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 | 917.1 | ||
Root | \(1.40126 + 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.917 |
Dual form | 1620.2.x.b.53.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(7\) | 1.36603 | − | 0.366025i | 0.516309 | − | 0.138345i | 0.00875026 | − | 0.999962i | \(-0.497215\pi\) |
0.507559 | + | 0.861617i | \(0.330548\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.87298 | − | 2.23607i | −1.16775 | − | 0.674200i | −0.214600 | − | 0.976702i | \(-0.568845\pi\) |
−0.953149 | + | 0.302502i | \(0.902178\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.09808 | + | 1.09808i | 1.13660 | + | 0.304552i | 0.777584 | − | 0.628779i | \(-0.216445\pi\) |
0.359018 | + | 0.933331i | \(0.383112\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23607 | − | 2.23607i | 0.542326 | − | 0.542326i | −0.381884 | − | 0.924210i | \(-0.624725\pi\) |
0.924210 | + | 0.381884i | \(0.124725\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | −0.818458 | + | 3.05453i | −0.170660 | + | 0.636913i | 0.826590 | + | 0.562805i | \(0.190278\pi\) |
−0.997250 | + | 0.0741081i | \(0.976389\pi\) | |||||||
\(24\) | 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 | \(-0.697035\pi\) |
0.995452 | + | 0.0952614i | \(0.0303687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 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 | −0.962697 | − | 0.270580i | \(-0.912784\pi\) |
−0.247019 | + | 0.969011i | \(0.579451\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.09808 | − | 4.09808i | −0.167455 | − | 0.624951i | −0.997714 | − | 0.0675734i | \(-0.978474\pi\) |
0.830259 | − | 0.557377i | \(-0.188192\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.45537 | − | 9.16358i | −0.358153 | − | 1.33665i | −0.876470 | − | 0.481457i | \(-0.840108\pi\) |
0.518317 | − | 0.855189i | \(-0.326559\pi\) | |||||||
\(48\) | 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 | 0.843802 | − | 0.536655i | \(-0.180312\pi\) |
−0.536655 | + | 0.843802i | \(0.680312\pi\) | |||||||
\(54\) | 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 | −0.995215 | − | 0.0977047i | \(-0.968850\pi\) |
0.412993 | − | 0.910734i | \(-0.364483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.45537 | − | 9.16358i | −0.304552 | − | 1.13660i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.366025 | + | 1.36603i | −0.0447171 | + | 0.166887i | −0.984673 | − | 0.174408i | \(-0.944199\pi\) |
0.939956 | + | 0.341295i | \(0.110865\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.47214i | − | 0.530745i | −0.964146 | − | 0.265372i | \(-0.914505\pi\) | ||
0.964146 | − | 0.265372i | \(-0.0854949\pi\) | |||||||
\(72\) | 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 | ||||||||
\(77\) | −6.10905 | − | 1.63692i | −0.696191 | − | 0.186544i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.19615 | + | 3.00000i | 0.584613 | + | 0.337526i | 0.762964 | − | 0.646440i | \(-0.223743\pi\) |
−0.178352 | + | 0.983967i | \(0.557076\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.16358 | + | 2.45537i | −1.00583 | + | 0.269512i | −0.723887 | − | 0.689918i | \(-0.757647\pi\) |
−0.281946 | + | 0.959430i | \(0.590980\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.83013 | − | 1.83013i | −0.740831 | − | 0.198505i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.47214 | 0.474045 | 0.237023 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237023 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | −12.2942 | + | 3.29423i | −1.24829 | + | 0.334478i | −0.821676 | − | 0.569955i | \(-0.806960\pi\) |
−0.426614 | + | 0.904434i | \(0.640294\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.74597 | − | 4.47214i | −0.770752 | − | 0.444994i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
−0.833143 | + | 0.553058i | \(0.813461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.36603 | − | 0.366025i | −0.134598 | − | 0.0360656i | 0.190891 | − | 0.981611i | \(-0.438862\pi\) |
−0.325489 | + | 0.945546i | \(0.605529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.23607 | − | 2.23607i | 0.216169 | − | 0.216169i | −0.590713 | − | 0.806882i | \(-0.701153\pi\) |
