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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_155.44', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.30901699437494745, 0.9510565162951535], 'a3': [0.6691306063588582, -0.7431448254773942], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.5, 0.8660254037844386], 'a7': [0.10452846326765347, -0.9945218953682733], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [-0.10452846326765347, -0.9945218953682733], 'algebraic': True, 'analytic_conductor': 16.65706334316688, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [31, [1]]], 'bad_primes': [5, 31], 'central_character': '155.44', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 155, 'conductor_radical': 155, 'conjugate': 'dirichlet_L_155.74', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^26', 'a^18', 0, 'a^5', 'a^23', 'a^27', 'a^22', 0, 'a^13', 'a^14', 'a^16', 'a^2', 0, 'a^6', 'a^2', 'a^1', 'a^14', 0, 'a^19', 'a^22', 'a^12', 'a^23', 0, 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'z2': {'__RealLiteral__': 0, 'data': '1.7854521743', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.6785224593', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.65706334316688, 'bad_primes': [5, 31], 'central_character': '155.44', 'conductor': 155, 'conductor_radical': 155, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/155/44'], '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': '1-155-155.44-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': '1-155-155.44-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.65706334316688, 'root_angle': -0.39481583003758874, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.184809874104', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_155.44', 'Lhash_array': ['dirichlet_L_155.44'], 'label': '1-155-155.44-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/155/44'}