Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7488,2,Mod(1,7488)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7488, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7488.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7488 = 2^{6} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7488.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: | \(59.7919810335\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 416) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7488.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.561553 | 0.251134 | 0.125567 | − | 0.992085i | \(-0.459925\pi\) | ||||
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.561553 | −0.212247 | −0.106124 | − | 0.994353i | \(-0.533844\pi\) | ||||
−0.106124 | + | 0.994353i | \(0.533844\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.561553 | 0.136197 | 0.0680983 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680983 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.68466 | −0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.24621 | −1.53128 | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.12311 | 1.27935 | 0.639674 | − | 0.768647i | \(-0.279069\pi\) | ||||
0.639674 | + | 0.768647i | \(0.279069\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.315342 | −0.0533025 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.68466 | 1.59215 | 0.796074 | − | 0.605199i | \(-0.206907\pi\) | ||||
0.796074 | + | 0.605199i | \(0.206907\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.12311 | −1.11244 | −0.556221 | − | 0.831034i | \(-0.687749\pi\) | ||||
−0.556221 | + | 0.831034i | \(0.687749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.80776 | 1.34317 | 0.671586 | − | 0.740927i | \(-0.265614\pi\) | ||||
0.671586 | + | 0.740927i | \(0.265614\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.68466 | −0.245733 | −0.122866 | − | 0.992423i | \(-0.539209\pi\) | ||||
−0.122866 | + | 0.992423i | \(0.539209\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68466 | −0.954951 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.87689 | −0.669893 | −0.334946 | − | 0.942237i | \(-0.608718\pi\) | ||||
−0.334946 | + | 0.942237i | \(0.608718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.12311 | 0.151440 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.3693 | −1.71177 | −0.855883 | − | 0.517170i | \(-0.826986\pi\) | ||||
−0.855883 | + | 0.517170i | \(0.826986\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.561553 | 0.0696521 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | −0.733017 | −0.366508 | − | 0.930415i | \(-0.619447\pi\) | ||||
−0.366508 | + | 0.930415i | \(0.619447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.68466 | 0.199932 | 0.0999661 | − | 0.994991i | \(-0.468127\pi\) | ||||
0.0999661 | + | 0.994991i | \(0.468127\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.12311 | −0.127990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.3693 | −1.90653 | −0.953265 | − | 0.302135i | \(-0.902301\pi\) | ||||
−0.953265 | + | 0.302135i | \(0.902301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.315342 | 0.0342036 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.24621 | 0.874097 | 0.437048 | − | 0.899438i | \(-0.356024\pi\) | ||||
0.437048 | + | 0.899438i | \(0.356024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.561553 | −0.0588667 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.36932 | −0.345685 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.12311 | −0.708776 | −0.354388 | − | 0.935099i | \(-0.615311\pi\) | ||||
−0.354388 | + | 0.935099i | \(0.615311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.68466 | 0.161361 | 0.0806805 | − | 0.996740i | \(-0.474291\pi\) | ||||
0.0806805 | + | 0.996740i | \(0.474291\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.24621 | −0.775738 | −0.387869 | − | 0.921714i | \(-0.626789\pi\) | ||||
−0.387869 | + | 0.921714i | \(0.626789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.315342 | −0.0289073 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.43845 | −0.486430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.24621 | 0.199319 | 0.0996595 | − | 0.995022i | \(-0.468225\pi\) | ||||
0.0996595 | + | 0.995022i | \(0.468225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.6847 | 1.37037 | 0.685187 | − | 0.728367i | \(-0.259720\pi\) | ||||
