Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(53,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 10, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 377.2 | ||
Root | \(0.535233 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.377 |
Dual form | 1620.2.x.b.593.2 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.11803 | − | 1.93649i | 0.500000 | − | 0.866025i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.366025 | + | 1.36603i | −0.138345 | + | 0.516309i | 0.861617 | + | 0.507559i | \(0.169452\pi\) |
−0.999962 | + | 0.00875026i | \(0.997215\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.87298 | + | 2.23607i | −1.16775 | + | 0.674200i | −0.953149 | − | 0.302502i | \(-0.902178\pi\) |
−0.214600 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.09808 | − | 4.09808i | −0.304552 | − | 1.13660i | −0.933331 | − | 0.359018i | \(-0.883112\pi\) |
0.628779 | − | 0.777584i | \(-0.283555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.23607 | + | 2.23607i | −0.542326 | + | 0.542326i | −0.924210 | − | 0.381884i | \(-0.875275\pi\) |
0.381884 | + | 0.924210i | \(0.375275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.05453 | + | 0.818458i | −0.636913 | + | 0.170660i | −0.562805 | − | 0.826590i | \(-0.690278\pi\) |
−0.0741081 | + | 0.997250i | \(0.523611\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.50000 | − | 4.33013i | −0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.23607 | − | 3.87298i | −0.415227 | − | 0.719195i | 0.580225 | − | 0.814456i | \(-0.302965\pi\) |
−0.995452 | + | 0.0952614i | \(0.969631\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.23607 | + | 2.23607i | 0.377964 | + | 0.377964i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.74597 | − | 4.47214i | −1.20972 | − | 0.698430i | −0.247019 | − | 0.969011i | \(-0.579451\pi\) |
−0.962697 | + | 0.270580i | \(0.912784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.09808 | + | 1.09808i | 0.624951 | + | 0.167455i | 0.557377 | − | 0.830259i | \(-0.311808\pi\) |
0.0675734 | + | 0.997714i | \(0.478474\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.16358 | − | 2.45537i | −1.33665 | − | 0.358153i | −0.481457 | − | 0.876470i | \(-0.659892\pi\) |
−0.855189 | + | 0.518317i | \(0.826559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.33013 | + | 2.50000i | 0.618590 | + | 0.357143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.23607 | − | 2.23607i | −0.307148 | − | 0.307148i | 0.536655 | − | 0.843802i | \(-0.319688\pi\) |
−0.843802 | + | 0.536655i | \(0.819688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0000i | 1.34840i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.47214 | − | 7.74597i | 0.582223 | − | 1.00844i | −0.412993 | − | 0.910734i | \(-0.635517\pi\) |
0.995215 | − | 0.0977047i | \(-0.0311501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 5.19615i | 0.384111 | + | 0.665299i | 0.991645 | − | 0.128994i | \(-0.0411748\pi\) |
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.16358 | − | 2.45537i | −1.13660 | − | 0.304552i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.36603 | − | 0.366025i | 0.166887 | − | 0.0447171i | −0.174408 | − | 0.984673i | \(-0.555801\pi\) |
0.341295 | + | 0.939956i | \(0.389135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.47214i | 0.530745i | 0.964146 | + | 0.265372i | \(0.0854949\pi\) | ||||
−0.964146 | + | 0.265372i | \(0.914505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | − | 1.00000i | 0.117041 | − | 0.117041i | −0.646160 | − | 0.763202i | \(-0.723626\pi\) |
0.763202 | + | 0.646160i | \(0.223626\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.63692 | − | 6.10905i | −0.186544 | − | 0.696191i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.19615 | + | 3.00000i | −0.584613 | + | 0.337526i | −0.762964 | − | 0.646440i | \(-0.776257\pi\) |
0.178352 | + | 0.983967i | \(0.442924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.45537 | + | 9.16358i | −0.269512 | + | 1.00583i | 0.689918 | + | 0.723887i | \(0.257647\pi\) |
−0.959430 | + | 0.281946i | \(0.909020\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.83013 | + | 6.83013i | 0.198505 | + | 0.740831i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.47214 | −0.474045 | −0.237023 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.87298 | − | 2.23607i | −0.397360 | − | 0.229416i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.29423 | − | 12.2942i | 0.334478 | − | 1.24829i | −0.569955 | − | 0.821676i | \(-0.693040\pi\) |
0.904434 | − | 0.426614i | \(-0.140294\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.74597 | + | 4.47214i | −0.770752 | + | 0.444994i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
0.0623905 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.366025 | + | 1.36603i | 0.0360656 | + | 0.134598i | 0.981611 | − | 0.190891i | \(-0.0611377\pi\) |
−0.945546 | + | 0.325489i | \(0.894471\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.23607 | + | 2.23607i | −0.216169 | + | 0.216169i | −0.806882 | − | 0.590713i | \(-0.798847\pi\) |
0.590713 | + | 0.806882i | \(0.298847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000i | 0.766261i | 0.923694 | + | 0.383131i | \(0.125154\pi\) | ||||
−0.923694 | + | 0.383131i | \(0.874846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.05453 | − | 0.818458i | 0.287346 | − | 0.0769940i | −0.112267 | − | 0.993678i | \(-0.535811\pi\) |
