# Stored data for newform 8005.2.a.g, downloaded from the LMFDB on 08 June 2024. {"Nk2": 32020, "analytic_conductor": 63.92024681803495, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, 1], [1601, -1]], "atkin_lehner_string": "+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [8005, 1, [1602, 4806], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 137, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [16394986737, 2118574090425, 31231252939025, -757384921012166, -9616202238218105, 129444636101117643, 973934215043343018, -11370960239885047075, -51549017432471521756, 583954601858464200408, 1760316863672388297877, -19624800688194018790242, -43699151228826183108605, 465370620439004598855235, 846130832064510657272575, -8185050521828490859610288, -13245413488379014249303870, 110525168597657667980088420, 169867386897349012929572549, -1175372160034468924840009796, -1790794556018196193074858097, 10044030914371876942135509481, 15558776652537024346228867023, -70143016485267287137361338017, -111974676233998857769923518374, 406220329663304041047106328641, 672659491628385781087720812243, -1976278821693757294443396601902, -3403492074181620493009137621542, 8170015594016572996952646343407, 14641688987318005340886341950139, -28994453794380610062151999399915, -54044830303817575617568896030051, 89139507754549435246733683572404, 172625357500831975854690460561672, -239337342066784639339155476651608, -480847699460297147614036490537956, 565309987792262830325924289089763, 1176234656772462921539839626144996, -1182297618003832788870547507898847, -2542592409182718859675711504995241, 2202304075177839819016989434592455, 4884015052744377997690410445542332, -3673143639630063445859384096735508, -8378251718770535169379758102918738, 5511771785173417333779591415347477, 12892312893284619256589811001619494, -7473534846561650308271776614707129, -17865969800420441545461218370316626, 9192977615279146018278642745952902, 22375553183810055215985258012763083, -10295195828012041970616833177068522, -25406314411153396401179094161284031, 10530863152341612222634578285311064, 26227281565927547695104475885123774, -9867433513935869681824774383683077, -24677458438635238356402520894090622, 8491372616272687261198460717260678, 21210775825631087693824856066276534, -6726269823743617237038612121659693, -16687357995696541005466361246919946, 4914199874288198354745478755101229, 12038188271622594630214925374347507, -3317010735411158989530041663986505, -7975432066894305883481355956446734, 2071420516743282842599992716746380, 4859143423013605551468410380575714, -1198154443039322201985491204398133, -2725785340067124447498565334840839, 642490870747935308022693709771703, 1409254779292643628771904490552867, -319606507203170922967901592353272, -672081100552122744535850527598827, 147553745195733473232628864964183, 295861171794647124488557988724206, -63237874379885318723681727832940, -120287766600947521997792320646776, 25160888578503969516681781339850, 45184505427902751371143498624827, -9292990563686888201297258010153, -15685349889254050746403504916470, 3185374464429559889684575350733, 