Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(1471,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.m (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.3 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1471 |
Dual form | 2352.3.m.g.1471.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.27492 | −0.854983 | −0.427492 | − | 0.904019i | \(-0.640603\pi\) | ||||
−0.427492 | + | 0.904019i | \(0.640603\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.10302i | − 0.282093i | −0.990003 | − | 0.141046i | \(-0.954953\pi\) | ||||
0.990003 | − | 0.141046i | \(-0.0450466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.72508 | 0.209622 | 0.104811 | − | 0.994492i | \(-0.466576\pi\) | ||||
0.104811 | + | 0.994492i | \(0.466576\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 7.40437i | − 0.493625i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.09967 | 0.299981 | 0.149990 | − | 0.988687i | \(-0.452076\pi\) | ||||
0.149990 | + | 0.988687i | \(0.452076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.7348i | 1.35446i | 0.735771 | + | 0.677231i | \(0.236820\pi\) | ||||
−0.735771 | + | 0.677231i | \(0.763180\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.1819i | 0.529648i | 0.964297 | + | 0.264824i | \(0.0853138\pi\) | ||||
−0.964297 | + | 0.264824i | \(0.914686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.72508 | −0.269003 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.0241 | 1.41462 | 0.707312 | − | 0.706902i | \(-0.249908\pi\) | ||||
0.707312 | + | 0.706902i | \(0.249908\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.172632i | − 0.00556876i | −0.999996 | − | 0.00278438i | \(-0.999114\pi\) | ||||
0.999996 | − | 0.00278438i | \(-0.000886297\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.37459 | 0.162866 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16.9244 | −0.457417 | −0.228708 | − | 0.973495i | \(-0.573450\pi\) | ||||
−0.228708 | + | 0.973495i | \(0.573450\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.71998i | 0.121025i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 36.7492 | 0.896321 | 0.448161 | − | 0.893953i | \(-0.352079\pi\) | ||||
0.448161 | + | 0.893953i | \(0.352079\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 53.3325i | − 1.24029i | −0.784487 | − | 0.620145i | \(-0.787074\pi\) | ||||
0.784487 | − | 0.620145i | \(-0.212926\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.8248 | 0.284994 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24.2487i | 0.515930i | 0.966154 | + | 0.257965i | \(0.0830519\pi\) | ||||
−0.966154 | + | 0.257965i | \(0.916948\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.83289i | 0.173194i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −103.375 | −1.95046 | −0.975232 | − | 0.221185i | \(-0.929008\pi\) | ||||
−0.975232 | + | 0.221185i | \(0.929008\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.2651i | 0.241185i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −44.5739 | −0.781999 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 29.2564i | 0.495871i | 0.968776 | + | 0.247936i | \(0.0797522\pi\) | ||||
−0.968776 | + | 0.247936i | \(0.920248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −32.9003 | −0.539350 | −0.269675 | − | 0.962951i | \(-0.586916\pi\) | ||||
−0.269675 | + | 0.962951i | \(0.586916\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.6495 | −0.179223 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17.0170i | 0.253985i | 0.991904 | + | 0.126992i | \(0.0405324\pi\) | ||||
−0.991904 | + | 0.126992i | \(0.959468\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.0997 | −0.305792 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 76.7857i | 1.08149i | 0.841187 | + | 0.540744i | \(0.181857\pi\) | ||||
−0.841187 | + | 0.540744i | \(0.818143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 99.2749 | 1.35993 | 0.679965 | − | 0.733244i | \(-0.261995\pi\) | ||||
0.679965 | + | 0.733244i | \(0.261995\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 11.6482i | − 0.155309i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 87.7275i | − 1.11047i | −0.831692 | − | 0.555237i | \(-0.812627\pi\) | ||||
0.831692 | − | 0.555237i | \(-0.187373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 151.452i | 1.82473i | 0.409381 | + | 0.912363i | \(0.365745\pi\) | ||||
−0.409381 | + | 0.912363i | \(0.634255\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.8007 | −0.256478 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 71.0558i | 0.816733i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −68.5498 | −0.770223 | −0.385111 | − | 0.922870i | \(-0.625837\pi\) | ||||
−0.385111 | + | 0.922870i | \(0.625837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.299007 | 0.00321512 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 110.014i | − 1.15804i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −104.522 | −1.07755 | −0.538775 | − | 0.842449i | \(-0.681113\pi\) | ||||
−0.538775 | + | 0.842449i | \(0.681113\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.30906i | 0.0940309i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −157.698 | −1.56136 | −0.780682 | − | 0.624929i | \(-0.785128\pi\) | ||||
−0.780682 | + | 0.624929i | \(0.785128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 120.448i | − 1.16940i | −0.811250 | − | 0.584699i | \(-0.801213\pi\) | ||||
0.811250 | − | 0.584699i | \(-0.198787\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 104.022i | − 0.972171i | −0.873911 | − | 0.486086i | \(-0.838424\pi\) | ||||
0.873911 | − | 0.486086i | \(-0.161576\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −103.625 | −0.950692 | −0.475346 | − | 0.879799i | \(-0.657677\pi\) | ||||
−0.475346 | + | 0.879799i | \(0.657677\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 29.3140i | − 0.264090i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −177.849 | −1.57388 | −0.786942 | − | 0.617027i | \(-0.788337\pi\) | ||||
