Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3328,2,Mod(1665,3328)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3328, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3328.1665");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3328 = 2^{8} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3328.b (of order \(2\), degree \(1\), not 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: | \(26.5742137927\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 416) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1665.1 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3328.1665 |
Dual form | 3328.2.b.ba.1665.4 |
$q$-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 \(\left(\mathbb{Z}/3328\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(769\) | \(1535\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.56155i | − 1.47891i | −0.673204 | − | 0.739457i | \(-0.735083\pi\) | ||||
0.673204 | − | 0.739457i | \(-0.264917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.561553i | − 0.251134i | −0.992085 | − | 0.125567i | \(-0.959925\pi\) | ||||
0.992085 | − | 0.125567i | \(-0.0400750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.561553 | −0.212247 | −0.106124 | − | 0.994353i | \(-0.533844\pi\) | ||||
−0.106124 | + | 0.994353i | \(0.533844\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.56155 | −1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.43845 | −0.371405 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.561553 | −0.136197 | −0.0680983 | − | 0.997679i | \(-0.521693\pi\) | ||||
−0.0680983 | + | 0.997679i | \(0.521693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.00000i | − 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.43845i | 0.313895i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 1.43845i | 0.276829i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.24621i | − 1.53128i | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
0.643268 | − | 0.765641i | \(-0.277578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.12311 | −1.27935 | −0.639674 | − | 0.768647i | \(-0.720931\pi\) | ||||
−0.639674 | + | 0.768647i | \(0.720931\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.12311 | 0.891818 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.315342i | 0.0533025i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.68466i | 1.59215i | 0.605199 | + | 0.796074i | \(0.293093\pi\) | ||||
−0.605199 | + | 0.796074i | \(0.706907\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.56155 | −0.410177 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.12311 | −1.11244 | −0.556221 | − | 0.831034i | \(-0.687749\pi\) | ||||
−0.556221 | + | 0.831034i | \(0.687749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.80776i | − 1.34317i | −0.740927 | − | 0.671586i | \(-0.765614\pi\) | ||||
0.740927 | − | 0.671586i | \(-0.234386\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000i | 0.298142i | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 1.43845i | 0.201423i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.87689i | 0.669893i | 0.942237 | + | 0.334946i | \(0.108718\pi\) | ||||
−0.942237 | + | 0.334946i | \(0.891282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.12311 | 0.151440 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.3693 | −2.03572 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.00000i | − 0.781133i | −0.920575 | − | 0.390567i | \(-0.872279\pi\) | ||||
0.920575 | − | 0.390567i | \(-0.127721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3693i | 1.71177i | 0.517170 | + | 0.855883i | \(0.326986\pi\) | ||||
−0.517170 | + | 0.855883i | \(0.673014\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.561553 | −0.0696521 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.00000i | − 0.733017i | −0.930415 | − | 0.366508i | \(-0.880553\pi\) | ||||
0.930415 | − | 0.366508i | \(-0.119447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.68466 | −0.199932 | −0.0999661 | − | 0.994991i | \(-0.531873\pi\) | ||||
−0.0999661 | + | 0.994991i | \(0.531873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 12.0000i | − 1.38564i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.12311i | − 0.127990i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.3693i | 1.90653i | 0.302135 | + | 0.953265i | \(0.402301\pi\) | ||||
−0.302135 | + | 0.953265i | \(0.597699\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.315342i | 0.0342036i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.1231 | −2.26463 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.24621 | 0.874097 | 0.437048 | − | 0.899438i | \(-0.356024\pi\) | ||||
0.437048 | + | 0.899438i | \(0.356024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.561553i | 0.0588667i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.2462i | 1.89204i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 7.12311i | − 0.715899i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.12311i | 0.708776i | 0.935099 | + | 0.354388i | \(0.115311\pi\) | ||||
−0.935099 | + | 0.354388i | \(0.884689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.807764 | 0.0788297 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.0000i | − 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.68466i | − 0.161361i | −0.996740 | − | 0.0806805i | \(-0.974291\pi\) | ||||
0.996740 | − | 0.0806805i | \(-0.0257093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.8078 | 2.35465 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.24621 | 0.775738 | 0.387869 | − | 0.921714i | \(-0.373211\pi\) | ||||
