Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,4,Mod(1,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, 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("600.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.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: | \(35.4011460034\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 600.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −20.0000 | −1.07990 | −0.539949 | − | 0.841698i | \(-0.681557\pi\) | ||||
−0.539949 | + | 0.841698i | \(0.681557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −56.0000 | −1.53497 | −0.767483 | − | 0.641069i | \(-0.778491\pi\) | ||||
−0.767483 | + | 0.641069i | \(0.778491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 86.0000 | 1.83478 | 0.917389 | − | 0.397992i | \(-0.130293\pi\) | ||||
0.917389 | + | 0.397992i | \(0.130293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 106.000 | 1.51228 | 0.756140 | − | 0.654409i | \(-0.227083\pi\) | ||||
0.756140 | + | 0.654409i | \(0.227083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.0482980 | 0.0241490 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241490 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −60.0000 | −0.623480 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −136.000 | −1.23295 | −0.616477 | − | 0.787373i | \(-0.711441\pi\) | ||||
−0.616477 | + | 0.787373i | \(0.711441\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −206.000 | −1.31908 | −0.659539 | − | 0.751671i | \(-0.729248\pi\) | ||||
−0.659539 | + | 0.751671i | \(0.729248\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −152.000 | −0.880645 | −0.440323 | − | 0.897840i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897840i | \(0.645136\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −168.000 | −0.886214 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −282.000 | −1.25299 | −0.626493 | − | 0.779427i | \(-0.715510\pi\) | ||||
−0.626493 | + | 0.779427i | \(0.715510\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 258.000 | 1.05931 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −246.000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −412.000 | −1.46115 | −0.730575 | − | 0.682833i | \(-0.760748\pi\) | ||||
−0.730575 | + | 0.682833i | \(0.760748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −40.0000 | −0.124140 | −0.0620702 | − | 0.998072i | \(-0.519770\pi\) | ||||
−0.0620702 | + | 0.998072i | \(0.519770\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.0000 | 0.166181 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 318.000 | 0.873116 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 126.000 | 0.326555 | 0.163278 | − | 0.986580i | \(-0.447793\pi\) | ||||
0.163278 | + | 0.986580i | \(0.447793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0000 | 0.0278849 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 56.0000 | 0.123569 | 0.0617846 | − | 0.998090i | \(-0.480321\pi\) | ||||
0.0617846 | + | 0.998090i | \(0.480321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.00419793 | −0.00209897 | − | 0.999998i | \(-0.500668\pi\) | ||||
−0.00209897 | + | 0.999998i | \(0.500668\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −180.000 | −0.359966 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 388.000 | 0.707489 | 0.353744 | − | 0.935342i | \(-0.384908\pi\) | ||||
0.353744 | + | 0.935342i | \(0.384908\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −408.000 | −0.711847 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −672.000 | −1.12326 | −0.561632 | − | 0.827387i | \(-0.689826\pi\) | ||||
−0.561632 | + | 0.827387i | \(0.689826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1170.00 | −1.87586 | −0.937932 | − | 0.346818i | \(-0.887262\pi\) | ||||
−0.937932 | + | 0.346818i | \(0.887262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1120.00 | 1.65761 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 408.000 | 0.581058 | 0.290529 | − | 0.956866i | \(-0.406169\pi\) | ||||
0.290529 | + | 0.956866i | \(0.406169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −668.000 | −0.883404 | −0.441702 | − | 0.897162i | \(-0.645625\pi\) | ||||
−0.441702 | + | 0.897162i | \(0.645625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −618.000 | −0.761570 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 66.0000 | 0.0786066 | 0.0393033 | − | 0.999227i | \(-0.487486\pi\) | ||||
0.0393033 | + | 0.999227i | \(0.487486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1720.00 | −1.98137 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −456.000 | −0.508441 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 926.000 | 0.969289 | 0.484645 | − | 0.874711i | \(-0.338949\pi\) | ||||
0.484645 | + | 0.874711i | \(0.338949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −504.000 | −0.511656 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −198.000 | −0.195067 | −0.0975333 | − | 0.995232i | \(-0.531095\pi\) | ||||
−0.0975333 | + | 0.995232i | \(0.531095\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1532.00 | 1.46556 | 0.732779 | − | 0.680467i | \(-0.238223\pi\) | ||||
0.732779 | + | 0.680467i | \(0.238223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 444.000 | 0.401150 | 0.200575 | − | 0.979678i | \(-0.435719\pi\) | ||||
0.200575 | + | 0.979678i | \(0.435719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 62.0000 | 0.0544819 | 0.0272409 | − | 0.999629i | \(-0.491328\pi\) | ||||
0.0272409 | + | 0.999629i | \(0.491328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −846.000 | −0.723412 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −414.000 | −0.344653 | −0.172327 | − | 0.985040i | \(-0.555128\pi\) | ||||
