# Stored data for newform 825.6.a.b, downloaded from the LMFDB on 25 April 2024.
{"label": "825.6.a.b", "space_label": "825.6.a", "level": 825, "weight": 6, "hecke_orbit": 2, "hecke_orbit_code": 4503599728034617, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 907803729091212453, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-2, 1]]], "qexp_display": "q+2q^{2}+9q^{3}-28q^{4}+18q^{6}-148q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 29700, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 132.31665134570903, "hecke_ring_index": 1, "level_radical": 165, "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": [825, 1, [551, 727, 376], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "0.972", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.898", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.626", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [11, -1]], "trace_display": [2, 9, 0, -148], "traces": [0, 1, 2, 9, -28, 0, 18, -148, -120, 81, 0, 121, -252, -574, -296, 0, 656, 722, 162, 2160, 0, -1332, 242, 2536, -1080, 0, -1148, 729, 4144, 4650, 0, 5032, 5152, 1089, 1444, 0, -2268, -8118, 4320, -5166, 0, -5138, -2664, -8304, -3388, 0, 5072, -24728, 5904, 5097, 0, 6498, 16072, 28746, 1458, 0, 17760, 19440, 9300, -5860, 0, -53658, 10064, -11988, -10688, 0, 2178, -30908, -20216, 22824, 0, -69648, -9720, 18446, -16236, 0, -60480, -17908, -10332, -25300, 0, 6561, -10276, 17556, 37296, 0, -16608, 41850, -14520, 132570, 0, 84952, -71008, 45288, -49456, 0, 46368, -70658, 10194, 9801, 0, -101998, 12996, -130904, 68880, 0, 57492, 141612, -20412, -239810, 0, -73062, -97088, 42726, 38880, 0, -130200, -46494, -11720, -106856, 0, 14641, -107316, -46242, -140896, 0, -23976, -51788, -186240, -74736, 0, 53652, -30492, -319680, -61816, 0, -86640, 228862, 45648, 374920, 0, -222552, -139296, -69454, 53136, 0, 36892, 45873, 227304, -65830, 0, 154052, -259200, 58482, -35816, 0, 144648, -287678, -50600, 258714, 0, -375328, 13122, -105124, 143864, 0, 35112, -150528, 159840, -41817, 0, 174960, 232512, 2166, 83700, 0, 79376, -52740, 265140, 672780, 0, -526778, 169904, -482922, -304320, 0, 90576, 87362, 692384, -107892, 0, -305608, -96192, -116434, -141316, 0, -142716, 247742, 19602, -513360, 0, -278172, -203996, -688200, -181944, 0, -261808, 205416, -376544, 261360, 0, -620688, -804888, -626832, 283224, 0, -87480, -744736, -479620, 166014, 0, -414428, -146124, 1318016, -762496, 0, 85452, 887412, -544320, -237450, 0, -161172, -558000, 914706, -92988, 0, 164080, -227700, -213712, 1408920, 0, -826358, 29282, 59049, 1502424, 0, -92484, -1239840, -603840, 158004, 0, -1603868, 335664, 306856, -103576, 0, -30464, -397618, -149472, 1201464, 0, 376650, 107304, -2131664, -130680, 0, -639360, 1193130, 865424, -725810, 0, -1467868, 473632, 764568, 457724, 0, -639072, -1520998, 749840, 407592, 0, 464382, -445104, 415136, 1950144, 0, -138908, 760424, 417312, -898573, 0, -635922, -516488, 2593206, 91746, 0, 974160, 88209, -131660, -1455664, 0, 1228992, 308104, -917982, 1416960, 0, 116964, 930832, 501424, -1178136, 0, 2485272, 619920, -1317194, -575356, 0, 708400, -2255398, 517428, 562650, 0, 1274508, -750656, 1559520, -183708, 0, -210248, -2158290, 616560, 3659744, 0, -3170708, -491568, -657558, -301056, 0, -873792, -1276298, -83634, 384534, 0, 608872, 349920, 1733080, 996480, 0, 4332, -3693028, -1171800, 1709190, 0, -418446, 623392, -4368594, -105480, 0, -3711960, -961704, 1345560, -3512840, 0, 2189501, -1053556, 131769, -2378656, 0, -965844, 