Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("525.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.56155 | 1.25920 | 0.629600 | − | 0.776920i | \(-0.283219\pi\) | ||||
0.629600 | + | 0.776920i | \(0.283219\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.68466 | 0.585582 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −10.6847 | −0.726999 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −11.8078 | −0.521834 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.19224 | −0.142320 | −0.0711599 | − | 0.997465i | \(-0.522670\pi\) | ||||
−0.0711599 | + | 0.997465i | \(0.522670\pi\) | |||||||
\(12\) | −14.0540 | −0.338086 | ||||||||
\(13\) | 54.5464 | 1.16373 | 0.581863 | − | 0.813287i | \(-0.302324\pi\) | ||||
0.581863 | + | 0.813287i | \(0.302324\pi\) | |||||||
\(14\) | −24.9309 | −0.475933 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.5312 | −1.24268 | ||||||||
\(17\) | 16.1619 | 0.230579 | 0.115289 | − | 0.993332i | \(-0.463220\pi\) | ||||
0.115289 | + | 0.993332i | \(0.463220\pi\) | |||||||
\(18\) | 32.0540 | 0.419733 | ||||||||
\(19\) | 87.4470 | 1.05588 | 0.527940 | − | 0.849282i | \(-0.322965\pi\) | ||||
0.527940 | + | 0.849282i | \(0.322965\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | −18.4924 | −0.179209 | ||||||||
\(23\) | 176.477 | 1.59992 | 0.799958 | − | 0.600056i | \(-0.204855\pi\) | ||||
0.799958 | + | 0.600056i | \(0.204855\pi\) | |||||||
\(24\) | 35.4233 | 0.301281 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 194.270 | 1.46536 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −32.7926 | −0.221329 | ||||||||
\(29\) | 142.170 | 0.910358 | 0.455179 | − | 0.890400i | \(-0.349575\pi\) | ||||
0.455179 | + | 0.890400i | \(0.349575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −94.3002 | −0.546349 | −0.273174 | − | 0.961965i | \(-0.588074\pi\) | ||||
−0.273174 | + | 0.961965i | \(0.588074\pi\) | |||||||
\(32\) | −188.793 | −1.04294 | ||||||||
\(33\) | 15.5767 | 0.0821684 | ||||||||
\(34\) | 57.5616 | 0.290345 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 42.1619 | 0.195194 | ||||||||
\(37\) | 17.3305 | 0.0770031 | 0.0385016 | − | 0.999259i | \(-0.487742\pi\) | ||||
0.0385016 | + | 0.999259i | \(0.487742\pi\) | |||||||
\(38\) | 311.447 | 1.32956 | ||||||||
\(39\) | −163.639 | −0.671878 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 210.270 | 0.800942 | 0.400471 | − | 0.916309i | \(-0.368846\pi\) | ||||
0.400471 | + | 0.916309i | \(0.368846\pi\) | |||||||
\(42\) | 74.7926 | 0.274780 | ||||||||
\(43\) | 521.570 | 1.84974 | 0.924868 | − | 0.380287i | \(-0.124175\pi\) | ||||
0.924868 | + | 0.380287i | \(0.124175\pi\) | |||||||
\(44\) | −24.3239 | −0.0833400 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 628.533 | 2.01461 | ||||||||
\(47\) | −105.417 | −0.327162 | −0.163581 | − | 0.986530i | \(-0.552304\pi\) | ||||
−0.163581 | + | 0.986530i | \(0.552304\pi\) | |||||||
\(48\) | 238.594 | 0.717459 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −48.4858 | −0.133125 | ||||||||
\(52\) | 255.531 | 0.681458 | ||||||||
\(53\) | −108.978 | −0.282440 | −0.141220 | − | 0.989978i | \(-0.545102\pi\) | ||||
−0.141220 | + | 0.989978i | \(0.545102\pi\) | |||||||
\(54\) | −96.1619 | −0.242333 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 82.6543 | 0.197235 | ||||||||
\(57\) | −262.341 | −0.609612 | ||||||||
\(58\) | 506.348 | 1.14632 | ||||||||
\(59\) | 210.365 | 0.464189 | 0.232094 | − | 0.972693i | \(-0.425442\pi\) | ||||
0.232094 | + | 0.972693i | \(0.425442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −674.304 | −1.41534 | −0.707670 | − | 0.706543i | \(-0.750254\pi\) | ||||
−0.707670 | + | 0.706543i | \(0.750254\pi\) | |||||||
\(62\) | −335.855 | −0.687962 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −36.1449 | −0.0705955 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 55.4773 | 0.103466 | ||||||||
\(67\) | 324.929 | 0.592484 | 0.296242 | − | 0.955113i | \(-0.404267\pi\) | ||||
0.296242 | + | 0.955113i | \(0.404267\pi\) | |||||||
\(68\) | 75.7131 | 0.135023 | ||||||||
\(69\) | −529.432 | −0.923712 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 793.965 | 1.32713 | 0.663565 | − | 0.748118i | \(-0.269042\pi\) | ||||
0.663565 | + | 0.748118i | \(0.269042\pi\) | |||||||
\(72\) | −106.270 | −0.173945 | ||||||||
\(73\) | 315.417 | 0.505709 | 0.252854 | − | 0.967504i | \(-0.418631\pi\) | ||||
0.252854 | + | 0.967504i | \(0.418631\pi\) | |||||||
\(74\) | 61.7235 | 0.0969623 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 409.659 | 0.618304 | ||||||||
\(77\) | 36.3457 | 0.0537918 | ||||||||
\(78\) | −582.810 | −0.846028 | ||||||||
\(79\) | −425.840 | −0.606465 | −0.303233 | − | 0.952917i | \(-0.598066\pi\) | ||||
−0.303233 | + | 0.952917i | \(0.598066\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 748.887 | 1.00855 | ||||||||
\(83\) | −283.029 | −0.374295 | −0.187148 | − | 0.982332i | \(-0.559924\pi\) | ||||
−0.187148 | + | 0.982332i | \(0.559924\pi\) | |||||||
\(84\) | 98.3778 | 0.127785 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1857.60 | 2.32919 | ||||||||
\(87\) | −426.511 | −0.525596 | ||||||||
\(88\) | 61.3087 | 0.0742674 | ||||||||
\(89\) | −843.131 | −1.00418 | −0.502088 | − | 0.864817i | \(-0.667435\pi\) | ||||
−0.502088 | + | 0.864817i | \(0.667435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −381.825 | −0.439847 | ||||||||
\(92\) | 826.736 | 0.936882 | ||||||||
\(93\) | 282.901 | 0.315435 | ||||||||
\(94\) | −375.447 | −0.411962 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 566.378 | 0.602143 | ||||||||
\(97\) | 1537.33 | 1.60920 | 0.804601 | − | 0.593816i | \(-0.202379\pi\) | ||||
0.804601 | + | 0.593816i | \(0.202379\pi\) | |||||||
\(98\) | 174.516 | 0.179886 | ||||||||
\(99\) | −46.7301 | −0.0474399 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1589.99 | −1.56644 | −0.783219 | − | 0.621745i | \(-0.786424\pi\) | ||||
−0.783219 | + | 0.621745i | \(0.786424\pi\) | |||||||
\(102\) | −172.685 | −0.167631 | ||||||||
\(103\) | −164.793 | −0.157646 | −0.0788228 | − | 0.996889i | \(-0.525116\pi\) | ||||
−0.0788228 | + | 0.996889i | \(0.525116\pi\) | |||||||
\(104\) | −644.071 | −0.607273 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −388.132 | −0.355648 | ||||||||
\(107\) | 1184.08 | 1.06981 | 0.534904 | − | 0.844913i | \(-0.320348\pi\) | ||||
0.534904 | + | 0.844913i | \(0.320348\pi\) | |||||||
\(108\) | −126.486 | −0.112695 | ||||||||
\(109\) | 333.247 | 0.292837 | 0.146419 | − | 0.989223i | \(-0.453225\pi\) | ||||
0.146419 | + | 0.989223i | \(0.453225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −51.9915 | −0.0444578 | ||||||||
\(112\) | 556.719 | 0.469687 | ||||||||
\(113\) | 1881.49 | 1.56634 | 0.783168 | − | 0.621810i | \(-0.213602\pi\) | ||||
0.783168 | + | 0.621810i | \(0.213602\pi\) | |||||||
\(114\) | −934.341 | −0.767623 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 666.020 | 0.533090 | ||||||||
