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 | 129.8 | ||
Root | \(3.86852 - 1.41699i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.129 |
Dual form | 224.3.s.b.33.8 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0.974102 | + | 0.226109i | \(0.0726004\pi\) |
0.682867 | + | 0.730543i | \(0.260733\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.45949 | − | 3.15204i | 1.09190 | − | 0.630408i | 0.157817 | − | 0.987468i | \(-0.449554\pi\) |
0.934081 | + | 0.357060i | \(0.116221\pi\) | |||||||
\(6\) | 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 | \(-0.912437\pi\) |
0.716440 | + | 0.697648i | \(0.245770\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 15.9368i | − | 1.22591i | −0.790118 | − | 0.612955i | \(-0.789981\pi\) | ||
0.790118 | − | 0.612955i | \(-0.210019\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 36.1848 | 2.41232 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.7354 | − | 10.2395i | −1.04326 | − | 0.602326i | −0.122505 | − | 0.992468i | \(-0.539093\pi\) |
−0.920755 | + | 0.390142i | \(0.872426\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.7669 | − | 6.79363i | 0.619311 | − | 0.357560i | −0.157289 | − | 0.987553i | \(-0.550276\pi\) |
0.776601 | + | 0.629993i | \(0.216942\pi\) | |||||||
\(20\) | 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 | \(-0.199258\pi\) |
−0.912594 | + | 0.408866i | \(0.865924\pi\) | |||||||
\(24\) | 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 | \(-0.404494\pi\) |
−0.679556 | + | 0.733623i | \(0.737828\pi\) | |||||||
\(32\) | 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 | 0.786593 | − | 0.617472i | \(-0.211843\pi\) |
−0.928043 | + | 0.372474i | \(0.878510\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 45.7380 | − | 79.2205i | 1.17277 | − | 2.03130i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.2412i | − | 0.274175i | −0.990559 | − | 0.137088i | \(-0.956226\pi\) | ||
0.990559 | − | 0.137088i | \(-0.0437742\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 49.1704 | 1.14350 | 0.571749 | − | 0.820428i | \(-0.306265\pi\) | ||||
0.571749 | + | 0.820428i | \(0.306265\pi\) | |||||||
\(44\) | 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 | \(-0.702024\pi\) |
0.400921 | + | 0.916113i | \(0.368690\pi\) | |||||||
\(48\) | 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 | −0.976779 | − | 0.214251i | \(-0.931269\pi\) |
0.673936 | + | 0.738789i | \(0.264602\pi\) | |||||||
\(54\) | 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 | \(-0.522754\pi\) |
−0.899526 | + | 0.436868i | \(0.856088\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27.6804 | + | 15.9813i | −0.453778 | + | 0.261989i | −0.709424 | − | 0.704782i | \(-0.751045\pi\) |
0.255647 | + | 0.966770i | \(0.417712\pi\) | |||||||
\(62\) | 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 | 0.219211 | + | 0.975677i | \(0.429652\pi\) |
−0.954567 | + | 0.297996i | \(0.903682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 26.9867i | − | 0.391112i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61.7537 | 0.869770 | 0.434885 | − | 0.900486i | \(-0.356789\pi\) | ||||
0.434885 | + | 0.900486i | \(0.356789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6253 | + | 9.02127i | 0.214045 | + | 0.123579i | 0.603190 | − | 0.797598i | \(-0.293896\pi\) |
−0.389145 | + | 0.921177i | \(0.627229\pi\) | |||||||
\(74\) | 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 | \(-0.227482\pi\) |
−0.945215 | + | 0.326447i | \(0.894149\pi\) | |||||||
\(80\) | 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 | 0.351938 | − | 0.936023i | \(-0.385523\pi\) |
0.986589 | + | 0.163224i | \(0.0521894\pi\) | |||||||
