Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [52,2,Mod(9,52)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(52, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("52.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 52 = 2^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 52.e (of order \(3\), degree \(2\), 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: | \(0.415222090511\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 52.9 |
Dual form | 52.2.e.b.29.1 |
$q$-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 \(\left(\mathbb{Z}/52\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.00000 | − | 1.73205i | 0.577350 | − | 1.00000i | −0.418432 | − | 0.908248i | \(-0.637420\pi\) |
0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.50000 | − | 0.866025i | −0.970725 | − | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | + | 5.19615i | −0.774597 | + | 1.34164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.00000 | 1.74574 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.50000 | + | 7.79423i | −0.835629 | + | 1.44735i | 0.0578882 | + | 0.998323i | \(0.481563\pi\) |
−0.893517 | + | 0.449029i | \(0.851770\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | − | 10.3923i | −1.01419 | − | 1.75662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.00000 | + | 5.19615i | −0.800641 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.50000 | + | 2.59808i | 0.223607 | + | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.00000 | 1.23625 | 0.618123 | − | 0.786082i | \(-0.287894\pi\) | ||||
0.618123 | + | 0.786082i | \(0.287894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | − | 4.33013i | −0.320092 | − | 0.554416i | 0.660415 | − | 0.750901i | \(-0.270381\pi\) |
−0.980507 | + | 0.196485i | \(0.937047\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | − | 3.46410i | 0.251976 | − | 0.436436i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.5000 | + | 2.59808i | 1.30236 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | − | 10.3923i | −0.722315 | − | 1.25109i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000 | − | 6.92820i | 0.461880 | − | 0.800000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.50000 | + | 7.79423i | 0.488094 | + | 0.845403i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.00000 | + | 15.5885i | 0.964901 | + | 1.67126i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | − | 13.8564i | −0.419314 | − | 1.45255i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | + | 5.19615i | 0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | − | 12.1244i | −0.710742 | − | 1.23104i | −0.964579 | − | 0.263795i | \(-0.915026\pi\) |
0.253837 | − | 0.967247i | \(-0.418307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | + | 7.79423i | −0.447767 | + | 0.775555i | −0.998240 | − | 0.0592978i | \(-0.981114\pi\) |
0.550474 | + | 0.834853i | \(0.314447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | 0.197066 | 0.0985329 | − | 0.995134i | \(-0.468585\pi\) | ||||
0.0985329 | + | 0.995134i | \(0.468585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −24.0000 | −2.34216 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | + | 5.19615i | −0.290021 | + | 0.502331i | −0.973814 | − | 0.227345i | \(-0.926996\pi\) |
0.683793 | + | 0.729676i | \(0.260329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.00000 | − | 12.1244i | −0.664411 | − | 1.15079i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50000 | + | 7.79423i | 0.423324 | + | 0.733219i | 0.996262 | − | 0.0863794i | \(-0.0275297\pi\) |
−0.572938 | + | 0.819599i | \(0.694196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | + | 15.5885i | −0.839254 | + | 1.45363i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | + | 3.46410i | 0.0924500 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | − | 10.3923i | 0.550019 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | − | 8.66025i | 0.443678 | − | 0.768473i | −0.554281 | − | 0.832330i | \(-0.687007\pi\) |
0.997959 | + | 0.0638564i | \(0.0203400\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | − | 6.92820i | 0.346844 | − | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.0000 | −1.03280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.50000 | − | 12.9904i | −0.640768 | − | 1.10984i | −0.985262 | − | 0.171054i | \(-0.945283\pi\) |
0.344493 | − | 0.938789i | \(-0.388051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | + | 13.8564i | 0.678551 | + | 1.17529i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) |
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | + | 10.3923i | −0.505291 | + | 0.875190i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.5000 | − | 23.3827i | 1.12111 | − | 1.94183i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.00000 | + | 15.5885i | 0.742307 | + | 1.28571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.50000 | − | 7.79423i | −0.368654 | − | 0.638528i | 0.620701 | − | 0.784047i | \(-0.286848\pi\) |
−0.989355 | + | 0.145519i | \(0.953515\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50000 | + | 2.59808i | −0.121268 | + | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | −0.558661 | −0.279330 | − | 0.960195i | \(-0.590112\pi\) | ||||
−0.279330 | + | 0.960195i | \(0.590112\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.00000 | − | 15.5885i | 0.713746 | − | 1.23625i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0000 | 1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | − | 6.92820i | −0.313304 | − | 0.542659i | 0.665771 | − | 0.746156i | \(-0.268103\pi\) |
