# Stored data for newform 4003.2.a.b, downloaded from the LMFDB on 27 April 2024.
{"label": "4003.2.a.b", "space_label": "4003.2.a", "level": 4003, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660928931, "dim": 152, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-67141, 25070181, -700074204, -181189477579, 3565430972352, 74182692228277, -1328687248138609, -14102898529466637, 206753922225676261, 1579209216547403558, -17767375748616074344, -112114944801971880437, 966968655667477505724, 5344798515868959367061, -36127881469941669966491, -179945464294220413846796, 976106605557619715300410, 4462620208120624271904675, -19776599296275909134412722, -84391479009851744024720698, 308821241203280080369396285, 1251849726999921542695278624, -3799137485439568420604626748, -14907016504291702868683466435, 37490822927228637714832164281, 145222872170528188412286894360, -301219213550457872566018925772, -1175602183760966847158573028678, 1994039771752796209213389739870, 8011420019528265752173601476429, -10973707543096062451466243763425, -46466467697480292143206881508756, 50482139938981484225567961599721, 231531272176172890554435882246658, -194323346697419888708760155805768, -999119680813124401519993108390464, 622018179322322570091277660890391, 3760113029610417171400793663953595, -1621365751385548628560370382451821, -12416820970192859096467033518796206, 3238376051440677786582760212091256, 36171223529052578212950680804597885, -3888464999598160671327229081806832, -93386025552027105494513429238902559, -3004548317470103907444909193407300, 214546885755735061520465437234755617, 34622601313819905650583922621502214, -440139790803228075698450004053418019, -124591225460770715694937951508708225, 808634885857607345775137516911257413, 323600558434504403350760948104852145, -1333611600954714951665324208558863760, -687809374879302207728871544929886792, 1977803115434394524145267235629072743, 1252331208882602729526935909803999395, -2640460918426392801809904244277888389, -1997949126200976723205412365169711874, 3174121831526357946130841976007604395, 2830249420913181985636070087412514361, -3432711761983641788082749565223410207, -3590907453087674674600841160359214900, 3331532508233841630667496185537727836, 4105480095515053529510617991081186321, -2886999652552949463600200759537638322, -4248584257445756695093616805090868536, 2212306717472370348704077045984864150, 3993083799314346860520395298416105763, -1470703956288842885846313911261447875, -3417185455598896386099511341977738173, 812595851986853807216193943413098622, 2667824714768909891045303723307191761, -328864447102586687616411338434420398, -1902686604119508513835987010882889952, 38544237431618562077959931444191678, 1240701549946180794055178630998374732, 92883564207795485435922921131039537, -739944982144698591227401559932642052, -122291122486669838047950283858154402, 403510231998555336084002544739379749, 102509577972120667276000200308607811, -201011565176366914646838278278603718, -69259075439767623832915800371642932, 91304032452042247670571444504336188, 