# Stored data for newform 1815.4.a.r, downloaded from the LMFDB on 24 April 2024.
{"label": "1815.4.a.r", "space_label": "1815.4.a", "level": 1815, "weight": 4, "hecke_orbit": 18, "hecke_orbit_code": 76561193732409111, "dim": 3, "is_polredabs": true, "nf_label": "3.3.47528.1", "trace_hash": 1097131909433504076, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [48, -25, -2, 1]], [7, [-3448, -604, 10, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{2}+3q^{3}+(10+\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 29040, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 107.08846666041921, "hecke_ring_index": 1, "level_radical": 165, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1815, 1, [1211, 727, 1696], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 47528, "field_disc_factorization": [[2, 3], [13, 1], [457, 1]], "field_poly": [-22, -26, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.036", "prec": 17}, {"__RealLiteral__": 0, "data": "2.992", "prec": 17}, {"__RealLiteral__": 0, "data": "0.270", "prec": 17}, {"__RealLiteral__": 0, "data": "24.728", "prec": 20}, {"__RealLiteral__": 0, "data": "4.779", "prec": 17}, {"__RealLiteral__": 0, "data": "310.176", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [11, -1]], "trace_display": [2, 9, -15, -10], "traces": [0, 3, 2, 9, 30, -15, 6, -10, -18, 27, -10, 0, 90, -114, -68, -45, 178, 104, 18, 58, -150, -30, 0, 120, -54, 75, -120, 81, -676, 220, -30, 248, 258, 0, -80, 50, 270, 838, 600, -342, 90, -156, -204, -122, 0, -135, 1256, 504, 534, 279, 50, 312, -520, 282, 54, 0, -1644, 174, -1644, 548, -450, -414, 2448, -90, -58, 570, 0, -428, 1704, 360, 340, -912, -162, -618, 1612, 225, 2752, 0, -360, 542, -890, 243, 3372, 0, -2028, -520, -1548, 660, 0, 790, -90, -772, 1912, 744, 424, -290, 774, 2074, 3978, 0, 750, 2276, -240, 676, 1528, 150, 4892, 1984, 810, -3226, 0, 2514, -3596, 866, 1800, -600, 2948, -1026, -1496, -1376, 270, 0, 1852, -468, -880, -375, -612, -1186, -34, -366, 600, -3324, 0, -5660, -5200, -405, -640, 1506, 3768, 330, 3380, 1512, -3152, 0, 1602, -1100, 648, 837, 7940, 5472, 150, 2806, 9048, 936, 0, -1240, -1560, -86, 5488, 846, -1290, -4176, 162, 5088, -3012, 0, -8292, -6348, -4932, -1019, 400, 522, 3604, -268, -4932, -250, 0, 1644, -3588, 2356, -1350, 3106, -432, -1242, 11288, -4190, 7344, 0, 3800, -270, -3000, -2768, -174, 4914, -2916, 1710, 1206, 1772, 0, -1136, -450, -1284, -4292, 1352, 5112, 780, 4720, 1080, -3752, 0, 1020, -7278, 5668, -2736, 572, 610, -486, 1328, 692, -1854, 0, -2624, 4836, 5380, 156, 675, 8044, 3160, 8256, 246, -6280, 0, -15940, 2548, -1080, -2520, 8664, 1626, -3952, 11316, -2670, 3598, 0, 729, -25484, -1395, 10116, 2140, 12336, 0, -250, 14508, -6084, 0, 13460, -1560, -20494, -6058, -4644, -4020, 2600, 1980, -14240, 5268, 0, -1410, -23328, 2370, -7040, -12846, -270, 4266, 9192, -2316, -20052, 0, 5736, 9710, -7216, 2232, 8220, 6084, 1272, -6274, -16480, -870, 0, -3528, 2322, -9507, 8220, 6222, 4808, 13056, 11934, -2740, 3572, 0, -1492, -3136, 