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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_5077.32', 'a10': [-0.2701595103737845, 0.9628155788906809], 'a2': [0.9999808475147489, 0.0061890713103398935], 'a3': [-0.2891739927104988, 0.9572765545754625], 'a4': [0.999923390792631, 0.012377905548485809], 'a5': [-0.264195401871286, 0.9644691750543766], 'a6': [-0.2950931071698525, 0.9554685018883887], 'a7': [-0.5951709920615447, 0.8035990854950475], 'a8': [0.9998276320345244, 0.018566265651324812], 'a9': [-0.8327568038797367, -0.5536389668294724], 'algebraic': True, 'analytic_conductor': 545.5994231823113, 'analytic_normalization': 0, 'bad_lfactors': [[5077, [1]]], 'bad_primes': [5077], 'central_character': '5077.32', 'coeff_info': ['x^5076 - 1', '0.999999233898242 + 0.00123782184843572*I', '\\\\zeta_{5076}'], 'conductor': 5077, 'conductor_radical': 5077, 'conjugate': 'dirichlet_L_5077.476', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^1506', 'a^10', 'a^1485', 'a^1511', 'a^1784', 'a^15', 'a^3012', 'a^1490', 'a^1633', 'a^1516', 'a^663', 'a^1789', 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'198.6991504678565270033372176260', '199.05910896147259581193332556185', '199.85999948821630012843752193244'], 'prelabel': '1-5077-5077.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 545.5994231823113, 'root_angle': 0.18261058465999933, 'root_number': '0.839905052530188089166068334128+0.542733362466563305076134927965*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(5076)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.25538144198493899727182243248+0.742583088554789000510203651400*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.283979177147', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.09201384278', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.52066777148', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 545.5994231823113, 'bad_primes': [5077], 'central_character': '5077.32', 'conductor': 5077, 'conductor_radical': 5077, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5077/32'], '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': '1-5077-5077.32-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': '1-5077-5077.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 545.5994231823113, 'root_angle': 0.09130529232999966, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.283979177147', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_5077.32', 'Lhash_array': ['dirichlet_L_5077.32'], 'label': '1-5077-5077.32-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5077/32'}