Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,4,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(2.53708213025\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-4.15251\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.15251 | 1.82169 | 0.910844 | − | 0.412750i | \(-0.135432\pi\) | ||||
0.910844 | + | 0.412750i | \(0.135432\pi\) | |||||||
\(3\) | −6.49933 | −1.25080 | −0.625398 | − | 0.780306i | \(-0.715063\pi\) | ||||
−0.625398 | + | 0.780306i | \(0.715063\pi\) | |||||||
\(4\) | 18.5484 | 2.31855 | ||||||||
\(5\) | 17.2665 | 1.54437 | 0.772183 | − | 0.635400i | \(-0.219165\pi\) | ||||
0.772183 | + | 0.635400i | \(0.219165\pi\) | |||||||
\(6\) | −33.4879 | −2.27856 | ||||||||
\(7\) | −23.3206 | −1.25919 | −0.629597 | − | 0.776922i | \(-0.716780\pi\) | ||||
−0.629597 | + | 0.776922i | \(0.716780\pi\) | |||||||
\(8\) | 54.3507 | 2.40199 | ||||||||
\(9\) | 15.2413 | 0.564491 | ||||||||
\(10\) | 88.9661 | 2.81336 | ||||||||
\(11\) | −60.5580 | −1.65990 | −0.829951 | − | 0.557836i | \(-0.811632\pi\) | ||||
−0.829951 | + | 0.557836i | \(0.811632\pi\) | |||||||
\(12\) | −120.552 | −2.90003 | ||||||||
\(13\) | 10.9419 | 0.233441 | 0.116721 | − | 0.993165i | \(-0.462762\pi\) | ||||
0.116721 | + | 0.993165i | \(0.462762\pi\) | |||||||
\(14\) | −120.160 | −2.29386 | ||||||||
\(15\) | −112.221 | −1.93169 | ||||||||
\(16\) | 131.656 | 2.05712 | ||||||||
\(17\) | −3.57473 | −0.0510000 | −0.0255000 | − | 0.999675i | \(-0.508118\pi\) | ||||
−0.0255000 | + | 0.999675i | \(0.508118\pi\) | |||||||
\(18\) | 78.5308 | 1.02833 | ||||||||
\(19\) | 33.2403 | 0.401361 | 0.200680 | − | 0.979657i | \(-0.435685\pi\) | ||||
0.200680 | + | 0.979657i | \(0.435685\pi\) | |||||||
\(20\) | 320.267 | 3.58069 | ||||||||
\(21\) | 151.568 | 1.57499 | ||||||||
\(22\) | −312.026 | −3.02383 | ||||||||
\(23\) | 63.7158 | 0.577637 | 0.288819 | − | 0.957384i | \(-0.406738\pi\) | ||||
0.288819 | + | 0.957384i | \(0.406738\pi\) | |||||||
\(24\) | −353.243 | −3.00440 | ||||||||
\(25\) | 173.134 | 1.38507 | ||||||||
\(26\) | 56.3783 | 0.425257 | ||||||||
\(27\) | 76.4239 | 0.544733 | ||||||||
\(28\) | −432.560 | −2.91950 | ||||||||
\(29\) | −89.3510 | −0.572140 | −0.286070 | − | 0.958209i | \(-0.592349\pi\) | ||||
−0.286070 | + | 0.958209i | \(0.592349\pi\) | |||||||
\(30\) | −578.220 | −3.51893 | ||||||||
\(31\) | 222.839 | 1.29106 | 0.645532 | − | 0.763733i | \(-0.276636\pi\) | ||||
0.645532 | + | 0.763733i | \(0.276636\pi\) | |||||||
\(32\) | 243.552 | 1.34545 | ||||||||
\(33\) | 393.586 | 2.07620 | ||||||||
\(34\) | −18.4188 | −0.0929061 | ||||||||
\(35\) | −402.666 | −1.94466 | ||||||||
\(36\) | 282.701 | 1.30880 | ||||||||
\(37\) | −59.6535 | −0.265053 | −0.132527 | − | 0.991179i | \(-0.542309\pi\) | ||||
−0.132527 | + | 0.991179i | \(0.542309\pi\) | |||||||
\(38\) | 171.271 | 0.731154 | ||||||||
\(39\) | −71.1150 | −0.291987 | ||||||||
\(40\) | 938.449 | 3.70955 | ||||||||
\(41\) | −143.837 | −0.547890 | −0.273945 | − | 0.961745i | \(-0.588329\pi\) | ||||
−0.273945 | + | 0.961745i | \(0.588329\pi\) | |||||||
\(42\) | 780.957 | 2.86915 | ||||||||
\(43\) | −43.0000 | −0.152499 | ||||||||
\(44\) | −1123.25 | −3.84857 | ||||||||
\(45\) | 263.164 | 0.871782 | ||||||||
\(46\) | 328.296 | 1.05228 | ||||||||
\(47\) | 379.013 | 1.17627 | 0.588135 | − | 0.808763i | \(-0.299862\pi\) | ||||
0.588135 | + | 0.808763i | \(0.299862\pi\) | |||||||
\(48\) | −855.674 | −2.57304 | ||||||||
\(49\) | 200.850 | 0.585569 | ||||||||
\(50\) | 892.073 | 2.52316 | ||||||||
\(51\) | 23.2334 | 0.0637906 | ||||||||
\(52\) | 202.955 | 0.541245 | ||||||||
\(53\) | −150.129 | −0.389090 | −0.194545 | − | 0.980894i | \(-0.562323\pi\) | ||||
−0.194545 | + | 0.980894i | \(0.562323\pi\) | |||||||
\(54\) | 393.775 | 0.992333 | ||||||||
\(55\) | −1045.63 | −2.56350 | ||||||||
\(56\) | −1267.49 | −3.02457 | ||||||||
\(57\) | −216.040 | −0.502021 | ||||||||
\(58\) | −460.382 | −1.04226 | ||||||||
\(59\) | 207.310 | 0.457448 | 0.228724 | − | 0.973491i | \(-0.426545\pi\) | ||||
0.228724 | + | 0.973491i | \(0.426545\pi\) | |||||||
\(60\) | −2081.52 | −4.47871 | ||||||||
\(61\) | −486.557 | −1.02127 | −0.510633 | − | 0.859799i | \(-0.670589\pi\) | ||||
−0.510633 | + | 0.859799i | \(0.670589\pi\) | |||||||
\(62\) | 1148.18 | 2.35192 | ||||||||
\(63\) | −355.435 | −0.710804 | ||||||||
\(64\) | 201.659 | 0.393866 | ||||||||
\(65\) | 188.929 | 0.360519 | ||||||||
\(66\) | 2027.96 | 3.78219 | ||||||||
\(67\) | 1019.41 | 1.85882 | 0.929408 | − | 0.369054i | \(-0.120318\pi\) | ||||
0.929408 | + | 0.369054i | \(0.120318\pi\) | |||||||
\(68\) | −66.3055 | −0.118246 | ||||||||
\(69\) | −414.110 | −0.722507 | ||||||||
\(70\) | −2074.74 | −3.54256 | ||||||||
\(71\) | 13.8437 | 0.0231400 | 0.0115700 | − | 0.999933i | \(-0.496317\pi\) | ||||
0.0115700 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(72\) | 828.374 | 1.35590 | ||||||||
\(73\) | 411.158 | 0.659211 | 0.329605 | − | 0.944119i | \(-0.393084\pi\) | ||||
0.329605 | + | 0.944119i | \(0.393084\pi\) | |||||||
\(74\) | −307.365 | −0.482844 | ||||||||
\(75\) | −1125.25 | −1.73244 | ||||||||
\(76\) | 616.555 | 0.930575 | ||||||||
\(77\) | 1412.25 | 2.09014 | ||||||||
\(78\) | −366.421 | −0.531910 | ||||||||
\(79\) | −1315.13 | −1.87296 | −0.936481 | − | 0.350718i | \(-0.885938\pi\) | ||||
−0.936481 | + | 0.350718i | \(0.885938\pi\) | |||||||
\(80\) | 2273.24 | 3.17695 | ||||||||
\(81\) | −908.218 | −1.24584 | ||||||||
\(82\) | −741.120 | −0.998085 | ||||||||
\(83\) | 813.425 | 1.07572 | 0.537861 | − | 0.843033i | \(-0.319232\pi\) | ||||
0.537861 | + | 0.843033i | \(0.319232\pi\) | |||||||
\(84\) | 2811.35 | 3.65170 | ||||||||
\(85\) | −61.7233 | −0.0787627 | ||||||||
\(86\) | −221.558 | −0.277805 | ||||||||
\(87\) | 580.721 | 0.715630 | ||||||||
\(88\) | −3291.37 | −3.98706 | ||||||||
\(89\) | −350.573 | −0.417535 | −0.208768 | − | 0.977965i | \(-0.566945\pi\) | ||||
−0.208768 | + | 0.977965i | \(0.566945\pi\) | |||||||
\(90\) | 1355.96 | 1.58811 | ||||||||
\(91\) | −255.171 | −0.293948 | ||||||||
\(92\) | 1181.83 | 1.33928 | ||||||||
\(93\) | −1448.30 | −1.61486 | ||||||||
\(94\) | 1952.87 | 2.14280 | ||||||||
\(95\) | 573.946 | 0.619848 | ||||||||
\(96\) | −1582.92 | −1.68288 | ||||||||
\(97\) | −1187.03 | −1.24252 | −0.621262 | − | 0.783603i | \(-0.713380\pi\) | ||||
−0.621262 | + | 0.783603i | \(0.713380\pi\) | |||||||
\(98\) | 1034.88 | 1.06672 | ||||||||
\(99\) | −922.981 | −0.937001 | ||||||||
\(100\) | 3211.35 | 3.21135 | ||||||||
\(101\) | 469.014 | 0.462066 | 0.231033 | − | 0.972946i | \(-0.425790\pi\) | ||||
0.231033 | + | 0.972946i | \(0.425790\pi\) | |||||||
\(102\) | 119.710 | 0.116207 | ||||||||
\(103\) | −1299.82 | −1.24345 | −0.621725 | − | 0.783235i | \(-0.713568\pi\) | ||||
−0.621725 | + | 0.783235i | \(0.713568\pi\) | |||||||
\(104\) | 594.700 | 0.560722 | ||||||||
\(105\) | 2617.06 | 2.43237 | ||||||||
\(106\) | −773.541 | −0.708801 | ||||||||
\(107\) | −1480.92 | −1.33800 | −0.669000 | − | 0.743263i | \(-0.733277\pi\) | ||||
−0.669000 | + | 0.743263i | \(0.733277\pi\) | |||||||
\(108\) | 1417.54 | 1.26299 | ||||||||
\(109\) | 350.586 | 0.308073 | 0.154037 | − | 0.988065i | \(-0.450773\pi\) | ||||
