Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,4,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(85.0217523183\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.36838 | −1.54445 | −0.772227 | − | 0.635347i | \(-0.780857\pi\) | ||||
−0.772227 | + | 0.635347i | \(0.780857\pi\) | |||||||
\(3\) | −5.97359 | −1.14962 | −0.574809 | − | 0.818288i | \(-0.694924\pi\) | ||||
−0.574809 | + | 0.818288i | \(0.694924\pi\) | |||||||
\(4\) | 11.0827 | 1.38534 | ||||||||
\(5\) | −7.42634 | −0.664232 | −0.332116 | − | 0.943238i | \(-0.607763\pi\) | ||||
−0.332116 | + | 0.943238i | \(0.607763\pi\) | |||||||
\(6\) | 26.0949 | 1.77553 | ||||||||
\(7\) | −29.1330 | −1.57303 | −0.786517 | − | 0.617568i | \(-0.788118\pi\) | ||||
−0.786517 | + | 0.617568i | \(0.788118\pi\) | |||||||
\(8\) | −13.4664 | −0.595138 | ||||||||
\(9\) | 8.68373 | 0.321620 | ||||||||
\(10\) | 32.4411 | 1.02588 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −66.2035 | −1.59261 | ||||||||
\(13\) | −62.3984 | −1.33125 | −0.665623 | − | 0.746288i | \(-0.731834\pi\) | ||||
−0.665623 | + | 0.746288i | \(0.731834\pi\) | |||||||
\(14\) | 127.264 | 2.42948 | ||||||||
\(15\) | 44.3619 | 0.763613 | ||||||||
\(16\) | −29.8352 | −0.466175 | ||||||||
\(17\) | 100.337 | 1.43149 | 0.715745 | − | 0.698362i | \(-0.246087\pi\) | ||||
0.715745 | + | 0.698362i | \(0.246087\pi\) | |||||||
\(18\) | −37.9338 | −0.496727 | ||||||||
\(19\) | −91.6168 | −1.10623 | −0.553114 | − | 0.833105i | \(-0.686561\pi\) | ||||
−0.553114 | + | 0.833105i | \(0.686561\pi\) | |||||||
\(20\) | −82.3040 | −0.920187 | ||||||||
\(21\) | 174.029 | 1.80839 | ||||||||
\(22\) | −48.0521 | −0.465670 | ||||||||
\(23\) | −188.629 | −1.71008 | −0.855039 | − | 0.518564i | \(-0.826467\pi\) | ||||
−0.855039 | + | 0.518564i | \(0.826467\pi\) | |||||||
\(24\) | 80.4430 | 0.684181 | ||||||||
\(25\) | −69.8494 | −0.558795 | ||||||||
\(26\) | 272.580 | 2.05605 | ||||||||
\(27\) | 109.414 | 0.779878 | ||||||||
\(28\) | −322.873 | −2.17919 | ||||||||
\(29\) | 52.8947 | 0.338700 | 0.169350 | − | 0.985556i | \(-0.445833\pi\) | ||||
0.169350 | + | 0.985556i | \(0.445833\pi\) | |||||||
\(30\) | −193.790 | −1.17937 | ||||||||
\(31\) | −318.944 | −1.84787 | −0.923935 | − | 0.382549i | \(-0.875046\pi\) | ||||
−0.923935 | + | 0.382549i | \(0.875046\pi\) | |||||||
\(32\) | 238.063 | 1.31512 | ||||||||
\(33\) | −65.7094 | −0.346623 | ||||||||
\(34\) | −438.310 | −2.21087 | ||||||||
\(35\) | 216.352 | 1.04486 | ||||||||
\(36\) | 96.2393 | 0.445552 | ||||||||
\(37\) | 304.879 | 1.35464 | 0.677321 | − | 0.735688i | \(-0.263141\pi\) | ||||
0.677321 | + | 0.735688i | \(0.263141\pi\) | |||||||
\(38\) | 400.217 | 1.70852 | ||||||||
\(39\) | 372.742 | 1.53042 | ||||||||
\(40\) | 100.006 | 0.395310 | ||||||||
\(41\) | 314.282 | 1.19714 | 0.598568 | − | 0.801072i | \(-0.295737\pi\) | ||||
0.598568 | + | 0.801072i | \(0.295737\pi\) | |||||||
\(42\) | −760.222 | −2.79297 | ||||||||
\(43\) | −253.267 | −0.898208 | −0.449104 | − | 0.893480i | \(-0.648257\pi\) | ||||
−0.449104 | + | 0.893480i | \(0.648257\pi\) | |||||||
\(44\) | 121.910 | 0.417695 | ||||||||
\(45\) | −64.4884 | −0.213630 | ||||||||
\(46\) | 824.001 | 2.64114 | ||||||||
\(47\) | 147.188 | 0.456800 | 0.228400 | − | 0.973567i | \(-0.426651\pi\) | ||||
0.228400 | + | 0.973567i | \(0.426651\pi\) | |||||||
\(48\) | 178.223 | 0.535923 | ||||||||
\(49\) | 505.732 | 1.47444 | ||||||||
\(50\) | 305.128 | 0.863034 | ||||||||
\(51\) | −599.372 | −1.64566 | ||||||||
\(52\) | −691.544 | −1.84423 | ||||||||
\(53\) | −337.028 | −0.873477 | −0.436739 | − | 0.899588i | \(-0.643867\pi\) | ||||
−0.436739 | + | 0.899588i | \(0.643867\pi\) | |||||||
\(54\) | −477.961 | −1.20449 | ||||||||
\(55\) | −81.6898 | −0.200274 | ||||||||
\(56\) | 392.318 | 0.936173 | ||||||||
\(57\) | 547.281 | 1.27174 | ||||||||
\(58\) | −231.064 | −0.523106 | ||||||||
\(59\) | −672.025 | −1.48288 | −0.741442 | − | 0.671017i | \(-0.765858\pi\) | ||||
−0.741442 | + | 0.671017i | \(0.765858\pi\) | |||||||
\(60\) | 491.650 | 1.05786 | ||||||||
\(61\) | −333.559 | −0.700129 | −0.350065 | − | 0.936726i | \(-0.613840\pi\) | ||||
−0.350065 | + | 0.936726i | \(0.613840\pi\) | |||||||
\(62\) | 1393.27 | 2.85395 | ||||||||
\(63\) | −252.983 | −0.505919 | ||||||||
\(64\) | −801.267 | −1.56497 | ||||||||
\(65\) | 463.392 | 0.884257 | ||||||||
\(66\) | 287.044 | 0.535343 | ||||||||
\(67\) | 673.598 | 1.22825 | 0.614127 | − | 0.789207i | \(-0.289508\pi\) | ||||
0.614127 | + | 0.789207i | \(0.289508\pi\) | |||||||
\(68\) | 1112.01 | 1.98310 | ||||||||
\(69\) | 1126.79 | 1.96593 | ||||||||
\(70\) | −945.106 | −1.61374 | ||||||||
\(71\) | −240.031 | −0.401217 | −0.200609 | − | 0.979671i | \(-0.564292\pi\) | ||||
−0.200609 | + | 0.979671i | \(0.564292\pi\) | |||||||
\(72\) | −116.939 | −0.191408 | ||||||||
\(73\) | 374.768 | 0.600866 | 0.300433 | − | 0.953803i | \(-0.402869\pi\) | ||||
0.300433 | + | 0.953803i | \(0.402869\pi\) | |||||||
\(74\) | −1331.82 | −2.09218 | ||||||||
\(75\) | 417.251 | 0.642401 | ||||||||
\(76\) | −1015.36 | −1.53250 | ||||||||
\(77\) | −320.463 | −0.474288 | ||||||||
\(78\) | −1628.28 | −2.36367 | ||||||||
\(79\) | −668.901 | −0.952623 | −0.476312 | − | 0.879277i | \(-0.658027\pi\) | ||||
−0.476312 | + | 0.879277i | \(0.658027\pi\) | |||||||
\(80\) | 221.566 | 0.309649 | ||||||||
\(81\) | −888.054 | −1.21818 | ||||||||
\(82\) | −1372.90 | −1.84892 | ||||||||
\(83\) | 1099.68 | 1.45428 | 0.727142 | − | 0.686488i | \(-0.240848\pi\) | ||||
0.727142 | + | 0.686488i | \(0.240848\pi\) | |||||||
\(84\) | 1928.71 | 2.50523 | ||||||||
\(85\) | −745.138 | −0.950842 | ||||||||
\(86\) | 1106.37 | 1.38724 | ||||||||
\(87\) | −315.971 | −0.389375 | ||||||||
\(88\) | −148.131 | −0.179441 | ||||||||
\(89\) | 381.951 | 0.454907 | 0.227453 | − | 0.973789i | \(-0.426960\pi\) | ||||
0.227453 | + | 0.973789i | \(0.426960\pi\) | |||||||
\(90\) | 281.710 | 0.329942 | ||||||||
\(91\) | 1817.85 | 2.09410 | ||||||||
\(92\) | −2090.52 | −2.36904 | ||||||||
\(93\) | 1905.24 | 2.12434 | ||||||||
\(94\) | −642.973 | −0.705506 | ||||||||
\(95\) | 680.378 | 0.734793 | ||||||||
\(96\) | −1422.09 | −1.51189 | ||||||||
\(97\) | 1133.16 | 1.18614 | 0.593069 | − | 0.805151i | \(-0.297916\pi\) | ||||
0.593069 | + | 0.805151i | \(0.297916\pi\) | |||||||
\(98\) | −2209.23 | −2.27720 | ||||||||
\(99\) | 95.5211 | 0.0969720 | ||||||||
\(100\) | −774.121 | −0.774121 | ||||||||
\(101\) | 1768.09 | 1.74189 | 0.870947 | − | 0.491376i | \(-0.163506\pi\) | ||||
0.870947 | + | 0.491376i | \(0.163506\pi\) | |||||||
\(102\) | 2618.28 | 2.54165 | ||||||||
\(103\) | 649.744 | 0.621565 | 0.310782 | − | 0.950481i | \(-0.399409\pi\) | ||||
0.310782 | + | 0.950481i | \(0.399409\pi\) | |||||||
\(104\) | 840.285 | 0.792276 | ||||||||
\(105\) | −1292.40 | −1.20119 | ||||||||
\(106\) | 1472.26 | 1.34905 | ||||||||
\(107\) | 1486.26 | 1.34283 | 0.671414 | − | 0.741082i | \(-0.265687\pi\) | ||||
0.671414 | + | 0.741082i | \(0.265687\pi\) | |||||||
\(108\) | 1212.60 | 1.08039 | ||||||||
\(109\) | −138.156 | −0.121403 | −0.0607016 | − | 0.998156i | \(-0.519334\pi\) | ||||
−0.0607016 | + | 0.998156i | \(0.519334\pi\) | |||||||
