Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(37,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.t (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(204\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 253.7 | ||
Character | \(\chi\) | \(=\) | 648.253 |
Dual form | 648.2.t.a.397.7 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.08004 | + | 0.912975i | −0.763701 | + | 0.645571i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.332954 | − | 1.97209i | 0.166477 | − | 0.986045i | ||||
\(5\) | −0.114718 | + | 0.136716i | −0.0513035 | + | 0.0611411i | −0.791086 | − | 0.611705i | \(-0.790484\pi\) |
0.739782 | + | 0.672846i | \(0.234928\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.42085 | + | 0.881117i | 0.914995 | + | 0.333031i | 0.756245 | − | 0.654288i | \(-0.227032\pi\) |
0.158749 | + | 0.987319i | \(0.449254\pi\) | |||||||
\(8\) | 1.44087 | + | 2.43391i | 0.509423 | + | 0.860516i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.000918366 | − | 0.252392i | −0.000290413 | − | 0.0798135i | ||||
\(11\) | 0.599296 | + | 0.714213i | 0.180695 | + | 0.215343i | 0.848787 | − | 0.528735i | \(-0.177333\pi\) |
−0.668093 | + | 0.744078i | \(0.732889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.368417 | − | 0.0649618i | −0.102180 | − | 0.0180172i | 0.122324 | − | 0.992490i | \(-0.460965\pi\) |
−0.224505 | + | 0.974473i | \(0.572076\pi\) | |||||||
\(14\) | −3.41904 | + | 1.25854i | −0.913777 | + | 0.336358i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.77828 | − | 1.31323i | −0.944571 | − | 0.328308i | ||||
\(17\) | 2.26254 | − | 3.91883i | 0.548746 | − | 0.950456i | −0.449615 | − | 0.893223i | \(-0.648439\pi\) |
0.998361 | − | 0.0572337i | \(-0.0182280\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.97566 | − | 1.14065i | 0.453246 | − | 0.261682i | −0.255954 | − | 0.966689i | \(-0.582390\pi\) |
0.709200 | + | 0.705007i | \(0.249056\pi\) | |||||||
\(20\) | 0.231420 | + | 0.271754i | 0.0517470 | + | 0.0607661i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.29932 | − | 0.224233i | −0.277016 | − | 0.0478067i | ||||
\(23\) | −4.40423 | + | 1.60301i | −0.918345 | + | 0.334250i | −0.757580 | − | 0.652742i | \(-0.773618\pi\) |
−0.160765 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.862710 | + | 4.89267i | 0.172542 | + | 0.978534i | ||||
\(26\) | 0.457212 | − | 0.266194i | 0.0896666 | − | 0.0522050i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.54367 | − | 4.48076i | 0.480709 | − | 0.846785i | ||||
\(29\) | 1.58682 | − | 0.279799i | 0.294665 | − | 0.0519574i | −0.0243613 | − | 0.999703i | \(-0.507755\pi\) |
0.319026 | + | 0.947746i | \(0.396644\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.17965 | − | 2.97715i | 1.46911 | − | 0.534712i | 0.521250 | − | 0.853404i | \(-0.325466\pi\) |
0.947858 | + | 0.318692i | \(0.103244\pi\) | |||||||
\(32\) | 5.27963 | − | 2.03114i | 0.933315 | − | 0.359059i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.13417 | + | 6.29812i | 0.194509 | + | 1.08012i | ||||
\(35\) | −0.398177 | + | 0.229888i | −0.0673043 | + | 0.0388581i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.82721 | + | 2.20964i | 0.629190 | + | 0.363263i | 0.780438 | − | 0.625233i | \(-0.214996\pi\) |
−0.151248 | + | 0.988496i | \(0.548329\pi\) | |||||||
\(38\) | −1.09240 | + | 3.03566i | −0.177210 | + | 0.492449i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.498046 | − | 0.0822239i | −0.0787481 | − | 0.0130007i | ||||
\(41\) | −0.238139 | + | 1.35055i | −0.0371910 | + | 0.210921i | −0.997740 | − | 0.0671892i | \(-0.978597\pi\) |
0.960549 | + | 0.278110i | \(0.0897080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.28437 | + | 3.91416i | 0.500862 | + | 0.596904i | 0.955945 | − | 0.293545i | \(-0.0948350\pi\) |
−0.455083 | + | 0.890449i | \(0.650391\pi\) | |||||||
\(44\) | 1.60803 | − | 0.944066i | 0.242420 | − | 0.142323i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.29322 | − | 5.75225i | 0.485558 | − | 0.848124i | ||||
\(47\) | 7.70413 | + | 2.80407i | 1.12376 | + | 0.409016i | 0.836024 | − | 0.548693i | \(-0.184874\pi\) |
0.287738 | + | 0.957709i | \(0.407097\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.278168 | − | 0.233411i | −0.0397383 | − | 0.0333444i | ||||
\(50\) | −5.39864 | − | 4.49663i | −0.763483 | − | 0.635919i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.250776 | + | 0.704922i | −0.0347764 | + | 0.0977551i | ||||
\(53\) | 9.07829i | 1.24700i | 0.781824 | + | 0.623500i | \(0.214290\pi\) | ||||
−0.781824 | + | 0.623500i | \(0.785710\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.166394 | −0.0224366 | ||||||||
\(56\) | 1.34357 | + | 7.16169i | 0.179541 | + | 0.957022i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.45837 | + | 1.75092i | −0.191494 | + | 0.229907i | ||||
\(59\) | 9.44865 | − | 11.2605i | 1.23011 | − | 1.46599i | 0.392469 | − | 0.919765i | \(-0.371621\pi\) |
0.837641 | − | 0.546222i | \(-0.183934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.07860 | + | 13.9533i | −0.650247 | + | 1.78654i | −0.0334206 | + | 0.999441i | \(0.510640\pi\) |
−0.616827 | + | 0.787099i | \(0.711582\pi\) | |||||||
\(62\) | −6.11625 | + | 10.6832i | −0.776765 | + | 1.35677i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.84780 | + | 7.01387i | −0.480975 | + | 0.876734i | ||||
\(65\) | 0.0511453 | − | 0.0429160i | 0.00634380 | − | 0.00532308i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.72274 | − | 0.303765i | −0.210466 | − | 0.0371108i | 0.0674209 | − | 0.997725i | \(-0.478523\pi\) |
−0.277887 | + | 0.960614i | \(0.589634\pi\) | |||||||
\(68\) | −6.97497 | − | 5.76672i | −0.845840 | − | 0.699318i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.220164 | − | 0.611813i | 0.0263146 | − | 0.0731256i | ||||
\(71\) | −2.77372 | + | 4.80422i | −0.329180 | + | 0.570156i | −0.982349 | − | 0.187055i | \(-0.940106\pi\) |
0.653169 | + | 0.757212i | \(0.273439\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.77001 | − | 8.26190i | −0.558287 | − | 0.966982i | −0.997640 | − | 0.0686670i | \(-0.978125\pi\) |
0.439352 | − | 0.898315i | \(-0.355208\pi\) | |||||||
\(74\) | −6.15087 | + | 1.10766i | −0.715024 | + | 0.128762i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.59165 | − | 4.27595i | −0.182575 | − | 0.490486i | ||||
\(77\) | 0.821500 | + | 2.25705i | 0.0936186 | + | 0.257215i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.704340 | − | 3.99451i | −0.0792444 | − | 0.449417i | −0.998451 | − | 0.0556413i | \(-0.982280\pi\) |
0.919206 | − | 0.393776i | \(-0.128831\pi\) | |||||||
\(80\) | 0.612976 | − | 0.365899i | 0.0685328 | − | 0.0409088i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.975822 | − | 1.67606i | −0.107761 | − | 0.185090i | ||||
\(83\) | 15.0319 | − | 2.65052i | 1.64996 | − | 0.290933i | 0.730148 | − | 0.683289i | \(-0.239451\pi\) |
0.919813 | + | 0.392357i | \(0.128340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.276212 | + | 0.758885i | 0.0299594 | + | 0.0823126i | ||||
\(86\) | −7.12077 | − | 1.22889i | −0.767852 | − | 0.132514i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.874822 | + | 2.48772i | −0.0932564 | + | 0.265191i | ||||
\(89\) | −8.16359 | − | 14.1397i | −0.865339 | − | 1.49881i | −0.866711 | − | 0.498811i | \(-0.833770\pi\) |
0.00137211 | − | 0.999999i | \(-0.499563\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.834643 | − | 0.481881i | −0.0874943 | − | 0.0505149i | ||||
\(92\) | 1.69487 | + | 9.21926i | 0.176703 | + | 0.961175i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.8808 | + | 4.00518i | −1.12227 | + | 0.413102i | ||||
\(95\) | −0.0706993 | + | 0.400955i | −0.00725359 | + | 0.0411372i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.94677 | + | 7.50723i | −0.908407 | + | 0.762244i | −0.971815 | − | 0.235744i | \(-0.924247\pi\) |
0.0634084 | + | 0.997988i | \(0.479803\pi\) | |||||||
\(98\) | 0.513530 | − | 0.00186855i | 0.0518744 | − | 0.000188752i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.93603 | − | 0.0723083i | 0.993603 | − | 0.00723083i | ||||
\(101\) | −0.733566 | + | 2.01546i | −0.0729926 | + | 0.200545i | −0.970824 | − | 0.239795i | \(-0.922920\pi\) |
0.897831 | + | 0.440340i | \(0.145142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.97851 | + | 7.53386i | 0.884679 | + | 0.742334i | 0.967136 | − | 0.254261i | \(-0.0818322\pi\) |
−0.0824568 | + | 0.996595i | \(0.526277\pi\) | |||||||
\(104\) | −0.372729 | − | 0.990294i | −0.0365491 | − | 0.0971063i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.28825 | − | 9.80488i | −0.805026 | − | 0.952334i | ||||
\(107\) | 7.40373i | 0.715745i | 0.933770 | + | 0.357873i | \(0.116498\pi\) | ||||
−0.933770 | + | 0.357873i | \(0.883502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.2321i | 1.26741i | 0.773575 | + | 0.633704i | \(0.218466\pi\) | ||||
−0.773575 | + | 0.633704i | \(0.781534\pi\) | |||||||
\(110\) | 0.179712 | − | 0.151914i | 0.0171348 | − | 0.0144844i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.98954 | − | 6.50824i | −0.754941 | − | 0.614971i | ||||
\(113\) | 7.02588 | + | 5.89541i | 0.660939 | + | 0.554594i | 0.910368 | − | 0.413799i | \(-0.135799\pi\) |
