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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1045.802', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.6427876096865394, -0.766044443118978], 'a3': [0.3420201433256687, 0.9396926207859084], 'a4': [-0.17364817766693036, -0.984807753012208], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9396926207859084, 0.3420201433256687], 'a7': [-0.8660254037844386, 0.5], 'a8': [-0.8660254037844386, -0.5], 'a9': [-0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.802', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.43', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 'a^7', 'a^26', 0, 'a^2', 'a^15', 'a^21', 'a^14', 0, 0, 'a^33', 'a^29', 'a^10', 0, 'a^16', 'a^31', 'a^9', 0, 0, 'a^22', 0, 'a^35', 'a^28', 0, 'a^24', 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'189.09848503826685855918632909360', '189.567313593266286739978333681550', '190.58261098707329116277528518948', '191.0259882784524463245545124829', '191.59655344140593419641816528197', '192.1730967560255552999852886337', '192.7481280125166090803475071411', '193.32989148317214309935886039105', '193.7641503755221950333450711113', '194.23682937198682087803259766251', '194.829158430964015315456336108216', '195.69102808412161627149732324264', '196.37018108761135275205958582978', '196.78924300555704837016647825058', '197.32058574497711193886210020774', '198.14192585514275243445188876371', '198.814158381254483207568839310018', '199.58239687850966119203791968079', '199.79730507741822651311107986803'], 'prelabel': '1-1045-1045.802-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.3361973032499449, 'root_number': '0.492187866624582205304896989298-0.870489002772316749771091105534*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.168098651625', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.38737241849629022602059786552-0.379319645060219841055672659294*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.733539704', 'prec': 37}, 'z2': {'__RealLiteral__': 0, 'data': '2.45961669162', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.00406496517', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.802', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/802'], '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': '1-1045-1045.802-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': '1-1045-1045.802-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.16809865162497245, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.733539704', 'prec': 37}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1045.802', 'Lhash_array': ['dirichlet_L_1045.802'], 'label': '1-1045-1045.802-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/802'}