Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (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: | \(9.44630255912\) |
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 | 170.6 | ||
Root | \(-0.181721 - 0.314749i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.h.508.6 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | −0.0419302 | − | 0.999121i | \(-0.513351\pi\) |
0.886229 | − | 0.463248i | \(-0.153316\pi\) | |||||||
\(3\) | 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 | ||||
\(5\) | −0.491140 | + | 0.850679i | −0.219644 | + | 0.380435i | −0.954699 | − | 0.297572i | \(-0.903823\pi\) |
0.735055 | + | 0.678008i | \(0.237156\pi\) | |||||||
\(6\) | 6.57063 | 2.68245 | ||||||||
\(7\) | −1.69505 | + | 2.03145i | −0.640669 | + | 0.767817i | ||||
\(8\) | −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 | \(0.805089\pi\) | |||||||
\(12\) | 5.09398 | − | 8.82303i | 1.47051 | − | 2.54699i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.17733 | + | 5.93113i | 0.581916 | + | 1.58516i | ||||
\(15\) | −2.70272 | −0.697840 | ||||||||
\(16\) | −1.15235 | + | 1.99593i | −0.288088 | + | 0.498983i | ||||
\(17\) | 3.22710 | + | 5.58950i | 0.782687 | + | 1.35565i | 0.930371 | + | 0.366619i | \(0.119485\pi\) |
−0.147685 | + | 0.989035i | \(0.547182\pi\) | |||||||
\(18\) | 5.45742 | + | 9.45253i | 1.28633 | + | 2.22798i | ||||
\(19\) | 1.91345 | − | 3.31419i | 0.438975 | − | 0.760327i | −0.558636 | − | 0.829413i | \(-0.688675\pi\) |
0.997611 | + | 0.0690863i | \(0.0220084\pi\) | |||||||
\(20\) | 3.63711 | 0.813282 | ||||||||
\(21\) | −7.17260 | − | 1.24430i | −1.56519 | − | 0.271528i | ||||
\(22\) | 1.40369 | 0.299269 | ||||||||
\(23\) | −4.13001 | + | 7.15338i | −0.861166 | + | 1.49158i | 0.00963902 | + | 0.999954i | \(0.496932\pi\) |
−0.870805 | + | 0.491629i | \(0.836402\pi\) | |||||||
\(24\) | −5.59398 | − | 9.68906i | −1.14187 | − | 1.97777i | ||||
\(25\) | 2.01756 | + | 3.49452i | 0.403513 | + | 0.698904i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.32156 | −0.831685 | ||||||||
\(28\) | 9.65231 | + | 1.67448i | 1.82412 | + | 0.316447i | ||||
\(29\) | −3.96018 | −0.735387 | −0.367694 | − | 0.929947i | \(-0.619853\pi\) | ||||
−0.367694 | + | 0.929947i | \(0.619853\pi\) | |||||||
\(30\) | −3.22710 | + | 5.58950i | −0.589185 | + | 1.02050i | ||||
\(31\) | 1.49436 | + | 2.58831i | 0.268395 | + | 0.464874i | 0.968448 | − | 0.249218i | \(-0.0801734\pi\) |
−0.700053 | + | 0.714091i | \(0.746840\pi\) | |||||||
\(32\) | −1.31430 | − | 2.27644i | −0.232338 | − | 0.402421i | ||||
\(33\) | −0.808663 | + | 1.40065i | −0.140770 | + | 0.243821i | ||||
\(34\) | 15.4129 | 2.64329 | ||||||||
\(35\) | −0.895609 | − | 2.43967i | −0.151386 | − | 0.412380i | ||||
\(36\) | 16.9238 | 2.82063 | ||||||||
\(37\) | −0.877941 | + | 1.52064i | −0.144333 | + | 0.249991i | −0.929124 | − | 0.369769i | \(-0.879437\pi\) |
0.784791 | + | 0.619760i | \(0.212770\pi\) | |||||||
\(38\) | −4.56938 | − | 7.91440i | −0.741252 | − | 1.28389i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.99705 | − | 3.45900i | 0.315762 | − | 0.546916i | ||||
\(41\) | 3.67169 | 0.573421 | 0.286710 | − | 0.958017i | \(-0.407438\pi\) | ||||
0.286710 | + | 0.958017i | \(0.407438\pi\) | |||||||
\(42\) | −11.1376 | + | 13.3479i | −1.71856 | + | 2.05963i | ||||
\(43\) | 6.38085 | 0.973070 | 0.486535 | − | 0.873661i | \(-0.338261\pi\) | ||||
0.486535 | + | 0.873661i | \(0.338261\pi\) | |||||||
\(44\) | 1.08823 | − | 1.88488i | 0.164058 | − | 0.284156i | ||||
\(45\) | −2.24482 | − | 3.88814i | −0.334638 | − | 0.579610i | ||||
\(46\) | 9.86261 | + | 17.0825i | 1.45416 | + | 2.51868i | ||||
\(47\) | 2.17030 | − | 3.75906i | 0.316570 | − | 0.548316i | −0.663200 | − | 0.748442i | \(-0.730802\pi\) |
0.979770 | + | 0.200127i | \(0.0641353\pi\) | |||||||
\(48\) | −6.34134 | −0.915294 | ||||||||
\(49\) | −1.25361 | − | 6.88683i | −0.179087 | − | 0.983833i | ||||
\(50\) | 9.63603 | 1.36274 | ||||||||
\(51\) | −8.87930 | + | 15.3794i | −1.24335 | + | 2.15355i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.212770 | − | 0.368529i | −0.0292263 | − | 0.0506214i | 0.851042 | − | 0.525097i | \(-0.175971\pi\) |
−0.880269 | + | 0.474476i | \(0.842638\pi\) | |||||||
\(54\) | −5.16002 | + | 8.93742i | −0.702190 | + | 1.21623i | ||||
\(55\) | −0.577387 | −0.0778548 | ||||||||
\(56\) | 6.89235 | − | 8.26022i | 0.921029 | − | 1.10382i | ||||
\(57\) | 10.5296 | 1.39468 | ||||||||
\(58\) | −4.72853 | + | 8.19006i | −0.620887 | + | 1.07541i | ||||
\(59\) | −3.00431 | − | 5.20362i | −0.391128 | − | 0.677454i | 0.601470 | − | 0.798895i | \(-0.294582\pi\) |
−0.992599 | + | 0.121441i | \(0.961248\pi\) | |||||||
\(60\) | 5.00371 | + | 8.66669i | 0.645977 | + | 1.11886i | ||||
\(61\) | −1.10337 | + | 1.91109i | −0.141272 | + | 0.244691i | −0.927976 | − | 0.372640i | \(-0.878453\pi\) |
0.786704 | + | 0.617331i | \(0.211786\pi\) | |||||||
\(62\) | 7.13717 | 0.906422 | ||||||||
\(63\) | −4.16735 | − | 11.3520i | −0.525036 | − | 1.43022i | ||||
\(64\) | −10.8866 | −1.36083 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.93112 | + | 3.34479i | 0.237704 | + | 0.411716i | ||||
\(67\) | −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 | ||||
\(69\) | −22.7272 | −2.73604 | ||||||||
\(70\) | −6.11486 | − | 1.06080i | −0.730866 | − | 0.126790i | ||||
\(71\) | 3.60253 | 0.427542 | 0.213771 | − | 0.976884i | \(-0.431425\pi\) | ||||
0.213771 | + | 0.976884i | \(0.431425\pi\) | |||||||
\(72\) | 9.29247 | − | 16.0950i | 1.09513 | − | 1.89682i | ||||
\(73\) | −2.46714 | − | 4.27321i | −0.288756 | − | 0.500141i | 0.684757 | − | 0.728772i | \(-0.259908\pi\) |
−0.973513 | + | 0.228631i | \(0.926575\pi\) | |||||||
\(74\) | 2.09656 | + | 3.63134i | 0.243720 | + | 0.422135i | ||||
\(75\) | −5.55128 | + | 9.61510i | −0.641007 | + | 1.11026i | ||||
\(76\) | −14.1699 | −1.62540 | ||||||||
\(77\) | −1.53229 | − | 0.265822i | −0.174621 | − | 0.0302932i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.39270 | + | 2.41223i | −0.156691 | + | 0.271397i | −0.933674 | − | 0.358125i | \(-0.883416\pi\) |
0.776982 | + | 0.629522i | \(0.216749\pi\) | |||||||
\(80\) | −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 | \(0.550315\pi\) | |||||||
\(84\) | 9.28903 | + | 25.3037i | 1.01352 | + | 2.76086i | ||||
\(85\) | −6.33983 | −0.687651 | ||||||||
\(86\) | 7.61885 | − | 13.1962i | 0.821562 | − | 1.42299i | ||||
\(87\) | −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 | −0.805213 | − | 0.592986i | \(-0.797949\pi\) |
0.916147 | + | 0.400842i | \(0.131282\pi\) | |||||||
\(90\) | −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 | ||||
\(96\) | 3.61628 | − | 6.26357i | 0.369085 | − | 0.639273i | ||||
\(97\) | 7.69704 | 0.781516 | 0.390758 | − | 0.920493i | \(-0.372213\pi\) | ||||
0.390758 | + | 0.920493i | \(0.372213\pi\) | |||||||
\(98\) | −15.7395 | − | 5.63041i | −1.58993 | − | 0.568758i | ||||
\(99\) | −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 | ||||
\(103\) | 5.43095 | − | 9.40669i | 0.535128 | − | 0.926868i | −0.464029 | − | 0.885820i | \(-0.653597\pi\) |
0.999157 | − | 0.0410486i | \(-0.0130699\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.58125 | − | 5.49045i | 0.447084 | − | 0.535813i | ||||
\(106\) | −1.01621 | −0.0987027 | ||||||||
\(107\) | 7.99024 | − | 13.8395i | 0.772446 | − | 1.33792i | −0.163773 | − | 0.986498i | \(-0.552366\pi\) |
0.936219 | − | 0.351418i | \(-0.114300\pi\) | |||||||
\(108\) | 8.00077 | + | 13.8577i | 0.769874 | + | 1.33346i | ||||
\(109\) | −4.61738 | − | 7.99754i | −0.442265 | − | 0.766026i | 0.555592 | − | 0.831455i | \(-0.312492\pi\) |
−0.997857 | + | 0.0654294i | \(0.979158\pi\) | |||||||
\(110\) | −0.689410 | + | 1.19409i | −0.0657327 | + | 0.113852i | ||||
\(111\) | −4.83127 | −0.458564 | ||||||||
\(112\) | −2.10135 | − | 5.72416i | −0.198559 | − | 0.540882i | ||||
