Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(19,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 11, 11, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.bn (of order \(22\), degree \(10\), 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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{22})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 339.4 | ||
Character | \(\chi\) | \(=\) | 920.339 |
Dual form | 920.2.bn.a.19.4 |
$q$-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 \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(281\) | \(461\) | \(737\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{22}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.587486 | − | 1.28641i | 0.415415 | − | 0.909632i | ||||
\(3\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(4\) | −1.30972 | − | 1.51150i | −0.654861 | − | 0.755750i | ||||
\(5\) | 1.20891 | + | 1.88110i | 0.540641 | + | 0.841254i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707757 | + | 0.101760i | 0.267507 | + | 0.0384617i | 0.274763 | − | 0.961512i | \(-0.411401\pi\) |
−0.00725596 | + | 0.999974i | \(0.502310\pi\) | |||||||
\(8\) | −2.71386 | + | 0.796860i | −0.959493 | + | 0.281733i | ||||
\(9\) | 2.52376 | + | 1.62192i | 0.841254 | + | 0.540641i | ||||
\(10\) | 3.13009 | − | 0.450039i | 0.989821 | − | 0.142315i | ||||
\(11\) | −2.39252 | + | 1.09263i | −0.721371 | + | 0.329439i | −0.742048 | − | 0.670347i | \(-0.766145\pi\) |
0.0206766 | + | 0.999786i | \(0.493418\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.02135 | + | 7.10362i | 0.283271 | + | 1.97019i | 0.238251 | + | 0.971203i | \(0.423426\pi\) |
0.0450190 | + | 0.998986i | \(0.485665\pi\) | |||||||
\(14\) | 0.546703 | − | 0.850686i | 0.146112 | − | 0.227355i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.569259 | + | 3.95929i | −0.142315 | + | 0.989821i | ||||
\(17\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(18\) | 3.56914 | − | 2.29374i | 0.841254 | − | 0.540641i | ||||
\(19\) | −5.86368 | + | 5.08091i | −1.34522 | + | 1.16564i | −0.374008 | + | 0.927425i | \(0.622017\pi\) |
−0.971212 | + | 0.238215i | \(0.923438\pi\) | |||||||
\(20\) | 1.25995 | − | 4.29098i | 0.281733 | − | 0.959493i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.71967i | 0.793036i | ||||||||
\(23\) | −3.44081 | − | 3.34078i | −0.717459 | − | 0.696601i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.07708 | + | 4.54816i | −0.415415 | + | 0.909632i | ||||
\(26\) | 9.73822 | + | 2.85940i | 1.90982 | + | 0.560774i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.773155 | − | 1.20305i | −0.146112 | − | 0.227355i | ||||
\(29\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(32\) | 4.75885 | + | 3.05833i | 0.841254 | + | 0.540641i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.664194 | + | 1.45438i | 0.112269 | + | 0.245835i | ||||
\(36\) | −0.853889 | − | 5.93893i | −0.142315 | − | 0.989821i | ||||
\(37\) | 5.71030 | − | 8.88540i | 0.938768 | − | 1.46075i | 0.0519407 | − | 0.998650i | \(-0.483459\pi\) |
0.886827 | − | 0.462101i | \(-0.152904\pi\) | |||||||
\(38\) | 3.09132 | + | 10.5281i | 0.501479 | + | 1.70788i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.77978 | − | 4.14170i | −0.755750 | − | 0.654861i | ||||
\(41\) | 1.38359 | − | 0.889181i | 0.216081 | − | 0.138867i | −0.428123 | − | 0.903720i | \(-0.640825\pi\) |
0.644204 | + | 0.764854i | \(0.277189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(44\) | 4.78504 | + | 2.18525i | 0.721371 | + | 0.329439i | ||||
\(45\) | 6.70820i | 1.00000i | ||||||||
\(46\) | −6.31905 | + | 2.46365i | −0.931694 | + | 0.363245i | ||||
\(47\) | 13.6824 | 1.99578 | 0.997890 | − | 0.0649306i | \(-0.0206826\pi\) | ||||
0.997890 | + | 0.0649306i | \(0.0206826\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.22589 | − | 1.82808i | −0.889412 | − | 0.261155i | ||||
\(50\) | 4.63056 | + | 5.34396i | 0.654861 | + | 0.755750i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.39944 | − | 10.8475i | 1.30347 | − | 1.50428i | ||||
\(53\) | 8.14452 | + | 1.17101i | 1.11874 | + | 0.160850i | 0.676779 | − | 0.736186i | \(-0.263375\pi\) |
0.441957 | + | 0.897036i | \(0.354284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.94768 | − | 3.17968i | −0.667145 | − | 0.428748i | ||||
\(56\) | −2.00184 | + | 0.287821i | −0.267507 | + | 0.0384617i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.607367 | − | 4.22433i | −0.0790725 | − | 0.549961i | −0.990395 | − | 0.138268i | \(-0.955847\pi\) |
0.911322 | − | 0.411693i | \(-0.135063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.62116 | + | 1.40475i | 0.204247 | + | 0.176981i | ||||
\(64\) | 6.73003 | − | 4.32513i | 0.841254 | − | 0.540641i | ||||
\(65\) | −12.1279 | + | 10.5089i | −1.50428 | + | 1.30347i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.26114 | 0.270258 | ||||||||
\(71\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(72\) | −8.14157 | − | 2.39058i | −0.959493 | − | 0.281733i | ||||
\(73\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(74\) | −8.07559 | − | 12.5659i | −0.938768 | − | 1.46075i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.3596 | + | 2.20837i | 1.76186 | + | 0.253318i | ||||
\(77\) | −1.80451 | + | 0.529851i | −0.205643 | + | 0.0603822i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(80\) | −8.13600 | + | 3.71558i | −0.909632 | + | 0.415415i | ||||
\(81\) | 3.73874 | + | 8.18669i | 0.415415 | + | 0.909632i | ||||
\(82\) | −0.331014 | − | 2.30225i | −0.0365544 | − | 0.254241i | ||||
\(83\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.62228 | − | 4.87173i | 0.599337 | − | 0.519328i | ||||
\(89\) | 4.41127 | − | 15.0234i | 0.467594 | − | 1.59248i | −0.301581 | − | 0.953440i | \(-0.597514\pi\) |
0.769175 | − | 0.639038i | \(-0.220667\pi\) | |||||||
