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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.30', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.9781476007338057, 0.20791169081775934], 'a3': [0.9135454576426009, 0.4067366430758002], 'a4': [0.9135454576426009, -0.4067366430758002], 'a5': [-0.30901699437494745, -0.9510565162951535], 'a6': [-0.9781476007338057, -0.20791169081775934], 'a7': [0.9135454576426009, -0.4067366430758002], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [0.6691306063588582, 0.7431448254773942], 'algebraic': True, 'analytic_conductor': 15.367484245631378, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.30', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.62', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^2', 'a^28', 'a^21', 'a^16', 'a^28', 'a^12', 'a^4', 'a^5', 0, 'a^0', 0, 'a^12', 'a^23', 'a^26', 'a^1', 'a^18', 'a^22', 'a^19', 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'191.83460148622320955319730987416', '192.30739143785937536928059919948', '192.71507317406887701608492819259', '193.74700669910895570923903557450', '194.9969631327590152732392813880', '195.78267378634194719978273294118', '196.628885977119779270888363754275', '196.91812430805719553703779811078', '197.9694819820336901555974343058', '198.62855474581660218794323787915', '198.98792911118315982518107348515', '199.79502072891481102253662977312'], 'prelabel': '1-143-143.30-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.367484245631378, 'root_angle': -0.17378488314973675, 'root_number': '0.854628534097366330499087354798-0.519239895141529697347023107416*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0868924415749', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07137065983772829739043940564-0.0718003711631261752091500354287*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.902054182663', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.26090237312', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.05758214367', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.367484245631378, 'bad_primes': [11, 13], 'central_character': '143.30', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/30'], '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': '1-143-143.30-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-143-143.30-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.367484245631378, 'root_angle': -0.08689244157486838, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.902054182663', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.30', 'Lhash_array': ['dirichlet_L_143.30'], 'label': '1-143-143.30-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/30'}
Lfunction data - 1-143-143.30-r1-0-0