0.387869 | + | 0.921714i | \(0.373211\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.56155i | 0.329266i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.315342 | 0.0289073 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.2462i | 1.64521i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 5.43845i | − 0.486430i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.24621 | −0.199319 | −0.0996595 | − | 0.995022i | \(-0.531775\pi\) | ||||
−0.0996595 | + | 0.995022i | \(0.531775\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.5616 | −1.98643 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 15.6847i | − 1.37037i | −0.728367 | − | 0.685187i | \(-0.759720\pi\) | ||||
0.728367 | − | 0.685187i | \(-0.240280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.36932i | 0.292157i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.807764 | 0.0695213 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.87689 | −0.416661 | −0.208331 | − | 0.978058i | \(-0.566803\pi\) | ||||
−0.208331 | + | 0.978058i | \(0.566803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.68466i | 0.651804i | 0.945404 | + | 0.325902i | \(0.105668\pi\) | ||||
−0.945404 | + | 0.325902i | \(0.894332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.31534i | 0.363417i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.63068 | −0.384557 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.1231i | 1.41229i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.24621i | 0.675556i | 0.941226 | + | 0.337778i | \(0.109675\pi\) | ||||
−0.941226 | + | 0.337778i | \(0.890325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3153 | 0.839451 | 0.419725 | − | 0.907651i | \(-0.362126\pi\) | ||||
0.419725 | + | 0.907651i | \(0.362126\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000i | 0.321288i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.4924 | 0.990714 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 9.36932i | − 0.733862i | −0.930248 | − | 0.366931i | \(-0.880409\pi\) | ||||
0.930248 | − | 0.366931i | \(-0.119591\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 2.87689i | − 0.223966i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.36932 | −0.725020 | −0.362510 | − | 0.931980i | \(-0.618080\pi\) | ||||
−0.362510 | + | 0.931980i | \(0.618080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.3693i | 1.63415i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3693i | 1.62468i | 0.583185 | + | 0.812340i | \(0.301806\pi\) | ||||
−0.583185 | + | 0.812340i | \(0.698194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.63068 | −0.198861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.3693 | −1.15523 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0540i | 1.42416i | 0.702098 | + | 0.712080i | \(0.252247\pi\) | ||||
−0.702098 | + | 0.712080i | \(0.747753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 17.3693i | − 1.29105i | −0.763739 | − | 0.645526i | \(-0.776638\pi\) | ||||
0.763739 | − | 0.645526i | \(-0.223362\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 34.2462 | 2.53155 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.43845 | 0.399843 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.12311i | − 0.0821296i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 0.807764i | − 0.0587562i | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 1.43845i | 0.103009i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 13.6847i | − 0.974992i | −0.873125 | − | 0.487496i | \(-0.837910\pi\) | ||||
0.873125 | − | 0.487496i | \(-0.162090\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.3693 | 1.08950 | 0.544751 | − | 0.838598i | \(-0.316624\pi\) | ||||
0.544751 | + | 0.838598i | \(0.316624\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.3693 | −1.08407 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.63068i | 0.325010i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000i | 0.279372i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.19224i | − 0.219763i | −0.993945 | − | 0.109881i | \(-0.964953\pi\) | ||||
0.993945 | − | 0.109881i | \(-0.0350471\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.31534i | 0.295682i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.94602 | −0.337316 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 25.6155i | 1.73094i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.561553i | 0.0377741i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8078 | −1.79518 | −0.897590 | − | 0.440831i | \(-0.854684\pi\) | ||||
−0.897590 | + | 0.440831i | \(0.854684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.6847 | −1.11231 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 21.3693i | − 1.41833i | −0.705042 | − | 0.709166i | \(-0.749072\pi\) | ||||
0.705042 | − | 0.709166i | \(-0.250928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 13.6847i | − 0.904308i | −0.891940 | − | 0.452154i | \(-0.850656\pi\) | ||||
0.891940 | − | 0.452154i | \(-0.149344\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.87689 | −0.189286 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.6847 | −0.896512 | −0.448256 | − | 0.893905i | \(-0.647955\pi\) | ||||
−0.448256 | + | 0.893905i | \(0.647955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.946025i | 0.0617118i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 30.7386i | 1.99669i | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 22.2462i | 1.42710i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.75379i | 0.239821i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 44.4924 | 2.81959 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 16.0000i | − 1.00991i | −0.863145 | − | 0.504956i | \(-0.831509\pi\) | ||||
