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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_475.436', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.30901699437494745, 0.9510565162951535], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [1.0, 0.0], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 51.04583927744689, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '475.436', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 475, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_475.341', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^1', 'a^6', 0, 'a^4', 'a^0', 'a^9', 'a^2', 0, 'a^8', 'a^7', 'a^7', 'a^3', 0, 'a^2', 'a^4', 'a^5', 0, 0, 'a^1', 'a^1', 'a^8', 'a^0', 0, 'a^0', 'a^3', 'a^6', 'a^1', 0, 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'spectral_label': 'r1-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.18187221153753826241113412355+0.556146847706895738499065180949*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.733380358171', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.23800736381', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.6957200638', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.04583927744689, 'bad_primes': [5, 19], 'central_character': '475.436', 'conductor': 475, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/475/436'], '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': '1-475-475.436-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-475-475.436-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.04583927744689, 'root_angle': 0.12000000000000001, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.733380358171', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_475.436', 'Lhash_array': ['dirichlet_L_475.436'], 'label': '1-475-475.436-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/475/436'}