Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(846,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.846");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 260x^{12} + 2030x^{10} + 11605x^{8} + 42100x^{6} + 106925x^{4} + 113575x^{2} + 87025 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 846.12 | ||
Root | \(-0.551501 - 0.955228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.846 |
Dual form | 847.2.b.f.846.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.672816i | 0.475753i | 0.971295 | + | 0.237877i | \(0.0764514\pi\) | ||||
−0.971295 | + | 0.237877i | \(0.923549\pi\) | |||||||
\(3\) | 2.65257i | 1.53146i | 0.643160 | + | 0.765732i | \(0.277623\pi\) | ||||
−0.643160 | + | 0.765732i | \(0.722377\pi\) | |||||||
\(4\) | 1.54732 | 0.773659 | ||||||||
\(5\) | 3.54984i | 1.58754i | 0.608221 | + | 0.793768i | \(0.291883\pi\) | ||||
−0.608221 | + | 0.793768i | \(0.708117\pi\) | |||||||
\(6\) | −1.78470 | −0.728599 | ||||||||
\(7\) | 1.10300 | − | 2.40487i | 0.416896 | − | 0.908954i | ||||
\(8\) | 2.38669i | 0.843824i | ||||||||
\(9\) | −4.03615 | −1.34538 | ||||||||
\(10\) | −2.38839 | −0.755275 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 4.10438i | 1.18483i | ||||||||
\(13\) | 1.10300 | 0.305918 | 0.152959 | − | 0.988233i | \(-0.451120\pi\) | ||||
0.152959 | + | 0.988233i | \(0.451120\pi\) | |||||||
\(14\) | 1.61803 | + | 0.742118i | 0.432438 | + | 0.198339i | ||||
\(15\) | −9.41620 | −2.43125 | ||||||||
\(16\) | 1.48883 | 0.372207 | ||||||||
\(17\) | −4.17308 | −1.01212 | −0.506061 | − | 0.862498i | \(-0.668899\pi\) | ||||
−0.506061 | + | 0.862498i | \(0.668899\pi\) | |||||||
\(18\) | − | 2.71559i | − | 0.640070i | ||||||
\(19\) | −1.24551 | −0.285741 | −0.142870 | − | 0.989741i | \(-0.545633\pi\) | ||||
−0.142870 | + | 0.989741i | \(0.545633\pi\) | |||||||
\(20\) | 5.49273i | 1.22821i | ||||||||
\(21\) | 6.37909 | + | 2.92579i | 1.39203 | + | 0.638461i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.85410 | 0.595121 | 0.297561 | − | 0.954703i | \(-0.403827\pi\) | ||||
0.297561 | + | 0.954703i | \(0.403827\pi\) | |||||||
\(24\) | −6.33088 | −1.29229 | ||||||||
\(25\) | −7.60134 | −1.52027 | ||||||||
\(26\) | 0.742118i | 0.145541i | ||||||||
\(27\) | − | 2.74846i | − | 0.528941i | ||||||
\(28\) | 1.70670 | − | 3.72109i | 0.322535 | − | 0.703221i | ||||
\(29\) | 2.04277i | 0.379333i | 0.981849 | + | 0.189666i | \(0.0607407\pi\) | ||||
−0.981849 | + | 0.189666i | \(0.939259\pi\) | |||||||
\(30\) | − | 6.33538i | − | 1.15668i | ||||||
\(31\) | − | 2.99530i | − | 0.537971i | −0.963144 | − | 0.268986i | \(-0.913312\pi\) | ||
0.963144 | − | 0.268986i | \(-0.0866884\pi\) | |||||||
\(32\) | 5.77510i | 1.02090i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.80772i | − | 0.481520i | ||||||
\(35\) | 8.53689 | + | 3.91548i | 1.44300 | + | 0.661837i | ||||
\(36\) | −6.24520 | −1.04087 | ||||||||
\(37\) | 2.76202 | 0.454074 | 0.227037 | − | 0.973886i | \(-0.427096\pi\) | ||||
0.227037 | + | 0.973886i | \(0.427096\pi\) | |||||||
\(38\) | − | 0.838003i | − | 0.135942i | ||||||
\(39\) | 2.92579i | 0.468502i | ||||||||
\(40\) | −8.47237 | −1.33960 | ||||||||
\(41\) | 5.49660 | 0.858424 | 0.429212 | − | 0.903204i | \(-0.358791\pi\) | ||||
0.429212 | + | 0.903204i | \(0.358791\pi\) | |||||||
\(42\) | −1.96852 | + | 4.29195i | −0.303750 | + | 0.662263i | ||||
\(43\) | − | 1.73205i | − | 0.264135i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) | ||
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 14.3277i | − | 2.13584i | ||||||
\(46\) | 1.92029i | 0.283131i | ||||||||
\(47\) | − | 6.82860i | − | 0.996053i | −0.867162 | − | 0.498027i | \(-0.834058\pi\) | ||
0.867162 | − | 0.498027i | \(-0.165942\pi\) | |||||||
\(48\) | 3.94923i | 0.570022i | ||||||||
\(49\) | −4.56677 | − | 5.30515i | −0.652396 | − | 0.757878i | ||||
\(50\) | − | 5.11431i | − | 0.723272i | ||||||
\(51\) | − | 11.0694i | − | 1.55003i | ||||||
\(52\) | 1.70670 | 0.236676 | ||||||||
\(53\) | 1.07985 | 0.148329 | 0.0741646 | − | 0.997246i | \(-0.476371\pi\) | ||||
0.0741646 | + | 0.997246i | \(0.476371\pi\) | |||||||
\(54\) | 1.84921 | 0.251645 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.73968 | + | 2.63253i | 0.766997 | + | 0.351786i | ||||
\(57\) | − | 3.30382i | − | 0.437602i | ||||||
\(58\) | −1.37441 | −0.180469 | ||||||||
\(59\) | − | 2.28980i | − | 0.298107i | −0.988829 | − | 0.149054i | \(-0.952377\pi\) | ||
0.988829 | − | 0.149054i | \(-0.0476227\pi\) | |||||||
\(60\) | −14.5699 | −1.88096 | ||||||||
\(61\) | 13.3518 | 1.70952 | 0.854761 | − | 0.519022i | \(-0.173704\pi\) | ||||
0.854761 | + | 0.519022i | \(0.173704\pi\) | |||||||
\(62\) | 2.01529 | 0.255941 | ||||||||
\(63\) | −4.45188 | + | 9.70640i | −0.560884 | + | 1.22289i | ||||
\(64\) | −0.907920 | −0.113490 | ||||||||
\(65\) | 3.91548i | 0.485655i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.489806 | 0.0598393 | 0.0299197 | − | 0.999552i | \(-0.490475\pi\) | ||||
0.0299197 | + | 0.999552i | \(0.490475\pi\) | |||||||
\(68\) | −6.45709 | −0.783037 | ||||||||
\(69\) | 7.57072i | 0.911407i | ||||||||
\(70\) | −2.63440 | + | 5.74376i | −0.314871 | + | 0.686510i | ||||
\(71\) | 10.2062 | 1.21125 | 0.605625 | − | 0.795750i | \(-0.292923\pi\) | ||||
0.605625 | + | 0.795750i | \(0.292923\pi\) | |||||||
\(72\) | − | 9.63305i | − | 1.13527i | ||||||
\(73\) | −12.5276 | −1.46624 | −0.733121 | − | 0.680098i | \(-0.761937\pi\) | ||||
−0.733121 | + | 0.680098i | \(0.761937\pi\) | |||||||
\(74\) | 1.85833i | 0.216027i | ||||||||
\(75\) | − | 20.1631i | − | 2.32824i | ||||||
\(76\) | −1.92721 | −0.221066 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.96852 | −0.222891 | ||||||||
\(79\) | − | 12.4332i | − | 1.39885i | −0.714708 | − | 0.699423i | \(-0.753440\pi\) | ||
0.714708 | − | 0.699423i | \(-0.246560\pi\) | |||||||
\(80\) | 5.28510i | 0.590892i | ||||||||
\(81\) | −4.81795 | −0.535328 | ||||||||
\(82\) | 3.69820i | 0.408398i | ||||||||
\(83\) | −1.61862 | −0.177666 | −0.0888332 | − | 0.996047i | \(-0.528314\pi\) | ||||
−0.0888332 | + | 0.996047i | \(0.528314\pi\) | |||||||
\(84\) | 9.87048 | + | 4.52714i | 1.07696 | + | 0.493951i | ||||
\(85\) | − | 14.8138i | − | 1.60678i | ||||||
\(86\) | 1.16535 | 0.125663 | ||||||||
\(87\) | −5.41860 | −0.580935 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.30985i | 0.244844i | 0.992478 | + | 0.122422i | \(0.0390661\pi\) | ||||
−0.992478 | + | 0.122422i | \(0.960934\pi\) | |||||||
\(90\) | 9.63989 | 1.01613 | ||||||||
\(91\) | 1.21661 | − | 2.65257i | 0.127536 | − | 0.278065i | ||||
\(92\) | 4.41620 | 0.460421 | ||||||||
\(93\) | 7.94525 | 0.823884 | ||||||||
\(94\) | 4.59439 | 0.473875 | ||||||||
\(95\) | − | 4.42137i | − | 0.453623i | ||||||
\(96\) | −15.3189 | −1.56348 | ||||||||
\(97\) | 12.6682i | 1.28626i | 0.765755 | + | 0.643132i | \(0.222366\pi\) | ||||
−0.765755 | + | 0.643132i | \(0.777634\pi\) | |||||||
\(98\) | 3.56939 | − | 3.07260i | 0.360563 | − | 0.310379i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.7617 | −1.17617 | ||||||||
\(101\) | −3.16649 | −0.315078 | −0.157539 | − | 0.987513i | \(-0.550356\pi\) | ||||
−0.157539 | + | 0.987513i | \(0.550356\pi\) | |||||||
\(102\) | 7.44768 | 0.737430 | ||||||||
\(103\) | 9.73220i | 0.958942i | 0.877558 | + | 0.479471i | \(0.159171\pi\) | ||||
−0.877558 | + | 0.479471i | \(0.840829\pi\) | |||||||
\(104\) | 2.63253i | 0.258141i | ||||||||
\(105\) | −10.3861 | + | 22.6447i | −1.01358 | + | 2.20990i | ||||
\(106\) | 0.726543i | 0.0705680i | ||||||||
\(107\) | 10.5567i | 1.02056i | 0.860010 | + | 0.510278i | \(0.170457\pi\) | ||||
−0.860010 | + | 0.510278i | \(0.829543\pi\) | |||||||
\(108\) | − | 4.25274i | − | 0.409220i | ||||||
