Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{37}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.54138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.1655 | −0.909232 | −0.454616 | − | 0.890687i | \(-0.650224\pi\) | ||||
−0.454616 | + | 0.890687i | \(0.650224\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.1655 | 0.991301 | 0.495651 | − | 0.868522i | \(-0.334930\pi\) | ||||
0.495651 | + | 0.868522i | \(0.334930\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 74.6621 | 1.59289 | 0.796444 | − | 0.604712i | \(-0.206712\pi\) | ||||
0.796444 | + | 0.604712i | \(0.206712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 30.4966 | 0.524945 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −91.1587 | −1.30054 | −0.650271 | − | 0.759702i | \(-0.725345\pi\) | ||||
−0.650271 | + | 0.759702i | \(0.725345\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 104.331 | 1.25975 | 0.629873 | − | 0.776698i | \(-0.283107\pi\) | ||||
0.629873 | + | 0.776698i | \(0.283107\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 36.8276 | 0.333874 | 0.166937 | − | 0.985968i | \(-0.446612\pi\) | ||||
0.166937 | + | 0.985968i | \(0.446612\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.6621 | −0.173297 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 262.993 | 1.68402 | 0.842010 | − | 0.539461i | \(-0.181372\pi\) | ||||
0.842010 | + | 0.539461i | \(0.181372\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −310.979 | −1.80173 | −0.900864 | − | 0.434102i | \(-0.857066\pi\) | ||||
−0.900864 | + | 0.434102i | \(0.857066\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −108.497 | −0.572328 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −71.1587 | −0.343657 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −285.311 | −1.26770 | −0.633848 | − | 0.773458i | \(-0.718526\pi\) | ||||
−0.633848 | + | 0.773458i | \(0.718526\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −223.986 | −0.919654 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 62.4966 | 0.238057 | 0.119028 | − | 0.992891i | \(-0.462022\pi\) | ||||
0.119028 | + | 0.992891i | \(0.462022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −386.648 | −1.37124 | −0.685620 | − | 0.727960i | \(-0.740469\pi\) | ||||
−0.685620 | + | 0.727960i | \(0.740469\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −91.4897 | −0.303077 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 430.290 | 1.33541 | 0.667705 | − | 0.744426i | \(-0.267277\pi\) | ||||
0.667705 | + | 0.744426i | \(0.267277\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 273.476 | 0.750869 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −111.959 | −0.290165 | −0.145082 | − | 0.989420i | \(-0.546345\pi\) | ||||
−0.145082 | + | 0.989420i | \(0.546345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −367.642 | −0.901323 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −312.993 | −0.727315 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 479.642 | 1.05837 | 0.529187 | − | 0.848506i | \(-0.322497\pi\) | ||||
0.529187 | + | 0.848506i | \(0.322497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 602.993 | 1.26566 | 0.632831 | − | 0.774290i | \(-0.281893\pi\) | ||||
0.632831 | + | 0.774290i | \(0.281893\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −758.979 | −1.44830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1020.97 | −1.86165 | −0.930827 | − | 0.365460i | \(-0.880912\pi\) | ||||
−0.930827 | + | 0.365460i | \(0.880912\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −110.483 | −0.192762 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 284.442 | 0.475451 | 0.237726 | − | 0.971332i | \(-0.423598\pi\) | ||||
0.237726 | + | 0.971332i | \(0.423598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −566.331 | −0.908000 | −0.454000 | − | 0.891002i | \(-0.650003\pi\) | ||||
−0.454000 | + | 0.891002i | \(0.650003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 64.9863 | 0.100053 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 253.159 | 0.374677 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −94.2900 | −0.134284 | −0.0671421 | − | 0.997743i | \(-0.521388\pi\) | ||||
−0.0671421 | + | 0.997743i | \(0.521388\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −626.621 | −0.828682 | −0.414341 | − | 0.910122i | \(-0.635988\pi\) | ||||
−0.414341 | + | 0.910122i | \(0.635988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 926.676 | 1.18250 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −788.979 | −0.972270 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1532.40 | 1.82510 | 0.912551 | − | 0.408962i | \(-0.134109\pi\) | ||||
0.912551 | + | 0.408962i | \(0.134109\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 522.635 | 0.602055 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 932.938 | 1.04023 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1060.58 | −1.14540 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 718.304 | 0.751883 | 0.375942 | − | 0.926643i | \(-0.377319\pi\) | ||||
0.375942 | + | 0.926643i | \(0.377319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 325.490 | 0.330434 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1420.12 | 1.39909 | 0.699543 | − | 0.714591i | \(-0.253387\pi\) | ||||
0.699543 | + | 0.714591i | \(0.253387\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1106.24 | 1.05826 | 0.529129 | − | 0.848541i | \(-0.322519\pi\) | ||||
0.529129 | + | 0.848541i | \(0.322519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 213.476 | 0.198411 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −157.213 | −0.142041 | −0.0710206 | − | 0.997475i | \(-0.522626\pi\) | ||||
−0.0710206 | + | 0.997475i | \(0.522626\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2153.89 | 1.89271 | 0.946355 | − | 0.323130i | \(-0.104735\pi\) | ||||
0.946355 | + | 0.323130i | \(0.104735\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 855.932 | 0.731905 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1253.23 | −1.04331 | −0.521654 | − | 0.853157i | \(-0.674685\pi\) | ||||
−0.521654 | + | 0.853157i | \(0.674685\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −374.372 | −0.303569 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 671.959 | 0.530963 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −638.111 | −0.491559 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.0548 | −0.0173214 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −187.490 | −0.137442 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1490.90 | 1.06680 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1381.02 | 0.964927 | 0.482464 | − | 0.875916i | \(-0.339742\pi\) | ||||
