Formats: - HTML - YAML - JSON - 2026-09-07T11:48:48.602993
  • lfunc_lfunctions • Show schema
    {'Lhash': '1180512409162328809171748738830', 'a10': [0.0, 0.0], 'a2': [-0.6566204310471103, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.568849609531507, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.3433795689528896, 0.0], 'a8': [2.34337956895289, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.47545968271595, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 37], 'central_character': '8325.1', 'coefficient_field': 'CDF', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6566204310471103, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3433795689528896, 0], [7.0, 0]], [[1.0, 0], [4.167837925921683, 0], [11.0, 0]], [[1.0, 0], [3.5688496095315068, 0], [13.0, 0]], [[1.0, 0], [-0.7443912525627138, 0], [17.0, 0]], [[1.0, 0], [1.7443912525627137, 0], 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[[1.0, 0], [-12.904525461374872, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 130, 'label': '2-8325-1.1-c1-0-130', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/8325/2/a/bo/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [-1.4889050225351364e-61, 0.11125669471454837, 0.22092213649944142, 0.3273812414271279, 0.42897407678183563, 0.5239802609534684, 0.6106109928714721, 0.687010390761446, 0.7512672036497288, 0.8014373143868209, 0.8355768284258123, 0.8517849738475186, 0.8482555466052344, 0.8233352294532867, 0.7755867930962111, 0.7038549481003601, 0.6073324487215929, 0.4856239485574356, 0.3388050686158756, 0.16747415942006186, -0.027205679176569495, -0.24347661154912725, -0.4789701932469853, -0.7307074122999412, -0.9951160981078377, -1.2680667360470723, -1.5449272475156048, 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'6.03952960387302177682255679537947', '6.98492143526365939775715279967435', '7.57260327553159590832016423342339'], 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.931260087716432175170713519188', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.29493719798171049368026411605', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.96689293307504430123651100023', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 66.47545968271595, 'bad_primes': [3, 5, 37], 'central_character': '1.1', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'index': 130, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8325/2/a/bo/1/2'], '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': '2-8325-1.1-c1-0-130', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.931260087716432175170713519188', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1180512409162328809171748738830', 'Lhash_array': ['1180512409162328809171748738830'], 'factors': ['2-8325-1.1-c1-0-130'], 'label': '2-8325-1.1-c1-0-130', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8325/2/a/bo/1/2'}