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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_407.141', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.9975640502598242, -0.0697564737441253], 'a3': [0.848048096156426, -0.5299192642332049], 'a4': [0.9902680687415704, -0.13917310096006544], 'a5': [-0.5591929034707468, 0.8290375725550417], 'a6': [0.8090169943749475, -0.5877852522924731], 'a7': [-0.6156614753256583, -0.7880107536067219], 'a8': [0.9781476007338057, -0.20791169081775934], 'a9': [0.4383711467890774, -0.898794046299167], 'algebraic': True, 'analytic_conductor': 1.8901000538530248, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [37, [1]]], 'bad_primes': [11, 37], 'central_character': '407.141', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 407, 'conductor_radical': 407, 'conjugate': 'dirichlet_L_407.280', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^89', 'a^82', 'a^88', 'a^31', 'a^81', 'a^58', 'a^87', 'a^74', 'a^30', 0, 'a^80', 'a^79', 'a^57', 'a^23', 'a^86', 'a^11', 'a^73', 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50}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.16881853392825457885531777222-0.475255371060235478449469954695*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.34716240197', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.81877083401', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.46592281893', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.8901000538530248, 'bad_primes': [11, 37], 'central_character': '407.141', 'conductor': 407, 'conductor_radical': 407, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/407/141'], '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': '1-407-407.141-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': '1-407-407.141-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8901000538530248, 'root_angle': -0.11070166287123274, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34716240197', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_407.141', 'Lhash_array': ['dirichlet_L_407.141'], 'factors': ['1-407-407.141-r0-0-0'], 'label': '1-407-407.141-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/407/141'}
Lfunction data - 1-407-407.141-r0-0-0