2152592, 1663616, -416178, 0, -4254408, -1268064, 2242466, 174724, 0, 2967360, -2669100, -215784, -2409860, 0, -466092, -611216, 1010656, -1676160, 0, -232868, -672624, 1978424, 1277790, 0, 1830992, -611640, 482868, 495484, 0, -274428, -5453998, -1026720, -2877120, 0, -1489798, -556344, -2888368, 2855944, 0, -1376400, -982278, -779760, -4398990, 0, 2059758, 3665312, 867280, 410832, 0, -2957248, 3374280, 522720, -280420, 0, 817462, -1241376, -2002968, -3449520, 0, -1253664, 7941384, -3965136, -625086, 0, 1885992, 478224, -5840674, -1489472, 0, 6714680, 5477760, 332028, -509540, 0, 412857, -828856, -4102684, 2045736, 0, 2636032, -592470, 1581824, 513410, 0, -621698, -1196328, 1386468, 1774824, 0, -2332800, -1227378, -474900, 526338, 0, -6409998, -322344, -6630304, 3050400, 0, 1829412, 4147692, 1301832, 4574384, 0, -2589102, 703200, -1004784, -455400, 0, 2991968, 2328426, 2817840, -5051320, 0, 4659732, -1652716, -3377952, -409948, 0, 118098, -2662208, 6438960, -946116, 0, -5546588, 1294776, 3357300, -2479680, 0, 3300992, 10307904, 316008, -6820, 0, -1354752, -3207736, 451136, 1438560, 0, 613712, -376353, 1450064, 393390, 0, -2730008, 5898752, 1574640, -795236, 0, 2092608, -2992088, 2402928, 19494, 0, 3284322, 753300, 1682656, -1502256, 0, -4263328, 3633104, 714384, -5047, 0, -474660, 8951040, 2949212, 2386260, 0, 3708960, 6055020, -1451620, 616737, 0, 9481582, -2935736, -4741002, 3719744, 0, 1529136, 6092392, -6408136, -4346298, 0, 10044000, -2738880, 3744400, -3041996, 0, -10497760, -8495938, 815184, 4766496, 0, 786258, 928764, 7022156, 6231456, 0, 830272, -971028, 8357760, 9418470, 0, 7296992, 1944712, -2750472, 1520848, 0, -865728, 3295902, -1797146, -1047906, 0, -2598288, -1271844, 3478266, -2213520, 0, 5186412, -4398268, -1284444, 10869120, 0, 2229678, -5325408, -9217814, 176418, 0, 1843240, -4620240, -2911328, 3771400, 0, 4197242, 2457984, -2503548, -4313456, 0, -1835964, 1001332, 11128320, -6193800, 0, 14193872, -1637496, 7382386, 1861664, 0, 2148960, 15402462, -2356272, -7124020, 0, 1848744, 4970544, -19620360, -3388896, 0, -2634388, 2352240, 8054984, -5861196, 0, 11669632, 3036000, -5586192, -4510796, 0, -7243992, -2925678, 1125300, -5641488, 0, -11027118, 2549016, 9560236, 10509184, 0, 3119040, 10994152, -787320, -709060, 0, -6702624, 2943472, 295346, -4316580, 0, -3370528, 1494126, 7319488, -16561340, 0, 1970422, -6341416, -3729852, -2106720, 0, -1315116, 11792400, 4214784, 11862144, 0, -6492618, -6862464, 1637326, -2552596, 0, 1170876, 6358782, 769068, 10457384, 0, 7986708, 1217744, -11103284, -4898880, 0, 3466160, -2137050, -5447424, -16500204, 0, 17018852, -60648, -1450548, -7386056, 0, -5022000, -3709636, 3418380, 8232354, 0, 15802082, -836892, -17534880, -1293248, 0, -8737188, 15095704, 1476720, 12483350, 0, -2049300, -15908400, 12761152, -1923408, 0, -18837840, 12680280, -7025680, 2007240, 0, 19373792, 4379002, -7437222, 14749784, 0, 263538, -6973008, -10194240, 531441, 0, -5995488, 13521816, 23496546, 4305184, 0, 13065472, -3739868, -832356, -13990120, 0, -11158560, -8508816, -24274504, -5434560, 0, 4484932, 1422036, -2446136, -20958576, 0, 15365992, -16221568, -14434812, -5338200, 0, 3020976, -20760518, -4819720, 2761704, 0, 5838102, -932184, 35491880, 8557024, 0, 2021312, 3363640, -274176, -13919710, 0, -3578562, 3260152, 4178826, -1345248, 0, 8478960, 10813176, 2555580, -11098080, 0, -8427408, 3661984, 3389850, 3343632, 0, 965736, -9667048, -6936776, -19184976, 0, -6323448, -1176120, 30799692, -10907996, 0, 14374080, 