Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
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([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (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: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 \) |
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 | 569.2 | ||
Root | \(0.874681 + 1.11128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.569 |
Dual form | 637.2.k.i.459.5 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.34523i | − | 0.951219i | −0.879657 | − | 0.475609i | \(-0.842228\pi\) | ||
0.879657 | − | 0.475609i | \(-0.157772\pi\) | |||||||
\(3\) | 1.02505 | − | 1.77544i | 0.591814 | − | 1.02505i | −0.402174 | − | 0.915563i | \(-0.631745\pi\) |
0.993988 | − | 0.109489i | \(-0.0349213\pi\) | |||||||
\(4\) | 0.190366 | 0.0951832 | ||||||||
\(5\) | −3.08979 | − | 1.78389i | −1.38179 | − | 0.797779i | −0.389422 | − | 0.921059i | \(-0.627325\pi\) |
−0.992372 | + | 0.123280i | \(0.960659\pi\) | |||||||
\(6\) | −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 | 0.323681 | − | 0.946166i | \(-0.395080\pi\) |
−0.657563 | + | 0.753399i | \(0.728413\pi\) | |||||||
\(12\) | 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 | ||||
\(16\) | −3.58303 | −0.895757 | ||||||||
\(17\) | 7.73920 | 1.87703 | 0.938515 | − | 0.345238i | \(-0.112202\pi\) | ||||
0.938515 | + | 0.345238i | \(0.112202\pi\) | |||||||
\(18\) | −1.40141 | + | 0.809103i | −0.330315 | + | 0.190707i | ||||
\(19\) | −0.817422 | + | 0.471939i | −0.187530 | + | 0.108270i | −0.590826 | − | 0.806799i | \(-0.701198\pi\) |
0.403296 | + | 0.915070i | \(0.367865\pi\) | |||||||
\(20\) | −0.588191 | − | 0.339592i | −0.131524 | − | 0.0759352i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.860052 | + | 1.48965i | −0.183364 | + | 0.317595i | ||||
\(23\) | −1.64727 | −0.343481 | −0.171740 | − | 0.985142i | \(-0.554939\pi\) | ||||
−0.171740 | + | 0.985142i | \(0.554939\pi\) | |||||||
\(24\) | −5.23141 | − | 3.02035i | −1.06786 | − | 0.616527i | ||||
\(25\) | 3.86451 | + | 6.69354i | 0.772903 | + | 1.33871i | ||||
\(26\) | 0.638275 | + | 4.80810i | 0.125176 | + | 0.942946i | ||||
\(27\) | 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 | \(0.955881\pi\) | |||||||
\(30\) | 4.91970 | + | 8.52117i | 0.898210 | + | 1.55575i | ||||
\(31\) | −4.46193 | + | 2.57610i | −0.801387 | + | 0.462681i | −0.843956 | − | 0.536413i | \(-0.819779\pi\) |
0.0425691 | + | 0.999094i | \(0.486446\pi\) | |||||||
\(32\) | − | 1.07309i | − | 0.189698i | ||||||
\(33\) | −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 | ||||
\(37\) | − | 1.05608i | − | 0.173619i | −0.996225 | − | 0.0868094i | \(-0.972333\pi\) | ||
0.996225 | − | 0.0868094i | \(-0.0276671\pi\) | |||||||
\(38\) | 0.634865 | + | 1.09962i | 0.102989 | + | 0.178382i | ||||
\(39\) | −2.82133 | + | 6.83214i | −0.451775 | + | 1.09402i | ||||
\(40\) | −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 | ||||
\(45\) | 4.29176i | 0.639778i | ||||||||
\(46\) | 2.21596i | 0.326725i | ||||||||
\(47\) | −0.774415 | − | 0.447109i | −0.112960 | − | 0.0652175i | 0.442456 | − | 0.896790i | \(-0.354107\pi\) |
−0.555416 | + | 0.831573i | \(0.687441\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | −0.680407 | + | 0.0903239i | −0.0943554 | + | 0.0125257i | ||||
\(53\) | 0.0399961 | + | 0.0692754i | 0.00549389 | + | 0.00951570i | 0.868759 | − | 0.495235i | \(-0.164918\pi\) |
−0.863265 | + | 0.504750i | \(0.831585\pi\) | |||||||
\(54\) | − | 4.95607i | − | 0.674436i | ||||||
\(55\) | 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 | ||||
\(59\) | − | 11.1847i | − | 1.45613i | −0.685509 | − | 0.728064i | \(-0.740420\pi\) | ||
0.685509 | − | 0.728064i | \(-0.259580\pi\) | |||||||
\(60\) | −1.20585 | + | 0.696200i | −0.155675 | + | 0.0898790i | ||||
\(61\) | −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 | ||||||||
\(65\) | 11.8899 | + | 4.90994i | 1.47476 | + | 0.609003i | ||||
\(66\) | 1.76319 | + | 3.05394i | 0.217034 | + | 0.375914i | ||||
\(67\) | 5.47418 | + | 3.16052i | 0.668777 | + | 0.386119i | 0.795613 | − | 0.605805i | \(-0.207149\pi\) |
−0.126836 | + | 0.991924i | \(0.540482\pi\) | |||||||
\(68\) | 1.47328 | 0.178662 | ||||||||
\(69\) | −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 | \(0.429562\pi\) | |||||||
\(72\) | −3.06959 | + | 1.77223i | −0.361755 | + | 0.208859i | ||||
\(73\) | −0.658617 | + | 0.380253i | −0.0770853 | + | 0.0445052i | −0.538047 | − | 0.842915i | \(-0.680838\pi\) |
0.460962 | + | 0.887420i | \(0.347504\pi\) | |||||||
\(74\) | −1.42067 | −0.165149 | ||||||||
\(75\) | 15.8453 | 1.82966 | ||||||||
\(76\) | −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 | −0.774469 | − | 0.632612i | \(-0.781983\pi\) |
0.935093 | + | 0.354404i | \(0.115316\pi\) | |||||||
\(80\) | 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 | \(-0.959275\pi\) | ||
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 | ||||
\(87\) | −8.29233 | −0.889032 | ||||||||
\(88\) | −1.88383 | + | 3.26289i | −0.200817 | + | 0.347825i | ||||
\(89\) | 7.57626i | 0.803082i | 0.915841 | + | 0.401541i | \(0.131525\pi\) | ||||
−0.915841 | + | 0.401541i | \(0.868475\pi\) | |||||||
\(90\) | 5.77339 | 0.608569 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.313586 | −0.0326936 | ||||||||
\(93\) | 10.5625i | 1.09528i | ||||||||
\(94\) | −0.601462 | + | 1.04176i | −0.0620361 | + | 0.107450i | ||||
\(95\) | 3.36755 | 0.345503 | ||||||||
\(96\) | −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 | ||||||||
\(100\) | 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 | ||||
\(103\) | 5.66755 | − | 9.81649i | 0.558441 | − | 0.967248i | −0.439186 | − | 0.898396i | \(-0.644733\pi\) |
0.997627 | − | 0.0688516i | \(-0.0219335\pi\) | |||||||
\(104\) | 1.39806 | + | 10.5315i | 0.137091 | + | 1.03270i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0931910 | − | 0.0538039i | 0.00905151 | − | 0.00522589i | ||||
\(107\) | −6.57206 | −0.635345 | −0.317673 | − | 0.948200i | \(-0.602901\pi\) | ||||