2250, -6308, 32352, 6828, 15424, 2070, -720, -2550, 0, 2028, -12240, -7448, 4584, 19978, -27244, 450, 872, -13970, 14676, 0, 290, 5952, -25808, 5232, 2430, -2850, -3416, -9678, 29316, 624, 0, 160, -12780, 7542, 14700, 2140, -10788, 11614, 3702, 2598, -8520, 0, 5400, -1916, -2820, -1800, 19384, 624, 8844, 14762, -1700, -3078, 0, -10586, -4488, 4560, 45716, -4128, 5736, 7992, 810, 5779, -3884, 0, 19920, 3090, 5556, 5636, 13032, -1404, -8060, -16044, -2640, -16246, 0, -1125, -4712, -6864, -1836, -3800, -13760, -3558, 4304, 5512, -102, 0, 10968, -1098, 9300, -6410, 1800, 3232, 29286, -9972, -20904, -2710, 0, -16866, 27520, -16980, 4450, -14814, -15600, -16144, 16764, -1215, 19176, 0, -1920, 11206, -16860, 4518, -13072, -4472, 11304, 0, -13208, 990, 0, 13540, 10140, 7250, -4216, 4536, 46340, 2600, -9456, 39812, 44820, 0, 7740, -8004, 4806, 2410, -21984, -3300, -26228, 24480, 1944, 8466, 0, 2511, 2080, 17844, 23820, -3950, 2136, 16416, 14028, -29922, 450, 0, -24540, 8418, 34644, 3860, 27144, 710, 10092, 2808, -9560, 30184, 0, 22044, 13212, -3720, -27528, 14292, -4680, 16776, -2120, -258, -13672, 0, 16464, 1450, -25728, 2538, -7016, 14652, -3870, -32724, 1332, -12528, 0, -10370, 486, 19824, -21052, 15264, -19890, -696, -9036, 12704, -7104, 0, 2480, 22848, -24876, -19724, -3750, -19044, 5208, -18492, -14796, -11380, 0, -3057, -41276, 3010, 1200, -22036, -6030, 1566, 46804, -3380, 10812, 0, -33208, -804, -7640, 23066, -14796, 42710, -36640, -750, 372, -2688, 0, -629, -24460, 4932, -60464, 3024, -10764, -9920, -47184, 7068, 748, 0, -4050, 2974, -23232, 9318, 3152, 16130, -1296, -23418, -33900, -3726, 0, -14832, 33864, -2964, 10712, -12570, 60552, 35184, 22032, 14284, 17980, 0, 11372, 3084, 11400, -4330, -12492, -810, -32144, -38792, -9000, 6454, 0, -8304, -43368, 3000, -522, -18762, -18738, 14742, -14740, 42144, -8748, 0, 35224, 5130, -25072, 36372, 3618, 9872, 7480, 5316, 49628, 7260, 0, 6880, 36412, -3408, -30176, 23880, -1350, -12774, -2712, -3852, -11144, 0, -12876, -32026, 8088, 4056, -9260, -21632, 15336, -27446, 24532, 2340, 0, 4290, 14160, 328, 4400, 3240, 32304, -70036, -11256, 1875, -7980, 0, -26804, 26064, 3060, -5152, 33792, -21834, -114924, 5930, 17004, -13770, 0, -8208, 170, 31038, 1716, 12944, -80272, 1830, 30864, 24824, -1458, 0, -3000, 3984, 129528, -47670, 2076, 16620, -9564, -5562, -5392, 6756, 0, 850, -38760, -7872, -100188, 28300, 14508, -31184, -62364, 16140, 26000, 0, 468, 10290, 75576, 2025, -66166, -3380, 24132, 24564, 3200, 9480, 0, 19068, 24768, -7530, -34168, 738, 13948, -5020, -18840, -19344, -89664, 0, 16332, -1650, -47820, -15264, -60164, 7644, -16900, 10040, -3240, 27428, 0, -7560, -93484, 16024, 25992, -43074, 15760, 4878, 33860, 51264, -11856, 0, -3448, 33948, 27544, 7368, -8010, 28872, 100090, 10794, 51596, 5500, 0, -4824, 60656, 2187, -3240, 8352, -76452, -36090, -32712, -4185, 32168, 0, 30348, 21534, -39700, 6420, -98744, 4816, 37008, -27360, -156976, 0, 0, -55072, -750, -48912, 23880, 43524, 37168, -14030, -18252, 