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{'Lhash': '854153255019110172275562811880,1484705028528369366383178520373,1723125001015888810385012966513,2578626268058295266420255890901', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.61767785549676, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 3, 2, 1]], [3, [1]], [19, [1, -16, 102, -304, 361]]], 'bad_primes': [2, 3, 19], 'central_character': '342.1', 'coefficient_field': '1.1.1.1', 'conductor': 13680577296, 'conductor_radical': 114, 'degree': 8, 'euler_factors': [[1, 2, 3, 2, 1], [1], [1, 0, 8, 0, 39, 0, 200, 0, 625], [1, 4, 22, 64, 235, 448, 1078, 1372, 2401], [1, 0, -4, 0, -138, 0, -484, 0, 14641], [1, -6, 23, -66, 108, -858, 3887, -13182, 28561], [1, -12, 92, -528, 2463, -8976, 26588, -58956, 83521], [1, -16, 102, -304, 361], [1, 0, 14, 0, -333, 0, 7406, 0, 279841], [1, 0, -52, 0, 1863, 0, -43732, 0, 707281], [1, 0, -34, 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'8-342e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 664876355761222122, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67380810995184899578608453205', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17122575279107761539823766299', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.35930594811035093376430293133', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 55.61767785549676, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 13680577296, 'conductor_radical': 114, 'degree': 8, 'dirichlet_coefficients': [1, -2, 0, 1, 0, 0, -4, 2, 0, 0, 0, 0, 6, 8, 0, -4, 12, 0, 16, 0, 0, 0, 0, 0, -8, -12, 0, -4, 0, 0, 0, 2, 0, -24, 0, 0, 0, -32, 0, 0, 0, 0, 2, 0, 0, 0, -12, 0, -6, 16, 0, 6, 0, 0, 0, -8, 0, 0, 24, 0, 2, 0, 0, 3, 0, 0, -6, 12, 0, 0, 12, 0, 14, 0, 0, 16, 0, 0, 18, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -24, 0, 0, 24, 0, 0, -36, 12, 0, -8], 'euler11': [1, 0, -4, 0, -138, 0, -484, 0, 14641], 'euler13': [1, -6, 23, -66, 108, -858, 3887, -13182, 28561], 'euler17': [1, -12, 92, -528, 2463, -8976, 26588, -58956, 83521], 'euler19': [1, -16, 102, -304, 361, 0, 0, 0, 0], 'euler2': [1, 2, 3, 2, 1, 0, 0, 0, 0], 'euler23': [1, 0, 14, 0, -333, 0, 7406, 0, 279841], 'euler29': [1, 0, -52, 0, 1863, 0, -43732, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -34, 0, 267, 0, -32674, 0, 923521], 'euler37': [1, 0, -106, 0, 5331, 0, -145114, 0, 1874161], 'euler41': [1, 0, -82, 0, 5043, 0, -137842, 0, 2825761], 'euler43': [1, -2, -59, 46, 1948, 1978, -109091, -159014, 3418801], 'euler47': [1, 12, 152, 1248, 10863, 58656, 335768, 1245876, 4879681], 'euler5': [1, 0, 8, 0, 39, 0, 200, 0, 625], 'euler53': [1, 0, -82, 0, 3915, 0, -230338, 0, 7890481], 'euler59': [1, -24, 320, -3312, 28071, -195408, 1113920, -4929096, 12117361], 'euler61': [1, -2, -113, 10, 9724, 610, -420473, -453962, 13845841], 'euler67': [1, 6, 77, 390, 540, 26130, 345653, 1804578, 20151121], 'euler7': [1, 4, 22, 64, 235, 448, 1078, 1372, 2401], 'euler71': [1, -12, -34, -432, 16419, -30672, -171394, -4294932, 25411681], 'euler73': [1, -14, 25, -350, 9604, -25550, 133225, -5446238, 28398241], 'euler79': [1, -18, 275, -3006, 30180, -237474, 1716275, -8874702, 38950081], 'euler83': [1, 0, -112, 0, 16050, 0, -771568, 0, 47458321], 'euler89': [1, 0, -28, 0, -7137, 0, -221788, 0, 62742241], 'euler97': [1, 36, 662, 8280, 85395, 803160, 6228758, 32856228, 88529281], 'euler_factors': [[1, 2, 3, 2, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 8, 0, 39, 0, 200, 0, 625], [1, 4, 22, 64, 235, 448, 1078, 1372, 2401], [1, 0, -4, 0, -138, 0, -484, 0, 14641], [1, -6, 23, -66, 108, -858, 3887, -13182, 28561], [1, -12, 92, -528, 2463, -8976, 26588, -58956, 83521], [1, -16, 102, -304, 361, 0, 0, 0, 0], [1, 0, 14, 0, -333, 0, 7406, 0, 279841], [1, 0, -52, 0, 1863, 0, -43732, 0, 707281], [1, 0, -34, 0, 267, 0, -32674, 0, 923521], [1, 0, -106, 0, 5331, 0, -145114, 0, 1874161], [1, 0, -82, 0, 5043, 0, -137842, 0, 2825761], [1, -2, -59, 46, 1948, 1978, -109091, -159014, 3418801], [1, 12, 152, 1248, 10863, 58656, 335768, 1245876, 4879681], [1, 0, -82, 0, 3915, 0, -230338, 0, 7890481], [1, -24, 320, -3312, 28071, -195408, 1113920, -4929096, 12117361], [1, -2, -113, 10, 9724, 610, -420473, -453962, 13845841], [1, 6, 77, 390, 540, 26130, 345653, 1804578, 20151121], [1, -12, -34, -432, 16419, -30672, -171394, -4294932, 25411681], [1, -14, 25, -350, 9604, -25550, 133225, -5446238, 28398241], [1, -18, 275, -3006, 30180, -237474, 1716275, -8874702, 38950081], [1, 0, -112, 0, 16050, 0, -771568, 0, 47458321], [1, 0, -28, 0, -7137, 0, -221788, 0, 62742241], [1, 36, 662, 8280, 85395, 803160, 6228758, 32856228, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/342/2/s/a'], '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': '8-342e4-1.1-c1e4-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-342e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 664876355761222122, 'z1': {'__RealLiteral__': 0, 'data': '0.67380810995184899578608453205', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '854153255019110172275562811880,1484705028528369366383178520373,1723125001015888810385012966513,2578626268058295266420255890901', 'Lhash_array': ['854153255019110172275562811880', '1484705028528369366383178520373', '1723125001015888810385012966513', '2578626268058295266420255890901'], 'label': '8-342e4-1.1-c1e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/342/2/s/a'}