Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1685,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1685");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.bm (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1685.1 | ||
Root | \(1.68124 - 0.416458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1685 |
Dual form | 1764.2.bm.a.1697.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.71501 | + | 0.242362i | −0.990162 | + | 0.139928i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.699656 | −0.312896 | −0.156448 | − | 0.987686i | \(-0.550004\pi\) | ||||
−0.156448 | + | 0.987686i | \(0.550004\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.88252 | − | 0.831308i | 0.960840 | − | 0.277103i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.265217i | 0.0799659i | 0.999200 | + | 0.0399829i | \(0.0127304\pi\) | ||||
−0.999200 | + | 0.0399829i | \(0.987270\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13823 | − | 0.657156i | 0.315688 | − | 0.182262i | −0.333781 | − | 0.942651i | \(-0.608325\pi\) |
0.649469 | + | 0.760388i | \(0.274991\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19992 | − | 0.169570i | 0.309817 | − | 0.0437829i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.86392 | − | 3.22840i | −0.452067 | − | 0.783003i | 0.546447 | − | 0.837493i | \(-0.315980\pi\) |
−0.998514 | + | 0.0544906i | \(0.982646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.382449 | + | 0.220807i | 0.0877398 | + | 0.0506566i | 0.543228 | − | 0.839585i | \(-0.317202\pi\) |
−0.455488 | + | 0.890242i | \(0.650535\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.96463i | 1.03520i | 0.855624 | + | 0.517598i | \(0.173174\pi\) | ||||
−0.855624 | + | 0.517598i | \(0.826826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.51048 | −0.902096 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.74208 | + | 2.12432i | −0.912613 | + | 0.408825i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.273287 | − | 0.157782i | −0.0507480 | − | 0.0292994i | 0.474411 | − | 0.880303i | \(-0.342661\pi\) |
−0.525159 | + | 0.851004i | \(0.675994\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.85521 | + | 2.80316i | 0.872022 | + | 0.503462i | 0.868020 | − | 0.496530i | \(-0.165393\pi\) |
0.00400255 | + | 0.999992i | \(0.498726\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0642786 | − | 0.454850i | −0.0111895 | − | 0.0791792i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.351124 | + | 0.608164i | −0.0577244 | + | 0.0999816i | −0.893444 | − | 0.449175i | \(-0.851718\pi\) |
0.835719 | + | 0.549157i | \(0.185051\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.79280 | + | 1.40289i | −0.287078 | + | 0.224643i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.39354 | − | 9.34189i | −0.842330 | − | 1.45896i | −0.887920 | − | 0.459998i | \(-0.847850\pi\) |
0.0455900 | − | 0.998960i | \(-0.485483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.73131 | − | 6.46283i | 0.569020 | − | 0.985572i | −0.427643 | − | 0.903948i | \(-0.640656\pi\) |
0.996663 | − | 0.0816240i | \(-0.0260106\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.01677 | + | 0.581630i | −0.300643 | + | 0.0867042i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50285 | + | 6.06712i | 0.510943 | + | 0.884980i | 0.999920 | + | 0.0126827i | \(0.00403713\pi\) |
−0.488976 | + | 0.872297i | \(0.662630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.97908 | + | 5.08500i | 0.557183 | + | 0.712043i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.51919 | + | 4.91856i | −1.17020 | + | 0.675616i | −0.953727 | − | 0.300672i | \(-0.902789\pi\) |
−0.216474 | + | 0.976288i | \(0.569456\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.185561i | − | 0.0250210i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.709419 | − | 0.285995i | −0.0939648 | − | 0.0378809i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.73182 | − | 11.6598i | 0.876408 | − | 1.51798i | 0.0211522 | − | 0.999776i | \(-0.493267\pi\) |
0.855256 | − | 0.518206i | \(-0.173400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.89484 | − | 2.82604i | 0.626720 | − | 0.361837i | −0.152761 | − | 0.988263i | \(-0.548816\pi\) |
0.779481 | + | 0.626426i | \(0.215483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.796368 | + | 0.459783i | −0.0987773 | + | 0.0570291i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.97060 | − | 5.14523i | 0.362916 | − | 0.628590i | −0.625523 | − | 0.780206i | \(-0.715114\pi\) |
0.988439 | + | 0.151616i | \(0.0484477\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.20324 | − | 8.51439i | −0.144853 | − | 1.02501i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.4323i | − | 1.59412i | −0.603900 | − | 0.797060i | \(-0.706387\pi\) | ||
0.603900 | − | 0.797060i | \(-0.293613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.66182 | − | 3.84620i | 0.779707 | − | 0.450164i | −0.0566194 | − | 0.998396i | \(-0.518032\pi\) |
0.836326 | + | 0.548232i | \(0.184699\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.73552 | − | 1.09317i | 0.893221 | − | 0.126229i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.698360 | − | 1.20959i | −0.0785716 | − | 0.136090i | 0.824062 | − | 0.566499i | \(-0.191703\pi\) |
−0.902634 | + | 0.430409i | \(0.858369\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.61785 | − | 4.79253i | 0.846428 | − | 0.532503i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.72399 | + | 6.45014i | −0.408761 | + | 0.707995i | −0.994751 | − | 0.102323i | \(-0.967372\pi\) |
0.585990 | + | 0.810318i | \(0.300706\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.30410 | + | 2.25877i | 0.141450 | + | 0.244998i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.506930 | + | 0.204363i | 0.0543486 | + | 0.0219101i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.59261 | − | 9.68668i | 0.592815 | − | 1.02679i | −0.401036 | − | 0.916062i | \(-0.631350\pi\) |
0.993851 | − | 0.110724i | \(-0.0353168\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.00612 | − | 3.63073i | −0.933892 | − | 0.376489i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.267582 | − | 0.154489i | −0.0274534 | − | 0.0158502i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.18225 | − | 5.30138i | −0.932316 | − | 0.538273i | −0.0447729 | − | 0.998997i | \(-0.514256\pi\) |
−0.887543 | + | 0.460724i | \(0.847590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.220477 | + | 0.764493i | 0.0221588 | + | 0.0768345i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.5071 | −1.74203 | −0.871013 | − | 0.491260i | \(-0.836537\pi\) | ||||
−0.871013 | + | 0.491260i | \(0.836537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.54219i | − | 0.841687i | −0.907133 | − | 0.420844i | \(-0.861734\pi\) | ||
0.907133 | − | 0.420844i | \(-0.138266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.09489 | − | 5.25093i | −0.879236 | − | 0.507627i | −0.00882940 | − | 0.999961i | \(-0.502811\pi\) |
