Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(163,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.163");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.z (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 163.5 | ||
Root | \(0.235136 - 1.39453i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.163 |
Dual form | 720.2.z.g.667.5 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.430311 | − | 1.34716i | −0.304276 | − | 0.952584i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.62967 | + | 1.15939i | −0.814833 | + | 0.579696i | ||||
\(5\) | 0.177336 | − | 2.22902i | 0.0793073 | − | 0.996850i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.115101 | + | 0.115101i | −0.0435040 | + | 0.0435040i | −0.728524 | − | 0.685020i | \(-0.759793\pi\) |
0.685020 | + | 0.728524i | \(0.259793\pi\) | |||||||
\(8\) | 2.26315 | + | 1.69652i | 0.800143 | + | 0.599809i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.07916 | + | 0.720273i | −0.973715 | + | 0.227770i | ||||
\(11\) | −2.95966 | − | 2.95966i | −0.892372 | − | 0.892372i | 0.102374 | − | 0.994746i | \(-0.467356\pi\) |
−0.994746 | + | 0.102374i | \(0.967356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.55822i | 0.432172i | 0.976374 | + | 0.216086i | \(0.0693292\pi\) | ||||
−0.976374 | + | 0.216086i | \(0.930671\pi\) | |||||||
\(14\) | 0.204588 | + | 0.105530i | 0.0546784 | + | 0.0282040i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.31162 | − | 3.77884i | 0.327905 | − | 0.944711i | ||||
\(17\) | −0.299668 | + | 0.299668i | −0.0726801 | + | 0.0726801i | −0.742512 | − | 0.669832i | \(-0.766366\pi\) |
0.669832 | + | 0.742512i | \(0.266366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.26261 | − | 2.26261i | −0.519079 | − | 0.519079i | 0.398214 | − | 0.917293i | \(-0.369630\pi\) |
−0.917293 | + | 0.398214i | \(0.869630\pi\) | |||||||
\(20\) | 2.29532 | + | 3.83817i | 0.513248 | + | 0.858240i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.71356 | + | 5.26071i | −0.578532 | + | 1.12159i | ||||
\(23\) | −4.14573 | − | 4.14573i | −0.864444 | − | 0.864444i | 0.127406 | − | 0.991851i | \(-0.459335\pi\) |
−0.991851 | + | 0.127406i | \(0.959335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.93710 | − | 0.790575i | −0.987421 | − | 0.158115i | ||||
\(26\) | 2.09917 | − | 0.670518i | 0.411680 | − | 0.131499i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0541288 | − | 0.321023i | 0.0102294 | − | 0.0606676i | ||||
\(29\) | −0.289656 | + | 0.289656i | −0.0537878 | + | 0.0537878i | −0.733489 | − | 0.679701i | \(-0.762109\pi\) |
0.679701 | + | 0.733489i | \(0.262109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.18508i | 0.751663i | 0.926688 | + | 0.375832i | \(0.122643\pi\) | ||||
−0.926688 | + | 0.375832i | \(0.877357\pi\) | |||||||
\(32\) | −5.65510 | − | 0.140879i | −0.999690 | − | 0.0249041i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.532650 | + | 0.274749i | 0.0913487 | + | 0.0471191i | ||||
\(35\) | 0.236151 | + | 0.276974i | 0.0399168 | + | 0.0468172i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.63643i | − | 0.269027i | −0.990912 | − | 0.134514i | \(-0.957053\pi\) | ||
0.990912 | − | 0.134514i | \(-0.0429472\pi\) | |||||||
\(38\) | −2.07447 | + | 4.02172i | −0.336523 | + | 0.652410i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.18292 | − | 4.74376i | 0.661377 | − | 0.750054i | ||||
\(41\) | 7.61648i | 1.18949i | 0.803913 | + | 0.594747i | \(0.202748\pi\) | ||||
−0.803913 | + | 0.594747i | \(0.797252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.72651i | − | 1.02578i | −0.858453 | − | 0.512892i | \(-0.828574\pi\) | ||
0.858453 | − | 0.512892i | \(-0.171426\pi\) | |||||||
\(44\) | 8.25467 | + | 1.39185i | 1.24444 | + | 0.209829i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.80100 | + | 7.36890i | −0.560427 | + | 1.08649i | ||||
\(47\) | −4.38366 | − | 4.38366i | −0.639423 | − | 0.639423i | 0.310990 | − | 0.950413i | \(-0.399339\pi\) |
−0.950413 | + | 0.310990i | \(0.899339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.97350i | 0.996215i | ||||||||
\(50\) | 1.05946 | + | 6.99125i | 0.149830 | + | 0.988712i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.80659 | − | 2.53938i | −0.250529 | − | 0.352148i | ||||
\(53\) | −11.4324 | −1.57036 | −0.785182 | − | 0.619265i | \(-0.787431\pi\) | ||||
−0.785182 | + | 0.619265i | \(0.787431\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.12202 | + | 6.07231i | −0.960333 | + | 0.818790i | ||||
\(56\) | −0.455760 | + | 0.0652196i | −0.0609035 | + | 0.00871533i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.514854 | + | 0.265570i | 0.0676037 | + | 0.0348711i | ||||
\(59\) | −1.63497 | + | 1.63497i | −0.212855 | + | 0.212855i | −0.805479 | − | 0.592624i | \(-0.798092\pi\) |
0.592624 | + | 0.805479i | \(0.298092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.23034 | − | 1.23034i | −0.157528 | − | 0.157528i | 0.623942 | − | 0.781471i | \(-0.285530\pi\) |
−0.781471 | + | 0.623942i | \(0.785530\pi\) | |||||||
\(62\) | 5.63796 | − | 1.80089i | 0.716022 | − | 0.228713i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.24366 | + | 7.67893i | 0.280458 | + | 0.959866i | ||||
\(65\) | 3.47331 | + | 0.276329i | 0.430811 | + | 0.0342744i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.49337i | − | 0.304614i | −0.988333 | − | 0.152307i | \(-0.951330\pi\) | ||
0.988333 | − | 0.152307i | \(-0.0486702\pi\) | |||||||
\(68\) | 0.140926 | − | 0.835791i | 0.0170897 | − | 0.101354i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.271509 | − | 0.437317i | 0.0324516 | − | 0.0522694i | ||||
\(71\) | −8.00096 | −0.949540 | −0.474770 | − | 0.880110i | \(-0.657469\pi\) | ||||
−0.474770 | + | 0.880110i | \(0.657469\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.12102 | + | 1.12102i | −0.131205 | + | 0.131205i | −0.769660 | − | 0.638454i | \(-0.779574\pi\) |
0.638454 | + | 0.769660i | \(0.279574\pi\) | |||||||
\(74\) | −2.20453 | + | 0.704173i | −0.256271 | + | 0.0818584i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.31056 | + | 1.06405i | 0.723871 | + | 0.122054i | ||||
\(77\) | 0.681319 | 0.0776435 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.62218 | 0.407527 | 0.203763 | − | 0.979020i | \(-0.434683\pi\) | ||||
0.203763 | + | 0.979020i | \(0.434683\pi\) | |||||||
\(80\) | −8.19054 | − | 3.59376i | −0.915730 | − | 0.401794i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.2606 | − | 3.27745i | 1.13309 | − | 0.361934i | ||||
\(83\) | −1.62629 | −0.178509 | −0.0892545 | − | 0.996009i | \(-0.528448\pi\) | ||||
−0.0892545 | + | 0.996009i | \(0.528448\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.614825 | + | 0.721109i | 0.0666871 | + | 0.0782152i | ||||
\(86\) | −9.06167 | + | 2.89449i | −0.977145 | + | 0.312121i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.67703 | − | 11.7193i | −0.178772 | − | 1.24928i | ||||
\(89\) | 15.7149 | 1.66577 | 0.832887 | − | 0.553443i | \(-0.186686\pi\) | ||||
0.832887 | + | 0.553443i | \(0.186686\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.179352 | − | 0.179352i | −0.0188012 | − | 0.0188012i | ||||
\(92\) | 11.5627 | + | 1.94962i | 1.20549 | + | 0.203262i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.01915 | + | 7.79182i | −0.414543 | + | 0.803665i | ||||
\(95\) | −5.44467 | + | 4.64218i | −0.558611 | + | 0.476277i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.69217 | − | 9.69217i | 0.984091 | − | 0.984091i | −0.0157848 | − | 0.999875i | \(-0.505025\pi\) |
0.999875 | + | 0.0157848i | \(0.00502467\pi\) | |||||||
\(98\) | 9.39441 | − | 3.00077i | 0.948978 | − | 0.303124i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.96241 | − | 4.43567i | 0.896241 | − | 0.443567i | ||||
\(101\) | 12.8067 | − | 12.8067i | 1.27432 | − | 1.27432i | 0.330516 | − | 0.943800i | \(-0.392777\pi\) |
0.943800 | − | 0.330516i | \(-0.107223\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.33738 | − | 4.33738i | −0.427375 | − | 0.427375i | 0.460358 | − | 0.887733i | \(-0.347721\pi\) |
−0.887733 | + | 0.460358i | \(0.847721\pi\) | |||||||
\(104\) | −2.64354 | + | 3.52648i | −0.259221 | + | 0.345800i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.91950 | + | 15.4013i | 0.477824 | + | 1.49590i | ||||
\(107\) | 11.9807 | 1.15822 | 0.579108 | − | 0.815251i | \(-0.303401\pi\) | ||||
0.579108 | + | 0.815251i | \(0.303401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.01503 | − | 4.01503i | 0.384570 | − | 0.384570i | −0.488175 | − | 0.872746i | \(-0.662337\pi\) |
0.872746 | + | 0.488175i | \(0.162337\pi\) | |||||||
\(110\) | 11.2450 | + | 6.98150i | 1.07217 | + | 0.665660i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.283980 | + | 0.585916i | 0.0268336 | + | 0.0553639i | ||||
\(113\) | −6.47754 | − | 6.47754i | −0.609356 | − | 0.609356i | 0.333422 | − | 0.942778i | \(-0.391797\pi\) |
−0.942778 | + | 0.333422i | \(0.891797\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.97612 | + | 8.50575i | −0.930278 | + | 0.793165i | ||||