−0.172327 | + | 0.985040i | \(0.555128\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 774.000 | 0.611593 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2120.00 | −1.63311 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1805.00 | 1.35612 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −738.000 | −0.541002 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 996.000 | 0.695911 | 0.347956 | − | 0.937511i | \(-0.386876\pi\) | ||||
0.347956 | + | 0.937511i | \(0.386876\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1236.00 | −0.843595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −264.000 | −0.176075 | −0.0880374 | − | 0.996117i | \(-0.528059\pi\) | ||||
−0.0880374 | + | 0.996117i | \(0.528059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −80.0000 | −0.0521570 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2278.00 | −1.42060 | −0.710302 | − | 0.703897i | \(-0.751442\pi\) | ||||
−0.710302 | + | 0.703897i | \(0.751442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1812.00 | 1.10570 | 0.552848 | − | 0.833282i | \(-0.313541\pi\) | ||||
0.552848 | + | 0.833282i | \(0.313541\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −120.000 | −0.0716725 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4816.00 | −2.81632 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 171.000 | 0.0959445 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1534.00 | −0.843424 | −0.421712 | − | 0.906730i | \(-0.638571\pi\) | ||||
−0.421712 | + | 0.906730i | \(0.638571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3016.00 | −1.62542 | −0.812711 | − | 0.582668i | \(-0.802009\pi\) | ||||
−0.812711 | + | 0.582668i | \(0.802009\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 954.000 | 0.504094 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1814.00 | 0.922121 | 0.461060 | − | 0.887369i | \(-0.347469\pi\) | ||||
0.461060 | + | 0.887369i | \(0.347469\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 378.000 | 0.188537 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2720.00 | 1.33147 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1844.00 | 0.886093 | 0.443047 | − | 0.896499i | \(-0.353898\pi\) | ||||
0.443047 | + | 0.896499i | \(0.353898\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3768.00 | −1.74597 | −0.872984 | − | 0.487749i | \(-0.837818\pi\) | ||||
−0.872984 | + | 0.487749i | \(0.837818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5199.00 | 2.36641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 36.0000 | 0.0160993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −938.000 | −0.412224 | −0.206112 | − | 0.978528i | \(-0.566081\pi\) | ||||
−0.206112 | + | 0.978528i | \(0.566081\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 168.000 | 0.0713427 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3968.00 | 1.65688 | 0.828442 | − | 0.560075i | \(-0.189228\pi\) | ||||
0.828442 | + | 0.560075i | \(0.189228\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3514.00 | −1.44306 | −0.721529 | − | 0.692384i | \(-0.756560\pi\) | ||||
−0.721529 | + | 0.692384i | \(0.756560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.00000 | −0.00242368 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5936.00 | −2.32130 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −540.000 | −0.207827 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1480.00 | −0.560676 | −0.280338 | − | 0.959901i | \(-0.590446\pi\) | ||||
−0.280338 | + | 0.959901i | \(0.590446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2774.00 | 1.03460 | 0.517298 | − | 0.855806i | \(-0.326938\pi\) | ||||
0.517298 | + | 0.855806i | \(0.326938\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3806.00 | 1.37648 | 0.688239 | − | 0.725484i | \(-0.258384\pi\) | ||||
0.688239 | + | 0.725484i | \(0.258384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −856.000 | −0.304926 | −0.152463 | − | 0.988309i | \(-0.548720\pi\) | ||||
−0.152463 | + | 0.988309i | \(0.548720\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1164.00 | 0.408469 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4120.00 | 1.42447 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1224.00 | −0.410985 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −224.000 | −0.0741359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3020.00 | 0.985334 | 0.492667 | − | 0.870218i | \(-0.336022\pi\) | ||||
0.492667 | + | 0.870218i | \(0.336022\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2016.00 | −0.648517 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3040.00 | 0.951008 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3510.00 | −1.08303 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9116.00 | 2.77470 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1684.00 | 0.505690 | 0.252845 | − | 0.967507i | \(-0.418634\pi\) | ||||
0.252845 | + | 0.967507i | \(0.418634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2004.00 | −0.585948 | −0.292974 | − | 0.956120i | \(-0.594645\pi\) | ||||
−0.292974 | + | 0.956120i | \(0.594645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5042.00 | −1.45496 | −0.727478 | − | 0.686131i | \(-0.759307\pi\) | ||||
−0.727478 | + | 0.686131i | \(0.759307\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3360.00 | 0.957021 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3090.00 | 0.868810 | 0.434405 | − | 0.900718i | \(-0.356959\pi\) | ||||
0.434405 | + | 0.900718i | \(0.356959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1224.00 | 0.335474 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2136.00 | 0.578102 | 0.289051 | − | 0.957314i | \(-0.406660\pi\) | ||||