−0.317673 | + | 0.948200i | \(0.602901\pi\) | |||||||
\(108\) | 0.701346 | 0.0674871 | ||||||||
\(109\) | −5.05684 | + | 2.91957i | −0.484358 | + | 0.279644i | −0.722231 | − | 0.691652i | \(-0.756883\pi\) |
0.237873 | + | 0.971296i | \(0.423550\pi\) | |||||||
\(110\) | 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 | −0.977761 | − | 0.209723i | \(-0.932744\pi\) |
0.670506 | + | 0.741904i | \(0.266077\pi\) | |||||||
\(114\) | 2.60308 | 0.243800 | ||||||||
\(115\) | 5.08973 | + | 2.93855i | 0.474619 | + | 0.274022i | ||||
\(116\) | −0.385001 | − | 0.666841i | −0.0357464 | − | 0.0619146i | ||||
\(117\) | 2.64403 | + | 3.43809i | 0.244441 | + | 0.317851i | ||||
\(118\) | −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 | ||||
\(122\) | −8.88187 | + | 5.12795i | −0.804127 | + | 0.464263i | ||||
\(123\) | − | 8.60802i | − | 0.776159i | ||||||
\(124\) | −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 | 0.982408 | + | 0.186748i | \(0.0597948\pi\) |
−0.329475 | + | 0.944164i | \(0.606872\pi\) | |||||||
\(128\) | 9.43568i | 0.834005i | ||||||||
\(129\) | −3.92661 | − | 6.80109i | −0.345719 | − | 0.598802i | ||||
\(130\) | 6.60498 | − | 15.9946i | 0.579295 | − | 1.40282i | ||||
\(131\) | 5.59335 | − | 9.68796i | 0.488693 | − | 0.846441i | −0.511222 | − | 0.859448i | \(-0.670807\pi\) |
0.999915 | + | 0.0130074i | \(0.00414049\pi\) | |||||||
\(132\) | −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 | ||||
\(136\) | − | 22.8038i | − | 1.95541i | ||||||
\(137\) | − | 17.6308i | − | 1.50630i | −0.657848 | − | 0.753151i | \(-0.728533\pi\) | ||
0.657848 | − | 0.753151i | \(-0.271467\pi\) | |||||||
\(138\) | 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 | ||||
\(143\) | 4.26128 | + | 1.75970i | 0.356346 | + | 0.147153i | ||||
\(144\) | 2.15506 | + | 3.73267i | 0.179588 | + | 0.311055i | ||||
\(145\) | 14.4311i | 1.19844i | ||||||||
\(146\) | 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 | −0.0798677 | − | 0.996805i | \(-0.525450\pi\) |
0.823325 | + | 0.567570i | \(0.192116\pi\) | |||||||
\(150\) | − | 21.3155i | − | 1.74041i | ||||||
\(151\) | −4.08249 | + | 2.35703i | −0.332229 | + | 0.191812i | −0.656830 | − | 0.754039i | \(-0.728103\pi\) |
0.324602 | + | 0.945851i | \(0.394770\pi\) | |||||||
\(152\) | 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 | ||||||||
\(156\) | −0.537087 | + | 1.30061i | −0.0430014 | + | 0.104132i | ||||
\(157\) | 4.50105 | + | 7.79604i | 0.359223 | + | 0.622192i | 0.987831 | − | 0.155530i | \(-0.0497085\pi\) |
−0.628608 | + | 0.777722i | \(0.716375\pi\) | |||||||
\(158\) | −3.32643 | − | 1.92052i | −0.264637 | − | 0.152788i | ||||
\(159\) | 0.163992 | 0.0130054 | ||||||||
\(160\) | −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 | −0.0329144 | − | 0.999458i | \(-0.510479\pi\) |
0.849099 | + | 0.528234i | \(0.177146\pi\) | |||||||
\(164\) | 0.692227 | − | 0.399657i | 0.0540538 | − | 0.0312080i | ||||
\(165\) | 9.35261 | 0.728099 | ||||||||
\(166\) | −3.12742 | −0.242735 | ||||||||
\(167\) | 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 | ||||
\(171\) | 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 | ||||
\(177\) | −19.8578 | − | 11.4649i | −1.49261 | − | 0.861757i | ||||
\(178\) | 10.1918 | 0.763907 | ||||||||
\(179\) | 2.71303 | − | 4.69911i | 0.202781 | − | 0.351228i | −0.746642 | − | 0.665226i | \(-0.768335\pi\) |
0.949424 | + | 0.313998i | \(0.101669\pi\) | |||||||
\(180\) | 0.817008i | 0.0608962i | ||||||||
\(181\) | 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 | ||||||||
\(184\) | 4.85376i | 0.357824i | ||||||||
\(185\) | −1.88393 | + | 3.26307i | −0.138509 | + | 0.239905i | ||||
\(186\) | 14.2090 | 1.04185 | ||||||||
\(187\) | −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 | ||||||
\(191\) | −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 | 0.982350 | − | 0.187050i | \(-0.0598928\pi\) |
0.329185 | + | 0.944266i | \(0.393226\pi\) | |||||||
\(194\) | 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 | \(0.266948\pi\) | |||||||
\(198\) | 2.06915 | 0.147048 | ||||||||
\(199\) | 10.6182 | 0.752703 | 0.376352 | − | 0.926477i | \(-0.377179\pi\) | ||||
0.376352 | + | 0.926477i | \(0.377179\pi\) | |||||||
\(200\) | 19.7228 | − | 11.3869i | 1.39461 | − | 0.805178i | ||||
\(201\) | 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 | ||||
\(205\) | −14.9805 | −1.04628 | ||||||||
\(206\) | −13.2054 | − | 7.62414i | −0.920064 | − | 0.531199i | ||||
\(207\) | 0.990773 | + | 1.71607i | 0.0688635 | + | 0.119275i | ||||
\(208\) | 12.8064 | − | 1.70005i | 0.887967 | − | 0.117877i | ||||
\(209\) | 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 | \(0.781993\pi\) | |||||||
\(212\) | 0.00761392 | + | 0.0131877i | 0.000522926 | + | 0.000905735i | ||||
\(213\) | 20.2826 | − | 11.7102i | 1.38974 | − | 0.802368i | ||||
\(214\) | 8.84091i | 0.604352i | ||||||||
\(215\) | −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 | ||||
\(219\) | 1.55912i | 0.105355i | ||||||||
\(220\) | 0.434227 | + | 0.752104i | 0.0292756 | + | 0.0507068i | ||||
\(221\) | −27.6614 | + | 3.67205i | −1.86071 | + | 0.247009i | ||||
\(222\) | −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 | ||||
\(227\) | 15.3753i | 1.02049i | 0.860028 | + | 0.510247i | \(0.170446\pi\) | ||||
−0.860028 | + | 0.510247i | \(0.829554\pi\) | |||||||
\(228\) | 0.368368i | 0.0243958i | ||||||||
\(229\) | 14.1608 | + | 8.17573i | 0.935771 | + | 0.540268i | 0.888632 | − | 0.458621i | \(-0.151656\pi\) |
0.0471389 | + | 0.998888i | \(0.484990\pi\) | |||||||
\(230\) | 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 | −0.215911 | + | 0.976413i | \(0.569272\pi\) |
−0.737643 | + | 0.675191i | \(0.764061\pi\) | |||||||
\(234\) | 4.62500 | − | 3.55682i | 0.302346 | − | 0.232517i | ||||
\(235\) | 1.59518 | + | 2.76294i | 0.104058 | + | 0.180234i | ||||
\(236\) | − | 2.12920i | − | 0.138599i | ||||||
\(237\) | −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 | \(-0.0902991\pi\) | |||||||