\(110\) | 356.852 | 0.309313 | ||||||||
\(111\) | −1821.22 | −1.55732 | ||||||||
\(112\) | 869.189 | 0.733309 | ||||||||
\(113\) | 1990.04 | 1.65670 | 0.828350 | − | 0.560211i | \(-0.189280\pi\) | ||||
0.828350 | + | 0.560211i | \(0.189280\pi\) | |||||||
\(114\) | −2390.73 | −1.96414 | ||||||||
\(115\) | 1400.82 | 1.13589 | ||||||||
\(116\) | 586.216 | 0.469214 | ||||||||
\(117\) | −541.851 | −0.428155 | ||||||||
\(118\) | 2935.66 | 2.29025 | ||||||||
\(119\) | −2923.12 | −2.25178 | ||||||||
\(120\) | −597.397 | −0.454455 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1457.11 | 1.08132 | ||||||||
\(123\) | −1877.39 | −1.37625 | ||||||||
\(124\) | −3534.76 | −2.55993 | ||||||||
\(125\) | 1447.02 | 1.03540 | ||||||||
\(126\) | 1105.13 | 0.781369 | ||||||||
\(127\) | 1397.51 | 0.976449 | 0.488225 | − | 0.872718i | \(-0.337645\pi\) | ||||
0.488225 | + | 0.872718i | \(0.337645\pi\) | |||||||
\(128\) | 1595.73 | 1.10191 | ||||||||
\(129\) | 1512.92 | 1.03260 | ||||||||
\(130\) | −2024.27 | −1.36569 | ||||||||
\(131\) | −131.000 | −0.0873704 | ||||||||
\(132\) | −728.239 | −0.480190 | ||||||||
\(133\) | 2669.07 | 1.74014 | ||||||||
\(134\) | −2942.53 | −1.89698 | ||||||||
\(135\) | −812.545 | −0.518020 | ||||||||
\(136\) | −1351.18 | −0.851934 | ||||||||
\(137\) | 1374.05 | 0.856884 | 0.428442 | − | 0.903569i | \(-0.359063\pi\) | ||||
0.428442 | + | 0.903569i | \(0.359063\pi\) | |||||||
\(138\) | −4922.24 | −3.03630 | ||||||||
\(139\) | 317.369 | 0.193661 | 0.0968304 | − | 0.995301i | \(-0.469130\pi\) | ||||
0.0968304 | + | 0.995301i | \(0.469130\pi\) | |||||||
\(140\) | 2397.76 | 1.44749 | ||||||||
\(141\) | −879.240 | −0.525145 | ||||||||
\(142\) | 1048.54 | 0.619661 | ||||||||
\(143\) | −686.382 | −0.401386 | ||||||||
\(144\) | −259.081 | −0.149931 | ||||||||
\(145\) | −392.814 | −0.224975 | ||||||||
\(146\) | −1637.13 | −0.928010 | ||||||||
\(147\) | −3021.03 | −1.69504 | ||||||||
\(148\) | 3378.88 | 1.87664 | ||||||||
\(149\) | −3327.61 | −1.82959 | −0.914793 | − | 0.403924i | \(-0.867646\pi\) | ||||
−0.914793 | + | 0.403924i | \(0.867646\pi\) | |||||||
\(150\) | −1822.71 | −0.992158 | ||||||||
\(151\) | −619.409 | −0.333820 | −0.166910 | − | 0.985972i | \(-0.553379\pi\) | ||||
−0.166910 | + | 0.985972i | \(0.553379\pi\) | |||||||
\(152\) | 1233.75 | 0.658359 | ||||||||
\(153\) | 871.301 | 0.460395 | ||||||||
\(154\) | 1399.90 | 0.732516 | ||||||||
\(155\) | 2368.59 | 1.22742 | ||||||||
\(156\) | 4131.00 | 2.12016 | ||||||||
\(157\) | 42.2200 | 0.0214619 | 0.0107310 | − | 0.999942i | \(-0.496584\pi\) | ||||
0.0107310 | + | 0.999942i | \(0.496584\pi\) | |||||||
\(158\) | 2922.01 | 1.47128 | ||||||||
\(159\) | 2013.26 | 1.00416 | ||||||||
\(160\) | −1767.94 | −0.873548 | ||||||||
\(161\) | 5495.32 | 2.69001 | ||||||||
\(162\) | 3879.35 | 1.88142 | ||||||||
\(163\) | −349.061 | −0.167734 | −0.0838668 | − | 0.996477i | \(-0.526727\pi\) | ||||
−0.0838668 | + | 0.996477i | \(0.526727\pi\) | |||||||
\(164\) | 3483.09 | 1.65844 | ||||||||
\(165\) | 487.981 | 0.230238 | ||||||||
\(166\) | −4803.81 | −2.24607 | ||||||||
\(167\) | −2142.85 | −0.992928 | −0.496464 | − | 0.868057i | \(-0.665368\pi\) | ||||
−0.496464 | + | 0.868057i | \(0.665368\pi\) | |||||||
\(168\) | −2343.55 | −1.07624 | ||||||||
\(169\) | 1696.56 | 0.772217 | ||||||||
\(170\) | 3255.04 | 1.46853 | ||||||||
\(171\) | −795.576 | −0.355785 | ||||||||
\(172\) | −2806.89 | −1.24432 | ||||||||
\(173\) | −4226.42 | −1.85739 | −0.928695 | − | 0.370844i | \(-0.879068\pi\) | ||||
−0.928695 | + | 0.370844i | \(0.879068\pi\) | |||||||
\(174\) | 1380.28 | 0.601372 | ||||||||
\(175\) | 2034.92 | 0.879004 | ||||||||
\(176\) | −328.187 | −0.140557 | ||||||||
\(177\) | 4014.40 | 1.70475 | ||||||||
\(178\) | −1668.50 | −0.702583 | ||||||||
\(179\) | −506.477 | −0.211485 | −0.105743 | − | 0.994394i | \(-0.533722\pi\) | ||||
−0.105743 | + | 0.994394i | \(0.533722\pi\) | |||||||
\(180\) | −714.706 | −0.295950 | ||||||||
\(181\) | 1521.98 | 0.625014 | 0.312507 | − | 0.949915i | \(-0.398831\pi\) | ||||
0.312507 | + | 0.949915i | \(0.398831\pi\) | |||||||
\(182\) | −7941.07 | −3.23424 | ||||||||
\(183\) | 1992.55 | 0.804881 | ||||||||
\(184\) | 2540.16 | 1.01773 | ||||||||
\(185\) | −2264.13 | −0.899797 | ||||||||
\(186\) | −8322.79 | −3.28095 | ||||||||
\(187\) | 1103.71 | 0.431610 | ||||||||
\(188\) | 1631.24 | 0.632822 | ||||||||
\(189\) | −3187.55 | −1.22677 | ||||||||
\(190\) | −2972.15 | −1.13485 | ||||||||
\(191\) | 4866.38 | 1.84355 | 0.921777 | − | 0.387721i | \(-0.126737\pi\) | ||||
0.921777 | + | 0.387721i | \(0.126737\pi\) | |||||||
\(192\) | 4786.44 | 1.79912 | ||||||||
\(193\) | 2772.11 | 1.03389 | 0.516944 | − | 0.856019i | \(-0.327069\pi\) | ||||
0.516944 | + | 0.856019i | \(0.327069\pi\) | |||||||
\(194\) | −4950.09 | −1.83194 | ||||||||
\(195\) | −2768.11 | −1.01656 | ||||||||
\(196\) | 5604.88 | 2.04259 | ||||||||
\(197\) | 1081.65 | 0.391188 | 0.195594 | − | 0.980685i | \(-0.437336\pi\) | ||||
0.195594 | + | 0.980685i | \(0.437336\pi\) | |||||||
\(198\) | −417.272 | −0.149769 | ||||||||
\(199\) | −3111.84 | −1.10851 | −0.554253 | − | 0.832348i | \(-0.686996\pi\) | ||||
−0.554253 | + | 0.832348i | \(0.686996\pi\) | |||||||
\(200\) | 940.623 | 0.332561 | ||||||||
\(201\) | −4023.80 | −1.41202 | ||||||||
\(202\) | −7723.68 | −2.69028 | ||||||||
\(203\) | −1540.98 | −0.532786 | ||||||||
\(204\) | −6642.67 | −2.27980 | ||||||||
\(205\) | −2333.96 | −0.795176 | ||||||||
\(206\) | −2838.33 | −0.959978 | ||||||||
\(207\) | −1638.00 | −0.549995 | ||||||||
\(208\) | 1861.67 | 0.620594 | ||||||||
\(209\) | −1007.78 | −0.333540 | ||||||||
\(210\) | 5645.67 | 1.85518 | ||||||||
\(211\) | 5629.59 | 1.83676 | 0.918381 | − | 0.395698i | \(-0.129497\pi\) | ||||
0.918381 | + | 0.395698i | \(0.129497\pi\) | |||||||
\(212\) | −3735.18 | −1.21006 | ||||||||
\(213\) | 1433.84 | 0.461246 | ||||||||
\(214\) | −6492.56 | −2.07394 | ||||||||
\(215\) | 1880.85 | 0.596619 | ||||||||
\(216\) | −1473.41 | −0.464135 | ||||||||
\(217\) | 9291.79 | 2.90676 | ||||||||
\(218\) | 603.517 | 0.187502 | ||||||||
\(219\) | −2238.71 | −0.690766 | ||||||||
\(220\) | −905.344 | −0.277447 | ||||||||
\(221\) | −6260.88 | −1.90567 | ||||||||
\(222\) | 7955.77 | 2.40521 | ||||||||
\(223\) | −122.755 | −0.0368622 | −0.0184311 | − | 0.999830i | \(-0.505867\pi\) | ||||
−0.0184311 | + | 0.999830i | \(0.505867\pi\) | |||||||
\(224\) | −6935.49 | −2.06874 | ||||||||
\(225\) | −606.554 | −0.179720 | ||||||||
\(226\) | −8693.24 | −2.55870 | ||||||||
\(227\) | −3544.13 | −1.03627 | −0.518133 | − | 0.855300i | \(-0.673373\pi\) | ||||
−0.518133 | + | 0.855300i | \(0.673373\pi\) | |||||||
\(228\) | 6065.36 | 1.76179 | ||||||||
\(229\) | 605.261 | 0.174658 | 0.0873292 | − | 0.996180i | \(-0.472167\pi\) | ||||
0.0873292 | + | 0.996180i | \(0.472167\pi\) | |||||||
\(230\) | −6119.31 | −1.75433 | ||||||||
\(231\) | 1914.31 | 0.545249 | ||||||||
\(232\) | −712.303 | −0.201573 | ||||||||
\(233\) | −2433.84 | −0.684319 | −0.342160 | − | 0.939642i | \(-0.611158\pi\) | ||||
−0.342160 | + | 0.939642i | \(0.611158\pi\) | |||||||