0.289051 | + | 0.957314i | \(0.406660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 98.0000 | 0.0261939 | 0.0130970 | − | 0.999914i | \(-0.495831\pi\) | ||||
0.0130970 | + | 0.999914i | \(0.495831\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 344.000 | 0.0886162 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2004.00 | −0.510033 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5040.00 | −1.26742 | −0.633709 | − | 0.773571i | \(-0.718468\pi\) | ||||
−0.633709 | + | 0.773571i | \(0.718468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7616.00 | 1.89254 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1986.00 | 0.482036 | 0.241018 | − | 0.970521i | \(-0.422519\pi\) | ||||
0.241018 | + | 0.970521i | \(0.422519\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5640.00 | 1.35310 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1854.00 | −0.439692 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1416.00 | −0.331994 | −0.165997 | − | 0.986126i | \(-0.553084\pi\) | ||||
−0.165997 | + | 0.986126i | \(0.553084\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 198.000 | 0.0453835 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6670.00 | −1.51181 | −0.755905 | − | 0.654681i | \(-0.772803\pi\) | ||||
−0.755905 | + | 0.654681i | \(0.772803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 48.0000 | 0.0107594 | 0.00537969 | − | 0.999986i | \(-0.498288\pi\) | ||||
0.00537969 | + | 0.999986i | \(0.498288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5160.00 | −1.14395 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6938.00 | −1.50492 | −0.752462 | − | 0.658636i | \(-0.771134\pi\) | ||||
−0.752462 | + | 0.658636i | \(0.771134\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1368.00 | −0.293548 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1694.00 | −0.359628 | −0.179814 | − | 0.983701i | \(-0.557550\pi\) | ||||
−0.179814 | + | 0.983701i | \(0.557550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6364.00 | 1.33675 | 0.668376 | − | 0.743824i | \(-0.266990\pi\) | ||||
0.668376 | + | 0.743824i | \(0.266990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4920.00 | 1.01191 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6323.00 | 1.28699 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2778.00 | 0.559619 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3134.00 | 0.624881 | 0.312441 | − | 0.949937i | \(-0.398853\pi\) | ||||
0.312441 | + | 0.949937i | \(0.398853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1512.00 | −0.295405 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11696.0 | −2.26220 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8240.00 | 1.57789 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −594.000 | −0.112622 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 236.000 | 0.0438737 | 0.0219369 | − | 0.999759i | \(-0.493017\pi\) | ||||
0.0219369 | + | 0.999759i | \(0.493017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4596.00 | 0.846140 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3776.00 | 0.688480 | 0.344240 | − | 0.938882i | \(-0.388137\pi\) | ||||
0.344240 | + | 0.938882i | \(0.388137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7918.00 | 1.42988 | 0.714939 | − | 0.699187i | \(-0.246454\pi\) | ||||
0.714939 | + | 0.699187i | \(0.246454\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4362.00 | −0.772853 | −0.386426 | − | 0.922320i | \(-0.626291\pi\) | ||||
−0.386426 | + | 0.922320i | \(0.626291\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11536.0 | 2.02474 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1332.00 | 0.231604 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 424.000 | 0.0730402 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 186.000 | 0.0314551 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 800.000 | 0.134059 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7980.00 | 1.32514 | 0.662569 | − | 0.749001i | \(-0.269466\pi\) | ||||
0.662569 | + | 0.749001i | \(0.269466\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2538.00 | −0.417662 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8294.00 | 1.34066 | 0.670331 | − | 0.742062i | \(-0.266152\pi\) | ||||
0.670331 | + | 0.742062i | \(0.266152\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1242.00 | −0.198986 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8512.00 | 1.35176 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5720.00 | 0.900440 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 964.000 | 0.149136 | 0.0745681 | − | 0.997216i | \(-0.476242\pi\) | ||||
0.0745681 | + | 0.997216i | \(0.476242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8670.00 | 1.32978 | 0.664892 | − | 0.746940i | \(-0.268478\pi\) | ||||
0.664892 | + | 0.746940i | \(0.268478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2322.00 | 0.353103 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2314.00 | 0.348900 | 0.174450 | − | 0.984666i | \(-0.444185\pi\) | ||||
0.174450 | + | 0.984666i | \(0.444185\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6360.00 | −0.942876 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1896.00 | −0.278738 | −0.139369 | − | 0.990240i | \(-0.544507\pi\) | ||||
−0.139369 | + | 0.990240i | \(0.544507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6843.00 | −0.997667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5415.00 | 0.782958 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1484.00 | −0.211074 | −0.105537 | − | 0.994415i | \(-0.533656\pi\) | ||||
