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lfunc_lfunctions • Show schema
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{'Lhash': '150294336202991581926317985905,1471813195432218170489914435303', 'a10': 0, 'a2': -4, 'a3': 0, 'a4': 8, 'a5': 0, 'a6': 0, 'a7': -58, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2163.7832267609574, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 4, 8]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 4, 8], [1], [1], [1, 58, 1682, 139258, 5764801], [1, -236, 43206, -3455276, 214358881], [1, 138, 9522, 3941418, 815730721], [1, 542, 146882, 45268382, 6975757441], [1, 0, -182242, 0, 16983563041], [1, -538, 144722, -150554458, 78310985281], [1, 0, -952162, 0, 500246412961], [1, -404, 1887846, -373102484, 852891037441], [1, -1302, 847602, -2440157622, 3512479453921], [1, 3364, 8480646, 9505860004, 7984925229121], [1, 2178, 2371842, 7446148578, 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'10.05745824261004230157177108355957', '10.68026061022661309246544134996210'], 'prelabel': '4-450e2-1.1-c4e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.8202993620316965, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c4e2-0', 'trace_hash': 1720911450754727239, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11856132610668302561315733702', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.16105588966488958368139802314', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.68467379930138418247203859424', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 2163.7832267609574, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -4, 0, 8, 0, 0, -58, 0, 0, 0, 236, 0, -138, 232, 0, -64, -542, 0, 0, 0, 0, -944, 538, 0, 0, 552, 0, -464, 0, 0, 404, 256, 0, 2168, 0, 0, 1302, 0, 0, 0, -3364, 0, -2178, 1888, 0, -2152, 2538, 0, 1682, 0, 0, -1104, -1222, 0, 0, 0, 0, 0, 0, 0, -11196, -1616, 0, -512, 0, 0, 1502, -4336, 0, 0, -12884, 0, 5902, -5208, 0, 0, -13688, 0, 0, 0, 0, 13456, -12462, 0, 0, 8712, 0, 0, 0, 0, 8004, 4304, 0, -10152, 0, 0, 14622, -6728, 0, 0], 'euler11': [1, -236, 43206, -3455276, 214358881], 'euler13': [1, 138, 9522, 3941418, 815730721], 'euler17': [1, 542, 146882, 45268382, 6975757441], 'euler19': [1, 0, -182242, 0, 16983563041], 'euler2': [1, 4, 8, 0, 0], 'euler23': [1, -538, 144722, -150554458, 78310985281], 'euler29': [1, 0, -952162, 0, 500246412961], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -404, 1887846, -373102484, 852891037441], 'euler37': [1, -1302, 847602, -2440157622, 3512479453921], 'euler41': [1, 3364, 8480646, 9505860004, 7984925229121], 'euler43': [1, 2178, 2371842, 7446148578, 11688200277601], 'euler47': [1, -2538, 3220722, -12384630378, 23811286661761], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 1222, 746642, 9642167782, 62259690411361], 'euler59': [1, 0, -22889122, 0, 146830437604321], 'euler61': [1, 11196, 59029286, 155018035836, 191707312997281], 'euler67': [1, -1502, 1128002, -30266983742, 406067677556641], 'euler7': [1, 58, 1682, 139258, 5764801], 'euler71': [1, 12884, 92322726, 327404098004, 645753531245761], 'euler73': [1, -5902, 17416802, -167606418382, 806460091894081], 'euler79': [1, 0, 33613438, 0, 1517108809906561], 'euler83': [1, 12462, 77650722, 591425596302, 2252292232139041], 'euler89': [1, 0, 84185918, 0, 3936588805702081], 'euler97': [1, -14622, 106901442, -1294475146782, 7837433594376961], 'euler_factors': [[1, 4, 8, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 58, 1682, 139258, 5764801], [1, -236, 43206, -3455276, 214358881], [1, 138, 9522, 3941418, 815730721], [1, 542, 146882, 45268382, 6975757441], [1, 0, -182242, 0, 16983563041], [1, -538, 144722, -150554458, 78310985281], [1, 0, -952162, 0, 500246412961], [1, -404, 1887846, -373102484, 852891037441], [1, -1302, 847602, -2440157622, 3512479453921], [1, 3364, 8480646, 9505860004, 7984925229121], [1, 2178, 2371842, 7446148578, 11688200277601], [1, -2538, 3220722, -12384630378, 23811286661761], [1, 1222, 746642, 9642167782, 62259690411361], [1, 0, -22889122, 0, 146830437604321], [1, 11196, 59029286, 155018035836, 191707312997281], [1, -1502, 1128002, -30266983742, 406067677556641], [1, 12884, 92322726, 327404098004, 645753531245761], [1, -5902, 17416802, -167606418382, 806460091894081], [1, 0, 33613438, 0, 1517108809906561], [1, 12462, 77650722, 591425596302, 2252292232139041], [1, 0, 84185918, 0, 3936588805702081], [1, -14622, 106901442, -1294475146782, 7837433594376961]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/5/g/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': '4-450e2-1.1-c4e2-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4, 4], 'order_of_vanishing': 0, 'prelabel': '4-450e2-1.1-c4e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.8202993620316965, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4e2-0', 'trace_hash': 1720911450754727239, 'z1': {'__RealLiteral__': 0, 'data': '0.11856132610668302561315733702', 'prec': 103}}
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{'Lhash': '150294336202991581926317985905,1471813195432218170489914435303', 'Lhash_array': ['150294336202991581926317985905', '1471813195432218170489914435303'], 'factors': ['2-450-5.2-c4-0-1', '2-450-5.3-c4-0-20'], 'label': '4-450e2-1.1-c4e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/5/g/a'}