\(117\) | 490.918 | 0.387909 | ||||||||
\(118\) | 749.224 | 0.584506 | ||||||||
\(119\) | −113.133 | −0.0871507 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1304.04 | −0.979745 | ||||||||
\(122\) | −2401.57 | −1.78220 | ||||||||
\(123\) | −630.810 | −0.462424 | ||||||||
\(124\) | −441.764 | −0.319932 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −224.378 | −0.158644 | ||||||||
\(127\) | 1638.79 | 1.14503 | 0.572516 | − | 0.819893i | \(-0.305967\pi\) | ||||
0.572516 | + | 0.819893i | \(0.305967\pi\) | |||||||
\(128\) | 1381.61 | 0.954048 | ||||||||
\(129\) | −1564.71 | −1.06795 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −598.142 | −0.398931 | −0.199465 | − | 0.979905i | \(-0.563921\pi\) | ||||
−0.199465 | + | 0.979905i | \(0.563921\pi\) | |||||||
\(132\) | 72.9716 | 0.0481164 | ||||||||
\(133\) | −612.129 | −0.399085 | ||||||||
\(134\) | 1157.25 | 0.746055 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −190.836 | −0.120324 | ||||||||
\(137\) | −1005.25 | −0.626894 | −0.313447 | − | 0.949606i | \(-0.601484\pi\) | ||||
−0.313447 | + | 0.949606i | \(0.601484\pi\) | |||||||
\(138\) | −1885.60 | −1.16314 | ||||||||
\(139\) | −1875.01 | −1.14414 | −0.572072 | − | 0.820204i | \(-0.693860\pi\) | ||||
−0.572072 | + | 0.820204i | \(0.693860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 316.250 | 0.188887 | ||||||||
\(142\) | 2827.75 | 1.67112 | ||||||||
\(143\) | −283.218 | −0.165621 | ||||||||
\(144\) | −715.781 | −0.414225 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1123.37 | 0.636788 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 81.1875 | 0.0450917 | ||||||||
\(149\) | −1051.80 | −0.578299 | −0.289150 | − | 0.957284i | \(-0.593373\pi\) | ||||
−0.289150 | + | 0.957284i | \(0.593373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −750.383 | −0.404406 | −0.202203 | − | 0.979344i | \(-0.564810\pi\) | ||||
−0.202203 | + | 0.979344i | \(0.564810\pi\) | |||||||
\(152\) | −1032.55 | −0.550994 | ||||||||
\(153\) | 145.457 | 0.0768597 | ||||||||
\(154\) | 129.447 | 0.0677346 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −766.594 | −0.393440 | ||||||||
\(157\) | −1453.90 | −0.739067 | −0.369533 | − | 0.929217i | \(-0.620482\pi\) | ||||
−0.369533 | + | 0.929217i | \(0.620482\pi\) | |||||||
\(158\) | −1516.65 | −0.763660 | ||||||||
\(159\) | 326.935 | 0.163067 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1235.34 | −0.604711 | ||||||||
\(162\) | 288.486 | 0.139911 | ||||||||
\(163\) | 1300.49 | 0.624921 | 0.312461 | − | 0.949931i | \(-0.398847\pi\) | ||||
0.312461 | + | 0.949931i | \(0.398847\pi\) | |||||||
\(164\) | 985.043 | 0.469018 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1008.02 | −0.471312 | ||||||||
\(167\) | −2111.46 | −0.978381 | −0.489191 | − | 0.872177i | \(-0.662708\pi\) | ||||
−0.489191 | + | 0.872177i | \(0.662708\pi\) | |||||||
\(168\) | −247.963 | −0.113874 | ||||||||
\(169\) | 778.310 | 0.354260 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 787.023 | 0.351960 | ||||||||
\(172\) | 2443.38 | 1.08317 | ||||||||
\(173\) | 335.292 | 0.147351 | 0.0736756 | − | 0.997282i | \(-0.476527\pi\) | ||||
0.0736756 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(174\) | −1519.04 | −0.661829 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 412.945 | 0.176857 | ||||||||
\(177\) | −631.094 | −0.267999 | ||||||||
\(178\) | −3002.85 | −1.26446 | ||||||||
\(179\) | 2322.23 | 0.969672 | 0.484836 | − | 0.874605i | \(-0.338879\pi\) | ||||
0.484836 | + | 0.874605i | \(0.338879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1525.59 | −0.626500 | −0.313250 | − | 0.949671i | \(-0.601418\pi\) | ||||
−0.313250 | + | 0.949671i | \(0.601418\pi\) | |||||||
\(182\) | −1359.89 | −0.553855 | ||||||||
\(183\) | 2022.91 | 0.817147 | ||||||||
\(184\) | −2083.80 | −0.834891 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1007.57 | 0.397195 | ||||||||
\(187\) | −83.9165 | −0.0328160 | ||||||||
\(188\) | −493.841 | −0.191580 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 293.912 | 0.111344 | 0.0556721 | − | 0.998449i | \(-0.482270\pi\) | ||||
0.0556721 | + | 0.998449i | \(0.482270\pi\) | |||||||
\(192\) | 108.435 | 0.0407583 | ||||||||
\(193\) | −3664.91 | −1.36687 | −0.683435 | − | 0.730012i | \(-0.739515\pi\) | ||||
−0.683435 | + | 0.730012i | \(0.739515\pi\) | |||||||
\(194\) | 5475.29 | 2.02630 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 229.548 | 0.0836546 | ||||||||
\(197\) | −5101.89 | −1.84515 | −0.922576 | − | 0.385816i | \(-0.873920\pi\) | ||||
−0.922576 | + | 0.385816i | \(0.873920\pi\) | |||||||
\(198\) | −166.432 | −0.0597363 | ||||||||
\(199\) | 5025.86 | 1.79032 | 0.895161 | − | 0.445743i | \(-0.147061\pi\) | ||||
0.895161 | + | 0.445743i | \(0.147061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −974.787 | −0.342071 | ||||||||
\(202\) | −5662.85 | −1.97246 | ||||||||
\(203\) | −995.193 | −0.344083 | ||||||||
\(204\) | −227.139 | −0.0779556 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −586.918 | −0.198507 | ||||||||
\(207\) | 1588.30 | 0.533305 | ||||||||
\(208\) | −4338.14 | −1.44614 | ||||||||
\(209\) | −454.045 | −0.150273 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3267.98 | −1.06624 | −0.533122 | − | 0.846039i | \(-0.678981\pi\) | ||||
−0.533122 | + | 0.846039i | \(0.678981\pi\) | |||||||
\(212\) | −510.526 | −0.165392 | ||||||||
\(213\) | −2381.89 | −0.766219 | ||||||||
\(214\) | 4217.17 | 1.34710 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 318.810 | 0.100427 | ||||||||
\(217\) | 660.101 | 0.206500 | ||||||||
\(218\) | 1186.88 | 0.368741 | ||||||||
\(219\) | −946.250 | −0.291971 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 881.575 | 0.268331 | ||||||||
\(222\) | −185.170 | −0.0559812 | ||||||||
\(223\) | 5457.65 | 1.63888 | 0.819442 | − | 0.573162i | \(-0.194283\pi\) | ||||
0.819442 | + | 0.573162i | \(0.194283\pi\) | |||||||
\(224\) | 1321.55 | 0.394195 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6701.04 | 1.97233 | ||||||||
\(227\) | 281.023 | 0.0821682 | 0.0410841 | − | 0.999156i | \(-0.486919\pi\) | ||||
0.0410841 | + | 0.999156i | \(0.486919\pi\) | |||||||
\(228\) | −1228.98 | −0.356978 | ||||||||
\(229\) | 2776.64 | 0.801248 | 0.400624 | − | 0.916243i | \(-0.368793\pi\) | ||||
0.400624 | + | 0.916243i | \(0.368793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −109.037 | −0.0310567 | ||||||||
\(232\) | −1678.71 | −0.475056 | ||||||||
\(233\) | 5781.09 | 1.62546 | 0.812729 | − | 0.582642i | \(-0.197981\pi\) | ||||
0.812729 | + | 0.582642i | \(0.197981\pi\) | |||||||
\(234\) | 1748.43 | 0.488455 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 985.486 | 0.271821 | ||||||||
\(237\) | 1277.52 | 0.350143 | ||||||||
\(238\) | −402.931 | −0.109740 | ||||||||
\(239\) | 1588.17 | 0.429833 | 0.214916 | − | 0.976632i | \(-0.431052\pi\) | ||||
