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  • lfunc_lfunctions • Show schema
    {'Lhash': '1416078394854289200399493350592', 'a10': [0, 0], 'a2': [105.55016388870413, 0], 'a3': [-6561.0, 0], 'a4': [-119931.1629030677, 0], 'a5': [0, 0], 'a6': [-692514.6252737878, 0], 'a7': [23938496.639604025, 0], 'a8': [-26493424.981001895, 0], 'a9': [43046721.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 137.41656550841986, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [6561.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.1', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-105.55016388870413, 0], [131072.0, 0]], [[1.0, 0], [6561.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-23938496.639604025, 0], [232630513987207.0, 0]], [[1.0, 0], [509412484.30742055, 0], [505447028499293760, 0]], [[1.0, 0], [4716823577.156807, 0], [8650415919381338000, 0]], [[1.0, 0], [-44499329376.77645, 0], [827240261886336800000, 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'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11708888442867196441015978010', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.51692356904465120434084502970', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.23528713247734365556383451858', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 137.41656550841986, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/18/a/d/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': '2-75-1.1-c17-0-35', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [17], 'order_of_vanishing': 1, 'prelabel': '2-75-1.1-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.722481201026508, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11708888442867196441015978010', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1416078394854289200399493350592', 'Lhash_array': ['1416078394854289200399493350592'], 'factors': ['2-75-1.1-c17-0-35'], 'label': '2-75-1.1-c17-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/18/a/d/1/2'}