Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.51 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.40394 | 1.55703 | 0.778513 | − | 0.627628i | \(-0.215974\pi\) | ||||
0.778513 | + | 0.627628i | \(0.215974\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 11.3946 | 1.42433 | ||||||||
\(5\) | −1.03938 | −0.0929653 | −0.0464826 | − | 0.998919i | \(-0.514801\pi\) | ||||
−0.0464826 | + | 0.998919i | \(0.514801\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.641944 | 0.0346617 | 0.0173309 | − | 0.999850i | \(-0.494483\pi\) | ||||
0.0173309 | + | 0.999850i | \(0.494483\pi\) | |||||||
\(8\) | 14.9498 | 0.660694 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.57738 | −0.144749 | ||||||||
\(11\) | 48.9987 | 1.34306 | 0.671531 | − | 0.740977i | \(-0.265637\pi\) | ||||
0.671531 | + | 0.740977i | \(0.265637\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −36.7063 | −0.783115 | −0.391557 | − | 0.920154i | \(-0.628064\pi\) | ||||
−0.391557 | + | 0.920154i | \(0.628064\pi\) | |||||||
\(14\) | 2.82708 | 0.0539692 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −25.3192 | −0.395612 | ||||||||
\(17\) | −37.8766 | −0.540378 | −0.270189 | − | 0.962807i | \(-0.587086\pi\) | ||||
−0.270189 | + | 0.962807i | \(0.587086\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −135.430 | −1.63526 | −0.817629 | − | 0.575746i | \(-0.804712\pi\) | ||||
−0.817629 | + | 0.575746i | \(0.804712\pi\) | |||||||
\(20\) | −11.8434 | −0.132413 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 215.787 | 2.09118 | ||||||||
\(23\) | 107.109 | 0.971031 | 0.485516 | − | 0.874228i | \(-0.338632\pi\) | ||||
0.485516 | + | 0.874228i | \(0.338632\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −123.920 | −0.991357 | ||||||||
\(26\) | −161.652 | −1.21933 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.31473 | 0.0493698 | ||||||||
\(29\) | 164.716 | 1.05473 | 0.527363 | − | 0.849640i | \(-0.323181\pi\) | ||||
0.527363 | + | 0.849640i | \(0.323181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −178.114 | −1.03194 | −0.515970 | − | 0.856606i | \(-0.672569\pi\) | ||||
−0.515970 | + | 0.856606i | \(0.672569\pi\) | |||||||
\(32\) | −231.103 | −1.27667 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −166.806 | −0.841382 | ||||||||
\(35\) | −0.667226 | −0.00322234 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −312.490 | −1.38846 | −0.694229 | − | 0.719754i | \(-0.744255\pi\) | ||||
−0.694229 | + | 0.719754i | \(0.744255\pi\) | |||||||
\(38\) | −596.427 | −2.54614 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −15.5386 | −0.0614216 | ||||||||
\(41\) | 128.393 | 0.489066 | 0.244533 | − | 0.969641i | \(-0.421365\pi\) | ||||
0.244533 | + | 0.969641i | \(0.421365\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −167.661 | −0.594606 | −0.297303 | − | 0.954783i | \(-0.596087\pi\) | ||||
−0.297303 | + | 0.954783i | \(0.596087\pi\) | |||||||
\(44\) | 558.323 | 1.91296 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 471.700 | 1.51192 | ||||||||
\(47\) | 59.1103 | 0.183449 | 0.0917247 | − | 0.995784i | \(-0.470762\pi\) | ||||
0.0917247 | + | 0.995784i | \(0.470762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.588 | −0.998799 | ||||||||
\(50\) | −545.734 | −1.54357 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −418.255 | −1.11541 | ||||||||
\(53\) | −261.864 | −0.678676 | −0.339338 | − | 0.940665i | \(-0.610203\pi\) | ||||
−0.339338 | + | 0.940665i | \(0.610203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −50.9285 | −0.124858 | ||||||||
\(56\) | 9.59694 | 0.0229008 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 725.399 | 1.64223 | ||||||||
\(59\) | 716.904 | 1.58191 | 0.790957 | − | 0.611872i | \(-0.209583\pi\) | ||||
0.790957 | + | 0.611872i | \(0.209583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 900.978 | 1.89112 | 0.945561 | − | 0.325446i | \(-0.105514\pi\) | ||||
0.945561 | + | 0.325446i | \(0.105514\pi\) | |||||||
\(62\) | −784.401 | −1.60676 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −815.207 | −1.59220 | ||||||||
\(65\) | 38.1519 | 0.0728024 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −397.047 | −0.723986 | −0.361993 | − | 0.932181i | \(-0.617904\pi\) | ||||
−0.361993 | + | 0.932181i | \(0.617904\pi\) | |||||||
\(68\) | −431.590 | −0.769677 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.93842 | −0.00501726 | ||||||||
\(71\) | −360.948 | −0.603333 | −0.301666 | − | 0.953414i | \(-0.597543\pi\) | ||||
−0.301666 | + | 0.953414i | \(0.597543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 145.439 | 0.233183 | 0.116592 | − | 0.993180i | \(-0.462803\pi\) | ||||
0.116592 | + | 0.993180i | \(0.462803\pi\) | |||||||
\(74\) | −1376.18 | −2.16187 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1543.18 | −2.32915 | ||||||||
\(77\) | 31.4545 | 0.0465529 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −227.148 | −0.323496 | −0.161748 | − | 0.986832i | \(-0.551713\pi\) | ||||
−0.161748 | + | 0.986832i | \(0.551713\pi\) | |||||||
\(80\) | 26.3163 | 0.0367782 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 565.437 | 0.761488 | ||||||||
\(83\) | −994.304 | −1.31493 | −0.657464 | − | 0.753486i | \(-0.728371\pi\) | ||||
−0.657464 | + | 0.753486i | \(0.728371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 39.3683 | 0.0502363 | ||||||||
\(86\) | −738.368 | −0.925817 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 732.522 | 0.887353 | ||||||||
\(89\) | −323.348 | −0.385111 | −0.192555 | − | 0.981286i | \(-0.561677\pi\) | ||||
−0.192555 | + | 0.981286i | \(0.561677\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.5634 | −0.0271441 | ||||||||
\(92\) | 1220.47 | 1.38307 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 260.318 | 0.285636 | ||||||||
\(95\) | 140.764 | 0.152022 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −198.509 | −0.207789 | −0.103895 | − | 0.994588i | \(-0.533130\pi\) | ||||
−0.103895 | + | 0.994588i | \(0.533130\pi\) | |||||||
\(98\) | −1508.74 | −1.55516 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1412.02 | −1.41202 | ||||||||
\(101\) | −1377.89 | −1.35748 | −0.678738 | − | 0.734380i | \(-0.737473\pi\) | ||||
−0.678738 | + | 0.734380i | \(0.737473\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −134.668 | −0.128828 | −0.0644140 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644140 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(104\) | −548.752 | −0.517399 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1153.23 | −1.05672 | ||||||||
\(107\) | −288.843 | −0.260967 | −0.130484 | − | 0.991450i | \(-0.541653\pi\) | ||||
−0.130484 | + | 0.991450i | \(0.541653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −885.572 | −0.778187 | −0.389094 | − | 0.921198i | \(-0.627212\pi\) | ||||