−0.870406 | + | 0.492334i | \(0.836144\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.12110 | − | 12.3341i | −0.682078 | − | 1.18139i | −0.974346 | − | 0.225057i | \(-0.927743\pi\) |
0.292268 | − | 0.956337i | \(-0.405590\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.454785 | − | 1.12811i | 0.0431663 | − | 0.107075i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3783 | − | 7.72396i | 1.25852 | − | 0.726609i | 0.285737 | − | 0.958308i | \(-0.407762\pi\) |
0.972788 | + | 0.231699i | \(0.0744284\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.47353i | − | 0.323908i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.73467 | − | 2.84048i | 0.252820 | − | 0.262603i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9297 | 0.993605 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.5141 | + | 14.7142i | 1.03819 | + | 1.32674i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.65406 | 0.595157 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.8304 | 1.93713 | 0.968566 | − | 0.248758i | \(-0.0800225\pi\) | ||||
0.968566 | + | 0.248758i | \(0.0800225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.83290 | + | 11.9881i | −0.425513 | + | 1.05550i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.20922 | −0.455132 | −0.227566 | − | 0.973763i | \(-0.573077\pi\) | ||||
−0.227566 | + | 0.973763i | \(0.573077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.31782 | − | 1.48629i | 0.285552 | − | 0.127920i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.69725i | − | 0.230442i | −0.993340 | − | 0.115221i | \(-0.963242\pi\) | ||
0.993340 | − | 0.115221i | \(-0.0367576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1448 | + | 5.85710i | −0.860470 | + | 0.496793i | −0.864170 | − | 0.503200i | \(-0.832156\pi\) |
0.00369951 | + | 0.999993i | \(0.498822\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.47787 | − | 9.55621i | −0.629750 | − | 0.804778i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.174289 | + | 0.301877i | 0.0145748 | + | 0.0252442i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.191206 | + | 0.110393i | 0.0158788 | + | 0.00916765i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 18.8280i | − | 1.54245i | −0.636564 | − | 0.771224i | \(-0.719645\pi\) | ||
0.636564 | − | 0.771224i | \(-0.280355\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0029 | 0.814021 | 0.407010 | − | 0.913424i | \(-0.366571\pi\) | ||||
0.407010 | + | 0.913424i | \(0.366571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.05659 | − | 7.75645i | −0.651336 | − | 0.627072i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.39698 | − | 1.96125i | −0.272852 | − | 0.157531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.218293 | + | 0.126032i | 0.0174217 | + | 0.0100584i | 0.508686 | − | 0.860952i | \(-0.330132\pi\) |
−0.491264 | + | 0.871011i | \(0.663465\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.4184 | − | 10.5001i | 1.06415 | − | 0.832713i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.29780 | − | 7.44400i | 0.336629 | − | 0.583059i | −0.647167 | − | 0.762348i | \(-0.724046\pi\) |
0.983796 | + | 0.179289i | \(0.0573797\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0449729 | + | 0.318238i | 0.00350114 | + | 0.0247748i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.24437 | + | 3.88736i | 0.173674 | + | 0.300813i | 0.939702 | − | 0.341995i | \(-0.111103\pi\) |
−0.766027 | + | 0.642808i | \(0.777769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.63629 | + | 9.76234i | −0.433561 | + | 0.750949i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.28598 | + | 0.318548i | 0.0983410 | + | 0.0243599i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.56072 | + | 6.16736i | 0.270717 | + | 0.468895i | 0.969046 | − | 0.246882i | \(-0.0794060\pi\) |
−0.698329 | + | 0.715777i | \(0.746073\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.71922 | + | 21.6283i | −0.655377 | + | 1.62568i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.1270 | + | 12.7750i | −1.65385 | + | 0.954848i | −0.678376 | + | 0.734715i | \(0.737316\pi\) |
−0.975470 | + | 0.220134i | \(0.929351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.943175i | − | 0.0701057i | −0.999385 | − | 0.0350528i | \(-0.988840\pi\) | ||
0.999385 | − | 0.0350528i | \(-0.0111599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.70977 | + | 6.03301i | −0.569923 | + | 0.445973i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.245666 | − | 0.425506i | 0.0180617 | − | 0.0312838i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.856227 | − | 0.494343i | 0.0626135 | − | 0.0361499i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.57413 | + | 1.48617i | −0.186258 | + | 0.107536i | −0.590229 | − | 0.807236i | \(-0.700963\pi\) |
0.403972 | + | 0.914771i | \(0.367629\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.25721 | − | 16.0340i | 0.666348 | − | 1.15415i | −0.312570 | − | 0.949895i | \(-0.601190\pi\) |
0.978918 | − | 0.204254i | \(-0.0654769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.25434 | − | 0.981542i | 0.0898255 | − | 0.0702897i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.1774i | − | 1.01010i | −0.863091 | − | 0.505048i | \(-0.831475\pi\) | ||
0.863091 | − | 0.505048i | \(-0.168525\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.5293 | − | 11.8526i | 1.45529 | − | 0.840209i | 0.456512 | − | 0.889717i | \(-0.349099\pi\) |
0.998774 | + | 0.0495081i | \(0.0157654\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.84760 | + | 9.54408i | −0.271389 | + | 0.673187i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.77362 | + | 6.53611i | 0.263561 | + | 0.456502i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.12714 | + | 14.3106i | 0.286856 | + | 0.994659i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0585617 | + | 0.101432i | −0.00405080 | + | 0.00701619i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.04004 | + | 5.26550i | 0.209285 | + | 0.362492i | 0.951489 | − | 0.307681i | \(-0.0995531\pi\) |
−0.742205 | + | 0.670173i | \(0.766220\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.25549 | + | 23.0365i | 0.223062 | + | 1.57844i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.61063 | + | 4.52175i | −0.178044 | + | 0.308381i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.4929 | + | 8.21085i | −0.709045 | + | 0.554838i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.24313 | − | 2.44977i | −0.285424 | − | 0.164790i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.796137 | + | 0.459650i | 0.0533133 | + | 0.0307804i | 0.526420 | − | 0.850225i | \(-0.323534\pi\) |
−0.473106 | + | 0.881005i | \(0.656867\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0016 | + | 3.74960i | −0.866771 | + | 0.249973i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.0059 | −0.664118 | −0.332059 | − | 0.943259i | \(-0.607743\pi\) | ||||
−0.332059 | + | 0.943259i | \(0.607743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.75025i | 0.181742i | 0.995863 | + | 0.0908710i | \(0.0289651\pi\) | ||||
