Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(1009,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1680.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.t (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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.3 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1009 |
Dual form | 1680.2.t.h.1009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214i | 1.24035i | 0.784465 | + | 0.620174i | \(0.212938\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 2.23607i | − 0.577350i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47214i | 0.599581i | 0.954005 | + | 0.299791i | \(0.0969168\pi\) | ||||
−0.954005 | + | 0.299791i | \(0.903083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4.00000i | − 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.472136 | −0.0876734 | −0.0438367 | − | 0.999039i | \(-0.513958\pi\) | ||||
−0.0438367 | + | 0.999039i | \(0.513958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.47214 | −1.52164 | −0.760820 | − | 0.648963i | \(-0.775203\pi\) | ||||
−0.760820 | + | 0.648963i | \(0.775203\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.23607i | − 0.377964i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.47214i | 1.06401i | 0.846740 | + | 0.532006i | \(0.178562\pi\) | ||||
−0.846740 | + | 0.532006i | \(0.821438\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.47214 | −0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4721 | −1.94782 | −0.973910 | − | 0.226934i | \(-0.927130\pi\) | ||||
−0.973910 | + | 0.226934i | \(0.927130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 6.47214i | − 0.986991i | −0.869748 | − | 0.493496i | \(-0.835719\pi\) | ||||
0.869748 | − | 0.493496i | \(-0.164281\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.23607 | 0.333333 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.47214i | − 0.360598i | −0.983612 | − | 0.180299i | \(-0.942293\pi\) | ||||
0.983612 | − | 0.180299i | \(-0.0577065\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.47214 | −0.346168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.47214 | −0.603023 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4721 | −1.59689 | −0.798447 | − | 0.602066i | \(-0.794345\pi\) | ||||
−0.798447 | + | 0.602066i | \(0.794345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.00000i | − 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 10.0000i | − 1.24035i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4721i | 1.27938i | 0.768635 | + | 0.639688i | \(0.220936\pi\) | ||||
−0.768635 | + | 0.639688i | \(0.779064\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.52786 | −0.418680 | −0.209340 | − | 0.977843i | \(-0.567132\pi\) | ||||
−0.209340 | + | 0.977843i | \(0.567132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.4721i | 1.92792i | 0.266051 | + | 0.963959i | \(0.414281\pi\) | ||||
−0.266051 | + | 0.963959i | \(0.585719\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.00000i | 0.577350i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 12.9443i | − 1.42082i | −0.703789 | − | 0.710409i | \(-0.748510\pi\) | ||||
0.703789 | − | 0.710409i | \(-0.251490\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5.52786i | − 0.599581i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 0.472136i | − 0.0506183i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.41641 | −0.998137 | −0.499069 | − | 0.866562i | \(-0.666324\pi\) | ||||
−0.499069 | + | 0.866562i | \(0.666324\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 8.47214i | − 0.878520i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.47214 | −0.458831 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 12.4721i | − 1.26635i | −0.774007 | − | 0.633177i | \(-0.781751\pi\) | ||||
0.774007 | − | 0.633177i | \(-0.218249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.47214 | −0.444994 | −0.222497 | − | 0.974933i | \(-0.571421\pi\) | ||||
−0.222497 | + | 0.974933i | \(0.571421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.94427i | 0.487174i | 0.969879 | + | 0.243587i | \(0.0783241\pi\) | ||||
−0.969879 | + | 0.243587i | \(0.921676\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.23607 | 0.218218 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.94427 | 0.282010 | 0.141005 | − | 0.990009i | \(-0.454967\pi\) | ||||
0.141005 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.47214 | −0.614308 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.94427i | − 0.276974i | −0.990364 | − | 0.138487i | \(-0.955776\pi\) | ||||
0.990364 | − | 0.138487i | \(-0.0442239\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.94427i | 0.834058i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.47214i | − 0.413449i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.47214 | −0.226620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 12.4721i | − 1.12457i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000i | 0.354943i | 0.984126 | + | 0.177471i | \(0.0567917\pi\) | ||||
−0.984126 | + | 0.177471i | \(0.943208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.47214 | 0.569840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.8885 | 1.91241 | 0.956205 | − | 0.292696i | \(-0.0945525\pi\) | ||||
0.956205 | + | 0.292696i | \(0.0945525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000i | 0.173422i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.23607i | 0.192450i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 15.8885i | − 1.35745i | −0.734393 | − | 0.678725i | \(-0.762533\pi\) | ||||
0.734393 | − | 0.678725i | \(-0.237467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.9443 | 1.26756 | 0.633778 | − | 0.773515i | \(-0.281503\pi\) | ||||