0.482464 | + | 0.875916i | \(0.339742\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1159.95 | 0.791686 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −413.269 | −0.275630 | −0.137815 | − | 0.990458i | \(-0.544008\pi\) | ||||
−0.137815 | + | 0.990458i | \(0.544008\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 730.317 | 0.476139 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 274.469 | 0.174982 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 147.655 | 0.0920806 | 0.0460403 | − | 0.998940i | \(-0.485340\pi\) | ||||
0.0460403 | + | 0.998940i | \(0.485340\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1949.82 | −1.18980 | −0.594898 | − | 0.803801i | \(-0.702808\pi\) | ||||
−0.594898 | + | 0.803801i | \(0.702808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1290.87 | −0.770999 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2700.19 | 1.57903 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2673.46 | −1.53117 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1004.07 | 0.552057 | 0.276029 | − | 0.961149i | \(-0.410982\pi\) | ||||
0.276029 | + | 0.961149i | \(0.410982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1285.79 | −0.692957 | −0.346478 | − | 0.938058i | \(-0.612623\pi\) | ||||
−0.346478 | + | 0.938058i | \(0.612623\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −820.428 | −0.433514 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3161.27 | 1.63819 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 408.345 | 0.207576 | 0.103788 | − | 0.994599i | \(-0.466904\pi\) | ||||
0.103788 | + | 0.994599i | \(0.466904\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 335.877 | 0.167527 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 257.793 | 0.126192 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1816.83 | 0.873037 | 0.436518 | − | 0.899695i | \(-0.356211\pi\) | ||||
0.436518 | + | 0.899695i | \(0.356211\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1102.92 | 0.520379 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3522.15 | −1.63205 | −0.816025 | − | 0.578016i | \(-0.803827\pi\) | ||||
−0.816025 | + | 0.578016i | \(0.803827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3377.43 | 1.53729 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 938.979 | 0.419916 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2395.57 | 1.05279 | 0.526393 | − | 0.850241i | \(-0.323544\pi\) | ||||
0.526393 | + | 0.850241i | \(0.323544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −151.635 | −0.0655000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1438.92 | −0.611052 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1505.08 | 0.628462 | 0.314231 | − | 0.949347i | \(-0.398253\pi\) | ||||
0.314231 | + | 0.949347i | \(0.398253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3034.42 | −1.24611 | −0.623056 | − | 0.782177i | \(-0.714109\pi\) | ||||
−0.623056 | + | 0.782177i | \(0.714109\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1808.98 | −0.730730 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2900.33 | 1.15263 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3296.80 | −1.28923 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −641.462 | −0.243008 | −0.121504 | − | 0.992591i | \(-0.538772\pi\) | ||||
−0.121504 | + | 0.992591i | \(0.538772\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2892.62 | 1.07884 | 0.539418 | − | 0.842038i | \(-0.318644\pi\) | ||||
0.539418 | + | 0.842038i | \(0.318644\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2276.94 | 0.836179 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3337.86 | 1.20717 | 0.603586 | − | 0.797298i | \(-0.293738\pi\) | ||||
0.603586 | + | 0.797298i | \(0.293738\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1401.82 | 0.499359 | 0.249680 | − | 0.968328i | \(-0.419675\pi\) | ||||
0.249680 | + | 0.968328i | \(0.419675\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3062.90 | 1.07483 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1840.95 | 0.636500 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −635.311 | −0.216449 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 331.449 | 0.111291 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3773.19 | 1.24879 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4967.62 | −1.62078 | −0.810391 | − | 0.585890i | \(-0.800745\pi\) | ||||
−0.810391 | + | 0.585890i | \(0.800745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −853.325 | −0.274502 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3930.48 | 1.24678 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2176.86 | −0.680989 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1698.99 | 0.524234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6806.10 | −2.07162 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 242.758 | 0.0728981 | 0.0364491 | − | 0.999336i | \(-0.488395\pi\) | ||||
0.0364491 | + | 0.999336i | \(0.488395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −194.959 | −0.0577656 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5873.30 | 1.71729 | 0.858644 | − | 0.512572i | \(-0.171307\pi\) | ||||
0.858644 | + | 0.512572i | \(0.171307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3979.27 | 1.14829 | 0.574143 | − | 0.818755i | \(-0.305335\pi\) | ||||
0.574143 | + | 0.818755i | \(0.305335\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −759.476 | −0.216320 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 601.724 | 0.169186 | 0.0845928 | − | 0.996416i | \(-0.473041\pi\) | ||||
0.0845928 | + | 0.996416i | \(0.473041\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4374.12 | −1.21420 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 282.870 | 0.0775290 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5140.22 | −1.39119 | −0.695593 | − | 0.718436i | \(-0.744858\pi\) | ||||
−0.695593 | + | 0.718436i | \(0.744858\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2036.43 | 0.544306 | 0.272153 | − | 0.962254i | \(-0.412264\pi\) | ||||