−0.249429 | + | 0.968393i | \(0.580243\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.286088 | − | 0.786020i | 0.0266778 | − | 0.0732968i | ||||
\(116\) | −0.0234515 | − | 3.22251i | −0.00217741 | − | 0.299203i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.0756404 | + | 20.7881i | 0.00696326 | + | 1.91370i | ||||
\(119\) | 8.93021 | − | 7.49334i | 0.818631 | − | 0.686913i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.75919 | − | 9.97684i | 0.159926 | − | 0.906985i | ||||
\(122\) | −7.25397 | − | 19.7067i | −0.656744 | − | 1.78416i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.14776 | − | 17.1223i | −0.282677 | − | 1.53762i | ||||
\(125\) | −1.54067 | − | 0.889506i | −0.137802 | − | 0.0795598i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.58464 | − | 16.6011i | −0.850500 | − | 1.47311i | −0.880758 | − | 0.473567i | \(-0.842966\pi\) |
0.0302583 | − | 0.999542i | \(-0.490367\pi\) | |||||||
\(128\) | −2.24772 | − | 11.0882i | −0.198673 | − | 0.980066i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0160575 | + | 0.0930453i | −0.00140834 | + | 0.00816061i | ||||
\(131\) | 0.312406 | + | 0.858328i | 0.0272950 | + | 0.0749924i | 0.952592 | − | 0.304252i | \(-0.0984063\pi\) |
−0.925297 | + | 0.379244i | \(0.876184\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.78780 | − | 1.02055i | 0.501866 | − | 0.0884926i | ||||
\(134\) | 2.13795 | − | 1.24474i | 0.184691 | − | 0.107529i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.7981 | − | 0.139708i | 1.09743 | − | 0.0119799i | ||||
\(137\) | −0.995947 | − | 5.64830i | −0.0850895 | − | 0.482566i | −0.997337 | − | 0.0729275i | \(-0.976766\pi\) |
0.912248 | − | 0.409639i | \(-0.134345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.23743 | − | 19.8847i | −0.613871 | − | 1.68660i | −0.721509 | − | 0.692406i | \(-0.756551\pi\) |
0.107638 | − | 0.994190i | \(-0.465671\pi\) | |||||||
\(140\) | 0.320785 | + | 0.861784i | 0.0271113 | + | 0.0728340i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.39042 | − | 7.72107i | −0.116681 | − | 0.647938i | ||||
\(143\) | −0.174394 | − | 0.302060i | −0.0145836 | − | 0.0252595i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.143784 | + | 0.249041i | −0.0119406 | + | 0.0206817i | ||||
\(146\) | 12.6947 | + | 4.56824i | 1.05062 | + | 0.378071i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.63190 | − | 6.81190i | 0.462939 | − | 0.559935i | ||||
\(149\) | −7.83652 | − | 1.38179i | −0.641992 | − | 0.113201i | −0.156831 | − | 0.987625i | \(-0.550128\pi\) |
−0.485161 | + | 0.874425i | \(0.661239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.04551 | + | 1.71638i | −0.166461 | + | 0.139677i | −0.722213 | − | 0.691671i | \(-0.756875\pi\) |
0.555752 | + | 0.831348i | \(0.312430\pi\) | |||||||
\(152\) | 5.62288 | + | 3.16504i | 0.456076 | + | 0.256719i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.94788 | − | 1.68769i | −0.237547 | − | 0.135998i | ||||
\(155\) | −0.531330 | + | 1.45982i | −0.0426775 | + | 0.117255i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.93100 | − | 9.45180i | 0.632963 | − | 0.754336i | −0.350278 | − | 0.936646i | \(-0.613913\pi\) |
0.983241 | + | 0.182310i | \(0.0583574\pi\) | |||||||
\(158\) | 4.40760 | + | 3.67117i | 0.350650 | + | 0.292062i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.327980 | + | 0.954816i | −0.0259291 | + | 0.0754848i | ||||
\(161\) | −12.0744 | −0.951597 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.6508i | − | 1.06922i | −0.845100 | − | 0.534608i | \(-0.820459\pi\) | ||
0.845100 | − | 0.534608i | \(-0.179541\pi\) | |||||||
\(164\) | 2.58412 | + | 0.919303i | 0.201786 | + | 0.0717855i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.8151 | + | 16.5864i | −1.07226 | + | 1.28735i | ||||
\(167\) | 3.21110 | + | 2.69443i | 0.248482 | + | 0.208502i | 0.758519 | − | 0.651651i | \(-0.225924\pi\) |
−0.510036 | + | 0.860153i | \(0.670368\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0845 | − | 4.39840i | −0.929576 | − | 0.338338i | ||||
\(170\) | −0.991161 | − | 0.567449i | −0.0760186 | − | 0.0435213i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.81262 | − | 5.17384i | 0.671956 | − | 0.394502i | ||||
\(173\) | −12.8781 | − | 15.3475i | −0.979103 | − | 1.16685i | −0.985978 | − | 0.166873i | \(-0.946633\pi\) |
0.00687524 | − | 0.999976i | \(-0.497812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.22253 | + | 12.6046i | −0.168007 | + | 0.952816i | ||||
\(176\) | −1.32638 | − | 3.48551i | −0.0999799 | − | 0.262730i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 21.7262 | + | 7.81828i | 1.62845 | + | 0.586005i | ||||
\(179\) | −6.96829 | − | 4.02315i | −0.520835 | − | 0.300704i | 0.216441 | − | 0.976296i | \(-0.430555\pi\) |
−0.737276 | + | 0.675592i | \(0.763888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.99841 | + | 4.04053i | −0.520188 | + | 0.300331i | −0.737011 | − | 0.675880i | \(-0.763764\pi\) |
0.216824 | + | 0.976211i | \(0.430430\pi\) | |||||||
\(182\) | 1.34139 | − | 0.241559i | 0.0994304 | − | 0.0179055i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.2475 | − | 8.40976i | −0.755454 | − | 0.619976i | ||||
\(185\) | −0.741143 | + | 0.269754i | −0.0544899 | + | 0.0198327i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.15481 | − | 0.732605i | 0.303830 | − | 0.0535734i | ||||
\(188\) | 8.09501 | − | 14.2596i | 0.590389 | − | 1.03999i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.289705 | − | 0.497593i | −0.0210174 | − | 0.0360992i | ||||
\(191\) | −2.88972 | − | 16.3884i | −0.209093 | − | 1.18582i | −0.890868 | − | 0.454262i | \(-0.849903\pi\) |
0.681776 | − | 0.731561i | \(-0.261208\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.775835 | + | 0.282381i | −0.0558458 | + | 0.0203262i | −0.369792 | − | 0.929115i | \(-0.620571\pi\) |
0.313946 | + | 0.949441i | \(0.398349\pi\) | |||||||
\(194\) | 2.80892 | − | 16.2763i | 0.201668 | − | 1.16857i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.552925 | + | 0.470858i | −0.0394946 | + | 0.0336327i | ||||
\(197\) | −13.0620 | + | 7.54137i | −0.930632 | + | 0.537301i | −0.887011 | − | 0.461748i | \(-0.847223\pi\) |
−0.0436205 | + | 0.999048i | \(0.513889\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.77810 | + | 13.4721i | −0.551375 | + | 0.955009i | 0.446801 | + | 0.894633i | \(0.352563\pi\) |
−0.998176 | + | 0.0603759i | \(0.980770\pi\) | |||||||
\(200\) | −10.6653 | + | 9.14944i | −0.754147 | + | 0.646963i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.04778 | − | 2.84649i | −0.0737218 | − | 0.200279i | ||||
\(203\) | 4.08799 | + | 0.720823i | 0.286921 | + | 0.0505918i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.157323 | − | 0.187490i | −0.0109879 | − | 0.0130949i | ||||
\(206\) | −16.5753 | + | 0.0603118i | −1.15486 | + | 0.00420212i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.30667 | + | 0.729260i | 0.0906015 | + | 0.0505651i | ||||
\(209\) | 1.99867 | + | 0.727455i | 0.138251 | + | 0.0503191i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.55232 | + | 4.23349i | −0.244552 | + | 0.291445i | −0.874332 | − | 0.485328i | \(-0.838700\pi\) |
0.629781 | + | 0.776773i | \(0.283145\pi\) | |||||||
\(212\) | 17.9032 | + | 3.02265i | 1.22960 | + | 0.207597i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.75942 | − | 7.99629i | −0.462064 | − | 0.546615i | ||||
\(215\) | −0.911903 | −0.0621913 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.4249 | 1.52230 | ||||||||
\(218\) | −12.0806 | − | 14.2912i | −0.818202 | − | 0.967920i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0554016 | + | 0.328144i | −0.00373517 | + | 0.0221235i | ||||
\(221\) | −1.08813 | + | 1.29679i | −0.0731957 | + | 0.0872312i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.91216 | + | 1.78788i | 0.328942 | + | 0.119725i | 0.501212 | − | 0.865325i | \(-0.332888\pi\) |
−0.172269 | + | 0.985050i | \(0.555110\pi\) | |||||||
\(224\) | 14.5709 | − | 0.265119i | 0.973556 | − | 0.0177140i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.9706 | + | 0.0471953i | −0.862789 | + | 0.00313938i | ||||
\(227\) | −5.65872 | − | 6.74381i | −0.375583 | − | 0.447602i | 0.544832 | − | 0.838545i | \(-0.316593\pi\) |
−0.920415 | + | 0.390943i | \(0.872149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.50987 | − | 1.50052i | −0.562348 | − | 0.0991572i | −0.114754 | − | 0.993394i | \(-0.536608\pi\) |
−0.447594 | + | 0.894237i | \(0.647719\pi\) | |||||||
\(230\) | 0.408632 | + | 1.11012i | 0.0269444 | + | 0.0731992i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.96740 | + | 3.45902i | 0.194820 | + | 0.227096i | ||||
\(233\) | 0.420645 | − | 0.728579i | 0.0275574 | − | 0.0477308i | −0.851918 | − | 0.523676i | \(-0.824560\pi\) |
0.879475 | + | 0.475945i | \(0.157894\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.26716 | + | 0.731597i | −0.0826606 | + | 0.0477241i | ||||
\(236\) | −19.0607 | − | 22.3828i | −1.24075 | − | 1.45700i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.80372 | + | 16.2461i | −0.181738 | + | 1.05308i | ||||