0.633778 | + | 0.773515i | \(0.281503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.47214 | 0.208191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.94427i | 0.747958i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.05573 | 0.0876734 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.00000i | − 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.52786 | 0.289014 | 0.144507 | − | 0.989504i | \(-0.453840\pi\) | ||||
0.144507 | + | 0.989504i | \(0.453840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8885 | −1.45575 | −0.727875 | − | 0.685710i | \(-0.759492\pi\) | ||||
−0.727875 | + | 0.685710i | \(0.759492\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 2.47214i | − 0.199860i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.9443 | 1.52164 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.4164i | 1.38998i | 0.719019 | + | 0.694990i | \(0.244591\pi\) | ||||
−0.719019 | + | 0.694990i | \(0.755409\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.41641i | 0.267594i | 0.991009 | + | 0.133797i | \(0.0427170\pi\) | ||||
−0.991009 | + | 0.133797i | \(0.957283\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 4.47214i | − 0.348155i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.52786i | 0.118230i | 0.998251 | + | 0.0591148i | \(0.0188278\pi\) | ||||
−0.998251 | + | 0.0591148i | \(0.981172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0000i | 0.912343i | 0.889892 | + | 0.456172i | \(0.150780\pi\) | ||||
−0.889892 | + | 0.456172i | \(0.849220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.00000i | 0.377964i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.05573 | −0.377883 | −0.188941 | − | 0.981988i | \(-0.560506\pi\) | ||||
−0.188941 | + | 0.981988i | \(0.560506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.52786 | 0.559542 | 0.279771 | − | 0.960067i | \(-0.409742\pi\) | ||||
0.279771 | + | 0.960067i | \(0.409742\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 12.4721i | − 0.921967i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 14.4721i | − 1.06401i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.94427i | 0.361561i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.41641 | −0.681347 | −0.340674 | − | 0.940182i | \(-0.610655\pi\) | ||||
−0.340674 | + | 0.940182i | \(0.610655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4.94427i | − 0.355896i | −0.984040 | − | 0.177948i | \(-0.943054\pi\) | ||||
0.984040 | − | 0.177948i | \(-0.0569460\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.0000 | 0.716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 15.8885i | − 1.13201i | −0.824401 | − | 0.566006i | \(-0.808488\pi\) | ||||
0.824401 | − | 0.566006i | \(-0.191512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5279 | 0.817189 | 0.408594 | − | 0.912716i | \(-0.366019\pi\) | ||||
0.408594 | + | 0.912716i | \(0.366019\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.4721 | −0.738648 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.472136i | − 0.0331374i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.8885 | 1.94782 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000i | 0.278019i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.88854 | 0.680755 | 0.340378 | − | 0.940289i | \(-0.389445\pi\) | ||||
0.340378 | + | 0.940289i | \(0.389445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3.52786i | − 0.241725i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.4721i | 0.986991i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 8.47214i | − 0.575126i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.4721 | −1.11308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.0557 | −0.743689 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.05573i | − 0.204627i | −0.994752 | − | 0.102313i | \(-0.967376\pi\) | ||||
0.994752 | − | 0.102313i | \(-0.0326244\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.8885i | 1.71828i | 0.511738 | + | 0.859142i | \(0.329002\pi\) | ||||
−0.511738 | + | 0.859142i | \(0.670998\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.3607 | −1.21331 | −0.606654 | − | 0.794966i | \(-0.707489\pi\) | ||||
−0.606654 | + | 0.794966i | \(0.707489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9443i | 0.979032i | 0.871994 | + | 0.489516i | \(0.162826\pi\) | ||||
−0.871994 | + | 0.489516i | \(0.837174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.52786i | 0.360598i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.94427i | − 0.580993i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.4721 | 1.58297 | 0.791485 | − | 0.611188i | \(-0.209308\pi\) | ||||
0.791485 | + | 0.611188i | \(0.209308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.8885 | 1.53880 | 0.769398 | − | 0.638769i | \(-0.220556\pi\) | ||||
0.769398 | + | 0.638769i | \(0.220556\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.23607 | 0.142857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94427i | 0.569110i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.9443 | 0.820310 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 8.00000i | − 0.502956i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.52786 | 0.346168 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.41641i | 0.213110i | 0.994307 | + | 0.106555i | \(0.0339820\pi\) | ||||
−0.994307 | + | 0.106555i | \(0.966018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.47214 | −0.402159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.472136 | 0.0292245 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 4.00000i | − 0.246651i | −0.992366 | − | 0.123325i | \(-0.960644\pi\) | ||||
0.992366 | − | 0.123325i | \(-0.0393559\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 4.47214i | − 0.274721i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 9.41641i | − 0.576275i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.3607 | 0.875586 | 0.437793 | − | 0.899076i | \(-0.355760\pi\) | ||||
