Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
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([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (of order \(6\), 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: | \(5.08647060876\) |
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: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 \) |
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 | 589.2 | ||
Root | \(0.874681 + 1.11128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.i.491.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16500 | − | 0.672613i | −0.823779 | − | 0.475609i | 0.0279386 | − | 0.999610i | \(-0.491106\pi\) |
−0.851718 | + | 0.524000i | \(0.824439\pi\) | |||||||
\(3\) | 1.02505 | − | 1.77544i | 0.591814 | − | 1.02505i | −0.402174 | − | 0.915563i | \(-0.631745\pi\) |
0.993988 | − | 0.109489i | \(-0.0349213\pi\) | |||||||
\(4\) | −0.0951832 | − | 0.164862i | −0.0475916 | − | 0.0824311i | ||||
\(5\) | − | 3.56778i | − | 1.59556i | −0.602950 | − | 0.797779i | \(-0.706008\pi\) | ||
0.602950 | − | 0.797779i | \(-0.293992\pi\) | |||||||
\(6\) | −2.38837 | + | 1.37893i | −0.975048 | + | 0.562944i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.94654i | 1.04176i | ||||||||
\(9\) | −0.601462 | − | 1.04176i | −0.200487 | − | 0.347254i | ||||
\(10\) | −2.39973 | + | 4.15646i | −0.758862 | + | 1.31439i | ||||
\(11\) | 1.10736 | + | 0.639336i | 0.333882 | + | 0.192767i | 0.657563 | − | 0.753399i | \(-0.271587\pi\) |
−0.323681 | + | 0.946166i | \(0.604920\pi\) | |||||||
\(12\) | −0.390271 | −0.112661 | ||||||||
\(13\) | −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 | \(-0.554465\pi\) | |||||||
\(18\) | 1.61821i | 0.381415i | ||||||||
\(19\) | 0.817422 | − | 0.471939i | 0.187530 | − | 0.108270i | −0.403296 | − | 0.915070i | \(-0.632135\pi\) |
0.590826 | + | 0.806799i | \(0.298802\pi\) | |||||||
\(20\) | −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 | \(0.111728\pi\) | |||||||
\(24\) | 5.23141 | + | 3.02035i | 1.06786 | + | 0.616527i | ||||
\(25\) | −7.72903 | −1.54581 | ||||||||
\(26\) | 3.84480 | + | 2.95681i | 0.754027 | + | 0.579879i | ||||
\(27\) | 3.68419 | 0.709023 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.02242 | + | 3.50293i | −0.375554 | + | 0.650478i | −0.990410 | − | 0.138161i | \(-0.955881\pi\) |
0.614856 | + | 0.788639i | \(0.289214\pi\) | |||||||
\(30\) | 4.91970 | + | 8.52117i | 0.898210 | + | 1.55575i | ||||
\(31\) | 5.15220i | 0.925362i | 0.886525 | + | 0.462681i | \(0.153112\pi\) | ||||
−0.886525 | + | 0.462681i | \(0.846888\pi\) | |||||||
\(32\) | 0.929326 | − | 0.536547i | 0.164283 | − | 0.0948490i | ||||
\(33\) | 2.27021 | − | 1.31071i | 0.395192 | − | 0.228164i | ||||
\(34\) | 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 | 0.422933 | − | 0.906161i | \(-0.361000\pi\) |
−0.573292 | + | 0.819351i | \(0.694334\pi\) | |||||||
\(38\) | −1.26973 | −0.205977 | ||||||||
\(39\) | −4.50614 | + | 5.85942i | −0.721559 | + | 0.938257i | ||||
\(40\) | 10.5126 | 1.66219 | ||||||||
\(41\) | 3.63629 | + | 2.09941i | 0.567893 | + | 0.327873i | 0.756307 | − | 0.654217i | \(-0.227002\pi\) |
−0.188415 | + | 0.982090i | \(0.560335\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.91532 | + | 3.31744i | 0.292084 | + | 0.505904i | 0.974302 | − | 0.225244i | \(-0.0723180\pi\) |
−0.682218 | + | 0.731148i | \(0.738985\pi\) | |||||||
\(44\) | − | 0.243416i | − | 0.0366964i | ||||||
\(45\) | −3.71678 | + | 2.14588i | −0.554064 | + | 0.319889i | ||||
\(46\) | −1.91908 | + | 1.10798i | −0.282952 | + | 0.163363i | ||||
\(47\) | − | 0.894217i | − | 0.130435i | −0.997871 | − | 0.0652175i | \(-0.979226\pi\) | ||
0.997871 | − | 0.0652175i | \(-0.0207741\pi\) | |||||||
\(48\) | −3.67279 | − | 6.36146i | −0.530121 | − | 0.918197i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.00432 | + | 5.19865i | 1.27340 | + | 0.735200i | ||||
\(51\) | −15.8662 | −2.22171 | ||||||||
\(52\) | 0.261981 | + | 0.634412i | 0.0363302 | + | 0.0879770i | ||||
\(53\) | −0.0799923 | −0.0109878 | −0.00549389 | − | 0.999985i | \(-0.501749\pi\) | ||||
−0.00549389 | + | 0.999985i | \(0.501749\pi\) | |||||||
\(54\) | −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 | ||||||
\(58\) | 4.71224 | − | 2.72061i | 0.618747 | − | 0.357234i | ||||
\(59\) | 9.68627 | − | 5.59237i | 1.26104 | − | 0.728064i | 0.287768 | − | 0.957700i | \(-0.407087\pi\) |
0.973277 | + | 0.229636i | \(0.0737535\pi\) | |||||||
\(60\) | 1.39240i | 0.179758i | ||||||||
\(61\) | −3.81196 | − | 6.60251i | −0.488072 | − | 0.845365i | 0.511834 | − | 0.859084i | \(-0.328966\pi\) |
−0.999906 | + | 0.0137195i | \(0.995633\pi\) | |||||||
\(62\) | 3.46543 | − | 6.00231i | 0.440111 | − | 0.762294i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.60961 | −1.07620 | ||||||||
\(65\) | −1.69282 | + | 12.7519i | −0.209968 | + | 1.58168i | ||||
\(66\) | −3.52639 | −0.434069 | ||||||||
\(67\) | −5.47418 | − | 3.16052i | −0.668777 | − | 0.386119i | 0.126836 | − | 0.991924i | \(-0.459518\pi\) |
−0.795613 | + | 0.605805i | \(0.792851\pi\) | |||||||
\(68\) | −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 | 0.219487 | − | 0.975616i | \(-0.429562\pi\) |
0.954651 | + | 0.297727i | \(0.0962285\pi\) | |||||||
\(72\) | 3.06959 | − | 1.77223i | 0.361755 | − | 0.208859i | ||||
\(73\) | 0.760506i | 0.0890105i | 0.999009 | + | 0.0445052i | \(0.0141711\pi\) | ||||
−0.999009 | + | 0.0445052i | \(0.985829\pi\) | |||||||
\(74\) | 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 | ||||
\(79\) | −2.85531 | −0.321247 | −0.160624 | − | 0.987016i | \(-0.551351\pi\) | ||||
−0.160624 | + | 0.987016i | \(0.551351\pi\) | |||||||
\(80\) | −11.0708 | − | 6.39172i | −1.23775 | − | 0.714616i | ||||
\(81\) | 5.58087 | − | 9.66636i | 0.620097 | − | 1.07404i | ||||
\(82\) | −2.82418 | − | 4.89163i | −0.311879 | − | 0.540190i | ||||
\(83\) | 2.32483i | 0.255183i | 0.991827 | + | 0.127591i | \(0.0407246\pi\) | ||||
−0.991827 | + | 0.127591i | \(0.959275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.9125 | + | 13.8059i | −2.59367 | + | 1.49746i | ||||
\(86\) | − | 5.15308i | − | 0.555671i | ||||||
\(87\) | 4.14617 | + | 7.18137i | 0.444516 | + | 0.769924i | ||||
\(88\) | −1.88383 | + | 3.26289i | −0.200817 | + | 0.347825i | ||||
\(89\) | 6.56124 | + | 3.78813i | 0.695490 | + | 0.401541i | 0.805665 | − | 0.592371i | \(-0.201808\pi\) |
−0.110176 | + | 0.993912i | \(0.535141\pi\) | |||||||
\(90\) | 5.77339 | 0.608569 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.313586 | −0.0326936 | ||||||||
\(93\) | 9.14742 | + | 5.28127i | 0.948544 | + | 0.547642i | ||||
\(94\) | −0.601462 | + | 1.04176i | −0.0620361 | + | 0.107450i | ||||
\(95\) | −1.68377 | − | 2.91638i | −0.172751 | − | 0.299214i | ||||
\(96\) | − | 2.19995i | − | 0.224532i | ||||||
\(97\) | 0.414443 | − | 0.239279i | 0.0420803 | − | 0.0242951i | −0.478812 | − | 0.877917i | \(-0.658933\pi\) |
0.520893 | + | 0.853622i | \(0.325599\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.53815i | − | 0.154589i | ||||||
\(100\) | 0.735674 | + | 1.27422i | 0.0735674 | + | 0.127422i | ||||
\(101\) | −1.43918 | + | 2.49273i | −0.143204 | + | 0.248036i | −0.928701 | − | 0.370829i | \(-0.879074\pi\) |
0.785498 | + | 0.618865i | \(0.212407\pi\) | |||||||
\(102\) | 18.4841 | + | 10.6718i | 1.83020 | + | 1.05666i | ||||
\(103\) | −11.3351 | −1.11688 | −0.558441 | − | 0.829544i | \(-0.688600\pi\) | ||||
−0.558441 | + | 0.829544i | \(0.688600\pi\) | |||||||
\(104\) | 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 | ||||
\(109\) | 5.83914i | 0.559288i | 0.960104 | + | 0.279644i | \(0.0902165\pi\) | ||||
−0.960104 | + | 0.279644i | \(0.909784\pi\) | |||||||
\(110\) | −5.31475 | + | 3.06847i | −0.506741 | + | 0.292567i | ||||
\(111\) | −1.87501 | + | 1.08254i | −0.177968 | + | 0.102750i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.26617 | − | 5.65717i | −0.307255 | − | 0.532181i | 0.670506 | − | 0.741904i | \(-0.266077\pi\) |
