Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(37,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.y (of order \(12\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 37.8 | ||
Character | \(\chi\) | \(=\) | 432.37 |
Dual form | 432.2.y.e.397.8 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.268956 | − | 1.38840i | −0.190180 | − | 0.981749i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.85533 | + | 0.746838i | −0.927663 | + | 0.373419i | ||||
\(5\) | −2.97932 | + | 0.798307i | −1.33239 | + | 0.357014i | −0.853607 | − | 0.520918i | \(-0.825590\pi\) |
−0.478786 | + | 0.877932i | \(0.658923\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.78208 | − | 1.02889i | 0.673564 | − | 0.388882i | −0.123862 | − | 0.992299i | \(-0.539528\pi\) |
0.797426 | + | 0.603417i | \(0.206195\pi\) | |||||||
\(8\) | 1.53591 | + | 2.37507i | 0.543027 | + | 0.839715i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.90968 | + | 3.92179i | 0.603893 | + | 1.24018i | ||||
\(11\) | −0.119598 | + | 0.446347i | −0.0360602 | + | 0.134579i | −0.981609 | − | 0.190901i | \(-0.938859\pi\) |
0.945549 | + | 0.325480i | \(0.105526\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.52075 | + | 5.67550i | 0.421779 | + | 1.57410i | 0.770857 | + | 0.637008i | \(0.219828\pi\) |
−0.349078 | + | 0.937094i | \(0.613505\pi\) | |||||||
\(14\) | −1.90781 | − | 2.19752i | −0.509883 | − | 0.587313i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.88447 | − | 2.77126i | 0.721117 | − | 0.692814i | ||||
\(17\) | −0.0443921 | −0.0107667 | −0.00538333 | − | 0.999986i | \(-0.501714\pi\) | ||||
−0.00538333 | + | 0.999986i | \(0.501714\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.10726 | + | 1.10726i | −0.254023 | + | 0.254023i | −0.822618 | − | 0.568595i | \(-0.807487\pi\) |
0.568595 | + | 0.822618i | \(0.307487\pi\) | |||||||
\(20\) | 4.93140 | − | 3.70619i | 1.10270 | − | 0.828729i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.651876 | + | 0.0460030i | 0.138980 | + | 0.00980788i | ||||
\(23\) | 7.89263 | + | 4.55681i | 1.64573 | + | 0.950161i | 0.978743 | + | 0.205089i | \(0.0657485\pi\) |
0.666984 | + | 0.745072i | \(0.267585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.90893 | − | 2.25682i | 0.781786 | − | 0.451364i | ||||
\(26\) | 7.47087 | − | 3.63787i | 1.46516 | − | 0.713445i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.53793 | + | 3.23984i | −0.479624 | + | 0.612273i | ||||
\(29\) | 6.95662 | + | 1.86402i | 1.29181 | + | 0.346140i | 0.838349 | − | 0.545134i | \(-0.183521\pi\) |
0.453464 | + | 0.891275i | \(0.350188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.542236 | − | 0.939180i | 0.0973884 | − | 0.168682i | −0.813214 | − | 0.581964i | \(-0.802284\pi\) |
0.910603 | + | 0.413282i | \(0.135618\pi\) | |||||||
\(32\) | −4.62341 | − | 3.25946i | −0.817312 | − | 0.576196i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0119395 | + | 0.0616341i | 0.00204761 | + | 0.0105702i | ||||
\(35\) | −4.48803 | + | 4.48803i | −0.758615 | + | 0.758615i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.769054 | − | 0.769054i | −0.126432 | − | 0.126432i | 0.641060 | − | 0.767491i | \(-0.278495\pi\) |
−0.767491 | + | 0.641060i | \(0.778495\pi\) | |||||||
\(38\) | 1.83513 | + | 1.23952i | 0.297697 | + | 0.201077i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.47201 | − | 5.84998i | −1.02332 | − | 0.924962i | ||||
\(41\) | −5.77193 | − | 3.33242i | −0.901423 | − | 0.520437i | −0.0237617 | − | 0.999718i | \(-0.507564\pi\) |
−0.877662 | + | 0.479281i | \(0.840898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.96351 | + | 11.0600i | −0.451932 | + | 1.68663i | 0.245023 | + | 0.969517i | \(0.421204\pi\) |
−0.696955 | + | 0.717115i | \(0.745462\pi\) | |||||||
\(44\) | −0.111455 | − | 0.917439i | −0.0168025 | − | 0.138309i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.20392 | − | 12.1837i | 0.619835 | − | 1.79639i | ||||
\(47\) | 1.22453 | + | 2.12095i | 0.178617 | + | 0.309373i | 0.941407 | − | 0.337273i | \(-0.109504\pi\) |
−0.762790 | + | 0.646646i | \(0.776171\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.38279 | + | 2.39506i | −0.197541 | + | 0.342151i | ||||
\(50\) | −4.18471 | − | 4.82019i | −0.591807 | − | 0.681677i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.06016 | − | 9.39416i | −0.979068 | − | 1.30274i | ||||
\(53\) | −2.44801 | − | 2.44801i | −0.336260 | − | 0.336260i | 0.518698 | − | 0.854958i | \(-0.326417\pi\) |
−0.854958 | + | 0.518698i | \(0.826417\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.42529i | − | 0.192186i | ||||||
\(56\) | 5.18080 | + | 2.65230i | 0.692314 | + | 0.354428i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.716989 | − | 10.1599i | 0.0941453 | − | 1.33407i | ||||
\(59\) | −3.59122 | + | 0.962265i | −0.467537 | + | 0.125276i | −0.484894 | − | 0.874573i | \(-0.661142\pi\) |
0.0173563 | + | 0.999849i | \(0.494475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.18758 | − | 0.318210i | −0.152054 | − | 0.0407426i | 0.181989 | − | 0.983301i | \(-0.441746\pi\) |
−0.334043 | + | 0.942558i | \(0.608413\pi\) | |||||||
\(62\) | −1.44980 | − | 0.500244i | −0.184124 | − | 0.0635310i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.28195 | + | 7.29581i | −0.410243 | + | 0.911976i | ||||
\(65\) | −9.06158 | − | 15.6951i | −1.12395 | − | 1.94674i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.48102 | + | 5.52723i | 0.180935 | + | 0.675258i | 0.995464 | + | 0.0951361i | \(0.0303286\pi\) |
−0.814529 | + | 0.580122i | \(0.803005\pi\) | |||||||
\(68\) | 0.0823618 | − | 0.0331537i | 0.00998783 | − | 0.00402048i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.43827 | + | 5.02411i | 0.889044 | + | 0.600496i | ||||
\(71\) | 6.88571i | 0.817184i | 0.912717 | + | 0.408592i | \(0.133980\pi\) | ||||
−0.912717 | + | 0.408592i | \(0.866020\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.1963i | − | 1.54451i | −0.635312 | − | 0.772255i | \(-0.719129\pi\) | ||
0.635312 | − | 0.772255i | \(-0.280871\pi\) | |||||||
\(74\) | −0.860915 | + | 1.27460i | −0.100079 | + | 0.148169i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.22738 | − | 2.88127i | 0.140791 | − | 0.330505i | ||||
\(77\) | 0.246106 | + | 0.918480i | 0.0280464 | + | 0.104670i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46441 | + | 6.00054i | 0.389777 | + | 0.675113i | 0.992419 | − | 0.122898i | \(-0.0392188\pi\) |
−0.602643 | + | 0.798011i | \(0.705885\pi\) | |||||||
\(80\) | −6.38144 | + | 10.5591i | −0.713466 | + | 1.18055i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.07435 | + | 8.91003i | −0.339506 | + | 0.983949i | ||||
\(83\) | 0.588112 | + | 0.157584i | 0.0645537 | + | 0.0172971i | 0.290951 | − | 0.956738i | \(-0.406028\pi\) |
−0.226398 | + | 0.974035i | \(0.572695\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.132258 | − | 0.0354385i | 0.0143454 | − | 0.00384385i | ||||
\(86\) | 16.1528 | + | 1.13991i | 1.74180 | + | 0.122919i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.24380 | + | 0.401495i | −0.132589 | + | 0.0427995i | ||||
\(89\) | 5.30004i | 0.561803i | 0.959737 | + | 0.280902i | \(0.0906335\pi\) | ||||
−0.959737 | + | 0.280902i | \(0.909367\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.54954 | + | 8.54954i | 0.896235 | + | 0.896235i | ||||
\(92\) | −18.0466 | − | 2.55985i | −1.88149 | − | 0.266883i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.61539 | − | 2.27059i | 0.269757 | − | 0.234193i | ||||
\(95\) | 2.41495 | − | 4.18282i | 0.247769 | − | 0.429148i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.88304 | − | 10.1897i | −0.597333 | − | 1.03461i | −0.993213 | − | 0.116309i | \(-0.962894\pi\) |
0.395880 | − | 0.918302i | \(-0.370439\pi\) | |||||||
\(98\) | 3.69722 | + | 1.27570i | 0.373475 | + | 0.128865i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.56686 | + | 7.10648i | −0.556686 | + | 0.710648i | ||||
\(101\) | −1.51464 | + | 5.65271i | −0.150712 | + | 0.562466i | 0.848722 | + | 0.528839i | \(0.177372\pi\) |
−0.999434 | + | 0.0336269i | \(0.989294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.13680 | + | 0.656334i | 0.112013 | + | 0.0646705i | 0.554960 | − | 0.831877i | \(-0.312734\pi\) |
−0.442947 | + | 0.896548i | \(0.646067\pi\) | |||||||
\(104\) | −11.1440 | + | 12.3290i | −1.09276 | + | 1.20895i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.74042 | + | 4.05723i | −0.266173 | + | 0.394073i | ||||
\(107\) | 2.92966 | + | 2.92966i | 0.283221 | + | 0.283221i | 0.834392 | − | 0.551171i | \(-0.185819\pi\) |
−0.551171 | + | 0.834392i | \(0.685819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5193 | − | 11.5193i | 1.10335 | − | 1.10335i | 0.109344 | − | 0.994004i | \(-0.465125\pi\) |
0.994004 | − | 0.109344i | \(-0.0348750\pi\) | |||||||
\(110\) | −1.97887 | + | 0.383339i | −0.188678 | + | 0.0365499i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.28905 | − | 7.90639i | 0.216295 | − | 0.747084i | ||||
\(113\) | −3.79250 | + | 6.56880i | −0.356768 | + | 0.617941i | −0.987419 | − | 0.158126i | \(-0.949455\pi\) |
