Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(89,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.r (of order \(6\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.1 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.89 |
Dual form | 1386.2.r.c.1277.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.0340742 | − | 0.0590182i | 0.0152384 | − | 0.0263937i | −0.858306 | − | 0.513139i | \(-0.828483\pi\) |
0.873544 | + | 0.486745i | \(0.161816\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.19067 | − | 1.48356i | −0.827996 | − | 0.560734i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0590182 | + | 0.0340742i | −0.0186632 | + | 0.0107752i | ||||
\(11\) | −0.866025 | + | 0.500000i | −0.261116 | + | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 1.15539 | + | 2.38014i | 0.308792 | + | 0.636119i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.817837 | − | 1.41654i | −0.198355 | − | 0.343560i | 0.749640 | − | 0.661845i | \(-0.230226\pi\) |
−0.947995 | + | 0.318285i | \(0.896893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.28497 | + | 3.62863i | 1.44187 | + | 0.832464i | 0.997975 | − | 0.0636147i | \(-0.0202629\pi\) |
0.443895 | + | 0.896079i | \(0.353596\pi\) | |||||||
\(20\) | 0.0681483 | 0.0152384 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −0.405083 | − | 0.233875i | −0.0844657 | − | 0.0487663i | 0.457172 | − | 0.889378i | \(-0.348862\pi\) |
−0.541638 | + | 0.840612i | \(0.682196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.49768 | + | 4.32611i | 0.499536 | + | 0.865221i | ||||
\(26\) | 1.22474 | − | 2.12132i | 0.240192 | − | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.189469 | − | 2.63896i | 0.0358062 | − | 0.498716i | ||||
\(29\) | − | 7.23143i | − | 1.34284i | −0.741076 | − | 0.671421i | \(-0.765684\pi\) | ||
0.741076 | − | 0.671421i | \(-0.234316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.201501 | + | 0.116337i | −0.0361906 | + | 0.0208947i | −0.517986 | − | 0.855389i | \(-0.673318\pi\) |
0.481796 | + | 0.876284i | \(0.339985\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.63567i | 0.280516i | ||||||||
\(35\) | −0.162203 | + | 0.0787382i | −0.0274172 | + | 0.0133092i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.74496 | − | 4.75442i | 0.451269 | − | 0.781621i | −0.547196 | − | 0.837004i | \(-0.684305\pi\) |
0.998465 | + | 0.0553835i | \(0.0176381\pi\) | |||||||
\(38\) | −3.62863 | − | 6.28497i | −0.588641 | − | 1.01956i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0590182 | − | 0.0340742i | −0.00933160 | − | 0.00538760i | ||||
\(41\) | −5.38891 | −0.841606 | −0.420803 | − | 0.907152i | \(-0.638252\pi\) | ||||
−0.420803 | + | 0.907152i | \(0.638252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.64100 | 1.47024 | 0.735119 | − | 0.677938i | \(-0.237126\pi\) | ||||
0.735119 | + | 0.677938i | \(0.237126\pi\) | |||||||
\(44\) | −0.866025 | − | 0.500000i | −0.130558 | − | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.233875 | + | 0.405083i | 0.0344830 | + | 0.0597263i | ||||
\(47\) | 4.31199 | − | 7.46859i | 0.628969 | − | 1.08941i | −0.358791 | − | 0.933418i | \(-0.616811\pi\) |
0.987759 | − | 0.155987i | \(-0.0498559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.59808 | + | 6.50000i | 0.371154 | + | 0.928571i | ||||
\(50\) | − | 4.99536i | − | 0.706450i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.12132 | + | 1.22474i | −0.294174 | + | 0.169842i | ||||
\(53\) | 7.34278 | − | 4.23936i | 1.00861 | − | 0.582320i | 0.0978246 | − | 0.995204i | \(-0.468812\pi\) |
0.910784 | + | 0.412883i | \(0.135478\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0681483i | 0.00918912i | ||||||||
\(56\) | −1.48356 | + | 2.19067i | −0.198250 | + | 0.292741i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.61571 | + | 6.26260i | −0.474767 | + | 0.822320i | ||||
\(59\) | −0.439158 | − | 0.760643i | −0.0571734 | − | 0.0990273i | 0.836022 | − | 0.548696i | \(-0.184875\pi\) |
−0.893196 | + | 0.449668i | \(0.851542\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.63223 | − | 4.98382i | −1.10524 | − | 0.638113i | −0.167651 | − | 0.985846i | \(-0.553618\pi\) |
−0.937593 | + | 0.347733i | \(0.886951\pi\) | |||||||
\(62\) | 0.232673 | 0.0295495 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.144564 | + | 0.0834643i | 0.0179310 | + | 0.0103525i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52993 | + | 2.64991i | 0.186910 | + | 0.323738i | 0.944219 | − | 0.329319i | \(-0.106819\pi\) |
−0.757308 | + | 0.653058i | \(0.773486\pi\) | |||||||
\(68\) | 0.817837 | − | 1.41654i | 0.0991773 | − | 0.171780i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.179841 | + | 0.0129120i | 0.0214951 | + | 0.00154328i | ||||
\(71\) | 15.8771i | 1.88426i | 0.335245 | + | 0.942131i | \(0.391181\pi\) | ||||
−0.335245 | + | 0.942131i | \(0.608819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.76696 | − | 3.90691i | 0.792013 | − | 0.457269i | −0.0486577 | − | 0.998816i | \(-0.515494\pi\) |
0.840671 | + | 0.541547i | \(0.182161\pi\) | |||||||
\(74\) | −4.75442 | + | 2.74496i | −0.552690 | + | 0.319095i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.25725i | 0.832464i | ||||||||
\(77\) | 2.63896 | + | 0.189469i | 0.300737 | + | 0.0215920i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.76612 | − | 9.98722i | 0.648740 | − | 1.12365i | −0.334684 | − | 0.942330i | \(-0.608630\pi\) |
0.983424 | − | 0.181320i | \(-0.0580370\pi\) | |||||||
\(80\) | 0.0340742 | + | 0.0590182i | 0.00380961 | + | 0.00659844i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.66693 | + | 2.69445i | 0.515376 | + | 0.297553i | ||||
\(83\) | 17.1270 | 1.87993 | 0.939967 | − | 0.341266i | \(-0.110856\pi\) | ||||
0.939967 | + | 0.341266i | \(0.110856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.111469 | −0.0120905 | ||||||||
\(86\) | −8.34935 | − | 4.82050i | −0.900333 | − | 0.519808i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | 5.33814 | − | 9.24592i | 0.565841 | − | 0.980066i | −0.431129 | − | 0.902290i | \(-0.641885\pi\) |
0.996971 | − | 0.0777760i | \(-0.0247819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.63397 | − | 5.36603i | 0.380944 | − | 0.562512i | ||||
\(92\) | − | 0.467750i | − | 0.0487663i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.46859 | + | 4.31199i | −0.770326 | + | 0.444748i | ||||
\(95\) | 0.428310 | − | 0.247285i | 0.0439437 | − | 0.0253709i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.99876i | 1.01522i | 0.861587 | + | 0.507610i | \(0.169471\pi\) | ||||
−0.861587 | + | 0.507610i | \(0.830529\pi\) | |||||||
\(98\) | 1.00000 | − | 6.92820i | 0.101015 | − | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.49768 | + | 4.32611i | −0.249768 | + | 0.432611i | ||||
\(101\) | 1.76028 | + | 3.04889i | 0.175154 | + | 0.303376i | 0.940215 | − | 0.340582i | \(-0.110624\pi\) |
−0.765060 | + | 0.643959i | \(0.777291\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8471 | + | 7.99465i | 1.36440 | + | 0.787736i | 0.990206 | − | 0.139614i | \(-0.0445862\pi\) |
0.374194 | + | 0.927351i | \(0.377920\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.47871 | −0.823525 | ||||||||
\(107\) | −5.25201 | − | 3.03225i | −0.507731 | − | 0.293139i | 0.224169 | − | 0.974550i | \(-0.428033\pi\) |
−0.731901 | + | 0.681412i | \(0.761366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.00877 | − | 15.6036i | −0.862883 | − | 1.49456i | −0.869134 | − | 0.494577i | \(-0.835323\pi\) |
0.00625046 | − | 0.999980i | \(-0.498010\pi\) | |||||||
\(110\) | 0.0340742 | − | 0.0590182i | 0.00324884 | − | 0.00562716i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.38014 | − | 1.15539i | 0.224902 | − | 0.109175i | ||||
\(113\) | 7.05521i | 0.663698i | 0.943332 | + | 0.331849i | \(0.107673\pi\) | ||||
−0.943332 | + | 0.331849i | \(0.892327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0276058 | + | 0.0159382i | −0.00257425 | + | 0.00148624i | ||||
\(116\) | 6.26260 | − | 3.61571i | 0.581468 | − | 0.335711i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.878315i | 0.0808555i | ||||||||
\(119\) | −0.309909 | + | 4.31648i | −0.0284093 | + | 0.395691i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 4.98382 | + | 8.63223i | 0.451214 | + | 0.781526i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.201501 | − | 0.116337i | −0.0180953 | − | 0.0104473i | ||||
