Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2640,2,Mod(529,2640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2640.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2640.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.0805061336\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 529.6 | ||
Root | \(-0.854638 - 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2640.529 |
Dual form | 2640.2.d.i.529.3 |
$q$-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 \(\left(\mathbb{Z}/2640\mathbb{Z}\right)^\times\).
\(n\) | \(661\) | \(881\) | \(991\) | \(1057\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.17009 | + | 0.539189i | 0.970492 | + | 0.241133i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.290725i | 0.109884i | 0.998490 | + | 0.0549418i | \(0.0174973\pi\) | ||||
−0.998490 | + | 0.0549418i | \(0.982503\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.97107i | 1.93343i | 0.255861 | + | 0.966714i | \(0.417641\pi\) | ||||
−0.255861 | + | 0.966714i | \(0.582359\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.539189 | + | 2.17009i | −0.139218 | + | 0.560314i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.78765i | − | 1.16118i | −0.814197 | − | 0.580588i | \(-0.802823\pi\) | ||
0.814197 | − | 0.580588i | \(-0.197177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.75872 | 1.77997 | 0.889987 | − | 0.455987i | \(-0.150714\pi\) | ||||
0.889987 | + | 0.455987i | \(0.150714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.290725 | −0.0634413 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.41855 | + | 2.34017i | 0.883710 | + | 0.468035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.41855 | 1.37759 | 0.688795 | − | 0.724956i | \(-0.258140\pi\) | ||||
0.688795 | + | 0.724956i | \(0.258140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.34017 | −1.13873 | −0.569364 | − | 0.822085i | \(-0.692811\pi\) | ||||
−0.569364 | + | 0.822085i | \(0.692811\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.156755 | + | 0.630898i | −0.0264965 | + | 0.106641i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.41855i | 0.562006i | 0.959707 | + | 0.281003i | \(0.0906671\pi\) | ||||
−0.959707 | + | 0.281003i | \(0.909333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.97107 | −1.11626 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.41855 | −1.15858 | −0.579291 | − | 0.815120i | \(-0.696671\pi\) | ||||
−0.579291 | + | 0.815120i | \(0.696671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.290725i | − | 0.0443351i | −0.999754 | − | 0.0221675i | \(-0.992943\pi\) | ||
0.999754 | − | 0.0221675i | \(-0.00705673\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.17009 | − | 0.539189i | −0.323497 | − | 0.0803775i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.26180i | 0.767512i | 0.923435 | + | 0.383756i | \(0.125370\pi\) | ||||
−0.923435 | + | 0.383756i | \(0.874630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.91548 | 0.987926 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.78765 | 0.670406 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.75872i | 0.791022i | 0.918461 | + | 0.395511i | \(0.129432\pi\) | ||||
−0.918461 | + | 0.395511i | \(0.870568\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.17009 | + | 0.539189i | 0.292614 | + | 0.0727042i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.75872i | 1.02767i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.60197 | 0.468936 | 0.234468 | − | 0.972124i | \(-0.424665\pi\) | ||||
0.234468 | + | 0.972124i | \(0.424665\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.68035 | −0.855331 | −0.427665 | − | 0.903937i | \(-0.640664\pi\) | ||||
−0.427665 | + | 0.903937i | \(0.640664\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.290725i | − | 0.0366279i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.75872 | + | 15.1278i | −0.466212 | + | 1.87638i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.15676i | 0.752167i | 0.926586 | + | 0.376084i | \(0.122729\pi\) | ||||
−0.926586 | + | 0.376084i | \(0.877271\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.07838 | 0.602693 | 0.301346 | − | 0.953515i | \(-0.402564\pi\) | ||||
0.301346 | + | 0.953515i | \(0.402564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.12783i | − | 0.132002i | −0.997820 | − | 0.0660010i | \(-0.978976\pi\) | ||
0.997820 | − | 0.0660010i | \(-0.0210241\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.34017 | + | 4.41855i | −0.270220 | + | 0.510210i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.290725i | 0.0331311i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.921622 | −0.103691 | −0.0518453 | − | 0.998655i | \(-0.516510\pi\) | ||||
−0.0518453 | + | 0.998655i | \(0.516510\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.70928i | − | 0.187617i | −0.995590 | − | 0.0938087i | \(-0.970096\pi\) | ||
0.995590 | − | 0.0938087i | \(-0.0299042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58145 | − | 10.3896i | 0.279997 | − | 1.12691i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.41855i | 0.795352i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.34017 | −0.460057 | −0.230029 | − | 0.973184i | \(-0.573882\pi\) | ||||