5032360506011564277968718564610, -1012920379832757206113719646609, -1492077698716645605025383849232, 298659527107960962789898820706, 408746131559417212095319523778, -81598625032022659272045998267, -103415808357790092804882485935, 20642173429754311226682977234, 24151498827666537572174417255, -4830514905800269119664293246, -5202321567855056470350963223, 1044551853472453046451693592, 1032597743326864220771315117, -208461349869497559503642439, -188640877330170088504894275, 38340617692137425055251144, 31673481246863193337144782, -6488101339181033622370358, -4879534594842823698199640, 1008283356864598649022380, 688363836686711199801785, -143586513172887125334520, -88715013874965042216227, 18690814882455565821908, 10416499147916285500100, -2217565280527474099446, -1110685672096410355217, 239006155144354670584, 107141543328993138915, -23309746174207823446, -9308431046774713015, 2047769478456134638, 724494327582068548, -161175035585855764, -50195238288525038, 11292535880448317, 3071858114431871, -698848381143397, -164483907489526, 37837892865567, 7614882638509, -1771097676204, -300194067973, 70582819385, 9876400014, -2347172396, -263769576, 63349643, 5492257, -1332787, -83626, 20500, 828, -205, -4, 1]], [3, [-320151626986633216, -115166496820731699200, 86345186900121179136, 51159040424467303429120, 175418385822960026177280, -6750073331030719156335360, -33521648462587118401098496, 385100576773950867425788096, 2113918914615109607771176072, -13129736806736966045896012560, -71725901146556374854010891828, 311167220676567374623141397832, 1556260677797886516318275523922, -5512168870605256617579765240472, -23555550300607672143259598436197, 75527842852988127469316366567444, 262109254611825292731637379382120, -815533911343607071050167554958918, -2220452929348897259937511981762724, 7039251628057230768357270247169711, 14671857420947233071730524455522522, -49231042957312877961701736182801182, -76834662308890506415152485388312442, 282680844758836422308916727620269988, 321436955951735886373275160055321288, -1349190855230544666294790994849627634, -1071117921905564654259993310938869598, 5413183706532997789379090042013964841, 2776588652541468915517503168469010816, -18440070389324706239910951081982192193, -5149226940640866186845700046691408904, 53799222063145167268168309354733309859, 4356806065619099605386740022337994936, -135438291586684535710676258623800078989, 12348785698005793766476845732490198449, 296088278531637075375451018588761966269, -72463503490388948243507073983004362101, -565099513445781026351829950263278771229, 218122261704676602810504517155108586951, 945649144804471032024083123961646964179, -492296520775224705814957367683260037188, -1392133339496941326391723316104816142486, 910644596568445393936201493712250474707, 1806991875537185271001897865253134949439, -1432671385858800306564019369874985626190, -2070078903308810418262505161602081285970, 1955397607059226775034948939864733574083, 2091629190600218309990295726604124009399, -2344041467145125668388560358477404473836, -1858228631925017737906845927246256616947, 2488798270259565504910664487992688306050, 