Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.a (trivial) |
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: | yes |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.414214 | −0.292893 | −0.146447 | − | 0.989219i | \(-0.546784\pi\) | ||||
−0.146447 | + | 0.989219i | \(0.546784\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 2.82843 | 1.26491 | 0.632456 | − | 0.774597i | \(-0.282047\pi\) | ||||
0.632456 | + | 0.774597i | \(0.282047\pi\) | |||||||
\(6\) | −0.414214 | −0.169102 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.17157 | −0.370484 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −1.82843 | −0.527821 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.17157 | 0.313116 | ||||||||
\(15\) | 2.82843 | 0.730297 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 7.65685 | 1.85706 | 0.928530 | − | 0.371257i | \(-0.121073\pi\) | ||||
0.928530 | + | 0.371257i | \(0.121073\pi\) | |||||||
\(18\) | −0.414214 | −0.0976311 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | −5.17157 | −1.15640 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | −0.828427 | −0.176621 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 1.58579 | 0.323697 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.17157 | 0.977335 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −1.17157 | −0.213899 | ||||||||
\(31\) | 1.17157 | 0.210421 | 0.105210 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105210 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | −3.17157 | −0.543920 | ||||||||
\(35\) | −8.00000 | −1.35225 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | 7.65685 | 1.25878 | 0.629390 | − | 0.777090i | \(-0.283305\pi\) | ||||
0.629390 | + | 0.777090i | \(0.283305\pi\) | |||||||
\(38\) | −1.17157 | −0.190054 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.48528 | 0.709185 | ||||||||
\(41\) | −5.17157 | −0.807664 | −0.403832 | − | 0.914833i | \(-0.632322\pi\) | ||||
−0.403832 | + | 0.914833i | \(0.632322\pi\) | |||||||
\(42\) | 1.17157 | 0.180778 | ||||||||
\(43\) | −1.65685 | −0.252668 | −0.126334 | − | 0.991988i | \(-0.540321\pi\) | ||||
−0.126334 | + | 0.991988i | \(0.540321\pi\) | |||||||
\(44\) | −3.65685 | −0.551292 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | 1.65685 | 0.244290 | ||||||||
\(47\) | 11.6569 | 1.70033 | 0.850163 | − | 0.526519i | \(-0.176503\pi\) | ||||
0.850163 | + | 0.526519i | \(0.176503\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.24264 | −0.175736 | ||||||||
\(51\) | 7.65685 | 1.07217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | −0.414214 | −0.0563673 | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | −4.48528 | −0.599371 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | −0.828427 | −0.108778 | ||||||||
\(59\) | −7.65685 | −0.996838 | −0.498419 | − | 0.866936i | \(-0.666086\pi\) | ||||
−0.498419 | + | 0.866936i | \(0.666086\pi\) | |||||||
\(60\) | −5.17157 | −0.667647 | ||||||||
\(61\) | 13.3137 | 1.70465 | 0.852323 | − | 0.523016i | \(-0.175193\pi\) | ||||
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(62\) | −0.485281 | −0.0616308 | ||||||||
\(63\) | −2.82843 | −0.356348 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.828427 | −0.101972 | ||||||||
\(67\) | −6.82843 | −0.834225 | −0.417113 | − | 0.908855i | \(-0.636958\pi\) | ||||
−0.417113 | + | 0.908855i | \(0.636958\pi\) | |||||||
\(68\) | −14.0000 | −1.69775 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 3.31371 | 0.396064 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 1.58579 | 0.186887 | ||||||||
\(73\) | −0.343146 | −0.0401622 | −0.0200811 | − | 0.999798i | \(-0.506392\pi\) | ||||
−0.0200811 | + | 0.999798i | \(0.506392\pi\) | |||||||
\(74\) | −3.17157 | −0.368688 | ||||||||
\(75\) | 3.00000 | 0.346410 | ||||||||
\(76\) | −5.17157 | −0.593220 | ||||||||
\(77\) | −5.65685 | −0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | 8.48528 | 0.948683 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.14214 | 0.236559 | ||||||||
\(83\) | −3.65685 | −0.401392 | −0.200696 | − | 0.979654i | \(-0.564320\pi\) | ||||
−0.200696 | + | 0.979654i | \(0.564320\pi\) | |||||||
\(84\) | 5.17157 | 0.564265 | ||||||||
\(85\) | 21.6569 | 2.34902 | ||||||||
\(86\) | 0.686292 | 0.0740047 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | 3.17157 | 0.338091 | ||||||||
\(89\) | −14.8284 | −1.57181 | −0.785905 | − | 0.618347i | \(-0.787803\pi\) | ||||
−0.785905 | + | 0.618347i | \(0.787803\pi\) | |||||||
\(90\) | −1.17157 | −0.123495 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.31371 | 0.762507 | ||||||||
\(93\) | 1.17157 | 0.121486 | ||||||||
\(94\) | −4.82843 | −0.498014 | ||||||||
\(95\) | 8.00000 | 0.820783 | ||||||||
\(96\) | −4.41421 | −0.450524 | ||||||||
\(97\) | −3.65685 | −0.371297 | −0.185649 | − | 0.982616i | \(-0.559439\pi\) | ||||
−0.185649 | + | 0.982616i | \(0.559439\pi\) | |||||||
\(98\) | −0.414214 | −0.0418419 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −5.48528 | −0.548528 | ||||||||
\(101\) | 7.65685 | 0.761885 | 0.380943 | − | 0.924599i | \(-0.375599\pi\) | ||||
0.380943 | + | 0.924599i | \(0.375599\pi\) | |||||||
\(102\) | −3.17157 | −0.314033 | ||||||||
\(103\) | 2.34315 | 0.230877 | 0.115439 | − | 0.993315i | \(-0.463173\pi\) | ||||
0.115439 | + | 0.993315i | \(0.463173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | 0.828427 | 0.0804640 | ||||||||
\(107\) | −11.3137 | −1.09374 | −0.546869 | − | 0.837218i | \(-0.684180\pi\) | ||||
−0.546869 | + | 0.837218i | \(0.684180\pi\) | |||||||
\(108\) | −1.82843 | −0.175940 | ||||||||
\(109\) | −5.31371 | −0.508961 | −0.254480 | − | 0.967078i | \(-0.581904\pi\) | ||||
−0.254480 | + | 0.967078i | \(0.581904\pi\) | |||||||
\(110\) | −2.34315 | −0.223410 | ||||||||
\(111\) | 7.65685 | 0.726756 | ||||||||
\(112\) | −8.48528 | −0.801784 | ||||||||
\(113\) | −5.31371 | −0.499872 | −0.249936 | − | 0.968262i | \(-0.580410\pi\) | ||||
−0.249936 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(114\) | −1.17157 | −0.109728 | ||||||||
\(115\) | −11.3137 | −1.05501 | ||||||||
\(116\) | −3.65685 | −0.339530 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.17157 | 0.291967 | ||||||||
\(119\) | −21.6569 | −1.98528 | ||||||||
\(120\) | 4.48528 | 0.409448 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −5.51472 | −0.499279 | ||||||||
\(123\) | −5.17157 | −0.466305 | ||||||||
\(124\) | −2.14214 | −0.192369 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 1.17157 | 0.104372 | ||||||||
\(127\) | 5.65685 | 0.501965 | 0.250982 | − | 0.967992i | \(-0.419246\pi\) | ||||
