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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_264.29', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.30901699437494745, -0.9510565162951535], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8090169943749475, -0.5877852522924731], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.2260108457425025, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '264.29', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 264, 'conductor_radical': 66, 'conjugate': 'dirichlet_L_264.173', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^8', 0, 'a^9', 0, 0, 0, 0, 0, 'a^12', 0, 0, 0, 'a^8', 0, 'a^6', 0, 0, 0, 'a^5', 0, 'a^6', 0, 0, 0, 'a^9', 0, 'a^2', 0, 0, 0, 'a^7', 0, 'a^9', 0, 0, 0, 'a^6', 0, 'a^0', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '-0.161066607033', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.14403568352872091301781526394-0.305582004848577752552030744513*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.04333786603', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.26485315095', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.14781829725', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.2260108457425025, 'bad_primes': [2, 3, 11], 'central_character': '264.29', 'conductor': 264, 'conductor_radical': 66, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/264/29'], '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': '1-264-264.29-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': '1-264-264.29-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2260108457425025, 'root_angle': -0.16106660703256495, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04333786603', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_264.29', 'Lhash_array': ['dirichlet_L_264.29'], 'factors': ['1-264-264.29-r0-0-0'], 'label': '1-264-264.29-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/264/29'}
Lfunction data - 1-264-264.29-r0-0-0