1441106198242710381255257153416484465527, -2354829512585962685803793301040675490756, -960891265257978538884584765701052677569, 1994682900827092670920929689575125933591, 532469000940085358071995948778362283381, -1517992769077796692288373158773824997713, -223395259748900291324179539992921239089, 1040707057777018304620666076360484405391, 44428376899002034114511380953197790608, -644074588992296982915768151711272131298, 32835838219257856664787978963835596626, 360339143768320018356377412888801682240, -49532650466352644211205363645638994847, -182393575396348408760608799522827111746, 40109837997754706583804090470450597801, 83541219868804192426412461650307303195, -25179714756367876865371229981095980975, -34603319033881232771440630672480626986, 13334755474699053397165217628279797579, 12940564199661845774328791054208333973, -6160720799322687325321802056316820319, -4355848946035646491624730359842773795, 2525171660997776436392069598948929471, 1312678807430326359370156962281083771, -927070102675262874984600510150996344, -350896346115284001141061452340755643, 306635816118255793270479697006285589, 81792028085574403998357376013224119, -91705478953079059956062551156344166, -16044136906049910792374963198460145, 24852844108354941932347411664900631, 2411193092572833278632224736993837, -6110124791849331390350840609636812, -175638403419043851316360840827102, 1363077061070512784335182421511672, -44940760014047183180538433389331, -275761709039785885830663047768495, 24997963198625431169437140407511, 50519809882534599655863816847681, -7406554335157880450536913454177, -8360435468591998073640509825379, 1699560919425737542154996173508, 1245006497508326140120195490690, -328338844631267829981701288097, -165867823667510578570171319001, 55121797711999133429964616589, 19591348534950655355241432578, -8159351659428707021523002901, -2020920152632869576967176185, 1072385740602965511322413907, 177052864091839090805641659, -125506494111460395608880352, -12370601590108471054853259, 13083057945058063623470668, 557215936574358459542205, -1212540484744636530955351, 7854109624645457728873, 99542356923199258988368, -5116114935900951662126, -7196004799349188400793, 680934931794119501980, 454122036462974573949, -63079068668086279809, -24696407256235236867, 4645801270526647590, 1134059704793901538, -282747668559195988, -42422945591889223, 14379076373676130, 1195532470360153, -609968080929281, -19326452458759, 21351671028111, -227759910498, -604314448394, 29078921776, 13363732929, -1130940064, -217288475, 27504948, 2278391, -441592, -9276, 4341, -87, -20, 1]]], "hecke_orbit": 7, "hecke_orbit_code": 27021597797785413, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "8005.2.a.g", "level": 8005, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [5, 1601], "level_radical": 8005, "minimal_twist": "8005.2.a.g", "prim_orbit_index": 1, "related_objects": [], "relative_dim": 137, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "8005.2.a", "trace_display": [4, 20, -137, -30], "traces": [137, 4, 20, 152, -137, 14, -30, 24, 163, -4, 51, 32, -6, 49, -20, 170, 46, 4, 47, -152, 28, -19, 29, 39, 137, 67, 77, -58, 27, -14, 23, 42, 