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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_85.2', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-1.0, -1.4081532572346456e-30], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [1.0, 0.0], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.7071067811865476, 0.7071067811865476], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 9.134518607543127, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [17, [1]]], 'bad_primes': [5, 17], 'central_character': '85.2', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 85, 'conductor_radical': 85, 'conjugate': 'dirichlet_L_85.43', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^5', 'a^0', 0, 'a^1', 'a^7', 'a^4', 'a^2', 0, 'a^1', 'a^5', 'a^2', 'a^3', 0, 'a^0', 0, 'a^6', 'a^6', 0, 'a^4', 'a^5', 'a^7', 'a^1', 0, 'a^6', 'a^7', 'a^7', 'a^7', 0, 'a^7', 'a^4', 'a^6', 0, 0, 'a^2', 'a^1', 'a^2', 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'0.655275236012774291522736957720-0.187260078191729823842659077012*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.822072992665', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.09276681916', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.63520506642', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.134518607543127, 'bad_primes': [5, 17], 'central_character': '85.2', 'conductor': 85, 'conductor_radical': 85, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/85/2'], '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': '1-85-85.2-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': '1-85-85.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.134518607543127, 'root_angle': -0.16930142995739483, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.822072992665', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_85.2', 'Lhash_array': ['dirichlet_L_85.2'], 'label': '1-85-85.2-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/85/2'}