Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7938,2,Mod(1,7938)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7938, 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("7938.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7938.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: | \(63.3852491245\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.239123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7938.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.76088 | 0.787488 | 0.393744 | − | 0.919220i | \(-0.371180\pi\) | ||||
0.393744 | + | 0.919220i | \(0.371180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.76088 | 0.556838 | ||||||||
\(11\) | 6.12476 | 1.84669 | 0.923343 | − | 0.383977i | \(-0.125446\pi\) | ||||
0.923343 | + | 0.383977i | \(0.125446\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.760877 | 0.211029 | 0.105515 | − | 0.994418i | \(-0.466351\pi\) | ||||
0.105515 | + | 0.994418i | \(0.466351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.84213 | 1.65946 | 0.829731 | − | 0.558164i | \(-0.188494\pi\) | ||||
0.829731 | + | 0.558164i | \(0.188494\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94282 | −0.445713 | −0.222857 | − | 0.974851i | \(-0.571538\pi\) | ||||
−0.222857 | + | 0.974851i | \(0.571538\pi\) | |||||||
\(20\) | 1.76088 | 0.393744 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.12476 | 1.30580 | ||||||||
\(23\) | −0.421067 | −0.0877985 | −0.0438992 | − | 0.999036i | \(-0.513978\pi\) | ||||
−0.0438992 | + | 0.999036i | \(0.513978\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.89931 | −0.379863 | ||||||||
\(26\) | 0.760877 | 0.149220 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.46457 | −0.271964 | −0.135982 | − | 0.990711i | \(-0.543419\pi\) | ||||
−0.135982 | + | 0.990711i | \(0.543419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.70370 | 1.38362 | 0.691812 | − | 0.722077i | \(-0.256813\pi\) | ||||
0.691812 | + | 0.722077i | \(0.256813\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.84213 | 1.17342 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.88564 | −0.474396 | −0.237198 | − | 0.971461i | \(-0.576229\pi\) | ||||
−0.237198 | + | 0.971461i | \(0.576229\pi\) | |||||||
\(38\) | −1.94282 | −0.315167 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.76088 | 0.278419 | ||||||||
\(41\) | 6.94282 | 1.08429 | 0.542143 | − | 0.840286i | \(-0.317613\pi\) | ||||
0.542143 | + | 0.840286i | \(0.317613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.66019 | −1.32067 | −0.660333 | − | 0.750973i | \(-0.729585\pi\) | ||||
−0.660333 | + | 0.750973i | \(0.729585\pi\) | |||||||
\(44\) | 6.12476 | 0.923343 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.421067 | −0.0620829 | ||||||||
\(47\) | 1.66019 | 0.242164 | 0.121082 | − | 0.992643i | \(-0.461364\pi\) | ||||
0.121082 | + | 0.992643i | \(0.461364\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.89931 | −0.268603 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.760877 | 0.105515 | ||||||||
\(53\) | 0.225450 | 0.0309680 | 0.0154840 | − | 0.999880i | \(-0.495071\pi\) | ||||
0.0154840 | + | 0.999880i | \(0.495071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7850 | 1.45424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.46457 | −0.192308 | ||||||||
\(59\) | 1.98633 | 0.258598 | 0.129299 | − | 0.991606i | \(-0.458727\pi\) | ||||
0.129299 | + | 0.991606i | \(0.458727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3502 | −1.32521 | −0.662605 | − | 0.748969i | \(-0.730549\pi\) | ||||
−0.662605 | + | 0.748969i | \(0.730549\pi\) | |||||||
\(62\) | 7.70370 | 0.978370 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.33981 | 0.166183 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.78495 | 0.828914 | 0.414457 | − | 0.910069i | \(-0.363972\pi\) | ||||
0.414457 | + | 0.910069i | \(0.363972\pi\) | |||||||
\(68\) | 6.84213 | 0.829731 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7850 | 1.27994 | 0.639969 | − | 0.768401i | \(-0.278947\pi\) | ||||
0.639969 | + | 0.768401i | \(0.278947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.306707 | −0.0358973 | −0.0179487 | − | 0.999839i | \(-0.505714\pi\) | ||||
−0.0179487 | + | 0.999839i | \(0.505714\pi\) | |||||||
\(74\) | −2.88564 | −0.335449 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.94282 | −0.222857 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4451 | −1.51270 | −0.756348 | − | 0.654169i | \(-0.773018\pi\) | ||||
−0.756348 | + | 0.654169i | \(0.773018\pi\) | |||||||
\(80\) | 1.76088 | 0.196872 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.94282 | 0.766706 | ||||||||
\(83\) | 3.12476 | 0.342987 | 0.171494 | − | 0.985185i | \(-0.445141\pi\) | ||||
0.171494 | + | 0.985185i | \(0.445141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0482 | 1.30681 | ||||||||
\(86\) | −8.66019 | −0.933852 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.12476 | 0.652902 | ||||||||
\(89\) | −2.60301 | −0.275919 | −0.137959 | − | 0.990438i | \(-0.544054\pi\) | ||||
−0.137959 | + | 0.990438i | \(0.544054\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.421067 | −0.0438992 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.66019 | 0.171236 | ||||||||
\(95\) | −3.42107 | −0.350994 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.63611 | 0.369191 | 0.184596 | − | 0.982815i | \(-0.440902\pi\) | ||||
0.184596 | + | 0.982815i | \(0.440902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.89931 | −0.189931 | ||||||||
\(101\) | −8.01040 | −0.797065 | −0.398532 | − | 0.917154i | \(-0.630480\pi\) | ||||
−0.398532 | + | 0.917154i | \(0.630480\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.82846 | −0.672828 | −0.336414 | − | 0.941714i | \(-0.609214\pi\) | ||||
−0.336414 | + | 0.941714i | \(0.609214\pi\) | |||||||
\(104\) | 0.760877 | 0.0746101 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.225450 | 0.0218977 | ||||||||
\(107\) | −3.54583 | −0.342788 | −0.171394 | − | 0.985203i | \(-0.554827\pi\) | ||||
−0.171394 | + | 0.985203i | \(0.554827\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.703697 | −0.0674019 | −0.0337010 | − | 0.999432i | \(-0.510729\pi\) | ||||
