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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_173.9', 'a10': [-0.934016108732548, -0.35723088980113277], 'a2': [-0.391104720490156, 0.9203461835691594], 'a3': [-0.9893433680751103, 0.14560116773500487], 'a4': [-0.6940741952206338, -0.7199034737579958], 'a5': [0.03652202305765884, 0.9993328483702394], 'a6': [0.25293338239168073, -0.9674836970574252], 'a7': [0.45724232330463854, -0.889342148882519], 'a8': [0.934016108732548, -0.35723088980113277], 'a9': [0.957600599908406, -0.2880990993652376], 'algebraic': True, 'analytic_conductor': 0.803408622399443, 'analytic_normalization': 0, 'bad_lfactors': [[173, [1]]], 'bad_primes': [173], 'central_character': '173.9', 'coeff_info': ['x^86 - 1', '0.997332283663552 + 0.0729953146609075*I', '\\\\zeta_{86}'], 'conductor': 173, 'conductor_radical': 173, 'conjugate': 'dirichlet_L_173.77', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^41', 'a^54', 'a^21', 'a^68', 'a^71', 'a^81', 'a^82', 'a^48', 'a^19', 'a^9', 'a^70', 'a^12', 'a^62', 'a^22', 'a^79', 'a^23', 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'186.894091208217353443578764533235', '187.41869403243622926517871037309', '187.89495997282667923240390616005', '188.76248735709560909346172891017', '189.410560846125834289085621163511', '189.95534910865467525287900177887', '190.59690955470608083172476264276', '191.5598658618770030409102592631', '192.05326271421314693414864060157', '193.65129430808765558825931542480', '193.816606143509671069537568298619', '194.72718267569982197664345171991', '195.24803171216540021716375741305', '195.93413125666006327017893511716', '196.78157978704524450516405219979', '197.86075322473087254401808393583', '198.28589427818219345887538347678', '198.707191022281909482140526329932', '199.49514217662208819999912277741'], 'prelabel': '1-173-173.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.803408622399443, 'root_angle': 0.5801513505836534, 'root_number': '-0.249150402779279276801356108174+0.968464804107471375495912918692*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.290075675292', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(86)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.576061575374333882514239703626+0.374109347381080455753963161120*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2998567985', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.82200380955', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.04381082148', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.803408622399443, 'bad_primes': [173], 'central_character': '173.9', 'conductor': 173, 'conductor_radical': 173, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/173/9'], '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': '1-173-173.9-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': '1-173-173.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.803408622399443, 'root_angle': 0.2900756752918267, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2998567985', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_173.9', 'Lhash_array': ['dirichlet_L_173.9'], 'label': '1-173-173.9-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/173/9'}