Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,4,Mod(1,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(2.89109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{65})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 35x^{2} + 36x + 194 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.11692\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.53113 | −1.24844 | −0.624221 | − | 0.781248i | \(-0.714584\pi\) | ||||
−0.624221 | + | 0.781248i | \(0.714584\pi\) | |||||||
\(3\) | −7.82220 | −1.50538 | −0.752691 | − | 0.658374i | \(-0.771245\pi\) | ||||
−0.752691 | + | 0.658374i | \(0.771245\pi\) | |||||||
\(4\) | 4.46887 | 0.558609 | ||||||||
\(5\) | −2.07730 | −0.185799 | −0.0928996 | − | 0.995675i | \(-0.529614\pi\) | ||||
−0.0928996 | + | 0.995675i | \(0.529614\pi\) | |||||||
\(6\) | 27.6212 | 1.87938 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 12.4689 | 0.551051 | ||||||||
\(9\) | 34.1868 | 1.26618 | ||||||||
\(10\) | 7.33521 | 0.231960 | ||||||||
\(11\) | 49.1868 | 1.34822 | 0.674108 | − | 0.738633i | \(-0.264528\pi\) | ||||
0.674108 | + | 0.738633i | \(0.264528\pi\) | |||||||
\(12\) | −34.9564 | −0.840920 | ||||||||
\(13\) | −44.8559 | −0.956983 | −0.478492 | − | 0.878092i | \(-0.658816\pi\) | ||||
−0.478492 | + | 0.878092i | \(0.658816\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.2490 | 0.279699 | ||||||||
\(16\) | −79.7802 | −1.24656 | ||||||||
\(17\) | 26.5179 | 0.378325 | 0.189163 | − | 0.981946i | \(-0.439423\pi\) | ||||
0.189163 | + | 0.981946i | \(0.439423\pi\) | |||||||
\(18\) | −120.718 | −1.58075 | ||||||||
\(19\) | 77.7350 | 0.938612 | 0.469306 | − | 0.883036i | \(-0.344504\pi\) | ||||
0.469306 | + | 0.883036i | \(0.344504\pi\) | |||||||
\(20\) | −9.28317 | −0.103789 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −173.685 | −1.68317 | ||||||||
\(23\) | 55.7510 | 0.505430 | 0.252715 | − | 0.967541i | \(-0.418677\pi\) | ||||
0.252715 | + | 0.967541i | \(0.418677\pi\) | |||||||
\(24\) | −97.5340 | −0.829543 | ||||||||
\(25\) | −120.685 | −0.965479 | ||||||||
\(26\) | 158.392 | 1.19474 | ||||||||
\(27\) | −56.2164 | −0.400698 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 121.436 | 0.777588 | 0.388794 | − | 0.921325i | \(-0.372892\pi\) | ||||
0.388794 | + | 0.921325i | \(0.372892\pi\) | |||||||
\(30\) | −57.3774 | −0.349188 | ||||||||
\(31\) | 305.553 | 1.77029 | 0.885143 | − | 0.465319i | \(-0.154060\pi\) | ||||
0.885143 | + | 0.465319i | \(0.154060\pi\) | |||||||
\(32\) | 181.963 | 1.00521 | ||||||||
\(33\) | −384.749 | −2.02958 | ||||||||
\(34\) | −93.6380 | −0.472317 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 152.776 | 0.707298 | ||||||||
\(37\) | 77.1868 | 0.342957 | 0.171479 | − | 0.985188i | \(-0.445146\pi\) | ||||
0.171479 | + | 0.985188i | \(0.445146\pi\) | |||||||
\(38\) | −274.492 | −1.17180 | ||||||||
\(39\) | 350.872 | 1.44063 | ||||||||
\(40\) | −25.9016 | −0.102385 | ||||||||
\(41\) | 248.720 | 0.947403 | 0.473702 | − | 0.880685i | \(-0.342917\pi\) | ||||
0.473702 | + | 0.880685i | \(0.342917\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −147.179 | −0.521967 | −0.260984 | − | 0.965343i | \(-0.584047\pi\) | ||||
−0.260984 | + | 0.965343i | \(0.584047\pi\) | |||||||
\(44\) | 219.809 | 0.753125 | ||||||||
\(45\) | −71.0161 | −0.235255 | ||||||||
\(46\) | −196.864 | −0.631000 | ||||||||
\(47\) | 269.851 | 0.837484 | 0.418742 | − | 0.908105i | \(-0.362471\pi\) | ||||
0.418742 | + | 0.908105i | \(0.362471\pi\) | |||||||
\(48\) | 624.056 | 1.87656 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 426.154 | 1.20534 | ||||||||
\(51\) | −207.428 | −0.569524 | ||||||||
\(52\) | −200.455 | −0.534579 | ||||||||
\(53\) | −141.121 | −0.365744 | −0.182872 | − | 0.983137i | \(-0.558539\pi\) | ||||
−0.182872 | + | 0.983137i | \(0.558539\pi\) | |||||||
\(54\) | 198.507 | 0.500248 | ||||||||
\(55\) | −102.176 | −0.250497 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −608.058 | −1.41297 | ||||||||
\(58\) | −428.805 | −0.970774 | ||||||||
\(59\) | −424.834 | −0.937434 | −0.468717 | − | 0.883348i | \(-0.655284\pi\) | ||||
−0.468717 | + | 0.883348i | \(0.655284\pi\) | |||||||
\(60\) | 72.6148 | 0.156242 | ||||||||
\(61\) | −587.996 | −1.23418 | −0.617092 | − | 0.786891i | \(-0.711689\pi\) | ||||
−0.617092 | + | 0.786891i | \(0.711689\pi\) | |||||||
\(62\) | −1078.95 | −2.21010 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.29373 | −0.00838618 | ||||||||
\(65\) | 93.1790 | 0.177807 | ||||||||
\(66\) | 1358.60 | 2.53381 | ||||||||
\(67\) | −179.634 | −0.327549 | −0.163775 | − | 0.986498i | \(-0.552367\pi\) | ||||
−0.163775 | + | 0.986498i | \(0.552367\pi\) | |||||||
\(68\) | 118.505 | 0.211336 | ||||||||
\(69\) | −436.095 | −0.760865 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 674.872 | 1.12806 | 0.564032 | − | 0.825753i | \(-0.309250\pi\) | ||||
0.564032 | + | 0.825753i | \(0.309250\pi\) | |||||||
\(72\) | 426.270 | 0.697729 | ||||||||
\(73\) | 237.489 | 0.380767 | 0.190383 | − | 0.981710i | \(-0.439027\pi\) | ||||
0.190383 | + | 0.981710i | \(0.439027\pi\) | |||||||
\(74\) | −272.556 | −0.428163 | ||||||||
\(75\) | 944.021 | 1.45341 | ||||||||
\(76\) | 347.388 | 0.524317 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1238.97 | −1.79854 | ||||||||
\(79\) | 495.852 | 0.706174 | 0.353087 | − | 0.935591i | \(-0.385132\pi\) | ||||
0.353087 | + | 0.935591i | \(0.385132\pi\) | |||||||
\(80\) | 165.727 | 0.231611 | ||||||||
\(81\) | −483.307 | −0.662973 | ||||||||
\(82\) | −878.262 | −1.18278 | ||||||||
\(83\) | −24.4406 | −0.0323217 | −0.0161609 | − | 0.999869i | \(-0.505144\pi\) | ||||
−0.0161609 | + | 0.999869i | \(0.505144\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −55.0855 | −0.0702925 | ||||||||
\(86\) | 519.708 | 0.651646 | ||||||||
\(87\) | −949.895 | −1.17057 | ||||||||
\(88\) | 613.304 | 0.742936 | ||||||||
\(89\) | 1072.29 | 1.27710 | 0.638552 | − | 0.769579i | \(-0.279534\pi\) | ||||
0.638552 | + | 0.769579i | \(0.279534\pi\) | |||||||
\(90\) | 250.767 | 0.293702 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 249.144 | 0.282337 | ||||||||
\(93\) | −2390.09 | −2.66496 | ||||||||
\(94\) | −952.877 | −1.04555 | ||||||||
\(95\) | −161.479 | −0.174393 | ||||||||
\(96\) | −1423.35 | −1.51323 | ||||||||
\(97\) | 1667.43 | 1.74538 | 0.872690 | − | 0.488275i | \(-0.162374\pi\) | ||||
0.872690 | + | 0.488275i | \(0.162374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1681.54 | 1.70708 | ||||||||
\(100\) | −539.325 | −0.539325 | ||||||||
\(101\) | −77.1187 | −0.0759762 | −0.0379881 | − | 0.999278i | \(-0.512095\pi\) | ||||
−0.0379881 | + | 0.999278i | \(0.512095\pi\) | |||||||
\(102\) | 732.455 | 0.711018 | ||||||||
\(103\) | 164.693 | 0.157550 | 0.0787749 | − | 0.996892i | \(-0.474899\pi\) | ||||
0.0787749 | + | 0.996892i | \(0.474899\pi\) | |||||||
\(104\) | −559.302 | −0.527347 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 498.315 | 0.456610 | ||||||||
\(107\) | 1022.62 | 0.923931 | 0.461966 | − | 0.886898i | \(-0.347144\pi\) | ||||
0.461966 | + | 0.886898i | \(0.347144\pi\) | |||||||
\(108\) | −251.224 | −0.223833 | ||||||||
\(109\) | 1362.52 | 1.19730 | 0.598649 | − | 0.801011i | \(-0.295704\pi\) | ||||