\(113\) | 10.1802 | 0.957677 | 0.478838 | − | 0.877903i | \(-0.341058\pi\) | ||||
0.478838 | + | 0.877903i | \(0.341058\pi\) | |||||||
\(114\) | 12.5726 | − | 21.7763i | 1.17753 | − | 2.03954i | ||||
\(115\) | −4.05682 | − | 7.02662i | −0.378301 | − | 0.655236i | ||||
\(116\) | 7.33173 | + | 12.6989i | 0.680734 | + | 1.17907i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.3488 | −1.32092 | ||||||||
\(119\) | −16.8249 | − | 2.91878i | −1.54234 | − | 0.267564i | ||||
\(120\) | 10.9897 | 1.00322 | ||||||||
\(121\) | 5.32724 | − | 9.22706i | 0.484295 | − | 0.838823i | ||||
\(122\) | 2.63489 | + | 4.56376i | 0.238552 | + | 0.413184i | ||||
\(123\) | 5.05128 | + | 8.74908i | 0.455459 | + | 0.788878i | ||||
\(124\) | 5.53320 | − | 9.58378i | 0.496896 | − | 0.860649i | ||||
\(125\) | −8.87502 | −0.793806 | ||||||||
\(126\) | −28.4530 | − | 4.93601i | −2.53479 | − | 0.439735i | ||||
\(127\) | 4.25026 | 0.377149 | 0.188575 | − | 0.982059i | \(-0.439613\pi\) | ||||
0.188575 | + | 0.982059i | \(0.439613\pi\) | |||||||
\(128\) | −10.3702 | + | 17.9617i | −0.916606 | + | 1.58761i | ||||
\(129\) | 8.77838 | + | 15.2046i | 0.772893 | + | 1.33869i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.08478 | − | 1.87890i | 0.0947779 | − | 0.164160i | −0.814738 | − | 0.579829i | \(-0.803119\pi\) |
0.909516 | + | 0.415669i | \(0.136453\pi\) | |||||||
\(132\) | 5.98851 | 0.521233 | ||||||||
\(133\) | 3.48923 | + | 9.50479i | 0.302555 | + | 0.824170i | ||||
\(134\) | −16.7474 | −1.44675 | ||||||||
\(135\) | 2.12249 | − | 3.67626i | 0.182675 | − | 0.316402i | ||||
\(136\) | −13.1219 | − | 22.7278i | −1.12519 | − | 1.94889i | ||||
\(137\) | −4.18158 | − | 7.24271i | −0.357257 | − | 0.618787i | 0.630245 | − | 0.776396i | \(-0.282955\pi\) |
−0.987501 | + | 0.157610i | \(0.949621\pi\) | |||||||
\(138\) | −27.1367 | + | 47.0022i | −2.31003 | + | 4.00110i | ||||
\(139\) | −0.576914 | −0.0489332 | −0.0244666 | − | 0.999701i | \(-0.507789\pi\) | ||||
−0.0244666 | + | 0.999701i | \(0.507789\pi\) | |||||||
\(140\) | −6.16508 | + | 7.38862i | −0.521045 | + | 0.624452i | ||||
\(141\) | 11.9430 | 1.00579 | ||||||||
\(142\) | 4.30149 | − | 7.45040i | 0.360973 | − | 0.625224i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.26698 | − | 9.12267i | −0.438915 | − | 0.760223i | ||||
\(145\) | 1.94500 | − | 3.36885i | 0.161524 | − | 0.279767i | ||||
\(146\) | −11.7832 | −0.975187 | ||||||||
\(147\) | 14.6856 | − | 12.4616i | 1.21125 | − | 1.02782i | ||||
\(148\) | 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 | ||||
\(151\) | 11.5054 | + | 19.9280i | 0.936300 | + | 1.62172i | 0.772300 | + | 0.635258i | \(0.219106\pi\) |
0.164000 | + | 0.986460i | \(0.447560\pi\) | |||||||
\(152\) | −7.78039 | + | 13.4760i | −0.631073 | + | 1.09305i | ||||
\(153\) | −29.4998 | −2.38492 | ||||||||
\(154\) | −2.37933 | + | 2.85154i | −0.191732 | + | 0.229784i | ||||
\(155\) | −2.93576 | −0.235806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2880 | − | 19.5513i | −0.900879 | − | 1.56037i | −0.826356 | − | 0.563148i | \(-0.809590\pi\) |
−0.0745227 | − | 0.997219i | \(-0.523743\pi\) | |||||||
\(158\) | 3.32583 | + | 5.76050i | 0.264588 | + | 0.458281i | ||||
\(159\) | 0.585433 | − | 1.01400i | 0.0464278 | − | 0.0804154i | ||||
\(160\) | 2.58203 | 0.204127 | ||||||||
\(161\) | −7.53119 | − | 20.5153i | −0.593541 | − | 1.61683i | ||||
\(162\) | 4.34913 | 0.341700 | ||||||||
\(163\) | −4.08857 | + | 7.08161i | −0.320242 | + | 0.554675i | −0.980538 | − | 0.196331i | \(-0.937097\pi\) |
0.660296 | + | 0.751005i | \(0.270431\pi\) | |||||||
\(164\) | −6.79761 | − | 11.7738i | −0.530804 | − | 0.919380i | ||||
\(165\) | −0.794333 | − | 1.37583i | −0.0618388 | − | 0.107108i | ||||
\(166\) | −3.42467 | + | 5.93170i | −0.265806 | + | 0.460389i | ||||
\(167\) | −2.32771 | −0.180124 | −0.0900619 | − | 0.995936i | \(-0.528707\pi\) | ||||
−0.0900619 | + | 0.995936i | \(0.528707\pi\) | |||||||
\(168\) | 29.1649 | + | 5.05953i | 2.25012 | + | 0.390351i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −7.56988 | + | 13.1114i | −0.580583 | + | 1.00560i | ||||
\(171\) | 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 | ||||||||
\(175\) | −10.5188 | − | 1.82480i | −0.795149 | − | 0.137942i | ||||
\(176\) | −1.35471 | −0.102115 | ||||||||
\(177\) | 8.26630 | − | 14.3177i | 0.621333 | − | 1.07618i | ||||
\(178\) | −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 | ||||
\(187\) | −1.89690 | + | 3.28552i | −0.138715 | + | 0.240261i | ||||
\(188\) | −16.0720 | −1.17217 | ||||||||
\(189\) | 7.32526 | − | 8.77905i | 0.532834 | − | 0.638582i | ||||
\(190\) | 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 | \(-0.489233\pi\) | |||||||
\(194\) | 9.19041 | − | 15.9183i | 0.659833 | − | 1.14286i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.7628 | + | 16.7699i | −1.41163 | + | 1.19785i | ||||
\(197\) | −1.47094 | −0.104800 | −0.0524002 | − | 0.998626i | \(-0.516687\pi\) | ||||
−0.0524002 | + | 0.998626i | \(0.516687\pi\) | |||||||
\(198\) | −3.20788 | + | 5.55622i | −0.227974 | + | 0.394863i | ||||
\(199\) | −4.69700 | − | 8.13543i | −0.332961 | − | 0.576706i | 0.650130 | − | 0.759823i | \(-0.274714\pi\) |
−0.983091 | + | 0.183117i | \(0.941381\pi\) | |||||||
\(200\) | −8.20374 | − | 14.2093i | −0.580092 | − | 1.00475i | ||||
\(201\) | 9.64810 | − | 16.7110i | 0.680524 | − | 1.17870i | ||||
\(202\) | 6.29802 | 0.443127 | ||||||||
\(203\) | 6.71271 | − | 8.04493i | 0.471140 | − | 0.564643i | ||||
\(204\) | 65.7551 | 4.60378 | ||||||||
\(205\) | −1.80331 | + | 3.12343i | −0.125949 | + | 0.218150i | ||||
\(206\) | −12.9693 | − | 22.4635i | −0.903615 | − | 1.56511i | ||||
\(207\) | −18.8767 | − | 32.6955i | −1.31202 | − | 2.27249i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.24946 | 0.155598 | ||||||||
\(210\) | −5.88472 | − | 16.0302i | −0.406084 | − | 1.10619i | ||||
\(211\) | −8.94219 | −0.615605 | −0.307803 | − | 0.951450i | \(-0.599594\pi\) | ||||
−0.307803 | + | 0.951450i | \(0.599594\pi\) | |||||||
\(212\) | −0.787829 | + | 1.36456i | −0.0541083 | + | 0.0937184i | ||||
\(213\) | 4.95615 | + | 8.58430i | 0.339589 | + | 0.588186i | ||||
\(214\) | −19.0810 | − | 33.0493i | −1.30435 | − | 2.25920i | ||||
\(215\) | −3.13389 | + | 5.42805i | −0.213729 | + | 0.370190i | ||||
\(216\) | 17.5722 | 1.19563 | ||||||||
\(217\) | −7.79104 | − | 1.35159i | −0.528890 | − | 0.0917518i | ||||
\(218\) | −22.0530 | −1.49362 | ||||||||
\(219\) | 6.78827 | − | 11.7576i | 0.458709 | − | 0.794507i | ||||
\(220\) | 1.06895 | + | 1.85148i | 0.0720686 | + | 0.124827i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.76863 | + | 9.99156i | −0.387165 | + | 0.670589i | ||||
\(223\) | 21.8196 | 1.46115 | 0.730574 | − | 0.682833i | \(-0.239252\pi\) | ||||
0.730574 | + | 0.682833i | \(0.239252\pi\) | |||||||
\(224\) | 6.85229 | + | 1.18873i | 0.457838 | + | 0.0794256i | ||||
\(225\) | −18.4431 | −1.22954 | ||||||||
\(226\) | 12.1554 | − | 21.0538i | 0.808565 | − | 1.40048i | ||||
\(227\) | 9.27627 | + | 16.0670i | 0.615687 | + | 1.06640i | 0.990263 | + | 0.139206i | \(0.0444549\pi\) |
−0.374576 | + | 0.927196i | \(0.622212\pi\) | |||||||
\(228\) | −19.4941 | − | 33.7648i | −1.29103 | − | 2.23613i | ||||
\(229\) | −9.67525 | + | 16.7580i | −0.639359 | + | 1.10740i | 0.346215 | + | 0.938155i | \(0.387467\pi\) |
−0.985574 | + | 0.169247i | \(0.945867\pi\) | |||||||
\(230\) | −19.3757 | −1.27759 | ||||||||
\(231\) | −1.47462 | − | 4.01692i | −0.0970230 | − | 0.264294i | ||||
\(232\) | 16.1027 | 1.05720 | ||||||||
\(233\) | −8.08170 | + | 13.9979i | −0.529450 | + | 0.917034i | 0.469960 | + | 0.882688i | \(0.344268\pi\) |
−0.999410 | + | 0.0343462i | \(0.989065\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.13184 | + | 3.69245i | 0.139066 | + | 0.240869i | ||||
\(236\) | −11.1241 | + | 19.2676i | −0.724119 | + | 1.25421i | ||||
\(237\) | −7.66398 | −0.497829 | ||||||||