−0.0337010 | + | 0.999432i | \(0.510729\pi\) | |||||||
\(110\) | 10.7850 | 1.02830 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.50232 | −0.799831 | −0.399916 | − | 0.916552i | \(-0.630961\pi\) | ||||
−0.399916 | + | 0.916552i | \(0.630961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.741446 | −0.0691402 | ||||||||
\(116\) | −1.46457 | −0.135982 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.98633 | 0.182856 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.5127 | 2.41025 | ||||||||
\(122\) | −10.3502 | −0.937064 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.70370 | 0.691812 | ||||||||
\(125\) | −12.1488 | −1.08663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.9532 | −1.68183 | −0.840913 | − | 0.541170i | \(-0.817982\pi\) | ||||
−0.840913 | + | 0.541170i | \(0.817982\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.33981 | 0.117509 | ||||||||
\(131\) | −7.29303 | −0.637195 | −0.318598 | − | 0.947890i | \(-0.603212\pi\) | ||||
−0.318598 | + | 0.947890i | \(0.603212\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.78495 | 0.586131 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.84213 | 0.586708 | ||||||||
\(137\) | −8.18194 | −0.699031 | −0.349515 | − | 0.936931i | \(-0.613654\pi\) | ||||
−0.349515 | + | 0.936931i | \(0.613654\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4646 | 1.05723 | 0.528616 | − | 0.848861i | \(-0.322711\pi\) | ||||
0.528616 | + | 0.848861i | \(0.322711\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.7850 | 0.905053 | ||||||||
\(143\) | 4.66019 | 0.389705 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.57893 | −0.214169 | ||||||||
\(146\) | −0.306707 | −0.0253832 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.88564 | −0.237198 | ||||||||
\(149\) | 8.82846 | 0.723256 | 0.361628 | − | 0.932323i | \(-0.382221\pi\) | ||||
0.361628 | + | 0.932323i | \(0.382221\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9863 | −1.21957 | −0.609785 | − | 0.792567i | \(-0.708744\pi\) | ||||
−0.609785 | + | 0.792567i | \(0.708744\pi\) | |||||||
\(152\) | −1.94282 | −0.157584 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.5653 | 1.08959 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.9806 | 1.51481 | 0.757407 | − | 0.652943i | \(-0.226466\pi\) | ||||
0.757407 | + | 0.652943i | \(0.226466\pi\) | |||||||
\(158\) | −13.4451 | −1.06964 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.76088 | 0.139210 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.0377 | 1.17785 | 0.588924 | − | 0.808189i | \(-0.299552\pi\) | ||||
0.588924 | + | 0.808189i | \(0.299552\pi\) | |||||||
\(164\) | 6.94282 | 0.542143 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.12476 | 0.242529 | ||||||||
\(167\) | −1.14419 | −0.0885404 | −0.0442702 | − | 0.999020i | \(-0.514096\pi\) | ||||
−0.0442702 | + | 0.999020i | \(0.514096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4211 | −0.955467 | ||||||||
\(170\) | 12.0482 | 0.924051 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.66019 | −0.660333 | ||||||||
\(173\) | 0.497677 | 0.0378377 | 0.0189188 | − | 0.999821i | \(-0.493978\pi\) | ||||
0.0189188 | + | 0.999821i | \(0.493978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.12476 | 0.461671 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.60301 | −0.195104 | ||||||||
\(179\) | −8.82846 | −0.659870 | −0.329935 | − | 0.944004i | \(-0.607027\pi\) | ||||
−0.329935 | + | 0.944004i | \(0.607027\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.32941 | 0.0988140 | 0.0494070 | − | 0.998779i | \(-0.484267\pi\) | ||||
0.0494070 | + | 0.998779i | \(0.484267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.421067 | −0.0310414 | ||||||||
\(185\) | −5.08126 | −0.373581 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 41.9064 | 3.06450 | ||||||||
\(188\) | 1.66019 | 0.121082 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.42107 | −0.248190 | ||||||||
\(191\) | −16.1683 | −1.16989 | −0.584947 | − | 0.811071i | \(-0.698885\pi\) | ||||
−0.584947 | + | 0.811071i | \(0.698885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1683 | −1.01985 | −0.509927 | − | 0.860218i | \(-0.670328\pi\) | ||||
−0.509927 | + | 0.860218i | \(0.670328\pi\) | |||||||
\(194\) | 3.63611 | 0.261058 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.8421 | 1.12871 | 0.564353 | − | 0.825534i | \(-0.309126\pi\) | ||||
0.564353 | + | 0.825534i | \(0.309126\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.94282 | 0.633940 | 0.316970 | − | 0.948436i | \(-0.397335\pi\) | ||||
0.316970 | + | 0.948436i | \(0.397335\pi\) | |||||||
\(200\) | −1.89931 | −0.134302 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.01040 | −0.563610 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.2255 | 0.853862 | ||||||||
\(206\) | −6.82846 | −0.475761 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.760877 | 0.0527573 | ||||||||
\(209\) | −11.8993 | −0.823093 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.7713 | −1.56764 | −0.783820 | − | 0.620988i | \(-0.786731\pi\) | ||||
−0.783820 | + | 0.620988i | \(0.786731\pi\) | |||||||
\(212\) | 0.225450 | 0.0154840 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.54583 | −0.242388 | ||||||||
\(215\) | −15.2495 | −1.04001 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.703697 | −0.0476604 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.7850 | 0.727121 | ||||||||
\(221\) | 5.20602 | 0.350195 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8856 | 0.862886 | 0.431443 | − | 0.902140i | \(-0.358005\pi\) | ||||
0.431443 | + | 0.902140i | \(0.358005\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.50232 | −0.565566 | ||||||||
\(227\) | 21.9967 | 1.45997 | 0.729987 | − | 0.683461i | \(-0.239526\pi\) | ||||
0.729987 | + | 0.683461i | \(0.239526\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.79863 | −0.251020 | −0.125510 | − | 0.992092i | \(-0.540057\pi\) | ||||
−0.125510 | + | 0.992092i | \(0.540057\pi\) | |||||||
\(230\) | −0.741446 | −0.0488895 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.46457 | −0.0961540 | ||||||||
