Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (of order \(6\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.5 | ||
Root | \(0.874681 + 1.11128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.361 |
Dual form | 637.2.u.g.30.5 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16500 | + | 0.672613i | 0.823779 | + | 0.475609i | 0.851718 | − | 0.524000i | \(-0.175561\pi\) |
−0.0279386 | + | 0.999610i | \(0.508894\pi\) | |||||||
\(3\) | −2.05010 | −1.18363 | −0.591814 | − | 0.806075i | \(-0.701588\pi\) | ||||
−0.591814 | + | 0.806075i | \(0.701588\pi\) | |||||||
\(4\) | −0.0951832 | − | 0.164862i | −0.0475916 | − | 0.0824311i | ||||
\(5\) | 3.08979 | − | 1.78389i | 1.38179 | − | 0.797779i | 0.389422 | − | 0.921059i | \(-0.372675\pi\) |
0.992372 | + | 0.123280i | \(0.0393415\pi\) | |||||||
\(6\) | −2.38837 | − | 1.37893i | −0.975048 | − | 0.562944i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.94654i | − | 1.04176i | ||||||
\(9\) | 1.20292 | 0.400975 | ||||||||
\(10\) | 4.79947 | 1.51772 | ||||||||
\(11\) | 1.27867i | 0.385534i | 0.981245 | + | 0.192767i | \(0.0617462\pi\) | ||||
−0.981245 | + | 0.192767i | \(0.938254\pi\) | |||||||
\(12\) | 0.195135 | + | 0.337984i | 0.0563307 | + | 0.0975677i | ||||
\(13\) | −3.57420 | + | 0.474474i | −0.991304 | + | 0.131595i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.33438 | + | 3.65716i | −1.63553 | + | 0.944273i | ||||
\(16\) | 1.79151 | − | 3.10299i | 0.447878 | − | 0.775748i | ||||
\(17\) | −3.86960 | − | 6.70234i | −0.938515 | − | 1.62556i | −0.768242 | − | 0.640159i | \(-0.778868\pi\) |
−0.170273 | − | 0.985397i | \(-0.554465\pi\) | |||||||
\(18\) | 1.40141 | + | 0.809103i | 0.330315 | + | 0.190707i | ||||
\(19\) | − | 0.943878i | − | 0.216540i | −0.994121 | − | 0.108270i | \(-0.965469\pi\) | ||
0.994121 | − | 0.108270i | \(-0.0345312\pi\) | |||||||
\(20\) | −0.588191 | − | 0.339592i | −0.131524 | − | 0.0759352i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.860052 | + | 1.48965i | −0.183364 | + | 0.317595i | ||||
\(23\) | 0.823637 | − | 1.42658i | 0.171740 | − | 0.297463i | −0.767288 | − | 0.641303i | \(-0.778394\pi\) |
0.939028 | + | 0.343840i | \(0.111728\pi\) | |||||||
\(24\) | 6.04071i | 1.23305i | ||||||||
\(25\) | 3.86451 | − | 6.69354i | 0.772903 | − | 1.33871i | ||||
\(26\) | −4.48308 | − | 1.85129i | −0.879203 | − | 0.363068i | ||||
\(27\) | 3.68419 | 0.709023 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.02242 | − | 3.50293i | −0.375554 | − | 0.650478i | 0.614856 | − | 0.788639i | \(-0.289214\pi\) |
−0.990410 | + | 0.138161i | \(0.955881\pi\) | |||||||
\(30\) | −9.83940 | −1.79642 | ||||||||
\(31\) | 4.46193 | + | 2.57610i | 0.801387 | + | 0.462681i | 0.843956 | − | 0.536413i | \(-0.180221\pi\) |
−0.0425691 | + | 0.999094i | \(0.513554\pi\) | |||||||
\(32\) | −0.929326 | + | 0.536547i | −0.164283 | + | 0.0948490i | ||||
\(33\) | − | 2.62141i | − | 0.456329i | ||||||
\(34\) | − | 10.4110i | − | 1.78547i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.114498 | − | 0.198317i | −0.0190830 | − | 0.0330528i | ||||
\(37\) | 0.914594 | + | 0.528041i | 0.150358 | + | 0.0868094i | 0.573292 | − | 0.819351i | \(-0.305666\pi\) |
−0.422933 | + | 0.906161i | \(0.639000\pi\) | |||||||
\(38\) | 0.634865 | − | 1.09962i | 0.102989 | − | 0.178382i | ||||
\(39\) | 7.32747 | − | 0.972721i | 1.17333 | − | 0.155760i | ||||
\(40\) | −5.25629 | − | 9.10417i | −0.831093 | − | 1.43950i | ||||
\(41\) | 3.63629 | − | 2.09941i | 0.567893 | − | 0.327873i | −0.188415 | − | 0.982090i | \(-0.560335\pi\) |
0.756307 | + | 0.654217i | \(0.227002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.91532 | − | 3.31744i | 0.292084 | − | 0.505904i | −0.682218 | − | 0.731148i | \(-0.738985\pi\) |
0.974302 | + | 0.225244i | \(0.0723180\pi\) | |||||||
\(44\) | 0.210805 | − | 0.121708i | 0.0317800 | − | 0.0183482i | ||||
\(45\) | 3.71678 | − | 2.14588i | 0.554064 | − | 0.319889i | ||||
\(46\) | 1.91908 | − | 1.10798i | 0.282952 | − | 0.163363i | ||||
\(47\) | 0.774415 | − | 0.447109i | 0.112960 | − | 0.0652175i | −0.442456 | − | 0.896790i | \(-0.645893\pi\) |
0.555416 | + | 0.831573i | \(0.312559\pi\) | |||||||
\(48\) | −3.67279 | + | 6.36146i | −0.530121 | + | 0.918197i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.00432 | − | 5.19865i | 1.27340 | − | 0.735200i | ||||
\(51\) | 7.93308 | + | 13.7405i | 1.11085 | + | 1.92405i | ||||
\(52\) | 0.418426 | + | 0.544088i | 0.0580253 | + | 0.0754514i | ||||
\(53\) | 0.0399961 | − | 0.0692754i | 0.00549389 | − | 0.00951570i | −0.863265 | − | 0.504750i | \(-0.831585\pi\) |
0.868759 | + | 0.495235i | \(0.164918\pi\) | |||||||
\(54\) | 4.29208 | + | 2.47804i | 0.584079 | + | 0.337218i | ||||
\(55\) | 2.28101 | + | 3.95082i | 0.307571 | + | 0.532729i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.93505i | 0.256303i | ||||||||
\(58\) | − | 5.44122i | − | 0.714467i | ||||||
\(59\) | −9.68627 | + | 5.59237i | −1.26104 | + | 0.728064i | −0.973277 | − | 0.229636i | \(-0.926246\pi\) |
−0.287768 | + | 0.957700i | \(0.592913\pi\) | |||||||
\(60\) | 1.20585 | + | 0.696200i | 0.155675 | + | 0.0898790i | ||||
\(61\) | 7.62392 | 0.976143 | 0.488072 | − | 0.872804i | \(-0.337701\pi\) | ||||
0.488072 | + | 0.872804i | \(0.337701\pi\) | |||||||
\(62\) | 3.46543 | + | 6.00231i | 0.440111 | + | 0.762294i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.60961 | −1.07620 | ||||||||
\(65\) | −10.1971 | + | 7.84199i | −1.26479 | + | 0.972679i | ||||
\(66\) | 1.76319 | − | 3.05394i | 0.217034 | − | 0.375914i | ||||
\(67\) | − | 6.32103i | − | 0.772237i | −0.922449 | − | 0.386119i | \(-0.873816\pi\) | ||
0.922449 | − | 0.386119i | \(-0.126184\pi\) | |||||||
\(68\) | −0.736641 | + | 1.27590i | −0.0893309 | + | 0.154726i | ||||
\(69\) | −1.68854 | + | 2.92464i | −0.203277 | + | 0.352085i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.89346 | + | 5.71199i | 1.17414 | + | 0.677889i | 0.954651 | − | 0.297727i | \(-0.0962285\pi\) |
0.219487 | + | 0.975616i | \(0.429562\pi\) | |||||||
\(72\) | − | 3.54446i | − | 0.417719i | ||||||
\(73\) | 0.658617 | + | 0.380253i | 0.0770853 | + | 0.0445052i | 0.538047 | − | 0.842915i | \(-0.319162\pi\) |
−0.460962 | + | 0.887420i | \(0.652496\pi\) | |||||||
\(74\) | 0.710335 | + | 1.23034i | 0.0825747 | + | 0.143024i | ||||
\(75\) | −7.92265 | + | 13.7224i | −0.914829 | + | 1.58453i | ||||
\(76\) | −0.155610 | + | 0.0898413i | −0.0178497 | + | 0.0103055i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.19077 | + | 3.79533i | 1.04065 | + | 0.429737i | ||||
\(79\) | 1.42765 | + | 2.47277i | 0.160624 | + | 0.278208i | 0.935093 | − | 0.354404i | \(-0.115316\pi\) |
−0.774469 | + | 0.632612i | \(0.781983\pi\) | |||||||
\(80\) | − | 12.7834i | − | 1.42923i | ||||||
\(81\) | −11.1617 | −1.24019 | ||||||||
\(82\) | 5.64837 | 0.623758 | ||||||||
\(83\) | − | 2.32483i | − | 0.255183i | −0.991827 | − | 0.127591i | \(-0.959275\pi\) | ||
0.991827 | − | 0.127591i | \(-0.0407246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.9125 | − | 13.8059i | −2.59367 | − | 1.49746i | ||||
\(86\) | 4.46270 | − | 2.57654i | 0.481226 | − | 0.277836i | ||||
\(87\) | 4.14617 | + | 7.18137i | 0.444516 | + | 0.769924i | ||||
\(88\) | 3.76766 | 0.401634 | ||||||||
\(89\) | −6.56124 | − | 3.78813i | −0.695490 | − | 0.401541i | 0.110176 | − | 0.993912i | \(-0.464859\pi\) |
−0.805665 | + | 0.592371i | \(0.798192\pi\) | |||||||
\(90\) | 5.77339 | 0.608569 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.313586 | −0.0326936 | ||||||||
\(93\) | −9.14742 | − | 5.28127i | −0.948544 | − | 0.547642i | ||||
\(94\) | 1.20292 | 0.124072 | ||||||||
\(95\) | −1.68377 | − | 2.91638i | −0.172751 | − | 0.299214i | ||||
\(96\) | 1.90522 | − | 1.09998i | 0.194450 | − | 0.112266i | ||||
\(97\) | 0.414443 | + | 0.239279i | 0.0420803 | + | 0.0242951i | 0.520893 | − | 0.853622i | \(-0.325599\pi\) |
−0.478812 | + | 0.877917i | \(0.658933\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.53815i | 0.154589i | ||||||||
\(100\) | −1.47135 | −0.147135 | ||||||||
\(101\) | 2.87836 | 0.286407 | 0.143204 | − | 0.989693i | \(-0.454260\pi\) | ||||
0.143204 | + | 0.989693i | \(0.454260\pi\) | |||||||
\(102\) | 21.3436i | 2.11333i | ||||||||
\(103\) | 5.66755 | + | 9.81649i | 0.558441 | + | 0.967248i | 0.997627 | + | 0.0688516i | \(0.0219335\pi\) |
−0.439186 | + | 0.898396i | \(0.644733\pi\) | |||||||
\(104\) | 1.39806 | + | 10.5315i | 0.137091 | + | 1.03270i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0931910 | − | 0.0538039i | 0.00905151 | − | 0.00522589i | ||||
\(107\) | 3.28603 | − | 5.69157i | 0.317673 | − | 0.550225i | −0.662329 | − | 0.749213i | \(-0.730432\pi\) |
0.980002 | + | 0.198988i | \(0.0637653\pi\) | |||||||
\(108\) | −0.350673 | − | 0.607384i | −0.0337435 | − | 0.0584455i | ||||
\(109\) | 5.05684 | + | 2.91957i | 0.484358 | + | 0.279644i | 0.722231 | − | 0.691652i | \(-0.243117\pi\) |
−0.237873 | + | 0.971296i | \(0.576450\pi\) | |||||||
\(110\) | 6.13694i | 0.585135i | ||||||||
\(111\) | −1.87501 | − | 1.08254i | −0.177968 | − | 0.102750i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.26617 | + | 5.65717i | −0.307255 | + | 0.532181i | −0.977761 | − | 0.209723i | \(-0.932744\pi\) |
0.670506 | + | 0.741904i | \(0.266077\pi\) | |||||||
\(114\) | −1.30154 | + | 2.25433i | −0.121900 | + | 0.211137i | ||||
\(115\) | − | 5.87711i | − | 0.548043i | ||||||