\(240\) | 22.6963 | − | 13.1037i | 1.46504 | − | 0.845840i | ||||
\(241\) | − | 18.1982i | − | 1.17225i | −0.810222 | − | 0.586124i | \(-0.800653\pi\) | ||
0.810222 | − | 0.586124i | \(-0.199347\pi\) | |||||||
\(242\) | −10.9102 | + | 6.29902i | −0.701336 | + | 0.404916i | ||||
\(243\) | −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 | ||||||||
\(247\) | 2.69770 | − | 2.07465i | 0.171651 | − | 0.132007i | ||||
\(248\) | 7.59057 | + | 13.1473i | 0.482002 | + | 0.834851i | ||||
\(249\) | −4.12759 | − | 2.38307i | −0.261576 | − | 0.151021i | ||||
\(250\) | −13.0979 | −0.828383 | ||||||||
\(251\) | −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 | ||||
\(254\) | 17.1446 | − | 9.89841i | 1.07574 | − | 0.621082i | ||||
\(255\) | −49.0230 | + | 28.3034i | −3.06994 | + | 1.77243i | ||||
\(256\) | −4.52609 | −0.282880 | ||||||||
\(257\) | −24.3267 | −1.51746 | −0.758730 | − | 0.651406i | \(-0.774180\pi\) | ||||
−0.758730 | + | 0.651406i | \(0.774180\pi\) | |||||||
\(258\) | −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 | ||||
\(262\) | −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 | ||||
\(268\) | 1.04210 | + | 0.601656i | 0.0636563 | + | 0.0367520i | ||||
\(269\) | 13.0407 | 0.795106 | 0.397553 | − | 0.917579i | \(-0.369859\pi\) | ||||
0.397553 | + | 0.917579i | \(0.369859\pi\) | |||||||
\(270\) | −8.84108 | + | 15.3132i | −0.538051 | + | 0.931931i | ||||
\(271\) | 26.9706i | 1.63835i | 0.573544 | + | 0.819174i | \(0.305568\pi\) | ||||
−0.573544 | + | 0.819174i | \(0.694432\pi\) | |||||||
\(272\) | −27.7298 | −1.68136 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.7174 | −1.43282 | ||||||||
\(275\) | − | 9.88289i | − | 0.595961i | ||||||
\(276\) | −0.321442 | + | 0.556753i | −0.0193485 | + | 0.0335126i | ||||
\(277\) | −12.7015 | −0.763156 | −0.381578 | − | 0.924337i | \(-0.624619\pi\) | ||||
−0.381578 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(278\) | 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 | \(-0.293601\pi\) | |||||||
\(282\) | 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 | ||||
\(285\) | 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 | ||||
\(289\) | 42.8952 | 2.52324 | ||||||||
\(290\) | 19.4131 | 1.13997 | ||||||||
\(291\) | 0.849651 | − | 0.490546i | 0.0498074 | − | 0.0287563i | ||||
\(292\) | −0.125379 | + | 0.0723874i | −0.00733723 | + | 0.00423615i | ||||
\(293\) | 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 | ||||
\(296\) | −3.11179 | −0.180869 | ||||||||
\(297\) | −4.07974 | − | 2.35544i | −0.236730 | − | 0.136676i | ||||
\(298\) | −7.04829 | − | 12.2080i | −0.408297 | − | 0.707190i | ||||
\(299\) | 5.88768 | − | 0.781589i | 0.340493 | − | 0.0452005i | ||||
\(300\) | 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 | ||||
\(304\) | 2.92885 | − | 1.69097i | 0.167981 | − | 0.0969838i | ||||
\(305\) | 27.2004i | 1.55749i | ||||||||
\(306\) | −10.8458 | + | 6.26180i | −0.620011 | + | 0.357963i | ||||
\(307\) | 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 | ||||
\(310\) | − | 24.7278i | − | 1.40444i | ||||||
\(311\) | 0.0753271 | + | 0.130470i | 0.00427141 | + | 0.00739830i | 0.868153 | − | 0.496296i | \(-0.165307\pi\) |
−0.863882 | + | 0.503695i | \(0.831974\pi\) | |||||||
\(312\) | 20.1312 | + | 8.31317i | 1.13970 | + | 0.470641i | ||||
\(313\) | −5.26057 | + | 9.11157i | −0.297345 | + | 0.515016i | −0.975528 | − | 0.219877i | \(-0.929434\pi\) |
0.678183 | + | 0.734893i | \(0.262768\pi\) | |||||||
\(314\) | 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 | \(-0.319860\pi\) |
−0.462907 | + | 0.886407i | \(0.653194\pi\) | |||||||
\(318\) | − | 0.220607i | − | 0.0123710i | ||||||
\(319\) | 5.17202i | 0.289578i | ||||||||
\(320\) | 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 | ||||
\(325\) | −16.9884 | − | 22.0904i | −0.942349 | − | 1.22535i | ||||
\(326\) | −8.09314 | − | 14.0177i | −0.448237 | − | 0.776370i | ||||
\(327\) | 11.9708i | 0.661989i | ||||||||
\(328\) | −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 | −0.960993 | − | 0.276574i | \(-0.910801\pi\) |
−0.240976 | + | 0.970531i | \(0.577467\pi\) | |||||||
\(332\) | − | 0.442569i | − | 0.0242891i | ||||||
\(333\) | −1.10019 | + | 0.635193i | −0.0602899 | + | 0.0348084i | ||||
\(334\) | −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 | \(0.159866\pi\) | |||||||
\(338\) | −4.56264 | − | 16.8823i | −0.248175 | − | 0.918273i | ||||
\(339\) | 6.69598 | + | 11.5978i | 0.363676 | + | 0.629905i | ||||
\(340\) | −4.55213 | − | 2.62817i | −0.246874 | − | 0.142533i | ||||
\(341\) | 6.58797 | 0.356759 | ||||||||
\(342\) | 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 | ||||
\(346\) | −16.7521 | + | 9.67185i | −0.900600 | + | 0.519962i | ||||
\(347\) | 24.7638 | 1.32939 | 0.664695 | − | 0.747115i | \(-0.268562\pi\) | ||||
0.664695 | + | 0.747115i | \(0.268562\pi\) | |||||||
\(348\) | −1.57858 | −0.0846209 | ||||||||
\(349\) | 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 | ||||
\(353\) | 17.3971 | + | 10.0442i | 0.925953 | + | 0.534599i | 0.885529 | − | 0.464583i | \(-0.153796\pi\) |
0.0404237 | + | 0.999183i | \(0.487129\pi\) | |||||||
\(354\) | −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 | ||||
\(359\) | 13.0346 | + | 7.52551i | 0.687938 | + | 0.397181i | 0.802839 | − | 0.596196i | \(-0.203322\pi\) |
−0.114901 | + | 0.993377i | \(0.536655\pi\) | |||||||
\(360\) | 12.6458 | 0.666495 | ||||||||
\(361\) | −9.05455 | + | 15.6829i | −0.476555 | + | 0.825418i | ||||
\(362\) | − | 20.8378i | − | 1.09521i | ||||||
\(363\) | −19.1992 | −1.00770 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.71331 | 0.142021 | ||||||||
\(366\) | 21.0257i | 1.09903i | ||||||||
\(367\) | 4.50178 | − | 7.79731i | 0.234991 | − | 0.407016i | −0.724279 | − | 0.689507i | \(-0.757827\pi\) |
0.959270 | + | 0.282491i | \(0.0911607\pi\) | |||||||
\(368\) | 5.90223 | 0.307675 | ||||||||
\(369\) | −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 | ||||||||