0.214916 | + | 0.976632i | \(0.431052\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4330.01 | −1.15735 | −0.578673 | − | 0.815560i | \(-0.696429\pi\) | ||||
−0.578673 | + | 0.815560i | \(0.696429\pi\) | |||||||
\(242\) | −4644.41 | −1.23369 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −3158.88 | −0.828798 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2246.66 | −0.582284 | ||||||||
\(247\) | 4769.92 | 1.22876 | ||||||||
\(248\) | 1113.47 | 0.285104 | ||||||||
\(249\) | 849.088 | 0.216099 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1400.53 | 0.352195 | 0.176097 | − | 0.984373i | \(-0.443653\pi\) | ||||
0.176097 | + | 0.984373i | \(0.443653\pi\) | |||||||
\(252\) | −295.133 | −0.0737764 | ||||||||
\(253\) | −916.312 | −0.227700 | ||||||||
\(254\) | 5836.64 | 1.44182 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5209.83 | 1.27193 | ||||||||
\(257\) | 4304.86 | 1.04486 | 0.522431 | − | 0.852681i | \(-0.325025\pi\) | ||||
0.522431 | + | 0.852681i | \(0.325025\pi\) | |||||||
\(258\) | −5572.80 | −1.34476 | ||||||||
\(259\) | −121.313 | −0.0291045 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1279.53 | 0.303453 | ||||||||
\(262\) | −2130.31 | −0.502333 | ||||||||
\(263\) | −1724.69 | −0.404369 | −0.202184 | − | 0.979347i | \(-0.564804\pi\) | ||||
−0.202184 | + | 0.979347i | \(0.564804\pi\) | |||||||
\(264\) | −183.926 | −0.0428783 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2180.13 | −0.502527 | ||||||||
\(267\) | 2529.39 | 0.579761 | ||||||||
\(268\) | 1522.18 | 0.346948 | ||||||||
\(269\) | 8004.82 | 1.81436 | 0.907180 | − | 0.420744i | \(-0.138231\pi\) | ||||
0.907180 | + | 0.420744i | \(0.138231\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1963.65 | −0.440160 | −0.220080 | − | 0.975482i | \(-0.570632\pi\) | ||||
−0.220080 | + | 0.975482i | \(0.570632\pi\) | |||||||
\(272\) | −1285.38 | −0.286535 | ||||||||
\(273\) | 1145.47 | 0.253946 | ||||||||
\(274\) | −3580.26 | −0.789384 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2480.21 | −0.540909 | ||||||||
\(277\) | −3278.33 | −0.711104 | −0.355552 | − | 0.934656i | \(-0.615707\pi\) | ||||
−0.355552 | + | 0.934656i | \(0.615707\pi\) | |||||||
\(278\) | −6677.93 | −1.44070 | ||||||||
\(279\) | −848.702 | −0.182116 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2859.04 | 0.606961 | 0.303480 | − | 0.952838i | \(-0.401851\pi\) | ||||
0.303480 | + | 0.952838i | \(0.401851\pi\) | |||||||
\(282\) | 1126.34 | 0.237846 | ||||||||
\(283\) | −5433.66 | −1.14134 | −0.570668 | − | 0.821181i | \(-0.693315\pi\) | ||||
−0.570668 | + | 0.821181i | \(0.693315\pi\) | |||||||
\(284\) | 3719.45 | 0.777144 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1008.70 | −0.208550 | ||||||||
\(287\) | −1471.89 | −0.302728 | ||||||||
\(288\) | −1699.13 | −0.347647 | ||||||||
\(289\) | −4651.79 | −0.946833 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4612.00 | −0.929073 | ||||||||
\(292\) | 1477.62 | 0.296134 | ||||||||
\(293\) | 8583.43 | 1.71143 | 0.855715 | − | 0.517447i | \(-0.173117\pi\) | ||||
0.855715 | + | 0.517447i | \(0.173117\pi\) | |||||||
\(294\) | −523.548 | −0.103857 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −204.634 | −0.0401829 | ||||||||
\(297\) | 140.190 | 0.0273895 | ||||||||
\(298\) | −3746.03 | −0.728194 | ||||||||
\(299\) | 9626.20 | 1.86186 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3650.99 | −0.699135 | ||||||||
\(302\) | −2672.53 | −0.509228 | ||||||||
\(303\) | 4769.98 | 0.904384 | ||||||||
\(304\) | −6954.77 | −1.31212 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 518.054 | 0.0967816 | ||||||||
\(307\) | −5269.83 | −0.979691 | −0.489846 | − | 0.871809i | \(-0.662947\pi\) | ||||
−0.489846 | + | 0.871809i | \(0.662947\pi\) | |||||||
\(308\) | 170.267 | 0.0314995 | ||||||||
\(309\) | 494.378 | 0.0910167 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4761.43 | −0.868154 | −0.434077 | − | 0.900876i | \(-0.642925\pi\) | ||||
−0.434077 | + | 0.900876i | \(0.642925\pi\) | |||||||
\(312\) | 1932.21 | 0.350609 | ||||||||
\(313\) | −7602.95 | −1.37298 | −0.686492 | − | 0.727137i | \(-0.740850\pi\) | ||||
−0.686492 | + | 0.727137i | \(0.740850\pi\) | |||||||
\(314\) | −5178.13 | −0.930632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1994.91 | −0.355135 | ||||||||
\(317\) | 8064.55 | 1.42886 | 0.714432 | − | 0.699704i | \(-0.246685\pi\) | ||||
0.714432 | + | 0.699704i | \(0.246685\pi\) | |||||||
\(318\) | 1164.39 | 0.205333 | ||||||||
\(319\) | −738.182 | −0.129562 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3552.24 | −0.617654 | ||||||||
\(322\) | −4399.73 | −0.761452 | ||||||||
\(323\) | 1413.31 | 0.243464 | ||||||||
\(324\) | 379.457 | 0.0650647 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4631.76 | 0.786901 | ||||||||
\(327\) | −999.741 | −0.169070 | ||||||||
\(328\) | −2482.82 | −0.417959 | ||||||||
\(329\) | 737.917 | 0.123655 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6960.79 | 1.15589 | 0.577945 | − | 0.816076i | \(-0.303855\pi\) | ||||
0.577945 | + | 0.816076i | \(0.303855\pi\) | |||||||
\(332\) | −1325.90 | −0.219181 | ||||||||
\(333\) | 155.974 | 0.0256677 | ||||||||
\(334\) | −7520.08 | −1.23198 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1670.16 | −0.271174 | ||||||||
\(337\) | 4731.61 | 0.764828 | 0.382414 | − | 0.923991i | \(-0.375093\pi\) | ||||
0.382414 | + | 0.923991i | \(0.375093\pi\) | |||||||
\(338\) | 2771.99 | 0.446084 | ||||||||
\(339\) | −5644.48 | −0.904325 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 489.629 | 0.0777563 | ||||||||
\(342\) | 2803.02 | 0.443187 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −6158.58 | −0.965256 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1194.16 | 0.185544 | ||||||||
\(347\) | 9796.67 | 1.51560 | 0.757800 | − | 0.652487i | \(-0.226274\pi\) | ||||
0.757800 | + | 0.652487i | \(0.226274\pi\) | |||||||
\(348\) | −1998.06 | −0.307779 | ||||||||
\(349\) | 12702.4 | 1.94827 | 0.974134 | − | 0.225971i | \(-0.0725554\pi\) | ||||
0.974134 | + | 0.225971i | \(0.0725554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1472.75 | −0.223959 | ||||||||
\(352\) | 980.256 | 0.148431 | ||||||||
\(353\) | −9970.21 | −1.50329 | −0.751644 | − | 0.659569i | \(-0.770739\pi\) | ||||
−0.751644 | + | 0.659569i | \(0.770739\pi\) | |||||||
\(354\) | −2247.67 | −0.337465 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3949.78 | −0.588028 | ||||||||
\(357\) | 339.400 | 0.0503165 | ||||||||
\(358\) | 8270.73 | 1.22101 | ||||||||
\(359\) | 4388.21 | 0.645128 | 0.322564 | − | 0.946548i | \(-0.395455\pi\) | ||||
0.322564 | + | 0.946548i | \(0.395455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 787.970 | 0.114881 | ||||||||
\(362\) | −5433.49 | −0.788889 | ||||||||
\(363\) | 3912.12 | 0.565656 | ||||||||
\(364\) | −1788.72 | −0.257567 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7204.71 | 1.02895 | ||||||||