−0.995863 | + | 0.0908710i | \(0.971035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.55513 | + | 3.20725i | 0.363928 | + | 0.210114i | 0.670803 | − | 0.741636i | \(-0.265950\pi\) |
−0.306874 | + | 0.951750i | \(0.599283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.45079 | − | 4.24489i | −0.159872 | − | 0.276906i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.49085 | + | 1.90521i | 0.0968414 | + | 0.123757i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.4288 | + | 6.59844i | −0.739270 | + | 0.426818i | −0.821804 | − | 0.569770i | \(-0.807032\pi\) |
0.0825337 | + | 0.996588i | \(0.473699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2.54868i | − | 0.164175i | −0.996625 | − | 0.0820874i | \(-0.973841\pi\) | ||
0.996625 | − | 0.0820874i | \(-0.0261587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.9032 | + | 10.0655i | −0.763589 | + | 0.645703i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.580418 | 0.0369311 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.82341 | − | 11.9646i | 0.305671 | − | 0.758227i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7893 | 1.18597 | 0.592986 | − | 0.805213i | \(-0.297949\pi\) | ||||
0.592986 | + | 0.805213i | \(0.297949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31670 | −0.0827804 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.78399 | − | 3.55775i | −0.174340 | − | 0.222795i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.3945 | −0.897907 | −0.448953 | − | 0.893555i | \(-0.648203\pi\) | ||||
−0.448953 | + | 0.893555i | \(0.648203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.918920 | − | 0.227625i | −0.0568797 | − | 0.0140896i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.84976i | 0.484037i | 0.970272 | + | 0.242019i | \(0.0778095\pi\) | ||||
−0.970272 | + | 0.242019i | \(0.922190\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.96050 | − | 3.44130i | 0.366151 | − | 0.211397i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.24369 | + | 17.9682i | −0.443307 | + | 1.09964i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.72267 | − | 13.3760i | −0.470859 | − | 0.815552i | 0.528585 | − | 0.848880i | \(-0.322723\pi\) |
−0.999444 | + | 0.0333281i | \(0.989389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9476 | − | 6.32057i | −0.665016 | − | 0.383947i | 0.129169 | − | 0.991623i | \(-0.458769\pi\) |
−0.794186 | + | 0.607675i | \(0.792102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.19626i | − | 0.0721369i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8906 | −0.714439 | −0.357219 | − | 0.934021i | \(-0.616275\pi\) | ||||
−0.357219 | + | 0.934021i | \(0.616275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.3255 | + | 4.04399i | 0.977385 | + | 0.242107i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.75411 | − | 1.59009i | −0.164297 | − | 0.0948568i | 0.415597 | − | 0.909549i | \(-0.363573\pi\) |
−0.579894 | + | 0.814692i | \(0.696906\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0195 | + | 9.24889i | 0.952263 | + | 0.549789i | 0.893783 | − | 0.448499i | \(-0.148041\pi\) |
0.0584799 | + | 0.998289i | \(0.481375\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.496349 | + | 0.200098i | 0.0294012 | + | 0.0118528i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.55161 | − | 2.68746i | 0.0912711 | − | 0.158086i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.0325 | + | 6.86648i | 0.998463 | + | 0.402520i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.42975 | − | 2.47639i | −0.0835266 | − | 0.144672i | 0.821236 | − | 0.570589i | \(-0.193285\pi\) |
−0.904762 | + | 0.425917i | \(0.859952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.70995 | + | 8.15788i | −0.274224 | + | 0.474970i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.563405 | − | 1.25768i | −0.0326921 | − | 0.0729779i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.26254 | + | 5.65088i | 0.188677 | + | 0.326799i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 30.0249 | − | 4.24308i | 1.72489 | − | 0.243758i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.42470 | + | 1.97725i | −0.196098 | + | 0.113217i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6746i | 1.23704i | 0.785771 | + | 0.618518i | \(0.212266\pi\) | ||||
−0.785771 | + | 0.618518i | \(0.787734\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.07031 | + | 14.6499i | 0.117776 | + | 0.833406i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.8462 | − | 20.5183i | 0.671738 | − | 1.16348i | −0.305673 | − | 0.952136i | \(-0.598881\pi\) |
0.977411 | − | 0.211348i | \(-0.0677852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.6283 | + | 13.6418i | −1.33555 | + | 0.771081i | −0.986144 | − | 0.165890i | \(-0.946950\pi\) |
−0.349407 | + | 0.936971i | \(0.613617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.2647 | + | 12.2772i | −1.19435 | + | 0.689556i | −0.959289 | − | 0.282426i | \(-0.908861\pi\) |
−0.235057 | + | 0.971982i | \(0.575528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0418465 | − | 0.0724802i | 0.00234295 | − | 0.00405811i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.8705 | + | 6.80115i | 0.941617 | + | 0.379603i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.64626i | − | 0.0916006i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.13396 | + | 2.96409i | −0.284781 | + | 0.164418i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.2021 | + | 19.4272i | 0.840678 | + | 1.07433i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.15579 | − | 14.1262i | −0.448283 | − | 0.776449i | 0.549991 | − | 0.835170i | \(-0.314631\pi\) |
−0.998274 | + | 0.0587215i | \(0.981298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.506550 | + | 2.04494i | −0.0277588 | + | 0.112062i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.07840 | + | 3.59989i | −0.113555 | + | 0.196683i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6580 | + | 23.6563i | 0.743998 | + | 1.28864i | 0.950661 | + | 0.310230i | \(0.100406\pi\) |
−0.206663 | + | 0.978412i | \(0.566261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.0719 | + | 16.4891i | −1.14447 | + | 0.895564i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.743445 | + | 1.28768i | −0.0402598 | + | 0.0697320i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.841854 | + | 5.95714i | 0.0453239 | + | 0.320722i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.37986 | − | 3.10606i | −0.288806 | − | 0.166742i | 0.348597 | − | 0.937273i | \(-0.386658\pi\) |
−0.637403 | + | 0.770530i | \(0.719991\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.6529 | + | 14.2334i | 1.31964 | + | 0.761896i | 0.983671 | − | 0.179977i | \(-0.0576023\pi\) |
0.335971 | + | 0.941872i | \(0.390936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00155 | + | 5.53424i | −0.213587 | + | 0.295396i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.98691 | −0.158977 | −0.0794887 | − | 0.996836i | \(-0.525329\pi\) | ||||
