Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(295,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 393.6 | ||
Root | \(-0.181721 + 0.314749i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.393 |
Dual form | 637.2.f.k.295.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19402 | + | 2.06810i | 0.844299 | + | 1.46237i | 0.886229 | + | 0.463248i | \(0.153316\pi\) |
−0.0419302 | + | 0.999121i | \(0.513351\pi\) | |||||||
\(3\) | 1.37574 | + | 2.38285i | 0.794283 | + | 1.37574i | 0.923293 | + | 0.384096i | \(0.125487\pi\) |
−0.129010 | + | 0.991643i | \(0.541180\pi\) | |||||||
\(4\) | −1.85136 | + | 3.20665i | −0.925680 | + | 1.60333i | ||||
\(5\) | 0.982280 | 0.439289 | 0.219644 | − | 0.975580i | \(-0.429510\pi\) | ||||
0.219644 | + | 0.975580i | \(0.429510\pi\) | |||||||
\(6\) | −3.28532 | + | 5.69033i | −1.34122 | + | 2.32307i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.06616 | −1.43761 | ||||||||
\(9\) | −2.28532 | + | 3.95828i | −0.761772 | + | 1.31943i | ||||
\(10\) | 1.17286 | + | 2.03145i | 0.370891 | + | 0.642402i | ||||
\(11\) | 0.293901 | + | 0.509052i | 0.0886146 | + | 0.153485i | 0.906926 | − | 0.421291i | \(-0.138423\pi\) |
−0.818311 | + | 0.574775i | \(0.805089\pi\) | |||||||
\(12\) | −10.1880 | −2.94101 | ||||||||
\(13\) | 2.39227 | − | 2.69760i | 0.663496 | − | 0.748179i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.35136 | + | 2.34063i | 0.348920 | + | 0.604347i | ||||
\(16\) | −1.15235 | − | 1.99593i | −0.288088 | − | 0.498983i | ||||
\(17\) | 3.22710 | − | 5.58950i | 0.782687 | − | 1.35565i | −0.147685 | − | 0.989035i | \(-0.547182\pi\) |
0.930371 | − | 0.366619i | \(-0.119485\pi\) | |||||||
\(18\) | −10.9148 | −2.57265 | ||||||||
\(19\) | 1.91345 | − | 3.31419i | 0.438975 | − | 0.760327i | −0.558636 | − | 0.829413i | \(-0.688675\pi\) |
0.997611 | + | 0.0690863i | \(0.0220084\pi\) | |||||||
\(20\) | −1.81855 | + | 3.14983i | −0.406641 | + | 0.704323i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.701847 | + | 1.21563i | −0.149634 | + | 0.259174i | ||||
\(23\) | −4.13001 | − | 7.15338i | −0.861166 | − | 1.49158i | −0.870805 | − | 0.491629i | \(-0.836402\pi\) |
0.00963902 | − | 0.999954i | \(-0.496932\pi\) | |||||||
\(24\) | −5.59398 | − | 9.68906i | −1.14187 | − | 1.97777i | ||||
\(25\) | −4.03513 | −0.807025 | ||||||||
\(26\) | 8.43532 | + | 1.72647i | 1.65430 | + | 0.338589i | ||||
\(27\) | −4.32156 | −0.831685 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.98009 | + | 3.42962i | 0.367694 | + | 0.636864i | 0.989205 | − | 0.146541i | \(-0.0468141\pi\) |
−0.621511 | + | 0.783406i | \(0.713481\pi\) | |||||||
\(30\) | −3.22710 | + | 5.58950i | −0.589185 | + | 1.02050i | ||||
\(31\) | −2.98872 | −0.536790 | −0.268395 | − | 0.963309i | \(-0.586493\pi\) | ||||
−0.268395 | + | 0.963309i | \(0.586493\pi\) | |||||||
\(32\) | −1.31430 | + | 2.27644i | −0.232338 | + | 0.402421i | ||||
\(33\) | −0.808663 | + | 1.40065i | −0.140770 | + | 0.243821i | ||||
\(34\) | 15.4129 | 2.64329 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.46189 | − | 14.6564i | −1.41031 | − | 2.44274i | ||||
\(37\) | −0.877941 | − | 1.52064i | −0.144333 | − | 0.249991i | 0.784791 | − | 0.619760i | \(-0.212770\pi\) |
−0.929124 | + | 0.369769i | \(0.879437\pi\) | |||||||
\(38\) | 9.13877 | 1.48250 | ||||||||
\(39\) | 9.71911 | + | 1.98923i | 1.55630 | + | 0.318532i | ||||
\(40\) | −3.99411 | −0.631524 | ||||||||
\(41\) | −1.83584 | − | 3.17977i | −0.286710 | − | 0.496597i | 0.686312 | − | 0.727307i | \(-0.259228\pi\) |
−0.973023 | + | 0.230710i | \(0.925895\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.19042 | + | 5.52598i | −0.486535 | + | 0.842703i | −0.999880 | − | 0.0154788i | \(-0.995073\pi\) |
0.513345 | + | 0.858182i | \(0.328406\pi\) | |||||||
\(44\) | −2.17647 | −0.328115 | ||||||||
\(45\) | −2.24482 | + | 3.88814i | −0.334638 | + | 0.579610i | ||||
\(46\) | 9.86261 | − | 17.0825i | 1.45416 | − | 2.51868i | ||||
\(47\) | −4.34059 | −0.633141 | −0.316570 | − | 0.948569i | \(-0.602531\pi\) | ||||
−0.316570 | + | 0.948569i | \(0.602531\pi\) | |||||||
\(48\) | 3.17067 | − | 5.49176i | 0.457647 | − | 0.792668i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.81802 | − | 8.34505i | −0.681370 | − | 1.18017i | ||||
\(51\) | 17.7586 | 2.48670 | ||||||||
\(52\) | 4.22130 | + | 12.6654i | 0.585389 | + | 1.75638i | ||||
\(53\) | 0.425541 | 0.0584525 | 0.0292263 | − | 0.999573i | \(-0.490696\pi\) | ||||
0.0292263 | + | 0.999573i | \(0.490696\pi\) | |||||||
\(54\) | −5.16002 | − | 8.93742i | −0.702190 | − | 1.21623i | ||||
\(55\) | 0.288693 | + | 0.500031i | 0.0389274 | + | 0.0674242i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.5296 | 1.39468 | ||||||||
\(58\) | −4.72853 | + | 8.19006i | −0.620887 | + | 1.07541i | ||||
\(59\) | −3.00431 | + | 5.20362i | −0.391128 | + | 0.677454i | −0.992599 | − | 0.121441i | \(-0.961248\pi\) |
0.601470 | + | 0.798895i | \(0.294582\pi\) | |||||||
\(60\) | −10.0074 | −1.29195 | ||||||||
\(61\) | −1.10337 | + | 1.91109i | −0.141272 | + | 0.244691i | −0.927976 | − | 0.372640i | \(-0.878453\pi\) |
0.786704 | + | 0.617331i | \(0.211786\pi\) | |||||||
\(62\) | −3.56859 | − | 6.18097i | −0.453211 | − | 0.784985i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.8866 | −1.36083 | ||||||||
\(65\) | 2.34988 | − | 2.64980i | 0.291467 | − | 0.328667i | ||||
\(66\) | −3.86223 | −0.475408 | ||||||||
\(67\) | −3.50651 | − | 6.07346i | −0.428389 | − | 0.741991i | 0.568341 | − | 0.822793i | \(-0.307585\pi\) |
−0.996730 | + | 0.0808015i | \(0.974252\pi\) | |||||||
\(68\) | 11.9491 | + | 20.6964i | 1.44904 | + | 2.50980i | ||||
\(69\) | 11.3636 | − | 19.6824i | 1.36802 | − | 2.36948i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.80127 | + | 3.11988i | −0.213771 | + | 0.370262i | −0.952892 | − | 0.303311i | \(-0.901908\pi\) |
0.739121 | + | 0.673573i | \(0.235241\pi\) | |||||||
\(72\) | 9.29247 | − | 16.0950i | 1.09513 | − | 1.89682i | ||||
\(73\) | 4.93427 | 0.577513 | 0.288756 | − | 0.957403i | \(-0.406758\pi\) | ||||
0.288756 | + | 0.957403i | \(0.406758\pi\) | |||||||
\(74\) | 2.09656 | − | 3.63134i | 0.243720 | − | 0.422135i | ||||
\(75\) | −5.55128 | − | 9.61510i | −0.641007 | − | 1.11026i | ||||
\(76\) | 7.08496 | + | 12.2715i | 0.812701 | + | 1.40764i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.49088 | + | 22.4753i | 0.848175 | + | 2.54483i | ||||
\(79\) | 2.78541 | 0.313383 | 0.156691 | − | 0.987648i | \(-0.449917\pi\) | ||||
0.156691 | + | 0.987648i | \(0.449917\pi\) | |||||||
\(80\) | −1.13193 | − | 1.96056i | −0.126554 | − | 0.219198i | ||||
\(81\) | 0.910609 | + | 1.57722i | 0.101179 | + | 0.175247i | ||||
\(82\) | 4.38406 | − | 7.59342i | 0.484138 | − | 0.838552i | ||||
\(83\) | −2.86819 | −0.314825 | −0.157412 | − | 0.987533i | \(-0.550315\pi\) | ||||
−0.157412 | + | 0.987533i | \(0.550315\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.16992 | − | 5.49045i | 0.343826 | − | 0.595523i | ||||
\(86\) | −15.2377 | −1.64312 | ||||||||
\(87\) | −5.44818 | + | 9.43652i | −0.584106 | + | 1.01170i | ||||
\(88\) | −1.19505 | − | 2.06989i | −0.127393 | − | 0.220651i | ||||
\(89\) | 1.04656 | + | 1.81269i | 0.110935 | + | 0.192145i | 0.916147 | − | 0.400842i | \(-0.131282\pi\) |
−0.805213 | + | 0.592986i | \(0.797949\pi\) | |||||||
\(90\) | −10.7214 | −1.13014 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 30.5845 | 3.18866 | ||||||||
\(93\) | −4.11170 | − | 7.12167i | −0.426363 | − | 0.738483i | ||||
\(94\) | −5.18275 | − | 8.97679i | −0.534560 | − | 0.925885i | ||||
\(95\) | 1.87954 | − | 3.25546i | 0.192837 | − | 0.334003i | ||||
\(96\) | −7.23255 | −0.738169 | ||||||||
\(97\) | −3.84852 | + | 6.66584i | −0.390758 | + | 0.676813i | −0.992550 | − | 0.121840i | \(-0.961120\pi\) |
0.601791 | + | 0.798653i | \(0.294454\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.68663 | −0.270016 | ||||||||
\(100\) | 7.47047 | − | 12.9392i | 0.747047 | − | 1.29392i | ||||
\(101\) | 1.31866 | + | 2.28399i | 0.131212 | + | 0.227265i | 0.924144 | − | 0.382045i | \(-0.124780\pi\) |
−0.792932 | + | 0.609310i | \(0.791447\pi\) | |||||||
\(102\) | 21.2041 | + | 36.7266i | 2.09952 | + | 3.63647i | ||||
\(103\) | −10.8619 | −1.07026 | −0.535128 | − | 0.844771i | \(-0.679737\pi\) | ||||
−0.535128 | + | 0.844771i | \(0.679737\pi\) | |||||||
\(104\) | −9.72736 | + | 10.9689i | −0.953846 | + | 1.07559i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.508103 | + | 0.880061i | 0.0493514 | + | 0.0854791i | ||||
\(107\) | 7.99024 | + | 13.8395i | 0.772446 | + | 1.33792i | 0.936219 | + | 0.351418i | \(0.114300\pi\) |
−0.163773 | + | 0.986498i | \(0.552366\pi\) | |||||||
\(108\) | 8.00077 | − | 13.8577i | 0.769874 | − | 1.33346i | ||||
\(109\) | 9.23477 | 0.884530 | 0.442265 | − | 0.896884i | \(-0.354175\pi\) | ||||
0.442265 | + | 0.896884i | \(0.354175\pi\) | |||||||
\(110\) | −0.689410 | + | 1.19409i | −0.0657327 | + | 0.113852i | ||||
\(111\) | 2.41564 | − | 4.18400i | 0.229282 | − | 0.397128i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.09012 | + | 8.81635i | −0.478838 | + | 0.829372i | −0.999706 | − | 0.0242655i | \(-0.992275\pi\) |
0.520867 | + | 0.853638i | \(0.325609\pi\) | |||||||
\(114\) | 12.5726 | + | 21.7763i | 1.17753 | + | 2.03954i | ||||