−0.977761 | + | 0.209723i | \(0.932744\pi\) | |||||||
\(114\) | −1.30154 | + | 2.25433i | −0.121900 | + | 0.211137i | ||||
\(115\) | −5.08973 | − | 2.93855i | −0.474619 | − | 0.274022i | ||||
\(116\) | 0.770001 | 0.0714928 | ||||||||
\(117\) | 1.65545 | + | 4.00884i | 0.153047 | + | 0.370618i | ||||
\(118\) | −15.0460 | −1.38510 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.7759 | − | 18.6645i | 0.983705 | − | 1.70383i | ||||
\(121\) | −4.68250 | − | 8.11033i | −0.425682 | − | 0.737302i | ||||
\(122\) | 10.2559i | 0.928525i | ||||||||
\(123\) | 7.45477 | − | 4.30401i | 0.672174 | − | 0.388080i | ||||
\(124\) | 0.849402 | − | 0.490402i | 0.0762786 | − | 0.0440394i | ||||
\(125\) | 9.73656i | 0.870865i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.35818 | − | 12.7447i | 0.652932 | − | 1.13091i | −0.329475 | − | 0.944164i | \(-0.606872\pi\) |
0.982408 | − | 0.186748i | \(-0.0597948\pi\) | |||||||
\(128\) | 8.17154 | + | 4.71784i | 0.722269 | + | 0.417002i | ||||
\(129\) | 7.85322 | 0.691437 | ||||||||
\(130\) | 10.5492 | − | 13.7174i | 0.925230 | − | 1.20309i | ||||
\(131\) | −11.1867 | −0.977386 | −0.488693 | − | 0.872456i | \(-0.662526\pi\) | ||||
−0.488693 | + | 0.872456i | \(0.662526\pi\) | |||||||
\(132\) | −0.432171 | − | 0.249514i | −0.0376157 | − | 0.0217174i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.25161 | + | 7.36400i | 0.367283 | + | 0.636153i | ||||
\(135\) | − | 13.1444i | − | 1.13129i | ||||||
\(136\) | 19.7487 | − | 11.4019i | 1.69344 | − | 0.977706i | ||||
\(137\) | 15.2687 | − | 8.81541i | 1.30450 | − | 0.753151i | 0.323324 | − | 0.946288i | \(-0.395200\pi\) |
0.981172 | + | 0.193137i | \(0.0618662\pi\) | |||||||
\(138\) | 4.54294i | 0.386721i | ||||||||
\(139\) | −2.92855 | − | 5.07240i | −0.248396 | − | 0.430235i | 0.714685 | − | 0.699447i | \(-0.246570\pi\) |
−0.963081 | + | 0.269212i | \(0.913237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.58763 | − | 0.916619i | −0.133703 | − | 0.0771932i | ||||
\(142\) | −15.3678 | −1.28964 | ||||||||
\(143\) | −3.65458 | − | 2.81053i | −0.305612 | − | 0.235028i | ||||
\(144\) | −4.31011 | −0.359176 | ||||||||
\(145\) | 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 | ||||||||
\(149\) | −9.07505 | + | 5.23948i | −0.743457 | + | 0.429235i | −0.823325 | − | 0.567570i | \(-0.807884\pi\) |
0.0798677 | + | 0.996805i | \(0.474550\pi\) | |||||||
\(150\) | 18.4598 | − | 10.6578i | 1.50724 | − | 0.870203i | ||||
\(151\) | 4.71406i | 0.383625i | 0.981432 | + | 0.191812i | \(0.0614365\pi\) | ||||
−0.981432 | + | 0.191812i | \(0.938564\pi\) | |||||||
\(152\) | 1.39059 | + | 2.40857i | 0.112791 | + | 0.195361i | ||||
\(153\) | −4.65483 | + | 8.06241i | −0.376321 | + | 0.651807i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.3819 | 1.47647 | ||||||||
\(156\) | 1.39490 | + | 0.185173i | 0.111682 | + | 0.0148257i | ||||
\(157\) | −9.00210 | −0.718445 | −0.359223 | − | 0.933252i | \(-0.616958\pi\) | ||||
−0.359223 | + | 0.933252i | \(0.616958\pi\) | |||||||
\(158\) | 3.32643 | + | 1.92052i | 0.264637 | + | 0.152788i | ||||
\(159\) | −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 | ||||
\(163\) | −10.4203 | + | 6.01619i | −0.816185 | + | 0.471224i | −0.849099 | − | 0.528234i | \(-0.822854\pi\) |
0.0329144 | + | 0.999458i | \(0.489521\pi\) | |||||||
\(164\) | − | 0.799315i | − | 0.0624160i | ||||||
\(165\) | −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 | 0.980672 | − | 0.195657i | \(-0.0626838\pi\) |
0.320893 | + | 0.947116i | \(0.396017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5497 | + | 3.39173i | 0.965365 | + | 0.260902i | ||||
\(170\) | 37.1440 | 2.84882 | ||||||||
\(171\) | −0.983297 | − | 0.567707i | −0.0751946 | − | 0.0434136i | ||||
\(172\) | 0.364613 | − | 0.631528i | 0.0278015 | − | 0.0481536i | ||||
\(173\) | −7.18976 | − | 12.4530i | −0.546627 | − | 0.946786i | −0.998503 | − | 0.0547049i | \(-0.982578\pi\) |
0.451875 | − | 0.892081i | \(-0.350755\pi\) | |||||||
\(174\) | − | 11.1551i | − | 0.845663i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.96771 | − | 2.29076i | 0.299077 | − | 0.172672i | ||||
\(177\) | − | 22.9299i | − | 1.72351i | ||||||
\(178\) | −5.09589 | − | 8.82635i | −0.381953 | − | 0.661563i | ||||
\(179\) | 2.71303 | − | 4.69911i | 0.202781 | − | 0.351228i | −0.746642 | − | 0.665226i | \(-0.768335\pi\) |
0.949424 | + | 0.313998i | \(0.101669\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | −1.88393 | + | 3.26307i | −0.138509 | + | 0.239905i | ||||
\(186\) | −7.10450 | − | 12.3054i | −0.520927 | − | 0.902272i | ||||
\(187\) | − | 9.89589i | − | 0.723659i | ||||||
\(188\) | −0.147423 | + | 0.0851144i | −0.0107519 | + | 0.00620761i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.53011i | 0.328649i | ||||||||
\(191\) | −2.37311 | − | 4.11035i | −0.171712 | − | 0.297414i | 0.767306 | − | 0.641281i | \(-0.221597\pi\) |
−0.939019 | + | 0.343866i | \(0.888263\pi\) | |||||||
\(192\) | −8.82529 | + | 15.2859i | −0.636911 | + | 1.10316i | ||||
\(193\) | −18.2204 | − | 10.5196i | −1.31154 | − | 0.757215i | −0.329185 | − | 0.944266i | \(-0.606774\pi\) |
−0.982350 | + | 0.187050i | \(0.940107\pi\) | |||||||
\(194\) | −0.643768 | −0.0462198 | ||||||||
\(195\) | 20.9051 | + | 16.0769i | 1.49704 | + | 1.15129i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.03342 | + | 2.90604i | 0.358616 | + | 0.207047i | 0.668474 | − | 0.743736i | \(-0.266948\pi\) |
−0.309857 | + | 0.950783i | \(0.600281\pi\) | |||||||
\(198\) | −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 | \(0.956155\pi\) | |||||||
\(200\) | − | 22.7739i | − | 1.61036i | ||||||
\(201\) | −11.2226 | + | 6.47939i | −0.791583 | + | 0.457021i | ||||
\(202\) | 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 | ||||
\(206\) | 13.2054 | + | 7.62414i | 0.920064 | + | 0.531199i | ||||
\(207\) | −1.98155 | −0.137727 | ||||||||
\(208\) | −7.87551 | + | 10.2407i | −0.546068 | + | 0.710063i | ||||
\(209\) | 1.20691 | 0.0834837 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.33275 | − | 4.04043i | 0.160593 | − | 0.278155i | −0.774489 | − | 0.632588i | \(-0.781993\pi\) |
0.935081 | + | 0.354433i | \(0.115326\pi\) | |||||||
\(212\) | 0.00761392 | + | 0.0131877i | 0.000522926 | + | 0.000905735i | ||||
\(213\) | − | 23.4203i | − | 1.60474i | ||||||
\(214\) | −7.65645 | + | 4.42046i | −0.523384 | + | 0.302176i | ||||
\(215\) | 11.8359 | − | 6.83344i | 0.807200 | − | 0.466037i | ||||
\(216\) | 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 | ||||
\(220\) | −0.868455 | −0.0585512 | ||||||||
\(221\) | 10.6506 | + | 25.7915i | 0.716438 | + | 1.73492i | ||||
\(222\) | 2.91252 | 0.195475 | ||||||||
\(223\) | −20.9798 | − | 12.1127i | −1.40491 | − | 0.811126i | −0.410020 | − | 0.912076i | \(-0.634478\pi\) |
−0.994891 | + | 0.100950i | \(0.967812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.64872 | + | 8.05182i | 0.309915 | + | 0.536788i | ||||
\(226\) | 8.78747i | 0.584534i | ||||||||
\(227\) | −13.3154 | + | 7.68764i | −0.883773 | + | 0.510247i | −0.871901 | − | 0.489683i | \(-0.837113\pi\) |
−0.0118726 | + | 0.999930i | \(0.503779\pi\) | |||||||
\(228\) | −0.319016 | + | 0.184184i | −0.0211274 | + | 0.0121979i | ||||
\(229\) | 16.3515i | 1.08054i | 0.841493 | + | 0.540268i | \(0.181677\pi\) | ||||
−0.841493 | + | 0.540268i | \(0.818323\pi\) | |||||||
\(230\) | 3.95302 | + | 6.84683i | 0.260654 | + | 0.451467i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.3215 | − | 5.95913i | −0.677641 | − | 0.391236i | ||||
\(233\) | 29.1107 | 1.90711 | 0.953554 | − | 0.301223i | \(-0.0973947\pi\) | ||||
0.953554 | + | 0.301223i | \(0.0973947\pi\) | |||||||
\(234\) | 0.767796 | − | 5.78378i | 0.0501924 | − | 0.378098i | ||||
\(235\) | −3.19037 | −0.208117 | ||||||||
\(236\) | −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 | \(0.0902991\pi\) | ||||
