Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.45 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.32699 | 1.52982 | 0.764911 | − | 0.644136i | \(-0.222783\pi\) | ||||
0.764911 | + | 0.644136i | \(0.222783\pi\) | |||||||
\(3\) | −4.31725 | −0.830855 | −0.415427 | − | 0.909626i | \(-0.636368\pi\) | ||||
−0.415427 | + | 0.909626i | \(0.636368\pi\) | |||||||
\(4\) | 10.7228 | 1.34036 | ||||||||
\(5\) | 7.58298 | 0.678242 | 0.339121 | − | 0.940743i | \(-0.389870\pi\) | ||||
0.339121 | + | 0.940743i | \(0.389870\pi\) | |||||||
\(6\) | −18.6807 | −1.27106 | ||||||||
\(7\) | 15.1566 | 0.818379 | 0.409189 | − | 0.912450i | \(-0.365812\pi\) | ||||
0.409189 | + | 0.912450i | \(0.365812\pi\) | |||||||
\(8\) | 11.7817 | 0.520683 | ||||||||
\(9\) | −8.36138 | −0.309681 | ||||||||
\(10\) | 32.8115 | 1.03759 | ||||||||
\(11\) | −4.61811 | −0.126583 | −0.0632914 | − | 0.997995i | \(-0.520160\pi\) | ||||
−0.0632914 | + | 0.997995i | \(0.520160\pi\) | |||||||
\(12\) | −46.2932 | −1.11364 | ||||||||
\(13\) | 4.43823 | 0.0946880 | 0.0473440 | − | 0.998879i | \(-0.484924\pi\) | ||||
0.0473440 | + | 0.998879i | \(0.484924\pi\) | |||||||
\(14\) | 65.5824 | 1.25197 | ||||||||
\(15\) | −32.7376 | −0.563521 | ||||||||
\(16\) | −34.8034 | −0.543803 | ||||||||
\(17\) | −58.9409 | −0.840898 | −0.420449 | − | 0.907316i | \(-0.638127\pi\) | ||||
−0.420449 | + | 0.907316i | \(0.638127\pi\) | |||||||
\(18\) | −36.1796 | −0.473756 | ||||||||
\(19\) | −40.0098 | −0.483099 | −0.241550 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241550 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(20\) | 81.3111 | 0.909086 | ||||||||
\(21\) | −65.4347 | −0.679953 | ||||||||
\(22\) | −19.9825 | −0.193649 | ||||||||
\(23\) | 205.181 | 1.86014 | 0.930071 | − | 0.367379i | \(-0.119745\pi\) | ||||
0.930071 | + | 0.367379i | \(0.119745\pi\) | |||||||
\(24\) | −50.8646 | −0.432612 | ||||||||
\(25\) | −67.4984 | −0.539987 | ||||||||
\(26\) | 19.2042 | 0.144856 | ||||||||
\(27\) | 152.664 | 1.08815 | ||||||||
\(28\) | 162.522 | 1.09692 | ||||||||
\(29\) | −248.436 | −1.59081 | −0.795403 | − | 0.606081i | \(-0.792741\pi\) | ||||
−0.795403 | + | 0.606081i | \(0.792741\pi\) | |||||||
\(30\) | −141.655 | −0.862086 | ||||||||
\(31\) | −63.1080 | −0.365630 | −0.182815 | − | 0.983147i | \(-0.558521\pi\) | ||||
−0.182815 | + | 0.983147i | \(0.558521\pi\) | |||||||
\(32\) | −244.848 | −1.35260 | ||||||||
\(33\) | 19.9375 | 0.105172 | ||||||||
\(34\) | −255.037 | −1.28642 | ||||||||
\(35\) | 114.932 | 0.555059 | ||||||||
\(36\) | −89.6578 | −0.415082 | ||||||||
\(37\) | −151.955 | −0.675167 | −0.337583 | − | 0.941296i | \(-0.609610\pi\) | ||||
−0.337583 | + | 0.941296i | \(0.609610\pi\) | |||||||
\(38\) | −173.122 | −0.739056 | ||||||||
\(39\) | −19.1609 | −0.0786720 | ||||||||
\(40\) | 89.3405 | 0.353150 | ||||||||
\(41\) | −292.670 | −1.11481 | −0.557407 | − | 0.830239i | \(-0.688204\pi\) | ||||
−0.557407 | + | 0.830239i | \(0.688204\pi\) | |||||||
\(42\) | −283.135 | −1.04021 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −49.5192 | −0.169666 | ||||||||
\(45\) | −63.4042 | −0.210039 | ||||||||
\(46\) | 887.818 | 2.84569 | ||||||||
\(47\) | −100.429 | −0.311682 | −0.155841 | − | 0.987782i | \(-0.549809\pi\) | ||||
−0.155841 | + | 0.987782i | \(0.549809\pi\) | |||||||
\(48\) | 150.255 | 0.451821 | ||||||||
\(49\) | −113.278 | −0.330257 | ||||||||
\(50\) | −292.065 | −0.826084 | ||||||||
\(51\) | 254.462 | 0.698664 | ||||||||
\(52\) | 47.5905 | 0.126916 | ||||||||
\(53\) | 566.570 | 1.46838 | 0.734192 | − | 0.678942i | \(-0.237561\pi\) | ||||
0.734192 | + | 0.678942i | \(0.237561\pi\) | |||||||
\(54\) | 660.575 | 1.66468 | ||||||||
\(55\) | −35.0190 | −0.0858539 | ||||||||
\(56\) | 178.571 | 0.426116 | ||||||||
\(57\) | 172.732 | 0.401385 | ||||||||
\(58\) | −1074.98 | −2.43365 | ||||||||
\(59\) | 730.172 | 1.61119 | 0.805596 | − | 0.592466i | \(-0.201846\pi\) | ||||
0.805596 | + | 0.592466i | \(0.201846\pi\) | |||||||
\(60\) | −351.040 | −0.755318 | ||||||||
\(61\) | −928.090 | −1.94803 | −0.974014 | − | 0.226486i | \(-0.927276\pi\) | ||||
−0.974014 | + | 0.226486i | \(0.927276\pi\) | |||||||
\(62\) | −273.068 | −0.559349 | ||||||||
\(63\) | −126.730 | −0.253436 | ||||||||
\(64\) | −781.026 | −1.52544 | ||||||||
\(65\) | 33.6550 | 0.0642214 | ||||||||
\(66\) | 86.2694 | 0.160894 | ||||||||
\(67\) | −61.7700 | −0.112633 | −0.0563164 | − | 0.998413i | \(-0.517936\pi\) | ||||
−0.0563164 | + | 0.998413i | \(0.517936\pi\) | |||||||
\(68\) | −632.014 | −1.12710 | ||||||||
\(69\) | −885.819 | −1.54551 | ||||||||
\(70\) | 497.310 | 0.849141 | ||||||||
\(71\) | −66.4400 | −0.111056 | −0.0555280 | − | 0.998457i | \(-0.517684\pi\) | ||||
−0.0555280 | + | 0.998457i | \(0.517684\pi\) | |||||||
\(72\) | −98.5114 | −0.161246 | ||||||||
\(73\) | −408.464 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(74\) | −657.506 | −1.03289 | ||||||||
\(75\) | 291.407 | 0.448651 | ||||||||
\(76\) | −429.019 | −0.647525 | ||||||||
\(77\) | −69.9947 | −0.103593 | ||||||||
\(78\) | −82.9092 | −0.120354 | ||||||||
\(79\) | 583.475 | 0.830962 | 0.415481 | − | 0.909602i | \(-0.363613\pi\) | ||||
0.415481 | + | 0.909602i | \(0.363613\pi\) | |||||||
\(80\) | −263.913 | −0.368830 | ||||||||
\(81\) | −433.330 | −0.594417 | ||||||||
\(82\) | −1266.38 | −1.70547 | ||||||||
\(83\) | −1149.74 | −1.52049 | −0.760246 | − | 0.649635i | \(-0.774922\pi\) | ||||
−0.760246 | + | 0.649635i | \(0.774922\pi\) | |||||||
\(84\) | −701.646 | −0.911379 | ||||||||
\(85\) | −446.948 | −0.570333 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1072.56 | 1.32173 | ||||||||
\(88\) | −54.4092 | −0.0659096 | ||||||||
\(89\) | 977.540 | 1.16426 | 0.582129 | − | 0.813096i | \(-0.302220\pi\) | ||||
0.582129 | + | 0.813096i | \(0.302220\pi\) | |||||||
\(90\) | −274.349 | −0.321322 | ||||||||
\(91\) | 67.2684 | 0.0774906 | ||||||||
\(92\) | 2200.13 | 2.49325 | ||||||||
\(93\) | 272.453 | 0.303785 | ||||||||
\(94\) | −434.554 | −0.476818 | ||||||||
\(95\) | −303.394 | −0.327658 | ||||||||
\(96\) | 1057.07 | 1.12382 | ||||||||
\(97\) | 254.707 | 0.266614 | 0.133307 | − | 0.991075i | \(-0.457440\pi\) | ||||
0.133307 | + | 0.991075i | \(0.457440\pi\) | |||||||
\(98\) | −490.153 | −0.505234 | ||||||||
\(99\) | 38.6137 | 0.0392003 | ||||||||
\(100\) | −723.775 | −0.723775 | ||||||||
\(101\) | −1396.17 | −1.37548 | −0.687742 | − | 0.725955i | \(-0.741398\pi\) | ||||
−0.687742 | + | 0.725955i | \(0.741398\pi\) | |||||||
\(102\) | 1101.06 | 1.06883 | ||||||||
\(103\) | −770.884 | −0.737451 | −0.368725 | − | 0.929538i | \(-0.620206\pi\) | ||||
−0.368725 | + | 0.929538i | \(0.620206\pi\) | |||||||
\(104\) | 52.2900 | 0.0493025 | ||||||||
\(105\) | −496.190 | −0.461173 | ||||||||
\(106\) | 2451.54 | 2.24637 | ||||||||
\(107\) | −559.189 | −0.505223 | −0.252611 | − | 0.967568i | \(-0.581289\pi\) | ||||
−0.252611 | + | 0.967568i | \(0.581289\pi\) | |||||||
\(108\) | 1636.99 | 1.45851 | ||||||||
\(109\) | 309.168 | 0.271678 | 0.135839 | − | 0.990731i | \(-0.456627\pi\) | ||||
0.135839 | + | 0.990731i | \(0.456627\pi\) | |||||||
\(110\) | −151.527 | −0.131341 | ||||||||