\(115\) | −4.05682 | − | 7.02662i | −0.378301 | − | 0.655236i | ||||
\(116\) | −14.6635 | −1.36147 | ||||||||
\(117\) | 5.21077 | + | 15.6342i | 0.481736 | + | 1.44538i | ||||
\(118\) | −14.3488 | −1.32092 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.49485 | − | 9.51736i | −0.501609 | − | 0.868813i | ||||
\(121\) | 5.32724 | − | 9.22706i | 0.484295 | − | 0.838823i | ||||
\(122\) | −5.26978 | −0.477104 | ||||||||
\(123\) | 5.05128 | − | 8.74908i | 0.455459 | − | 0.788878i | ||||
\(124\) | 5.53320 | − | 9.58378i | 0.496896 | − | 0.860649i | ||||
\(125\) | −8.87502 | −0.793806 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.12513 | − | 3.68083i | −0.188575 | − | 0.326621i | 0.756201 | − | 0.654340i | \(-0.227053\pi\) |
−0.944775 | + | 0.327719i | \(0.893720\pi\) | |||||||
\(128\) | −10.3702 | − | 17.9617i | −0.916606 | − | 1.58761i | ||||
\(129\) | −17.5568 | −1.54579 | ||||||||
\(130\) | 8.28585 | + | 1.69588i | 0.726717 | + | 0.148739i | ||||
\(131\) | −2.16957 | −0.189556 | −0.0947779 | − | 0.995498i | \(-0.530214\pi\) | ||||
−0.0947779 | + | 0.995498i | \(0.530214\pi\) | |||||||
\(132\) | −2.99425 | − | 5.18620i | −0.260616 | − | 0.451401i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.37369 | − | 14.5037i | 0.723376 | − | 1.25292i | ||||
\(135\) | −4.24498 | −0.365350 | ||||||||
\(136\) | −13.1219 | + | 22.7278i | −1.12519 | + | 1.94889i | ||||
\(137\) | −4.18158 | + | 7.24271i | −0.357257 | + | 0.618787i | −0.987501 | − | 0.157610i | \(-0.949621\pi\) |
0.630245 | + | 0.776396i | \(0.282955\pi\) | |||||||
\(138\) | 54.2735 | 4.62007 | ||||||||
\(139\) | 0.288457 | − | 0.499622i | 0.0244666 | − | 0.0423774i | −0.853533 | − | 0.521039i | \(-0.825545\pi\) |
0.877999 | + | 0.478662i | \(0.158878\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.97152 | − | 10.3430i | −0.502893 | − | 0.871036i | ||||
\(142\) | −8.60298 | −0.721946 | ||||||||
\(143\) | 2.07631 | + | 0.424962i | 0.173630 | + | 0.0355371i | ||||
\(144\) | 10.5340 | 0.877830 | ||||||||
\(145\) | 1.94500 | + | 3.36885i | 0.161524 | + | 0.279767i | ||||
\(146\) | 5.89161 | + | 10.2046i | 0.487593 | + | 0.844537i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.50154 | 0.534423 | ||||||||
\(149\) | −1.40331 | + | 2.43061i | −0.114964 | + | 0.199123i | −0.917765 | − | 0.397123i | \(-0.870009\pi\) |
0.802801 | + | 0.596246i | \(0.203342\pi\) | |||||||
\(150\) | 13.2567 | − | 22.9612i | 1.08240 | − | 1.87478i | ||||
\(151\) | −23.0109 | −1.87260 | −0.936300 | − | 0.351202i | \(-0.885773\pi\) | ||||
−0.936300 | + | 0.351202i | \(0.885773\pi\) | |||||||
\(152\) | −7.78039 | + | 13.4760i | −0.631073 | + | 1.09305i | ||||
\(153\) | 14.7499 | + | 25.5476i | 1.19246 | + | 2.06540i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.93576 | −0.235806 | ||||||||
\(156\) | −24.3724 | + | 27.4830i | −1.95135 | + | 2.20040i | ||||
\(157\) | 22.5760 | 1.80176 | 0.900879 | − | 0.434071i | \(-0.142923\pi\) | ||||
0.900879 | + | 0.434071i | \(0.142923\pi\) | |||||||
\(158\) | 3.32583 | + | 5.76050i | 0.264588 | + | 0.458281i | ||||
\(159\) | 0.585433 | + | 1.01400i | 0.0464278 | + | 0.0804154i | ||||
\(160\) | −1.29101 | + | 2.23610i | −0.102064 | + | 0.176779i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.17457 | + | 3.76646i | −0.170850 | + | 0.295921i | ||||
\(163\) | −4.08857 | + | 7.08161i | −0.320242 | + | 0.554675i | −0.980538 | − | 0.196331i | \(-0.937097\pi\) |
0.660296 | + | 0.751005i | \(0.270431\pi\) | |||||||
\(164\) | 13.5952 | 1.06161 | ||||||||
\(165\) | −0.794333 | + | 1.37583i | −0.0618388 | + | 0.107108i | ||||
\(166\) | −3.42467 | − | 5.93170i | −0.265806 | − | 0.460389i | ||||
\(167\) | 1.16386 | + | 2.01586i | 0.0900619 | + | 0.155992i | 0.907537 | − | 0.419972i | \(-0.137960\pi\) |
−0.817475 | + | 0.575964i | \(0.804627\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.55408 | − | 12.9068i | −0.119545 | − | 0.992829i | ||||
\(170\) | 15.1398 | 1.16117 | ||||||||
\(171\) | 8.74566 | + | 15.1479i | 0.668798 | + | 1.15839i | ||||
\(172\) | −11.8133 | − | 20.4611i | −0.900752 | − | 1.56015i | ||||
\(173\) | 4.06686 | − | 7.04401i | 0.309198 | − | 0.535546i | −0.668989 | − | 0.743272i | \(-0.733273\pi\) |
0.978187 | + | 0.207726i | \(0.0666061\pi\) | |||||||
\(174\) | −26.0209 | −1.97264 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.677355 | − | 1.17321i | 0.0510576 | − | 0.0884343i | ||||
\(177\) | −16.5326 | −1.24267 | ||||||||
\(178\) | −2.49922 | + | 4.32877i | −0.187324 | + | 0.324455i | ||||
\(179\) | 10.4963 | + | 18.1801i | 0.784528 | + | 1.35884i | 0.929281 | + | 0.369375i | \(0.120428\pi\) |
−0.144752 | + | 0.989468i | \(0.546239\pi\) | |||||||
\(180\) | −8.31194 | − | 14.3967i | −0.619536 | − | 1.07307i | ||||
\(181\) | −1.60807 | −0.119527 | −0.0597635 | − | 0.998213i | \(-0.519035\pi\) | ||||
−0.0597635 | + | 0.998213i | \(0.519035\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.07180 | −0.448841 | ||||||||
\(184\) | 16.7933 | + | 29.0868i | 1.23802 | + | 2.14431i | ||||
\(185\) | −0.862384 | − | 1.49369i | −0.0634037 | − | 0.109818i | ||||
\(186\) | 9.81889 | − | 17.0068i | 0.719956 | − | 1.24700i | ||||
\(187\) | 3.79379 | 0.277430 | ||||||||
\(188\) | 8.03601 | − | 13.9188i | 0.586086 | − | 1.01513i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.97683 | 0.651247 | ||||||||
\(191\) | 5.78111 | − | 10.0132i | 0.418307 | − | 0.724529i | −0.577463 | − | 0.816417i | \(-0.695957\pi\) |
0.995769 | + | 0.0918886i | \(0.0292904\pi\) | |||||||
\(192\) | −14.9771 | − | 25.9412i | −1.08088 | − | 1.87214i | ||||
\(193\) | −11.7894 | − | 20.4199i | −0.848621 | − | 1.46985i | −0.882439 | − | 0.470427i | \(-0.844100\pi\) |
0.0338178 | − | 0.999428i | \(-0.489233\pi\) | |||||||
\(194\) | −18.3808 | −1.31967 | ||||||||
\(195\) | 9.54689 | + | 1.95398i | 0.683667 | + | 0.139927i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.735472 | + | 1.27387i | 0.0524002 | + | 0.0907598i | 0.891036 | − | 0.453933i | \(-0.149980\pi\) |
−0.838636 | + | 0.544693i | \(0.816646\pi\) | |||||||
\(198\) | −3.20788 | − | 5.55622i | −0.227974 | − | 0.394863i | ||||
\(199\) | −4.69700 | + | 8.13543i | −0.332961 | + | 0.576706i | −0.983091 | − | 0.183117i | \(-0.941381\pi\) |
0.650130 | + | 0.759823i | \(0.274714\pi\) | |||||||
\(200\) | 16.4075 | 1.16018 | ||||||||
\(201\) | 9.64810 | − | 16.7110i | 0.680524 | − | 1.17870i | ||||
\(202\) | −3.14901 | + | 5.45425i | −0.221564 | + | 0.383760i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −32.8776 | + | 56.9456i | −2.30189 | + | 3.98699i | ||||
\(205\) | −1.80331 | − | 3.12343i | −0.125949 | − | 0.218150i | ||||
\(206\) | −12.9693 | − | 22.4635i | −0.903615 | − | 1.56511i | ||||
\(207\) | 37.7535 | 2.62405 | ||||||||
\(208\) | −8.14096 | − | 1.66623i | −0.564474 | − | 0.115532i | ||||
\(209\) | 2.24946 | 0.155598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.47109 | + | 7.74416i | 0.307803 | + | 0.533130i | 0.977881 | − | 0.209160i | \(-0.0670730\pi\) |
−0.670079 | + | 0.742290i | \(0.733740\pi\) | |||||||
\(212\) | −0.787829 | + | 1.36456i | −0.0541083 | + | 0.0937184i | ||||
\(213\) | −9.91229 | −0.679179 | ||||||||
\(214\) | −19.0810 | + | 33.0493i | −1.30435 | + | 2.25920i | ||||
\(215\) | −3.13389 | + | 5.42805i | −0.213729 | + | 0.370190i | ||||
\(216\) | 17.5722 | 1.19563 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 11.0265 | + | 19.0984i | 0.746808 | + | 1.29351i | ||||
\(219\) | 6.78827 | + | 11.7576i | 0.458709 | + | 0.794507i | ||||
\(220\) | −2.13790 | −0.144137 | ||||||||
\(221\) | −7.35814 | − | 22.0770i | −0.494962 | − | 1.48506i | ||||
\(222\) | 11.5373 | 0.774330 | ||||||||
\(223\) | −10.9098 | − | 18.8963i | −0.730574 | − | 1.26539i | −0.956638 | − | 0.291279i | \(-0.905919\pi\) |
0.226064 | − | 0.974112i | \(-0.427414\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.22154 | − | 15.9722i | 0.614769 | − | 1.06481i | ||||
\(226\) | −24.3108 | −1.61713 | ||||||||
\(227\) | 9.27627 | − | 16.0670i | 0.615687 | − | 1.06640i | −0.374576 | − | 0.927196i | \(-0.622212\pi\) |
0.990263 | − | 0.139206i | \(-0.0444549\pi\) | |||||||
\(228\) | −19.4941 | + | 33.7648i | −1.29103 | + | 2.23613i | ||||
\(229\) | 19.3505 | 1.27872 | 0.639359 | − | 0.768909i | \(-0.279200\pi\) | ||||
0.639359 | + | 0.768909i | \(0.279200\pi\) | |||||||
\(230\) | 9.68784 | − | 16.7798i | 0.638797 | − | 1.10643i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.05137 | − | 13.9454i | −0.528599 | − | 0.915560i | ||||
\(233\) | 16.1634 | 1.05890 | 0.529450 | − | 0.848341i | \(-0.322398\pi\) | ||||
0.529450 | + | 0.848341i | \(0.322398\pi\) | |||||||
\(234\) | −26.1113 | + | 29.4439i | −1.70695 | + | 1.92481i | ||||
\(235\) | −4.26368 | −0.278132 | ||||||||
\(236\) | −11.1241 | − | 19.2676i | −0.724119 | − | 1.25421i | ||||
\(237\) | 3.83199 | + | 6.63720i | 0.248915 | + | 0.431133i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.1037 | 1.04166 | 0.520831 | − | 0.853660i | \(-0.325622\pi\) | ||||
0.520831 | + | 0.853660i | \(0.325622\pi\) | |||||||
\(240\) | 3.11449 | − | 5.39445i | 0.201039 | − | 0.348210i | ||||
\(241\) | 2.00300 | − | 3.46930i | 0.129025 | − | 0.223477i | −0.794274 | − | 0.607559i | \(-0.792149\pi\) |
0.923299 | + | 0.384082i | \(0.125482\pi\) | |||||||
\(242\) | 25.4433 | 1.63556 | ||||||||