0.863145 | − | 0.504956i | \(-0.168491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.807764 | 0.0505841 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.9309 | 0.993740 | 0.496870 | − | 0.867825i | \(-0.334483\pi\) | ||||
0.496870 | + | 0.867825i | \(0.334483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5.43845i | − 0.337929i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29.3693i | 1.81792i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.7386 | 1.64877 | 0.824387 | − | 0.566026i | \(-0.191520\pi\) | ||||
0.824387 | + | 0.566026i | \(0.191520\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.73863 | 0.168233 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 21.1231i | − 1.29271i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 21.3693i | − 1.30291i | −0.758687 | − | 0.651455i | \(-0.774159\pi\) | ||||
0.758687 | − | 0.651455i | \(-0.225841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.68466 | −0.102336 | −0.0511679 | − | 0.998690i | \(-0.516294\pi\) | ||||
−0.0511679 | + | 0.998690i | \(0.516294\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.43845 | 0.0870588 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.36932i | 0.564991i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.36932i | 0.0822743i | 0.999154 | + | 0.0411371i | \(0.0130981\pi\) | ||||
−0.999154 | + | 0.0411371i | \(0.986902\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.3693 | 1.51882 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.2462 | −1.20779 | −0.603894 | − | 0.797065i | \(-0.706385\pi\) | ||||
−0.603894 | + | 0.797065i | \(0.706385\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.24621i | 0.133523i | 0.997769 | + | 0.0667617i | \(0.0212667\pi\) | ||||
−0.997769 | + | 0.0667617i | \(0.978733\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.63068i | 0.511238i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6847 | −0.981450 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.3693i | 0.900965i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4384i | 1.36929i | 0.728877 | + | 0.684644i | \(0.240042\pi\) | ||||
−0.728877 | + | 0.684644i | \(0.759958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.36932 | −0.196169 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.87689 | −0.166934 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.94602i | 0.285084i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.2462 | 1.04822 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.50758 | 0.429883 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.00000i | 0.342438i | 0.985233 | + | 0.171219i | \(0.0547706\pi\) | ||||
−0.985233 | + | 0.171219i | \(0.945229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.3693 | −0.871514 | −0.435757 | − | 0.900064i | \(-0.643519\pi\) | ||||
−0.435757 | + | 0.900064i | \(0.643519\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0540 | −0.963948 | −0.481974 | − | 0.876186i | \(-0.660080\pi\) | ||||
−0.481974 | + | 0.876186i | \(0.660080\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.12311i | − 0.0632798i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 32.2462i | − 1.81113i | −0.424210 | − | 0.905564i | \(-0.639448\pi\) | ||||
0.424210 | − | 0.905564i | \(-0.360552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.4924 | 0.923398 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.7386 | −1.71566 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.36932i | 0.187474i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.68466i | − 0.259858i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.31534 | −0.238639 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.946025 | 0.0521560 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.3693i | 1.17456i | 0.809382 | + | 0.587282i | \(0.199802\pi\) | ||||
−0.809382 | + | 0.587282i | \(0.800198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 34.4924i | − 1.89017i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 21.1231i | − 1.14725i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 14.2462i | − 0.771476i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 16.3153i | − 0.875853i | −0.899011 | − | 0.437927i | \(-0.855713\pi\) | ||||
0.899011 | − | 0.437927i | \(-0.144287\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.0540i | 1.55522i | 0.628745 | + | 0.777612i | \(0.283569\pi\) | ||||
−0.628745 | + | 0.777612i | \(0.716431\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.43845 | 0.0767786 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.8617 | −1.37648 | −0.688241 | − | 0.725482i | \(-0.741617\pi\) | ||||
−0.688241 | + | 0.725482i | \(0.741617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.946025i | 0.0502098i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 0.807764i | − 0.0427514i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3693 | −0.916717 | −0.458359 | − | 0.888767i | \(-0.651563\pi\) | ||||
−0.458359 | + | 0.888767i | \(0.651563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 17.9309i | − 0.941127i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.61553i | 0.293930i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3693 | 1.42867 | 0.714333 | − | 0.699806i | \(-0.246730\pi\) | ||||
0.714333 | + | 0.699806i | \(0.246730\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.3693 | 1.32067 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.73863i | − 0.142183i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3693i | 0.692237i | 0.938191 | + | 0.346118i | \(0.112500\pi\) | ||||
−0.938191 | + | 0.346118i | \(0.887500\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.9309 | −0.719387 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.24621 | −0.424701 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.8769i | 0.866908i | 0.901176 | + | 0.433454i | \(0.142705\pi\) | ||||