−0.389094 | + | 0.921198i | \(0.627212\pi\) | |||||||
\(110\) | −224.286 | −0.194407 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −16.2535 | −0.0137126 | ||||||||
\(113\) | −23.9012 | −0.0198976 | −0.00994882 | − | 0.999951i | \(-0.503167\pi\) | ||||
−0.00994882 | + | 0.999951i | \(0.503167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −111.327 | −0.0902722 | ||||||||
\(116\) | 1876.88 | 1.50228 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3157.20 | 2.46308 | ||||||||
\(119\) | −24.3147 | −0.0187304 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1069.88 | 0.803815 | ||||||||
\(122\) | 3967.85 | 2.94453 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2029.54 | −1.46983 | ||||||||
\(125\) | 258.723 | 0.185127 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 857.709 | 0.599286 | 0.299643 | − | 0.954051i | \(-0.403132\pi\) | ||||
0.299643 | + | 0.954051i | \(0.403132\pi\) | |||||||
\(128\) | −1741.30 | −1.20243 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 168.018 | 0.113355 | ||||||||
\(131\) | 1472.96 | 0.982392 | 0.491196 | − | 0.871049i | \(-0.336560\pi\) | ||||
0.491196 | + | 0.871049i | \(0.336560\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −86.9388 | −0.0566809 | ||||||||
\(134\) | −1748.57 | −1.12727 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −566.247 | −0.357024 | ||||||||
\(137\) | −1390.34 | −0.867041 | −0.433520 | − | 0.901144i | \(-0.642729\pi\) | ||||
−0.433520 | + | 0.901144i | \(0.642729\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −27.7276 | −0.0169196 | −0.00845981 | − | 0.999964i | \(-0.502693\pi\) | ||||
−0.00845981 | + | 0.999964i | \(0.502693\pi\) | |||||||
\(140\) | −7.60281 | −0.00458967 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1589.59 | −0.939405 | ||||||||
\(143\) | −1798.56 | −1.05177 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −171.203 | −0.0980528 | ||||||||
\(146\) | 640.505 | 0.363072 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3560.71 | −1.97762 | ||||||||
\(149\) | 995.083 | 0.547116 | 0.273558 | − | 0.961855i | \(-0.411799\pi\) | ||||
0.273558 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −659.208 | −0.355269 | −0.177634 | − | 0.984097i | \(-0.556844\pi\) | ||||
−0.177634 | + | 0.984097i | \(0.556844\pi\) | |||||||
\(152\) | −2024.66 | −1.08041 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 138.523 | 0.0724840 | ||||||||
\(155\) | 185.128 | 0.0959346 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −741.441 | −0.376901 | −0.188450 | − | 0.982083i | \(-0.560346\pi\) | ||||
−0.188450 | + | 0.982083i | \(0.560346\pi\) | |||||||
\(158\) | −1000.35 | −0.503692 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 240.204 | 0.118686 | ||||||||
\(161\) | 68.7579 | 0.0336576 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −181.036 | −0.0869926 | −0.0434963 | − | 0.999054i | \(-0.513850\pi\) | ||||
−0.0434963 | + | 0.999054i | \(0.513850\pi\) | |||||||
\(164\) | 1463.00 | 0.696591 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4378.85 | −2.04738 | ||||||||
\(167\) | −882.972 | −0.409140 | −0.204570 | − | 0.978852i | \(-0.565580\pi\) | ||||
−0.204570 | + | 0.978852i | \(0.565580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −849.649 | −0.386732 | ||||||||
\(170\) | 173.375 | 0.0782193 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1910.44 | −0.846916 | ||||||||
\(173\) | −589.731 | −0.259170 | −0.129585 | − | 0.991568i | \(-0.541365\pi\) | ||||
−0.129585 | + | 0.991568i | \(0.541365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −79.5495 | −0.0343622 | ||||||||
\(176\) | −1240.61 | −0.531332 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1424.00 | −0.599627 | ||||||||
\(179\) | 2060.21 | 0.860263 | 0.430132 | − | 0.902766i | \(-0.358467\pi\) | ||||
0.430132 | + | 0.902766i | \(0.358467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1514.84 | −0.622083 | −0.311041 | − | 0.950396i | \(-0.600678\pi\) | ||||
−0.311041 | + | 0.950396i | \(0.600678\pi\) | |||||||
\(182\) | −103.772 | −0.0422641 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1601.26 | 0.641555 | ||||||||
\(185\) | 324.796 | 0.129078 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1855.90 | −0.725760 | ||||||||
\(188\) | 673.541 | 0.261293 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 619.916 | 0.236702 | ||||||||
\(191\) | −1934.29 | −0.732777 | −0.366388 | − | 0.930462i | \(-0.619406\pi\) | ||||
−0.366388 | + | 0.930462i | \(0.619406\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4952.41 | 1.84706 | 0.923530 | − | 0.383526i | \(-0.125290\pi\) | ||||
0.923530 | + | 0.383526i | \(0.125290\pi\) | |||||||
\(194\) | −874.222 | −0.323534 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3903.67 | −1.42262 | ||||||||
\(197\) | 1761.04 | 0.636899 | 0.318449 | − | 0.947940i | \(-0.396838\pi\) | ||||
0.318449 | + | 0.947940i | \(0.396838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3690.29 | −1.31456 | −0.657281 | − | 0.753645i | \(-0.728294\pi\) | ||||
−0.657281 | + | 0.753645i | \(0.728294\pi\) | |||||||
\(200\) | −1852.58 | −0.654984 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6068.14 | −2.11363 | ||||||||
\(203\) | 105.739 | 0.0365586 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −133.450 | −0.0454661 | ||||||||
\(206\) | −593.071 | −0.200588 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 929.373 | 0.309810 | ||||||||
\(209\) | −6635.92 | −2.19625 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5426.38 | −1.77046 | −0.885231 | − | 0.465151i | \(-0.846000\pi\) | ||||
−0.885231 | + | 0.465151i | \(0.846000\pi\) | |||||||
\(212\) | −2983.85 | −0.966659 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1272.04 | −0.406333 | ||||||||
\(215\) | 174.264 | 0.0552777 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −114.339 | −0.0357689 | ||||||||
\(218\) | −3900.00 | −1.21166 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −580.312 | −0.177839 | ||||||||
\(221\) | 1390.31 | 0.423178 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2368.65 | 0.711286 | 0.355643 | − | 0.934622i | \(-0.384262\pi\) | ||||
0.355643 | + | 0.934622i | \(0.384262\pi\) | |||||||
\(224\) | −148.355 | −0.0442517 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −105.259 | −0.0309812 | ||||||||
\(227\) | −4653.98 | −1.36077 | −0.680387 | − | 0.732853i | \(-0.738188\pi\) | ||||
−0.680387 | + | 0.732853i | \(0.738188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2760.19 | −0.796500 | −0.398250 | − | 0.917277i | \(-0.630382\pi\) | ||||
−0.398250 | + | 0.917277i | \(0.630382\pi\) | |||||||
\(230\) | −490.277 | −0.140556 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2462.48 | 0.696851 | ||||||||
