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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_143.63', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.7431448254773942, -0.6691306063588582], 'a3': [-0.10452846326765347, -0.9945218953682733], 'a4': [0.10452846326765347, -0.9945218953682733], 'a5': [-0.9510565162951535, 0.30901699437494745], 'a6': [-0.7431448254773942, -0.6691306063588582], 'a7': [-0.9945218953682733, -0.10452846326765347], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.63', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.84', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^53', 'a^44', 'a^46', 'a^27', 'a^37', 'a^31', 'a^39', 'a^28', 'a^20', 0, 'a^30', 0, 'a^24', 'a^11', 'a^32', 'a^52', 'a^21', 'a^49', 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'3.51150472446', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.63', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/63'], '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': '1-143-143.63-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': '1-143-143.63-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.4994544901517354, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.668002155372', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_143.63', 'Lhash_array': ['dirichlet_L_143.63'], 'label': '1-143-143.63-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/63'}