# Stored data for newform 8009.2.a.b, downloaded from the LMFDB on 16 April 2024.
{"label": "8009.2.a.b", "space_label": "8009.2.a", "level": 8009, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660932937, "dim": 361, "analytic_rank": 0, "is_twist_minimal": true, "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32036, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 63.95218697884346, "level_radical": 8009, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8009, 1, [3], [1]], "inner_twist_count": 1, "level_primes": [8009], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 361, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[8009, -1]], "trace_display": [10, 23, 21, 106], "traces": [361, 10, 23, 414, 21, 49, 106, 30, 406, 65, 33, 52, 89, 32, 55, 512, 42, 34, 191, 48, 53, 61, 52, 139, 458, 57, 80, 194, 47, 32, 254, 55, 40, 122, 93, 519, 43, 25, 210, 184, 54, 48, 151, 56, 82, 101, 117, 77, 563, 38, 143, 241, 14, 164, 452, 52, 21, 55, 125, 39, 227, 58, 292, 710, 15, 105, 120, 125, 136, 88, 105, 78, 108, 41, 128, 461, 28, 13, 400, 59, 485, 175, 97, 76, 144, -14, 327, 145, 52, 60, 192, 11, 32, 366, 182, 275, 117, 42, 111, 657, 172, -54, 371, 123, 67, 169, 41, 135, 165, 31, 370, 342, -27, 18, 295, 74, 166, 250, 219, -10, 634, -24, 105, 427, 57, 14, 264, 99, 161, 78, 243, 48, 159, 63, 111, 332, -28, 100, 565, 127, 22, 125, 125, 694, 172, 43, 61, 48, 91, 34, 553, 32, 106, 157, 46, 259, 214, -15, 437, 308, 35, -4, 134, 135, 26, 302, 202, 84, 596, -88, 504, 273, 87, 37, 668, -6, -1, 219, 112, 94, 219, -58, 240, 259, 19, 77, 211, 141, 109, 40, 241, 6, 119, 178, 262, 910, 14, 18, 793, 23, 96, 129, -2, 188, 221, 95, 163, 490, 107, -167, 426, -34, 59, 94, 208, 368, 159, -93, 151, 745, -44, 31, 506, 11, 476, 185, 103, -125, 254, 4, 368, 47, 22, 132, 226, 144, 141, 34, 364, -155, 370, -49, 153, 606, 52, -137, 239, 76, 21, 152, 171, 323, 126, -10, 354, 976, 26, -62, 582, -191, 80, 60, 189, 145, 215, 4, 39, 132, 44, -169, 1039, 149, -57, 231, 15, 159, 169, -153, 591, 15, 34, -102, 432, 60, 48, 163, 128, -44, 657, -112, 117, 100, -29, 54, 471, -45, 24, 2, 269, 81, 228, -89, 223, 839, -47, 47, 349, -135, 59, 24, 505, -228, 219, 85, 283, 608, -37, -130, 601, 10, 267, -106, -5, 563, 446, -90, 221, 346, 53, -305, 451, -19, -119, 382, 348, -69, 130, -85, 280, 223, 56, -74, 731, -162, -163, 332, 108, 402, 476, -138, 694, 151, -4, 55, 504, -34, -99, 64, 183, -43, 686, -78, 35, 185, -32, -58, 560, -223, 80, 273, 95, -112, 192, -23, 36, 1009, 25, -60, 253, 74, 308, 28, 204, 376, 159, -69, 250, 147, -7, -279, 1228, 57, -25, 53, 89, -57, 192, -73, 562, 812, -106, -188, 228, 397, -3, 290, 175, -338, 449, -127, 194, 440, -72, 53, 656, 108, -12, -8, 126, -233, 204, -235, 327, 320, 56, 114, 360, -130, 50, 128, 246, 4, 215, -75, -39, 313, -42, -46, 1558, -98, 621, 12, 51, 404, 59, 120, 199, 370, -93, -219, 663, -328, -32, 227, -4, -179, 160, -67, 