0.437793 | + | 0.899076i | \(0.355760\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5279 | −0.943251 | −0.471625 | − | 0.881799i | \(-0.656332\pi\) | ||||
−0.471625 | + | 0.881799i | \(0.656332\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 4.47214i | − 0.270666i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0000 | 0.603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.41641i | 0.205272i | 0.994719 | + | 0.102636i | \(0.0327277\pi\) | ||||
−0.994719 | + | 0.102636i | \(0.967272\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.47214 | 0.507214 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.9443 | −0.891501 | −0.445750 | − | 0.895157i | \(-0.647063\pi\) | ||||
−0.445750 | + | 0.895157i | \(0.647063\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.944272i | 0.0561311i | 0.999606 | + | 0.0280656i | \(0.00893472\pi\) | ||||
−0.999606 | + | 0.0280656i | \(0.991065\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 4.47214i | − 0.264906i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 12.4721i | − 0.736207i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8885 | 0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.4721 | 0.731130 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.05573i | 0.412200i | 0.978531 | + | 0.206100i | \(0.0660772\pi\) | ||||
−0.978531 | + | 0.206100i | \(0.933923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.00000i | − 0.116052i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.8885 | 1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.47214 | 0.373048 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4.47214i | − 0.256917i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.8885 | 1.59689 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000i | 1.14146i | 0.821138 | + | 0.570730i | \(0.193340\pi\) | ||||
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.94427 | −0.281270 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0000 | −0.907277 | −0.453638 | − | 0.891186i | \(-0.649874\pi\) | ||||
−0.453638 | + | 0.891186i | \(0.649874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.41641i | 0.0800601i | 0.999198 | + | 0.0400301i | \(0.0127454\pi\) | ||||
−0.999198 | + | 0.0400301i | \(0.987255\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.23607i | 0.125988i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.9443i | 0.614692i | 0.951598 | + | 0.307346i | \(0.0994408\pi\) | ||||
−0.951598 | + | 0.307346i | \(0.900559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.944272 | −0.0528691 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.94427i | 0.275107i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.3607i | 1.24035i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.94427i | 0.162819i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.47214 | 0.136293 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.88854 | 0.103804 | 0.0519019 | − | 0.998652i | \(-0.483472\pi\) | ||||
0.0519019 | + | 0.998652i | \(0.483472\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.47214i | − 0.354671i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 23.4164i | − 1.27938i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.9443i | 1.57669i | 0.615230 | + | 0.788347i | \(0.289063\pi\) | ||||
−0.615230 | + | 0.788347i | \(0.710937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.94427 | 0.159911 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.9443 | −0.917584 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.94427 | −0.481543 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 22.8328i | − 1.22573i | −0.790188 | − | 0.612865i | \(-0.790017\pi\) | ||||
0.790188 | − | 0.612865i | \(-0.209983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.41641 | 0.0758186 | 0.0379093 | − | 0.999281i | \(-0.487930\pi\) | ||||
0.0379093 | + | 0.999281i | \(0.487930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.4721i | 1.40897i | 0.709719 | + | 0.704485i | \(0.248822\pi\) | ||||
−0.709719 | + | 0.704485i | \(0.751178\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.88854 | 0.418680 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2.47214i | − 0.130839i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.4164 | −0.708091 | −0.354045 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354045 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 7.00000i | − 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 36.8328i | − 1.92792i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.88854i | 0.516178i | 0.966121 | + | 0.258089i | \(0.0830927\pi\) | ||||
−0.966121 | + | 0.258089i | \(0.916907\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.4721 | 0.649273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | −0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.3607i | 1.46846i | 0.678901 | + | 0.734230i | \(0.262457\pi\) | ||||
−0.678901 | + | 0.734230i | \(0.737543\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 11.1803i | − 0.577350i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.11146i | − 0.108746i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.8885 | 1.53527 | 0.767636 | − | 0.640886i | \(-0.221433\pi\) | ||||
0.767636 | + | 0.640886i | \(0.221433\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 24.3607i | − 1.24477i | −0.782710 | − | 0.622386i | \(-0.786163\pi\) | ||||
0.782710 | − | 0.622386i | \(-0.213837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 4.47214i | − 0.227921i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.47214i | 0.328997i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.4164 | 1.49147 | 0.745736 | − | 0.666242i | \(-0.232098\pi\) | ||||
0.745736 | + | 0.666242i | \(0.232098\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.88854 | 0.500085 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.8885i | 1.10413i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.0000 | 1.00631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4721i | 0.826713i | 0.910569 | + | 0.413356i | \(0.135644\pi\) | ||||
