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  • lfunc_lfunctions • Show schema
    {'Lhash': '5561176889988406189565828642097', 'a10': [-18.0, 3.111507638930571e-61], 'a2': [-1.0, -1.7320508075688772], 'a3': [0.0, -5.196152422706632], 'a4': [-2.0, 3.4641016151377544], 'a5': [4.5, -7.794228634059948], 'a6': [-9.0, 5.196152422706632], 'a7': [15.5, 26.846787517317598], 'a8': [8.0, 0.0], 'a9': [-27.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.7320508075688772]]], [3, [[1.0, 0], [0, 5.196152422706632]]]], 'bad_primes': [2, 3], 'central_character': '18.13', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '2465618589489457348633280209795', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 5.196152422706632]], [[1.0, 0], [-4.5, 7.794228634059948], [-62.5, -108.25317547305482]], [[1.0, 0], [-15.5, -26.846787517317598], [-171.5, 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'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.38699503553042529087882060291', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.60179753450900366957381205288', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.509455018666476487755178860952', 'prec': 107}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/4/c/a/13/1'], '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': '2-18-9.4-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-18-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': 0.2222222222222222, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.38699503553042529087882060291', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '5561176889988406189565828642097', 'Lhash_array': ['5561176889988406189565828642097'], 'factors': ['2-18-9.4-c3-0-2'], 'label': '2-18-9.4-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/4/c/a/13/1'}