\(90\) | 8.62953 | + | 3.94097i | 0.909632 | + | 0.415415i | ||||
\(91\) | 5.13157i | 0.537935i | ||||||||
\(92\) | −0.543085 | + | 9.57628i | −0.0566205 | + | 0.998396i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.03820 | − | 17.6012i | 0.829077 | − | 1.81542i | ||||
\(95\) | −16.6464 | − | 4.88781i | −1.70788 | − | 0.501479i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(98\) | −6.00929 | + | 6.93509i | −0.607030 | + | 0.700550i | ||||
\(99\) | −7.81030 | − | 1.12295i | −0.784964 | − | 0.112861i | ||||
\(100\) | 9.59493 | − | 2.81733i | 0.959493 | − | 0.281733i | ||||
\(101\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.1590 | − | 6.00954i | 1.29660 | − | 0.592137i | 0.356901 | − | 0.934142i | \(-0.383833\pi\) |
0.939698 | + | 0.342005i | \(0.111106\pi\) | |||||||
\(104\) | −8.43238 | − | 18.4643i | −0.826863 | − | 1.81058i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.29119 | − | 9.78928i | 0.611054 | − | 0.950819i | ||||
\(107\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(110\) | −6.99707 | + | 4.49674i | −0.667145 | + | 0.428748i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.805795 | + | 2.74429i | −0.0761405 | + | 0.259311i | ||||
\(113\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.12472 | − | 10.5112i | 0.198131 | − | 0.980176i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.94389 | + | 19.5844i | −0.826863 | + | 1.81058i | ||||
\(118\) | −5.79106 | − | 1.70041i | −0.533110 | − | 0.156535i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.67316 | + | 3.08499i | −0.243015 | + | 0.280454i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0665 | + | 1.59113i | −0.989821 | + | 0.142315i | ||||
\(126\) | 2.75949 | − | 1.26022i | 0.245835 | − | 0.112269i | ||||
\(127\) | −7.96144 | − | 17.4331i | −0.706463 | − | 1.54694i | −0.831954 | − | 0.554844i | \(-0.812778\pi\) |
0.125491 | − | 0.992095i | \(-0.459949\pi\) | |||||||
\(128\) | −1.61011 | − | 11.1986i | −0.142315 | − | 0.989821i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.39381 | + | 21.7753i | 0.560774 | + | 1.90982i | ||||
\(131\) | −3.25768 | + | 22.6577i | −0.284625 | + | 1.97961i | −0.136702 | + | 0.990612i | \(0.543650\pi\) |
−0.147923 | + | 0.988999i | \(0.547259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.66710 | + | 2.99936i | −0.404689 | + | 0.260078i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.17129 | 0.438623 | 0.219312 | − | 0.975655i | \(-0.429619\pi\) | ||||
0.219312 | + | 0.975655i | \(0.429619\pi\) | |||||||
\(140\) | 1.32839 | − | 2.90876i | 0.112269 | − | 0.245835i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.2052 | − | 15.8796i | −0.853401 | − | 1.32792i | ||||
\(144\) | −7.85833 | + | 9.06899i | −0.654861 | + | 0.755750i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.9092 | + | 3.00629i | −1.71872 | + | 0.247115i | ||||
\(149\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(152\) | 11.8644 | − | 18.4614i | 0.962331 | − | 1.49742i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.378514 | + | 2.63262i | −0.0305015 | + | 0.212143i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8056 | − | 11.9627i | 1.10181 | − | 0.954724i | 0.102610 | − | 0.994722i | \(-0.467281\pi\) |
0.999200 | + | 0.0399981i | \(0.0127352\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.6491i | 1.00000i | ||||||||
\(161\) | −2.09530 | − | 2.71460i | −0.165133 | − | 0.213940i | ||||
\(162\) | 12.7279 | 1.00000 | ||||||||
\(163\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(164\) | −3.15612 | − | 0.926720i | −0.246451 | − | 0.0723647i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.58895 | + | 11.0662i | −0.742016 | + | 0.856332i | −0.993769 | − | 0.111460i | \(-0.964447\pi\) |
0.251753 | + | 0.967791i | \(0.418993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −36.9449 | + | 10.8480i | −2.84191 | + | 0.834461i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.0394 | + | 3.31256i | −1.76186 | + | 0.253318i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3676 | + | 22.7019i | 0.788235 | + | 1.72599i | 0.681635 | + | 0.731693i | \(0.261269\pi\) |
0.106601 | + | 0.994302i | \(0.466003\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.93289 | + | 3.00763i | −0.146112 | + | 0.227355i | ||||
\(176\) | −2.96406 | − | 10.0946i | −0.223424 | − | 0.760913i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.7348 | − | 14.5008i | −1.25432 | − | 1.08688i | ||||
\(179\) | 18.3445 | − | 11.7893i | 1.37113 | − | 0.881174i | 0.372236 | − | 0.928138i | \(-0.378591\pi\) |
0.998897 | + | 0.0469643i | \(0.0149547\pi\) | |||||||
\(180\) | 10.1394 | − | 8.78588i | 0.755750 | − | 0.654861i | ||||
\(181\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(182\) | 6.60132 | + | 3.01472i | 0.489323 | + | 0.223466i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0000 | + | 6.32456i | 0.884652 | + | 0.466252i | ||||
\(185\) | 23.6176 | 1.73640 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −17.9201 | − | 20.6809i | −1.30696 | − | 1.50831i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.0672 | + | 18.5426i | −1.16564 | + | 1.34522i | ||||
\(191\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.39103 | + | 11.8047i | 0.385073 | + | 0.843193i | ||||
\(197\) | 2.80615 | + | 19.5172i | 0.199930 | + | 1.39054i | 0.804481 | + | 0.593978i | \(0.202443\pi\) |
−0.604551 | + | 0.796566i | \(0.706648\pi\) | |||||||
\(198\) | −6.03302 | + | 9.38756i | −0.428748 | + | 0.667145i | ||||
\(199\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(200\) | 2.01264 | − | 13.9982i | 0.142315 | − | 0.989821i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.34528 | + | 1.52774i | 0.233644 | + | 0.106702i | ||||
\(206\) | − | 20.4585i | − | 1.42541i | ||||||
