Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
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, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (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: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 324.10 | ||
Character | \(\chi\) | \(=\) | 637.324 |
Dual form | 637.2.r.g.116.10 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.589067 | + | 0.340098i | 0.416533 | + | 0.240486i | 0.693593 | − | 0.720367i | \(-0.256027\pi\) |
−0.277060 | + | 0.960853i | \(0.589360\pi\) | |||||||
\(3\) | 1.16706 | + | 2.02141i | 0.673804 | + | 1.16706i | 0.976817 | + | 0.214077i | \(0.0686743\pi\) |
−0.303012 | + | 0.952987i | \(0.597992\pi\) | |||||||
\(4\) | −0.768667 | − | 1.33137i | −0.384333 | − | 0.665685i | ||||
\(5\) | −2.81123 | − | 1.62306i | −1.25722 | − | 0.725856i | −0.284686 | − | 0.958621i | \(-0.591889\pi\) |
−0.972533 | + | 0.232765i | \(0.925223\pi\) | |||||||
\(6\) | 1.58766i | 0.648161i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.40608i | − | 0.850678i | ||||||
\(9\) | −1.22407 | + | 2.12016i | −0.408025 | + | 0.706720i | ||||
\(10\) | −1.10400 | − | 1.91219i | −0.349116 | − | 0.604686i | ||||
\(11\) | 4.61728 | − | 2.66579i | 1.39216 | − | 0.803765i | 0.398607 | − | 0.917122i | \(-0.369494\pi\) |
0.993554 | + | 0.113357i | \(0.0361603\pi\) | |||||||
\(12\) | 1.79417 | − | 3.10759i | 0.517931 | − | 0.897083i | ||||
\(13\) | −1.47728 | − | 3.28902i | −0.409723 | − | 0.912210i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7.57687i | − | 1.95634i | ||||||
\(16\) | −0.719029 | + | 1.24540i | −0.179757 | + | 0.311349i | ||||
\(17\) | 1.33421 | + | 2.31092i | 0.323593 | + | 0.560480i | 0.981227 | − | 0.192858i | \(-0.0617758\pi\) |
−0.657633 | + | 0.753338i | \(0.728442\pi\) | |||||||
\(18\) | −1.44212 | + | 0.832611i | −0.339912 | + | 0.196248i | ||||
\(19\) | −0.603203 | − | 0.348259i | −0.138384 | − | 0.0798962i | 0.429209 | − | 0.903205i | \(-0.358792\pi\) |
−0.567594 | + | 0.823309i | \(0.692126\pi\) | |||||||
\(20\) | 4.99038i | 1.11588i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.62652 | 0.773176 | ||||||||
\(23\) | 4.48044 | − | 7.76035i | 0.934236 | − | 1.61814i | 0.158245 | − | 0.987400i | \(-0.449417\pi\) |
0.775991 | − | 0.630744i | \(-0.217250\pi\) | |||||||
\(24\) | 4.86368 | − | 2.80805i | 0.992795 | − | 0.573191i | ||||
\(25\) | 2.76867 | + | 4.79547i | 0.553733 | + | 0.959094i | ||||
\(26\) | 0.248375 | − | 2.43987i | 0.0487103 | − | 0.478498i | ||||
\(27\) | 1.28809 | 0.247893 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.28644 | −0.981667 | −0.490833 | − | 0.871253i | \(-0.663308\pi\) | ||||
−0.490833 | + | 0.871253i | \(0.663308\pi\) | |||||||
\(30\) | 2.57688 | − | 4.46329i | 0.470472 | − | 0.814881i | ||||
\(31\) | 4.72808 | − | 2.72976i | 0.849188 | − | 0.490279i | −0.0111891 | − | 0.999937i | \(-0.503562\pi\) |
0.860377 | + | 0.509659i | \(0.170228\pi\) | |||||||
\(32\) | −5.01457 | + | 2.89516i | −0.886459 | + | 0.511797i | ||||
\(33\) | 10.7773 | + | 6.22229i | 1.87609 | + | 1.08316i | ||||
\(34\) | 1.81505i | 0.311278i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.76362 | 0.627270 | ||||||||
\(37\) | −5.79541 | − | 3.34598i | −0.952760 | − | 0.550076i | −0.0588228 | − | 0.998268i | \(-0.518735\pi\) |
−0.893937 | + | 0.448192i | \(0.852068\pi\) | |||||||
\(38\) | −0.236885 | − | 0.410296i | −0.0384278 | − | 0.0665588i | ||||
\(39\) | 4.92440 | − | 6.82468i | 0.788534 | − | 1.09282i | ||||
\(40\) | −3.90522 | + | 6.76404i | −0.617470 | + | 1.06949i | ||||
\(41\) | 2.21339i | 0.345673i | 0.984951 | + | 0.172836i | \(0.0552932\pi\) | ||||
−0.984951 | + | 0.172836i | \(0.944707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.39014 | 0.364493 | 0.182246 | − | 0.983253i | \(-0.441663\pi\) | ||||
0.182246 | + | 0.983253i | \(0.441663\pi\) | |||||||
\(44\) | −7.09829 | − | 4.09820i | −1.07011 | − | 0.617827i | ||||
\(45\) | 6.88231 | − | 3.97350i | 1.02595 | − | 0.592335i | ||||
\(46\) | 5.27856 | − | 3.04758i | 0.778281 | − | 0.449341i | ||||
\(47\) | −5.01925 | − | 2.89787i | −0.732133 | − | 0.422697i | 0.0870689 | − | 0.996202i | \(-0.472250\pi\) |
−0.819202 | + | 0.573505i | \(0.805583\pi\) | |||||||
\(48\) | −3.35661 | −0.484485 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.76647i | 0.532660i | ||||||||
\(51\) | −3.11421 | + | 5.39397i | −0.436077 | + | 0.755307i | ||||
\(52\) | −3.24337 | + | 4.49496i | −0.449774 | + | 0.623339i | ||||
\(53\) | 2.35785 | + | 4.08392i | 0.323876 | + | 0.560969i | 0.981284 | − | 0.192565i | \(-0.0616807\pi\) |
−0.657409 | + | 0.753534i | \(0.728347\pi\) | |||||||
\(54\) | 0.758771 | + | 0.438077i | 0.103256 | + | 0.0596147i | ||||
\(55\) | −17.3070 | −2.33367 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.62576i | − | 0.215338i | ||||||
\(58\) | −3.11407 | − | 1.79791i | −0.408897 | − | 0.236077i | ||||
\(59\) | −2.58136 | + | 1.49035i | −0.336065 | + | 0.194027i | −0.658531 | − | 0.752554i | \(-0.728822\pi\) |
0.322466 | + | 0.946581i | \(0.395488\pi\) | |||||||
\(60\) | −10.0876 | + | 5.82409i | −1.30231 | + | 0.751886i | ||||
\(61\) | −1.09732 | + | 1.90062i | −0.140498 | + | 0.243350i | −0.927684 | − | 0.373366i | \(-0.878204\pi\) |
0.787186 | + | 0.616715i | \(0.211537\pi\) | |||||||
\(62\) | 3.71354 | 0.471620 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.06244 | −0.132805 | ||||||||
\(65\) | −1.18533 | + | 11.6439i | −0.147022 | + | 1.44425i | ||||
\(66\) | 4.23238 | + | 7.33069i | 0.520969 | + | 0.902345i | ||||
\(67\) | 7.53957 | − | 4.35297i | 0.921105 | − | 0.531800i | 0.0371174 | − | 0.999311i | \(-0.488182\pi\) |
0.883987 | + | 0.467511i | \(0.154849\pi\) | |||||||
\(68\) | 2.05112 | − | 3.55265i | 0.248735 | − | 0.430822i | ||||
\(69\) | 20.9158 | 2.51797 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.56190i | 1.01611i | 0.861325 | + | 0.508055i | \(0.169635\pi\) | ||||
−0.861325 | + | 0.508055i | \(0.830365\pi\) | |||||||
\(72\) | 5.10128 | + | 2.94522i | 0.601191 | + | 0.347098i | ||||
\(73\) | −5.09355 | + | 2.94076i | −0.596155 | + | 0.344190i | −0.767527 | − | 0.641016i | \(-0.778513\pi\) |
0.171373 | + | 0.985206i | \(0.445180\pi\) | |||||||
\(74\) | −2.27593 | − | 3.94202i | −0.264571 | − | 0.458250i | ||||
\(75\) | −6.46242 | + | 11.1932i | −0.746216 | + | 1.29248i | ||||
\(76\) | 1.07078i | 0.122827i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.22186 | − | 2.34542i | 0.591259 | − | 0.265566i | ||||
\(79\) | −0.455408 | + | 0.788790i | −0.0512374 | + | 0.0887458i | −0.890507 | − | 0.454970i | \(-0.849650\pi\) |
0.839269 | + | 0.543716i | \(0.182983\pi\) | |||||||
\(80\) | 4.04271 | − | 2.33406i | 0.451989 | − | 0.260956i | ||||
\(81\) | 5.17551 | + | 8.96424i | 0.575056 | + | 0.996027i | ||||
\(82\) | −0.752769 | + | 1.30383i | −0.0831294 | + | 0.143984i | ||||
\(83\) | 11.7481i | 1.28952i | 0.764387 | + | 0.644758i | \(0.223042\pi\) | ||||
−0.764387 | + | 0.644758i | \(0.776958\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 8.66202i | − | 0.939528i | ||||||
\(86\) | 1.40795 | + | 0.812881i | 0.151823 | + | 0.0876553i | ||||
\(87\) | −6.16961 | − | 10.6861i | −0.661451 | − | 1.14567i | ||||
\(88\) | −6.41410 | − | 11.1095i | −0.683745 | − | 1.18428i | ||||
\(89\) | 0.853918 | + | 0.493010i | 0.0905151 | + | 0.0522589i | 0.544574 | − | 0.838713i | \(-0.316691\pi\) |
−0.454059 | + | 0.890971i | \(0.650025\pi\) | |||||||
\(90\) | 5.40552 | 0.569792 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −13.7758 | −1.43623 | ||||||||
\(93\) | 11.0359 | + | 6.37160i | 1.14437 | + | 0.660704i | ||||
\(94\) | −1.97112 | − | 3.41408i | −0.203305 | − | 0.352135i | ||||
\(95\) | 1.13049 | + | 1.95807i | 0.115986 | + | 0.200894i | ||||
\(96\) | −11.7046 | − | 6.75768i | −1.19460 | − | 0.689702i | ||||
\(97\) | − | 15.3454i | − | 1.55809i | −0.626969 | − | 0.779044i | \(-0.715705\pi\) | ||
0.626969 | − | 0.779044i | \(-0.284295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.0525i | 1.31182i | ||||||||
\(100\) | 4.25636 | − | 7.37224i | 0.425636 | − | 0.737224i | ||||
\(101\) | −1.95463 | − | 3.38552i | −0.194493 | − | 0.336872i | 0.752241 | − | 0.658888i | \(-0.228973\pi\) |
−0.946734 | + | 0.322016i | \(0.895640\pi\) | |||||||
\(102\) | −3.66896 | + | 2.11828i | −0.363281 | + | 0.209741i | ||||
\(103\) | 9.28058 | − | 16.0744i | 0.914443 | − | 1.58386i | 0.106728 | − | 0.994288i | \(-0.465963\pi\) |
0.807715 | − | 0.589573i | \(-0.200704\pi\) | |||||||
\(104\) | −7.91365 | + | 3.55444i | −0.775997 | + | 0.348542i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.20760i | 0.311550i | ||||||||
\(107\) | −6.55292 | + | 11.3500i | −0.633495 | + | 1.09724i | 0.353337 | + | 0.935496i | \(0.385047\pi\) |
−0.986832 | + | 0.161749i | \(0.948287\pi\) | |||||||
\(108\) | −0.990111 | − | 1.71492i | −0.0952735 | − | 0.165018i | ||||
\(109\) | −13.3350 | + | 7.69895i | −1.27726 | + | 0.737426i | −0.976344 | − | 0.216225i | \(-0.930626\pi\) |
−0.300916 | + | 0.953651i | \(0.597292\pi\) | |||||||
\(110\) | −10.1950 | − | 5.88606i | −0.972052 | − | 0.561214i | ||||
\(111\) | − | 15.6199i | − | 1.48258i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.7346 | 1.19797 | 0.598985 | − | 0.800761i | \(-0.295571\pi\) | ||||