−0.0794887 | + | 0.996836i | \(0.525329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.39798i | 0.498793i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.5977 | + | 15.3562i | 1.40377 | + | 0.810468i | 0.994777 | − | 0.102070i | \(-0.0325465\pi\) |
0.408994 | + | 0.912537i | \(0.365880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.40249 | − | 16.2856i | −0.494868 | − | 0.857136i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.7445 | + | 2.64894i | −0.983830 | + | 0.139033i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.66098 | + | 2.69102i | −0.243967 | + | 0.140854i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.0384i | 0.993794i | 0.867809 | + | 0.496897i | \(0.165527\pi\) | ||||
−0.867809 | + | 0.496897i | \(0.834473\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.3130 | − | 22.4445i | −1.21363 | − | 1.16841i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.11738 | 0.213190 | 0.106595 | − | 0.994303i | \(-0.466005\pi\) | ||||
0.106595 | + | 0.994303i | \(0.466005\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.4118 | + | 1.61270i | −0.589302 | + | 0.0832792i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.414750 | −0.0213607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2436 | −0.577546 | −0.288773 | − | 0.957398i | \(-0.593247\pi\) | ||||
−0.288773 | + | 0.957398i | \(0.593247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.4393 | + | 5.29086i | −1.91807 | + | 0.271059i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.6093 | −1.61516 | −0.807580 | − | 0.589758i | \(-0.799223\pi\) | ||||
−0.807580 | + | 0.589758i | \(0.799223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.38299 | − | 21.7311i | 0.273633 | − | 1.10465i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.2485i | 1.07734i | 0.842516 | + | 0.538672i | \(0.181074\pi\) | ||||
−0.842516 | + | 0.538672i | \(0.818926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0278 | − | 9.25367i | 0.810562 | − | 0.467978i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.93387 | − | 1.26252i | 0.450654 | − | 0.0636857i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.488611 | + | 0.846300i | 0.0245847 | + | 0.0425820i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.6927 | − | 11.9469i | −1.03854 | − | 0.599599i | −0.119118 | − | 0.992880i | \(-0.538007\pi\) |
−0.919419 | + | 0.393281i | \(0.871340\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 25.4174i | − | 1.26928i | −0.772806 | − | 0.634642i | \(-0.781147\pi\) | ||
0.772806 | − | 0.634642i | \(-0.218853\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.36845 | 0.367049 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.32987 | + | 3.35312i | −0.264844 | + | 0.166618i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.161295 | − | 0.0931240i | −0.00799512 | − | 0.00461598i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3831 | + | 11.1908i | 0.958433 | + | 0.553351i | 0.895690 | − | 0.444678i | \(-0.146682\pi\) |
0.0627424 | + | 0.998030i | \(0.480015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.653713 | + | 4.62582i | 0.0322453 | + | 0.228175i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.60551 | − | 4.51288i | 0.127900 | − | 0.221528i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.9789 | − | 12.5037i | 0.782489 | − | 0.612309i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.04181 | + | 12.1968i | 0.344015 | + | 0.595851i | 0.985174 | − | 0.171556i | \(-0.0548796\pi\) |
−0.641159 | + | 0.767408i | \(0.721546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.07639 | − | 13.9887i | 0.393619 | − | 0.681768i | −0.599305 | − | 0.800521i | \(-0.704556\pi\) |
0.992924 | + | 0.118753i | \(0.0378896\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.1407 | + | 14.5766i | 0.736165 | + | 0.708740i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.40717 | + | 14.5617i | 0.407808 | + | 0.706344i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.372071 | − | 0.475482i | −0.0179638 | − | 0.0229565i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.16179 | − | 4.13486i | 0.344971 | − | 0.199169i | −0.317497 | − | 0.948259i | \(-0.602842\pi\) |
0.662468 | + | 0.749090i | \(0.269509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.35102i | − | 0.209097i | −0.994520 | − | 0.104548i | \(-0.966660\pi\) | ||
0.994520 | − | 0.104548i | \(-0.0333397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.354676 | − | 0.142984i | −0.0170054 | − | 0.00685556i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.09622 | + | 1.89872i | −0.0524395 | + | 0.0908279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0200 | − | 10.4039i | 0.860048 | − | 0.496549i | −0.00398054 | − | 0.999992i | \(-0.501267\pi\) |
0.864028 | + | 0.503443i | \(0.167934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.7927 | + | 15.4688i | −1.27296 | + | 0.734945i | −0.975544 | − | 0.219803i | \(-0.929459\pi\) |
−0.297417 | + | 0.954748i | \(0.596125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.91290 | + | 6.77734i | −0.185489 | + | 0.321277i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.56320 | + | 32.2902i | 0.215832 | + | 1.52727i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.9215i | 0.987346i | 0.869648 | + | 0.493673i | \(0.164346\pi\) | ||||
−0.869648 | + | 0.493673i | \(0.835654\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.47763 | − | 1.43046i | 0.116667 | − | 0.0673577i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.1550 | + | 2.42432i | −0.806012 | + | 0.113904i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.15058 | − | 1.99286i | −0.0538217 | − | 0.0932218i | 0.837859 | − | 0.545886i | \(-0.183807\pi\) |
−0.891681 | + | 0.452664i | \(0.850474\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.6970 | + | 11.3498i | 0.732673 | + | 0.529762i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.92497 | − | 15.4585i | 0.415677 | − | 0.719974i | −0.579822 | − | 0.814743i | \(-0.696878\pi\) |
0.995499 | + | 0.0947688i | \(0.0302112\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.24034 | − | 10.8086i | −0.290013 | − | 0.502318i | 0.683799 | − | 0.729670i | \(-0.260326\pi\) |
−0.973813 | + | 0.227353i | \(0.926993\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.30119 | + | 2.54026i | 0.292211 | + | 0.117802i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.42799 | + | 4.20541i | −0.112354 | + | 0.194603i | −0.916719 | − | 0.399533i | \(-0.869172\pi\) |
0.804365 | + | 0.594136i | \(0.202506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.404920 | − | 0.163239i | −0.0186577 | − | 0.00752168i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.71405 | + | 0.989607i | 0.0788121 | + | 0.0455022i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.72503 | − | 0.995945i | −0.0791497 | − | 0.0456971i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.4679 | + | 21.2599i | −0.937161 | + | 0.973425i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.81084 | −0.402577 | −0.201289 | − | 0.979532i | \(-0.564513\pi\) | ||||
