Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 200x^{3} - 99x^{2} + 5803x - 3615 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(13.2682\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −27.5365 | −1.76647 | −0.883233 | − | 0.468935i | \(-0.844638\pi\) | ||||
−0.883233 | + | 0.468935i | \(0.844638\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −79.9429 | −1.43006 | −0.715031 | − | 0.699093i | \(-0.753587\pi\) | ||||
−0.715031 | + | 0.699093i | \(0.753587\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 515.257 | 2.12040 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −455.152 | −1.13416 | −0.567080 | − | 0.823663i | \(-0.691927\pi\) | ||||
−0.567080 | + | 0.823663i | \(0.691927\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −581.059 | −0.953591 | −0.476795 | − | 0.879014i | \(-0.658202\pi\) | ||||
−0.476795 | + | 0.879014i | \(0.658202\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2201.35 | 2.52615 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2375.39 | −1.99348 | −0.996742 | − | 0.0806600i | \(-0.974297\pi\) | ||||
−0.996742 | + | 0.0806600i | \(0.974297\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 732.193 | 0.465309 | 0.232654 | − | 0.972559i | \(-0.425259\pi\) | ||||
0.232654 | + | 0.972559i | \(0.425259\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 593.164 | 0.233806 | 0.116903 | − | 0.993143i | \(-0.462703\pi\) | ||||
0.116903 | + | 0.993143i | \(0.462703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3265.86 | 1.04508 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7497.01 | −1.97915 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −930.360 | −0.205426 | −0.102713 | − | 0.994711i | \(-0.532752\pi\) | ||||
−0.102713 | + | 0.994711i | \(0.532752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 624.232 | 0.116665 | 0.0583327 | − | 0.998297i | \(-0.481422\pi\) | ||||
0.0583327 | + | 0.998297i | \(0.481422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12533.3 | 2.00346 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4077.82 | −0.489693 | −0.244847 | − | 0.969562i | \(-0.578738\pi\) | ||||
−0.244847 | + | 0.969562i | \(0.578738\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16000.3 | 1.68449 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6674.36 | 0.620083 | 0.310042 | − | 0.950723i | \(-0.399657\pi\) | ||||
0.310042 | + | 0.950723i | \(0.399657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8956.88 | 0.738730 | 0.369365 | − | 0.929284i | \(-0.379575\pi\) | ||||
0.369365 | + | 0.929284i | \(0.379575\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −41191.2 | −3.03230 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10280.9 | 0.678873 | 0.339436 | − | 0.940629i | \(-0.389764\pi\) | ||||
0.339436 | + | 0.940629i | \(0.389764\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 65409.9 | 3.52142 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13843.9 | 0.676970 | 0.338485 | − | 0.940972i | \(-0.390086\pi\) | ||||
0.338485 | + | 0.940972i | \(0.390086\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 36386.1 | 1.62192 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −20162.0 | −0.821952 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10723.2 | 0.401045 | 0.200522 | − | 0.979689i | \(-0.435736\pi\) | ||||
0.200522 | + | 0.979689i | \(0.435736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22151.0 | −0.762199 | −0.381099 | − | 0.924534i | \(-0.624454\pi\) | ||||
−0.381099 | + | 0.924534i | \(0.624454\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 46451.5 | 1.36369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20042.4 | 0.545460 | 0.272730 | − | 0.962091i | \(-0.412073\pi\) | ||||
0.272730 | + | 0.962091i | \(0.412073\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16333.6 | −0.413010 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 35780.7 | 0.842370 | 0.421185 | − | 0.906975i | \(-0.361614\pi\) | ||||
0.421185 | + | 0.906975i | \(0.361614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55858.6 | 1.22683 | 0.613413 | − | 0.789763i | \(-0.289796\pi\) | ||||
0.613413 | + | 0.789763i | \(0.289796\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −89930.4 | −1.84609 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 55116.7 | 0.993608 | 0.496804 | − | 0.867863i | \(-0.334507\pi\) | ||||
0.496804 | + | 0.867863i | \(0.334507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81233.6 | 1.37570 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 87650.6 | 1.39656 | 0.698280 | − | 0.715825i | \(-0.253949\pi\) | ||||
0.698280 | + | 0.715825i | \(0.253949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 189896. | 2.85080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 25618.8 | 0.362878 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −75763.0 | −1.01387 | −0.506935 | − | 0.861985i | \(-0.669221\pi\) | ||||
−0.506935 | + | 0.861985i | \(0.669221\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17189.2 | −0.206085 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −58533.6 | −0.665420 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 32072.1 | 0.346097 | 0.173048 | − | 0.984913i | \(-0.444638\pi\) | ||||
0.173048 | + | 0.984913i | \(0.444638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −234520. | −2.40487 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −187860. | −1.83245 | −0.916223 | − | 0.400669i | \(-0.868778\pi\) | ||||
−0.916223 | + | 0.400669i | \(0.868778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 160995. | 1.49527 | 0.747633 | − | 0.664112i | \(-0.231190\pi\) | ||||
0.747633 | + | 0.664112i | \(0.231190\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −153336. | −1.29475 | −0.647375 | − | 0.762172i | \(-0.724133\pi\) | ||||
−0.647375 | + | 0.762172i | \(0.724133\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −42063.0 | −0.339105 | −0.169552 | − | 0.985521i | \(-0.554232\pi\) | ||||
