Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(737,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 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("4140.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.s (of order \(4\), degree \(2\), 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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.17 | ||
Character | \(\chi\) | \(=\) | 4140.737 |
Dual form | 4140.2.s.b.2393.17 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.52812 | + | 1.63243i | 0.683398 | + | 0.730046i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.30479 | − | 2.30479i | −0.871130 | − | 0.871130i | 0.121465 | − | 0.992596i | \(-0.461241\pi\) |
−0.992596 | + | 0.121465i | \(0.961241\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.32736i | − | 1.00324i | −0.865089 | − | 0.501618i | \(-0.832738\pi\) | ||
0.865089 | − | 0.501618i | \(-0.167262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.34641 | + | 3.34641i | −0.928128 | + | 0.928128i | −0.997585 | − | 0.0694574i | \(-0.977873\pi\) |
0.0694574 | + | 0.997585i | \(0.477873\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.668244 | − | 0.668244i | 0.162073 | − | 0.162073i | −0.621411 | − | 0.783484i | \(-0.713440\pi\) |
0.783484 | + | 0.621411i | \(0.213440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.73320i | − | 0.397624i | −0.980038 | − | 0.198812i | \(-0.936292\pi\) | ||
0.980038 | − | 0.198812i | \(-0.0637083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.329672 | + | 4.98912i | −0.0659343 | + | 0.997824i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.39260 | −0.815686 | −0.407843 | − | 0.913052i | \(-0.633719\pi\) | ||||
−0.407843 | + | 0.913052i | \(0.633719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.04377 | 0.367072 | 0.183536 | − | 0.983013i | \(-0.441246\pi\) | ||||
0.183536 | + | 0.983013i | \(0.441246\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.240409 | − | 7.28443i | 0.0406365 | − | 1.23129i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.47227 | + | 4.47227i | 0.735237 | + | 0.735237i | 0.971652 | − | 0.236415i | \(-0.0759725\pi\) |
−0.236415 | + | 0.971652i | \(0.575972\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.40057i | 1.15578i | 0.816116 | + | 0.577888i | \(0.196123\pi\) | ||||
−0.816116 | + | 0.577888i | \(0.803877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.11206 | + | 5.11206i | −0.779581 | + | 0.779581i | −0.979760 | − | 0.200178i | \(-0.935848\pi\) |
0.200178 | + | 0.979760i | \(0.435848\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.48003 | − | 1.48003i | 0.215884 | − | 0.215884i | −0.590877 | − | 0.806761i | \(-0.701218\pi\) |
0.806761 | + | 0.590877i | \(0.201218\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.62415i | 0.517736i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.98341 | + | 3.98341i | 0.547163 | + | 0.547163i | 0.925619 | − | 0.378456i | \(-0.123545\pi\) |
−0.378456 | + | 0.925619i | \(0.623545\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.43168 | − | 5.08461i | 0.732408 | − | 0.685609i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.36490 | 0.177695 | 0.0888473 | − | 0.996045i | \(-0.471682\pi\) | ||||
0.0888473 | + | 0.996045i | \(0.471682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.91418 | 0.501159 | 0.250580 | − | 0.968096i | \(-0.419379\pi\) | ||||
0.250580 | + | 0.968096i | \(0.419379\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.5765 | − | 0.349058i | −1.31186 | − | 0.0432953i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6961 | + | 10.6961i | 1.30673 | + | 1.30673i | 0.923760 | + | 0.382972i | \(0.125099\pi\) |
0.382972 | + | 0.923760i | \(0.374901\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3416i | 1.22732i | 0.789571 | + | 0.613660i | \(0.210303\pi\) | ||||
−0.789571 | + | 0.613660i | \(0.789697\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.13556 | + | 2.13556i | −0.249948 | + | 0.249948i | −0.820949 | − | 0.571001i | \(-0.806555\pi\) |
0.571001 | + | 0.820949i | \(0.306555\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.66887 | + | 7.66887i | −0.873949 | + | 0.873949i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.87969i | − | 0.999044i | −0.866301 | − | 0.499522i | \(-0.833509\pi\) | ||
0.866301 | − | 0.499522i | \(-0.166491\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.21101 | − | 2.21101i | −0.242690 | − | 0.242690i | 0.575272 | − | 0.817962i | \(-0.304896\pi\) |
−0.817962 | + | 0.575272i | \(0.804896\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.11202 | + | 0.0697032i | 0.229081 | + | 0.00756038i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.17165 | −0.230194 | −0.115097 | − | 0.993354i | \(-0.536718\pi\) | ||||
−0.115097 | + | 0.993354i | \(0.536718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.4256 | 1.61704 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.82934 | − | 2.64855i | 0.290284 | − | 0.271736i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.81888 | + | 9.81888i | 0.996956 | + | 0.996956i | 0.999995 | − | 0.00303933i | \(-0.000967451\pi\) |
−0.00303933 | + | 0.999995i | \(0.500967\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.82234i | 0.479841i | 0.970793 | + | 0.239920i | \(0.0771213\pi\) | ||||
−0.970793 | + | 0.239920i | \(0.922879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.43010 | + | 3.43010i | −0.337978 | + | 0.337978i | −0.855606 | − | 0.517628i | \(-0.826815\pi\) |
0.517628 | + | 0.855606i | \(0.326815\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.14994 | + | 5.14994i | −0.497864 | + | 0.497864i | −0.910772 | − | 0.412909i | \(-0.864513\pi\) |