0.598649 | + | 0.801011i | \(0.295704\pi\) | |||||||
\(110\) | 360.795 | 0.312731 | ||||||||
\(111\) | −603.770 | −0.516282 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1538.41 | −1.28072 | −0.640360 | − | 0.768075i | \(-0.721215\pi\) | ||||
−0.640360 | + | 0.768075i | \(0.721215\pi\) | |||||||
\(114\) | 2147.13 | 1.76401 | ||||||||
\(115\) | −115.811 | −0.0939084 | ||||||||
\(116\) | 542.681 | 0.434368 | ||||||||
\(117\) | −1533.48 | −1.21171 | ||||||||
\(118\) | 1500.14 | 1.17033 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 202.607 | 0.154128 | ||||||||
\(121\) | 1088.34 | 0.817685 | ||||||||
\(122\) | 2076.29 | 1.54081 | ||||||||
\(123\) | −1945.54 | −1.42620 | ||||||||
\(124\) | 1365.48 | 0.988898 | ||||||||
\(125\) | 510.360 | 0.365184 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −170.358 | −0.119030 | −0.0595151 | − | 0.998227i | \(-0.518955\pi\) | ||||
−0.0595151 | + | 0.998227i | \(0.518955\pi\) | |||||||
\(128\) | −1440.54 | −0.994744 | ||||||||
\(129\) | 1151.26 | 0.785760 | ||||||||
\(130\) | −329.027 | −0.221981 | ||||||||
\(131\) | −751.935 | −0.501503 | −0.250751 | − | 0.968051i | \(-0.580678\pi\) | ||||
−0.250751 | + | 0.968051i | \(0.580678\pi\) | |||||||
\(132\) | −1719.39 | −1.13374 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 634.312 | 0.408927 | ||||||||
\(135\) | 116.778 | 0.0744493 | ||||||||
\(136\) | 330.648 | 0.208477 | ||||||||
\(137\) | 518.623 | 0.323423 | 0.161711 | − | 0.986838i | \(-0.448299\pi\) | ||||
0.161711 | + | 0.986838i | \(0.448299\pi\) | |||||||
\(138\) | 1539.91 | 0.949896 | ||||||||
\(139\) | −2975.72 | −1.81581 | −0.907905 | − | 0.419177i | \(-0.862319\pi\) | ||||
−0.907905 | + | 0.419177i | \(0.862319\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2110.83 | −1.26073 | ||||||||
\(142\) | −2383.06 | −1.40832 | ||||||||
\(143\) | −2206.32 | −1.29022 | ||||||||
\(144\) | −2727.43 | −1.57837 | ||||||||
\(145\) | −252.258 | −0.144475 | ||||||||
\(146\) | −838.604 | −0.475365 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 344.938 | 0.191579 | ||||||||
\(149\) | −2717.94 | −1.49438 | −0.747188 | − | 0.664612i | \(-0.768597\pi\) | ||||
−0.747188 | + | 0.664612i | \(0.768597\pi\) | |||||||
\(150\) | −3333.46 | −1.81450 | ||||||||
\(151\) | 707.650 | 0.381376 | 0.190688 | − | 0.981651i | \(-0.438928\pi\) | ||||
0.190688 | + | 0.981651i | \(0.438928\pi\) | |||||||
\(152\) | 969.267 | 0.517224 | ||||||||
\(153\) | 906.561 | 0.479027 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −634.724 | −0.328918 | ||||||||
\(156\) | 1568.00 | 0.804747 | ||||||||
\(157\) | 3117.91 | 1.58495 | 0.792473 | − | 0.609906i | \(-0.208793\pi\) | ||||
0.792473 | + | 0.609906i | \(0.208793\pi\) | |||||||
\(158\) | −1750.92 | −0.881618 | ||||||||
\(159\) | 1103.87 | 0.550584 | ||||||||
\(160\) | −377.991 | −0.186768 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1706.62 | 0.827684 | ||||||||
\(163\) | 1808.77 | 0.869167 | 0.434583 | − | 0.900632i | \(-0.356896\pi\) | ||||
0.434583 | + | 0.900632i | \(0.356896\pi\) | |||||||
\(164\) | 1111.50 | 0.529228 | ||||||||
\(165\) | 799.237 | 0.377094 | ||||||||
\(166\) | 86.3028 | 0.0403518 | ||||||||
\(167\) | 3147.38 | 1.45839 | 0.729197 | − | 0.684303i | \(-0.239894\pi\) | ||||
0.729197 | + | 0.684303i | \(0.239894\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −184.949 | −0.0841827 | ||||||||
\(170\) | 194.514 | 0.0877562 | ||||||||
\(171\) | 2657.51 | 1.18845 | ||||||||
\(172\) | −657.724 | −0.291576 | ||||||||
\(173\) | −3284.36 | −1.44338 | −0.721691 | − | 0.692215i | \(-0.756635\pi\) | ||||
−0.721691 | + | 0.692215i | \(0.756635\pi\) | |||||||
\(174\) | 3354.20 | 1.46139 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3924.13 | −1.68064 | ||||||||
\(177\) | 3323.13 | 1.41120 | ||||||||
\(178\) | −3786.39 | −1.59439 | ||||||||
\(179\) | 2798.83 | 1.16868 | 0.584341 | − | 0.811508i | \(-0.301353\pi\) | ||||
0.584341 | + | 0.811508i | \(0.301353\pi\) | |||||||
\(180\) | −317.362 | −0.131415 | ||||||||
\(181\) | −3723.04 | −1.52890 | −0.764451 | − | 0.644682i | \(-0.776990\pi\) | ||||
−0.764451 | + | 0.644682i | \(0.776990\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4599.42 | 1.85792 | ||||||||
\(184\) | 695.152 | 0.278518 | ||||||||
\(185\) | −160.340 | −0.0637212 | ||||||||
\(186\) | 8439.73 | 3.32705 | ||||||||
\(187\) | 1304.33 | 0.510064 | ||||||||
\(188\) | 1205.93 | 0.467826 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 570.202 | 0.217720 | ||||||||
\(191\) | 959.650 | 0.363549 | 0.181774 | − | 0.983340i | \(-0.441816\pi\) | ||||
0.181774 | + | 0.983340i | \(0.441816\pi\) | |||||||
\(192\) | 33.5864 | 0.0126244 | ||||||||
\(193\) | −3790.25 | −1.41362 | −0.706808 | − | 0.707406i | \(-0.749865\pi\) | ||||
−0.706808 | + | 0.707406i | \(0.749865\pi\) | |||||||
\(194\) | −5887.91 | −2.17901 | ||||||||
\(195\) | −728.865 | −0.267667 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5117.99 | 1.85097 | 0.925487 | − | 0.378779i | \(-0.123656\pi\) | ||||
0.925487 | + | 0.378779i | \(0.123656\pi\) | |||||||
\(198\) | −5937.72 | −2.13119 | ||||||||
\(199\) | 864.855 | 0.308080 | 0.154040 | − | 0.988065i | \(-0.450772\pi\) | ||||
0.154040 | + | 0.988065i | \(0.450772\pi\) | |||||||
\(200\) | −1504.80 | −0.532028 | ||||||||
\(201\) | 1405.13 | 0.493087 | ||||||||
\(202\) | 272.316 | 0.0948519 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −926.969 | −0.318141 | ||||||||
\(205\) | −516.665 | −0.176027 | ||||||||
\(206\) | −581.550 | −0.196692 | ||||||||
\(207\) | 1905.95 | 0.639963 | ||||||||
\(208\) | 3578.61 | 1.19294 | ||||||||
\(209\) | 3823.53 | 1.26545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1344.61 | −0.438707 | −0.219353 | − | 0.975645i | \(-0.570395\pi\) | ||||
−0.219353 | + | 0.975645i | \(0.570395\pi\) | |||||||
\(212\) | −630.650 | −0.204308 | ||||||||
\(213\) | −5278.98 | −1.69817 | ||||||||
\(214\) | −3611.01 | −1.15348 | ||||||||
\(215\) | 305.735 | 0.0969811 | ||||||||
\(216\) | −700.955 | −0.220805 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4811.23 | −1.49476 | ||||||||
\(219\) | −1857.68 | −0.573200 | ||||||||
\(220\) | −456.609 | −0.139930 | ||||||||
\(221\) | −1189.48 | −0.362051 | ||||||||
\(222\) | 2131.99 | 0.644549 | ||||||||
\(223\) | −864.916 | −0.259727 | −0.129863 | − | 0.991532i | \(-0.541454\pi\) | ||||
−0.129863 | + | 0.991532i | \(0.541454\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4125.83 | −1.22247 | ||||||||
\(226\) | 5432.32 | 1.59890 | ||||||||
\(227\) | 1715.34 | 0.501548 | 0.250774 | − | 0.968046i | \(-0.419315\pi\) | ||||
0.250774 | + | 0.968046i | \(0.419315\pi\) | |||||||
\(228\) | −2717.33 | −0.789298 | ||||||||
\(229\) | 1045.46 | 0.301685 | 0.150842 | − | 0.988558i | \(-0.451801\pi\) | ||||
0.150842 | + | 0.988558i | \(0.451801\pi\) | |||||||
\(230\) | 408.945 | 0.117239 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1514.17 | 0.428491 | ||||||||
\(233\) | 1448.67 | 0.407320 | 0.203660 | − | 0.979042i | \(-0.434716\pi\) | ||||
0.203660 | + | 0.979042i | \(0.434716\pi\) | |||||||
\(234\) | 5414.91 | 1.51275 | ||||||||
\(235\) | −560.560 | −0.155604 | ||||||||