−0.169552 | + | 0.985521i | \(0.554232\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 112289. | 0.865026 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 92809.7 | 0.683750 | 0.341875 | − | 0.939745i | \(-0.388938\pi\) | ||||
0.341875 | + | 0.939745i | \(0.388938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −47419.2 | −0.334357 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −299395. | −2.02199 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 46112.2 | 0.286320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −183788. | −1.09536 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11261.1 | −0.0644622 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 59778.1 | 0.328877 | 0.164438 | − | 0.986387i | \(-0.447419\pi\) | ||||
0.164438 | + | 0.986387i | \(0.447419\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −246641. | −1.30494 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −261722. | −1.33249 | −0.666243 | − | 0.745735i | \(-0.732099\pi\) | ||||
−0.666243 | + | 0.745735i | \(0.732099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 599332. | 2.83031 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 51875.5 | 0.236135 | 0.118068 | − | 0.993006i | \(-0.462330\pi\) | ||||
0.118068 | + | 0.993006i | \(0.462330\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −299390. | −1.31432 | −0.657159 | − | 0.753752i | \(-0.728242\pi\) | ||||
−0.657159 | + | 0.753752i | \(0.728242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −283101. | −1.19920 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 264470. | 1.08152 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 74375.6 | 0.293772 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −281682. | −1.03943 | −0.519713 | − | 0.854341i | \(-0.673961\pi\) | ||||
−0.519713 | + | 0.854341i | \(0.673961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −222399. | −0.793761 | −0.396881 | − | 0.917870i | \(-0.629907\pi\) | ||||
−0.396881 | + | 0.917870i | \(0.629907\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.22394e6 | −4.22698 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −49902.9 | −0.166839 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −59674.9 | −0.193216 | −0.0966078 | − | 0.995323i | \(-0.530799\pi\) | ||||
−0.0966078 | + | 0.995323i | \(0.530799\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −381213. | −1.19584 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 378987. | 1.11726 | 0.558631 | − | 0.829416i | \(-0.311327\pi\) | ||||
0.558631 | + | 0.829416i | \(0.311327\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.00195e6 | −2.86507 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 143609. | 0.398465 | 0.199233 | − | 0.979952i | \(-0.436155\pi\) | ||||
0.199233 | + | 0.979952i | \(0.436155\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −33663.2 | −0.0906648 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 377268. | 0.986641 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 774133. | 1.96653 | 0.983265 | − | 0.182181i | \(-0.0583156\pi\) | ||||
0.983265 | + | 0.182181i | \(0.0583156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −295278. | −0.708432 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −466552. | −1.08835 | −0.544173 | − | 0.838973i | \(-0.683157\pi\) | ||||
−0.544173 | + | 0.838973i | \(0.683157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 575239. | 1.30512 | 0.652562 | − | 0.757736i | \(-0.273694\pi\) | ||||
0.652562 | + | 0.757736i | \(0.273694\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 609960. | 1.34640 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 325993. | 0.700292 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.08116e6 | 2.26093 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −280046. | −0.555451 | −0.277726 | − | 0.960660i | \(-0.589581\pi\) | ||||
−0.277726 | + | 0.960660i | \(0.589581\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 28761.8 | 0.0555805 | 0.0277902 | − | 0.999614i | \(-0.491153\pi\) | ||||
0.0277902 | + | 0.999614i | \(0.491153\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.27911e6 | −2.40892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −174264. | −0.319921 | −0.159960 | − | 0.987123i | \(-0.551137\pi\) | ||||
−0.159960 | + | 0.987123i | \(0.551137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 654406. | 1.17143 | 0.585713 | − | 0.810519i | \(-0.300815\pi\) | ||||
0.585713 | + | 0.810519i | \(0.300815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −551898. | −0.963537 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −533568. | −0.886757 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 305632. | 0.495762 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −333259. | −0.527735 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 610071. | 0.943354 | 0.471677 | − | 0.881771i | \(-0.343649\pi\) | ||||
0.471677 | + | 0.881771i | \(0.343649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −985274. | −1.48802 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −716039. | −1.05643 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.53815e6 | −2.16714 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.38024e6 | 1.90097 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −862752. | −1.16178 | −0.580890 | − | 0.813982i | \(-0.697295\pi\) | ||||
−0.580890 | + | 0.813982i | \(0.697295\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.68276e6 | 2.21598 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26778.5 | 0.0344923 | 0.0172461 | − | 0.999851i | \(-0.494510\pi\) | ||||
0.0172461 | + | 0.999851i | \(0.494510\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −812554. | −1.02391 | −0.511957 | − | 0.859011i | \(-0.671079\pi\) | ||||
−0.511957 | + | 0.859011i | \(0.671079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.25004e6 | 1.50846 | 0.754228 | − | 0.656612i | \(-0.228011\pi\) | ||||