\(116\) | −0.385001 | + | 0.666841i | −0.0357464 | + | 0.0619146i | ||||
\(117\) | −4.29949 | + | 0.570756i | −0.397488 | + | 0.0527664i | ||||
\(118\) | −15.0460 | −1.38510 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.7759 | + | 18.6645i | 0.983705 | + | 1.70383i | ||||
\(121\) | 9.36500 | 0.851363 | ||||||||
\(122\) | 8.88187 | + | 5.12795i | 0.804127 | + | 0.464263i | ||||
\(123\) | −7.45477 | + | 4.30401i | −0.672174 | + | 0.388080i | ||||
\(124\) | − | 0.980805i | − | 0.0880789i | ||||||
\(125\) | − | 9.73656i | − | 0.870865i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.35818 | + | 12.7447i | 0.652932 | + | 1.13091i | 0.982408 | + | 0.186748i | \(0.0597948\pi\) |
−0.329475 | + | 0.944164i | \(0.606872\pi\) | |||||||
\(128\) | −8.17154 | − | 4.71784i | −0.722269 | − | 0.417002i | ||||
\(129\) | −3.92661 | + | 6.80109i | −0.345719 | + | 0.598802i | ||||
\(130\) | −17.1542 | + | 2.27722i | −1.50453 | + | 0.199726i | ||||
\(131\) | 5.59335 | + | 9.68796i | 0.488693 | + | 0.846441i | 0.999915 | − | 0.0130074i | \(-0.00414049\pi\) |
−0.511222 | + | 0.859448i | \(0.670807\pi\) | |||||||
\(132\) | −0.432171 | + | 0.249514i | −0.0376157 | + | 0.0217174i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.25161 | − | 7.36400i | 0.367283 | − | 0.636153i | ||||
\(135\) | 11.3834 | − | 6.57219i | 0.979724 | − | 0.565644i | ||||
\(136\) | −19.7487 | + | 11.4019i | −1.69344 | + | 0.977706i | ||||
\(137\) | −15.2687 | + | 8.81541i | −1.30450 | + | 0.753151i | −0.981172 | − | 0.193137i | \(-0.938134\pi\) |
−0.323324 | + | 0.946288i | \(0.604800\pi\) | |||||||
\(138\) | −3.93430 | + | 2.27147i | −0.334910 | + | 0.193360i | ||||
\(139\) | −2.92855 | + | 5.07240i | −0.248396 | + | 0.430235i | −0.963081 | − | 0.269212i | \(-0.913237\pi\) |
0.714685 | + | 0.699447i | \(0.246570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.58763 | + | 0.916619i | −0.133703 | + | 0.0771932i | ||||
\(142\) | 7.68392 | + | 13.3089i | 0.644820 | + | 1.11686i | ||||
\(143\) | −0.606697 | − | 4.57022i | −0.0507345 | − | 0.382181i | ||||
\(144\) | 2.15506 | − | 3.73267i | 0.179588 | − | 0.311055i | ||||
\(145\) | −12.4977 | − | 7.21554i | −1.03788 | − | 0.599218i | ||||
\(146\) | 0.511526 | + | 0.885989i | 0.0423342 | + | 0.0733250i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 0.201043i | − | 0.0165256i | ||||||
\(149\) | 10.4790i | 0.858470i | 0.903193 | + | 0.429235i | \(0.141217\pi\) | ||||
−0.903193 | + | 0.429235i | \(0.858783\pi\) | |||||||
\(150\) | −18.4598 | + | 10.6578i | −1.50724 | + | 0.870203i | ||||
\(151\) | 4.08249 | + | 2.35703i | 0.332229 | + | 0.191812i | 0.656830 | − | 0.754039i | \(-0.271897\pi\) |
−0.324602 | + | 0.945851i | \(0.605230\pi\) | |||||||
\(152\) | −2.78117 | −0.225583 | ||||||||
\(153\) | −4.65483 | − | 8.06241i | −0.376321 | − | 0.651807i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.3819 | 1.47647 | ||||||||
\(156\) | −0.857817 | − | 1.11544i | −0.0686803 | − | 0.0893063i | ||||
\(157\) | 4.50105 | − | 7.79604i | 0.359223 | − | 0.622192i | −0.628608 | − | 0.777722i | \(-0.716375\pi\) |
0.987831 | + | 0.155530i | \(0.0497085\pi\) | |||||||
\(158\) | 3.84103i | 0.305576i | ||||||||
\(159\) | −0.0819962 | + | 0.142022i | −0.00650272 | + | 0.0112630i | ||||
\(160\) | −1.91428 | + | 3.31563i | −0.151337 | + | 0.262123i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −13.0034 | − | 7.50754i | −1.02165 | − | 0.589848i | ||||
\(163\) | 12.0324i | 0.942449i | 0.882013 | + | 0.471224i | \(0.156188\pi\) | ||||
−0.882013 | + | 0.471224i | \(0.843812\pi\) | |||||||
\(164\) | −0.692227 | − | 0.399657i | −0.0540538 | − | 0.0312080i | ||||
\(165\) | −4.67630 | − | 8.09959i | −0.364050 | − | 0.630553i | ||||
\(166\) | 1.56371 | − | 2.70842i | 0.121367 | − | 0.210214i | ||||
\(167\) | 16.8199 | − | 9.71099i | 1.30157 | − | 0.751459i | 0.320893 | − | 0.947116i | \(-0.396017\pi\) |
0.980672 | + | 0.195657i | \(0.0626838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5497 | − | 3.39173i | 0.965365 | − | 0.260902i | ||||
\(170\) | −18.5720 | − | 32.1677i | −1.42441 | − | 2.46715i | ||||
\(171\) | − | 1.13541i | − | 0.0868273i | ||||||
\(172\) | −0.729226 | −0.0556030 | ||||||||
\(173\) | 14.3795 | 1.09325 | 0.546627 | − | 0.837376i | \(-0.315912\pi\) | ||||
0.546627 | + | 0.837376i | \(0.315912\pi\) | |||||||
\(174\) | 11.1551i | 0.845663i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.96771 | + | 2.29076i | 0.299077 | + | 0.172672i | ||||
\(177\) | 19.8578 | − | 11.4649i | 1.49261 | − | 0.861757i | ||||
\(178\) | −5.09589 | − | 8.82635i | −0.381953 | − | 0.661563i | ||||
\(179\) | −5.42606 | −0.405563 | −0.202781 | − | 0.979224i | \(-0.564998\pi\) | ||||
−0.202781 | + | 0.979224i | \(0.564998\pi\) | |||||||
\(180\) | −0.707550 | − | 0.408504i | −0.0527376 | − | 0.0304481i | ||||
\(181\) | 15.4902 | 1.15138 | 0.575688 | − | 0.817669i | \(-0.304734\pi\) | ||||
0.575688 | + | 0.817669i | \(0.304734\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.6298 | −1.15539 | ||||||||
\(184\) | −4.20348 | − | 2.42688i | −0.309885 | − | 0.178912i | ||||
\(185\) | 3.76786 | 0.277019 | ||||||||
\(186\) | −7.10450 | − | 12.3054i | −0.520927 | − | 0.902272i | ||||
\(187\) | 8.57010 | − | 4.94795i | 0.626707 | − | 0.361830i | ||||
\(188\) | −0.147423 | − | 0.0851144i | −0.0107519 | − | 0.00620761i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 4.53011i | − | 0.328649i | ||||||
\(191\) | 4.74622 | 0.343425 | 0.171712 | − | 0.985147i | \(-0.445070\pi\) | ||||
0.171712 | + | 0.985147i | \(0.445070\pi\) | |||||||
\(192\) | 17.6506 | 1.27382 | ||||||||
\(193\) | − | 21.0391i | − | 1.51443i | −0.653166 | − | 0.757215i | \(-0.726559\pi\) | ||
0.653166 | − | 0.757215i | \(-0.273441\pi\) | |||||||
\(194\) | 0.321884 | + | 0.557519i | 0.0231099 | + | 0.0400276i | ||||
\(195\) | 20.9051 | − | 16.0769i | 1.49704 | − | 1.15129i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.03342 | − | 2.90604i | 0.358616 | − | 0.207047i | −0.309857 | − | 0.950783i | \(-0.600281\pi\) |
0.668474 | + | 0.743736i | \(0.266948\pi\) | |||||||
\(198\) | −1.03458 | + | 1.79194i | −0.0735242 | + | 0.127348i | ||||
\(199\) | −5.30909 | − | 9.19562i | −0.376352 | − | 0.651860i | 0.614177 | − | 0.789168i | \(-0.289488\pi\) |
−0.990528 | + | 0.137309i | \(0.956155\pi\) | |||||||
\(200\) | −19.7228 | − | 11.3869i | −1.39461 | − | 0.805178i | ||||
\(201\) | 12.9588i | 0.914041i | ||||||||
\(202\) | 3.35329 | + | 1.93602i | 0.235936 | + | 0.136218i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.51019 | − | 2.61573i | 0.105735 | − | 0.183138i | ||||
\(205\) | 7.49023 | − | 12.9735i | 0.523140 | − | 0.906106i | ||||
\(206\) | 15.2483i | 1.06240i | ||||||||
\(207\) | 0.990773 | − | 1.71607i | 0.0688635 | − | 0.119275i | ||||
\(208\) | −4.93093 | + | 11.9407i | −0.341899 | + | 0.827941i | ||||
\(209\) | 1.20691 | 0.0834837 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.33275 | + | 4.04043i | 0.160593 | + | 0.278155i | 0.935081 | − | 0.354433i | \(-0.115326\pi\) |
−0.774489 | + | 0.632588i | \(0.781993\pi\) | |||||||
\(212\) | −0.0152278 | −0.00104585 | ||||||||
\(213\) | −20.2826 | − | 11.7102i | −1.38974 | − | 0.802368i | ||||
\(214\) | 7.65645 | − | 4.42046i | 0.523384 | − | 0.302176i | ||||
\(215\) | − | 13.6669i | − | 0.932074i | ||||||
\(216\) | − | 10.8556i | − | 0.738631i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.92748 | + | 6.80260i | 0.266003 | + | 0.460730i | ||||
\(219\) | −1.35023 | − | 0.779558i | −0.0912403 | − | 0.0526776i | ||||
\(220\) | 0.434227 | − | 0.752104i | 0.0292756 | − | 0.0507068i | ||||
\(221\) | 17.0108 | + | 22.1195i | 1.14427 | + | 1.48792i | ||||
\(222\) | −1.45626 | − | 2.52232i | −0.0977377 | − | 0.169287i | ||||
\(223\) | −20.9798 | + | 12.1127i | −1.40491 | + | 0.811126i | −0.994891 | − | 0.100950i | \(-0.967812\pi\) |
−0.410020 | + | 0.912076i | \(0.634478\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.64872 | − | 8.05182i | 0.309915 | − | 0.536788i | ||||
\(226\) | −7.61017 | + | 4.39373i | −0.506221 | + | 0.292267i | ||||
\(227\) | 13.3154 | − | 7.68764i | 0.883773 | − | 0.510247i | 0.0118726 | − | 0.999930i | \(-0.496221\pi\) |
0.871901 | + | 0.489683i | \(0.162887\pi\) | |||||||
\(228\) | 0.319016 | − | 0.184184i | 0.0211274 | − | 0.0121979i | ||||
\(229\) | −14.1608 | + | 8.17573i | −0.935771 | + | 0.540268i | −0.888632 | − | 0.458621i | \(-0.848344\pi\) |
−0.0471389 | + | 0.998888i | \(0.515010\pi\) | |||||||
\(230\) | 3.95302 | − | 6.84683i | 0.260654 | − | 0.451467i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.3215 | + | 5.95913i | −0.677641 | + | 0.391236i | ||||
\(233\) | −14.5554 | − | 25.2106i | −0.953554 | − | 1.65160i | −0.737643 | − | 0.675191i | \(-0.764061\pi\) |
−0.215911 | − | 0.976413i | \(-0.569272\pi\) | |||||||
\(234\) | −5.39280 | − | 2.22696i | −0.352538 | − | 0.145581i | ||||
\(235\) | 1.59518 | − | 2.76294i | 0.104058 | − | 0.180234i | ||||
\(236\) | 1.84394 | + | 1.06460i | 0.120030 | + | 0.0692995i | ||||
\(237\) | −2.92684 | − | 5.06943i | −0.190119 | − | 0.329295i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.65409i | − | 0.559787i | −0.960031 | − | 0.279893i | \(-0.909701\pi\) | ||
0.960031 | − | 0.279893i | \(-0.0902991\pi\) | |||||||
\(240\) | 26.2074i | 1.69168i | ||||||||
\(241\) | −15.7601 | + | 9.09909i | −1.01520 | + | 0.586124i | −0.912709 | − | 0.408611i | \(-0.866013\pi\) |