\(234\) | 2367.01 | 0.661266 | ||||||||
\(235\) | −1093.07 | −0.303421 | ||||||||
\(236\) | −7447.86 | −2.05430 | ||||||||
\(237\) | 3995.74 | 1.09515 | ||||||||
\(238\) | 12769.3 | 3.47777 | ||||||||
\(239\) | −1270.44 | −0.343839 | −0.171920 | − | 0.985111i | \(-0.554997\pi\) | ||||
−0.171920 | + | 0.985111i | \(0.554997\pi\) | |||||||
\(240\) | −1323.55 | −0.355977 | ||||||||
\(241\) | −5515.94 | −1.47433 | −0.737163 | − | 0.675715i | \(-0.763835\pi\) | ||||
−0.737163 | + | 0.675715i | \(0.763835\pi\) | |||||||
\(242\) | −528.574 | −0.140405 | ||||||||
\(243\) | 2350.69 | 0.620564 | ||||||||
\(244\) | −3696.74 | −0.969917 | ||||||||
\(245\) | −3755.74 | −0.979369 | ||||||||
\(246\) | 8201.14 | 2.12555 | ||||||||
\(247\) | 5716.74 | 1.47266 | ||||||||
\(248\) | 4295.04 | 1.09974 | ||||||||
\(249\) | −6569.03 | −1.67187 | ||||||||
\(250\) | −6321.12 | −1.59913 | ||||||||
\(251\) | 3679.95 | 0.925403 | 0.462702 | − | 0.886514i | \(-0.346880\pi\) | ||||
0.462702 | + | 0.886514i | \(0.346880\pi\) | |||||||
\(252\) | −2803.74 | −0.700869 | ||||||||
\(253\) | −2074.91 | −0.515608 | ||||||||
\(254\) | −6104.85 | −1.50808 | ||||||||
\(255\) | 4451.15 | 1.09310 | ||||||||
\(256\) | −560.622 | −0.136871 | ||||||||
\(257\) | −433.341 | −0.105179 | −0.0525896 | − | 0.998616i | \(-0.516748\pi\) | ||||
−0.0525896 | + | 0.998616i | \(0.516748\pi\) | |||||||
\(258\) | −6608.98 | −1.59480 | ||||||||
\(259\) | −8882.03 | −2.13090 | ||||||||
\(260\) | 5135.64 | 1.22500 | ||||||||
\(261\) | 459.323 | 0.108933 | ||||||||
\(262\) | 572.257 | 0.134940 | ||||||||
\(263\) | −5523.85 | −1.29511 | −0.647557 | − | 0.762017i | \(-0.724209\pi\) | ||||
−0.647557 | + | 0.762017i | \(0.724209\pi\) | |||||||
\(264\) | 884.873 | 0.206288 | ||||||||
\(265\) | 2502.88 | 0.580192 | ||||||||
\(266\) | −11659.5 | −2.68756 | ||||||||
\(267\) | −2281.62 | −0.522969 | ||||||||
\(268\) | 7465.29 | 1.70155 | ||||||||
\(269\) | −5505.06 | −1.24777 | −0.623883 | − | 0.781517i | \(-0.714446\pi\) | ||||
−0.623883 | + | 0.781517i | \(0.714446\pi\) | |||||||
\(270\) | 3549.50 | 0.800058 | ||||||||
\(271\) | −929.326 | −0.208312 | −0.104156 | − | 0.994561i | \(-0.533214\pi\) | ||||
−0.104156 | + | 0.994561i | \(0.533214\pi\) | |||||||
\(272\) | −2993.58 | −0.667324 | ||||||||
\(273\) | −10859.1 | −2.40741 | ||||||||
\(274\) | −6002.37 | −1.32342 | ||||||||
\(275\) | −768.343 | −0.168483 | ||||||||
\(276\) | 12487.9 | 2.72349 | ||||||||
\(277\) | −149.106 | −0.0323427 | −0.0161714 | − | 0.999869i | \(-0.505148\pi\) | ||||
−0.0161714 | + | 0.999869i | \(0.505148\pi\) | |||||||
\(278\) | −1386.39 | −0.299100 | ||||||||
\(279\) | −2769.62 | −0.594312 | ||||||||
\(280\) | −2913.49 | −0.621837 | ||||||||
\(281\) | 5667.28 | 1.20314 | 0.601569 | − | 0.798821i | \(-0.294543\pi\) | ||||
0.601569 | + | 0.798821i | \(0.294543\pi\) | |||||||
\(282\) | 3840.85 | 0.811062 | ||||||||
\(283\) | −5028.35 | −1.05620 | −0.528099 | − | 0.849183i | \(-0.677095\pi\) | ||||
−0.528099 | + | 0.849183i | \(0.677095\pi\) | |||||||
\(284\) | −2660.19 | −0.555822 | ||||||||
\(285\) | −4064.30 | −0.844730 | ||||||||
\(286\) | 2998.38 | 0.619922 | ||||||||
\(287\) | −9155.97 | −1.88313 | ||||||||
\(288\) | 2067.27 | 0.422970 | ||||||||
\(289\) | 5154.53 | 1.04916 | ||||||||
\(290\) | 1715.96 | 0.347464 | ||||||||
\(291\) | −6769.06 | −1.36361 | ||||||||
\(292\) | 4153.44 | 0.832403 | ||||||||
\(293\) | 5616.21 | 1.11980 | 0.559902 | − | 0.828559i | \(-0.310839\pi\) | ||||
0.559902 | + | 0.828559i | \(0.310839\pi\) | |||||||
\(294\) | 13197.0 | 2.61791 | ||||||||
\(295\) | 4990.69 | 0.984980 | ||||||||
\(296\) | −4105.63 | −0.806199 | ||||||||
\(297\) | 1203.55 | 0.235142 | ||||||||
\(298\) | 14536.2 | 2.82571 | ||||||||
\(299\) | 11770.1 | 2.27653 | ||||||||
\(300\) | 4624.28 | 0.889943 | ||||||||
\(301\) | 7378.44 | 1.41291 | ||||||||
\(302\) | 2705.81 | 0.515569 | ||||||||
\(303\) | −10561.8 | −2.00251 | ||||||||
\(304\) | 2733.41 | 0.515696 | ||||||||
\(305\) | 2477.13 | 0.465049 | ||||||||
\(306\) | −3806.17 | −0.711059 | ||||||||
\(307\) | 4594.43 | 0.854130 | 0.427065 | − | 0.904221i | \(-0.359548\pi\) | ||||
0.427065 | + | 0.904221i | \(0.359548\pi\) | |||||||
\(308\) | −3551.60 | −0.657049 | ||||||||
\(309\) | −3881.30 | −0.714562 | ||||||||
\(310\) | −10346.9 | −1.89569 | ||||||||
\(311\) | 2948.13 | 0.537534 | 0.268767 | − | 0.963205i | \(-0.413384\pi\) | ||||
0.268767 | + | 0.963205i | \(0.413384\pi\) | |||||||
\(312\) | −5019.51 | −0.910814 | ||||||||
\(313\) | −5038.96 | −0.909964 | −0.454982 | − | 0.890501i | \(-0.650354\pi\) | ||||
−0.454982 | + | 0.890501i | \(0.650354\pi\) | |||||||
\(314\) | −184.433 | −0.0331470 | ||||||||
\(315\) | 1878.74 | 0.336048 | ||||||||
\(316\) | −7413.23 | −1.31971 | ||||||||
\(317\) | −2854.70 | −0.505792 | −0.252896 | − | 0.967493i | \(-0.581383\pi\) | ||||
−0.252896 | + | 0.967493i | \(0.581383\pi\) | |||||||
\(318\) | −8794.69 | −1.55089 | ||||||||
\(319\) | 581.841 | 0.102122 | ||||||||
\(320\) | 5950.48 | 1.03951 | ||||||||
\(321\) | −8878.33 | −1.54374 | ||||||||
\(322\) | −24005.6 | −4.15460 | ||||||||
\(323\) | −9192.57 | −1.58355 | ||||||||
\(324\) | −9842.04 | −1.68759 | ||||||||
\(325\) | 4358.49 | 0.743894 | ||||||||
\(326\) | 1524.83 | 0.259057 | ||||||||
\(327\) | 825.287 | 0.139567 | ||||||||
\(328\) | −4232.26 | −0.712461 | ||||||||
\(329\) | −4288.03 | −0.718561 | ||||||||
\(330\) | −2131.68 | −0.355592 | ||||||||
\(331\) | −7671.02 | −1.27383 | −0.636915 | − | 0.770934i | \(-0.719790\pi\) | ||||
−0.636915 | + | 0.770934i | \(0.719790\pi\) | |||||||
\(332\) | 12187.4 | 2.01468 | ||||||||
\(333\) | 2647.48 | 0.435679 | ||||||||
\(334\) | 9360.79 | 1.53353 | ||||||||
\(335\) | −5002.37 | −0.815847 | ||||||||
\(336\) | −5192.17 | −0.843025 | ||||||||
\(337\) | −3129.55 | −0.505868 | −0.252934 | − | 0.967484i | \(-0.581396\pi\) | ||||
−0.252934 | + | 0.967484i | \(0.581396\pi\) | |||||||
\(338\) | −7411.22 | −1.19265 | ||||||||
\(339\) | −11887.7 | −1.90457 | ||||||||
\(340\) | −8258.15 | −1.31724 | ||||||||
\(341\) | −3508.38 | −0.557154 | ||||||||
\(342\) | 3475.38 | 0.549494 | ||||||||
\(343\) | −4740.87 | −0.746305 | ||||||||
\(344\) | 3410.61 | 0.534558 | ||||||||
\(345\) | −8367.92 | −1.30584 | ||||||||
\(346\) | 18462.6 | 2.86865 | ||||||||
\(347\) | −7868.55 | −1.21731 | −0.608654 | − | 0.793436i | \(-0.708290\pi\) | ||||
−0.608654 | + | 0.793436i | \(0.708290\pi\) | |||||||
\(348\) | −3501.81 | −0.539417 | ||||||||
\(349\) | −10383.1 | −1.59254 | −0.796268 | − | 0.604944i | \(-0.793195\pi\) | ||||
−0.796268 | + | 0.604944i | \(0.793195\pi\) | |||||||
\(350\) | −8889.31 | −1.35758 | ||||||||
\(351\) | −6827.25 | −1.03821 | ||||||||
\(352\) | 2618.69 | 0.396525 | ||||||||
\(353\) | −10876.3 | −1.63990 | −0.819950 | − | 0.572436i | \(-0.805999\pi\) | ||||
−0.819950 | + | 0.572436i | \(0.805999\pi\) | |||||||
\(354\) | −17536.4 | −2.63291 | ||||||||
\(355\) | 1782.55 | 0.266501 | ||||||||
\(356\) | 4233.05 | 0.630200 | ||||||||
\(357\) | 17461.5 | 2.58869 | ||||||||
\(358\) | 2212.48 | 0.326629 | ||||||||
\(359\) | 3839.16 | 0.564410 | 0.282205 | − | 0.959354i | \(-0.408934\pi\) | ||||
