Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(17,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.t (of order \(6\), 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: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.89 |
Dual form | 252.2.t.a.17.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.22474 | + | 2.12132i | −0.547723 | + | 0.948683i | 0.450708 | + | 0.892672i | \(0.351172\pi\) |
−0.998430 | + | 0.0560116i | \(0.982162\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.67423 | + | 2.12132i | −1.10782 | + | 0.639602i | −0.938265 | − | 0.345918i | \(-0.887568\pi\) |
−0.169559 | + | 0.985520i | \(0.554234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.73205i | − | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) | ||
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.44949 | + | 4.24264i | 0.594089 | + | 1.02899i | 0.993675 | + | 0.112296i | \(0.0358205\pi\) |
−0.399586 | + | 0.916696i | \(0.630846\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.50000 | + | 2.59808i | 1.03237 | + | 0.596040i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.48528i | − | 1.57568i | −0.615882 | − | 0.787839i | \(-0.711200\pi\) | ||
0.615882 | − | 0.787839i | \(-0.288800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 0.866025i | −0.269408 | + | 0.155543i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.12372 | − | 2.12132i | −1.03510 | − | 0.358569i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | − | 4.33013i | 0.410997 | − | 0.711868i | −0.584002 | − | 0.811752i | \(-0.698514\pi\) |
0.994999 | + | 0.0998840i | \(0.0318472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.2474 | 1.91273 | 0.956365 | − | 0.292174i | \(-0.0943788\pi\) | ||||
0.956365 | + | 0.292174i | \(0.0943788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0000 | −1.67748 | −0.838742 | − | 0.544529i | \(-0.816708\pi\) | ||||
−0.838742 | + | 0.544529i | \(0.816708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.22474 | + | 2.12132i | −0.178647 | + | 0.309426i | −0.941417 | − | 0.337243i | \(-0.890505\pi\) |
0.762770 | + | 0.646670i | \(0.223839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.34847 | − | 4.24264i | 1.00939 | − | 0.582772i | 0.0983769 | − | 0.995149i | \(-0.468635\pi\) |
0.911013 | + | 0.412378i | \(0.135302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.3923i | − | 1.40130i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.44949 | − | 4.24264i | −0.318896 | − | 0.552345i | 0.661362 | − | 0.750067i | \(-0.269979\pi\) |
−0.980258 | + | 0.197722i | \(0.936646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 1.73205i | −0.384111 | − | 0.221766i | 0.295495 | − | 0.955344i | \(-0.404516\pi\) |
−0.679605 | + | 0.733578i | \(0.737849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.67423 | + | 2.12132i | 0.455733 | + | 0.263117i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.7279i | − | 1.51053i | −0.655422 | − | 0.755263i | \(-0.727509\pi\) | ||
0.655422 | − | 0.755263i | \(-0.272491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5000 | − | 7.79423i | 1.58006 | − | 0.912245i | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.34847 | − | 8.48528i | −0.837436 | − | 0.966988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | + | 9.52628i | −0.618798 | + | 1.07179i | 0.370907 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143120i | \(0.954286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2474 | 1.34433 | 0.672166 | − | 0.740400i | \(-0.265364\pi\) | ||||
0.672166 | + | 0.740400i | \(0.265364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | −1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.34847 | + | 12.7279i | −0.778936 | + | 1.34916i | 0.153619 | + | 0.988130i | \(0.450907\pi\) |
−0.932555 | + | 0.361027i | \(0.882426\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.50000 | − | 0.866025i | 0.471728 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.0227 | + | 6.36396i | −1.13091 | + | 0.652929i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.46410i | − | 0.351726i | −0.984415 | − | 0.175863i | \(-0.943728\pi\) | ||
0.984415 | − | 0.175863i | \(-0.0562716\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.67423 | + | 6.36396i | 0.365600 | + | 0.633238i | 0.988872 | − | 0.148767i | \(-0.0475305\pi\) |
−0.623272 | + | 0.782005i | \(0.714197\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.50000 | + | 4.33013i | 0.738997 | + | 0.426660i | 0.821705 | − | 0.569914i | \(-0.193023\pi\) |
−0.0827075 | + | 0.996574i | \(0.526357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.34847 | + | 4.24264i | 0.710403 | + | 0.410152i | 0.811210 | − | 0.584754i | \(-0.198809\pi\) |
−0.100807 | + | 0.994906i | \(0.532142\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.50000 | + | 4.33013i | 0.239457 | + | 0.414751i | 0.960558 | − | 0.278078i | \(-0.0896974\pi\) |
−0.721102 | + | 0.692829i | \(0.756364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24264i | 0.399114i | 0.979886 | + | 0.199557i | \(0.0639503\pi\) | ||||