\(125\) | 0.681167 | 0.0609254 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.83939 | 0.606898 | 0.303449 | − | 0.952848i | \(-0.401862\pi\) | ||||
0.303449 | + | 0.952848i | \(0.401862\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0834643 | − | 0.144564i | −0.00732031 | − | 0.0126791i | ||||
\(131\) | 0.757359 | − | 1.31178i | 0.0661708 | − | 0.114611i | −0.831042 | − | 0.556210i | \(-0.812255\pi\) |
0.897213 | + | 0.441599i | \(0.145588\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.38499 | − | 17.2733i | −0.727071 | − | 1.49778i | ||||
\(134\) | − | 3.05986i | − | 0.264331i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.41654 | + | 0.817837i | −0.121467 | + | 0.0701290i | ||||
\(137\) | 4.27427 | − | 2.46775i | 0.365175 | − | 0.210834i | −0.306173 | − | 0.951976i | \(-0.599049\pi\) |
0.671349 | + | 0.741142i | \(0.265715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.10583i | 0.0937952i | 0.998900 | + | 0.0468976i | \(0.0149334\pi\) | ||||
−0.998900 | + | 0.0468976i | \(0.985067\pi\) | |||||||
\(140\) | −0.149291 | − | 0.101102i | −0.0126174 | − | 0.00854471i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.93854 | − | 13.7499i | 0.666187 | − | 1.15387i | ||||
\(143\) | −1.22474 | − | 2.12132i | −0.102418 | − | 0.177394i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.426786 | − | 0.246405i | −0.0354426 | − | 0.0204628i | ||||
\(146\) | −7.81382 | −0.646676 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.48993 | 0.451269 | ||||||||
\(149\) | −0.275702 | − | 0.159176i | −0.0225863 | − | 0.0130402i | 0.488664 | − | 0.872472i | \(-0.337484\pi\) |
−0.511251 | + | 0.859432i | \(0.670818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.76941 | − | 3.06471i | −0.143992 | − | 0.249402i | 0.785004 | − | 0.619491i | \(-0.212661\pi\) |
−0.928997 | + | 0.370088i | \(0.879327\pi\) | |||||||
\(152\) | 3.62863 | − | 6.28497i | 0.294320 | − | 0.509778i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.19067 | − | 1.48356i | −0.176529 | − | 0.119549i | ||||
\(155\) | 0.0158563i | 0.00127361i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.64589 | + | 3.25966i | −0.450591 | + | 0.260149i | −0.708080 | − | 0.706132i | \(-0.750438\pi\) |
0.257489 | + | 0.966281i | \(0.417105\pi\) | |||||||
\(158\) | −9.98722 | + | 5.76612i | −0.794541 | + | 0.458728i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 0.0681483i | − | 0.00538760i | ||||||
\(161\) | 0.540436 | + | 1.11331i | 0.0425923 | + | 0.0877411i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.553536 | − | 0.958753i | 0.0433563 | − | 0.0750954i | −0.843533 | − | 0.537078i | \(-0.819528\pi\) |
0.886889 | + | 0.461982i | \(0.152862\pi\) | |||||||
\(164\) | −2.69445 | − | 4.66693i | −0.210401 | − | 0.364426i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.8324 | − | 8.56350i | −1.15122 | − | 0.664657i | ||||
\(167\) | 9.93426 | 0.768736 | 0.384368 | − | 0.923180i | \(-0.374419\pi\) | ||||
0.384368 | + | 0.923180i | \(0.374419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0.0965346 | + | 0.0557343i | 0.00740386 | + | 0.00427462i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.82050 | + | 8.34935i | 0.367560 | + | 0.636632i | ||||
\(173\) | 6.61107 | − | 11.4507i | 0.502630 | − | 0.870581i | −0.497365 | − | 0.867541i | \(-0.665699\pi\) |
0.999995 | − | 0.00303994i | \(-0.000967644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.946464 | − | 13.1825i | 0.0715459 | − | 0.996506i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.24592 | + | 5.33814i | −0.693011 | + | 0.400110i | ||||
\(179\) | −9.79227 | + | 5.65357i | −0.731909 | + | 0.422568i | −0.819120 | − | 0.573622i | \(-0.805538\pi\) |
0.0872113 | + | 0.996190i | \(0.472204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.26670i | 0.614459i | 0.951635 | + | 0.307230i | \(0.0994020\pi\) | ||||
−0.951635 | + | 0.307230i | \(0.900598\pi\) | |||||||
\(182\) | −5.83013 | + | 2.83013i | −0.432158 | + | 0.209783i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.233875 | + | 0.405083i | −0.0172415 | + | 0.0298631i | ||||
\(185\) | −0.187065 | − | 0.324006i | −0.0137533 | − | 0.0238214i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.41654 | + | 0.817837i | 0.103587 | + | 0.0598062i | ||||
\(188\) | 8.62398 | 0.628969 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.494570 | −0.0358799 | ||||||||
\(191\) | −10.3133 | − | 5.95439i | −0.746245 | − | 0.430845i | 0.0780906 | − | 0.996946i | \(-0.475118\pi\) |
−0.824335 | + | 0.566102i | \(0.808451\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7134 | − | 22.0203i | −0.915132 | − | 1.58506i | −0.806707 | − | 0.590951i | \(-0.798753\pi\) |
−0.108425 | − | 0.994105i | \(-0.534581\pi\) | |||||||
\(194\) | 4.99938 | − | 8.65918i | 0.358934 | − | 0.621693i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.33013 | + | 5.50000i | −0.309295 | + | 0.392857i | ||||
\(197\) | − | 8.37821i | − | 0.596923i | −0.954422 | − | 0.298461i | \(-0.903527\pi\) | ||
0.954422 | − | 0.298461i | \(-0.0964734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.3736 | − | 10.0306i | 1.23158 | − | 0.711053i | 0.264220 | − | 0.964462i | \(-0.414885\pi\) |
0.967359 | + | 0.253410i | \(0.0815521\pi\) | |||||||
\(200\) | 4.32611 | − | 2.49768i | 0.305902 | − | 0.176612i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3.52056i | − | 0.247706i | ||||||
\(203\) | −10.7283 | + | 15.8417i | −0.752978 | + | 1.11187i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.183622 | + | 0.318043i | −0.0128248 | + | 0.0222131i | ||||
\(206\) | −7.99465 | − | 13.8471i | −0.557014 | − | 0.964776i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.12132 | − | 1.22474i | −0.147087 | − | 0.0849208i | ||||
\(209\) | −7.25725 | −0.501995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.96399 | 0.204050 | 0.102025 | − | 0.994782i | \(-0.467468\pi\) | ||||
0.102025 | + | 0.994782i | \(0.467468\pi\) | |||||||
\(212\) | 7.34278 | + | 4.23936i | 0.504304 | + | 0.291160i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.03225 | + | 5.25201i | 0.207280 | + | 0.359020i | ||||
\(215\) | 0.328509 | − | 0.568994i | 0.0224041 | − | 0.0388051i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.614014 | + | 0.0440843i | 0.0416820 | + | 0.00299263i | ||||
\(218\) | 18.0175i | 1.22030i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0590182 | + | 0.0340742i | −0.00397901 | + | 0.00229728i | ||||
\(221\) | 3.46979 | − | 2.00328i | 0.233403 | − | 0.134755i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.8238i | 0.925709i | 0.886434 | + | 0.462854i | \(0.153175\pi\) | ||||
−0.886434 | + | 0.462854i | \(0.846825\pi\) | |||||||
\(224\) | −2.63896 | − | 0.189469i | −0.176323 | − | 0.0126594i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.52761 | − | 6.10999i | 0.234653 | − | 0.406431i | ||||
\(227\) | 11.1257 | + | 19.2702i | 0.738437 | + | 1.27901i | 0.953199 | + | 0.302345i | \(0.0977693\pi\) |
−0.214761 | + | 0.976667i | \(0.568897\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3195 | + | 7.11269i | 0.814098 | + | 0.470020i | 0.848377 | − | 0.529393i | \(-0.177580\pi\) |
−0.0342790 | + | 0.999412i | \(0.510913\pi\) | |||||||
\(230\) | 0.0318764 | 0.00210187 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.23143 | −0.474767 | ||||||||
\(233\) | 0.445759 | + | 0.257359i | 0.0292027 | + | 0.0168602i | 0.514530 | − | 0.857472i | \(-0.327966\pi\) |
−0.485328 | + | 0.874332i | \(0.661300\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.293855 | − | 0.508972i | −0.0191690 | − | 0.0332017i | ||||
\(236\) | 0.439158 | − | 0.760643i | 0.0285867 | − | 0.0495137i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.42663 | − | 3.58322i | 0.157295 | − | 0.232266i | ||||
\(239\) | 21.8238i | 1.41166i | 0.708380 | + | 0.705832i | \(0.249426\pi\) | ||||
−0.708380 | + | 0.705832i | \(0.750574\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.95439 | + | 4.59247i | −0.512387 | + | 0.295827i | −0.733814 | − | 0.679350i | \(-0.762262\pi\) |
0.221427 | + | 0.975177i | \(0.428929\pi\) | |||||||
\(242\) | −0.866025 | + | 0.500000i | −0.0556702 | + | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9.96764i | − | 0.638113i | ||||||
\(245\) | 0.472146 | + | 0.0681483i | 0.0301643 | + | 0.00435384i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.88828 | + | 15.3950i | −0.565548 | + | 0.979558i | ||||