0.399613 | + | 0.916684i | \(0.369145\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.83013 | + | 6.83013i | −0.170660 | + | 0.636913i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.23607 | − | 3.87298i | −0.204980 | − | 0.355036i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.50000 | − | 7.79423i | 0.409091 | − | 0.708566i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | − | 13.0000i | −1.15356 | − | 1.15356i | −0.985833 | − | 0.167731i | \(-0.946356\pi\) |
−0.167731 | − | 0.985833i | \(-0.553644\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.87298 | + | 2.23607i | 0.338384 | + | 0.195366i | 0.659557 | − | 0.751654i | \(-0.270744\pi\) |
−0.321173 | + | 0.947020i | \(0.604077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.73205 | + | 0.732051i | 0.236899 | + | 0.0634769i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.16358 | − | 2.45537i | −0.782897 | − | 0.209777i | −0.154836 | − | 0.987940i | \(-0.549485\pi\) |
−0.628062 | + | 0.778164i | \(0.716151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1244 | − | 7.00000i | −1.02837 | − | 0.593732i | −0.111856 | − | 0.993724i | \(-0.535679\pi\) |
−0.916519 | + | 0.399992i | \(0.869013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.4164 | + | 13.4164i | 1.12194 | + | 1.12194i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.0000 | −0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.70820 | + | 11.6190i | −0.549557 | + | 0.951861i | 0.448747 | + | 0.893659i | \(0.351870\pi\) |
−0.998305 | + | 0.0582028i | \(0.981463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | − | 3.46410i | −0.162758 | − | 0.281905i | 0.773099 | − | 0.634285i | \(-0.218706\pi\) |
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.47214 | + | 7.74597i | 0.359211 | + | 0.622171i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2942 | + | 3.29423i | −0.981186 | + | 0.262908i | −0.713544 | − | 0.700610i | \(-0.752911\pi\) |
−0.267642 | + | 0.963518i | \(0.586244\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.47214i | − | 0.352454i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0000 | − | 17.0000i | 1.33154 | − | 1.33154i | 0.427552 | − | 0.903991i | \(-0.359376\pi\) |
0.903991 | − | 0.427552i | \(-0.140624\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.09229 | − | 15.2726i | −0.316671 | − | 1.18183i | −0.922424 | − | 0.386179i | \(-0.873795\pi\) |
0.605753 | − | 0.795653i | \(-0.292872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.33013 | + | 2.50000i | −0.333087 | + | 0.192308i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.72920 | − | 21.3817i | 0.435583 | − | 1.62562i | −0.304083 | − | 0.952645i | \(-0.598350\pi\) |
0.739667 | − | 0.672974i | \(-0.234983\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.83013 | − | 1.83013i | 0.516309 | − | 0.138345i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.94427 | 0.668526 | 0.334263 | − | 0.942480i | \(-0.391513\pi\) | ||||
0.334263 | + | 0.942480i | \(0.391513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.16358 | + | 2.45537i | −0.673720 | + | 0.180523i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.66025 | − | 13.6603i | 0.267664 | − | 0.998937i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.87298 | − | 2.23607i | 0.280239 | − | 0.161796i | −0.353292 | − | 0.935513i | \(-0.614938\pi\) |
0.633532 | + | 0.773717i | \(0.281605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.09808 | − | 4.09808i | −0.0790413 | − | 0.294986i | 0.915078 | − | 0.403277i | \(-0.132129\pi\) |
−0.994119 | + | 0.108291i | \(0.965462\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.70820 | − | 6.70820i | 0.477940 | − | 0.477940i | −0.426532 | − | 0.904472i | \(-0.640265\pi\) |
0.904472 | + | 0.426532i | \(0.140265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0000i | 1.27599i | 0.770042 | + | 0.637993i | \(0.220235\pi\) | ||||
−0.770042 | + | 0.637993i | \(0.779765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.10905 | − | 1.63692i | 0.428771 | − | 0.114889i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.3205 | + | 10.0000i | −1.20972 | + | 0.698430i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.47214 | + | 7.74597i | 0.309344 | + | 0.535800i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | − | 13.8564i | 0.550743 | − | 0.953914i | −0.447478 | − | 0.894295i | \(-0.647678\pi\) |
0.998221 | − | 0.0596196i | \(-0.0189888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.70820 | − | 6.70820i | 0.457496 | − | 0.457496i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | − | 4.00000i | −0.271538 | − | 0.271538i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.6190 | + | 6.70820i | 0.781575 | + | 0.451243i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.09808 | + | 1.09808i | 0.274427 | + | 0.0735326i | 0.393408 | − | 0.919364i | \(-0.371296\pi\) |
−0.118981 | + | 0.992897i | \(0.537963\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.2726 | + | 4.09229i | 1.01368 | + | 0.271615i | 0.727166 | − | 0.686461i | \(-0.240837\pi\) |
0.286514 | + | 0.958076i | \(0.407504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3923 | + | 6.00000i | 0.686743 | + | 0.396491i | 0.802391 | − | 0.596799i | \(-0.203561\pi\) |
−0.115648 | + | 0.993290i | \(0.536894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.1246 | − | 20.1246i | −1.31841 | − | 1.31841i | −0.915037 | − | 0.403370i | \(-0.867839\pi\) |
−0.403370 | − | 0.915037i | \(-0.632161\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.0000 | + | 15.0000i | −0.978492 | + | 0.978492i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0000 | + | 22.5167i | 0.837404 | + | 1.45043i | 0.892058 | + | 0.451920i | \(0.149261\pi\) |