\(238\) | −26.1256 | + | 31.3105i | −1.69347 | + | 2.02956i | ||||
\(239\) | 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 | 0.923299 | − | 0.384082i | \(-0.125482\pi\) |
−0.794274 | + | 0.607559i | \(0.792149\pi\) | |||||||
\(242\) | −12.7217 | − | 22.0346i | −0.817779 | − | 1.41643i | ||||
\(243\) | −8.98786 | + | 15.5674i | −0.576572 | + | 0.998651i | ||||
\(244\) | 8.17095 | 0.523092 | ||||||||
\(245\) | 6.47418 | + | 2.31598i | 0.413620 | + | 0.147962i | ||||
\(246\) | 24.1253 | 1.53817 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.07631 | − | 10.5245i | −0.385846 | − | 0.668305i | ||||
\(249\) | −3.94588 | − | 6.83446i | −0.250060 | − | 0.433116i | ||||
\(250\) | −10.5969 | + | 18.3544i | −0.670209 | + | 1.16084i | ||||
\(251\) | 3.24688 | 0.204941 | 0.102471 | − | 0.994736i | \(-0.467325\pi\) | ||||
0.102471 | + | 0.994736i | \(0.467325\pi\) | |||||||
\(252\) | −28.6867 | + | 34.3799i | −1.80709 | + | 2.16573i | ||||
\(253\) | −4.85525 | −0.305247 | ||||||||
\(254\) | 5.07489 | − | 8.78996i | 0.318427 | − | 0.551531i | ||||
\(255\) | −8.72195 | − | 15.1069i | −0.546190 | − | 0.946029i | ||||
\(256\) | 13.8778 | + | 24.0371i | 0.867365 | + | 1.50232i | ||||
\(257\) | 13.4462 | − | 23.2895i | 0.838751 | − | 1.45276i | −0.0521891 | − | 0.998637i | \(-0.516620\pi\) |
0.890940 | − | 0.454122i | \(-0.150047\pi\) | |||||||
\(258\) | 41.9262 | 2.61021 | ||||||||
\(259\) | −1.60095 | − | 4.36106i | −0.0994784 | − | 0.270983i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.05027 | − | 15.6755i | 0.560198 | − | 0.970291i | ||||
\(262\) | −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 | ||||||||
\(266\) | 23.8231 | + | 4.13282i | 1.46069 | + | 0.253399i | ||||
\(267\) | 5.75915 | 0.352455 | ||||||||
\(268\) | −12.9836 | + | 22.4883i | −0.793102 | + | 1.37369i | ||||
\(269\) | 11.9190 | + | 20.6444i | 0.726716 | + | 1.25871i | 0.958264 | + | 0.285886i | \(0.0922878\pi\) |
−0.231548 | + | 0.972824i | \(0.574379\pi\) | |||||||
\(270\) | −5.06859 | − | 8.77905i | −0.308464 | − | 0.534276i | ||||
\(271\) | −4.95068 | + | 8.57482i | −0.300732 | + | 0.520883i | −0.976302 | − | 0.216413i | \(-0.930564\pi\) |
0.675570 | + | 0.737296i | \(0.263898\pi\) | |||||||
\(272\) | −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 | 0.632889 | − | 0.774243i | \(-0.281869\pi\) |
−0.986958 | + | 0.160977i | \(0.948536\pi\) | |||||||
\(278\) | −0.688846 | + | 1.19312i | −0.0413142 | + | 0.0715584i | ||||
\(279\) | −13.6603 | −0.817823 | ||||||||
\(280\) | 3.64169 | + | 9.92010i | 0.217633 | + | 0.592840i | ||||
\(281\) | 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 | ||||
\(285\) | −5.17151 | + | 8.95733i | −0.306334 | + | 0.530586i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.22369 | + | 7.45886i | −0.367373 | + | 0.440283i | ||||
\(288\) | 12.0144 | 0.707955 | ||||||||
\(289\) | −12.3283 | + | 21.3533i | −0.725197 | + | 1.25608i | ||||
\(290\) | −4.64474 | − | 8.04493i | −0.272749 | − | 0.472414i | ||||
\(291\) | 10.5891 | + | 18.3409i | 0.620746 | + | 1.07516i | ||||
\(292\) | −9.13512 | + | 15.8225i | −0.534592 | + | 0.925941i | ||||
\(293\) | −14.0956 | −0.823476 | −0.411738 | − | 0.911302i | \(-0.635078\pi\) | ||||
−0.411738 | + | 0.911302i | \(0.635078\pi\) | |||||||
\(294\) | −8.23701 | − | 45.2508i | −0.480392 | − | 2.63908i | ||||
\(295\) | 5.90215 | 0.343637 | ||||||||
\(296\) | 3.56985 | − | 6.18316i | 0.207493 | − | 0.359389i | ||||
\(297\) | −1.27011 | − | 2.19990i | −0.0736994 | − | 0.127651i | ||||
\(298\) | 3.35116 | + | 5.80438i | 0.194128 | + | 0.336239i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 41.1097 | 2.37347 | ||||||||
\(301\) | −10.8159 | + | 12.9624i | −0.623416 | + | 0.747140i | ||||
\(302\) | 54.9508 | 3.16207 | ||||||||
\(303\) | −3.62827 | + | 6.28434i | −0.208439 | + | 0.361026i | ||||
\(304\) | 4.40993 | + | 7.63822i | 0.252927 | + | 0.438082i | ||||
\(305\) | −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 | \(0.350311\pi\) | |||||||
\(308\) | 1.98443 | + | 5.40566i | 0.113073 | + | 0.308016i | ||||
\(309\) | 29.8863 | 1.70017 | ||||||||
\(310\) | −3.50535 | + | 6.07145i | −0.199091 | + | 0.344835i | ||||
\(311\) | 14.3017 | + | 24.7713i | 0.810975 | + | 1.40465i | 0.912183 | + | 0.409784i | \(0.134396\pi\) |
−0.101208 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.28962 | − | 16.0901i | 0.525080 | − | 0.909465i | −0.474493 | − | 0.880259i | \(-0.657369\pi\) |
0.999573 | − | 0.0292063i | \(-0.00929798\pi\) | |||||||
\(314\) | −53.9122 | −3.04244 | ||||||||
\(315\) | 11.7037 | + | 2.03035i | 0.659427 | + | 0.114397i | ||||
\(316\) | 10.3136 | 0.580184 | ||||||||
\(317\) | −15.3223 | + | 26.5389i | −0.860584 | + | 1.49057i | 0.0107826 | + | 0.999942i | \(0.496568\pi\) |
−0.871366 | + | 0.490633i | \(0.836766\pi\) | |||||||
\(318\) | −1.39804 | − | 2.42147i | −0.0783979 | − | 0.135789i | ||||
\(319\) | −1.16390 | − | 2.01594i | −0.0651660 | − | 0.112871i | ||||
\(320\) | 5.34685 | − | 9.26102i | 0.298898 | − | 0.517707i | ||||
\(321\) | 43.9700 | 2.45416 | ||||||||
\(322\) | −51.4200 | − | 8.92033i | −2.86552 | − | 0.497110i | ||||
\(323\) | 24.6995 | 1.37432 | ||||||||
\(324\) | 3.37173 | − | 5.84001i | 0.187318 | − | 0.324445i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.76366 | + | 16.9112i | 0.540759 | + | 0.936622i | ||||
\(327\) | 12.7046 | − | 22.0051i | 0.702568 | − | 1.21688i | ||||
\(328\) | −14.9297 | −0.824353 | ||||||||
\(329\) | 3.95760 | + | 10.7807i | 0.218190 | + | 0.594357i | ||||
\(330\) | −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 | ||||
\(333\) | −4.01275 | − | 6.95028i | −0.219897 | − | 0.380873i | ||||
\(334\) | −2.77933 | + | 4.81395i | −0.152078 | + | 0.263407i | ||||
\(335\) | 6.88876 | 0.376373 | ||||||||
\(336\) | 10.7489 | − | 12.8821i | 0.586400 | − | 0.702779i | ||||
\(337\) | −12.3160 | −0.670898 | −0.335449 | − | 0.942058i | \(-0.608888\pi\) | ||||
−0.335449 | + | 0.942058i | \(0.608888\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.0054 | + | 24.2580i | 0.760666 | + | 1.31751i | ||||
\(340\) | 11.7373 | + | 20.3296i | 0.636545 | + | 1.10253i | ||||
\(341\) | −0.878389 | + | 1.52141i | −0.0475674 | + | 0.0823892i | ||||
\(342\) | 41.7699 | 2.25866 | ||||||||
\(343\) | 16.1152 | + | 9.12688i | 0.870140 | + | 0.492805i | ||||
\(344\) | −25.9456 | −1.39889 | ||||||||
\(345\) | 11.1623 | − | 19.3336i | 0.600956 | − | 1.04089i | ||||
\(346\) | −9.71182 | − | 16.8214i | −0.522111 | − | 0.904322i | ||||
\(347\) | −3.07253 | − | 5.32177i | −0.164942 | − | 0.285688i | 0.771693 | − | 0.635996i | \(-0.219410\pi\) |
−0.936635 | + | 0.350308i | \(0.886077\pi\) | |||||||
\(348\) | −20.1731 | + | 34.9408i | −1.08139 | + | 1.87302i | ||||
\(349\) | 13.0313 | 0.697547 | 0.348774 | − | 0.937207i | \(-0.386598\pi\) | ||||
0.348774 | + | 0.937207i | \(0.386598\pi\) | |||||||
\(350\) | −16.3336 | + | 19.5752i | −0.873065 | + | 1.04634i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.772550 | − | 1.33810i | 0.0411771 | − | 0.0713208i | ||||
\(353\) | −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 | ||||||||
\(357\) | −16.1917 | − | 44.1067i | −0.856954 | − | 2.33438i | ||||
\(358\) | 50.1310 | 2.64950 | ||||||||
\(359\) | −9.96610 | + | 17.2618i | −0.525991 | + | 0.911043i | 0.473551 | + | 0.880767i | \(0.342972\pi\) |
−0.999542 | + | 0.0302764i | \(0.990361\pi\) | |||||||
\(360\) | 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 | ||||
\(369\) | −8.39096 | + | 14.5336i | −0.436816 | + | 0.756588i | ||||
\(370\) | −4.11881 | −0.214127 | ||||||||
\(371\) | 1.10931 | + | 0.192442i | 0.0575923 | + | 0.00999109i | ||||
\(372\) | 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 | ||||
\(376\) | −8.82478 | + | 15.2850i | −0.455103 | + | 0.788262i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −9.40946 | − | 25.6317i | −0.483971 | − | 1.31835i | ||||