0.630651 | + | 0.776067i | \(0.282788\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.1524 | − | 7.27547i | −2.53198 | − | 0.678441i | ||||
\(116\) | −14.2989 | + | 1.73710i | −1.32762 | + | 0.161286i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.30189 | + | 4.72726i | 0.211906 | + | 0.435179i | ||||
\(119\) | −0.0791104 | + | 0.0456744i | −0.00725204 | + | 0.00418696i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.34136 | + | 5.39324i | 0.849214 | + | 0.490294i | ||||
\(122\) | −0.122398 | + | 1.73442i | −0.0110814 | + | 0.157027i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.304609 | + | 2.14745i | −0.0273547 | + | 0.192846i | ||||
\(125\) | 1.06075 | − | 1.06075i | 0.0948761 | − | 0.0948761i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6374 | −0.943915 | −0.471958 | − | 0.881621i | \(-0.656452\pi\) | ||||
−0.471958 | + | 0.881621i | \(0.656452\pi\) | |||||||
\(128\) | 11.0122 | + | 2.59441i | 0.973352 | + | 0.229316i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19.3540 | + | 16.8024i | −1.69746 | + | 1.47367i | ||||
\(131\) | −4.98338 | − | 18.5982i | −0.435400 | − | 1.62493i | −0.740108 | − | 0.672488i | \(-0.765226\pi\) |
0.304708 | − | 0.952446i | \(-0.401441\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.833985 | + | 3.11247i | −0.0723157 | + | 0.269886i | ||||
\(134\) | 7.27569 | − | 3.54283i | 0.628524 | − | 0.306054i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0681824 | − | 0.105434i | −0.00584659 | − | 0.00904093i | ||||
\(137\) | 8.30213 | − | 4.79324i | 0.709299 | − | 0.409514i | −0.101502 | − | 0.994835i | \(-0.532365\pi\) |
0.810802 | + | 0.585321i | \(0.199032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.81465 | − | 1.82598i | 0.578011 | − | 0.154878i | 0.0420428 | − | 0.999116i | \(-0.486613\pi\) |
0.535968 | + | 0.844238i | \(0.319947\pi\) | |||||||
\(140\) | 4.97492 | − | 11.6786i | 0.420458 | − | 0.987020i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.56014 | − | 1.85195i | 0.802270 | − | 0.155412i | ||||
\(143\) | −2.71512 | −0.227050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.2141 | −1.84478 | ||||||||
\(146\) | −18.3218 | + | 3.54922i | −1.51632 | + | 0.293736i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00120 | + | 0.852487i | 0.164498 | + | 0.0700740i | ||||
\(149\) | −19.4991 | + | 5.22476i | −1.59743 | + | 0.428029i | −0.944264 | − | 0.329189i | \(-0.893225\pi\) |
−0.653162 | + | 0.757218i | \(0.726558\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.86699 | − | 2.23261i | 0.314691 | − | 0.181687i | −0.334333 | − | 0.942455i | \(-0.608511\pi\) |
0.649024 | + | 0.760768i | \(0.275178\pi\) | |||||||
\(152\) | −4.33048 | − | 0.929169i | −0.351248 | − | 0.0753656i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.20903 | − | 0.588725i | 0.0974263 | − | 0.0474408i | ||||
\(155\) | −0.865741 | + | 3.23099i | −0.0695380 | + | 0.259519i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.26421 | − | 15.9143i | −0.340321 | − | 1.27010i | −0.897984 | − | 0.440029i | \(-0.854968\pi\) |
0.557662 | − | 0.830068i | \(-0.311698\pi\) | |||||||
\(158\) | 7.39939 | − | 6.42388i | 0.588664 | − | 0.511056i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.3767 | + | 6.02006i | 1.29469 | + | 0.475928i | ||||
\(161\) | 18.7538 | 1.47800 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.24124 | − | 5.24124i | 0.410525 | − | 0.410525i | −0.471396 | − | 0.881922i | \(-0.656250\pi\) |
0.881922 | + | 0.471396i | \(0.156250\pi\) | |||||||
\(164\) | 13.1976 | + | 1.87204i | 1.03056 | + | 0.146181i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0606142 | − | 0.858920i | 0.00470457 | − | 0.0666651i | ||||
\(167\) | 11.2974 | + | 6.52257i | 0.874220 | + | 0.504731i | 0.868748 | − | 0.495254i | \(-0.164925\pi\) |
0.00547195 | + | 0.999985i | \(0.498258\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.6403 | + | 10.7620i | −1.43387 | + | 0.827847i | ||||
\(170\) | −0.0847745 | − | 0.174096i | −0.00650191 | − | 0.0133526i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.76173 | − | 22.7331i | −0.210580 | − | 1.73339i | ||||
\(173\) | −1.38769 | − | 0.371831i | −0.105504 | − | 0.0282698i | 0.205681 | − | 0.978619i | \(-0.434059\pi\) |
−0.311185 | + | 0.950349i | \(0.600726\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.64402 | − | 8.04369i | 0.351055 | − | 0.608046i | ||||
\(176\) | 0.891964 | + | 1.61891i | 0.0672343 | + | 0.122030i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.35859 | − | 1.42548i | 0.551550 | − | 0.106844i | ||||
\(179\) | 2.50772 | − | 2.50772i | 0.187436 | − | 0.187436i | −0.607151 | − | 0.794587i | \(-0.707688\pi\) |
0.794587 | + | 0.607151i | \(0.207688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.8795 | + | 10.8795i | 0.808666 | + | 0.808666i | 0.984432 | − | 0.175766i | \(-0.0562403\pi\) |
−0.175766 | + | 0.984432i | \(0.556240\pi\) | |||||||
\(182\) | 9.57076 | − | 14.1697i | 0.709432 | − | 1.05032i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.29963 | + | 25.7444i | 0.0958098 | + | 1.89791i | ||||
\(185\) | 2.90520 | + | 1.67732i | 0.213594 | + | 0.123319i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.00530922 | − | 0.0198143i | 0.000388248 | − | 0.00144896i | ||||
\(188\) | −3.85592 | − | 3.02053i | −0.281222 | − | 0.220295i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.45695 | − | 2.22793i | −0.468436 | − | 0.161631i | ||||
\(191\) | 6.59227 | + | 11.4182i | 0.477000 | + | 0.826188i | 0.999653 | − | 0.0263575i | \(-0.00839081\pi\) |
−0.522653 | + | 0.852546i | \(0.675057\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.71808 | − | 15.1002i | 0.627541 | − | 1.08693i | −0.360503 | − | 0.932758i | \(-0.617395\pi\) |
0.988044 | − | 0.154175i | \(-0.0492718\pi\) | |||||||
\(194\) | −12.5652 | + | 10.9086i | −0.902127 | + | 0.783194i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.776801 | − | 5.47633i | 0.0554858 | − | 0.391167i | ||||
\(197\) | 8.36275 | + | 8.36275i | 0.595822 | + | 0.595822i | 0.939198 | − | 0.343376i | \(-0.111571\pi\) |
−0.343376 | + | 0.939198i | \(0.611571\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.6420i | − | 1.10883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) | ||
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(200\) | 11.3639 | + | 5.81772i | 0.803549 | + | 0.411375i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.25561 | + | 0.582601i | 0.580863 | + | 0.0409916i | ||||
\(203\) | 14.3151 | − | 3.83573i | 1.00473 | − | 0.269216i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.8567 | + | 5.32059i | 1.38685 | + | 0.371606i | ||||
\(206\) | 0.605506 | − | 1.75487i | 0.0421876 | − | 0.122267i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.1148 | + | 12.1564i | 1.39471 | + | 0.842896i | ||||
\(209\) | −0.361796 | − | 0.626649i | −0.0250259 | − | 0.0433462i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.00865 | + | 18.6925i | 0.344810 | + | 1.28685i | 0.892834 | + | 0.450386i | \(0.148713\pi\) |
−0.548024 | + | 0.836462i | \(0.684620\pi\) | |||||||
\(212\) | 6.37012 | + | 2.71359i | 0.437502 | + | 0.186370i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.27960 | − | 4.85550i | 0.224189 | − | 0.331915i | ||||
\(215\) | − | 35.3170i | − | 2.40860i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.23159i | − | 0.151491i | ||||||
\(218\) | −19.0916 | − | 12.8952i | −1.29305 | − | 0.873376i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.06446 | + | 2.64437i | 0.0717657 | + | 0.178283i | ||||
\(221\) | −0.0675091 | − | 0.251948i | −0.00454116 | − | 0.0169478i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.07790 | − | 3.59904i | −0.139147 | − | 0.241009i | 0.788027 | − | 0.615641i | \(-0.211103\pi\) |
−0.927174 | + | 0.374631i | \(0.877769\pi\) | |||||||
\(224\) | −11.5929 | − | 1.05166i | −0.774584 | − | 0.0702667i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.1402 | + | 3.49880i | 0.674513 | + | 0.232737i | ||||
\(227\) | −6.22983 | − | 1.66928i | −0.413488 | − | 0.110794i | 0.0460768 | − | 0.998938i | \(-0.485328\pi\) |
−0.459565 | + | 0.888144i | \(0.651995\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.37974 | + | 2.51329i | −0.619831 | + | 0.166083i | −0.555051 | − | 0.831816i | \(-0.687301\pi\) |
−0.0647799 | + | 0.997900i | \(0.520635\pi\) | |||||||
\(230\) | −2.79848 | + | 39.6553i | −0.184526 | + | 2.61479i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.25758 | + | 19.3855i | 0.410830 | + | 1.27272i | ||||
\(233\) | − | 22.2096i | − | 1.45500i | −0.686108 | − | 0.727499i | \(-0.740682\pi\) | ||
0.686108 | − | 0.727499i | \(-0.259318\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.34145 | − | 5.34145i | −0.348438 | − | 0.348438i | ||||
\(236\) | 5.94423 | − | 4.46738i | 0.386937 | − | 0.290801i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.0846917 | + | 0.0975527i | 0.00548974 | + | 0.00632340i | ||||
\(239\) | 4.02723 | − | 6.97537i | 0.260500 | − | 0.451199i | −0.705875 | − | 0.708337i | \(-0.749446\pi\) |