−0.979076 | + | 0.203497i | \(0.934769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | − | 20.7846i | 0.928588 | − | 1.60836i | 0.142901 | − | 0.989737i | \(-0.454357\pi\) |
0.785687 | − | 0.618624i | \(-0.212310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | + | 1.73205i | −0.0764719 | + | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | + | 13.8564i | 0.604743 | + | 1.04745i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | + | 20.7846i | −0.896922 | + | 1.55351i | −0.0655145 | + | 0.997852i | \(0.520869\pi\) |
−0.831408 | + | 0.555663i | \(0.812464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5000 | + | 18.1865i | −0.771975 | + | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000 | + | 13.8564i | 0.581914 | + | 1.00791i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | + | 9.52628i | −0.395899 | + | 0.685717i | −0.993215 | − | 0.116289i | \(-0.962900\pi\) |
0.597317 | + | 0.802005i | \(0.296234\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.0000 | − | 15.5885i | 1.07417 | − | 1.11631i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | + | 5.19615i | −0.213741 | + | 0.370211i | −0.952882 | − | 0.303340i | \(-0.901898\pi\) |
0.739141 | + | 0.673550i | \(0.235232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0000 | − | 22.5167i | −0.921546 | − | 1.59616i | −0.797025 | − | 0.603947i | \(-0.793594\pi\) |
−0.124521 | − | 0.992217i | \(-0.539739\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | + | 3.46410i | 0.141069 | + | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −36.0000 | −2.52670 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | + | 1.73205i | −0.0688428 | + | 0.119239i | −0.898392 | − | 0.439194i | \(-0.855264\pi\) |
0.829549 | + | 0.558433i | \(0.188597\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | 0.822226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.00000 | − | 10.3923i | −0.409197 | − | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | + | 6.92820i | 0.271538 | + | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00000 | + | 1.73205i | −0.0675737 | + | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 10.3923i | 0.201802 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0000 | + | 22.5167i | −0.870544 | + | 1.50783i | −0.00910984 | + | 0.999959i | \(0.502900\pi\) |
−0.861435 | + | 0.507869i | \(0.830434\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | − | 3.46410i | −0.133333 | − | 0.230940i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.00000 | − | 5.19615i | −0.199117 | − | 0.344881i | 0.749125 | − | 0.662428i | \(-0.230474\pi\) |
−0.948242 | + | 0.317547i | \(0.897141\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0000 | 1.17419 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.00000 | + | 6.92820i | −0.259828 | + | 0.450035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.00000 | − | 8.66025i | −0.320750 | − | 0.555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.5000 | − | 23.3827i | 0.862483 | − | 1.49387i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000 | + | 6.92820i | 0.127257 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | − | 20.7846i | 0.760469 | − | 1.31717i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.00000 | + | 5.19615i | 0.189358 | + | 0.327978i | 0.945036 | − | 0.326965i | \(-0.106026\pi\) |
−0.755678 | + | 0.654943i | \(0.772693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.0000 | 1.12720 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.50000 | + | 2.59808i | −0.0935674 | + | 0.162064i | −0.909010 | − | 0.416775i | \(-0.863160\pi\) |
0.815442 | + | 0.578838i | \(0.196494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.0000 | 1.73984 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | 0.557086 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.0000 | −1.65860 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000 | + | 10.3923i | 0.367194 | + | 0.635999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0000 | − | 25.9808i | −0.914566 | − | 1.58408i | −0.807535 | − | 0.589819i | \(-0.799199\pi\) |
−0.107031 | − | 0.994256i | \(-0.534134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28.0000 | − | 6.92820i | −1.69464 | − | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.50000 | + | 16.4545i | 0.570800 | + | 0.988654i | 0.996484 | + | 0.0837823i | \(0.0267000\pi\) |
−0.425684 | + | 0.904872i | \(0.639967\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | − | 1.73205i | −0.0598684 | − | 0.103695i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | − | 13.8564i | 0.475551 | − | 0.823678i | −0.524057 | − | 0.851683i | \(-0.675582\pi\) |
0.999608 | + | 0.0280052i | \(0.00891551\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0000 | 0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.0000 | −1.64139 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.50000 | − | 7.79423i | −0.262893 | − | 0.455344i | 0.704117 | − | 0.710084i | \(-0.251343\pi\) |
−0.967009 | + | 0.254741i | \(0.918010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.0000 | + | 15.5885i | −0.867472 | + | 0.901504i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | + | 13.8564i | −0.461112 | + | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | + | 15.5885i | 0.517036 | + | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.50000 | + | 12.9904i | 0.429449 | + | 0.743827i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0000 | 1.48390 | 0.741949 | − | 0.670456i | \(-0.233902\pi\) | ||||