\(379\) | −11.7014 | −0.601058 | −0.300529 | − | 0.953773i | \(-0.597163\pi\) | ||||
−0.300529 | + | 0.953773i | \(0.597163\pi\) | |||||||
\(380\) | 6.95942 | − | 12.0541i | 0.357010 | − | 0.618360i | ||||
\(381\) | 5.84725 | + | 10.1277i | 0.299563 | + | 0.518859i | ||||
\(382\) | −13.8055 | − | 23.9119i | −0.706352 | − | 1.22344i | ||||
\(383\) | 10.7644 | − | 18.6445i | 0.550036 | − | 0.952690i | −0.448235 | − | 0.893916i | \(-0.647947\pi\) |
0.998271 | − | 0.0587748i | \(-0.0187194\pi\) | |||||||
\(384\) | −57.0669 | −2.91218 | ||||||||
\(385\) | 0.978699 | − | 1.17293i | 0.0498791 | − | 0.0597783i | ||||
\(386\) | −56.3072 | −2.86596 | ||||||||
\(387\) | −14.5823 | + | 25.2572i | −0.741258 | + | 1.28390i | ||||
\(388\) | −14.2500 | − | 24.6817i | −0.723435 | − | 1.25303i | ||||
\(389\) | −13.2455 | − | 22.9419i | −0.671574 | − | 1.16320i | −0.977458 | − | 0.211131i | \(-0.932285\pi\) |
0.305884 | − | 0.952069i | \(-0.401048\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.3118 | −2.69609 | ||||||||
\(392\) | 5.09738 | + | 28.0030i | 0.257457 | + | 1.41436i | ||||
\(393\) | 5.96951 | 0.301122 | ||||||||
\(394\) | −1.75633 | + | 3.04206i | −0.0884828 | + | 0.153257i | ||||
\(395\) | −1.36802 | − | 2.36949i | −0.0688327 | − | 0.119222i | ||||
\(396\) | 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 | ||||||||
\(399\) | −17.8482 | + | 21.3904i | −0.893529 | + | 1.07086i | ||||
\(400\) | −9.29977 | −0.464989 | ||||||||
\(401\) | −10.8059 | + | 18.7164i | −0.539623 | + | 0.934655i | 0.459301 | + | 0.888281i | \(0.348100\pi\) |
−0.998924 | + | 0.0463741i | \(0.985233\pi\) | |||||||
\(402\) | −23.0400 | − | 39.9065i | −1.14913 | − | 1.99035i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.88264 | − | 8.45697i | 0.242920 | − | 0.420750i | ||||
\(405\) | −1.78895 | −0.0888934 | ||||||||
\(406\) | −8.62262 | − | 23.4884i | −0.427934 | − | 1.16571i | ||||
\(407\) | −1.03211 | −0.0511599 | ||||||||
\(408\) | 36.1047 | − | 62.5351i | 1.78745 | − | 3.09595i | ||||
\(409\) | −3.87109 | − | 6.70492i | −0.191413 | − | 0.331537i | 0.754306 | − | 0.656523i | \(-0.227974\pi\) |
−0.945719 | + | 0.324986i | \(0.894640\pi\) | |||||||
\(410\) | 4.30637 | + | 7.45886i | 0.212677 | + | 0.368367i | ||||
\(411\) | 11.5055 | − | 19.9282i | 0.567526 | − | 0.982984i | ||||
\(412\) | −40.2186 | −1.98143 | ||||||||
\(413\) | 15.6634 | + | 2.71728i | 0.770744 | + | 0.133709i | ||||
\(414\) | −90.1567 | −4.43096 | ||||||||
\(415\) | 1.40868 | − | 2.43991i | 0.0691495 | − | 0.119770i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.793683 | − | 1.37470i | −0.0388668 | − | 0.0673193i | ||||
\(418\) | 2.68589 | − | 4.65211i | 0.131371 | − | 0.227542i | ||||
\(419\) | −8.10194 | −0.395806 | −0.197903 | − | 0.980222i | \(-0.563413\pi\) | ||||
−0.197903 | + | 0.980222i | \(0.563413\pi\) | |||||||
\(420\) | −26.0875 | − | 4.52565i | −1.27294 | − | 0.220829i | ||||
\(421\) | −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 | ||||
\(424\) | 0.865159 | + | 1.49850i | 0.0420158 | + | 0.0727735i | ||||
\(425\) | −13.0218 | + | 22.5543i | −0.631648 | + | 1.09405i | ||||
\(426\) | 23.6709 | 1.14686 | ||||||||
\(427\) | −2.01203 | − | 5.48085i | −0.0973690 | − | 0.265237i | ||||
\(428\) | −59.1713 | −2.86015 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.48384 | + | 12.9624i | 0.360903 | + | 0.625102i | ||||
\(431\) | 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 | ||||
\(433\) | 22.0910 | 1.06163 | 0.530813 | − | 0.847489i | \(-0.321887\pi\) | ||||
0.530813 | + | 0.847489i | \(0.321887\pi\) | |||||||
\(434\) | −12.0979 | + | 14.4988i | −0.580716 | + | 0.695967i | ||||
\(435\) | 10.7033 | 0.513183 | ||||||||
\(436\) | −17.0969 | + | 29.6127i | −0.818792 | + | 1.41819i | ||||
\(437\) | 15.8051 | + | 27.3752i | 0.756060 | + | 1.30953i | ||||
\(438\) | −16.2106 | − | 28.0777i | −0.774575 | − | 1.34160i | ||||
\(439\) | 3.17790 | − | 5.50428i | 0.151673 | − | 0.262705i | −0.780170 | − | 0.625568i | \(-0.784867\pi\) |
0.931843 | + | 0.362863i | \(0.118201\pi\) | |||||||
\(440\) | 2.34775 | 0.111924 | ||||||||
\(441\) | 30.1249 | + | 10.7764i | 1.43452 | + | 0.513164i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.78135 | − | 11.7456i | 0.322192 | − | 0.558052i | −0.658748 | − | 0.752363i | \(-0.728914\pi\) |
0.980940 | + | 0.194311i | \(0.0622472\pi\) | |||||||
\(444\) | 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 | ||||||||
\(448\) | 18.4534 | − | 22.1157i | 0.871839 | − | 1.04487i | ||||
\(449\) | 21.9118 | 1.03408 | 0.517041 | − | 0.855961i | \(-0.327034\pi\) | ||||
0.517041 | + | 0.855961i | \(0.327034\pi\) | |||||||
\(450\) | −22.0214 | + | 38.1421i | −1.03810 | + | 1.79804i | ||||
\(451\) | 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 | −0.987264 | − | 0.159091i | \(-0.949144\pi\) |
0.631409 | + | 0.775450i | \(0.282477\pi\) | |||||||
\(458\) | 23.1049 | + | 40.0188i | 1.07962 | + | 1.86996i | ||||
\(459\) | −13.9461 | − | 24.1554i | −0.650949 | − | 1.12748i | ||||
\(460\) | −15.0213 | + | 26.0176i | −0.700371 | + | 1.21308i | ||||
\(461\) | −16.2163 | −0.755267 | −0.377633 | − | 0.925955i | \(-0.623262\pi\) | ||||
−0.377633 | + | 0.925955i | \(0.623262\pi\) | |||||||
\(462\) | −10.0681 | − | 1.74662i | −0.468412 | − | 0.0812600i | ||||
\(463\) | −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 | ||||
\(467\) | −7.00337 | + | 12.1302i | −0.324078 | + | 0.561319i | −0.981325 | − | 0.192356i | \(-0.938387\pi\) |
0.657248 | + | 0.753675i | \(0.271721\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.2817 | + | 3.17150i | 0.844169 | + | 0.146446i | ||||
\(470\) | 10.1818 | 0.469652 | ||||||||
\(471\) | 31.0586 | − | 53.7951i | 1.43111 | − | 2.47875i | ||||
\(472\) | 12.2160 | + | 21.1588i | 0.562288 | + | 0.973912i | ||||
\(473\) | 1.87534 | + | 3.24818i | 0.0862282 | + | 0.149352i | ||||
\(474\) | −9.15094 | + | 15.8499i | −0.420316 | + | 0.728009i | ||||
\(475\) | 15.4420 | 0.708528 | ||||||||
\(476\) | 21.7895 | + | 59.3553i | 0.998719 | + | 2.72055i | ||||
\(477\) | 1.94499 | 0.0890550 | ||||||||
\(478\) | 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 | \(0.592732\pi\) | |||||||
\(480\) | 3.55219 | + | 6.15258i | 0.162135 | + | 0.280826i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 9.56649 | 0.435742 | ||||||||
\(483\) | 38.5238 | − | 46.1693i | 1.75289 | − | 2.10078i | ||||
\(484\) | −39.4506 | −1.79321 | ||||||||
\(485\) | −3.78033 | + | 6.54772i | −0.171656 | + | 0.297317i | ||||
\(486\) | 21.4633 | + | 37.1756i | 0.973597 | + | 1.68632i | ||||
\(487\) | 14.2452 | + | 24.6733i | 0.645510 | + | 1.11806i | 0.984184 | + | 0.177152i | \(0.0566884\pi\) |
−0.338674 | + | 0.940904i | \(0.609978\pi\) | |||||||
\(488\) | 4.48649 | − | 7.77082i | 0.203094 | − | 0.351769i | ||||
\(489\) | −22.4992 | −1.01745 | ||||||||
\(490\) | 12.5200 | − | 10.6239i | 0.565595 | − | 0.479941i | ||||
\(491\) | −28.4677 | −1.28473 | −0.642365 | − | 0.766399i | \(-0.722047\pi\) | ||||
−0.642365 | + | 0.766399i | \(0.722047\pi\) | |||||||
\(492\) | 18.7035 | − | 32.3954i | 0.843218 | − | 1.46050i | ||||
\(493\) | −12.7799 | − | 22.1354i | −0.575578 | − | 0.996930i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.31951 | − | 2.28546i | 0.0593076 | − | 0.102724i | ||||
\(496\) | −6.88812 | −0.309286 | ||||||||
\(497\) | −6.10647 | + | 7.31838i | −0.273913 | + | 0.328274i | ||||
\(498\) | −18.8458 | −0.844501 | ||||||||
\(499\) | 13.1164 | − | 22.7183i | 0.587172 | − | 1.01701i | −0.407429 | − | 0.913237i | \(-0.633575\pi\) |
0.994601 | − | 0.103775i | \(-0.0330921\pi\) | |||||||
\(500\) | 16.4309 | + | 28.4591i | 0.734811 | + | 1.27273i | ||||
\(501\) | −3.20233 | − | 5.54659i | −0.143069 | − | 0.247803i | ||||
\(502\) | 3.87684 | − | 6.71488i | 0.173032 | − | 0.299700i | ||||
\(503\) | 8.53175 | 0.380412 | 0.190206 | − | 0.981744i | \(-0.439084\pi\) | ||||
