# Stored data for newform 207.6.a.b, downloaded from the LMFDB on 19 April 2024.
{"label": "207.6.a.b", "space_label": "207.6.a", "level": 207, "weight": 6, "hecke_orbit": 2, "hecke_orbit_code": 4503599728033999, "dim": 3, "is_polredabs": true, "nf_label": "3.3.7925.1", "trace_hash": 1822094335560698957, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [8, -48, -4, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{2}+(2-6\\beta _{1}+4\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 7452, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 33.19945070128699, "hecke_ring_index": 2, "level_radical": 69, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [207, 1, [47, 28], [1, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 1, "level_primes": [3, 23], "conrey_indexes": [1], "field_disc": 7925, "field_disc_factorization": [[5, 2], [317, 1]], "field_poly": [12, -13, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.860", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.262", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "265.904", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [23, -1]], "trace_display": [4, 0, 58, -282], "traces": [0, 3, 4, 0, 16, 58, 0, -282, 360, 0, -156, -136, 0, -1116, -2016, 0, 128, 896, 0, 1654, -1504, 0, 1352, 1587, 0, -7347, -1998, 0, -10264, 844, 0, -3020, -6656, 0, -11212, -1072, 0, 8938, -10728, 0, 3440, 12792, 0, -16730, -5112, 0, 2116, -22500, 0, 2887, -15156, 0, -47412, -17108, 0, -436, -42640, 0, -55678, -54176, 0, -71324, 72710, 0, -49984, -846, 0, -62960, 8352, 0, 9224, -98400, 0, -81772, 59044, 0, 31488, 304, 0, 58224, 17568, 0, 61926, -9892, 0, 15536, -191140, 0, -58400, -27542, 0, 151974, 8464, 0, -146990, 20644, 0, -273672, 401276, 0, -97504, 127930, 0, -173434, -291600, 0, 474356, 333390, 0, -266200, 37312, 0, -33472, 186012, 0, 30682, -451252, 0, 113192, 48676, 0, -377281, -234292, 0, 509420, -294132, 0, 330608, -467200, 0, 133812, -286256, 0, -35876, 439400, 0, 320320, 283202, 0, 614888, 99536, 0, -208350, 317862, 0, 244194, -453826, 0, 912416, 590592, 0, 525336, 496080, 0, 19192, -321150, 0, -312544, 875972, 0, 9344, -149178, 0, -141044, 996404, 0, 16444, 159412, 0, 274623, -227432, 0, -1283560, -444622, 0, 807898, 416704, 0, -297356, -482352, 0, 88998, 1417752, 0, 190440, -259572, 0, -623932, -227260, 0, -312408, -427590, 0, 507188, -749116, 0, 2319984, -1284264, 0, -26522, -1029160, 0, 700680, 1001254, 0, -216778, 995008, 0, 1185264, -815648, 0, -772200, 1872264, 0, 1643040, 273720, 0, -1085750, 437680, 0, -169392, -1705842, 0, -1018768, 1308864, 0, -212484, 618868, 0, -991176, -82524, 0, -812880, 626308, 0, -381370, -262272, 0, 460888, 883212, 0, -3037844, -1056068, 0, -1006008, -1096478, 0, -2514888, 511920, 0, 911144, 117108, 0, -71944, -2203006, 0, -366592, -2337336, 0, -2223312, -305712, 0, -1553038, -1002732, 0, -1312508, -287488, 0, 1384840, 654412, 0, -450856, -2358944, 0, 3873596, 500104, 0, 238968, 826674, 0, 121920, -1759432, 0, -2622792, -1744780, 0, -1115964, -2624198, 0, -437299, 72372, 0, -1952924, -1911512, 0, -1060736, 3777520, 0, 1240156, -590364, 0, 4624120, -1891922, 0, -3034496, -1066124, 0, -2663388, 430928, 0, 180300, 4444264, 0, -4849134, -2413272, 0, 1163448, -1925946, 0, 595862, -182144, 0, -1066464, 4890928, 0, 3621744, 1806698, 0, 4529840, 3509150, 0, -2740952, 5528496, 0, -4311104, -2077540, 