0.598985 | + | 0.800761i | \(0.295571\pi\) | |||||||
\(114\) | 0.552919 | − | 0.957684i | 0.0517856 | − | 0.0896953i | ||||
\(115\) | −25.1911 | + | 14.5441i | −2.34908 | + | 1.35624i | ||||
\(116\) | 4.06351 | + | 7.03820i | 0.377287 | + | 0.653481i | ||||
\(117\) | 8.78154 | + | 0.893946i | 0.811854 | + | 0.0826454i | ||||
\(118\) | −2.02746 | −0.186643 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −18.2306 | −1.66422 | ||||||||
\(121\) | 8.71284 | − | 15.0911i | 0.792076 | − | 1.37192i | ||||
\(122\) | −1.29280 | + | 0.746396i | −0.117044 | + | 0.0675755i | ||||
\(123\) | −4.47417 | + | 2.58316i | −0.403422 | + | 0.232916i | ||||
\(124\) | −7.26863 | − | 4.19654i | −0.652742 | − | 0.376861i | ||||
\(125\) | − | 1.74425i | − | 0.156011i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2763 | 0.911878 | 0.455939 | − | 0.890011i | \(-0.349303\pi\) | ||||
0.455939 | + | 0.890011i | \(0.349303\pi\) | |||||||
\(128\) | 9.40329 | + | 5.42899i | 0.831141 | + | 0.479859i | ||||
\(129\) | 2.78944 | + | 4.83146i | 0.245597 | + | 0.425386i | ||||
\(130\) | −4.65831 | + | 6.45591i | −0.408560 | + | 0.566221i | ||||
\(131\) | 6.29063 | − | 10.8957i | 0.549615 | − | 0.951961i | −0.448686 | − | 0.893690i | \(-0.648108\pi\) |
0.998301 | − | 0.0582718i | \(-0.0185590\pi\) | |||||||
\(132\) | − | 19.1315i | − | 1.66518i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.92175 | 0.511561 | ||||||||
\(135\) | −3.62111 | − | 2.09065i | −0.311656 | − | 0.179934i | ||||
\(136\) | 5.56025 | − | 3.21021i | 0.476788 | − | 0.275274i | ||||
\(137\) | 1.49466 | − | 0.862942i | 0.127697 | − | 0.0737261i | −0.434791 | − | 0.900532i | \(-0.643178\pi\) |
0.562488 | + | 0.826805i | \(0.309844\pi\) | |||||||
\(138\) | 12.3208 | + | 7.11343i | 1.04882 | + | 0.605536i | ||||
\(139\) | 2.93311 | 0.248783 | 0.124391 | − | 0.992233i | \(-0.460302\pi\) | ||||
0.124391 | + | 0.992233i | \(0.460302\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 13.5280i | − | 1.13926i | ||||||
\(142\) | −2.91188 | + | 5.04353i | −0.244360 | + | 0.423244i | ||||
\(143\) | −15.5888 | − | 11.2482i | −1.30360 | − | 0.940623i | ||||
\(144\) | −1.76029 | − | 3.04891i | −0.146691 | − | 0.254076i | ||||
\(145\) | 14.8614 | + | 8.58022i | 1.23417 | + | 0.712548i | ||||
\(146\) | −4.00059 | −0.331091 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.2878i | 0.845650i | ||||||||
\(149\) | 11.4661 | + | 6.61994i | 0.939338 | + | 0.542327i | 0.889753 | − | 0.456443i | \(-0.150877\pi\) |
0.0495851 | + | 0.998770i | \(0.484210\pi\) | |||||||
\(150\) | −7.61360 | + | 4.39571i | −0.621648 | + | 0.358909i | ||||
\(151\) | 8.01838 | − | 4.62942i | 0.652527 | − | 0.376736i | −0.136897 | − | 0.990585i | \(-0.543713\pi\) |
0.789424 | + | 0.613849i | \(0.210380\pi\) | |||||||
\(152\) | −0.837940 | + | 1.45135i | −0.0679659 | + | 0.117720i | ||||
\(153\) | −6.53268 | −0.528136 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.7223 | −1.42349 | ||||||||
\(156\) | −12.8714 | − | 1.31029i | −1.03054 | − | 0.104907i | ||||
\(157\) | −0.828132 | − | 1.43437i | −0.0660922 | − | 0.114475i | 0.831086 | − | 0.556144i | \(-0.187720\pi\) |
−0.897178 | + | 0.441669i | \(0.854386\pi\) | |||||||
\(158\) | −0.536532 | + | 0.309767i | −0.0426842 | + | 0.0246437i | ||||
\(159\) | −5.50352 | + | 9.53238i | −0.436458 | + | 0.755967i | ||||
\(160\) | 18.7961 | 1.48596 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.04072i | 0.553171i | ||||||||
\(163\) | 8.57328 | + | 4.94978i | 0.671511 | + | 0.387697i | 0.796649 | − | 0.604442i | \(-0.206604\pi\) |
−0.125138 | + | 0.992139i | \(0.539937\pi\) | |||||||
\(164\) | 2.94684 | − | 1.70136i | 0.230109 | − | 0.132854i | ||||
\(165\) | −20.1983 | − | 34.9845i | −1.57244 | − | 2.72354i | ||||
\(166\) | −3.99549 | + | 6.92039i | −0.310110 | + | 0.537127i | ||||
\(167\) | 6.10891i | 0.472721i | 0.971665 | + | 0.236361i | \(0.0759547\pi\) | ||||
−0.971665 | + | 0.236361i | \(0.924045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.63531 | + | 9.71758i | −0.664255 | + | 0.747506i | ||||
\(170\) | 2.94594 | − | 5.10251i | 0.225943 | − | 0.391345i | ||||
\(171\) | 1.47673 | − | 0.852591i | 0.112928 | − | 0.0651992i | ||||
\(172\) | −1.83722 | − | 3.18216i | −0.140087 | − | 0.242637i | ||||
\(173\) | −9.36059 | + | 16.2130i | −0.711672 | + | 1.23265i | 0.252557 | + | 0.967582i | \(0.418729\pi\) |
−0.964229 | + | 0.265070i | \(0.914605\pi\) | |||||||
\(174\) | − | 8.39309i | − | 0.636278i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.66712i | 0.577931i | ||||||||
\(177\) | −6.02523 | − | 3.47867i | −0.452884 | − | 0.261473i | ||||
\(178\) | 0.335343 | + | 0.580832i | 0.0251350 | + | 0.0435352i | ||||
\(179\) | −4.96878 | − | 8.60618i | −0.371384 | − | 0.643256i | 0.618395 | − | 0.785868i | \(-0.287783\pi\) |
−0.989779 | + | 0.142612i | \(0.954450\pi\) | |||||||
\(180\) | −10.5804 | − | 6.10859i | −0.788616 | − | 0.455308i | ||||
\(181\) | 22.6991 | 1.68721 | 0.843606 | − | 0.536962i | \(-0.180428\pi\) | ||||
0.843606 | + | 0.536962i | \(0.180428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.12259 | −0.378673 | ||||||||
\(184\) | −18.6720 | − | 10.7803i | −1.37652 | − | 0.794734i | ||||
\(185\) | 10.8615 | + | 18.8126i | 0.798552 | + | 1.38313i | ||||
\(186\) | 4.33394 | + | 7.50660i | 0.317780 | + | 0.550411i | ||||
\(187\) | 12.3208 | + | 7.11343i | 0.900988 | + | 0.520186i | ||||
\(188\) | 8.90997i | 0.649827i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.53791i | 0.111572i | ||||||||
\(191\) | −2.71463 | + | 4.70188i | −0.196424 | + | 0.340216i | −0.947366 | − | 0.320152i | \(-0.896266\pi\) |
0.750943 | + | 0.660368i | \(0.229600\pi\) | |||||||
\(192\) | −1.23993 | − | 2.14763i | −0.0894845 | − | 0.154992i | ||||
\(193\) | −1.70611 | + | 0.985026i | −0.122809 | + | 0.0709037i | −0.560146 | − | 0.828394i | \(-0.689255\pi\) |
0.437337 | + | 0.899298i | \(0.355922\pi\) | |||||||
\(194\) | 5.21894 | − | 9.03947i | 0.374698 | − | 0.648996i | ||||
\(195\) | −24.9205 | + | 11.1931i | −1.78459 | + | 0.801557i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.1476i | 1.36421i | 0.731253 | + | 0.682107i | \(0.238936\pi\) | ||||
−0.731253 | + | 0.682107i | \(0.761064\pi\) | |||||||
\(198\) | −4.43913 | + | 7.68879i | −0.315475 | + | 0.546419i | ||||
\(199\) | 0.0974054 | + | 0.168711i | 0.00690489 | + | 0.0119596i | 0.869457 | − | 0.494008i | \(-0.164469\pi\) |
−0.862552 | + | 0.505968i | \(0.831135\pi\) | |||||||
\(200\) | 11.5383 | − | 6.66164i | 0.815880 | − | 0.471049i | ||||
\(201\) | 17.5983 | + | 10.1604i | 1.24129 | + | 0.716659i | ||||
\(202\) | − | 2.65907i | − | 0.187091i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.57516 | 0.670396 | ||||||||
\(205\) | 3.59247 | − | 6.22233i | 0.250909 | − | 0.434587i | ||||
\(206\) | 10.9338 | − | 6.31262i | 0.761792 | − | 0.439821i | ||||
\(207\) | 10.9688 | + | 18.9985i | 0.762383 | + | 1.32049i | ||||
\(208\) | 5.15834 | + | 0.525110i | 0.357666 | + | 0.0364098i | ||||
\(209\) | −3.71354 | −0.256871 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2618 | 0.844139 | 0.422070 | − | 0.906563i | \(-0.361304\pi\) | ||||
0.422070 | + | 0.906563i | \(0.361304\pi\) | |||||||
\(212\) | 3.62480 | − | 6.27834i | 0.248952 | − | 0.431198i | ||||
\(213\) | −17.3071 | + | 9.99228i | −1.18587 | + | 0.684660i | ||||
\(214\) | −7.72022 | + | 4.45727i | −0.527743 | + | 0.304693i | ||||
\(215\) | −6.71922 | − | 3.87934i | −0.458247 | − | 0.264569i | ||||
\(216\) | − | 3.09925i | − | 0.210877i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.4736 | −0.709362 | ||||||||
\(219\) | −11.8890 | − | 6.86411i | −0.803383 | − | 0.463834i | ||||
\(220\) | 13.3033 | + | 23.0420i | 0.896907 | + | 1.55349i | ||||
\(221\) | 5.62966 | − | 7.80210i | 0.378692 | − | 0.524826i | ||||
\(222\) | 5.31230 | − | 9.20117i | 0.356538 | − | 0.617542i | ||||
\(223\) | 27.1733i | 1.81966i | 0.414981 | + | 0.909830i | \(0.363788\pi\) | ||||
−0.414981 | + | 0.909830i | \(0.636212\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.5562 | −0.903748 | ||||||||
\(226\) | 7.50153 | + | 4.33101i | 0.498994 | + | 0.288094i | ||||
\(227\) | −6.24651 | + | 3.60642i | −0.414595 | + | 0.239367i | −0.692762 | − | 0.721166i | \(-0.743606\pi\) |
0.278167 | + | 0.960533i | \(0.410273\pi\) | |||||||
\(228\) | −2.16449 | + | 1.24967i | −0.143347 | + | 0.0827614i | ||||
\(229\) | −14.8200 | − | 8.55635i | −0.979335 | − | 0.565419i | −0.0772656 | − | 0.997011i | \(-0.524619\pi\) |
−0.902069 | + | 0.431591i | \(0.857952\pi\) | |||||||
\(230\) | −19.7856 | −1.30463 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.7196i | 0.835082i | ||||||||
\(233\) | −6.31766 | + | 10.9425i | −0.413883 | + | 0.716867i | −0.995311 | − | 0.0967314i | \(-0.969161\pi\) |
0.581427 | + | 0.813599i | \(0.302495\pi\) | |||||||
\(234\) | 4.86889 | + | 3.51318i | 0.318289 | + | 0.229664i | ||||
\(235\) | 9.40684 | + | 16.2931i | 0.613635 | + | 1.06285i | ||||
\(236\) | 3.96842 | + | 2.29117i | 0.258322 | + | 0.149142i | ||||
\(237\) | −2.12596 | −0.138096 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.70807i | 0.498594i | 0.968427 | + | 0.249297i | \(0.0801995\pi\) | ||||
−0.968427 | + | 0.249297i | \(0.919801\pi\) | |||||||
\(240\) | 9.43620 | + | 5.44799i | 0.609104 | + | 0.351666i | ||||