0.190206 | + | 0.981744i | \(0.439084\pi\) | |||||||
\(504\) | 16.9451 | + | 46.1591i | 0.754795 | + | 2.05609i | ||||
\(505\) | −2.59059 | −0.115280 | ||||||||
\(506\) | −5.79726 | + | 10.0412i | −0.257720 | + | 0.446384i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.86876 | − | 13.6291i | −0.349120 | − | 0.604693i | ||||
\(509\) | 6.51298 | − | 11.2808i | 0.288683 | − | 0.500014i | −0.684813 | − | 0.728719i | \(-0.740116\pi\) |
0.973496 | + | 0.228706i | \(0.0734493\pi\) | |||||||
\(510\) | −41.6567 | −1.84459 | ||||||||
\(511\) | 12.8627 | + | 2.23142i | 0.569014 | + | 0.0987124i | ||||
\(512\) | 24.8008 | 1.09605 | ||||||||
\(513\) | −8.26908 | + | 14.3225i | −0.365089 | + | 0.632352i | ||||
\(514\) | −32.1100 | − | 55.6162i | −1.41631 | − | 2.45312i | ||||
\(515\) | 5.33472 | + | 9.24000i | 0.235076 | + | 0.407163i | ||||
\(516\) | 32.5039 | − | 56.2984i | 1.43090 | − | 2.47840i | ||||
\(517\) | 2.55141 | 0.112211 | ||||||||
\(518\) | −10.9307 | − | 1.89625i | −0.480266 | − | 0.0833164i | ||||
\(519\) | 22.3798 | 0.982363 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.23285 | − | 3.86741i | −0.0978230 | − | 0.169434i | 0.812960 | − | 0.582319i | \(-0.197855\pi\) |
−0.910783 | + | 0.412885i | \(0.864521\pi\) | |||||||
\(522\) | −21.6124 | − | 37.4337i | −0.945948 | − | 1.63843i | ||||
\(523\) | 1.45406 | − | 2.51850i | 0.0635815 | − | 0.110126i | −0.832482 | − | 0.554051i | \(-0.813081\pi\) |
0.896064 | + | 0.443925i | \(0.146414\pi\) | |||||||
\(524\) | −8.03330 | −0.350936 | ||||||||
\(525\) | −10.1229 | − | 27.5752i | −0.441801 | − | 1.20348i | ||||
\(526\) | 9.09140 | 0.396404 | ||||||||
\(527\) | −9.64490 | + | 16.7055i | −0.420138 | + | 0.727701i | ||||
\(528\) | −1.86373 | − | 3.22807i | −0.0811084 | − | 0.140484i | ||||
\(529\) | −22.6139 | − | 39.1684i | −0.983213 | − | 1.70297i | ||||
\(530\) | 0.499100 | − | 0.864466i | 0.0216795 | − | 0.0375500i | ||||
\(531\) | 27.4632 | 1.19180 | ||||||||
\(532\) | 24.0187 | − | 28.7855i | 1.04134 | − | 1.24801i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.87654 | − | 11.9105i | 0.297577 | − | 0.515418i | ||||
\(535\) | 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 | ||||||||
\(539\) | 3.13732 | − | 2.66220i | 0.135134 | − | 0.114669i | ||||
\(540\) | −15.7180 | −0.676394 | ||||||||
\(541\) | 9.23193 | − | 15.9902i | 0.396912 | − | 0.687471i | −0.596431 | − | 0.802664i | \(-0.703415\pi\) |
0.993343 | + | 0.115193i | \(0.0367486\pi\) | |||||||
\(542\) | 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 | ||||
\(551\) | −7.57760 | + | 13.1248i | −0.322817 | + | 0.559135i | ||||
\(552\) | 92.4127 | 3.93334 | ||||||||
\(553\) | −2.53964 | − | 6.91806i | −0.107996 | − | 0.294186i | ||||
\(554\) | −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 | \(0.833692\pi\) | |||||||
\(558\) | −16.3107 | + | 28.2510i | −0.690487 | + | 1.19596i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5.90148 | + | 1.02379i | 0.249383 | + | 0.0432629i | ||||
\(561\) | −10.4385 | −0.440716 | ||||||||
\(562\) | 15.5194 | − | 26.8804i | 0.654646 | − | 1.13388i | ||||
\(563\) | −3.99253 | − | 6.91527i | −0.168265 | − | 0.291444i | 0.769545 | − | 0.638593i | \(-0.220483\pi\) |
−0.937810 | + | 0.347149i | \(0.887150\pi\) | |||||||
\(564\) | −22.1109 | − | 38.2972i | −0.931037 | − | 1.61260i | ||||
\(565\) | −4.99992 | + | 8.66012i | −0.210348 | + | 0.364334i | ||||
\(566\) | 40.1309 | 1.68683 | ||||||||
\(567\) | −4.74758 | − | 0.823608i | −0.199380 | − | 0.0345883i | ||||
\(568\) | −14.6485 | −0.614637 | ||||||||
\(569\) | 13.3621 | − | 23.1438i | 0.560167 | − | 0.970237i | −0.437315 | − | 0.899308i | \(-0.644070\pi\) |
0.997481 | − | 0.0709285i | \(-0.0225962\pi\) | |||||||
\(570\) | 12.3498 | + | 21.3904i | 0.517275 | + | 0.895946i | ||||
\(571\) | −6.74647 | − | 11.6852i | −0.282331 | − | 0.489012i | 0.689627 | − | 0.724164i | \(-0.257774\pi\) |
−0.971958 | + | 0.235153i | \(0.924441\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.8132 | 1.32902 | ||||||||
\(574\) | 7.99447 | + | 21.7772i | 0.333683 | + | 0.908964i | ||||
\(575\) | −33.3302 | −1.38996 | ||||||||
\(576\) | 24.8794 | − | 43.0923i | 1.03664 | − | 1.79551i | ||||
\(577\) | −6.00662 | − | 10.4038i | −0.250059 | − | 0.433115i | 0.713483 | − | 0.700673i | \(-0.247117\pi\) |
−0.963542 | + | 0.267558i | \(0.913783\pi\) | |||||||
\(578\) | 29.4406 | + | 50.9925i | 1.22457 | + | 2.12101i | ||||
\(579\) | 32.4383 | − | 56.1848i | 1.34809 | − | 2.33496i | ||||
\(580\) | −14.4036 | −0.598078 | ||||||||
\(581\) | 4.86172 | − | 5.82659i | 0.201698 | − | 0.241728i | ||||
\(582\) | 50.5745 | 2.09638 | ||||||||
\(583\) | 0.125067 | − | 0.216622i | 0.00517974 | − | 0.00897158i | ||||
\(584\) | 10.0318 | + | 17.3756i | 0.415118 | + | 0.719005i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.8305 | + | 29.1512i | −0.695260 | + | 1.20422i | ||||
\(587\) | 10.4235 | 0.430225 | 0.215113 | − | 0.976589i | \(-0.430988\pi\) | ||||
0.215113 | + | 0.976589i | \(0.430988\pi\) | |||||||
\(588\) | −67.1486 | − | 24.0207i | −2.76916 | − | 0.990599i | ||||
\(589\) | 11.4375 | 0.471275 | ||||||||
\(590\) | 7.04728 | − | 12.2062i | 0.290132 | − | 0.502523i | ||||
\(591\) | −2.02364 | − | 3.50504i | −0.0832412 | − | 0.144178i | ||||
\(592\) | −2.02339 | − | 3.50462i | −0.0831610 | − | 0.144039i | ||||
\(593\) | 11.1751 | − | 19.3558i | 0.458905 | − | 0.794847i | −0.539998 | − | 0.841666i | \(-0.681575\pi\) |
0.998903 | + | 0.0468194i | \(0.0149085\pi\) | |||||||
\(594\) | −6.06615 | −0.248897 | ||||||||
\(595\) | 10.7463 | − | 12.8791i | 0.440557 | − | 0.527991i | ||||
\(596\) | 10.3921 | 0.425679 | ||||||||
\(597\) | 12.9237 | − | 22.3845i | 0.528931 | − | 0.916135i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.579463 | − | 1.00366i | −0.0236762 | − | 0.0410084i | 0.853945 | − | 0.520364i | \(-0.174204\pi\) |
−0.877621 | + | 0.479356i | \(0.840870\pi\) | |||||||
\(600\) | 22.5724 | − | 39.0966i | 0.921515 | − | 1.59611i | ||||
\(601\) | 42.1813 | 1.72061 | 0.860306 | − | 0.509778i | \(-0.170272\pi\) | ||||
0.860306 | + | 0.509778i | \(0.170272\pi\) | |||||||
\(602\) | 13.8932 | + | 37.8456i | 0.566245 | + | 1.54247i | ||||
\(603\) | 32.0540 | 1.30534 | ||||||||
\(604\) | 42.6014 | − | 73.7879i | 1.73343 | − | 3.00239i | ||||
\(605\) | 5.23284 | + | 9.06355i | 0.212745 | + | 0.368486i | ||||
\(606\) | 8.66444 | + | 15.0072i | 0.351969 | + | 0.609628i | ||||
\(607\) | 9.07844 | − | 15.7243i | 0.368482 | − | 0.638230i | −0.620846 | − | 0.783932i | \(-0.713211\pi\) |
0.989328 | + | 0.145702i | \(0.0465441\pi\) | |||||||
\(608\) | −10.0594 | −0.407962 | ||||||||
\(609\) | 28.4048 | + | 4.92765i | 1.15102 | + | 0.199679i | ||||
\(610\) | −5.17640 | −0.209586 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 54.6147 | + | 94.5955i | 2.20767 | + | 3.82380i | ||||
\(613\) | 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 | ||||
\(615\) | −9.92354 | −0.400156 | ||||||||
\(616\) | 6.23055 | + | 1.08087i | 0.251036 | + | 0.0435497i | ||||
\(617\) | −26.0436 | −1.04848 | −0.524238 | − | 0.851572i | \(-0.675650\pi\) | ||||
−0.524238 | + | 0.851572i | \(0.675650\pi\) | |||||||
\(618\) | 35.6848 | − | 61.8079i | 1.43545 | − | 2.48628i | ||||
\(619\) | −13.4171 | − | 23.2390i | −0.539277 | − | 0.934056i | −0.998943 | − | 0.0459638i | \(-0.985364\pi\) |
0.459666 | − | 0.888092i | \(-0.347969\pi\) | |||||||
\(620\) | 5.43515 | + | 9.41396i | 0.218281 | + | 0.378074i | ||||
\(621\) | 17.8481 | − | 30.9138i | 0.716218 | − | 1.24053i | ||||
\(622\) | 68.3060 | 2.73882 | ||||||||
\(623\) | 1.90843 | + | 5.19863i | 0.0764596 | + | 0.208279i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.72894 | + | 9.92281i | −0.229158 | + | 0.396912i | ||||
\(626\) | −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 | ||||||||