0.754228 | + | 0.656612i | \(0.228011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −821888. | −0.970830 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.51772e6 | −1.75517 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.59397e6 | −1.80504 | −0.902518 | − | 0.430653i | \(-0.858283\pi\) | ||||
−0.902518 | + | 0.430653i | \(0.858283\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.57916e6 | 1.75139 | 0.875696 | − | 0.482864i | \(-0.160403\pi\) | ||||
0.875696 | + | 0.482864i | \(0.160403\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −415115. | −0.450975 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −425447. | −0.443714 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.41359e6 | −2.46697 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.47838e6 | −1.48116 | −0.740581 | − | 0.671967i | \(-0.765450\pi\) | ||||
−0.740581 | + | 0.671967i | \(0.765450\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −269980. | −0.265173 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.22905e6 | −5.03585 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.04962e6 | −0.991286 | −0.495643 | − | 0.868526i | \(-0.665067\pi\) | ||||
−0.495643 | + | 0.868526i | \(0.665067\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −479375. | −0.435586 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −159846. | −0.142499 | −0.0712497 | − | 0.997459i | \(-0.522699\pi\) | ||||
−0.0712497 | + | 0.997459i | \(0.522699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.10672e6 | −0.968109 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.08624e6 | 1.79096 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 226510. | 0.190856 | 0.0954280 | − | 0.995436i | \(-0.469578\pi\) | ||||
0.0954280 | + | 0.995436i | \(0.469578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.50643e6 | −1.24602 | −0.623011 | − | 0.782213i | \(-0.714091\pi\) | ||||
−0.623011 | + | 0.782213i | \(0.714091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.48646e6 | −1.18528 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.91164e6 | −1.49695 | −0.748474 | − | 0.663164i | \(-0.769213\pi\) | ||||
−0.748474 | + | 0.663164i | \(0.769213\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 321640. | 0.247377 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.17933e6 | 0.890987 | 0.445493 | − | 0.895285i | \(-0.353028\pi\) | ||||
0.445493 | + | 0.895285i | \(0.353028\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 353544. | 0.262408 | 0.131204 | − | 0.991355i | \(-0.458116\pi\) | ||||
0.131204 | + | 0.991355i | \(0.458116\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.61181e6 | 1.17544 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.22262e6 | 2.97398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −883151. | −0.611368 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 61933.0 | 0.0421457 | 0.0210728 | − | 0.999778i | \(-0.493292\pi\) | ||||
0.0210728 | + | 0.999778i | \(0.493292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −857240. | −0.573519 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.41228e6 | 2.24467 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −344663. | −0.222955 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.17301e6 | 3.23695 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.77081e6 | 1.08999 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.90020e6 | 1.15068 | 0.575338 | − | 0.817915i | \(-0.304870\pi\) | ||||
0.575338 | + | 0.817915i | \(0.304870\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.43323e6 | −2.64134 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.63063e6 | 1.54226 | 0.771131 | − | 0.636676i | \(-0.219691\pi\) | ||||
0.771131 | + | 0.636676i | \(0.219691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.76044e6 | −1.59264 | −0.796319 | − | 0.604877i | \(-0.793222\pi\) | ||||
−0.796319 | + | 0.604877i | \(0.793222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 621404. | 0.347317 | 0.173658 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173658 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 423455. | 0.232986 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.22234e6 | 2.28713 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.73924e6 | −0.927586 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.89766e6 | −0.996575 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.15827e6 | 0.599017 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 878316. | 0.440637 | 0.220318 | − | 0.975428i | \(-0.429290\pi\) | ||||
0.220318 | + | 0.975428i | \(0.429290\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.10113e6 | −1.03835 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.60225e6 | −0.780042 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.72499e6 | 0.827392 | 0.413696 | − | 0.910415i | \(-0.364238\pi\) | ||||
0.413696 | + | 0.910415i | \(0.364238\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.55565e6 | −1.20782 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −284121. | −0.132317 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.30576e6 | 0.590629 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 925574. | 0.412655 | 0.206328 | − | 0.978483i | \(-0.433849\pi\) | ||||
0.206328 | + | 0.978483i | \(0.433849\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.27452e6 | 1.43908 | 0.719539 | − | 0.694452i | \(-0.244353\pi\) | ||||
0.719539 | + | 0.694452i | \(0.244353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.35621e6 | 1.88730 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.90831e6 | −0.815103 | −0.407551 | − | 0.913182i | \(-0.633617\pi\) | ||||
−0.407551 | + | 0.913182i | \(0.633617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.86041e6 | −1.20464 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.44900e6 | −0.593379 | −0.296690 | − | 0.954974i | \(-0.595883\pi\) | ||||
−0.296690 | + | 0.954974i | \(0.595883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.93999e6 | −0.783488 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.26977e6 | −0.505775 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.46550e6 | −1.75444 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.87979e6 | 0.728524 | 0.364262 | − | 0.931296i | \(-0.381321\pi\) | ||||