−0.979886 | + | 0.199557i | \(0.936050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.79796 | + | 8.48528i | −0.898177 | + | 0.777844i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.67423 | + | 6.36396i | −0.321019 | + | 0.556022i | −0.980699 | − | 0.195525i | \(-0.937359\pi\) |
0.659679 | + | 0.751547i | \(0.270692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.50000 | + | 12.9904i | −0.390199 | + | 1.12641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.73205i | 0.146911i | 0.997299 | + | 0.0734553i | \(0.0234026\pi\) | ||||
−0.997299 | + | 0.0734553i | \(0.976597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.67423 | + | 6.36396i | 0.307255 | + | 0.532181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.0000 | + | 10.3923i | 1.49482 | + | 0.863034i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.6969 | − | 8.48528i | −1.20402 | − | 0.695141i | −0.242574 | − | 0.970133i | \(-0.577992\pi\) |
−0.961447 | + | 0.274992i | \(0.911325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.24264i | − | 0.340777i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | + | 5.19615i | −0.718278 | + | 0.414698i | −0.814119 | − | 0.580699i | \(-0.802779\pi\) |
0.0958404 | + | 0.995397i | \(0.469446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | − | 19.0526i | 0.861586 | − | 1.49231i | −0.00881059 | − | 0.999961i | \(-0.502805\pi\) |
0.870397 | − | 0.492350i | \(-0.163862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.1464 | 1.32683 | 0.663415 | − | 0.748251i | \(-0.269106\pi\) | ||||
0.663415 | + | 0.748251i | \(0.269106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0000 | 0.769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 1.73205i | 0.151186 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.0227 | + | 6.36396i | −0.823876 | + | 0.475665i | −0.851751 | − | 0.523947i | \(-0.824459\pi\) |
0.0278755 | + | 0.999611i | \(0.491126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.19615i | 0.386227i | 0.981176 | + | 0.193113i | \(0.0618586\pi\) | ||||
−0.981176 | + | 0.193113i | \(0.938141\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.12372 | + | 10.6066i | 0.450225 | + | 0.779813i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.0000 | − | 10.3923i | −1.31629 | − | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.67423 | + | 2.12132i | 0.265858 | + | 0.153493i | 0.627004 | − | 0.779016i | \(-0.284281\pi\) |
−0.361146 | + | 0.932509i | \(0.617614\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.50000 | − | 16.4545i | −0.683825 | − | 1.18442i | −0.973805 | − | 0.227387i | \(-0.926982\pi\) |
0.289980 | − | 0.957033i | \(-0.406351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.48528i | − | 0.604551i | −0.953221 | − | 0.302276i | \(-0.902254\pi\) | ||
0.953221 | − | 0.302276i | \(-0.0977463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0000 | + | 6.92820i | −0.850657 | + | 0.491127i | −0.860873 | − | 0.508821i | \(-0.830082\pi\) |
0.0102152 | + | 0.999948i | \(0.496748\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.0454 | − | 4.24264i | 1.54728 | − | 0.297775i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.0000 | + | 25.9808i | −1.04765 | + | 1.81458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.0454 | −1.52491 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.00000 | −0.137686 | −0.0688428 | − | 0.997628i | \(-0.521931\pi\) | ||||
−0.0688428 | + | 0.997628i | \(0.521931\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4722 | − | 23.3345i | 0.918796 | − | 1.59140i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | − | 3.46410i | −0.203653 | − | 0.235159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.34847 | − | 4.24264i | 0.494312 | − | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.7846i | − | 1.39184i | −0.718119 | − | 0.695920i | \(-0.754997\pi\) | ||
0.718119 | − | 0.695920i | \(-0.245003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0227 | − | 19.0919i | −0.731603 | − | 1.26717i | −0.956198 | − | 0.292721i | \(-0.905439\pi\) |
0.224595 | − | 0.974452i | \(-0.427894\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.50000 | + | 0.866025i | 0.0991228 | + | 0.0572286i | 0.548742 | − | 0.835992i | \(-0.315107\pi\) |
−0.449619 | + | 0.893220i | \(0.648440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.67423 | + | 2.12132i | 0.240707 | + | 0.138972i | 0.615502 | − | 0.788136i | \(-0.288953\pi\) |
−0.374795 | + | 0.927108i | \(0.622287\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | − | 5.19615i | −0.195698 | − | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.24264i | 0.274434i | 0.990541 | + | 0.137217i | \(0.0438157\pi\) | ||||
−0.990541 | + | 0.137217i | \(0.956184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0000 | − | 6.92820i | 0.772988 | − | 0.446285i | −0.0609515 | − | 0.998141i | \(-0.519414\pi\) |
0.833939 | + | 0.551856i | \(0.186080\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.44949 | − | 16.9706i | 0.156492 | − | 1.08421i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.50000 | − | 7.79423i | 0.286328 | − | 0.495935i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.79796 | 0.618442 | 0.309221 | − | 0.950990i | \(-0.399932\pi\) | ||||
