Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(589,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 589.3 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.589 |
Dual form | 980.2.e.f.589.1 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.63746 | + | 1.52274i | −0.732294 | + | 0.680989i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.27492 | −1.59045 | −0.795224 | − | 0.606316i | \(-0.792647\pi\) | ||||
−0.795224 | + | 0.606316i | \(0.792647\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62685i | 0.728557i | 0.931290 | + | 0.364278i | \(0.118684\pi\) | ||||
−0.931290 | + | 0.364278i | \(0.881316\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.63746 | − | 2.83616i | −0.680989 | − | 0.732294i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.418627i | − | 0.101532i | −0.998711 | − | 0.0507659i | \(-0.983834\pi\) | ||
0.998711 | − | 0.0507659i | \(-0.0161663\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.27492 | −0.751318 | −0.375659 | − | 0.926758i | \(-0.622584\pi\) | ||||
−0.375659 | + | 0.926758i | \(0.622584\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.82300i | − | 1.63121i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) | ||
0.578610 | − | 0.815604i | \(-0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.362541 | − | 4.98684i | 0.0725083 | − | 0.997368i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.27492 | −0.793832 | −0.396916 | − | 0.917855i | \(-0.629920\pi\) | ||||
−0.396916 | + | 0.917855i | \(0.629920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.27492 | 0.588192 | 0.294096 | − | 0.955776i | \(-0.404981\pi\) | ||||
0.294096 | + | 0.955776i | \(0.404981\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 9.13642i | − | 1.59045i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.97368i | 1.63966i | 0.572605 | + | 0.819831i | \(0.305933\pi\) | ||||
−0.572605 | + | 0.819831i | \(0.694067\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.54983 | −0.728557 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.72508 | −0.581760 | −0.290880 | − | 0.956760i | \(-0.593948\pi\) | ||||
−0.290880 | + | 0.956760i | \(0.593948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.15068i | − | 0.327975i | −0.986462 | − | 0.163988i | \(-0.947564\pi\) | ||
0.986462 | − | 0.163988i | \(-0.0524357\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.50958i | − | 0.949519i | −0.880115 | − | 0.474760i | \(-0.842535\pi\) | ||
0.880115 | − | 0.474760i | \(-0.157465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.725083 | 0.101532 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.67232i | − | 0.779153i | −0.920994 | − | 0.389577i | \(-0.872621\pi\) | ||
0.920994 | − | 0.389577i | \(-0.127379\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.63746 | − | 8.03231i | 1.16467 | − | 1.08308i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.67232i | − | 0.751318i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.27492 | 0.426358 | 0.213179 | − | 0.977013i | \(-0.431618\pi\) | ||||
0.213179 | + | 0.977013i | \(0.431618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5498 | −1.73488 | −0.867439 | − | 0.497543i | \(-0.834236\pi\) | ||||
−0.867439 | + | 0.497543i | \(0.834236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.00000 | − | 4.30136i | −0.496139 | − | 0.533517i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.52165i | − | 0.430237i | −0.976588 | − | 0.215119i | \(-0.930986\pi\) | ||
0.976588 | − | 0.215119i | \(-0.0690139\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.5498 | 1.63121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.54983 | −0.539966 | −0.269983 | − | 0.962865i | \(-0.587018\pi\) | ||||
−0.269983 | + | 0.962865i | \(0.587018\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.50958i | 0.761888i | 0.924598 | + | 0.380944i | \(0.124401\pi\) | ||||
−0.924598 | + | 0.380944i | \(0.875599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.63746 | + | 0.627940i | 0.997368 | + | 0.0725083i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.27492 | −0.818492 | −0.409246 | − | 0.912424i | \(-0.634208\pi\) | ||||
−0.409246 | + | 0.912424i | \(0.634208\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.40437i | − | 0.812736i | −0.913710 | − | 0.406368i | \(-0.866795\pi\) | ||
0.913710 | − | 0.406368i | \(-0.133205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.637459 | + | 0.685484i | 0.0691421 | + | 0.0743512i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.40437i | − | 0.793832i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.00000 | 0.741999 | 0.370999 | − | 0.928633i | \(-0.379015\pi\) | ||||