\(111\) | 656.025 | 0.560966 | ||||||||
\(112\) | −527.500 | −0.445036 | ||||||||
\(113\) | 1649.23 | 1.37298 | 0.686490 | − | 0.727139i | \(-0.259150\pi\) | ||||
0.686490 | + | 0.727139i | \(0.259150\pi\) | |||||||
\(114\) | 747.411 | 0.614048 | ||||||||
\(115\) | 1555.89 | 1.26163 | ||||||||
\(116\) | −2663.94 | −2.13225 | ||||||||
\(117\) | −37.1098 | −0.0293231 | ||||||||
\(118\) | 3159.45 | 2.46484 | ||||||||
\(119\) | −893.343 | −0.688173 | ||||||||
\(120\) | −385.705 | −0.293416 | ||||||||
\(121\) | −1309.67 | −0.983977 | ||||||||
\(122\) | −4015.84 | −2.98014 | ||||||||
\(123\) | 1263.53 | 0.926249 | ||||||||
\(124\) | −676.697 | −0.490074 | ||||||||
\(125\) | −1459.71 | −1.04448 | ||||||||
\(126\) | −548.359 | −0.387712 | ||||||||
\(127\) | −1484.24 | −1.03705 | −0.518525 | − | 0.855062i | \(-0.673519\pi\) | ||||
−0.518525 | + | 0.855062i | \(0.673519\pi\) | |||||||
\(128\) | −1420.71 | −0.981050 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 145.625 | 0.0982474 | ||||||||
\(131\) | 2344.14 | 1.56343 | 0.781713 | − | 0.623638i | \(-0.214346\pi\) | ||||
0.781713 | + | 0.623638i | \(0.214346\pi\) | |||||||
\(132\) | 213.787 | 0.140968 | ||||||||
\(133\) | −606.412 | −0.395358 | ||||||||
\(134\) | −267.278 | −0.172308 | ||||||||
\(135\) | 1157.65 | 0.738032 | ||||||||
\(136\) | −694.425 | −0.437842 | ||||||||
\(137\) | −1016.32 | −0.633797 | −0.316899 | − | 0.948459i | \(-0.602641\pi\) | ||||
−0.316899 | + | 0.948459i | \(0.602641\pi\) | |||||||
\(138\) | −3832.93 | −2.36435 | ||||||||
\(139\) | 1637.27 | 0.999073 | 0.499536 | − | 0.866293i | \(-0.333504\pi\) | ||||
0.499536 | + | 0.866293i | \(0.333504\pi\) | |||||||
\(140\) | 1232.40 | 0.743976 | ||||||||
\(141\) | 433.576 | 0.258962 | ||||||||
\(142\) | −287.485 | −0.169896 | ||||||||
\(143\) | −20.4962 | −0.0119859 | ||||||||
\(144\) | 291.004 | 0.168405 | ||||||||
\(145\) | −1883.88 | −1.07895 | ||||||||
\(146\) | −1767.42 | −1.00187 | ||||||||
\(147\) | 489.049 | 0.274395 | ||||||||
\(148\) | −1629.39 | −0.904964 | ||||||||
\(149\) | −2190.65 | −1.20446 | −0.602232 | − | 0.798321i | \(-0.705722\pi\) | ||||
−0.602232 | + | 0.798321i | \(0.705722\pi\) | |||||||
\(150\) | 1260.92 | 0.686356 | ||||||||
\(151\) | −2993.00 | −1.61302 | −0.806512 | − | 0.591218i | \(-0.798647\pi\) | ||||
−0.806512 | + | 0.591218i | \(0.798647\pi\) | |||||||
\(152\) | −471.385 | −0.251542 | ||||||||
\(153\) | 492.827 | 0.260410 | ||||||||
\(154\) | −302.866 | −0.158478 | ||||||||
\(155\) | −478.546 | −0.247986 | ||||||||
\(156\) | −205.460 | −0.105448 | ||||||||
\(157\) | −1276.61 | −0.648948 | −0.324474 | − | 0.945895i | \(-0.605187\pi\) | ||||
−0.324474 | + | 0.945895i | \(0.605187\pi\) | |||||||
\(158\) | 2524.69 | 1.27122 | ||||||||
\(159\) | −2446.02 | −1.22001 | ||||||||
\(160\) | −1856.67 | −0.917394 | ||||||||
\(161\) | 3109.85 | 1.52230 | ||||||||
\(162\) | −1875.01 | −0.909352 | ||||||||
\(163\) | −1124.07 | −0.540148 | −0.270074 | − | 0.962840i | \(-0.587048\pi\) | ||||
−0.270074 | + | 0.962840i | \(0.587048\pi\) | |||||||
\(164\) | −3138.26 | −1.49425 | ||||||||
\(165\) | 151.186 | 0.0713321 | ||||||||
\(166\) | −4974.93 | −2.32608 | ||||||||
\(167\) | 3171.73 | 1.46968 | 0.734838 | − | 0.678242i | \(-0.237258\pi\) | ||||
0.734838 | + | 0.678242i | \(0.237258\pi\) | |||||||
\(168\) | −770.933 | −0.354040 | ||||||||
\(169\) | −2177.30 | −0.991034 | ||||||||
\(170\) | −1933.94 | −0.872508 | ||||||||
\(171\) | 334.537 | 0.149607 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −364.520 | −0.160196 | −0.0800982 | − | 0.996787i | \(-0.525523\pi\) | ||||
−0.0800982 | + | 0.996787i | \(0.525523\pi\) | |||||||
\(174\) | 4640.95 | 2.02201 | ||||||||
\(175\) | −1023.05 | −0.441914 | ||||||||
\(176\) | 160.726 | 0.0688361 | ||||||||
\(177\) | −3152.33 | −1.33867 | ||||||||
\(178\) | 4229.81 | 1.78111 | ||||||||
\(179\) | 2292.73 | 0.957355 | 0.478677 | − | 0.877991i | \(-0.341116\pi\) | ||||
0.478677 | + | 0.877991i | \(0.341116\pi\) | |||||||
\(180\) | −679.873 | −0.281526 | ||||||||
\(181\) | 989.703 | 0.406431 | 0.203216 | − | 0.979134i | \(-0.434861\pi\) | ||||
0.203216 | + | 0.979134i | \(0.434861\pi\) | |||||||
\(182\) | 291.070 | 0.118547 | ||||||||
\(183\) | 4006.79 | 1.61853 | ||||||||
\(184\) | 2417.39 | 0.968545 | ||||||||
\(185\) | −1152.27 | −0.457927 | ||||||||
\(186\) | 1178.90 | 0.464737 | ||||||||
\(187\) | 272.195 | 0.106443 | ||||||||
\(188\) | −1076.88 | −0.417764 | ||||||||
\(189\) | 2313.86 | 0.890522 | ||||||||
\(190\) | −1312.78 | −0.501259 | ||||||||
\(191\) | 1523.76 | 0.577254 | 0.288627 | − | 0.957442i | \(-0.406801\pi\) | ||||
0.288627 | + | 0.957442i | \(0.406801\pi\) | |||||||
\(192\) | 3371.88 | 1.26742 | ||||||||
\(193\) | −794.523 | −0.296326 | −0.148163 | − | 0.988963i | \(-0.547336\pi\) | ||||
−0.148163 | + | 0.988963i | \(0.547336\pi\) | |||||||
\(194\) | 1102.12 | 0.407872 | ||||||||
\(195\) | −145.297 | −0.0533587 | ||||||||
\(196\) | −1214.66 | −0.442661 | ||||||||
\(197\) | −5363.39 | −1.93973 | −0.969863 | − | 0.243652i | \(-0.921655\pi\) | ||||
−0.969863 | + | 0.243652i | \(0.921655\pi\) | |||||||
\(198\) | 167.081 | 0.0599695 | ||||||||
\(199\) | −4058.33 | −1.44566 | −0.722832 | − | 0.691024i | \(-0.757160\pi\) | ||||
−0.722832 | + | 0.691024i | \(0.757160\pi\) | |||||||
\(200\) | −795.247 | −0.281162 | ||||||||
\(201\) | 266.676 | 0.0935815 | ||||||||
\(202\) | −6041.21 | −2.10425 | ||||||||
\(203\) | −3765.44 | −1.30188 | ||||||||
\(204\) | 2728.56 | 0.936458 | ||||||||
\(205\) | −2219.31 | −0.756114 | ||||||||
\(206\) | −3335.61 | −1.12817 | ||||||||
\(207\) | −1715.60 | −0.576050 | ||||||||
\(208\) | −154.465 | −0.0514916 | ||||||||
\(209\) | 184.770 | 0.0611521 | ||||||||
\(210\) | −2147.01 | −0.705513 | ||||||||
\(211\) | 1338.34 | 0.436658 | 0.218329 | − | 0.975875i | \(-0.429939\pi\) | ||||
0.218329 | + | 0.975875i | \(0.429939\pi\) | |||||||
\(212\) | 6075.24 | 1.96816 | ||||||||
\(213\) | 286.838 | 0.0922715 | ||||||||
\(214\) | −2419.60 | −0.772901 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1798.64 | 0.566584 | ||||||||
\(217\) | −956.501 | −0.299224 | ||||||||
\(218\) | 1337.77 | 0.415619 | ||||||||
\(219\) | 1763.44 | 0.544120 | ||||||||
\(220\) | −375.503 | −0.115075 | ||||||||
\(221\) | −261.593 | −0.0796230 | ||||||||
\(222\) | 2838.62 | 0.858177 | ||||||||
\(223\) | −334.702 | −0.100508 | −0.0502540 | − | 0.998736i | \(-0.516003\pi\) | ||||
−0.0502540 | + | 0.998736i | \(0.516003\pi\) | |||||||
\(224\) | −3711.05 | −1.10694 | ||||||||
\(225\) | 564.380 | 0.167224 | ||||||||
\(226\) | 7136.22 | 2.10042 | ||||||||
\(227\) | 1321.17 | 0.386294 | 0.193147 | − | 0.981170i | \(-0.438131\pi\) | ||||
0.193147 | + | 0.981170i | \(0.438131\pi\) | |||||||
\(228\) | 1852.18 | 0.537999 | ||||||||
\(229\) | −1838.72 | −0.530594 | −0.265297 | − | 0.964167i | \(-0.585470\pi\) | ||||
−0.265297 | + | 0.964167i | \(0.585470\pi\) | |||||||
\(230\) | 6732.31 | 1.93007 | ||||||||
\(231\) | 302.184 | 0.0860705 | ||||||||
\(232\) | −2927.00 | −0.828306 | ||||||||
\(233\) | 2469.71 | 0.694403 | 0.347202 | − | 0.937791i | \(-0.387132\pi\) | ||||
0.347202 | + | 0.937791i | \(0.387132\pi\) | |||||||