−0.901176 | + | 0.433454i | \(0.857295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.75379i | 0.294776i | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 31.3693i | 1.59459i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 20.2462i | − 1.02652i | −0.858232 | − | 0.513262i | \(-0.828437\pi\) | ||||
0.858232 | − | 0.513262i | \(-0.171563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −40.1771 | −2.02667 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.73863i | 0.339057i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6.00000i | − 0.301131i | −0.988600 | − | 0.150566i | \(-0.951890\pi\) | ||||
0.988600 | − | 0.150566i | \(-0.0481095\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.63068 | 0.432075 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.1231 | 1.55421 | 0.777107 | − | 0.629369i | \(-0.216686\pi\) | ||||
0.777107 | + | 0.629369i | \(0.216686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.12311i | 0.354827i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.93087i | 0.195326i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.3693 | −0.960101 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.63068 | 0.327866 | 0.163933 | − | 0.986471i | \(-0.447582\pi\) | ||||
0.163933 | + | 0.986471i | \(0.447582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.4924i | 0.616206i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.36932i | 0.165793i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.75379 | 0.478795 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.6847 | 0.963962 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 15.0540i | − 0.735435i | −0.929938 | − | 0.367717i | \(-0.880139\pi\) | ||||
0.929938 | − | 0.367717i | \(-0.119861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.6847i | 1.64169i | 0.571151 | + | 0.820845i | \(0.306497\pi\) | ||||
−0.571151 | + | 0.820845i | \(0.693503\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.63068 | −0.127607 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 7.50758i | − 0.363317i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 5.12311i | − 0.247346i | ||||||||
\(430\) | 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 | ||||||||
\(435\) | 11.8617i | 0.568727i | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 23.8078 | 1.13370 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 7.68466i | − 0.365109i | −0.983196 | − | 0.182555i | \(-0.941563\pi\) | ||||
0.983196 | − | 0.182555i | \(-0.0584366\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 4.63068i | − 0.219515i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.1231 | 0.999089 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 14.2462i | − 0.670828i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 26.4233i | − 1.24147i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.315342 | 0.0147834 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.0000 | 0.654892 | 0.327446 | − | 0.944870i | \(-0.393812\pi\) | ||||
0.327446 | + | 0.944870i | \(0.393812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 0.807764i | − 0.0377032i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 21.1922i | − 0.987021i | −0.869740 | − | 0.493510i | \(-0.835713\pi\) | ||||
0.869740 | − | 0.493510i | \(-0.164287\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.6155 | −1.09751 | −0.548753 | − | 0.835984i | \(-0.684897\pi\) | ||||
−0.548753 | + | 0.835984i | \(0.684897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.2462 | 0.475157 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 14.7386i | − 0.682023i | −0.940059 | − | 0.341011i | \(-0.889231\pi\) | ||||
0.940059 | − | 0.341011i | \(-0.110769\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.36932i | 0.155581i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.12311 | 0.236060 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.6155 | 0.809963 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 28.1080i | − 1.28968i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 17.3693i | − 0.795286i | ||||||||
\(478\) | 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 | ||||||||
\(485\) | 3.36932i | 0.152993i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.1231 | −0.866551 | −0.433275 | − | 0.901262i | \(-0.642642\pi\) | ||||
−0.433275 | + | 0.901262i | \(0.642642\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.6847i | 1.61043i | 0.592986 | + | 0.805213i | \(0.297949\pi\) | ||||
−0.592986 | + | 0.805213i | \(0.702051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.63068i | 0.208555i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.946025 | 0.0424350 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 16.8769i | − 0.755514i | −0.925905 | − | 0.377757i | \(-0.876696\pi\) | ||||
0.925905 | − | 0.377757i | \(-0.123304\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0000i | 1.07224i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.63068 | −0.206472 | −0.103236 | − | 0.994657i | \(-0.532920\pi\) | ||||
−0.103236 | + | 0.994657i | \(0.532920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.56155i | 0.113763i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 10.4924i | − 0.465068i | −0.972588 | − | 0.232534i | \(-0.925298\pi\) | ||||
0.972588 | − | 0.232534i | \(-0.0747018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.61553 | 0.248416 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.63068 | 0.381054 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3.36932i | − 0.148182i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 54.7386 | 2.40276 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5616 | −0.550332 | −0.275166 | − | 0.961397i | \(-0.588733\pi\) | ||||
