# Stored data for newform 138.6.a.e, downloaded from the LMFDB on 23 April 2024. {"label": "138.6.a.e", "space_label": "138.6.a", "level": 138, "weight": 6, "hecke_orbit": 5, "hecke_orbit_code": 18014398610145418, "dim": 2, "is_polredabs": true, "nf_label": "2.2.616.1", "trace_hash": 246954846105783326, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [-1382, 4, 1]]], "qexp_display": "q-4q^{2}+9q^{3}+2^{4}q^{4}+(-2+3\\beta )q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 4968, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 22.13296713419133, "hecke_ring_index": 1, "level_radical": 138, "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": 0, "analytic_rank_proved": true, "char_values": [138, 1, [47, 97], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 3, 23], "conrey_indexes": [1], "field_disc": 616, "field_disc_factorization": [[2, 3], [7, 1], [11, 1]], "field_poly": [-154, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.966", "prec": 17}, {"__RealLiteral__": 0, "data": "0.065", "prec": 17}, {"__RealLiteral__": 0, "data": "9.361", "prec": 17}, {"__RealLiteral__": 0, "data": "1.291", "prec": 17}, {"__RealLiteral__": 0, "data": "61.972", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [23, -1]], "trace_display": [-8, 18, -4, -40], "traces": [0, 2, -8, 18, 32, -4, -72, -40, -128, 162, 16, -160, 288, -1456, 160, -36, 512, -436, -648, -448, -64, -360, 640, 1058, -1152, -3470, 5824, 1458, -640, 6364, 144, -2360, -2048, -1440, 1744, -4540, 2592, -19388, 1792, -13104, 256, -17476, 1440, -23760, -2560, -324, -4232, -35684, 4608, -25114, 13880, -3924, -23296, 1476, -5832, -18160, 2560, -4032, -25456, 23092, -576, -70884, 9440, -3240, 8192, 14000, 5760, -81824, -6976, 9522, 18160, 15552, -10368, 49644, 77552, -31230, -7168, 34000, 52416, 102680, -1024, 13122, 69904, 39096, -5760, -123868, 95040, 57276, 10240, -21228, 1296, 10640, 16928, -21240, 142736, 164444, -18432, -25772, 100456, -12960, -55520, 206828, 15696, 107640, 93184, -40860, -5904, 21408, 23328, 120956, 72640, -174492, -10240, 49108, 16128, -2116, 101824, -117936, -92368, 216620, 2304, -186102, 283536, -157284, -37760, 8352, 12960, -9472, -32768, -213840, -56000, 27912, -23040, -263620, 327296, -2916, 27904, -58516, -38088, 1416, -72640, -321156, -62208, 42560, 41472, 247840, -198576, -226026, -310208, 120036, 124920, -57520, 28672, -35316, -136000, -518264, -209664, 528356, -410720, 13284, 4096, -21160, -52488, -752352, -279616, -163440, -156384, 3664, 23040, 361734, 495472, -36288, -380160, 808396, -229104, 87880, -40960, 207828, 84912, -369652, -5184, 116212, -42560, -637956, -67712, 410224, 84960, 866480, -570944, -29160, -657776, 935240, 73728, 845904, 103088, 126000, -401824, -130876, 51840, -1060440, 222080, -736416, -827312, -561560, -62784, 862856, -430560, 85698, -372736, -1054480, 163440, 500512, 23616, 139968, -85632, -422796, -93312, 918840, -483824, 446796, -290560, -181552, 697968, -123496, 40960, -281070, -196432, 952832, -64512, 1315052, 8464, 306000, -407296, -1125524, 471744, -806432, 369472, 924120, -866480, -1437792, -9216, 898764, 744408, 118098, -1134144, 235028, 629136, 980336, 151040, 351864, -33408, -10104, -51840, -84640, 37888, -1114812, 131072, -95204, 855360, -231320, 224000, 515484, -111648, -1346280, 92160, 849900, 1054480, -191052, -1309184, 1624260, 11664, -2828720, -111616, 95760, 234064, 351520, 152352, 1034828, -5664, -191160, 290560, 3052060, 1284624, 1300288, 248832, 1479996, -170240, -1030320, -165888, 2868634, -991360, -231948, 794304, 1357324, 904104, 2568736, 1240832, -116640, -480144, -770224, -499680, 1259060, 230080, 1861452, -114688, 361680, 141264, 1504072, 544000, 968760, 2073056, -2638388, 838656, -1415124, -2113424, -367740, 1642880, -3323868, -53136, -2246240, -16384, 192672, 84640, -7261996, 209952, 2481808, 3009408, 1088604, 1118464, 2176680, 653760, -1441064, 625536, -1570428, -14656, 621028, -92160, -637532, -1446936, 441972, -1981888, 3675360, 145152, 866560, 1520640, -19044, -3233584, -3797236, 916416, 1425440, -351520, -1061424, 163840, -6125516, -831312, -4089312, -339648, 1949580, 1478608, -5856504, 20736, 4797486, -464848, -1674918, 