0.272153 | + | 0.962254i | \(0.412264\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −498.111 | −0.129890 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7789.58 | 2.00663 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1879.86 | 0.478440 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6583.70 | 1.65561 | 0.827807 | − | 0.561013i | \(-0.189588\pi\) | ||||
0.827807 | + | 0.561013i | \(0.189588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1331.89 | 0.330969 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2780.03 | −0.682714 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1277.78 | 0.310139 | 0.155069 | − | 0.987904i | \(-0.450440\pi\) | ||||
0.155069 | + | 0.987904i | \(0.450440\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1997.17 | −0.479144 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2366.94 | 0.561340 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4266.18 | 1.00024 | 0.500121 | − | 0.865955i | \(-0.333289\pi\) | ||||
0.500121 | + | 0.865955i | \(0.333289\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1138.12 | 0.263827 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4597.20 | −1.05372 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 317.560 | 0.0719777 | 0.0359889 | − | 0.999352i | \(-0.488542\pi\) | ||||
0.0359889 | + | 0.999352i | \(0.488542\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 896.687 | 0.200996 | 0.100498 | − | 0.994937i | \(-0.467956\pi\) | ||||
0.100498 | + | 0.994937i | \(0.467956\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1567.90 | −0.347597 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −783.421 | −0.171789 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1919.24 | −0.416304 | −0.208152 | − | 0.978097i | \(-0.566745\pi\) | ||||
−0.208152 | + | 0.978097i | \(0.566745\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2798.82 | −0.600576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −744.541 | −0.158063 | −0.0790313 | − | 0.996872i | \(-0.525183\pi\) | ||||
−0.0790313 | + | 0.996872i | \(0.525183\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2447.23 | 0.514038 | 0.257019 | − | 0.966406i | \(-0.417260\pi\) | ||||
0.257019 | + | 0.966406i | \(0.417260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3181.74 | 0.661298 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 437.476 | 0.0899770 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3396.90 | 0.691411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2154.91 | −0.434100 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1825.72 | −0.364027 | −0.182014 | − | 0.983296i | \(-0.558261\pi\) | ||||
−0.182014 | + | 0.983296i | \(0.558261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4875.81 | −0.962307 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −976.469 | −0.190776 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2749.63 | 0.531823 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2706.54 | −0.518280 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4260.37 | −0.807763 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6129.74 | −1.15078 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −905.267 | −0.168294 | −0.0841471 | − | 0.996453i | \(-0.526817\pi\) | ||||
−0.0841471 | + | 0.996453i | \(0.526817\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3318.71 | −0.610986 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1943.29 | 0.354320 | 0.177160 | − | 0.984182i | \(-0.443309\pi\) | ||||
0.177160 | + | 0.984182i | \(0.443309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8197.97 | 1.48044 | 0.740219 | − | 0.672366i | \(-0.234722\pi\) | ||||
0.740219 | + | 0.672366i | \(0.234722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −640.428 | −0.114552 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3657.78 | −0.648080 | −0.324040 | − | 0.946043i | \(-0.605041\pi\) | ||||
−0.324040 | + | 0.946043i | \(0.605041\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9511.29 | 1.66937 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 471.640 | 0.0820075 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9510.68 | −1.63835 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1617.34 | −0.276042 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6461.67 | −1.09276 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3012.03 | 0.504737 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −123.087 | −0.0204395 | −0.0102197 | − | 0.999948i | \(-0.503253\pi\) | ||||
−0.0102197 | + | 0.999948i | \(0.503253\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2567.79 | −0.422565 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10378.7 | 1.69268 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6104.63 | 0.986766 | 0.493383 | − | 0.869812i | \(-0.335760\pi\) | ||||
0.493383 | + | 0.869812i | \(0.335760\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3759.68 | 0.602354 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11246.7 | −1.78606 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1123.12 | 0.175265 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3875.62 | −0.599579 | −0.299790 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299790 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2621.15 | 0.402025 | 0.201013 | − | 0.979589i | \(-0.435577\pi\) | ||||
0.201013 | + | 0.979589i | \(0.435577\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2015.88 | −0.306551 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −168.784 | −0.0254490 | −0.0127245 | − | 0.999919i | \(-0.504050\pi\) | ||||
−0.0127245 | + | 0.999919i | \(0.504050\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2891.50 | −0.432295 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1914.33 | 0.283802 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2644.83 | −0.388826 | −0.194413 | − | 0.980920i | \(-0.562280\pi\) | ||||
−0.194413 | + | 0.980920i | \(0.562280\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4025.97 | 0.586961 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 69.1644 | 0.0100005 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5757.05 | 0.825583 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4909.52 | −0.698296 | −0.349148 | − | 0.937068i | \(-0.613529\pi\) | ||||
−0.349148 | + | 0.937068i | \(0.613529\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 562.469 | 0.0793522 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −783.712 | −0.109672 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5574.80 | 0.773867 | 0.386933 | − | 0.922108i | \(-0.373534\pi\) | ||||