−0.275166 | + | 0.961397i | \(0.588733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 40.4924i | − 1.77061i | −0.465011 | − | 0.885305i | \(-0.653950\pi\) | ||||
0.465011 | − | 0.885305i | \(-0.346050\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.73863i | 0.294098i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000 | 0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.3693i | 0.927349i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.12311i | 0.308536i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.73863 | −0.291337 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 48.8078 | 2.10621 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 13.3693i | − 0.575857i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 18.3153i | − 0.787438i | −0.919231 | − | 0.393719i | \(-0.871188\pi\) | ||||
0.919231 | − | 0.393719i | \(-0.128812\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −44.4924 | −1.90935 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.946025 | −0.0405232 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 23.0540i | − 0.985717i | −0.870110 | − | 0.492858i | \(-0.835952\pi\) | ||||
0.870110 | − | 0.492858i | \(-0.164048\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 47.6155i | − 2.03218i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.4773 | −2.10780 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.73863 | 0.286556 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 13.9309i | − 0.591332i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 43.3002i | − 1.83469i | −0.398096 | − | 0.917344i | \(-0.630329\pi\) | ||||
0.398096 | − | 0.917344i | \(-0.369671\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.80776 | −0.372529 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.87689 | −0.121463 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 43.6847i | − 1.84109i | −0.390638 | − | 0.920544i | \(-0.627746\pi\) | ||||
0.390638 | − | 0.920544i | \(-0.372254\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.63068i | − 0.194814i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.93087 | 0.165081 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.6847 | 1.07676 | 0.538378 | − | 0.842703i | \(-0.319037\pi\) | ||||
0.538378 | + | 0.842703i | \(0.319037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 17.4384i | − 0.729776i | −0.931051 | − | 0.364888i | \(-0.881107\pi\) | ||||
0.931051 | − | 0.364888i | \(-0.118893\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 49.6155i | − 2.07272i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | − 3.50758i | − 0.145770i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 9.75379i | − 0.404655i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.75379 | −0.403961 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 9.36932i | − 0.386713i | −0.981129 | − | 0.193357i | \(-0.938063\pi\) | ||||
0.981129 | − | 0.193357i | \(-0.0619374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.7386i | 1.76101i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.0540 | −1.44193 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.2462 | 0.831412 | 0.415706 | − | 0.909499i | \(-0.363534\pi\) | ||||
0.415706 | + | 0.909499i | \(0.363534\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 0.177081i | − 0.00725961i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 39.3693i | − 1.61128i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.3693 | 1.44515 | 0.722576 | − | 0.691292i | \(-0.242958\pi\) | ||||
0.722576 | + | 0.691292i | \(0.242958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0540 | 0.858810 | 0.429405 | − | 0.903112i | \(-0.358723\pi\) | ||||
0.429405 | + | 0.903112i | \(0.358723\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.3693i | 0.870226i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.93087i | − 0.159813i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8617 | −1.29323 | −0.646614 | − | 0.762817i | \(-0.723816\pi\) | ||||
−0.646614 | + | 0.762817i | \(0.723816\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.8617 | 0.480662 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.68466i | 0.0681540i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 10.0000i | − 0.403896i | −0.979396 | − | 0.201948i | \(-0.935273\pi\) | ||||
0.979396 | − | 0.201948i | \(-0.0647272\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.2462 | 0.413167 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6155 | 0.950725 | 0.475363 | − | 0.879790i | \(-0.342317\pi\) | ||||
0.475363 | + | 0.879790i | \(0.342317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.36932i | 0.376585i | 0.982113 | + | 0.188292i | \(0.0602952\pi\) | ||||
−0.982113 | + | 0.188292i | \(0.939705\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.63068 | −0.185524 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 30.7386i | − 1.22758i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 5.43845i | − 0.216845i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.0540 | 1.63433 | 0.817166 | − | 0.576402i | \(-0.195544\pi\) | ||||
0.817166 | + | 0.576402i | \(0.195544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.17708 | −0.325010 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.26137i | 0.0500558i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.68466i | 0.264856i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.4924 | 0.414426 | 0.207213 | − | 0.978296i | \(-0.433561\pi\) | ||||
0.207213 | + | 0.978296i | \(0.433561\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0000i | 0.709851i | 0.934895 | + | 0.354925i | \(0.115494\pi\) | ||||