170240, -3902472, 2551824, 482232, 270848, -1415556, -1640896, -1450940, -339840, -311116, -3465920, 75168, 2283776, -3590720, 116640, -2597760, 2631104, -85248, -3740960, -631936, -294912, 671200, -3383616, -1924560, -412352, 6112780, -504000, -230644, 1607296, 251208, 523504, 636404, -207360, -3977044, 4241760, -2372580, -888320, -7798948, 2945664, -373856, 3309248, -26244, 2246240, -925280, 251136, -2855832, -3451424, -526644, 1722240, -4820040, -342792, 4996416, 1490944, 12744, 4217920, -1764984, -653760, 7045348, -2002048, -2890404, -94464, 1255420, -559872, 1051160, 342528, 383040, 1691184, -6162792, 373248, -4551036, -3675360, 2230560, 1935296, -236992, -1787184, -5588400, 1162240, -2034234, 726208, -3611336, -2791872, -4384428, 493984, 1080324, -163840, -2985724, 1124280, -4121280, 785728, -517680, -3811328, 3120320, 258048, 8994860, -5260208, -317844, -33856, 8184876, -1224000, -7708520, 1629184, -4664376, 4502096, 9229528, -1886976, 874180, 3225728, 4755204, -1477888, 5036240, -3696480, 123088, 3465920, 119556, 5751168, 13754680, 36864, 15600256, -3595056, -190440, -2977632, 6558352, -472392, -3178792, 4536576, -6771168, -940112, 8874500, -2516544, -13112912, -3921344, -1470960, -604160, 6452640, -1407456, -285520, 133632, 32976, 40416, 7498424, 207360, 3703688, 338560, 3255606, -151552, 9620244, 4459248, 5345760, -524288, -326592, 380816, -5896956, -3421440, 8706720, 925280, 7275564, -896000, 9336132, -2061936, -19532176, 446592, 790920, 5385120, 24048760, -368640, 559682, -3399600, 1870452, -4217920, 16034144, 764208, -8961264, 5236736, -3326868, -6497040, 777120, -46656, 21041000, 11314880, 1045908, 446464, 3701720, -383040, 3234640, -936256, -5741604, -1406080, 13947976, -609408, -3456540, -4139312, 3692016, 22656, -6628708, 764640, 15416016, -1162240, 7798320, -12208240, 7038208, -5138496, 14320804, -5201152, -262440, -995328, 3307156, -5919984, -15498576, 680960, 8417160, 4121280, -1835630, 663552, -12964320, -11474536, 7613136, 3965440, -9239600, 927792, -5803760, -3177216, 1134000, -5429296, -6018616, -3616416, -30327416, -10274944, -1177884, -4963328, -6343756, 466560, 3068720, 1920576, -9543960, 3080896, 8301856, 1998720, -7187648, -5036240, -6627744, -920320, 3329004, -7445808, -20121760, 458752, -5054040, -1446720, 22466752, -565056, -20079996, -6016288, 7765704, -2176000, -20952540, -3875040, -6997776, -8292224, 771282, 10553552, 7802700, -3354624, -2622698, 5660496, -9490320, 8453696, -12488576, 1470960, -9621496, -6571520, 4504608, 13295472, -5586040, 212544, 19022192, 8984960, 1259712, 65536, 13105436, -770688, -13155520, -338560, -3805164, 29047984, -6085900, -839808, -19280160, -9927232, 8269560, -12037632, -14295452, -4354416, -20158368, -4473856, 4021164, -8706720, -6053816, -2615040, 4642404, 5764256, -1633968, -2502144, -1708840, 6281712, 3366556, 58624, -1111464, -2484112, 4204640, 368640, -4765112, 2550128, -2529630, 5787744, -7194044, -1767888, -10329240, 7927552, 8575488, -14701440, -26125208, -580608, -593524, -3466240, 11835468, -6082560, 2336880, 76176, 24257968, 12934336, 2754000, 15188944, 16780704, -3665664, -33445912, -5701760, -10129716, 1406080, 15346860, 4245696, 26258344, -655360, -7257888, 24502064, -10998800, 3325248, 1381932, 16357248, 8317080, 1358592, -1248440, -7798320, 12481280, -5914432, -12940128, 23426016, -35580972, -82944, 7316660, -19189944, 8088876, 1859392, -12083812, 6699672, 4047624, -680960, 1062882, 15609888, 26343900, -10207296, 11032276, -1928928, 2115252, -1083392, 3496720, 5662224, -7873144, 6563584, 8823024, 5803760, 10953408, 1359360, 6738900, 1244464, 3166776, 13863680, 14435920, -300672, -22520024, -9135104, -90936, 14362880, -32916112, -466560, 41563156, 10391040, -761760, -10524416, -7736316, 340992, -8991840, 14963840, -10033308, 2527744, -6351296, 1179648, -20777700, -2684800, -856836, 13534464, -46430396, 7698240, 6186536, 1649408, -2081880, -24451120, 52760960, 2016000, 25810560, 922576, 4639356, -6429184, -16921792, -1004832, -30171824, -2094016, -12116520, -2545616, -25013860, 829440, 52483200, 15908176, 7649100, -16967040, -47218332, 9490320, 47280112, 3553280, -1719468, 31195792, 