\(248\) | 0.116337 | + | 0.201501i | 0.00738738 | + | 0.0127953i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.589908 | − | 0.340583i | −0.0373091 | − | 0.0215404i | ||||
\(251\) | −31.3044 | −1.97592 | −0.987959 | − | 0.154718i | \(-0.950553\pi\) | ||||
−0.987959 | + | 0.154718i | \(0.950553\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.467750 | 0.0294072 | ||||||||
\(254\) | −5.92309 | − | 3.41970i | −0.371647 | − | 0.214571i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2.01033 | − | 3.48200i | 0.125401 | − | 0.217201i | −0.796489 | − | 0.604654i | \(-0.793312\pi\) |
0.921890 | + | 0.387453i | \(0.126645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.0668 | + | 6.34303i | −0.811931 | + | 0.394137i | ||||
\(260\) | 0.166929i | 0.0103525i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.31178 | + | 0.757359i | −0.0810423 | + | 0.0467898i | ||||
\(263\) | 11.6746 | − | 6.74032i | 0.719885 | − | 0.415626i | −0.0948253 | − | 0.995494i | \(-0.530229\pi\) |
0.814710 | + | 0.579868i | \(0.196896\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.577810i | − | 0.0354946i | ||||||
\(266\) | −1.37502 | + | 19.1516i | −0.0843080 | + | 1.17426i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.52993 | + | 2.64991i | −0.0934552 | + | 0.161869i | ||||
\(269\) | 15.7399 | + | 27.2624i | 0.959681 | + | 1.66222i | 0.723273 | + | 0.690562i | \(0.242637\pi\) |
0.236408 | + | 0.971654i | \(0.424030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.89157 | − | 2.82415i | −0.297142 | − | 0.171555i | 0.344017 | − | 0.938964i | \(-0.388212\pi\) |
−0.641158 | + | 0.767409i | \(0.721546\pi\) | |||||||
\(272\) | 1.63567 | 0.0991773 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.93550 | −0.298164 | ||||||||
\(275\) | −4.32611 | − | 2.49768i | −0.260874 | − | 0.150616i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.45982 | − | 5.99259i | −0.207881 | − | 0.360060i | 0.743166 | − | 0.669107i | \(-0.233323\pi\) |
−0.951047 | + | 0.309047i | \(0.899990\pi\) | |||||||
\(278\) | 0.552914 | − | 0.957676i | 0.0331616 | − | 0.0574376i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0787382 | + | 0.162203i | 0.00470551 | + | 0.00969346i | ||||
\(281\) | 30.4582i | 1.81698i | 0.417902 | + | 0.908492i | \(0.362766\pi\) | ||||
−0.417902 | + | 0.908492i | \(0.637234\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.8490 | + | 13.1919i | −1.35823 | + | 0.784175i | −0.989385 | − | 0.145315i | \(-0.953580\pi\) |
−0.368846 | + | 0.929490i | \(0.620247\pi\) | |||||||
\(284\) | −13.7499 | + | 7.93854i | −0.815909 | + | 0.471065i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.44949i | 0.144841i | ||||||||
\(287\) | 11.8053 | + | 7.99479i | 0.696846 | + | 0.471917i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.16228 | − | 12.4054i | 0.421311 | − | 0.729732i | ||||
\(290\) | 0.246405 | + | 0.426786i | 0.0144694 | + | 0.0250617i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.76696 | + | 3.90691i | 0.396007 | + | 0.228634i | ||||
\(293\) | −15.0095 | −0.876862 | −0.438431 | − | 0.898765i | \(-0.644466\pi\) | ||||
−0.438431 | + | 0.898765i | \(0.644466\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0598557 | −0.00348494 | ||||||||
\(296\) | −4.75442 | − | 2.74496i | −0.276345 | − | 0.159548i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.159176 | + | 0.275702i | 0.00922084 | + | 0.0159710i | ||||
\(299\) | 0.572874 | − | 0.992248i | 0.0331302 | − | 0.0573832i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.1203 | − | 14.3030i | −1.21735 | − | 0.824413i | ||||
\(302\) | 3.53882i | 0.203636i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.28497 | + | 3.62863i | −0.360467 | + | 0.208116i | ||||
\(305\) | −0.588272 | + | 0.339639i | −0.0336844 | + | 0.0194477i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.0711i | − | 0.860151i | −0.902793 | − | 0.430076i | \(-0.858487\pi\) | ||
0.902793 | − | 0.430076i | \(-0.141513\pi\) | |||||||
\(308\) | 1.15539 | + | 2.38014i | 0.0658347 | + | 0.135621i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.00792814 | − | 0.0137319i | 0.000450288 | − | 0.000779922i | ||||
\(311\) | 9.93645 | + | 17.2104i | 0.563445 | + | 0.975915i | 0.997193 | + | 0.0748804i | \(0.0238575\pi\) |
−0.433748 | + | 0.901034i | \(0.642809\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.81257 | − | 4.51059i | −0.441593 | − | 0.254954i | 0.262680 | − | 0.964883i | \(-0.415394\pi\) |
−0.704273 | + | 0.709929i | \(0.748727\pi\) | |||||||
\(314\) | 6.51931 | 0.367906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.5322 | 0.648740 | ||||||||
\(317\) | −10.2958 | − | 5.94427i | −0.578268 | − | 0.333863i | 0.182177 | − | 0.983266i | \(-0.441686\pi\) |
−0.760445 | + | 0.649403i | \(0.775019\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.61571 | + | 6.26260i | 0.202441 | + | 0.350638i | ||||
\(320\) | −0.0340742 | + | 0.0590182i | −0.00190480 | + | 0.00329922i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0886240 | − | 1.23437i | 0.00493882 | − | 0.0687889i | ||||
\(323\) | − | 11.8705i | − | 0.660492i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.5967 | + | 6.11804i | −0.587802 | + | 0.339368i | ||||
\(326\) | −0.958753 | + | 0.553536i | −0.0531004 | + | 0.0306575i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.38891i | 0.297553i | ||||||||
\(329\) | −20.5263 | + | 9.96410i | −1.13165 | + | 0.549339i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.5175 | + | 19.9489i | −0.633061 | + | 1.09649i | 0.353862 | + | 0.935298i | \(0.384868\pi\) |
−0.986922 | + | 0.161196i | \(0.948465\pi\) | |||||||
\(332\) | 8.56350 | + | 14.8324i | 0.469983 | + | 0.814035i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.60332 | − | 4.96713i | −0.470753 | − | 0.271789i | ||||
\(335\) | 0.208524 | 0.0113929 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.8191 | −1.13409 | −0.567045 | − | 0.823687i | \(-0.691914\pi\) | ||||
−0.567045 | + | 0.823687i | \(0.691914\pi\) | |||||||
\(338\) | −6.06218 | − | 3.50000i | −0.329739 | − | 0.190375i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.0557343 | − | 0.0965346i | −0.00302261 | − | 0.00523532i | ||||
\(341\) | 0.116337 | − | 0.201501i | 0.00629998 | − | 0.0109119i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.95164 | − | 18.0938i | 0.213368 | − | 0.976972i | ||||
\(344\) | − | 9.64100i | − | 0.519808i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.4507 | + | 6.61107i | −0.615594 | + | 0.355413i | ||||
\(347\) | 6.30751 | − | 3.64165i | 0.338605 | − | 0.195494i | −0.321050 | − | 0.947062i | \(-0.604036\pi\) |
0.659655 | + | 0.751569i | \(0.270702\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.7366i | 1.80588i | 0.429767 | + | 0.902940i | \(0.358596\pi\) | ||||
−0.429767 | + | 0.902940i | \(0.641404\pi\) | |||||||
\(350\) | −7.41093 | + | 10.9432i | −0.396131 | + | 0.584938i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 8.71467 | + | 15.0943i | 0.463835 | + | 0.803386i | 0.999148 | − | 0.0412678i | \(-0.0131397\pi\) |
−0.535313 | + | 0.844654i | \(0.679806\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.937036 | + | 0.540998i | 0.0497327 | + | 0.0287132i | ||||
\(356\) | 10.6763 | 0.565841 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.3071 | 0.597601 | ||||||||
\(359\) | −22.6722 | − | 13.0898i | −1.19659 | − | 0.690852i | −0.236798 | − | 0.971559i | \(-0.576098\pi\) |
−0.959794 | + | 0.280707i | \(0.909431\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.8339 | + | 29.1571i | 0.885992 | + | 1.53458i | ||||
\(362\) | 4.13335 | − | 7.15918i | 0.217244 | − | 0.376278i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.46410 | + | 0.464102i | 0.338811 | + | 0.0243255i | ||||
\(365\) | − | 0.532499i | − | 0.0278723i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.91510 | − | 5.72449i | 0.517564 | − | 0.298816i | −0.218373 | − | 0.975865i | \(-0.570075\pi\) |
0.735937 | + | 0.677050i | \(0.236742\pi\) | |||||||
\(368\) | 0.405083 | − | 0.233875i | 0.0211164 | − | 0.0121916i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.374129i | 0.0194501i | ||||||||
\(371\) | −22.3750 | − | 1.60645i | −1.16165 | − | 0.0834028i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.1189 | − | 24.4546i | 0.731048 | − | 1.26621i | −0.225388 | − | 0.974269i | \(-0.572365\pi\) |