0.364262 | + | 0.931296i | \(0.381321\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.43901e6 | 1.31482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.50861e6 | 1.67792 | 0.838959 | − | 0.544194i | \(-0.183165\pi\) | ||||
0.838959 | + | 0.544194i | \(0.183165\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 310091. | 0.113870 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 540594. | 0.195893 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.33971e6 | 0.836688 | 0.418344 | − | 0.908289i | \(-0.362611\pi\) | ||||
0.418344 | + | 0.908289i | \(0.362611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.64608e6 | −0.580949 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.71181e6 | −0.596293 | −0.298146 | − | 0.954520i | \(-0.596368\pi\) | ||||
−0.298146 | + | 0.954520i | \(0.596368\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.61510e6 | 1.56640 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.07773e6 | 0.361108 | 0.180554 | − | 0.983565i | \(-0.442211\pi\) | ||||
0.180554 | + | 0.983565i | \(0.442211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.40900e6 | −0.466088 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.20691e6 | 2.35379 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.40619e6 | −1.42092 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −288083. | −0.0917363 | −0.0458682 | − | 0.998948i | \(-0.514605\pi\) | ||||
−0.0458682 | + | 0.998948i | \(0.514605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.46431e6 | −1.69697 | −0.848485 | − | 0.529220i | \(-0.822485\pi\) | ||||
−0.848485 | + | 0.529220i | \(0.822485\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −362716. | −0.111251 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.49405e6 | −1.96733 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.85603e6 | 0.555391 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.45675e6 | −0.726195 | −0.363098 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363098 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.42847e6 | −0.417125 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.00704e6 | −1.99717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.24414e6 | 2.32170 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −267685. | −0.0744884 | −0.0372442 | − | 0.999306i | \(-0.511858\pi\) | ||||
−0.0372442 | + | 0.999306i | \(0.511858\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.11613e6 | −0.306908 | −0.153454 | − | 0.988156i | \(-0.549040\pi\) | ||||
−0.153454 | + | 0.988156i | \(0.549040\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.29733e6 | 1.43948 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.75770e6 | −2.08334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.28257e6 | −1.91048 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.56045e6 | −0.404629 | −0.202314 | − | 0.979321i | \(-0.564846\pi\) | ||||
−0.202314 | + | 0.979321i | \(0.564846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.91249e6 | −0.746525 | −0.373263 | − | 0.927726i | \(-0.621761\pi\) | ||||
−0.373263 | + | 0.927726i | \(0.621761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.04804e6 | −0.518938 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 434310. | 0.108792 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.10541e6 | 0.273754 | 0.136877 | − | 0.990588i | \(-0.456293\pi\) | ||||
0.136877 | + | 0.990588i | \(0.456293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.78806e6 | −0.432885 | −0.216443 | − | 0.976295i | \(-0.569445\pi\) | ||||
−0.216443 | + | 0.976295i | \(0.569445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.05671e6 | 1.44990 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.75654e6 | 1.83611 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.24314e6 | −0.993279 | −0.496639 | − | 0.867957i | \(-0.665433\pi\) | ||||
−0.496639 | + | 0.867957i | \(0.665433\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.03785e6 | −0.703274 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.12408e6 | 1.40215 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.65975e6 | 0.371750 | 0.185875 | − | 0.982573i | \(-0.440488\pi\) | ||||
0.185875 | + | 0.982573i | \(0.440488\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.78083e7 | 3.94540 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.34155e6 | 1.82808 | 0.914038 | − | 0.405628i | \(-0.132947\pi\) | ||||
0.914038 | + | 0.405628i | \(0.132947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −487990. | −0.105793 | −0.0528967 | − | 0.998600i | \(-0.516845\pi\) | ||||
−0.0528967 | + | 0.998600i | \(0.516845\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.37415e6 | 0.294715 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.98913e6 | 1.27078 | 0.635392 | − | 0.772190i | \(-0.280839\pi\) | ||||
0.635392 | + | 0.772190i | \(0.280839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.64324e6 | 0.341309 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.07674e6 | −0.837838 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.39124e6 | 0.486283 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.13318e6 | 1.43545 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.97080e6 | 0.790751 | 0.395375 | − | 0.918520i | \(-0.370615\pi\) | ||||
0.395375 | + | 0.918520i | \(0.370615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.36946e6 | 0.466967 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.56393e6 | −0.494940 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.63822e6 | −1.45938 | −0.729692 | − | 0.683775i | \(-0.760337\pi\) | ||||
−0.729692 | + | 0.683775i | \(0.760337\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.04360e7 | −1.97361 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.30768e6 | −1.55516 | −0.777581 | − | 0.628782i | \(-0.783554\pi\) | ||||