\(233\) | 4125.32 | 1.15991 | 0.579955 | − | 0.814649i | \(-0.303070\pi\) | ||||
0.579955 | + | 0.814649i | \(0.303070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −61.4382 | −0.0170544 | ||||||||
\(236\) | 8168.87 | 2.25317 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −107.080 | −0.0291638 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3229.52 | −0.863202 | −0.431601 | − | 0.902065i | \(-0.642051\pi\) | ||||
−0.431601 | + | 0.902065i | \(0.642051\pi\) | |||||||
\(242\) | 4711.67 | 1.25156 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10266.3 | 2.69358 | ||||||||
\(245\) | 356.080 | 0.0928536 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4971.15 | 1.28059 | ||||||||
\(248\) | −2662.77 | −0.681797 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1139.40 | 0.288248 | ||||||||
\(251\) | −1164.25 | −0.292777 | −0.146389 | − | 0.989227i | \(-0.546765\pi\) | ||||
−0.146389 | + | 0.989227i | \(0.546765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5248.20 | 1.30416 | ||||||||
\(254\) | 3777.29 | 0.933105 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1146.91 | −0.280008 | ||||||||
\(257\) | 7690.46 | 1.86661 | 0.933303 | − | 0.359090i | \(-0.116913\pi\) | ||||
0.933303 | + | 0.359090i | \(0.116913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −200.601 | −0.0481264 | ||||||||
\(260\) | 434.727 | 0.103695 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6486.83 | 1.52961 | ||||||||
\(263\) | 3236.93 | 0.758927 | 0.379463 | − | 0.925207i | \(-0.376109\pi\) | ||||
0.379463 | + | 0.925207i | \(0.376109\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 272.177 | 0.0630933 | ||||||||
\(266\) | −382.873 | −0.0882536 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4524.22 | −1.03120 | ||||||||
\(269\) | 709.861 | 0.160896 | 0.0804479 | − | 0.996759i | \(-0.474365\pi\) | ||||
0.0804479 | + | 0.996759i | \(0.474365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6243.22 | −1.39944 | −0.699721 | − | 0.714416i | \(-0.746692\pi\) | ||||
−0.699721 | + | 0.714416i | \(0.746692\pi\) | |||||||
\(272\) | 959.005 | 0.213780 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6122.96 | −1.35001 | ||||||||
\(275\) | −6071.91 | −1.33145 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5525.13 | 1.19846 | 0.599229 | − | 0.800578i | \(-0.295474\pi\) | ||||
0.599229 | + | 0.800578i | \(0.295474\pi\) | |||||||
\(278\) | −122.111 | −0.0263443 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.97490 | −0.00212898 | ||||||||
\(281\) | 148.471 | 0.0315197 | 0.0157598 | − | 0.999876i | \(-0.494983\pi\) | ||||
0.0157598 | + | 0.999876i | \(0.494983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2136.10 | −0.448685 | −0.224342 | − | 0.974510i | \(-0.572023\pi\) | ||||
−0.224342 | + | 0.974510i | \(0.572023\pi\) | |||||||
\(284\) | −4112.87 | −0.859346 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7920.75 | −1.63764 | ||||||||
\(287\) | 82.4215 | 0.0169519 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3478.36 | −0.707992 | ||||||||
\(290\) | −753.968 | −0.152671 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1657.23 | 0.332130 | ||||||||
\(293\) | −5523.29 | −1.10128 | −0.550639 | − | 0.834744i | \(-0.685616\pi\) | ||||
−0.550639 | + | 0.834744i | \(0.685616\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −745.138 | −0.147063 | ||||||||
\(296\) | −4671.66 | −0.917347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4382.28 | 0.851875 | ||||||||
\(299\) | −3931.56 | −0.760429 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −107.629 | −0.0206101 | ||||||||
\(302\) | −2903.11 | −0.553163 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3428.99 | 0.646928 | ||||||||
\(305\) | −936.461 | −0.175809 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1415.87 | −0.263218 | −0.131609 | − | 0.991302i | \(-0.542014\pi\) | ||||
−0.131609 | + | 0.991302i | \(0.542014\pi\) | |||||||
\(308\) | 358.413 | 0.0663067 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 815.293 | 0.149373 | ||||||||
\(311\) | 6245.37 | 1.13872 | 0.569361 | − | 0.822088i | \(-0.307191\pi\) | ||||
0.569361 | + | 0.822088i | \(0.307191\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3634.14 | −0.656273 | −0.328137 | − | 0.944630i | \(-0.606421\pi\) | ||||
−0.328137 | + | 0.944630i | \(0.606421\pi\) | |||||||
\(314\) | −3265.26 | −0.586844 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2588.27 | −0.460765 | ||||||||
\(317\) | −1405.97 | −0.249107 | −0.124553 | − | 0.992213i | \(-0.539750\pi\) | ||||
−0.124553 | + | 0.992213i | \(0.539750\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8070.89 | 1.41656 | ||||||||
\(320\) | 847.313 | 0.148019 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 302.805 | 0.0524058 | ||||||||
\(323\) | 5129.64 | 0.883656 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4548.63 | 0.776346 | ||||||||
\(326\) | −797.269 | −0.135450 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1919.46 | 0.323123 | ||||||||
\(329\) | 37.9455 | 0.00635867 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9057.14 | 1.50400 | 0.752002 | − | 0.659161i | \(-0.229088\pi\) | ||||
0.752002 | + | 0.659161i | \(0.229088\pi\) | |||||||
\(332\) | −11329.7 | −1.87289 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3888.55 | −0.637042 | ||||||||
\(335\) | 412.684 | 0.0673056 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1855.81 | 0.299977 | 0.149988 | − | 0.988688i | \(-0.452076\pi\) | ||||
0.149988 | + | 0.988688i | \(0.452076\pi\) | |||||||
\(338\) | −3741.80 | −0.602151 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 448.588 | 0.0715532 | ||||||||
\(341\) | −8727.35 | −1.38596 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −440.109 | −0.0692818 | ||||||||
\(344\) | −2506.50 | −0.392853 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2597.14 | −0.403535 | ||||||||
\(347\) | 11986.1 | 1.85432 | 0.927161 | − | 0.374663i | \(-0.122241\pi\) | ||||
0.927161 | + | 0.374663i | \(0.122241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6042.16 | 0.926732 | 0.463366 | − | 0.886167i | \(-0.346641\pi\) | ||||
0.463366 | + | 0.886167i | \(0.346641\pi\) | |||||||
\(350\) | −350.331 | −0.0535028 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11323.7 | −1.71465 | ||||||||
\(353\) | 5817.21 | 0.877107 | 0.438554 | − | 0.898705i | \(-0.355491\pi\) | ||||
0.438554 | + | 0.898705i | \(0.355491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 375.163 | 0.0560890 | ||||||||
\(356\) | −3684.44 | −0.548525 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9073.02 | 1.33945 | ||||||||
\(359\) | −3414.05 | −0.501912 | −0.250956 | − | 0.967998i | \(-0.580745\pi\) | ||||