0.386933 | + | 0.922108i | \(0.373534\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4472.69 | −0.615917 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19635.6 | 2.68246 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8099.04 | 1.09768 | 0.548839 | − | 0.835928i | \(-0.315070\pi\) | ||||
0.548839 | + | 0.835928i | \(0.315070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4143.06 | −0.557101 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4779.21 | −0.637614 | −0.318807 | − | 0.947820i | \(-0.603282\pi\) | ||||
−0.318807 | + | 0.947820i | \(0.603282\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2573.49 | −0.340668 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3479.84 | −0.457080 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11688.8 | 1.52351 | 0.761757 | − | 0.647863i | \(-0.224337\pi\) | ||||
0.761757 | + | 0.647863i | \(0.224337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3357.16 | −0.434217 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1239.81 | 0.159135 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 958.507 | 0.122095 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2563.24 | −0.324044 | −0.162022 | − | 0.986787i | \(-0.551802\pi\) | ||||
−0.162022 | + | 0.986787i | \(0.551802\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2190.95 | −0.274899 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4139.96 | −0.515560 | −0.257780 | − | 0.966204i | \(-0.582991\pi\) | ||||
−0.257780 | + | 0.966204i | \(0.582991\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23218.4 | −2.86995 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −823.408 | −0.101026 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10318.4 | −1.25667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2015.71 | −0.243693 | −0.121847 | − | 0.992549i | \(-0.538882\pi\) | ||||
−0.121847 | + | 0.992549i | \(0.538882\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −442.966 | −0.0531627 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3357.49 | 0.400027 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6369.93 | 0.753464 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5849.47 | 0.686929 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14830.8 | 1.72919 | 0.864594 | − | 0.502471i | \(-0.167575\pi\) | ||||
0.864594 | + | 0.502471i | \(0.167575\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9103.21 | 1.05383 | 0.526916 | − | 0.849917i | \(-0.323348\pi\) | ||||
0.526916 | + | 0.849917i | \(0.323348\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3872.61 | 0.445136 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1974.69 | 0.225380 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4220.95 | 0.478375 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8100.58 | −0.911655 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14680.9 | 1.64072 | 0.820362 | − | 0.571845i | \(-0.193772\pi\) | ||||
0.820362 | + | 0.571845i | \(0.193772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5929.64 | −0.658107 | −0.329053 | − | 0.944311i | \(-0.606730\pi\) | ||||
−0.329053 | + | 0.944311i | \(0.606730\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8020.39 | 0.884019 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3842.26 | 0.420596 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16070.6 | 1.74717 | 0.873587 | − | 0.486669i | \(-0.161788\pi\) | ||||
0.873587 | + | 0.486669i | \(0.161788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −610.567 | −0.0654829 | −0.0327415 | − | 0.999464i | \(-0.510424\pi\) | ||||
−0.0327415 | + | 0.999464i | \(0.510424\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15577.7 | −1.65944 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3012.21 | −0.318730 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1092.21 | 0.114798 | 0.0573991 | − | 0.998351i | \(-0.481719\pi\) | ||||
0.0573991 | + | 0.998351i | \(0.481719\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2260.22 | 0.235986 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3857.38 | 0.400079 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5312.86 | −0.547408 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 672.511 | 0.0688375 | 0.0344188 | − | 0.999407i | \(-0.489042\pi\) | ||||
0.0344188 | + | 0.999407i | \(0.489042\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2461.28 | 0.250290 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10504.7 | −1.06128 | −0.530642 | − | 0.847596i | \(-0.678049\pi\) | ||||
−0.530642 | + | 0.847596i | \(0.678049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6034.32 | −0.605699 | −0.302849 | − | 0.953038i | \(-0.597938\pi\) | ||||
−0.302849 | + | 0.953038i | \(0.597938\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9483.81 | −0.945809 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16545.7 | 1.63949 | 0.819747 | − | 0.572726i | \(-0.194114\pi\) | ||||
0.819747 | + | 0.572726i | \(0.194114\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7146.76 | −0.703639 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1225.03 | −0.119844 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13983.3 | −1.35931 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2260.03 | −0.218310 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1007.63 | −0.0967216 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11914.9 | −1.13655 | −0.568274 | − | 0.822839i | \(-0.692389\pi\) | ||||
−0.568274 | + | 0.822839i | \(0.692389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21301.9 | −2.01930 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −773.380 | −0.0728572 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7301.93 | −0.683637 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 943.059 | 0.0877497 | 0.0438748 | − | 0.999037i | \(-0.486030\pi\) | ||||
0.0438748 | + | 0.999037i | \(0.486030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5450.49 | −0.504048 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7491.83 | 0.688598 | 0.344299 | − | 0.938860i | \(-0.388117\pi\) | ||||
0.344299 | + | 0.938860i | \(0.388117\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23974.1 | −2.19014 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3308.77 | −0.300441 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1991.09 | 0.179704 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19551.1 | −1.75396 | −0.876980 | − | 0.480527i | \(-0.840446\pi\) | ||||