−0.0546547 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.68246 | − | 5.59017i | 0.618590 | − | 0.357143i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.19615 | + | 2.19615i | −0.521509 | + | 0.139738i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4164i | 0.846836i | 0.905934 | + | 0.423418i | \(0.139170\pi\) | ||||
−0.905934 | + | 0.423418i | \(0.860830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0000 | − | 10.0000i | 0.628695 | − | 0.628695i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.72920 | + | 21.3817i | 0.357378 | + | 1.33375i | 0.877466 | + | 0.479640i | \(0.159233\pi\) |
−0.520088 | + | 0.854113i | \(0.674101\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.19615 | − | 3.00000i | 0.322873 | − | 0.186411i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.72920 | + | 21.3817i | −0.353278 | + | 1.31845i | 0.529360 | + | 0.848397i | \(0.322432\pi\) |
−0.882638 | + | 0.470054i | \(0.844235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.83013 | + | 1.83013i | −0.419571 | + | 0.112424i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.3607 | −1.36335 | −0.681677 | − | 0.731653i | \(-0.738749\pi\) | ||||
−0.681677 | + | 0.731653i | \(0.738749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.3649 | + | 11.1803i | 1.16775 | + | 0.674200i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.29423 | − | 12.2942i | 0.197931 | − | 0.738689i | −0.793558 | − | 0.608495i | \(-0.791773\pi\) |
0.991489 | − | 0.130193i | \(-0.0415598\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.2379 | − | 13.4164i | 1.38626 | − | 0.800356i | 0.393366 | − | 0.919382i | \(-0.371311\pi\) |
0.992891 | + | 0.119026i | \(0.0379773\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.22243 | + | 23.2224i | 0.369885 | + | 1.38043i | 0.860676 | + | 0.509153i | \(0.170041\pi\) |
−0.490791 | + | 0.871277i | \(0.663292\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.94427 | − | 8.94427i | 0.527964 | − | 0.527964i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000i | 0.411765i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.16358 | + | 2.45537i | −0.535342 | + | 0.143444i | −0.516354 | − | 0.856375i | \(-0.672711\pi\) |
−0.0189880 | + | 0.999820i | \(0.506044\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.0000 | − | 17.3205i | −0.582223 | − | 1.00844i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.70820 | + | 11.6190i | 0.387945 | + | 0.671941i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | + | 5.19615i | −0.172917 | + | 0.299501i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.4164 | 0.768221 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.0000 | − | 21.0000i | −1.19853 | − | 1.19853i | −0.974606 | − | 0.223928i | \(-0.928112\pi\) |
−0.223928 | − | 0.974606i | \(-0.571888\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.87298 | − | 2.23607i | −0.219617 | − | 0.126796i | 0.386156 | − | 0.922433i | \(-0.373803\pi\) |
−0.605773 | + | 0.795638i | \(0.707136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.09808 | + | 1.09808i | 0.231637 | + | 0.0620669i | 0.372770 | − | 0.927924i | \(-0.378408\pi\) |
−0.141133 | + | 0.989991i | \(0.545075\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.4907 | + | 7.36612i | 1.54403 | + | 0.413722i | 0.927566 | − | 0.373658i | \(-0.121897\pi\) |
0.616467 | + | 0.787381i | \(0.288563\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.3205 | + | 10.0000i | 0.969762 | + | 0.559893i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.47214 | + | 4.47214i | 0.248836 | + | 0.248836i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0000 | + | 15.0000i | −0.832050 | + | 0.832050i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.70820 | − | 11.6190i | 0.369835 | − | 0.640573i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.818458 | − | 3.05453i | 0.0447171 | − | 0.166887i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.2942 | + | 3.29423i | −0.669709 | + | 0.179448i | −0.577624 | − | 0.816303i | \(-0.696020\pi\) |
−0.0920854 | + | 0.995751i | \(0.529353\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 17.8885i | − | 0.968719i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.00303 | + | 33.5998i | 0.483308 | + | 1.80373i | 0.587561 | + | 0.809180i | \(0.300088\pi\) |
−0.104253 | + | 0.994551i | \(0.533245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.46410 | − | 2.00000i | 0.185429 | − | 0.107058i | −0.404412 | − | 0.914577i | \(-0.632524\pi\) |
0.589841 | + | 0.807519i | \(0.299190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.45537 | − | 9.16358i | 0.130686 | − | 0.487728i | −0.869292 | − | 0.494299i | \(-0.835425\pi\) |
0.999978 | + | 0.00657077i | \(0.00209155\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.66025 | + | 5.00000i | 0.459639 | + | 0.265372i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.7771 | 1.88824 | 0.944121 | − | 0.329598i | \(-0.106913\pi\) | ||||
0.944121 | + | 0.329598i | \(0.106913\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.818458 | − | 3.05453i | −0.0428400 | − | 0.159881i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.366025 | + | 1.36603i | −0.0191064 | + | 0.0713059i | −0.974821 | − | 0.222990i | \(-0.928418\pi\) |
0.955714 | + | 0.294296i | \(0.0950850\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.87298 | − | 2.23607i | 0.201075 | − | 0.116091i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.41858 | − | 31.4186i | −0.435898 | − | 1.62679i | −0.738909 | − | 0.673806i | \(-0.764659\pi\) |