−0.230029 | + | 0.973184i | \(0.573882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.02666 | −0.212452 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 6.34017i | − | 0.657445i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.8371 | + | 4.18342i | 1.72745 | + | 0.429210i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.68035i | − | 0.475217i | −0.971361 | − | 0.237609i | \(-0.923636\pi\) | ||
0.971361 | − | 0.237609i | \(-0.0763635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.58145 | −0.853886 | −0.426943 | − | 0.904279i | \(-0.640410\pi\) | ||||
−0.426943 | + | 0.904279i | \(0.640410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.73820i | − | 0.663935i | −0.943291 | − | 0.331968i | \(-0.892288\pi\) | ||
0.943291 | − | 0.331968i | \(-0.107712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.630898 | − | 0.156755i | −0.0615693 | − | 0.0152978i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.2329i | 1.18260i | 0.806453 | + | 0.591298i | \(0.201384\pi\) | ||||
−0.806453 | + | 0.591298i | \(0.798616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.31351 | 0.604725 | 0.302362 | − | 0.953193i | \(-0.402225\pi\) | ||||
0.302362 | + | 0.953193i | \(0.402225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.41855 | −0.324474 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.4969i | − | 1.55190i | −0.630794 | − | 0.775950i | \(-0.717271\pi\) | ||
0.630794 | − | 0.775950i | \(-0.282729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.15676 | − | 8.68035i | 0.201118 | − | 0.809446i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 6.97107i | − | 0.644476i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.39189 | 0.127594 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 7.41855i | − | 0.668908i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.32684 | + | 7.46081i | 0.744775 | + | 0.667315i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.87217i | 0.432336i | 0.976356 | + | 0.216168i | \(0.0693558\pi\) | ||||
−0.976356 | + | 0.216168i | \(0.930644\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.290725 | 0.0255969 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.68035 | 0.758405 | 0.379203 | − | 0.925314i | \(-0.376198\pi\) | ||||
0.379203 | + | 0.925314i | \(0.376198\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.25565i | 0.195590i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.539189 | − | 2.17009i | 0.0464060 | − | 0.186771i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.5958i | 1.07613i | 0.842902 | + | 0.538067i | \(0.180845\pi\) | ||||
−0.842902 | + | 0.538067i | \(0.819155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.91548 | −0.841020 | −0.420510 | − | 0.907288i | \(-0.638149\pi\) | ||||
−0.420510 | + | 0.907288i | \(0.638149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.26180 | −0.443123 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.97107i | 0.582950i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0989 | + | 4.00000i | 1.33694 | + | 0.332182i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.91548i | 0.570379i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.26180 | 0.103370 | 0.0516851 | − | 0.998663i | \(-0.483541\pi\) | ||||
0.0516851 | + | 0.998663i | \(0.483541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.60197 | −0.130366 | −0.0651832 | − | 0.997873i | \(-0.520763\pi\) | ||||
−0.0651832 | + | 0.997873i | \(0.520763\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.78765i | 0.387059i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.7587 | − | 3.41855i | −1.10513 | − | 0.274585i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.10504i | 0.567044i | 0.958966 | + | 0.283522i | \(0.0915029\pi\) | ||||
−0.958966 | + | 0.283522i | \(0.908497\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.75872 | −0.456696 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.16290 | 0.0916492 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.9360i | 1.79649i | 0.439499 | + | 0.898243i | \(0.355156\pi\) | ||||
−0.439499 | + | 0.898243i | \(0.644844\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.539189 | + | 2.17009i | −0.0419758 | + | 0.168941i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.81432i | 0.372543i | 0.982498 | + | 0.186271i | \(0.0596404\pi\) | ||||
−0.982498 | + | 0.186271i | \(0.940360\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.5958 | −2.73814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.75872 | −0.593324 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.8865i | − | 0.979746i | −0.871794 | − | 0.489873i | \(-0.837043\pi\) | ||
0.871794 | − | 0.489873i | \(-0.162957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.680346 | + | 1.28458i | −0.0514293 | + | 0.0971052i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.60197i | 0.270741i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.84324 | 0.137771 | 0.0688853 | − | 0.997625i | \(-0.478056\pi\) | ||||
0.0688853 | + | 0.997625i | \(0.478056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2823 | 0.764278 | 0.382139 | − | 0.924105i | \(-0.375187\pi\) | ||||
0.382139 | + | 0.924105i | \(0.375187\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.68035i | − | 0.493825i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.84324 | + | 7.41855i | −0.135518 | + | 0.545423i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.78765i | − | 0.350108i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.290725 | 0.0211471 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5174 | 0.833373 | 0.416687 | − | 0.909050i | \(-0.363191\pi\) | ||||