0.956436 | − | 0.291943i | \(-0.0943016\pi\) | |||||||
\(374\) | −0.817837 | − | 1.41654i | −0.0422894 | − | 0.0732473i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.46859 | − | 4.31199i | −0.385163 | − | 0.222374i | ||||
\(377\) | 17.7133 | 0.912282 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.93550 | 0.510352 | 0.255176 | − | 0.966895i | \(-0.417867\pi\) | ||||
0.255176 | + | 0.966895i | \(0.417867\pi\) | |||||||
\(380\) | 0.428310 | + | 0.247285i | 0.0219718 | + | 0.0126854i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.95439 | + | 10.3133i | 0.304653 | + | 0.527675i | ||||
\(383\) | −6.97381 | + | 12.0790i | −0.356345 | + | 0.617208i | −0.987347 | − | 0.158573i | \(-0.949311\pi\) |
0.631002 | + | 0.775781i | \(0.282644\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.101102 | − | 0.149291i | 0.00515266 | − | 0.00760855i | ||||
\(386\) | 25.4269i | 1.29419i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.65918 | + | 4.99938i | −0.439603 | + | 0.253805i | ||||
\(389\) | 1.53141 | − | 0.884161i | 0.0776457 | − | 0.0448288i | −0.460674 | − | 0.887569i | \(-0.652392\pi\) |
0.538320 | + | 0.842740i | \(0.319059\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.765087i | 0.0386921i | ||||||||
\(392\) | 6.50000 | − | 2.59808i | 0.328300 | − | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.18910 | + | 7.25574i | −0.211044 | + | 0.365539i | ||||
\(395\) | −0.392952 | − | 0.680613i | −0.0197716 | − | 0.0342453i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.04114 | − | 0.601102i | −0.0522533 | − | 0.0301685i | 0.473646 | − | 0.880715i | \(-0.342938\pi\) |
−0.525899 | + | 0.850547i | \(0.676271\pi\) | |||||||
\(398\) | −20.0613 | −1.00558 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.99536 | −0.249768 | ||||||||
\(401\) | −15.4934 | − | 8.94510i | −0.773702 | − | 0.446697i | 0.0604915 | − | 0.998169i | \(-0.480733\pi\) |
−0.834194 | + | 0.551472i | \(0.814067\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.284965 | − | 0.493574i | −0.0141951 | − | 0.0245867i | ||||
\(404\) | −1.76028 | + | 3.04889i | −0.0875771 | + | 0.151688i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.2118 | − | 8.35515i | 0.854208 | − | 0.414659i | ||||
\(407\) | 5.48993i | 0.272126i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.35436 | + | 0.781939i | −0.0669687 | + | 0.0386644i | −0.533110 | − | 0.846046i | \(-0.678977\pi\) |
0.466142 | + | 0.884710i | \(0.345644\pi\) | |||||||
\(410\) | 0.318043 | − | 0.183622i | 0.0157070 | − | 0.00906847i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.9893i | 0.787736i | ||||||||
\(413\) | −0.166413 | + | 2.31784i | −0.00818866 | + | 0.114053i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.583589 | − | 1.01081i | 0.0286472 | − | 0.0496185i | ||||
\(416\) | 1.22474 | + | 2.12132i | 0.0600481 | + | 0.104006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.28497 | + | 3.62863i | 0.307408 | + | 0.177482i | ||||
\(419\) | 4.99020 | 0.243787 | 0.121894 | − | 0.992543i | \(-0.461103\pi\) | ||||
0.121894 | + | 0.992543i | \(0.461103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.0235 | −1.80441 | −0.902207 | − | 0.431302i | \(-0.858054\pi\) | ||||
−0.902207 | + | 0.431302i | \(0.858054\pi\) | |||||||
\(422\) | −2.56689 | − | 1.48200i | −0.124954 | − | 0.0721425i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.23936 | − | 7.34278i | −0.205881 | − | 0.356597i | ||||
\(425\) | 4.08539 | − | 7.07610i | 0.198170 | − | 0.343241i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.5166 | + | 23.7244i | 0.557325 | + | 1.14810i | ||||
\(428\) | − | 6.06450i | − | 0.293139i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.568994 | + | 0.328509i | −0.0274393 | + | 0.0158421i | ||||
\(431\) | 11.4567 | − | 6.61453i | 0.551850 | − | 0.318611i | −0.198018 | − | 0.980198i | \(-0.563450\pi\) |
0.749868 | + | 0.661588i | \(0.230117\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.5794i | − | 0.604527i | −0.953224 | − | 0.302263i | \(-0.902258\pi\) | ||
0.953224 | − | 0.302263i | \(-0.0977422\pi\) | |||||||
\(434\) | −0.509710 | − | 0.345185i | −0.0244669 | − | 0.0165694i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00877 | − | 15.6036i | 0.431442 | − | 0.747279i | ||||
\(437\) | −1.69729 | − | 2.93979i | −0.0811924 | − | 0.140629i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.2358 | − | 8.79639i | −0.727165 | − | 0.419829i | 0.0902191 | − | 0.995922i | \(-0.471243\pi\) |
−0.817384 | + | 0.576093i | \(0.804577\pi\) | |||||||
\(440\) | 0.0681483 | 0.00324884 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00657 | −0.190573 | ||||||||
\(443\) | −23.4746 | − | 13.5531i | −1.11531 | − | 0.643926i | −0.175112 | − | 0.984549i | \(-0.556029\pi\) |
−0.940200 | + | 0.340623i | \(0.889362\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.363785 | − | 0.630094i | −0.0172451 | − | 0.0298693i | ||||
\(446\) | 6.91189 | − | 11.9717i | 0.327288 | − | 0.566879i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.19067 | + | 1.48356i | 0.103499 | + | 0.0700918i | ||||
\(449\) | − | 14.9950i | − | 0.707658i | −0.935310 | − | 0.353829i | \(-0.884879\pi\) | ||
0.935310 | − | 0.353829i | \(-0.115121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.66693 | − | 2.69445i | 0.219757 | − | 0.126877i | ||||
\(452\) | −6.10999 | + | 3.52761i | −0.287390 | + | 0.165925i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 22.2514i | − | 1.04431i | ||||||
\(455\) | −0.192868 | − | 0.397314i | −0.00904181 | − | 0.0186263i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.475430 | − | 0.823468i | 0.0222397 | − | 0.0385202i | −0.854691 | − | 0.519136i | \(-0.826254\pi\) |
0.876931 | + | 0.480616i | \(0.159587\pi\) | |||||||
\(458\) | −7.11269 | − | 12.3195i | −0.332354 | − | 0.575654i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0276058 | − | 0.0159382i | −0.00128713 | − | 0.000743122i | ||||
\(461\) | 17.7698 | 0.827621 | 0.413810 | − | 0.910363i | \(-0.364198\pi\) | ||||
0.413810 | + | 0.910363i | \(0.364198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.21592 | 0.0565088 | 0.0282544 | − | 0.999601i | \(-0.491005\pi\) | ||||
0.0282544 | + | 0.999601i | \(0.491005\pi\) | |||||||
\(464\) | 6.26260 | + | 3.61571i | 0.290734 | + | 0.167855i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.257359 | − | 0.445759i | −0.0119219 | − | 0.0206494i | ||||
\(467\) | −4.45982 | + | 7.72464i | −0.206376 | + | 0.357454i | −0.950570 | − | 0.310510i | \(-0.899500\pi\) |
0.744194 | + | 0.667963i | \(0.232834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.579747 | − | 8.07483i | 0.0267702 | − | 0.372861i | ||||
\(470\) | 0.587710i | 0.0271090i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.760643 | + | 0.439158i | −0.0350114 | + | 0.0202139i | ||||
\(473\) | −8.34935 | + | 4.82050i | −0.383903 | + | 0.221647i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 36.2526i | 1.66338i | ||||||||
\(476\) | −3.89313 | + | 1.88985i | −0.178441 | + | 0.0866211i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.9119 | − | 18.9000i | 0.499098 | − | 0.864464i | ||||
\(479\) | 10.3161 | + | 17.8680i | 0.471355 | + | 0.816411i | 0.999463 | − | 0.0327661i | \(-0.0104317\pi\) |
−0.528108 | + | 0.849177i | \(0.677098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6459 | + | 6.72376i | 0.531007 | + | 0.306577i | ||||
\(482\) | 9.18494 | 0.418363 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0.590109 | + | 0.340699i | 0.0267954 | + | 0.0154704i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.0189644 | − | 0.0328473i | −0.000859360 | − | 0.00148845i | 0.865595 | − | 0.500744i | \(-0.166940\pi\) |
−0.866455 | + | 0.499256i | \(0.833607\pi\) | |||||||
\(488\) | −4.98382 | + | 8.63223i | −0.225607 | + | 0.390763i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.374816 | − | 0.295091i | −0.0169325 | − | 0.0133309i | ||||
\(491\) | 34.6919i | 1.56562i | 0.622258 | + | 0.782812i | \(0.286215\pi\) | ||||
−0.622258 | + | 0.782812i | \(0.713785\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2436 | + | 5.91413i | −0.461347 | + | 0.266359i | ||||
\(494\) | 15.3950 | − | 8.88828i | 0.692652 | − | 0.399903i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.232673i | − | 0.0104473i | ||||||
