Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(844,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.844");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.d (of order \(2\), degree \(1\), 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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 844.5 | ||
Root | \(1.09445 - 0.895644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.844 |
Dual form | 845.2.d.c.844.6 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.456850 | 0.323042 | 0.161521 | − | 0.986869i | \(-0.448360\pi\) | ||||
0.161521 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | −0.957427 | − | 0.288675i | \(-0.906785\pi\) | ||
0.957427 | − | 0.288675i | \(-0.0932147\pi\) | |||||||
\(4\) | −1.79129 | −0.895644 | ||||||||
\(5\) | 2.18890 | + | 0.456850i | 0.978906 | + | 0.204310i | ||||
\(6\) | − | 0.456850i | − | 0.186508i | ||||||
\(7\) | −1.73205 | −0.654654 | −0.327327 | − | 0.944911i | \(-0.606148\pi\) | ||||
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 1.00000 | + | 0.208712i | 0.316228 | + | 0.0660006i | ||||
\(11\) | − | 2.64575i | − | 0.797724i | −0.917011 | − | 0.398862i | \(-0.869405\pi\) | ||
0.917011 | − | 0.398862i | \(-0.130595\pi\) | |||||||
\(12\) | 1.79129i | 0.517100i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.791288 | −0.211481 | ||||||||
\(15\) | 0.456850 | − | 2.18890i | 0.117958 | − | 0.565172i | ||||
\(16\) | 2.79129 | 0.697822 | ||||||||
\(17\) | − | 4.58258i | − | 1.11144i | −0.831370 | − | 0.555719i | \(-0.812443\pi\) | ||
0.831370 | − | 0.555719i | \(-0.187557\pi\) | |||||||
\(18\) | 0.913701 | 0.215361 | ||||||||
\(19\) | 1.73205i | 0.397360i | 0.980064 | + | 0.198680i | \(0.0636654\pi\) | ||||
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(20\) | −3.92095 | − | 0.818350i | −0.876751 | − | 0.182989i | ||||
\(21\) | 1.73205i | 0.377964i | ||||||||
\(22\) | − | 1.20871i | − | 0.257698i | ||||||
\(23\) | − | 4.58258i | − | 0.955533i | −0.878487 | − | 0.477767i | \(-0.841446\pi\) | ||
0.878487 | − | 0.477767i | \(-0.158554\pi\) | |||||||
\(24\) | 1.73205i | 0.353553i | ||||||||
\(25\) | 4.58258 | + | 2.00000i | 0.916515 | + | 0.400000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.00000i | − | 0.962250i | ||||||
\(28\) | 3.10260 | 0.586337 | ||||||||
\(29\) | −4.58258 | −0.850963 | −0.425481 | − | 0.904967i | \(-0.639895\pi\) | ||||
−0.425481 | + | 0.904967i | \(0.639895\pi\) | |||||||
\(30\) | 0.208712 | − | 1.00000i | 0.0381055 | − | 0.182574i | ||||
\(31\) | − | 6.20520i | − | 1.11449i | −0.830349 | − | 0.557244i | \(-0.811859\pi\) | ||
0.830349 | − | 0.557244i | \(-0.188141\pi\) | |||||||
\(32\) | 4.73930 | 0.837798 | ||||||||
\(33\) | −2.64575 | −0.460566 | ||||||||
\(34\) | − | 2.09355i | − | 0.359041i | ||||||
\(35\) | −3.79129 | − | 0.791288i | −0.640845 | − | 0.133752i | ||||
\(36\) | −3.58258 | −0.597096 | ||||||||
\(37\) | 7.93725 | 1.30488 | 0.652438 | − | 0.757842i | \(-0.273746\pi\) | ||||
0.652438 | + | 0.757842i | \(0.273746\pi\) | |||||||
\(38\) | 0.791288i | 0.128364i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.79129 | − | 0.791288i | −0.599455 | − | 0.125114i | ||||
\(41\) | 2.64575i | 0.413197i | 0.978426 | + | 0.206598i | \(0.0662394\pi\) | ||||
−0.978426 | + | 0.206598i | \(0.933761\pi\) | |||||||
\(42\) | 0.791288i | 0.122098i | ||||||||
\(43\) | − | 10.5826i | − | 1.61383i | −0.590669 | − | 0.806914i | \(-0.701136\pi\) | ||
0.590669 | − | 0.806914i | \(-0.298864\pi\) | |||||||
\(44\) | 4.73930i | 0.714477i | ||||||||
\(45\) | 4.37780 | + | 0.913701i | 0.652604 | + | 0.136206i | ||||
\(46\) | − | 2.09355i | − | 0.308677i | ||||||
\(47\) | −1.82740 | −0.266554 | −0.133277 | − | 0.991079i | \(-0.542550\pi\) | ||||
−0.133277 | + | 0.991079i | \(0.542550\pi\) | |||||||
\(48\) | − | 2.79129i | − | 0.402888i | ||||||
\(49\) | −4.00000 | −0.571429 | ||||||||
\(50\) | 2.09355 | + | 0.913701i | 0.296073 | + | 0.129217i | ||||
\(51\) | −4.58258 | −0.641689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.58258i | − | 1.04155i | −0.853695 | − | 0.520773i | \(-0.825644\pi\) | ||
0.853695 | − | 0.520773i | \(-0.174356\pi\) | |||||||
\(54\) | − | 2.28425i | − | 0.310847i | ||||||
\(55\) | 1.20871 | − | 5.79129i | 0.162983 | − | 0.780897i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 1.73205 | 0.229416 | ||||||||
\(58\) | −2.09355 | −0.274897 | ||||||||
\(59\) | 13.9518i | 1.81636i | 0.418576 | + | 0.908182i | \(0.362530\pi\) | ||||
−0.418576 | + | 0.908182i | \(0.637470\pi\) | |||||||
\(60\) | −0.818350 | + | 3.92095i | −0.105649 | + | 0.506193i | ||||
\(61\) | −1.41742 | −0.181483 | −0.0907413 | − | 0.995874i | \(-0.528924\pi\) | ||||
−0.0907413 | + | 0.995874i | \(0.528924\pi\) | |||||||
\(62\) | − | 2.83485i | − | 0.360026i | ||||||
\(63\) | −3.46410 | −0.436436 | ||||||||
\(64\) | −3.41742 | −0.427178 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.20871 | −0.148782 | ||||||||
\(67\) | −1.00905 | −0.123275 | −0.0616376 | − | 0.998099i | \(-0.519632\pi\) | ||||
−0.0616376 | + | 0.998099i | \(0.519632\pi\) | |||||||
\(68\) | 8.20871i | 0.995453i | ||||||||
\(69\) | −4.58258 | −0.551677 | ||||||||
\(70\) | −1.73205 | − | 0.361500i | −0.207020 | − | 0.0432075i | ||||
\(71\) | − | 7.02355i | − | 0.833542i | −0.909011 | − | 0.416771i | \(-0.863162\pi\) | ||
0.909011 | − | 0.416771i | \(-0.136838\pi\) | |||||||
\(72\) | −3.46410 | −0.408248 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 3.62614 | 0.421530 | ||||||||
\(75\) | 2.00000 | − | 4.58258i | 0.230940 | − | 0.529150i | ||||
\(76\) | − | 3.10260i | − | 0.355893i | ||||||
\(77\) | 4.58258i | 0.522233i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | 0.675053 | 0.337526 | − | 0.941316i | \(-0.390410\pi\) | ||||
0.337526 | + | 0.941316i | \(0.390410\pi\) | |||||||
\(80\) | 6.10985 | + | 1.27520i | 0.683102 | + | 0.142572i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.20871i | 0.133480i | ||||||||
\(83\) | 6.01450 | 0.660177 | 0.330089 | − | 0.943950i | \(-0.392921\pi\) | ||||
0.330089 | + | 0.943950i | \(0.392921\pi\) | |||||||
\(84\) | − | 3.10260i | − | 0.338522i | ||||||
\(85\) | 2.09355 | − | 10.0308i | 0.227077 | − | 1.08799i | ||||
\(86\) | − | 4.83465i | − | 0.521334i | ||||||
\(87\) | 4.58258i | 0.491304i | ||||||||
\(88\) | 4.58258i | 0.488504i | ||||||||
\(89\) | 9.57395i | 1.01484i | 0.861700 | + | 0.507419i | \(0.169400\pi\) | ||||
−0.861700 | + | 0.507419i | \(0.830600\pi\) | |||||||
\(90\) | 2.00000 | + | 0.417424i | 0.210819 | + | 0.0440004i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.20871i | 0.855817i | ||||||||
\(93\) | −6.20520 | −0.643450 | ||||||||
\(94\) | −0.834849 | −0.0861081 | ||||||||
\(95\) | −0.791288 | + | 3.79129i | −0.0811844 | + | 0.388978i | ||||
\(96\) | − | 4.73930i | − | 0.483703i | ||||||
\(97\) | −11.4014 | −1.15763 | −0.578816 | − | 0.815458i | \(-0.696485\pi\) | ||||
−0.578816 | + | 0.815458i | \(0.696485\pi\) | |||||||
\(98\) | −1.82740 | −0.184595 | ||||||||
\(99\) | − | 5.29150i | − | 0.531816i | ||||||
\(100\) | −8.20871 | − | 3.58258i | −0.820871 | − | 0.358258i | ||||
\(101\) | 9.00000 | 0.895533 | 0.447767 | − | 0.894150i | \(-0.352219\pi\) | ||||
0.447767 | + | 0.894150i | \(0.352219\pi\) | |||||||
\(102\) | −2.09355 | −0.207292 | ||||||||
\(103\) | − | 3.16515i | − | 0.311872i | −0.987767 | − | 0.155936i | \(-0.950161\pi\) | ||
0.987767 | − | 0.155936i | \(-0.0498393\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.791288 | + | 3.79129i | −0.0772218 | + | 0.369992i | ||||
\(106\) | − | 3.46410i | − | 0.336463i | ||||||
\(107\) | − | 10.5826i | − | 1.02306i | −0.859267 | − | 0.511528i | \(-0.829080\pi\) | ||
0.859267 | − | 0.511528i | \(-0.170920\pi\) | |||||||
\(108\) | 8.95644i | 0.861834i | ||||||||
\(109\) | 13.1334i | 1.25795i | 0.777425 | + | 0.628976i | \(0.216526\pi\) | ||||