286, 396, 151, -334, 448, -45, -193, 60, 117, 213, 310, -211, 217, 573, -135, -121, 726, 118, -242, -69, 371, -186, 554, -148, -61, 971, -153, 204, 340, -305, 73, -41, 265, -215, 91, -155, 989, 526, -46, -202, 320, -180, -35, 44, 283, -224, 98, -182, -5, 312, -7, -239, 948, -107, -218, 553, -95, 275, 132, -208, 665, -118, 18, -194, 553, 411, -233, 68, 37, -142, 707, -174, 386, 209, -129, -84, 1157, 23, -134, 136, 33, -452, 376, -241, 179, 525, -3, -222, 469, -331, 448, 6, 345, -127, 124, -241, 19, 1091, -145, -5, 1252, -203, -216, -98, 39, -249, 174, -81, 540, 160, -112, -328, 553, -265, -174, 215, 95, 759, 245, -266, 580, 81, -56, -453, 322, -33, -330, 476, 145, -344, 447, -244, 826, -175, 44, 143, 152, -72, -212, 98, 245, -195, 519, -418, 22, 691, -94, -87, 937, -264, -49, -166, 59, -20, 94, -7, 504, 212, -226, -448, 414, -182, 178, -58, 122, 135, 635, -229, -31, 198, 73, -375, 926, -298, 59, 396, 11, 370, 274, -202, 206, 374, -181, -273, 358, -206, -133, 141, 434, -243, 313, -304, 254, 15, 23, -209, 489, -25, -45, -107, 24, -629, 358, -214, 286, 793, -180, -211, 223, 41, -87, 212, 801, -203, 131, -224, 198, 969, -44, -191, 1568, -757, -30, 110, -40, 832, 264, -263, -3, 313, 7, -352, 729, -54, -271, -104, 259, -220, -37, -82, 260, 748, -25, -512, 852, -396, -220, 446, 18, -459, 255, -233, 794, 313, -229, -39, 352, -135, -73, -77, 486, -237, 479, -465, -105, 195, -185, -196, 1032, -283, 376, -132, 374, -86, 190, -137, -206, 236, -221, -90, 502, -334, -52, -297, 51, -116, 473, -351, 233, -65, -16, -567, 655, -111, -79, 97, 129, -322, 165, -355, 453, -280, 167, -521, 433, -74, -23, 558, 73, -494, 610, -585, 136, -136, -150, -462, 962, 345, -134, -268, 29, -145, 142, -172, 1061, 1220, -348, -285, 279, -237, 298, -146, 467, -621, -89, 64, -390, 1171, -247, -669, 951, -349, -105, -79, 103, -276, 192, -355, 328, -25, -48, -654, 851, -614, -149, -39, 189, -108, 183, -216, -115, 143, -45, -310, 565, -40, -350, -229, -119, -452, 456, -761, 1264, 579, -157, -465, 520, -10, -299, -288, 285, -1082, 704, -316, 93, 485, -249, 479, 690, -545, -16, -233, -129, -415, 273, -39, 346, -104, -34, -823, 987, -352, -133, -249, -46, 309, 42, -74, -61, -78, -192, -954, 1860, -544, -58, 142, 85, -323, -40, -267, 220, 924, -179, -643, 299, -580, -206, 253, 322, -352, 50, -525, -228, 476, -89, -280, 439, -426, -435, -96, 342, -160, 577, -570, 123, 3, -389, -290, 164, -287, 340, -502, 114, -988, 169, -536, -83, 255, -149, -676, 1574, -674, -29, -9, -123, -121, -184, -440, 619, -324, -11, -1022, 863, -427, -386, 285, 24, 23, 388, -579, -44, -278, 22, -649, 733, 89, -172, -310, -164, -145, 251, -510, 476, -446, -299, -259, 207, 190, -435, -48, 140, -1291, 665, -577, -167, 620, -24, -592, 727, -528, -227, 42, 163, -186, 27, -254, 308, 902, -397, -488, 987, -527, -194, -363, 50, -865, 381, -297, -247, -265, -76, -690, 1118, -365, -143, -68, -208, -611, 449, -405, 