\(236\) | −1898.53 | −0.523659 | ||||||||
\(237\) | −3878.65 | −1.06306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3153.12 | −0.853383 | −0.426691 | − | 0.904397i | \(-0.640321\pi\) | ||||
−0.426691 | + | 0.904397i | \(0.640321\pi\) | |||||||
\(240\) | −1296.35 | −0.348663 | ||||||||
\(241\) | 381.012 | 0.101839 | 0.0509194 | − | 0.998703i | \(-0.483785\pi\) | ||||
0.0509194 | + | 0.998703i | \(0.483785\pi\) | |||||||
\(242\) | −3843.06 | −1.02083 | ||||||||
\(243\) | 5298.37 | 1.39873 | ||||||||
\(244\) | −2627.68 | −0.689426 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6869.94 | 1.78053 | ||||||||
\(247\) | −3486.87 | −0.898236 | ||||||||
\(248\) | 3809.90 | 0.975519 | ||||||||
\(249\) | 191.179 | 0.0486565 | ||||||||
\(250\) | −1802.15 | −0.455912 | ||||||||
\(251\) | −3776.23 | −0.949617 | −0.474808 | − | 0.880089i | \(-0.657483\pi\) | ||||
−0.474808 | + | 0.880089i | \(0.657483\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2742.21 | 0.681428 | ||||||||
\(254\) | 601.556 | 0.148602 | ||||||||
\(255\) | 430.890 | 0.105817 | ||||||||
\(256\) | 5121.09 | 1.25027 | ||||||||
\(257\) | −4258.42 | −1.03359 | −0.516795 | − | 0.856109i | \(-0.672875\pi\) | ||||
−0.516795 | + | 0.856109i | \(0.672875\pi\) | |||||||
\(258\) | −4065.26 | −0.980977 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 416.405 | 0.0993244 | ||||||||
\(261\) | 4151.50 | 0.984564 | ||||||||
\(262\) | 2655.18 | 0.626098 | ||||||||
\(263\) | 4198.83 | 0.984451 | 0.492226 | − | 0.870468i | \(-0.336184\pi\) | ||||
0.492226 | + | 0.870468i | \(0.336184\pi\) | |||||||
\(264\) | −4797.38 | −1.11840 | ||||||||
\(265\) | 293.150 | 0.0679548 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8387.65 | −1.92253 | ||||||||
\(268\) | −802.762 | −0.182972 | ||||||||
\(269\) | −3740.59 | −0.847835 | −0.423917 | − | 0.905701i | \(-0.639345\pi\) | ||||
−0.423917 | + | 0.905701i | \(0.639345\pi\) | |||||||
\(270\) | −412.359 | −0.0929457 | ||||||||
\(271\) | −4356.30 | −0.976480 | −0.488240 | − | 0.872709i | \(-0.662361\pi\) | ||||
−0.488240 | + | 0.872709i | \(0.662361\pi\) | |||||||
\(272\) | −2115.60 | −0.471607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1831.32 | −0.403775 | ||||||||
\(275\) | −5936.10 | −1.30167 | ||||||||
\(276\) | −1948.85 | −0.425026 | ||||||||
\(277\) | −1344.30 | −0.291593 | −0.145797 | − | 0.989315i | \(-0.546575\pi\) | ||||
−0.145797 | + | 0.989315i | \(0.546575\pi\) | |||||||
\(278\) | 10507.7 | 2.26693 | ||||||||
\(279\) | 10445.9 | 2.24150 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4205.54 | 0.892817 | 0.446408 | − | 0.894829i | \(-0.352703\pi\) | ||||
0.446408 | + | 0.894829i | \(0.352703\pi\) | |||||||
\(282\) | 7453.60 | 1.57395 | ||||||||
\(283\) | −4752.03 | −0.998159 | −0.499079 | − | 0.866556i | \(-0.666328\pi\) | ||||
−0.499079 | + | 0.866556i | \(0.666328\pi\) | |||||||
\(284\) | 3015.91 | 0.630146 | ||||||||
\(285\) | 1263.12 | 0.262529 | ||||||||
\(286\) | 7790.79 | 1.61077 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6220.73 | 1.27278 | ||||||||
\(289\) | −4209.80 | −0.856870 | ||||||||
\(290\) | 890.757 | 0.180369 | ||||||||
\(291\) | −13043.0 | −2.62746 | ||||||||
\(292\) | 1061.31 | 0.212700 | ||||||||
\(293\) | 4961.17 | 0.989196 | 0.494598 | − | 0.869122i | \(-0.335315\pi\) | ||||
0.494598 | + | 0.869122i | \(0.335315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 882.506 | 0.174174 | ||||||||
\(296\) | 962.432 | 0.188987 | ||||||||
\(297\) | −2765.10 | −0.540227 | ||||||||
\(298\) | 9597.39 | 1.86564 | ||||||||
\(299\) | −2500.76 | −0.483688 | ||||||||
\(300\) | 4218.71 | 0.811890 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2498.80 | −0.476126 | ||||||||
\(303\) | 603.237 | 0.114373 | ||||||||
\(304\) | −6201.71 | −1.17004 | ||||||||
\(305\) | 1221.44 | 0.229310 | ||||||||
\(306\) | −3201.18 | −0.598037 | ||||||||
\(307\) | 4234.00 | 0.787124 | 0.393562 | − | 0.919298i | \(-0.371243\pi\) | ||||
0.393562 | + | 0.919298i | \(0.371243\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1288.26 | −0.237173 | ||||||||
\(310\) | 2241.29 | 0.410635 | ||||||||
\(311\) | 684.700 | 0.124842 | 0.0624209 | − | 0.998050i | \(-0.480118\pi\) | ||||
0.0624209 | + | 0.998050i | \(0.480118\pi\) | |||||||
\(312\) | 4374.97 | 0.793859 | ||||||||
\(313\) | 5944.07 | 1.07341 | 0.536707 | − | 0.843768i | \(-0.319668\pi\) | ||||
0.536707 | + | 0.843768i | \(0.319668\pi\) | |||||||
\(314\) | −11009.8 | −1.97872 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2215.90 | 0.394475 | ||||||||
\(317\) | −2823.89 | −0.500333 | −0.250166 | − | 0.968203i | \(-0.580485\pi\) | ||||
−0.250166 | + | 0.968203i | \(0.580485\pi\) | |||||||
\(318\) | −3897.92 | −0.687373 | ||||||||
\(319\) | 5973.04 | 1.04836 | ||||||||
\(320\) | 8.91935 | 0.00155815 | ||||||||
\(321\) | −7999.16 | −1.39087 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2061.37 | 0.355101 | ||||||||
\(324\) | −2159.84 | −0.370343 | ||||||||
\(325\) | 5413.43 | 0.923947 | ||||||||
\(326\) | −6387.02 | −1.08510 | ||||||||
\(327\) | −10657.9 | −1.80239 | ||||||||
\(328\) | 3101.26 | 0.522068 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2822.21 | −0.470780 | ||||||||
\(331\) | −2812.97 | −0.467114 | −0.233557 | − | 0.972343i | \(-0.575037\pi\) | ||||
−0.233557 | + | 0.972343i | \(0.575037\pi\) | |||||||
\(332\) | −109.222 | −0.0180552 | ||||||||
\(333\) | 2638.77 | 0.434245 | ||||||||
\(334\) | −11113.8 | −1.82072 | ||||||||
\(335\) | 373.154 | 0.0608584 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4260.10 | 0.688612 | 0.344306 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344306 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(338\) | 653.080 | 0.105097 | ||||||||
\(339\) | 12033.7 | 1.92797 | ||||||||
\(340\) | −246.170 | −0.0392660 | ||||||||
\(341\) | 15029.2 | 2.38673 | ||||||||
\(342\) | −9384.00 | −1.48371 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1835.16 | −0.287631 | ||||||||
\(345\) | 905.899 | 0.141368 | ||||||||
\(346\) | 11597.5 | 1.80198 | ||||||||
\(347\) | 36.0584 | 0.00557843 | 0.00278922 | − | 0.999996i | \(-0.499112\pi\) | ||||
0.00278922 | + | 0.999996i | \(0.499112\pi\) | |||||||
\(348\) | −4244.96 | −0.653890 | ||||||||
\(349\) | 242.692 | 0.0372236 | 0.0186118 | − | 0.999827i | \(-0.494075\pi\) | ||||
0.0186118 | + | 0.999827i | \(0.494075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2521.63 | 0.383461 | ||||||||
\(352\) | 8950.18 | 1.35524 | ||||||||
\(353\) | 109.990 | 0.0165840 | 0.00829201 | − | 0.999966i | \(-0.497361\pi\) | ||||
0.00829201 | + | 0.999966i | \(0.497361\pi\) | |||||||
\(354\) | −11734.4 | −1.76180 | ||||||||
\(355\) | −1401.91 | −0.209593 | ||||||||
\(356\) | 4791.92 | 0.713402 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9883.01 | −1.45903 | ||||||||
\(359\) | 12404.5 | 1.82363 | 0.911814 | − | 0.410604i | \(-0.134682\pi\) | ||||
0.911814 | + | 0.410604i | \(0.134682\pi\) | |||||||
\(360\) | −885.491 | −0.129637 | ||||||||
\(361\) | −816.273 | −0.119008 | ||||||||
\(362\) | 13146.5 | 1.90875 | ||||||||
\(363\) | −8513.20 | −1.23093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −493.335 | −0.0707461 | ||||||||