0, -1959210, -533746, 0, 770832, -88630, 0, -2208084, -4083600, 0, -5325256, -2545304, 0, 7478088, 6294384, 0, 568512, -3766976, 0, -1292410, -4721064, 0, 1000374, 2790096, 0, -985725, -522036, 0, 8894088, -822522, 0, 3760626, 67712, 0, -1534496, -5824188, 0, 2420778, 2697744, 0, -1257200, 5086782, 0, 4370126, 859328, 0, 9578300, 2390712, 0, -208776, 5672854, 0, -2895664, -9062620, 0, 473984, 3205960, 0, 918578, 699204, 0, 4892672, 1882924, 0, 566528, 12194044, 0, -3941100, 10828240, 0, 11381432, -4337716, 0, -4435768, -1893364, 0, 8096472, 3026184, 0, -2981872, 5477472, 0, 3458736, -2789726, 0, -4216106, 2179040, 0, -2153600, -2843624, 0, 8861196, 5466720, 0, 894960, 2110816, 0, -4378308, -12759760, 0, -2234720, 874966, 0, 12929444, -1326880, 0, 9022104, -7473624, 0, 1754608, -1356904, 0, 13015936, 5205518, 0, -5058014, -10191056, 0, -9850236, -1103616, 0, 4165200, -15976728, 0, -795616, 2842336, 0, 1211880, 4168304, 0, 5655694, 7298066, 0, -1559200, -253340, 0, -9361280, 1521260, 0, -5144246, 979232, 0, -3516334, 2023834, 0, -19849806, 1545488, 0, -3707312, -4572952, 0, 3998396, -8834240, 0, 804676, 14073068, 0, -705202, 9010836, 0, -2826160, 11318230, 0, 15802328, 7593376, 0, -3319956, 3312584, 0, -2599660, 715208, 0, -14534284, 3788696, 0, 12996138, 7514624, 0, -9670018, -7863784, 0, -3493730, -23218936, 0, -3465360, 14245806, 0, 12946388, -7619452, 0, -13120516, -2899570, 0, 839523, 3922936, 0, -3677552, -23087034, 0, 4601220, -9046240, 0, -10200734, 1621216, 0, -483448, -2638848, 0, -1848192, -4739040, 0, -7092968, 12941944, 0, -3337688, -3009208, 0, -15107716, 3760134, 0, -746364, -10248188, 0, 18309060, -1453632, 0, 6205804, -1745358, 0, 9187792, -19119696, 0, -15453520, -12487252, 0, 9432992, -2452176, 0, -26557224, -3886563, 0, -1967440, -22594052, 0, -5223792, -4977372, 0, 9403516, -10363120, 0, -17532216, -3700356, 0, -1479160, 5359792, 0, -18619232, 10303382, 0, 581256, -6006616, 0, -1056942, 5880112, 0, -8481808, 44352560, 0, -22496148, -6446526, 0, 3261276, -4887808, 0, 3011368, -1083780, 0, -11304758, -28303184, 0, 1453120, 9167166, 0, -6641302, 6015840, 0, 37272122, 10030088, 0, 12691783, 14656828, 0, 7174272, 21225776, 0, 5139780, -2374880, 0, -37339488, 14540518, 0, -16978824, 2857156, 0, -3152640, 19322238, 0, -7024500, -5429656, 0, -22785816, 12585340, 0, 10613512, 8779302, 0, 10761652, -33898664, 0, -2487906, -20899888, 0, 27258000, 15032940, 0, 20415748, 35906474, 0, 20663840, 1049504, 0, 446476, -44754096, 0, 7159520, 1348948, 0, -27045676, 5273980, 0, 11681996, -33261264, 0, 31387668, 8586560, 0, -6239660, 15653084, 0, -240528, -38394352, 0, 6439520, 9224136, 0, 11346108, -3085664, 0, -10761552, 13900718, 0, 25314994, -8176306, 0, 33947896, 19692410, 0, 32142084, -14364672, 0, -12688878, -28002540, 0, -12745754, 6476660, 0, -17431600, -1597580, 0, 8219052, -10668324, 0, -25125372, 2033736, 0, -6207444, -38883900, 0, -17419984, 5346664, 0, -19341918, 31129200, 0, 2458604, -1991860, 0, -6632122, 26073528, 0, -3521024, 14360400, 0, 3822064, 10207856, 0, -62701024, 26936462, 0, 15996332, 39114364, 0, 5920416, -48211020, 0, -16095116, -19053840, 0, 41352786, 22805466, 0, -14272194, 20236388, 0, 10913120, -34183920, 0, 17119040, 70545040, 0, 52162616, 38685132, 0, 19377996, -611408, 0, 5636676, 21596700, 0, -635720, -32437440, 0, 12736800, 38205856, 0, 9528910, -5931148, 0, -497088, -10463104, 