21383040, -11782656, -2401660, 1495424, 14618340, -13236992, -17331124, 104976, -34615616, -8984960, -25458480, 3701120, 12735000, -1004544, -22426404, 11423328, 861840, 13805696, -4166980, 2106576, 4863904, -6888960, 3163680, 19280160, -20820264, 1371168, 45059752, -19985664, 9313452, -5963776, -2841148, -50976, 19060336, -16871680, -1720440, 7059936, 18963368, 2615040, 3721342, -28181392, 27468540, 8008192, -16867596, 11561616, -1205960, 377856, 11702592, -5021680, -10256252, 2239488, 25002884, -4204640, 13319964, -1370112, -71204244, -1532160, -43963184, -6764736, -9272880, 24651168, 7524860, -1492992, 5388976, 18204144, 25817706, 14701440, -13826160, -8922240, 61397392, -7741184, -2087532, 947968, 22249200, 7148736, -13508444, 22353600, 12215916, -4648960, 52565788, 8136936, -2761400, -2904832, 23118624, 14445344, 22073748, 11167488, 9531080, 17537712, -1049760, -1975936, -43796984, -4321296, 13034048, 655360, -6932016, 11942896, -56670016, -4497120, -38700108, 16485120, 11331540, -3142912, -2701352, 2070720, -18023888, 15245312, 16753068, -12481280, 70699000, -1032192, -36958400, -35979440, 3255120, 21040832, 32946000, 1271376, 51510120, 135424, 13536648, -32739504, -27554688, 4896000, 32152388, 30834080, 8718840, -6516736, -46646020, 18657504, 16528736, -18008384, -23745492, -36918112, 12274880, 7547904, 12163620, -3496720, -12736116, -12902912, 3493676, -19020816, -9244804, 5911552, -3309660, -20144960, 594028, 14785920, -51353568, -492352, -29914812, -13863680, 21172772, -478224, -11740648, -23004672, -20216160, -55018720, 2354580, -147456, 44196146, -62401024, 1734048, 14380224, -13770336, 761760, 13564152, 11910528, -65357964, -26233408, 35937040, 1889568, -28000880, 12715168, 22336272, -18146304, -32608684, 27084672, 31210800, 3760448, 9797436, -35498000, -2714040, 10066176, 35678672, 52451648, 19590120, 15685376, -12569040, 5883840, 1815584, 2416640, -12969576, -25810560, -19817652, 5629824, -72923568, 1142080, -14133852, -534528, -21795200, -131904, -122705456, -161664, 5589252, -29993696, 49987644, -829440, 77065332, -14814752, -5737788, -1354240, -18158460, -13022424, -18789080, 606208, 3977748, -38480976, -4679176, -17836992, 17890500, -21383040, 33078240, 2097152, 27009244, 1306368, -71383984, -1523264, 7799040, 23587824, 34678640, 13685760, 50425260, -34826880, -171396, -3701120, 5556672, -29102256, 4434656, 3584000, -34175124, -37344528, -14032340, 8247744, -6835360, 78128704, 12828960, -1786368, -44425860, -3163680, -30871536, -21540480, -9552816, -96195040, 65761672, 1474560, 56202320, -2238728, -55129644, 13598400, -56427196, -7481808, -23142440, 16871680, -36803808, -64136576, -41316960, -3056832, 92443836, 35845056, 17546220, -20946944, -26776504, 13307472, 43104864, 25988160, -52708536, -3108480, -8163456, 186624, -18876836, -84164000, 43177374, -45259520, 14073600, -4183632, -36362904, -1785856, -15074262, -14806880, 86016128, 1532160, -35136380, -12938560, -35122248, 3745024, -73712292, 22966416, 15874680, 5624320, 4340088, -55791904, 134871784, 2437632, 88756640, 13826160, -12740004, 16557248, 56139988, -14768064, -43995200, -90624, -13058460, 26514832, 69051728, -3058560, -40913812, -61664064, -2800044, 4648960, 149107672, -31193280, 42916208, 48832960, 676512, -28152832, -13285306, 20553984, 7263572, -57283216, -32316480, 20804608, 29266640, 1049760, -30011896, 3981312, -23379840, -13228624, -2744468, 23679936, -3670120, 61994304, -767232, -2723840, 41459480, -33668640, -47202016, -16485120, -5687424, 7342520, 53416100, -2654208, -23147372, 51857280, 6040800, 45898144, -2253552, -30452544, 28852824, -15861760, -17321040, 36958400, -1174808, -3711168, -53096552, 23215040, 55015020, 12708864, -31852720, -4536000, 68805232, 21717184, -2075796, 24074464, 65422940, 14465664, 57743680, 121309664, 2260872, 41099776, -53414228, 4711536, 19672200, 19853312, 5727636, 25375024, -19786472, -1866240, 22214344, -12274880, -35793396, -7682304, 104850900, 38175840, 39587952, -12323584, -21353220, -33207424, -35967360, -7994880, -13819972, 28750592, -70190532, 20144960, 8202000, 26510976, 179229024, 3681280, -3364704, -13316016, -27844200, 29783232, 132030516, 