0.966375 | + | 0.257137i | \(0.0827792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.07653 | + | 8.79280i | 0.327008 | + | 0.566394i | 0.981917 | − | 0.189314i | \(-0.0606263\pi\) |
−0.654909 | + | 0.755708i | \(0.727293\pi\) | |||||||
\(242\) | 4.97557 | − | 14.4201i | 0.319842 | − | 0.926960i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.44099 | − | 0.296544i | 0.156268 | − | 0.0189843i | ||||
\(245\) | 2.20778 | − | 8.23954i | 0.141050 | − | 0.526405i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.96812 | − | 4.60040i | −0.507000 | − | 0.292716i | ||||
\(248\) | 3.06345 | − | 0.154649i | 0.194529 | − | 0.00982020i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.75804 | − | 1.18745i | −0.111188 | − | 0.0751010i | ||||
\(251\) | −11.0682 | − | 11.0682i | −0.698617 | − | 0.698617i | 0.265495 | − | 0.964112i | \(-0.414465\pi\) |
−0.964112 | + | 0.265495i | \(0.914465\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.97786 | + | 2.97786i | −0.187217 | + | 0.187217i | ||||
\(254\) | 2.86099 | + | 14.7690i | 0.179514 | + | 0.926688i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.640289 | − | 15.9872i | 0.0400181 | − | 0.999199i | ||||
\(257\) | 10.3807 | − | 17.9800i | 0.647533 | − | 1.12156i | −0.336177 | − | 0.941799i | \(-0.609134\pi\) |
0.983710 | − | 0.179761i | \(-0.0575326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.16179 | − | 0.579249i | −0.134327 | − | 0.0359928i | ||||
\(260\) | 28.5339 | + | 22.3520i | 1.76960 | + | 1.38621i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.4815 | + | 11.9210i | −1.51247 | + | 0.736484i | ||||
\(263\) | 9.13436 | − | 5.27373i | 0.563249 | − | 0.325192i | −0.191200 | − | 0.981551i | \(-0.561238\pi\) |
0.754448 | + | 0.656359i | \(0.227904\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.24767 | + | 5.33914i | 0.568080 | + | 0.327981i | ||||
\(266\) | 4.54567 | + | 0.320789i | 0.278713 | + | 0.0196689i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.87571 | − | 9.14873i | −0.420001 | − | 0.558848i | ||||
\(269\) | 0.529850 | − | 0.529850i | 0.0323055 | − | 0.0323055i | −0.690770 | − | 0.723075i | \(-0.742728\pi\) |
0.723075 | + | 0.690770i | \(0.242728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.3682 | 0.872804 | 0.436402 | − | 0.899752i | \(-0.356253\pi\) | ||||
0.436402 | + | 0.899752i | \(0.356253\pi\) | |||||||
\(272\) | −0.128047 | + | 0.123022i | −0.00776402 | + | 0.00745929i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.88786 | − | 10.2375i | −0.536935 | − | 0.618472i | ||||
\(275\) | 0.539824 | + | 2.01465i | 0.0325526 | + | 0.121488i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.19602 | − | 8.19567i | 0.131946 | − | 0.492430i | −0.868046 | − | 0.496485i | \(-0.834624\pi\) |
0.999992 | + | 0.00405455i | \(0.00129061\pi\) | |||||||
\(278\) | −4.36803 | − | 8.97037i | −0.261977 | − | 0.538007i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −17.5526 | − | 3.76618i | −1.04897 | − | 0.225072i | ||||
\(281\) | −6.21827 | + | 3.59012i | −0.370951 | + | 0.214169i | −0.673874 | − | 0.738847i | \(-0.735371\pi\) |
0.302923 | + | 0.953015i | \(0.402038\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.8817 | + | 3.98753i | −0.884623 | + | 0.237034i | −0.672401 | − | 0.740187i | \(-0.734737\pi\) |
−0.212222 | + | 0.977221i | \(0.568070\pi\) | |||||||
\(284\) | −5.14251 | − | 12.7752i | −0.305152 | − | 0.758071i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.730248 | + | 3.76968i | 0.0431805 | + | 0.222906i | ||||
\(287\) | −13.7147 | −0.809555 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9980 | −0.999884 | ||||||||
\(290\) | 5.97460 | + | 30.8421i | 0.350841 | + | 1.81111i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.85550 | + | 24.4834i | 0.576750 | + | 1.43278i | ||||
\(293\) | 15.3492 | − | 4.11281i | 0.896711 | − | 0.240273i | 0.219108 | − | 0.975701i | \(-0.429685\pi\) |
0.677603 | + | 0.735428i | \(0.263019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.93122 | − | 5.73379i | 0.578218 | − | 0.333834i | ||||
\(296\) | 0.645360 | − | 3.00776i | 0.0375108 | − | 0.174822i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.4985 | + | 25.6673i | 0.724016 | + | 1.48687i | ||||
\(299\) | −13.8595 | + | 51.7244i | −0.801517 | + | 2.99130i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.09824 | + | 22.7589i | 0.351496 | + | 1.31180i | ||||
\(302\) | −4.13981 | − | 4.76846i | −0.238219 | − | 0.274394i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.125354 | + | 6.26236i | −0.00718954 | + | 0.359171i | ||||
\(305\) | 3.79220 | 0.217141 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.37130 | − | 7.37130i | 0.420702 | − | 0.420702i | −0.464743 | − | 0.885446i | \(-0.653853\pi\) |
0.885446 | + | 0.464743i | \(0.153853\pi\) | |||||||
\(308\) | −1.14256 | − | 1.52028i | −0.0651035 | − | 0.0866259i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.71876 | + | 0.333004i | 0.268008 | + | 0.0189134i | ||||
\(311\) | 6.23360 | + | 3.59897i | 0.353475 | + | 0.204079i | 0.666215 | − | 0.745760i | \(-0.267913\pi\) |
−0.312740 | + | 0.949839i | \(0.601247\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.23161 | + | 5.32987i | −0.521801 | + | 0.301262i | −0.737671 | − | 0.675160i | \(-0.764075\pi\) |
0.215870 | + | 0.976422i | \(0.430741\pi\) | |||||||
\(314\) | −20.9485 | + | 10.2007i | −1.18219 | + | 0.575658i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.9090 | − | 8.54560i | −0.613681 | − | 0.480727i | ||||
\(317\) | −14.5196 | − | 3.89052i | −0.815503 | − | 0.218513i | −0.173123 | − | 0.984900i | \(-0.555386\pi\) |
−0.642379 | + | 0.766387i | \(0.722053\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.66400 | + | 2.88213i | −0.0931662 | + | 0.161369i | ||||
\(320\) | 3.95367 | − | 24.3566i | 0.221017 | − | 1.36157i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.04393 | − | 26.0378i | −0.281087 | − | 1.45103i | ||||
\(323\) | 0.0491536 | − | 0.0491536i | 0.00273498 | − | 0.00273498i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.7531 | + | 18.7531i | 1.04023 | + | 1.04023i | ||||
\(326\) | −8.68661 | − | 5.86729i | −0.481107 | − | 0.324959i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.950425 | − | 18.8271i | −0.0524785 | − | 1.03955i | ||||
\(329\) | 4.36444 | + | 2.51981i | 0.240619 | + | 0.138922i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.53309 | − | 24.3818i | 0.359091 | − | 1.34015i | −0.516166 | − | 0.856488i | \(-0.672641\pi\) |
0.875257 | − | 0.483658i | \(-0.160692\pi\) | |||||||
\(332\) | −1.20883 | + | 0.146855i | −0.0663431 | + | 0.00805969i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.01745 | − | 17.4396i | 0.329260 | − | 0.954255i | ||||
\(335\) | −8.82485 | − | 15.2851i | −0.482153 | − | 0.835113i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.80217 | − | 3.12146i | 0.0981707 | − | 0.170037i | −0.812757 | − | 0.582603i | \(-0.802034\pi\) |
0.910928 | + | 0.412566i | \(0.135368\pi\) | |||||||
\(338\) | 19.9554 | + | 22.9858i | 1.08543 | + | 1.25026i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.218915 | + | 0.164525i | −0.0118724 | + | 0.00892265i | ||||
\(341\) | 0.354350 | + | 0.354350i | 0.0191891 | + | 0.0191891i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0953i | 1.08505i | ||||||||
\(344\) | −30.8200 | + | 9.94861i | −1.66170 | + | 0.536393i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.143023 | + | 2.02668i | −0.00768899 | + | 0.108955i | ||||
\(347\) | −15.4243 | + | 4.13293i | −0.828020 | + | 0.221867i | −0.647850 | − | 0.761768i | \(-0.724331\pi\) |
−0.180170 | + | 0.983635i | \(0.557665\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.1326 | − | 4.05477i | −0.810029 | − | 0.217047i | −0.170047 | − | 0.985436i | \(-0.554392\pi\) |
−0.639983 | + | 0.768389i | \(0.721058\pi\) | |||||||
\(350\) | −12.4169 | − | 4.28438i | −0.663712 | − | 0.229010i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00780 | − | 1.67382i | 0.107016 | − | 0.0892149i | ||||
\(353\) | −2.05577 | − | 3.56070i | −0.109418 | − | 0.189517i | 0.806117 | − | 0.591756i | \(-0.201565\pi\) |
−0.915534 | + | 0.402239i | \(0.868232\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.49691 | − | 20.5147i | −0.291746 | − | 1.08881i | ||||
\(356\) | −3.95827 | − | 9.83330i | −0.209788 | − | 0.521164i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.15619 | − | 2.80726i | −0.219662 | − | 0.148368i | ||||
\(359\) | 20.1902i | 1.06560i | 0.846242 | + | 0.532800i | \(0.178860\pi\) | ||||
−0.846242 | + | 0.532800i | \(0.821140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.5479i | 0.870945i | ||||||||
\(362\) | 12.1790 | − | 18.0312i | 0.640114 | − | 0.947699i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −22.2473 | − | 9.47706i | −1.16608 | − | 0.496733i | ||||
\(365\) | 10.5347 | + | 39.3160i | 0.551411 | + | 2.05789i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2398 | + | 19.4679i | 0.586714 | + | 1.01622i | 0.994659 | + | 0.103212i | \(0.0329120\pi\) |
−0.407946 | + | 0.913006i | \(0.633755\pi\) | |||||||