0.282205 | + | 0.959354i | \(0.408934\pi\) | |||||||
\(360\) | 868.429 | 0.127140 | ||||||||
\(361\) | 1534.64 | 0.223741 | ||||||||
\(362\) | −6648.56 | −0.965305 | ||||||||
\(363\) | −722.804 | −0.104511 | ||||||||
\(364\) | 20146.7 | 2.90103 | ||||||||
\(365\) | −2783.15 | −0.399115 | ||||||||
\(366\) | −8704.19 | −1.24310 | ||||||||
\(367\) | −7993.78 | −1.13698 | −0.568490 | − | 0.822690i | \(-0.692472\pi\) | ||||
−0.568490 | + | 0.822690i | \(0.692472\pi\) | |||||||
\(368\) | 5627.77 | 0.797195 | ||||||||
\(369\) | 2729.14 | 0.385022 | ||||||||
\(370\) | 9890.59 | 1.38970 | ||||||||
\(371\) | 9818.63 | 1.37401 | ||||||||
\(372\) | 21115.2 | 2.94294 | ||||||||
\(373\) | 991.175 | 0.137590 | 0.0687950 | − | 0.997631i | \(-0.478085\pi\) | ||||
0.0687950 | + | 0.997631i | \(0.478085\pi\) | |||||||
\(374\) | −4821.41 | −0.666602 | ||||||||
\(375\) | −8643.89 | −1.19032 | ||||||||
\(376\) | −1982.10 | −0.271859 | ||||||||
\(377\) | −3300.54 | −0.450893 | ||||||||
\(378\) | 13924.4 | 1.89470 | ||||||||
\(379\) | 135.414 | 0.0183530 | 0.00917648 | − | 0.999958i | \(-0.497079\pi\) | ||||
0.00917648 | + | 0.999958i | \(0.497079\pi\) | |||||||
\(380\) | 7540.43 | 1.01794 | ||||||||
\(381\) | −8348.15 | −1.12254 | ||||||||
\(382\) | −21258.2 | −2.84728 | ||||||||
\(383\) | 8755.87 | 1.16816 | 0.584078 | − | 0.811697i | \(-0.301456\pi\) | ||||
0.584078 | + | 0.811697i | \(0.301456\pi\) | |||||||
\(384\) | −9532.24 | −1.26677 | ||||||||
\(385\) | 2379.87 | 0.315037 | ||||||||
\(386\) | −12109.6 | −1.59679 | ||||||||
\(387\) | −2199.31 | −0.288881 | ||||||||
\(388\) | 12558.5 | 1.64320 | ||||||||
\(389\) | −1509.22 | −0.196710 | −0.0983552 | − | 0.995151i | \(-0.531358\pi\) | ||||
−0.0983552 | + | 0.995151i | \(0.531358\pi\) | |||||||
\(390\) | 12092.2 | 1.57003 | ||||||||
\(391\) | −18926.4 | −2.44796 | ||||||||
\(392\) | −6810.41 | −0.877494 | ||||||||
\(393\) | 782.540 | 0.100443 | ||||||||
\(394\) | −4725.04 | −0.604173 | ||||||||
\(395\) | 4967.49 | 0.632763 | ||||||||
\(396\) | 1058.63 | 0.134339 | ||||||||
\(397\) | 6588.49 | 0.832914 | 0.416457 | − | 0.909155i | \(-0.363272\pi\) | ||||
0.416457 | + | 0.909155i | \(0.363272\pi\) | |||||||
\(398\) | 13593.7 | 1.71204 | ||||||||
\(399\) | −15943.9 | −2.00049 | ||||||||
\(400\) | 2083.97 | 0.260496 | ||||||||
\(401\) | 5549.47 | 0.691091 | 0.345545 | − | 0.938402i | \(-0.387694\pi\) | ||||
0.345545 | + | 0.938402i | \(0.387694\pi\) | |||||||
\(402\) | 17577.5 | 2.18080 | ||||||||
\(403\) | 19901.6 | 2.45997 | ||||||||
\(404\) | 19595.2 | 2.41311 | ||||||||
\(405\) | 6594.99 | 0.809155 | ||||||||
\(406\) | 6731.58 | 0.822864 | ||||||||
\(407\) | 3353.66 | 0.408440 | ||||||||
\(408\) | 8071.41 | 0.979398 | ||||||||
\(409\) | 6275.97 | 0.758745 | 0.379372 | − | 0.925244i | \(-0.376140\pi\) | ||||
0.379372 | + | 0.925244i | \(0.376140\pi\) | |||||||
\(410\) | 10195.6 | 1.22811 | ||||||||
\(411\) | −8208.02 | −0.985089 | ||||||||
\(412\) | 7200.92 | 0.861078 | ||||||||
\(413\) | 19578.1 | 2.33263 | ||||||||
\(414\) | 7155.40 | 0.849441 | ||||||||
\(415\) | −8166.60 | −0.965982 | ||||||||
\(416\) | −14854.7 | −1.75075 | ||||||||
\(417\) | −1895.83 | −0.222636 | ||||||||
\(418\) | 4402.38 | 0.515138 | ||||||||
\(419\) | 11299.9 | 1.31751 | 0.658755 | − | 0.752358i | \(-0.271084\pi\) | ||||
0.658755 | + | 0.752358i | \(0.271084\pi\) | |||||||
\(420\) | −14323.2 | −1.66405 | ||||||||
\(421\) | −5919.18 | −0.685233 | −0.342616 | − | 0.939475i | \(-0.611313\pi\) | ||||
−0.342616 | + | 0.939475i | \(0.611313\pi\) | |||||||
\(422\) | −24592.1 | −2.83679 | ||||||||
\(423\) | 1278.14 | 0.146916 | ||||||||
\(424\) | 4538.56 | 0.519840 | ||||||||
\(425\) | −7008.49 | −0.799909 | ||||||||
\(426\) | −6263.57 | −0.712373 | ||||||||
\(427\) | 9717.58 | 1.10133 | ||||||||
\(428\) | 16471.8 | 1.86027 | ||||||||
\(429\) | 4100.16 | 0.461440 | ||||||||
\(430\) | −8216.27 | −0.921450 | ||||||||
\(431\) | 7920.77 | 0.885220 | 0.442610 | − | 0.896714i | \(-0.354053\pi\) | ||||
0.442610 | + | 0.896714i | \(0.354053\pi\) | |||||||
\(432\) | −3264.38 | −0.363559 | ||||||||
\(433\) | 7889.32 | 0.875604 | 0.437802 | − | 0.899071i | \(-0.355757\pi\) | ||||
0.437802 | + | 0.899071i | \(0.355757\pi\) | |||||||
\(434\) | −40590.0 | −4.48936 | ||||||||
\(435\) | 2346.51 | 0.258636 | ||||||||
\(436\) | −1531.14 | −0.168185 | ||||||||
\(437\) | 17281.5 | 1.89174 | ||||||||
\(438\) | 9779.51 | 1.06686 | ||||||||
\(439\) | 8745.97 | 0.950849 | 0.475424 | − | 0.879757i | \(-0.342295\pi\) | ||||
0.475424 | + | 0.879757i | \(0.342295\pi\) | |||||||
\(440\) | 1100.07 | 0.119191 | ||||||||
\(441\) | 4391.64 | 0.474208 | ||||||||
\(442\) | 27349.9 | 2.94321 | ||||||||
\(443\) | 1097.78 | 0.117736 | 0.0588679 | − | 0.998266i | \(-0.481251\pi\) | ||||
0.0588679 | + | 0.998266i | \(0.481251\pi\) | |||||||
\(444\) | −20184.0 | −2.15742 | ||||||||
\(445\) | −2836.50 | −0.302164 | ||||||||
\(446\) | 536.239 | 0.0569320 | ||||||||
\(447\) | 19877.8 | 2.10332 | ||||||||
\(448\) | 23343.3 | 2.46176 | ||||||||
\(449\) | 6722.81 | 0.706612 | 0.353306 | − | 0.935508i | \(-0.385057\pi\) | ||||
0.353306 | + | 0.935508i | \(0.385057\pi\) | |||||||
\(450\) | 2649.65 | 0.277569 | ||||||||
\(451\) | 3457.10 | 0.360950 | ||||||||
\(452\) | 22055.0 | 2.29509 | ||||||||
\(453\) | 3700.09 | 0.383765 | ||||||||
\(454\) | 15482.1 | 1.60046 | ||||||||
\(455\) | −13500.0 | −1.39097 | ||||||||
\(456\) | −7369.93 | −0.756861 | ||||||||
\(457\) | −713.291 | −0.0730117 | −0.0365058 | − | 0.999333i | \(-0.511623\pi\) | ||||
−0.0365058 | + | 0.999333i | \(0.511623\pi\) | |||||||
\(458\) | −2644.01 | −0.269752 | ||||||||
\(459\) | 10978.3 | 1.11639 | ||||||||
\(460\) | 15524.9 | 1.57359 | ||||||||
\(461\) | −600.992 | −0.0607180 | −0.0303590 | − | 0.999539i | \(-0.509665\pi\) | ||||
−0.0303590 | + | 0.999539i | \(0.509665\pi\) | |||||||
\(462\) | −8362.44 | −0.842113 | ||||||||
\(463\) | −8635.45 | −0.866789 | −0.433395 | − | 0.901204i | \(-0.642684\pi\) | ||||
−0.433395 | + | 0.901204i | \(0.642684\pi\) | |||||||
\(464\) | −1578.12 | −0.157893 | ||||||||
\(465\) | −14149.0 | −1.41106 | ||||||||
\(466\) | 10631.9 | 1.05690 | ||||||||
\(467\) | −802.667 | −0.0795353 | −0.0397677 | − | 0.999209i | \(-0.512662\pi\) | ||||
−0.0397677 | + | 0.999209i | \(0.512662\pi\) | |||||||
\(468\) | −6005.18 | −0.593140 | ||||||||
\(469\) | −19623.9 | −1.93209 | ||||||||
\(470\) | 4774.94 | 0.468620 | ||||||||
\(471\) | −252.205 | −0.0246730 | ||||||||
\(472\) | 9049.79 | 0.882522 | ||||||||
\(473\) | −2785.94 | −0.270820 | ||||||||
\(474\) | −17454.9 | −1.69141 | ||||||||
\(475\) | 6399.38 | 0.618155 | ||||||||
\(476\) | −32396.1 | −3.11948 | ||||||||
\(477\) | −2926.66 | −0.280928 | ||||||||
\(478\) | 5549.74 | 0.531044 | ||||||||
\(479\) | 10548.8 | 1.00624 | 0.503120 | − | 0.864216i | \(-0.332185\pi\) | ||||
0.503120 | + | 0.864216i | \(0.332185\pi\) | |||||||
\(480\) | 10560.9 | 1.00425 | ||||||||
\(481\) | −19023.9 | −1.80336 | ||||||||
\(482\) | 24095.7 | 2.27703 | ||||||||
\(483\) | −32826.7 | −3.09248 | ||||||||
\(484\) | 1341.01 | 0.125940 | ||||||||
\(485\) | −8415.27 | −0.787872 | ||||||||