−0.105537 | + | 0.994415i | \(0.533656\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2214.00 | −0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2520.00 | −0.352647 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12370.0 | −1.71714 | −0.858571 | − | 0.512694i | \(-0.828648\pi\) | ||||
−0.858571 | + | 0.512694i | \(0.828648\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17716.0 | −2.42021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5620.00 | 0.761689 | 0.380844 | − | 0.924639i | \(-0.375633\pi\) | ||||
0.380844 | + | 0.924639i | \(0.375633\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2988.00 | 0.401784 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5880.00 | −0.784475 | −0.392238 | − | 0.919864i | \(-0.628299\pi\) | ||||
−0.392238 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3708.00 | −0.487050 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2082.00 | 0.271367 | 0.135683 | − | 0.990752i | \(-0.456677\pi\) | ||||
0.135683 | + | 0.990752i | \(0.456677\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14416.0 | −1.86457 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −792.000 | −0.101657 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1742.00 | 0.220223 | 0.110111 | − | 0.993919i | \(-0.464879\pi\) | ||||
0.110111 | + | 0.993919i | \(0.464879\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −240.000 | −0.0301129 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3270.00 | −0.407222 | −0.203611 | − | 0.979052i | \(-0.565268\pi\) | ||||
−0.203611 | + | 0.979052i | \(0.565268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13072.0 | −1.61579 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15792.0 | 1.92329 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6134.00 | −0.741581 | −0.370791 | − | 0.928716i | \(-0.620913\pi\) | ||||
−0.370791 | + | 0.928716i | \(0.620913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6834.00 | −0.820186 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1120.00 | −0.133442 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5436.00 | 0.638374 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10392.0 | −1.21165 | −0.605826 | − | 0.795597i | \(-0.707157\pi\) | ||||
−0.605826 | + | 0.795597i | \(0.707157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12690.0 | −1.46906 | −0.734528 | − | 0.678578i | \(-0.762596\pi\) | ||||
−0.734528 | + | 0.678578i | \(0.762596\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −360.000 | −0.0413801 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 40.0000 | 0.00453334 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14448.0 | −1.62600 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7408.00 | −0.827914 | −0.413957 | − | 0.910297i | \(-0.635854\pi\) | ||||
−0.413957 | + | 0.910297i | \(0.635854\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5062.00 | 0.561811 | 0.280906 | − | 0.959735i | \(-0.409365\pi\) | ||||
0.280906 | + | 0.959735i | \(0.409365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −544.000 | −0.0595493 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7160.00 | −0.778424 | −0.389212 | − | 0.921148i | \(-0.627253\pi\) | ||||
−0.389212 | + | 0.921148i | \(0.627253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 513.000 | 0.0553936 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17100.0 | −1.83396 | −0.916981 | − | 0.398930i | \(-0.869382\pi\) | ||||
−0.916981 | + | 0.398930i | \(0.869382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4602.00 | −0.486951 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8634.00 | 0.907491 | 0.453746 | − | 0.891131i | \(-0.350087\pi\) | ||||
0.453746 | + | 0.891131i | \(0.350087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13776.0 | 1.43833 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9048.00 | −0.938437 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2986.00 | −0.305644 | −0.152822 | − | 0.988254i | \(-0.548836\pi\) | ||||
−0.152822 | + | 0.988254i | \(0.548836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2862.00 | 0.291039 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2406.00 | −0.243077 | −0.121539 | − | 0.992587i | \(-0.538783\pi\) | ||||
−0.121539 | + | 0.992587i | \(0.538783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14316.0 | 1.43698 | 0.718489 | − | 0.695538i | \(-0.244834\pi\) | ||||
0.718489 | + | 0.695538i | \(0.244834\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 292.000 | 0.0289339 | 0.0144670 | − | 0.999895i | \(-0.495395\pi\) | ||||
0.0144670 | + | 0.999895i | \(0.495395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7760.00 | −0.764016 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5442.00 | 0.532387 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23072.0 | 2.24282 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1134.00 | 0.108852 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14056.0 | 1.34078 | 0.670391 | − | 0.742008i | \(-0.266126\pi\) | ||||
0.670391 | + | 0.742008i | \(0.266126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24252.0 | −2.29895 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8160.00 | 0.768722 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11204.0 | 1.04251 | 0.521254 | − | 0.853401i | \(-0.325464\pi\) | ||||
0.521254 | + | 0.853401i | \(0.325464\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5532.00 | 0.511586 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4608.00 | 0.423536 | 0.211768 | − | 0.977320i | \(-0.432078\pi\) | ||||
0.211768 | + | 0.977320i | \(0.432078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21836.0 | −1.99482 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13440.0 | 1.21301 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2468.00 | 0.221409 | 0.110704 | − | 0.993853i | \(-0.464689\pi\) | ||||