\(367\) | −9441.30 | −1.34287 | −0.671433 | − | 0.741065i | \(-0.734321\pi\) | ||||
−0.671433 | + | 0.741065i | \(0.734321\pi\) | |||||||
\(368\) | −14035.5 | −1.98818 | ||||||||
\(369\) | 1892.43 | 0.266981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 762.847 | 0.106752 | ||||||||
\(372\) | 1325.29 | 0.184713 | ||||||||
\(373\) | −3219.40 | −0.446901 | −0.223451 | − | 0.974715i | \(-0.571732\pi\) | ||||
−0.223451 | + | 0.974715i | \(0.571732\pi\) | |||||||
\(374\) | −298.873 | −0.0413218 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1244.73 | 0.170724 | ||||||||
\(377\) | 7754.89 | 1.05941 | ||||||||
\(378\) | 673.133 | 0.0915933 | ||||||||
\(379\) | −14011.4 | −1.89899 | −0.949495 | − | 0.313783i | \(-0.898403\pi\) | ||||
−0.949495 | + | 0.313783i | \(0.898403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4916.37 | −0.661085 | ||||||||
\(382\) | 1046.78 | 0.140204 | ||||||||
\(383\) | 5322.87 | 0.710147 | 0.355073 | − | 0.934838i | \(-0.384456\pi\) | ||||
0.355073 | + | 0.934838i | \(0.384456\pi\) | |||||||
\(384\) | −4144.83 | −0.550820 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13052.8 | −1.72116 | ||||||||
\(387\) | 4694.13 | 0.616579 | ||||||||
\(388\) | 7201.88 | 0.942320 | ||||||||
\(389\) | −3844.51 | −0.501091 | −0.250545 | − | 0.968105i | \(-0.580610\pi\) | ||||
−0.250545 | + | 0.968105i | \(0.580610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2852.21 | 0.368907 | ||||||||
\(392\) | −578.580 | −0.0745478 | ||||||||
\(393\) | 1794.43 | 0.230323 | ||||||||
\(394\) | −18170.7 | −2.32341 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −218.915 | −0.0277800 | ||||||||
\(397\) | −8046.40 | −1.01722 | −0.508611 | − | 0.860996i | \(-0.669841\pi\) | ||||
−0.508611 | + | 0.860996i | \(0.669841\pi\) | |||||||
\(398\) | 17899.9 | 2.25437 | ||||||||
\(399\) | 1836.39 | 0.230412 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7741.38 | 0.964055 | 0.482027 | − | 0.876156i | \(-0.339901\pi\) | ||||
0.482027 | + | 0.876156i | \(0.339901\pi\) | |||||||
\(402\) | −3471.76 | −0.430735 | ||||||||
\(403\) | −5143.74 | −0.635801 | ||||||||
\(404\) | −7448.58 | −0.917279 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3544.43 | −0.433269 | ||||||||
\(407\) | −89.9840 | −0.0109591 | ||||||||
\(408\) | 572.509 | 0.0694691 | ||||||||
\(409\) | −8966.94 | −1.08407 | −0.542037 | − | 0.840354i | \(-0.682347\pi\) | ||||
−0.542037 | + | 0.840354i | \(0.682347\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3015.76 | 0.361937 | ||||||||
\(412\) | −771.997 | −0.0923145 | ||||||||
\(413\) | −1472.55 | −0.175447 | ||||||||
\(414\) | 5656.80 | 0.671537 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10298.0 | −1.21370 | ||||||||
\(417\) | 5625.02 | 0.660571 | ||||||||
\(418\) | −1617.11 | −0.189223 | ||||||||
\(419\) | −12413.6 | −1.44736 | −0.723681 | − | 0.690135i | \(-0.757551\pi\) | ||||
−0.723681 | + | 0.690135i | \(0.757551\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1672.14 | −0.193575 | −0.0967875 | − | 0.995305i | \(-0.530857\pi\) | ||||
−0.0967875 | + | 0.995305i | \(0.530857\pi\) | |||||||
\(422\) | −11639.1 | −1.34261 | ||||||||
\(423\) | −948.750 | −0.109054 | ||||||||
\(424\) | 1286.79 | 0.147387 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8483.24 | −0.964823 | ||||||||
\(427\) | 4720.13 | 0.534948 | ||||||||
\(428\) | 5547.02 | 0.626461 | ||||||||
\(429\) | 849.653 | 0.0956216 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16021.8 | 1.79059 | 0.895296 | − | 0.445472i | \(-0.146964\pi\) | ||||
0.895296 | + | 0.445472i | \(0.146964\pi\) | |||||||
\(432\) | 2147.34 | 0.239153 | ||||||||
\(433\) | 10882.7 | 1.20782 | 0.603912 | − | 0.797051i | \(-0.293608\pi\) | ||||
0.603912 | + | 0.797051i | \(0.293608\pi\) | |||||||
\(434\) | 2350.99 | 0.260025 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1561.15 | 0.171480 | ||||||||
\(437\) | 15432.4 | 1.68932 | ||||||||
\(438\) | −3370.12 | −0.367650 | ||||||||
\(439\) | 7738.40 | 0.841307 | 0.420653 | − | 0.907221i | \(-0.361801\pi\) | ||||
0.420653 | + | 0.907221i | \(0.361801\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 3139.78 | 0.337882 | ||||||||
\(443\) | 8766.56 | 0.940207 | 0.470103 | − | 0.882611i | \(-0.344217\pi\) | ||||
0.470103 | + | 0.882611i | \(0.344217\pi\) | |||||||
\(444\) | −243.562 | −0.0260337 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19437.7 | 2.06368 | ||||||||
\(447\) | 3155.39 | 0.333881 | ||||||||
\(448\) | 253.014 | 0.0266826 | ||||||||
\(449\) | 3099.58 | 0.325786 | 0.162893 | − | 0.986644i | \(-0.447917\pi\) | ||||
0.162893 | + | 0.986644i | \(0.447917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1091.77 | −0.113990 | ||||||||
\(452\) | 8814.15 | 0.917219 | ||||||||
\(453\) | 2251.15 | 0.233484 | ||||||||
\(454\) | 1000.88 | 0.103466 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3097.66 | 0.318117 | ||||||||
\(457\) | −6122.94 | −0.626737 | −0.313369 | − | 0.949632i | \(-0.601458\pi\) | ||||
−0.313369 | + | 0.949632i | \(0.601458\pi\) | |||||||
\(458\) | 9889.16 | 1.00893 | ||||||||
\(459\) | −436.372 | −0.0443749 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10412.2 | −1.05194 | −0.525970 | − | 0.850503i | \(-0.676297\pi\) | ||||
−0.525970 | + | 0.850503i | \(0.676297\pi\) | |||||||
\(462\) | −388.341 | −0.0391066 | ||||||||
\(463\) | −11278.5 | −1.13209 | −0.566043 | − | 0.824376i | \(-0.691526\pi\) | ||||
−0.566043 | + | 0.824376i | \(0.691526\pi\) | |||||||
\(464\) | −11307.0 | −1.13128 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20589.6 | 2.04677 | ||||||||
\(467\) | 14923.2 | 1.47872 | 0.739359 | − | 0.673311i | \(-0.235128\pi\) | ||||
0.739359 | + | 0.673311i | \(0.235128\pi\) | |||||||
\(468\) | 2299.78 | 0.227153 | ||||||||
\(469\) | −2274.50 | −0.223938 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4361.69 | 0.426701 | ||||||||
\(472\) | −2483.93 | −0.242230 | ||||||||
\(473\) | −2708.11 | −0.263254 | ||||||||
\(474\) | 4549.95 | 0.440899 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −529.992 | −0.0510339 | ||||||||
\(477\) | −980.804 | −0.0941466 | ||||||||
\(478\) | 5656.34 | 0.541245 | ||||||||
\(479\) | −4674.21 | −0.445867 | −0.222933 | − | 0.974834i | \(-0.571563\pi\) | ||||
−0.222933 | + | 0.974834i | \(0.571563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 945.316 | 0.0896106 | ||||||||
\(482\) | −15421.6 | −1.45733 | ||||||||
\(483\) | 3706.02 | 0.349130 | ||||||||
\(484\) | −6108.99 | −0.573721 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −865.457 | −0.0807777 | ||||||||
\(487\) | 17081.7 | 1.58941 | 0.794706 | − | 0.606994i | \(-0.207625\pi\) | ||||
0.794706 | + | 0.606994i | \(0.207625\pi\) | |||||||
\(488\) | 7962.02 | 0.738573 | ||||||||
\(489\) | −3901.47 | −0.360799 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18203.9 | 1.67318 | 0.836588 | − | 0.547832i | \(-0.184547\pi\) | ||||