0.250982 | + | 0.967992i | \(0.419246\pi\) | |||||||
\(128\) | 10.5563 | 0.933058 | ||||||||
\(129\) | −1.65685 | −0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | −3.65685 | −0.318288 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 2.82843 | 0.244339 | ||||||||
\(135\) | 2.82843 | 0.243432 | ||||||||
\(136\) | 12.1421 | 1.04118 | ||||||||
\(137\) | 10.8284 | 0.925135 | 0.462567 | − | 0.886584i | \(-0.346928\pi\) | ||||
0.462567 | + | 0.886584i | \(0.346928\pi\) | |||||||
\(138\) | 1.65685 | 0.141041 | ||||||||
\(139\) | −7.31371 | −0.620341 | −0.310170 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310170 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(140\) | 14.6274 | 1.23624 | ||||||||
\(141\) | 11.6569 | 0.981684 | ||||||||
\(142\) | 0.828427 | 0.0695201 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 5.65685 | 0.469776 | ||||||||
\(146\) | 0.142136 | 0.0117632 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −14.0000 | −1.15079 | ||||||||
\(149\) | 9.17157 | 0.751365 | 0.375682 | − | 0.926749i | \(-0.377408\pi\) | ||||
0.375682 | + | 0.926749i | \(0.377408\pi\) | |||||||
\(150\) | −1.24264 | −0.101461 | ||||||||
\(151\) | 3.51472 | 0.286024 | 0.143012 | − | 0.989721i | \(-0.454321\pi\) | ||||
0.143012 | + | 0.989721i | \(0.454321\pi\) | |||||||
\(152\) | 4.48528 | 0.363804 | ||||||||
\(153\) | 7.65685 | 0.619020 | ||||||||
\(154\) | 2.34315 | 0.188816 | ||||||||
\(155\) | 3.31371 | 0.266163 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 4.68629 | 0.372821 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | −12.4853 | −0.987048 | ||||||||
\(161\) | 11.3137 | 0.891645 | ||||||||
\(162\) | −0.414214 | −0.0325437 | ||||||||
\(163\) | −18.8284 | −1.47476 | −0.737378 | − | 0.675480i | \(-0.763936\pi\) | ||||
−0.737378 | + | 0.675480i | \(0.763936\pi\) | |||||||
\(164\) | 9.45584 | 0.738377 | ||||||||
\(165\) | 5.65685 | 0.440386 | ||||||||
\(166\) | 1.51472 | 0.117565 | ||||||||
\(167\) | 3.65685 | 0.282976 | 0.141488 | − | 0.989940i | \(-0.454811\pi\) | ||||
0.141488 | + | 0.989940i | \(0.454811\pi\) | |||||||
\(168\) | −4.48528 | −0.346047 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.97056 | −0.688011 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 3.02944 | 0.230992 | ||||||||
\(173\) | −11.6569 | −0.886254 | −0.443127 | − | 0.896459i | \(-0.646131\pi\) | ||||
−0.443127 | + | 0.896459i | \(0.646131\pi\) | |||||||
\(174\) | −0.828427 | −0.0628029 | ||||||||
\(175\) | −8.48528 | −0.641427 | ||||||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | −7.65685 | −0.575524 | ||||||||
\(178\) | 6.14214 | 0.460373 | ||||||||
\(179\) | −23.3137 | −1.74255 | −0.871274 | − | 0.490797i | \(-0.836706\pi\) | ||||
−0.871274 | + | 0.490797i | \(0.836706\pi\) | |||||||
\(180\) | −5.17157 | −0.385466 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3137 | 0.984178 | ||||||||
\(184\) | −6.34315 | −0.467623 | ||||||||
\(185\) | 21.6569 | 1.59224 | ||||||||
\(186\) | −0.485281 | −0.0355826 | ||||||||
\(187\) | 15.3137 | 1.11985 | ||||||||
\(188\) | −21.3137 | −1.55446 | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | −3.31371 | −0.240402 | ||||||||
\(191\) | 3.31371 | 0.239772 | 0.119886 | − | 0.992788i | \(-0.461747\pi\) | ||||
0.119886 | + | 0.992788i | \(0.461747\pi\) | |||||||
\(192\) | −4.17157 | −0.301057 | ||||||||
\(193\) | −5.31371 | −0.382489 | −0.191245 | − | 0.981542i | \(-0.561252\pi\) | ||||
−0.191245 | + | 0.981542i | \(0.561252\pi\) | |||||||
\(194\) | 1.51472 | 0.108750 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.82843 | −0.130602 | ||||||||
\(197\) | −0.485281 | −0.0345749 | −0.0172874 | − | 0.999851i | \(-0.505503\pi\) | ||||
−0.0172874 | + | 0.999851i | \(0.505503\pi\) | |||||||
\(198\) | −0.828427 | −0.0588738 | ||||||||
\(199\) | 21.6569 | 1.53521 | 0.767607 | − | 0.640921i | \(-0.221447\pi\) | ||||
0.767607 | + | 0.640921i | \(0.221447\pi\) | |||||||
\(200\) | 4.75736 | 0.336396 | ||||||||
\(201\) | −6.82843 | −0.481640 | ||||||||
\(202\) | −3.17157 | −0.223151 | ||||||||
\(203\) | −5.65685 | −0.397033 | ||||||||
\(204\) | −14.0000 | −0.980196 | ||||||||
\(205\) | −14.6274 | −1.02162 | ||||||||
\(206\) | −0.970563 | −0.0676223 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 3.31371 | 0.228668 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 3.65685 | 0.251154 | ||||||||
\(213\) | −2.00000 | −0.137038 | ||||||||
\(214\) | 4.68629 | 0.320348 | ||||||||
\(215\) | −4.68629 | −0.319602 | ||||||||
\(216\) | 1.58579 | 0.107899 | ||||||||
\(217\) | −3.31371 | −0.224949 | ||||||||
\(218\) | 2.20101 | 0.149071 | ||||||||
\(219\) | −0.343146 | −0.0231876 | ||||||||
\(220\) | −10.3431 | −0.697335 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.17157 | −0.212862 | ||||||||
\(223\) | 12.4853 | 0.836076 | 0.418038 | − | 0.908429i | \(-0.362718\pi\) | ||||
0.418038 | + | 0.908429i | \(0.362718\pi\) | |||||||
\(224\) | 12.4853 | 0.834208 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 2.20101 | 0.146409 | ||||||||
\(227\) | 17.3137 | 1.14915 | 0.574576 | − | 0.818452i | \(-0.305167\pi\) | ||||
0.574576 | + | 0.818452i | \(0.305167\pi\) | |||||||
\(228\) | −5.17157 | −0.342496 | ||||||||
\(229\) | 1.31371 | 0.0868123 | 0.0434062 | − | 0.999058i | \(-0.486179\pi\) | ||||
0.0434062 | + | 0.999058i | \(0.486179\pi\) | |||||||
\(230\) | 4.68629 | 0.309005 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | 3.17157 | 0.208224 | ||||||||
\(233\) | 6.97056 | 0.456657 | 0.228328 | − | 0.973584i | \(-0.426674\pi\) | ||||
0.228328 | + | 0.973584i | \(0.426674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.9706 | 2.15076 | ||||||||
\(236\) | 14.0000 | 0.911322 | ||||||||
\(237\) | −11.3137 | −0.734904 | ||||||||
\(238\) | 8.97056 | 0.581475 | ||||||||
\(239\) | −2.00000 | −0.129369 | −0.0646846 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646846 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(240\) | 8.48528 | 0.547723 | ||||||||
\(241\) | −0.343146 | −0.0221040 | −0.0110520 | − | 0.999939i | \(-0.503518\pi\) | ||||
−0.0110520 | + | 0.999939i | \(0.503518\pi\) | |||||||
\(242\) | 2.89949 | 0.186387 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −24.3431 | −1.55841 | ||||||||
\(245\) | 2.82843 | 0.180702 | ||||||||
\(246\) | 2.14214 | 0.136578 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.85786 | 0.117975 | ||||||||
\(249\) | −3.65685 | −0.231744 | ||||||||
\(250\) | 2.34315 | 0.148194 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 5.17157 | 0.325778 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | −2.34315 | −0.147022 | ||||||||
