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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_175.52', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.7431448254773942, 0.6691306063588582], 'a3': [-0.9945218953682733, -0.10452846326765347], 'a4': [0.10452846326765347, -0.9945218953682733], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.8090169943749475, -0.5877852522924731], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 0.8126965833520376, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '175.52', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 175, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_175.138', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^31', 'a^46', 0, 'a^54', 0, 'a^9', 'a^2', 0, 'a^28', 'a^17', 'a^27', 0, 0, 'a^32', 'a^49', 'a^25', 'a^44', 0, 0, 'a^51', 'a^53', 'a^40', 0, 'a^50', 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'188.81702718096553615663497672002', '189.39720541874847743400550100138', '190.18957342010863224825827263456', '190.95907446101032741281590329165', '191.39024232770684909436287958003', '192.51109161246103320456898805277', '193.314047876029685511516362162525', '193.92187499767631917959378495684', '194.89406125620073299774268477473', '195.56836650175242190710276363042', '196.14825311992065871207143645521', '196.8111522567908795843388125066', '197.73501733129405541558520005704', '198.61145610783246488299573457906', '199.03295620344650502145019210812', '199.66007722069201754161561037776'], 'prelabel': '1-175-175.52-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8126965833520376, 'root_angle': -0.3529874272254411, 'root_number': '0.445608282921949141407207526510-0.895228048148264917376865787343*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.176493713613', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.475555915036907886462656509428+0.0150107951539868445511715958605*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.443128846337', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.27933382553', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.79302943591', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8126965833520376, 'bad_primes': [5, 7], 'central_character': '175.52', 'conductor': 175, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/175/52'], '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': '1-175-175.52-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': '1-175-175.52-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8126965833520376, 'root_angle': -0.17649371361272054, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.443128846337', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_175.52', 'Lhash_array': ['dirichlet_L_175.52'], 'label': '1-175-175.52-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/175/52'}