−0.910569 | + | 0.413356i | \(0.864356\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.00000 | −0.100125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.8885 | 0.993186 | 0.496593 | − | 0.867983i | \(-0.334584\pi\) | ||||
0.496593 | + | 0.867983i | \(0.334584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 37.8885i | − 1.88736i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.23607 | −0.111111 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.9443i | 0.641624i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.8885 | −1.37900 | −0.689500 | − | 0.724286i | \(-0.742170\pi\) | ||||
−0.689500 | + | 0.724286i | \(0.742170\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.8885 | 0.783724 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.9443i | 1.42082i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.9443i | 0.731824i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.00000 | −0.195413 | −0.0977064 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977064 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.94427 | 0.338443 | 0.169222 | − | 0.985578i | \(-0.445875\pi\) | ||||
0.169222 | + | 0.985578i | \(0.445875\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.47214i | 0.120199i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.3607i | 0.599581i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 12.4721i | − 0.603569i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.94427 | −0.431834 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.41641 | −0.260899 | −0.130450 | − | 0.991455i | \(-0.541642\pi\) | ||||
−0.130450 | + | 0.991455i | \(0.541642\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 5.41641i | − 0.260296i | −0.991495 | − | 0.130148i | \(-0.958455\pi\) | ||||
0.991495 | − | 0.130148i | \(-0.0415452\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.05573i | 0.0506183i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.00000i | − 0.382692i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.4721 | 1.93163 | 0.965815 | − | 0.259233i | \(-0.0834697\pi\) | ||||
0.965815 | + | 0.259233i | \(0.0834697\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0557i | 0.905365i | 0.891672 | + | 0.452682i | \(0.149533\pi\) | ||||
−0.891672 | + | 0.452682i | \(0.850467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.0557 | 0.998137 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.52786i | 0.166862i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.9443 | 1.27158 | 0.635789 | − | 0.771863i | \(-0.280675\pi\) | ||||
0.635789 | + | 0.771863i | \(0.280675\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.9443 | −1.17458 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 17.8885i | − 0.840477i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.0000 | 0.468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 8.94427i | − 0.418395i | −0.977873 | − | 0.209198i | \(-0.932915\pi\) | ||||
0.977873 | − | 0.209198i | \(-0.0670852\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.47214 | 0.115389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.52786 | −0.164309 | −0.0821545 | − | 0.996620i | \(-0.526180\pi\) | ||||
−0.0821545 | + | 0.996620i | \(0.526180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 18.8328i | − 0.875235i | −0.899161 | − | 0.437618i | \(-0.855822\pi\) | ||||
0.899161 | − | 0.437618i | \(-0.144178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.9443i | 0.878520i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 36.9443i | − 1.70958i | −0.518976 | − | 0.854789i | \(-0.673687\pi\) | ||||
0.518976 | − | 0.854789i | \(-0.326313\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4721 | −0.483558 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.4164 | −0.802506 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 12.9443i | − 0.595178i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0000 | 0.458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.00000i | − 0.0915737i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0000 | −0.731059 | −0.365529 | − | 0.930800i | \(-0.619112\pi\) | ||||
−0.365529 | + | 0.930800i | \(0.619112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.9443 | −1.31975 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000i | 0.182006i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.8885i | 1.26635i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 21.8885i | − 0.991865i | −0.868361 | − | 0.495932i | \(-0.834826\pi\) | ||||
0.868361 | − | 0.495932i | \(-0.165174\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.41641 | −0.154495 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9443 | −0.854943 | −0.427472 | − | 0.904029i | \(-0.640596\pi\) | ||||
−0.427472 | + | 0.904029i | \(0.640596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.16718i | − 0.0525673i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.47214 | 0.201008 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 3.52786i | − 0.158246i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.8885 | 1.33799 | 0.668997 | − | 0.743265i | \(-0.266724\pi\) | ||||
0.668997 | + | 0.743265i | \(0.266724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.52786 | −0.0682599 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.5836i | 0.561075i | 0.959843 | + | 0.280537i | \(0.0905126\pi\) | ||||
−0.959843 | + | 0.280537i | \(0.909487\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 7.00000i | − 0.310881i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.4164 | 1.65845 | 0.829227 | − | 0.558913i | \(-0.188781\pi\) | ||||