0, 16095354, 2608732, 0, 6443272, -1236508, 0, 27609948, -23857534, 0, 54498976, 17653936, 0, 21654250, 20671104, 0, -17958968, -1191206, 0, -567088, -55017990, 0, 47453680, -34381750, 0, 14473080, 71340488, 0, 10245952, -8483794, 0, -11537140, 13144406, 0, 9878864, -62442490, 0, 9121912, -4346320, 0, 19317872, -32986118, 0, -6673790, -10233256, 0, -6089472, -24710096, 0, 25884112, 7066384, 0, -30888628, 31947618, 0, -3949985, -12898248, 0, -22833040, 200708, 0, 43242854, 27916512, 0, 29379628, 4728202, 0, -63886562, 69841328, 0, 35585040, 19268644, 0, 27490080, -2355360, 0, 19193768, -36043396, 0, -8238852, -79172504, 0, -79304920, 27315372, 0, 35001990, -47885760, 0, -5675112, 4149808, 0, -35951806, 9159202, 0, 12299904, -6900504, 0, -59250588, 21922776, 0, -45575622, 48789528, 0, 14302358, 6931664, 0, 10751024, 22008600, 0, -5277582, 70451200, 0, -38576056, -66531140, 0, -70659596, 13467388, 0, -15043040, 10667948, 0, 11151950, -77360464, 0, -7058088, 38973500, 0, -37286836, -8077020, 0, -60924432, 45885814, 0, 31401118, 1819760, 0, 3166978, 58814280, 0, -38745762, -49736840, 0, 32759392, -40983396, 0, -18304034, -6932284, 0, 30217688, -16686712, 0, -76563076, -30601480, 0, 19683360, -53736718, 0, 6766968, 30953664, 0, 2546680, -12029784, 0, 32273694, 26193992, 0, 2383840, 31490522, 0, -44679500, 26841444, 0, 72481792, -76508448, 0, -4913483, -38537388, 0, -1901608, 8339798, 0, -8047568, -43205880, 0, 11724024, 49070474, 0, -53848762, 83888858, 0, -8635104, -63614548, 0, 21539284, 12690304, 0, -23097226, -69662852, 0, -29558174, -3890696, 0, 12156984, -8850170, 0, 13025192, -33593120, 0, 91368000, -27832972, 0, -29917090, 29444574, 0, -19500640, -8794008, 0, -66384992, -39877584, 0, -95154868, -80293544, 0, -5979690, -19522760, 0, -2704248, 54826140, 0, -13642656, 16783920, 0, 60471738, 66463800, 0, -154959812, 108734584, 0, -22892544, -49683548, 0, 39859092, -98050652, 0, 8143208, 69543866, 0, -87207750, 9094780, 0, -149585584, -5719628, 0, 99007048, 34431264, 0, 856668, -51338908, 0, -21477448, -56132876, 0, -39979920, 14780408, 0, -22288948, -45597464, 0, 24002200, -5571880, 0, 4432426, 1119364, 0, 6034624, 219316, 0, 24153876, -14415520, 0, -39072042, 5169124, 0, 50650106, -7934280, 0, 38549440, -108689566, 0, 59480770, 14756684, 0, -31057752, -131389146, 0, -11902500, 41390566, 0, 39774528, 15765960, 0, 94816492, 97162752, 0, 26568960, 127349678, 0, -81287872, 33255066, 0, 23774480, -29870262, 0, 42499976, 9031928, 0, -26576204, -49523022, 0, -48489912, -123770928, 0, 48135316, 10184338, 0, -52966320, 57574320, 0, 103454216, -27788408, 0, 24149454, 136444680, 0, -5540736, -91580768, 0, 11597830, 79300896, 0, 63603436, 1527223, 0, 21242816, 6246616, 0, -17716824, -106432, 0, 52295328, 20645360, 0, -30425096, -100444860, 0, -20198074, -58826804, 0, 46190160, 8656344, 0, 103769090, -169444136, 0, -8017524, -50890680, 0, -101694240, 150771790, 0, -51016928, 96480864, 0, -23278232, 7250160, 0, -79738376, 113543624, 0, 17244918, -63820392, 0, -18393712, 80379752, 0, 26580640, -27422624, 0, 133884882, 52080680, 0, 12999240, 55246780, 0, 10687648, 149296542, 0, -26132892, -83600256, 0, -24957664, -133630912, 0, -115988354, 1573408, 0, 27002080, 37396946, 0, 6009942, -25080948, 0, 125282416, 53440240, 0, 44236624, 4135486, 0, 258950240, -65881764, 0, -52624670, 3326480, 0, 15266532, 94565508, 