\(116\) | 0.136217 | − | 0.807867i | 0.0126475 | − | 0.0750086i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.90611 | + | 1.49902i | 0.267529 | + | 0.137996i | ||||
\(119\) | − | 0.0689840i | − | 0.00632375i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.51921i | 0.592655i | ||||||||
\(122\) | −1.12803 | + | 2.18688i | −0.102127 | + | 0.197991i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.85215 | − | 6.82028i | −0.435736 | − | 0.612480i | ||||
\(125\) | −2.63774 | + | 10.8647i | −0.235927 | + | 0.971771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2756 | − | 12.2756i | −1.08928 | − | 1.08928i | −0.995603 | − | 0.0936781i | \(-0.970138\pi\) |
−0.0936781 | − | 0.995603i | \(-0.529862\pi\) | |||||||
\(128\) | 9.37925 | − | 6.32690i | 0.829017 | − | 0.559224i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.12234 | − | 4.79800i | −0.0984360 | − | 0.420813i | ||||
\(131\) | −7.99562 | + | 7.99562i | −0.698581 | + | 0.698581i | −0.964104 | − | 0.265524i | \(-0.914455\pi\) |
0.265524 | + | 0.964104i | \(0.414455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.520857 | 0.0451641 | ||||||||
\(134\) | −3.35896 | + | 1.07292i | −0.290170 | + | 0.0926865i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.18658 | + | 0.169801i | −0.101749 | + | 0.0145603i | ||||
\(137\) | 3.08551 | + | 3.08551i | 0.263613 | + | 0.263613i | 0.826520 | − | 0.562907i | \(-0.190317\pi\) |
−0.562907 | + | 0.826520i | \(0.690317\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2206 | − | 12.2206i | 1.03654 | − | 1.03654i | 0.0372284 | − | 0.999307i | \(-0.488147\pi\) |
0.999307 | − | 0.0372284i | \(-0.0118529\pi\) | |||||||
\(140\) | −0.705969 | − | 0.177583i | −0.0596653 | − | 0.0150085i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.44290 | + | 10.7786i | 0.288922 | + | 0.904516i | ||||
\(143\) | 4.61180 | − | 4.61180i | 0.385658 | − | 0.385658i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.594284 | + | 0.697017i | 0.0493526 | + | 0.0578841i | ||||
\(146\) | 1.99258 | + | 1.02780i | 0.164907 | + | 0.0850616i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.89726 | + | 2.66683i | 0.155954 | + | 0.219212i | ||||
\(149\) | −2.59172 | − | 2.59172i | −0.212322 | − | 0.212322i | 0.592931 | − | 0.805253i | \(-0.297971\pi\) |
−0.805253 | + | 0.592931i | \(0.797971\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9594 | −1.38014 | −0.690068 | − | 0.723745i | \(-0.742419\pi\) | ||||
−0.690068 | + | 0.723745i | \(0.742419\pi\) | |||||||
\(152\) | −1.28207 | − | 8.95919i | −0.103989 | − | 0.726686i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.293179 | − | 0.917844i | −0.0236250 | − | 0.0739620i | ||||
\(155\) | 9.32865 | + | 0.742168i | 0.749296 | + | 0.0596124i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.55235 | 0.682552 | 0.341276 | − | 0.939963i | \(-0.389141\pi\) | ||||
0.341276 | + | 0.939963i | \(0.389141\pi\) | |||||||
\(158\) | −1.55866 | − | 4.87964i | −0.124000 | − | 0.388203i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.31688 | + | 12.5804i | −0.104108 | + | 0.994566i | ||||
\(161\) | 0.954354 | 0.0752136 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.57797 | −0.280248 | −0.140124 | − | 0.990134i | \(-0.544750\pi\) | ||||
−0.140124 | + | 0.990134i | \(0.544750\pi\) | |||||||
\(164\) | −8.83049 | − | 12.4123i | −0.689545 | − | 0.969238i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.699812 | + | 2.19087i | 0.0543159 | + | 0.170045i | ||||
\(167\) | −0.482874 | + | 0.482874i | −0.0373659 | + | 0.0373659i | −0.725543 | − | 0.688177i | \(-0.758411\pi\) |
0.688177 | + | 0.725543i | \(0.258411\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5720 | 0.813227 | ||||||||
\(170\) | 0.706881 | − | 1.13857i | 0.0542153 | − | 0.0873241i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.79867 | + | 10.9620i | 0.594643 | + | 0.835842i | ||||
\(173\) | − | 11.8189i | − | 0.898576i | −0.893387 | − | 0.449288i | \(-0.851678\pi\) | ||
0.893387 | − | 0.449288i | \(-0.148322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.659260 | − | 0.477269i | 0.0498354 | − | 0.0360781i | ||||
\(176\) | −15.0661 | + | 7.30216i | −1.13565 | + | 0.550421i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.76228 | − | 21.1704i | −0.506855 | − | 1.58679i | ||||
\(179\) | 4.71524 | + | 4.71524i | 0.352433 | + | 0.352433i | 0.861014 | − | 0.508581i | \(-0.169830\pi\) |
−0.508581 | + | 0.861014i | \(0.669830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1843 | − | 13.1843i | 0.979983 | − | 0.979983i | −0.0198205 | − | 0.999804i | \(-0.506309\pi\) |
0.999804 | + | 0.0198205i | \(0.00630948\pi\) | |||||||
\(182\) | −0.164439 | + | 0.318793i | −0.0121890 | + | 0.0236305i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.34910 | − | 16.4157i | −0.173178 | − | 1.21018i | ||||
\(185\) | −3.64764 | − | 0.290199i | −0.268180 | − | 0.0213358i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.77383 | 0.129715 | ||||||||
\(188\) | 12.2263 | + | 2.06152i | 0.891694 | + | 0.150352i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.59664 | + | 5.33724i | 0.623666 | + | 0.387204i | ||||
\(191\) | − | 13.9872i | − | 1.01208i | −0.862510 | − | 0.506040i | \(-0.831109\pi\) | ||
0.862510 | − | 0.506040i | \(-0.168891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.88875 | + | 3.88875i | 0.279919 | + | 0.279919i | 0.833076 | − | 0.553158i | \(-0.186577\pi\) |
−0.553158 | + | 0.833076i | \(0.686577\pi\) | |||||||
\(194\) | −17.2275 | − | 8.88623i | −1.23686 | − | 0.637994i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.08503 | − | 11.3645i | −0.577502 | − | 0.811748i | ||||
\(197\) | − | 22.3277i | − | 1.59078i | −0.606097 | − | 0.795391i | \(-0.707266\pi\) | ||
0.606097 | − | 0.795391i | \(-0.292734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.83847i | 0.697431i | 0.937229 | + | 0.348715i | \(0.113382\pi\) | ||||
−0.937229 | + | 0.348715i | \(0.886618\pi\) | |||||||
\(200\) | −9.83217 | − | 10.1651i | −0.695239 | − | 0.718779i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −22.7635 | − | 11.7418i | −1.60164 | − | 0.826150i | ||||
\(203\) | − | 0.0666793i | − | 0.00467997i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.9773 | + | 1.35068i | 1.18575 | + | 0.0943355i | ||||
\(206\) | −3.97671 | + | 7.70955i | −0.277071 | + | 0.537150i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.88827 | + | 2.04379i | 0.408278 | + | 0.141711i | ||||
\(209\) | 13.3931i | 0.926423i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0531 | − | 11.0531i | 0.760925 | − | 0.760925i | −0.215565 | − | 0.976490i | \(-0.569159\pi\) |
0.976490 | + | 0.215565i | \(0.0691592\pi\) | |||||||
\(212\) | 18.6310 | − | 13.2547i | 1.27958 | − | 0.910334i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.15541 | − | 16.1398i | −0.352417 | − | 1.10330i | ||||
\(215\) | −14.9936 | − | 1.19286i | −1.02255 | − | 0.0813521i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.481706 | − | 0.481706i | −0.0327004 | − | 0.0327004i | ||||
\(218\) | −7.13659 | − | 3.68117i | −0.483351 | − | 0.249320i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.56632 | − | 18.1530i | 0.307861 | − | 1.22388i | ||||
\(221\) | −0.466948 | − | 0.466948i | −0.0314103 | − | 0.0314103i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.93975 | − | 5.93975i | 0.397755 | − | 0.397755i | −0.479686 | − | 0.877440i | \(-0.659249\pi\) |
0.877440 | + | 0.479686i | \(0.159249\pi\) | |||||||
\(224\) | 0.667122 | − | 0.634691i | 0.0445740 | − | 0.0424071i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.93891 | + | 11.5136i | −0.395051 | + | 0.765875i | ||||
\(227\) | − | 23.2105i | − | 1.54054i | −0.637720 | − | 0.770269i | \(-0.720122\pi\) | ||
0.637720 | − | 0.770269i | \(-0.279878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.59944 | + | 5.59944i | 0.370021 | + | 0.370021i | 0.867485 | − | 0.497464i | \(-0.165735\pi\) |
−0.497464 | + | 0.867485i | \(0.665735\pi\) | |||||||
\(230\) | 15.7514 | + | 9.77929i | 1.03862 | + | 0.644828i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.14694 | + | 0.164128i | −0.0753003 | + | 0.0107755i | ||||
\(233\) | −3.01998 | + | 3.01998i | −0.197845 | + | 0.197845i | −0.799076 | − | 0.601230i | \(-0.794677\pi\) |
0.601230 | + | 0.799076i | \(0.294677\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.5487 | + | 8.99391i | −0.688120 | + | 0.586698i | ||||
\(236\) | 0.768884 | − | 4.56004i | 0.0500501 | − | 0.296833i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0929323 | + | 0.0296846i | −0.00602391 | + | 0.00192416i | ||||
\(239\) | 0.00138865 | 8.98241e−5 | 4.49120e−5 | − | 1.00000i | \(-0.499986\pi\) | ||||
4.49120e−5 | 1.00000i | \(0.499986\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8578 | −0.828245 | −0.414123 | − | 0.910221i | \(-0.635912\pi\) | ||||
−0.414123 | + | 0.910221i | \(0.635912\pi\) | |||||||