0.309221 | + | 0.950990i | \(0.399932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.67423 | − | 6.36396i | 0.229192 | − | 0.396973i | −0.728377 | − | 0.685177i | \(-0.759725\pi\) |
0.957569 | + | 0.288204i | \(0.0930581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5000 | + | 4.33013i | 0.776712 | + | 0.269061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0454 | − | 12.7279i | 1.35938 | − | 0.784837i | 0.369838 | − | 0.929096i | \(-0.379413\pi\) |
0.989540 | + | 0.144259i | \(0.0460798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.7846i | 1.27679i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.12372 | − | 10.6066i | −0.373370 | − | 0.646696i | 0.616712 | − | 0.787189i | \(-0.288464\pi\) |
−0.990082 | + | 0.140493i | \(0.955131\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0000 | − | 13.8564i | −1.45790 | − | 0.841717i | −0.458988 | − | 0.888442i | \(-0.651788\pi\) |
−0.998908 | + | 0.0467255i | \(0.985121\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.67423 | + | 2.12132i | 0.221565 | + | 0.127920i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.50000 | − | 9.52628i | −0.330463 | − | 0.572379i | 0.652140 | − | 0.758099i | \(-0.273872\pi\) |
−0.982603 | + | 0.185720i | \(0.940538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9706i | 1.01238i | 0.862422 | + | 0.506189i | \(0.168946\pi\) | ||||
−0.862422 | + | 0.506189i | \(0.831054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.50000 | + | 4.33013i | −0.445829 | + | 0.257399i | −0.706067 | − | 0.708145i | \(-0.749532\pi\) |
0.260238 | + | 0.965544i | \(0.416199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.12372 | + | 31.8198i | 0.361472 | + | 1.87826i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50000 | + | 6.06218i | −0.205882 | + | 0.356599i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.4949 | −1.43101 | −0.715504 | − | 0.698609i | \(-0.753803\pi\) | ||||
−0.715504 | + | 0.698609i | \(0.753803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.50000 | − | 28.5788i | −0.317015 | − | 1.64726i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.34847 | − | 4.24264i | 0.420772 | − | 0.242933i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0526i | 1.08739i | 0.839284 | + | 0.543693i | \(0.182975\pi\) | ||||
−0.839284 | + | 0.543693i | \(0.817025\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.57321 | − | 14.8492i | −0.486142 | − | 0.842023i | 0.513731 | − | 0.857951i | \(-0.328263\pi\) |
−0.999873 | + | 0.0159282i | \(0.994930\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.5000 | − | 7.79423i | −0.763065 | − | 0.440556i | 0.0673300 | − | 0.997731i | \(-0.478552\pi\) |
−0.830395 | + | 0.557175i | \(0.811885\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.34847 | − | 4.24264i | −0.412731 | − | 0.238290i | 0.279231 | − | 0.960224i | \(-0.409920\pi\) |
−0.691963 | + | 0.721933i | \(0.743254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | + | 31.1769i | 1.00781 | + | 1.74557i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4558i | 1.41640i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.50000 | + | 0.866025i | −0.0832050 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.12372 | − | 2.12132i | −0.337612 | − | 0.116952i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.50000 | − | 4.33013i | 0.137412 | − | 0.238005i | −0.789104 | − | 0.614260i | \(-0.789455\pi\) |
0.926516 | + | 0.376254i | \(0.122788\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.1464 | −0.936809 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.00000 | 0.381314 | 0.190657 | − | 0.981657i | \(-0.438938\pi\) | ||||
0.190657 | + | 0.981657i | \(0.438938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.67423 | − | 6.36396i | 0.198971 | − | 0.344628i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.34847 | + | 4.24264i | −0.394486 | + | 0.227757i | −0.684102 | − | 0.729386i | \(-0.739806\pi\) |
0.289616 | + | 0.957143i | \(0.406472\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.2487i | 1.29800i | 0.760787 | + | 0.649002i | \(0.224813\pi\) | ||||
−0.760787 | + | 0.649002i | \(0.775187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4722 | + | 23.3345i | 0.717053 | + | 1.24197i | 0.962163 | + | 0.272476i | \(0.0878426\pi\) |
−0.245110 | + | 0.969495i | \(0.578824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0000 | + | 15.5885i | 1.43301 | + | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.6969 | − | 8.48528i | −0.775675 | − | 0.447836i | 0.0592205 | − | 0.998245i | \(-0.481138\pi\) |
−0.834895 | + | 0.550409i | \(0.814472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.00000 | + | 6.92820i | 0.210526 | + | 0.364642i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.1838i | 1.99863i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.5000 | − | 12.9904i | 1.17449 | − | 0.678092i | 0.219757 | − | 0.975555i | \(-0.429474\pi\) |