5798842, -5754240, -17853616, 0, 10738170, -2979596, 2231966, 7788816, 0, -5776736, -6532290, 12239760, -19254330, 0, -13193768, 19269600, -13210812, -1964556, 0, 4262688, -17936640, -8797980, 6881112, 0, 13377922, 4119516, 18861336, 15708480, 0, 1734560, -16267988, -5751648, -21809810, 0, -13688982, 6134912, 3680034, 6748560, 0, -7318080, 3668328, -560840, 11777080, 0, 1111351, 1634924, 4179438, 17379264, 0, -4005936, -2166868, 18857376, 3736224, 0, -20587248, 17551296, 14399266, 15882768, 0, -16993440, -6276038, -1250172, -4717380, 0, 6843816, 3771984, -7539264, 3755808, 0, -11681348, -8087157, 20852608, -3061300, 0, 17741192, 28777200, -5723298, 10955520, 0, -4648392, 10433082, -1019080, 23338854, 0, 39107642, 825714, -12928204, 11603984, 0, -8205368, -33646568, 8767440, 7664624, 0, 793881, -36904448, -53412480, -1184940, 0, 27563520, -13100976, 1026820, 23398800, 0, 20754612, -1243396, 11060928, -5127120, 0, 2772936, 41962932, -24847536, -8261838, 0, -1925208, 12752640, 2124276, -2454756, 0, 6648600, -7940496, 1052676, -17248100, 0, 8377488, -12819996, 39977952, 4512816, 0, -13260608, -10603224, 23956800, 2511450, 0, 11009520, -25611768, 22367448, 8295384, 0, 5579280, -17985338, 9148768, -11854746, 0, -32258598, -5178204, -13029968, -3844160, 0, -2009568, -44165868, 6375600, -10588004, 0, -20298582, 12822720, -18748774, 4656852, 0, -39449760, 5063850, -10102640, -33871576, 0, -3308127, 9319464, 11470572, 23138024, 0, -6755904, -10867348, -1756920, 14035680, 0, -47912308, -1653372, -55488160, -5324416, 0, -35199648, -40138458, -1892232, 16040970, 0, -19424610, -11093176, -3226824, 5549040, 0, 6714600, 32937696, 34715520, -21058944, 0, -5953448, 25924864, -28536372, 20615808, 0, -4424112, -32078318, -13640, -5918022, 0, 10279192, -2709504, -4230920, 44908304, 0, 902272, 62091360, -7864128, -23533270, 0, -11486682, -8591968, 11989386, -752706, 0, 6214560, 3460806, 786780, 46036700, 0, 26382622, -5460016, 5479848, 12772352, 0, 3149280, 14522200, 11133304, 15597720, 0, -20996488, 8968320, 7675966, -5984176, 0, -33640992, -38741076, 38988, 3892160, 0, -33237252, 6568644, 9742840, -10546200, 0, 3365312, 15382710, -6438240, 36495410, 0, 24366512, 59686592, -3766014, 7266208, 0, 5610528, -22799696, -10094, -39317346, 0, -55875418, -949320, -42417284, 38361600, 0, 5898424, -8549618, -33407640, 58410790, 0, -8655336, -20275648, -37748700, 12110040, 0, 20322680, -31615560, 1233474, -10077144, 0, -62710208, 18963164, 19705509, 41100304, 0, -9482004, -17790008, -7716736, 1185921, 0, 5100452, -21407904, -21094614, 12184784, 0, -27463440, 59023002, -8692596, 42576344, 0, 19373328, 20088000, -48452904, 14972544, 0, 7488800, -3745602, 42587944, -14732250, 0, -12341758, -44990400, -38289672, -16991876, 0, -11412576, 74139762, 9532992, 20182194, 0, -12657600, 1572516, -7014804, -13002696, 0, 14044312, 12925992, 26706240, -62055310, 0, -24021900, -11623808, -15839384, -1942056, 0, -45689088, -21688740, 18836940, -22315576, 0, 15558352, 14593984, -4194828, 8334480, 0, -5500944, -40849776, -21291872, 9095904, 0, 14076152, -15085440, 40897006, 6591804, 0, 25160044, -76095180, -2095812, -115901280, 0, -6053616, -5196576, 4959596, 17805816, 0, 6956532, 11500110, 12100576, 22278144, 0, 33200172, -72609768, 16478928, -8796536, 0, -5504760, 17135052, 21738240, 4345812, 0, -13836378, 4459356, 6188916, -41823936, 0, -18435628, -13630788, -2469852, -23891700, 0, -49085982, 7899600, 406806, -9240480, 0, 40758592, -25894080, 7542800, -29017010, 0, 36013442, 