0, -17097640, 95162408, 0, 102626688, -80915094, 0, -9050132, 34799392, 0, 105052590, 145204412, 0, -39489543, 235764736, 0, -166266096, -41617672, 0, -35316432, -10268096, 0, -47695832, -61406028, 0, 76533992, -176982116, 0, -17359440, 15377866, 0, 49126796, 102132228, 0, 110577824, 144783460, 0, 77956296, 62579684, 0, 57904392, 35358258, 0, 22515168, 29804160, 0, -96055592, 67857534, 0, 97582194, 167301640, 0, 122085344, -230644, 0, 16576528, -116763552, 0, -21609996, 107044360, 0, -126618480, -299160342, 0, -20218256, -115893236, 0, 38037486, 34838528, 0, 196316524, 37586928, 0, -2396066, -68460600, 0, -22556560, -55681096, 0, -39217096, -39467264, 0, 149420090, 25879928, 0, 8027056, -57338784, 0, 129545748, 78138920, 0, -37205124, -2785840, 0, -23736762, 84444922, 0, 10575368, 10671732, 0, -96645984, -243836100, 0, 738628, 131753080, 0, 131432460, 175395624, 0, 61043910, 76738924, 0, 195163956, 21570012, 0, -6834064, -173569632, 0, 5482832, 25986168, 0, -159186800, -29453662, 0, -90909280, -144264680, 0, -31846302, 21269840, 0, -17723976, -171820692, 0, 7018722, -94784918, 0, -117714680, -89019200, 0, -105569982, 88222680, 0, 4522788, -29806096, 0, -28659104, 240028584, 0, -67011264, 52060268, 0, 3073140, 20418640, 0, 33155662, -20379122, 0, 113053357, 11354336, 0, -252385168, 29489400, 0, 7848824, 128512960, 0, -364577292, 82322446, 0, 161931240, -43374016, 0, 19506800, -18810362, 0, -3693096, 102524672, 0, -23827116, -91268100, 0, -73248512, -121088648, 0, -77577724, -19876626, 0, -50627722, 132029200, 0, -34193200, -37730396, 0, -78357952, -80546008, 0, 43056640, 150047232, 0, 192582536, -229398532, 0, -285867760, -48843012, 0, 201232800, 81420848, 0, 29589440, -284814144, 0, 105163342, 97241888, 0, 38463590, -112542712, 0, 21671792, -29790864, 0, -116561520, 33256360, 0, 26989712, -150489448, 0, -155284192, -31327792, 0, 2914862, -129136952, 0, -84985200, 15887886, 0, -211745460, -50647600, 0, 170802902, 96411432, 0, -20061114, -200747724, 0, -28607616, -13065930, 0, 100867688, 39346576, 0, 39500920, 15245472, 0, -28341952, -275783976, 0, 43713032, 159924006, 0, 181577650, -26441536, 0, -93325720, 140619984, 0, 56006400, 106846722, 0, 34234720, -222466466, 0, -12822650, -352141616, 0, -117182864, 110781266, 0, -307234486, -6060104, 0, 100147216, -369657506, 0, -447534, -94354080, 0, -387234480, 303405572, 0, -196688768, 49467312, 0, 61386400, -27744480, 0, 64460476, 134870364, 0, -13014772, -278534152, 0, -103248404, 335269988, 0, -107956808, 362029302, 0, 350764920, -85642176, 0, -148615310, 162434378, 0, 182033076, 119776000, 0, 77616560, 612494, 0, -107021860, 202681584, 0, -107319024, 24538512, 0, -241903464, 236305008, 0, 7563968, -33305840, 0, -337803876, -7356400, 0, -67128120, 5066388, 0, -20139476, -217457230, 0, -36418592, -300738454, 0, 46707694, -827920, 0, -106679332, 184738948, 0, 79563752, -51198260, 0, 4418208, -135633144, 0, 48697936, -185053184, 0, -29381712, 79344830, 0, 125065152, 32032772, 0, -158374000, 263533544, 0, -137577606, -83872672, 0, 84191736, -196551142, 0, 16010964, 152422164, 0, -207034276, 139916828, 0, -313775080, 184686480, 0, 361399668, 23218092, 0, 107451346, -25507640, 0, 128693056, 122229836, 0, 310015464, -117541992, 0, -574228, -239107504, 0, -249554160, 4879496, 0, -155735820, 55201598, 0, 127334048, -221672320, 0, -103843440, -53148632, 0, 144275322, -204438530, 