\(90\) | 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 | \(-0.763866\pi\) | ||
0.737228 | − | 0.675644i | \(-0.236134\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −129.578 | −1.30887 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −99.2877 | − | 57.3238i | −0.983046 | − | 0.567562i | −0.0798578 | − | 0.996806i | \(-0.525447\pi\) |
−0.903188 | + | 0.429244i | \(0.858780\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −173.736 | + | 100.307i | −1.68676 | + | 0.973851i | −0.729786 | + | 0.683675i | \(0.760380\pi\) |
−0.956973 | + | 0.290176i | \(0.906286\pi\) | |||||||
\(104\) | 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 | \(-0.320446\pi\) |
−0.999181 | + | 0.0404762i | \(0.987113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.59446 | − | 13.1540i | 0.0696740 | − | 0.120679i | −0.829084 | − | 0.559124i | \(-0.811137\pi\) |
0.898758 | + | 0.438445i | \(0.144471\pi\) | |||||||
\(110\) | 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 | \(-0.534841\pi\) | ||||
−0.109239 | + | 0.994016i | \(0.534841\pi\) | |||||||
\(128\) | 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 | \(-0.420954\pi\) |
0.962352 | + | 0.271805i | \(0.0876206\pi\) | |||||||
\(132\) | 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 | −0.989410 | − | 0.145147i | \(-0.953635\pi\) |
0.620406 | + | 0.784281i | \(0.286968\pi\) | |||||||
\(138\) | 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 | 0.996541 | − | 0.0831082i | \(-0.0264847\pi\) |
−0.570244 | + | 0.821475i | \(0.693151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −145.693 | + | 252.347i | −0.964852 | + | 1.67117i | −0.254841 | + | 0.966983i | \(0.582023\pi\) |
−0.710011 | + | 0.704190i | \(0.751310\pi\) | |||||||
\(152\) | 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 | 0.958008 | − | 0.286741i | \(-0.0925719\pi\) |
0.230679 | + | 0.973030i | \(0.425905\pi\) | |||||||
\(158\) | 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 | 0.999221 | + | 0.0394714i | \(0.0125674\pi\) |
−0.465427 | + | 0.885086i | \(0.654099\pi\) | |||||||
\(164\) | 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 | −0.931204 | − | 0.364499i | \(-0.881240\pi\) |
−0.149937 | + | 0.988696i | \(0.547907\pi\) | |||||||
\(174\) | 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 | \(-0.999051\pi\) |
0.502581 | + | 0.864530i | \(0.332384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 172.429i | 0.952648i | 0.879270 | + | 0.476324i | \(0.158031\pi\) | ||||
−0.879270 | + | 0.476324i | \(0.841969\pi\) | |||||||
\(182\) | 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 | \(-0.285433\pi\) |
−0.988699 | + | 0.149916i | \(0.952100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.6165 | − | 37.4409i | 0.112003 | − | 0.193994i | −0.804575 | − | 0.593851i | \(-0.797607\pi\) |
0.916578 | + | 0.399857i | \(0.130940\pi\) | |||||||
\(194\) | 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 | \(-0.0599900\pi\) |
0.328896 | + | 0.944366i | \(0.393323\pi\) | |||||||
\(200\) | 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 | \(-0.762742\pi\) | ||||
−0.734839 | + | 0.678241i | \(0.762742\pi\) | |||||||
\(212\) | 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 | \(-0.567869\pi\) |
−0.952217 | + | 0.305422i | \(0.901202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 171.968 | − | 99.2857i | 0.750952 | − | 0.433562i | −0.0750860 | − | 0.997177i | \(-0.523923\pi\) |
0.826038 | + | 0.563615i | \(0.190590\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 87.7954 | − | 198.901i | 0.380066 | − | 0.861045i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 123.928 | + | 214.650i | 0.531881 | + | 0.921246i | 0.999307 | + | 0.0372134i | \(0.0118481\pi\) |