−0.960031 | + | 0.279893i | \(0.909701\pi\) | |||||||
\(240\) | −22.6963 | + | 13.1037i | −1.46504 | + | 0.845840i | ||||
\(241\) | 15.7601 | − | 9.09909i | 1.01520 | − | 0.586124i | 0.102487 | − | 0.994734i | \(-0.467320\pi\) |
0.912709 | + | 0.408611i | \(0.133987\pi\) | |||||||
\(242\) | 12.5980i | 0.809833i | ||||||||
\(243\) | −5.91508 | − | 10.2452i | −0.379453 | − | 0.657231i | ||||
\(244\) | −0.725669 | + | 1.25690i | −0.0464562 | + | 0.0804645i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.5797 | −0.738297 | ||||||||
\(247\) | −3.14555 | + | 1.29896i | −0.200147 | + | 0.0826506i | ||||
\(248\) | −15.1811 | −0.964003 | ||||||||
\(249\) | 4.12759 | + | 2.38307i | 0.261576 | + | 0.151021i | ||||
\(250\) | 6.54894 | − | 11.3431i | 0.414191 | − | 0.717400i | ||||
\(251\) | −7.93598 | − | 13.7455i | −0.500915 | − | 0.867610i | −0.999999 | − | 0.00105678i | \(-0.999664\pi\) |
0.499085 | − | 0.866553i | \(-0.333670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.82413 | − | 1.05316i | 0.114682 | − | 0.0662117i | ||||
\(254\) | −17.1446 | + | 9.89841i | −1.07574 | + | 0.621082i | ||||
\(255\) | 56.6069i | 3.54486i | ||||||||
\(256\) | 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 | ||||
\(261\) | 4.86563 | 0.301175 | ||||||||
\(262\) | 13.0325 | + | 7.52432i | 0.805150 | + | 0.464854i | ||||
\(263\) | −7.71727 | + | 13.3667i | −0.475867 | + | 0.824226i | −0.999618 | − | 0.0276456i | \(-0.991199\pi\) |
0.523751 | + | 0.851872i | \(0.324532\pi\) | |||||||
\(264\) | 3.86204 | + | 6.68925i | 0.237692 | + | 0.411695i | ||||
\(265\) | 0.285395i | 0.0175317i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.4512 | − | 7.76606i | 0.823201 | − | 0.475275i | ||||
\(268\) | 1.20331i | 0.0735040i | ||||||||
\(269\) | −6.52035 | − | 11.2936i | −0.397553 | − | 0.688582i | 0.595870 | − | 0.803081i | \(-0.296807\pi\) |
−0.993423 | + | 0.114499i | \(0.963474\pi\) | |||||||
\(270\) | −8.84108 | + | 15.3132i | −0.538051 | + | 0.931931i | ||||
\(271\) | 23.3572 | + | 13.4853i | 1.41885 | + | 0.819174i | 0.996198 | − | 0.0871168i | \(-0.0277653\pi\) |
0.422654 | + | 0.906291i | \(0.361099\pi\) | |||||||
\(272\) | −27.7298 | −1.68136 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.7174 | −1.43282 | ||||||||
\(275\) | −8.55884 | − | 4.94145i | −0.516117 | − | 0.297980i | ||||
\(276\) | −0.321442 | + | 0.556753i | −0.0193485 | + | 0.0335126i | ||||
\(277\) | 6.35073 | + | 10.9998i | 0.381578 | + | 0.660913i | 0.991288 | − | 0.131712i | \(-0.0420474\pi\) |
−0.609710 | + | 0.792625i | \(0.708714\pi\) | |||||||
\(278\) | 7.87912i | 0.472558i | ||||||||
\(279\) | 5.36737 | − | 3.09885i | 0.321336 | − | 0.185523i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.7216i | 1.59408i | 0.603930 | + | 0.797038i | \(0.293601\pi\) | ||||
−0.603930 | + | 0.797038i | \(0.706399\pi\) | |||||||
\(282\) | 1.23306 | + | 2.13572i | 0.0734276 | + | 0.127180i | ||||
\(283\) | −7.37113 | + | 12.7672i | −0.438168 | + | 0.758929i | −0.997548 | − | 0.0699819i | \(-0.977706\pi\) |
0.559380 | + | 0.828911i | \(0.311039\pi\) | |||||||
\(284\) | −1.88338 | − | 1.08737i | −0.111758 | − | 0.0645236i | ||||
\(285\) | −6.90382 | −0.408947 | ||||||||
\(286\) | 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 | ||||
\(291\) | − | 0.981092i | − | 0.0575126i | ||||||
\(292\) | 0.125379 | − | 0.0723874i | 0.00733723 | − | 0.00423615i | ||||
\(293\) | 10.0312 | − | 5.79153i | 0.586030 | − | 0.338345i | −0.177496 | − | 0.984121i | \(-0.556800\pi\) |
0.763526 | + | 0.645777i | \(0.223466\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.9523 | − | 34.5584i | −1.16167 | − | 2.01207i | ||||
\(296\) | 1.55589 | − | 2.69489i | 0.0904344 | − | 0.156637i | ||||
\(297\) | 4.07974 | + | 2.35544i | 0.236730 | + | 0.136676i | ||||
\(298\) | 14.0966 | 0.816593 | ||||||||
\(299\) | −3.62072 | + | 4.70809i | −0.209391 | + | 0.272276i | ||||
\(300\) | 3.01641 | 0.174153 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.17074 | − | 5.49188i | 0.182455 | − | 0.316022i | ||||
\(303\) | 2.95047 | + | 5.11036i | 0.169500 | + | 0.293582i | ||||
\(304\) | − | 3.38194i | − | 0.193968i | ||||||
\(305\) | −23.5563 | + | 13.6002i | −1.34883 | + | 0.778746i | ||||
\(306\) | 10.8458 | − | 6.26180i | 0.620011 | − | 0.357963i | ||||
\(307\) | − | 29.3335i | − | 1.67415i | −0.547086 | − | 0.837076i | \(-0.684263\pi\) | ||
0.547086 | − | 0.837076i | \(-0.315737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.6191 | + | 20.1248i | −0.660986 | + | 1.14486i | ||||
\(310\) | −21.4149 | − | 12.3639i | −1.21628 | − | 0.702222i | ||||
\(311\) | −0.150654 | −0.00854282 | −0.00427141 | − | 0.999991i | \(-0.501360\pi\) | ||||
−0.00427141 | + | 0.999991i | \(0.501360\pi\) | |||||||
\(312\) | −17.2650 | − | 13.2775i | −0.977438 | − | 0.751691i | ||||
\(313\) | 10.5211 | 0.594690 | 0.297345 | − | 0.954770i | \(-0.403899\pi\) | ||||
0.297345 | + | 0.954770i | \(0.403899\pi\) | |||||||
\(314\) | 10.4874 | + | 6.05493i | 0.591841 | + | 0.341699i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.271777 | + | 0.470732i | 0.0152887 | + | 0.0264808i | ||||
\(317\) | 1.50676i | 0.0846281i | 0.999104 | + | 0.0423140i | \(0.0134730\pi\) | ||||
−0.999104 | + | 0.0423140i | \(0.986527\pi\) | |||||||
\(318\) | 0.191051 | − | 0.110303i | 0.0107136 | − | 0.00618551i | ||||
\(319\) | −4.47910 | + | 2.58601i | −0.250782 | + | 0.144789i | ||||
\(320\) | 30.7172i | 1.71714i | ||||||||
\(321\) | −6.73671 | − | 11.6683i | −0.376006 | − | 0.651262i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.32619 | − | 3.65243i | −0.351999 | − | 0.203227i | ||||
\(324\) | −2.12482 | −0.118046 | ||||||||
\(325\) | 27.6251 | + | 3.66722i | 1.53236 | + | 0.203421i | ||||
\(326\) | 16.1863 | 0.896475 | ||||||||
\(327\) | 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 | ||||||||
\(331\) | 21.8679 | − | 12.6254i | 1.20197 | − | 0.693957i | 0.240976 | − | 0.970531i | \(-0.422533\pi\) |
0.960993 | + | 0.276574i | \(0.0891992\pi\) | |||||||
\(332\) | 0.383276 | − | 0.221284i | 0.0210350 | − | 0.0121446i | ||||
\(333\) | 1.27039i | 0.0696167i | ||||||||
\(334\) | −13.0635 | − | 22.6266i | −0.714802 | − | 1.23807i | ||||
\(335\) | −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 | \(0.159866\pi\) | |||||||
\(338\) | −12.3391 | − | 12.3925i | −0.671161 | − | 0.674062i | ||||
\(339\) | −13.3920 | −0.727351 | ||||||||
\(340\) | 4.55213 | + | 2.62817i | 0.246874 | + | 0.142533i | ||||
\(341\) | −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 | ||||
\(345\) | −10.4345 | + | 6.02434i | −0.561773 | + | 0.324340i | ||||
\(346\) | 19.3437i | 1.03992i | ||||||||
\(347\) | −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 | 0.743330 | − | 0.668925i | \(-0.233245\pi\) |
−0.207642 | + | 0.978205i | \(0.566579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.1680 | − | 1.74805i | −0.702857 | − | 0.0933042i | ||||
\(352\) | 1.37213 | 0.0731350 | ||||||||
\(353\) | −17.3971 | − | 10.0442i | −0.925953 | − | 0.534599i | −0.0404237 | − | 0.999183i | \(-0.512871\pi\) |
−0.885529 | + | 0.464583i | \(0.846204\pi\) | |||||||
\(354\) | −15.4229 | + | 26.7133i | −0.819719 | + | 1.41980i | ||||
\(355\) | −20.3791 | − | 35.2977i | −1.08161 | − | 1.87340i | ||||
\(356\) | − | 1.44227i | − | 0.0764399i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.32136 | + | 3.64964i | −0.334094 | + | 0.192890i | ||||
\(359\) | 15.0510i | 0.794363i | 0.917740 | + | 0.397181i | \(0.130012\pi\) | ||||
−0.917740 | + | 0.397181i | \(0.869988\pi\) | |||||||
\(360\) | −6.32292 | − | 10.9516i | −0.333247 | − | 0.577201i | ||||
\(361\) | −9.05455 | + | 15.6829i | −0.476555 | + | 0.825418i | ||||
\(362\) | −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 | ||||
\(367\) | 4.50178 | − | 7.79731i | 0.234991 | − | 0.407016i | −0.724279 | − | 0.689507i | \(-0.757827\pi\) |