−0.876980 | + | 0.480527i | \(0.840446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10566.5 | 0.942265 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16168.0 | −1.43319 | −0.716596 | − | 0.697488i | \(-0.754301\pi\) | ||||
−0.716596 | + | 0.697488i | \(0.754301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14436.3 | −1.27209 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10132.3 | −0.887556 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6152.87 | 0.535798 | 0.267899 | − | 0.963447i | \(-0.413671\pi\) | ||||
0.267899 | + | 0.963447i | \(0.413671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3964.32 | −0.343192 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2816.94 | −0.242438 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11245.5 | −0.962202 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15561.7 | 1.32379 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7186.72 | −0.607826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21054.8 | −1.77049 | −0.885245 | − | 0.465125i | \(-0.846009\pi\) | ||||
−0.885245 | + | 0.465125i | \(0.846009\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7707.01 | 0.644367 | 0.322184 | − | 0.946677i | \(-0.395583\pi\) | ||||
0.322184 | + | 0.946677i | \(0.395583\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 454.904 | 0.0378165 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28348.5 | 2.34322 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10810.7 | −0.888528 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4316.77 | 0.352791 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4666.13 | 0.379198 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1598.16 | 0.129148 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4515.23 | −0.362843 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1772.11 | 0.141614 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20382.6 | 1.61981 | 0.809905 | − | 0.586561i | \(-0.199519\pi\) | ||||
0.809905 | + | 0.586561i | \(0.199519\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9103.25 | 0.719443 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21895.4 | −1.72091 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2378.87 | −0.185947 | −0.0929736 | − | 0.995669i | \(-0.529637\pi\) | ||||
−0.0929736 | + | 0.995669i | \(0.529637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5426.94 | 0.421887 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27438.4 | 2.12144 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −660.030 | −0.0507546 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8700.99 | −0.665471 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9909.32 | −0.753808 | −0.376904 | − | 0.926252i | \(-0.623011\pi\) | ||||
−0.376904 | + | 0.926252i | \(0.623011\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28868.0 | −2.18423 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9890.40 | 0.744337 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11964.2 | 0.895612 | 0.447806 | − | 0.894131i | \(-0.352206\pi\) | ||||
0.447806 | + | 0.894131i | \(0.352206\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12739.7 | 0.948609 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1008.95 | 0.0743365 | 0.0371683 | − | 0.999309i | \(-0.488166\pi\) | ||||
0.0371683 | + | 0.999309i | \(0.488166\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4128.83 | 0.302603 | 0.151301 | − | 0.988488i | \(-0.451654\pi\) | ||||
0.151301 | + | 0.988488i | \(0.451654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1924.39 | 0.140301 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −797.764 | −0.0578592 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1693.04 | 0.122153 | 0.0610763 | − | 0.998133i | \(-0.480547\pi\) | ||||
0.0610763 | + | 0.998133i | \(0.480547\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8677.86 | −0.622866 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4386.35 | −0.313212 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4049.05 | −0.287641 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6830.82 | −0.482768 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10416.6 | 0.732433 | 0.366217 | − | 0.930530i | \(-0.380653\pi\) | ||||
0.366217 | + | 0.930530i | \(0.380653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32444.8 | −2.26972 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10013.6 | −0.696961 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12079.7 | 0.836513 | 0.418257 | − | 0.908329i | \(-0.362641\pi\) | ||||
0.418257 | + | 0.908329i | \(0.362641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6486.73 | 0.446941 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4205.47 | −0.288305 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6531.39 | 0.445518 | 0.222759 | − | 0.974874i | \(-0.428494\pi\) | ||||
0.222759 | + | 0.974874i | \(0.428494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14001.5 | −0.950303 | −0.475151 | − | 0.879904i | \(-0.657607\pi\) | ||||
−0.475151 | + | 0.879904i | \(0.657607\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9188.69 | −0.620551 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 234.364 | 0.0157492 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1272.28 | −0.0850745 | −0.0425372 | − | 0.999095i | \(-0.513544\pi\) | ||||
−0.0425372 | + | 0.999095i | \(0.513544\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5522.86 | −0.367483 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32126.4 | 2.12716 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6823.22 | −0.449571 | −0.224786 | − | 0.974408i | \(-0.572168\pi\) | ||||
−0.224786 | + | 0.974408i | \(0.572168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1905.93 | 0.124967 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3787.85 | −0.247153 | −0.123576 | − | 0.992335i | \(-0.539436\pi\) | ||||
−0.123576 | + | 0.992335i | \(0.539436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30311.6 | −1.96822 | −0.984108 | − | 0.177570i | \(-0.943176\pi\) | ||||
