Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(33,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.33");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.s (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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} + \cdots + 208849 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{20}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Root | \(-3.16141 - 2.64174i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.33 |
Dual form | 224.3.s.b.129.1 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −4.97091 | + | 2.86995i | −1.65697 | + | 0.956651i | −0.682867 | + | 0.730543i | \(0.739267\pi\) |
−0.974102 | + | 0.226109i | \(0.927400\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.45949 | + | 3.15204i | 1.09190 | + | 0.630408i | 0.934081 | − | 0.357060i | \(-0.116221\pi\) |
0.157817 | + | 0.987468i | \(0.449554\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.64993 | + | 4.13259i | 0.807133 | + | 0.590370i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.9733 | − | 20.7383i | 1.33036 | − | 2.30426i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.70557 | + | 4.68619i | 0.245961 | + | 0.426017i | 0.962401 | − | 0.271631i | \(-0.0875632\pi\) |
−0.716440 | + | 0.697648i | \(0.754230\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.9368i | 1.22591i | 0.790118 | + | 0.612955i | \(0.210019\pi\) | ||||
−0.790118 | + | 0.612955i | \(0.789981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −36.1848 | −2.41232 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.7354 | + | 10.2395i | −1.04326 | + | 0.602326i | −0.920755 | − | 0.390142i | \(-0.872426\pi\) |
−0.122505 | + | 0.992468i | \(0.539093\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.7669 | − | 6.79363i | −0.619311 | − | 0.357560i | 0.157289 | − | 0.987553i | \(-0.449724\pi\) |
−0.776601 | + | 0.629993i | \(0.783058\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −39.9456 | − | 4.32768i | −1.90217 | − | 0.206080i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.35080 | − | 4.07170i | 0.102209 | − | 0.177030i | −0.810386 | − | 0.585897i | \(-0.800742\pi\) |
0.912594 | + | 0.408866i | \(0.134076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.37071 | + | 12.7664i | 0.294828 | + | 0.510658i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 85.7918i | 3.17748i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.76543 | 0.0608770 | 0.0304385 | − | 0.999537i | \(-0.490310\pi\) | ||||
0.0304385 | + | 0.999537i | \(0.490310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.9039 | − | 6.87274i | 0.383998 | − | 0.221701i | −0.295558 | − | 0.955325i | \(-0.595506\pi\) |
0.679556 | + | 0.733623i | \(0.262172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −26.8983 | − | 15.5297i | −0.815099 | − | 0.470598i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.8197 | + | 40.3706i | 0.509133 | + | 1.15345i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.23363 | + | 9.06491i | −0.141449 | + | 0.244998i | −0.928043 | − | 0.372474i | \(-0.878510\pi\) |
0.786593 | + | 0.617472i | \(0.211843\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −45.7380 | − | 79.2205i | −1.17277 | − | 2.03130i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2412i | 0.274175i | 0.990559 | + | 0.137088i | \(0.0437742\pi\) | ||||
−0.990559 | + | 0.137088i | \(0.956226\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −49.1704 | −1.14350 | −0.571749 | − | 0.820428i | \(-0.693735\pi\) | ||||
−0.571749 | + | 0.820428i | \(0.693735\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 130.736 | − | 75.4805i | 2.90525 | − | 1.67734i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.02382 | + | 5.20991i | 0.191996 | + | 0.110849i | 0.592917 | − | 0.805264i | \(-0.297976\pi\) |
−0.400921 | + | 0.916113i | \(0.631310\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8434 | + | 46.6977i | 0.302927 | + | 0.953014i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 58.7740 | − | 101.800i | 1.15243 | − | 1.99607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −16.0506 | − | 27.8005i | −0.302842 | − | 0.524538i | 0.673936 | − | 0.738789i | \(-0.264602\pi\) |
−0.976779 | + | 0.214251i | \(0.931269\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 34.1123i | 0.620223i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 77.9897 | 1.36824 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 57.2860 | − | 33.0741i | 0.970950 | − | 0.560578i | 0.0714242 | − | 0.997446i | \(-0.477246\pi\) |
0.899526 | + | 0.436868i | \(0.143912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27.6804 | − | 15.9813i | −0.453778 | − | 0.261989i | 0.255647 | − | 0.966770i | \(-0.417712\pi\) |
−0.709424 | + | 0.704782i | \(0.751045\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 153.351 | − | 67.6894i | 2.43415 | − | 1.07444i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −50.2335 | + | 87.0070i | −0.772824 | + | 1.33857i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49.2688 | + | 85.3361i | 0.735356 | + | 1.27367i | 0.954567 | + | 0.297996i | \(0.0963182\pi\) |
−0.219211 | + | 0.975677i | \(0.570348\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 26.9867i | 0.391112i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61.7537 | −0.869770 | −0.434885 | − | 0.900486i | \(-0.643211\pi\) | ||||
−0.434885 | + | 0.900486i | \(0.643211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6253 | − | 9.02127i | 0.214045 | − | 0.123579i | −0.389145 | − | 0.921177i | \(-0.627229\pi\) |
0.603190 | + | 0.797598i | \(0.293896\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −73.2782 | − | 42.3072i | −0.977043 | − | 0.564096i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.07980 | + | 37.6576i | −0.0529844 | + | 0.489060i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0018 | − | 25.9839i | 0.189896 | − | 0.328910i | −0.755319 | − | 0.655357i | \(-0.772518\pi\) |
0.945215 | + | 0.326447i | \(0.105851\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −138.459 | − | 239.818i | −1.70937 | − | 2.96072i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 63.4583i | − | 0.764558i | −0.924047 | − | 0.382279i | \(-0.875139\pi\) | ||
0.924047 | − | 0.382279i | \(-0.124861\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −129.102 | −1.51884 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.77580 | + | 5.06671i | −0.100871 | + | 0.0582381i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 119.129 | + | 68.7791i | 1.33853 | + | 0.772799i | 0.986589 | − | 0.163224i | \(-0.0521894\pi\) |
0.351938 | + | 0.936023i | \(0.385523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −65.8604 | + | 90.0420i | −0.723741 | + | 0.989472i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −39.4489 | + | 68.3275i | −0.424182 | + | 0.734705i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −42.8276 | − | 74.1796i | −0.450817 | − | 0.780838i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 131.075i | 1.35129i | 0.737228 | + | 0.675644i | \(0.236134\pi\) | ||||
−0.737228 | + | 0.675644i | \(0.763866\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 129.578 | 1.30887 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −99.2877 | + | 57.3238i | −0.983046 | + | 0.567562i | −0.903188 | − | 0.429244i | \(-0.858780\pi\) |
−0.0798578 | + | 0.996806i | \(0.525447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 173.736 | + | 100.307i | 1.68676 | + | 0.973851i | 0.956973 | + | 0.290176i | \(0.0937137\pi\) |
0.729786 | + | 0.683675i | \(0.239620\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −204.442 | − | 149.537i | −1.94706 | − | 1.42416i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 49.7054 | − | 86.0923i | 0.464537 | − | 0.804601i | −0.534644 | − | 0.845078i | \(-0.679554\pi\) |
0.999181 | + | 0.0404762i | \(0.0128875\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.59446 | + | 13.1540i | 0.0696740 | + | 0.120679i | 0.898758 | − | 0.438445i | \(-0.144471\pi\) |