\(233\) | 6.67059 | 0.437005 | 0.218503 | − | 0.975836i | \(-0.429883\pi\) | ||||
0.218503 | + | 0.975836i | \(0.429883\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.92339 | 0.190701 | ||||||||
\(236\) | 1.98633 | 0.129299 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6408 | 1.01172 | 0.505858 | − | 0.862617i | \(-0.331176\pi\) | ||||
0.505858 | + | 0.862617i | \(0.331176\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.4120 | 1.37927 | 0.689635 | − | 0.724157i | \(-0.257771\pi\) | ||||
0.689635 | + | 0.724157i | \(0.257771\pi\) | |||||||
\(242\) | 26.5127 | 1.70430 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.3502 | −0.662605 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.47825 | −0.0940586 | ||||||||
\(248\) | 7.70370 | 0.489185 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.1488 | −0.768360 | ||||||||
\(251\) | −23.6030 | −1.48981 | −0.744904 | − | 0.667171i | \(-0.767505\pi\) | ||||
−0.744904 | + | 0.667171i | \(0.767505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.57893 | −0.162136 | ||||||||
\(254\) | −18.9532 | −1.18923 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.2599 | 1.26378 | 0.631890 | − | 0.775058i | \(-0.282279\pi\) | ||||
0.631890 | + | 0.775058i | \(0.282279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.33981 | 0.0830915 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.29303 | −0.450565 | ||||||||
\(263\) | −22.4887 | −1.38671 | −0.693355 | − | 0.720596i | \(-0.743868\pi\) | ||||
−0.693355 | + | 0.720596i | \(0.743868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.396990 | 0.0243869 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.78495 | 0.414457 | ||||||||
\(269\) | 25.3412 | 1.54508 | 0.772540 | − | 0.634966i | \(-0.218986\pi\) | ||||
0.772540 | + | 0.634966i | \(0.218986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7576 | 0.835715 | 0.417858 | − | 0.908513i | \(-0.362781\pi\) | ||||
0.417858 | + | 0.908513i | \(0.362781\pi\) | |||||||
\(272\) | 6.84213 | 0.414865 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.18194 | −0.494289 | ||||||||
\(275\) | −11.6328 | −0.701487 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.28263 | −0.197234 | −0.0986171 | − | 0.995125i | \(-0.531442\pi\) | ||||
−0.0986171 | + | 0.995125i | \(0.531442\pi\) | |||||||
\(278\) | 12.4646 | 0.747575 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.26896 | −0.0756996 | −0.0378498 | − | 0.999283i | \(-0.512051\pi\) | ||||
−0.0378498 | + | 0.999283i | \(0.512051\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.19235 | −0.486984 | −0.243492 | − | 0.969903i | \(-0.578293\pi\) | ||||
−0.243492 | + | 0.969903i | \(0.578293\pi\) | |||||||
\(284\) | 10.7850 | 0.639969 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.66019 | 0.275563 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.8148 | 1.75381 | ||||||||
\(290\) | −2.57893 | −0.151440 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.306707 | −0.0179487 | ||||||||
\(293\) | −15.4509 | −0.902651 | −0.451326 | − | 0.892359i | \(-0.649049\pi\) | ||||
−0.451326 | + | 0.892359i | \(0.649049\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.49768 | 0.203643 | ||||||||
\(296\) | −2.88564 | −0.167724 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.82846 | 0.511419 | ||||||||
\(299\) | −0.320380 | −0.0185280 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.9863 | −0.862366 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.94282 | −0.111428 | ||||||||
\(305\) | −18.2255 | −1.04359 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.89931 | 0.279619 | 0.139809 | − | 0.990178i | \(-0.455351\pi\) | ||||
0.139809 | + | 0.990178i | \(0.455351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.5653 | 0.770455 | ||||||||
\(311\) | −7.69002 | −0.436061 | −0.218031 | − | 0.975942i | \(-0.569963\pi\) | ||||
−0.218031 | + | 0.975942i | \(0.569963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.72313 | −0.0973969 | −0.0486985 | − | 0.998814i | \(-0.515507\pi\) | ||||
−0.0486985 | + | 0.998814i | \(0.515507\pi\) | |||||||
\(314\) | 18.9806 | 1.07114 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.4451 | −0.756348 | ||||||||
\(317\) | 33.2028 | 1.86485 | 0.932426 | − | 0.361361i | \(-0.117688\pi\) | ||||
0.932426 | + | 0.361361i | \(0.117688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.97017 | −0.502233 | ||||||||
\(320\) | 1.76088 | 0.0984360 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.2930 | −0.739644 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.44514 | −0.0801621 | ||||||||
\(326\) | 15.0377 | 0.832864 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.94282 | 0.383353 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.88891 | 0.158789 | 0.0793944 | − | 0.996843i | \(-0.474701\pi\) | ||||
0.0793944 | + | 0.996843i | \(0.474701\pi\) | |||||||
\(332\) | 3.12476 | 0.171494 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.14419 | −0.0626075 | ||||||||
\(335\) | 11.9475 | 0.652760 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.72313 | 0.475179 | 0.237590 | − | 0.971366i | \(-0.423643\pi\) | ||||
0.237590 | + | 0.971366i | \(0.423643\pi\) | |||||||
\(338\) | −12.4211 | −0.675617 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.0482 | 0.653403 | ||||||||
\(341\) | 47.1833 | 2.55512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.66019 | −0.466926 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.497677 | 0.0267553 | ||||||||
\(347\) | 9.69467 | 0.520437 | 0.260219 | − | 0.965550i | \(-0.416205\pi\) | ||||
0.260219 | + | 0.965550i | \(0.416205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.3984 | −1.52013 | −0.760065 | − | 0.649847i | \(-0.774833\pi\) | ||||
−0.760065 | + | 0.649847i | \(0.774833\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.12476 | 0.326451 | ||||||||
\(353\) | −4.39372 | −0.233854 | −0.116927 | − | 0.993141i | \(-0.537304\pi\) | ||||
−0.116927 | + | 0.993141i | \(0.537304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.9910 | 1.00794 | ||||||||
\(356\) | −2.60301 | −0.137959 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.82846 | −0.466599 | ||||||||