\(242\) | 8.78240 | − | 2.80529i | 0.564554 | − | 0.180331i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.43148 | + | 0.578593i | 0.219678 | + | 0.0370407i | ||||
\(245\) | 15.5441 | + | 1.23666i | 0.993077 | + | 0.0790071i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.52565 | − | 3.52565i | 0.224332 | − | 0.224332i | ||||
\(248\) | −7.10006 | + | 9.47146i | −0.450854 | + | 0.601438i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.7715 | − | 1.12176i | 0.997480 | − | 0.0709463i | ||||
\(251\) | 9.14111 | + | 9.14111i | 0.576982 | + | 0.576982i | 0.934071 | − | 0.357089i | \(-0.116231\pi\) |
−0.357089 | + | 0.934071i | \(0.616231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.5399i | 1.54281i | ||||||||
\(254\) | −11.2548 | + | 21.8194i | −0.706190 | + | 1.36907i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.5593 | − | 9.91280i | −0.784957 | − | 0.619550i | ||||
\(257\) | −21.2733 | + | 21.2733i | −1.32699 | + | 1.32699i | −0.419013 | + | 0.907980i | \(0.637624\pi\) |
−0.907980 | + | 0.419013i | \(0.862376\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.188354 | + | 0.188354i | 0.0117038 | + | 0.0117038i | ||||
\(260\) | −5.98071 | + | 3.57660i | −0.370908 | + | 0.221812i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.2120 | + | 7.33076i | 0.878018 | + | 0.452896i | ||||
\(263\) | 16.7214 | + | 16.7214i | 1.03108 | + | 1.03108i | 0.999501 | + | 0.0315818i | \(0.0100545\pi\) |
0.0315818 | + | 0.999501i | \(0.489946\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.02739 | + | 25.4832i | −0.124541 | + | 1.56542i | ||||
\(266\) | −0.224131 | − | 0.701677i | −0.0137423 | − | 0.0430226i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.89079 | + | 4.06336i | 0.176583 | + | 0.248209i | ||||
\(269\) | −15.9096 | + | 15.9096i | −0.970026 | + | 0.970026i | −0.999564 | − | 0.0295378i | \(-0.990596\pi\) |
0.0295378 | + | 0.999564i | \(0.490596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.3601i | − | 0.750824i | −0.926858 | − | 0.375412i | \(-0.877501\pi\) | ||
0.926858 | − | 0.375412i | \(-0.122499\pi\) | |||||||
\(272\) | 0.739348 | + | 1.52545i | 0.0448295 | + | 0.0924938i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.82894 | − | 5.48440i | 0.170902 | − | 0.331324i | ||||
\(275\) | 12.2723 | + | 16.9520i | 0.740049 | + | 1.02224i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.0270i | − | 1.26339i | −0.775217 | − | 0.631695i | \(-0.782359\pi\) | ||
0.775217 | − | 0.631695i | \(-0.217641\pi\) | |||||||
\(278\) | −21.7217 | − | 11.2044i | −1.30278 | − | 0.671994i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0645531 | + | 1.02747i | 0.00385779 | + | 0.0614029i | ||||
\(281\) | 10.6807i | 0.637158i | 0.947896 | + | 0.318579i | \(0.103206\pi\) | ||||
−0.947896 | + | 0.318579i | \(0.896794\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5946i | 0.748673i | 0.927293 | + | 0.374336i | \(0.122129\pi\) | ||||
−0.927293 | + | 0.374336i | \(0.877871\pi\) | |||||||
\(284\) | 13.0389 | − | 9.27626i | 0.773716 | − | 0.550445i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.19733 | − | 4.22832i | −0.484718 | − | 0.250026i | ||||
\(287\) | −0.876663 | − | 0.876663i | −0.0517478 | − | 0.0517478i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8204i | 0.989435i | ||||||||
\(290\) | 0.683265 | − | 1.10053i | 0.0401227 | − | 0.0646252i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.527185 | − | 3.12659i | 0.0308512 | − | 0.182970i | ||||
\(293\) | −3.43132 | −0.200460 | −0.100230 | − | 0.994964i | \(-0.531958\pi\) | ||||
−0.100230 | + | 0.994964i | \(0.531958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.35446 | + | 3.93434i | 0.195304 | + | 0.229066i | ||||
\(296\) | 2.77623 | − | 3.70348i | 0.161365 | − | 0.215260i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.37621 | + | 4.60670i | −0.137650 | + | 0.266859i | ||||
\(299\) | 6.45996 | − | 6.45996i | 0.373589 | − | 0.373589i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.774227 | + | 0.774227i | 0.0446257 | + | 0.0446257i | ||||
\(302\) | 7.29781 | + | 22.8470i | 0.419942 | + | 1.31470i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.5177 | + | 5.58238i | −0.660588 | + | 0.320171i | ||||
\(305\) | −2.96063 | + | 2.52427i | −0.169525 | + | 0.144539i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.8104i | 0.674053i | 0.941495 | + | 0.337027i | \(0.109421\pi\) | ||||
−0.941495 | + | 0.337027i | \(0.890579\pi\) | |||||||
\(308\) | −1.11032 | + | 0.789916i | −0.0632665 | + | 0.0450097i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.01440 | − | 12.8865i | −0.171207 | − | 0.731906i | ||||
\(311\) | −22.6262 | −1.28301 | −0.641506 | − | 0.767118i | \(-0.721690\pi\) | ||||
−0.641506 | + | 0.767118i | \(0.721690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.08945 | − | 7.08945i | 0.400719 | − | 0.400719i | −0.477767 | − | 0.878486i | \(-0.658554\pi\) |
0.878486 | + | 0.477767i | \(0.158554\pi\) | |||||||
\(314\) | −3.68017 | − | 11.5214i | −0.207684 | − | 0.650188i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.90294 | + | 4.19952i | −0.332066 | + | 0.236242i | ||||
\(317\) | 25.1265 | 1.41124 | 0.705621 | − | 0.708589i | \(-0.250668\pi\) | ||||
0.705621 | + | 0.708589i | \(0.250668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.71457 | 0.0959974 | ||||||||
\(320\) | 17.5144 | − | 3.63943i | 0.979085 | − | 0.203450i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.410669 | − | 1.28566i | −0.0228857 | − | 0.0716473i | ||||
\(323\) | 1.35606 | 0.0754535 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.23189 | − | 7.69309i | 0.0683329 | − | 0.426736i | ||||
\(326\) | 1.53964 | + | 4.82008i | 0.0852726 | + | 0.266960i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.9215 | + | 17.2372i | −0.713469 | + | 0.951765i | ||||
\(329\) | 1.00913 | 0.0556349 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.80829 | + | 5.80829i | 0.319253 | + | 0.319253i | 0.848480 | − | 0.529227i | \(-0.177518\pi\) |
−0.529227 | + | 0.848480i | \(0.677518\pi\) | |||||||
\(332\) | 2.65032 | − | 1.88551i | 0.145455 | − | 0.103481i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.858293 | + | 0.442721i | 0.0469637 | + | 0.0242246i | ||||
\(335\) | −5.55778 | − | 0.442166i | −0.303654 | − | 0.0241581i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.41679 | + | 7.41679i | −0.404019 | + | 0.404019i | −0.879647 | − | 0.475628i | \(-0.842221\pi\) |
0.475628 | + | 0.879647i | \(0.342221\pi\) | |||||||
\(338\) | −4.54923 | − | 14.2421i | −0.247445 | − | 0.774667i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.83801 | − | 0.462343i | −0.0996799 | − | 0.0250741i | ||||
\(341\) | 12.3864 | − | 12.3864i | 0.670763 | − | 0.670763i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.60836 | − | 1.60836i | −0.0868434 | − | 0.0868434i | ||||
\(344\) | 11.4116 | − | 15.2231i | 0.615274 | − | 0.820774i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.9220 | + | 5.08581i | −0.855970 | + | 0.273415i | ||||
\(347\) | 18.2493 | 0.979673 | 0.489837 | − | 0.871814i | \(-0.337056\pi\) | ||||
0.489837 | + | 0.871814i | \(0.337056\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.4413 | + | 19.4413i | −1.04067 | + | 1.04067i | −0.0415330 | + | 0.999137i | \(0.513224\pi\) |
−0.999137 | + | 0.0415330i | \(0.986776\pi\) | |||||||
\(350\) | −0.926643 | − | 0.682754i | −0.0495312 | − | 0.0364947i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.3202 | + | 17.1541i | 0.869871 | + | 0.914319i | ||||
\(353\) | 1.13598 | + | 1.13598i | 0.0604622 | + | 0.0604622i | 0.736691 | − | 0.676229i | \(-0.236387\pi\) |
−0.676229 | + | 0.736691i | \(0.736387\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.41886 | + | 17.8343i | −0.0753054 | + | 0.946549i | ||||
\(356\) | −25.6100 | + | 18.2197i | −1.35733 | + | 0.965643i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.32315 | − | 8.38118i | 0.228485 | − | 0.442959i | ||||
\(359\) | 28.4140i | 1.49963i | 0.661645 | + | 0.749817i | \(0.269859\pi\) | ||||
−0.661645 | + | 0.749817i | \(0.730141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 8.76116i | − | 0.461114i | ||||||
\(362\) | −23.4347 | − | 12.0880i | −1.23170 | − | 0.635331i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.500224 | + | 0.0843445i | 0.0262189 | + | 0.00442085i | ||||
\(365\) | 2.29998 | + | 2.69758i | 0.120387 | + | 0.141198i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.29692 | − | 2.29692i | −0.119898 | − | 0.119898i | 0.644612 | − | 0.764510i | \(-0.277019\pi\) |
−0.764510 | + | 0.644612i | \(0.777019\pi\) | |||||||
\(368\) | −21.1037 | + | 10.2285i | −1.10011 | + | 0.533195i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.17868 | + | 5.03882i | 0.0612764 | + | 0.261956i | ||||
\(371\) | 1.31588 | − | 1.31588i | 0.0683172 | − | 0.0683172i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0787 | −0.936081 | −0.468040 | − | 0.883707i | \(-0.655040\pi\) | ||||
−0.468040 | + | 0.883707i | \(0.655040\pi\) | |||||||