\(207\) | −3.26529 | − | 14.0121i | −0.226954 | − | 0.973906i | ||||
\(208\) | −28.7067 | −1.99045 | ||||||||
\(209\) | 8.47743 | − | 18.5630i | 0.586396 | − | 1.28403i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.40236 | − | 6.23466i | −0.371914 | − | 0.429212i | 0.538682 | − | 0.842509i | \(-0.318922\pi\) |
−0.910596 | + | 0.413297i | \(0.864377\pi\) | |||||||
\(212\) | −8.89708 | − | 13.8441i | −0.611054 | − | 0.950819i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.67400 | + | 11.6429i | 0.112861 | + | 0.784964i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.80701 | + | 12.5680i | −0.121006 | + | 0.841617i | 0.835414 | + | 0.549622i | \(0.185228\pi\) |
−0.956420 | + | 0.291995i | \(0.905681\pi\) | |||||||
\(224\) | 3.05689 | + | 2.64881i | 0.204247 | + | 0.176981i | ||||
\(225\) | −12.6188 | + | 8.10961i | −0.841254 | + | 0.540641i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | −12.2735 | − | 8.90845i | −0.809293 | − | 0.587406i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(234\) | 19.9392 | + | 23.0111i | 1.30347 | + | 1.50428i | ||||
\(235\) | 16.5408 | + | 25.7379i | 1.07900 | + | 1.67896i | ||||
\(236\) | −5.58959 | + | 6.45073i | −0.363852 | + | 0.419907i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.9318 | − | 5.90574i | 0.833008 | − | 0.380422i | 0.0471945 | − | 0.998886i | \(-0.484972\pi\) |
0.785813 | + | 0.618464i | \(0.212245\pi\) | |||||||
\(242\) | 2.39813 | + | 5.25118i | 0.154158 | + | 0.337558i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.08772 | − | 13.9215i | −0.261155 | − | 0.889412i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −42.0817 | − | 36.4640i | −2.67759 | − | 2.32015i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.45458 | + | 15.1709i | −0.281733 | + | 0.959493i | ||||
\(251\) | 25.1823 | + | 11.5004i | 1.58949 | + | 0.725897i | 0.996831 | − | 0.0795541i | \(-0.0253496\pi\) |
0.592662 | + | 0.805451i | \(0.298077\pi\) | |||||||
\(252\) | − | 4.29021i | − | 0.270258i | ||||||
\(253\) | 11.8824 | + | 4.23336i | 0.747042 | + | 0.266149i | ||||
\(254\) | −27.1034 | −1.70062 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.3519 | − | 4.50772i | −0.959493 | − | 0.281733i | ||||
\(257\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.94569 | − | 5.70763i | 0.307310 | − | 0.354655i | ||||
\(260\) | 31.7684 | + | 4.56760i | 1.97019 | + | 0.283271i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 27.2333 | + | 17.5018i | 1.68248 | + | 1.08126i | ||||
\(263\) | 30.6081 | − | 4.40079i | 1.88738 | − | 0.271364i | 0.900749 | − | 0.434340i | \(-0.143019\pi\) |
0.986630 | + | 0.162976i | \(0.0521094\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.64321 | + | 16.7363i | 0.469519 | + | 1.02810i | ||||
\(266\) | 1.11657 | + | 7.76590i | 0.0684612 | + | 0.476158i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 13.1510i | − | 0.793036i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.6750 | −1.18216 | −0.591080 | − | 0.806613i | \(-0.701298\pi\) | ||||
−0.591080 | + | 0.806613i | \(0.701298\pi\) | |||||||
\(278\) | 3.03806 | − | 6.65242i | 0.182211 | − | 0.398986i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.96146 | − | 3.41771i | −0.176981 | − | 0.204247i | ||||
\(281\) | −9.77227 | − | 15.2060i | −0.582965 | − | 0.907111i | 0.417034 | − | 0.908891i | \(-0.363070\pi\) |
−0.999998 | + | 0.00178007i | \(0.999433\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.4231 | + | 3.79907i | −1.56243 | + | 0.224644i | ||||
\(287\) | 1.06973 | − | 0.488530i | 0.0631443 | − | 0.0288370i | ||||
\(288\) | 7.04983 | + | 15.4370i | 0.415415 | + | 0.909632i | ||||
\(289\) | 2.41935 | + | 16.8270i | 0.142315 | + | 0.989821i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.1724 | + | 14.8800i | 1.00322 | + | 0.869298i | 0.991431 | − | 0.130632i | \(-0.0417008\pi\) |
0.0117925 | + | 0.999930i | \(0.496246\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.21214 | − | 6.24936i | 0.419907 | − | 0.363852i | ||||
\(296\) | −8.41652 | + | 28.6640i | −0.489200 | + | 1.66606i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.2174 | − | 27.8543i | 1.16920 | − | 1.61086i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.7788 | − | 26.1083i | −0.962331 | − | 1.49742i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(308\) | 3.16427 | + | 2.03355i | 0.180301 | + | 0.115873i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(314\) | −7.27831 | − | 24.7876i | −0.410739 | − | 1.39885i | ||||
\(315\) | −0.682628 | + | 4.74778i | −0.0384617 | + | 0.267507i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.0248 | + | 11.5839i | −1.01238 | + | 0.650614i | −0.938007 | − | 0.346617i | \(-0.887330\pi\) |
−0.0743686 | + | 0.997231i | \(0.523694\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 16.2720 | + | 7.43117i | 0.909632 | + | 0.415415i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.72306 | + | 1.10064i | −0.263206 | + | 0.0613360i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.47747 | − | 16.3734i | 0.415415 | − | 0.909632i | ||||
\(325\) | −34.4298 | − | 10.1095i | −1.90982 | − | 0.560774i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.04632 | + | 3.51564i | −0.168205 | + | 0.194119i | ||||
\(329\) | 9.68380 | + | 1.39232i | 0.533885 | + | 0.0767611i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.0241 | − | 14.1540i | −1.21055 | − | 0.777974i | −0.229801 | − | 0.973238i | \(-0.573807\pi\) |
−0.980751 | + | 0.195264i | \(0.937444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 28.8229 | − | 13.1630i | 1.57948 | − | 0.721326i | ||||
\(334\) | 8.60240 | + | 18.8366i | 0.470702 | + | 1.03069i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(338\) | −7.74957 | + | 53.8994i | −0.421521 | + | 2.93174i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.27397 | + | 31.5842i | −0.501479 | + | 1.70788i | ||||