\(241\) | 16.6296 | − | 9.60112i | 1.07121 | − | 0.618463i | 0.142697 | − | 0.989766i | \(-0.454422\pi\) |
0.928512 | + | 0.371304i | \(0.121089\pi\) | |||||||
\(242\) | 10.2649 | − | 5.92644i | 0.659853 | − | 0.380966i | ||||
\(243\) | −10.1482 | + | 17.5771i | −0.651005 | + | 1.12757i | ||||
\(244\) | 3.37390 | 0.215992 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.51412 | −0.224052 | ||||||||
\(247\) | −0.254335 | + | 2.49842i | −0.0161830 | + | 0.158971i | ||||
\(248\) | −6.56801 | − | 11.3761i | −0.417069 | − | 0.722385i | ||||
\(249\) | −23.7477 | + | 13.7107i | −1.50495 | + | 0.868882i | ||||
\(250\) | 0.593216 | − | 1.02748i | 0.0375183 | − | 0.0649836i | ||||
\(251\) | 17.6761 | 1.11570 | 0.557851 | − | 0.829941i | \(-0.311626\pi\) | ||||
0.557851 | + | 0.829941i | \(0.311626\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 47.7756i | − | 3.00362i | ||||||
\(254\) | 6.05346 | + | 3.49497i | 0.379828 | + | 0.219294i | ||||
\(255\) | 17.5095 | − | 10.1091i | 1.09649 | − | 0.633058i | ||||
\(256\) | 4.75522 | + | 8.23628i | 0.297201 | + | 0.514767i | ||||
\(257\) | 1.30967 | − | 2.26842i | 0.0816952 | − | 0.141500i | −0.822283 | − | 0.569079i | \(-0.807300\pi\) |
0.903978 | + | 0.427579i | \(0.140633\pi\) | |||||||
\(258\) | 3.79474i | 0.236250i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.4135 | − | 7.37216i | 1.01792 | − | 0.457202i | ||||
\(261\) | 6.47099 | − | 11.2081i | 0.400544 | − | 0.693763i | ||||
\(262\) | 7.41121 | − | 4.27887i | 0.457866 | − | 0.264349i | ||||
\(263\) | −2.81437 | − | 4.87464i | −0.173542 | − | 0.300583i | 0.766114 | − | 0.642705i | \(-0.222188\pi\) |
−0.939656 | + | 0.342122i | \(0.888854\pi\) | |||||||
\(264\) | 14.9713 | − | 25.9311i | 0.921421 | − | 1.59595i | ||||
\(265\) | − | 15.3078i | − | 0.940348i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.30149i | 0.140849i | ||||||||
\(268\) | −11.5908 | − | 6.69197i | −0.708022 | − | 0.408777i | ||||
\(269\) | −6.92905 | − | 12.0015i | −0.422472 | − | 0.731743i | 0.573709 | − | 0.819059i | \(-0.305504\pi\) |
−0.996181 | + | 0.0873166i | \(0.972171\pi\) | |||||||
\(270\) | −1.42205 | − | 2.46307i | −0.0865433 | − | 0.149897i | ||||
\(271\) | −6.93575 | − | 4.00436i | −0.421317 | − | 0.243247i | 0.274324 | − | 0.961637i | \(-0.411546\pi\) |
−0.695641 | + | 0.718390i | \(0.744879\pi\) | |||||||
\(272\) | −3.83734 | −0.232673 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.17394 | 0.0709203 | ||||||||
\(275\) | 25.5674 | + | 14.7613i | 1.54177 | + | 0.890143i | ||||
\(276\) | −16.0773 | − | 27.8467i | −0.967739 | − | 1.67617i | ||||
\(277\) | 9.14650 | + | 15.8422i | 0.549560 | + | 0.951866i | 0.998305 | + | 0.0582057i | \(0.0185379\pi\) |
−0.448745 | + | 0.893660i | \(0.648129\pi\) | |||||||
\(278\) | 1.72780 | + | 0.997544i | 0.103626 | + | 0.0598287i | ||||
\(279\) | 13.3657i | 0.800184i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.3790i | − | 1.15605i | −0.816018 | − | 0.578026i | \(-0.803823\pi\) | ||
0.816018 | − | 0.578026i | \(-0.196177\pi\) | |||||||
\(282\) | 4.60084 | − | 7.96889i | 0.273976 | − | 0.474540i | ||||
\(283\) | −3.21864 | − | 5.57486i | −0.191329 | − | 0.331391i | 0.754362 | − | 0.656458i | \(-0.227946\pi\) |
−0.945691 | + | 0.325068i | \(0.894613\pi\) | |||||||
\(284\) | 11.3990 | − | 6.58124i | 0.676409 | − | 0.390525i | ||||
\(285\) | −2.63872 | + | 4.57039i | −0.156304 | + | 0.270726i | ||||
\(286\) | −5.35737 | − | 11.9277i | −0.316788 | − | 0.705299i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 14.1756i | − | 0.835304i | ||||||
\(289\) | 4.93977 | − | 8.55594i | 0.290575 | − | 0.503291i | ||||
\(290\) | 5.83623 | + | 10.1087i | 0.342715 | + | 0.593601i | ||||
\(291\) | 31.0194 | − | 17.9090i | 1.81839 | − | 1.04985i | ||||
\(292\) | 7.83048 | + | 4.52093i | 0.458244 | + | 0.264567i | ||||
\(293\) | 7.66381i | 0.447725i | 0.974621 | + | 0.223862i | \(0.0718666\pi\) | ||||
−0.974621 | + | 0.223862i | \(0.928133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.67573 | 0.563343 | ||||||||
\(296\) | −8.05071 | + | 13.9442i | −0.467938 | + | 0.810492i | ||||
\(297\) | 5.94747 | − | 3.43377i | 0.345107 | − | 0.199248i | ||||
\(298\) | 4.50286 | + | 7.79918i | 0.260844 | + | 0.451795i | ||||
\(299\) | −32.1428 | − | 3.27208i | −1.85886 | − | 0.189229i | ||||
\(300\) | 19.8698 | 1.14718 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.29782 | 0.362399 | ||||||||
\(303\) | 4.56236 | − | 7.90224i | 0.262101 | − | 0.453972i | ||||
\(304\) | 0.867441 | − | 0.500817i | 0.0497512 | − | 0.0287238i | ||||
\(305\) | 6.16965 | − | 3.56205i | 0.353273 | − | 0.203962i | ||||
\(306\) | −3.84819 | − | 2.22175i | −0.219986 | − | 0.127009i | ||||
\(307\) | − | 0.312144i | − | 0.0178150i | −0.999960 | − | 0.00890751i | \(-0.997165\pi\) | ||
0.999960 | − | 0.00890751i | \(-0.00283539\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 43.3241 | 2.46462 | ||||||||
\(310\) | −10.4396 | − | 6.02731i | −0.592930 | − | 0.342328i | ||||
\(311\) | 1.40754 | + | 2.43792i | 0.0798141 | + | 0.138242i | 0.903170 | − | 0.429284i | \(-0.141234\pi\) |
−0.823356 | + | 0.567526i | \(0.807901\pi\) | |||||||
\(312\) | −16.4207 | − | 11.8485i | −0.929641 | − | 0.670789i | ||||
\(313\) | −6.64651 | + | 11.5121i | −0.375683 | + | 0.650702i | −0.990429 | − | 0.138023i | \(-0.955925\pi\) |
0.614746 | + | 0.788725i | \(0.289258\pi\) | |||||||
\(314\) | − | 1.12658i | − | 0.0635769i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.40023 | 0.0787690 | ||||||||
\(317\) | −0.841932 | − | 0.486090i | −0.0472876 | − | 0.0273015i | 0.476170 | − | 0.879353i | \(-0.342025\pi\) |
−0.523457 | + | 0.852052i | \(0.675358\pi\) | |||||||
\(318\) | −6.48389 | + | 3.74347i | −0.363598 | + | 0.209924i | ||||
\(319\) | −24.4090 | + | 14.0925i | −1.36664 | + | 0.789029i | ||||
\(320\) | 2.98676 | + | 1.72440i | 0.166965 | + | 0.0963972i | ||||
\(321\) | −30.5907 | −1.70741 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.85860i | − | 0.103415i | ||||||
\(324\) | 7.95648 | − | 13.7810i | 0.442026 | − | 0.765612i | ||||
\(325\) | 11.6823 | − | 16.1904i | 0.648018 | − | 0.898084i | ||||
\(326\) | 3.36682 | + | 5.83151i | 0.186471 | + | 0.322978i | ||||
\(327\) | −31.1255 | − | 17.9703i | −1.72125 | − | 0.993762i | ||||
\(328\) | 5.32559 | 0.294056 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 27.4776i | − | 1.51259i | ||||||
\(331\) | −6.68651 | − | 3.86046i | −0.367524 | − | 0.212190i | 0.304852 | − | 0.952400i | \(-0.401393\pi\) |
−0.672376 | + | 0.740210i | \(0.734726\pi\) | |||||||
\(332\) | 15.6410 | − | 9.03033i | 0.858411 | − | 0.495604i | ||||
\(333\) | 14.1880 | − | 8.19147i | 0.777500 | − | 0.448890i | ||||
\(334\) | −2.07763 | + | 3.59856i | −0.113683 | + | 0.196904i | ||||
\(335\) | −28.2606 | −1.54404 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.4858 | −1.49725 | −0.748624 | − | 0.662995i | \(-0.769285\pi\) | ||||
−0.748624 | + | 0.662995i | \(0.769285\pi\) | |||||||
\(338\) | −8.39171 | + | 2.78746i | −0.456449 | + | 0.151618i | ||||
\(339\) | 14.8621 | + | 25.7419i | 0.807197 | + | 1.39811i | ||||
\(340\) | −11.5323 | + | 6.65820i | −0.625429 | + | 0.361092i | ||||
\(341\) | 14.5539 | − | 25.2081i | 0.788138 | − | 1.36509i | ||||
\(342\) | 1.15986 | 0.0627179 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 5.75086i | − | 0.310066i | ||||||
\(345\) | −58.7991 | − | 33.9477i | −3.16564 | − | 1.82768i | ||||
\(346\) | −11.0280 | + | 6.36704i | −0.592871 | + | 0.342294i | ||||
\(347\) | 1.84773 | + | 3.20036i | 0.0991914 | + | 0.171804i | 0.911350 | − | 0.411632i | \(-0.135041\pi\) |
−0.812159 | + | 0.583436i | \(0.801708\pi\) | |||||||
\(348\) | −9.48474 | + | 16.4281i | −0.508436 | + | 0.880636i | ||||
\(349\) | − | 26.7513i | − | 1.43197i | −0.698118 | − | 0.715983i | \(-0.745979\pi\) | ||
0.698118 | − | 0.715983i | \(-0.254021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.90286 | − | 4.23655i | −0.101567 | − | 0.226130i | ||||
\(352\) | −15.4358 | + | 26.7355i | −0.822729 | + | 1.42501i | ||||
\(353\) | −2.38444 | + | 1.37666i | −0.126911 | + | 0.0732722i | −0.562112 | − | 0.827061i | \(-0.690011\pi\) |
0.435200 | + | 0.900334i | \(0.356678\pi\) | |||||||
\(354\) | −2.36618 | − | 4.09834i | −0.125761 | − | 0.217824i | ||||
\(355\) | 13.8965 | − | 24.0694i | 0.737549 | − | 1.27747i | ||||
\(356\) | − | 1.51584i | − | 0.0803394i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 6.75949i | − | 0.357250i | ||||||
\(359\) | 30.3581 | + | 17.5273i | 1.60224 | + | 0.925053i | 0.991038 | + | 0.133578i | \(0.0426466\pi\) |
0.611201 | + | 0.791475i | \(0.290687\pi\) | |||||||
\(360\) | −9.56056 | − | 16.5594i | −0.503886 | − | 0.872756i | ||||
\(361\) | −9.25743 | − | 16.0343i | −0.487233 | − | 0.843913i | ||||
\(362\) | 13.3713 | + | 7.71993i | 0.702781 | + | 0.405751i | ||||
\(363\) | 40.6737 | 2.13482 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.0922 | 0.999329 | ||||||||
\(366\) | −3.01755 | − | 1.74218i | −0.157730 | − | 0.0910653i | ||||
\(367\) | 7.50027 | + | 12.9908i | 0.391511 | + | 0.678117i | 0.992649 | − | 0.121028i | \(-0.0386192\pi\) |
−0.601138 | + | 0.799145i | \(0.705286\pi\) | |||||||
\(368\) | 6.44313 | + | 11.1598i | 0.335872 | + | 0.581747i | ||||
