Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,2,Mod(1351,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.1452461474\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1351 |
Dual form | 1521.2.b.h.1351.1 |
$q$-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 \(\left(\mathbb{Z}/1521\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56155i | 1.81129i | 0.424035 | + | 0.905646i | \(0.360613\pi\) | ||||
−0.424035 | + | 0.905646i | \(0.639387\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.56155 | −2.28078 | ||||||||
\(5\) | 0.561553i | 0.251134i | 0.992085 | + | 0.125567i | \(0.0400750\pi\) | ||||
−0.992085 | + | 0.125567i | \(0.959925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.56155i | − 1.34614i | −0.739579 | − | 0.673070i | \(-0.764975\pi\) | ||||
0.739579 | − | 0.673070i | \(-0.235025\pi\) | |||||||
\(8\) | − 6.56155i | − 2.31986i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.43845 | −0.454877 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 9.12311 | 2.43825 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.68466 | 1.92116 | ||||||||
\(17\) | 2.56155 | 0.621268 | 0.310634 | − | 0.950530i | \(-0.399459\pi\) | ||||
0.310634 | + | 0.950530i | \(0.399459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12311i | 0.257658i | 0.991667 | + | 0.128829i | \(0.0411218\pi\) | ||||
−0.991667 | + | 0.128829i | \(0.958878\pi\) | |||||||
\(20\) | − 2.56155i | − 0.572781i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.12311 | −1.09225 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.68466 | 0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.2462i | 3.07025i | ||||||||
\(29\) | 5.68466 | 1.05561 | 0.527807 | − | 0.849364i | \(-0.323014\pi\) | ||||
0.527807 | + | 0.849364i | \(0.323014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56155i | 0.280463i | 0.990119 | + | 0.140232i | \(0.0447847\pi\) | ||||
−0.990119 | + | 0.140232i | \(0.955215\pi\) | |||||||
\(32\) | 6.56155i | 1.15993i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.56155i | 1.12530i | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.43845i | 0.565277i | 0.959226 | + | 0.282639i | \(0.0912097\pi\) | ||||
−0.959226 | + | 0.282639i | \(0.908790\pi\) | |||||||
\(38\) | −2.87689 | −0.466694 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.68466 | 0.582596 | ||||||||
\(41\) | 2.56155i | 0.400047i | 0.979791 | + | 0.200024i | \(0.0641019\pi\) | ||||
−0.979791 | + | 0.200024i | \(0.935898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.438447 | −0.0668626 | −0.0334313 | − | 0.999441i | \(-0.510643\pi\) | ||||
−0.0334313 | + | 0.999441i | \(0.510643\pi\) | |||||||
\(44\) | − 9.12311i | − 1.37536i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.12311i | 0.755361i | ||||||||
\(47\) | 8.24621i | 1.20283i | 0.798935 | + | 0.601417i | \(0.205397\pi\) | ||||
−0.798935 | + | 0.601417i | \(0.794603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.68466 | −0.812094 | ||||||||
\(50\) | 12.0000i | 1.69706i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6847 | −1.60501 | −0.802506 | − | 0.596645i | \(-0.796500\pi\) | ||||
−0.802506 | + | 0.596645i | \(0.796500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.12311 | −0.151440 | ||||||||
\(56\) | −23.3693 | −3.12286 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.5616i | 1.91203i | ||||||||
\(59\) | 11.1231i | 1.44811i | 0.689745 | + | 0.724053i | \(0.257723\pi\) | ||||
−0.689745 | + | 0.724053i | \(0.742277\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.1231 | 1.55220 | 0.776102 | − | 0.630607i | \(-0.217194\pi\) | ||||
0.776102 | + | 0.630607i | \(0.217194\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.43845 | −0.179806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.438447i | − 0.0535648i | −0.999641 | − | 0.0267824i | \(-0.991474\pi\) | ||||
0.999641 | − | 0.0267824i | \(-0.00852613\pi\) | |||||||
\(68\) | −11.6847 | −1.41697 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.12311i | 0.612328i | ||||||||
\(71\) | 14.0000i | 1.66149i | 0.556650 | + | 0.830747i | \(0.312086\pi\) | ||||
−0.556650 | + | 0.830747i | \(0.687914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1.87689i | − 0.219674i | −0.993950 | − | 0.109837i | \(-0.964967\pi\) | ||||
0.993950 | − | 0.109837i | \(-0.0350329\pi\) | |||||||
\(74\) | −8.80776 | −1.02388 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 5.12311i | − 0.587661i | ||||||||
\(77\) | 7.12311 | 0.811753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.56155 | 1.07576 | 0.537879 | − | 0.843022i | \(-0.319226\pi\) | ||||
0.537879 | + | 0.843022i | \(0.319226\pi\) | |||||||
\(80\) | 4.31534i | 0.482470i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.56155 | −0.724602 | ||||||||
\(83\) | − 9.12311i | − 1.00139i | −0.865624 | − | 0.500695i | \(-0.833078\pi\) | ||||
0.865624 | − | 0.500695i | \(-0.166922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.43845i | 0.156022i | ||||||||
\(86\) | − 1.12311i | − 0.121108i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.1231 | 1.39893 | ||||||||
\(89\) | − 13.1231i | − 1.39105i | −0.718504 | − | 0.695523i | \(-0.755173\pi\) | ||||
0.718504 | − | 0.695523i | \(-0.244827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.12311 | −0.951150 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.1231 | −2.17868 | ||||||||
\(95\) | −0.630683 | −0.0647067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.43845i | 0.450656i | 0.974283 | + | 0.225328i | \(0.0723454\pi\) | ||||
−0.974283 | + | 0.225328i | \(0.927655\pi\) | |||||||
\(98\) | − 14.5616i | − 1.47094i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −21.3693 | −2.13693 | ||||||||
\(101\) | −3.43845 | −0.342138 | −0.171069 | − | 0.985259i | \(-0.554722\pi\) | ||||
−0.171069 | + | 0.985259i | \(0.554722\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.56155 | 0.745062 | 0.372531 | − | 0.928020i | \(-0.378490\pi\) | ||||
0.372531 | + | 0.928020i | \(0.378490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 29.9309i | − 2.90714i | ||||||||
\(107\) | −8.24621 | −0.797191 | −0.398596 | − | 0.917127i | \(-0.630502\pi\) | ||||
−0.398596 | + | 0.917127i | \(0.630502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 17.8078i | − 1.70567i | −0.522177 | − | 0.852837i | \(-0.674880\pi\) | ||||
0.522177 | − | 0.852837i | \(-0.325120\pi\) | |||||||
