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  • lfunc_lfunctions • Show schema
    {'Lhash': '763281574209207621576879730364', 'a10': [-1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.596915527892125, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.529033218405047, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '2070.1', 'coefficient_field': 'CDF', 'conductor': 2070, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.596915527892125, 0], [7.0, 0]], [[1.0, 0], [5.131632370575728, 0], [11.0, 0]], [[1.0, 0], [1.2221164044197774, 0], [13.0, 0]], [[1.0, 0], [-4.687399561736173, 0], [17.0, 0]], [[1.0, 0], [4.596915527892125, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], 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'group': 'GL2', 'index': 2, 'label': '2-2070-1.1-c1-0-2', 'leading_term': '0.75618240483761126394141207700926', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2070/2/a/z/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [0.7561824048376112, 0.7494454154356339, 0.7291569220027834, 0.6950940536108298, 0.6469169329729407, 0.5842134406790208, 0.5065570726737093, 0.41357386436017946, 0.30501409861424716, 0.18082462400355362, 0.041217963206978916, -0.1132651347095569, -0.2817025490799882, -0.46274944131460805, -0.6546106959362646, -0.8550287806895221, -1.0612883223021343, -1.270238351274067, -1.4783327912023567, -1.6816893365771812, -1.8761663680474159, -2.0574569957239723, -2.2211987077840885, -2.3630964496184874, -2.479056290375321, -2.5653261761602923, -2.6186396529393026, -2.636357899974696, 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'7.56456030324053744079270194696329', '8.375757539500270428583267452795308', '9.417246562727572730971649577342134'], 'prelabel': '2-2070-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.065591373761639, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60212299356919442244351812269', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.38399835308151187172869194962', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.90532806023335387889832660096', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 16.529033218405047, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 2070, 'conductor_radical': 690, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2070/2/a/z/1/1'], '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': '2-2070-1.1-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2070-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.065591373761639, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60212299356919442244351812269', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '763281574209207621576879730364', 'Lhash_array': ['763281574209207621576879730364'], 'factors': ['2-2070-1.1-c1-0-2'], 'label': '2-2070-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2070/2/a/z/1/1'}