25482, -91080, 0, -45240, 17040, 40380, -6996, -151776, -4680, -85008, -14456, -61482, 22346, 0, -18174, 79016, 23602, -13932, 6200, -74012, -12060, 40908, 34032, 7800, 0, 57024, 5940, 16218, 430, -42720, -23850, -18176, 15804, -27440, 48580, 0, -26956, 87284, -4230, 2096, -1034, -69984, 14816, 6450, 7110, -129796, 0, -21120, 20880, -78144, -38538, -77932, -16080, -810, -34398, 9496, 12798, 0, -25440, 27576, 15700, 53724, -6948, 15060, -9948, -60156, -48044, -5296, 0, -1744, -25200, 17208, -29794, 41460, 29130, -15768, -1080, -21648, 31740, 0, 6696, -47848, 31976, 24660, 3849, -94716, 18252, -94704, 5095, 3816, 0, 40380, -18822, -2000, 57040, -49440, -32222, 103400, -2610, 31300, 39576, 0, -24912, -18020, -10584, -143744, -28248, 6966, 1340, 38620, -28521, -102304, 0, 24660, 10744, 57004, 18666, 122976, 1250, 14424, -55358, -121192, 39168, 0, 48642, 35802, -1748, -39872, -8220, -7144, 2696, 10716, 34284, 17940, 0, 19512, 1056, -4476, -11780, 20884, -9408, 32060, -59424, 6750, 6064, 0, -18924, -4396, -15530, 97056, 8744, -66820, 20484, 2160, -53496, 46272, 0, 26512, 6210, -51020, 41928, -2160, 36290, -56440, -7650, -39556, 19936, 0, 20950, 22296, 6084, -21676, -24966, -36720, 45810, 162224, -22344, -82576, 0, 13752, 80050, 104896, 59934, -19000, -69636, -81732, 71376, 44712, 1350, 0, -9676, 2616, 45460, 15000, -41910, -42992, 26728, 44028, 13840, 154136, 0, 128136, 135012, 870, 49315, -60560, 17856, 13564, -24570, -77424, 58950, 0, 15696, 14580, -58412, 7290, -100732, -2504, -8550, -127028, 44282, -10248, 0, -6030, -29034, 105464, 30048, 87948, -8860, -93904, 1872, -77312, -20784, 0, -35896, 82704, 480, 105536, 5680, -38340, -34998, 33816, 22626, 2250, 0, 44100, 29088, 78360, 6420, -30404, 94092, -32364, -70498, 21460, 34842, 0, -4806, 11106, -6760, 76540, 7794, -81588, -85844, -25560, 59262, -68880, 0, -90586, -3900, 16200, -29692, 3612, -5748, -23600, -27112, -8460, -54858, 0, -5400, -223576, -61296, 58152, 46060, 18760, 1872, 46188, 28656, 26532, 0, 57884, 44286, -95072, -32814, -5100, 15590, 88284, -9234, 100800, 36390, 0, 8092, 109842, -31758, -28340, -24158, -13464, -1082, -149760, 13680, -82992, 0, 137148, -46094, -2860, -12384, -49024, 25640, 17208, -3050, -173260, 23976, 0, -25560, 2430, 17312, -41964, 17337, -9016, -6640, -11652, -11184, -24120, 0, -3460, 16796, 59760, -109670, -210484, 9270, -296460, 130688, 16668, 106548, 0, 16908, -51744, -25488, 39096, 13120, -67024, -4212, 100744, 86346, -24180, 0, 45600, -48132, 48776, -26900, -7920, -31714, 59376, -48738, -780, 10008, 0, -125080, 178108, -3375, 88964, 95832, -14136, 104742, -40220, -20592, -76716, 0, -5508, -15800, -96000, -11400, 46868, -10528, -41280, -160640, -121872, -10674, 0, -1230, 12912, 114928, -79512, 16536, 31400, -66036, -306, -20914, 85132, 0, -58606, 45612, 32904, -148964, 79700, -3294, 209352, -28104, 27900, -12740, 0, -19230, 20392, -18936, 5400, 63684, 187384, 9696, 177376, 12600, 87858, 0, 99456, -29916, -43320, 48166, -62712, 106586, 95948, -8130, 23856, -40412, 