\(374\) | −0.763298 | − | 2.38963i | −0.0394692 | − | 0.123565i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.48392 | − | 17.3578i | −0.128098 | − | 0.895162i | ||||
\(377\) | −0.451348 | − | 0.451348i | −0.0232456 | − | 0.0232456i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.79031 | + | 2.79031i | −0.143328 | + | 0.143328i | −0.775130 | − | 0.631802i | \(-0.782316\pi\) |
0.631802 | + | 0.775130i | \(0.282316\pi\) | |||||||
\(380\) | 3.49088 | − | 13.8777i | 0.179078 | − | 0.711911i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.8430 | + | 6.01885i | −0.964090 | + | 0.307951i | ||||
\(383\) | 8.12206 | − | 8.12206i | 0.415018 | − | 0.415018i | −0.468464 | − | 0.883482i | \(-0.655193\pi\) |
0.883482 | + | 0.468464i | \(0.155193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.120823 | − | 1.51868i | 0.00615770 | − | 0.0773990i | ||||
\(386\) | 3.56539 | − | 6.91213i | 0.181474 | − | 0.351818i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.55796 | + | 27.0320i | −0.231396 | + | 1.37234i | ||||
\(389\) | 14.4341 | + | 14.4341i | 0.731839 | + | 0.731839i | 0.970984 | − | 0.239145i | \(-0.0768670\pi\) |
−0.239145 | + | 0.970984i | \(0.576867\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.48468 | 0.125656 | ||||||||
\(392\) | −11.8307 | + | 15.7821i | −0.597539 | + | 0.797114i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −30.0789 | + | 9.60785i | −1.51535 | + | 0.484036i | ||||
\(395\) | 0.642344 | − | 8.07392i | 0.0323198 | − | 0.406243i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.1624 | −1.76475 | −0.882374 | − | 0.470549i | \(-0.844056\pi\) | ||||
−0.882374 | + | 0.470549i | \(0.844056\pi\) | |||||||
\(398\) | 13.2540 | − | 4.23360i | 0.664362 | − | 0.212211i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.46305 | + | 17.6196i | −0.473153 | + | 0.880980i | ||||
\(401\) | 23.5164 | 1.17435 | 0.587176 | − | 0.809459i | \(-0.300240\pi\) | ||||
0.587176 | + | 0.809459i | \(0.300240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.52128 | −0.324848 | ||||||||
\(404\) | −6.02265 | + | 35.7187i | −0.299638 | + | 1.77707i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0898275 | + | 0.0286928i | −0.00445806 | + | 0.00142400i | ||||
\(407\) | −4.84328 | + | 4.84328i | −0.240072 | + | 0.240072i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2595 | 1.15011 | 0.575054 | − | 0.818115i | \(-0.304981\pi\) | ||||
0.575054 | + | 0.818115i | \(0.304981\pi\) | |||||||
\(410\) | −5.48594 | − | 23.4523i | −0.270931 | − | 1.15823i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.0972 | + | 2.03975i | 0.595986 | + | 0.100491i | ||||
\(413\) | − | 0.376374i | − | 0.0185201i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.288401 | + | 3.62505i | −0.0141571 | + | 0.177947i | ||||
\(416\) | 0.219520 | − | 8.81188i | 0.0107628 | − | 0.432038i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.0427 | − | 5.76322i | 0.882496 | − | 0.281888i | ||||
\(419\) | −6.63975 | − | 6.63975i | −0.324373 | − | 0.324373i | 0.526069 | − | 0.850442i | \(-0.323665\pi\) |
−0.850442 | + | 0.526069i | \(0.823665\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.28216 | − | 7.28216i | 0.354911 | − | 0.354911i | −0.507022 | − | 0.861933i | \(-0.669254\pi\) |
0.861933 | + | 0.507022i | \(0.169254\pi\) | |||||||
\(422\) | −19.6465 | − | 10.1340i | −0.956376 | − | 0.493314i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.8733 | − | 19.3953i | −1.25652 | − | 0.941919i | ||||
\(425\) | 1.71640 | − | 1.24258i | 0.0832576 | − | 0.0602740i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.283225 | 0.0137062 | ||||||||
\(428\) | −19.5245 | + | 13.8903i | −0.943751 | + | 0.671413i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.84493 | + | 20.7120i | 0.233643 | + | 0.998821i | ||||
\(431\) | − | 11.7250i | − | 0.564771i | −0.959301 | − | 0.282386i | \(-0.908874\pi\) | ||
0.959301 | − | 0.282386i | \(-0.0911258\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.8827 | − | 20.8827i | −1.00356 | − | 1.00356i | −0.999994 | − | 0.00356603i | \(-0.998865\pi\) |
−0.00356603 | − | 0.999994i | \(-0.501135\pi\) | |||||||
\(434\) | −0.441651 | + | 0.856218i | −0.0211999 | + | 0.0410998i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.88816 | + | 11.1982i | −0.0904265 | + | 0.536294i | ||||
\(437\) | 18.7604i | 0.897430i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.53661i | 0.359703i | 0.983694 | + | 0.179851i | \(0.0575617\pi\) | ||||
−0.983694 | + | 0.179851i | \(0.942438\pi\) | |||||||
\(440\) | −26.4199 | + | 1.65990i | −1.25952 | + | 0.0791325i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.428120 | + | 0.829985i | −0.0203636 | + | 0.0394784i | ||||
\(443\) | 25.7280i | 1.22237i | 0.791486 | + | 0.611187i | \(0.209308\pi\) | ||||
−0.791486 | + | 0.611187i | \(0.790692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.78682 | − | 35.0289i | 0.132108 | − | 1.66053i | ||||
\(446\) | −10.5577 | − | 5.44584i | −0.499922 | − | 0.257868i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.14210 | − | 0.625604i | −0.0539591 | − | 0.0295570i | ||||
\(449\) | 2.33824i | 0.110348i | 0.998477 | + | 0.0551741i | \(0.0175714\pi\) | ||||
−0.998477 | + | 0.0551741i | \(0.982429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5422 | − | 22.5422i | 1.06147 | − | 1.06147i | ||||
\(452\) | 18.0662 | + | 3.04621i | 0.849765 | + | 0.143282i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.2682 | + | 9.98774i | −1.46749 | + | 0.468748i | ||||
\(455\) | −0.431586 | + | 0.367975i | −0.0202331 | + | 0.0172509i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4561 | + | 10.4561i | 0.489115 | + | 0.489115i | 0.908027 | − | 0.418912i | \(-0.137588\pi\) |
−0.418912 | + | 0.908027i | \(0.637588\pi\) | |||||||
\(458\) | 5.13383 | − | 9.95282i | 0.239888 | − | 0.465065i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.39625 | − | 25.4278i | 0.298226 | − | 1.18558i | ||||
\(461\) | −15.6903 | − | 15.6903i | −0.730769 | − | 0.730769i | 0.240003 | − | 0.970772i | \(-0.422852\pi\) |
−0.970772 | + | 0.240003i | \(0.922852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.6332 | + | 19.6332i | −0.912434 | + | 0.912434i | −0.996463 | − | 0.0840297i | \(-0.973221\pi\) |
0.0840297 | + | 0.996463i | \(0.473221\pi\) | |||||||
\(464\) | 0.714647 | + | 1.47448i | 0.0331766 | + | 0.0684511i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.36791 | + | 2.76886i | 0.248664 | + | 0.128265i | ||||
\(467\) | − | 24.4862i | − | 1.13309i | −0.824032 | − | 0.566543i | \(-0.808281\pi\) | ||
0.824032 | − | 0.566543i | \(-0.191719\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.286989 | + | 0.286989i | 0.0132519 | + | 0.0132519i | ||||
\(470\) | 16.6554 | + | 10.3406i | 0.768257 | + | 0.476974i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.47395 | + | 0.926426i | −0.297987 | + | 0.0426422i | ||||
\(473\) | −19.9082 | + | 19.9082i | −0.915380 | + | 0.915380i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.38199 | + | 12.9595i | 0.430475 | + | 0.594624i | ||||
\(476\) | 0.0799795 | + | 0.112421i | 0.00366586 | + | 0.00515280i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.000597550 | − | 0.00187073i | −2.73313e−5 | − | 8.55650e-5i | ||||
\(479\) | −37.0609 | −1.69335 | −0.846677 | − | 0.532108i | \(-0.821400\pi\) | ||||
−0.846677 | + | 0.532108i | \(0.821400\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.54991 | 0.116266 | ||||||||
\(482\) | 5.53286 | + | 17.3215i | 0.252015 | + | 0.788973i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.55832 | − | 10.6241i | −0.343560 | − | 0.482915i | ||||
\(485\) | −19.8853 | − | 23.3229i | −0.902945 | − | 1.05904i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.1912 | − | 20.1912i | 0.914950 | − | 0.914950i | −0.0817061 | − | 0.996656i | \(-0.526037\pi\) |
0.996656 | + | 0.0817061i | \(0.0260369\pi\) | |||||||
\(488\) | −0.697145 | − | 4.87172i | −0.0315583 | − | 0.220532i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.02283 | − | 21.4725i | −0.226908 | − | 0.970029i | ||||
\(491\) | 7.45822 | + | 7.45822i | 0.336585 | + | 0.336585i | 0.855080 | − | 0.518496i | \(-0.173508\pi\) |
−0.518496 | + | 0.855080i | \(0.673508\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.173601i | − | 0.00781860i | ||||||
\(494\) | −6.26673 | − | 3.23248i | −0.281953 | − | 0.145436i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.8148 | + | 5.48923i | 0.710104 | + | 0.246474i | ||||
\(497\) | 0.920917 | − | 0.920917i | 0.0413088 | − | 0.0413088i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.17420 | + | 8.17420i | 0.365927 | + | 0.365927i | 0.865990 | − | 0.500062i | \(-0.166689\pi\) |
−0.500062 | + | 0.865990i | \(0.666689\pi\) | |||||||
\(500\) | −8.29785 | − | 20.7640i | −0.371091 | − | 0.928596i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.38100 | − | 16.2480i | 0.374062 | − | 0.725185i | ||||
\(503\) | 29.2327 | + | 29.2327i | 1.30342 | + | 1.30342i | 0.926072 | + | 0.377348i | \(0.123164\pi\) |