0.303011 | − | 0.952987i | \(-0.402008\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.4164 | + | 13.4164i | −0.690980 | + | 0.690980i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.00000i | − | 0.102733i | −0.998680 | − | 0.0513665i | \(-0.983642\pi\) | ||
0.998680 | − | 0.0513665i | \(-0.0163577\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.16358 | − | 2.45537i | 0.468237 | − | 0.125464i | −0.0169831 | − | 0.999856i | \(-0.505406\pi\) |
0.485220 | + | 0.874392i | \(0.338739\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.6603 | − | 3.66025i | −0.696191 | − | 0.186544i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.70820 | − | 11.6190i | −0.340119 | − | 0.589104i | 0.644335 | − | 0.764743i | \(-0.277134\pi\) |
−0.984455 | + | 0.175639i | \(0.943801\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.00000 | − | 8.66025i | 0.252861 | − | 0.437968i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.4164i | 0.675053i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0000 | − | 11.0000i | −0.552074 | − | 0.552074i | 0.374965 | − | 0.927039i | \(-0.377655\pi\) |
−0.927039 | + | 0.374965i | \(0.877655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.3923 | + | 4.39230i | 0.816559 | + | 0.218796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.3272 | + | 4.91075i | 0.908443 | + | 0.243417i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.3923 | + | 6.00000i | 0.513866 | + | 0.296681i | 0.734422 | − | 0.678694i | \(-0.237454\pi\) |
−0.220555 | + | 0.975375i | \(0.570787\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.94427 | + | 8.94427i | 0.440119 | + | 0.440119i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0000 | + | 15.0000i | 0.736321 | + | 0.736321i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4164 | + | 23.2379i | −0.655434 | + | 1.13525i | 0.326350 | + | 0.945249i | \(0.394181\pi\) |
−0.981785 | + | 0.189997i | \(0.939152\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | − | 1.73205i | −0.0487370 | − | 0.0844150i | 0.840628 | − | 0.541613i | \(-0.182186\pi\) |
−0.889365 | + | 0.457198i | \(0.848853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.2726 | + | 4.09229i | 0.740831 | + | 0.198505i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.19615 | + | 2.19615i | −0.396640 | + | 0.106279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 31.3050i | − | 1.50791i | −0.656928 | − | 0.753953i | \(-0.728145\pi\) | ||
0.656928 | − | 0.753953i | \(-0.271855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | − | 17.0000i | 0.816968 | − | 0.816968i | −0.168700 | − | 0.985668i | \(-0.553957\pi\) |
0.985668 | + | 0.168700i | \(0.0539568\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.63692 | + | 6.10905i | 0.0783043 | + | 0.292236i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.0526 | + | 11.0000i | −0.909329 | + | 0.525001i | −0.880215 | − | 0.474575i | \(-0.842602\pi\) |
−0.0291138 | + | 0.999576i | \(0.509269\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.36612 | − | 27.4907i | 0.349975 | − | 1.30612i | −0.536717 | − | 0.843763i | \(-0.680336\pi\) |
0.886692 | − | 0.462361i | \(-0.152998\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.00000 | + | 8.66025i | −0.237023 | + | 0.410535i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.47214 | 0.211053 | 0.105527 | − | 0.994416i | \(-0.466347\pi\) | ||||
0.105527 | + | 0.994416i | \(0.466347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0000 | 1.88353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.70820 | − | 11.6190i | 0.314485 | − | 0.544705i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.09808 | + | 4.09808i | −0.0513658 | + | 0.191700i | −0.986841 | − | 0.161692i | \(-0.948305\pi\) |
0.935475 | + | 0.353392i | \(0.114972\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.74597 | − | 4.47214i | 0.360766 | − | 0.208288i | −0.308651 | − | 0.951175i | \(-0.599877\pi\) |
0.669417 | + | 0.742887i | \(0.266544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.95448 | − | 25.9545i | −0.323202 | − | 1.20621i | −0.916107 | − | 0.400934i | \(-0.868686\pi\) |
0.592905 | − | 0.805273i | \(-0.297981\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.23607 | + | 2.23607i | −0.103473 | + | 0.103473i | −0.756948 | − | 0.653475i | \(-0.773310\pi\) |
0.653475 | + | 0.756948i | \(0.273310\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000i | 0.0923514i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.3272 | + | 4.91075i | −0.842683 | + | 0.225796i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.66025 | + | 5.00000i | −0.397360 | + | 0.229416i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.8885 | + | 30.9839i | 0.817348 | + | 1.41569i | 0.907629 | + | 0.419773i | \(0.137890\pi\) |
−0.0902809 | + | 0.995916i | \(0.528776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.00000 | + | 15.5885i | −0.410365 | + | 0.710772i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.1246 | − | 20.1246i | −0.913812 | − | 0.913812i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.0000 | − | 21.0000i | −0.951601 | − | 0.951601i | 0.0472808 | − | 0.998882i | \(-0.484944\pi\) |
−0.998882 | + | 0.0472808i | \(0.984944\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3649 | + | 11.1803i | 0.873926 | + | 0.504562i | 0.868651 | − | 0.495424i | \(-0.164987\pi\) |