0.829227 | + | 0.558913i | \(0.188781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.4721 | −0.728684 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 2.00000i | − 0.0883022i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 11.0557i | − 0.487174i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4.94427i | − 0.217449i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.4164 | 0.763027 | 0.381513 | − | 0.924363i | \(-0.375403\pi\) | ||||
0.381513 | + | 0.924363i | \(0.375403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.9443i | 1.09074i | 0.838196 | + | 0.545368i | \(0.183610\pi\) | ||||
−0.838196 | + | 0.545368i | \(0.816390\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.00000 | −0.218218 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 20.9443i | − 0.912347i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 55.7771i | − 2.41597i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 5.05573i | − 0.218171i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.05573 | −0.217363 | −0.108681 | − | 0.994077i | \(-0.534663\pi\) | ||||
−0.108681 | + | 0.994077i | \(0.534663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.52786i | 0.323052i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.58359 | −0.282010 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 25.3050i | − 1.08196i | −0.841035 | − | 0.540981i | \(-0.818053\pi\) | ||||
0.841035 | − | 0.540981i | \(-0.181947\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.4721 | 0.532298 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.944272 | −0.0402273 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 8.94427i | − 0.380349i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.4721 | 0.614308 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 22.9443i | − 0.972180i | −0.873909 | − | 0.486090i | \(-0.838423\pi\) | ||||
0.873909 | − | 0.486090i | \(-0.161577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.9443 | 1.22421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.94427 | −0.208747 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.8328i | 0.793709i | 0.917882 | + | 0.396854i | \(0.129898\pi\) | ||||
−0.917882 | + | 0.396854i | \(0.870102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.58359i | 0.276974i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.8885 | 1.92038 | 0.960188 | − | 0.279355i | \(-0.0901206\pi\) | ||||
0.960188 | + | 0.279355i | \(0.0901206\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9.41641i | − 0.393376i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 20.0000i | − 0.834058i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 15.5279i | − 0.646433i | −0.946325 | − | 0.323217i | \(-0.895236\pi\) | ||||
0.946325 | − | 0.323217i | \(-0.104764\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.94427 | 0.205477 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.9443 | 0.537019 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.0000i | 0.413449i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 32.9443i | − 1.35976i | −0.733325 | − | 0.679878i | \(-0.762033\pi\) | ||||
0.733325 | − | 0.679878i | \(-0.237967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.9443 | −0.698177 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.8885 | 0.653567 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.3050i | 1.69619i | 0.529843 | + | 0.848096i | \(0.322251\pi\) | ||||
−0.529843 | + | 0.848096i | \(0.677749\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52786 | 0.226620 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.5279i | 0.471804i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.3607 | −1.07707 | −0.538534 | − | 0.842604i | \(-0.681022\pi\) | ||||
−0.538534 | + | 0.842604i | \(0.681022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 10.4721i | − 0.426458i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.6525 | 0.636364 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9443i | 0.525392i | 0.964879 | + | 0.262696i | \(0.0846116\pi\) | ||||
−0.964879 | + | 0.262696i | \(0.915388\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.472136 | 0.0191319 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0557 | 0.447267 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.4164i | 0.784221i | 0.919918 | + | 0.392111i | \(0.128255\pi\) | ||||
−0.919918 | + | 0.392111i | \(0.871745\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.8885i | 1.12457i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1115i | 0.487589i | 0.969827 | + | 0.243794i | \(0.0783922\pi\) | ||||
−0.969827 | + | 0.243794i | \(0.921608\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.8885 | −0.960162 | −0.480081 | − | 0.877224i | \(-0.659393\pi\) | ||||
−0.480081 | + | 0.877224i | \(0.659393\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 9.41641i | − 0.377260i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.00000i | 0.159745i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.9443 | −1.62997 | −0.814983 | − | 0.579485i | \(-0.803254\pi\) | ||||
−0.814983 | + | 0.579485i | \(0.803254\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.88854i | 0.393034i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 8.94427i | − 0.354943i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.47214i | − 0.177192i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.52786 | 0.139560 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.0000 | −1.65890 | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.9443i | 0.983706i | 0.870678 | + | 0.491853i | \(0.163680\pi\) | ||||
−0.870678 | + | 0.491853i | \(0.836320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.4721 | −0.569840 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.2492i | 1.66099i | 0.557027 | + | 0.830494i | \(0.311942\pi\) | ||||
−0.557027 | + | 0.830494i | \(0.688058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.47214 | 0.332049 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.9443i | 0.741347i | 0.928763 | + | 0.370673i | \(0.120873\pi\) | ||||