\(373\) | 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 | ||||
\(376\) | −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 | \(0.465137\pi\) | |||||||
\(380\) | 0.641068 | 0.0328861 | ||||||||
\(381\) | 30.1700 | 1.54566 | ||||||||
\(382\) | −5.52935 | + | 3.19237i | −0.282906 | + | 0.163336i | ||||
\(383\) | −21.3327 | + | 12.3164i | −1.09005 | + | 0.629339i | −0.933589 | − | 0.358345i | \(-0.883341\pi\) |
−0.156459 | + | 0.987685i | \(0.550008\pi\) | |||||||
\(384\) | 16.7525 | + | 9.67207i | 0.854898 | + | 0.493576i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.1512 | − | 24.5106i | 0.720277 | − | 1.24756i | ||||
\(387\) | −4.60798 | −0.234237 | ||||||||
\(388\) | 0.0788960 | + | 0.0455506i | 0.00400534 | + | 0.00231248i | ||||
\(389\) | −9.42834 | − | 16.3304i | −0.478036 | − | 0.827982i | 0.521647 | − | 0.853161i | \(-0.325318\pi\) |
−0.999683 | + | 0.0251791i | \(0.991984\pi\) | |||||||
\(390\) | −21.6270 | − | 28.1221i | −1.09513 | − | 1.42402i | ||||
\(391\) | −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 | ||||
\(395\) | −8.82229 | + | 5.09355i | −0.443897 | + | 0.256284i | ||||
\(396\) | 0.292811i | 0.0147143i | ||||||||
\(397\) | 12.5600 | − | 7.25149i | 0.630366 | − | 0.363942i | −0.150528 | − | 0.988606i | \(-0.548097\pi\) |
0.780894 | + | 0.624664i | \(0.214764\pi\) | |||||||
\(398\) | − | 14.2839i | − | 0.715985i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.8467 | − | 23.9831i | −0.692333 | − | 1.19916i | ||||
\(401\) | − | 20.9889i | − | 1.04814i | −0.851676 | − | 0.524069i | \(-0.824413\pi\) | ||
0.851676 | − | 0.524069i | \(-0.175587\pi\) | |||||||
\(402\) | −8.71624 | − | 15.0970i | −0.434727 | − | 0.752968i | ||||
\(403\) | 14.7255 | − | 11.3245i | 0.733531 | − | 0.564116i | ||||
\(404\) | −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 | ||||
\(409\) | 21.4276i | 1.05953i | 0.848146 | + | 0.529763i | \(0.177719\pi\) | ||||
−0.848146 | + | 0.529763i | \(0.822281\pi\) | |||||||
\(410\) | 20.1521i | 0.995242i | ||||||||
\(411\) | −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 | ||||
\(416\) | 0.509155 | + | 3.83545i | 0.0249634 | + | 0.188048i | ||||
\(417\) | 6.00383 | + | 10.3989i | 0.294009 | + | 0.509238i | ||||
\(418\) | − | 1.62357i | − | 0.0794113i | ||||||
\(419\) | 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 | \(0.978125\pi\) | |||||||
\(422\) | 5.43530 | − | 3.13807i | 0.264586 | − | 0.152759i | ||||
\(423\) | 1.07568i | 0.0523011i | ||||||||
\(424\) | 0.204122 | − | 0.117850i | 0.00991306 | − | 0.00572331i | ||||
\(425\) | 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 | ||||||||
\(429\) | 7.49227 | − | 5.76187i | 0.361730 | − | 0.278186i | ||||
\(430\) | 9.19253 | + | 15.9219i | 0.443303 | + | 0.767823i | ||||
\(431\) | 4.96775 | + | 2.86813i | 0.239288 | + | 0.138153i | 0.614849 | − | 0.788645i | \(-0.289217\pi\) |
−0.375561 | + | 0.926797i | \(0.622550\pi\) | |||||||
\(432\) | −13.2006 | −0.635112 | ||||||||
\(433\) | 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 | ||||
\(436\) | −0.962653 | + | 0.555788i | −0.0461027 | + | 0.0266174i | ||||
\(437\) | 1.34652 | − | 0.777413i | 0.0644128 | − | 0.0371887i | ||||
\(438\) | 2.09736 | 0.100216 | ||||||||
\(439\) | 36.6423 | 1.74884 | 0.874420 | − | 0.485169i | \(-0.161242\pi\) | ||||
0.874420 | + | 0.485169i | \(0.161242\pi\) | |||||||
\(440\) | 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 | 0.340996 | + | 0.940065i | \(0.389236\pi\) |
−0.984618 | + | 0.174721i | \(0.944098\pi\) | |||||||
\(444\) | −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 | 0.941699 | − | 0.336456i | \(-0.109228\pi\) |
0.179470 | + | 0.983764i | \(0.442562\pi\) | |||||||
\(450\) | −10.8315 | − | 6.25358i | −0.510602 | − | 0.294796i | ||||
\(451\) | −5.36892 | −0.252812 | ||||||||
\(452\) | −0.621768 | + | 1.07693i | −0.0292455 | + | 0.0506547i | ||||
\(453\) | 9.66431i | 0.454069i | ||||||||
\(454\) | 20.6832 | 0.970712 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.70169 | 0.267006 | ||||||||
\(457\) | 39.6639i | 1.85540i | 0.373327 | + | 0.927700i | \(0.378217\pi\) | ||||
−0.373327 | + | 0.927700i | \(0.621783\pi\) | |||||||
\(458\) | 10.9982 | − | 19.0495i | 0.513913 | − | 0.890123i | ||||
\(459\) | 28.5127 | 1.33086 | ||||||||
\(460\) | 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 | \(-0.0349221\pi\) | |||||||
\(464\) | 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 | ||||
\(467\) | −16.0081 | + | 27.7268i | −0.740765 | + | 1.28304i | 0.211383 | + | 0.977403i | \(0.432203\pi\) |
−0.952147 | + | 0.305639i | \(0.901130\pi\) | |||||||
\(468\) | 0.503335 | + | 0.654496i | 0.0232667 | + | 0.0302541i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.71678 | − | 2.14588i | 0.171442 | − | 0.0989822i | ||||
\(471\) | 18.4552 | 0.850372 | ||||||||
\(472\) | −32.9563 | −1.51693 | ||||||||
\(473\) | −4.24191 | + | 2.44907i | −0.195043 | + | 0.112608i | ||||
\(474\) | −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 | ||||
\(478\) | −11.6417 | −0.532480 | ||||||||
\(479\) | −15.6097 | − | 9.01224i | −0.713224 | − | 0.411780i | 0.0990298 | − | 0.995084i | \(-0.468426\pi\) |
−0.812254 | + | 0.583305i | \(0.801759\pi\) | |||||||
\(480\) | 3.92447 | + | 6.79738i | 0.179127 | + | 0.310257i | ||||
\(481\) | 0.501083 | + | 3.77464i | 0.0228474 | + | 0.172109i | ||||
\(482\) | −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 | ||||
\(486\) | −13.7821 | + | 7.95712i | −0.625170 | + | 0.360942i | ||||
\(487\) | − | 17.6004i | − | 0.797550i | −0.917049 | − | 0.398775i | \(-0.869435\pi\) | ||
0.917049 | − | 0.398775i | \(-0.130565\pi\) | |||||||
\(488\) | −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 | 0.906318 | − | 0.422595i | \(-0.138881\pi\) |
−0.819138 | + | 0.573597i | \(0.805547\pi\) | |||||||
\(492\) | − | 1.63868i | − | 0.0738773i | ||||||
\(493\) | −15.6519 | − | 27.1099i | −0.704926 | − | 1.22097i | ||||
\(494\) | −2.79087 | − | 3.62902i | −0.125567 | − | 0.163277i | ||||