−0.102487 | + | 0.994734i | \(0.532680\pi\) | |||||||
\(242\) | 10.9102 | + | 6.29902i | 0.701336 | + | 0.404916i | ||||
\(243\) | 11.8302 | 0.758905 | ||||||||
\(244\) | −0.725669 | − | 1.25690i | −0.0464562 | − | 0.0804645i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.5797 | −0.738297 | ||||||||
\(247\) | 0.447846 | + | 3.37360i | 0.0284957 | + | 0.214657i | ||||
\(248\) | 7.59057 | − | 13.1473i | 0.482002 | − | 0.834851i | ||||
\(249\) | 4.76614i | 0.302042i | ||||||||
\(250\) | 6.54894 | − | 11.3431i | 0.414191 | − | 0.717400i | ||||
\(251\) | −7.93598 | + | 13.7455i | −0.500915 | + | 0.867610i | 0.499085 | + | 0.866553i | \(0.333670\pi\) |
−0.999999 | + | 0.00105678i | \(0.999664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.82413 | + | 1.05316i | 0.114682 | + | 0.0662117i | ||||
\(254\) | 19.7968i | 1.24216i | ||||||||
\(255\) | 49.0230 | + | 28.3034i | 3.06994 | + | 1.77243i | ||||
\(256\) | 2.26304 | + | 3.91971i | 0.141440 | + | 0.244982i | ||||
\(257\) | 12.1634 | − | 21.0676i | 0.758730 | − | 1.31416i | −0.184769 | − | 0.982782i | \(-0.559154\pi\) |
0.943499 | − | 0.331376i | \(-0.107513\pi\) | |||||||
\(258\) | −9.14900 | + | 5.28218i | −0.569592 | + | 0.328854i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.26344 | + | 0.934688i | 0.140372 | + | 0.0579669i | ||||
\(261\) | −2.43282 | − | 4.21376i | −0.150588 | − | 0.260825i | ||||
\(262\) | 15.0486i | 0.929708i | ||||||||
\(263\) | 15.4345 | 0.951734 | 0.475867 | − | 0.879517i | \(-0.342134\pi\) | ||||
0.475867 | + | 0.879517i | \(0.342134\pi\) | |||||||
\(264\) | −7.72409 | −0.475385 | ||||||||
\(265\) | − | 0.285395i | − | 0.0175317i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.4512 | + | 7.76606i | 0.823201 | + | 0.475275i | ||||
\(268\) | −1.04210 | + | 0.601656i | −0.0636563 | + | 0.0367520i | ||||
\(269\) | −6.52035 | − | 11.2936i | −0.397553 | − | 0.688582i | 0.595870 | − | 0.803081i | \(-0.296807\pi\) |
−0.993423 | + | 0.114499i | \(0.963474\pi\) | |||||||
\(270\) | 17.6822 | 1.07610 | ||||||||
\(271\) | −23.3572 | − | 13.4853i | −1.41885 | − | 0.819174i | −0.422654 | − | 0.906291i | \(-0.638901\pi\) |
−0.996198 | + | 0.0871168i | \(0.972235\pi\) | |||||||
\(272\) | −27.7298 | −1.68136 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.7174 | −1.43282 | ||||||||
\(275\) | 8.55884 | + | 4.94145i | 0.516117 | + | 0.297980i | ||||
\(276\) | 0.642883 | 0.0386970 | ||||||||
\(277\) | 6.35073 | + | 10.9998i | 0.381578 | + | 0.660913i | 0.991288 | − | 0.131712i | \(-0.0420474\pi\) |
−0.609710 | + | 0.792625i | \(0.708714\pi\) | |||||||
\(278\) | −6.82352 | + | 3.93956i | −0.409248 | + | 0.236279i | ||||
\(279\) | 5.36737 | + | 3.09885i | 0.321336 | + | 0.185523i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 26.7216i | − | 1.59408i | −0.603930 | − | 0.797038i | \(-0.706399\pi\) | ||
0.603930 | − | 0.797038i | \(-0.293601\pi\) | |||||||
\(282\) | −2.46612 | −0.146855 | ||||||||
\(283\) | 14.7423 | 0.876336 | 0.438168 | − | 0.898893i | \(-0.355627\pi\) | ||||
0.438168 | + | 0.898893i | \(0.355627\pi\) | |||||||
\(284\) | − | 2.17474i | − | 0.129047i | ||||||
\(285\) | 3.45191 | + | 5.97888i | 0.204473 | + | 0.354158i | ||||
\(286\) | 2.36719 | − | 5.73238i | 0.139975 | − | 0.338963i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.11791 | + | 0.645425i | −0.0658734 | + | 0.0380320i | ||||
\(289\) | −21.4476 | + | 37.1483i | −1.26162 | + | 2.18519i | ||||
\(290\) | −9.70653 | − | 16.8122i | −0.569987 | − | 0.987247i | ||||
\(291\) | −0.849651 | − | 0.490546i | −0.0498074 | − | 0.0287563i | ||||
\(292\) | − | 0.144775i | − | 0.00847230i | ||||||
\(293\) | 10.0312 | + | 5.79153i | 0.586030 | + | 0.338345i | 0.763526 | − | 0.645777i | \(-0.223466\pi\) |
−0.177496 | + | 0.984121i | \(0.556800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.9523 | + | 34.5584i | −1.16167 | + | 2.01207i | ||||
\(296\) | 1.55589 | − | 2.69489i | 0.0904344 | − | 0.156637i | ||||
\(297\) | 4.71087i | 0.273353i | ||||||||
\(298\) | −7.04829 | + | 12.2080i | −0.408297 | + | 0.707190i | ||||
\(299\) | −2.26697 | + | 5.48968i | −0.131102 | + | 0.317476i | ||||
\(300\) | 3.01641 | 0.174153 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.17074 | + | 5.49188i | 0.182455 | + | 0.316022i | ||||
\(303\) | −5.90093 | −0.339000 | ||||||||
\(304\) | −2.92885 | − | 1.69097i | −0.167981 | − | 0.0969838i | ||||
\(305\) | 23.5563 | − | 13.6002i | 1.34883 | − | 0.778746i | ||||
\(306\) | − | 12.5236i | − | 0.715927i | ||||||
\(307\) | 29.3335i | 1.67415i | 0.547086 | + | 0.837076i | \(0.315737\pi\) | ||||
−0.547086 | + | 0.837076i | \(0.684263\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.6191 | − | 20.1248i | −0.660986 | − | 1.14486i | ||||
\(310\) | 21.4149 | + | 12.3639i | 1.21628 | + | 0.702222i | ||||
\(311\) | 0.0753271 | − | 0.130470i | 0.00427141 | − | 0.00739830i | −0.863882 | − | 0.503695i | \(-0.831974\pi\) |
0.868153 | + | 0.496296i | \(0.165307\pi\) | |||||||
\(312\) | −2.86616 | − | 21.5907i | −0.162264 | − | 1.22233i | ||||
\(313\) | −5.26057 | − | 9.11157i | −0.297345 | − | 0.515016i | 0.678183 | − | 0.734893i | \(-0.262768\pi\) |
−0.975528 | + | 0.219877i | \(0.929434\pi\) | |||||||
\(314\) | 10.4874 | − | 6.05493i | 0.591841 | − | 0.341699i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.271777 | − | 0.470732i | 0.0152887 | − | 0.0264808i | ||||
\(317\) | −1.30489 | + | 0.753380i | −0.0732901 | + | 0.0423140i | −0.536197 | − | 0.844093i | \(-0.680140\pi\) |
0.462907 | + | 0.886407i | \(0.346806\pi\) | |||||||
\(318\) | −0.191051 | + | 0.110303i | −0.0107136 | + | 0.00618551i | ||||
\(319\) | 4.47910 | − | 2.58601i | 0.250782 | − | 0.144789i | ||||
\(320\) | −26.6018 | + | 15.3586i | −1.48709 | + | 0.858571i | ||||
\(321\) | −6.73671 | + | 11.6683i | −0.376006 | + | 0.651262i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.32619 | + | 3.65243i | −0.351999 | + | 0.203227i | ||||
\(324\) | 1.06241 | + | 1.84015i | 0.0590228 | + | 0.102231i | ||||
\(325\) | −10.6366 | + | 25.7576i | −0.590014 | + | 1.42878i | ||||
\(326\) | −8.09314 | + | 14.0177i | −0.448237 | + | 0.776370i | ||||
\(327\) | −10.3671 | − | 5.98542i | −0.573299 | − | 0.330995i | ||||
\(328\) | −6.18600 | − | 10.7145i | −0.341565 | − | 0.591607i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 12.5814i | − | 0.692582i | ||||||
\(331\) | − | 25.2509i | − | 1.38791i | −0.720017 | − | 0.693957i | \(-0.755866\pi\) | ||
0.720017 | − | 0.693957i | \(-0.244134\pi\) | |||||||
\(332\) | −0.383276 | + | 0.221284i | −0.0210350 | + | 0.0121446i | ||||
\(333\) | 1.10019 | + | 0.635193i | 0.0602899 | + | 0.0348084i | ||||
\(334\) | 26.1270 | 1.42960 | ||||||||
\(335\) | −11.2760 | − | 19.5306i | −0.616075 | − | 1.06707i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.1811 | 1.75302 | 0.876509 | − | 0.481386i | \(-0.159866\pi\) | ||||
0.876509 | + | 0.481386i | \(0.159866\pi\) | |||||||
\(338\) | 16.9018 | + | 4.48977i | 0.919335 | + | 0.244211i | ||||
\(339\) | 6.69598 | − | 11.5978i | 0.363676 | − | 0.629905i | ||||
\(340\) | 5.25634i | 0.285065i | ||||||||
\(341\) | −3.29398 | + | 5.70535i | −0.178379 | + | 0.308962i | ||||
\(342\) | 0.763694 | − | 1.32276i | 0.0412959 | − | 0.0715265i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.77495 | − | 5.64357i | −0.527030 | − | 0.304281i | ||||
\(345\) | 12.0487i | 0.648679i | ||||||||
\(346\) | 16.7521 | + | 9.67185i | 0.900600 | + | 0.519962i | ||||
\(347\) | −12.3819 | − | 21.4461i | −0.664695 | − | 1.15128i | −0.979368 | − | 0.202085i | \(-0.935228\pi\) |
0.314673 | − | 0.949200i | \(-0.398105\pi\) | |||||||
\(348\) | 0.789291 | − | 1.36709i | 0.0423104 | − | 0.0732838i | ||||
\(349\) | 10.0075 | − | 5.77782i | 0.535688 | − | 0.309280i | −0.207642 | − | 0.978205i | \(-0.566579\pi\) |
0.743330 | + | 0.668925i | \(0.233245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.1680 | + | 1.74805i | −0.702857 | + | 0.0933042i | ||||
\(352\) | −0.686067 | − | 1.18830i | −0.0365675 | − | 0.0633368i | ||||
\(353\) | − | 20.0884i | − | 1.06920i | −0.845106 | − | 0.534599i | \(-0.820463\pi\) | ||
0.845106 | − | 0.534599i | \(-0.179537\pi\) | |||||||
\(354\) | 30.8459 | 1.63944 | ||||||||
\(355\) | 40.7582 | 2.16322 | ||||||||
\(356\) | 1.44227i | 0.0764399i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.32136 | − | 3.64964i | −0.334094 | − | 0.192890i | ||||
\(359\) | −13.0346 | + | 7.52551i | −0.687938 | + | 0.397181i | −0.802839 | − | 0.596196i | \(-0.796678\pi\) |
0.114901 | + | 0.993377i | \(0.463345\pi\) | |||||||
\(360\) | −6.32292 | − | 10.9516i | −0.333247 | − | 0.577201i | ||||
\(361\) | 18.1091 | 0.953110 | ||||||||
\(362\) | 18.0461 | + | 10.4189i | 0.948481 | + | 0.547606i | ||||
\(363\) | −19.1992 | −1.00770 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.71331 | 0.142021 | ||||||||
\(366\) | −18.2087 | − | 10.5128i | −0.951787 | − | 0.549514i | ||||
\(367\) | −9.00355 | −0.469982 | −0.234991 | − | 0.971998i | \(-0.575506\pi\) | ||||
−0.234991 | + | 0.971998i | \(0.575506\pi\) | |||||||
\(368\) | −2.95112 | − | 5.11148i | −0.153838 | − | 0.266454i | ||||
\(369\) | 4.37418 | − | 2.52543i | 0.227711 | − | 0.131469i | ||||
\(370\) | 4.38956 | + | 2.53431i | 0.228202 | + | 0.131753i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.01075i | 0.104253i | ||||||||
\(373\) | −16.1391 | −0.835649 | −0.417824 | − | 0.908528i | \(-0.637207\pi\) | ||||
