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lfunc_lfunctions • Show schema
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{'Lhash': '229044901039461106342154119488,2251425870124078962026590304366', 'a10': 0, 'a2': 1, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': -2, 'a7': 0, 'a8': -1, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8069734733433876, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1, 2, 1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1', 'coefficient_field': '1.1.1.1', 'conductor': 3240000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, 2, 1], [1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 4, 6, 4, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 2, 3, 2, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, 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'5.36970526932147481326199900939364', '6.10830087856580903077164341735721', '6.42028049841365022151502090050368', '6.62827361643327361832839757442960', '6.91336963670413770661341706545561', '7.52731592307891002553681013779407', '8.092650685060006443180412257156039', '8.484988356238490620612424190934641', '8.931788012563920906567232087794027', '9.221672433493689494542748373485329', '9.910023944342792120838150622732805'], 'prelabel': '4-1800e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9477958760932674, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 1077550387795151139, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18068456797024635616045494218', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77606184994408508858255127027', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.44656023537320876925877225840', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8069734733433876, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 3240000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 1, -2, 0, 0, -2, 0, -1, 3, 0, -2, 0, 0, 0, 0, -1, -4, 3, -2, 0, 0, -2, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, -1, 0, 8, 0, 0, -4, 0, 0, 4, 0, 1, 0, 0, 0, 0, 1, 0, 4, -1, 0, 0, 0, 0, -3, 2, 0, 0, 0, 0, 0, 0, 0, 5, 1, -1, 0, 0, -1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, -6, 0], 'euler11': [1, 2, 3, 2, 1], 'euler13': [1, 0, 1, 0, 1], 'euler17': [1, 4, 6, 4, 1], 'euler19': [1, 2, 3, 2, 1], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, -1, 0, -1, 1], 'euler43': [1, 1, 0, 1, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, -1, 0, -1, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, 1, 0, 1, 1], 'euler7': [1, 0, 1, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, -2, 3, -2, 1], 'euler79': [1, 0, 1, 0, 1], 'euler83': [1, 1, 0, 1, 1], 'euler89': [1, 2, 3, 2, 1], 'euler97': [1, 1, 0, 1, 1], 'euler_factors': [[1, -1, 1, 0, 0], [1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 4, 6, 4, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 2, 3, 2, 1], [1, 1, 0, 1, 1]], 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/1/bk/c', 'ArtinRepresentation/2.1800.12t18.b'], 'is_instance_Artin': True, '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': '4-1800e2-1.1-c0e2-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-1800e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9477958760932674, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1077550387795151139, 'z1': {'__RealLiteral__': 0, 'data': '0.18068456797024635616045494218', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24605253
{'Lhash': '229044901039461106342154119488,2251425870124078962026590304366', 'Lhash_array': ['229044901039461106342154119488', '2251425870124078962026590304366'], 'label': '4-1800e2-1.1-c0e2-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1800.12t18.b'}
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id: 19837799
{'Lhash': '229044901039461106342154119488,2251425870124078962026590304366', 'Lhash_array': ['229044901039461106342154119488', '2251425870124078962026590304366'], 'label': '4-1800e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/1/bk/c'}