Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(126,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.d (of order \(5\), degree \(4\), 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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 126.4 | ||
Root | \(0.991969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.126 |
Dual form | 625.2.d.p.501.4 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.520202 | + | 1.60102i | 0.367839 | + | 1.13209i | 0.948184 | + | 0.317721i | \(0.102917\pi\) |
−0.580346 | + | 0.814370i | \(0.697083\pi\) | |||||||
\(3\) | 0.574677 | − | 0.417528i | 0.331790 | − | 0.241060i | −0.409400 | − | 0.912355i | \(-0.634262\pi\) |
0.741190 | + | 0.671295i | \(0.234262\pi\) | |||||||
\(4\) | −0.674615 | + | 0.490137i | −0.337308 | + | 0.245068i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.967418 | + | 0.702870i | 0.394947 | + | 0.286946i | ||||
\(7\) | −4.59110 | −1.73527 | −0.867637 | − | 0.497198i | \(-0.834362\pi\) | ||||
−0.867637 | + | 0.497198i | \(0.834362\pi\) | |||||||
\(8\) | 1.58816 | + | 1.15387i | 0.561500 | + | 0.407953i | ||||
\(9\) | −0.771126 | + | 2.37328i | −0.257042 | + | 0.791094i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.20974 | + | 3.72319i | 0.364749 | + | 1.12258i | 0.950138 | + | 0.311830i | \(0.100942\pi\) |
−0.585389 | + | 0.810753i | \(0.699058\pi\) | |||||||
\(12\) | −0.183041 | + | 0.563341i | −0.0528393 | + | 0.162623i | ||||
\(13\) | −0.177048 | + | 0.544898i | −0.0491043 | + | 0.151127i | −0.972602 | − | 0.232476i | \(-0.925317\pi\) |
0.923498 | + | 0.383604i | \(0.125317\pi\) | |||||||
\(14\) | −2.38830 | − | 7.35044i | −0.638301 | − | 1.96449i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.53656 | + | 4.72903i | −0.384139 | + | 1.18226i | ||||
\(17\) | 0.188186 | + | 0.136725i | 0.0456419 | + | 0.0331608i | 0.610372 | − | 0.792115i | \(-0.291020\pi\) |
−0.564730 | + | 0.825275i | \(0.691020\pi\) | |||||||
\(18\) | −4.20081 | −0.990140 | ||||||||
\(19\) | 4.49012 | + | 3.26227i | 1.03010 | + | 0.748415i | 0.968330 | − | 0.249675i | \(-0.0803238\pi\) |
0.0617752 | + | 0.998090i | \(0.480324\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.63840 | + | 1.91691i | −0.575747 | + | 0.418305i | ||||
\(22\) | −5.33158 | + | 3.87362i | −1.13670 | + | 0.825858i | ||||
\(23\) | −1.52428 | − | 4.69124i | −0.317834 | − | 0.978192i | −0.974572 | − | 0.224073i | \(-0.928064\pi\) |
0.656738 | − | 0.754118i | \(-0.271936\pi\) | |||||||
\(24\) | 1.39445 | 0.284641 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.964492 | −0.189152 | ||||||||
\(27\) | 1.20628 | + | 3.71256i | 0.232149 | + | 0.714482i | ||||
\(28\) | 3.09723 | − | 2.25027i | 0.585321 | − | 0.425261i | ||||
\(29\) | −3.34174 | + | 2.42792i | −0.620546 | + | 0.450853i | −0.853112 | − | 0.521727i | \(-0.825288\pi\) |
0.232566 | + | 0.972581i | \(0.425288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.82777 | + | 2.05449i | 0.507882 | + | 0.368998i | 0.812020 | − | 0.583630i | \(-0.198368\pi\) |
−0.304138 | + | 0.952628i | \(0.598368\pi\) | |||||||
\(32\) | −4.44444 | −0.785674 | ||||||||
\(33\) | 2.24974 | + | 1.63453i | 0.391630 | + | 0.284536i | ||||
\(34\) | −0.121005 | + | 0.372415i | −0.0207522 | + | 0.0638686i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.643019 | − | 1.97901i | −0.107170 | − | 0.329835i | ||||
\(37\) | −1.67378 | + | 5.15138i | −0.275169 | + | 0.846882i | 0.714006 | + | 0.700139i | \(0.246879\pi\) |
−0.989175 | + | 0.146742i | \(0.953121\pi\) | |||||||
\(38\) | −2.88717 | + | 8.88581i | −0.468361 | + | 1.44147i | ||||
\(39\) | 0.125764 | + | 0.387063i | 0.0201384 | + | 0.0619797i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.22079 | − | 9.91257i | 0.503003 | − | 1.54808i | −0.301100 | − | 0.953593i | \(-0.597354\pi\) |
0.804103 | − | 0.594491i | \(-0.202646\pi\) | |||||||
\(42\) | −4.44152 | − | 3.22695i | −0.685341 | − | 0.497929i | ||||
\(43\) | 1.38833 | 0.211718 | 0.105859 | − | 0.994381i | \(-0.466241\pi\) | ||||
0.105859 | + | 0.994381i | \(0.466241\pi\) | |||||||
\(44\) | −2.64098 | − | 1.91878i | −0.398142 | − | 0.289267i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.71783 | − | 4.88079i | 0.990491 | − | 0.719634i | ||||
\(47\) | −0.744634 | + | 0.541008i | −0.108616 | + | 0.0789142i | −0.640767 | − | 0.767735i | \(-0.721384\pi\) |
0.532151 | + | 0.846649i | \(0.321384\pi\) | |||||||
\(48\) | 1.09148 | + | 3.35922i | 0.157541 | + | 0.484862i | ||||
\(49\) | 14.0782 | 2.01118 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.165233 | 0.0231373 | ||||||||
\(52\) | −0.147635 | − | 0.454374i | −0.0204733 | − | 0.0630103i | ||||
\(53\) | −0.996044 | + | 0.723668i | −0.136817 | + | 0.0994034i | −0.654089 | − | 0.756418i | \(-0.726948\pi\) |
0.517272 | + | 0.855821i | \(0.326948\pi\) | |||||||
\(54\) | −5.31636 | + | 3.86256i | −0.723466 | + | 0.525628i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.29141 | − | 5.29752i | −0.974356 | − | 0.707911i | ||||
\(57\) | 3.94246 | 0.522191 | ||||||||
\(58\) | −5.62552 | − | 4.08718i | −0.738668 | − | 0.536673i | ||||
\(59\) | 1.39299 | − | 4.28718i | 0.181352 | − | 0.558143i | −0.818515 | − | 0.574485i | \(-0.805202\pi\) |
0.999866 | + | 0.0163426i | \(0.00520224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.60276 | − | 11.0881i | −0.461286 | − | 1.41969i | −0.863594 | − | 0.504187i | \(-0.831792\pi\) |
0.402309 | − | 0.915504i | \(-0.368208\pi\) | |||||||
\(62\) | −1.81827 | + | 5.59606i | −0.230921 | + | 0.710700i | ||||
\(63\) | 3.54032 | − | 10.8960i | 0.446038 | − | 1.37277i | ||||
\(64\) | 0.761103 | + | 2.34244i | 0.0951379 | + | 0.292804i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.44660 | + | 4.45216i | −0.178064 | + | 0.548023i | ||||
\(67\) | 2.39022 | + | 1.73660i | 0.292012 | + | 0.212159i | 0.724140 | − | 0.689653i | \(-0.242237\pi\) |
−0.432128 | + | 0.901812i | \(0.642237\pi\) | |||||||
\(68\) | −0.193968 | −0.0235220 | ||||||||
\(69\) | −2.83469 | − | 2.05952i | −0.341257 | − | 0.247938i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.59331 | + | 1.88415i | −0.307770 | + | 0.223608i | −0.730939 | − | 0.682443i | \(-0.760918\pi\) |
0.423169 | + | 0.906051i | \(0.360918\pi\) | |||||||
\(72\) | −3.96312 | + | 2.87938i | −0.467058 | + | 0.339338i | ||||
\(73\) | −3.18047 | − | 9.78847i | −0.372245 | − | 1.14565i | −0.945318 | − | 0.326149i | \(-0.894249\pi\) |
0.573073 | − | 0.819504i | \(-0.305751\pi\) | |||||||
\(74\) | −9.11816 | −1.05996 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.62806 | −0.530875 | ||||||||
\(77\) | −5.55402 | − | 17.0935i | −0.632940 | − | 1.94799i | ||||
\(78\) | −0.554272 | + | 0.402702i | −0.0627589 | + | 0.0455970i | ||||
\(79\) | 7.77877 | − | 5.65161i | 0.875180 | − | 0.635856i | −0.0567919 | − | 0.998386i | \(-0.518087\pi\) |
0.931972 | + | 0.362531i | \(0.118087\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.81318 | − | 2.77044i | −0.423687 | − | 0.307827i | ||||
\(82\) | 17.5457 | 1.93759 | ||||||||
\(83\) | 8.48125 | + | 6.16199i | 0.930938 | + | 0.676366i | 0.946222 | − | 0.323517i | \(-0.104865\pi\) |
−0.0152844 | + | 0.999883i | \(0.504865\pi\) | |||||||
\(84\) | 0.840358 | − | 2.58636i | 0.0916906 | − | 0.282195i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.722211 | + | 2.22274i | 0.0778780 | + | 0.239684i | ||||
\(87\) | −0.906701 | + | 2.79054i | −0.0972086 | + | 0.299177i | ||||
\(88\) | −2.37480 | + | 7.30889i | −0.253155 | + | 0.779130i | ||||
\(89\) | 2.24293 | + | 6.90303i | 0.237750 | + | 0.731720i | 0.996745 | + | 0.0806230i | \(0.0256910\pi\) |
−0.758994 | + | 0.651097i | \(0.774309\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.812846 | − | 2.50168i | 0.0852094 | − | 0.262248i | ||||
\(92\) | 3.32765 | + | 2.41768i | 0.346932 | + | 0.252061i | ||||
\(93\) | 2.48286 | 0.257461 | ||||||||
\(94\) | −1.25352 | − | 0.910739i | −0.129291 | − | 0.0939356i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.55412 | + | 1.85568i | −0.260679 | + | 0.189394i | ||||
\(97\) | 6.73079 | − | 4.89020i | 0.683408 | − | 0.496525i | −0.191079 | − | 0.981575i | \(-0.561199\pi\) |
0.874487 | + | 0.485050i | \(0.161199\pi\) | |||||||
\(98\) | 7.32353 | + | 22.5395i | 0.739788 | + | 2.27683i | ||||
\(99\) | −9.76903 | −0.981824 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.56513 | −0.354744 | −0.177372 | − | 0.984144i | \(-0.556760\pi\) | ||||
−0.177372 | + | 0.984144i | \(0.556760\pi\) | |||||||
\(102\) | 0.0859547 | + | 0.264541i | 0.00851078 | + | 0.0261935i | ||||
\(103\) | 0.323059 | − | 0.234716i | 0.0318320 | − | 0.0231273i | −0.571756 | − | 0.820424i | \(-0.693737\pi\) |
0.603587 | + | 0.797297i | \(0.293737\pi\) | |||||||
\(104\) | −0.909920 | + | 0.661095i | −0.0892250 | + | 0.0648257i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.67675 | − | 1.21823i | −0.162860 | − | 0.118325i | ||||
\(107\) | −1.64372 | −0.158904 | −0.0794522 | − | 0.996839i | \(-0.525317\pi\) | ||||
−0.0794522 | + | 0.996839i | \(0.525317\pi\) | |||||||
\(108\) | −2.63344 | − | 1.91331i | −0.253403 | − | 0.184108i | ||||
\(109\) | 0.0231501 | − | 0.0712488i | 0.00221738 | − | 0.00682440i | −0.949942 | − | 0.312427i | \(-0.898858\pi\) |
0.952159 | + | 0.305603i | \(0.0988580\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.18896 | + | 3.65923i | 0.112851 | + | 0.347319i | ||||
\(112\) | 7.05449 | − | 21.7115i | 0.666587 | − | 2.05154i | ||||