80487040, -236196, -1835008, -59973172, 20216160, 780804, 5786880, -8327520, -89867008, 18576592, 2260224, 42833590, 80319984, -25702488, 24065152, 73515180, -31062816, 80098952, 8704000, -4739796, 83810160, -123507328, 15500160, -40787300, 27991104, -43380360, 33168896, 160320888, -3085128, -100055440, -42214208, 44967744, -31210800, -119814024, 13418496, 77065236, 10490792, 114696, -22641984, -13098200, 37961280, 3004728, -33814784, -15884856, 49954304, -198160, -5883840, 44789248, 38485984, 63408132, 26286080, -9606640, -18018432, 1790640, -53181888, -26013636, 22344160, -135576208, -850176, 45313996, -76088768, 11298780, -35939840, 15048004, -5038848, -163376600, -262144, 9460440, -52421744, -44641884, 3082752, -290072, 52622080, 3447360, 1354240, -54907340, 15220656, -178742992, -116191936, -55465128, 24343600, 37819960, 3359232, 17458748, 77120640, -40959324, 39708928, 183069060, -33078240, 691560, 48150528, 20075040, 57181808, -127789336, 17417664, -40676000, 80633472, -2132928, 17895424, -134101408, -16084656, 26943864, 34826880, -50295600, 24215264, 90653456, 10460160, -2109732, -18569616, -18308106, -23057024, -5972268, 6535872, -129687808, 10008576, -32502024, 6835360, 20944320, -25126848, 116769752, -13466224, -39459852, -234496, -2254520, 4445856, -101088624, 9936448, 9722916, -16818560, -60263620, -1474560, 22795344, 19060448, -26871516, -10200512, -242917920, 10118520, 3212800, -23150976, -37091520, 28776176, -17444408, 7071552, 12215668, 41316960, -4659120, -31710208, -6825588, -34301952, -196059688, 58805760, 28082880, 104500832, 79703520, 2322432, 99033390, 2374096, 80953740, 13864960, -40330572, -47341872, 88996800, 24330240, -2860596, -9347520, -56410680, -304704, 41098784, -97031872, 73663884, -51737344, -6682264, -11016000, -235508112, -60755776, -69376680, -67122816, -51258816, 14662656, 57773020, 133783648, -41979384, 22807040, 38124320, 40518864, -147095304, -5624320, 83065752, -61387440, -37497636, -16982784, -47056724, -105033376, 7867620, 2621440, -79183460, 29031552, -236880288, -98008256, 42796836, 43995200, -109678316, -13300992, -72281440, -5527728, 45326160, -65428992, -62541548, -33268320, -77625464, -5434368, 1107792, 4993760, 85355016, 31193280, -64468616, -49925120, 1076004, 23657728, 57023508, 51760512, 25872120, -93704064, 123792120, 142323888, -70283076, 331776, 131784000, -29266640, 140402304, 76759776, 48649372, -32355504, 139060488, -7437568, -1713960, 48335248, 3696456, -26798688, -64057192, -16190496, 59025168, 2723840, 207718720, -4251528, -20337232, -62439552, -28609128, -105375600, 35996800, 40829184, 18168676, -44129104, -60940512, 7715712, 21925456, -8461008, -44622184, 4333568, 79870500, -13986880, -50524300, -22648896, -121281400, 31492576, -118016208, -26254336, -254517820, -35292096, 18226080, -23215040, -13238640, -43813632, 197689800, -5437440, -155172572, -26955600, 58073760, -4977856, -53994044, -12667104, 7406000, -55454720, -2569680, -57743680, -196719720, 1202688, 26663756, 90080096, 296784, 36540416, 61773800, 363744, 9418320, -57451520, 67485816, 131664448, 47453228, 1866240, 203837484, -166252624, 33333192, -41564160, 280351480, 3047040, -5231080, 42097664, 29300454, 30945264, -120625568, -1363968, 122104092, 35967360, 86582196, -59855360, -112003520, 40133232, -71917680, -10110976, 48111840, 25405184, 158128216, -4718592, 84864720, 83110800, -2939328, 10739200, -43284896, 3427344, 70825872, -54137856, -53072604, 185721584, -143691520, -30792960, -45509128, -24746144, 78360480, -6597632, -69162244, 8327520, -47962256, 97804480, 65480076, -211043840, -90628448, -8064000, -112204640, -103242240, 84025188, -3690304, -144614280, -18557424, 123178392, 25716736, -175789584, 67687168, 120954184, 4019328, 147309456, 120687296, 7118280, 8376064, 290644368, 48466080, -52086432, 10182464, 216438840, 100055440, 107460928, -3317760, 41709840, -209932800, 5037138, -63632704, 27787080, -30596400, 167307096, 67868160, 16834068, 188873328, -75156320, -37961280, 154559052, -189120448, 144307296, -14213120, 38644924, 6877872, -99783680, -124783168, -80651376, -85532160, 11314992, 47130624, 143112204, 9606640, -29941812, -5981696, 51786324, -58473360, 