\(343\) | −8.77332 | − | 4.00664i | −0.473715 | − | 0.216338i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 35.2949 | 1.89746 | ||||||||
\(347\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(350\) | 2.73351 | + | 4.25343i | 0.146112 | + | 0.227355i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.7272 | − | 2.11746i | −0.784964 | − | 0.112861i | ||||
\(353\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −28.4854 | + | 13.0089i | −1.50972 | + | 0.689468i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.38879 | − | 30.5247i | −0.231955 | − | 1.61328i | ||||
\(359\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(360\) | −5.34550 | − | 18.2051i | −0.281733 | − | 0.959493i | ||||
\(361\) | 5.86314 | − | 40.7790i | 0.308586 | − | 2.14627i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.75637 | − | 6.72093i | 0.406544 | − | 0.352272i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.99021i | 0.103888i | 0.998650 | + | 0.0519440i | \(0.0165417\pi\) | ||||
−0.998650 | + | 0.0519440i | \(0.983458\pi\) | |||||||
\(368\) | 15.1858 | − | 11.7214i | 0.791616 | − | 0.611019i | ||||
\(369\) | 4.93404 | 0.256856 | ||||||||
\(370\) | 13.8750 | − | 30.3820i | 0.721326 | − | 1.57948i | ||||
\(371\) | 5.64518 | + | 1.65758i | 0.293083 | + | 0.0860570i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3287 | − | 31.6320i | −1.05258 | − | 1.63784i | −0.718837 | − | 0.695179i | \(-0.755325\pi\) |
−0.333741 | − | 0.942665i | \(-0.608311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −37.1320 | + | 10.9029i | −1.91494 | + | 0.562276i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.3023 | + | 16.1220i | −1.81336 | + | 0.828133i | −0.873231 | + | 0.487306i | \(0.837980\pi\) |
−0.940126 | + | 0.340827i | \(0.889293\pi\) | |||||||
\(380\) | 14.4142 | + | 31.5626i | 0.739431 | + | 1.61913i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.35368 | + | 18.2330i | 0.273560 | + | 0.931660i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) |
−0.702046 | + | 0.712132i | \(0.747730\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.17819 | − | 2.75392i | −0.161976 | − | 0.140353i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 18.3529 | 0.926961 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26.7558 | + | 7.85621i | 1.34794 | + | 0.395790i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.53197 | + | 13.2760i | 0.428748 | + | 0.667145i | ||||
\(397\) | 8.10822 | − | 9.35739i | 0.406940 | − | 0.469634i | −0.514874 | − | 0.857266i | \(-0.672161\pi\) |
0.921814 | + | 0.387632i | \(0.126707\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.8251 | − | 10.8128i | −0.841254 | − | 0.540641i | ||||
\(401\) | 39.4153 | − | 5.66707i | 1.96831 | − | 0.283000i | 0.968946 | − | 0.247272i | \(-0.0795342\pi\) |
0.999362 | − | 0.0357278i | \(-0.0113749\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.8802 | + | 16.9299i | −0.540641 | + | 0.841254i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.95357 | + | 27.4977i | −0.195971 | + | 1.36301i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.1459 | − | 15.5176i | 1.19394 | − | 0.767298i | 0.216041 | − | 0.976384i | \(-0.430685\pi\) |
0.977897 | + | 0.209087i | \(0.0670491\pi\) | |||||||
\(410\) | 3.93061 | − | 3.40589i | 0.194119 | − | 0.168205i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −26.3181 | − | 12.0191i | −1.29660 | − | 0.592137i | ||||
\(413\) | − | 3.05161i | − | 0.150160i | ||||||
\(414\) | −19.9436 | − | 4.03136i | −0.980176 | − | 0.198131i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.8648 | + | 36.9287i | −0.826863 | + | 1.81058i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.8993 | − | 21.8110i | −0.924395 | − | 1.06681i | ||||
\(419\) | −19.8886 | − | 30.9472i | −0.971620 | − | 1.51187i | −0.854958 | − | 0.518698i | \(-0.826417\pi\) |
−0.116662 | − | 0.993172i | \(-0.537219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(422\) | −11.1942 | + | 3.28690i | −0.544924 | + | 0.160004i | ||||
\(423\) | 34.5310 | + | 22.1918i | 1.67896 | + | 1.07900i | ||||
\(424\) | −23.0362 | + | 3.31210i | −1.11874 | + | 0.160850i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.1500 | + | 2.10683i | 1.77713 | + | 0.100783i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(440\) | 15.9610 | + | 4.68658i | 0.760913 | + | 0.223424i | ||||
\(441\) | −12.7476 | − | 14.7116i | −0.607030 | − | 0.700550i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.5934 | − | 9.86390i | 1.59248 | − | 0.467594i | ||||
\(446\) | 15.1061 | + | 9.70809i | 0.715294 | + | 0.459691i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.20335 | − | 2.37629i | 0.245835 | − | 0.112269i | ||||
\(449\) | −1.30696 | − | 2.86183i | −0.0616791 | − | 0.135058i | 0.876282 | − | 0.481798i | \(-0.160016\pi\) |
−0.937961 | + | 0.346740i | \(0.887289\pi\) | |||||||
\(450\) | 3.01895 | + | 20.9973i | 0.142315 | + | 0.989821i | ||||
\(451\) | −2.33873 | + | 3.63913i | −0.110126 | + | 0.171360i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.65300 | + | 6.20361i | −0.452540 | + | 0.290830i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18.6705 | + | 10.5553i | −0.870515 | + | 0.492141i | ||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0801 | + | 5.30880i | 0.840255 | + | 0.246721i | 0.673417 | − | 0.739263i | \(-0.264826\pi\) |
0.166838 | + | 0.985984i | \(0.446644\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(468\) | 41.3158 | − | 12.1314i | 1.90982 | − | 0.560774i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 42.8271 | − | 6.15760i | 1.97547 | − | 0.284029i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.01451 | + | 10.9802i | 0.230812 | + | 0.505407i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.9295 | − | 37.2224i | −0.501479 | − | 1.70788i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.6555 | + | 16.1651i | 0.854179 | + | 0.740150i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 68.9507 | + | 31.4887i | 3.14388 | + | 1.43576i | ||||