−0.786942 | + | 0.617027i | \(0.788337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 52.0766i | − 0.452840i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.17525 | −0.0698739 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 111.371 | 0.920424 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 63.6514i | 0.517491i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 135.622 | 1.08498 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 171.672i | − 1.35174i | −0.737019 | − | 0.675872i | \(-0.763767\pi\) | ||||
0.737019 | − | 0.675872i | \(-0.236233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 92.3746 | 0.716082 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 125.152i | − 0.955360i | −0.878534 | − | 0.477680i | \(-0.841478\pi\) | ||||
0.878534 | − | 0.477680i | \(-0.158522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 22.2131i | 0.164542i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −180.949 | −1.32079 | −0.660396 | − | 0.750918i | \(-0.729612\pi\) | ||||
−0.660396 | + | 0.750918i | \(0.729612\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 155.204i | 1.11658i | 0.829647 | + | 0.558288i | \(0.188542\pi\) | ||||
−0.829647 | + | 0.558288i | \(0.811458\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −42.0000 | −0.297872 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 8.45598i | − 0.0591327i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −175.375 | −1.20948 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −39.1478 | −0.262737 | −0.131369 | − | 0.991334i | \(-0.541937\pi\) | ||||
−0.131369 | + | 0.991334i | \(0.541937\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 135.084i | − 0.894597i | −0.894385 | − | 0.447298i | \(-0.852386\pi\) | ||||
0.894385 | − | 0.447298i | \(-0.147614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.2990 | −0.0999935 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.737986i | 0.00476120i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 56.0482 | 0.356995 | 0.178497 | − | 0.983940i | \(-0.442876\pi\) | ||||
0.178497 | + | 0.983940i | \(0.442876\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 179.050i | − 1.12610i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25.5780i | 0.156920i | 0.996917 | + | 0.0784600i | \(0.0250003\pi\) | ||||
−0.996917 | + | 0.0784600i | \(0.975000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −22.9759 | −0.139248 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 77.9998i | − 0.467065i | −0.972349 | − | 0.233532i | \(-0.924971\pi\) | ||||
0.972349 | − | 0.233532i | \(-0.0750285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −161.574 | −0.956059 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 77.2043i | − 0.451487i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −287.148 | −1.65981 | −0.829907 | − | 0.557902i | \(-0.811607\pi\) | ||||
−0.829907 | + | 0.557902i | \(0.811607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −50.6736 | −0.286291 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 65.8496i | − 0.367875i | −0.982938 | − | 0.183937i | \(-0.941116\pi\) | ||||
0.982938 | − | 0.183937i | \(-0.0588844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 205.323 | 1.13438 | 0.567191 | − | 0.823586i | \(-0.308030\pi\) | ||||
0.567191 | + | 0.823586i | \(0.308030\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 56.9850i | − 0.311394i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 72.3505 | 0.391084 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.8244i | − 0.0846223i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 98.9830i | 0.518235i | 0.965846 | + | 0.259118i | \(0.0834318\pi\) | ||||
−0.965846 | + | 0.259118i | \(0.916568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −54.5531 | −0.282659 | −0.141329 | − | 0.989963i | \(-0.545138\pi\) | ||||
−0.141329 | + | 0.989963i | \(0.545138\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 20.1775i | − 0.103475i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −127.450 | −0.646955 | −0.323478 | − | 0.946236i | \(-0.604852\pi\) | ||||
−0.323478 | + | 0.946236i | \(0.604852\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 12.1819i | − 0.0612156i | −0.999531 | − | 0.0306078i | \(-0.990256\pi\) | ||||
0.999531 | − | 0.0306078i | \(-0.00974428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.4743 | −0.146638 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −157.100 | −0.766340 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 36.5457i | − 0.176549i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 79.8555 | 0.382084 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 210.243i | − 0.996411i | −0.867059 | − | 0.498206i | \(-0.833992\pi\) | ||||
0.867059 | − | 0.498206i | \(-0.166008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −132.997 | −0.624398 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 227.992i | 1.06043i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 171.949i | 0.785156i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8970 | 0.0628824 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 264.323i | − 1.18531i | −0.805458 | − | 0.592653i | \(-0.798080\pi\) | ||||
0.805458 | − | 0.592653i | \(-0.201920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.1752 | 0.0896678 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 351.878i | 1.55012i | 0.631885 | + | 0.775062i | \(0.282281\pi\) | ||||
−0.631885 | + | 0.775062i | \(0.717719\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −205.371 | −0.896818 | −0.448409 | − | 0.893829i | \(-0.648009\pi\) | ||||
−0.448409 | + | 0.893829i | \(0.648009\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 33.8488 | 0.145274 | 0.0726370 | − | 0.997358i | \(-0.476859\pi\) | ||||
0.0726370 | + | 0.997358i | \(0.476859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 103.661i | − 0.441112i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 151.949 | 0.641133 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 78.4285i | 0.328153i | 0.986448 | + | 0.164076i | \(0.0524644\pi\) | ||||