\(359\) | −32.1592 | −1.69730 | −0.848650 | − | 0.528955i | \(-0.822584\pi\) | ||||
−0.848650 | + | 0.528955i | \(0.822584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2255 | −0.801339 | ||||||||
\(362\) | 1.32941 | 0.0698721 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.540073 | −0.0282687 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.6030 | 1.80626 | 0.903131 | − | 0.429365i | \(-0.141262\pi\) | ||||
0.903131 | + | 0.429365i | \(0.141262\pi\) | |||||||
\(368\) | −0.421067 | −0.0219496 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.08126 | −0.264162 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9759 | 0.568312 | 0.284156 | − | 0.958778i | \(-0.408287\pi\) | ||||
0.284156 | + | 0.958778i | \(0.408287\pi\) | |||||||
\(374\) | 41.9064 | 2.16693 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.66019 | 0.0856178 | ||||||||
\(377\) | −1.11436 | −0.0573925 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.9877 | 1.74583 | 0.872916 | − | 0.487871i | \(-0.162226\pi\) | ||||
0.872916 | + | 0.487871i | \(0.162226\pi\) | |||||||
\(380\) | −3.42107 | −0.175497 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.1683 | −0.827241 | ||||||||
\(383\) | −21.0241 | −1.07428 | −0.537140 | − | 0.843493i | \(-0.680495\pi\) | ||||
−0.537140 | + | 0.843493i | \(0.680495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.1683 | −0.721146 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.63611 | 0.184596 | ||||||||
\(389\) | 13.7382 | 0.696553 | 0.348277 | − | 0.937392i | \(-0.386767\pi\) | ||||
0.348277 | + | 0.937392i | \(0.386767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.88099 | −0.145698 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.8421 | 0.798115 | ||||||||
\(395\) | −23.6752 | −1.19123 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.15787 | 0.359243 | 0.179622 | − | 0.983736i | \(-0.442513\pi\) | ||||
0.179622 | + | 0.983736i | \(0.442513\pi\) | |||||||
\(398\) | 8.94282 | 0.448263 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.89931 | −0.0949657 | ||||||||
\(401\) | −9.27936 | −0.463389 | −0.231695 | − | 0.972789i | \(-0.574427\pi\) | ||||
−0.231695 | + | 0.972789i | \(0.574427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.86156 | 0.291985 | ||||||||
\(404\) | −8.01040 | −0.398532 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.6739 | −0.876061 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1683 | 0.750023 | 0.375011 | − | 0.927020i | \(-0.377639\pi\) | ||||
0.375011 | + | 0.927020i | \(0.377639\pi\) | |||||||
\(410\) | 12.2255 | 0.603772 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.82846 | −0.336414 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.50232 | 0.270098 | ||||||||
\(416\) | 0.760877 | 0.0373051 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.8993 | −0.582014 | ||||||||
\(419\) | 8.33654 | 0.407267 | 0.203633 | − | 0.979047i | \(-0.434725\pi\) | ||||
0.203633 | + | 0.979047i | \(0.434725\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.00465 | 0.341386 | 0.170693 | − | 0.985324i | \(-0.445399\pi\) | ||||
0.170693 | + | 0.985324i | \(0.445399\pi\) | |||||||
\(422\) | −22.7713 | −1.10849 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.225450 | 0.0109488 | ||||||||
\(425\) | −12.9954 | −0.630367 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.54583 | −0.171394 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.2495 | −0.735397 | ||||||||
\(431\) | 3.45090 | 0.166224 | 0.0831120 | − | 0.996540i | \(-0.473514\pi\) | ||||
0.0831120 | + | 0.996540i | \(0.473514\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2599 | 1.35809 | 0.679043 | − | 0.734099i | \(-0.262395\pi\) | ||||
0.679043 | + | 0.734099i | \(0.262395\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.703697 | −0.0337010 | ||||||||
\(437\) | 0.818057 | 0.0391330 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.8960 | −1.37913 | −0.689566 | − | 0.724222i | \(-0.742199\pi\) | ||||
−0.689566 | + | 0.724222i | \(0.742199\pi\) | |||||||
\(440\) | 10.7850 | 0.514152 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.20602 | 0.247625 | ||||||||
\(443\) | −13.7609 | −0.653799 | −0.326899 | − | 0.945059i | \(-0.606004\pi\) | ||||
−0.326899 | + | 0.945059i | \(0.606004\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.58358 | −0.217283 | ||||||||
\(446\) | 12.8856 | 0.610153 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.2003 | −0.953309 | −0.476655 | − | 0.879091i | \(-0.658151\pi\) | ||||
−0.476655 | + | 0.879091i | \(0.658151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.5231 | 2.00234 | ||||||||
\(452\) | −8.50232 | −0.399916 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.9967 | 1.03236 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.0298 | 0.936956 | 0.468478 | − | 0.883475i | \(-0.344803\pi\) | ||||
0.468478 | + | 0.883475i | \(0.344803\pi\) | |||||||
\(458\) | −3.79863 | −0.177498 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.741446 | −0.0345701 | ||||||||
\(461\) | −11.9532 | −0.556717 | −0.278359 | − | 0.960477i | \(-0.589790\pi\) | ||||
−0.278359 | + | 0.960477i | \(0.589790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2905 | −0.617664 | −0.308832 | − | 0.951117i | \(-0.599938\pi\) | ||||
−0.308832 | + | 0.951117i | \(0.599938\pi\) | |||||||
\(464\) | −1.46457 | −0.0679911 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.67059 | 0.309009 | ||||||||
\(467\) | 11.2301 | 0.519667 | 0.259833 | − | 0.965653i | \(-0.416332\pi\) | ||||
0.259833 | + | 0.965653i | \(0.416332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.92339 | 0.134846 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.98633 | 0.0914281 | ||||||||
\(473\) | −53.0416 | −2.43886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.69002 | 0.169310 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.6408 | 0.715392 | ||||||||
\(479\) | −32.6271 | −1.49077 | −0.745385 | − | 0.666634i | \(-0.767734\pi\) | ||||
−0.745385 | + | 0.666634i | \(0.767734\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.19562 | −0.100111 | ||||||||