−0.467426 | + | 0.884032i | \(0.654819\pi\) | |||||||
\(234\) | 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 | \(-0.581383\pi\) | ||||
−0.252895 | + | 0.967494i | \(0.581383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 125.956 | + | 72.7209i | 0.522640 | + | 0.301746i | 0.738014 | − | 0.674785i | \(-0.235764\pi\) |
−0.215374 | + | 0.976532i | \(0.569097\pi\) | |||||||
\(242\) | 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 | −0.482942 | − | 0.875652i | \(-0.660432\pi\) |
0.516866 | + | 0.856066i | \(0.327099\pi\) | |||||||
\(258\) | 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 | \(-0.833384\pi\) |
0.865946 | + | 0.500138i | \(0.166717\pi\) | |||||||
\(264\) | 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 | 0.497947 | − | 0.867207i | \(-0.334087\pi\) |
−0.502050 | + | 0.864839i | \(0.667421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 309.749 | − | 178.834i | 1.14298 | − | 0.659903i | 0.195817 | − | 0.980641i | \(-0.437264\pi\) |
0.947168 | + | 0.320738i | \(0.103931\pi\) | |||||||
\(272\) | 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 | −0.671918 | − | 0.740626i | \(-0.734529\pi\) |
0.977360 | + | 0.211585i | \(0.0678625\pi\) | |||||||
\(278\) | 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 | \(-0.466324\pi\) |
−0.808383 | + | 0.588657i | \(0.799657\pi\) | |||||||
\(284\) | 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 | \(-0.872693\pi\) | ||
0.921081 | − | 0.389370i | \(-0.127307\pi\) | |||||||
\(294\) | 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 | \(-0.202223\pi\) |
−0.111471 | + | 0.993768i | \(0.535556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.5147 | + | 19.9271i | −0.110271 | + | 0.0636648i | −0.554121 | − | 0.832436i | \(-0.686946\pi\) |
0.443850 | + | 0.896101i | \(0.353612\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1050.58 | + | 113.819i | −3.33517 | + | 0.361330i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 221.206 | + | 383.140i | 0.697811 | + | 1.20864i | 0.969224 | + | 0.246181i | \(0.0791756\pi\) |
−0.271413 | + | 0.962463i | \(0.587491\pi\) | |||||||
\(318\) | 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 | \(-0.236429\pi\) |
−0.954017 | + | 0.299753i | \(0.903096\pi\) | |||||||
\(332\) | 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 | \(-0.948477\pi\) |
0.633031 | + | 0.774126i | \(0.281811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 675.578i | 1.93575i | 0.251428 | + | 0.967876i | \(0.419100\pi\) | ||||
−0.251428 | + | 0.967876i | \(0.580900\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1367.25 | 3.89530 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −492.343 | − | 284.254i | −1.39474 | − | 0.805252i | −0.400903 | − | 0.916121i | \(-0.631304\pi\) |
−0.993835 | + | 0.110868i | \(0.964637\pi\) | |||||||
\(354\) | 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 | −0.768092 | − | 0.640339i | \(-0.778794\pi\) |
−0.170504 | − | 0.985357i | \(-0.554540\pi\) | |||||||
\(360\) | 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 | \(-0.352041\pi\) |
−0.550004 | + | 0.835162i | \(0.685374\pi\) | |||||||
\(368\) | 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 | −0.882328 | − | 0.470636i | \(-0.844025\pi\) |
0.0335811 | − | 0.999436i | \(-0.489309\pi\) | |||||||
\(374\) | 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 | \(-0.201136\pi\) | ||||
0.806914 | + | 0.590669i | \(0.201136\pi\) | |||||||
\(380\) | 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 | \(-0.351016\pi\) |
0.998457 | + | 0.0555219i | \(0.0176823\pi\) | |||||||