\(234\) | −160.574 | −0.0448591 | ||||||||
\(235\) | −761.550 | −0.211396 | ||||||||
\(236\) | 7829.52 | 2.15957 | ||||||||
\(237\) | −2519.00 | −0.690409 | ||||||||
\(238\) | −3865.48 | −1.05278 | ||||||||
\(239\) | −6493.53 | −1.75746 | −0.878728 | − | 0.477324i | \(-0.841607\pi\) | ||||
−0.878728 | + | 0.477324i | \(0.841607\pi\) | |||||||
\(240\) | 1139.38 | 0.306444 | ||||||||
\(241\) | −546.111 | −0.145967 | −0.0729836 | − | 0.997333i | \(-0.523252\pi\) | ||||
−0.0729836 | + | 0.997333i | \(0.523252\pi\) | |||||||
\(242\) | −5666.94 | −1.50531 | ||||||||
\(243\) | −2251.13 | −0.594280 | ||||||||
\(244\) | −9951.76 | −2.61105 | ||||||||
\(245\) | −858.985 | −0.223994 | ||||||||
\(246\) | 5467.28 | 1.41700 | ||||||||
\(247\) | −177.573 | −0.0457437 | ||||||||
\(248\) | −743.520 | −0.190377 | ||||||||
\(249\) | 4963.73 | 1.26331 | ||||||||
\(250\) | −6316.16 | −1.59788 | ||||||||
\(251\) | 3433.75 | 0.863493 | 0.431746 | − | 0.901995i | \(-0.357898\pi\) | ||||
0.431746 | + | 0.901995i | \(0.357898\pi\) | |||||||
\(252\) | −1358.91 | −0.339694 | ||||||||
\(253\) | −947.550 | −0.235462 | ||||||||
\(254\) | −6422.31 | −1.58650 | ||||||||
\(255\) | 1929.58 | 0.473864 | ||||||||
\(256\) | 100.803 | 0.0246101 | ||||||||
\(257\) | −485.127 | −0.117749 | −0.0588743 | − | 0.998265i | \(-0.518751\pi\) | ||||
−0.0588743 | + | 0.998265i | \(0.518751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2303.11 | −0.552542 | ||||||||
\(260\) | 360.878 | 0.0860795 | ||||||||
\(261\) | 2077.27 | 0.492642 | ||||||||
\(262\) | 10143.1 | 2.39176 | ||||||||
\(263\) | −1318.47 | −0.309126 | −0.154563 | − | 0.987983i | \(-0.549397\pi\) | ||||
−0.154563 | + | 0.987983i | \(0.549397\pi\) | |||||||
\(264\) | 234.898 | 0.0547613 | ||||||||
\(265\) | 4296.29 | 0.995920 | ||||||||
\(266\) | −2623.94 | −0.604827 | ||||||||
\(267\) | −4220.28 | −0.967330 | ||||||||
\(268\) | −662.350 | −0.150968 | ||||||||
\(269\) | −1988.06 | −0.450610 | −0.225305 | − | 0.974288i | \(-0.572338\pi\) | ||||
−0.225305 | + | 0.974288i | \(0.572338\pi\) | |||||||
\(270\) | 5009.13 | 1.12906 | ||||||||
\(271\) | 7179.43 | 1.60930 | 0.804648 | − | 0.593752i | \(-0.202354\pi\) | ||||
0.804648 | + | 0.593752i | \(0.202354\pi\) | |||||||
\(272\) | 2051.34 | 0.457283 | ||||||||
\(273\) | −290.414 | −0.0643834 | ||||||||
\(274\) | −4397.61 | −0.969597 | ||||||||
\(275\) | 311.715 | 0.0683531 | ||||||||
\(276\) | −9498.50 | −2.07153 | ||||||||
\(277\) | 3471.68 | 0.753043 | 0.376521 | − | 0.926408i | \(-0.377120\pi\) | ||||
0.376521 | + | 0.926408i | \(0.377120\pi\) | |||||||
\(278\) | 7084.44 | 1.52840 | ||||||||
\(279\) | 527.670 | 0.113229 | ||||||||
\(280\) | 1354.10 | 0.289010 | ||||||||
\(281\) | 2360.71 | 0.501168 | 0.250584 | − | 0.968095i | \(-0.419377\pi\) | ||||
0.250584 | + | 0.968095i | \(0.419377\pi\) | |||||||
\(282\) | 1876.08 | 0.396166 | ||||||||
\(283\) | −3584.19 | −0.752854 | −0.376427 | − | 0.926446i | \(-0.622847\pi\) | ||||
−0.376427 | + | 0.926446i | \(0.622847\pi\) | |||||||
\(284\) | −712.426 | −0.148855 | ||||||||
\(285\) | 1309.83 | 0.272236 | ||||||||
\(286\) | −88.6870 | −0.0183363 | ||||||||
\(287\) | −4435.88 | −0.912340 | ||||||||
\(288\) | 2047.26 | 0.418876 | ||||||||
\(289\) | −1438.97 | −0.292890 | ||||||||
\(290\) | −8151.55 | −1.65060 | ||||||||
\(291\) | −1099.63 | −0.221518 | ||||||||
\(292\) | −4379.90 | −0.877788 | ||||||||
\(293\) | −218.871 | −0.0436403 | −0.0218201 | − | 0.999762i | \(-0.506946\pi\) | ||||
−0.0218201 | + | 0.999762i | \(0.506946\pi\) | |||||||
\(294\) | 2116.11 | 0.419776 | ||||||||
\(295\) | 5536.88 | 1.09278 | ||||||||
\(296\) | −1790.29 | −0.351548 | ||||||||
\(297\) | −705.018 | −0.137742 | ||||||||
\(298\) | −9478.93 | −1.84262 | ||||||||
\(299\) | 910.643 | 0.176133 | ||||||||
\(300\) | 3124.72 | 0.601352 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12950.7 | −2.46764 | ||||||||
\(303\) | 6027.60 | 1.14283 | ||||||||
\(304\) | 1392.48 | 0.262711 | ||||||||
\(305\) | −7037.69 | −1.32124 | ||||||||
\(306\) | 2132.46 | 0.398381 | ||||||||
\(307\) | −2450.11 | −0.455488 | −0.227744 | − | 0.973721i | \(-0.573135\pi\) | ||||
−0.227744 | + | 0.973721i | \(0.573135\pi\) | |||||||
\(308\) | −750.542 | −0.138851 | ||||||||
\(309\) | 3328.09 | 0.612714 | ||||||||
\(310\) | −2070.67 | −0.379374 | ||||||||
\(311\) | −818.907 | −0.149312 | −0.0746559 | − | 0.997209i | \(-0.523786\pi\) | ||||
−0.0746559 | + | 0.997209i | \(0.523786\pi\) | |||||||
\(312\) | −225.749 | −0.0409632 | ||||||||
\(313\) | −1988.86 | −0.359159 | −0.179579 | − | 0.983743i | \(-0.557474\pi\) | ||||
−0.179579 | + | 0.983743i | \(0.557474\pi\) | |||||||
\(314\) | −5523.89 | −0.992775 | ||||||||
\(315\) | −960.991 | −0.171891 | ||||||||
\(316\) | 6256.51 | 1.11379 | ||||||||
\(317\) | −4046.09 | −0.716880 | −0.358440 | − | 0.933553i | \(-0.616691\pi\) | ||||
−0.358440 | + | 0.933553i | \(0.616691\pi\) | |||||||
\(318\) | −10583.9 | −1.86640 | ||||||||
\(319\) | 1147.30 | 0.201369 | ||||||||
\(320\) | −5922.51 | −1.03462 | ||||||||
\(321\) | 2414.16 | 0.419767 | ||||||||
\(322\) | 13456.3 | 2.32885 | ||||||||
\(323\) | 2358.22 | 0.406237 | ||||||||
\(324\) | −4646.53 | −0.796730 | ||||||||
\(325\) | −299.574 | −0.0511303 | ||||||||
\(326\) | −4863.85 | −0.826330 | ||||||||
\(327\) | −1334.75 | −0.225725 | ||||||||
\(328\) | −3448.16 | −0.580465 | ||||||||
\(329\) | −1522.16 | −0.255074 | ||||||||
\(330\) | 654.179 | 0.109125 | ||||||||
\(331\) | 11197.4 | 1.85940 | 0.929702 | − | 0.368313i | \(-0.120065\pi\) | ||||
0.929702 | + | 0.368313i | \(0.120065\pi\) | |||||||
\(332\) | −12328.5 | −2.03800 | ||||||||
\(333\) | 1270.55 | 0.209086 | ||||||||
\(334\) | 13724.1 | 2.24834 | ||||||||
\(335\) | −468.400 | −0.0763924 | ||||||||
\(336\) | 2277.35 | 0.369760 | ||||||||
\(337\) | 9070.66 | 1.46620 | 0.733102 | − | 0.680119i | \(-0.238072\pi\) | ||||
0.733102 | + | 0.680119i | \(0.238072\pi\) | |||||||
\(338\) | −9421.16 | −1.51611 | ||||||||
\(339\) | −7120.15 | −1.14075 | ||||||||
\(340\) | −4792.55 | −0.764449 | ||||||||
\(341\) | 291.439 | 0.0462825 | ||||||||
\(342\) | 1447.54 | 0.228871 | ||||||||
\(343\) | −6915.62 | −1.08865 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6717.15 | −1.04823 | ||||||||
\(346\) | −1577.28 | −0.245072 | ||||||||
\(347\) | −2409.25 | −0.372724 | −0.186362 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186362 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(348\) | 11500.9 | 1.77159 | ||||||||
\(349\) | 10646.2 | 1.63289 | 0.816443 | − | 0.577426i | \(-0.195943\pi\) | ||||
0.816443 | + | 0.577426i | \(0.195943\pi\) | |||||||
\(350\) | −4426.71 | −0.676050 | ||||||||
\(351\) | 677.557 | 0.103035 | ||||||||
\(352\) | 1130.73 | 0.171217 | ||||||||
\(353\) | 6413.78 | 0.967056 | 0.483528 | − | 0.875329i | \(-0.339355\pi\) | ||||
0.483528 | + | 0.875329i | \(0.339355\pi\) | |||||||
\(354\) | −13640.1 | −2.04792 | ||||||||
\(355\) | −503.814 | −0.0753229 | ||||||||
\(356\) | 10482.0 | 1.56052 | ||||||||
\(357\) | 3856.78 | 0.571772 | ||||||||
\(358\) | 9920.61 | 1.46458 | ||||||||
\(359\) | 3428.56 | 0.504046 | 0.252023 | − | 0.967721i | \(-0.418904\pi\) | ||||
