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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_245.114', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.7330518718298263, -0.6801727377709194], 'a3': [0.9888308262251285, -0.14904226617617444], 'a4': [0.07473009358642425, -0.9972037971811801], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.6234898018587335, -0.7818314824680298], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6234898018587335, -0.7818314824680298], 'a9': [0.9555728057861407, -0.2947551744109042], 'algebraic': True, 'analytic_conductor': 1.1377752166928528, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '245.114', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 245, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_245.144', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 'a^41', 'a^32', 0, 'a^36', 0, 'a^27', 'a^40', 0, 'a^2', 'a^31', 'a^9', 0, 0, 'a^22', 'a^17', 'a^35', 'a^28', 0, 0, 'a^39', 'a^25', 'a^26', 0, 'a^4', 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'199.30926934602143883495394136685'], 'prelabel': '1-245-245.114-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1377752166928528, 'root_angle': -0.2108843537414966, 'root_number': '0.243304086743308689627615364703-0.969950061278416807934283432993*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.210884353741', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.76843923412249465768720300982-0.908373484427507409531516035572*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.57487905548', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.44393545052', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.88187454828', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.1377752166928528, 'bad_primes': [5, 7], 'central_character': '245.114', 'conductor': 245, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/245/114'], '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': '1-245-245.114-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': '1-245-245.114-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1377752166928528, 'root_angle': -0.2108843537414966, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57487905548', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_245.114', 'Lhash_array': ['dirichlet_L_245.114'], 'factors': ['1-245-245.114-r0-0-0'], 'label': '1-245-245.114-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/245/114'}
Lfunction data - 1-245-245.114-r0-0-0