\(255\) | 21.6569 | 1.35620 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −4.34315 | −0.270918 | −0.135459 | − | 0.990783i | \(-0.543251\pi\) | ||||
−0.135459 | + | 0.990783i | \(0.543251\pi\) | |||||||
\(258\) | 0.686292 | 0.0427266 | ||||||||
\(259\) | −21.6569 | −1.34569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 3.31371 | 0.204722 | ||||||||
\(263\) | 12.0000 | 0.739952 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(264\) | 3.17157 | 0.195197 | ||||||||
\(265\) | −5.65685 | −0.347498 | ||||||||
\(266\) | 3.31371 | 0.203177 | ||||||||
\(267\) | −14.8284 | −0.907485 | ||||||||
\(268\) | 12.4853 | 0.762660 | ||||||||
\(269\) | 18.0000 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(270\) | −1.17157 | −0.0712997 | ||||||||
\(271\) | 27.7990 | 1.68867 | 0.844334 | − | 0.535817i | \(-0.179996\pi\) | ||||
0.844334 | + | 0.535817i | \(0.179996\pi\) | |||||||
\(272\) | 22.9706 | 1.39279 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.48528 | −0.270966 | ||||||||
\(275\) | 6.00000 | 0.361814 | ||||||||
\(276\) | 7.31371 | 0.440234 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 3.02944 | 0.181694 | ||||||||
\(279\) | 1.17157 | 0.0701402 | ||||||||
\(280\) | −12.6863 | −0.758151 | ||||||||
\(281\) | −21.1716 | −1.26299 | −0.631495 | − | 0.775380i | \(-0.717558\pi\) | ||||
−0.631495 | + | 0.775380i | \(0.717558\pi\) | |||||||
\(282\) | −4.82843 | −0.287529 | ||||||||
\(283\) | 28.9706 | 1.72212 | 0.861061 | − | 0.508502i | \(-0.169801\pi\) | ||||
0.861061 | + | 0.508502i | \(0.169801\pi\) | |||||||
\(284\) | 3.65685 | 0.216994 | ||||||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.6274 | 0.863429 | ||||||||
\(288\) | −4.41421 | −0.260110 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | −2.34315 | −0.137594 | ||||||||
\(291\) | −3.65685 | −0.214369 | ||||||||
\(292\) | 0.627417 | 0.0367168 | ||||||||
\(293\) | −2.14214 | −0.125145 | −0.0625724 | − | 0.998040i | \(-0.519930\pi\) | ||||
−0.0625724 | + | 0.998040i | \(0.519930\pi\) | |||||||
\(294\) | −0.414214 | −0.0241574 | ||||||||
\(295\) | −21.6569 | −1.26091 | ||||||||
\(296\) | 12.1421 | 0.705747 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | −3.79899 | −0.220070 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.48528 | −0.316693 | ||||||||
\(301\) | 4.68629 | 0.270113 | ||||||||
\(302\) | −1.45584 | −0.0837744 | ||||||||
\(303\) | 7.65685 | 0.439875 | ||||||||
\(304\) | 8.48528 | 0.486664 | ||||||||
\(305\) | 37.6569 | 2.15623 | ||||||||
\(306\) | −3.17157 | −0.181307 | ||||||||
\(307\) | 22.8284 | 1.30289 | 0.651444 | − | 0.758697i | \(-0.274164\pi\) | ||||
0.651444 | + | 0.758697i | \(0.274164\pi\) | |||||||
\(308\) | 10.3431 | 0.589355 | ||||||||
\(309\) | 2.34315 | 0.133297 | ||||||||
\(310\) | −1.37258 | −0.0779575 | ||||||||
\(311\) | −10.6274 | −0.602626 | −0.301313 | − | 0.953525i | \(-0.597425\pi\) | ||||
−0.301313 | + | 0.953525i | \(0.597425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 4.14214 | 0.233754 | ||||||||
\(315\) | −8.00000 | −0.450749 | ||||||||
\(316\) | 20.6863 | 1.16369 | ||||||||
\(317\) | −8.48528 | −0.476581 | −0.238290 | − | 0.971194i | \(-0.576587\pi\) | ||||
−0.238290 | + | 0.971194i | \(0.576587\pi\) | |||||||
\(318\) | 0.828427 | 0.0464559 | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | −11.7990 | −0.659584 | ||||||||
\(321\) | −11.3137 | −0.631470 | ||||||||
\(322\) | −4.68629 | −0.261157 | ||||||||
\(323\) | 21.6569 | 1.20502 | ||||||||
\(324\) | −1.82843 | −0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.79899 | 0.431946 | ||||||||
\(327\) | −5.31371 | −0.293849 | ||||||||
\(328\) | −8.20101 | −0.452825 | ||||||||
\(329\) | −32.9706 | −1.81773 | ||||||||
\(330\) | −2.34315 | −0.128986 | ||||||||
\(331\) | −26.1421 | −1.43690 | −0.718451 | − | 0.695578i | \(-0.755148\pi\) | ||||
−0.718451 | + | 0.695578i | \(0.755148\pi\) | |||||||
\(332\) | 6.68629 | 0.366958 | ||||||||
\(333\) | 7.65685 | 0.419593 | ||||||||
\(334\) | −1.51472 | −0.0828817 | ||||||||
\(335\) | −19.3137 | −1.05522 | ||||||||
\(336\) | −8.48528 | −0.462910 | ||||||||
\(337\) | 9.31371 | 0.507350 | 0.253675 | − | 0.967290i | \(-0.418361\pi\) | ||||
0.253675 | + | 0.967290i | \(0.418361\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.31371 | −0.288601 | ||||||||
\(340\) | −39.5980 | −2.14750 | ||||||||
\(341\) | 2.34315 | 0.126888 | ||||||||
\(342\) | −1.17157 | −0.0633514 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | −2.62742 | −0.141661 | ||||||||
\(345\) | −11.3137 | −0.609110 | ||||||||
\(346\) | 4.82843 | 0.259578 | ||||||||
\(347\) | −8.68629 | −0.466305 | −0.233152 | − | 0.972440i | \(-0.574904\pi\) | ||||
−0.233152 | + | 0.972440i | \(0.574904\pi\) | |||||||
\(348\) | −3.65685 | −0.196028 | ||||||||
\(349\) | −3.65685 | −0.195747 | −0.0978735 | − | 0.995199i | \(-0.531204\pi\) | ||||
−0.0978735 | + | 0.995199i | \(0.531204\pi\) | |||||||
\(350\) | 3.51472 | 0.187870 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.82843 | −0.470557 | ||||||||
\(353\) | 33.4558 | 1.78067 | 0.890337 | − | 0.455301i | \(-0.150468\pi\) | ||||
0.890337 | + | 0.455301i | \(0.150468\pi\) | |||||||
\(354\) | 3.17157 | 0.168567 | ||||||||
\(355\) | −5.65685 | −0.300235 | ||||||||
\(356\) | 27.1127 | 1.43697 | ||||||||
\(357\) | −21.6569 | −1.14620 | ||||||||
\(358\) | 9.65685 | 0.510381 | ||||||||
\(359\) | −34.9706 | −1.84568 | −0.922838 | − | 0.385189i | \(-0.874136\pi\) | ||||
−0.922838 | + | 0.385189i | \(0.874136\pi\) | |||||||
\(360\) | 4.48528 | 0.236395 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −5.79899 | −0.304788 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.970563 | −0.0508016 | ||||||||
\(366\) | −5.51472 | −0.288259 | ||||||||
\(367\) | −24.0000 | −1.25279 | −0.626395 | − | 0.779506i | \(-0.715470\pi\) | ||||
−0.626395 | + | 0.779506i | \(0.715470\pi\) | |||||||
\(368\) | −12.0000 | −0.625543 | ||||||||
\(369\) | −5.17157 | −0.269221 | ||||||||
\(370\) | −8.97056 | −0.466357 | ||||||||
\(371\) | 5.65685 | 0.293689 | ||||||||
\(372\) | −2.14214 | −0.111065 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | −6.34315 | −0.327996 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 18.4853 | 0.953306 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.17157 | 0.0602592 | ||||||||
\(379\) | −0.485281 | −0.0249272 | −0.0124636 | − | 0.999922i | \(-0.503967\pi\) | ||||
−0.0124636 | + | 0.999922i | \(0.503967\pi\) | |||||||
\(380\) | −14.6274 | −0.750371 | ||||||||
\(381\) | 5.65685 | 0.289809 | ||||||||
\(382\) | −1.37258 | −0.0702275 | ||||||||