−0.250956 | + | 0.967998i | \(0.580745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11482.4 | 1.67407 | ||||||||
\(362\) | −6671.25 | −0.968599 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −268.496 | −0.0386622 | ||||||||
\(365\) | −151.167 | −0.0216779 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6466.51 | 0.919753 | 0.459876 | − | 0.887983i | \(-0.347894\pi\) | ||||
0.459876 | + | 0.887983i | \(0.347894\pi\) | |||||||
\(368\) | −2711.91 | −0.384152 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1430.38 | 0.200978 | ||||||||
\(371\) | −168.102 | −0.0235241 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6467.86 | 0.897836 | 0.448918 | − | 0.893573i | \(-0.351810\pi\) | ||||
0.448918 | + | 0.893573i | \(0.351810\pi\) | |||||||
\(374\) | −8173.29 | −1.13003 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 883.687 | 0.121204 | ||||||||
\(377\) | −6046.12 | −0.825971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4816.72 | −0.652818 | −0.326409 | − | 0.945229i | \(-0.605839\pi\) | ||||
−0.326409 | + | 0.945229i | \(0.605839\pi\) | |||||||
\(380\) | 1603.96 | 0.216530 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8518.49 | −1.14095 | ||||||||
\(383\) | 2548.11 | 0.339954 | 0.169977 | − | 0.985448i | \(-0.445631\pi\) | ||||
0.169977 | + | 0.985448i | \(0.445631\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −32.6932 | −0.00432780 | ||||||||
\(386\) | 21810.1 | 2.87592 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2261.94 | −0.295961 | ||||||||
\(389\) | −526.077 | −0.0685685 | −0.0342843 | − | 0.999412i | \(-0.510915\pi\) | ||||
−0.0342843 | + | 0.999412i | \(0.510915\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4056.91 | −0.524724 | ||||||||
\(392\) | −5121.62 | −0.659901 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7755.52 | 0.991668 | ||||||||
\(395\) | 236.094 | 0.0300739 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 385.566 | 0.0487431 | 0.0243715 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243715 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(398\) | −16251.8 | −2.04681 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3137.55 | 0.392193 | ||||||||
\(401\) | 3502.48 | 0.436173 | 0.218087 | − | 0.975929i | \(-0.430018\pi\) | ||||
0.218087 | + | 0.975929i | \(0.430018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6537.89 | 0.808128 | ||||||||
\(404\) | −15700.6 | −1.93350 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 465.666 | 0.0569227 | ||||||||
\(407\) | −15311.6 | −1.86479 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14696.0 | 1.77670 | 0.888352 | − | 0.459163i | \(-0.151851\pi\) | ||||
0.888352 | + | 0.459163i | \(0.151851\pi\) | |||||||
\(410\) | −587.705 | −0.0707919 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1534.50 | −0.183494 | ||||||||
\(413\) | 460.212 | 0.0548319 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1033.46 | 0.122243 | ||||||||
\(416\) | 8482.91 | 0.999781 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −29224.2 | −3.41962 | ||||||||
\(419\) | 4073.53 | 0.474952 | 0.237476 | − | 0.971393i | \(-0.423680\pi\) | ||||
0.237476 | + | 0.971393i | \(0.423680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16058.5 | 1.85901 | 0.929503 | − | 0.368814i | \(-0.120236\pi\) | ||||
0.929503 | + | 0.368814i | \(0.120236\pi\) | |||||||
\(422\) | −23897.4 | −2.75666 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3914.82 | −0.448397 | ||||||||
\(425\) | 4693.65 | 0.535707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 578.378 | 0.0655496 | ||||||||
\(428\) | −3291.26 | −0.371703 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 767.447 | 0.0860688 | ||||||||
\(431\) | −92.4432 | −0.0103314 | −0.00516570 | − | 0.999987i | \(-0.501644\pi\) | ||||
−0.00516570 | + | 0.999987i | \(0.501644\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3712.65 | −0.412053 | −0.206026 | − | 0.978546i | \(-0.566053\pi\) | ||||
−0.206026 | + | 0.978546i | \(0.566053\pi\) | |||||||
\(434\) | −503.542 | −0.0556931 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10090.8 | −1.10840 | ||||||||
\(437\) | −14505.8 | −1.58789 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12513.8 | −1.36048 | −0.680241 | − | 0.732989i | \(-0.738125\pi\) | ||||
−0.680241 | + | 0.732989i | \(0.738125\pi\) | |||||||
\(440\) | −761.371 | −0.0824930 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6122.83 | 0.658899 | ||||||||
\(443\) | 9236.58 | 0.990617 | 0.495308 | − | 0.868717i | \(-0.335055\pi\) | ||||
0.495308 | + | 0.868717i | \(0.335055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 336.083 | 0.0358019 | ||||||||
\(446\) | 10431.4 | 1.10749 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −523.318 | −0.0551885 | ||||||||
\(449\) | 1911.77 | 0.200939 | 0.100470 | − | 0.994940i | \(-0.467965\pi\) | ||||
0.100470 | + | 0.994940i | \(0.467965\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6291.12 | 0.656845 | ||||||||
\(452\) | −272.345 | −0.0283408 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20495.8 | −2.11876 | ||||||||
\(455\) | 24.4914 | 0.00252346 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11969.9 | 1.22523 | 0.612615 | − | 0.790381i | \(-0.290117\pi\) | ||||
0.612615 | + | 0.790381i | \(0.290117\pi\) | |||||||
\(458\) | −12155.7 | −1.24017 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1268.53 | −0.128577 | ||||||||
\(461\) | −1178.25 | −0.119038 | −0.0595190 | − | 0.998227i | \(-0.518957\pi\) | ||||
−0.0595190 | + | 0.998227i | \(0.518957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13223.2 | −1.32729 | −0.663643 | − | 0.748050i | \(-0.730990\pi\) | ||||
−0.663643 | + | 0.748050i | \(0.730990\pi\) | |||||||
\(464\) | −4170.48 | −0.417262 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18167.7 | 1.80601 | ||||||||
\(467\) | −3290.43 | −0.326045 | −0.163022 | − | 0.986622i | \(-0.552124\pi\) | ||||
−0.163022 | + | 0.986622i | \(0.552124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −254.882 | −0.0250946 | ||||||||
\(470\) | −270.570 | −0.0265542 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10717.6 | 1.04516 | ||||||||
\(473\) | −8215.18 | −0.798592 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16782.5 | 1.62112 | ||||||||
\(476\) | −277.057 | −0.0266783 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1052.54 | 0.100716 | ||||||||
\(479\) | −11053.9 | −1.05441 | −0.527207 | − | 0.849737i | \(-0.676761\pi\) | ||||
−0.527207 | + | 0.849737i | \(0.676761\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11470.3 | 1.08732 | ||||||||
\(482\) | −14222.6 | −1.34403 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12190.9 | 1.14490 | ||||||||