0, 223409520, 17549244, 0, -139543644, 54853328, 0, 12233108, -101627142, 0, -52053600, -32632520, 0, 127708084, -192337744, 0, 57693076, 43795920, 0, -223509160, 349548060, 0, 11324760, -228753154, 0, -70455744, -28108904, 0, 6742584, 115453888, 0, -84760484, -157882922, 0, 11142272, -266930800, 0, 125020496, 36613698, 0, 345447292, 325837440, 0, 109296612, -113172114, 0, 16621854, 19588016, 0, -124952000, -53519458, 0, 140409200, -621112, 0, 277468464, -43257388, 0, 63794035, 188880750, 0, 15846168, 15754720, 0, 209701696, -218860800, 0, -47313816, -155278156, 0, 118684466, 328732432, 0, -119324864, 219056442, 0, 180686054, 4076192, 0, 31234276, 136046772, 0, -12159180, -162148336, 0, 367955152, 379649642, 0, -11403828, 116715840, 0, 35462622, 77614736, 0, 262226040, -251227930, 0, 9105600, 128973630, 0, -33269406, 154332672, 0, -208169018, -137564152, 0, 74825532, -41704936, 0, -410001336, 372980520, 0, -107259024, -243353520, 0, -102961944, 49376710, 0, 8053372, -355396140, 0, 160562560, 203306798, 0, 140123934, 16657152, 0, -57073296, -60961828, 0, 23512170, 238827832, 0, 143119588, 67731108, 0, 141486266, 11783552, 0, -229313492, -352771220, 0, 31825794, 260884096, 0, -261363600, 56234988, 0, 160816, -93534588, 0, 412377914, 264272260, 0, -105510180, 260237824, 0, -62845824, -26446284, 0, -225610712, -57537600, 0, -84454220, -314493856, 0, 259330162, 64283004, 0, 194728448, 15560838, 0, 136626836, -292270464, 0, -287517910, 377383714, 0, 246631924, 333690432, 0, 56672432, 20806650, 0, -128394396, 281064352, 0, 22191584, -119301026, 0, 419298002, 222615880, 0, -77573920, 30800496, 0, -96583680, -10142352, 0, 528079340, -215176100, 0, 217768728, 85089312, 0, 121490160, 93981420, 0, 108594034, -107011200, 0, 389178032, 60877256, 0, 108438976, -400626136, 0, 9293472, 264125308, 0, -92053696, -151684068, 0, 119758590, 68888154, 0, 50513971, -210836836, 0, -429949520, -328013360, 0, 47938672, 166774528, 0, -252689338, -124466906, 0, 248935896, 278276168, 0, -43063280, 3183508, 0, 77592604, 56924032, 0, 63363504, -344799996, 0, -310996582, -310152608, 0, -176031600, 90465932, 0, 37982188, 37022480, 0, 4932336, 49024902, 0, 44474022, 32758854, 0, 112344832, 4223850, 0, -30330000, -9360080, 0, 277762098, 150121176, 0, 22616144, 314507142, 0, -60992672, -678764376, 0, -187802576, 51910336, 0, 541854456, -373911252, 0, -5232868, 18661520, 0, 269612560, -110366778, 0, -48745128, 657956648, 0, -676424144, 397593140, 0, -225530296, 167523766, 0, -246698352, -9325056, 0, 41658200, -396875520, 0, 37715324, 287364314, 0, -320931856, -85561174, 0, -63609536, 53776116, 0, -107180422, 140955376, 0, -422220088, -222012490, 0, -198963680, -353432336, 0, 139532852, 95394724, 0, -41999750, 207742528, 0, 305721816, 8218544, 0, -61473412, -43259208, 0, -93690960, 80765252, 0, 162388728, -46700244, 0, -290934956, -17366772, 0, 152495034, 84698468, 0, 159738136, 99638124, 0, -124631176, -397332000, 0, -101113060, -22544952, 0, 422120088, -181046144, 0, -257450240, 211155922, 0, -214358424, 508390840, 0, -81045696, 92396404, 0, 258117512, -554060760, 0, 319704396, -56292724, 0, -32265654, -65925312, 0, -12811464, 249477048, 0, 327039964, 394817664, 0, -92338080, 440769108, 0, -603004858, -678165912, 0, 550929608, -8836290, 0, -636618524, -303640800, 0, 110305440, 194334000, 0, 331911626, -30893600, 0, 175382910, -264948968, 