\(368\) | 35.3941 | − | 8.72852i | 1.84505 | − | 0.455006i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.54742 | − | 4.48471i | 0.0804466 | − | 0.233149i | ||||
\(371\) | −6.88128 | − | 1.84383i | −0.357258 | − | 0.0957270i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.6543 | + | 6.87405i | −1.32833 | + | 0.355925i | −0.852092 | − | 0.523392i | \(-0.824666\pi\) |
−0.476237 | + | 0.879317i | \(0.658000\pi\) | |||||||
\(374\) | −0.0289381 | − | 0.00204217i | −0.00149636 | − | 0.000105598i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.15665 | + | 6.16596i | −0.162792 | + | 0.317985i | ||||
\(377\) | 42.3171i | 2.17944i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.62881 | − | 6.62881i | −0.340499 | − | 0.340499i | 0.516056 | − | 0.856555i | \(-0.327400\pi\) |
−0.856555 | + | 0.516056i | \(0.827400\pi\) | |||||||
\(380\) | −1.35663 | + | 9.56407i | −0.0695938 | + | 0.490626i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.0800 | − | 12.2237i | 0.720394 | − | 0.625419i | ||||
\(383\) | −1.98902 | + | 3.44509i | −0.101634 | + | 0.176036i | −0.912358 | − | 0.409393i | \(-0.865741\pi\) |
0.810724 | + | 0.585429i | \(0.199074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.46646 | − | 2.53998i | −0.0747376 | − | 0.129449i | ||||
\(386\) | −23.3099 | − | 8.04293i | −1.18644 | − | 0.409374i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.5250 | + | 14.5116i | 0.940467 | + | 0.736714i | ||||
\(389\) | −1.21847 | + | 4.54738i | −0.0617787 | + | 0.230561i | −0.989911 | − | 0.141688i | \(-0.954747\pi\) |
0.928133 | + | 0.372250i | \(0.121414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.350370 | − | 0.202286i | −0.0177190 | − | 0.0102301i | ||||
\(392\) | −7.81228 | + | 0.394379i | −0.394580 | + | 0.0199191i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.36166 | − | 13.8601i | 0.471634 | − | 0.698261i | ||||
\(395\) | −15.1119 | − | 15.1119i | −0.760360 | − | 0.760360i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.1361 | + | 18.1361i | −0.910223 | + | 0.910223i | −0.996289 | − | 0.0860661i | \(-0.972570\pi\) |
0.0860661 | + | 0.996289i | \(0.472570\pi\) | |||||||
\(398\) | −21.7174 | + | 4.20700i | −1.08859 | + | 0.210878i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.02095 | − | 17.3424i | 0.251047 | − | 0.867119i | ||||
\(401\) | 2.47526 | − | 4.28727i | 0.123608 | − | 0.214096i | −0.797580 | − | 0.603214i | \(-0.793887\pi\) |
0.921188 | + | 0.389118i | \(0.127220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.15492 | + | 1.64921i | 0.306599 | + | 0.0821528i | ||||
\(404\) | −1.41151 | − | 11.6188i | −0.0702253 | − | 0.578057i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.17568 | − | 18.8435i | −0.455381 | − | 0.935189i | ||||
\(407\) | 0.435242 | − | 0.251287i | 0.0215742 | − | 0.0124558i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4390 | − | 7.18164i | −0.615067 | − | 0.355109i | 0.159879 | − | 0.987137i | \(-0.448890\pi\) |
−0.774946 | + | 0.632027i | \(0.782223\pi\) | |||||||
\(410\) | 2.04655 | − | 29.0001i | 0.101072 | − | 1.43221i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.59931 | − | 0.368705i | −0.128059 | − | 0.0181648i | ||||
\(413\) | −5.40979 | + | 5.40979i | −0.266199 | + | 0.266199i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.87798 | −0.0921862 | ||||||||
\(416\) | 11.4680 | − | 31.1970i | 0.562266 | − | 1.52956i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.772734 | + | 0.670859i | −0.0377956 | + | 0.0328128i | ||||
\(419\) | 6.54483 | + | 24.4257i | 0.319736 | + | 1.19327i | 0.919499 | + | 0.393093i | \(0.128595\pi\) |
−0.599763 | + | 0.800178i | \(0.704738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.33131 | − | 4.96853i | 0.0648842 | − | 0.242151i | −0.925865 | − | 0.377853i | \(-0.876662\pi\) |
0.990750 | + | 0.135702i | \(0.0433290\pi\) | |||||||
\(422\) | 24.6057 | − | 11.9815i | 1.19779 | − | 0.583250i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.05427 | − | 9.57413i | 0.0997643 | − | 0.464961i | ||||
\(425\) | −0.173526 | + | 0.100185i | −0.00841723 | + | 0.00485969i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.44376 | + | 0.654803i | −0.118262 | + | 0.0316882i | ||||
\(428\) | −7.62346 | − | 3.24749i | −0.368494 | − | 0.156974i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −49.0343 | + | 9.49872i | −2.36464 | + | 0.458069i | ||||
\(431\) | −20.0912 | −0.967760 | −0.483880 | − | 0.875134i | \(-0.660773\pi\) | ||||
−0.483880 | + | 0.875134i | \(0.660773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.8262 | 1.04890 | 0.524449 | − | 0.851442i | \(-0.324271\pi\) | ||||
0.524449 | + | 0.851442i | \(0.324271\pi\) | |||||||
\(434\) | −3.09835 | + | 0.600200i | −0.148726 | + | 0.0288105i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.7690 | + | 29.9751i | −0.611524 | + | 1.43555i | ||||
\(437\) | −13.7848 | + | 3.69362i | −0.659415 | + | 0.176690i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.7554 | − | 14.8699i | 1.22924 | − | 0.709700i | 0.262367 | − | 0.964968i | \(-0.415497\pi\) |
0.966870 | + | 0.255268i | \(0.0821636\pi\) | |||||||
\(440\) | 3.38516 | − | 2.18912i | 0.161381 | − | 0.104362i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.331648 | + | 0.161493i | −0.0157749 | + | 0.00768142i | ||||
\(443\) | 9.06164 | − | 33.8185i | 0.430532 | − | 1.60677i | −0.321007 | − | 0.947077i | \(-0.604021\pi\) |
0.751539 | − | 0.659689i | \(-0.229312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.23106 | − | 15.7905i | −0.200571 | − | 0.748543i | ||||
\(446\) | −4.43805 | + | 3.85295i | −0.210148 | + | 0.182442i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.65786 | + | 16.3785i | 0.0783264 | + | 0.773810i | ||||
\(449\) | −27.6805 | −1.30633 | −0.653163 | − | 0.757217i | \(-0.726558\pi\) | ||||
−0.653163 | + | 0.757217i | \(0.726558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.17773 | − | 2.17773i | 0.102545 | − | 0.102545i | ||||
\(452\) | 2.13049 | − | 15.0196i | 0.100210 | − | 0.706465i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.642082 | + | 9.09848i | −0.0301344 | + | 0.427013i | ||||
\(455\) | −32.2970 | − | 18.6467i | −1.51411 | − | 0.874169i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.8114 | − | 7.97402i | 0.646070 | − | 0.373009i | −0.140879 | − | 0.990027i | \(-0.544993\pi\) |
0.786949 | + | 0.617018i | \(0.211659\pi\) | |||||||
\(458\) | 6.01220 | + | 12.3469i | 0.280932 | + | 0.576932i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 55.8102 | − | 6.78009i | 2.60216 | − | 0.316123i | ||||
\(461\) | 18.1773 | + | 4.87059i | 0.846600 | + | 0.226846i | 0.655943 | − | 0.754811i | \(-0.272271\pi\) |
0.190658 | + | 0.981657i | \(0.438938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.07529 | − | 10.5227i | 0.282343 | − | 0.489032i | −0.689619 | − | 0.724173i | \(-0.742222\pi\) |
0.971961 | + | 0.235141i | \(0.0755552\pi\) | |||||||
\(464\) | 25.2318 | − | 13.9019i | 1.17136 | − | 0.645378i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.8359 | + | 5.97340i | −1.42844 | + | 0.276712i | ||||
\(467\) | 15.9698 | − | 15.9698i | 0.738992 | − | 0.738992i | −0.233391 | − | 0.972383i | \(-0.574982\pi\) |
0.972383 | + | 0.233391i | \(0.0749822\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.32618 | + | 8.32618i | 0.384467 | + | 0.384467i | ||||
\(470\) | −5.97947 | + | 8.85270i | −0.275812 | + | 0.408345i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.80126 | − | 7.05146i | −0.359082 | − | 0.324570i | ||||
\(473\) | −4.58216 | − | 2.64551i | −0.210688 | − | 0.121641i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.82931 | + | 6.82710i | −0.0839347 | + | 0.313249i | ||||
\(476\) | 0.112664 | − | 0.143823i | 0.00516395 | − | 0.00659214i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.7678 | − | 3.71536i | −0.492507 | − | 0.169936i | ||||
\(479\) | 9.27240 | + | 16.0603i | 0.423667 | + | 0.733813i | 0.996295 | − | 0.0860026i | \(-0.0274094\pi\) |
−0.572628 | + | 0.819815i | \(0.694076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.19523 | − | 5.53430i | 0.145690 | − | 0.252343i | ||||
\(482\) | 10.8426 | − | 9.41314i | 0.493866 | − | 0.428757i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.3591 | − | 3.02973i | −0.970870 | − | 0.137715i | ||||
\(485\) | 25.6620 | + | 25.6620i | 1.16525 | + | 1.16525i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.58835i | 0.298547i | 0.988796 | + | 0.149273i | \(0.0476934\pi\) | ||||
−0.988796 | + | 0.149273i | \(0.952307\pi\) | |||||||
\(488\) | −1.06824 | − | 3.30932i | −0.0483570 | − | 0.149806i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.0336 | − | 0.849214i | −0.543623 | − | 0.0383636i | ||||
\(491\) | 4.86361 | − | 1.30320i | 0.219491 | − | 0.0588126i | −0.147397 | − | 0.989077i | \(-0.547090\pi\) |
0.366889 | + | 0.930265i | \(0.380423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.308819 | − | 0.0827478i | −0.0139085 | − | 0.00372678i | ||||
\(494\) | −4.24413 | + | 12.3003i | −0.190953 | + | 0.553415i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.03865 | − | 4.21171i | −0.0466366 | − | 0.189111i | ||||