0, -129624, 19760, -50598, -115708, 8838, 82560, -56580, -38880, -50940, -138704, 0, 13350, 37354, 61220, -44442, 25336, -17990, -46800, -41248, 179088, -48432, 0, 135736, 50292, -4606, -143500, -3645, -44048, 147568, 57528, 135568, 127420, 0, -27232, -80400, -5760, 6975, -77808, 33618, 179524, -95328, -50580, 103046, 0, 13554, -76004, -10700, -39216, 61722, -134088, -13416, -61680, -1568, 33912, 0, 11024, 0, -178968, 40920, -39624, -34922, 1250, 2970, 134076, 37832, 0, -72540, -296052, 40620, 29440, 89412, 30420, -101692, 223152, 21750, 19672, 0, -12648, -39516, -19780, 13608, -67300, 137760, 139020, -99160, -108504, 7800, 0, -6018, -28368, -177060, 102470, 119436, 120972, -56508, 134460, 30290, -125496, 0, -259184, 13272, 23220, 3804, 98640, -24012, 232864, 20100, 14418, -101438, 0, 7230, -13000, 5810, -65952, -77256, 65496, -9900, -58036, 59628, -78684, 0, 71200, 73440, 65388, -98480, 5832, -26340, -102032, 25398, -95832, -45504, 0, -103406, -178164, 7533, -179496, 7050, 6240, -69318, -80484, 53532, 116640, 0, 71460, -107344, 22928, -11850, 210708, 245120, 6408, -65352, 35200, 49248, 0, -560, 42084, 64230, -51112, -89766, 142552, -112128, 1350, -91516, -66406, 0, -105696, -21330, -73620, -10016, 90408, 25254, -45960, -53092, 103932, 33968, 0, 11580, -163456, 39288, 81432, 103189, 100260, 2130, 43912, 61642, 30276, 0, -60588, 8424, -112784, 110056, -28680, -90466, -111112, 90552, 3704, -48550, 0, 90796, 84420, 66132, 36080, -25432, 39636, -79680, 175056, -11160, 48116, 0, -82584, -32418, -41100, 42876, -82940, -50864, -14040, -30420, 223920, 50328, 0, -98126, -6360, -8976, 28908, -774, 77336, 31370, -41016, 134652, -11884, 0, 82400, -108468, 49392, -106644, 227724, 4350, 115008, -9516, -77184, -42694, 0, 7614, -30664, 43314, -21048, 17640, 26120, 43956, 154432, 344, -11610, 0, 35360, -98172, 124678, 47535, 3996, -73886, -31156, -37584, -41100, 136800, 0, 24142, -50816, -31110, 92560, 55104, 1458, -15254, -24040, 59472, -60432, 0, -63156, -65280, -223792, 45792, 296600, -99308, -59670, 39558, 11384, -2088, 0, 13700, -27108, 66836, 181760, 38112, -17860, 117192, -21312, 98500, -276472, 0, -52092, -19904, 7440, 86694, 7460, 68544, 15904, 34776, -74628, 15680, 0, -59172, -182840, 50108, -11250, 45868, -205520, -57132, 50152, 31540, 15624, 0, -69232, -55476, -161760, 16016, -44388, 111248, 39060, -34140, -115320, 25944, 0, 187416, -77120, -9171, -13164, 133788, -123828, -10350, -8552, 9030, -176240, 0, 3600, 131702, 48848, -66108, 35488, 12750, -18090, -139256, -140924, 4698, 0, -146112, 140412, -108392, 99496, -10140, -1348, 28352, 32436, -60014, 61200, 0, 57260, 109844, -99624, 37240, -46876, -2412, 154656, -33424, -22920, 53544, 0, 69198, 59936, -99890, -44388, -208464, 109962, 128130, 136220, -120948, -109920, 0, 47540, -2250, -281192, -218328, 1116, -14362, -4360, -8064, 60104, 152608, 0, 69850, -119888, -1887, 41660, 121232, -73380, -63412, 288224, 14796, -193068, 0, -181392, 182910, -11520, 9072, -1450, 13420, -32292, 86284, -13820, -29760, 