0.954734 | + | 0.297462i | \(0.0961403\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.6969 | + | 16.9706i | 0.763027 | + | 0.881068i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.50000 | − | 6.06218i | 0.181223 | − | 0.313888i | −0.761074 | − | 0.648665i | \(-0.775328\pi\) |
0.942297 | + | 0.334777i | \(0.108661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.6969 | −0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.89898 | − | 8.48528i | 0.250326 | − | 0.433578i | −0.713289 | − | 0.700870i | \(-0.752795\pi\) |
0.963616 | + | 0.267292i | \(0.0861288\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.0000 | − | 5.19615i | 1.37605 | − | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.67423 | + | 2.12132i | −0.186291 | + | 0.107555i | −0.590245 | − | 0.807224i | \(-0.700969\pi\) |
0.403954 | + | 0.914779i | \(0.367636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.4722 | − | 23.3345i | −0.677860 | − | 1.17409i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | + | 4.33013i | 0.376414 | + | 0.217323i | 0.676257 | − | 0.736666i | \(-0.263601\pi\) |
−0.299843 | + | 0.953989i | \(0.596934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.34847 | + | 4.24264i | 0.366965 | + | 0.211867i | 0.672132 | − | 0.740432i | \(-0.265379\pi\) |
−0.305167 | + | 0.952299i | \(0.598712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.50000 | + | 2.59808i | 0.0747203 | + | 0.129419i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.2132i | 1.05150i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.50000 | + | 4.33013i | −0.370851 | + | 0.214111i | −0.673830 | − | 0.738886i | \(-0.735352\pi\) |
0.302979 | + | 0.952997i | \(0.402019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.79796 | − | 8.48528i | 0.482126 | − | 0.417533i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0000 | + | 25.9808i | −0.736321 | + | 1.27535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.9444 | −1.31632 | −0.658160 | − | 0.752878i | \(-0.728665\pi\) | ||||
−0.658160 | + | 0.752878i | \(0.728665\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0000 | 1.70580 | 0.852898 | − | 0.522078i | \(-0.174843\pi\) | ||||
0.852898 | + | 0.522078i | \(0.174843\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.44949 | − | 4.24264i | 0.118818 | − | 0.205798i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.00000 | − | 8.66025i | 0.145180 | − | 0.419099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3712 | + | 10.6066i | −0.884908 | + | 0.510902i | −0.872274 | − | 0.489018i | \(-0.837355\pi\) |
−0.0126347 | + | 0.999920i | \(0.504022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1244i | 0.582659i | 0.956623 | + | 0.291330i | \(0.0940977\pi\) | ||||
−0.956623 | + | 0.291330i | \(0.905902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.0000 | − | 20.7846i | −1.71819 | − | 0.991995i | −0.922231 | − | 0.386640i | \(-0.873635\pi\) |
−0.795956 | − | 0.605355i | \(-0.793031\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0000 | − | 31.1769i | −0.853282 | − | 1.47793i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7279i | 0.600668i | 0.953834 | + | 0.300334i | \(0.0970981\pi\) | ||||
−0.953834 | + | 0.300334i | \(0.902902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −45.0000 | + | 25.9808i | −2.11897 | + | 1.22339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.67423 | + | 10.6066i | −0.172251 | + | 0.497245i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.50000 | + | 11.2583i | −0.304057 | + | 0.526642i | −0.977051 | − | 0.213006i | \(-0.931675\pi\) |
0.672994 | + | 0.739648i | \(0.265008\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.89898 | 0.228168 | 0.114084 | − | 0.993471i | \(-0.463607\pi\) | ||||
0.114084 | + | 0.993471i | \(0.463607\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.0000 | 1.34774 | 0.673872 | − | 0.738848i | \(-0.264630\pi\) | ||||
0.673872 | + | 0.738848i | \(0.264630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.67423 | + | 6.36396i | −0.170023 | + | 0.294489i | −0.938428 | − | 0.345476i | \(-0.887718\pi\) |
0.768404 | + | 0.639965i | \(0.221051\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | + | 12.1244i | −0.646460 | + | 0.559851i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.4166 | − | 23.3345i | 1.85836 | − | 1.07292i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.19615i | − | 0.238416i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.44949 | − | 4.24264i | −0.111920 | − | 0.193851i | 0.804624 | − | 0.593784i | \(-0.202367\pi\) |
−0.916544 | + | 0.399933i | \(0.869033\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.50000 | − | 4.33013i | −0.341971 | − | 0.197437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.34847 | + | 4.24264i | 0.333677 | + | 0.192648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.50000 | − | 6.06218i | −0.158600 | − | 0.274703i | 0.775764 | − | 0.631023i | \(-0.217365\pi\) |
−0.934364 | + | 0.356320i | \(0.884031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 33.9411i | − | 1.53174i | −0.642995 | − | 0.765871i | \(-0.722308\pi\) | ||