\(495\) | 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 | \(-0.424691\pi\) |
−0.724706 | + | 0.689058i | \(0.758024\pi\) | |||||||
\(500\) | − | 1.85351i | − | 0.0828917i | ||||||
\(501\) | − | 39.8171i | − | 1.77890i | ||||||
\(502\) | 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 | ||||
\(507\) | 6.84233 | − | 25.7580i | 0.303879 | − | 1.14395i | ||||
\(508\) | 1.40075 | + | 2.42617i | 0.0621482 | + | 0.107644i | ||||
\(509\) | − | 15.6702i | − | 0.694568i | −0.937760 | − | 0.347284i | \(-0.887104\pi\) | ||
0.937760 | − | 0.347284i | \(-0.112896\pi\) | |||||||
\(510\) | 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 | ||||
\(514\) | 32.7249i | 1.44344i | ||||||||
\(515\) | −35.0230 | + | 20.2206i | −1.54330 | + | 0.891025i | ||||
\(516\) | −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 | ||||||||
\(520\) | 14.4673 | − | 35.0341i | 0.634435 | − | 1.53635i | ||||
\(521\) | −12.6207 | − | 21.8598i | −0.552925 | − | 0.957694i | −0.998062 | − | 0.0622317i | \(-0.980178\pi\) |
0.445137 | − | 0.895463i | \(-0.353155\pi\) | |||||||
\(522\) | 5.66846 | + | 3.27269i | 0.248102 | + | 0.143242i | ||||
\(523\) | 13.2477 | 0.579279 | 0.289640 | − | 0.957136i | \(-0.406465\pi\) | ||||
0.289640 | + | 0.957136i | \(0.406465\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 8.13422 | − | 4.69629i | 0.353996 | − | 0.204380i | ||||
\(529\) | −20.2865 | −0.882021 | ||||||||
\(530\) | −0.383920 | −0.0166764 | ||||||||
\(531\) | −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 | ||||
\(535\) | 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 | ||||
\(541\) | −12.4737 | − | 7.20170i | −0.536287 | − | 0.309625i | 0.207286 | − | 0.978280i | \(-0.433537\pi\) |
−0.743573 | + | 0.668655i | \(0.766870\pi\) | |||||||
\(542\) | 36.2816 | 1.55843 | ||||||||
\(543\) | 15.8782 | − | 27.5019i | 0.681401 | − | 1.18022i | ||||
\(544\) | − | 8.30488i | − | 0.356069i | ||||||
\(545\) | 20.8328 | 0.892377 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00679 | 0.0858042 | 0.0429021 | − | 0.999079i | \(-0.486340\pi\) | ||||
0.0429021 | + | 0.999079i | \(0.486340\pi\) | |||||||
\(548\) | − | 3.35631i | − | 0.143375i | ||||||
\(549\) | −4.58550 | + | 7.94232i | −0.195704 | + | 0.338970i | ||||
\(550\) | −13.2947 | −0.566889 | ||||||||
\(551\) | 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 | ||||||||
\(555\) | 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 | 0.334267 | − | 0.942478i | \(-0.391511\pi\) |
−0.649077 | + | 0.760723i | \(0.724845\pi\) | |||||||
\(558\) | 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 | ||||
\(562\) | −35.9466 | −1.51631 | ||||||||
\(563\) | −12.7744 | −0.538375 | −0.269188 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269188 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(564\) | −0.302231 | + | 0.174493i | −0.0127262 | + | 0.00734750i | ||||
\(565\) | 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 | ||||
\(569\) | 5.79116 | 0.242778 | 0.121389 | − | 0.992605i | \(-0.461265\pi\) | ||||
0.121389 | + | 0.992605i | \(0.461265\pi\) | |||||||
\(570\) | −8.04295 | − | 4.64360i | −0.336882 | − | 0.194499i | ||||
\(571\) | −22.0666 | − | 38.2204i | −0.923458 | − | 1.59948i | −0.794023 | − | 0.607888i | \(-0.792017\pi\) |
−0.129435 | − | 0.991588i | \(-0.541316\pi\) | |||||||
\(572\) | 0.811204 | + | 0.334987i | 0.0339182 | + | 0.0140065i | ||||
\(573\) | −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 | ||||
\(577\) | −10.3343 | + | 5.96649i | −0.430221 | + | 0.248388i | −0.699441 | − | 0.714691i | \(-0.746568\pi\) |
0.269220 | + | 0.963079i | \(0.413234\pi\) | |||||||
\(578\) | − | 57.7037i | − | 2.40016i | ||||||
\(579\) | 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 | ||||
\(583\) | − | 0.102284i | − | 0.00423617i | ||||||
\(584\) | 1.12043 | + | 1.94064i | 0.0463637 | + | 0.0803043i | ||||
\(585\) | −2.03633 | − | 15.3396i | −0.0841919 | − | 0.634215i | ||||
\(586\) | 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 | ||||
\(591\) | − | 11.9154i | − | 0.490133i | ||||||
\(592\) | 3.78397i | 0.155520i | ||||||||
\(593\) | −15.7443 | − | 9.09000i | −0.646543 | − | 0.373282i | 0.140588 | − | 0.990068i | \(-0.455101\pi\) |
−0.787130 | + | 0.616787i | \(0.788434\pi\) | |||||||
\(594\) | −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 | ||||
\(598\) | −1.05141 | − | 7.92026i | −0.0429955 | − | 0.323884i | ||||
\(599\) | 19.1341 | + | 33.1412i | 0.781797 | + | 1.35411i | 0.930894 | + | 0.365290i | \(0.119030\pi\) |
−0.149096 | + | 0.988823i | \(0.547636\pi\) | |||||||
\(600\) | − | 46.6888i | − | 1.90606i | ||||||
\(601\) | −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 | ||||||
\(604\) | −0.777170 | + | 0.448699i | −0.0316226 | + | 0.0182573i | ||||
\(605\) | 33.4122i | 1.35840i | ||||||||
\(606\) | 6.87459 | − | 3.96904i | 0.279261 | − | 0.161231i | ||||
\(607\) | −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 | ||||||||
\(611\) | 2.98005 | + | 1.23061i | 0.120560 | + | 0.0497853i | ||||
\(612\) | −0.886124 | − | 1.53481i | −0.0358194 | − | 0.0620411i | ||||
\(613\) | 11.5089 | + | 6.64469i | 0.464842 | + | 0.268376i | 0.714078 | − | 0.700066i | \(-0.246846\pi\) |
−0.249236 | + | 0.968443i | \(0.580180\pi\) | |||||||
\(614\) | 39.4602 | 1.59248 | ||||||||
\(615\) | −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 | \(0.739223\pi\) | |||||||
\(618\) | −27.0724 | + | 15.6303i | −1.08901 | + | 0.628742i | ||||
\(619\) | 8.04109 | − | 4.64253i | 0.323199 | − | 0.186599i | −0.329619 | − | 0.944114i | \(-0.606920\pi\) |
0.652817 | + | 0.757515i | \(0.273587\pi\) | |||||||
\(620\) | 3.49929 | 0.140535 | ||||||||
\(621\) | −6.06888 | −0.243536 | ||||||||
\(622\) | 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 | ||||
\(626\) | 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 | 0.668484 | − | 0.743726i | \(-0.266943\pi\) |
−0.309844 | + | 0.950787i | \(0.600277\pi\) | |||||||
\(632\) | −7.28611 | − | 4.20664i | −0.289826 | − | 0.167331i | ||||