\(482\) | − | 20.1051i | − | 0.915764i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.16406 | 0.371093 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.8356 | + | 33.2781i | 1.30667 | + | 1.50797i | 0.704925 | + | 0.709281i | \(0.250980\pi\) |
0.601741 | + | 0.798692i | \(0.294474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.3103 | − | 2.92018i | −0.917526 | − | 0.131920i | ||||
\(491\) | 30.8465 | − | 9.05735i | 1.39208 | − | 0.408752i | 0.502125 | − | 0.864795i | \(-0.332552\pi\) |
0.889958 | + | 0.456043i | \(0.150734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −71.6302 | + | 32.7124i | −3.22279 | + | 1.47180i | ||||
\(495\) | −7.32956 | − | 16.0495i | −0.329439 | − | 0.721371i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.11489 | − | 42.5300i | 0.273740 | − | 1.90391i | −0.134298 | − | 0.990941i | \(-0.542878\pi\) |
0.408039 | − | 0.912965i | \(-0.366213\pi\) | |||||||
\(500\) | 16.8991 | + | 14.6431i | 0.755750 | + | 0.654861i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.5885 | − | 25.6386i | 1.32060 | − | 1.14430i | ||||
\(503\) | 11.6414 | − | 39.6469i | 0.519064 | − | 1.76777i | −0.113797 | − | 0.993504i | \(-0.536301\pi\) |
0.632861 | − | 0.774265i | \(-0.281880\pi\) | |||||||
\(504\) | −5.51899 | − | 2.52044i | −0.245835 | − | 0.112269i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.4266 | − | 12.7987i | 0.552430 | − | 0.568971i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.9229 | + | 34.8662i | −0.706463 | + | 1.54694i | ||||
\(509\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14.8178 | + | 17.1007i | −0.654861 | + | 0.755750i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.2126 | + | 17.4885i | 1.19913 | + | 0.770635i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.7353 | + | 14.9497i | −1.43970 | + | 0.657488i | ||||
\(518\) | −4.43685 | − | 9.71535i | −0.194944 | − | 0.426868i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.5393 | − | 38.1839i | 1.07612 | − | 1.67447i | ||||
\(521\) | −12.7583 | − | 43.4509i | −0.558953 | − | 1.90362i | −0.400658 | − | 0.916228i | \(-0.631218\pi\) |
−0.158295 | − | 0.987392i | \(-0.550600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(524\) | 38.5137 | − | 24.7513i | 1.68248 | − | 1.08126i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.3206 | − | 41.9601i | 0.537204 | − | 1.82955i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.678358 | + | 22.9900i | 0.0294938 | + | 0.999565i | ||||
\(530\) | 26.0201 | 1.13024 | ||||||||
\(531\) | 5.31869 | − | 11.6463i | 0.230812 | − | 0.505407i | ||||
\(532\) | 10.6461 | + | 3.12599i | 0.461568 | + | 0.135529i | ||||
\(533\) | 7.72953 | + | 8.92036i | 0.334803 | + | 0.386384i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.8930 | − | 2.42884i | 0.727631 | − | 0.104618i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.9177 | − | 7.72603i | −0.721371 | − | 0.329439i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.5588 | + | 25.3103i | −0.491087 | + | 1.07533i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.77295 | − | 7.81640i | −0.287237 | − | 0.331489i | ||||
\(557\) | −13.8527 | − | 21.5552i | −0.586957 | − | 0.913323i | −0.999997 | − | 0.00260984i | \(-0.999169\pi\) |
0.413040 | − | 0.910713i | \(-0.364467\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6.13641 | + | 1.80181i | −0.259311 | + | 0.0761405i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.3022 | + | 3.63791i | −1.06731 | + | 0.153456i | ||||
\(563\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.81304 | + | 6.17464i | 0.0761405 | + | 0.259311i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.55956 | − | 8.28341i | −0.400758 | − | 0.347258i | 0.431045 | − | 0.902331i | \(-0.358145\pi\) |
−0.831802 | + | 0.555072i | \(0.812691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.2733 | + | 22.7660i | −1.09950 | + | 0.952726i | −0.999108 | − | 0.0422218i | \(-0.986556\pi\) |
−0.100396 | + | 0.994948i | \(0.532011\pi\) | |||||||
\(572\) | −10.6360 | + | 36.2230i | −0.444714 | + | 1.51456i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1.66312i | − | 0.0694174i | ||||||
\(575\) | 22.3412 | − | 8.71030i | 0.931694 | − | 0.363245i | ||||
\(576\) | 24.0000 | 1.00000 | ||||||||
\(577\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(578\) | 23.0678 | + | 6.77331i | 0.959493 | + | 0.281733i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.7654 | + | 6.09727i | −0.860014 | + | 0.252523i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −47.6525 | + | 6.85140i | −1.97019 | + | 0.283271i | ||||
\(586\) | 29.2304 | − | 13.3491i | 1.20750 | − | 0.551445i | ||||
\(587\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.80223 | − | 12.9492i | −0.156535 | − | 0.533110i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 31.9292 | + | 27.6668i | 1.31228 | + | 1.13710i | ||||
\(593\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23.9547 | − | 42.3719i | −0.979582 | − | 1.73272i | ||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.5049 | − | 13.3615i | −1.85619 | − | 0.545025i | −0.999578 | − | 0.0290573i | \(-0.990749\pi\) |
−0.856608 | − | 0.515968i | \(-0.827432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.03479 | − | 1.29901i | −0.367316 | − | 0.0528121i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.3723 | + | 13.0925i | 0.826886 | + | 0.531407i | 0.884287 | − | 0.466944i | \(-0.154645\pi\) |
−0.0574012 | + | 0.998351i | \(0.518281\pi\) | |||||||