\(113\) | 4.36729 | − | 13.4411i | 0.410840 | − | 1.26444i | −0.505079 | − | 0.863073i | \(-0.668537\pi\) |
0.915919 | − | 0.401363i | \(-0.131463\pi\) | |||||||
\(114\) | 2.05088 | + | 6.31195i | 0.192082 | + | 0.591168i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.06438 | − | 3.27582i | 0.0988251 | − | 0.304152i | ||||
\(117\) | −1.15667 | − | 0.840370i | −0.106934 | − | 0.0776922i | ||||
\(118\) | 7.58848 | 0.698576 | ||||||||
\(119\) | −0.863983 | − | 0.627721i | −0.0792012 | − | 0.0575431i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.49946 | + | 2.54251i | −0.318133 | + | 0.231137i | ||||
\(122\) | 15.8782 | − | 11.5362i | 1.43754 | − | 1.04443i | ||||
\(123\) | −2.28786 | − | 7.04130i | −0.206289 | − | 0.634892i | ||||
\(124\) | −2.91464 | −0.261742 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 19.2864 | 1.71817 | ||||||||
\(127\) | 3.65025 | + | 11.2343i | 0.323907 | + | 0.996883i | 0.971932 | + | 0.235264i | \(0.0755954\pi\) |
−0.648025 | + | 0.761619i | \(0.724405\pi\) | |||||||
\(128\) | −10.5456 | + | 7.66184i | −0.932109 | + | 0.677217i | ||||
\(129\) | 0.797840 | − | 0.579665i | 0.0702459 | − | 0.0510366i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.5407 | + | 9.83791i | 1.18306 | + | 0.859542i | 0.992513 | − | 0.122136i | \(-0.0389744\pi\) |
0.190545 | + | 0.981678i | \(0.438974\pi\) | |||||||
\(132\) | −2.31885 | −0.201830 | ||||||||
\(133\) | −20.6146 | − | 14.9774i | −1.78751 | − | 1.29871i | ||||
\(134\) | −1.53692 | + | 4.73017i | −0.132770 | + | 0.408624i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.141107 | + | 0.434284i | 0.0120999 | + | 0.0372395i | ||||
\(137\) | 3.22062 | − | 9.91204i | 0.275156 | − | 0.846843i | −0.714022 | − | 0.700123i | \(-0.753128\pi\) |
0.989178 | − | 0.146720i | \(-0.0468715\pi\) | |||||||
\(138\) | 1.82272 | − | 5.60976i | 0.155160 | − | 0.477535i | ||||
\(139\) | 2.05803 | + | 6.33397i | 0.174560 | + | 0.537241i | 0.999613 | − | 0.0278147i | \(-0.00885484\pi\) |
−0.825053 | + | 0.565055i | \(0.808855\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.202038 | + | 0.621811i | −0.0170147 | + | 0.0523659i | ||||
\(142\) | −4.36561 | − | 3.17180i | −0.366354 | − | 0.266172i | ||||
\(143\) | −2.24294 | −0.187564 | ||||||||
\(144\) | −10.0385 | − | 7.29336i | −0.836538 | − | 0.607780i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.0170 | − | 10.1840i | 1.16006 | − | 0.842831i | ||||
\(147\) | 8.09044 | − | 5.87805i | 0.667289 | − | 0.484814i | ||||
\(148\) | −1.39572 | − | 4.29558i | −0.114727 | − | 0.353095i | ||||
\(149\) | −12.0316 | −0.985667 | −0.492834 | − | 0.870124i | \(-0.664039\pi\) | ||||
−0.492834 | + | 0.870124i | \(0.664039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.54218 | −0.125501 | −0.0627505 | − | 0.998029i | \(-0.519987\pi\) | ||||
−0.0627505 | + | 0.998029i | \(0.519987\pi\) | |||||||
\(152\) | 3.36682 | + | 10.3620i | 0.273085 | + | 0.840469i | ||||
\(153\) | −0.469603 | + | 0.341187i | −0.0379652 | + | 0.0275833i | ||||
\(154\) | 24.4778 | − | 17.7842i | 1.97248 | − | 1.43309i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.274556 | − | 0.199477i | −0.0219821 | − | 0.0159709i | ||||
\(157\) | −9.82482 | −0.784106 | −0.392053 | − | 0.919943i | \(-0.628235\pi\) | ||||
−0.392053 | + | 0.919943i | \(0.628235\pi\) | |||||||
\(158\) | 13.0949 | + | 9.51397i | 1.04177 | + | 0.756891i | ||||
\(159\) | −0.270252 | + | 0.831751i | −0.0214324 | + | 0.0659622i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.99812 | + | 21.5380i | 0.551529 | + | 1.69743i | ||||
\(162\) | 2.45190 | − | 7.54617i | 0.192639 | − | 0.592883i | ||||
\(163\) | −1.72465 | + | 5.30792i | −0.135085 | + | 0.415748i | −0.995603 | − | 0.0936712i | \(-0.970140\pi\) |
0.860518 | + | 0.509419i | \(0.170140\pi\) | |||||||
\(164\) | 2.68572 | + | 8.26580i | 0.209720 | + | 0.645450i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.45349 | + | 16.7841i | −0.423273 | + | 1.30270i | ||||
\(167\) | 17.6857 | + | 12.8494i | 1.36856 | + | 0.994318i | 0.997848 | + | 0.0655703i | \(0.0208867\pi\) |
0.370713 | + | 0.928747i | \(0.379113\pi\) | |||||||
\(168\) | −6.40207 | −0.493930 | ||||||||
\(169\) | 10.2517 | + | 7.44826i | 0.788589 | + | 0.572943i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.2047 | + | 8.14071i | −0.856847 | + | 0.622536i | ||||
\(172\) | −0.936586 | + | 0.680470i | −0.0714140 | + | 0.0518853i | ||||
\(173\) | 7.24291 | + | 22.2914i | 0.550668 | + | 1.69478i | 0.707117 | + | 0.707096i | \(0.249995\pi\) |
−0.156449 | + | 0.987686i | \(0.550005\pi\) | |||||||
\(174\) | −4.93937 | −0.374453 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.4659 | −1.46730 | ||||||||
\(177\) | −0.989495 | − | 3.04535i | −0.0743750 | − | 0.228903i | ||||
\(178\) | −9.88511 | + | 7.18195i | −0.740920 | + | 0.538310i | ||||
\(179\) | 5.11196 | − | 3.71406i | 0.382086 | − | 0.277602i | −0.380119 | − | 0.924938i | \(-0.624117\pi\) |
0.762205 | + | 0.647336i | \(0.224117\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7904 | + | 7.83972i | 0.802047 | + | 0.582722i | 0.911514 | − | 0.411269i | \(-0.134914\pi\) |
−0.109467 | + | 0.993990i | \(0.534914\pi\) | |||||||
\(182\) | 4.42808 | 0.328231 | ||||||||
\(183\) | −6.70003 | − | 4.86786i | −0.495280 | − | 0.359842i | ||||
\(184\) | 2.99227 | − | 9.20926i | 0.220593 | − | 0.678916i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.29159 | + | 3.97511i | 0.0947040 | + | 0.291469i | ||||
\(187\) | −0.281398 | + | 0.866054i | −0.0205779 | + | 0.0633322i | ||||
\(188\) | 0.237174 | − | 0.729945i | 0.0172977 | − | 0.0532367i | ||||
\(189\) | −5.53817 | − | 17.0447i | −0.402843 | − | 1.23982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.859323 | + | 2.64472i | −0.0621784 | + | 0.191365i | −0.977320 | − | 0.211766i | \(-0.932078\pi\) |
0.915142 | + | 0.403132i | \(0.132078\pi\) | |||||||
\(192\) | 1.41542 | + | 1.02836i | 0.102149 | + | 0.0742157i | ||||
\(193\) | 22.5667 | 1.62438 | 0.812192 | − | 0.583391i | \(-0.198274\pi\) | ||||
0.812192 | + | 0.583391i | \(0.198274\pi\) | |||||||
\(194\) | 11.3307 | + | 8.23222i | 0.813495 | + | 0.591039i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.49739 | + | 6.90026i | −0.678385 | + | 0.492876i | ||||
\(197\) | −1.02892 | + | 0.747558i | −0.0733079 | + | 0.0532613i | −0.623836 | − | 0.781556i | \(-0.714427\pi\) |
0.550528 | + | 0.834817i | \(0.314427\pi\) | |||||||
\(198\) | −5.08187 | − | 15.6404i | −0.361153 | − | 1.11151i | ||||
\(199\) | −8.62648 | −0.611515 | −0.305757 | − | 0.952109i | \(-0.598910\pi\) | ||||
−0.305757 | + | 0.952109i | \(0.598910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.09868 | 0.148030 | ||||||||
\(202\) | −1.85459 | − | 5.70784i | −0.130488 | − | 0.401602i | ||||
\(203\) | 15.3423 | − | 11.1468i | 1.07682 | − | 0.782354i | ||||
\(204\) | −0.111469 | + | 0.0809868i | −0.00780438 | + | 0.00567021i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.543841 | + | 0.395124i | 0.0378912 | + | 0.0275296i | ||||
\(207\) | 12.3091 | 0.855538 | ||||||||
\(208\) | −2.30480 | − | 1.67453i | −0.159809 | − | 0.116108i | ||||
\(209\) | −6.71415 | + | 20.6640i | −0.464428 | + | 1.42936i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.49912 | − | 20.0022i | −0.447418 | − | 1.37701i | −0.879810 | − | 0.475325i | \(-0.842330\pi\) |
0.432392 | − | 0.901686i | \(-0.357670\pi\) | |||||||
\(212\) | 0.317250 | − | 0.976395i | 0.0217888 | − | 0.0670591i | ||||
\(213\) | −0.703633 | + | 2.16556i | −0.0482121 | + | 0.148382i | ||||
\(214\) | −0.855067 | − | 2.63162i | −0.0584511 | − | 0.179894i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.36803 | + | 7.28803i | −0.161124 | + | 0.495888i | ||||
\(217\) | −12.9826 | − | 9.43239i | −0.881315 | − | 0.640313i | ||||
\(218\) | 0.126113 | 0.00854148 | ||||||||
\(219\) | −5.91470 | − | 4.29728i | −0.399678 | − | 0.290383i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.107819 | + | 0.0783354i | −0.00725272 | + | 0.00526941i | ||||
\(222\) | −5.24000 | + | 3.80708i | −0.351686 | + | 0.255515i | ||||
\(223\) | −1.95774 | − | 6.02530i | −0.131100 | − | 0.403484i | 0.863863 | − | 0.503726i | \(-0.168038\pi\) |
−0.994963 | + | 0.100243i | \(0.968038\pi\) | |||||||
\(224\) | 20.4049 | 1.36336 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.7914 | 1.58258 | ||||||||
\(227\) | −3.48028 | − | 10.7112i | −0.230994 | − | 0.710926i | −0.997628 | − | 0.0688416i | \(-0.978070\pi\) |
0.766634 | − | 0.642085i | \(-0.221930\pi\) | |||||||
\(228\) | −2.65964 | + | 1.93234i | −0.176139 | + | 0.127973i | ||||
\(229\) | −12.1683 | + | 8.84079i | −0.804104 | + | 0.584216i | −0.912115 | − | 0.409934i | \(-0.865552\pi\) |
0.108011 | + | 0.994150i | \(0.465552\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.3288 | − | 7.50431i | −0.679585 | − | 0.493747i | ||||
\(232\) | −8.10872 | −0.532363 | ||||||||
\(233\) | 6.33257 | + | 4.60088i | 0.414861 | + | 0.301414i | 0.775567 | − | 0.631266i | \(-0.217464\pi\) |
−0.360706 | + | 0.932680i | \(0.617464\pi\) | |||||||
\(234\) | 0.743745 | − | 2.28901i | 0.0486201 | − | 0.149637i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.16157 | + | 3.57495i | 0.0756119 | + | 0.232709i | ||||
\(237\) | 2.11058 | − | 6.49570i | 0.137097 | − | 0.421941i | ||||
\(238\) | 0.555546 | − | 1.70979i | 0.0360107 | − | 0.110830i | ||||
\(239\) | 2.70046 | + | 8.31115i | 0.174678 | + | 0.537603i | 0.999619 | − | 0.0276159i | \(-0.00879153\pi\) |
