165, 0.0], 'a6': [0.0, 0.0], 'a7': [1.3973024910749616, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.2229162381692915, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.79269013540588, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 23], 'central_character': '4232.1', 'coefficient_field': 'CDF', 'conductor': 4232, 'conductor_radical': 46, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8815235458175288, 0], [3.0, 0]], [[1.0, 0], [-2.4684178195659165, 0], [5.0, 0]], [[1.0, 0], [-1.3973024910749616, 0], [7.0, 0]], [[1.0, 0], [0.7600303735093401, 0], [11.0, 0]], [[1.0, 0], [3.31151200918882, 0], [13.0, 0]], [[1.0, 0], [-2.1405850958884387, 0], [17.0, 0]], [[1.0, 0], [-0.4164166087348136, 0], 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0], [-6.575816685319375, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 100, 'label': '2-4232-1.1-c1-0-100', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4232/2/a/y/1/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-8.593108987202787e-61, 0.17051778291633776, 0.3403980802801951, 0.5089691644483894, 0.6754929886678996, 0.8391372894134206, 0.9989536006475976, 1.153862535184291, 1.3026472584799873, 1.4439556406839738, 1.5763111591866537, 1.698132260359296, 1.80775958747566, 1.9034902430596732, 1.9836180717287517, 2.046478813707497, 2.0904988785196092, 2.1142464133640115, 2.1164832845232757, 2.096216549155879, 2.052747968229423, 1.9857201007521061, 1.8951575280745891, 1.781501788979253, 1.6456386658976383, 1.4889165539285485, 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'5.74243309592567614079088960304740', '6.31469292752256436629081775592729', '7.43051885280097440426214807664815', '7.85271676301761034247046461803029'], 'prelabel': '2-4232-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.813148040038708, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50348501760894694313632997160', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34540412074306358990396610274', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23230938615260306920248855120', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 33.79269013540588, 'bad_primes': [2, 23], 'central_character': '1.1', 'conductor': 4232, 'conductor_radical': 46, 'degree': 2, 'index': 100, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4232/2/a/y/1/6'], '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': '2-4232-1.1-c1-0-100', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4232-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.813148040038708, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50348501760894694313632997160', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '1905893685006131643563084810846', 'Lhash_array': ['1905893685006131643563084810846'], 'factors': ['2-4232-1.1-c1-0-100'], 'label': '2-4232-1.1-c1-0-100', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4232/2/a/y/1/6'}