989, 180, -187, -975, -52, -255, -301, 104, 213, -260, -29, -834, 621, -266, -155, -283, 575, -435, -561, 54, -24, -572, 383, -638, -239, 1099, -244, -773, 265, -336, -177, -362, 553, -849, -38, -610, 18, 857, -438, -345, 1938, -962, 122, -288, -159, -690, -1, -395, -243, -68, -74, -966, 763, -288, 10, -106, 308, -322, -74, -527, -140, 11, -65, -114, 1107, -432, -546, -142, -83, -787, 838, -412, 790, -229, -338, -196, 349, -568, -321, -255, 73, -1183, 253, -486, -304, 1409, -396, -622, 532, -196, 507, -312, 172, -1082, 6, -397, 264, 428, -224, -944, 402, -830, -265, 2, -40, -163, -186, -82, -81, -27, -119, -875, 985, -852, -264, -317, -389, 322, 95, -548, 592, -717, -291, -1013, 254, -406, -292, 504, -70, -685, 169, -455, -210, 556, -284, -897, 1032, -339, -303, -259, -88, -691, 661, -940, 205, 54, -536, -580, 318, -561, -307, -650, 815, -765, -37, -234, -441, 502, -190, -451, 829, -793, 11, -335, -215, -733, 382, -621, 226, -372, -376, -687, 199, -751, -452, 240, 90, -602, -165, -569, 527, 72, 2, -446, 966, -694, -616, 232, -61, -812, 485, -1168, 154, -215, -341, -388, 452, -222, -118, -323, 233, -825, 303, -726, -209, -127, -375, -571, 699, -818, 75, -314, -291, -811, -96, -331, -383, 1103, -142, -1201, 265, -802, -83, -259, 671, -439, 805, -607, -350, 277, -111, -1091, 2026, -1225, -533, 168, -223, -460, -110, -419, 404, -528, -384, -740, -42, 242, -515, -511, -295, -1400, 666, -835, 1113, -3, -399, -1058, 236, -428, -444, -203, 14, -562, 137, -650, 128, 422, -234, -430, 177, -852, -348, -491, 434, -1251, 256, -748, -387, 323, -16, -758, 1051, -704, -379, -434, -318, 231, -376, -359, -118, -909, -157, -898, 720, -984, -131, 181, -109, 57, -33, -783, -97, 607, -11, -1232, 394, -851, -305, -416, -386, -483, 318, -929, 444, 254, -454, -775, 437, -651, -379, -517, 833, -1723, 249, -470, -410, 313, -502, -695, 1133, -620, -382, -662, -90, -1500, 106, -567, 434, 599, -234, -533, 500, -154, 93, -288, 227, -1195, -324, -938, -44, -329, -212, -774, 938, -834, -413, -365, -308, -614, -178, -726, 988, -261, -6, -1404, 444, -622, -681, -55, -256, -840, 644, -1125, -21, 576, -242, -432, 2170, -814, -486, -422, -35, -1842, 349, -492, 63, 394, -458, -836, -48, -459, -264, -823, 217, -180, 119, -864, -475, 883, -422, -1090, 1186, -1189, -493, -811, 101, -164, 352, -866, 200, -308, -441, -1010, 383, -760, -33, -14, 145, -755, -119, -584, -231, 181, -304, -1216, 145, -573, -813, 661, 164, -1731, 282, -933, 1180, -262, -375, -571, -97, -641, -402, -240, -137, -1794, 552, -765, -263, 701, -273, -1011, 1234, -888, -665, -737, -172, -1280, -15, -703, 98, -442, -680, -955, 965, -965, -166, -593, -427, -675, -199, -260, -340, 261, -183, -1059, 917, -1331, -342, -390, 7, -656, -187, -859, -44, 161, -173, -1347, 317, -618, -724, -174, 135, -1465, 218, -515, -157, -81, -379, -269, 897, -945, -509, -133, -175, -1603, 332, -781, 391, 1691, -774, -1039, 