0.806882 | + | 0.590713i | \(0.201153\pi\) | |||||||
\(108\) | 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 | ||||||||
\(113\) | 0.818458 | − | 3.05453i | 0.0769940 | − | 0.287346i | −0.916684 | − | 0.399613i | \(-0.869145\pi\) |
0.993678 | + | 0.112267i | \(0.0358113\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.83013 | − | 1.83013i | 0.636913 | − | 0.170660i | ||||
\(116\) | 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 | −0.321173 | − | 0.947020i | \(-0.604077\pi\) |
0.659557 | + | 0.751654i | \(0.270744\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.732051 | − | 2.73205i | −0.0634769 | − | 0.236899i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.45537 | − | 9.16358i | −0.209777 | − | 0.782897i | −0.987940 | − | 0.154836i | \(-0.950515\pi\) |
0.778164 | − | 0.628062i | \(-0.216151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1244 | − | 7.00000i | 1.02837 | − | 0.593732i | 0.111856 | − | 0.993724i | \(-0.464321\pi\) |
0.916519 | + | 0.399992i | \(0.130987\pi\) | |||||||
\(140\) | 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 | 0.998305 | + | 0.0582028i | \(0.0185370\pi\) |
−0.448747 | + | 0.893659i | \(0.648130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | + | 3.46410i | −0.162758 | + | 0.281905i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
0.773099 | + | 0.634285i | \(0.218706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.47214 | + | 7.74597i | −0.359211 | + | 0.622171i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.29423 | − | 12.2942i | 0.262908 | − | 0.981186i | −0.700610 | − | 0.713544i | \(-0.747089\pi\) |
0.963518 | − | 0.267642i | \(-0.0862445\pi\) | |||||||
\(158\) | 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 | ||||||||
\(167\) | −15.2726 | − | 4.09229i | −1.18183 | − | 0.316671i | −0.386179 | − | 0.922424i | \(-0.626205\pi\) |
−0.795653 | + | 0.605753i | \(0.792872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.33013 | + | 2.50000i | 0.333087 | + | 0.192308i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3817 | − | 5.72920i | 1.62562 | − | 0.435583i | 0.672974 | − | 0.739667i | \(-0.265017\pi\) |
0.952645 | + | 0.304083i | \(0.0983501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.83013 | + | 6.83013i | −0.138345 | + | 0.516309i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.94427 | −0.668526 | −0.334263 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334263 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | −2.45537 | + | 9.16358i | −0.180523 | + | 0.673720i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.6603 | + | 3.66025i | −0.998937 | + | 0.267664i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.87298 | + | 2.23607i | 0.280239 | + | 0.161796i | 0.633532 | − | 0.773717i | \(-0.281605\pi\) |
−0.353292 | + | 0.935513i | \(0.614938\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.09808 | + | 1.09808i | 0.294986 | + | 0.0790413i | 0.403277 | − | 0.915078i | \(-0.367871\pi\) |
−0.108291 | + | 0.994119i | \(0.534538\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.70820 | + | 6.70820i | −0.477940 | + | 0.477940i | −0.904472 | − | 0.426532i | \(-0.859735\pi\) |
0.426532 | + | 0.904472i | \(0.359735\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 1.63692 | − | 6.10905i | 0.114889 | − | 0.428771i | ||||
\(204\) | 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 | 0.998221 | + | 0.0596196i | \(0.0189888\pi\) |
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 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 | ||||||||
\(223\) | −1.09808 | − | 4.09808i | −0.0735326 | − | 0.274427i | 0.919364 | − | 0.393408i | \(-0.128704\pi\) |
−0.992897 | + | 0.118981i | \(0.962037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.09229 | + | 15.2726i | 0.271615 | + | 1.01368i | 0.958076 | + | 0.286514i | \(0.0924964\pi\) |
−0.686461 | + | 0.727166i | \(0.740837\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.3923 | + | 6.00000i | −0.686743 | + | 0.396491i | −0.802391 | − | 0.596799i | \(-0.796439\pi\) |