−0.777581 | + | 0.628782i | \(0.783554\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.20997e6 | 0.409514 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.87482e7 | 3.43912 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.70382e6 | 1.02545 | 0.512725 | − | 0.858553i | \(-0.328636\pi\) | ||||
0.512725 | + | 0.858553i | \(0.328636\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.95448e6 | −0.703875 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −58117.5 | −0.0102421 | −0.00512103 | − | 0.999987i | \(-0.501630\pi\) | ||||
−0.00512103 | + | 0.999987i | \(0.501630\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.50181e7 | 2.62051 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 926966. | 0.160156 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.76812e6 | 0.302494 | 0.151247 | − | 0.988496i | \(-0.451671\pi\) | ||||
0.151247 | + | 0.988496i | \(0.451671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.48925e6 | −0.920916 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.28704e7 | −2.13832 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.67939e6 | −0.769950 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.13169e7 | −3.47381 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.94082e6 | 1.28165 | 0.640827 | − | 0.767685i | \(-0.278592\pi\) | ||||
0.640827 | + | 0.767685i | \(0.278592\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.76839e6 | −1.24187 | −0.620936 | − | 0.783862i | \(-0.713247\pi\) | ||||
−0.620936 | + | 0.783862i | \(0.713247\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.48280e6 | −0.232571 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.08450e6 | −0.945335 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.52519e6 | 0.850376 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.87820e6 | −0.591306 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.22581e7 | 1.85157 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.28472e7 | 1.92253 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.88500e6 | −0.717582 | −0.358791 | − | 0.933418i | \(-0.616811\pi\) | ||||
−0.358791 | + | 0.933418i | \(0.616811\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.58400e7 | −2.30546 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.36264e6 | 0.484941 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.12743e6 | 1.16141 | 0.580704 | − | 0.814115i | \(-0.302777\pi\) | ||||
0.580704 | + | 0.814115i | \(0.302777\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.14135e7 | −1.61617 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −681202. | −0.0955866 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.97670e6 | −1.23704 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.09229e6 | −0.832037 | −0.416018 | − | 0.909356i | \(-0.636575\pi\) | ||||
−0.416018 | + | 0.909356i | \(0.636575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.20448e6 | −0.704446 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.97714e7 | −3.99386 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.34382e6 | 0.444602 | 0.222301 | − | 0.974978i | \(-0.428643\pi\) | ||||
0.222301 | + | 0.974978i | \(0.428643\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.41948e6 | −0.977805 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.93388e6 | 1.02732 | 0.513659 | − | 0.857994i | \(-0.328290\pi\) | ||||
0.513659 | + | 0.857994i | \(0.328290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.99862e6 | 0.769948 | 0.384974 | − | 0.922928i | \(-0.374210\pi\) | ||||
0.384974 | + | 0.922928i | \(0.374210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.71148e6 | 0.981185 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.93719e6 | 0.244345 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.42929e6 | 0.428810 | 0.214405 | − | 0.976745i | \(-0.431219\pi\) | ||||
0.214405 | + | 0.976745i | \(0.431219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −791997. | −0.0981810 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.30108e6 | −0.767792 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.39345e7 | 2.89158 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.04291e6 | −0.484282 | −0.242141 | − | 0.970241i | \(-0.577850\pi\) | ||||
−0.242141 | + | 0.970241i | \(0.577850\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 457058. | 0.0542855 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.79862e6 | 0.565129 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.46937e6 | −0.171591 | −0.0857956 | − | 0.996313i | \(-0.527343\pi\) | ||||
−0.0857956 | + | 0.996313i | \(0.527343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.80200e7 | −2.06928 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.35233e6 | 1.06501 | 0.532504 | − | 0.846427i | \(-0.321251\pi\) | ||||
0.532504 | + | 0.846427i | \(0.321251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.19824e6 | −0.474112 | −0.237056 | − | 0.971496i | \(-0.576182\pi\) | ||||
−0.237056 | + | 0.971496i | \(0.576182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.03270e7 | 1.15659 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.68634e6 | −0.409456 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.21401e7 | 1.33737 | 0.668683 | − | 0.743548i | \(-0.266859\pi\) | ||||
0.668683 | + | 0.743548i | \(0.266859\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.97384e6 | −0.647367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.99084e6 | 0.751412 | 0.375706 | − | 0.926739i | \(-0.377400\pi\) | ||||
0.375706 | + | 0.926739i | \(0.377400\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.46926e7 | 1.56643 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.72855e6 | −1.02881 | −0.514405 | − | 0.857547i | \(-0.671987\pi\) | ||||
−0.514405 | + | 0.857547i | \(0.671987\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.66808e6 | 0.909277 | 0.454639 | − | 0.890676i | \(-0.349768\pi\) | ||||