\(369\) | −4.69273 | − | 2.70935i | −0.244294 | − | 0.141043i | ||||
\(370\) | 14.7759i | 0.768161i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 19.5905i | − | 1.01572i | ||||||
\(373\) | −10.4971 | + | 18.1816i | −0.543521 | + | 0.941406i | 0.455177 | + | 0.890401i | \(0.349576\pi\) |
−0.998698 | + | 0.0510055i | \(0.983757\pi\) | |||||||
\(374\) | 4.83853 | + | 8.38058i | 0.250194 | + | 0.433349i | ||||
\(375\) | 3.52585 | − | 2.03565i | 0.182074 | − | 0.105121i | ||||
\(376\) | −6.97250 | + | 12.0767i | −0.359579 | + | 0.622810i | ||||
\(377\) | 7.80953 | + | 17.3872i | 0.402211 | + | 0.895486i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.2425i | − | 0.782956i | −0.920187 | − | 0.391478i | \(-0.871964\pi\) | ||
0.920187 | − | 0.391478i | \(-0.128036\pi\) | |||||||
\(380\) | 1.73794 | − | 3.01021i | 0.0891547 | − | 0.154420i | ||||
\(381\) | 11.9931 | + | 20.7727i | 0.614428 | + | 1.06422i | ||||
\(382\) | −3.19820 | + | 1.84648i | −0.163634 | + | 0.0944742i | ||||
\(383\) | 21.2834 | + | 12.2880i | 1.08753 | + | 0.627887i | 0.932918 | − | 0.360088i | \(-0.117253\pi\) |
0.154613 | + | 0.987975i | \(0.450587\pi\) | |||||||
\(384\) | 25.3439i | 1.29333i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.34002 | −0.0682053 | ||||||||
\(387\) | −2.92571 | + | 5.06747i | −0.148722 | + | 0.257594i | ||||
\(388\) | −20.4304 | + | 11.7955i | −1.03720 | + | 0.598825i | ||||
\(389\) | 9.62037 | + | 16.6630i | 0.487772 | + | 0.844846i | 0.999901 | − | 0.0140622i | \(-0.00447629\pi\) |
−0.512129 | + | 0.858909i | \(0.671143\pi\) | |||||||
\(390\) | −18.4866 | − | 1.88190i | −0.936105 | − | 0.0952940i | ||||
\(391\) | 23.9114 | 1.20925 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.3663 | 1.48133 | ||||||||
\(394\) | −6.51208 | + | 11.2792i | −0.328074 | + | 0.568240i | ||||
\(395\) | 2.56051 | − | 1.47831i | 0.128833 | − | 0.0743820i | ||||
\(396\) | 17.3777 | − | 10.0330i | 0.873262 | − | 0.504178i | ||||
\(397\) | −0.516813 | − | 0.298382i | −0.0259381 | − | 0.0149754i | 0.486975 | − | 0.873416i | \(-0.338100\pi\) |
−0.512913 | + | 0.858441i | \(0.671434\pi\) | |||||||
\(398\) | 0.132510i | 0.00664211i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.96301 | −0.398151 | ||||||||
\(401\) | −1.38104 | − | 0.797343i | −0.0689657 | − | 0.0398174i | 0.465121 | − | 0.885247i | \(-0.346011\pi\) |
−0.534086 | + | 0.845430i | \(0.679344\pi\) | |||||||
\(402\) | 6.91106 | + | 11.9703i | 0.344692 | + | 0.597024i | ||||
\(403\) | −15.9629 | − | 11.5181i | −0.795169 | − | 0.573759i | ||||
\(404\) | −3.00492 | + | 5.20468i | −0.149500 | + | 0.258942i | ||||
\(405\) | − | 33.6007i | − | 1.66963i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.6787 | −1.76853 | ||||||||
\(408\) | 12.9783 | + | 7.49305i | 0.642523 | + | 0.370961i | ||||
\(409\) | 25.1047 | − | 14.4942i | 1.24135 | − | 0.716691i | 0.271978 | − | 0.962304i | \(-0.412322\pi\) |
0.969368 | + | 0.245612i | \(0.0789890\pi\) | |||||||
\(410\) | 4.23241 | − | 2.44358i | 0.209024 | − | 0.120680i | ||||
\(411\) | 3.48873 | + | 2.01422i | 0.172086 | + | 0.0993540i | ||||
\(412\) | −28.5347 | −1.40580 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14.9218i | 0.733369i | ||||||||
\(415\) | 19.0678 | − | 33.0264i | 0.936003 | − | 1.62120i | ||||
\(416\) | 16.9301 | + | 12.2161i | 0.830069 | + | 0.598942i | ||||
\(417\) | 3.42312 | + | 5.92902i | 0.167631 | + | 0.290345i | ||||
\(418\) | −2.18752 | − | 1.26297i | −0.106995 | − | 0.0617738i | ||||
\(419\) | 5.18611 | 0.253358 | 0.126679 | − | 0.991944i | \(-0.459568\pi\) | ||||
0.126679 | + | 0.991944i | \(0.459568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.84363i | 0.138590i | 0.997596 | + | 0.0692950i | \(0.0220750\pi\) | ||||
−0.997596 | + | 0.0692950i | \(0.977925\pi\) | |||||||
\(422\) | 7.22304 | + | 4.17023i | 0.351612 | + | 0.203003i | ||||
\(423\) | 12.2879 | − | 7.09441i | 0.597457 | − | 0.344942i | ||||
\(424\) | 9.82623 | − | 5.67318i | 0.477204 | − | 0.275514i | ||||
\(425\) | −7.38796 | + | 12.7963i | −0.358369 | + | 0.620713i | ||||
\(426\) | −13.5934 | −0.658603 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 20.1480 | 0.973892 | ||||||||
\(429\) | 4.54416 | − | 44.6388i | 0.219394 | − | 2.15518i | ||||
\(430\) | −2.63872 | − | 4.57039i | −0.127250 | − | 0.220404i | ||||
\(431\) | 3.44770 | − | 1.99053i | 0.166070 | − | 0.0958804i | −0.414662 | − | 0.909976i | \(-0.636100\pi\) |
0.580731 | + | 0.814095i | \(0.302767\pi\) | |||||||
\(432\) | −0.926174 | + | 1.60418i | −0.0445606 | + | 0.0771812i | ||||
\(433\) | −7.42082 | −0.356622 | −0.178311 | − | 0.983974i | \(-0.557063\pi\) | ||||
−0.178311 | + | 0.983974i | \(0.557063\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40.0546i | 1.92047i | ||||||||
\(436\) | 20.5003 | + | 11.8359i | 0.981787 | + | 0.566835i | ||||
\(437\) | −5.40522 | + | 3.12071i | −0.258567 | + | 0.149284i | ||||
\(438\) | −4.66894 | − | 8.08685i | −0.223091 | − | 0.386404i | ||||
\(439\) | 15.2835 | − | 26.4718i | 0.729442 | − | 1.26343i | −0.227678 | − | 0.973737i | \(-0.573113\pi\) |
0.957119 | − | 0.289694i | \(-0.0935534\pi\) | |||||||
\(440\) | 41.6419i | 1.98520i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.96973 | − | 2.68133i | 0.283951 | − | 0.127538i | ||||
\(443\) | 2.15488 | − | 3.73235i | 0.102381 | − | 0.177329i | −0.810284 | − | 0.586037i | \(-0.800687\pi\) |
0.912665 | + | 0.408708i | \(0.134021\pi\) | |||||||
\(444\) | −20.7959 | + | 12.0065i | −0.986928 | + | 0.569803i | ||||
\(445\) | −1.60037 | − | 2.77192i | −0.0758649 | − | 0.131402i | ||||
\(446\) | −9.24160 | + | 16.0069i | −0.437602 | + | 0.757949i | ||||
\(447\) | 30.9036i | 1.46169i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.7830i | 1.45274i | 0.687305 | + | 0.726369i | \(0.258794\pi\) | ||||
−0.687305 | + | 0.726369i | \(0.741206\pi\) | |||||||
\(450\) | −7.98552 | − | 4.61044i | −0.376441 | − | 0.217338i | ||||
\(451\) | 5.90042 | + | 10.2198i | 0.277840 | + | 0.481233i | ||||
\(452\) | −9.78865 | − | 16.9544i | −0.460419 | − | 0.797470i | ||||
\(453\) | 18.7159 | + | 10.8056i | 0.879351 | + | 0.507693i | ||||
\(454\) | −4.90615 | −0.230257 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.91172 | −0.183183 | ||||||||
\(457\) | −11.6873 | − | 6.74769i | −0.546711 | − | 0.315644i | 0.201083 | − | 0.979574i | \(-0.435554\pi\) |
−0.747794 | + | 0.663930i | \(0.768887\pi\) | |||||||
\(458\) | −5.81999 | − | 10.0805i | −0.271950 | − | 0.471032i | ||||
\(459\) | 1.71858 | + | 2.97667i | 0.0802164 | + | 0.138939i | ||||
\(460\) | 38.7270 | + | 22.3591i | 1.80566 | + | 1.04250i | ||||
\(461\) | − | 27.4778i | − | 1.27977i | −0.768471 | − | 0.639885i | \(-0.778982\pi\) | ||
0.768471 | − | 0.639885i | \(-0.221018\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.06521i | 0.374822i | 0.982282 | + | 0.187411i | \(0.0600096\pi\) | ||||
−0.982282 | + | 0.187411i | \(0.939990\pi\) | |||||||
\(464\) | 3.80110 | − | 6.58371i | 0.176462 | − | 0.305641i | ||||
\(465\) | −20.6830 | − | 35.8240i | −0.959152 | − | 1.66130i | ||||
\(466\) | −7.44305 | + | 4.29725i | −0.344793 | + | 0.199066i | ||||
\(467\) | 6.31626 | − | 10.9401i | 0.292282 | − | 0.506247i | −0.682067 | − | 0.731290i | \(-0.738919\pi\) |
0.974349 | + | 0.225043i | \(0.0722521\pi\) | |||||||
\(468\) | −5.55991 | − | 12.3786i | −0.257007 | − | 0.572202i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12.7970i | 0.590281i | ||||||||
\(471\) | 1.93297 | − | 3.34800i | 0.0890664 | − | 0.154267i | ||||
\(472\) | 3.58590 | + | 6.21097i | 0.165055 | + | 0.285883i | ||||
\(473\) | 11.0359 | − | 6.37160i | 0.507433 | − | 0.292966i | ||||
\(474\) | −1.25233 | − | 0.723036i | −0.0575216 | − | 0.0332101i | ||||
\(475\) | − | 3.85685i | − | 0.176965i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.5447 | −0.528597 | ||||||||
\(478\) | −2.62150 | + | 4.54057i | −0.119905 | + | 0.207681i | ||||
\(479\) | 27.3127 | − | 15.7690i | 1.24795 | − | 0.720504i | 0.277249 | − | 0.960798i | \(-0.410577\pi\) |
0.970700 | + | 0.240295i | \(0.0772441\pi\) | |||||||
\(480\) | 21.9363 | + | 37.9947i | 1.00125 | + | 1.73421i | ||||
\(481\) | −2.44358 | + | 24.0042i | −0.111418 | + | 1.09450i | ||||
\(482\) | 13.0613 | 0.594926 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.7891 | −1.21769 | ||||||||
\(485\) | −24.9065 | + | 43.1394i | −1.13095 | + | 1.95886i | ||||
\(486\) | −11.9559 | + | 6.90274i | −0.542330 | + | 0.313115i | ||||
\(487\) | 36.4786 | − | 21.0609i | 1.65300 | − | 0.954362i | 0.677175 | − | 0.735822i | \(-0.263204\pi\) |
0.975828 | − | 0.218539i | \(-0.0701292\pi\) | |||||||
\(488\) | 4.57305 | + | 2.64025i | 0.207012 | + | 0.119519i | ||||
\(489\) | 23.1068i | 1.04493i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.2284 | −1.36419 | −0.682095 | − | 0.731264i | \(-0.738931\pi\) | ||||
−0.682095 | + | 0.731264i | \(0.738931\pi\) | |||||||
\(492\) | 6.87829 | + | 3.97118i | 0.310097 | + | 0.179035i | ||||
\(493\) | −7.05321 | − | 12.2165i | −0.317661 | − | 0.550204i | ||||
\(494\) | −0.999529 | + | 1.38524i | −0.0449709 | + | 0.0623249i | ||||
\(495\) | 21.1850 | − | 36.6935i | 0.952196 | − | 1.64925i | ||||
\(496\) | 7.85110i | 0.352525i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −18.6520 | −0.835815 | ||||||||