0.377348 | + | 0.926072i | \(0.376836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.2754 | − | 30.8176i | −1.16924 | − | 1.37136i | ||||
\(506\) | 33.0591 | − | 10.5598i | 1.46966 | − | 0.469440i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 34.2373 | + | 5.77287i | 1.51903 | + | 0.256130i | ||||
\(509\) | 20.0340 | − | 20.0340i | 0.887992 | − | 0.887992i | −0.106338 | − | 0.994330i | \(-0.533912\pi\) |
0.994330 | + | 0.106338i | \(0.0339125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.258061i | − | 0.0114159i | ||||||
\(512\) | −7.94969 | + | 21.1850i | −0.351330 | + | 0.936252i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 37.8126 | + | 19.5044i | 1.66784 | + | 0.860301i | ||||
\(515\) | −10.4373 | + | 8.89895i | −0.459922 | + | 0.392135i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.9483i | 1.14121i | ||||||||
\(518\) | 0.172692 | − | 0.334794i | 0.00758765 | − | 0.0147100i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.39181 | + | 6.51790i | 0.324152 | + | 0.285829i | ||||
\(521\) | − | 5.89264i | − | 0.258161i | −0.991634 | − | 0.129081i | \(-0.958797\pi\) | ||
0.991634 | − | 0.129081i | \(-0.0412026\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.6537i | − | 1.07803i | −0.842296 | − | 0.539015i | \(-0.818797\pi\) | ||
0.842296 | − | 0.539015i | \(-0.181203\pi\) | |||||||
\(524\) | 3.76012 | − | 22.3003i | 0.164262 | − | 0.974191i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.3309 | − | 29.7217i | 0.668460 | − | 1.29593i | ||||
\(527\) | −1.25413 | − | 1.25413i | −0.0546309 | − | 0.0546309i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3742i | 0.494528i | ||||||||
\(530\) | 35.2022 | − | 8.23447i | 1.52909 | − | 0.357683i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.848823 | + | 0.603878i | −0.0368012 | + | 0.0261814i | ||||
\(533\) | −11.8681 | −0.514066 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.12461 | − | 26.7052i | 0.0918549 | − | 1.15457i | ||||
\(536\) | 4.23004 | − | 5.64286i | 0.182710 | − | 0.243735i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 28.2788 | + | 14.5867i | 1.21919 | + | 0.628876i | ||||
\(539\) | 20.6392 | − | 20.6392i | 0.888994 | − | 0.888994i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.1762 | − | 27.1762i | −1.16840 | − | 1.16840i | −0.982585 | − | 0.185812i | \(-0.940508\pi\) |
−0.185812 | − | 0.982585i | \(-0.559492\pi\) | |||||||
\(542\) | −16.6510 | + | 5.31869i | −0.715223 | + | 0.228457i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.73687 | − | 1.65243i | 0.0744676 | − | 0.0708475i | ||||
\(545\) | −8.23759 | − | 9.66162i | −0.352860 | − | 0.413858i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.69225i | − | 0.157869i | −0.996880 | − | 0.0789347i | \(-0.974848\pi\) | ||
0.996880 | − | 0.0789347i | \(-0.0251519\pi\) | |||||||
\(548\) | −8.60567 | − | 1.45103i | −0.367616 | − | 0.0619850i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.5561 | − | 23.8274i | 0.748594 | − | 1.01600i | ||||
\(551\) | 1.31076 | 0.0558402 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.416915 | + | 0.416915i | −0.0177290 | + | 0.0177290i | ||||
\(554\) | −28.3267 | + | 9.04815i | −1.20349 | + | 0.384419i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.74700 | + | 34.0839i | −0.243727 | + | 1.44548i | ||||
\(557\) | −12.2117 | −0.517426 | −0.258713 | − | 0.965954i | \(-0.583298\pi\) | ||||
−0.258713 | + | 0.965954i | \(0.583298\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4814 | 0.443315 | ||||||||
\(560\) | 1.35638 | − | 0.529093i | 0.0573176 | − | 0.0223583i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.3886 | − | 4.59603i | 0.606947 | − | 0.193872i | ||||
\(563\) | 12.2211 | 0.515057 | 0.257528 | − | 0.966271i | \(-0.417092\pi\) | ||||
0.257528 | + | 0.966271i | \(0.417092\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.5873 | + | 13.2899i | −0.655763 | + | 0.559110i | ||||
\(566\) | 16.9669 | − | 5.41960i | 0.713174 | − | 0.227803i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.1074 | − | 13.5738i | −0.759768 | − | 0.569543i | ||||
\(569\) | 30.9592 | 1.29788 | 0.648938 | − | 0.760841i | \(-0.275213\pi\) | ||||
0.648938 | + | 0.760841i | \(0.275213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.1508 | + | 30.1508i | 1.26177 | + | 1.26177i | 0.950233 | + | 0.311539i | \(0.100844\pi\) |
0.311539 | + | 0.950233i | \(0.399156\pi\) | |||||||
\(572\) | −2.16881 | + | 12.8626i | −0.0906823 | + | 0.537812i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.803765 | + | 1.55824i | −0.0335485 | + | 0.0650397i | ||||
\(575\) | 17.1904 | + | 23.7454i | 0.716889 | + | 0.990252i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.98215 | − | 1.98215i | 0.0825181 | − | 0.0825181i | −0.664643 | − | 0.747161i | \(-0.731416\pi\) |
0.747161 | + | 0.664643i | \(0.231416\pi\) | |||||||
\(578\) | 22.6597 | − | 7.23800i | 0.942520 | − | 0.301061i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.77660 | − | 0.446896i | −0.0737693 | − | 0.0185564i | ||||
\(581\) | 0.187188 | − | 0.187188i | 0.00776586 | − | 0.00776586i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.8361 | + | 33.8361i | 1.40135 | + | 1.40135i | ||||
\(584\) | −4.43886 | + | 0.635204i | −0.183681 | + | 0.0262849i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.47653 | + | 4.62253i | 0.0609951 | + | 0.190955i | ||||
\(587\) | −26.9680 | −1.11309 | −0.556544 | − | 0.830818i | \(-0.687873\pi\) | ||||
−0.556544 | + | 0.830818i | \(0.687873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.46923 | − | 9.46923i | 0.390173 | − | 0.390173i | ||||
\(590\) | 3.85671 | − | 6.21197i | 0.158778 | − | 0.255743i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.18381 | − | 2.14637i | −0.254153 | − | 0.0882152i | ||||
\(593\) | −16.6701 | − | 16.6701i | −0.684560 | − | 0.684560i | 0.276464 | − | 0.961024i | \(-0.410837\pi\) |
−0.961024 | + | 0.276464i | \(0.910837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.153767 | − | 0.0122334i | −0.00630383 | − | 0.000501520i | ||||
\(596\) | 7.22846 | + | 1.21882i | 0.296089 | + | 0.0499247i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.4824 | − | 5.92279i | −0.469549 | − | 0.242201i | ||||
\(599\) | − | 28.8376i | − | 1.17827i | −0.808033 | − | 0.589137i | \(-0.799468\pi\) | ||
0.808033 | − | 0.589137i | \(-0.200532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.91377i | 0.0780642i | 0.999238 | + | 0.0390321i | \(0.0124275\pi\) | ||||
−0.999238 | + | 0.0390321i | \(0.987573\pi\) | |||||||
\(602\) | 0.709847 | − | 1.37616i | 0.0289312 | − | 0.0560882i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 27.6381 | − | 19.6626i | 1.12458 | − | 0.800059i | ||||
\(605\) | 14.5315 | + | 1.15609i | 0.590789 | + | 0.0470019i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.89049 | − | 7.89049i | −0.320265 | − | 0.320265i | 0.528604 | − | 0.848869i | \(-0.322716\pi\) |
−0.848869 | + | 0.528604i | \(0.822716\pi\) | |||||||
\(608\) | 12.4766 | + | 13.1141i | 0.505991 | + | 0.531845i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.67457 | + | 2.90222i | 0.189268 | + | 0.117507i | ||||
\(611\) | 6.83071 | − | 6.83071i | 0.276341 | − | 0.276341i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.1035 | −1.61976 | −0.809882 | − | 0.586592i | \(-0.800469\pi\) | ||||
−0.809882 | + | 0.586592i | \(0.800469\pi\) | |||||||
\(614\) | 15.9104 | − | 5.08213i | 0.642092 | − | 0.205098i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.54193 | + | 1.15587i | 0.0621259 | + | 0.0465713i | ||||
\(617\) | −14.5821 | − | 14.5821i | −0.587052 | − | 0.587052i | 0.349780 | − | 0.936832i | \(-0.386256\pi\) |
−0.936832 | + | 0.349780i | \(0.886256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.01752 | + | 4.01752i | −0.161478 | + | 0.161478i | −0.783221 | − | 0.621743i | \(-0.786425\pi\) |
0.621743 | + | 0.783221i | \(0.286425\pi\) | |||||||
\(620\) | −16.0630 | + | 9.60609i | −0.645108 | + | 0.385790i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.73628 | + | 30.4810i | 0.390389 | + | 1.22218i | ||||
\(623\) | −1.80880 | + | 1.80880i | −0.0724679 | + | 0.0724679i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.7500 | + | 7.80630i | 0.949999 | + | 0.312252i | ||||
\(626\) | −12.6013 | − | 6.49993i | −0.503648 | − | 0.259790i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.9375 | + | 9.91553i | −0.556166 | + | 0.395673i | ||||
\(629\) | 0.490385 | + | 0.490385i | 0.0195529 | + | 0.0195529i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.9309 | −1.07210 | −0.536052 | − | 0.844185i | \(-0.680085\pi\) | ||||
−0.536052 | + | 0.844185i | \(0.680085\pi\) | |||||||
\(632\) | 8.19752 | + | 6.14508i | 0.326080 | + | 0.244438i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.8122 | − | 33.8493i | −0.429407 | − | 1.34433i | ||||
\(635\) | −29.5395 | + | 25.1856i | −1.17224 | + | 0.999462i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.8662 | −0.430536 | ||||||||