0.252023 | + | 0.967721i | \(0.418904\pi\) | |||||||
\(360\) | −747.010 | −0.109364 | ||||||||
\(361\) | −5258.21 | −0.766615 | ||||||||
\(362\) | 4282.44 | 0.621768 | ||||||||
\(363\) | 5654.18 | 0.817542 | ||||||||
\(364\) | 721.309 | 0.103865 | ||||||||
\(365\) | −3097.38 | −0.444175 | ||||||||
\(366\) | 17337.4 | 2.47606 | ||||||||
\(367\) | −10004.5 | −1.42297 | −0.711483 | − | 0.702703i | \(-0.751976\pi\) | ||||
−0.711483 | + | 0.702703i | \(0.751976\pi\) | |||||||
\(368\) | −7141.00 | −1.01155 | ||||||||
\(369\) | 2447.13 | 0.345237 | ||||||||
\(370\) | −4985.85 | −0.700547 | ||||||||
\(371\) | 8587.26 | 1.20169 | ||||||||
\(372\) | 2921.47 | 0.407180 | ||||||||
\(373\) | −6168.67 | −0.856305 | −0.428153 | − | 0.903706i | \(-0.640835\pi\) | ||||
−0.428153 | + | 0.903706i | \(0.640835\pi\) | |||||||
\(374\) | 1177.79 | 0.162839 | ||||||||
\(375\) | 6301.94 | 0.867815 | ||||||||
\(376\) | −1183.22 | −0.162288 | ||||||||
\(377\) | −1102.62 | −0.150630 | ||||||||
\(378\) | 10012.1 | 1.36234 | ||||||||
\(379\) | 12794.7 | 1.73409 | 0.867045 | − | 0.498230i | \(-0.166016\pi\) | ||||
0.867045 | + | 0.498230i | \(0.166016\pi\) | |||||||
\(380\) | −3253.24 | −0.439179 | ||||||||
\(381\) | 6407.85 | 0.861638 | ||||||||
\(382\) | 6593.30 | 0.883096 | ||||||||
\(383\) | 3461.90 | 0.461867 | 0.230933 | − | 0.972970i | \(-0.425822\pi\) | ||||
0.230933 | + | 0.972970i | \(0.425822\pi\) | |||||||
\(384\) | 6133.56 | 0.815110 | ||||||||
\(385\) | −530.768 | −0.0702610 | ||||||||
\(386\) | −3437.89 | −0.453327 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2731.18 | 0.357358 | ||||||||
\(389\) | 13493.8 | 1.75877 | 0.879384 | − | 0.476113i | \(-0.157955\pi\) | ||||
0.879384 | + | 0.476113i | \(0.157955\pi\) | |||||||
\(390\) | −628.699 | −0.0816293 | ||||||||
\(391\) | −12093.6 | −1.56419 | ||||||||
\(392\) | −1334.61 | −0.171959 | ||||||||
\(393\) | −10120.2 | −1.29898 | ||||||||
\(394\) | −23207.3 | −2.96743 | ||||||||
\(395\) | 4424.48 | 0.563594 | ||||||||
\(396\) | 414.049 | 0.0525423 | ||||||||
\(397\) | −8336.42 | −1.05389 | −0.526943 | − | 0.849900i | \(-0.676662\pi\) | ||||
−0.526943 | + | 0.849900i | \(0.676662\pi\) | |||||||
\(398\) | −17560.3 | −2.21161 | ||||||||
\(399\) | 2618.03 | 0.328485 | ||||||||
\(400\) | 2349.17 | 0.293647 | ||||||||
\(401\) | −1635.58 | −0.203684 | −0.101842 | − | 0.994801i | \(-0.532474\pi\) | ||||
−0.101842 | + | 0.994801i | \(0.532474\pi\) | |||||||
\(402\) | 1153.91 | 0.143163 | ||||||||
\(403\) | −280.088 | −0.0346208 | ||||||||
\(404\) | −14970.9 | −1.84364 | ||||||||
\(405\) | −3285.93 | −0.403159 | ||||||||
\(406\) | −16293.0 | −1.99165 | ||||||||
\(407\) | 701.742 | 0.0854646 | ||||||||
\(408\) | 2998.00 | 0.363783 | ||||||||
\(409\) | 13688.6 | 1.65490 | 0.827452 | − | 0.561536i | \(-0.189789\pi\) | ||||
0.827452 | + | 0.561536i | \(0.189789\pi\) | |||||||
\(410\) | −9602.94 | −1.15672 | ||||||||
\(411\) | 4387.71 | 0.526593 | ||||||||
\(412\) | −8266.07 | −0.988446 | ||||||||
\(413\) | 11066.9 | 1.31856 | ||||||||
\(414\) | −7423.38 | −0.881255 | ||||||||
\(415\) | −8718.49 | −1.03126 | ||||||||
\(416\) | −1086.69 | −0.128075 | ||||||||
\(417\) | −7068.48 | −0.830084 | ||||||||
\(418\) | 799.496 | 0.0935518 | ||||||||
\(419\) | −253.682 | −0.0295780 | −0.0147890 | − | 0.999891i | \(-0.504708\pi\) | ||||
−0.0147890 | + | 0.999891i | \(0.504708\pi\) | |||||||
\(420\) | −5320.57 | −0.618136 | ||||||||
\(421\) | 11417.5 | 1.32174 | 0.660872 | − | 0.750498i | \(-0.270187\pi\) | ||||
0.660872 | + | 0.750498i | \(0.270187\pi\) | |||||||
\(422\) | 5790.96 | 0.668009 | ||||||||
\(423\) | 839.724 | 0.0965219 | ||||||||
\(424\) | 6675.17 | 0.764563 | ||||||||
\(425\) | 3978.42 | 0.454074 | ||||||||
\(426\) | 1241.15 | 0.141159 | ||||||||
\(427\) | −14066.7 | −1.59422 | ||||||||
\(428\) | −5996.10 | −0.677178 | ||||||||
\(429\) | 88.4873 | 0.00995852 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4723.09 | −0.527850 | −0.263925 | − | 0.964543i | \(-0.585017\pi\) | ||||
−0.263925 | + | 0.964543i | \(0.585017\pi\) | |||||||
\(432\) | −5313.21 | −0.591741 | ||||||||
\(433\) | 5231.32 | 0.580604 | 0.290302 | − | 0.956935i | \(-0.406244\pi\) | ||||
0.290302 | + | 0.956935i | \(0.406244\pi\) | |||||||
\(434\) | −4138.77 | −0.457759 | ||||||||
\(435\) | 8133.19 | 0.896452 | ||||||||
\(436\) | 3315.16 | 0.364145 | ||||||||
\(437\) | −8209.27 | −0.898633 | ||||||||
\(438\) | 7630.39 | 0.832407 | ||||||||
\(439\) | 12258.1 | 1.33268 | 0.666342 | − | 0.745646i | \(-0.267859\pi\) | ||||
0.666342 | + | 0.745646i | \(0.267859\pi\) | |||||||
\(440\) | −412.584 | −0.0447027 | ||||||||
\(441\) | 947.161 | 0.102274 | ||||||||
\(442\) | −1131.91 | −0.121809 | ||||||||
\(443\) | −15064.2 | −1.61563 | −0.807813 | − | 0.589439i | \(-0.799349\pi\) | ||||
−0.807813 | + | 0.589439i | \(0.799349\pi\) | |||||||
\(444\) | 7034.46 | 0.751893 | ||||||||
\(445\) | 7412.67 | 0.789649 | ||||||||
\(446\) | −1448.25 | −0.153759 | ||||||||
\(447\) | 9457.59 | 1.00073 | ||||||||
\(448\) | −11837.7 | −1.24839 | ||||||||
\(449\) | 1007.95 | 0.105943 | 0.0529713 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529713 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(450\) | 2442.07 | 0.255822 | ||||||||
\(451\) | 1351.58 | 0.141116 | ||||||||
\(452\) | 17684.5 | 1.84028 | ||||||||
\(453\) | 12921.5 | 1.34019 | ||||||||
\(454\) | 5716.67 | 0.590962 | ||||||||
\(455\) | 510.095 | 0.0525574 | ||||||||
\(456\) | 2035.08 | 0.208995 | ||||||||
\(457\) | −2569.85 | −0.263047 | −0.131523 | − | 0.991313i | \(-0.541987\pi\) | ||||
−0.131523 | + | 0.991313i | \(0.541987\pi\) | |||||||
\(458\) | −7956.13 | −0.811715 | ||||||||
\(459\) | −8998.14 | −0.915027 | ||||||||
\(460\) | 16683.5 | 1.69103 | ||||||||
\(461\) | −2634.42 | −0.266155 | −0.133077 | − | 0.991106i | \(-0.542486\pi\) | ||||
−0.133077 | + | 0.991106i | \(0.542486\pi\) | |||||||
\(462\) | 1307.55 | 0.131672 | ||||||||
\(463\) | 9459.74 | 0.949528 | 0.474764 | − | 0.880113i | \(-0.342533\pi\) | ||||
0.474764 | + | 0.880113i | \(0.342533\pi\) | |||||||
\(464\) | 8646.40 | 0.865085 | ||||||||
\(465\) | 2066.00 | 0.206040 | ||||||||
\(466\) | 10686.4 | 1.06231 | ||||||||
\(467\) | 4529.63 | 0.448835 | 0.224418 | − | 0.974493i | \(-0.427952\pi\) | ||||
0.224418 | + | 0.974493i | \(0.427952\pi\) | |||||||
\(468\) | −397.922 | −0.0393033 | ||||||||
\(469\) | −936.221 | −0.0921763 | ||||||||
\(470\) | −3295.22 | −0.323398 | ||||||||
\(471\) | 5511.45 | 0.539181 | ||||||||
\(472\) | 8602.68 | 0.838920 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10899.7 | −1.05620 | ||||||||
\(475\) | 2700.60 | 0.260867 | ||||||||
\(476\) | −9579.17 | −0.922396 | ||||||||
\(477\) | −4737.31 | −0.454730 | ||||||||
\(478\) | −28097.5 | −2.68859 | ||||||||
\(479\) | −14764.9 | −1.40841 | −0.704203 | − | 0.709999i | \(-0.748695\pi\) | ||||
−0.704203 | + | 0.709999i | \(0.748695\pi\) | |||||||
\(480\) | 8015.72 | 0.762221 | ||||||||
\(481\) | −674.410 | −0.0639302 | ||||||||
\(482\) | −2363.02 | −0.223304 | ||||||||
\(483\) | −13426.0 | −1.26481 | ||||||||
\(484\) | −14043.4 | −1.31888 | ||||||||
\(485\) | 1931.44 | 0.180829 | ||||||||