\(482\) | 21.4120 | 0.975292 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 26.5127 | 1.20512 | ||||||||
\(485\) | 6.40275 | 0.290734 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.69794 | −0.167570 | −0.0837848 | − | 0.996484i | \(-0.526701\pi\) | ||||
−0.0837848 | + | 0.996484i | \(0.526701\pi\) | |||||||
\(488\) | −10.3502 | −0.468532 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.5609 | 1.69510 | 0.847549 | − | 0.530717i | \(-0.178077\pi\) | ||||
0.847549 | + | 0.530717i | \(0.178077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0208 | −0.451314 | ||||||||
\(494\) | −1.47825 | −0.0665095 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.70370 | 0.345906 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.7954 | −1.42336 | −0.711678 | − | 0.702506i | \(-0.752064\pi\) | ||||
−0.711678 | + | 0.702506i | \(0.752064\pi\) | |||||||
\(500\) | −12.1488 | −0.543313 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.6030 | −1.05345 | ||||||||
\(503\) | 30.8252 | 1.37443 | 0.687214 | − | 0.726455i | \(-0.258834\pi\) | ||||
0.687214 | + | 0.726455i | \(0.258834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.1053 | −0.627679 | ||||||||
\(506\) | −2.57893 | −0.114648 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.9532 | −0.840913 | ||||||||
\(509\) | 8.01616 | 0.355310 | 0.177655 | − | 0.984093i | \(-0.443149\pi\) | ||||
0.177655 | + | 0.984093i | \(0.443149\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.2599 | 0.893627 | ||||||||
\(515\) | −12.0241 | −0.529844 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1683 | 0.447200 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.33981 | 0.0587546 | ||||||||
\(521\) | −29.7292 | −1.30246 | −0.651229 | − | 0.758881i | \(-0.725746\pi\) | ||||
−0.651229 | + | 0.758881i | \(0.725746\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.9396 | −1.17798 | −0.588992 | − | 0.808139i | \(-0.700475\pi\) | ||||
−0.588992 | + | 0.808139i | \(0.700475\pi\) | |||||||
\(524\) | −7.29303 | −0.318598 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.4887 | −0.980552 | ||||||||
\(527\) | 52.7097 | 2.29607 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8227 | −0.992291 | ||||||||
\(530\) | 0.396990 | 0.0172441 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.28263 | 0.228816 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.24377 | −0.269942 | ||||||||
\(536\) | 6.78495 | 0.293065 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.3412 | 1.09254 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.3114 | −0.615293 | −0.307647 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307647 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(542\) | 13.7576 | 0.590940 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.84213 | 0.293354 | ||||||||
\(545\) | −1.23912 | −0.0530782 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.04926 | −0.0876202 | −0.0438101 | − | 0.999040i | \(-0.513950\pi\) | ||||
−0.0438101 | + | 0.999040i | \(0.513950\pi\) | |||||||
\(548\) | −8.18194 | −0.349515 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11.6328 | −0.496026 | ||||||||
\(551\) | 2.84540 | 0.121218 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.28263 | −0.139466 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.4646 | 0.528616 | ||||||||
\(557\) | −17.6868 | −0.749412 | −0.374706 | − | 0.927144i | \(-0.622256\pi\) | ||||
−0.374706 | + | 0.927144i | \(0.622256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.58934 | −0.278699 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.26896 | −0.0535277 | ||||||||
\(563\) | 0.937063 | 0.0394925 | 0.0197462 | − | 0.999805i | \(-0.493714\pi\) | ||||
0.0197462 | + | 0.999805i | \(0.493714\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.9715 | −0.629858 | ||||||||
\(566\) | −8.19235 | −0.344350 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.7850 | 0.452527 | ||||||||
\(569\) | 23.5264 | 0.986278 | 0.493139 | − | 0.869951i | \(-0.335849\pi\) | ||||
0.493139 | + | 0.869951i | \(0.335849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.484004 | −0.0202549 | −0.0101275 | − | 0.999949i | \(-0.503224\pi\) | ||||
−0.0101275 | + | 0.999949i | \(0.503224\pi\) | |||||||
\(572\) | 4.66019 | 0.194852 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.799737 | 0.0333514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.46130 | 0.185727 | 0.0928633 | − | 0.995679i | \(-0.470398\pi\) | ||||
0.0928633 | + | 0.995679i | \(0.470398\pi\) | |||||||
\(578\) | 29.8148 | 1.24013 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.57893 | −0.107084 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.38083 | 0.0571881 | ||||||||
\(584\) | −0.306707 | −0.0126916 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.4509 | −0.638271 | ||||||||
\(587\) | −16.6304 | −0.686408 | −0.343204 | − | 0.939261i | \(-0.611512\pi\) | ||||
−0.343204 | + | 0.939261i | \(0.611512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.9669 | −0.616700 | ||||||||
\(590\) | 3.49768 | 0.143997 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.88564 | −0.118599 | ||||||||
\(593\) | −41.5264 | −1.70528 | −0.852642 | − | 0.522495i | \(-0.825001\pi\) | ||||
−0.852642 | + | 0.522495i | \(0.825001\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.82846 | 0.361628 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.320380 | −0.0131013 | ||||||||
\(599\) | 15.0766 | 0.616014 | 0.308007 | − | 0.951384i | \(-0.400338\pi\) | ||||
0.308007 | + | 0.951384i | \(0.400338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.1111 | 0.657185 | 0.328593 | − | 0.944472i | \(-0.393426\pi\) | ||||
0.328593 | + | 0.944472i | \(0.393426\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.9863 | −0.609785 | ||||||||
\(605\) | 46.6856 | 1.89804 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.5732 | 0.794451 | 0.397225 | − | 0.917721i | \(-0.369973\pi\) | ||||
0.397225 | + | 0.917721i | \(0.369973\pi\) | |||||||
\(608\) | −1.94282 | −0.0787918 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.2255 | −0.737927 | ||||||||
