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lfunc_lfunctions • Show schema
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{'Lhash': '578223105512552592732509053915,1488235378289360218339417958185', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 577.5735203685758, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '882.1', 'coefficient_field': '1.1.1.1', 'conductor': 777924, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 0, 2], [1], [1, 0, -48, 0, 625], [1], [1, 0, -192, 0, 14641], [1, 30, 563, 5070, 28561], [1, 0, -450, 0, 83521], [1, -26, 891, -9386, 130321], [1, 0, -546, 0, 279841], [1, 0, -1170, 0, 707281], [1, 6, 1931, 5766, 923521], [1, -34, 3027, -46546, 1874161], [1, 0, 3136, 0, 2825761], [1, 170, 10923, 314330, 3418801], [1, 0, 784, 0, 4879681], [1, 0, -4466, 0, 7890481], [1, 0, 1230, 0, 12117361], [1, -144, 12626, -535824, 13845841], [1, -86, 10827, -386054, 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'9.941460077108236694753244515271834'], 'prelabel': '4-882e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.902321829151794, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 708763739121673397, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45613760243433685964316918352', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17401070769927964154356917892', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.20227081949867521130733780516', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 577.5735203685758, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 777924, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 4, 0, 0, 26, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, -170, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, -8, 0, 0, 86, 0, 0, 0, 0, 0, 190, 0, 0, -52, 0, 0, 138, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, -96], 'euler11': [1, 0, -192, 0, 14641], 'euler13': [1, 30, 563, 5070, 28561], 'euler17': [1, 0, -450, 0, 83521], 'euler19': [1, -26, 891, -9386, 130321], 'euler2': [1, 0, 2, 0, 0], 'euler23': [1, 0, -546, 0, 279841], 'euler29': [1, 0, -1170, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 6, 1931, 5766, 923521], 'euler37': [1, -34, 3027, -46546, 1874161], 'euler41': [1, 0, 3136, 0, 2825761], 'euler43': [1, 170, 10923, 314330, 3418801], 'euler47': [1, 0, 784, 0, 4879681], 'euler5': [1, 0, -48, 0, 625], 'euler53': [1, 0, -4466, 0, 7890481], 'euler59': [1, 0, 1230, 0, 12117361], 'euler61': [1, -144, 12626, -535824, 13845841], 'euler67': [1, -86, 10827, -386054, 20151121], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -7344, 0, 25411681], 'euler73': [1, -190, 19683, -1012510, 28398241], 'euler79': [1, -138, 17243, -861258, 38950081], 'euler83': [1, 0, -10080, 0, 47458321], 'euler89': [1, 0, 2590, 0, 62742241], 'euler97': [1, 32, 19074, 301088, 88529281], 'euler_factors': [[1, 0, 2, 0, 0], [1, 0, 0, 0, 0], [1, 0, -48, 0, 625], [1, 0, 0, 0, 0], [1, 0, -192, 0, 14641], [1, 30, 563, 5070, 28561], [1, 0, -450, 0, 83521], [1, -26, 891, -9386, 130321], [1, 0, -546, 0, 279841], [1, 0, -1170, 0, 707281], [1, 6, 1931, 5766, 923521], [1, -34, 3027, -46546, 1874161], [1, 0, 3136, 0, 2825761], [1, 170, 10923, 314330, 3418801], [1, 0, 784, 0, 4879681], [1, 0, -4466, 0, 7890481], [1, 0, 1230, 0, 12117361], [1, -144, 12626, -535824, 13845841], [1, -86, 10827, -386054, 20151121], [1, 0, -7344, 0, 25411681], [1, -190, 19683, -1012510, 28398241], [1, -138, 17243, -861258, 38950081], [1, 0, -10080, 0, 47458321], [1, 0, 2590, 0, 62742241], [1, 32, 19074, 301088, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/3/b/d'], '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': '4-882e2-1.1-c2e2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-882e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.902321829151794, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 708763739121673397, 'z1': {'__RealLiteral__': 0, 'data': '0.45613760243433685964316918352', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '578223105512552592732509053915,1488235378289360218339417958185', 'Lhash_array': ['578223105512552592732509053915', '1488235378289360218339417958185'], 'label': '4-882e2-1.1-c2e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/3/b/d'}