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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_89.33', 'a10': [0.9096319953545183, 0.41541501300188644], 'a2': [-0.9594929736144974, 0.28173255684142967], 'a3': [0.9771468659711595, -0.21256528955297668], 'a4': [0.8412535328311812, -0.5406408174555976], 'a5': [-0.7557495743542583, -0.6548607339452851], 'a6': [-0.8776789895672557, 0.47924898672005684], 'a7': [0.07133918319923234, 0.9974521146102535], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [0.9096319953545183, -0.41541501300188644], 'algebraic': True, 'analytic_conductor': 9.564378306721627, 'analytic_normalization': 0, 'bad_lfactors': [[89, [1]]], 'bad_primes': [89], 'central_character': '89.33', 'coeff_info': ['x^88 - 1', '0.997452114610254 + 0.0713391831992323*I', '\\\\zeta_{88}'], 'conductor': 89, 'conductor_radical': 89, 'conjugate': 'dirichlet_L_89.27', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^40', 'a^85', 'a^80', 'a^54', 'a^37', 'a^21', 'a^32', 'a^82', 'a^6', 'a^12', 'a^77', 'a^19', 'a^61', 'a^51', 'a^72', 'a^70', 'a^34', 'a^71', 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9.564378306721627, 'root_angle': 0.08917547693872006, 'root_number': '0.961013138224584529161804812578+0.276502709136340271260951758587*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0445877384694', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(88)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.00695888837074591260949500664+0.0753417488455442891765784641478*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2552768742', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.754904255', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '4.718330373', 'prec': 37}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.564378306721627, 'bad_primes': [89], 'central_character': '89.33', 'conductor': 89, 'conductor_radical': 89, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/89/33'], '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': '1-89-89.33-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': '1-89-89.33-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.564378306721627, 'root_angle': 0.04458773846936003, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2552768742', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_89.33', 'Lhash_array': ['dirichlet_L_89.33'], 'label': '1-89-89.33-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/89/33'}