−0.824941 | + | 0.565219i | \(0.808792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.185686 | + | 0.571482i | −0.0119611 | + | 0.0368124i | −0.956859 | − | 0.290553i | \(-0.906161\pi\) |
0.944898 | + | 0.327365i | \(0.106161\pi\) | |||||||
\(242\) | −5.89102 | − | 4.28008i | −0.378689 | − | 0.275134i | ||||
\(243\) | −15.0589 | −0.966031 | ||||||||
\(244\) | 7.86518 | + | 5.71439i | 0.503517 | + | 0.365826i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.0831 | − | 7.32580i | 0.642875 | − | 0.467076i | ||||
\(247\) | −2.57257 | + | 1.86908i | −0.163689 | + | 0.118927i | ||||
\(248\) | 2.12034 | + | 6.52573i | 0.134642 | + | 0.414384i | ||||
\(249\) | 7.44678 | 0.471921 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1908 | −0.895712 | −0.447856 | − | 0.894106i | \(-0.647812\pi\) | ||||
−0.447856 | + | 0.894106i | \(0.647812\pi\) | |||||||
\(252\) | 2.95217 | + | 9.08584i | 0.185969 | + | 0.572354i | ||||
\(253\) | 15.6224 | − | 11.3503i | 0.982171 | − | 0.713589i | ||||
\(254\) | −16.0875 | + | 11.6882i | −1.00942 | + | 0.733384i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.7674 | − | 10.0026i | −0.860463 | − | 0.625163i | ||||
\(257\) | −17.6859 | −1.10322 | −0.551609 | − | 0.834103i | \(-0.685986\pi\) | ||||
−0.551609 | + | 0.834103i | \(0.685986\pi\) | |||||||
\(258\) | 1.34309 | + | 0.975813i | 0.0836173 | + | 0.0607515i | ||||
\(259\) | 7.68452 | − | 23.6505i | 0.477493 | − | 1.46957i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.18523 | − | 9.80313i | −0.197161 | − | 0.606799i | ||||
\(262\) | −8.70676 | + | 26.7967i | −0.537906 | + | 1.65550i | ||||
\(263\) | −7.51987 | + | 23.1438i | −0.463695 | + | 1.42711i | 0.396922 | + | 0.917852i | \(0.370078\pi\) |
−0.860617 | + | 0.509254i | \(0.829922\pi\) | |||||||
\(264\) | 1.68692 | + | 5.19180i | 0.103823 | + | 0.319533i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.2553 | − | 40.7957i | 0.812736 | − | 2.50134i | ||||
\(267\) | 4.17117 | + | 3.03053i | 0.255271 | + | 0.185466i | ||||
\(268\) | −2.46365 | −0.150491 | ||||||||
\(269\) | −24.2558 | − | 17.6229i | −1.47890 | − | 1.07449i | −0.977908 | − | 0.209037i | \(-0.932967\pi\) |
−0.500996 | − | 0.865449i | \(-0.667033\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.4083 | − | 16.2806i | 1.36121 | − | 0.988974i | 0.362838 | − | 0.931852i | \(-0.381808\pi\) |
0.998367 | − | 0.0571213i | \(-0.0181922\pi\) | |||||||
\(272\) | −0.935738 | + | 0.679854i | −0.0567375 | + | 0.0412222i | ||||
\(273\) | −0.577397 | − | 1.77705i | −0.0349457 | − | 0.107552i | ||||
\(274\) | 17.5447 | 1.05992 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.92177 | 0.175870 | ||||||||
\(277\) | 0.708908 | + | 2.18179i | 0.0425941 | + | 0.131091i | 0.970092 | − | 0.242737i | \(-0.0780451\pi\) |
−0.927498 | + | 0.373828i | \(0.878045\pi\) | |||||||
\(278\) | −9.07021 | + | 6.58990i | −0.543995 | + | 0.395236i | ||||
\(279\) | −7.05646 | + | 5.12682i | −0.422459 | + | 0.306934i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.30922 | + | 0.951204i | 0.0781015 | + | 0.0567441i | 0.626151 | − | 0.779702i | \(-0.284629\pi\) |
−0.548049 | + | 0.836446i | \(0.684629\pi\) | |||||||
\(282\) | −1.10063 | −0.0655416 | ||||||||
\(283\) | 10.5109 | + | 7.63662i | 0.624808 | + | 0.453950i | 0.854598 | − | 0.519291i | \(-0.173804\pi\) |
−0.229789 | + | 0.973240i | \(0.573804\pi\) | |||||||
\(284\) | 0.825997 | − | 2.54216i | 0.0490139 | − | 0.150849i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.16678 | − | 3.59098i | −0.0689932 | − | 0.212339i | ||||
\(287\) | −14.7870 | + | 45.5096i | −0.872848 | + | 2.68635i | ||||
\(288\) | 3.42723 | − | 10.5479i | 0.201951 | − | 0.621542i | ||||
\(289\) | −5.23657 | − | 16.1165i | −0.308033 | − | 0.948029i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.82624 | − | 5.62058i | 0.107056 | − | 0.329484i | ||||
\(292\) | 6.94328 | + | 5.04459i | 0.406325 | + | 0.295212i | ||||
\(293\) | −11.7009 | −0.683572 | −0.341786 | − | 0.939778i | \(-0.611032\pi\) | ||||
−0.341786 | + | 0.939778i | \(0.611032\pi\) | |||||||
\(294\) | 13.6195 | + | 9.89517i | 0.794308 | + | 0.577098i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.60224 | + | 6.24990i | −0.499995 | + | 0.363268i | ||||
\(297\) | −12.3633 | + | 8.98244i | −0.717389 | + | 0.521214i | ||||
\(298\) | −6.25887 | − | 19.2628i | −0.362566 | − | 1.11586i | ||||
\(299\) | 2.82612 | 0.163439 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.37395 | −0.367388 | ||||||||
\(302\) | −0.802247 | − | 2.46906i | −0.0461641 | − | 0.142079i | ||||
\(303\) | −2.04880 | + | 1.48854i | −0.117701 | + | 0.0855144i | ||||
\(304\) | −22.3267 | + | 16.2213i | −1.28052 | + | 0.930355i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.790535 | − | 0.574358i | −0.0451919 | − | 0.0328338i | ||||
\(307\) | 26.5673 | 1.51628 | 0.758138 | − | 0.652094i | \(-0.226109\pi\) | ||||
0.758138 | + | 0.652094i | \(0.226109\pi\) | |||||||
\(308\) | 12.1250 | + | 8.80933i | 0.690886 | + | 0.501958i | ||||
\(309\) | 0.0876543 | − | 0.269772i | 0.00498648 | − | 0.0153468i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.16895 | − | 12.8307i | −0.236399 | − | 0.727563i | −0.996933 | − | 0.0782636i | \(-0.975062\pi\) |
0.760533 | − | 0.649299i | \(-0.224938\pi\) | |||||||
\(312\) | −0.246885 | + | 0.759833i | −0.0139771 | + | 0.0430171i | ||||
\(313\) | 5.25155 | − | 16.1626i | 0.296835 | − | 0.913564i | −0.685764 | − | 0.727824i | \(-0.740532\pi\) |
0.982599 | − | 0.185740i | \(-0.0594683\pi\) | |||||||
\(314\) | −5.11089 | − | 15.7297i | −0.288424 | − | 0.887679i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.47762 | + | 7.62532i | −0.139377 | + | 0.428958i | ||||
\(317\) | −13.5882 | − | 9.87237i | −0.763187 | − | 0.554488i | 0.136699 | − | 0.990613i | \(-0.456351\pi\) |
−0.899886 | + | 0.436125i | \(0.856351\pi\) | |||||||
\(318\) | −1.47224 | −0.0825588 | ||||||||
\(319\) | −13.0822 | − | 9.50479i | −0.732464 | − | 0.532166i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.944608 | + | 0.686298i | −0.0527229 | + | 0.0383054i | ||||
\(322\) | −30.8423 | + | 22.4082i | −1.71877 | + | 1.24876i | ||||
\(323\) | 0.398945 | + | 1.22783i | 0.0221979 | + | 0.0683182i | ||||
\(324\) | 3.93033 | 0.218351 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.39524 | −0.520354 | ||||||||
\(327\) | −0.0164445 | − | 0.0506109i | −0.000909382 | − | 0.00279879i | ||||
\(328\) | 16.5529 | − | 12.0264i | 0.913982 | − | 0.664047i | ||||
\(329\) | 3.41869 | − | 2.48383i | 0.188479 | − | 0.136938i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3832 | − | 7.54386i | −0.570714 | − | 0.414648i | 0.264650 | − | 0.964344i | \(-0.414743\pi\) |
−0.835365 | + | 0.549696i | \(0.814743\pi\) | |||||||
\(332\) | −8.74180 | −0.479768 | ||||||||
\(333\) | −10.9350 | − | 7.94473i | −0.599233 | − | 0.435368i | ||||
\(334\) | −11.3720 | + | 34.9994i | −0.622249 | + | 1.91508i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.01109 | − | 15.4225i | −0.273377 | − | 0.841369i | ||||
\(337\) | 6.56274 | − | 20.1980i | 0.357495 | − | 1.10026i | −0.597053 | − | 0.802202i | \(-0.703662\pi\) |
0.954548 | − | 0.298056i | \(-0.0963382\pi\) | |||||||
\(338\) | −6.59187 | + | 20.2877i | −0.358550 | + | 1.10350i | ||||
\(339\) | −3.10226 | − | 9.54778i | −0.168492 | − | 0.518564i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.22841 | + | 13.0137i | −0.228981 | + | 0.704731i | ||||
\(342\) | −18.8622 | − | 13.7042i | −1.01995 | − | 0.741036i | ||||
\(343\) | −32.4969 | −1.75467 | ||||||||
\(344\) | 2.20489 | + | 1.60194i | 0.118879 | + | 0.0863710i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.9211 | + | 23.1921i | −1.71609 | + | 1.24681i | ||||
\(347\) | −23.1606 | + | 16.8272i | −1.24333 | + | 0.903331i | −0.997815 | − | 0.0660623i | \(-0.978956\pi\) |
−0.245513 | + | 0.969393i | \(0.578956\pi\) | |||||||
\(348\) | −0.756071 | − | 2.32695i | −0.0405297 | − | 0.124738i | ||||
\(349\) | 19.9124 | 1.06588 | 0.532942 | − | 0.846152i | \(-0.321086\pi\) | ||||
0.532942 | + | 0.846152i | \(0.321086\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.23654 | −0.119377 | ||||||||
\(352\) | −5.37660 | − | 16.5475i | −0.286574 | − | 0.881984i | ||||
\(353\) | −19.9759 | + | 14.5133i | −1.06321 | + | 0.772467i | −0.974679 | − | 0.223607i | \(-0.928217\pi\) |
−0.0885298 | + | 0.996074i | \(0.528217\pi\) | |||||||
\(354\) | 4.36093 | − | 3.16840i | 0.231781 | − | 0.168399i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.89655 | − | 3.55755i | −0.259516 | − | 0.188550i | ||||
\(357\) | −0.758602 | −0.0401495 | ||||||||
\(358\) | 8.60552 | + | 6.25228i | 0.454816 | + | 0.330443i | ||||
\(359\) | 6.64419 | − | 20.4487i | 0.350667 | − | 1.07924i | −0.607812 | − | 0.794081i | \(-0.707953\pi\) |
0.958479 | − | 0.285162i | \(-0.0920473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.64751 | + | 11.2259i | 0.191974 | + | 0.590835i | ||||
\(362\) | −6.93832 | + | 21.3539i | −0.364670 | + | 1.12234i | ||||
\(363\) | −0.949494 | + | 2.92224i | −0.0498355 | + | 0.153378i | ||||
\(364\) | 0.677808 | + | 2.08608i | 0.0355268 | + | 0.109340i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.30816 | − | 13.2591i | 0.225191 | − | 0.693066i | ||||
\(367\) | 0.925379 | + | 0.672327i | 0.0483044 | + | 0.0350952i | 0.611675 | − | 0.791109i | \(-0.290496\pi\) |
−0.563371 | + | 0.826204i | \(0.690496\pi\) | |||||||
\(368\) | 24.5272 | 1.27857 | ||||||||
\(369\) | 21.0417 | + | 15.2877i | 1.09539 | + | 0.795845i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.57294 | − | 3.32244i | 0.237415 | − | 0.172492i | ||||