0.454639 | + | 0.890676i | \(0.349768\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.44695e6 | −0.462736 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.30558e6 | −0.952892 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.17677e6 | 0.932226 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.68642e6 | 0.976195 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.83557e6 | −0.483476 | −0.241738 | − | 0.970342i | \(-0.577717\pi\) | ||||
−0.241738 | + | 0.970342i | \(0.577717\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.67992e7 | −1.66640 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.77884e6 | −0.470314 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.84363e7 | 1.78616 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.78219e7 | −1.71320 | −0.856601 | − | 0.515980i | \(-0.827428\pi\) | ||||
−0.856601 | + | 0.515980i | \(0.827428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.58095e7 | 1.50796 | 0.753980 | − | 0.656897i | \(-0.228132\pi\) | ||||
0.753980 | + | 0.656897i | \(0.228132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.97172e7 | 1.86615 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −786375. | −0.0738532 | −0.0369266 | − | 0.999318i | \(-0.511757\pi\) | ||||
−0.0369266 | + | 0.999318i | \(0.511757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.88067e6 | −0.454849 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.18512e6 | 0.108762 | 0.0543812 | − | 0.998520i | \(-0.482681\pi\) | ||||
0.0543812 | + | 0.998520i | \(0.482681\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.09228e7 | 1.90554 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.87815e7 | 2.60136 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.81475e6 | 0.252479 | 0.126240 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126240 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 295576. | 0.0263127 | 0.0131564 | − | 0.999913i | \(-0.495812\pi\) | ||||
0.0131564 | + | 0.999913i | \(0.495812\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.80070e7 | −3.35799 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −551856. | −0.0480298 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.37571e7 | 2.05224 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.00821e7 | 0.864456 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.29325e6 | −0.280277 | −0.140138 | − | 0.990132i | \(-0.544755\pi\) | ||||
−0.140138 | + | 0.990132i | \(0.544755\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.44842e7 | −2.06836 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.49842e7 | 1.25650 | 0.628248 | − | 0.778013i | \(-0.283772\pi\) | ||||
0.628248 | + | 0.778013i | \(0.283772\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −737385. | −0.0609294 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.74204e6 | −0.224917 | −0.112458 | − | 0.993656i | \(-0.535872\pi\) | ||||
−0.112458 | + | 0.993656i | \(0.535872\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.14708e6 | −0.337688 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.23749e7 | 1.80871 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.04413e6 | −0.645552 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.95290e7 | 1.55591 | 0.777955 | − | 0.628321i | \(-0.216257\pi\) | ||||
0.777955 | + | 0.628321i | \(0.216257\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.39341e7 | 1.87955 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.58542e7 | −1.23613 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.44216e7 | −2.66464 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.97976e6 | 0.613331 | 0.306665 | − | 0.951817i | \(-0.400787\pi\) | ||||
0.306665 | + | 0.951817i | \(0.400787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.98575e6 | −0.227859 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.26319e7 | 1.71494 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.20987e6 | 0.613368 | 0.306684 | − | 0.951811i | \(-0.400781\pi\) | ||||
0.306684 | + | 0.951811i | \(0.400781\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.83993e7 | 2.10685 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 370272. | 0.0272770 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.11425e7 | −1.54665 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.38924e7 | 3.18853 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.88944e6 | −0.713427 | −0.356714 | − | 0.934214i | \(-0.616103\pi\) | ||||
−0.356714 | + | 0.934214i | \(0.616103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.34845e7 | −3.09377 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.03843e6 | −0.214686 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.40610e7 | 0.986691 | 0.493345 | − | 0.869834i | \(-0.335774\pi\) | ||||
0.493345 | + | 0.869834i | \(0.335774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.30898e6 | −0.579067 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.12761e7 | −1.47265 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.26419e7 | −1.55651 | −0.778257 | − | 0.627946i | \(-0.783896\pi\) | ||||
−0.778257 | + | 0.627946i | \(0.783896\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.12234e6 | −0.618640 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.94357e7 | −1.30915 | −0.654576 | − | 0.755996i | \(-0.727153\pi\) | ||||
−0.654576 | + | 0.755996i | \(0.727153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.17153e7 | 0.783806 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.54899e6 | −0.435214 | −0.217607 | − | 0.976037i | \(-0.569825\pi\) | ||||
−0.217607 | + | 0.976037i | \(0.569825\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.25185e7 | 1.48644 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.51626e7 | 2.96127 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.01572e7 | 0.657163 | 0.328582 | − | 0.944476i | \(-0.393429\pi\) | ||||
0.328582 | + | 0.944476i | \(0.393429\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.07094e7 | 2.61642 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.77792e7 | 1.13513 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.02731e6 | −0.509132 | −0.254566 | − | 0.967055i | \(-0.581933\pi\) | ||||