0.642995 | − | 0.765871i | \(-0.277692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.0000 | − | 20.7846i | 1.62136 | − | 0.936092i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.0681 | − | 6.36396i | 1.48331 | − | 0.285463i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5000 | − | 30.3109i | 0.783408 | − | 1.35690i | −0.146538 | − | 0.989205i | \(-0.546813\pi\) |
0.929946 | − | 0.367697i | \(-0.119854\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.44949 | −0.109217 | −0.0546087 | − | 0.998508i | \(-0.517391\pi\) | ||||
−0.0546087 | + | 0.998508i | \(0.517391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.57321 | − | 14.8492i | 0.380001 | − | 0.658181i | −0.611061 | − | 0.791584i | \(-0.709257\pi\) |
0.991062 | + | 0.133402i | \(0.0425903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.0000 | + | 31.1769i | 1.19441 | + | 1.37919i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.3712 | + | 10.6066i | −0.809531 | + | 0.467383i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.3923i | − | 0.457053i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.44949 | − | 4.24264i | −0.107314 | − | 0.185873i | 0.807367 | − | 0.590049i | \(-0.200892\pi\) |
−0.914681 | + | 0.404176i | \(0.867558\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.50000 | − | 4.33013i | −0.327952 | − | 0.189343i | 0.326979 | − | 0.945031i | \(-0.393969\pi\) |
−0.654932 | + | 0.755688i | \(0.727303\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.34847 | − | 4.24264i | −0.320104 | − | 0.184812i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21.2132i | − | 0.918846i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 10.3923i | −0.778208 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.3712 | − | 23.3345i | 0.791302 | − | 1.00509i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.50000 | − | 16.4545i | 0.408437 | − | 0.707433i | −0.586278 | − | 0.810110i | \(-0.699407\pi\) |
0.994715 | + | 0.102677i | \(0.0327407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.2474 | −0.524623 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00000 | 0.0855138 | 0.0427569 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427569 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.0454 | − | 38.1838i | 0.939166 | − | 1.62668i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.5000 | − | 9.52628i | −1.16942 | − | 0.405099i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.3712 | − | 10.6066i | 0.778412 | − | 0.449416i | −0.0574555 | − | 0.998348i | \(-0.518299\pi\) |
0.835867 | + | 0.548932i | \(0.184965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.0526i | 0.805837i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.67423 | + | 6.36396i | 0.154851 | + | 0.268209i | 0.933005 | − | 0.359864i | \(-0.117177\pi\) |
−0.778154 | + | 0.628073i | \(0.783844\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | − | 5.19615i | −0.378633 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.3712 | − | 10.6066i | −0.770160 | − | 0.444652i | 0.0627719 | − | 0.998028i | \(-0.480006\pi\) |
−0.832932 | + | 0.553376i | \(0.813339\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50000 | + | 6.06218i | 0.146470 | + | 0.253694i | 0.929921 | − | 0.367760i | \(-0.119875\pi\) |
−0.783450 | + | 0.621455i | \(0.786542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.5000 | + | 19.9186i | −1.43625 | + | 0.829222i | −0.997587 | − | 0.0694283i | \(-0.977883\pi\) |
−0.438667 | + | 0.898650i | \(0.644549\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.12372 | + | 31.8198i | 0.254055 | + | 1.32011i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | + | 31.1769i | −0.745484 | + | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.6969 | 0.606608 | 0.303304 | − | 0.952894i | \(-0.401910\pi\) | ||||
0.303304 | + | 0.952894i | \(0.401910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | −0.370839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.22474 | − | 2.12132i | 0.0502942 | − | 0.0871122i | −0.839782 | − | 0.542923i | \(-0.817317\pi\) |
0.890077 | + | 0.455811i | \(0.150651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | − | 31.1769i | −0.245976 | − | 1.27813i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.6969 | + | 8.48528i | −0.600501 | + | 0.346699i | −0.769238 | − | 0.638962i | \(-0.779364\pi\) |
0.168738 | + | 0.985661i | \(0.446031\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 43.3013i | − | 1.76630i | −0.469095 | − | 0.883148i | \(-0.655420\pi\) | ||
0.469095 | − | 0.883148i | \(-0.344580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.57321 | + | 14.8492i | 0.348551 | + | 0.603708i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.5000 | + | 12.9904i | 0.913247 | + | 0.527263i | 0.881474 | − | 0.472232i | \(-0.156551\pi\) |
0.0317724 | + | 0.999495i | \(0.489885\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.67423 | + | 2.12132i | 0.148644 | + | 0.0858194i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | − | 6.92820i | −0.161558 | − | 0.279827i | 0.773869 | − | 0.633345i | \(-0.218319\pi\) |
