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lfunc_lfunctions • Show schema
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2.9758374605662943, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e4-0', 'trace_hash': 159680607562325642, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19922200987649567890267980118', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.66923307631524300125628859900', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.861243579343531291392818016906', 'prec': 107}}
-
lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6149.979268829188, 'bad_primes': [5, 13], 'central_character': '1.1', 'conductor': 11156640625, 'conductor_radical': 65, 'degree': 8, 'dirichlet_coefficients': [1, -4, -6, 11, 0, 24, -20, -18, 4, 0, 4, -66, 0, 80, 0, 24, -30, -16, -10, 0, 120, -16, 30, 108, 0, 0, 48, -220, -2, 0, -20, -40, -24, 120, 0, 44, -38, 40, 0, 0, 100, -480, 0, 44, 0, -120, -68, -144, 236, 0, 180, 0, 0, -192, 0, 360, 60, 8, 164, 0, -124, 80, -80, 97, 0, 96, 170, -330, -180, 0, -86, -72, -58, 152, 0, -110, -80, 0, 40, 0, -123, -400, -188, 1320, 0, 0, 12, -72, 110, 0, 0, 330, 120, 272, 0, 240, 146, -944, 16, 0], 'euler11': [1, -4, 200, 960, 17471, 116160, 2928200, -7086244, 214358881], 'euler13': [1, 0, -169, 0, 28561, 0, 0, 0, 0], 'euler17': [1, 30, 109, 6390, 282060, 1846710, 9103789, 724127070, 6975757441], 'euler19': [1, 10, 74, 1752, -96625, 632472, 9643754, 470458810, 16983563041], 'euler2': [1, 4, 5, -6, -31, -24, 80, 256, 256], 'euler23': [1, -30, -356, -5940, 821595, -3142260, -99623396, -4441076670, 78310985281], 'euler29': [1, 2, -1571, -214, 1769980, -179974, -1111138451, 1189646642, 500246412961], 'euler3': [1, 6, 32, 120, 427, 1080, 2592, 4374, 6561], 'euler31': [1, 20, 200, 18300, 1672334, 17586300, 184704200, 17750073620, 852891037441], 'euler37': [1, 38, 1517, -52158, -1571608, -71404302, 2843102237, 97497603542, 3512479453921], 'euler41': [1, -100, 3461, 7272, -4096804, 12224232, 9779958821, -475010424100, 7984925229121], 'euler43': [1, 0, -998, 0, -2422797, 0, -3411963398, 0, 11688200277601], 'euler47': [1, 68, 2312, 148716, 9565454, 328513644, 11281822472, 732986642372, 23811286661761], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -4814, 0, 12616659, 0, -37984775534, 0, 62259690411361], 'euler59': [1, -164, 6980, 551844, -68910913, 1920968964, 84579179780, -6917607517124, 146830437604321], 'euler61': [1, 124, 5413, 312604, 28201432, 1163199484, 74947537333, 6388526420764, 191707312997281], 'euler67': [1, -170, 10706, -134496, -16049425, -603752544, 215737901426, -15377924968730, 406067677556641], 'euler7': [1, 20, 164, 636, 1871, 31164, 393764, 2352980, 5764801], 'euler71': [1, 86, 4658, 258336, 1457087, 1302271776, 118367610098, 11016624417206, 645753531245761], 'euler73': [1, 58, 1682, 201144, 20590727, 1071896376, 47765841362, 8777385124762, 806460091894081], 'euler79': [1, -40, 14980, -541240, 136037062, -3377878840, 583472213380, -9723498220840, 1517108809906561], 'euler83': [1, 188, 17672, 1935084, 200304482, 13330793676, 838683448712, 61464790193372, 2252292232139041], 'euler89': [1, -110, 12050, -1194180, 87746159, -9459099780, 756044004050, -54667942005710, 3936588805702081], 'euler97': [1, -146, 13250, -1056876, 58176719, -9944146284, 1173012973250, -121613912719634, 7837433594376961], 'euler_factors': [[1, 4, 5, -6, -31, -24, 80, 256, 256], [1, 6, 32, 120, 427, 1080, 2592, 4374, 6561], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 20, 164, 636, 1871, 31164, 393764, 2352980, 5764801], [1, -4, 200, 960, 17471, 116160, 2928200, -7086244, 214358881], [1, 0, -169, 0, 28561, 0, 0, 0, 0], [1, 30, 109, 6390, 282060, 1846710, 9103789, 724127070, 6975757441], [1, 10, 74, 1752, -96625, 632472, 9643754, 470458810, 16983563041], [1, -30, -356, -5940, 821595, -3142260, -99623396, -4441076670, 78310985281], [1, 2, -1571, -214, 1769980, -179974, -1111138451, 1189646642, 500246412961], [1, 20, 200, 18300, 1672334, 17586300, 184704200, 17750073620, 852891037441], [1, 38, 1517, -52158, -1571608, -71404302, 2843102237, 97497603542, 3512479453921], [1, -100, 3461, 7272, -4096804, 12224232, 9779958821, -475010424100, 7984925229121], [1, 0, -998, 0, -2422797, 0, -3411963398, 0, 11688200277601], [1, 68, 2312, 148716, 9565454, 328513644, 11281822472, 732986642372, 23811286661761], [1, 0, -4814, 0, 12616659, 0, -37984775534, 0, 62259690411361], [1, -164, 6980, 551844, -68910913, 1920968964, 84579179780, -6917607517124, 146830437604321], [1, 124, 5413, 312604, 28201432, 1163199484, 74947537333, 6388526420764, 191707312997281], [1, -170, 10706, -134496, -16049425, -603752544, 215737901426, -15377924968730, 406067677556641], [1, 86, 4658, 258336, 1457087, 1302271776, 118367610098, 11016624417206, 645753531245761], [1, 58, 1682, 201144, 20590727, 1071896376, 47765841362, 8777385124762, 806460091894081], [1, -40, 14980, -541240, 136037062, -3377878840, 583472213380, -9723498220840, 1517108809906561], [1, 188, 17672, 1935084, 200304482, 13330793676, 838683448712, 61464790193372, 2252292232139041], [1, -110, 12050, -1194180, 87746159, -9459099780, 756044004050, -54667942005710, 3936588805702081], [1, -146, 13250, -1056876, 58176719, -9944146284, 1173012973250, -121613912719634, 7837433594376961]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/325/3/w/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': '8-325e4-1.1-c2e4-0-1', 'motivic_weight': 2, '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': [2, 2, 2, 2], 'order_of_vanishing': 0, 'prelabel': '8-325e4-1.1-c2e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.9758374605662943, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e4-0', 'trace_hash': 159680607562325642, 'z1': {'__RealLiteral__': 0, 'data': '0.19922200987649567890267980118', 'prec': 103}}
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{'Lhash': '252543900398613993337472295234,848353710883602244157560407796,1091755940297536154309333161151,2409543454339253943417759401196', 'Lhash_array': ['252543900398613993337472295234', '848353710883602244157560407796', '1091755940297536154309333161151', '2409543454339253943417759401196'], 'label': '8-325e4-1.1-c2e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/325/3/w/a'}