−0.417824 | + | 0.908528i | \(0.637207\pi\) | |||||||
\(374\) | 13.3122 | 0.688358 | ||||||||
\(375\) | 19.9610i | 1.03078i | ||||||||
\(376\) | −1.31742 | − | 2.28184i | −0.0679409 | − | 0.117677i | ||||
\(377\) | 8.89057 | + | 11.5606i | 0.457888 | + | 0.595400i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5668 | + | 7.83277i | −0.696878 | + | 0.402342i | −0.806183 | − | 0.591666i | \(-0.798471\pi\) |
0.109306 | + | 0.994008i | \(0.465137\pi\) | |||||||
\(380\) | −0.320534 | + | 0.555181i | −0.0164430 | + | 0.0284802i | ||||
\(381\) | −15.0850 | − | 26.1280i | −0.772829 | − | 1.33858i | ||||
\(382\) | 5.52935 | + | 3.19237i | 0.282906 | + | 0.163336i | ||||
\(383\) | − | 24.6328i | − | 1.25868i | −0.777131 | − | 0.629339i | \(-0.783326\pi\) | ||
0.777131 | − | 0.629339i | \(-0.216674\pi\) | |||||||
\(384\) | 16.7525 | + | 9.67207i | 0.854898 | + | 0.493576i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.1512 | − | 24.5106i | 0.720277 | − | 1.24756i | ||||
\(387\) | 2.30399 | − | 3.99062i | 0.117118 | − | 0.202855i | ||||
\(388\) | − | 0.0911013i | − | 0.00462497i | ||||||
\(389\) | −9.42834 | + | 16.3304i | −0.478036 | + | 0.827982i | −0.999683 | − | 0.0251791i | \(-0.991984\pi\) |
0.521647 | + | 0.853161i | \(0.325318\pi\) | |||||||
\(390\) | 35.1680 | − | 4.66854i | 1.78080 | − | 0.236401i | ||||
\(391\) | −12.7486 | −0.644724 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.4669 | − | 19.8613i | −0.578431 | − | 1.00187i | ||||
\(394\) | 7.81857 | 0.393894 | ||||||||
\(395\) | 8.82229 | + | 5.09355i | 0.443897 | + | 0.256284i | ||||
\(396\) | 0.253582 | − | 0.146406i | 0.0127430 | − | 0.00735716i | ||||
\(397\) | 14.5030i | 0.727884i | 0.931422 | + | 0.363942i | \(0.118569\pi\) | ||||
−0.931422 | + | 0.363942i | \(0.881431\pi\) | |||||||
\(398\) | − | 14.2839i | − | 0.715985i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.8467 | − | 23.9831i | −0.692333 | − | 1.19916i | ||||
\(401\) | 18.1770 | + | 10.4945i | 0.907714 | + | 0.524069i | 0.879695 | − | 0.475539i | \(-0.157747\pi\) |
0.0280189 | + | 0.999607i | \(0.491080\pi\) | |||||||
\(402\) | −8.71624 | + | 15.0970i | −0.434727 | + | 0.752968i | ||||
\(403\) | −17.1701 | − | 7.09041i | −0.855304 | − | 0.353198i | ||||
\(404\) | −0.273971 | − | 0.474532i | −0.0136306 | − | 0.0236089i | ||||
\(405\) | −34.4874 | + | 19.9113i | −1.71369 | + | 0.989401i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.675191 | + | 1.16947i | −0.0334680 | + | 0.0579683i | ||||
\(408\) | 40.4869 | − | 23.3751i | 2.00440 | − | 1.15724i | ||||
\(409\) | 18.5568 | − | 10.7138i | 0.917576 | − | 0.529763i | 0.0347148 | − | 0.999397i | \(-0.488948\pi\) |
0.882861 | + | 0.469635i | \(0.155614\pi\) | |||||||
\(410\) | 17.4522 | − | 10.0761i | 0.861905 | − | 0.497621i | ||||
\(411\) | 31.3025 | − | 18.0725i | 1.54404 | − | 0.891451i | ||||
\(412\) | 1.07891 | − | 1.86873i | 0.0531542 | − | 0.0920657i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.30850 | − | 1.33281i | 0.113457 | − | 0.0655043i | ||||
\(415\) | −4.14723 | − | 7.18321i | −0.203580 | − | 0.352610i | ||||
\(416\) | 3.06702 | − | 2.35866i | 0.150373 | − | 0.115643i | ||||
\(417\) | 6.00383 | − | 10.3989i | 0.294009 | − | 0.509238i | ||||
\(418\) | 1.40605 | + | 0.811784i | 0.0687722 | + | 0.0397056i | ||||
\(419\) | 3.98203 | + | 6.89708i | 0.194535 | + | 0.336944i | 0.946748 | − | 0.321976i | \(-0.104347\pi\) |
−0.752213 | + | 0.658920i | \(0.771014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.81786i | 0.137334i | 0.997640 | + | 0.0686670i | \(0.0218746\pi\) | ||||
−0.997640 | + | 0.0686670i | \(0.978125\pi\) | |||||||
\(422\) | 6.27614i | 0.305518i | ||||||||
\(423\) | 0.931562 | − | 0.537838i | 0.0452941 | − | 0.0261506i | ||||
\(424\) | −0.204122 | − | 0.117850i | −0.00991306 | − | 0.00572331i | ||||
\(425\) | −59.8165 | −2.90152 | ||||||||
\(426\) | −15.7528 | − | 27.2847i | −0.763227 | − | 1.32195i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.25110 | −0.0604742 | ||||||||
\(429\) | 1.24379 | + | 9.36943i | 0.0600508 | + | 0.452360i | ||||
\(430\) | 9.19253 | − | 15.9219i | 0.443303 | − | 0.767823i | ||||
\(431\) | − | 5.73626i | − | 0.276306i | −0.990411 | − | 0.138153i | \(-0.955883\pi\) | ||
0.990411 | − | 0.138153i | \(-0.0441166\pi\) | |||||||
\(432\) | 6.60028 | − | 11.4320i | 0.317556 | − | 0.550023i | ||||
\(433\) | 12.2628 | − | 21.2398i | 0.589314 | − | 1.02072i | −0.405009 | − | 0.914313i | \(-0.632732\pi\) |
0.994322 | − | 0.106409i | \(-0.0339351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.6215 | + | 14.7926i | 1.22846 | + | 0.709251i | ||||
\(436\) | − | 1.11158i | − | 0.0532349i | ||||||
\(437\) | −1.34652 | − | 0.777413i | −0.0644128 | − | 0.0371887i | ||||
\(438\) | −1.04868 | − | 1.81637i | −0.0501079 | − | 0.0867895i | ||||
\(439\) | −18.3211 | + | 31.7332i | −0.874420 | + | 1.51454i | −0.0170416 | + | 0.999855i | \(0.505425\pi\) |
−0.857379 | + | 0.514686i | \(0.827909\pi\) | |||||||
\(440\) | 11.6412 | − | 6.72108i | 0.554975 | − | 0.320415i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.93973 | + | 37.2108i | 0.234959 | + | 1.76994i | ||||
\(443\) | −13.5467 | − | 23.4635i | −0.643622 | − | 1.11479i | −0.984618 | − | 0.174721i | \(-0.944098\pi\) |
0.340996 | − | 0.940065i | \(-0.389236\pi\) | |||||||
\(444\) | 0.412158i | 0.0195602i | ||||||||
\(445\) | −27.0304 | −1.28136 | ||||||||
\(446\) | −32.5886 | −1.54312 | ||||||||
\(447\) | − | 21.4830i | − | 1.01611i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.7571 | + | 13.7162i | 1.12117 | + | 0.647307i | 0.941699 | − | 0.336456i | \(-0.109228\pi\) |
0.179470 | + | 0.983764i | \(0.442562\pi\) | |||||||
\(450\) | 10.8315 | − | 6.25358i | 0.510602 | − | 0.294796i | ||||
\(451\) | 2.68446 | + | 4.64962i | 0.126406 | + | 0.218942i | ||||
\(452\) | 1.24354 | 0.0584911 | ||||||||
\(453\) | −8.36953 | − | 4.83215i | −0.393235 | − | 0.227034i | ||||
\(454\) | 20.6832 | 0.970712 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.70169 | 0.267006 | ||||||||
\(457\) | −34.3500 | − | 19.8320i | −1.60682 | − | 0.927700i | −0.990075 | − | 0.140539i | \(-0.955116\pi\) |
−0.616748 | − | 0.787161i | \(-0.711550\pi\) | |||||||
\(458\) | −21.9964 | −1.02783 | ||||||||
\(459\) | −14.2563 | − | 24.6927i | −0.665429 | − | 1.15256i | ||||
\(460\) | −0.968913 | + | 0.559402i | −0.0451758 | + | 0.0260823i | ||||
\(461\) | 4.23988 | + | 2.44790i | 0.197471 | + | 0.114010i | 0.595475 | − | 0.803374i | \(-0.296964\pi\) |
−0.398004 | + | 0.917384i | \(0.630297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.71193i | − | 0.218982i | −0.993988 | − | 0.109491i | \(-0.965078\pi\) | ||
0.993988 | − | 0.109491i | \(-0.0349221\pi\) | |||||||
\(464\) | −14.4928 | −0.672810 | ||||||||
\(465\) | −37.6848 | −1.74759 | ||||||||
\(466\) | − | 39.1605i | − | 1.81408i | ||||||
\(467\) | −16.0081 | − | 27.7268i | −0.740765 | − | 1.28304i | −0.952147 | − | 0.305639i | \(-0.901130\pi\) |
0.211383 | − | 0.977403i | \(-0.432203\pi\) | |||||||
\(468\) | 0.503335 | + | 0.654496i | 0.0232667 | + | 0.0302541i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.71678 | − | 2.14588i | 0.171442 | − | 0.0989822i | ||||
\(471\) | −9.22761 | + | 15.9827i | −0.425186 | + | 0.736444i | ||||
\(472\) | 16.4781 | + | 28.5410i | 0.758467 | + | 1.31370i | ||||
\(473\) | 4.24191 | + | 2.44907i | 0.195043 | + | 0.112608i | ||||
\(474\) | − | 7.87452i | − | 0.361689i | ||||||
\(475\) | −6.31788 | − | 3.64763i | −0.289884 | − | 0.167365i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0481123 | − | 0.0833330i | 0.00220291 | − | 0.00381556i | ||||
\(478\) | 5.82086 | − | 10.0820i | 0.266240 | − | 0.461141i | ||||
\(479\) | 18.0245i | 0.823560i | 0.911283 | + | 0.411780i | \(0.135093\pi\) | ||||
−0.911283 | + | 0.411780i | \(0.864907\pi\) | |||||||
\(480\) | 3.92447 | − | 6.79738i | 0.179127 | − | 0.310257i | ||||
\(481\) | −3.51948 | − | 1.45337i | −0.160474 | − | 0.0662680i | ||||
\(482\) | −24.4807 | −1.11506 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.891390 | − | 1.54393i | −0.0405177 | − | 0.0701788i | ||||
\(485\) | 1.70739 | 0.0775284 | ||||||||
\(486\) | 13.7821 | + | 7.95712i | 0.625170 | + | 0.360942i | ||||
\(487\) | −15.2424 | + | 8.80020i | −0.690699 | + | 0.398775i | −0.803874 | − | 0.594800i | \(-0.797231\pi\) |
0.113175 | + | 0.993575i | \(0.463898\pi\) | |||||||
\(488\) | − | 22.4642i | − | 1.01691i | ||||||
\(489\) | − | 24.6676i | − | 1.11551i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.93180 | + | 3.34598i | 0.0871810 | + | 0.151002i | 0.906318 | − | 0.422595i | \(-0.138881\pi\) |
−0.819138 | + | 0.573597i | \(0.805547\pi\) | |||||||
\(492\) | 1.41914 | + | 0.819339i | 0.0639796 | + | 0.0369387i | ||||
\(493\) | −15.6519 | + | 27.1099i | −0.704926 | + | 1.22097i | ||||
\(494\) | −1.74739 | + | 4.23148i | −0.0786188 | + | 0.190383i | ||||
\(495\) | 2.74388 | + | 4.75254i | 0.123328 | + | 0.213611i | ||||
\(496\) | 15.9872 | − | 9.23023i | 0.717848 | − | 0.414450i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.20576 | + | 5.55255i | −0.143654 | + | 0.248816i | ||||
\(499\) | 10.9528 | − | 6.32363i | 0.490317 | − | 0.283084i | −0.234389 | − | 0.972143i | \(-0.575309\pi\) |
0.724706 | + | 0.689058i | \(0.241976\pi\) | |||||||
\(500\) | −1.60519 | + | 0.926757i | −0.0717863 | + | 0.0414458i | ||||
\(501\) | −34.4826 | + | 19.9085i | −1.54057 | + | 0.889448i | ||||