40, 38, 30, 222, -56, 87, 44, -24, 66, 34, 15, 87, -163, 37, 52, 56, 195, 4, 106, -31, 45, 83, -51, 148, 4, -101, 239, -32, 46, 63, -59, 200, 6, 108, -18, 152, 63, -49, 110, 6, -19, 81, 20, 94, 43, -3, 40, -170, 229, 3, 235, 94, -46, 110, 31, -105, 150, -4, 110, 76, 11, 56, -47, 146, 17, 75, 125, 152, 66, 29, -16, 175, -28, 37, 147, 125, 5, 19, 77, -99, 58, 96, -29, 128, 18, 22, 143, -39, 142, 138, -16, 89, -137, 189, -150, 123, 79, -67, 252, 120, -30, 127, -77, 124, 74, 82, 127, 58, 73, -46, 94, 318, -27, 161, 146, -156, 98, 14, 18, 256, 138, 59, -23, 57, 9, -16, 136, -42, 123, 20, -134, 190, -40, 146, 98, 135, 155, -38, 250, -64, 96, 67, -30, 153, 13, 55, 382, -222, 193, 46, -17, 66, 56, 124, -19, 123, 73, -87, 198, 146, -72, 210, -44, 287, 62, 60, 37, 24, 97, -70, 336, 148, -66, 117, -23, -63, 157, -34, 143, 168, 115, 40, -15, 279, -69, 90, 175, -87, 176, 139, -168, 377, 163, 47, 231, 9, 125, -37, 183, -192, 44, 185, -52, 519, 83, -71, 128, -56, 95, 31, 301, 110, -195, 256, -251, 250, 61, -4, 567, -82, -86, 188, -106, 338, 231, 21, 173, 31, 173, -70, 162, 217, -45, 119, 132, -69, 264, -83, 83, 428, 24, 132, 51, 327, -164, 184, 182, -148, 104, 64, 38, 233, -4, 76, 170, 44, 223, 101, 373, -154, 91, 83, -239, 297, 114, -4, 440, 32, 20, 39, -71, 175, -46, 370, 25, 230, 86, -63, 374, -129, 28, 260, 59, 264, 47, 88, 135, -200, 130, -77, 183, 424, -6, 146, 53, -52, 126, -108, 163, 456, -115, 29, 18, 281, -19, 80, 476, -152, 283, 189, -279, 282, -63, 207, 219, 168, -24, 49, 118, -221, 195, 79, -110, 362, -18, -41, 161, -6, 284, 214, 207, 320, 19, 183, -191, 190, 95, -81, 373, -31, -137, 263, -20, 211, 106, 15, 104, -94, 102, -7, 238, 253, -43, 251, 101, 64, 203, 3, 199, 97, -82, 186, -40, 371, -50, 130, 191, 170, 201, 87, -68, 235, -229, 52, 82, 117, 71, -3, 366, -19, 69, -1, -235, 269, -62, -88, 612, -94, 105, -8, 115, 112, 46, 139, 6, 315, 65, -110, 182, -20, 26, 206, -31, -46, 78, 37, 157, 105, 209, -307, 310, 180, -150, 185, 61, -112, 112, 4, 414, -36, -59, 78, -110, -21, -110, 242, 341, -76, 154, -604, -370, 177, -11, -8, 501, 105, 58, -56, 145, -100, 116, -97, 47, 131, -5, -20, 184, -146, 102, 135, 17, 107, -17, -116, -531, 455, 121, -75, 365, -471, 49, 225, -125, 48, 115, 176, 109, -152, -11, -291, 200, 93, -66, 29, 123, -236, 209, -29, 156, -35, 82, -144, 16, -174, -91, 17, 92, -175, 184, -768, 301, 256, 28, 5, -110, 148, 148, -37, 628, -326, 66, -210, -147, -17, 90, 0, 271, -125, -106, -203, 14, 260, -5, -490, -39, 162, 81, -19, 314, -68, -49, 16, -77, 38, 95, 207, 267, 99, 17, -271, 584, -232, -58, 27, -288, -339, 178, -96, 58, -61, 236, -39, 29, 169, -85, 54, 292, -128, 159, -271, -410, 213, -18, -233, 534, 51, 83, -22, 56, -771, 194, 251, -143, -78, -73, -21, 189, 39, 65, -279, 142, -31, -142, -466, -231, 582, 71, -138, 515, -193, -57, 81, 16, -62, 13, -2, 340, -89, 133, -303, 69, -223, 137, -26, -23, 41, 198, -189, 151, -237, 184, -214, 150, -135, -340, 200, 214, -123, 195, -280, 112, 281, -79, -307, 251, 35, 55, 67, 122, -536, 37, -196, -252, -3, -177, -97, 396, -120, -31, -271, 214, 336, 30, -90, -22, 381, 35, -127, 228, -354, -174, -31, 