\(239\) | −12.9749 | + | 4.72248i | −0.839276 | + | 0.305472i | −0.725660 | − | 0.688053i | \(-0.758466\pi\) |
−0.113616 | + | 0.993525i | \(0.536243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.61837 | + | 14.8495i | 0.168664 | + | 0.956542i | 0.945206 | + | 0.326476i | \(0.105861\pi\) |
−0.776541 | + | 0.630066i | \(0.783028\pi\) | |||||||
\(242\) | 7.20862 | + | 12.3814i | 0.463387 | + | 0.795908i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 25.8263 | + | 14.6613i | 1.65336 | + | 0.938591i | ||||
\(245\) | 0.0638218 | − | 0.0112535i | 0.00407743 | − | 0.000718960i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.801963 | + | 0.291891i | −0.0510277 | + | 0.0185726i | ||||
\(248\) | 19.0319 | + | 15.6188i | 1.20853 | + | 0.991797i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.47607 | − | 0.445894i | 0.156601 | − | 0.0282008i | ||||
\(251\) | −9.73582 | + | 5.62098i | −0.614520 | + | 0.354793i | −0.774732 | − | 0.632289i | \(-0.782115\pi\) |
0.160213 | + | 0.987083i | \(0.448782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.78432 | − | 2.18488i | −0.237918 | − | 0.137362i | ||||
\(254\) | 25.5081 | + | 9.17923i | 1.60052 | + | 0.575956i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.5509 | + | 9.92351i | 0.784428 | + | 0.620220i | ||||
\(257\) | −1.23538 | + | 7.00619i | −0.0770609 | + | 0.437034i | 0.921728 | + | 0.387837i | \(0.126778\pi\) |
−0.998789 | + | 0.0491976i | \(0.984334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.31815 | + | 8.72143i | 0.454728 | + | 0.541923i | ||||
\(260\) | −0.0676053 | − | 0.115152i | −0.00419270 | − | 0.00714144i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.12104 | − | 0.641806i | −0.0692581 | − | 0.0396509i | ||||
\(263\) | 18.0450 | + | 6.56783i | 1.11270 | + | 0.404990i | 0.831983 | − | 0.554801i | \(-0.187205\pi\) |
0.280717 | + | 0.959790i | \(0.409428\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.24114 | − | 1.04144i | −0.0762429 | − | 0.0639754i | ||||
\(266\) | −5.31930 | + | 6.38635i | −0.326147 | + | 0.391572i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.17265 | + | 3.29626i | −0.0716307 | + | 0.201351i | ||||
\(269\) | − | 16.5198i | − | 1.00723i | −0.863928 | − | 0.503616i | \(-0.832003\pi\) | ||
0.863928 | − | 0.503616i | \(-0.167997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.17854 | −0.0715913 | −0.0357956 | − | 0.999359i | \(-0.511397\pi\) | ||||
−0.0357956 | + | 0.999359i | \(0.511397\pi\) | |||||||
\(272\) | −13.6948 | + | 11.8352i | −0.830372 | + | 0.717616i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.23241 | + | 5.19109i | 0.376514 | + | 0.313605i | ||||
\(275\) | −2.97739 | + | 3.54832i | −0.179543 | + | 0.213972i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.87030 | − | 21.6235i | 0.472880 | − | 1.29923i | −0.442547 | − | 0.896745i | \(-0.645925\pi\) |
0.915428 | − | 0.402483i | \(-0.131853\pi\) | |||||||
\(278\) | 25.9709 | + | 14.8686i | 1.55763 | + | 0.891757i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.13325 | − | 0.637889i | −0.0677244 | − | 0.0381212i | ||||
\(281\) | −16.4336 | + | 13.7895i | −0.980348 | + | 0.822610i | −0.984142 | − | 0.177383i | \(-0.943237\pi\) |
0.00379366 | + | 0.999993i | \(0.498792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.339199 | + | 0.0598100i | 0.0201633 | + | 0.00355534i | 0.183721 | − | 0.982978i | \(-0.441186\pi\) |
−0.163557 | + | 0.986534i | \(0.552297\pi\) | |||||||
\(284\) | 8.55084 | + | 7.06961i | 0.507399 | + | 0.419504i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.464125 | + | 0.167018i | 0.0274443 | + | 0.00987596i | ||||
\(287\) | −1.76649 | + | 3.05966i | −0.104273 | + | 0.180606i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.73816 | − | 3.01059i | −0.102245 | − | 0.177093i | ||||
\(290\) | −0.0720765 | − | 0.400244i | −0.00423248 | − | 0.0235032i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17.8814 | + | 6.65606i | −1.04643 | + | 0.389516i | ||||
\(293\) | 9.01139 | + | 24.7586i | 0.526451 | + | 1.44641i | 0.863221 | + | 0.504826i | \(0.168443\pi\) |
−0.336770 | + | 0.941587i | \(0.609335\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.455551 | + | 2.58356i | 0.0265232 | + | 0.150420i | ||||
\(296\) | 0.136442 | + | 12.4989i | 0.00793051 | + | 0.726482i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.72525 | − | 5.66216i | 0.563369 | − | 0.328000i | ||||
\(299\) | 1.72673 | − | 0.304468i | 0.0998591 | − | 0.0176079i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.50213 | + | 12.3695i | 0.259499 | + | 0.712967i | ||||
\(302\) | 0.642205 | − | 3.72125i | 0.0369547 | − | 0.214134i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.96252 | + | 1.71519i | −0.514036 | + | 0.0983729i | ||||
\(305\) | −1.32503 | − | 2.29502i | −0.0758711 | − | 0.131413i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.2917 | − | 8.25134i | −0.815673 | − | 0.470929i | 0.0332493 | − | 0.999447i | \(-0.489414\pi\) |
−0.848922 | + | 0.528518i | \(0.822748\pi\) | |||||||
\(308\) | 4.72463 | − | 0.868578i | 0.269211 | − | 0.0494918i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.758922 | − | 2.06175i | −0.0431039 | − | 0.117099i | ||||
\(311\) | −3.58763 | + | 20.3464i | −0.203436 | + | 1.15374i | 0.696447 | + | 0.717609i | \(0.254763\pi\) |
−0.899882 | + | 0.436133i | \(0.856348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.65918 | + | 8.10501i | −0.545969 | + | 0.458122i | −0.873573 | − | 0.486693i | \(-0.838203\pi\) |
0.327604 | + | 0.944815i | \(0.393759\pi\) | |||||||
\(314\) | 0.0634910 | + | 17.4491i | 0.00358300 | + | 0.984709i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.11205 | + | 0.0590345i | −0.456338 | + | 0.00332095i | ||||
\(317\) | −4.18467 | + | 11.4973i | −0.235034 | + | 0.645752i | 0.764964 | + | 0.644073i | \(0.222757\pi\) |
−0.999999 | + | 0.00167879i | \(0.999466\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.15081 | + | 0.965645i | 0.0644331 | + | 0.0540658i | ||||
\(320\) | −0.517493 | − | 1.33067i | −0.0289288 | − | 0.0743868i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.0408 | − | 11.0236i | 0.726735 | − | 0.614323i | ||||
\(323\) | − | 10.3230i | − | 0.574388i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.85859i | − | 0.103096i | ||||||
\(326\) | 12.4629 | + | 14.7434i | 0.690254 | + | 0.816561i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.63024 | + | 1.36636i | −0.200447 | + | 0.0754445i | ||||
\(329\) | 16.1798 | + | 13.5765i | 0.892022 | + | 0.748495i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.93586 | − | 19.0561i | 0.381230 | − | 1.04742i | −0.589610 | − | 0.807688i | \(-0.700718\pi\) |
0.970839 | − | 0.239731i | \(-0.0770593\pi\) | |||||||
\(332\) | −0.222154 | − | 30.5267i | −0.0121923 | − | 1.67537i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.92805 | + | 0.0215701i | −0.324369 | + | 0.00118026i | ||||
\(335\) | 0.239159 | − | 0.200678i | 0.0130666 | − | 0.0109642i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.99094 | − | 16.9625i | 0.162927 | − | 0.924006i | −0.788249 | − | 0.615357i | \(-0.789012\pi\) |
0.951176 | − | 0.308649i | \(-0.0998769\pi\) | |||||||
\(338\) | 17.0673 | − | 6.28241i | 0.928339 | − | 0.341718i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.58856 | − | 0.292041i | 0.0861515 | − | 0.0158381i | ||||
\(341\) | 7.02835 | + | 4.05782i | 0.380606 | + | 0.219743i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.48449 | − | 16.4276i | −0.512114 | − | 0.887008i | ||||
\(344\) | −4.79436 | + | 13.6336i | −0.258495 | + | 0.735076i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.9207 | + | 4.81849i | 1.50103 | + | 0.259043i | ||||
\(347\) | −2.18170 | − | 5.99416i | −0.117120 | − | 0.321783i | 0.867257 | − | 0.497861i | \(-0.165881\pi\) |
−0.984376 | + | 0.176078i | \(0.943659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.1972 | + | 2.32702i | −0.706430 | + | 0.124563i | −0.515310 | − | 0.857004i | \(-0.672323\pi\) |
−0.191120 | + | 0.981567i | \(0.561212\pi\) | |||||||
\(350\) | −9.10725 | − | 15.6425i | −0.486803 | − | 0.836126i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.61473 | + | 2.55352i | 0.245966 | + | 0.136103i | ||||
\(353\) | 1.95983 | + | 11.1147i | 0.104311 | + | 0.591577i | 0.991493 | + | 0.130158i | \(0.0415484\pi\) |
−0.887182 | + | 0.461419i | \(0.847340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.338617 | − | 0.930342i | −0.0179719 | − | 0.0493774i | ||||
\(356\) | −30.6030 | + | 11.3915i | −1.62195 | + | 0.603746i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.1990 | − | 2.01674i | 0.591888 | − | 0.106588i | ||||
\(359\) | 13.5862 | + | 23.5320i | 0.717053 | + | 1.24197i | 0.962162 | + | 0.272477i | \(0.0878428\pi\) |
−0.245109 | + | 0.969495i | \(0.578824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.89786 | + | 11.9474i | −0.363045 | + | 0.628813i | ||||
\(362\) | 3.86963 | − | 10.7533i | 0.203383 | − | 0.565181i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.22821 | + | 1.48555i | −0.0643757 | + | 0.0778638i | ||||
\(365\) | 1.67674 | + | 0.295654i | 0.0877644 | + | 0.0154752i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.5436 | − | 14.7209i | 0.915771 | − | 0.768423i | −0.0574375 | − | 0.998349i | \(-0.518293\pi\) |