\(243\) | −8.98786 | + | 15.5674i | −0.576572 | + | 0.998651i | ||||
\(244\) | −4.08548 | − | 7.07625i | −0.261546 | − | 0.453011i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 24.1253 | 1.53817 | ||||||||
\(247\) | −4.36287 | − | 13.0901i | −0.277603 | − | 0.832906i | ||||
\(248\) | 12.1526 | 0.771692 | ||||||||
\(249\) | −3.94588 | − | 6.83446i | −0.250060 | − | 0.433116i | ||||
\(250\) | −10.5969 | − | 18.3544i | −0.670209 | − | 1.16084i | ||||
\(251\) | −1.62344 | + | 2.81188i | −0.102471 | + | 0.177484i | −0.912702 | − | 0.408626i | \(-0.866008\pi\) |
0.810231 | + | 0.586110i | \(0.199341\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.42763 | − | 4.20477i | 0.152624 | − | 0.264352i | ||||
\(254\) | 5.07489 | − | 8.78996i | 0.318427 | − | 0.551531i | ||||
\(255\) | 17.4439 | 1.09238 | ||||||||
\(256\) | 13.8778 | − | 24.0371i | 0.867365 | − | 1.50232i | ||||
\(257\) | 13.4462 | + | 23.2895i | 0.838751 | + | 1.45276i | 0.890940 | + | 0.454122i | \(0.150047\pi\) |
−0.0521891 | + | 0.998637i | \(0.516620\pi\) | |||||||
\(258\) | −20.9631 | − | 36.3092i | −1.30511 | − | 2.26051i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.14650 | + | 12.4410i | 0.257155 | + | 0.771556i | ||||
\(261\) | −18.1005 | −1.12040 | ||||||||
\(262\) | −2.59050 | − | 4.48688i | −0.160042 | − | 0.277200i | ||||
\(263\) | 1.90353 | + | 3.29701i | 0.117377 | + | 0.203302i | 0.918727 | − | 0.394893i | \(-0.129218\pi\) |
−0.801351 | + | 0.598195i | \(0.795885\pi\) | |||||||
\(264\) | 3.28815 | − | 5.69525i | 0.202372 | − | 0.350518i | ||||
\(265\) | 0.418000 | 0.0256775 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.87958 | + | 4.98757i | −0.176227 | + | 0.305235i | ||||
\(268\) | 25.9673 | 1.58620 | ||||||||
\(269\) | 11.9190 | − | 20.6444i | 0.726716 | − | 1.25871i | −0.231548 | − | 0.972824i | \(-0.574379\pi\) |
0.958264 | − | 0.285886i | \(-0.0922878\pi\) | |||||||
\(270\) | −5.06859 | − | 8.77905i | −0.308464 | − | 0.534276i | ||||
\(271\) | −4.95068 | − | 8.57482i | −0.300732 | − | 0.520883i | 0.675570 | − | 0.737296i | \(-0.263898\pi\) |
−0.976302 | + | 0.216413i | \(0.930564\pi\) | |||||||
\(272\) | −14.8750 | −0.901931 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.9715 | −1.20653 | ||||||||
\(275\) | −1.18593 | − | 2.05409i | −0.0715142 | − | 0.123866i | ||||
\(276\) | 42.0763 | + | 72.8783i | 2.53270 | + | 4.38676i | ||||
\(277\) | −5.89289 | + | 10.2068i | −0.354069 | + | 0.613266i | −0.986958 | − | 0.160977i | \(-0.948536\pi\) |
0.632889 | + | 0.774243i | \(0.281869\pi\) | |||||||
\(278\) | 1.37769 | 0.0826285 | ||||||||
\(279\) | 6.83017 | − | 11.8302i | 0.408912 | − | 0.708256i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9976 | 0.775372 | 0.387686 | − | 0.921791i | \(-0.373274\pi\) | ||||
0.387686 | + | 0.921791i | \(0.373274\pi\) | |||||||
\(282\) | 14.2602 | − | 24.6994i | 0.849184 | − | 1.47083i | ||||
\(283\) | 8.40249 | + | 14.5535i | 0.499476 | + | 0.865118i | 1.00000 | 0.000604910i | \(-0.000192549\pi\) | |
−0.500524 | + | 0.865723i | \(0.666859\pi\) | |||||||
\(284\) | −6.66959 | − | 11.5521i | −0.395767 | − | 0.685489i | ||||
\(285\) | 10.3430 | 0.612668 | ||||||||
\(286\) | 1.60029 | + | 4.80143i | 0.0946270 | + | 0.283914i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.00719 | − | 10.4048i | −0.353977 | − | 0.613107i | ||||
\(289\) | −12.3283 | − | 21.3533i | −0.725197 | − | 1.25608i | ||||
\(290\) | −4.64474 | + | 8.04493i | −0.272749 | + | 0.472414i | ||||
\(291\) | −21.1783 | −1.24149 | ||||||||
\(292\) | −9.13512 | + | 15.8225i | −0.534592 | + | 0.925941i | ||||
\(293\) | 7.04782 | − | 12.2072i | 0.411738 | − | 0.713151i | −0.583342 | − | 0.812227i | \(-0.698255\pi\) |
0.995080 | + | 0.0990757i | \(0.0315886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.95108 | + | 5.11141i | −0.171818 | + | 0.297598i | ||||
\(296\) | 3.56985 | + | 6.18316i | 0.207493 | + | 0.359389i | ||||
\(297\) | −1.27011 | − | 2.19990i | −0.0736994 | − | 0.127651i | ||||
\(298\) | −6.70232 | −0.388255 | ||||||||
\(299\) | −29.1770 | − | 5.97172i | −1.68735 | − | 0.345353i | ||||
\(300\) | 41.1097 | 2.37347 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −27.4754 | − | 47.5888i | −1.58103 | − | 2.73843i | ||||
\(303\) | −3.62827 | + | 6.28434i | −0.208439 | + | 0.361026i | ||||
\(304\) | −8.81986 | −0.505854 | ||||||||
\(305\) | −1.08382 | + | 1.87723i | −0.0620593 | + | 0.107490i | ||||
\(306\) | −35.2233 | + | 61.0085i | −2.01358 | + | 3.48762i | ||||
\(307\) | 15.8786 | 0.906240 | 0.453120 | − | 0.891450i | \(-0.350311\pi\) | ||||
0.453120 | + | 0.891450i | \(0.350311\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.9431 | − | 25.8823i | −0.850086 | − | 1.47239i | ||||
\(310\) | −3.50535 | − | 6.07145i | −0.199091 | − | 0.344835i | ||||
\(311\) | −28.6034 | −1.62195 | −0.810975 | − | 0.585081i | \(-0.801063\pi\) | ||||
−0.810975 | + | 0.585081i | \(0.801063\pi\) | |||||||
\(312\) | −39.5195 | − | 8.08853i | −2.23735 | − | 0.457923i | ||||
\(313\) | −18.5792 | −1.05016 | −0.525080 | − | 0.851053i | \(-0.675965\pi\) | ||||
−0.525080 | + | 0.851053i | \(0.675965\pi\) | |||||||
\(314\) | 26.9561 | + | 46.6893i | 1.52122 | + | 2.63483i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.15679 | + | 8.93182i | −0.290092 | + | 0.502454i | ||||
\(317\) | 30.6445 | 1.72117 | 0.860584 | − | 0.509309i | \(-0.170099\pi\) | ||||
0.860584 | + | 0.509309i | \(0.170099\pi\) | |||||||
\(318\) | −1.39804 | + | 2.42147i | −0.0783979 | + | 0.135789i | ||||
\(319\) | −1.16390 | + | 2.01594i | −0.0651660 | + | 0.112871i | ||||
\(320\) | −10.6937 | −0.597796 | ||||||||
\(321\) | −21.9850 | + | 38.0791i | −1.22708 | + | 2.12537i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.3498 | − | 21.3904i | −0.687160 | − | 1.19020i | ||||
\(324\) | −6.74346 | −0.374637 | ||||||||
\(325\) | −9.65311 | + | 10.8852i | −0.535458 | + | 0.603800i | ||||
\(326\) | −19.5273 | −1.08152 | ||||||||
\(327\) | 12.7046 | + | 22.0051i | 0.702568 | + | 1.21688i | ||||
\(328\) | 7.46483 | + | 12.9295i | 0.412177 | + | 0.713911i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.79379 | −0.208842 | ||||||||
\(331\) | −13.6138 | + | 23.5799i | −0.748284 | + | 1.29607i | 0.200360 | + | 0.979722i | \(0.435789\pi\) |
−0.948644 | + | 0.316344i | \(0.897545\pi\) | |||||||
\(332\) | 5.31005 | − | 9.19728i | 0.291427 | − | 0.504766i | ||||
\(333\) | 8.02549 | 0.439794 | ||||||||
\(334\) | −2.77933 | + | 4.81395i | −0.152078 | + | 0.263407i | ||||
\(335\) | −3.44438 | − | 5.96584i | −0.188187 | − | 0.325949i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.3160 | −0.670898 | −0.335449 | − | 0.942058i | \(-0.608888\pi\) | ||||
−0.335449 | + | 0.942058i | \(0.608888\pi\) | |||||||
\(338\) | 24.8369 | − | 18.6249i | 1.35095 | − | 1.01306i | ||||
\(339\) | −28.0107 | −1.52133 | ||||||||
\(340\) | 11.7373 | + | 20.3296i | 0.636545 | + | 1.10253i | ||||
\(341\) | −0.878389 | − | 1.52141i | −0.0475674 | − | 0.0823892i | ||||
\(342\) | −20.8850 | + | 36.1738i | −1.12933 | + | 1.95606i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.9728 | − | 22.4695i | 0.699445 | − | 1.21148i | ||||
\(345\) | 11.1623 | − | 19.3336i | 0.600956 | − | 1.04089i | ||||
\(346\) | 19.4236 | 1.04422 | ||||||||
\(347\) | −3.07253 | + | 5.32177i | −0.164942 | + | 0.285688i | −0.936635 | − | 0.350308i | \(-0.886077\pi\) |
0.771693 | + | 0.635996i | \(0.219410\pi\) | |||||||
\(348\) | −20.1731 | − | 34.9408i | −1.08139 | − | 1.87302i | ||||
\(349\) | −6.51563 | − | 11.2854i | −0.348774 | − | 0.604094i | 0.637258 | − | 0.770650i | \(-0.280068\pi\) |
−0.986032 | + | 0.166557i | \(0.946735\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.3383 | + | 11.6578i | −0.551820 | + | 0.622249i | ||||
\(352\) | −1.54510 | −0.0823541 | ||||||||
\(353\) | −15.8332 | − | 27.4240i | −0.842718 | − | 1.45963i | −0.887589 | − | 0.460637i | \(-0.847621\pi\) |
0.0448710 | − | 0.998993i | \(-0.485712\pi\) | |||||||
\(354\) | −19.7402 | − | 34.1911i | −1.04918 | − | 1.81724i | ||||
\(355\) | −1.76935 | + | 3.06460i | −0.0939072 | + | 0.162652i | ||||
\(356\) | −7.75021 | −0.410761 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.0655 | + | 43.4147i | −1.32475 | + | 2.29454i | ||||
\(359\) | 19.9322 | 1.05198 | 0.525991 | − | 0.850490i | \(-0.323695\pi\) | ||||
0.525991 | + | 0.850490i | \(0.323695\pi\) | |||||||
\(360\) | 9.12780 | − | 15.8098i | 0.481077 | − | 0.833251i | ||||
\(361\) | 2.17744 | + | 3.77144i | 0.114602 | + | 0.198497i | ||||
\(362\) | −1.92007 | − | 3.32566i | −0.100917 | − | 0.174793i | ||||
\(363\) | 29.3156 | 1.53867 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.84684 | 0.253695 | ||||||||
\(366\) | −7.24984 | − | 12.5571i | −0.378955 | − | 0.656370i | ||||
\(367\) | −9.85950 | − | 17.0772i | −0.514662 | − | 0.891420i | −0.999855 | − | 0.0170133i | \(-0.994584\pi\) |
0.485194 | − | 0.874407i | \(-0.338749\pi\) | |||||||
\(368\) | −9.51844 | + | 16.4864i | −0.496183 | + | 0.859414i | ||||
\(369\) | 16.7819 | 0.873632 | ||||||||
\(370\) | 2.05940 | − | 3.56699i | 0.107063 | − | 0.185439i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 30.4490 | 1.57870 | ||||||||
\(373\) | −8.77345 | + | 15.1961i | −0.454272 | + | 0.786823i | −0.998646 | − | 0.0520202i | \(-0.983434\pi\) |