0.115648 | + | 0.993290i | \(0.463106\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.1246 | + | 20.1246i | 1.31841 | + | 1.31841i | 0.915037 | + | 0.403370i | \(0.132161\pi\) |
0.403370 | + | 0.915037i | \(0.367839\pi\) | |||||||
\(234\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0000 | − | 22.5167i | 0.837404 | − | 1.45043i | −0.0546547 | − | 0.998505i | \(-0.517406\pi\) |
0.892058 | − | 0.451920i | \(-0.149261\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.68246 | + | 5.59017i | 0.618590 | + | 0.357143i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.19615 | − | 8.19615i | 0.139738 | − | 0.521509i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.4164i | − | 0.846836i | −0.905934 | − | 0.423418i | \(-0.860830\pi\) | ||
0.905934 | − | 0.423418i | \(-0.139170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0000 | − | 10.0000i | 0.628695 | − | 0.628695i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.3817 | + | 5.72920i | 1.33375 | + | 0.357378i | 0.854113 | − | 0.520088i | \(-0.174101\pi\) |
0.479640 | + | 0.877466i | \(0.340767\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.19615 | − | 3.00000i | −0.322873 | − | 0.186411i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.3817 | + | 5.72920i | −1.31845 | + | 0.353278i | −0.848397 | − | 0.529360i | \(-0.822432\pi\) |
−0.470054 | + | 0.882638i | \(0.655765\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.83013 | − | 6.83013i | 0.112424 | − | 0.419571i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.3607 | 1.36335 | 0.681677 | − | 0.731653i | \(-0.261251\pi\) | ||||
0.681677 | + | 0.731653i | \(0.261251\pi\) | |||||||
\(270\) | 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 | ||||||||
\(277\) | −12.2942 | + | 3.29423i | −0.738689 | + | 0.197931i | −0.608495 | − | 0.793558i | \(-0.708227\pi\) |
−0.130193 | + | 0.991489i | \(0.541560\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.2379 | + | 13.4164i | 1.38626 | + | 0.800356i | 0.992891 | − | 0.119026i | \(-0.0379773\pi\) |
0.393366 | + | 0.919382i | \(0.371311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.2224 | − | 6.22243i | −1.38043 | − | 0.369885i | −0.509153 | − | 0.860676i | \(-0.670041\pi\) |
−0.871277 | + | 0.490791i | \(0.836708\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | −2.45537 | + | 9.16358i | −0.143444 | + | 0.535342i | 0.856375 | + | 0.516354i | \(0.172711\pi\) |
−0.999820 | + | 0.0189880i | \(0.993956\pi\) | |||||||
\(294\) | 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 | −0.605773 | − | 0.795638i | \(-0.707136\pi\) |
0.386156 | + | 0.922433i | \(0.373803\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.09808 | − | 4.09808i | −0.0620669 | − | 0.231637i | 0.927924 | − | 0.372770i | \(-0.121592\pi\) |
−0.989991 | + | 0.141133i | \(0.954925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.36612 | + | 27.4907i | 0.413722 | + | 1.54403i | 0.787381 | + | 0.616467i | \(0.211437\pi\) |
−0.373658 | + | 0.927566i | \(0.621897\pi\) | |||||||
\(318\) | 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 | −0.734905 | − | 0.678170i | \(-0.762773\pi\) |
0.954765 | + | 0.297361i | \(0.0961066\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.05453 | − | 0.818458i | 0.166887 | − | 0.0447171i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.29423 | − | 12.2942i | 0.179448 | − | 0.669709i | −0.816303 | − | 0.577624i | \(-0.803980\pi\) |
0.995751 | − | 0.0920854i | \(-0.0293533\pi\) | |||||||
\(338\) | 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 | ||||||||
\(347\) | 33.5998 | + | 9.00303i | 1.80373 | + | 0.483308i | 0.994551 | − | 0.104253i | \(-0.0332451\pi\) |
0.809180 | + | 0.587561i | \(0.199912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.46410 | − | 2.00000i | −0.185429 | − | 0.107058i | 0.404412 | − | 0.914577i | \(-0.367476\pi\) |
−0.589841 | + | 0.807519i | \(0.700810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.16358 | − | 2.45537i | 0.487728 | − | 0.130686i | −0.00657077 | − | 0.999978i | \(-0.502092\pi\) |
0.494299 | + | 0.869292i | \(0.335425\pi\) | |||||||
