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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3895.107', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.4067366430758002, -0.9135454576426009], 'a3': [0.8660254037844386, 0.5], 'a4': [-0.6691306063588582, 0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.10452846326765347, -0.9945218953682733], 'a7': [0.5877852522924731, 0.8090169943749475], 'a8': [0.9510565162951535, 0.30901699437494745], 'a9': [0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 18.08830395517821, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]], [41, [1]]], 'bad_primes': [5, 19, 41], 'central_character': '3895.107', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 3895, 'conductor_radical': 3895, 'conjugate': 'dirichlet_L_3895.3713', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 'a^5', 'a^22', 0, 'a^46', 'a^9', 'a^3', 'a^10', 0, 'a^18', 'a^27', 'a^1', 'a^50', 0, 'a^44', 'a^53', 'a^51', 0, 0, 'a^14', 'a^59', 'a^1', 'a^8', 0, 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'196.36571530474072803582610383059', '197.04313797003484150049656944963', '197.6733802173112886937408586764', '198.06881565037304412311684959687', '198.688575533470910553847316485084', '199.11102852051392048465035455214', '199.49286517664436164291203376559', '199.948767084845987617646356803234'], 'prelabel': '1-3895-3895.107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.08830395517821, 'root_angle': 0.21987083833365392, 'root_number': '0.770771828998083735992125225247+0.637111283547033691702131956399*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.32922194128242513006111987272+0.0508881565275408408454719460669*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17719801172', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.91829173689', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.61280059626', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.08830395517821, 'bad_primes': [5, 19, 41], 'central_character': '3895.107', 'conductor': 3895, 'conductor_radical': 3895, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3895/107'], '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': '1-3895-3895.107-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': '1-3895-3895.107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.08830395517821, 'root_angle': 0.10993541916682696, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17719801172', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3895.107', 'Lhash_array': ['dirichlet_L_3895.107'], 'label': '1-3895-3895.107-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3895/107'}
Lfunction data - 1-3895-3895.107-r0-0-0