\(110\) | − 2.87689i | − 0.274301i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 27.3693i | − 2.58616i | ||||||||
\(113\) | 14.8078 | 1.39300 | 0.696499 | − | 0.717558i | \(-0.254740\pi\) | ||||
0.696499 | + | 0.717558i | \(0.254740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.12311i | 0.104730i | ||||||||
\(116\) | −25.9309 | −2.40762 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −28.4924 | −2.62294 | ||||||||
\(119\) | − 9.12311i | − 0.836314i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 31.0540i | 2.81149i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 7.12311i | − 0.639674i | ||||||||
\(125\) | 5.43845i | 0.486430i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.56155 | −0.848451 | −0.424225 | − | 0.905557i | \(-0.639454\pi\) | ||||
−0.424225 | + | 0.905557i | \(0.639454\pi\) | |||||||
\(128\) | 9.43845i | 0.834249i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3693 | 1.51756 | 0.758782 | − | 0.651345i | \(-0.225795\pi\) | ||||
0.758782 | + | 0.651345i | \(0.225795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 1.12311 | 0.0970215 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 16.8078i | − 1.44125i | ||||||||
\(137\) | 1.43845i | 0.122895i | 0.998110 | + | 0.0614474i | \(0.0195717\pi\) | ||||
−0.998110 | + | 0.0614474i | \(0.980428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9309 | 0.927144 | 0.463572 | − | 0.886059i | \(-0.346567\pi\) | ||||
0.463572 | + | 0.886059i | \(0.346567\pi\) | |||||||
\(140\) | −9.12311 | −0.771043 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −35.8617 | −3.00945 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.19224i | 0.265101i | ||||||||
\(146\) | 4.80776 | 0.397893 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 15.6847i | − 1.28927i | ||||||||
\(149\) | − 6.56155i | − 0.537543i | −0.963204 | − | 0.268772i | \(-0.913382\pi\) | ||||
0.963204 | − | 0.268772i | \(-0.0866177\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3693i | 1.25074i | 0.780329 | + | 0.625369i | \(0.215051\pi\) | ||||
−0.780329 | + | 0.625369i | \(0.784949\pi\) | |||||||
\(152\) | 7.36932 | 0.597731 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 18.2462i | 1.47032i | ||||||||
\(155\) | −0.876894 | −0.0704339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.36932 | −0.348709 | −0.174355 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174355 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(158\) | 24.4924i | 1.94851i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.68466 | −0.291298 | ||||||||
\(161\) | − 7.12311i | − 0.561379i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.8078i | 1.23816i | 0.785328 | + | 0.619080i | \(0.212494\pi\) | ||||
−0.785328 | + | 0.619080i | \(0.787506\pi\) | |||||||
\(164\) | − 11.6847i | − 0.912419i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.3693 | 1.81381 | ||||||||
\(167\) | 6.24621i | 0.483346i | 0.970358 | + | 0.241673i | \(0.0776962\pi\) | ||||
−0.970358 | + | 0.241673i | \(0.922304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3.68466 | −0.282600 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 3.75379 | 0.285395 | 0.142698 | − | 0.989766i | \(-0.454422\pi\) | ||||
0.142698 | + | 0.989766i | \(0.454422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 16.6847i | − 1.26124i | ||||||||
\(176\) | 15.3693i | 1.15851i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 33.6155 | 2.51959 | ||||||||
\(179\) | −13.1231 | −0.980867 | −0.490433 | − | 0.871479i | \(-0.663162\pi\) | ||||
−0.490433 | + | 0.871479i | \(0.663162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.68466 | −0.719855 | −0.359927 | − | 0.932980i | \(-0.617199\pi\) | ||||
−0.359927 | + | 0.932980i | \(0.617199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 13.1231i | − 0.967448i | ||||||||
\(185\) | −1.93087 | −0.141960 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.12311i | 0.374639i | ||||||||
\(188\) | − 37.6155i | − 2.74339i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − 1.61553i | − 0.117203i | ||||||||
\(191\) | 0.876894 | 0.0634499 | 0.0317249 | − | 0.999497i | \(-0.489900\pi\) | ||||
0.0317249 | + | 0.999497i | \(0.489900\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.4924i | 1.40310i | 0.712623 | + | 0.701548i | \(0.247507\pi\) | ||||
−0.712623 | + | 0.701548i | \(0.752493\pi\) | |||||||
\(194\) | −11.3693 | −0.816269 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 25.9309 | 1.85220 | ||||||||
\(197\) | − 11.3693i | − 0.810030i | −0.914310 | − | 0.405015i | \(-0.867266\pi\) | ||||
0.914310 | − | 0.405015i | \(-0.132734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.1771 | 1.64298 | 0.821490 | − | 0.570223i | \(-0.193143\pi\) | ||||
0.821490 | + | 0.570223i | \(0.193143\pi\) | |||||||
\(200\) | − 30.7386i | − 2.17355i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 8.80776i | − 0.619712i | ||||||||
\(203\) | − 20.2462i | − 1.42101i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.43845 | −0.100466 | ||||||||
\(206\) | 19.3693i | 1.34952i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.24621 | −0.155374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.31534 | 0.503609 | 0.251804 | − | 0.967778i | \(-0.418976\pi\) | ||||
0.251804 | + | 0.967778i | \(0.418976\pi\) | |||||||
\(212\) | 53.3002 | 3.66067 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − 21.1231i | − 1.44395i | ||||||||
\(215\) | − 0.246211i | − 0.0167915i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.56155 | 0.377543 | ||||||||
\(218\) | 45.6155 | 3.08947 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.12311 | 0.345400 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 8.00000i | − 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 23.3693 | 1.56143 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 37.9309i | 2.52312i | ||||||||
\(227\) | − 1.12311i | − 0.0745431i | −0.999305 | − | 0.0372716i | \(-0.988133\pi\) | ||||
0.999305 | − | 0.0372716i | \(-0.0118667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.246211i | 0.0162701i | 0.999967 | + | 0.00813505i | \(0.00258949\pi\) | ||||
−0.999967 | + | 0.00813505i | \(0.997411\pi\) | |||||||
\(230\) | −2.87689 | −0.189697 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 37.3002i | − 2.44888i | ||||||||
\(233\) | 26.0000 | 1.70332 | 0.851658 | − | 0.524097i | \(-0.175597\pi\) | ||||