−0.829084 | + | 0.559124i | \(0.811137\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 60.0811i | − | 0.541271i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 114.050 | 1.00929 | 0.504645 | − | 0.863327i | \(-0.331623\pi\) | ||||
0.504645 | + | 0.863327i | \(0.331623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.6683 | − | 14.8196i | 0.223203 | − | 0.128866i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 330.503 | + | 190.816i | 2.82481 | + | 1.63091i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −142.520 | − | 15.4405i | −1.19764 | − | 0.129752i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 45.8598 | − | 79.4315i | 0.379006 | − | 0.656458i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −32.2617 | − | 55.8789i | −0.262290 | − | 0.454300i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 64.6709i | − | 0.517367i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 27.7466 | 0.218477 | 0.109239 | − | 0.994016i | \(-0.465159\pi\) | ||||
0.109239 | + | 0.994016i | \(0.465159\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 244.422 | − | 141.117i | 1.89474 | − | 1.09393i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −158.266 | − | 91.3750i | −1.20814 | − | 0.697519i | −0.245786 | − | 0.969324i | \(-0.579046\pi\) |
−0.962352 | + | 0.271805i | \(0.912379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −38.4069 | − | 87.0114i | −0.288774 | − | 0.654221i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −270.419 | + | 468.380i | −2.00311 | + | 3.46948i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −50.5536 | − | 87.5614i | −0.369004 | − | 0.639134i | 0.620406 | − | 0.784281i | \(-0.286968\pi\) |
−0.989410 | + | 0.145147i | \(0.953635\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 88.5595i | 0.637119i | 0.947903 | + | 0.318559i | \(0.103199\pi\) | ||||
−0.947903 | + | 0.318559i | \(0.896801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −59.8088 | −0.424176 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −74.6830 | + | 43.1182i | −0.522258 | + | 0.301526i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.63837 | + | 5.56472i | 0.0664715 | + | 0.0383773i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −207.805 | − | 189.530i | −1.41364 | − | 1.28932i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 63.5182 | − | 110.017i | 0.426296 | − | 0.738367i | −0.570244 | − | 0.821475i | \(-0.693151\pi\) |
0.996541 | + | 0.0831082i | \(0.0264847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 145.693 | + | 252.347i | 0.964852 | + | 1.67117i | 0.710011 | + | 0.704190i | \(0.248690\pi\) |
0.254841 | + | 0.966983i | \(0.417977\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 490.403i | 3.20525i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 86.6526 | 0.559049 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 186.624 | − | 107.747i | 1.18869 | − | 0.686289i | 0.230679 | − | 0.973030i | \(-0.425905\pi\) |
0.958008 | + | 0.286741i | \(0.0925719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 159.572 | + | 92.1292i | 1.00360 | + | 0.579429i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.1085 | − | 13.2899i | 0.187009 | − | 0.0825462i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −87.0084 | + | 150.703i | −0.533794 | + | 0.924558i | 0.465427 | + | 0.885086i | \(0.345901\pi\) |
−0.999221 | + | 0.0394714i | \(0.987433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −97.9006 | − | 169.569i | −0.593337 | − | 1.02769i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 241.170i | − | 1.44413i | −0.691823 | − | 0.722067i | \(-0.743192\pi\) | ||
0.691823 | − | 0.722067i | \(-0.256808\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −84.9827 | −0.502856 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −281.777 | + | 162.684i | −1.64782 | + | 0.951369i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −187.037 | − | 107.986i | −1.08114 | − | 0.624197i | −0.149937 | − | 0.988696i | \(-0.547907\pi\) |
−0.931204 | + | 0.364499i | \(0.881240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.1145 | + | 102.590i | −0.0635114 | + | 0.586227i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −189.842 | + | 328.817i | −1.07256 | + | 1.85772i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 89.0372 | + | 154.217i | 0.497414 | + | 0.861547i | 0.999996 | − | 0.00298291i | \(-0.000949492\pi\) |
−0.502581 | + | 0.864530i | \(0.667616\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 172.429i | − | 0.952648i | −0.879270 | − | 0.476324i | \(-0.841969\pi\) | ||
0.879270 | − | 0.476324i | \(-0.158031\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 183.462 | 1.00253 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −57.1459 | + | 32.9932i | −0.308897 | + | 0.178342i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −95.9688 | − | 55.4076i | −0.513202 | − | 0.296297i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −354.543 | + | 484.718i | −1.87589 | + | 2.56464i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 69.6230 | − | 120.591i | 0.364518 | − | 0.631364i | −0.624181 | − | 0.781280i | \(-0.714567\pi\) |
0.988699 | + | 0.149916i | \(0.0479004\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.6165 | + | 37.4409i | 0.112003 | + | 0.193994i | 0.916578 | − | 0.399857i | \(-0.130940\pi\) |
−0.804575 | + | 0.593851i | \(0.797607\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 576.672i | − | 2.95729i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 205.910 | 1.04523 | 0.522614 | − | 0.852570i | \(-0.324957\pi\) | ||||
0.522614 | + | 0.852570i | \(0.324957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −260.927 | + | 150.646i | −1.31119 | + | 0.757016i | −0.982293 | − | 0.187350i | \(-0.940010\pi\) |
−0.328896 | + | 0.944366i | \(0.606677\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −489.822 | − | 282.799i | −2.43692 | − | 1.40696i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.97457 | + | 7.29581i | 0.0491358 | + | 0.0359400i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.4327 | + | 61.3712i | −0.172842 | + | 0.299372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −56.2935 | − | 97.5032i | −0.271949 | − | 0.471030i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 73.5226i | − | 0.351783i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 310.102 | 1.46968 | 0.734839 | − | 0.678241i | \(-0.237258\pi\) | ||||
0.734839 | + | 0.678241i | \(0.237258\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 306.972 | − | 177.230i | 1.44118 | − | 0.832067i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −268.446 | − | 154.987i | −1.24858 | − | 0.720871i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 95.6586 | + | 10.3636i | 0.440823 | + | 0.0477585i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −51.7812 | + | 89.6877i | −0.236444 | + | 0.409533i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −163.186 | − | 282.646i | −0.738398 | − | 1.27894i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 266.090i | 1.19323i | 0.802528 | + | 0.596614i | \(0.203488\pi\) | ||||
−0.802528 | + | 0.596614i | \(0.796512\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 353.006 | 1.56892 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 264.188 | − | 152.529i | 1.16382 | − | 0.671933i | 0.211605 | − | 0.977355i | \(-0.432131\pi\) |
0.952217 | + | 0.305422i | \(0.0987976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 171.968 | + | 99.2857i | 0.750952 | + | 0.433562i | 0.826038 | − | 0.563615i | \(-0.190590\pi\) |
−0.0750860 | + | 0.997177i | \(0.523923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −87.7954 | − | 198.901i | −0.380066 | − | 0.861045i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 123.928 | − | 214.650i | 0.531881 | − | 0.921246i | −0.467426 | − | 0.884032i | \(-0.654819\pi\) |