\(497\) | 7.08461 | + | 12.2709i | 0.317788 | + | 0.550425i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.62008 | + | 20.9744i | 0.251589 | + | 0.938944i | 0.969956 | + | 0.243279i | \(0.0782232\pi\) |
−0.718367 | + | 0.695664i | \(0.755110\pi\) | |||||||
\(500\) | −1.17583 | + | 2.76024i | −0.0525845 | + | 0.123442i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.3902 | + | 18.3439i | −0.553003 | + | 0.818730i | ||||
\(503\) | 9.04140i | 0.403136i | 0.979475 | + | 0.201568i | \(0.0646037\pi\) | ||||
−0.979475 | + | 0.201568i | \(0.935396\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.0504i | − | 0.803232i | ||||||
\(506\) | 4.93539 | + | 3.33356i | 0.219405 | + | 0.148195i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.7358 | − | 7.94440i | 0.875635 | − | 0.352476i | ||||
\(509\) | −3.80331 | − | 14.1941i | −0.168579 | − | 0.629144i | −0.997557 | − | 0.0698626i | \(-0.977744\pi\) |
0.828978 | − | 0.559281i | \(-0.188923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.5775 | − | 23.5169i | −0.600633 | − | 1.04033i | ||||
\(512\) | −22.3689 | + | 3.41087i | −0.988573 | + | 0.150740i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.7554 | − | 9.57684i | −1.22424 | − | 0.422416i | ||||
\(515\) | −3.91086 | − | 1.04791i | −0.172333 | − | 0.0461765i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.09313 | + | 0.292904i | −0.0480760 | + | 0.0128819i | ||||
\(518\) | −0.222806 | + | 3.15722i | −0.00978953 | + | 0.138720i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.3593 | − | 45.6283i | 1.02437 | − | 2.00093i | ||||
\(521\) | 7.25761i | 0.317962i | 0.987282 | + | 0.158981i | \(0.0508208\pi\) | ||||
−0.987282 | + | 0.158981i | \(0.949179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0736 | − | 19.0736i | −0.834028 | − | 0.834028i | 0.154037 | − | 0.988065i | \(-0.450773\pi\) |
−0.988065 | + | 0.154037i | \(0.950773\pi\) | |||||||
\(524\) | 23.1356 | + | 30.7840i | 1.01069 | + | 1.34480i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.77879 | − | 11.2638i | −0.426376 | − | 0.491124i | ||||
\(527\) | −0.0240710 | + | 0.0416922i | −0.00104855 | + | 0.00181614i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.0291 | + | 52.0119i | 1.30561 | + | 2.26139i | ||||
\(530\) | 4.92567 | − | 14.2755i | 0.213957 | − | 0.620087i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.777200 | − | 6.39750i | −0.0336959 | − | 0.277367i | ||||
\(533\) | 10.1355 | − | 37.8264i | 0.439019 | − | 1.63844i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.0672 | − | 6.38963i | −0.478476 | − | 0.276248i | ||||
\(536\) | −10.8529 | + | 12.0069i | −0.468772 | + | 0.518617i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.878151 | − | 0.593139i | −0.0378598 | − | 0.0255720i | ||||
\(539\) | −0.903648 | − | 0.903648i | −0.0389229 | − | 0.0389229i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1246 | − | 12.1246i | 0.521279 | − | 0.521279i | −0.396679 | − | 0.917957i | \(-0.629837\pi\) |
0.917957 | + | 0.396679i | \(0.129837\pi\) | |||||||
\(542\) | −3.86440 | − | 19.9488i | −0.165990 | − | 0.856875i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.205243 | + | 0.144694i | 0.00879972 | + | 0.00620371i | ||||
\(545\) | −25.1237 | + | 43.5156i | −1.07618 | + | 1.86400i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.1224 | + | 9.94693i | 1.58724 | + | 0.425300i | 0.941158 | − | 0.337967i | \(-0.109739\pi\) |
0.646083 | + | 0.763267i | \(0.276406\pi\) | |||||||
\(548\) | −11.8234 | + | 15.0934i | −0.505070 | + | 0.644757i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.65196 | − | 1.29135i | 0.113080 | − | 0.0550632i | ||||
\(551\) | −9.76675 | + | 5.63884i | −0.416078 | + | 0.240223i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.3477 | + | 7.12897i | 0.525079 | + | 0.303155i | ||||
\(554\) | −11.9695 | − | 0.844692i | −0.508536 | − | 0.0358875i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.2797 | + | 8.47722i | −0.478365 | + | 0.359514i | ||||
\(557\) | 7.00897 | − | 7.00897i | 0.296979 | − | 0.296979i | −0.542850 | − | 0.839830i | \(-0.682655\pi\) |
0.839830 | + | 0.542850i | \(0.182655\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −67.2778 | −2.84555 | ||||||||
\(560\) | −0.508094 | + | 25.3830i | −0.0214709 | + | 1.07263i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.65697 | + | 7.66788i | 0.280807 | + | 0.323450i | ||||
\(563\) | −1.62398 | − | 6.06076i | −0.0684424 | − | 0.255430i | 0.923224 | − | 0.384262i | \(-0.125544\pi\) |
−0.991667 | + | 0.128831i | \(0.958877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.05515 | − | 22.5981i | 0.254742 | − | 0.950711i | ||||
\(566\) | 9.53881 | + | 19.5893i | 0.400946 | + | 0.823399i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.3541 | + | 10.5759i | −0.686202 | + | 0.443753i | ||||
\(569\) | 5.33529 | − | 3.08033i | 0.223667 | − | 0.129134i | −0.383980 | − | 0.923341i | \(-0.625447\pi\) |
0.607647 | + | 0.794207i | \(0.292113\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0529 | − | 4.83727i | 0.755491 | − | 0.202433i | 0.139539 | − | 0.990217i | \(-0.455438\pi\) |
0.615952 | + | 0.787783i | \(0.288771\pi\) | |||||||
\(572\) | 5.03744 | − | 2.02776i | 0.210626 | − | 0.0847847i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.68866 | + | 19.0416i | 0.153962 | + | 0.794780i | ||||
\(575\) | 41.1357 | 1.71548 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.2964 | 0.470277 | 0.235138 | − | 0.971962i | \(-0.424446\pi\) | ||||
0.235138 | + | 0.971962i | \(0.424446\pi\) | |||||||
\(578\) | 4.57172 | + | 23.6001i | 0.190158 | + | 0.981635i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 41.2143 | − | 16.5903i | 1.71133 | − | 0.688875i | ||||
\(581\) | 1.21020 | − | 0.324272i | 0.0502076 | − | 0.0134531i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.38544 | − | 0.799884i | 0.0573790 | − | 0.0331278i | ||||
\(584\) | 31.3422 | − | 20.2684i | 1.29695 | − | 0.838711i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.83850 | − | 20.2047i | −0.406425 | − | 0.834650i | ||||
\(587\) | 9.93836 | − | 37.0905i | 0.410200 | − | 1.53089i | −0.384059 | − | 0.923309i | \(-0.625474\pi\) |
0.794259 | − | 0.607579i | \(-0.207859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.439521 | + | 1.64031i | 0.0181101 | + | 0.0675879i | ||||
\(590\) | −10.6319 | − | 12.2464i | −0.437707 | − | 0.504176i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.34955 | − | 0.0870653i | −0.178766 | − | 0.00357836i | ||||
\(593\) | −7.39166 | −0.303539 | −0.151770 | − | 0.988416i | \(-0.548497\pi\) | ||||
−0.151770 | + | 0.988416i | \(0.548497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.199233 | − | 0.199233i | 0.00816776 | − | 0.00816776i | ||||
\(596\) | 32.2751 | − | 24.2563i | 1.32204 | − | 0.993576i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 75.5419 | + | 5.33101i | 3.08914 | + | 0.218001i | ||||
\(599\) | −22.9017 | − | 13.2223i | −0.935739 | − | 0.540249i | −0.0471171 | − | 0.998889i | \(-0.515003\pi\) |
−0.888622 | + | 0.458640i | \(0.848337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.6284 | + | 19.4154i | −1.37173 | + | 0.791970i | −0.991146 | − | 0.132775i | \(-0.957611\pi\) |
−0.380587 | + | 0.924745i | \(0.624278\pi\) | |||||||
\(602\) | 29.9584 | − | 14.5880i | 1.22101 | − | 0.594561i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.50713 | + | 7.03022i | −0.224082 | + | 0.286056i | ||||
\(605\) | −32.1364 | − | 8.61091i | −1.30653 | − | 0.350083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.86964 | − | 3.23831i | 0.0758863 | − | 0.131439i | −0.825585 | − | 0.564278i | \(-0.809155\pi\) |
0.901471 | + | 0.432839i | \(0.142488\pi\) | |||||||
\(608\) | 8.72839 | − | 1.51026i | 0.353983 | − | 0.0612489i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.01993 | − | 5.26510i | −0.0412959 | − | 0.213178i | ||||
\(611\) | −10.1753 | + | 10.1753i | −0.411648 | + | 0.411648i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.21378 | − | 4.21378i | −0.170193 | − | 0.170193i | 0.616871 | − | 0.787064i | \(-0.288400\pi\) |
−0.787064 | + | 0.616871i | \(0.788400\pi\) | |||||||
\(614\) | −12.2169 | − | 8.25178i | −0.493034 | − | 0.333015i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.80346 | + | 1.99522i | −0.0726635 | + | 0.0803899i | ||||
\(617\) | 19.3833 | + | 11.1910i | 0.780343 | + | 0.450531i | 0.836552 | − | 0.547888i | \(-0.184568\pi\) |
−0.0562088 | + | 0.998419i | \(0.517901\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.10361 | + | 15.3149i | −0.164938 | + | 0.615557i | 0.833110 | + | 0.553107i | \(0.186558\pi\) |
−0.998048 | + | 0.0624496i | \(0.980109\pi\) | |||||||
\(620\) | −0.806794 | − | 6.64110i | −0.0324016 | − | 0.266713i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.32026 | − | 9.62271i | 0.133130 | − | 0.385836i | ||||
\(623\) | 5.45314 | + | 9.44511i | 0.218475 | + | 0.378410i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.5976 | + | 23.5518i | −0.543905 | + | 0.942071i | ||||
\(626\) | 9.88290 | + | 11.3837i | 0.395000 | + | 0.454984i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.7969 | + | 26.3415i | 0.789982 | + | 1.05114i | ||||