−0.935428 | + | 0.353518i | \(0.884985\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 21.2132i | − | 0.854011i | −0.904249 | − | 0.427006i | \(-0.859568\pi\) | ||
0.904249 | − | 0.427006i | \(-0.140432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.50000 | − | 4.33013i | 0.301450 | − | 0.174042i | −0.341644 | − | 0.939829i | \(-0.610984\pi\) |
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.7423 | − | 12.7279i | −1.47205 | − | 0.509933i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.4949 | 0.976676 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0000 | −0.875806 | −0.437903 | − | 0.899022i | \(-0.644279\pi\) | ||||
−0.437903 | + | 0.899022i | \(0.644279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.12372 | + | 10.6066i | −0.243013 | + | 0.420910i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.50000 | + | 11.2583i | 0.178296 | + | 0.446071i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.34847 | + | 4.24264i | −0.290247 | + | 0.167574i | −0.638053 | − | 0.769992i | \(-0.720260\pi\) |
0.347806 | + | 0.937566i | \(0.386927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.9090i | 1.29780i | 0.760872 | + | 0.648901i | \(0.224771\pi\) | ||||
−0.760872 | + | 0.648901i | \(0.775229\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0227 | + | 19.0919i | 0.433347 | + | 0.750579i | 0.997159 | − | 0.0753238i | \(-0.0239991\pi\) |
−0.563812 | + | 0.825903i | \(0.690666\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000 | + | 10.3923i | 0.706562 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.3712 | + | 10.6066i | 0.718920 | + | 0.415068i | 0.814355 | − | 0.580367i | \(-0.197091\pi\) |
−0.0954353 | + | 0.995436i | \(0.530424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.00000 | − | 15.5885i | −0.351659 | − | 0.609091i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9706i | 0.661079i | 0.943792 | + | 0.330540i | \(0.107231\pi\) | ||||
−0.943792 | + | 0.330540i | \(0.892769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.50000 | − | 2.59808i | 0.175030 | − | 0.101053i | −0.409926 | − | 0.912119i | \(-0.634445\pi\) |
0.584955 | + | 0.811065i | \(0.301112\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.0454 | − | 25.4558i | −0.854884 | − | 0.987135i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.6969 | 0.567369 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0000 | 0.732396 | 0.366198 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366198 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6969 | + | 25.4558i | −0.564849 | + | 0.978348i | 0.432214 | + | 0.901771i | \(0.357732\pi\) |
−0.997064 | + | 0.0765767i | \(0.975601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.00000 | − | 1.73205i | 0.345388 | − | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.34847 | − | 4.24264i | 0.281181 | − | 0.162340i | −0.352777 | − | 0.935708i | \(-0.614762\pi\) |
0.633958 | + | 0.773367i | \(0.281429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.34847 | − | 12.7279i | −0.279954 | − | 0.484895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.5000 | + | 9.52628i | 0.627690 | + | 0.362397i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.67423 | − | 2.12132i | −0.139372 | − | 0.0804663i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.0000 | + | 51.9615i | 1.13633 | + | 1.96818i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.9411i | 1.28194i | 0.767567 | + | 0.640969i | \(0.221467\pi\) | ||||
−0.767567 | + | 0.640969i | \(0.778533\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.5000 | − | 12.9904i | 0.848604 | − | 0.489942i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.6969 | + | 12.7279i | −0.552735 | + | 0.478683i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.00000 | + | 13.8564i | −0.300446 | + | 0.520388i | −0.976237 | − | 0.216705i | \(-0.930469\pi\) |
0.675791 | + | 0.737093i | \(0.263802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.4722 | + | 23.3345i | −0.502428 | + | 0.870231i | 0.497568 | + | 0.867425i | \(0.334226\pi\) |
−0.999996 | + | 0.00280593i | \(0.999107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.50000 | + | 21.6506i | −0.279315 | + | 0.806312i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.34847 | + | 4.24264i | −0.272915 | + | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 39.8372i | − | 1.47748i | −0.673991 | − | 0.738739i | \(-0.735421\pi\) | ||
0.673991 | − | 0.738739i | \(-0.264579\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.9444 | − | 46.6690i | −0.996574 | − | 1.72612i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.50000 | + | 4.33013i | 0.277019 | + | 0.159937i | 0.632073 | − | 0.774909i | \(-0.282204\pi\) |
−0.355054 | + | 0.934846i | \(0.615538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.7196 | − | 14.8492i | −0.947395 | − | 0.546979i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.50000 | + | 16.4545i | 0.349463 | + | 0.605288i | 0.986154 | − | 0.165831i | \(-0.0530307\pi\) |
