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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_475.386', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.882947592858927, -0.46947156278589075], 'a3': [-0.24192189559966773, -0.9702957262759965], 'a4': [0.5591929034707468, 0.8290375725550417], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.24192189559966773, 0.9702957262759965], 'a7': [-0.5, -0.8660254037844386], 'a8': [-0.10452846326765347, -0.9945218953682733], 'a9': [-0.882947592858927, 0.46947156278589075], 'algebraic': True, 'analytic_conductor': 2.205890726241245, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '475.386', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 475, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_475.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^32', 'a^7', 0, 'a^13', 'a^30', 'a^33', 'a^19', 0, 'a^6', 'a^39', 'a^4', 'a^11', 0, 'a^14', 'a^8', 'a^0', 0, 0, 'a^17', 'a^32', 'a^16', 'a^20', 0, 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'data': '-0.104633884473', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.633838090779820189229427479444-0.245037087357260217930026205388*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.06986494676', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.81499826783', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.2273237501', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.205890726241245, 'bad_primes': [5, 19], 'central_character': '475.386', 'conductor': 475, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/475/386'], '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': '1-475-475.386-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': '1-475-475.386-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.205890726241245, 'root_angle': -0.10463388447279034, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06986494676', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_475.386', 'Lhash_array': ['dirichlet_L_475.386'], 'factors': ['1-475-475.386-r0-0-0'], 'label': '1-475-475.386-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/475/386'}
Lfunction data - 1-475-475.386-r0-0-0