\(608\) | −43.4434 | + | 6.24622i | −1.76186 | + | 0.253318i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.9744 | + | 97.1944i | 0.565345 | + | 3.93206i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.54990 | + | 12.0898i | 0.143379 | + | 0.488304i | 0.999599 | − | 0.0283068i | \(-0.00901155\pi\) |
−0.856220 | + | 0.516611i | \(0.827193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.47496 | − | 2.87588i | 0.180301 | − | 0.115873i | ||||
\(617\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.2591 | + | 7.88195i | 0.693700 | + | 0.316802i | 0.730880 | − | 0.682506i | \(-0.239110\pi\) |
−0.0371796 | + | 0.999309i | \(0.511837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.65089 | − | 10.1840i | 0.186334 | − | 0.408015i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3715 | − | 18.8937i | −0.654861 | − | 0.755750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.1631 | − | 5.19947i | −1.44306 | − | 0.207481i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 5.70658 | + | 3.66739i | 0.227355 | + | 0.146112i | ||||
\(631\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.31231 | + | 29.9927i | 0.171264 | + | 1.19116i | ||||
\(635\) | 23.1688 | − | 36.0513i | 0.919425 | − | 1.43065i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.62723 | − | 46.0934i | 0.262581 | − | 1.82629i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19.1191 | − | 16.5668i | 0.755750 | − | 0.654861i | ||||
\(641\) | −13.8360 | + | 47.1211i | −0.546489 | + | 1.86117i | −0.0394976 | + | 0.999220i | \(0.512576\pi\) |
−0.506991 | + | 0.861951i | \(0.669242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | −1.35886 | + | 6.72242i | −0.0535464 | + | 0.264900i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.7278 | − | 6.67348i | −0.893522 | − | 0.262362i | −0.197432 | − | 0.980317i | \(-0.563260\pi\) |
−0.696090 | + | 0.717955i | \(0.745078\pi\) | |||||||
\(648\) | −16.6700 | − | 19.2382i | −0.654861 | − | 0.755750i | ||||
\(649\) | 6.06875 | + | 9.44317i | 0.238219 | + | 0.370677i | ||||
\(650\) | −33.2320 | + | 38.3518i | −1.30347 | + | 1.50428i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.8907 | + | 19.8523i | 1.20885 | + | 0.776879i | 0.980465 | − | 0.196692i | \(-0.0630200\pi\) |
0.228382 | + | 0.973572i | \(0.426656\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.5596 | + | 21.2631i | −1.81923 | + | 0.830817i | ||||
\(656\) | 2.73290 | + | 5.98422i | 0.106702 | + | 0.233644i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.48019 | − | 11.6394i | 0.291608 | − | 0.453751i | ||||
\(659\) | 9.02556 | + | 30.7382i | 0.351586 | + | 1.19739i | 0.925586 | + | 0.378536i | \(0.123573\pi\) |
−0.574001 | + | 0.818855i | \(0.694609\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(662\) | −31.1467 | + | 20.0168i | −1.21055 | + | 0.777974i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.2842 | − | 5.15332i | −0.437582 | − | 0.199837i | ||||
\(666\) | − | 44.8112i | − | 1.73640i | ||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 29.2855 | 1.13309 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 64.7842 | + | 41.6343i | 2.49170 | + | 1.60132i | ||||
\(677\) | −44.5819 | + | 6.40991i | −1.71342 | + | 0.246353i | −0.927993 | − | 0.372597i | \(-0.878467\pi\) |
−0.785430 | + | 0.618950i | \(0.787558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(684\) | 35.1821 | + | 30.4855i | 1.34522 | + | 1.16564i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.3084 | + | 8.93228i | −0.393577 | + | 0.341036i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 59.0516i | 2.24969i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.2125 | −1.75801 | −0.879004 | − | 0.476815i | \(-0.841791\pi\) | ||||
−0.879004 | + | 0.476815i | \(0.841791\pi\) | |||||||
\(692\) | 20.7352 | − | 45.4038i | 0.788235 | − | 1.72599i | ||||
\(693\) | −5.41352 | − | 1.58955i | −0.205643 | − | 0.0603822i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.25162 | + | 9.72771i | 0.237138 | + | 0.368993i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.07757 | − | 1.01760i | 0.267507 | − | 0.0384617i | ||||
\(701\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.6625 | + | 81.1147i | 0.439861 | + | 3.05930i | ||||
\(704\) | −11.3760 | + | 17.7013i | −0.428748 | + | 0.667145i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 44.2865i | 1.65971i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.5339 | − | 38.3940i | 0.655732 | − | 1.43585i | ||||
\(716\) | −41.8457 | − | 12.2870i | −1.56385 | − | 0.459187i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(720\) | −26.5597 | − | 3.81871i | −0.989821 | − | 0.142315i | ||||
\(721\) | 9.92494 | − | 2.91423i | 0.369624 | − | 0.108531i | ||||
\(722\) | −49.0142 | − | 31.4995i | −1.82412 | − | 1.17229i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1025 | + | 45.2843i | −1.07935 | + | 1.67950i | −0.489421 | + | 0.872048i | \(0.662792\pi\) |
−0.589930 | + | 0.807455i | \(0.700845\pi\) | |||||||
\(728\) | −4.08914 | − | 13.9263i | −0.151554 | − | 0.516145i | ||||
\(729\) | −3.84250 | + | 26.7252i | −0.142315 | + | 0.989821i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.1058 | − | 51.4456i | 0.557945 | − | 1.90019i | 0.145000 | − | 0.989432i | \(-0.453682\pi\) |
0.412946 | − | 0.910756i | \(-0.364500\pi\) | |||||||
\(734\) | 2.56023 | + | 1.16922i | 0.0944998 | + | 0.0431566i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.15710 | − | 26.4214i | −0.226954 | − | 0.973906i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.89868 | − | 6.34722i | 0.106702 | − | 0.233644i | ||||
\(739\) | 46.8684 | + | 13.7618i | 1.72408 | + | 0.506236i | 0.985752 | − | 0.168206i | \(-0.0537973\pi\) |
0.738328 | + | 0.674441i | \(0.235615\pi\) | |||||||