0.973208 | + | 0.229926i | \(0.0738485\pi\) | |||||||
\(368\) | 18.7455 | − | 0.272851i | 0.977179 | − | 0.0142234i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.554182 | − | 0.967988i | 0.0288105 | − | 0.0503233i | ||||
\(371\) | −7.99904 | + | 21.9772i | −0.415289 | + | 1.14100i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.2082 | − | 21.6997i | 0.942786 | − | 1.12357i | −0.0493967 | − | 0.998779i | \(-0.515730\pi\) |
0.992183 | − | 0.124790i | \(-0.0398257\pi\) | |||||||
\(374\) | −3.81849 | + | 4.58448i | −0.197450 | + | 0.237058i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.27577 | + | 22.7914i | 0.220506 | + | 1.17538i | ||||
\(377\) | −0.602788 | −0.0310451 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.20463i | 0.472810i | 0.971655 | + | 0.236405i | \(0.0759692\pi\) | ||||
−0.971655 | + | 0.236405i | \(0.924031\pi\) | |||||||
\(380\) | 0.767181 | + | 0.272925i | 0.0393556 | + | 0.0140008i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.0832 | + | 15.0618i | 0.925217 | + | 0.770630i | ||||
\(383\) | −18.0654 | − | 15.1587i | −0.923100 | − | 0.774573i | 0.0514658 | − | 0.998675i | \(-0.483611\pi\) |
−0.974566 | + | 0.224102i | \(0.928055\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.402815 | − | 0.146613i | −0.0205294 | − | 0.00747207i | ||||
\(386\) | 0.580123 | − | 1.01330i | 0.0295275 | − | 0.0515756i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.8261 | + | 20.1434i | 0.600378 | + | 1.02263i | ||||
\(389\) | −19.3453 | − | 23.0548i | −0.980844 | − | 1.16892i | −0.985627 | − | 0.168936i | \(-0.945967\pi\) |
0.00478250 | − | 0.999989i | \(-0.498478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.68282 | + | 20.8863i | −0.186248 | + | 1.05627i | ||||
\(392\) | 0.167297 | − | 1.01335i | 0.00844977 | − | 0.0511819i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.22239 | − | 20.0703i | 0.363859 | − | 1.01113i | ||||
\(395\) | 0.626912 | + | 0.361948i | 0.0315434 | + | 0.0182116i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4854 | + | 8.94051i | −0.777191 | + | 0.448711i | −0.835434 | − | 0.549591i | \(-0.814783\pi\) |
0.0582431 | + | 0.998302i | \(0.481450\pi\) | |||||||
\(398\) | −3.89903 | − | 21.6515i | −0.195441 | − | 1.08529i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.16564 | − | 19.6188i | 0.158282 | − | 0.980942i | ||||
\(401\) | 9.33220 | − | 3.39664i | 0.466028 | − | 0.169620i | −0.0983243 | − | 0.995154i | \(-0.531348\pi\) |
0.564352 | + | 0.825534i | \(0.309126\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.20692 | + | 0.565467i | −0.159748 | + | 0.0281679i | ||||
\(404\) | 3.73042 | + | 2.11771i | 0.185595 | + | 0.105360i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.07327 | + | 2.95372i | −0.251782 | + | 0.146590i | ||||
\(407\) | 0.715477 | + | 4.05767i | 0.0354649 | + | 0.201131i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.20287 | + | 1.89369i | −0.257265 | + | 0.0936369i | −0.467433 | − | 0.884028i | \(-0.654821\pi\) |
0.210168 | + | 0.977665i | \(0.432599\pi\) | |||||||
\(410\) | 0.341088 | + | 0.0588641i | 0.0168451 | + | 0.00290709i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.8469 | − | 15.1980i | 0.879253 | − | 0.748752i | ||||
\(413\) | 32.7955 | − | 18.9345i | 1.61376 | − | 0.931706i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.36206 | + | 2.35915i | −0.0668608 | + | 0.115806i | ||||
\(416\) | −2.07705 | + | 0.405333i | −0.101836 | + | 0.0198731i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.82278 | + | 1.03905i | −0.138067 | + | 0.0508218i | ||||
\(419\) | 4.02902 | + | 0.710424i | 0.196830 | + | 0.0347065i | 0.271194 | − | 0.962525i | \(-0.412581\pi\) |
−0.0743638 | + | 0.997231i | \(0.523693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7920 | − | 18.8201i | −0.769653 | − | 0.917237i | 0.228764 | − | 0.973482i | \(-0.426532\pi\) |
−0.998417 | + | 0.0562453i | \(0.982087\pi\) | |||||||
\(422\) | −0.0284378 | − | 7.81549i | −0.00138433 | − | 0.380452i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22.0957 | + | 13.0806i | −1.07306 | + | 0.635251i | ||||
\(425\) | 21.1255 | + | 7.68904i | 1.02474 | + | 0.372973i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.5890 | + | 29.3041i | −1.18995 | + | 1.41812i | ||||
\(428\) | 14.6008 | + | 2.46510i | 0.705757 | + | 0.119155i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.984888 | − | 0.832545i | 0.0474955 | − | 0.0401489i | ||||
\(431\) | −14.0058 | −0.674635 | −0.337318 | − | 0.941391i | \(-0.609520\pi\) | ||||
−0.337318 | + | 0.941391i | \(0.609520\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4899 | 0.600227 | 0.300113 | − | 0.953904i | \(-0.402976\pi\) | ||||
0.300113 | + | 0.953904i | \(0.402976\pi\) | |||||||
\(434\) | −24.2197 | + | 20.4734i | −1.16258 | + | 0.982754i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.0950 | + | 4.40569i | 1.24972 | + | 0.210994i | ||||
\(437\) | −6.87277 | + | 8.19065i | −0.328769 | + | 0.391812i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.1446 | − | 3.69232i | −0.484174 | − | 0.176225i | 0.0883886 | − | 0.996086i | \(-0.471828\pi\) |
−0.572562 | + | 0.819861i | \(0.694050\pi\) | |||||||
\(440\) | −0.239752 | − | 0.404988i | −0.0114297 | − | 0.0193070i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.00871096 | − | 2.39401i | −0.000414338 | − | 0.113872i | ||||
\(443\) | −18.6993 | − | 22.2849i | −0.888430 | − | 1.05879i | −0.997898 | − | 0.0647991i | \(-0.979359\pi\) |
0.109469 | − | 0.993990i | \(-0.465085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.86963 | + | 0.505994i | 0.136034 | + | 0.0239864i | ||||
\(446\) | −6.93759 | + | 2.55370i | −0.328504 | + | 0.120921i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15.4950 | + | 13.5892i | −0.732070 | + | 0.642027i | ||||
\(449\) | 15.0485 | − | 26.0648i | 0.710184 | − | 1.23007i | −0.254604 | − | 0.967045i | \(-0.581945\pi\) |
0.964788 | − | 0.263029i | \(-0.0847216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.10730 | + | 0.639299i | −0.0521406 | + | 0.0301034i | ||||
\(452\) | 13.9656 | − | 11.8928i | 0.656886 | − | 0.559389i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.2685 | + | 2.11728i | 0.575792 | + | 0.0993687i | ||||
\(455\) | 0.161629 | − | 0.0588282i | 0.00757729 | − | 0.00275791i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.71160 | + | 15.3782i | 0.126843 | + | 0.719363i | 0.980196 | + | 0.198029i | \(0.0634542\pi\) |
−0.853353 | + | 0.521334i | \(0.825435\pi\) | |||||||
\(458\) | 10.5609 | − | 6.14868i | 0.493479 | − | 0.287309i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.45485 | − | 0.825900i | −0.0678327 | − | 0.0385078i | ||||
\(461\) | 12.7088 | − | 2.24090i | 0.591908 | − | 0.104369i | 0.130332 | − | 0.991470i | \(-0.458396\pi\) |
0.461575 | + | 0.887101i | \(0.347284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.6243 | − | 11.8743i | 1.51618 | − | 0.551845i | 0.555990 | − | 0.831189i | \(-0.312339\pi\) |
0.960191 | + | 0.279345i | \(0.0901172\pi\) | |||||||
\(464\) | −6.36290 | − | 1.02670i | −0.295390 | − | 0.0476634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.210862 | + | 1.17093i | 0.00976801 | + | 0.0542423i | ||||
\(467\) | −12.4213 | + | 7.17141i | −0.574787 | + | 0.331853i | −0.759059 | − | 0.651022i | \(-0.774341\pi\) |
0.184272 | + | 0.982875i | \(0.441007\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.90284 | − | 2.25330i | −0.180216 | − | 0.104048i | ||||
\(470\) | 0.700651 | − | 1.94704i | 0.0323186 | − | 0.0898102i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 41.0212 | + | 6.77230i | 1.88815 | + | 0.311720i | ||||
\(473\) | −0.827235 | + | 4.69148i | −0.0380363 | + | 0.215715i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.28522 | + | 8.68219i | 0.334269 | + | 0.398366i | ||||
\(476\) | −11.8042 | − | 20.1061i | −0.541044 | − | 0.921563i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.70185 | − | 16.9462i | 0.443752 | − | 0.775101i | ||||
\(479\) | −0.567163 | − | 0.206430i | −0.0259143 | − | 0.00943204i | 0.329030 | − | 0.944319i | \(-0.393278\pi\) |
−0.354945 | + | 0.934887i | \(0.615500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.26647 | − | 1.06269i | −0.0577459 | − | 0.0484546i | ||||
\(482\) | −16.3852 | − | 13.6475i | −0.746324 | − | 0.621627i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.0895 | − | 6.79110i | −0.867704 | − | 0.308686i | ||||
\(485\) | − | 2.08438i | − | 0.0946467i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.8735 | −1.03650 | −0.518249 | − | 0.855230i | \(-0.673416\pi\) | ||||
−0.518249 | + | 0.855230i | \(0.673416\pi\) | |||||||
\(488\) | −41.2787 | + | 7.74406i | −1.86860 | + | 0.350557i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0586557 | + | 0.0704219i | −0.00264979 | + | 0.00318134i | ||||
\(491\) | −5.76980 | + | 6.87618i | −0.260387 | + | 0.310318i | −0.880360 | − | 0.474306i | \(-0.842699\pi\) |
0.619973 | + | 0.784623i | \(0.287144\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.49376 | − | 6.85154i | 0.112313 | − | 0.308578i | ||||
