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{'Lhash': '1382613635323024463643893048074,1851588870593464727467765731976,2559360599486645760697822130958', 'a10': 0, 'a2': 2, 'a3': -9, 'a4': 5, 'a5': 0, 'a6': -18, 'a7': -10, 'a8': -4, 'a9': 54, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 115334.71800677532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 9, 27, 27]], [5, [1]], [11, [1, -33, 363, -1331]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'euler_factors': [[1, -2, -1, 16, -8, -128, 512], [1, 9, 27, 27], [1], [1, 10, 425, 3412, 145775, 1176490, 40353607], [1, -33, 363, -1331], [1, 114, 10303, 538132, 22635691, 550256226, 10604499373], [1, -104, 17531, -1030352, 86129803, -2510307176, 118587876497], [1, 58, 9081, 861164, 62286579, 2728661098, 322687697779], [1, 120, 25765, 2771856, 313482755, 17764306680, 1801152661463], [1, 220, 58859, 10101400, 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'7.59864198458999920060838161953315', '7.66971650226535703084286455319801', '8.400916356948033273541867174937411', '8.507383788613095679588096596368887', '8.789070329456716328700463922895257', '9.455059253445627846431972477339149', '9.545219535754985454645743513720873', '9.909247981780164681614435621155321'], 'prelabel': '6-825e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.976860021151063, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3e3-0', 'trace_hash': 1816758521490722677, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09068984393183498145687599081', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.46064607255351147116592512346', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.01897951929802681699068491839', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 115334.71800677532, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'dirichlet_coefficients': [1, 2, -9, 5, 0, -18, -10, -4, 54, 0, 33, -45, -114, -20, 0, -27, 104, 108, -58, 0, 90, 66, -120, 36, 0, -228, -270, -50, -220, 0, 248, 6, -297, 208, 0, 270, -838, -116, 1026, 0, 156, 180, -122, 165, 0, -240, -504, 243, -325, 0, -936, -570, -282, -540, 0, 40, 522, -440, 548, 0, 414, 496, -540, -167, 0, -594, 428, 520, 1080, 0, -912, -216, -618, -1676, 0, -290, -330, 2052, -542, 0, 1215, 312, 0, 450, 0, -244, 1980, -132, 790, 0, 1140, -600, -2232, -1008, 0, -54, -2074, -650, 1782, 0], 'euler11': [1, -33, 363, -1331, 0, 0, 0], 'euler13': [1, 114, 10303, 538132, 22635691, 550256226, 10604499373], 'euler17': [1, -104, 17531, -1030352, 86129803, -2510307176, 118587876497], 'euler19': [1, 58, 9081, 861164, 62286579, 2728661098, 322687697779], 'euler2': [1, -2, -1, 16, -8, -128, 512], 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1801152661463], [1, 220, 58859, 10101400, 1435512151, 130861130620, 14507145975869], [1, -248, 50781, -5187088, 1512816771, -220100912888, 26439622160671], [1, 838, 375507, 103501764, 19020556071, 2150078730742, 129961739795077], [1, -156, 100167, -24516984, 6903609807, -741016261596, 327381934393961], [1, 122, 193581, 17954308, 15391044567, 771206291978, 502592611936843], [1, 504, 393661, 109025808, 40871066003, 5432724525816, 1119130473102767], [1, 282, 224563, 87620892, 33432265751, 6250349838378, 3299763591802133], [1, -548, 673721, -226302104, 138368145259, -23114932435268, 8662995818654939], [1, -414, -389, 154404524, -88295609, -21329434985454, 11694146092834141], [1, -428, 695537, -249317576, 209191794731, -38716187568332, 27206534396294947], [1, 912, 1171621, 649961952, 419336043731, 116827458935952, 45848500718449031], [1, 618, 1066507, 454366420, 414889353619, 93524551846602, 58871586708267913], [1, 542, 1317893, 445950836, 649772646827, 131753400892382, 119851595982618319], [1, 0, 624021, 434328048, 356807095527, 0, 186940255267540403], [1, -790, -3625, 827778380, -2555512625, -392615219859190, 350356403707485209], [1, 2074, 3705231, 3687692268, 3381664292463, 1727583938222746, 760231058654565217]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/4/a/r'], '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': '6-825e3-1.1-c3e3-0-2', 'motivic_weight': 3, '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}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'prelabel': '6-825e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.976860021151063, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 1816758521490722677, 'z1': {'__RealLiteral__': 0, 'data': '1.09068984393183498145687599081', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1382613635323024463643893048074,1851588870593464727467765731976,2559360599486645760697822130958', 'Lhash_array': ['1382613635323024463643893048074', '1851588870593464727467765731976', '2559360599486645760697822130958'], 'label': '6-825e3-1.1-c3e3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/4/a/r'}