\(109\) | − | 3.04683i | − | 0.291833i | −0.989297 | − | 0.145917i | \(-0.953387\pi\) | ||
0.989297 | − | 0.145917i | \(-0.0466131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.32647i | 0.695397i | ||||||||
\(112\) | 1.64218 | − | 3.58044i | 0.155172 | − | 0.338320i | ||||
\(113\) | 7.25710 | 0.682691 | 0.341345 | − | 0.939938i | \(-0.389117\pi\) | ||||
0.341345 | + | 0.939938i | \(0.389117\pi\) | |||||||
\(114\) | 2.22286 | 0.208190 | ||||||||
\(115\) | 10.1316i | 0.944776i | ||||||||
\(116\) | 3.16082i | 0.293474i | ||||||||
\(117\) | −4.45188 | −0.411576 | ||||||||
\(118\) | 1.54062 | 0.141825 | ||||||||
\(119\) | −4.60292 | + | 10.0357i | −0.421949 | + | 0.919972i | ||||
\(120\) | − | 22.4736i | − | 2.05155i | ||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 8.98330i | 0.813310i | ||||||||
\(123\) | 14.5801i | 1.31465i | ||||||||
\(124\) | − | 4.63468i | − | 0.416206i | ||||||
\(125\) | − | 9.23433i | − | 0.825944i | ||||||
\(126\) | −6.53062 | − | 2.99530i | −0.581794 | − | 0.266842i | ||||
\(127\) | − | 6.12976i | − | 0.543928i | −0.962307 | − | 0.271964i | \(-0.912327\pi\) | ||
0.962307 | − | 0.271964i | \(-0.0876732\pi\) | |||||||
\(128\) | 10.9393i | 0.966909i | ||||||||
\(129\) | 4.59439 | 0.404514 | ||||||||
\(130\) | −2.63440 | −0.231052 | ||||||||
\(131\) | −18.8287 | −1.64507 | −0.822534 | − | 0.568715i | \(-0.807441\pi\) | ||||
−0.822534 | + | 0.568715i | \(0.807441\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.37381 | + | 2.99530i | −0.119124 | + | 0.259725i | ||||
\(134\) | 0.329550i | 0.0284687i | ||||||||
\(135\) | 9.75658 | 0.839713 | ||||||||
\(136\) | − | 9.95987i | − | 0.854052i | ||||||
\(137\) | −2.95939 | −0.252837 | −0.126419 | − | 0.991977i | \(-0.540348\pi\) | ||||
−0.126419 | + | 0.991977i | \(0.540348\pi\) | |||||||
\(138\) | −5.09370 | −0.433605 | ||||||||
\(139\) | 14.7735 | 1.25307 | 0.626534 | − | 0.779394i | \(-0.284473\pi\) | ||||
0.626534 | + | 0.779394i | \(0.284473\pi\) | |||||||
\(140\) | 13.2093 | + | 6.05849i | 1.11639 | + | 0.512036i | ||||
\(141\) | 18.1134 | 1.52542 | ||||||||
\(142\) | 6.86688i | 0.576256i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.00914 | −0.500761 | ||||||||
\(145\) | −7.25150 | −0.602204 | ||||||||
\(146\) | − | 8.42876i | − | 0.697569i | ||||||
\(147\) | 14.0723 | − | 12.1137i | 1.16066 | − | 0.999121i | ||||
\(148\) | 4.27373 | 0.351298 | ||||||||
\(149\) | 7.51223i | 0.615426i | 0.951479 | + | 0.307713i | \(0.0995637\pi\) | ||||
−0.951479 | + | 0.307713i | \(0.900436\pi\) | |||||||
\(150\) | 13.5661 | 1.10767 | ||||||||
\(151\) | − | 12.7284i | − | 1.03582i | −0.855434 | − | 0.517912i | \(-0.826710\pi\) | ||
0.855434 | − | 0.517912i | \(-0.173290\pi\) | |||||||
\(152\) | − | 2.97266i | − | 0.241115i | ||||||
\(153\) | 16.8432 | 1.36169 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.6328 | 0.854048 | ||||||||
\(156\) | 4.52714i | 0.362461i | ||||||||
\(157\) | − | 15.2616i | − | 1.21800i | −0.793168 | − | 0.609002i | \(-0.791570\pi\) | ||
0.793168 | − | 0.609002i | \(-0.208430\pi\) | |||||||
\(158\) | 8.36527 | 0.665505 | ||||||||
\(159\) | 2.86439i | 0.227161i | ||||||||
\(160\) | −20.5006 | −1.62072 | ||||||||
\(161\) | 3.14808 | − | 6.86374i | 0.248104 | − | 0.540938i | ||||
\(162\) | − | 3.24160i | − | 0.254684i | ||||||
\(163\) | 21.0339 | 1.64750 | 0.823751 | − | 0.566951i | \(-0.191877\pi\) | ||||
0.823751 | + | 0.566951i | \(0.191877\pi\) | |||||||
\(164\) | 8.50499 | 0.664128 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 1.08903i | − | 0.0845253i | ||||||
\(167\) | −8.34102 | −0.645447 | −0.322724 | − | 0.946493i | \(-0.604598\pi\) | ||||
−0.322724 | + | 0.946493i | \(0.604598\pi\) | |||||||
\(168\) | −6.98298 | + | 15.2249i | −0.538748 | + | 1.17463i | ||||
\(169\) | −11.7834 | −0.906414 | ||||||||
\(170\) | 9.96694 | 0.764430 | ||||||||
\(171\) | 5.02708 | 0.384431 | ||||||||
\(172\) | − | 2.68003i | − | 0.204351i | ||||||
\(173\) | 16.0588 | 1.22093 | 0.610466 | − | 0.792043i | \(-0.290982\pi\) | ||||
0.610466 | + | 0.792043i | \(0.290982\pi\) | |||||||
\(174\) | − | 3.64572i | − | 0.276381i | ||||||
\(175\) | −8.38430 | + | 18.2802i | −0.633793 | + | 1.38185i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.07388 | 0.456540 | ||||||||
\(178\) | −1.55410 | −0.116485 | ||||||||
\(179\) | 7.36816 | 0.550722 | 0.275361 | − | 0.961341i | \(-0.411203\pi\) | ||||
0.275361 | + | 0.961341i | \(0.411203\pi\) | |||||||
\(180\) | − | 22.1695i | − | 1.65241i | ||||||
\(181\) | − | 14.4786i | − | 1.07619i | −0.842885 | − | 0.538094i | \(-0.819145\pi\) | ||
0.842885 | − | 0.538094i | \(-0.180855\pi\) | |||||||
\(182\) | 1.78470 | + | 0.818558i | 0.132290 | + | 0.0606755i | ||||
\(183\) | 35.4166i | 2.61807i | ||||||||
\(184\) | 6.81187i | 0.502178i | ||||||||
\(185\) | 9.80473i | 0.720858i | ||||||||
\(186\) | 5.34569i | 0.391965i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 10.5660i | − | 0.770606i | ||||||
\(189\) | −6.60968 | − | 3.03156i | −0.480783 | − | 0.220513i | ||||
\(190\) | 2.97477 | 0.215813 | ||||||||
\(191\) | 1.58944 | 0.115008 | 0.0575040 | − | 0.998345i | \(-0.481686\pi\) | ||||
0.0575040 | + | 0.998345i | \(0.481686\pi\) | |||||||
\(192\) | − | 2.40832i | − | 0.173806i | ||||||
\(193\) | 11.2031i | 0.806419i | 0.915108 | + | 0.403209i | \(0.132105\pi\) | ||||
−0.915108 | + | 0.403209i | \(0.867895\pi\) | |||||||
\(194\) | −8.52340 | −0.611944 | ||||||||
\(195\) | −10.3861 | −0.743764 | ||||||||
\(196\) | −7.06625 | − | 8.20875i | −0.504732 | − | 0.586339i | ||||
\(197\) | − | 15.0339i | − | 1.07112i | −0.844496 | − | 0.535561i | \(-0.820100\pi\) | ||
0.844496 | − | 0.535561i | \(-0.179900\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.9453i | 1.55566i | 0.628476 | + | 0.777829i | \(0.283679\pi\) | ||||
−0.628476 | + | 0.777829i | \(0.716321\pi\) | |||||||
\(200\) | − | 18.1421i | − | 1.28284i | ||||||
\(201\) | 1.29925i | 0.0916418i | ||||||||
\(202\) | − | 2.13047i | − | 0.149899i | ||||||
\(203\) | 4.91259 | + | 2.25318i | 0.344796 | + | 0.158142i | ||||
\(204\) | − | 17.1279i | − | 1.19919i | ||||||
\(205\) | 19.5120i | 1.36278i | ||||||||
\(206\) | −6.54798 | −0.456220 | ||||||||
\(207\) | −11.5196 | −0.800666 | ||||||||
\(208\) | 1.64218 | 0.113865 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −15.2357 | − | 6.98793i | −1.05137 | − | 0.482213i | ||||
\(211\) | 14.3700i | 0.989271i | 0.869101 | + | 0.494635i | \(0.164698\pi\) | ||||
−0.869101 | + | 0.494635i | \(0.835302\pi\) | |||||||
\(212\) | 1.67088 | 0.114756 | ||||||||
\(213\) | 27.0726i | 1.85499i | ||||||||
\(214\) | −7.10273 | −0.485532 | ||||||||
\(215\) | 6.14850 | 0.419324 | ||||||||
\(216\) | 6.55973 | 0.446333 | ||||||||
\(217\) | −7.20329 | − | 3.30382i | −0.488991 | − | 0.224278i | ||||
\(218\) | 2.04996 | 0.138840 | ||||||||
\(219\) | − | 33.2303i | − | 2.24550i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.60292 | −0.309626 | ||||||||
\(222\) | −4.92937 | −0.330837 | ||||||||
\(223\) | 17.7224i | 1.18678i | 0.804916 | + | 0.593388i | \(0.202210\pi\) | ||||
−0.804916 | + | 0.593388i | \(0.797790\pi\) | |||||||
\(224\) | 13.8883 | + | 6.36994i | 0.927954 | + | 0.425610i | ||||
\(225\) | 30.6801 | 2.04534 | ||||||||
\(226\) | 4.88270i | 0.324792i | ||||||||
\(227\) | 4.10131 | 0.272214 | 0.136107 | − | 0.990694i | \(-0.456541\pi\) | ||||
0.136107 | + | 0.990694i | \(0.456541\pi\) | |||||||
\(228\) | − | 5.11206i | − | 0.338554i | ||||||
\(229\) | 9.80126i | 0.647686i | 0.946111 | + | 0.323843i | \(0.104975\pi\) | ||||
−0.946111 | + | 0.323843i | \(0.895025\pi\) | |||||||
\(230\) | −6.81670 | −0.449480 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.87547 | −0.320090 | ||||||||