0.959270 | + | 0.282491i | \(0.0911607\pi\) | |||||||
\(368\) | −2.95112 | − | 5.11148i | −0.153838 | − | 0.266454i | ||||
\(369\) | − | 5.05087i | − | 0.262938i | ||||||
\(370\) | 4.38956 | − | 2.53431i | 0.228202 | − | 0.131753i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 2.01075i | − | 0.104253i | ||||||
\(373\) | 8.06953 | + | 13.9768i | 0.417824 | + | 0.723693i | 0.995720 | − | 0.0924174i | \(-0.0294594\pi\) |
−0.577896 | + | 0.816110i | \(0.696126\pi\) | |||||||
\(374\) | −6.65611 | + | 11.5287i | −0.344179 | + | 0.596136i | ||||
\(375\) | 17.2867 | + | 9.98048i | 0.892681 | + | 0.515390i | ||||
\(376\) | 2.63484 | 0.135882 | ||||||||
\(377\) | 8.89057 | − | 11.5606i | 0.457888 | − | 0.595400i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5668 | − | 7.83277i | −0.696878 | − | 0.402342i | 0.109306 | − | 0.994008i | \(-0.465137\pi\) |
−0.806183 | + | 0.591666i | \(0.798471\pi\) | |||||||
\(380\) | −0.320534 | + | 0.555181i | −0.0164430 | + | 0.0284802i | ||||
\(381\) | −15.0850 | − | 26.1280i | −0.772829 | − | 1.33858i | ||||
\(382\) | 6.38474i | 0.326672i | ||||||||
\(383\) | 21.3327 | − | 12.3164i | 1.09005 | − | 0.629339i | 0.156459 | − | 0.987685i | \(-0.449992\pi\) |
0.933589 | + | 0.358345i | \(0.116659\pi\) | |||||||
\(384\) | 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 | ||||
\(388\) | −0.0788960 | − | 0.0455506i | −0.00400534 | − | 0.00231248i | ||||
\(389\) | 18.8567 | 0.956071 | 0.478036 | − | 0.878340i | \(-0.341349\pi\) | ||||
0.478036 | + | 0.878340i | \(0.341349\pi\) | |||||||
\(390\) | −13.5409 | − | 32.7906i | −0.685670 | − | 1.66042i | ||||
\(391\) | −12.7486 | −0.644724 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.4669 | + | 19.8613i | −0.578431 | + | 1.00187i | ||||
\(394\) | −3.90929 | − | 6.77108i | −0.196947 | − | 0.341122i | ||||
\(395\) | 10.1871i | 0.512569i | ||||||||
\(396\) | −0.253582 | + | 0.146406i | −0.0127430 | + | 0.00735716i | ||||
\(397\) | −12.5600 | + | 7.25149i | −0.630366 | + | 0.363942i | −0.780894 | − | 0.624664i | \(-0.785236\pi\) |
0.150528 | + | 0.988606i | \(0.451903\pi\) | |||||||
\(398\) | 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 | −0.0280189 | − | 0.999607i | \(-0.508920\pi\) |
−0.879695 | + | 0.475539i | \(0.842253\pi\) | |||||||
\(402\) | 17.4325 | 0.869453 | ||||||||
\(403\) | 2.44458 | − | 18.4150i | 0.121773 | − | 0.917314i | ||||
\(404\) | 0.547943 | 0.0272612 | ||||||||
\(405\) | −34.4874 | − | 19.9113i | −1.71369 | − | 0.989401i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.675191 | − | 1.16947i | −0.0334680 | − | 0.0579683i | ||||
\(408\) | − | 46.7502i | − | 2.31448i | ||||||
\(409\) | −18.5568 | + | 10.7138i | −0.917576 | + | 0.529763i | −0.882861 | − | 0.469635i | \(-0.844386\pi\) |
−0.0347148 | + | 0.999397i | \(0.511052\pi\) | |||||||
\(410\) | −17.4522 | + | 10.0761i | −0.861905 | + | 0.497621i | ||||
\(411\) | − | 36.1450i | − | 1.78290i | ||||||
\(412\) | 1.07891 | + | 1.86873i | 0.0531542 | + | 0.0920657i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.30850 | + | 1.33281i | 0.113457 | + | 0.0655043i | ||||
\(415\) | 8.29446 | 0.407159 | ||||||||
\(416\) | −3.57617 | + | 1.47678i | −0.175336 | + | 0.0724052i | ||||
\(417\) | −12.0077 | −0.588018 | ||||||||
\(418\) | −1.40605 | − | 0.811784i | −0.0687722 | − | 0.0397056i | ||||
\(419\) | 3.98203 | − | 6.89708i | 0.194535 | − | 0.336944i | −0.752213 | − | 0.658920i | \(-0.771014\pi\) |
0.946748 | + | 0.321976i | \(0.104347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.81786i | − | 0.137334i | −0.997640 | − | 0.0686670i | \(-0.978125\pi\) | ||
0.997640 | − | 0.0686670i | \(-0.0218746\pi\) | |||||||
\(422\) | −5.43530 | + | 3.13807i | −0.264586 | + | 0.152759i | ||||
\(423\) | −0.931562 | + | 0.537838i | −0.0452941 | + | 0.0261506i | ||||
\(424\) | − | 0.235700i | − | 0.0114466i | ||||||
\(425\) | 29.9082 | + | 51.8026i | 1.45076 | + | 2.51279i | ||||
\(426\) | −15.7528 | + | 27.2847i | −0.763227 | + | 1.32195i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.25110 | −0.0604742 | ||||||||
\(429\) | −8.73606 | + | 3.60756i | −0.421781 | + | 0.174175i | ||||
\(430\) | −18.3851 | −0.886606 | ||||||||
\(431\) | −4.96775 | − | 2.86813i | −0.239288 | − | 0.138153i | 0.375561 | − | 0.926797i | \(-0.377450\pi\) |
−0.614849 | + | 0.788645i | \(0.710783\pi\) | |||||||
\(432\) | 6.60028 | − | 11.4320i | 0.317556 | − | 0.550023i | ||||
\(433\) | 12.2628 | + | 21.2398i | 0.589314 | + | 1.02072i | 0.994322 | + | 0.106409i | \(0.0339351\pi\) |
−0.405009 | + | 0.914313i | \(0.632732\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.6215 | − | 14.7926i | 1.22846 | − | 0.709251i | ||||
\(436\) | 0.962653 | − | 0.555788i | 0.0461027 | − | 0.0266174i | ||||
\(437\) | − | 1.55483i | − | 0.0743774i | ||||||
\(438\) | −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 | ||||
\(443\) | 27.0933 | 1.28724 | 0.643622 | − | 0.765344i | \(-0.277431\pi\) | ||||
0.643622 | + | 0.765344i | \(0.277431\pi\) | |||||||
\(444\) | 0.356939 | + | 0.206079i | 0.0169396 | + | 0.00978008i | ||||
\(445\) | 13.5152 | − | 23.4090i | 0.640682 | − | 1.10969i | ||||
\(446\) | 16.2943 | + | 28.2226i | 0.771558 | + | 1.33638i | ||||
\(447\) | 21.4830i | 1.01611i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.7571 | − | 13.7162i | 1.12117 | − | 0.647307i | 0.179470 | − | 0.983764i | \(-0.442562\pi\) |
0.941699 | + | 0.336456i | \(0.109228\pi\) | |||||||
\(450\) | − | 12.5072i | − | 0.589593i | ||||||
\(451\) | 2.68446 | + | 4.64962i | 0.126406 | + | 0.218942i | ||||
\(452\) | −0.621768 | + | 1.07693i | −0.0292455 | + | 0.0506547i | ||||
\(453\) | 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 | \(0.0448835\pi\) |
0.616748 | + | 0.787161i | \(0.288450\pi\) | |||||||
\(458\) | 10.9982 | − | 19.0495i | 0.513913 | − | 0.890123i | ||||
\(459\) | −14.2563 | − | 24.6927i | −0.665429 | − | 1.15256i | ||||
\(460\) | 1.11880i | 0.0521645i | ||||||||
\(461\) | 4.23988 | − | 2.44790i | 0.197471 | − | 0.114010i | −0.398004 | − | 0.917384i | \(-0.630297\pi\) |
0.595475 | + | 0.803374i | \(0.296964\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.71193i | 0.218982i | 0.993988 | + | 0.109491i | \(0.0349221\pi\) | ||||
−0.993988 | + | 0.109491i | \(0.965078\pi\) | |||||||
\(464\) | 7.24638 | + | 12.5511i | 0.336405 | + | 0.582670i | ||||
\(465\) | 18.8424 | − | 32.6360i | 0.873794 | − | 1.51346i | ||||
\(466\) | −33.9140 | − | 19.5803i | −1.57104 | − | 0.907038i | ||||
\(467\) | 32.0161 | 1.48153 | 0.740765 | − | 0.671764i | \(-0.234463\pi\) | ||||
0.740765 | + | 0.671764i | \(0.234463\pi\) | |||||||
\(468\) | 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 | ||||
\(473\) | 4.89814i | 0.225217i | ||||||||
\(474\) | 6.81953 | − | 3.93726i | 0.313232 | − | 0.180844i | ||||
\(475\) | −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 | ||||
\(479\) | 15.6097 | + | 9.01224i | 0.713224 | + | 0.411780i | 0.812254 | − | 0.583305i | \(-0.198241\pi\) |
−0.0990298 | + | 0.995084i | \(0.531574\pi\) | |||||||
\(480\) | −7.84894 | −0.358253 | ||||||||
\(481\) | 3.01840 | + | 2.32127i | 0.137627 | + | 0.105841i | ||||
\(482\) | −24.4807 | −1.11506 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.891390 | + | 1.54393i | −0.0405177 | + | 0.0701788i | ||||
\(485\) | −0.853693 | − | 1.47864i | −0.0387642 | − | 0.0671416i | ||||
\(486\) | 15.9142i | 0.721885i | ||||||||
\(487\) | 15.2424 | − | 8.80020i | 0.690699 | − | 0.398775i | −0.113175 | − | 0.993575i | \(-0.536102\pi\) |
0.803874 | + | 0.594800i | \(0.202769\pi\) | |||||||
\(488\) | 19.4545 | − | 11.2321i | 0.880666 | − | 0.508453i | ||||
\(489\) | 24.6676i | 1.11551i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.93180 | − | 3.34598i | 0.0871810 | − | 0.151002i | −0.819138 | − | 0.573597i | \(-0.805547\pi\) |
0.906318 | + | 0.422595i | \(0.138881\pi\) | |||||||
\(492\) | −1.41914 | − | 0.819339i | −0.0639796 | − | 0.0369387i | ||||