6812288, 52947968, 6994080, 69324496, -92479416, -419904, -54539244, 138462464, 189369000, 35939840, -59879232, 101833920, 82045840, -14804480, 9413172, -50940000, 114756480, 4018176, 8227008, 89705616, 33315480, -45693312, 270548940, -3447360, -56129360, -55222784, 29111760, 16667920, -162646424, -8426304, 95632680, -19455616, -51674436, 27555840, -287188064, -12654720, -15524320, -77120640, 125531784, 83281056, 42693592, -5484672, 24520640, -180239008, -31108860, 79942656, 224809280, -37253808, 47182312, 23855104, 33228144, 11364592, -41800416, 203904, 95013124, -76241344, -59658372, 67486720, -32431440, 6881760, 140135120, -28239744, 138744144, -75853472, 26261676, -10460160, 168260214, -14885368, 70184880, 112725568, 73459792, -109874160, -34641160, -32032768, 63343872, 67470384, -256431084, -46246464, -116604796, 4823840, 128887236, -1511424, 20966844, -46810368, -291318976, 20086720, -2361960, 41025008, -100730112, -8957952, 56294400, -100011536, 29764404, 16818560, -184439468, -53279856, 319281224, 5480448, -139487184, 284816976, 130232560, 6128640, -230368984, 175852736, 75754440, 27058944, 265219292, 37091520, -221841136, -98604672, -16520670, -30099440, 63498720, 5971968, 182971040, -21555904, -116678880, -72816576, 321185324, -103270824, -26868880, -58805760, 68518224, 55304640, 228295496, 35688960, -286523452, -245589568, -83156400, 30964736, -180377152, 8350128, -109176352, -3791872, -52233840, -88996800, 232209900, -28594944, -246025292, 54033776, 10206000, -89414400, -4772120, -48863664, 137959464, 18595840, -54167544, -210263152, 67147168, -32547744, 90382624, 11045600, -272946744, 11619328, -204881160, -92474496, 17986000, -57781376, -10600956, -88294992, -10749888, -44669952, -43102564, -38124320, -57093804, -70150848, 39757424, 4199040, -267346224, 7903744, 27618480, 175187936, 61328692, 17285184, -201785260, -52136192, -85895640, -2621440, -14680480, 27728064, 53675544, -47771584, 74716704, 226680064, 2704880, 17988480, -199649708, 154800432, -64688832, -65940480, -82864476, -45326160, 66103296, 12571648, -59649696, 10805408, -46660992, -8282880, 268218316, 72095552, 29961036, -60981248, 54317720, -67012272, 396663216, 49925120, -181095840, -282796000, 290792748, 4128768, -70919604, 147833600, -45486360, 143917760, -520596800, -13020480, 77546136, -84163328, 202200768, -131784000, -150305964, -5085504, -127410880, -206040480, -180719964, -541696, -13493240, -54146592, 389674600, 130958016, 69891336, 110218752, 192992152, -19584000, 68048862, -128609552, -188572860, -123336320, -203831848, -34875360, -17564720, 26066944, -62979984, 186584080, 78688800, -74630016, -265215532, -66114944, 6941538, 72033536, 354626960, 94981968, 314945304, 147672448, 70224300, -49099520, -166432396, -30191616, -362125332, -48654480, -23604282, 13986880, 67755324, 50944464, -305767272, 51611648, -85412880, -13974704, -75891640, 76083264, -147230048, 36979216, -112397184, -23646208, 350981164, 13238640, 42153056, 80579840, -86593464, -2376112, -210758988, -59143680, 95077480, 205414272, 40541472, 1969408, 67574388, 119659248, -111376800, 55454720, -50274360, -84691088, 155448160, 1912896, 20681784, 46962592, 171199728, 92018688, -285685220, 80864640, -179269096, 220074880, 11337408, -9418320, 196593824, 589824, -659561444, -176784584, 117948924, 249604096, -61946800, -6936192, 49637192, -57520896, -118399680, 55081344, 26981808, -3047040, 340859664, -54256608, -34246476, -47642112, -59470320, 261431856, -13008880, 104933632, -54773100, -143748160, -217370248, -7558272, -127817036, 112003520, -173521440, -50860672, 340583516, -89345088, 532912664, 72585216, 74426040, 130434736, -65526172, -108338688, -359330244, -124843200, -128659068, -15041792, 99973824, -39189744, -90250048, 141992000, -181425312, 10856160, 7213140, -40264704, -52392800, -142714688, 36190476, -209806592, -63889124, -78360480, -181516856, -62741504, -54484344, 50276160, -24718520, -23535360, 152457140, -7262336, 41781636, -9666560, -242353816, 51878304, 273590944, 103242240, -14705712, 79270608, 7162560, -22519296, -89633716, 291694272, -15379560, -4568320, 24832412, 56535408, -187352264, 2138112, 30299004, 