0.412909 | + | 0.910772i | \(0.364513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.69664i | − | 0.449856i | −0.974375 | − | 0.224928i | \(-0.927785\pi\) | ||
0.974375 | − | 0.224928i | \(-0.0722147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.4656 | + | 10.4656i | 0.984525 | + | 0.984525i | 0.999882 | − | 0.0153569i | \(-0.00488843\pi\) |
−0.0153569 | + | 0.999882i | \(0.504888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0737570 | + | 2.23485i | −0.00687787 | + | 0.208401i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.08033 | −0.282373 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0712980 | −0.00648164 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.64818 | + | 7.08583i | −0.773517 | + | 0.633776i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.50076 | + | 4.50076i | 0.399378 | + | 0.399378i | 0.878014 | − | 0.478636i | \(-0.158869\pi\) |
−0.478636 | + | 0.878014i | \(0.658869\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.33197i | 0.640597i | 0.947317 | + | 0.320299i | \(0.103783\pi\) | ||||
−0.947317 | + | 0.320299i | \(0.896217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.99468 | + | 3.99468i | −0.346382 | + | 0.346382i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.943223 | + | 0.943223i | −0.0805850 | + | 0.0805850i | −0.746250 | − | 0.665665i | \(-0.768148\pi\) |
0.665665 | + | 0.746250i | \(0.268148\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.8696i | − | 0.921948i | −0.887414 | − | 0.460974i | \(-0.847500\pi\) | ||
0.887414 | − | 0.460974i | \(-0.152500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.1347 | + | 11.1347i | 0.931131 | + | 0.931131i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.71245 | − | 7.17063i | −0.557438 | − | 0.595488i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.38387 | −0.522987 | −0.261494 | − | 0.965205i | \(-0.584215\pi\) | ||||
−0.261494 | + | 0.965205i | \(0.584215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.15277 | −0.337948 | −0.168974 | − | 0.985621i | \(-0.554045\pi\) | ||||
−0.168974 | + | 0.985621i | \(0.554045\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.12314 | + | 3.33632i | 0.250857 | + | 0.267980i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.94797 | + | 6.94797i | 0.554509 | + | 0.554509i | 0.927739 | − | 0.373230i | \(-0.121750\pi\) |
−0.373230 | + | 0.927739i | \(0.621750\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.25947i | − | 0.256882i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.0078 | − | 13.0078i | 1.01885 | − | 1.01885i | 0.0190341 | − | 0.999819i | \(-0.493941\pi\) |
0.999819 | − | 0.0190341i | \(-0.00605912\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.40719 | + | 5.40719i | −0.418421 | + | 0.418421i | −0.884659 | − | 0.466238i | \(-0.845609\pi\) |
0.466238 | + | 0.884659i | \(0.345609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.39694i | − | 0.722841i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.48767 | − | 7.48767i | −0.569277 | − | 0.569277i | 0.362649 | − | 0.931926i | \(-0.381872\pi\) |
−0.931926 | + | 0.362649i | \(0.881872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2587 | − | 10.7391i | 0.926672 | − | 0.811797i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.99794 | −0.523051 | −0.261525 | − | 0.965197i | \(-0.584226\pi\) | ||||
−0.261525 | + | 0.965197i | \(0.584226\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.8405 | −0.954426 | −0.477213 | − | 0.878788i | \(-0.658353\pi\) | ||||
−0.477213 | + | 0.878788i | \(0.658353\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.466494 | + | 14.1349i | −0.0342973 | + | 1.03922i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.22349 | − | 2.22349i | −0.162597 | − | 0.162597i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6720i | 1.56813i | 0.620678 | + | 0.784066i | \(0.286857\pi\) | ||||
−0.620678 | + | 0.784066i | \(0.713143\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.21213 | − | 1.21213i | 0.0872509 | − | 0.0872509i | −0.662134 | − | 0.749385i | \(-0.730349\pi\) |
0.749385 | + | 0.662134i | \(0.230349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.8261 | + | 15.8261i | −1.12756 | + | 1.12756i | −0.136990 | + | 0.990572i | \(0.543743\pi\) |
−0.990572 | + | 0.136990i | \(0.956257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17.0772i | − | 1.21057i | −0.796010 | − | 0.605284i | \(-0.793060\pi\) | ||
0.796010 | − | 0.605284i | \(-0.206940\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.1240 | + | 10.1240i | 0.710569 | + | 0.710569i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0809 | + | 11.3090i | −0.843769 | + | 0.789854i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.76698 | −0.398911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.4031 | 1.33576 | 0.667881 | − | 0.744268i | \(-0.267201\pi\) | ||||
0.667881 | + | 0.744268i | \(0.267201\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.1569 | − | 0.533229i | −1.10189 | − | 0.0363659i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.71048 | − | 4.71048i | −0.319768 | − | 0.319768i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.47244i | 0.300849i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.624745 | + | 0.624745i | −0.0418360 | + | 0.0418360i | −0.727715 | − | 0.685879i | \(-0.759418\pi\) |
0.685879 | + | 0.727715i | \(0.259418\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9001 | − | 12.9001i | 0.856209 | − | 0.856209i | −0.134680 | − | 0.990889i | \(-0.543001\pi\) |
0.990889 | + | 0.134680i | \(0.0430007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.6374i | 1.09943i | 0.835353 | + | 0.549714i | \(0.185263\pi\) | ||||