−0.201289 | + | 0.979532i | \(0.564513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.922973i | 0.0420839i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.42441 | + | 3.70914i | 0.291718 | + | 0.168423i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.66185 | + | 8.07456i | 0.211249 | + | 0.365893i | 0.952106 | − | 0.305770i | \(-0.0989137\pi\) |
−0.740857 | + | 0.671663i | \(0.765580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.56662 | + | 13.8082i | −0.251731 | + | 0.624427i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.9192 | + | 15.5418i | −1.21485 | + | 0.701391i | −0.963811 | − | 0.266587i | \(-0.914104\pi\) |
−0.251034 | + | 0.967978i | \(0.580771\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.17637i | 0.0529811i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.154258 | − | 0.534882i | −0.00693338 | − | 0.0240412i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.3388 | −1.00002 | −0.500010 | − | 0.866020i | \(-0.666670\pi\) | ||||
−0.500010 | + | 0.866020i | \(0.666670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.79127 | − | 6.12291i | −0.214058 | − | 0.273552i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.2396 | −0.545738 | −0.272869 | − | 0.962051i | \(-0.587973\pi\) | ||||
−0.272869 | + | 0.962051i | \(0.587973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2490 | 0.545072 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.30027 | − | 18.1085i | 0.324216 | − | 0.804229i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.1099 | 0.625411 | 0.312706 | − | 0.949850i | \(-0.398765\pi\) | ||||
0.312706 | + | 0.949850i | \(0.398765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.28266 | − | 0.234640i | −0.100782 | − | 0.0103596i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.97659i | 0.263360i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.60910 | + | 0.929015i | −0.0707682 | + | 0.0408580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.60141 | − | 9.71409i | −0.333665 | − | 0.426401i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.81632 | + | 4.87800i | 0.123385 | + | 0.213709i | 0.921101 | − | 0.389325i | \(-0.127292\pi\) |
−0.797715 | + | 0.603034i | \(0.793958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.2293 | + | 19.1849i | 1.45302 | + | 0.838899i | 0.998651 | − | 0.0519176i | \(-0.0165333\pi\) |
0.454364 | + | 0.890816i | \(0.349867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 20.8995i | − | 0.910395i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.64754 | −0.0716321 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.71167 | − | 39.2060i | 0.421451 | − | 1.70139i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.2782 | − | 7.08880i | −0.531826 | − | 0.307050i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.36329 | + | 3.67385i | 0.275109 | + | 0.158834i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.8518 | − | 27.2720i | 1.50396 | − | 1.17687i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.21673 | + | 5.57154i | −0.138298 | + | 0.239539i | −0.926852 | − | 0.375426i | \(-0.877496\pi\) |
0.788555 | + | 0.614965i | \(0.210830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.228590 | + | 1.61756i | 0.00980975 | + | 0.0694159i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.98232 | + | 8.62963i | 0.213419 | + | 0.369653i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.52889 | + | 11.3084i | −0.279155 | + | 0.483511i | −0.971175 | − | 0.238368i | \(-0.923388\pi\) |
0.692020 | + | 0.721878i | \(0.256721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.7602 | − | 12.2152i | 0.501912 | − | 0.521333i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0696787 | − | 0.120687i | −0.00296841 | − | 0.00514144i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.318193 | + | 0.789287i | −0.0135065 | + | 0.0335034i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.5409 | − | 14.7460i | 1.08220 | − | 0.624809i | 0.150712 | − | 0.988578i | \(-0.451843\pi\) |
0.931489 | + | 0.363769i | \(0.118510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.80822i | − | 0.414844i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.34863 | + | 1.05532i | −0.0569391 | + | 0.0445557i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.25934 | − | 9.10944i | 0.221655 | − | 0.383917i | −0.733656 | − | 0.679521i | \(-0.762188\pi\) |
0.955311 | + | 0.295604i | \(0.0955209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.36020 | + | 5.40411i | −0.393787 | + | 0.227353i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.8054 | + | 13.1667i | −0.956053 | + | 0.551977i | −0.894956 | − | 0.446155i | \(-0.852793\pi\) |
−0.0610967 | + | 0.998132i | \(0.519460\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0295 | − | 38.1562i | 0.921906 | − | 1.59679i | 0.125444 | − | 0.992101i | \(-0.459965\pi\) |
0.796463 | − | 0.604688i | \(-0.206702\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.05447 | − | 3.17268i | 0.169378 | − | 0.132540i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 22.3929i | − | 0.933847i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.1535 | + | 7.01684i | −0.505957 | + | 0.292115i | −0.731170 | − | 0.682195i | \(-0.761026\pi\) |
0.225213 | + | 0.974310i | \(0.427692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.9902 | + | 29.7420i | −0.498295 | + | 1.23604i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.30448 | − | 2.25943i | −0.0540262 | − | 0.0935762i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.91332 | + | 1.98736i | −0.0791062 | + | 0.0821673i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.52469 | − | 2.64085i | 0.0629308 | − | 0.108999i | −0.832843 | − | 0.553509i | \(-0.813289\pi\) |
0.895774 | + | 0.444509i | \(0.146622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.23791 | + | 2.14413i | 0.0510073 | + | 0.0883473i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.43607 | + | 24.3144i | 0.141341 | + | 1.00016i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.3041 | − | 23.0434i | 0.546334 | − | 0.946278i | −0.452188 | − | 0.891923i | \(-0.649356\pi\) |
0.998522 | − | 0.0543552i | \(-0.0173103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.3354 | + | 25.3029i | −1.32340 | + | 1.03558i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.86333 | − | 2.23050i | −0.157852 | − | 0.0911356i | 0.418993 | − | 0.907989i | \(-0.362383\pi\) |
−0.576845 | + | 0.816854i | \(0.695716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.25019 | + | 3.03120i | 0.214160 | + | 0.123645i | 0.603243 | − | 0.797557i | \(-0.293875\pi\) |
−0.389083 | + | 0.921203i | \(0.627208\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.28554 | − | 17.3007i | 0.174521 | − | 0.704539i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.64700 | −0.310895 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 45.3313i | − | 1.83994i | −0.391986 | − | 0.919971i | \(-0.628212\pi\) | ||
0.391986 | − | 0.919971i | \(-0.371788\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.97409 | + | 4.60384i | 0.322597 | + | 0.186251i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6294 | + | 28.8029i | 0.671654 | + | 1.16334i | 0.977435 | + | 0.211237i | \(0.0677492\pi\) |