−0.984108 | + | 0.177570i | \(0.943176\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −994.346 | −0.0642540 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10726.8 | 0.689824 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12448.0 | −0.796671 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11319.6 | −0.720988 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26008.5 | 1.64869 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4357.18 | −0.274892 | −0.137446 | − | 0.990509i | \(-0.543889\pi\) | ||||
−0.137446 | + | 0.990509i | \(0.543889\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14902.8 | 0.935758 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14038.8 | −0.877343 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3658.44 | 0.227555 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2559.98 | 0.158484 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7843.40 | −0.483301 | −0.241650 | − | 0.970363i | \(-0.577689\pi\) | ||||
−0.241650 | + | 0.970363i | \(0.577689\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13730.3 | 0.842101 | 0.421050 | − | 0.907037i | \(-0.361662\pi\) | ||||
0.421050 | + | 0.907037i | \(0.361662\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11791.5 | −0.719826 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18378.8 | −1.11676 | −0.558380 | − | 0.829585i | \(-0.688577\pi\) | ||||
−0.558380 | + | 0.829585i | \(0.688577\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17346.5 | 1.04917 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6530.57 | 0.393169 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29631.0 | −1.77573 | −0.887864 | − | 0.460107i | \(-0.847811\pi\) | ||||
−0.887864 | + | 0.460107i | \(0.847811\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4201.10 | 0.250612 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5096.98 | −0.302667 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11311.1 | 0.668616 | 0.334308 | − | 0.942464i | \(-0.391497\pi\) | ||||
0.334308 | + | 0.942464i | \(0.391497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12315.4 | 0.724682 | 0.362341 | − | 0.932046i | \(-0.381978\pi\) | ||||
0.362341 | + | 0.932046i | \(0.381978\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20418.3 | 1.19605 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7424.06 | −0.432921 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9685.41 | 0.562250 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −728.274 | −0.0420877 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21807.6 | 1.25465 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14615.5 | −0.837127 | −0.418564 | − | 0.908187i | \(-0.637466\pi\) | ||||
−0.418564 | + | 0.908187i | \(0.637466\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 584.877 | 0.0333510 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12450.9 | 0.706835 | 0.353418 | − | 0.935466i | \(-0.385019\pi\) | ||||
0.353418 | + | 0.935466i | \(0.385019\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5028.13 | 0.284185 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17619.9 | −0.991477 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22985.2 | −1.28771 | −0.643853 | − | 0.765149i | \(-0.722665\pi\) | ||||
−0.643853 | + | 0.765149i | \(0.722665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1500.99 | −0.0837226 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11937.8 | −0.662963 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8359.09 | −0.462200 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6824.13 | 0.375691 | 0.187845 | − | 0.982199i | \(-0.439850\pi\) | ||||
0.187845 | + | 0.982199i | \(0.439850\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2278.43 | 0.124892 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19821.0 | 1.08180 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5697.11 | −0.309603 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1805.17 | −0.0976793 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 443.637 | 0.0239029 | 0.0119515 | − | 0.999929i | \(-0.496196\pi\) | ||||
0.0119515 | + | 0.999929i | \(0.496196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29766.7 | −1.59698 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13122.4 | 0.701017 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9940.87 | 0.528805 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24146.1 | −1.27902 | −0.639510 | − | 0.768783i | \(-0.720863\pi\) | ||||
−0.639510 | + | 0.768783i | \(0.720863\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −848.610 | −0.0447614 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11452.6 | −0.601549 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27448.9 | −1.43571 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15420.7 | 0.803201 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19205.6 | 0.996171 | 0.498085 | − | 0.867128i | \(-0.334037\pi\) | ||||
0.498085 | + | 0.867128i | \(0.334037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7743.65 | 0.399984 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6109.28 | −0.314255 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5696.98 | −0.291835 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6045.94 | 0.308434 | 0.154217 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154217 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35246.4 | 1.78336 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3004.60 | 0.151402 | 0.0757008 | − | 0.997131i | \(-0.475881\pi\) | ||||
0.0757008 | + | 0.997131i | \(0.475881\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1494.33 | 0.0749922 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36923.8 | −1.84546 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31957.4 | −1.59076 | −0.795380 | − | 0.606111i | \(-0.792729\pi\) | ||||
−0.795380 | + | 0.606111i | \(0.792729\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23368.7 | −1.15853 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16854.1 | 0.832190 | 0.416095 | − | 0.909321i | \(-0.363398\pi\) | ||||
0.416095 | + | 0.909321i | \(0.363398\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10206.9 | −0.501948 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5639.59 | −0.276227 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1100.49 | −0.0536865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13020.8 | −0.632671 | −0.316335 | − | 0.948647i | \(-0.602453\pi\) | ||||