−0.928763 | + | 0.370673i | \(0.879127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.9443 | −1.91241 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 16.4721i | − 0.642639i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.8885 | −1.86547 | −0.932736 | − | 0.360559i | \(-0.882586\pi\) | ||||
−0.932736 | + | 0.360559i | \(0.882586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.2492 | −1.25435 | −0.627175 | − | 0.778879i | \(-0.715789\pi\) | ||||
−0.627175 | + | 0.778879i | \(0.715789\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 11.0557i | − 0.429369i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 4.47214i | − 0.173422i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.88854i | 0.0731247i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.05573 | 0.118141 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.9443 | −0.962963 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 13.8885i | − 0.535364i | −0.963507 | − | 0.267682i | \(-0.913742\pi\) | ||||
0.963507 | − | 0.267682i | \(-0.0862577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 5.00000i | − 0.192450i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 37.8885i | − 1.45618i | −0.685484 | − | 0.728088i | \(-0.740409\pi\) | ||||
0.685484 | − | 0.728088i | \(-0.259591\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.4721 | 0.478637 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.8885 | −0.992051 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.8885i | 1.90893i | 0.298320 | + | 0.954466i | \(0.403574\pi\) | ||||
−0.298320 | + | 0.954466i | \(0.596426\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.5279i | 1.35745i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 18.3607i | − 0.700504i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.94427 | −0.340750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.83282 | −0.183849 | −0.0919245 | − | 0.995766i | \(-0.529302\pi\) | ||||
−0.0919245 | + | 0.995766i | \(0.529302\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.00000i | − 0.0759737i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.4164 | −1.26756 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 30.8328i | − 1.16788i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.9443 | −0.565244 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.47214 | 0.319988 | 0.159994 | − | 0.987118i | \(-0.448852\pi\) | ||||
0.159994 | + | 0.987118i | \(0.448852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.9443i | 0.488202i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.52786 | −0.208191 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.47214i | − 0.168192i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.111456 | −0.00418582 | −0.00209291 | − | 0.999998i | \(-0.500666\pi\) | ||||
−0.00209291 | + | 0.999998i | \(0.500666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.94427 | 0.335436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.8885i | 1.26914i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 20.0000i | − 0.747958i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.4721i | 0.913929i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.94427 | −0.333565 | −0.166783 | − | 0.985994i | \(-0.553338\pi\) | ||||
−0.166783 | + | 0.985994i | \(0.553338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.94427 | −0.184134 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.8885i | 0.888425i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.36068 | −0.0876734 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 36.9443i | − 1.37019i | −0.728455 | − | 0.685094i | \(-0.759761\pi\) | ||||
0.728455 | − | 0.685094i | \(-0.240239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0000 | 0.591781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 50.3607i | − 1.86011i | −0.367415 | − | 0.930057i | \(-0.619757\pi\) | ||||
0.367415 | − | 0.930057i | \(-0.380243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.23607i | 0.0824786i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.9443i | 0.771492i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.94427 | −0.328576 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.8328i | 1.86488i | 0.361331 | + | 0.932438i | \(0.382322\pi\) | ||||
−0.361331 | + | 0.932438i | \(0.617678\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.88854 | −0.289014 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.9443i | 0.473606i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.8328 | 0.979143 | 0.489572 | − | 0.871963i | \(-0.337153\pi\) | ||||
0.489572 | + | 0.871963i | \(0.337153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 24.0000i | − 0.874609i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.0000 | 1.45575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.5279i | 0.782444i | 0.920296 | + | 0.391222i | \(0.127947\pi\) | ||||
−0.920296 | + | 0.391222i | \(0.872053\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.5279 | −0.562885 | −0.281442 | − | 0.959578i | \(-0.590813\pi\) | ||||
−0.281442 | + | 0.959578i | \(0.590813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.94427i | 0.106590i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.52786i | 0.199860i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.9443 | −0.683148 | −0.341574 | − | 0.939855i | \(-0.610960\pi\) | ||||
−0.341574 | + | 0.939855i | \(0.610960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.41641 | −0.123039 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.944272i | 0.0339631i | 0.999856 | + | 0.0169815i | \(0.00540566\pi\) | ||||