\(486\) | −10268.7 | −0.958432 | ||||||||
\(487\) | 7389.88 | 0.687612 | 0.343806 | − | 0.939041i | \(-0.388284\pi\) | ||||
0.343806 | + | 0.939041i | \(0.388284\pi\) | |||||||
\(488\) | 4491.86 | 0.416674 | ||||||||
\(489\) | 2085.15 | 0.192829 | ||||||||
\(490\) | 16406.5 | 1.51259 | ||||||||
\(491\) | 6737.63 | 0.619277 | 0.309638 | − | 0.950854i | \(-0.399792\pi\) | ||||
0.309638 | + | 0.950854i | \(0.399792\pi\) | |||||||
\(492\) | −20806.6 | −1.90657 | ||||||||
\(493\) | 5307.30 | 0.484845 | ||||||||
\(494\) | −24972.9 | −2.27446 | ||||||||
\(495\) | −709.372 | −0.0644120 | ||||||||
\(496\) | 9515.75 | 0.861431 | ||||||||
\(497\) | 6992.82 | 0.631128 | ||||||||
\(498\) | 28696.0 | 2.58213 | ||||||||
\(499\) | −2089.51 | −0.187453 | −0.0937267 | − | 0.995598i | \(-0.529878\pi\) | ||||
−0.0937267 | + | 0.995598i | \(0.529878\pi\) | |||||||
\(500\) | 16036.9 | 1.43438 | ||||||||
\(501\) | 12800.5 | 1.14149 | ||||||||
\(502\) | −16075.4 | −1.42924 | ||||||||
\(503\) | −8722.86 | −0.773227 | −0.386614 | − | 0.922242i | \(-0.626355\pi\) | ||||
−0.386614 | + | 0.922242i | \(0.626355\pi\) | |||||||
\(504\) | 3406.78 | 0.301092 | ||||||||
\(505\) | −13130.4 | −1.15702 | ||||||||
\(506\) | 9064.01 | 0.796332 | ||||||||
\(507\) | −10134.6 | −0.887754 | ||||||||
\(508\) | 15488.2 | 1.35271 | ||||||||
\(509\) | −1337.90 | −0.116506 | −0.0582530 | − | 0.998302i | \(-0.518553\pi\) | ||||
−0.0582530 | + | 0.998302i | \(0.518553\pi\) | |||||||
\(510\) | −19444.3 | −1.68825 | ||||||||
\(511\) | −10918.1 | −0.945183 | ||||||||
\(512\) | −10316.8 | −0.890517 | ||||||||
\(513\) | −10024.1 | −0.862723 | ||||||||
\(514\) | 1892.99 | 0.162444 | ||||||||
\(515\) | −4825.22 | −0.412863 | ||||||||
\(516\) | 16767.2 | 1.43049 | ||||||||
\(517\) | 1619.07 | 0.137730 | ||||||||
\(518\) | 38800.0 | 3.29107 | ||||||||
\(519\) | 25246.9 | 2.13529 | ||||||||
\(520\) | −6240.24 | −0.526255 | ||||||||
\(521\) | −10353.1 | −0.870588 | −0.435294 | − | 0.900288i | \(-0.643356\pi\) | ||||
−0.435294 | + | 0.900288i | \(0.643356\pi\) | |||||||
\(522\) | −2006.50 | −0.168241 | ||||||||
\(523\) | 8062.52 | 0.674090 | 0.337045 | − | 0.941488i | \(-0.390572\pi\) | ||||
0.337045 | + | 0.941488i | \(0.390572\pi\) | |||||||
\(524\) | −1451.84 | −0.121038 | ||||||||
\(525\) | −12155.8 | −1.01052 | ||||||||
\(526\) | 24130.3 | 2.00025 | ||||||||
\(527\) | −32001.9 | −2.64521 | ||||||||
\(528\) | 1960.45 | 0.161587 | ||||||||
\(529\) | 23413.7 | 1.92436 | ||||||||
\(530\) | −10933.5 | −0.896080 | ||||||||
\(531\) | −5835.69 | −0.476925 | ||||||||
\(532\) | 29580.6 | 2.41068 | ||||||||
\(533\) | −19610.7 | −1.59368 | ||||||||
\(534\) | 9966.96 | 0.807701 | ||||||||
\(535\) | −11037.5 | −0.891950 | ||||||||
\(536\) | −9070.97 | −0.730982 | ||||||||
\(537\) | 3025.48 | 0.243127 | ||||||||
\(538\) | 24048.2 | 1.92712 | ||||||||
\(539\) | 5563.05 | 0.444559 | ||||||||
\(540\) | −9005.20 | −0.717633 | ||||||||
\(541\) | −5804.10 | −0.461253 | −0.230627 | − | 0.973042i | \(-0.574078\pi\) | ||||
−0.230627 | + | 0.973042i | \(0.574078\pi\) | |||||||
\(542\) | 4059.65 | 0.321728 | ||||||||
\(543\) | −9091.65 | −0.718527 | ||||||||
\(544\) | 23886.5 | 1.88259 | ||||||||
\(545\) | 1025.99 | 0.0806399 | ||||||||
\(546\) | 47436.6 | 3.71813 | ||||||||
\(547\) | 7089.14 | 0.554131 | 0.277065 | − | 0.960851i | \(-0.410638\pi\) | ||||
0.277065 | + | 0.960851i | \(0.410638\pi\) | |||||||
\(548\) | 15228.2 | 1.18708 | ||||||||
\(549\) | −2896.54 | −0.225175 | ||||||||
\(550\) | 3356.41 | 0.260214 | ||||||||
\(551\) | −4846.04 | −0.374679 | ||||||||
\(552\) | −15173.8 | −1.17000 | ||||||||
\(553\) | 19487.1 | 1.49851 | ||||||||
\(554\) | 651.353 | 0.0499519 | ||||||||
\(555\) | 13525.0 | 1.03442 | ||||||||
\(556\) | 3517.30 | 0.268286 | ||||||||
\(557\) | −12824.8 | −0.975588 | −0.487794 | − | 0.872959i | \(-0.662198\pi\) | ||||
−0.487794 | + | 0.872959i | \(0.662198\pi\) | |||||||
\(558\) | 12098.8 | 0.917887 | ||||||||
\(559\) | 15803.5 | 1.19574 | ||||||||
\(560\) | −6454.90 | −0.487088 | ||||||||
\(561\) | −6593.10 | −0.496187 | ||||||||
\(562\) | −24756.8 | −1.85819 | ||||||||
\(563\) | −12853.2 | −0.962162 | −0.481081 | − | 0.876676i | \(-0.659756\pi\) | ||||
−0.481081 | + | 0.876676i | \(0.659756\pi\) | |||||||
\(564\) | −9744.37 | −0.727503 | ||||||||
\(565\) | −14778.7 | −1.10043 | ||||||||
\(566\) | 21965.7 | 1.63125 | ||||||||
\(567\) | 25871.7 | 1.91624 | ||||||||
\(568\) | 3232.36 | 0.238780 | ||||||||
\(569\) | −17699.9 | −1.30407 | −0.652037 | − | 0.758187i | \(-0.726085\pi\) | ||||
−0.652037 | + | 0.758187i | \(0.726085\pi\) | |||||||
\(570\) | 17754.4 | 1.30465 | ||||||||
\(571\) | −2068.46 | −0.151598 | −0.0757988 | − | 0.997123i | \(-0.524151\pi\) | ||||
−0.0757988 | + | 0.997123i | \(0.524151\pi\) | |||||||
\(572\) | −7606.98 | −0.556056 | ||||||||
\(573\) | −29069.7 | −2.11938 | ||||||||
\(574\) | 39996.7 | 2.90842 | ||||||||
\(575\) | 13175.6 | 0.955583 | ||||||||
\(576\) | −6957.99 | −0.503327 | ||||||||
\(577\) | 13464.4 | 0.971460 | 0.485730 | − | 0.874109i | \(-0.338554\pi\) | ||||
0.485730 | + | 0.874109i | \(0.338554\pi\) | |||||||
\(578\) | −22516.9 | −1.62038 | ||||||||
\(579\) | −16559.4 | −1.18858 | ||||||||
\(580\) | −4353.45 | −0.311667 | ||||||||
\(581\) | −32037.0 | −2.28764 | ||||||||
\(582\) | 29569.8 | 2.10603 | ||||||||
\(583\) | −3707.30 | −0.263363 | ||||||||
\(584\) | −5046.79 | −0.357598 | ||||||||
\(585\) | 4023.97 | 0.284395 | ||||||||
\(586\) | −24533.7 | −1.72949 | ||||||||
\(587\) | 16533.2 | 1.16252 | 0.581260 | − | 0.813718i | \(-0.302560\pi\) | ||||
0.581260 | + | 0.813718i | \(0.302560\pi\) | |||||||
\(588\) | −33481.2 | −2.34820 | ||||||||
\(589\) | 29220.6 | 2.04417 | ||||||||
\(590\) | −21801.2 | −1.52126 | ||||||||
\(591\) | −6461.31 | −0.449717 | ||||||||
\(592\) | −9096.11 | −0.631500 | ||||||||
\(593\) | −20303.6 | −1.40602 | −0.703009 | − | 0.711181i | \(-0.748161\pi\) | ||||
−0.703009 | + | 0.711181i | \(0.748161\pi\) | |||||||
\(594\) | −5257.57 | −0.363166 | ||||||||
\(595\) | 21708.1 | 1.49571 | ||||||||
\(596\) | −36878.9 | −2.53460 | ||||||||
\(597\) | 18588.9 | 1.27436 | ||||||||
\(598\) | −51416.3 | −3.51600 | ||||||||
\(599\) | −24323.8 | −1.65917 | −0.829585 | − | 0.558380i | \(-0.811423\pi\) | ||||
−0.829585 | + | 0.558380i | \(0.811423\pi\) | |||||||
\(600\) | −5618.89 | −0.382317 | ||||||||
\(601\) | −6599.62 | −0.447927 | −0.223964 | − | 0.974598i | \(-0.571900\pi\) | ||||
−0.223964 | + | 0.974598i | \(0.571900\pi\) | |||||||
\(602\) | −32231.8 | −2.18218 | ||||||||
\(603\) | 5849.34 | 0.395031 | ||||||||
\(604\) | −6864.73 | −0.462453 | ||||||||
\(605\) | −898.588 | −0.0603848 | ||||||||
\(606\) | 46138.0 | 3.09279 | ||||||||
\(607\) | 22101.8 | 1.47790 | 0.738951 | − | 0.673760i | \(-0.235322\pi\) | ||||
0.738951 | + | 0.673760i | \(0.235322\pi\) | |||||||
\(608\) | −21810.6 | −1.45483 | ||||||||
\(609\) | 9205.18 | 0.612500 | ||||||||
\(610\) | −10821.0 | −0.718246 | ||||||||
\(611\) | −9184.30 | −0.608113 | ||||||||
\(612\) | 9656.37 | 0.637804 | ||||||||
\(613\) | 2778.73 | 0.183086 | 0.0915430 | − | 0.995801i | \(-0.470820\pi\) | ||||