\(630\) | 18.1734 | − | 21.7801i | 0.724044 | − | 0.867739i | ||||
\(631\) | −33.6121 | −1.33808 | −0.669039 | − | 0.743228i | \(-0.733294\pi\) | ||||
−0.669039 | + | 0.743228i | \(0.733294\pi\) | |||||||
\(632\) | 5.66296 | − | 9.80853i | 0.225260 | − | 0.390162i | ||||
\(633\) | −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 | 0.577414 | − | 0.816452i | \(-0.304062\pi\) |
−0.995775 | + | 0.0918294i | \(0.970729\pi\) | |||||||
\(642\) | 52.5010 | − | 90.9343i | 2.07205 | − | 3.58889i | ||||
\(643\) | 0.661539 | 0.0260886 | 0.0130443 | − | 0.999915i | \(-0.495848\pi\) | ||||
0.0130443 | + | 0.999915i | \(0.495848\pi\) | |||||||
\(644\) | −51.8423 | + | 62.1310i | −2.04287 | + | 2.44831i | ||||
\(645\) | −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 | ||||
\(649\) | 1.76594 | − | 3.05870i | 0.0693193 | − | 0.120065i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.49781 | − | 20.4243i | −0.293862 | − | 0.800492i | ||||
\(652\) | 30.2777 | 1.18577 | ||||||||
\(653\) | −6.35602 | + | 11.0089i | −0.248730 | + | 0.430813i | −0.963174 | − | 0.268880i | \(-0.913347\pi\) |
0.714444 | + | 0.699693i | \(0.246680\pi\) | |||||||
\(654\) | −30.3391 | − | 52.5489i | −1.18635 | − | 2.05482i | ||||
\(655\) | 1.06556 | + | 1.84560i | 0.0416349 | + | 0.0721138i | ||||
\(656\) | −4.23107 | + | 7.32844i | −0.165196 | + | 0.286127i | ||||
\(657\) | 22.5527 | 0.879867 | ||||||||
\(658\) | 27.0209 | + | 4.68759i | 1.05339 | + | 0.182741i | ||||
\(659\) | −14.1904 | −0.552781 | −0.276391 | − | 0.961045i | \(-0.589138\pi\) | ||||
−0.276391 | + | 0.961045i | \(0.589138\pi\) | |||||||
\(660\) | −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 | \(-0.596567\pi\) | |||||||
\(662\) | 32.5104 | + | 56.3096i | 1.26355 | + | 2.18853i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.6625 | 0.452594 | ||||||||
\(665\) | −9.79923 | − | 1.69997i | −0.379998 | − | 0.0659219i | ||||
\(666\) | −19.1652 | −0.742635 | ||||||||
\(667\) | 16.3556 | − | 28.3287i | 0.633290 | − | 1.09689i | ||||
\(668\) | 4.30944 | + | 7.46417i | 0.166737 | + | 0.288797i | ||||
\(669\) | 30.0181 | + | 51.9928i | 1.16057 | + | 2.01016i | ||||
\(670\) | 8.22530 | − | 14.2466i | 0.317771 | − | 0.550396i | ||||
\(671\) | −1.29713 | −0.0500751 | ||||||||
\(672\) | 6.59439 | + | 17.9634i | 0.254384 | + | 0.692952i | ||||
\(673\) | −1.87427 | −0.0722479 | −0.0361240 | − | 0.999347i | \(-0.511501\pi\) | ||||
−0.0361240 | + | 0.999347i | \(0.511501\pi\) | |||||||
\(674\) | −14.7056 | + | 25.4708i | −0.566438 | + | 0.981100i | ||||
\(675\) | −8.71902 | − | 15.1018i | −0.335595 | − | 0.581268i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.00439 | − | 1.73966i | 0.0386020 | − | 0.0668607i | −0.846079 | − | 0.533058i | \(-0.821043\pi\) |
0.884681 | + | 0.466197i | \(0.154376\pi\) | |||||||
\(678\) | 66.8906 | 2.56892 | ||||||||
\(679\) | −13.0469 | + | 15.6362i | −0.500693 | + | 0.600062i | ||||
\(680\) | 25.7788 | 0.988571 | ||||||||
\(681\) | −25.5234 | + | 44.2079i | −0.978061 | + | 1.69405i | ||||
\(682\) | 2.09762 | + | 3.63319i | 0.0803222 | + | 0.139122i | ||||
\(683\) | 7.05061 | + | 12.2120i | 0.269784 | + | 0.467280i | 0.968806 | − | 0.247820i | \(-0.0797143\pi\) |
−0.699022 | + | 0.715100i | \(0.746381\pi\) | |||||||
\(684\) | 32.3828 | − | 56.0886i | 1.23819 | − | 2.14460i | ||||
\(685\) | 8.21497 | 0.313878 | ||||||||
\(686\) | 38.1172 | − | 22.4302i | 1.45532 | − | 0.856390i | ||||
\(687\) | −53.2425 | −2.03133 | ||||||||
\(688\) | −7.35298 | + | 12.7357i | −0.280330 | + | 0.485546i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −26.6559 | − | 46.1693i | −1.01477 | − | 1.75764i | ||||
\(691\) | 17.8460 | − | 30.9102i | 0.678895 | − | 1.17588i | −0.296419 | − | 0.955058i | \(-0.595793\pi\) |
0.975314 | − | 0.220822i | \(-0.0708741\pi\) | |||||||
\(692\) | −30.1169 | −1.14487 | ||||||||
\(693\) | 4.55397 | − | 5.45776i | 0.172991 | − | 0.207323i | ||||
\(694\) | −14.6746 | −0.557041 | ||||||||
\(695\) | 0.283346 | − | 0.490769i | 0.0107479 | − | 0.0186159i | ||||
\(696\) | 22.1532 | + | 38.3704i | 0.839714 | + | 1.45443i | ||||
\(697\) | 11.8489 | + | 20.5229i | 0.448809 | + | 0.777360i | ||||
\(698\) | 15.5596 | − | 26.9500i | 0.588938 | − | 1.02007i | ||||
\(699\) | −44.4732 | −1.68213 | ||||||||
\(700\) | 13.6226 | + | 37.1086i | 0.514888 | + | 1.40257i | ||||
\(701\) | −6.15865 | −0.232609 | −0.116305 | − | 0.993214i | \(-0.537105\pi\) | ||||
−0.116305 | + | 0.993214i | \(0.537105\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.35979 | + | 5.81932i | 0.126717 | + | 0.219480i | ||||
\(704\) | −3.19959 | − | 5.54185i | −0.120589 | − | 0.208866i | ||||
\(705\) | −5.86571 | + | 10.1597i | −0.220915 | + | 0.382637i | ||||
\(706\) | −75.6207 | −2.84602 | ||||||||
\(707\) | −6.87501 | − | 1.19268i | −0.258561 | − | 0.0448552i | ||||
\(708\) | −61.2156 | −2.30062 | ||||||||
\(709\) | −17.0185 | + | 29.4770i | −0.639144 | + | 1.10703i | 0.346477 | + | 0.938059i | \(0.387378\pi\) |
−0.985621 | + | 0.168972i | \(0.945955\pi\) | |||||||
\(710\) | 4.22527 | + | 7.31838i | 0.158571 | + | 0.274654i | ||||
\(711\) | −6.36553 | − | 11.0254i | −0.238726 | − | 0.413486i | ||||
\(712\) | −4.25547 | + | 7.37069i | −0.159480 | + | 0.276228i | ||||
\(713\) | −24.6869 | −0.924530 | ||||||||
\(714\) | −110.550 | − | 19.1782i | −4.13724 | − | 0.717727i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 38.8648 | − | 67.3158i | 1.45244 | − | 2.51571i | ||||
\(717\) | 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 | ||||||||
\(721\) | 9.90351 | + | 26.9775i | 0.368826 | + | 1.00470i | ||||
\(722\) | 10.3996 | 0.387034 | ||||||||
\(723\) | −5.51122 | + | 9.54571i | −0.204964 | + | 0.355009i | ||||
\(724\) | 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 | ||||
\(733\) | 13.1689 | − | 22.8092i | 0.486404 | − | 0.842476i | −0.513474 | − | 0.858105i | \(-0.671642\pi\) |
0.999878 | + | 0.0156289i | \(0.00497504\pi\) | |||||||
\(734\) | −47.0897 | −1.73811 | ||||||||
\(735\) | 3.38816 | + | 18.6132i | 0.124974 | + | 0.686558i | ||||
\(736\) | 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 | \(-0.383328\pi\) | |||||||
\(740\) | −3.19317 | + | 5.53073i | −0.117383 | + | 0.203314i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.72252 | − | 2.06438i | 0.0632358 | − | 0.0757857i | ||||
\(743\) | 22.4782 | 0.824644 | 0.412322 | − | 0.911038i | \(-0.364718\pi\) | ||||
0.412322 | + | 0.911038i | \(0.364718\pi\) | |||||||
\(744\) | 16.7188 | − | 28.9579i | 0.612942 | − | 1.06165i | ||||
\(745\) | −1.37845 | − | 2.38754i | −0.0505023 | − | 0.0874726i | ||||
\(746\) | 20.9513 | + | 36.2888i | 0.767083 | + | 1.32863i | ||||
\(747\) | 6.55472 | − | 11.3531i | 0.239825 | − | 0.415388i | ||||
\(748\) | 14.0474 | 0.513623 | ||||||||
\(749\) | 14.5705 | + | 39.6905i | 0.532393 | + | 1.45026i | ||||
\(750\) | −58.3145 | −2.12934 | ||||||||
\(751\) | 21.2712 | − | 36.8428i | 0.776197 | − | 1.34441i | −0.157923 | − | 0.987451i | \(-0.550480\pi\) |
0.934119 | − | 0.356961i | \(-0.116187\pi\) | |||||||
\(752\) | 5.00189 | + | 8.66353i | 0.182400 | + | 0.315927i | ||||
\(753\) | 4.46686 | + | 7.73683i | 0.162781 | + | 0.281946i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.6031 | −0.822612 | ||||||||
\(756\) | −41.7131 | − | 7.23637i | −1.51709 | − | 0.263184i | ||||
\(757\) | −11.2380 | −0.408454 | −0.204227 | − | 0.978924i | \(-0.565468\pi\) | ||||
−0.204227 | + | 0.978924i | \(0.565468\pi\) | |||||||
\(758\) | −13.9716 | + | 24.1996i | −0.507473 | + | 0.878969i | ||||
\(759\) | −6.67956 | − | 11.5693i | −0.242453 | − | 0.419941i | ||||
\(760\) | −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 | ||||||||
\(763\) | 24.0733 | + | 4.17623i | 0.871513 | + | 0.151190i | ||||
\(764\) | −42.8117 | −1.54887 | ||||||||
\(765\) | 14.4885 | − | 25.0948i | 0.523833 | − | 0.907306i | ||||