0.00527540 | + | 0.999986i | \(0.498321\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.6603 | + | 3.66025i | 0.615227 | + | 0.164850i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.10905 | − | 1.63692i | −0.274028 | − | 0.0734257i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.9090 | − | 19.0000i | −1.47321 | − | 0.850557i | −0.473662 | − | 0.880707i | \(-0.657068\pi\) |
−0.999545 | + | 0.0301498i | \(0.990402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.70820 | − | 6.70820i | −0.299104 | − | 0.299104i | 0.541559 | − | 0.840663i | \(-0.317834\pi\) |
−0.840663 | + | 0.541559i | \(0.817834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0000i | 0.889988i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.23607 | + | 3.87298i | −0.0991120 | + | 0.171667i | −0.911317 | − | 0.411705i | \(-0.864934\pi\) |
0.812205 | + | 0.583372i | \(0.198267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | + | 1.73205i | 0.0442374 | + | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.05453 | + | 0.818458i | 0.134598 | + | 0.0360656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.9808 | − | 10.9808i | 1.80233 | − | 0.482933i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00000 | + | 3.00000i | −0.131181 | + | 0.131181i | −0.769649 | − | 0.638468i | \(-0.779569\pi\) |
0.638468 | + | 0.769649i | \(0.279569\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.27383 | − | 12.2181i | −0.142610 | − | 0.532229i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2583 | + | 6.50000i | −0.489493 | + | 0.282609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.82149 | + | 36.6543i | −0.425416 | + | 1.58767i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.83013 | + | 6.83013i | 0.0791233 | + | 0.295292i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.3607 | −0.963143 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.0000 | −1.11783 | −0.558914 | − | 0.829226i | \(-0.688782\pi\) | ||||
−0.558914 | + | 0.829226i | \(0.688782\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.4919 | + | 8.94427i | 0.663602 | + | 0.383131i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.88269 | − | 36.8827i | 0.422553 | − | 1.57699i | −0.346656 | − | 0.937992i | \(-0.612683\pi\) |
0.769209 | − | 0.638997i | \(-0.220651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.74597 | + | 4.47214i | −0.329989 | + | 0.190519i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.19615 | − | 8.19615i | −0.0933899 | − | 0.348536i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.70820 | − | 6.70820i | 0.284236 | − | 0.284236i | −0.550560 | − | 0.834796i | \(-0.685586\pi\) |
0.834796 | + | 0.550560i | \(0.185586\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18.0000i | − | 0.761319i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.16358 | − | 2.45537i | 0.386199 | − | 0.103482i | −0.0604952 | − | 0.998168i | \(-0.519268\pi\) |
0.446694 | + | 0.894687i | \(0.352601\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.83013 | − | 6.83013i | 0.0769940 | − | 0.287346i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.1803 | − | 19.3649i | −0.468704 | − | 0.811820i | 0.530656 | − | 0.847587i | \(-0.321946\pi\) |
−0.999360 | + | 0.0357678i | \(0.988612\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | − | 13.8564i | 0.334790 | − | 0.579873i | −0.648655 | − | 0.761083i | \(-0.724668\pi\) |
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1803 | + | 11.1803i | 0.466252 | + | 0.466252i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.0000 | − | 11.0000i | −0.457936 | − | 0.457936i | 0.440041 | − | 0.897977i | \(-0.354964\pi\) |
−0.897977 | + | 0.440041i | \(0.854964\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6190 | − | 6.70820i | −0.482035 | − | 0.278303i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.6603 | + | 3.66025i | 0.565750 | + | 0.151592i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.16358 | − | 2.45537i | −0.378221 | − | 0.101344i | 0.0646996 | − | 0.997905i | \(-0.479391\pi\) |
−0.442921 | + | 0.896561i | \(0.646058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.92820 | + | 4.00000i | 0.285472 | + | 0.164817i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.1803 | − | 11.1803i | −0.459122 | − | 0.459122i | 0.439246 | − | 0.898367i | \(-0.355246\pi\) |
−0.898367 | + | 0.439246i | \(0.855246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.0000 | −0.409960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8885 | − | 30.9839i | 0.730906 | − | 1.26597i | −0.225590 | − | 0.974222i | \(-0.572431\pi\) |
0.956496 | − | 0.291744i | \(-0.0942356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00000 | − | 12.1244i | −0.285536 | − | 0.494563i | 0.687203 | − | 0.726465i | \(-0.258838\pi\) |
−0.972739 | + | 0.231903i | \(0.925505\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.0623 | − | 17.4284i | −0.409091 | − | 0.708566i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.8827 | + | 9.88269i | −1.49702 | + | 0.401126i | −0.912101 | − | 0.409965i | \(-0.865541\pi\) |
−0.584921 | + | 0.811091i | \(0.698874\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.2492i | 1.62831i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0000 | − | 21.0000i | 0.848182 | − | 0.848182i | −0.141724 | − | 0.989906i | \(-0.545265\pi\) |
0.989906 | + | 0.141724i | \(0.0452646\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.36612 | − | 27.4907i | −0.296549 | − | 1.10674i | −0.939980 | − | 0.341231i | \(-0.889156\pi\) |