0.544374 | + | 0.838843i | \(0.316767\pi\) | |||||||
\(374\) | 4.52986 | + | 7.84595i | 0.234234 | + | 0.405704i | ||||
\(375\) | −12.2097 | − | 21.1478i | −0.630507 | − | 1.09207i | ||||
\(376\) | 17.6496 | 0.910207 | ||||||||
\(377\) | 13.9887 | + | 2.86308i | 0.720452 | + | 0.147456i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.85068 | + | 10.1337i | 0.300529 | + | 0.520532i | 0.976256 | − | 0.216620i | \(-0.0695034\pi\) |
−0.675727 | + | 0.737152i | \(0.736170\pi\) | |||||||
\(380\) | 6.95942 | + | 12.0541i | 0.357010 | + | 0.618360i | ||||
\(381\) | 5.84725 | − | 10.1277i | 0.299563 | − | 0.518859i | ||||
\(382\) | 27.6110 | 1.41270 | ||||||||
\(383\) | 10.7644 | − | 18.6445i | 0.550036 | − | 0.952690i | −0.448235 | − | 0.893916i | \(-0.647947\pi\) |
0.998271 | − | 0.0587748i | \(-0.0187194\pi\) | |||||||
\(384\) | 28.5334 | − | 49.4213i | 1.45609 | − | 2.52202i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 28.1536 | − | 48.7634i | 1.43298 | − | 2.48199i | ||||
\(387\) | −14.5823 | − | 25.2572i | −0.741258 | − | 1.28390i | ||||
\(388\) | −14.2500 | − | 24.6817i | −0.723435 | − | 1.25303i | ||||
\(389\) | 26.4910 | 1.34315 | 0.671574 | − | 0.740938i | \(-0.265619\pi\) | ||||
0.671574 | + | 0.740938i | \(0.265619\pi\) | |||||||
\(390\) | 7.35814 | + | 22.0770i | 0.372594 | + | 1.11791i | ||||
\(391\) | −53.3118 | −2.69609 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.98476 | − | 5.16975i | −0.150561 | − | 0.260779i | ||||
\(394\) | −1.75633 | + | 3.04206i | −0.0884828 | + | 0.153257i | ||||
\(395\) | 2.73605 | 0.137665 | ||||||||
\(396\) | 4.97392 | − | 8.61508i | 0.249949 | − | 0.432924i | ||||
\(397\) | 16.8995 | − | 29.2707i | 0.848160 | − | 1.46906i | −0.0346887 | − | 0.999398i | \(-0.511044\pi\) |
0.882849 | − | 0.469658i | \(-0.155623\pi\) | |||||||
\(398\) | −22.4332 | −1.12447 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.64989 | + | 8.05384i | 0.232494 | + | 0.402692i | ||||
\(401\) | −10.8059 | − | 18.7164i | −0.539623 | − | 0.934655i | −0.998924 | − | 0.0463741i | \(-0.985233\pi\) |
0.459301 | − | 0.888281i | \(-0.348100\pi\) | |||||||
\(402\) | 46.0800 | 2.29826 | ||||||||
\(403\) | −7.14983 | + | 8.06237i | −0.356158 | + | 0.401615i | ||||
\(404\) | −9.76527 | −0.485840 | ||||||||
\(405\) | 0.894473 | + | 1.54927i | 0.0444467 | + | 0.0769839i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.516056 | − | 0.893835i | 0.0255799 | − | 0.0443058i | ||||
\(408\) | −72.2093 | −3.57489 | ||||||||
\(409\) | −3.87109 | + | 6.70492i | −0.191413 | + | 0.331537i | −0.945719 | − | 0.324986i | \(-0.894640\pi\) |
0.754306 | + | 0.656523i | \(0.227974\pi\) | |||||||
\(410\) | 4.30637 | − | 7.45886i | 0.212677 | − | 0.368367i | ||||
\(411\) | −23.0111 | −1.13505 | ||||||||
\(412\) | 20.1093 | − | 34.8303i | 0.990714 | − | 1.71597i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 45.0783 | + | 78.0780i | 2.21548 | + | 3.83732i | ||||
\(415\) | −2.81736 | −0.138299 | ||||||||
\(416\) | 2.99675 | + | 8.99132i | 0.146928 | + | 0.440836i | ||||
\(417\) | 1.58737 | 0.0777337 | ||||||||
\(418\) | 2.68589 | + | 4.65211i | 0.131371 | + | 0.227542i | ||||
\(419\) | 4.05097 | + | 7.01649i | 0.197903 | + | 0.342778i | 0.947848 | − | 0.318722i | \(-0.103254\pi\) |
−0.749945 | + | 0.661500i | \(0.769920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.1124 | −1.56506 | −0.782530 | − | 0.622612i | \(-0.786071\pi\) | ||||
−0.782530 | + | 0.622612i | \(0.786071\pi\) | |||||||
\(422\) | −10.6771 | + | 18.4933i | −0.519755 | + | 0.900242i | ||||
\(423\) | 9.91963 | − | 17.1813i | 0.482309 | − | 0.835384i | ||||
\(424\) | −1.73032 | −0.0840316 | ||||||||
\(425\) | −13.0218 | + | 22.5543i | −0.631648 | + | 1.09405i | ||||
\(426\) | −11.8355 | − | 20.4996i | −0.573430 | − | 0.993210i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −59.1713 | −2.86015 | ||||||||
\(429\) | 1.84384 | + | 5.53217i | 0.0890214 | + | 0.267096i | ||||
\(430\) | −14.9677 | −0.721806 | ||||||||
\(431\) | 14.7640 | + | 25.5721i | 0.711159 | + | 1.23176i | 0.964422 | + | 0.264366i | \(0.0851627\pi\) |
−0.253263 | + | 0.967397i | \(0.581504\pi\) | |||||||
\(432\) | 4.97996 | + | 8.62554i | 0.239598 | + | 0.414997i | ||||
\(433\) | −11.0455 | + | 19.1314i | −0.530813 | + | 0.919395i | 0.468540 | + | 0.883442i | \(0.344780\pi\) |
−0.999353 | + | 0.0359531i | \(0.988553\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.35164 | + | 9.26931i | −0.256591 | + | 0.444429i | ||||
\(436\) | −17.0969 | + | 29.6127i | −0.818792 | + | 1.41819i | ||||
\(437\) | −31.6102 | −1.51212 | ||||||||
\(438\) | −16.2106 | + | 28.0777i | −0.774575 | + | 1.34160i | ||||
\(439\) | 3.17790 | + | 5.50428i | 0.151673 | + | 0.262705i | 0.931843 | − | 0.362863i | \(-0.118201\pi\) |
−0.780170 | + | 0.625568i | \(0.784867\pi\) | |||||||
\(440\) | −1.17387 | − | 2.03321i | −0.0559622 | − | 0.0969294i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.8718 | − | 41.5777i | 1.75381 | − | 1.97765i | ||||
\(443\) | −13.5627 | −0.644383 | −0.322192 | − | 0.946675i | \(-0.604420\pi\) | ||||
−0.322192 | + | 0.946675i | \(0.604420\pi\) | |||||||
\(444\) | 8.94443 | + | 15.4922i | 0.424484 | + | 0.735227i | ||||
\(445\) | 1.02801 | + | 1.78057i | 0.0487324 | + | 0.0844070i | ||||
\(446\) | 26.0530 | − | 45.1251i | 1.23365 | − | 2.13674i | ||||
\(447\) | −7.72237 | −0.365255 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.9559 | + | 18.9762i | −0.517041 | + | 0.895541i | 0.482763 | + | 0.875751i | \(0.339633\pi\) |
−0.999804 | + | 0.0197900i | \(0.993700\pi\) | |||||||
\(450\) | 44.0428 | 2.07620 | ||||||||
\(451\) | 1.07911 | − | 1.86908i | 0.0508134 | − | 0.0880115i | ||||
\(452\) | −18.8473 | − | 32.6445i | −0.886502 | − | 1.53547i | ||||
\(453\) | −31.6570 | − | 54.8315i | −1.48737 | − | 2.57621i | ||||
\(454\) | 44.3041 | 2.07930 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −42.8151 | −2.00500 | ||||||||
\(457\) | −7.60732 | − | 13.1763i | −0.355855 | − | 0.616359i | 0.631409 | − | 0.775450i | \(-0.282477\pi\) |
−0.987264 | + | 0.159091i | \(0.949144\pi\) | |||||||
\(458\) | 23.1049 | + | 40.0188i | 1.07962 | + | 1.86996i | ||||
\(459\) | −13.9461 | + | 24.1554i | −0.650949 | + | 1.12748i | ||||
\(460\) | 30.0426 | 1.40074 | ||||||||
\(461\) | 8.10813 | − | 14.0437i | 0.377633 | − | 0.654080i | −0.613084 | − | 0.790018i | \(-0.710071\pi\) |
0.990717 | + | 0.135937i | \(0.0434046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44769 | −0.0672799 | −0.0336400 | − | 0.999434i | \(-0.510710\pi\) | ||||
−0.0336400 | + | 0.999434i | \(0.510710\pi\) | |||||||
\(464\) | 4.56353 | − | 7.90426i | 0.211856 | − | 0.366946i | ||||
\(465\) | −4.03884 | − | 6.99547i | −0.187297 | − | 0.324407i | ||||
\(466\) | 19.2994 | + | 33.4275i | 0.894027 | + | 1.54850i | ||||
\(467\) | 14.0067 | 0.648155 | 0.324078 | − | 0.946031i | \(-0.394946\pi\) | ||||
0.324078 | + | 0.946031i | \(0.394946\pi\) | |||||||
\(468\) | −59.7803 | − | 12.2353i | −2.76334 | − | 0.565579i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.09091 | − | 8.81772i | −0.234826 | − | 0.406731i | ||||
\(471\) | 31.0586 | + | 53.7951i | 1.43111 | + | 2.47875i | ||||
\(472\) | 12.2160 | − | 21.1588i | 0.562288 | − | 0.973912i | ||||
\(473\) | −3.75068 | −0.172456 | ||||||||
\(474\) | −9.15094 | + | 15.8499i | −0.420316 | + | 0.728009i | ||||
\(475\) | −7.72100 | + | 13.3732i | −0.354264 | + | 0.613603i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.972495 | + | 1.68441i | −0.0445275 | + | 0.0771239i | ||||
\(478\) | 19.2281 | + | 33.3041i | 0.879474 | + | 1.52329i | ||||
\(479\) | 15.0122 | + | 26.0018i | 0.685923 | + | 1.18805i | 0.973146 | + | 0.230189i | \(0.0739345\pi\) |
−0.287223 | + | 0.957864i | \(0.592732\pi\) | |||||||
\(480\) | −7.10439 | −0.324270 | ||||||||
\(481\) | −6.20235 | − | 1.26945i | −0.282803 | − | 0.0578817i | ||||
\(482\) | 9.56649 | 0.435742 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.7253 | + | 34.1652i | 0.896605 | + | 1.55296i | ||||
\(485\) | −3.78033 | + | 6.54772i | −0.171656 | + | 0.297317i | ||||
\(486\) | −42.9267 | −1.94719 | ||||||||
\(487\) | 14.2452 | − | 24.6733i | 0.645510 | − | 1.11806i | −0.338674 | − | 0.940904i | \(-0.609978\pi\) |
0.984184 | − | 0.177152i | \(-0.0566884\pi\) | |||||||
\(488\) | 4.48649 | − | 7.77082i | 0.203094 | − | 0.351769i | ||||
\(489\) | −22.4992 | −1.01745 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2339 | + | 24.6538i | 0.642365 | + | 1.11261i | 0.984903 | + | 0.173105i | \(0.0553799\pi\) |
−0.342539 | + | 0.939504i | \(0.611287\pi\) | |||||||
\(492\) | 18.7035 | + | 32.3954i | 0.843218 | + | 1.46050i | ||||
\(493\) | 25.5598 | 1.15116 | ||||||||
\(494\) | 21.8624 | − | 24.6527i | 0.983636 | − | 1.10918i | ||||
\(495\) | −2.63902 | −0.118615 | ||||||||
\(496\) | 3.44406 | + | 5.96528i | 0.154643 | + | 0.267849i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.42290 | − | 16.3209i | 0.422250 | − | 0.731359i | ||||
\(499\) | −26.2329 | −1.17434 | −0.587172 | − | 0.809462i | \(-0.699759\pi\) | ||||
−0.587172 | + | 0.809462i | \(0.699759\pi\) | |||||||
\(500\) | 16.4309 | − | 28.4591i | 0.734811 | − | 1.27273i | ||||
\(501\) | −3.20233 | + | 5.54659i | −0.143069 | + | 0.247803i | ||||
\(502\) | −7.75367 | −0.346063 | ||||||||