−0.316335 | + | 0.948647i | \(0.602453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19751.1 | −0.955869 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13070.8 | 0.630059 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17832.8 | 0.856203 | 0.428102 | − | 0.903731i | \(-0.359183\pi\) | ||||
0.428102 | + | 0.903731i | \(0.359183\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3995.67 | −0.191085 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11732.4 | 0.558869 | 0.279434 | − | 0.960165i | \(-0.409853\pi\) | ||||
0.279434 | + | 0.960165i | \(0.409853\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15077.2 | 0.715377 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8340.08 | 0.394165 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35811.0 | 1.68587 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12233.1 | 0.573651 | 0.286826 | − | 0.957983i | \(-0.407400\pi\) | ||||
0.286826 | + | 0.957983i | \(0.407400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3833.34 | −0.179059 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7475.30 | 0.347824 | 0.173912 | − | 0.984761i | \(-0.444359\pi\) | ||||
0.173912 | + | 0.984761i | \(0.444359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6736.47 | 0.312234 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5991.52 | 0.276634 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6520.33 | 0.299891 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10287.0 | 0.471315 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7100.82 | −0.324090 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4151.04 | −0.188735 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30616.2 | 1.38672 | 0.693360 | − | 0.720591i | \(-0.256129\pi\) | ||||
0.693360 | + | 0.720591i | \(0.256129\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12798.5 | −0.577491 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8772.60 | −0.394333 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45020.7 | 2.01606 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3414.36 | −0.152321 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32993.8 | −1.46637 | −0.733187 | − | 0.680027i | \(-0.761968\pi\) | ||||
−0.733187 | + | 0.680027i | \(0.761968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39224.7 | −1.73676 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13791.6 | 0.608368 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20481.7 | −0.900102 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2620.61 | −0.114738 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −952.681 | −0.0415564 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40725.3 | 1.76987 | 0.884936 | − | 0.465713i | \(-0.154202\pi\) | ||||
0.884936 | + | 0.465713i | \(0.154202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22387.3 | 0.969327 | 0.484663 | − | 0.874701i | \(-0.338942\pi\) | ||||
0.484663 | + | 0.874701i | \(0.338942\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2690.06 | −0.116045 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18469.0 | −0.793793 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40339.4 | −1.72742 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4703.71 | 0.200685 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12101.2 | 0.514416 | 0.257208 | − | 0.966356i | \(-0.417197\pi\) | ||||
0.257208 | + | 0.966356i | \(0.417197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17732.5 | 0.751051 | 0.375526 | − | 0.926812i | \(-0.377462\pi\) | ||||
0.375526 | + | 0.926812i | \(0.377462\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2350.26 | 0.0991826 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3150.77 | −0.132482 | −0.0662412 | − | 0.997804i | \(-0.521101\pi\) | ||||
−0.0662412 | + | 0.997804i | \(0.521101\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17769.5 | −0.744465 | −0.372232 | − | 0.928140i | \(-0.621408\pi\) | ||||
−0.372232 | + | 0.928140i | \(0.621408\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5757.73 | 0.240353 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4466.78 | −0.185792 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35804.5 | 1.48391 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8396.45 | 0.346743 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19970.0 | 0.821741 | 0.410871 | − | 0.911694i | \(-0.365225\pi\) | ||||
0.410871 | + | 0.911694i | \(0.365225\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44776.4 | 1.83593 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2233.62 | 0.0912575 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34333.3 | −1.39775 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −161.384 | −0.00654688 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7341.69 | −0.296780 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10507.3 | −0.423250 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37094.0 | 1.48895 | 0.744476 | − | 0.667650i | \(-0.232700\pi\) | ||||
0.744476 | + | 0.667650i | \(0.232700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9545.22 | −0.381801 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28630.4 | 1.14119 | 0.570593 | − | 0.821233i | \(-0.306714\pi\) | ||||
0.570593 | + | 0.821233i | \(0.306714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33096.6 | −1.31460 | −0.657301 | − | 0.753628i | \(-0.728302\pi\) | ||||
−0.657301 | + | 0.753628i | \(0.728302\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1312.43 | −0.0519482 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19554.7 | −0.771323 | −0.385661 | − | 0.922640i | \(-0.626027\pi\) | ||||
−0.385661 | + | 0.922640i | \(0.626027\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24352.2 | −0.957227 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10190.7 | −0.399187 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3410.05 | −0.133116 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −76227.4 | −2.96541 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6464.73 | 0.250628 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10436.3 | 0.403212 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8043.01 | −0.309684 | −0.154842 | − | 0.987939i | \(-0.549487\pi\) | ||||
−0.154842 | + | 0.987939i | \(0.549487\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5477.17 | 0.210171 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27751.2 | −1.06125 | −0.530625 | − | 0.847606i | \(-0.678043\pi\) | ||||