0.999307 | − | 0.0372134i | \(-0.0118481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.8437 | + | 56.8869i | 0.139760 | + | 0.242072i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 172.218i | 0.726658i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 120.884 | 0.505790 | 0.252895 | − | 0.967494i | \(-0.418617\pi\) | ||||
0.252895 | + | 0.967494i | \(0.418617\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 125.956 | − | 72.7209i | 0.522640 | − | 0.301746i | −0.215374 | − | 0.976532i | \(-0.569097\pi\) |
0.738014 | + | 0.674785i | \(0.235764\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 707.854 | + | 408.680i | 2.91298 | + | 1.68181i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −66.1555 | + | 301.733i | −0.270023 | + | 1.23156i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 108.269 | − | 187.527i | 0.438336 | − | 0.759220i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 182.123 | + | 315.446i | 0.731416 | + | 1.26685i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 212.061i | 0.844865i | 0.906394 | + | 0.422432i | \(0.138824\pi\) | ||||
−0.906394 | + | 0.422432i | \(0.861176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.4410 | 0.100557 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 641.753 | − | 370.516i | 2.51668 | − | 1.45300i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.71846 | + | 5.03361i | 0.0339240 | + | 0.0195860i | 0.516866 | − | 0.856066i | \(-0.327099\pi\) |
−0.482942 | + | 0.875652i | \(0.660432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −67.0312 | + | 29.5877i | −0.258808 | + | 0.114238i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.1380 | − | 36.6121i | 0.0809886 | − | 0.140276i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0417642 | + | 0.0723377i | 0.000158799 | + | 0.000275048i | 0.866105 | − | 0.499862i | \(-0.166616\pi\) |
−0.865946 | + | 0.500138i | \(0.833283\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 202.369i | − | 0.763657i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −789.572 | −2.95720 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.10371 | + | 0.637226i | −0.00410301 | + | 0.00236887i | −0.502050 | − | 0.864839i | \(-0.667421\pi\) |
0.497947 | + | 0.867207i | \(0.334087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −309.749 | − | 178.834i | −1.14298 | − | 0.659903i | −0.195817 | − | 0.980641i | \(-0.562736\pi\) |
−0.947168 | + | 0.320738i | \(0.896069\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 68.9695 | − | 636.607i | 0.252636 | − | 2.33189i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −39.8840 | + | 69.0810i | −0.145033 | + | 0.251204i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 84.6074 | + | 146.544i | 0.305442 | + | 0.529041i | 0.977360 | − | 0.211585i | \(-0.0678625\pi\) |
−0.671918 | + | 0.740626i | \(0.734529\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 329.157i | − | 1.17977i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 246.835 | 0.878418 | 0.439209 | − | 0.898385i | \(-0.355259\pi\) | ||||
0.439209 | + | 0.898385i | \(0.355259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 198.888 | − | 114.828i | 0.702783 | − | 0.405752i | −0.105600 | − | 0.994409i | \(-0.533676\pi\) |
0.808383 | + | 0.588657i | \(0.200343\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 425.784 | + | 245.827i | 1.49398 | + | 0.862549i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −46.4552 | + | 63.5119i | −0.161865 | + | 0.221296i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 65.1965 | − | 112.924i | 0.225593 | − | 0.390739i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −376.179 | − | 651.561i | −1.29271 | − | 2.23904i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 228.171i | 0.778740i | 0.921081 | + | 0.389370i | \(0.127307\pi\) | ||||
−0.921081 | + | 0.389370i | \(0.872693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 417.004 | 1.41357 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −402.036 | + | 232.116i | −1.35366 | + | 0.781535i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 64.8900 | + | 37.4643i | 0.217023 | + | 0.125299i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −277.810 | − | 203.201i | −0.922955 | − | 0.675087i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 329.033 | − | 569.902i | 1.08592 | − | 1.88087i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −100.747 | − | 174.500i | −0.330319 | − | 0.572130i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 333.745i | 1.08712i | 0.839371 | + | 0.543559i | \(0.182924\pi\) | ||||
−0.839371 | + | 0.543559i | \(0.817076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1151.50 | −3.72654 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −215.654 | + | 124.508i | −0.693421 | + | 0.400347i | −0.804892 | − | 0.593421i | \(-0.797777\pi\) |
0.111471 | + | 0.993768i | \(0.464444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.5147 | − | 19.9271i | −0.110271 | − | 0.0636648i | 0.443850 | − | 0.896101i | \(-0.353612\pi\) |
−0.554121 | + | 0.832436i | \(0.686946\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1050.58 | + | 113.819i | 3.33517 | + | 0.361330i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 221.206 | − | 383.140i | 0.697811 | − | 1.20864i | −0.271413 | − | 0.962463i | \(-0.587491\pi\) |
0.969224 | − | 0.246181i | \(-0.0791756\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.77650 | + | 8.27315i | 0.0149734 | + | 0.0259346i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 570.609i | 1.77760i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 278.255 | 0.861470 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −203.457 | + | 117.466i | −0.626021 | + | 0.361433i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −75.5027 | − | 43.5915i | −0.230895 | − | 0.133307i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.4535 | + | 66.7274i | 0.0895245 | + | 0.202819i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 71.9641 | − | 124.646i | 0.217414 | − | 0.376573i | −0.736602 | − | 0.676326i | \(-0.763571\pi\) |
0.954017 | + | 0.299753i | \(0.0969044\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 125.327 | + | 217.073i | 0.376359 | + | 0.651872i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 621.189i | 1.85430i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −428.372 | −1.27113 | −0.635567 | − | 0.772046i | \(-0.719234\pi\) | ||||
−0.635567 | + | 0.772046i | \(0.719234\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −566.930 | + | 327.317i | −1.67236 | + | 0.965538i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 64.4139 | + | 37.1894i | 0.188897 | + | 0.109060i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −109.118 | + | 325.180i | −0.318129 | + | 0.948047i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −85.0632 | + | 147.334i | −0.246560 | + | 0.427054i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 122.803 | + | 212.700i | 0.353898 | + | 0.612969i | 0.986929 | − | 0.161158i | \(-0.0515228\pi\) |
−0.633031 | + | 0.774126i | \(0.718189\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 675.578i | − | 1.93575i | −0.251428 | − | 0.967876i | \(-0.580900\pi\) | ||
0.251428 | − | 0.967876i | \(-0.419100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1367.25 | −3.89530 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −492.343 | + | 284.254i | −1.39474 | + | 0.805252i | −0.993835 | − | 0.110868i | \(-0.964637\pi\) |
−0.400903 | + | 0.916121i | \(0.631304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −337.144 | − | 194.650i | −0.949701 | − | 0.548310i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 752.765 | − | 332.272i | 2.10859 | − | 0.930733i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 336.956 | − | 583.625i | 0.938596 | − | 1.62570i | 0.170504 | − | 0.985357i | \(-0.445460\pi\) |
0.768092 | − | 0.640339i | \(-0.221206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −88.1931 | − | 152.755i | −0.244302 | − | 0.423144i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 526.462i | 1.45031i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 113.742 | 0.311621 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 37.3366 | − | 21.5563i | 0.101735 | − | 0.0587366i | −0.448269 | − | 0.893899i | \(-0.647959\pi\) |
