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'4.67690953548421880162400296571376', '6.35768279052953653401815202474055', '6.61602891824790078042385517180553', '7.64301859820724922477637115105823', '7.83814457472610941962957315535963', '8.413589837211907911686011685924850', '8.574426353822105208231083551620258', '9.474688155985932296916650904218342', '9.778131687861258099697008710542502', '10.69385456385676065266010132856056', '11.16655365200357594354097215650620', '11.66690750246370816148884638083283', '11.88285438318654672660724487482585'], 'prelabel': '4-78e2-1.1-c9e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.338201260671841, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c9e2-0', 'trace_hash': 1325746134718613023, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46494253786047836419387462334', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.69565793131419739956162422808', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92528648570127623628235811743', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1613.8534758508947, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 6084, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, -32, 162, 768, -2314, -5184, 3738, -16384, 19683, 74048, 15020, 124416, 57122, -119616, -374868, 327680, -484180, -629856, -68538, -1777152, 605556, -480640, -431976, -2654208, 1340346, -1827904, 2125764, 2870784, -1864872, 11995776, 8299954, -6291456, 2433240, 15493760, -8649732, 15116544, 9131400, 2193216, 9253764, 37912576, -11131186, -19377792, -18866232, 11535360, -45546462, 13823232, -85216336, 53084160, -68997082, -42891072, -78437160, 43869696, -153856132, -68024448, -34756280, -61243392, -11103156, 59675904, -144173624, -287898624, -59443008, -265598528, 73575054, 117440512, -132180308, -77863680, -166548854, -371850240, -69980112, 276791424, -15061388, -322486272, -9417608, -292204800, 217136052, -52637184, 56144760, -296120448, -839937320, -758251520, 215233605, 356197952, 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'euler79': [1, 839937320, 413909200502022942, 100667828327363197443765080, 14364405059580771582276370834385761], 'euler83': [1, 699318048, 451612178615361238, 130730694406318072387093344, 34946659039493167390823397237402409], 'euler89': [1, -456025130, 700638627502586962, -159771324547038424407302170, 122749609618842355502421774953773681], 'euler97': [1, -1429586424, 1704235462005901102, -1086816000555714139845814008, 577951262543040979328274795306257089], 'euler_factors': [[1, 32, 256, 0, 0], [1, -162, 6561, 0, 0], [1, 2314, 4014250, 4519531250, 3814697265625], [1, -3738, 82969726, -150841782966, 1628413597910449], [1, -15020, 419343382, -35416374318820, 5559917313492231481], [1, -57122, 815730721, 0, 0], [1, 484180, 295618325494, 57417878042317460, 14063084452067724991009], [1, 68538, 642219890158, 22116369430377102, 104127350297911241532841], [1, 431976, 3189924689326, 778054722088140888, 3244150909895248285300369], [1, 1864872, 1964400640198, 27053970330310773768, 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'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9, 9], 'order_of_vanishing': 2, 'prelabel': '4-78e2-1.1-c9e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.338201260671841, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9e2-0', 'trace_hash': 1325746134718613023, 'z1': {'__RealLiteral__': 0, 'data': '1.46494253786047836419387462334', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1857035287418701073300342135483,2149501794412200116879709834704', 'Lhash_array': ['1857035287418701073300342135483', '2149501794412200116879709834704'], 'label': '4-78e2-1.1-c9e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/10/a/b'}