−0.254566 | + | 0.967055i | \(0.581933\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.43429e6 | 0.468419 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.31336e6 | −0.332589 | −0.166294 | − | 0.986076i | \(-0.553180\pi\) | ||||
−0.166294 | + | 0.986076i | \(0.553180\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.78451e7 | 6.04485 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.23079e6 | −0.382433 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.32376e6 | −0.385620 | −0.192810 | − | 0.981236i | \(-0.561760\pi\) | ||||
−0.192810 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.89028e7 | 1.75107 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.03024e6 | 0.182402 | 0.0912009 | − | 0.995833i | \(-0.470929\pi\) | ||||
0.0912009 | + | 0.995833i | \(0.470929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.03866e6 | 0.121924 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.88692e6 | 0.288530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.62856e7 | −0.955383 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.97491e6 | 0.406569 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.77058e6 | 0.276310 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.44622e6 | 0.140786 | 0.0703930 | − | 0.997519i | \(-0.477575\pi\) | ||||
0.0703930 | + | 0.997519i | \(0.477575\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.40160e6 | 0.251720 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.28710e7 | 0.726826 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.04752e7 | 1.71013 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.16846e6 | −0.343978 | −0.171989 | − | 0.985099i | \(-0.555019\pi\) | ||||
−0.171989 | + | 0.985099i | \(0.555019\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.44212e7 | −1.35332 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.90374e7 | −2.14981 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.54241e7 | −1.39142 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.23727e6 | −0.337140 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.08989e7 | 1.65986 | 0.829930 | − | 0.557868i | \(-0.188380\pi\) | ||||
0.829930 | + | 0.557868i | \(0.188380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.16479e6 | 0.435906 | 0.217953 | − | 0.975959i | \(-0.430062\pi\) | ||||
0.217953 | + | 0.975959i | \(0.430062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.14817e7 | 2.20105 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.02973e7 | −1.59775 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.55816e6 | 0.343737 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.77929e7 | 0.921272 | 0.460636 | − | 0.887589i | \(-0.347621\pi\) | ||||
0.460636 | + | 0.887589i | \(0.347621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.09125e7 | −1.07623 | −0.538116 | − | 0.842871i | \(-0.680864\pi\) | ||||
−0.538116 | + | 0.842871i | \(0.680864\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.09320e7 | 2.09376 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.17379e7 | 1.10523 | 0.552617 | − | 0.833435i | \(-0.313629\pi\) | ||||
0.552617 | + | 0.833435i | \(0.313629\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.51536e7 | 1.77657 | 0.888287 | − | 0.459288i | \(-0.151895\pi\) | ||||
0.888287 | + | 0.459288i | \(0.151895\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.26398e7 | 2.64431 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.14805e7 | −0.569830 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.67988e6 | −0.230898 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.68616e6 | −0.426013 | −0.213007 | − | 0.977051i | \(-0.568326\pi\) | ||||
−0.213007 | + | 0.977051i | \(0.568326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.96456e7 | −0.957800 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.24747e7 | −1.57390 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.69113e6 | 0.129656 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.73536e6 | −0.463535 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.41882e6 | −0.114493 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 125857. | 0.00592247 | 0.00296124 | − | 0.999996i | \(-0.499057\pi\) | ||||
0.00296124 | + | 0.999996i | \(0.499057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.01599e7 | −1.41096 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.49143e7 | −0.693669 | −0.346834 | − | 0.937926i | \(-0.612743\pi\) | ||||
−0.346834 | + | 0.937926i | \(0.612743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.06866e7 | −1.88134 | −0.940672 | − | 0.339317i | \(-0.889804\pi\) | ||||
−0.940672 | + | 0.339317i | \(0.889804\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.14409e7 | 1.43704 | 0.718518 | − | 0.695508i | \(-0.244821\pi\) | ||||
0.718518 | + | 0.695508i | \(0.244821\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.18865e7 | −2.81226 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.16276e8 | −5.25343 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.50864e7 | −1.12691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.16458e7 | −0.520146 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.65254e7 | 0.733864 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.71647e7 | −1.19263 | −0.596315 | − | 0.802751i | \(-0.703369\pi\) | ||||
−0.596315 | + | 0.802751i | \(0.703369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.70542e6 | −0.0744489 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.03892e6 | 0.0450966 | 0.0225483 | − | 0.999746i | \(-0.492822\pi\) | ||||
0.0225483 | + | 0.999746i | \(0.492822\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.29747e7 | −0.991625 | −0.495812 | − | 0.868430i | \(-0.665130\pi\) | ||||
−0.495812 | + | 0.868430i | \(0.665130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.36054e7 | 1.01310 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.42677e7 | −1.46243 | −0.731217 | − | 0.682145i | \(-0.761047\pi\) | ||||