87180800, -278967988, 527616, 8062676, 490821824, -10003176, 646656, 274639732, -22357008, -318918432, 119974784, 37841760, -199950576, 368396224, 3317760, -341444752, -308261328, -42886008, 59259008, 572859320, 22951152, -148017080, 5416960, -22766670, 72633840, 497492936, 52089696, -253956516, 75156320, -64746396, -2424832, -530983824, -15910992, 151279840, 153923904, -92963160, 18716704, -303564008, 71347968, -448103488, -71562000, 77179392, 85532160, 19597536, -132312960, -11229612, -8388608, -235126872, -108036976, -61952020, -5225472, -416423144, 285535936, -5341716, 6093056, -92485764, -31196160, -331985088, -94351296, 106519212, -138714560, -31082308, -54743040, -96000840, -201701040, 21031920, 139307520, -231216644, 685584, 205580144, 14804480, 218321712, -22226688, -88129992, 116409024, 10259960, -17738624, 24786000, -14336000, -232805500, 136700496, -298972080, 149378112, 151026336, 56129360, -138386032, -32990976, 405429900, 27341440, -301013208, -312514816, 5628560, -51315840, -135158736, 7145472, -91167444, 177703440, -11977608, 12654720, -9018080, 123486144, 138121740, 86161920, -220741448, 38211264, 266999920, 384780160, 236325096, -263046688, -227087308, -5898240, -479217940, -224809280, -65320992, 8954912, -199532088, 220518576, 592633440, -54393600, -98989200, 225708784, 12851200, 29927232, 603417744, 92569760, 12437388, -67486720, 194693740, 147215232, -361844656, 256546304, 74853720, 165267840, 157241480, 12227328, 610734852, -369775344, -11235960, -143380224, 131394940, -70184880, 168010176, 83787776, 112331520, 107106016, 839721988, -53229888, -298642040, -172419456, -116461152, -103952640, 245384020, 210834144, -65379120, 12433920, -320228748, 32653824, 254289176, -746496, 92297380, 75507344, 65849940, 336656000, 160723080, -172709496, -225642720, 181038080, 72799884, -56294400, 73603264, 16734528, 241821176, 145451616, -108754308, 7143424, 141499480, 60297048, 248405904, 59227520, 36428616, -344064512, 126545432, -6128640, 86990876, 140545520, 9565938, 51754240, 231092080, 140488992, 274043360, -14980096, 237095100, 294849168, 8667216, -91865664, 212683744, -63498720, 99290484, -22497280, 747297216, -17360352, 54373400, 223167616, 19037268, -539487136, -510244376, -9750528, 455953914, -355026560, 31470480, -55304640, -238130988, 50960016, 239483008, -66228992, -70858296, -224559952, 8040520, 59072256, -418819740, 175980800, 79407216, 362496, 54538116, 52233840, 898529664, -106059328, 98580672, -276206912, -13633388, 12234240, 177672800, 163655248, 60650100, 246656256, 532184204, 11200176, 382255880, -18595840, 28500984, -596430688, -35459624, 124773120, -6443416, -171664832, 129923280, -195331840, -560489216, -2706048, -504884720, 112611328, -202680216, 53141224, 103488480, -82215936, 716617704, -29054288, -818424, 229132864, 158092760, 129265920, 658954128, -83218432, -296245008, -117066560, -5365828, -4199040, -486632508, 120047584, 374068404, -15925248, -175685428, 93519360, -31026800, 52914496, -6855840, 10977872, -162235436, -94719744, -68767184, 14680480, -69626844, -247977216, 14485184, 3068928, 285739656, 10895360, -80926560, -165837920, 405853576, 134674560, -319628968, 188808064, -90299772, 65940480, -664898036, 22749696, 216138048, -29370080, -57161664, -213664400, 389563988, 10616832, -296679936, 92589488, -186999300, -207429120, -149710572, -24163200, 177619384, -183592576, -7711524, 9014208, 217015360, 121810176, -37531160, -115411296, -417873564, 63447040, -485125600, 69284160, 109412012, -147833600, 55678824, 4699232, 318285632, 14844672, 44731508, 212386208, -18736920, -92860160, -122196140, -220060080, -74839688, -50835456, 474848640, 127410880, -671097928, 18144000, -287372736, -275220928, 232295040, -86868736, 178117480, 8303184, 245203048, -96297856, 41754204, -261691760, 447785928, -57862656, -94478048, -230974720, -152296128, -485238656, -65275460, -9043488, -107557240, -164399104, -271546416, 213656912, -755567808, -18846144, 247095200, -78688800, -109048680, -79413248, 56941560, -22910544, 378422600, -101500096, -225124740, 79145888, -795405744, 7464960, -151578856, -88857376, 472348800, 49099520, -203662148, 143173584, 132732264, 