\(493\) | 31.3038 | 1.40985 | ||||||||
\(494\) | 4.53826 | + | 0.602454i | 0.204186 | + | 0.0271057i | ||||
\(495\) | −5.48776 | −0.246656 | ||||||||
\(496\) | 15.9872 | + | 9.23023i | 0.717848 | + | 0.414450i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.20576 | − | 5.55255i | −0.143654 | − | 0.248816i | ||||
\(499\) | − | 12.6473i | − | 0.566169i | −0.959095 | − | 0.283084i | \(-0.908642\pi\) | ||
0.959095 | − | 0.283084i | \(-0.0913577\pi\) | |||||||
\(500\) | 1.60519 | − | 0.926757i | 0.0717863 | − | 0.0414458i | ||||
\(501\) | 34.4826 | − | 19.9085i | 1.54057 | − | 0.889448i | ||||
\(502\) | 21.3514i | 0.952959i | ||||||||
\(503\) | 11.0180 | + | 19.0837i | 0.491268 | + | 0.850902i | 0.999949 | − | 0.0100533i | \(-0.00320011\pi\) |
−0.508681 | + | 0.860955i | \(0.669867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.89351 | + | 5.13467i | 0.395756 | + | 0.228490i | ||||
\(506\) | −2.83348 | −0.125964 | ||||||||
\(507\) | 18.8860 | − | 18.8047i | 0.838755 | − | 0.835144i | ||||
\(508\) | −2.80150 | −0.124296 | ||||||||
\(509\) | −13.5708 | − | 7.83509i | −0.601514 | − | 0.347284i | 0.168123 | − | 0.985766i | \(-0.446229\pi\) |
−0.769637 | + | 0.638482i | \(0.779563\pi\) | |||||||
\(510\) | 38.0745 | − | 65.9470i | 1.68597 | − | 2.92018i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 24.9600i | − | 1.10309i | ||||||
\(513\) | 3.01154 | − | 1.73871i | 0.132963 | − | 0.0767661i | ||||
\(514\) | −28.3406 | + | 16.3625i | −1.25005 | + | 0.721718i | ||||
\(515\) | 40.4411i | 1.78205i | ||||||||
\(516\) | −0.747495 | − | 1.29470i | −0.0329066 | − | 0.0569959i | ||||
\(517\) | 0.571705 | − | 0.990222i | 0.0251436 | − | 0.0435499i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.4795 | −1.29401 | ||||||||
\(520\) | −37.5741 | − | 4.98795i | −1.64773 | − | 0.218736i | ||||
\(521\) | 25.2415 | 1.10585 | 0.552925 | − | 0.833231i | \(-0.313512\pi\) | ||||
0.552925 | + | 0.833231i | \(0.313512\pi\) | |||||||
\(522\) | −5.66846 | − | 3.27269i | −0.248102 | − | 0.143242i | ||||
\(523\) | −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 | ||||
\(527\) | 34.5318 | − | 19.9369i | 1.50423 | − | 0.868466i | ||||
\(528\) | − | 9.39259i | − | 0.408760i | ||||||
\(529\) | 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 | ||||
\(534\) | −20.8942 | −0.904181 | ||||||||
\(535\) | −20.3063 | − | 11.7238i | −0.877916 | − | 0.506865i | ||||
\(536\) | 9.31258 | − | 16.1299i | 0.402242 | − | 0.696704i | ||||
\(537\) | −5.56200 | − | 9.63366i | −0.240018 | − | 0.415723i | ||||
\(538\) | 17.5427i | 0.756320i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.16701 | + | 1.25112i | −0.0932532 | + | 0.0538398i | ||||
\(541\) | − | 14.4034i | − | 0.619250i | −0.950859 | − | 0.309625i | \(-0.899796\pi\) | ||
0.950859 | − | 0.309625i | \(-0.100204\pi\) | |||||||
\(542\) | −18.1408 | − | 31.4208i | −0.779214 | − | 1.34964i | ||||
\(543\) | 15.8782 | − | 27.5019i | 0.681401 | − | 1.18022i | ||||
\(544\) | −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 | ||||
\(549\) | −4.58550 | + | 7.94232i | −0.195704 | + | 0.338970i | ||||
\(550\) | 6.64736 | + | 11.5136i | 0.283445 | + | 0.490940i | ||||
\(551\) | 3.81783i | 0.162645i | ||||||||
\(552\) | 8.61757 | − | 4.97535i | 0.366788 | − | 0.211765i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 17.0863i | − | 0.725928i | ||||||
\(555\) | 3.86226 | + | 6.68962i | 0.163944 | + | 0.283959i | ||||
\(556\) | −0.557497 | + | 0.965614i | −0.0236432 | + | 0.0409512i | ||||
\(557\) | 7.42977 | + | 4.28958i | 0.314810 | + | 0.181755i | 0.649077 | − | 0.760723i | \(-0.275155\pi\) |
−0.334267 | + | 0.942478i | \(0.608489\pi\) | |||||||
\(558\) | −8.33731 | −0.352946 | ||||||||
\(559\) | −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 | \(0.746578\pi\) | |||||||
\(564\) | 0.348987i | 0.0146950i | ||||||||
\(565\) | −20.1835 | + | 11.6530i | −0.849126 | + | 0.490243i | ||||
\(566\) | 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 | \(0.205402\pi\) | |||||||
\(570\) | 8.04295 | + | 4.64360i | 0.336882 | + | 0.194499i | ||||
\(571\) | 44.1332 | 1.84692 | 0.923458 | − | 0.383700i | \(-0.125350\pi\) | ||||
0.923458 | + | 0.383700i | \(0.125350\pi\) | |||||||
\(572\) | −0.115495 | + | 0.870017i | −0.00482907 | + | 0.0363772i | ||||
\(573\) | −9.73025 | −0.406487 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.36592 | + | 11.0261i | −0.265477 | + | 0.459820i | ||||
\(576\) | 5.17835 | + | 8.96917i | 0.215765 | + | 0.373715i | ||||
\(577\) | 11.9330i | 0.496776i | 0.968661 | + | 0.248388i | \(0.0799009\pi\) | ||||
−0.968661 | + | 0.248388i | \(0.920099\pi\) | |||||||
\(578\) | 49.9729 | − | 28.8518i | 2.07860 | − | 1.20008i | ||||
\(579\) | −37.3538 | + | 21.5662i | −1.55237 | + | 0.896261i | ||||
\(580\) | − | 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 | ||||
\(584\) | −2.24086 | −0.0927274 | ||||||||
\(585\) | 14.3027 | − | 5.90629i | 0.591342 | − | 0.244195i | ||||
\(586\) | −15.5818 | −0.643679 | ||||||||
\(587\) | −17.6250 | − | 10.1758i | −0.727462 | − | 0.420000i | 0.0900312 | − | 0.995939i | \(-0.471303\pi\) |
−0.817493 | + | 0.575939i | \(0.804637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.43152 | + | 4.21152i | 0.100189 | + | 0.173533i | ||||
\(590\) | 53.6808i | 2.21000i | ||||||||
\(591\) | 10.3190 | − | 5.95769i | 0.424468 | − | 0.245067i | ||||
\(592\) | −3.27701 | + | 1.89199i | −0.134684 | + | 0.0777601i | ||||
\(593\) | − | 18.1800i | − | 0.746563i | −0.927718 | − | 0.373282i | \(-0.878232\pi\) | ||
0.927718 | − | 0.373282i | \(-0.121768\pi\) | |||||||
\(594\) | −3.16859 | − | 5.48817i | −0.130009 | − | 0.225182i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.72759 | + | 0.997422i | 0.0707646 | + | 0.0408560i | ||||
\(597\) | −21.7684 | −0.890920 | ||||||||
\(598\) | 7.38486 | − | 3.04958i | 0.301989 | − | 0.124707i | ||||
\(599\) | −38.2682 | −1.56359 | −0.781797 | − | 0.623532i | \(-0.785697\pi\) | ||||
−0.781797 | + | 0.623532i | \(0.785697\pi\) | |||||||
\(600\) | −40.4337 | − | 23.3444i | −1.65070 | − | 0.953031i | ||||
\(601\) | −13.4360 | + | 23.2718i | −0.548064 | + | 0.949275i | 0.450343 | + | 0.892856i | \(0.351302\pi\) |
−0.998407 | + | 0.0564195i | \(0.982032\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.60372i | 0.309648i | ||||||||
\(604\) | 0.777170 | − | 0.448699i | 0.0316226 | − | 0.0182573i | ||||
\(605\) | −28.9358 | + | 16.7061i | −1.17641 | + | 0.679200i | ||||
\(606\) | − | 7.93809i | − | 0.322463i | ||||||
\(607\) | −4.70105 | − | 8.14245i | −0.190810 | − | 0.330492i | 0.754709 | − | 0.656059i | \(-0.227778\pi\) |
−0.945519 | + | 0.325568i | \(0.894445\pi\) | |||||||
\(608\) | 0.506435 | − | 0.877171i | 0.0205386 | − | 0.0355740i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.5908 | 1.48152 | ||||||||
\(611\) | −0.424283 | + | 3.19611i | −0.0171646 | + | 0.129301i | ||||
\(612\) | 1.77225 | 0.0716389 | ||||||||
\(613\) | −11.5089 | − | 6.64469i | −0.464842 | − | 0.268376i | 0.249236 | − | 0.968443i | \(-0.419820\pi\) |
−0.714078 | + | 0.700066i | \(0.753154\pi\) | |||||||
\(614\) | −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 | −0.682765 | − | 0.730638i | \(-0.739223\pi\) |
0.291368 | + | 0.956611i | \(0.405890\pi\) | |||||||
\(618\) | 27.0724 | − | 15.6303i | 1.08901 | − | 0.628742i | ||||
\(619\) | − | 9.28505i | − | 0.373198i | −0.982436 | − | 0.186599i | \(-0.940254\pi\) | ||
0.982436 | − | 0.186599i | \(-0.0597465\pi\) | |||||||
\(620\) | −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 | ||||
\(625\) | −3.90726 | −0.156290 | ||||||||
\(626\) | −12.2571 | − | 7.07665i | −0.489893 | − | 0.282840i | ||||
\(627\) | 1.23715 | − | 2.14280i | 0.0494068 | − | 0.0855752i | ||||
\(628\) | 0.856848 | + | 1.48410i | 0.0341920 | + | 0.0592222i | ||||