0.154037 | + | 0.988065i | \(0.450773\pi\) | |||||||
\(110\) | −5387.61 | −4.66990 | ||||||||
\(111\) | 387.707 | 0.331528 | ||||||||
\(112\) | −3070.29 | −2.59031 | ||||||||
\(113\) | 785.106 | 0.653598 | 0.326799 | − | 0.945094i | \(-0.394030\pi\) | ||||
0.326799 | + | 0.945094i | \(0.394030\pi\) | |||||||
\(114\) | −1113.15 | −0.914525 | ||||||||
\(115\) | 1100.15 | 0.892084 | ||||||||
\(116\) | −1657.32 | −1.32653 | ||||||||
\(117\) | 166.768 | 0.131776 | ||||||||
\(118\) | 1068.17 | 0.833329 | ||||||||
\(119\) | 83.3649 | 0.0642189 | ||||||||
\(120\) | −6099.29 | −4.63989 | ||||||||
\(121\) | 2336.27 | 1.75528 | ||||||||
\(122\) | −2506.99 | −1.86043 | ||||||||
\(123\) | 934.841 | 0.685299 | ||||||||
\(124\) | 4133.30 | 2.99340 | ||||||||
\(125\) | 831.100 | 0.594687 | ||||||||
\(126\) | −1831.39 | −1.29486 | ||||||||
\(127\) | −731.562 | −0.511147 | −0.255573 | − | 0.966790i | \(-0.582264\pi\) | ||||
−0.255573 | + | 0.966790i | \(0.582264\pi\) | |||||||
\(128\) | −909.364 | −0.627947 | ||||||||
\(129\) | 279.471 | 0.190745 | ||||||||
\(130\) | 973.458 | 0.656753 | ||||||||
\(131\) | 2462.56 | 1.64240 | 0.821202 | − | 0.570638i | \(-0.193304\pi\) | ||||
0.821202 | + | 0.570638i | \(0.193304\pi\) | |||||||
\(132\) | 7300.40 | 4.81377 | ||||||||
\(133\) | −775.184 | −0.505391 | ||||||||
\(134\) | 5252.52 | 3.38618 | ||||||||
\(135\) | 1319.58 | 0.841267 | ||||||||
\(136\) | −194.289 | −0.122501 | ||||||||
\(137\) | 2384.64 | 1.48710 | 0.743552 | − | 0.668678i | \(-0.233139\pi\) | ||||
0.743552 | + | 0.668678i | \(0.233139\pi\) | |||||||
\(138\) | −2133.71 | −1.31618 | ||||||||
\(139\) | −3086.87 | −1.88363 | −0.941816 | − | 0.336129i | \(-0.890882\pi\) | ||||
−0.941816 | + | 0.336129i | \(0.890882\pi\) | |||||||
\(140\) | −7468.81 | −4.50878 | ||||||||
\(141\) | −2463.33 | −1.47127 | ||||||||
\(142\) | 71.3297 | 0.0421539 | ||||||||
\(143\) | −662.619 | −0.387490 | ||||||||
\(144\) | 2006.60 | 1.16123 | ||||||||
\(145\) | −1542.78 | −0.883594 | ||||||||
\(146\) | 2118.50 | 1.20088 | ||||||||
\(147\) | −1305.39 | −0.732427 | ||||||||
\(148\) | −1106.48 | −0.614539 | ||||||||
\(149\) | −1445.58 | −0.794808 | −0.397404 | − | 0.917644i | \(-0.630089\pi\) | ||||
−0.397404 | + | 0.917644i | \(0.630089\pi\) | |||||||
\(150\) | −5797.88 | −3.15596 | ||||||||
\(151\) | −825.878 | −0.445093 | −0.222546 | − | 0.974922i | \(-0.571437\pi\) | ||||
−0.222546 | + | 0.974922i | \(0.571437\pi\) | |||||||
\(152\) | 1806.64 | 0.964063 | ||||||||
\(153\) | −54.4834 | −0.0287891 | ||||||||
\(154\) | 7276.63 | 3.80758 | ||||||||
\(155\) | 3847.65 | 1.99388 | ||||||||
\(156\) | −1319.07 | −0.676987 | ||||||||
\(157\) | 1187.82 | 0.603809 | 0.301904 | − | 0.953338i | \(-0.402378\pi\) | ||||
0.301904 | + | 0.953338i | \(0.402378\pi\) | |||||||
\(158\) | −6776.24 | −3.41195 | ||||||||
\(159\) | 975.737 | 0.486673 | ||||||||
\(160\) | 4205.30 | 2.07786 | ||||||||
\(161\) | −1485.89 | −0.727357 | ||||||||
\(162\) | −4679.61 | −2.26953 | ||||||||
\(163\) | 1514.60 | 0.727809 | 0.363904 | − | 0.931436i | \(-0.381443\pi\) | ||||
0.363904 | + | 0.931436i | \(0.381443\pi\) | |||||||
\(164\) | −2667.94 | −1.27031 | ||||||||
\(165\) | 6795.88 | 3.20641 | ||||||||
\(166\) | 4191.18 | 1.95963 | ||||||||
\(167\) | −3354.48 | −1.55435 | −0.777177 | − | 0.629282i | \(-0.783349\pi\) | ||||
−0.777177 | + | 0.629282i | \(0.783349\pi\) | |||||||
\(168\) | 8237.84 | 3.78312 | ||||||||
\(169\) | −2077.27 | −0.945505 | ||||||||
\(170\) | −318.030 | −0.143481 | ||||||||
\(171\) | 506.625 | 0.226565 | ||||||||
\(172\) | −797.581 | −0.353575 | ||||||||
\(173\) | 1654.64 | 0.727166 | 0.363583 | − | 0.931562i | \(-0.381553\pi\) | ||||
0.363583 | + | 0.931562i | \(0.381553\pi\) | |||||||
\(174\) | 2992.17 | 1.30366 | ||||||||
\(175\) | −4037.58 | −1.74407 | ||||||||
\(176\) | −7972.81 | −3.41462 | ||||||||
\(177\) | −1347.38 | −0.572175 | ||||||||
\(178\) | −1806.33 | −0.760619 | ||||||||
\(179\) | −1334.05 | −0.557049 | −0.278524 | − | 0.960429i | \(-0.589845\pi\) | ||||
−0.278524 | + | 0.960429i | \(0.589845\pi\) | |||||||
\(180\) | 4881.27 | 2.02127 | ||||||||
\(181\) | 2771.58 | 1.13817 | 0.569087 | − | 0.822277i | \(-0.307297\pi\) | ||||
0.569087 | + | 0.822277i | \(0.307297\pi\) | |||||||
\(182\) | −1314.77 | −0.535481 | ||||||||
\(183\) | 3162.29 | 1.27740 | ||||||||
\(184\) | 3463.00 | 1.38748 | ||||||||
\(185\) | −1030.01 | −0.409339 | ||||||||
\(186\) | −7462.39 | −2.94177 | ||||||||
\(187\) | 216.479 | 0.0846550 | ||||||||
\(188\) | 7030.08 | 2.72724 | ||||||||
\(189\) | −1782.25 | −0.685924 | ||||||||
\(190\) | 2957.26 | 1.12917 | ||||||||
\(191\) | 81.5135 | 0.0308802 | 0.0154401 | − | 0.999881i | \(-0.495085\pi\) | ||||
0.0154401 | + | 0.999881i | \(0.495085\pi\) | |||||||
\(192\) | −1310.65 | −0.492646 | ||||||||
\(193\) | 3305.29 | 1.23275 | 0.616373 | − | 0.787454i | \(-0.288601\pi\) | ||||
0.616373 | + | 0.787454i | \(0.288601\pi\) | |||||||
\(194\) | −6116.20 | −2.26349 | ||||||||
\(195\) | −1227.91 | −0.450936 | ||||||||
\(196\) | 3725.45 | 1.35767 | ||||||||
\(197\) | 2241.99 | 0.810840 | 0.405420 | − | 0.914131i | \(-0.367125\pi\) | ||||
0.405420 | + | 0.914131i | \(0.367125\pi\) | |||||||
\(198\) | −4755.67 | −1.70692 | ||||||||
\(199\) | −4074.29 | −1.45135 | −0.725675 | − | 0.688037i | \(-0.758472\pi\) | ||||
−0.725675 | + | 0.688037i | \(0.758472\pi\) | |||||||
\(200\) | 9409.94 | 3.32691 | ||||||||
\(201\) | −6625.48 | −2.32500 | ||||||||
\(202\) | 2416.60 | 0.841740 | ||||||||
\(203\) | 2083.72 | 0.720435 | ||||||||
\(204\) | 430.941 | 0.147902 | ||||||||
\(205\) | −2483.56 | −0.846143 | ||||||||
\(206\) | −6697.36 | −2.26518 | ||||||||
\(207\) | 971.109 | 0.326071 | ||||||||
\(208\) | 1440.56 | 0.480217 | ||||||||
\(209\) | −2012.97 | −0.666220 | ||||||||
\(210\) | 13484.4 | 4.43102 | ||||||||
\(211\) | 4267.62 | 1.39239 | 0.696196 | − | 0.717851i | \(-0.254874\pi\) | ||||
0.696196 | + | 0.717851i | \(0.254874\pi\) | |||||||
\(212\) | −2784.65 | −0.902125 | ||||||||
\(213\) | −89.9746 | −0.0289435 | ||||||||
\(214\) | −7630.46 | −2.43742 | ||||||||
\(215\) | −742.461 | −0.235514 | ||||||||
\(216\) | 4153.69 | 1.30844 | ||||||||
\(217\) | −5196.73 | −1.62570 | ||||||||
\(218\) | 1806.40 | 0.561214 | ||||||||
\(219\) | −2672.25 | −0.824538 | ||||||||
\(220\) | −19394.7 | −5.94360 | ||||||||
\(221\) | −39.1143 | −0.0119055 | ||||||||
\(222\) | 1997.67 | 0.603940 | ||||||||
\(223\) | −889.370 | −0.267070 | −0.133535 | − | 0.991044i | \(-0.542633\pi\) | ||||
−0.133535 | + | 0.991044i | \(0.542633\pi\) | |||||||
\(224\) | −5679.78 | −1.69418 | ||||||||
\(225\) | 2638.78 | 0.781859 | ||||||||
\(226\) | 4045.27 | 1.19065 | ||||||||
\(227\) | 232.389 | 0.0679479 | 0.0339739 | − | 0.999423i | \(-0.489184\pi\) | ||||
0.0339739 | + | 0.999423i | \(0.489184\pi\) | |||||||
\(228\) | −4007.19 | −1.16396 | ||||||||
\(229\) | 851.806 | 0.245803 | 0.122902 | − | 0.992419i | \(-0.460780\pi\) | ||||
0.122902 | + | 0.992419i | \(0.460780\pi\) | |||||||
\(230\) | 5668.54 | 1.62510 | ||||||||
\(231\) | −9178.67 | −2.61434 | ||||||||
\(232\) | −4856.29 | −1.37427 | ||||||||
\(233\) | −2083.62 | −0.585848 | −0.292924 | − | 0.956136i | \(-0.594628\pi\) | ||||
−0.292924 | + | 0.956136i | \(0.594628\pi\) | |||||||