−0.835353 | + | 0.549714i | \(0.814737\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.3269 | − | 10.3269i | −0.676536 | − | 0.676536i | 0.282679 | − | 0.959215i | \(-0.408777\pi\) |
−0.959215 | + | 0.282679i | \(0.908777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.67771 | + | 0.154379i | 0.305140 | + | 0.0100706i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3787 | −1.12414 | −0.562068 | − | 0.827091i | \(-0.689994\pi\) | ||||
−0.562068 | + | 0.827091i | \(0.689994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.6714 | −1.39598 | −0.697990 | − | 0.716108i | \(-0.745922\pi\) | ||||
−0.697990 | + | 0.716108i | \(0.745922\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.91618 | + | 5.53815i | −0.377971 | + | 0.353820i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.80001 | + | 5.80001i | 0.369046 | + | 0.369046i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4963i | 0.725642i | 0.931859 | + | 0.362821i | \(0.118186\pi\) | ||||
−0.931859 | + | 0.362821i | \(0.881814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.35280 | − | 2.35280i | 0.147919 | − | 0.147919i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.2208 | − | 10.2208i | 0.637557 | − | 0.637557i | −0.312395 | − | 0.949952i | \(-0.601131\pi\) |
0.949952 | + | 0.312395i | \(0.101131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 20.6153i | − | 1.28097i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.174750 | + | 0.174750i | 0.0107756 | + | 0.0107756i | 0.712474 | − | 0.701698i | \(-0.247575\pi\) |
−0.701698 | + | 0.712474i | \(0.747575\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.415501 | + | 12.5898i | −0.0255241 | + | 0.773384i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.7405 | −0.898742 | −0.449371 | − | 0.893345i | \(-0.648352\pi\) | ||||
−0.449371 | + | 0.893345i | \(0.648352\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2858 | 0.624821 | 0.312410 | − | 0.949947i | \(-0.398864\pi\) | ||||
0.312410 | + | 0.949947i | \(0.398864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.6006 | + | 1.09694i | 1.00105 | + | 0.0661477i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.7038 | + | 10.7038i | 0.643128 | + | 0.643128i | 0.951323 | − | 0.308195i | \(-0.0997249\pi\) |
−0.308195 | + | 0.951323i | \(0.599725\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 33.1367i | − | 1.97677i | −0.151971 | − | 0.988385i | \(-0.548562\pi\) | ||
0.151971 | − | 0.988385i | \(-0.451438\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.3141 | + | 16.3141i | −0.969771 | + | 0.969771i | −0.999556 | − | 0.0297850i | \(-0.990518\pi\) |
0.0297850 | + | 0.999556i | \(0.490518\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.0568 | − | 17.0568i | 1.00683 | − | 1.00683i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1069i | 0.947465i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.68206 | − | 2.68206i | −0.156688 | − | 0.156688i | 0.624410 | − | 0.781097i | \(-0.285340\pi\) |
−0.781097 | + | 0.624410i | \(0.785340\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.08573 | + | 2.22810i | 0.121436 | + | 0.129725i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.73254 | −0.273690 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.5645 | 1.35823 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.98135 | + | 6.38963i | 0.342491 | + | 0.365869i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.34372 | + | 5.34372i | 0.304982 | + | 0.304982i | 0.842959 | − | 0.537977i | \(-0.180811\pi\) |
−0.537977 | + | 0.842959i | \(0.680811\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.73509i | 0.325207i | 0.986691 | + | 0.162604i | \(0.0519892\pi\) | ||||
−0.986691 | + | 0.162604i | \(0.948011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3170 | − | 13.3170i | 0.752721 | − | 0.752721i | −0.222265 | − | 0.974986i | \(-0.571345\pi\) |
0.974986 | + | 0.222265i | \(0.0713450\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.1119 | + | 14.1119i | −0.792602 | + | 0.792602i | −0.981917 | − | 0.189314i | \(-0.939373\pi\) |
0.189314 | + | 0.981917i | \(0.439373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.6158i | 0.818325i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.15820 | − | 1.15820i | −0.0644441 | − | 0.0644441i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.5924 | − | 17.7989i | −0.864912 | − | 0.987303i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.82231 | −0.376126 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.6832 | −1.19182 | −0.595909 | − | 0.803052i | \(-0.703208\pi\) | ||||
−0.595909 | + | 0.803052i | \(0.703208\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.11569 | + | 33.8055i | −0.0609564 | + | 1.84699i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.6800 | + | 16.6800i | 0.908619 | + | 0.908619i | 0.996161 | − | 0.0875421i | \(-0.0279012\pi\) |
−0.0875421 | + | 0.996161i | \(0.527901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.80036i | − | 0.368260i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.78064 | + | 7.78064i | −0.420115 | + | 0.420115i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.3065 | + | 11.3065i | −0.606967 | + | 0.606967i | −0.942152 | − | 0.335185i | \(-0.891201\pi\) |
0.335185 | + | 0.942152i | \(0.391201\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.3389i | 0.606958i | 0.952838 | + | 0.303479i | \(0.0981482\pi\) | ||||
−0.952838 | + | 0.303479i | \(0.901852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7921 | − | 13.7921i | −0.734082 | − | 0.734082i | 0.237344 | − | 0.971426i | \(-0.423723\pi\) |
−0.971426 | + | 0.237344i | \(0.923723\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.8819 | + | 15.8032i | −0.896000 | + | 0.838748i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.8705 | −1.52373 | −0.761863 | − | 0.647738i | \(-0.775715\pi\) | ||||