7, -741, -481, -407, 425, -930, -162, -892, -664, -77, -174, -1320, 934, -918, -107, -433, -307, 66, 336, -662, -373, -528, -328, -1701, 1808, -495, -811, -500, -10, 65, -177, -822, 879, -902, -419, -1236, 1113, -730, -710, 814, -579, -972, 15, -806, 448, -249, -407, -1703, 83, -639, -193, -841, 979, -1787, 250, -1254, -565, 1372, -717, -1205, 538, -556, -393, -587, -287, -1516, 72, -585, 803, -456, -565, -936, 543, -794, -183, -606, 100, -1597, 213, -848, -473, -238, -411, -1482, 1278, -865, -886, -64, -362, -727, -128, -870, 767, 696, -236, -680, 340, -1275, -865, -270, -240, -1665, 149, -1616, -214, -350, -45, -1029, 964, -28, -959, -782, 67, -1343, 162, -968, 108, -11, -827, -1012, 98, -1194, -323, -230, 84, -2033, -320, -310, -369, 614, -383, -2062, 967, -1398, -158, -728, -573, -674, -103, -568, 364, 72, -510, -1595, 534, -1548, -585, -567, -465, -689, 462, -984, -178, -116, -428, -1229, 258, -808, -1042, -465, -330, -1440, 355, -1516, 373, -732, -593, -1010, -94, -493, -734, -159, 885, -1998, 873, -940, -440, 51, -572, -1165, 891, -1423, -615, -770, -77, -1299, 278, -1124, -500, -81, -392, -1317, 682, -527, -695, -920, -96, -608, -251, -598, -146, -358, -566, -1731, 1886, -1491, -688, -118, -252, -1321, -233, -703, 326, -610, -378, -1999, -279, -514, -580, 229, -147, -1375, 90, -1462, -356, -167, -263, -1037, 1294, -1245, -729, -654, -59, -2044, 597, -1038, -308, -407, -664, -296, -99, -1211, -160, -932, 205, -1293, -128, -940, 30, 2166, -481, -2019, 2002, -876, -717, -530, -535, -349, -109, -980, 118, -781, -505, -1512, 332, -675, -744, -224, -546, -713, 76, -1048, -696, -956, -381, -1858, 855, -262, -1168, -484, -387, -1343, 287, -1298, 1501, -346, -547, -1515, 811, -1435, -597, -477, 141, -1829, -62, -1222, -399, 632, -379, -1715, 276, -1596, -422, -819, 347, -1427, -366, -833, -867, -6, -642, -1108, 1076, -1922, -160, -891, 221, -1967, -251, -1010, -900, -537, -607, -1287, 790, -970, -563, 199, -775, -926, -46, -900, 753, -273, -530, -1946, -99, -585, -572, -536, -18, -2337, 760, -1121, -349, -309, -631, -593, 978, -1128, -853, -377, -519, -2239, 599, -1653, -458, -650, -628, -1126, 669, -786, -412, -1454, 265, -924, -232, -952, -502, -255, -609, -1686, 2276, -1367, -369, -739, -599, -988, -571, -968, -471, 993, -131, -2826, 219, -1842, -784, -394, -261, -1602, -97, -1330, 13, 260, -603, -1864, 534, -1118, -818, -264, -150, -1670, 589, -732, 707, -1024, -606, -1272, 12, -278, -706, -806, -101, -1691, 531, -965, -247, 502, -904, -1595, 248, -1020, -848, -1063, -241, -2222, -282, -759, -85, 866, -700, -1601, 546, -1805, -471, -330, -305, -749, -130, -1425, -811, -633, -228, -2097, 1640, -1534, -755, 31, -600, -1433, -150, -1252, 1017, -1263, -313, -2271, 653, -780, -1044, -15, -206, -2010, -86, -1379, -235, -885, -625, -1806, 1050, -1225, -752, -1053, -53, -623, 312, -1697, -500, 155, -798, -1033, 161, -1329, -1268, -1026, 