40262394515132623551654321444515342, -37695088241261436759137085455526930, -20700761066720428407634351527898304, 14071616720671514694335830932495317, 9546344391981271324702793333329280, -4708530268818045687796034710889940, -3980080193691731041366477739823496, 1390536796131932825119566879177496, 1507182680593957028539306997417342, -351399160583689640787631997614567, -519760077469444508011357336628990, 70387820470893891464059274429564, 163433048030270543193213682725727, -8197616122278085717971473395441, -46862977716224111367680196793737, -1266301564659048308979890762023, 12242736996893963632818487348481, 1220251406656463051162856107942, -2908104172111862467651509872873, -497667734087290215829717511929, 625965959828698915334068152093, 153448054779579229515699627002, -121445810100226082860457411582, -39678228073165937869823701982, 21059015759973944935744789669, 8927052431452048781876081446, -3218110186028909664803319271, -1776261536490134198890238836, 422235592941768983369615345, 314941395619711814955748616, -44887510562891437075242975, -49903572761777497062879406, 3205509437941347511704336, 7065361433115652209028251, 26578514303037349233531, -891371943621848104735284, -59013171410677405095207, 99671899752675632579267, 12688380039202135450829, -9791112346751070761754, -1879227359132532856002, 832881925943062110773, 222919632175106962346, -59830422484415216824, -22126715145423863081, 3448467522683545836, 1864353337255747578, -138184087170472709, -133533781846388543, 1199716306044726, 8071886038985793, 384842805900084, -405274544509635, -41435576309478, 16417164378504, 2671747557270, -507066240764, -125079143245, 10342502763, 4379836354, -55907926, -112086616, -4595767, 1945411, 177403, -18712, -3036, 21, 22, 1]]], "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16012, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 31.964115929118538, "level_radical": 4003, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [4003, 1, [2], [1]], "inner_twist_count": 1, "level_primes": [4003], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 152, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[4003, 1]], "trace_display": [-22, -18, -59, -19], "traces": [152, -22, -18, 138, -59, -17, -19, -66, 106, -15, -40, -53, -59, -36, -40, 118, -93, -59, -16, -108, -62, -37, -107, -31, 101, -64, -63, -53, -124, -68, -15, -129, -49, 0, -76, 45, -98, -125, -47, -7, -56, -84, -62, -114, -142, -3, -111, -92, 117, -64, -21, -85, -347, 3, -16, -73, -115, -29, -50, -54, -62, -55, -70, 64, -147, 34, -86, -174, -104, -7, -86, -139, -27, -52, -49, -11, -346, -59, -17, -149, -8, -31, -106, -51, -69, -85, -32, -113, -59, 10, -9, -314, -230, 7, -74, -54, -60, -77, -96, 25, -169, -27, -24, -122, -24, 49, -184, -103, -62, -28, -9, -122, -289, -45, -9, -211, -183, -18, -53, -98, 94, -110, -117, 29, -279, 24, -60, -210, -71, -21, -49, -45, -136, -115, -40, -20, -364, 76, 47, -114, -120, -34, -46, -33, 13, -40, -80, -123, -296, 118, 12, -268, -217, 54, -180, -7, -197, -132, 