0.370999 | + | 0.928633i | \(0.379015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.67232i | 0.588192i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.36254 | − | 4.98684i | 0.550185 | − | 0.511639i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820i | 0.703452i | 0.936103 | + | 0.351726i | \(0.114405\pi\) | ||||
−0.936103 | + | 0.351726i | \(0.885595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5498 | −1.34826 | −0.674129 | − | 0.738613i | \(-0.735481\pi\) | ||||
−0.674129 | + | 0.738613i | \(0.735481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2871i | 1.11215i | 0.831132 | + | 0.556076i | \(0.187694\pi\) | ||||
−0.831132 | + | 0.556076i | \(0.812306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.52165i | − | 0.340450i | −0.985405 | − | 0.170225i | \(-0.945550\pi\) | ||
0.985405 | − | 0.170225i | \(-0.0544495\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5498 | 1.10627 | 0.553137 | − | 0.833090i | \(-0.313431\pi\) | ||||
0.553137 | + | 0.833090i | \(0.313431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.2749 | −1.63966 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.30136i | 0.404637i | 0.979320 | + | 0.202319i | \(0.0648477\pi\) | ||||
−0.979320 | + | 0.202319i | \(0.935152\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.9124 | + | 12.8098i | 1.11083 | + | 1.19452i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.8248 | 1.52952 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 6.45203i | − | 0.581760i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.00000 | + | 8.71780i | 0.626099 | + | 0.779744i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6460i | 1.38836i | 0.719802 | + | 0.694179i | \(0.244232\pi\) | ||||
−0.719802 | + | 0.694179i | \(0.755768\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.72508 | 0.327975 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7251 | −0.937055 | −0.468527 | − | 0.883449i | \(-0.655215\pi\) | ||||
−0.468527 | + | 0.883449i | \(0.655215\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.91238 | − | 8.50848i | −0.680989 | − | 0.732294i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.3183i | 1.82135i | 0.413126 | + | 0.910674i | \(0.364437\pi\) | ||||
−0.413126 | + | 0.910674i | \(0.635563\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0997 | −1.11110 | −0.555550 | − | 0.831483i | \(-0.687492\pi\) | ||||
−0.555550 | + | 0.831483i | \(0.687492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.2749 | 0.949519 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 13.8564i | − | 1.15873i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.00000 | − | 6.50958i | 0.581318 | − | 0.540591i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.54983 | 0.618507 | 0.309253 | − | 0.950980i | \(-0.399921\pi\) | ||||
0.309253 | + | 0.950980i | \(0.399921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7251 | −1.03555 | −0.517776 | − | 0.855516i | \(-0.673240\pi\) | ||||
−0.517776 | + | 0.855516i | \(0.673240\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.36254 | + | 4.98684i | −0.430730 | + | 0.400553i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.20822i | 0.176235i | 0.996110 | + | 0.0881176i | \(0.0280851\pi\) | ||||
−0.996110 | + | 0.0881176i | \(0.971915\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.82475 | 0.779153 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.67232i | 0.444291i | 0.975014 | + | 0.222145i | \(0.0713059\pi\) | ||||
−0.975014 | + | 0.222145i | \(0.928694\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.9124 | + | 14.9605i | 1.08308 | + | 1.16467i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.476171i | 0.0368472i | 0.999830 | + | 0.0184236i | \(0.00586474\pi\) | ||||
−0.999830 | + | 0.0184236i | \(0.994135\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.09967 | 0.469205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.4811i | 1.55715i | 0.627553 | + | 0.778573i | \(0.284056\pi\) | ||||
−0.627553 | + | 0.778573i | \(0.715944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.67232i | 0.426358i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.27492 | 0.543753 | 0.271876 | − | 0.962332i | \(-0.412356\pi\) | ||||
0.271876 | + | 0.962332i | \(0.412356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2749 | −1.80434 | −0.902170 | − | 0.431380i | \(-0.858027\pi\) | ||||