\(366\) | −16241.2 | −2.31951 | ||||||||
\(367\) | −13859.6 | −1.97130 | −0.985649 | − | 0.168807i | \(-0.946009\pi\) | ||||
−0.985649 | + | 0.168807i | \(0.946009\pi\) | |||||||
\(368\) | −4447.82 | −0.630051 | ||||||||
\(369\) | 8502.93 | 1.19958 | ||||||||
\(370\) | 566.181 | 0.0795523 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10681.0 | −1.48867 | ||||||||
\(373\) | 4898.06 | 0.679925 | 0.339963 | − | 0.940439i | \(-0.389586\pi\) | ||||
0.339963 | + | 0.940439i | \(0.389586\pi\) | |||||||
\(374\) | −4605.75 | −0.636786 | ||||||||
\(375\) | −3992.14 | −0.549742 | ||||||||
\(376\) | 3364.73 | 0.461497 | ||||||||
\(377\) | −5447.11 | −0.744139 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9806.25 | −1.32906 | −0.664530 | − | 0.747262i | \(-0.731368\pi\) | ||||
−0.664530 | + | 0.747262i | \(0.731368\pi\) | |||||||
\(380\) | −721.627 | −0.0974176 | ||||||||
\(381\) | 1332.57 | 0.179186 | ||||||||
\(382\) | −3388.65 | −0.453870 | ||||||||
\(383\) | −10729.7 | −1.43149 | −0.715746 | − | 0.698361i | \(-0.753913\pi\) | ||||
−0.715746 | + | 0.698361i | \(0.753913\pi\) | |||||||
\(384\) | 11268.2 | 1.49747 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13383.8 | 1.76482 | ||||||||
\(387\) | −5031.58 | −0.660903 | ||||||||
\(388\) | 7451.53 | 0.974984 | ||||||||
\(389\) | 5264.05 | 0.686113 | 0.343057 | − | 0.939315i | \(-0.388538\pi\) | ||||
0.343057 | + | 0.939315i | \(0.388538\pi\) | |||||||
\(390\) | 2573.72 | 0.334167 | ||||||||
\(391\) | 1478.40 | 0.191217 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5881.79 | 0.754954 | ||||||||
\(394\) | −18072.3 | −2.31083 | ||||||||
\(395\) | −1030.03 | −0.131206 | ||||||||
\(396\) | 7514.57 | 0.953590 | ||||||||
\(397\) | −1214.90 | −0.153587 | −0.0767935 | − | 0.997047i | \(-0.524468\pi\) | ||||
−0.0767935 | + | 0.997047i | \(0.524468\pi\) | |||||||
\(398\) | −3053.91 | −0.384620 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9628.26 | 1.20353 | ||||||||
\(401\) | 2295.45 | 0.285859 | 0.142929 | − | 0.989733i | \(-0.454348\pi\) | ||||
0.142929 | + | 0.989733i | \(0.454348\pi\) | |||||||
\(402\) | −4961.71 | −0.615591 | ||||||||
\(403\) | −13705.8 | −1.69413 | ||||||||
\(404\) | −344.633 | −0.0424410 | ||||||||
\(405\) | 1003.97 | 0.123180 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3796.57 | 0.462381 | ||||||||
\(408\) | −2586.39 | −0.313837 | ||||||||
\(409\) | −4646.54 | −0.561753 | −0.280876 | − | 0.959744i | \(-0.590625\pi\) | ||||
−0.280876 | + | 0.959744i | \(0.590625\pi\) | |||||||
\(410\) | 1824.41 | 0.219759 | ||||||||
\(411\) | −4056.77 | −0.486875 | ||||||||
\(412\) | 735.990 | 0.0880087 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6730.14 | −0.798957 | ||||||||
\(415\) | 50.7703 | 0.00600535 | ||||||||
\(416\) | −8162.11 | −0.961973 | ||||||||
\(417\) | 23276.7 | 2.73349 | ||||||||
\(418\) | −13501.4 | −1.57984 | ||||||||
\(419\) | −7541.24 | −0.879269 | −0.439634 | − | 0.898177i | \(-0.644892\pi\) | ||||
−0.439634 | + | 0.898177i | \(0.644892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6243.63 | −0.722794 | −0.361397 | − | 0.932412i | \(-0.617700\pi\) | ||||
−0.361397 | + | 0.932412i | \(0.617700\pi\) | |||||||
\(422\) | 4748.01 | 0.547700 | ||||||||
\(423\) | 9225.32 | 1.06040 | ||||||||
\(424\) | −1759.62 | −0.201544 | ||||||||
\(425\) | −3200.31 | −0.365265 | ||||||||
\(426\) | 18640.8 | 2.12006 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4569.97 | 0.516116 | ||||||||
\(429\) | 17258.2 | 1.94227 | ||||||||
\(430\) | −1079.59 | −0.121075 | ||||||||
\(431\) | 11465.8 | 1.28141 | 0.640706 | − | 0.767786i | \(-0.278642\pi\) | ||||
0.640706 | + | 0.767786i | \(0.278642\pi\) | |||||||
\(432\) | 4484.95 | 0.499496 | ||||||||
\(433\) | −5156.40 | −0.572289 | −0.286144 | − | 0.958187i | \(-0.592374\pi\) | ||||
−0.286144 | + | 0.958187i | \(0.592374\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1973.21 | 0.217491 | ||||||||
\(436\) | 6088.92 | 0.668822 | ||||||||
\(437\) | 4333.80 | 0.474402 | ||||||||
\(438\) | 6559.72 | 0.715607 | ||||||||
\(439\) | 5064.25 | 0.550577 | 0.275289 | − | 0.961362i | \(-0.411227\pi\) | ||||
0.275289 | + | 0.961362i | \(0.411227\pi\) | |||||||
\(440\) | −1274.01 | −0.138037 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4200.22 | 0.452000 | ||||||||
\(443\) | 12703.6 | 1.36246 | 0.681228 | − | 0.732071i | \(-0.261446\pi\) | ||||
0.681228 | + | 0.732071i | \(0.261446\pi\) | |||||||
\(444\) | −2698.17 | −0.288400 | ||||||||
\(445\) | −2227.46 | −0.237285 | ||||||||
\(446\) | 3054.13 | 0.324254 | ||||||||
\(447\) | 21260.2 | 2.24961 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13942.2 | 1.46542 | 0.732709 | − | 0.680542i | \(-0.238256\pi\) | ||||
0.732709 | + | 0.680542i | \(0.238256\pi\) | |||||||
\(450\) | 14568.8 | 1.52618 | ||||||||
\(451\) | 12233.7 | 1.27730 | ||||||||
\(452\) | −6874.95 | −0.715421 | ||||||||
\(453\) | −5535.38 | −0.574116 | ||||||||
\(454\) | −6057.10 | −0.626154 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7581.80 | −0.778619 | ||||||||
\(457\) | −15214.0 | −1.55729 | −0.778646 | − | 0.627464i | \(-0.784093\pi\) | ||||
−0.778646 | + | 0.627464i | \(0.784093\pi\) | |||||||
\(458\) | −3691.65 | −0.376636 | ||||||||
\(459\) | −1490.74 | −0.151594 | ||||||||
\(460\) | −517.546 | −0.0524581 | ||||||||
\(461\) | 11430.2 | 1.15479 | 0.577394 | − | 0.816465i | \(-0.304070\pi\) | ||||
0.577394 | + | 0.816465i | \(0.304070\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9347.88 | −0.938300 | −0.469150 | − | 0.883119i | \(-0.655440\pi\) | ||||
−0.469150 | + | 0.883119i | \(0.655440\pi\) | |||||||
\(464\) | −9688.17 | −0.969314 | ||||||||
\(465\) | 4964.94 | 0.495147 | ||||||||
\(466\) | −5115.44 | −0.508515 | ||||||||
\(467\) | −3630.84 | −0.359776 | −0.179888 | − | 0.983687i | \(-0.557573\pi\) | ||||
−0.179888 | + | 0.983687i | \(0.557573\pi\) | |||||||
\(468\) | −6852.92 | −0.676872 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1979.41 | 0.194262 | ||||||||
\(471\) | −24388.9 | −2.38595 | ||||||||
\(472\) | −5297.20 | −0.516575 | ||||||||
\(473\) | −7239.26 | −0.703724 | ||||||||
\(474\) | 13696.0 | 1.32717 | ||||||||
\(475\) | −9381.43 | −0.906210 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4824.46 | −0.463096 | ||||||||
\(478\) | 11134.1 | 1.06540 | ||||||||
\(479\) | −6521.25 | −0.622053 | −0.311027 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311027 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(480\) | 2956.72 | 0.281157 | ||||||||
\(481\) | −3462.28 | −0.328205 | ||||||||
\(482\) | −1345.40 | −0.127140 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4863.65 | 0.456766 | ||||||||
\(485\) | −3463.75 | −0.324290 | ||||||||
\(486\) | −18709.2 | −1.74623 | ||||||||
\(487\) | −3666.29 | −0.341140 | −0.170570 | − | 0.985346i | \(-0.554561\pi\) | ||||
−0.170570 | + | 0.985346i | \(0.554561\pi\) | |||||||
\(488\) | −7331.65 | −0.680099 | ||||||||
\(489\) | −14148.6 | −1.30843 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12470.7 | −1.14623 | −0.573113 | − | 0.819476i | \(-0.694264\pi\) | ||||
−0.573113 | + | 0.819476i | \(0.694264\pi\) | |||||||