\(494\) | 0.599660 | − | 1.04742i | 0.0269800 | − | 0.0471259i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −34.8147 | + | 0.506747i | −1.56323 | + | 0.0227536i | ||||
\(497\) | −10.9478 | + | 9.18633i | −0.491078 | + | 0.412063i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.2976 | + | 7.63454i | 1.93827 | + | 0.341769i | 0.999992 | − | 0.00411738i | \(-0.00131061\pi\) |
0.938276 | + | 0.345886i | \(0.112422\pi\) | |||||||
\(500\) | −2.26716 | + | 2.74217i | −0.101390 | + | 0.122634i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.38322 | − | 14.9594i | 0.240265 | − | 0.667671i | ||||
\(503\) | −8.29388 | + | 14.3654i | −0.369806 | + | 0.640523i | −0.989535 | − | 0.144293i | \(-0.953909\pi\) |
0.619729 | + | 0.784816i | \(0.287242\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.191391 | − | 0.331499i | −0.00851679 | − | 0.0147515i | ||||
\(506\) | 6.08195 | − | 1.09524i | 0.270376 | − | 0.0486895i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −35.9301 | + | 13.3744i | −1.59414 | + | 0.593393i | ||||
\(509\) | −9.18363 | − | 25.2318i | −0.407057 | − | 1.11838i | −0.958730 | − | 0.284320i | \(-0.908232\pi\) |
0.551672 | − | 0.834061i | \(-0.313990\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.26777 | − | 24.2037i | −0.188795 | − | 1.07071i | ||||
\(512\) | −22.6153 | + | 0.740862i | −0.999464 | + | 0.0327418i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.06222 | − | 8.69481i | −0.223285 | − | 0.383512i | ||||
\(515\) | −2.05999 | + | 0.363232i | −0.0907742 | + | 0.0160059i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.61435 | + | 7.18286i | 0.114979 | + | 0.315902i | ||||
\(518\) | −15.8663 | − | 2.73817i | −0.697126 | − | 0.120308i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.178147 | + | 0.0626467i | 0.00781228 | + | 0.00274724i | ||||
\(521\) | −1.11230 | − | 1.92655i | −0.0487306 | − | 0.0844039i | 0.840631 | − | 0.541608i | \(-0.182184\pi\) |
−0.889362 | + | 0.457204i | \(0.848851\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.08920 | + | 1.78355i | 0.135081 | + | 0.0779892i | 0.566018 | − | 0.824393i | \(-0.308483\pi\) |
−0.430937 | + | 0.902382i | \(0.641817\pi\) | |||||||
\(524\) | 1.79672 | − | 0.330309i | 0.0784899 | − | 0.0144296i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.4855 | + | 9.38111i | −1.11122 | + | 0.409036i | ||||
\(527\) | 6.83983 | − | 38.7906i | 0.297948 | − | 1.68974i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.791437 | + | 0.664094i | −0.0344103 | + | 0.0288737i | ||||
\(530\) | 2.29129 | − | 0.00833720i | 0.0995274 | − | 0.000362145i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0855374 | − | 11.7539i | −0.00370852 | − | 0.509595i | ||||
\(533\) | 0.175469 | − | 0.482096i | 0.00760039 | − | 0.0208819i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.01220 | − | 0.849341i | −0.0437614 | − | 0.0367202i | ||||
\(536\) | −1.74290 | − | 4.63067i | −0.0752819 | − | 0.200015i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.0822 | + | 17.8420i | 0.650239 | + | 0.769224i | ||||
\(539\) | − | 0.338554i | − | 0.0145825i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 16.0298i | − | 0.689174i | −0.938754 | − | 0.344587i | \(-0.888019\pi\) | ||
0.938754 | − | 0.344587i | \(-0.111981\pi\) | |||||||
\(542\) | 1.27287 | − | 1.07598i | 0.0546743 | − | 0.0462172i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.98566 | − | 25.2855i | 0.170884 | − | 1.08411i | ||||
\(545\) | −1.80904 | − | 1.51796i | −0.0774907 | − | 0.0650224i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.0856 | + | 30.4574i | −0.473985 | + | 1.30226i | 0.440539 | + | 0.897733i | \(0.354787\pi\) |
−0.914525 | + | 0.404530i | \(0.867435\pi\) | |||||||
\(548\) | −11.4706 | + | 0.0834756i | −0.489998 | + | 0.00356590i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0238353 | − | 6.55059i | −0.00101634 | − | 0.279318i | ||||
\(551\) | 2.81586 | − | 2.36279i | 0.119960 | − | 0.100658i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.81453 | − | 10.2907i | 0.0771616 | − | 0.437605i | ||||
\(554\) | 11.2415 | + | 30.5395i | 0.477605 | + | 1.29750i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −41.6241 | + | 7.65219i | −1.76526 | + | 0.324525i | ||||
\(557\) | 29.5913 | + | 17.0845i | 1.25382 | + | 0.723895i | 0.971867 | − | 0.235532i | \(-0.0756833\pi\) |
0.281956 | + | 0.959427i | \(0.409017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.955747 | − | 1.65540i | −0.0404238 | − | 0.0700160i | ||||
\(560\) | 1.80632 | − | 0.345683i | 0.0763311 | − | 0.0146078i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.15948 | − | 29.8966i | 0.217640 | − | 1.26111i | ||||
\(563\) | −2.63340 | − | 7.23520i | −0.110984 | − | 0.304927i | 0.871749 | − | 0.489952i | \(-0.162986\pi\) |
−0.982734 | + | 0.185025i | \(0.940763\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.61199 | + | 0.284237i | −0.0678169 | + | 0.0119580i | ||||
\(566\) | −0.420952 | + | 0.245084i | −0.0176939 | + | 0.0103016i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.6896 | + | 0.171273i | −0.658321 | + | 0.00718644i | ||||
\(569\) | −2.70678 | − | 15.3509i | −0.113474 | − | 0.643544i | −0.987494 | − | 0.157654i | \(-0.949607\pi\) |
0.874020 | − | 0.485890i | \(-0.161504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.83178 | + | 21.5176i | 0.327750 | + | 0.900485i | 0.988680 | + | 0.150038i | \(0.0479396\pi\) |
−0.660930 | + | 0.750447i | \(0.729838\pi\) | |||||||
\(572\) | −0.653754 | + | 0.243349i | −0.0273348 | + | 0.0101749i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.885513 | − | 4.91730i | −0.0369606 | − | 0.205244i | ||||
\(575\) | −11.6426 | − | 20.1655i | −0.485528 | − | 0.840960i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.3039 | − | 23.0431i | 0.553850 | − | 0.959297i | −0.444141 | − | 0.895957i | \(-0.646491\pi\) |
0.997992 | − | 0.0633405i | \(-0.0201754\pi\) | |||||||
\(578\) | 4.62587 | + | 1.66464i | 0.192411 | + | 0.0692400i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.443258 | + | 0.366474i | 0.0184053 | + | 0.0152170i | ||||
\(581\) | 38.7253 | + | 6.82831i | 1.60660 | + | 0.283286i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.48384 | + | 5.44058i | −0.268533 | + | 0.225326i | ||||
\(584\) | 13.2357 | − | 23.5140i | 0.547699 | − | 0.973018i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.3366 | − | 18.5130i | −1.33581 | − | 0.764765i | ||||
\(587\) | −14.1595 | + | 38.9028i | −0.584424 | + | 1.60569i | 0.196113 | + | 0.980581i | \(0.437168\pi\) |
−0.780537 | + | 0.625110i | \(0.785054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.7643 | − | 15.2119i | 0.525944 | − | 0.626795i | ||||
\(590\) | −2.85073 | − | 2.37443i | −0.117363 | − | 0.0977536i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.5585 | − | 13.3747i | −0.475052 | − | 0.549695i | ||||
\(593\) | 12.1474 | 0.498833 | 0.249417 | − | 0.968396i | \(-0.419761\pi\) | ||||
0.249417 | + | 0.968396i | \(0.419761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.08052i | 0.0852930i | ||||||||
\(596\) | −5.33421 | + | 14.9942i | −0.218498 | + | 0.614188i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.58695 | + | 1.90529i | −0.0648954 | + | 0.0779133i | ||||
\(599\) | −25.1300 | − | 21.0866i | −1.02679 | − | 0.861575i | −0.0363204 | − | 0.999340i | \(-0.511564\pi\) |
−0.990465 | + | 0.137765i | \(0.956008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.6419 | + | 9.69685i | 1.08674 | + | 0.395543i | 0.822414 | − | 0.568889i | \(-0.192627\pi\) |
0.264331 | + | 0.964432i | \(0.414849\pi\) | |||||||
\(602\) | −16.1555 | − | 9.24917i | −0.658450 | − | 0.376968i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.70380 | + | 4.60540i | 0.110016 | + | 0.187391i | ||||
\(605\) | 1.16218 | + | 1.38503i | 0.0472493 | + | 0.0563095i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.218532 | + | 1.23936i | −0.00886995 | + | 0.0503040i | −0.988921 | − | 0.148440i | \(-0.952575\pi\) |
0.980052 | + | 0.198744i | \(0.0636861\pi\) | |||||||
\(608\) | 8.11391 | − | 10.0350i | 0.329063 | − | 0.406974i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.52638 | + | 1.26898i | 0.142779 | + | 0.0513797i | ||||
\(611\) | −2.65617 | − | 1.53354i | −0.107457 | − | 0.0620405i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.4944 | − | 15.8739i | 1.11049 | − | 0.641141i | 0.171532 | − | 0.985179i | \(-0.445128\pi\) |
0.938956 | + | 0.344038i | \(0.111795\pi\) | |||||||
\(614\) | 22.9689 | − | 4.13626i | 0.926947 | − | 0.166926i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.30978 | + | 5.25157i | −0.173646 | + | 0.211592i | ||||
\(617\) | 29.6509 | − | 10.7920i | 1.19370 | − | 0.434471i | 0.332679 | − | 0.943040i | \(-0.392047\pi\) |
0.861021 | + | 0.508569i | \(0.169825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.3688 | − | 5.17850i | 1.18043 | − | 0.208142i | 0.451208 | − | 0.892419i | \(-0.350993\pi\) |
0.729222 | + | 0.684277i | \(0.239882\pi\) | |||||||
\(620\) | 2.70199 | + | 1.53388i | 0.108514 | + | 0.0616023i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.7010 | − | 25.2503i | −0.589458 | − | 1.01244i | ||||