−0.761863 | + | 0.647738i | \(0.775715\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9960 | 0.841895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.74955 | − | 0.222756i | −0.353288 | − | 0.0116596i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.8404 | + | 22.8404i | 1.19226 | + | 1.19226i | 0.976432 | + | 0.215825i | \(0.0692442\pi\) |
0.215825 | + | 0.976432i | \(0.430756\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 18.3619i | − | 0.953300i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.25000 | + | 2.25000i | −0.116501 | + | 0.116501i | −0.762954 | − | 0.646453i | \(-0.776252\pi\) |
0.646453 | + | 0.762954i | \(0.276252\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6995 | − | 14.6995i | 0.757061 | − | 0.757061i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.64580i | 0.341372i | 0.985325 | + | 0.170686i | \(0.0545984\pi\) | ||||
−0.985325 | + | 0.170686i | \(0.945402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.1236 | + | 12.1236i | 0.619486 | + | 0.619486i | 0.945400 | − | 0.325914i | \(-0.105672\pi\) |
−0.325914 | + | 0.945400i | \(0.605672\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.2379 | − | 0.799925i | −1.23528 | − | 0.0407680i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.47535 | 0.0748033 | 0.0374017 | − | 0.999300i | \(-0.488092\pi\) | ||||
0.0374017 | + | 0.999300i | \(0.488092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.945040 | 0.0477927 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.4955 | − | 13.5693i | 0.729348 | − | 0.682744i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.4685 | − | 18.4685i | −0.926910 | − | 0.926910i | 0.0705954 | − | 0.997505i | \(-0.477510\pi\) |
−0.997505 | + | 0.0705954i | \(0.977510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 25.3860i | − | 1.26772i | −0.773448 | − | 0.633859i | \(-0.781470\pi\) | ||
0.773448 | − | 0.633859i | \(-0.218530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.83931 | + | 6.83931i | −0.340690 | + | 0.340690i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.8808 | − | 14.8808i | 0.737616 | − | 0.737616i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.4786i | 1.25983i | 0.776662 | + | 0.629917i | \(0.216911\pi\) | ||||
−0.776662 | + | 0.629917i | \(0.783089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.14581 | − | 3.14581i | −0.154795 | − | 0.154795i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.230626 | − | 6.98802i | 0.0113210 | − | 0.343028i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.6109 | 0.811497 | 0.405748 | − | 0.913985i | \(-0.367011\pi\) | ||||
0.405748 | + | 0.913985i | \(0.367011\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.0022 | 1.41348 | 0.706742 | − | 0.707472i | \(-0.250164\pi\) | ||||
0.706742 | + | 0.707472i | \(0.250164\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.11365 | + | 3.55425i | 0.151034 | + | 0.172406i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.02138 | − | 9.02138i | −0.436575 | − | 0.436575i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.1768i | 1.30906i | 0.756036 | + | 0.654530i | \(0.227133\pi\) | ||||
−0.756036 | + | 0.654530i | \(0.772867\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.9196 | − | 21.9196i | 1.05339 | − | 1.05339i | 0.0548950 | − | 0.998492i | \(-0.482518\pi\) |
0.998492 | − | 0.0548950i | \(-0.0174824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.22556 | − | 1.22556i | 0.0586265 | − | 0.0586265i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.35097i | 0.159933i | 0.996798 | + | 0.0799665i | \(0.0254813\pi\) | ||||
−0.996798 | + | 0.0799665i | \(0.974519\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0480 | − | 10.0480i | −0.477397 | − | 0.477397i | 0.426901 | − | 0.904298i | \(-0.359605\pi\) |
−0.904298 | + | 0.426901i | \(0.859605\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.31855 | − | 3.54507i | −0.157314 | − | 0.168052i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.2261 | 1.14330 | 0.571651 | − | 0.820497i | \(-0.306303\pi\) | ||||
0.571651 | + | 0.820497i | \(0.306303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.6243 | 1.15951 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.5722 | + | 25.1812i | 1.10508 | + | 1.18051i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.91796 | + | 8.91796i | 0.417164 | + | 0.417164i | 0.884225 | − | 0.467061i | \(-0.154687\pi\) |
−0.467061 | + | 0.884225i | \(0.654687\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.48346i | − | 0.208816i | −0.994535 | − | 0.104408i | \(-0.966705\pi\) | ||
0.994535 | − | 0.104408i | \(-0.0332947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.9675 | − | 14.9675i | 0.695598 | − | 0.695598i | −0.267860 | − | 0.963458i | \(-0.586316\pi\) |
0.963458 | + | 0.267860i | \(0.0863163\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.50750 | − | 6.50750i | 0.301131 | − | 0.301131i | −0.540325 | − | 0.841456i | \(-0.681699\pi\) |
0.841456 | + | 0.540325i | \(0.181699\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 49.3044i | − | 2.27667i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.0096 | + | 17.0096i | 0.782104 | + | 0.782104i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.64716 | + | 0.571388i | 0.396759 | + | 0.0262171i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.6866 | 1.26503 | 0.632516 | − | 0.774548i | \(-0.282022\pi\) | ||||