30729216, 68841900, -419403600, -179582400, -152703360, 106759636, -158351808, -424964988, 49294336, -620377572, 85412880, 181018960, 132829696, 425521008, 143869440, -505818768, 31979520, 184816998, 55279888, -15475212, -115002368, -409101728, 280762128, 601416624, -80579840, 192447360, -32808000, -413303808, -106043904, -328572328, -716916096, -21614940, -14725120, 243090788, 13458816, 579211544, 53264064, 131565060, 111376800, 73727068, -119132928, 18687188, -528122064, -155980116, -321948160, 133383640, 944784, -574766080, 7340032, -311540544, 239892688, -4697152, -80864640, -269525508, -3123216, -229126320, -23147520, 434480844, 33310080, 267368320, 359468032, 114615000, -74306368, -209849184, -9040896, -279975208, -171334360, -201837636, -321279936, -448818560, 102809952, -458406448, -96260608, 7756560, -294060720, -103109896, 124251264, 11324832, -320395808, -37502820, -34816000, -427500680, 18959184, 561204888, -335240640, 43775136, 494029312, -7709000, -62000640, 276699524, 163149200, 28473120, -111964416, 407634020, 173521440, 854490776, -132675584, -187382376, -641283552, -720335392, 12340512, 32333760, 400221760, 405537768, 168856832, -1192302384, -179870976, -296404592, 124843200, 83821068, 479256096, -436545640, -53673984, 111148320, -308260944, -25570332, -41963168, 685064776, -458784, 326453240, 90567936, 171543024, 52392800, 63985724, -151845120, -664132224, -12018912, -15483960, 135259136, 47192520, 63539424, 234401840, -199817216, 170670312, 792640, -399134720, 23535360, -181438836, -179156992, 33492078, -153943936, -375315956, -253632528, 26166120, -105144320, 247216860, 38426560, -431045020, 72073728, -340221588, -7162560, -151808364, 212727552, -717997720, 104054544, 785755360, -89376640, -10853640, 542304832, -462773440, 3400704, -111431664, -181255984, 105323328, 304355072, 332488620, -45195120, -687279496, 143759360, -92306268, -60192016, -49305480, 20155392, 3741140, 653506400, 225025956, 1048576, 236945408, -37841760, 459025920, 209686976, 119879676, 178567536, 1498941200, -12331008, 239257860, 1160288, -640838196, -210488320, -1003542656, -13789440, -164028696, -5416960, -395668656, 219629360, 873211624, -60882624, -483674592, 714971968, -83455920, 464767744, 382530720, 221860512, 684246192, -97374400, 67723740, -151279840, -195389760, -13436928, 32865644, -69834992, 48500784, -308482560, 38322668, 163837296, 25978132, -158835712, 232359354, -732276240, -28815220, 132312960, 349952916, -2766240, -124435440, -192602112, 615348916, -80300160, -583785560, -228727232, 552576528, 511157344, -55321324, -69670656, 574611984, 162704000, -18787788, -322533888, 292392548, 8531712, 804790184, -71581696, 200242800, 536405632, -694560960, 64338624, -129725760, -107775456, -121575996, -139307520, -851158804, 201182400, 213106192, -96861056, 109943244, -362613824, 329166880, -41840640, 989911440, 8438928, 473092092, 74278464, -1119364, 73232424, 23593312, 92228096, -24852600, 23889072, -138564640, -26143488, 411879380, 518751232, 208067616, -40034304, 779865476, 130008096, -196639504, -27341440, 198663732, -83777280, -765065104, 100507392, -731669344, -467079008, 85779720, 53864896, 598746992, 157839408, -377163240, 937984, -9447840, 9018080, -1469088, -17783424, 414007708, 404354496, -394172856, -39745792, 313527000, -38891664, 295660992, 67274240, 117306432, 241054480, 225753104, 5898240, -404310628, -91181376, -62388144, -76241792, -278738476, 107486064, 215715120, 40802048, -510030144, 971671680, 557135756, -40474080, -990875592, -12851200, -348300972, 92603904, 158740160, 148366080, -586484000, -115104704, 101983860, 69777632, -985757184, -28286208, 998077692, -48862672, -24312168, -165267840, 731884160, 18636480, 275135880, 126840832, -162214992, 27302352, 70396860, 137207808, -225633188, 784238752, 150777612, -235223040, 1084311924, -112331520, -267937232, -418003328, 636291000, -318814080, -3510632, -9289728, 114591980, -396133560, -332625600, -9496384, -655623180, -323814960, -97321952, -55459840, 29296080, 161322288, 851582272, 189367488, -74497116, -355987200, 296514000, -97320960, -165488692, 11442384, 434146552, 37390080, 463591080, 225642720, 