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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_465.257', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.5877852522924731, 0.8090169943749475], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.30901699437494745, -0.9510565162951535], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7431448254773942, 0.6691306063588582], 'a8': [0.9510565162951535, 0.30901699437494745], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.1594509214782716, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1]]], 'bad_primes': [3, 5, 31], 'central_character': '465.257', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 465, 'conductor_radical': 465, 'conjugate': 'dirichlet_L_465.38', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^21', 0, 'a^42', 0, 0, 'a^7', 'a^3', 0, 0, 'a^2', 0, 'a^29', 'a^28', 0, 'a^24', 'a^13', 0, 'a^46', 0, 0, 'a^23', 'a^3', 0, 0, 'a^50', 0, 'a^49', 'a^36', 0, 0, 'a^45', 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'190.47257740757325409818781266621', '191.50353375053006521550655464439', '192.030104108485289411923608053512', '192.73934591057673680001176438804', '193.19823320283563310042486473114', '194.42277495189207241395793254192', '194.926488672625465141474493919104', '195.73232917989561967701202292746', '196.01200610952526652755158451310', '196.75859270211976991811627264820', '197.53501711666028379709418247614', '198.10228793724406491914629882512', '198.69353516862472319724988866294', '199.26187402191900259187498975423', '199.78918627914152834045578414856'], 'prelabel': '1-465-465.257-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1594509214782716, 'root_angle': 0.23775056134644582, 'root_number': '0.0768895288889955963586868765016+0.997039618243542171638247846948*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.237750561346', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.794712563542926737517955165371+0.386374434945900186653250089525*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.24951712198', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.38632191721', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.22517408989', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.1594509214782716, 'bad_primes': [3, 5, 31], 'central_character': '465.257', 'conductor': 465, 'conductor_radical': 465, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/465/257'], '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': '1-465-465.257-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': '1-465-465.257-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1594509214782716, 'root_angle': 0.23775056134644582, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24951712198', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_465.257', 'Lhash_array': ['dirichlet_L_465.257'], 'factors': ['1-465-465.257-r0-0-0'], 'label': '1-465-465.257-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/465/257'}
Lfunction data - 1-465-465.257-r0-0-0