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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_80.53', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, 0.0], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-5.8869658587496495e-30, 1.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 8.597193983570001, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '80.53', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 80, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_80.77', 'degree': 1, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 'I', 0, 1, 0, 'I', 0, 1, 0, 0, 0, '-I', 0, 'I', 0, 'I', 0, '-I', 0, 0, 0, 1, 0, 'I', 0, 1, 0, 'I', 0, 0, 0, 1, 0, 1, 0, -1, 0, -1, 0, 0, 0, '-I', 0, -1, 0, '-I', 0, -1, 0, 0, 0, 'I', 0, '-I', 0, '-I', 0, 'I', 0, 0, 0, -1, 0, '-I', 0, -1, 0, '-I', 0, 0, 0, -1, 0, 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'198.04750958836960300097527135566', '198.90727505472187074105781498353', '199.53176184090747802512369699257'], 'prelabel': '1-80-80.53-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.597193983570001, 'root_angle': 0.19879180882521663, 'root_number': '0.811242185175560853981676916722+0.584710284663764943254761894084*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0993959044126', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.55051335268229298490650634281+0.251613678933111631605052494981*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.82248746392', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.17620358134', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.77715492487', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.597193983570001, 'bad_primes': [2, 5], 'central_character': '80.53', 'conductor': 80, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/80/53'], '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': '1-80-80.53-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-80-80.53-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.597193983570001, 'root_angle': 0.09939590441260832, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82248746392', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_80.53', 'Lhash_array': ['dirichlet_L_80.53'], 'label': '1-80-80.53-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/80/53'}