\(354\) | 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 | \(-0.893087\pi\) | ||||
−0.944121 | + | 0.329598i | \(0.893087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.05453 | − | 0.818458i | −0.159881 | − | 0.0428400i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.36603 | − | 0.366025i | 0.0713059 | − | 0.0191064i | −0.222990 | − | 0.974821i | \(-0.571582\pi\) |
0.294296 | + | 0.955714i | \(0.404915\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.87298 | + | 2.23607i | 0.201075 | + | 0.116091i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.4186 | + | 8.41858i | 1.62679 | + | 0.435898i | 0.952987 | − | 0.303011i | \(-0.0979919\pi\) |
0.673806 | + | 0.738909i | \(0.264659\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | 2.45537 | − | 9.16358i | 0.125464 | − | 0.468237i | −0.874392 | − | 0.485220i | \(-0.838739\pi\) |
0.999856 | + | 0.0169831i | \(0.00540616\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.66025 | + | 13.6603i | 0.186544 | + | 0.696191i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.70820 | − | 11.6190i | 0.340119 | − | 0.589104i | −0.644335 | − | 0.764743i | \(-0.722866\pi\) |
0.984455 | + | 0.175639i | \(0.0561992\pi\) | |||||||
\(390\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.39230 | − | 16.3923i | −0.218796 | − | 0.816559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.91075 | + | 18.3272i | 0.243417 | + | 0.908443i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.3923 | + | 6.00000i | −0.513866 | + | 0.296681i | −0.734422 | − | 0.678694i | \(-0.762546\pi\) |
0.220555 | + | 0.975375i | \(0.429213\pi\) | |||||||
\(410\) | 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 | 0.981785 | + | 0.189997i | \(0.0608478\pi\) |
−0.326350 | + | 0.945249i | \(0.605819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | + | 1.73205i | −0.0487370 | + | 0.0844150i | −0.889365 | − | 0.457198i | \(-0.848853\pi\) |
0.840628 | + | 0.541613i | \(0.182186\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.09229 | + | 15.2726i | 0.198505 | + | 0.740831i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.19615 | − | 8.19615i | 0.106279 | − | 0.396640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.3050i | 1.50791i | 0.656928 | + | 0.753953i | \(0.271855\pi\) | ||||
−0.656928 | + | 0.753953i | \(0.728145\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | 6.10905 | + | 1.63692i | 0.292236 | + | 0.0783043i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.0526 | + | 11.0000i | 0.909329 | + | 0.525001i | 0.880215 | − | 0.474575i | \(-0.157398\pi\) |
0.0291138 | + | 0.999576i | \(0.490731\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4907 | − | 7.36612i | 1.30612 | − | 0.349975i | 0.462361 | − | 0.886692i | \(-0.347002\pi\) |
0.843763 | + | 0.536717i | \(0.180336\pi\) | |||||||
\(444\) | 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 | \(-0.533653\pi\) | ||||
−0.105527 | + | 0.994416i | \(0.533653\pi\) | |||||||
\(450\) | 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 | ||||||||
\(457\) | 4.09808 | − | 1.09808i | 0.191700 | − | 0.0513658i | −0.161692 | − | 0.986841i | \(-0.551695\pi\) |
0.353392 | + | 0.935475i | \(0.385028\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.74597 | + | 4.47214i | 0.360766 | + | 0.208288i | 0.669417 | − | 0.742887i | \(-0.266544\pi\) |
−0.308651 | + | 0.951175i | \(0.599877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.9545 | + | 6.95448i | 1.20621 | + | 0.323202i | 0.805273 | − | 0.592905i | \(-0.202019\pi\) |
0.400934 | + | 0.916107i | \(0.368686\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.23607 | − | 2.23607i | 0.103473 | − | 0.103473i | −0.653475 | − | 0.756948i | \(-0.726690\pi\) |
0.756948 | + | 0.653475i | \(0.226690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000i | 0.0923514i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.91075 | + | 18.3272i | −0.225796 | + | 0.842683i | ||||
\(474\) | 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 | 0.0902809 | + | 0.995916i | \(0.471224\pi\) |
−0.907629 | + | 0.419773i | \(0.862110\pi\) | |||||||