\(499\) | 3.03799 | + | 1.75398i | 0.135999 | + | 0.0785191i | 0.566456 | − | 0.824092i | \(-0.308314\pi\) |
−0.430457 | + | 0.902611i | \(0.641648\pi\) | |||||||
\(500\) | −2.32224 | + | 1.34075i | −0.103854 | + | 0.0599600i | ||||
\(501\) | −12.3486 | + | 7.12948i | −0.551696 | + | 0.318522i | ||||
\(502\) | 10.4124 | + | 6.01159i | 0.464727 | + | 0.268310i | ||||
\(503\) | −22.8622 | −1.01937 | −0.509687 | − | 0.860360i | \(-0.670239\pi\) | ||||
−0.509687 | + | 0.860360i | \(0.670239\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.6900i | 0.564696i | ||||||||
\(506\) | 16.2484 | − | 28.1430i | 0.722329 | − | 1.25111i | ||||
\(507\) | −29.7212 | − | 6.11450i | −1.31997 | − | 0.271555i | ||||
\(508\) | −7.89908 | − | 13.6816i | −0.350465 | − | 0.607023i | ||||
\(509\) | −18.8582 | − | 10.8878i | −0.835873 | − | 0.482592i | 0.0199862 | − | 0.999800i | \(-0.493638\pi\) |
−0.855859 | + | 0.517209i | \(0.826971\pi\) | |||||||
\(510\) | 13.7524 | 0.608966 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 15.2470i | − | 0.673829i | ||||||
\(513\) | −0.776979 | − | 0.448589i | −0.0343045 | − | 0.0198057i | ||||
\(514\) | 1.54297 | − | 0.890835i | 0.0680575 | − | 0.0392930i | ||||
\(515\) | −52.1797 | + | 30.1259i | −2.29931 | + | 1.32751i | ||||
\(516\) | 4.28830 | − | 7.42756i | 0.188782 | − | 0.326980i | ||||
\(517\) | −30.9004 | −1.35900 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −43.6976 | −1.91811 | ||||||||
\(520\) | 28.0162 | + | 2.85200i | 1.22859 | + | 0.125068i | ||||
\(521\) | −7.26177 | − | 12.5777i | −0.318144 | − | 0.551041i | 0.661957 | − | 0.749542i | \(-0.269726\pi\) |
−0.980101 | + | 0.198501i | \(0.936393\pi\) | |||||||
\(522\) | 7.62370 | − | 4.40155i | 0.333680 | − | 0.192650i | ||||
\(523\) | −8.20941 | + | 14.2191i | −0.358973 | + | 0.621759i | −0.987789 | − | 0.155795i | \(-0.950206\pi\) |
0.628817 | + | 0.777553i | \(0.283539\pi\) | |||||||
\(524\) | −19.3416 | −0.844942 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 3.82865i | − | 0.166937i | ||||||
\(527\) | 12.6165 | + | 7.28413i | 0.549583 | + | 0.317302i | ||||
\(528\) | −15.4984 | + | 8.94801i | −0.674482 | + | 0.389412i | ||||
\(529\) | −28.6486 | − | 49.6209i | −1.24559 | − | 2.15743i | ||||
\(530\) | 5.20614 | − | 9.01730i | 0.226140 | − | 0.391686i | ||||
\(531\) | − | 7.29720i | − | 0.316672i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.27987 | − | 3.26978i | 0.315326 | − | 0.141630i | ||||
\(534\) | −0.782734 | + | 1.35573i | −0.0338722 | + | 0.0586684i | ||||
\(535\) | 36.8435 | − | 21.2716i | 1.59288 | − | 0.919651i | ||||
\(536\) | −10.4736 | − | 18.1408i | −0.452391 | − | 0.783564i | ||||
\(537\) | 11.5978 | − | 20.0879i | 0.500481 | − | 0.866858i | ||||
\(538\) | − | 9.42623i | − | 0.406394i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.42805i | 0.276619i | ||||||||
\(541\) | −11.6873 | − | 6.74769i | −0.502478 | − | 0.290106i | 0.227258 | − | 0.973835i | \(-0.427024\pi\) |
−0.729736 | + | 0.683729i | \(0.760357\pi\) | |||||||
\(542\) | −2.72375 | − | 4.71767i | −0.116995 | − | 0.202641i | ||||
\(543\) | 26.4913 | + | 45.8843i | 1.13685 | + | 1.96908i | ||||
\(544\) | −13.3810 | − | 7.72550i | −0.573704 | − | 0.331228i | ||||
\(545\) | 49.9835 | 2.14106 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.5615 | 0.579847 | 0.289924 | − | 0.957050i | \(-0.406370\pi\) | ||||
0.289924 | + | 0.957050i | \(0.406370\pi\) | |||||||
\(548\) | −2.29779 | − | 1.32663i | −0.0981567 | − | 0.0566708i | ||||
\(549\) | −2.68641 | − | 4.65300i | −0.114653 | − | 0.198585i | ||||
\(550\) | 10.0406 | + | 17.3909i | 0.428133 | + | 0.741549i | ||||
\(551\) | 3.18879 | + | 1.84105i | 0.135847 | + | 0.0784314i | ||||
\(552\) | − | 50.3252i | − | 2.14198i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.4428i | 0.528645i | ||||||||
\(555\) | −25.3521 | + | 43.9111i | −1.07614 | + | 1.86392i | ||||
\(556\) | −2.25458 | − | 3.90505i | −0.0956155 | − | 0.165611i | ||||
\(557\) | −30.5478 | + | 17.6368i | −1.29435 | + | 0.747294i | −0.979422 | − | 0.201821i | \(-0.935314\pi\) |
−0.314929 | + | 0.949115i | \(0.601981\pi\) | |||||||
\(558\) | −4.54565 | + | 7.87330i | −0.192433 | + | 0.333303i | ||||
\(559\) | −3.53089 | − | 7.86121i | −0.149341 | − | 0.332494i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.2073i | 1.40201i | ||||||||
\(562\) | 6.59075 | − | 11.4155i | 0.278014 | − | 0.481534i | ||||
\(563\) | 18.0551 | + | 31.2723i | 0.760931 | + | 1.31797i | 0.942371 | + | 0.334569i | \(0.108591\pi\) |
−0.181440 | + | 0.983402i | \(0.558076\pi\) | |||||||
\(564\) | −18.0107 | + | 10.3985i | −0.758389 | + | 0.437856i | ||||
\(565\) | −35.7998 | − | 20.6690i | −1.50611 | − | 0.869553i | ||||
\(566\) | − | 4.37862i | − | 0.184047i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.6006 | 0.864383 | ||||||||
\(569\) | 5.91808 | − | 10.2504i | 0.248099 | − | 0.429719i | −0.714900 | − | 0.699227i | \(-0.753528\pi\) |
0.962998 | + | 0.269508i | \(0.0868610\pi\) | |||||||
\(570\) | −3.10876 | + | 1.79484i | −0.130212 | + | 0.0751778i | ||||
\(571\) | −22.9707 | − | 39.7864i | −0.961294 | − | 1.66501i | −0.719260 | − | 0.694741i | \(-0.755519\pi\) |
−0.242034 | − | 0.970268i | \(-0.577815\pi\) | |||||||
\(572\) | −2.99293 | + | 29.4006i | −0.125141 | + | 1.22930i | ||||
\(573\) | −12.6726 | −0.529405 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 49.6193 | 2.06927 | ||||||||
\(576\) | 1.30050 | − | 2.25254i | 0.0541877 | − | 0.0938558i | ||||
\(577\) | −25.7617 | + | 14.8735i | −1.07247 | + | 0.619192i | −0.928856 | − | 0.370441i | \(-0.879206\pi\) |
−0.143616 | + | 0.989633i | \(0.545873\pi\) | |||||||
\(578\) | 5.81972 | − | 3.36002i | 0.242068 | − | 0.139758i | ||||
\(579\) | −3.98229 | − | 2.29918i | −0.165498 | − | 0.0955505i | ||||
\(580\) | − | 26.3813i | − | 1.09542i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 24.3633 | 1.00989 | ||||||||
\(583\) | 21.7737 | + | 12.5711i | 0.901774 | + | 0.520640i | ||||
\(584\) | 7.07571 | + | 12.2555i | 0.292795 | + | 0.507136i | ||||
\(585\) | −23.2360 | − | 16.7661i | −0.960690 | − | 0.693192i | ||||
\(586\) | −2.60645 | + | 4.51450i | −0.107671 | + | 0.186492i | ||||
\(587\) | − | 11.3406i | − | 0.468078i | −0.972227 | − | 0.234039i | \(-0.924806\pi\) | ||
0.972227 | − | 0.234039i | \(-0.0751943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.80265 | −0.156686 | ||||||||
\(590\) | 5.69966 | + | 3.29070i | 0.234651 | + | 0.135476i | ||||
\(591\) | −38.7053 | + | 22.3465i | −1.59212 | + | 0.919213i | ||||
\(592\) | 8.33415 | − | 4.81172i | 0.342531 | − | 0.197761i | ||||
\(593\) | −2.48622 | − | 1.43542i | −0.102097 | − | 0.0589455i | 0.448082 | − | 0.893992i | \(-0.352107\pi\) |
−0.550179 | + | 0.835047i | \(0.685440\pi\) | |||||||
\(594\) | 4.67128 | 0.191665 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 20.3541i | − | 0.833737i | ||||||
\(597\) | −0.227357 | + | 0.393793i | −0.00930509 | + | 0.0161169i | ||||
\(598\) | −17.8214 | − | 12.8592i | −0.728772 | − | 0.525851i | ||||
\(599\) | 2.70779 | + | 4.69004i | 0.110637 | + | 0.191630i | 0.916027 | − | 0.401116i | \(-0.131377\pi\) |
−0.805390 | + | 0.592745i | \(0.798044\pi\) | |||||||
\(600\) | 26.9318 | + | 15.5491i | 1.09949 | + | 0.634789i | ||||
\(601\) | 34.1648 | 1.39361 | 0.696805 | − | 0.717261i | \(-0.254604\pi\) | ||||
0.696805 | + | 0.717261i | \(0.254604\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.3134i | 0.867951i | ||||||||
\(604\) | −12.3269 | − | 7.11695i | −0.501575 | − | 0.289585i | ||||
\(605\) | −48.9875 | + | 28.2830i | −1.99163 | + | 1.14987i | ||||
\(606\) | 5.37508 | − | 3.10330i | 0.218348 | − | 0.126063i | ||||
\(607\) | −11.0215 | + | 19.0898i | −0.447349 | + | 0.774830i | −0.998212 | − | 0.0597646i | \(-0.980965\pi\) |
0.550864 | + | 0.834595i | \(0.314298\pi\) | |||||||
\(608\) | 4.03307 | 0.163562 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.84579 | 0.196200 | ||||||||
\(611\) | −2.11632 | + | 20.7894i | −0.0856173 | + | 0.841048i | ||||
\(612\) | 5.02146 | + | 8.69742i | 0.202980 | + | 0.351572i | ||||
\(613\) | 21.4294 | − | 12.3723i | 0.865527 | − | 0.499712i | −0.000332251 | − | 1.00000i | \(-0.500106\pi\) |
0.865859 | + | 0.500288i | \(0.166772\pi\) | |||||||
\(614\) | 0.106160 | − | 0.183874i | 0.00428426 | − | 0.00742055i | ||||
\(615\) | 16.7705 | 0.676254 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.9659i | 0.803797i | 0.915684 | + | 0.401898i | \(0.131650\pi\) | ||||
−0.915684 | + | 0.401898i | \(0.868350\pi\) | |||||||
\(618\) | 25.5208 | + | 14.7345i | 1.02660 | + | 0.592707i | ||||
\(619\) | −8.72521 | + | 5.03750i | −0.350696 | + | 0.202474i | −0.664992 | − | 0.746851i | \(-0.731565\pi\) |
0.314296 | + | 0.949325i | \(0.398232\pi\) | |||||||
\(620\) | 13.6225 | + | 23.5949i | 0.547093 | + | 0.947593i | ||||
\(621\) | 5.77120 | − | 9.99602i | 0.231590 | − | 0.401126i | ||||
\(622\) | 1.91480i | 0.0767766i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.95864 | + | 11.0400i | 0.198505 | + | 0.441952i | ||||
\(625\) | 11.0123 | − | 19.0739i | 0.440492 | − | 0.762955i | ||||
\(626\) | −7.83048 | + | 4.52093i | −0.312969 | + | 0.180693i | ||||
\(627\) | −4.33394 | − | 7.50660i | −0.173081 | − | 0.299785i | ||||