0.416687 | + | 0.909050i | \(0.363191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.86603i | 0.278283i | 0.990273 | + | 0.139141i | \(0.0444343\pi\) | ||||
−0.990273 | + | 0.139141i | \(0.955566\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.1278 | − | 3.75872i | −1.08333 | − | 0.269168i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.57304i | 0.610804i | 0.952224 | + | 0.305402i | \(0.0987908\pi\) | ||||
−0.952224 | + | 0.305402i | \(0.901209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.31351 | 0.589329 | 0.294665 | − | 0.955601i | \(-0.404792\pi\) | ||||
0.294665 | + | 0.955601i | \(0.404792\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.15676 | −0.434264 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.15676i | 0.151375i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.0989 | − | 4.00000i | −1.12440 | − | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000i | 0.278019i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.75872 | 0.536682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.9155 | −1.78410 | −0.892048 | − | 0.451941i | \(-0.850732\pi\) | ||||
−0.892048 | + | 0.451941i | \(0.850732\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.07838i | 0.347965i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.156755 | − | 0.630898i | 0.0106906 | − | 0.0430269i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.84324i | − | 0.125128i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.12783 | 0.0762114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.3751 | 2.24505 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.62863i | 0.644781i | 0.946607 | + | 0.322390i | \(0.104486\pi\) | ||||
−0.946607 | + | 0.322390i | \(0.895514\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41855 | − | 2.34017i | −0.294570 | − | 0.156012i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 18.3896i | − | 1.22056i | −0.792185 | − | 0.610281i | \(-0.791057\pi\) | ||
0.792185 | − | 0.610281i | \(-0.208943\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.1506 | −1.13334 | −0.566672 | − | 0.823943i | \(-0.691769\pi\) | ||||
−0.566672 | + | 0.823943i | \(0.691769\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.290725 | −0.0191283 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.10731i | − | 0.269079i | −0.990908 | − | 0.134539i | \(-0.957045\pi\) | ||
0.990908 | − | 0.134539i | \(-0.0429555\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.83710 | + | 11.4186i | −0.185072 | + | 0.744864i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 0.921622i | − | 0.0598658i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.36683 | −0.282467 | −0.141234 | − | 0.989976i | \(-0.545107\pi\) | ||||
−0.141234 | + | 0.989976i | \(0.545107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.20394 | −0.335215 | −0.167608 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167608 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.0072 | + | 3.72875i | 0.958774 | + | 0.238221i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 54.0866i | 3.44145i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.70928 | 0.108321 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.28231 | 0.522775 | 0.261388 | − | 0.965234i | \(-0.415820\pi\) | ||||
0.261388 | + | 0.965234i | \(0.415820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.00000i | − | 0.251478i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.3896 | + | 2.58145i | 0.650623 | + | 0.161657i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.0205i | − | 0.687441i | −0.939072 | − | 0.343721i | \(-0.888313\pi\) | ||
0.939072 | − | 0.343721i | \(-0.111687\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.993857 | −0.0617553 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.41855 | −0.459197 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.97107i | 0.183204i | 0.995796 | + | 0.0916020i | \(0.0291988\pi\) | ||||
−0.995796 | + | 0.0916020i | \(0.970801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.10504 | + | 12.4969i | −0.190741 | + | 0.767680i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.34017i | − | 0.265614i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8432 | 0.965980 | 0.482990 | − | 0.875626i | \(-0.339551\pi\) | ||||
0.482990 | + | 0.875626i | \(0.339551\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.28231 | 0.381623 | 0.190812 | − | 0.981627i | \(-0.438888\pi\) | ||||
0.190812 | + | 0.981627i | \(0.438888\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.02666i | − | 0.122659i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.41855 | + | 2.34017i | 0.266449 | + | 0.141118i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.12783i | − | 0.308101i | −0.988063 | − | 0.154051i | \(-0.950768\pi\) | ||
0.988063 | − | 0.154051i | \(-0.0492319\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.34017 | 0.379576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.8888 | 1.30578 | 0.652889 | − | 0.757454i | \(-0.273557\pi\) | ||||
0.652889 | + | 0.757454i | \(0.273557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 25.9649i | − | 1.54345i | −0.635954 | − | 0.771727i | \(-0.719393\pi\) | ||