−0.934895 | + | 0.354925i | \(0.884506\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.6695i | 0.498861i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.1080 | −1.18367 | −0.591833 | − | 0.806061i | \(-0.701595\pi\) | ||||
−0.591833 | + | 0.806061i | \(0.701595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 10.2462i | − 0.401581i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 47.6155i | − 1.86334i | −0.363306 | − | 0.931670i | \(-0.618352\pi\) | ||||
0.363306 | − | 0.931670i | \(-0.381648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.80776 | −0.344148 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35.6155 | 1.38949 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 12.0000i | − 0.467454i | −0.972302 | − | 0.233727i | \(-0.924908\pi\) | ||||
0.972302 | − | 0.233727i | \(-0.0750921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.7386i | 0.806639i | 0.915059 | + | 0.403320i | \(0.132144\pi\) | ||||
−0.915059 | + | 0.403320i | \(0.867856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.43845 | 0.0558647 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.89205 | 0.0733705 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 68.6695i | 2.65492i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 6.73863i | 0.259370i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 21.3693i | − 0.821290i | −0.911795 | − | 0.410645i | \(-0.865304\pi\) | ||||
0.911795 | − | 0.410645i | \(-0.134696\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.36932 | 0.129303 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −54.7386 | −2.09759 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.36932i | − 0.205451i | −0.994710 | − | 0.102726i | \(-0.967244\pi\) | ||||
0.994710 | − | 0.102726i | \(-0.0327564\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.73863i | 0.104638i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.0540 | −1.33739 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.87689 | 0.185795 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.87689i | 0.185526i | 0.995688 | + | 0.0927629i | \(0.0295699\pi\) | ||||
−0.995688 | + | 0.0927629i | \(0.970430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000i | 0.151947i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.31534 | 0.163690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.0540i | 1.32586i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.36932i | 0.353874i | 0.984222 | + | 0.176937i | \(0.0566189\pi\) | ||||
−0.984222 | + | 0.176937i | \(0.943381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.1080 | 2.19158 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.42329 | 0.0912665 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.00000i | − 0.150435i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 16.7386i | − 0.628633i | −0.949318 | − | 0.314316i | \(-0.898225\pi\) | ||||
0.949318 | − | 0.314316i | \(-0.101775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.7386 | 1.60282 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.12311i | − 0.0420018i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 55.5464i | 2.07442i | ||||||||
\(718\) | 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 | ||||||||
\(723\) | − 5.12311i | − 0.190530i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 38.6307i | − 1.43471i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.6155 | −1.54343 | −0.771717 | − | 0.635966i | \(-0.780602\pi\) | ||||
−0.771717 | + | 0.635966i | \(0.780602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 35.9848 | 1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.94602i | 0.182935i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 25.0540i | − 0.925390i | −0.886518 | − | 0.462695i | \(-0.846883\pi\) | ||||
0.886518 | − | 0.462695i | \(-0.153117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.61553 | 0.354674 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.0000 | 0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.1080i | 1.91682i | 0.285392 | + | 0.958411i | \(0.407876\pi\) | ||||
−0.285392 | + | 0.958411i | \(0.592124\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.3693i | 0.564606i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.6847 | 0.502041 | 0.251021 | − | 0.967982i | \(-0.419234\pi\) | ||||
0.251021 | + | 0.967982i | \(0.419234\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.63068 | 0.169655 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 61.8617i | − 2.26340i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.73863i | 0.246224i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.2462 | 0.957738 | 0.478869 | − | 0.877886i | \(-0.341047\pi\) | ||||
0.478869 | + | 0.877886i | \(0.341047\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −40.9848 | −1.49357 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 5.79261i | − 0.210815i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.36932i | 0.340534i | 0.985398 | + | 0.170267i | \(0.0544630\pi\) | ||||
−0.985398 | + | 0.170267i | \(0.945537\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 0.946025i | 0.0342484i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.12311i | − 0.0406060i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 40.8078i | − 1.46966i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.6847i | 0.923813i | 0.886929 | + | 0.461906i | \(0.152834\pi\) | ||||