−0.777425 | + | 0.628976i | \(0.783474\pi\) | |||||||
\(110\) | 0.552200 | − | 2.64575i | 0.0526502 | − | 0.252262i | ||||
\(111\) | − | 7.93725i | − | 0.753371i | ||||||
\(112\) | −4.83465 | −0.456832 | ||||||||
\(113\) | 7.41742i | 0.697773i | 0.937165 | + | 0.348886i | \(0.113440\pi\) | ||||
−0.937165 | + | 0.348886i | \(0.886560\pi\) | |||||||
\(114\) | 0.791288 | 0.0741109 | ||||||||
\(115\) | 2.09355 | − | 10.0308i | 0.195225 | − | 0.935377i | ||||
\(116\) | 8.20871 | 0.762160 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.37386i | 0.586762i | ||||||||
\(119\) | 7.93725i | 0.727607i | ||||||||
\(120\) | −0.791288 | + | 3.79129i | −0.0722344 | + | 0.346096i | ||||
\(121\) | 4.00000 | 0.363636 | ||||||||
\(122\) | −0.647551 | −0.0586265 | ||||||||
\(123\) | 2.64575 | 0.238559 | ||||||||
\(124\) | 11.1153i | 0.998184i | ||||||||
\(125\) | 9.11710 | + | 6.47135i | 0.815459 | + | 0.578815i | ||||
\(126\) | −1.58258 | −0.140987 | ||||||||
\(127\) | 17.7477i | 1.57486i | 0.616407 | + | 0.787428i | \(0.288588\pi\) | ||||
−0.616407 | + | 0.787428i | \(0.711412\pi\) | |||||||
\(128\) | −11.0399 | −0.975795 | ||||||||
\(129\) | −10.5826 | −0.931744 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.58258 | −0.662493 | −0.331246 | − | 0.943544i | \(-0.607469\pi\) | ||||
−0.331246 | + | 0.943544i | \(0.607469\pi\) | |||||||
\(132\) | 4.73930 | 0.412503 | ||||||||
\(133\) | − | 3.00000i | − | 0.260133i | ||||||
\(134\) | −0.460985 | −0.0398230 | ||||||||
\(135\) | 2.28425 | − | 10.9445i | 0.196597 | − | 0.941953i | ||||
\(136\) | 7.93725i | 0.680614i | ||||||||
\(137\) | 10.4877 | 0.896021 | 0.448010 | − | 0.894028i | \(-0.352133\pi\) | ||||
0.448010 | + | 0.894028i | \(0.352133\pi\) | |||||||
\(138\) | −2.09355 | −0.178215 | ||||||||
\(139\) | 21.7477 | 1.84462 | 0.922309 | − | 0.386453i | \(-0.126300\pi\) | ||||
0.922309 | + | 0.386453i | \(0.126300\pi\) | |||||||
\(140\) | 6.79129 | + | 1.41742i | 0.573969 | + | 0.119794i | ||||
\(141\) | 1.82740i | 0.153895i | ||||||||
\(142\) | − | 3.20871i | − | 0.269269i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.58258 | 0.465215 | ||||||||
\(145\) | −10.0308 | − | 2.09355i | −0.833013 | − | 0.173860i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.00000i | 0.329914i | ||||||||
\(148\) | −14.2179 | −1.16870 | ||||||||
\(149\) | 16.6929i | 1.36753i | 0.729701 | + | 0.683766i | \(0.239659\pi\) | ||||
−0.729701 | + | 0.683766i | \(0.760341\pi\) | |||||||
\(150\) | 0.913701 | − | 2.09355i | 0.0746033 | − | 0.170938i | ||||
\(151\) | 9.66930i | 0.786877i | 0.919351 | + | 0.393438i | \(0.128715\pi\) | ||||
−0.919351 | + | 0.393438i | \(0.871285\pi\) | |||||||
\(152\) | − | 3.00000i | − | 0.243332i | ||||||
\(153\) | − | 9.16515i | − | 0.740959i | ||||||
\(154\) | 2.09355i | 0.168703i | ||||||||
\(155\) | 2.83485 | − | 13.5826i | 0.227701 | − | 1.09098i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.16515i | 0.731459i | 0.930721 | + | 0.365729i | \(0.119180\pi\) | ||||
−0.930721 | + | 0.365729i | \(0.880820\pi\) | |||||||
\(158\) | 2.74110 | 0.218070 | ||||||||
\(159\) | −7.58258 | −0.601337 | ||||||||
\(160\) | 10.3739 | + | 2.16515i | 0.820126 | + | 0.171170i | ||||
\(161\) | 7.93725i | 0.625543i | ||||||||
\(162\) | 0.456850 | 0.0358935 | ||||||||
\(163\) | 21.0707 | 1.65038 | 0.825191 | − | 0.564854i | \(-0.191068\pi\) | ||||
0.825191 | + | 0.564854i | \(0.191068\pi\) | |||||||
\(164\) | − | 4.73930i | − | 0.370077i | ||||||
\(165\) | −5.79129 | − | 1.20871i | −0.450851 | − | 0.0940981i | ||||
\(166\) | 2.74773 | 0.213265 | ||||||||
\(167\) | −9.57395 | −0.740855 | −0.370427 | − | 0.928861i | \(-0.620789\pi\) | ||||
−0.370427 | + | 0.928861i | \(0.620789\pi\) | |||||||
\(168\) | − | 3.00000i | − | 0.231455i | ||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.956439 | − | 4.58258i | 0.0733555 | − | 0.351468i | ||||
\(171\) | 3.46410i | 0.264906i | ||||||||
\(172\) | 18.9564i | 1.44541i | ||||||||
\(173\) | 16.5826i | 1.26075i | 0.776291 | + | 0.630375i | \(0.217099\pi\) | ||||
−0.776291 | + | 0.630375i | \(0.782901\pi\) | |||||||
\(174\) | 2.09355i | 0.158712i | ||||||||
\(175\) | −7.93725 | − | 3.46410i | −0.600000 | − | 0.261861i | ||||
\(176\) | − | 7.38505i | − | 0.556669i | ||||||
\(177\) | 13.9518 | 1.04868 | ||||||||
\(178\) | 4.37386i | 0.327835i | ||||||||
\(179\) | −18.1652 | −1.35773 | −0.678864 | − | 0.734264i | \(-0.737527\pi\) | ||||
−0.678864 | + | 0.734264i | \(0.737527\pi\) | |||||||
\(180\) | −7.84190 | − | 1.63670i | −0.584501 | − | 0.121992i | ||||
\(181\) | 8.74773 | 0.650213 | 0.325107 | − | 0.945677i | \(-0.394600\pi\) | ||||
0.325107 | + | 0.945677i | \(0.394600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.41742i | 0.104779i | ||||||||
\(184\) | 7.93725i | 0.585142i | ||||||||
\(185\) | 17.3739 | + | 3.62614i | 1.27735 | + | 0.266599i | ||||
\(186\) | −2.83485 | −0.207861 | ||||||||
\(187\) | −12.1244 | −0.886621 | ||||||||
\(188\) | 3.27340 | 0.238737 | ||||||||
\(189\) | 8.66025i | 0.629941i | ||||||||
\(190\) | −0.361500 | + | 1.73205i | −0.0262260 | + | 0.125656i | ||||
\(191\) | −16.5826 | −1.19987 | −0.599937 | − | 0.800048i | \(-0.704808\pi\) | ||||
−0.599937 | + | 0.800048i | \(0.704808\pi\) | |||||||
\(192\) | 3.41742i | 0.246631i | ||||||||
\(193\) | 14.8655 | 1.07004 | 0.535020 | − | 0.844840i | \(-0.320304\pi\) | ||||
0.535020 | + | 0.844840i | \(0.320304\pi\) | |||||||
\(194\) | −5.20871 | −0.373964 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.16515 | 0.511797 | ||||||||
\(197\) | −14.6748 | −1.04553 | −0.522767 | − | 0.852476i | \(-0.675100\pi\) | ||||
−0.522767 | + | 0.852476i | \(0.675100\pi\) | |||||||
\(198\) | − | 2.41742i | − | 0.171799i | ||||||
\(199\) | −10.5826 | −0.750179 | −0.375089 | − | 0.926989i | \(-0.622388\pi\) | ||||
−0.375089 | + | 0.926989i | \(0.622388\pi\) | |||||||
\(200\) | −7.93725 | − | 3.46410i | −0.561249 | − | 0.244949i | ||||
\(201\) | 1.00905i | 0.0711729i | ||||||||
\(202\) | 4.11165 | 0.289295 | ||||||||
\(203\) | 7.93725 | 0.557086 | ||||||||
\(204\) | 8.20871 | 0.574725 | ||||||||
\(205\) | −1.20871 | + | 5.79129i | −0.0844201 | + | 0.404481i | ||||
\(206\) | − | 1.44600i | − | 0.100748i | ||||||
\(207\) | − | 9.16515i | − | 0.637022i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.58258 | 0.316983 | ||||||||
\(210\) | −0.361500 | + | 1.73205i | −0.0249459 | + | 0.119523i | ||||
\(211\) | −0.165151 | −0.0113695 | −0.00568475 | − | 0.999984i | \(-0.501810\pi\) | ||||
−0.00568475 | + | 0.999984i | \(0.501810\pi\) | |||||||
\(212\) | 13.5826i | 0.932855i | ||||||||
\(213\) | −7.02355 | −0.481246 | ||||||||
\(214\) | − | 4.83465i | − | 0.330490i | ||||||
\(215\) | 4.83465 | − | 23.1642i | 0.329721 | − | 1.57979i | ||||
\(216\) | 8.66025i | 0.589256i | ||||||||
\(217\) | 10.7477i | 0.729603i | ||||||||
\(218\) | 6.00000i | 0.406371i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.16515 | + | 10.3739i | −0.145974 | + | 0.699406i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 3.62614i | − | 0.243370i | ||||||
\(223\) | −8.66025 | −0.579934 | −0.289967 | − | 0.957037i | \(-0.593644\pi\) | ||||
−0.289967 | + | 0.957037i | \(0.593644\pi\) | |||||||
\(224\) | −8.20871 | −0.548468 | ||||||||
\(225\) | 9.16515 | + | 4.00000i | 0.611010 | + | 0.266667i | ||||
\(226\) | 3.38865i | 0.225410i | ||||||||
\(227\) | 0.818350 | 0.0543158 | 0.0271579 | − | 0.999631i | \(-0.491354\pi\) | ||||
0.0271579 | + | 0.999631i | \(0.491354\pi\) | |||||||
\(228\) | −3.10260 | −0.205475 | ||||||||
\(229\) | − | 26.2668i | − | 1.73576i | −0.496774 | − | 0.867880i | \(-0.665482\pi\) | ||
0.496774 | − | 0.867880i | \(-0.334518\pi\) | |||||||
\(230\) | 0.956439 | − | 4.58258i | 0.0630657 | − | 0.302166i | ||||
\(231\) | 4.58258 | 0.301511 | ||||||||
\(232\) | 7.93725 | 0.521106 | ||||||||
\(233\) | − | 2.83485i | − | 0.185717i | −0.995679 | − | 0.0928586i | \(-0.970400\pi\) | ||