0.635954 | − | 0.771727i | \(-0.280607\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.18342 | + | 16.8371i | −0.247804 | + | 0.997344i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.15676i | − | 0.127309i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.92162 | −0.348331 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.68035 | 0.274367 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4163i | 0.608526i | 0.952588 | + | 0.304263i | \(0.0984101\pi\) | ||||
−0.952588 | + | 0.304263i | \(0.901590\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.81658 | + | 1.94214i | 0.455099 | + | 0.113076i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.8843 | 1.61259 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0845208 | 0.00487170 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 8.58145i | − | 0.492991i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.4969 | − | 3.60197i | −0.830092 | − | 0.206248i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.0700i | − | 1.65911i | −0.558425 | − | 0.829555i | \(-0.688594\pi\) | ||
0.558425 | − | 0.829555i | \(-0.311406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.73820 | 0.383323 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.44521 | −0.308770 | −0.154385 | − | 0.988011i | \(-0.549340\pi\) | ||||
−0.154385 | + | 0.988011i | \(0.549340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.0928i | 1.41833i | 0.705044 | + | 0.709163i | \(0.250927\pi\) | ||||
−0.705044 | + | 0.709163i | \(0.749073\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.156755 | − | 0.630898i | 0.00883217 | − | 0.0355471i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 21.1773i | − | 1.18943i | −0.803935 | − | 0.594717i | \(-0.797264\pi\) | ||
0.803935 | − | 0.594717i | \(-0.202736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.41855 | 0.415359 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2329 | −0.682772 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 37.1461i | − | 2.06686i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.3135 | + | 30.8020i | −0.904911 | + | 1.70859i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.31351i | 0.349138i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.52973 | −0.0843369 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.70701 | 0.368650 | 0.184325 | − | 0.982865i | \(-0.440990\pi\) | ||||
0.184325 | + | 0.982865i | \(0.440990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.41855i | − | 0.187335i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.31965 | + | 13.3607i | −0.181372 | + | 0.729973i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.7503i | − | 1.29376i | −0.762591 | − | 0.646881i | \(-0.776073\pi\) | ||
0.762591 | − | 0.646881i | \(-0.223927\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.4969 | 0.895990 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.34017 | −0.343340 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.04557i | 0.218440i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.68035 | + | 2.15676i | 0.467334 | + | 0.116116i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 31.1689i | − | 1.67323i | −0.547790 | − | 0.836616i | \(-0.684531\pi\) | ||
0.547790 | − | 0.836616i | \(-0.315469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.0472 | −0.591342 | −0.295671 | − | 0.955290i | \(-0.595543\pi\) | ||||
−0.295671 | + | 0.955290i | \(0.595543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.97107 | 0.372088 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 27.4329i | − | 1.46011i | −0.683390 | − | 0.730054i | \(-0.739495\pi\) | ||
0.683390 | − | 0.730054i | \(-0.260505\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.0205 | + | 2.73820i | 0.584908 | + | 0.145329i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.39189i | 0.0736666i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.1506 | −1.01073 | −0.505365 | − | 0.862905i | \(-0.668642\pi\) | ||||
−0.505365 | + | 0.862905i | \(0.668642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.1978 | 2.16830 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.608111 | − | 2.44748i | 0.0318300 | − | 0.128107i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.5692i | − | 0.760504i | −0.924883 | − | 0.380252i | \(-0.875837\pi\) | ||
0.924883 | − | 0.380252i | \(-0.124163\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.41855 | 0.386194 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.67420 | −0.0869203 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.81432i | − | 0.456388i | −0.973616 | − | 0.228194i | \(-0.926718\pi\) | ||
0.973616 | − | 0.228194i | \(-0.0732820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.46081 | + | 8.32684i | −0.385275 | + | 0.429996i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 51.7152i | 2.66347i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.5174 | −1.20801 | −0.604005 | − | 0.796980i | \(-0.706429\pi\) | ||||
−0.604005 | + | 0.796980i | \(0.706429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.87217 | −0.249609 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.3028i | 0.986329i | 0.869936 | + | 0.493164i | \(0.164160\pi\) | ||||
−0.869936 | + | 0.493164i | \(0.835840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.156755 | + | 0.630898i | −0.00798900 | + | 0.0321535i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.290725i | 0.0147784i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0410 | 1.01612 | 0.508060 | − | 0.861321i | \(-0.330363\pi\) | ||||