0.632516 | + | 0.774548i | \(0.282022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.9321 | −1.36479 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.02419 | + | 31.0331i | −0.0465060 | + | 1.40914i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.45385 | + | 6.45385i | 0.292452 | + | 0.292452i | 0.838048 | − | 0.545596i | \(-0.183697\pi\) |
−0.545596 | + | 0.838048i | \(0.683697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 40.6025i | − | 1.83237i | −0.400759 | − | 0.916183i | \(-0.631254\pi\) | ||
0.400759 | − | 0.916183i | \(-0.368746\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.93533 | + | 2.93533i | −0.132201 | + | 0.132201i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.8352 | − | 23.8352i | 1.06916 | − | 1.06916i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.65115i | − | 0.163448i | −0.996655 | − | 0.0817239i | \(-0.973957\pi\) | ||
0.996655 | − | 0.0817239i | \(-0.0260426\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.5058 | + | 28.5058i | 1.27101 | + | 1.27101i | 0.945559 | + | 0.325450i | \(0.105516\pi\) |
0.325450 | + | 0.945559i | \(0.394484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.87214 | + | 7.36913i | −0.350306 | + | 0.327922i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.9364 | −1.45988 | −0.729940 | − | 0.683511i | \(-0.760452\pi\) | ||||
−0.729940 | + | 0.683511i | \(0.760452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.84404 | 0.435475 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.8410 | − | 0.357787i | −0.477713 | − | 0.0157660i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.92458 | − | 4.92458i | −0.216583 | − | 0.216583i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.2827i | 0.669549i | 0.942298 | + | 0.334775i | \(0.108660\pi\) | ||||
−0.942298 | + | 0.334775i | \(0.891340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.2400 | + | 13.2400i | −0.578946 | + | 0.578946i | −0.934613 | − | 0.355667i | \(-0.884254\pi\) |
0.355667 | + | 0.934613i | \(0.384254\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.36574 | − | 1.36574i | 0.0594925 | − | 0.0594925i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.7654 | − | 24.7654i | −1.07271 | − | 1.07271i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.2767 | − | 0.537181i | −0.703703 | − | 0.0232244i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0588 | 0.519411 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7418 | 0.805772 | 0.402886 | − | 0.915250i | \(-0.368007\pi\) | ||||
0.402886 | + | 0.915250i | \(0.368007\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.66694 | − | 7.17705i | 0.328416 | − | 0.307431i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.35624 | − | 6.35624i | −0.271773 | − | 0.271773i | 0.558040 | − | 0.829814i | \(-0.311553\pi\) |
−0.829814 | + | 0.558040i | \(0.811553\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.61328i | 0.324336i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.4659 | + | 20.4659i | −0.870297 | + | 0.870297i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.88154 | − | 1.88154i | 0.0797233 | − | 0.0797233i | −0.666121 | − | 0.745844i | \(-0.732046\pi\) |
0.745844 | + | 0.666121i | \(0.232046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.2141i | − | 1.44710i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.64046 | + | 3.64046i | 0.153427 | + | 0.153427i | 0.779647 | − | 0.626220i | \(-0.215399\pi\) |
−0.626220 | + | 0.779647i | \(0.715399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.09165 | + | 33.0773i | −0.0459261 | + | 1.39157i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.6487 | 0.781793 | 0.390897 | − | 0.920435i | \(-0.372165\pi\) | ||||
0.390897 | + | 0.920435i | \(0.372165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.07667 | −0.337998 | −0.168999 | − | 0.985616i | \(-0.554053\pi\) | ||||
−0.168999 | + | 0.985616i | \(0.554053\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.76095 | + | 3.29473i | −0.156843 | + | 0.137400i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.11139 | − | 8.11139i | −0.337682 | − | 0.337682i | 0.517813 | − | 0.855494i | \(-0.326746\pi\) |
−0.855494 | + | 0.517813i | \(0.826746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.1918i | 0.422829i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.2542 | − | 13.2542i | 0.548933 | − | 0.548933i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.1304 | + | 15.1304i | −0.624499 | + | 0.624499i | −0.946679 | − | 0.322180i | \(-0.895585\pi\) |
0.322180 | + | 0.946679i | \(0.395585\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.54227i | − | 0.145957i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.6097 | + | 13.6097i | 0.558883 | + | 0.558883i | 0.928989 | − | 0.370106i | \(-0.120679\pi\) |
−0.370106 | + | 0.928989i | \(0.620679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.70713 | − | 5.02843i | −0.192973 | − | 0.206145i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.2874 | −0.869780 | −0.434890 | − | 0.900484i | \(-0.643213\pi\) | ||||
−0.434890 | + | 0.900484i | \(0.643213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.3467 | 1.27866 | 0.639329 | − | 0.768933i | \(-0.279212\pi\) | ||||
0.639329 | + | 0.768933i | \(0.279212\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.108952 | − | 0.116389i | −0.00442954 | − | 0.00473190i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.66528 | − | 6.66528i | −0.270535 | − | 0.270535i | 0.558780 | − | 0.829316i | \(-0.311269\pi\) |
−0.829316 | + | 0.558780i | \(0.811269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.90556i | 0.400736i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.392499 | + | 0.392499i | −0.0158529 | + | 0.0158529i | −0.714989 | − | 0.699136i | \(-0.753568\pi\) |