8394484, -13408182, -34411776, 0, -5007096, -50285856, -18486240, -25995312, 0, -320568, 25703496, 47221106, 2002664, 0, -23086080, 33261522, -12387600, 72899856, 0, -8840502, 28387744, 55440136, -7017840, 0, 14764772, -39590910, -26063296, -71711070, 0, -59816148, -11747648, 18537822, 30804924, 0, 32987808, -40154118, -14248040, 7805520, 0, 13318012, 3697488, 5169846, -69587616, 0, -39240720, -38613600, -26615232, 63758890, 0, 30368520, 36881432, -99571440, 4704480, 0, 34521360, -2523780, -11722392, -13139980, 0, 40557692, 23339264, 7357158, -16596800, 0, -11172384, 77963144, 63151144, -18026712, 0, -25854416, -31045680, -66761280, -5851356, 0, -15754200, -35737078, -11282976, 7982160, 0, 71472456, -22054236, 6599196, -35686224, 0, 19120472, -5625774, 45039360, -7013130, 0, 17815972, -43666560, 16973928, 21988304, 0, 4304016, -4325298, -1418120, -52566066, 0, 16146102, -13405248, -31641024, 12614880, 0, 590692, -71880988, 60432120, -12929576, 0, 49299840, -26470976, 58546852, 2988252, 0, -102472832, -4585860, -33122680, 40657560, 0, -51568198, 3940844, 3715713, 88779824, 0, -7459704, 55169692, 11516736, -36924156, 0, 1771561, 18411624, -41785728, 23584800, 0, 18063360, 45229984, 23724288, 75138896, 0, -5332230, -12985236, -18266600, 14236416, 0, 3274652, 4620690, 35736344, -150439680, 0, 17232232, 5018040, -5595282, 12717564, 0, -10766952, -14860960, 20914768, 12478212, 0, -66366378, 15973416, -114985200, -17048416, 0, -22206568, -66478368, -20995200, -3442033, 0, -11046402, -48526240, -33408174, -4274100, 0, -42782208, 4737042, -33000408, -36665816, 0, -62411498, 34037704, -57689982, -259920, 0, -2901096, 39843360, 103404784, -59672736, 0, -81285288, 27453600, 75977280, -7419272, 0, -47857320, -6266348, 16464708, 31955700, 0, 37329228, 31604164, -136076688, 11716488, 0, -35069760, 41169456, -22535040, 115322730, 0, 12675432, 122320632, -23301918, 30191408, 0, 6328800, 137650940, 24966700, -9043056, 0, 23701050, -4098600, 297376, 86965920, 0, 25522304, 98508732, 26927712, 83844350, 0, 20955834, -80733600, 12507246, 25360560, 0, 98359520, -45461880, 4014480, -39082320, 0, 6491892, 38747584, 41937588, -61306028, 0, -14874444, -100561948, 63213360, -30401568, 0, 111847972, -3689532, 55651586, -13946016, 0, 55728512, -124431296, 1062882, -129032240, 0, -23959872, -11990976, -38681280, 57950640, 0, 46993092, -8515044, -60272576, -24524724, 0, 82771852, -27104768, -49919292, -7479736, 0, 11652984, 91861824, -27980240, 30215700, 0, 145504502, -22317120, -66544324, 119123424, 0, -48549008, 68868752, 29708928, 17175330, 0, 92771136, -62789048, 57198486, 2844072, 0, -10483440, -61380, -41917152, 150882580, 0, -54648000, 30731984, -12192768, -127398656, 0, -28869624, 27692302, 74734800, 4060224, 0, 75086872, 12947040, 95715540, -41521036, 0, 67476080, 41710284, 5523408, 25648104, 0, -3387177, 11676204, 61087436, 13050576, 0, 70983760, 3540510, 36672960, 45365320, 0, 103746752, -28298368, -24570072, 6727280, 0, 53088768, 133668900, -27839420, 14171760, 0, -78382688, -7157124, 49090896, 13972080, 0, 8357652, 61335344, 18833472, -32291730, 0, -26928792, -46351648, 134116346, 21626352, 0, -35778120, 175446, -22196160, 118972200, 0, -195066368, -16854816, 29558898, -51267776, 0, 6779700, 30707992, 26259744, 15143904, 0, 24228812, -13520304, -8403934, -19334096, 0, -29729040, 37920960, -38369952, -154222800, 0, 32697936, -12646896, 158209616, 6429456, 0, 61599384, -45423, 152711944, -131336976, 0, 67411872, 61603200, -4271940, 11597684, 0, 80559360, -100674478, -35707232, 