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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_311.265', 'a10': [-0.9948693233918952, 0.10116832198743218], 'a2': [-0.6121059825476628, -0.7907757369376985], 'a3': [-0.6121059825476628, 0.7907757369376985], 'a4': [-0.25065253225872053, 0.9680771188662043], 'a5': [0.5289640103269625, -0.8486442574947509], 'a6': [1.0, 0.0], 'a7': [-0.05064916883871271, -0.9987165071710528], 'a8': [0.9189578116202306, -0.39435585511331855], 'a9': [-0.25065253225872053, -0.9680771188662043], 'algebraic': True, 'analytic_conductor': 1.4442779281284783, 'analytic_normalization': 0, 'bad_lfactors': [[311, [1]]], 'bad_primes': [311], 'central_character': '311.265', 'coeff_info': ['x^31 - 1', '0.979529941252494 + 0.201298520088660*I', '\\\\zeta_{31}'], 'conductor': 311, 'conductor_radical': 311, 'conjugate': 'dirichlet_L_311.169', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^20', 'a^11', 'a^9', 'a^26', 'a^0', 'a^23', 'a^29', 'a^22', 'a^15', 'a^10', 'a^20', 'a^22', 'a^12', 'a^6', 'a^18', 'a^15', 'a^11', 'a^5', 'a^4', 'a^3', 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'191.259140742435033399070381816193', '191.976907323477744043476357392912', '192.69085808900246224963990198944', '193.18099806195006198313589790860', '193.845953582610577568186438389220', '194.271775975412585870567113278387', '195.15612146240207571521155371430', '195.86011705953852068327270582560', '196.91126314707225839386110946218', '197.81079986277670063317147804229', '198.0033289735716115120214330194', '199.09243852803766746345867723599', '199.519333913576434100621078908268'], 'prelabel': '1-311-311.265-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4442779281284783, 'root_angle': -0.8488523925859056, 'root_number': '-0.889363958188828827006561945317-0.457199901437761827982768754726*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.424426196293', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(31)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.509778837881405605742320879081-0.255107305589835719921762654391*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.374295811575', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.80013117341', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.42655685232', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4442779281284783, 'bad_primes': [311], 'central_character': '311.265', 'conductor': 311, 'conductor_radical': 311, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/311/265'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-311-311.265-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-311-311.265-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4442779281284783, 'root_angle': -0.4244261962929528, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.374295811575', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_311.265', 'Lhash_array': ['dirichlet_L_311.265'], 'label': '1-311-311.265-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/311/265'}