\(485\) | 206.327 | 0.0193172 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16349.3 | 1.52127 | 0.760635 | − | 0.649180i | \(-0.224888\pi\) | ||||
0.760635 | + | 0.649180i | \(0.224888\pi\) | |||||||
\(488\) | 13469.4 | 1.24945 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1568.15 | 0.144575 | ||||||||
\(491\) | −2008.83 | −0.184638 | −0.0923189 | − | 0.995729i | \(-0.529428\pi\) | ||||
−0.0923189 | + | 0.995729i | \(0.529428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6238.89 | −0.569950 | ||||||||
\(494\) | 21892.6 | 1.99392 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4509.70 | 0.408249 | ||||||||
\(497\) | −231.708 | −0.0209126 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15817.0 | 1.41897 | 0.709486 | − | 0.704719i | \(-0.248927\pi\) | ||||
0.709486 | + | 0.704719i | \(0.248927\pi\) | |||||||
\(500\) | 2948.06 | 0.263682 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5127.30 | −0.455862 | ||||||||
\(503\) | 8353.62 | 0.740496 | 0.370248 | − | 0.928933i | \(-0.379273\pi\) | ||||
0.370248 | + | 0.928933i | \(0.379273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1432.15 | 0.126198 | ||||||||
\(506\) | 23112.7 | 2.03060 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9773.29 | 0.853582 | ||||||||
\(509\) | −21578.9 | −1.87911 | −0.939557 | − | 0.342394i | \(-0.888762\pi\) | ||||
−0.939557 | + | 0.342394i | \(0.888762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 93.3639 | 0.00808253 | ||||||||
\(512\) | 8879.47 | 0.766447 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 33868.3 | 2.90635 | ||||||||
\(515\) | 139.972 | 0.0119765 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2896.33 | 0.246384 | ||||||||
\(518\) | −883.433 | −0.0749340 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 570.363 | 0.0481002 | ||||||||
\(521\) | −8204.63 | −0.689926 | −0.344963 | − | 0.938616i | \(-0.612109\pi\) | ||||
−0.344963 | + | 0.938616i | \(0.612109\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2955.61 | −0.247112 | −0.123556 | − | 0.992338i | \(-0.539430\pi\) | ||||
−0.123556 | + | 0.992338i | \(0.539430\pi\) | |||||||
\(524\) | 16783.9 | 1.39925 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14255.2 | 1.18167 | ||||||||
\(527\) | 6746.34 | 0.557638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −694.712 | −0.0570980 | ||||||||
\(530\) | 1198.65 | 0.0982379 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −990.637 | −0.0807323 | ||||||||
\(533\) | −4712.85 | −0.382994 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 300.218 | 0.0242609 | ||||||||
\(536\) | −5935.78 | −0.478334 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3126.18 | 0.250519 | ||||||||
\(539\) | −16786.4 | −1.34145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6432.08 | 0.511158 | 0.255579 | − | 0.966788i | \(-0.417734\pi\) | ||||
0.255579 | + | 0.966788i | \(0.417734\pi\) | |||||||
\(542\) | −27494.8 | −2.17897 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8753.37 | 0.689886 | ||||||||
\(545\) | 920.449 | 0.0723444 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16502.9 | −1.28997 | −0.644983 | − | 0.764197i | \(-0.723135\pi\) | ||||
−0.644983 | + | 0.764197i | \(0.723135\pi\) | |||||||
\(548\) | −15842.4 | −1.23495 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26740.3 | −2.07311 | ||||||||
\(551\) | −22307.6 | −1.72475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −145.817 | −0.0112129 | ||||||||
\(554\) | 24332.3 | 1.86603 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −315.947 | −0.0240991 | ||||||||
\(557\) | 1129.33 | 0.0859092 | 0.0429546 | − | 0.999077i | \(-0.486323\pi\) | ||||
0.0429546 | + | 0.999077i | \(0.486323\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6154.21 | 0.465645 | ||||||||
\(560\) | 16.8936 | 0.00127480 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 653.856 | 0.0490770 | ||||||||
\(563\) | 2308.16 | 0.172784 | 0.0863920 | − | 0.996261i | \(-0.472466\pi\) | ||||
0.0863920 | + | 0.996261i | \(0.472466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.8425 | 0.00184979 | ||||||||
\(566\) | −9407.24 | −0.698614 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5396.10 | −0.398619 | ||||||||
\(569\) | 7530.78 | 0.554845 | 0.277423 | − | 0.960748i | \(-0.410520\pi\) | ||||
0.277423 | + | 0.960748i | \(0.410520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −873.313 | −0.0640053 | −0.0320026 | − | 0.999488i | \(-0.510188\pi\) | ||||
−0.0320026 | + | 0.999488i | \(0.510188\pi\) | |||||||
\(572\) | −20494.0 | −1.49807 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 362.979 | 0.0263945 | ||||||||
\(575\) | −13272.9 | −0.962639 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6904.84 | −0.498184 | −0.249092 | − | 0.968480i | \(-0.580132\pi\) | ||||
−0.249092 | + | 0.968480i | \(0.580132\pi\) | |||||||
\(578\) | −15318.5 | −1.10236 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1950.80 | −0.139660 | ||||||||
\(581\) | −638.288 | −0.0455777 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12831.0 | −0.911503 | ||||||||
\(584\) | 2174.29 | 0.154063 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24324.2 | −1.71472 | ||||||||
\(587\) | −16415.9 | −1.15427 | −0.577134 | − | 0.816649i | \(-0.695829\pi\) | ||||
−0.577134 | + | 0.816649i | \(0.695829\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24122.0 | 1.68749 | ||||||||
\(590\) | −3281.54 | −0.228981 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7911.98 | 0.549291 | ||||||||
\(593\) | −15126.7 | −1.04752 | −0.523761 | − | 0.851865i | \(-0.675472\pi\) | ||||
−0.523761 | + | 0.851865i | \(0.675472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.2722 | 0.00174128 | ||||||||
\(596\) | 11338.6 | 0.779275 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17314.4 | −1.18401 | ||||||||
\(599\) | 2800.89 | 0.191054 | 0.0955270 | − | 0.995427i | \(-0.469546\pi\) | ||||
0.0955270 | + | 0.995427i | \(0.469546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 751.290 | 0.0509913 | 0.0254956 | − | 0.999675i | \(-0.491884\pi\) | ||||
0.0254956 | + | 0.999675i | \(0.491884\pi\) | |||||||
\(602\) | −473.991 | −0.0320904 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7511.44 | −0.506020 | ||||||||
\(605\) | −1112.01 | −0.0747268 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13057.4 | −0.873118 | −0.436559 | − | 0.899676i | \(-0.643803\pi\) | ||||
−0.436559 | + | 0.899676i | \(0.643803\pi\) | |||||||
\(608\) | 31298.3 | 2.08769 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4124.12 | −0.273739 | ||||||||
\(611\) | −2169.72 | −0.143662 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10446.0 | −0.688270 | −0.344135 | − | 0.938920i | \(-0.611828\pi\) | ||||