−0.986448 | + | 0.164076i | \(0.947536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 174.474 | 0.723960 | 0.361980 | − | 0.932186i | \(-0.382101\pi\) | ||||
0.361980 | + | 0.932186i | \(0.382101\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 70.1294i | 0.283925i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −262.323 | −1.05351 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 128.124i | − 0.510455i | −0.966881 | − | 0.255228i | \(-0.917850\pi\) | ||||
0.966881 | − | 0.255228i | \(-0.0821504\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.8007 | 0.149410 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 37.7599i | − 0.148078i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −285.601 | −1.11129 | −0.555645 | − | 0.831420i | \(-0.687528\pi\) | ||||
−0.555645 | + | 0.831420i | \(0.687528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −123.072 | −0.471541 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 510.227i | − 1.94003i | −0.243051 | − | 0.970013i | \(-0.578148\pi\) | ||||
0.243051 | − | 0.970013i | \(-0.421852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 441.918 | 1.66761 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 118.732i | − 0.444688i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 233.471 | 0.867922 | 0.433961 | − | 0.900932i | \(-0.357116\pi\) | ||||
0.433961 | + | 0.900932i | \(0.357116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 317.582i | − 1.17189i | −0.810350 | − | 0.585945i | \(-0.800723\pi\) | ||||
0.810350 | − | 0.585945i | \(-0.199277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.8681i | 0.0758838i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −522.265 | −1.88543 | −0.942717 | − | 0.333595i | \(-0.891738\pi\) | ||||
−0.942717 | + | 0.333595i | \(0.891738\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.517895i | 0.00185625i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −307.752 | −1.09520 | −0.547602 | − | 0.836739i | \(-0.684459\pi\) | ||||
−0.547602 | + | 0.836739i | \(0.684459\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 207.888i | − 0.734586i | −0.930105 | − | 0.367293i | \(-0.880285\pi\) | ||||
0.930105 | − | 0.367293i | \(-0.119715\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 190.550 | 0.668596 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −262.993 | −0.910012 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 181.038i | − 0.622124i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −341.670 | −1.16611 | −0.583055 | − | 0.812433i | \(-0.698143\pi\) | ||||
−0.583055 | + | 0.812433i | \(0.698143\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 125.069i | − 0.423962i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.1238 | −0.0542887 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 33.1967i | 0.111026i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 273.140i | − 0.901453i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 140.646 | 0.461135 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 179.913i | 0.586036i | 0.956107 | + | 0.293018i | \(0.0946597\pi\) | ||||
−0.956107 | + | 0.293018i | \(0.905340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 208.622 | 0.675152 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 262.665i | 0.844581i | 0.906461 | + | 0.422290i | \(0.138774\pi\) | ||||
−0.906461 | + | 0.422290i | \(0.861226\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 547.042 | 1.74774 | 0.873868 | − | 0.486163i | \(-0.161604\pi\) | ||||
0.873868 | + | 0.486163i | \(0.161604\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.2815 | −0.0765979 | −0.0382990 | − | 0.999266i | \(-0.512194\pi\) | ||||
−0.0382990 | + | 0.999266i | \(0.512194\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 127.299i | − 0.399055i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 180.172 | 0.561283 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 131.239i | 0.406312i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.3264 | −0.0563889 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 179.484i | − 0.548882i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 306.819i | 0.926946i | 0.886111 | + | 0.463473i | \(0.153397\pi\) | ||||
−0.886111 | + | 0.463473i | \(0.846603\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 50.7733 | 0.152472 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 72.7461i | − 0.217153i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 312.093 | 0.926092 | 0.463046 | − | 0.886334i | \(-0.346756\pi\) | ||||
0.463046 | + | 0.886334i | \(0.346756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 308.043i | − 0.908682i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.535679 | −0.00157091 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 90.1993 | 0.261447 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 380.004i | 1.09511i | 0.836769 | + | 0.547556i | \(0.184442\pi\) | ||||
−0.836769 | + | 0.547556i | \(0.815558\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −201.395 | −0.577064 | −0.288532 | − | 0.957470i | \(-0.593167\pi\) | ||||
−0.288532 | + | 0.957470i | \(0.593167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 14.1599i | − 0.0403417i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 319.746 | 0.905796 | 0.452898 | − | 0.891562i | \(-0.350390\pi\) | ||||
0.452898 | + | 0.891562i | \(0.350390\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 328.252i | − 0.924655i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 547.463i | − 1.52497i | −0.647007 | − | 0.762484i | \(-0.723980\pi\) | ||||
0.647007 | − | 0.762484i | \(-0.276020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −301.278 | −0.834566 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 192.901i | 0.531407i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −424.392 | −1.16272 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 186.250i | 0.507494i | 0.967271 | + | 0.253747i | \(0.0816630\pi\) | ||||