−0.305781 | + | 0.952102i | \(0.598917\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.05591 | − | 10.2949i | −0.324846 | − | 0.415131i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.3001 | − | 18.0711i | 1.26010 | − | 0.727516i | 0.287002 | − | 0.957930i | \(-0.407341\pi\) |
0.973093 | + | 0.230414i | \(0.0740079\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26.4462i | − | 1.06296i | −0.847069 | − | 0.531482i | \(-0.821635\pi\) | ||
0.847069 | − | 0.531482i | \(-0.178365\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.5464 | − | 23.5426i | −0.423214 | − | 0.944734i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8969 | 0.715874 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0758507 | − | 0.188150i | 0.00302918 | − | 0.00751398i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.61787 | 0.104381 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0484 | −1.27583 | −0.637914 | − | 0.770107i | \(-0.720203\pi\) | ||||
−0.637914 | + | 0.770107i | \(0.720203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.48985 | − | 8.29359i | −0.257949 | − | 0.329641i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.2737 | −0.606120 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.1664 | − | 38.7189i | −0.441735 | − | 1.53170i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 24.4154i | − | 0.964351i | −0.876075 | − | 0.482176i | \(-0.839847\pi\) | ||
0.876075 | − | 0.482176i | \(-0.160153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.9014 | + | 18.4183i | −1.25807 | + | 0.726346i | −0.972699 | − | 0.232071i | \(-0.925450\pi\) |
−0.285370 | + | 0.958418i | \(0.592116\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.38136 | − | 8.38757i | 0.133141 | − | 0.330260i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.2847 | + | 23.0098i | 0.522276 | + | 0.904608i | 0.999664 | + | 0.0259155i | \(0.00825009\pi\) |
−0.477389 | + | 0.878692i | \(0.658417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.09239 | + | 1.78539i | 0.121387 | + | 0.0700827i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 30.3418i | − | 1.18737i | −0.804699 | − | 0.593683i | \(-0.797673\pi\) | ||
0.804699 | − | 0.593683i | \(-0.202327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.64466 | 0.142409 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.0055 | − | 16.6248i | 0.624432 | − | 0.648595i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.9873 | + | 23.6640i | 1.59664 | + | 0.921820i | 0.992129 | + | 0.125223i | \(0.0399647\pi\) |
0.604511 | + | 0.796597i | \(0.293369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.4187 | − | 17.5623i | −1.18315 | − | 0.683092i | −0.226409 | − | 0.974032i | \(-0.572699\pi\) |
−0.956741 | + | 0.290940i | \(0.906032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.87075 | + | 3.17301i | 0.305674 | + | 0.123229i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.783329 | − | 1.35677i | 0.0303306 | − | 0.0525342i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.47679 | − | 0.595351i | −0.0570958 | − | 0.0230176i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.749513 | + | 1.29819i | 0.0289346 | + | 0.0501162i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.54758 | + | 4.41254i | −0.0982020 | + | 0.170091i | −0.910940 | − | 0.412538i | \(-0.864642\pi\) |
0.812738 | + | 0.582629i | \(0.197976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.3890 | − | 9.58169i | 0.823265 | − | 0.368800i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.42072 | + | 14.5851i | 0.323635 | + | 0.560551i | 0.981235 | − | 0.192815i | \(-0.0617618\pi\) |
−0.657601 | + | 0.753367i | \(0.728429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.1603 | − | 2.42506i | 0.657584 | − | 0.0929287i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7555 | + | 9.09645i | −0.602868 | + | 0.348066i | −0.770169 | − | 0.637840i | \(-0.779828\pi\) |
0.167301 | + | 0.985906i | \(0.446495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.88715i | 0.0721042i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.666559 | − | 4.71672i | −0.0254308 | − | 0.179954i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.46452 | + | 11.1969i | −0.246279 | + | 0.426567i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.05405 | − | 1.76326i | 0.116182 | − | 0.0670775i | −0.440783 | − | 0.897614i | \(-0.645299\pi\) |
0.556965 | + | 0.830536i | \(0.311966\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.09786 | − | 4.09795i | 0.269237 | − | 0.155444i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.1063 | + | 34.8251i | −0.761579 | + | 1.31909i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.3044 | − | 4.15412i | −0.389749 | − | 0.157123i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.3502i | − | 0.504229i | −0.967697 | − | 0.252114i | \(-0.918874\pi\) | ||
0.967697 | − | 0.252114i | \(-0.0811259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.268574 | + | 0.155061i | −0.0101295 | + | 0.00584824i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.23193 | + | 6.68605i | 0.197046 | + | 0.251811i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1447 | + | 36.6237i | 0.794107 | + | 1.37543i | 0.923405 | + | 0.383827i | \(0.125394\pi\) |
−0.129298 | + | 0.991606i | \(0.541273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.01858 | − | 2.90613i | −0.113206 | − | 0.108988i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.9166 | + | 24.1043i | −0.521182 | + | 0.902715i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.121942 | − | 0.211210i | −0.00456038 | − | 0.00789881i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.0014 | − | 14.0863i | 0.672273 | − | 0.526063i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.2035 | − | 26.3332i | 0.566994 | − | 0.982062i | −0.429868 | − | 0.902892i | \(-0.641440\pi\) |
0.996861 | − | 0.0791697i | \(-0.0252269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.617704 | + | 4.37101i | 0.0229727 | + | 0.162560i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.23265 | + | 0.711673i | 0.0457796 | + | 0.0264309i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.3671 | − | 6.56280i | −0.421583 | − | 0.243401i | 0.274171 | − | 0.961681i | \(-0.411596\pi\) |
−0.695754 | + | 0.718280i | \(0.744930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.9746 | − | 20.1473i | 0.665724 | − | 0.746198i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.8195 | −1.02894 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.7588i | 1.39465i | 0.716753 | + | 0.697327i | \(0.245628\pi\) | ||||
−0.716753 | + | 0.697327i | \(0.754372\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.36460 | + | 0.787853i | 0.0502657 | + | 0.0290209i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1215 | − | 22.7271i | −0.482683 | − | 0.836031i | 0.517119 | − | 0.855913i | \(-0.327004\pi\) |