0.995679 | − | 0.0928586i | \(-0.0296004\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | − | 0.834849i | −0.260931 | − | 0.0544595i | ||||
\(236\) | − | 24.9916i | − | 1.62682i | ||||||
\(237\) | − | 6.00000i | − | 0.389742i | ||||||
\(238\) | 3.62614i | 0.235048i | ||||||||
\(239\) | − | 0.190700i | − | 0.0123354i | −0.999981 | − | 0.00616769i | \(-0.998037\pi\) | ||
0.999981 | − | 0.00616769i | \(-0.00196325\pi\) | |||||||
\(240\) | 1.27520 | − | 6.10985i | 0.0823138 | − | 0.394389i | ||||
\(241\) | 1.73205i | 0.111571i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) | ||||
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 1.82740 | 0.117470 | ||||||||
\(243\) | − | 16.0000i | − | 1.02640i | ||||||
\(244\) | 2.53901 | 0.162544 | ||||||||
\(245\) | −8.75560 | − | 1.82740i | −0.559375 | − | 0.116748i | ||||
\(246\) | 1.20871 | 0.0770647 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.7477i | 0.682481i | ||||||||
\(249\) | − | 6.01450i | − | 0.381154i | ||||||
\(250\) | 4.16515 | + | 2.95644i | 0.263427 | + | 0.186982i | ||||
\(251\) | −0.165151 | −0.0104243 | −0.00521213 | − | 0.999986i | \(-0.501659\pi\) | ||||
−0.00521213 | + | 0.999986i | \(0.501659\pi\) | |||||||
\(252\) | 6.20520 | 0.390891 | ||||||||
\(253\) | −12.1244 | −0.762252 | ||||||||
\(254\) | 8.10805i | 0.508745i | ||||||||
\(255\) | −10.0308 | − | 2.09355i | −0.628153 | − | 0.131103i | ||||
\(256\) | 1.79129 | 0.111955 | ||||||||
\(257\) | − | 18.1652i | − | 1.13311i | −0.824024 | − | 0.566556i | \(-0.808276\pi\) | ||
0.824024 | − | 0.566556i | \(-0.191724\pi\) | |||||||
\(258\) | −4.83465 | −0.300992 | ||||||||
\(259\) | −13.7477 | −0.854242 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.16515 | −0.567309 | ||||||||
\(262\) | −3.46410 | −0.214013 | ||||||||
\(263\) | − | 9.00000i | − | 0.554964i | −0.960731 | − | 0.277482i | \(-0.910500\pi\) | ||
0.960731 | − | 0.277482i | \(-0.0894999\pi\) | |||||||
\(264\) | 4.58258 | 0.282038 | ||||||||
\(265\) | 3.46410 | − | 16.5975i | 0.212798 | − | 1.01958i | ||||
\(266\) | − | 1.37055i | − | 0.0840339i | ||||||
\(267\) | 9.57395 | 0.585917 | ||||||||
\(268\) | 1.80750 | 0.110411 | ||||||||
\(269\) | 15.0000 | 0.914566 | 0.457283 | − | 0.889321i | \(-0.348823\pi\) | ||||
0.457283 | + | 0.889321i | \(0.348823\pi\) | |||||||
\(270\) | 1.04356 | − | 5.00000i | 0.0635091 | − | 0.304290i | ||||
\(271\) | 8.66025i | 0.526073i | 0.964786 | + | 0.263036i | \(0.0847240\pi\) | ||||
−0.964786 | + | 0.263036i | \(0.915276\pi\) | |||||||
\(272\) | − | 12.7913i | − | 0.775586i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.79129 | 0.289452 | ||||||||
\(275\) | 5.29150 | − | 12.1244i | 0.319090 | − | 0.731126i | ||||
\(276\) | 8.20871 | 0.494106 | ||||||||
\(277\) | − | 7.41742i | − | 0.445670i | −0.974856 | − | 0.222835i | \(-0.928469\pi\) | ||
0.974856 | − | 0.222835i | \(-0.0715311\pi\) | |||||||
\(278\) | 9.93545 | 0.595889 | ||||||||
\(279\) | − | 12.4104i | − | 0.742992i | ||||||
\(280\) | 6.56670 | + | 1.37055i | 0.392436 | + | 0.0819061i | ||||
\(281\) | − | 3.65480i | − | 0.218027i | −0.994040 | − | 0.109014i | \(-0.965231\pi\) | ||
0.994040 | − | 0.109014i | \(-0.0347692\pi\) | |||||||
\(282\) | 0.834849i | 0.0497145i | ||||||||
\(283\) | 27.7477i | 1.64943i | 0.565548 | + | 0.824716i | \(0.308665\pi\) | ||||
−0.565548 | + | 0.824716i | \(0.691335\pi\) | |||||||
\(284\) | 12.5812i | 0.746557i | ||||||||
\(285\) | 3.79129 | + | 0.791288i | 0.224577 | + | 0.0468718i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.58258i | − | 0.270501i | ||||||
\(288\) | 9.47860 | 0.558532 | ||||||||
\(289\) | −4.00000 | −0.235294 | ||||||||
\(290\) | −4.58258 | − | 0.956439i | −0.269098 | − | 0.0561640i | ||||
\(291\) | 11.4014i | 0.668359i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.1389 | −1.05968 | −0.529842 | − | 0.848097i | \(-0.677749\pi\) | ||||
−0.529842 | + | 0.848097i | \(0.677749\pi\) | |||||||
\(294\) | 1.82740i | 0.106576i | ||||||||
\(295\) | −6.37386 | + | 30.5390i | −0.371101 | + | 1.77805i | ||||
\(296\) | −13.7477 | −0.799070 | ||||||||
\(297\) | −13.2288 | −0.767610 | ||||||||
\(298\) | 7.62614i | 0.441770i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.58258 | + | 8.20871i | −0.206840 | + | 0.473930i | ||||
\(301\) | 18.3296i | 1.05650i | ||||||||
\(302\) | 4.41742i | 0.254194i | ||||||||
\(303\) | − | 9.00000i | − | 0.517036i | ||||||
\(304\) | 4.83465i | 0.277286i | ||||||||
\(305\) | −3.10260 | − | 0.647551i | −0.177654 | − | 0.0370786i | ||||
\(306\) | − | 4.18710i | − | 0.239361i | ||||||
\(307\) | −24.2487 | −1.38395 | −0.691974 | − | 0.721923i | \(-0.743259\pi\) | ||||
−0.691974 | + | 0.721923i | \(0.743259\pi\) | |||||||
\(308\) | − | 8.20871i | − | 0.467735i | ||||||
\(309\) | −3.16515 | −0.180059 | ||||||||
\(310\) | 1.29510 | − | 6.20520i | 0.0735568 | − | 0.352432i | ||||
\(311\) | 7.58258 | 0.429968 | 0.214984 | − | 0.976618i | \(-0.431030\pi\) | ||||
0.214984 | + | 0.976618i | \(0.431030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.25227i | 0.183829i | 0.995767 | + | 0.0919147i | \(0.0292987\pi\) | ||||
−0.995767 | + | 0.0919147i | \(0.970701\pi\) | |||||||
\(314\) | 4.18710i | 0.236292i | ||||||||
\(315\) | −7.58258 | − | 1.58258i | −0.427230 | − | 0.0891680i | ||||
\(316\) | −10.7477 | −0.604607 | ||||||||
\(317\) | 0.190700 | 0.0107108 | 0.00535540 | − | 0.999986i | \(-0.498295\pi\) | ||||
0.00535540 | + | 0.999986i | \(0.498295\pi\) | |||||||
\(318\) | −3.46410 | −0.194257 | ||||||||
\(319\) | 12.1244i | 0.678834i | ||||||||
\(320\) | −7.48040 | − | 1.56125i | −0.418167 | − | 0.0872766i | ||||
\(321\) | −10.5826 | −0.590662 | ||||||||
\(322\) | 3.62614i | 0.202077i | ||||||||
\(323\) | 7.93725 | 0.441641 | ||||||||
\(324\) | −1.79129 | −0.0995160 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.62614 | 0.533142 | ||||||||
\(327\) | 13.1334 | 0.726279 | ||||||||
\(328\) | − | 4.58258i | − | 0.253030i | ||||||
\(329\) | 3.16515 | 0.174500 | ||||||||
\(330\) | −2.64575 | − | 0.552200i | −0.145644 | − | 0.0303976i | ||||
\(331\) | 4.47315i | 0.245867i | 0.992415 | + | 0.122933i | \(0.0392301\pi\) | ||||
−0.992415 | + | 0.122933i | \(0.960770\pi\) | |||||||
\(332\) | −10.7737 | −0.591284 | ||||||||
\(333\) | 15.8745 | 0.869918 | ||||||||
\(334\) | −4.37386 | −0.239327 | ||||||||
\(335\) | −2.20871 | − | 0.460985i | −0.120675 | − | 0.0251863i | ||||
\(336\) | 4.83465i | 0.263752i | ||||||||
\(337\) | 30.7477i | 1.67494i | 0.546487 | + | 0.837468i | \(0.315965\pi\) | ||||
−0.546487 | + | 0.837468i | \(0.684035\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.41742 | 0.402859 | ||||||||
\(340\) | −3.75015 | + | 17.9681i | −0.203381 | + | 0.974455i | ||||
\(341\) | −16.4174 | −0.889053 | ||||||||
\(342\) | 1.58258i | 0.0855759i | ||||||||
\(343\) | 19.0526 | 1.02874 | ||||||||
\(344\) | 18.3296i | 0.988264i | ||||||||
\(345\) | −10.0308 | − | 2.09355i | −0.540040 | − | 0.112713i | ||||
\(346\) | 7.57575i | 0.407275i | ||||||||
\(347\) | − | 21.3303i | − | 1.14507i | −0.819880 | − | 0.572535i | \(-0.805960\pi\) | ||
0.819880 | − | 0.572535i | \(-0.194040\pi\) | |||||||
\(348\) | − | 8.20871i | − | 0.440033i | ||||||
\(349\) | 2.45505i | 0.131416i | 0.997839 | + | 0.0657079i | \(0.0209306\pi\) | ||||
−0.997839 | + | 0.0657079i | \(0.979069\pi\) | |||||||
\(350\) | −3.62614 | − | 1.58258i | −0.193825 | − | 0.0845922i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 12.5390i | − | 0.668332i | ||||||
\(353\) | 6.83285 | 0.363676 | 0.181838 | − | 0.983328i | \(-0.441795\pi\) | ||||
0.181838 | + | 0.983328i | \(0.441795\pi\) | |||||||
\(354\) | 6.37386 | 0.338767 | ||||||||
\(355\) | 3.20871 | − | 15.3739i | 0.170301 | − | 0.815960i | ||||
\(356\) | − | 17.1497i | − | 0.908933i | ||||||
\(357\) | 7.93725 | 0.420084 | ||||||||
\(358\) | −8.29875 | −0.438603 | ||||||||