\(480\) | 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 | 0.00527540 | − | 0.999986i | \(-0.498321\pi\) |
0.868651 | + | 0.495424i | \(0.164987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.66025 | − | 13.6603i | −0.164850 | − | 0.615227i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.63692 | − | 6.10905i | −0.0734257 | − | 0.274028i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.9090 | − | 19.0000i | 1.47321 | − | 0.850557i | 0.473662 | − | 0.880707i | \(-0.342932\pi\) |
0.999545 | + | 0.0301498i | \(0.00959843\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.70820 | + | 6.70820i | 0.299104 | + | 0.299104i | 0.840663 | − | 0.541559i | \(-0.182166\pi\) |
−0.541559 | + | 0.840663i | \(0.682166\pi\) | |||||||
\(504\) | 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 | \(-0.135066\pi\) |
−0.812205 | + | 0.583372i | \(0.801733\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | − | 1.73205i | 0.0442374 | − | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.818458 | + | 3.05453i | 0.0360656 | + | 0.134598i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.9808 | + | 40.9808i | −0.482933 | + | 1.80233i | ||||
\(518\) | 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 | ||||||||
\(527\) | −12.2181 | − | 3.27383i | −0.532229 | − | 0.142610i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2583 | + | 6.50000i | 0.489493 | + | 0.282609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.6543 | + | 9.82149i | −1.58767 | + | 0.425416i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.83013 | − | 1.83013i | −0.295292 | − | 0.0791233i | ||||
\(536\) | 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 | ||||||||
\(547\) | −36.8827 | + | 9.88269i | −1.57699 | + | 0.422553i | −0.937992 | − | 0.346656i | \(-0.887317\pi\) |
−0.638997 | + | 0.769209i | \(0.720651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.74597 | − | 4.47214i | −0.329989 | − | 0.190519i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.19615 | + | 2.19615i | 0.348536 | + | 0.0933899i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.70820 | + | 6.70820i | −0.284236 | + | 0.284236i | −0.834796 | − | 0.550560i | \(-0.814414\pi\) |
0.550560 | + | 0.834796i | \(0.314414\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18.0000i | − | 0.761319i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.45537 | − | 9.16358i | 0.103482 | − | 0.386199i | −0.894687 | − | 0.446694i | \(-0.852601\pi\) |
0.998168 | + | 0.0604952i | \(0.0192680\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.83013 | + | 1.83013i | −0.287346 | + | 0.0769940i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.1803 | − | 19.3649i | 0.468704 | − | 0.811820i | −0.530656 | − | 0.847587i | \(-0.678054\pi\) |
0.999360 | + | 0.0357678i | \(0.0113877\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | + | 13.8564i | 0.334790 | + | 0.579873i | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | 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 | ||||||||
\(583\) | −3.66025 | − | 13.6603i | −0.151592 | − | 0.565750i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.45537 | − | 9.16358i | −0.101344 | − | 0.378221i | 0.896561 | − | 0.442921i | \(-0.146058\pi\) |
−0.997905 | + | 0.0646996i | \(0.979391\pi\) | |||||||
\(588\) | 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 | 0.898367 | − | 0.439246i | \(-0.144754\pi\) |
−0.439246 | + | 0.898367i | \(0.644754\pi\) | |||||||
\(594\) | 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 | −0.956496 | − | 0.291744i | \(-0.905764\pi\) |
0.225590 | − | 0.974222i | \(-0.427569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00000 | + | 12.1244i | −0.285536 | + | 0.494563i | −0.972739 | − | 0.231903i | \(-0.925505\pi\) |
0.687203 | + | 0.726465i | \(0.258838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0623 | − | 17.4284i | 0.409091 | − | 0.708566i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.88269 | − | 36.8827i | 0.401126 | − | 1.49702i | −0.409965 | − | 0.912101i | \(-0.634459\pi\) |
0.811091 | − | 0.584921i | \(-0.198874\pi\) | |||||||