0.851658 | + | 0.524097i | \(0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.63068 | −0.302072 | ||||||||
\(236\) | − 50.7386i | − 3.30280i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.3693 | 1.51481 | ||||||||
\(239\) | − 0.630683i | − 0.0407955i | −0.999792 | − | 0.0203977i | \(-0.993507\pi\) | ||||
0.999792 | − | 0.0203977i | \(-0.00649326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.80776i | 0.180864i | 0.995903 | + | 0.0904320i | \(0.0288248\pi\) | ||||
−0.995903 | + | 0.0904320i | \(0.971175\pi\) | |||||||
\(242\) | 17.9309i | 1.15264i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −55.3002 | −3.54023 | ||||||||
\(245\) | − 3.19224i | − 0.203944i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.2462 | 0.650635 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.9309 | −0.881066 | ||||||||
\(251\) | −30.7386 | −1.94021 | −0.970103 | − | 0.242695i | \(-0.921969\pi\) | ||||
−0.970103 | + | 0.242695i | \(0.921969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000i | 0.251478i | ||||||||
\(254\) | − 24.4924i | − 1.53679i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.0540 | −1.69087 | ||||||||
\(257\) | −16.1771 | −1.00910 | −0.504549 | − | 0.863383i | \(-0.668341\pi\) | ||||
−0.504549 | + | 0.863383i | \(0.668341\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.2462 | 0.760943 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 44.4924i | 2.74875i | ||||||||
\(263\) | 15.3693 | 0.947713 | 0.473856 | − | 0.880602i | \(-0.342862\pi\) | ||||
0.473856 | + | 0.880602i | \(0.342862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 6.56155i | − 0.403073i | ||||||||
\(266\) | 10.2462i | 0.628236i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000i | 0.122169i | ||||||||
\(269\) | −3.36932 | −0.205431 | −0.102715 | − | 0.994711i | \(-0.532753\pi\) | ||||
−0.102715 | + | 0.994711i | \(0.532753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1.06913i | − 0.0649450i | −0.999473 | − | 0.0324725i | \(-0.989662\pi\) | ||||
0.999473 | − | 0.0324725i | \(-0.0103381\pi\) | |||||||
\(272\) | 19.6847 | 1.19356 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.68466 | −0.222598 | ||||||||
\(275\) | 9.36932i | 0.564991i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.6847 | −1.06257 | −0.531284 | − | 0.847194i | \(-0.678290\pi\) | ||||
−0.531284 | + | 0.847194i | \(0.678290\pi\) | |||||||
\(278\) | 28.0000i | 1.67933i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − 13.1231i | − 0.784256i | ||||||||
\(281\) | 2.80776i | 0.167497i | 0.996487 | + | 0.0837486i | \(0.0266893\pi\) | ||||
−0.996487 | + | 0.0837486i | \(0.973311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.31534 | 0.0781889 | 0.0390945 | − | 0.999236i | \(-0.487553\pi\) | ||||
0.0390945 | + | 0.999236i | \(0.487553\pi\) | |||||||
\(284\) | − 63.8617i | − 3.78950i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.12311 | 0.538520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4384 | −0.614026 | ||||||||
\(290\) | −8.17708 | −0.480175 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.56155i | 0.501027i | ||||||||
\(293\) | − 24.5616i | − 1.43490i | −0.696609 | − | 0.717451i | \(-0.745309\pi\) | ||||
0.696609 | − | 0.717451i | \(-0.254691\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.24621 | −0.363668 | ||||||||
\(296\) | 22.5616 | 1.31136 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.8078 | 0.973648 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.56155i | 0.0900064i | ||||||||
\(302\) | −39.3693 | −2.26545 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.63068i | 0.495004i | ||||||||
\(305\) | 6.80776i | 0.389811i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.1922i | 0.581702i | 0.956768 | + | 0.290851i | \(0.0939383\pi\) | ||||
−0.956768 | + | 0.290851i | \(0.906062\pi\) | |||||||
\(308\) | −32.4924 | −1.85143 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 2.24621i | − 0.127576i | ||||||||
\(311\) | −10.8769 | −0.616772 | −0.308386 | − | 0.951261i | \(-0.599789\pi\) | ||||
−0.308386 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.31534 | −0.0743475 | −0.0371738 | − | 0.999309i | \(-0.511835\pi\) | ||||
−0.0371738 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(314\) | − 11.1922i | − 0.631614i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −43.6155 | −2.45357 | ||||||||
\(317\) | − 23.0540i | − 1.29484i | −0.762133 | − | 0.647420i | \(-0.775848\pi\) | ||||
0.762133 | − | 0.647420i | \(-0.224152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3693i | 0.636560i | ||||||||
\(320\) | − 0.807764i | − 0.0451554i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.2462 | 1.01682 | ||||||||
\(323\) | 2.87689i | 0.160075i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −40.4924 | −2.24267 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.8078 | 0.928054 | ||||||||
\(329\) | 29.3693 | 1.61918 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8078i | 1.30859i | 0.756238 | + | 0.654297i | \(0.227035\pi\) | ||||
−0.756238 | + | 0.654297i | \(0.772965\pi\) | |||||||
\(332\) | 41.6155i | 2.28395i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.0000 | −0.875481 | ||||||||
\(335\) | 0.246211 | 0.0134520 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.12311 | −0.115653 | −0.0578265 | − | 0.998327i | \(-0.518417\pi\) | ||||
−0.0578265 | + | 0.998327i | \(0.518417\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 6.56155i | − 0.355850i | ||||||||
\(341\) | −3.12311 | −0.169126 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 4.68466i | − 0.252948i | ||||||||
\(344\) | 2.87689i | 0.155112i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.61553i | 0.516934i | ||||||||
\(347\) | 13.6155 | 0.730920 | 0.365460 | − | 0.930827i | \(-0.380912\pi\) | ||||
0.365460 | + | 0.930827i | \(0.380912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 13.8078i | − 0.739113i | −0.929208 | − | 0.369556i | \(-0.879510\pi\) | ||||
0.929208 | − | 0.369556i | \(-0.120490\pi\) | |||||||
\(350\) | 42.7386 | 2.28448 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.1231 | −0.699464 | ||||||||
\(353\) | 17.6847i | 0.941259i | 0.882331 | + | 0.470630i | \(0.155973\pi\) | ||||
−0.882331 | + | 0.470630i | \(0.844027\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.86174 | −0.417258 | ||||||||