\(359\) | 19.5293i | 1.03072i | 0.856975 | + | 0.515359i | \(0.172341\pi\) | ||||
−0.856975 | + | 0.515359i | \(0.827659\pi\) | |||||||
\(360\) | −7.58258 | − | 1.58258i | −0.399637 | − | 0.0834091i | ||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 3.99640 | 0.210046 | ||||||||
\(363\) | − | 4.00000i | − | 0.209946i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.647551i | 0.0338480i | ||||||||
\(367\) | − | 1.74773i | − | 0.0912306i | −0.998959 | − | 0.0456153i | \(-0.985475\pi\) | ||
0.998959 | − | 0.0456153i | \(-0.0145248\pi\) | |||||||
\(368\) | − | 12.7913i | − | 0.666792i | ||||||
\(369\) | 5.29150i | 0.275465i | ||||||||
\(370\) | 7.93725 | + | 1.65660i | 0.412638 | + | 0.0861226i | ||||
\(371\) | 13.1334i | 0.681852i | ||||||||
\(372\) | 11.1153 | 0.576302 | ||||||||
\(373\) | 13.0000i | 0.673114i | 0.941663 | + | 0.336557i | \(0.109263\pi\) | ||||
−0.941663 | + | 0.336557i | \(0.890737\pi\) | |||||||
\(374\) | −5.53901 | −0.286416 | ||||||||
\(375\) | 6.47135 | − | 9.11710i | 0.334179 | − | 0.470805i | ||||
\(376\) | 3.16515 | 0.163230 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.95644i | 0.203497i | ||||||||
\(379\) | − | 10.6784i | − | 0.548510i | −0.961657 | − | 0.274255i | \(-0.911569\pi\) | ||
0.961657 | − | 0.274255i | \(-0.0884313\pi\) | |||||||
\(380\) | 1.41742 | − | 6.79129i | 0.0727123 | − | 0.348386i | ||||
\(381\) | 17.7477 | 0.909244 | ||||||||
\(382\) | −7.57575 | −0.387609 | ||||||||
\(383\) | 23.6211 | 1.20698 | 0.603490 | − | 0.797371i | \(-0.293776\pi\) | ||||
0.603490 | + | 0.797371i | \(0.293776\pi\) | |||||||
\(384\) | 11.0399i | 0.563375i | ||||||||
\(385\) | −2.09355 | + | 10.0308i | −0.106697 | + | 0.511217i | ||||
\(386\) | 6.79129 | 0.345667 | ||||||||
\(387\) | − | 21.1652i | − | 1.07589i | ||||||
\(388\) | 20.4231 | 1.03683 | ||||||||
\(389\) | 3.16515 | 0.160480 | 0.0802398 | − | 0.996776i | \(-0.474431\pi\) | ||||
0.0802398 | + | 0.996776i | \(0.474431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.0000 | −1.06202 | ||||||||
\(392\) | 6.92820 | 0.349927 | ||||||||
\(393\) | 7.58258i | 0.382490i | ||||||||
\(394\) | −6.70417 | −0.337751 | ||||||||
\(395\) | 13.1334 | + | 2.74110i | 0.660813 | + | 0.137920i | ||||
\(396\) | 9.47860i | 0.476318i | ||||||||
\(397\) | −20.3477 | −1.02122 | −0.510610 | − | 0.859812i | \(-0.670580\pi\) | ||||
−0.510610 | + | 0.859812i | \(0.670580\pi\) | |||||||
\(398\) | −4.83465 | −0.242339 | ||||||||
\(399\) | −3.00000 | −0.150188 | ||||||||
\(400\) | 12.7913 | + | 5.58258i | 0.639564 | + | 0.279129i | ||||
\(401\) | − | 29.8263i | − | 1.48945i | −0.667370 | − | 0.744726i | \(-0.732580\pi\) | ||
0.667370 | − | 0.744726i | \(-0.267420\pi\) | |||||||
\(402\) | 0.460985i | 0.0229918i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −16.1216 | −0.802079 | ||||||||
\(405\) | 2.18890 | + | 0.456850i | 0.108767 | + | 0.0227011i | ||||
\(406\) | 3.62614 | 0.179962 | ||||||||
\(407\) | − | 21.0000i | − | 1.04093i | ||||||
\(408\) | 7.93725 | 0.392953 | ||||||||
\(409\) | − | 8.66025i | − | 0.428222i | −0.976809 | − | 0.214111i | \(-0.931315\pi\) | ||
0.976809 | − | 0.214111i | \(-0.0686854\pi\) | |||||||
\(410\) | −0.552200 | + | 2.64575i | −0.0272712 | + | 0.130664i | ||||
\(411\) | − | 10.4877i | − | 0.517318i | ||||||
\(412\) | 5.66970i | 0.279326i | ||||||||
\(413\) | − | 24.1652i | − | 1.18909i | ||||||
\(414\) | − | 4.18710i | − | 0.205785i | ||||||
\(415\) | 13.1652 | + | 2.74773i | 0.646252 | + | 0.134881i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 21.7477i | − | 1.06499i | ||||||
\(418\) | 2.09355 | 0.102399 | ||||||||
\(419\) | 5.83485 | 0.285051 | 0.142526 | − | 0.989791i | \(-0.454478\pi\) | ||||
0.142526 | + | 0.989791i | \(0.454478\pi\) | |||||||
\(420\) | 1.41742 | − | 6.79129i | 0.0691632 | − | 0.331381i | ||||
\(421\) | − | 5.48220i | − | 0.267186i | −0.991036 | − | 0.133593i | \(-0.957348\pi\) | ||
0.991036 | − | 0.133593i | \(-0.0426515\pi\) | |||||||
\(422\) | −0.0754495 | −0.00367282 | ||||||||
\(423\) | −3.65480 | −0.177703 | ||||||||
\(424\) | 13.1334i | 0.637815i | ||||||||
\(425\) | 9.16515 | − | 21.0000i | 0.444575 | − | 1.01865i | ||||
\(426\) | −3.20871 | −0.155463 | ||||||||
\(427\) | 2.45505 | 0.118808 | ||||||||
\(428\) | 18.9564i | 0.916294i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.20871 | − | 10.5826i | 0.106514 | − | 0.510337i | ||||
\(431\) | 8.46955i | 0.407964i | 0.978975 | + | 0.203982i | \(0.0653884\pi\) | ||||
−0.978975 | + | 0.203982i | \(0.934612\pi\) | |||||||
\(432\) | − | 13.9564i | − | 0.671479i | ||||||
\(433\) | − | 9.74773i | − | 0.468446i | −0.972183 | − | 0.234223i | \(-0.924745\pi\) | ||
0.972183 | − | 0.234223i | \(-0.0752546\pi\) | |||||||
\(434\) | 4.91010i | 0.235692i | ||||||||
\(435\) | −2.09355 | + | 10.0308i | −0.100378 | + | 0.480940i | ||||
\(436\) | − | 23.5257i | − | 1.12668i | ||||||
\(437\) | 7.93725 | 0.379690 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4955 | 0.691830 | 0.345915 | − | 0.938266i | \(-0.387569\pi\) | ||||
0.345915 | + | 0.938266i | \(0.387569\pi\) | |||||||
\(440\) | −2.09355 | + | 10.0308i | −0.0998061 | + | 0.478200i | ||||
\(441\) | −8.00000 | −0.380952 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 19.9129i | − | 0.946089i | −0.881038 | − | 0.473045i | \(-0.843155\pi\) | ||
0.881038 | − | 0.473045i | \(-0.156845\pi\) | |||||||
\(444\) | 14.2179i | 0.674752i | ||||||||
\(445\) | −4.37386 | + | 20.9564i | −0.207341 | + | 0.993430i | ||||
\(446\) | −3.95644 | −0.187343 | ||||||||
\(447\) | 16.6929 | 0.789545 | ||||||||
\(448\) | 5.91915 | 0.279654 | ||||||||
\(449\) | − | 11.0200i | − | 0.520064i | −0.965600 | − | 0.260032i | \(-0.916267\pi\) | ||
0.965600 | − | 0.260032i | \(-0.0837331\pi\) | |||||||
\(450\) | 4.18710 | + | 1.82740i | 0.197382 | + | 0.0861445i | ||||
\(451\) | 7.00000 | 0.329617 | ||||||||
\(452\) | − | 13.2867i | − | 0.624956i | ||||||
\(453\) | 9.66930 | 0.454304 | ||||||||
\(454\) | 0.373864 | 0.0175463 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | 1.73205 | 0.0810219 | 0.0405110 | − | 0.999179i | \(-0.487101\pi\) | ||||
0.0405110 | + | 0.999179i | \(0.487101\pi\) | |||||||
\(458\) | − | 12.0000i | − | 0.560723i | ||||||
\(459\) | −22.9129 | −1.06948 | ||||||||
\(460\) | −3.75015 | + | 17.9681i | −0.174852 | + | 0.837765i | ||||
\(461\) | − | 35.8408i | − | 1.66927i | −0.550803 | − | 0.834635i | \(-0.685678\pi\) | ||
0.550803 | − | 0.834635i | \(-0.314322\pi\) | |||||||
\(462\) | 2.09355 | 0.0974008 | ||||||||
\(463\) | −39.4002 | −1.83108 | −0.915542 | − | 0.402223i | \(-0.868238\pi\) | ||||
−0.915542 | + | 0.402223i | \(0.868238\pi\) | |||||||
\(464\) | −12.7913 | −0.593821 | ||||||||
\(465\) | −13.5826 | − | 2.83485i | −0.629877 | − | 0.131463i | ||||
\(466\) | − | 1.29510i | − | 0.0599944i | ||||||
\(467\) | − | 24.3303i | − | 1.12587i | −0.826500 | − | 0.562936i | \(-0.809672\pi\) | ||
0.826500 | − | 0.562936i | \(-0.190328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.74773 | 0.0807025 | ||||||||
\(470\) | −1.82740 | − | 0.381401i | −0.0842917 | − | 0.0175927i | ||||
\(471\) | 9.16515 | 0.422308 | ||||||||
\(472\) | − | 24.1652i | − | 1.11229i | ||||||
\(473\) | −27.9989 | −1.28739 | ||||||||
\(474\) | − | 2.74110i | − | 0.125903i | ||||||
\(475\) | −3.46410 | + | 7.93725i | −0.158944 | + | 0.364186i | ||||
\(476\) | − | 14.2179i | − | 0.651677i | ||||||
\(477\) | − | 15.1652i | − | 0.694365i | ||||||
\(478\) | − | 0.0871215i | − | 0.00398485i | ||||||
\(479\) | 4.66385i | 0.213097i | 0.994308 | + | 0.106548i | \(0.0339799\pi\) | ||||
−0.994308 | + | 0.106548i | \(0.966020\pi\) | |||||||
\(480\) | 2.16515 | − | 10.3739i | 0.0988252 | − | 0.473500i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.791288i | 0.0360422i | ||||||||
\(483\) | 7.93725 | 0.361158 | ||||||||
\(484\) | −7.16515 | −0.325689 | ||||||||