0.0915430 | + | 0.995801i | \(0.470820\pi\) | |||||||
\(614\) | −20070.2 | −1.31916 | ||||||||
\(615\) | 13942.1 | 0.914148 | ||||||||
\(616\) | 4315.50 | 0.282267 | ||||||||
\(617\) | 21046.8 | 1.37328 | 0.686638 | − | 0.726999i | \(-0.259086\pi\) | ||||
0.686638 | + | 0.726999i | \(0.259086\pi\) | |||||||
\(618\) | 16955.0 | 1.10361 | ||||||||
\(619\) | −16016.8 | −1.04002 | −0.520009 | − | 0.854161i | \(-0.674072\pi\) | ||||
−0.520009 | + | 0.854161i | \(0.674072\pi\) | |||||||
\(620\) | 26250.4 | 1.70039 | ||||||||
\(621\) | −20638.6 | −1.33365 | ||||||||
\(622\) | −12878.5 | −0.830197 | ||||||||
\(623\) | −11127.4 | −0.715584 | ||||||||
\(624\) | −11120.8 | −0.713445 | ||||||||
\(625\) | −2014.89 | −0.128953 | ||||||||
\(626\) | 22012.1 | 1.40540 | ||||||||
\(627\) | 6020.09 | 0.383444 | ||||||||
\(628\) | 467.912 | 0.0297320 | ||||||||
\(629\) | 30590.6 | 1.93916 | ||||||||
\(630\) | −8207.05 | −0.519010 | ||||||||
\(631\) | −10915.3 | −0.688636 | −0.344318 | − | 0.938853i | \(-0.611890\pi\) | ||||
−0.344318 | + | 0.938853i | \(0.611890\pi\) | |||||||
\(632\) | 9007.72 | 0.566943 | ||||||||
\(633\) | −33628.8 | −2.11157 | ||||||||
\(634\) | 12470.4 | 0.781173 | ||||||||
\(635\) | −10378.4 | −0.648589 | ||||||||
\(636\) | 22312.4 | 1.39111 | ||||||||
\(637\) | −31556.9 | −1.96284 | ||||||||
\(638\) | −2541.70 | −0.157723 | ||||||||
\(639\) | −2084.36 | −0.129039 | ||||||||
\(640\) | −11850.5 | −0.731922 | ||||||||
\(641\) | −9647.47 | −0.594465 | −0.297233 | − | 0.954805i | \(-0.596064\pi\) | ||||
−0.297233 | + | 0.954805i | \(0.596064\pi\) | |||||||
\(642\) | 38783.9 | 2.38423 | ||||||||
\(643\) | 16731.0 | 1.02614 | 0.513070 | − | 0.858347i | \(-0.328508\pi\) | ||||
0.513070 | + | 0.858347i | \(0.328508\pi\) | |||||||
\(644\) | 60903.0 | 3.72658 | ||||||||
\(645\) | −11235.4 | −0.685883 | ||||||||
\(646\) | 40156.6 | 2.44573 | ||||||||
\(647\) | 11230.6 | 0.682410 | 0.341205 | − | 0.939989i | \(-0.389165\pi\) | ||||
0.341205 | + | 0.939989i | \(0.389165\pi\) | |||||||
\(648\) | 11958.9 | 0.724986 | ||||||||
\(649\) | −7392.27 | −0.447107 | ||||||||
\(650\) | −19039.5 | −1.14891 | ||||||||
\(651\) | −55505.3 | −3.34166 | ||||||||
\(652\) | −3868.54 | −0.232368 | ||||||||
\(653\) | −697.645 | −0.0418085 | −0.0209043 | − | 0.999781i | \(-0.506655\pi\) | ||||
−0.0209043 | + | 0.999781i | \(0.506655\pi\) | |||||||
\(654\) | −3605.16 | −0.215555 | ||||||||
\(655\) | 972.851 | 0.0580343 | ||||||||
\(656\) | −9376.65 | −0.558074 | ||||||||
\(657\) | 3254.38 | 0.193250 | ||||||||
\(658\) | 18731.7 | 1.10979 | ||||||||
\(659\) | 4169.03 | 0.246437 | 0.123219 | − | 0.992380i | \(-0.460678\pi\) | ||||
0.123219 | + | 0.992380i | \(0.460678\pi\) | |||||||
\(660\) | 5408.15 | 0.318958 | ||||||||
\(661\) | 28394.9 | 1.67085 | 0.835426 | − | 0.549603i | \(-0.185221\pi\) | ||||
0.835426 | + | 0.549603i | \(0.185221\pi\) | |||||||
\(662\) | 33509.9 | 1.96737 | ||||||||
\(663\) | 37399.9 | 2.19079 | ||||||||
\(664\) | −14808.8 | −0.865500 | ||||||||
\(665\) | −19821.5 | −1.15585 | ||||||||
\(666\) | −11565.2 | −0.672887 | ||||||||
\(667\) | −9977.45 | −0.579203 | ||||||||
\(668\) | −23748.6 | −1.37554 | ||||||||
\(669\) | 733.287 | 0.0423774 | ||||||||
\(670\) | 21852.2 | 1.26004 | ||||||||
\(671\) | −3669.15 | −0.211097 | ||||||||
\(672\) | 41429.7 | 2.37825 | ||||||||
\(673\) | 6420.75 | 0.367759 | 0.183880 | − | 0.982949i | \(-0.441134\pi\) | ||||
0.183880 | + | 0.982949i | \(0.441134\pi\) | |||||||
\(674\) | 13671.1 | 0.781290 | ||||||||
\(675\) | −7642.49 | −0.435792 | ||||||||
\(676\) | 18802.5 | 1.06978 | ||||||||
\(677\) | 32510.1 | 1.84559 | 0.922794 | − | 0.385294i | \(-0.125900\pi\) | ||||
0.922794 | + | 0.385294i | \(0.125900\pi\) | |||||||
\(678\) | 51929.8 | 2.94152 | ||||||||
\(679\) | −33012.5 | −1.86584 | ||||||||
\(680\) | 10034.4 | 0.565882 | ||||||||
\(681\) | 21171.2 | 1.19131 | ||||||||
\(682\) | 15325.9 | 0.860499 | ||||||||
\(683\) | −4235.83 | −0.237305 | −0.118653 | − | 0.992936i | \(-0.537858\pi\) | ||||
−0.118653 | + | 0.992936i | \(0.537858\pi\) | |||||||
\(684\) | −8817.14 | −0.492883 | ||||||||
\(685\) | −10204.2 | −0.569170 | ||||||||
\(686\) | 20709.9 | 1.15263 | ||||||||
\(687\) | −3615.58 | −0.200790 | ||||||||
\(688\) | 7556.28 | 0.418722 | ||||||||
\(689\) | 21030.0 | 1.16281 | ||||||||
\(690\) | 36554.2 | 2.01681 | ||||||||
\(691\) | −10628.2 | −0.585117 | −0.292559 | − | 0.956248i | \(-0.594507\pi\) | ||||
−0.292559 | + | 0.956248i | \(0.594507\pi\) | |||||||
\(692\) | −46840.2 | −2.57311 | ||||||||
\(693\) | −2782.82 | −0.152540 | ||||||||
\(694\) | 34372.8 | 1.88008 | ||||||||
\(695\) | −2356.89 | −0.128636 | ||||||||
\(696\) | 4255.00 | 0.231732 | ||||||||
\(697\) | 31534.1 | 1.71369 | ||||||||
\(698\) | 45357.3 | 2.45960 | ||||||||
\(699\) | 14538.8 | 0.786705 | ||||||||
\(700\) | 22552.5 | 1.21772 | ||||||||
\(701\) | 25593.2 | 1.37895 | 0.689473 | − | 0.724311i | \(-0.257842\pi\) | ||||
0.689473 | + | 0.724311i | \(0.257842\pi\) | |||||||
\(702\) | 29824.0 | 1.60347 | ||||||||
\(703\) | −27932.0 | −1.49854 | ||||||||
\(704\) | −8813.94 | −0.471858 | ||||||||
\(705\) | 6529.54 | 0.348818 | ||||||||
\(706\) | 47511.6 | 2.53275 | ||||||||
\(707\) | −51509.7 | −2.74006 | ||||||||
\(708\) | 44490.4 | 2.36166 | ||||||||
\(709\) | 16184.8 | 0.857310 | 0.428655 | − | 0.903468i | \(-0.358988\pi\) | ||||
0.428655 | + | 0.903468i | \(0.358988\pi\) | |||||||
\(710\) | −7786.86 | −0.411599 | ||||||||
\(711\) | −5808.56 | −0.306382 | ||||||||
\(712\) | −5143.52 | −0.270733 | ||||||||
\(713\) | 60161.9 | 3.16000 | ||||||||
\(714\) | −76278.5 | −3.99811 | ||||||||
\(715\) | 5097.31 | 0.266614 | ||||||||
\(716\) | −5613.13 | −0.292979 | ||||||||
\(717\) | 7589.05 | 0.395284 | ||||||||
\(718\) | −16770.9 | −0.871706 | ||||||||
\(719\) | −19063.7 | −0.988813 | −0.494406 | − | 0.869231i | \(-0.664615\pi\) | ||||
−0.494406 | + | 0.869231i | \(0.664615\pi\) | |||||||
\(720\) | 1924.02 | 0.0995891 | ||||||||
\(721\) | −18929.0 | −0.977743 | ||||||||
\(722\) | −6703.89 | −0.345558 | ||||||||
\(723\) | 32949.9 | 1.69491 | ||||||||
\(724\) | 16867.6 | 0.865856 | ||||||||
\(725\) | −3694.66 | −0.189264 | ||||||||
\(726\) | 3157.48 | 0.161412 | ||||||||
\(727\) | −17468.5 | −0.891158 | −0.445579 | − | 0.895243i | \(-0.647002\pi\) | ||||
−0.445579 | + | 0.895243i | \(0.647002\pi\) | |||||||
\(728\) | −24480.0 | −1.24628 | ||||||||
\(729\) | 9935.38 | 0.504770 | ||||||||
\(730\) | 12157.9 | 0.616414 | ||||||||
\(731\) | −25412.1 | −1.28577 | ||||||||
\(732\) | 22082.8 | 1.11503 | ||||||||
\(733\) | −15298.7 | −0.770900 | −0.385450 | − | 0.922729i | \(-0.625954\pi\) | ||||
−0.385450 | + | 0.922729i | \(0.625954\pi\) | |||||||
\(734\) | 34919.8 | 1.75601 | ||||||||
\(735\) | 22435.2 | 1.12590 | ||||||||
\(736\) | −44905.5 | −2.24896 | ||||||||
\(737\) | 7409.58 | 0.370333 | ||||||||
\(738\) | −11921.9 | −0.594649 | ||||||||
\(739\) | 3717.46 | 0.185046 | 0.0925230 | − | 0.995711i | \(-0.470507\pi\) | ||||
0.0925230 | + | 0.995711i | \(0.470507\pi\) | |||||||
\(740\) | −25092.7 | −1.24652 | ||||||||
\(741\) | −34149.5 | −1.69300 | ||||||||
\(742\) | −42891.5 | −2.12210 | ||||||||