\(383\) | −30.9706 | −1.58252 | −0.791261 | − | 0.611479i | \(-0.790575\pi\) | ||||
−0.791261 | + | 0.611479i | \(0.790575\pi\) | |||||||
\(384\) | 10.5563 | 0.538701 | ||||||||
\(385\) | −16.0000 | −0.815436 | ||||||||
\(386\) | 2.20101 | 0.112028 | ||||||||
\(387\) | −1.65685 | −0.0842226 | ||||||||
\(388\) | 6.68629 | 0.339445 | ||||||||
\(389\) | −26.9706 | −1.36746 | −0.683731 | − | 0.729734i | \(-0.739644\pi\) | ||||
−0.683731 | + | 0.729734i | \(0.739644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.6274 | −1.54890 | ||||||||
\(392\) | 1.58579 | 0.0800943 | ||||||||
\(393\) | −8.00000 | −0.403547 | ||||||||
\(394\) | 0.201010 | 0.0101267 | ||||||||
\(395\) | −32.0000 | −1.61009 | ||||||||
\(396\) | −3.65685 | −0.183764 | ||||||||
\(397\) | −30.9706 | −1.55437 | −0.777184 | − | 0.629273i | \(-0.783353\pi\) | ||||
−0.777184 | + | 0.629273i | \(0.783353\pi\) | |||||||
\(398\) | −8.97056 | −0.449654 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 9.00000 | 0.450000 | ||||||||
\(401\) | −26.1421 | −1.30548 | −0.652738 | − | 0.757584i | \(-0.726380\pi\) | ||||
−0.652738 | + | 0.757584i | \(0.726380\pi\) | |||||||
\(402\) | 2.82843 | 0.141069 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 2.82843 | 0.140546 | ||||||||
\(406\) | 2.34315 | 0.116288 | ||||||||
\(407\) | 15.3137 | 0.759072 | ||||||||
\(408\) | 12.1421 | 0.601125 | ||||||||
\(409\) | 34.9706 | 1.72918 | 0.864592 | − | 0.502475i | \(-0.167577\pi\) | ||||
0.864592 | + | 0.502475i | \(0.167577\pi\) | |||||||
\(410\) | 6.05887 | 0.299226 | ||||||||
\(411\) | 10.8284 | 0.534127 | ||||||||
\(412\) | −4.28427 | −0.211071 | ||||||||
\(413\) | 21.6569 | 1.06566 | ||||||||
\(414\) | 1.65685 | 0.0814299 | ||||||||
\(415\) | −10.3431 | −0.507725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.31371 | −0.358154 | ||||||||
\(418\) | −2.34315 | −0.114607 | ||||||||
\(419\) | 14.6274 | 0.714596 | 0.357298 | − | 0.933990i | \(-0.383698\pi\) | ||||
0.357298 | + | 0.933990i | \(0.383698\pi\) | |||||||
\(420\) | 14.6274 | 0.713745 | ||||||||
\(421\) | −37.3137 | −1.81856 | −0.909279 | − | 0.416186i | \(-0.863366\pi\) | ||||
−0.909279 | + | 0.416186i | \(0.863366\pi\) | |||||||
\(422\) | 4.97056 | 0.241963 | ||||||||
\(423\) | 11.6569 | 0.566776 | ||||||||
\(424\) | −3.17157 | −0.154025 | ||||||||
\(425\) | 22.9706 | 1.11424 | ||||||||
\(426\) | 0.828427 | 0.0401374 | ||||||||
\(427\) | −37.6569 | −1.82234 | ||||||||
\(428\) | 20.6863 | 0.999910 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.94113 | 0.0936094 | ||||||||
\(431\) | −8.34315 | −0.401875 | −0.200938 | − | 0.979604i | \(-0.564399\pi\) | ||||
−0.200938 | + | 0.979604i | \(0.564399\pi\) | |||||||
\(432\) | 3.00000 | 0.144338 | ||||||||
\(433\) | −21.3137 | −1.02427 | −0.512136 | − | 0.858905i | \(-0.671146\pi\) | ||||
−0.512136 | + | 0.858905i | \(0.671146\pi\) | |||||||
\(434\) | 1.37258 | 0.0658861 | ||||||||
\(435\) | 5.65685 | 0.271225 | ||||||||
\(436\) | 9.71573 | 0.465299 | ||||||||
\(437\) | −11.3137 | −0.541208 | ||||||||
\(438\) | 0.142136 | 0.00679150 | ||||||||
\(439\) | 16.9706 | 0.809961 | 0.404980 | − | 0.914325i | \(-0.367278\pi\) | ||||
0.404980 | + | 0.914325i | \(0.367278\pi\) | |||||||
\(440\) | 8.97056 | 0.427655 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.9411 | −1.23250 | −0.616250 | − | 0.787551i | \(-0.711349\pi\) | ||||
−0.616250 | + | 0.787551i | \(0.711349\pi\) | |||||||
\(444\) | −14.0000 | −0.664411 | ||||||||
\(445\) | −41.9411 | −1.98820 | ||||||||
\(446\) | −5.17157 | −0.244881 | ||||||||
\(447\) | 9.17157 | 0.433801 | ||||||||
\(448\) | 11.7990 | 0.557450 | ||||||||
\(449\) | 31.7990 | 1.50069 | 0.750344 | − | 0.661048i | \(-0.229888\pi\) | ||||
0.750344 | + | 0.661048i | \(0.229888\pi\) | |||||||
\(450\) | −1.24264 | −0.0585786 | ||||||||
\(451\) | −10.3431 | −0.487040 | ||||||||
\(452\) | 9.71573 | 0.456989 | ||||||||
\(453\) | 3.51472 | 0.165136 | ||||||||
\(454\) | −7.17157 | −0.336579 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.48528 | 0.210043 | ||||||||
\(457\) | 7.65685 | 0.358173 | 0.179086 | − | 0.983833i | \(-0.442686\pi\) | ||||
0.179086 | + | 0.983833i | \(0.442686\pi\) | |||||||
\(458\) | −0.544156 | −0.0254267 | ||||||||
\(459\) | 7.65685 | 0.357391 | ||||||||
\(460\) | 20.6863 | 0.964503 | ||||||||
\(461\) | −5.17157 | −0.240864 | −0.120432 | − | 0.992722i | \(-0.538428\pi\) | ||||
−0.120432 | + | 0.992722i | \(0.538428\pi\) | |||||||
\(462\) | 2.34315 | 0.109013 | ||||||||
\(463\) | 24.4853 | 1.13793 | 0.568964 | − | 0.822363i | \(-0.307344\pi\) | ||||
0.568964 | + | 0.822363i | \(0.307344\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 3.31371 | 0.153670 | ||||||||
\(466\) | −2.88730 | −0.133752 | ||||||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.3137 | 0.891824 | ||||||||
\(470\) | −13.6569 | −0.629944 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | −12.1421 | −0.558887 | ||||||||
\(473\) | −3.31371 | −0.152364 | ||||||||
\(474\) | 4.68629 | 0.215248 | ||||||||
\(475\) | 8.48528 | 0.389331 | ||||||||
\(476\) | 39.5980 | 1.81497 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0.828427 | 0.0378914 | ||||||||
\(479\) | −25.3137 | −1.15661 | −0.578306 | − | 0.815820i | \(-0.696286\pi\) | ||||
−0.578306 | + | 0.815820i | \(0.696286\pi\) | |||||||
\(480\) | −12.4853 | −0.569873 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.142136 | 0.00647410 | ||||||||
\(483\) | 11.3137 | 0.514792 | ||||||||
\(484\) | 12.7990 | 0.581772 | ||||||||
\(485\) | −10.3431 | −0.469658 | ||||||||
\(486\) | −0.414214 | −0.0187891 | ||||||||
\(487\) | 7.79899 | 0.353406 | 0.176703 | − | 0.984264i | \(-0.443457\pi\) | ||||
0.176703 | + | 0.984264i | \(0.443457\pi\) | |||||||
\(488\) | 21.1127 | 0.955727 | ||||||||
\(489\) | −18.8284 | −0.851451 | ||||||||
\(490\) | −1.17157 | −0.0529263 | ||||||||
\(491\) | 30.6274 | 1.38220 | 0.691098 | − | 0.722761i | \(-0.257127\pi\) | ||||
0.691098 | + | 0.722761i | \(0.257127\pi\) | |||||||
\(492\) | 9.45584 | 0.426302 | ||||||||
\(493\) | 15.3137 | 0.689695 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | 3.51472 | 0.157816 | ||||||||
\(497\) | 5.65685 | 0.253745 | ||||||||
\(498\) | 1.51472 | 0.0678762 | ||||||||
\(499\) | −26.1421 | −1.17028 | −0.585141 | − | 0.810931i | \(-0.698961\pi\) | ||||
−0.585141 | + | 0.810931i | \(0.698961\pi\) | |||||||
\(500\) | 10.3431 | 0.462560 | ||||||||
\(501\) | 3.65685 | 0.163376 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.31371 | −0.326102 | −0.163051 | − | 0.986618i | \(-0.552134\pi\) | ||||