0.508060 | + | 0.861321i | \(0.330363\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.1506 | −0.968488 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.68035i | 0.437866i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.00000 | − | 0.496928i | −0.100631 | − | 0.0250032i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.3607i | 1.67433i | 0.546954 | + | 0.837163i | \(0.315787\pi\) | ||||
−0.546954 | + | 0.837163i | \(0.684213\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.25565 | −0.112924 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.6475 | −1.88003 | −0.940014 | − | 0.341135i | \(-0.889189\pi\) | ||||
−0.940014 | + | 0.341135i | \(0.889189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 44.1978i | − | 2.20165i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.17009 | + | 0.539189i | 0.107832 | + | 0.0267925i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.41855i | 0.169451i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.2039 | 1.24625 | 0.623127 | − | 0.782120i | \(-0.285862\pi\) | ||||
0.623127 | + | 0.782120i | \(0.285862\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.5958 | −0.621306 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.04718i | 0.0515284i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.921622 | − | 3.70928i | 0.0452407 | − | 0.182081i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.91548i | − | 0.485563i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.8432 | 0.871700 | 0.435850 | − | 0.900019i | \(-0.356448\pi\) | ||||
0.435850 | + | 0.900019i | \(0.356448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.8120 | −0.575684 | −0.287842 | − | 0.957678i | \(-0.592938\pi\) | ||||
−0.287842 | + | 0.957678i | \(0.592938\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.26180i | − | 0.255837i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.2039 | − | 21.1545i | 0.543471 | − | 1.02614i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.94214i | − | 0.0939868i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.97107 | −0.336566 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6803 | −0.803464 | −0.401732 | − | 0.915757i | \(-0.631592\pi\) | ||||
−0.401732 | + | 0.915757i | \(0.631592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.3135i | − | 1.36066i | −0.732906 | − | 0.680330i | \(-0.761836\pi\) | ||
0.732906 | − | 0.680330i | \(-0.238164\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.00000 | + | 16.0989i | −0.191785 | + | 0.771883i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 31.0349i | − | 1.48460i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.4452 | −1.30989 | −0.654944 | − | 0.755677i | \(-0.727308\pi\) | ||||
−0.654944 | + | 0.755677i | \(0.727308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.91548 | −0.329309 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 0.412408i | − | 0.0195941i | −0.999952 | − | 0.00979704i | \(-0.996881\pi\) | ||
0.999952 | − | 0.00979704i | \(-0.00311854\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.41855 | − | 2.34017i | −0.446482 | − | 0.110935i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.26180i | 0.0596809i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.33403 | −0.0629568 | −0.0314784 | − | 0.999504i | \(-0.510022\pi\) | ||||
−0.0314784 | + | 0.999504i | \(0.510022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.41855 | −0.349326 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1.60197i | − | 0.0752670i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.39803 | − | 1.09275i | −0.206183 | − | 0.0512291i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 11.6514i | − | 0.545030i | −0.962151 | − | 0.272515i | \(-0.912145\pi\) | ||
0.962151 | − | 0.272515i | \(-0.0878555\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.78765 | −0.223469 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.05786 | −0.0958440 | −0.0479220 | − | 0.998851i | \(-0.515260\pi\) | ||||
−0.0479220 | + | 0.998851i | \(0.515260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.7792i | − | 1.33748i | −0.743494 | − | 0.668742i | \(-0.766833\pi\) | ||
0.743494 | − | 0.668742i | \(-0.233167\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.41855 | − | 13.7587i | 0.158531 | − | 0.638046i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.84324i | 0.0852952i | 0.999090 | + | 0.0426476i | \(0.0135793\pi\) | ||||
−0.999090 | + | 0.0426476i | \(0.986421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.78992 | −0.0826509 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.10504 | −0.327383 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.290725i | − | 0.0133675i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 34.2823 | + | 18.1568i | 1.57298 | + | 0.833089i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 5.75872i | − | 0.263674i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.8371 | 1.22622 | 0.613109 | − | 0.789998i | \(-0.289919\pi\) | ||||
0.613109 | + | 0.789998i | \(0.289919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.8310 | −1.08660 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.16290i | 0.0529137i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.52359 | − | 10.1568i | 0.114590 | − | 0.461195i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5646i | 1.29439i | 0.762326 | + | 0.647193i | \(0.224057\pi\) | ||||