\(234\) | 859.276 | 0.240054 | ||||||||
\(235\) | 6544.24 | 1.81659 | ||||||||
\(236\) | 3845.27 | 1.06062 | ||||||||
\(237\) | 8547.48 | 2.34269 | ||||||||
\(238\) | 429.539 | 0.116987 | ||||||||
\(239\) | 986.983 | 0.267124 | 0.133562 | − | 0.991040i | \(-0.457358\pi\) | ||||
0.133562 | + | 0.991040i | \(0.457358\pi\) | |||||||
\(240\) | −14774.5 | −3.97372 | ||||||||
\(241\) | 14.8772 | 0.00397644 | 0.00198822 | − | 0.999998i | \(-0.499367\pi\) | ||||
0.00198822 | + | 0.999998i | \(0.499367\pi\) | |||||||
\(242\) | 12037.7 | 3.19757 | ||||||||
\(243\) | 3839.36 | 1.01356 | ||||||||
\(244\) | −9024.85 | −2.36786 | ||||||||
\(245\) | 3467.99 | 0.904333 | ||||||||
\(246\) | 4816.78 | 1.24840 | ||||||||
\(247\) | 363.712 | 0.0936942 | ||||||||
\(248\) | 12111.4 | 3.10112 | ||||||||
\(249\) | −5286.72 | −1.34551 | ||||||||
\(250\) | 4282.26 | 1.08333 | ||||||||
\(251\) | −3027.27 | −0.761274 | −0.380637 | − | 0.924725i | \(-0.624295\pi\) | ||||
−0.380637 | + | 0.924725i | \(0.624295\pi\) | |||||||
\(252\) | −6592.76 | −1.64803 | ||||||||
\(253\) | −3858.50 | −0.958822 | ||||||||
\(254\) | −3769.38 | −0.931150 | ||||||||
\(255\) | 401.160 | 0.0985161 | ||||||||
\(256\) | −6298.79 | −1.53779 | ||||||||
\(257\) | 5759.92 | 1.39803 | 0.699016 | − | 0.715106i | \(-0.253622\pi\) | ||||
0.699016 | + | 0.715106i | \(0.253622\pi\) | |||||||
\(258\) | 1439.98 | 0.347477 | ||||||||
\(259\) | 1391.15 | 0.333753 | ||||||||
\(260\) | 3504.32 | 0.835881 | ||||||||
\(261\) | −1361.82 | −0.322968 | ||||||||
\(262\) | 12688.4 | 2.99195 | ||||||||
\(263\) | 2545.09 | 0.596719 | 0.298359 | − | 0.954454i | \(-0.403561\pi\) | ||||
0.298359 | + | 0.954454i | \(0.403561\pi\) | |||||||
\(264\) | 21391.7 | 4.98700 | ||||||||
\(265\) | −2592.21 | −0.600898 | ||||||||
\(266\) | −3994.15 | −0.920665 | ||||||||
\(267\) | 2278.49 | 0.522252 | ||||||||
\(268\) | 18908.4 | 4.30976 | ||||||||
\(269\) | 6757.89 | 1.53173 | 0.765866 | − | 0.643001i | \(-0.222311\pi\) | ||||
0.765866 | + | 0.643001i | \(0.222311\pi\) | |||||||
\(270\) | 6799.13 | 1.53253 | ||||||||
\(271\) | 2485.54 | 0.557143 | 0.278571 | − | 0.960415i | \(-0.410139\pi\) | ||||
0.278571 | + | 0.960415i | \(0.410139\pi\) | |||||||
\(272\) | −470.634 | −0.104913 | ||||||||
\(273\) | 1658.44 | 0.367669 | ||||||||
\(274\) | 12286.9 | 2.70904 | ||||||||
\(275\) | −10484.6 | −2.29908 | ||||||||
\(276\) | −7681.07 | −1.67517 | ||||||||
\(277\) | −2090.19 | −0.453385 | −0.226692 | − | 0.973966i | \(-0.572791\pi\) | ||||
−0.226692 | + | 0.973966i | \(0.572791\pi\) | |||||||
\(278\) | −15905.1 | −3.43139 | ||||||||
\(279\) | 3396.34 | 0.728795 | ||||||||
\(280\) | −21885.2 | −4.67104 | ||||||||
\(281\) | −6049.22 | −1.28422 | −0.642111 | − | 0.766612i | \(-0.721941\pi\) | ||||
−0.642111 | + | 0.766612i | \(0.721941\pi\) | |||||||
\(282\) | −12692.3 | −2.68020 | ||||||||
\(283\) | −650.183 | −0.136570 | −0.0682851 | − | 0.997666i | \(-0.521753\pi\) | ||||
−0.0682851 | + | 0.997666i | \(0.521753\pi\) | |||||||
\(284\) | 256.778 | 0.0536513 | ||||||||
\(285\) | −3730.26 | −0.775304 | ||||||||
\(286\) | −3414.16 | −0.705885 | ||||||||
\(287\) | 3354.35 | 0.689900 | ||||||||
\(288\) | 3712.04 | 0.759494 | ||||||||
\(289\) | −4900.22 | −0.997399 | ||||||||
\(290\) | −7949.21 | −1.60963 | ||||||||
\(291\) | 7714.92 | 1.55415 | ||||||||
\(292\) | 7626.31 | 1.52841 | ||||||||
\(293\) | −2172.20 | −0.433110 | −0.216555 | − | 0.976270i | \(-0.569482\pi\) | ||||
−0.216555 | + | 0.976270i | \(0.569482\pi\) | |||||||
\(294\) | −6726.04 | −1.33425 | ||||||||
\(295\) | 3579.53 | 0.706468 | ||||||||
\(296\) | −3242.21 | −0.636654 | ||||||||
\(297\) | −4628.08 | −0.904203 | ||||||||
\(298\) | −7448.36 | −1.44789 | ||||||||
\(299\) | 697.171 | 0.134844 | ||||||||
\(300\) | −20871.6 | −4.01674 | ||||||||
\(301\) | 1002.79 | 0.192025 | ||||||||
\(302\) | −4255.35 | −0.810820 | ||||||||
\(303\) | −3048.28 | −0.577950 | ||||||||
\(304\) | 4376.28 | 0.825648 | ||||||||
\(305\) | −8401.16 | −1.57721 | ||||||||
\(306\) | −280.727 | −0.0524447 | ||||||||
\(307\) | 1257.47 | 0.233771 | 0.116885 | − | 0.993145i | \(-0.462709\pi\) | ||||
0.116885 | + | 0.993145i | \(0.462709\pi\) | |||||||
\(308\) | 26194.9 | 4.84609 | ||||||||
\(309\) | 8447.98 | 1.55530 | ||||||||
\(310\) | 19825.1 | 3.63222 | ||||||||
\(311\) | −1316.02 | −0.239950 | −0.119975 | − | 0.992777i | \(-0.538281\pi\) | ||||
−0.119975 | + | 0.992777i | \(0.538281\pi\) | |||||||
\(312\) | −3865.15 | −0.701350 | ||||||||
\(313\) | 3137.09 | 0.566514 | 0.283257 | − | 0.959044i | \(-0.408585\pi\) | ||||
0.283257 | + | 0.959044i | \(0.408585\pi\) | |||||||
\(314\) | 6120.24 | 1.09995 | ||||||||
\(315\) | −6137.14 | −1.09774 | ||||||||
\(316\) | −24393.6 | −4.34256 | ||||||||
\(317\) | 571.518 | 0.101261 | 0.0506303 | − | 0.998717i | \(-0.483877\pi\) | ||||
0.0506303 | + | 0.998717i | \(0.483877\pi\) | |||||||
\(318\) | 5027.50 | 0.886566 | ||||||||
\(319\) | 5410.92 | 0.949696 | ||||||||
\(320\) | 3481.96 | 0.608273 | ||||||||
\(321\) | 9624.99 | 1.67356 | ||||||||
\(322\) | −7656.07 | −1.32502 | ||||||||
\(323\) | −118.825 | −0.0204694 | ||||||||
\(324\) | −16846.0 | −2.88854 | ||||||||
\(325\) | 1894.41 | 0.323332 | ||||||||
\(326\) | 7804.01 | 1.32584 | ||||||||
\(327\) | −2278.57 | −0.385337 | ||||||||
\(328\) | −7817.62 | −1.31602 | ||||||||
\(329\) | −8838.80 | −1.48115 | ||||||||
\(330\) | 35015.8 | 5.84109 | ||||||||
\(331\) | −2257.30 | −0.374841 | −0.187420 | − | 0.982280i | \(-0.560013\pi\) | ||||
−0.187420 | + | 0.982280i | \(0.560013\pi\) | |||||||
\(332\) | 15087.7 | 2.49412 | ||||||||
\(333\) | −909.194 | −0.149620 | ||||||||
\(334\) | −17284.0 | −2.83155 | ||||||||
\(335\) | 17601.7 | 2.87069 | ||||||||
\(336\) | 19954.8 | 3.23995 | ||||||||
\(337\) | −9222.66 | −1.49077 | −0.745386 | − | 0.666633i | \(-0.767735\pi\) | ||||
−0.745386 | + | 0.666633i | \(0.767735\pi\) | |||||||
\(338\) | −10703.2 | −1.72242 | ||||||||
\(339\) | −5102.66 | −0.817517 | ||||||||
\(340\) | −1144.87 | −0.182615 | ||||||||
\(341\) | −13494.7 | −2.14304 | ||||||||
\(342\) | 2610.39 | 0.412730 | ||||||||
\(343\) | 3315.02 | 0.521849 | ||||||||
\(344\) | −2337.08 | −0.366299 | ||||||||
\(345\) | −7150.24 | −1.11582 | ||||||||
\(346\) | 8525.54 | 1.32467 | ||||||||
\(347\) | 8840.48 | 1.36767 | 0.683835 | − | 0.729636i | \(-0.260311\pi\) | ||||
0.683835 | + | 0.729636i | \(0.260311\pi\) | |||||||
\(348\) | 10771.4 | 1.65922 | ||||||||
\(349\) | 1431.64 | 0.219581 | 0.109791 | − | 0.993955i | \(-0.464982\pi\) | ||||
0.109791 | + | 0.993955i | \(0.464982\pi\) | |||||||
\(350\) | −20803.7 | −3.17715 | ||||||||
\(351\) | 836.222 | 0.127163 | ||||||||
\(352\) | −14749.0 | −2.23331 | ||||||||
\(353\) | −8308.06 | −1.25267 | −0.626336 | − | 0.779553i | \(-0.715446\pi\) | ||||
−0.626336 | + | 0.779553i | \(0.715446\pi\) | |||||||
\(354\) | −6942.37 | −1.04232 | ||||||||
\(355\) | 239.032 | 0.0357367 | ||||||||
\(356\) | −6502.56 | −0.968076 | ||||||||
\(357\) | −541.816 | −0.0803247 | ||||||||
\(358\) | −6873.72 | −1.01477 | ||||||||
\(359\) | 11642.2 | 1.71157 | 0.855786 | − | 0.517330i | \(-0.173074\pi\) | ||||
0.855786 | + | 0.517330i | \(0.173074\pi\) | |||||||