\(629\) | 0.0341399 | + | 0.0341399i | 0.00136125 | + | 0.00136125i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.2887i | 1.52425i | 0.647429 | + | 0.762125i | \(0.275844\pi\) | ||||
−0.647429 | + | 0.762125i | \(0.724156\pi\) | |||||||
\(632\) | −8.93068 | + | 17.4445i | −0.355243 | + | 0.693906i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.49647 | + | 21.2054i | −0.0594326 | + | 0.842176i | ||||
\(635\) | 31.6922 | − | 8.49189i | 1.25767 | − | 0.336990i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.6960 | − | 4.20574i | −0.621900 | − | 0.166638i | ||||
\(638\) | 4.44911 | + | 1.53514i | 0.176142 | + | 0.0607767i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −34.8801 | + | 1.06154i | −1.37876 | + | 0.0419611i | ||||
\(641\) | 8.82135 | + | 15.2790i | 0.348422 | + | 0.603485i | 0.985969 | − | 0.166926i | \(-0.0533841\pi\) |
−0.637547 | + | 0.770412i | \(0.720051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.49737 | + | 27.9805i | 0.295667 | + | 1.10345i | 0.940686 | + | 0.339278i | \(0.110183\pi\) |
−0.645019 | + | 0.764167i | \(0.723150\pi\) | |||||||
\(644\) | −34.7943 | + | 14.0060i | −1.37109 | + | 0.551914i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.0814652 | − | 0.0550249i | −0.00320520 | − | 0.00216492i | ||||
\(647\) | 5.73725i | 0.225555i | 0.993620 | + | 0.112777i | \(0.0359747\pi\) | ||||
−0.993620 | + | 0.112777i | \(0.964025\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.71802i | − | 0.0674380i | ||||||
\(650\) | 20.9931 | − | 31.0806i | 0.823417 | − | 1.21908i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.80985 | + | 13.6386i | −0.227531 | + | 0.534127i | ||||
\(653\) | −10.0743 | − | 37.5980i | −0.394239 | − | 1.47132i | −0.823072 | − | 0.567938i | \(-0.807741\pi\) |
0.428832 | − | 0.903384i | \(-0.358925\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.6942 | + | 51.4318i | 1.16025 | + | 2.00961i | ||||
\(656\) | −25.8839 | + | 6.38322i | −1.01060 | + | 0.249223i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.32467 | − | 6.73732i | 0.0906251 | − | 0.262648i | ||||
\(659\) | 38.3072 | + | 10.2644i | 1.49224 | + | 0.399844i | 0.910492 | − | 0.413528i | \(-0.135703\pi\) |
0.581745 | + | 0.813371i | \(0.302370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.49909 | − | 1.47348i | 0.213890 | − | 0.0573116i | −0.150283 | − | 0.988643i | \(-0.548018\pi\) |
0.364173 | + | 0.931331i | \(0.381352\pi\) | |||||||
\(662\) | −35.6089 | − | 2.51293i | −1.38398 | − | 0.0976678i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.529015 | + | 1.63885i | 0.0205298 | + | 0.0635995i | ||||
\(665\) | − | 9.93883i | − | 0.385411i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.4121 | + | 46.4121i | 1.79708 | + | 1.79708i | ||||
\(668\) | −25.8317 | − | 3.66415i | −0.999458 | − | 0.141770i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.8484 | + | 16.3635i | −0.728176 | + | 0.632175i | ||||
\(671\) | 0.284064 | − | 0.492013i | 0.0109662 | − | 0.0189940i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.23206 | − | 3.86604i | −0.0860396 | − | 0.149025i | 0.819794 | − | 0.572658i | \(-0.194088\pi\) |
−0.905834 | + | 0.423633i | \(0.860754\pi\) | |||||||
\(674\) | −4.81855 | − | 1.66261i | −0.185604 | − | 0.0640414i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.5464 | − | 33.8883i | 1.02102 | − | 1.30340i | ||||
\(677\) | −2.16066 | + | 8.06369i | −0.0830409 | + | 0.309913i | −0.994936 | − | 0.100511i | \(-0.967952\pi\) |
0.911895 | + | 0.410423i | \(0.134619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.9681 | − | 12.1060i | −0.804683 | − | 0.464584i | ||||
\(680\) | 0.287306 | + | 0.259693i | 0.0110177 | + | 0.00995876i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.396676 | − | 0.587284i | 0.0151895 | − | 0.0224883i | ||||
\(683\) | −3.00972 | − | 3.00972i | −0.115164 | − | 0.115164i | 0.647177 | − | 0.762340i | \(-0.275950\pi\) |
−0.762340 | + | 0.647177i | \(0.775950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.9082 | + | 20.9082i | −0.798863 | + | 0.798863i | ||||
\(686\) | 27.9004 | − | 5.40475i | 1.06524 | − | 0.206354i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 22.1019 | + | 40.1148i | 0.842627 | + | 1.52936i | ||||
\(689\) | 10.1709 | − | 17.6165i | 0.387480 | − | 0.671135i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5847 | − | 7.65924i | −1.08741 | − | 0.291371i | −0.329783 | − | 0.944057i | \(-0.606976\pi\) |
−0.757629 | + | 0.652686i | \(0.773642\pi\) | |||||||
\(692\) | 2.85232 | − | 0.346514i | 0.108429 | − | 0.0131725i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.88662 | + | 20.3036i | 0.375291 | + | 0.770713i | ||||
\(695\) | −18.8453 | + | 10.8804i | −0.714844 | + | 0.412715i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.256228 | + | 0.147933i | 0.00970532 | + | 0.00560337i | ||||
\(698\) | −1.55965 | + | 22.1007i | −0.0590337 | + | 0.836524i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.60885 | + | 18.3920i | −0.0986052 | + | 0.695152i | ||||
\(701\) | 1.29990 | − | 1.29990i | 0.0490966 | − | 0.0490966i | −0.682132 | − | 0.731229i | \(-0.738947\pi\) |
0.731229 | + | 0.682132i | \(0.238947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.70309 | 0.0642331 | ||||||||
\(704\) | −2.86395 | − | 2.33745i | −0.107939 | − | 0.0880960i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.39077 | + | 3.81191i | −0.165249 | + | 0.143463i | ||||
\(707\) | 3.11678 | + | 11.6320i | 0.117219 | + | 0.437466i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.80720 | − | 36.6010i | 0.368317 | − | 1.37458i | −0.494551 | − | 0.869149i | \(-0.664667\pi\) |
0.862868 | − | 0.505429i | \(-0.168666\pi\) | |||||||
\(710\) | −27.0043 | + | 13.1495i | −1.01345 | + | 0.493491i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.5880 | + | 8.14040i | −0.471755 | + | 0.305074i | ||||
\(713\) | 8.55933 | − | 4.94173i | 0.320550 | − | 0.185069i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.08922 | − | 2.16750i | 0.302520 | − | 0.0810599i | ||||
\(716\) | −2.77978 | + | 6.52550i | −0.103885 | + | 0.243869i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.0322 | − | 5.43028i | 1.04615 | − | 0.202656i | ||||
\(719\) | −5.11125 | −0.190617 | −0.0953087 | − | 0.995448i | \(-0.530384\pi\) | ||||
−0.0953087 | + | 0.995448i | \(0.530384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.70117 | 0.100597 | ||||||||
\(722\) | 22.9752 | − | 4.45067i | 0.855049 | − | 0.165637i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28.3102 | − | 12.0598i | −1.05214 | − | 0.448198i | ||||
\(725\) | 31.3997 | − | 8.41353i | 1.16616 | − | 0.312471i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.6355 | + | 10.7592i | −0.691154 | + | 0.399038i | −0.804044 | − | 0.594570i | \(-0.797322\pi\) |
0.112890 | + | 0.993607i | \(0.463989\pi\) | |||||||
\(728\) | −7.17444 | + | 33.4371i | −0.265902 | + | 1.23926i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 51.7531 | − | 25.2007i | 1.91547 | − | 0.932719i | ||||
\(731\) | 0.131557 | − | 0.490976i | 0.00486580 | − | 0.0181594i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.799079 | − | 2.98220i | −0.0295147 | − | 0.110150i | 0.949597 | − | 0.313473i | \(-0.101493\pi\) |
−0.979112 | + | 0.203323i | \(0.934826\pi\) | |||||||
\(734\) | 24.0063 | − | 20.8414i | 0.886090 | − | 0.769271i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.6382 | − | 46.7937i | −0.797593 | − | 1.72484i | ||||
\(737\) | −2.64419 | −0.0973999 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.9990 | − | 23.9990i | 0.882818 | − | 0.882818i | −0.111002 | − | 0.993820i | \(-0.535406\pi\) |
0.993820 | + | 0.111002i | \(0.0354060\pi\) | |||||||
\(740\) | −6.64277 | − | 0.942257i | −0.244193 | − | 0.0346381i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.709223 | + | 10.0499i | −0.0260364 | + | 0.368943i | ||||
\(743\) | −14.4499 | − | 8.34266i | −0.530116 | − | 0.306062i | 0.210948 | − | 0.977497i | \(-0.432345\pi\) |
−0.741064 | + | 0.671435i | \(0.765678\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.9230 | − | 31.1325i | 1.97559 | − | 1.14061i | ||||
\(746\) | 16.4438 | + | 33.7697i | 0.602051 | + | 1.23640i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.00494772 | + | 0.0407271i | 0.000180907 | + | 0.00148913i | ||||
\(749\) | 8.23519 | + | 2.20661i | 0.300907 | + | 0.0806278i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.1635 | − | 29.7281i | 0.626305 | − | 1.08479i | −0.361982 | − | 0.932185i | \(-0.617900\pi\) |
0.988287 | − | 0.152607i | \(-0.0487669\pi\) | |||||||
\(752\) | 9.40983 | + | 2.72433i | 0.343141 | + | 0.0993460i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 58.7531 | − | 11.3814i | 2.13966 | − | 0.414487i | ||||
\(755\) | −9.73869 | + | 9.73869i | −0.354427 | + | 0.354427i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.0162 | − | 24.0162i | −0.872884 | − | 0.872884i | 0.119902 | − | 0.992786i | \(-0.461742\pi\) |
−0.992786 | + | 0.119902i | \(0.961742\pi\) | |||||||