\(611\) | 1.26320 | 0.0511036 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.55159 | 0.224226 | 0.112113 | − | 0.993695i | \(-0.464238\pi\) | ||||
0.112113 | + | 0.993695i | \(0.464238\pi\) | |||||||
\(614\) | 4.89931 | 0.197720 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.26896 | −0.0510863 | −0.0255431 | − | 0.999674i | \(-0.508132\pi\) | ||||
−0.0255431 | + | 0.999674i | \(0.508132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.50232 | 0.180964 | 0.0904818 | − | 0.995898i | \(-0.471159\pi\) | ||||
0.0904818 | + | 0.995898i | \(0.471159\pi\) | |||||||
\(620\) | 13.5653 | 0.544794 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.69002 | −0.308342 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.8960 | −0.475842 | ||||||||
\(626\) | −1.72313 | −0.0688700 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.9806 | 0.757407 | ||||||||
\(629\) | −19.7439 | −0.787242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.69905 | −0.0676381 | −0.0338191 | − | 0.999428i | \(-0.510767\pi\) | ||||
−0.0338191 | + | 0.999428i | \(0.510767\pi\) | |||||||
\(632\) | −13.4451 | −0.534819 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 33.2028 | 1.31865 | ||||||||
\(635\) | −33.3743 | −1.32442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.97017 | −0.355132 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.76088 | 0.0696048 | ||||||||
\(641\) | −0.948577 | −0.0374666 | −0.0187333 | − | 0.999825i | \(-0.505963\pi\) | ||||
−0.0187333 | + | 0.999825i | \(0.505963\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.6979 | 0.776811 | 0.388405 | − | 0.921489i | \(-0.373026\pi\) | ||||
0.388405 | + | 0.921489i | \(0.373026\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.2930 | −0.523007 | ||||||||
\(647\) | −23.4542 | −0.922079 | −0.461039 | − | 0.887380i | \(-0.652523\pi\) | ||||
−0.461039 | + | 0.887380i | \(0.652523\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.1658 | 0.477549 | ||||||||
\(650\) | −1.44514 | −0.0566832 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.0377 | 0.588924 | ||||||||
\(653\) | 22.7907 | 0.891869 | 0.445935 | − | 0.895065i | \(-0.352871\pi\) | ||||
0.445935 | + | 0.895065i | \(0.352871\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.8421 | −0.501784 | ||||||||
\(656\) | 6.94282 | 0.271072 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.4796 | 1.03150 | 0.515750 | − | 0.856739i | \(-0.327513\pi\) | ||||
0.515750 | + | 0.856739i | \(0.327513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.7382 | −1.03999 | −0.519997 | − | 0.854168i | \(-0.674067\pi\) | ||||
−0.519997 | + | 0.854168i | \(0.674067\pi\) | |||||||
\(662\) | 2.88891 | 0.112281 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.12476 | 0.121264 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.616683 | 0.0238781 | ||||||||
\(668\) | −1.14419 | −0.0442702 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.9475 | 0.461571 | ||||||||
\(671\) | −63.3926 | −2.44724 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7713 | 0.800674 | 0.400337 | − | 0.916368i | \(-0.368893\pi\) | ||||
0.400337 | + | 0.916368i | \(0.368893\pi\) | |||||||
\(674\) | 8.72313 | 0.336002 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4211 | −0.477733 | ||||||||
\(677\) | −20.6979 | −0.795486 | −0.397743 | − | 0.917497i | \(-0.630207\pi\) | ||||
−0.397743 | + | 0.917497i | \(0.630207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.0482 | 0.462026 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 47.1833 | 1.80674 | ||||||||
\(683\) | −28.5836 | −1.09372 | −0.546860 | − | 0.837224i | \(-0.684177\pi\) | ||||
−0.546860 | + | 0.837224i | \(0.684177\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4074 | −0.550478 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.66019 | −0.330167 | ||||||||
\(689\) | 0.171540 | 0.00653515 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.69794 | −0.254802 | −0.127401 | − | 0.991851i | \(-0.540663\pi\) | ||||
−0.127401 | + | 0.991851i | \(0.540663\pi\) | |||||||
\(692\) | 0.497677 | 0.0189188 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.69467 | 0.368005 | ||||||||
\(695\) | 21.9486 | 0.832557 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.5037 | 1.79933 | ||||||||
\(698\) | −28.3984 | −1.07489 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.1442 | −0.949683 | −0.474842 | − | 0.880071i | \(-0.657495\pi\) | ||||
−0.474842 | + | 0.880071i | \(0.657495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.60628 | 0.211445 | ||||||||
\(704\) | 6.12476 | 0.230836 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.39372 | −0.165360 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.86621 | 0.332977 | 0.166489 | − | 0.986043i | \(-0.446757\pi\) | ||||
0.166489 | + | 0.986043i | \(0.446757\pi\) | |||||||
\(710\) | 18.9910 | 0.712719 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.60301 | −0.0975519 | ||||||||
\(713\) | −3.24377 | −0.121480 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.20602 | 0.306888 | ||||||||
\(716\) | −8.82846 | −0.329935 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −32.1592 | −1.20017 | ||||||||
\(719\) | −23.6030 | −0.880244 | −0.440122 | − | 0.897938i | \(-0.645065\pi\) | ||||
−0.440122 | + | 0.897938i | \(0.645065\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.2255 | −0.566633 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.32941 | 0.0494070 | ||||||||
\(725\) | 2.78168 | 0.103309 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.51384 | −0.241585 | −0.120792 | − | 0.992678i | \(-0.538544\pi\) | ||||
−0.120792 | + | 0.992678i | \(0.538544\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.540073 | −0.0199890 | ||||||||
\(731\) | −59.2542 | −2.19159 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.1981 | −0.856842 | −0.428421 | − | 0.903579i | \(-0.640930\pi\) | ||||
−0.428421 | + | 0.903579i | \(0.640930\pi\) | |||||||
\(734\) | 34.6030 | 1.27722 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.421067 | −0.0155207 | ||||||||
\(737\) | 41.5562 | 1.53074 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.1568 | 0.557550 | 0.278775 | − | 0.960356i | \(-0.410072\pi\) | ||||