\(497\) | 23.5546 | − | 34.7814i | 1.05657 | − | 1.56016i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2268 | − | 17.7133i | 0.457814 | − | 0.792957i | −0.541031 | − | 0.841002i | \(-0.681966\pi\) |
0.998845 | + | 0.0480457i | \(0.0152993\pi\) | |||||||
\(500\) | 0.340583 | + | 0.589908i | 0.0152314 | + | 0.0263815i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.1104 | + | 15.6522i | 1.21000 | + | 0.698592i | ||||
\(503\) | −31.4660 | −1.40300 | −0.701501 | − | 0.712669i | \(-0.747486\pi\) | ||||
−0.701501 | + | 0.712669i | \(0.747486\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.239920 | 0.0106763 | ||||||||
\(506\) | −0.405083 | − | 0.233875i | −0.0180082 | − | 0.0103970i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.41970 | + | 5.92309i | 0.151724 | + | 0.262794i | ||||
\(509\) | −4.97798 | + | 8.62211i | −0.220645 | + | 0.382168i | −0.955004 | − | 0.296593i | \(-0.904150\pi\) |
0.734359 | + | 0.678761i | \(0.237483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.6203 | − | 1.48047i | −0.912190 | − | 0.0654923i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.48200 | + | 2.01033i | −0.153584 | + | 0.0886720i | ||||
\(515\) | 0.943660 | − | 0.544822i | 0.0415826 | − | 0.0240077i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.62398i | 0.379282i | ||||||||
\(518\) | 14.4877 | + | 1.04017i | 0.636552 | + | 0.0457024i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0834643 | − | 0.144564i | 0.00366015 | − | 0.00633957i | ||||
\(521\) | −20.4947 | − | 35.4979i | −0.897891 | − | 1.55519i | −0.830186 | − | 0.557487i | \(-0.811766\pi\) |
−0.0677047 | − | 0.997705i | \(-0.521568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.0347 | + | 18.4952i | 1.40078 | + | 0.808741i | 0.994473 | − | 0.104996i | \(-0.0334829\pi\) |
0.406307 | + | 0.913736i | \(0.366816\pi\) | |||||||
\(524\) | 1.51472 | 0.0661708 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.4806 | −0.587784 | ||||||||
\(527\) | 0.329590 | + | 0.190289i | 0.0143571 | + | 0.00828910i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3906 | − | 19.7291i | −0.495244 | − | 0.857787i | ||||
\(530\) | −0.288905 | + | 0.500398i | −0.0125492 | + | 0.0217359i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.7666 | − | 15.8983i | 0.466791 | − | 0.689277i | ||||
\(533\) | − | 13.2001i | − | 0.571758i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.357916 | + | 0.206643i | −0.0154741 | + | 0.00893395i | ||||
\(536\) | 2.64991 | − | 1.52993i | 0.114459 | − | 0.0660828i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 31.4799i | − | 1.35719i | ||||||
\(539\) | −5.50000 | − | 4.33013i | −0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.7301 | − | 30.7095i | 0.762277 | − | 1.32030i | −0.179397 | − | 0.983777i | \(-0.557415\pi\) |
0.941674 | − | 0.336526i | \(-0.109252\pi\) | |||||||
\(542\) | 2.82415 | + | 4.89157i | 0.121308 | + | 0.210111i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.41654 | − | 0.817837i | −0.0607335 | − | 0.0350645i | ||||
\(545\) | −1.22786 | −0.0525960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.2066 | 1.41981 | 0.709907 | − | 0.704296i | \(-0.248737\pi\) | ||||
0.709907 | + | 0.704296i | \(0.248737\pi\) | |||||||
\(548\) | 4.27427 | + | 2.46775i | 0.182588 | + | 0.105417i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.49768 | + | 4.32611i | 0.106501 | + | 0.184466i | ||||
\(551\) | 26.2402 | − | 45.4493i | 1.11787 | − | 1.93620i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.4484 | + | 13.3243i | −1.16722 | + | 0.566607i | ||||
\(554\) | 6.91964i | 0.293987i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.957676 | + | 0.552914i | −0.0406145 | + | 0.0234488i | ||||
\(557\) | 1.95592 | − | 1.12925i | 0.0828748 | − | 0.0478478i | −0.457990 | − | 0.888957i | \(-0.651430\pi\) |
0.540865 | + | 0.841110i | \(0.318097\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.6155i | 0.998830i | ||||||||
\(560\) | 0.0129120 | − | 0.179841i | 0.000545631 | − | 0.00759965i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.2291 | − | 26.3776i | 0.642401 | − | 1.11267i | ||||
\(563\) | 4.02066 | + | 6.96399i | 0.169451 | + | 0.293497i | 0.938227 | − | 0.346021i | \(-0.112467\pi\) |
−0.768776 | + | 0.639518i | \(0.779134\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.416386 | + | 0.240401i | 0.0175175 | + | 0.0101137i | ||||
\(566\) | 26.3837 | 1.10899 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.8771 | 0.666187 | ||||||||
\(569\) | −15.6841 | − | 9.05521i | −0.657511 | − | 0.379614i | 0.133817 | − | 0.991006i | \(-0.457277\pi\) |
−0.791328 | + | 0.611392i | \(0.790610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.15006 | − | 12.3843i | −0.299221 | − | 0.518266i | 0.676737 | − | 0.736225i | \(-0.263393\pi\) |
−0.975958 | + | 0.217959i | \(0.930060\pi\) | |||||||
\(572\) | 1.22474 | − | 2.12132i | 0.0512092 | − | 0.0886969i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.22631 | − | 12.8263i | −0.259881 | − | 0.535361i | ||||
\(575\) | − | 2.33658i | − | 0.0974420i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.3960 | + | 15.8171i | −1.14051 | + | 0.658475i | −0.946557 | − | 0.322536i | \(-0.895465\pi\) |
−0.193955 | + | 0.981011i | \(0.562131\pi\) | |||||||
\(578\) | −12.4054 | + | 7.16228i | −0.515998 | + | 0.297912i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 0.492810i | − | 0.0204628i | ||||||
\(581\) | −37.5196 | − | 25.4090i | −1.55658 | − | 1.05414i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.23936 | + | 7.34278i | −0.175576 | + | 0.304107i | ||||
\(584\) | −3.90691 | − | 6.76696i | −0.161669 | − | 0.280019i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.9986 | + | 7.50473i | 0.536966 | + | 0.310017i | ||||
\(587\) | 25.9909 | 1.07276 | 0.536381 | − | 0.843976i | \(-0.319791\pi\) | ||||
0.536381 | + | 0.843976i | \(0.319791\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.68857 | −0.0695762 | ||||||||
\(590\) | 0.0518366 | + | 0.0299279i | 0.00213408 | + | 0.00123211i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.74496 | + | 4.75442i | 0.112817 | + | 0.195405i | ||||
\(593\) | 15.0260 | − | 26.0258i | 0.617043 | − | 1.06875i | −0.372979 | − | 0.927840i | \(-0.621664\pi\) |
0.990022 | − | 0.140911i | \(-0.0450030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.244191 | + | 0.165371i | 0.0100108 | + | 0.00677954i | ||||
\(596\) | − | 0.318353i | − | 0.0130402i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.992248 | + | 0.572874i | −0.0405760 | + | 0.0234266i | ||||
\(599\) | −8.18991 | + | 4.72844i | −0.334631 | + | 0.193199i | −0.657895 | − | 0.753110i | \(-0.728553\pi\) |
0.323265 | + | 0.946309i | \(0.395220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.30182i | 0.0938931i | 0.998897 | + | 0.0469465i | \(0.0149490\pi\) | ||||
−0.998897 | + | 0.0469465i | \(0.985051\pi\) | |||||||
\(602\) | 11.1392 | + | 22.9469i | 0.453998 | + | 0.935247i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.76941 | − | 3.06471i | 0.0719962 | − | 0.124701i | ||||
\(605\) | −0.0340742 | − | 0.0590182i | −0.00138531 | − | 0.00239943i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.13710 | − | 1.81121i | −0.127331 | − | 0.0735145i | 0.434982 | − | 0.900439i | \(-0.356755\pi\) |
−0.562313 | + | 0.826925i | \(0.690088\pi\) | |||||||
\(608\) | 7.25725 | 0.294320 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.679278 | 0.0275032 | ||||||||
\(611\) | 18.2942 | + | 10.5622i | 0.740105 | + | 0.427300i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.97209 | + | 8.61192i | 0.200821 | + | 0.347832i | 0.948793 | − | 0.315898i | \(-0.102306\pi\) |
−0.747972 | + | 0.663730i | \(0.768972\pi\) | |||||||
\(614\) | −7.53553 | + | 13.0519i | −0.304109 | + | 0.526733i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.189469 | − | 2.63896i | 0.00763391 | − | 0.106327i | ||||
\(617\) | − | 5.20936i | − | 0.209721i | −0.994487 | − | 0.104860i | \(-0.966560\pi\) | ||
0.994487 | − | 0.104860i | \(-0.0334396\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.6324 | − | 6.13859i | 0.427350 | − | 0.246731i | −0.270867 | − | 0.962617i | \(-0.587310\pi\) |
0.698217 | + | 0.715886i | \(0.253977\pi\) | |||||||
\(620\) | −0.0137319 | + | 0.00792814i | −0.000551488 | + | 0.000318402i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 19.8729i | − | 0.796831i | ||||||