\(360\) | 14303.2 | 2.09401 | ||||||||
\(361\) | −5754.08 | −0.838909 | ||||||||
\(362\) | 14280.6 | 2.07340 | ||||||||
\(363\) | −15184.2 | −2.19549 | ||||||||
\(364\) | −4733.02 | −0.681532 | ||||||||
\(365\) | 7099.27 | 1.01806 | ||||||||
\(366\) | 16293.8 | 2.32702 | ||||||||
\(367\) | 4373.93 | 0.622119 | 0.311059 | − | 0.950391i | \(-0.399316\pi\) | ||||
0.311059 | + | 0.950391i | \(0.399316\pi\) | |||||||
\(368\) | 8388.55 | 1.18827 | ||||||||
\(369\) | −2192.25 | −0.309279 | ||||||||
\(370\) | −5307.14 | −0.745689 | ||||||||
\(371\) | 3501.09 | 0.489940 | ||||||||
\(372\) | −26863.7 | −3.74413 | ||||||||
\(373\) | 7970.63 | 1.10644 | 0.553222 | − | 0.833034i | \(-0.313398\pi\) | ||||
0.553222 | + | 0.833034i | \(0.313398\pi\) | |||||||
\(374\) | 1115.41 | 0.154215 | ||||||||
\(375\) | −5401.59 | −0.743832 | ||||||||
\(376\) | 20599.6 | 2.82538 | ||||||||
\(377\) | −977.669 | −0.133561 | ||||||||
\(378\) | −9183.07 | −1.24954 | ||||||||
\(379\) | −2020.56 | −0.273850 | −0.136925 | − | 0.990581i | \(-0.543722\pi\) | ||||
−0.136925 | + | 0.990581i | \(0.543722\pi\) | |||||||
\(380\) | 10645.8 | 1.43715 | ||||||||
\(381\) | 4754.66 | 0.639340 | ||||||||
\(382\) | 420.000 | 0.0562540 | ||||||||
\(383\) | 11625.0 | 1.55094 | 0.775468 | − | 0.631386i | \(-0.217514\pi\) | ||||
0.775468 | + | 0.631386i | \(0.217514\pi\) | |||||||
\(384\) | 5910.26 | 0.785434 | ||||||||
\(385\) | 24384.7 | 3.22794 | ||||||||
\(386\) | 17030.5 | 2.24568 | ||||||||
\(387\) | −655.375 | −0.0860841 | ||||||||
\(388\) | −22017.6 | −2.88086 | ||||||||
\(389\) | 6212.26 | 0.809702 | 0.404851 | − | 0.914383i | \(-0.367323\pi\) | ||||
0.404851 | + | 0.914383i | \(0.367323\pi\) | |||||||
\(390\) | −6326.82 | −0.821464 | ||||||||
\(391\) | −227.767 | −0.0294595 | ||||||||
\(392\) | 10916.4 | 1.40653 | ||||||||
\(393\) | −16005.0 | −2.05431 | ||||||||
\(394\) | 11551.9 | 1.47710 | ||||||||
\(395\) | −22707.8 | −2.89254 | ||||||||
\(396\) | −17119.8 | −2.17248 | ||||||||
\(397\) | −1647.75 | −0.208307 | −0.104154 | − | 0.994561i | \(-0.533213\pi\) | ||||
−0.104154 | + | 0.994561i | \(0.533213\pi\) | |||||||
\(398\) | −20992.8 | −2.64391 | ||||||||
\(399\) | 5038.18 | 0.632141 | ||||||||
\(400\) | 22794.0 | 2.84925 | ||||||||
\(401\) | 6893.37 | 0.858450 | 0.429225 | − | 0.903198i | \(-0.358787\pi\) | ||||
0.429225 | + | 0.903198i | \(0.358787\pi\) | |||||||
\(402\) | −34137.8 | −4.23543 | ||||||||
\(403\) | 2438.28 | 0.301388 | ||||||||
\(404\) | 8699.46 | 1.07132 | ||||||||
\(405\) | −15681.8 | −1.92404 | ||||||||
\(406\) | 10736.4 | 1.31241 | ||||||||
\(407\) | 3612.49 | 0.439962 | ||||||||
\(408\) | 1262.75 | 0.153224 | ||||||||
\(409\) | −2962.23 | −0.358125 | −0.179062 | − | 0.983838i | \(-0.557306\pi\) | ||||
−0.179062 | + | 0.983838i | \(0.557306\pi\) | |||||||
\(410\) | −12796.6 | −1.54141 | ||||||||
\(411\) | −15498.5 | −1.86006 | ||||||||
\(412\) | −24109.6 | −2.88300 | ||||||||
\(413\) | −4834.59 | −0.576016 | ||||||||
\(414\) | 5003.65 | 0.594000 | ||||||||
\(415\) | 14045.0 | 1.66131 | ||||||||
\(416\) | 2664.92 | 0.314083 | ||||||||
\(417\) | 20062.6 | 2.35604 | ||||||||
\(418\) | −10371.8 | −1.21365 | ||||||||
\(419\) | −5520.25 | −0.643633 | −0.321816 | − | 0.946802i | \(-0.604293\pi\) | ||||
−0.321816 | + | 0.946802i | \(0.604293\pi\) | |||||||
\(420\) | 48542.2 | 5.63957 | ||||||||
\(421\) | 11017.9 | 1.27548 | 0.637742 | − | 0.770250i | \(-0.279868\pi\) | ||||
0.637742 | + | 0.770250i | \(0.279868\pi\) | |||||||
\(422\) | 21989.0 | 2.53651 | ||||||||
\(423\) | 5776.63 | 0.663994 | ||||||||
\(424\) | −8159.61 | −0.934589 | ||||||||
\(425\) | −618.906 | −0.0706385 | ||||||||
\(426\) | −463.595 | −0.0527260 | ||||||||
\(427\) | 11346.8 | 1.28597 | ||||||||
\(428\) | −27468.7 | −3.10222 | ||||||||
\(429\) | 4306.58 | 0.484671 | ||||||||
\(430\) | −3825.54 | −0.429033 | ||||||||
\(431\) | 8825.55 | 0.986338 | 0.493169 | − | 0.869934i | \(-0.335838\pi\) | ||||
0.493169 | + | 0.869934i | \(0.335838\pi\) | |||||||
\(432\) | 10061.6 | 1.12058 | ||||||||
\(433\) | 4570.88 | 0.507303 | 0.253652 | − | 0.967296i | \(-0.418368\pi\) | ||||
0.253652 | + | 0.967296i | \(0.418368\pi\) | |||||||
\(434\) | −26776.2 | −2.96152 | ||||||||
\(435\) | 10027.0 | 1.10520 | ||||||||
\(436\) | 6502.80 | 0.714283 | ||||||||
\(437\) | 2117.93 | 0.231841 | ||||||||
\(438\) | −13768.8 | −1.50205 | ||||||||
\(439\) | −3059.73 | −0.332649 | −0.166325 | − | 0.986071i | \(-0.553190\pi\) | ||||
−0.166325 | + | 0.986071i | \(0.553190\pi\) | |||||||
\(440\) | −56830.6 | −6.15749 | ||||||||
\(441\) | 3061.21 | 0.330549 | ||||||||
\(442\) | −201.537 | −0.0216881 | ||||||||
\(443\) | −2764.55 | −0.296496 | −0.148248 | − | 0.988950i | \(-0.547363\pi\) | ||||
−0.148248 | + | 0.988950i | \(0.547363\pi\) | |||||||
\(444\) | 7191.35 | 0.768663 | ||||||||
\(445\) | −6053.18 | −0.644828 | ||||||||
\(446\) | −4582.49 | −0.486518 | ||||||||
\(447\) | 9395.29 | 0.994143 | ||||||||
\(448\) | −4702.82 | −0.495954 | ||||||||
\(449\) | 7567.33 | 0.795377 | 0.397688 | − | 0.917521i | \(-0.369812\pi\) | ||||
0.397688 | + | 0.917521i | \(0.369812\pi\) | |||||||
\(450\) | 13596.3 | 1.42430 | ||||||||
\(451\) | 8710.46 | 0.909444 | ||||||||
\(452\) | 14562.4 | 1.51540 | ||||||||
\(453\) | 5367.65 | 0.556720 | ||||||||
\(454\) | 1197.38 | 0.123780 | ||||||||
\(455\) | −4405.93 | −0.453963 | ||||||||
\(456\) | −11741.9 | −1.20585 | ||||||||
\(457\) | −8079.05 | −0.826963 | −0.413482 | − | 0.910512i | \(-0.635687\pi\) | ||||
−0.413482 | + | 0.910512i | \(0.635687\pi\) | |||||||
\(458\) | 4388.94 | 0.447777 | ||||||||
\(459\) | −273.195 | −0.0277813 | ||||||||
\(460\) | 20406.0 | 2.06834 | ||||||||
\(461\) | 14466.4 | 1.46154 | 0.730770 | − | 0.682624i | \(-0.239161\pi\) | ||||
0.730770 | + | 0.682624i | \(0.239161\pi\) | |||||||
\(462\) | −47293.2 | −4.76251 | ||||||||
\(463\) | −7966.79 | −0.799672 | −0.399836 | − | 0.916587i | \(-0.630933\pi\) | ||||
−0.399836 | + | 0.916587i | \(0.630933\pi\) | |||||||
\(464\) | −11763.6 | −1.17696 | ||||||||
\(465\) | −25007.2 | −2.49393 | ||||||||
\(466\) | −10735.9 | −1.06723 | ||||||||
\(467\) | 6737.29 | 0.667590 | 0.333795 | − | 0.942646i | \(-0.391671\pi\) | ||||
0.333795 | + | 0.942646i | \(0.391671\pi\) | |||||||
\(468\) | 3093.29 | 0.305528 | ||||||||
\(469\) | −23773.2 | −2.34061 | ||||||||
\(470\) | 33719.3 | 3.30927 | ||||||||
\(471\) | −7720.00 | −0.755242 | ||||||||
\(472\) | 11267.4 | 1.09878 | ||||||||
\(473\) | 2603.99 | 0.253133 | ||||||||
\(474\) | 44041.0 | 4.26766 | ||||||||
\(475\) | 5755.02 | 0.555912 | ||||||||
\(476\) | 1546.28 | 0.148895 | ||||||||
\(477\) | −2288.15 | −0.219638 | ||||||||
\(478\) | 5085.44 | 0.486616 | ||||||||
\(479\) | −18115.7 | −1.72803 | −0.864014 | − | 0.503468i | \(-0.832057\pi\) | ||||
−0.864014 | + | 0.503468i | \(0.832057\pi\) | |||||||
\(480\) | −27331.6 | −2.59899 | ||||||||
\(481\) | −652.722 | −0.0618743 | ||||||||
\(482\) | 76.6548 | 0.00724384 | ||||||||
\(483\) | 9657.28 | 0.909776 | ||||||||
\(484\) | 43334.1 | 4.06969 | ||||||||
\(485\) | −20496.0 | −1.91891 | ||||||||
\(486\) | 19782.4 | 1.84639 | ||||||||
\(487\) | −14966.4 | −1.39260 | −0.696298 | − | 0.717753i | \(-0.745171\pi\) | ||||