\(233\) | 0.101962i | 0.00667974i | 0.999994 | + | 0.00333987i | \(0.00106312\pi\) | ||||
−0.999994 | + | 0.00333987i | \(0.998937\pi\) | |||||||
\(234\) | − | 2.99530i | − | 0.195809i | ||||||
\(235\) | 24.2404 | 1.58127 | ||||||||
\(236\) | − | 3.54306i | − | 0.230633i | ||||||
\(237\) | 32.9800 | 2.14228 | ||||||||
\(238\) | −6.75219 | − | 3.09692i | −0.437680 | − | 0.200744i | ||||
\(239\) | 6.13574i | 0.396888i | 0.980112 | + | 0.198444i | \(0.0635888\pi\) | ||||
−0.980112 | + | 0.198444i | \(0.936411\pi\) | |||||||
\(240\) | −14.0191 | −0.904931 | ||||||||
\(241\) | −4.31560 | −0.277992 | −0.138996 | − | 0.990293i | \(-0.544388\pi\) | ||||
−0.138996 | + | 0.990293i | \(0.544388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 21.0254i | − | 1.34878i | ||||||
\(244\) | 20.6595 | 1.32259 | ||||||||
\(245\) | 18.8324 | − | 16.2113i | 1.20316 | − | 1.03570i | ||||
\(246\) | −9.80975 | −0.625447 | ||||||||
\(247\) | −1.37381 | −0.0874132 | ||||||||
\(248\) | 7.14886 | 0.453953 | ||||||||
\(249\) | − | 4.29350i | − | 0.272090i | ||||||
\(250\) | 6.21301 | 0.392945 | ||||||||
\(251\) | − | 30.6941i | − | 1.93739i | −0.248245 | − | 0.968697i | \(-0.579854\pi\) | ||
0.248245 | − | 0.968697i | \(-0.420146\pi\) | |||||||
\(252\) | −6.88847 | + | 15.0189i | −0.433933 | + | 0.946101i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.12420 | 0.258776 | ||||||||
\(255\) | 39.2946 | 2.46072 | ||||||||
\(256\) | −9.17600 | −0.573500 | ||||||||
\(257\) | 6.73271i | 0.419975i | 0.977704 | + | 0.209988i | \(0.0673424\pi\) | ||||
−0.977704 | + | 0.209988i | \(0.932658\pi\) | |||||||
\(258\) | 3.09118i | 0.192449i | ||||||||
\(259\) | 3.04652 | − | 6.64230i | 0.189301 | − | 0.412732i | ||||
\(260\) | 6.05849i | 0.375732i | ||||||||
\(261\) | − | 8.24492i | − | 0.510348i | ||||||
\(262\) | − | 12.6682i | − | 0.782646i | ||||||
\(263\) | 24.4460i | 1.50741i | 0.657215 | + | 0.753703i | \(0.271734\pi\) | ||||
−0.657215 | + | 0.753703i | \(0.728266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.83330i | 0.235478i | ||||||||
\(266\) | −2.01529 | − | 0.924319i | −0.123565 | − | 0.0566736i | ||||
\(267\) | −6.12705 | −0.374969 | ||||||||
\(268\) | 0.757886 | 0.0462952 | ||||||||
\(269\) | − | 25.3199i | − | 1.54378i | −0.635755 | − | 0.771891i | \(-0.719311\pi\) | ||
0.635755 | − | 0.771891i | \(-0.280689\pi\) | |||||||
\(270\) | 6.56439i | 0.399496i | ||||||||
\(271\) | 27.3409 | 1.66084 | 0.830421 | − | 0.557136i | \(-0.188100\pi\) | ||||
0.830421 | + | 0.557136i | \(0.188100\pi\) | |||||||
\(272\) | −6.21301 | −0.376719 | ||||||||
\(273\) | 7.03615 | + | 3.22716i | 0.425847 | + | 0.195316i | ||||
\(274\) | − | 1.99112i | − | 0.120288i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.7143i | 0.705118i | ||||||||
\(277\) | 22.4190i | 1.34703i | 0.739175 | + | 0.673513i | \(0.235216\pi\) | ||||
−0.739175 | + | 0.673513i | \(0.764784\pi\) | |||||||
\(278\) | 9.93983i | 0.596151i | ||||||||
\(279\) | 12.0895i | 0.723777i | ||||||||
\(280\) | −9.34505 | + | 20.3749i | −0.558473 | + | 1.21764i | ||||
\(281\) | − | 21.5172i | − | 1.28361i | −0.766868 | − | 0.641805i | \(-0.778186\pi\) | ||
0.766868 | − | 0.641805i | \(-0.221814\pi\) | |||||||
\(282\) | 12.1870i | 0.725723i | ||||||||
\(283\) | −30.9433 | −1.83939 | −0.919694 | − | 0.392637i | \(-0.871563\pi\) | ||||
−0.919694 | + | 0.392637i | \(0.871563\pi\) | |||||||
\(284\) | 15.7922 | 0.937094 | ||||||||
\(285\) | 11.7280 | 0.694708 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.06276 | − | 13.2186i | 0.357873 | − | 0.780269i | ||||
\(288\) | − | 23.3091i | − | 1.37350i | ||||||
\(289\) | 0.414624 | 0.0243896 | ||||||||
\(290\) | − | 4.87893i | − | 0.286500i | ||||||
\(291\) | −33.6034 | −1.96987 | ||||||||
\(292\) | −19.3842 | −1.13437 | ||||||||
\(293\) | −24.8510 | −1.45181 | −0.725904 | − | 0.687796i | \(-0.758579\pi\) | ||||
−0.725904 | + | 0.687796i | \(0.758579\pi\) | |||||||
\(294\) | 8.15030 | + | 9.46807i | 0.475335 | + | 0.552189i | ||||
\(295\) | 8.12843 | 0.473256 | ||||||||
\(296\) | 6.59210i | 0.383158i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.05435 | −0.292791 | ||||||||
\(299\) | 3.14808 | 0.182058 | ||||||||
\(300\) | − | 31.1988i | − | 1.80126i | ||||||
\(301\) | −4.16535 | − | 1.91046i | −0.240087 | − | 0.110117i | ||||
\(302\) | 8.56389 | 0.492796 | ||||||||
\(303\) | − | 8.39936i | − | 0.482531i | ||||||
\(304\) | −1.85436 | −0.106355 | ||||||||
\(305\) | 47.3967i | 2.71393i | ||||||||
\(306\) | 11.3324i | 0.647828i | ||||||||
\(307\) | 10.0029 | 0.570896 | 0.285448 | − | 0.958394i | \(-0.407858\pi\) | ||||
0.285448 | + | 0.958394i | \(0.407858\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.8154 | −1.46859 | ||||||||
\(310\) | 7.15393i | 0.406316i | ||||||||
\(311\) | − | 18.7190i | − | 1.06146i | −0.847542 | − | 0.530728i | \(-0.821919\pi\) | ||
0.847542 | − | 0.530728i | \(-0.178081\pi\) | |||||||
\(312\) | −6.98298 | −0.395333 | ||||||||
\(313\) | − | 5.28598i | − | 0.298781i | −0.988778 | − | 0.149391i | \(-0.952269\pi\) | ||
0.988778 | − | 0.149391i | \(-0.0477312\pi\) | |||||||
\(314\) | 10.2682 | 0.579469 | ||||||||
\(315\) | −34.4561 | − | 15.8034i | −1.94138 | − | 0.890423i | ||||
\(316\) | − | 19.2381i | − | 1.08223i | ||||||
\(317\) | −28.7541 | −1.61499 | −0.807497 | − | 0.589872i | \(-0.799178\pi\) | ||||
−0.807497 | + | 0.589872i | \(0.799178\pi\) | |||||||
\(318\) | −1.92721 | −0.108072 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 3.22297i | − | 0.180169i | ||||||
\(321\) | −28.0025 | −1.56294 | ||||||||
\(322\) | 4.61803 | + | 2.11808i | 0.257353 | + | 0.118036i | ||||
\(323\) | 5.19764 | 0.289204 | ||||||||
\(324\) | −7.45491 | −0.414162 | ||||||||
\(325\) | −8.38430 | −0.465077 | ||||||||
\(326\) | 14.1520i | 0.783804i | ||||||||
\(327\) | 8.08193 | 0.446932 | ||||||||
\(328\) | 13.1187i | 0.724359i | ||||||||
\(329\) | −16.4219 | − | 7.53196i | −0.905367 | − | 0.415250i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.2266 | 0.672035 | 0.336017 | − | 0.941856i | \(-0.390920\pi\) | ||||
0.336017 | + | 0.941856i | \(0.390920\pi\) | |||||||
\(332\) | −2.50452 | −0.137453 | ||||||||
\(333\) | −11.1479 | −0.610903 | ||||||||
\(334\) | − | 5.61197i | − | 0.307073i | ||||||
\(335\) | 1.73873i | 0.0949971i | ||||||||
\(336\) | 9.49738 | + | 4.35601i | 0.518124 | + | 0.237640i | ||||
\(337\) | − | 36.0841i | − | 1.96563i | −0.184603 | − | 0.982813i | \(-0.559100\pi\) | ||
0.184603 | − | 0.982813i | \(-0.440900\pi\) | |||||||
\(338\) | − | 7.92806i | − | 0.431229i | ||||||
\(339\) | 19.2500i | 1.04552i | ||||||||
\(340\) | − | 22.9216i | − | 1.24310i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.38230i | 0.182894i | ||||||||
\(343\) | −17.7953 | + | 5.13089i | −0.960858 | + | 0.277042i | ||||
\(344\) | 4.13387 | 0.222884 | ||||||||
\(345\) | −26.8748 | −1.44689 | ||||||||
\(346\) | 10.8047i | 0.580862i | ||||||||
\(347\) | 27.5091i | 1.47677i | 0.674380 | + | 0.738384i | \(0.264411\pi\) | ||||
−0.674380 | + | 0.738384i | \(0.735589\pi\) | |||||||
\(348\) | −8.38430 | −0.449445 | ||||||||
\(349\) | 14.1265 | 0.756174 | 0.378087 | − | 0.925770i | \(-0.376582\pi\) | ||||
0.378087 | + | 0.925770i | \(0.376582\pi\) | |||||||
\(350\) | −12.2992 | − | 5.64109i | −0.657421 | − | 0.301529i | ||||
\(351\) | − | 3.03156i | − | 0.161812i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.23958i | − | 0.438549i | −0.975663 | − | 0.219274i | \(-0.929631\pi\) | ||
0.975663 | − | 0.219274i | \(-0.0703690\pi\) | |||||||
\(354\) | 4.08660i | 0.217200i | ||||||||
\(355\) | 36.2302i | 1.92290i | ||||||||
\(356\) | 3.57407i | 0.189425i | ||||||||
\(357\) | −26.6205 | − | 12.2096i | −1.40890 | − | 0.646200i | ||||