\(623\) | −25.4110 | + | 12.3353i | −1.01807 | + | 0.494204i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4652 | + | 21.5903i | −0.498607 | + | 0.863613i | ||||
\(626\) | 4.51059 | + | 7.81257i | 0.180279 | + | 0.312253i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.64589 | − | 3.25966i | −0.225296 | − | 0.130074i | ||||
\(629\) | −8.97973 | −0.358045 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.18708 | 0.0472568 | 0.0236284 | − | 0.999721i | \(-0.492478\pi\) | ||||
0.0236284 | + | 0.999721i | \(0.492478\pi\) | |||||||
\(632\) | −9.98722 | − | 5.76612i | −0.397270 | − | 0.229364i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.94427 | + | 10.2958i | 0.236077 | + | 0.408897i | ||||
\(635\) | 0.233047 | − | 0.403649i | 0.00924817 | − | 0.0160183i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.9217 | + | 6.36396i | −0.630840 | + | 0.252149i | ||||
\(638\) | − | 7.23143i | − | 0.286295i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.0590182 | − | 0.0340742i | 0.00233290 | − | 0.00134690i | ||||
\(641\) | 32.2791 | − | 18.6364i | 1.27495 | − | 0.736092i | 0.299033 | − | 0.954243i | \(-0.403336\pi\) |
0.975915 | + | 0.218151i | \(0.0700025\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.75684i | 0.108719i | 0.998521 | + | 0.0543597i | \(0.0173117\pi\) | ||||
−0.998521 | + | 0.0543597i | \(0.982688\pi\) | |||||||
\(644\) | −0.693937 | + | 1.02469i | −0.0273450 | + | 0.0403783i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.93525 | + | 10.2802i | −0.233519 | + | 0.404467i | ||||
\(647\) | 15.2508 | + | 26.4151i | 0.599570 | + | 1.03849i | 0.992884 | + | 0.119081i | \(0.0379950\pi\) |
−0.393315 | + | 0.919404i | \(0.628672\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.760643 | + | 0.439158i | 0.0298579 | + | 0.0172384i | ||||
\(650\) | 12.2361 | 0.479938 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.10707 | 0.0433563 | ||||||||
\(653\) | −9.77473 | − | 5.64344i | −0.382515 | − | 0.220845i | 0.296397 | − | 0.955065i | \(-0.404215\pi\) |
−0.678912 | + | 0.734220i | \(0.737548\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0516128 | − | 0.0893960i | −0.00201668 | − | 0.00349299i | ||||
\(656\) | 2.69445 | − | 4.66693i | 0.105201 | − | 0.182213i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.7583 | + | 1.63397i | 0.887212 | + | 0.0636990i | ||||
\(659\) | 10.2338i | 0.398652i | 0.979933 | + | 0.199326i | \(0.0638753\pi\) | ||||
−0.979933 | + | 0.199326i | \(0.936125\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.6739 | + | 11.3587i | −0.765226 | + | 0.441803i | −0.831169 | − | 0.556020i | \(-0.812328\pi\) |
0.0659431 | + | 0.997823i | \(0.478994\pi\) | |||||||
\(662\) | 19.9489 | − | 11.5175i | 0.775338 | − | 0.447642i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 17.1270i | − | 0.664657i | ||||||
\(665\) | −1.30515 | − | 0.0937055i | −0.0506115 | − | 0.00363374i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.69125 | + | 2.92933i | −0.0654855 | + | 0.113424i | ||||
\(668\) | 4.96713 | + | 8.60332i | 0.192184 | + | 0.332872i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.180587 | − | 0.104262i | −0.00697669 | − | 0.00402799i | ||||
\(671\) | 9.96764 | 0.384797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.2268 | −1.08806 | −0.544031 | − | 0.839065i | \(-0.683103\pi\) | ||||
−0.544031 | + | 0.839065i | \(0.683103\pi\) | |||||||
\(674\) | 18.0299 | + | 10.4096i | 0.694486 | + | 0.400962i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | + | 6.06218i | 0.134615 | + | 0.233161i | ||||
\(677\) | 8.40665 | − | 14.5607i | 0.323094 | − | 0.559615i | −0.658031 | − | 0.752991i | \(-0.728610\pi\) |
0.981125 | + | 0.193376i | \(0.0619437\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.8338 | − | 21.9040i | 0.569269 | − | 0.840598i | ||||
\(680\) | 0.111469i | 0.00427462i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.201501 | + | 0.116337i | −0.00771586 | + | 0.00445476i | ||||
\(683\) | 17.9178 | − | 10.3448i | 0.685604 | − | 0.395834i | −0.116359 | − | 0.993207i | \(-0.537122\pi\) |
0.801963 | + | 0.597374i | \(0.203789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.336346i | − | 0.0128511i | ||||||
\(686\) | −12.4691 | + | 13.6938i | −0.476073 | + | 0.522834i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.82050 | + | 8.34935i | −0.183780 | + | 0.318316i | ||||
\(689\) | 10.3843 | + | 17.9861i | 0.395609 | + | 0.685215i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.3537 | + | 23.2982i | 1.53513 | + | 0.886306i | 0.999114 | + | 0.0420972i | \(0.0134039\pi\) |
0.536014 | + | 0.844209i | \(0.319929\pi\) | |||||||
\(692\) | 13.2221 | 0.502630 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.28329 | −0.276470 | ||||||||
\(695\) | 0.0652640 | + | 0.0376802i | 0.00247561 | + | 0.00142929i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.40725 | + | 7.63358i | 0.166936 | + | 0.289142i | ||||
\(698\) | 16.8683 | − | 29.2168i | 0.638475 | − | 1.10587i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.8896 | − | 5.77161i | 0.449386 | − | 0.218146i | ||||
\(701\) | − | 25.8612i | − | 0.976765i | −0.872630 | − | 0.488382i | \(-0.837587\pi\) | ||
0.872630 | − | 0.488382i | \(-0.162413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.5040 | − | 19.9209i | 1.30134 | − | 0.751331i | ||||
\(704\) | 0.866025 | − | 0.500000i | 0.0326396 | − | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 17.4293i | − | 0.655962i | ||||||
\(707\) | 0.667035 | − | 9.29061i | 0.0250864 | − | 0.349409i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.3750 | + | 17.9700i | −0.389641 | + | 0.674878i | −0.992401 | − | 0.123044i | \(-0.960734\pi\) |
0.602760 | + | 0.797923i | \(0.294068\pi\) | |||||||
\(710\) | −0.540998 | − | 0.937036i | −0.0203033 | − | 0.0351663i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.24592 | − | 5.33814i | −0.346506 | − | 0.200055i | ||||
\(713\) | 0.108833 | 0.00407582 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.166929 | −0.00624278 | ||||||||
\(716\) | −9.79227 | − | 5.65357i | −0.365954 | − | 0.211284i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.0898 | + | 22.6722i | 0.488506 | + | 0.846118i | ||||
\(719\) | 12.4722 | − | 21.6025i | 0.465136 | − | 0.805639i | −0.534072 | − | 0.845439i | \(-0.679339\pi\) |
0.999208 | + | 0.0398001i | \(0.0126721\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.4740 | − | 38.0568i | −0.688006 | − | 1.41731i | ||||
\(722\) | − | 33.6677i | − | 1.25298i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.15918 | + | 4.13335i | −0.266069 | + | 0.153615i | ||||
\(725\) | 31.2839 | − | 18.0618i | 1.16186 | − | 0.670798i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.4534i | − | 0.721487i | −0.932665 | − | 0.360743i | \(-0.882523\pi\) | ||
0.932665 | − | 0.360743i | \(-0.117477\pi\) | |||||||
\(728\) | −5.36603 | − | 3.63397i | −0.198878 | − | 0.134684i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.266249 | + | 0.461157i | −0.00985433 | + | 0.0170682i | ||||
\(731\) | −7.88477 | − | 13.6568i | −0.291629 | − | 0.505116i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.02326 | + | 1.16813i | 0.0747309 | + | 0.0431459i | 0.536900 | − | 0.843646i | \(-0.319595\pi\) |
−0.462169 | + | 0.886792i | \(0.652929\pi\) | |||||||
\(734\) | −11.4490 | −0.422589 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.467750 | −0.0172415 | ||||||||
\(737\) | −2.64991 | − | 1.52993i | −0.0976108 | − | 0.0563556i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.2066 | − | 31.5348i | −0.669742 | − | 1.16003i | −0.977976 | − | 0.208717i | \(-0.933071\pi\) |
0.308234 | − | 0.951310i | \(-0.400262\pi\) | |||||||
\(740\) | 0.187065 | − | 0.324006i | 0.00687663 | − | 0.0119107i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.5741 | + | 12.5787i | 0.681876 | + | 0.461779i | ||||
\(743\) | − | 52.1166i | − | 1.91197i | −0.293409 | − | 0.955987i | \(-0.594790\pi\) | ||
0.293409 | − | 0.955987i | \(-0.405210\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0187886 | + | 0.0108476i | −0.000688361 | + | 0.000397425i | ||||
\(746\) | −24.4546 | + | 14.1189i | −0.895347 | + | 0.516929i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.63567i | 0.0598062i | ||||||||
\(749\) | 7.00689 | + | 14.4344i | 0.256026 | + | 0.527420i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.88661 | − | 8.46385i | 0.178315 | − | 0.308850i | −0.762989 | − | 0.646412i | \(-0.776269\pi\) |