\(485\) | −24.9564 | − | 5.20871i | −1.13321 | − | 0.236515i | ||||
\(486\) | − | 7.30960i | − | 0.331570i | ||||||
\(487\) | 10.6784 | 0.483882 | 0.241941 | − | 0.970291i | \(-0.422216\pi\) | ||||
0.241941 | + | 0.970291i | \(0.422216\pi\) | |||||||
\(488\) | 2.45505 | 0.111135 | ||||||||
\(489\) | − | 21.0707i | − | 0.952848i | ||||||
\(490\) | −4.00000 | − | 0.834849i | −0.180702 | − | 0.0377146i | ||||
\(491\) | 19.4174 | 0.876296 | 0.438148 | − | 0.898903i | \(-0.355635\pi\) | ||||
0.438148 | + | 0.898903i | \(0.355635\pi\) | |||||||
\(492\) | −4.73930 | −0.213664 | ||||||||
\(493\) | 21.0000i | 0.945792i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.41742 | − | 11.5826i | 0.108655 | − | 0.520598i | ||||
\(496\) | − | 17.3205i | − | 0.777714i | ||||||
\(497\) | 12.1652i | 0.545682i | ||||||||
\(498\) | − | 2.74773i | − | 0.123129i | ||||||
\(499\) | − | 0.723000i | − | 0.0323659i | −0.999869 | − | 0.0161830i | \(-0.994849\pi\) | ||
0.999869 | − | 0.0161830i | \(-0.00515142\pi\) | |||||||
\(500\) | −16.3314 | − | 11.5921i | −0.730361 | − | 0.518413i | ||||
\(501\) | 9.57395i | 0.427733i | ||||||||
\(502\) | −0.0754495 | −0.00336747 | ||||||||
\(503\) | − | 0.165151i | − | 0.00736374i | −0.999993 | − | 0.00368187i | \(-0.998828\pi\) | ||
0.999993 | − | 0.00368187i | \(-0.00117198\pi\) | |||||||
\(504\) | 6.00000 | 0.267261 | ||||||||
\(505\) | 19.7001 | + | 4.11165i | 0.876643 | + | 0.182966i | ||||
\(506\) | −5.53901 | −0.246239 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 31.7913i | − | 1.41051i | ||||||
\(509\) | − | 8.46955i | − | 0.375406i | −0.982226 | − | 0.187703i | \(-0.939896\pi\) | ||
0.982226 | − | 0.187703i | \(-0.0601043\pi\) | |||||||
\(510\) | −4.58258 | − | 0.956439i | −0.202920 | − | 0.0423518i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.8981 | 1.01196 | ||||||||
\(513\) | 8.66025 | 0.382360 | ||||||||
\(514\) | − | 8.29875i | − | 0.366042i | ||||||
\(515\) | 1.44600 | − | 6.92820i | 0.0637184 | − | 0.305293i | ||||
\(516\) | 18.9564 | 0.834511 | ||||||||
\(517\) | 4.83485i | 0.212636i | ||||||||
\(518\) | −6.28065 | −0.275956 | ||||||||
\(519\) | 16.5826 | 0.727894 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.4955 | 1.20460 | 0.602299 | − | 0.798271i | \(-0.294252\pi\) | ||||
0.602299 | + | 0.798271i | \(0.294252\pi\) | |||||||
\(522\) | −4.18710 | −0.183264 | ||||||||
\(523\) | − | 0.165151i | − | 0.00722157i | −0.999993 | − | 0.00361078i | \(-0.998851\pi\) | ||
0.999993 | − | 0.00361078i | \(-0.00114935\pi\) | |||||||
\(524\) | 13.5826 | 0.593358 | ||||||||
\(525\) | −3.46410 | + | 7.93725i | −0.151186 | + | 0.346410i | ||||
\(526\) | − | 4.11165i | − | 0.179277i | ||||||
\(527\) | −28.4358 | −1.23868 | ||||||||
\(528\) | −7.38505 | −0.321393 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | 1.58258 | − | 7.58258i | 0.0687427 | − | 0.329366i | ||||
\(531\) | 27.9035i | 1.21091i | ||||||||
\(532\) | 5.37386i | 0.232987i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.37386 | 0.189276 | ||||||||
\(535\) | 4.83465 | − | 23.1642i | 0.209020 | − | 1.00148i | ||||
\(536\) | 1.74773 | 0.0754903 | ||||||||
\(537\) | 18.1652i | 0.783884i | ||||||||
\(538\) | 6.85275 | 0.295443 | ||||||||
\(539\) | 10.5830i | 0.455842i | ||||||||
\(540\) | −4.09175 | + | 19.6048i | −0.176081 | + | 0.843655i | ||||
\(541\) | 10.3923i | 0.446800i | 0.974727 | + | 0.223400i | \(0.0717156\pi\) | ||||
−0.974727 | + | 0.223400i | \(0.928284\pi\) | |||||||
\(542\) | 3.95644i | 0.169944i | ||||||||
\(543\) | − | 8.74773i | − | 0.375401i | ||||||
\(544\) | − | 21.7182i | − | 0.931161i | ||||||
\(545\) | −6.00000 | + | 28.7477i | −0.257012 | + | 1.23142i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.7477i | 1.22916i | 0.788853 | + | 0.614582i | \(0.210675\pi\) | ||||
−0.788853 | + | 0.614582i | \(0.789325\pi\) | |||||||
\(548\) | −18.7864 | −0.802516 | ||||||||
\(549\) | −2.83485 | −0.120988 | ||||||||
\(550\) | 2.41742 | − | 5.53901i | 0.103079 | − | 0.236184i | ||||
\(551\) | − | 7.93725i | − | 0.338138i | ||||||
\(552\) | 7.93725 | 0.337832 | ||||||||
\(553\) | −10.3923 | −0.441926 | ||||||||
\(554\) | − | 3.38865i | − | 0.143970i | ||||||
\(555\) | 3.62614 | − | 17.3739i | 0.153921 | − | 0.737479i | ||||
\(556\) | −38.9564 | −1.65212 | ||||||||
\(557\) | 7.74655 | 0.328232 | 0.164116 | − | 0.986441i | \(-0.447523\pi\) | ||||
0.164116 | + | 0.986441i | \(0.447523\pi\) | |||||||
\(558\) | − | 5.66970i | − | 0.240017i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.5826 | − | 2.20871i | −0.447195 | − | 0.0933351i | ||||
\(561\) | 12.1244i | 0.511891i | ||||||||
\(562\) | − | 1.66970i | − | 0.0704319i | ||||||
\(563\) | 9.00000i | 0.379305i | 0.981851 | + | 0.189652i | \(0.0607361\pi\) | ||||
−0.981851 | + | 0.189652i | \(0.939264\pi\) | |||||||
\(564\) | − | 3.27340i | − | 0.137835i | ||||||
\(565\) | −3.38865 | + | 16.2360i | −0.142562 | + | 0.683054i | ||||
\(566\) | 12.6766i | 0.532835i | ||||||||
\(567\) | −1.73205 | −0.0727393 | ||||||||
\(568\) | 12.1652i | 0.510438i | ||||||||
\(569\) | −7.74773 | −0.324802 | −0.162401 | − | 0.986725i | \(-0.551924\pi\) | ||||
−0.162401 | + | 0.986725i | \(0.551924\pi\) | |||||||
\(570\) | 1.73205 | + | 0.361500i | 0.0725476 | + | 0.0151416i | ||||
\(571\) | −35.0780 | −1.46797 | −0.733985 | − | 0.679166i | \(-0.762342\pi\) | ||||
−0.733985 | + | 0.679166i | \(0.762342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.5826i | 0.692747i | ||||||||
\(574\) | − | 2.09355i | − | 0.0873831i | ||||||
\(575\) | 9.16515 | − | 21.0000i | 0.382213 | − | 0.875761i | ||||
\(576\) | −6.83485 | −0.284785 | ||||||||
\(577\) | 6.92820 | 0.288425 | 0.144212 | − | 0.989547i | \(-0.453935\pi\) | ||||
0.144212 | + | 0.989547i | \(0.453935\pi\) | |||||||
\(578\) | −1.82740 | −0.0760099 | ||||||||
\(579\) | − | 14.8655i | − | 0.617787i | ||||||
\(580\) | 17.9681 | + | 3.75015i | 0.746083 | + | 0.155717i | ||||
\(581\) | −10.4174 | −0.432188 | ||||||||
\(582\) | 5.20871i | 0.215908i | ||||||||
\(583\) | −20.0616 | −0.830867 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.28674 | −0.342322 | ||||||||
\(587\) | 39.4956 | 1.63016 | 0.815078 | − | 0.579351i | \(-0.196694\pi\) | ||||
0.815078 | + | 0.579351i | \(0.196694\pi\) | |||||||
\(588\) | − | 7.16515i | − | 0.295486i | ||||||
\(589\) | 10.7477 | 0.442852 | ||||||||
\(590\) | −2.91190 | + | 13.9518i | −0.119881 | + | 0.574385i | ||||
\(591\) | 14.6748i | 0.603639i | ||||||||
\(592\) | 22.1552 | 0.910571 | ||||||||
\(593\) | 21.1660 | 0.869184 | 0.434592 | − | 0.900627i | \(-0.356893\pi\) | ||||
0.434592 | + | 0.900627i | \(0.356893\pi\) | |||||||
\(594\) | −6.04356 | −0.247970 | ||||||||
\(595\) | −3.62614 | + | 17.3739i | −0.148657 | + | 0.712259i | ||||
\(596\) | − | 29.9017i | − | 1.22482i | ||||||
\(597\) | 10.5826i | 0.433116i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.4955 | −0.633127 | −0.316564 | − | 0.948571i | \(-0.602529\pi\) | ||||
−0.316564 | + | 0.948571i | \(0.602529\pi\) | |||||||
\(600\) | −3.46410 | + | 7.93725i | −0.141421 | + | 0.324037i | ||||
\(601\) | 16.9129 | 0.689891 | 0.344945 | − | 0.938623i | \(-0.387897\pi\) | ||||
0.344945 | + | 0.938623i | \(0.387897\pi\) | |||||||
\(602\) | 8.37386i | 0.341293i | ||||||||
\(603\) | −2.01810 | −0.0821834 | ||||||||
\(604\) | − | 17.3205i | − | 0.704761i | ||||||
\(605\) | 8.75560 | + | 1.82740i | 0.355966 | + | 0.0742944i | ||||
\(606\) | − | 4.11165i | − | 0.167024i | ||||||
\(607\) | 7.74773i | 0.314471i | 0.987561 | + | 0.157235i | \(0.0502581\pi\) | ||||
−0.987561 | + | 0.157235i | \(0.949742\pi\) | |||||||
\(608\) | 8.20871i | 0.332907i | ||||||||
\(609\) | − | 7.93725i | − | 0.321634i | ||||||
\(610\) | −1.41742 | − | 0.295834i | −0.0573898 | − | 0.0119780i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 16.4174i | 0.663635i | ||||||||