\(356\) | 59.8617i | 3.17267i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 33.6155i | − 1.77664i | ||||||||
\(359\) | − 15.3693i | − 0.811162i | −0.914059 | − | 0.405581i | \(-0.867069\pi\) | ||||
0.914059 | − | 0.405581i | \(-0.132931\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7386 | 0.933612 | ||||||||
\(362\) | − 24.8078i | − 1.30387i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.05398 | 0.0551676 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0540 | 1.04681 | 0.523404 | − | 0.852084i | \(-0.324662\pi\) | ||||
0.523404 | + | 0.852084i | \(0.324662\pi\) | |||||||
\(368\) | 15.3693 | 0.801181 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 4.94602i | − 0.257132i | ||||||||
\(371\) | 41.6155i | 2.16057i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.63068 | 0.187990 | 0.0939948 | − | 0.995573i | \(-0.470036\pi\) | ||||
0.0939948 | + | 0.995573i | \(0.470036\pi\) | |||||||
\(374\) | −13.1231 | −0.678580 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 54.1080 | 2.79040 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 11.3153i | − 0.581230i | −0.956840 | − | 0.290615i | \(-0.906140\pi\) | ||||
0.956840 | − | 0.290615i | \(-0.0938599\pi\) | |||||||
\(380\) | 2.87689 | 0.147582 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.24621i | 0.114926i | ||||||||
\(383\) | 26.7386i | 1.36628i | 0.730287 | + | 0.683140i | \(0.239386\pi\) | ||||
−0.730287 | + | 0.683140i | \(0.760614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000i | 0.203859i | ||||||||
\(386\) | −49.9309 | −2.54141 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 20.2462i | − 1.02785i | ||||||||
\(389\) | −3.05398 | −0.154843 | −0.0774213 | − | 0.996998i | \(-0.524669\pi\) | ||||
−0.0774213 | + | 0.996998i | \(0.524669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.12311 | 0.259087 | ||||||||
\(392\) | 37.3002i | 1.88394i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 29.1231 | 1.46720 | ||||||||
\(395\) | 5.36932i | 0.270160i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12.0540i | − 0.604972i | −0.953154 | − | 0.302486i | \(-0.902184\pi\) | ||||
0.953154 | − | 0.302486i | \(-0.0978165\pi\) | |||||||
\(398\) | 59.3693i | 2.97591i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 36.0000 | 1.80000 | ||||||||
\(401\) | − 18.5616i | − 0.926920i | −0.886118 | − | 0.463460i | \(-0.846608\pi\) | ||||
0.886118 | − | 0.463460i | \(-0.153392\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 15.6847 | 0.780341 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 51.8617 | 2.57385 | ||||||||
\(407\) | −6.87689 | −0.340875 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.3693i | 0.908304i | 0.890924 | + | 0.454152i | \(0.150058\pi\) | ||||
−0.890924 | + | 0.454152i | \(0.849942\pi\) | |||||||
\(410\) | − 3.68466i | − 0.181972i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −34.4924 | −1.69932 | ||||||||
\(413\) | 39.6155 | 1.94935 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.12311 | 0.251483 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 5.75379i | − 0.281427i | ||||||||
\(419\) | 17.7538 | 0.867329 | 0.433665 | − | 0.901074i | \(-0.357220\pi\) | ||||
0.433665 | + | 0.901074i | \(0.357220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 14.7538i | − 0.719056i | −0.933134 | − | 0.359528i | \(-0.882938\pi\) | ||||
0.933134 | − | 0.359528i | \(-0.117062\pi\) | |||||||
\(422\) | 18.7386i | 0.912182i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 76.6695i | 3.72340i | ||||||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 43.1771i | − 2.08949i | ||||||||
\(428\) | 37.6155 | 1.81822 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.630683 | 0.0304142 | ||||||||
\(431\) | − 2.87689i | − 0.138575i | −0.997597 | − | 0.0692876i | \(-0.977927\pi\) | ||||
0.997597 | − | 0.0692876i | \(-0.0220726\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.2462 | −1.21326 | −0.606628 | − | 0.794986i | \(-0.707478\pi\) | ||||
−0.606628 | + | 0.794986i | \(0.707478\pi\) | |||||||
\(434\) | 14.2462i | 0.683840i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 81.2311i | 3.89026i | ||||||||
\(437\) | 2.24621i | 0.107451i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.31534 | 0.0627778 | 0.0313889 | − | 0.999507i | \(-0.490007\pi\) | ||||
0.0313889 | + | 0.999507i | \(0.490007\pi\) | |||||||
\(440\) | 7.36932i | 0.351318i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.7386 | −0.700254 | −0.350127 | − | 0.936702i | \(-0.613862\pi\) | ||||
−0.350127 | + | 0.936702i | \(0.613862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.36932 | 0.349339 | ||||||||
\(446\) | 20.4924 | 0.970344 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.12311i | 0.242044i | ||||||||
\(449\) | − 8.24621i | − 0.389163i | −0.980886 | − | 0.194581i | \(-0.937665\pi\) | ||||
0.980886 | − | 0.194581i | \(-0.0623348\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.12311 | −0.241238 | ||||||||
\(452\) | −67.5464 | −3.17712 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.87689 | 0.135019 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.6155i | 1.33858i | 0.743002 | + | 0.669289i | \(0.233401\pi\) | ||||
−0.743002 | + | 0.669289i | \(0.766599\pi\) | |||||||
\(458\) | −0.630683 | −0.0294699 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 5.12311i | − 0.238866i | ||||||||
\(461\) | − 36.8078i | − 1.71431i | −0.515060 | − | 0.857154i | \(-0.672230\pi\) | ||||
0.515060 | − | 0.857154i | \(-0.327770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 26.6847i | − 1.24014i | −0.784546 | − | 0.620071i | \(-0.787104\pi\) | ||||
0.784546 | − | 0.620071i | \(-0.212896\pi\) | |||||||
\(464\) | 43.6847 | 2.02801 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 66.6004i | 3.08520i | ||||||||
\(467\) | −26.0000 | −1.20314 | −0.601568 | − | 0.798821i | \(-0.705457\pi\) | ||||
−0.601568 | + | 0.798821i | \(0.705457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.56155 | −0.0721058 | ||||||||
\(470\) | − 11.8617i | − 0.547141i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 72.9848 | 3.35940 | ||||||||
\(473\) | − 0.876894i | − 0.0403196i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.26137i | 0.241408i | ||||||||
\(476\) | 41.6155i | 1.90744i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.61553 | 0.0738925 | ||||||||
\(479\) | 6.24621i | 0.285397i | 0.989766 | + | 0.142698i | \(0.0455779\pi\) | ||||