0.550004 | + | 0.835162i | \(0.314626\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 233.123 | + | 134.594i | 0.631771 | + | 0.364753i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.2032 | − | 223.402i | 0.0652377 | − | 0.602161i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −316.582 | + | 548.337i | −0.848746 | + | 1.47007i | 0.0335811 | + | 0.999436i | \(0.489309\pi\) |
−0.882328 | + | 0.470636i | \(0.844025\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 185.603 | + | 321.473i | 0.494940 | + | 0.857261i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.1354i | 0.0746297i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −611.641 | −1.61383 | −0.806914 | − | 0.590669i | \(-0.798864\pi\) | ||||
−0.806914 | + | 0.590669i | \(0.798864\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −137.926 | + | 79.6316i | −0.362010 | + | 0.209007i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −555.198 | − | 320.544i | −1.44960 | − | 0.836929i | −0.451145 | − | 0.892450i | \(-0.648984\pi\) |
−0.998457 | + | 0.0555219i | \(0.982318\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −140.972 | + | 192.732i | −0.366161 | + | 0.500602i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −588.731 | + | 1019.71i | −1.52127 | + | 2.63492i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 177.180 | + | 306.884i | 0.455475 | + | 0.788905i | 0.998715 | − | 0.0506717i | \(-0.0161362\pi\) |
−0.543241 | + | 0.839577i | \(0.682803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 96.2843i | 0.246251i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1048.97 | 2.66913 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 163.805 | − | 94.5726i | 0.414695 | − | 0.239424i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 271.796 | + | 156.922i | 0.684625 | + | 0.395268i | 0.801595 | − | 0.597867i | \(-0.203985\pi\) |
−0.116970 | + | 0.993135i | \(0.537318\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 440.636 | + | 322.299i | 1.10435 | + | 0.807768i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −161.060 | + | 278.963i | −0.401645 | + | 0.695669i | −0.993925 | − | 0.110063i | \(-0.964895\pi\) |
0.592280 | + | 0.805732i | \(0.298228\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 109.530 | + | 189.711i | 0.271786 | + | 0.470747i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1745.72i | − | 4.31041i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −56.6398 | −0.139164 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 413.847 | − | 238.935i | 1.01185 | − | 0.584192i | 0.100117 | − | 0.994976i | \(-0.468078\pi\) |
0.911733 | + | 0.410784i | \(0.134745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 502.594 | + | 290.173i | 1.22286 | + | 0.706017i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 460.344 | + | 49.8733i | 1.11463 | + | 0.120759i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 200.023 | − | 346.450i | 0.481984 | − | 0.834820i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −254.162 | − | 440.221i | −0.609500 | − | 1.05569i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 194.885i | 0.465119i | 0.972582 | + | 0.232560i | \(0.0747101\pi\) | ||||
−0.972582 | + | 0.232560i | \(0.925290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 290.331 | 0.689621 | 0.344811 | − | 0.938672i | \(-0.387943\pi\) | ||||
0.344811 | + | 0.938672i | \(0.387943\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 216.089 | − | 124.759i | 0.510850 | − | 0.294939i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −261.445 | − | 150.945i | −0.615165 | − | 0.355166i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −90.3483 | − | 204.685i | −0.211589 | − | 0.479356i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 247.495 | − | 428.673i | 0.576911 | − | 0.999239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −191.169 | − | 331.115i | −0.443549 | − | 0.768249i | 0.554401 | − | 0.832249i | \(-0.312947\pi\) |
−0.997950 | + | 0.0640009i | \(0.979614\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 295.254i | 0.681879i | 0.940085 | + | 0.340940i | \(0.110745\pi\) | ||||
−0.940085 | + | 0.340940i | \(0.889255\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −63.8819 | −0.146855 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −55.3233 | + | 31.9409i | −0.126598 | + | 0.0730913i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −42.5045 | − | 24.5400i | −0.0968212 | − | 0.0558997i | 0.450808 | − | 0.892621i | \(-0.351136\pi\) |
−0.547629 | + | 0.836721i | \(0.684469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1146.16 | + | 251.297i | 2.59899 | + | 0.569835i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 316.862 | − | 548.821i | 0.715264 | − | 1.23887i | −0.247594 | − | 0.968864i | \(-0.579640\pi\) |
0.962858 | − | 0.270010i | \(-0.0870269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 433.589 | + | 750.998i | 0.974357 | + | 1.68764i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 729.177i | 1.63127i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.3296 | −0.0608677 | −0.0304339 | − | 0.999537i | \(-0.509689\pi\) | ||||
−0.0304339 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −52.6783 | + | 30.4138i | −0.116803 | + | 0.0674364i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1448.45 | − | 836.263i | −3.19746 | − | 1.84605i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −643.380 | + | 283.989i | −1.41402 | + | 0.624152i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −169.555 | + | 293.677i | −0.371017 | + | 0.642620i | −0.989722 | − | 0.143003i | \(-0.954324\pi\) |
0.618705 | + | 0.785623i | \(0.287658\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −878.469 | − | 1521.55i | −1.91388 | − | 3.31493i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 580.237i | 1.25865i | 0.777143 | + | 0.629324i | \(0.216668\pi\) | ||||
−0.777143 | + | 0.629324i | \(0.783332\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 433.685 | 0.936684 | 0.468342 | − | 0.883547i | \(-0.344852\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −430.742 | + | 248.689i | −0.926327 | + | 0.534815i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 86.6558 | + | 50.0308i | 0.185558 | + | 0.107132i | 0.589902 | − | 0.807475i | \(-0.299167\pi\) |
−0.404343 | + | 0.914607i | \(0.632500\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −74.2938 | + | 685.751i | −0.158409 | + | 1.46216i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −618.460 | + | 1071.20i | −1.31308 | + | 2.27432i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −133.034 | − | 230.422i | −0.281256 | − | 0.487150i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 200.296i | − | 0.421675i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −768.715 | −1.61156 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −418.996 | + | 241.907i | −0.874730 | + | 0.505026i | −0.868917 | − | 0.494957i | \(-0.835184\pi\) |
−0.00581309 | + | 0.999983i | \(0.501850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −144.466 | − | 83.4075i | −0.300345 | − | 0.173404i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −111.525 | + | 152.473i | −0.230901 | + | 0.315679i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −413.154 | + | 715.603i | −0.851863 | + | 1.47547i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 114.763 | + | 198.776i | 0.235654 | + | 0.408164i | 0.959462 | − | 0.281836i | \(-0.0909436\pi\) |
−0.723809 | + | 0.690001i | \(0.757610\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 998.840i | − | 2.04262i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −221.445 | −0.451008 | −0.225504 | − | 0.974242i | \(-0.572403\pi\) | ||||