0, 64110972, -43416168, 0, 49164528, -39255780, 0, -122856416, 444142892, 0, -186625600, 133765786, 0, -309195252, -294415466, 0, 582879256, -161440938, 0, -14569718, 187801600, 0, -226776894, 361728888, 0, 264637442, -652854204, 0, -517962640, -21918752, 0, 128781760, 172604912, 0, -45029072, -21565612, 0, 8849104, 130062660, 0, 92777200, 255386224, 0, -457002800, -493636800, 0, 200903136, -97198932, 0, 371739050, -155225486, 0, 19245312, -338971704, 0, -189395052, 146281512, 0, -300274224, 276318332, 0, -257342820, 83228416, 0, -118473104, 80394246, 0, -61063416, -32776336, 0, -347533196, -600876720, 0, -33715660, -405846134, 0, -92789440, -100677416, 0, -807832170, -164046200, 0, 122504640, 261398536, 0, -815180886, 259756608, 0, 4477456, 161697814, 0, -26043012, -196129440, 0, 412195598, 181332914, 0, -113147824, 45346428, 0, 65931904, -94803092, 0, -594778582, -298783548, 0, -78588608, 10968736, 0, -254986876, -295211952, 0, -196253280, -415491240, 0, 266256484, -944960, 0, -638938028, -300031384, 0, 674691832, 598129460, 0, 300767920, -339685964, 0, -30728384, 27455912, 0, 8767512, 233575266, 0, -389099070, -77757710, 0, 185721844, 108677892, 0, 110404838, 147216960, 0, 45118200, 601206876, 0, 38482608, -45120094, 0, -198060800, -841001106, 0, 355798920, 42604800, 0, 39926884, -405475456, 0, 10920676, -198572586, 0, -345656556, -294957756, 0, 139706416, 289536992, 0, 179005824, 212887974, 0, -33816618, 257101168, 0, 149543200, -62119430, 0, -289187912, 78756664, 0, -228911436, -572793338, 0, -287705771, 184814424, 0, -587250672, 104041634, 0, -117652434, 161055280, 0, -374665216, 670017924, 0, 177933768, 134715680, 0, 156315248, 156093038, 0, 15415658, 181031744, 0, 20627376, -144772488, 0, -55304248, 408518832, 0, 710683920, 277579224, 0, -168709836, -2130944, 0, 475186256, -996168904, 0, 260656628, 321477400, 0, 6778880, -306726696, 0, -184989610, -136587976, 0, 212275004, -139612524, 0, -280910284, 170057998, 0, -296916656, -71817432, 0, -166728200, -79687200, 0, -145521816, -345355444, 0, 318486566, -20314456, 0, 308624160, -206821320, 0, -494127126, 328296696, 0, 564275120, -630681720, 0, 506341180, -257454832, 0, 362018704, 30889320, 0, -127897868, -137039328, 0, -42354768, -63604508, 0, 93689408, 800370220, 0, -567764720, 211653458, 0, -104735858, -51579616, 0, 30607200, -313110680, 0, 138373426, -249774990, 0, 432907220, -175240254, 0, -779767744, 104961240, 0, 199489392, 241636120, 0, -387304722, 128561144, 0, 172663584, 310397680, 0, 67674970, -635412064, 0, 277026832, 549908784, 0, -463060196, 55465804, 0, -33325888, -390887526, 0, 132095436, 301668384, 0, 984068336, -598440996, 0, 285592108, 431593680, 0, -58556480, 53713400, 0, 146268264, 1182540948, 0, 439312470, 273662872, 0, 343472634, -2778960, 0, -70045640, 831660910, 0, 204682440, -170294400, 0, 408517256, 34822826, 0, 38147760, -256814856, 0, 43639936, -91746586, 0, 190331924, -302412816, 0, -478859656, -147189576, 0, -395781308, -738504442, 0, -45001888, 455014634, 0, -811807044, 401501472, 0, -796079212, 54776240, 0, 93911686, -155904284, 0, -154256400, 751901322, 0, -284453976, 548793824, 0, -276492640, -478285494, 0, 789599447, 237346112, 0, 215514644, -313346556, 0, -731361306, 881054400, 0, 207710688, -139956216, 0, 266296544, 444880600, 0, 354952336, -207973504, 0, -515283084, 202728768, 0, 735419584, -372640652, 