−0.967271 | + | 0.253747i | \(0.918337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −110.248 | −0.298774 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.8729 | 0.0854502 | 0.0427251 | − | 0.999087i | \(-0.486396\pi\) | ||||
0.0427251 | + | 0.999087i | \(0.486396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 234.904i | 0.626412i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 111.794 | 0.296536 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 644.960i | 1.70174i | 0.525375 | + | 0.850871i | \(0.323925\pi\) | ||||
−0.525375 | + | 0.850871i | \(0.676075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 297.344 | 0.780430 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 539.678i | 1.40908i | 0.709664 | + | 0.704540i | \(0.248847\pi\) | ||||
−0.709664 | + | 0.704540i | \(0.751153\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 159.997i | 0.413430i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 255.704 | 0.657338 | 0.328669 | − | 0.944445i | \(-0.393400\pi\) | ||||
0.328669 | + | 0.944445i | \(0.393400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 62.1237i | 0.158884i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 216.770 | 0.551577 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 375.028i | 0.949438i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −193.419 | −0.487203 | −0.243601 | − | 0.969875i | \(-0.578329\pi\) | ||||
−0.243601 | + | 0.969875i | \(0.578329\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.0000 | 0.0798005 | 0.0399002 | − | 0.999204i | \(-0.487296\pi\) | ||||
0.0399002 | + | 0.999204i | \(0.487296\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.470435i | − 0.00116733i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −38.4743 | −0.0949982 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 52.5168i | 0.129034i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −370.739 | −0.906453 | −0.453226 | − | 0.891395i | \(-0.649727\pi\) | ||||
−0.453226 | + | 0.891395i | \(0.649727\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 313.412i | − 0.762560i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 647.446i | − 1.56011i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −268.821 | −0.644656 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 735.457i | 1.75527i | 0.479332 | + | 0.877634i | \(0.340879\pi\) | ||||
−0.479332 | + | 0.877634i | \(0.659121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −483.021 | −1.14732 | −0.573659 | − | 0.819094i | \(-0.694476\pi\) | ||||
−0.573659 | + | 0.819094i | \(0.694476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 72.7461i | − 0.171977i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.2957 | −0.0806958 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.6462 | 0.0341403 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 569.117i | − 1.32046i | −0.751065 | − | 0.660228i | \(-0.770460\pi\) | ||||
0.751065 | − | 0.660228i | \(-0.229540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 45.3297 | 0.104688 | 0.0523438 | − | 0.998629i | \(-0.483331\pi\) | ||||
0.0523438 | + | 0.998629i | \(0.483331\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 303.758i | − 0.698294i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −313.498 | −0.717388 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 59.1041i | − 0.134633i | −0.997732 | − | 0.0673167i | \(-0.978556\pi\) | ||||
0.997732 | − | 0.0673167i | \(-0.0214438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 218.191i | − 0.492530i | −0.969202 | − | 0.246265i | \(-0.920797\pi\) | ||||
0.969202 | − | 0.246265i | \(-0.0792034\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 293.045 | 0.658528 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 67.8061i | − 0.151691i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −369.643 | −0.823258 | −0.411629 | − | 0.911351i | \(-0.635040\pi\) | ||||
−0.411629 | + | 0.911351i | \(0.635040\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 114.033i | − 0.252846i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 233.973 | 0.516496 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 514.650 | 1.12615 | 0.563074 | − | 0.826407i | \(-0.309619\pi\) | ||||
0.563074 | + | 0.826407i | \(0.309619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 26.4987i | − 0.0577313i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −656.440 | −1.42395 | −0.711974 | − | 0.702206i | \(-0.752199\pi\) | ||||
−0.711974 | + | 0.702206i | \(0.752199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 90.7673i | 0.196042i | 0.995184 | + | 0.0980208i | \(0.0312512\pi\) | ||||
−0.995184 | + | 0.0980208i | \(0.968749\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.27823 | −0.00274888 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 341.010i | 0.730214i | 0.930966 | + | 0.365107i | \(0.118968\pi\) | ||||
−0.930966 | + | 0.365107i | \(0.881032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 97.0783i | 0.206111i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −165.492 | −0.349877 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 173.068i | − 0.364355i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 310.124 | 0.650155 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 252.376i | − 0.526881i | −0.964676 | − | 0.263440i | \(-0.915143\pi\) | ||||
0.964676 | − | 0.263440i | \(-0.0848573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.1204 | −0.0958845 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 446.825 | 0.921288 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 586.411i | 1.20413i | 0.798447 | + | 0.602065i | \(0.205655\pi\) | ||||
−0.798447 | + | 0.602065i | \(0.794345\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44.3023 | −0.0905978 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 462.384i | 0.941719i | 0.882208 | + | 0.470860i | \(0.156056\pi\) | ||||
−0.882208 | + | 0.470860i | \(0.843944\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 209.209 | 0.424360 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 39.7954i | − 0.0803948i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 882.142i | 1.76782i | 0.467658 | + | 0.883910i | \(0.345098\pi\) | ||||