17, -12, -143, -76, -43, -15, -146, 42, -66, -194, 79, -142, -23, -127, -270, 48, 0, -174, -152, 16, -169, -88, -139, -109, -136, 95, -126, 29, -33, -230, -209, 78, -141, 3, -19, -82, 4, 108, -418, -72, -2, -143, -71, 5, -177, 11, -138, -46, -239, -19, -59, 174, -11, -527, -234, 115, -34, 1, -28, -266, 59, 84, -289, 147, -77, -50, -125, 82, -67, -46, -125, 111, 7, -5, -313, 59, -67, -53, -220, 77, -102, 94, 23, -170, -97, 79, -419, 39, -142, -108, 21, 159, -50, 62, -216, -52, 66, 74, -296, 129, 12, -75, -271, 58, -301, 181, 105, 66, -80, -44, -283, -14, 21, -297, -155, 108, -120, 83, -195, -44, 84, 133, -180, 5, -19, -87, -124, 161, -254, -116, 95, 7, 6, 49, -324, 184, 10, -147, -113, 51, 25, 55, -79, -294, -59, 123, -200, 37, 28, -437, -310, 56, -84, 81, -84, 13, 63, 155, -535, 215, 36, -117, -1, -7, -227, -62, -31, 17, 15, 128, -92, 239, -32, -133, -420, 139, -17, 223, -46, -107, 71, 139, -312, 26, -26, -206, 4, 182, -234, 204, -50, -3, 9, -95, -111, 87, 61, 10, -68, 133, -81, 319, 80, -15, 1, 126, -437, 97, -90, -533, 105, 182, 50, -197, -294, 60, 94, 244, -175, -77, 110, -6, -67, 2, -171, 70, 204, -20, -108, 132, -572, 235, 152, -27, -89, 195, -45, 85, -125, 6, -10, 70, -207, 197, 25, -160, -90, 176, -279, 124, 56, -88, 162, 161, -488, 256, 53, -76, -186, 287, -63, 291, -111, -141, -81, 177, -233, 260, -7, -234, -178, 256, -86, 15, -47, 20, 129, 118, -393, 47, 96, 88, 15, 254, -236, 290, -161, 88, 207, 10, -90, 213, 114, -402, -146, 109, -76, 126, -108, -30, 0, 303, -120, 289, -51, -278, 93, 184, -287, 41, 26, 17, 26, 249, -327, 192, 65, 19, -754, 86, -9, 141, 179, -32, 230, 379, -576, 331, -25, -64, 154, 260, -146, -83, -238, 82, 131, 395, -201, 168, 89, -87, -19, 150, -102, 309, 104, -29, 71, -21, -338, 505, 26, -190, -81, 333, 3, 295, -49, -142, 61, 169, -192, 161, -96, 243, -73, 136, -313, 169, 95, 164, 97, 60, -681, 218, 259, -221, -49, 191, 46, 330, 114, -81, -249, 343, -133, 589, 51, -484, 40, 235, 67, 426, -60, 126, 139, 399, -779, 298, 15, 60, -20, 58, -137, 359, 105, 192, 46, 133, -93, 717, 162, 10, -137, 366, -284, 241, -27, 169, 285, 345, -424, 206, 81, 237, -80, 262, -164, 23, 26, 200, 107, 97, -322, 483, 182, -212, -339, 365, -141, 630, 202, 41, 17, 327, -325, 330, 73, -356, 128, 350, -95, 26, -156, 141, 325, 556, -371, 323, 45, -140, 27, 326, -101, 424, 54, 258, 128, 70, -10, 398, 33, -399, -2, 290, 202, 430, -32, -25, 120, 417, -322, 233, -63, 104, 64, 459, -285, 224, 64, 219, 153, 248, -908, 242, 192, 344, 77, 316, -79, 253, 124, -12, 62, 254, -185, 423, 99, 96, -58, 424, 50, 89, -148, 0, 116, 282, -501, 396, 206, -159, 141, 233, -162, 398, 164, 329, 61, -8, 111, 495, 74, -202, -424, 295, -168, 475, 32, 102, 190, 442, -429, 406, 110, 55, 169, 421, -172, 256, -116, 311, 141, 332, -163, 677, 303, -37, 48, 163, -88, 482, 236, 25, 147, 261, -553, 540, 100, 183, -125, 408, -8, 117, 46, 448, 300, 505, -277, 398, 251, 66, 134, 362, 12, 564, 322, 210, 80, 558, -483, 264, 78, -226, -263, 568, 198, 325, -597, 93, 250, 549, -38, 466, 152, 50, -27, 338, -234, 