\(492\) | −8694.35 | −0.796691 | ||||||||
\(493\) | 3220.22 | 0.294181 | ||||||||
\(494\) | 12312.6 | 1.12140 | ||||||||
\(495\) | −3493.05 | −0.317174 | ||||||||
\(496\) | −24377.0 | −2.20678 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −675.078 | −0.0607449 | ||||||||
\(499\) | −2303.93 | −0.206690 | −0.103345 | − | 0.994646i | \(-0.532955\pi\) | ||||
−0.103345 | + | 0.994646i | \(0.532955\pi\) | |||||||
\(500\) | 2280.74 | 0.203995 | ||||||||
\(501\) | −24619.5 | −2.19544 | ||||||||
\(502\) | 13334.4 | 1.18554 | ||||||||
\(503\) | 10520.4 | 0.932570 | 0.466285 | − | 0.884635i | \(-0.345592\pi\) | ||||
0.466285 | + | 0.884635i | \(0.345592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 160.198 | 0.0141163 | ||||||||
\(506\) | −9683.10 | −0.850724 | ||||||||
\(507\) | 1446.71 | 0.126727 | ||||||||
\(508\) | −761.308 | −0.0664913 | ||||||||
\(509\) | 9662.22 | 0.841395 | 0.420698 | − | 0.907201i | \(-0.361785\pi\) | ||||
0.420698 | + | 0.907201i | \(0.361785\pi\) | |||||||
\(510\) | −1521.53 | −0.132107 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6558.89 | −0.566142 | ||||||||
\(513\) | −4369.98 | −0.376100 | ||||||||
\(514\) | 15037.0 | 1.29038 | ||||||||
\(515\) | −342.115 | −0.0292726 | ||||||||
\(516\) | 5144.85 | 0.438933 | ||||||||
\(517\) | 13273.1 | 1.12911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25690.9 | 2.17284 | ||||||||
\(520\) | 1161.84 | 0.0979806 | ||||||||
\(521\) | −8607.81 | −0.723829 | −0.361914 | − | 0.932211i | \(-0.617877\pi\) | ||||
−0.361914 | + | 0.932211i | \(0.617877\pi\) | |||||||
\(522\) | −14659.5 | −1.22917 | ||||||||
\(523\) | 10482.7 | 0.876439 | 0.438219 | − | 0.898868i | \(-0.355609\pi\) | ||||
0.438219 | + | 0.898868i | \(0.355609\pi\) | |||||||
\(524\) | −3360.30 | −0.280144 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14826.6 | −1.22903 | ||||||||
\(527\) | 8102.61 | 0.669744 | ||||||||
\(528\) | 30695.3 | 2.53000 | ||||||||
\(529\) | −9058.83 | −0.744541 | ||||||||
\(530\) | −1035.15 | −0.0848377 | ||||||||
\(531\) | −14523.7 | −1.18696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11156.6 | −0.906649 | ||||||||
\(534\) | 29617.9 | 2.40017 | ||||||||
\(535\) | −2124.29 | −0.171666 | ||||||||
\(536\) | −2239.84 | −0.180497 | ||||||||
\(537\) | −21893.0 | −1.75931 | ||||||||
\(538\) | 13208.5 | 1.05847 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 521.866 | 0.0415881 | ||||||||
\(541\) | 20722.6 | 1.64683 | 0.823416 | − | 0.567438i | \(-0.192066\pi\) | ||||
0.823416 | + | 0.567438i | \(0.192066\pi\) | |||||||
\(542\) | 15382.6 | 1.21908 | ||||||||
\(543\) | 29122.3 | 2.30158 | ||||||||
\(544\) | 4825.27 | 0.380298 | ||||||||
\(545\) | −2830.35 | −0.222457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4175.09 | −0.326351 | −0.163176 | − | 0.986597i | \(-0.552174\pi\) | ||||
−0.163176 | + | 0.986597i | \(0.552174\pi\) | |||||||
\(548\) | 2317.66 | 0.180667 | ||||||||
\(549\) | −20101.7 | −1.56270 | ||||||||
\(550\) | 20961.1 | 1.62506 | ||||||||
\(551\) | 9439.81 | 0.729854 | ||||||||
\(552\) | −5437.61 | −0.419276 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4746.91 | 0.364038 | ||||||||
\(555\) | 1254.21 | 0.0959248 | ||||||||
\(556\) | −13298.1 | −1.01433 | ||||||||
\(557\) | −10161.7 | −0.773011 | −0.386505 | − | 0.922287i | \(-0.626318\pi\) | ||||
−0.386505 | + | 0.922287i | \(0.626318\pi\) | |||||||
\(558\) | −36885.7 | −2.79838 | ||||||||
\(559\) | 6601.85 | 0.499514 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10202.7 | −0.767841 | ||||||||
\(562\) | −14850.3 | −1.11463 | ||||||||
\(563\) | 17104.4 | 1.28040 | 0.640201 | − | 0.768208i | \(-0.278851\pi\) | ||||
0.640201 | + | 0.768208i | \(0.278851\pi\) | |||||||
\(564\) | −9433.01 | −0.704257 | ||||||||
\(565\) | 3195.73 | 0.237957 | ||||||||
\(566\) | 16780.0 | 1.24614 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8414.89 | 0.621621 | ||||||||
\(569\) | −18257.6 | −1.34516 | −0.672581 | − | 0.740023i | \(-0.734815\pi\) | ||||
−0.672581 | + | 0.740023i | \(0.734815\pi\) | |||||||
\(570\) | −4460.23 | −0.327752 | ||||||||
\(571\) | 13630.5 | 0.998982 | 0.499491 | − | 0.866319i | \(-0.333520\pi\) | ||||
0.499491 | + | 0.866319i | \(0.333520\pi\) | |||||||
\(572\) | −9859.74 | −0.720728 | ||||||||
\(573\) | −7506.57 | −0.547280 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6728.30 | −0.487981 | ||||||||
\(576\) | −146.789 | −0.0106184 | ||||||||
\(577\) | −4442.08 | −0.320496 | −0.160248 | − | 0.987077i | \(-0.551229\pi\) | ||||
−0.160248 | + | 0.987077i | \(0.551229\pi\) | |||||||
\(578\) | 14865.4 | 1.06975 | ||||||||
\(579\) | 29648.0 | 2.12803 | ||||||||
\(580\) | −1127.31 | −0.0807052 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 46056.4 | 3.28024 | ||||||||
\(583\) | −6941.27 | −0.493101 | ||||||||
\(584\) | 2961.22 | 0.209822 | ||||||||
\(585\) | 3185.49 | 0.225135 | ||||||||
\(586\) | −17518.5 | −1.23495 | ||||||||
\(587\) | −3103.38 | −0.218211 | −0.109106 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109106 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23752.1 | 1.66161 | ||||||||
\(590\) | −3116.24 | −0.217447 | ||||||||
\(591\) | −40033.9 | −2.78642 | ||||||||
\(592\) | −6157.97 | −0.427519 | ||||||||
\(593\) | −5937.71 | −0.411185 | −0.205592 | − | 0.978638i | \(-0.565912\pi\) | ||||
−0.205592 | + | 0.978638i | \(0.565912\pi\) | |||||||
\(594\) | 9763.93 | 0.674443 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12146.1 | −0.834772 | ||||||||
\(597\) | −6765.07 | −0.463778 | ||||||||
\(598\) | 8830.50 | 0.603856 | ||||||||
\(599\) | −2600.33 | −0.177373 | −0.0886866 | − | 0.996060i | \(-0.528267\pi\) | ||||
−0.0886866 | + | 0.996060i | \(0.528267\pi\) | |||||||
\(600\) | 11770.9 | 0.800906 | ||||||||
\(601\) | 13881.4 | 0.942156 | 0.471078 | − | 0.882092i | \(-0.343865\pi\) | ||||
0.471078 | + | 0.882092i | \(0.343865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6141.11 | −0.414735 | ||||||||
\(604\) | 3162.40 | 0.213040 | ||||||||
\(605\) | −2260.80 | −0.151925 | ||||||||
\(606\) | −2130.11 | −0.142788 | ||||||||
\(607\) | 12284.6 | 0.821442 | 0.410721 | − | 0.911761i | \(-0.365277\pi\) | ||||
0.410721 | + | 0.911761i | \(0.365277\pi\) | |||||||
\(608\) | 14144.9 | 0.943505 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4313.07 | −0.286281 | ||||||||
\(611\) | −12104.4 | −0.801459 | ||||||||
\(612\) | 4051.30 | 0.267589 | ||||||||
\(613\) | 22062.0 | 1.45363 | 0.726815 | − | 0.686833i | \(-0.241000\pi\) | ||||
0.726815 | + | 0.686833i | \(0.241000\pi\) | |||||||
\(614\) | −14950.8 | −0.982679 | ||||||||
\(615\) | 4041.46 | 0.264988 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12182.2 | −0.794871 | −0.397436 | − | 0.917630i | \(-0.630100\pi\) | ||||
−0.397436 | + | 0.917630i | \(0.630100\pi\) | |||||||
\(618\) | 4549.00 | 0.296097 | ||||||||
\(619\) | −23248.6 | −1.50960 | −0.754799 | − | 0.655956i | \(-0.772266\pi\) | ||||
−0.754799 | + | 0.655956i | \(0.772266\pi\) | |||||||
\(620\) | −2836.50 | −0.183736 | ||||||||
\(621\) | −3134.12 | −0.202525 | ||||||||
\(622\) | −2417.76 | −0.155858 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −27992.6 | −1.79583 | ||||||||