\(502\) | −18.4908 | + | 10.6757i | −0.825287 | + | 0.476480i | ||||
\(503\) | 11.0180 | − | 19.0837i | 0.491268 | − | 0.850902i | −0.508681 | − | 0.860955i | \(-0.669867\pi\) |
0.999949 | + | 0.0100533i | \(0.00320011\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.89351 | − | 5.13467i | 0.395756 | − | 0.228490i | ||||
\(506\) | 1.41674 | + | 2.45387i | 0.0629818 | + | 0.109088i | ||||
\(507\) | −25.7283 | + | 6.95339i | −1.14263 | + | 0.308811i | ||||
\(508\) | 1.40075 | − | 2.42617i | 0.0621482 | − | 0.107644i | ||||
\(509\) | 13.5708 | + | 7.83509i | 0.601514 | + | 0.347284i | 0.769637 | − | 0.638482i | \(-0.220437\pi\) |
−0.168123 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(510\) | 38.0745 | + | 65.9470i | 1.68597 | + | 2.92018i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.9600i | 1.10309i | ||||||||
\(513\) | − | 3.47743i | − | 0.153532i | ||||||
\(514\) | 28.3406 | − | 16.3625i | 1.25005 | − | 0.721718i | ||||
\(515\) | 35.0230 | + | 20.2206i | 1.54330 | + | 0.891025i | ||||
\(516\) | 1.49499 | 0.0658132 | ||||||||
\(517\) | 0.571705 | + | 0.990222i | 0.0251436 | + | 0.0435499i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.4795 | −1.29401 | ||||||||
\(520\) | 23.1067 | + | 30.0461i | 1.01330 | + | 1.31761i | ||||
\(521\) | −12.6207 | + | 21.8598i | −0.552925 | + | 0.957694i | 0.445137 | + | 0.895463i | \(0.353155\pi\) |
−0.998062 | + | 0.0622317i | \(0.980178\pi\) | |||||||
\(522\) | − | 6.54538i | − | 0.286483i | ||||||
\(523\) | −6.62383 | + | 11.4728i | −0.289640 | + | 0.501671i | −0.973724 | − | 0.227733i | \(-0.926869\pi\) |
0.684084 | + | 0.729403i | \(0.260202\pi\) | |||||||
\(524\) | 1.06479 | − | 1.84426i | 0.0465154 | − | 0.0805670i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.9812 | + | 10.3815i | 0.784019 | + | 0.452654i | ||||
\(527\) | − | 39.8738i | − | 1.73693i | ||||||
\(528\) | −8.13422 | − | 4.69629i | −0.353996 | − | 0.204380i | ||||
\(529\) | 10.1432 | + | 17.5686i | 0.441011 | + | 0.763853i | ||||
\(530\) | 0.191960 | − | 0.332485i | 0.00833822 | − | 0.0144422i | ||||
\(531\) | −11.6518 | + | 6.72720i | −0.505647 | + | 0.291935i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0007 | + | 9.22903i | −0.519807 | + | 0.399754i | ||||
\(534\) | 10.4471 | + | 18.0949i | 0.452091 | + | 0.783044i | ||||
\(535\) | − | 23.4477i | − | 1.01373i | ||||||
\(536\) | −18.6252 | −0.804485 | ||||||||
\(537\) | 11.1240 | 0.480036 | ||||||||
\(538\) | − | 17.5427i | − | 0.756320i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.16701 | − | 1.25112i | −0.0932532 | − | 0.0538398i | ||||
\(541\) | 12.4737 | − | 7.20170i | 0.536287 | − | 0.309625i | −0.207286 | − | 0.978280i | \(-0.566463\pi\) |
0.743573 | + | 0.668655i | \(0.233130\pi\) | |||||||
\(542\) | −18.1408 | − | 31.4208i | −0.779214 | − | 1.34964i | ||||
\(543\) | −31.7565 | −1.36280 | ||||||||
\(544\) | 7.19224 | + | 4.15244i | 0.308365 | + | 0.178034i | ||||
\(545\) | 20.8328 | 0.892377 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00679 | 0.0858042 | 0.0429021 | − | 0.999079i | \(-0.486340\pi\) | ||||
0.0429021 | + | 0.999079i | \(0.486340\pi\) | |||||||
\(548\) | 2.90665 | + | 1.67816i | 0.124166 | + | 0.0716873i | ||||
\(549\) | 9.17100 | 0.391409 | ||||||||
\(550\) | 6.64736 | + | 11.5136i | 0.283445 | + | 0.490940i | ||||
\(551\) | −3.30634 | + | 1.90892i | −0.140855 | + | 0.0813226i | ||||
\(552\) | 8.61757 | + | 4.97535i | 0.366788 | + | 0.211765i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 17.0863i | 0.725928i | ||||||||
\(555\) | −7.72451 | −0.327887 | ||||||||
\(556\) | 1.11499 | 0.0472863 | ||||||||
\(557\) | 8.57916i | 0.363511i | 0.983344 | + | 0.181755i | \(0.0581779\pi\) | ||||
−0.983344 | + | 0.181755i | \(0.941822\pi\) | |||||||
\(558\) | 4.16865 | + | 7.22032i | 0.176473 | + | 0.305661i | ||||
\(559\) | −5.27170 | + | 12.7659i | −0.222969 | + | 0.539942i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.5696 | + | 10.1438i | −0.741788 | + | 0.428272i | ||||
\(562\) | 17.9733 | − | 31.1306i | 0.758157 | − | 1.31317i | ||||
\(563\) | 6.38718 | + | 11.0629i | 0.269188 | + | 0.466247i | 0.968652 | − | 0.248421i | \(-0.0799115\pi\) |
−0.699465 | + | 0.714667i | \(0.746578\pi\) | |||||||
\(564\) | 0.302231 | + | 0.174493i | 0.0127262 | + | 0.00734750i | ||||
\(565\) | 23.3059i | 0.980487i | ||||||||
\(566\) | 17.1747 | + | 9.91583i | 0.721908 | + | 0.416794i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.8306 | − | 29.1515i | 0.706196 | − | 1.22317i | ||||
\(569\) | −2.89558 | + | 5.01530i | −0.121389 | + | 0.210252i | −0.920316 | − | 0.391176i | \(-0.872068\pi\) |
0.798927 | + | 0.601429i | \(0.205402\pi\) | |||||||
\(570\) | 9.28720i | 0.388998i | ||||||||
\(571\) | −22.0666 | + | 38.2204i | −0.923458 | + | 1.59948i | −0.129435 | + | 0.991588i | \(0.541316\pi\) |
−0.794023 | + | 0.607888i | \(0.792017\pi\) | |||||||
\(572\) | −0.695710 | + | 0.535030i | −0.0290891 | + | 0.0223707i | ||||
\(573\) | −9.73025 | −0.406487 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.36592 | − | 11.0261i | −0.265477 | − | 0.459820i | ||||
\(576\) | −10.3567 | −0.431529 | ||||||||
\(577\) | 10.3343 | + | 5.96649i | 0.430221 | + | 0.248388i | 0.699441 | − | 0.714691i | \(-0.253432\pi\) |
−0.269220 | + | 0.963079i | \(0.586766\pi\) | |||||||
\(578\) | −49.9729 | + | 28.8518i | −2.07860 | + | 1.20008i | ||||
\(579\) | 43.1324i | 1.79252i | ||||||||
\(580\) | 2.74719i | 0.114071i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.659895 | − | 1.14297i | −0.0273535 | − | 0.0473777i | ||||
\(583\) | 0.0885805 | + | 0.0511420i | 0.00366863 | + | 0.00211808i | ||||
\(584\) | 1.12043 | − | 1.94064i | 0.0463637 | − | 0.0803043i | ||||
\(585\) | −12.2663 | + | 9.43332i | −0.507150 | + | 0.390020i | ||||
\(586\) | 7.79091 | + | 13.4943i | 0.321840 | + | 0.557443i | ||||
\(587\) | −17.6250 | + | 10.1758i | −0.727462 | + | 0.420000i | −0.817493 | − | 0.575939i | \(-0.804637\pi\) |
0.0900312 | + | 0.995939i | \(0.471303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.43152 | − | 4.21152i | 0.100189 | − | 0.173533i | ||||
\(590\) | −46.4889 | + | 26.8404i | −1.91392 | + | 1.10500i | ||||
\(591\) | −10.3190 | + | 5.95769i | −0.424468 | + | 0.245067i | ||||
\(592\) | 3.27701 | − | 1.89199i | 0.134684 | − | 0.0777601i | ||||
\(593\) | 15.7443 | − | 9.09000i | 0.646543 | − | 0.373282i | −0.140588 | − | 0.990068i | \(-0.544899\pi\) |
0.787130 | + | 0.616787i | \(0.211566\pi\) | |||||||
\(594\) | −3.16859 | + | 5.48817i | −0.130009 | + | 0.225182i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.72759 | − | 0.997422i | 0.0707646 | − | 0.0408560i | ||||
\(597\) | 10.8842 | + | 18.8520i | 0.445460 | + | 0.771560i | ||||
\(598\) | −6.33344 | + | 4.87068i | −0.258994 | + | 0.199177i | ||||
\(599\) | 19.1341 | − | 33.1412i | 0.781797 | − | 1.35411i | −0.149096 | − | 0.988823i | \(-0.547636\pi\) |
0.930894 | − | 0.365290i | \(-0.119030\pi\) | |||||||
\(600\) | 40.4337 | + | 23.3444i | 1.65070 | + | 0.953031i | ||||
\(601\) | −13.4360 | − | 23.2718i | −0.548064 | − | 0.949275i | −0.998407 | − | 0.0564195i | \(-0.982032\pi\) |
0.450343 | − | 0.892856i | \(-0.351302\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7.60372i | − | 0.309648i | ||||||
\(604\) | − | 0.897398i | − | 0.0365146i | ||||||
\(605\) | 28.9358 | − | 16.7061i | 1.17641 | − | 0.679200i | ||||
\(606\) | −6.87459 | − | 3.96904i | −0.279261 | − | 0.161231i | ||||
\(607\) | 9.40209 | 0.381619 | 0.190810 | − | 0.981627i | \(-0.438889\pi\) | ||||
0.190810 | + | 0.981627i | \(0.438889\pi\) | |||||||
\(608\) | 0.506435 | + | 0.877171i | 0.0205386 | + | 0.0355740i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.5908 | 1.48152 | ||||||||
\(611\) | −2.55577 | + | 1.96549i | −0.103395 | + | 0.0795153i | ||||
\(612\) | −0.886124 | + | 1.53481i | −0.0358194 | + | 0.0620411i | ||||
\(613\) | − | 13.2894i | − | 0.536753i | −0.963314 | − | 0.268376i | \(-0.913513\pi\) | ||
0.963314 | − | 0.268376i | \(-0.0864871\pi\) | |||||||
\(614\) | −19.7301 | + | 34.1735i | −0.796242 | + | 1.37913i | ||||
\(615\) | −15.3557 | + | 26.5969i | −0.619204 | + | 1.07249i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.72211 | − | 5.61306i | −0.391397 | − | 0.225973i | 0.291368 | − | 0.956611i | \(-0.405890\pi\) |
−0.682765 | + | 0.730638i | \(0.739223\pi\) | |||||||
\(618\) | − | 31.2606i | − | 1.25748i | ||||||
\(619\) | −8.04109 | − | 4.64253i | −0.323199 | − | 0.186599i | 0.329619 | − | 0.944114i | \(-0.393080\pi\) |
−0.652817 | + | 0.757515i | \(0.726413\pi\) | |||||||
\(620\) | −1.74965 | − | 3.03048i | −0.0702675 | − | 0.121707i | ||||
\(621\) | 3.03444 | − | 5.25580i | 0.121768 | − | 0.210908i | ||||
\(622\) | 0.175512 | − | 0.101332i | 0.00703740 | − | 0.00406304i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 10.1089 | − | 24.4797i | 0.404681 | − | 0.979974i | ||||
\(625\) | 1.95363 | + | 3.38379i | 0.0781452 | + | 0.135351i | ||||
\(626\) | − | 14.1533i | − | 0.565680i | ||||||
\(627\) | −2.47429 | −0.0988137 | ||||||||
\(628\) | −1.71370 | −0.0683839 | ||||||||
\(629\) | − | 8.17322i | − | 0.325888i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.00894 | + | 5.20132i | 0.358640 | + | 0.207061i | 0.668484 | − | 0.743726i | \(-0.266943\pi\) |
−0.309844 | + | 0.950787i | \(0.600277\pi\) | |||||||
\(632\) | 7.28611 | − | 4.20664i | 0.289826 | − | 0.167331i | ||||
\(633\) | −4.78237 | − | 8.28331i | −0.190082 | − | 0.329232i | ||||