\(503\) | −4.26588 | + | 7.38872i | −0.190206 | + | 0.329447i | −0.945318 | − | 0.326149i | \(-0.894249\pi\) |
0.755112 | + | 0.655595i | \(0.227582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.29529 | + | 2.24352i | 0.0576398 | + | 0.0998351i | ||||
\(506\) | 11.5945 | 0.515440 | ||||||||
\(507\) | 28.6169 | − | 21.4595i | 1.27092 | − | 0.953050i | ||||
\(508\) | 15.7375 | 0.698240 | ||||||||
\(509\) | 6.51298 | + | 11.2808i | 0.288683 | + | 0.500014i | 0.973496 | − | 0.228706i | \(-0.0734493\pi\) |
−0.684813 | + | 0.728719i | \(0.740116\pi\) | |||||||
\(510\) | 20.8283 | + | 36.0758i | 0.922295 | + | 1.59746i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.8008 | 1.09605 | ||||||||
\(513\) | −8.26908 | + | 14.3225i | −0.365089 | + | 0.632352i | ||||
\(514\) | −32.1100 | + | 55.6162i | −1.41631 | + | 2.45312i | ||||
\(515\) | −10.6694 | −0.470151 | ||||||||
\(516\) | 32.5039 | − | 56.2984i | 1.43090 | − | 2.47840i | ||||
\(517\) | −1.27571 | − | 2.20959i | −0.0561055 | − | 0.0971775i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.3798 | 0.982363 | ||||||||
\(520\) | −9.55499 | + | 10.7745i | −0.419014 | + | 0.472493i | ||||
\(521\) | 4.46570 | 0.195646 | 0.0978230 | − | 0.995204i | \(-0.468812\pi\) | ||||
0.0978230 | + | 0.995204i | \(0.468812\pi\) | |||||||
\(522\) | −21.6124 | − | 37.4337i | −0.945948 | − | 1.63843i | ||||
\(523\) | 1.45406 | + | 2.51850i | 0.0635815 | + | 0.110126i | 0.896064 | − | 0.443925i | \(-0.146414\pi\) |
−0.832482 | + | 0.554051i | \(0.813081\pi\) | |||||||
\(524\) | 4.01665 | − | 6.95704i | 0.175468 | − | 0.303920i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.54570 | + | 7.87339i | −0.198202 | + | 0.343296i | ||||
\(527\) | −9.64490 | + | 16.7055i | −0.420138 | + | 0.727701i | ||||
\(528\) | 3.72746 | 0.162217 | ||||||||
\(529\) | −22.6139 | + | 39.1684i | −0.983213 | + | 1.70297i | ||||
\(530\) | 0.499100 | + | 0.864466i | 0.0216795 | + | 0.0375500i | ||||
\(531\) | −13.7316 | − | 23.7838i | −0.595901 | − | 1.03213i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.9696 | − | 2.65451i | −0.561775 | − | 0.114980i | ||||
\(534\) | −13.7531 | −0.595154 | ||||||||
\(535\) | 7.84866 | + | 13.5943i | 0.339327 | + | 0.587732i | ||||
\(536\) | 14.2581 | + | 24.6957i | 0.615854 | + | 1.06669i | ||||
\(537\) | −28.8803 | + | 50.0221i | −1.24628 | + | 2.15861i | ||||
\(538\) | 56.9262 | 2.45426 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.85899 | − | 13.6122i | 0.338197 | − | 0.585775i | ||||
\(541\) | −18.4639 | −0.793824 | −0.396912 | − | 0.917857i | \(-0.629918\pi\) | ||||
−0.396912 | + | 0.917857i | \(0.629918\pi\) | |||||||
\(542\) | 11.8224 | − | 20.4770i | 0.507815 | − | 0.879562i | ||||
\(543\) | −2.21229 | − | 3.83180i | −0.0949384 | − | 0.164438i | ||||
\(544\) | 8.48277 | + | 14.6926i | 0.363696 | + | 0.629940i | ||||
\(545\) | 9.07112 | 0.388564 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.9817 | 1.49571 | 0.747856 | − | 0.663861i | \(-0.231083\pi\) | ||||
0.747856 | + | 0.663861i | \(0.231083\pi\) | |||||||
\(548\) | −15.4832 | − | 26.8177i | −0.661411 | − | 1.14560i | ||||
\(549\) | −5.04310 | − | 8.73491i | −0.215234 | − | 0.372797i | ||||
\(550\) | 2.83204 | − | 4.90524i | 0.120759 | − | 0.209160i | ||||
\(551\) | 15.1552 | 0.645633 | ||||||||
\(552\) | −46.2063 | + | 80.0317i | −1.96667 | + | 3.40638i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −28.1449 | −1.19576 | ||||||||
\(555\) | 2.37283 | − | 4.10986i | 0.100721 | − | 0.174454i | ||||
\(556\) | 1.06808 | + | 1.84996i | 0.0452965 | + | 0.0784559i | ||||
\(557\) | −0.0265706 | − | 0.0460217i | −0.00112583 | − | 0.00195000i | 0.865462 | − | 0.500975i | \(-0.167025\pi\) |
−0.866588 | + | 0.499025i | \(0.833692\pi\) | |||||||
\(558\) | 32.6214 | 1.38097 | ||||||||
\(559\) | 7.27451 | + | 21.8261i | 0.307679 | + | 0.923146i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.21927 | + | 9.04004i | 0.220358 | + | 0.381671i | ||||
\(562\) | 15.5194 | + | 26.8804i | 0.654646 | + | 1.13388i | ||||
\(563\) | −3.99253 | + | 6.91527i | −0.168265 | + | 0.291444i | −0.937810 | − | 0.347149i | \(-0.887150\pi\) |
0.769545 | + | 0.638593i | \(0.220483\pi\) | |||||||
\(564\) | 44.2218 | 1.86207 | ||||||||
\(565\) | −4.99992 | + | 8.66012i | −0.210348 | + | 0.364334i | ||||
\(566\) | −20.0655 | + | 34.7544i | −0.843414 | + | 1.46084i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.32424 | − | 12.6860i | 0.307318 | − | 0.532291i | ||||
\(569\) | 13.3621 | + | 23.1438i | 0.560167 | + | 0.970237i | 0.997481 | + | 0.0709285i | \(0.0225962\pi\) |
−0.437315 | + | 0.899308i | \(0.644070\pi\) | |||||||
\(570\) | 12.3498 | + | 21.3904i | 0.517275 | + | 0.895946i | ||||
\(571\) | 13.4929 | 0.564662 | 0.282331 | − | 0.959317i | \(-0.408892\pi\) | ||||
0.282331 | + | 0.959317i | \(0.408892\pi\) | |||||||
\(572\) | −5.20670 | + | 5.87124i | −0.217703 | + | 0.245489i | ||||
\(573\) | 31.8132 | 1.32902 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.6651 | + | 28.8648i | 0.694982 | + | 1.20374i | ||||
\(576\) | 24.8794 | − | 43.0923i | 1.03664 | − | 1.79551i | ||||
\(577\) | 12.0132 | 0.500118 | 0.250059 | − | 0.968231i | \(-0.419550\pi\) | ||||
0.250059 | + | 0.968231i | \(0.419550\pi\) | |||||||
\(578\) | 29.4406 | − | 50.9925i | 1.22457 | − | 2.12101i | ||||
\(579\) | 32.4383 | − | 56.1848i | 1.34809 | − | 2.33496i | ||||
\(580\) | −14.4036 | −0.598078 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −25.2872 | − | 43.7988i | −1.04819 | − | 1.81552i | ||||
\(583\) | 0.125067 | + | 0.216622i | 0.00517974 | + | 0.00897158i | ||||
\(584\) | −20.0636 | −0.830236 | ||||||||
\(585\) | 5.11843 | + | 15.3571i | 0.211621 | + | 0.634939i | ||||
\(586\) | 33.6609 | 1.39052 | ||||||||
\(587\) | −5.21177 | − | 9.02705i | −0.215113 | − | 0.372586i | 0.738195 | − | 0.674588i | \(-0.235679\pi\) |
−0.953307 | + | 0.302002i | \(0.902345\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.71876 | + | 9.90518i | −0.235637 | + | 0.408136i | ||||
\(590\) | −14.0946 | −0.580264 | ||||||||
\(591\) | −2.02364 | + | 3.50504i | −0.0832412 | + | 0.144178i | ||||
\(592\) | −2.02339 | + | 3.50462i | −0.0831610 | + | 0.144039i | ||||
\(593\) | −22.3501 | −0.917810 | −0.458905 | − | 0.888485i | \(-0.651758\pi\) | ||||
−0.458905 | + | 0.888485i | \(0.651758\pi\) | |||||||
\(594\) | 3.03307 | − | 5.25344i | 0.124449 | − | 0.215551i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.19607 | − | 8.99986i | −0.212839 | − | 0.368649i | ||||
\(597\) | −25.8474 | −1.05786 | ||||||||
\(598\) | −22.4878 | − | 67.4714i | −0.919595 | − | 2.75911i | ||||
\(599\) | 1.15893 | 0.0473524 | 0.0236762 | − | 0.999720i | \(-0.492463\pi\) | ||||
0.0236762 | + | 0.999720i | \(0.492463\pi\) | |||||||
\(600\) | 22.5724 | + | 39.0966i | 0.921515 | + | 1.59611i | ||||
\(601\) | −21.0907 | − | 36.5301i | −0.860306 | − | 1.49009i | −0.871633 | − | 0.490158i | \(-0.836939\pi\) |
0.0113271 | − | 0.999936i | \(-0.496394\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.0540 | 1.30534 | ||||||||
\(604\) | 42.6014 | − | 73.7879i | 1.73343 | − | 3.00239i | ||||
\(605\) | 5.23284 | − | 9.06355i | 0.212745 | − | 0.368486i | ||||
\(606\) | −17.3289 | −0.703937 | ||||||||
\(607\) | 9.07844 | − | 15.7243i | 0.368482 | − | 0.638230i | −0.620846 | − | 0.783932i | \(-0.713211\pi\) |
0.989328 | + | 0.145702i | \(0.0465441\pi\) | |||||||
\(608\) | 5.02970 | + | 8.71169i | 0.203981 | + | 0.353306i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.17640 | −0.209586 | ||||||||
\(611\) | −10.3839 | + | 11.7092i | −0.420087 | + | 0.473703i | ||||
\(612\) | −109.229 | −4.41534 | ||||||||
\(613\) | 0.451323 | + | 0.781714i | 0.0182288 | + | 0.0315731i | 0.874996 | − | 0.484130i | \(-0.160864\pi\) |
−0.856767 | + | 0.515703i | \(0.827531\pi\) | |||||||
\(614\) | 18.9594 | + | 32.8386i | 0.765137 | + | 1.32526i | ||||
\(615\) | 4.96177 | − | 8.59404i | 0.200078 | − | 0.346545i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.0218 | − | 22.5544i | 0.524238 | − | 0.908008i | −0.475363 | − | 0.879790i | \(-0.657683\pi\) |
0.999602 | − | 0.0282180i | \(-0.00898327\pi\) | |||||||
\(618\) | 35.6848 | − | 61.8079i | 1.43545 | − | 2.48628i | ||||
\(619\) | 26.8341 | 1.07855 | 0.539277 | − | 0.842128i | \(-0.318697\pi\) | ||||
0.539277 | + | 0.842128i | \(0.318697\pi\) | |||||||
\(620\) | 5.43515 | − | 9.41396i | 0.218281 | − | 0.378074i | ||||
\(621\) | 17.8481 | + | 30.9138i | 0.716218 | + | 1.24053i | ||||
\(622\) | −34.1530 | − | 59.1547i | −1.36941 | − | 2.37189i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.22948 | − | 21.6910i | −0.289411 | − | 0.868335i | ||||
\(625\) | 11.4579 | 0.458315 | ||||||||
\(626\) | −22.1839 | − | 38.4237i | −0.886649 | − | 1.53572i | ||||
\(627\) | 3.09467 | + | 5.36012i | 0.123589 | + | 0.214063i | ||||
\(628\) | −41.7962 | + | 72.3932i | −1.66785 | + | 2.88880i | ||||
\(629\) | −11.3328 | −0.451869 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8061 | − | 29.1089i | 0.669039 | − | 1.15881i | −0.309135 | − | 0.951018i | \(-0.600039\pi\) |
0.978173 | − | 0.207791i | \(-0.0666273\pi\) | |||||||
\(632\) | −11.3259 | −0.450521 | ||||||||
\(633\) | −12.3021 | + | 21.3079i | −0.488965 | + | 0.846913i | ||||