−0.902170 | + | 0.431380i | \(0.858027\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 23.4690i | − | 1.73488i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.1873 | − | 16.3315i | −1.11659 | − | 1.20071i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.20822i | 0.161481i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.175248 | 0.0126805 | 0.00634026 | − | 0.999980i | \(-0.497982\pi\) | ||||
0.00634026 | + | 0.999980i | \(0.497982\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.3183i | 1.53453i | 0.641332 | + | 0.767263i | \(0.278382\pi\) | ||||
−0.641332 | + | 0.767263i | \(0.721618\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.45017 | − | 6.92820i | 0.533517 | − | 0.496139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.60271i | − | 0.612918i | −0.951884 | − | 0.306459i | \(-0.900856\pi\) | ||
0.951884 | − | 0.306459i | \(-0.0991442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2749 | −1.22459 | −0.612293 | − | 0.790631i | \(-0.709753\pi\) | ||||
−0.612293 | + | 0.790631i | \(0.709753\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.09967 | 0.430237 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.09967 | − | 5.67232i | 0.426019 | − | 0.396172i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.2749 | 1.19493 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.6495 | 1.76578 | 0.882892 | − | 0.469576i | \(-0.155593\pi\) | ||||
0.882892 | + | 0.469576i | \(0.155593\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 7.88054i | − | 0.539966i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.27492 | + | 3.52165i | 0.223348 | + | 0.240174i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.2749 | −0.761888 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.09967 | 0.0739717 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.71780i | − | 0.583787i | −0.956451 | − | 0.291893i | \(-0.905715\pi\) | ||
0.956451 | − | 0.291893i | \(-0.0942853\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.5287i | 1.29617i | 0.761569 | + | 0.648084i | \(0.224429\pi\) | ||||
−0.761569 | + | 0.648084i | \(0.775571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.27492 | −0.216413 | −0.108206 | − | 0.994128i | \(-0.534511\pi\) | ||||
−0.108206 | + | 0.994128i | \(0.534511\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.2750i | 0.935189i | 0.883943 | + | 0.467594i | \(0.154879\pi\) | ||||
−0.883943 | + | 0.467594i | \(0.845121\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.91238 | + | 10.6592i | 0.646612 | + | 0.695327i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 12.6005i | − | 0.818492i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.549834 | −0.0355658 | −0.0177829 | − | 0.999842i | \(-0.505661\pi\) | ||||
−0.0177829 | + | 0.999842i | \(0.505661\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.82475 | 0.632868 | 0.316434 | − | 0.948615i | \(-0.397514\pi\) | ||||
0.316434 | + | 0.948615i | \(0.397514\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.60271i | − | 0.547377i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.8248 | 0.812736 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5498 | −1.29709 | −0.648547 | − | 0.761175i | \(-0.724623\pi\) | ||||
−0.648547 | + | 0.761175i | \(0.724623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.2657i | 2.59435i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.18729 | + | 1.10411i | −0.0743512 | + | 0.0691421i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.6482i | 0.726594i | 0.931673 | + | 0.363297i | \(0.118349\pi\) | ||||
−0.931673 | + | 0.363297i | \(0.881651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.779710i | 0.0480790i | 0.999711 | + | 0.0240395i | \(0.00765274\pi\) | ||||
−0.999711 | + | 0.0240395i | \(0.992347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.63746 | + | 9.28819i | 0.530595 | + | 0.570569i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1244i | 0.741999i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.4502 | 0.881042 | 0.440521 | − | 0.897742i | \(-0.354794\pi\) | ||||
0.440521 | + | 0.897742i | \(0.354794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.82475 | 0.596811 | 0.298406 | − | 0.954439i | \(-0.403545\pi\) | ||||
0.298406 | + | 0.954439i | \(0.403545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.91238 | + | 26.3052i | −0.115321 | + | 1.58626i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 14.2750i | − | 0.857704i | −0.903375 | − | 0.428852i | \(-0.858918\pi\) | ||
0.903375 | − | 0.428852i | \(-0.141082\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.9260i | 0.649484i | 0.945803 | + | 0.324742i | \(0.105278\pi\) | ||||