−0.696298 | + | 0.717753i | \(0.745171\pi\) | |||||||
\(488\) | −26444.7 | −2.45307 | ||||||||
\(489\) | −9843.90 | −0.910341 | ||||||||
\(490\) | 17868.8 | 1.64741 | ||||||||
\(491\) | −15713.8 | −1.44430 | −0.722151 | − | 0.691736i | \(-0.756846\pi\) | ||||
−0.722151 | + | 0.691736i | \(0.756846\pi\) | |||||||
\(492\) | 17339.8 | 1.58890 | ||||||||
\(493\) | 319.406 | 0.0291791 | ||||||||
\(494\) | 1874.03 | 0.170682 | ||||||||
\(495\) | −15936.7 | −1.44707 | ||||||||
\(496\) | 29338.0 | 2.65588 | ||||||||
\(497\) | −322.843 | −0.0291378 | ||||||||
\(498\) | −27239.9 | −2.45110 | ||||||||
\(499\) | −15391.5 | −1.38080 | −0.690398 | − | 0.723430i | \(-0.742565\pi\) | ||||
−0.690398 | + | 0.723430i | \(0.742565\pi\) | |||||||
\(500\) | 15415.6 | 1.37881 | ||||||||
\(501\) | 21801.8 | 1.94418 | ||||||||
\(502\) | −15598.1 | −1.38680 | ||||||||
\(503\) | −12150.9 | −1.07710 | −0.538548 | − | 0.842595i | \(-0.681027\pi\) | ||||
−0.538548 | + | 0.842595i | \(0.681027\pi\) | |||||||
\(504\) | −19318.2 | −1.70734 | ||||||||
\(505\) | 8098.25 | 0.713599 | ||||||||
\(506\) | −19881.0 | −1.74667 | ||||||||
\(507\) | 13500.9 | 1.18263 | ||||||||
\(508\) | −13569.3 | −1.18512 | ||||||||
\(509\) | 16646.6 | 1.44960 | 0.724799 | − | 0.688960i | \(-0.241933\pi\) | ||||
0.724799 | + | 0.688960i | \(0.241933\pi\) | |||||||
\(510\) | 2066.98 | 0.179466 | ||||||||
\(511\) | −9588.44 | −0.830074 | ||||||||
\(512\) | −25179.7 | −2.17343 | ||||||||
\(513\) | 2540.35 | 0.218634 | ||||||||
\(514\) | 29678.1 | 2.54678 | ||||||||
\(515\) | −22443.5 | −1.92034 | ||||||||
\(516\) | 5183.74 | 0.442251 | ||||||||
\(517\) | −22952.3 | −1.95249 | ||||||||
\(518\) | 7167.94 | 0.607995 | ||||||||
\(519\) | −10754.0 | −0.909536 | ||||||||
\(520\) | 10268.4 | 0.865961 | ||||||||
\(521\) | 16675.9 | 1.40227 | 0.701135 | − | 0.713028i | \(-0.252677\pi\) | ||||
0.701135 | + | 0.713028i | \(0.252677\pi\) | |||||||
\(522\) | −7016.81 | −0.588347 | ||||||||
\(523\) | 14326.5 | 1.19781 | 0.598903 | − | 0.800821i | \(-0.295603\pi\) | ||||
0.598903 | + | 0.800821i | \(0.295603\pi\) | |||||||
\(524\) | 45676.5 | 3.80799 | ||||||||
\(525\) | 26241.5 | 2.18148 | ||||||||
\(526\) | 13113.6 | 1.08704 | ||||||||
\(527\) | −796.588 | −0.0658443 | ||||||||
\(528\) | 51817.9 | 4.27099 | ||||||||
\(529\) | −8107.30 | −0.666335 | ||||||||
\(530\) | −13356.4 | −1.09465 | ||||||||
\(531\) | 3159.67 | 0.258226 | ||||||||
\(532\) | −14378.4 | −1.17177 | ||||||||
\(533\) | −1573.84 | −0.127900 | ||||||||
\(534\) | 11739.9 | 0.951380 | ||||||||
\(535\) | −25570.4 | −2.06636 | ||||||||
\(536\) | 55405.6 | 4.46485 | ||||||||
\(537\) | 8670.44 | 0.696754 | ||||||||
\(538\) | 34820.1 | 2.79034 | ||||||||
\(539\) | −12163.1 | −0.971987 | ||||||||
\(540\) | 24476.0 | 1.95052 | ||||||||
\(541\) | −8159.73 | −0.648455 | −0.324228 | − | 0.945979i | \(-0.605104\pi\) | ||||
−0.324228 | + | 0.945979i | \(0.605104\pi\) | |||||||
\(542\) | 12806.8 | 1.01494 | ||||||||
\(543\) | −18013.4 | −1.42362 | ||||||||
\(544\) | −870.633 | −0.0686178 | ||||||||
\(545\) | 6053.40 | 0.475778 | ||||||||
\(546\) | 8545.15 | 0.669778 | ||||||||
\(547\) | −6089.67 | −0.476006 | −0.238003 | − | 0.971264i | \(-0.576493\pi\) | ||||
−0.238003 | + | 0.971264i | \(0.576493\pi\) | |||||||
\(548\) | 44231.2 | 3.44793 | ||||||||
\(549\) | −7415.74 | −0.576496 | ||||||||
\(550\) | −54022.2 | −4.18821 | ||||||||
\(551\) | −2970.06 | −0.229635 | ||||||||
\(552\) | −22507.2 | −1.73545 | ||||||||
\(553\) | 30669.7 | 2.35842 | ||||||||
\(554\) | −10769.8 | −0.825926 | ||||||||
\(555\) | 6694.37 | 0.512000 | ||||||||
\(556\) | −57256.5 | −4.36729 | ||||||||
\(557\) | 4160.66 | 0.316504 | 0.158252 | − | 0.987399i | \(-0.449414\pi\) | ||||
0.158252 | + | 0.987399i | \(0.449414\pi\) | |||||||
\(558\) | 17499.7 | 1.32764 | ||||||||
\(559\) | −470.501 | −0.0355995 | ||||||||
\(560\) | −53013.3 | −4.00039 | ||||||||
\(561\) | −1406.97 | −0.105886 | ||||||||
\(562\) | −31168.7 | −2.33945 | ||||||||
\(563\) | 7731.24 | 0.578744 | 0.289372 | − | 0.957217i | \(-0.406554\pi\) | ||||
0.289372 | + | 0.957217i | \(0.406554\pi\) | |||||||
\(564\) | −45690.8 | −3.41122 | ||||||||
\(565\) | 13556.1 | 1.00939 | ||||||||
\(566\) | −3350.08 | −0.248788 | ||||||||
\(567\) | 21180.2 | 1.56875 | ||||||||
\(568\) | 752.414 | 0.0555820 | ||||||||
\(569\) | 9134.32 | 0.672989 | 0.336494 | − | 0.941685i | \(-0.390759\pi\) | ||||
0.336494 | + | 0.941685i | \(0.390759\pi\) | |||||||
\(570\) | −19220.2 | −1.41236 | ||||||||
\(571\) | 10421.5 | 0.763797 | 0.381898 | − | 0.924204i | \(-0.375270\pi\) | ||||
0.381898 | + | 0.924204i | \(0.375270\pi\) | |||||||
\(572\) | −12290.5 | −0.898414 | ||||||||
\(573\) | −529.783 | −0.0386248 | ||||||||
\(574\) | 17283.4 | 1.25678 | ||||||||
\(575\) | 11031.3 | 0.800067 | ||||||||
\(576\) | 3073.54 | 0.222334 | ||||||||
\(577\) | 806.571 | 0.0581941 | 0.0290971 | − | 0.999577i | \(-0.490737\pi\) | ||||
0.0290971 | + | 0.999577i | \(0.490737\pi\) | |||||||
\(578\) | −25248.5 | −1.81695 | ||||||||
\(579\) | −21482.2 | −1.54191 | ||||||||
\(580\) | −28616.1 | −2.04866 | ||||||||
\(581\) | −18969.6 | −1.35454 | ||||||||
\(582\) | 39751.2 | 2.83117 | ||||||||
\(583\) | 9091.50 | 0.645852 | ||||||||
\(584\) | 22346.7 | 1.58341 | ||||||||
\(585\) | 2879.51 | 0.203510 | ||||||||
\(586\) | −11192.3 | −0.788992 | ||||||||
\(587\) | 11514.2 | 0.809614 | 0.404807 | − | 0.914402i | \(-0.367339\pi\) | ||||
0.404807 | + | 0.914402i | \(0.367339\pi\) | |||||||
\(588\) | −24212.9 | −1.69817 | ||||||||
\(589\) | 7407.23 | 0.518183 | ||||||||
\(590\) | 18443.6 | 1.28696 | ||||||||
\(591\) | −14571.5 | −1.01420 | ||||||||
\(592\) | −7853.72 | −0.545246 | ||||||||
\(593\) | 2702.41 | 0.187141 | 0.0935706 | − | 0.995613i | \(-0.470172\pi\) | ||||
0.0935706 | + | 0.995613i | \(0.470172\pi\) | |||||||
\(594\) | −23846.2 | −1.64718 | ||||||||
\(595\) | 1439.42 | 0.0991775 | ||||||||
\(596\) | −26813.1 | −1.84280 | ||||||||
\(597\) | 26480.1 | 1.81534 | ||||||||
\(598\) | 3592.18 | 0.245644 | ||||||||
\(599\) | −27360.1 | −1.86628 | −0.933142 | − | 0.359507i | \(-0.882945\pi\) | ||||
−0.933142 | + | 0.359507i | \(0.882945\pi\) | |||||||
\(600\) | −61158.3 | −4.16129 | ||||||||
\(601\) | −11506.8 | −0.780985 | −0.390492 | − | 0.920606i | \(-0.627695\pi\) | ||||
−0.390492 | + | 0.920606i | \(0.627695\pi\) | |||||||
\(602\) | 5166.87 | 0.349810 | ||||||||
\(603\) | 15537.1 | 1.04929 | ||||||||
\(604\) | −15318.7 | −1.03197 | ||||||||
\(605\) | 40339.4 | 2.71079 | ||||||||
\(606\) | −15706.3 | −1.05285 | ||||||||
\(607\) | 8189.12 | 0.547588 | 0.273794 | − | 0.961788i | \(-0.411721\pi\) | ||||
0.273794 | + | 0.961788i | \(0.411721\pi\) | |||||||
\(608\) | 8095.75 | 0.540010 | ||||||||
\(609\) | −13542.8 | −0.901117 | ||||||||
\(610\) | −43287.1 | −2.87318 | ||||||||
\(611\) | 4147.12 | 0.274590 | ||||||||
\(612\) | −1010.58 | −0.0667488 | ||||||||
\(613\) | −24210.1 | −1.59517 | −0.797583 | − | 0.603209i | \(-0.793889\pi\) | ||||
−0.797583 | + | 0.603209i | \(0.793889\pi\) | |||||||
\(614\) | 6479.14 | 0.425858 | ||||||||
\(615\) | 16141.5 | 1.05835 | ||||||||
\(616\) | 76756.8 | 5.02048 | ||||||||
\(617\) | −8779.45 | −0.572848 | −0.286424 | − | 0.958103i | \(-0.592467\pi\) | ||||