\(486\) | −9740.62 | −0.909143 | ||||||||
\(487\) | −6246.07 | −0.581184 | −0.290592 | − | 0.956847i | \(-0.593852\pi\) | ||||
−0.290592 | + | 0.956847i | \(0.593852\pi\) | |||||||
\(488\) | −10934.5 | −1.01431 | ||||||||
\(489\) | 4852.89 | 0.448784 | ||||||||
\(490\) | −3716.82 | −0.342671 | ||||||||
\(491\) | 9471.49 | 0.870555 | 0.435277 | − | 0.900296i | \(-0.356650\pi\) | ||||
0.435277 | + | 0.900296i | \(0.356650\pi\) | |||||||
\(492\) | 13548.6 | 1.24150 | ||||||||
\(493\) | 14643.0 | 1.33771 | ||||||||
\(494\) | −768.356 | −0.0699797 | ||||||||
\(495\) | 292.807 | 0.0265873 | ||||||||
\(496\) | 2196.37 | 0.198830 | ||||||||
\(497\) | −1007.00 | −0.0908859 | ||||||||
\(498\) | 21478.0 | 1.93264 | ||||||||
\(499\) | −9708.83 | −0.870996 | −0.435498 | − | 0.900190i | \(-0.643428\pi\) | ||||
−0.435498 | + | 0.900190i | \(0.643428\pi\) | |||||||
\(500\) | −15652.3 | −1.39998 | ||||||||
\(501\) | −13693.2 | −1.22109 | ||||||||
\(502\) | 14857.8 | 1.32099 | ||||||||
\(503\) | −5971.16 | −0.529306 | −0.264653 | − | 0.964344i | \(-0.585257\pi\) | ||||
−0.264653 | + | 0.964344i | \(0.585257\pi\) | |||||||
\(504\) | −1493.10 | −0.131960 | ||||||||
\(505\) | −10587.1 | −0.932912 | ||||||||
\(506\) | −4100.04 | −0.360215 | ||||||||
\(507\) | 9399.95 | 0.823405 | ||||||||
\(508\) | −15915.3 | −1.39002 | ||||||||
\(509\) | −10850.7 | −0.944887 | −0.472443 | − | 0.881361i | \(-0.656628\pi\) | ||||
−0.472443 | + | 0.881361i | \(0.656628\pi\) | |||||||
\(510\) | 8349.29 | 0.724927 | ||||||||
\(511\) | −6190.92 | −0.535949 | ||||||||
\(512\) | 11801.9 | 1.01870 | ||||||||
\(513\) | −6108.05 | −0.525686 | ||||||||
\(514\) | −2099.14 | −0.180134 | ||||||||
\(515\) | −5845.60 | −0.500170 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 463.791 | 0.0394536 | ||||||||
\(518\) | −9965.54 | −0.845291 | ||||||||
\(519\) | 1573.72 | 0.133100 | ||||||||
\(520\) | 396.514 | 0.0334390 | ||||||||
\(521\) | 13234.7 | 1.11290 | 0.556450 | − | 0.830881i | \(-0.312163\pi\) | ||||
0.556450 | + | 0.830881i | \(0.312163\pi\) | |||||||
\(522\) | 8988.31 | 0.753655 | ||||||||
\(523\) | 15760.1 | 1.31767 | 0.658836 | − | 0.752286i | \(-0.271049\pi\) | ||||
0.658836 | + | 0.752286i | \(0.271049\pi\) | |||||||
\(524\) | 25135.9 | 2.09555 | ||||||||
\(525\) | 4416.74 | 0.367166 | ||||||||
\(526\) | −5705.00 | −0.472908 | ||||||||
\(527\) | 3719.64 | 0.307457 | ||||||||
\(528\) | −693.892 | −0.0571928 | ||||||||
\(529\) | 29932.4 | 2.46013 | ||||||||
\(530\) | 18590.0 | 1.52358 | ||||||||
\(531\) | −6105.24 | −0.498955 | ||||||||
\(532\) | −6502.46 | −0.529920 | ||||||||
\(533\) | −1298.94 | −0.105560 | ||||||||
\(534\) | −18261.1 | −1.47984 | ||||||||
\(535\) | −4240.32 | −0.342663 | ||||||||
\(536\) | −727.756 | −0.0586461 | ||||||||
\(537\) | −9898.27 | −0.795423 | ||||||||
\(538\) | −8602.31 | −0.689353 | ||||||||
\(539\) | 523.130 | 0.0418048 | ||||||||
\(540\) | 12413.3 | 0.989226 | ||||||||
\(541\) | −8717.14 | −0.692753 | −0.346376 | − | 0.938096i | \(-0.612588\pi\) | ||||
−0.346376 | + | 0.938096i | \(0.612588\pi\) | |||||||
\(542\) | 31065.3 | 2.46194 | ||||||||
\(543\) | −4272.79 | −0.337685 | ||||||||
\(544\) | 14431.5 | 1.13740 | ||||||||
\(545\) | 2344.41 | 0.184263 | ||||||||
\(546\) | −1256.62 | −0.0984952 | ||||||||
\(547\) | 13375.8 | 1.04553 | 0.522766 | − | 0.852476i | \(-0.324900\pi\) | ||||
0.522766 | + | 0.852476i | \(0.324900\pi\) | |||||||
\(548\) | −10897.9 | −0.849514 | ||||||||
\(549\) | 7760.11 | 0.603267 | ||||||||
\(550\) | 1348.79 | 0.104568 | ||||||||
\(551\) | 9939.88 | 0.768517 | ||||||||
\(552\) | −10436.5 | −0.804720 | ||||||||
\(553\) | 8843.48 | 0.680042 | ||||||||
\(554\) | 15021.9 | 1.15202 | ||||||||
\(555\) | 4974.63 | 0.380471 | ||||||||
\(556\) | 17556.2 | 1.33911 | ||||||||
\(557\) | 18892.9 | 1.43720 | 0.718598 | − | 0.695426i | \(-0.244784\pi\) | ||||
0.718598 | + | 0.695426i | \(0.244784\pi\) | |||||||
\(558\) | 2283.22 | 0.173220 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4000.02 | −0.301843 | ||||||||
\(561\) | −1175.13 | −0.0884389 | ||||||||
\(562\) | 10214.8 | 0.766698 | ||||||||
\(563\) | −24531.2 | −1.83635 | −0.918177 | − | 0.396170i | \(-0.870339\pi\) | ||||
−0.918177 | + | 0.396170i | \(0.870339\pi\) | |||||||
\(564\) | 4649.17 | 0.347102 | ||||||||
\(565\) | 12506.1 | 0.931214 | ||||||||
\(566\) | −15508.7 | −1.15173 | ||||||||
\(567\) | −6567.80 | −0.486458 | ||||||||
\(568\) | −782.778 | −0.0578251 | ||||||||
\(569\) | 18497.1 | 1.36281 | 0.681403 | − | 0.731908i | \(-0.261370\pi\) | ||||
0.681403 | + | 0.731908i | \(0.261370\pi\) | |||||||
\(570\) | 5667.60 | 0.416473 | ||||||||
\(571\) | 4775.61 | 0.350006 | 0.175003 | − | 0.984568i | \(-0.444007\pi\) | ||||
0.175003 | + | 0.984568i | \(0.444007\pi\) | |||||||
\(572\) | −219.778 | −0.0160653 | ||||||||
\(573\) | −6578.46 | −0.479614 | ||||||||
\(574\) | −19194.0 | −1.39572 | ||||||||
\(575\) | −13849.4 | −1.00445 | ||||||||
\(576\) | 6530.46 | 0.472400 | ||||||||
\(577\) | 17822.1 | 1.28586 | 0.642932 | − | 0.765923i | \(-0.277718\pi\) | ||||
0.642932 | + | 0.765923i | \(0.277718\pi\) | |||||||
\(578\) | −6226.41 | −0.448070 | ||||||||
\(579\) | 3430.15 | 0.246204 | ||||||||
\(580\) | −20200.6 | −1.44618 | ||||||||
\(581\) | −17426.2 | −1.24434 | ||||||||
\(582\) | −4758.10 | −0.338883 | ||||||||
\(583\) | −2616.48 | −0.185872 | ||||||||
\(584\) | −4812.41 | −0.340991 | ||||||||
\(585\) | −281.403 | −0.0198881 | ||||||||
\(586\) | −947.054 | −0.0667618 | ||||||||
\(587\) | 8344.83 | 0.586760 | 0.293380 | − | 0.955996i | \(-0.405220\pi\) | ||||
0.293380 | + | 0.955996i | \(0.405220\pi\) | |||||||
\(588\) | 5244.00 | 0.367787 | ||||||||
\(589\) | 2524.94 | 0.176635 | ||||||||
\(590\) | 23958.0 | 1.67176 | ||||||||
\(591\) | 23155.1 | 1.61163 | ||||||||
\(592\) | 5288.53 | 0.367158 | ||||||||
\(593\) | −12261.2 | −0.849084 | −0.424542 | − | 0.905408i | \(-0.639565\pi\) | ||||
−0.424542 | + | 0.905408i | \(0.639565\pi\) | |||||||
\(594\) | −3050.60 | −0.210720 | ||||||||
\(595\) | −6774.20 | −0.466748 | ||||||||
\(596\) | −23490.0 | −1.61441 | ||||||||
\(597\) | 17520.8 | 1.20114 | ||||||||
\(598\) | 3940.34 | 0.269452 | ||||||||
\(599\) | 20681.9 | 1.41075 | 0.705374 | − | 0.708835i | \(-0.250779\pi\) | ||||
0.705374 | + | 0.708835i | \(0.250779\pi\) | |||||||
\(600\) | 3433.28 | 0.233605 | ||||||||
\(601\) | 7757.58 | 0.526519 | 0.263260 | − | 0.964725i | \(-0.415202\pi\) | ||||
0.263260 | + | 0.964725i | \(0.415202\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 516.482 | 0.0348802 | ||||||||
\(604\) | −32093.4 | −2.16203 | ||||||||
\(605\) | −9931.22 | −0.667375 | ||||||||
\(606\) | 26081.4 | 1.74832 | ||||||||
\(607\) | 1766.42 | 0.118116 | 0.0590582 | − | 0.998255i | \(-0.481190\pi\) | ||||
0.0590582 | + | 0.998255i | \(0.481190\pi\) | |||||||
\(608\) | 9796.31 | 0.653442 | ||||||||
\(609\) | 16256.3 | 1.08167 | ||||||||
\(610\) | −30452.0 | −2.02126 | ||||||||
\(611\) | −445.726 | −0.0295125 | ||||||||
\(612\) | 5284.51 | 0.349042 | ||||||||
\(613\) | 10071.3 | 0.663584 | 0.331792 | − | 0.943352i | \(-0.392347\pi\) | ||||
0.331792 | + | 0.943352i | \(0.392347\pi\) | |||||||