\(743\) | −4968.60 | −0.245330 | −0.122665 | − | 0.992448i | \(-0.539144\pi\) | ||||
−0.122665 | + | 0.992448i | \(0.539144\pi\) | |||||||
\(744\) | −25656.8 | −1.26428 | ||||||||
\(745\) | 24712.0 | 1.21527 | ||||||||
\(746\) | −4329.83 | −0.212502 | ||||||||
\(747\) | 9549.32 | 0.467726 | ||||||||
\(748\) | 12232.1 | 0.597927 | ||||||||
\(749\) | −43299.4 | −2.11232 | ||||||||
\(750\) | 37759.8 | 1.83839 | ||||||||
\(751\) | −8781.91 | −0.426706 | −0.213353 | − | 0.976975i | \(-0.568438\pi\) | ||||
−0.213353 | + | 0.976975i | \(0.568438\pi\) | |||||||
\(752\) | −4391.38 | −0.212949 | ||||||||
\(753\) | −21982.5 | −1.06386 | ||||||||
\(754\) | 14418.0 | 0.696384 | ||||||||
\(755\) | 4599.94 | 0.221734 | ||||||||
\(756\) | −35326.7 | −1.69950 | ||||||||
\(757\) | −12187.9 | −0.585176 | −0.292588 | − | 0.956239i | \(-0.594516\pi\) | ||||
−0.292588 | + | 0.956239i | \(0.594516\pi\) | |||||||
\(758\) | −591.541 | −0.0283453 | ||||||||
\(759\) | 12394.7 | 0.592751 | ||||||||
\(760\) | −9162.27 | −0.437303 | ||||||||
\(761\) | −6853.23 | −0.326451 | −0.163226 | − | 0.986589i | \(-0.552190\pi\) | ||||
−0.163226 | + | 0.986589i | \(0.552190\pi\) | |||||||
\(762\) | 36467.9 | 1.73372 | ||||||||
\(763\) | 4024.90 | 0.190971 | ||||||||
\(764\) | 53932.7 | 2.55395 | ||||||||
\(765\) | −6470.58 | −0.305810 | ||||||||
\(766\) | −38248.9 | −1.80416 | ||||||||
\(767\) | 41933.3 | 1.97409 | ||||||||
\(768\) | 3348.93 | 0.157349 | ||||||||
\(769\) | −31870.3 | −1.49450 | −0.747252 | − | 0.664541i | \(-0.768627\pi\) | ||||
−0.747252 | + | 0.664541i | \(0.768627\pi\) | |||||||
\(770\) | −10396.2 | −0.486561 | ||||||||
\(771\) | 2588.60 | 0.120916 | ||||||||
\(772\) | 30722.4 | 1.43229 | ||||||||
\(773\) | 14611.4 | 0.679864 | 0.339932 | − | 0.940450i | \(-0.389596\pi\) | ||||
0.339932 | + | 0.940450i | \(0.389596\pi\) | |||||||
\(774\) | 9607.40 | 0.446164 | ||||||||
\(775\) | 22278.0 | 1.03258 | ||||||||
\(776\) | −15259.7 | −0.705917 | ||||||||
\(777\) | 53057.6 | 2.44972 | ||||||||
\(778\) | 6592.83 | 0.303810 | ||||||||
\(779\) | −28793.5 | −1.32430 | ||||||||
\(780\) | −30678.2 | −1.40828 | ||||||||
\(781\) | −2640.34 | −0.120972 | ||||||||
\(782\) | 82677.8 | 3.78076 | ||||||||
\(783\) | 5787.41 | 0.264144 | ||||||||
\(784\) | −15088.6 | −0.687345 | ||||||||
\(785\) | −313.540 | −0.0142557 | ||||||||
\(786\) | −3418.43 | −0.155129 | ||||||||
\(787\) | −11397.5 | −0.516235 | −0.258118 | − | 0.966113i | \(-0.583102\pi\) | ||||
−0.258118 | + | 0.966113i | \(0.583102\pi\) | |||||||
\(788\) | 11987.6 | 0.541928 | ||||||||
\(789\) | 32997.2 | 1.48889 | ||||||||
\(790\) | −21699.9 | −0.977274 | ||||||||
\(791\) | −57975.8 | −2.60605 | ||||||||
\(792\) | −1286.33 | −0.0577118 | ||||||||
\(793\) | 20813.6 | 0.932045 | ||||||||
\(794\) | −28781.0 | −1.28640 | ||||||||
\(795\) | −14951.2 | −0.666999 | ||||||||
\(796\) | −34487.7 | −1.53566 | ||||||||
\(797\) | 21032.0 | 0.934744 | 0.467372 | − | 0.884061i | \(-0.345201\pi\) | ||||
0.467372 | + | 0.884061i | \(0.345201\pi\) | |||||||
\(798\) | 69649.1 | 3.08966 | ||||||||
\(799\) | 14768.4 | 0.653904 | ||||||||
\(800\) | −16628.6 | −0.734885 | ||||||||
\(801\) | 3316.76 | 0.146307 | ||||||||
\(802\) | −24242.2 | −1.06736 | ||||||||
\(803\) | 4122.44 | 0.181168 | ||||||||
\(804\) | −44594.6 | −1.95613 | ||||||||
\(805\) | −40810.1 | −1.78679 | ||||||||
\(806\) | −86937.6 | −3.79931 | ||||||||
\(807\) | 32884.9 | 1.43445 | ||||||||
\(808\) | −23809.9 | −1.03667 | ||||||||
\(809\) | 40850.3 | 1.77530 | 0.887652 | − | 0.460515i | \(-0.152335\pi\) | ||||
0.887652 | + | 0.460515i | \(0.152335\pi\) | |||||||
\(810\) | −28809.4 | −1.24970 | ||||||||
\(811\) | −20130.2 | −0.871598 | −0.435799 | − | 0.900044i | \(-0.643534\pi\) | ||||
−0.435799 | + | 0.900044i | \(0.643534\pi\) | |||||||
\(812\) | −17078.2 | −0.738090 | ||||||||
\(813\) | 5551.41 | 0.239479 | ||||||||
\(814\) | −14650.1 | −0.630817 | ||||||||
\(815\) | 2592.25 | 0.111414 | ||||||||
\(816\) | 17882.4 | 0.767168 | ||||||||
\(817\) | 23203.6 | 0.993623 | ||||||||
\(818\) | −27415.8 | −1.17185 | ||||||||
\(819\) | 15785.8 | 0.673503 | ||||||||
\(820\) | −25866.6 | −1.10159 | ||||||||
\(821\) | 42406.1 | 1.80266 | 0.901330 | − | 0.433132i | \(-0.142592\pi\) | ||||
0.901330 | + | 0.433132i | \(0.142592\pi\) | |||||||
\(822\) | 35855.7 | 1.52142 | ||||||||
\(823\) | 20389.0 | 0.863569 | 0.431785 | − | 0.901977i | \(-0.357884\pi\) | ||||
0.431785 | + | 0.901977i | \(0.357884\pi\) | |||||||
\(824\) | −8749.74 | −0.369917 | ||||||||
\(825\) | 4589.77 | 0.193691 | ||||||||
\(826\) | −85524.5 | −3.60264 | ||||||||
\(827\) | −14308.2 | −0.601627 | −0.300814 | − | 0.953683i | \(-0.597258\pi\) | ||||
−0.300814 | + | 0.953683i | \(0.597258\pi\) | |||||||
\(828\) | −18153.5 | −0.761929 | ||||||||
\(829\) | 20206.3 | 0.846553 | 0.423276 | − | 0.906001i | \(-0.360880\pi\) | ||||
0.423276 | + | 0.906001i | \(0.360880\pi\) | |||||||
\(830\) | 35674.8 | 1.49192 | ||||||||
\(831\) | 890.700 | 0.0371818 | ||||||||
\(832\) | 49997.8 | 2.08337 | ||||||||
\(833\) | 50743.7 | 2.11064 | ||||||||
\(834\) | 8281.69 | 0.343851 | ||||||||
\(835\) | 15913.6 | 0.659535 | ||||||||
\(836\) | −11169.0 | −0.462067 | ||||||||
\(837\) | −34896.8 | −1.44111 | ||||||||
\(838\) | −49362.2 | −2.03483 | ||||||||
\(839\) | 41965.6 | 1.72683 | 0.863417 | − | 0.504490i | \(-0.168320\pi\) | ||||
0.863417 | + | 0.504490i | \(0.168320\pi\) | |||||||
\(840\) | 17404.0 | 0.714874 | ||||||||
\(841\) | −21591.2 | −0.885282 | ||||||||
\(842\) | 25857.2 | 1.05831 | ||||||||
\(843\) | −33854.0 | −1.38315 | ||||||||
\(844\) | 62391.1 | 2.54454 | ||||||||
\(845\) | −12599.2 | −0.512932 | ||||||||
\(846\) | −5583.40 | −0.226905 | ||||||||
\(847\) | −3525.09 | −0.143003 | ||||||||
\(848\) | 10055.3 | 0.407193 | ||||||||
\(849\) | 30037.3 | 1.21422 | ||||||||
\(850\) | 30615.7 | 1.23542 | ||||||||
\(851\) | −57508.8 | −2.31654 | ||||||||
\(852\) | 15890.9 | 0.638982 | ||||||||
\(853\) | −38914.5 | −1.56203 | −0.781013 | − | 0.624515i | \(-0.785297\pi\) | ||||
−0.781013 | + | 0.624515i | \(0.785297\pi\) | |||||||
\(854\) | −42450.1 | −1.70095 | ||||||||
\(855\) | 5908.22 | 0.236324 | ||||||||
\(856\) | −20014.7 | −0.799169 | ||||||||
\(857\) | −10165.5 | −0.405188 | −0.202594 | − | 0.979263i | \(-0.564937\pi\) | ||||
−0.202594 | + | 0.979263i | \(0.564937\pi\) | |||||||
\(858\) | −17911.1 | −0.712673 | ||||||||
\(859\) | −2582.90 | −0.102593 | −0.0512965 | − | 0.998683i | \(-0.516335\pi\) | ||||
−0.0512965 | + | 0.998683i | \(0.516335\pi\) | |||||||
\(860\) | 20844.9 | 0.826519 | ||||||||
\(861\) | 54694.0 | 2.16488 | ||||||||
\(862\) | −34600.9 | −1.36718 | ||||||||
\(863\) | 26171.0 | 1.03230 | 0.516148 | − | 0.856499i | \(-0.327365\pi\) | ||||
0.516148 | + | 0.856499i | \(0.327365\pi\) | |||||||
\(864\) | 26047.4 | 1.02564 | ||||||||
\(865\) | 31386.8 | 1.23374 | ||||||||
\(866\) | −34463.5 | −1.35233 | ||||||||
\(867\) | −30791.0 | −1.20613 | ||||||||
\(868\) | 102978. | 4.02685 | ||||||||
\(869\) | −7357.91 | −0.287227 | ||||||||
\(870\) | −10250.4 | −0.399451 | ||||||||
\(871\) | −42031.4 | −1.63511 | ||||||||