−0.286424 | + | 0.958103i | \(0.592467\pi\) | |||||||
\(618\) | 43528.3 | 2.83328 | ||||||||
\(619\) | −6089.56 | −0.395412 | −0.197706 | − | 0.980261i | \(-0.563349\pi\) | ||||
−0.197706 | + | 0.980261i | \(0.563349\pi\) | |||||||
\(620\) | 71367.8 | 4.62290 | ||||||||
\(621\) | 4869.40 | 0.314658 | ||||||||
\(622\) | −6780.79 | −0.437114 | ||||||||
\(623\) | 8175.57 | 0.525758 | ||||||||
\(624\) | −9362.69 | −0.600653 | ||||||||
\(625\) | −7291.47 | −0.466654 | ||||||||
\(626\) | 16163.9 | 1.03201 | ||||||||
\(627\) | 13082.9 | 0.833305 | ||||||||
\(628\) | 22032.1 | 1.39996 | ||||||||
\(629\) | 213.245 | 0.0135177 | ||||||||
\(630\) | −31621.7 | −1.99974 | ||||||||
\(631\) | 13768.3 | 0.868634 | 0.434317 | − | 0.900760i | \(-0.356990\pi\) | ||||
0.434317 | + | 0.900760i | \(0.356990\pi\) | |||||||
\(632\) | −71478.5 | −4.49883 | ||||||||
\(633\) | −27736.6 | −1.74160 | ||||||||
\(634\) | 2944.75 | 0.184465 | ||||||||
\(635\) | −12631.5 | −0.789398 | ||||||||
\(636\) | 18098.3 | 1.12837 | ||||||||
\(637\) | 2197.68 | 0.136696 | ||||||||
\(638\) | 27879.8 | 1.73005 | ||||||||
\(639\) | 210.995 | 0.0130623 | ||||||||
\(640\) | −15701.6 | −0.969780 | ||||||||
\(641\) | 393.612 | 0.0242539 | 0.0121269 | − | 0.999926i | \(-0.496140\pi\) | ||||
0.0121269 | + | 0.999926i | \(0.496140\pi\) | |||||||
\(642\) | 49592.9 | 3.04871 | ||||||||
\(643\) | −29944.9 | −1.83656 | −0.918281 | − | 0.395929i | \(-0.870423\pi\) | ||||
−0.918281 | + | 0.395929i | \(0.870423\pi\) | |||||||
\(644\) | −27560.9 | −1.68641 | ||||||||
\(645\) | 4825.50 | 0.294580 | ||||||||
\(646\) | −612.249 | −0.0372889 | ||||||||
\(647\) | −8372.05 | −0.508716 | −0.254358 | − | 0.967110i | \(-0.581864\pi\) | ||||
−0.254358 | + | 0.967110i | \(0.581864\pi\) | |||||||
\(648\) | −49362.3 | −2.99249 | ||||||||
\(649\) | −12554.3 | −0.759320 | ||||||||
\(650\) | 9760.97 | 0.589010 | ||||||||
\(651\) | 33775.3 | 2.03342 | ||||||||
\(652\) | 28093.4 | 1.68746 | ||||||||
\(653\) | 7203.34 | 0.431682 | 0.215841 | − | 0.976429i | \(-0.430751\pi\) | ||||
0.215841 | + | 0.976429i | \(0.430751\pi\) | |||||||
\(654\) | −11740.4 | −0.701964 | ||||||||
\(655\) | 42519.9 | 2.53647 | ||||||||
\(656\) | −18936.9 | −1.12708 | ||||||||
\(657\) | 6266.56 | 0.372119 | ||||||||
\(658\) | −45542.0 | −2.69820 | ||||||||
\(659\) | −28054.8 | −1.65836 | −0.829182 | − | 0.558979i | \(-0.811193\pi\) | ||||
−0.829182 | + | 0.558979i | \(0.811193\pi\) | |||||||
\(660\) | 126053. | 7.43423 | ||||||||
\(661\) | −11582.1 | −0.681531 | −0.340766 | − | 0.940148i | \(-0.610686\pi\) | ||||
−0.340766 | + | 0.940148i | \(0.610686\pi\) | |||||||
\(662\) | −11630.8 | −0.682843 | ||||||||
\(663\) | 254.217 | 0.0148914 | ||||||||
\(664\) | 44210.2 | 2.58387 | ||||||||
\(665\) | −13384.8 | −0.780509 | ||||||||
\(666\) | −4684.64 | −0.272561 | ||||||||
\(667\) | −5693.07 | −0.330489 | ||||||||
\(668\) | −62220.1 | −3.60385 | ||||||||
\(669\) | 5780.31 | 0.334050 | ||||||||
\(670\) | 90692.9 | 5.22951 | ||||||||
\(671\) | 29464.9 | 1.69520 | ||||||||
\(672\) | 36914.7 | 2.11907 | ||||||||
\(673\) | 9582.65 | 0.548862 | 0.274431 | − | 0.961607i | \(-0.411511\pi\) | ||||
0.274431 | + | 0.961607i | \(0.411511\pi\) | |||||||
\(674\) | −47519.9 | −2.71572 | ||||||||
\(675\) | 13231.5 | 0.754492 | ||||||||
\(676\) | −38530.1 | −2.19220 | ||||||||
\(677\) | 8247.63 | 0.468216 | 0.234108 | − | 0.972211i | \(-0.424783\pi\) | ||||
0.234108 | + | 0.972211i | \(0.424783\pi\) | |||||||
\(678\) | −26291.5 | −1.48926 | ||||||||
\(679\) | 27682.3 | 1.56458 | ||||||||
\(680\) | −3354.70 | −0.189187 | ||||||||
\(681\) | −1510.37 | −0.0849890 | ||||||||
\(682\) | −69531.5 | −3.90395 | ||||||||
\(683\) | 23171.1 | 1.29812 | 0.649061 | − | 0.760736i | \(-0.275162\pi\) | ||||
0.649061 | + | 0.760736i | \(0.275162\pi\) | |||||||
\(684\) | 9397.08 | 0.525301 | ||||||||
\(685\) | 41174.4 | 2.29663 | ||||||||
\(686\) | 17080.7 | 0.950647 | ||||||||
\(687\) | −5536.16 | −0.307450 | ||||||||
\(688\) | −5661.20 | −0.313708 | ||||||||
\(689\) | −1642.69 | −0.0908297 | ||||||||
\(690\) | −36841.7 | −2.03267 | ||||||||
\(691\) | 24019.8 | 1.32237 | 0.661185 | − | 0.750223i | \(-0.270054\pi\) | ||||
0.661185 | + | 0.750223i | \(0.270054\pi\) | |||||||
\(692\) | 30690.8 | 1.68597 | ||||||||
\(693\) | 21524.5 | 1.17987 | ||||||||
\(694\) | 45550.7 | 2.49147 | ||||||||
\(695\) | −53299.6 | −2.90902 | ||||||||
\(696\) | 31562.6 | 1.71893 | ||||||||
\(697\) | 514.177 | 0.0279424 | ||||||||
\(698\) | 7376.54 | 0.400009 | ||||||||
\(699\) | 13542.1 | 0.732776 | ||||||||
\(700\) | −74890.6 | −4.04371 | ||||||||
\(701\) | −756.339 | −0.0407511 | −0.0203755 | − | 0.999792i | \(-0.506486\pi\) | ||||
−0.0203755 | + | 0.999792i | \(0.506486\pi\) | |||||||
\(702\) | 4308.64 | 0.231651 | ||||||||
\(703\) | −1982.90 | −0.106382 | ||||||||
\(704\) | −12212.1 | −0.653779 | ||||||||
\(705\) | −42533.2 | −2.27219 | ||||||||
\(706\) | −42807.4 | −2.28198 | ||||||||
\(707\) | −10937.7 | −0.581830 | ||||||||
\(708\) | −24991.7 | −1.32662 | ||||||||
\(709\) | −26580.1 | −1.40795 | −0.703975 | − | 0.710224i | \(-0.748594\pi\) | ||||
−0.703975 | + | 0.710224i | \(0.748594\pi\) | |||||||
\(710\) | 1231.62 | 0.0651011 | ||||||||
\(711\) | −20044.3 | −1.05727 | ||||||||
\(712\) | −19053.9 | −1.00291 | ||||||||
\(713\) | 14198.3 | 0.745767 | ||||||||
\(714\) | −2791.71 | −0.146327 | ||||||||
\(715\) | −11441.1 | −0.598426 | ||||||||
\(716\) | −24744.5 | −1.29154 | ||||||||
\(717\) | −6414.72 | −0.334118 | ||||||||
\(718\) | 59986.8 | 3.11795 | ||||||||
\(719\) | 14125.2 | 0.732656 | 0.366328 | − | 0.930486i | \(-0.380615\pi\) | ||||
0.366328 | + | 0.930486i | \(0.380615\pi\) | |||||||
\(720\) | 34647.1 | 1.79336 | ||||||||
\(721\) | 30312.7 | 1.56575 | ||||||||
\(722\) | −29648.0 | −1.52823 | ||||||||
\(723\) | −96.6916 | −0.00497372 | ||||||||
\(724\) | 51408.3 | 2.63891 | ||||||||
\(725\) | −15469.6 | −0.792453 | ||||||||
\(726\) | −78236.8 | −3.99951 | ||||||||
\(727\) | −19206.2 | −0.979805 | −0.489903 | − | 0.871777i | \(-0.662968\pi\) | ||||
−0.489903 | + | 0.871777i | \(0.662968\pi\) | |||||||
\(728\) | −13868.8 | −0.706058 | ||||||||
\(729\) | −431.393 | −0.0219170 | ||||||||
\(730\) | 36579.1 | 1.85459 | ||||||||
\(731\) | 153.713 | 0.00777742 | ||||||||
\(732\) | 58655.5 | 2.96170 | ||||||||
\(733\) | −29831.4 | −1.50320 | −0.751602 | − | 0.659617i | \(-0.770718\pi\) | ||||
−0.751602 | + | 0.659617i | \(0.770718\pi\) | |||||||
\(734\) | 22536.8 | 1.13331 | ||||||||
\(735\) | −22539.6 | −1.13114 | ||||||||
\(736\) | 15518.1 | 0.777181 | ||||||||
\(737\) | −61733.4 | −3.08545 | ||||||||
\(738\) | −11295.6 | −0.563411 | ||||||||
\(739\) | 11720.8 | 0.583431 | 0.291715 | − | 0.956505i | \(-0.405774\pi\) | ||||
0.291715 | + | 0.956505i | \(0.405774\pi\) | |||||||
\(740\) | −19105.0 | −0.949073 | ||||||||
\(741\) | −2363.89 | −0.117192 | ||||||||
\(742\) | 18039.4 | 0.892518 | ||||||||
\(743\) | 4257.57 | 0.210222 | 0.105111 | − | 0.994460i | \(-0.466480\pi\) | ||||
0.105111 | + | 0.994460i | \(0.466480\pi\) | |||||||
\(744\) | −78716.3 | −3.87887 | ||||||||
\(745\) | −24960.1 | −1.22747 | ||||||||
\(746\) | 41068.8 | 2.01560 | ||||||||