\(614\) | −10601.6 | −0.696816 | ||||||||
\(615\) | 9581.32 | 0.628221 | ||||||||
\(616\) | −824.658 | −0.0539390 | ||||||||
\(617\) | 21039.4 | 1.37280 | 0.686399 | − | 0.727225i | \(-0.259191\pi\) | ||||
0.686399 | + | 0.727225i | \(0.259191\pi\) | |||||||
\(618\) | 14400.6 | 0.937344 | ||||||||
\(619\) | 9690.78 | 0.629249 | 0.314625 | − | 0.949216i | \(-0.398121\pi\) | ||||
0.314625 | + | 0.949216i | \(0.398121\pi\) | |||||||
\(620\) | −5131.38 | −0.332389 | ||||||||
\(621\) | 31323.8 | 2.02412 | ||||||||
\(622\) | −3543.40 | −0.228420 | ||||||||
\(623\) | 14816.2 | 0.952804 | ||||||||
\(624\) | 666.865 | 0.0427820 | ||||||||
\(625\) | −2631.66 | −0.168426 | ||||||||
\(626\) | −8605.76 | −0.549449 | ||||||||
\(627\) | −797.696 | −0.0508085 | ||||||||
\(628\) | −13688.9 | −0.869821 | ||||||||
\(629\) | 8956.34 | 0.567747 | ||||||||
\(630\) | −4158.20 | −0.262963 | ||||||||
\(631\) | −20307.8 | −1.28121 | −0.640603 | − | 0.767872i | \(-0.721316\pi\) | ||||
−0.640603 | + | 0.767872i | \(0.721316\pi\) | |||||||
\(632\) | 6874.34 | 0.432668 | ||||||||
\(633\) | −5777.92 | −0.362799 | ||||||||
\(634\) | −17507.4 | −1.09670 | ||||||||
\(635\) | −11255.0 | −0.703372 | ||||||||
\(636\) | −26228.3 | −1.63525 | ||||||||
\(637\) | −502.754 | −0.0312713 | ||||||||
\(638\) | 4964.37 | 0.308058 | ||||||||
\(639\) | 555.531 | 0.0343919 | ||||||||
\(640\) | −10773.2 | −0.665390 | ||||||||
\(641\) | 29060.8 | 1.79069 | 0.895344 | − | 0.445374i | \(-0.146929\pi\) | ||||
0.895344 | + | 0.445374i | \(0.146929\pi\) | |||||||
\(642\) | 10446.0 | 0.642168 | ||||||||
\(643\) | 13231.3 | 0.811494 | 0.405747 | − | 0.913985i | \(-0.367011\pi\) | ||||
0.405747 | + | 0.913985i | \(0.367011\pi\) | |||||||
\(644\) | 33346.4 | 2.04042 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10204.0 | 0.621471 | ||||||||
\(647\) | 25154.9 | 1.52850 | 0.764252 | − | 0.644918i | \(-0.223109\pi\) | ||||
0.764252 | + | 0.644918i | \(0.223109\pi\) | |||||||
\(648\) | −5105.37 | −0.309503 | ||||||||
\(649\) | −3372.01 | −0.203949 | ||||||||
\(650\) | −1296.25 | −0.0782203 | ||||||||
\(651\) | 4129.45 | 0.248611 | ||||||||
\(652\) | −12053.2 | −0.723990 | ||||||||
\(653\) | −6734.12 | −0.403563 | −0.201781 | − | 0.979431i | \(-0.564673\pi\) | ||||
−0.201781 | + | 0.979431i | \(0.564673\pi\) | |||||||
\(654\) | −5775.46 | −0.345319 | ||||||||
\(655\) | 17775.6 | 1.06038 | ||||||||
\(656\) | 10185.9 | 0.606239 | ||||||||
\(657\) | 3415.32 | 0.202807 | ||||||||
\(658\) | −6586.36 | −0.390217 | ||||||||
\(659\) | −3685.41 | −0.217850 | −0.108925 | − | 0.994050i | \(-0.534741\pi\) | ||||
−0.108925 | + | 0.994050i | \(0.534741\pi\) | |||||||
\(660\) | 1621.14 | 0.0956103 | ||||||||
\(661\) | 3938.81 | 0.231773 | 0.115887 | − | 0.993262i | \(-0.463029\pi\) | ||||
0.115887 | + | 0.993262i | \(0.463029\pi\) | |||||||
\(662\) | 48450.9 | 2.84456 | ||||||||
\(663\) | 1129.36 | 0.0661551 | ||||||||
\(664\) | −13546.0 | −0.791695 | ||||||||
\(665\) | −4598.41 | −0.268149 | ||||||||
\(666\) | 5497.66 | 0.319865 | ||||||||
\(667\) | −50974.4 | −2.95913 | ||||||||
\(668\) | 34010.0 | 1.96989 | ||||||||
\(669\) | 1444.99 | 0.0835076 | ||||||||
\(670\) | −2026.76 | −0.116867 | ||||||||
\(671\) | 4286.02 | 0.246587 | ||||||||
\(672\) | 16021.5 | 0.919708 | ||||||||
\(673\) | 31975.1 | 1.83143 | 0.915714 | − | 0.401831i | \(-0.131626\pi\) | ||||
0.915714 | + | 0.401831i | \(0.131626\pi\) | |||||||
\(674\) | 39248.7 | 2.24303 | ||||||||
\(675\) | −10304.6 | −0.587589 | ||||||||
\(676\) | −23346.9 | −1.32834 | ||||||||
\(677\) | 10683.3 | 0.606487 | 0.303244 | − | 0.952913i | \(-0.401930\pi\) | ||||
0.303244 | + | 0.952913i | \(0.401930\pi\) | |||||||
\(678\) | −30808.8 | −1.74514 | ||||||||
\(679\) | 3860.49 | 0.218191 | ||||||||
\(680\) | −5265.81 | −0.296963 | ||||||||
\(681\) | −5703.80 | −0.320954 | ||||||||
\(682\) | 1261.06 | 0.0708039 | ||||||||
\(683\) | −15614.9 | −0.874800 | −0.437400 | − | 0.899267i | \(-0.644101\pi\) | ||||
−0.437400 | + | 0.899267i | \(0.644101\pi\) | |||||||
\(684\) | 3587.19 | 0.200526 | ||||||||
\(685\) | −7706.75 | −0.429868 | ||||||||
\(686\) | −29923.8 | −1.66545 | ||||||||
\(687\) | 7938.21 | 0.440847 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2514.57 | 0.139038 | ||||||||
\(690\) | −29065.0 | −1.60360 | ||||||||
\(691\) | 25222.6 | 1.38858 | 0.694292 | − | 0.719693i | \(-0.255717\pi\) | ||||
0.694292 | + | 0.719693i | \(0.255717\pi\) | |||||||
\(692\) | −3908.70 | −0.214720 | ||||||||
\(693\) | 585.252 | 0.0320807 | ||||||||
\(694\) | −10424.8 | −0.570201 | ||||||||
\(695\) | 12415.4 | 0.677614 | ||||||||
\(696\) | 12636.6 | 0.688202 | ||||||||
\(697\) | 17250.2 | 0.937445 | ||||||||
\(698\) | 46065.9 | 2.49802 | ||||||||
\(699\) | −10662.3 | −0.576948 | ||||||||
\(700\) | −10970.0 | −0.592322 | ||||||||
\(701\) | −4178.65 | −0.225143 | −0.112572 | − | 0.993644i | \(-0.535909\pi\) | ||||
−0.112572 | + | 0.993644i | \(0.535909\pi\) | |||||||
\(702\) | 2931.78 | 0.157625 | ||||||||
\(703\) | 6079.68 | 0.326173 | ||||||||
\(704\) | 3606.86 | 0.193095 | ||||||||
\(705\) | 3287.80 | 0.175639 | ||||||||
\(706\) | 27752.3 | 1.47942 | ||||||||
\(707\) | −21161.1 | −1.12567 | ||||||||
\(708\) | −33802.0 | −1.79429 | ||||||||
\(709\) | −27765.1 | −1.47072 | −0.735360 | − | 0.677677i | \(-0.762987\pi\) | ||||
−0.735360 | + | 0.677677i | \(0.762987\pi\) | |||||||
\(710\) | −2180.00 | −0.115231 | ||||||||
\(711\) | −4878.65 | −0.257333 | ||||||||
\(712\) | 11517.1 | 0.606210 | ||||||||
\(713\) | −12948.6 | −0.680124 | ||||||||
\(714\) | 16688.3 | 0.874709 | ||||||||
\(715\) | −155.423 | −0.00812933 | ||||||||
\(716\) | 24584.6 | 1.28320 | ||||||||
\(717\) | 28034.2 | 1.46019 | ||||||||
\(718\) | 14835.4 | 0.771101 | ||||||||
\(719\) | −25705.2 | −1.33330 | −0.666649 | − | 0.745372i | \(-0.732272\pi\) | ||||
−0.666649 | + | 0.745372i | \(0.732272\pi\) | |||||||
\(720\) | 2206.68 | 0.114220 | ||||||||
\(721\) | −11684.0 | −0.603514 | ||||||||
\(722\) | −22752.2 | −1.17278 | ||||||||
\(723\) | 2357.69 | 0.121277 | ||||||||
\(724\) | 10612.4 | 0.544763 | ||||||||
\(725\) | 16769.0 | 0.859015 | ||||||||
\(726\) | 24465.6 | 1.25069 | ||||||||
\(727\) | −27877.2 | −1.42216 | −0.711080 | − | 0.703111i | \(-0.751793\pi\) | ||||
−0.711080 | + | 0.703111i | \(0.751793\pi\) | |||||||
\(728\) | 792.538 | 0.0403481 | ||||||||
\(729\) | 21418.6 | 1.08818 | ||||||||
\(730\) | −13402.3 | −0.679509 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 42964.2 | 2.16940 | ||||||||
\(733\) | −1914.75 | −0.0964841 | −0.0482420 | − | 0.998836i | \(-0.515362\pi\) | ||||
−0.0482420 | + | 0.998836i | \(0.515362\pi\) | |||||||
\(734\) | −43289.2 | −2.17689 | ||||||||
\(735\) | 3708.45 | 0.186106 | ||||||||
\(736\) | −50238.2 | −2.51604 | ||||||||
\(737\) | 285.260 | 0.0142574 | ||||||||
\(738\) | 10588.7 | 0.528151 | ||||||||
\(739\) | 397.742 | 0.0197986 | 0.00989932 | − | 0.999951i | \(-0.496849\pi\) | ||||
0.00989932 | + | 0.999951i | \(0.496849\pi\) | |||||||
\(740\) | −12355.6 | −0.613785 | ||||||||
\(741\) | 766.626 | 0.0380064 | ||||||||
\(742\) | 37157.0 | 1.83838 | ||||||||
\(743\) | −9023.68 | −0.445554 | −0.222777 | − | 0.974869i | \(-0.571512\pi\) | ||||