0.836588 | + | 0.547832i | \(0.184547\pi\) | |||||||
\(492\) | −2955.13 | −0.270787 | ||||||||
\(493\) | 2297.75 | 0.209909 | ||||||||
\(494\) | 16988.3 | 1.54725 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7499.81 | 0.678934 | ||||||||
\(497\) | −5557.75 | −0.501608 | ||||||||
\(498\) | 3024.07 | 0.272112 | ||||||||
\(499\) | 7109.47 | 0.637803 | 0.318901 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6334.38 | 0.564869 | ||||||||
\(502\) | 4988.07 | 0.443483 | ||||||||
\(503\) | −15402.0 | −1.36529 | −0.682647 | − | 0.730748i | \(-0.739171\pi\) | ||||
−0.682647 | + | 0.730748i | \(0.739171\pi\) | |||||||
\(504\) | 743.889 | 0.0657450 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3263.49 | −0.286719 | ||||||||
\(507\) | −2334.93 | −0.204532 | ||||||||
\(508\) | 7677.17 | 0.670511 | ||||||||
\(509\) | 6404.72 | 0.557730 | 0.278865 | − | 0.960330i | \(-0.410042\pi\) | ||||
0.278865 | + | 0.960330i | \(0.410042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2207.92 | −0.191140 | ||||||||
\(512\) | 7502.22 | 0.647567 | ||||||||
\(513\) | −2361.07 | −0.203204 | ||||||||
\(514\) | 15332.0 | 1.31569 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7330.13 | −0.625370 | ||||||||
\(517\) | 547.348 | 0.0465616 | ||||||||
\(518\) | −432.064 | −0.0366483 | ||||||||
\(519\) | −1005.88 | −0.0850732 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8916.72 | −0.749806 | −0.374903 | − | 0.927064i | \(-0.622324\pi\) | ||||
−0.374903 | + | 0.927064i | \(0.622324\pi\) | |||||||
\(522\) | 4557.13 | 0.382107 | ||||||||
\(523\) | −6929.40 | −0.579353 | −0.289677 | − | 0.957125i | \(-0.593548\pi\) | ||||
−0.289677 | + | 0.957125i | \(0.593548\pi\) | |||||||
\(524\) | −2802.09 | −0.233607 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6142.58 | −0.509181 | ||||||||
\(527\) | −1524.07 | −0.125977 | ||||||||
\(528\) | −1238.83 | −0.102109 | ||||||||
\(529\) | 18977.2 | 1.55973 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1893.28 | 0.154730 | ||||||||
\(532\) | −2867.61 | −0.233697 | ||||||||
\(533\) | 11469.5 | 0.932078 | ||||||||
\(534\) | 9008.56 | 0.730035 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3836.69 | −0.309178 | ||||||||
\(537\) | −6966.68 | −0.559840 | ||||||||
\(538\) | 28509.6 | 2.28464 | ||||||||
\(539\) | −254.420 | −0.0203314 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6929.23 | −0.550667 | −0.275334 | − | 0.961349i | \(-0.588788\pi\) | ||||
−0.275334 | + | 0.961349i | \(0.588788\pi\) | |||||||
\(542\) | −6993.65 | −0.554249 | ||||||||
\(543\) | 4576.78 | 0.361710 | ||||||||
\(544\) | −3051.25 | −0.240480 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4079.67 | 0.319769 | ||||||||
\(547\) | −8509.95 | −0.665190 | −0.332595 | − | 0.943070i | \(-0.607924\pi\) | ||||
−0.332595 | + | 0.943070i | \(0.607924\pi\) | |||||||
\(548\) | −4709.26 | −0.367098 | ||||||||
\(549\) | −6068.74 | −0.471780 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12432.4 | 0.961228 | ||||||||
\(552\) | 6251.41 | 0.482024 | ||||||||
\(553\) | 2980.88 | 0.229222 | ||||||||
\(554\) | −11676.0 | −0.895422 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8783.76 | −0.669990 | ||||||||
\(557\) | −4043.94 | −0.307625 | −0.153813 | − | 0.988100i | \(-0.549155\pi\) | ||||
−0.153813 | + | 0.988100i | \(0.549155\pi\) | |||||||
\(558\) | −3022.70 | −0.229321 | ||||||||
\(559\) | 28449.8 | 2.15259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 251.750 | 0.0189463 | ||||||||
\(562\) | 10182.6 | 0.764285 | ||||||||
\(563\) | 15878.9 | 1.18866 | 0.594331 | − | 0.804221i | \(-0.297417\pi\) | ||||
0.594331 | + | 0.804221i | \(0.297417\pi\) | |||||||
\(564\) | 1481.52 | 0.110609 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19352.3 | −1.43717 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | −9374.95 | −0.692543 | ||||||||
\(569\) | 11611.6 | 0.855510 | 0.427755 | − | 0.903895i | \(-0.359305\pi\) | ||||
0.427755 | + | 0.903895i | \(0.359305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17395.7 | 1.27493 | 0.637466 | − | 0.770478i | \(-0.279982\pi\) | ||||
0.637466 | + | 0.770478i | \(0.279982\pi\) | |||||||
\(572\) | −1326.78 | −0.0969850 | ||||||||
\(573\) | −881.736 | −0.0642846 | ||||||||
\(574\) | −5242.21 | −0.381195 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −325.304 | −0.0235318 | ||||||||
\(577\) | −11474.0 | −0.827848 | −0.413924 | − | 0.910311i | \(-0.635842\pi\) | ||||
−0.413924 | + | 0.910311i | \(0.635842\pi\) | |||||||
\(578\) | −16567.6 | −1.19225 | ||||||||
\(579\) | 10994.7 | 0.789162 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1981.20 | 0.141470 | ||||||||
\(582\) | −16425.9 | −1.16989 | ||||||||
\(583\) | 565.841 | 0.0401968 | ||||||||
\(584\) | −3724.37 | −0.263896 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30570.3 | 2.15503 | ||||||||
\(587\) | 11870.4 | 0.834659 | 0.417330 | − | 0.908755i | \(-0.362966\pi\) | ||||
0.417330 | + | 0.908755i | \(0.362966\pi\) | |||||||
\(588\) | −688.645 | −0.0482980 | ||||||||
\(589\) | −8246.26 | −0.576878 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15305.7 | 1.06530 | ||||||||
\(592\) | −1378.32 | −0.0956899 | ||||||||
\(593\) | −5760.65 | −0.398923 | −0.199462 | − | 0.979906i | \(-0.563919\pi\) | ||||
−0.199462 | + | 0.979906i | \(0.563919\pi\) | |||||||
\(594\) | 499.295 | 0.0344888 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4927.31 | −0.338642 | ||||||||
\(597\) | −15077.6 | −1.03364 | ||||||||
\(598\) | 34284.2 | 2.34446 | ||||||||
\(599\) | −21696.5 | −1.47996 | −0.739978 | − | 0.672631i | \(-0.765164\pi\) | ||||
−0.739978 | + | 0.672631i | \(0.765164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12403.0 | −0.841812 | −0.420906 | − | 0.907104i | \(-0.638288\pi\) | ||||
−0.420906 | + | 0.907104i | \(0.638288\pi\) | |||||||
\(602\) | −13003.2 | −0.880350 | ||||||||
\(603\) | 2924.36 | 0.197495 | ||||||||
\(604\) | −3515.29 | −0.236813 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16988.5 | 1.13880 | ||||||||
\(607\) | 17066.5 | 1.14120 | 0.570600 | − | 0.821228i | \(-0.306711\pi\) | ||||
0.570600 | + | 0.821228i | \(0.306711\pi\) | |||||||
\(608\) | −16509.3 | −1.10122 | ||||||||
\(609\) | 2985.58 | 0.198656 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5750.10 | −0.380727 | ||||||||
\(612\) | 681.418 | 0.0450077 | ||||||||
\(613\) | 2707.50 | 0.178393 | 0.0891965 | − | 0.996014i | \(-0.471570\pi\) | ||||
0.0891965 | + | 0.996014i | \(0.471570\pi\) | |||||||
\(614\) | −18768.8 | −1.23363 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −429.161 | −0.0280704 | ||||||||
\(617\) | −23226.3 | −1.51549 | −0.757743 | − | 0.652553i | \(-0.773698\pi\) | ||||
−0.757743 | + | 0.652553i | \(0.773698\pi\) | |||||||
\(618\) | 1760.75 | 0.114608 | ||||||||
\(619\) | −2298.43 | −0.149243 | −0.0746216 | − | 0.997212i | \(-0.523775\pi\) | ||||