0.741949 | + | 0.670456i | \(0.233902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.00000 | − | 3.46410i | 0.113776 | − | 0.197066i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00000 | 0.340229 | 0.170114 | − | 0.985424i | \(-0.445586\pi\) | ||||
0.170114 | + | 0.985424i | \(0.445586\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.00000 | + | 10.3923i | −0.338062 | + | 0.585540i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.0000 | −0.842484 | −0.421242 | − | 0.906948i | \(-0.638406\pi\) | ||||
−0.421242 | + | 0.906948i | \(0.638406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | + | 10.3923i | 0.334887 | + | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | + | 5.19615i | −0.166924 | + | 0.289122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.0000 | − | 3.46410i | −0.776580 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.0000 | + | 17.3205i | −0.553001 | + | 0.957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | − | 20.7846i | −0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | − | 27.7128i | −0.879440 | − | 1.52323i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) |
−0.0274825 | − | 0.999622i | \(-0.508749\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.00000 | −0.383598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00000 | − | 5.19615i | 0.163908 | − | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.0000 | −1.36184 | −0.680918 | − | 0.732359i | \(-0.738419\pi\) | ||||
−0.680918 | + | 0.732359i | \(0.738419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.0000 | 0.977626 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.0000 | + | 31.1769i | 0.969087 | + | 1.67851i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00000 | − | 15.5885i | −0.483145 | − | 0.836832i | 0.516667 | − | 0.856186i | \(-0.327172\pi\) |
−0.999813 | + | 0.0193540i | \(0.993839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.00000 | + | 12.1244i | −0.374701 | + | 0.649002i | −0.990282 | − | 0.139072i | \(-0.955588\pi\) |
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.0000 | − | 3.46410i | −0.747265 | − | 0.184900i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.5000 | + | 23.3827i | −0.718532 | + | 1.24453i | 0.243049 | + | 0.970014i | \(0.421853\pi\) |
−0.961581 | + | 0.274521i | \(0.911481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00000 | − | 15.5885i | −0.477670 | − | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0000 | − | 20.7846i | −0.635107 | − | 1.10004i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.0000 | 1.90001 | 0.950004 | − | 0.312239i | \(-0.101079\pi\) | ||||
0.950004 | + | 0.312239i | \(0.101079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.0000 | 1.15470 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.00000 | 0.157027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | − | 19.0526i | 0.574195 | − | 0.994535i | −0.421933 | − | 0.906627i | \(-0.638648\pi\) |
0.996129 | − | 0.0879086i | \(-0.0280183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00000 | 0.156174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.0000 | + | 31.1769i | 0.934513 | + | 1.61862i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.50000 | + | 6.06218i | 0.181223 | + | 0.313888i | 0.942297 | − | 0.334777i | \(-0.108661\pi\) |
−0.761074 | + | 0.648665i | \(0.775328\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.00000 | − | 5.19615i | 0.154919 | − | 0.268328i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.5000 | − | 23.3827i | 1.15881 | − | 1.20427i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.00000 | − | 8.66025i | 0.256833 | − | 0.444847i | −0.708559 | − | 0.705652i | \(-0.750654\pi\) |
0.965392 | + | 0.260804i | \(0.0839877\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.0000 | − | 17.3205i | −0.512316 | − | 0.887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0000 | + | 31.1769i | 0.919757 | + | 1.59307i | 0.799783 | + | 0.600289i | \(0.204948\pi\) |
0.119974 | + | 0.992777i | \(0.461719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000 | − | 3.46410i | 0.101666 | − | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0000 | 1.06474 | 0.532371 | − | 0.846511i | \(-0.321301\pi\) | ||||
0.532371 | + | 0.846511i | \(0.321301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00000 | − | 10.3923i | 0.302660 | − | 0.524222i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0000 | 0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00000 | + | 8.66025i | 0.250943 | + | 0.434646i | 0.963786 | − | 0.266678i | \(-0.0859261\pi\) |
−0.712843 | + | 0.701324i | \(0.752593\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | − | 13.8564i | −0.400501 | − | 0.693688i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5000 | − | 28.5788i | 0.823971 | − | 1.42716i | −0.0787327 | − | 0.996896i | \(-0.525087\pi\) |
0.902703 | − | 0.430263i | \(-0.141579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.00000 | − | 1.73205i | −0.348695 | − | 0.0862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.5000 | + | 28.5788i | −0.819892 | + | 1.42009i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5000 | + | 21.6506i | 0.618085 | + | 1.07056i | 0.989835 | + | 0.142222i | \(0.0454247\pi\) |