−0.731217 | + | 0.682145i | \(0.761047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.69736e7 | −1.56026 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.52763e6 | 0.315885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.72975e7 | 1.55640 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.49081e6 | 0.393842 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −580761. | −0.0239661 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.28847e7 | −1.34953 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.59862e7 | −1.86641 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.29823e7 | 1.33126 | 0.665630 | − | 0.746282i | \(-0.268163\pi\) | ||||
0.665630 | + | 0.746282i | \(0.268163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.67963e7 | −3.88552 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.04563e7 | 0.417429 | 0.208714 | − | 0.977977i | \(-0.433072\pi\) | ||||
0.208714 | + | 0.977977i | \(0.433072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.98943e7 | −1.58392 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.87619e7 | −1.92543 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.06514e6 | −0.236893 | −0.118446 | − | 0.992960i | \(-0.537791\pi\) | ||||
−0.118446 | + | 0.992960i | \(0.537791\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.23248e7 | −2.03263 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.07907e7 | −0.803276 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.33176e7 | −0.511767 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.29537e7 | 3.17056 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.43259e7 | −1.30492 | −0.652459 | − | 0.757824i | \(-0.726263\pi\) | ||||
−0.652459 | + | 0.757824i | \(0.726263\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.24382e7 | −2.72435 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.64313e7 | −3.23327 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.21642e7 | −0.452621 | −0.226310 | − | 0.974055i | \(-0.572666\pi\) | ||||
−0.226310 | + | 0.974055i | \(0.572666\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.60127e7 | 2.81334 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.28376e7 | −0.840770 | −0.420385 | − | 0.907346i | \(-0.638105\pi\) | ||||
−0.420385 | + | 0.907346i | \(0.638105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.95899e6 | 0.144979 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.84801e7 | −0.669623 | −0.334811 | − | 0.942285i | \(-0.608673\pi\) | ||||
−0.334811 | + | 0.942285i | \(0.608673\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.24571e7 | −1.16989 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.71113e7 | −0.613523 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.03848e7 | −0.370394 | −0.185197 | − | 0.982701i | \(-0.559292\pi\) | ||||
−0.185197 | + | 0.982701i | \(0.559292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.23877e7 | 0.794329 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.16605e7 | −0.411562 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.82395e7 | −0.986389 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.90077e7 | −2.74539 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.29930e6 | −0.0794835 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.47893e7 | 1.88421 | 0.942105 | − | 0.335318i | \(-0.108844\pi\) | ||||
0.942105 | + | 0.335318i | \(0.108844\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.78926e7 | 1.63855 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.66991e7 | 0.568387 | 0.284194 | − | 0.958767i | \(-0.408274\pi\) | ||||
0.284194 | + | 0.958767i | \(0.408274\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.22549e7 | 1.76042 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.99527e7 | −1.00392 | −0.501961 | − | 0.864890i | \(-0.667388\pi\) | ||||
−0.501961 | + | 0.864890i | \(0.667388\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.44836e7 | 1.14989 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.16733e7 | −0.719038 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.42575e7 | 1.79092 | 0.895460 | − | 0.445141i | \(-0.146847\pi\) | ||||
0.895460 | + | 0.445141i | \(0.146847\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.39312e7 | 0.457506 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.31290e6 | 0.172719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.93896e7 | 1.92099 | 0.960497 | − | 0.278290i | \(-0.0897677\pi\) | ||||
0.960497 | + | 0.278290i | \(0.0897677\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.41857e7 | −0.778370 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.23151e7 | −1.67521 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.67971e7 | −0.853786 | −0.426893 | − | 0.904302i | \(-0.640392\pi\) | ||||
−0.426893 | + | 0.904302i | \(0.640392\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.05715e7 | 0.969176 |
(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 | 784.6.a.bk.1.1 | 5 | ||
4.3 | odd | 2 | 392.6.a.k.1.5 | 5 | |||
7.2 | even | 3 | 112.6.i.f.81.5 | 10 | |||
7.4 | even | 3 | 112.6.i.f.65.5 | 10 | |||
7.6 | odd | 2 | 784.6.a.bl.1.5 | 5 | |||
28.3 | even | 6 | 392.6.i.o.177.5 | 10 | |||
28.11 | odd | 6 | 56.6.i.b.9.1 | ✓ | 10 | ||
28.19 | even | 6 | 392.6.i.o.361.5 | 10 | |||
28.23 | odd | 6 | 56.6.i.b.25.1 | yes | 10 | ||
28.27 | even | 2 | 392.6.a.j.1.1 | 5 | |||
84.11 | even | 6 | 504.6.s.b.289.2 | 10 | |||
84.23 | even | 6 | 504.6.s.b.361.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.i.b.9.1 | ✓ | 10 | 28.11 | odd | 6 | ||
56.6.i.b.25.1 | yes | 10 | 28.23 | odd | 6 | ||
112.6.i.f.65.5 | 10 | 7.4 | even | 3 | |||
112.6.i.f.81.5 | 10 | 7.2 | even | 3 | |||
392.6.a.j.1.1 | 5 | 28.27 | even | 2 | |||
392.6.a.k.1.5 | 5 | 4.3 | odd | 2 | |||
392.6.i.o.177.5 | 10 | 28.3 | even | 6 | |||
392.6.i.o.361.5 | 10 | 28.19 | even | 6 | |||
504.6.s.b.289.2 | 10 | 84.11 | even | 6 | |||
504.6.s.b.361.2 | 10 | 84.23 | even | 6 | |||
784.6.a.bk.1.1 | 5 | 1.1 | even | 1 | trivial | ||
784.6.a.bl.1.5 | 5 | 7.6 | odd | 2 |