\(625\) | 14025.4 | 0.897628 | ||||||||
\(626\) | −20989.3 | −1.34010 | ||||||||
\(627\) | −29908.4 | −1.90499 | ||||||||
\(628\) | 13933.6 | 0.885365 | ||||||||
\(629\) | 2046.83 | 0.129749 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19184.4 | 1.21033 | 0.605165 | − | 0.796100i | \(-0.293107\pi\) | ||||
0.605165 | + | 0.796100i | \(0.293107\pi\) | |||||||
\(632\) | 6182.72 | 0.389138 | ||||||||
\(633\) | 10517.8 | 0.660421 | ||||||||
\(634\) | 9971.52 | 0.624637 | ||||||||
\(635\) | 353.884 | 0.0221157 | ||||||||
\(636\) | 4933.07 | 0.307561 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21091.6 | −1.30881 | ||||||||
\(639\) | 23071.7 | 1.42833 | ||||||||
\(640\) | 2992.44 | 0.184823 | ||||||||
\(641\) | −19433.4 | −1.19746 | −0.598730 | − | 0.800951i | \(-0.704328\pi\) | ||||
−0.598730 | + | 0.800951i | \(0.704328\pi\) | |||||||
\(642\) | 28246.0 | 1.73642 | ||||||||
\(643\) | −5777.47 | −0.354341 | −0.177170 | − | 0.984180i | \(-0.556694\pi\) | ||||
−0.177170 | + | 0.984180i | \(0.556694\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2391.52 | −0.145994 | ||||||||
\(646\) | −7278.95 | −0.443323 | ||||||||
\(647\) | 29231.5 | 1.77621 | 0.888106 | − | 0.459640i | \(-0.152021\pi\) | ||||
0.888106 | + | 0.459640i | \(0.152021\pi\) | |||||||
\(648\) | −6026.30 | −0.365332 | ||||||||
\(649\) | −20896.2 | −1.26386 | ||||||||
\(650\) | −19115.5 | −1.15349 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8083.18 | 0.485524 | ||||||||
\(653\) | −7093.27 | −0.425086 | −0.212543 | − | 0.977152i | \(-0.568174\pi\) | ||||
−0.212543 | + | 0.977152i | \(0.568174\pi\) | |||||||
\(654\) | 37634.4 | 2.25018 | ||||||||
\(655\) | 1561.99 | 0.0931788 | ||||||||
\(656\) | −19842.9 | −1.18100 | ||||||||
\(657\) | 8118.98 | 0.482118 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19014.2 | 1.12396 | 0.561980 | − | 0.827151i | \(-0.310040\pi\) | ||||
0.561980 | + | 0.827151i | \(0.310040\pi\) | |||||||
\(660\) | 3571.69 | 0.210648 | ||||||||
\(661\) | 21058.4 | 1.23915 | 0.619573 | − | 0.784939i | \(-0.287306\pi\) | ||||
0.619573 | + | 0.784939i | \(0.287306\pi\) | |||||||
\(662\) | 9932.96 | 0.583165 | ||||||||
\(663\) | 9304.37 | 0.545025 | ||||||||
\(664\) | −304.746 | −0.0178109 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9317.83 | −0.542130 | ||||||||
\(667\) | 6770.16 | 0.393016 | ||||||||
\(668\) | 14065.3 | 0.814672 | ||||||||
\(669\) | 6765.54 | 0.390988 | ||||||||
\(670\) | −1317.65 | −0.0759782 | ||||||||
\(671\) | −28921.6 | −1.66395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9634.87 | 0.551853 | 0.275926 | − | 0.961179i | \(-0.411015\pi\) | ||||
0.275926 | + | 0.961179i | \(0.411015\pi\) | |||||||
\(674\) | −15043.0 | −0.859693 | ||||||||
\(675\) | 6784.46 | 0.386865 | ||||||||
\(676\) | −826.515 | −0.0470252 | ||||||||
\(677\) | −8371.31 | −0.475237 | −0.237619 | − | 0.971359i | \(-0.576367\pi\) | ||||
−0.237619 | + | 0.971359i | \(0.576367\pi\) | |||||||
\(678\) | −42492.7 | −2.40696 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −686.854 | −0.0387348 | ||||||||
\(681\) | −13417.8 | −0.755022 | ||||||||
\(682\) | −53069.9 | −2.97969 | ||||||||
\(683\) | −12068.8 | −0.676137 | −0.338069 | − | 0.941121i | \(-0.609774\pi\) | ||||
−0.338069 | + | 0.941121i | \(0.609774\pi\) | |||||||
\(684\) | 11876.1 | 0.663878 | ||||||||
\(685\) | −1077.33 | −0.0600917 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8177.78 | −0.454151 | ||||||||
\(688\) | 11742.0 | 0.650666 | ||||||||
\(689\) | 6330.09 | 0.350011 | ||||||||
\(690\) | −3198.85 | −0.176490 | ||||||||
\(691\) | −2981.29 | −0.164130 | −0.0820648 | − | 0.996627i | \(-0.526151\pi\) | ||||
−0.0820648 | + | 0.996627i | \(0.526151\pi\) | |||||||
\(692\) | −14677.4 | −0.806286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −127.327 | −0.00696435 | ||||||||
\(695\) | 6181.46 | 0.337376 | ||||||||
\(696\) | −11844.1 | −0.645043 | ||||||||
\(697\) | 6595.53 | 0.358427 | ||||||||
\(698\) | −856.978 | −0.0464715 | ||||||||
\(699\) | −11331.8 | −0.613172 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28978.0 | −1.56132 | −0.780660 | − | 0.624956i | \(-0.785117\pi\) | ||||
−0.780660 | + | 0.624956i | \(0.785117\pi\) | |||||||
\(702\) | −8904.22 | −0.478729 | ||||||||
\(703\) | 6000.11 | 0.321904 | ||||||||
\(704\) | −211.195 | −0.0113064 | ||||||||
\(705\) | 4384.81 | 0.234243 | ||||||||
\(706\) | −388.388 | −0.0207042 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 14850.7 | 0.788307 | ||||||||
\(709\) | −16372.4 | −0.867249 | −0.433625 | − | 0.901094i | \(-0.642766\pi\) | ||||
−0.433625 | + | 0.901094i | \(0.642766\pi\) | |||||||
\(710\) | 4950.32 | 0.261665 | ||||||||
\(711\) | 16951.6 | 0.894141 | ||||||||
\(712\) | 13370.2 | 0.703750 | ||||||||
\(713\) | 17034.9 | 0.894755 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4583.18 | 0.239722 | ||||||||
\(716\) | 12507.6 | 0.652836 | ||||||||
\(717\) | 24664.3 | 1.28467 | ||||||||
\(718\) | −43801.7 | −2.27669 | ||||||||
\(719\) | −23010.5 | −1.19353 | −0.596765 | − | 0.802416i | \(-0.703547\pi\) | ||||
−0.596765 | + | 0.802416i | \(0.703547\pi\) | |||||||
\(720\) | 5665.68 | 0.293260 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2882.36 | 0.148574 | ||||||||
\(723\) | −2980.35 | −0.153306 | ||||||||
\(724\) | −16637.8 | −0.854058 | ||||||||
\(725\) | −14655.5 | −0.750745 | ||||||||
\(726\) | 30061.2 | 1.53674 | ||||||||
\(727\) | 24636.8 | 1.25685 | 0.628423 | − | 0.777872i | \(-0.283701\pi\) | ||||
0.628423 | + | 0.777872i | \(0.283701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28395.6 | −1.44264 | ||||||||
\(730\) | 1742.03 | 0.0883225 | ||||||||
\(731\) | −3902.87 | −0.197473 | ||||||||
\(732\) | 20554.2 | 1.03785 | ||||||||
\(733\) | −6904.76 | −0.347931 | −0.173965 | − | 0.984752i | \(-0.555658\pi\) | ||||
−0.173965 | + | 0.984752i | \(0.555658\pi\) | |||||||
\(734\) | 48940.1 | 2.46105 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10144.6 | 0.508065 | ||||||||
\(737\) | −8835.63 | −0.441607 | ||||||||
\(738\) | −30025.0 | −1.49761 | ||||||||
\(739\) | −9234.89 | −0.459690 | −0.229845 | − | 0.973227i | \(-0.573822\pi\) | ||||
−0.229845 | + | 0.973227i | \(0.573822\pi\) | |||||||
\(740\) | −716.538 | −0.0355952 | ||||||||
\(741\) | 27275.0 | 1.35219 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20216.9 | 0.998232 | 0.499116 | − | 0.866535i | \(-0.333658\pi\) | ||||
0.499116 | + | 0.866535i | \(0.333658\pi\) | |||||||
\(744\) | −29801.8 | −1.46853 | ||||||||
\(745\) | 5645.97 | 0.277654 | ||||||||
\(746\) | −17295.7 | −0.848847 | ||||||||
\(747\) | −835.544 | −0.0409250 | ||||||||
\(748\) | 5828.88 | 0.284926 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14096.8 | 0.686321 | ||||||||
\(751\) | 24054.9 | 1.16881 | 0.584405 | − | 0.811462i | \(-0.301328\pi\) | ||||
0.584405 | + | 0.811462i | \(0.301328\pi\) | |||||||
\(752\) | −21528.7 | −1.04398 | ||||||||
\(753\) | 29538.4 | 1.42954 | ||||||||
\(754\) | 19234.5 | 0.929015 | ||||||||
\(755\) | −1470.00 | −0.0708593 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30328.2 | −1.45614 | −0.728069 | − | 0.685504i | \(-0.759582\pi\) | ||||
−0.728069 | + | 0.685504i | \(0.759582\pi\) | |||||||