\(628\) | −1.27312 | + | 2.20510i | −0.0508028 | + | 0.0879931i | ||||
\(629\) | − | 17.8570i | − | 0.712004i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 26.2386i | − | 1.04454i | −0.852780 | − | 0.522271i | \(-0.825085\pi\) | ||
0.852780 | − | 0.522271i | \(-0.174915\pi\) | |||||||
\(632\) | 1.89789 | + | 1.09575i | 0.0754941 | + | 0.0435866i | ||||
\(633\) | 14.3103 | + | 24.7862i | 0.568785 | + | 0.985164i | ||||
\(634\) | −0.330636 | − | 0.572679i | −0.0131312 | − | 0.0227440i | ||||
\(635\) | −28.8891 | − | 16.6792i | −1.14643 | − | 0.661892i | ||||
\(636\) | 16.9215 | 0.670981 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −19.1714 | −0.759001 | ||||||||
\(639\) | −18.1526 | − | 10.4804i | −0.718105 | − | 0.414598i | ||||
\(640\) | −17.6232 | − | 30.5243i | −0.696618 | − | 1.20658i | ||||
\(641\) | 18.6107 | + | 32.2346i | 0.735077 | + | 1.27319i | 0.954690 | + | 0.297603i | \(0.0961872\pi\) |
−0.219613 | + | 0.975587i | \(0.570479\pi\) | |||||||
\(642\) | −18.0200 | − | 10.4038i | −0.711192 | − | 0.410607i | ||||
\(643\) | 10.8569i | 0.428155i | 0.976817 | + | 0.214077i | \(0.0686744\pi\) | ||||
−0.976817 | + | 0.214077i | \(0.931326\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 18.1098i | − | 0.713071i | ||||||
\(646\) | 0.632107 | − | 1.09484i | 0.0248699 | − | 0.0430760i | ||||
\(647\) | 5.61938 | + | 9.73305i | 0.220921 | + | 0.382646i | 0.955088 | − | 0.296323i | \(-0.0957605\pi\) |
−0.734167 | + | 0.678969i | \(0.762427\pi\) | |||||||
\(648\) | 21.5687 | − | 12.4527i | 0.847298 | − | 0.489188i | ||||
\(649\) | −7.94592 | + | 13.7627i | −0.311904 | + | 0.540234i | ||||
\(650\) | 12.3880 | − | 5.56412i | 0.485898 | − | 0.218243i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 15.2189i | − | 0.596019i | ||||||
\(653\) | 7.91231 | − | 13.7045i | 0.309632 | − | 0.536299i | −0.668649 | − | 0.743578i | \(-0.733127\pi\) |
0.978282 | + | 0.207279i | \(0.0664607\pi\) | |||||||
\(654\) | −12.2234 | − | 21.1715i | −0.477971 | − | 0.827870i | ||||
\(655\) | −35.3688 | + | 20.4202i | −1.38197 | + | 0.797883i | ||||
\(656\) | −2.75654 | − | 1.59149i | −0.107625 | − | 0.0621372i | ||||
\(657\) | − | 14.3988i | − | 0.561753i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.8237 | −1.08386 | −0.541928 | − | 0.840425i | \(-0.682306\pi\) | ||||
−0.541928 | + | 0.840425i | \(0.682306\pi\) | |||||||
\(660\) | −31.0515 | + | 53.7829i | −1.20868 | + | 2.09349i | ||||
\(661\) | −15.1140 | + | 8.72604i | −0.587865 | + | 0.339404i | −0.764253 | − | 0.644917i | \(-0.776892\pi\) |
0.176388 | + | 0.984321i | \(0.443559\pi\) | |||||||
\(662\) | −2.62587 | − | 4.54814i | −0.102057 | − | 0.176768i | ||||
\(663\) | 22.3414 | + | 2.27432i | 0.867670 | + | 0.0883273i | ||||
\(664\) | 28.2668 | 1.09696 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.1436 | 0.431806 | ||||||||
\(667\) | −23.6855 | + | 41.0246i | −0.917108 | + | 1.58848i | ||||
\(668\) | 8.13321 | − | 4.69571i | 0.314683 | − | 0.181683i | ||||
\(669\) | −54.9285 | + | 31.7130i | −2.12366 | + | 1.22610i | ||||
\(670\) | −16.6474 | − | 9.61137i | −0.643145 | − | 0.371320i | ||||
\(671\) | 11.7009i | 0.451709i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.6883 | −1.18295 | −0.591474 | − | 0.806324i | \(-0.701454\pi\) | ||||
−0.591474 | + | 0.806324i | \(0.701454\pi\) | |||||||
\(674\) | −16.1910 | − | 9.34788i | −0.623654 | − | 0.360067i | ||||
\(675\) | 3.56629 | + | 6.17699i | 0.137267 | + | 0.237753i | ||||
\(676\) | 19.5754 | + | 4.02721i | 0.752899 | + | 0.154893i | ||||
\(677\) | 1.73778 | − | 3.00992i | 0.0667883 | − | 0.115681i | −0.830698 | − | 0.556724i | \(-0.812058\pi\) |
0.897486 | + | 0.441043i | \(0.145391\pi\) | |||||||
\(678\) | 20.2183i | 0.776477i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −20.8415 | −0.799236 | ||||||||
\(681\) | −14.5801 | − | 8.41785i | −0.558712 | − | 0.322573i | ||||
\(682\) | 17.1464 | − | 9.89951i | 0.656571 | − | 0.379072i | ||||
\(683\) | 2.58740 | − | 1.49384i | 0.0990042 | − | 0.0571601i | −0.449680 | − | 0.893190i | \(-0.648462\pi\) |
0.548685 | + | 0.836029i | \(0.315129\pi\) | |||||||
\(684\) | −2.27023 | − | 1.31072i | −0.0868043 | − | 0.0501165i | ||||
\(685\) | −5.60244 | −0.214058 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 39.9432i | − | 1.52393i | ||||||
\(688\) | −1.71858 | + | 2.97667i | −0.0655202 | + | 0.113484i | ||||
\(689\) | 9.94889 | − | 13.7881i | 0.379022 | − | 0.525284i | ||||
\(690\) | −23.0911 | − | 39.9949i | −0.879063 | − | 1.52258i | ||||
\(691\) | 9.95176 | + | 5.74565i | 0.378583 | + | 0.218575i | 0.677202 | − | 0.735798i | \(-0.263193\pi\) |
−0.298619 | + | 0.954373i | \(0.596526\pi\) | |||||||
\(692\) | 28.7807 | 1.09408 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.51364i | 0.0954164i | ||||||||
\(695\) | −8.24563 | − | 4.76061i | −0.312774 | − | 0.180580i | ||||
\(696\) | −25.7116 | + | 14.8446i | −0.974594 | + | 0.562682i | ||||
\(697\) | −5.11495 | + | 2.95312i | −0.193743 | + | 0.111857i | ||||
\(698\) | 9.09807 | − | 15.7583i | 0.344367 | − | 0.596461i | ||||
\(699\) | −29.4924 | −1.11551 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.977624 | −0.0369244 | −0.0184622 | − | 0.999830i | \(-0.505877\pi\) | ||||
−0.0184622 | + | 0.999830i | \(0.505877\pi\) | |||||||
\(702\) | 0.319929 | − | 3.14277i | 0.0120749 | − | 0.118616i | ||||
\(703\) | 2.33054 | + | 4.03661i | 0.0878979 | + | 0.152244i | ||||
\(704\) | −4.90557 | + | 2.83223i | −0.184886 | + | 0.106744i | ||||
\(705\) | −21.9568 | + | 38.0302i | −0.826939 | + | 1.43230i | ||||
\(706\) | −1.87280 | −0.0704836 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.6957i | 0.401971i | ||||||||
\(709\) | −8.53524 | − | 4.92782i | −0.320548 | − | 0.185068i | 0.331089 | − | 0.943600i | \(-0.392584\pi\) |
−0.651637 | + | 0.758531i | \(0.725917\pi\) | |||||||
\(710\) | 16.3719 | − | 9.45235i | 0.614428 | − | 0.354740i | ||||
\(711\) | −1.11491 | − | 1.93108i | −0.0418123 | − | 0.0724210i | ||||
\(712\) | 1.18622 | − | 2.05460i | 0.0444555 | − | 0.0769992i | ||||
\(713\) | − | 48.9220i | − | 1.83214i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.5672 | + | 56.9229i | 0.956157 | + | 2.12880i | ||||
\(716\) | −7.63867 | + | 13.2306i | −0.285471 | + | 0.494449i | ||||
\(717\) | −15.5812 | + | 8.99581i | −0.581890 | + | 0.335955i | ||||
\(718\) | 11.9220 | + | 20.6495i | 0.444924 | + | 0.770631i | ||||
\(719\) | 9.76729 | − | 16.9174i | 0.364258 | − | 0.630914i | −0.624398 | − | 0.781106i | \(-0.714656\pi\) |
0.988657 | + | 0.150192i | \(0.0479892\pi\) | |||||||
\(720\) | 11.4283i | 0.425906i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 12.5937i | − | 0.468690i | ||||||
\(723\) | 38.8157 | + | 22.4102i | 1.44357 | + | 0.833446i | ||||
\(724\) | −17.4481 | − | 30.2209i | −0.648452 | − | 1.12315i | ||||
\(725\) | −14.6364 | − | 25.3510i | −0.543582 | − | 0.941511i | ||||
\(726\) | 23.9596 | + | 13.8331i | 0.889223 | + | 0.513393i | ||||
\(727\) | −24.4958 | −0.908498 | −0.454249 | − | 0.890875i | \(-0.650092\pi\) | ||||
−0.454249 | + | 0.890875i | \(0.650092\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.3211 | −0.604486 | ||||||||
\(730\) | 11.2466 | + | 6.49321i | 0.416254 | + | 0.240324i | ||||
\(731\) | 3.18894 | + | 5.52341i | 0.117947 | + | 0.204291i | ||||
\(732\) | 3.93756 | + | 6.82006i | 0.145536 | + | 0.252077i | ||||
\(733\) | −26.6977 | − | 15.4140i | −0.986104 | − | 0.569327i | −0.0819964 | − | 0.996633i | \(-0.526130\pi\) |
−0.904107 | + | 0.427305i | \(0.859463\pi\) | |||||||
\(734\) | 10.2033i | 0.376611i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 51.8864i | 1.91256i | ||||||||
\(737\) | 23.2082 | − | 40.1978i | 0.854885 | − | 1.48070i | ||||
\(738\) | −1.84289 | − | 3.19198i | −0.0678377 | − | 0.117498i | ||||
\(739\) | 2.33709 | − | 1.34932i | 0.0859712 | − | 0.0496355i | −0.456398 | − | 0.889776i | \(-0.650861\pi\) |
0.542369 | + | 0.840140i | \(0.317527\pi\) | |||||||
\(740\) | 16.6977 | − | 28.9213i | 0.613820 | − | 1.06317i | ||||
\(741\) | −5.34717 | + | 2.40170i | −0.196433 | + | 0.0882287i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 15.2204i | − | 0.558382i | −0.960236 | − | 0.279191i | \(-0.909934\pi\) | ||
0.960236 | − | 0.279191i | \(-0.0900662\pi\) | |||||||
\(744\) | 15.3306 | − | 26.5533i | 0.562046 | − | 0.973493i | ||||
\(745\) | −21.4892 | − | 37.2203i | −0.787302 | − | 1.36365i | ||||
\(746\) | −12.3670 | + | 7.14011i | −0.452790 | + | 0.261418i | ||||
\(747\) | −24.9077 | − | 14.3805i | −0.911327 | − | 0.526155i | ||||
\(748\) | − | 21.8714i | − | 0.799699i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.76929 | 0.101120 | ||||||||
\(751\) | −12.2741 | + | 21.2594i | −0.447888 | + | 0.775765i | −0.998248 | − | 0.0591620i | \(-0.981157\pi\) |
0.550360 | + | 0.834927i | \(0.314490\pi\) | |||||||
\(752\) | 7.21798 | − | 4.16730i | 0.263213 | − | 0.151966i | ||||
\(753\) | 20.6291 | + | 35.7306i | 0.751765 | + | 1.30210i | ||||
\(754\) | −1.31302 | + | 12.8982i | −0.0478173 | + | 0.469726i | ||||
\(755\) | −30.0553 | −1.09383 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.0892 | 0.403043 | 0.201522 | − | 0.979484i | \(-0.435411\pi\) | ||||
0.201522 | + | 0.979484i | \(0.435411\pi\) | |||||||