\(613\) | −5.91915 | −0.239072 | −0.119536 | − | 0.992830i | \(-0.538141\pi\) | ||||
−0.119536 | + | 0.992830i | \(0.538141\pi\) | |||||||
\(614\) | −11.0780 | −0.447073 | ||||||||
\(615\) | 5.79129 | + | 1.20871i | 0.233527 | + | 0.0487400i | ||||
\(616\) | − | 7.93725i | − | 0.319801i | ||||||
\(617\) | −13.9518 | −0.561677 | −0.280838 | − | 0.959755i | \(-0.590612\pi\) | ||||
−0.280838 | + | 0.959755i | \(0.590612\pi\) | |||||||
\(618\) | −1.44600 | −0.0581667 | ||||||||
\(619\) | 29.7309i | 1.19499i | 0.801874 | + | 0.597493i | \(0.203836\pi\) | ||||
−0.801874 | + | 0.597493i | \(0.796164\pi\) | |||||||
\(620\) | −5.07803 | + | 24.3303i | −0.203939 | + | 0.977128i | ||||
\(621\) | −22.9129 | −0.919462 | ||||||||
\(622\) | 3.46410 | 0.138898 | ||||||||
\(623\) | − | 16.5826i | − | 0.664367i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0000 | + | 18.3303i | 0.680000 | + | 0.733212i | ||||
\(626\) | 1.48580i | 0.0593846i | ||||||||
\(627\) | − | 4.58258i | − | 0.183010i | ||||||
\(628\) | − | 16.4174i | − | 0.655127i | ||||||
\(629\) | − | 36.3731i | − | 1.45029i | ||||||
\(630\) | −3.46410 | − | 0.723000i | −0.138013 | − | 0.0288050i | ||||
\(631\) | 5.91915i | 0.235638i | 0.993035 | + | 0.117819i | \(0.0375902\pi\) | ||||
−0.993035 | + | 0.117819i | \(0.962410\pi\) | |||||||
\(632\) | −10.3923 | −0.413384 | ||||||||
\(633\) | 0.165151i | 0.00656418i | ||||||||
\(634\) | 0.0871215 | 0.00346004 | ||||||||
\(635\) | −8.10805 | + | 38.8480i | −0.321758 | + | 1.54164i | ||||
\(636\) | 13.5826 | 0.538584 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.53901i | 0.219292i | ||||||||
\(639\) | − | 14.0471i | − | 0.555695i | ||||||
\(640\) | −24.1652 | − | 5.04356i | −0.955211 | − | 0.199364i | ||||
\(641\) | 18.1652 | 0.717480 | 0.358740 | − | 0.933437i | \(-0.383206\pi\) | ||||
0.358740 | + | 0.933437i | \(0.383206\pi\) | |||||||
\(642\) | −4.83465 | −0.190809 | ||||||||
\(643\) | −21.7937 | −0.859458 | −0.429729 | − | 0.902958i | \(-0.641391\pi\) | ||||
−0.429729 | + | 0.902958i | \(0.641391\pi\) | |||||||
\(644\) | − | 14.2179i | − | 0.560264i | ||||||
\(645\) | −23.1642 | − | 4.83465i | −0.912090 | − | 0.190364i | ||||
\(646\) | 3.62614 | 0.142668 | ||||||||
\(647\) | 27.0000i | 1.06148i | 0.847535 | + | 0.530740i | \(0.178086\pi\) | ||||
−0.847535 | + | 0.530740i | \(0.821914\pi\) | |||||||
\(648\) | −1.73205 | −0.0680414 | ||||||||
\(649\) | 36.9129 | 1.44896 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.7477 | 0.421237 | ||||||||
\(652\) | −37.7436 | −1.47815 | ||||||||
\(653\) | 42.8258i | 1.67590i | 0.545746 | + | 0.837951i | \(0.316246\pi\) | ||||
−0.545746 | + | 0.837951i | \(0.683754\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | −16.5975 | − | 3.46410i | −0.648518 | − | 0.135354i | ||||
\(656\) | 7.38505i | 0.288338i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.44600 | 0.0563710 | ||||||||
\(659\) | −30.4955 | −1.18793 | −0.593967 | − | 0.804489i | \(-0.702439\pi\) | ||||
−0.593967 | + | 0.804489i | \(0.702439\pi\) | |||||||
\(660\) | 10.3739 | + | 2.16515i | 0.403802 | + | 0.0842784i | ||||
\(661\) | 18.3296i | 0.712937i | 0.934307 | + | 0.356469i | \(0.116019\pi\) | ||||
−0.934307 | + | 0.356469i | \(0.883981\pi\) | |||||||
\(662\) | 2.04356i | 0.0794252i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.4174 | −0.404274 | ||||||||
\(665\) | 1.37055 | − | 6.56670i | 0.0531477 | − | 0.254646i | ||||
\(666\) | 7.25227 | 0.281020 | ||||||||
\(667\) | 21.0000i | 0.813123i | ||||||||
\(668\) | 17.1497 | 0.663542 | ||||||||
\(669\) | 8.66025i | 0.334825i | ||||||||
\(670\) | −1.00905 | − | 0.210601i | −0.0389830 | − | 0.00813623i | ||||
\(671\) | 3.75015i | 0.144773i | ||||||||
\(672\) | 8.20871i | 0.316658i | ||||||||
\(673\) | 24.1652i | 0.931498i | 0.884917 | + | 0.465749i | \(0.154215\pi\) | ||||
−0.884917 | + | 0.465749i | \(0.845785\pi\) | |||||||
\(674\) | 14.0471i | 0.541074i | ||||||||
\(675\) | 10.0000 | − | 22.9129i | 0.384900 | − | 0.881917i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.83485i | − | 0.108952i | −0.998515 | − | 0.0544760i | \(-0.982651\pi\) | ||
0.998515 | − | 0.0544760i | \(-0.0173489\pi\) | |||||||
\(678\) | 3.38865 | 0.130140 | ||||||||
\(679\) | 19.7477 | 0.757848 | ||||||||
\(680\) | −3.62614 | + | 17.3739i | −0.139056 | + | 0.666257i | ||||
\(681\) | − | 0.818350i | − | 0.0313593i | ||||||
\(682\) | −7.50030 | −0.287202 | ||||||||
\(683\) | 33.0997 | 1.26652 | 0.633262 | − | 0.773938i | \(-0.281716\pi\) | ||||
0.633262 | + | 0.773938i | \(0.281716\pi\) | |||||||
\(684\) | − | 6.20520i | − | 0.237262i | ||||||
\(685\) | 22.9564 | + | 4.79129i | 0.877120 | + | 0.183066i | ||||
\(686\) | 8.70417 | 0.332327 | ||||||||
\(687\) | −26.2668 | −1.00214 | ||||||||
\(688\) | − | 29.5390i | − | 1.12616i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4.58258 | − | 0.956439i | −0.174456 | − | 0.0364110i | ||||
\(691\) | 19.7756i | 0.752298i | 0.926559 | + | 0.376149i | \(0.122752\pi\) | ||||
−0.926559 | + | 0.376149i | \(0.877248\pi\) | |||||||
\(692\) | − | 29.7042i | − | 1.12918i | ||||||
\(693\) | 9.16515i | 0.348155i | ||||||||
\(694\) | − | 9.74475i | − | 0.369906i | ||||||
\(695\) | 47.6036 | + | 9.93545i | 1.80571 | + | 0.376873i | ||||
\(696\) | − | 7.93725i | − | 0.300861i | ||||||
\(697\) | 12.1244 | 0.459243 | ||||||||
\(698\) | 1.12159i | 0.0424528i | ||||||||
\(699\) | −2.83485 | −0.107224 | ||||||||
\(700\) | 14.2179 | + | 6.20520i | 0.537386 | + | 0.234535i | ||||
\(701\) | −21.1652 | −0.799397 | −0.399698 | − | 0.916647i | \(-0.630885\pi\) | ||||
−0.399698 | + | 0.916647i | \(0.630885\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7477i | 0.518505i | ||||||||
\(704\) | 9.04165i | 0.340770i | ||||||||
\(705\) | −0.834849 | + | 4.00000i | −0.0314422 | + | 0.150649i | ||||
\(706\) | 3.12159 | 0.117483 | ||||||||
\(707\) | −15.5885 | −0.586264 | ||||||||
\(708\) | −24.9916 | −0.939242 | ||||||||
\(709\) | − | 36.3731i | − | 1.36602i | −0.730409 | − | 0.683010i | \(-0.760671\pi\) | ||
0.730409 | − | 0.683010i | \(-0.239329\pi\) | |||||||
\(710\) | 1.46590 | − | 7.02355i | 0.0550143 | − | 0.263589i | ||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | − | 16.5826i | − | 0.621458i | ||||||
\(713\) | −28.4358 | −1.06493 | ||||||||
\(714\) | 3.62614 | 0.135705 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.5390 | 1.21604 | ||||||||
\(717\) | −0.190700 | −0.00712184 | ||||||||
\(718\) | 8.92197i | 0.332965i | ||||||||
\(719\) | 24.4955 | 0.913526 | 0.456763 | − | 0.889588i | \(-0.349009\pi\) | ||||
0.456763 | + | 0.889588i | \(0.349009\pi\) | |||||||
\(720\) | 12.2197 | + | 2.55040i | 0.455402 | + | 0.0950478i | ||||
\(721\) | 5.48220i | 0.204168i | ||||||||
\(722\) | 7.30960 | 0.272035 | ||||||||
\(723\) | 1.73205 | 0.0644157 | ||||||||
\(724\) | −15.6697 | −0.582360 | ||||||||
\(725\) | −21.0000 | − | 9.16515i | −0.779920 | − | 0.340385i | ||||
\(726\) | − | 1.82740i | − | 0.0678212i | ||||||
\(727\) | − | 15.2523i | − | 0.565675i | −0.959168 | − | 0.282838i | \(-0.908724\pi\) | ||
0.959168 | − | 0.282838i | \(-0.0912758\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.4955 | −1.79367 | ||||||||
\(732\) | − | 2.53901i | − | 0.0938447i | ||||||
\(733\) | −22.8027 | −0.842237 | −0.421119 | − | 0.907006i | \(-0.638362\pi\) | ||||
−0.421119 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(734\) | − | 0.798450i | − | 0.0294713i | ||||||
\(735\) | −1.82740 | + | 8.75560i | −0.0674047 | + | 0.322955i | ||||
\(736\) | − | 21.7182i | − | 0.800544i | ||||||
\(737\) | 2.66970i | 0.0983396i | ||||||||
\(738\) | 2.41742i | 0.0889866i | ||||||||
\(739\) | − | 17.0345i | − | 0.626623i | −0.949650 | − | 0.313311i | \(-0.898562\pi\) | ||
0.949650 | − | 0.313311i | \(-0.101438\pi\) | |||||||
\(740\) | −31.1216 | − | 6.49545i | −1.14405 | − | 0.238778i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000i | 0.220267i | ||||||||