\(372\) | −1.67498 | + | 1.21694i | −0.0868435 | + | 0.0630955i | ||||
\(373\) | 3.56590 | + | 10.9747i | 0.184636 | + | 0.568250i | 0.999942 | − | 0.0107800i | \(-0.00343146\pi\) |
−0.815306 | + | 0.579030i | \(0.803431\pi\) | |||||||
\(374\) | −1.53295 | −0.0792671 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.80685 | −0.0931812 | ||||||||
\(377\) | −0.731318 | − | 2.25077i | −0.0376648 | − | 0.115920i | ||||
\(378\) | 24.4080 | − | 17.7334i | 1.25541 | − | 0.912110i | ||||
\(379\) | −17.0745 | + | 12.4054i | −0.877059 | + | 0.637221i | −0.932472 | − | 0.361243i | \(-0.882352\pi\) |
0.0554129 | + | 0.998464i | \(0.482352\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.78835 | + | 4.93202i | 0.347778 | + | 0.252675i | ||||
\(382\) | −4.68127 | −0.239515 | ||||||||
\(383\) | 0.694241 | + | 0.504395i | 0.0354740 | + | 0.0257734i | 0.605381 | − | 0.795936i | \(-0.293021\pi\) |
−0.569907 | + | 0.821709i | \(0.693021\pi\) | |||||||
\(384\) | −2.86130 | + | 8.80617i | −0.146015 | + | 0.449388i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.7392 | + | 36.1296i | 0.597511 | + | 1.83895i | ||||
\(387\) | −1.07057 | + | 3.29489i | −0.0544204 | + | 0.167489i | ||||
\(388\) | −2.14382 | + | 6.59801i | −0.108836 | + | 0.334963i | ||||
\(389\) | −10.4864 | − | 32.2738i | −0.531681 | − | 1.63634i | −0.750714 | − | 0.660627i | \(-0.770290\pi\) |
0.219034 | − | 0.975717i | \(-0.429710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.354564 | − | 1.09124i | 0.0179311 | − | 0.0551862i | ||||
\(392\) | 22.3585 | + | 16.2444i | 1.12927 | + | 0.820466i | ||||
\(393\) | 11.8891 | 0.599728 | ||||||||
\(394\) | −1.73210 | − | 1.25845i | −0.0872621 | − | 0.0633996i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.59034 | − | 4.78816i | 0.331177 | − | 0.240614i | ||||
\(397\) | 21.7048 | − | 15.7695i | 1.08933 | − | 0.791446i | 0.110046 | − | 0.993926i | \(-0.464900\pi\) |
0.979286 | + | 0.202480i | \(0.0649001\pi\) | |||||||
\(398\) | −4.48751 | − | 13.8112i | −0.224939 | − | 0.692290i | ||||
\(399\) | −18.1002 | −0.906145 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.79757 | 0.189642 | 0.0948208 | − | 0.995494i | \(-0.469772\pi\) | ||||
0.0948208 | + | 0.995494i | \(0.469772\pi\) | |||||||
\(402\) | 1.09174 | + | 3.36003i | 0.0544510 | + | 0.167583i | ||||
\(403\) | −1.62014 | + | 1.17710i | −0.0807049 | + | 0.0586355i | ||||
\(404\) | 2.40509 | − | 1.74740i | 0.119658 | − | 0.0869365i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.8274 | + | 18.7647i | 1.28179 | + | 0.931276i | ||||
\(407\) | −21.2044 | −1.05106 | ||||||||
\(408\) | 0.262417 | + | 0.190657i | 0.0129916 | + | 0.00943892i | ||||
\(409\) | −4.38043 | + | 13.4816i | −0.216598 | + | 0.666621i | 0.782438 | + | 0.622728i | \(0.213976\pi\) |
−0.999036 | + | 0.0438924i | \(0.986024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.28773 | − | 7.04092i | −0.112846 | − | 0.347303i | ||||
\(412\) | −0.102898 | + | 0.316686i | −0.00506940 | + | 0.0156020i | ||||
\(413\) | −6.39535 | + | 19.6829i | −0.314695 | + | 0.968531i | ||||
\(414\) | 6.40320 | + | 19.7070i | 0.314700 | + | 0.968547i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.786879 | − | 2.42177i | 0.0385799 | − | 0.118737i | ||||
\(417\) | 3.82731 | + | 2.78071i | 0.187424 | + | 0.136172i | ||||
\(418\) | −36.5762 | −1.78900 | ||||||||
\(419\) | 15.8542 | + | 11.5187i | 0.774528 | + | 0.562727i | 0.903332 | − | 0.428943i | \(-0.141114\pi\) |
−0.128804 | + | 0.991670i | \(0.541114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8597 | − | 15.1555i | 1.01664 | − | 0.738632i | 0.0510485 | − | 0.998696i | \(-0.483744\pi\) |
0.965591 | + | 0.260064i | \(0.0837437\pi\) | |||||||
\(422\) | 28.6431 | − | 20.8104i | 1.39432 | − | 1.01304i | ||||
\(423\) | −0.709759 | − | 2.18441i | −0.0345096 | − | 0.106210i | ||||
\(424\) | −2.41689 | −0.117375 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.83313 | −0.185716 | ||||||||
\(427\) | 16.5406 | + | 50.9068i | 0.800457 | + | 2.46355i | ||||
\(428\) | 1.10888 | − | 0.805647i | 0.0535996 | − | 0.0389424i | ||||
\(429\) | −1.28896 | + | 0.936488i | −0.0622318 | + | 0.0452141i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.62525 | − | 5.54007i | −0.367296 | − | 0.266856i | 0.388793 | − | 0.921325i | \(-0.372892\pi\) |
−0.756089 | + | 0.654469i | \(0.772892\pi\) | |||||||
\(432\) | −19.4103 | −0.933881 | ||||||||
\(433\) | 1.41708 | + | 1.02957i | 0.0681006 | + | 0.0494780i | 0.621315 | − | 0.783561i | \(-0.286599\pi\) |
−0.553214 | + | 0.833039i | \(0.686599\pi\) | |||||||
\(434\) | 8.34787 | − | 25.6921i | 0.400710 | − | 1.23326i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.0193042 | + | 0.0594123i | 0.000924504 | + | 0.00284533i | ||||
\(437\) | 8.45989 | − | 26.0369i | 0.404691 | − | 1.24551i | ||||
\(438\) | 3.80318 | − | 11.7050i | 0.181723 | − | 0.559286i | ||||
\(439\) | 8.67814 | + | 26.7086i | 0.414185 | + | 1.27473i | 0.912978 | + | 0.408009i | \(0.133777\pi\) |
−0.498793 | + | 0.866721i | \(0.666223\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.8561 | + | 33.4116i | −0.516957 | + | 1.59103i | ||||
\(442\) | −0.181504 | − | 0.131871i | −0.00863328 | − | 0.00627244i | ||||
\(443\) | 29.9110 | 1.42111 | 0.710557 | − | 0.703640i | \(-0.248443\pi\) | ||||
0.710557 | + | 0.703640i | \(0.248443\pi\) | |||||||
\(444\) | −2.59561 | − | 1.88582i | −0.123182 | − | 0.0894972i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.62819 | − | 6.26875i | 0.408557 | − | 0.296834i | ||||
\(447\) | −6.91429 | + | 5.02352i | −0.327035 | + | 0.237605i | ||||
\(448\) | −3.49431 | − | 10.7544i | −0.165090 | − | 0.508096i | ||||
\(449\) | 6.29974 | 0.297303 | 0.148652 | − | 0.988890i | \(-0.452507\pi\) | ||||
0.148652 | + | 0.988890i | \(0.452507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.8026 | 1.92132 | ||||||||
\(452\) | 3.64175 | + | 11.2082i | 0.171294 | + | 0.527188i | ||||
\(453\) | −0.886258 | + | 0.643904i | −0.0416400 | + | 0.0302532i | ||||
\(454\) | 15.3384 | − | 11.1440i | 0.719865 | − | 0.523012i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.26126 | + | 4.54907i | 0.293210 | + | 0.213030i | ||||
\(457\) | −19.1809 | −0.897243 | −0.448622 | − | 0.893722i | \(-0.648085\pi\) | ||||
−0.448622 | + | 0.893722i | \(0.648085\pi\) | |||||||
\(458\) | −20.4842 | − | 14.8827i | −0.957166 | − | 0.695422i | ||||
\(459\) | −0.280595 | + | 0.863583i | −0.0130971 | + | 0.0403086i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.18509 | + | 6.72502i | 0.101770 | + | 0.313215i | 0.988959 | − | 0.148191i | \(-0.0473450\pi\) |
−0.887189 | + | 0.461406i | \(0.847345\pi\) | |||||||
\(462\) | 6.64147 | − | 20.4403i | 0.308989 | − | 0.950971i | ||||
\(463\) | 2.97225 | − | 9.14766i | 0.138132 | − | 0.425128i | −0.857932 | − | 0.513764i | \(-0.828251\pi\) |
0.996064 | + | 0.0886360i | \(0.0282508\pi\) | |||||||
\(464\) | −6.34693 | − | 19.5339i | −0.294649 | − | 0.906836i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.07188 | + | 12.5320i | −0.188626 | + | 0.580531i | ||||
\(467\) | −15.5509 | − | 11.2984i | −0.719611 | − | 0.522828i | 0.166649 | − | 0.986016i | \(-0.446705\pi\) |
−0.886260 | + | 0.463188i | \(0.846705\pi\) | |||||||
\(468\) | 1.19220 | 0.0551096 | ||||||||
\(469\) | −10.9737 | − | 7.97289i | −0.506720 | − | 0.368154i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.64610 | + | 4.10213i | −0.260159 | + | 0.189016i | ||||
\(472\) | 7.15912 | − | 5.20140i | 0.329525 | − | 0.239414i | ||||
\(473\) | 1.67951 | + | 5.16900i | 0.0772239 | + | 0.237671i | ||||
\(474\) | 11.4977 | 0.528105 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.890525 | 0.0408172 | ||||||||
\(477\) | −0.949393 | − | 2.92193i | −0.0434697 | − | 0.133786i | ||||
\(478\) | −11.9015 | + | 8.64696i | −0.544363 | + | 0.395503i | ||||
\(479\) | 30.7423 | − | 22.3356i | 1.40465 | − | 1.02054i | 0.410579 | − | 0.911825i | \(-0.365327\pi\) |
0.994073 | − | 0.108714i | \(-0.0346734\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.51063 | − | 1.82408i | −0.114475 | − | 0.0831710i | ||||
\(482\) | −1.01155 | −0.0460747 | ||||||||
\(483\) | 13.0144 | + | 9.45549i | 0.592174 | + | 0.430240i | ||||
\(484\) | 1.11461 | − | 3.43043i | 0.0506642 | − | 0.155928i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.83369 | − | 24.1096i | −0.355344 | − | 1.09364i | ||||
\(487\) | 5.17572 | − | 15.9292i | 0.234534 | − | 0.721823i | −0.762648 | − | 0.646813i | \(-0.776101\pi\) |
0.997183 | − | 0.0750094i | \(-0.0238987\pi\) | |||||||
\(488\) | 7.07248 | − | 21.7669i | 0.320156 | − | 0.985339i | ||||
\(489\) | 1.22509 | + | 3.77043i | 0.0554003 | + | 0.170505i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.76587 | + | 8.51248i | −0.124822 | + | 0.384163i | −0.993869 | − | 0.110567i | \(-0.964733\pi\) |
0.869047 | + | 0.494730i | \(0.164733\pi\) | |||||||
\(492\) | 4.99462 | + | 3.62880i | 0.225175 | + | 0.163599i | ||||
\(493\) | −0.960829 | −0.0432736 | ||||||||
\(494\) | −4.33069 | − | 3.14643i | −0.194847 | − | 0.141565i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.0608 | + | 10.2158i | −0.631348 | + | 0.458701i | ||||
\(497\) | 11.9062 | − | 8.65034i | 0.534065 | − | 0.388021i | ||||
\(498\) | 3.87383 | + | 11.9224i | 0.173591 | + | 0.534257i | ||||
\(499\) | −36.3310 | −1.62640 | −0.813200 | − | 0.581985i | \(-0.802276\pi\) | ||||