860254488, 1218816, -19088480, -164395136, 121829832, 388127488, -247113000, -294655536, 746067160, 206949376, -247992192, 26729056, -341350584, 44064000, -1240065464, 942032448, 289371492, 243023104, 987659444, 277506720, 496720720, 268491264, 78469560, 205035264, -98447958, -58650624, -31263676, -231092080, -419814180, -535134592, -274729892, 167917536, -838827472, -91228160, 148758624, -152497280, 179832576, -162075456, -1021202844, 588381216, -213709428, 22497280, 244065444, -332263008, -1657488, 245549760, 110473920, 149990544, 168537660, 67931136, -572907566, 188226896, 109472580, 420133504, 529633448, -31470480, -328574600, -10485760, -114625044, 316733840, -125868668, -116126208, -605270400, 947521152, 31443084, 392033024, -142878460, -171187344, 10819520, -175980800, -83203236, 438713264, 384871284, 53203968, -65920184, 289125760, -29786940, 22110912, 103105780, -181304640, -858843632, 261715968, 5346252, 250166192, 723153512, 133073280, -328241156, 310501856, -462182112, 21737472, -230543200, -4431168, -31647056, -19975040, -269233308, -341420064, -418017876, -124773120, -674069908, 257874464, 190554948, 199700480, 760184172, -4304016, 33973520, -94630912, -105665832, -228094032, 1195073528, -207042048, -1935953488, -103488480, -181945440, 374816256, 647627748, -495168480, 4418208, -569295552, 21191220, 281132304, -1247232436, -1327104, 894466980, -527136000, 397765314, 117066560, 358546464, -561609216, -758552672, -307039104, 15606432, -194597488, -115638244, 129422016, -53972960, -556241952, -123933024, 29750272, 244303236, 6855840, 365124032, -193340992, 122077368, -14785824, -702282688, 107194752, -173324720, 256228768, -588221676, 64761984, -16114588, -236100672, -1347944832, -10895360, 323433360, -830874880, -70258880, 17006112, 955935436, 81348928, -252007920, 249758208, -5010688, 114436512, -882583544, 421502400, 201026448, -143987200, -487751920, -163316736, 1045157032, -72674704, -293478156, 176516416, 266447520, 243762048, -452235808, -30862848, 280897200, -87701824, 1295545260, 33844032, -491489888, 178488736, 88176924, -17334272, -15183392, -319482000, 203510960, 55947520, -24426360, 202097200, -806086624, 90595584, 703350788, 485125600, 321108048, -125970304, 245391300, 472064832, -303566560, 105017344, 176311080, 1018071280, 158947816, 141168384, -794034712, -72904320, -113121360, 92860160, 326588036, 52954560, -984742568, 175254528, 16340256, -790759200, -389843540, 21749760, -780999520, 620690288, -116726184, 107822400, 380309920, -232295040, -1054391464, 19911424, -178358868, 215976176, -191567064, 50668416, 904751188, -29624000, -656312112, 221818880, -1569673560, 10278720, 262366672, 230974720, -127204668, 786878880, -732560076, -4810752], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "138.6.a.e", "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], [1, 0], [-4, 0], [9, 0], [16, 0], [-2, 3], [-36, 0], [-20, -5], [-64, 0], [81, 0], [8, -12], [-80, -20], [144, 0], [-728, 12], [80, 20], [-18, 27], [256, 0], [-218, -135], [-324, 0], [-224, 177], [-32, 48], [-180, -45], [320, 80], [529, 0], [-576, 0], [-1735, -12], [2912, -48], [729, 0], [-320, -80], [3182, 282], [72, -108], [-1180, -566], [-1024, 0], [-720, -180], [872, 540], [-2270, -50], [1296, 0], [-9694, 402], [896, -708], [-6552, 108], [128, -192], [-8738, 896], [720, 180], [-11880, -509], [-1280, -320], [-162, 243], [-2116, 0], [-17842, -950], [2304, 0], [-12557, 200], [6940, 48], [-1962, -1215], [-11648, 192], [738, 923], [-2916, 0], [-9080, -200], [1280, 320], [-2016, 1593], [-12728, -1128], [11546, 2830], [-288, 432], [-35442, 238], [4720, 2264], [-1620, -405], [4096, 0], [7000, -2208], [2880, 720], [-40912, 495], [-3488, -2160], [4761, 0], [9080, 200], [7776, -4392], [-5184, 0], [24822, -4116], [38776, -1608], [-15615, -108], [-3584, 2832], [17000, 800], [26208, -432], [51340, 911], [-512, 768], [6561, 0], [34952, -3584], [19548, 5492], [-2880, -720], [-61934, -384], [47520, 2036], [28638, 2538], [5120, 1280], [-10614, -4791], [648, -972], [5320, 3400], [8464, 0], [-10620, -5094], [71368, 3800], [82222, -1026], [-9216, 0], [-12886, 7042], [50228, -800], [-6480, -1620], [-27760, -192]]}