−0.989766 | + | 0.142698i | \(0.954422\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −7.19224 | −0.327597 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.9309 | −1.45140 | ||||||||
\(485\) | −2.49242 | −0.113175 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.12311i | 0.0508928i | 0.999676 | + | 0.0254464i | \(0.00810071\pi\) | ||||
−0.999676 | + | 0.0254464i | \(0.991899\pi\) | |||||||
\(488\) | − 79.5464i | − 3.60090i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.17708 | 0.369403 | ||||||||
\(491\) | −19.7538 | −0.891476 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.5616 | 0.655819 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0000i | 0.538816i | ||||||||
\(497\) | 49.8617 | 2.23660 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.4924i | 1.27550i | 0.770245 | + | 0.637748i | \(0.220134\pi\) | ||||
−0.770245 | + | 0.637748i | \(0.779866\pi\) | |||||||
\(500\) | − 24.8078i | − 1.10944i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 78.7386i | − 3.51428i | ||||||||
\(503\) | 11.7538 | 0.524076 | 0.262038 | − | 0.965058i | \(-0.415605\pi\) | ||||
0.262038 | + | 0.965058i | \(0.415605\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 1.93087i | − 0.0859226i | ||||||||
\(506\) | −10.2462 | −0.455500 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 43.6155 | 1.93513 | ||||||||
\(509\) | 6.80776i | 0.301749i | 0.988553 | + | 0.150874i | \(0.0482089\pi\) | ||||
−0.988553 | + | 0.150874i | \(0.951791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.68466 | −0.295712 | ||||||||
\(512\) | − 50.4233i | − 2.22842i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 41.4384i | − 1.82777i | ||||||||
\(515\) | 4.24621i | 0.187110i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.4924 | −0.725336 | ||||||||
\(518\) | 31.3693i | 1.37829i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.9309 | 1.66178 | 0.830891 | − | 0.556436i | \(-0.187831\pi\) | ||||
0.830891 | + | 0.556436i | \(0.187831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.8617 | −1.04340 | −0.521701 | − | 0.853129i | \(-0.674702\pi\) | ||||
−0.521701 | + | 0.853129i | \(0.674702\pi\) | |||||||
\(524\) | −79.2311 | −3.46122 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 39.3693i | 1.71658i | ||||||||
\(527\) | 4.00000i | 0.174243i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 16.8078 | 0.730083 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18.2462 | −0.791074 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.63068i | − 0.200202i | ||||||||
\(536\) | −2.87689 | −0.124263 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 8.63068i | − 0.372095i | ||||||||
\(539\) | − 11.3693i | − 0.489711i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 29.7386i | − 1.27856i | −0.768972 | − | 0.639282i | \(-0.779232\pi\) | ||||
0.768972 | − | 0.639282i | \(-0.220768\pi\) | |||||||
\(542\) | 2.73863 | 0.117634 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.8078i | 0.720627i | ||||||||
\(545\) | 10.0000 | 0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9309 | −1.06597 | −0.532984 | − | 0.846126i | \(-0.678929\pi\) | ||||
−0.532984 | + | 0.846126i | \(0.678929\pi\) | |||||||
\(548\) | − 6.56155i | − 0.280296i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.0000 | −1.02336 | ||||||||
\(551\) | 6.38447i | 0.271988i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 34.0540i | − 1.44812i | ||||||||
\(554\) | − 45.3002i | − 1.92462i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −49.8617 | −2.11461 | ||||||||
\(557\) | 14.0691i | 0.596128i | 0.954546 | + | 0.298064i | \(0.0963409\pi\) | ||||
−0.954546 | + | 0.298064i | \(0.903659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 15.3693 | 0.649472 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.19224 | −0.303386 | ||||||||
\(563\) | 1.36932 | 0.0577098 | 0.0288549 | − | 0.999584i | \(-0.490814\pi\) | ||||
0.0288549 | + | 0.999584i | \(0.490814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.31534i | 0.349829i | ||||||||
\(566\) | 3.36932i | 0.141623i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 91.8617 | 3.85443 | ||||||||
\(569\) | 40.7386 | 1.70785 | 0.853926 | − | 0.520394i | \(-0.174215\pi\) | ||||
0.853926 | + | 0.520394i | \(0.174215\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.3693 | −0.810581 | −0.405290 | − | 0.914188i | \(-0.632830\pi\) | ||||
−0.405290 | + | 0.914188i | \(0.632830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 23.3693i | 0.975416i | ||||||||
\(575\) | 9.36932 | 0.390728 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.6847i | 1.23579i | 0.786261 | + | 0.617894i | \(0.212014\pi\) | ||||
−0.786261 | + | 0.617894i | \(0.787986\pi\) | |||||||
\(578\) | − 26.7386i | − 1.11218i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 14.5616i | − 0.604636i | ||||||||
\(581\) | −32.4924 | −1.34801 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 23.3693i | − 0.967858i | ||||||||
\(584\) | −12.3153 | −0.509612 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 62.9157 | 2.59902 | ||||||||
\(587\) | 14.6307i | 0.603873i | 0.953328 | + | 0.301936i | \(0.0976330\pi\) | ||||
−0.953328 | + | 0.301936i | \(0.902367\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.75379 | −0.0722636 | ||||||||
\(590\) | − 16.0000i | − 0.658710i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26.4233i | 1.08599i | ||||||||
\(593\) | − 44.4233i | − 1.82425i | −0.409917 | − | 0.912123i | \(-0.634442\pi\) | ||||
0.409917 | − | 0.912123i | \(-0.365558\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.12311 | 0.210027 | ||||||||
\(596\) | 29.9309i | 1.22602i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.384472 | 0.0157091 | 0.00785455 | − | 0.999969i | \(-0.497500\pi\) | ||||
0.00785455 | + | 0.999969i | \(0.497500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.9309 | −1.46565 | −0.732825 | − | 0.680417i | \(-0.761799\pi\) | ||||
−0.732825 | + | 0.680417i | \(0.761799\pi\) | |||||||
\(602\) | −4.00000 | −0.163028 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 70.1080i | − 2.85265i | ||||||||
\(605\) | 3.93087i | 0.159813i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | −7.36932 | −0.298865 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.4384 | −0.706062 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 22.8617i | − 0.923377i | −0.887042 | − | 0.461688i | \(-0.847244\pi\) | ||||