\(623\) | −7.30404 | − | 41.4233i | −0.292630 | − | 1.65959i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0443 | + | 8.38744i | −0.921772 | + | 0.335498i | ||||
\(626\) | 3.03258 | − | 17.5723i | 0.121206 | − | 0.702330i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.9991 | − | 18.7877i | −0.638435 | − | 0.749710i | ||||
\(629\) | 17.3184 | − | 9.99880i | 0.690531 | − | 0.398678i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.5109 | + | 26.8656i | −0.617478 | + | 1.06950i | 0.372466 | + | 0.928046i | \(0.378512\pi\) |
−0.989944 | + | 0.141458i | \(0.954821\pi\) | |||||||
\(632\) | 8.70740 | − | 7.46985i | 0.346362 | − | 0.297135i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.97714 | − | 16.2380i | −0.237382 | − | 0.644892i | ||||
\(635\) | 3.36916 | + | 0.594074i | 0.133701 | + | 0.0235751i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0873191 | + | 0.104063i | 0.00345971 | + | 0.00412312i | ||||
\(638\) | −2.12453 | + | 0.00773040i | −0.0841108 | + | 0.000306049i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.77378 | + | 0.964715i | 0.0701149 | + | 0.0381337i | ||||
\(641\) | −34.7901 | − | 12.6626i | −1.37413 | − | 0.500142i | −0.453735 | − | 0.891137i | \(-0.649909\pi\) |
−0.920393 | + | 0.390995i | \(0.872131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.1010 | + | 25.1472i | −0.832143 | + | 0.991710i | 0.167839 | + | 0.985814i | \(0.446321\pi\) |
−0.999983 | + | 0.00589543i | \(0.998123\pi\) | |||||||
\(644\) | −4.02022 | + | 23.8118i | −0.158419 | + | 0.938317i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.42465 | + | 11.1492i | 0.370808 | + | 0.438660i | ||||
\(647\) | 32.3509 | 1.27185 | 0.635923 | − | 0.771752i | \(-0.280620\pi\) | ||||
0.635923 | + | 0.771752i | \(0.280620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.7049 | 0.537965 | ||||||||
\(650\) | 1.69684 | + | 2.00734i | 0.0665556 | + | 0.0787343i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −26.9207 | − | 4.54510i | −1.05430 | − | 0.178000i | ||||
\(653\) | −7.14706 | + | 8.51753i | −0.279686 | + | 0.333317i | −0.887539 | − | 0.460733i | \(-0.847587\pi\) |
0.607853 | + | 0.794050i | \(0.292031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.153185 | − | 0.0557549i | −0.00598545 | − | 0.00217852i | ||||
\(656\) | 2.67334 | − | 4.79004i | 0.104376 | − | 0.187020i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.8698 | + | 0.108685i | −1.16444 | + | 0.00423700i | ||||
\(659\) | 21.7371 | + | 25.9052i | 0.846757 | + | 1.00913i | 0.999782 | + | 0.0209028i | \(0.00665406\pi\) |
−0.153025 | + | 0.988222i | \(0.548901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.9698 | − | 4.75551i | −1.04901 | − | 0.184968i | −0.377532 | − | 0.925997i | \(-0.623227\pi\) |
−0.671473 | + | 0.741029i | \(0.734338\pi\) | |||||||
\(662\) | 9.90679 | + | 26.9136i | 0.385038 | + | 1.04603i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.1100 | + | 32.7671i | 1.09088 | + | 1.27161i | ||||
\(665\) | −0.524441 | + | 0.908358i | −0.0203369 | + | 0.0352246i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.54020 | + | 3.77598i | −0.253237 | + | 0.146207i | ||||
\(668\) | 6.38282 | − | 5.43546i | 0.246959 | − | 0.210304i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.0750860 | + | 0.435085i | −0.00290082 | + | 0.0168088i | ||||
\(671\) | −13.0092 | + | 4.73497i | −0.502216 | + | 0.182792i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.55472 | − | 20.1598i | −0.137024 | − | 0.777103i | −0.973429 | − | 0.228990i | \(-0.926458\pi\) |
0.836404 | − | 0.548113i | \(-0.184654\pi\) | |||||||
\(674\) | 12.2560 | + | 21.0508i | 0.472083 | + | 0.810845i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6976 | + | 22.3673i | −0.488370 | + | 0.860279i | ||||
\(677\) | 32.7893 | − | 5.78165i | 1.26020 | − | 0.222207i | 0.496645 | − | 0.867954i | \(-0.334565\pi\) |
0.763552 | + | 0.645747i | \(0.223454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.2735 | + | 10.2907i | −1.08504 | + | 0.394922i | ||||
\(680\) | −1.44907 | + | 1.76573i | −0.0555693 | + | 0.0677125i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.2956 | + | 2.03412i | −0.432529 | + | 0.0778904i | ||||
\(683\) | 11.8895 | − | 6.86440i | 0.454939 | − | 0.262659i | −0.254975 | − | 0.966948i | \(-0.582067\pi\) |
0.709914 | + | 0.704289i | \(0.248734\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.886463 | + | 0.511800i | 0.0338700 | + | 0.0195549i | ||||
\(686\) | 25.2416 | + | 9.08331i | 0.963728 | + | 0.346802i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.26909 | − | 19.1019i | −0.277131 | − | 0.728255i | ||||
\(689\) | 0.589743 | − | 3.34460i | 0.0224674 | − | 0.127419i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4903 | − | 19.6524i | −0.627321 | − | 0.747612i | 0.354990 | − | 0.934870i | \(-0.384484\pi\) |
−0.982311 | + | 0.187258i | \(0.940040\pi\) | |||||||
\(692\) | −34.5545 | + | 20.2867i | −1.31356 | + | 0.771187i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.82883 | + | 4.48207i | 0.297178 | + | 0.170137i | ||||
\(695\) | 3.54881 | + | 1.29166i | 0.134614 | + | 0.0489955i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.75379 | + | 3.98890i | 0.180063 | + | 0.151090i | ||||
\(698\) | 12.1289 | − | 14.5620i | 0.459087 | − | 0.551179i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.1174 | + | 8.57976i | 0.911550 | + | 0.324284i | ||||
\(701\) | − | 0.366433i | − | 0.0138400i | −0.999976 | − | 0.00692000i | \(-0.997797\pi\) | ||
0.999976 | − | 0.00692000i | \(-0.00220272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0817 | 0.380237 | ||||||||
\(704\) | −7.31537 | + | 1.45523i | −0.275708 | + | 0.0548462i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.2641 | − | 10.2150i | −0.461567 | − | 0.384447i | ||||
\(707\) | −3.55171 | + | 4.23276i | −0.133576 | + | 0.159189i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.32486 | − | 6.38749i | 0.0873118 | − | 0.239887i | −0.888350 | − | 0.459166i | \(-0.848148\pi\) |
0.975662 | + | 0.219279i | \(0.0703705\pi\) | |||||||
\(710\) | 1.21510 | + | 0.695654i | 0.0456018 | + | 0.0261074i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.6522 | − | 40.2429i | 0.848926 | − | 1.50817i | ||||
\(713\) | −31.2526 | + | 26.2241i | −1.17042 | + | 0.982100i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0613024 | + | 0.0108093i | 0.00229258 | + | 0.000404244i | ||||
\(716\) | −10.2541 | + | 12.4026i | −0.383215 | + | 0.463506i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36.1577 | − | 13.0115i | −1.34939 | − | 0.485586i | ||||
\(719\) | 6.07495 | − | 10.5221i | 0.226558 | − | 0.392409i | −0.730228 | − | 0.683203i | \(-0.760586\pi\) |
0.956786 | + | 0.290794i | \(0.0939195\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0974 | + | 26.1495i | 0.562257 | + | 0.973857i | ||||
\(722\) | −3.45778 | − | 19.2012i | −0.128685 | − | 0.714596i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.63815 | + | 15.1468i | 0.209540 | + | 0.562927i | ||||
\(725\) | 2.73793 | + | 7.52240i | 0.101684 | + | 0.279375i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.337498 | + | 1.91405i | 0.0125171 | + | 0.0709881i | 0.990426 | − | 0.138041i | \(-0.0440807\pi\) |
−0.977909 | + | 0.209029i | \(0.932970\pi\) | |||||||
\(728\) | −0.0297554 | − | 2.72577i | −0.00110281 | − | 0.101024i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.08086 | + | 1.21150i | −0.0770160 | + | 0.0448397i | ||||
\(731\) | 22.7700 | − | 4.01496i | 0.842177 | − | 0.148499i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.2681 | + | 39.2014i | 0.527006 | + | 1.44794i | 0.862579 | + | 0.505923i | \(0.168848\pi\) |
−0.335572 | + | 0.942014i | \(0.608930\pi\) | |||||||
\(734\) | −5.50798 | + | 31.9160i | −0.203303 | + | 1.17804i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.9967 | + | 17.4089i | −0.737090 | + | 0.641700i | ||||
\(737\) | −0.815477 | − | 1.41245i | −0.0300385 | − | 0.0520282i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.3170 | + | 12.8847i | 0.820943 | + | 0.473971i | 0.850741 | − | 0.525584i | \(-0.176153\pi\) |
−0.0297988 | + | 0.999556i | \(0.509487\pi\) | |||||||
\(740\) | 0.285213 | + | 1.55142i | 0.0104846 | + | 0.0570312i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.4254 | − | 31.0391i | −0.419438 | − | 1.13948i | ||||
\(743\) | 0.466716 | − | 2.64688i | 0.0171222 | − | 0.0971046i | −0.975049 | − | 0.221989i | \(-0.928745\pi\) |
0.992171 | + | 0.124885i | \(0.0398561\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.08790 | − | 0.912858i | 0.0398576 | − | 0.0334445i | ||||
\(746\) | 0.145765 | + | 40.0601i | 0.00533682 | + | 1.46671i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.0614036 | − | 8.43759i | −0.00224514 | − | 0.308509i | ||||
\(749\) | −6.52355 | + | 17.9233i | −0.238365 | + | 0.654903i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.3934 | − | 29.6986i | −1.29153 | − | 1.08372i | −0.991544 | − | 0.129773i | \(-0.958575\pi\) |
−0.299982 | − | 0.953945i | \(-0.596981\pi\) | |||||||
\(752\) | −25.4260 | − | 20.7119i | −0.927190 | − | 0.755284i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.651032 | − | 0.550330i | 0.0237092 | − | 0.0200418i | ||||