0, 684142368, 372720440, 0, 746691072, 204204896, 0, 368532504, -388902400, 0, 80857388, 18198286, 0, 142293838, 250934324, 0, -36919200, -132691136, 0, -385861422, 690765660, 0, -646125234, -71796900, 0, 199600480, -1202313964, 0, 1245323944, -67041624, 0, 332957618, -531820000, 0, -692497576, 250879252, 0, 176363310, -617702176, 0, -32185728, -95383512, 0, 649913416, -852527728, 0, 252731016, 647732414, 0, 82582892, 112726286, 0, -262567544, 419101680, 0, -192783460, -149054880, 0, 138688808, -593006670, 0, -5194360, -23393632, 0, 345486640, -64196608, 0, -470983340, 727810816, 0, 1084817480, 187799018, 0, 56179604, 236277648, 0, 533818496, -370362756, 0, 82202762, -584787760, 0, 297661344, -140819800, 0, 255915594, 26249304, 0, -663617344, 220401436, 0, 411959804, -413245168, 0, 465078492, -225081768, 0, 795132762, 473189472, 0, 77900160, -512126490, 0, 585651750, -216136768, 0, 19738048, -823485700, 0, -282765116, 266275944, 0, -100735920, 234191160, 0, 719697984, -281059264, 0, 936541550, -287311716, 0, -138720134, 789164400, 0, -1114403508, 892200482, 0, -649559236, -55084080, 0, 992200602, -5524592, 0, 330547252, -300591732, 0, 190393344, 515958498, 0, 260443274, 1032510696, 0, 578063354, -50980338, 0, -608808164, 200961212, 0, -265591480, 684106350, 0, 282675546, -17706688, 0, -498562858, 468047528, 0, 580029664, 1359581722, 0, 793615360, -123250660, 0, -1143941706, 34887860, 0, 107504784, 616749918, 0, 246744114, -134664302, 0, -10019776, 1760376948, 0, 98400348, 812323440, 0, 138908270, -460922364, 0, 240266976, -92374352, 0, -7427024, -1163205494, 0, -709542792, 119166452, 0, -717770104, 344057088, 0, -304361544, -37107296, 0, 117234528, 481141894, 0, 622851840, 44015104, 0, -449847180, -693909690, 0, -406183554, -32328376, 0, 511982320, -100387734, 0, 18232560, -89612720, 0, -630315208, -966172878, 0, 135399984, -691840660, 0, -117448504, 16230778, 0, -467525200, -122762000, 0, -1360760164, 289431608, 0, -438032784, 541963438, 0, -380851456, 608042700, 0, -589262064, -36662752, 0, -317041616, 792107248, 0, -358522974, -1212745600, 0, -238712308, 780403232, 0, -40116084, 633786752, 0, -1718400120, -842490270, 0, 166000974, -793016496, 0, -278777760, -953383048, 0, -809410192, 130529216, 0, 514564944, 17365026, 0, 21317204, -211588364, 0, -146378372, 332179138, 0, 21938796, -790347600, 0, 404018900, -1267806792, 0, -399419002, -834499736, 0, -480821072, -103496778, 0, 185897764, 24033432, 0, -89441568, -474101162, 0, -913522384, 59878568, 0, 1244099776, 491401116, 0, -254521564, -76062592, 0, -741981806, 531357000, 0, 706313720, 605855550, 0, 170873520, -252627140, 0, 364189492, 362934668, 0, -492142036, 16782982, 0, 25749604, 581586636, 0, -212116256, -685828166, 0, 1082539980, -660201120, 0, 647926870, -311055070, 0, 482663528, -211397728, 0, 929069440, 528521108, 0, -105580908, -1099727928, 0, 484369608, -570985460, 0, 121781724, 845180930, 0, -484883904, -38744416, 0, -1176218246, -866877952, 0, -57966836, -172421118, 0, 2684740, -25527668, 0, 276847040, 213169304, 0, 107409422, -397458464, 0, -1133093340, -199581649, 0, -315976008, -974429416, 0, -447795832, 1065857584, 0, -385214340, 717880560, 0, 347823052, 47457360, 0, 556555824, 678664084, 0, 45981248, -1271510204, 0, -88736456, 34066440, 0, -123940468, -587268616, 0, 1188485769, 33845384, 0, -266862912, 95597714, 0, 29896112, 290968064, 