0.887042 | − | 0.461688i | \(-0.152756\pi\) | |||||||
\(614\) | −26.1080 | −1.05363 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − 46.7386i | − 1.88315i | ||||||||
\(617\) | − 10.8078i | − 0.435104i | −0.976049 | − | 0.217552i | \(-0.930193\pi\) | ||||
0.976049 | − | 0.217552i | \(-0.0698072\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 24.3002i | − 0.976707i | −0.872646 | − | 0.488353i | \(-0.837598\pi\) | ||||
0.872646 | − | 0.488353i | \(-0.162402\pi\) | |||||||
\(620\) | 4.00000 | 0.160644 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 27.8617i | − 1.11715i | ||||||||
\(623\) | −46.7386 | −1.87254 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | − 3.36932i | − 0.134665i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.9309 | 0.795328 | ||||||||
\(629\) | 8.80776i | 0.351189i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 14.4384i | − 0.574786i | −0.957813 | − | 0.287393i | \(-0.907212\pi\) | ||||
0.957813 | − | 0.287393i | \(-0.0927885\pi\) | |||||||
\(632\) | − 62.7386i | − 2.49561i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 59.0540 | 2.34533 | ||||||||
\(635\) | − 5.36932i | − 0.213075i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −29.1231 | −1.15299 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.30019 | −0.209508 | ||||||||
\(641\) | 26.1771 | 1.03393 | 0.516966 | − | 0.856006i | \(-0.327061\pi\) | ||||
0.516966 | + | 0.856006i | \(0.327061\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 38.5464i | − 1.52012i | −0.649852 | − | 0.760061i | \(-0.725169\pi\) | ||||
0.649852 | − | 0.760061i | \(-0.274831\pi\) | |||||||
\(644\) | 32.4924i | 1.28038i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.36932 | −0.289942 | ||||||||
\(647\) | −47.6155 | −1.87196 | −0.935980 | − | 0.352054i | \(-0.885483\pi\) | ||||
−0.935980 | + | 0.352054i | \(0.885483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.2462 | −0.873240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 72.1080i | − 2.82397i | ||||||||
\(653\) | −14.8769 | −0.582178 | −0.291089 | − | 0.956696i | \(-0.594018\pi\) | ||||
−0.291089 | + | 0.956696i | \(0.594018\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.75379i | 0.381112i | ||||||||
\(656\) | 19.6847i | 0.768557i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 75.2311i | 2.93281i | ||||||||
\(659\) | −14.2462 | −0.554954 | −0.277477 | − | 0.960732i | \(-0.589498\pi\) | ||||
−0.277477 | + | 0.960732i | \(0.589498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.3693i | 1.18123i | 0.806954 | + | 0.590615i | \(0.201115\pi\) | ||||
−0.806954 | + | 0.590615i | \(0.798885\pi\) | |||||||
\(662\) | −60.9848 | −2.37024 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −59.8617 | −2.32309 | ||||||||
\(665\) | 2.24621i | 0.0871043i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3693 | 0.440222 | ||||||||
\(668\) | − 28.4924i | − 1.10240i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.630683i | 0.0243654i | ||||||||
\(671\) | 24.2462i | 0.936015i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.75379 | 0.260339 | 0.130170 | − | 0.991492i | \(-0.458448\pi\) | ||||
0.130170 | + | 0.991492i | \(0.458448\pi\) | |||||||
\(674\) | − 5.43845i | − 0.209481i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.6155 | −0.984485 | −0.492242 | − | 0.870458i | \(-0.663823\pi\) | ||||
−0.492242 | + | 0.870458i | \(0.663823\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.8078 | 0.606646 | ||||||||
\(680\) | 9.43845 | 0.361948 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 8.00000i | − 0.306336i | ||||||||
\(683\) | − 36.1080i | − 1.38163i | −0.723030 | − | 0.690816i | \(-0.757251\pi\) | ||||
0.723030 | − | 0.690816i | \(-0.242749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.807764 | −0.0308631 | ||||||||
\(686\) | 12.0000 | 0.458162 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.36932 | −0.128454 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.30019i | − 0.0875032i | −0.999042 | − | 0.0437516i | \(-0.986069\pi\) | ||||
0.999042 | − | 0.0437516i | \(-0.0139310\pi\) | |||||||
\(692\) | −17.1231 | −0.650923 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.8769i | 1.32391i | ||||||||
\(695\) | 6.13826i | 0.232837i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.56155i | 0.248537i | ||||||||
\(698\) | 35.3693 | 1.33875 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 76.1080i | 2.87661i | ||||||||
\(701\) | 19.3693 | 0.731569 | 0.365785 | − | 0.930700i | \(-0.380801\pi\) | ||||
0.365785 | + | 0.930700i | \(0.380801\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.86174 | −0.145648 | ||||||||
\(704\) | − 2.87689i | − 0.108427i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.3002 | −1.70490 | ||||||||
\(707\) | 12.2462i | 0.460566i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.4924i | 0.957388i | 0.877982 | + | 0.478694i | \(0.158890\pi\) | ||||
−0.877982 | + | 0.478694i | \(0.841110\pi\) | |||||||
\(710\) | − 20.1383i | − 0.755775i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −86.1080 | −3.22703 | ||||||||
\(713\) | 3.12311i | 0.116961i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 59.8617 | 2.23714 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 39.3693 | 1.46925 | ||||||||
\(719\) | 1.36932 | 0.0510669 | 0.0255335 | − | 0.999674i | \(-0.491872\pi\) | ||||
0.0255335 | + | 0.999674i | \(0.491872\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 26.9309i | − 1.00296i | ||||||||
\(722\) | 45.4384i | 1.69104i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 44.1771 | 1.64183 | ||||||||
\(725\) | 26.6307 | 0.989039 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.6695 | −1.47126 | −0.735630 | − | 0.677383i | \(-0.763114\pi\) | ||||
−0.735630 | + | 0.677383i | \(0.763114\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.69981i | 0.0999246i | ||||||||
\(731\) | −1.12311 | −0.0415396 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 53.4924i | − 1.97579i | −0.155131 | − | 0.987894i | \(-0.549580\pi\) | ||||
0.155131 | − | 0.987894i | \(-0.450420\pi\) | |||||||
\(734\) | 51.3693i | 1.89608i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.1231i | 0.483724i | ||||||||
\(737\) | 0.876894 | 0.0323008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 6.24621i | − 0.229771i | −0.993379 | − | 0.114885i | \(-0.963350\pi\) | ||||