−0.945803 | + | 0.324742i | \(0.894722\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.63746 | + | 9.28819i | 0.511639 | + | 0.550185i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8248 | 0.989691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92820i | 0.404750i | 0.979308 | + | 0.202375i | \(0.0648660\pi\) | ||||
−0.979308 | + | 0.202375i | \(0.935134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.36254 | + | 4.98684i | −0.312219 | + | 0.290345i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 27.4093i | − | 1.59045i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.5498 | 1.18843 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 23.4690i | − | 1.34826i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.1873 | − | 20.6328i | 1.27044 | − | 1.18143i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.5145i | − | 1.51326i | −0.653843 | − | 0.756631i | \(-0.726844\pi\) | ||
0.653843 | − | 0.756631i | \(-0.273156\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.5498 | −1.11215 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.82475 | −0.557111 | −0.278555 | − | 0.960420i | \(-0.589856\pi\) | ||||
−0.278555 | + | 0.960420i | \(0.589856\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 33.5002i | − | 1.89354i | −0.321904 | − | 0.946772i | \(-0.604323\pi\) | ||
0.321904 | − | 0.946772i | \(-0.395677\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 25.6197i | − | 1.43894i | −0.694521 | − | 0.719472i | \(-0.744384\pi\) | ||
0.694521 | − | 0.719472i | \(-0.255616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.5498 | 1.26255 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.09967 | 0.340450 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.37097i | 0.0762827i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0997 | + | 0.952341i | 0.726639 | + | 0.0528264i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.0049i | 1.10627i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.8248 | 0.979737 | 0.489868 | − | 0.871796i | \(-0.337045\pi\) | ||||
0.489868 | + | 0.871796i | \(0.337045\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.36254 | + | 5.76655i | 0.292987 | + | 0.315060i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.30136i | 0.234310i | 0.993114 | + | 0.117155i | \(0.0373774\pi\) | ||||
−0.993114 | + | 0.117155i | \(0.962623\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.45017 | −0.404637 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2749 | −0.935489 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −22.1873 | + | 20.6328i | −1.19452 | + | 1.11083i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 12.1244i | − | 0.650870i | −0.945564 | − | 0.325435i | \(-0.894489\pi\) | ||
0.945564 | − | 0.325435i | \(-0.105511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.72508 | 0.199399 | 0.0996996 | − | 0.995018i | \(-0.468212\pi\) | ||||
0.0996996 | + | 0.995018i | \(0.468212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.6495 | −0.728557 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.18408i | 0.435595i | 0.975994 | + | 0.217797i | \(0.0698872\pi\) | ||||
−0.975994 | + | 0.217797i | \(0.930113\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.45017 | − | 6.92820i | 0.395414 | − | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.3746 | −1.91978 | −0.959889 | − | 0.280382i | \(-0.909539\pi\) | ||||
−0.959889 | + | 0.280382i | \(0.909539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.27492 | −0.435522 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.1413i | 1.52952i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.91238 | − | 10.6592i | −0.518837 | − | 0.557926i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.03341i | 0.314941i | 0.987524 | + | 0.157471i | \(0.0503340\pi\) | ||||
−0.987524 | + | 0.157471i | \(0.949666\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.97368i | 0.516417i | 0.966089 | + | 0.258209i | \(0.0831322\pi\) | ||||
−0.966089 | + | 0.258209i | \(0.916868\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.0997 | + | 12.1244i | −0.779744 | + | 0.626099i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.2296i | − | 0.578352i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6495 | 1.11206 | 0.556030 | − | 0.831162i | \(-0.312324\pi\) | ||||
0.556030 | + | 0.831162i | \(0.312324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.0997 | −1.38836 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 6.14849i | − | 0.314173i | −0.987585 | − | 0.157087i | \(-0.949790\pi\) | ||