−0.0746216 | + | 0.997212i | \(0.523775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4764.89 | −0.307904 | ||||||||
\(622\) | −16958.1 | −1.09318 | ||||||||
\(623\) | 5901.91 | 0.379543 | ||||||||
\(624\) | 13014.4 | 0.834926 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27078.3 | −1.72886 | ||||||||
\(627\) | 1362.14 | 0.0867599 | ||||||||
\(628\) | −6811.01 | −0.432785 | ||||||||
\(629\) | 280.094 | 0.0177553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −663.913 | −0.0418858 | −0.0209429 | − | 0.999781i | \(-0.506667\pi\) | ||||
−0.0209429 | + | 0.999781i | \(0.506667\pi\) | |||||||
\(632\) | 5028.22 | 0.316474 | ||||||||
\(633\) | 9803.95 | 0.615596 | ||||||||
\(634\) | 28722.3 | 1.79923 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1531.58 | 0.0954890 | ||||||||
\(637\) | 2672.77 | 0.166247 | ||||||||
\(638\) | −2629.08 | −0.163144 | ||||||||
\(639\) | 7145.68 | 0.442377 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15215.6 | 0.937566 | 0.468783 | − | 0.883313i | \(-0.344693\pi\) | ||||
0.468783 | + | 0.883313i | \(0.344693\pi\) | |||||||
\(642\) | −12651.5 | −0.777749 | ||||||||
\(643\) | 12904.0 | 0.791420 | 0.395710 | − | 0.918375i | \(-0.370498\pi\) | ||||
0.395710 | + | 0.918375i | \(0.370498\pi\) | |||||||
\(644\) | −5787.15 | −0.354108 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5033.58 | 0.306569 | ||||||||
\(647\) | −9425.54 | −0.572730 | −0.286365 | − | 0.958121i | \(-0.592447\pi\) | ||||
−0.286365 | + | 0.958121i | \(0.592447\pi\) | |||||||
\(648\) | −956.429 | −0.0579816 | ||||||||
\(649\) | −1092.26 | −0.0660632 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1980.30 | −0.119223 | ||||||||
\(652\) | 6092.35 | 0.365943 | ||||||||
\(653\) | −29894.7 | −1.79153 | −0.895765 | − | 0.444528i | \(-0.853372\pi\) | ||||
−0.895765 | + | 0.444528i | \(0.853372\pi\) | |||||||
\(654\) | −3560.63 | −0.212892 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16723.0 | −0.995312 | ||||||||
\(657\) | 2838.75 | 0.168570 | ||||||||
\(658\) | 2628.13 | 0.155707 | ||||||||
\(659\) | −11593.6 | −0.685313 | −0.342656 | − | 0.939461i | \(-0.611327\pi\) | ||||
−0.342656 | + | 0.939461i | \(0.611327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17149.2 | −1.00911 | −0.504557 | − | 0.863378i | \(-0.668344\pi\) | ||||
−0.504557 | + | 0.863378i | \(0.668344\pi\) | |||||||
\(662\) | 24791.2 | 1.45550 | ||||||||
\(663\) | −2644.72 | −0.154921 | ||||||||
\(664\) | 3341.94 | 0.195320 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 555.511 | 0.0323208 | ||||||||
\(667\) | 25089.9 | 1.45650 | ||||||||
\(668\) | −9891.47 | −0.572923 | ||||||||
\(669\) | −16372.9 | −0.946210 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3501.15 | 0.201431 | ||||||||
\(672\) | −3964.64 | −0.227589 | ||||||||
\(673\) | −16475.0 | −0.943633 | −0.471817 | − | 0.881697i | \(-0.656402\pi\) | ||||
−0.471817 | + | 0.881697i | \(0.656402\pi\) | |||||||
\(674\) | 16851.9 | 0.963071 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3646.11 | 0.207448 | ||||||||
\(677\) | −4559.89 | −0.258864 | −0.129432 | − | 0.991588i | \(-0.541315\pi\) | ||||
−0.129432 | + | 0.991588i | \(0.541315\pi\) | |||||||
\(678\) | −20103.1 | −1.13872 | ||||||||
\(679\) | −10761.3 | −0.608221 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −843.070 | −0.0474398 | ||||||||
\(682\) | 1743.84 | 0.0979106 | ||||||||
\(683\) | −27895.9 | −1.56282 | −0.781411 | − | 0.624017i | \(-0.785500\pi\) | ||||
−0.781411 | + | 0.624017i | \(0.785500\pi\) | |||||||
\(684\) | 3686.93 | 0.206101 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1221.61 | −0.0679904 | ||||||||
\(687\) | −8329.93 | −0.462601 | ||||||||
\(688\) | −41481.1 | −2.29862 | ||||||||
\(689\) | −5944.37 | −0.328683 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28178.5 | −1.55132 | −0.775659 | − | 0.631152i | \(-0.782582\pi\) | ||||
−0.775659 | + | 0.631152i | \(0.782582\pi\) | |||||||
\(692\) | 1570.73 | 0.0862862 | ||||||||
\(693\) | 327.111 | 0.0179306 | ||||||||
\(694\) | 34891.4 | 1.90844 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5036.14 | 0.274274 | ||||||||
\(697\) | 3398.37 | 0.184680 | ||||||||
\(698\) | 45240.4 | 2.45326 | ||||||||
\(699\) | −17343.3 | −0.938458 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3912.96 | 0.210828 | 0.105414 | − | 0.994428i | \(-0.466383\pi\) | ||||
0.105414 | + | 0.994428i | \(0.466383\pi\) | |||||||
\(702\) | −5245.29 | −0.282009 | ||||||||
\(703\) | 1515.50 | 0.0813060 | ||||||||
\(704\) | 187.673 | 0.0100471 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35509.4 | −1.89294 | ||||||||
\(707\) | 11130.0 | 0.592058 | ||||||||
\(708\) | −2956.46 | −0.156936 | ||||||||
\(709\) | −7782.72 | −0.412251 | −0.206126 | − | 0.978526i | \(-0.566086\pi\) | ||||
−0.206126 | + | 0.978526i | \(0.566086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3832.56 | −0.202155 | ||||||||
\(712\) | 9955.49 | 0.524014 | ||||||||
\(713\) | −16641.8 | −0.874112 | ||||||||
\(714\) | 1208.79 | 0.0633584 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10878.8 | 0.567823 | ||||||||
\(717\) | −4764.50 | −0.248164 | ||||||||
\(718\) | 15628.9 | 0.812345 | ||||||||
\(719\) | −27868.8 | −1.44552 | −0.722762 | − | 0.691097i | \(-0.757128\pi\) | ||||
−0.722762 | + | 0.691097i | \(0.757128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1153.55 | 0.0595844 | ||||||||
\(722\) | 2806.40 | 0.144658 | ||||||||
\(723\) | 12990.0 | 0.668194 | ||||||||
\(724\) | −7146.89 | −0.366868 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13933.2 | 0.712274 | ||||||||
\(727\) | −34202.4 | −1.74484 | −0.872419 | − | 0.488759i | \(-0.837450\pi\) | ||||
−0.872419 | + | 0.488759i | \(0.837450\pi\) | |||||||
\(728\) | 4508.50 | 0.229527 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8429.58 | 0.426510 | ||||||||
\(732\) | 9476.65 | 0.478507 | ||||||||
\(733\) | −12544.2 | −0.632101 | −0.316051 | − | 0.948742i | \(-0.602357\pi\) | ||||
−0.316051 | + | 0.948742i | \(0.602357\pi\) | |||||||
\(734\) | −33625.7 | −1.69094 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33317.6 | −1.66862 | ||||||||
\(737\) | −1687.11 | −0.0843221 | ||||||||
\(738\) | 6739.99 | 0.336182 | ||||||||
\(739\) | 4563.19 | 0.227144 | 0.113572 | − | 0.993530i | \(-0.463771\pi\) | ||||
0.113572 | + | 0.993530i | \(0.463771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14309.7 | −0.709422 | ||||||||
\(742\) | 2716.92 | 0.134422 | ||||||||
\(743\) | 10369.7 | 0.512017 | 0.256009 | − | 0.966674i | \(-0.417592\pi\) | ||||
0.256009 | + | 0.966674i | \(0.417592\pi\) | |||||||
\(744\) | −3340.42 | −0.164605 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11466.1 | −0.562738 | ||||||||
\(747\) | −2547.26 | −0.124765 | ||||||||
\(748\) | −393.120 | −0.0192164 | ||||||||
\(749\) | −8288.57 | −0.404349 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36808.0 | −1.78847 | −0.894237 | − | 0.447595i | \(-0.852281\pi\) | ||||