0.110704 | + | 0.993853i | \(0.464689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11304.0 | −1.00803 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12192.0 | −1.08074 | −0.540372 | − | 0.841426i | \(-0.681717\pi\) | ||||
−0.540372 | + | 0.841426i | \(0.681717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15597.0 | 1.36625 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1714.00 | 0.149257 | 0.0746284 | − | 0.997211i | \(-0.476223\pi\) | ||||
0.0746284 | + | 0.997211i | \(0.476223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23400.0 | 2.02574 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 108.000 | 0.00929496 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2240.00 | 0.190551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2814.00 | −0.237998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18014.0 | −1.51479 | −0.757397 | − | 0.652955i | \(-0.773529\pi\) | ||||
−0.757397 | + | 0.652955i | \(0.773529\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16748.0 | 1.40027 | 0.700133 | − | 0.714013i | \(-0.253124\pi\) | ||||
0.700133 | + | 0.714013i | \(0.253124\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16112.0 | −1.33178 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6329.00 | 0.520178 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 504.000 | 0.0411897 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21156.0 | −1.71926 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11904.0 | 0.956602 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3192.00 | −0.255082 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14018.0 | −1.11401 | −0.557006 | − | 0.830508i | \(-0.688050\pi\) | ||||
−0.557006 | + | 0.830508i | \(0.688050\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10542.0 | −0.833150 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 412.000 | 0.0322045 | 0.0161022 | − | 0.999870i | \(-0.494874\pi\) | ||||
0.0161022 | + | 0.999870i | \(0.494874\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.0000 | −0.00139931 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −824.000 | −0.0637089 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8160.00 | −0.627484 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18218.0 | −1.38586 | −0.692928 | − | 0.721007i | \(-0.743679\pi\) | ||||
−0.692928 | + | 0.721007i | \(0.743679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35432.0 | −2.68088 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17808.0 | −1.34020 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23524.0 | −1.76096 | −0.880478 | − | 0.474087i | \(-0.842778\pi\) | ||||
−0.880478 | + | 0.474087i | \(0.842778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1620.00 | −0.119989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23330.0 | 1.71888 | 0.859442 | − | 0.511234i | \(-0.170811\pi\) | ||||
0.859442 | + | 0.511234i | \(0.170811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13124.0 | −0.961860 | −0.480930 | − | 0.876759i | \(-0.659701\pi\) | ||||
−0.480930 | + | 0.876759i | \(0.659701\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4440.00 | −0.323706 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11714.0 | −0.845165 | −0.422582 | − | 0.906324i | \(-0.638876\pi\) | ||||
−0.422582 | + | 0.906324i | \(0.638876\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8322.00 | 0.597324 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13360.0 | 0.953987 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7056.00 | −0.501252 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17628.0 | 1.23950 | 0.619749 | − | 0.784800i | \(-0.287234\pi\) | ||||
0.619749 | + | 0.784800i | \(0.287234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −608.000 | −0.0425335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11418.0 | 0.794710 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2802.00 | 0.194038 | 0.0970188 | − | 0.995283i | \(-0.469069\pi\) | ||||
0.0970188 | + | 0.995283i | \(0.469069\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2568.00 | −0.176049 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2664.00 | −0.181716 | −0.0908582 | − | 0.995864i | \(-0.528961\pi\) | ||||
−0.0908582 | + | 0.995864i | \(0.528961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23962.0 | 1.62634 | 0.813170 | − | 0.582026i | \(-0.197740\pi\) | ||||
0.813170 | + | 0.582026i | \(0.197740\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3492.00 | 0.235830 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11940.0 | −0.798401 | −0.399201 | − | 0.916864i | \(-0.630712\pi\) | ||||
−0.399201 | + | 0.916864i | \(0.630712\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12360.0 | 0.822418 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3440.00 | −0.227770 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16794.0 | −1.10653 | −0.553265 | − | 0.833005i | \(-0.686618\pi\) | ||||
−0.553265 | + | 0.833005i | \(0.686618\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20706.0 | 1.35104 | 0.675520 | − | 0.737341i | \(-0.263919\pi\) | ||||
0.675520 | + | 0.737341i | \(0.263919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10724.0 | 0.696339 | 0.348170 | − | 0.937432i | \(-0.386803\pi\) | ||||
0.348170 | + | 0.937432i | \(0.386803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3672.00 | −0.237282 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1320.00 | −0.0848871 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −672.000 | −0.0428024 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29892.0 | −1.89487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5744.00 | −0.362385 | −0.181193 | − | 0.983448i | \(-0.557996\pi\) | ||||