−0.163051 | + | 0.986618i | \(0.552134\pi\) | |||||||
\(504\) | −4.48528 | −0.199790 | ||||||||
\(505\) | 21.6569 | 0.963717 | ||||||||
\(506\) | 3.31371 | 0.147312 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.3431 | −0.458903 | ||||||||
\(509\) | −11.7990 | −0.522981 | −0.261491 | − | 0.965206i | \(-0.584214\pi\) | ||||
−0.261491 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(510\) | −8.97056 | −0.397223 | ||||||||
\(511\) | 0.970563 | 0.0429352 | ||||||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | 2.82843 | 0.124878 | ||||||||
\(514\) | 1.79899 | 0.0793500 | ||||||||
\(515\) | 6.62742 | 0.292039 | ||||||||
\(516\) | 3.02944 | 0.133364 | ||||||||
\(517\) | 23.3137 | 1.02534 | ||||||||
\(518\) | 8.97056 | 0.394144 | ||||||||
\(519\) | −11.6569 | −0.511679 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.3137 | 1.10901 | 0.554507 | − | 0.832179i | \(-0.312907\pi\) | ||||
0.554507 | + | 0.832179i | \(0.312907\pi\) | |||||||
\(522\) | −0.828427 | −0.0362593 | ||||||||
\(523\) | −15.3137 | −0.669622 | −0.334811 | − | 0.942285i | \(-0.608672\pi\) | ||||
−0.334811 | + | 0.942285i | \(0.608672\pi\) | |||||||
\(524\) | 14.6274 | 0.639002 | ||||||||
\(525\) | −8.48528 | −0.370328 | ||||||||
\(526\) | −4.97056 | −0.216727 | ||||||||
\(527\) | 8.97056 | 0.390764 | ||||||||
\(528\) | 6.00000 | 0.261116 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 2.34315 | 0.101780 | ||||||||
\(531\) | −7.65685 | −0.332279 | ||||||||
\(532\) | 14.6274 | 0.634179 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.14214 | 0.265796 | ||||||||
\(535\) | −32.0000 | −1.38348 | ||||||||
\(536\) | −10.8284 | −0.467717 | ||||||||
\(537\) | −23.3137 | −1.00606 | ||||||||
\(538\) | −7.45584 | −0.321444 | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | −5.17157 | −0.222549 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | −11.5147 | −0.494600 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | −33.7990 | −1.44912 | ||||||||
\(545\) | −15.0294 | −0.643790 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3137 | 0.996822 | 0.498411 | − | 0.866941i | \(-0.333917\pi\) | ||||
0.498411 | + | 0.866941i | \(0.333917\pi\) | |||||||
\(548\) | −19.7990 | −0.845771 | ||||||||
\(549\) | 13.3137 | 0.568215 | ||||||||
\(550\) | −2.48528 | −0.105973 | ||||||||
\(551\) | 5.65685 | 0.240990 | ||||||||
\(552\) | −6.34315 | −0.269982 | ||||||||
\(553\) | 32.0000 | 1.36078 | ||||||||
\(554\) | 0.828427 | 0.0351965 | ||||||||
\(555\) | 21.6569 | 0.919282 | ||||||||
\(556\) | 13.3726 | 0.567124 | ||||||||
\(557\) | 7.79899 | 0.330454 | 0.165227 | − | 0.986256i | \(-0.447164\pi\) | ||||
0.165227 | + | 0.986256i | \(0.447164\pi\) | |||||||
\(558\) | −0.485281 | −0.0205436 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −24.0000 | −1.01419 | ||||||||
\(561\) | 15.3137 | 0.646545 | ||||||||
\(562\) | 8.76955 | 0.369921 | ||||||||
\(563\) | 4.00000 | 0.168580 | 0.0842900 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842900 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(564\) | −21.3137 | −0.897469 | ||||||||
\(565\) | −15.0294 | −0.632293 | ||||||||
\(566\) | −12.0000 | −0.504398 | ||||||||
\(567\) | −2.82843 | −0.118783 | ||||||||
\(568\) | −3.17157 | −0.133076 | ||||||||
\(569\) | −42.9706 | −1.80142 | −0.900710 | − | 0.434421i | \(-0.856953\pi\) | ||||
−0.900710 | + | 0.434421i | \(0.856953\pi\) | |||||||
\(570\) | −3.31371 | −0.138796 | ||||||||
\(571\) | −12.9706 | −0.542801 | −0.271401 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271401 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.31371 | 0.138432 | ||||||||
\(574\) | −6.05887 | −0.252893 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | −4.17157 | −0.173816 | ||||||||
\(577\) | 31.9411 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(578\) | −17.2426 | −0.717199 | ||||||||
\(579\) | −5.31371 | −0.220830 | ||||||||
\(580\) | −10.3431 | −0.429476 | ||||||||
\(581\) | 10.3431 | 0.429106 | ||||||||
\(582\) | 1.51472 | 0.0627871 | ||||||||
\(583\) | −4.00000 | −0.165663 | ||||||||
\(584\) | −0.544156 | −0.0225173 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.887302 | 0.0366541 | ||||||||
\(587\) | 10.9706 | 0.452804 | 0.226402 | − | 0.974034i | \(-0.427304\pi\) | ||||
0.226402 | + | 0.974034i | \(0.427304\pi\) | |||||||
\(588\) | −1.82843 | −0.0754031 | ||||||||
\(589\) | 3.31371 | 0.136539 | ||||||||
\(590\) | 8.97056 | 0.369312 | ||||||||
\(591\) | −0.485281 | −0.0199618 | ||||||||
\(592\) | 22.9706 | 0.944084 | ||||||||
\(593\) | 20.4853 | 0.841230 | 0.420615 | − | 0.907239i | \(-0.361814\pi\) | ||||
0.420615 | + | 0.907239i | \(0.361814\pi\) | |||||||
\(594\) | −0.828427 | −0.0339908 | ||||||||
\(595\) | −61.2548 | −2.51120 | ||||||||
\(596\) | −16.7696 | −0.686908 | ||||||||
\(597\) | 21.6569 | 0.886356 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.3137 | −0.952572 | −0.476286 | − | 0.879290i | \(-0.658017\pi\) | ||||
−0.476286 | + | 0.879290i | \(0.658017\pi\) | |||||||
\(600\) | 4.75736 | 0.194218 | ||||||||
\(601\) | −0.627417 | −0.0255929 | −0.0127964 | − | 0.999918i | \(-0.504073\pi\) | ||||
−0.0127964 | + | 0.999918i | \(0.504073\pi\) | |||||||
\(602\) | −1.94113 | −0.0791144 | ||||||||
\(603\) | −6.82843 | −0.278075 | ||||||||
\(604\) | −6.42641 | −0.261487 | ||||||||
\(605\) | −19.7990 | −0.804943 | ||||||||
\(606\) | −3.17157 | −0.128836 | ||||||||
\(607\) | 41.9411 | 1.70234 | 0.851169 | − | 0.524892i | \(-0.175894\pi\) | ||||
0.851169 | + | 0.524892i | \(0.175894\pi\) | |||||||
\(608\) | −12.4853 | −0.506345 | ||||||||
\(609\) | −5.65685 | −0.229227 | ||||||||
\(610\) | −15.5980 | −0.631544 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | 47.6569 | 1.92484 | 0.962421 | − | 0.271561i | \(-0.0875400\pi\) | ||||
0.962421 | + | 0.271561i | \(0.0875400\pi\) | |||||||
\(614\) | −9.45584 | −0.381607 | ||||||||
\(615\) | −14.6274 | −0.589834 | ||||||||
\(616\) | −8.97056 | −0.361434 | ||||||||
\(617\) | 34.8284 | 1.40214 | 0.701070 | − | 0.713093i | \(-0.252706\pi\) | ||||
0.701070 | + | 0.713093i | \(0.252706\pi\) | |||||||
\(618\) | −0.970563 | −0.0390418 | ||||||||
\(619\) | −23.7990 | −0.956562 | −0.478281 | − | 0.878207i | \(-0.658740\pi\) | ||||
−0.478281 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(620\) | −6.05887 | −0.243330 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 4.40202 | 0.176505 | ||||||||
\(623\) | 41.9411 | 1.68034 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | −2.48528 | −0.0993318 | ||||||||
\(627\) | 5.65685 | 0.225913 | ||||||||
\(628\) | 18.2843 | 0.729622 | ||||||||