−0.467658 | + | 0.883910i | \(0.654902\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 135.100 | 0.269660 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.1303i | 0.0380323i | 0.999819 | + | 0.0190162i | \(0.00605340\pi\) | ||||
−0.999819 | + | 0.0190162i | \(0.993947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 674.145 | 1.33494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 279.854i | − 0.551981i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −427.725 | −0.840324 | −0.420162 | − | 0.907449i | \(-0.638027\pi\) | ||||
−0.420162 | + | 0.907449i | \(0.638027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 133.722 | 0.260666 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 514.905i | 0.999816i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 75.2442 | 0.145540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 497.355i | − 0.958294i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −787.244 | −1.51103 | −0.755513 | − | 0.655134i | \(-0.772612\pi\) | ||||
−0.755513 | + | 0.655134i | \(0.772612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 603.935i | − 1.15475i | −0.816479 | − | 0.577376i | \(-0.804077\pi\) | ||||
0.816479 | − | 0.577376i | \(-0.195923\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 0.880364i | − 0.00167052i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 380.601 | 0.719473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 87.7692i | − 0.165290i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 100.145 | 0.187888 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 444.687i | 0.831190i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 114.055 | 0.212393 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −851.914 | −1.57470 | −0.787352 | − | 0.616504i | \(-0.788548\pi\) | ||||
−0.787352 | + | 0.616504i | \(0.788548\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 355.630i | 0.654936i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 442.990 | 0.812826 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 887.898i | − 1.62321i | −0.584204 | − | 0.811607i | \(-0.698593\pi\) | ||||
0.584204 | − | 0.811607i | \(-0.301407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 98.7010 | 0.179783 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1055.75i | 1.91605i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 125.315i | 0.225792i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 592.908 | 1.06447 | 0.532233 | − | 0.846598i | \(-0.321353\pi\) | ||||
0.532233 | + | 0.846598i | \(0.321353\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 145.335i | − 0.259992i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.4086 | 0.0488567 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 153.849i | − 0.273266i | −0.990622 | − | 0.136633i | \(-0.956372\pi\) | ||||
0.990622 | − | 0.136633i | \(-0.0436282\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 760.289 | 1.34564 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 289.450 | 0.508700 | 0.254350 | − | 0.967112i | \(-0.418139\pi\) | ||||
0.254350 | + | 0.967112i | \(0.418139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 640.702i | 1.12207i | 0.827792 | + | 0.561035i | \(0.189597\pi\) | ||||
−0.827792 | + | 0.561035i | \(0.810403\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −171.444 | −0.299203 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 81.9243i | − 0.142477i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −190.209 | −0.329652 | −0.164826 | − | 0.986323i | \(-0.552706\pi\) | ||||
−0.164826 | + | 0.986323i | \(0.552706\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 94.4888i | − 0.163193i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 320.773i | 0.550211i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 34.9485 | 0.0597410 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 338.241i | − 0.576219i | −0.957597 | − | 0.288109i | \(-0.906973\pi\) | ||||
0.957597 | − | 0.288109i | \(-0.0930267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.44263 | 0.00754267 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 220.750i | − 0.373520i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −736.736 | −1.24239 | −0.621194 | − | 0.783657i | \(-0.713352\pi\) | ||||
−0.621194 | + | 0.783657i | \(0.713352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.0997 | 0.0353428 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 371.266i | − 0.619810i | −0.950768 | − | 0.309905i | \(-0.899703\pi\) | ||||
0.950768 | − | 0.309905i | \(-0.100297\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −965.894 | −1.60714 | −0.803572 | − | 0.595207i | \(-0.797070\pi\) | ||||
−0.803572 | + | 0.595207i | \(0.797070\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 51.0509i | − 0.0846615i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −476.103 | −0.786947 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 304.887i | 0.502285i | 0.967950 | + | 0.251143i | \(0.0808063\pi\) | ||||
−0.967950 | + | 0.251143i | \(0.919194\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 66.0797i | 0.108150i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 425.341 | 0.693867 | 0.346934 | − | 0.937890i | \(-0.387223\pi\) | ||||
0.346934 | + | 0.937890i | \(0.387223\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 272.105i | − 0.442447i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 821.189 | 1.33094 | 0.665470 | − | 0.746425i | \(-0.268231\pi\) | ||||
0.665470 | + | 0.746425i | \(0.268231\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 897.086i | − 1.44925i | −0.689143 | − | 0.724625i | \(-0.742013\pi\) | ||||