\(608\) | 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 | ||||||||
\(617\) | −27.4907 | − | 7.36612i | −1.10674 | − | 0.296549i | −0.341231 | − | 0.939980i | \(-0.610844\pi\) |
−0.765504 | + | 0.643431i | \(0.777510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.3731 | + | 21.0000i | 1.46196 | + | 0.844061i | 0.999102 | − | 0.0423727i | \(-0.0134917\pi\) |
0.462855 | + | 0.886434i | \(0.346825\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.10905 | − | 1.63692i | 0.244754 | − | 0.0655816i | ||||
\(624\) | 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 | ||||||||
\(635\) | −10.6399 | + | 39.7088i | −0.422234 | + | 1.57580i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.4904 | + | 5.49038i | −0.811858 | + | 0.217537i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.74597 | − | 4.47214i | −0.305947 | − | 0.176639i | 0.339164 | − | 0.940727i | \(-0.389856\pi\) |
−0.645112 | + | 0.764088i | \(0.723189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.6865 | − | 7.68653i | −1.13129 | − | 0.303127i | −0.355844 | − | 0.934545i | \(-0.615807\pi\) |
−0.775443 | + | 0.631418i | \(0.782473\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.6525 | + | 15.6525i | −0.615362 | + | 0.615362i | −0.944338 | − | 0.328976i | \(-0.893296\pi\) |
0.328976 | + | 0.944338i | \(0.393296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0000i | 1.57014i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.36612 | − | 27.4907i | 0.288259 | − | 1.07580i | −0.658167 | − | 0.752872i | \(-0.728668\pi\) |
0.946425 | − | 0.322923i | \(-0.104666\pi\) | |||||||
\(654\) | 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 | \(-0.777596\pi\) |
0.939887 | + | 0.341484i | \(0.110930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.00000 | − | 1.73205i | −0.0388955 | − | 0.0673690i | 0.845922 | − | 0.533306i | \(-0.179051\pi\) |
−0.884818 | + | 0.465937i | \(0.845717\pi\) | |||||||
\(662\) | 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 | ||||||||
\(673\) | 0.366025 | + | 1.36603i | 0.0141092 | + | 0.0526564i | 0.972622 | − | 0.232395i | \(-0.0746561\pi\) |
−0.958512 | + | 0.285051i | \(0.907989\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.00303 | − | 33.5998i | −0.346015 | − | 1.29134i | −0.891422 | − | 0.453174i | \(-0.850292\pi\) |
0.545408 | − | 0.838171i | \(-0.316375\pi\) | |||||||
\(678\) | 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 | 0.208068 | − | 0.978114i | \(-0.433283\pi\) |
−0.978114 | + | 0.208068i | \(0.933283\pi\) | |||||||
\(684\) | 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 | 0.103204 | − | 0.994660i | \(-0.467091\pi\) |
0.809799 | − | 0.586707i | \(-0.199576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.1109 | − | 15.6525i | −1.02837 | − | 0.593732i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.32051 | + | 27.3205i | −0.277284 | + | 1.03484i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.7771i | − | 1.35128i | −0.737231 | − | 0.675641i | \(-0.763867\pi\) | ||
0.737231 | − | 0.675641i | \(-0.236133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | + | 6.00000i | −0.226294 | + | 0.226294i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.2181 | − | 3.27383i | −0.459509 | − | 0.123125i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.2487 | − | 14.0000i | −0.910679 | − | 0.525781i | −0.0300298 | − | 0.999549i | \(-0.509560\pi\) |
−0.880650 | + | 0.473768i | \(0.842894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.2181 | − | 3.27383i | 0.457572 | − | 0.122606i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.9808 | + | 40.9808i | −0.410657 | + | 1.53259i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.7771 | 1.33426 | 0.667130 | − | 0.744941i | \(-0.267522\pi\) | ||||
0.667130 | + | 0.744941i | \(0.267522\pi\) | |||||||
\(720\) | 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 | ||||||||
\(727\) | 28.6865 | − | 7.68653i | 1.06392 | − | 0.285078i | 0.315930 | − | 0.948783i | \(-0.397684\pi\) |