−0.225504 | + | 0.974242i | \(0.572403\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.3107 | + | 18.0772i | −0.0635105 | + | 0.0366678i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 707.431 | + | 408.436i | 1.42915 | + | 0.825122i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −348.904 | − | 255.203i | −0.702020 | − | 0.513486i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 256.703 | − | 444.622i | 0.514435 | − | 0.891027i | −0.485425 | − | 0.874278i | \(-0.661335\pi\) |
0.999860 | − | 0.0167486i | \(-0.00533150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 692.148 | + | 1198.83i | 1.38153 | + | 2.39288i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 360.553i | − | 0.716806i | −0.933567 | − | 0.358403i | \(-0.883321\pi\) | ||
0.933567 | − | 0.358403i | \(-0.116679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −722.747 | −1.43118 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 422.441 | − | 243.896i | 0.833217 | − | 0.481058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 163.560 | + | 94.4312i | 0.321335 | + | 0.185523i | 0.651988 | − | 0.758230i | \(-0.273935\pi\) |
−0.330652 | + | 0.943753i | \(0.607269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 125.563 | + | 13.6034i | 0.245720 | + | 0.0266212i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 582.838 | − | 1009.51i | 1.13614 | − | 1.96785i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 632.341 | + | 1095.25i | 1.22785 | + | 2.12669i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 56.3831i | 0.109058i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1239.66 | 2.38856 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −409.657 | + | 236.516i | −0.786291 | + | 0.453965i | −0.838655 | − | 0.544663i | \(-0.816658\pi\) |
0.0523644 | + | 0.998628i | \(0.483324\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −362.994 | − | 209.575i | −0.694061 | − | 0.400716i | 0.111071 | − | 0.993812i | \(-0.464572\pi\) |
−0.805131 | + | 0.593096i | \(0.797905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −239.178 | − | 541.862i | −0.455578 | − | 1.03212i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −140.747 | + | 243.782i | −0.267073 | + | 0.462584i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 253.448 | + | 438.984i | 0.479107 | + | 0.829837i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1584.02i | − | 2.98309i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −179.149 | −0.336114 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 542.733 | − | 313.347i | 1.01445 | − | 0.585695i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −885.191 | − | 511.065i | −1.64840 | − | 0.951705i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −178.674 | + | 195.903i | −0.331492 | + | 0.363456i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 309.243 | − | 535.625i | 0.571614 | − | 0.990065i | −0.424786 | − | 0.905294i | \(-0.639651\pi\) |
0.996400 | − | 0.0847712i | \(-0.0270159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 494.864 | + | 857.129i | 0.911352 | + | 1.57851i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 95.7522i | 0.175692i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −255.031 | −0.466236 | −0.233118 | − | 0.972448i | \(-0.574893\pi\) | ||||
−0.233118 | + | 0.972448i | \(0.574893\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −662.851 | + | 382.697i | −1.20738 | + | 0.697081i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.7737 | − | 11.9937i | −0.0377018 | − | 0.0217672i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 192.140 | − | 84.8108i | 0.347450 | − | 0.153365i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 189.378 | − | 328.013i | 0.341222 | − | 0.591014i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −244.130 | − | 422.845i | −0.438294 | − | 0.759148i | 0.559264 | − | 0.828990i | \(-0.311084\pi\) |
−0.997558 | + | 0.0698419i | \(0.977751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 783.621i | − | 1.40183i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 636.069 | 1.13381 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.5152 | + | 24.5462i | −0.0755155 | + | 0.0435989i | −0.537282 | − | 0.843402i | \(-0.680549\pi\) |
0.461767 | + | 0.887001i | \(0.347216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 622.654 | + | 359.489i | 1.10204 | + | 0.636264i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 208.786 | − | 1927.15i | 0.368230 | − | 3.39886i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 304.056 | − | 526.641i | 0.534370 | − | 0.925556i | −0.464824 | − | 0.885403i | \(-0.653882\pi\) |
0.999194 | − | 0.0401523i | \(-0.0127843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 150.396 | + | 260.494i | 0.263391 | + | 0.456207i | 0.967141 | − | 0.254241i | \(-0.0818257\pi\) |
−0.703750 | + | 0.710448i | \(0.748492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 799.259i | 1.39487i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 69.3082 | 0.120536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −150.719 | + | 87.0176i | −0.261211 | + | 0.150810i | −0.624887 | − | 0.780715i | \(-0.714855\pi\) |
0.363676 | + | 0.931526i | \(0.381522\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −214.907 | − | 124.077i | −0.371170 | − | 0.214295i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 262.247 | − | 358.535i | 0.451372 | − | 0.617100i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 86.8523 | − | 150.433i | 0.148975 | − | 0.258032i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1202.92 | + | 2083.52i | 2.05627 | + | 3.56157i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 477.592i | − | 0.813614i | −0.913514 | − | 0.406807i | \(-0.866642\pi\) | ||
0.913514 | − | 0.406807i | \(-0.133358\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −186.764 | −0.317086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1023.56 | + | 590.952i | −1.73191 | + | 0.999918i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 382.387 | + | 220.771i | 0.644834 | + | 0.372295i | 0.786474 | − | 0.617623i | \(-0.211904\pi\) |
−0.141640 | + | 0.989918i | \(0.545238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −729.416 | − | 533.525i | −1.22591 | − | 0.896680i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 864.695 | − | 1497.70i | 1.44840 | − | 2.50870i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −146.046 | − | 252.959i | −0.243816 | − | 0.422302i | 0.717982 | − | 0.696062i | \(-0.245066\pi\) |
−0.961798 | + | 0.273759i | \(0.911733\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 614.010i | − | 1.02165i | −0.859685 | − | 0.510824i | \(-0.829340\pi\) | ||
0.859685 | − | 0.510824i | \(-0.170660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2359.64 | 3.91316 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 500.742 | − | 289.104i | 0.827673 | − | 0.477857i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −281.659 | − | 162.616i | −0.464019 | − | 0.267901i | 0.249714 | − | 0.968320i | \(-0.419663\pi\) |
−0.713732 | + | 0.700418i | \(0.752997\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −70.5213 | − | 7.64023i | −0.115799 | − | 0.0125455i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −83.0294 | + | 143.811i | −0.135891 | + | 0.235370i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −278.468 | − | 482.321i | −0.454271 | − | 0.786820i | 0.544375 | − | 0.838842i | \(-0.316767\pi\) |
−0.998646 | + | 0.0520217i | \(0.983434\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 406.761i | − | 0.661399i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 277.944 | 0.450476 | 0.225238 | − | 0.974304i | \(-0.427684\pi\) | ||||
0.225238 | + | 0.974304i | \(0.427684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 111.665 | − | 64.4696i | 0.180395 | − | 0.104151i | −0.407083 | − | 0.913391i | \(-0.633454\pi\) |