\(634\) | 36.5901 | + | 63.3760i | 1.45318 | + | 2.51698i | ||||
\(635\) | −2.08747 | − | 3.61561i | −0.0828388 | − | 0.143481i | ||||
\(636\) | −4.33539 | −0.171909 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.55889 | −0.220078 | ||||||||
\(639\) | −8.23293 | − | 14.2598i | −0.325690 | − | 0.564111i | ||||
\(640\) | −10.1865 | − | 17.6435i | −0.402655 | − | 0.697419i | ||||
\(641\) | −10.5921 | + | 18.3460i | −0.418361 | + | 0.724622i | −0.995775 | − | 0.0918294i | \(-0.970729\pi\) |
0.577414 | + | 0.816452i | \(0.304062\pi\) | |||||||
\(642\) | −105.002 | −4.14410 | ||||||||
\(643\) | −0.330770 | + | 0.572910i | −0.0130443 | + | 0.0225933i | −0.872474 | − | 0.488661i | \(-0.837486\pi\) |
0.859430 | + | 0.511254i | \(0.170819\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.2457 | −0.679047 | ||||||||
\(646\) | 29.4917 | − | 51.0811i | 1.16034 | − | 2.00976i | ||||
\(647\) | 20.0162 | + | 34.6690i | 0.786916 | + | 1.36298i | 0.927848 | + | 0.372960i | \(0.121657\pi\) |
−0.140931 | + | 0.990019i | \(0.545010\pi\) | |||||||
\(648\) | −3.70268 | − | 6.41323i | −0.145455 | − | 0.251936i | ||||
\(649\) | −3.53188 | −0.138639 | ||||||||
\(650\) | −34.0376 | − | 6.96654i | −1.33506 | − | 0.273250i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.1388 | − | 26.2212i | −0.592883 | − | 1.02690i | ||||
\(653\) | −6.35602 | − | 11.0089i | −0.248730 | − | 0.430813i | 0.714444 | − | 0.699693i | \(-0.246680\pi\) |
−0.963174 | + | 0.268880i | \(0.913347\pi\) | |||||||
\(654\) | −30.3391 | + | 52.5489i | −1.18635 | + | 2.05482i | ||||
\(655\) | −2.13112 | −0.0832698 | ||||||||
\(656\) | −4.23107 | + | 7.32844i | −0.165196 | + | 0.286127i | ||||
\(657\) | −11.2764 | + | 19.5313i | −0.439933 | + | 0.761987i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.09522 | − | 12.2893i | 0.276391 | − | 0.478723i | −0.694094 | − | 0.719884i | \(-0.744195\pi\) |
0.970485 | + | 0.241161i | \(0.0775283\pi\) | |||||||
\(660\) | −2.94119 | − | 5.09430i | −0.114486 | − | 0.198295i | ||||
\(661\) | −25.0890 | − | 43.4554i | −0.975848 | − | 1.69022i | −0.677106 | − | 0.735885i | \(-0.736766\pi\) |
−0.298742 | − | 0.954334i | \(-0.596567\pi\) | |||||||
\(662\) | −65.0207 | −2.52710 | ||||||||
\(663\) | 42.4834 | − | 47.9056i | 1.64992 | − | 1.86050i | ||||
\(664\) | 11.6625 | 0.452594 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.58259 | + | 16.5975i | 0.371318 | + | 0.643141i | ||||
\(667\) | 16.3556 | − | 28.3287i | 0.633290 | − | 1.09689i | ||||
\(668\) | −8.61888 | −0.333474 | ||||||||
\(669\) | 30.0181 | − | 51.9928i | 1.16057 | − | 2.01016i | ||||
\(670\) | 8.22530 | − | 14.2466i | 0.317771 | − | 0.550396i | ||||
\(671\) | −1.29713 | −0.0500751 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.937137 | + | 1.62317i | 0.0361240 | + | 0.0625685i | 0.883522 | − | 0.468389i | \(-0.155166\pi\) |
−0.847398 | + | 0.530958i | \(0.821832\pi\) | |||||||
\(674\) | −14.7056 | − | 25.4708i | −0.566438 | − | 0.981100i | ||||
\(675\) | 17.4380 | 0.671191 | ||||||||
\(676\) | 44.2647 | + | 18.9117i | 1.70249 | + | 0.727373i | ||||
\(677\) | −2.00879 | −0.0772041 | −0.0386020 | − | 0.999255i | \(-0.512290\pi\) | ||||
−0.0386020 | + | 0.999255i | \(0.512290\pi\) | |||||||
\(678\) | −33.4453 | − | 57.9290i | −1.28446 | − | 2.22475i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.8894 | + | 22.3251i | −0.494286 | + | 0.856128i | ||||
\(681\) | 51.0469 | 1.95612 | ||||||||
\(682\) | 2.09762 | − | 3.63319i | 0.0803222 | − | 0.139122i | ||||
\(683\) | 7.05061 | − | 12.2120i | 0.269784 | − | 0.467280i | −0.699022 | − | 0.715100i | \(-0.746381\pi\) |
0.968806 | + | 0.247820i | \(0.0797143\pi\) | |||||||
\(684\) | −64.7655 | −2.47637 | ||||||||
\(685\) | −4.10748 | + | 7.11437i | −0.156939 | + | 0.271826i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.6212 | + | 46.1094i | 1.01566 | + | 1.75918i | ||||
\(688\) | 14.7060 | 0.560660 | ||||||||
\(689\) | 1.01801 | − | 1.14794i | 0.0387830 | − | 0.0437330i | ||||
\(690\) | 53.3118 | 2.02954 | ||||||||
\(691\) | 17.8460 | + | 30.9102i | 0.678895 | + | 1.17588i | 0.975314 | + | 0.220822i | \(0.0708741\pi\) |
−0.296419 | + | 0.955058i | \(0.595793\pi\) | |||||||
\(692\) | 15.0585 | + | 26.0820i | 0.572437 | + | 0.991489i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.6746 | −0.557041 | ||||||||
\(695\) | 0.283346 | − | 0.490769i | 0.0107479 | − | 0.0186159i | ||||
\(696\) | 22.1532 | − | 38.3704i | 0.839714 | − | 1.45443i | ||||
\(697\) | −23.6978 | −0.897618 | ||||||||
\(698\) | 15.5596 | − | 26.9500i | 0.588938 | − | 1.02007i | ||||
\(699\) | 22.2366 | + | 38.5150i | 0.841066 | + | 1.45677i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.15865 | −0.232609 | −0.116305 | − | 0.993214i | \(-0.537105\pi\) | ||||
−0.116305 | + | 0.993214i | \(0.537105\pi\) | |||||||
\(702\) | −36.4538 | − | 7.46106i | −1.37586 | − | 0.281600i | ||||
\(703\) | −6.71957 | −0.253434 | ||||||||
\(704\) | −3.19959 | − | 5.54185i | −0.120589 | − | 0.208866i | ||||
\(705\) | −5.86571 | − | 10.1597i | −0.220915 | − | 0.382637i | ||||
\(706\) | 37.8103 | − | 65.4894i | 1.42301 | − | 2.46473i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 30.6078 | − | 53.0143i | 1.15031 | − | 1.99240i | ||||
\(709\) | −17.0185 | + | 29.4770i | −0.639144 | + | 1.10703i | 0.346477 | + | 0.938059i | \(0.387378\pi\) |
−0.985621 | + | 0.168972i | \(0.945955\pi\) | |||||||
\(710\) | −8.45054 | −0.317143 | ||||||||
\(711\) | −6.36553 | + | 11.0254i | −0.238726 | + | 0.413486i | ||||
\(712\) | −4.25547 | − | 7.37069i | −0.159480 | − | 0.276228i | ||||
\(713\) | 12.3434 | + | 21.3794i | 0.462265 | + | 0.800667i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.03952 | + | 0.417432i | 0.0762736 | + | 0.0156111i | ||||
\(716\) | −77.7295 | −2.90489 | ||||||||
\(717\) | 22.1545 | + | 38.3727i | 0.827375 | + | 1.43306i | ||||
\(718\) | 23.7994 | + | 41.2218i | 0.888187 | + | 1.53838i | ||||
\(719\) | 11.4824 | − | 19.8881i | 0.428222 | − | 0.741702i | −0.568493 | − | 0.822688i | \(-0.692474\pi\) |
0.996715 | + | 0.0809859i | \(0.0258069\pi\) | |||||||
\(720\) | 10.3473 | 0.385621 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.19981 | + | 9.00633i | −0.193517 | + | 0.335181i | ||||
\(723\) | 11.0224 | 0.409929 | ||||||||
\(724\) | 2.97712 | − | 5.15653i | 0.110644 | − | 0.191641i | ||||
\(725\) | −7.98992 | − | 13.8389i | −0.296738 | − | 0.513966i | ||||
\(726\) | 35.0034 | + | 60.6276i | 1.29910 | + | 2.25010i | ||||
\(727\) | 1.06558 | 0.0395203 | 0.0197601 | − | 0.999805i | \(-0.493710\pi\) | ||||
0.0197601 | + | 0.999805i | \(0.493710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.9962 | −1.62949 | ||||||||
\(730\) | 5.78721 | + | 10.0237i | 0.214194 | + | 0.370996i | ||||
\(731\) | 20.5916 | + | 35.6658i | 0.761609 | + | 1.31915i | ||||
\(732\) | 11.2411 | − | 19.4702i | 0.415483 | − | 0.719637i | ||||
\(733\) | −26.3378 | −0.972808 | −0.486404 | − | 0.873734i | \(-0.661692\pi\) | ||||
−0.486404 | + | 0.873734i | \(0.661692\pi\) | |||||||
\(734\) | 23.5448 | − | 40.7809i | 0.869056 | − | 1.50525i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.7123 | 0.800326 | ||||||||
\(737\) | 2.06114 | − | 3.57000i | 0.0759230 | − | 0.131502i | ||||
\(738\) | 20.0379 | + | 34.7067i | 0.737606 | + | 1.27757i | ||||
\(739\) | −17.1075 | − | 29.6310i | −0.629308 | − | 1.08999i | −0.987691 | − | 0.156419i | \(-0.950005\pi\) |
0.358383 | − | 0.933575i | \(-0.383328\pi\) | |||||||
\(740\) | 6.38633 | 0.234766 | ||||||||
\(741\) | 25.1897 | − | 28.4047i | 0.925366 | − | 1.04347i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.2391 | − | 19.4667i | −0.412322 | − | 0.714163i | 0.582821 | − | 0.812600i | \(-0.301949\pi\) |
−0.995143 | + | 0.0984379i | \(0.968615\pi\) | |||||||
\(744\) | 16.7188 | + | 28.9579i | 0.612942 | + | 1.06165i | ||||
\(745\) | −1.37845 | + | 2.38754i | −0.0505023 | + | 0.0874726i | ||||
\(746\) | −41.9027 | −1.53417 | ||||||||
\(747\) | 6.55472 | − | 11.3531i | 0.239825 | − | 0.415388i | ||||
\(748\) | −7.02368 | + | 12.1654i | −0.256811 | + | 0.444810i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 29.1573 | − | 50.5018i | 1.06467 | − | 1.84407i | ||||
\(751\) | 21.2712 | + | 36.8428i | 0.776197 | + | 1.34441i | 0.934119 | + | 0.356961i | \(0.116187\pi\) |
−0.157923 | + | 0.987451i | \(0.550480\pi\) | |||||||
\(752\) | 5.00189 | + | 8.66353i | 0.182400 | + | 0.315927i | ||||
\(753\) | −8.93372 | −0.325563 | ||||||||
\(754\) | 10.7816 | + | 32.3485i | 0.392641 | + | 1.17806i | ||||
\(755\) | −22.6031 | −0.822612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.61902 | + | 9.73243i | 0.204227 | + | 0.353731i | 0.949886 | − | 0.312596i | \(-0.101199\pi\) |
−0.745659 | + | 0.666327i | \(0.767865\pi\) | |||||||
\(758\) | −13.9716 | + | 24.1996i | −0.507473 | + | 0.878969i | ||||
\(759\) | 13.3591 | 0.484906 | ||||||||
\(760\) | −7.64252 | + | 13.2372i | −0.277223 | + | 0.480165i | ||||
\(761\) | −6.40422 | + | 11.0924i | −0.232153 | + | 0.402101i | −0.958441 | − | 0.285289i | \(-0.907910\pi\) |
0.726289 | + | 0.687390i | \(0.241244\pi\) | |||||||
\(762\) | 27.9269 | 1.01168 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.4059 | + | 37.0760i | 0.774437 | + | 1.34136i | ||||
\(765\) | 14.4885 | + | 25.0948i | 0.523833 | + | 0.907306i | ||||
