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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3381.11', 'a10': [-0.7775737186139037, -0.6287917875743494], 'a2': [0.8760444770061827, 0.48223031251359944], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5349078513860724, 0.8449104038450086], 'a5': [-0.9844116218848333, -0.17587995536180925], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.061161660821842705, 0.9981278731933669], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.701297990361368, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.11', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.2459', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 0, 'a^74', 'a^244', 0, 0, 'a^111', 0, 'a^281', 'a^128', 0, 'a^72', 0, 0, 'a^148', 'a^80', 0, 'a^217', 'a^318', 0, 'a^165', 0, 0, 'a^26', 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'199.18524252728766497724225695639'], 'prelabel': '1-3381-3381.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.9305725138166407, 'root_number': '-0.976307536760117501747254448612+0.216387600535224321386902341802*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.18181826332598529972985212789+0.819300520953229548490039902324*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.38707865795', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.3250707453', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.31730095773', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.11', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/11'], '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': '1-3381-3381.11-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': '1-3381-3381.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.4652862569083204, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38707865795', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3381.11', 'Lhash_array': ['dirichlet_L_3381.11'], 'label': '1-3381-3381.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/11'}
Lfunction data - 1-3381-3381.11-r0-0-0