474, 142, 454, 210, 332, -466, 604, 409, 273, 10, 321, -227, 773, -18, 42, 105, 445, -159, 303, 109, -267, 192, 662, 156, 230, -113, 411, 271, 408, -562, 495, 353, 114, 222, 313, -231, 306, 7, 191, 0, 327, -184, 511, 325, -11, -97, 320, -25, 472, -13, -47, 467, 447, -343, 389, 77, 488, 225, 558, -199, -156, 72, 150, 444, 210, -589, 588, 209, 283, -664, 441, 118, 981, 170, -118, 255, 396, -347, 930, 318, -629, 44, 494, 44, 114, 178, 473, 482, 602, 32, 714, 241, 369, 39, 291, -303, 471, 193, 287, 160, 481, -154, 434, 233, -515, 238, 625, -56, 631, -143, 129, 392, 681, -90, 447, 35, -73, 100, 384, 129, 649, 220, 447, 217, 316, -972, 556, 476, 477, 46, 236, 143, 146, 277, 79, 543, 451, -181, 966, 205, -1, 98, 794, -12, 478, 75, 240, 485, 460, -711, 371, 236, 402, -1, 212, -13, 595, -129, 414, 322, 425, 40, 851, 363, -248, -455, 652, -60, 446, 69, 295, 282, 248, -187, 475, 361, 335, 294, 693, 31, 316, 123, 108, 396, 543, -566, 581, 479, 277, -102, 548, 181, 798, -11, 241, -44, 474, -143, 877, 244, -13, 454, 532, -85, 473, -378, 130, 557, 926, -452, 706, 265, 26, 229, 320, 71, 596, 204, 538, 245, 201, -351, 829, 279, 209, 305, 498, 68, 661, -192, 285, 332, 679, 180, 418, 183, 266, -53, 371, 181, 740, 267, 187, 305, 183, -597, 335, 369, 166, -369, 221, -51, 599, 9, 89, 426, 157, 152, 603, 245, -376, 6, 511, -25, 367, -162, 322, 337, 404, -1073, 302, 119, 483, 201, 311, 24, -55, -60, 60, 127, 251, -182, 457, 244, -639, 46, 40, 314, 625, -135, 94, 300, 539, -266, -9, 4, 277, -90, -89, -147, -1, -138, 260, 288, 111, -514, 360, 223, -220, -181, -62, -148, 174, 177, -146, 386, 66, 12, 429, 117, -209, 101, 490, 143, -45, -342, -32, 534, 294, -218, -109, 279, -166, -204, 258, -299, 198, 253, 61, -91, -324, -633, 609, 180, -105, 267, 91, -89, 644, -190, 141, 128, -340, -187, -333, 133, -115, -60, 376, -297, 183, 73, 211, 261, -52, -272, 218, 248, 270, -102, -14, 157, -61, -24, 73, 153, 344, -338, 192, -145, -318, -210, 96, 310, -191, -46, 142, 316, 202, -1269, 285, 131, -81, -26, 506, -94, -355, 44, 63, -216, 110, -329, 277, 239, -378, -324, -566, 77, 463, -42, -164, 275, 339, -224, -233, -74, -141, 165, 403, -247, -128, -122, -44, 101, -433, -497, -126, -34, 370, -467, 371, 13, 34, 196, -164, 45, -131, -829, 28, 237, -656, 25, -298, -78, -40, -595, 314, 458, 183, -71, 511, 463, -350, 150, -322, -227, -386, 168, 50, 38, -54, -241, -102, 80, -732, -630, -355, 53, 141, -371, -6, 181, 138, -478, 123, 46, -529, 90, 357, -477, 78, 102, 83, 178, -281, -325, -234, -166, 420, -316, -128, -25, 3, -62, -590, 139, 86, -167, 294, 23, -786, -261, 108, -93, 523, -99, -168, 272, 85, -991, -357, 319, -186, 190, -429, -181, 275, -139, 1, 441, -127, -303, -957, 62, -598, -236, -110, 177, -246, 40, -105, -221, -229, -437, -292, -27, -390, 542, 216, -152, 350, -255, -225, 201, 313, -477, 0, 133, 133, -622, -338, 211, 83, 165, -162, 151, -58, -1085, 578, 257, -323, 152, -92, -81, -1534, 55, 34, 443, -118, -74, 18, -207, 213, -426, -40, -225, -118, -81, 310, 250, 232, -340, 211, 477, 145, -203, -367, -62, 