26542908, 0, -24438298, 21476340, 35142600, 41714344, 0, 4463932, 47872752, 33380640, -104922790, 0, 54495180, 80874304, -74846274, -13064580, 0, -66910688, 5550633, -38508660, 46316380, 0, 109146502, -26387536, 85334238, 82584000, 0, -26421624, 49871592, 27503784, -42669018, 0, -135376488, 33477696, -176627328, -35873280, 0, 123171720, -81663918, 13762224, -7965430, 0, 54831528, 26755844, 144649872, -57673224, 0, 37722672, -39116682, -85873024, -51015076, 0, 29726312, -24283840, 90396000, -32535976, 0, -24649920, 134854982, -43619620, 33699600, 0, 18640292, -27377964, 103386476, 106901760, 0, 7360068, -26905188, -94479840, -185495290, 0, -76463442, -31363200, -208520160, 7336656, 0, 7851760, 42898464, 23554160, 46779056, 0, -89457157, 2222702, 7076322, -22888936, 0, 8358876, 122300984, 74482560, 63199404, 0, 286351200, 56083104, -46795014, -4333736, 0, 148099392, -107436258, 7472448, -193434020, 0, -8739252, -41174496, -30796248, 75219840, 0, 28798532, 84766230, -222358752, -89251650, 0, -27249000, 92897472, 65672928, -12552076, 0, 17502408, -73642556, -9434760, -24754248, 0, 167522082, 13687632, -171678824, -52807776, 0, -15078528, -34809038, -7791552, 183496320, 0, 29663118, 163538872, 234310206, -16174314, 0, 89368320, -9431154, -6122600, 200741904, 0, 160624622, 35482384, -23384592, -157315360, 0, -11446596, -123415428, -153377280, 31304394, 0, -94512688, -19921680, -189471274, 20866164, 0, 14267120, 237372464, 46677708, 174925700, 0, -39584412, 78215284, 42665952, -11559996, 0, -25856408, 97822080, 49731360, -249509700, 0, -45414688, 114875152, 20067102, -67293136, 0, -47928672, 75583942, 15329248, -82960326, 0, -131366788, 1587762, -163155584, -158161920, 0, -106824960, -31198788, 16589160, 134335750, 0, -41582160, 4508672, -12720004, -26201952, 0, -14375480, 33942600, 46797600, 58847464, 0, -175387718, 41509224, 37775178, 17407544, 0, 22121856, -215204080, 28028256, -22531932, 0, 46288932, -38821104, -41377446, 83925864, 0, -106489440, -64160800, -16523676, 102243864, 0, 9011988, -3850416, 167335736, 100154880, 0, 4248552, -55744200, 34366584, -29487520, 0, -18146608, 28494000, 127744848, -15880992, 0, -14737464, -18213888, -34496200, 66441474, 0, 315486272, 16754976, -152621280, 179479944, 0, 79955904, -7708568, 19340640, -78052027, 0, 138622158, 185648512, -173142820, -21206448, 0, -49699200, -64116180, 5022900, -5059857, 0, -45259858, 22019040, 16638696, -109764720, 0, 44734896, -17871088, -116135376, -176583240, 0, 120380832, -30500064, 5600046, -35970676, 0, -128082752, 236065422, -23709492, -271292960, 0, 21170160, -64517196, 107419880, 72494856, 0, -26059936, -52750764, -30190720, 37015510, 0, -270007056, 28133952, 105026688, -88331736, 0, 27324000, 217244464, -21176008, -50275728, 0, -16062778, -40597164, 262086, -70097536, 0, -37497548, -227079908, -65195928, 44522016, 0, -26331102, -169070400, 113602386, 10127700, 0, 141436960, -50773392, -67743152, -220315680, 0, 30848172, -6616254, -99244062, -130472496, 0, 22941144, 127052464, 99162960, 86042124, 0, 49587132, 94582656, -323219094, -21734696, 0, 9604496, 37786420, 28071360, 225107704, 0, 98947368, -95824616, -143722200, -7085880, 0, -110976320, -6381540, 74541824, 113215010, 0, -186342488, -276446016, -60323616, -80276916, 0, 26491248, -282752640, 32081940, 2658114, 0, -233360028, -38849220, -88425848, 155304464, 0, -6453648, -68728536, -30334752, 81406380, 0, 13447134, -94004400, 65888186, 65875392, 0, 148780800, -149052060, -42117888, -6181500, 