−0.886929 | + | 0.461906i | \(0.847166\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.3693 | −1.19866 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.9309 | −0.499767 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.7386i | 1.53127i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 3.36932i | − 0.120564i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.8617 | 0.423904 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.12311 | 0.0400854 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 35.6155i | − 1.26956i | −0.772694 | − | 0.634778i | \(-0.781091\pi\) | ||||
0.772694 | − | 0.634778i | \(-0.218909\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 68.4924i | − 2.43839i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.63068 | −0.164648 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.3693 | 0.474758 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 7.01515i | − 0.248802i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 12.7386i | − 0.451226i | −0.974217 | − | 0.225613i | \(-0.927562\pi\) | ||||
0.974217 | − | 0.225613i | \(-0.0724384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.946025 | 0.0334679 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.3693 | −1.03771 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 20.0000i | − 0.705785i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −54.7386 | −1.92689 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9309 | 1.40389 | 0.701947 | − | 0.712229i | \(-0.252314\pi\) | ||||
0.701947 | + | 0.712229i | \(0.252314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.8617i | 0.908128i | 0.890969 | + | 0.454064i | \(0.150026\pi\) | ||||
−0.890969 | + | 0.454064i | \(0.849974\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.31534i | 0.151346i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.26137 | −0.184298 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52.8466 | −1.84887 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 2.00000i | − 0.0698857i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 5.05398i | − 0.176385i | −0.996103 | − | 0.0881925i | \(-0.971891\pi\) | ||||
0.996103 | − | 0.0881925i | \(-0.0281091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.3693 | −1.37233 | −0.686164 | − | 0.727447i | \(-0.740707\pi\) | ||||
−0.686164 | + | 0.727447i | \(0.740707\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.0000 | 0.835573 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 36.7386i | − 1.27753i | −0.769403 | − | 0.638764i | \(-0.779446\pi\) | ||||
0.769403 | − | 0.638764i | \(-0.220554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 32.7386i | − 1.13706i | −0.822663 | − | 0.568530i | \(-0.807512\pi\) | ||||
0.822663 | − | 0.568530i | \(-0.192488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.50758 | 0.121677 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.75379 | 0.130061 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.26137i | 0.182077i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 10.2462i | − 0.354161i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.1080 | 1.24658 | 0.623292 | − | 0.781989i | \(-0.285795\pi\) | ||||
0.623292 | + | 0.781989i | \(0.285795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.0000 | −1.34483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 51.8617i | 1.78621i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.561553i | 0.0193180i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.93087 | −0.135066 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.75379 | 0.197470 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 21.6847i | − 0.742469i | −0.928539 | − | 0.371234i | \(-0.878935\pi\) | ||||
0.928539 | − | 0.371234i | \(-0.121065\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.0000 | 0.410391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.2462 | 1.10151 | 0.550755 | − | 0.834667i | \(-0.314340\pi\) | ||||
0.550755 | + | 0.834667i | \(0.314340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 36.0000i | − 1.22830i | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||||
0.789188 | − | 0.614152i | \(-0.210502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 10.2462i | − 0.349190i | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 42.7386i | 1.45148i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 24.0000i | − 0.814144i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | −0.203302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.3693 | 0.723242 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.05398i | 0.103243i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 31.7926i | − 1.07356i | −0.843722 | − | 0.536780i | \(-0.819640\pi\) | ||||
0.843722 | − | 0.536780i | \(-0.180360\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 60.0388 | 2.02506 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.3002 | −0.650240 | −0.325120 | − | 0.945673i | \(-0.605405\pi\) | ||||
−0.325120 | + | 0.945673i | \(0.605405\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.4384i | 0.586850i | 0.955982 | + | 0.293425i | \(0.0947952\pi\) | ||||
−0.955982 | + | 0.293425i | \(0.905205\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.63068i | 0.290117i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000 | 0.402921 | 0.201460 | − | 0.979497i | \(-0.435431\pi\) | ||||
0.201460 | + | 0.979497i | \(0.435431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.26137 | 0.0423049 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 14.0000i | − 0.469018i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.1080i | 0.338250i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.6998 | 0.357655 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.7386i | 1.95904i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.73863i | − 0.0912371i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.6695 | 0.421615 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.75379 | −0.324227 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.4233i | 0.877371i | 0.898641 | + | 0.438686i | \(0.144556\pi\) | ||||