\(747\) | 12397.6 | 0.607236 | ||||||||
\(748\) | 4015.33 | 0.196277 | ||||||||
\(749\) | 34535.9 | 1.68480 | ||||||||
\(750\) | −27831.8 | −1.35503 | ||||||||
\(751\) | −16414.4 | −0.797564 | −0.398782 | − | 0.917046i | \(-0.630567\pi\) | ||||
−0.398782 | + | 0.917046i | \(0.630567\pi\) | |||||||
\(752\) | 49899.2 | 2.41973 | ||||||||
\(753\) | 19675.2 | 0.952199 | ||||||||
\(754\) | −5037.45 | −0.243307 | ||||||||
\(755\) | −14260.1 | −0.687386 | ||||||||
\(756\) | −33057.9 | −1.59035 | ||||||||
\(757\) | −22813.5 | −1.09534 | −0.547668 | − | 0.836696i | \(-0.684484\pi\) | ||||
−0.547668 | + | 0.836696i | \(0.684484\pi\) | |||||||
\(758\) | −10410.9 | −0.498869 | ||||||||
\(759\) | 25077.7 | 1.19929 | ||||||||
\(760\) | 31194.4 | 1.48887 | ||||||||
\(761\) | 1695.44 | 0.0807617 | 0.0403808 | − | 0.999184i | \(-0.487143\pi\) | ||||
0.0403808 | + | 0.999184i | \(0.487143\pi\) | |||||||
\(762\) | 24498.5 | 1.16468 | ||||||||
\(763\) | −8175.86 | −0.387924 | ||||||||
\(764\) | 1511.95 | 0.0715972 | ||||||||
\(765\) | −940.741 | −0.0444609 | ||||||||
\(766\) | 59897.9 | 2.82532 | ||||||||
\(767\) | 2268.36 | 0.106787 | ||||||||
\(768\) | 40937.9 | 1.92346 | ||||||||
\(769\) | 21604.9 | 1.01313 | 0.506563 | − | 0.862203i | \(-0.330916\pi\) | ||||
0.506563 | + | 0.862203i | \(0.330916\pi\) | |||||||
\(770\) | 125642. | 5.88030 | ||||||||
\(771\) | −37435.6 | −1.74865 | ||||||||
\(772\) | 61307.8 | 2.85818 | ||||||||
\(773\) | 34435.4 | 1.60227 | 0.801136 | − | 0.598482i | \(-0.204229\pi\) | ||||
0.801136 | + | 0.598482i | \(0.204229\pi\) | |||||||
\(774\) | −3376.83 | −0.156818 | ||||||||
\(775\) | 38580.9 | 1.78821 | ||||||||
\(776\) | −64516.1 | −2.98453 | ||||||||
\(777\) | −9041.57 | −0.417457 | ||||||||
\(778\) | 32008.8 | 1.47503 | ||||||||
\(779\) | −4781.18 | −0.219902 | ||||||||
\(780\) | −22775.8 | −1.04552 | ||||||||
\(781\) | −838.345 | −0.0384102 | ||||||||
\(782\) | −1173.57 | −0.0536660 | ||||||||
\(783\) | −6828.54 | −0.311663 | ||||||||
\(784\) | 26443.1 | 1.20459 | ||||||||
\(785\) | 20509.5 | 0.932502 | ||||||||
\(786\) | −82465.9 | −3.74232 | ||||||||
\(787\) | −12352.5 | −0.559490 | −0.279745 | − | 0.960074i | \(-0.590250\pi\) | ||||
−0.279745 | + | 0.960074i | \(0.590250\pi\) | |||||||
\(788\) | 41585.4 | 1.87997 | ||||||||
\(789\) | −16541.4 | −0.746374 | ||||||||
\(790\) | −117002. | −5.26931 | ||||||||
\(791\) | −18309.1 | −0.823006 | ||||||||
\(792\) | −50164.7 | −2.25066 | ||||||||
\(793\) | −5323.85 | −0.238406 | ||||||||
\(794\) | −8490.03 | −0.379471 | ||||||||
\(795\) | 16847.6 | 0.751601 | ||||||||
\(796\) | −75571.5 | −3.36503 | ||||||||
\(797\) | 29811.8 | 1.32495 | 0.662477 | − | 0.749083i | \(-0.269505\pi\) | ||||
0.662477 | + | 0.749083i | \(0.269505\pi\) | |||||||
\(798\) | 25959.3 | 1.15156 | ||||||||
\(799\) | −1354.87 | −0.0599897 | ||||||||
\(800\) | 42167.0 | 1.86354 | ||||||||
\(801\) | −5343.17 | −0.235695 | ||||||||
\(802\) | 35518.2 | 1.56383 | ||||||||
\(803\) | −24898.9 | −1.09423 | ||||||||
\(804\) | −122892. | −5.39063 | ||||||||
\(805\) | −25656.2 | −1.12331 | ||||||||
\(806\) | 12563.3 | 0.549035 | ||||||||
\(807\) | −43921.7 | −1.91588 | ||||||||
\(808\) | 25491.3 | 1.10988 | ||||||||
\(809\) | −1273.45 | −0.0553424 | −0.0276712 | − | 0.999617i | \(-0.508809\pi\) | ||||
−0.0276712 | + | 0.999617i | \(0.508809\pi\) | |||||||
\(810\) | −80800.6 | −3.50499 | ||||||||
\(811\) | 37825.5 | 1.63777 | 0.818886 | − | 0.573956i | \(-0.194592\pi\) | ||||
0.818886 | + | 0.573956i | \(0.194592\pi\) | |||||||
\(812\) | 38649.6 | 1.67036 | ||||||||
\(813\) | −16154.3 | −0.696872 | ||||||||
\(814\) | 18613.4 | 0.801475 | ||||||||
\(815\) | 26152.0 | 1.12400 | ||||||||
\(816\) | 3058.80 | 0.131225 | ||||||||
\(817\) | −1429.33 | −0.0612070 | ||||||||
\(818\) | −15262.9 | −0.652391 | ||||||||
\(819\) | −3889.14 | −0.165931 | ||||||||
\(820\) | −46066.1 | −1.96182 | ||||||||
\(821\) | 189.193 | 0.00804247 | 0.00402124 | − | 0.999992i | \(-0.498720\pi\) | ||||
0.00402124 | + | 0.999992i | \(0.498720\pi\) | |||||||
\(822\) | −79856.4 | −3.38846 | ||||||||
\(823\) | 26388.5 | 1.11767 | 0.558837 | − | 0.829278i | \(-0.311248\pi\) | ||||
0.558837 | + | 0.829278i | \(0.311248\pi\) | |||||||
\(824\) | −70646.4 | −2.98675 | ||||||||
\(825\) | 68143.0 | 2.87568 | ||||||||
\(826\) | −24910.3 | −1.04932 | ||||||||
\(827\) | −37247.2 | −1.56616 | −0.783079 | − | 0.621923i | \(-0.786352\pi\) | ||||
−0.783079 | + | 0.621923i | \(0.786352\pi\) | |||||||
\(828\) | 18012.5 | 0.756012 | ||||||||
\(829\) | −18429.8 | −0.772128 | −0.386064 | − | 0.922472i | \(-0.626166\pi\) | ||||
−0.386064 | + | 0.922472i | \(0.626166\pi\) | |||||||
\(830\) | 72367.2 | 3.02639 | ||||||||
\(831\) | 13584.9 | 0.567092 | ||||||||
\(832\) | 2206.54 | 0.0919445 | ||||||||
\(833\) | −717.985 | −0.0298640 | ||||||||
\(834\) | 103373. | 4.29197 | ||||||||
\(835\) | −57920.2 | −2.40049 | ||||||||
\(836\) | −37337.3 | −1.54466 | ||||||||
\(837\) | 17030.2 | 0.703285 | ||||||||
\(838\) | −28443.2 | −1.17250 | ||||||||
\(839\) | 24344.3 | 1.00174 | 0.500870 | − | 0.865523i | \(-0.333014\pi\) | ||||
0.500870 | + | 0.865523i | \(0.333014\pi\) | |||||||
\(840\) | 142239. | 5.84252 | ||||||||
\(841\) | −16405.4 | −0.672656 | ||||||||
\(842\) | 56769.8 | 2.32354 | ||||||||
\(843\) | 39315.9 | 1.60630 | ||||||||
\(844\) | 79157.5 | 3.22833 | ||||||||
\(845\) | −35867.4 | −1.46021 | ||||||||
\(846\) | 29764.2 | 1.20959 | ||||||||
\(847\) | −54483.3 | −2.21023 | ||||||||
\(848\) | −19765.3 | −0.800406 | ||||||||
\(849\) | 4225.75 | 0.170822 | ||||||||
\(850\) | −3188.92 | −0.128681 | ||||||||
\(851\) | −3800.87 | −0.153105 | ||||||||
\(852\) | −1668.88 | −0.0671068 | ||||||||
\(853\) | 14146.8 | 0.567852 | 0.283926 | − | 0.958846i | \(-0.408363\pi\) | ||||
0.283926 | + | 0.958846i | \(0.408363\pi\) | |||||||
\(854\) | 58464.5 | 2.34264 | ||||||||
\(855\) | 8747.66 | 0.349899 | ||||||||
\(856\) | −80489.1 | −3.21386 | ||||||||
\(857\) | 8682.05 | 0.346060 | 0.173030 | − | 0.984917i | \(-0.444644\pi\) | ||||
0.173030 | + | 0.984917i | \(0.444644\pi\) | |||||||
\(858\) | 22189.7 | 0.882919 | ||||||||
\(859\) | −25428.8 | −1.01003 | −0.505017 | − | 0.863110i | \(-0.668514\pi\) | ||||
−0.505017 | + | 0.863110i | \(0.668514\pi\) | |||||||
\(860\) | −13771.5 | −0.546050 | ||||||||
\(861\) | −21801.0 | −0.862924 | ||||||||
\(862\) | 45473.7 | 1.79680 | ||||||||
\(863\) | −39552.6 | −1.56012 | −0.780062 | − | 0.625703i | \(-0.784812\pi\) | ||||
−0.780062 | + | 0.625703i | \(0.784812\pi\) | |||||||
\(864\) | 18613.2 | 0.732909 | ||||||||
\(865\) | 28569.9 | 1.12301 | ||||||||
\(866\) | 23551.5 | 0.924148 | ||||||||
\(867\) | 31848.1 | 1.24754 | ||||||||
\(868\) | −96391.0 | −3.76927 | ||||||||
\(869\) | 79641.9 | 3.10894 | ||||||||
\(870\) | 51664.5 | 2.01332 | ||||||||
\(871\) | 11154.3 | 0.433924 | ||||||||
\(872\) | 19054.6 | 0.739988 | ||||||||
\(873\) | −18091.9 | −0.701395 | ||||||||
\(874\) | 10912.7 | 0.422342 | ||||||||
\(875\) | −19381.8 | −0.748826 | ||||||||
\(876\) | −49565.9 | −1.91173 | ||||||||
\(877\) | 1955.60 | 0.0752975 | 0.0376487 | − | 0.999291i | \(-0.488013\pi\) | ||||
0.0376487 | + | 0.999291i | \(0.488013\pi\) | |||||||
\(878\) | −15765.3 | −0.605983 | ||||||||