77, -139, 20, 37, 51, -124, -69, -308, 137, 122, -74, -206, -473, -32, 323, -82, 158, 26, 116, 56, -127, -412, -130, 268, 442, -58, 101, -663, -110, -249, -73, -108, 269, -62, 166, 46, 39, -301, 325, -396, -94, 388, -243, -145, 559, -318, -76, -300, 179, 213, 27, -517, -257, 311, 202, -161, 315, -451, -87, 87, -146, -222, 177, -8, 232, 156, 95, -581, -148, 273, -98, -280, 524, -63, 218, -14, 3, -122, 214, 141, -18, -371, -293, 216, 158, -256, 154, -240, -79, 198, -138, -148, -408, 405, 176, -59, 281, -551, 188, -260, 23, -67, -73, -213, 589, -57, -33, -375, 162, 366, -9, -571, -66, 97, 262, 16, 182, -768, -126, 91, -136, -17, 262, -22, 69, 42, 288, -580, 738, 63, -123, -197, -328, 6, 102, -20, 158, 47, -71, 158, 134, -103, -148, 371, 739, -190, 35, -828, -399, -41, 40, -419, 343, 255, 124, -146, 130, -550, 281, -200, -98, 115, -380, -67, 414, -135, 54, -312, 365, 233, -155, -362, -438, 390, 10, 38, 394, -508, -87, -185, -250, -49, 152, 83, 322, 64, -44, -217, 78, 268, -96, -406, 437, -303, 360, -67, 191, -278, 186, 6, 30, -521, -315, -33, 179, -153, 224, -841, 73, 392, -13, -247, 92, 265, 118, -55, 72, -950, 57, 355, -382, 333, -102, -183, 457, 222, 99, -776, -60, -61, -193, -647, -241, 520, 238, -46, 273, -750, -71, -63, 17, 6, 125, 36, 192, -66, -187, -272, 328, -194, -56, -181, 186, -637, 151, -124, 266, -252, -44, 301, 19, -521, 46, 150, 455, -123, 242, -674, -201, 955, -73, -375, 91, 214, 115, 87, 78, -421, 324, -365, -198, -478, -1, -136, 274, -146, 276, -303, 482, -352, 72, -364, -425, 200, 266, -210, 941, 40, -142, -173, 44, -214, 139, 215, 382, -287, 42, -534, 120, -64, -62, -120, 50, -273, 233, -60, 71, -200, 224, 179, -37, -337, -384, 98, 376, -24, 11, -652, -173, 1045, -97, -593, -30, 53, 123, 70, 95, -927, 185, -382, -336, 291, -18, 72, 645, -148, 146, -466, 43, 354, 66, -591, -12, 718, 87, -117, 227, -938, -185, 100, 23, -138, -12, -39, 293, 63, 64, -269, 303, 229, -157, -3, -439, -222, 370, 34, 236, -120, 213, -382, -143, -177, -413, 69, 479, -168, 69, -735, -97, -512, -115, -283, 760, 343, 142, -40, 113, -540, 272, -477, 15, 266, -144, -122, 706, -279, 88, -957, 274, -8, 69, -623, -497, 961, 170, -90, 665, -835, -308, 282, -175, -256, 146, 163, 206, 87, 13, -258, 74, 25, -176, -109, -230, -602, 508, -139, 86, 261, 212, 121, 168, -733, -460, 459, 416, -377, -27, -725, 123, -80, -163, -111, -76, 241, 261, -47, 143, -643, 146, -167, -231, -55, -113, -280, 946, -9, 65, -317, -310, 438, -125, -933, 0, 424, 173, 37, 126, -751, 26, -57, -183, -246, -48, 243, -6, 192, 141, -540, 217, 243, -44, -331, -230, -325, 411, -185, 259, -637, -45, -122, 52, -285, -271, 366, 644, -519, 41, -514, -530, 344, -83, -98, 189, 757, 76, 71, 131, -515, 383, -123, -128, 95, -300, -261, 352, 56, -70, -368, 326, -267, -95, -555, -393, 480, 161, -31, 481, -856, -163, -102, -301, -119, 127, -118, 426, -110, -83, -820, 314, 417, 195, -419, -220, -57, 39, -256, 76, 36, 16, -8, 251, -1159, -187, 474, 465, -250, 145, -692, -257, 906, -61, -93, 227, 39, 58, 4, 353, -546, 133, -220, -567, 376, -492, 211, 898, 82, -213, -261, 160, 228, 86, -757, -299, 102, 271, -188, 