\(634\) | −2.02693 | −0.0804998 | ||||||||
\(635\) | 45.4704 | + | 26.2523i | 1.80444 | + | 1.04179i | ||||
\(636\) | 0.0312187 | 0.00123790 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.95754 | 0.275452 | ||||||||
\(639\) | 11.9011 | + | 6.87109i | 0.470800 | + | 0.271816i | ||||
\(640\) | −33.6644 | −1.33070 | ||||||||
\(641\) | 7.42955 | + | 12.8684i | 0.293449 | + | 0.508269i | 0.974623 | − | 0.223853i | \(-0.0718634\pi\) |
−0.681174 | + | 0.732122i | \(0.738530\pi\) | |||||||
\(642\) | −15.6965 | + | 9.06239i | −0.619492 | + | 0.357664i | ||||
\(643\) | −1.98945 | − | 1.14861i | −0.0784563 | − | 0.0452968i | 0.460259 | − | 0.887785i | \(-0.347757\pi\) |
−0.538715 | + | 0.842488i | \(0.681090\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.0185i | 1.10323i | ||||||||
\(646\) | −9.82669 | −0.386626 | ||||||||
\(647\) | 7.99865 | 0.314459 | 0.157230 | − | 0.987562i | \(-0.449744\pi\) | ||||
0.157230 | + | 0.987562i | \(0.449744\pi\) | |||||||
\(648\) | 32.8885i | 1.29198i | ||||||||
\(649\) | −7.15081 | − | 12.3856i | −0.280694 | − | 0.486176i | ||||
\(650\) | −29.7166 | + | 22.8533i | −1.16558 | + | 0.896380i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.98368 | − | 1.14528i | 0.0776871 | − | 0.0448526i | ||||
\(653\) | −1.99222 | + | 3.45062i | −0.0779615 | + | 0.135033i | −0.902370 | − | 0.430962i | \(-0.858174\pi\) |
0.824409 | + | 0.565995i | \(0.191508\pi\) | |||||||
\(654\) | −8.05175 | − | 13.9460i | −0.314848 | − | 0.545333i | ||||
\(655\) | 34.5645 | + | 19.9558i | 1.35055 | + | 0.779738i | ||||
\(656\) | − | 15.0445i | − | 0.587389i | ||||||
\(657\) | 0.792267 | + | 0.457415i | 0.0309093 | + | 0.0178455i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.7501 | − | 23.8159i | 0.535629 | − | 0.927737i | −0.463504 | − | 0.886095i | \(-0.653408\pi\) |
0.999133 | − | 0.0416417i | \(-0.0132588\pi\) | |||||||
\(660\) | −0.890211 | + | 1.54189i | −0.0346514 | + | 0.0600180i | ||||
\(661\) | 6.98621i | 0.271732i | 0.990727 | + | 0.135866i | \(0.0433817\pi\) | ||||
−0.990727 | + | 0.135866i | \(0.956618\pi\) | |||||||
\(662\) | 16.9841 | − | 29.4173i | 0.660105 | − | 1.14333i | ||||
\(663\) | −34.8739 | − | 45.3472i | −1.35439 | − | 1.76114i | ||||
\(664\) | −6.85019 | −0.265839 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.854479 | + | 1.48000i | 0.0331104 | + | 0.0573488i | ||||
\(667\) | −6.66296 | −0.257991 | ||||||||
\(668\) | −3.20195 | − | 1.84865i | −0.123887 | − | 0.0715263i | ||||
\(669\) | 43.0108 | − | 24.8323i | 1.66289 | − | 0.960071i | ||||
\(670\) | − | 30.3376i | − | 1.17204i | ||||||
\(671\) | 9.74849i | 0.376336i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.72783 | + | 4.72474i | 0.105150 | + | 0.182125i | 0.913800 | − | 0.406166i | \(-0.133134\pi\) |
−0.808649 | + | 0.588291i | \(0.799801\pi\) | |||||||
\(674\) | 37.4910 | + | 21.6455i | 1.44410 | + | 0.833752i | ||||
\(675\) | 14.2376 | − | 24.6603i | 0.548006 | − | 0.949174i | ||||
\(676\) | −1.75369 | − | 1.74614i | −0.0674497 | − | 0.0671594i | ||||
\(677\) | 16.8961 | + | 29.2649i | 0.649371 | + | 1.12474i | 0.983273 | + | 0.182135i | \(0.0583009\pi\) |
−0.333903 | + | 0.942607i | \(0.608366\pi\) | |||||||
\(678\) | 15.6016 | − | 9.00761i | 0.599177 | − | 0.345935i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −40.6795 | + | 70.4590i | −1.55999 | + | 2.70198i | ||||
\(681\) | −27.2979 | + | 15.7605i | −1.04606 | + | 0.603942i | ||||
\(682\) | −7.67498 | + | 4.43115i | −0.293890 | + | 0.169678i | ||||
\(683\) | −10.6511 | + | 6.14942i | −0.407553 | + | 0.235301i | −0.689738 | − | 0.724059i | \(-0.742274\pi\) |
0.282185 | + | 0.959360i | \(0.408941\pi\) | |||||||
\(684\) | −0.187187 | + | 0.108072i | −0.00715726 | + | 0.00413225i | ||||
\(685\) | −31.4514 | + | 54.4754i | −1.20170 | + | 2.08140i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.0311 | − | 16.7611i | 1.10760 | − | 0.639476i | ||||
\(688\) | −6.86265 | − | 11.8865i | −0.261636 | − | 0.453167i | ||||
\(689\) | −0.110085 | + | 0.266581i | −0.00419389 | + | 0.0101559i | ||||
\(690\) | −8.10410 | + | 14.0367i | −0.308518 | + | 0.534369i | ||||
\(691\) | −9.60393 | − | 5.54483i | −0.365351 | − | 0.210935i | 0.306075 | − | 0.952008i | \(-0.400984\pi\) |
−0.671425 | + | 0.741072i | \(0.734318\pi\) | |||||||
\(692\) | −1.36869 | − | 2.37064i | −0.0520297 | − | 0.0901181i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 33.3129i | − | 1.26454i | ||||||
\(695\) | 20.8968i | 0.792662i | ||||||||
\(696\) | 21.1602 | − | 12.2168i | 0.802075 | − | 0.463078i | ||||
\(697\) | −28.1419 | − | 16.2478i | −1.06595 | − | 0.615428i | ||||
\(698\) | 15.5449 | 0.588385 | ||||||||
\(699\) | 29.8400 | + | 51.6844i | 1.12865 | + | 1.95488i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.6470 | 0.402133 | 0.201066 | − | 0.979578i | \(-0.435559\pi\) | ||||
0.201066 | + | 0.979578i | \(0.435559\pi\) | |||||||
\(702\) | −16.5165 | − | 6.82050i | −0.623375 | − | 0.257423i | ||||
\(703\) | 0.498406 | − | 0.863265i | 0.0187977 | − | 0.0325587i | ||||
\(704\) | − | 11.0089i | − | 0.414912i | ||||||
\(705\) | −3.27029 | + | 5.66431i | −0.123166 | + | 0.213330i | ||||
\(706\) | 13.5117 | − | 23.4030i | 0.508521 | − | 0.880784i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.78027 | − | 2.18254i | −0.142071 | − | 0.0820248i | ||||
\(709\) | 40.7069i | 1.52878i | 0.644754 | + | 0.764391i | \(0.276960\pi\) | ||||
−0.644754 | + | 0.764391i | \(0.723040\pi\) | |||||||
\(710\) | 47.4833 | + | 27.4145i | 1.78202 | + | 1.02885i | ||||
\(711\) | 1.71736 | + | 2.97455i | 0.0644060 | + | 0.111554i | ||||
\(712\) | −11.1619 | + | 19.3329i | −0.418309 | + | 0.724532i | ||||
\(713\) | 7.35003 | − | 4.24354i | 0.275261 | − | 0.158922i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0273 | − | 13.0387i | −0.375001 | − | 0.487621i | ||||
\(716\) | 0.516470 | + | 0.894552i | 0.0193014 | + | 0.0334310i | ||||
\(717\) | 17.7418i | 0.662579i | ||||||||
\(718\) | −20.2470 | −0.755612 | ||||||||
\(719\) | −9.77537 | −0.364560 | −0.182280 | − | 0.983247i | \(-0.558348\pi\) | ||||
−0.182280 | + | 0.983247i | \(0.558348\pi\) | |||||||
\(720\) | − | 15.3775i | − | 0.573086i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.0971 | + | 12.1804i | 0.785153 | + | 0.453308i | ||||
\(723\) | 32.3098 | − | 18.6541i | 1.20161 | − | 0.693752i | ||||
\(724\) | −1.47441 | − | 2.55375i | −0.0547959 | − | 0.0949092i | ||||
\(725\) | −31.2627 | −1.16107 | ||||||||
\(726\) | −22.3671 | − | 12.9136i | −0.830120 | − | 0.479270i | ||||
\(727\) | 12.2091 | 0.452811 | 0.226406 | − | 0.974033i | \(-0.427303\pi\) | ||||
0.226406 | + | 0.974033i | \(0.427303\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.23219 | 0.341933 | ||||||||
\(730\) | 3.16101 | + | 1.82501i | 0.116994 | + | 0.0675467i | ||||
\(731\) | −29.6461 | −1.09650 | ||||||||
\(732\) | 1.48770 | + | 2.57677i | 0.0549869 | + | 0.0952400i | ||||
\(733\) | −19.3256 | + | 11.1577i | −0.713809 | + | 0.412118i | −0.812470 | − | 0.583003i | \(-0.801877\pi\) |
0.0986608 | + | 0.995121i | \(0.468544\pi\) | |||||||
\(734\) | −10.4891 | − | 6.05591i | −0.387161 | − | 0.223528i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.76768i | 0.0651576i | ||||||||
\(737\) | 8.08253 | 0.297724 | ||||||||
\(738\) | 6.79456 | 0.250111 | ||||||||
\(739\) | 42.3729i | 1.55871i | 0.626580 | + | 0.779357i | \(0.284454\pi\) | ||||
−0.626580 | + | 0.779357i | \(0.715546\pi\) | |||||||
\(740\) | −0.358637 | − | 0.621178i | −0.0131838 | − | 0.0228350i | ||||
\(741\) | −0.918130 | − | 6.91624i | −0.0337283 | − | 0.254074i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.8296 | + | 15.4901i | −0.984282 | + | 0.568276i | −0.903560 | − | 0.428461i | \(-0.859056\pi\) |
−0.0807220 | + | 0.996737i | \(0.525723\pi\) | |||||||
\(744\) | −15.5615 | + | 26.9532i | −0.570511 | + | 0.988153i | ||||
\(745\) | 18.6933 | + | 32.3778i | 0.684870 | + | 1.18623i | ||||
\(746\) | −18.8020 | − | 10.8553i | −0.688390 | − | 0.397442i | ||||
\(747\) | − | 2.79659i | − | 0.102322i | ||||||
\(748\) | −1.63146 | − | 0.941923i | −0.0596520 | − | 0.0344401i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.4260 | + | 23.2545i | −0.490248 | + | 0.849135i | ||||
\(751\) | 11.2830 | − | 19.5427i | 0.411722 | − | 0.713123i | −0.583356 | − | 0.812216i | \(-0.698261\pi\) |
0.995078 | + | 0.0990930i | \(0.0315941\pi\) | |||||||
\(752\) | − | 3.20400i | − | 0.116838i | ||||||
\(753\) | 16.2696 | − | 28.1798i | 0.592897 | − | 1.02693i | ||||
\(754\) | 2.58172 | + | 19.4480i | 0.0940206 | + | 0.708254i | ||||
\(755\) | 16.8187 | 0.612095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.1404 | − | 27.9560i | −0.586633 | − | 1.01608i | −0.994670 | − | 0.103112i | \(-0.967120\pi\) |
0.408037 | − | 0.912965i | \(-0.366213\pi\) | |||||||
\(758\) | −21.0737 | −0.765431 | ||||||||
\(759\) | −3.73966 | − | 2.15909i | −0.135741 | − | 0.0783701i | ||||
\(760\) | −8.59323 | + | 4.96130i | −0.311709 | + | 0.179965i | ||||
\(761\) | 29.7517i | 1.07850i | 0.842147 | + | 0.539249i | \(0.181292\pi\) | ||||
−0.842147 | + | 0.539249i | \(0.818708\pi\) | |||||||
\(762\) | − | 40.5855i | − | 1.47026i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.451761 | − | 0.782473i | −0.0163441 | − | 0.0283089i | ||||
\(765\) | −28.7649 | − | 16.6074i | −1.04000 | − | 0.600442i | ||||
\(766\) | 16.5684 | − | 28.6972i | 0.598639 | − | 1.03687i | ||||