−0.371750 | + | 0.928333i | \(0.621242\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.0000 | −1.47979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.0000 | −1.76717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.0000 | 1.56705 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0000 | + | 25.9808i | −0.732798 | + | 1.26924i | 0.222885 | + | 0.974845i | \(0.428453\pi\) |
−0.955683 | + | 0.294398i | \(0.904881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | 0.243685 | 0.121843 | − | 0.992549i | \(-0.461120\pi\) | ||||
0.121843 | + | 0.992549i | \(0.461120\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | + | 5.19615i | 0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000 | − | 17.3205i | 0.483934 | − | 0.838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | − | 10.3923i | 0.289010 | − | 0.500580i | −0.684564 | − | 0.728953i | \(-0.740007\pi\) |
0.973574 | + | 0.228373i | \(0.0733406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.500000 | + | 0.866025i | 0.0240285 | + | 0.0416185i | 0.877790 | − | 0.479046i | \(-0.159017\pi\) |
−0.853761 | + | 0.520665i | \(0.825684\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −27.0000 | − | 46.7654i | −1.29455 | − | 2.24223i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | −0.574038 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | + | 27.7128i | −0.763638 | + | 1.32266i | 0.177325 | + | 0.984152i | \(0.443256\pi\) |
−0.940963 | + | 0.338508i | \(0.890078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | 0.570137 | 0.285069 | − | 0.958507i | \(-0.407984\pi\) | ||||
0.285069 | + | 0.958507i | \(0.407984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.0000 | −0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0000 | − | 25.9808i | −0.707894 | − | 1.22611i | −0.965637 | − | 0.259895i | \(-0.916312\pi\) |
0.257743 | − | 0.966213i | \(-0.417021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.0000 | + | 17.3205i | −0.469841 | + | 0.813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000 | + | 41.5692i | 0.562569 | + | 1.94880i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | + | 19.9186i | −0.537947 | + | 0.931752i | 0.461067 | + | 0.887365i | \(0.347467\pi\) |
−0.999014 | + | 0.0443868i | \(0.985867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.00000 | − | 10.3923i | −0.280056 | − | 0.485071i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.5000 | + | 33.7750i | 0.908206 | + | 1.57306i | 0.816556 | + | 0.577267i | \(0.195881\pi\) |
0.0916500 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.00000 | + | 10.3923i | −0.278243 | + | 0.481932i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | − | 6.92820i | −0.183533 | − | 0.317888i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.50000 | − | 7.79423i | −0.206041 | − | 0.356873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.00000 | + | 15.5885i | −0.411220 | + | 0.712255i | −0.995023 | − | 0.0996406i | \(-0.968231\pi\) |
0.583803 | + | 0.811895i | \(0.301564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5000 | + | 18.1865i | −0.797931 | + | 0.829235i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.0000 | − | 41.5692i | 1.09204 | − | 1.89146i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0000 | + | 36.3731i | 0.953561 | + | 1.65162i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | + | 13.8564i | 0.362515 | + | 0.627894i | 0.988374 | − | 0.152042i | \(-0.0485850\pi\) |
−0.625859 | + | 0.779936i | \(0.715252\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | − | 20.7846i | 0.541552 | − | 0.937996i | −0.457263 | − | 0.889332i | \(-0.651170\pi\) |
0.998815 | − | 0.0486647i | \(-0.0154966\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0000 | 1.21602 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | + | 20.7846i | −0.538274 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.0000 | − | 41.5692i | −1.07224 | − | 1.85718i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.00000 | − | 10.3923i | −0.267527 | − | 0.463370i | 0.700696 | − | 0.713460i | \(-0.252873\pi\) |
−0.968223 | + | 0.250090i | \(0.919540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5000 | − | 23.3827i | 0.600742 | − | 1.04052i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.0000 | − | 13.8564i | 0.977054 | − | 0.615385i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.50000 | − | 12.9904i | 0.332432 | − | 0.575789i | −0.650556 | − | 0.759458i | \(-0.725464\pi\) |
0.982988 | + | 0.183669i | \(0.0587976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | − | 3.46410i | −0.0884748 | − | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | − | 6.92820i | −0.176604 | − | 0.305888i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.00000 | −0.264392 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | −0.394297 | −0.197149 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197149 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0000 | + | 17.3205i | −0.437269 | + | 0.757373i | −0.997478 | − | 0.0709788i | \(-0.977388\pi\) |
0.560208 | + | 0.828352i | \(0.310721\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.0000 | 1.39659 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.00000 | − | 5.19615i | −0.130682 | − | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.50000 | − | 7.79423i | 0.324861 | − | 0.337606i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | − | 15.5885i | 0.389104 | − | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.0000 | + | 41.5692i | 1.03568 | + | 1.79384i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0000 | −0.816874 | −0.408437 | − | 0.912787i | \(-0.633926\pi\) | ||||