−0.222777 | + | 0.974869i | \(0.571512\pi\) | |||||||
\(744\) | 3209.96 | 0.158176 | ||||||||
\(745\) | −16611.7 | −0.816919 | ||||||||
\(746\) | −26691.8 | −1.30999 | ||||||||
\(747\) | 9613.45 | 0.470867 | ||||||||
\(748\) | 2918.71 | 0.142672 | ||||||||
\(749\) | −8475.39 | −0.413463 | ||||||||
\(750\) | 27268.4 | 1.32760 | ||||||||
\(751\) | −19915.2 | −0.967665 | −0.483832 | − | 0.875161i | \(-0.660756\pi\) | ||||
−0.483832 | + | 0.875161i | \(0.660756\pi\) | |||||||
\(752\) | 3495.26 | 0.169493 | ||||||||
\(753\) | −14824.4 | −0.717437 | ||||||||
\(754\) | −4771.01 | −0.230438 | ||||||||
\(755\) | −22695.8 | −1.09402 | ||||||||
\(756\) | 24811.2 | 1.19362 | ||||||||
\(757\) | −24897.3 | −1.19539 | −0.597694 | − | 0.801724i | \(-0.703916\pi\) | ||||
−0.597694 | + | 0.801724i | \(0.703916\pi\) | |||||||
\(758\) | 55362.6 | 2.65285 | ||||||||
\(759\) | 4090.81 | 0.195635 | ||||||||
\(760\) | −3574.50 | −0.170606 | ||||||||
\(761\) | −34554.9 | −1.64601 | −0.823006 | − | 0.568033i | \(-0.807705\pi\) | ||||
−0.823006 | + | 0.568033i | \(0.807705\pi\) | |||||||
\(762\) | 27726.7 | 1.31815 | ||||||||
\(763\) | 4685.93 | 0.222335 | ||||||||
\(764\) | 16339.1 | 0.773726 | ||||||||
\(765\) | 3737.10 | 0.176621 | ||||||||
\(766\) | 14979.6 | 0.706574 | ||||||||
\(767\) | 3240.67 | 0.152560 | ||||||||
\(768\) | −435.191 | −0.0204474 | ||||||||
\(769\) | −12520.7 | −0.587138 | −0.293569 | − | 0.955938i | \(-0.594843\pi\) | ||||
−0.293569 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(770\) | −2296.63 | −0.107487 | ||||||||
\(771\) | 2094.41 | 0.0978319 | ||||||||
\(772\) | −8519.54 | −0.397183 | ||||||||
\(773\) | −23875.0 | −1.11090 | −0.555450 | − | 0.831550i | \(-0.687454\pi\) | ||||
−0.555450 | + | 0.831550i | \(0.687454\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4259.69 | 0.197435 | ||||||||
\(776\) | 3000.89 | 0.138822 | ||||||||
\(777\) | 9943.10 | 0.459082 | ||||||||
\(778\) | 58387.4 | 2.69060 | ||||||||
\(779\) | 11709.7 | 0.538566 | ||||||||
\(780\) | −1558.00 | −0.0715196 | ||||||||
\(781\) | 306.827 | 0.0140578 | ||||||||
\(782\) | −52328.8 | −2.39293 | ||||||||
\(783\) | −37927.2 | −1.73104 | ||||||||
\(784\) | 3942.46 | 0.179594 | ||||||||
\(785\) | −9680.53 | −0.440144 | ||||||||
\(786\) | −43790.2 | −1.98721 | ||||||||
\(787\) | 3612.43 | 0.163620 | 0.0818102 | − | 0.996648i | \(-0.473930\pi\) | ||||
0.0818102 | + | 0.996648i | \(0.473930\pi\) | |||||||
\(788\) | −57510.8 | −2.59992 | ||||||||
\(789\) | 5692.15 | 0.256839 | ||||||||
\(790\) | 19144.7 | 0.862198 | ||||||||
\(791\) | 24996.7 | 1.12362 | ||||||||
\(792\) | 454.936 | 0.0204109 | ||||||||
\(793\) | −4119.08 | −0.184455 | ||||||||
\(794\) | −36071.6 | −1.61226 | ||||||||
\(795\) | −18548.1 | −0.827465 | ||||||||
\(796\) | −43516.8 | −1.93770 | ||||||||
\(797\) | 14565.8 | 0.647363 | 0.323682 | − | 0.946166i | \(-0.395079\pi\) | ||||
0.323682 | + | 0.946166i | \(0.395079\pi\) | |||||||
\(798\) | 11328.2 | 0.502524 | ||||||||
\(799\) | 5919.36 | 0.262093 | ||||||||
\(800\) | 16526.8 | 0.730389 | ||||||||
\(801\) | −8173.58 | −0.360549 | ||||||||
\(802\) | −7077.16 | −0.311600 | ||||||||
\(803\) | 1886.33 | 0.0828981 | ||||||||
\(804\) | 2859.53 | 0.125433 | ||||||||
\(805\) | 23581.9 | 1.03249 | ||||||||
\(806\) | −1211.94 | −0.0529636 | ||||||||
\(807\) | 8582.94 | 0.374391 | ||||||||
\(808\) | −16449.3 | −0.716192 | ||||||||
\(809\) | −22200.5 | −0.964806 | −0.482403 | − | 0.875949i | \(-0.660236\pi\) | ||||
−0.482403 | + | 0.875949i | \(0.660236\pi\) | |||||||
\(810\) | −14218.2 | −0.616761 | ||||||||
\(811\) | 805.377 | 0.0348713 | 0.0174356 | − | 0.999848i | \(-0.494450\pi\) | ||||
0.0174356 | + | 0.999848i | \(0.494450\pi\) | |||||||
\(812\) | −40376.2 | −1.74498 | ||||||||
\(813\) | −30995.4 | −1.33709 | ||||||||
\(814\) | 3036.43 | 0.130746 | ||||||||
\(815\) | −8523.81 | −0.366351 | ||||||||
\(816\) | −8856.15 | −0.379935 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 59230.3 | 2.53171 | ||||||||
\(819\) | −562.457 | −0.0239974 | ||||||||
\(820\) | −23797.3 | −1.01346 | ||||||||
\(821\) | −30715.5 | −1.30570 | −0.652848 | − | 0.757489i | \(-0.726426\pi\) | ||||
−0.652848 | + | 0.757489i | \(0.726426\pi\) | |||||||
\(822\) | 18985.6 | 0.805594 | ||||||||
\(823\) | −10776.3 | −0.456424 | −0.228212 | − | 0.973611i | \(-0.573288\pi\) | ||||
−0.228212 | + | 0.973611i | \(0.573288\pi\) | |||||||
\(824\) | −9082.34 | −0.383978 | ||||||||
\(825\) | −1345.75 | −0.0567915 | ||||||||
\(826\) | 47886.4 | 2.01717 | ||||||||
\(827\) | −26112.2 | −1.09796 | −0.548978 | − | 0.835837i | \(-0.684983\pi\) | ||||
−0.548978 | + | 0.835837i | \(0.684983\pi\) | |||||||
\(828\) | −18396.1 | −0.772112 | ||||||||
\(829\) | −44126.9 | −1.84872 | −0.924362 | − | 0.381518i | \(-0.875402\pi\) | ||||
−0.924362 | + | 0.381518i | \(0.875402\pi\) | |||||||
\(830\) | −37724.8 | −1.57765 | ||||||||
\(831\) | −14988.1 | −0.625669 | ||||||||
\(832\) | −3466.38 | −0.144441 | ||||||||
\(833\) | 6676.71 | 0.277712 | ||||||||
\(834\) | −30585.3 | −1.26988 | ||||||||
\(835\) | 24051.2 | 0.996797 | ||||||||
\(836\) | 1981.26 | 0.0819655 | ||||||||
\(837\) | −9634.30 | −0.397862 | ||||||||
\(838\) | −1097.68 | −0.0452491 | ||||||||
\(839\) | −2366.99 | −0.0973986 | −0.0486993 | − | 0.998813i | \(-0.515508\pi\) | ||||
−0.0486993 | + | 0.998813i | \(0.515508\pi\) | |||||||
\(840\) | −5845.97 | −0.240125 | ||||||||
\(841\) | 37331.4 | 1.53066 | ||||||||
\(842\) | 49403.4 | 2.02203 | ||||||||
\(843\) | −10191.8 | −0.416398 | ||||||||
\(844\) | 14350.8 | 0.585277 | ||||||||
\(845\) | −16510.4 | −0.672161 | ||||||||
\(846\) | 3633.48 | 0.147661 | ||||||||
\(847\) | −19850.2 | −0.805265 | ||||||||
\(848\) | −19718.5 | −0.798511 | ||||||||
\(849\) | 15473.8 | 0.625512 | ||||||||
\(850\) | 17214.6 | 0.694653 | ||||||||
\(851\) | −31178.3 | −1.25591 | ||||||||
\(852\) | 3075.72 | 0.123677 | ||||||||
\(853\) | −24301.3 | −0.975452 | −0.487726 | − | 0.872997i | \(-0.662173\pi\) | ||||
−0.487726 | + | 0.872997i | \(0.662173\pi\) | |||||||
\(854\) | −60866.4 | −2.43888 | ||||||||
\(855\) | 2536.79 | 0.101469 | ||||||||
\(856\) | −6588.21 | −0.263061 | ||||||||
\(857\) | −40357.3 | −1.60861 | −0.804304 | − | 0.594218i | \(-0.797462\pi\) | ||||
−0.804304 | + | 0.594218i | \(0.797462\pi\) | |||||||
\(858\) | 382.884 | 0.0152348 | ||||||||
\(859\) | −10352.8 | −0.411212 | −0.205606 | − | 0.978635i | \(-0.565917\pi\) | ||||
−0.205606 | + | 0.978635i | \(0.565917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19150.8 | 0.758022 | ||||||||
\(862\) | −20436.8 | −0.807516 | ||||||||
\(863\) | −15149.6 | −0.597563 | −0.298781 | − | 0.954322i | \(-0.596580\pi\) | ||||
−0.298781 | + | 0.954322i | \(0.596580\pi\) | |||||||
\(864\) | −37379.4 | −1.47184 | ||||||||
\(865\) | −2764.15 | −0.108652 | ||||||||
\(866\) | 22635.9 | 0.888220 | ||||||||
\(867\) | 6212.39 | 0.243349 | ||||||||
\(868\) | −10256.4 | −0.401066 | ||||||||
\(869\) | −2694.55 | −0.105186 | ||||||||
\(870\) | 35192.2 | 1.37141 | ||||||||
\(871\) | −274.149 | −0.0106650 | ||||||||
\(872\) | 3642.53 | 0.141458 | ||||||||
\(873\) | −2129.70 | −0.0825653 | ||||||||