0.587478 | + | 0.809240i | \(0.300121\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 349.319 | + | 201.679i | 0.562510 | + | 0.324765i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 388.834 | + | 880.908i | 0.624132 | + | 1.41398i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 388.113 | − | 672.231i | 0.620981 | − | 1.07557i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 211.006 | + | 365.474i | 0.336533 | + | 0.582893i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 214.360i | − | 0.340795i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 279.339 | 0.442692 | 0.221346 | − | 0.975195i | \(-0.428955\pi\) | ||||
0.221346 | + | 0.975195i | \(0.428955\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1541.49 | + | 889.979i | −2.43521 | + | 1.40597i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 151.483 | + | 87.4585i | 0.238555 | + | 0.137730i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −744.213 | + | 236.557i | −1.16831 | + | 0.371361i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −739.394 | + | 1280.67i | −1.15711 | + | 2.00417i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 441.133 | + | 764.064i | 0.688194 | + | 1.19199i | 0.972421 | + | 0.233231i | \(0.0749297\pi\) |
−0.284227 | + | 0.958757i | \(0.591737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 575.210i | − | 0.894572i | −0.894391 | − | 0.447286i | \(-0.852391\pi\) | ||
0.894391 | − | 0.447286i | \(-0.147609\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1779.22 | 2.75849 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 406.207 | − | 234.524i | 0.627832 | − | 0.362479i | −0.152080 | − | 0.988368i | \(-0.548597\pi\) |
0.779912 | + | 0.625889i | \(0.215264\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 309.983 | + | 178.969i | 0.477632 | + | 0.275761i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −505.253 | + | 223.019i | −0.776119 | + | 0.342580i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −412.463 | + | 714.407i | −0.631644 | + | 1.09404i | 0.355572 | + | 0.934649i | \(0.384286\pi\) |
−0.987216 | + | 0.159390i | \(0.949047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −576.035 | − | 997.722i | −0.879443 | − | 1.52324i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 432.056i | − | 0.657620i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 888.926 | 1.34890 | 0.674451 | − | 0.738320i | \(-0.264381\pi\) | ||||
0.674451 | + | 0.738320i | \(0.264381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −131.019 | + | 75.6439i | −0.198214 | + | 0.114439i | −0.595822 | − | 0.803117i | \(-0.703174\pi\) |
0.397608 | + | 0.917555i | \(0.369840\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1622.36 | + | 936.672i | 2.44700 | + | 1.41278i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 64.5809 | − | 596.098i | 0.0971141 | − | 0.896388i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.15017 | − | 7.18831i | 0.00622215 | − | 0.0107771i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −763.666 | − | 1322.71i | −1.14150 | − | 1.97714i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 172.954i | − | 0.257756i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −904.158 | −1.34347 | −0.671737 | − | 0.740790i | \(-0.734452\pi\) | ||||
−0.671737 | + | 0.740790i | \(0.734452\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1095.26 | + | 632.347i | −1.62260 | + | 0.936810i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −762.576 | − | 440.273i | −1.12640 | − | 0.650330i | −0.183376 | − | 0.983043i | \(-0.558703\pi\) |
−0.943028 | + | 0.332713i | \(0.892036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −541.679 | + | 740.564i | −0.797760 | + | 1.09067i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −875.501 | + | 1516.41i | −1.28561 | + | 2.22674i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 272.776 | + | 472.461i | 0.399379 | + | 0.691744i | 0.993649 | − | 0.112521i | \(-0.0358926\pi\) |
−0.594271 | + | 0.804265i | \(0.702559\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 637.388i | − | 0.930493i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1139.78 | −1.65907 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 443.052 | − | 255.796i | 0.643037 | − | 0.371257i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −815.732 | − | 470.963i | −1.18051 | − | 0.681568i | −0.224377 | − | 0.974502i | \(-0.572035\pi\) |
−0.956132 | + | 0.292935i | \(0.905368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 732.107 | + | 535.493i | 1.05643 | + | 0.772718i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −279.143 | + | 483.490i | −0.401645 | + | 0.695669i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −115.105 | − | 199.367i | −0.165143 | − | 0.286036i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1422.67i | 2.03530i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −304.580 | −0.434494 | −0.217247 | − | 0.976117i | \(-0.569708\pi\) | ||||
−0.217247 | + | 0.976117i | \(0.569708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 123.167 | − | 71.1107i | 0.175203 | − | 0.101153i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −326.526 | − | 188.520i | −0.463157 | − | 0.267404i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −797.864 | − | 86.4400i | −1.12852 | − | 0.122263i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 321.938 | − | 557.614i | 0.454074 | − | 0.786479i | −0.544561 | − | 0.838722i | \(-0.683304\pi\) |
0.998634 | + | 0.0522425i | \(0.0166369\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −359.242 | − | 622.225i | −0.505262 | − | 0.875140i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 64.6257i | − | 0.0906391i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −543.641 | −0.760338 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −600.902 | + | 346.931i | −0.838079 | + | 0.483865i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 628.047 | + | 362.603i | 0.873500 | + | 0.504316i | 0.868510 | − | 0.495672i | \(-0.165078\pi\) |
0.00499056 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 567.071 | + | 1284.71i | 0.786506 | + | 1.78184i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −417.411 | + | 722.977i | −0.577332 | + | 0.999968i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.0125 | + | 22.5383i | 0.0179483 | + | 0.0310873i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1090.68i | − | 1.50025i | −0.661295 | − | 0.750126i | \(-0.729993\pi\) | ||
0.661295 | − | 0.750126i | \(-0.270007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2199.30 | −3.01688 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 872.058 | − | 503.483i | 1.19297 | − | 0.688759i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −204.559 | − | 118.102i | −0.279071 | − | 0.161122i | 0.353932 | − | 0.935271i | \(-0.384845\pi\) |
−0.633003 | + | 0.774149i | \(0.718178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −537.106 | − | 1689.75i | −0.730757 | − | 2.29898i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −266.601 | + | 461.766i | −0.361738 | + | 0.626548i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.140534 | + | 0.243412i | 0.000190168 | + | 0.000329381i | 0.866120 | − | 0.499835i | \(-0.166606\pi\) |
−0.865930 | + | 0.500165i | \(0.833273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1242.91i | 1.67734i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −172.285 | −0.231878 | −0.115939 | − | 0.993256i | \(-0.536988\pi\) | ||||
−0.115939 | + | 0.993256i | \(0.536988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 693.554 | − | 400.424i | 0.930945 | − | 0.537481i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1316.02 | − | 759.804i | −1.76174 | − | 1.01714i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 636.617 | − | 281.003i | 0.849955 | − | 0.375172i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.4735 | − | 44.1215i | 0.0339195 | − | 0.0587503i | −0.848567 | − | 0.529087i | \(-0.822534\pi\) |
0.882487 | + | 0.470337i | \(0.155868\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −608.606 | − | 1054.14i | −0.808241 | − | 1.39991i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1836.92i | 2.43300i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −472.598 | −0.624304 | −0.312152 | − | 0.950032i | \(-0.601050\pi\) | ||||
