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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_143.108', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.10452846326765347, -0.9945218953682733], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [0.8090169943749475, -0.5877852522924731], 'a6': [0.10452846326765347, 0.9945218953682733], 'a7': [0.9781476007338057, 0.20791169081775934], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.108', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.49', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^14', 'a^16', 'a^27', 'a^7', 'a^1', 'a^9', 'a^28', 'a^20', 0, 'a^0', 0, 'a^24', 'a^11', 'a^2', 'a^22', 'a^21', 'a^19', 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'2.38333172476', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.530006437', 'prec': 37}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.108', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/108'], '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': '1-143-143.108-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': '1-143-143.108-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.2906761786770401, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03556202668', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_143.108', 'Lhash_array': ['dirichlet_L_143.108'], 'label': '1-143-143.108-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/108'}