\(758\) | 34627.1 | 1.65925 | ||||||||
\(759\) | −21450.1 | −1.02581 | ||||||||
\(760\) | −2013.46 | −0.0960997 | ||||||||
\(761\) | 33834.1 | 1.61168 | 0.805839 | − | 0.592135i | \(-0.201715\pi\) | ||||
0.805839 | + | 0.592135i | \(0.201715\pi\) | |||||||
\(762\) | −4705.49 | −0.223703 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4288.55 | 0.203082 | ||||||||
\(765\) | −1883.20 | −0.0890027 | ||||||||
\(766\) | 37887.9 | 1.78713 | ||||||||
\(767\) | 19056.3 | 0.897109 | ||||||||
\(768\) | −40058.2 | −1.88213 | ||||||||
\(769\) | −31738.1 | −1.48830 | −0.744151 | − | 0.668011i | \(-0.767146\pi\) | ||||
−0.744151 | + | 0.668011i | \(0.767146\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33310.2 | 1.55595 | ||||||||
\(772\) | −16938.1 | −0.789658 | ||||||||
\(773\) | −27494.2 | −1.27930 | −0.639650 | − | 0.768667i | \(-0.720920\pi\) | ||||
−0.639650 | + | 0.768667i | \(0.720920\pi\) | |||||||
\(774\) | 17767.1 | 0.825099 | ||||||||
\(775\) | −36875.6 | −1.70917 | ||||||||
\(776\) | 20791.0 | 0.961794 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18588.0 | −0.856573 | ||||||||
\(779\) | 19334.2 | 0.889244 | ||||||||
\(780\) | −3257.20 | −0.149521 | ||||||||
\(781\) | 33194.8 | 1.52087 | ||||||||
\(782\) | −5220.41 | −0.238723 | ||||||||
\(783\) | −6826.68 | −0.311578 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6476.84 | −0.294482 | ||||||||
\(786\) | −20769.3 | −0.942517 | ||||||||
\(787\) | 468.356 | 0.0212136 | 0.0106068 | − | 0.999944i | \(-0.496624\pi\) | ||||
0.0106068 | + | 0.999944i | \(0.496624\pi\) | |||||||
\(788\) | 22871.6 | 1.03397 | ||||||||
\(789\) | −32844.0 | −1.48198 | ||||||||
\(790\) | 3637.18 | 0.163804 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 20966.9 | 0.940688 | ||||||||
\(793\) | 26375.1 | 1.18109 | ||||||||
\(794\) | 4289.97 | 0.191745 | ||||||||
\(795\) | −2293.07 | −0.102298 | ||||||||
\(796\) | 3864.93 | 0.172096 | ||||||||
\(797\) | −37723.8 | −1.67659 | −0.838297 | − | 0.545214i | \(-0.816449\pi\) | ||||
−0.838297 | + | 0.545214i | \(0.816449\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7155.87 | 0.316841 | ||||||||
\(800\) | −21960.2 | −0.970512 | ||||||||
\(801\) | 36658.1 | 1.61704 | ||||||||
\(802\) | −8105.53 | −0.356878 | ||||||||
\(803\) | 11681.3 | 0.513356 | ||||||||
\(804\) | 6279.36 | 0.275443 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 48397.1 | 2.11503 | ||||||||
\(807\) | 29259.6 | 1.27632 | ||||||||
\(808\) | −961.583 | −0.0418668 | ||||||||
\(809\) | −7797.13 | −0.338854 | −0.169427 | − | 0.985543i | \(-0.554192\pi\) | ||||
−0.169427 | + | 0.985543i | \(0.554192\pi\) | |||||||
\(810\) | −3545.16 | −0.153783 | ||||||||
\(811\) | −16925.9 | −0.732860 | −0.366430 | − | 0.930446i | \(-0.619420\pi\) | ||||
−0.366430 | + | 0.930446i | \(0.619420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34075.8 | 1.46998 | ||||||||
\(814\) | −13406.2 | −0.577256 | ||||||||
\(815\) | −3757.36 | −0.161490 | ||||||||
\(816\) | 16548.6 | 0.709949 | ||||||||
\(817\) | −11441.0 | −0.489925 | ||||||||
\(818\) | 16407.5 | 0.701316 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2308.91 | −0.0983301 | ||||||||
\(821\) | −30009.3 | −1.27568 | −0.637840 | − | 0.770169i | \(-0.720172\pi\) | ||||
−0.637840 | + | 0.770169i | \(0.720172\pi\) | |||||||
\(822\) | 14325.0 | 0.607835 | ||||||||
\(823\) | −23385.6 | −0.990486 | −0.495243 | − | 0.868754i | \(-0.664921\pi\) | ||||
−0.495243 | + | 0.868754i | \(0.664921\pi\) | |||||||
\(824\) | 2053.53 | 0.0868181 | ||||||||
\(825\) | 46433.3 | 1.95952 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37325.9 | −1.56947 | −0.784734 | − | 0.619833i | \(-0.787200\pi\) | ||||
−0.784734 | + | 0.619833i | \(0.787200\pi\) | |||||||
\(828\) | 8517.43 | 0.357489 | ||||||||
\(829\) | 24671.3 | 1.03362 | 0.516809 | − | 0.856100i | \(-0.327120\pi\) | ||||
0.516809 | + | 0.856100i | \(0.327120\pi\) | |||||||
\(830\) | −179.277 | −0.00749733 | ||||||||
\(831\) | 10515.4 | 0.438960 | ||||||||
\(832\) | 192.599 | 0.00802544 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −82193.0 | −3.41260 | ||||||||
\(835\) | −6538.05 | −0.270969 | ||||||||
\(836\) | 17086.9 | 0.706892 | ||||||||
\(837\) | −17177.1 | −0.709350 | ||||||||
\(838\) | 26629.1 | 1.09772 | ||||||||
\(839\) | −14147.4 | −0.582147 | −0.291074 | − | 0.956701i | \(-0.594013\pi\) | ||||
−0.291074 | + | 0.956701i | \(0.594013\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9642.35 | −0.395356 | ||||||||
\(842\) | 22047.1 | 0.902366 | ||||||||
\(843\) | −32896.6 | −1.34403 | ||||||||
\(844\) | −6008.91 | −0.245065 | ||||||||
\(845\) | 384.195 | 0.0156411 | ||||||||
\(846\) | −32575.8 | −1.32385 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11258.6 | 0.455923 | ||||||||
\(849\) | 37171.3 | 1.50261 | ||||||||
\(850\) | 11300.7 | 0.456012 | ||||||||
\(851\) | 4303.24 | 0.173341 | ||||||||
\(852\) | −23591.1 | −0.948611 | ||||||||
\(853\) | −27963.6 | −1.12246 | −0.561229 | − | 0.827661i | \(-0.689671\pi\) | ||||
−0.561229 | + | 0.827661i | \(0.689671\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5520.44 | −0.220813 | ||||||||
\(856\) | 12750.9 | 0.509134 | ||||||||
\(857\) | −33855.8 | −1.34947 | −0.674734 | − | 0.738061i | \(-0.735741\pi\) | ||||
−0.674734 | + | 0.738061i | \(0.735741\pi\) | |||||||
\(858\) | −60941.1 | −2.42482 | ||||||||
\(859\) | 24282.7 | 0.964511 | 0.482255 | − | 0.876031i | \(-0.339818\pi\) | ||||
0.482255 | + | 0.876031i | \(0.339818\pi\) | |||||||
\(860\) | 1366.29 | 0.0541745 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −40487.2 | −1.59977 | ||||||||
\(863\) | −19667.0 | −0.775750 | −0.387875 | − | 0.921712i | \(-0.626791\pi\) | ||||
−0.387875 | + | 0.921712i | \(0.626791\pi\) | |||||||
\(864\) | −10229.3 | −0.402787 | ||||||||
\(865\) | 6822.59 | 0.268179 | ||||||||
\(866\) | 18207.9 | 0.714469 | ||||||||
\(867\) | 32929.9 | 1.28992 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24389.4 | 0.952075 | ||||||||
\(870\) | −6967.67 | −0.271524 | ||||||||
\(871\) | 8057.65 | 0.313459 | ||||||||
\(872\) | 16989.1 | 0.659773 | ||||||||
\(873\) | 57004.0 | 2.20996 | ||||||||
\(874\) | −15303.2 | −0.592264 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8301.75 | −0.320194 | ||||||||
\(877\) | −36061.0 | −1.38848 | −0.694238 | − | 0.719745i | \(-0.744259\pi\) | ||||
−0.694238 | + | 0.719745i | \(0.744259\pi\) | |||||||
\(878\) | −17882.5 | −0.687364 | ||||||||
\(879\) | −38807.2 | −1.48912 | ||||||||
\(880\) | 8151.58 | 0.312261 | ||||||||
\(881\) | 15889.7 | 0.607646 | 0.303823 | − | 0.952728i | \(-0.401737\pi\) | ||||
0.303823 | + | 0.952728i | \(0.401737\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14861.3 | 0.566390 | 0.283195 | − | 0.959062i | \(-0.408606\pi\) | ||||
0.283195 | + | 0.959062i | \(0.408606\pi\) | |||||||
\(884\) | −5315.65 | −0.202245 | ||||||||
\(885\) | −6903.13 | −0.262199 | ||||||||
\(886\) | −44858.2 | −1.70095 | ||||||||
\(887\) | 38189.9 | 1.44565 | 0.722824 | − | 0.691032i | \(-0.242844\pi\) | ||||
0.722824 | + | 0.691032i | \(0.242844\pi\) | |||||||
\(888\) | −7528.33 | −0.284498 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7865.45 | 0.296237 | ||||||||