−0.344135 | + | 0.938920i | \(0.611828\pi\) | |||||||
\(614\) | −6235.39 | −0.409837 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 470.238 | 0.0307572 | ||||||||
\(617\) | 23077.9 | 1.50580 | 0.752902 | − | 0.658133i | \(-0.228654\pi\) | ||||
0.752902 | + | 0.658133i | \(0.228654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15208.7 | −0.987541 | −0.493771 | − | 0.869592i | \(-0.664382\pi\) | ||||
−0.493771 | + | 0.869592i | \(0.664382\pi\) | |||||||
\(620\) | 2109.47 | 0.136643 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27504.2 | 1.77302 | ||||||||
\(623\) | −207.572 | −0.0133486 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15221.0 | 0.974147 | ||||||||
\(626\) | −16004.5 | −1.02184 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8448.46 | −0.536831 | ||||||||
\(629\) | 11836.0 | 0.750292 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12789.5 | 0.806881 | 0.403440 | − | 0.915006i | \(-0.367814\pi\) | ||||
0.403440 | + | 0.915006i | \(0.367814\pi\) | |||||||
\(632\) | −3395.82 | −0.213732 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6191.78 | −0.387866 | ||||||||
\(635\) | −891.488 | −0.0557128 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12575.1 | 0.782174 | ||||||||
\(638\) | 35543.7 | 2.20562 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1809.88 | 0.111784 | ||||||||
\(641\) | −26876.5 | −1.65610 | −0.828048 | − | 0.560657i | \(-0.810549\pi\) | ||||
−0.828048 | + | 0.560657i | \(0.810549\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19135.9 | −1.17363 | −0.586816 | − | 0.809720i | \(-0.699619\pi\) | ||||
−0.586816 | + | 0.809720i | \(0.699619\pi\) | |||||||
\(644\) | 783.472 | 0.0479396 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22590.6 | 1.37588 | ||||||||
\(647\) | −21262.7 | −1.29200 | −0.645999 | − | 0.763338i | \(-0.723559\pi\) | ||||
−0.645999 | + | 0.763338i | \(0.723559\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35127.4 | 2.12461 | ||||||||
\(650\) | 20031.9 | 1.20879 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2062.84 | −0.123906 | ||||||||
\(653\) | 20411.0 | 1.22319 | 0.611597 | − | 0.791169i | \(-0.290527\pi\) | ||||
0.611597 | + | 0.791169i | \(0.290527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1530.97 | −0.0913283 | ||||||||
\(656\) | −3250.82 | −0.193480 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 167.110 | 0.00990062 | ||||||||
\(659\) | −9829.73 | −0.581050 | −0.290525 | − | 0.956867i | \(-0.593830\pi\) | ||||
−0.290525 | + | 0.956867i | \(0.593830\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12394.9 | −0.729355 | −0.364678 | − | 0.931134i | \(-0.618821\pi\) | ||||
−0.364678 | + | 0.931134i | \(0.618821\pi\) | |||||||
\(662\) | 39887.1 | 2.34177 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14864.7 | −0.868766 | ||||||||
\(665\) | 90.3628 | 0.00526935 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17642.5 | 1.02417 | ||||||||
\(668\) | −10061.2 | −0.582751 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1817.44 | 0.104797 | ||||||||
\(671\) | 44146.8 | 2.53989 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24772.1 | 1.41886 | 0.709430 | − | 0.704776i | \(-0.248952\pi\) | ||||
0.709430 | + | 0.704776i | \(0.248952\pi\) | |||||||
\(674\) | 8172.85 | 0.467072 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9681.46 | −0.550834 | ||||||||
\(677\) | 25646.0 | 1.45592 | 0.727959 | − | 0.685621i | \(-0.240469\pi\) | ||||
0.727959 | + | 0.685621i | \(0.240469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −127.432 | −0.00720234 | ||||||||
\(680\) | 588.548 | 0.0331909 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −38434.7 | −2.15798 | ||||||||
\(683\) | 31682.3 | 1.77495 | 0.887475 | − | 0.460857i | \(-0.152458\pi\) | ||||
0.887475 | + | 0.460857i | \(0.152458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1445.09 | 0.0806047 | ||||||||
\(686\) | −1938.21 | −0.107874 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4245.04 | 0.235233 | ||||||||
\(689\) | 9612.06 | 0.531481 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26145.5 | −1.43939 | −0.719696 | − | 0.694289i | \(-0.755719\pi\) | ||||
−0.719696 | + | 0.694289i | \(0.755719\pi\) | |||||||
\(692\) | −6719.78 | −0.369144 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 52786.2 | 2.88723 | ||||||||
\(695\) | 28.8196 | 0.00157294 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4863.10 | −0.264280 | ||||||||
\(698\) | 26609.3 | 1.44295 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −906.439 | −0.0489431 | ||||||||
\(701\) | 14749.5 | 0.794694 | 0.397347 | − | 0.917668i | \(-0.369931\pi\) | ||||
0.397347 | + | 0.917668i | \(0.369931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42320.6 | 2.27049 | ||||||||
\(704\) | −39944.1 | −2.13842 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25618.6 | 1.36568 | ||||||||
\(707\) | −884.528 | −0.0470525 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17166.5 | −0.909313 | −0.454657 | − | 0.890667i | \(-0.650238\pi\) | ||||
−0.454657 | + | 0.890667i | \(0.650238\pi\) | |||||||
\(710\) | 1652.19 | 0.0873320 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4833.99 | −0.254440 | ||||||||
\(713\) | −19077.5 | −1.00205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1869.39 | 0.0977782 | ||||||||
\(716\) | 23475.3 | 1.22530 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15035.2 | −0.781491 | ||||||||
\(719\) | 7064.10 | 0.366407 | 0.183203 | − | 0.983075i | \(-0.441353\pi\) | ||||
0.183203 | + | 0.983075i | \(0.441353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −86.4496 | −0.00446540 | ||||||||
\(722\) | 50567.8 | 2.60656 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17261.0 | −0.886052 | ||||||||
\(725\) | −20411.6 | −1.04561 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5129.92 | 0.261703 | 0.130852 | − | 0.991402i | \(-0.458229\pi\) | ||||
0.130852 | + | 0.991402i | \(0.458229\pi\) | |||||||
\(728\) | −352.268 | −0.0179340 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −665.730 | −0.0337531 | ||||||||
\(731\) | 6350.42 | 0.321312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36422.5 | −1.83533 | −0.917664 | − | 0.397357i | \(-0.869928\pi\) | ||||
−0.917664 | + | 0.397357i | \(0.869928\pi\) | |||||||
\(734\) | 28478.1 | 1.43208 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24753.1 | −1.23969 | ||||||||
\(737\) | −19454.8 | −0.972358 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2073.74 | 0.103226 | 0.0516129 | − | 0.998667i | \(-0.483564\pi\) | ||||
0.0516129 | + | 0.998667i | \(0.483564\pi\) | |||||||
\(740\) | 3700.94 | 0.183850 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −740.311 | −0.0366276 | ||||||||