\(743\) | 5.72845 | 0.210157 | 0.105078 | − | 0.994464i | \(-0.466491\pi\) | ||||
0.105078 | + | 0.994464i | \(0.466491\pi\) | |||||||
\(744\) | 10.7477 | 0.394031 | ||||||||
\(745\) | −7.62614 | + | 36.5390i | −0.279400 | + | 1.33869i | ||||
\(746\) | 5.93905i | 0.217444i | ||||||||
\(747\) | 12.0290 | 0.440118 | ||||||||
\(748\) | 21.7182 | 0.794096 | ||||||||
\(749\) | 18.3296i | 0.669748i | ||||||||
\(750\) | 2.95644 | − | 4.16515i | 0.107954 | − | 0.152090i | ||||
\(751\) | 11.7477 | 0.428681 | 0.214340 | − | 0.976759i | \(-0.431240\pi\) | ||||
0.214340 | + | 0.976759i | \(0.431240\pi\) | |||||||
\(752\) | −5.10080 | −0.186007 | ||||||||
\(753\) | 0.165151i | 0.00601845i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.41742 | + | 21.1652i | −0.160767 | + | 0.770279i | ||||
\(756\) | − | 15.5130i | − | 0.564203i | ||||||
\(757\) | 9.74773i | 0.354287i | 0.984185 | + | 0.177144i | \(0.0566857\pi\) | ||||
−0.984185 | + | 0.177144i | \(0.943314\pi\) | |||||||
\(758\) | − | 4.87841i | − | 0.177192i | ||||||
\(759\) | 12.1244i | 0.440086i | ||||||||
\(760\) | 1.37055 | − | 6.56670i | 0.0497151 | − | 0.238199i | ||||
\(761\) | 35.4594i | 1.28540i | 0.766118 | + | 0.642701i | \(0.222186\pi\) | ||||
−0.766118 | + | 0.642701i | \(0.777814\pi\) | |||||||
\(762\) | 8.10805 | 0.293724 | ||||||||
\(763\) | − | 22.7477i | − | 0.823523i | ||||||
\(764\) | 29.7042 | 1.07466 | ||||||||
\(765\) | 4.18710 | − | 20.0616i | 0.151385 | − | 0.725329i | ||||
\(766\) | 10.7913 | 0.389905 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 1.79129i | − | 0.0646375i | ||||||
\(769\) | − | 15.5885i | − | 0.562134i | −0.959688 | − | 0.281067i | \(-0.909312\pi\) | ||
0.959688 | − | 0.281067i | \(-0.0906883\pi\) | |||||||
\(770\) | −0.956439 | + | 4.58258i | −0.0344677 | + | 0.165145i | ||||
\(771\) | −18.1652 | −0.654202 | ||||||||
\(772\) | −26.6283 | −0.958374 | ||||||||
\(773\) | −24.1534 | −0.868736 | −0.434368 | − | 0.900735i | \(-0.643028\pi\) | ||||
−0.434368 | + | 0.900735i | \(0.643028\pi\) | |||||||
\(774\) | − | 9.66930i | − | 0.347556i | ||||||
\(775\) | 12.4104 | − | 28.4358i | 0.445795 | − | 1.02144i | ||||
\(776\) | 19.7477 | 0.708902 | ||||||||
\(777\) | 13.7477i | 0.493197i | ||||||||
\(778\) | 1.44600 | 0.0518416 | ||||||||
\(779\) | −4.58258 | −0.164188 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.5826 | −0.664937 | ||||||||
\(782\) | −9.59386 | −0.343076 | ||||||||
\(783\) | 22.9129i | 0.818839i | ||||||||
\(784\) | −11.1652 | −0.398755 | ||||||||
\(785\) | −4.18710 | + | 20.0616i | −0.149444 | + | 0.716030i | ||||
\(786\) | 3.46410i | 0.123560i | ||||||||
\(787\) | 16.3115 | 0.581441 | 0.290720 | − | 0.956808i | \(-0.406105\pi\) | ||||
0.290720 | + | 0.956808i | \(0.406105\pi\) | |||||||
\(788\) | 26.2867 | 0.936425 | ||||||||
\(789\) | −9.00000 | −0.320408 | ||||||||
\(790\) | 6.00000 | + | 1.25227i | 0.213470 | + | 0.0445539i | ||||
\(791\) | − | 12.8474i | − | 0.456799i | ||||||
\(792\) | 9.16515i | 0.325669i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9.29583 | −0.329897 | ||||||||
\(795\) | −16.5975 | − | 3.46410i | −0.588653 | − | 0.122859i | ||||
\(796\) | 18.9564 | 0.671893 | ||||||||
\(797\) | 44.0780i | 1.56132i | 0.624954 | + | 0.780662i | \(0.285118\pi\) | ||||
−0.624954 | + | 0.780662i | \(0.714882\pi\) | |||||||
\(798\) | −1.37055 | −0.0485170 | ||||||||
\(799\) | 8.37420i | 0.296258i | ||||||||
\(800\) | 21.7182 | + | 9.47860i | 0.767855 | + | 0.335119i | ||||
\(801\) | 19.1479i | 0.676558i | ||||||||
\(802\) | − | 13.6261i | − | 0.481156i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 1.80750i | − | 0.0637456i | ||||||
\(805\) | −3.62614 | + | 17.3739i | −0.127805 | + | 0.612348i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 15.0000i | − | 0.528025i | ||||||
\(808\) | −15.5885 | −0.548400 | ||||||||
\(809\) | 54.8258 | 1.92757 | 0.963785 | − | 0.266679i | \(-0.0859263\pi\) | ||||
0.963785 | + | 0.266679i | \(0.0859263\pi\) | |||||||
\(810\) | 1.00000 | + | 0.208712i | 0.0351364 | + | 0.00733340i | ||||
\(811\) | 50.5155i | 1.77384i | 0.461923 | + | 0.886920i | \(0.347160\pi\) | ||||
−0.461923 | + | 0.886920i | \(0.652840\pi\) | |||||||
\(812\) | −14.2179 | −0.498951 | ||||||||
\(813\) | 8.66025 | 0.303728 | ||||||||
\(814\) | − | 9.59386i | − | 0.336264i | ||||||
\(815\) | 46.1216 | + | 9.62614i | 1.61557 | + | 0.337189i | ||||
\(816\) | −12.7913 | −0.447785 | ||||||||
\(817\) | 18.3296 | 0.641270 | ||||||||
\(818\) | − | 3.95644i | − | 0.138334i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.16515 | − | 10.3739i | 0.0756104 | − | 0.362271i | ||||
\(821\) | 18.1389i | 0.633051i | 0.948584 | + | 0.316525i | \(0.102516\pi\) | ||||
−0.948584 | + | 0.316525i | \(0.897484\pi\) | |||||||
\(822\) | − | 4.79129i | − | 0.167115i | ||||||
\(823\) | 31.4174i | 1.09514i | 0.836759 | + | 0.547571i | \(0.184448\pi\) | ||||
−0.836759 | + | 0.547571i | \(0.815552\pi\) | |||||||
\(824\) | 5.48220i | 0.190982i | ||||||||
\(825\) | −12.1244 | − | 5.29150i | −0.422116 | − | 0.184226i | ||||
\(826\) | − | 11.0399i | − | 0.384126i | ||||||
\(827\) | −10.7737 | −0.374638 | −0.187319 | − | 0.982299i | \(-0.559980\pi\) | ||||
−0.187319 | + | 0.982299i | \(0.559980\pi\) | |||||||
\(828\) | 16.4174i | 0.570545i | ||||||||
\(829\) | 33.3303 | 1.15761 | 0.578805 | − | 0.815466i | \(-0.303519\pi\) | ||||
0.578805 | + | 0.815466i | \(0.303519\pi\) | |||||||
\(830\) | 6.01450 | + | 1.25530i | 0.208766 | + | 0.0435721i | ||||
\(831\) | −7.41742 | −0.257308 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.3303i | 0.635107i | ||||||||
\(834\) | − | 9.93545i | − | 0.344037i | ||||||
\(835\) | −20.9564 | − | 4.37386i | −0.725227 | − | 0.151364i | ||||
\(836\) | −8.20871 | −0.283904 | ||||||||
\(837\) | −31.0260 | −1.07242 | ||||||||
\(838\) | 2.66565 | 0.0920834 | ||||||||
\(839\) | − | 43.6827i | − | 1.50809i | −0.656821 | − | 0.754047i | \(-0.728099\pi\) | ||
0.656821 | − | 0.754047i | \(-0.271901\pi\) | |||||||
\(840\) | 1.37055 | − | 6.56670i | 0.0472885 | − | 0.226573i | ||||
\(841\) | −8.00000 | −0.275862 | ||||||||
\(842\) | − | 2.50455i | − | 0.0863123i | ||||||
\(843\) | −3.65480 | −0.125878 | ||||||||
\(844\) | 0.295834 | 0.0101830 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.66970 | −0.0574054 | ||||||||
\(847\) | −6.92820 | −0.238056 | ||||||||
\(848\) | − | 21.1652i | − | 0.726814i | ||||||
\(849\) | 27.7477 | 0.952300 | ||||||||
\(850\) | 4.18710 | − | 9.59386i | 0.143616 | − | 0.329067i | ||||
\(851\) | − | 36.3731i | − | 1.24685i | ||||||
\(852\) | 12.5812 | 0.431025 | ||||||||
\(853\) | 5.63310 | 0.192874 | 0.0964369 | − | 0.995339i | \(-0.469255\pi\) | ||||
0.0964369 | + | 0.995339i | \(0.469255\pi\) | |||||||
\(854\) | 1.12159 | 0.0383800 | ||||||||
\(855\) | −1.58258 | + | 7.58258i | −0.0541229 | + | 0.259319i | ||||
\(856\) | 18.3296i | 0.626491i | ||||||||
\(857\) | − | 4.74773i | − | 0.162179i | −0.996707 | − | 0.0810896i | \(-0.974160\pi\) | ||
0.996707 | − | 0.0810896i | \(-0.0258400\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.2432 | 1.50956 | 0.754779 | − | 0.655979i | \(-0.227744\pi\) | ||||
0.754779 | + | 0.655979i | \(0.227744\pi\) | |||||||
\(860\) | −8.66025 | + | 41.4938i | −0.295312 | + | 1.41493i | ||||
\(861\) | −4.58258 | −0.156174 | ||||||||
\(862\) | 3.86932i | 0.131789i | ||||||||
\(863\) | −13.6657 | −0.465186 | −0.232593 | − | 0.972574i | \(-0.574721\pi\) | ||||
−0.232593 | + | 0.972574i | \(0.574721\pi\) | |||||||
\(864\) | − | 23.6965i | − | 0.806172i | ||||||
\(865\) | −7.57575 | + | 36.2976i | −0.257583 | + | 1.23416i | ||||
\(866\) | − | 4.45325i | − | 0.151328i | ||||||
\(867\) | 4.00000i | 0.135847i | ||||||||
\(868\) | − | 19.2523i | − | 0.653465i | ||||||
\(869\) | − | 15.8745i | − | 0.538506i | ||||||