\(638\) | −0.737797 | − | 2.30979i | −0.0292097 | − | 0.0914456i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.4395 | − | 22.0286i | −0.491715 | − | 0.870756i | ||||
\(641\) | −18.6880 | −0.738131 | −0.369065 | − | 0.929403i | \(-0.620322\pi\) | ||||
−0.369065 | + | 0.929403i | \(0.620322\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.6249 | 1.16829 | 0.584146 | − | 0.811648i | \(-0.301429\pi\) | ||||
0.584146 | + | 0.811648i | \(0.301429\pi\) | |||||||
\(644\) | −1.55528 | + | 1.10647i | −0.0612865 | + | 0.0436011i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.583529 | − | 1.82683i | −0.0229586 | − | 0.0718758i | ||||
\(647\) | 5.04426 | − | 5.04426i | 0.198310 | − | 0.198310i | −0.600965 | − | 0.799275i | \(-0.705217\pi\) |
0.799275 | + | 0.600965i | \(0.205217\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.67794 | 0.379893 | ||||||||
\(650\) | −10.8939 | + | 1.65087i | −0.427294 | + | 0.0647525i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.83089 | − | 4.14827i | 0.228355 | − | 0.162459i | ||||
\(653\) | − | 3.04934i | − | 0.119330i | −0.998218 | − | 0.0596649i | \(-0.980997\pi\) | ||
0.998218 | − | 0.0596649i | \(-0.0190032\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.4045 | + | 19.2404i | 0.640978 | + | 0.751783i | ||||
\(656\) | 28.7815 | + | 9.98991i | 1.12373 | + | 0.390040i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.434238 | − | 1.35945i | −0.0169284 | − | 0.0529970i | ||||
\(659\) | −22.0441 | − | 22.0441i | −0.858718 | − | 0.858718i | 0.132469 | − | 0.991187i | \(-0.457709\pi\) |
−0.991187 | + | 0.132469i | \(0.957709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.09788 | − | 8.09788i | 0.314971 | − | 0.314971i | −0.531861 | − | 0.846832i | \(-0.678507\pi\) |
0.846832 | + | 0.531861i | \(0.178507\pi\) | |||||||
\(662\) | 5.32531 | − | 10.3241i | 0.206974 | − | 0.401256i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.68054 | − | 2.75904i | −0.142833 | − | 0.107071i | ||||
\(665\) | 0.0923670 | − | 1.16100i | 0.00358184 | − | 0.0450218i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.40167 | 0.0929931 | ||||||||
\(668\) | 0.227083 | − | 1.34676i | 0.00878609 | − | 0.0521078i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.79591 | + | 7.67748i | 0.0693820 | + | 0.296607i | ||||
\(671\) | 7.28276i | 0.281148i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.1768 | − | 27.1768i | −1.04759 | − | 1.04759i | −0.998810 | − | 0.0487786i | \(-0.984467\pi\) |
−0.0487786 | − | 0.998810i | \(-0.515533\pi\) | |||||||
\(674\) | 13.1831 | + | 6.80006i | 0.507795 | + | 0.261929i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.2287 | + | 12.2570i | −0.662644 | + | 0.471425i | ||||
\(677\) | 28.6501i | 1.10111i | 0.834798 | + | 0.550557i | \(0.185585\pi\) | ||||
−0.834798 | + | 0.550557i | \(0.814415\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.23115i | 0.0856238i | ||||||||
\(680\) | 0.168066 | + | 2.67504i | 0.00644502 | + | 0.102583i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.0165 | − | 11.3565i | −0.843055 | − | 0.434861i | ||||
\(683\) | − | 30.8472i | − | 1.18034i | −0.807281 | − | 0.590168i | \(-0.799062\pi\) | ||
0.807281 | − | 0.590168i | \(-0.200938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.42485 | − | 6.33051i | 0.283689 | − | 0.241876i | ||||
\(686\) | −1.47462 | + | 2.85881i | −0.0563013 | + | 0.109150i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25.4184 | − | 8.82261i | −0.969069 | − | 0.336359i | ||||
\(689\) | − | 17.8142i | − | 0.678668i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.253186 | − | 0.253186i | 0.00963164 | − | 0.00963164i | −0.702275 | − | 0.711906i | \(-0.747832\pi\) |
0.711906 | + | 0.702275i | \(0.247832\pi\) | |||||||
\(692\) | 13.7028 | + | 19.2609i | 0.520901 | + | 0.732189i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.85286 | − | 24.5847i | −0.298091 | − | 0.933221i | ||||
\(695\) | −25.0728 | − | 29.4071i | −0.951066 | − | 1.11548i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.28241 | − | 2.28241i | −0.0864525 | − | 0.0864525i | ||||
\(698\) | 34.5563 | + | 17.8247i | 1.30798 | + | 0.674675i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.521032 | + | 1.54213i | −0.0196932 | + | 0.0582870i | ||||
\(701\) | −10.5238 | − | 10.5238i | −0.397479 | − | 0.397479i | 0.479864 | − | 0.877343i | \(-0.340686\pi\) |
−0.877343 | + | 0.479864i | \(0.840686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.70261 | + | 3.70261i | −0.139646 | + | 0.139646i | ||||
\(704\) | 16.0866 | − | 29.3675i | 0.606285 | − | 1.10683i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.04152 | − | 2.01917i | 0.0391982 | − | 0.0759925i | ||||
\(707\) | 2.94813i | 0.110876i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.58968 | + | 1.58968i | 0.0597015 | + | 0.0597015i | 0.736327 | − | 0.676626i | \(-0.236558\pi\) |
−0.676626 | + | 0.736327i | \(0.736558\pi\) | |||||||
\(710\) | 24.6362 | − | 5.76288i | 0.924581 | − | 0.216277i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 35.5651 | + | 26.6606i | 1.33286 | + | 0.999147i | ||||
\(713\) | 17.3502 | − | 17.3502i | 0.649771 | − | 0.649771i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.46198 | − | 11.0977i | −0.353858 | − | 0.415029i | ||||
\(716\) | −13.1511 | − | 2.21745i | −0.491478 | − | 0.0828699i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 38.2781 | − | 12.2269i | 1.42853 | − | 0.456302i | ||||
\(719\) | 22.8919 | 0.853722 | 0.426861 | − | 0.904317i | \(-0.359619\pi\) | ||||
0.426861 | + | 0.904317i | \(0.359619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.998472 | 0.0371850 | ||||||||
\(722\) | −11.8027 | + | 3.77002i | −0.439249 | + | 0.140306i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.20023 | + | 36.7718i | −0.230430 | + | 1.36661i | ||||
\(725\) | 1.65906 | − | 1.20107i | 0.0616158 | − | 0.0446065i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.1893 | − | 20.1893i | 0.748780 | − | 0.748780i | −0.225470 | − | 0.974250i | \(-0.572392\pi\) |
0.974250 | + | 0.225470i | \(0.0723919\pi\) | |||||||
\(728\) | −0.101626 | − | 0.710175i | −0.00376653 | − | 0.0263208i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.64436 | − | 4.25924i | 0.0978720 | − | 0.157641i | ||||
\(731\) | 2.01572 | + | 2.01572i | 0.0745540 | + | 0.0745540i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.3253i | − | 0.529118i | −0.964370 | − | 0.264559i | \(-0.914774\pi\) | ||
0.964370 | − | 0.264559i | \(-0.0852263\pi\) | |||||||
\(734\) | −2.10592 | + | 4.08270i | −0.0777311 | + | 0.150695i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.8605 | + | 24.0286i | 0.842648 | + | 0.885705i | ||||
\(737\) | −7.37954 | + | 7.37954i | −0.271829 | + | 0.271829i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.3401 | − | 32.3401i | −1.18965 | − | 1.18965i | −0.977164 | − | 0.212487i | \(-0.931844\pi\) |
−0.212487 | − | 0.977164i | \(-0.568156\pi\) | |||||||
\(740\) | 6.28089 | − | 3.75612i | 0.230890 | − | 0.138078i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.33894 | − | 1.20646i | −0.0858651 | − | 0.0442906i | ||||
\(743\) | 6.06842 | + | 6.06842i | 0.222629 | + | 0.222629i | 0.809605 | − | 0.586976i | \(-0.199682\pi\) |
−0.586976 | + | 0.809605i | \(0.699682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.23662 | + | 5.31741i | −0.228492 | + | 0.194815i | ||||
\(746\) | 7.77947 | + | 24.3549i | 0.284827 | + | 0.891696i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.89075 | + | 2.05657i | −0.105696 | + | 0.0751955i | ||||
\(749\) | −1.37898 | + | 1.37898i | −0.0503870 | + | 0.0503870i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.6431i | 1.81150i | 0.423810 | + | 0.905751i | \(0.360692\pi\) | ||||
−0.423810 | + | 0.905751i | \(0.639308\pi\) | |||||||
\(752\) | −22.3149 | + | 10.8155i | −0.813740 | + | 0.394400i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.413816 | + | 0.802256i | −0.0150703 | + | 0.0292164i | ||||
\(755\) | −3.00752 | + | 37.8029i | −0.109455 | + | 1.37579i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.18443i | 0.333814i | 0.985973 | + | 0.166907i | \(0.0533779\pi\) | ||||
−0.985973 | + | 0.166907i | \(0.946622\pi\) | |||||||
\(758\) | 4.95968 | + | 2.55828i | 0.180144 | + | 0.0929211i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.1976 | + | 1.26896i | −0.732644 | + | 0.0460302i | ||||
\(761\) | 4.75310i | 0.172300i | 0.996282 | + | 0.0861499i | \(0.0274564\pi\) | ||||
−0.996282 | + | 0.0861499i | \(0.972544\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.924267i | 0.0334607i | ||||||||
\(764\) | 16.2167 | + | 22.7945i | 0.586698 | + | 0.824675i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.4367 | − | 7.44668i | −0.521619 | − | 0.269060i | ||||
\(767\) | −2.54765 | − | 2.54765i | −0.0919902 | − | 0.0919902i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 19.4153i | − | 0.700135i | −0.936724 | − | 0.350067i | \(-0.886159\pi\) | ||