\(629\) | 58.6274 | 2.33763 | ||||||||
\(630\) | 3.31371 | 0.132021 | ||||||||
\(631\) | −43.1127 | −1.71629 | −0.858145 | − | 0.513408i | \(-0.828383\pi\) | ||||
−0.858145 | + | 0.513408i | \(0.828383\pi\) | |||||||
\(632\) | −17.9411 | −0.713660 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 3.51472 | 0.139587 | ||||||||
\(635\) | 16.0000 | 0.634941 | ||||||||
\(636\) | 3.65685 | 0.145004 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.65685 | −0.0655955 | ||||||||
\(639\) | −2.00000 | −0.0791188 | ||||||||
\(640\) | 29.8579 | 1.18024 | ||||||||
\(641\) | 30.2843 | 1.19616 | 0.598078 | − | 0.801438i | \(-0.295931\pi\) | ||||
0.598078 | + | 0.801438i | \(0.295931\pi\) | |||||||
\(642\) | 4.68629 | 0.184953 | ||||||||
\(643\) | −22.8284 | −0.900265 | −0.450133 | − | 0.892962i | \(-0.648623\pi\) | ||||
−0.450133 | + | 0.892962i | \(0.648623\pi\) | |||||||
\(644\) | −20.6863 | −0.815154 | ||||||||
\(645\) | −4.68629 | −0.184523 | ||||||||
\(646\) | −8.97056 | −0.352942 | ||||||||
\(647\) | 11.3137 | 0.444788 | 0.222394 | − | 0.974957i | \(-0.428613\pi\) | ||||
0.222394 | + | 0.974957i | \(0.428613\pi\) | |||||||
\(648\) | 1.58579 | 0.0622956 | ||||||||
\(649\) | −15.3137 | −0.601116 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.31371 | −0.129874 | ||||||||
\(652\) | 34.4264 | 1.34824 | ||||||||
\(653\) | −25.3137 | −0.990602 | −0.495301 | − | 0.868721i | \(-0.664942\pi\) | ||||
−0.495301 | + | 0.868721i | \(0.664942\pi\) | |||||||
\(654\) | 2.20101 | 0.0860663 | ||||||||
\(655\) | −22.6274 | −0.884126 | ||||||||
\(656\) | −15.5147 | −0.605748 | ||||||||
\(657\) | −0.343146 | −0.0133874 | ||||||||
\(658\) | 13.6569 | 0.532400 | ||||||||
\(659\) | −47.3137 | −1.84308 | −0.921540 | − | 0.388283i | \(-0.873068\pi\) | ||||
−0.921540 | + | 0.388283i | \(0.873068\pi\) | |||||||
\(660\) | −10.3431 | −0.402606 | ||||||||
\(661\) | 34.9706 | 1.36020 | 0.680099 | − | 0.733121i | \(-0.261937\pi\) | ||||
0.680099 | + | 0.733121i | \(0.261937\pi\) | |||||||
\(662\) | 10.8284 | 0.420859 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.79899 | −0.225044 | ||||||||
\(665\) | −22.6274 | −0.877454 | ||||||||
\(666\) | −3.17157 | −0.122896 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | −6.68629 | −0.258700 | ||||||||
\(669\) | 12.4853 | 0.482709 | ||||||||
\(670\) | 8.00000 | 0.309067 | ||||||||
\(671\) | 26.6274 | 1.02794 | ||||||||
\(672\) | 12.4853 | 0.481630 | ||||||||
\(673\) | 16.6274 | 0.640940 | 0.320470 | − | 0.947259i | \(-0.396159\pi\) | ||||
0.320470 | + | 0.947259i | \(0.396159\pi\) | |||||||
\(674\) | −3.85786 | −0.148599 | ||||||||
\(675\) | 3.00000 | 0.115470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.6863 | 1.02564 | 0.512819 | − | 0.858497i | \(-0.328601\pi\) | ||||
0.512819 | + | 0.858497i | \(0.328601\pi\) | |||||||
\(678\) | 2.20101 | 0.0845293 | ||||||||
\(679\) | 10.3431 | 0.396934 | ||||||||
\(680\) | 34.3431 | 1.31700 | ||||||||
\(681\) | 17.3137 | 0.663463 | ||||||||
\(682\) | −0.970563 | −0.0371648 | ||||||||
\(683\) | −47.9411 | −1.83442 | −0.917208 | − | 0.398408i | \(-0.869563\pi\) | ||||
−0.917208 | + | 0.398408i | \(0.869563\pi\) | |||||||
\(684\) | −5.17157 | −0.197740 | ||||||||
\(685\) | 30.6274 | 1.17021 | ||||||||
\(686\) | −7.02944 | −0.268385 | ||||||||
\(687\) | 1.31371 | 0.0501211 | ||||||||
\(688\) | −4.97056 | −0.189501 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.68629 | 0.178404 | ||||||||
\(691\) | 5.85786 | 0.222844 | 0.111422 | − | 0.993773i | \(-0.464460\pi\) | ||||
0.111422 | + | 0.993773i | \(0.464460\pi\) | |||||||
\(692\) | 21.3137 | 0.810226 | ||||||||
\(693\) | −5.65685 | −0.214886 | ||||||||
\(694\) | 3.59798 | 0.136577 | ||||||||
\(695\) | −20.6863 | −0.784676 | ||||||||
\(696\) | 3.17157 | 0.120218 | ||||||||
\(697\) | −39.5980 | −1.49988 | ||||||||
\(698\) | 1.51472 | 0.0573329 | ||||||||
\(699\) | 6.97056 | 0.263651 | ||||||||
\(700\) | 15.5147 | 0.586401 | ||||||||
\(701\) | 5.02944 | 0.189959 | 0.0949796 | − | 0.995479i | \(-0.469721\pi\) | ||||
0.0949796 | + | 0.995479i | \(0.469721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.6569 | 0.816804 | ||||||||
\(704\) | −8.34315 | −0.314444 | ||||||||
\(705\) | 32.9706 | 1.24174 | ||||||||
\(706\) | −13.8579 | −0.521548 | ||||||||
\(707\) | −21.6569 | −0.814490 | ||||||||
\(708\) | 14.0000 | 0.526152 | ||||||||
\(709\) | 4.62742 | 0.173786 | 0.0868931 | − | 0.996218i | \(-0.472306\pi\) | ||||
0.0868931 | + | 0.996218i | \(0.472306\pi\) | |||||||
\(710\) | 2.34315 | 0.0879367 | ||||||||
\(711\) | −11.3137 | −0.424297 | ||||||||
\(712\) | −23.5147 | −0.881251 | ||||||||
\(713\) | −4.68629 | −0.175503 | ||||||||
\(714\) | 8.97056 | 0.335715 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.6274 | 1.59306 | ||||||||
\(717\) | −2.00000 | −0.0746914 | ||||||||
\(718\) | 14.4853 | 0.540586 | ||||||||
\(719\) | −29.9411 | −1.11662 | −0.558308 | − | 0.829634i | \(-0.688549\pi\) | ||||
−0.558308 | + | 0.829634i | \(0.688549\pi\) | |||||||
\(720\) | 8.48528 | 0.316228 | ||||||||
\(721\) | −6.62742 | −0.246818 | ||||||||
\(722\) | 4.55635 | 0.169570 | ||||||||
\(723\) | −0.343146 | −0.0127617 | ||||||||
\(724\) | −25.5980 | −0.951341 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 2.89949 | 0.107610 | ||||||||
\(727\) | −10.3431 | −0.383606 | −0.191803 | − | 0.981433i | \(-0.561433\pi\) | ||||
−0.191803 | + | 0.981433i | \(0.561433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.402020 | 0.0148794 | ||||||||
\(731\) | −12.6863 | −0.469219 | ||||||||
\(732\) | −24.3431 | −0.899749 | ||||||||
\(733\) | 36.6274 | 1.35286 | 0.676432 | − | 0.736505i | \(-0.263525\pi\) | ||||
0.676432 | + | 0.736505i | \(0.263525\pi\) | |||||||
\(734\) | 9.94113 | 0.366934 | ||||||||
\(735\) | 2.82843 | 0.104328 | ||||||||
\(736\) | 17.6569 | 0.650840 | ||||||||
\(737\) | −13.6569 | −0.503057 | ||||||||
\(738\) | 2.14214 | 0.0788531 | ||||||||
\(739\) | 18.1421 | 0.667369 | 0.333685 | − | 0.942685i | \(-0.391708\pi\) | ||||
0.333685 | + | 0.942685i | \(0.391708\pi\) | |||||||
\(740\) | −39.5980 | −1.45565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.34315 | −0.0860196 | ||||||||
\(743\) | −2.00000 | −0.0733729 | −0.0366864 | − | 0.999327i | \(-0.511680\pi\) | ||||
−0.0366864 | + | 0.999327i | \(0.511680\pi\) | |||||||
\(744\) | 1.85786 | 0.0681126 | ||||||||
\(745\) | 25.9411 | 0.950409 | ||||||||
\(746\) | −4.14214 | −0.151654 | ||||||||
\(747\) | −3.65685 | −0.133797 | ||||||||
\(748\) | −28.0000 | −1.02378 | ||||||||
\(749\) | 32.0000 | 1.16925 | ||||||||
\(750\) | 2.34315 | 0.0855596 | ||||||||