\(758\) | 5.18396 | − | 8.97888i | 0.188290 | − | 0.326128i | ||||
\(759\) | 96.5742 | − | 55.7571i | 3.50542 | − | 2.02386i | ||||
\(760\) | 4.71128 | − | 2.72006i | 0.170896 | − | 0.0986669i | ||||
\(761\) | 14.6802 | + | 8.47561i | 0.532157 | + | 0.307241i | 0.741894 | − | 0.670517i | \(-0.233928\pi\) |
−0.209738 | + | 0.977758i | \(0.567261\pi\) | |||||||
\(762\) | 16.3154i | 0.591044i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.34659 | 0.301969 | ||||||||
\(765\) | 18.3649 | + | 10.6030i | 0.663983 | + | 0.383351i | ||||
\(766\) | 8.35824 | + | 14.4769i | 0.301996 | + | 0.523072i | ||||
\(767\) | 8.71518 | + | 6.28850i | 0.314687 | + | 0.227064i | ||||
\(768\) | −11.0993 | + | 19.2245i | −0.400511 | + | 0.693705i | ||||
\(769\) | 50.7371i | 1.82962i | 0.403879 | + | 0.914812i | \(0.367662\pi\) | ||||
−0.403879 | + | 0.914812i | \(0.632338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.11389 | 0.220186 | ||||||||
\(772\) | 2.62287 | + | 1.51431i | 0.0943990 | + | 0.0545013i | ||||
\(773\) | −26.7221 | + | 15.4280i | −0.961128 | + | 0.554907i | −0.896520 | − | 0.443003i | \(-0.853913\pi\) |
−0.0646079 | + | 0.997911i | \(0.520580\pi\) | |||||||
\(774\) | −3.44688 | + | 1.99006i | −0.123895 | + | 0.0715311i | ||||
\(775\) | 26.1809 | + | 15.1156i | 0.940447 | + | 0.542967i | ||||
\(776\) | −36.9223 | −1.32543 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.0875i | 0.469209i | ||||||||
\(779\) | 0.770832 | − | 1.33512i | 0.0276179 | − | 0.0478357i | ||||
\(780\) | 34.0577 | + | 24.5746i | 1.21946 | + | 0.879911i | ||||
\(781\) | 22.8242 | + | 39.5327i | 0.816714 | + | 1.41459i | ||||
\(782\) | 14.0854 | + | 8.13221i | 0.503693 | + | 0.290807i | ||||
\(783\) | −6.80940 | −0.243348 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.37644i | 0.191893i | ||||||||
\(786\) | 17.2987 | + | 9.98742i | 0.617025 | + | 0.356239i | ||||
\(787\) | 3.46788 | − | 2.00218i | 0.123616 | − | 0.0713700i | −0.436917 | − | 0.899502i | \(-0.643930\pi\) |
0.560533 | + | 0.828132i | \(0.310596\pi\) | |||||||
\(788\) | 25.4926 | − | 14.7182i | 0.908136 | − | 0.524312i | ||||
\(789\) | 6.56911 | − | 11.3780i | 0.233866 | − | 0.405069i | ||||
\(790\) | 2.01109 | 0.0715512 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 31.4053 | 1.11594 | ||||||||
\(793\) | 7.87223 | + | 0.801380i | 0.279551 | + | 0.0284578i | ||||
\(794\) | −0.202958 | − | 0.351534i | −0.00720272 | − | 0.0124755i | ||||
\(795\) | 30.9433 | − | 17.8651i | 1.09745 | − | 0.633611i | ||||
\(796\) | 0.149745 | − | 0.259365i | 0.00530756 | − | 0.00919296i | ||||
\(797\) | −17.3993 | −0.616316 | −0.308158 | − | 0.951335i | \(-0.599713\pi\) | ||||
−0.308158 | + | 0.951335i | \(0.599713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.4654i | − | 0.547128i | ||||||
\(800\) | −27.7673 | − | 16.0315i | −0.981723 | − | 0.566798i | ||||
\(801\) | −2.09052 | + | 1.20696i | −0.0738648 | + | 0.0426459i | ||||
\(802\) | −0.542349 | − | 0.939377i | −0.0191510 | − | 0.0331705i | ||||
\(803\) | −15.6789 | + | 27.1566i | −0.553296 | + | 0.958337i | ||||
\(804\) | − | 31.2398i | − | 1.10174i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.48592 | − | 12.2139i | −0.193233 | − | 0.430217i | ||||
\(807\) | 16.1733 | − | 28.0130i | 0.569327 | − | 0.986103i | ||||
\(808\) | −8.14584 | + | 4.70300i | −0.286570 | + | 0.165451i | ||||
\(809\) | −22.6592 | − | 39.2469i | −0.796656 | − | 1.37985i | −0.921782 | − | 0.387708i | \(-0.873267\pi\) |
0.125126 | − | 0.992141i | \(-0.460066\pi\) | |||||||
\(810\) | 11.4275 | − | 19.7931i | 0.401523 | − | 0.695457i | ||||
\(811\) | 3.47248i | 0.121935i | 0.998140 | + | 0.0609676i | \(0.0194186\pi\) | ||||
−0.998140 | + | 0.0609676i | \(0.980581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 18.6934i | − | 0.655605i | ||||||
\(814\) | −21.0172 | − | 12.1343i | −0.736651 | − | 0.425306i | ||||
\(815\) | −16.0676 | − | 27.8299i | −0.562824 | − | 0.974840i | ||||
\(816\) | −4.47842 | − | 7.75685i | −0.156776 | − | 0.271544i | ||||
\(817\) | −1.44174 | − | 0.832388i | −0.0504400 | − | 0.0291216i | ||||
\(818\) | 19.7178 | 0.689416 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.0456 | −0.385730 | ||||||||
\(821\) | −10.4883 | − | 6.05541i | −0.366043 | − | 0.211335i | 0.305685 | − | 0.952133i | \(-0.401114\pi\) |
−0.671728 | + | 0.740797i | \(0.734448\pi\) | |||||||
\(822\) | 1.37006 | + | 2.37302i | 0.0477864 | + | 0.0827685i | ||||
\(823\) | 6.17222 | + | 10.6906i | 0.215150 | + | 0.372651i | 0.953319 | − | 0.301965i | \(-0.0976426\pi\) |
−0.738169 | + | 0.674616i | \(0.764309\pi\) | |||||||
\(824\) | −38.6764 | − | 22.3298i | −1.34736 | − | 0.777896i | ||||
\(825\) | 68.9097i | 2.39913i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0214i | 1.14827i | 0.818762 | + | 0.574133i | \(0.194661\pi\) | ||||
−0.818762 | + | 0.574133i | \(0.805339\pi\) | |||||||
\(828\) | 16.8627 | − | 29.2070i | 0.586018 | − | 1.01501i | ||||
\(829\) | 12.9259 | + | 22.3883i | 0.448935 | + | 0.777578i | 0.998317 | − | 0.0579933i | \(-0.0184702\pi\) |
−0.549382 | + | 0.835571i | \(0.685137\pi\) | |||||||
\(830\) | 22.4645 | − | 12.9699i | 0.779753 | − | 0.450191i | ||||
\(831\) | −21.3491 | + | 36.9777i | −0.740592 | + | 1.28274i | ||||
\(832\) | 1.56951 | + | 3.49438i | 0.0544131 | + | 0.121146i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.65679i | 0.161251i | ||||||||
\(835\) | 9.91514 | − | 17.1735i | 0.343127 | − | 0.594314i | ||||
\(836\) | 2.85447 | + | 4.94409i | 0.0987240 | + | 0.170995i | ||||
\(837\) | 6.09018 | − | 3.51617i | 0.210508 | − | 0.121537i | ||||
\(838\) | 3.05497 | + | 1.76379i | 0.105532 | + | 0.0609290i | ||||
\(839\) | 24.3723i | 0.841424i | 0.907194 | + | 0.420712i | \(0.138220\pi\) | ||||
−0.907194 | + | 0.420712i | \(0.861780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.05359 | −0.0363305 | ||||||||
\(842\) | −0.967113 | + | 1.67509i | −0.0333289 | + | 0.0577273i | ||||
\(843\) | 39.1729 | − | 22.6165i | 1.34919 | − | 0.778953i | ||||
\(844\) | −9.42526 | − | 16.3250i | −0.324431 | − | 0.561931i | ||||
\(845\) | 40.0481 | − | 13.3027i | 1.37770 | − | 0.457626i | ||||
\(846\) | 9.65118 | 0.331815 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.78145 | −0.232876 | ||||||||
\(849\) | 7.51273 | − | 13.0124i | 0.257836 | − | 0.446585i | ||||
\(850\) | −8.70401 | + | 5.02526i | −0.298545 | + | 0.172365i | ||||
\(851\) | −51.9320 | + | 29.9829i | −1.78020 | + | 1.02780i | ||||
\(852\) | 26.6068 | + | 15.3615i | 0.911535 | + | 0.526275i | ||||
\(853\) | − | 16.2919i | − | 0.557825i | −0.960316 | − | 0.278913i | \(-0.910026\pi\) | ||
0.960316 | − | 0.278913i | \(-0.0899740\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.53523 | −0.189301 | ||||||||
\(856\) | 27.3090 | + | 15.7669i | 0.933402 | + | 0.538900i | ||||
\(857\) | −14.1483 | − | 24.5056i | −0.483296 | − | 0.837094i | 0.516520 | − | 0.856275i | \(-0.327227\pi\) |
−0.999816 | + | 0.0191815i | \(0.993894\pi\) | |||||||
\(858\) | 17.8584 | − | 24.7498i | 0.609676 | − | 0.844945i | ||||
\(859\) | 2.65355 | − | 4.59609i | 0.0905380 | − | 0.156816i | −0.817200 | − | 0.576355i | \(-0.804475\pi\) |
0.907738 | + | 0.419538i | \(0.137808\pi\) | |||||||
\(860\) | 11.9277i | 0.406731i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.70790 | 0.0922314 | ||||||||
\(863\) | −30.7323 | − | 17.7433i | −1.04614 | − | 0.603990i | −0.124575 | − | 0.992210i | \(-0.539757\pi\) |
−0.921567 | + | 0.388220i | \(0.873090\pi\) | |||||||
\(864\) | −6.45921 | + | 3.72923i | −0.219747 | + | 0.126871i | ||||
\(865\) | 52.6295 | − | 30.3856i | 1.78946 | − | 1.03314i | ||||
\(866\) | −4.37136 | − | 2.52381i | −0.148545 | − | 0.0857624i | ||||
\(867\) | 23.0601 | 0.783163 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.85609i | 0.164731i | ||||||||
\(870\) | −13.6225 | + | 23.5949i | −0.461846 | + | 0.799941i | ||||
\(871\) | −25.4550 | − | 18.3673i | −0.862511 | − | 0.622351i | ||||
\(872\) | 18.5243 | + | 32.0850i | 0.627312 | + | 1.08654i | ||||
\(873\) | 32.5347 | + | 18.7839i | 1.10113 | + | 0.635739i | ||||
\(874\) | −4.24539 | −0.143602 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.1048i | 0.713067i | ||||||||
\(877\) | −36.7183 | − | 21.1993i | −1.23989 | − | 0.715850i | −0.270817 | − | 0.962631i | \(-0.587294\pi\) |
−0.969071 | + | 0.246781i | \(0.920627\pi\) | |||||||
\(878\) | 18.0060 | − | 10.3958i | 0.607674 | − | 0.350841i | ||||
\(879\) | −15.4917 | + | 8.94416i | −0.522523 | + | 0.301679i | ||||
\(880\) | 12.4442 | − | 21.5540i | 0.419494 | − | 0.726586i | ||||
\(881\) | −33.1997 | −1.11853 | −0.559263 | − | 0.828990i | \(-0.688916\pi\) | ||||
−0.559263 | + | 0.828990i | \(0.688916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.9618 | −0.402546 | −0.201273 | − | 0.979535i | \(-0.564508\pi\) | ||||
−0.201273 | + | 0.979535i | \(0.564508\pi\) | |||||||
\(884\) | −14.7148 | − | 1.49794i | −0.494913 | − | 0.0503813i | ||||
\(885\) | 11.2922 | + | 19.5587i | 0.379583 | + | 0.657457i | ||||
\(886\) | 2.53873 | − | 1.46574i | 0.0852904 | − | 0.0492424i | ||||
\(887\) | −3.16331 | + | 5.47902i | −0.106214 | + | 0.183967i | −0.914233 | − | 0.405188i | \(-0.867206\pi\) |
0.808020 | + | 0.589155i | \(0.200539\pi\) | |||||||