0, -61440128, -11906896, 17733798, -53782016, 0, -57072744, 83215552, -288621312, -33568668, 0, -63740138, -18960480, 18658566, -64156636, 0, 190960, -15189858, -11836044, -121146260, 0, 106131600, 20558384, 101467196, 37933056, 0, -8461840, 106759296, 192464160, -26188386, 0, -257898748, -12631808, -58433562, 124182720, 0, -61762176, 26803502, -47066540, 14735934, 0, 205341312, -22973364, 132988804, -36822720, 0, 23978772, -161410308, 10537884, 336891870, 0, 57229038, -33972928, 305881920, 6921612, 0, -11014920, 94116456, 92073400, 153149400, 0, 165127172, 52765244, 71880372, 76440224, 0, 10959696, 336197520, -163215360, -99929556, 0, -383794488, -44089920, 168439266, 29044400, 0, 47714160, 10570802, 31195440, -323863200, 0, -19233450, -41992976, -143630904, -49026816, 0, 15351932, -148501836, 83778464, 76395070, 0, -517989600, -144175680, 153169668, -77482152, 0, -545832, -155529056, 7784320, -13054932, 0, 304023942, -66474504, 275792836, -91961016, 0, 19485680, 60922272, -45198000, 283145330, 0, -33386724, -47114368, 215438272, 30765420, 0, 35195712, 74091186, 72990820, -60146380, 0, -36978568, 48733024, 142218738, 255799680, 0, -7532028, -42325488, -101726912, -157813920, 0, -112389008, -11639232, 44423246, -45599392, 0, 141316, 85773900, -78634692, 60341176, 0, 135861336, -111750836, -14088514, 13290480, 0, -84834568, 112350150, -209710080, 377809070, 0, 127954672, -82577936, -18443700, -17099236, 0, -143175600, -140245978, 116821580, 114850368, 0, -181215118, -17310672, -99885704, -159238016, 0, -75497400, 92288160, -169540560, -137763136, 0, 114122520, 87097200, -44521774, -63231120, 0, -17268636, 18065160, -20154288, -37390936, 0, 184870802, -125420416, 174364128, -265484296, 0, 39411018, 29976782, 176144160, -66934998, 0, 86403072, 132748056, -147696948, -35580016, 0, -134465280, -367820256, 2371842, 148304700, 0, -62757072, 10200904, 47571480, -91748160, 0, -42189228, 4782969, -170586976, -62116560, 0, 194944712, 150133472, -53959392, 118046004, 0, 121696344, 237125140, 85152688, 211468914, 0, -350468736, 38746656, -338344724, -281232000, 0, -96905808, -197609928, 117589248, 382128977, 0, -33658812, -104843200, 132764126, -7491204, 0, 182519760, -125911080, -29464500, 333798904, 0, 125855182, -24683516, -100427040, 245947520, 0, -76579344, 38736744, 237886264, -218470536, 0, -179188688, -48911040, -83272200, 148279524, 0, -133461888, -100747398, 40364388, 324981020, 0, 12798324, -25315200, -125732284, -22015224, 0, -14029608, -188627184, -55725840, -1243284, 0, -116743008, -196620368, 138293928, 25851984, 0, -145994112, 435595644, -124110620, -129913308, 0, -230808960, -48043800, 92820272, -49816320, 0, -31678768, 80157252, 27188784, 263203390, 0, -186844662, -358826496, -217674454, -43377480, 0, -263717160, 24855336, -44631152, -238706784, 0, 117097162, 31116704, 52542918, -204315776, 0, -8389656, -69973628, -45561824, 319426920, 0, -117645000, 77013216, 387703306, -81699552, 0, -91250880, -143307978, 18191808, 31624560, 0, 30272760, 28152304, -126038616, -2467584, 0, 81794012, -125277390, -92285256, -235602150, 0, 153836552, 107828760, -32207058, -152190360, 0, 29341368, 469264784, -231802560, 37609434, 0, -75103248, -12107232, -258666928, 72752064, 0, 9919192, -386175720, 76310640, 165238364, 0, 97318584, -97391448, 60555826, 23000220, 0, 95033792, -99882720, 44556288, 86399980, 0, -168311018, 66400344, -75846672, -311184720, 0, 32957856, 292265332, 123151504, 30508650, 0, 203734272, 30092688, 302370572, 34270104, 0, -304335360, 