−0.813200 | + | 0.581985i | \(0.802276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.5286 | 0.693765 | ||||||||
\(502\) | −7.38206 | − | 22.7197i | −0.329478 | − | 1.01403i | ||||
\(503\) | 9.94645 | − | 7.22652i | 0.443490 | − | 0.322215i | −0.343530 | − | 0.939142i | \(-0.611623\pi\) |
0.787020 | + | 0.616927i | \(0.211623\pi\) | |||||||
\(504\) | 18.1951 | − | 13.2195i | 0.810475 | − | 0.588844i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.2989 | + | 19.1073i | 1.16913 | + | 0.849422i | ||||
\(507\) | 9.00125 | 0.399759 | ||||||||
\(508\) | −7.96886 | − | 5.78971i | −0.353561 | − | 0.256877i | ||||
\(509\) | −9.61945 | + | 29.6056i | −0.426375 | + | 1.31225i | 0.475297 | + | 0.879825i | \(0.342341\pi\) |
−0.901672 | + | 0.432421i | \(0.857659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6018 | + | 44.9399i | 0.645948 | + | 1.98802i | ||||
\(512\) | 0.796386 | − | 2.45102i | 0.0351956 | − | 0.108321i | ||||
\(513\) | −6.69499 | + | 20.6051i | −0.295591 | + | 0.909736i | ||||
\(514\) | −9.20026 | − | 28.3155i | −0.405806 | − | 1.24894i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.254120 | + | 0.782101i | −0.0111870 | + | 0.0344301i | ||||
\(517\) | −2.91508 | − | 2.11793i | −0.128205 | − | 0.0931466i | ||||
\(518\) | 41.8624 | 1.83933 | ||||||||
\(519\) | 13.4696 | + | 9.78624i | 0.591250 | + | 0.429568i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.1198 | + | 9.53206i | −0.574787 | + | 0.417607i | −0.836841 | − | 0.547446i | \(-0.815600\pi\) |
0.262054 | + | 0.965053i | \(0.415600\pi\) | |||||||
\(522\) | 14.0380 | − | 10.1992i | 0.614428 | − | 0.446408i | ||||
\(523\) | 9.45381 | + | 29.0958i | 0.413386 | + | 1.27227i | 0.913686 | + | 0.406420i | \(0.133223\pi\) |
−0.500300 | + | 0.865852i | \(0.666777\pi\) | |||||||
\(524\) | −13.9567 | −0.609701 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −40.9655 | −1.78618 | ||||||||
\(527\) | 0.251246 | + | 0.773255i | 0.0109444 | + | 0.0336835i | ||||
\(528\) | −11.1866 | + | 8.12755i | −0.486835 | + | 0.353706i | ||||
\(529\) | −1.07695 | + | 0.782451i | −0.0468240 | + | 0.0340196i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.10051 | + | 6.61191i | 0.394928 | + | 0.286932i | ||||
\(532\) | 21.2479 | 0.921214 | ||||||||
\(533\) | 4.83110 | + | 3.51000i | 0.209258 | + | 0.152035i | ||||
\(534\) | −2.68208 | + | 8.25461i | −0.116065 | + | 0.357212i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.79225 | + | 5.51599i | 0.0774135 | + | 0.238254i | ||||
\(537\) | 1.38701 | − | 4.26877i | 0.0598538 | − | 0.184211i | ||||
\(538\) | 15.5966 | − | 48.0015i | 0.672419 | − | 2.06949i | ||||
\(539\) | 17.0310 | + | 52.4159i | 0.733575 | + | 2.25771i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.65545 | − | 17.4057i | 0.243147 | − | 0.748329i | −0.752789 | − | 0.658262i | \(-0.771292\pi\) |
0.995936 | − | 0.0900672i | \(-0.0287082\pi\) | |||||||
\(542\) | 37.7223 | + | 27.4069i | 1.62031 | + | 1.17723i | ||||
\(543\) | 9.47432 | 0.406582 | ||||||||
\(544\) | −0.836383 | − | 0.607668i | −0.0358596 | − | 0.0260536i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.54472 | − | 1.84885i | 0.108904 | − | 0.0791233i | ||||
\(547\) | −5.30394 | + | 3.85354i | −0.226780 | + | 0.164765i | −0.695373 | − | 0.718649i | \(-0.744761\pi\) |
0.468593 | + | 0.883414i | \(0.344761\pi\) | |||||||
\(548\) | 2.68558 | + | 8.26536i | 0.114722 | + | 0.353078i | ||||
\(549\) | 29.0935 | 1.24168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.9254 | −0.976653 | ||||||||
\(552\) | −2.12553 | − | 6.54171i | −0.0904686 | − | 0.278434i | ||||
\(553\) | −35.7131 | + | 25.9471i | −1.51868 | + | 1.10338i | ||||
\(554\) | −3.12432 | + | 2.26995i | −0.132739 | + | 0.0964409i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.49289 | − | 3.26428i | −0.190541 | − | 0.138436i | ||||
\(557\) | 35.5383 | 1.50581 | 0.752904 | − | 0.658131i | \(-0.228653\pi\) | ||||
0.752904 | + | 0.658131i | \(0.228653\pi\) | |||||||
\(558\) | −11.8789 | − | 8.63054i | −0.502875 | − | 0.365360i | ||||
\(559\) | −0.245800 | + | 0.756496i | −0.0103963 | + | 0.0319964i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.199888 | + | 0.615193i | 0.00843930 | + | 0.0259735i | ||||
\(562\) | −0.841836 | + | 2.59090i | −0.0355107 | + | 0.109291i | ||||
\(563\) | −11.8193 | + | 36.3760i | −0.498123 | + | 1.53306i | 0.313911 | + | 0.949453i | \(0.398361\pi\) |
−0.812033 | + | 0.583611i | \(0.801639\pi\) | |||||||
\(564\) | −0.168474 | − | 0.518509i | −0.00709403 | − | 0.0218332i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.75857 | + | 20.8007i | −0.284084 | + | 0.874320i | ||||
\(567\) | 17.5067 | + | 12.7194i | 0.735213 | + | 0.534164i | ||||
\(568\) | −6.29266 | −0.264034 | ||||||||
\(569\) | −6.11534 | − | 4.44305i | −0.256368 | − | 0.186262i | 0.452176 | − | 0.891929i | \(-0.350648\pi\) |
−0.708544 | + | 0.705666i | \(0.750648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.6286 | + | 13.5345i | −0.779583 | + | 0.566400i | −0.904854 | − | 0.425723i | \(-0.860020\pi\) |
0.125271 | + | 0.992123i | \(0.460020\pi\) | |||||||
\(572\) | 1.51312 | − | 1.09935i | 0.0632667 | − | 0.0459659i | ||||
\(573\) | 0.610412 | + | 1.87865i | 0.0255003 | + | 0.0784819i | ||||
\(574\) | −80.5540 | −3.36226 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.14617 | −0.256090 | ||||||||
\(577\) | −6.89626 | − | 21.2245i | −0.287095 | − | 0.883587i | −0.985763 | − | 0.168141i | \(-0.946223\pi\) |
0.698668 | − | 0.715446i | \(-0.253777\pi\) | |||||||
\(578\) | 23.0787 | − | 16.7677i | 0.959949 | − | 0.697444i | ||||
\(579\) | 12.9685 | − | 9.42220i | 0.538954 | − | 0.391573i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.9383 | − | 28.2903i | −1.61543 | − | 1.17368i | ||||
\(582\) | 9.94866 | 0.412385 | ||||||||
\(583\) | −3.89930 | − | 2.83301i | −0.161493 | − | 0.117331i | ||||
\(584\) | 6.24349 | − | 19.2155i | 0.258358 | − | 0.795143i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.08682 | − | 18.7333i | −0.251444 | − | 0.773866i | ||||
\(587\) | 6.51365 | − | 20.0470i | 0.268847 | − | 0.827426i | −0.721935 | − | 0.691961i | \(-0.756747\pi\) |
0.990782 | − | 0.135465i | \(-0.0432529\pi\) | |||||||
\(588\) | −2.57689 | + | 7.93085i | −0.106269 | + | 0.327063i | ||||
\(589\) | 5.99472 | + | 18.4499i | 0.247008 | + | 0.760213i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.279174 | + | 0.859209i | −0.0114837 | + | 0.0353431i | ||||
\(592\) | −21.7892 | − | 15.8308i | −0.895530 | − | 0.650641i | ||||
\(593\) | −34.3547 | −1.41078 | −0.705390 | − | 0.708819i | \(-0.749228\pi\) | ||||
−0.705390 | + | 0.708819i | \(0.749228\pi\) | |||||||
\(594\) | −20.8124 | − | 15.1211i | −0.853945 | − | 0.620427i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.11670 | − | 5.89713i | 0.332473 | − | 0.241556i | ||||
\(597\) | −4.95744 | + | 3.60179i | −0.202895 | + | 0.147412i | ||||
\(598\) | 1.47015 | + | 4.52467i | 0.0601190 | + | 0.185027i | ||||
\(599\) | 0.498231 | 0.0203572 | 0.0101786 | − | 0.999948i | \(-0.496760\pi\) | ||||
0.0101786 | + | 0.999948i | \(0.496760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.8635 | 1.13657 | 0.568287 | − | 0.822830i | \(-0.307606\pi\) | ||||
0.568287 | + | 0.822830i | \(0.307606\pi\) | |||||||
\(602\) | −3.31574 | − | 10.2048i | −0.135140 | − | 0.415917i | ||||
\(603\) | −5.96459 | + | 4.33353i | −0.242897 | + | 0.176475i | ||||
\(604\) | 1.04038 | − | 0.755880i | 0.0423325 | − | 0.0307563i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.44897 | − | 2.50582i | −0.140105 | − | 0.101792i | ||||
\(607\) | 14.1000 | 0.572303 | 0.286152 | − | 0.958184i | \(-0.407624\pi\) | ||||
0.286152 | + | 0.958184i | \(0.407624\pi\) | |||||||
\(608\) | −19.9561 | − | 14.4989i | −0.809326 | − | 0.588010i | ||||
\(609\) | 4.16276 | − | 12.8117i | 0.168684 | − | 0.519155i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.162958 | − | 0.501534i | −0.00659258 | − | 0.0202899i | ||||
\(612\) | 0.149573 | − | 0.460340i | 0.00604615 | − | 0.0186081i | ||||
\(613\) | 9.83468 | − | 30.2680i | 0.397219 | − | 1.22251i | −0.530001 | − | 0.847997i | \(-0.677808\pi\) |
0.927220 | − | 0.374518i | \(-0.122192\pi\) | |||||||
\(614\) | 13.8204 | + | 42.5348i | 0.557745 | + | 1.71656i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9030 | − | 33.5559i | 0.439293 | − | 1.35200i | ||||
\(617\) | −27.4793 | − | 19.9649i | −1.10627 | − | 0.803755i | −0.124201 | − | 0.992257i | \(-0.539637\pi\) |
−0.982073 | + | 0.188502i | \(0.939637\pi\) | |||||||
\(618\) | 0.477508 | 0.0192082 | ||||||||
\(619\) | −0.912910 | − | 0.663268i | −0.0366929 | − | 0.0266590i | 0.569288 | − | 0.822138i | \(-0.307219\pi\) |
−0.605981 | + | 0.795479i | \(0.707219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.5778 | − | 11.3179i | 0.625116 | − | 0.454173i | ||||
\(622\) | 18.3735 | − | 13.3491i | 0.736710 | − | 0.535251i | ||||
\(623\) | −10.2975 | − | 31.6925i | −0.412562 | − | 1.26974i | ||||
\(624\) | −2.02368 | −0.0810119 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.6085 | 1.14343 | ||||||||
\(627\) | 4.76933 | + | 14.6785i | 0.190469 | + | 0.586203i | ||||
\(628\) | 6.62797 | − | 4.81550i | 0.264485 | − | 0.192159i | ||||
\(629\) | −1.01931 | + | 0.740571i | −0.0406425 | + | 0.0295285i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.5197 | − | 19.2677i | −1.05573 | − | 0.767034i | −0.0824380 | − | 0.996596i | \(-0.526271\pi\) |
−0.973294 | + | 0.229562i | \(0.926271\pi\) | |||||||