0, -8424, -141552, 235946, 129040, 21204, 73664, 161696, 2244, -26160, 93444, 0, 105516, -64064, -12150, 104950, 72848, 8922, 148312, 14250, -69696, -17022, 0, 27954, 17080, -223528, 9456, -126976, 23520, 48390, 217876, 31246, -3888, 0, -146580, -70254, -76796, 188688, -101700, -3120, -199936, -11178, -50512, 57616, 0, -13764, -90960, -44496, 70892, -800, 101592, 173738, -449916, -8892, 63900, 0, 32136, 87074, 22392, -37710, 178992, -24396, 181656, 126150, -73500, 105552, 0, -90552, 66096, -10700, 225336, 42852, -151776, 44672, 53940, 30765, -366674, 0, 259676, -58070, 34116, 34972, 5544, 9252, -18510, 260196, 34200, 75626, 0, -12990, 111644, 68414, -37476, 123652, 42600, -2430, 391536, 119512, -96432, 0, 93024, -116376, 268552, -180094, -27000, 103472, 241116, 19362, -144880, 9580, 0, 78528, 45816, -24912, 14100, 204770, -130104, -117838, 167888, 9000, 253216, 0, -1566, 207352, -96920, -56286, 70004, 135948, -56214, -3120, -444960, 44226, 0, 142544, -44220, 33414, 124032, 126432, -155564, -73810, -26244, -92560, 452928, 0, 8500, -24768, 105672, 84998, -206496, 15390, -68112, 94008, -75216, 44202, 0, 109116, 103268, -90456, 10854, 52930, 76008, 29616, 22944, -102712, 22440, 0, 429448, 15948, -130052, -22800, 148884, 93862, -24632, 21780, -228580, -155148, 0, 109152, -113912, 20640, 69408, -4348, 109236, 124714, -28680, -10224, 160212, 0, -90528, -39960, -366668, 71640, 197472, -209876, -4050, 160194, 233376, -38322, 0, -28895, -8136, 101964, -99684, -11556, 19420, 17964, -33432, 153774, -67296, 0, 77036, 126528, -38628, 120240, -99600, -96078, 69552, -39620, 24264, -15450, 0, 12168, -166816, -54624, -27780, -223560, -19084, -64896, 288128, -28180, 46008, 0, -319496, -82338, -65160, -82488, 73596, -111604, 176364, 7020, 68096, 199248, 0, -133757, 40300, 12870, 225688, -105456, 42480, 80220, -74588, 984, 65524, 0, 13200, 123570, 258552, 9720, -4840, 81230, 96912, -151194, 507472, -210108, 0, -90272, -33768, 140826, 59616, 5625, 316320, 26844, -23940, -2920, 23560, 0, -56260, 113796, -80412, 34320, 68976, 78192, -4696, 289028, 9180, 221648, 0, -15456, -368624, 19000, 101376, 141284, 43232, -65502, 68800, -20234, -344772, 0, -147552, 17790, -72472, 99988, 51012, -250128, -21520, -41310, -116984, 92476, 0, -27560, -43704, -24624, 596520, -85296, 510, -51312, 62146, 93114, -126960, 0, 5148, -20400, -76020, 38832, -54840, -6132, -240816, -17878, -348412, 5490, 0, -244552, 92592, -48132, -46500, 74472, 206120, 135712, -4374, 32050, -232016, 0, 341976, -65928, -9000, 37400, 94460, 11952, -246612, -16160, 388584, -85816, 0, -143010, -146430, 172852, 6228, -185036, -39176, 49860, -300688, -269448, -28692, 0, 104520, -16686, 207104, -251430, -16176, 13550, -287040, 20268, 27024, -299688, 0, 65484, -109152, 2550, 149840, 84330, -116280, -288870, 390496, -23616, -137600, 0, -300564, 159906, 59696, 84900, -49608, -284400, 43524, -33498, -22250, -93552, 0, 76092, -187092, 74070, -101312, 48420, -260664, 235764, 78000, -116828, -353644, 0, 452304, 80720, 1404, -46598, 