−0.762326 | + | 0.647193i | \(0.775943\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.9360 | −1.03720 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.9877 | −1.17281 | −0.586405 | − | 0.810018i | \(-0.699457\pi\) | ||||
−0.586405 | + | 0.810018i | \(0.699457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 35.5174i | − | 1.59963i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.17009 | − | 0.539189i | −0.0975381 | − | 0.0242347i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.47641i | 0.0662260i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.5174 | −1.23185 | −0.615925 | − | 0.787805i | \(-0.711218\pi\) | ||||
−0.615925 | + | 0.787805i | \(0.711218\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.81432 | −0.215088 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 22.6576i | − | 1.01025i | −0.863046 | − | 0.505125i | \(-0.831446\pi\) | ||
0.863046 | − | 0.505125i | \(-0.168554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.6225 | − | 4.62702i | −0.828690 | − | 0.205900i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 35.5958i | − | 1.58087i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.8432 | 1.23413 | 0.617065 | − | 0.786912i | \(-0.288322\pi\) | ||||
0.617065 | + | 0.786912i | \(0.288322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.327887 | 0.0145049 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.75872i | − | 0.342556i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.63317 | − | 14.6225i | 0.160096 | − | 0.644344i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.26180i | 0.231413i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.8865 | 0.565657 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.7009 | 1.30122 | 0.650609 | − | 0.759413i | \(-0.274514\pi\) | ||||
0.650609 | + | 0.759413i | \(0.274514\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.7565i | − | 1.08252i | −0.840854 | − | 0.541262i | \(-0.817947\pi\) | ||
0.840854 | − | 0.541262i | \(-0.182053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.28458 | − | 0.680346i | −0.0560637 | − | 0.0296927i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.3545i | 1.32226i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.60197 | −0.156312 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 51.7152i | − | 2.24004i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.59583 | + | 26.5464i | −0.285162 | + | 1.14770i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.84324i | 0.0795419i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.91548 | 0.297871 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5236 | −0.538431 | −0.269216 | − | 0.963080i | \(-0.586764\pi\) | ||||
−0.269216 | + | 0.963080i | \(0.586764\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.2823i | 0.441256i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.7009 | + | 3.40417i | 0.586881 | + | 0.145819i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.2784i | − | 0.610502i | −0.952272 | − | 0.305251i | \(-0.901260\pi\) | ||
0.952272 | − | 0.305251i | \(-0.0987404\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.68035 | 0.285110 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 57.5585 | 2.45207 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.267938i | − | 0.0113939i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.41855 | − | 1.84324i | −0.314900 | − | 0.0782414i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.57918i | 0.151655i | 0.997121 | + | 0.0758274i | \(0.0241598\pi\) | ||||
−0.997121 | + | 0.0758274i | \(0.975840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.02666 | 0.0857187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.78765 | 0.202135 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 28.9588i | − | 1.22047i | −0.792222 | − | 0.610234i | \(-0.791076\pi\) | ||
0.792222 | − | 0.610234i | \(-0.208924\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.89496 | − | 35.7998i | 0.374214 | − | 1.50611i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.290725i | 0.0122093i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.8264 | 1.08270 | 0.541350 | − | 0.840797i | \(-0.317913\pi\) | ||||
0.541350 | + | 0.840797i | \(0.317913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.1194 | −0.716425 | −0.358213 | − | 0.933640i | \(-0.616614\pi\) | ||||
−0.358213 | + | 0.933640i | \(0.616614\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.5174i | 0.481148i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.36069 | − | 17.6742i | 0.390368 | − | 0.737065i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22.5692i | − | 0.939567i | −0.882782 | − | 0.469783i | \(-0.844332\pi\) | ||
0.882782 | − | 0.469783i | \(-0.155668\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.86603 | −0.160667 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.496928 | 0.0206161 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.75872i | 0.238502i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.75872 | − | 15.1278i | 0.155404 | − | 0.625459i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.63317i | 0.149957i | 0.997185 | + | 0.0749784i | \(0.0238888\pi\) | ||||
−0.997185 | + | 0.0749784i | \(0.976111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.1917 | −2.02691 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.57304 | −0.352648 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.3051i | 0.505310i | 0.967556 | + | 0.252655i | \(0.0813037\pi\) | ||||