\(632\) | 18.8751 | 0.750813 | ||||||||
\(633\) | −12.0864 | − | 8.78127i | −0.480391 | − | 0.349024i | ||||
\(634\) | 8.73726 | − | 26.8905i | 0.347001 | − | 1.06796i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.225355 | − | 0.693573i | −0.00893593 | − | 0.0275020i | ||||
\(637\) | −2.49252 | + | 7.67120i | −0.0987574 | + | 0.303944i | ||||
\(638\) | 8.41194 | − | 25.8893i | 0.333032 | − | 1.02497i | ||||
\(639\) | −2.47185 | − | 7.60758i | −0.0977850 | − | 0.300951i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.39802 | − | 28.9241i | 0.371199 | − | 1.14243i | −0.574808 | − | 0.818288i | \(-0.694923\pi\) |
0.946007 | − | 0.324146i | \(-0.105077\pi\) | |||||||
\(642\) | −1.59016 | − | 1.15532i | −0.0627587 | − | 0.0455969i | ||||
\(643\) | −1.06932 | −0.0421700 | −0.0210850 | − | 0.999778i | \(-0.506712\pi\) | ||||
−0.0210850 | + | 0.999778i | \(0.506712\pi\) | |||||||
\(644\) | −15.2776 | − | 11.0998i | −0.602022 | − | 0.437394i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.75824 | + | 1.27744i | −0.0691771 | + | 0.0502601i | ||||
\(647\) | 24.7300 | − | 17.9674i | 0.972237 | − | 0.706372i | 0.0162768 | − | 0.999868i | \(-0.494819\pi\) |
0.955960 | + | 0.293496i | \(0.0948187\pi\) | |||||||
\(648\) | −2.85923 | − | 8.79981i | −0.112321 | − | 0.345689i | ||||
\(649\) | 17.6471 | 0.692709 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3991 | −0.446765 | ||||||||
\(652\) | −1.43813 | − | 4.42611i | −0.0563216 | − | 0.173340i | ||||
\(653\) | −26.9808 | + | 19.6027i | −1.05584 | + | 0.767114i | −0.973315 | − | 0.229475i | \(-0.926299\pi\) |
−0.0825273 | + | 0.996589i | \(0.526299\pi\) | |||||||
\(654\) | 0.0724745 | − | 0.0526558i | 0.00283398 | − | 0.00205901i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.9280 | + | 30.4624i | 1.63701 | + | 1.18936i | ||||
\(657\) | 25.6833 | 1.00200 | ||||||||
\(658\) | 5.75506 | + | 4.18130i | 0.224356 | + | 0.163004i | ||||
\(659\) | −3.12572 | + | 9.61998i | −0.121761 | + | 0.374741i | −0.993297 | − | 0.115590i | \(-0.963124\pi\) |
0.871536 | + | 0.490331i | \(0.163124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.52955 | − | 29.3290i | −0.370657 | − | 1.14076i | −0.946362 | − | 0.323107i | \(-0.895273\pi\) |
0.575706 | − | 0.817657i | \(-0.304727\pi\) | |||||||
\(662\) | 6.67648 | − | 20.5481i | 0.259489 | − | 0.798624i | ||||
\(663\) | −0.0292542 | + | 0.0900351i | −0.00113614 | + | 0.00349667i | ||||
\(664\) | 6.35948 | + | 19.5725i | 0.246796 | + | 0.759558i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.03125 | − | 21.6400i | 0.272455 | − | 0.838532i | ||||
\(667\) | 16.4837 | + | 11.9761i | 0.638251 | + | 0.463717i | ||||
\(668\) | −18.2290 | −0.705302 | ||||||||
\(669\) | −3.64079 | − | 2.64519i | −0.140761 | − | 0.102269i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.9248 | − | 26.8275i | 1.42547 | − | 1.03566i | ||||
\(672\) | 11.7262 | − | 8.51961i | 0.452349 | − | 0.328651i | ||||
\(673\) | 9.52544 | + | 29.3163i | 0.367179 | + | 1.13006i | 0.948606 | + | 0.316461i | \(0.102495\pi\) |
−0.581427 | + | 0.813599i | \(0.697505\pi\) | |||||||
\(674\) | 35.7514 | 1.37709 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.5666 | −0.406407 | ||||||||
\(677\) | −12.7476 | − | 39.2331i | −0.489930 | − | 1.50785i | −0.824712 | − | 0.565553i | \(-0.808663\pi\) |
0.334782 | − | 0.942296i | \(-0.391337\pi\) | |||||||
\(678\) | 13.6724 | − | 9.93356i | 0.525084 | − | 0.381496i | ||||
\(679\) | −30.9017 | + | 22.4514i | −1.18590 | + | 0.861607i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.47225 | − | 4.70237i | −0.248017 | − | 0.180195i | ||||
\(682\) | −23.0348 | −0.882048 | ||||||||
\(683\) | 18.0827 | + | 13.1379i | 0.691915 | + | 0.502706i | 0.877289 | − | 0.479962i | \(-0.159350\pi\) |
−0.185374 | + | 0.982668i | \(0.559350\pi\) | |||||||
\(684\) | 3.56882 | − | 10.9837i | 0.136457 | − | 0.419972i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.9050 | − | 52.0282i | −0.645435 | − | 1.98644i | ||||
\(687\) | −3.30157 | + | 10.1612i | −0.125963 | + | 0.387674i | ||||
\(688\) | −2.13324 | + | 6.56544i | −0.0813291 | + | 0.250305i | ||||
\(689\) | −0.217978 | − | 0.670866i | −0.00830428 | − | 0.0255580i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.83956 | − | 8.73927i | 0.108022 | − | 0.332457i | −0.882406 | − | 0.470489i | \(-0.844078\pi\) |
0.990428 | + | 0.138032i | \(0.0440776\pi\) | |||||||
\(692\) | −15.8120 | − | 11.4881i | −0.601082 | − | 0.436712i | ||||
\(693\) | 44.8506 | 1.70373 | ||||||||
\(694\) | −38.9889 | − | 28.3271i | −1.48000 | − | 1.07528i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.65990 | + | 3.38561i | −0.176633 | + | 0.128331i | ||||
\(697\) | 1.96141 | − | 1.42505i | 0.0742937 | − | 0.0539775i | ||||
\(698\) | 10.3585 | + | 31.8801i | 0.392073 | + | 1.20668i | ||||
\(699\) | 5.56018 | 0.210305 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.9929 | −1.35943 | −0.679717 | − | 0.733475i | \(-0.737897\pi\) | ||||
−0.679717 | + | 0.733475i | \(0.737897\pi\) | |||||||
\(702\) | −1.16345 | − | 3.58073i | −0.0439116 | − | 0.135146i | ||||
\(703\) | −24.3207 | + | 17.6700i | −0.917271 | + | 0.666437i | ||||
\(704\) | −7.80059 | + | 5.66746i | −0.293996 | + | 0.213600i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.6276 | − | 24.4319i | −1.26559 | − | 0.919506i | ||||
\(707\) | 16.3679 | 0.615578 | ||||||||
\(708\) | 2.16017 | + | 1.56945i | 0.0811841 | + | 0.0589837i | ||||
\(709\) | 6.25640 | − | 19.2552i | 0.234964 | − | 0.723145i | −0.762162 | − | 0.647386i | \(-0.775862\pi\) |
0.997126 | − | 0.0757586i | \(-0.0241378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.41445 | + | 22.8193i | 0.278063 | + | 0.855791i | ||||
\(712\) | −4.40304 | + | 13.5512i | −0.165011 | + | 0.507852i | ||||
\(713\) | 5.32783 | − | 16.3974i | 0.199529 | − | 0.614086i | ||||
\(714\) | −0.394627 | − | 1.21454i | −0.0147685 | − | 0.0454529i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.62821 | + | 5.01112i | −0.0608491 | + | 0.187274i | ||||
\(717\) | 5.02202 | + | 3.64871i | 0.187551 | + | 0.136264i | ||||
\(718\) | 36.1951 | 1.35079 | ||||||||
\(719\) | 29.9551 | + | 21.7637i | 1.11714 | + | 0.811647i | 0.983773 | − | 0.179420i | \(-0.0574220\pi\) |
0.133364 | + | 0.991067i | \(0.457422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.48320 | + | 1.07761i | −0.0552372 | + | 0.0401322i | ||||
\(722\) | −16.0754 | + | 11.6794i | −0.598264 | + | 0.434664i | ||||
\(723\) | 0.131900 | + | 0.405947i | 0.00490542 | + | 0.0150973i | ||||
\(724\) | −11.1219 | −0.413343 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.17249 | −0.191969 | ||||||||
\(727\) | 3.73261 | + | 11.4878i | 0.138435 | + | 0.426059i | 0.996108 | − | 0.0881356i | \(-0.0280909\pi\) |
−0.857673 | + | 0.514195i | \(0.828091\pi\) | |||||||
\(728\) | 4.17754 | − | 3.03516i | 0.154830 | − | 0.112490i | ||||
\(729\) | 2.78552 | − | 2.02380i | 0.103167 | − | 0.0749555i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.261264 | + | 0.189820i | 0.00966320 | + | 0.00702073i | ||||
\(732\) | 6.90586 | 0.255248 | ||||||||
\(733\) | 36.0916 | + | 26.2221i | 1.33307 | + | 0.968534i | 0.999668 | + | 0.0257496i | \(0.00819725\pi\) |
0.333404 | + | 0.942784i | \(0.391803\pi\) | |||||||
\(734\) | −0.595024 | + | 1.83130i | −0.0219627 | + | 0.0675943i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.77456 | + | 20.8500i | 0.249714 | + | 0.768540i | ||||
\(737\) | −3.57413 | + | 11.0001i | −0.131655 | + | 0.405192i | ||||
\(738\) | −13.5299 | + | 41.6408i | −0.498043 | + | 1.53282i | ||||
\(739\) | −4.52596 | − | 13.9295i | −0.166490 | − | 0.512404i | 0.832653 | − | 0.553795i | \(-0.186821\pi\) |
−0.999143 | + | 0.0413910i | \(0.986821\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.698004 | + | 2.14824i | −0.0256418 | + | 0.0789174i | ||||
\(742\) | 7.69813 | + | 5.59302i | 0.282607 | + | 0.205326i | ||||
\(743\) | −24.4397 | −0.896604 | −0.448302 | − | 0.893882i | \(-0.647971\pi\) | ||||
−0.448302 | + | 0.893882i | \(0.647971\pi\) | |||||||
\(744\) | 3.94318 | + | 2.86489i | 0.144564 | + | 0.105032i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.7157 | + | 11.4182i | −0.575394 | + | 0.418048i | ||||
\(747\) | −21.1642 | + | 15.3767i | −0.774359 | + | 0.562605i | ||||
\(748\) | −0.234650 | − | 0.722177i | −0.00857964 | − | 0.0264054i | ||||
\(749\) | 7.54648 | 0.275743 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.2863 | 1.14165 | 0.570826 | − | 0.821071i | \(-0.306623\pi\) | ||||
0.570826 | + | 0.821071i | \(0.306623\pi\) | |||||||
\(752\) | −1.41427 | − | 4.35269i | −0.0515733 | − | 0.158726i | ||||
\(753\) | −8.15510 | + | 5.92503i | −0.297189 | + | 0.215920i | ||||
\(754\) | 3.22308 | − | 2.34171i | 0.117378 | − | 0.0852800i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.0904 | + | 8.78418i | 0.439723 | + | 0.319478i | ||||
\(757\) | 11.3251 | 0.411617 | 0.205808 | − | 0.978592i | \(-0.434018\pi\) | ||||
0.205808 | + | 0.978592i | \(0.434018\pi\) | |||||||
\(758\) | −28.7434 | − | 20.8833i | −1.04401 | − | 0.758516i | ||||
\(759\) | 4.23876 | − | 13.0456i | 0.153857 | − | 0.473524i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.7728 | − | 39.3108i | −0.463015 | − | 1.42501i | −0.861462 | − | 0.507822i | \(-0.830451\pi\) |
0.398447 | − | 0.917191i | \(-0.369549\pi\) | |||||||
\(762\) | −4.36494 | + | 13.4339i | −0.158125 | + | 0.486659i | ||||
\(763\) | −0.106285 | + | 0.327111i | −0.00384776 | + | 0.0118422i | ||||