−0.894237 | + | 0.447595i | \(0.852281\pi\) | |||||||
\(752\) | 8383.92 | 0.406556 | ||||||||
\(753\) | −4201.60 | −0.203340 | ||||||||
\(754\) | 27619.4 | 1.33401 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 885.400 | 0.0425948 | ||||||||
\(757\) | −12516.6 | −0.600955 | −0.300477 | − | 0.953789i | \(-0.597146\pi\) | ||||
−0.300477 | + | 0.953789i | \(0.597146\pi\) | |||||||
\(758\) | −49902.3 | −2.39121 | ||||||||
\(759\) | 2748.93 | 0.131462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11745.1 | 0.559473 | 0.279736 | − | 0.960077i | \(-0.409753\pi\) | ||||
0.279736 | + | 0.960077i | \(0.409753\pi\) | |||||||
\(762\) | −17509.9 | −0.832438 | ||||||||
\(763\) | −2332.73 | −0.110682 | ||||||||
\(764\) | 1376.88 | 0.0652011 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18957.7 | 0.894216 | ||||||||
\(767\) | 11474.6 | 0.540189 | ||||||||
\(768\) | −15629.5 | −0.734350 | ||||||||
\(769\) | 36497.1 | 1.71147 | 0.855735 | − | 0.517414i | \(-0.173105\pi\) | ||||
0.855735 | + | 0.517414i | \(0.173105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12914.6 | −0.603252 | ||||||||
\(772\) | −17168.8 | −0.800414 | ||||||||
\(773\) | −29858.1 | −1.38929 | −0.694644 | − | 0.719353i | \(-0.744438\pi\) | ||||
−0.694644 | + | 0.719353i | \(0.744438\pi\) | |||||||
\(774\) | 16718.4 | 0.776396 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18152.5 | −0.839737 | ||||||||
\(777\) | 363.940 | 0.0168035 | ||||||||
\(778\) | −13692.4 | −0.630973 | ||||||||
\(779\) | 18387.5 | 0.845699 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4122.45 | −0.188877 | ||||||||
\(782\) | 10158.3 | 0.464527 | ||||||||
\(783\) | −3838.60 | −0.175199 | ||||||||
\(784\) | −3897.03 | −0.177525 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6390.94 | 0.290022 | ||||||||
\(787\) | 3168.00 | 0.143491 | 0.0717453 | − | 0.997423i | \(-0.477143\pi\) | ||||
0.0717453 | + | 0.997423i | \(0.477143\pi\) | |||||||
\(788\) | −23900.6 | −1.08049 | ||||||||
\(789\) | 5174.07 | 0.233463 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13170.5 | −0.592019 | ||||||||
\(792\) | 551.778 | 0.0247558 | ||||||||
\(793\) | −36780.8 | −1.64707 | ||||||||
\(794\) | −28657.7 | −1.28089 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23544.5 | 1.04838 | ||||||||
\(797\) | 29317.0 | 1.30296 | 0.651481 | − | 0.758665i | \(-0.274148\pi\) | ||||
0.651481 | + | 0.758665i | \(0.274148\pi\) | |||||||
\(798\) | 6540.39 | 0.290134 | ||||||||
\(799\) | −1703.74 | −0.0754366 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7588.18 | −0.334725 | ||||||||
\(802\) | 27571.3 | 1.21394 | ||||||||
\(803\) | −1637.72 | −0.0719724 | ||||||||
\(804\) | −4566.54 | −0.200310 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18319.7 | −0.800600 | ||||||||
\(807\) | −24014.5 | −1.04752 | ||||||||
\(808\) | 18774.3 | 0.817422 | ||||||||
\(809\) | 16657.3 | 0.723904 | 0.361952 | − | 0.932197i | \(-0.382110\pi\) | ||||
0.361952 | + | 0.932197i | \(0.382110\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5144.55 | 0.222749 | 0.111375 | − | 0.993779i | \(-0.464475\pi\) | ||||
0.111375 | + | 0.993779i | \(0.464475\pi\) | |||||||
\(812\) | −4662.14 | −0.201489 | ||||||||
\(813\) | 5890.95 | 0.254126 | ||||||||
\(814\) | −320.483 | −0.0137997 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3856.13 | 0.165431 | ||||||||
\(817\) | 45609.7 | 1.95310 | ||||||||
\(818\) | −31936.2 | −1.36507 | ||||||||
\(819\) | −3436.42 | −0.146616 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5217.18 | −0.221779 | −0.110890 | − | 0.993833i | \(-0.535370\pi\) | ||||
−0.110890 | + | 0.993833i | \(0.535370\pi\) | |||||||
\(822\) | 10740.8 | 0.455751 | ||||||||
\(823\) | 42326.5 | 1.79272 | 0.896360 | − | 0.443327i | \(-0.146202\pi\) | ||||
0.896360 | + | 0.443327i | \(0.146202\pi\) | |||||||
\(824\) | 1945.83 | 0.0822649 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5244.57 | −0.220922 | ||||||||
\(827\) | −31675.8 | −1.33189 | −0.665946 | − | 0.746000i | \(-0.731972\pi\) | ||||
−0.665946 | + | 0.746000i | \(0.731972\pi\) | |||||||
\(828\) | 7440.62 | 0.312294 | ||||||||
\(829\) | −3471.22 | −0.145429 | −0.0727144 | − | 0.997353i | \(-0.523166\pi\) | ||||
−0.0727144 | + | 0.997353i | \(0.523166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9835.00 | 0.410556 | ||||||||
\(832\) | −1971.57 | −0.0821539 | ||||||||
\(833\) | 791.934 | 0.0329399 | ||||||||
\(834\) | 20033.8 | 0.831791 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2127.05 | −0.0879970 | ||||||||
\(837\) | 2546.11 | 0.105145 | ||||||||
\(838\) | −44211.7 | −1.82252 | ||||||||
\(839\) | −20964.9 | −0.862682 | −0.431341 | − | 0.902189i | \(-0.641959\pi\) | ||||
−0.431341 | + | 0.902189i | \(0.641959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4176.57 | −0.171248 | ||||||||
\(842\) | −5955.41 | −0.243749 | ||||||||
\(843\) | −8577.12 | −0.350429 | ||||||||
\(844\) | −15309.4 | −0.624373 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3379.02 | −0.137321 | ||||||||
\(847\) | 9128.28 | 0.370309 | ||||||||
\(848\) | 8667.17 | 0.350981 | ||||||||
\(849\) | 16301.0 | 0.658950 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3058.44 | 0.123199 | ||||||||
\(852\) | −11158.4 | −0.448685 | ||||||||
\(853\) | 1084.77 | 0.0435426 | 0.0217713 | − | 0.999763i | \(-0.493069\pi\) | ||||
0.0217713 | + | 0.999763i | \(0.493069\pi\) | |||||||
\(854\) | 16811.0 | 0.673607 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13981.4 | −0.558263 | ||||||||
\(857\) | −12661.6 | −0.504679 | −0.252340 | − | 0.967639i | \(-0.581200\pi\) | ||||
−0.252340 | + | 0.967639i | \(0.581200\pi\) | |||||||
\(858\) | 3026.09 | 0.120407 | ||||||||
\(859\) | −39678.7 | −1.57604 | −0.788021 | − | 0.615648i | \(-0.788894\pi\) | ||||
−0.788021 | + | 0.615648i | \(0.788894\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4415.67 | 0.174780 | ||||||||
\(862\) | 57062.6 | 2.25471 | ||||||||
\(863\) | −41614.0 | −1.64143 | −0.820717 | − | 0.571334i | \(-0.806426\pi\) | ||||
−0.820717 | + | 0.571334i | \(0.806426\pi\) | |||||||
\(864\) | 5097.40 | 0.200714 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 38759.2 | 1.52089 | ||||||||
\(867\) | 13955.4 | 0.546654 | ||||||||
\(868\) | 3092.35 | 0.120923 | ||||||||
\(869\) | 2211.06 | 0.0863120 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17723.7 | 0.689489 | ||||||||
\(872\) | −3934.90 | −0.152813 | ||||||||
\(873\) | 13836.0 | 0.536400 | ||||||||
\(874\) | 54963.3 | 2.12719 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4432.86 | −0.170973 | ||||||||
\(877\) | −37061.0 | −1.42698 | −0.713490 | − | 0.700665i | \(-0.752887\pi\) | ||||
−0.713490 | + | 0.700665i | \(0.752887\pi\) | |||||||
\(878\) | 27560.7 | 1.05937 | ||||||||
\(879\) | −25750.3 | −0.988095 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25468.7 | −0.973962 | −0.486981 | − | 0.873412i | \(-0.661902\pi\) | ||||