0.685187 | + | 0.728367i | \(0.259720\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.36932 | 0.292157 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.87689 | −0.416661 | −0.208331 | − | 0.978058i | \(-0.566803\pi\) | ||||
−0.208331 | + | 0.978058i | \(0.566803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.68466 | −0.651804 | −0.325902 | − | 0.945404i | \(-0.605668\pi\) | ||||
−0.325902 | + | 0.945404i | \(0.605668\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.63068 | −0.384557 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.24621 | −0.675556 | −0.337778 | − | 0.941226i | \(-0.609675\pi\) | ||||
−0.337778 | + | 0.941226i | \(0.609675\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3153 | 0.839451 | 0.419725 | − | 0.907651i | \(-0.362126\pi\) | ||||
0.419725 | + | 0.907651i | \(0.362126\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.36932 | −0.733862 | −0.366931 | − | 0.930248i | \(-0.619591\pi\) | ||||
−0.366931 | + | 0.930248i | \(0.619591\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.36932 | 0.725020 | 0.362510 | − | 0.931980i | \(-0.381920\pi\) | ||||
0.362510 | + | 0.931980i | \(0.381920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3693 | 1.62468 | 0.812340 | − | 0.583185i | \(-0.198194\pi\) | ||||
0.812340 | + | 0.583185i | \(0.198194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.63068 | 0.198861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.0540 | −1.42416 | −0.712080 | − | 0.702098i | \(-0.752247\pi\) | ||||
−0.712080 | + | 0.702098i | \(0.752247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3693 | −1.29105 | −0.645526 | − | 0.763739i | \(-0.723362\pi\) | ||||
−0.645526 | + | 0.763739i | \(0.723362\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.43845 | 0.399843 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.12311 | 0.0821296 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3693 | 1.40151 | 0.700757 | − | 0.713400i | \(-0.252846\pi\) | ||||
0.700757 | + | 0.713400i | \(0.252846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.36932 | 0.0985656 | 0.0492828 | − | 0.998785i | \(-0.484306\pi\) | ||||
0.0492828 | + | 0.998785i | \(0.484306\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.6847 | 0.974992 | 0.487496 | − | 0.873125i | \(-0.337910\pi\) | ||||
0.487496 | + | 0.873125i | \(0.337910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.3693 | 1.08950 | 0.544751 | − | 0.838598i | \(-0.316624\pi\) | ||||
0.544751 | + | 0.838598i | \(0.316624\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.63068 | 0.325010 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | −0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.19224 | −0.219763 | −0.109881 | − | 0.993945i | \(-0.535047\pi\) | ||||
−0.109881 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.94602 | 0.337316 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.561553 | 0.0377741 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.8078 | 1.79518 | 0.897590 | − | 0.440831i | \(-0.145316\pi\) | ||||
0.897590 | + | 0.440831i | \(0.145316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.3693 | 1.41833 | 0.709166 | − | 0.705042i | \(-0.249072\pi\) | ||||
0.709166 | + | 0.705042i | \(0.249072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6847 | −0.904308 | −0.452154 | − | 0.891940i | \(-0.649344\pi\) | ||||
−0.452154 | + | 0.891940i | \(0.649344\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.6847 | −0.896512 | −0.448256 | − | 0.893905i | \(-0.647955\pi\) | ||||
−0.448256 | + | 0.893905i | \(0.647955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.946025 | −0.0617118 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.6847 | −1.40266 | −0.701332 | − | 0.712835i | \(-0.747411\pi\) | ||||
−0.701332 | + | 0.712835i | \(0.747411\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.75379 | −0.239821 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.0000 | −1.00991 | −0.504956 | − | 0.863145i | \(-0.668491\pi\) | ||||
−0.504956 | + | 0.863145i | \(0.668491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.9309 | −0.993740 | −0.496870 | − | 0.867825i | \(-0.665517\pi\) | ||||
−0.496870 | + | 0.867825i | \(0.665517\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.43845 | −0.337929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.7386 | −1.64877 | −0.824387 | − | 0.566026i | \(-0.808480\pi\) | ||||