\(755\) | − | 0.476553i | − | 0.0173435i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.2974i | 1.50098i | 0.660883 | + | 0.750489i | \(0.270182\pi\) | ||||
−0.660883 | + | 0.750489i | \(0.729818\pi\) | |||||||
\(758\) | −8.40360 | − | 9.94133i | −0.305232 | − | 0.361085i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.07776 | + | 0.405648i | −0.0390943 | + | 0.0147144i | ||||
\(761\) | −16.6555 | − | 13.9756i | −0.603762 | − | 0.506616i | 0.288891 | − | 0.957362i | \(-0.406714\pi\) |
−0.892652 | + | 0.450746i | \(0.851158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.6591 | + | 32.0330i | −0.422086 | + | 1.15967i | ||||
\(764\) | −33.2816 | + | 0.242203i | −1.20408 | + | 0.00876258i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.3508 | − | 0.121352i | 1.20501 | − | 0.00438462i | ||||
\(767\) | −4.21254 | + | 3.53474i | −0.152106 | + | 0.127632i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.86149 | − | 27.5709i | 0.175310 | − | 0.994232i | −0.762476 | − | 0.647017i | \(-0.776016\pi\) |
0.937786 | − | 0.347215i | \(-0.112873\pi\) | |||||||
\(770\) | 0.568908 | − | 0.209413i | 0.0205020 | − | 0.00754672i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.298563 | + | 1.62404i | 0.0107455 | + | 0.0584504i | ||||
\(773\) | −23.6486 | − | 13.6535i | −0.850580 | − | 0.491083i | 0.0102662 | − | 0.999947i | \(-0.496732\pi\) |
−0.860847 | + | 0.508864i | \(0.830065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.6229 | + | 37.4519i | 0.776717 | + | 1.34531i | ||||
\(776\) | −31.1630 | − | 10.9587i | −1.11869 | − | 0.393394i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41.9420 | + | 7.23826i | 1.50370 | + | 0.259504i | ||||
\(779\) | 1.07002 | + | 2.93986i | 0.0383375 | + | 0.105331i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.09352 | + | 0.898125i | −0.182260 | + | 0.0321374i | ||||
\(782\) | −15.0911 | − | 25.9203i | −0.539656 | − | 0.926907i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.744476 | + | 1.24719i | 0.0265884 | + | 0.0445426i | ||||
\(785\) | 0.382380 | + | 2.16858i | 0.0136477 | + | 0.0774001i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.72182 | − | 21.2155i | −0.275253 | − | 0.756252i | −0.997884 | − | 0.0650180i | \(-0.979290\pi\) |
0.722631 | − | 0.691234i | \(-0.242933\pi\) | |||||||
\(788\) | 10.5232 | + | 28.2705i | 0.374874 | + | 1.00709i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.00754 | + | 0.181438i | −0.0358465 | + | 0.00645529i | ||||
\(791\) | 11.8140 | + | 20.4625i | 0.420059 | + | 0.727564i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.77747 | − | 4.81073i | 0.0986310 | − | 0.170834i | ||||
\(794\) | 8.56234 | − | 23.7939i | 0.303866 | − | 0.844412i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.9784 | + | 19.8247i | 0.849891 | + | 0.702668i | ||||
\(797\) | −19.2857 | − | 3.40058i | −0.683133 | − | 0.120455i | −0.178697 | − | 0.983904i | \(-0.557188\pi\) |
−0.504436 | + | 0.863449i | \(0.668299\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.4196 | − | 23.8469i | 1.00541 | − | 0.843641i | ||||
\(800\) | 14.4925 | + | 24.0792i | 0.512387 | + | 0.851328i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.97806 | + | 12.1886i | −0.246404 | + | 0.430393i | ||||
\(803\) | 3.04211 | − | 8.35812i | 0.107354 | − | 0.294952i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.38515 | − | 1.65076i | 0.0488202 | − | 0.0581816i | ||||
\(806\) | 2.94733 | − | 3.53856i | 0.103815 | − | 0.124641i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.96241 | + | 1.11857i | −0.209757 | + | 0.0393513i | ||||
\(809\) | 27.8483 | 0.979094 | 0.489547 | − | 0.871977i | \(-0.337162\pi\) | ||||
0.489547 | + | 0.871977i | \(0.337162\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.82601i | − | 0.274808i | −0.990515 | − | 0.137404i | \(-0.956124\pi\) | ||
0.990515 | − | 0.137404i | \(-0.0438759\pi\) | |||||||
\(812\) | 2.78264 | − | 7.82188i | 0.0976515 | − | 0.274494i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.47730 | − | 3.72922i | −0.156929 | − | 0.130709i | ||||
\(815\) | 1.86628 | + | 1.56600i | 0.0653730 | + | 0.0548545i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9535 | + | 3.98673i | 0.383213 | + | 0.139478i | ||||
\(818\) | 3.89039 | − | 6.79534i | 0.136024 | − | 0.237593i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.422128 | + | 0.247829i | −0.0147414 | + | 0.00865457i | ||||
\(821\) | −9.82911 | − | 11.7139i | −0.343038 | − | 0.408817i | 0.566750 | − | 0.823890i | \(-0.308201\pi\) |
−0.909788 | + | 0.415073i | \(0.863756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.11133 | + | 23.3165i | −0.143312 | + | 0.812763i | 0.825395 | + | 0.564556i | \(0.190953\pi\) |
−0.968707 | + | 0.248207i | \(0.920159\pi\) | |||||||
\(824\) | −5.39988 | + | 32.7082i | −0.188114 | + | 1.13944i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.1336 | + | 50.3914i | −0.630949 | + | 1.75334i | ||||
\(827\) | −0.0403168 | − | 0.0232769i | −0.00140195 | − | 0.000809419i | 0.499299 | − | 0.866430i | \(-0.333591\pi\) |
−0.500701 | + | 0.865620i | \(0.666924\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.44307 | − | 3.71991i | 0.223777 | − | 0.129198i | −0.383921 | − | 0.923366i | \(-0.625426\pi\) |
0.607698 | + | 0.794168i | \(0.292093\pi\) | |||||||
\(830\) | −0.682776 | − | 3.79149i | −0.0236995 | − | 0.131605i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.87323 | − | 2.33407i | 0.0649426 | − | 0.0809193i | ||||
\(833\) | −1.54406 | + | 0.561994i | −0.0534987 | + | 0.0194719i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.736742 | + | 0.129908i | −0.0254960 | + | 0.00449564i | ||||
\(836\) | 2.10007 | − | 3.69934i | 0.0726325 | − | 0.127944i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.00008 | + | 2.91111i | −0.172725 | + | 0.100562i | ||||
\(839\) | 3.69536 | + | 20.9574i | 0.127578 | + | 0.723531i | 0.979743 | + | 0.200258i | \(0.0641780\pi\) |
−0.852165 | + | 0.523273i | \(0.824711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.8114 | + | 9.03060i | −0.855565 | + | 0.311400i | ||||
\(842\) | 34.2382 | + | 5.90874i | 1.17993 | + | 0.203629i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.16606 | + | 8.41505i | 0.246666 | + | 0.289658i | ||||
\(845\) | 1.98764 | − | 1.14756i | 0.0683768 | − | 0.0394774i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.0495 | − | 22.6024i | 0.448385 | − | 0.776626i | ||||
\(848\) | 11.9219 | − | 34.3004i | 0.409399 | − | 1.17788i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −29.8362 | + | 10.9826i | −1.02337 | + | 0.376700i | ||||
\(851\) | −20.3980 | − | 3.59671i | −0.699234 | − | 0.123294i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.8527 | + | 14.1255i | 0.405829 | + | 0.483648i | 0.929788 | − | 0.368095i | \(-0.119990\pi\) |
−0.523959 | + | 0.851744i | \(0.675545\pi\) | |||||||
\(854\) | −0.196846 | − | 54.0986i | −0.00673591 | − | 1.85122i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.0200 | + | 10.6678i | −0.615910 | + | 0.364617i | ||||
\(857\) | 18.6167 | + | 6.77591i | 0.635933 | + | 0.231461i | 0.639812 | − | 0.768532i | \(-0.279012\pi\) |
−0.00387866 | + | 0.999992i | \(0.501235\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.06270 | + | 6.03349i | −0.172737 | + | 0.205860i | −0.845466 | − | 0.534029i | \(-0.820677\pi\) |
0.672729 | + | 0.739889i | \(0.265122\pi\) | |||||||
\(860\) | −0.303622 | + | 1.79836i | −0.0103534 | + | 0.0613234i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.1268 | − | 12.7869i | 0.515219 | − | 0.435525i | ||||
\(863\) | 3.41425 | 0.116222 | 0.0581111 | − | 0.998310i | \(-0.481492\pi\) | ||||
0.0581111 | + | 0.998310i | \(0.481492\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.57559 | 0.121574 | ||||||||
\(866\) | −13.4895 | + | 11.4030i | −0.458393 | + | 0.387489i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.46646 | − | 44.2240i | 0.253428 | − | 1.50106i | ||||
\(869\) | 2.43082 | − | 2.89694i | 0.0824600 | − | 0.0982720i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.614953 | + | 0.223825i | 0.0208369 | + | 0.00758401i | ||||
\(872\) | −32.2058 | + | 19.0657i | −1.09063 | + | 0.645648i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.0550194 | − | 15.1209i | −0.00186106 | − | 0.511471i | ||||
\(875\) | −2.94597 | − | 3.51087i | −0.0995919 | − | 0.118689i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.1746 | − | 2.32305i | −0.444876 | − | 0.0784437i | −0.0532774 | − | 0.998580i | \(-0.516967\pi\) |
−0.391599 | + | 0.920136i | \(0.628078\pi\) | |||||||
\(878\) | 14.3275 | − | 5.27389i | 0.483529 | − | 0.177985i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.628684 | + | 0.218514i | 0.0211929 | + | 0.00736610i | ||||
\(881\) | −28.5441 | + | 49.4399i | −0.961676 | + | 1.66567i | −0.243384 | + | 0.969930i | \(0.578257\pi\) |
−0.718292 | + | 0.695742i | \(0.755076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.0975 | − | 9.87122i | 0.575375 | − | 0.332193i | −0.183918 | − | 0.982942i | \(-0.558878\pi\) |
0.759293 | + | 0.650749i | \(0.225545\pi\) | |||||||