0.278775 | + | 0.960356i | \(0.410072\pi\) | |||||||
\(740\) | −5.08126 | −0.186791 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.4347 | 0.382813 | 0.191407 | − | 0.981511i | \(-0.438695\pi\) | ||||
0.191407 | + | 0.981511i | \(0.438695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.5458 | 0.569555 | ||||||||
\(746\) | 10.9759 | 0.401857 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 41.9064 | 1.53225 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.2118 | 1.46735 | 0.733674 | − | 0.679501i | \(-0.237804\pi\) | ||||
0.733674 | + | 0.679501i | \(0.237804\pi\) | |||||||
\(752\) | 1.66019 | 0.0605409 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.11436 | −0.0405826 | ||||||||
\(755\) | −26.3891 | −0.960397 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.5206 | −0.782181 | −0.391091 | − | 0.920352i | \(-0.627902\pi\) | ||||
−0.391091 | + | 0.920352i | \(0.627902\pi\) | |||||||
\(758\) | 33.9877 | 1.23449 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.42107 | −0.124095 | ||||||||
\(761\) | −23.6627 | −0.857771 | −0.428886 | − | 0.903359i | \(-0.641094\pi\) | ||||
−0.428886 | + | 0.903359i | \(0.641094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.1683 | −0.584947 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.0241 | −0.759631 | ||||||||
\(767\) | 1.51135 | 0.0545717 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.2553 | 0.405876 | 0.202938 | − | 0.979192i | \(-0.434951\pi\) | ||||
0.202938 | + | 0.979192i | \(0.434951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.1683 | −0.509927 | ||||||||
\(773\) | −0.277984 | −0.00999839 | −0.00499919 | − | 0.999988i | \(-0.501591\pi\) | ||||
−0.00499919 | + | 0.999988i | \(0.501591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.6317 | −0.525587 | ||||||||
\(776\) | 3.63611 | 0.130529 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.7382 | 0.492538 | ||||||||
\(779\) | −13.4887 | −0.483281 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 66.0553 | 2.36364 | ||||||||
\(782\) | −2.88099 | −0.103024 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.4224 | 1.19290 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.3880 | −1.04757 | −0.523784 | − | 0.851851i | \(-0.675480\pi\) | ||||
−0.523784 | + | 0.851851i | \(0.675480\pi\) | |||||||
\(788\) | 15.8421 | 0.564353 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −23.6752 | −0.842327 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.87524 | −0.279658 | ||||||||
\(794\) | 7.15787 | 0.254023 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.94282 | 0.316970 | ||||||||
\(797\) | −0.866210 | −0.0306827 | −0.0153414 | − | 0.999882i | \(-0.504883\pi\) | ||||
−0.0153414 | + | 0.999882i | \(0.504883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.3592 | 0.401861 | ||||||||
\(800\) | −1.89931 | −0.0671509 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.27936 | −0.327666 | ||||||||
\(803\) | −1.87851 | −0.0662910 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.86156 | 0.206465 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.01040 | −0.281805 | ||||||||
\(809\) | −19.3341 | −0.679749 | −0.339875 | − | 0.940471i | \(-0.610385\pi\) | ||||
−0.339875 | + | 0.940471i | \(0.610385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.0391 | −1.65177 | −0.825884 | − | 0.563841i | \(-0.809323\pi\) | ||||
−0.825884 | + | 0.563841i | \(0.809323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.6739 | −0.619469 | ||||||||
\(815\) | 26.4796 | 0.927541 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.8252 | 0.588639 | ||||||||
\(818\) | 15.1683 | 0.530346 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.2255 | 0.426931 | ||||||||
\(821\) | 1.41066 | 0.0492325 | 0.0246162 | − | 0.999697i | \(-0.492164\pi\) | ||||
0.0246162 | + | 0.999697i | \(0.492164\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.0391 | −1.22139 | −0.610694 | − | 0.791867i | \(-0.709109\pi\) | ||||
−0.610694 | + | 0.791867i | \(0.709109\pi\) | |||||||
\(824\) | −6.82846 | −0.237881 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.5997 | −0.646776 | −0.323388 | − | 0.946266i | \(-0.604822\pi\) | ||||
−0.323388 | + | 0.946266i | \(0.604822\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.1696 | −1.32569 | −0.662843 | − | 0.748758i | \(-0.730650\pi\) | ||||
−0.662843 | + | 0.748758i | \(0.730650\pi\) | |||||||
\(830\) | 5.50232 | 0.190988 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.760877 | 0.0263787 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.01478 | −0.0697245 | ||||||||
\(836\) | −11.8993 | −0.411546 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.33654 | 0.287981 | ||||||||
\(839\) | −34.7382 | −1.19930 | −0.599648 | − | 0.800264i | \(-0.704693\pi\) | ||||
−0.599648 | + | 0.800264i | \(0.704693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8550 | −0.926035 | ||||||||
\(842\) | 7.00465 | 0.241396 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.7713 | −0.783820 | ||||||||
\(845\) | −21.8720 | −0.752419 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.225450 | 0.00774199 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.9954 | −0.445737 | ||||||||
\(851\) | 1.21505 | 0.0416513 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.3171 | 1.44891 | 0.724455 | − | 0.689322i | \(-0.242091\pi\) | ||||
0.724455 | + | 0.689322i | \(0.242091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.54583 | −0.121194 | ||||||||
\(857\) | 14.9234 | 0.509773 | 0.254887 | − | 0.966971i | \(-0.417962\pi\) | ||||
0.254887 | + | 0.966971i | \(0.417962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.4132 | 0.662368 | 0.331184 | − | 0.943566i | \(-0.392552\pi\) | ||||
0.331184 | + | 0.943566i | \(0.392552\pi\) | |||||||
\(860\) | −15.2495 | −0.520005 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.45090 | 0.117538 | ||||||||
\(863\) | 1.08453 | 0.0369177 | 0.0184588 | − | 0.999830i | \(-0.494124\pi\) | ||||
0.0184588 | + | 0.999830i | \(0.494124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.876348 | 0.0297967 | ||||||||