\(358\) | 4.95742i | 0.262008i | ||||||||
\(359\) | − | 29.9242i | − | 1.57934i | −0.613533 | − | 0.789669i | \(-0.710252\pi\) | ||
0.613533 | − | 0.789669i | \(-0.289748\pi\) | |||||||
\(360\) | 34.1957 | 1.80227 | ||||||||
\(361\) | −17.4487 | −0.918352 | ||||||||
\(362\) | 9.74145 | 0.511999 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.88249 | − | 4.10438i | 0.0986692 | − | 0.215128i | ||||
\(365\) | − | 44.4709i | − | 2.32771i | ||||||
\(366\) | −23.8289 | −1.24556 | ||||||||
\(367\) | − | 4.63468i | − | 0.241928i | −0.992657 | − | 0.120964i | \(-0.961401\pi\) | ||
0.992657 | − | 0.120964i | \(-0.0385986\pi\) | |||||||
\(368\) | 4.24927 | 0.221509 | ||||||||
\(369\) | −22.1851 | −1.15491 | ||||||||
\(370\) | −6.59678 | −0.342950 | ||||||||
\(371\) | 1.19108 | − | 2.59690i | 0.0618378 | − | 0.134824i | ||||
\(372\) | 12.2938 | 0.637405 | ||||||||
\(373\) | − | 15.2702i | − | 0.790662i | −0.918539 | − | 0.395331i | \(-0.870630\pi\) | ||
0.918539 | − | 0.395331i | \(-0.129370\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.4947 | 1.26490 | ||||||||
\(376\) | 16.2978 | 0.840493 | ||||||||
\(377\) | 2.25318i | 0.116045i | ||||||||
\(378\) | 2.03968 | − | 4.44710i | 0.104910 | − | 0.228734i | ||||
\(379\) | 22.7591 | 1.16906 | 0.584529 | − | 0.811373i | \(-0.301279\pi\) | ||||
0.584529 | + | 0.811373i | \(0.301279\pi\) | |||||||
\(380\) | − | 6.84127i | − | 0.350950i | ||||||
\(381\) | 16.2596 | 0.833007 | ||||||||
\(382\) | 1.06940i | 0.0547154i | ||||||||
\(383\) | 28.9146i | 1.47746i | 0.673999 | + | 0.738732i | \(0.264575\pi\) | ||||
−0.673999 | + | 0.738732i | \(0.735425\pi\) | |||||||
\(384\) | −29.0174 | −1.48079 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.53765 | −0.383656 | ||||||||
\(387\) | 6.99081i | 0.355363i | ||||||||
\(388\) | 19.6018i | 0.995130i | ||||||||
\(389\) | −21.9665 | −1.11375 | −0.556873 | − | 0.830598i | \(-0.687999\pi\) | ||||
−0.556873 | + | 0.830598i | \(0.687999\pi\) | |||||||
\(390\) | − | 6.98793i | − | 0.353848i | ||||||
\(391\) | −11.9104 | −0.602335 | ||||||||
\(392\) | 12.6618 | − | 10.8995i | 0.639516 | − | 0.550507i | ||||
\(393\) | − | 49.9444i | − | 2.51936i | ||||||
\(394\) | 10.1151 | 0.509590 | ||||||||
\(395\) | 44.1359 | 2.22072 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.02008i | 0.151573i | 0.997124 | + | 0.0757866i | \(0.0241468\pi\) | ||||
−0.997124 | + | 0.0757866i | \(0.975853\pi\) | |||||||
\(398\) | −14.7651 | −0.740109 | ||||||||
\(399\) | −7.94525 | − | 3.64412i | −0.397760 | − | 0.182434i | ||||
\(400\) | −11.3171 | −0.565855 | ||||||||
\(401\) | 7.88407 | 0.393712 | 0.196856 | − | 0.980432i | \(-0.436927\pi\) | ||||
0.196856 | + | 0.980432i | \(0.436927\pi\) | |||||||
\(402\) | −0.874155 | −0.0435989 | ||||||||
\(403\) | − | 3.30382i | − | 0.164575i | ||||||
\(404\) | −4.89957 | −0.243763 | ||||||||
\(405\) | − | 17.1030i | − | 0.849852i | ||||||
\(406\) | −1.51598 | + | 3.30527i | −0.0752366 | + | 0.164038i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 26.4193 | 1.30795 | ||||||||
\(409\) | −26.5465 | −1.31264 | −0.656320 | − | 0.754483i | \(-0.727888\pi\) | ||||
−0.656320 | + | 0.754483i | \(0.727888\pi\) | |||||||
\(410\) | −13.1280 | −0.648346 | ||||||||
\(411\) | − | 7.84999i | − | 0.387211i | ||||||
\(412\) | 15.0588i | 0.741894i | ||||||||
\(413\) | −5.50668 | − | 2.52566i | −0.270966 | − | 0.124280i | ||||
\(414\) | − | 7.75056i | − | 0.380919i | ||||||
\(415\) | − | 5.74583i | − | 0.282052i | ||||||
\(416\) | 6.36994i | 0.312312i | ||||||||
\(417\) | 39.1877i | 1.91903i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.28466i | 0.355879i | 0.984041 | + | 0.177940i | \(0.0569431\pi\) | ||||
−0.984041 | + | 0.177940i | \(0.943057\pi\) | |||||||
\(420\) | −16.0706 | + | 35.0386i | −0.784165 | + | 1.70971i | ||||
\(421\) | −23.8041 | −1.16014 | −0.580070 | − | 0.814567i | \(-0.696975\pi\) | ||||
−0.580070 | + | 0.814567i | \(0.696975\pi\) | |||||||
\(422\) | −9.66836 | −0.470648 | ||||||||
\(423\) | 27.5612i | 1.34007i | ||||||||
\(424\) | 2.57728i | 0.125164i | ||||||||
\(425\) | 31.7210 | 1.53870 | ||||||||
\(426\) | −18.2149 | −0.882515 | ||||||||
\(427\) | 14.7271 | − | 32.1093i | 0.712692 | − | 1.55388i | ||||
\(428\) | 16.3346i | 0.789562i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.13681i | 0.199495i | ||||||||
\(431\) | 0.640406i | 0.0308473i | 0.999881 | + | 0.0154236i | \(0.00490969\pi\) | ||||
−0.999881 | + | 0.0154236i | \(0.995090\pi\) | |||||||
\(432\) | − | 4.09199i | − | 0.196876i | ||||||
\(433\) | − | 17.2215i | − | 0.827611i | −0.910365 | − | 0.413806i | \(-0.864199\pi\) | ||
0.910365 | − | 0.413806i | \(-0.135801\pi\) | |||||||
\(434\) | 2.22286 | − | 4.84649i | 0.106701 | − | 0.232639i | ||||
\(435\) | − | 19.2351i | − | 0.922254i | ||||||
\(436\) | − | 4.71441i | − | 0.225779i | ||||||
\(437\) | −3.55483 | −0.170050 | ||||||||
\(438\) | 22.3579 | 1.06830 | ||||||||
\(439\) | −0.0381286 | −0.00181978 | −0.000909889 | − | 1.00000i | \(-0.500290\pi\) | ||||
−0.000909889 | 1.00000i | \(0.500290\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4322 | + | 21.4124i | 0.877722 | + | 1.01964i | ||||
\(442\) | − | 3.09692i | − | 0.147305i | ||||||
\(443\) | 30.6420 | 1.45585 | 0.727923 | − | 0.685658i | \(-0.240486\pi\) | ||||
0.727923 | + | 0.685658i | \(0.240486\pi\) | |||||||
\(444\) | 11.3364i | 0.538001i | ||||||||
\(445\) | −8.19959 | −0.388698 | ||||||||
\(446\) | −11.9239 | −0.564613 | ||||||||
\(447\) | −19.9267 | −0.942503 | ||||||||
\(448\) | −1.00144 | + | 2.18343i | −0.0473135 | + | 0.103157i | ||||
\(449\) | −29.5218 | −1.39322 | −0.696609 | − | 0.717451i | \(-0.745309\pi\) | ||||
−0.696609 | + | 0.717451i | \(0.745309\pi\) | |||||||
\(450\) | 20.6421i | 0.973078i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 11.2290 | 0.528170 | ||||||||
\(453\) | 33.7631 | 1.58633 | ||||||||
\(454\) | 2.75943i | 0.129506i | ||||||||
\(455\) | 9.41620 | + | 4.31878i | 0.441438 | + | 0.202468i | ||||
\(456\) | 7.88521 | 0.369259 | ||||||||
\(457\) | − | 4.24787i | − | 0.198707i | −0.995052 | − | 0.0993534i | \(-0.968323\pi\) | ||
0.995052 | − | 0.0993534i | \(-0.0316774\pi\) | |||||||
\(458\) | −6.59445 | −0.308138 | ||||||||
\(459\) | 11.4695i | 0.535353i | ||||||||
\(460\) | 15.6768i | 0.730935i | ||||||||
\(461\) | −11.8930 | −0.553913 | −0.276957 | − | 0.960882i | \(-0.589326\pi\) | ||||
−0.276957 | + | 0.960882i | \(0.589326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.5007 | 1.37102 | 0.685508 | − | 0.728066i | \(-0.259580\pi\) | ||||
0.685508 | + | 0.728066i | \(0.259580\pi\) | |||||||
\(464\) | 3.04134i | 0.141191i | ||||||||
\(465\) | 28.2043i | 1.30794i | ||||||||
\(466\) | −0.0686016 | −0.00317791 | ||||||||
\(467\) | − | 11.1490i | − | 0.515913i | −0.966156 | − | 0.257957i | \(-0.916951\pi\) | ||
0.966156 | − | 0.257957i | \(-0.0830492\pi\) | |||||||
\(468\) | −6.88847 | −0.318420 | ||||||||
\(469\) | 0.540257 | − | 1.17792i | 0.0249468 | − | 0.0543912i | ||||
\(470\) | 16.3093i | 0.752294i | ||||||||
\(471\) | 40.4824 | 1.86533 | ||||||||
\(472\) | 5.46506 | 0.251550 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 22.1895i | 1.01920i | ||||||||
\(475\) | 9.46758 | 0.434402 | ||||||||
\(476\) | −7.12218 | + | 15.5284i | −0.326445 | + | 0.711745i | ||||
\(477\) | −4.35844 | −0.199559 | ||||||||
\(478\) | −4.12823 | −0.188821 | ||||||||
\(479\) | −11.3316 | −0.517753 | −0.258877 | − | 0.965910i | \(-0.583352\pi\) | ||||
−0.258877 | + | 0.965910i | \(0.583352\pi\) | |||||||
\(480\) | − | 54.3795i | − | 2.48207i | ||||||
\(481\) | 3.04652 | 0.138909 | ||||||||
\(482\) | − | 2.90360i | − | 0.132256i | ||||||