\(743\) | −24869.6 | −1.22797 | −0.613983 | − | 0.789319i | \(-0.710434\pi\) | ||||
−0.613983 | + | 0.789319i | \(0.710434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1034.27 | −0.0508628 | ||||||||
\(746\) | 28484.0 | 1.39795 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21147.4 | −1.03372 | ||||||||
\(749\) | −185.421 | −0.00904557 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3087.87 | −0.150037 | −0.0750187 | − | 0.997182i | \(-0.523902\pi\) | ||||
−0.0750187 | + | 0.997182i | \(0.523902\pi\) | |||||||
\(752\) | −1496.62 | −0.0725749 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −26626.7 | −1.28606 | ||||||||
\(755\) | 685.170 | 0.0330277 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 536.550 | 0.0257612 | 0.0128806 | − | 0.999917i | \(-0.495900\pi\) | ||||
0.0128806 | + | 0.999917i | \(0.495900\pi\) | |||||||
\(758\) | −21212.5 | −1.01646 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2104.40 | 0.100440 | ||||||||
\(761\) | 35832.5 | 1.70687 | 0.853435 | − | 0.521199i | \(-0.174515\pi\) | ||||
0.853435 | + | 0.521199i | \(0.174515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −568.488 | −0.0269733 | ||||||||
\(764\) | −22040.6 | −1.04372 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11221.7 | 0.529317 | ||||||||
\(767\) | −26314.9 | −1.23882 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2680.19 | −0.125683 | −0.0628415 | − | 0.998024i | \(-0.520016\pi\) | ||||
−0.0628415 | + | 0.998024i | \(0.520016\pi\) | |||||||
\(770\) | −143.979 | −0.00673849 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 56431.0 | 2.63082 | ||||||||
\(773\) | 29716.1 | 1.38268 | 0.691342 | − | 0.722528i | \(-0.257020\pi\) | ||||
0.691342 | + | 0.722528i | \(0.257020\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22071.8 | 1.02302 | ||||||||
\(776\) | −2967.68 | −0.137285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2316.81 | −0.106763 | ||||||||
\(779\) | −17388.4 | −0.799748 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17686.0 | −0.810313 | ||||||||
\(782\) | −17866.4 | −0.817008 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8674.05 | 0.395137 | ||||||||
\(785\) | 770.641 | 0.0350387 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24465.5 | −1.10813 | −0.554067 | − | 0.832472i | \(-0.686925\pi\) | ||||
−0.554067 | + | 0.832472i | \(0.686925\pi\) | |||||||
\(788\) | 20066.5 | 0.907155 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1039.74 | 0.0468258 | ||||||||
\(791\) | −15.3432 | −0.000689687 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33071.5 | −1.48096 | ||||||||
\(794\) | 1698.01 | 0.0758942 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −42049.6 | −1.87237 | ||||||||
\(797\) | 40634.3 | 1.80595 | 0.902974 | − | 0.429695i | \(-0.141379\pi\) | ||||
0.902974 | + | 0.429695i | \(0.141379\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2238.90 | −0.0991319 | ||||||||
\(800\) | 28638.2 | 1.26564 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15424.7 | 0.679133 | ||||||||
\(803\) | 7126.34 | 0.313179 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −71.4658 | −0.00312899 | ||||||||
\(806\) | 28792.4 | 1.25828 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20599.2 | −0.896877 | ||||||||
\(809\) | −29160.3 | −1.26727 | −0.633636 | − | 0.773631i | \(-0.718438\pi\) | ||||
−0.633636 | + | 0.773631i | \(0.718438\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30266.4 | −1.31048 | −0.655239 | − | 0.755422i | \(-0.727432\pi\) | ||||
−0.655239 | + | 0.755422i | \(0.727432\pi\) | |||||||
\(812\) | 1204.85 | 0.0520715 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −67431.3 | −2.90352 | ||||||||
\(815\) | 188.165 | 0.00808729 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22706.4 | 0.972334 | ||||||||
\(818\) | 64720.4 | 2.76637 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1520.62 | −0.0647588 | ||||||||
\(821\) | 6700.52 | 0.284835 | 0.142418 | − | 0.989807i | \(-0.454512\pi\) | ||||
0.142418 | + | 0.989807i | \(0.454512\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26517.6 | 1.12314 | 0.561570 | − | 0.827429i | \(-0.310198\pi\) | ||||
0.561570 | + | 0.827429i | \(0.310198\pi\) | |||||||
\(824\) | −2013.27 | −0.0851159 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2026.75 | 0.0853747 | ||||||||
\(827\) | 30173.6 | 1.26873 | 0.634364 | − | 0.773034i | \(-0.281262\pi\) | ||||
0.634364 | + | 0.773034i | \(0.281262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3774.02 | −0.158115 | −0.0790573 | − | 0.996870i | \(-0.525191\pi\) | ||||
−0.0790573 | + | 0.996870i | \(0.525191\pi\) | |||||||
\(830\) | 4551.30 | 0.190335 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 29923.2 | 1.24688 | ||||||||
\(833\) | 12976.1 | 0.539728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 917.747 | 0.0380358 | ||||||||
\(836\) | −75614.0 | −3.12819 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17939.6 | 0.739513 | ||||||||
\(839\) | 8724.67 | 0.359010 | 0.179505 | − | 0.983757i | \(-0.442550\pi\) | ||||
0.179505 | + | 0.983757i | \(0.442550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2742.42 | 0.112445 | ||||||||
\(842\) | 70720.4 | 2.89452 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −61831.7 | −2.52172 | ||||||||
\(845\) | 883.111 | 0.0359526 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 686.802 | 0.0278616 | ||||||||
\(848\) | 6630.19 | 0.268493 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20670.5 | 0.834110 | ||||||||
\(851\) | −33470.4 | −1.34824 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26434.7 | −1.06109 | −0.530543 | − | 0.847658i | \(-0.678012\pi\) | ||||
−0.530543 | + | 0.847658i | \(0.678012\pi\) | |||||||
\(854\) | 2547.14 | 0.102062 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4318.14 | −0.172419 | ||||||||
\(857\) | 927.595 | 0.0369732 | 0.0184866 | − | 0.999829i | \(-0.494115\pi\) | ||||
0.0184866 | + | 0.999829i | \(0.494115\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45670.7 | 1.81405 | 0.907023 | − | 0.421081i | \(-0.138349\pi\) | ||||
0.907023 | + | 0.421081i | \(0.138349\pi\) | |||||||
\(860\) | 1985.68 | 0.0787337 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −407.114 | −0.0160863 | ||||||||
\(863\) | −4030.68 | −0.158987 | −0.0794936 | − | 0.996835i | \(-0.525330\pi\) | ||||
−0.0794936 | + | 0.996835i | \(0.525330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 612.957 | 0.0240938 | ||||||||
\(866\) | −16350.3 | −0.641577 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1302.85 | −0.0509467 | ||||||||
\(869\) | −11130.0 | −0.434475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14574.1 | 0.566964 | ||||||||