0.643431 | − | 0.765504i | \(-0.277510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.3731 | + | 21.0000i | −1.46196 | + | 0.844061i | −0.999102 | − | 0.0423727i | \(-0.986508\pi\) |
−0.462855 | + | 0.886434i | \(0.653175\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.63692 | − | 6.10905i | 0.0655816 | − | 0.244754i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4164 | 0.534947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | 0.159237 | 0.0796187 | − | 0.996825i | \(-0.474630\pi\) | ||||
0.0796187 | + | 0.996825i | \(0.474630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −39.7088 | + | 10.6399i | −1.57580 | + | 0.422234i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.49038 | − | 20.4904i | 0.217537 | − | 0.811858i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.74597 | + | 4.47214i | −0.305947 | + | 0.176639i | −0.645112 | − | 0.764088i | \(-0.723189\pi\) |
0.339164 | + | 0.940727i | \(0.389856\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.68653 | + | 28.6865i | 0.303127 | + | 1.13129i | 0.934545 | + | 0.355844i | \(0.115807\pi\) |
−0.631418 | + | 0.775443i | \(0.717527\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.6525 | − | 15.6525i | 0.615362 | − | 0.615362i | −0.328976 | − | 0.944338i | \(-0.606704\pi\) |
0.944338 | + | 0.328976i | \(0.106704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0000i | 1.57014i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.4907 | − | 7.36612i | 1.07580 | − | 0.288259i | 0.322923 | − | 0.946425i | \(-0.395334\pi\) |
0.752872 | + | 0.658167i | \(0.228668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.66025 | − | 5.00000i | 0.338384 | − | 0.195366i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.47214 | − | 7.74597i | −0.174210 | − | 0.301740i | 0.765678 | − | 0.643224i | \(-0.222404\pi\) |
−0.939887 | + | 0.341484i | \(0.889070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.00000 | + | 1.73205i | −0.0388955 | + | 0.0673690i | −0.884818 | − | 0.465937i | \(-0.845717\pi\) |
0.845922 | + | 0.533306i | \(0.179051\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.47214 | − | 4.47214i | 0.173422 | − | 0.173422i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000 | + | 10.0000i | 0.387202 | + | 0.387202i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.2379 | − | 13.4164i | −0.897089 | − | 0.517935i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.36603 | − | 0.366025i | −0.0526564 | − | 0.0141092i | 0.232395 | − | 0.972622i | \(-0.425344\pi\) |
−0.285051 | + | 0.958512i | \(0.592011\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.5998 | − | 9.00303i | −1.29134 | − | 0.346015i | −0.453174 | − | 0.891422i | \(-0.649708\pi\) |
−0.838171 | + | 0.545408i | \(0.816375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.5885 | + | 9.00000i | 0.598230 | + | 0.345388i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.1246 | + | 20.1246i | 0.770047 | + | 0.770047i | 0.978114 | − | 0.208068i | \(-0.0667174\pi\) |
−0.208068 | + | 0.978114i | \(0.566717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0000 | + | 15.0000i | −0.573121 | + | 0.573121i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.70820 | + | 11.6190i | −0.255562 | + | 0.442647i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0000 | + | 41.5692i | 0.913003 | + | 1.58137i | 0.809799 | + | 0.586707i | \(0.199576\pi\) |
0.103204 | + | 0.994660i | \(0.467091\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.1109 | + | 15.6525i | −1.02837 | + | 0.593732i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.3205 | − | 7.32051i | 1.03484 | − | 0.277284i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.7771i | 1.35128i | 0.737231 | + | 0.675641i | \(0.236133\pi\) | ||||
−0.737231 | + | 0.675641i | \(0.763867\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | + | 6.00000i | −0.226294 | + | 0.226294i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.27383 | − | 12.2181i | −0.123125 | − | 0.459509i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.2487 | − | 14.0000i | 0.910679 | − | 0.525781i | 0.0300298 | − | 0.999549i | \(-0.490440\pi\) |
0.880650 | + | 0.473768i | \(0.157106\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.27383 | − | 12.2181i | 0.122606 | − | 0.457572i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.9808 | − | 10.9808i | 1.53259 | − | 0.410657i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.7771 | −1.33426 | −0.667130 | − | 0.744941i | \(-0.732478\pi\) | ||||
−0.667130 | + | 0.744941i | \(0.732478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.00000 | −0.0744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.1803 | + | 19.3649i | −0.415227 | + | 0.719195i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.68653 | + | 28.6865i | −0.285078 | + | 1.06392i | 0.663705 | + | 0.747995i | \(0.268983\pi\) |
−0.948783 | + | 0.315930i | \(0.897684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6190 | + | 6.70820i | −0.429742 | + | 0.248112i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.366025 | + | 1.36603i | 0.0135195 | + | 0.0504553i | 0.972356 | − | 0.233503i | \(-0.0750189\pi\) |
−0.958837 | + | 0.283958i | \(0.908352\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.47214 | + | 4.47214i | −0.164733 | + | 0.164733i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.0000i | 0.514998i | 0.966279 | + | 0.257499i | \(0.0828985\pi\) | ||||
−0.966279 | + | 0.257499i | \(0.917102\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.2726 | + | 4.09229i | −0.560298 | + | 0.150132i | −0.527843 | − | 0.849342i | \(-0.676999\pi\) |