\(483\) | 18.2066 | + | 8.35052i | 0.828427 | + | 0.379962i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −44.9702 | −2.04199 | ||||||||
\(486\) | 14.1462 | 0.641685 | ||||||||
\(487\) | 15.5058 | 0.702637 | 0.351318 | − | 0.936256i | \(-0.385733\pi\) | ||||
0.351318 | + | 0.936256i | \(0.385733\pi\) | |||||||
\(488\) | 31.8666i | 1.44253i | ||||||||
\(489\) | 55.7940i | 2.52309i | ||||||||
\(490\) | 10.9072 | + | 12.6708i | 0.492738 | + | 0.572406i | ||||
\(491\) | 10.4088i | 0.469742i | 0.972027 | + | 0.234871i | \(0.0754668\pi\) | ||||
−0.972027 | + | 0.234871i | \(0.924533\pi\) | |||||||
\(492\) | 22.5601i | 1.01709i | ||||||||
\(493\) | − | 8.52465i | − | 0.383931i | ||||||
\(494\) | − | 0.924319i | − | 0.0415871i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.45949i | − | 0.200237i | ||||||
\(497\) | 11.2574 | − | 24.5445i | 0.504965 | − | 1.10097i | ||||
\(498\) | 2.88874 | 0.129447 | ||||||||
\(499\) | −23.2190 | −1.03942 | −0.519712 | − | 0.854342i | \(-0.673961\pi\) | ||||
−0.519712 | + | 0.854342i | \(0.673961\pi\) | |||||||
\(500\) | − | 14.2885i | − | 0.638999i | ||||||
\(501\) | − | 22.1252i | − | 0.988479i | ||||||
\(502\) | 20.6515 | 0.921721 | ||||||||
\(503\) | 1.15636 | 0.0515596 | 0.0257798 | − | 0.999668i | \(-0.491793\pi\) | ||||
0.0257798 | + | 0.999668i | \(0.491793\pi\) | |||||||
\(504\) | −23.1662 | − | 10.6253i | −1.03190 | − | 0.473287i | ||||
\(505\) | − | 11.2405i | − | 0.500197i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 31.2563i | − | 1.38814i | ||||||
\(508\) | − | 9.48469i | − | 0.420815i | ||||||
\(509\) | − | 17.8327i | − | 0.790420i | −0.918591 | − | 0.395210i | \(-0.870672\pi\) | ||
0.918591 | − | 0.395210i | \(-0.129328\pi\) | |||||||
\(510\) | 26.4381i | 1.17070i | ||||||||
\(511\) | −13.8180 | + | 30.1272i | −0.611270 | + | 1.33275i | ||||
\(512\) | 15.7049i | 0.694065i | ||||||||
\(513\) | 3.42325i | 0.151140i | ||||||||
\(514\) | −4.52988 | −0.199804 | ||||||||
\(515\) | −34.5477 | −1.52235 | ||||||||
\(516\) | 7.10899 | 0.312956 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.46905 | + | 2.04975i | 0.196359 | + | 0.0900607i | ||||
\(519\) | 42.5973i | 1.86981i | ||||||||
\(520\) | −9.34505 | −0.409807 | ||||||||
\(521\) | − | 35.9158i | − | 1.57350i | −0.617273 | − | 0.786749i | \(-0.711763\pi\) | ||
0.617273 | − | 0.786749i | \(-0.288237\pi\) | |||||||
\(522\) | 5.54732 | 0.242800 | ||||||||
\(523\) | −9.86251 | −0.431257 | −0.215629 | − | 0.976475i | \(-0.569180\pi\) | ||||
−0.215629 | + | 0.976475i | \(0.569180\pi\) | |||||||
\(524\) | −29.1339 | −1.27272 | ||||||||
\(525\) | −48.4896 | − | 22.2400i | −2.11626 | − | 0.970632i | ||||
\(526\) | −16.4477 | −0.717153 | ||||||||
\(527\) | 12.4996i | 0.544492i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.8541 | −0.645831 | ||||||||
\(530\) | −2.57911 | −0.112029 | ||||||||
\(531\) | 9.24199i | 0.401068i | ||||||||
\(532\) | −2.12571 | + | 4.63468i | −0.0921614 | + | 0.200939i | ||||
\(533\) | 6.06276 | 0.262607 | ||||||||
\(534\) | − | 4.12238i | − | 0.178393i | ||||||
\(535\) | −37.4746 | −1.62017 | ||||||||
\(536\) | 1.16902i | 0.0504938i | ||||||||
\(537\) | 19.5446i | 0.843411i | ||||||||
\(538\) | 17.0356 | 0.734459 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 15.0965 | 0.649651 | ||||||||
\(541\) | − | 20.6287i | − | 0.886897i | −0.896300 | − | 0.443449i | \(-0.853755\pi\) | ||
0.896300 | − | 0.443449i | \(-0.146245\pi\) | |||||||
\(542\) | 18.3954i | 0.790151i | ||||||||
\(543\) | 38.4056 | 1.64814 | ||||||||
\(544\) | − | 24.1000i | − | 1.03328i | ||||||
\(545\) | 10.8157 | 0.463295 | ||||||||
\(546\) | −2.17128 | + | 4.73404i | −0.0929224 | + | 0.202598i | ||||
\(547\) | 28.8672i | 1.23427i | 0.786856 | + | 0.617136i | \(0.211707\pi\) | ||||
−0.786856 | + | 0.617136i | \(0.788293\pi\) | |||||||
\(548\) | −4.57911 | −0.195610 | ||||||||
\(549\) | −53.8898 | −2.29996 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.54430i | − | 0.108391i | ||||||
\(552\) | −18.0690 | −0.769067 | ||||||||
\(553\) | −29.9002 | − | 13.7139i | −1.27149 | − | 0.583173i | ||||
\(554\) | −15.0839 | −0.640852 | ||||||||
\(555\) | −26.0078 | −1.10397 | ||||||||
\(556\) | 22.8592 | 0.969448 | ||||||||
\(557\) | 14.5467i | 0.616365i | 0.951327 | + | 0.308183i | \(0.0997208\pi\) | ||||
−0.951327 | + | 0.308183i | \(0.900279\pi\) | |||||||
\(558\) | −8.13399 | −0.344339 | ||||||||
\(559\) | − | 1.91046i | − | 0.0808037i | ||||||
\(560\) | 12.7100 | + | 5.82948i | 0.537094 | + | 0.246340i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.4771 | 0.610681 | ||||||||
\(563\) | 6.04411 | 0.254729 | 0.127365 | − | 0.991856i | \(-0.459348\pi\) | ||||
0.127365 | + | 0.991856i | \(0.459348\pi\) | |||||||
\(564\) | 28.0271 | 1.18016 | ||||||||
\(565\) | 25.7615i | 1.08380i | ||||||||
\(566\) | − | 20.8191i | − | 0.875094i | ||||||
\(567\) | −5.31421 | + | 11.5865i | −0.223176 | + | 0.486589i | ||||
\(568\) | 24.3590i | 1.02208i | ||||||||
\(569\) | − | 13.1065i | − | 0.549455i | −0.961522 | − | 0.274727i | \(-0.911412\pi\) | ||
0.961522 | − | 0.274727i | \(-0.0885876\pi\) | |||||||
\(570\) | 7.89080i | 0.330509i | ||||||||
\(571\) | 14.5264i | 0.607910i | 0.952686 | + | 0.303955i | \(0.0983073\pi\) | ||||
−0.952686 | + | 0.303955i | \(0.901693\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.21612i | 0.176131i | ||||||||
\(574\) | 8.89368 | + | 4.07912i | 0.371215 | + | 0.170259i | ||||
\(575\) | −21.6950 | −0.904744 | ||||||||
\(576\) | 3.66450 | 0.152687 | ||||||||
\(577\) | − | 27.4793i | − | 1.14398i | −0.820261 | − | 0.571990i | \(-0.806172\pi\) | ||
0.820261 | − | 0.571990i | \(-0.193828\pi\) | |||||||
\(578\) | 0.278966i | 0.0116034i | ||||||||
\(579\) | −29.7171 | −1.23500 | ||||||||
\(580\) | −11.2204 | −0.465901 | ||||||||
\(581\) | −1.78534 | + | 3.89256i | −0.0740683 | + | 0.161491i | ||||
\(582\) | − | 22.6089i | − | 0.937171i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 29.8995i | − | 1.23725i | ||||||
\(585\) | − | 15.8034i | − | 0.653392i | ||||||
\(586\) | − | 16.7201i | − | 0.690702i | ||||||
\(587\) | − | 14.3085i | − | 0.590575i | −0.955408 | − | 0.295287i | \(-0.904585\pi\) | ||
0.955408 | − | 0.295287i | \(-0.0954154\pi\) | |||||||
\(588\) | 21.7743 | − | 18.7437i | 0.897958 | − | 0.772979i | ||||
\(589\) | 3.73069i | 0.153720i | ||||||||
\(590\) | 5.46894i | 0.225153i | ||||||||
\(591\) | 39.8786 | 1.64039 | ||||||||
\(592\) | 4.11218 | 0.169010 | ||||||||
\(593\) | 31.8607 | 1.30836 | 0.654181 | − | 0.756338i | \(-0.273013\pi\) | ||||
0.654181 | + | 0.756338i | \(0.273013\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.6251 | − | 16.3396i | −1.46049 | − | 0.669859i | ||||
\(596\) | 11.6238i | 0.476130i | ||||||||
\(597\) | −58.2114 | −2.38243 | ||||||||
\(598\) | 2.11808i | 0.0866147i | ||||||||
\(599\) | 22.5485 | 0.921307 | 0.460653 | − | 0.887580i | \(-0.347615\pi\) | ||||
0.460653 | + | 0.887580i | \(0.347615\pi\) | |||||||
\(600\) | 48.1232 | 1.96462 | ||||||||
\(601\) | 28.9546 | 1.18108 | 0.590542 | − | 0.807007i | \(-0.298914\pi\) | ||||
0.590542 | + | 0.807007i | \(0.298914\pi\) | |||||||
\(602\) | 1.28539 | − | 2.80252i | 0.0523884 | − | 0.114222i | ||||
\(603\) | −1.97693 | −0.0805068 | ||||||||
\(604\) | − | 19.6949i | − | 0.801374i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.65123 | 0.229565 | ||||||||
\(607\) | 28.4019 | 1.15280 | 0.576400 | − | 0.817168i | \(-0.304457\pi\) | ||||
0.576400 | + | 0.817168i | \(0.304457\pi\) | |||||||
\(608\) | − | 7.19297i | − | 0.291713i | ||||||
\(609\) | −5.97673 | + | 13.0310i | −0.242189 | + | 0.528043i | ||||
\(610\) | −31.8893 | −1.29116 | ||||||||
\(611\) | − | 7.53196i | − | 0.304710i | ||||||
\(612\) | 26.0618 | 1.05348 | ||||||||