122724, 30870, -83820, -39792, 226728, -16438, 0, 6075, -181524, 129092, -198498, -244126, -95880, -10140, -188948, 227688, 72396, 0, -151564, 73692, -176136, 127728, 9600, -48620, 118436, 28440, -32880, -56030, 0, 84112, 910, 57204, 84300, -89616, 74304, 67346, -162912, -22590, 622316, 0, -102504, 19616, 65360, 2214, 355240, 376580, 41844, 22360, -112032, -15060, 0, -80314, -56520, 25684, -617384, -58032, 74752, 0, -268992, -209888, 155168, 0, 66040, 44604, 48996, -62876, -70988, -4950, 68056, -27684, -143460, 48774, 0, -45792, 434668, 81664, -180492, -67700, -238272, 22932, -261484, 437908, -50700, 0, -200192, 30120, 11340, -36250, -9720, -116946, -55296, 82284, 21080, 207872, 0, 49854, -316080, -22680, 260494, -81360, -280452, -36048, -231700, 48072, 189308, 0, 77976, -13000, -20460, -129222, -394256, -26808, 47280, -307086, 87408, 14634, 0, -199060, 101580, -63138, -483420, 153792, -224100, -40176, -35568, -141448, -128976, 0, -343144, -144324, -10344, -454012, -38700, 101844, 71284, 59940, 82632, 40020, 0, 22104, 147888, -128448, -24030, 17182, 175904, 86616, 360940, -12050, 300270, 0, -363632, 32382, 109920, 243456, 154788, 295800, -269392, 16500, 61792, -220720, 0, 122628, 131140, -14472, -99000, 115848, 181968, -122400, -200620, 6561, 18684, 0, -9720, 107412, -197556, 25056, 29736, -42330, -229356, 177228, 592600, -108270, 0, -118272, -98136, 244692, -206640, -12555, 280856, -141132, 96504, -221837, -10400, 0, -262368, -164788, 91044, -89220, -12824, 64602, 103668, 17948, -119100, -177970, 0, 19260, 290968, 19750, -296232, -97984, 77152, 14448, -10680, -65968, 111024, 0, 364304, -82080, -139088, -7098, -470928, -70298, -70140, 0, 82272, 135216, 0, 149610, -65424, -165216, 263876, -163784, -2250, -269074, -381476, -146736, 263304, 0, 71640, -73084, 274588, 130572, 122700, -164832, 111504, -96592, -65092, -42090, 0, 82684, -54756, -34986, -173220, 76446, -102416, 23956, -273240, -19300, -590364, 0, -239840, -75084, -135720, -196058, -478288, 51120, -57224, -3550, 121140, 2270, 0, -20988, -50460, -134560, -455328, -50698, 673248, -14040, -436440, 74310, -255024, 0, 47800, -43368, -392464, 53208, -184446, -150920, -413604, 67038, 78420, -202920, 0, 180020, 18370, -54522, 218416, -110220, 237048, 439392, -582672, 70806, -66060, 0, -41796, -72368, 468456, 18600, 73708, -143544, -222036, -3600, 137640, -36180, 0, -98718, 122724, -71460, -74840, 102096, -165720, 89024, 23400, 59738, 584008, 0, -268672, -83880, 171072, 346872, 349088, 17820, 10600, -126416, 48654, -76956, 0, 1290, 598976, 66194, -128160, -227204, 68360, -71550, 452556, 140816, -54528, 0, 288852, 47412, 25172, 50176, -82320, -59422, -95976, 145740, -174076, -7250, 0, -14978, 468552, -80868, 128640, 100386, 261852, -125002, 222852, -12690, 341396, 0, 6288, 198194, 35080, -3102, -248992, 302880, -209952, -73260, -105712, 44448, 0, -182040, 19350, -149673, -110892, 21330, 99420, 163620, -389388, 281928, 228120, 0, -6660, -39440, -63360, -58748, -117600, 62640, 31432, 