0.941303 | + | 0.337562i | \(0.109602\pi\) | |||||||
\(752\) | 4.31199 | + | 7.46859i | 0.157242 | + | 0.272351i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.3402 | − | 8.85666i | −0.558656 | − | 0.322540i | ||||
\(755\) | −0.241165 | −0.00877688 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6251 | 1.00405 | 0.502026 | − | 0.864852i | \(-0.332588\pi\) | ||||
0.502026 | + | 0.864852i | \(0.332588\pi\) | |||||||
\(758\) | −8.60440 | − | 4.96775i | −0.312526 | − | 0.180437i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.247285 | − | 0.428310i | −0.00896997 | − | 0.0155364i | ||||
\(761\) | 10.0318 | − | 17.3755i | 0.363651 | − | 0.629863i | −0.624907 | − | 0.780699i | \(-0.714863\pi\) |
0.988559 | + | 0.150836i | \(0.0481966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.41376 | + | 47.5475i | −0.123586 | + | 1.72134i | ||||
\(764\) | − | 11.9088i | − | 0.430845i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0790 | − | 6.97381i | 0.436432 | − | 0.251974i | ||||
\(767\) | 1.86319 | − | 1.07571i | 0.0672758 | − | 0.0388417i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.4568i | − | 1.13436i | −0.823593 | − | 0.567181i | \(-0.808034\pi\) | ||
0.823593 | − | 0.567181i | \(-0.191966\pi\) | |||||||
\(770\) | −0.162203 | + | 0.0787382i | −0.00584537 | + | 0.00283753i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.7134 | − | 22.0203i | 0.457566 | − | 0.792528i | ||||
\(773\) | −3.56548 | − | 6.17559i | −0.128241 | − | 0.222121i | 0.794754 | − | 0.606932i | \(-0.207600\pi\) |
−0.922995 | + | 0.384811i | \(0.874267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00657 | − | 0.581142i | −0.0361570 | − | 0.0208752i | ||||
\(776\) | 9.99876 | 0.358934 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.76832 | −0.0633974 | ||||||||
\(779\) | −33.8691 | − | 19.5543i | −1.21349 | − | 0.700606i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.93854 | − | 13.7499i | −0.284063 | − | 0.492012i | ||||
\(782\) | 0.382543 | − | 0.662585i | 0.0136797 | − | 0.0236940i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.92820 | − | 1.00000i | −0.247436 | − | 0.0357143i | ||||
\(785\) | 0.444280i | 0.0158570i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7613 | − | 11.9865i | 0.740061 | − | 0.427274i | −0.0820306 | − | 0.996630i | \(-0.526141\pi\) |
0.822091 | + | 0.569356i | \(0.192807\pi\) | |||||||
\(788\) | 7.25574 | − | 4.18910i | 0.258475 | − | 0.149231i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.785904i | 0.0279612i | ||||||||
\(791\) | 10.4669 | − | 15.4556i | 0.372159 | − | 0.549539i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.2078 | − | 21.1446i | 0.433512 | − | 0.750866i | ||||
\(794\) | 0.601102 | + | 1.04114i | 0.0213323 | + | 0.0369487i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.3736 | + | 10.0306i | 0.615790 | + | 0.355526i | ||||
\(797\) | −7.65551 | −0.271172 | −0.135586 | − | 0.990766i | \(-0.543292\pi\) | ||||
−0.135586 | + | 0.990766i | \(0.543292\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.1060 | −0.499035 | ||||||||
\(800\) | 4.32611 | + | 2.49768i | 0.152951 | + | 0.0883062i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.94510 | + | 15.4934i | 0.315863 | + | 0.547090i | ||||
\(803\) | −3.90691 | + | 6.76696i | −0.137872 | + | 0.238801i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0841205 | + | 0.00603958i | 0.00296486 | + | 0.000212867i | ||||
\(806\) | 0.569930i | 0.0200749i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.04889 | − | 1.76028i | 0.107260 | − | 0.0619264i | ||||
\(809\) | −22.9383 | + | 13.2434i | −0.806467 | + | 0.465614i | −0.845728 | − | 0.533615i | \(-0.820833\pi\) |
0.0392603 | + | 0.999229i | \(0.487500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.2759i | 1.76543i | 0.469911 | + | 0.882714i | \(0.344286\pi\) | ||||
−0.469911 | + | 0.882714i | \(0.655714\pi\) | |||||||
\(812\) | −19.0834 | − | 1.37013i | −0.669697 | − | 0.0480821i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.74496 | − | 4.75442i | 0.0962109 | − | 0.166642i | ||||
\(815\) | −0.0377226 | − | 0.0653375i | −0.00132136 | − | 0.00228867i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 60.5933 | + | 34.9836i | 2.11989 | + | 1.22392i | ||||
\(818\) | 1.56388 | 0.0546797 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.367245 | −0.0128248 | ||||||||
\(821\) | 5.84233 | + | 3.37307i | 0.203899 | + | 0.117721i | 0.598473 | − | 0.801143i | \(-0.295774\pi\) |
−0.394574 | + | 0.918864i | \(0.629108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5276 | + | 26.8946i | 0.541258 | + | 0.937487i | 0.998832 | + | 0.0483153i | \(0.0153852\pi\) |
−0.457574 | + | 0.889172i | \(0.651281\pi\) | |||||||
\(824\) | 7.99465 | − | 13.8471i | 0.278507 | − | 0.482388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.30304 | − | 1.92410i | 0.0453384 | − | 0.0669480i | ||||
\(827\) | 17.0506i | 0.592906i | 0.955047 | + | 0.296453i | \(0.0958039\pi\) | ||||
−0.955047 | + | 0.296453i | \(0.904196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.5417 | − | 17.6332i | 1.06076 | − | 0.612428i | 0.135115 | − | 0.990830i | \(-0.456860\pi\) |
0.925641 | + | 0.378402i | \(0.123526\pi\) | |||||||
\(830\) | −1.01081 | + | 0.583589i | −0.0350856 | + | 0.0202567i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.44949i | − | 0.0849208i | ||||||
\(833\) | 7.08268 | − | 8.99621i | 0.245400 | − | 0.311700i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.338502 | − | 0.586302i | 0.0117143 | − | 0.0202898i | ||||
\(836\) | −3.62863 | − | 6.28497i | −0.125499 | − | 0.217370i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.32164 | − | 2.49510i | −0.149288 | − | 0.0861917i | ||||
\(839\) | −20.8253 | −0.718969 | −0.359484 | − | 0.933151i | \(-0.617047\pi\) | ||||
−0.359484 | + | 0.933151i | \(0.617047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.2936 | −0.803226 | ||||||||
\(842\) | 32.0633 | + | 18.5117i | 1.10497 | + | 0.637957i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.48200 | + | 2.56689i | 0.0510125 | + | 0.0883562i | ||||
\(845\) | 0.238519 | − | 0.413127i | 0.00820531 | − | 0.0142120i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.38014 | + | 1.15539i | −0.0817826 | + | 0.0396998i | ||||
\(848\) | 8.47871i | 0.291160i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.07610 | + | 4.08539i | −0.242708 | + | 0.140128i | ||||
\(851\) | −2.22388 | + | 1.28396i | −0.0762335 | + | 0.0440135i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.3869i | 0.526837i | 0.964682 | + | 0.263419i | \(0.0848501\pi\) | ||||
−0.964682 | + | 0.263419i | \(0.915150\pi\) | |||||||
\(854\) | 1.88856 | − | 26.3042i | 0.0646251 | − | 0.900111i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.03225 | + | 5.25201i | −0.103640 | + | 0.179510i | ||||
\(857\) | 21.0768 | + | 36.5061i | 0.719969 | + | 1.24702i | 0.961011 | + | 0.276509i | \(0.0891775\pi\) |
−0.241042 | + | 0.970515i | \(0.577489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.86724 | − | 3.96481i | −0.234307 | − | 0.135277i | 0.378250 | − | 0.925703i | \(-0.376526\pi\) |
−0.612558 | + | 0.790426i | \(0.709859\pi\) | |||||||
\(860\) | 0.657018 | 0.0224041 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.2291 | −0.450584 | ||||||||
\(863\) | 20.6857 | + | 11.9429i | 0.704150 | + | 0.406541i | 0.808891 | − | 0.587958i | \(-0.200068\pi\) |
−0.104741 | + | 0.994500i | \(0.533401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.450534 | − | 0.780347i | −0.0153186 | − | 0.0265326i | ||||
\(866\) | −6.28969 | + | 10.8941i | −0.213732 | + | 0.370195i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.268829 | + | 0.553794i | 0.00912465 | + | 0.0187970i | ||||
\(869\) | 11.5322i | 0.391205i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.49093 | + | 3.74754i | −0.219937 | + | 0.126981i | ||||
\(872\) | −15.6036 | + | 9.00877i | −0.528406 | + | 0.305075i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.39458i | 0.114823i | ||||||||
\(875\) | −1.49221 | − | 1.01055i | −0.0504460 | − | 0.0341630i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.3033 | + | 24.7741i | −0.482989 | + | 0.836562i | −0.999809 | − | 0.0195322i | \(-0.993782\pi\) |
0.516820 | + | 0.856094i | \(0.327116\pi\) | |||||||