\(872\) | −13239.1 | −0.514144 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −63882.6 | −2.47238 | ||||||||
\(875\) | 166.086 | 0.00641682 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28143.7 | −1.08363 | −0.541816 | − | 0.840497i | \(-0.682263\pi\) | ||||
−0.541816 | + | 0.840497i | \(0.682263\pi\) | |||||||
\(878\) | −55110.0 | −2.11831 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1289.47 | 0.0493954 | ||||||||
\(881\) | 2213.18 | 0.0846354 | 0.0423177 | − | 0.999104i | \(-0.486526\pi\) | ||||
0.0423177 | + | 0.999104i | \(0.486526\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35722.9 | 1.36146 | 0.680732 | − | 0.732533i | \(-0.261662\pi\) | ||||
0.680732 | + | 0.732533i | \(0.261662\pi\) | |||||||
\(884\) | 15842.1 | 0.602745 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40677.3 | 1.54242 | ||||||||
\(887\) | −10710.8 | −0.405449 | −0.202725 | − | 0.979236i | \(-0.564980\pi\) | ||||
−0.202725 | + | 0.979236i | \(0.564980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 550.601 | 0.0207723 | ||||||||
\(890\) | 1480.09 | 0.0557445 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26990.0 | 1.01311 | ||||||||
\(893\) | −8005.33 | −0.299987 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2141.34 | −0.0799746 | ||||||||
\(896\) | −1117.82 | −0.0416782 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8419.29 | 0.312868 | ||||||||
\(899\) | −29338.2 | −1.08841 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9918.52 | 0.366741 | ||||||||
\(902\) | 27705.7 | 1.02273 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −357.318 | −0.0131463 | ||||||||
\(905\) | 1574.50 | 0.0578321 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1897.49 | 0.0694655 | 0.0347327 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347327 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(908\) | −53030.5 | −1.93819 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 107.858 | 0.00392909 | ||||||||
\(911\) | −29031.1 | −1.05581 | −0.527905 | − | 0.849303i | \(-0.677022\pi\) | ||||
−0.527905 | + | 0.849303i | \(0.677022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48719.7 | −1.76603 | ||||||||
\(914\) | 52714.9 | 1.90772 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31451.4 | −1.13448 | ||||||||
\(917\) | 945.560 | 0.0340514 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28486.3 | −1.02250 | −0.511249 | − | 0.859433i | \(-0.670817\pi\) | ||||
−0.511249 | + | 0.859433i | \(0.670817\pi\) | |||||||
\(920\) | −1664.32 | −0.0596423 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5188.93 | −0.185345 | ||||||||
\(923\) | 13249.1 | 0.472479 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38723.6 | 1.37646 | ||||||||
\(926\) | −58234.0 | −2.06662 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −38066.3 | −1.34654 | ||||||||
\(929\) | 10167.6 | 0.359084 | 0.179542 | − | 0.983750i | \(-0.442538\pi\) | ||||
0.179542 | + | 0.983750i | \(0.442538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46396.8 | 1.63329 | ||||||||
\(932\) | 47006.6 | 1.65209 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14490.8 | −0.507660 | ||||||||
\(935\) | 1929.00 | 0.0674705 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19728.5 | −0.687835 | −0.343917 | − | 0.939000i | \(-0.611754\pi\) | ||||
−0.343917 | + | 0.939000i | \(0.611754\pi\) | |||||||
\(938\) | −1122.49 | −0.0390730 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −700.067 | −0.0242911 | ||||||||
\(941\) | −7614.04 | −0.263773 | −0.131887 | − | 0.991265i | \(-0.542103\pi\) | ||||
−0.131887 | + | 0.991265i | \(0.542103\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13752.1 | 0.474898 | ||||||||
\(944\) | −18151.4 | −0.625825 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36179.1 | −1.24343 | ||||||||
\(947\) | 5187.12 | 0.177992 | 0.0889962 | − | 0.996032i | \(-0.471634\pi\) | ||||
0.0889962 | + | 0.996032i | \(0.471634\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5338.53 | −0.182609 | ||||||||
\(950\) | 73909.1 | 2.52413 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −363.499 | −0.0123751 | ||||||||
\(953\) | −4786.50 | −0.162697 | −0.0813483 | − | 0.996686i | \(-0.525923\pi\) | ||||
−0.0813483 | + | 0.996686i | \(0.525923\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2010.47 | 0.0681228 | ||||||||
\(956\) | 2723.32 | 0.0921323 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −48680.5 | −1.64175 | ||||||||
\(959\) | −892.519 | −0.0300531 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1933.49 | 0.0649018 | ||||||||
\(962\) | 50514.6 | 1.69299 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −36799.2 | −1.22949 | ||||||||
\(965\) | −5147.46 | −0.171712 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26758.4 | −0.889858 | −0.444929 | − | 0.895566i | \(-0.646771\pi\) | ||||
−0.444929 | + | 0.895566i | \(0.646771\pi\) | |||||||
\(968\) | 15994.5 | 0.531076 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 908.652 | 0.0300774 | ||||||||
\(971\) | −151.922 | −0.00502102 | −0.00251051 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00251051 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.7996 | −0.000586464 0 | ||||||||
\(974\) | 72001.3 | 2.36866 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22812.0 | −0.748151 | ||||||||
\(977\) | 49782.9 | 1.63019 | 0.815096 | − | 0.579326i | \(-0.196684\pi\) | ||||
0.815096 | + | 0.579326i | \(0.196684\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15843.7 | −0.517227 | ||||||||
\(980\) | 4057.41 | 0.132254 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8846.75 | −0.287486 | ||||||||
\(983\) | −14715.5 | −0.477469 | −0.238734 | − | 0.971085i | \(-0.576732\pi\) | ||||
−0.238734 | + | 0.971085i | \(0.576732\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1830.40 | −0.0592095 | ||||||||
\(986\) | −27475.6 | −0.887427 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 56644.5 | 1.82399 | ||||||||
\(989\) | −17958.0 | −0.577381 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30000.8 | −0.961662 | −0.480831 | − | 0.876813i | \(-0.659665\pi\) | ||||
−0.480831 | + | 0.876813i | \(0.659665\pi\) | |||||||
\(992\) | 41162.5 | 1.31745 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1020.43 | −0.0325614 | ||||||||
\(995\) | 3835.63 | 0.122209 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48254.9 | −1.53285 | −0.766424 | − | 0.642335i | \(-0.777966\pi\) | ||||
−0.766424 | + | 0.642335i | \(0.777966\pi\) | |||||||
\(998\) | 69657.2 | 2.20938 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.g.1.51 | ✓ | 59 | |
3.2 | odd | 2 | 2151.4.a.h.1.9 | yes | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.51 | ✓ | 59 | 1.1 | even | 1 | trivial | |
2151.4.a.h.1.9 | yes | 59 | 3.2 | odd | 2 |