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  • lfunc_lfunctions • Show schema
    {'Lhash': '1973932984350682628284325436636', 'a10': [-3.640451108543371, 3.0547011824976624], 'a2': [-1.8610339645456269, -0.4410731521139416], 'a3': [-1.4311357024719593, 0.9756283109412577], 'a4': [1.4816366110298604, 0.7441058734655658], 'a5': [1.4837799211056641, -1.9930623191225354], 'a6': [3.093715604572642, -1.1844418880418552], 'a7': [3.8040341616764843, 2.501952627165416], 'a8': [0.5010839196576774, 0.4204593321736229], 'a9': [1.096298797779817, -2.792513016260896], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6467882563723715, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [1.4311357024719593, -0.9756283109412577]]]], 'bad_primes': [3], 'central_character': '81.16', 'coefficient_field': 'CDF', 'conductor': 81, 'conductor_radical': 3, 'conjugate': '1973955500906412549024443722048', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8610339645456269, 0.4410731521139416], [1.7872652806468246, 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0.1272879542603917*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0203136153398', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55715856088049282814925727753', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.91140310499595560865078058590', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.81646742689473388577838871609', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.6467882563723715, 'bad_primes': [3], 'central_character': '81.16', 'conductor': 81, 'conductor_radical': 3, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/81/2/g/a/16/3'], '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': '2-3e4-81.16-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3e4-81.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8042314693994332, 'root_angle': 0.02031361533983531, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55715856088049282814925727753', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1973932984350682628284325436636', 'Lhash_array': ['1973932984350682628284325436636'], 'factors': ['2-3e4-81.16-c1-0-1'], 'label': '2-3e4-81.16-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/81/2/g/a/16/3'}