\(758\) | −7.42061 | + | 10.9863i | −0.269529 | + | 0.399041i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.6437 | − | 0.688757i | 0.494907 | − | 0.0249838i | ||||
\(761\) | −13.2713 | − | 7.66221i | −0.481086 | − | 0.277755i | 0.239783 | − | 0.970826i | \(-0.422924\pi\) |
−0.720869 | + | 0.693072i | \(0.756257\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.67629 | − | 32.3804i | 0.314103 | − | 1.17225i | ||||
\(764\) | −20.7583 | − | 16.2610i | −0.751010 | − | 0.588303i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.31813 | + | 1.83499i | 0.192152 | + | 0.0663009i | ||||
\(767\) | −10.9227 | − | 18.9186i | −0.394395 | − | 0.683112i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.6394 | − | 35.7485i | 0.744276 | − | 1.28912i | −0.206256 | − | 0.978498i | \(-0.566128\pi\) |
0.950532 | − | 0.310626i | \(-0.100539\pi\) | |||||||
\(770\) | −3.13210 | + | 2.71917i | −0.112873 | + | 0.0979923i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.89750 | + | 34.5267i | −0.176265 | + | 1.24264i | ||||
\(773\) | −36.3711 | − | 36.3711i | −1.30818 | − | 1.30818i | −0.922730 | − | 0.385448i | \(-0.874047\pi\) |
−0.385448 | − | 0.922730i | \(-0.625953\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.89492i | − | 0.175831i | ||||||
\(776\) | 15.1655 | − | 29.6232i | 0.544410 | − | 1.06341i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.64131 | + | 0.468679i | 0.238103 | + | 0.0168030i | ||||
\(779\) | 10.0809 | − | 2.70117i | 0.361185 | − | 0.0967793i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.07342 | − | 0.823519i | −0.109975 | − | 0.0294678i | ||||
\(782\) | −0.186621 | + | 0.540861i | −0.00667355 | + | 0.0193412i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.64872 | + | 10.7405i | 0.0945970 | + | 0.383590i | ||||
\(785\) | 25.4089 | + | 44.0096i | 0.906883 | + | 1.57077i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.98650 | − | 29.8060i | −0.284688 | − | 1.06247i | −0.949067 | − | 0.315074i | \(-0.897971\pi\) |
0.664379 | − | 0.747396i | \(-0.268696\pi\) | |||||||
\(788\) | −21.7613 | − | 9.27001i | −0.775213 | − | 0.330230i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.9169 | + | 25.0458i | −0.601877 | + | 0.891089i | ||||
\(791\) | 15.6082i | 0.554963i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.22401i | − | 0.256532i | ||||||
\(794\) | 30.0580 | + | 20.3024i | 1.06672 | + | 0.720504i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.6820 | + | 29.0210i | 0.414059 | + | 1.02862i | ||||
\(797\) | −6.90917 | − | 25.7854i | −0.244735 | − | 0.913364i | −0.973516 | − | 0.228617i | \(-0.926580\pi\) |
0.728781 | − | 0.684747i | \(-0.240087\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0543596 | − | 0.0941536i | −0.00192311 | − | 0.00333092i | ||||
\(800\) | −25.4286 | − | 2.30677i | −0.899037 | − | 0.0815566i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.61819 | − | 2.28357i | −0.233697 | − | 0.0806356i | ||||
\(803\) | 5.89013 | + | 1.57826i | 0.207858 | + | 0.0556954i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −55.8735 | + | 14.9712i | −1.96928 | + | 0.527667i | ||||
\(806\) | 0.634361 | − | 8.98908i | 0.0223444 | − | 0.316627i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.7520 | + | 5.08469i | −0.554152 | + | 0.178879i | ||||
\(809\) | − | 41.9379i | − | 1.47446i | −0.675644 | − | 0.737228i | \(-0.736134\pi\) | ||
0.675644 | − | 0.737228i | \(-0.263866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.250947 | + | 0.250947i | 0.00881196 | + | 0.00881196i | 0.711499 | − | 0.702687i | \(-0.248017\pi\) |
−0.702687 | + | 0.711499i | \(0.748017\pi\) | |||||||
\(812\) | −23.6946 | + | 17.8076i | −0.831517 | + | 0.624925i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.465949 | − | 0.536706i | −0.0163315 | − | 0.0188116i | ||||
\(815\) | −11.4312 | + | 19.7994i | −0.400418 | + | 0.693544i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.96490 | − | 15.5277i | −0.313642 | − | 0.543244i | ||||
\(818\) | −6.62548 | + | 19.2018i | −0.231654 | + | 0.671377i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −40.8143 | + | 4.95832i | −1.42530 | + | 0.173152i | ||||
\(821\) | 5.03635 | − | 18.7959i | 0.175770 | − | 0.655982i | −0.820650 | − | 0.571432i | \(-0.806388\pi\) |
0.996419 | − | 0.0845497i | \(-0.0269452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.7295 | − | 20.0511i | −1.21059 | − | 0.698936i | −0.247705 | − | 0.968836i | \(-0.579676\pi\) |
−0.962889 | + | 0.269899i | \(0.913010\pi\) | |||||||
\(824\) | 0.187190 | + | 3.70806i | 0.00652107 | + | 0.129176i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.96597 | + | 6.05598i | 0.311966 | + | 0.210714i | ||||
\(827\) | 39.0429 | + | 39.0429i | 1.35765 | + | 1.35765i | 0.876801 | + | 0.480853i | \(0.159673\pi\) |
0.480853 | + | 0.876801i | \(0.340327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.5103 | + | 18.5103i | −0.642891 | + | 0.642891i | −0.951265 | − | 0.308374i | \(-0.900215\pi\) |
0.308374 | + | 0.951265i | \(0.400215\pi\) | |||||||
\(830\) | 0.505092 | + | 2.60739i | 0.0175320 | + | 0.0905037i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −46.3984 | − | 7.53161i | −1.60858 | − | 0.261112i | ||||
\(833\) | 0.0613849 | − | 0.106322i | 0.00212686 | − | 0.00368383i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.8656 | − | 10.4140i | −1.34500 | − | 0.360392i | ||||
\(836\) | 1.13925 | + | 0.892435i | 0.0394019 | + | 0.0308655i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 32.1524 | − | 15.6563i | 1.11069 | − | 0.540837i | ||||
\(839\) | −9.12331 | + | 5.26735i | −0.314972 | + | 0.181849i | −0.649149 | − | 0.760661i | \(-0.724875\pi\) |
0.334177 | + | 0.942510i | \(0.391542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.8053 | + | 11.4346i | 0.682942 | + | 0.394297i | ||||
\(842\) | −7.25638 | − | 0.512085i | −0.250072 | − | 0.0176476i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.2530 | − | 30.9401i | −0.800401 | − | 1.06500i | ||||
\(845\) | 46.9442 | − | 46.9442i | 1.61493 | − | 1.61493i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.1961 | 0.762667 | ||||||||
\(848\) | −13.8453 | − | 0.277141i | −0.475448 | − | 0.00951707i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.185768 | + | 0.213978i | 0.00637179 | + | 0.00733939i | ||||
\(851\) | −2.56542 | − | 9.57429i | −0.0879416 | − | 0.328203i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.50035 | − | 31.7237i | 0.291046 | − | 1.08620i | −0.653260 | − | 0.757133i | \(-0.726599\pi\) |
0.944307 | − | 0.329067i | \(-0.106734\pi\) | |||||||
\(854\) | 1.56639 | + | 3.21681i | 0.0536009 | + | 0.110077i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.45846 | + | 11.4579i | −0.0840283 | + | 0.391622i | ||||
\(857\) | −32.9302 | + | 19.0123i | −1.12487 | + | 0.649447i | −0.942641 | − | 0.333808i | \(-0.891666\pi\) |
−0.182234 | + | 0.983255i | \(0.558333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.8849 | + | 11.2230i | −1.42910 | + | 0.382925i | −0.888701 | − | 0.458487i | \(-0.848392\pi\) |
−0.540395 | + | 0.841412i | \(0.681725\pi\) | |||||||
\(860\) | 26.3761 | + | 65.5246i | 0.899418 | + | 2.23437i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.40365 | + | 27.8947i | 0.184049 | + | 0.950097i | ||||
\(863\) | 19.8437 | 0.675487 | 0.337744 | − | 0.941238i | \(-0.390336\pi\) | ||||
0.337744 | + | 0.941238i | \(0.390336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.43121 | 0.150666 | ||||||||
\(866\) | −5.87027 | − | 30.3035i | −0.199480 | − | 1.02975i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.66664 | + | 4.14033i | 0.0565694 | + | 0.140532i | ||||
\(869\) | −3.09266 | + | 0.828675i | −0.104911 | + | 0.0281109i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.1176 | + | 16.8110i | −0.986611 | + | 0.569620i | ||||
\(872\) | 45.0518 | + | 9.66654i | 1.52565 | + | 0.327350i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.83573 | + | 18.1454i | 0.298873 | + | 0.613778i | ||||
\(875\) | 0.798951 | − | 2.98173i | 0.0270095 | − | 0.100801i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.2670 | − | 49.5131i | −0.447995 | − | 1.67194i | −0.707906 | − | 0.706307i | \(-0.750360\pi\) |
0.259911 | − | 0.965633i | \(-0.416307\pi\) | |||||||
\(878\) | −27.5724 | − | 31.7595i | −0.930525 | − | 1.07183i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.94983 | − | 4.11119i | −0.133149 | − | 0.138588i | ||||
\(881\) | 31.7902 | 1.07104 | 0.535519 | − | 0.844523i | \(-0.320116\pi\) | ||||
0.535519 | + | 0.844523i | \(0.320116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.7423 | − | 28.7423i | 0.967255 | − | 0.967255i | −0.0322259 | − | 0.999481i | \(-0.510260\pi\) |
0.999481 | + | 0.0322259i | \(0.0102596\pi\) | |||||||
\(884\) | 0.313415 | + | 0.417026i | 0.0105413 | + | 0.0140261i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.3909 | − | 3.48553i | −1.65932 | − | 0.117099i | ||||
\(887\) | 23.1996 | + | 13.3943i | 0.778966 | + | 0.449736i | 0.836064 | − | 0.548632i | \(-0.184851\pi\) |
−0.0570976 | + | 0.998369i | \(0.518185\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.9567 | + | 10.9447i | −0.635787 | + | 0.367072i | ||||
