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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.83', 'a10': [1.0, 0.0], 'a2': [-0.5877852522924731, -0.8090169943749475], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [-0.30901699437494745, 0.9510565162951535], 'a5': [-0.5877852522924731, 0.8090169943749475], 'a6': [0.5877852522924731, -0.8090169943749475], 'a7': [-0.9510565162951535, -0.30901699437494745], 'a8': [0.9510565162951535, -0.30901699437494745], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.83', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.112', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^4', 'a^6', 'a^7', 'a^17', 'a^11', 'a^19', 'a^8', 'a^0', 0, 'a^10', 0, 'a^4', 'a^11', 'a^12', 'a^12', 'a^1', 'a^9', 'a^13', 'a^15', 0, 'a^10', 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'194.34954101819753773092127500838', '194.801715185697527524555169087', '196.10649092546402751219917413795', '197.32448820013245386183274506922', '197.75514350907048217971886571074', '198.36996791536796043440532881564', '199.17515965151276132832953990123', '199.66914456958724804493240910367'], 'prelabel': '1-143-143.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.8005817865619425, 'root_number': '-0.810089958962382518119133619164+0.586305601532447758779122500571*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.400290893281', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.517486996456198004931400708539+0.134895396285240310828225287081*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.53869593337', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.49038793897', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.42113434573', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.83', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/83'], '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': '1-143-143.83-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': '1-143-143.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.4002908932809712, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.53869593337', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.83', 'Lhash_array': ['dirichlet_L_143.83'], 'label': '1-143-143.83-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/83'}
Lfunction data - 1-143-143.83-r0-0-0