0.747995 | + | 0.663705i | \(0.231017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6190 | − | 6.70820i | −0.429742 | − | 0.248112i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.36603 | − | 0.366025i | −0.0504553 | − | 0.0135195i | 0.233503 | − | 0.972356i | \(-0.424981\pi\) |
−0.283958 | + | 0.958837i | \(0.591648\pi\) | |||||||
\(734\) | 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 | ||||||||
\(743\) | −4.09229 | + | 15.2726i | −0.150132 | + | 0.560298i | 0.849342 | + | 0.527843i | \(0.176999\pi\) |
−0.999473 | + | 0.0324550i | \(0.989667\pi\) | |||||||
\(744\) | 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 | 0.735542 | − | 0.677479i | \(-0.236928\pi\) |
−0.954485 | + | 0.298259i | \(0.903594\pi\) | |||||||
\(752\) | 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 | −0.192198 | − | 0.981356i | \(-0.561562\pi\) |
0.753780 | + | 0.657127i | \(0.228228\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.92820 | + | 10.9282i | 0.106008 | + | 0.395628i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.82149 | − | 36.6543i | −0.354634 | − | 1.32351i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.92820 | − | 4.00000i | 0.249837 | − | 0.144244i | −0.369852 | − | 0.929091i | \(-0.620592\pi\) |
0.619690 | + | 0.784847i | \(0.287258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.70820 | − | 6.70820i | −0.241277 | − | 0.241277i | 0.576101 | − | 0.817378i | \(-0.304573\pi\) |
−0.817378 | + | 0.576101i | \(0.804573\pi\) | |||||||
\(774\) | 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 | ||||||||
\(785\) | −27.4907 | + | 7.36612i | −0.981186 | + | 0.262908i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.95448 | − | 25.9545i | 0.247901 | − | 0.925177i | −0.724003 | − | 0.689797i | \(-0.757700\pi\) |
0.971903 | − | 0.235380i | \(-0.0756336\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | −27.4907 | − | 7.36612i | −0.973772 | − | 0.260921i | −0.263352 | − | 0.964700i | \(-0.584828\pi\) |
−0.710420 | + | 0.703778i | \(0.751495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.9808 | − | 15.0000i | −0.919133 | − | 0.530662i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.10905 | + | 1.63692i | −0.215584 | + | 0.0577655i | ||||
\(804\) | 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 | \(-0.474950\pi\) | ||||
0.0786160 | + | 0.996905i | \(0.474950\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | −51.9269 | − | 13.9138i | −1.81892 | − | 0.487378i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.19615 | + | 2.19615i | −0.286747 | + | 0.0768336i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4919 | − | 8.94427i | −0.540672 | − | 0.312157i | 0.204679 | − | 0.978829i | \(-0.434385\pi\) |
−0.745351 | + | 0.666672i | \(0.767718\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2224 | − | 6.22243i | −0.809483 | − | 0.216900i | −0.169740 | − | 0.985489i | \(-0.554293\pi\) |
−0.639743 | + | 0.768589i | \(0.720959\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.1246 | − | 20.1246i | 0.699801 | − | 0.699801i | −0.264566 | − | 0.964368i | \(-0.585229\pi\) |
0.964368 | + | 0.264566i | \(0.0852288\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | −4.09229 | + | 15.2726i | −0.141789 | + | 0.529165i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.15064 | + | 34.1506i | 0.316671 | + | 1.18183i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.8885 | − | 30.9839i | 0.617581 | − | 1.06968i | −0.372345 | − | 0.928095i | \(-0.621446\pi\) |
0.989926 | − | 0.141587i | \(-0.0452206\pi\) | |||||||
\(840\) | 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 | ||||||||
\(853\) | 13.5429 | + | 50.5429i | 0.463701 | + | 1.73056i | 0.661159 | + | 0.750246i | \(0.270065\pi\) |
−0.197458 | + | 0.980311i | \(0.563268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.45537 | − | 9.16358i | −0.0838739 | − | 0.313022i | 0.911225 | − | 0.411910i | \(-0.135138\pi\) |
−0.995099 | + | 0.0988880i | \(0.968471\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1244 | − | 7.00000i | 0.413678 | − | 0.238837i | −0.278691 | − | 0.960381i | \(-0.589901\pi\) |
0.692369 | + | 0.721544i | \(0.256567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.5967 | + | 24.5967i | 0.837283 | + | 0.837283i | 0.988501 | − | 0.151217i | \(-0.0483194\pi\) |