0.987585 | − | 0.157087i | \(-0.0502102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.3746 | −1.64146 | −0.820728 | − | 0.571319i | \(-0.806432\pi\) | ||||
−0.820728 | + | 0.571319i | \(0.806432\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.27492 | −0.165620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 18.5764i | − | 0.937055i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.9124 | − | 11.0778i | 0.599377 | − | 0.557384i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.8109i | − | 0.542585i | −0.962497 | − | 0.271293i | \(-0.912549\pi\) | ||
0.962497 | − | 0.271293i | \(-0.0874511\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | 0.149813 | 0.0749064 | − | 0.997191i | \(-0.476134\pi\) | ||||
0.0749064 | + | 0.997191i | \(0.476134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.60271i | 0.428532i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.7371 | − | 13.7046i | 0.732294 | − | 0.680989i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 52.6103i | − | 2.60780i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0997 | 0.993865 | 0.496932 | − | 0.867789i | \(-0.334460\pi\) | ||||
0.496932 | + | 0.867789i | \(0.334460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.9244 | −1.82135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2749 | + | 12.1244i | 0.553464 | + | 0.595161i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 22.6893i | − | 1.11110i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0997 | 0.639961 | 0.319980 | − | 0.947424i | \(-0.396324\pi\) | ||||
0.319980 | + | 0.947424i | \(0.396324\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.27492 | −0.208347 | −0.104173 | − | 0.994559i | \(-0.533220\pi\) | ||||
−0.104173 | + | 0.994559i | \(0.533220\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.08762 | − | 0.151770i | −0.101265 | − | 0.00736190i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.0000 | 1.15873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3746 | −0.885073 | −0.442536 | − | 0.896751i | \(-0.645921\pi\) | ||||
−0.442536 | + | 0.896751i | \(0.645921\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.1578i | − | 0.872606i | −0.899800 | − | 0.436303i | \(-0.856288\pi\) | ||
0.899800 | − | 0.436303i | \(-0.143712\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.2749 | + | 12.1244i | 0.540591 | + | 0.581318i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.6197i | 1.22556i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.8248 | −1.13709 | −0.568547 | − | 0.822651i | \(-0.692494\pi\) | ||||
−0.568547 | + | 0.822651i | \(0.692494\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12.1244i | − | 0.576046i | −0.957624 | − | 0.288023i | \(-0.907002\pi\) | ||
0.957624 | − | 0.288023i | \(-0.0929979\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.4622 | + | 10.6592i | −0.543361 | + | 0.505293i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.0767i | 0.618507i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.17525 | 0.149849 | 0.0749246 | − | 0.997189i | \(-0.476128\pi\) | ||||
0.0749246 | + | 0.997189i | \(0.476128\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.6495 | 0.925259 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 22.0405i | − | 1.03555i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.37097i | 0.0641312i | 0.999486 | + | 0.0320656i | \(0.0102085\pi\) | ||||
−0.999486 | + | 0.0320656i | \(0.989791\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.17525 | 0.101532 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.15068i | 0.0999505i | 0.998750 | + | 0.0499752i | \(0.0159142\pi\) | ||||
−0.998750 | + | 0.0499752i | \(0.984086\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.63746 | − | 9.28819i | −0.400553 | − | 0.430730i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15.7035i | − | 0.726673i | −0.931658 | − | 0.363337i | \(-0.881637\pi\) | ||
0.931658 | − | 0.363337i | \(-0.118363\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.82475 | −0.176235 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.3446i | 0.521627i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.18729 | + | 16.3315i | −0.0544767 | + | 0.749340i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.82475 | −0.448904 | −0.224452 | − | 0.974485i | \(-0.572059\pi\) | ||||
−0.224452 | + | 0.974485i | \(0.572059\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1993 | −1.19459 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.5498 | − | 11.3446i | −0.479043 | − | 0.515134i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.93039i | − | 0.132789i | −0.997793 | − | 0.0663943i | \(-0.978850\pi\) | ||