\(740\) | −30.9324 | − | 35.6979i | −1.13710 | − | 1.31228i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.44879 | − | 6.28824i | 0.200031 | − | 0.230849i | ||||
\(743\) | 30.3551 | + | 4.36440i | 1.11362 | + | 0.160114i | 0.674472 | − | 0.738300i | \(-0.264371\pi\) |
0.439148 | + | 0.898415i | \(0.355280\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −52.6347 | + | 7.56772i | −1.92709 | + | 0.277074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(752\) | −7.78882 | + | 54.1724i | −0.284029 | + | 1.97547i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.2746 | − | 22.5029i | −1.79091 | − | 0.817883i | −0.968507 | − | 0.248985i | \(-0.919903\pi\) |
−0.822407 | − | 0.568899i | \(-0.807370\pi\) | |||||||
\(758\) | 54.8848i | 1.99351i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 49.0707 | 1.77998 | ||||||||
\(761\) | 9.89988 | − | 21.6777i | 0.358870 | − | 0.785817i | −0.640963 | − | 0.767572i | \(-0.721465\pi\) |
0.999834 | − | 0.0182449i | \(-0.00580787\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.6003 | + | 3.82455i | 0.961109 | + | 0.138187i | ||||
\(767\) | 29.3877 | − | 8.62901i | 1.06113 | − | 0.311576i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.4190 | + | 6.24271i | −1.56573 | + | 0.225118i | −0.869951 | − | 0.493138i | \(-0.835850\pi\) |
−0.695779 | + | 0.718256i | \(0.744941\pi\) | |||||||
\(770\) | −5.40982 | + | 2.47058i | −0.194956 | + | 0.0890336i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.0596 | − | 46.7736i | 1.08117 | − | 1.68233i | 0.528337 | − | 0.849035i | \(-0.322816\pi\) |
0.552830 | − | 0.833294i | \(-0.313548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.59510 | + | 12.2438i | −0.128808 | + | 0.438679i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.7821 | − | 23.6094i | 0.385073 | − | 0.843193i | ||||
\(785\) | 39.1927 | + | 11.5080i | 1.39885 | + | 0.410739i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(788\) | 25.8250 | − | 29.8036i | 0.919977 | − | 1.06171i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 22.0909 | − | 3.17619i | 0.784964 | − | 0.112861i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −7.27401 | − | 15.9279i | −0.258145 | − | 0.565259i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.8585 | − | 50.6034i | −0.526315 | − | 1.79246i | −0.605787 | − | 0.795627i | \(-0.707142\pi\) |
0.0794719 | − | 0.996837i | \(-0.474677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −23.7942 | + | 15.2916i | −0.841254 | + | 0.540641i | ||||
\(801\) | 35.4998 | − | 30.7608i | 1.25432 | − | 1.08688i | ||||
\(802\) | 15.8657 | − | 54.0337i | 0.560239 | − | 1.90800i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.57341 | − | 7.22318i | 0.0907006 | − | 0.254584i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.2195 | − | 40.6454i | −1.23825 | − | 1.42902i | −0.865366 | − | 0.501140i | \(-0.832914\pi\) |
−0.372885 | − | 0.927878i | \(-0.621631\pi\) | |||||||
\(810\) | 15.3869 | + | 23.9425i | 0.540641 | + | 0.841254i | ||||
\(811\) | −34.4509 | + | 39.7585i | −1.20973 | + | 1.39611i | −0.315251 | + | 0.949008i | \(0.602089\pi\) |
−0.894484 | + | 0.447100i | \(0.852457\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.0508 | + | 21.2404i | 1.15843 | + | 0.744477i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −5.77673 | − | 40.1780i | −0.201979 | − | 1.40479i | ||||
\(819\) | −8.32301 | + | 12.9509i | −0.290830 | + | 0.452540i | ||||
\(820\) | −2.07221 | − | 7.05730i | −0.0723647 | − | 0.246451i | ||||
\(821\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.7591 | + | 26.1943i | −1.42077 | + | 0.913076i | −0.420792 | + | 0.907157i | \(0.638248\pi\) |
−0.999982 | + | 0.00591934i | \(0.998116\pi\) | |||||||
\(824\) | −30.9230 | + | 26.7949i | −1.07725 | + | 0.933446i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.92563 | − | 1.79278i | −0.136590 | − | 0.0623787i | ||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | −16.9026 | + | 23.2874i | −0.587406 | + | 0.809293i | ||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 37.5977 | + | 43.3901i | 1.30347 | + | 1.50428i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.4089 | − | 4.65969i | −1.12156 | − | 0.161255i | ||||
\(836\) | −39.1610 | + | 11.4987i | −1.35441 | + | 0.397691i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −51.4951 | + | 7.40388i | −1.77887 | + | 0.255763i | ||||
\(839\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.12713 | − | 28.7048i | −0.142315 | − | 0.989821i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.34809 | + | 16.3313i | −0.0808247 | + | 0.562148i | ||||
\(845\) | −65.0691 | − | 56.3827i | −2.23845 | − | 1.93963i | ||||
\(846\) | 48.8343 | − | 31.3839i | 1.67896 | − | 1.07900i | ||||
\(847\) | −2.20588 | + | 1.91140i | −0.0757949 | + | 0.0656766i | ||||
\(848\) | −9.27269 | + | 31.5799i | −0.318426 | + | 1.08446i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −49.3323 | + | 11.4961i | −1.69109 | + | 0.394082i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.9450 | − | 50.2425i | 0.785622 | − | 1.72027i | 0.0968435 | − | 0.995300i | \(-0.469125\pi\) |
0.688778 | − | 0.724972i | \(-0.258147\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −34.0838 | − | 39.3348i | −1.16564 | − | 1.34522i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.2757 | + | 8.30249i | −0.964754 | + | 0.283277i | −0.725917 | − | 0.687782i | \(-0.758584\pi\) |
−0.238837 | + | 0.971060i | \(0.576766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0225 | − | 35.0844i | −0.545413 | − | 1.19429i | −0.958891 | − | 0.283774i | \(-0.908413\pi\) |
0.413478 | − | 0.910514i | \(-0.364314\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.1711 | + | 46.9471i | −1.02585 | + | 1.59625i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.5354 | − | 46.5526i | 0.829921 | − | 1.57466i | ||||