\(767\) | 31.9672 | − | 24.5841i | 1.15427 | − | 0.887680i | ||||
\(768\) | −4.63947 | − | 8.03581i | −0.167413 | − | 0.289967i | ||||
\(769\) | 36.2090 | − | 20.9053i | 1.30573 | − | 0.753863i | 0.324349 | − | 0.945938i | \(-0.394855\pi\) |
0.981380 | + | 0.192075i | \(0.0615215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9361 | + | 43.1907i | −0.898053 | + | 1.55547i | ||||
\(772\) | −3.46856 | + | 2.00257i | −0.124836 | + | 0.0720742i | ||||
\(773\) | −35.8826 | + | 20.7168i | −1.29061 | + | 0.745132i | −0.978762 | − | 0.205001i | \(-0.934280\pi\) |
−0.311845 | + | 0.950133i | \(0.600947\pi\) | |||||||
\(774\) | 5.36829 | − | 3.09938i | 0.192959 | − | 0.111405i | ||||
\(775\) | 34.4864 | − | 19.9107i | 1.23879 | − | 0.715215i | ||||
\(776\) | 0.705044 | − | 1.22117i | 0.0253096 | − | 0.0438375i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.9680 | + | 12.6832i | −0.787592 | + | 0.454716i | ||||
\(779\) | −1.98159 | − | 3.43221i | −0.0709978 | − | 0.122972i | ||||
\(780\) | −4.64028 | − | 1.91621i | −0.166149 | − | 0.0686112i | ||||
\(781\) | −7.30376 | + | 12.6505i | −0.261349 | + | 0.452670i | ||||
\(782\) | −14.8521 | − | 8.57486i | −0.531110 | − | 0.306637i | ||||
\(783\) | −7.45098 | − | 12.9055i | −0.266276 | − | 0.461204i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 32.1175i | − | 1.14632i | ||||||
\(786\) | − | 30.8513i | − | 1.10043i | ||||||
\(787\) | −20.6657 | + | 11.9313i | −0.736651 | + | 0.425306i | −0.820851 | − | 0.571143i | \(-0.806500\pi\) |
0.0841992 | + | 0.996449i | \(0.473167\pi\) | |||||||
\(788\) | −0.958193 | − | 0.553213i | −0.0341342 | − | 0.0197074i | ||||
\(789\) | −31.6424 | −1.12650 | ||||||||
\(790\) | 6.85198 | + | 11.8680i | 0.243782 | + | 0.422243i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.53221 | 0.161045 | ||||||||
\(793\) | −27.2494 | + | 3.61735i | −0.967654 | + | 0.128456i | ||||
\(794\) | −9.75490 | + | 16.8960i | −0.346188 | + | 0.599616i | ||||
\(795\) | 0.585088i | 0.0207509i | ||||||||
\(796\) | −1.01067 | + | 1.75054i | −0.0358223 | + | 0.0620461i | ||||
\(797\) | −25.4115 | + | 44.0141i | −0.900123 | + | 1.55906i | −0.0727899 | + | 0.997347i | \(0.523190\pi\) |
−0.827333 | + | 0.561712i | \(0.810143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.99335 | − | 3.46026i | −0.212029 | − | 0.122415i | ||||
\(800\) | 8.29397i | 0.293236i | ||||||||
\(801\) | −7.89267 | − | 4.55683i | −0.278874 | − | 0.161008i | ||||
\(802\) | 14.1174 | + | 24.4521i | 0.498504 | + | 0.863434i | ||||
\(803\) | −0.486219 | + | 0.842156i | −0.0171583 | + | 0.0297190i | ||||
\(804\) | 2.13641 | − | 1.23346i | 0.0753454 | − | 0.0435007i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.2341 | − | 19.8092i | −0.536598 | − | 0.697748i | ||||
\(807\) | 13.3674 | + | 23.1530i | 0.470555 | + | 0.815025i | ||||
\(808\) | − | 8.48119i | − | 0.298367i | ||||||
\(809\) | 4.41176 | 0.155109 | 0.0775547 | − | 0.996988i | \(-0.475289\pi\) | ||||
0.0775547 | + | 0.996988i | \(0.475289\pi\) | |||||||
\(810\) | −53.5704 | −1.88227 | ||||||||
\(811\) | 17.6493i | 0.619750i | 0.950777 | + | 0.309875i | \(0.100287\pi\) | ||||
−0.950777 | + | 0.309875i | \(0.899713\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.8848 | + | 27.6463i | 1.67939 | + | 0.969598i | ||||
\(814\) | −1.57320 | + | 0.908285i | −0.0551405 | + | 0.0318354i | ||||
\(815\) | 21.4644 | + | 37.1775i | 0.751866 | + | 1.30227i | ||||
\(816\) | 56.8489 | 1.99011 | ||||||||
\(817\) | −3.13126 | − | 1.80783i | −0.109549 | − | 0.0632480i | ||||
\(818\) | 28.8249 | 1.00784 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.85178 | −0.0995884 | ||||||||
\(821\) | 3.08342 | + | 1.78022i | 0.107612 | + | 0.0621299i | 0.552840 | − | 0.833287i | \(-0.313544\pi\) |
−0.445228 | + | 0.895417i | \(0.646877\pi\) | |||||||
\(822\) | 48.6232 | 1.69593 | ||||||||
\(823\) | 10.9332 | + | 18.9369i | 0.381109 | + | 0.660100i | 0.991221 | − | 0.132215i | \(-0.0422091\pi\) |
−0.610112 | + | 0.792315i | \(0.708876\pi\) | |||||||
\(824\) | 28.9247 | − | 16.6997i | 1.00764 | − | 0.581760i | ||||
\(825\) | −17.5465 | − | 10.1305i | −0.610891 | − | 0.352698i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.1361i | − | 0.630653i | −0.948983 | − | 0.315327i | \(-0.897886\pi\) | ||
0.948983 | − | 0.315327i | \(-0.102114\pi\) | |||||||
\(828\) | −0.377220 | −0.0131093 | ||||||||
\(829\) | 30.8994 | 1.07318 | 0.536590 | − | 0.843843i | \(-0.319712\pi\) | ||||
0.536590 | + | 0.843843i | \(0.319712\pi\) | |||||||
\(830\) | − | 11.1579i | − | 0.387297i | ||||||
\(831\) | −13.0196 | − | 22.5507i | −0.451646 | − | 0.782275i | ||||
\(832\) | 30.7724 | − | 4.08504i | 1.06684 | − | 0.141623i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.9889 | − | 8.07651i | 0.484397 | − | 0.279667i | ||||
\(835\) | 34.6466 | − | 60.0097i | 1.19900 | − | 2.07672i | ||||
\(836\) | −0.114878 | − | 0.198974i | −0.00397313 | − | 0.00688165i | ||||
\(837\) | 16.4386 | + | 9.49084i | 0.568202 | + | 0.328051i | ||||
\(838\) | 10.7135i | 0.370090i | ||||||||
\(839\) | 13.3333 | + | 7.69796i | 0.460315 | + | 0.265763i | 0.712177 | − | 0.702000i | \(-0.247709\pi\) |
−0.251862 | + | 0.967763i | \(0.581043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.31965 | − | 10.9459i | 0.217919 | − | 0.377446i | ||||
\(842\) | −1.89533 | + | 3.28280i | −0.0653173 | + | 0.113133i | ||||
\(843\) | 54.7820i | 1.88679i | ||||||||
\(844\) | 0.444076 | − | 0.769163i | 0.0152857 | − | 0.0264757i | ||||
\(845\) | 32.7256 | − | 32.8671i | 1.12579 | − | 1.13066i | ||||
\(846\) | 1.44703 | 0.0497498 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.143307 | − | 0.248216i | −0.00492119 | − | 0.00852376i | ||||
\(849\) | −30.2231 | −1.03726 | ||||||||
\(850\) | −69.6862 | − | 40.2333i | −2.39022 | − | 1.37999i | ||||
\(851\) | 1.50659 | − | 0.869829i | 0.0516451 | − | 0.0298173i | ||||
\(852\) | 4.45845i | 0.152744i | ||||||||
\(853\) | − | 23.7772i | − | 0.814116i | −0.913402 | − | 0.407058i | \(-0.866555\pi\) | ||
0.913402 | − | 0.407058i | \(-0.133445\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.02545 | − | 3.50818i | −0.0692690 | − | 0.119977i | ||||
\(856\) | −16.7704 | − | 9.68242i | −0.573202 | − | 0.330938i | ||||
\(857\) | 15.0525 | − | 26.0717i | 0.514184 | − | 0.890592i | −0.485681 | − | 0.874136i | \(-0.661428\pi\) |
0.999865 | − | 0.0164561i | \(-0.00523837\pi\) | |||||||
\(858\) | −4.85299 | + | 11.7520i | −0.165678 | + | 0.401206i | ||||
\(859\) | −7.56717 | − | 13.1067i | −0.258188 | − | 0.447195i | 0.707568 | − | 0.706645i | \(-0.249792\pi\) |
−0.965757 | + | 0.259450i | \(0.916459\pi\) | |||||||
\(860\) | −2.25315 | + | 1.30086i | −0.0768318 | + | 0.0443589i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.85828 | − | 6.68274i | 0.131414 | − | 0.227615i | ||||
\(863\) | −15.8186 | + | 9.13287i | −0.538471 | + | 0.310886i | −0.744459 | − | 0.667668i | \(-0.767293\pi\) |
0.205988 | + | 0.978555i | \(0.433959\pi\) | |||||||
\(864\) | −3.42382 | + | 1.97674i | −0.116481 | + | 0.0672501i | ||||
\(865\) | 44.4296 | − | 25.6514i | 1.51065 | − | 0.872175i | ||||
\(866\) | 28.5724 | − | 16.4963i | 0.970929 | − | 0.560566i | ||||
\(867\) | 43.9697 | − | 76.1578i | 1.49329 | − | 2.58646i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.16186 | + | 1.82550i | −0.107259 | + | 0.0619259i | ||||
\(870\) | 19.8994 | + | 34.4668i | 0.674653 | + | 1.16853i | ||||
\(871\) | 2.99917 | + | 22.5926i | 0.101623 | + | 0.765521i | ||||
\(872\) | 8.60263 | − | 14.9002i | 0.291322 | − | 0.504584i | ||||
\(873\) | 0.498543 | + | 0.287834i | 0.0168731 | + | 0.00974171i | ||||
\(874\) | −1.04580 | − | 1.81137i | −0.0353746 | − | 0.0612706i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.296803i | 0.0100281i | ||||||||
\(877\) | − | 6.99639i | − | 0.236251i | −0.992999 | − | 0.118126i | \(-0.962311\pi\) | ||
0.992999 | − | 0.118126i | \(-0.0376886\pi\) | |||||||
\(878\) | −42.6883 | + | 24.6461i | −1.44066 | + | 0.831765i | ||||
\(879\) | −20.5650 | − | 11.8732i | −0.693641 | − | 0.400474i | ||||
\(880\) | 16.3458 | 0.551018 | ||||||||
\(881\) | −12.8873 | − | 22.3215i | −0.434184 | − | 0.752029i | 0.563045 | − | 0.826427i | \(-0.309630\pi\) |
−0.997229 | + | 0.0743977i | \(0.976297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.4526 | −0.553674 | −0.276837 | − | 0.960917i | \(-0.589286\pi\) | ||||
−0.276837 | + | 0.960917i | \(0.589286\pi\) | |||||||
\(884\) | 2.02752 | − | 4.90983i | 0.0681928 | − | 0.165136i | ||||
\(885\) | 40.9043 | − | 70.8484i | 1.37498 | − | 2.38154i | ||||
\(886\) | − | 36.4467i | − | 1.22445i | ||||||
\(887\) | 27.6227 | − | 47.8440i | 0.927481 | − | 1.60644i | 0.139958 | − | 0.990157i | \(-0.455303\pi\) |
0.787522 | − | 0.616286i | \(-0.211364\pi\) | |||||||
\(888\) | −3.18974 | + | 5.52479i | −0.107041 | + | 0.185400i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −31.4904 | − | 18.1810i | −1.05556 | − | 0.609429i | ||||
\(891\) | − | 14.2722i | − | 0.478137i | ||||||
\(892\) | 3.99385 | + | 2.30585i | 0.133724 | + | 0.0772056i | ||||
\(893\) | −0.422016 | − | 0.730953i | −0.0141222 | − | 0.0244604i | ||||
\(894\) | 14.4497 | − | 25.0277i | 0.483271 | − | 0.837050i | ||||
\(895\) | −16.7654 | + | 9.67949i | −0.560404 | + | 0.323550i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.64751 | − | 11.2544i | 0.155176 | − | 0.375774i | ||||