0.997793 | − | 0.0663943i | \(-0.0211495\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.82475 | −0.444291 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.5498 | −1.28844 | −0.644218 | − | 0.764842i | \(-0.722817\pi\) | ||||
−0.644218 | + | 0.764842i | \(0.722817\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.78959i | 0.0805993i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.62541 | −0.0727635 | −0.0363818 | − | 0.999338i | \(-0.511583\pi\) | ||||
−0.0363818 | + | 0.999338i | \(0.511583\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.824752 | −0.0368472 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7682i | 1.41647i | 0.705975 | + | 0.708236i | \(0.250509\pi\) | ||||
−0.705975 | + | 0.708236i | \(0.749491\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.1873 | − | 20.6328i | 0.987322 | − | 0.918149i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.5649i | 0.469205i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.4502 | 0.640492 | 0.320246 | − | 0.947334i | \(-0.396234\pi\) | ||||
0.320246 | + | 0.947334i | \(0.396234\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 17.0170i | − | 0.751318i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.1873 | − | 18.4822i | −0.757363 | − | 0.814421i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.3375i | 1.51016i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −35.4743 | −1.55715 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.82475 | 0.430430 | 0.215215 | − | 0.976567i | \(-0.430955\pi\) | ||||
0.215215 | + | 0.976567i | \(0.430955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.34683i | 0.321254i | 0.987015 | + | 0.160627i | \(0.0513517\pi\) | ||||
−0.987015 | + | 0.160627i | \(0.948648\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.37097i | − | 0.0597203i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −38.1993 | −1.66084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.78523i | − | 0.423845i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.36254 | + | 5.76655i | 0.231843 | + | 0.249310i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.6005i | 0.543753i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5498 | −0.754526 | −0.377263 | − | 0.926106i | \(-0.623135\pi\) | ||||
−0.377263 | + | 0.926106i | \(0.623135\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 42.0454i | − | 1.80434i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.9124 | + | 17.5874i | −0.810117 | + | 0.753360i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.5386i | 0.878168i | 0.898446 | + | 0.439084i | \(0.144697\pi\) | ||||
−0.898446 | + | 0.439084i | \(0.855303\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0000 | 0.596420 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 28.2870 | − | 26.3052i | 1.20071 | − | 1.11659i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 9.97368i | − | 0.422598i | −0.977421 | − | 0.211299i | \(-0.932231\pi\) | ||
0.977421 | − | 0.211299i | \(-0.0677694\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.64950 | 0.238949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.82475 | −0.161481 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 22.6317i | − | 0.953814i | −0.878954 | − | 0.476907i | \(-0.841758\pi\) | ||
0.878954 | − | 0.476907i | \(-0.158242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.54983 | − | 7.04329i | −0.275554 | − | 0.296313i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.37459 | −0.351081 | −0.175540 | − | 0.984472i | \(-0.556167\pi\) | ||||
−0.175540 | + | 0.984472i | \(0.556167\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.27492 | 0.304446 | 0.152223 | − | 0.988346i | \(-0.451357\pi\) | ||||
0.152223 | + | 0.988346i | \(0.451357\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.303539i | 0.0126805i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.0120 | − | 2.83616i | −1.62691 | − | 0.118276i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.88273i | 0.161640i | 0.996729 | + | 0.0808200i | \(0.0257539\pi\) | ||||
−0.996729 | + | 0.0808200i | \(0.974246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.9244 | −1.53453 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.9210i | 1.23920i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 20.8997i | − | 0.862623i | −0.902203 | − | 0.431311i | \(-0.858051\pi\) | ||