\(613\) | − | 17.0228i | − | 0.687545i | −0.939053 | − | 0.343773i | \(-0.888295\pi\) | ||
0.939053 | − | 0.343773i | \(-0.111705\pi\) | |||||||
\(614\) | 6.73012i | 0.271606i | ||||||||
\(615\) | −51.7571 | −2.08705 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.0794 | 0.768109 | 0.384055 | − | 0.923310i | \(-0.374527\pi\) | ||||
0.384055 | + | 0.923310i | \(0.374527\pi\) | |||||||
\(618\) | − | 17.3690i | − | 0.698684i | ||||||
\(619\) | − | 22.6115i | − | 0.908834i | −0.890789 | − | 0.454417i | \(-0.849848\pi\) | ||
0.890789 | − | 0.454417i | \(-0.150152\pi\) | |||||||
\(620\) | 16.4524 | 0.660742 | ||||||||
\(621\) | − | 7.84438i | − | 0.314784i | ||||||
\(622\) | 12.5944 | 0.504991 | ||||||||
\(623\) | 5.55488 | + | 2.54777i | 0.222552 | + | 0.102074i | ||||
\(624\) | 4.35601i | 0.174380i | ||||||||
\(625\) | −5.22633 | −0.209053 | ||||||||
\(626\) | 3.55649 | 0.142146 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 23.6145i | − | 0.942320i | ||||||
\(629\) | −11.5261 | −0.459578 | ||||||||
\(630\) | 10.6328 | − | 23.1826i | 0.423622 | − | 0.923619i | ||||
\(631\) | −6.59183 | −0.262417 | −0.131208 | − | 0.991355i | \(-0.541886\pi\) | ||||
−0.131208 | + | 0.991355i | \(0.541886\pi\) | |||||||
\(632\) | 29.6743 | 1.18038 | ||||||||
\(633\) | −38.1174 | −1.51503 | ||||||||
\(634\) | − | 19.3463i | − | 0.768338i | ||||||
\(635\) | 21.7597 | 0.863505 | ||||||||
\(636\) | 4.43212i | 0.175745i | ||||||||
\(637\) | −5.03716 | − | 5.85159i | −0.199580 | − | 0.231848i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −41.1936 | −1.62959 | ||||||||
\(640\) | −38.8328 | −1.53500 | ||||||||
\(641\) | 10.3555 | 0.409017 | 0.204509 | − | 0.978865i | \(-0.434440\pi\) | ||||
0.204509 | + | 0.978865i | \(0.434440\pi\) | |||||||
\(642\) | − | 18.8405i | − | 0.743576i | ||||||
\(643\) | − | 29.1774i | − | 1.15065i | −0.817926 | − | 0.575323i | \(-0.804876\pi\) | ||
0.817926 | − | 0.575323i | \(-0.195124\pi\) | |||||||
\(644\) | 4.87108 | − | 10.6204i | 0.191948 | − | 0.418502i | ||||
\(645\) | 16.3093i | 0.642180i | ||||||||
\(646\) | 3.49706i | 0.137590i | ||||||||
\(647\) | 1.57539i | 0.0619349i | 0.999520 | + | 0.0309675i | \(0.00985882\pi\) | ||||
−0.999520 | + | 0.0309675i | \(0.990141\pi\) | |||||||
\(648\) | − | 11.4990i | − | 0.451723i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 5.64109i | − | 0.221262i | ||||||
\(651\) | 8.76363 | − | 19.1073i | 0.343474 | − | 0.748873i | ||||
\(652\) | 32.5461 | 1.27461 | ||||||||
\(653\) | 14.5691 | 0.570134 | 0.285067 | − | 0.958508i | \(-0.407984\pi\) | ||||
0.285067 | + | 0.958508i | \(0.407984\pi\) | |||||||
\(654\) | 5.43766i | 0.212629i | ||||||||
\(655\) | − | 66.8387i | − | 2.61160i | ||||||
\(656\) | 8.18350 | 0.319512 | ||||||||
\(657\) | 50.5632 | 1.97266 | ||||||||
\(658\) | 5.06763 | − | 11.0489i | 0.197557 | − | 0.430731i | ||||
\(659\) | − | 28.4616i | − | 1.10871i | −0.832281 | − | 0.554353i | \(-0.812966\pi\) | ||
0.832281 | − | 0.554353i | \(-0.187034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.7887i | − | 1.27533i | −0.770313 | − | 0.637666i | \(-0.779900\pi\) | ||
0.770313 | − | 0.637666i | \(-0.220100\pi\) | |||||||
\(662\) | 8.22626i | 0.319723i | ||||||||
\(663\) | − | 12.2096i | − | 0.474181i | ||||||
\(664\) | − | 3.86314i | − | 0.149919i | ||||||
\(665\) | −10.6328 | − | 4.87679i | −0.412323 | − | 0.189114i | ||||
\(666\) | − | 7.50051i | − | 0.290639i | ||||||
\(667\) | 5.83027i | 0.225749i | ||||||||
\(668\) | −12.9062 | −0.499356 | ||||||||
\(669\) | −47.0099 | −1.81751 | ||||||||
\(670\) | −1.16985 | −0.0451951 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −16.8967 | + | 36.8398i | −0.651806 | + | 1.42113i | ||||
\(673\) | 10.2694i | 0.395858i | 0.980216 | + | 0.197929i | \(0.0634215\pi\) | ||||
−0.980216 | + | 0.197929i | \(0.936579\pi\) | |||||||
\(674\) | 24.2780 | 0.935153 | ||||||||
\(675\) | 20.8920i | 0.804132i | ||||||||
\(676\) | −18.2326 | −0.701256 | ||||||||
\(677\) | 35.0099 | 1.34554 | 0.672769 | − | 0.739852i | \(-0.265105\pi\) | ||||
0.672769 | + | 0.739852i | \(0.265105\pi\) | |||||||
\(678\) | −12.9517 | −0.497408 | ||||||||
\(679\) | 30.4654 | + | 13.9731i | 1.16916 | + | 0.536238i | ||||
\(680\) | 35.3559 | 1.35584 | ||||||||
\(681\) | 10.8790i | 0.416885i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.0603 | −0.691059 | −0.345529 | − | 0.938408i | \(-0.612301\pi\) | ||||
−0.345529 | + | 0.938408i | \(0.612301\pi\) | |||||||
\(684\) | 7.77850 | 0.297418 | ||||||||
\(685\) | − | 10.5053i | − | 0.401388i | ||||||
\(686\) | −3.45215 | − | 11.9730i | −0.131804 | − | 0.457131i | ||||
\(687\) | −25.9986 | −0.991907 | ||||||||
\(688\) | − | 2.57873i | − | 0.0983131i | ||||||
\(689\) | 1.19108 | 0.0453765 | ||||||||
\(690\) | − | 18.0818i | − | 0.688363i | ||||||
\(691\) | − | 23.6161i | − | 0.898398i | −0.893432 | − | 0.449199i | \(-0.851709\pi\) | ||
0.893432 | − | 0.449199i | \(-0.148291\pi\) | |||||||
\(692\) | 24.8481 | 0.944585 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.5086 | −0.702577 | ||||||||
\(695\) | 52.4434i | 1.98929i | ||||||||
\(696\) | − | 12.9325i | − | 0.490206i | ||||||
\(697\) | −22.9378 | −0.868830 | ||||||||
\(698\) | 9.50453i | 0.359752i | ||||||||
\(699\) | −0.270461 | −0.0102298 | ||||||||
\(700\) | −12.9732 | + | 28.2853i | −0.490340 | + | 1.06908i | ||||
\(701\) | 36.7279i | 1.38719i | 0.720363 | + | 0.693597i | \(0.243975\pi\) | ||||
−0.720363 | + | 0.693597i | \(0.756025\pi\) | |||||||
\(702\) | 2.03968 | 0.0769828 | ||||||||
\(703\) | −3.44014 | −0.129747 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 64.2995i | 2.42166i | ||||||||
\(706\) | 5.54373 | 0.208641 | ||||||||
\(707\) | −3.49265 | + | 7.61500i | −0.131355 | + | 0.286391i | ||||
\(708\) | 9.39822 | 0.353207 | ||||||||
\(709\) | −25.4613 | −0.956219 | −0.478109 | − | 0.878300i | \(-0.658678\pi\) | ||||
−0.478109 | + | 0.878300i | \(0.658678\pi\) | |||||||
\(710\) | −24.3763 | −0.914826 | ||||||||
\(711\) | 50.1823i | 1.88198i | ||||||||
\(712\) | −5.51290 | −0.206605 | ||||||||
\(713\) | − | 8.54889i | − | 0.320158i | ||||||
\(714\) | 8.21481 | − | 17.9107i | 0.307431 | − | 0.670290i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.4009 | 0.426071 | ||||||||
\(717\) | −16.2755 | −0.607820 | ||||||||
\(718\) | 20.1335 | 0.751375 | ||||||||
\(719\) | − | 30.5473i | − | 1.13922i | −0.821914 | − | 0.569612i | \(-0.807094\pi\) | ||
0.821914 | − | 0.569612i | \(-0.192906\pi\) | |||||||
\(720\) | − | 21.3315i | − | 0.794976i | ||||||
\(721\) | 23.4047 | + | 10.7346i | 0.871635 | + | 0.399779i | ||||
\(722\) | − | 11.7398i | − | 0.436909i | ||||||
\(723\) | − | 11.4474i | − | 0.425735i | ||||||
\(724\) | − | 22.4030i | − | 0.832602i | ||||||
\(725\) | − | 15.5278i | − | 0.576688i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.80772i | − | 0.104133i | −0.998644 | − | 0.0520663i | \(-0.983419\pi\) | ||
0.998644 | − | 0.0520663i | \(-0.0165807\pi\) | |||||||
\(728\) | 6.33088 | + | 2.90368i | 0.234638 | + | 0.107618i | ||||
\(729\) | 41.3174 | 1.53028 | ||||||||
\(730\) | 29.9207 | 1.10742 | ||||||||
\(731\) | 7.22799i | 0.267337i | ||||||||
\(732\) | 54.8008i | 2.02549i | ||||||||
\(733\) | 6.75560 | 0.249524 | 0.124762 | − | 0.992187i | \(-0.460183\pi\) | ||||
0.124762 | + | 0.992187i | \(0.460183\pi\) | |||||||
\(734\) | 3.11829 | 0.115098 | ||||||||
\(735\) | 43.0017 | + | 49.9544i | 1.58614 | + | 1.84259i | ||||
\(736\) | 16.4827i | 0.607561i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 14.9265i | − | 0.549452i | ||||||
\(739\) | − | 12.6084i | − | 0.463809i | −0.972739 | − | 0.231905i | \(-0.925504\pi\) | ||
0.972739 | − | 0.231905i | \(-0.0744957\pi\) | |||||||