\(766\) | −25.7058 | − | 44.5238i | −0.928789 | − | 1.60871i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −38.1846 | + | 66.1377i | −1.37787 | + | 2.38654i | ||||
\(769\) | −51.3517 | −1.85179 | −0.925895 | − | 0.377781i | \(-0.876687\pi\) | ||||
−0.925895 | + | 0.377781i | \(0.876687\pi\) | |||||||
\(770\) | −1.25716 | − | 3.42455i | −0.0453049 | − | 0.123412i | ||||
\(771\) | 73.9938 | 2.66482 | ||||||||
\(772\) | −43.6529 | + | 75.6091i | −1.57110 | + | 2.72123i | ||||
\(773\) | −10.0023 | − | 17.3245i | −0.359759 | − | 0.623120i | 0.628162 | − | 0.778083i | \(-0.283808\pi\) |
−0.987920 | + | 0.154963i | \(0.950474\pi\) | |||||||
\(774\) | 34.8230 | + | 60.3151i | 1.25169 | + | 2.16798i | ||||
\(775\) | −6.02993 | + | 10.4441i | −0.216602 | + | 0.375165i | ||||
\(776\) | −31.2974 | −1.12351 | ||||||||
\(777\) | 8.18925 | − | 9.81450i | 0.293788 | − | 0.352093i | ||||
\(778\) | −63.2615 | −2.26804 | ||||||||
\(779\) | 7.02558 | − | 12.1687i | 0.251717 | − | 0.435987i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.05879 | + | 1.83388i | 0.0378864 | + | 0.0656212i | ||||
\(782\) | −63.6552 | + | 110.254i | −2.27631 | + | 3.94268i | ||||
\(783\) | 17.1142 | 0.611611 | ||||||||
\(784\) | 15.1903 | + | 5.43394i | 0.542509 | + | 0.194069i | ||||
\(785\) | 22.1759 | 0.791492 | ||||||||
\(786\) | 7.12771 | − | 12.3456i | 0.254237 | − | 0.440351i | ||||
\(787\) | −14.6596 | − | 25.3911i | −0.522558 | − | 0.905096i | −0.999656 | − | 0.0262462i | \(-0.991645\pi\) |
0.477098 | − | 0.878850i | \(-0.341689\pi\) | |||||||
\(788\) | 2.72325 | + | 4.71680i | 0.0970117 | + | 0.168029i | ||||
\(789\) | −5.23752 | + | 9.07166i | −0.186461 | + | 0.322959i | ||||
\(790\) | −6.53378 | −0.232462 | ||||||||
\(791\) | −17.2560 | + | 20.6807i | −0.613553 | + | 0.735321i | ||||
\(792\) | 10.9243 | 0.388177 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −40.3566 | − | 69.8996i | −1.43220 | − | 2.48064i | ||||
\(795\) | 0.575059 | + | 0.996031i | 0.0203952 | + | 0.0353256i | ||||
\(796\) | −17.3917 | + | 30.1232i | −0.616431 | + | 1.06769i | ||||
\(797\) | 3.10100 | 0.109843 | 0.0549215 | − | 0.998491i | \(-0.482509\pi\) | ||||
0.0549215 | + | 0.998491i | \(0.482509\pi\) | |||||||
\(798\) | 22.9264 | + | 62.4525i | 0.811588 | + | 2.21079i | ||||
\(799\) | 28.0151 | 0.991102 | ||||||||
\(800\) | 5.30338 | − | 9.18572i | 0.187503 | − | 0.324764i | ||||
\(801\) | 4.78343 | + | 8.28514i | 0.169014 | + | 0.292741i | ||||
\(802\) | 25.8050 | + | 44.6956i | 0.911206 | + | 1.57826i | ||||
\(803\) | 1.45019 | − | 2.51180i | 0.0511761 | − | 0.0886395i | ||||
\(804\) | −71.4484 | −2.51979 | ||||||||
\(805\) | 21.1508 | + | 3.66923i | 0.745467 | + | 0.129323i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.7950 | + | 56.8025i | −1.15444 | + | 1.99954i | ||||
\(808\) | −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 | \(0.821737\pi\) | |||||||
\(812\) | −38.2249 | − | 6.63125i | −1.34143 | − | 0.232711i | ||||
\(813\) | −27.2434 | −0.955466 | ||||||||
\(814\) | −1.23236 | + | 2.13451i | −0.0431942 | + | 0.0748146i | ||||
\(815\) | −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 | −0.518972 | − | 0.854791i | \(-0.673685\pi\) |
0.999757 | + | 0.0220477i | \(0.00701856\pi\) | |||||||
\(822\) | −27.4756 | − | 47.5892i | −0.958323 | − | 1.65986i | ||||
\(823\) | −10.2137 | − | 17.6907i | −0.356028 | − | 0.616659i | 0.631265 | − | 0.775567i | \(-0.282536\pi\) |
−0.987293 | + | 0.158908i | \(0.949203\pi\) | |||||||
\(824\) | −22.0831 | + | 38.2491i | −0.769303 | + | 1.33247i | ||||
\(825\) | −6.52611 | −0.227210 | ||||||||
\(826\) | 24.3220 | − | 29.1490i | 0.846270 | − | 1.01422i | ||||
\(827\) | −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 | ||||
\(831\) | 16.2142 | − | 28.0837i | 0.562463 | − | 0.974214i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.4484 | − | 29.2315i | 1.19357 | − | 1.01281i | ||||
\(834\) | −3.79069 | −0.131261 | ||||||||
\(835\) | 1.14323 | − | 1.98014i | 0.0395632 | − | 0.0685255i | ||||
\(836\) | −4.16456 | − | 7.21323i | −0.144034 | − | 0.249475i | ||||
\(837\) | −6.45797 | − | 11.1855i | −0.223220 | − | 0.386628i | ||||
\(838\) | −9.67387 | + | 16.7556i | −0.334178 | + | 0.578814i | ||||
\(839\) | −30.3739 | −1.04862 | −0.524312 | − | 0.851526i | \(-0.675677\pi\) | ||||
−0.524312 | + | 0.851526i | \(0.675677\pi\) | |||||||
\(840\) | −18.6281 | + | 22.3251i | −0.642731 | + | 0.770288i | ||||
\(841\) | −13.3170 | −0.459205 | ||||||||
\(842\) | −38.3428 | + | 66.4116i | −1.32138 | + | 2.28869i | ||||
\(843\) | 17.8813 | + | 30.9713i | 0.615865 | + | 1.06671i | ||||
\(844\) | 16.5552 | + | 28.6745i | 0.569854 | + | 0.987016i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 47.3769 | 1.62885 | ||||||||
\(847\) | 9.71440 | + | 26.4624i | 0.333791 | + | 0.909258i | ||||
\(848\) | 0.980745 | 0.0336789 | ||||||||
\(849\) | −23.1193 | + | 40.0437i | −0.793451 | + | 1.37430i | ||||
\(850\) | 31.0964 | + | 53.8606i | 1.06660 | + | 1.84740i | ||||
\(851\) | −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 | \(0.528964\pi\) | |||||||
\(854\) | −13.7374 | − | 2.38315i | −0.470082 | − | 0.0815498i | ||||
\(855\) | −17.1814 | −0.587591 | ||||||||
\(856\) | −32.4896 | + | 56.2737i | −1.11047 | + | 1.92340i | ||||
\(857\) | 8.31857 | + | 14.4082i | 0.284157 | + | 0.492175i | 0.972404 | − | 0.233302i | \(-0.0749529\pi\) |
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.29426 | − | 9.16993i | 0.180638 | − | 0.312874i | −0.761460 | − | 0.648212i | \(-0.775517\pi\) |
0.942098 | + | 0.335338i | \(0.108850\pi\) | |||||||
\(860\) | 23.2078 | 0.791381 | ||||||||
\(861\) | −26.3355 | − | 4.56868i | −0.897512 | − | 0.155700i | ||||
\(862\) | 70.5142 | 2.40172 | ||||||||
\(863\) | 28.0316 | − | 48.5522i | 0.954207 | − | 1.65273i | 0.218033 | − | 0.975941i | \(-0.430036\pi\) |
0.736173 | − | 0.676793i | \(-0.236631\pi\) | |||||||
\(864\) | 5.67984 | + | 9.83777i | 0.193232 | + | 0.334688i | ||||
\(865\) | 3.99480 | + | 6.91919i | 0.135827 | + | 0.235260i | ||||
\(866\) | 26.3771 | − | 45.6864i | 0.896329 | − | 1.55249i | ||||
\(867\) | −67.8424 | −2.30405 | ||||||||
\(868\) | 10.0900 | + | 27.4854i | 0.342476 | + | 0.932916i | ||||
\(869\) | −1.63727 | −0.0555405 | ||||||||
\(870\) | 12.7799 | − | 22.1354i | 0.433279 | − | 0.750462i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 18.7750 | + | 32.5193i | 0.635803 | + | 1.10124i | ||||
\(873\) | −17.5902 | + | 30.4671i | −0.595337 | + | 1.03115i | ||||
\(874\) | 75.4863 | 2.55336 | ||||||||
\(875\) | 15.0436 | − | 18.0292i | 0.508567 | − | 0.609498i | ||||
\(876\) | −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 | ||||
\(879\) | −19.3919 | − | 33.5878i | −0.654073 | − | 1.13289i | ||||
\(880\) | 0.665353 | − | 1.15242i | 0.0224290 | − | 0.0388482i | ||||
\(881\) | 10.2299 | 0.344653 | 0.172326 | − | 0.985040i | \(-0.444872\pi\) | ||||
0.172326 | + | 0.985040i | \(0.444872\pi\) | |||||||
\(882\) | 58.2565 | − | 49.4341i | 1.96160 | − | 1.66453i | ||||
\(883\) | −3.98979 | −0.134267 | −0.0671335 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671335 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.11982 | + | 14.0639i | 0.272945 | + | 0.472754i | ||||
\(886\) | −16.1941 | − | 28.0490i | −0.544052 | − | 0.942325i | ||||
\(887\) | 7.11039 | − | 12.3155i | 0.238743 | − | 0.413516i | −0.721611 | − | 0.692299i | \(-0.756598\pi\) |
0.960354 | + | 0.278784i | \(0.0899312\pi\) | |||||||
\(888\) | 19.6447 | 0.659234 | ||||||||
\(889\) | −7.20440 | + | 8.63420i | −0.241628 | + | 0.289582i | ||||
\(890\) | 4.90986 | 0.164579 | ||||||||
\(891\) | −0.535258 | + | 0.927094i | −0.0179318 | + | 0.0310588i | ||||
\(892\) | −40.3960 | − | 69.9678i | −1.35256 | − | 2.34270i | ||||
\(893\) | −8.30550 | − | 14.3855i | −0.277933 | − | 0.481394i | ||||
\(894\) | −9.22065 | + | 15.9706i | −0.308385 | + | 0.534138i | ||||
\(895\) | −20.6206 | −0.689269 | ||||||||