24, -230, 132, 134, -80, 9, -283, 204, -685, -77, 225, -229, -187, 38, 317, 701, -357, -1130, -144, 215, -238, -364, 282, -210, -286, -24, 127, 296, -147, -8, 318, -98, -844, 266, -279, 57, -212, -52, 69, -321, 427, -789, 184, -48, -304, 329, -207, 9, -389, 124, 60, 97, -462, -406, -77, 81, -204, -408, -603, 188, -219, -83, -27, 239, -516, -527, -237, -138, -84, 234, -322, -278, 110, -19, -414, 52, -258, -136, -602, 524, -190, -510, 251, -180, 471, 197, -865, 61, -505, -330, 336, 67, -68, -241, -362, 150, -493, -776, -390, 85, -53, -410, -369, 209, -561, 41, -361, 33, -157, 247, 235, 270, -479, -401, -114, 181, -954, 103, -85, -155, -84, -25, -495, -27, -203, -33, -597, -26, 294, -549, -153, -1, -164, 40, -156, 560, -416, -593, -1069, 232, 378, -252, -590, -141, -704, 116, -359, 445, 151, -255, -194, -381, -232, -114, 34, 169, -392, 44, -386, 292, 79, -933, -596, 195, 17, 182, 400, -273, -996, -224, 317, 161, -536, 11, 249, 133, -533, -519, -790, -96, 402, 125, -319, -107, 136, -356, -308, -26, -133, 72, -143, 61, -303, -485, -215, 212, -675, -226, -479, 435, -476, -546, 48, 339, -164, 230, -600, 89, -230, -663, -46, 140, -109, -43, -520, 322, -433, -312, -722, 95, 466, -715, 513, 61, 141, 298, -888, -316, -893, 203, 209, 429, -830, -376, 378, 236, -341, -229, -96, 300, 35, -577, -616, 288, 71, 166, -238, 185, -912, -185, -216, -215, -60, 47, 127, 75, -573, -741, 0, 187, -175, 350, 4, -26, 27, -215, -348, 344, -703, -265, -426, 188, -202, -593, -444, 8, -66, -153, 266, 246, 21, -915, -515, -35, -1072, 184, -442, -161, -568, 162, 465, -294, 288, 137, -963, 211, -660, -749, -261, 17, 816, 227, 103, 232, -292, -737, -149, 166, -495, 172, -241, -413, -711, -261, -500, 837, 192, -527, -325, 17, -69, -720, -561, -52, -417, 24, -297, 450, -875, -227, -267, -24, -413, -500, 332, 293, -933, -223, 224, -21, -484, -213, -279, 14, -451, -68, 2, -379, -87, -45, -3, 67, 40, -586, -774, 429, -305, 54, -842, 15, -266, -935, 96, 30, 196, -285, -468, -126, -599, -139, 583, 28, -755, 191, -337, 302, -564, -1003, -602, 57, -87, 98, -754, 165, -125, -173, 134, 219, -183, -385, -696, 354, -110, -334, -790, 200, -900, -10, -203, 536, 361, -751, -209, -300, 274, 104, -229, -167, -203, -519, 0, 497, -285, -223, 0, 648, -961, -607, -181, -45, 385, 1, 40, 46, -1182, 113, -759, 362, -940, 125, -54, -463, 270, -83, -330, 230, -362, -878, -1185, 252, -216, -663, -666, 72, 5, 78, -276, -42, -671, -753, -158, 120, -492, -195, 3, -19, -679, -736, -225, 211, 214, -298, 146, 113, -636, -410, -1266, -33, -660, 369, 270, -196, -120, -697, -103, 227, -573, 34, -196, -259, 155, -203, -478, 144, -307, 395, -312, -86, 172, -294, 108, 121, -203, -56, -263, 536, -461, -547, -1541, 507, -233, -629, -237, 16, -407, 97, -218, -153, -112, 500, 109, 232, -1089, -426, 124, -444, -230, 145, -540, 360, -924, -705, -452, 87, 262, 252, -132, -219, -501, -254, -82, -224, 204, -266, -406, 287, -318, -262, -428, 599, 620, 9, 50, 195, 97, -826, -1132, 125, -255, 235, 267, 8, -908, 172, 159, 459, -638, -621, -1092, 