−0.824387 | + | 0.566026i | \(0.808480\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.73863 | −0.168233 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.3693 | −1.30291 | −0.651455 | − | 0.758687i | \(-0.725841\pi\) | ||||
−0.651455 | + | 0.758687i | \(0.725841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.68466 | 0.102336 | 0.0511679 | − | 0.998690i | \(-0.483706\pi\) | ||||
0.0511679 | + | 0.998690i | \(0.483706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.36932 | −0.564991 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.36932 | 0.0822743 | 0.0411371 | − | 0.999154i | \(-0.486902\pi\) | ||||
0.0411371 | + | 0.999154i | \(0.486902\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.2462 | −1.20779 | −0.603894 | − | 0.797065i | \(-0.706385\pi\) | ||||
−0.603894 | + | 0.797065i | \(0.706385\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.24621 | −0.133523 | −0.0667617 | − | 0.997769i | \(-0.521267\pi\) | ||||
−0.0667617 | + | 0.997769i | \(0.521267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6847 | −0.981450 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.4384 | −1.36929 | −0.684644 | − | 0.728877i | \(-0.740042\pi\) | ||||
−0.684644 | + | 0.728877i | \(0.740042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.36932 | −0.196169 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.94602 | −0.285084 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.50758 | −0.429883 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.00000 | 0.342438 | 0.171219 | − | 0.985233i | \(-0.445229\pi\) | ||||
0.171219 | + | 0.985233i | \(0.445229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.3693 | 0.871514 | 0.435757 | − | 0.900064i | \(-0.356481\pi\) | ||||
0.435757 | + | 0.900064i | \(0.356481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0540 | 0.963948 | 0.481974 | − | 0.876186i | \(-0.339920\pi\) | ||||
0.481974 | + | 0.876186i | \(0.339920\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.2462 | −1.81113 | −0.905564 | − | 0.424210i | \(-0.860552\pi\) | ||||
−0.905564 | + | 0.424210i | \(0.860552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.4924 | −0.923398 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.36932 | −0.187474 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.68466 | −0.259858 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.946025 | 0.0521560 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.3693 | −1.17456 | −0.587282 | − | 0.809382i | \(-0.699802\pi\) | ||||
−0.587282 | + | 0.809382i | \(0.699802\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.36932 | −0.184085 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.05398 | 0.0574137 | 0.0287068 | − | 0.999588i | \(-0.490861\pi\) | ||||
0.0287068 | + | 0.999588i | \(0.490861\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2462 | 0.771476 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.3153 | −0.875853 | −0.437927 | − | 0.899011i | \(-0.644287\pi\) | ||||
−0.437927 | + | 0.899011i | \(0.644287\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.0540 | −1.55522 | −0.777612 | − | 0.628745i | \(-0.783569\pi\) | ||||
−0.777612 | + | 0.628745i | \(0.783569\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.8617 | 1.37648 | 0.688241 | − | 0.725482i | \(-0.258383\pi\) | ||||
0.688241 | + | 0.725482i | \(0.258383\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.946025 | 0.0502098 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.3693 | 0.916717 | 0.458359 | − | 0.888767i | \(-0.348437\pi\) | ||||
0.458359 | + | 0.888767i | \(0.348437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.61553 | 0.293930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.3693 | −1.42867 | −0.714333 | − | 0.699806i | \(-0.753270\pi\) | ||||
−0.714333 | + | 0.699806i | \(0.753270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.73863 | 0.142183 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3693 | 0.692237 | 0.346118 | − | 0.938191i | \(-0.387500\pi\) | ||||
0.346118 | + | 0.938191i | \(0.387500\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.24621 | −0.424701 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.8769 | −0.866908 | −0.433454 | − | 0.901176i | \(-0.642705\pi\) | ||||
−0.433454 | + | 0.901176i | \(0.642705\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.68466 | 0.0860820 | 0.0430410 | − | 0.999073i | \(-0.486295\pi\) | ||||