\(384\) | 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 | −0.543241 | − | 0.839577i | \(-0.682803\pi\) |
0.998715 | + | 0.0506717i | \(0.0161362\pi\) | |||||||
\(390\) | 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 | −0.116970 | − | 0.993135i | \(-0.537318\pi\) |
0.801595 | + | 0.597867i | \(0.203985\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −440.636 | + | 322.299i | −1.10435 | + | 0.807768i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −161.060 | − | 278.963i | −0.401645 | − | 0.695669i | 0.592280 | − | 0.805732i | \(-0.298228\pi\) |
−0.993925 | + | 0.110063i | \(0.964895\pi\) | |||||||
\(402\) | 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 | 0.911733 | − | 0.410784i | \(-0.134745\pi\) |
0.100117 | + | 0.994976i | \(0.468078\pi\) | |||||||
\(410\) | 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 | \(-0.687053\pi\) |
0.997950 | + | 0.0640009i | \(0.0203861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 295.254i | − | 0.681879i | −0.940085 | − | 0.340940i | \(-0.889255\pi\) | ||
0.940085 | − | 0.340940i | \(-0.110745\pi\) | |||||||
\(434\) | 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 | \(-0.648864\pi\) |
0.547629 | + | 0.836721i | \(0.315531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1146.16 | − | 251.297i | 2.59899 | − | 0.569835i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −316.862 | − | 548.821i | −0.715264 | − | 1.23887i | −0.962858 | − | 0.270010i | \(-0.912973\pi\) |
0.247594 | − | 0.968864i | \(-0.420360\pi\) | |||||||
\(444\) | 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 | 0.618705 | − | 0.785623i | \(-0.287658\pi\) |
−0.989722 | + | 0.143003i | \(0.954324\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 878.469 | − | 1521.55i | 1.91388 | − | 3.31493i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 580.237i | − | 1.25865i | −0.777143 | − | 0.629324i | \(-0.783332\pi\) | ||
0.777143 | − | 0.629324i | \(-0.216668\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −433.685 | −0.936684 | −0.468342 | − | 0.883547i | \(-0.655148\pi\) | ||||
−0.468342 | + | 0.883547i | \(0.655148\pi\) | |||||||
\(464\) | 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 | \(-0.700833\pi\) |
0.404343 | + | 0.914607i | \(0.367500\pi\) | |||||||
\(468\) | 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 | \(-0.164816\pi\) |
0.00581309 | + | 0.999983i | \(0.498150\pi\) | |||||||
\(480\) | 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 | \(-0.909056\pi\) |
0.723809 | + | 0.690001i | \(0.242390\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 998.840i | 2.04262i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 221.445 | 0.451008 | 0.225504 | − | 0.974242i | \(-0.427597\pi\) | ||||
0.225504 | + | 0.974242i | \(0.427597\pi\) | |||||||
\(492\) | 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 | −0.999860 | − | 0.0167486i | \(-0.994668\pi\) |
0.485425 | − | 0.874278i | \(-0.338665\pi\) | |||||||
\(500\) | 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 | −0.330652 | − | 0.943753i | \(-0.607269\pi\) |
0.651988 | + | 0.758230i | \(0.273935\pi\) | |||||||
\(510\) | 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 | 0.0523644 | − | 0.998628i | \(-0.483324\pi\) |
−0.838655 | + | 0.544663i | \(0.816658\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 362.994 | − | 209.575i | 0.694061 | − | 0.400716i | −0.111071 | − | 0.993812i | \(-0.535428\pi\) |
0.805131 | + | 0.593096i | \(0.202095\pi\) | |||||||
\(524\) | 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 | 0.996400 | + | 0.0847712i | \(0.0270159\pi\) |
−0.424786 | + | 0.905294i | \(0.639651\pi\) | |||||||