−0.999856 | + | 0.0169815i | \(0.994594\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.3607 | −1.52164 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 6.47214i | − 0.232187i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.9443 | −0.893721 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.05573 | −0.252474 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.472136i | 0.0168728i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 38.9443i | − 1.38998i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.0000i | 1.28326i | 0.767014 | + | 0.641631i | \(0.221742\pi\) | ||||
−0.767014 | + | 0.641631i | \(0.778258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.00000 | 0.142404 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.94427 | 0.104686 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 55.7771i | − 1.98070i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.47214 | 0.158610 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 28.0000i | − 0.991811i | −0.868377 | − | 0.495905i | \(-0.834836\pi\) | ||||
0.868377 | − | 0.495905i | \(-0.165164\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.11146 | 0.216208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.41641 | 0.332712 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.9443i | 1.16258i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.94427 | −0.315244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.3607i | 0.505520i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.8328 | −1.01371 | −0.506854 | − | 0.862032i | \(-0.669192\pi\) | ||||
−0.506854 | + | 0.862032i | \(0.669192\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.9443 | −1.08660 | −0.543300 | − | 0.839539i | \(-0.682825\pi\) | ||||
−0.543300 | + | 0.839539i | \(0.682825\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 15.5279i | − 0.544586i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 7.63932i | − 0.267594i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 12.9443i | − 0.452863i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.47214 | 0.156269 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.3050 | −1.51135 | −0.755677 | − | 0.654945i | \(-0.772692\pi\) | ||||
−0.755677 | + | 0.654945i | \(0.772692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 32.9443i | − 1.14837i | −0.818727 | − | 0.574183i | \(-0.805320\pi\) | ||||
0.818727 | − | 0.574183i | \(-0.194680\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.0000i | 0.348155i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 56.7214i | 1.97239i | 0.165573 | + | 0.986197i | \(0.447053\pi\) | ||||
−0.165573 | + | 0.986197i | \(0.552947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.4721 | −0.433175 | −0.216588 | − | 0.976263i | \(-0.569493\pi\) | ||||
−0.216588 | + | 0.976263i | \(0.569493\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.41641 | −0.118514 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2.47214i | − 0.0856544i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3.41641i | − 0.118230i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.47214i | 0.292840i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.0557 | 0.519781 | 0.259891 | − | 0.965638i | \(-0.416313\pi\) | ||||
0.259891 | + | 0.965638i | \(0.416313\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7771 | −0.992313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 14.9443i | − 0.514708i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.6525 | 0.538462 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 7.00000i | − 0.240523i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.944272 | −0.0324073 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.8885 | 0.887448 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 40.4721i | − 1.38574i | −0.721063 | − | 0.692870i | \(-0.756346\pi\) | ||||
0.721063 | − | 0.692870i | \(-0.243654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.47214 | 0.152944 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.4164i | 1.48308i | 0.670911 | + | 0.741538i | \(0.265903\pi\) | ||||
−0.670911 | + | 0.741538i | \(0.734097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.9443 | −1.32876 | −0.664381 | − | 0.747394i | \(-0.731305\pi\) | ||||
−0.664381 | + | 0.747394i | \(0.731305\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.4721 | 0.425049 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.8328i | 1.18572i | 0.805305 | + | 0.592861i | \(0.202002\pi\) | ||||
−0.805305 | + | 0.592861i | \(0.797998\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 26.8328i | − 0.912343i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.8885i | 0.369794i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.8885 | −0.606827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.8328 | −1.58687 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.4721i | 0.422118i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 11.1803i | − 0.377964i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.3050i | 0.449276i | 0.974442 | + | 0.224638i | \(0.0721200\pi\) | ||||
−0.974442 | + | 0.224638i | \(0.927880\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.05573 | −0.237984 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.4721 | 1.22878 | 0.614389 | − | 0.789003i | \(-0.289403\pi\) | ||||
0.614389 | + | 0.789003i | \(0.289403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 28.3607i | − 0.954413i | −0.878791 | − | 0.477206i | \(-0.841649\pi\) | ||||
0.878791 | − | 0.477206i | \(-0.158351\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 31.4164i | − 1.05486i | −0.849599 | − | 0.527430i | \(-0.823156\pi\) | ||||
0.849599 | − | 0.527430i | \(-0.176844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.94427i | − 0.165454i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3050 | 0.377883 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.8885i | 0.597281i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00000 | 0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.94427 | −0.164718 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.47214i | 0.215379i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.8328 | −0.559542 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.3607i | 0.941701i | 0.882213 | + | 0.470850i | \(0.156053\pi\) | ||||