−0.999802 | + | 0.0198820i | \(0.993671\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.995424 | + | 0.140672i | −0.0365678 | + | 0.00516770i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.78379 | + | 5.07132i | −0.322246 | + | 0.186049i | −0.652393 | − | 0.757881i | \(-0.726235\pi\) |
0.330147 | + | 0.943929i | \(0.392902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.1731i | 0.482625i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.37242 | + | 21.6884i | −0.196567 | + | 0.793539i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.90737 | 0.288544 | 0.144272 | − | 0.989538i | \(-0.453916\pi\) | ||||
0.144272 | + | 0.989538i | \(0.453916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −32.2239 | + | 4.55383i | −1.17430 | + | 0.165951i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.99855 | −0.254703 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.8903 | 1.08638 | 0.543191 | − | 0.839609i | \(-0.317216\pi\) | ||||
0.543191 | + | 0.839609i | \(0.317216\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.25816 | − | 0.319119i | 0.0819660 | − | 0.0115833i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.11374 | 0.221623 | 0.110811 | − | 0.993841i | \(-0.464655\pi\) | ||||
0.110811 | + | 0.993841i | \(0.464655\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.63684 | + | 5.42684i | 0.203800 | + | 0.196208i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 17.6954i | − | 0.638944i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.79863 | + | 5.65724i | −0.353348 | + | 0.204005i | −0.666159 | − | 0.745810i | \(-0.732063\pi\) |
0.312811 | + | 0.949815i | \(0.398729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6868 | − | 3.48870i | 0.889073 | − | 0.125642i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.2106 | + | 33.2737i | 0.690956 | + | 1.19677i | 0.971525 | + | 0.236937i | \(0.0761437\pi\) |
−0.280569 | + | 0.959834i | \(0.590523\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.8994 | − | 12.6436i | −0.786648 | − | 0.454172i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 4.76373i | − | 0.170678i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.56247 | 0.127475 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.63112 | + | 0.167667i | 0.0582916 | + | 0.00599193i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.152730 | − | 0.0881788i | −0.00545117 | − | 0.00314723i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.2747 | − | 23.8300i | −1.47129 | − | 0.849447i | −0.471806 | − | 0.881703i | \(-0.656398\pi\) |
−0.999480 | + | 0.0322557i | \(0.989731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.90249 | − | 13.4624i | −0.0677304 | − | 0.479275i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.71430 | − | 6.43335i | 0.131898 | − | 0.228455i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.38828 | + | 7.34646i | −0.332968 | + | 0.260552i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.1359 | − | 26.2161i | −0.536139 | − | 0.928621i | −0.999107 | − | 0.0422457i | \(-0.986549\pi\) |
0.462968 | − | 0.886375i | \(-0.346785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.0581 | − | 22.6172i | 0.461961 | − | 0.800140i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.06819 | − | 32.5712i | 0.285075 | − | 1.15085i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.02008 | + | 1.76683i | 0.0359978 | + | 0.0623500i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.4863 | + | 21.0684i | 0.580345 | + | 0.741642i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.219373 | + | 0.126655i | −0.00771273 | + | 0.00445295i | −0.503851 | − | 0.863790i | \(-0.668084\pi\) |
0.496139 | + | 0.868243i | \(0.334751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.0629i | − | 0.774735i | −0.921925 | − | 0.387367i | \(-0.873385\pi\) | ||
0.921925 | − | 0.387367i | \(-0.126615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.3070 | + | 8.18657i | 0.712199 | + | 0.287116i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.00698 | + | 5.20824i | −0.105330 | + | 0.182437i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.85407 | − | 1.64780i | 0.0998514 | − | 0.0576492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.2467 | − | 13.9988i | 0.846214 | − | 0.488562i | −0.0131576 | − | 0.999913i | \(-0.504188\pi\) |
0.859372 | + | 0.511352i | \(0.170855\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.4771 | + | 42.3955i | −0.853217 | + | 1.47782i | 0.0250719 | + | 0.999686i | \(0.492019\pi\) |
−0.878289 | + | 0.478130i | \(0.841315\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.289928 | + | 2.05159i | 0.0100940 | + | 0.0714272i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.641658i | 0.0223126i | 0.999938 | + | 0.0111563i | \(0.00355124\pi\) | ||||
−0.999938 | + | 0.0111563i | \(0.996449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.57180 | + | 5.52628i | −0.332442 | + | 0.191936i | −0.656925 | − | 0.753956i | \(-0.728143\pi\) |
0.324483 | + | 0.945892i | \(0.394810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.3926 | − | 2.88184i | 0.707410 | − | 0.0999700i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.57029 | − | 2.71981i | −0.0543420 | − | 0.0941230i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.9786 | − | 2.97878i | −1.00165 | − | 0.102962i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.62330 | + | 8.00780i | −0.159614 | + | 0.276460i | −0.934730 | − | 0.355360i | \(-0.884358\pi\) |
0.775115 | + | 0.631820i | \(0.217692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4502 | − | 25.0285i | −0.498283 | − | 0.863052i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.10871 | + | 2.05952i | 0.175953 | + | 0.0709338i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.94346 | − | 6.83028i | 0.135659 | − | 0.234969i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.7153 | − | 11.9794i | −1.01983 | − | 0.411132i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.01931 | − | 1.74320i | −0.103501 | − | 0.0597561i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.3256 | − | 19.8179i | −1.17529 | − | 0.678551i | −0.220366 | − | 0.975417i | \(-0.570725\pi\) |
−0.954919 | + | 0.296866i | \(0.904059\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.899740 | − | 0.222874i | −0.0307705 | − | 0.00762212i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.8520 | 0.814770 | 0.407385 | − | 0.913256i | \(-0.366441\pi\) | ||||
0.407385 | + | 0.913256i | \(0.366441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.1138i | 0.379197i | 0.981862 | + | 0.189598i | \(0.0607186\pi\) | ||||
−0.981862 | + | 0.189598i | \(0.939281\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.7780 | + | 22.3885i | 1.32002 | + | 0.762113i | 0.983731 | − | 0.179646i | \(-0.0574954\pi\) |
0.336287 | + | 0.941759i | \(0.390829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.49128 | − | 4.31503i | −0.0847061 | − | 0.146715i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.00968 | + | 4.98508i | −0.0682525 | + | 0.169302i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.320805 | − | 0.185217i | 0.0108826 | − | 0.00628305i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 7.80859i | − | 0.264584i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.8751 | − | 7.64804i | −1.04496 | − | 0.258847i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.68191 | 0.124329 | 0.0621647 | − | 0.998066i | \(-0.480200\pi\) | ||||