\(542\) | 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 | \(-0.425107\pi\) | ||||
0.233118 | + | 0.972448i | \(0.425107\pi\) | |||||||
\(548\) | 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 | −0.997558 | − | 0.0698419i | \(-0.977751\pi\) |
0.559264 | + | 0.828990i | \(0.311084\pi\) | |||||||
\(558\) | 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 | \(-0.319451\pi\) |
−0.461767 | + | 0.887001i | \(0.652784\pi\) | |||||||
\(564\) | 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 | 0.999194 | + | 0.0401523i | \(0.0127843\pi\) |
−0.464824 | + | 0.885403i | \(0.653882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −150.396 | + | 260.494i | −0.263391 | + | 0.456207i | −0.967141 | − | 0.254241i | \(-0.918174\pi\) |
0.703750 | + | 0.710448i | \(0.251508\pi\) | |||||||
\(572\) | 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 | 0.363676 | − | 0.931526i | \(-0.381522\pi\) |
−0.624887 | + | 0.780715i | \(0.714855\pi\) | |||||||
\(578\) | 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 | −0.141640 | − | 0.989918i | \(-0.545238\pi\) |
0.786474 | + | 0.617623i | \(0.211904\pi\) | |||||||
\(594\) | 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 | \(-0.754934\pi\) |
0.961798 | + | 0.273759i | \(0.0882672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 614.010i | 1.02165i | 0.859685 | + | 0.510824i | \(0.170660\pi\) | ||||
−0.859685 | + | 0.510824i | \(0.829340\pi\) | |||||||
\(602\) | 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 | \(-0.580337\pi\) |
0.713732 | + | 0.700418i | \(0.247003\pi\) | |||||||
\(608\) | 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 | −0.998646 | − | 0.0520217i | \(-0.983434\pi\) |
0.544375 | + | 0.838842i | \(0.316767\pi\) | |||||||
\(614\) | 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 | \(-0.366546\pi\) |
−0.587478 | + | 0.809240i | \(0.699879\pi\) | |||||||
\(620\) | 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 | \(-0.571045\pi\) | ||||
−0.221346 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(632\) | 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 | −0.284227 | − | 0.958757i | \(-0.591737\pi\) |
0.972421 | − | 0.233231i | \(-0.0749297\pi\) | |||||||
\(642\) | 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 | \(-0.451403\pi\) |
−0.779912 | + | 0.625889i | \(0.784736\pi\) | |||||||
\(648\) | 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 | −0.987216 | − | 0.159390i | \(-0.949047\pi\) |
0.355572 | − | 0.934649i | \(-0.384286\pi\) | |||||||
\(654\) | 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 | \(-0.735619\pi\) | ||||
−0.674451 | + | 0.738320i | \(0.735619\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −131.019 | − | 75.6439i | −0.198214 | − | 0.114439i | 0.397608 | − | 0.917555i | \(-0.369840\pi\) |
−0.595822 | + | 0.803117i | \(0.703174\pi\) | |||||||
\(662\) | 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 | −0.943028 | − | 0.332713i | \(-0.892036\pi\) |
−0.183376 | + | 0.983043i | \(0.558703\pi\) | |||||||
\(678\) | 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 | \(-0.964107\pi\) |
0.594271 | + | 0.804265i | \(0.297441\pi\) | |||||||
\(684\) | 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 | \(-0.427965\pi\) |
0.956132 | + | 0.292935i | \(0.0946318\pi\) | |||||||
\(692\) | 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 | 0.998634 | − | 0.0522425i | \(-0.0166369\pi\) |
−0.544561 | + | 0.838722i | \(0.683304\pi\) | |||||||
\(710\) | 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 | \(-0.834922\pi\) |
−0.00499056 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(720\) | 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 | −0.633003 | − | 0.774149i | \(-0.718178\pi\) |
