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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_139.24', 'a10': [-0.06824241336467098, -0.9976687691905392], 'a2': [-0.41917652041666414, 0.9079047553192889], 'a3': [0.8981277053636961, 0.4397347210059058], 'a4': [-0.648582089462756, -0.7611447124089648], 'a5': [-0.8771826024025943, 0.4801569348059156], 'a6': [-0.7757112907044198, 0.6310879443260528], 'a7': [0.9343938371606711, -0.35624171158941687], 'a8': [0.9629172873477992, -0.2697967711570243], 'a9': [0.6132667502837162, 0.7898758718915586], 'algebraic': True, 'analytic_conductor': 0.6455132862053328, 'analytic_normalization': 0, 'bad_lfactors': [[139, [1]]], 'bad_primes': [139], 'central_character': '139.24', 'coeff_info': ['x^69 - 1', '0.995856842531531 + 0.0909348623088469*I', '\\\\zeta_{69}'], 'conductor': 139, 'conductor_radical': 139, 'conjugate': 'dirichlet_L_139.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 'a^5', 'a^44', 'a^29', 'a^27', 'a^65', 'a^66', 'a^10', 'a^51', 'a^16', 'a^49', 'a^28', 'a^18', 'a^34', 'a^19', 'a^8', 'a^32', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-139-139.24-r0-0-0', 'leading_term': '0.501854055000639890795237666160+0.879083574572054784824894999258*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/139/24', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0122477086182842, 1.4284329683814054, 2.0481159928360606, 2.533293277270425, 2.558743843775216, 1.925058050636959, 0.6425501639514379, -1.0274781780707454, -2.6217384047942307, -3.626706376498535, -3.690670933384157, -2.8063915549774046, -1.364866153338964, -0.024925008863832764, 0.569500802097928, 0.10282684314194429, -1.2294332966159311, -2.784769895505371, -3.779611084705175, -3.693301836739416, -2.551493938357597, -0.9165218017856701, 0.42984716424695263, 0.9394605507609596, 0.6151794372943281, -0.014982871858651253, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6455132862053328, 'bad_primes': [139], 'central_character': '139.24', 'conductor': 139, 'conductor_radical': 139, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/139/24'], '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': '1-139-139.24-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': '1-139-139.24-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6455132862053328, 'root_angle': 0.3348815527530151, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99970638342', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_139.24', 'Lhash_array': ['dirichlet_L_139.24'], 'label': '1-139-139.24-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/139/24'}