\(872\) | 1860.47 | 0.0722517 | ||||||||
\(873\) | 9840.10 | 0.381486 | ||||||||
\(874\) | −75492.3 | −2.92170 | ||||||||
\(875\) | −42156.0 | −1.62872 | ||||||||
\(876\) | −24810.9 | −0.956945 | ||||||||
\(877\) | 1732.50 | 0.0667075 | 0.0333537 | − | 0.999444i | \(-0.489381\pi\) | ||||
0.0333537 | + | 0.999444i | \(0.489381\pi\) | |||||||
\(878\) | −38205.7 | −1.46854 | ||||||||
\(879\) | −33548.9 | −1.28735 | ||||||||
\(880\) | 2437.23 | 0.0933625 | ||||||||
\(881\) | 31267.6 | 1.19572 | 0.597861 | − | 0.801600i | \(-0.296017\pi\) | ||||
0.597861 | + | 0.801600i | \(0.296017\pi\) | |||||||
\(882\) | −19184.3 | −0.732393 | ||||||||
\(883\) | 32065.6 | 1.22208 | 0.611038 | − | 0.791601i | \(-0.290752\pi\) | ||||
0.611038 | + | 0.791601i | \(0.290752\pi\) | |||||||
\(884\) | −69387.5 | −2.63999 | ||||||||
\(885\) | −29812.3 | −1.13235 | ||||||||
\(886\) | −4795.50 | −0.181837 | ||||||||
\(887\) | −36264.0 | −1.37275 | −0.686373 | − | 0.727250i | \(-0.740798\pi\) | ||||
−0.686373 | + | 0.727250i | \(0.740798\pi\) | |||||||
\(888\) | 24525.3 | 0.926821 | ||||||||
\(889\) | −40713.7 | −1.53599 | ||||||||
\(890\) | 12390.9 | 0.466678 | ||||||||
\(891\) | −9768.59 | −0.367295 | ||||||||
\(892\) | −1360.46 | −0.0510667 | ||||||||
\(893\) | −13484.9 | −0.505325 | ||||||||
\(894\) | −86833.5 | −3.24849 | ||||||||
\(895\) | 3761.27 | 0.140475 | ||||||||
\(896\) | −46488.5 | −1.73334 | ||||||||
\(897\) | −70309.8 | −2.61714 | ||||||||
\(898\) | −29367.7 | −1.09133 | ||||||||
\(899\) | −16870.4 | −0.625873 | ||||||||
\(900\) | −6722.26 | −0.248973 | ||||||||
\(901\) | −33816.4 | −1.25037 | ||||||||
\(902\) | −15101.9 | −0.557471 | ||||||||
\(903\) | −44075.8 | −1.62431 | ||||||||
\(904\) | −26798.7 | −0.985966 | ||||||||
\(905\) | −11302.7 | −0.415155 | ||||||||
\(906\) | −16163.4 | −0.592707 | ||||||||
\(907\) | 19470.5 | 0.712799 | 0.356400 | − | 0.934334i | \(-0.384004\pi\) | ||||
0.356400 | + | 0.934334i | \(0.384004\pi\) | |||||||
\(908\) | −39278.6 | −1.43558 | ||||||||
\(909\) | 15353.6 | 0.560228 | ||||||||
\(910\) | 58973.1 | 2.14828 | ||||||||
\(911\) | 31598.9 | 1.14920 | 0.574598 | − | 0.818436i | \(-0.305158\pi\) | ||||
0.574598 | + | 0.818436i | \(0.305158\pi\) | |||||||
\(912\) | −16328.2 | −0.592853 | ||||||||
\(913\) | 12096.5 | 0.438483 | ||||||||
\(914\) | 3115.92 | 0.112763 | ||||||||
\(915\) | −14797.3 | −0.534628 | ||||||||
\(916\) | 6707.93 | 0.241961 | ||||||||
\(917\) | 3816.42 | 0.137437 | ||||||||
\(918\) | −47957.2 | −1.72421 | ||||||||
\(919\) | −23034.5 | −0.826811 | −0.413405 | − | 0.910547i | \(-0.635661\pi\) | ||||
−0.413405 | + | 0.910547i | \(0.635661\pi\) | |||||||
\(920\) | −18864.1 | −0.676011 | ||||||||
\(921\) | −27445.2 | −0.981922 | ||||||||
\(922\) | 2625.36 | 0.0937762 | ||||||||
\(923\) | 14977.5 | 0.534119 | ||||||||
\(924\) | 21215.8 | 0.755355 | ||||||||
\(925\) | −21295.6 | −0.756967 | ||||||||
\(926\) | 37722.9 | 1.33872 | ||||||||
\(927\) | 5642.20 | 0.199908 | ||||||||
\(928\) | 12592.3 | 0.445432 | ||||||||
\(929\) | 28197.6 | 0.995839 | 0.497919 | − | 0.867223i | \(-0.334097\pi\) | ||||
0.497919 | + | 0.867223i | \(0.334097\pi\) | |||||||
\(930\) | 61807.9 | 2.17931 | ||||||||
\(931\) | −46333.5 | −1.63106 | ||||||||
\(932\) | −26973.6 | −0.948014 | ||||||||
\(933\) | −17610.9 | −0.617958 | ||||||||
\(934\) | 3506.35 | 0.122839 | ||||||||
\(935\) | −8196.52 | −0.286690 | ||||||||
\(936\) | 7296.81 | 0.254812 | ||||||||
\(937\) | 18488.6 | 0.644608 | 0.322304 | − | 0.946636i | \(-0.395543\pi\) | ||||
0.322304 | + | 0.946636i | \(0.395543\pi\) | |||||||
\(938\) | 85724.7 | 2.98402 | ||||||||
\(939\) | 30100.6 | 1.04611 | ||||||||
\(940\) | −12114.2 | −0.420341 | ||||||||
\(941\) | 13165.0 | 0.456075 | 0.228037 | − | 0.973652i | \(-0.426769\pi\) | ||||
0.228037 | + | 0.973652i | \(0.426769\pi\) | |||||||
\(942\) | 1101.73 | 0.0381063 | ||||||||
\(943\) | −59282.5 | −2.04719 | ||||||||
\(944\) | 20050.0 | 0.691284 | ||||||||
\(945\) | 23671.9 | 0.814863 | ||||||||
\(946\) | 12170.0 | 0.418269 | ||||||||
\(947\) | −25346.9 | −0.869761 | −0.434880 | − | 0.900488i | \(-0.643209\pi\) | ||||
−0.434880 | + | 0.900488i | \(0.643209\pi\) | |||||||
\(948\) | 44283.6 | 1.51716 | ||||||||
\(949\) | −23384.9 | −0.799901 | ||||||||
\(950\) | −27954.9 | −0.954712 | ||||||||
\(951\) | 17052.8 | 0.581467 | ||||||||
\(952\) | 39364.0 | 1.34012 | ||||||||
\(953\) | 3143.07 | 0.106835 | 0.0534176 | − | 0.998572i | \(-0.482989\pi\) | ||||
0.0534176 | + | 0.998572i | \(0.482989\pi\) | |||||||
\(954\) | 12784.7 | 0.433880 | ||||||||
\(955\) | −36139.4 | −1.22455 | ||||||||
\(956\) | −14079.9 | −0.476334 | ||||||||
\(957\) | −3475.68 | −0.117401 | ||||||||
\(958\) | −46081.3 | −1.55409 | ||||||||
\(959\) | −40030.3 | −1.34791 | ||||||||
\(960\) | −35545.7 | −1.19503 | ||||||||
\(961\) | 71934.1 | 2.41462 | ||||||||
\(962\) | 83103.7 | 2.78521 | ||||||||
\(963\) | 12906.3 | 0.431880 | ||||||||
\(964\) | −61131.5 | −2.04244 | ||||||||
\(965\) | −20586.6 | −0.686743 | ||||||||
\(966\) | 143400. | 4.77620 | ||||||||
\(967\) | −30936.4 | −1.02880 | −0.514398 | − | 0.857551i | \(-0.671985\pi\) | ||||
−0.514398 | + | 0.857551i | \(0.671985\pi\) | |||||||
\(968\) | −1629.44 | −0.0541035 | ||||||||
\(969\) | 54912.6 | 1.82048 | ||||||||
\(970\) | 36761.1 | 1.21683 | ||||||||
\(971\) | 43550.4 | 1.43934 | 0.719670 | − | 0.694316i | \(-0.244293\pi\) | ||||
0.719670 | + | 0.694316i | \(0.244293\pi\) | |||||||
\(972\) | 26052.0 | 0.859691 | ||||||||
\(973\) | −9245.90 | −0.304635 | ||||||||
\(974\) | −32281.8 | −1.06199 | ||||||||
\(975\) | −26035.8 | −0.855194 | ||||||||
\(976\) | 9951.81 | 0.326383 | ||||||||
\(977\) | −29342.8 | −0.960860 | −0.480430 | − | 0.877033i | \(-0.659519\pi\) | ||||
−0.480430 | + | 0.877033i | \(0.659519\pi\) | |||||||
\(978\) | −9108.71 | −0.297816 | ||||||||
\(979\) | 4201.46 | 0.137160 | ||||||||
\(980\) | −41623.8 | −1.35676 | ||||||||
\(981\) | −1199.71 | −0.0390457 | ||||||||
\(982\) | −29432.5 | −0.956445 | ||||||||
\(983\) | 34339.7 | 1.11421 | 0.557104 | − | 0.830443i | \(-0.311913\pi\) | ||||
0.557104 | + | 0.830443i | \(0.311913\pi\) | |||||||
\(984\) | 25281.7 | 0.819058 | ||||||||
\(985\) | −8032.68 | −0.259840 | ||||||||
\(986\) | −23184.3 | −0.748821 | ||||||||
\(987\) | 25614.9 | 0.826071 | ||||||||
\(988\) | 63357.0 | 2.04014 | ||||||||
\(989\) | 47773.5 | 1.53600 | ||||||||
\(990\) | 3098.81 | 0.0994813 | ||||||||
\(991\) | −44515.6 | −1.42693 | −0.713464 | − | 0.700692i | \(-0.752875\pi\) | ||||
−0.713464 | + | 0.700692i | \(0.752875\pi\) | |||||||
\(992\) | −75928.7 | −2.43018 | ||||||||
\(993\) | 45823.5 | 1.46442 | ||||||||
\(994\) | −30547.3 | −0.974749 | ||||||||
\(995\) | 23109.6 | 0.736306 | ||||||||
\(996\) | −72802.7 | −2.31611 | ||||||||
\(997\) | 34834.3 | 1.10653 | 0.553267 | − | 0.833004i | \(-0.313381\pi\) | ||||
0.553267 | + | 0.833004i | \(0.313381\pi\) | |||||||
\(998\) | 9127.76 | 0.289513 | ||||||||
\(999\) | 33357.9 | 1.05645 |
(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 | 1441.4.a.b.1.12 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.4.a.b.1.12 | ✓ | 79 | 1.1 | even | 1 | trivial |