−0.882213 | + | 0.470850i | \(0.843947\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.47214 | 0.148331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.41641 | −0.0469277 | −0.0234638 | − | 0.999725i | \(-0.507469\pi\) | ||||
−0.0234638 | + | 0.999725i | \(0.507469\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 25.8885i | − 0.856786i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.8885i | 0.921967i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.8885i | 0.722823i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.7214 | 1.73912 | 0.869559 | − | 0.493830i | \(-0.164403\pi\) | ||||
0.869559 | + | 0.493830i | \(0.164403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | −0.659022 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 15.7771i | − 0.519309i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.3607i | 1.06401i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 4.94427i | − 0.162391i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.3050 | 1.42079 | 0.710395 | − | 0.703804i | \(-0.248516\pi\) | ||||
0.710395 | + | 0.703804i | \(0.248516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.00000 | −0.0655474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 16.0000i | − 0.523816i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 11.0557i | − 0.361561i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 47.3050i | − 1.54539i | −0.634780 | − | 0.772693i | \(-0.718909\pi\) | ||||
0.634780 | − | 0.772693i | \(-0.281091\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.41641 | −0.0462227 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.4721 | 1.44975 | 0.724875 | − | 0.688880i | \(-0.241897\pi\) | ||||
0.724875 | + | 0.688880i | \(0.241897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.8885i | 1.62459i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.23607 | −0.0727393 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 16.0000i | − 0.519930i | −0.965618 | − | 0.259965i | \(-0.916289\pi\) | ||||
0.965618 | − | 0.259965i | \(-0.0837111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −73.6656 | −2.39129 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.9443 | −0.354892 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000i | 0.583077i | 0.956559 | + | 0.291539i | \(0.0941672\pi\) | ||||
−0.956559 | + | 0.291539i | \(0.905833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.0557 | 0.681347 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 0.944272i | − 0.0305240i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.8885 | 0.513068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.7771 | 1.31539 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0557i | 0.355896i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 9.88854i | − 0.317994i | −0.987279 | − | 0.158997i | \(-0.949174\pi\) | ||||
0.987279 | − | 0.158997i | \(-0.0508260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.94427 | −0.158833 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.88854 | −0.0606063 | −0.0303031 | − | 0.999541i | \(-0.509647\pi\) | ||||
−0.0303031 | + | 0.999541i | \(0.509647\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.9443i | 0.479091i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.3607 | −0.716115 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 0.832816i | − 0.0266441i | −0.999911 | − | 0.0133221i | \(-0.995759\pi\) | ||||
0.999911 | − | 0.0133221i | \(-0.00424067\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.8328 | −0.601899 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.94427 | −0.0940034 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.4721i | 1.09949i | 0.835332 | + | 0.549745i | \(0.185275\pi\) | ||||
−0.835332 | + | 0.549745i | \(0.814725\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.5279i | 1.13201i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.47214i | 0.0786890i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.8885 | −0.823208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.0557 | 1.24065 | 0.620323 | − | 0.784346i | \(-0.287002\pi\) | ||||
0.620323 | + | 0.784346i | \(0.287002\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.88854i | 0.0599311i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.7771 | −0.817189 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.3607i | 1.59494i | 0.603359 | + | 0.797469i | \(0.293828\pi\) | ||||
−0.603359 | + | 0.797469i | \(0.706172\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.47214 | 0.204769 |
(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 | 1680.2.t.h.1009.3 | 4 | ||
3.2 | odd | 2 | 5040.2.t.u.1009.4 | 4 | |||
4.3 | odd | 2 | 840.2.t.c.169.1 | ✓ | 4 | ||
5.2 | odd | 4 | 8400.2.a.db.1.2 | 2 | |||
5.3 | odd | 4 | 8400.2.a.cz.1.1 | 2 | |||
5.4 | even | 2 | inner | 1680.2.t.h.1009.1 | 4 | ||
12.11 | even | 2 | 2520.2.t.f.1009.3 | 4 | |||
15.14 | odd | 2 | 5040.2.t.u.1009.3 | 4 | |||
20.3 | even | 4 | 4200.2.a.bk.1.1 | 2 | |||
20.7 | even | 4 | 4200.2.a.bj.1.2 | 2 | |||
20.19 | odd | 2 | 840.2.t.c.169.3 | yes | 4 | ||
60.59 | even | 2 | 2520.2.t.f.1009.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.c.169.1 | ✓ | 4 | 4.3 | odd | 2 | ||
840.2.t.c.169.3 | yes | 4 | 20.19 | odd | 2 | ||
1680.2.t.h.1009.1 | 4 | 5.4 | even | 2 | inner | ||
1680.2.t.h.1009.3 | 4 | 1.1 | even | 1 | trivial | ||
2520.2.t.f.1009.3 | 4 | 12.11 | even | 2 | |||
2520.2.t.f.1009.4 | 4 | 60.59 | even | 2 | |||
4200.2.a.bj.1.2 | 2 | 20.7 | even | 4 | |||
4200.2.a.bk.1.1 | 2 | 20.3 | even | 4 | |||
5040.2.t.u.1009.3 | 4 | 15.14 | odd | 2 | |||
5040.2.t.u.1009.4 | 4 | 3.2 | odd | 2 | |||
8400.2.a.cz.1.1 | 2 | 5.3 | odd | 4 | |||
8400.2.a.db.1.2 | 2 | 5.2 | odd | 4 |