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{'Lhash': 'dirichlet_L_1080.317', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.984807753012208, 0.17364817766693036], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 5.015498914401147, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.317', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1080, 'conductor_radical': 30, 'conjugate': 'dirichlet_L_1080.293', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^17', 0, 0, 0, 'a^20', 0, 'a^49', 0, 0, 0, 'a^3', 0, 'a^24', 0, 0, 0, 'a^1', 0, 0, 0, 0, 0, 'a^50', 0, 'a^28', 0, 0, 0, 0, 0, 'a^39', 0, 0, 0, 'a^22', 0, 'a^29', 0, 0, 0, 'a^35', 0, 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'data': '0.449740909976', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.06039707248', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.92688049931', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.015498914401147, 'bad_primes': [2, 3, 5], 'central_character': '1080.317', 'conductor': 1080, 'conductor_radical': 30, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1080/317'], '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': '1-1080-1080.317-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': '1-1080-1080.317-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015498914401147, 'root_angle': -0.1711551636718676, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.449740909976', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1080.317', 'Lhash_array': ['dirichlet_L_1080.317'], 'factors': ['1-1080-1080.317-r0-0-0'], 'label': '1-1080-1080.317-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1080/317'}