\(874\) | −35521.4 | −1.37475 | ||||||||
\(875\) | −22124.2 | −0.854784 | ||||||||
\(876\) | 18909.1 | 0.729314 | ||||||||
\(877\) | 19411.3 | 0.747405 | 0.373703 | − | 0.927549i | \(-0.378088\pi\) | ||||
0.373703 | + | 0.927549i | \(0.378088\pi\) | |||||||
\(878\) | 53040.8 | 2.03877 | ||||||||
\(879\) | 944.921 | 0.0362587 | ||||||||
\(880\) | 1218.78 | 0.0466876 | ||||||||
\(881\) | −44659.5 | −1.70785 | −0.853926 | − | 0.520394i | \(-0.825785\pi\) | ||||
−0.853926 | + | 0.520394i | \(0.825785\pi\) | |||||||
\(882\) | 4098.36 | 0.156461 | ||||||||
\(883\) | 21280.2 | 0.811024 | 0.405512 | − | 0.914090i | \(-0.367093\pi\) | ||||
0.405512 | + | 0.914090i | \(0.367093\pi\) | |||||||
\(884\) | −2805.03 | −0.106723 | ||||||||
\(885\) | −23904.1 | −0.907940 | ||||||||
\(886\) | −65182.7 | −2.47162 | ||||||||
\(887\) | 12849.9 | 0.486423 | 0.243211 | − | 0.969973i | \(-0.421799\pi\) | ||||
0.243211 | + | 0.969973i | \(0.421799\pi\) | |||||||
\(888\) | 7729.11 | 0.292085 | ||||||||
\(889\) | −22496.1 | −0.848700 | ||||||||
\(890\) | 32074.5 | 1.20802 | ||||||||
\(891\) | 2001.16 | 0.0752430 | ||||||||
\(892\) | −3588.96 | −0.134717 | ||||||||
\(893\) | 4018.14 | 0.150573 | ||||||||
\(894\) | 40922.9 | 1.53095 | ||||||||
\(895\) | 17385.7 | 0.649319 | ||||||||
\(896\) | −21533.1 | −0.802870 | ||||||||
\(897\) | −3931.47 | −0.146341 | ||||||||
\(898\) | 4361.40 | 0.162073 | ||||||||
\(899\) | 15678.3 | 0.581646 | ||||||||
\(900\) | 6051.76 | 0.224139 | ||||||||
\(901\) | −33394.1 | −1.23476 | ||||||||
\(902\) | 5848.28 | 0.215883 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19430.8 | 0.714888 | ||||||||
\(905\) | 7504.90 | 0.275659 | ||||||||
\(906\) | 55911.2 | 2.05025 | ||||||||
\(907\) | 38267.7 | 1.40094 | 0.700472 | − | 0.713680i | \(-0.252973\pi\) | ||||
0.700472 | + | 0.713680i | \(0.252973\pi\) | |||||||
\(908\) | 14166.6 | 0.517772 | ||||||||
\(909\) | 11673.9 | 0.425961 | ||||||||
\(910\) | 2207.18 | 0.0804035 | ||||||||
\(911\) | 33801.3 | 1.22929 | 0.614646 | − | 0.788803i | \(-0.289299\pi\) | ||||
0.614646 | + | 0.788803i | \(0.289299\pi\) | |||||||
\(912\) | −6011.67 | −0.218274 | ||||||||
\(913\) | 5309.64 | 0.192468 | ||||||||
\(914\) | −11119.7 | −0.402415 | ||||||||
\(915\) | 30383.4 | 1.09775 | ||||||||
\(916\) | −19716.3 | −0.711185 | ||||||||
\(917\) | 35529.2 | 1.27947 | ||||||||
\(918\) | −38934.9 | −1.39983 | ||||||||
\(919\) | 18924.2 | 0.679274 | 0.339637 | − | 0.940557i | \(-0.389696\pi\) | ||||
0.339637 | + | 0.940557i | \(0.389696\pi\) | |||||||
\(920\) | 18331.0 | 0.656908 | ||||||||
\(921\) | 10577.7 | 0.378445 | ||||||||
\(922\) | −11399.1 | −0.407170 | ||||||||
\(923\) | −294.876 | −0.0105157 | ||||||||
\(924\) | 3240.28 | 0.115365 | ||||||||
\(925\) | 10256.7 | 0.364582 | ||||||||
\(926\) | 40932.2 | 1.45261 | ||||||||
\(927\) | 6445.65 | 0.228374 | ||||||||
\(928\) | 60828.9 | 2.15173 | ||||||||
\(929\) | −47171.0 | −1.66591 | −0.832955 | − | 0.553340i | \(-0.813353\pi\) | ||||
−0.832955 | + | 0.553340i | \(0.813353\pi\) | |||||||
\(930\) | 8939.58 | 0.315205 | ||||||||
\(931\) | 4532.23 | 0.159547 | ||||||||
\(932\) | 26482.3 | 0.930747 | ||||||||
\(933\) | 3535.42 | 0.124056 | ||||||||
\(934\) | 19599.6 | 0.686638 | ||||||||
\(935\) | 2064.05 | 0.0721944 | ||||||||
\(936\) | −437.217 | −0.0152680 | ||||||||
\(937\) | −39747.2 | −1.38579 | −0.692894 | − | 0.721039i | \(-0.743665\pi\) | ||||
−0.692894 | + | 0.721039i | \(0.743665\pi\) | |||||||
\(938\) | −4051.02 | −0.141013 | ||||||||
\(939\) | 8586.38 | 0.298409 | ||||||||
\(940\) | −8165.98 | −0.283346 | ||||||||
\(941\) | 9781.20 | 0.338850 | 0.169425 | − | 0.985543i | \(-0.445809\pi\) | ||||
0.169425 | + | 0.985543i | \(0.445809\pi\) | |||||||
\(942\) | 23848.0 | 0.824852 | ||||||||
\(943\) | −60050.5 | −2.07371 | ||||||||
\(944\) | −25412.4 | −0.876170 | ||||||||
\(945\) | 17546.0 | 0.603990 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33077.2 | 1.13502 | 0.567511 | − | 0.823366i | \(-0.307906\pi\) | ||||
0.567511 | + | 0.823366i | \(0.307906\pi\) | |||||||
\(948\) | −27010.9 | −0.925393 | ||||||||
\(949\) | −1812.86 | −0.0620104 | ||||||||
\(950\) | 11685.5 | 0.399081 | ||||||||
\(951\) | 17468.0 | 0.595623 | ||||||||
\(952\) | −10525.1 | −0.358320 | ||||||||
\(953\) | 4221.07 | 0.143477 | 0.0717386 | − | 0.997423i | \(-0.477145\pi\) | ||||
0.0717386 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(954\) | −20498.3 | −0.695657 | ||||||||
\(955\) | 11554.7 | 0.391518 | ||||||||
\(956\) | −69629.2 | −2.35561 | ||||||||
\(957\) | −4953.19 | −0.167308 | ||||||||
\(958\) | −63887.6 | −2.15461 | ||||||||
\(959\) | −15404.0 | −0.518686 | ||||||||
\(960\) | 25568.9 | 0.859618 | ||||||||
\(961\) | −25808.4 | −0.866315 | ||||||||
\(962\) | −2918.16 | −0.0978019 | ||||||||
\(963\) | 4675.59 | 0.156458 | ||||||||
\(964\) | −5855.86 | −0.195648 | ||||||||
\(965\) | −6024.85 | −0.200981 | ||||||||
\(966\) | −58094.1 | −1.93493 | ||||||||
\(967\) | 17701.1 | 0.588655 | 0.294328 | − | 0.955705i | \(-0.404904\pi\) | ||||
0.294328 | + | 0.955705i | \(0.404904\pi\) | |||||||
\(968\) | −15430.2 | −0.512340 | ||||||||
\(969\) | −10181.0 | −0.337524 | ||||||||
\(970\) | 8357.32 | 0.276636 | ||||||||
\(971\) | 22881.9 | 0.756248 | 0.378124 | − | 0.925755i | \(-0.376569\pi\) | ||||
0.378124 | + | 0.925755i | \(0.376569\pi\) | |||||||
\(972\) | −24138.5 | −0.796547 | ||||||||
\(973\) | 24815.4 | 0.817620 | ||||||||
\(974\) | −27026.7 | −0.889108 | ||||||||
\(975\) | 1293.33 | 0.0424819 | ||||||||
\(976\) | 32300.7 | 1.05934 | ||||||||
\(977\) | 27596.4 | 0.903671 | 0.451835 | − | 0.892101i | \(-0.350769\pi\) | ||||
0.451835 | + | 0.892101i | \(0.350769\pi\) | |||||||
\(978\) | 20998.4 | 0.686560 | ||||||||
\(979\) | −4514.38 | −0.147375 | ||||||||
\(980\) | −9210.76 | −0.300232 | ||||||||
\(981\) | −2585.07 | −0.0841334 | ||||||||
\(982\) | 40983.0 | 1.33179 | ||||||||
\(983\) | 13288.7 | 0.431175 | 0.215587 | − | 0.976485i | \(-0.430833\pi\) | ||||
0.215587 | + | 0.976485i | \(0.430833\pi\) | |||||||
\(984\) | 14886.5 | 0.482282 | ||||||||
\(985\) | −40670.5 | −1.31560 | ||||||||
\(986\) | 63360.3 | 2.04645 | ||||||||
\(987\) | 6571.53 | 0.211929 | ||||||||
\(988\) | −1904.09 | −0.0613128 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 1266.97 | 0.0406738 | ||||||||
\(991\) | 43350.5 | 1.38958 | 0.694789 | − | 0.719213i | \(-0.255498\pi\) | ||||
0.694789 | + | 0.719213i | \(0.255498\pi\) | |||||||
\(992\) | 15451.8 | 0.494553 | ||||||||
\(993\) | −48341.8 | −1.54489 | ||||||||
\(994\) | −4357.30 | −0.139039 | ||||||||
\(995\) | −30774.2 | −0.980510 | ||||||||
\(996\) | 53225.3 | 1.69328 | ||||||||
\(997\) | 45404.7 | 1.44231 | 0.721154 | − | 0.692775i | \(-0.243612\pi\) | ||||
0.721154 | + | 0.692775i | \(0.243612\pi\) | |||||||
\(998\) | −42010.0 | −1.33247 | ||||||||
\(999\) | −23198.0 | −0.734686 |
(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 | 1849.4.a.i.1.45 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.6 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.45 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.6 | yes | 50 | 43.42 | odd | 2 |