\(751\) | −0.970563 | −0.0354163 | −0.0177082 | − | 0.999843i | \(-0.505637\pi\) | ||||
−0.0177082 | + | 0.999843i | \(0.505637\pi\) | |||||||
\(752\) | 34.9706 | 1.27525 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.94113 | 0.361795 | ||||||||
\(756\) | 5.17157 | 0.188088 | ||||||||
\(757\) | 51.9411 | 1.88783 | 0.943916 | − | 0.330185i | \(-0.107111\pi\) | ||||
0.943916 | + | 0.330185i | \(0.107111\pi\) | |||||||
\(758\) | 0.201010 | 0.00730102 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 12.6863 | 0.460180 | ||||||||
\(761\) | −32.4853 | −1.17759 | −0.588795 | − | 0.808282i | \(-0.700398\pi\) | ||||
−0.588795 | + | 0.808282i | \(0.700398\pi\) | |||||||
\(762\) | −2.34315 | −0.0848832 | ||||||||
\(763\) | 15.0294 | 0.544102 | ||||||||
\(764\) | −6.05887 | −0.219202 | ||||||||
\(765\) | 21.6569 | 0.783005 | ||||||||
\(766\) | 12.8284 | 0.463510 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.97056 | 0.143275 | ||||||||
\(769\) | −42.0000 | −1.51456 | −0.757279 | − | 0.653091i | \(-0.773472\pi\) | ||||
−0.757279 | + | 0.653091i | \(0.773472\pi\) | |||||||
\(770\) | 6.62742 | 0.238836 | ||||||||
\(771\) | −4.34315 | −0.156415 | ||||||||
\(772\) | 9.71573 | 0.349677 | ||||||||
\(773\) | −34.1421 | −1.22801 | −0.614004 | − | 0.789303i | \(-0.710442\pi\) | ||||
−0.614004 | + | 0.789303i | \(0.710442\pi\) | |||||||
\(774\) | 0.686292 | 0.0246682 | ||||||||
\(775\) | 3.51472 | 0.126252 | ||||||||
\(776\) | −5.79899 | −0.208172 | ||||||||
\(777\) | −21.6569 | −0.776935 | ||||||||
\(778\) | 11.1716 | 0.400520 | ||||||||
\(779\) | −14.6274 | −0.524082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 12.6863 | 0.453661 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | −28.2843 | −1.00951 | ||||||||
\(786\) | 3.31371 | 0.118196 | ||||||||
\(787\) | 40.7696 | 1.45328 | 0.726639 | − | 0.687020i | \(-0.241081\pi\) | ||||
0.726639 | + | 0.687020i | \(0.241081\pi\) | |||||||
\(788\) | 0.887302 | 0.0316088 | ||||||||
\(789\) | 12.0000 | 0.427211 | ||||||||
\(790\) | 13.2548 | 0.471586 | ||||||||
\(791\) | 15.0294 | 0.534385 | ||||||||
\(792\) | 3.17157 | 0.112697 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.8284 | 0.455264 | ||||||||
\(795\) | −5.65685 | −0.200628 | ||||||||
\(796\) | −39.5980 | −1.40351 | ||||||||
\(797\) | 24.3431 | 0.862278 | 0.431139 | − | 0.902285i | \(-0.358112\pi\) | ||||
0.431139 | + | 0.902285i | \(0.358112\pi\) | |||||||
\(798\) | 3.31371 | 0.117304 | ||||||||
\(799\) | 89.2548 | 3.15761 | ||||||||
\(800\) | −13.2426 | −0.468198 | ||||||||
\(801\) | −14.8284 | −0.523937 | ||||||||
\(802\) | 10.8284 | 0.382365 | ||||||||
\(803\) | −0.686292 | −0.0242187 | ||||||||
\(804\) | 12.4853 | 0.440322 | ||||||||
\(805\) | 32.0000 | 1.12785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | 12.1421 | 0.427159 | ||||||||
\(809\) | 18.6863 | 0.656975 | 0.328488 | − | 0.944508i | \(-0.393461\pi\) | ||||
0.328488 | + | 0.944508i | \(0.393461\pi\) | |||||||
\(810\) | −1.17157 | −0.0411649 | ||||||||
\(811\) | 30.1421 | 1.05843 | 0.529217 | − | 0.848487i | \(-0.322486\pi\) | ||||
0.529217 | + | 0.848487i | \(0.322486\pi\) | |||||||
\(812\) | 10.3431 | 0.362973 | ||||||||
\(813\) | 27.7990 | 0.974953 | ||||||||
\(814\) | −6.34315 | −0.222327 | ||||||||
\(815\) | −53.2548 | −1.86544 | ||||||||
\(816\) | 22.9706 | 0.804131 | ||||||||
\(817\) | −4.68629 | −0.163953 | ||||||||
\(818\) | −14.4853 | −0.506466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.7452 | 0.933982 | ||||||||
\(821\) | 23.7990 | 0.830590 | 0.415295 | − | 0.909687i | \(-0.363678\pi\) | ||||
0.415295 | + | 0.909687i | \(0.363678\pi\) | |||||||
\(822\) | −4.48528 | −0.156442 | ||||||||
\(823\) | 15.0294 | 0.523893 | 0.261947 | − | 0.965082i | \(-0.415636\pi\) | ||||
0.261947 | + | 0.965082i | \(0.415636\pi\) | |||||||
\(824\) | 3.71573 | 0.129444 | ||||||||
\(825\) | 6.00000 | 0.208893 | ||||||||
\(826\) | −8.97056 | −0.312126 | ||||||||
\(827\) | 26.0000 | 0.904109 | 0.452054 | − | 0.891990i | \(-0.350691\pi\) | ||||
0.452054 | + | 0.891990i | \(0.350691\pi\) | |||||||
\(828\) | 7.31371 | 0.254169 | ||||||||
\(829\) | −17.3137 | −0.601330 | −0.300665 | − | 0.953730i | \(-0.597209\pi\) | ||||
−0.300665 | + | 0.953730i | \(0.597209\pi\) | |||||||
\(830\) | 4.28427 | 0.148709 | ||||||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.65685 | 0.265294 | ||||||||
\(834\) | 3.02944 | 0.104901 | ||||||||
\(835\) | 10.3431 | 0.357939 | ||||||||
\(836\) | −10.3431 | −0.357725 | ||||||||
\(837\) | 1.17157 | 0.0404955 | ||||||||
\(838\) | −6.05887 | −0.209300 | ||||||||
\(839\) | −43.2548 | −1.49332 | −0.746661 | − | 0.665204i | \(-0.768344\pi\) | ||||
−0.746661 | + | 0.665204i | \(0.768344\pi\) | |||||||
\(840\) | −12.6863 | −0.437719 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 15.4558 | 0.532644 | ||||||||
\(843\) | −21.1716 | −0.729188 | ||||||||
\(844\) | 21.9411 | 0.755245 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.82843 | −0.166005 | ||||||||
\(847\) | 19.7990 | 0.680301 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 28.9706 | 0.994267 | ||||||||
\(850\) | −9.51472 | −0.326352 | ||||||||
\(851\) | −30.6274 | −1.04989 | ||||||||
\(852\) | 3.65685 | 0.125282 | ||||||||
\(853\) | −3.65685 | −0.125208 | −0.0626042 | − | 0.998038i | \(-0.519941\pi\) | ||||
−0.0626042 | + | 0.998038i | \(0.519941\pi\) | |||||||
\(854\) | 15.5980 | 0.533752 | ||||||||
\(855\) | 8.00000 | 0.273594 | ||||||||
\(856\) | −17.9411 | −0.613215 | ||||||||
\(857\) | −49.5980 | −1.69423 | −0.847117 | − | 0.531406i | \(-0.821664\pi\) | ||||
−0.847117 | + | 0.531406i | \(0.821664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.686292 | −0.0234160 | −0.0117080 | − | 0.999931i | \(-0.503727\pi\) | ||||
−0.0117080 | + | 0.999931i | \(0.503727\pi\) | |||||||
\(860\) | 8.56854 | 0.292185 | ||||||||
\(861\) | 14.6274 | 0.498501 | ||||||||
\(862\) | 3.45584 | 0.117707 | ||||||||
\(863\) | 28.3431 | 0.964812 | 0.482406 | − | 0.875948i | \(-0.339763\pi\) | ||||
0.482406 | + | 0.875948i | \(0.339763\pi\) | |||||||
\(864\) | −4.41421 | −0.150175 | ||||||||
\(865\) | −32.9706 | −1.12103 | ||||||||
\(866\) | 8.82843 | 0.300002 | ||||||||
\(867\) | 41.6274 | 1.41374 | ||||||||
\(868\) | 6.05887 | 0.205652 | ||||||||
\(869\) | −22.6274 | −0.767583 | ||||||||
\(870\) | −2.34315 | −0.0794401 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.42641 | −0.285354 | ||||||||
\(873\) | −3.65685 | −0.123766 | ||||||||
\(874\) | 4.68629 | 0.158516 | ||||||||
\(875\) | 16.0000 | 0.540899 | ||||||||
\(876\) | 0.627417 | 0.0211985 | ||||||||