0.902203 | − | 0.431311i | \(-0.141949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.7251 | −0.441919 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.9003 | 0.612918 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.3851i | 1.37096i | 0.728090 | + | 0.685482i | \(0.240408\pi\) | ||||
−0.728090 | + | 0.685482i | \(0.759592\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 29.9210i | − | 1.22459i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.27492 | −0.215527 | −0.107764 | − | 0.994177i | \(-0.534369\pi\) | ||||
−0.107764 | + | 0.994177i | \(0.534369\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.5498 | + | 25.6197i | −1.12006 | + | 1.04159i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 11.4022i | − | 0.462801i | −0.972859 | − | 0.231400i | \(-0.925669\pi\) | ||
0.972859 | − | 0.231400i | \(-0.0743307\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.0997 | 0.691779 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 28.3616i | − | 1.14551i | −0.819725 | − | 0.572757i | \(-0.805874\pi\) | ||
0.819725 | − | 0.572757i | \(-0.194126\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.82475 | + | 10.5649i | 0.396172 | + | 0.426019i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.2920i | 1.25977i | 0.776689 | + | 0.629884i | \(0.216898\pi\) | ||||
−0.776689 | + | 0.629884i | \(0.783102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.92442 | 0.358703 | 0.179351 | − | 0.983785i | \(-0.442600\pi\) | ||||
0.179351 | + | 0.983785i | \(0.442600\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40.6495 | 1.63121 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7371 | − | 3.61587i | −0.989485 | − | 0.144635i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.9210i | 1.19493i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.17525 | 0.166478 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0997 | 1.31768 | 0.658839 | − | 0.752284i | \(-0.271048\pi\) | ||||
0.658839 | + | 0.752284i | \(0.271048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 44.4262i | 1.76578i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.8248 | − | 25.6197i | −0.945456 | − | 1.01669i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.09967 | −0.0829319 | −0.0414660 | − | 0.999140i | \(-0.513203\pi\) | ||||
−0.0414660 | + | 0.999140i | \(0.513203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 31.4071i | − | 1.23857i | −0.785164 | − | 0.619287i | \(-0.787422\pi\) | ||
0.785164 | − | 0.619287i | \(-0.212578\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.09967 | + | 5.67232i | −0.240174 | + | 0.223348i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 26.9331i | − | 1.05885i | −0.848357 | − | 0.529425i | \(-0.822408\pi\) | ||
0.848357 | − | 0.529425i | \(-0.177592\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.2749 | −0.678100 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.3616i | 1.10988i | 0.831892 | + | 0.554938i | \(0.187258\pi\) | ||||
−0.831892 | + | 0.554938i | \(0.812742\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.5619 | − | 16.3315i | 0.686199 | − | 0.638124i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.5498 | 1.57960 | 0.789799 | − | 0.613366i | \(-0.210185\pi\) | ||||
0.789799 | + | 0.613366i | \(0.210185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.450166 | −0.0175094 | −0.00875471 | − | 0.999962i | \(-0.502787\pi\) | ||||
−0.00875471 | + | 0.999962i | \(0.502787\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.90468i | 0.0739717i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.4427i | 1.29491i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.0997 | 0.583787 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 71.4743 | 2.75923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 31.2920i | − | 1.20622i | −0.797659 | − | 0.603109i | \(-0.793928\pi\) | ||
0.797659 | − | 0.603109i | \(-0.206072\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9124 | + | 1.88382i | 0.997368 | + | 0.0725083i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 46.4043i | − | 1.78346i | −0.452566 | − | 0.891731i | \(-0.649491\pi\) | ||
0.452566 | − | 0.891731i | \(-0.350509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.8248 | −1.29617 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.1676i | 0.733430i | 0.930333 | + | 0.366715i | \(0.119518\pi\) | ||||
−0.930333 | + | 0.366715i | \(0.880482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.4622 | − | 34.9079i | −1.24032 | − | 1.33376i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5.67232i | − | 0.216413i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.9003 | 0.567657 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3746 | 1.15550 | 0.577752 | − | 0.816212i | \(-0.303930\pi\) | ||||