\(764\) | −0.716564 | − | 2.20536i | −0.0259244 | − | 0.0797870i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.446401 | + | 1.37388i | −0.0161291 | + | 0.0496403i | ||||
\(767\) | 2.08945 | + | 1.51807i | 0.0754455 | + | 0.0548144i | ||||
\(768\) | −12.0882 | −0.436195 | ||||||||
\(769\) | −18.3235 | − | 13.3128i | −0.660762 | − | 0.480072i | 0.206158 | − | 0.978519i | \(-0.433904\pi\) |
−0.866920 | + | 0.498447i | \(0.833904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.1637 | + | 7.38436i | −0.366037 | + | 0.265941i | ||||
\(772\) | −15.2238 | + | 11.0607i | −0.547917 | + | 0.398085i | ||||
\(773\) | −5.20820 | − | 16.0292i | −0.187326 | − | 0.576530i | 0.812655 | − | 0.582746i | \(-0.198022\pi\) |
−0.999981 | + | 0.00621531i | \(0.998022\pi\) | |||||||
\(774\) | −5.83210 | −0.209630 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.3322 | 0.586292 | ||||||||
\(777\) | −5.45862 | − | 16.7999i | −0.195827 | − | 0.602694i | ||||
\(778\) | 46.2158 | − | 33.5778i | 1.65692 | − | 1.20382i | ||||
\(779\) | 46.7992 | − | 34.0016i | 1.67675 | − | 1.21823i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1523 | − | 7.37606i | −0.363277 | − | 0.263936i | ||||
\(782\) | 1.93153 | 0.0690715 | ||||||||
\(783\) | −13.0449 | − | 9.47766i | −0.466186 | − | 0.338704i | ||||
\(784\) | −21.6320 | + | 66.5765i | −0.772572 | + | 2.37773i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.18476 | + | 19.0347i | 0.220603 | + | 0.678947i | ||||
\(787\) | −6.21393 | + | 19.1245i | −0.221503 | + | 0.681716i | 0.777125 | + | 0.629346i | \(0.216677\pi\) |
−0.998628 | + | 0.0523693i | \(0.983323\pi\) | |||||||
\(788\) | 0.327723 | − | 1.00863i | 0.0116746 | − | 0.0359309i | ||||
\(789\) | 5.34166 | + | 16.4400i | 0.190168 | + | 0.585278i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.0507 | + | 61.7097i | −0.712920 | + | 2.19414i | ||||
\(792\) | −15.5148 | − | 11.2722i | −0.551294 | − | 0.400539i | ||||
\(793\) | 6.67976 | 0.237205 | ||||||||
\(794\) | 36.5381 | + | 26.5465i | 1.29669 | + | 0.942099i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.81955 | − | 4.22815i | 0.206269 | − | 0.149863i | ||||
\(797\) | −43.8266 | + | 31.8419i | −1.55242 | + | 1.12790i | −0.610521 | + | 0.792000i | \(0.709040\pi\) |
−0.941898 | + | 0.335898i | \(0.890960\pi\) | |||||||
\(798\) | −9.41579 | − | 28.9788i | −0.333315 | − | 1.02584i | ||||
\(799\) | −0.214100 | −0.00757430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.1124 | −0.639971 | ||||||||
\(802\) | 1.97550 | + | 6.07998i | 0.0697575 | + | 0.214691i | ||||
\(803\) | 32.5967 | − | 23.6829i | 1.15031 | − | 0.835752i | ||||
\(804\) | −1.41580 | + | 1.02864i | −0.0499315 | + | 0.0362774i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.72736 | − | 1.98154i | −0.0960671 | − | 0.0697969i | ||||
\(807\) | −21.2973 | −0.749701 | ||||||||
\(808\) | −5.66200 | − | 4.11368i | −0.199189 | − | 0.144719i | ||||
\(809\) | 4.73927 | − | 14.5860i | 0.166624 | − | 0.512815i | −0.832528 | − | 0.553982i | \(-0.813108\pi\) |
0.999152 | + | 0.0411669i | \(0.0131075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.57428 | + | 11.0005i | 0.125510 | + | 0.386279i | 0.993994 | − | 0.109438i | \(-0.0349051\pi\) |
−0.868484 | + | 0.495717i | \(0.834905\pi\) | |||||||
\(812\) | −4.88667 | + | 15.0396i | −0.171489 | + | 0.527788i | ||||
\(813\) | 6.07994 | − | 18.7121i | 0.213233 | − | 0.656263i | ||||
\(814\) | −11.0306 | − | 33.9486i | −0.386621 | − | 1.18990i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.253890 | + | 0.781393i | −0.00888793 | + | 0.0273542i | ||||
\(817\) | 6.23376 | + | 4.52909i | 0.218092 | + | 0.158453i | ||||
\(818\) | −23.8630 | −0.834349 | ||||||||
\(819\) | 5.31039 | + | 3.85822i | 0.185560 | + | 0.134817i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.9949 | + | 19.6129i | −0.942128 | + | 0.684496i | −0.948932 | − | 0.315480i | \(-0.897834\pi\) |
0.00680360 | + | 0.999977i | \(0.497834\pi\) | |||||||
\(822\) | 10.0826 | − | 7.32541i | 0.351670 | − | 0.255503i | ||||
\(823\) | −9.26497 | − | 28.5146i | −0.322956 | − | 0.993958i | −0.972355 | − | 0.233509i | \(-0.924979\pi\) |
0.649398 | − | 0.760449i | \(-0.275021\pi\) | |||||||
\(824\) | 0.783901 | 0.0273085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34.8395 | −1.21222 | ||||||||
\(827\) | 7.63982 | + | 23.5130i | 0.265663 | + | 0.817626i | 0.991540 | + | 0.129801i | \(0.0414340\pi\) |
−0.725877 | + | 0.687824i | \(0.758566\pi\) | |||||||
\(828\) | −8.30388 | + | 6.03312i | −0.288580 | + | 0.209665i | ||||
\(829\) | 0.171031 | − | 0.124261i | 0.00594015 | − | 0.00431577i | −0.584811 | − | 0.811169i | \(-0.698831\pi\) |
0.590751 | + | 0.806854i | \(0.298831\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.31835 | + | 0.957839i | 0.0457331 | + | 0.0332271i | ||||
\(832\) | −1.41114 | −0.0489225 | ||||||||
\(833\) | 2.64933 | + | 1.92485i | 0.0917939 | + | 0.0666922i | ||||
\(834\) | −2.46098 | + | 7.57413i | −0.0852169 | + | 0.262271i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.59873 | − | 17.2311i | −0.193636 | − | 0.595951i | ||||
\(837\) | −4.21634 | + | 12.9766i | −0.145738 | + | 0.448535i | ||||
\(838\) | −10.1943 | + | 31.3749i | −0.352157 | + | 1.08383i | ||||
\(839\) | −1.70489 | − | 5.24712i | −0.0588594 | − | 0.181151i | 0.917304 | − | 0.398188i | \(-0.130361\pi\) |
−0.976163 | + | 0.217037i | \(0.930361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.68903 | + | 11.3537i | −0.127208 | + | 0.391506i | ||||
\(842\) | 35.1154 | + | 25.5129i | 1.21016 | + | 0.879231i | ||||
\(843\) | 1.14953 | 0.0395920 | ||||||||
\(844\) | 14.1882 | + | 10.3084i | 0.488379 | + | 0.354828i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.12807 | − | 2.27267i | 0.107545 | − | 0.0781361i | ||||
\(847\) | 16.0664 | − | 11.6729i | 0.552047 | − | 0.401086i | ||||
\(848\) | −1.89177 | − | 5.82228i | −0.0649638 | − | 0.199938i | ||||
\(849\) | 9.22888 | 0.316734 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.7177 | 0.915871 | ||||||||
\(852\) | −0.586739 | − | 1.80580i | −0.0201013 | − | 0.0618656i | ||||
\(853\) | 1.24545 | − | 0.904870i | 0.0426433 | − | 0.0309822i | −0.566259 | − | 0.824227i | \(-0.691610\pi\) |
0.608903 | + | 0.793245i | \(0.291610\pi\) | |||||||
\(854\) | −72.8983 | + | 52.9637i | −2.49453 | + | 1.81238i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.61049 | − | 1.89663i | −0.0892247 | − | 0.0648255i | ||||
\(857\) | −45.3407 | −1.54881 | −0.774404 | − | 0.632691i | \(-0.781950\pi\) | ||||
−0.774404 | + | 0.632691i | \(0.781950\pi\) | |||||||
\(858\) | −2.16986 | − | 1.57649i | −0.0740777 | − | 0.0538206i | ||||
\(859\) | −6.73547 | + | 20.7296i | −0.229811 | + | 0.707286i | 0.767956 | + | 0.640502i | \(0.221274\pi\) |
−0.997767 | + | 0.0667839i | \(0.978726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.5038 | + | 32.3273i | 0.357968 | + | 1.10171i | ||||
\(862\) | 4.90308 | − | 15.0901i | 0.167000 | − | 0.513972i | ||||
\(863\) | −3.95176 | + | 12.1623i | −0.134519 | + | 0.414008i | −0.995515 | − | 0.0946043i | \(-0.969841\pi\) |
0.860996 | + | 0.508613i | \(0.169841\pi\) | |||||||
\(864\) | −5.36126 | − | 16.5003i | −0.182394 | − | 0.561350i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.911192 | + | 2.80436i | −0.0309636 | + | 0.0952960i | ||||
\(867\) | −9.73842 | − | 7.07538i | −0.330734 | − | 0.240292i | ||||
\(868\) | 13.3814 | 0.454194 | ||||||||
\(869\) | 30.4522 | + | 22.1248i | 1.03302 | + | 0.750534i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.36945 | + | 0.994964i | −0.0464021 | + | 0.0337131i | ||||
\(872\) | 0.118978 | − | 0.0864424i | 0.00402909 | − | 0.00292731i | ||||
\(873\) | 6.41555 | + | 19.7450i | 0.217133 | + | 0.668268i | ||||
\(874\) | 46.0863 | 1.55889 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.09640 | 0.205978 | ||||||||
\(877\) | 2.95216 | + | 9.08583i | 0.0996875 | + | 0.306807i | 0.988447 | − | 0.151567i | \(-0.0484321\pi\) |
−0.888759 | + | 0.458374i | \(0.848432\pi\) | |||||||
\(878\) | −38.2465 | + | 27.7877i | −1.29076 | + | 0.937790i | ||||
\(879\) | −6.72423 | + | 4.88544i | −0.226803 | + | 0.164782i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.6595 | + | 23.0020i | 1.06664 | + | 0.774956i | 0.975305 | − | 0.220864i | \(-0.0708877\pi\) |
0.0913314 | + | 0.995821i | \(0.470888\pi\) | |||||||
\(882\) | −59.1400 | −1.99135 | ||||||||
\(883\) | 28.3361 | + | 20.5874i | 0.953586 | + | 0.692821i | 0.951652 | − | 0.307177i | \(-0.0993844\pi\) |
0.00193394 | + | 0.999998i | \(0.499384\pi\) | |||||||
\(884\) | 0.0343416 | − | 0.105692i | 0.00115503 | − | 0.00355482i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.5598 | + | 47.8880i | 0.522741 | + | 1.60883i | ||||
\(887\) | 11.2000 | − | 34.4699i | 0.376058 | − | 1.15739i | −0.566705 | − | 0.823921i | \(-0.691782\pi\) |
0.942762 | − | 0.333465i | \(-0.108218\pi\) | |||||||
\(888\) | −2.33401 | + | 7.18335i | −0.0783243 | + | 0.241057i | ||||
\(889\) | −16.7587 | − | 51.5779i | −0.562068 | − | 1.72987i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.70191 | − | 17.5487i | 0.191021 | − | 0.587903i | ||||
\(892\) | 4.27394 | + | 3.10520i | 0.143102 | + | 0.103970i | ||||
\(893\) | −5.10841 | −0.170946 | ||||||||
\(894\) | −11.6396 | − | 8.45665i | −0.389286 | − | 0.282833i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 48.4160 | − | 35.1763i | 1.61747 | − | 1.17516i | ||||
\(897\) | 1.62411 | − | 1.17998i | 0.0542273 | − | 0.0393985i | ||||