\(888\) | −37.5827 | −1.26119 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 2.17713i | − | 0.0729777i | ||||||
\(891\) | 47.7935 | + | 27.5936i | 1.60114 | + | 0.924420i | ||||
\(892\) | 36.1777 | − | 20.8872i | 1.21132 | − | 0.699356i | ||||
\(893\) | 2.01842 | + | 3.49600i | 0.0675438 | + | 0.116989i | ||||
\(894\) | −10.5102 | + | 18.2043i | −0.351515 | + | 0.608842i | ||||
\(895\) | 32.2586i | 1.07829i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.8984 | − | 68.7926i | −1.03167 | − | 2.29692i | ||||
\(898\) | −10.4692 | + | 18.1332i | −0.349363 | + | 0.605114i | ||||
\(899\) | −24.9947 | + | 14.4307i | −0.833619 | + | 0.481290i | ||||
\(900\) | 10.4202 | + | 18.0483i | 0.347340 | + | 0.601611i | ||||
\(901\) | −6.29173 | + | 10.8976i | −0.209608 | + | 0.363051i | ||||
\(902\) | 8.02688i | 0.267266i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 30.6404i | − | 1.01909i | ||||||
\(905\) | −63.8124 | − | 36.8421i | −2.12120 | − | 1.22467i | ||||
\(906\) | 7.34996 | + | 12.7305i | 0.244186 | + | 0.422943i | ||||
\(907\) | 4.65667 | + | 8.06558i | 0.154622 | + | 0.267813i | 0.932921 | − | 0.360080i | \(-0.117251\pi\) |
−0.778299 | + | 0.627894i | \(0.783917\pi\) | |||||||
\(908\) | 9.60296 | + | 5.54427i | 0.318686 | + | 0.183993i | ||||
\(909\) | 9.57047 | 0.317432 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.4873 | 0.943826 | 0.471913 | − | 0.881645i | \(-0.343564\pi\) | ||||
0.471913 | + | 0.881645i | \(0.343564\pi\) | |||||||
\(912\) | 2.02472 | + | 1.16897i | 0.0670451 | + | 0.0387085i | ||||
\(913\) | 31.3178 | + | 54.2440i | 1.03647 | + | 1.79522i | ||||
\(914\) | −4.58975 | − | 7.94969i | −0.151816 | − | 0.262952i | ||||
\(915\) | 14.4008 | + | 8.31428i | 0.476074 | + | 0.274862i | ||||
\(916\) | 26.3079i | 0.869238i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.33794i | 0.0771636i | ||||||||
\(919\) | −27.3916 | + | 47.4437i | −0.903566 | + | 1.56502i | −0.0807363 | + | 0.996735i | \(0.525727\pi\) |
−0.822830 | + | 0.568287i | \(0.807606\pi\) | |||||||
\(920\) | 34.9942 | + | 60.6117i | 1.15372 | + | 1.99831i | ||||
\(921\) | 0.630973 | − | 0.364292i | 0.0207913 | − | 0.0120038i | ||||
\(922\) | 9.34515 | − | 16.1863i | 0.307766 | − | 0.533067i | ||||
\(923\) | 28.1603 | − | 12.6483i | 0.926906 | − | 0.416323i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 37.0556i | − | 1.21838i | ||||||
\(926\) | −2.74296 | + | 4.75095i | −0.0901393 | + | 0.156126i | ||||
\(927\) | 22.7203 | + | 39.3526i | 0.746231 | + | 1.29251i | ||||
\(928\) | 26.5092 | − | 15.3051i | 0.870207 | − | 0.502414i | ||||
\(929\) | 11.5496 | + | 6.66817i | 0.378930 | + | 0.218776i | 0.677353 | − | 0.735658i | \(-0.263127\pi\) |
−0.298422 | + | 0.954434i | \(0.596460\pi\) | |||||||
\(930\) | − | 28.1370i | − | 0.922649i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.4247 | 0.636277 | ||||||||
\(933\) | −3.28537 | + | 5.69043i | −0.107558 | + | 0.186296i | ||||
\(934\) | 7.44141 | − | 4.29630i | 0.243490 | − | 0.140579i | ||||
\(935\) | −23.0911 | − | 39.9949i | −0.755160 | − | 1.30797i | ||||
\(936\) | 2.15091 | − | 21.1291i | 0.0703046 | − | 0.690626i | ||||
\(937\) | −15.4989 | −0.506327 | −0.253164 | − | 0.967423i | \(-0.581471\pi\) | ||||
−0.253164 | + | 0.967423i | \(0.581471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.0276 | −1.01255 | ||||||||
\(940\) | 14.4614 | − | 25.0480i | 0.471680 | − | 0.816974i | ||||
\(941\) | 18.8503 | − | 10.8832i | 0.614502 | − | 0.354783i | −0.160223 | − | 0.987081i | \(-0.551221\pi\) |
0.774725 | + | 0.632298i | \(0.217888\pi\) | |||||||
\(942\) | 2.27729 | − | 1.31480i | 0.0741982 | − | 0.0428384i | ||||
\(943\) | 17.1766 | + | 9.91694i | 0.559348 | + | 0.322940i | ||||
\(944\) | − | 4.28642i | − | 0.139511i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.66787 | 0.281817 | ||||||||
\(947\) | −14.0527 | − | 8.11331i | −0.456650 | − | 0.263647i | 0.253985 | − | 0.967208i | \(-0.418259\pi\) |
−0.710635 | + | 0.703561i | \(0.751592\pi\) | |||||||
\(948\) | 1.63416 | + | 2.83044i | 0.0530749 | + | 0.0919284i | ||||
\(949\) | 17.1968 | + | 12.4085i | 0.558232 | + | 0.402796i | ||||
\(950\) | 1.31171 | − | 2.27195i | 0.0425575 | − | 0.0737117i | ||||
\(951\) | − | 2.26919i | − | 0.0735835i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.2125 | 0.816712 | 0.408356 | − | 0.912823i | \(-0.366102\pi\) | ||||
0.408356 | + | 0.912823i | \(0.366102\pi\) | |||||||
\(954\) | −6.80063 | − | 3.92634i | −0.220178 | − | 0.127120i | ||||
\(955\) | 15.2629 | − | 8.81204i | 0.493896 | − | 0.285151i | ||||
\(956\) | 10.2623 | − | 5.92494i | 0.331906 | − | 0.191626i | ||||
\(957\) | −56.9736 | − | 32.8937i | −1.84169 | − | 1.06330i | ||||
\(958\) | 21.4520 | 0.693083 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.04996i | 0.259811i | ||||||||
\(961\) | −0.596863 | + | 1.03380i | −0.0192537 | + | 0.0333483i | ||||
\(962\) | −9.60321 | + | 13.3090i | −0.309620 | + | 0.429100i | ||||
\(963\) | −16.0425 | − | 27.7865i | −0.516963 | − | 0.895406i | ||||
\(964\) | −25.5653 | − | 14.7601i | −0.823402 | − | 0.475392i | ||||
\(965\) | 6.39504 | 0.205863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 32.6302i | − | 1.04932i | −0.851313 | − | 0.524658i | \(-0.824193\pi\) | ||
0.851313 | − | 0.524658i | \(-0.175807\pi\) | |||||||
\(968\) | −36.3104 | − | 20.9638i | −1.16706 | − | 0.673802i | ||||
\(969\) | 3.75700 | − | 2.16911i | 0.120692 | − | 0.0696817i | ||||
\(970\) | −29.3433 | + | 16.9413i | −0.942155 | + | 0.543953i | ||||
\(971\) | −17.0162 | + | 29.4730i | −0.546077 | + | 0.945832i | 0.452462 | + | 0.891784i | \(0.350546\pi\) |
−0.998538 | + | 0.0540486i | \(0.982787\pi\) | |||||||
\(972\) | 31.2022 | 1.00081 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28.6511 | 0.918041 | ||||||||
\(975\) | 46.3616 | + | 4.71953i | 1.48476 | + | 0.151146i | ||||
\(976\) | −1.57802 | − | 2.73320i | −0.0505111 | − | 0.0874878i | ||||
\(977\) | 4.20500 | − | 2.42776i | 0.134530 | − | 0.0776708i | −0.431225 | − | 0.902245i | \(-0.641918\pi\) |
0.565754 | + | 0.824574i | \(0.308585\pi\) | |||||||
\(978\) | −7.85860 | + | 13.6115i | −0.251290 | + | 0.435247i | ||||
\(979\) | 5.25703 | 0.168016 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 37.6964i | − | 1.20355i | ||||||
\(982\) | −17.8066 | − | 10.2806i | −0.568231 | − | 0.328068i | ||||
\(983\) | −23.8899 | + | 13.7928i | −0.761968 | + | 0.439922i | −0.830002 | − | 0.557761i | \(-0.811661\pi\) |
0.0680339 | + | 0.997683i | \(0.478327\pi\) | |||||||
\(984\) | 6.21530 | + | 10.7652i | 0.198136 | + | 0.343182i | ||||
\(985\) | 31.0778 | − | 53.8284i | 0.990222 | − | 1.71511i | ||||
\(986\) | − | 9.59513i | − | 0.305571i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.52182 | − | 1.58184i | 0.112044 | − | 0.0503250i | ||||
\(989\) | 10.7089 | − | 18.5483i | 0.340522 | − | 0.589801i | ||||
\(990\) | 24.9588 | − | 14.4100i | 0.793243 | − | 0.457979i | ||||
\(991\) | 0.996052 | + | 1.72521i | 0.0316406 | + | 0.0548032i | 0.881412 | − | 0.472348i | \(-0.156593\pi\) |
−0.849771 | + | 0.527151i | \(0.823260\pi\) | |||||||
\(992\) | −15.8062 | + | 27.3771i | −0.501846 | + | 0.869224i | ||||
\(993\) | − | 18.0216i | − | 0.571898i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 0.632380i | − | 0.0200478i | ||||||
\(996\) | 36.5081 | + | 21.0779i | 1.15680 | + | 0.667880i | ||||
\(997\) | 15.7800 | + | 27.3318i | 0.499758 | + | 0.865607i | 1.00000 | 0.000279244i | \(-8.88862e-5\pi\) | |
−0.500242 | + | 0.865886i | \(0.666756\pi\) | |||||||
\(998\) | 1.19305 | + | 2.06643i | 0.0377654 | + | 0.0654116i | ||||
\(999\) | −7.46501 | − | 4.30992i | −0.236182 | − | 0.136360i |
(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.r.g.324.10 | 32 | ||
7.2 | even | 3 | 637.2.c.g.246.7 | ✓ | 16 | ||
7.3 | odd | 6 | inner | 637.2.r.g.116.7 | 32 | ||
7.4 | even | 3 | inner | 637.2.r.g.116.8 | 32 | ||
7.5 | odd | 6 | 637.2.c.g.246.8 | yes | 16 | ||
7.6 | odd | 2 | inner | 637.2.r.g.324.9 | 32 | ||
13.12 | even | 2 | inner | 637.2.r.g.324.8 | 32 | ||
91.5 | even | 12 | 8281.2.a.cs.1.8 | 16 | |||
91.12 | odd | 6 | 637.2.c.g.246.10 | yes | 16 | ||
91.25 | even | 6 | inner | 637.2.r.g.116.10 | 32 | ||
91.38 | odd | 6 | inner | 637.2.r.g.116.9 | 32 | ||
91.44 | odd | 12 | 8281.2.a.cs.1.7 | 16 | |||
91.47 | even | 12 | 8281.2.a.cs.1.10 | 16 | |||
91.51 | even | 6 | 637.2.c.g.246.9 | yes | 16 | ||
91.86 | odd | 12 | 8281.2.a.cs.1.9 | 16 | |||
91.90 | odd | 2 | inner | 637.2.r.g.324.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.7 | ✓ | 16 | 7.2 | even | 3 | ||
637.2.c.g.246.8 | yes | 16 | 7.5 | odd | 6 | ||
637.2.c.g.246.9 | yes | 16 | 91.51 | even | 6 | ||
637.2.c.g.246.10 | yes | 16 | 91.12 | odd | 6 | ||
637.2.r.g.116.7 | 32 | 7.3 | odd | 6 | inner | ||
637.2.r.g.116.8 | 32 | 7.4 | even | 3 | inner | ||
637.2.r.g.116.9 | 32 | 91.38 | odd | 6 | inner | ||
637.2.r.g.116.10 | 32 | 91.25 | even | 6 | inner | ||
637.2.r.g.324.7 | 32 | 91.90 | odd | 2 | inner | ||
637.2.r.g.324.8 | 32 | 13.12 | even | 2 | inner | ||
637.2.r.g.324.9 | 32 | 7.6 | odd | 2 | inner | ||
637.2.r.g.324.10 | 32 | 1.1 | even | 1 | trivial | ||
8281.2.a.cs.1.7 | 16 | 91.44 | odd | 12 | |||
8281.2.a.cs.1.8 | 16 | 91.5 | even | 12 | |||
8281.2.a.cs.1.9 | 16 | 91.86 | odd | 12 | |||
8281.2.a.cs.1.10 | 16 | 91.47 | even | 12 |