0.993379 | − | 0.114885i | \(-0.0366501\pi\) | |||||||
\(740\) | 8.80776 | 0.323780 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −106.600 | −3.91342 | ||||||||
\(743\) | − 37.3693i | − 1.37095i | −0.728097 | − | 0.685474i | \(-0.759595\pi\) | ||||
0.728097 | − | 0.685474i | \(-0.240405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.68466 | 0.134995 | ||||||||
\(746\) | 9.30019i | 0.340504i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 23.3693i | − 0.854467i | ||||||||
\(749\) | 29.3693i | 1.07313i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.1080 | 1.09865 | 0.549327 | − | 0.835607i | \(-0.314884\pi\) | ||||
0.549327 | + | 0.835607i | \(0.314884\pi\) | |||||||
\(752\) | 63.3693i | 2.31084i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.63068 | −0.314103 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0000 | 1.09037 | 0.545184 | − | 0.838316i | \(-0.316460\pi\) | ||||
0.545184 | + | 0.838316i | \(0.316460\pi\) | |||||||
\(758\) | 28.9848 | 1.05278 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.13826i | 0.150110i | ||||||||
\(761\) | 15.3693i | 0.557137i | 0.960416 | + | 0.278569i | \(0.0898600\pi\) | ||||
−0.960416 | + | 0.278569i | \(0.910140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −63.4233 | −2.29608 | ||||||||
\(764\) | −4.00000 | −0.144715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −68.4924 | −2.47473 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000i | 0.649097i | 0.945869 | + | 0.324548i | \(0.105212\pi\) | ||||
−0.945869 | + | 0.324548i | \(0.894788\pi\) | |||||||
\(770\) | −10.2462 | −0.369248 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 88.9157i | − 3.20015i | ||||||||
\(773\) | − 7.75379i | − 0.278884i | −0.990230 | − | 0.139442i | \(-0.955469\pi\) | ||||
0.990230 | − | 0.139442i | \(-0.0445309\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.31534i | 0.262775i | ||||||||
\(776\) | 29.1231 | 1.04546 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 7.82292i | − 0.280465i | ||||||||
\(779\) | −2.87689 | −0.103075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0000 | −1.00192 | ||||||||
\(782\) | 13.1231i | 0.469281i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −43.6847 | −1.56017 | ||||||||
\(785\) | − 2.45360i | − 0.0875728i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.17708i | − 0.0419584i | −0.999780 | − | 0.0209792i | \(-0.993322\pi\) | ||||
0.999780 | − | 0.0209792i | \(-0.00667838\pi\) | |||||||
\(788\) | 51.8617i | 1.84750i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.7538 | −0.489338 | ||||||||
\(791\) | − 52.7386i | − 1.87517i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 30.8769 | 1.09578 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −105.723 | −3.74727 | ||||||||
\(797\) | −41.6155 | −1.47410 | −0.737049 | − | 0.675840i | \(-0.763781\pi\) | ||||
−0.737049 | + | 0.675840i | \(0.763781\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.1231i | 0.747282i | ||||||||
\(800\) | 30.7386i | 1.08677i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 47.5464 | 1.67892 | ||||||||
\(803\) | 3.75379 | 0.132468 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.5616i | 0.793713i | ||||||||
\(809\) | −37.3002 | −1.31140 | −0.655702 | − | 0.755019i | \(-0.727627\pi\) | ||||
−0.655702 | + | 0.755019i | \(0.727627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.56155i | 0.0548335i | 0.999624 | + | 0.0274168i | \(0.00872812\pi\) | ||||
−0.999624 | + | 0.0274168i | \(0.991272\pi\) | |||||||
\(812\) | 92.3542i | 3.24100i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − 17.6155i | − 0.617424i | ||||||||
\(815\) | −8.87689 | −0.310944 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 0.492423i | − 0.0172277i | ||||||||
\(818\) | −47.0540 | −1.64520 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.56155 | 0.229139 | ||||||||
\(821\) | − 26.4924i | − 0.924592i | −0.886726 | − | 0.462296i | \(-0.847026\pi\) | ||||
0.886726 | − | 0.462296i | \(-0.152974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(824\) | − 49.6155i | − 1.72844i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 101.477i | 3.53085i | ||||||||
\(827\) | − 34.7386i | − 1.20798i | −0.796992 | − | 0.603990i | \(-0.793577\pi\) | ||||
0.796992 | − | 0.603990i | \(-0.206423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.4924 | 0.677000 | 0.338500 | − | 0.940966i | \(-0.390081\pi\) | ||||
0.338500 | + | 0.940966i | \(0.390081\pi\) | |||||||
\(830\) | 13.1231i | 0.455510i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.5616 | −0.504528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.50758 | −0.121385 | ||||||||
\(836\) | 10.2462 | 0.354373 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 45.4773i | 1.57099i | ||||||||
\(839\) | 19.6155i | 0.677203i | 0.940930 | + | 0.338602i | \(0.109954\pi\) | ||||
−0.940930 | + | 0.338602i | \(0.890046\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | 37.7926 | 1.30242 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33.3693 | −1.14862 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 24.9309i | − 0.856635i | ||||||||
\(848\) | −89.7926 | −3.08349 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.7386i | 1.05433i | ||||||||
\(851\) | 6.87689i | 0.235737i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 6.12311i | − 0.209651i | −0.994491 | − | 0.104826i | \(-0.966572\pi\) | ||||
0.994491 | − | 0.104826i | \(-0.0334284\pi\) | |||||||
\(854\) | 110.600 | 3.78467 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54.1080i | 1.84937i | ||||||||
\(857\) | 31.4384 | 1.07392 | 0.536958 | − | 0.843609i | \(-0.319573\pi\) | ||||
0.536958 | + | 0.843609i | \(0.319573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.4384 | 0.697351 | 0.348675 | − | 0.937244i | \(-0.386632\pi\) | ||||
0.348675 | + | 0.937244i | \(0.386632\pi\) | |||||||
\(860\) | 1.12311i | 0.0382976i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.36932 | 0.251000 | ||||||||
\(863\) | − 2.49242i | − 0.0848430i | −0.999100 | − | 0.0424215i | \(-0.986493\pi\) | ||||
0.999100 | − | 0.0424215i | \(-0.0135072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.10795i | 0.0716725i | ||||||||
\(866\) | − 64.6695i | − 2.19756i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −25.3693 | −0.861091 | ||||||||