\(766\) | 51.4117 | 1.85758 | ||||||||
\(767\) | 6.85016 | + | 20.5529i | 0.247345 | + | 0.742122i | ||||
\(768\) | 76.3692 | 2.75574 | ||||||||
\(769\) | 25.6759 | + | 44.4719i | 0.925895 | + | 1.60370i | 0.790115 | + | 0.612958i | \(0.210021\pi\) |
0.135780 | + | 0.990739i | \(0.456646\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.9969 | + | 64.0805i | −1.33241 | + | 2.30780i | ||||
\(772\) | 87.3059 | 3.14221 | ||||||||
\(773\) | −10.0023 | + | 17.3245i | −0.359759 | + | 0.623120i | −0.987920 | − | 0.154963i | \(-0.950474\pi\) |
0.628162 | + | 0.778083i | \(0.283808\pi\) | |||||||
\(774\) | 34.8230 | − | 60.3151i | 1.25169 | − | 2.16798i | ||||
\(775\) | 12.0599 | 0.433203 | ||||||||
\(776\) | 15.6487 | − | 27.1044i | 0.561756 | − | 0.972990i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.6308 | + | 54.7861i | 1.13402 | + | 1.96418i | ||||
\(779\) | −14.0512 | −0.503435 | ||||||||
\(780\) | −23.9405 | + | 26.9960i | −0.857206 | + | 0.966613i | ||||
\(781\) | −2.11758 | −0.0757729 | ||||||||
\(782\) | −63.6552 | − | 110.254i | −2.27631 | − | 3.94268i | ||||
\(783\) | −8.55708 | − | 14.8213i | −0.305805 | − | 0.529670i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.1759 | 0.791492 | ||||||||
\(786\) | 7.12771 | − | 12.3456i | 0.254237 | − | 0.440351i | ||||
\(787\) | −14.6596 | + | 25.3911i | −0.522558 | + | 0.905096i | 0.477098 | + | 0.878850i | \(0.341689\pi\) |
−0.999656 | + | 0.0262462i | \(0.991645\pi\) | |||||||
\(788\) | −5.44650 | −0.194023 | ||||||||
\(789\) | −5.23752 | + | 9.07166i | −0.186461 | + | 0.322959i | ||||
\(790\) | 3.26689 | + | 5.65842i | 0.116231 | + | 0.201318i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.9243 | 0.388177 | ||||||||
\(793\) | 2.51581 | + | 7.54831i | 0.0893389 | + | 0.268048i | ||||
\(794\) | 80.7131 | 2.86440 | ||||||||
\(795\) | 0.575059 | + | 0.996031i | 0.0203952 | + | 0.0353256i | ||||
\(796\) | −17.3917 | − | 30.1232i | −0.616431 | − | 1.06769i | ||||
\(797\) | −1.55050 | + | 2.68554i | −0.0549215 | + | 0.0951269i | −0.892179 | − | 0.451682i | \(-0.850824\pi\) |
0.837258 | + | 0.546809i | \(0.184158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0075 | + | 24.2618i | −0.495551 | + | 0.858319i | ||||
\(800\) | 5.30338 | − | 9.18572i | 0.187503 | − | 0.324764i | ||||
\(801\) | −9.56685 | −0.338028 | ||||||||
\(802\) | 25.8050 | − | 44.6956i | 0.911206 | − | 1.57826i | ||||
\(803\) | 1.45019 | + | 2.51180i | 0.0511761 | + | 0.0886395i | ||||
\(804\) | 35.7242 | + | 61.8762i | 1.25990 | + | 2.18220i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25.2108 | − | 5.15995i | −0.888013 | − | 0.181751i | ||||
\(807\) | 65.5899 | 2.30887 | ||||||||
\(808\) | −5.36189 | − | 9.28707i | −0.188631 | − | 0.326718i | ||||
\(809\) | −3.99501 | − | 6.91957i | −0.140457 | − | 0.243279i | 0.787212 | − | 0.616683i | \(-0.211524\pi\) |
−0.927669 | + | 0.373404i | \(0.878191\pi\) | |||||||
\(810\) | −2.13603 | + | 3.69972i | −0.0750526 | + | 0.129995i | ||||
\(811\) | −48.2554 | −1.69448 | −0.847239 | − | 0.531213i | \(-0.821737\pi\) | ||||
−0.847239 | + | 0.531213i | \(0.821737\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.6217 | − | 23.5934i | 0.477733 | − | 0.827458i | ||||
\(814\) | 2.46472 | 0.0863884 | ||||||||
\(815\) | −4.01612 | + | 6.95612i | −0.140679 | + | 0.243662i | ||||
\(816\) | −20.4642 | − | 35.4449i | −0.716389 | − | 1.24082i | ||||
\(817\) | 12.2094 | + | 21.1473i | 0.427153 | + | 0.739851i | ||||
\(818\) | −18.4886 | −0.646439 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.3543 | 0.466353 | ||||||||
\(821\) | 13.7760 | + | 23.8607i | 0.480785 | + | 0.832743i | 0.999757 | − | 0.0220477i | \(-0.00701856\pi\) |
−0.518972 | + | 0.854791i | \(0.673685\pi\) | |||||||
\(822\) | −27.4756 | − | 47.5892i | −0.958323 | − | 1.65986i | ||||
\(823\) | −10.2137 | + | 17.6907i | −0.356028 | + | 0.616659i | −0.987293 | − | 0.158908i | \(-0.949203\pi\) |
0.631265 | + | 0.775567i | \(0.282536\pi\) | |||||||
\(824\) | 44.1663 | 1.53861 | ||||||||
\(825\) | 3.26306 | − | 5.65178i | 0.113605 | − | 0.196770i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.7142 | −0.963719 | −0.481859 | − | 0.876249i | \(-0.660038\pi\) | ||||
−0.481859 | + | 0.876249i | \(0.660038\pi\) | |||||||
\(828\) | −69.8953 | + | 121.062i | −2.42903 | + | 4.20720i | ||||
\(829\) | −4.62832 | − | 8.01648i | −0.160748 | − | 0.278424i | 0.774389 | − | 0.632710i | \(-0.218057\pi\) |
−0.935137 | + | 0.354286i | \(0.884724\pi\) | |||||||
\(830\) | −3.36398 | − | 5.82659i | −0.116766 | − | 0.202244i | ||||
\(831\) | −32.4283 | −1.12493 | ||||||||
\(832\) | −26.0437 | + | 29.3677i | −0.902904 | + | 1.01814i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.89535 | + | 3.28283i | 0.0656304 | + | 0.113675i | ||||
\(835\) | 1.14323 | + | 1.98014i | 0.0395632 | + | 0.0685255i | ||||
\(836\) | −4.16456 | + | 7.21323i | −0.144034 | + | 0.249475i | ||||
\(837\) | 12.9159 | 0.446440 | ||||||||
\(838\) | −9.67387 | + | 16.7556i | −0.334178 | + | 0.578814i | ||||
\(839\) | 15.1870 | − | 26.3046i | 0.524312 | − | 0.908135i | −0.475287 | − | 0.879831i | \(-0.657656\pi\) |
0.999599 | − | 0.0283045i | \(-0.00901080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.65848 | − | 11.5328i | 0.229603 | − | 0.397683i | ||||
\(842\) | −38.3428 | − | 66.4116i | −1.32138 | − | 2.28869i | ||||
\(843\) | 17.8813 | + | 30.9713i | 0.615865 | + | 1.06671i | ||||
\(844\) | −33.1104 | −1.13971 | ||||||||
\(845\) | −1.52654 | − | 12.6781i | −0.0525147 | − | 0.436139i | ||||
\(846\) | 47.3769 | 1.62885 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.490373 | − | 0.849350i | −0.0168395 | − | 0.0291668i | ||||
\(849\) | −23.1193 | + | 40.0437i | −0.793451 | + | 1.37430i | ||||
\(850\) | −62.1929 | −2.13320 | ||||||||
\(851\) | −7.25180 | + | 12.5605i | −0.248589 | + | 0.430568i | ||||
\(852\) | 18.3512 | − | 31.7853i | 0.628703 | − | 1.08894i | ||||
\(853\) | −5.30773 | −0.181733 | −0.0908666 | − | 0.995863i | \(-0.528964\pi\) | ||||
−0.0908666 | + | 0.995863i | \(0.528964\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.59069 | + | 14.8795i | 0.293795 | + | 0.508868i | ||||
\(856\) | −32.4896 | − | 56.2737i | −1.11047 | − | 1.92340i | ||||
\(857\) | −16.6371 | −0.568314 | −0.284157 | − | 0.958778i | \(-0.591714\pi\) | ||||
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(858\) | −9.23951 | + | 10.4188i | −0.315432 | + | 0.355691i | ||||
\(859\) | −10.5885 | −0.361276 | −0.180638 | − | 0.983550i | \(-0.557816\pi\) | ||||
−0.180638 | + | 0.983550i | \(0.557816\pi\) | |||||||
\(860\) | −11.6039 | − | 20.0986i | −0.395690 | − | 0.685356i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −35.2571 | + | 61.0671i | −1.20086 | + | 2.07995i | ||||
\(863\) | −56.0632 | −1.90841 | −0.954207 | − | 0.299148i | \(-0.903298\pi\) | ||||
−0.954207 | + | 0.299148i | \(0.903298\pi\) | |||||||
\(864\) | 5.67984 | − | 9.83777i | 0.193232 | − | 0.334688i | ||||
\(865\) | 3.99480 | − | 6.91919i | 0.135827 | − | 0.235260i | ||||
\(866\) | −52.7541 | −1.79266 | ||||||||
\(867\) | 33.9212 | − | 58.7532i | 1.15202 | − | 1.99536i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.818634 | + | 1.41792i | 0.0277703 | + | 0.0480995i | ||||
\(870\) | −25.5598 | −0.866559 | ||||||||
\(871\) | −24.7723 | − | 5.07019i | −0.839377 | − | 0.171797i | ||||
\(872\) | −37.5501 | −1.27161 | ||||||||
\(873\) | −17.5902 | − | 30.4671i | −0.595337 | − | 1.03115i | ||||
\(874\) | −37.7432 | − | 65.3731i | −1.27668 | − | 2.21128i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −50.2702 | −1.69847 | ||||||||
\(877\) | 1.83026 | − | 3.17010i | 0.0618033 | − | 0.107047i | −0.833468 | − | 0.552567i | \(-0.813648\pi\) |
0.895272 | + | 0.445521i | \(0.146982\pi\) | |||||||
\(878\) | −7.58894 | + | 13.1444i | −0.256114 | + | 0.443603i | ||||
\(879\) | 38.7838 | 1.30815 | ||||||||
\(880\) | 0.665353 | − | 1.15242i | 0.0224290 | − | 0.0388482i | ||||
\(881\) | −5.11493 | − | 8.85932i | −0.172326 | − | 0.298478i | 0.766906 | − | 0.641759i | \(-0.221795\pi\) |
−0.939233 | + | 0.343281i | \(0.888462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.98979 | −0.134267 | −0.0671335 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671335 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(884\) | 84.4159 | + | 17.2776i | 2.83921 | + | 0.581107i | ||||
\(885\) | −16.2396 | −0.545890 | ||||||||
\(886\) | −16.1941 | − | 28.0490i | −0.544052 | − | 0.942325i | ||||
\(887\) | 7.11039 | + | 12.3155i | 0.238743 | + | 0.413516i | 0.960354 | − | 0.278784i | \(-0.0899312\pi\) |
−0.721611 | + | 0.692299i | \(0.756598\pi\) | |||||||
\(888\) | −9.82237 | + | 17.0128i | −0.329617 | + | 0.570913i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.45493 | + | 4.25206i | −0.0822894 | + | 0.142529i | ||||
\(891\) | −0.535258 | + | 0.927094i | −0.0179318 | + | 0.0310588i | ||||
\(892\) | 80.7919 | 2.70511 | ||||||||
\(893\) | −8.30550 | + | 14.3855i | −0.277933 | + | 0.481394i | ||||
\(894\) | −9.22065 | − | 15.9706i | −0.308385 | − | 0.534138i | ||||
\(895\) | 10.3103 | + | 17.8579i | 0.344635 | + | 0.596924i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.9103 | − | 77.7400i | −0.865119 | − | 2.59566i | ||||
\(898\) | −52.3262 | −1.74615 | ||||||||