214, -873, -68, 21, 106, -384, 266, -157, 270, -338, -146, -647, 530, -175, -231, -501, -85, -308, 136, -21, 306, -695, 134, 85, -173, 144, -261, 169, 285, -31, 380, -980, -434, 265, -173, -196, 430, 393, 88, 70, -75, -672, 107, -133, -162, -511, -336, -268, 401, -217, 13, -210, 538, 95, 45, -990, -543, 906, 392, -119, 522, -1209, -76, -699, -132, -379, 52, 23, 89, 69, -191, -718, 483, 322, -264, -198, 327, -1, 409, 83, 76, -205, -76, 109, -83, -304, -353, 410, 154, -428, 242, -905, -21, 681, -24, -316, -234, 625, 411, -132, 121, -1191, 123, -548, -51, 82, 188, 195, 700, -327, -72, -289, -537, 80, 164, -545, 26, 441, 44, -184, 400, -710, -313, 213, -182, -772, -110, 426, 341, 148, 101, -685, 548, -496, -104, -279, -573, -591, 333, -64, 140, 186, 485, -174, -38, -455, -304, 235, 708, -233, 63, -1165, -727, 156, 4, -550, 303, 248, -104, -76, 71, -742, 567, -446, -170, 71, -340, 213, 259, -44, 238, -1277, 198, 271, -223, -1041, -296, 517, 81, -101, 257, -681, -155, -143, -373, 113, -216, 111, 468, 154, -180, -363, 550, 60, -91, 362, -647, -56, 469, -83, 0, -153, 159, -222, 239, -603, -489, 479, 336, -297, 61, -1108, 362, -121, -114, -214, -6, -210, 289, 4, -152, -822, 311, 574, -440, -1037, -213, -81, 669, -32, -41, -311, 135, 124, -20, -871, -213, 329, 9, -39, 763, -948, -186, -115, 71, -135, 98, 51, 269, -175, 331, -500, 389, -653, 46, -568, -642, 21, 232, -370, 400, 124, 142, -302, -25, -705, -592, 780, 652, -230, -26, -984, -402, 398, -86, -504, 130, 95, 118, 63, 66, -366, 239, -183, -374, 50, -215, -254, 275, 129, -76, -620, 380, 105, -28, -890, -517, 455, 305, -260, 954, -2016, 265, 24, -59, -127, 36, 95, 366, -264, -39, -880, 121, 31, -47, -872, 249, 20, 487, -88, -146, -334, -27, 336, -135, -590, -425, 567, 276, 200, 137, -1002, 7, -13, -130, -580, 3, 488, 23, 77, 648, -596, 333, -1138, -183, -69, -661, -319, 581, -424, -73, -656, -109, -261, 6, -566, -213, -150, 339, -146, -68, -490, -342, 184, -53, -386, 195, -54, 106, 52, 95, -985, 678, 507, -126, -296, -210, -23, -233, 108, 176, -740, -27, -135, -163, -1407, -410, 195, 160, -456, 80, -1374, -126, 341, 115, -528, 552, -260, 197, -29, -274, -872, 332, -692, -18, 70, -864, -57, 307, -281, 445, -848, 100, 139, 19, -681, -578, -88, -241, -80, 314, -987, -22, 3, -476, -343, -62, -99, 550, 152, -50, -1002, 63, 45, -283, -195, 216, -128, 197, -189, 86, -1216, 234, -153, 279, -1137, -257, 172, 577, -282, -35, -1508, -410, -150, 63, -693, -180, -9, 58, -207, 188, -659, 176, -1043, -219, 0, -330, -568, 1116, -168, 71, -304, -390, -87, 24, -551, -393, 357, -386, -49, 305, -917, -107, -211, -118, -445, -525, 87, 0, 221, -370, -940, 759, -779, -195, -447, -206, -778, 625, -79, 234, -245, -498, -157, 110, -1564, -85, -26, 131, -362, 213, -1110, -477, 115, 18, -546, 363, 9, -196, 41, 167, -1138, -229, -92, -161, -419, -355, 16, 155, 6, -58, -513, -309, 50, -284, -1092, -793, 141, -181, -214, 887, -1461, -617, -241, -207, -540, 104, -263, 370, -320, -574, -804, 539, -942, -19, -305, 234, -494, -22, -183, -225, -130, -465, -15, 191, -337, -176, -184, -174, -190, -233, -1710, -616, 492, -95, -563, 264, -1254, 