\(869\) | 19.1231i | 0.648707i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −116.847 | −3.95692 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.75379 | −0.194625 | ||||||||
\(875\) | 19.3693 | 0.654802 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 19.4384i | − 0.656390i | −0.944610 | − | 0.328195i | \(-0.893560\pi\) | ||||
0.944610 | − | 0.328195i | \(-0.106440\pi\) | |||||||
\(878\) | 3.36932i | 0.113709i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.63068 | −0.290940 | ||||||||
\(881\) | −37.9309 | −1.27792 | −0.638962 | − | 0.769239i | \(-0.720636\pi\) | ||||
−0.638962 | + | 0.769239i | \(0.720636\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8078 | 0.397363 | 0.198681 | − | 0.980064i | \(-0.436334\pi\) | ||||
0.198681 | + | 0.980064i | \(0.436334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 37.7538i | − 1.26836i | ||||||||
\(887\) | −49.3693 | −1.65766 | −0.828830 | − | 0.559501i | \(-0.810993\pi\) | ||||
−0.828830 | + | 0.559501i | \(0.810993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.0540i | 1.14213i | ||||||||
\(890\) | 18.8769i | 0.632755i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.4924i | 1.22186i | ||||||||
\(893\) | −9.26137 | −0.309920 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 7.36932i | − 0.246329i | ||||||||
\(896\) | 33.6155 | 1.12302 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.1231 | 0.704887 | ||||||||
\(899\) | 8.87689i | 0.296061i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.9309 | −0.997142 | ||||||||
\(902\) | − 13.1231i | − 0.436952i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 97.1619i | − 3.23156i | ||||||||
\(905\) | − 5.43845i | − 0.180780i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0000 | −0.929725 | −0.464862 | − | 0.885383i | \(-0.653896\pi\) | ||||
−0.464862 | + | 0.885383i | \(0.653896\pi\) | |||||||
\(908\) | 5.12311i | 0.170016i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.7386 | 0.355787 | 0.177893 | − | 0.984050i | \(-0.443072\pi\) | ||||
0.177893 | + | 0.984050i | \(0.443072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.2462 | 0.603861 | ||||||||
\(914\) | −73.3002 | −2.42455 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 1.12311i | − 0.0371085i | ||||||||
\(917\) | − 61.8617i | − 2.04285i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.4924 | 1.46767 | 0.733835 | − | 0.679328i | \(-0.237729\pi\) | ||||
0.733835 | + | 0.679328i | \(0.237729\pi\) | |||||||
\(920\) | 7.36932 | 0.242959 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 94.2850 | 3.10511 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.1080i | 0.529626i | ||||||||
\(926\) | 68.3542 | 2.24626 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 37.3002i | 1.22444i | ||||||||
\(929\) | 12.8078i | 0.420209i | 0.977679 | + | 0.210105i | \(0.0673804\pi\) | ||||
−0.977679 | + | 0.210105i | \(0.932620\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6.38447i | − 0.209243i | ||||||||
\(932\) | −118.600 | −3.88488 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 66.6004i | − 2.17923i | ||||||||
\(935\) | −2.87689 | −0.0940845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.43845 | −0.112329 | −0.0561646 | − | 0.998422i | \(-0.517887\pi\) | ||||
−0.0561646 | + | 0.998422i | \(0.517887\pi\) | |||||||
\(938\) | − 4.00000i | − 0.130605i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.1231 | 0.688960 | ||||||||
\(941\) | − 2.49242i | − 0.0812507i | −0.999174 | − | 0.0406253i | \(-0.987065\pi\) | ||||
0.999174 | − | 0.0406253i | \(-0.0129350\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.12311i | 0.166831i | ||||||||
\(944\) | 85.4773i | 2.78205i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.24621 | 0.0730306 | ||||||||
\(947\) | − 10.7386i | − 0.348959i | −0.984661 | − | 0.174479i | \(-0.944176\pi\) | ||||
0.984661 | − | 0.174479i | \(-0.0558242\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −13.4773 | −0.437260 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −59.8617 | −1.94013 | ||||||||
\(953\) | −34.9848 | −1.13327 | −0.566635 | − | 0.823969i | \(-0.691755\pi\) | ||||
−0.566635 | + | 0.823969i | \(0.691755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.492423i | 0.0159344i | ||||||||
\(956\) | 2.87689i | 0.0930454i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.0000 | −0.516937 | ||||||||
\(959\) | 5.12311 | 0.165434 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.5616 | 0.921340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 12.8078i | − 0.412510i | ||||||||
\(965\) | −10.9460 | −0.352365 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.12311i | 0.293379i | 0.989183 | + | 0.146690i | \(0.0468619\pi\) | ||||
−0.989183 | + | 0.146690i | \(0.953138\pi\) | |||||||
\(968\) | − 45.9309i | − 1.47627i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − 6.38447i | − 0.204993i | ||||||||
\(971\) | −52.9848 | −1.70036 | −0.850182 | − | 0.526488i | \(-0.823508\pi\) | ||||
−0.850182 | + | 0.526488i | \(0.823508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 38.9309i | − 1.24807i | ||||||||
\(974\) | −2.87689 | −0.0921816 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 93.1619 | 2.98204 | ||||||||
\(977\) | 15.8229i | 0.506220i | 0.967438 | + | 0.253110i | \(0.0814535\pi\) | ||||
−0.967438 | + | 0.253110i | \(0.918547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.2462 | 0.838833 | ||||||||
\(980\) | 14.5616i | 0.465152i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 50.6004i | − 1.61472i | ||||||||
\(983\) | 27.6155i | 0.880799i | 0.897802 | + | 0.440399i | \(0.145163\pi\) | ||||
−0.897802 | + | 0.440399i | \(0.854837\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.38447 | 0.203426 | ||||||||
\(986\) | 37.3002i | 1.18788i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.876894 | −0.0278836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.3542 | 1.28189 | 0.640946 | − | 0.767586i | \(-0.278542\pi\) | ||||
0.640946 | + | 0.767586i | \(0.278542\pi\) | |||||||
\(992\) | −10.2462 | −0.325318 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 127.723i | 4.05114i | ||||||||
\(995\) | 13.0152i | 0.412608i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.6155 | 0.652900 | 0.326450 | − | 0.945214i | \(-0.394147\pi\) | ||||
0.326450 | + | 0.945214i | \(0.394147\pi\) | |||||||
\(998\) | −72.9848 | −2.31029 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))