−0.530625 | + | 0.847606i | \(0.678043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20355.2 | 0.775771 | 0.387885 | − | 0.921708i | \(-0.373206\pi\) | ||||
0.387885 | + | 0.921708i | \(0.373206\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14627.4 | 0.555588 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11001.2 | −0.416443 | −0.208221 | − | 0.978082i | \(-0.566767\pi\) | ||||
−0.208221 | + | 0.978082i | \(0.566767\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9667.14 | 0.364708 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2929.41 | 0.110145 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44892.6 | 1.68228 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15299.9 | −0.571418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8248.88 | −0.307048 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −81785.5 | −3.03415 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10206.0 | 0.377372 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8119.62 | 0.299229 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30846.4 | 1.13301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11666.9 | 0.427116 | 0.213558 | − | 0.976930i | \(-0.431495\pi\) | ||||
0.213558 | + | 0.976930i | \(0.431495\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12781.1 | 0.466362 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3478.55 | 0.126509 | 0.0632543 | − | 0.997997i | \(-0.479852\pi\) | ||||
0.0632543 | + | 0.997997i | \(0.479852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22662.1 | −0.821473 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18389.2 | 0.664403 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2892.89 | −0.104178 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14907.0 | −0.535079 | −0.267540 | − | 0.963547i | \(-0.586211\pi\) | ||||
−0.267540 | + | 0.963547i | \(0.586211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2715.80 | 0.0971647 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21237.0 | 0.757340 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6180.42 | 0.219688 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9956.12 | 0.352753 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31359.5 | 1.10751 | 0.553753 | − | 0.832681i | \(-0.313195\pi\) | ||||
0.553753 | + | 0.832681i | \(0.313195\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5112.22 | 0.179964 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5829.86 | −0.204567 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33513.7 | 1.17221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28359.5 | 0.988757 | 0.494378 | − | 0.869247i | \(-0.335396\pi\) | ||||
0.494378 | + | 0.869247i | \(0.335396\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24593.9 | −0.854731 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4772.62 | 0.165338 | 0.0826690 | − | 0.996577i | \(-0.473656\pi\) | ||||
0.0826690 | + | 0.996577i | \(0.473656\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2301.60 | 0.0794808 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1921.28 | 0.0661369 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50905.8 | −1.74679 | −0.873397 | − | 0.487008i | \(-0.838088\pi\) | ||||
−0.873397 | + | 0.487008i | \(0.838088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42283.5 | −1.44634 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10973.3 | 0.374169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16818.3 | 0.571666 | 0.285833 | − | 0.958279i | \(-0.407730\pi\) | ||||
0.285833 | + | 0.958279i | \(0.407730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6520.80 | 0.220951 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28533.9 | −0.963813 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1033.59 | 0.0348032 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66917.2 | 2.24622 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1414.92 | −0.0473470 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29405.0 | −0.980913 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45160.6 | −1.50183 | −0.750913 | − | 0.660401i | \(-0.770386\pi\) | ||||
−0.750913 | + | 0.660401i | \(0.770386\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28532.0 | 0.945904 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29892.4 | −0.987943 | −0.493972 | − | 0.869478i | \(-0.664455\pi\) | ||||
−0.493972 | + | 0.869478i | \(0.664455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13648.8 | −0.449701 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4852.01 | 0.159373 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36169.1 | 1.18439 | 0.592197 | − | 0.805793i | \(-0.298261\pi\) | ||||
0.592197 | + | 0.805793i | \(0.298261\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 55420.1 | 1.80923 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19385.0 | 0.630903 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13732.3 | 0.445567 | 0.222784 | − | 0.974868i | \(-0.428486\pi\) | ||||
0.222784 | + | 0.974868i | \(0.428486\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33931.1 | −1.09760 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9036.09 | −0.291410 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14239.3 | −0.457821 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31284.6 | −1.00281 | −0.501407 | − | 0.865211i | \(-0.667184\pi\) | ||||
−0.501407 | + | 0.865211i | \(0.667184\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 369.260 | 0.0118007 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14250.3 | −0.454034 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20015.1 | −0.635790 | −0.317895 | − | 0.948126i | \(-0.602976\pi\) | ||||
−0.317895 | + | 0.948126i | \(0.602976\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7703.38 | 0.243968 |
(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 | 1344.4.a.bh.1.1 | 2 | ||
4.3 | odd | 2 | 1344.4.a.bp.1.1 | 2 | |||
8.3 | odd | 2 | 672.4.a.f.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 672.4.a.k.1.2 | yes | 2 | ||
24.5 | odd | 2 | 2016.4.a.n.1.1 | 2 | |||
24.11 | even | 2 | 2016.4.a.m.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.f.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
672.4.a.k.1.2 | yes | 2 | 8.5 | even | 2 | ||
1344.4.a.bh.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.a.bp.1.1 | 2 | 4.3 | odd | 2 | |||
2016.4.a.m.1.1 | 2 | 24.11 | even | 2 | |||
2016.4.a.n.1.1 | 2 | 24.5 | odd | 2 |