125, -1886, -17, -812, -1563, -408, -726, -1022, 871, -2077, -348, -1423, -798, -1469, -105, -1041, 393, -739, -512, -1588, 511, -670, -765, -333, 376, -1652, -366, -1116, 512, -797, -48, -1057, 938, -1323, -348, -52, -640, -1107, 357, -1045, 885, -447, -678, -516, -128, -870, -693, -525, 245, -1565, -142, -575, -455, 569, -458, -1135, 70, -853, -295, -546, 177, -1519, 188, -743, 62, 1378, -460, -1307, 577, -977, -42, -639, 653, -292, -328, -615, -310, -436, -496, -864, 1463, -820, -746, -223, -194, 289, 192, -606, 552, -970, -342, -553, -135, -546, -791, -337, -109, -1169, 805, -792, 14, 662, -648, -398, 1115, 337, -486, -381, -104, -1540, -129, -294, 43, -32, -395, -379, 364, -646, -182, 9, 225, -478, -237, -825, -226, 639, -294, -518, 2121, -655, -445, -95, -672, -370, 229, 427, 328, -58, -142, -919, 864, -558, -27, -274, -341, 62, -421, -426, -112, 1436, 284, -568, 276, 14, -808, -277, 143, -955, 248, -358, 1418, 30, -243, -318, 548, -483, -396, -422, 279, -1542, 511, -715, -709, 596, -585, -137, 324, -831, 223, -222, -115, 324, -89, -440, 1350, 570, -272, -451, 498, -13, -695, -304, -241, -1000, 147, -296, -351, 408, 131, -802, 1831, -332, -796, 300, -101, 1184, 454, 127, 104, -543, -287, -420, 334, -211, -689, 391, -157, -585, 692, 410, 945, -317, -359, -681, 839, -550, -22, -232, -119, 317, 371, -895, -170, 2433, -921, -433, 169, -353, 30, -981, 403, 801, -147, 142, -281, 1675, -252, -532, 3179, -692, -505, -233, -158, -1190, -92, 345, -435, -859, -414, -111, 477, 386, -672, -644, -316, -341, 141, -519, 428, 62, -220, 569, 1167, -496, -318, 830, -286, 66, 61, 186, 763, -196, -444, 95, -132, -208, -676, -154, 559, -575, 411, 75, -359, 655, -121, 139, 1571, -366, -841, 256, -128, -754, -360, -189, 425, 838, -166, -193, 1074, -603, -263, -411, -265, 613, -395, -683, 0, 986, -86, -561, 1721, -387, -684, -724, -82, 737, 143, -396, 276, -237, -453, -314, 479, -170, -541, 627, 450, -1303, 699, -63, 703, 178, -543, 203, 103, 188, -336, -313, 410, -1335, 816, 462, 200, 1092, -727, 931, -10, 65, -358, 1107, 157, -1124, -71, -134, -366, 1078, -311, -1080, 1252, 538, -280, 204, -179, 1671, 451, -629, 1020, -1048, -452, -847, 1388, 187, -799, -87, 240, 460, -361, 180, -22, -530, -227, 266, 1130, -722, -35, 648, 184, -475, 259, -174, 702, 756, -461, -393, 543, 1201, -322, -173, 522, 101, 1113, 549, -231, 904, -1019, 823, 753, -646, -1010, -212, 410, -51, -105, 124, -53, 749, -270, -1052, 655, -992, -122, 771, -101, 8, -16, -261, 193, 1195, -303, 517, 1159, -362, -730, 74, -133, 270, 15, -733, 2235, -677, 643, 713, -168, 283, -971, 83, -24, -92, 469, 732, -40, -49, -151, -967, 1467, 500, -270, -232, -478, 343, 196, 546, -181, -103, -865, 660, 655, -910, 451, -238, 943, 352, -117, 134, -931, 689, 100, -616, 1025, 100, 459, -644, -234, -339, -32, 446, 364, -145, -738, 516, 547, 584, -42, -94, 580, 855, 181, -537, 195, 1153, -870, -331, 350, 