\(633\) | 9.56474 | 0.380164 | ||||||||
\(634\) | 1.01347 | − | 1.75538i | 0.0402499 | − | 0.0697149i | ||||
\(635\) | − | 52.5046i | − | 2.08358i | ||||||
\(636\) | 0.0312187 | 0.00123790 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.95754 | 0.275452 | ||||||||
\(639\) | − | 13.7422i | − | 0.543632i | ||||||
\(640\) | 16.8322 | − | 29.1542i | 0.665351 | − | 1.15242i | ||||
\(641\) | −14.8591 | −0.586899 | −0.293449 | − | 0.955975i | \(-0.594803\pi\) | ||||
−0.293449 | + | 0.955975i | \(0.594803\pi\) | |||||||
\(642\) | 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 | ||||||||
\(646\) | 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 | ||||
\(649\) | −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 | ||||
\(653\) | 3.98444 | 0.155923 | 0.0779615 | − | 0.996956i | \(-0.475159\pi\) | ||||
0.0779615 | + | 0.996956i | \(0.475159\pi\) | |||||||
\(654\) | 16.1035 | 0.629696 | ||||||||
\(655\) | −34.5645 | + | 19.9558i | −1.35055 | + | 0.779738i | ||||
\(656\) | −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 | −0.463504 | − | 0.886095i | \(-0.653408\pi\) |
0.999133 | − | 0.0416417i | \(-0.0132588\pi\) | |||||||
\(660\) | 1.78042 | 0.0693028 | ||||||||
\(661\) | −6.05023 | − | 3.49310i | −0.235327 | − | 0.135866i | 0.377700 | − | 0.925928i | \(-0.376715\pi\) |
−0.613027 | + | 0.790062i | \(0.710048\pi\) | |||||||
\(662\) | 16.9841 | + | 29.4173i | 0.660105 | + | 1.14333i | ||||
\(663\) | −21.8349 | + | 52.8752i | −0.847996 | + | 2.05350i | ||||
\(664\) | −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 | ||||
\(668\) | 3.20195 | − | 1.84865i | 0.123887 | − | 0.0715263i | ||||
\(669\) | 49.6646i | 1.92014i | ||||||||
\(670\) | −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 | 0.913800 | − | 0.406166i | \(-0.133134\pi\) |
−0.808649 | + | 0.588291i | \(0.799801\pi\) | |||||||
\(674\) | − | 43.2909i | − | 1.66750i | ||||||
\(675\) | 14.2376 | + | 24.6603i | 0.548006 | + | 0.949174i | ||||
\(676\) | 2.38905 | − | 0.645671i | 0.0918866 | − | 0.0248335i | ||||
\(677\) | 16.8961 | − | 29.2649i | 0.649371 | − | 1.12474i | −0.333903 | − | 0.942607i | \(-0.608366\pi\) |
0.983273 | − | 0.182135i | \(-0.0583009\pi\) | |||||||
\(678\) | 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 | ||||
\(682\) | − | 8.86231i | − | 0.339355i | ||||||
\(683\) | − | 12.2988i | − | 0.470602i | −0.971923 | − | 0.235301i | \(-0.924392\pi\) | ||
0.971923 | − | 0.235301i | \(-0.0756076\pi\) | |||||||
\(684\) | 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 | ||||
\(689\) | −0.175823 | − | 0.228627i | −0.00669834 | − | 0.00870998i | ||||
\(690\) | −8.10410 | − | 14.0367i | −0.308518 | − | 0.534369i | ||||
\(691\) | 11.0897i | 0.421871i | 0.977500 | + | 0.210935i | \(0.0676509\pi\) | ||||
−0.977500 | + | 0.210935i | \(0.932349\pi\) | |||||||
\(692\) | −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 | ||||
\(696\) | 24.4337i | 0.926156i | ||||||||
\(697\) | 28.1419 | − | 16.2478i | 1.06595 | − | 0.615428i | ||||
\(698\) | −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 | \(0.435559\pi\) | |||||||
\(702\) | 2.35153 | + | 17.7140i | 0.0887526 | + | 0.668571i | ||||
\(703\) | 0.498406 | + | 0.863265i | 0.0187977 | + | 0.0325587i | ||||
\(704\) | 9.53396 | + | 5.50443i | 0.359325 | + | 0.207456i | ||||
\(705\) | 6.54058 | 0.246333 | ||||||||
\(706\) | 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 | 0.339605 | − | 0.940568i | \(-0.389707\pi\) |
0.984358 | + | 0.176178i | \(0.0563733\pi\) | |||||||
\(710\) | −47.4833 | + | 27.4145i | −1.78202 | + | 1.02885i | ||||
\(711\) | −3.43472 | −0.128812 | ||||||||
\(712\) | 22.3237 | 0.836618 | ||||||||
\(713\) | 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 | ||||
\(717\) | −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 | ||||
\(723\) | −32.3098 | − | 18.6541i | −1.20161 | − | 0.693752i | ||||
\(724\) | 2.94881 | 0.109592 | ||||||||
\(725\) | 15.6313 | − | 27.0743i | 0.580533 | − | 1.00551i | ||||
\(726\) | 25.8273i | 0.958540i | ||||||||
\(727\) | 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 | ||||||||
\(730\) | − | 3.65002i | − | 0.135093i | ||||||
\(731\) | 14.8231 | − | 25.6743i | 0.548251 | − | 0.949598i | ||||
\(732\) | −2.97539 | −0.109974 | ||||||||
\(733\) | 19.3256 | + | 11.1577i | 0.713809 | + | 0.412118i | 0.812470 | − | 0.583003i | \(-0.198123\pi\) |
−0.0986608 | + | 0.995121i | \(0.531456\pi\) | |||||||
\(734\) | −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 | −0.361653 | − | 0.932313i | \(-0.617787\pi\) |
−0.988233 | + | 0.152956i | \(0.951121\pi\) | |||||||
\(740\) | −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 | \(0.525723\pi\) | |||||||
\(744\) | 31.1229 | 1.14102 | ||||||||
\(745\) | −37.3866 | −1.36974 | ||||||||
\(746\) | 18.8020 | − | 10.8553i | 0.688390 | − | 0.397442i | ||||
\(747\) | −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 | ||||
\(751\) | −22.5660 | −0.823444 | −0.411722 | − | 0.911309i | \(-0.635073\pi\) | ||||
−0.411722 | + | 0.911309i | \(0.635073\pi\) | |||||||
\(752\) | 2.77475 | + | 1.60200i | 0.101185 | + | 0.0584190i | ||||
\(753\) | 16.2696 | + | 28.1798i | 0.592897 | + | 1.02693i | ||||
\(754\) | 15.5516 | − | 11.9598i | 0.566356 | − | 0.435551i | ||||
\(755\) | 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 | \(-0.366213\pi\) | |||||||
\(758\) | 10.5368 | + | 18.2504i | 0.382716 | + | 0.662883i | ||||
\(759\) | 3.73966 | − | 2.15909i | 0.135741 | − | 0.0783701i | ||||
\(760\) | − | 9.92260i | − | 0.359931i | ||||||
\(761\) | 25.7657 | − | 14.8758i | 0.934006 | − | 0.539249i | 0.0459296 | − | 0.998945i | \(-0.485375\pi\) |
0.888076 | + | 0.459696i | \(0.152042\pi\) | |||||||
\(762\) | − | 40.5855i | − | 1.47026i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.451761 | − | 0.782473i | −0.0163441 | − | 0.0283089i | ||||
\(765\) | 33.2148i | 1.20088i | ||||||||
\(766\) | 16.5684 | + | 28.6972i | 0.598639 | + | 1.03687i | ||||