\(890\) | −20.7856 | + | 10.1214i | −0.696736 | + | 0.339269i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.54309 | + | 5.12553i | 0.219079 | + | 0.171615i | ||||
\(893\) | −3.70433 | − | 0.992572i | −0.123961 | − | 0.0332151i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.46938 | + | 9.47324i | −0.182821 | + | 0.316655i | ||||
\(896\) | 22.2940 | − | 6.70686i | 0.744792 | − | 0.224060i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.44484 | + | 38.4318i | 0.248438 | + | 1.28248i | ||||
\(899\) | 5.52278 | − | 5.52278i | 0.184195 | − | 0.184195i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.108672 | + | 0.108672i | 0.00362040 | + | 0.00362040i | ||||
\(902\) | −3.60928 | − | 2.43785i | −0.120176 | − | 0.0811716i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.4263 | + | 1.08164i | −0.712629 | + | 0.0359749i | ||||
\(905\) | −41.0986 | − | 23.7283i | −1.36616 | − | 0.788756i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.28704 | − | 15.9995i | 0.142349 | − | 0.531253i | −0.857510 | − | 0.514467i | \(-0.827990\pi\) |
0.999859 | − | 0.0167863i | \(-0.00534350\pi\) | |||||||
\(908\) | 12.8050 | − | 1.55562i | 0.424950 | − | 0.0516251i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17.2026 | + | 49.8563i | −0.570262 | + | 1.65272i | ||||
\(911\) | −0.940538 | − | 1.62906i | −0.0311614 | − | 0.0539731i | 0.850024 | − | 0.526744i | \(-0.176587\pi\) |
−0.881186 | + | 0.472771i | \(0.843254\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.140674 | + | 0.243655i | −0.00465564 | + | 0.00806381i | ||||
\(914\) | −14.7858 | − | 17.0311i | −0.489071 | − | 0.563340i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.5254 | − | 11.6681i | 0.512975 | − | 0.385526i | ||||
\(917\) | −28.0162 | − | 28.0162i | −0.925177 | − | 0.925177i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.7898i | 1.93930i | 0.244501 | + | 0.969649i | \(0.421376\pi\) | ||||
−0.244501 | + | 0.969649i | \(0.578624\pi\) | |||||||
\(920\) | −24.4240 | − | 75.6635i | −0.805234 | − | 2.49455i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.87345 | − | 26.5474i | 0.0616989 | − | 0.874291i | ||||
\(923\) | −39.0799 | + | 10.4714i | −1.28633 | + | 0.344671i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.74180 | − | 1.27056i | −0.155909 | − | 0.0417758i | ||||
\(926\) | −16.2437 | − | 5.60480i | −0.533802 | − | 0.184185i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.0876 | − | 31.2930i | −0.856369 | − | 1.02724i | ||||
\(929\) | −17.0265 | − | 29.4908i | −0.558622 | − | 0.967562i | −0.997612 | − | 0.0690699i | \(-0.977997\pi\) |
0.438990 | − | 0.898492i | \(-0.355336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.12085 | − | 4.18306i | −0.0367343 | − | 0.137094i | ||||
\(932\) | 16.5870 | + | 41.2060i | 0.543324 | + | 1.34975i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.4676 | − | 17.8773i | −0.866047 | − | 0.584963i | ||||
\(935\) | 0.0632715i | 0.00206920i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.8098i | − | 0.777833i | −0.921273 | − | 0.388916i | \(-0.872849\pi\) | ||
0.921273 | − | 0.388916i | \(-0.127151\pi\) | |||||||
\(938\) | 9.32072 | − | 13.7995i | 0.304332 | − | 0.450569i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.8993 | + | 5.92093i | 0.453346 | + | 0.193120i | ||||
\(941\) | −3.51153 | − | 13.1052i | −0.114473 | − | 0.427217i | 0.884774 | − | 0.466020i | \(-0.154312\pi\) |
−0.999247 | + | 0.0388023i | \(0.987646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.3705 | − | 52.6032i | −0.988998 | − | 1.71300i | ||||
\(944\) | −7.69208 | + | 12.7278i | −0.250356 | + | 0.414255i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.44064 | + | 7.07341i | −0.0793519 | + | 0.229976i | ||||
\(947\) | 19.1830 | + | 5.14006i | 0.623363 | + | 0.167030i | 0.556656 | − | 0.830743i | \(-0.312084\pi\) |
0.0667069 | + | 0.997773i | \(0.478751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 74.8957 | − | 20.0682i | 2.43122 | − | 0.651442i | ||||
\(950\) | 9.97076 | + | 0.703639i | 0.323494 | + | 0.0228291i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.229987 | − | 0.117741i | −0.00745391 | − | 0.00381601i | ||||
\(953\) | − | 13.2336i | − | 0.428678i | −0.976759 | − | 0.214339i | \(-0.931240\pi\) | ||
0.976759 | − | 0.214339i | \(-0.0687598\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.7557 | − | 28.7557i | −0.930512 | − | 0.930512i | ||||
\(956\) | −2.26236 | + | 15.9493i | −0.0731698 | + | 0.515837i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.8043 | − | 17.1933i | 0.639847 | − | 0.555492i | ||||
\(959\) | 9.86339 | − | 17.0839i | 0.318506 | − | 0.551668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9120 | + | 25.8283i | 0.481031 | + | 0.833170i | ||||
\(962\) | −8.54322 | − | 2.94779i | −0.275444 | − | 0.0950404i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.9854 | − | 12.5222i | −0.514855 | − | 0.403312i | ||||
\(965\) | −13.9194 | + | 51.9479i | −0.448081 | + | 1.67226i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.2656 | + | 26.1341i | 1.45564 | + | 0.840417i | 0.998793 | − | 0.0491262i | \(-0.0156437\pi\) |
0.456852 | + | 0.889543i | \(0.348977\pi\) | |||||||
\(968\) | 1.53818 | + | 30.4699i | 0.0494390 | + | 0.979341i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 28.7273 | − | 42.5312i | 0.922377 | − | 1.36559i | ||||
\(971\) | 33.2081 | + | 33.2081i | 1.06570 | + | 1.06570i | 0.997684 | + | 0.0680139i | \(0.0216662\pi\) |
0.0680139 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.2655 | − | 10.2655i | 0.329098 | − | 0.329098i | ||||
\(974\) | 9.14728 | − | 1.77197i | 0.293098 | − | 0.0567777i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.30736 | + | 2.37321i | −0.137875 | + | 0.0759646i | ||||
\(977\) | −15.0366 | + | 26.0441i | −0.481063 | + | 0.833226i | −0.999764 | − | 0.0217300i | \(-0.993083\pi\) |
0.518701 | + | 0.854956i | \(0.326416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.36566 | − | 0.633876i | −0.0756067 | − | 0.0202588i | ||||
\(980\) | 2.05745 | + | 16.9359i | 0.0657230 | + | 0.540997i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.11746 | − | 6.40214i | −0.0994822 | − | 0.204301i | ||||
\(983\) | 18.8575 | − | 10.8874i | 0.601460 | − | 0.347253i | −0.168155 | − | 0.985760i | \(-0.553781\pi\) |
0.769616 | + | 0.638507i | \(0.220448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.5914 | − | 18.2393i | −1.00658 | − | 0.581152i | ||||
\(986\) | −0.0318287 | + | 0.451021i | −0.00101363 | + | 0.0143634i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.2192 | + | 2.58434i | 0.579631 | + | 0.0822188i | ||||
\(989\) | −73.7882 | + | 73.7882i | −2.34633 | + | 2.34633i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5288 | 0.683884 | 0.341942 | − | 0.939721i | \(-0.388915\pi\) | ||||
0.341942 | + | 0.939721i | \(0.388915\pi\) | |||||||
\(992\) | −5.56820 | + | 2.57482i | −0.176790 | + | 0.0817507i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.1315 | − | 13.1366i | 0.479943 | − | 0.416669i | ||||
\(995\) | 12.4871 | + | 46.6025i | 0.395868 | + | 1.47740i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.21836 | + | 30.6713i | −0.260278 | + | 0.971371i | 0.704799 | + | 0.709407i | \(0.251037\pi\) |
−0.965078 | + | 0.261964i | \(0.915630\pi\) | |||||||
\(998\) | 27.6094 | − | 13.4441i | 0.873960 | − | 0.425566i | ||||
\(999\) | 0 | 0 |
(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 | 432.2.y.e.37.8 | 72 | ||
3.2 | odd | 2 | 144.2.x.e.85.11 | yes | 72 | ||
4.3 | odd | 2 | 1728.2.bc.e.1009.3 | 72 | |||
9.2 | odd | 6 | 144.2.x.e.133.14 | yes | 72 | ||
9.7 | even | 3 | inner | 432.2.y.e.181.5 | 72 | ||
12.11 | even | 2 | 576.2.bb.e.49.9 | 72 | |||
16.3 | odd | 4 | 1728.2.bc.e.145.16 | 72 | |||
16.13 | even | 4 | inner | 432.2.y.e.253.5 | 72 | ||
36.7 | odd | 6 | 1728.2.bc.e.1585.16 | 72 | |||
36.11 | even | 6 | 576.2.bb.e.241.2 | 72 | |||
48.29 | odd | 4 | 144.2.x.e.13.14 | ✓ | 72 | ||
48.35 | even | 4 | 576.2.bb.e.337.2 | 72 | |||
144.29 | odd | 12 | 144.2.x.e.61.11 | yes | 72 | ||
144.61 | even | 12 | inner | 432.2.y.e.397.8 | 72 | ||
144.83 | even | 12 | 576.2.bb.e.529.9 | 72 | |||
144.115 | odd | 12 | 1728.2.bc.e.721.3 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.14 | ✓ | 72 | 48.29 | odd | 4 | ||
144.2.x.e.61.11 | yes | 72 | 144.29 | odd | 12 | ||
144.2.x.e.85.11 | yes | 72 | 3.2 | odd | 2 | ||
144.2.x.e.133.14 | yes | 72 | 9.2 | odd | 6 | ||
432.2.y.e.37.8 | 72 | 1.1 | even | 1 | trivial | ||
432.2.y.e.181.5 | 72 | 9.7 | even | 3 | inner | ||
432.2.y.e.253.5 | 72 | 16.13 | even | 4 | inner | ||
432.2.y.e.397.8 | 72 | 144.61 | even | 12 | inner | ||
576.2.bb.e.49.9 | 72 | 12.11 | even | 2 | |||
576.2.bb.e.241.2 | 72 | 36.11 | even | 6 | |||
576.2.bb.e.337.2 | 72 | 48.35 | even | 4 | |||
576.2.bb.e.529.9 | 72 | 144.83 | even | 12 | |||
1728.2.bc.e.145.16 | 72 | 16.3 | odd | 4 | |||
1728.2.bc.e.721.3 | 72 | 144.115 | odd | 12 | |||
1728.2.bc.e.1009.3 | 72 | 4.3 | odd | 2 | |||
1728.2.bc.e.1585.16 | 72 | 36.7 | odd | 6 |