−0.408437 | + | 0.912787i | \(0.633926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.00000 | + | 12.1244i | −0.300399 | + | 0.520306i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.0000 | 1.28506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.0000 | −0.940652 | −0.470326 | − | 0.882493i | \(-0.655864\pi\) | ||||
−0.470326 | + | 0.882493i | \(0.655864\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.50000 | + | 4.33013i | −0.106697 | + | 0.184805i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.0000 | 0.766826 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | − | 13.8564i | −0.340195 | − | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.0000 | + | 36.3731i | 0.891400 | + | 1.54395i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.50000 | − | 2.59808i | 0.0635570 | − | 0.110084i | −0.832496 | − | 0.554031i | \(-0.813089\pi\) |
0.896053 | + | 0.443947i | \(0.146422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | − | 13.8564i | −0.169182 | − | 0.586064i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | − | 31.1769i | −0.758610 | − | 1.31395i | −0.943560 | − | 0.331202i | \(-0.892546\pi\) |
0.184950 | − | 0.982748i | \(-0.440788\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.5000 | − | 23.3827i | −0.567949 | − | 0.983717i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 44.0000 | 1.84783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00000 | − | 15.5885i | 0.377300 | − | 0.653502i | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | −0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | − | 20.7846i | 0.500435 | − | 0.866778i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.0000 | 0.457936 | 0.228968 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228968 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.0000 | + | 19.0526i | 0.457144 | + | 0.791797i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | + | 41.5692i | 0.995688 | + | 1.72458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.00000 | − | 10.3923i | −0.124035 | − | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | − | 3.46410i | −0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | + | 10.3923i | 0.246807 | + | 0.427482i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.00000 | −0.369586 | −0.184793 | − | 0.982777i | \(-0.559161\pi\) | ||||
−0.184793 | + | 0.982777i | \(0.559161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0000 | + | 31.1769i | −0.737928 | + | 1.27813i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −52.0000 | −2.12822 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.500000 | − | 0.866025i | 0.0203954 | − | 0.0353259i | −0.855648 | − | 0.517559i | \(-0.826841\pi\) |
0.876043 | + | 0.482233i | \(0.160174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.5000 | − | 28.5788i | −0.670820 | − | 1.16190i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0000 | + | 19.0526i | 0.446476 | + | 0.773320i | 0.998154 | − | 0.0607380i | \(-0.0193454\pi\) |
−0.551678 | + | 0.834058i | \(0.686012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36.0000 | + | 62.3538i | −1.45879 | + | 2.52670i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.0000 | + | 5.19615i | 0.849569 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.50000 | − | 16.4545i | 0.383701 | − | 0.664590i | −0.607887 | − | 0.794024i | \(-0.707983\pi\) |
0.991588 | + | 0.129433i | \(0.0413159\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.00000 | − | 15.5885i | −0.362915 | − | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5000 | − | 23.3827i | −0.543490 | − | 0.941351i | −0.998700 | − | 0.0509678i | \(-0.983769\pi\) |
0.455211 | − | 0.890384i | \(-0.349564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.0000 | −1.60774 | −0.803868 | − | 0.594808i | \(-0.797228\pi\) | ||||
−0.803868 | + | 0.594808i | \(0.797228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.0000 | − | 20.7846i | 0.481543 | − | 0.834058i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.0000 | −0.961540 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | + | 24.2487i | 0.557331 | + | 0.965326i | 0.997718 | + | 0.0675178i | \(0.0215080\pi\) |
−0.440387 | + | 0.897808i | \(0.645159\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.00000 | + | 3.46410i | 0.0794929 | + | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.0000 | + | 25.9808i | −0.595257 | + | 1.03102i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.5000 | − | 23.3827i | 0.891482 | − | 0.926456i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.00000 | − | 5.19615i | 0.118678 | − | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.50000 | − | 12.9904i | −0.296232 | − | 0.513089i | 0.679039 | − | 0.734103i | \(-0.262397\pi\) |
−0.975271 | + | 0.221013i | \(0.929064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.00000 | + | 13.8564i | 0.315489 | + | 0.546443i | 0.979541 | − | 0.201243i | \(-0.0644981\pi\) |
−0.664052 | + | 0.747686i | \(0.731165\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.0000 | −0.944999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.00000 | + | 5.19615i | −0.117942 | + | 0.204282i | −0.918952 | − | 0.394369i | \(-0.870963\pi\) |
0.801010 | + | 0.598651i | \(0.204296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0000 | 0.627089 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.0000 | − | 36.3731i | 0.821794 | − | 1.42339i | −0.0825519 | − | 0.996587i | \(-0.526307\pi\) |