\(767\) | 5.30687 | + | 39.9764i | 0.191620 | + | 1.44347i | ||||
\(768\) | −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 | ||||
\(773\) | − | 41.4336i | − | 1.49026i | −0.666917 | − | 0.745132i | \(-0.732387\pi\) | ||
0.666917 | − | 0.745132i | \(-0.267613\pi\) | |||||||
\(774\) | 6.19877i | 0.222810i | ||||||||
\(775\) | −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 | ||||
\(780\) | 3.97963 | − | 3.06050i | 0.142493 | − | 0.109583i | ||||
\(781\) | −7.30376 | − | 12.6505i | −0.261349 | − | 0.452670i | ||||
\(782\) | 17.1497i | 0.613273i | ||||||||
\(783\) | −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 | ||||
\(787\) | − | 23.8627i | − | 0.850612i | −0.905050 | − | 0.425306i | \(-0.860167\pi\) | ||
0.905050 | − | 0.425306i | \(-0.139833\pi\) | |||||||
\(788\) | 0.958193 | − | 0.553213i | 0.0341342 | − | 0.0197074i | ||||
\(789\) | 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 | ||||||||
\(793\) | 16.7574 | + | 21.7900i | 0.595073 | + | 0.773785i | ||||
\(794\) | −9.75490 | − | 16.8960i | −0.346188 | − | 0.599616i | ||||
\(795\) | −0.506701 | − | 0.292544i | −0.0179708 | − | 0.0103755i | ||||
\(796\) | 2.02135 | 0.0716447 | ||||||||
\(797\) | −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 | ||||
\(800\) | 7.18279 | − | 4.14699i | 0.253950 | − | 0.146618i | ||||
\(801\) | 7.89267 | − | 4.55683i | 0.278874 | − | 0.161008i | ||||
\(802\) | −28.2349 | −0.997008 | ||||||||
\(803\) | 0.972438 | 0.0343166 | ||||||||
\(804\) | 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 | ||||
\(808\) | 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 | \(0.100287\pi\) | ||||
−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 | ||||
\(815\) | −42.9288 | −1.50373 | ||||||||
\(816\) | −28.4244 | + | 49.2326i | −0.995054 | + | 1.72348i | ||||
\(817\) | 3.61566i | 0.126496i | ||||||||
\(818\) | 28.8249 | 1.00784 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.85178 | −0.0995884 | ||||||||
\(821\) | − | 3.56043i | − | 0.124260i | −0.998068 | − | 0.0621299i | \(-0.980211\pi\) | ||
0.998068 | − | 0.0621299i | \(-0.0197893\pi\) | |||||||
\(822\) | −24.3116 | + | 42.1089i | −0.847964 | + | 1.46872i | ||||
\(823\) | −21.8665 | −0.762217 | −0.381109 | − | 0.924530i | \(-0.624458\pi\) | ||||
−0.381109 | + | 0.924530i | \(0.624458\pi\) | |||||||
\(824\) | −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 | \(-0.102114\pi\) | |||||||
\(828\) | 0.188610 | + | 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 | ||||
\(831\) | −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 | ||||
\(835\) | −69.2933 | −2.39799 | ||||||||
\(836\) | 0.229755 | 0.00794625 | ||||||||
\(837\) | −16.4386 | + | 9.49084i | −0.568202 | + | 0.328051i | ||||
\(838\) | 9.27813 | − | 5.35673i | 0.320508 | − | 0.185045i | ||||
\(839\) | 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 | ||||
\(842\) | 3.79065 | 0.130635 | ||||||||
\(843\) | −47.4426 | − | 27.3910i | −1.63401 | − | 0.943396i | ||||
\(844\) | 0.444076 | + | 0.769163i | 0.0152857 | + | 0.0264757i | ||||
\(845\) | −44.8265 | − | 11.9076i | −1.54208 | − | 0.409636i | ||||
\(846\) | 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 | ||||
\(850\) | 69.6862 | − | 40.2333i | 2.39022 | − | 1.37999i | ||||
\(851\) | 1.73966i | 0.0596347i | ||||||||
\(852\) | 3.86113 | − | 2.22922i | 0.132280 | − | 0.0763719i | ||||
\(853\) | − | 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 | ||||
\(856\) | 19.3648i | 0.661877i | ||||||||
\(857\) | 15.0525 | + | 26.0717i | 0.514184 | + | 0.890592i | 0.999865 | + | 0.0164561i | \(0.00523837\pi\) |
−0.485681 | + | 0.874136i | \(0.661428\pi\) | |||||||
\(858\) | −7.75102 | − | 10.0788i | −0.264615 | − | 0.344085i | ||||
\(859\) | −7.56717 | + | 13.1067i | −0.258188 | + | 0.447195i | −0.965757 | − | 0.259450i | \(-0.916459\pi\) |
0.707568 | + | 0.706645i | \(0.249792\pi\) | |||||||
\(860\) | −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 | \(-0.232707\pi\) |
−0.205988 | + | 0.978555i | \(0.566041\pi\) | |||||||
\(864\) | − | 3.95348i | − | 0.134500i | ||||||
\(865\) | 51.3029i | 1.74435i | ||||||||
\(866\) | −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 | ||||
\(871\) | −21.0654 | − | 8.69895i | −0.713772 | − | 0.294753i | ||||
\(872\) | 8.60263 | + | 14.9002i | 0.291322 | + | 0.504584i | ||||
\(873\) | − | 0.575668i | − | 0.0194834i | ||||||
\(874\) | −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 | −0.598799 | − | 0.800899i | \(-0.704355\pi\) |
0.394199 | + | 0.919025i | \(0.371022\pi\) | |||||||
\(878\) | − | 49.2922i | − | 1.66353i | ||||||
\(879\) | 20.5650 | − | 11.8732i | 0.693641 | − | 0.400474i | ||||
\(880\) | −8.17292 | − | 14.1559i | −0.275509 | − | 0.477195i | ||||
\(881\) | −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 | \(0.589286\pi\) | |||||||
\(884\) | −5.26580 | + | 0.699034i | −0.177108 | + | 0.0235111i | ||||
\(885\) | 40.9043 | + | 70.8484i | 1.37498 | + | 2.38154i | ||||
\(886\) | 31.5637 | + | 18.2233i | 1.06040 | + | 0.612225i | ||||
\(887\) | −55.2455 | −1.85496 | −0.927481 | − | 0.373871i | \(-0.878030\pi\) | ||||
−0.927481 | + | 0.373871i | \(0.878030\pi\) | |||||||
\(888\) | −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 | ||||
\(892\) | −3.99385 | + | 2.30585i | −0.133724 | + | 0.0772056i | ||||
\(893\) | 0.844032 | 0.0282444 | ||||||||
\(894\) | −28.8995 | −0.966542 | ||||||||
\(895\) | −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 | ||||
\(899\) | 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 | ||||
\(905\) | −47.8614 | − | 27.6328i | −1.59097 | − | 0.918544i | ||||
\(906\) | 13.0007 | 0.431919 | ||||||||
\(907\) | 23.9212 | − | 41.4327i | 0.794290 | − | 1.37575i | −0.128998 | − | 0.991645i | \(-0.541176\pi\) |
0.923289 | − | 0.384107i | \(-0.125490\pi\) | |||||||
\(908\) | 2.92694i | 0.0971338i | ||||||||
\(909\) | 3.46245 | 0.114842 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.0711 | −0.764380 | −0.382190 | − | 0.924084i | \(-0.624830\pi\) | ||||
