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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.113', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9510565162951535, 0.30901699437494745], 'a3': [0.5877852522924731, 0.8090169943749475], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.30901699437494745, 0.9510565162951535], 'a7': [-0.5877852522924731, 0.8090169943749475], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [-0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.113', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.37', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^3', 'a^2', 0, 'a^4', 'a^7', 'a^3', 'a^6', 0, 0, 'a^5', 'a^11', 'a^8', 0, 'a^4', 'a^19', 'a^7', 0, 0, 'a^10', 0, 'a^5', 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'192.02599617946629528277409939749', '192.39260849687694812176096764588', '193.37244207490020541959000700953', '193.64803947733698111494902626218', '193.8422504395970070609017150290', '194.766946193637477845458217898734', '195.64132669144961752402366219705', '196.11065954527954607471903955929', '196.592286034608940275097552960895', '197.124712795730128414234623885321', '197.7930191192878816367239820497', '198.37767809893795457903808985424', '198.79150130487547453357107847329', '199.51019601089058987461717383373'], 'prelabel': '1-1045-1045.113-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.8162243346208732, 'root_number': '-0.837912913260305516403854005021+0.545803948127555892904722397471*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.40811216731', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.51896917312065286831126756972+1.29228327979491688573626393936*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.99841797281', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.90242799658', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.46526126276', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.113', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/113'], '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': '1-1045-1045.113-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': '1-1045-1045.113-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.4081121673104366, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99841797281', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.113', 'Lhash_array': ['dirichlet_L_1045.113'], 'label': '1-1045-1045.113-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/113'}
Lfunction data - 1-1045-1045.113-r0-0-0