0.577752 | + | 0.816212i | \(0.303930\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.4502 | − | 19.9474i | 0.813651 | − | 0.756646i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.55942i | 0.0590672i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.7251 | −0.935189 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.82475 | 0.333306 | 0.166653 | − | 0.986016i | \(-0.446704\pi\) | ||||
0.166653 | + | 0.986016i | \(0.446704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.6630i | − | 1.23191i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.4622 | + | 17.1687i | −0.695327 | + | 0.646612i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.4502 | 0.392464 | 0.196232 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196232 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 25.6197i | − | 0.959465i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.0997 | + | 22.6893i | 0.789083 | + | 0.848531i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.952341i | − | 0.0355658i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.3746 | 1.13278 | 0.566390 | − | 0.824137i | \(-0.308339\pi\) | ||||
0.566390 | + | 0.824137i | \(0.308339\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.0170i | 0.632868i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.54983 | + | 21.3183i | −0.0575594 | + | 0.791743i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.10302i | − | 0.115085i | −0.998343 | − | 0.0575423i | \(-0.981674\pi\) | ||
0.998343 | − | 0.0575423i | \(-0.0183264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.900331 | −0.0332999 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.6865i | 1.39198i | 0.718050 | + | 0.695991i | \(0.245035\pi\) | ||||
−0.718050 | + | 0.695991i | \(0.754965\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.5764i | 0.684270i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.9244 | 0.769717 | 0.384859 | − | 0.922976i | \(-0.374250\pi\) | ||||
0.384859 | + | 0.922976i | \(0.374250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.9003 | 0.547377 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.45203i | − | 0.236702i | −0.992972 | − | 0.118351i | \(-0.962239\pi\) | ||
0.992972 | − | 0.118351i | \(-0.0377608\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.3625 | + | 11.4964i | −0.452928 | + | 0.421196i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.7251 | −0.537326 | −0.268663 | − | 0.963234i | \(-0.586582\pi\) | ||||
−0.268663 | + | 0.963234i | \(0.586582\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 35.5934i | − | 1.29709i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.8368 | − | 19.3770i | 0.758329 | − | 0.705200i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 35.5934i | − | 1.29366i | −0.762633 | − | 0.646831i | \(-0.776094\pi\) | ||
0.762633 | − | 0.646831i | \(-0.223906\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −71.4743 | −2.59435 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.9244 | 0.831010 | 0.415505 | − | 0.909591i | \(-0.363605\pi\) | ||||
0.415505 | + | 0.909591i | \(0.363605\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.60271i | 0.310626i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.1752 | −0.726594 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 40.3133i | − | 1.44997i | −0.688765 | − | 0.724985i | \(-0.741847\pi\) | ||
0.688765 | − | 0.724985i | \(-0.258153\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.18729 | − | 16.3315i | 0.0426488 | − | 0.586644i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.1993 | 0.437087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 22.2131i | − | 0.793832i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.36254 | − | 3.61587i | −0.120014 | − | 0.129056i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.73205i | 0.0617409i | 0.999523 | + | 0.0308705i | \(0.00982794\pi\) | ||||
−0.999523 | + | 0.0308705i | \(0.990172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.35050 | −0.0480790 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35.5934i | − | 1.26396i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.0876 | + | 14.9605i | −0.570569 | + | 0.530595i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.8229i | 1.65855i | 0.558839 | + | 0.829276i | \(0.311247\pi\) | ||||
−0.558839 | + | 0.829276i | \(0.688753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.72508 | −0.0964065 | ||||||||
\(800\) | 0 | 0 | ||||||||