288, -470, 145, -90, -369, -126, 461, 922, 224, -456, -633, 608, 188, -263, 733, 836, -852, 399, 661, -788, 812, 229, 467, 1025, -627, -230, -601, 406, 1224, -574, -347, -311, 1250, -265, -959, 1681, 548, -471, -344, -144, 206, -56, 1299, 898, 270, -36, -390, 3542, -683, -657, -125, 20, -23, 32, -74, 342, 17, -370, 1557, 5, -896, -532, -183, 195, -322, 592, -92, 315, 439, -598, 373, 1501, 284, 9, -515, -216, -172, 63, -336, 104, 690, -185, -36, 316, 594, -330, -881, 627, -86, 257, -24, 26, 954, -275, 760, 1398, -363, 587, 584, 214, -253, 32, 54, 540, -567, 454, 163, 242, 2375, -982, 1116, -317, 159, 366, -1059, 51, 708, -301, -382, 990, -476, -334, 636, 69, -1170, 30, 384, 1949, 398, -796, 558, 1190, -473, 374, -384, 920, 1329, 85, 286, -700, 311, -312, 758, 751, -468, -94, 34, 352, 573, 410, -3, 121, 1321, -343, -308, 1266, 608, 353, 528, -134, -877, -288, 725, -13, -332, 37, 91, 1488, 1107, -789, -81, 207, 1656, 321, -32, 1660, 290, -401, 1235, 112, 1274, -741, 1628, 336, -66, -296, 84, 877, 517, -179, 673, 2280, 229, 248, -695, -322, 2208, 930, 1408, 176, 1307, -220, -333, 1087, -164, -803, -594, 735, -98, -319, 930, -264, 2911, -585, -1117, 2476, -460, 524, 229, -67, 391, -87, 140, 1238, 808, -259, 1533, 531, -560, 228, -310, 457, 1654, 187, 92, -13, -65, 393, 1417, 1295, -482, -622, 1153, 91, -384, 653, 154, -62, 1521, -407, 110, -72, 1139, -303, -1001, 341, -202, 515, 580, 61, 1374, -475, -63, 1039, -204, -606, 890, 548, 826, -479, 1601, 512, 120, -321, 188, 1618, 541, -414, -127, -322, 331, 733, -459, -345, -660, -16, -277, 3912, 1829, -72, 612, -479, 1141, -294, -399, 2039, 924, 202, 600, -85, -216, -596, 296, 416, -1061, 565, 173, -632, 1452, -402, 550, 970, -474, -216, -402, 323, -592, 102, 688, -53, 1080, -1026, 1657, 151, 330, -325, 793, 594, 464, 251, -400, 475, 573, -38, -701, 533, 904, -84, 12, -471, 876, -351, -200, 1288, 313, -793, 939, 996, 210, -1030, 1177, 654, 581, 600, -460, 323, 339, 25, 544, 339, 492, -453, 941, 251, -26, 840, 312, 1340, -110, -153, -128, 836, 538, -360, -317, 319, 732, 386, 2418, -164, 1282, -546, 1057, 1509, -1175, 215, -333, 334, 2120, -357, -252, 425, 995, -368, -533, 1531, 1152, -658, -382, 645, -797, -391, 927, -229, 1071, -58, 1359, 3879, -271, -645, -163, -802, 672, 306, 362, 181, 54, -492, 258, 736, 1340, -174, 346, 348, 46, 289, -357, 588, 438, -661, 581, 959, 1166, -687, -411, 606, 175, 22, 1812, 7, -322, -267, 1269, 295, -919, -616, 654, 251, 1361, -197, 543, 201, 814, 13, 69, 2474, -836, -453, 387, 173, 344, -27, 298, 563, -617, -426, -68, 760, 525, -493, 48, 772, 708, -214, -7, 313, 2116, 30, 931, 876, -562, -758, 1054, 358, -110, 215, 2550, 637, -388, -987, 402, -73, 554, -588, -694, 1469, -701], "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": "8009.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "hecke_cutters": 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}