278, 81, 139, -1221, -203, -566, -373, -744, -363, -140, 325, 31, -140, -396, -592, -383, 137, -1476, -172, 1017, -280, -263, -42, -1239, -172, -450, 20, -535, 18, -465, 155, -211, -471, -592, 161, -357, -106, -281, -988, -249, 120, -15, 277, -483, -223, 160, -104, -1140, -427, 94, 259, 94, -136, -2199, -367, -113, -102, -615, 1002, -423, -353, 7, -841, -452, -509, -545, -238, -489, 151, -699, 527, -253, -113, -683, 197, -430, 43, -914, -783, 588, -281, -251, 436, -1532, -310, -265, -101, -1021, -28, -323, 368, -64, -168, -717, 5, -327, -203, -1423, 226, -1544, 26, -3, 318, 136, -785, -122, -199, -1119, -689, 208, 170, -97, -70, -904, 126, -299, 82, -70, -225, -1029, -123, -186, -195, -819, 100, -1079, 40, -54, -17, -761, 593, -371, -230, -944, -574, -315, 50, -1131, -112, 355, 33, -130, 158, -1332, -218, 165, -191, -683, 133, 529, -36, -170, -471, -933, 398, -913, -201, -83, -967, -586, -36, -87, 178, -97, -271, -93, 68, -969, -656, 69, 236, -235, 123, -636, -857, -151, 229, -321, 810, -168, -50, -52, -144, -876, -385, -416, -82, 67, -461, -176, 262, -117, -42, -743, 156, 685, -71, -730, -461, -77, -329, 3, 342, -631, -418, -647, -366, -699, 389, 341, 305, 19, -171, -680, -16, -650, -69, 83, 164, 69, 75, 1, 191, -1780, -337, 180, 235, -1163, 80, 130, 120, -269, -168, -1007, -79, 165, 62, -264, 134, -1393, 220, 88, -192, 285, -77, 621, -612, -144, -217, 175, 1021, 94, -243, -425, -342, 268, -105, -565, -143, -12, -810, 8, -153, -207, -41, -111, -115, 93, 178, 405, 74, -112, -97, -577, 711, 841, -46, -570, -295, -384, 288, -139, 369, 89, 14, 42, -6, -336, -469, 547, -33, -315, 3, -1843, -792, 716, -65, -11, 442, 938, -384, 110, 155, -646, -97, -270, -182, 12, -325, 320, 655, 20, 145, -23, -14, 40, -26, -543, -587, 794, -271, -206, 266, -750, -294, -191, 31, 432, 63, -98, 346, 46, 112, -509, 325, -695, -78, -1070, 377, 69, -202, -37, 12, 39, -1059, 478, -157, -480, -255, 576, -81, -105, 46, -1068, -153, 160, -209, 442, -276, 536, 335, 307, 125, -949, 105, 323, -310, -469, -89, 583, 873, -180, 12, -333, -886, 29, 150, 9, -128, 348, -206, -185, 268, -565, -272, 39, -61, 306, 39, 108, 183, 112, -335, -246, 621, 827, -112, 388, -531, -48, -11, -4, 424, -366, -499, -144, -414, -1430, -189, 240, 1109, 36, 233, -1138, -499, 266, 59, -195, 677, 299, -37, -78, 296, -1036, 344, 92, 110, 431, -450, 119, 174, 21, -52, -234, 217, -150, 110, 182, -302, 491, -659, -242, 435, -183, -290, 825, -341, 572, 33, 619, 532, 76, -68, -330, -322, 56, -154, -1223, 54, -186, -83, 604, 339, -434, 466, 438, 370, 245, 94, 321, -32, -177, -39, -1494, 366, -14, 11, 112, 48, 130, -53, 8, -185, -708, -155, 65, -501, 198, 462, 726, 309, -105, -41, -1096, -554, 734, -58, -207, -274, 1431, -244, 56, 697, -566, -568, 9, -145, 176, -110, -109, 263, 100, -520, -695, 786, -555, -116, 37, 236, -1140, 487, 97, 478, 308, -716, 165, -47, 345, -388, 1176, 741, -131, 57, 101, -271, -264, 5, 318, -22, 196, -260, 20, -198, -596, -241, 1012, -184, 416, -625, 396, 372, 146, 357, 175, 461, 955, -102, -549, -451, -220, -551, -135, 631, -421, -216, -41, -17, -228, -103, 535, 171, -107, 251, 48, 