−0.151217 | + | 0.988501i | \(0.548319\pi\) | |||||||
\(864\) | 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 | ||||||||
\(875\) | 15.2726 | − | 4.09229i | 0.516309 | − | 0.138345i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.29423 | − | 12.2942i | 0.111238 | − | 0.415147i | −0.887740 | − | 0.460346i | \(-0.847726\pi\) |
0.998978 | + | 0.0451990i | \(0.0143922\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7214i | 1.50670i | 0.657619 | + | 0.753350i | \(0.271564\pi\) | ||||
−0.657619 | + | 0.753350i | \(0.728436\pi\) | |||||||
\(882\) | 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 | ||||||||
\(887\) | −27.4907 | − | 7.36612i | −0.923048 | − | 0.247330i | −0.234160 | − | 0.972198i | \(-0.575234\pi\) |
−0.688888 | + | 0.724868i | \(0.741901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.5167 | − | 13.0000i | −0.755185 | − | 0.436006i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.3272 | + | 4.91075i | −0.613295 | + | 0.164332i | ||||
\(894\) | 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 | ||||||||
\(907\) | −9.56218 | + | 2.56218i | −0.317507 | + | 0.0850757i | −0.414053 | − | 0.910253i | \(-0.635887\pi\) |
0.0965460 | + | 0.995329i | \(0.469220\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.6028 | − | 24.5967i | −1.41149 | − | 0.814927i | −0.415965 | − | 0.909381i | \(-0.636556\pi\) |
−0.995529 | + | 0.0944540i | \(0.969889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.9808 | + | 10.9808i | 1.35627 | + | 0.363410i | ||||
\(914\) | 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 | ||||||||
\(923\) | 4.91075 | − | 18.3272i | 0.161639 | − | 0.603246i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.4904 | − | 5.49038i | 0.673720 | − | 0.180523i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.23607 | − | 3.87298i | 0.0733630 | − | 0.127068i | −0.827010 | − | 0.562187i | \(-0.809960\pi\) |
0.900373 | + | 0.435118i | \(0.143293\pi\) | |||||||
\(930\) | 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 | −0.828410 | − | 0.560123i | \(-0.810754\pi\) |
0.0708757 | + | 0.997485i | \(0.477421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.32051 | − | 27.3205i | −0.238389 | − | 0.889678i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.09229 | + | 15.2726i | 0.132982 | + | 0.496294i | 0.999998 | − | 0.00198565i | \(-0.000632053\pi\) |
−0.867017 | + | 0.498279i | \(0.833965\pi\) | |||||||
\(948\) | 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 | \(-0.971117\pi\) |
−0.0906141 | − | 0.995886i | \(-0.528883\pi\) | |||||||
\(954\) | 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 | ||||||||
\(965\) | −2.45537 | − | 9.16358i | −0.0790413 | − | 0.294986i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.56218 | − | 9.56218i | 0.0823941 | − | 0.307499i | −0.912414 | − | 0.409269i | \(-0.865784\pi\) |
0.994808 | + | 0.101770i | \(0.0324505\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.3607i | 0.717588i | 0.933417 | + | 0.358794i | \(0.116812\pi\) | ||||
−0.933417 | + | 0.358794i | \(0.883188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0000 | − | 14.0000i | 0.448819 | − | 0.448819i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.16358 | + | 2.45537i | 0.293169 | + | 0.0785543i | 0.402406 | − | 0.915461i | \(-0.368174\pi\) |
−0.109237 | + | 0.994016i | \(0.534841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.3205 | − | 10.0000i | −0.553566 | − | 0.319601i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.2726 | − | 4.09229i | 0.487121 | − | 0.130524i | −0.00689536 | − | 0.999976i | \(-0.502195\pi\) |
0.494017 | + | 0.869452i | \(0.335528\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.4904 | + | 5.49038i | 0.652878 | + | 0.174938i | ||||
\(986\) | 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 | ||||||||
\(997\) | 31.4186 | − | 8.41858i | 0.995037 | − | 0.266619i | 0.275672 | − | 0.961252i | \(-0.411100\pi\) |
0.719365 | + | 0.694633i | \(0.244433\pi\) | |||||||
\(998\) | 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 \(a_p\))