0.0430410 | + | 0.999073i | \(0.486295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.630683 | −0.0321426 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.2462 | 1.02652 | 0.513262 | − | 0.858232i | \(-0.328437\pi\) | ||||
0.513262 | + | 0.858232i | \(0.328437\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.73863 | 0.339057 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000 | 0.301131 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.1231 | −1.55421 | −0.777107 | − | 0.629369i | \(-0.783314\pi\) | ||||
−0.777107 | + | 0.629369i | \(0.783314\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.12311 | 0.354827 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.3693 | 0.960101 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.63068 | −0.327866 | −0.163933 | − | 0.986471i | \(-0.552418\pi\) | ||||
−0.163933 | + | 0.986471i | \(0.552418\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.36932 | 0.165793 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.75379 | −0.478795 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.0540 | 0.735435 | 0.367717 | − | 0.929938i | \(-0.380139\pi\) | ||||
0.367717 | + | 0.929938i | \(0.380139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.6847 | 1.64169 | 0.820845 | − | 0.571151i | \(-0.193503\pi\) | ||||
0.820845 | + | 0.571151i | \(0.193503\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.63068 | −0.127607 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.50758 | 0.363317 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.68466 | −0.273820 | −0.136910 | − | 0.990583i | \(-0.543717\pi\) | ||||
−0.136910 | + | 0.990583i | \(0.543717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3153 | 0.687951 | 0.343976 | − | 0.938979i | \(-0.388226\pi\) | ||||
0.343976 | + | 0.938979i | \(0.388226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.6155 | −1.98620 | −0.993100 | − | 0.117267i | \(-0.962587\pi\) | ||||
−0.993100 | + | 0.117267i | \(0.962587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.68466 | −0.365109 | −0.182555 | − | 0.983196i | \(-0.558437\pi\) | ||||
−0.182555 | + | 0.983196i | \(0.558437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.63068 | 0.219515 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.2462 | −0.670828 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.315342 | −0.0147834 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0000 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.1922 | −0.987021 | −0.493510 | − | 0.869740i | \(-0.664287\pi\) | ||||
−0.493510 | + | 0.869740i | \(0.664287\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.6155 | 1.09751 | 0.548753 | − | 0.835984i | \(-0.315103\pi\) | ||||
0.548753 | + | 0.835984i | \(0.315103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7386 | 0.682023 | 0.341011 | − | 0.940059i | \(-0.389231\pi\) | ||||
0.341011 | + | 0.940059i | \(0.389231\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.36932 | 0.155581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.6155 | 0.809963 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.1080 | 1.28968 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.6847 | −1.53909 | −0.769546 | − | 0.638592i | \(-0.779517\pi\) | ||||
−0.769546 | + | 0.638592i | \(0.779517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.68466 | 0.441582 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.36932 | −0.152993 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.1231 | −0.866551 | −0.433275 | − | 0.901262i | \(-0.642642\pi\) | ||||
−0.433275 | + | 0.901262i | \(0.642642\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.6847 | 1.61043 | 0.805213 | − | 0.592986i | \(-0.202051\pi\) | ||||
0.805213 | + | 0.592986i | \(0.202051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.63068 | −0.208555 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.946025 | −0.0424350 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8769 | −0.755514 | −0.377757 | − | 0.925905i | \(-0.623304\pi\) | ||||
−0.377757 | + | 0.925905i | \(0.623304\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.63068 | 0.206472 | 0.103236 | − | 0.994657i | \(-0.467080\pi\) | ||||
0.103236 | + | 0.994657i | \(0.467080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | −0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.4924 | −0.465068 | −0.232534 | − | 0.972588i | \(-0.574702\pi\) | ||||