\(898\) | 3.27714 | + | 10.0860i | 0.109360 | + | 0.336574i | ||||
\(899\) | −14.4378 | −0.481528 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.286386 | −0.00954089 | ||||||||
\(902\) | 21.2256 | + | 65.3258i | 0.706736 | + | 2.17511i | ||||
\(903\) | −3.66297 | + | 2.66130i | −0.121896 | + | 0.0885625i | ||||
\(904\) | 22.4452 | − | 16.3074i | 0.746517 | − | 0.542377i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.49194 | − | 1.08395i | −0.0495662 | − | 0.0360120i | ||||
\(907\) | −40.8532 | −1.35651 | −0.678255 | − | 0.734827i | \(-0.737263\pi\) | ||||
−0.678255 | + | 0.734827i | \(0.737263\pi\) | |||||||
\(908\) | 7.59779 | + | 5.52012i | 0.252142 | + | 0.183192i | ||||
\(909\) | 2.74917 | − | 8.46106i | 0.0911841 | − | 0.280636i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.93897 | + | 12.1229i | 0.130504 | + | 0.401650i | 0.994864 | − | 0.101224i | \(-0.0322759\pi\) |
−0.864360 | + | 0.502874i | \(0.832276\pi\) | |||||||
\(912\) | −6.05781 | + | 18.6440i | −0.200594 | + | 0.617365i | ||||
\(913\) | −12.6821 | + | 39.0316i | −0.419718 | + | 1.29176i | ||||
\(914\) | −9.97794 | − | 30.7089i | −0.330041 | − | 1.01576i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.87573 | − | 11.9283i | 0.128058 | − | 0.394121i | ||||
\(917\) | −62.1669 | − | 45.1669i | −2.05293 | − | 1.49154i | ||||
\(918\) | −1.52858 | −0.0504506 | ||||||||
\(919\) | −7.82486 | − | 5.68509i | −0.258118 | − | 0.187534i | 0.451199 | − | 0.892423i | \(-0.350997\pi\) |
−0.709317 | + | 0.704890i | \(0.750997\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.2676 | − | 11.0926i | 0.503086 | − | 0.365513i | ||||
\(922\) | −9.63019 | + | 6.99674i | −0.317153 | + | 0.230425i | ||||
\(923\) | −0.567529 | − | 1.74668i | −0.0186805 | − | 0.0574925i | ||||
\(924\) | 10.6461 | 0.350231 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.1917 | 0.532094 | ||||||||
\(927\) | 0.307928 | + | 0.947706i | 0.0101137 | + | 0.0311268i | ||||
\(928\) | 14.8522 | − | 10.7907i | 0.487547 | − | 0.354223i | ||||
\(929\) | −8.83405 | + | 6.41831i | −0.289836 | + | 0.210578i | −0.723196 | − | 0.690643i | \(-0.757328\pi\) |
0.433360 | + | 0.901221i | \(0.357328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 63.2130 | + | 45.9269i | 2.07172 | + | 1.50519i | ||||
\(932\) | −6.52711 | −0.213803 | ||||||||
\(933\) | −7.75297 | − | 5.63287i | −0.253821 | − | 0.184412i | ||||
\(934\) | 9.99933 | − | 30.7748i | 0.327188 | − | 1.00698i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.867303 | − | 2.66928i | −0.0283487 | − | 0.0872483i | ||||
\(937\) | 4.92778 | − | 15.1661i | 0.160984 | − | 0.495456i | −0.837734 | − | 0.546078i | \(-0.816120\pi\) |
0.998718 | + | 0.0506216i | \(0.0161202\pi\) | |||||||
\(938\) | 7.05618 | − | 21.7167i | 0.230392 | − | 0.709075i | ||||
\(939\) | −3.73039 | − | 11.4809i | −0.121737 | − | 0.374667i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.83155 | − | 5.63692i | 0.0597067 | − | 0.183758i | −0.916755 | − | 0.399451i | \(-0.869201\pi\) |
0.976461 | + | 0.215692i | \(0.0692009\pi\) | |||||||
\(942\) | −9.50470 | − | 6.90557i | −0.309680 | − | 0.224996i | ||||
\(943\) | −51.4117 | −1.67419 | ||||||||
\(944\) | 18.1338 | + | 13.1750i | 0.590205 | + | 0.428809i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.40197 | + | 5.37785i | −0.240659 | + | 0.174849i | ||||
\(947\) | 0.801236 | − | 0.582132i | 0.0260367 | − | 0.0189168i | −0.574691 | − | 0.818371i | \(-0.694878\pi\) |
0.600727 | + | 0.799454i | \(0.294878\pi\) | |||||||
\(948\) | 1.75995 | + | 5.41657i | 0.0571606 | + | 0.175922i | ||||
\(949\) | 5.89681 | 0.191418 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.9308 | −0.386882 | ||||||||
\(952\) | −0.647839 | − | 1.99384i | −0.0209966 | − | 0.0646208i | ||||
\(953\) | 43.3627 | − | 31.5049i | 1.40466 | − | 1.02054i | 0.410584 | − | 0.911823i | \(-0.365325\pi\) |
0.994072 | − | 0.108720i | \(-0.0346750\pi\) | |||||||
\(954\) | 4.18419 | − | 3.03999i | 0.135468 | − | 0.0984234i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.89537 | − | 4.28324i | −0.190670 | − | 0.138530i | ||||
\(957\) | −11.4866 | −0.371308 | ||||||||
\(958\) | 51.7519 | + | 37.6000i | 1.67203 | + | 1.21480i | ||||
\(959\) | −14.7862 | + | 45.5072i | −0.477471 | + | 1.46950i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.80420 | − | 17.8635i | −0.187232 | − | 0.576242i | ||||
\(962\) | 1.61435 | − | 4.96846i | 0.0520488 | − | 0.160190i | ||||
\(963\) | 1.26751 | − | 3.90101i | 0.0408451 | − | 0.125708i | ||||
\(964\) | −0.154838 | − | 0.476542i | −0.00498699 | − | 0.0153484i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.36831 | + | 25.7550i | −0.269246 | + | 0.828654i | ||||
\(967\) | 24.0561 | + | 17.4778i | 0.773592 | + | 0.562047i | 0.903049 | − | 0.429538i | \(-0.141323\pi\) |
−0.129457 | + | 0.991585i | \(0.541323\pi\) | |||||||
\(968\) | −8.49141 | −0.272924 | ||||||||
\(969\) | 0.741917 | + | 0.539034i | 0.0238338 | + | 0.0173163i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.0399 | + | 35.6296i | −1.57376 | + | 1.14341i | −0.650330 | + | 0.759652i | \(0.725369\pi\) |
−0.923435 | + | 0.383755i | \(0.874631\pi\) | |||||||
\(972\) | 10.1590 | − | 7.38094i | 0.325850 | − | 0.236744i | ||||
\(973\) | −9.44864 | − | 29.0799i | −0.302910 | − | 0.932260i | ||||
\(974\) | 28.1954 | 0.903440 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 57.9720 | 1.85564 | ||||||||
\(977\) | 13.7553 | + | 42.3343i | 0.440070 | + | 1.35440i | 0.887801 | + | 0.460227i | \(0.152232\pi\) |
−0.447731 | + | 0.894168i | \(0.647768\pi\) | |||||||
\(978\) | −5.39923 | + | 3.92277i | −0.172648 | + | 0.125436i | ||||
\(979\) | −22.9879 | + | 16.7017i | −0.734697 | + | 0.533789i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.151242 | + | 0.109884i | 0.00482878 | + | 0.00350831i | ||||
\(982\) | −15.0675 | −0.480822 | ||||||||
\(983\) | −30.9369 | − | 22.4769i | −0.986732 | − | 0.716903i | −0.0275293 | − | 0.999621i | \(-0.508764\pi\) |
−0.959203 | + | 0.282718i | \(0.908764\pi\) | |||||||
\(984\) | 4.49123 | − | 13.8226i | 0.143175 | − | 0.440648i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.499825 | − | 1.53830i | −0.0159177 | − | 0.0489896i | ||||
\(987\) | 0.927580 | − | 2.85480i | 0.0295252 | − | 0.0908692i | ||||
\(988\) | 0.819389 | − | 2.52182i | 0.0260682 | − | 0.0802298i | ||||
\(989\) | −2.11619 | − | 6.51298i | −0.0672911 | − | 0.207101i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.01721 | − | 21.5968i | 0.222909 | − | 0.686044i | −0.775588 | − | 0.631239i | \(-0.782547\pi\) |
0.998497 | − | 0.0548043i | \(-0.0174535\pi\) | |||||||
\(992\) | −12.5678 | − | 9.13108i | −0.399030 | − | 0.289912i | ||||
\(993\) | −9.11678 | −0.289312 | ||||||||
\(994\) | 20.0430 | + | 14.5621i | 0.635725 | + | 0.461881i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.02371 | + | 3.64994i | −0.159182 | + | 0.115653i | ||||
\(997\) | −16.6887 | + | 12.1251i | −0.528538 | + | 0.384005i | −0.819811 | − | 0.572635i | \(-0.805921\pi\) |
0.291273 | + | 0.956640i | \(0.405921\pi\) | |||||||
\(998\) | −18.8995 | − | 58.1666i | −0.598253 | − | 1.84123i | ||||
\(999\) | −21.1439 | −0.668962 |
(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 | 625.2.d.p.126.4 | 16 | ||
5.2 | odd | 4 | 625.2.e.k.499.3 | 32 | |||
5.3 | odd | 4 | 625.2.e.k.499.6 | 32 | |||
5.4 | even | 2 | 625.2.d.n.126.1 | 16 | |||
25.2 | odd | 20 | 625.2.b.d.624.12 | 16 | |||
25.3 | odd | 20 | 625.2.e.k.124.3 | 32 | |||
25.4 | even | 10 | 625.2.d.n.501.1 | 16 | |||
25.6 | even | 5 | 625.2.d.q.376.1 | 16 | |||
25.8 | odd | 20 | 625.2.e.j.249.3 | 32 | |||
25.9 | even | 10 | 625.2.d.m.251.4 | 16 | |||
25.11 | even | 5 | 625.2.a.e.1.7 | ✓ | 8 | ||
25.12 | odd | 20 | 625.2.e.j.374.3 | 32 | |||
25.13 | odd | 20 | 625.2.e.j.374.6 | 32 | |||
25.14 | even | 10 | 625.2.a.g.1.2 | yes | 8 | ||
25.16 | even | 5 | 625.2.d.q.251.1 | 16 | |||
25.17 | odd | 20 | 625.2.e.j.249.6 | 32 | |||
25.19 | even | 10 | 625.2.d.m.376.4 | 16 | |||
25.21 | even | 5 | inner | 625.2.d.p.501.4 | 16 | ||
25.22 | odd | 20 | 625.2.e.k.124.6 | 32 | |||
25.23 | odd | 20 | 625.2.b.d.624.5 | 16 | |||
75.11 | odd | 10 | 5625.2.a.be.1.2 | 8 | |||
75.14 | odd | 10 | 5625.2.a.s.1.7 | 8 | |||
100.11 | odd | 10 | 10000.2.a.bn.1.4 | 8 | |||
100.39 | odd | 10 | 10000.2.a.be.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.7 | ✓ | 8 | 25.11 | even | 5 | ||
625.2.a.g.1.2 | yes | 8 | 25.14 | even | 10 | ||
625.2.b.d.624.5 | 16 | 25.23 | odd | 20 | |||
625.2.b.d.624.12 | 16 | 25.2 | odd | 20 | |||
625.2.d.m.251.4 | 16 | 25.9 | even | 10 | |||
625.2.d.m.376.4 | 16 | 25.19 | even | 10 | |||
625.2.d.n.126.1 | 16 | 5.4 | even | 2 | |||
625.2.d.n.501.1 | 16 | 25.4 | even | 10 | |||
625.2.d.p.126.4 | 16 | 1.1 | even | 1 | trivial | ||
625.2.d.p.501.4 | 16 | 25.21 | even | 5 | inner | ||
625.2.d.q.251.1 | 16 | 25.16 | even | 5 | |||
625.2.d.q.376.1 | 16 | 25.6 | even | 5 | |||
625.2.e.j.249.3 | 32 | 25.8 | odd | 20 | |||
625.2.e.j.249.6 | 32 | 25.17 | odd | 20 | |||
625.2.e.j.374.3 | 32 | 25.12 | odd | 20 | |||
625.2.e.j.374.6 | 32 | 25.13 | odd | 20 | |||
625.2.e.k.124.3 | 32 | 25.3 | odd | 20 | |||
625.2.e.k.124.6 | 32 | 25.22 | odd | 20 | |||
625.2.e.k.499.3 | 32 | 5.2 | odd | 4 | |||
625.2.e.k.499.6 | 32 | 5.3 | odd | 4 | |||
5625.2.a.s.1.7 | 8 | 75.14 | odd | 10 | |||
5625.2.a.be.1.2 | 8 | 75.11 | odd | 10 | |||
10000.2.a.be.1.5 | 8 | 100.39 | odd | 10 | |||
10000.2.a.bn.1.4 | 8 | 100.11 | odd | 10 |