264384, -234432, -151344, 0, -115614, 214976, 178720, -233796, 51850, -114660, -48240, -328796, -190272, -2430, 0, -209352, -103194, 212840, -99120, 28488, -184814, 453808, 38394, 105260, -169444, 0, 289812, -47328, -76320, -53436, 178808, 82728, 286256, 99450, 47100, -216512, 0, 161172, 3480, 661436, -20844, 170420, -140336, 45180, 161264, 4216, -29844, 0, -63520, -180468, 159652, -185260, -144132, 35520, -61396, -15888, 108366, 251548, 0, -94632, 369120, -5232, -217848, -12400, -75600, 91456, -143008, 51624, -114240, 0, -89382, 551120, -259800, 124380, 35984, -475448, 87390, -237960, 98620, -47304, 0, -345948, -3240, 18750, 161976, -64944, -131626, -442964, 95220, 42000, -36688, 0, -126980, -26040, 20088, -189196, 36528, -143544, 92460, 427664, 95928, -64232, 0, 73980, 176930, -25552, 11547, -130528, 56900, -284148, -345514, 172464, 54756, 0, 189588, -284112, 163360, -98344, 15285, -626836, 63240, 11448, -328968, 206380, 0, -162144, -592192, 121140, -15050, -492768, -56466, 17496, 66468, -6000, -279094, 0, 171120, 563716, 110180, -148320, -103102, 15776, -96666, 30150, -139128, 310200, 0, 254052, -7830, 331332, -42096, 93900, -426328, -234020, 118728, -94888, -229440, 0, 16900, -486384, -74736, 296764, 301452, -54060, 197832, -737224, -31752, 307632, 0, -431232, 70080, -5760, -84744, 166040, -186548, 20898, -107014, 203040, 4020, 0, 364914, 115860, 81040, 38200, -85563, -350060, -657348, -306912, -115330, -154080, 0, 681512, -100712, 73980, -10284, -789404, 32232, -76272, -213550, 171012, 392174, 0, 55998, 183200, 528494, 368928, -328796, 139548, 3750, 24400, -305632, 43272, 0, -1860, -166074, -272560, 157374, -363576, 13440, 427128, 117504, -266680, -59424, 0, 360292, 413956, 145926, 355092, 3145, 107406, -107674, -712952, -5244, 122300, 0, -119616, 344400, 222428, -24660, -123012, 83664, -21432, -613130, 302320, 8088, 0, 217968, 32148, -15120, 16224, 102852, -541872, -496, 53820, 48856, -333204, 0, 708928, 49600, 58536, -120538, -208832, 3168, 235920, 171536, -13428, -138314, 0, -35340, 232784, 48936, 62652, -210678, -3740, -28224, -376440, -156990, 96180, 0, 593640, -178272, -571104, 172116, 20250, -151428, -413712, 18192, -331578, -14870, 0, 86324, 466040, -56772, 116160, 66576, -13188, 21798, 234528, -46590, -166712, 0, 291168, 277662, -15760, 26232, 461092, -103444, -200460, -80650, -225584, 61452, 0, -230466, 6480, -382272, 63328, -160488, 156960, 117090, 138816, -175744, 620366, 0, 169500, -275516, 79536, 232716, -158376, 18630, 429020, -302112, -153060, 375146, 0, 125784, -168956, 295458, -6480, 74160, -121200, 108870, 528576, -401808, -169320, 0, -259284, -22950, -2008, 14820, -118668, -241546, -411696, 59808, -53560, 347296, 0, 79328, 276000, 62850, 295860, -73482, 66888, -561476, -302760, 18252, 38576, 0, -65028, -175920, -507424, -74898, -248064, -133224, -110160, -115554, -917628, 137430, 0, -71420, 486672, 16174, -473936, -67032, -89900, -51300, -247728, -616892, 299076, 0, -745680, 20580, 41256, 77029, -56860, 240150, 1008992, 298248, 