\(891\) | −23772.3 | −0.893831 | ||||||||
\(892\) | −3865.20 | −0.145086 | ||||||||
\(893\) | 20976.8 | 0.786073 | ||||||||
\(894\) | −75072.7 | −2.80851 | ||||||||
\(895\) | −5813.99 | −0.217140 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19561.4 | 0.728135 | ||||||||
\(898\) | −49231.7 | −1.82949 | ||||||||
\(899\) | 37105.0 | 1.37655 | ||||||||
\(900\) | −18437.8 | −0.682881 | ||||||||
\(901\) | −3742.22 | −0.138370 | ||||||||
\(902\) | −43198.9 | −1.59464 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19182.2 | −0.705742 | ||||||||
\(905\) | 7733.86 | 0.284069 | ||||||||
\(906\) | 19546.1 | 0.716751 | ||||||||
\(907\) | 16865.5 | 0.617431 | 0.308715 | − | 0.951154i | \(-0.400101\pi\) | ||||
0.308715 | + | 0.951154i | \(0.400101\pi\) | |||||||
\(908\) | 7665.65 | 0.280169 | ||||||||
\(909\) | −2636.44 | −0.0961993 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26754.1 | 0.973000 | 0.486500 | − | 0.873681i | \(-0.338273\pi\) | ||||
0.486500 | + | 0.873681i | \(0.338273\pi\) | |||||||
\(912\) | 48511.0 | 1.76136 | ||||||||
\(913\) | −1202.15 | −0.0435766 | ||||||||
\(914\) | 53722.7 | 1.94419 | ||||||||
\(915\) | −9554.37 | −0.345200 | ||||||||
\(916\) | 4672.02 | 0.168524 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5263.99 | 0.189257 | ||||||||
\(919\) | −41527.5 | −1.49061 | −0.745303 | − | 0.666726i | \(-0.767695\pi\) | ||||
−0.745303 | + | 0.666726i | \(0.767695\pi\) | |||||||
\(920\) | −1444.04 | −0.0517484 | ||||||||
\(921\) | −33119.2 | −1.18492 | ||||||||
\(922\) | −40361.5 | −1.44169 | ||||||||
\(923\) | −30272.0 | −1.07954 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9315.27 | −0.331118 | ||||||||
\(926\) | 33008.6 | 1.17141 | ||||||||
\(927\) | 5630.31 | 0.199486 | ||||||||
\(928\) | 22096.8 | 0.781642 | ||||||||
\(929\) | −4584.68 | −0.161914 | −0.0809572 | − | 0.996718i | \(-0.525798\pi\) | ||||
−0.0809572 | + | 0.996718i | \(0.525798\pi\) | |||||||
\(930\) | −17531.8 | −0.618163 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6473.92 | 0.227532 | ||||||||
\(933\) | −5355.86 | −0.187935 | ||||||||
\(934\) | 12821.0 | 0.449159 | ||||||||
\(935\) | −2709.48 | −0.0947694 | ||||||||
\(936\) | −19120.7 | −0.667715 | ||||||||
\(937\) | 6928.18 | 0.241552 | 0.120776 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120776 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46495.7 | −1.61590 | ||||||||
\(940\) | −2505.07 | −0.0869217 | ||||||||
\(941\) | −20944.9 | −0.725596 | −0.362798 | − | 0.931868i | \(-0.618178\pi\) | ||||
−0.362798 | + | 0.931868i | \(0.618178\pi\) | |||||||
\(942\) | 86120.5 | 2.97872 | ||||||||
\(943\) | 13866.4 | 0.478846 | ||||||||
\(944\) | 33893.3 | 1.16857 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25562.8 | 0.878559 | ||||||||
\(947\) | 29278.9 | 1.00468 | 0.502342 | − | 0.864669i | \(-0.332472\pi\) | ||||
0.502342 | + | 0.864669i | \(0.332472\pi\) | |||||||
\(948\) | −17333.2 | −0.593836 | ||||||||
\(949\) | −10652.8 | −0.364387 | ||||||||
\(950\) | 33127.1 | 1.13135 | ||||||||
\(951\) | 22089.0 | 0.753192 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2136.81 | 0.0726316 | 0.0363158 | − | 0.999340i | \(-0.488438\pi\) | ||||
0.0363158 | + | 0.999340i | \(0.488438\pi\) | |||||||
\(954\) | 17035.8 | 0.578149 | ||||||||
\(955\) | −1993.48 | −0.0675470 | ||||||||
\(956\) | −14090.9 | −0.476707 | ||||||||
\(957\) | −46722.3 | −1.57818 | ||||||||
\(958\) | 23027.4 | 0.776597 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −69.7689 | −0.00234561 | ||||||||
\(961\) | 63571.4 | 2.13391 | ||||||||
\(962\) | 12225.8 | 0.409745 | ||||||||
\(963\) | 34960.2 | 1.16986 | ||||||||
\(964\) | 1702.70 | 0.0568881 | ||||||||
\(965\) | 7873.47 | 0.262649 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3921.32 | −0.130405 | −0.0652023 | − | 0.997872i | \(-0.520769\pi\) | ||||
−0.0652023 | + | 0.997872i | \(0.520769\pi\) | |||||||
\(968\) | 13570.4 | 0.450586 | ||||||||
\(969\) | −16124.4 | −0.534562 | ||||||||
\(970\) | 12230.9 | 0.404857 | ||||||||
\(971\) | −47809.1 | −1.58009 | −0.790045 | − | 0.613049i | \(-0.789943\pi\) | ||||
−0.790045 | + | 0.613049i | \(0.789943\pi\) | |||||||
\(972\) | 23677.7 | 0.781341 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12946.1 | 0.425894 | ||||||||
\(975\) | −42344.9 | −1.39089 | ||||||||
\(976\) | 46910.5 | 1.53849 | ||||||||
\(977\) | −51329.1 | −1.68082 | −0.840411 | − | 0.541949i | \(-0.817686\pi\) | ||||
−0.840411 | + | 0.541949i | \(0.817686\pi\) | |||||||
\(978\) | 49960.5 | 1.63350 | ||||||||
\(979\) | 52742.4 | 1.72181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46580.1 | 1.51599 | ||||||||
\(982\) | 44035.8 | 1.43100 | ||||||||
\(983\) | 16326.3 | 0.529734 | 0.264867 | − | 0.964285i | \(-0.414672\pi\) | ||||
0.264867 | + | 0.964285i | \(0.414672\pi\) | |||||||
\(984\) | −24258.7 | −0.785912 | ||||||||
\(985\) | −10631.6 | −0.343909 | ||||||||
\(986\) | −11371.0 | −0.367268 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15582.4 | −0.501763 | ||||||||
\(989\) | −8205.37 | −0.263818 | ||||||||
\(990\) | 12334.4 | 0.395973 | ||||||||
\(991\) | 33770.0 | 1.08248 | 0.541242 | − | 0.840867i | \(-0.317954\pi\) | ||||
0.541242 | + | 0.840867i | \(0.317954\pi\) | |||||||
\(992\) | 55599.3 | 1.77952 | ||||||||
\(993\) | 22003.6 | 0.703185 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1796.56 | −0.0572410 | ||||||||
\(996\) | 854.354 | 0.0271800 | ||||||||
\(997\) | −50695.4 | −1.61037 | −0.805185 | − | 0.593023i | \(-0.797934\pi\) | ||||
−0.805185 | + | 0.593023i | \(0.797934\pi\) | |||||||
\(998\) | 8135.48 | 0.258040 | ||||||||
\(999\) | −4339.16 | −0.137422 |
(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 | 49.4.a.e.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 441.4.a.u.1.4 | 4 | |||
4.3 | odd | 2 | 784.4.a.bf.1.4 | 4 | |||
5.4 | even | 2 | 1225.4.a.bb.1.4 | 4 | |||
7.2 | even | 3 | 49.4.c.e.18.4 | 8 | |||
7.3 | odd | 6 | 49.4.c.e.30.3 | 8 | |||
7.4 | even | 3 | 49.4.c.e.30.4 | 8 | |||
7.5 | odd | 6 | 49.4.c.e.18.3 | 8 | |||
7.6 | odd | 2 | inner | 49.4.a.e.1.2 | yes | 4 | |
21.2 | odd | 6 | 441.4.e.y.361.1 | 8 | |||
21.5 | even | 6 | 441.4.e.y.361.2 | 8 | |||
21.11 | odd | 6 | 441.4.e.y.226.1 | 8 | |||
21.17 | even | 6 | 441.4.e.y.226.2 | 8 | |||
21.20 | even | 2 | 441.4.a.u.1.3 | 4 | |||
28.27 | even | 2 | 784.4.a.bf.1.1 | 4 | |||
35.34 | odd | 2 | 1225.4.a.bb.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.a.e.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
49.4.a.e.1.2 | yes | 4 | 7.6 | odd | 2 | inner | |
49.4.c.e.18.3 | 8 | 7.5 | odd | 6 | |||
49.4.c.e.18.4 | 8 | 7.2 | even | 3 | |||
49.4.c.e.30.3 | 8 | 7.3 | odd | 6 | |||
49.4.c.e.30.4 | 8 | 7.4 | even | 3 | |||
441.4.a.u.1.3 | 4 | 21.20 | even | 2 | |||
441.4.a.u.1.4 | 4 | 3.2 | odd | 2 | |||
441.4.e.y.226.1 | 8 | 21.11 | odd | 6 | |||
441.4.e.y.226.2 | 8 | 21.17 | even | 6 | |||
441.4.e.y.361.1 | 8 | 21.2 | odd | 6 | |||
441.4.e.y.361.2 | 8 | 21.5 | even | 6 | |||
784.4.a.bf.1.1 | 4 | 28.27 | even | 2 | |||
784.4.a.bf.1.4 | 4 | 4.3 | odd | 2 | |||
1225.4.a.bb.1.3 | 4 | 35.34 | odd | 2 | |||
1225.4.a.bb.1.4 | 4 | 5.4 | even | 2 |