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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_67.54', 'a10': [-0.7860530947427875, -0.6181589862206052], 'a2': [0.23575893550942723, -0.9718115683235417], 'a3': [-0.14231483827328514, -0.9898214418809327], 'a4': [-0.8888354486549235, -0.4582265217274104], 'a5': [0.41541501300188644, -0.9096319953545183], 'a6': [-0.9954719225730846, -0.09505604330418266], 'a7': [0.7237340381050702, 0.690079011482112], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [-0.9594929736144974, 0.28173255684142967], 'algebraic': True, 'analytic_conductor': 0.311146691911923, 'analytic_normalization': 0, 'bad_lfactors': [[67, [1]]], 'bad_primes': [67], 'central_character': '67.54', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 67, 'conductor_radical': 67, 'conjugate': 'dirichlet_L_67.36', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^24', 'a^19', 'a^27', 'a^17', 'a^4', 'a^12', 'a^15', 'a^20', 'a^16', 'a^10', 'a^32', 'a^30', 'a^18', 'a^5', 'a^14', 'a^8', 'a^29', 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'0.667894732598149240620350894256-0.814311813228899775754669012603*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.31418359504', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.57499843492', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.87783103538', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.311146691911923, 'bad_primes': [67], 'central_character': '67.54', 'conductor': 67, 'conductor_radical': 67, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/67/54'], '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': '1-67-67.54-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': '1-67-67.54-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': -0.4024235430265302, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31418359504', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_67.54', 'Lhash_array': ['dirichlet_L_67.54'], 'label': '1-67-67.54-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/67/54'}