\(899\) | −5.91794 | − | 10.2502i | −0.197374 | − | 0.341862i | ||||
\(900\) | 34.1448 | + | 59.1405i | 1.13816 | + | 1.97135i | ||||
\(901\) | 1.37326 | − | 2.37856i | 0.0457500 | − | 0.0792413i | ||||
\(902\) | 5.15392 | 0.171607 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.6973 | − | 35.8487i | 0.688381 | − | 1.19231i | ||||
\(905\) | −1.57958 | −0.0525069 | ||||||||
\(906\) | 75.5980 | − | 130.940i | 2.51158 | − | 4.35018i | ||||
\(907\) | −21.7126 | − | 37.6074i | −0.720956 | − | 1.24873i | −0.960617 | − | 0.277876i | \(-0.910370\pi\) |
0.239661 | − | 0.970857i | \(-0.422964\pi\) | |||||||
\(908\) | 34.3474 | + | 59.4915i | 1.13986 | + | 1.97429i | ||||
\(909\) | −12.0542 | −0.399814 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.8617 | 0.823706 | 0.411853 | − | 0.911250i | \(-0.364882\pi\) | ||||
0.411853 | + | 0.911250i | \(0.364882\pi\) | |||||||
\(912\) | −12.1338 | − | 21.0164i | −0.401791 | − | 0.695923i | ||||
\(913\) | −0.842964 | − | 1.46006i | −0.0278980 | − | 0.0483208i | ||||
\(914\) | 18.1666 | − | 31.4654i | 0.600896 | − | 1.04078i | ||||
\(915\) | −5.96421 | −0.197171 | ||||||||
\(916\) | −35.8248 | + | 62.0503i | −1.18368 | + | 2.05020i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −66.6076 | −2.19838 | ||||||||
\(919\) | 0.831637 | − | 1.44044i | 0.0274332 | − | 0.0475157i | −0.851983 | − | 0.523570i | \(-0.824600\pi\) |
0.879416 | + | 0.476054i | \(0.157933\pi\) | |||||||
\(920\) | 16.4957 | + | 28.5714i | 0.543847 | + | 0.941971i | ||||
\(921\) | 21.8448 | + | 37.8363i | 0.719811 | + | 1.24675i | ||||
\(922\) | 38.7250 | 1.27534 | ||||||||
\(923\) | 4.10708 | + | 12.3227i | 0.135186 | + | 0.405607i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.54260 | + | 6.13597i | 0.116480 | + | 0.201749i | ||||
\(926\) | −1.72857 | − | 2.99397i | −0.0568044 | − | 0.0983880i | ||||
\(927\) | 24.8229 | − | 42.9945i | 0.815291 | − | 1.41212i | ||||
\(928\) | −10.4098 | −0.341717 | ||||||||
\(929\) | −4.74761 | + | 8.22310i | −0.155764 | + | 0.269791i | −0.933337 | − | 0.359002i | \(-0.883117\pi\) |
0.777573 | + | 0.628793i | \(0.216451\pi\) | |||||||
\(930\) | 9.64490 | − | 16.7055i | 0.316269 | − | 0.547793i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −29.9243 | + | 51.8304i | −0.980202 | + | 1.69776i | ||||
\(933\) | −39.3508 | − | 68.1576i | −1.28829 | − | 2.23138i | ||||
\(934\) | 16.7243 | + | 28.9674i | 0.547236 | + | 0.947841i | ||||
\(935\) | 3.72657 | 0.121872 | ||||||||
\(936\) | −21.1878 | − | 63.5710i | −0.692546 | − | 2.07788i | ||||
\(937\) | −6.41678 | −0.209627 | −0.104813 | − | 0.994492i | \(-0.533425\pi\) | ||||
−0.104813 | + | 0.994492i | \(0.533425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.5602 | − | 44.2715i | −0.834125 | − | 1.44475i | ||||
\(940\) | 7.89361 | − | 13.6721i | 0.257461 | − | 0.445936i | ||||
\(941\) | −51.5186 | −1.67946 | −0.839730 | − | 0.543005i | \(-0.817287\pi\) | ||||
−0.839730 | + | 0.543005i | \(0.817287\pi\) | |||||||
\(942\) | −74.1691 | + | 128.465i | −2.41656 | + | 4.18561i | ||||
\(943\) | −15.1641 | + | 26.2650i | −0.493810 | + | 0.855305i | ||||
\(944\) | 13.8481 | 0.450717 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.47838 | − | 7.75678i | −0.145605 | − | 0.252195i | ||||
\(947\) | 4.20109 | + | 7.27651i | 0.136517 | + | 0.236455i | 0.926176 | − | 0.377091i | \(-0.123076\pi\) |
−0.789659 | + | 0.613546i | \(0.789742\pi\) | |||||||
\(948\) | −28.3776 | −0.921661 | ||||||||
\(949\) | 11.8041 | − | 13.3107i | 0.383178 | − | 0.432083i | ||||
\(950\) | −36.8761 | −1.19642 | ||||||||
\(951\) | 42.1589 | + | 73.0213i | 1.36709 | + | 2.36788i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0455 | − | 31.2558i | 0.584552 | − | 1.01247i | −0.410379 | − | 0.911915i | \(-0.634604\pi\) |
0.994931 | − | 0.100559i | \(-0.0320631\pi\) | |||||||
\(954\) | −4.64471 | −0.150378 | ||||||||
\(955\) | 5.67867 | − | 9.83575i | 0.183758 | − | 0.318277i | ||||
\(956\) | −29.8138 | + | 51.6390i | −0.964246 | + | 1.67012i | ||||
\(957\) | −6.40491 | −0.207041 | ||||||||
\(958\) | −35.8496 | + | 62.0933i | −1.15825 | + | 2.00614i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −14.7117 | − | 25.4815i | −0.474820 | − | 0.822412i | ||||
\(961\) | −22.0676 | −0.711857 | ||||||||
\(962\) | −4.78037 | − | 14.3428i | −0.154125 | − | 0.462431i | ||||
\(963\) | −73.0409 | −2.35371 | ||||||||
\(964\) | 7.41656 | + | 12.8459i | 0.238871 | + | 0.413737i | ||||
\(965\) | −11.5805 | − | 20.0580i | −0.372790 | − | 0.645691i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.18338 | 0.102371 | 0.0511853 | − | 0.998689i | \(-0.483700\pi\) | ||||
0.0511853 | + | 0.998689i | \(0.483700\pi\) | |||||||
\(968\) | −21.6614 | + | 37.5187i | −0.696225 | + | 1.20590i | ||||
\(969\) | 33.9801 | − | 58.8553i | 1.09160 | − | 1.89070i | ||||
\(970\) | −18.0551 | −0.579715 | ||||||||
\(971\) | −18.8738 | + | 32.6904i | −0.605690 | + | 1.04909i | 0.386253 | + | 0.922393i | \(0.373769\pi\) |
−0.991942 | + | 0.126692i | \(0.959564\pi\) | |||||||
\(972\) | −33.2795 | − | 57.6419i | −1.06744 | − | 1.84886i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 68.0359 | 2.18001 | ||||||||
\(975\) | −39.2179 | − | 8.02679i | −1.25598 | − | 0.257063i | ||||
\(976\) | 5.08589 | 0.162795 | ||||||||
\(977\) | 10.6538 | + | 18.4530i | 0.340846 | + | 0.590363i | 0.984590 | − | 0.174878i | \(-0.0559532\pi\) |
−0.643744 | + | 0.765241i | \(0.722620\pi\) | |||||||
\(978\) | −26.8645 | − | 46.5307i | −0.859032 | − | 1.48789i | ||||
\(979\) | −0.615168 | + | 1.06550i | −0.0196609 | + | 0.0340536i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.1044 | + | 36.5538i | −0.673810 | + | 1.16707i | ||||
\(982\) | −33.9910 | + | 58.8741i | −1.08470 | + | 1.87875i | ||||
\(983\) | −22.0316 | −0.702700 | −0.351350 | − | 0.936244i | \(-0.614277\pi\) | ||||
−0.351350 | + | 0.936244i | \(0.614277\pi\) | |||||||
\(984\) | −20.5393 | + | 35.5752i | −0.654770 | + | 1.13409i | ||||
\(985\) | 0.722439 | + | 1.25130i | 0.0230188 | + | 0.0398698i | ||||
\(986\) | 30.5189 | + | 52.8603i | 0.971919 | + | 1.68341i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 50.0528 | + | 10.2444i | 1.59239 | + | 0.325918i | ||||
\(989\) | 52.7059 | 1.67595 | ||||||||
\(990\) | −3.15104 | − | 5.45776i | −0.100147 | − | 0.173459i | ||||
\(991\) | 11.0129 | + | 19.0750i | 0.349838 | + | 0.605937i | 0.986220 | − | 0.165437i | \(-0.0529033\pi\) |
−0.636383 | + | 0.771374i | \(0.719570\pi\) | |||||||
\(992\) | 3.92808 | − | 6.80364i | 0.124717 | − | 0.216016i | ||||
\(993\) | −74.9164 | −2.37740 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.61376 | + | 7.99127i | −0.146266 | + | 0.253340i | ||||
\(996\) | 29.2210 | 0.925902 | ||||||||
\(997\) | −5.04102 | + | 8.73130i | −0.159651 | + | 0.276523i | −0.934743 | − | 0.355325i | \(-0.884370\pi\) |
0.775092 | + | 0.631848i | \(0.217703\pi\) | |||||||
\(998\) | −31.3225 | − | 54.2522i | −0.991497 | − | 1.71732i | ||||
\(999\) | 3.79408 | + | 6.57153i | 0.120039 | + | 0.207914i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.f.k.393.6 | 12 | ||
7.2 | even | 3 | 91.2.g.b.81.6 | yes | 12 | ||
7.3 | odd | 6 | 637.2.h.l.471.1 | 12 | |||
7.4 | even | 3 | 91.2.h.b.16.1 | yes | 12 | ||
7.5 | odd | 6 | 637.2.g.l.263.6 | 12 | |||
7.6 | odd | 2 | 637.2.f.j.393.6 | 12 | |||
13.3 | even | 3 | 8281.2.a.bz.1.1 | 6 | |||
13.9 | even | 3 | inner | 637.2.f.k.295.6 | 12 | ||
13.10 | even | 6 | 8281.2.a.ce.1.6 | 6 | |||
21.2 | odd | 6 | 819.2.n.d.172.1 | 12 | |||
21.11 | odd | 6 | 819.2.s.d.289.6 | 12 | |||
91.9 | even | 3 | 91.2.h.b.74.1 | yes | 12 | ||
91.16 | even | 3 | 1183.2.e.h.508.6 | 12 | |||
91.23 | even | 6 | 1183.2.e.g.508.1 | 12 | |||
91.48 | odd | 6 | 637.2.f.j.295.6 | 12 | |||
91.55 | odd | 6 | 8281.2.a.ca.1.1 | 6 | |||
91.61 | odd | 6 | 637.2.h.l.165.1 | 12 | |||
91.62 | odd | 6 | 8281.2.a.cf.1.6 | 6 | |||
91.74 | even | 3 | 91.2.g.b.9.6 | ✓ | 12 | ||
91.81 | even | 3 | 1183.2.e.h.170.6 | 12 | |||
91.87 | odd | 6 | 637.2.g.l.373.6 | 12 | |||
91.88 | even | 6 | 1183.2.e.g.170.1 | 12 | |||
273.74 | odd | 6 | 819.2.n.d.100.1 | 12 | |||
273.191 | odd | 6 | 819.2.s.d.802.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.6 | ✓ | 12 | 91.74 | even | 3 | ||
91.2.g.b.81.6 | yes | 12 | 7.2 | even | 3 | ||
91.2.h.b.16.1 | yes | 12 | 7.4 | even | 3 | ||
91.2.h.b.74.1 | yes | 12 | 91.9 | even | 3 | ||
637.2.f.j.295.6 | 12 | 91.48 | odd | 6 | |||
637.2.f.j.393.6 | 12 | 7.6 | odd | 2 | |||
637.2.f.k.295.6 | 12 | 13.9 | even | 3 | inner | ||
637.2.f.k.393.6 | 12 | 1.1 | even | 1 | trivial | ||
637.2.g.l.263.6 | 12 | 7.5 | odd | 6 | |||
637.2.g.l.373.6 | 12 | 91.87 | odd | 6 | |||
637.2.h.l.165.1 | 12 | 91.61 | odd | 6 | |||
637.2.h.l.471.1 | 12 | 7.3 | odd | 6 | |||
819.2.n.d.100.1 | 12 | 273.74 | odd | 6 | |||
819.2.n.d.172.1 | 12 | 21.2 | odd | 6 | |||
819.2.s.d.289.6 | 12 | 21.11 | odd | 6 | |||
819.2.s.d.802.6 | 12 | 273.191 | odd | 6 | |||
1183.2.e.g.170.1 | 12 | 91.88 | even | 6 | |||
1183.2.e.g.508.1 | 12 | 91.23 | even | 6 | |||
1183.2.e.h.170.6 | 12 | 91.81 | even | 3 | |||
1183.2.e.h.508.6 | 12 | 91.16 | even | 3 | |||
8281.2.a.bz.1.1 | 6 | 13.3 | even | 3 | |||
8281.2.a.ca.1.1 | 6 | 91.55 | odd | 6 | |||
8281.2.a.ce.1.6 | 6 | 13.10 | even | 6 | |||
8281.2.a.cf.1.6 | 6 | 91.62 | odd | 6 |