102, 115, -498, 181, 144, -1031, 481, -128, -28, -386, -793, 55, -31, -131, 130, -639, 193, -357, -86, -920, 763, 166, -523, -356, -123, -700, -12, 561, 3, -730, 408, 534, 168, -384, -461, 334, 297, -587, 333, -217, 180, 125, -850, 58, 68, 262, 227, -812, 443, -122, -56, -770, 50, -170, -187, -183, 392, -310, -1195, -527, -8, 41, 392, -174, 224, -1058, -79, -895, 95, -286, -415, 454, 163, -227, -695, -236, 647, 16, -268, 33, 398, 355, -1100, 421, 343, -338, 270, -312, -378, -1761, -96, -259, -60, -40, 34, -377, 113, -326, 348, -606, 299, 533, 283, -637, -3, 319, -318, -1323, 206, 6, -598, 592, -472, -47, -496, -77, 504, -594, 238, 224, 659, -225, 135, -395, -146, 186, 429, -267, 161, -384, -615, -54, -46, -424, 20, -345, 143, -180, -569, 33, 646, 236, -433, -1414, 283, -285, 227, 502, -348, -432, 249, -468, 110, 72, -1087, -791, 178, -604, 209, -1769, 247, 298, -621, 331, 230, -81, 75, -269, 259, -224, 200, 127, -238, -54, 234, -439, 716, -1543, -941, -440, -31, 553, -441, 120, -280, 1, 113, -674, 345, -67, 40, -106, -240, -432, -791, -711, 271, -463, 18, -367, 219, 87, -421, -629, 251, -113, 290, 246, -623, -447, 89, 10, 510, 118, -109, -121, 401, -1114, -866, -33, -193, -357, -377, 315, 507, -417, 148, -909, 22, -774, 808, -194, 228, -785, -188, 203, 590, 520, -705, -539, 38, 236, -887, -300, 30, -449, 333, -624, 586, -598, -492, 584, 172, -108, -314, 6, 334, -1324, -10, -167, 448, 1153, 51, -515, -362, -301, 141, -864, -162, -384, 434, 63, 216, 483, -225, -1638, 15, -667, -367, -88, 86, 305, -586, -228, 532, -923, -136, -167, 239, -350, -343, 300, -155, 471, -157, -7, 410, -1083, -1312, -850, 725, 313, 363, 303, 117, -191, 121, 381, 40, -371, -114, 472, -181, -1291, 104, -68, 173, -272, 838, 46, 139, -109, -999, -102, 194, 213, 558, -1554, 152, -569, 90, 99, 231, -252, -174, -69, 827, -497, -597, -1197, 298, -443, 509, -269, 340, 122, -518, -98, -98, -258, 501, 126, -239, 200, -303, -214, 598, 307, 191, -1394, 264, -146, -666, 72, 132, 706, 344, -538, 447, -126, -187, -47, 259, -498, -288, -621, 119, 264, -263, -153, 553, 651, -1032, 89, 178, -472, 376, 338, -65, -498, -7, 776, 303, -1072, -70, -537, 532, 233, 146, -82, 350, -737, -577, -501, 82, 1022, 92, -155, 370, -690, -261, -644, 141, 714, 191, -537, 890, 214, -1449, -127, 310, 427, -112, 605, 276, -998, 203, -57, 546, -1625, 296, 272, 198, 104, -755, 72, 720, -2013, 197, 136, 572, 332, -632, 263, 553, 591, 226, -664, -280, 96, -178, 283, -384, 270, -190, 130, 296, -587, -28, -179, 438, 1435, 331, -506, 330, -69, -455, -640, 406, -72, 737, -40, 211, -405, -576, 499, 133, 601, -298, -672, 484, -188, 289, -361, 198, -812, 516, -74, 96, 109, -283, 564, -340, 497, 142, 15, 204, -462, -121, -119, 698, 643, -903, -304, 536, -711, -536, -112, -40, -586, 462, 352, 752, 35, -743, -847, 151, -979, 161, -837, -112, 688, -211, -392, 1251, 658, 179, -720, -91, 96, -598, 101, -286, -117, -101, 372, 321, -520, -468, -212, 609, 520, -164, 197, 2, 802, 64, 17, 463, 174, 217, 46, 291, -595, -277, -921, 