\(877\) | −42.2843 | −1.42784 | −0.713919 | − | 0.700228i | \(-0.753082\pi\) | ||||
−0.713919 | + | 0.700228i | \(0.753082\pi\) | |||||||
\(878\) | −7.02944 | −0.237232 | ||||||||
\(879\) | −2.14214 | −0.0722524 | ||||||||
\(880\) | 16.9706 | 0.572078 | ||||||||
\(881\) | −25.5980 | −0.862418 | −0.431209 | − | 0.902252i | \(-0.641913\pi\) | ||||
−0.431209 | + | 0.902252i | \(0.641913\pi\) | |||||||
\(882\) | −0.414214 | −0.0139473 | ||||||||
\(883\) | 27.5980 | 0.928746 | 0.464373 | − | 0.885640i | \(-0.346280\pi\) | ||||
0.464373 | + | 0.885640i | \(0.346280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.6569 | −0.727987 | ||||||||
\(886\) | 10.7452 | 0.360991 | ||||||||
\(887\) | −8.00000 | −0.268614 | −0.134307 | − | 0.990940i | \(-0.542881\pi\) | ||||
−0.134307 | + | 0.990940i | \(0.542881\pi\) | |||||||
\(888\) | 12.1421 | 0.407463 | ||||||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 17.3726 | 0.582330 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | −22.8284 | −0.764352 | ||||||||
\(893\) | 32.9706 | 1.10332 | ||||||||
\(894\) | −3.79899 | −0.127057 | ||||||||
\(895\) | −65.9411 | −2.20417 | ||||||||
\(896\) | −29.8579 | −0.997481 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.1716 | −0.439541 | ||||||||
\(899\) | 2.34315 | 0.0781483 | ||||||||
\(900\) | −5.48528 | −0.182843 | ||||||||
\(901\) | −15.3137 | −0.510174 | ||||||||
\(902\) | 4.28427 | 0.142651 | ||||||||
\(903\) | 4.68629 | 0.155950 | ||||||||
\(904\) | −8.42641 | −0.280258 | ||||||||
\(905\) | 39.5980 | 1.31628 | ||||||||
\(906\) | −1.45584 | −0.0483672 | ||||||||
\(907\) | −12.9706 | −0.430680 | −0.215340 | − | 0.976539i | \(-0.569086\pi\) | ||||
−0.215340 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(908\) | −31.6569 | −1.05057 | ||||||||
\(909\) | 7.65685 | 0.253962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | 8.48528 | 0.280976 | ||||||||
\(913\) | −7.31371 | −0.242048 | ||||||||
\(914\) | −3.17157 | −0.104906 | ||||||||
\(915\) | 37.6569 | 1.24490 | ||||||||
\(916\) | −2.40202 | −0.0793650 | ||||||||
\(917\) | 22.6274 | 0.747223 | ||||||||
\(918\) | −3.17157 | −0.104678 | ||||||||
\(919\) | 3.31371 | 0.109309 | 0.0546546 | − | 0.998505i | \(-0.482594\pi\) | ||||
0.0546546 | + | 0.998505i | \(0.482594\pi\) | |||||||
\(920\) | −17.9411 | −0.591501 | ||||||||
\(921\) | 22.8284 | 0.752222 | ||||||||
\(922\) | 2.14214 | 0.0705475 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 10.3431 | 0.340265 | ||||||||
\(925\) | 22.9706 | 0.755267 | ||||||||
\(926\) | −10.1421 | −0.333291 | ||||||||
\(927\) | 2.34315 | 0.0769590 | ||||||||
\(928\) | −8.82843 | −0.289807 | ||||||||
\(929\) | −11.7990 | −0.387112 | −0.193556 | − | 0.981089i | \(-0.562002\pi\) | ||||
−0.193556 | + | 0.981089i | \(0.562002\pi\) | |||||||
\(930\) | −1.37258 | −0.0450088 | ||||||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | −12.7452 | −0.417482 | ||||||||
\(933\) | −10.6274 | −0.347926 | ||||||||
\(934\) | 3.31371 | 0.108428 | ||||||||
\(935\) | 43.3137 | 1.41651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.3137 | −0.696289 | −0.348144 | − | 0.937441i | \(-0.613188\pi\) | ||||
−0.348144 | + | 0.937441i | \(0.613188\pi\) | |||||||
\(938\) | −8.00000 | −0.261209 | ||||||||
\(939\) | 6.00000 | 0.195803 | ||||||||
\(940\) | −60.2843 | −1.96626 | ||||||||
\(941\) | −34.1421 | −1.11300 | −0.556501 | − | 0.830847i | \(-0.687856\pi\) | ||||
−0.556501 | + | 0.830847i | \(0.687856\pi\) | |||||||
\(942\) | 4.14214 | 0.134958 | ||||||||
\(943\) | 20.6863 | 0.673638 | ||||||||
\(944\) | −22.9706 | −0.747628 | ||||||||
\(945\) | −8.00000 | −0.260240 | ||||||||
\(946\) | 1.37258 | 0.0446265 | ||||||||
\(947\) | 21.0294 | 0.683365 | 0.341682 | − | 0.939815i | \(-0.389003\pi\) | ||||
0.341682 | + | 0.939815i | \(0.389003\pi\) | |||||||
\(948\) | 20.6863 | 0.671860 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.51472 | −0.114033 | ||||||||
\(951\) | −8.48528 | −0.275154 | ||||||||
\(952\) | −34.3431 | −1.11307 | ||||||||
\(953\) | 40.3431 | 1.30684 | 0.653421 | − | 0.756994i | \(-0.273333\pi\) | ||||
0.653421 | + | 0.756994i | \(0.273333\pi\) | |||||||
\(954\) | 0.828427 | 0.0268213 | ||||||||
\(955\) | 9.37258 | 0.303290 | ||||||||
\(956\) | 3.65685 | 0.118271 | ||||||||
\(957\) | 4.00000 | 0.129302 | ||||||||
\(958\) | 10.4853 | 0.338764 | ||||||||
\(959\) | −30.6274 | −0.989011 | ||||||||
\(960\) | −11.7990 | −0.380811 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.3137 | −0.364579 | ||||||||
\(964\) | 0.627417 | 0.0202077 | ||||||||
\(965\) | −15.0294 | −0.483815 | ||||||||
\(966\) | −4.68629 | −0.150779 | ||||||||
\(967\) | −18.1421 | −0.583412 | −0.291706 | − | 0.956508i | \(-0.594223\pi\) | ||||
−0.291706 | + | 0.956508i | \(0.594223\pi\) | |||||||
\(968\) | −11.1005 | −0.356784 | ||||||||
\(969\) | 21.6569 | 0.695718 | ||||||||
\(970\) | 4.28427 | 0.137560 | ||||||||
\(971\) | −15.3137 | −0.491440 | −0.245720 | − | 0.969341i | \(-0.579024\pi\) | ||||
−0.245720 | + | 0.969341i | \(0.579024\pi\) | |||||||
\(972\) | −1.82843 | −0.0586468 | ||||||||
\(973\) | 20.6863 | 0.663172 | ||||||||
\(974\) | −3.23045 | −0.103510 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.9411 | 1.27848 | ||||||||
\(977\) | −42.1421 | −1.34825 | −0.674123 | − | 0.738619i | \(-0.735478\pi\) | ||||
−0.674123 | + | 0.738619i | \(0.735478\pi\) | |||||||
\(978\) | 7.79899 | 0.249384 | ||||||||
\(979\) | −29.6569 | −0.947837 | ||||||||
\(980\) | −5.17157 | −0.165200 | ||||||||
\(981\) | −5.31371 | −0.169654 | ||||||||
\(982\) | −12.6863 | −0.404836 | ||||||||
\(983\) | −25.3137 | −0.807382 | −0.403691 | − | 0.914895i | \(-0.632273\pi\) | ||||
−0.403691 | + | 0.914895i | \(0.632273\pi\) | |||||||
\(984\) | −8.20101 | −0.261439 | ||||||||
\(985\) | −1.37258 | −0.0437341 | ||||||||
\(986\) | −6.34315 | −0.202007 | ||||||||
\(987\) | −32.9706 | −1.04946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.62742 | 0.210740 | ||||||||
\(990\) | −2.34315 | −0.0744701 | ||||||||
\(991\) | 4.68629 | 0.148865 | 0.0744325 | − | 0.997226i | \(-0.476285\pi\) | ||||
0.0744325 | + | 0.997226i | \(0.476285\pi\) | |||||||
\(992\) | −5.17157 | −0.164198 | ||||||||
\(993\) | −26.1421 | −0.829596 | ||||||||
\(994\) | −2.34315 | −0.0743201 | ||||||||
\(995\) | 61.2548 | 1.94191 | ||||||||
\(996\) | 6.68629 | 0.211863 | ||||||||
\(997\) | −39.2548 | −1.24321 | −0.621607 | − | 0.783330i | \(-0.713520\pi\) | ||||
−0.621607 | + | 0.783330i | \(0.713520\pi\) | |||||||
\(998\) | 10.8284 | 0.342768 | ||||||||
\(999\) | 7.65685 | 0.242252 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))