\(740\) | 15.1710i | 0.557698i | ||||||||
\(741\) | − | 3.64412i | − | 0.133870i | ||||||
\(742\) | 1.74724 | + | 0.801378i | 0.0641431 | + | 0.0294195i | ||||
\(743\) | − | 7.01399i | − | 0.257318i | −0.991689 | − | 0.128659i | \(-0.958933\pi\) | ||
0.991689 | − | 0.128659i | \(-0.0410673\pi\) | |||||||
\(744\) | 18.9629i | 0.695213i | ||||||||
\(745\) | −26.6672 | −0.977010 | ||||||||
\(746\) | 10.2741 | 0.376160 | ||||||||
\(747\) | 6.53298 | 0.239029 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.3875 | + | 11.6441i | 0.927639 | + | 0.425465i | ||||
\(750\) | 16.4805i | 0.601782i | ||||||||
\(751\) | 8.92542 | 0.325693 | 0.162847 | − | 0.986651i | \(-0.447932\pi\) | ||||
0.162847 | + | 0.986651i | \(0.447932\pi\) | |||||||
\(752\) | − | 10.1666i | − | 0.370738i | ||||||
\(753\) | 81.4184 | 2.96705 | ||||||||
\(754\) | −1.51598 | −0.0552086 | ||||||||
\(755\) | 45.1838 | 1.64441 | ||||||||
\(756\) | −10.2273 | − | 4.69078i | −0.371962 | − | 0.170602i | ||||
\(757\) | 28.3234 | 1.02943 | 0.514716 | − | 0.857361i | \(-0.327897\pi\) | ||||
0.514716 | + | 0.857361i | \(0.327897\pi\) | |||||||
\(758\) | 15.3127i | 0.556183i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.5525 | 0.382778 | ||||||||
\(761\) | −7.02091 | −0.254508 | −0.127254 | − | 0.991870i | \(-0.540616\pi\) | ||||
−0.127254 | + | 0.991870i | \(0.540616\pi\) | |||||||
\(762\) | 10.9398i | 0.396305i | ||||||||
\(763\) | −7.32721 | − | 3.36066i | −0.265263 | − | 0.121664i | ||||
\(764\) | 2.45937 | 0.0889770 | ||||||||
\(765\) | 59.7905i | 2.16173i | ||||||||
\(766\) | −19.4542 | −0.702908 | ||||||||
\(767\) | − | 2.52566i | − | 0.0911963i | ||||||
\(768\) | − | 24.3400i | − | 0.878295i | ||||||
\(769\) | 27.4453 | 0.989703 | 0.494851 | − | 0.868978i | \(-0.335222\pi\) | ||||
0.494851 | + | 0.868978i | \(0.335222\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.8590 | −0.643177 | ||||||||
\(772\) | 17.3348i | 0.623893i | ||||||||
\(773\) | 28.6264i | 1.02962i | 0.857305 | + | 0.514809i | \(0.172137\pi\) | ||||
−0.857305 | + | 0.514809i | \(0.827863\pi\) | |||||||
\(774\) | −4.70353 | −0.169065 | ||||||||
\(775\) | 22.7683i | 0.817861i | ||||||||
\(776\) | −30.2352 | −1.08538 | ||||||||
\(777\) | 17.6192 | + | 8.08111i | 0.632085 | + | 0.289908i | ||||
\(778\) | − | 14.7794i | − | 0.529868i | ||||||
\(779\) | −6.84609 | −0.245287 | ||||||||
\(780\) | −16.0706 | −0.575419 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 8.01352i | − | 0.286563i | ||||||
\(783\) | 5.61447 | 0.200645 | ||||||||
\(784\) | −6.79915 | − | 7.89846i | −0.242827 | − | 0.282088i | ||||
\(785\) | 54.1760 | 1.93363 | ||||||||
\(786\) | 33.6034 | 1.19860 | ||||||||
\(787\) | 7.62353 | 0.271749 | 0.135875 | − | 0.990726i | \(-0.456616\pi\) | ||||
0.135875 | + | 0.990726i | \(0.456616\pi\) | |||||||
\(788\) | − | 23.2623i | − | 0.828684i | ||||||
\(789\) | −64.8449 | −2.30854 | ||||||||
\(790\) | 29.6954i | 1.05651i | ||||||||
\(791\) | 8.00460 | − | 17.4524i | 0.284611 | − | 0.620535i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.7271 | 0.522973 | ||||||||
\(794\) | −2.03196 | −0.0721114 | ||||||||
\(795\) | −10.1681 | −0.360626 | ||||||||
\(796\) | 33.9563i | 1.20355i | ||||||||
\(797\) | 34.7434i | 1.23067i | 0.788264 | + | 0.615337i | \(0.210980\pi\) | ||||
−0.788264 | + | 0.615337i | \(0.789020\pi\) | |||||||
\(798\) | 2.45182 | − | 5.34569i | 0.0867936 | − | 0.189235i | ||||
\(799\) | 28.4963i | 1.00813i | ||||||||
\(800\) | − | 43.8985i | − | 1.55205i | ||||||
\(801\) | − | 9.32290i | − | 0.329408i | ||||||
\(802\) | 5.30453i | 0.187309i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.01035i | 0.0708995i | ||||||||
\(805\) | 24.3651 | + | 11.1752i | 0.858758 | + | 0.393873i | ||||
\(806\) | 2.22286 | 0.0782971 | ||||||||
\(807\) | 67.1629 | 2.36425 | ||||||||
\(808\) | − | 7.55745i | − | 0.265870i | ||||||
\(809\) | 22.4247i | 0.788412i | 0.919022 | + | 0.394206i | \(0.128980\pi\) | ||||
−0.919022 | + | 0.394206i | \(0.871020\pi\) | |||||||
\(810\) | 11.5071 | 0.404320 | ||||||||
\(811\) | −19.5492 | −0.686464 | −0.343232 | − | 0.939251i | \(-0.611522\pi\) | ||||
−0.343232 | + | 0.939251i | \(0.611522\pi\) | |||||||
\(812\) | 7.60134 | + | 3.48639i | 0.266755 | + | 0.122348i | ||||
\(813\) | 72.5238i | 2.54352i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 74.6669i | 2.61547i | ||||||||
\(816\) | − | 16.4805i | − | 0.576932i | ||||||
\(817\) | 2.15729i | 0.0754742i | ||||||||
\(818\) | − | 17.8609i | − | 0.624493i | ||||||
\(819\) | −4.91043 | + | 10.7062i | −0.171584 | + | 0.374104i | ||||
\(820\) | 30.1913i | 1.05433i | ||||||||
\(821\) | − | 18.3901i | − | 0.641818i | −0.947110 | − | 0.320909i | \(-0.896012\pi\) | ||
0.947110 | − | 0.320909i | \(-0.103988\pi\) | |||||||
\(822\) | 5.28160 | 0.184217 | ||||||||
\(823\) | 22.2604 | 0.775950 | 0.387975 | − | 0.921670i | \(-0.373175\pi\) | ||||
0.387975 | + | 0.921670i | \(0.373175\pi\) | |||||||
\(824\) | −23.2278 | −0.809178 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.69931 | − | 3.70498i | 0.0591264 | − | 0.128913i | ||||
\(827\) | − | 46.5155i | − | 1.61750i | −0.588151 | − | 0.808751i | \(-0.700144\pi\) | ||
0.588151 | − | 0.808751i | \(-0.299856\pi\) | |||||||
\(828\) | −17.8245 | −0.619442 | ||||||||
\(829\) | − | 20.7816i | − | 0.721776i | −0.932609 | − | 0.360888i | \(-0.882474\pi\) | ||
0.932609 | − | 0.360888i | \(-0.117526\pi\) | |||||||
\(830\) | 3.86589 | 0.134187 | ||||||||
\(831\) | −59.4680 | −2.06292 | ||||||||
\(832\) | −1.00144 | −0.0347186 | ||||||||
\(833\) | 19.0575 | + | 22.1388i | 0.660304 | + | 0.767065i | ||||
\(834\) | −26.3661 | −0.912984 | ||||||||
\(835\) | − | 29.6092i | − | 1.02467i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.23245 | −0.284555 | ||||||||
\(838\) | −4.90124 | −0.169311 | ||||||||
\(839\) | − | 7.54175i | − | 0.260370i | −0.991490 | − | 0.130185i | \(-0.958443\pi\) | ||
0.991490 | − | 0.130185i | \(-0.0415571\pi\) | |||||||
\(840\) | −54.0460 | − | 24.7884i | −1.86476 | − | 0.855282i | ||||
\(841\) | 24.8271 | 0.856107 | ||||||||
\(842\) | − | 16.0158i | − | 0.551940i | ||||||
\(843\) | 57.0760 | 1.96580 | ||||||||
\(844\) | 22.2349i | 0.765358i | ||||||||
\(845\) | − | 41.8291i | − | 1.43896i | ||||||
\(846\) | −18.5436 | −0.637544 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.60772 | 0.0552092 | ||||||||
\(849\) | − | 82.0793i | − | 2.81696i | ||||||
\(850\) | 21.3424i | 0.732039i | ||||||||
\(851\) | 7.88309 | 0.270229 | ||||||||
\(852\) | 41.8900i | 1.43513i | ||||||||
\(853\) | −1.58216 | −0.0541720 | −0.0270860 | − | 0.999633i | \(-0.508623\pi\) | ||||
−0.0270860 | + | 0.999633i | \(0.508623\pi\) | |||||||
\(854\) | 21.6037 | + | 9.90860i | 0.739262 | + | 0.339065i | ||||
\(855\) | 17.8453i | 0.610297i | ||||||||
\(856\) | −25.1956 | −0.861169 | ||||||||
\(857\) | −52.3232 | −1.78733 | −0.893664 | − | 0.448737i | \(-0.851874\pi\) | ||||
−0.893664 | + | 0.448737i | \(0.851874\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.18932i | − | 0.245296i | −0.992450 | − | 0.122648i | \(-0.960861\pi\) | ||
0.992450 | − | 0.122648i | \(-0.0391387\pi\) | |||||||
\(860\) | 9.51368 | 0.324414 | ||||||||
\(861\) | 35.0633 | + | 16.0819i | 1.19495 | + | 0.548070i | ||||
\(862\) | −0.430876 | −0.0146757 | ||||||||
\(863\) | −43.8560 | −1.49288 | −0.746438 | − | 0.665455i | \(-0.768238\pi\) | ||||
−0.746438 | + | 0.665455i | \(0.768238\pi\) | |||||||
\(864\) | 15.8726 | 0.539997 | ||||||||
\(865\) | 57.0063i | 1.93827i | ||||||||
\(866\) | 11.5869 | 0.393738 | ||||||||
\(867\) | 1.09982i | 0.0373519i | ||||||||
\(868\) | −11.1458 | − | 5.11206i | −0.378313 | − | 0.173515i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.9417 | 0.438765 | ||||||||