−0.967556 | + | 0.252655i | \(0.918696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.02052 | + | 0.750491i | 0.123829 | + | 0.0307671i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.31351i | 0.340249i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.6865 | 0.804368 | 0.402184 | − | 0.915559i | \(-0.368251\pi\) | ||||
0.402184 | + | 0.915559i | \(0.368251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.8843 | 1.05584 | 0.527921 | − | 0.849294i | \(-0.322972\pi\) | ||||
0.527921 | + | 0.849294i | \(0.322972\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6.15676i | − | 0.250722i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.17009 | + | 0.539189i | 0.0882266 | + | 0.0219211i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 41.5357i | − | 1.68588i | −0.538006 | − | 0.842941i | \(-0.680822\pi\) | ||
0.538006 | − | 0.842941i | \(-0.319178\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.15676 | −0.0873961 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.6803 | −1.48393 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.6453i | − | 0.833855i | −0.908940 | − | 0.416927i | \(-0.863107\pi\) | ||
0.908940 | − | 0.416927i | \(-0.136893\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.00000 | − | 16.0989i | 0.161296 | − | 0.649170i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.69472i | − | 0.350036i | −0.984565 | − | 0.175018i | \(-0.944002\pi\) | ||
0.984565 | − | 0.175018i | \(-0.0559984\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.65368 | 0.106661 | 0.0533303 | − | 0.998577i | \(-0.483016\pi\) | ||||
0.0533303 | + | 0.998577i | \(0.483016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.26180i | − | 0.0505528i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | + | 20.6803i | 0.561887 | + | 0.827214i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.75872i | 0.309854i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.3668 | 0.652588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.6393 | 0.423544 | 0.211772 | − | 0.977319i | \(-0.432077\pi\) | ||||
0.211772 | + | 0.977319i | \(0.432077\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 25.9155i | − | 1.03005i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.62702 | + | 10.5730i | −0.104250 | + | 0.419578i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 48.2083i | 1.91008i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.07838 | −0.200898 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.8576 | −1.41629 | −0.708145 | − | 0.706067i | \(-0.750468\pi\) | ||||
−0.708145 | + | 0.706067i | \(0.750468\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.2146i | − | 0.481697i | −0.970563 | − | 0.240849i | \(-0.922574\pi\) | ||
0.970563 | − | 0.240849i | \(-0.0774258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.630898 | + | 0.156755i | 0.0248416 | + | 0.00617224i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.9421i | 1.01989i | 0.860207 | + | 0.509945i | \(0.170334\pi\) | ||||
−0.860207 | + | 0.509945i | \(0.829666\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.60197 | 0.141390 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.84324 | 0.0722424 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 14.3402i | − | 0.561174i | −0.959829 | − | 0.280587i | \(-0.909471\pi\) | ||
0.959829 | − | 0.280587i | \(-0.0905292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.8371 | + | 4.68035i | 0.736026 | + | 0.182876i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.12783i | 0.0440007i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.52359 | 0.254123 | 0.127062 | − | 0.991895i | \(-0.459445\pi\) | ||||
0.127062 | + | 0.991895i | \(0.459445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.16290 | 0.123022 | 0.0615112 | − | 0.998106i | \(-0.480408\pi\) | ||||
0.0615112 | + | 0.998106i | \(0.480408\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33.3751i | 1.29618i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.21622 | + | 4.89496i | −0.0471631 | + | 0.189818i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29.6742i | − | 1.14899i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.62863 | −0.372264 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.68035 | −0.257892 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.4885i | − | 0.712680i | −0.934356 | − | 0.356340i | \(-0.884024\pi\) | ||
0.934356 | − | 0.356340i | \(-0.115976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.34017 | − | 4.41855i | 0.0900733 | − | 0.170070i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 15.0966i | − | 0.580211i | −0.956995 | − | 0.290105i | \(-0.906310\pi\) | ||
0.956995 | − | 0.290105i | \(-0.0936903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.36069 | 0.0522186 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.3896 | 0.704692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.4657i | 0.476988i | 0.971144 | + | 0.238494i | \(0.0766537\pi\) | ||||
−0.971144 | + | 0.238494i | \(0.923346\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.79153 | + | 27.3340i | −0.259491 | + | 1.04438i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 17.1506i | − | 0.654337i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.1445 | −1.52938 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.7214 | 1.16870 | 0.584348 | − | 0.811503i | \(-0.301350\pi\) | ||||