−0.0324550 | + | 0.999473i | \(0.510333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0000 | + | 25.9808i | 0.549557 | + | 0.951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.23607 | − | 3.87298i | −0.0817041 | − | 0.141516i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.00000 | + | 10.3923i | −0.218943 | + | 0.379221i | −0.954485 | − | 0.298259i | \(-0.903594\pi\) |
0.735542 | + | 0.677479i | \(0.236928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.94427 | −0.325515 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | + | 9.00000i | 0.327111 | + | 0.327111i | 0.851487 | − | 0.524376i | \(-0.175701\pi\) |
−0.524376 | + | 0.851487i | \(0.675701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4919 | + | 8.94427i | 0.561582 | + | 0.324230i | 0.753780 | − | 0.657127i | \(-0.228228\pi\) |
−0.192198 | + | 0.981356i | \(0.561562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9282 | − | 2.92820i | −0.395628 | − | 0.106008i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.6543 | − | 9.82149i | −1.32351 | − | 0.354634i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.92820 | − | 4.00000i | −0.249837 | − | 0.144244i | 0.369852 | − | 0.929091i | \(-0.379408\pi\) |
−0.619690 | + | 0.784847i | \(0.712742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.70820 | + | 6.70820i | 0.241277 | + | 0.241277i | 0.817378 | − | 0.576101i | \(-0.195427\pi\) |
−0.576101 | + | 0.817378i | \(0.695427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.0000 | 0.718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.94427 | + | 15.4919i | −0.320462 | + | 0.555056i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0000 | − | 17.3205i | −0.357828 | − | 0.619777i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.36612 | + | 27.4907i | −0.262908 | + | 0.981186i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.9545 | + | 6.95448i | −0.925177 | + | 0.247901i | −0.689797 | − | 0.724003i | \(-0.742300\pi\) |
−0.235380 | + | 0.971903i | \(0.575634\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.47214i | 0.159011i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | − | 18.0000i | 0.639199 | − | 0.639199i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.36612 | − | 27.4907i | −0.260921 | − | 0.973772i | −0.964700 | − | 0.263352i | \(-0.915172\pi\) |
0.703778 | − | 0.710420i | \(-0.251495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.9808 | − | 15.0000i | 0.919133 | − | 0.530662i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.63692 | + | 6.10905i | −0.0577655 | + | 0.215584i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.66025 | − | 5.00000i | −0.305234 | − | 0.176227i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.47214 | −0.157232 | −0.0786160 | − | 0.996905i | \(-0.525050\pi\) | ||||
−0.0786160 | + | 0.996905i | \(0.525050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.9138 | − | 51.9269i | −0.487378 | − | 1.81892i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.19615 | − | 8.19615i | 0.0768336 | − | 0.286747i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4919 | + | 8.94427i | −0.540672 | + | 0.312157i | −0.745351 | − | 0.666672i | \(-0.767718\pi\) |
0.204679 | + | 0.978829i | \(0.434385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.22243 | + | 23.2224i | 0.216900 | + | 0.809483i | 0.985489 | + | 0.169740i | \(0.0542927\pi\) |
−0.768589 | + | 0.639743i | \(0.779041\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.1246 | + | 20.1246i | −0.699801 | + | 0.699801i | −0.964368 | − | 0.264566i | \(-0.914771\pi\) |
0.264566 | + | 0.964368i | \(0.414771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 16.0000i | − | 0.555703i | −0.960624 | − | 0.277851i | \(-0.910378\pi\) | ||
0.960624 | − | 0.277851i | \(-0.0896223\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.2726 | + | 4.09229i | −0.529165 | + | 0.141789i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.1506 | − | 9.15064i | −1.18183 | − | 0.316671i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.8885 | − | 30.9839i | −0.617581 | − | 1.06968i | −0.989926 | − | 0.141587i | \(-0.954779\pi\) |
0.372345 | − | 0.928095i | \(-0.378554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.50000 | − | 7.79423i | 0.155172 | − | 0.268767i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.1803i | 0.384615i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000 | + | 9.00000i | 0.309244 | + | 0.309244i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.6190 | + | 6.70820i | 0.398292 | + | 0.229954i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.5429 | − | 13.5429i | −1.73056 | − | 0.463701i | −0.750246 | − | 0.661159i | \(-0.770065\pi\) |
−0.980311 | + | 0.197458i | \(0.936732\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.16358 | − | 2.45537i | −0.313022 | − | 0.0838739i | 0.0988880 | − | 0.995099i | \(-0.468471\pi\) |
−0.411910 | + | 0.911225i | \(0.635138\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.1244 | − | 7.00000i | −0.413678 | − | 0.238837i | 0.278691 | − | 0.960381i | \(-0.410099\pi\) |
−0.692369 | + | 0.721544i | \(0.743433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.5967 | − | 24.5967i | −0.837283 | − | 0.837283i | 0.151217 | − | 0.988501i | \(-0.451681\pi\) |