−0.382190 | + | 0.924084i | \(0.624830\pi\) | |||||||
\(912\) | − | 6.93333i | − | 0.229585i | ||||||
\(913\) | −1.48635 | + | 2.57443i | −0.0491909 | + | 0.0852011i | ||||
\(914\) | 53.3569 | 1.76489 | ||||||||
\(915\) | 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 | ||||||
\(919\) | 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 | ||||
\(922\) | 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 | ||||
\(926\) | −6.33861 | −0.208300 | ||||||||
\(927\) | −13.6353 | −0.447841 | ||||||||
\(928\) | −3.75897 | + | 2.17024i | −0.123394 | + | 0.0712418i | ||||
\(929\) | −11.0695 | + | 6.39095i | −0.363177 | + | 0.209680i | −0.670474 | − | 0.741933i | \(-0.733909\pi\) |
0.307296 | + | 0.951614i | \(0.400576\pi\) | |||||||
\(930\) | −43.9027 | − | 25.3473i | −1.43963 | − | 0.831169i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.77085 | + | 4.79926i | −0.0907623 | + | 0.157205i | ||||
\(933\) | 0.308857 | 0.0101115 | ||||||||
\(934\) | 37.2988 | + | 21.5345i | 1.22045 | + | 0.704629i | ||||
\(935\) | 17.6532 | + | 30.5762i | 0.577320 | + | 0.999948i | ||||
\(936\) | 10.1305 | − | 7.79074i | 0.331124 | − | 0.254648i | ||||
\(937\) | −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 | ||||
\(941\) | −39.1000 | + | 22.5744i | −1.27462 | + | 0.735905i | −0.975855 | − | 0.218420i | \(-0.929910\pi\) |
−0.298770 | + | 0.954325i | \(0.596576\pi\) | |||||||
\(942\) | − | 24.8265i | − | 0.808890i | ||||||
\(943\) | −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 | ||||
\(947\) | − | 19.8557i | − | 0.645225i | −0.946531 | − | 0.322612i | \(-0.895439\pi\) | ||
0.946531 | − | 0.322612i | \(-0.104561\pi\) | |||||||
\(948\) | −0.557172 | − | 0.965050i | −0.0180961 | − | 0.0313434i | ||||
\(949\) | 2.17361 | − | 1.67160i | 0.0705583 | − | 0.0542623i | ||||
\(950\) | −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 | ||||
\(955\) | 16.9335i | 0.547954i | ||||||||
\(956\) | − | 1.64745i | − | 0.0532823i | ||||||
\(957\) | 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 | ||||
\(962\) | 5.07775 | − | 0.674070i | 0.163713 | − | 0.0217329i | ||||
\(963\) | 3.95285 | + | 6.84653i | 0.127379 | + | 0.220626i | ||||
\(964\) | − | 3.46432i | − | 0.111578i | ||||||
\(965\) | −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 | \(0.683037\pi\) | |||||||
\(968\) | −23.8974 | + | 13.7972i | −0.768091 | + | 0.443458i | ||||
\(969\) | 14.9757i | 0.481089i | ||||||||
\(970\) | −1.98910 | + | 1.14841i | −0.0638663 | + | 0.0368732i | ||||
\(971\) | −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 | ||||||||
\(975\) | −56.6342 | + | 7.51819i | −1.81375 | + | 0.240775i | ||||
\(976\) | 13.6584 | + | 23.6570i | 0.437193 | + | 0.757241i | ||||
\(977\) | −35.5369 | − | 20.5172i | −1.13693 | − | 0.656405i | −0.191259 | − | 0.981540i | \(-0.561257\pi\) |
−0.945668 | + | 0.325135i | \(0.894590\pi\) | |||||||
\(978\) | −33.1835 | −1.06109 | ||||||||
\(979\) | 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 | ||||
\(983\) | 23.2379 | − | 13.4164i | 0.741173 | − | 0.427916i | −0.0813229 | − | 0.996688i | \(-0.525915\pi\) |
0.822496 | + | 0.568772i | \(0.192581\pi\) | |||||||
\(984\) | −25.3639 | −0.808571 | ||||||||
\(985\) | −20.7362 | −0.660711 | ||||||||
\(986\) | −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 | ||||
\(990\) | −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 | ||||
\(996\) | −0.785755 | − | 0.453656i | −0.0248976 | − | 0.0143746i | ||||
\(997\) | 53.9097 | 1.70734 | 0.853669 | − | 0.520816i | \(-0.174372\pi\) | ||||
0.853669 | + | 0.520816i | \(0.174372\pi\) | |||||||
\(998\) | −8.50671 | + | 14.7341i | −0.269275 | + | 0.466398i | ||||
\(999\) | − | 3.89081i | − | 0.123100i |
(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.k.i.569.2 | 12 | ||
7.2 | even | 3 | 637.2.q.i.491.2 | 12 | |||
7.3 | odd | 6 | 91.2.u.b.88.5 | yes | 12 | ||
7.4 | even | 3 | 637.2.u.g.361.5 | 12 | |||
7.5 | odd | 6 | 637.2.q.g.491.2 | 12 | |||
7.6 | odd | 2 | 91.2.k.b.23.2 | yes | 12 | ||
13.4 | even | 6 | 637.2.u.g.30.5 | 12 | |||
21.17 | even | 6 | 819.2.do.e.361.2 | 12 | |||
21.20 | even | 2 | 819.2.bm.f.478.5 | 12 | |||
91.2 | odd | 12 | 8281.2.a.co.1.4 | 12 | |||
91.4 | even | 6 | inner | 637.2.k.i.459.5 | 12 | ||
91.17 | odd | 6 | 91.2.k.b.4.5 | ✓ | 12 | ||
91.24 | even | 12 | 1183.2.e.j.508.4 | 24 | |||
91.30 | even | 6 | 637.2.q.i.589.2 | 12 | |||
91.37 | odd | 12 | 8281.2.a.co.1.9 | 12 | |||
91.41 | even | 12 | 1183.2.e.j.170.9 | 24 | |||
91.54 | even | 12 | 8281.2.a.cp.1.4 | 12 | |||
91.69 | odd | 6 | 91.2.u.b.30.5 | yes | 12 | ||
91.76 | even | 12 | 1183.2.e.j.170.4 | 24 | |||
91.80 | even | 12 | 1183.2.e.j.508.9 | 24 | |||
91.82 | odd | 6 | 637.2.q.g.589.2 | 12 | |||
91.89 | even | 12 | 8281.2.a.cp.1.9 | 12 | |||
273.17 | even | 6 | 819.2.bm.f.550.2 | 12 | |||
273.251 | even | 6 | 819.2.do.e.667.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.5 | ✓ | 12 | 91.17 | odd | 6 | ||
91.2.k.b.23.2 | yes | 12 | 7.6 | odd | 2 | ||
91.2.u.b.30.5 | yes | 12 | 91.69 | odd | 6 | ||
91.2.u.b.88.5 | yes | 12 | 7.3 | odd | 6 | ||
637.2.k.i.459.5 | 12 | 91.4 | even | 6 | inner | ||
637.2.k.i.569.2 | 12 | 1.1 | even | 1 | trivial | ||
637.2.q.g.491.2 | 12 | 7.5 | odd | 6 | |||
637.2.q.g.589.2 | 12 | 91.82 | odd | 6 | |||
637.2.q.i.491.2 | 12 | 7.2 | even | 3 | |||
637.2.q.i.589.2 | 12 | 91.30 | even | 6 | |||
637.2.u.g.30.5 | 12 | 13.4 | even | 6 | |||
637.2.u.g.361.5 | 12 | 7.4 | even | 3 | |||
819.2.bm.f.478.5 | 12 | 21.20 | even | 2 | |||
819.2.bm.f.550.2 | 12 | 273.17 | even | 6 | |||
819.2.do.e.361.2 | 12 | 21.17 | even | 6 | |||
819.2.do.e.667.2 | 12 | 273.251 | even | 6 | |||
1183.2.e.j.170.4 | 24 | 91.76 | even | 12 | |||
1183.2.e.j.170.9 | 24 | 91.41 | even | 12 | |||
1183.2.e.j.508.4 | 24 | 91.24 | even | 12 | |||
1183.2.e.j.508.9 | 24 | 91.80 | even | 12 | |||
8281.2.a.co.1.4 | 12 | 91.2 | odd | 12 | |||
8281.2.a.co.1.9 | 12 | 91.37 | odd | 12 | |||
8281.2.a.cp.1.4 | 12 | 91.54 | even | 12 | |||
8281.2.a.cp.1.9 | 12 | 91.89 | even | 12 |