−0.181193 | + | 0.983448i | \(0.557996\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9060.00 | 0.568883 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4902.00 | 0.304905 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6048.00 | −0.374421 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27906.0 | 1.71953 | 0.859767 | − | 0.510687i | \(-0.170609\pi\) | ||||
0.859767 | + | 0.510687i | \(0.170609\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20556.0 | −1.26073 | −0.630365 | − | 0.776299i | \(-0.717095\pi\) | ||||
−0.630365 | + | 0.776299i | \(0.717095\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10224.0 | 0.621247 | 0.310624 | − | 0.950533i | \(-0.399462\pi\) | ||||
0.310624 | + | 0.950533i | \(0.399462\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3136.00 | −0.189675 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9120.00 | 0.549064 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12982.0 | 0.777986 | 0.388993 | − | 0.921241i | \(-0.372823\pi\) | ||||
0.388993 | + | 0.921241i | \(0.372823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10530.0 | −0.625288 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1512.00 | −0.0893766 | −0.0446883 | − | 0.999001i | \(-0.514229\pi\) | ||||
−0.0446883 | + | 0.999001i | \(0.514229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16710.0 | 0.983273 | 0.491637 | − | 0.870800i | \(-0.336399\pi\) | ||||
0.491637 | + | 0.870800i | \(0.336399\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27348.0 | 1.60197 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28016.0 | 1.62636 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5052.00 | 0.291961 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 112.000 | 0.00644368 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7962.00 | −0.456036 | −0.228018 | − | 0.973657i | \(-0.573225\pi\) | ||||
−0.228018 | + | 0.973657i | \(0.573225\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12226.0 | −0.694067 | −0.347033 | − | 0.937853i | \(-0.612811\pi\) | ||||
−0.347033 | + | 0.937853i | \(0.612811\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18520.0 | −1.04673 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6012.00 | −0.338297 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8748.00 | 0.490092 | 0.245046 | − | 0.969511i | \(-0.421197\pi\) | ||||
0.245046 | + | 0.969511i | \(0.421197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15126.0 | −0.840019 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10836.0 | 0.599156 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7324.00 | −0.403210 | −0.201605 | − | 0.979467i | \(-0.564616\pi\) | ||||
−0.201605 | + | 0.979467i | \(0.564616\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10080.0 | 0.552536 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26076.0 | −1.41707 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9270.00 | 0.501607 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21934.0 | −1.18179 | −0.590896 | − | 0.806748i | \(-0.701226\pi\) | ||||
−0.590896 | + | 0.806748i | \(0.701226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1128.00 | −0.0605168 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3960.00 | 0.210652 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10690.0 | −0.566250 | −0.283125 | − | 0.959083i | \(-0.591371\pi\) | ||||
−0.283125 | + | 0.959083i | \(0.591371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3672.00 | 0.193686 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20672.0 | 1.08580 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6408.00 | 0.333767 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13792.0 | 0.715375 | 0.357688 | − | 0.933841i | \(-0.383565\pi\) | ||||
0.357688 | + | 0.933841i | \(0.383565\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30640.0 | −1.58265 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 294.000 | 0.0151231 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24004.0 | 1.22457 | 0.612283 | − | 0.790639i | \(-0.290251\pi\) | ||||
0.612283 | + | 0.790639i | \(0.290251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43672.0 | −2.20967 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8562.00 | −0.431439 | −0.215719 | − | 0.976455i | \(-0.569210\pi\) | ||||
−0.215719 | + | 0.976455i | \(0.569210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21728.0 | −1.08597 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13836.0 | −0.688722 | −0.344361 | − | 0.938837i | \(-0.611904\pi\) | ||||
−0.344361 | + | 0.938837i | \(0.611904\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1032.00 | 0.0511626 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22224.0 | 1.09733 | 0.548667 | − | 0.836041i | \(-0.315135\pi\) | ||||
0.548667 | + | 0.836041i | \(0.315135\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6012.00 | −0.294468 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8880.00 | −0.433202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11544.0 | 0.560914 | 0.280457 | − | 0.959867i | \(-0.409514\pi\) | ||||
0.280457 | + | 0.959867i | \(0.409514\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15120.0 | −0.731744 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3814.00 | 0.183120 | 0.0915602 | − | 0.995800i | \(-0.470815\pi\) | ||||
0.0915602 | + | 0.995800i | \(0.470815\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22848.0 | 1.09266 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25662.0 | −1.22240 | −0.611200 | − | 0.791476i | \(-0.709313\pi\) | ||||