527, -122, -226, -246, 472, 378, -662, 860, 257, -615, 363, -524, 26, -1221, 37, 493, 73, 729, -124, 186, 929, -53, -429, -615, -138, 1297, -150, -92, 167, -87, -725, -251, 275, 249, 355, -187, -200, -25, 118, -126, 803, -51, -460, -67, -30, 1100, -870, 247, 220, -780, 593, -636, 752, -1136, -457, -305, 239, -305, 162, 1192, -172, -1712, -132, -287, 414, 90, -286, 25, 268, 95, -22, 243, 143, 457, 695, 461, -77, 437, -669, -1728, 502, 133, 126, -1356, 147, 818, -956, 145, 908, -745, 167, 175, 196, -1158, -186, 250, 334, -522, 126, 414, 420, 216, -1352, -832, 199, 674, 246, -1044, 496, -196, 235, -758, 159, 902, -189, 326, -1, -241, -202, -70, 269, 432, 416, 54, 925, -462, -1696, -1, 324, 353, 472, -351, 353, -1883, -280, 652, 326, 562, -413, -211, 547, -1416, -73, 181, 566, -566, -225, 673, 259, -1040, 245, -206, 527, 132, 603, 214, -838, -20, 217, -24, 599, -1313, -835, -914, 882, -154, -434, -554, 281, 944, -237, -14, 162, 766, -356, -187, 456, -304, 347, -336, 441, -1026, -126, 471, 696, 364, -357, 106, 9, 5, 16, -321, -39, -146, 410, 407, 126, 345, -798, -60, 356, -360, -49, -647, -82, 715, -498, -99, 5, 178, 298, -529, 487, -430, -365, -350, -277, 614, 334, -143, 794, -50, -1005, -1222, 211, 214, -274, 380, 226, 123, -139, 252, 276, -2485, 377, 187, -32, -262, -270, 133, 296, 85, -162, -92, 745, 488, -971, -1285, 157, -168, 386, -1325, 292, -294, 40, 638, 315, 240, -9, -995, 331, -351, -257, -195, 548, 1190, 303, 46, 76, -364, -518, -1067, 330, 615, 45, 674, 87, -633, 25, -377, 762, -856, -831, 96, 7, 395, -104, -263, 112, -716, 891, -547, 209, -100, -597, 1336, -6, 393, 127, -230, 213, -1438, -86, -557, 631, 743, -252, 178, 553, -141, -914, -339, -236, -447, 375, -351, 113, -209, -304, 279, 809, -69, 728, -1537, 440, 804, -261, -466, 23, 307, 33, -1203, 78, -141, 477, -185, -152, 374, 495, 443, 452, -818, -838, -670, 377, 954, -63, 50, 13, -954, -55, -236, 822, 690, -345, -322, 216, -146, 77, -1360, 925, -35, 362, 290, 1033, -18, -1659, 397, 112, 154, 809, 200, -662, -1462, 799, 681, 73, -283, 282, -917, 120, 227, -67, -560, 457, 1028, -175, -504, 728, 448, -469, -982, 502, -177, -267, 161, 351, -240, -358, 403, 1026, 170, 321, -433, 320, -94, -400, 474, 239, -144, 553, -283, 342, -1823, -709, -142, 334, 278, 81, -305, 287, 1138, -702, -159, 596, 629, -83, 127, 169, -1166, 923, -1323, -86, 289, 435, 375, -31, 411, -1296, -147, 118, 231, -353, -442, 349, -308, 165, -67, 926, 760, 330, 362, 592, -1033, 170, 418, -284, -834, 611, 915, 888, -1228, -806, 103, 447, 1804, 102, -590, 261, 271, 262, -1443, 1331, -111, 2, -357, 505, 826, -926, -288, 361, 397, 451, 389, 664, -13, -1215, 290, 693, -738, 224, 453, -59, 217, 309, 431, 175, 508, -232, -1079, 640, 314, 55, -535, 1070, -74, 77, 454, -264, 877, -521, -728, -142, 290, 814, 377, 73, 269, 164, 215, 973, -338, -805, -1133, 581, -384, -510, -439, 589, 57], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "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": "4003.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}