0.904345 | − | 0.426801i | \(-0.140360\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | −0.703318 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.500000 | + | 0.866025i | 0.0195069 | + | 0.0337869i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | + | 10.3923i | 0.233727 | + | 0.404827i | 0.958902 | − | 0.283738i | \(-0.0915745\pi\) |
−0.725175 | + | 0.688565i | \(0.758241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.50000 | − | 6.06218i | 0.136134 | − | 0.235791i | −0.789896 | − | 0.613241i | \(-0.789865\pi\) |
0.926030 | + | 0.377450i | \(0.123199\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.0000 | + | 5.19615i | 0.815572 | + | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | + | 20.7846i | −0.465340 | + | 0.805993i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.0000 | + | 46.7654i | 1.04544 | + | 1.81076i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.0000 | + | 45.0333i | 1.00522 | + | 1.74109i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.50000 | − | 11.2583i | 0.250557 | − | 0.433977i | −0.713123 | − | 0.701039i | \(-0.752720\pi\) |
0.963679 | + | 0.267063i | \(0.0860531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.0000 | 0.615840 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.0000 | − | 48.4974i | 1.07454 | − | 1.86116i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.00000 | + | 5.19615i | 0.114792 | + | 0.198825i | 0.917697 | − | 0.397282i | \(-0.130047\pi\) |
−0.802905 | + | 0.596107i | \(0.796713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.5000 | + | 38.9711i | 0.859681 | + | 1.48901i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0000 | − | 24.2487i | 0.534133 | − | 0.925146i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −31.5000 | − | 7.79423i | −1.20005 | − | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | − | 34.6410i | 0.760836 | − | 1.31781i | −0.181584 | − | 0.983375i | \(-0.558123\pi\) |
0.942420 | − | 0.334431i | \(-0.108544\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.0000 | − | 41.5692i | −0.910372 | − | 1.57681i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | 0.340899 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.0000 | + | 31.1769i | −0.680823 | + | 1.17922i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.0000 | − | 31.1769i | 0.677919 | − | 1.17419i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.0000 | −1.35392 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5000 | + | 26.8468i | 0.582115 | + | 1.00825i | 0.995228 | + | 0.0975728i | \(0.0311079\pi\) |
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00000 | + | 3.46410i | 0.0750059 | + | 0.129914i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.00000 | − | 10.3923i | 0.224702 | − | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.0000 | − | 41.5692i | 0.896296 | − | 1.55243i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.00000 | − | 10.3923i | −0.223762 | − | 0.387568i | 0.732185 | − | 0.681106i | \(-0.238501\pi\) |
−0.955947 | + | 0.293538i | \(0.905167\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | + | 6.92820i | 0.148968 | + | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00000 | 0.0743808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0000 | + | 31.1769i | −0.668503 | + | 1.15788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0000 | 1.07114 | 0.535570 | − | 0.844491i | \(-0.320097\pi\) | ||||
0.535570 | + | 0.844491i | \(0.320097\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −27.0000 | − | 46.7654i | −0.995910 | − | 1.72497i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.0000 | + | 17.3205i | −0.367856 | + | 0.637145i | −0.989230 | − | 0.146369i | \(-0.953241\pi\) |
0.621374 | + | 0.783514i | \(0.286575\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.0000 | + | 3.46410i | 0.514303 | + | 0.127257i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0000 | − | 20.7846i | 0.440237 | − | 0.762513i | −0.557470 | − | 0.830197i | \(-0.688228\pi\) |
0.997707 | + | 0.0676840i | \(0.0215610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5000 | + | 23.3827i | 0.494602 | + | 0.856675i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.00000 | − | 10.3923i | −0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.0000 | −0.876941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | − | 3.46410i | 0.0729810 | − | 0.126407i | −0.827225 | − | 0.561870i | \(-0.810082\pi\) |
0.900207 | + | 0.435463i | \(0.143415\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000 | 0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.0000 | 1.09181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.0000 | + | 32.9090i | −0.690567 | + | 1.19610i | 0.281086 | + | 0.959683i | \(0.409305\pi\) |
−0.971652 | + | 0.236414i | \(0.924028\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.00000 | + | 15.5885i | 0.326250 | + | 0.565081i | 0.981764 | − | 0.190101i | \(-0.0608816\pi\) |
−0.655515 | + | 0.755182i | \(0.727548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.0000 | − | 34.6410i | −0.724049 | − | 1.25409i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.50000 | − | 7.79423i | 0.162698 | − | 0.281801i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.00000 | + | 12.1244i | −0.252426 | + | 0.437215i | −0.964193 | − | 0.265200i | \(-0.914562\pi\) |