0.689143 | − | 0.724625i | \(-0.257987\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 63.2990 | 0.101931 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −411.646 | −0.658634 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 138.314i | 0.220596i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −86.3089 | −0.137216 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 347.398i | − 0.550552i | −0.961365 | − | 0.275276i | \(-0.911231\pi\) | ||||
0.961365 | − | 0.275276i | \(-0.0887693\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 364.151 | 0.575278 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 733.882i | 1.15572i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 230.357i | − 0.360496i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 405.855 | 0.633160 | 0.316580 | − | 0.948566i | \(-0.397465\pi\) | ||||
0.316580 | + | 0.948566i | \(0.397465\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 52.5787i | − 0.0817709i | −0.999164 | − | 0.0408854i | \(-0.986982\pi\) | ||||
0.999164 | − | 0.0408854i | \(-0.0130179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −394.894 | −0.612238 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1121.44i | 1.73329i | 0.498928 | + | 0.866644i | \(0.333727\pi\) | ||||
−0.498928 | + | 0.866644i | \(0.666273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 90.7832 | 0.139882 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.9660 | −0.0642664 | −0.0321332 | − | 0.999484i | \(-0.510230\pi\) | ||||
−0.0321332 | + | 0.999484i | \(0.510230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 535.015i | 0.816817i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −297.825 | −0.453310 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1224.43i | 1.85801i | 0.370069 | + | 0.929004i | \(0.379334\pi\) | ||||
−0.370069 | + | 0.929004i | \(0.620666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.1171 | 0.0410244 | 0.0205122 | − | 0.999790i | \(-0.493470\pi\) | ||||
0.0205122 | + | 0.999790i | \(0.493470\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.0703i | 0.0363052i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 499.751i | 0.749252i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 457.821 | 0.684337 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 102.090i | 0.152147i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −418.238 | −0.621453 | −0.310726 | − | 0.950499i | \(-0.600572\pi\) | ||||
−0.310726 | + | 0.950499i | \(0.600572\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 34.9446i | 0.0517697i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −233.410 | −0.344770 | −0.172385 | − | 0.985030i | \(-0.555147\pi\) | ||||
−0.172385 | + | 0.985030i | \(0.555147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −609.471 | −0.894965 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 414.221i | − 0.606472i | −0.952915 | − | 0.303236i | \(-0.901933\pi\) | ||||
0.952915 | − | 0.303236i | \(-0.0980671\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 773.540 | 1.12926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 355.713i | − 0.517778i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −281.704 | −0.408860 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 471.232i | 0.681956i | 0.940071 | + | 0.340978i | \(0.110758\pi\) | ||||
−0.940071 | + | 0.340978i | \(0.889242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 663.485i | − 0.954654i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 187.409 | 0.268879 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 58.6279i | 0.0838740i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1150.00 | 1.64051 | 0.820257 | − | 0.571995i | \(-0.193830\pi\) | ||||
0.820257 | + | 0.571995i | \(0.193830\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 435.546i | − 0.619553i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 179.547 | 0.254676 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1388.97 | 1.95906 | 0.979528 | − | 0.201310i | \(-0.0645198\pi\) | ||||
0.979528 | + | 0.201310i | \(0.0645198\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 263.183i | 0.370158i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.10298 | 0.00294948 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.1486i | 0.0505575i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −135.842 | −0.189459 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1179.12i | 1.63995i | 0.572400 | + | 0.819975i | \(0.306013\pi\) | ||||
−0.572400 | + | 0.819975i | \(0.693987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 302.198i | 0.417978i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −275.890 | −0.380538 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1168.99i | − 1.60796i | −0.594656 | − | 0.803980i | \(-0.702712\pi\) | ||||
0.594656 | − | 0.803980i | \(-0.297288\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 271.978i | − 0.372063i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 768.375 | 1.04826 | 0.524130 | − | 0.851638i | \(-0.324391\pi\) | ||||
0.524130 | + | 0.851638i | \(0.324391\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.8040 | 0.0716472 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 378.288i | 0.511891i | 0.966691 | + | 0.255946i | \(0.0823868\pi\) | ||||
−0.966691 | + | 0.255946i | \(0.917613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −121.468 | −0.163924 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1461.21i | 1.96664i | 0.181889 | + | 0.983319i | \(0.441779\pi\) | ||||
−0.181889 | + | 0.983319i | \(0.558221\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 167.354 | 0.224636 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 454.357i | − 0.608242i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1109.38i | − 1.47721i | −0.674139 | − | 0.738605i | \(-0.735485\pi\) | ||||
0.674139 | − | 0.738605i | \(-0.264515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 221.918 | 0.294712 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 577.474i | 0.764866i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 925.286 | 1.22231 | 0.611153 | − | 0.791512i | \(-0.290706\pi\) | ||||