\(629\) | 8.17322i | 0.325888i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.00894 | − | 5.20132i | 0.358640 | − | 0.207061i | −0.309844 | − | 0.950787i | \(-0.600277\pi\) |
0.668484 | + | 0.743726i | \(0.266943\pi\) | |||||||
\(632\) | − | 8.41327i | − | 0.334662i | ||||||
\(633\) | −4.78237 | − | 8.28331i | −0.190082 | − | 0.329232i | ||||
\(634\) | 1.01347 | − | 1.75538i | 0.0402499 | − | 0.0697149i | ||||
\(635\) | −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 | ||||
\(640\) | 16.8322 | − | 29.1542i | 0.665351 | − | 1.15242i | ||||
\(641\) | 7.42955 | + | 12.8684i | 0.293449 | + | 0.508269i | 0.974623 | − | 0.223853i | \(-0.0718634\pi\) |
−0.681174 | + | 0.732122i | \(0.738530\pi\) | |||||||
\(642\) | 18.1248i | 0.715328i | ||||||||
\(643\) | −1.98945 | + | 1.14861i | −0.0784563 | + | 0.0452968i | −0.538715 | − | 0.842488i | \(-0.681090\pi\) |
0.460259 | + | 0.887785i | \(0.347757\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 28.0185i | − | 1.10323i | ||||||
\(646\) | 4.91334 | + | 8.51016i | 0.193313 | + | 0.334828i | ||||
\(647\) | −3.99932 | + | 6.92703i | −0.157230 | + | 0.272330i | −0.933869 | − | 0.357616i | \(-0.883590\pi\) |
0.776639 | + | 0.629946i | \(0.216923\pi\) | |||||||
\(648\) | 28.4823 | + | 16.4443i | 1.11889 | + | 0.645991i | ||||
\(649\) | 14.3016 | 0.561387 | ||||||||
\(650\) | −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 | ||||
\(655\) | 39.9116i | 1.55948i | ||||||||
\(656\) | 13.0289 | − | 7.52225i | 0.508694 | − | 0.293695i | ||||
\(657\) | 0.792267 | − | 0.457415i | 0.0309093 | − | 0.0178455i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.7501 | + | 23.8159i | 0.535629 | + | 0.927737i | 0.999133 | + | 0.0416417i | \(0.0132588\pi\) |
−0.463504 | + | 0.886095i | \(0.653408\pi\) | |||||||
\(660\) | −0.890211 | + | 1.54189i | −0.0346514 | + | 0.0600180i | ||||
\(661\) | 6.05023 | + | 3.49310i | 0.235327 | + | 0.135866i | 0.613027 | − | 0.790062i | \(-0.289952\pi\) |
−0.377700 | + | 0.925928i | \(0.623285\pi\) | |||||||
\(662\) | −33.9681 | −1.32021 | ||||||||
\(663\) | 56.7087 | + | 7.52808i | 2.20238 | + | 0.292366i | ||||
\(664\) | −6.85019 | −0.265839 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.854479 | − | 1.48000i | 0.0331104 | − | 0.0573488i | ||||
\(667\) | 3.33148 | + | 5.77029i | 0.128995 | + | 0.223427i | ||||
\(668\) | − | 3.69729i | − | 0.143053i | ||||||
\(669\) | −43.0108 | + | 24.8323i | −1.66289 | + | 0.960071i | ||||
\(670\) | 26.2731 | − | 15.1688i | 1.01502 | − | 0.586022i | ||||
\(671\) | − | 9.74849i | − | 0.376336i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.72783 | − | 4.72474i | 0.105150 | − | 0.182125i | −0.808649 | − | 0.588291i | \(-0.799801\pi\) |
0.913800 | + | 0.406166i | \(0.133134\pi\) | |||||||
\(674\) | −37.4910 | − | 21.6455i | −1.44410 | − | 0.833752i | ||||
\(675\) | −28.4752 | −1.09601 | ||||||||
\(676\) | −0.635358 | − | 2.39181i | −0.0244369 | − | 0.0919928i | ||||
\(677\) | −33.7922 | −1.29874 | −0.649371 | − | 0.760472i | \(-0.724968\pi\) | ||||
−0.649371 | + | 0.760472i | \(0.724968\pi\) | |||||||
\(678\) | 15.6016 | + | 9.00761i | 0.599177 | + | 0.345935i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −40.6795 | − | 70.4590i | −1.55999 | − | 2.70198i | ||||
\(681\) | 31.5209i | 1.20788i | ||||||||
\(682\) | 7.67498 | − | 4.43115i | 0.293890 | − | 0.169678i | ||||
\(683\) | 10.6511 | − | 6.14942i | 0.407553 | − | 0.235301i | −0.282185 | − | 0.959360i | \(-0.591059\pi\) |
0.689738 | + | 0.724059i | \(0.257726\pi\) | |||||||
\(684\) | 0.216145i | 0.00826450i | ||||||||
\(685\) | −31.4514 | − | 54.4754i | −1.20170 | − | 2.08140i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.0311 | + | 16.7611i | 1.10760 | + | 0.639476i | ||||
\(688\) | 13.7253 | 0.523272 | ||||||||
\(689\) | 0.285908 | + | 0.0379543i | 0.0108922 | + | 0.00144594i | ||||
\(690\) | 16.2082 | 0.617036 | ||||||||
\(691\) | 9.60393 | + | 5.54483i | 0.365351 | + | 0.210935i | 0.671425 | − | 0.741072i | \(-0.265682\pi\) |
−0.306075 | + | 0.952008i | \(0.599016\pi\) | |||||||
\(692\) | −1.36869 | + | 2.37064i | −0.0520297 | + | 0.0901181i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.3129i | 1.26454i | ||||||||
\(695\) | −18.0972 | + | 10.4484i | −0.686465 | + | 0.396331i | ||||
\(696\) | −21.1602 | + | 12.2168i | −0.802075 | + | 0.463078i | ||||
\(697\) | − | 32.4955i | − | 1.23086i | ||||||
\(698\) | −7.77247 | − | 13.4623i | −0.294193 | − | 0.509556i | ||||
\(699\) | 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 | \(0.435559\pi\) | |||||||
\(702\) | 14.1650 | + | 10.8935i | 0.534623 | + | 0.411147i | ||||
\(703\) | −0.996813 | −0.0375955 | ||||||||
\(704\) | −9.53396 | − | 5.50443i | −0.359325 | − | 0.207456i | ||||
\(705\) | −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 | ||||
\(709\) | −35.2532 | + | 20.3535i | −1.32396 | + | 0.764391i | −0.984358 | − | 0.176178i | \(-0.943627\pi\) |
−0.339605 | + | 0.940568i | \(0.610293\pi\) | |||||||
\(710\) | 54.8290i | 2.05770i | ||||||||
\(711\) | 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 | ||||
\(716\) | −1.03294 | −0.0386028 | ||||||||
\(717\) | 15.3648 | + | 8.87089i | 0.573810 | + | 0.331290i | ||||
\(718\) | 10.1235 | − | 17.5344i | 0.377806 | − | 0.654380i | ||||
\(719\) | 4.88769 | + | 8.46572i | 0.182280 | + | 0.315718i | 0.942657 | − | 0.333764i | \(-0.108319\pi\) |
−0.760377 | + | 0.649482i | \(0.774986\pi\) | |||||||
\(720\) | 15.3775i | 0.573086i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.0971 | − | 12.1804i | 0.785153 | − | 0.453308i | ||||
\(723\) | − | 37.3081i | − | 1.38750i | ||||||
\(724\) | −1.47441 | − | 2.55375i | −0.0547959 | − | 0.0949092i | ||||
\(725\) | 15.6313 | − | 27.0743i | 0.580533 | − | 1.00551i | ||||
\(726\) | 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 | ||||
\(731\) | 14.8231 | − | 25.6743i | 0.548251 | − | 0.949598i | ||||
\(732\) | 1.48770 | + | 2.57677i | 0.0549869 | + | 0.0952400i | ||||
\(733\) | 22.3153i | 0.824236i | 0.911131 | + | 0.412118i | \(0.135211\pi\) | ||||
−0.911131 | + | 0.412118i | \(0.864789\pi\) | |||||||
\(734\) | −10.4891 | + | 6.05591i | −0.387161 | + | 0.223528i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.76768i | − | 0.0651576i | ||||||
\(737\) | −4.04126 | − | 6.99968i | −0.148862 | − | 0.257836i | ||||
\(738\) | −3.39728 | + | 5.88426i | −0.125056 | + | 0.216603i | ||||
\(739\) | 36.6960 | + | 21.1865i | 1.34989 | + | 0.779357i | 0.988233 | − | 0.152956i | \(-0.0488793\pi\) |
0.361653 | + | 0.932313i | \(0.382213\pi\) | |||||||
\(740\) | 0.717275 | 0.0263675 | ||||||||
\(741\) | −0.918130 | + | 6.91624i | −0.0337283 | + | 0.254074i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.8296 | − | 15.4901i | −0.984282 | − | 0.568276i | −0.0807220 | − | 0.996737i | \(-0.525723\pi\) |
−0.903560 | + | 0.428461i | \(0.859056\pi\) | |||||||
\(744\) | −15.5615 | + | 26.9532i | −0.570511 | + | 0.988153i | ||||
\(745\) | 18.6933 | + | 32.3778i | 0.684870 | + | 1.18623i | ||||
\(746\) | − | 21.7107i | − | 0.794885i | ||||||
\(747\) | 2.42192 | − | 1.39830i | 0.0886133 | − | 0.0511609i | ||||
\(748\) | −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 | \(0.0315941\pi\) | |||||||
\(752\) | −2.77475 | − | 1.60200i | −0.101185 | − | 0.0584190i | ||||
\(753\) | −32.5392 | −1.18579 | ||||||||
\(754\) | −18.1333 | + | 7.48816i | −0.660376 | + | 0.272703i | ||||
\(755\) | 16.8187 | 0.612095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.1404 | + | 27.9560i | −0.586633 | + | 1.01608i | 0.408037 | + | 0.912965i | \(0.366213\pi\) |
−0.994670 | + | 0.103112i | \(0.967120\pi\) | |||||||
\(758\) | 10.5368 | + | 18.2504i | 0.382716 | + | 0.662883i | ||||
\(759\) | − | 4.31818i | − | 0.156740i | ||||||
\(760\) | 8.59323 | − | 4.96130i | 0.311709 | − | 0.179965i | ||||
\(761\) | −25.7657 | + | 14.8758i | −0.934006 | + | 0.539249i | −0.888076 | − | 0.459696i | \(-0.847958\pi\) |
−0.0459296 | + | 0.998945i | \(0.514625\pi\) | |||||||