0.936724 | − | 0.350067i | \(-0.113841\pi\) | |||||||
\(770\) | −2.09789 | + | 0.490736i | −0.0756027 | + | 0.0176849i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.8460 | − | 1.82877i | −0.390355 | − | 0.0658190i | ||||
\(773\) | −26.0890 | −0.938356 | −0.469178 | − | 0.883104i | \(-0.655450\pi\) | ||||
−0.469178 | + | 0.883104i | \(0.655450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.30862 | − | 20.6622i | 0.118849 | − | 0.742208i | ||||
\(776\) | 38.3777 | − | 5.49187i | 1.37768 | − | 0.197147i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.2339 | − | 25.6562i | 0.474458 | − | 0.919819i | ||||
\(779\) | 17.2331 | − | 17.2331i | 0.617442 | − | 0.617442i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.6802 | + | 23.6802i | 0.847343 | + | 0.847343i | ||||
\(782\) | −1.06919 | − | 3.34726i | −0.0382340 | − | 0.119698i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 26.3518 | + | 9.14657i | 0.941135 | + | 0.326663i | ||||
\(785\) | 1.51664 | − | 19.0634i | 0.0541313 | − | 0.680402i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.2339i | 0.507384i | 0.967285 | + | 0.253692i | \(0.0816449\pi\) | ||||
−0.967285 | + | 0.253692i | \(0.918355\pi\) | |||||||
\(788\) | 25.8866 | + | 36.3867i | 0.922170 | + | 1.29622i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11.1532 | + | 2.60896i | −0.396815 | + | 0.0928225i | ||||
\(791\) | 1.49114 | 0.0530189 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.91713 | − | 1.91713i | 0.0680794 | − | 0.0680794i | ||||
\(794\) | 15.1307 | + | 47.3692i | 0.536970 | + | 1.68107i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.4067 | − | 16.0334i | −0.404298 | − | 0.568289i | ||||
\(797\) | −19.8283 | −0.702353 | −0.351176 | − | 0.936309i | \(-0.614218\pi\) | ||||
−0.351176 | + | 0.936309i | \(0.614218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.62729 | 0.0929467 | ||||||||
\(800\) | 27.8084 | + | 5.16631i | 0.983177 | + | 0.182657i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.1194 | − | 31.6803i | −0.357327 | − | 1.11867i | ||||
\(803\) | 6.63568 | 0.234168 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.169242 | − | 2.12728i | 0.00596499 | − | 0.0749767i | ||||
\(806\) | 2.80618 | + | 8.78518i | 0.0988433 | + | 0.309445i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 50.7103 | − | 7.25667i | 1.78398 | − | 0.255289i | ||||
\(809\) | −21.3864 | −0.751907 | −0.375954 | − | 0.926639i | \(-0.622685\pi\) | ||||
−0.375954 | + | 0.926639i | \(0.622685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.90624 | − | 9.90624i | −0.347855 | − | 0.347855i | 0.511455 | − | 0.859310i | \(-0.329107\pi\) |
−0.859310 | + | 0.511455i | \(0.829107\pi\) | |||||||
\(812\) | 0.0773075 | + | 0.108665i | 0.00271296 | + | 0.00381339i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.60877 | + | 4.44054i | 0.301737 | + | 0.155641i | ||||
\(815\) | −0.634504 | + | 7.97538i | −0.0222257 | + | 0.279365i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.2195 | + | 15.2195i | −0.532463 | + | 0.532463i | ||||
\(818\) | −10.0088 | − | 31.3342i | −0.349950 | − | 1.09557i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.2333 | + | 17.4822i | −1.02087 | + | 0.610506i | ||||
\(821\) | −22.6209 | + | 22.6209i | −0.789474 | + | 0.789474i | −0.981408 | − | 0.191934i | \(-0.938524\pi\) |
0.191934 | + | 0.981408i | \(0.438524\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.89892 | + | 4.89892i | 0.170766 | + | 0.170766i | 0.787316 | − | 0.616550i | \(-0.211470\pi\) |
−0.616550 | + | 0.787316i | \(0.711470\pi\) | |||||||
\(824\) | −2.45769 | − | 17.1746i | −0.0856177 | − | 0.598304i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.507034 | + | 0.161958i | −0.0176420 | + | 0.00563523i | ||||
\(827\) | −1.05434 | −0.0366630 | −0.0183315 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183315 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7754 | − | 11.7754i | 0.408978 | − | 0.408978i | −0.472404 | − | 0.881382i | \(-0.656614\pi\) |
0.881382 | + | 0.472404i | \(0.156614\pi\) | |||||||
\(830\) | 5.00762 | − | 1.17138i | 0.173817 | − | 0.0406591i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.9655 | + | 3.49612i | −0.414828 | + | 0.121206i | ||||
\(833\) | −2.08973 | − | 2.08973i | −0.0724050 | − | 0.0724050i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.990707 | + | 1.16197i | 0.0342848 | + | 0.0402116i | ||||
\(836\) | −15.5279 | − | 21.8263i | −0.537044 | − | 0.754880i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.08763 | + | 11.8019i | −0.210294 | + | 0.407691i | ||||
\(839\) | − | 41.1678i | − | 1.42127i | −0.703560 | − | 0.710636i | \(-0.748407\pi\) | ||
0.703560 | − | 0.710636i | \(-0.251593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8322i | 0.994214i | ||||||||
\(842\) | −12.9438 | − | 6.67662i | −0.446073 | − | 0.230092i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.19796 | + | 30.8277i | −0.178921 | + | 1.06113i | ||||
\(845\) | 1.87479 | − | 23.5651i | 0.0644948 | − | 0.810666i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.750366 | − | 0.750366i | −0.0257829 | − | 0.0257829i | ||||
\(848\) | −14.9950 | + | 43.2013i | −0.514930 | + | 1.48354i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.41254 | − | 1.77757i | −0.0827493 | − | 0.0609700i | ||||
\(851\) | −6.78419 | + | 6.78419i | −0.232559 | + | 0.232559i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7179 | 0.401212 | 0.200606 | − | 0.979672i | \(-0.435709\pi\) | ||||
0.200606 | + | 0.979672i | \(0.435709\pi\) | |||||||
\(854\) | −0.121875 | − | 0.381549i | −0.00417047 | − | 0.0130563i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.1140 | + | 20.3254i | 0.926738 | + | 0.694708i | ||||
\(857\) | 12.2154 | + | 12.2154i | 0.417270 | + | 0.417270i | 0.884262 | − | 0.466992i | \(-0.154662\pi\) |
−0.466992 | + | 0.884262i | \(0.654662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.2170 | − | 17.2170i | 0.587436 | − | 0.587436i | −0.349500 | − | 0.936936i | \(-0.613649\pi\) |
0.936936 | + | 0.349500i | \(0.113649\pi\) | |||||||
\(860\) | 25.8175 | − | 15.4395i | 0.880369 | − | 0.526482i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.7954 | + | 5.04537i | −0.537992 | + | 0.171846i | ||||
\(863\) | 11.1929 | − | 11.1929i | 0.381011 | − | 0.381011i | −0.490455 | − | 0.871466i | \(-0.663169\pi\) |
0.871466 | + | 0.490455i | \(0.163169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.3447 | − | 2.09593i | −0.895746 | − | 0.0712637i | ||||
\(866\) | −19.1463 | + | 37.1184i | −0.650616 | + | 1.26133i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.34351 | + | 0.226533i | 0.0456016 | + | 0.00768905i | ||||
\(869\) | −10.7204 | − | 10.7204i | −0.363665 | − | 0.363665i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.88522 | 0.131646 | ||||||||
\(872\) | 15.8982 | − | 2.27504i | 0.538380 | − | 0.0770425i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.2732 | − | 8.07279i | 0.854878 | − | 0.273066i | ||||
\(875\) | −0.946933 | − | 1.55415i | −0.0320122 | − | 0.0525397i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.1739 | 1.45788 | 0.728940 | − | 0.684578i | \(-0.240013\pi\) | ||||
0.728940 | + | 0.684578i | \(0.240013\pi\) | |||||||
\(878\) | 10.1530 | − | 3.24308i | 0.342647 | − | 0.109449i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.6049 | + | 34.8775i | 0.458622 | + | 1.17572i | ||||
\(881\) | 33.4204 | 1.12596 | 0.562981 | − | 0.826470i | \(-0.309654\pi\) | ||||
0.562981 | + | 0.826470i | \(0.309654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00362 | 0.0674270 | 0.0337135 | − | 0.999432i | \(-0.489267\pi\) | ||||
0.0337135 | + | 0.999432i | \(0.489267\pi\) | |||||||
\(884\) | 1.30234 | + | 0.219593i | 0.0438026 | + | 0.00738571i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.6597 | − | 11.0710i | 1.16441 | − | 0.371939i | ||||
\(887\) | 16.1765 | − | 16.1765i | 0.543154 | − | 0.543154i | −0.381298 | − | 0.924452i | \(-0.624523\pi\) |
0.924452 | + | 0.381298i | \(0.124523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.82586 | 0.0947762 | ||||||||
\(890\) | −48.3886 | + | 11.3190i | −1.62199 | + | 0.379414i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.79330 | + | 16.5663i | −0.0935266 | + | 0.554681i | ||||
\(893\) | 19.8371i | 0.663822i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3466 | − | 9.67419i | 0.379274 | − | 0.323373i | ||||
\(896\) | −0.351329 | + | 1.80779i | −0.0117371 | + | 0.0603940i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.14997 | − | 1.00617i | 0.105116 | − | 0.0335763i | ||||
\(899\) | −1.21223 | − | 1.21223i | −0.0404303 | − | 0.0404303i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.42593 | − | 3.42593i | 0.114134 | − | 0.114134i | ||||
\(902\) | −40.0680 | − | 20.6677i | −1.33412 | − | 0.688161i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.67037 | − | 25.6489i | −0.122075 | − | 0.853070i | ||||