\(896\) | −18.9104 | − | 51.5127i | −0.631753 | − | 1.72092i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.1631 | − | 45.3158i | 0.873074 | − | 1.51221i | ||||
\(899\) | −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 | ||||||||
\(903\) | −45.7672 | − | 7.93969i | −1.52304 | − | 0.264216i | ||||
\(904\) | −41.3945 | −1.37676 | ||||||||
\(905\) | 0.789789 | − | 1.36795i | 0.0262535 | − | 0.0454723i | ||||
\(906\) | 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 | ||||
\(915\) | 2.98210 | − | 5.16516i | 0.0985853 | − | 0.170755i | ||||
\(916\) | 71.6495 | 2.36737 | ||||||||
\(917\) | 1.97814 | + | 5.38852i | 0.0653238 | + | 0.177944i | ||||
\(918\) | −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 | ||||
\(922\) | −19.3625 | + | 33.5369i | −0.637671 | + | 1.10448i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −10.1508 | + | 12.1654i | −0.333937 | + | 0.400211i | ||||
\(925\) | −7.08521 | −0.232960 | ||||||||
\(926\) | −1.72857 | + | 2.99397i | −0.0568044 | + | 0.0983880i | ||||
\(927\) | 24.8229 | + | 42.9945i | 0.815291 | + | 1.41212i | ||||
\(928\) | 5.20488 | + | 9.01512i | 0.170859 | + | 0.295936i | ||||
\(929\) | −4.74761 | + | 8.22310i | −0.155764 | + | 0.269791i | −0.933337 | − | 0.359002i | \(-0.883117\pi\) |
0.777573 | + | 0.628793i | \(0.216451\pi\) | |||||||
\(930\) | −19.2898 | −0.632537 | ||||||||
\(931\) | −25.2230 | − | 9.02289i | −0.826649 | − | 0.295713i | ||||
\(932\) | 59.8486 | 1.96040 | ||||||||
\(933\) | −39.3508 | + | 68.1576i | −1.28829 | + | 2.23138i | ||||
\(934\) | 16.7243 | + | 28.9674i | 0.547236 | + | 0.947841i | ||||
\(935\) | −1.86328 | − | 3.22730i | −0.0609359 | − | 0.105544i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.41678 | −0.209627 | −0.104813 | − | 0.994492i | \(-0.533425\pi\) | ||||
−0.104813 | + | 0.994492i | \(0.533425\pi\) | |||||||
\(938\) | 28.3876 | − | 34.0215i | 0.926889 | − | 1.11084i | ||||
\(939\) | 51.1203 | 1.66825 | ||||||||
\(940\) | 7.89361 | − | 13.6721i | 0.257461 | − | 0.445936i | ||||
\(941\) | 25.7593 | + | 44.6164i | 0.839730 | + | 1.45445i | 0.890121 | + | 0.455725i | \(0.150620\pi\) |
−0.0503911 | + | 0.998730i | \(0.516047\pi\) | |||||||
\(942\) | −74.1691 | − | 128.465i | −2.41656 | − | 4.18561i | ||||
\(943\) | −15.1641 | + | 26.2650i | −0.493810 | + | 0.855305i | ||||
\(944\) | 13.8481 | 0.450717 | ||||||||
\(945\) | 3.87043 | + | 10.5432i | 0.125905 | + | 0.342970i | ||||
\(946\) | 8.95676 | 0.291209 | ||||||||
\(947\) | 4.20109 | − | 7.27651i | 0.136517 | − | 0.236455i | −0.789659 | − | 0.613546i | \(-0.789742\pi\) |
0.926176 | + | 0.377091i | \(0.123076\pi\) | |||||||
\(948\) | 14.1888 | + | 24.5757i | 0.460831 | + | 0.798182i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 18.4380 | − | 31.9356i | 0.598209 | − | 1.03613i | ||||
\(951\) | −84.3177 | −2.73419 | ||||||||
\(952\) | 68.4128 | + | 11.8682i | 2.21727 | + | 0.384652i | ||||
\(953\) | −36.0911 | −1.16910 | −0.584552 | − | 0.811356i | \(-0.698730\pi\) | ||||
−0.584552 | + | 0.811356i | \(0.698730\pi\) | |||||||
\(954\) | 2.32235 | − | 4.02244i | 0.0751890 | − | 0.130231i | ||||
\(955\) | 5.67867 | + | 9.83575i | 0.183758 | + | 0.318277i | ||||
\(956\) | −29.8138 | − | 51.6390i | −0.964246 | − | 1.67012i | ||||
\(957\) | 3.20245 | − | 5.54681i | 0.103521 | − | 0.179303i | ||||
\(958\) | 71.6991 | 2.31649 | ||||||||
\(959\) | 21.8012 | + | 3.78207i | 0.703998 | + | 0.122129i | ||||
\(960\) | 29.4235 | 0.949639 | ||||||||
\(961\) | 11.0338 | − | 19.1111i | 0.355928 | − | 0.616486i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.5205 | + | 63.2553i | 1.17686 | + | 2.03837i | ||||
\(964\) | 7.41656 | − | 12.8459i | 0.238871 | − | 0.413737i | ||||
\(965\) | 23.1610 | 0.745580 | ||||||||
\(966\) | −49.4847 | − | 134.798i | −1.59214 | − | 4.33706i | ||||
\(967\) | 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 | ||||
\(970\) | 9.02756 | + | 15.6362i | 0.289857 | + | 0.502048i | ||||
\(971\) | −18.8738 | + | 32.6904i | −0.605690 | + | 1.04909i | 0.386253 | + | 0.922393i | \(0.373769\pi\) |
−0.991942 | + | 0.126692i | \(0.959564\pi\) | |||||||
\(972\) | 66.5591 | 2.13488 | ||||||||
\(973\) | 0.977898 | − | 1.17197i | 0.0313500 | − | 0.0375718i | ||||
\(974\) | 68.0359 | 2.18001 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.54294 | − | 4.40451i | −0.0813977 | − | 0.140985i | ||||
\(977\) | 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 | ||||
\(979\) | 1.23034 | 0.0393217 | ||||||||
\(980\) | −4.55951 | − | 25.0482i | −0.145648 | − | 0.800134i | ||||
\(981\) | 42.2087 | 1.34762 | ||||||||
\(982\) | −33.9910 | + | 58.8741i | −1.08470 | + | 1.87875i | ||||
\(983\) | 11.0158 | + | 19.0799i | 0.351350 | + | 0.608556i | 0.986486 | − | 0.163844i | \(-0.0523895\pi\) |
−0.635136 | + | 0.772400i | \(0.719056\pi\) | |||||||
\(984\) | −20.5393 | − | 35.5752i | −0.654770 | − | 1.13409i | ||||
\(985\) | 0.722439 | − | 1.25130i | 0.0230188 | − | 0.0398698i | ||||
\(986\) | −61.0378 | −1.94384 | ||||||||
\(987\) | −20.2441 | + | 24.2618i | −0.644376 | + | 0.772260i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.3529 | + | 45.6446i | −0.837975 | + | 1.45141i | ||||
\(990\) | −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 | ||||||||
\(994\) | 7.84390 | + | 21.3671i | 0.248793 | + | 0.677723i | ||||
\(995\) | 9.22753 | 0.292532 | ||||||||
\(996\) | −14.6105 | + | 25.3061i | −0.462951 | + | 0.801855i | ||||
\(997\) | −5.04102 | − | 8.73130i | −0.159651 | − | 0.276523i | 0.775092 | − | 0.631848i | \(-0.217703\pi\) |
−0.934743 | + | 0.355325i | \(0.884370\pi\) | |||||||
\(998\) | −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 | 1183.2.e.h.170.6 | 12 | ||
7.2 | even | 3 | 8281.2.a.bz.1.1 | 6 | |||
7.4 | even | 3 | inner | 1183.2.e.h.508.6 | 12 | ||
7.5 | odd | 6 | 8281.2.a.ca.1.1 | 6 | |||
13.3 | even | 3 | 91.2.g.b.9.6 | ✓ | 12 | ||
13.9 | even | 3 | 91.2.h.b.16.1 | yes | 12 | ||
13.12 | even | 2 | 1183.2.e.g.170.1 | 12 | |||
39.29 | odd | 6 | 819.2.n.d.100.1 | 12 | |||
39.35 | odd | 6 | 819.2.s.d.289.6 | 12 | |||
91.3 | odd | 6 | 637.2.h.l.165.1 | 12 | |||
91.9 | even | 3 | 637.2.f.k.393.6 | 12 | |||
91.12 | odd | 6 | 8281.2.a.cf.1.6 | 6 | |||
91.16 | even | 3 | 637.2.f.k.295.6 | 12 | |||
91.25 | even | 6 | 1183.2.e.g.508.1 | 12 | |||
91.48 | odd | 6 | 637.2.h.l.471.1 | 12 | |||
91.51 | even | 6 | 8281.2.a.ce.1.6 | 6 | |||
91.55 | odd | 6 | 637.2.g.l.373.6 | 12 | |||
91.61 | odd | 6 | 637.2.f.j.393.6 | 12 | |||
91.68 | odd | 6 | 637.2.f.j.295.6 | 12 | |||
91.74 | even | 3 | 91.2.g.b.81.6 | yes | 12 | ||
91.81 | even | 3 | 91.2.h.b.74.1 | yes | 12 | ||
91.87 | odd | 6 | 637.2.g.l.263.6 | 12 | |||
273.74 | odd | 6 | 819.2.n.d.172.1 | 12 | |||
273.263 | 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 | 13.3 | even | 3 | ||
91.2.g.b.81.6 | yes | 12 | 91.74 | even | 3 | ||
91.2.h.b.16.1 | yes | 12 | 13.9 | even | 3 | ||
91.2.h.b.74.1 | yes | 12 | 91.81 | even | 3 | ||
637.2.f.j.295.6 | 12 | 91.68 | odd | 6 | |||
637.2.f.j.393.6 | 12 | 91.61 | odd | 6 | |||
637.2.f.k.295.6 | 12 | 91.16 | even | 3 | |||
637.2.f.k.393.6 | 12 | 91.9 | even | 3 | |||
637.2.g.l.263.6 | 12 | 91.87 | odd | 6 | |||
637.2.g.l.373.6 | 12 | 91.55 | odd | 6 | |||
637.2.h.l.165.1 | 12 | 91.3 | odd | 6 | |||
637.2.h.l.471.1 | 12 | 91.48 | odd | 6 | |||
819.2.n.d.100.1 | 12 | 39.29 | odd | 6 | |||
819.2.n.d.172.1 | 12 | 273.74 | odd | 6 | |||
819.2.s.d.289.6 | 12 | 39.35 | odd | 6 | |||
819.2.s.d.802.6 | 12 | 273.263 | odd | 6 | |||
1183.2.e.g.170.1 | 12 | 13.12 | even | 2 | |||
1183.2.e.g.508.1 | 12 | 91.25 | even | 6 | |||
1183.2.e.h.170.6 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.e.h.508.6 | 12 | 7.4 | even | 3 | inner | ||
8281.2.a.bz.1.1 | 6 | 7.2 | even | 3 | |||
8281.2.a.ca.1.1 | 6 | 7.5 | odd | 6 | |||
8281.2.a.ce.1.6 | 6 | 91.51 | even | 6 | |||
8281.2.a.cf.1.6 | 6 | 91.12 | odd | 6 |