−0.611200 | + | 0.791476i | \(0.709313\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1240.00 | −0.0588349 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4816.00 | 0.226722 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30658.0 | 1.43765 | 0.718827 | − | 0.695189i | \(-0.244679\pi\) | ||||
0.718827 | + | 0.695189i | \(0.244679\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5958.00 | 0.278304 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30894.0 | 1.43749 | 0.718745 | − | 0.695274i | \(-0.244717\pi\) | ||||
0.718745 | + | 0.695274i | \(0.244717\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16920.0 | 0.781212 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −984.000 | −0.0452573 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37632.0 | 1.72417 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5562.00 | −0.253857 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21596.0 | −0.978163 | −0.489081 | − | 0.872238i | \(-0.662668\pi\) | ||||
−0.489081 | + | 0.872238i | \(0.662668\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4248.00 | −0.191677 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8280.00 | 0.372191 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −172.000 | −0.00770227 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8646.00 | 0.384262 | 0.192131 | − | 0.981369i | \(-0.438460\pi\) | ||||
0.192131 | + | 0.981369i | \(0.438460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4240.00 | −0.187735 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 594.000 | 0.0262022 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 65520.0 | 2.87939 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20010.0 | −0.872844 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24954.0 | 1.08447 | 0.542235 | − | 0.840227i | \(-0.317578\pi\) | ||||
0.542235 | + | 0.840227i | \(0.317578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40004.0 | 1.73210 | 0.866048 | − | 0.499960i | \(-0.166652\pi\) | ||||
0.866048 | + | 0.499960i | \(0.166652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 144.000 | 0.00621193 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1648.00 | −0.0705707 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15480.0 | −0.660458 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16570.0 | 0.704381 | 0.352191 | − | 0.935928i | \(-0.385437\pi\) | ||||
0.352191 | + | 0.935928i | \(0.385437\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4388.00 | 0.185852 | 0.0929259 | − | 0.995673i | \(-0.470378\pi\) | ||||
0.0929259 | + | 0.995673i | \(0.470378\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14364.0 | −0.603972 | −0.301986 | − | 0.953312i | \(-0.597650\pi\) | ||||
−0.301986 | + | 0.953312i | \(0.597650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21170.0 | −0.886929 | −0.443465 | − | 0.896292i | \(-0.646251\pi\) | ||||
−0.443465 | + | 0.896292i | \(0.646251\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20814.0 | −0.868868 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6042.00 | 0.251312 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4104.00 | −0.169480 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10664.0 | 0.438811 | 0.219405 | − | 0.975634i | \(-0.429588\pi\) | ||||
0.219405 | + | 0.975634i | \(0.429588\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18047.0 | 0.739965 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5082.00 | −0.207632 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36100.0 | −1.46448 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19092.0 | 0.771774 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38352.0 | 1.54488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3190.00 | 0.128046 | 0.0640232 | − | 0.997948i | \(-0.479607\pi\) | ||||
0.0640232 | + | 0.997948i | \(0.479607\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20814.0 | −0.829630 | −0.414815 | − | 0.909906i | \(-0.636154\pi\) | ||||
−0.414815 | + | 0.909906i | \(0.636154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18988.0 | −0.754205 | −0.377103 | − | 0.926172i | \(-0.623080\pi\) | ||||
−0.377103 | + | 0.926172i | \(0.623080\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14760.0 | 0.584227 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11664.0 | −0.460078 | −0.230039 | − | 0.973181i | \(-0.573885\pi\) | ||||
−0.230039 | + | 0.973181i | \(0.573885\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18969.0 | 0.743046 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22848.0 | −0.891905 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33368.0 | 1.29808 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8334.00 | 0.323096 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8246.00 | 0.317500 | 0.158750 | − | 0.987319i | \(-0.449254\pi\) | ||||
0.158750 | + | 0.987319i | \(0.449254\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9402.00 | 0.360775 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22890.0 | 0.875350 | 0.437675 | − | 0.899133i | \(-0.355802\pi\) | ||||
0.437675 | + | 0.899133i | \(0.355802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33548.0 | −1.27857 | −0.639287 | − | 0.768969i | \(-0.720770\pi\) | ||||
−0.639287 | + | 0.768969i | \(0.720770\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32264.0 | 1.22133 | 0.610665 | − | 0.791889i | \(-0.290902\pi\) | ||||
0.610665 | + | 0.791889i | \(0.290902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19920.0 | −0.751513 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4536.00 | −0.170552 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −160.000 | −0.00599574 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35088.0 | −1.30608 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31312.0 | 1.16164 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13356.0 | 0.493843 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24720.0 | 0.910997 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51228.0 | −1.87541 | −0.937706 | − | 0.347431i | \(-0.887054\pi\) | ||||