\(875\) | −7.99434 | −0.270258 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.2666 | − | 14.4660i | −1.66361 | − | 0.488481i | −0.691381 | − | 0.722491i | \(-0.742997\pi\) |
−0.972234 | + | 0.234009i | \(0.924815\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.4058 | − | 17.7792i | 0.519328 | − | 0.599337i | ||||
\(881\) | 28.1874 | + | 4.05273i | 0.949656 | + | 0.136540i | 0.599699 | − | 0.800226i | \(-0.295287\pi\) |
0.349957 | + | 0.936766i | \(0.386196\pi\) | |||||||
\(882\) | −26.4142 | + | 7.75591i | −0.889412 | + | 0.261155i | ||||
\(883\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.76708 | − | 47.0661i | −0.227216 | − | 1.58032i | −0.709754 | − | 0.704450i | \(-0.751194\pi\) |
0.482538 | − | 0.875875i | \(-0.339715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.86077 | − | 13.1486i | −0.129486 | − | 0.440989i | ||||
\(890\) | 7.04656 | − | 49.0099i | 0.236201 | − | 1.64281i | ||||
\(891\) | −17.8900 | − | 15.5018i | −0.599337 | − | 0.519328i | ||||
\(892\) | 21.3632 | − | 13.7293i | 0.715294 | − | 0.459691i | ||||
\(893\) | −80.2291 | + | 69.5189i | −2.68476 | + | 2.32636i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.3537 | + | 20.2557i | 1.48258 | + | 0.677072i | ||||
\(896\) | − | 8.08970i | − | 0.270258i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.44932 | −0.148476 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 28.7848 | + | 8.45198i | 0.959493 | + | 0.281733i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.30746 | + | 5.14651i | 0.110126 | + | 0.171360i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.30941 | + | 16.0623i | 0.0765561 | + | 0.532459i | ||||
\(911\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.61130 | + | 15.7046i | −0.152278 | + | 0.518613i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 2.60979 | + | 30.2190i | 0.0860424 | + | 0.996291i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.5515 | + | 44.4270i | 0.938768 | + | 1.46075i | ||||
\(926\) | 17.4511 | − | 20.1397i | 0.573480 | − | 0.661831i | ||||
\(927\) | 42.9573 | + | 6.17633i | 1.41090 | + | 0.202857i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.8360 | + | 17.2465i | 0.880461 | + | 0.565838i | 0.900936 | − | 0.433952i | \(-0.142881\pi\) |
−0.0204747 | + | 0.999790i | \(0.506518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.7949 | − | 20.9138i | 1.50087 | − | 0.685424i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.66641 | − | 60.2762i | 0.283271 | − | 1.97019i | ||||
\(937\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17.2391 | − | 58.7108i | 0.562276 | − | 1.91494i | ||||
\(941\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.73124 | − | 1.56278i | −0.251764 | − | 0.0508910i | ||||
\(944\) | 17.0711 | 0.555617 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −54.3043 | − | 7.80778i | −1.76186 | − | 0.253318i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(954\) | 31.7549 | − | 14.5020i | 1.02810 | − | 0.469519i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.0789 | − | 16.7599i | 0.841254 | − | 0.540641i | ||||
\(962\) | 81.0151 | − | 70.2000i | 2.61203 | − | 2.26334i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.8635 | − | 11.8115i | −0.833008 | − | 0.380422i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.7436 | 1.37454 | 0.687271 | − | 0.726401i | \(-0.258808\pi\) | ||||
0.687271 | + | 0.726401i | \(0.258808\pi\) | |||||||
\(968\) | 4.79626 | − | 10.5024i | 0.154158 | − | 0.337558i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.6919 | − | 50.8696i | −1.04913 | − | 1.63248i | −0.728175 | − | 0.685391i | \(-0.759631\pi\) |
−0.320959 | − | 0.947093i | \(-0.604005\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.66002 | + | 0.526231i | 0.117335 | + | 0.0168702i | ||||
\(974\) | 59.7499 | − | 17.5441i | 1.91451 | − | 0.562151i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.86093 | + | 40.7636i | 0.187316 | + | 1.30281i | ||||
\(980\) | −15.6886 | + | 24.4119i | −0.501153 | + | 0.779809i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.47037 | − | 45.0024i | 0.206478 | − | 1.43608i | ||||
\(983\) | 45.2358 | + | 39.1971i | 1.44280 | + | 1.25019i | 0.916585 | + | 0.399840i | \(0.130934\pi\) |
0.526214 | + | 0.850352i | \(0.323611\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.3215 | + | 28.8732i | −1.06171 | + | 0.919977i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 111.364i | 3.54296i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −24.9523 | −0.793036 | ||||||||
\(991\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.5528 | − | 17.7799i | 1.91773 | − | 0.563095i | 0.948652 | − | 0.316322i | \(-0.102448\pi\) |
0.969073 | − | 0.246773i | \(-0.0793702\pi\) | |||||||
\(998\) | −51.1188 | − | 32.8521i | −1.61814 | − | 1.03991i | ||||
\(999\) | 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 | 920.2.bn.a.339.4 | yes | 40 | |
5.4 | even | 2 | inner | 920.2.bn.a.339.1 | yes | 40 | |
8.3 | odd | 2 | inner | 920.2.bn.a.339.1 | yes | 40 | |
23.19 | odd | 22 | inner | 920.2.bn.a.19.4 | yes | 40 | |
40.19 | odd | 2 | CM | 920.2.bn.a.339.4 | yes | 40 | |
115.19 | odd | 22 | inner | 920.2.bn.a.19.1 | ✓ | 40 | |
184.19 | even | 22 | inner | 920.2.bn.a.19.1 | ✓ | 40 | |
920.19 | even | 22 | inner | 920.2.bn.a.19.4 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.bn.a.19.1 | ✓ | 40 | 115.19 | odd | 22 | inner | |
920.2.bn.a.19.1 | ✓ | 40 | 184.19 | even | 22 | inner | |
920.2.bn.a.19.4 | yes | 40 | 23.19 | odd | 22 | inner | |
920.2.bn.a.19.4 | yes | 40 | 920.19 | even | 22 | inner | |
920.2.bn.a.339.1 | yes | 40 | 5.4 | even | 2 | inner | |
920.2.bn.a.339.1 | yes | 40 | 8.3 | odd | 2 | inner | |
920.2.bn.a.339.4 | yes | 40 | 1.1 | even | 1 | trivial | |
920.2.bn.a.339.4 | yes | 40 | 40.19 | odd | 2 | CM |