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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6001.965', 'a10': [-0.9238795325112867, -0.3826834323650898], 'a2': [-0.9898214418809327, 0.14231483827328514], 'a3': [0.5102700330608996, -0.8600142402077006], 'a4': [0.9594929736144974, -0.28173255684142967], 'a5': [0.8600142402077006, 0.5102700330608996], 'a6': [-0.3826834323650898, 0.9238795325112867], 'a7': [-0.3826834323650898, -0.9238795325112867], 'a8': [-0.9096319953545183, 0.41541501300188644], 'a9': [-0.47924898672005684, -0.8776789895672557], 'algebraic': True, 'analytic_conductor': 27.868526838260447, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [353, [1]]], 'bad_primes': [17, 353], 'central_character': '6001.965', 'coeff_info': ['x^176 - 1', '0.999362825656992 + 0.0356923338389805*I', '\\\\zeta_{176}'], 'conductor': 6001, 'conductor_radical': 6001, 'conjugate': 'dirichlet_L_6001.4067', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^84', 'a^147', 'a^168', 'a^15', 'a^55', 'a^121', 'a^76', 'a^118', 'a^99', 'a^152', 'a^139', 'a^39', 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'199.887241322840234942218922649414'], 'prelabel': '1-6001-6001.965-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': 0.8219570266313333, 'root_number': '-0.847606306793708350474740422062+0.530625620078346723429404609609*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(176)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.729041536349356466027694887956-0.242724401712657788340601317335*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0881068053309', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.21231232875', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.80051227766', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.868526838260447, 'bad_primes': [17, 353], 'central_character': '6001.965', 'conductor': 6001, 'conductor_radical': 6001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6001/965'], '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': '1-6001-6001.965-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': '1-6001-6001.965-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': 0.41097851331566665, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0881068053309', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6001.965', 'Lhash_array': ['dirichlet_L_6001.965'], 'label': '1-6001-6001.965-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6001/965'}