−0.636691 | + | 0.771119i | \(0.719697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 12.7279i | − | 0.466942i | −0.972364 | − | 0.233471i | \(-0.924992\pi\) | ||
0.972364 | − | 0.233471i | \(-0.0750084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.0000 | − | 20.7846i | 1.31894 | − | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.34847 | + | 21.2132i | −0.268507 | + | 0.775114i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.50000 | − | 4.33013i | 0.0912263 | − | 0.158009i | −0.816801 | − | 0.576919i | \(-0.804255\pi\) |
0.908027 | + | 0.418911i | \(0.137588\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.89898 | −0.178292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.508839 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.1464 | + | 29.6985i | −0.621558 | + | 1.07657i | 0.367638 | + | 0.929969i | \(0.380166\pi\) |
−0.989196 | + | 0.146600i | \(0.953167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | + | 8.66025i | −0.362024 | + | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.34847 | + | 4.24264i | −0.265338 | + | 0.153193i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5885i | 0.562134i | 0.959688 | + | 0.281067i | \(0.0906883\pi\) | ||||
−0.959688 | + | 0.281067i | \(0.909312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.8207 | + | 36.0624i | 0.748867 | + | 1.29708i | 0.948366 | + | 0.317178i | \(0.102735\pi\) |
−0.199499 | + | 0.979898i | \(0.563931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50000 | + | 0.866025i | 0.0538816 | + | 0.0311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 55.1135 | + | 31.8198i | 1.97465 | + | 1.14006i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | + | 46.7654i | 0.966136 | + | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 25.4558i | − | 0.908558i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | − | 8.66025i | 0.534692 | − | 0.308705i | −0.208233 | − | 0.978079i | \(-0.566771\pi\) |
0.742925 | + | 0.669375i | \(0.233438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0227 | + | 2.12132i | −0.391922 | + | 0.0754255i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.00000 | + | 5.19615i | −0.106533 | + | 0.184521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.0681 | + | 57.2756i | −1.16695 | + | 2.02121i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.3712 | + | 10.6066i | −0.645896 | + | 0.372908i | −0.786882 | − | 0.617103i | \(-0.788306\pi\) |
0.140986 | + | 0.990012i | \(0.454973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.9444 | + | 46.6690i | 0.943821 | + | 1.63475i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −49.5000 | − | 28.5788i | −1.73179 | − | 0.999847i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3712 | + | 10.6066i | 0.641158 | + | 0.370173i | 0.785061 | − | 0.619419i | \(-0.212632\pi\) |
−0.143902 | + | 0.989592i | \(0.545965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0000 | − | 22.5167i | −0.453152 | − | 0.784881i | 0.545428 | − | 0.838157i | \(-0.316367\pi\) |
−0.998580 | + | 0.0532760i | \(0.983034\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29.6985i | − | 1.03272i | −0.856372 | − | 0.516359i | \(-0.827287\pi\) | ||
0.856372 | − | 0.516359i | \(-0.172713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5000 | − | 18.1865i | 1.09404 | − | 0.631644i | 0.159391 | − | 0.987216i | \(-0.449047\pi\) |
0.934649 | + | 0.355571i | \(0.115714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.9444 | − | 21.2132i | −0.933568 | − | 0.734994i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.0000 | + | 36.3731i | −0.726735 | + | 1.25874i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.8888 | 1.86045 | 0.930224 | − | 0.366993i | \(-0.119613\pi\) | ||||
0.930224 | + | 0.366993i | \(0.119613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.0000 | −1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.2474 | + | 21.2132i | −0.421325 | + | 0.729756i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.5000 | + | 6.06218i | 0.601307 | + | 0.208299i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.9808i | 0.889564i | 0.895639 | + | 0.444782i | \(0.146719\pi\) | ||||
−0.895639 | + | 0.444782i | \(0.853281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.5959 | − | 33.9411i | −0.669384 | − | 1.15941i | −0.978077 | − | 0.208245i | \(-0.933225\pi\) |
0.308693 | − | 0.951162i | \(-0.400108\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.0000 | + | 22.5167i | 1.33066 | + | 0.768259i | 0.985401 | − | 0.170248i | \(-0.0544569\pi\) |
0.345262 | + | 0.938506i | \(0.387790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.0681 | − | 19.0919i | −1.12565 | − | 0.649895i | −0.182814 | − | 0.983148i | \(-0.558521\pi\) |
−0.942838 | + | 0.333252i | \(0.891854\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 46.6690i | − | 1.58314i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5000 | − | 6.06218i | 0.355779 | − | 0.205409i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.89898 | − | 25.4558i | −0.165616 | − | 0.860565i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | − | 24.2487i | 0.472746 | − | 0.818821i | −0.526767 | − | 0.850010i | \(-0.676596\pi\) |