0.699136 | + | 0.714989i | \(0.253568\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.2561 | + | 18.2561i | −0.734964 | + | 0.734964i | −0.971599 | − | 0.236635i | \(-0.923956\pi\) |
0.236635 | + | 0.971599i | \(0.423956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.8938i | 0.598631i | 0.954154 | + | 0.299316i | \(0.0967584\pi\) | ||||
−0.954154 | + | 0.299316i | \(0.903242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.00520 | + | 5.00520i | 0.200529 | + | 0.200529i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7826 | − | 3.28954i | −0.991305 | − | 0.131582i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.97714 | 0.238324 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.5944 | −1.13833 | −0.569163 | − | 0.822225i | \(-0.692733\pi\) | ||||
−0.569163 | + | 0.822225i | \(0.692733\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.469466 | + | 14.2249i | −0.0186302 | + | 0.564498i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.1279 | − | 12.1279i | −0.480525 | − | 0.480525i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 24.3383i | − | 0.961304i | −0.876911 | − | 0.480652i | \(-0.840400\pi\) | ||
0.876911 | − | 0.480652i | \(-0.159600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.5022 | − | 13.5022i | 0.532474 | − | 0.532474i | −0.388834 | − | 0.921308i | \(-0.627122\pi\) |
0.921308 | + | 0.388834i | \(0.127122\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.7471 | − | 10.7471i | 0.422511 | − | 0.422511i | −0.463557 | − | 0.886067i | \(-0.653427\pi\) |
0.886067 | + | 0.463557i | \(0.153427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.54150i | − | 0.178269i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.0250 | − | 14.0250i | −0.548840 | − | 0.548840i | 0.377265 | − | 0.926105i | \(-0.376864\pi\) |
−0.926105 | + | 0.377265i | \(0.876864\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.9689 | + | 11.2042i | −0.467665 | + | 0.437783i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.4088 | −1.65201 | −0.826006 | − | 0.563661i | \(-0.809393\pi\) | ||||
−0.826006 | + | 0.563661i | \(0.809393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.734309 | −0.0285613 | −0.0142806 | − | 0.999898i | \(-0.504546\pi\) | ||||
−0.0142806 | + | 0.999898i | \(0.504546\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.6254 | − | 0.416677i | −0.489592 | − | 0.0161580i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.10604 | − | 3.10604i | −0.120266 | − | 0.120266i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 13.0239i | − | 0.502781i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1053 | + | 16.1053i | −0.620816 | + | 0.620816i | −0.945740 | − | 0.324924i | \(-0.894661\pi\) |
0.324924 | + | 0.945740i | \(0.394661\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.09950 | + | 9.09950i | −0.349722 | + | 0.349722i | −0.860006 | − | 0.510284i | \(-0.829540\pi\) |
0.510284 | + | 0.860006i | \(0.329540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 45.2610i | − | 1.73696i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.71416 | + | 3.71416i | 0.142118 | + | 0.142118i | 0.774586 | − | 0.632468i | \(-0.217958\pi\) |
−0.632468 | + | 0.774586i | \(0.717958\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.98111 | − | 0.0983858i | −0.113902 | − | 0.00375913i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.6602 | −1.01567 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.44413 | −0.169063 | −0.0845313 | − | 0.996421i | \(-0.526939\pi\) | ||||
−0.0845313 | + | 0.996421i | \(0.526939\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.7439 | − | 16.6101i | 0.673065 | − | 0.630058i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.94539 | + | 4.94539i | 0.187320 | + | 0.187320i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 50.9289i | − | 1.92356i | −0.273824 | − | 0.961780i | \(-0.588289\pi\) | ||
0.273824 | − | 0.961780i | \(-0.411711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.75136 | − | 7.75136i | 0.292348 | − | 0.292348i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.1145 | − | 11.1145i | 0.418004 | − | 0.418004i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 39.9766i | − | 1.50135i | −0.660670 | − | 0.750677i | \(-0.729728\pi\) | ||
0.660670 | − | 0.750677i | \(-0.270272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.44517 | + | 1.44517i | 0.0541219 | + | 0.0541219i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.16144 | + | 35.1919i | −0.0434354 | + | 1.31610i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.9771 | −1.19255 | −0.596273 | − | 0.802782i | \(-0.703352\pi\) | ||||
−0.596273 | + | 0.802782i | \(0.703352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.8114 | 0.588846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.44812 | − | 21.9152i | 0.0537817 | − | 0.813911i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.30489 | + | 7.30489i | 0.270923 | + | 0.270923i | 0.829472 | − | 0.558549i | \(-0.188642\pi\) |
−0.558549 | + | 0.829472i | \(0.688642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.83220i | 0.252698i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.4176 | + | 31.4176i | −1.16044 | + | 1.16044i | −0.176056 | + | 0.984380i | \(0.556334\pi\) |
−0.984380 | + | 0.176056i | \(0.943666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.5896 | − | 35.5896i | 1.31096 | − | 1.31096i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 39.9278i | − | 1.46877i | −0.678734 | − | 0.734384i | \(-0.737471\pi\) | ||
0.678734 | − | 0.734384i | \(-0.262529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.2758 | − | 12.2758i | −0.450354 | − | 0.450354i | 0.445118 | − | 0.895472i | \(-0.353162\pi\) |