\(866\) | 28.2599 | 0.960312 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −82.3483 | −2.79348 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.16251 | 0.174925 | ||||||||
\(872\) | −0.703697 | −0.0238302 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.818057 | 0.0276712 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.5699 | −0.964737 | −0.482369 | − | 0.875968i | \(-0.660223\pi\) | ||||
−0.482369 | + | 0.875968i | \(0.660223\pi\) | |||||||
\(878\) | −28.8960 | −0.975194 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.7850 | 0.363561 | ||||||||
\(881\) | 45.9967 | 1.54967 | 0.774835 | − | 0.632164i | \(-0.217833\pi\) | ||||
0.774835 | + | 0.632164i | \(0.217833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.9384 | 1.10847 | 0.554233 | − | 0.832361i | \(-0.313012\pi\) | ||||
0.554233 | + | 0.832361i | \(0.313012\pi\) | |||||||
\(884\) | 5.20602 | 0.175097 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.7609 | −0.462306 | ||||||||
\(887\) | −28.3398 | −0.951558 | −0.475779 | − | 0.879565i | \(-0.657834\pi\) | ||||
−0.475779 | + | 0.879565i | \(0.657834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.58358 | −0.153642 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.8856 | 0.431443 | ||||||||
\(893\) | −3.22545 | −0.107936 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.5458 | −0.519640 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.2003 | −0.674091 | ||||||||
\(899\) | −11.2826 | −0.376297 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.54256 | 0.0513901 | ||||||||
\(902\) | 42.5231 | 1.41587 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.50232 | −0.282783 | ||||||||
\(905\) | 2.34092 | 0.0778149 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.94747 | 0.263891 | 0.131946 | − | 0.991257i | \(-0.457878\pi\) | ||||
0.131946 | + | 0.991257i | \(0.457878\pi\) | |||||||
\(908\) | 21.9967 | 0.729987 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.01616 | 0.265587 | 0.132794 | − | 0.991144i | \(-0.457605\pi\) | ||||
0.132794 | + | 0.991144i | \(0.457605\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.1384 | 0.633390 | ||||||||
\(914\) | 20.0298 | 0.662528 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.79863 | −0.125510 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0449 | 0.793168 | 0.396584 | − | 0.917999i | \(-0.370196\pi\) | ||||
0.396584 | + | 0.917999i | \(0.370196\pi\) | |||||||
\(920\) | −0.741446 | −0.0244448 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.9532 | −0.393658 | ||||||||
\(923\) | 8.20602 | 0.270104 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.48073 | 0.180205 | ||||||||
\(926\) | −13.2905 | −0.436754 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.46457 | −0.0480770 | ||||||||
\(929\) | 27.8662 | 0.914261 | 0.457130 | − | 0.889400i | \(-0.348877\pi\) | ||||
0.457130 | + | 0.889400i | \(0.348877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.67059 | 0.218503 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.2301 | 0.367460 | ||||||||
\(935\) | 73.7921 | 2.41326 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.2211 | 1.73866 | 0.869328 | − | 0.494235i | \(-0.164552\pi\) | ||||
0.869328 | + | 0.494235i | \(0.164552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.92339 | 0.0953505 | ||||||||
\(941\) | −30.0482 | −0.979542 | −0.489771 | − | 0.871851i | \(-0.662920\pi\) | ||||
−0.489771 | + | 0.871851i | \(0.662920\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.92339 | −0.0951987 | ||||||||
\(944\) | 1.98633 | 0.0646494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −53.0416 | −1.72453 | ||||||||
\(947\) | −39.6889 | −1.28972 | −0.644858 | − | 0.764302i | \(-0.723084\pi\) | ||||
−0.644858 | + | 0.764302i | \(0.723084\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.233366 | −0.00757538 | ||||||||
\(950\) | 3.69002 | 0.119720 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.0643 | 0.747126 | 0.373563 | − | 0.927605i | \(-0.378136\pi\) | ||||
0.373563 | + | 0.927605i | \(0.378136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.4703 | −0.921278 | ||||||||
\(956\) | 15.6408 | 0.505858 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32.6271 | −1.05413 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.3469 | 0.914418 | ||||||||
\(962\) | −2.19562 | −0.0707895 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.4120 | 0.689635 | ||||||||
\(965\) | −24.9486 | −0.803123 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.5803 | −0.983396 | −0.491698 | − | 0.870766i | \(-0.663624\pi\) | ||||
−0.491698 | + | 0.870766i | \(0.663624\pi\) | |||||||
\(968\) | 26.5127 | 0.852151 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.40275 | 0.205580 | ||||||||
\(971\) | −26.2060 | −0.840991 | −0.420496 | − | 0.907295i | \(-0.638144\pi\) | ||||
−0.420496 | + | 0.907295i | \(0.638144\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.69794 | −0.118490 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.3502 | −0.331302 | ||||||||
\(977\) | 21.0539 | 0.673574 | 0.336787 | − | 0.941581i | \(-0.390660\pi\) | ||||
0.336787 | + | 0.941581i | \(0.390660\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.9428 | −0.509535 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 37.5609 | 1.19862 | ||||||||
\(983\) | −19.5297 | −0.622900 | −0.311450 | − | 0.950263i | \(-0.600815\pi\) | ||||
−0.311450 | + | 0.950263i | \(0.600815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.8960 | 0.888842 | ||||||||
\(986\) | −10.0208 | −0.319128 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.47825 | −0.0470293 | ||||||||
\(989\) | 3.64652 | 0.115952 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.9967 | 0.476387 | 0.238193 | − | 0.971218i | \(-0.423445\pi\) | ||||
0.238193 | + | 0.971218i | \(0.423445\pi\) | |||||||
\(992\) | 7.70370 | 0.244593 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.7472 | 0.499220 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58.5641 | −1.85475 | −0.927373 | − | 0.374139i | \(-0.877938\pi\) | ||||
−0.927373 | + | 0.374139i | \(0.877938\pi\) | |||||||
\(998\) | −31.7954 | −1.00646 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))