352670202, 8691624, 188892104, 0, -87003432, -27672756, 270692240, -62430984, 0, 12377832, -172664784, 86765184, -331972544, 0, -358248208, 258098792, -56911032, -27261576, 0, -10585080, 366087222, -47783400, 277197228, 0, 528607662, -98171964, -399554364, -43184480, 0, 813612, -90113056, 129366720, 85381630, 0, 52189578, 174679680, -82516854, -51788160, 0, -105599200, -160682544, -58034020, 341039640, 0, -342161119, 72026884, 96643530, -117522776, 0, -26816364, 81635400, -147479040, 20087694, 0, -551371948, 70099344, -111862080, -100571712, 0, 101058112, 54797122, -51990624, 30108680, 0, -58790610, -641136, -300629744, 110157840, 0, 94442212, -173288970, -28037296, 546568144, 0, -50145788, -402278400, -118743912, 66523044, 0, 173426400, 132893122, 145799712, -118897308, 0, -564961218, -17681004, -252960120, -397428416, 0, 110880272, -226842528, 38364192, -127309600, 0, -161429760, -206706808, 159479936, -79181820, 0, -111699840, 61930008, -143422140, -268882700, 0, 359128032, -119632296, 120401298, -92262016, 0, 37075644, -402924108, -431268936, 169752024, 0, 646551912, 141376320, 42645206, -80308236, 0, 199472560, -358758498, 15611040, 250911144, 0, -146411892, 26636024, 175418992, -51764832, 0, 10339692, -196288290, -298232640, 115888320, 0, -710831088, 549370080, -123200838, -77227200, 0, 55214208, 107376852, 127517780, 33120306, 0, 275694804, 60737040, -181710644, 158063280, 0, -199142880, -608158160, -65862720, 66833116, 0, 33014952, -188716768, 519900320, -5047560, 0, 164113488, 105993720, -26279960, -28731450, 0, 394261002, 81115384, 10002159, -326749696, 0, 14714316, -324046148, -130345600, 37614942, 0, 357452532, 156413376, -47529260, 155926288, 0, 270647760, 48661440, -36053424, -96625140, 0, -19501812, -51708832, -326065024, 169716384, 0, -133522560, 33626016, 81918984, -419175230, 0, -188451908, -67518000, -185285232, -71474156, 0, 157961664, -582823918, 15964320, 129593394, 0, -142203908, 142944912, 110679426, 308759304, 0, 13198392, 111225544, -152940960, -318583616, 0, -56484342, -267686608, 88341792, -11251548, 0, -246215168, -42456420, -14026260, -181906180, 0, 616450500, 35631944, 61594344, -187142400, 0, 33947856, 294668640, -307836256, -67853376, 0, -343381288, 33802272, 636918766, -8650596, 0, 19853680, 146518362, -105132132, 108353136, 0, -72784413, 32292204, 494341920, 187673472, 0, -63282048, -27551700, -68961344, 80700750, 0, -331884968, -8269688, 159670728, -143761976, 0, 258994800, -231337218, -25859152, -51509682, 0, -143188298, 98599680, 445576032, 54914944, 0, 117093704, 565402464, -41835528, 170479320, 0, 93897738, -439169280, 259829526, -9171720, 0, 463717520, 210049686, 81315120, 395026800, 0, 809827200, -103136396, 351968778, -55171816, 0, 7431426, -550665908, 380484960, -116353836, 0, -99989318, 104435856, 356659280, 110339384, 0, 90448512, 640287442, -73848312, 298368280, 0, -302819112, 3543122, -367429824, 78906960, 0, -83571456, 68981616, -330187200, -207703516, 0, 573600072, -98746368, 7144929, 90459968, 0, -332140032, 423155482, 150277792, -480712320, 0, -149577088, -10664460, -105282224, 181793304, 0, -36533200, -262107608, 248071680, -440123710, 0, -117908784, -45845128, 188494106, 9241380, 0, 153155760, 210589200, -300879360, -375029260, 0, -149744628, 34464464, 186791508, -27431952, 0, -11190564, -307027228, -178045896, 99548352, 0, 100251912, -46144080, 678341486, -29721920, 0, -292806752, -150020640, 24956424, 472991420, 0, 377666388, -132732756, -189112920, -223627824, 