0.0621647 | + | 0.998066i | \(0.480200\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.05221 | + | 3.90052i | 0.102949 | + | 0.131561i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.3992 | 0.586194 | 0.293097 | − | 0.956083i | \(-0.405314\pi\) | ||||
0.293097 | + | 0.956083i | \(0.405314\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.02834 | −0.0682592 | −0.0341296 | − | 0.999417i | \(-0.510866\pi\) | ||||
−0.0341296 | + | 0.999417i | \(0.510866\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.10045 | − | 15.1324i | 0.205065 | − | 0.508669i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.3780 | −1.55722 | −0.778610 | − | 0.627508i | \(-0.784075\pi\) | ||||
−0.778610 | + | 0.627508i | \(0.784075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.27106 | + | 2.02038i | 0.0425821 | + | 0.0676854i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.09381i | 0.103531i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4812 | − | 8.93810i | 0.517481 | − | 0.298768i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.96484 | − | 8.90060i | −0.232549 | − | 0.297182i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.884576 | − | 1.53213i | −0.0295023 | − | 0.0510994i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.7582 | + | 18.3356i | 1.05802 | + | 0.610847i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.659898i | 0.0219357i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0391 | 0.532571 | 0.266285 | − | 0.963894i | \(-0.414204\pi\) | ||||
0.266285 | + | 0.963894i | \(0.414204\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −50.4647 | + | 14.5538i | −1.67381 | + | 0.482720i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7833 | + | 10.2672i | 0.589187 | + | 0.340167i | 0.764776 | − | 0.644296i | \(-0.222850\pi\) |
−0.175589 | + | 0.984464i | \(0.556183\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.71069 | − | 0.987665i | −0.0566154 | − | 0.0326869i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.39419 | − | 4.22103i | 0.178326 | − | 0.139543i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.7069 | + | 30.6693i | −0.584097 | + | 1.01169i | 0.410890 | + | 0.911685i | \(0.365218\pi\) |
−0.994987 | + | 0.100001i | \(0.968115\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.25311 | − | 37.1722i | −0.173096 | − | 1.22486i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.82712 | − | 15.2890i | −0.290548 | − | 0.503244i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.58374 | − | 2.74311i | 0.0520730 | − | 0.0901930i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.10119 | − | 24.6230i | −0.233234 | − | 0.808727i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.8626 | + | 34.4030i | 0.651670 | + | 1.12873i | 0.982718 | + | 0.185111i | \(0.0592646\pi\) |
−0.331048 | + | 0.943614i | \(0.607402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.3435 | + | 38.0601i | −0.502325 | + | 1.24603i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.599064 | + | 0.345870i | −0.0195915 | + | 0.0113112i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.2142i | − | 0.758376i | −0.925320 | − | 0.379188i | \(-0.876203\pi\) | ||
0.925320 | − | 0.379188i | \(-0.123797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37.2165 | − | 29.1225i | 1.21452 | − | 0.950376i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.9616 | − | 31.1104i | 0.585531 | − | 1.01417i | −0.409278 | − | 0.912410i | \(-0.634219\pi\) |
0.994809 | − | 0.101760i | \(-0.0324474\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.3790 | − | 26.7769i | 1.51031 | − | 0.871977i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.7365 | + | 15.4363i | −0.868818 | + | 0.501612i | −0.866955 | − | 0.498386i | \(-0.833926\pi\) |
−0.00186277 | + | 0.999998i | \(0.500593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.05511 | − | 8.75571i | 0.164096 | − | 0.284222i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.4937 | − | 26.2093i | 1.08611 | − | 0.849894i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.4640i | 0.986826i | 0.869795 | + | 0.493413i | \(0.164251\pi\) | ||||
−0.869795 | + | 0.493413i | \(0.835749\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.80100 | − | 1.03981i | 0.0582791 | − | 0.0336475i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0542006 | + | 0.134446i | −0.00175206 | + | 0.00434603i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.215406 | + | 0.373095i | 0.00694859 | + | 0.0120353i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.5813 | − | 7.57527i | −0.985470 | − | 0.244110i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.47686 | + | 11.2182i | −0.208497 | + | 0.361128i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.75865 | − | 11.7063i | −0.217343 | − | 0.376450i | 0.736652 | − | 0.676272i | \(-0.236406\pi\) |
−0.953995 | + | 0.299823i | \(0.903072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.398993 | + | 2.82336i | 0.0128175 | + | 0.0906994i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.6428 | − | 28.8261i | 0.534092 | − | 0.925074i | −0.465115 | − | 0.885250i | \(-0.653987\pi\) |
0.999207 | − | 0.0398238i | \(-0.0126797\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.08640 | − | 6.32773i | 0.258972 | − | 0.202649i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.9127 | + | 22.4662i | 1.24493 | + | 0.718758i | 0.970093 | − | 0.242734i | \(-0.0780441\pi\) |
0.274833 | + | 0.961492i | \(0.411377\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.56907 | + | 1.48325i | 0.0821079 | + | 0.0474050i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.7802 | − | 29.6335i | −0.982736 | − | 0.946125i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.8949 | 0.857813 | 0.428907 | − | 0.903349i | \(-0.358899\pi\) | ||||
0.428907 | + | 0.903349i | \(0.358899\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.91929i | 0.316055i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0855 | + | 18.5246i | 1.02026 | + | 0.589048i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7201 | + | 30.6920i | 0.562896 | + | 0.974965i | 0.997242 | + | 0.0742186i | \(0.0236463\pi\) |
−0.434346 | + | 0.900746i | \(0.643020\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.4109 | + | 22.2500i | 0.552520 | + | 0.706082i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.3635 | + | 8.29275i | −0.455352 | + | 0.262898i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 32.4953i | − | 1.02914i | −0.857449 | − | 0.514568i | \(-0.827952\pi\) | ||
0.857449 | − | 0.514568i | \(-0.172048\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.373122 | − | 3.62986i | 0.0118050 | − | 0.114844i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))