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lfunc_lfunctions • Show schema
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{'Lhash': '1140768243501520001506712934247,2668915444765533276969405914488', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.369859079893637, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 3]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, 3], [1, -4, 54, -100, 625], [1, 0, -50, 0, 2401], [1, 0, -194, 0, 14641], [1, 4, 342, 676, 28561], [1, -20, 678, -5780, 83521], [1, 0, -290, 0, 130321], [1, 0, -290, 0, 279841], [1, -52, 2358, -43732, 707281], [1, 0, -1874, 0, 923521], [1, 52, 3414, 71188, 1874161], [1, -116, 6726, -194996, 2825761], [1, 0, -1346, 0, 3418801], [1, 0, 382, 0, 4879681], [1, -148, 11094, -415732, 7890481], [1, 0, 1150, 0, 12117361], [1, 52, 8118, 193492, 13845841], [1, 0, -8930, 0, 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'4-192e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2872737212055974, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 229205241110540773, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.899907469215992686316824256879', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.10540305371607791461657824528', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.76962669435860102907115344980', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 27.369859079893637, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 0, 0, -3, 0, 0, 0, -4, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 116, 0, 0, 0, -12, 0, 0, 0, 50, 0, 0, 0, 148, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 80, 0, 0, 0, 164, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, -194, 0, 14641], 'euler13': [1, 4, 342, 676, 28561], 'euler17': [1, -20, 678, -5780, 83521], 'euler19': [1, 0, -290, 0, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -290, 0, 279841], 'euler29': [1, -52, 2358, -43732, 707281], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, -1874, 0, 923521], 'euler37': [1, 52, 3414, 71188, 1874161], 'euler41': [1, -116, 6726, -194996, 2825761], 'euler43': [1, 0, -1346, 0, 3418801], 'euler47': [1, 0, 382, 0, 4879681], 'euler5': [1, -4, 54, -100, 625], 'euler53': [1, -148, 11094, -415732, 7890481], 'euler59': [1, 0, 1150, 0, 12117361], 'euler61': [1, 52, 8118, 193492, 13845841], 'euler67': [1, 0, -8930, 0, 20151121], 'euler7': [1, 0, -50, 0, 2401], 'euler71': [1, 0, -10082, 0, 25411681], 'euler73': [1, 92, 12774, 490268, 28398241], 'euler79': [1, 0, 1390, 0, 38950081], 'euler83': [1, 0, -11426, 0, 47458321], 'euler89': [1, -164, 22566, -1299044, 62742241], 'euler97': [1, -4, 18822, -37636, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 0], [1, -4, 54, -100, 625], [1, 0, -50, 0, 2401], [1, 0, -194, 0, 14641], [1, 4, 342, 676, 28561], [1, -20, 678, -5780, 83521], [1, 0, -290, 0, 130321], [1, 0, -290, 0, 279841], [1, -52, 2358, -43732, 707281], [1, 0, -1874, 0, 923521], [1, 52, 3414, 71188, 1874161], [1, -116, 6726, -194996, 2825761], [1, 0, -1346, 0, 3418801], [1, 0, 382, 0, 4879681], [1, -148, 11094, -415732, 7890481], [1, 0, 1150, 0, 12117361], [1, 52, 8118, 193492, 13845841], [1, 0, -8930, 0, 20151121], [1, 0, -10082, 0, 25411681], [1, 92, 12774, 490268, 28398241], [1, 0, 1390, 0, 38950081], [1, 0, -11426, 0, 47458321], [1, -164, 22566, -1299044, 62742241], [1, -4, 18822, -37636, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/3/g/b'], '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': '4-192e2-1.1-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': '4-192e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2872737212055974, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 229205241110540773, 'z1': {'__RealLiteral__': 0, 'data': '0.899907469215992686316824256879', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1140768243501520001506712934247,2668915444765533276969405914488', 'Lhash_array': ['1140768243501520001506712934247', '2668915444765533276969405914488'], 'label': '4-192e2-1.1-c2e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/3/g/b'}