−0.895472 | + | 0.445118i | \(0.853162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.75535 | − | 10.4212i | −0.357408 | − | 0.381805i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.7391 | 0.867409 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4987 | 1.00344 | 0.501721 | − | 0.865029i | \(-0.332700\pi\) | ||||
0.501721 | + | 0.865029i | \(0.332700\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.34595 | − | 6.77912i | −0.230953 | − | 0.246717i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3031 | − | 17.3031i | −0.628890 | − | 0.628890i | 0.318899 | − | 0.947789i | \(-0.396687\pi\) |
−0.947789 | + | 0.318899i | \(0.896687\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 39.6747i | − | 1.43821i | −0.694902 | − | 0.719104i | \(-0.744552\pi\) | ||
0.694902 | − | 0.719104i | \(-0.255448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8248 | + | 10.8248i | −0.391883 | + | 0.391883i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.56751 | + | 4.56751i | −0.164923 | + | 0.164923i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.77095i | 0.208106i | 0.994572 | + | 0.104053i | \(0.0331811\pi\) | ||||
−0.994572 | + | 0.104053i | \(0.966819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.24325 | + | 9.24325i | 0.332457 | + | 0.332457i | 0.853519 | − | 0.521062i | \(-0.174464\pi\) |
−0.521062 | + | 0.853519i | \(0.674464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.673774 | + | 10.1966i | −0.0242027 | + | 0.366274i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.8267 | 0.459564 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.4101 | 1.23129 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.724730 | + | 21.9595i | −0.0258667 | + | 0.783767i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.1273 | − | 35.1273i | −1.25215 | − | 1.25215i | −0.954752 | − | 0.297402i | \(-0.903880\pi\) |
−0.297402 | − | 0.954752i | \(-0.596120\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 48.2423i | − | 1.71530i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0985 | + | 13.0985i | −0.465140 | + | 0.465140i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0455 | + | 17.0455i | −0.603784 | + | 0.603784i | −0.941314 | − | 0.337531i | \(-0.890408\pi\) |
0.337531 | + | 0.941314i | \(0.390408\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.97804i | − | 0.0699780i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.10576 | + | 7.10576i | 0.250757 | + | 0.250757i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.32087 | − | 4.98088i | 0.187536 | − | 0.175553i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.1490 | −0.391977 | −0.195988 | − | 0.980606i | \(-0.562792\pi\) | ||||
−0.195988 | + | 0.980606i | \(0.562792\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0660 | 0.529039 | 0.264519 | − | 0.964380i | \(-0.414787\pi\) | ||||
0.264519 | + | 0.964380i | \(0.414787\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.1120 | + | 1.35682i | 1.44009 | + | 0.0475275i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.86023 | + | 8.86023i | 0.309980 | + | 0.309980i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 43.9646i | − | 1.53437i | −0.641423 | − | 0.767187i | \(-0.721656\pi\) | ||
0.641423 | − | 0.767187i | \(-0.278344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.8602 | + | 20.8602i | −0.727139 | + | 0.727139i | −0.970049 | − | 0.242910i | \(-0.921898\pi\) |
0.242910 | + | 0.970049i | \(0.421898\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.61299 | + | 9.61299i | −0.334276 | + | 0.334276i | −0.854208 | − | 0.519932i | \(-0.825957\pi\) |
0.519932 | + | 0.854208i | \(0.325957\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.7708i | 1.86754i | 0.357879 | + | 0.933768i | \(0.383500\pi\) | ||||
−0.357879 | + | 0.933768i | \(0.616500\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.42182 | + | 2.42182i | 0.0839110 | + | 0.0839110i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.0897 | − | 0.564013i | −0.591414 | − | 0.0195185i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.5784 | 0.917590 | 0.458795 | − | 0.888542i | \(-0.348281\pi\) | ||||
0.458795 | + | 0.888542i | \(0.348281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.70503 | −0.334656 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.3399 | − | 14.3597i | 0.527707 | − | 0.493988i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.164327 | + | 0.164327i | 0.00564635 | + | 0.00564635i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.32475i | 0.216810i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.2333 | − | 38.2333i | 1.30908 | − | 1.30908i | 0.387004 | − | 0.922078i | \(-0.373510\pi\) |
0.922078 | − | 0.387004i | \(-0.126490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.94602 | + | 1.94602i | −0.0664749 | + | 0.0664749i | −0.739563 | − | 0.673088i | \(-0.764968\pi\) |
0.673088 | + | 0.739563i | \(0.264968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 50.5755i | − | 1.72561i | −0.505533 | − | 0.862807i | \(-0.668704\pi\) | ||
0.505533 | − | 0.862807i | \(-0.331296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.6077 | + | 22.6077i | 0.769577 | + | 0.769577i | 0.978032 | − | 0.208455i | \(-0.0668436\pi\) |
−0.208455 | + | 0.978032i | \(0.566844\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.781024 | − | 23.6652i | 0.0265556 | − | 0.804641i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.5459 | −1.00228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −71.5868 | −2.42563 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.2637 | + | 3.60090i | 1.22594 | + | 0.121733i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.5411 | − | 26.5411i | −0.896228 | − | 0.896228i | 0.0988722 | − | 0.995100i | \(-0.468476\pi\) |