−0.312152 | + | 0.950032i | \(0.601050\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −126.465 | + | 73.0145i | −0.166620 | + | 0.0961982i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −370.248 | − | 213.763i | −0.486528 | − | 0.280897i | 0.236605 | − | 0.971606i | \(-0.423965\pi\) |
−0.723133 | + | 0.690709i | \(0.757299\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.4519 | + | 105.704i | −0.0150090 | + | 0.138537i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1545.77 | + | 2677.35i | −2.02062 | + | 3.49981i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 527.097 | + | 912.958i | 0.687219 | + | 1.19030i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 199.651i | − | 0.259625i | −0.991539 | − | 0.129812i | \(-0.958563\pi\) | ||
0.991539 | − | 0.129812i | \(-0.0414375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −57.7849 | −0.0749480 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.7213 | + | 21.2011i | −0.0475049 | + | 0.0274270i | −0.523564 | − | 0.851986i | \(-0.675398\pi\) |
0.476059 | + | 0.879413i | \(0.342065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 175.481 | + | 101.314i | 0.226427 | + | 0.130728i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 248.291 | − | 339.454i | 0.319550 | − | 0.436878i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 76.3685 | − | 132.274i | 0.0980340 | − | 0.169800i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −167.079 | − | 289.389i | −0.213929 | − | 0.370537i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 151.460i | 0.193435i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1358.50 | 1.73057 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 524.104 | − | 302.591i | 0.665951 | − | 0.384487i | −0.128589 | − | 0.991698i | \(-0.541045\pi\) |
0.794541 | + | 0.607211i | \(0.207712\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.415212 | − | 0.239723i | −0.000526251 | − | 0.000303831i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 644.373 | + | 471.321i | 0.814631 | + | 0.595854i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 254.691 | − | 441.139i | 0.321175 | − | 0.556291i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 580.790 | + | 1005.96i | 0.730553 | + | 1.26536i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 349.434i | − | 0.438437i | −0.975676 | − | 0.219219i | \(-0.929649\pi\) | ||
0.975676 | − | 0.219219i | \(-0.0703508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −213.388 | −0.267069 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2852.73 | − | 1647.02i | 3.56146 | − | 2.05621i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 84.5507 | + | 48.8153i | 0.105293 | + | 0.0607912i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 206.268 | + | 22.3469i | 0.256233 | + | 0.0277601i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.65762 | − | 6.33519i | 0.00453237 | − | 0.00785029i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.7935 | + | 51.6039i | 0.0368276 | + | 0.0637873i | 0.883852 | − | 0.467767i | \(-0.154941\pi\) |
−0.847024 | + | 0.531554i | \(0.821608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 157.670i | − | 0.194414i | −0.995264 | − | 0.0972069i | \(-0.969009\pi\) | ||
0.995264 | − | 0.0972069i | \(-0.0309909\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2052.98 | 2.52519 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −950.043 | + | 548.508i | −1.16570 | + | 0.673015i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 578.584 | + | 334.046i | 0.708182 | + | 0.408869i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1078.75 | + | 2443.93i | 1.31716 | + | 2.98404i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 169.068 | − | 292.835i | 0.205930 | − | 0.356681i | −0.744499 | − | 0.667624i | \(-0.767312\pi\) |
0.950429 | + | 0.310943i | \(0.100645\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −557.669 | − | 965.911i | −0.677605 | − | 1.17365i | −0.975700 | − | 0.219111i | \(-0.929684\pi\) |
0.298095 | − | 0.954536i | \(-0.403649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 457.861i | − | 0.554982i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1368.45 | −1.65472 | −0.827359 | − | 0.561673i | \(-0.810158\pi\) | ||||
−0.827359 | + | 0.561673i | \(0.810158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 293.704 | − | 169.570i | 0.354288 | − | 0.204548i | −0.312284 | − | 0.949989i | \(-0.601094\pi\) |
0.666572 | + | 0.745441i | \(0.267761\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −841.151 | − | 485.639i | −1.01222 | − | 0.584403i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −741.417 | − | 676.213i | −0.890056 | − | 0.811780i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 760.178 | − | 1316.67i | 0.910393 | − | 1.57685i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 589.625 | + | 1021.26i | 0.704451 | + | 1.22014i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 402.959i | − | 0.480284i | −0.970738 | − | 0.240142i | \(-0.922806\pi\) | ||
0.970738 | − | 0.240142i | \(-0.0771941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −837.883 | −0.996294 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1227.00 | + | 708.406i | −1.45551 | + | 0.840340i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −463.962 | − | 267.869i | −0.549068 | − | 0.317004i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 587.362 | − | 259.262i | 0.693462 | − | 0.306095i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −659.101 | + | 1141.60i | −0.776326 | + | 1.34464i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.6064 | + | 42.6195i | 0.0289147 | + | 0.0500817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1179.46i | − | 1.38272i | −0.722512 | − | 0.691359i | \(-0.757012\pi\) | ||
0.722512 | − | 0.691359i | \(-0.242988\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2051.15 | −2.39900 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 579.907 | − | 334.810i | 0.676671 | − | 0.390676i | −0.121929 | − | 0.992539i | \(-0.538908\pi\) |
0.798600 | + | 0.601863i | \(0.205575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 753.231 | + | 434.878i | 0.876869 | + | 0.506261i | 0.869625 | − | 0.493713i | \(-0.164361\pi\) |
0.00724440 | + | 0.999974i | \(0.497694\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 48.6483 | − | 449.036i | 0.0565021 | − | 0.521529i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.9704 | − | 79.6231i | 0.0532681 | − | 0.0922631i | −0.838162 | − | 0.545422i | \(-0.816370\pi\) |
0.891430 | + | 0.453159i | \(0.149703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −680.753 | − | 1179.10i | −0.786998 | − | 1.36312i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 748.444i | 0.863257i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 162.354 | 0.186828 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1359.99 | + | 785.189i | −1.56141 | + | 0.901480i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2718.27 | + | 1569.40i | 3.11372 | + | 1.79771i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 267.258 | − | 365.386i | 0.305438 | − | 0.417584i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 218.160 | − | 377.864i | 0.248757 | − | 0.430860i | −0.714424 | − | 0.699713i | \(-0.753311\pi\) |
0.963181 | + | 0.268853i | \(0.0866445\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −654.840 | − | 1134.22i | −0.744983 | − | 1.29035i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 884.017i | 1.00342i | 0.865035 | + | 0.501712i | \(0.167296\pi\) | ||||
−0.865035 | + | 0.501712i | \(0.832704\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −62.8499 | −0.0711776 | −0.0355888 | − | 0.999367i | \(-0.511331\pi\) | ||||