−0.988501 | + | 0.151217i | \(0.951681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.0000 | − | 35.0000i | −1.19004 | − | 1.19004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.4164 | − | 23.2379i | 0.455120 | − | 0.788292i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00000 | − | 5.19615i | −0.101651 | − | 0.176065i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.09229 | − | 15.2726i | 0.138345 | − | 0.516309i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.2942 | + | 3.29423i | −0.415147 | + | 0.111238i | −0.460346 | − | 0.887740i | \(-0.652274\pi\) |
0.0451990 | + | 0.998978i | \(0.485608\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 44.7214i | − | 1.50670i | −0.657619 | − | 0.753350i | \(-0.728436\pi\) | ||
0.657619 | − | 0.753350i | \(-0.271564\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.0000 | + | 23.0000i | −0.774012 | + | 0.774012i | −0.978805 | − | 0.204794i | \(-0.934348\pi\) |
0.204794 | + | 0.978805i | \(0.434348\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.36612 | − | 27.4907i | −0.247330 | − | 0.923048i | −0.972198 | − | 0.234160i | \(-0.924766\pi\) |
0.724868 | − | 0.688888i | \(-0.241901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.5167 | − | 13.0000i | 0.755185 | − | 0.436006i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.91075 | + | 18.3272i | −0.164332 | + | 0.613295i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0000 | − | 17.3205i | 0.334263 | − | 0.578961i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.8885 | 0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | 0.333148 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.6525 | − | 27.1109i | 0.520306 | − | 0.901196i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.56218 | − | 9.56218i | 0.0850757 | − | 0.317507i | −0.910253 | − | 0.414053i | \(-0.864113\pi\) |
0.995329 | + | 0.0965460i | \(0.0307795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.6028 | + | 24.5967i | −1.41149 | + | 0.814927i | −0.995529 | − | 0.0944540i | \(-0.969889\pi\) |
−0.415965 | + | 0.909381i | \(0.636556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.9808 | − | 40.9808i | −0.363410 | − | 1.35627i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.47214 | + | 4.47214i | −0.147683 | + | 0.147683i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.0000i | − | 0.725713i | −0.931845 | − | 0.362857i | \(-0.881802\pi\) | ||
0.931845 | − | 0.362857i | \(-0.118198\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.3272 | − | 4.91075i | 0.603246 | − | 0.161639i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.49038 | + | 20.4904i | −0.180523 | + | 0.673720i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.23607 | − | 3.87298i | −0.0733630 | − | 0.127068i | 0.827010 | − | 0.562187i | \(-0.190040\pi\) |
−0.900373 | + | 0.435118i | \(0.856707\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | − | 8.66025i | 0.163868 | − | 0.283828i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.3607 | − | 22.3607i | −0.731272 | − | 0.731272i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.0000 | − | 11.0000i | −0.359354 | − | 0.359354i | 0.504221 | − | 0.863575i | \(-0.331780\pi\) |
−0.863575 | + | 0.504221i | \(0.831780\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.2379 | − | 13.4164i | −0.757534 | − | 0.437362i | 0.0708757 | − | 0.997485i | \(-0.477421\pi\) |
−0.828410 | + | 0.560123i | \(0.810754\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.3205 | + | 7.32051i | 0.889678 | + | 0.238389i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.2726 | + | 4.09229i | 0.496294 | + | 0.132982i | 0.498279 | − | 0.867017i | \(-0.333965\pi\) |
−0.00198565 | + | 0.999998i | \(0.500632\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.19615 | − | 3.00000i | −0.168674 | − | 0.0973841i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.5410 | + | 33.5410i | 1.08650 | + | 1.08650i | 0.995886 | + | 0.0906141i | \(0.0288830\pi\) |
0.0906141 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 10.0000i | − | 0.323592i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.70820 | − | 11.6190i | 0.216619 | − | 0.375195i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.16358 | − | 2.45537i | −0.294986 | − | 0.0790413i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.56218 | + | 2.56218i | −0.307499 | + | 0.0823941i | −0.409269 | − | 0.912414i | \(-0.634216\pi\) |
0.101770 | + | 0.994808i | \(0.467549\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 22.3607i | − | 0.717588i | −0.933417 | − | 0.358794i | \(-0.883188\pi\) | ||
0.933417 | − | 0.358794i | \(-0.116812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0000 | − | 14.0000i | 0.448819 | − | 0.448819i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.45537 | + | 9.16358i | 0.0785543 | + | 0.293169i | 0.994016 | − | 0.109237i | \(-0.0348408\pi\) |
−0.915461 | + | 0.402406i | \(0.868174\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3205 | − | 10.0000i | 0.553566 | − | 0.319601i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.09229 | − | 15.2726i | 0.130524 | − | 0.487121i | −0.869452 | − | 0.494017i | \(-0.835528\pi\) |
0.999976 | + | 0.00689536i | \(0.00219488\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.49038 | − | 20.4904i | −0.174938 | − | 0.652878i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.4164 | −0.426617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.8569 | + | 20.1246i | 1.10504 | + | 0.637993i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.41858 | + | 31.4186i | −0.266619 | + | 0.995037i | 0.694633 | + | 0.719365i | \(0.255567\pi\) |
−0.961252 | + | 0.275672i | \(0.911100\pi\) | |||||||
\(998\) | 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 \(a_p\))