\(878\) | 8.79639 | + | 15.2358i | 0.296864 | + | 0.514183i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0590182 | − | 0.0340742i | −0.00198950 | − | 0.00114864i | ||||
\(881\) | −10.9836 | −0.370048 | −0.185024 | − | 0.982734i | \(-0.559236\pi\) | ||||
−0.185024 | + | 0.982734i | \(0.559236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.61872 | 0.222738 | 0.111369 | − | 0.993779i | \(-0.464477\pi\) | ||||
0.111369 | + | 0.993779i | \(0.464477\pi\) | |||||||
\(884\) | 3.46979 | + | 2.00328i | 0.116702 | + | 0.0673777i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.5531 | + | 23.4746i | 0.455324 | + | 0.788645i | ||||
\(887\) | −13.1198 | + | 22.7241i | −0.440519 | + | 0.763001i | −0.997728 | − | 0.0673712i | \(-0.978539\pi\) |
0.557209 | + | 0.830372i | \(0.311872\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.9829 | − | 10.1467i | −0.502509 | − | 0.340308i | ||||
\(890\) | 0.727570i | 0.0243882i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.9717 | + | 6.91189i | −0.400844 | + | 0.231427i | ||||
\(893\) | 54.2014 | − | 31.2932i | 1.81378 | − | 1.04719i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.770563i | 0.0257571i | ||||||||
\(896\) | −1.15539 | − | 2.38014i | −0.0385990 | − | 0.0795149i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.49750 | + | 12.9861i | −0.250195 | + | 0.433350i | ||||
\(899\) | 0.841279 | + | 1.45714i | 0.0280582 | + | 0.0485983i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0104 | − | 6.93421i | −0.400124 | − | 0.231012i | ||||
\(902\) | −5.38891 | −0.179431 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.05521 | 0.234653 | ||||||||
\(905\) | 0.487886 | + | 0.281681i | 0.0162179 | + | 0.00936340i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.03536 | + | 3.52534i | 0.0675830 | + | 0.117057i | 0.897837 | − | 0.440328i | \(-0.145138\pi\) |
−0.830254 | + | 0.557385i | \(0.811805\pi\) | |||||||
\(908\) | −11.1257 | + | 19.2702i | −0.369219 | + | 0.639506i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.0316278 | + | 0.440518i | −0.00104845 | + | 0.0146030i | ||||
\(911\) | − | 48.6470i | − | 1.61175i | −0.592089 | − | 0.805873i | \(-0.701696\pi\) | ||
0.592089 | − | 0.805873i | \(-0.298304\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.8324 | + | 8.56350i | −0.490882 | + | 0.283411i | ||||
\(914\) | −0.823468 | + | 0.475430i | −0.0272379 | + | 0.0157258i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.2254i | 0.470020i | ||||||||
\(917\) | −3.60524 | + | 1.75010i | −0.119056 | + | 0.0577933i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.5377 | − | 26.9121i | 0.512542 | − | 0.887750i | −0.487352 | − | 0.873206i | \(-0.662037\pi\) |
0.999894 | − | 0.0145439i | \(-0.00462962\pi\) | |||||||
\(920\) | 0.0159382 | + | 0.0276058i | 0.000525467 | + | 0.000910135i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.3891 | − | 8.88488i | −0.506812 | − | 0.292608i | ||||
\(923\) | −38.8907 | −1.28010 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.4241 | 0.901700 | ||||||||
\(926\) | −1.05302 | − | 0.607962i | −0.0346044 | − | 0.0199789i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.61571 | − | 6.26260i | −0.118692 | − | 0.205580i | ||||
\(929\) | −23.7632 | + | 41.1591i | −0.779645 | + | 1.35039i | 0.152501 | + | 0.988303i | \(0.451267\pi\) |
−0.932146 | + | 0.362082i | \(0.882066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.25725 | + | 50.2797i | −0.237847 | + | 1.64785i | ||||
\(932\) | 0.514719i | 0.0168602i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.72464 | − | 4.45982i | 0.252758 | − | 0.145930i | ||||
\(935\) | 0.0965346 | − | 0.0557343i | 0.00315702 | − | 0.00182271i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 40.0691i | − | 1.30900i | −0.756062 | − | 0.654500i | \(-0.772879\pi\) | ||
0.756062 | − | 0.654500i | \(-0.227121\pi\) | |||||||
\(938\) | −4.53949 | + | 6.70314i | −0.148220 | + | 0.218865i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.293855 | − | 0.508972i | 0.00958450 | − | 0.0166008i | ||||
\(941\) | −13.3932 | − | 23.1977i | −0.436606 | − | 0.756223i | 0.560819 | − | 0.827938i | \(-0.310486\pi\) |
−0.997425 | + | 0.0717148i | \(0.977153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.18296 | + | 1.26033i | 0.0710868 | + | 0.0410420i | ||||
\(944\) | 0.878315 | 0.0285867 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.64100 | 0.313456 | ||||||||
\(947\) | 7.02383 | + | 4.05521i | 0.228244 | + | 0.131777i | 0.609762 | − | 0.792585i | \(-0.291265\pi\) |
−0.381518 | + | 0.924362i | \(0.624598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.56993 | + | 16.5756i | 0.310653 | + | 0.538067i | ||||
\(950\) | 18.1263 | − | 31.3956i | 0.588094 | − | 1.01861i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.31648 | + | 0.309909i | 0.139898 | + | 0.0100442i | ||||
\(953\) | 1.34315i | 0.0435088i | 0.999763 | + | 0.0217544i | \(0.00692518\pi\) | ||||
−0.999763 | + | 0.0217544i | \(0.993075\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.702835 | + | 0.405782i | −0.0227432 | + | 0.0131308i | ||||
\(956\) | −18.9000 | + | 10.9119i | −0.611268 | + | 0.352916i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 20.6322i | − | 0.666597i | ||||||
\(959\) | −13.0246 | − | 0.935123i | −0.420586 | − | 0.0301967i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4729 | + | 26.7999i | −0.499127 | + | 0.864513i | ||||
\(962\) | −6.72376 | − | 11.6459i | −0.216783 | − | 0.375479i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.95439 | − | 4.59247i | −0.256194 | − | 0.147914i | ||||
\(965\) | −1.73280 | −0.0557807 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.5361 | −1.07845 | −0.539224 | − | 0.842162i | \(-0.681282\pi\) | ||||
−0.539224 | + | 0.842162i | \(0.681282\pi\) | |||||||
\(968\) | −0.866025 | − | 0.500000i | −0.0278351 | − | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.340699 | − | 0.590109i | −0.0109392 | − | 0.0189472i | ||||
\(971\) | −26.6106 | + | 46.0910i | −0.853976 | + | 1.47913i | 0.0236161 | + | 0.999721i | \(0.492482\pi\) |
−0.877592 | + | 0.479408i | \(0.840851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.64057 | − | 2.42251i | 0.0525942 | − | 0.0776620i | ||||
\(974\) | 0.0379288i | 0.00121532i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.63223 | − | 4.98382i | 0.276311 | − | 0.159528i | ||||
\(977\) | −0.171724 | + | 0.0991448i | −0.00549393 | + | 0.00317192i | −0.502744 | − | 0.864435i | \(-0.667676\pi\) |
0.497251 | + | 0.867607i | \(0.334343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6763i | 0.341215i | ||||||||
\(980\) | 0.177055 | + | 0.442964i | 0.00565580 | + | 0.0141500i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.3460 | − | 30.0441i | 0.553532 | − | 0.958745i | ||||
\(983\) | 13.7122 | + | 23.7503i | 0.437352 | + | 0.757516i | 0.997484 | − | 0.0708872i | \(-0.0225830\pi\) |
−0.560132 | + | 0.828403i | \(0.689250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.494467 | − | 0.285481i | −0.0157550 | − | 0.00909617i | ||||
\(986\) | 11.8283 | 0.376689 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.7766 | −0.565548 | ||||||||
\(989\) | −3.90541 | − | 2.25479i | −0.124185 | − | 0.0716981i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4729 | − | 18.1396i | −0.332682 | − | 0.576222i | 0.650355 | − | 0.759631i | \(-0.274620\pi\) |
−0.983037 | + | 0.183408i | \(0.941287\pi\) | |||||||
\(992\) | −0.116337 | + | 0.201501i | −0.00369369 | + | 0.00639765i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −37.7896 | + | 18.3443i | −1.19861 | + | 0.581845i | ||||
\(995\) | − | 1.36714i | − | 0.0433413i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.8774 | + | 10.8989i | −0.597853 | + | 0.345170i | −0.768196 | − | 0.640214i | \(-0.778846\pi\) |
0.170344 | + | 0.985385i | \(0.445512\pi\) | |||||||
\(998\) | −17.7133 | + | 10.2268i | −0.560705 | + | 0.323723i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1386.2.r.c.89.1 | yes | 8 | |
3.2 | odd | 2 | 1386.2.r.a.89.4 | ✓ | 8 | ||
7.3 | odd | 6 | 1386.2.r.a.1277.4 | yes | 8 | ||
21.17 | even | 6 | inner | 1386.2.r.c.1277.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.a.89.4 | ✓ | 8 | 3.2 | odd | 2 | ||
1386.2.r.a.1277.4 | yes | 8 | 7.3 | odd | 6 | ||
1386.2.r.c.89.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1386.2.r.c.1277.1 | yes | 8 | 21.17 | even | 6 | inner |