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  • lfunc_lfunctions • Show schema
    {'Lhash': '246924213189078820203850901724', 'a10': [0, 0], 'a2': [3.3722813232690143, 0], 'a3': [0, -7.364352513263748], 'a4': [3.3722813232690143, 0], 'a5': [0, 0], 'a6': [0, -24.834668438448563], 'a7': [0, 17.470315925184817], 'a8': [-15.6059692628831, 0], 'a9': [-27.233687939614086, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.075811752439773, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-12.2119385257662, -69.02078351803105]]]], 'bad_primes': [5, 17], 'central_character': '425.101', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '2465977023752928946925081231275', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.3722813232690143, 0], [8.0, 0]], [[1.0, 0], [0, 7.364352513263748], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -17.470315925184817], [-343.0, 0]], [[1.0, 0], [0, -51.55046759284624], [-1331.0, 0]], [[1.0, 0], 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1.7046415703460176, 1.5745564507632759, 1.36885876574581], 'positive_zeros': ['0.19478885833732282037913097518950', '2.94350644163360497697122408865812', '3.66254797152423182490380305925830', '4.71145478897404407931429842764401', '5.14742351689751084623101779631067', '6.37448369584037951678784924889624', '7.62958694075698906486270221891266', '9.005799860583317784123243562422040', '9.683555526835593196192335364646716', '10.62290353977539911452079953624326'], 'prelabel': '2-425-17.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.00757543652013, 'root_angle': -0.2778710518489221, 'root_number': '-0.1742253025442341241214494235836753333941704886651501632 - 0.9847058159437112243242355191245761531710006085797621256*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2778710518489221', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19478885833732282037913097519', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.94350644163360497697122408866', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.66254797152423182490380305926', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 25.075811752439773, 'bad_primes': [5, 17], 'central_character': '17.16', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/4/d/c/101/3'], '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': '2-425-17.16-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-425-17.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.00757543652013, 'root_angle': -0.2778710518489221, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19478885833732282037913097519', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '246924213189078820203850901724', 'Lhash_array': ['246924213189078820203850901724'], 'factors': ['2-425-17.16-c3-0-5'], 'label': '2-425-17.16-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/4/d/c/101/3'}