\(905\) | −27.0501 | − | 31.7262i | −0.899176 | − | 1.05462i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.7116 | −0.986559 | −0.493279 | − | 0.869871i | \(-0.664202\pi\) | ||||
−0.493279 | + | 0.869871i | \(0.664202\pi\) | |||||||
\(908\) | 26.9101 | + | 37.8254i | 0.893044 | + | 1.25528i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.681436 | + | 0.423071i | 0.0225894 | + | 0.0140247i | ||||
\(911\) | 44.6931i | 1.48075i | 0.672195 | + | 0.740374i | \(0.265352\pi\) | ||||
−0.672195 | + | 0.740374i | \(0.734648\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.81328 | + | 4.81328i | 0.159296 | + | 0.159296i | ||||
\(914\) | 9.58663 | − | 18.5854i | 0.317097 | − | 0.614749i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.6172 | − | 2.63326i | −0.516005 | − | 0.0870055i | ||||
\(917\) | − | 1.84061i | − | 0.0607821i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.1278i | 1.32369i | 0.749639 | + | 0.661847i | \(0.230227\pi\) | ||||
−0.749639 | + | 0.661847i | \(0.769773\pi\) | |||||||
\(920\) | −37.0076 | + | 2.32509i | −1.22010 | + | 0.0766560i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.3856 | + | 27.8890i | −0.473764 | + | 0.918474i | ||||
\(923\) | − | 12.4673i | − | 0.410365i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.29372 | + | 8.07922i | −0.0425372 | + | 0.265643i | ||||
\(926\) | 34.8974 | + | 18.0007i | 1.14680 | + | 0.591538i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.67884 | − | 1.59723i | 0.0551106 | − | 0.0524316i | ||||
\(929\) | 27.7519i | 0.910512i | 0.890361 | + | 0.455256i | \(0.150452\pi\) | ||||
−0.890361 | + | 0.455256i | \(0.849548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.7783 | − | 15.7783i | 0.517114 | − | 0.517114i | ||||
\(932\) | 1.42021 | − | 8.42289i | 0.0465206 | − | 0.275901i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.9867 | + | 10.5367i | −1.07936 | + | 0.344770i | ||||
\(935\) | 0.314565 | − | 3.95391i | 0.0102874 | − | 0.129307i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.2805 | − | 17.2805i | −0.564531 | − | 0.564531i | 0.366060 | − | 0.930591i | \(-0.380706\pi\) |
−0.930591 | + | 0.366060i | \(0.880706\pi\) | |||||||
\(938\) | 0.263125 | − | 0.510114i | 0.00859133 | − | 0.0166558i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.76334 | − | 26.8871i | 0.220596 | − | 0.876961i | ||||
\(941\) | 4.81532 | + | 4.81532i | 0.156975 | + | 0.156975i | 0.781225 | − | 0.624250i | \(-0.214595\pi\) |
−0.624250 | + | 0.781225i | \(0.714595\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.5759 | − | 31.5759i | 1.02825 | − | 1.02825i | ||||
\(944\) | 4.03385 | + | 8.32277i | 0.131291 | + | 0.270883i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.3862 | + | 18.2528i | 1.15050 | + | 0.593449i | ||||
\(947\) | 3.37347i | 0.109623i | 0.998497 | + | 0.0548115i | \(0.0174558\pi\) | ||||
−0.998497 | + | 0.0548115i | \(0.982544\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.74680 | − | 1.74680i | −0.0567034 | − | 0.0567034i | ||||
\(950\) | 13.4213 | − | 18.2156i | 0.435446 | − | 0.590993i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.117032 | − | 0.156121i | 0.00379304 | − | 0.00505991i | ||||
\(953\) | −14.3663 | + | 14.3663i | −0.465369 | + | 0.465369i | −0.900410 | − | 0.435041i | \(-0.856734\pi\) |
0.435041 | + | 0.900410i | \(0.356734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.1778 | − | 2.48044i | −1.00889 | − | 0.0802652i | ||||
\(956\) | −0.00226303 | + | 0.00160999i | −7.31916e−5 | + | 5.20707e-5i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.9477 | + | 49.9268i | 0.515246 | + | 1.61306i | ||||
\(959\) | −0.710289 | −0.0229364 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.4851 | 0.435003 | ||||||||
\(962\) | −1.09726 | − | 3.43514i | −0.0353769 | − | 0.110753i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.9539 | − | 14.9073i | 0.674881 | − | 0.480131i | ||||
\(965\) | 9.35775 | − | 7.97851i | 0.301236 | − | 0.256837i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.8576 | + | 11.8576i | −0.381315 | + | 0.381315i | −0.871576 | − | 0.490260i | \(-0.836902\pi\) |
0.490260 | + | 0.871576i | \(0.336902\pi\) | |||||||
\(968\) | −11.0599 | + | 14.7539i | −0.355480 | + | 0.474209i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.8627 | + | 36.8247i | −0.734077 | + | 1.18237i | ||||
\(971\) | 14.6082 | + | 14.6082i | 0.468799 | + | 0.468799i | 0.901525 | − | 0.432726i | \(-0.142448\pi\) |
−0.432726 | + | 0.901525i | \(0.642448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.81319i | 0.0901869i | ||||||||
\(974\) | −35.8892 | − | 18.5122i | −1.14996 | − | 0.593170i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.26298 | + | 3.03552i | −0.200473 | + | 0.0971645i | ||||
\(977\) | −12.9249 | + | 12.9249i | −0.413504 | + | 0.413504i | −0.882957 | − | 0.469454i | \(-0.844451\pi\) |
0.469454 | + | 0.882957i | \(0.344451\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.5108 | − | 46.5108i | −1.48649 | − | 1.48649i | ||||
\(980\) | −26.7655 | + | 16.0064i | −0.854992 | + | 0.511305i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.83804 | − | 13.2567i | 0.218211 | − | 0.423040i | ||||
\(983\) | 0.133323 | + | 0.133323i | 0.00425235 | + | 0.00425235i | 0.709230 | − | 0.704977i | \(-0.249043\pi\) |
−0.704977 | + | 0.709230i | \(0.749043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49.7690 | − | 3.95951i | −1.58577 | − | 0.126161i | ||||
\(986\) | −0.233868 | + | 0.0747024i | −0.00744787 | + | 0.00237901i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.65802 | + | 9.83324i | −0.0527485 | + | 0.312837i | ||||
\(989\) | −27.8863 | + | 27.8863i | −0.886733 | + | 0.886733i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 47.9032i | − | 1.52170i | −0.648930 | − | 0.760848i | \(-0.724783\pi\) | ||
0.648930 | − | 0.760848i | \(-0.275217\pi\) | |||||||
\(992\) | 0.589589 | − | 23.6671i | 0.0187195 | − | 0.751430i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.63690 | − | 0.844340i | −0.0519194 | − | 0.0267808i | ||||
\(995\) | 21.9302 | + | 1.74472i | 0.695234 | + | 0.0553114i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.9379i | 1.73990i | 0.493138 | + | 0.869951i | \(0.335850\pi\) | ||||
−0.493138 | + | 0.869951i | \(0.664150\pi\) | |||||||
\(998\) | 7.49449 | − | 14.5294i | 0.237234 | − | 0.459919i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 720.2.z.g.163.5 | 18 | ||
3.2 | odd | 2 | 80.2.s.b.3.5 | yes | 18 | ||
5.2 | odd | 4 | 720.2.bd.g.307.9 | 18 | |||
12.11 | even | 2 | 320.2.s.b.303.9 | 18 | |||
15.2 | even | 4 | 80.2.j.b.67.1 | yes | 18 | ||
15.8 | even | 4 | 400.2.j.d.307.9 | 18 | |||
15.14 | odd | 2 | 400.2.s.d.243.5 | 18 | |||
16.11 | odd | 4 | 720.2.bd.g.523.9 | 18 | |||
24.5 | odd | 2 | 640.2.s.d.223.9 | 18 | |||
24.11 | even | 2 | 640.2.s.c.223.1 | 18 | |||
48.5 | odd | 4 | 320.2.j.b.143.9 | 18 | |||
48.11 | even | 4 | 80.2.j.b.43.1 | ✓ | 18 | ||
48.29 | odd | 4 | 640.2.j.c.543.1 | 18 | |||
48.35 | even | 4 | 640.2.j.d.543.9 | 18 | |||
60.23 | odd | 4 | 1600.2.j.d.1007.9 | 18 | |||
60.47 | odd | 4 | 320.2.j.b.47.1 | 18 | |||
60.59 | even | 2 | 1600.2.s.d.943.1 | 18 | |||
80.27 | even | 4 | inner | 720.2.z.g.667.5 | 18 | ||
120.77 | even | 4 | 640.2.j.d.607.1 | 18 | |||
120.107 | odd | 4 | 640.2.j.c.607.9 | 18 | |||
240.53 | even | 4 | 1600.2.s.d.207.1 | 18 | |||
240.59 | even | 4 | 400.2.j.d.43.9 | 18 | |||
240.77 | even | 4 | 640.2.s.c.287.1 | 18 | |||
240.107 | odd | 4 | 80.2.s.b.27.5 | yes | 18 | ||
240.149 | odd | 4 | 1600.2.j.d.143.1 | 18 | |||
240.197 | even | 4 | 320.2.s.b.207.9 | 18 | |||
240.203 | odd | 4 | 400.2.s.d.107.5 | 18 | |||
240.227 | odd | 4 | 640.2.s.d.287.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.1 | ✓ | 18 | 48.11 | even | 4 | ||
80.2.j.b.67.1 | yes | 18 | 15.2 | even | 4 | ||
80.2.s.b.3.5 | yes | 18 | 3.2 | odd | 2 | ||
80.2.s.b.27.5 | yes | 18 | 240.107 | odd | 4 | ||
320.2.j.b.47.1 | 18 | 60.47 | odd | 4 | |||
320.2.j.b.143.9 | 18 | 48.5 | odd | 4 | |||
320.2.s.b.207.9 | 18 | 240.197 | even | 4 | |||
320.2.s.b.303.9 | 18 | 12.11 | even | 2 | |||
400.2.j.d.43.9 | 18 | 240.59 | even | 4 | |||
400.2.j.d.307.9 | 18 | 15.8 | even | 4 | |||
400.2.s.d.107.5 | 18 | 240.203 | odd | 4 | |||
400.2.s.d.243.5 | 18 | 15.14 | odd | 2 | |||
640.2.j.c.543.1 | 18 | 48.29 | odd | 4 | |||
640.2.j.c.607.9 | 18 | 120.107 | odd | 4 | |||
640.2.j.d.543.9 | 18 | 48.35 | even | 4 | |||
640.2.j.d.607.1 | 18 | 120.77 | even | 4 | |||
640.2.s.c.223.1 | 18 | 24.11 | even | 2 | |||
640.2.s.c.287.1 | 18 | 240.77 | even | 4 | |||
640.2.s.d.223.9 | 18 | 24.5 | odd | 2 | |||
640.2.s.d.287.9 | 18 | 240.227 | odd | 4 | |||
720.2.z.g.163.5 | 18 | 1.1 | even | 1 | trivial | ||
720.2.z.g.667.5 | 18 | 80.27 | even | 4 | inner | ||
720.2.bd.g.307.9 | 18 | 5.2 | odd | 4 | |||
720.2.bd.g.523.9 | 18 | 16.11 | odd | 4 | |||
1600.2.j.d.143.1 | 18 | 240.149 | odd | 4 | |||
1600.2.j.d.1007.9 | 18 | 60.23 | odd | 4 | |||
1600.2.s.d.207.1 | 18 | 240.53 | even | 4 | |||
1600.2.s.d.943.1 | 18 | 60.59 | even | 2 |