0.584348 | + | 0.811503i | \(0.301350\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 0.290725i | − | 0.0110437i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.5174 | − | 5.34632i | −0.816203 | − | 0.202797i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.5174i | 1.34532i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.10731 | 0.155353 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.9955 | 0.679679 | 0.339840 | − | 0.940483i | \(-0.389627\pi\) | ||||
0.339840 | + | 0.940483i | \(0.389627\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.5236i | 1.00036i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.4186 | − | 2.83710i | −0.430047 | − | 0.106851i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2.49484i | − | 0.0938281i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.5897 | −0.885929 | −0.442965 | − | 0.896539i | \(-0.646073\pi\) | ||||
−0.442965 | + | 0.896539i | \(0.646073\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.921622 | 0.0345635 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.3607i | 0.949765i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.75872 | + | 15.1278i | −0.140568 | + | 0.565749i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 4.36683i | − | 0.163082i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.5646 | 0.916106 | 0.458053 | − | 0.888925i | \(-0.348547\pi\) | ||||
0.458053 | + | 0.888925i | \(0.348547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.95896 | 0.0729556 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.20394i | − | 0.193536i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.7792 | + | 17.3607i | 1.21739 | + | 0.644760i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.51130i | 0.315667i | 0.987466 | + | 0.157833i | \(0.0504509\pi\) | ||||
−0.987466 | + | 0.157833i | \(0.949549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.39189 | −0.0514809 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 29.8615i | − | 1.10296i | −0.834188 | − | 0.551480i | \(-0.814063\pi\) | ||
0.834188 | − | 0.551480i | \(-0.185937\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.72875 | + | 15.0072i | −0.137537 | + | 0.553548i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.15676i | 0.226787i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.7526 | −1.35197 | −0.675983 | − | 0.736917i | \(-0.736281\pi\) | ||||
−0.675983 | + | 0.736917i | \(0.736281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −54.0866 | −1.98692 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.17501i | 0.0797933i | 0.999204 | + | 0.0398966i | \(0.0127029\pi\) | ||||
−0.999204 | + | 0.0398966i | \(0.987297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.73820 | + | 0.680346i | 0.100320 | + | 0.0249259i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.70928i | 0.0625391i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.55640 | −0.129948 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.4580 | 1.62229 | 0.811147 | − | 0.584842i | \(-0.198843\pi\) | ||||
0.811147 | + | 0.584842i | \(0.198843\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.28231i | 0.301824i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.47641 | − | 0.863763i | −0.126519 | − | 0.0314356i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.4247i | 0.960422i | 0.877153 | + | 0.480211i | \(0.159440\pi\) | ||||
−0.877153 | + | 0.480211i | \(0.840560\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.6163 | −1.00109 | −0.500546 | − | 0.865710i | \(-0.666867\pi\) | ||||
−0.500546 | + | 0.865710i | \(0.666867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.83549i | 0.0664493i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.58145 | + | 10.3896i | −0.0933325 | + | 0.375638i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.1096i | 0.906654i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.8432 | −1.00405 | −0.502027 | − | 0.864852i | \(-0.667412\pi\) | ||||
−0.502027 | + | 0.864852i | \(0.667412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0205 | 0.396894 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 18.0267i | − | 0.648374i | −0.945993 | − | 0.324187i | \(-0.894909\pi\) | ||
0.945993 | − | 0.324187i | \(-0.105091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.0144 | − | 14.8371i | −1.00631 | − | 0.532964i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 0.993857i | − | 0.0356544i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.5585 | −2.06225 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.07838 | 0.181719 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 7.41855i | − | 0.265117i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.83096 | + | 15.4186i | −0.136733 | + | 0.550312i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.6391i | 1.27040i | 0.772349 | + | 0.635199i | \(0.219082\pi\) | ||||
−0.772349 | + | 0.635199i | \(0.780918\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.97107 | −0.105773 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.79606 | 0.170528 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 46.5692i | − | 1.65372i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.4969 | − | 3.10504i | −0.443220 | − | 0.110124i | ||||
\(796\) | 0 | 0 |