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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2668.215', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.7557495743542583, 0.6548607339452851], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.14231483827328514, -0.9898214418809327], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.41541501300188644, -0.9096319953545183], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.14231483827328514, 0.9898214418809327], 'algebraic': True, 'analytic_conductor': 12.390139910761352, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [23, [1]], [29, [1]]], 'bad_primes': [2, 23, 29], 'central_character': '2668.215', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 2668, 'conductor_radical': 1334, 'conjugate': 'dirichlet_L_2668.2395', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^49', 0, 'a^34', 0, 'a^30', 0, 'a^10', 0, 'a^53', 0, 'a^14', 0, 'a^39', 0, 'a^7', 0, 'a^37', 0, 'a^35', 0, 0, 0, 'a^24', 0, 'a^59', 0, 0, 0, 'a^61', 0, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21795105826', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.26769035452320311848955438114+0.260356598789371409528723079895*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.19998892753', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.93068186058', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.02501839903', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.390139910761352, 'bad_primes': [2, 23, 29], 'central_character': '2668.215', 'conductor': 2668, 'conductor_radical': 1334, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2668/215'], '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': '1-2668-2668.215-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': '1-2668-2668.215-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.390139910761352, 'root_angle': 0.2179510582595518, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19998892753', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2668.215', 'Lhash_array': ['dirichlet_L_2668.215'], 'factors': ['1-2668-2668.215-r0-0-0'], 'label': '1-2668-2668.215-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2668/215'}
Lfunction data - 1-2668-2668.215-r0-0-0