0.353932 | + | 0.935271i | \(0.384845\pi\) | |||||||
\(734\) | 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 | \(-0.833394\pi\) |
0.865930 | + | 0.500165i | \(0.166727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1242.91i | − | 1.67734i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 172.285 | 0.231878 | 0.115939 | − | 0.993256i | \(-0.463012\pi\) | ||||
0.115939 | + | 0.993256i | \(0.463012\pi\) | |||||||
\(744\) | 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 | \(-0.177466\pi\) |
−0.882487 | + | 0.470337i | \(0.844132\pi\) | |||||||
\(752\) | 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 | −0.723133 | − | 0.690709i | \(-0.757299\pi\) |
0.236605 | + | 0.971606i | \(0.423965\pi\) | |||||||
\(762\) | 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 | \(0.0414375\pi\) | ||||
−0.991539 | + | 0.129812i | \(0.958563\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 57.7849 | 0.0749480 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.7213 | − | 21.2011i | −0.0475049 | − | 0.0274270i | 0.476059 | − | 0.879413i | \(-0.342065\pi\) |
−0.523564 | + | 0.851986i | \(0.675398\pi\) | |||||||
\(774\) | 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 | \(-0.458955\pi\) |
−0.794541 | + | 0.607211i | \(0.792288\pi\) | |||||||
\(788\) | 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 | \(0.0703508\pi\) | ||||
−0.975676 | + | 0.219219i | \(0.929649\pi\) | |||||||
\(798\) | 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 | −0.847024 | − | 0.531554i | \(-0.821608\pi\) |
0.883852 | + | 0.467767i | \(0.154941\pi\) | |||||||
\(810\) | 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 | 0.950429 | − | 0.310943i | \(-0.100645\pi\) |
−0.744499 | + | 0.667624i | \(0.767312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 557.669 | − | 965.911i | 0.677605 | − | 1.17365i | −0.298095 | − | 0.954536i | \(-0.596351\pi\) |
0.975700 | − | 0.219111i | \(-0.0703155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 457.861i | 0.554982i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1368.45 | 1.65472 | 0.827359 | − | 0.561673i | \(-0.189842\pi\) | ||||
0.827359 | + | 0.561673i | \(0.189842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 293.704 | + | 169.570i | 0.354288 | + | 0.204548i | 0.666572 | − | 0.745441i | \(-0.267761\pi\) |
−0.312284 | + | 0.949989i | \(0.601094\pi\) | |||||||
\(830\) | 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 | \(0.242988\pi\) | ||||
−0.722512 | + | 0.691359i | \(0.757012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2051.15 | 2.39900 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 579.907 | + | 334.810i | 0.676671 | + | 0.390676i | 0.798600 | − | 0.601863i | \(-0.205575\pi\) |
−0.121929 | + | 0.992539i | \(0.538908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −753.231 | + | 434.878i | −0.876869 | + | 0.506261i | −0.869625 | − | 0.493713i | \(-0.835639\pi\) |
−0.00724440 | + | 0.999974i | \(0.502306\pi\) | |||||||
\(860\) | 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 | \(-0.183630\pi\) |
−0.891430 | + | 0.453159i | \(0.850297\pi\) | |||||||
\(864\) | 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 | 0.963181 | − | 0.268853i | \(-0.0866445\pi\) |
−0.714424 | + | 0.699713i | \(0.753311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 654.840 | − | 1134.22i | 0.744983 | − | 1.29035i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 884.017i | − | 1.00342i | −0.865035 | − | 0.501712i | \(-0.832704\pi\) | ||
0.865035 | − | 0.501712i | \(-0.167296\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 62.8499 | 0.0711776 | 0.0355888 | − | 0.999367i | \(-0.488669\pi\) | ||||