−0.232534 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.61553 | −0.248416 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.36932 | −0.148182 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5616 | −0.550332 | −0.275166 | − | 0.961397i | \(-0.588733\pi\) | ||||
−0.275166 | + | 0.961397i | \(0.588733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.4924 | 1.77061 | 0.885305 | − | 0.465011i | \(-0.153950\pi\) | ||||
0.885305 | + | 0.465011i | \(0.153950\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000 | 0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.12311 | −0.308536 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.73863 | −0.291337 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.3693 | −0.575857 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.3153 | 0.787438 | 0.393719 | − | 0.919231i | \(-0.371188\pi\) | ||||
0.393719 | + | 0.919231i | \(0.371188\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.946025 | 0.0405232 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.0540 | −0.985717 | −0.492858 | − | 0.870110i | \(-0.664048\pi\) | ||||
−0.492858 | + | 0.870110i | \(0.664048\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 49.4773 | 2.10780 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.73863 | −0.286556 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.3002 | −1.83469 | −0.917344 | − | 0.398096i | \(-0.869671\pi\) | ||||
−0.917344 | + | 0.398096i | \(0.869671\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.80776 | 0.372529 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.6847 | 1.84109 | 0.920544 | − | 0.390638i | \(-0.127746\pi\) | ||||
0.920544 | + | 0.390638i | \(0.127746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.63068 | −0.194814 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.6847 | 1.07676 | 0.538378 | − | 0.842703i | \(-0.319037\pi\) | ||||
0.538378 | + | 0.842703i | \(0.319037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4384 | 0.729776 | 0.364888 | − | 0.931051i | \(-0.381107\pi\) | ||||
0.364888 | + | 0.931051i | \(0.381107\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.73863 | −0.197272 | −0.0986360 | − | 0.995124i | \(-0.531448\pi\) | ||||
−0.0986360 | + | 0.995124i | \(0.531448\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.75379 | 0.404655 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.75379 | −0.403961 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.36932 | −0.386713 | −0.193357 | − | 0.981129i | \(-0.561937\pi\) | ||||
−0.193357 | + | 0.981129i | \(0.561937\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.7386 | −1.76101 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.2462 | −0.831412 | −0.415706 | − | 0.909499i | \(-0.636466\pi\) | ||||
−0.415706 | + | 0.909499i | \(0.636466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.177081 | −0.00725961 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.3693 | −1.44515 | −0.722576 | − | 0.691292i | \(-0.757042\pi\) | ||||
−0.722576 | + | 0.691292i | \(0.757042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0540 | −0.858810 | −0.429405 | − | 0.903112i | \(-0.641277\pi\) | ||||
−0.429405 | + | 0.903112i | \(0.641277\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.93087 | −0.159813 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.8617 | 1.29323 | 0.646614 | − | 0.762817i | \(-0.276184\pi\) | ||||
0.646614 | + | 0.762817i | \(0.276184\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.68466 | −0.0681540 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0000 | −0.403896 | −0.201948 | − | 0.979396i | \(-0.564727\pi\) | ||||
−0.201948 | + | 0.979396i | \(0.564727\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6155 | 0.950725 | 0.475363 | − | 0.879790i | \(-0.342317\pi\) | ||||
0.475363 | + | 0.879790i | \(0.342317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.36932 | −0.376585 | −0.188292 | − | 0.982113i | \(-0.560295\pi\) | ||||
−0.188292 | + | 0.982113i | \(0.560295\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.63068 | −0.185524 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.43845 | 0.216845 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.0540 | 1.63433 | 0.817166 | − | 0.576402i | \(-0.195544\pi\) | ||||
0.817166 | + | 0.576402i | \(0.195544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.26137 | 0.0500558 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.68466 | −0.264856 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.4924 | −0.414426 | −0.207213 | − | 0.978296i | \(-0.566439\pi\) | ||||
