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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6001.180', 'a10': [0.19509032201612828, 0.9807852804032304], 'a2': [-0.5406408174555976, 0.8412535328311812], 'a3': [0.9998406937250033, 0.01784901037884606], 'a4': [-0.41541501300188644, -0.9096319953545183], 'a5': [0.7196152909155629, -0.6943729783628607], 'a6': [-0.5555702330196022, 0.8314696123025452], 'a7': [0.19509032201612828, -0.9807852804032304], 'a8': [0.9898214418809327, 0.14231483827328514], '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': '6001.180', 'coeff_info': ['x^352 - 1', '0.999840693725003 + 0.0178490103788461*I', '\\\\zeta_{352}'], 'conductor': 6001, 'conductor_radical': 6001, 'conjugate': 'dirichlet_L_6001.1967', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^120', 'a^1', 'a^240', 'a^309', 'a^121', 'a^275', 'a^8', 'a^2', 'a^77', 'a^82', 'a^241', 'a^183', 'a^43', 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'199.071860036609658074478170913048'], 'prelabel': '1-6001-6001.180-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': -0.7509049101344117, 'root_number': '-0.709114126014576145982812620504-0.705093721633219353658603649159*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, '1.03003324716234172022220245450+0.0146030212172667134489463925296*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.181193453954', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.37234009604', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.87249055166', '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': '6001.180', 'conductor': 6001, 'conductor_radical': 6001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6001/180'], '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': '1-6001-6001.180-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': '1-6001-6001.180-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': -0.37545245506720587, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.181193453954', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6001.180', 'Lhash_array': ['dirichlet_L_6001.180'], 'label': '1-6001-6001.180-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6001/180'}