\(762\) | 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 | ||||
\(766\) | −33.1367 | −1.19728 | ||||||||
\(767\) | −37.2740 | + | 15.3923i | −1.34589 | + | 0.555785i | ||||
\(768\) | 9.27895 | 0.334825 | ||||||||
\(769\) | 36.2090 | + | 20.9053i | 1.30573 | + | 0.753863i | 0.981380 | − | 0.192075i | \(-0.0615215\pi\) |
0.324349 | + | 0.945938i | \(0.394855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9361 | − | 43.1907i | −0.898053 | − | 1.55547i | ||||
\(772\) | 4.00514i | 0.144148i | ||||||||
\(773\) | 35.8826 | − | 20.7168i | 1.29061 | − | 0.745132i | 0.311845 | − | 0.950133i | \(-0.399053\pi\) |
0.978762 | + | 0.205001i | \(0.0657198\pi\) | |||||||
\(774\) | −5.36829 | + | 3.09938i | −0.192959 | + | 0.111405i | ||||
\(775\) | − | 39.8215i | − | 1.43043i | ||||||
\(776\) | 0.705044 | + | 1.22117i | 0.0253096 | + | 0.0438375i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.9680 | − | 12.6832i | −0.787592 | − | 0.454716i | ||||
\(779\) | 3.96318 | 0.141996 | ||||||||
\(780\) | 0.660657 | − | 4.97671i | 0.0236553 | − | 0.178195i | ||||
\(781\) | 14.6075 | 0.522698 | ||||||||
\(782\) | 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 | ||||||||
\(786\) | 26.7180 | − | 15.4256i | 0.952998 | − | 0.550214i | ||||
\(787\) | 20.6657 | − | 11.9313i | 0.736651 | − | 0.425306i | −0.0841992 | − | 0.996449i | \(-0.526833\pi\) |
0.820851 | + | 0.571143i | \(0.193500\pi\) | |||||||
\(788\) | − | 1.10643i | − | 0.0394148i | ||||||
\(789\) | 15.8212 | + | 27.4031i | 0.563250 | + | 0.975577i | ||||
\(790\) | 6.85198 | − | 11.8680i | 0.243782 | − | 0.422243i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.53221 | 0.161045 | ||||||||
\(793\) | 10.4920 | + | 25.4073i | 0.372581 | + | 0.902241i | ||||
\(794\) | 19.5098 | 0.692377 | ||||||||
\(795\) | 0.506701 | + | 0.292544i | 0.0179708 | + | 0.0103755i | ||||
\(796\) | −1.01067 | + | 1.75054i | −0.0358223 | + | 0.0620461i | ||||
\(797\) | −25.4115 | − | 44.0141i | −0.900123 | − | 1.55906i | −0.827333 | − | 0.561712i | \(-0.810143\pi\) |
−0.0727899 | − | 0.997347i | \(-0.523190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.99335 | + | 3.46026i | −0.212029 | + | 0.122415i | ||||
\(800\) | −7.18279 | + | 4.14699i | −0.253950 | + | 0.146618i | ||||
\(801\) | − | 9.11367i | − | 0.322016i | ||||||
\(802\) | 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 | ||||
\(807\) | −26.7348 | −0.941110 | ||||||||
\(808\) | −7.34493 | − | 4.24060i | −0.258394 | − | 0.149184i | ||||
\(809\) | −2.20588 | + | 3.82070i | −0.0775547 | + | 0.134329i | −0.902194 | − | 0.431330i | \(-0.858045\pi\) |
0.824640 | + | 0.565658i | \(0.191378\pi\) | |||||||
\(810\) | 26.7852 | + | 46.3933i | 0.941136 | + | 1.63010i | ||||
\(811\) | − | 17.6493i | − | 0.619750i | −0.950777 | − | 0.309875i | \(-0.899713\pi\) | ||
0.950777 | − | 0.309875i | \(-0.100287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.8848 | − | 27.6463i | 1.67939 | − | 0.969598i | ||||
\(814\) | 1.81657i | 0.0636707i | ||||||||
\(815\) | 21.4644 | + | 37.1775i | 0.751866 | + | 1.30227i | ||||
\(816\) | −28.4244 | + | 49.2326i | −0.995054 | + | 1.72348i | ||||
\(817\) | 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 | 0.445228 | − | 0.895417i | \(-0.353123\pi\) |
−0.552840 | + | 0.833287i | \(0.686456\pi\) | |||||||
\(822\) | −24.3116 | + | 42.1089i | −0.847964 | + | 1.46872i | ||||
\(823\) | 10.9332 | + | 18.9369i | 0.381109 | + | 0.660100i | 0.991221 | − | 0.132215i | \(-0.0422091\pi\) |
−0.610112 | + | 0.792315i | \(0.708876\pi\) | |||||||
\(824\) | − | 33.3993i | − | 1.16352i | ||||||
\(825\) | −17.5465 | + | 10.1305i | −0.610891 | + | 0.352698i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.1361i | 0.630653i | 0.948983 | + | 0.315327i | \(0.102114\pi\) | ||||
−0.948983 | + | 0.315327i | \(0.897886\pi\) | |||||||
\(828\) | 0.188610 | + | 0.326682i | 0.00655465 | + | 0.0113530i | ||||
\(829\) | −15.4497 | + | 26.7596i | −0.536590 | + | 0.929401i | 0.462495 | + | 0.886622i | \(0.346954\pi\) |
−0.999085 | + | 0.0427787i | \(0.986379\pi\) | |||||||
\(830\) | −9.66305 | − | 5.57896i | −0.335409 | − | 0.193649i | ||||
\(831\) | 26.0393 | 0.903293 | ||||||||
\(832\) | 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 | ||||
\(837\) | 18.9817i | 0.656103i | ||||||||
\(838\) | −9.27813 | + | 5.35673i | −0.320508 | + | 0.185045i | ||||
\(839\) | 13.3333 | − | 7.69796i | 0.460315 | − | 0.265763i | −0.251862 | − | 0.967763i | \(-0.581043\pi\) |
0.712177 | + | 0.702000i | \(0.247709\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.31965 | + | 10.9459i | 0.217919 | + | 0.377446i | ||||
\(842\) | −1.89533 | + | 3.28280i | −0.0653173 | + | 0.113133i | ||||
\(843\) | 47.4426 | + | 27.3910i | 1.63401 | + | 0.943396i | ||||
\(844\) | −0.888153 | −0.0305715 | ||||||||
\(845\) | 12.1009 | − | 44.7747i | 0.416284 | − | 1.54030i | ||||
\(846\) | 1.44703 | 0.0497498 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.143307 | + | 0.248216i | −0.00492119 | + | 0.00852376i | ||||
\(849\) | 15.1116 | + | 26.1740i | 0.518628 | + | 0.898290i | ||||
\(850\) | − | 80.4667i | − | 2.75998i | ||||||
\(851\) | −1.50659 | + | 0.869829i | −0.0516451 | + | 0.0298173i | ||||
\(852\) | −3.86113 | + | 2.22922i | −0.132280 | + | 0.0763719i | ||||
\(853\) | 23.7772i | 0.814116i | 0.913402 | + | 0.407058i | \(0.133445\pi\) | ||||
−0.913402 | + | 0.407058i | \(0.866555\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.02545 | + | 3.50818i | −0.0692690 | + | 0.119977i | ||||
\(856\) | 16.7704 | + | 9.68242i | 0.573202 | + | 0.330938i | ||||
\(857\) | −30.1050 | −1.02837 | −0.514184 | − | 0.857680i | \(-0.671905\pi\) | ||||
−0.514184 | + | 0.857680i | \(0.671905\pi\) | |||||||
\(858\) | 12.6040 | + | 1.67318i | 0.430294 | + | 0.0571214i | ||||
\(859\) | 15.1343 | 0.516377 | 0.258188 | − | 0.966095i | \(-0.416874\pi\) | ||||
0.258188 | + | 0.966095i | \(0.416874\pi\) | |||||||
\(860\) | −2.25315 | − | 1.30086i | −0.0768318 | − | 0.0443589i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.85828 | + | 6.68274i | 0.131414 | + | 0.227615i | ||||
\(863\) | 18.2657i | 0.621773i | 0.950447 | + | 0.310886i | \(0.100626\pi\) | ||||
−0.950447 | + | 0.310886i | \(0.899374\pi\) | |||||||
\(864\) | 3.42382 | − | 1.97674i | 0.116481 | − | 0.0672501i | ||||
\(865\) | −44.4296 | + | 25.6514i | −1.51065 | + | 0.872175i | ||||
\(866\) | − | 32.9925i | − | 1.12113i | ||||||
\(867\) | 43.9697 | + | 76.1578i | 1.49329 | + | 2.58646i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.16186 | − | 1.82550i | −0.107259 | − | 0.0619259i | ||||
\(870\) | −39.7988 | −1.34931 | ||||||||
\(871\) | 18.0662 | + | 13.8937i | 0.612150 | + | 0.470769i | ||||
\(872\) | −17.2053 | −0.582643 | ||||||||
\(873\) | −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 | ||||||
\(877\) | 6.05906 | − | 3.49820i | 0.204600 | − | 0.118126i | −0.394199 | − | 0.919025i | \(-0.628978\pi\) |
0.598799 | + | 0.800899i | \(0.295645\pi\) | |||||||
\(878\) | 42.6883 | − | 24.6461i | 1.44066 | − | 0.831765i | ||||
\(879\) | − | 23.7465i | − | 0.800948i | ||||||
\(880\) | −8.17292 | − | 14.1559i | −0.275509 | − | 0.477195i | ||||
\(881\) | −12.8873 | + | 22.3215i | −0.434184 | + | 0.752029i | −0.997229 | − | 0.0743977i | \(-0.976297\pi\) |
0.563045 | + | 0.826427i | \(0.309630\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.4526 | −0.553674 | −0.276837 | − | 0.960917i | \(-0.589286\pi\) | ||||
−0.276837 | + | 0.960917i | \(0.589286\pi\) | |||||||
\(884\) | 3.23828 | − | 4.21080i | 0.108915 | − | 0.141625i | ||||
\(885\) | −81.8086 | −2.74997 | ||||||||
\(886\) | −31.5637 | − | 18.2233i | −1.06040 | − | 0.612225i | ||||
\(887\) | 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 | ||||
\(891\) | 12.3601 | − | 7.13611i | 0.414079 | − | 0.239069i | ||||
\(892\) | 4.61170i | 0.154411i | ||||||||
\(893\) | −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 | ||||