−0.937706 | + | 0.347431i | \(0.887054\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1782.00 | −0.0650222 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2144.00 | −0.0779735 | −0.0389868 | − | 0.999240i | \(-0.512413\pi\) | ||||
−0.0389868 | + | 0.999240i | \(0.512413\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37408.0 | 1.35600 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5280.00 | 0.190143 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33584.0 | 1.20548 | 0.602739 | − | 0.797939i | \(-0.294076\pi\) | ||||
0.602739 | + | 0.797939i | \(0.294076\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 708.000 | 0.0253305 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −57792.0 | −2.06094 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13788.0 | 0.488519 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3590.00 | −0.126786 | −0.0633929 | − | 0.997989i | \(-0.520192\pi\) | ||||
−0.0633929 | + | 0.997989i | \(0.520192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 228.000 | 0.00802621 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11328.0 | 0.397494 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21686.0 | 0.756084 | 0.378042 | − | 0.925788i | \(-0.376597\pi\) | ||||
0.378042 | + | 0.925788i | \(0.376597\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23754.0 | 0.825540 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5174.00 | −0.179243 | −0.0896215 | − | 0.995976i | \(-0.528566\pi\) | ||||
−0.0896215 | + | 0.995976i | \(0.528566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33456.0 | 1.15533 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35524.0 | −1.21898 | −0.609490 | − | 0.792793i | \(-0.708626\pi\) | ||||
−0.609490 | + | 0.792793i | \(0.708626\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −100620. | −3.44179 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13086.0 | −0.446207 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16122.0 | 0.547999 | 0.273999 | − | 0.961730i | \(-0.411653\pi\) | ||||
0.273999 | + | 0.961730i | \(0.411653\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34608.0 | 1.16898 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45560.0 | 1.53411 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6687.00 | −0.224464 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3996.00 | 0.133717 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19188.0 | −0.638102 | −0.319051 | − | 0.947738i | \(-0.603364\pi\) | ||||
−0.319051 | + | 0.947738i | \(0.603364\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1272.00 | 0.0421698 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38464.0 | −1.27123 | −0.635617 | − | 0.772004i | \(-0.719254\pi\) | ||||
−0.635617 | + | 0.772004i | \(0.719254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36240.0 | −1.19404 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43930.0 | 1.43853 | 0.719266 | − | 0.694735i | \(-0.244478\pi\) | ||||
0.719266 | + | 0.694735i | \(0.244478\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3696.00 | −0.120659 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 558.000 | 0.0181606 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17328.0 | −0.562235 | −0.281118 | − | 0.959673i | \(-0.590705\pi\) | ||||
−0.281118 | + | 0.959673i | \(0.590705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2400.00 | 0.0773990 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56032.0 | 1.80153 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18160.0 | −0.582110 | −0.291055 | − | 0.956706i | \(-0.594006\pi\) | ||||
−0.291055 | + | 0.956706i | \(0.594006\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23940.0 | 0.765068 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9102.00 | 0.289131 | 0.144565 | − | 0.989495i | \(-0.453822\pi\) | ||||
0.144565 | + | 0.989495i | \(0.453822\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7614.00 | −0.241137 |
(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 | 600.4.a.i.1.1 | 1 | ||
3.2 | odd | 2 | 1800.4.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 1200.4.a.p.1.1 | 1 | |||
5.2 | odd | 4 | 600.4.f.a.49.1 | 2 | |||
5.3 | odd | 4 | 600.4.f.a.49.2 | 2 | |||
5.4 | even | 2 | 120.4.a.b.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 1800.4.f.v.649.1 | 2 | |||
15.8 | even | 4 | 1800.4.f.v.649.2 | 2 | |||
15.14 | odd | 2 | 360.4.a.n.1.1 | 1 | |||
20.3 | even | 4 | 1200.4.f.t.49.1 | 2 | |||
20.7 | even | 4 | 1200.4.f.t.49.2 | 2 | |||
20.19 | odd | 2 | 240.4.a.g.1.1 | 1 | |||
40.19 | odd | 2 | 960.4.a.k.1.1 | 1 | |||
40.29 | even | 2 | 960.4.a.bj.1.1 | 1 | |||
60.59 | even | 2 | 720.4.a.q.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.a.b.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
240.4.a.g.1.1 | 1 | 20.19 | odd | 2 | |||
360.4.a.n.1.1 | 1 | 15.14 | odd | 2 | |||
600.4.a.i.1.1 | 1 | 1.1 | even | 1 | trivial | ||
600.4.f.a.49.1 | 2 | 5.2 | odd | 4 | |||
600.4.f.a.49.2 | 2 | 5.3 | odd | 4 | |||
720.4.a.q.1.1 | 1 | 60.59 | even | 2 | |||
960.4.a.k.1.1 | 1 | 40.19 | odd | 2 | |||
960.4.a.bj.1.1 | 1 | 40.29 | even | 2 | |||
1200.4.a.p.1.1 | 1 | 4.3 | odd | 2 | |||
1200.4.f.t.49.1 | 2 | 20.3 | even | 4 | |||
1200.4.f.t.49.2 | 2 | 20.7 | even | 4 | |||
1800.4.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
1800.4.f.v.649.1 | 2 | 15.2 | even | 4 | |||
1800.4.f.v.649.2 | 2 | 15.8 | even | 4 |