0.999514 | + | 0.0311889i | \(0.00992933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3939 | 0.990305 | 0.495152 | − | 0.868806i | \(-0.335112\pi\) | ||||
0.495152 | + | 0.868806i | \(0.335112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.00000 | 0.0336527 | 0.0168263 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168263 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.1691 | − | 48.7904i | 0.945827 | − | 1.63822i | 0.191740 | − | 0.981446i | \(-0.438587\pi\) |
0.754087 | − | 0.656774i | \(-0.228080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.50000 | + | 12.9904i | 0.0838473 | + | 0.435683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.0227 | + | 6.36396i | −0.368861 | + | 0.212962i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 31.1769i | − | 1.04213i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.34847 | + | 12.7279i | 0.245085 | + | 0.424500i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | + | 20.7846i | 1.19933 | + | 0.692436i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.0227 | − | 6.36396i | −0.366407 | − | 0.211545i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.50000 | − | 6.06218i | −0.116216 | − | 0.201291i | 0.802049 | − | 0.597258i | \(-0.203743\pi\) |
−0.918265 | + | 0.395966i | \(0.870410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.48528i | 0.281130i | 0.990071 | + | 0.140565i | \(0.0448919\pi\) | ||||
−0.990071 | + | 0.140565i | \(0.955108\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.0000 | + | 25.9808i | −1.48928 | + | 0.859838i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.3712 | − | 6.36396i | −0.606670 | − | 0.210157i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.5000 | − | 35.5070i | 0.676233 | − | 1.17127i | −0.299874 | − | 0.953979i | \(-0.596945\pi\) |
0.976107 | − | 0.217291i | \(-0.0697219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.0454 | −0.725633 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.00000 | −0.164399 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.4722 | − | 23.3345i | 0.442008 | − | 0.765581i | −0.555830 | − | 0.831296i | \(-0.687599\pi\) |
0.997838 | + | 0.0657150i | \(0.0209328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.0000 | − | 5.19615i | −1.17985 | − | 0.170297i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 44.0908 | − | 25.4558i | 1.44192 | − | 0.832495i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.0526i | − | 0.622420i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) | ||
0.950341 | − | 0.311210i | \(-0.100734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.79796 | − | 16.9706i | −0.319404 | − | 0.553225i | 0.660960 | − | 0.750422i | \(-0.270149\pi\) |
−0.980364 | + | 0.197197i | \(0.936816\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.7650 | + | 27.5772i | 1.55216 | + | 0.896137i | 0.997966 | + | 0.0637469i | \(0.0203050\pi\) |
0.554189 | + | 0.832391i | \(0.313028\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.5000 | − | 23.3827i | −0.438229 | − | 0.759034i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33.9411i | − | 1.09946i | −0.835342 | − | 0.549730i | \(-0.814730\pi\) | ||
0.835342 | − | 0.549730i | \(-0.185270\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.00000 | + | 5.19615i | −0.291233 | + | 0.168144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | + | 24.2487i | −0.451613 | + | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.5403 | 1.49819 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.0000 | −1.38279 | −0.691393 | − | 0.722478i | \(-0.743003\pi\) | ||||
−0.691393 | + | 0.722478i | \(0.743003\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.89898 | − | 8.48528i | 0.157216 | − | 0.272306i | −0.776648 | − | 0.629935i | \(-0.783082\pi\) |
0.933864 | + | 0.357629i | \(0.116415\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.50000 | + | 0.866025i | −0.144263 | + | 0.0277635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.0681 | + | 19.0919i | −1.05794 | + | 0.610803i | −0.924862 | − | 0.380302i | \(-0.875820\pi\) |
−0.133080 | + | 0.991105i | \(0.542487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 62.3538i | − | 1.99284i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.9444 | + | 46.6690i | 0.859392 | + | 1.48851i | 0.872509 | + | 0.488597i | \(0.162491\pi\) |
−0.0131168 | + | 0.999914i | \(0.504175\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | + | 10.3923i | 0.573528 | + | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.50000 | − | 11.2583i | −0.206479 | − | 0.357633i | 0.744124 | − | 0.668042i | \(-0.232867\pi\) |
−0.950603 | + | 0.310409i | \(0.899534\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 33.9411i | − | 1.07601i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.5000 | + | 25.1147i | −1.37766 | + | 0.795392i | −0.991877 | − | 0.127198i | \(-0.959401\pi\) |
−0.385782 | + | 0.922590i | \(0.626068\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))