\(879\) | 14117.8 | 0.541733 | ||||||||
\(880\) | −137663. | −5.27343 | ||||||||
\(881\) | 3037.09 | 0.116143 | 0.0580716 | − | 0.998312i | \(-0.481505\pi\) | ||||
0.0580716 | + | 0.998312i | \(0.481505\pi\) | |||||||
\(882\) | 15772.9 | 0.602157 | ||||||||
\(883\) | 15702.3 | 0.598443 | 0.299222 | − | 0.954184i | \(-0.403273\pi\) | ||||
0.299222 | + | 0.954184i | \(0.403273\pi\) | |||||||
\(884\) | −725.508 | −0.0276035 | ||||||||
\(885\) | −23264.5 | −0.883648 | ||||||||
\(886\) | −14244.4 | −0.540123 | ||||||||
\(887\) | 2964.83 | 0.112231 | 0.0561157 | − | 0.998424i | \(-0.482128\pi\) | ||||
0.0561157 | + | 0.998424i | \(0.482128\pi\) | |||||||
\(888\) | 21072.2 | 0.796324 | ||||||||
\(889\) | 17060.5 | 0.643633 | ||||||||
\(890\) | −31189.1 | −1.17467 | ||||||||
\(891\) | 54999.9 | 2.06797 | ||||||||
\(892\) | −16496.4 | −0.619215 | ||||||||
\(893\) | 12598.5 | 0.472109 | ||||||||
\(894\) | 48409.3 | 1.81102 | ||||||||
\(895\) | −23034.5 | −0.860287 | ||||||||
\(896\) | 21206.9 | 0.790707 | ||||||||
\(897\) | −4531.14 | −0.168663 | ||||||||
\(898\) | 38990.8 | 1.44893 | ||||||||
\(899\) | −19910.9 | −0.738670 | ||||||||
\(900\) | 48945.0 | 1.81278 | ||||||||
\(901\) | 536.670 | 0.0198436 | ||||||||
\(902\) | 44880.7 | 1.65672 | ||||||||
\(903\) | −6517.43 | −0.240184 | ||||||||
\(904\) | 42671.1 | 1.56993 | ||||||||
\(905\) | 47855.5 | 1.75776 | ||||||||
\(906\) | 27656.9 | 1.01417 | ||||||||
\(907\) | 47065.4 | 1.72302 | 0.861511 | − | 0.507738i | \(-0.169518\pi\) | ||||
0.861511 | + | 0.507738i | \(0.169518\pi\) | |||||||
\(908\) | 4310.43 | 0.157540 | ||||||||
\(909\) | 7148.37 | 0.260832 | ||||||||
\(910\) | −22701.6 | −0.826979 | ||||||||
\(911\) | −40218.3 | −1.46267 | −0.731335 | − | 0.682018i | \(-0.761102\pi\) | ||||
−0.731335 | + | 0.682018i | \(0.761102\pi\) | |||||||
\(912\) | −28442.9 | −1.03272 | ||||||||
\(913\) | −49259.4 | −1.78559 | ||||||||
\(914\) | −41627.4 | −1.50647 | ||||||||
\(915\) | 54601.9 | 1.97277 | ||||||||
\(916\) | 15799.6 | 0.569906 | ||||||||
\(917\) | −57428.4 | −2.06810 | ||||||||
\(918\) | −1407.64 | −0.0506090 | ||||||||
\(919\) | −13015.3 | −0.467175 | −0.233587 | − | 0.972336i | \(-0.575047\pi\) | ||||
−0.233587 | + | 0.972336i | \(0.575047\pi\) | |||||||
\(920\) | 59794.0 | 2.14277 | ||||||||
\(921\) | −8172.72 | −0.292400 | ||||||||
\(922\) | 74538.6 | 2.66247 | ||||||||
\(923\) | 151.476 | 0.00540184 | ||||||||
\(924\) | −170250. | −6.06147 | ||||||||
\(925\) | −10328.0 | −0.367117 | ||||||||
\(926\) | −41049.0 | −1.45675 | ||||||||
\(927\) | −19811.0 | −0.701917 | ||||||||
\(928\) | −21761.6 | −0.769784 | ||||||||
\(929\) | −17365.8 | −0.613298 | −0.306649 | − | 0.951823i | \(-0.599208\pi\) | ||||
−0.306649 | + | 0.951823i | \(0.599208\pi\) | |||||||
\(930\) | −128850. | −4.54317 | ||||||||
\(931\) | 6676.32 | 0.235024 | ||||||||
\(932\) | −38647.8 | −1.35832 | ||||||||
\(933\) | 8553.22 | 0.300128 | ||||||||
\(934\) | 34714.0 | 1.21614 | ||||||||
\(935\) | 3737.84 | 0.130738 | ||||||||
\(936\) | 9063.98 | 0.316523 | ||||||||
\(937\) | −41655.6 | −1.45232 | −0.726162 | − | 0.687523i | \(-0.758698\pi\) | ||||
−0.726162 | + | 0.687523i | \(0.758698\pi\) | |||||||
\(938\) | −122492. | −4.26386 | ||||||||
\(939\) | −20389.0 | −0.708593 | ||||||||
\(940\) | 121385. | 4.21186 | ||||||||
\(941\) | −11377.5 | −0.394149 | −0.197075 | − | 0.980388i | \(-0.563144\pi\) | ||||
−0.197075 | + | 0.980388i | \(0.563144\pi\) | |||||||
\(942\) | −39777.4 | −1.37582 | ||||||||
\(943\) | −9164.66 | −0.316482 | ||||||||
\(944\) | 27293.5 | 0.941027 | ||||||||
\(945\) | −30773.3 | −1.05932 | ||||||||
\(946\) | 13417.1 | 0.461129 | ||||||||
\(947\) | 39835.0 | 1.36691 | 0.683455 | − | 0.729992i | \(-0.260476\pi\) | ||||
0.683455 | + | 0.729992i | \(0.260476\pi\) | |||||||
\(948\) | 158542. | 5.43165 | ||||||||
\(949\) | 4498.84 | 0.153887 | ||||||||
\(950\) | 29652.8 | 1.01270 | ||||||||
\(951\) | −3714.48 | −0.126656 | ||||||||
\(952\) | 4530.94 | 0.154253 | ||||||||
\(953\) | 16468.3 | 0.559769 | 0.279885 | − | 0.960034i | \(-0.409704\pi\) | ||||
0.279885 | + | 0.960034i | \(0.409704\pi\) | |||||||
\(954\) | −11789.7 | −0.400112 | ||||||||
\(955\) | 1407.46 | 0.0476903 | ||||||||
\(956\) | 18306.9 | 0.619340 | ||||||||
\(957\) | −35167.3 | −1.18788 | ||||||||
\(958\) | −93341.2 | −3.14793 | ||||||||
\(959\) | −55611.2 | −1.87255 | ||||||||
\(960\) | −22630.4 | −0.760826 | ||||||||
\(961\) | 19866.1 | 0.666848 | ||||||||
\(962\) | −3363.16 | −0.112716 | ||||||||
\(963\) | −22571.1 | −0.755289 | ||||||||
\(964\) | 275.948 | 0.00921958 | ||||||||
\(965\) | 57070.9 | 1.90381 | ||||||||
\(966\) | 49759.3 | 1.65733 | ||||||||
\(967\) | 55135.3 | 1.83354 | 0.916770 | − | 0.399416i | \(-0.130787\pi\) | ||||
0.916770 | + | 0.399416i | \(0.130787\pi\) | |||||||
\(968\) | 126978. | 4.21615 | ||||||||
\(969\) | 772.284 | 0.0256030 | ||||||||
\(970\) | −105606. | −3.49566 | ||||||||
\(971\) | −13040.1 | −0.430975 | −0.215488 | − | 0.976507i | \(-0.569134\pi\) | ||||
−0.215488 | + | 0.976507i | \(0.569134\pi\) | |||||||
\(972\) | 71214.0 | 2.34999 | ||||||||
\(973\) | 71987.6 | 2.37186 | ||||||||
\(974\) | −77114.7 | −2.53687 | ||||||||
\(975\) | −12312.4 | −0.404423 | ||||||||
\(976\) | −64058.0 | −2.10087 | ||||||||
\(977\) | −45144.9 | −1.47831 | −0.739157 | − | 0.673534i | \(-0.764776\pi\) | ||||
−0.739157 | + | 0.673534i | \(0.764776\pi\) | |||||||
\(978\) | −50720.8 | −1.65836 | ||||||||
\(979\) | 21230.0 | 0.693068 | ||||||||
\(980\) | 64325.6 | 2.09674 | ||||||||
\(981\) | 5343.37 | 0.173905 | ||||||||
\(982\) | −80965.4 | −2.63107 | ||||||||
\(983\) | −26573.6 | −0.862225 | −0.431113 | − | 0.902298i | \(-0.641879\pi\) | ||||
−0.431113 | + | 0.902298i | \(0.641879\pi\) | |||||||
\(984\) | 50809.3 | 1.64608 | ||||||||
\(985\) | 38711.5 | 1.25223 | ||||||||
\(986\) | 1645.74 | 0.0531553 | ||||||||
\(987\) | 57446.3 | 1.85262 | ||||||||
\(988\) | 6746.28 | 0.217235 | ||||||||
\(989\) | −2739.78 | −0.0880889 | ||||||||
\(990\) | −82114.0 | −2.63612 | ||||||||
\(991\) | 20658.0 | 0.662183 | 0.331092 | − | 0.943599i | \(-0.392583\pi\) | ||||
0.331092 | + | 0.943599i | \(0.392583\pi\) | |||||||
\(992\) | 54272.8 | 1.73706 | ||||||||
\(993\) | 14670.9 | 0.468850 | ||||||||
\(994\) | −1663.45 | −0.0530800 | ||||||||
\(995\) | −70348.9 | −2.24142 | ||||||||
\(996\) | −98060.1 | −3.11963 | ||||||||
\(997\) | −27284.2 | −0.866701 | −0.433350 | − | 0.901226i | \(-0.642669\pi\) | ||||
−0.433350 | + | 0.901226i | \(0.642669\pi\) | |||||||
\(998\) | −79304.8 | −2.51538 | ||||||||
\(999\) | −4558.95 | −0.144383 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.4.a.b.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 387.4.a.h.1.1 | 6 | |||
4.3 | odd | 2 | 688.4.a.i.1.5 | 6 | |||
5.4 | even | 2 | 1075.4.a.b.1.1 | 6 | |||
7.6 | odd | 2 | 2107.4.a.c.1.6 | 6 | |||
43.42 | odd | 2 | 1849.4.a.c.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.a.b.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
387.4.a.h.1.1 | 6 | 3.2 | odd | 2 | |||
688.4.a.i.1.5 | 6 | 4.3 | odd | 2 | |||
1075.4.a.b.1.1 | 6 | 5.4 | even | 2 | |||
1849.4.a.c.1.1 | 6 | 43.42 | odd | 2 | |||
2107.4.a.c.1.6 | 6 | 7.6 | odd | 2 |