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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3895.1013', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.882947592858927, 0.46947156278589075], 'a3': [0.9961946980917455, -0.08715574274765818], 'a4': [0.5591929034707468, 0.8290375725550417], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9205048534524404, 0.39073112848927377], 'a7': [0.052335956242943835, 0.9986295347545738], 'a8': [0.10452846326765347, 0.9945218953682733], 'a9': [0.984807753012208, -0.17364817766693036], 'algebraic': True, 'analytic_conductor': 18.08830395517821, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]], [41, [1]]], 'bad_primes': [5, 19, 41], 'central_character': '3895.1013', 'coeff_info': ['x^360 - 1', '0.999847695156391 + 0.0174524064372835*I', '\\\\zeta_{360}'], 'conductor': 3895, 'conductor_radical': 3895, 'conjugate': 'dirichlet_L_3895.1042', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^28', 'a^355', 'a^56', 0, 'a^23', 'a^87', 'a^84', 'a^350', 0, 'a^309', 'a^51', 'a^203', 'a^115', 0, 'a^112', 'a^109', 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'194.52544349732712021198973046071', '194.90801630494834943276611044569', '195.65900124405359660261081290680', '195.93431401374282347675001876656', '196.46924814747632672858802322109', '197.09540315072324567020933574551', '197.20231057767893956900591131081', '198.06227940740086099776973714679', '198.43632778258296003830548103817', '198.9163957127063032710031037977', '199.584037419305119971974031599743'], 'prelabel': '1-3895-3895.1013-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.08830395517821, 'root_angle': 0.5839121824106797, 'root_number': '-0.260575160032048919893376345775+0.965453564898007974174544088467*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(360)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.20373755812906419722217319432+1.17627422177419200044997704903*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.4166936844', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.28016354691', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98111033521', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.08830395517821, 'bad_primes': [5, 19, 41], 'central_character': '3895.1013', 'conductor': 3895, 'conductor_radical': 3895, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3895/1013'], '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': '1-3895-3895.1013-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': '1-3895-3895.1013-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.08830395517821, 'root_angle': 0.29195609120533983, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.4166936844', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3895.1013', 'Lhash_array': ['dirichlet_L_3895.1013'], 'label': '1-3895-3895.1013-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3895/1013'}
Lfunction data - 1-3895-3895.1013-r0-0-0