−0.207213 | + | 0.978296i | \(0.566439\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0000 | 0.709851 | 0.354925 | − | 0.934895i | \(-0.384506\pi\) | ||||
0.354925 | + | 0.934895i | \(0.384506\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.1080 | 1.18367 | 0.591833 | − | 0.806061i | \(-0.298405\pi\) | ||||
0.591833 | + | 0.806061i | \(0.298405\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.6155 | −1.86334 | −0.931670 | − | 0.363306i | \(-0.881648\pi\) | ||||
−0.931670 | + | 0.363306i | \(0.881648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.80776 | 0.344148 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.7386 | 0.806639 | 0.403320 | − | 0.915059i | \(-0.367856\pi\) | ||||
0.403320 | + | 0.915059i | \(0.367856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.89205 | 0.0733705 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.7386 | −1.03223 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0540 | −0.811571 | −0.405786 | − | 0.913968i | \(-0.633002\pi\) | ||||
−0.405786 | + | 0.913968i | \(0.633002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.3693 | 0.821290 | 0.410645 | − | 0.911795i | \(-0.365304\pi\) | ||||
0.410645 | + | 0.911795i | \(0.365304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.36932 | 0.129303 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.36932 | −0.205451 | −0.102726 | − | 0.994710i | \(-0.532756\pi\) | ||||
−0.102726 | + | 0.994710i | \(0.532756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.73863 | −0.104638 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.87689 | −0.185795 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.87689 | 0.185526 | 0.0927629 | − | 0.995688i | \(-0.470430\pi\) | ||||
0.0927629 | + | 0.995688i | \(0.470430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.31534 | −0.163690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.36932 | 0.353874 | 0.176937 | − | 0.984222i | \(-0.443381\pi\) | ||||
0.176937 | + | 0.984222i | \(0.443381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −58.1080 | −2.19158 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.00000 | 0.150435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.7386 | −0.628633 | −0.314316 | − | 0.949318i | \(-0.601775\pi\) | ||||
−0.314316 | + | 0.949318i | \(0.601775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.12311 | 0.0420018 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.3693 | 0.573179 | 0.286589 | − | 0.958054i | \(-0.407478\pi\) | ||||
0.286589 | + | 0.958054i | \(0.407478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.6307 | 1.43471 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.6155 | −1.54343 | −0.771717 | − | 0.635966i | \(-0.780602\pi\) | ||||
−0.771717 | + | 0.635966i | \(0.780602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.94602 | 0.182935 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.0540 | 0.925390 | 0.462695 | − | 0.886518i | \(-0.346883\pi\) | ||||
0.462695 | + | 0.886518i | \(0.346883\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.1080 | 1.91682 | 0.958411 | − | 0.285392i | \(-0.0921237\pi\) | ||||
0.958411 | + | 0.285392i | \(0.0921237\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.6847 | −0.502041 | −0.251021 | − | 0.967982i | \(-0.580766\pi\) | ||||
−0.251021 | + | 0.967982i | \(0.580766\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.63068 | −0.169655 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.73863 | 0.246224 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.2462 | −0.957738 | −0.478869 | − | 0.877886i | \(-0.658953\pi\) | ||||
−0.478869 | + | 0.877886i | \(0.658953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.79261 | 0.210815 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.36932 | 0.340534 | 0.170267 | − | 0.985398i | \(-0.445537\pi\) | ||||
0.170267 | + | 0.985398i | \(0.445537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.946025 | −0.0342484 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.36932 | 0.337866 | 0.168933 | − | 0.985628i | \(-0.445968\pi\) | ||||
0.168933 | + | 0.985628i | \(0.445968\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.6847 | −0.923813 | −0.461906 | − | 0.886929i | \(-0.652834\pi\) | ||||
