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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6001.1006', 'a10': [-0.19509032201612828, -0.9807852804032304], 'a2': [0.8412535328311812, 0.5406408174555976], 'a3': [0.01784901037884606, -0.9998406937250033], 'a4': [0.41541501300188644, 0.9096319953545183], 'a5': [-0.6943729783628607, -0.7196152909155629], 'a6': [0.5555702330196022, -0.8314696123025452], 'a7': [0.9807852804032304, 0.19509032201612828], 'a8': [-0.14231483827328514, 0.9898214418809327], 'a9': [-0.9993628256569916, -0.035692333838980454], 'algebraic': True, 'analytic_conductor': 27.868526838260447, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [353, [1]]], 'bad_primes': [17, 353], 'central_character': '6001.1006', 'coeff_info': ['x^352 - 1', '0.999840693725003 + 0.0178490103788461*I', '\\\\zeta_{352}'], 'conductor': 6001, 'conductor_radical': 6001, 'conjugate': 'dirichlet_L_6001.686', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 'a^265', 'a^64', 'a^221', 'a^297', 'a^11', 'a^96', 'a^178', 'a^253', 'a^302', 'a^329', 'a^315', 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'199.98703999711615938942828402254'], 'prelabel': '1-6001-6001.1006-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': -0.05764271035711991, 'root_number': '0.983647981377687507167961517333-0.180101773260566568770204337042*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(352)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.82730583329617849878143990726-0.0741792309088879581873012808612*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.875765442099', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.48763653067', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.46871604965', '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': '6001.1006', 'conductor': 6001, 'conductor_radical': 6001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6001/1006'], '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': '1-6001-6001.1006-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': '1-6001-6001.1006-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': -0.028821355178559955, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.875765442099', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6001.1006', 'Lhash_array': ['dirichlet_L_6001.1006'], 'label': '1-6001-6001.1006-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6001/1006'}