0.0355888 | + | 0.999367i | \(0.488669\pi\) | |||||||
\(884\) | 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 | \(-0.467125\pi\) |
0.912959 | + | 0.408050i | \(0.133791\pi\) | |||||||
\(888\) | 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 | 0.319297 | + | 0.947655i | \(0.396553\pi\) |
−0.980341 | + | 0.197308i | \(0.936780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2745.41i | − | 3.02026i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1588.16 | −1.74331 | −0.871657 | − | 0.490116i | \(-0.836954\pi\) | ||||
−0.871657 | + | 0.490116i | \(0.836954\pi\) | |||||||
\(912\) | 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 | −0.988813 | − | 0.149161i | \(-0.952343\pi\) |
0.365229 | − | 0.930918i | \(-0.380991\pi\) | |||||||
\(920\) | 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 | −0.650922 | − | 0.759145i | \(-0.725617\pi\) |
0.331978 | + | 0.943287i | \(0.392284\pi\) | |||||||
\(930\) | 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 | \(-0.986873\pi\) | ||
0.999150 | − | 0.0412274i | \(-0.0131268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −228.759 | −0.243620 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 415.988 | + | 240.171i | 0.442070 | + | 0.255229i | 0.704475 | − | 0.709728i | \(-0.251182\pi\) |
−0.262405 | + | 0.964958i | \(0.584516\pi\) | |||||||
\(942\) | 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 | \(-0.100566\pi\) |
−0.744334 | + | 0.667808i | \(0.767233\pi\) | |||||||
\(948\) | 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 | \(-0.378742\pi\) | ||||
0.371797 | + | 0.928314i | \(0.378742\pi\) | |||||||
\(968\) | 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 | \(-0.500691\pi\) |
0.864938 | + | 0.501879i | \(0.167358\pi\) | |||||||
\(972\) | 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 | −0.289498 | − | 0.957179i | \(-0.593488\pi\) |
0.973690 | − | 0.227877i | \(-0.0731783\pi\) | |||||||
\(978\) | 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 | \(-0.421496\pi\) |
−0.717753 | + | 0.696297i | \(0.754830\pi\) | |||||||
\(984\) | 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 | \(-0.773369\pi\) |
0.944340 | + | 0.328971i | \(0.106702\pi\) | |||||||
\(992\) | 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 | 0.104751 | − | 0.994498i | \(-0.466595\pi\) |
−0.808885 | + | 0.587966i | \(0.799929\pi\) | |||||||
\(998\) | 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.129.8 | yes | 16 | |
4.3 | odd | 2 | inner | 224.3.s.b.129.1 | yes | 16 | |
7.3 | odd | 6 | 1568.3.c.g.97.15 | 16 | |||
7.4 | even | 3 | 1568.3.c.g.97.2 | 16 | |||
7.5 | odd | 6 | inner | 224.3.s.b.33.8 | yes | 16 | |
8.3 | odd | 2 | 448.3.s.h.129.8 | 16 | |||
8.5 | even | 2 | 448.3.s.h.129.1 | 16 | |||
28.3 | even | 6 | 1568.3.c.g.97.1 | 16 | |||
28.11 | odd | 6 | 1568.3.c.g.97.16 | 16 | |||
28.19 | even | 6 | inner | 224.3.s.b.33.1 | ✓ | 16 | |
56.5 | odd | 6 | 448.3.s.h.257.1 | 16 | |||
56.19 | even | 6 | 448.3.s.h.257.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.b.33.1 | ✓ | 16 | 28.19 | even | 6 | inner | |
224.3.s.b.33.8 | yes | 16 | 7.5 | odd | 6 | inner | |
224.3.s.b.129.1 | yes | 16 | 4.3 | odd | 2 | inner | |
224.3.s.b.129.8 | yes | 16 | 1.1 | even | 1 | trivial | |
448.3.s.h.129.1 | 16 | 8.5 | even | 2 | |||
448.3.s.h.129.8 | 16 | 8.3 | odd | 2 | |||
448.3.s.h.257.1 | 16 | 56.5 | odd | 6 | |||
448.3.s.h.257.8 | 16 | 56.19 | even | 6 | |||
1568.3.c.g.97.1 | 16 | 28.3 | even | 6 | |||
1568.3.c.g.97.2 | 16 | 7.4 | even | 3 | |||
1568.3.c.g.97.15 | 16 | 7.3 | odd | 6 | |||
1568.3.c.g.97.16 | 16 | 28.11 | odd | 6 |