−0.461906 | + | 0.886929i | \(0.652834\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.3693 | −1.19866 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.7386 | 1.53127 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.36932 | 0.120564 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.12311 | −0.0400854 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.6155 | −1.26956 | −0.634778 | − | 0.772694i | \(-0.718909\pi\) | ||||
−0.634778 | + | 0.772694i | \(0.718909\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.63068 | 0.164648 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.3693 | −0.474758 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.7386 | −0.451226 | −0.225613 | − | 0.974217i | \(-0.572438\pi\) | ||||
−0.225613 | + | 0.974217i | \(0.572438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.946025 | −0.0334679 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0000 | 0.705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9309 | 1.40389 | 0.701947 | − | 0.712229i | \(-0.252314\pi\) | ||||
0.701947 | + | 0.712229i | \(0.252314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.8617 | −0.908128 | −0.454064 | − | 0.890969i | \(-0.650026\pi\) | ||||
−0.454064 | + | 0.890969i | \(0.650026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.26137 | −0.184298 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52.8466 | −1.84887 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.05398 | 0.176385 | 0.0881925 | − | 0.996103i | \(-0.471891\pi\) | ||||
0.0881925 | + | 0.996103i | \(0.471891\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.3693 | −1.37233 | −0.686164 | − | 0.727447i | \(-0.740707\pi\) | ||||
−0.686164 | + | 0.727447i | \(0.740707\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.7386 | −1.27753 | −0.638764 | − | 0.769403i | \(-0.720554\pi\) | ||||
−0.638764 | + | 0.769403i | \(0.720554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.7386 | 1.13706 | 0.568530 | − | 0.822663i | \(-0.307512\pi\) | ||||
0.568530 | + | 0.822663i | \(0.307512\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.75379 | −0.130061 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.26137 | 0.182077 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.1080 | −1.24658 | −0.623292 | − | 0.781989i | \(-0.714205\pi\) | ||||
−0.623292 | + | 0.781989i | \(0.714205\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.561553 | 0.0193180 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.93087 | 0.135066 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.6847 | −0.742469 | −0.371234 | − | 0.928539i | \(-0.621065\pi\) | ||||
−0.371234 | + | 0.928539i | \(0.621065\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.2462 | 1.10151 | 0.550755 | − | 0.834667i | \(-0.314340\pi\) | ||||
0.550755 | + | 0.834667i | \(0.314340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.0000 | 1.22830 | 0.614152 | − | 0.789188i | \(-0.289498\pi\) | ||||
0.614152 | + | 0.789188i | \(0.289498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.0540 | 0.852847 | 0.426424 | − | 0.904524i | \(-0.359773\pi\) | ||||
0.426424 | + | 0.904524i | \(0.359773\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | −0.203302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.05398 | 0.103243 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.7926 | 1.07356 | 0.536780 | − | 0.843722i | \(-0.319640\pi\) | ||||
0.536780 | + | 0.843722i | \(0.319640\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.3002 | 0.650240 | 0.325120 | − | 0.945673i | \(-0.394595\pi\) | ||||
0.325120 | + | 0.945673i | \(0.394595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.4384 | 0.586850 | 0.293425 | − | 0.955982i | \(-0.405205\pi\) | ||||
0.293425 | + | 0.955982i | \(0.405205\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | −0.402921 | −0.201460 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201460 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.26137 | −0.0423049 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.1080 | 0.338250 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.6998 | −0.357655 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.7386 | −1.95904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.73863 | −0.0912371 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.75379 | −0.324227 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.4233 | −0.877371 | −0.438686 | − | 0.898641i | \(-0.644556\pi\) | ||||
−0.438686 | + | 0.898641i | \(0.644556\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.3693 | 0.906786 | 0.453393 | − | 0.891311i | \(-0.350213\pi\) | ||||