0, -229970400, -74356542, -73064640, -593922630, 0, -524813588, 310891952, -17326872, -132956736, 0, 114773760, -270986816, -6884066, 19118484, 0, 67829282, -22092804, 356274912, -207969600, 0, -66816348, 158805304, 59837400, -178597450, 0, -71464464, 88753152, -574746394, 9474084, 0, 462005712, -155232900, -73331632, 667092240, 0, -194068028, -124822996, 75397392, -476527856, 0, -115379964, 295536852, 1420896, 359801568, 0, -75899528, 40615344, 144906080, 79686720, 0, 443163360, 6075702, -119345472, 807191704, 0, -95429016, -162570576, 37129576, 215611200, 0, 151954560, 22603050, 103869808, 95751130, 0, -37748028, -205102800, 99085680, -12532696, 0, -230505912, -694414878, 63911400, 201307032, 0, 651488182, 74658456, -393681644, -442458296, 0, -272153376, 220490104, 50213520, 408137023, 0, -161868042, 490976640, -328559700, 82338912, 0, -3686144, -106692714, 230645460, 295930940, 0, 427478464, 25350864, -290327382, 524231280, 0, -46603836, -48111778, -422679712, -117269712, 0, -142192800, -34597440, -1619874, 275301880, 0, -349533800, -353016298, -18086112, -108681216, 0, -397492812, 47402100, -22002724, 57380400, 0, 594752, -95292036, 683000640, 145377144, 0, 718452152, -357312256, -182687238, 197017464, 0, 115404480, 828251422, 167688700, -168738966, 0, -280936218, 41911668, 651050520, 441343680, 0, 25014492, 1326855024, -355047840, 332752320, 0, 45574650, 421540800, -30191874, -90923760, 0, -56202720, -304844184, -78164640, -269375080, 0, 256660032, 12983784, -29773143, -542466176, 0, 83875176, 796154472, -262740120, 103235148, 0, -29868420, 208242216, -257931344, -201123896, 0, -345566368, 372610462, -60803136, -756541184, 0, -97806132, 223695944, -412892064, -15812280, 0, 111303172, 126321120, 195244224, -680902450, 0, 357851424, 437672704, -431210772, -248862592, 0, -14880348, 632744402, -258064480, -499393440, 0, -131334368, -47919744, 205385400, 167873664, 0, -77362560, -61701768, -316796832, -474290700, 0, -361246122, -657903288, 41502160, -17030088, 0, -258311040, 144368730, -49049448, -153206060, 0, 1563852, 165543704, -174821490, -472304640, 0, -99838584, -120984376, 104716304, -29041416, 0, -509374488, 49941360, -549684394, 183723648, 0, 391723360, -444988158, 60431400, -87823010, 0, 296439264, 291009004, -251138844, 312439680, 0, -133088648, -189530496, 510528960, 929706430, 0, -545626628, 679686112, -53581032, 137737504, 0, 233323776, 136296300, 34350660, -256827348, 0, -177612028, 185542272, -621384480, -269095920, 0, 114396972, -608703600, -39817008, -273494826, 0, -288704862, 57309472, -94775548, -122760, 0, 586840128, -53262198, 301765160, -620531360, 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": "33.6.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], [1], [2], [9], [-28], [0], [18], [-148], [-120], [81], [0], [121], [-252], [-574], [-296], [0], [656], [722], [162], [2160], [0], [-1332], [242], [2536], [-1080], [0], [-1148], [729], [4144], [4650], [0], [5032], [5152], [1089], [1444], [0], [-2268], [-8118], [4320], [-5166], [0], [-5138], [-2664], [-8304], [-3388], [0], [5072], [-24728], [5904], [5097], [0], [6498], [16072], [28746], [1458], [0], [17760], [19440], [9300], [-5860], [0], [-53658], [10064], [-11988], [-10688], [0], [2178], [-30908], [-20216], [22824], [0], [-69648], [-9720], [18446], [-16236], [0], [-60480], [-17908], [-10332], [-25300], [0], [6561], [-10276], [17556], [37296], [0], [-16608], [41850], [-14520], [132570], [0], [84952], [-71008], [45288], [-49456], [0], [46368], [-70658], [10194], [9801], [0]]}