0.611153 | + | 0.791512i | \(0.290706\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 65.4727i | 0.0862617i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1373.79 | 1.80524 | 0.902620 | − | 0.430439i | \(-0.141641\pi\) | ||||
0.902620 | + | 0.430439i | \(0.141641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 65.4020 | 0.0854928 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 79.7261i | 0.103945i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1212.84 | −1.57716 | −0.788580 | − | 0.614933i | \(-0.789183\pi\) | ||||
−0.788580 | + | 0.614933i | \(0.789183\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 494.676i | − 0.641603i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −796.392 | −1.03026 | −0.515131 | − | 0.857112i | \(-0.672257\pi\) | ||||
−0.515131 | + | 0.857112i | \(0.672257\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.16096i | 0.00149801i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 945.731i | 1.21403i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 238.267 | 0.305080 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 213.167i | − 0.272244i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −239.601 | −0.305225 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 169.301i | 0.215122i | 0.994199 | + | 0.107561i | \(0.0343040\pi\) | ||||
−0.994199 | + | 0.107561i | \(0.965696\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 883.739 | 1.12008 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −89.6561 | −0.113059 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 765.424i | 0.962798i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −181.725 | −0.228011 | −0.114006 | − | 0.993480i | \(-0.536368\pi\) | ||||
−0.114006 | + | 0.993480i | \(0.536368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 123.660i | 0.154769i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 205.650 | 0.256741 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 308.052i | − 0.383626i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 404.384i | 0.501095i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1284.05 | 1.58720 | 0.793602 | − | 0.608437i | \(-0.208203\pi\) | ||||
0.793602 | + | 0.608437i | \(0.208203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 627.609i | 0.773871i | 0.922107 | + | 0.386936i | \(0.126466\pi\) | ||||
−0.922107 | + | 0.386936i | \(0.873534\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 550.069 | 0.676592 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 109.344i | − 0.134164i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1372.50 | 1.67993 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 644.577 | 0.785112 | 0.392556 | − | 0.919728i | \(-0.371591\pi\) | ||||
0.392556 | + | 0.919728i | \(0.371591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 698.701i | − 0.848969i | −0.905435 | − | 0.424484i | \(-0.860455\pi\) | ||||
0.905435 | − | 0.424484i | \(-0.139545\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.1445 | −0.0438116 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 736.603i | 0.890693i | 0.895358 | + | 0.445347i | \(0.146920\pi\) | ||||
−0.895358 | + | 0.445347i | \(0.853080\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 854.107 | 1.03029 | 0.515143 | − | 0.857104i | \(-0.327739\pi\) | ||||
0.515143 | + | 0.857104i | \(0.327739\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 904.589i | − 1.08856i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 333.443i | 0.399333i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.897020 | −0.00107171 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 261.597i | 0.311796i | 0.987773 | + | 0.155898i | \(0.0498272\pi\) | ||||
−0.987773 | + | 0.155898i | \(0.950173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.976 | 1.00116 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 533.043i | − 0.632317i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 690.715 | 0.817414 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 360.072 | 0.424113 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 206.172i | − 0.242270i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −300.278 | −0.352026 | −0.176013 | − | 0.984388i | \(-0.556320\pi\) | ||||
−0.176013 | + | 0.984388i | \(0.556320\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 330.042i | 0.386014i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −256.344 | −0.299118 | −0.149559 | − | 0.988753i | \(-0.547785\pi\) | ||||
−0.149559 | + | 0.988753i | \(0.547785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 887.342i | − 1.03299i | −0.856289 | − | 0.516497i | \(-0.827236\pi\) | ||||
0.856289 | − | 0.516497i | \(-0.172764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1543.01i | − 1.78796i | −0.448106 | − | 0.893980i | \(-0.647901\pi\) | ||||
0.448106 | − | 0.893980i | \(-0.352099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1227.53 | 1.41911 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 455.518i | − 0.525395i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −272.220 | −0.313257 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.3726i | 0.0532407i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 313.567 | 0.359184 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −574.028 | −0.654536 | −0.327268 | − | 0.944932i | \(-0.606128\pi\) | ||||
−0.327268 | + | 0.944932i | \(0.606128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 591.790i | − 0.673254i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 201.842 | 0.229106 | 0.114553 | − | 0.993417i | \(-0.463456\pi\) | ||||
0.114553 | + | 0.993417i | \(0.463456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 661.078i | 0.748673i | 0.927293 | + | 0.374336i | \(0.122129\pi\) | ||||
−0.927293 | + | 0.374336i | \(0.877871\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 216.625 | 0.244774 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 430.783i | − 0.485663i | −0.970069 | − | 0.242831i | \(-0.921924\pi\) | ||||