0, 1147400986, 385035832, 0, 1052575110, -657300432, 0, -1166609200, -230697748, 0, 410142602, -1825751280, 0, -74874576, -286126944, 0, 171801356, -439860960, 0, -568387608, 138132508, 0, -368417336, -140358000, 0, -1631247942, 40874124, 0, -438867892, 108587896, 0, 398787264, 153432184, 0, -285129170, 269483180, 0, -1343358726, 26516472, 0, 831140666, -911897654, 0, -108938736, 70254216, 0, 55950282, 540890448, 0, 2782680, 683346640, 0, -93855952, 124539016, 0, 134859680, 703328806, 0, -155595828, -970465568, 0, -1106063946, -10112248, 0, -313660900, -21737444, 0, -912607168, -259737290, 0, -306929340, 163914600, 0, -188044932, 358647936, 0, -203055196, -548183300, 0, 458536928, 339651534, 0, -21433104, 1167460628, 0, -378344224, 1288849128, 0, 208203848, 61754408, 0, -844803936, 566779786, 0, -859501940, -958079808, 0, -618841770, 223540296, 0, 172524740, -1118147196, 0, 19346000, 174891632, 0, -570658876, 319925680, 0, -32296144, -1568595736, 0, -1269652340, -75915056, 0, -434713544, 546835744, 0, -672678306, 208950800, 0, 182218968, -106957140, 0, 1147282336, 1584451100, 0, -247148800, 2481300, 0, 438026404, 2733120, 0, -236419048, 661239954, 0, -371768316, 510860400, 0, 59947028, 142090956, 0, -606829834, -600692352, 0, 1299073752, 706222462, 0, 377880812, 468605460, 0, -1104252640, -880603138, 0, -814859428, -761476136, 0, 174815448, -116823924, 0, 228952872, -1082550228, 0, -539173536, -366511648, 0, 948568608, 65252400, 0, -570168708, -1179910782, 0, -593195796, 70786548, 0, 326897408, -497559018, 0, -145034448, -2007365040, 0, 1149355426, 23592712, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "23.6.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [1, -1, 0], [0, 0, 0], [2, -6, 4], [21, 3, -2], [0, 0, 0], [-87, 17, -4], [112, -8, 16], [0, 0, 0], [-50, -2, -8], [-37, -3, -28], [0, 0, 0], [-324, 45, -99], [-592, 180, -60], [0, 0, 0], [88, 8, -128], [269, 57, 146], [0, 0, 0], [498, 40, 200], [-544, -40, 88], [0, 0, 0], [454, 78, 68], [529, 0, 0], [0, 0, 0], [-2391, 86, -88], [-423, 747, 18], [0, 0, 0], [-2908, 1068, -472], [704, 745, -523], [0, 0, 0], [-1471, -914, 479], [-1968, 464, -288], [0, 0, 0], [-3656, -276, -520], [-460, -160, 148], [0, 0, 0], [2053, -1117, 1662], [-3622, -698, -560], [0, 0, 0], [1144, 232, 240], [3258, -1171, 1847], [0, 0, 0], [-4510, 2050, -1150], [-1888, -104, 448], [0, 0, 0], [529, -529, 0], [-7613, 682, 1021], [0, 0, 0], [-949, -4306, 1428], [-3997, 2997, -168], [0, 0, 0], [-14958, 2682, 144], [-7006, -4444, -534], [0, 0, 0], [130, -14, -840], [-12600, 3432, -1408], [0, 0, 0], [-16559, 4067, -1934], [-17710, -934, -1980], [0, 0, 0], [-23320, 1322, -42], [21985, -4057, 2698], [0, 0, 0], [-16064, 4608, 2816], [351, -351, -2250], [0, 0, 0], [-21949, -4323, -1436], [4124, 1492, -2528], [0, 0, 0], [2748, -636, 344], [-31515, 1628, -2227], [0, 0, 0], [-26170, 3241, -21], [15646, -10962, 1144], [0, 0, 0], [11316, -28, -2488], [-368, -532, 876], [0, 0, 0], [20036, -4778, -6662], [7536, 816, -4224], [0, 0, 0], [16043, -12807, 990], [-9839, -5867, 13758], [0, 0, 0], [3856, 508, 4476], [-56060, 17060, -5900], [0, 0, 0], [-19256, -2024, -2656], [-4304, 5964, -8666], [0, 0, 0], [43587, -14229, 6984], [1058, -3174, 2116], [0, 0, 0], [-44413, 8981, -4770], [5298, 894, 5644], [0, 0, 0], [-90313, 3351, 618], [121157, -23437, 14368], [0, 0, 0], [-24034, 16566, -8836]]}