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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_143.8', 'a10': [1.0, 0.0], 'a2': [-0.9510565162951535, -0.30901699437494745], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [-0.9510565162951535, 0.30901699437494745], 'a6': [0.9510565162951535, -0.30901699437494745], 'a7': [0.5877852522924731, -0.8090169943749475], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.8', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.18', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^8', 'a^2', 'a^9', 'a^19', 'a^17', 'a^13', 'a^16', 'a^0', 0, 'a^10', 0, 'a^8', 'a^17', 'a^4', 'a^4', 'a^7', 'a^3', 'a^11', 'a^5', 0, 'a^10', 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'192.05348662733952528568018037017', '192.67020174594942128664279835711', '193.61711927334738038525525778518', '194.31467206743396201322971003895', '194.875566679714156099085260857737', '195.6177674133080091532990842408', '196.80406042875511613101131243017', '197.805016009883496964758321389110', '198.457173891919220737482432029788', '198.74393975490949226453517892165', '199.57825975261192334158770326443'], 'prelabel': '1-143-143.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.2285496931596305, 'root_number': '0.753116390810882759089093987159+0.657887301816952313537833256077*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11427484658', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.517873127893077965964204072984+0.0662743111874795338399810216751*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.15252202753', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.40333086076', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.40296764732', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.8', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/8'], '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': '1-143-143.8-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': '1-143-143.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.11427484657981525, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15252202753', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_143.8', 'Lhash_array': ['dirichlet_L_143.8'], 'label': '1-143-143.8-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/8'}