−0.0355888 | + | 0.999367i | \(0.511331\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2072.89 | + | 1196.78i | −2.34224 | + | 1.35230i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −901.243 | − | 520.333i | −1.01606 | − | 0.586621i | −0.103098 | − | 0.994671i | \(-0.532875\pi\) |
−0.912959 | + | 0.408050i | \(0.866209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 156.767 | + | 114.665i | 0.176340 | + | 0.128983i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 749.222 | − | 1297.69i | 0.840878 | − | 1.45644i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −70.7884 | − | 122.609i | −0.0792703 | − | 0.137300i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1122.60i | 1.25430i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −430.083 | −0.479468 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.0156 | − | 12.1334i | 0.0233766 | − | 0.0134965i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 569.329 | + | 328.702i | 0.631886 | + | 0.364820i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1964.14 | + | 212.794i | 2.17513 | + | 0.235652i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 543.504 | − | 941.376i | 0.600557 | − | 1.04019i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 599.568 | + | 1038.48i | 0.661045 | + | 1.14496i | 0.980341 | + | 0.197308i | \(0.0632200\pi\) |
−0.319297 | + | 0.947655i | \(0.603447\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2745.41i | 3.02026i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1588.16 | 1.74331 | 0.871657 | − | 0.490116i | \(-0.163046\pi\) | ||||
0.871657 | + | 0.490116i | \(0.163046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 297.378 | − | 171.691i | 0.325715 | − | 0.188052i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1001.61 | + | 578.281i | 1.09466 | + | 0.632001i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −516.577 | − | 1170.31i | −0.563334 | − | 1.27624i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 573.073 | − | 992.592i | 0.623584 | − | 1.08008i | −0.365229 | − | 0.930918i | \(-0.619009\pi\) |
0.988813 | − | 0.149161i | \(-0.0476572\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −957.834 | − | 1659.02i | −1.03999 | − | 1.80132i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 984.158i | − | 1.06626i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −154.302 | −0.166813 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4160.38 | − | 2402.00i | 4.48801 | − | 2.59115i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −296.299 | − | 171.068i | −0.318944 | − | 0.184142i | 0.331978 | − | 0.943287i | \(-0.392284\pi\) |
−0.650922 | + | 0.759145i | \(0.725617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 142.586 | − | 650.328i | 0.153153 | − | 0.698527i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 714.664 | − | 1237.83i | 0.765985 | − | 1.32672i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −349.294 | − | 604.995i | −0.373576 | − | 0.647053i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 77.2601i | 0.0824548i | 0.999150 | + | 0.0412274i | \(0.0131268\pi\) | ||||
−0.999150 | + | 0.0412274i | \(0.986873\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 228.759 | 0.243620 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 415.988 | − | 240.171i | 0.442070 | − | 0.255229i | −0.262405 | − | 0.964958i | \(-0.584516\pi\) |
0.704475 | + | 0.709728i | \(0.251182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.7707 | + | 26.4257i | 0.0485374 | + | 0.0280231i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3463.47 | + | 1528.78i | −3.66505 | + | 1.61776i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −195.244 | + | 338.173i | −0.206171 | + | 0.357099i | −0.950505 | − | 0.310708i | \(-0.899434\pi\) |
0.744334 | + | 0.667808i | \(0.232767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 143.770 | + | 249.018i | 0.151497 | + | 0.262400i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2539.40i | 2.67025i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1234.80 | −1.29570 | −0.647851 | − | 0.761767i | \(-0.724332\pi\) | ||||
−0.647851 | + | 0.761767i | \(0.724332\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 760.212 | − | 438.909i | 0.796034 | − | 0.459590i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.4871 | − | 27.4167i | −0.0496208 | − | 0.0286486i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 76.2311 | − | 703.633i | 0.0794902 | − | 0.733715i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −386.031 | + | 668.625i | −0.401697 | + | 0.695760i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1190.27 | − | 2061.61i | −1.23601 | − | 2.14083i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 272.545i | 0.282430i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −719.055 | −0.743593 | −0.371797 | − | 0.928314i | \(-0.621258\pi\) | ||||
−0.371797 | + | 0.928314i | \(0.621258\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1383.18 | + | 798.578i | −1.42743 | + | 0.824126i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −837.747 | − | 483.674i | −0.862767 | − | 0.498119i | 0.00217068 | − | 0.999998i | \(-0.499309\pi\) |
−0.864938 | + | 0.501879i | \(0.832642\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −365.980 | + | 500.355i | −0.376136 | + | 0.514239i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 674.243 | − | 1167.82i | 0.691531 | − | 1.19777i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 668.456 | + | 1157.80i | 0.684192 | + | 1.18506i | 0.973690 | + | 0.227877i | \(0.0731783\pi\) |
−0.289498 | + | 0.957179i | \(0.593488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 744.347i | 0.760313i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 363.722 | 0.370767 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 465.567 | − | 268.795i | 0.473619 | − | 0.273444i | −0.244134 | − | 0.969741i | \(-0.578504\pi\) |
0.717753 | + | 0.696297i | \(0.245170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1124.16 | + | 649.036i | 1.14128 | + | 0.658920i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −337.915 | − | 247.165i | −0.342366 | − | 0.250421i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −115.590 | + | 200.207i | −0.116875 | + | 0.202434i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −185.587 | − | 321.446i | −0.187273 | − | 0.324366i | 0.757067 | − | 0.653337i | \(-0.226631\pi\) |
−0.944340 | + | 0.328971i | \(0.893298\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 826.135i | 0.831959i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1899.37 | −1.90891 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −702.022 | + | 405.313i | −0.704134 | + | 0.406532i | −0.808885 | − | 0.587966i | \(-0.799929\pi\) |
0.104751 | + | 0.994498i | \(0.466595\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −777.696 | − | 449.003i | −0.778474 | − | 0.449452i |
(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 | 224.3.s.b.33.1 | ✓ | 16 | |
4.3 | odd | 2 | inner | 224.3.s.b.33.8 | yes | 16 | |
7.2 | even | 3 | 1568.3.c.g.97.1 | 16 | |||
7.3 | odd | 6 | inner | 224.3.s.b.129.1 | yes | 16 | |
7.5 | odd | 6 | 1568.3.c.g.97.16 | 16 | |||
8.3 | odd | 2 | 448.3.s.h.257.1 | 16 | |||
8.5 | even | 2 | 448.3.s.h.257.8 | 16 | |||
28.3 | even | 6 | inner | 224.3.s.b.129.8 | yes | 16 | |
28.19 | even | 6 | 1568.3.c.g.97.2 | 16 | |||
28.23 | odd | 6 | 1568.3.c.g.97.15 | 16 | |||
56.3 | even | 6 | 448.3.s.h.129.1 | 16 | |||
56.45 | odd | 6 | 448.3.s.h.129.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.b.33.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
224.3.s.b.33.8 | yes | 16 | 4.3 | odd | 2 | inner | |
224.3.s.b.129.1 | yes | 16 | 7.3 | odd | 6 | inner | |
224.3.s.b.129.8 | yes | 16 | 28.3 | even | 6 | inner | |
448.3.s.h.129.1 | 16 | 56.3 | even | 6 | |||
448.3.s.h.129.8 | 16 | 56.45 | odd | 6 | |||
448.3.s.h.257.1 | 16 | 8.3 | odd | 2 | |||
448.3.s.h.257.8 | 16 | 8.5 | even | 2 | |||
1568.3.c.g.97.1 | 16 | 7.2 | even | 3 | |||
1568.3.c.g.97.2 | 16 | 28.19 | even | 6 | |||
1568.3.c.g.97.15 | 16 | 28.23 | odd | 6 | |||
1568.3.c.g.97.16 | 16 | 7.5 | odd | 6 |