\(898\) | 18.4514 | + | 31.9587i | 0.615731 | + | 1.06648i | ||||
\(899\) | − | 20.8398i | − | 0.695046i | ||||||
\(900\) | −1.76992 | −0.0589973 | ||||||||
\(901\) | −0.619076 | −0.0206244 | ||||||||
\(902\) | 7.22241i | 0.240480i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.6691 | + | 9.62388i | 0.554405 | + | 0.320086i | ||||
\(905\) | 47.8614 | − | 27.6328i | 1.59097 | − | 0.918544i | ||||
\(906\) | −6.50034 | − | 11.2589i | −0.215959 | − | 0.374052i | ||||
\(907\) | −47.8424 | −1.58858 | −0.794290 | − | 0.607538i | \(-0.792157\pi\) | ||||
−0.794290 | + | 0.607538i | \(0.792157\pi\) | |||||||
\(908\) | −2.53480 | − | 1.46347i | −0.0841204 | − | 0.0485669i | ||||
\(909\) | 3.46245 | 0.114842 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.0711 | −0.764380 | −0.382190 | − | 0.924084i | \(-0.624830\pi\) | ||||
−0.382190 | + | 0.924084i | \(0.624830\pi\) | |||||||
\(912\) | 6.00444 | + | 3.46666i | 0.198827 | + | 0.114793i | ||||
\(913\) | 2.97269 | 0.0983817 | ||||||||
\(914\) | −26.6785 | − | 46.2085i | −0.882445 | − | 1.52844i | ||||
\(915\) | −48.2928 | + | 27.8819i | −1.59651 | + | 0.921746i | ||||
\(916\) | 2.69574 | + | 1.55638i | 0.0890697 | + | 0.0514244i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 38.3560i | − | 1.26594i | ||||||
\(919\) | −43.4368 | −1.43285 | −0.716424 | − | 0.697665i | \(-0.754222\pi\) | ||||
−0.716424 | + | 0.697665i | \(0.754222\pi\) | |||||||
\(920\) | −17.3171 | −0.570929 | ||||||||
\(921\) | − | 60.1367i | − | 1.98157i | ||||||
\(922\) | 3.29298 | + | 5.70360i | 0.108448 | + | 0.187838i | ||||
\(923\) | −38.0714 | − | 15.7216i | −1.25313 | − | 0.517482i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.06892 | − | 4.08124i | 0.232425 | − | 0.134190i | ||||
\(926\) | 3.16931 | − | 5.48940i | 0.104150 | − | 0.180393i | ||||
\(927\) | 6.81764 | + | 11.8085i | 0.223921 | + | 0.387842i | ||||
\(928\) | 3.75897 | + | 2.17024i | 0.123394 | + | 0.0712418i | ||||
\(929\) | − | 12.7819i | − | 0.419361i | −0.977770 | − | 0.209680i | \(-0.932758\pi\) | ||
0.977770 | − | 0.209680i | \(-0.0672424\pi\) | |||||||
\(930\) | −43.9027 | − | 25.3473i | −1.43963 | − | 0.831169i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.77085 | + | 4.79926i | −0.0907623 | + | 0.157205i | ||||
\(933\) | −0.154428 | + | 0.267478i | −0.00505576 | + | 0.00875683i | ||||
\(934\) | − | 43.0689i | − | 1.40926i | ||||||
\(935\) | 17.6532 | − | 30.5762i | 0.577320 | − | 0.999948i | ||||
\(936\) | 1.68175 | + | 12.6686i | 0.0549699 | + | 0.414086i | ||||
\(937\) | −16.2533 | −0.530971 | −0.265486 | − | 0.964115i | \(-0.585532\pi\) | ||||
−0.265486 | + | 0.964115i | \(0.585532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.7847 | + | 18.6797i | 0.351946 | + | 0.609588i | ||||
\(940\) | −0.607339 | −0.0198092 | ||||||||
\(941\) | 39.1000 | + | 22.5744i | 1.27462 | + | 0.735905i | 0.975855 | − | 0.218420i | \(-0.0700904\pi\) |
0.298770 | + | 0.954325i | \(0.403424\pi\) | |||||||
\(942\) | −21.5003 | + | 12.4132i | −0.700519 | + | 0.404445i | ||||
\(943\) | − | 6.91662i | − | 0.225236i | ||||||
\(944\) | 40.0752i | 1.30434i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.29455 | + | 5.70633i | 0.107115 | + | 0.185529i | ||||
\(947\) | 17.1956 | + | 9.92787i | 0.558781 | + | 0.322612i | 0.752656 | − | 0.658414i | \(-0.228772\pi\) |
−0.193875 | + | 0.981026i | \(0.562106\pi\) | |||||||
\(948\) | −0.557172 | + | 0.965050i | −0.0180961 | + | 0.0313434i | ||||
\(949\) | −2.53445 | − | 1.04660i | −0.0822716 | − | 0.0339741i | ||||
\(950\) | −4.90689 | − | 8.49898i | −0.159200 | − | 0.275743i | ||||
\(951\) | 2.67516 | − | 1.54451i | 0.0867482 | − | 0.0500841i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.86433 | − | 13.6214i | 0.254751 | − | 0.441241i | −0.710077 | − | 0.704124i | \(-0.751340\pi\) |
0.964828 | + | 0.262883i | \(0.0846733\pi\) | |||||||
\(954\) | 0.112102 | − | 0.0647220i | 0.00362943 | − | 0.00209545i | ||||
\(955\) | 14.6648 | − | 8.46673i | 0.474542 | − | 0.273977i | ||||
\(956\) | −1.42673 | + | 0.823724i | −0.0461438 | + | 0.0266412i | ||||
\(957\) | −9.18262 | + | 5.30159i | −0.296832 | + | 0.171376i | ||||
\(958\) | −12.1235 | + | 20.9985i | −0.391693 | + | 0.678432i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 54.5365 | − | 31.4867i | 1.76016 | − | 1.01623i | ||||
\(961\) | −2.22744 | − | 3.85804i | −0.0718529 | − | 0.124453i | ||||
\(962\) | −3.12264 | − | 4.06042i | −0.100678 | − | 0.130913i | ||||
\(963\) | 3.95285 | − | 6.84653i | 0.127379 | − | 0.220626i | ||||
\(964\) | 3.00019 | + | 1.73216i | 0.0966296 | + | 0.0557891i | ||||
\(965\) | −37.5315 | − | 65.0064i | −1.20818 | − | 2.09263i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.1912i | 1.67835i | 0.543858 | + | 0.839177i | \(0.316963\pi\) | ||||
−0.543858 | + | 0.839177i | \(0.683037\pi\) | |||||||
\(968\) | − | 27.5943i | − | 0.886915i | ||||||
\(969\) | 12.9693 | − | 7.48786i | 0.416635 | − | 0.240545i | ||||
\(970\) | 1.98910 | + | 1.14841i | 0.0638663 | + | 0.0368732i | ||||
\(971\) | 22.4584 | 0.720724 | 0.360362 | − | 0.932813i | \(-0.382653\pi\) | ||||
0.360362 | + | 0.932813i | \(0.382653\pi\) | |||||||
\(972\) | −1.12603 | − | 1.95035i | −0.0361175 | − | 0.0625574i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23.6765 | −0.758645 | ||||||||
\(975\) | 21.8062 | − | 52.8058i | 0.698357 | − | 1.69114i | ||||
\(976\) | 13.6584 | − | 23.6570i | 0.437193 | − | 0.757241i | ||||
\(977\) | 41.0345i | 1.31281i | 0.754409 | + | 0.656405i | \(0.227924\pi\) | ||||
−0.754409 | + | 0.656405i | \(0.772076\pi\) | |||||||
\(978\) | 16.5918 | − | 28.7378i | 0.530546 | − | 0.918933i | ||||
\(979\) | 4.84378 | − | 8.38967i | 0.154808 | − | 0.268135i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.08300 | + | 3.51202i | 0.194215 | + | 0.112130i | ||||
\(982\) | 5.19742i | 0.165856i | ||||||||
\(983\) | −23.2379 | − | 13.4164i | −0.741173 | − | 0.427916i | 0.0813229 | − | 0.996688i | \(-0.474085\pi\) |
−0.822496 | + | 0.568772i | \(0.807419\pi\) | |||||||
\(984\) | 12.6819 | + | 21.9658i | 0.404285 | + | 0.700243i | ||||
\(985\) | 10.3681 | − | 17.9581i | 0.330356 | − | 0.572193i | ||||
\(986\) | −36.4689 | + | 21.0553i | −1.16141 | + | 0.670539i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.513552 | − | 0.394943i | 0.0163383 | − | 0.0125648i | ||||
\(989\) | −3.15506 | − | 5.46473i | −0.100325 | − | 0.173768i | ||||
\(990\) | 7.38228i | 0.234624i | ||||||||
\(991\) | 10.3751 | 0.329576 | 0.164788 | − | 0.986329i | \(-0.447306\pi\) | ||||
0.164788 | + | 0.986329i | \(0.447306\pi\) | |||||||
\(992\) | −5.52879 | −0.175539 | ||||||||
\(993\) | 51.7669i | 1.64277i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.8079 | − | 18.9417i | −1.04008 | − | 0.600491i | ||||
\(996\) | 0.785755 | − | 0.453656i | 0.0248976 | − | 0.0143746i | ||||
\(997\) | −26.9549 | − | 46.6872i | −0.853669 | − | 1.47860i | −0.877874 | − | 0.478891i | \(-0.841039\pi\) |
0.0242056 | − | 0.999707i | \(-0.492294\pi\) | |||||||
\(998\) | 17.0134 | 0.538550 | ||||||||
\(999\) | 3.36954 | + | 1.94540i | 0.106607 | + | 0.0615499i |
(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 | 637.2.u.g.361.5 | 12 | ||
7.2 | even | 3 | 637.2.k.i.569.2 | 12 | |||
7.3 | odd | 6 | 637.2.q.g.491.2 | 12 | |||
7.4 | even | 3 | 637.2.q.i.491.2 | 12 | |||
7.5 | odd | 6 | 91.2.k.b.23.2 | yes | 12 | ||
7.6 | odd | 2 | 91.2.u.b.88.5 | yes | 12 | ||
13.4 | even | 6 | 637.2.k.i.459.5 | 12 | |||
21.5 | even | 6 | 819.2.bm.f.478.5 | 12 | |||
21.20 | even | 2 | 819.2.do.e.361.2 | 12 | |||
91.4 | even | 6 | 637.2.q.i.589.2 | 12 | |||
91.11 | odd | 12 | 8281.2.a.co.1.9 | 12 | |||
91.17 | odd | 6 | 637.2.q.g.589.2 | 12 | |||
91.24 | even | 12 | 8281.2.a.cp.1.9 | 12 | |||
91.30 | even | 6 | inner | 637.2.u.g.30.5 | 12 | ||
91.41 | even | 12 | 1183.2.e.j.508.9 | 24 | |||
91.54 | even | 12 | 1183.2.e.j.170.9 | 24 | |||
91.67 | odd | 12 | 8281.2.a.co.1.4 | 12 | |||
91.69 | odd | 6 | 91.2.k.b.4.5 | ✓ | 12 | ||
91.76 | even | 12 | 1183.2.e.j.508.4 | 24 | |||
91.80 | even | 12 | 8281.2.a.cp.1.4 | 12 | |||
91.82 | odd | 6 | 91.2.u.b.30.5 | yes | 12 | ||
91.89 | even | 12 | 1183.2.e.j.170.4 | 24 | |||
273.173 | even | 6 | 819.2.do.e.667.2 | 12 | |||
273.251 | even | 6 | 819.2.bm.f.550.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.5 | ✓ | 12 | 91.69 | odd | 6 | ||
91.2.k.b.23.2 | yes | 12 | 7.5 | odd | 6 | ||
91.2.u.b.30.5 | yes | 12 | 91.82 | odd | 6 | ||
91.2.u.b.88.5 | yes | 12 | 7.6 | odd | 2 | ||
637.2.k.i.459.5 | 12 | 13.4 | even | 6 | |||
637.2.k.i.569.2 | 12 | 7.2 | even | 3 | |||
637.2.q.g.491.2 | 12 | 7.3 | odd | 6 | |||
637.2.q.g.589.2 | 12 | 91.17 | odd | 6 | |||
637.2.q.i.491.2 | 12 | 7.4 | even | 3 | |||
637.2.q.i.589.2 | 12 | 91.4 | even | 6 | |||
637.2.u.g.30.5 | 12 | 91.30 | even | 6 | inner | ||
637.2.u.g.361.5 | 12 | 1.1 | even | 1 | trivial | ||
819.2.bm.f.478.5 | 12 | 21.5 | even | 6 | |||
819.2.bm.f.550.2 | 12 | 273.251 | even | 6 | |||
819.2.do.e.361.2 | 12 | 21.20 | even | 2 | |||
819.2.do.e.667.2 | 12 | 273.173 | even | 6 | |||
1183.2.e.j.170.4 | 24 | 91.89 | even | 12 | |||
1183.2.e.j.170.9 | 24 | 91.54 | even | 12 | |||
1183.2.e.j.508.4 | 24 | 91.76 | even | 12 | |||
1183.2.e.j.508.9 | 24 | 91.41 | even | 12 | |||
8281.2.a.co.1.4 | 12 | 91.67 | odd | 12 | |||
8281.2.a.co.1.9 | 12 | 91.11 | odd | 12 | |||
8281.2.a.cp.1.4 | 12 | 91.80 | even | 12 | |||
8281.2.a.cp.1.9 | 12 | 91.24 | even | 12 |