0.711767 | + | 0.702416i | \(0.247895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | + | 5.19615i | 0.108042 | + | 0.187135i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.00000 | + | 5.19615i | 0.107903 | + | 0.186893i | 0.914920 | − | 0.403634i | \(-0.132253\pi\) |
−0.807018 | + | 0.590527i | \(0.798920\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.0000 | − | 48.4974i | 1.00449 | − | 1.73984i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.0000 | + | 31.1769i | −0.643268 | + | 1.11417i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.0000 | 0.749522 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0000 | − | 32.9090i | −0.677277 | − | 1.17308i | −0.975798 | − | 0.218675i | \(-0.929827\pi\) |
0.298521 | − | 0.954403i | \(-0.403507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0000 | + | 31.1769i | −0.640006 | + | 1.10852i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.00000 | + | 17.3205i | 0.177555 | + | 0.615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.0000 | + | 46.7654i | −0.957591 | + | 1.65860i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.00000 | + | 15.5885i | 0.318796 | + | 0.552171i | 0.980237 | − | 0.197826i | \(-0.0633881\pi\) |
−0.661441 | + | 0.749997i | \(0.730055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.00000 | + | 15.5885i | 0.318397 | + | 0.551480i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −72.0000 | −2.53767 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −60.0000 | −2.11210 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.50000 | + | 12.9904i | −0.263686 | + | 0.456717i | −0.967219 | − | 0.253946i | \(-0.918272\pi\) |
0.703533 | + | 0.710663i | \(0.251605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0000 | −0.351147 | −0.175574 | − | 0.984466i | \(-0.556178\pi\) | ||||
−0.175574 | + | 0.984466i | \(0.556178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | + | 13.8564i | 0.280572 | + | 0.485965i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | + | 20.7846i | 0.420342 | + | 0.728053i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | − | 6.92820i | 0.139942 | − | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.0000 | + | 10.3923i | −0.349428 | + | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | − | 27.7128i | −0.557725 | − | 0.966008i | −0.997686 | − | 0.0679910i | \(-0.978341\pi\) |
0.439961 | − | 0.898017i | \(-0.354992\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.50000 | − | 16.4545i | 0.329949 | − | 0.571488i | −0.652553 | − | 0.757743i | \(-0.726302\pi\) |
0.982501 | + | 0.186256i | \(0.0596352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.0000 | 1.31821 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.0000 | 0.935495 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.0000 | + | 62.3538i | −1.24583 | + | 2.15784i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0000 | − | 36.3731i | −0.725001 | − | 1.25574i | −0.958974 | − | 0.283495i | \(-0.908506\pi\) |
0.233973 | − | 0.972243i | \(-0.424827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.00000 | − | 5.19615i | 0.103325 | − | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.5000 | − | 18.1865i | −1.18684 | − | 0.625636i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.0000 | + | 38.1051i | −0.755929 | + | 1.30931i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.0000 | − | 27.7128i | −0.549119 | − | 0.951101i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.0000 | − | 36.3731i | −0.719871 | − | 1.24685i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.00000 | 0.171197 | 0.0855984 | − | 0.996330i | \(-0.472720\pi\) | ||||
0.0855984 | + | 0.996330i | \(0.472720\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | − | 5.19615i | 0.102598 | − | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | 0.102478 | 0.0512390 | − | 0.998686i | \(-0.483683\pi\) | ||||
0.0512390 | + | 0.998686i | \(0.483683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | 0.0682391 | 0.0341196 | − | 0.999418i | \(-0.489137\pi\) | ||||
0.0341196 | + | 0.999418i | \(0.489137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | + | 20.7846i | −0.408959 | + | 0.708338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.0000 | 1.22545 | 0.612727 | − | 0.790295i | \(-0.290072\pi\) | ||||
0.612727 | + | 0.790295i | \(0.290072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | − | 13.8564i | −0.271694 | − | 0.470588i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.00000 | − | 5.19615i | 0.169419 | − | 0.176065i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.00000 | + | 12.1244i | −0.236914 | + | 0.410347i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | + | 10.3923i | 0.202837 | + | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.50000 | − | 4.33013i | −0.0844190 | − | 0.146218i | 0.820724 | − | 0.571324i | \(-0.193570\pi\) |
−0.905143 | + | 0.425106i | \(0.860237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.0000 | −0.607125 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.5000 | + | 44.1673i | −0.859117 | + | 1.48803i | 0.0136556 | + | 0.999907i | \(0.495653\pi\) |
−0.872772 | + | 0.488127i | \(0.837680\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.0000 | 0.874970 | 0.437485 | − | 0.899226i | \(-0.355869\pi\) | ||||
0.437485 | + | 0.899226i | \(0.355869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.00000 | + | 10.3923i | −0.201460 | + | 0.348939i | −0.948999 | − | 0.315279i | \(-0.897902\pi\) |