0.970069 | − | 0.242831i | \(-0.0780762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 27.9272i | − 0.0313436i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −624.035 | −0.698807 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 281.501i | 0.314527i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −57.4983 | −0.0641007 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 7.08205i | − 0.00787770i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −527.176 | −0.585101 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −877.739 | −0.969878 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1012.97i | 1.11684i | 0.829559 | + | 0.558419i | \(0.188592\pi\) | ||||
−0.829559 | + | 0.558419i | \(0.811408\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 473.093 | 0.520454 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 507.799i | 0.557408i | 0.960377 | + | 0.278704i | \(0.0899049\pi\) | ||||
−0.960377 | + | 0.278704i | \(0.910095\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 469.959 | 0.514742 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 243.606i | 0.266236i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 179.536i | − 0.195360i | −0.995218 | − | 0.0976802i | \(-0.968858\pi\) | ||||
0.995218 | − | 0.0976802i | \(-0.0311422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −311.619 | −0.338348 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 209.247i | 0.226703i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 113.818 | 0.123047 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 361.344i | 0.389799i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 298.578 | 0.321397 | 0.160699 | − | 0.987004i | \(-0.448625\pi\) | ||||
0.160699 | + | 0.987004i | \(0.448625\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −454.949 | −0.487619 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 67.6479i | 0.0723507i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 568.691 | 0.606927 | 0.303464 | − | 0.952843i | \(-0.401857\pi\) | ||||
0.303464 | + | 0.952843i | \(0.401857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 947.504i | 1.00906i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −570.715 | −0.606499 | −0.303249 | − | 0.952911i | \(-0.598071\pi\) | ||||
−0.303249 | + | 0.952911i | \(0.598071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 447.675i | 0.474735i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 435.346i | 0.459711i | 0.973225 | + | 0.229855i | \(0.0738253\pi\) | ||||
−0.973225 | + | 0.229855i | \(0.926175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 270.532 | 0.285071 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 42.0569i | − 0.0442238i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1282.02 | −1.34525 | −0.672624 | − | 0.739984i | \(-0.734833\pi\) | ||||
−0.672624 | + | 0.739984i | \(0.734833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 423.144i | − 0.443083i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 220.488 | 0.230394 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.970 | 0.999969 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 312.067i | 0.324057i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 233.210 | 0.241669 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 625.993i | − 0.647355i | −0.946167 | − | 0.323678i | \(-0.895081\pi\) | ||||
0.946167 | − | 0.323678i | \(-0.104919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −227.312 | −0.234584 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1260.98i | 1.29864i | 0.760516 | + | 0.649319i | \(0.224946\pi\) | ||||
−0.760516 | + | 0.649319i | \(0.775054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 31.7423i | − 0.0325562i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1575.49 | 1.61257 | 0.806287 | − | 0.591524i | \(-0.201474\pi\) | ||||
0.806287 | + | 0.591524i | \(0.201474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 212.711i | 0.217274i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 310.876 | 0.316897 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1047.12i | 1.06523i | 0.846358 | + | 0.532614i | \(0.178790\pi\) | ||||
−0.846358 | + | 0.532614i | \(0.821210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 544.839 | 0.553136 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 649.691 | 0.656917 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 781.385i | − 0.788481i | −0.919007 | − | 0.394241i | \(-0.871008\pi\) | ||||
0.919007 | − | 0.394241i | \(-0.128992\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −531.426 | −0.535172 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.0766i | 0.0523383i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −700.155 | −0.702262 | −0.351131 | − | 0.936326i | \(-0.614203\pi\) | ||||
−0.351131 | + | 0.936326i | \(0.614203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 87.9419i | 0.0880299i |
(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 | 2352.3.m.g.1471.3 | 4 | ||
4.3 | odd | 2 | inner | 2352.3.m.g.1471.1 | 4 | ||
7.2 | even | 3 | 336.3.be.a.319.2 | yes | 4 | ||
7.4 | even | 3 | 336.3.be.b.79.2 | yes | 4 | ||
7.6 | odd | 2 | 2352.3.m.h.1471.2 | 4 | |||
21.2 | odd | 6 | 1008.3.cd.g.991.1 | 4 | |||
21.11 | odd | 6 | 1008.3.cd.f.415.1 | 4 | |||
28.11 | odd | 6 | 336.3.be.a.79.2 | ✓ | 4 | ||
28.23 | odd | 6 | 336.3.be.b.319.2 | yes | 4 | ||
28.27 | even | 2 | 2352.3.m.h.1471.4 | 4 | |||
84.11 | even | 6 | 1008.3.cd.g.415.1 | 4 | |||
84.23 | even | 6 | 1008.3.cd.f.991.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.3.be.a.79.2 | ✓ | 4 | 28.11 | odd | 6 | ||
336.3.be.a.319.2 | yes | 4 | 7.2 | even | 3 | ||
336.3.be.b.79.2 | yes | 4 | 7.4 | even | 3 | ||
336.3.be.b.319.2 | yes | 4 | 28.23 | odd | 6 | ||
1008.3.cd.f.415.1 | 4 | 21.11 | odd | 6 | |||
1008.3.cd.f.991.1 | 4 | 84.23 | even | 6 | |||
1008.3.cd.g.415.1 | 4 | 84.11 | even | 6 | |||
1008.3.cd.g.991.1 | 4 | 21.2 | odd | 6 | |||
2352.3.m.g.1471.1 | 4 | 4.3 | odd | 2 | inner | ||
2352.3.m.g.1471.3 | 4 | 1.1 | even | 1 | trivial | ||
2352.3.m.h.1471.2 | 4 | 7.6 | odd | 2 | |||
2352.3.m.h.1471.4 | 4 | 28.27 | even | 2 |