314688, -15420, 0, 179802, -112924, -364660, -57000, -281632, -440160, -208908, -444788, 21650, -245196, 0, -220152, 214128, 62460, -112632, 134136, -410990, 84944, 4050, -132148, -679992, 0, -255696, 160720, -29028, 264996, -287252, 7848, 193960, 257872, 136380, -169732, 0, 45000, 103286, 825408, -125730, 392684, -32270, -128976, -146250, 200116, 80184, 0, 749286, 132084, -341492, 13080, 41520, 57532, 15824, 462408, 167356, 216840, 0, 44392, -156040, 384408, -15000, -365392, 405036, 336208, 238932, 2610, 86888, 0, 147945, -76576, 93810, -181680, 1620, 965238, 53568, 93690, -83052, 40692, 0, 374916, -73710, 275060, -208170, -232272, -273016, 73700, 176850, 658112, 143324, 0, -210720, 283796, 47088, -86112, 210602, 43740, -120480, -175216, -175236, 381504, 0, 21870, 474778, -412176, -302196, -176120, 176912, -7512, 253932, 158016, -25650, 0, 277640, -381084, 364424, 125360, 132846, -311760, -111256, -30744, -181860, 118440, 0, -346640, -279960, -18090, -222384, -771480, -87102, -461608, -49360, 316392, -199420, 0, 90144, -37400, -316920, 263844, -170658, 286336, -26580, -298584, -15270, -281712, 0, -248140, 5616, -16244, -95492, -231936, -36300, 726384, -62352, -928232, -118332, 0, -115936, 228284, -107688, 125604, -34400, 248112, -116308, -86372, 1440, -182060, 0, 316608, -589828, -861104, 17040, 767840, -95584, -115020, 114714, 150880, -104994, 0, 102096, 101448, -119400, -718296, 67878, -708360, 208420, 6750], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "165.4.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, 0], [1, 0, 0], [1, -1, 0], [3, 0, 0], [10, 0, 1], [-5, 0, 0], [3, -3, 0], [-4, 2, -2], [-3, -9, 2], [9, 0, 0], [-5, 5, 0], [0, 0, 0], [30, 0, 3], [-38, 0, 2], [-28, 16, -6], [-15, 0, 0], [60, -2, 5], [34, 2, 2], [9, -9, 0], [24, -14, 8], [-50, 0, -5], [-12, 6, -6], [0, 0, 0], [48, -24, 4], [-9, -27, 6], [25, 0, 0], [-48, 24, 4], [27, 0, 0], [-238, 38, -12], [62, 34, 0], [-15, 15, 0], [96, -40, -8], [93, -21, -4], [0, 0, 0], [-10, -50, 2], [20, -10, 10], [90, 0, 9], [286, -20, 0], [222, -66, 30], [-114, 0, 6], [15, 45, -10], [-30, -66, 0], [-84, 48, -18], [-48, 22, 14], [0, 0, 0], [-45, 0, 0], [436, -52, 32], [168, 0, -4], [180, -6, 15], [117, -72, 0], [25, -25, 0], [102, 6, 6], [-172, -4, -32], [126, -96, 16], [27, -27, 0], [0, 0, 0], [-600, 156, -14], [72, -42, 24], [-516, -96, -34], [172, 32, 8], [-150, 0, -15], [-134, -12, -68], [816, 0, 24], [-36, 18, -18], [-10, -28, -27], [190, 0, -10], [0, 0, 0], [-176, 100, -16], [558, 30, 38], [144, -72, 12], [140, -80, 30], [-324, 60, -28], [-27, -81, 18], [-194, -36, 38], [626, -266, 20], [75, 0, 0], [1002, -254, 62], [0, 0, 0], [-144, 72, 12], [212, -94, -8], [-300, 10, -25], [81, 0, 0], [1092, 96, 66], [-60, 180, -54], [-714, 114, -36], [-170, -10, -10], [-492, -72, 6], [186, 102, 0], [0, 0, 0], [254, 28, 120], [-45, 45, 0], [-244, -40, 92], [776, -416, 84], [288, -120, -24], [188, -140, -8], [-120, 70, -40], [279, -63, -12], [658, 100, -44], [1341, -45, 72], [0, 0, 0], [250, 0, 25]]}