\(884\) | 2.19508 | + | 2.57766i | 0.0738285 | + | 0.0866962i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40.5415 | + | 6.99655i | 1.36202 | + | 0.235054i | ||||
\(887\) | 53.6182 | − | 19.5154i | 1.80032 | − | 0.655264i | 0.802004 | − | 0.597319i | \(-0.203767\pi\) |
0.998320 | − | 0.0579452i | \(-0.0184549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.57547 | − | 48.6339i | −0.287612 | − | 1.63113i | ||||
\(890\) | −3.56127 | + | 2.07341i | −0.119374 | + | 0.0695010i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.16138 | − | 9.09194i | 0.172816 | − | 0.304421i | ||||
\(893\) | 18.4192 | − | 3.24779i | 0.616373 | − | 0.108683i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.34942 | − | 0.491147i | 0.0451060 | − | 0.0164172i | ||||
\(896\) | 4.32858 | − | 28.8233i | 0.144608 | − | 0.962919i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.54357 | + | 41.8899i | 0.251732 | + | 1.39788i | ||||
\(899\) | 12.1466 | − | 7.01286i | 0.405113 | − | 0.233892i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.5763 | + | 20.5400i | 1.18522 | + | 0.684286i | ||||
\(902\) | 0.612257 | − | 1.70140i | 0.0203859 | − | 0.0566504i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.22553 | + | 25.5948i | −0.140539 | + | 0.851272i | ||||
\(905\) | 0.250440 | − | 1.42031i | 0.00832490 | − | 0.0472128i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.5646 | − | 18.5491i | −0.516813 | − | 0.615914i | 0.443011 | − | 0.896516i | \(-0.353910\pi\) |
−0.959824 | + | 0.280602i | \(0.909466\pi\) | |||||||
\(908\) | −15.1835 | + | 8.91414i | −0.503882 | + | 0.295826i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.120857 | + | 0.211100i | −0.00400636 | + | 0.00699790i | ||||
\(911\) | −21.3962 | − | 7.78758i | −0.708888 | − | 0.258014i | −0.0376870 | − | 0.999290i | \(-0.511999\pi\) |
−0.671201 | + | 0.741275i | \(0.734221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9016 | + | 9.14750i | 0.360789 | + | 0.302738i | ||||
\(914\) | −16.9686 | − | 14.1334i | −0.561270 | − | 0.467492i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.79256 | + | 16.2826i | −0.191391 | + | 0.537993i | ||||
\(917\) | 2.35315i | 0.0777078i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.40847 | 0.112435 | 0.0562174 | − | 0.998419i | \(-0.482096\pi\) | ||||
0.0562174 | + | 0.998419i | \(0.482096\pi\) | |||||||
\(920\) | 2.32532 | − | 0.436239i | 0.0766634 | − | 0.0143824i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.6801 | + | 14.0231i | −0.384662 | + | 0.461825i | ||||
\(923\) | 1.33398 | − | 1.58977i | 0.0439084 | − | 0.0523279i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.50928 | + | 20.6316i | −0.246904 | + | 0.678362i | ||||
\(926\) | −24.3945 | + | 42.6098i | −0.801653 | + | 1.40025i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.80951 | − | 4.70029i | 0.256360 | − | 0.154295i | ||||
\(929\) | 16.2267 | − | 13.6158i | 0.532381 | − | 0.446721i | −0.336541 | − | 0.941669i | \(-0.609257\pi\) |
0.868923 | + | 0.494948i | \(0.164813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.815804 | − | 0.143848i | −0.0267369 | − | 0.00471443i | ||||
\(932\) | −1.29677 | − | 1.07213i | −0.0424771 | − | 0.0351189i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.86807 | − | 19.0857i | 0.224730 | − | 0.624502i | ||||
\(935\) | −0.376473 | + | 0.652071i | −0.0123120 | + | 0.0213250i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.8301 | + | 36.0788i | 0.680489 | + | 1.17864i | 0.974832 | + | 0.222942i | \(0.0715661\pi\) |
−0.294342 | + | 0.955700i | \(0.595101\pi\) | |||||||
\(938\) | 6.27241 | − | 1.12954i | 0.204802 | − | 0.0368809i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.02087 | + | 2.74255i | 0.0332971 | + | 0.0894520i | ||||
\(941\) | −17.2670 | − | 47.4407i | −0.562888 | − | 1.54652i | −0.815382 | − | 0.578924i | \(-0.803473\pi\) |
0.252493 | − | 0.967599i | \(-0.418749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.11613 | − | 6.32988i | −0.0363461 | − | 0.206129i | ||||
\(944\) | −50.4873 | + | 30.1370i | −1.64322 | + | 0.980874i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.38976 | − | 5.82221i | −0.110211 | − | 0.189296i | ||||
\(947\) | 38.1758 | − | 6.73142i | 1.24055 | − | 0.218742i | 0.485396 | − | 0.874294i | \(-0.338675\pi\) |
0.755149 | + | 0.655553i | \(0.227564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.22064 | + | 3.35369i | 0.0396238 | + | 0.108865i | ||||
\(950\) | −15.7949 | − | 2.72585i | −0.512455 | − | 0.0884382i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 31.1053 | + | 10.9384i | 1.00813 | + | 0.354516i | ||||
\(953\) | 17.7159 | + | 30.6848i | 0.573873 | + | 0.993977i | 0.996163 | + | 0.0875165i | \(0.0278931\pi\) |
−0.422290 | + | 0.906461i | \(0.638774\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.57205 | + | 1.48498i | 0.0832297 | + | 0.0480527i | ||||
\(956\) | 4.99311 | + | 27.1600i | 0.161489 | + | 0.878419i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.801022 | − | 0.294853i | 0.0258798 | − | 0.00952627i | ||||
\(959\) | 2.56577 | − | 14.5512i | 0.0828531 | − | 0.469883i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.2959 | − | 28.7776i | 1.10632 | − | 0.928311i | ||||
\(962\) | 2.33804 | − | 0.00850730i | 0.0753815 | − | 0.000274286i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30.1564 | − | 0.219460i | 0.971272 | − | 0.00706832i | ||||
\(965\) | 0.0503964 | − | 0.138463i | 0.00162232 | − | 0.00445728i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.48262 | − | 1.24406i | −0.0476777 | − | 0.0400064i | 0.618637 | − | 0.785677i | \(-0.287685\pi\) |
−0.666315 | + | 0.745670i | \(0.732129\pi\) | |||||||
\(968\) | 26.8174 | − | 10.0936i | 0.861945 | − | 0.324421i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.90298 | + | 2.25120i | 0.0611011 | + | 0.0722817i | ||||
\(971\) | 30.4220i | 0.976288i | 0.872763 | + | 0.488144i | \(0.162326\pi\) | ||||
−0.872763 | + | 0.488144i | \(0.837674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 54.5148i | − | 1.74766i | ||||||
\(974\) | 24.7042 | − | 20.8830i | 0.791574 | − | 0.669133i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37.5123 | − | 46.0503i | 1.20074 | − | 1.47403i | ||||
\(977\) | −2.40690 | − | 2.01963i | −0.0770035 | − | 0.0646136i | 0.603473 | − | 0.797383i | \(-0.293783\pi\) |
−0.680477 | + | 0.732769i | \(0.738227\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.20639 | − | 14.3044i | 0.166397 | − | 0.457172i | ||||
\(980\) | −0.000943217 | − | 0.129609i | −3.01300e−5 | − | 0.00414022i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.0461897 | − | 12.6942i | −0.00147397 | − | 0.405088i | ||||
\(983\) | −44.9828 | + | 37.7451i | −1.43473 | + | 1.20388i | −0.491880 | + | 0.870663i | \(0.663690\pi\) |
−0.942850 | + | 0.333218i | \(0.891865\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.467428 | − | 2.65092i | 0.0148935 | − | 0.0844652i | ||||
\(986\) | 3.56194 | + | 9.67664i | 0.113435 | + | 0.308167i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.308618 | + | 1.67873i | 0.00981845 | + | 0.0534075i | ||||
\(989\) | −20.7395 | − | 11.9740i | −0.659479 | − | 0.380750i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.3807 | + | 17.9799i | 0.329754 | + | 0.571150i | 0.982463 | − | 0.186458i | \(-0.0597009\pi\) |
−0.652709 | + | 0.757609i | \(0.726368\pi\) | |||||||
\(992\) | 37.1385 | − | 32.3323i | 1.17915 | − | 1.02655i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.43717 | − | 19.9167i | 0.109020 | − | 0.631718i | ||||
\(995\) | −0.949553 | − | 2.60888i | −0.0301029 | − | 0.0827069i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.5454 | + | 5.73863i | −1.03072 | + | 0.181744i | −0.663335 | − | 0.748323i | \(-0.730859\pi\) |
−0.367389 | + | 0.930067i | \(0.619748\pi\) | |||||||
\(998\) | −53.7331 | + | 31.2841i | −1.70089 | + | 0.990280i | ||||
\(999\) | 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 | 648.2.t.a.253.7 | 204 | ||
3.2 | odd | 2 | 216.2.t.a.13.28 | yes | 204 | ||
8.5 | even | 2 | inner | 648.2.t.a.253.30 | 204 | ||
12.11 | even | 2 | 864.2.bf.a.337.22 | 204 | |||
24.5 | odd | 2 | 216.2.t.a.13.5 | ✓ | 204 | ||
24.11 | even | 2 | 864.2.bf.a.337.13 | 204 | |||
27.2 | odd | 18 | 216.2.t.a.133.5 | yes | 204 | ||
27.25 | even | 9 | inner | 648.2.t.a.397.30 | 204 | ||
108.83 | even | 18 | 864.2.bf.a.241.13 | 204 | |||
216.29 | odd | 18 | 216.2.t.a.133.28 | yes | 204 | ||
216.83 | even | 18 | 864.2.bf.a.241.22 | 204 | |||
216.133 | even | 18 | inner | 648.2.t.a.397.7 | 204 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.t.a.13.5 | ✓ | 204 | 24.5 | odd | 2 | ||
216.2.t.a.13.28 | yes | 204 | 3.2 | odd | 2 | ||
216.2.t.a.133.5 | yes | 204 | 27.2 | odd | 18 | ||
216.2.t.a.133.28 | yes | 204 | 216.29 | odd | 18 | ||
648.2.t.a.253.7 | 204 | 1.1 | even | 1 | trivial | ||
648.2.t.a.253.30 | 204 | 8.5 | even | 2 | inner | ||
648.2.t.a.397.7 | 204 | 216.133 | even | 18 | inner | ||
648.2.t.a.397.30 | 204 | 27.25 | even | 9 | inner | ||
864.2.bf.a.241.13 | 204 | 108.83 | even | 18 | |||
864.2.bf.a.241.22 | 204 | 216.83 | even | 18 | |||
864.2.bf.a.337.13 | 204 | 24.11 | even | 2 | |||
864.2.bf.a.337.22 | 204 | 12.11 | even | 2 |