92, -725, 17, 268, 167, 187, -334, 116, 393, 446, -424, 278, 531, -772, -448, 35, 188, -455, -236, -294, -216, 1311, -121, -494, 143, 837, -225, 75, 426, -98, 298, 436, -365, -28, -47, 759, 351, 471, -22, -216, 74, -20, -49, 39, 526, 418, -212, -225, 246, -1404, -526, 214, 125, 363, 42, 861, -216, -48, 130, 128, 905, 1057, -115, -349, -429, 403, 358, -176, 757, -74, -1322, 725, -109, -1217, -244, 1003, 117, 152, 246, -264, -591, -495, 11, -63, 264, 1128, -268, 291, 120, 591, -187, -368, -200, -288, -173, 507, 808, -93, 188, -371, 537, 249, 66, -41, -973, 221, -1113, -29, 314, 224, -110, 111, -123, -337, 82, 858, 638, 236, 14, -680, -236, 444, -209, -378, 596, 415, -94, 29, 293, 124, -329, 310, -156, 686, -469, 794, -18, 35, -204, -1373, -5, 219, -82, 974, 397, 189, -189, 144, -315, -25, -215, -369, -16, 569, -22, -56, 781, 174, -173, 39, -38, -251, 91, -657, -394, 1210, -959, -17, 209, -302, 361, 1175, -92, 884, 709, 175, 220, 175, 47, 87, 1258, -155, -184, -346, -173, -230, -261, 768, 507, -955, -426, 37, -301, -289, 163, 146, 1332, -256, -289, -450, -628, 412, -28, -216, 868, -332, 81, -5, 128, 158, -140, -133, 110, 251, 129, 848, -41, -148, -205, 106, 378, 520, -148, -1110, -290, -31, -531, 37, 523, 451, -515, 465, -628, 1592, -425, 752, 177, 326, -542, -329, -178, -4, -66, -190, 53, 370, -187, 210, 114, 139, -90, 992, 147, -269, 244, 217, -277, 17, -1, 372, -468, -213, -90, 754, 971, 57, 115, 0, 649, -612, -126, 489, -271, 165, 6, 584, 33, 125, 469, -518, 133, -67, 106, -1469, 68, 308, -999, 203, 10, 182, -49, 216, -14, 159, -248, 505, 610, -260, 72, -512, 472, 275, 5, -137, -371, 867, 445, 490, 429, -186, 45, 275, 39, 298, 101, 191, 243, -162, 7, -102, -509, 500, -81, 372, 452, -52, -126, 19, 828, -98, -90, 860, -314, -664, 176, 279, 418, 68, 257, -522, 102, 1425, 49, -5, -689, 753, -578, -16, 677, -449, -87, 26, 77, -83, 403, 1155, 374, -38, -911, -57, 319, -1329, -95, 476, 188, 859, 266, -207, 118, 875, -261, 625, -267, 150, -247, 627, 319, -99, 225, -951, 133, -121, -17, 191, 260, -38, -6, 271, 409, -52, -176, -150, -584, -1105, -144, 1514, 841, 232, -313, 221, -655, 289, 58, 175, 593, 710, -653, -27, 401, -1067, -273, -305, 288, 936, -500, 742, -15, 339, 147, 199, 915, 1286, -178, -750, 240, 547, -803, 96, 610, 196, -476, 363, -58, -1575, 71, -261, 577, 61, -53, -232, -262, 222, -236, 151, 298, 369, 246, 39, 55, -216, 389, 77, -29, 1520, 47, 347, 172, -169, 240, -707, 358, 230, 85, -284, -795, 406, -868, -54, 834, -458, -1162, 1290, -292, 659, 279, 1809, 341, 128, -56, -36, 530, -136, -159, 76, 678, -81, -25, 271, 361, -803, -137, -187, 410, -65, 91, 1090, -36, -213, 18, -1299, -263, 161, 18, 1456, -602, 375, 257, 233, 297, 208, -918, 142, -534, -184, -28, 748, 1129, -51, -216, -329, -90, 1212, -83, 232, -148, 1487, -561, 22, 421, -1118, -236, 54, -56, 510, 161, -71, 267, 771, 100, 509, 620, 476, -194, -11, 264, -13, 298, -251, 664, -1319, -763, 1029, 143, 1843, 19, 781, 471, 78, -172, -653, -863, -334, 73, 252, 960, 1556, -280, 21, -405, -584, -41, 298, -189, 641, -786, 466, 576, -39], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}