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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_899.314', 'a10': [0.9839295885986297, -0.17855689479863665], 'a2': [-0.3930250316539236, -0.9195277725514507], 'a3': [0.9839295885986297, 0.17855689479863665], 'a4': [-0.6910626489868646, 0.7227948638273916], 'a5': [-0.2225209339563144, 0.9749279121818236], 'a6': [-0.2225209339563144, -0.9749279121818236], 'a7': [0.1342332658176555, 0.9909497617679347], 'a8': [0.9362348706397372, 0.3513748240813427], 'a9': [0.9362348706397372, 0.3513748240813427], 'algebraic': True, 'analytic_conductor': 4.174938448191325, 'analytic_normalization': 0, 'bad_lfactors': [[29, [1]], [31, [1]]], 'bad_primes': [29, 31], 'central_character': '899.314', 'coeff_info': ['x^35 - 1', '0.983929588598630 + 0.178556894798637*I', '\\\\zeta_{35}'], 'conductor': 899, 'conductor_radical': 899, 'conjugate': 'dirichlet_L_899.690', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^24', 'a^1', 'a^13', 'a^10', 'a^25', 'a^8', 'a^2', 'a^2', 'a^34', 'a^33', 'a^14', 'a^26', 'a^32', 'a^11', 'a^26', 'a^7', 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'st_group': 'mu(35)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.26966786048989920349225037268-0.0599919827406192779369441633335*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.30039668147', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.40212595016', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.13700333043', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.174938448191325, 'bad_primes': [29, 31], 'central_character': '899.314', 'conductor': 899, 'conductor_radical': 899, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/899/314'], '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': '1-899-899.314-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': '1-899-899.314-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.174938448191325, 'root_angle': 0.03646835533572701, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30039668147', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_899.314', 'Lhash_array': ['dirichlet_L_899.314'], 'label': '1-899-899.314-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/899/314'}
Lfunction data - 1-899-899.314-r0-0-0