0.453393 | + | 0.891311i | \(0.350213\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.7386 | −1.14968 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.80776 | −0.290858 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.7538 | 1.11343 | 0.556717 | − | 0.830702i | \(-0.312061\pi\) | ||||
0.556717 | + | 0.830702i | \(0.312061\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.68466 | 0.0554512 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −45.3693 | −1.49173 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.6155 | −1.16851 | −0.584254 | − | 0.811571i | \(-0.698613\pi\) | ||||
−0.584254 | + | 0.811571i | \(0.698613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.1080 | 1.31448 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.630683 | 0.0206255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7386 | 1.33087 | 0.665437 | − | 0.746454i | \(-0.268245\pi\) | ||||
0.665437 | + | 0.746454i | \(0.268245\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.6847 | 1.22848 | 0.614242 | − | 0.789117i | \(-0.289462\pi\) | ||||
0.614242 | + | 0.789117i | \(0.289462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.00000 | 0.0649913 | 0.0324956 | − | 0.999472i | \(-0.489654\pi\) | ||||
0.0324956 | + | 0.999472i | \(0.489654\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0000 | 0.324614 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.1922 | 0.686484 | 0.343242 | − | 0.939247i | \(-0.388475\pi\) | ||||
0.343242 | + | 0.939247i | \(0.388475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.8769 | 0.351968 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.73863 | 0.0884351 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7386 | 0.636730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.768944 | 0.0247532 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.42329 | −0.270875 | −0.135437 | − | 0.990786i | \(-0.543244\pi\) | ||||
−0.135437 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.6847 | −0.503345 | −0.251672 | − | 0.967813i | \(-0.580981\pi\) | ||||
−0.251672 | + | 0.967813i | \(0.580981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.31534 | 0.138343 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.9848 | −1.63115 | −0.815575 | − | 0.578652i | \(-0.803579\pi\) | ||||
−0.815575 | + | 0.578652i | \(0.803579\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.4924 | 0.527100 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.4233 | −1.28930 | −0.644651 | − | 0.764477i | \(-0.722997\pi\) | ||||
−0.644651 | + | 0.764477i | \(0.722997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.68466 | 0.244854 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.36932 | 0.107030 | 0.0535149 | − | 0.998567i | \(-0.482958\pi\) | ||||
0.0535149 | + | 0.998567i | \(0.482958\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.63068 | 0.273611 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.7386 | −1.41689 | −0.708443 | − | 0.705768i | \(-0.750602\pi\) | ||||
−0.708443 | + | 0.705768i | \(0.750602\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 7488.2.a.cf.1.2 | 2 | ||
3.2 | odd | 2 | 832.2.a.l.1.1 | 2 | |||
4.3 | odd | 2 | 7488.2.a.ce.1.2 | 2 | |||
8.3 | odd | 2 | 3744.2.a.x.1.1 | 2 | |||
8.5 | even | 2 | 3744.2.a.y.1.1 | 2 | |||
12.11 | even | 2 | 832.2.a.o.1.2 | 2 | |||
24.5 | odd | 2 | 416.2.a.e.1.2 | yes | 2 | ||
24.11 | even | 2 | 416.2.a.c.1.1 | ✓ | 2 | ||
48.5 | odd | 4 | 3328.2.b.u.1665.4 | 4 | |||
48.11 | even | 4 | 3328.2.b.ba.1665.1 | 4 | |||
48.29 | odd | 4 | 3328.2.b.u.1665.1 | 4 | |||
48.35 | even | 4 | 3328.2.b.ba.1665.4 | 4 | |||
312.77 | odd | 2 | 5408.2.a.bd.1.2 | 2 | |||
312.155 | even | 2 | 5408.2.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
416.2.a.c.1.1 | ✓ | 2 | 24.11 | even | 2 | ||
416.2.a.e.1.2 | yes | 2 | 24.5 | odd | 2 | ||
832.2.a.l.1.1 | 2 | 3.2 | odd | 2 | |||
832.2.a.o.1.2 | 2 | 12.11 | even | 2 | |||
3328.2.b.u.1665.1 | 4 | 48.29 | odd | 4 | |||
3328.2.b.u.1665.4 | 4 | 48.5 | odd | 4 | |||
3328.2.b.ba.1665.1 | 4 | 48.11 | even | 4 | |||
3328.2.b.ba.1665.4 | 4 | 48.35 | even | 4 | |||
3744.2.a.x.1.1 | 2 | 8.3 | odd | 2 | |||
3744.2.a.y.1.1 | 2 | 8.5 | even | 2 | |||
5408.2.a.p.1.1 | 2 | 312.155 | even | 2 | |||
5408.2.a.bd.1.2 | 2 | 312.77 | odd | 2 | |||
7488.2.a.ce.1.2 | 2 | 4.3 | odd | 2 | |||
7488.2.a.cf.1.2 | 2 | 1.1 | even | 1 | trivial |