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lfunc_lfunctions • Show schema
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{'Lhash': '1201942515968412069342624910222', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.8915383985257197], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [6.274587767933326, 0], 'a8': [0, 0], 'a9': [-6.144071107200124, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.67046080286829, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [18.39754939647369, -13.803266867097465]]]], 'bad_primes': [2, 5, 23], 'central_character': '2300.1149', 'coefficient_field': 'CDF', 'conductor': 2300, 'conductor_radical': 230, 'conjugate': '752047481167793814376326611385', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.8915383985257197], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.274587767933326, 0], [49.0, 0]], [[1.0, 0], [0, 11.167242759643136], [-121.0, 0]], [[1.0, 0], [0, 15.96812974900393], [-169.0, 0]], [[1.0, 0], [23.908580104234606, 0], [289.0, 0]], 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'positive_zeros': ['0.948165461170461981889839983834526', '2.04385729832616212318000505176505', '2.36053554134757671587296772954034', '4.29713751790085049094754406654852', '4.56938070308778691423984017602836', '5.89967530241927343045713468620949', '6.78703272979987744785494629910500', '7.07759880038936750829719706354159', '7.979611481582977821647433770313148', '8.608935182506003765110582964828096'], 'prelabel': '2-2300-115.114-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.916467697329933, 'root_angle': -0.057305665817384215, 'root_number': '0.9838381318804458826401487898907527516579687675786871676 - 0.179060130285874568773160492664417010979659034527021135*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.028652832908692107', 'prec': 70}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.948165461170461981889839983835', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.04385729832616212318000505177', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.36053554134757671587296772954', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.67046080286829, 'bad_primes': [2, 5, 23], 'central_character': '115.114', 'conductor': 2300, 'conductor_radical': 230, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2300/3/d/c/1149/24'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-2300-115.114-c2-0-45', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2300-115.114-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.916467697329933, 'root_angle': -0.028652832908692107, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.948165461170461981889839983835', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1201942515968412069342624910222', 'Lhash_array': ['1201942515968412069342624910222'], 'label': '2-2300-115.114-c2-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2300/3/d/c/1149/24'}