\(870\) | −0.956439 | + | 4.58258i | −0.0324263 | + | 0.155364i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 22.7477i | − | 0.770335i | ||||||
\(873\) | −22.8027 | −0.771755 | ||||||||
\(874\) | 3.62614 | 0.122656 | ||||||||
\(875\) | −15.7913 | − | 11.2087i | −0.533843 | − | 0.378924i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.93725 | −0.268022 | −0.134011 | − | 0.990980i | \(-0.542786\pi\) | ||||
−0.134011 | + | 0.990980i | \(0.542786\pi\) | |||||||
\(878\) | 6.62225 | 0.223490 | ||||||||
\(879\) | 18.1389i | 0.611809i | ||||||||
\(880\) | 3.37386 | − | 16.1652i | 0.113733 | − | 0.544927i | ||||
\(881\) | 36.4955 | 1.22956 | 0.614782 | − | 0.788697i | \(-0.289244\pi\) | ||||
0.614782 | + | 0.788697i | \(0.289244\pi\) | |||||||
\(882\) | −3.65480 | −0.123064 | ||||||||
\(883\) | − | 36.2432i | − | 1.21968i | −0.792524 | − | 0.609840i | \(-0.791234\pi\) | ||
0.792524 | − | 0.609840i | \(-0.208766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.5390 | + | 6.37386i | 1.02656 | + | 0.214255i | ||||
\(886\) | − | 9.09720i | − | 0.305627i | ||||||
\(887\) | 54.4955i | 1.82978i | 0.403705 | + | 0.914889i | \(0.367722\pi\) | ||||
−0.403705 | + | 0.914889i | \(0.632278\pi\) | |||||||
\(888\) | 13.7477i | 0.461344i | ||||||||
\(889\) | − | 30.7400i | − | 1.03099i | ||||||
\(890\) | −1.99820 | + | 9.57395i | −0.0669798 | + | 0.320920i | ||||
\(891\) | − | 2.64575i | − | 0.0886360i | ||||||
\(892\) | 15.5130 | 0.519414 | ||||||||
\(893\) | − | 3.16515i | − | 0.105918i | ||||||
\(894\) | 7.62614 | 0.255056 | ||||||||
\(895\) | −39.7617 | − | 8.29875i | −1.32909 | − | 0.277397i | ||||
\(896\) | 19.1216 | 0.638808 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 5.03447i | − | 0.168002i | ||||||
\(899\) | 28.4358i | 0.948387i | ||||||||
\(900\) | −16.4174 | − | 7.16515i | −0.547247 | − | 0.238838i | ||||
\(901\) | −34.7477 | −1.15761 | ||||||||
\(902\) | 3.19795 | 0.106480 | ||||||||
\(903\) | 18.3296 | 0.609970 | ||||||||
\(904\) | − | 12.8474i | − | 0.427297i | ||||||
\(905\) | 19.1479 | + | 3.99640i | 0.636498 | + | 0.132845i | ||||
\(906\) | 4.41742 | 0.146759 | ||||||||
\(907\) | − | 6.25227i | − | 0.207603i | −0.994598 | − | 0.103802i | \(-0.966899\pi\) | ||
0.994598 | − | 0.103802i | \(-0.0331007\pi\) | |||||||
\(908\) | −1.46590 | −0.0486476 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.91288 | −0.262165 | −0.131083 | − | 0.991371i | \(-0.541845\pi\) | ||||
−0.131083 | + | 0.991371i | \(0.541845\pi\) | |||||||
\(912\) | 4.83465 | 0.160091 | ||||||||
\(913\) | − | 15.9129i | − | 0.526639i | ||||||
\(914\) | 0.791288 | 0.0261735 | ||||||||
\(915\) | −0.647551 | + | 3.10260i | −0.0214074 | + | 0.102569i | ||||
\(916\) | 47.0514i | 1.55462i | ||||||||
\(917\) | 13.1334 | 0.433703 | ||||||||
\(918\) | −10.4678 | −0.345487 | ||||||||
\(919\) | −54.1652 | −1.78674 | −0.893372 | − | 0.449318i | \(-0.851667\pi\) | ||||
−0.893372 | + | 0.449318i | \(0.851667\pi\) | |||||||
\(920\) | −3.62614 | + | 17.3739i | −0.119550 | + | 0.572799i | ||||
\(921\) | 24.2487i | 0.799022i | ||||||||
\(922\) | − | 16.3739i | − | 0.539244i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −8.20871 | −0.270047 | ||||||||
\(925\) | 36.3731 | + | 15.8745i | 1.19594 | + | 0.521951i | ||||
\(926\) | −18.0000 | −0.591517 | ||||||||
\(927\) | − | 6.33030i | − | 0.207914i | ||||||
\(928\) | −21.7182 | −0.712935 | ||||||||
\(929\) | − | 26.3622i | − | 0.864915i | −0.901654 | − | 0.432457i | \(-0.857647\pi\) | ||
0.901654 | − | 0.432457i | \(-0.142353\pi\) | |||||||
\(930\) | −6.20520 | − | 1.29510i | −0.203477 | − | 0.0424680i | ||||
\(931\) | − | 6.92820i | − | 0.227063i | ||||||
\(932\) | 5.07803i | 0.166336i | ||||||||
\(933\) | − | 7.58258i | − | 0.248242i | ||||||
\(934\) | − | 11.1153i | − | 0.363704i | ||||||
\(935\) | −26.5390 | − | 5.53901i | −0.867919 | − | 0.181145i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.4955i | 1.02891i | 0.857517 | + | 0.514456i | \(0.172006\pi\) | ||||
−0.857517 | + | 0.514456i | \(0.827994\pi\) | |||||||
\(938\) | 0.798450 | 0.0260703 | ||||||||
\(939\) | 3.25227 | 0.106134 | ||||||||
\(940\) | 7.16515 | + | 1.49545i | 0.233701 | + | 0.0487763i | ||||
\(941\) | 26.4575i | 0.862490i | 0.902235 | + | 0.431245i | \(0.141926\pi\) | ||||
−0.902235 | + | 0.431245i | \(0.858074\pi\) | |||||||
\(942\) | 4.18710 | 0.136423 | ||||||||
\(943\) | 12.1244 | 0.394823 | ||||||||
\(944\) | 38.9434i | 1.26750i | ||||||||
\(945\) | −3.95644 | + | 18.9564i | −0.128703 | + | 0.616653i | ||||
\(946\) | −12.7913 | −0.415881 | ||||||||
\(947\) | 14.3332 | 0.465765 | 0.232883 | − | 0.972505i | \(-0.425184\pi\) | ||||
0.232883 | + | 0.972505i | \(0.425184\pi\) | |||||||
\(948\) | 10.7477i | 0.349070i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.58258 | + | 3.62614i | −0.0513455 | + | 0.117647i | ||||
\(951\) | − | 0.190700i | − | 0.00618388i | ||||||
\(952\) | − | 13.7477i | − | 0.445566i | ||||||
\(953\) | 8.07803i | 0.261673i | 0.991404 | + | 0.130837i | \(0.0417663\pi\) | ||||
−0.991404 | + | 0.130837i | \(0.958234\pi\) | |||||||
\(954\) | − | 6.92820i | − | 0.224309i | ||||||
\(955\) | −36.2976 | − | 7.57575i | −1.17456 | − | 0.245146i | ||||
\(956\) | 0.341599i | 0.0110481i | ||||||||
\(957\) | 12.1244 | 0.391925 | ||||||||
\(958\) | 2.13068i | 0.0688392i | ||||||||
\(959\) | −18.1652 | −0.586583 | ||||||||
\(960\) | −1.56125 | + | 7.48040i | −0.0503892 | + | 0.241429i | ||||
\(961\) | −7.50455 | −0.242082 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 21.1652i | − | 0.682037i | ||||||
\(964\) | − | 3.10260i | − | 0.0999281i | ||||||
\(965\) | 32.5390 | + | 6.79129i | 1.04747 | + | 0.218619i | ||||
\(966\) | 3.62614 | 0.116669 | ||||||||
\(967\) | 37.3821 | 1.20213 | 0.601064 | − | 0.799201i | \(-0.294744\pi\) | ||||
0.601064 | + | 0.799201i | \(0.294744\pi\) | |||||||
\(968\) | −6.92820 | −0.222681 | ||||||||
\(969\) | − | 7.93725i | − | 0.254981i | ||||||
\(970\) | −11.4014 | − | 2.37960i | −0.366075 | − | 0.0764044i | ||||
\(971\) | −18.4955 | −0.593547 | −0.296774 | − | 0.954948i | \(-0.595911\pi\) | ||||
−0.296774 | + | 0.954948i | \(0.595911\pi\) | |||||||
\(972\) | 28.6606i | 0.919289i | ||||||||
\(973\) | −37.6682 | −1.20759 | ||||||||
\(974\) | 4.87841 | 0.156314 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.95644 | −0.126643 | ||||||||
\(977\) | −35.3085 | −1.12962 | −0.564809 | − | 0.825222i | \(-0.691050\pi\) | ||||
−0.564809 | + | 0.825222i | \(0.691050\pi\) | |||||||
\(978\) | − | 9.62614i | − | 0.307810i | ||||||
\(979\) | 25.3303 | 0.809560 | ||||||||
\(980\) | 15.6838 | + | 3.27340i | 0.501001 | + | 0.104565i | ||||
\(981\) | 26.2668i | 0.838635i | ||||||||
\(982\) | 8.87086 | 0.283080 | ||||||||
\(983\) | −55.0840 | −1.75691 | −0.878454 | − | 0.477827i | \(-0.841424\pi\) | ||||
−0.878454 | + | 0.477827i | \(0.841424\pi\) | |||||||
\(984\) | −4.58258 | −0.146087 | ||||||||
\(985\) | −32.1216 | − | 6.70417i | −1.02348 | − | 0.213613i | ||||
\(986\) | 9.59386i | 0.305531i | ||||||||
\(987\) | − | 3.16515i | − | 0.100748i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.4955 | −1.54207 | ||||||||
\(990\) | 1.10440 | − | 5.29150i | 0.0351002 | − | 0.168175i | ||||
\(991\) | −13.0000 | −0.412959 | −0.206479 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206479 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(992\) | − | 29.4083i | − | 0.933715i | ||||||
\(993\) | 4.47315 | 0.141951 | ||||||||
\(994\) | 5.55765i | 0.176278i | ||||||||
\(995\) | −23.1642 | − | 4.83465i | −0.734355 | − | 0.153269i | ||||
\(996\) | 10.7737i | 0.341378i | ||||||||
\(997\) | 0.165151i | 0.00523040i | 0.999997 | + | 0.00261520i | \(0.000832444\pi\) | ||||
−0.999997 | + | 0.00261520i | \(0.999168\pi\) | |||||||
\(998\) | − | 0.330303i | − | 0.0104556i | ||||||
\(999\) | − | 39.6863i | − | 1.25562i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))