−0.898641 | + | 0.438686i | \(0.855444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 25.3693i | − 0.841447i | ||||||||
\(910\) | 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 | ||||||||
\(915\) | − 19.2311i | − 0.635759i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.80776i | 0.290858i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.7538 | 1.11343 | 0.556717 | − | 0.830702i | \(-0.312061\pi\) | ||||
0.556717 | + | 0.830702i | \(0.312061\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.3693 | 0.506436 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.68466i | 0.0554512i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.3693i | 1.49173i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.6155 | 1.16851 | 0.584254 | − | 0.811571i | \(-0.301387\pi\) | ||||
0.584254 | + | 0.811571i | \(0.301387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.1080i | 1.31448i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39.3693i | 1.28889i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.630683 | −0.0206255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.7386 | −1.33087 | −0.665437 | − | 0.746454i | \(-0.731755\pi\) | ||||
−0.665437 | + | 0.746454i | \(0.731755\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.6847i | 1.42559i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.6847i | 1.22848i | 0.789117 | + | 0.614242i | \(0.210538\pi\) | ||||
−0.789117 | + | 0.614242i | \(0.789462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.453602 | −0.0147557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.00000i | − 0.0649913i | −0.999472 | − | 0.0324956i | \(-0.989654\pi\) | ||||
0.999472 | − | 0.0324956i | \(-0.0103455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0000i | 0.324614i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −82.6004 | −2.67850 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.1922 | 0.686484 | 0.343242 | − | 0.939247i | \(-0.388475\pi\) | ||||
0.343242 | + | 0.939247i | \(0.388475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 10.8769i | − 0.351968i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 42.2462i | − 1.36563i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.73863 | 0.0884351 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7386 | 0.636730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.7386i | 1.37723i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 0.768944i | − 0.0247532i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.42329 | −0.270875 | −0.135437 | − | 0.990786i | \(-0.543244\pi\) | ||||
−0.135437 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.63068 | 0.277257 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 15.6847i | − 0.503345i | −0.967813 | − | 0.251672i | \(-0.919019\pi\) | ||||
0.967813 | − | 0.251672i | \(-0.0809805\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.31534i | − 0.138343i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0000 | −0.384308 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.9848 | 1.63115 | 0.815575 | − | 0.578652i | \(-0.196421\pi\) | ||||
0.815575 | + | 0.578652i | \(0.196421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.4924i | 0.527100i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000i | 0.191565i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.4233 | 1.28930 | 0.644651 | − | 0.764477i | \(-0.277003\pi\) | ||||
0.644651 | + | 0.764477i | \(0.277003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.68466 | −0.244854 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.42329i | − 0.0771342i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.36932 | −0.107030 | −0.0535149 | − | 0.998567i | \(-0.517042\pi\) | ||||
−0.0535149 | + | 0.998567i | \(0.517042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 54.7386 | 1.73708 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 8.63068i | − 0.273611i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 44.7386i | − 1.41689i | −0.705768 | − | 0.708443i | \(-0.749398\pi\) | ||||
0.705768 | − | 0.708443i | \(-0.250602\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.9309 | −0.440753 |
(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 | 3328.2.b.ba.1665.1 | 4 | ||
4.3 | odd | 2 | 3328.2.b.u.1665.4 | 4 | |||
8.3 | odd | 2 | 3328.2.b.u.1665.1 | 4 | |||
8.5 | even | 2 | inner | 3328.2.b.ba.1665.4 | 4 | ||
16.3 | odd | 4 | 832.2.a.l.1.1 | 2 | |||
16.5 | even | 4 | 416.2.a.c.1.1 | ✓ | 2 | ||
16.11 | odd | 4 | 416.2.a.e.1.2 | yes | 2 | ||
16.13 | even | 4 | 832.2.a.o.1.2 | 2 | |||
48.5 | odd | 4 | 3744.2.a.x.1.1 | 2 | |||
48.11 | even | 4 | 3744.2.a.y.1.1 | 2 | |||
48.29 | odd | 4 | 7488.2.a.ce.1.2 | 2 | |||
48.35 | even | 4 | 7488.2.a.cf.1.2 | 2 | |||
208.155 | odd | 4 | 5408.2.a.bd.1.2 | 2 | |||
208.181 | even | 4 | 5408.2.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
416.2.a.c.1.1 | ✓ | 2 | 16.5 | even | 4 | ||
416.2.a.e.1.2 | yes | 2 | 16.11 | odd | 4 | ||
832.2.a.l.1.1 | 2 | 16.3 | odd | 4 | |||
832.2.a.o.1.2 | 2 | 16.13 | even | 4 | |||
3328.2.b.u.1665.1 | 4 | 8.3 | odd | 2 | |||
3328.2.b.u.1665.4 | 4 | 4.3 | odd | 2 | |||
3328.2.b.ba.1665.1 | 4 | 1.1 | even | 1 | trivial | ||
3328.2.b.ba.1665.4 | 4 | 8.5 | even | 2 | inner | ||
3744.2.a.x.1.1 | 2 | 48.5 | odd | 4 | |||
3744.2.a.y.1.1 | 2 | 48.11 | even | 4 | |||
5408.2.a.p.1.1 | 2 | 208.181 | even | 4 | |||
5408.2.a.bd.1.2 | 2 | 208.155 | odd | 4 | |||
7488.2.a.ce.1.2 | 2 | 48.29 | odd | 4 | |||
7488.2.a.cf.1.2 | 2 | 48.35 | even | 4 |