\(898\) | −36.9028 | −1.23146 | ||||||||
\(899\) | −18.0478 | − | 10.4199i | −0.601927 | − | 0.347523i | ||||
\(900\) | 0.884960 | − | 1.53280i | 0.0294987 | − | 0.0510932i | ||||
\(901\) | 0.309538 | + | 0.536136i | 0.0103122 | + | 0.0178613i | ||||
\(902\) | − | 7.22241i | − | 0.240480i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.6691 | − | 9.62388i | 0.554405 | − | 0.320086i | ||||
\(905\) | − | 55.2655i | − | 1.83709i | ||||||
\(906\) | −6.50034 | − | 11.2589i | −0.215959 | − | 0.374052i | ||||
\(907\) | 23.9212 | − | 41.4327i | 0.794290 | − | 1.37575i | −0.128998 | − | 0.991645i | \(-0.541176\pi\) |
0.923289 | − | 0.384107i | \(-0.125490\pi\) | |||||||
\(908\) | 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 | ||||
\(913\) | −1.48635 | + | 2.57443i | −0.0491909 | + | 0.0852011i | ||||
\(914\) | −26.6785 | − | 46.2085i | −0.882445 | − | 1.52844i | ||||
\(915\) | 55.7637i | 1.84349i | ||||||||
\(916\) | 2.69574 | − | 1.55638i | 0.0890697 | − | 0.0514244i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 38.3560i | 1.26594i | ||||||||
\(919\) | 21.7184 | + | 37.6174i | 0.716424 | + | 1.24088i | 0.962408 | + | 0.271609i | \(0.0875557\pi\) |
−0.245984 | + | 0.969274i | \(0.579111\pi\) | |||||||
\(920\) | 8.65856 | − | 14.9971i | 0.285464 | − | 0.494439i | ||||
\(921\) | −52.0799 | − | 30.0684i | −1.71609 | − | 0.990787i | ||||
\(922\) | −6.58595 | −0.216897 | ||||||||
\(923\) | −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 | ||||
\(928\) | 4.34049i | 0.142484i | ||||||||
\(929\) | 11.0695 | − | 6.39095i | 0.363177 | − | 0.209680i | −0.307296 | − | 0.951614i | \(-0.599424\pi\) |
0.670474 | + | 0.741933i | \(0.266091\pi\) | |||||||
\(930\) | −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 | ||||
\(934\) | −37.2988 | − | 21.5345i | −1.22045 | − | 0.704629i | ||||
\(935\) | −35.3063 | −1.15464 | ||||||||
\(936\) | −11.8122 | + | 4.87786i | −0.386094 | + | 0.159438i | ||||
\(937\) | −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 | ||||
\(940\) | 0.303669 | + | 0.525971i | 0.00990460 | + | 0.0171553i | ||||
\(941\) | 45.1488i | 1.47181i | 0.677085 | + | 0.735905i | \(0.263243\pi\) | ||||
−0.677085 | + | 0.735905i | \(0.736757\pi\) | |||||||
\(942\) | 21.5003 | − | 12.4132i | 0.700519 | − | 0.404445i | ||||
\(943\) | 5.98997 | − | 3.45831i | 0.195060 | − | 0.112618i | ||||
\(944\) | − | 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 | 0.193875 | − | 0.981026i | \(-0.437894\pi\) |
−0.752656 | + | 0.658414i | \(0.771228\pi\) | |||||||
\(948\) | 1.11434 | 0.0361922 | ||||||||
\(949\) | 0.360840 | − | 2.71820i | 0.0117134 | − | 0.0882364i | ||||
\(950\) | 9.81378 | 0.318401 | ||||||||
\(951\) | 2.67516 | + | 1.54451i | 0.0867482 | + | 0.0500841i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.86433 | + | 13.6214i | 0.254751 | + | 0.441241i | 0.964828 | − | 0.262883i | \(-0.0846733\pi\) |
−0.710077 | + | 0.704124i | \(0.751340\pi\) | |||||||
\(954\) | − | 0.129444i | − | 0.00419090i | ||||||
\(955\) | −14.6648 | + | 8.46673i | −0.474542 | + | 0.273977i | ||||
\(956\) | 1.42673 | − | 0.823724i | 0.0461438 | − | 0.0266412i | ||||
\(957\) | 10.6032i | 0.342752i | ||||||||
\(958\) | −12.1235 | − | 20.9985i | −0.391693 | − | 0.678432i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 54.5365 | + | 31.4867i | 1.76016 | + | 1.01623i | ||||
\(961\) | 4.45488 | 0.143706 | ||||||||
\(962\) | −1.95511 | − | 4.73450i | −0.0630354 | − | 0.152646i | ||||
\(963\) | −7.90569 | −0.254757 | ||||||||
\(964\) | −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 | \(-0.683037\pi\) | ||
0.543858 | − | 0.839177i | \(-0.316963\pi\) | |||||||
\(968\) | 23.8974 | − | 13.7972i | 0.768091 | − | 0.443458i | ||||
\(969\) | −12.9693 | + | 7.48786i | −0.416635 | + | 0.240545i | ||||
\(970\) | 2.29682i | 0.0737465i | ||||||||
\(971\) | −11.2292 | − | 19.4495i | −0.360362 | − | 0.624165i | 0.627658 | − | 0.778489i | \(-0.284013\pi\) |
−0.988020 | + | 0.154324i | \(0.950680\pi\) | |||||||
\(972\) | −1.12603 | + | 1.95035i | −0.0361175 | + | 0.0625574i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23.6765 | −0.758645 | ||||||||
\(975\) | 34.8281 | − | 45.2876i | 1.11539 | − | 1.45036i | ||||
\(976\) | −27.3167 | −0.874387 | ||||||||
\(977\) | 35.5369 | + | 20.5172i | 1.13693 | + | 0.656405i | 0.945668 | − | 0.325135i | \(-0.105410\pi\) |
0.191259 | + | 0.981540i | \(0.438743\pi\) | |||||||
\(978\) | 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 | ||||
\(982\) | −4.50110 | + | 2.59871i | −0.143636 | + | 0.0829282i | ||||
\(983\) | − | 26.8328i | − | 0.855832i | −0.903818 | − | 0.427916i | \(-0.859248\pi\) | ||
0.903818 | − | 0.427916i | \(-0.140752\pi\) | |||||||
\(984\) | 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 | ||||
\(989\) | 6.31013 | 0.200650 | ||||||||
\(990\) | 6.39324 | + | 3.69114i | 0.203191 | + | 0.117312i | ||||
\(991\) | −5.18755 | + | 8.98510i | −0.164788 | + | 0.285421i | −0.936580 | − | 0.350454i | \(-0.886027\pi\) |
0.771792 | + | 0.635875i | \(0.219361\pi\) | |||||||
\(992\) | 2.76439 | + | 4.78807i | 0.0877696 | + | 0.152021i | ||||
\(993\) | − | 51.7669i | − | 1.64277i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.8079 | + | 18.9417i | −1.04008 | + | 0.600491i | ||||
\(996\) | − | 0.907312i | − | 0.0287493i | ||||||
\(997\) | −26.9549 | − | 46.6872i | −0.853669 | − | 1.47860i | −0.877874 | − | 0.478891i | \(-0.841039\pi\) |
0.0242056 | − | 0.999707i | \(-0.492294\pi\) | |||||||
\(998\) | −8.50671 | + | 14.7341i | −0.269275 | + | 0.466398i | ||||
\(999\) | −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.q.i.589.2 | 12 | ||
7.2 | even | 3 | 637.2.k.i.459.5 | 12 | |||
7.3 | odd | 6 | 91.2.u.b.30.5 | yes | 12 | ||
7.4 | even | 3 | 637.2.u.g.30.5 | 12 | |||
7.5 | odd | 6 | 91.2.k.b.4.5 | ✓ | 12 | ||
7.6 | odd | 2 | 637.2.q.g.589.2 | 12 | |||
13.6 | odd | 12 | 8281.2.a.co.1.9 | 12 | |||
13.7 | odd | 12 | 8281.2.a.co.1.4 | 12 | |||
13.10 | even | 6 | inner | 637.2.q.i.491.2 | 12 | ||
21.5 | even | 6 | 819.2.bm.f.550.2 | 12 | |||
21.17 | even | 6 | 819.2.do.e.667.2 | 12 | |||
91.6 | even | 12 | 8281.2.a.cp.1.9 | 12 | |||
91.10 | odd | 6 | 91.2.k.b.23.2 | yes | 12 | ||
91.19 | even | 12 | 1183.2.e.j.508.4 | 24 | |||
91.20 | even | 12 | 8281.2.a.cp.1.4 | 12 | |||
91.23 | even | 6 | 637.2.u.g.361.5 | 12 | |||
91.33 | even | 12 | 1183.2.e.j.508.9 | 24 | |||
91.45 | even | 12 | 1183.2.e.j.170.4 | 24 | |||
91.59 | even | 12 | 1183.2.e.j.170.9 | 24 | |||
91.62 | odd | 6 | 637.2.q.g.491.2 | 12 | |||
91.75 | odd | 6 | 91.2.u.b.88.5 | yes | 12 | ||
91.88 | even | 6 | 637.2.k.i.569.2 | 12 | |||
273.101 | even | 6 | 819.2.bm.f.478.5 | 12 | |||
273.257 | even | 6 | 819.2.do.e.361.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.5 | ✓ | 12 | 7.5 | odd | 6 | ||
91.2.k.b.23.2 | yes | 12 | 91.10 | odd | 6 | ||
91.2.u.b.30.5 | yes | 12 | 7.3 | odd | 6 | ||
91.2.u.b.88.5 | yes | 12 | 91.75 | odd | 6 | ||
637.2.k.i.459.5 | 12 | 7.2 | even | 3 | |||
637.2.k.i.569.2 | 12 | 91.88 | even | 6 | |||
637.2.q.g.491.2 | 12 | 91.62 | odd | 6 | |||
637.2.q.g.589.2 | 12 | 7.6 | odd | 2 | |||
637.2.q.i.491.2 | 12 | 13.10 | even | 6 | inner | ||
637.2.q.i.589.2 | 12 | 1.1 | even | 1 | trivial | ||
637.2.u.g.30.5 | 12 | 7.4 | even | 3 | |||
637.2.u.g.361.5 | 12 | 91.23 | even | 6 | |||
819.2.bm.f.478.5 | 12 | 273.101 | even | 6 | |||
819.2.bm.f.550.2 | 12 | 21.5 | even | 6 | |||
819.2.do.e.361.2 | 12 | 273.257 | even | 6 | |||
819.2.do.e.667.2 | 12 | 21.17 | even | 6 | |||
1183.2.e.j.170.4 | 24 | 91.45 | even | 12 | |||
1183.2.e.j.170.9 | 24 | 91.59 | even | 12 | |||
1183.2.e.j.508.4 | 24 | 91.19 | even | 12 | |||
1183.2.e.j.508.9 | 24 | 91.33 | even | 12 | |||
8281.2.a.co.1.4 | 12 | 13.7 | odd | 12 | |||
8281.2.a.co.1.9 | 12 | 13.6 | odd | 12 | |||
8281.2.a.cp.1.4 | 12 | 91.20 | even | 12 | |||
8281.2.a.cp.1.9 | 12 | 91.6 | even | 12 |