−0.486981 | + | 0.873412i | \(0.661902\pi\) | |||||||
\(882\) | 1570.64 | 0.0599619 | ||||||||
\(883\) | 34428.3 | 1.31212 | 0.656062 | − | 0.754707i | \(-0.272221\pi\) | ||||
0.656062 | + | 0.754707i | \(0.272221\pi\) | |||||||
\(884\) | 4129.88 | 0.157130 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31222.6 | 1.18391 | ||||||||
\(887\) | 41295.4 | 1.56321 | 0.781603 | − | 0.623777i | \(-0.214403\pi\) | ||||
0.781603 | + | 0.623777i | \(0.214403\pi\) | |||||||
\(888\) | 613.903 | 0.0231996 | ||||||||
\(889\) | −11471.5 | −0.432782 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −420.571 | −0.0158133 | ||||||||
\(892\) | 25567.2 | 0.959702 | ||||||||
\(893\) | −9218.37 | −0.345443 | ||||||||
\(894\) | 11238.1 | 0.420423 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9671.26 | −0.360596 | ||||||||
\(897\) | −28878.6 | −1.07495 | ||||||||
\(898\) | 11039.3 | 0.410230 | ||||||||
\(899\) | −13406.7 | −0.497373 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1761.30 | −0.0651247 | ||||||||
\(902\) | −3888.40 | −0.143536 | ||||||||
\(903\) | 10953.0 | 0.403646 | ||||||||
\(904\) | −22216.2 | −0.817368 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8017.59 | 0.294003 | ||||||||
\(907\) | −53733.8 | −1.96715 | −0.983573 | − | 0.180509i | \(-0.942225\pi\) | ||||
−0.983573 | + | 0.180509i | \(0.942225\pi\) | |||||||
\(908\) | 1316.50 | 0.0481162 | ||||||||
\(909\) | −14309.9 | −0.522146 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24296.8 | 0.883634 | 0.441817 | − | 0.897105i | \(-0.354334\pi\) | ||||
0.441817 | + | 0.897105i | \(0.354334\pi\) | |||||||
\(912\) | 20864.3 | 0.757550 | ||||||||
\(913\) | 1469.55 | 0.0532696 | ||||||||
\(914\) | −21807.2 | −0.789187 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13007.6 | 0.469197 | ||||||||
\(917\) | 4186.99 | 0.150782 | ||||||||
\(918\) | −1554.16 | −0.0558769 | ||||||||
\(919\) | 4280.46 | 0.153645 | 0.0768223 | − | 0.997045i | \(-0.475523\pi\) | ||||
0.0768223 | + | 0.997045i | \(0.475523\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15809.5 | 0.565625 | ||||||||
\(922\) | −37083.6 | −1.32460 | ||||||||
\(923\) | 43307.9 | 1.54442 | ||||||||
\(924\) | −510.801 | −0.0181863 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −40168.9 | −1.42552 | ||||||||
\(927\) | −1483.13 | −0.0525485 | ||||||||
\(928\) | −26840.7 | −0.949450 | ||||||||
\(929\) | −31884.5 | −1.12604 | −0.563022 | − | 0.826442i | \(-0.690361\pi\) | ||||
−0.563022 | + | 0.826442i | \(0.690361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4284.90 | 0.150840 | ||||||||
\(932\) | 27082.4 | 0.951839 | ||||||||
\(933\) | 14284.3 | 0.501229 | ||||||||
\(934\) | 53149.6 | 1.86200 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5796.64 | −0.202424 | ||||||||
\(937\) | −44523.1 | −1.55230 | −0.776151 | − | 0.630548i | \(-0.782830\pi\) | ||||
−0.776151 | + | 0.630548i | \(0.782830\pi\) | |||||||
\(938\) | −8100.76 | −0.281982 | ||||||||
\(939\) | 22808.8 | 0.792693 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46374.9 | 1.60657 | 0.803283 | − | 0.595598i | \(-0.203085\pi\) | ||||
0.803283 | + | 0.595598i | \(0.203085\pi\) | |||||||
\(942\) | 15534.4 | 0.537301 | ||||||||
\(943\) | 37107.9 | 1.28144 | ||||||||
\(944\) | −16730.6 | −0.576836 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9645.09 | −0.331489 | ||||||||
\(947\) | −20348.2 | −0.698234 | −0.349117 | − | 0.937079i | \(-0.613518\pi\) | ||||
−0.349117 | + | 0.937079i | \(0.613518\pi\) | |||||||
\(948\) | 5984.74 | 0.205037 | ||||||||
\(949\) | 17204.8 | 0.588507 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24193.6 | −0.824956 | ||||||||
\(952\) | 1335.85 | 0.0454782 | ||||||||
\(953\) | −45012.9 | −1.53002 | −0.765010 | − | 0.644018i | \(-0.777266\pi\) | ||||
−0.765010 | + | 0.644018i | \(0.777266\pi\) | |||||||
\(954\) | −3493.18 | −0.118549 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7440.02 | 0.251702 | ||||||||
\(957\) | 2214.55 | 0.0748027 | ||||||||
\(958\) | −16647.4 | −0.561435 | ||||||||
\(959\) | 7036.76 | 0.236944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20898.5 | −0.701503 | ||||||||
\(962\) | 3366.79 | 0.112838 | ||||||||
\(963\) | 10656.7 | 0.356603 | ||||||||
\(964\) | −20284.6 | −0.677721 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13199.2 | 0.439624 | ||||||||
\(967\) | −40305.8 | −1.34038 | −0.670190 | − | 0.742190i | \(-0.733787\pi\) | ||||
−0.670190 | + | 0.742190i | \(0.733787\pi\) | |||||||
\(968\) | 15397.8 | 0.511265 | ||||||||
\(969\) | −4239.93 | −0.140564 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33991.8 | 1.12343 | 0.561713 | − | 0.827332i | \(-0.310142\pi\) | ||||
0.561713 | + | 0.827332i | \(0.310142\pi\) | |||||||
\(972\) | −1138.37 | −0.0375651 | ||||||||
\(973\) | 13125.0 | 0.432445 | ||||||||
\(974\) | 60837.2 | 2.00139 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 53628.2 | 1.75881 | ||||||||
\(977\) | −18219.0 | −0.596600 | −0.298300 | − | 0.954472i | \(-0.596420\pi\) | ||||
−0.298300 | + | 0.954472i | \(0.596420\pi\) | |||||||
\(978\) | −13895.3 | −0.454317 | ||||||||
\(979\) | 4377.73 | 0.142914 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2999.22 | 0.0976125 | ||||||||
\(982\) | 64834.1 | 2.10686 | ||||||||
\(983\) | 7676.89 | 0.249089 | 0.124545 | − | 0.992214i | \(-0.460253\pi\) | ||||
0.124545 | + | 0.992214i | \(0.460253\pi\) | |||||||
\(984\) | 7448.45 | 0.241309 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8183.55 | 0.264318 | ||||||||
\(987\) | −2213.75 | −0.0713925 | ||||||||
\(988\) | 22345.4 | 0.719537 | ||||||||
\(989\) | 92045.3 | 2.95942 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50585.6 | 1.62150 | 0.810748 | − | 0.585395i | \(-0.199061\pi\) | ||||
0.810748 | + | 0.585395i | \(0.199061\pi\) | |||||||
\(992\) | 17803.2 | 0.569810 | ||||||||
\(993\) | −20882.4 | −0.667354 | ||||||||
\(994\) | −19794.2 | −0.631625 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3977.69 | 0.126544 | ||||||||
\(997\) | −53060.5 | −1.68550 | −0.842750 | − | 0.538305i | \(-0.819065\pi\) | ||||
−0.842750 | + | 0.538305i | \(0.819065\pi\) | |||||||
\(998\) | 25320.8 | 0.803121 | ||||||||
\(999\) | −467.923 | −0.0148193 |
(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 | 525.4.a.m.1.2 | yes | 2 | |
3.2 | odd | 2 | 1575.4.a.o.1.1 | 2 | |||
5.2 | odd | 4 | 525.4.d.m.274.4 | 4 | |||
5.3 | odd | 4 | 525.4.d.m.274.1 | 4 | |||
5.4 | even | 2 | 525.4.a.j.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 1575.4.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.4.a.j.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
525.4.a.m.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
525.4.d.m.274.1 | 4 | 5.3 | odd | 4 | |||
525.4.d.m.274.4 | 4 | 5.2 | odd | 4 | |||
1575.4.a.o.1.1 | 2 | 3.2 | odd | 2 | |||
1575.4.a.x.1.2 | 2 | 15.14 | odd | 2 |