−0.995100 | + | 0.0988722i | \(0.968476\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.54565i | − | 0.254219i | −0.991889 | − | 0.127110i | \(-0.959430\pi\) | ||
0.991889 | − | 0.127110i | \(-0.0405700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.6779 | − | 13.6779i | 0.460297 | − | 0.460297i | −0.438456 | − | 0.898753i | \(-0.644474\pi\) |
0.898753 | + | 0.438456i | \(0.144474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.9261 | − | 17.9261i | 0.601899 | − | 0.601899i | −0.338917 | − | 0.940816i | \(-0.610061\pi\) |
0.940816 | + | 0.338917i | \(0.110061\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 20.7466i | − | 0.695820i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.56519 | − | 2.56519i | −0.0858407 | − | 0.0858407i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.6937 | − | 11.4237i | −0.357452 | − | 0.381851i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.97749 | −0.299416 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.32377 | 0.177361 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.6219 | − | 20.9612i | −0.652253 | − | 0.696775i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.3530 | − | 26.3530i | −0.875038 | − | 0.875038i | 0.117978 | − | 0.993016i | \(-0.462359\pi\) |
−0.993016 | + | 0.117978i | \(0.962359\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33.9264i | − | 1.12403i | −0.827126 | − | 0.562016i | \(-0.810026\pi\) | ||
0.827126 | − | 0.562016i | \(-0.189974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.35681 | + | 7.35681i | −0.243475 | + | 0.243475i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.8987 | − | 16.8987i | 0.558044 | − | 0.558044i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.6588i | − | 1.14329i | −0.820501 | − | 0.571645i | \(-0.806306\pi\) | ||
0.820501 | − | 0.571645i | \(-0.193694\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.6072 | − | 34.6072i | −1.13911 | − | 1.13911i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.7871 | + | 20.8383i | −0.782115 | + | 0.685160i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.0724 | 1.51159 | 0.755794 | − | 0.654810i | \(-0.227251\pi\) | ||||
0.755794 | + | 0.654810i | \(0.227251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.28139 | 0.205864 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.231928 | − | 7.02745i | 0.00758484 | − | 0.229822i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.4255 | + | 12.4255i | 0.405923 | + | 0.405923i | 0.880314 | − | 0.474391i | \(-0.157332\pi\) |
−0.474391 | + | 0.880314i | \(0.657332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.6602i | 1.71667i | 0.513088 | + | 0.858336i | \(0.328502\pi\) | ||||
−0.513088 | + | 0.858336i | \(0.671498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.23299 | + | 5.23299i | −0.170410 | + | 0.170410i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.94840 | − | 2.94840i | 0.0958103 | − | 0.0958103i | −0.657577 | − | 0.753387i | \(-0.728419\pi\) |
0.753387 | + | 0.657577i | \(0.228419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 14.2929i | − | 0.463967i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.6925 | − | 28.6925i | −0.929442 | − | 0.929442i | 0.0682275 | − | 0.997670i | \(-0.478266\pi\) |
−0.997670 | + | 0.0682275i | \(0.978266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.3781 | + | 33.1175i | −1.14481 | + | 1.07166i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.34787 | 0.140400 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8230 | −0.865258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.83100 | + | 0.126435i | 0.123324 | + | 0.00407008i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.0078 | − | 20.0078i | −0.643408 | − | 0.643408i | 0.307984 | − | 0.951392i | \(-0.400346\pi\) |
−0.951392 | + | 0.307984i | \(0.900346\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24.5560i | − | 0.788040i | −0.919102 | − | 0.394020i | \(-0.871084\pi\) | ||
0.919102 | − | 0.394020i | \(-0.128916\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.0522 | + | 25.0522i | −0.803137 | + | 0.803137i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.2875 | − | 21.2875i | 0.681046 | − | 0.681046i | −0.279190 | − | 0.960236i | \(-0.590066\pi\) |
0.960236 | + | 0.279190i | \(0.0900659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.22585i | 0.230939i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.2091 | − | 16.2091i | −0.516990 | − | 0.516990i | 0.399669 | − | 0.916659i | \(-0.369125\pi\) |
−0.916659 | + | 0.399669i | \(0.869125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.0192 | − | 1.65079i | −1.59375 | − | 0.0525985i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.22954 | −0.229886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0424 | 1.43082 | 0.715410 | − | 0.698705i | \(-0.246240\pi\) | ||||
0.715410 | + | 0.698705i | \(0.246240\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.8773 | − | 26.0960i | 0.883770 | − | 0.827299i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.6571 | + | 31.6571i | 1.00259 | + | 1.00259i | 0.999997 | + | 0.00259275i | \(0.000825300\pi\) |
0.00259275 | + | 0.999997i | \(0.499175\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4140.2.s.b.737.17 | yes | 44 | |
3.2 | odd | 2 | inner | 4140.2.s.b.737.6 | ✓ | 44 | |
5.3 | odd | 4 | inner | 4140.2.s.b.2393.6 | yes | 44 | |
15.8 | even | 4 | inner | 4140.2.s.b.2393.17 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.s.b.737.6 | ✓ | 44 | 3.2 | odd | 2 | inner | |
4140.2.s.b.737.17 | yes | 44 | 1.1 | even | 1 | trivial | |
4140.2.s.b.2393.6 | yes | 44 | 5.3 | odd | 4 | inner | |
4140.2.s.b.2393.17 | yes | 44 | 15.8 | even | 4 | inner |