0.747539 | + | 0.664218i | \(0.231235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.0000 | 1.34156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.00000 | + | 10.3923i | 0.200782 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0000 | − | 62.3538i | 1.20335 | − | 2.08426i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | + | 41.5692i | 0.400668 | + | 1.38796i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.00000 | + | 15.5885i | −0.300167 | + | 0.519904i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.5000 | − | 23.3827i | −0.449750 | − | 0.778990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.0000 | + | 27.7128i | 0.532447 | + | 0.922225i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0000 | 0.698064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | + | 6.92820i | −0.132818 | + | 0.230047i | −0.924762 | − | 0.380547i | \(-0.875736\pi\) |
0.791944 | + | 0.610594i | \(0.209069\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.00000 | 0.298511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.0000 | 0.991769 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0000 | + | 20.7846i | 0.396275 | + | 0.686368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.0000 | − | 32.9090i | −0.626752 | − | 1.08557i | −0.988199 | − | 0.153174i | \(-0.951051\pi\) |
0.361447 | − | 0.932393i | \(-0.382283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.0000 | − | 45.0333i | 0.856729 | − | 1.48390i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.00000 | − | 20.7846i | −0.197492 | − | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | − | 24.2487i | 0.460317 | − | 0.797293i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.00000 | − | 1.73205i | −0.0328443 | − | 0.0568880i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.5000 | + | 18.1865i | 0.344494 | + | 0.596681i | 0.985262 | − | 0.171054i | \(-0.0547172\pi\) |
−0.640768 | + | 0.767735i | \(0.721384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | 0.589926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.00000 | − | 10.3923i | 0.196431 | − | 0.340229i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.0000 | 1.53542 | 0.767712 | − | 0.640796i | \(-0.221395\pi\) | ||||
0.767712 | + | 0.640796i | \(0.221395\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | − | 24.2487i | 0.456873 | − | 0.791327i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | + | 15.5885i | 0.293080 | + | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.0000 | − | 41.5692i | −0.780720 | − | 1.35225i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.00000 | − | 15.5885i | 0.292461 | − | 0.506557i | −0.681930 | − | 0.731417i | \(-0.738859\pi\) |
0.974391 | + | 0.224860i | \(0.0721926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.50000 | + | 0.866025i | 0.113615 | + | 0.0281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.0000 | + | 25.9808i | −0.486408 | + | 0.842484i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.00000 | + | 5.19615i | 0.0971795 | + | 0.168320i | 0.910516 | − | 0.413473i | \(-0.135685\pi\) |
−0.813337 | + | 0.581793i | \(0.802351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.00000 | + | 15.5885i | 0.291233 | + | 0.504431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.0000 | − | 51.9615i | 0.968751 | − | 1.67793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | 0.193347 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.5000 | − | 28.5788i | 0.531154 | − | 0.919985i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.0000 | −1.86515 | −0.932577 | − | 0.360971i | \(-0.882445\pi\) | ||||
−0.932577 | + | 0.360971i | \(0.882445\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.00000 | + | 10.3923i | 0.192748 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0000 | − | 25.9808i | −0.481373 | − | 0.833762i | 0.518399 | − | 0.855139i | \(-0.326528\pi\) |
−0.999771 | + | 0.0213768i | \(0.993195\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.0000 | + | 55.4256i | −1.02587 | + | 1.77686i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.0000 | + | 20.7846i | −0.640513 | + | 0.665640i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5000 | + | 33.7750i | −0.623860 | + | 1.08056i | 0.364900 | + | 0.931047i | \(0.381103\pi\) |
−0.988760 | + | 0.149511i | \(0.952230\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.00000 | + | 8.66025i | 0.159638 | + | 0.276501i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.00000 | −0.191370 | −0.0956851 | − | 0.995412i | \(-0.530504\pi\) | ||||
−0.0956851 | + | 0.995412i | \(0.530504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | − | 15.5885i | 0.286764 | − | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −48.0000 | −1.52786 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00000 | + | 1.73205i | −0.0317660 | + | 0.0550204i | −0.881471 | − | 0.472237i | \(-0.843446\pi\) |
0.849705 | + | 0.527258i | \(0.176780\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −64.0000 | −2.03098 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.0000 | + | 67.5500i | 1.23638 | + | 2.14148i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50000 | − | 4.33013i | −0.0791758 | − | 0.137136i | 0.823719 | − | 0.566999i | \(-0.191896\pi\) |
−0.902895 | + | 0.429862i | \(0.858562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.0000 | − | 24.2487i | 0.442940 | − | 0.767195i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))