\(871\) | 0.540257 | 0.0183059 | ||||||||
\(872\) | 7.27184 | 0.246256 | ||||||||
\(873\) | − | 51.1309i | − | 1.73052i | ||||||
\(874\) | − | 2.39175i | − | 0.0809020i | ||||||
\(875\) | −22.2073 | − | 10.1855i | −0.750745 | − | 0.344332i | ||||
\(876\) | − | 51.4179i | − | 1.73725i | ||||||
\(877\) | − | 14.3775i | − | 0.485494i | −0.970090 | − | 0.242747i | \(-0.921952\pi\) | ||
0.970090 | − | 0.242747i | \(-0.0780484\pi\) | |||||||
\(878\) | − | 0.0256535i | − | 0.000865765i | ||||||
\(879\) | − | 65.9190i | − | 2.22339i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.45261i | − | 0.0826304i | −0.999146 | − | 0.0413152i | \(-0.986845\pi\) | ||
0.999146 | − | 0.0413152i | \(-0.0131548\pi\) | |||||||
\(882\) | −14.4066 | + | 12.4015i | −0.485095 | + | 0.417579i | ||||
\(883\) | 4.78704 | 0.161097 | 0.0805484 | − | 0.996751i | \(-0.474333\pi\) | ||||
0.0805484 | + | 0.996751i | \(0.474333\pi\) | |||||||
\(884\) | −7.12218 | −0.239545 | ||||||||
\(885\) | 21.5613i | 0.724774i | ||||||||
\(886\) | 20.6165i | 0.692624i | ||||||||
\(887\) | −35.8413 | −1.20343 | −0.601717 | − | 0.798709i | \(-0.705517\pi\) | ||||
−0.601717 | + | 0.798709i | \(0.705517\pi\) | |||||||
\(888\) | −17.4860 | −0.586793 | ||||||||
\(889\) | −14.7413 | − | 6.76114i | −0.494406 | − | 0.226761i | ||||
\(890\) | − | 5.51682i | − | 0.184924i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.4221i | 0.918161i | ||||||||
\(893\) | 8.50512i | 0.284613i | ||||||||
\(894\) | − | 13.4070i | − | 0.448399i | ||||||
\(895\) | 26.1558i | 0.874291i | ||||||||
\(896\) | 26.3076 | + | 12.0661i | 0.878876 | + | 0.403100i | ||||
\(897\) | 8.35052i | 0.278816i | ||||||||
\(898\) | − | 19.8627i | − | 0.662828i | ||||||
\(899\) | 6.11870 | 0.204070 | ||||||||
\(900\) | 47.4719 | 1.58240 | ||||||||
\(901\) | −4.50631 | −0.150127 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.06763 | − | 11.0489i | 0.168640 | − | 0.367685i | ||||
\(904\) | 17.3205i | 0.576071i | ||||||||
\(905\) | 51.3967 | 1.70849 | ||||||||
\(906\) | 22.7163i | 0.754700i | ||||||||
\(907\) | 7.18813 | 0.238678 | 0.119339 | − | 0.992854i | \(-0.461922\pi\) | ||||
0.119339 | + | 0.992854i | \(0.461922\pi\) | |||||||
\(908\) | 6.34603 | 0.210601 | ||||||||
\(909\) | 12.7804 | 0.423900 | ||||||||
\(910\) | −2.90575 | + | 6.33538i | −0.0963245 | + | 0.210016i | ||||
\(911\) | 20.0130 | 0.663060 | 0.331530 | − | 0.943445i | \(-0.392435\pi\) | ||||
0.331530 | + | 0.943445i | \(0.392435\pi\) | |||||||
\(912\) | − | 4.91883i | − | 0.162879i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 2.85803 | 0.0945354 | ||||||||
\(915\) | −125.723 | −4.15628 | ||||||||
\(916\) | 15.1657i | 0.501088i | ||||||||
\(917\) | −20.7681 | + | 45.2805i | −0.685822 | + | 1.49529i | ||||
\(918\) | −7.71690 | −0.254696 | ||||||||
\(919\) | − | 3.54390i | − | 0.116903i | −0.998290 | − | 0.0584513i | \(-0.981384\pi\) | ||
0.998290 | − | 0.0584513i | \(-0.0186162\pi\) | |||||||
\(920\) | −24.1810 | −0.797224 | ||||||||
\(921\) | 26.5335i | 0.874307i | ||||||||
\(922\) | − | 8.00182i | − | 0.263526i | ||||||
\(923\) | 11.2574 | 0.370543 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.9951 | −0.690314 | ||||||||
\(926\) | 19.8486i | 0.652265i | ||||||||
\(927\) | − | 39.2806i | − | 1.29014i | ||||||
\(928\) | −11.7972 | −0.387262 | ||||||||
\(929\) | 27.2210i | 0.893092i | 0.894761 | + | 0.446546i | \(0.147346\pi\) | ||||
−0.894761 | + | 0.446546i | \(0.852654\pi\) | |||||||
\(930\) | −18.9763 | −0.622259 | ||||||||
\(931\) | 5.68798 | + | 6.60764i | 0.186416 | + | 0.216557i | ||||
\(932\) | 0.157767i | 0.00516784i | ||||||||
\(933\) | 49.6535 | 1.62558 | ||||||||
\(934\) | 7.50122 | 0.245447 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 10.6253i | − | 0.347298i | ||||||
\(937\) | 47.9616 | 1.56684 | 0.783418 | − | 0.621495i | \(-0.213474\pi\) | ||||
0.783418 | + | 0.621495i | \(0.213474\pi\) | |||||||
\(938\) | 0.792523 | + | 0.363494i | 0.0258768 | + | 0.0118685i | ||||
\(939\) | 14.0214 | 0.457573 | ||||||||
\(940\) | 37.5076 | 1.22336 | ||||||||
\(941\) | 10.4613 | 0.341028 | 0.170514 | − | 0.985355i | \(-0.445457\pi\) | ||||
0.170514 | + | 0.985355i | \(0.445457\pi\) | |||||||
\(942\) | 27.2372i | 0.887437i | ||||||||
\(943\) | 15.6879 | 0.510867 | ||||||||
\(944\) | − | 3.40913i | − | 0.110958i | ||||||
\(945\) | 10.7615 | − | 23.4633i | 0.350073 | − | 0.763260i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.5419 | −1.02497 | −0.512487 | − | 0.858695i | \(-0.671276\pi\) | ||||
−0.512487 | + | 0.858695i | \(0.671276\pi\) | |||||||
\(948\) | 51.0306 | 1.65740 | ||||||||
\(949\) | −13.8180 | −0.448550 | ||||||||
\(950\) | 6.36994i | 0.206668i | ||||||||
\(951\) | − | 76.2725i | − | 2.47330i | ||||||
\(952\) | −23.9522 | − | 10.9858i | −0.776294 | − | 0.356051i | ||||
\(953\) | − | 3.69767i | − | 0.119779i | −0.998205 | − | 0.0598897i | \(-0.980925\pi\) | ||
0.998205 | − | 0.0598897i | \(-0.0190749\pi\) | |||||||
\(954\) | − | 2.93243i | − | 0.0949410i | ||||||
\(955\) | 5.64226i | 0.182579i | ||||||||
\(956\) | 9.49395i | 0.307056i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 7.62407i | − | 0.246323i | ||||||
\(959\) | −3.26421 | + | 7.11693i | −0.105407 | + | 0.229818i | ||||
\(960\) | 8.54916 | 0.275923 | ||||||||
\(961\) | 22.0282 | 0.710587 | ||||||||
\(962\) | 2.04975i | 0.0660865i | ||||||||
\(963\) | − | 42.6084i | − | 1.37304i | ||||||
\(964\) | −6.67760 | −0.215071 | ||||||||
\(965\) | −39.7693 | −1.28022 | ||||||||
\(966\) | −5.61836 | + | 12.2497i | −0.180768 | + | 0.394127i | ||||
\(967\) | 22.8572i | 0.735038i | 0.930016 | + | 0.367519i | \(0.119793\pi\) | ||||
−0.930016 | + | 0.367519i | \(0.880207\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.7871i | 0.442906i | ||||||||
\(970\) | − | 30.2567i | − | 0.971483i | ||||||
\(971\) | − | 1.02730i | − | 0.0329675i | −0.999864 | − | 0.0164837i | \(-0.994753\pi\) | ||
0.999864 | − | 0.0164837i | \(-0.00524718\pi\) | |||||||
\(972\) | − | 32.5329i | − | 1.04349i | ||||||
\(973\) | 16.2952 | − | 35.5282i | 0.522399 | − | 1.13898i | ||||
\(974\) | 10.4326i | 0.334282i | ||||||||
\(975\) | − | 22.2400i | − | 0.712249i | ||||||
\(976\) | 19.8785 | 0.636297 | ||||||||
\(977\) | 20.2745 | 0.648638 | 0.324319 | − | 0.945948i | \(-0.394865\pi\) | ||||
0.324319 | + | 0.945948i | \(0.394865\pi\) | |||||||
\(978\) | −37.5391 | −1.20037 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 29.1397 | − | 25.0840i | 0.930834 | − | 0.801280i | ||||
\(981\) | 12.2974i | 0.392627i | ||||||||
\(982\) | −7.00320 | −0.223481 | ||||||||
\(983\) | − | 19.6549i | − | 0.626894i | −0.949606 | − | 0.313447i | \(-0.898516\pi\) | ||
0.949606 | − | 0.313447i | \(-0.101484\pi\) | |||||||
\(984\) | −34.7983 | −1.10933 | ||||||||
\(985\) | 53.3680 | 1.70044 | ||||||||
\(986\) | 5.73552 | 0.182656 | ||||||||
\(987\) | 19.9791 | − | 43.5602i | 0.635941 | − | 1.38654i | ||||
\(988\) | −2.12571 | −0.0676280 | ||||||||
\(989\) | − | 4.94345i | − | 0.157193i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4581 | 0.395744 | 0.197872 | − | 0.980228i | \(-0.436597\pi\) | ||||
0.197872 | + | 0.980228i | \(0.436597\pi\) | |||||||
\(992\) | 17.2981 | 0.549216 | ||||||||
\(993\) | 32.4320i | 1.02920i | ||||||||
\(994\) | 16.5139 | + | 7.57418i | 0.523790 | + | 0.240238i | ||||
\(995\) | −77.9021 | −2.46966 | ||||||||
\(996\) | − | 6.64341i | − | 0.210505i | ||||||
\(997\) | −20.0672 | −0.635533 | −0.317767 | − | 0.948169i | \(-0.602933\pi\) | ||||
−0.317767 | + | 0.948169i | \(0.602933\pi\) | |||||||
\(998\) | − | 15.6221i | − | 0.494509i | ||||||
\(999\) | − | 7.59130i | − | 0.240178i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))