Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (of order \(3\), degree \(2\), not 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.11 | ||
Character | \(\chi\) | \(=\) | 3024.1873 |
Dual form | 3024.2.t.k.289.11 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.22296 | 1.88857 | 0.944283 | − | 0.329134i | \(-0.106757\pi\) | ||||
0.944283 | + | 0.329134i | \(0.106757\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37802 | − | 1.15974i | 0.898809 | − | 0.438341i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.92915 | 0.581660 | 0.290830 | − | 0.956775i | \(-0.406069\pi\) | ||||
0.290830 | + | 0.956775i | \(0.406069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.291529 | + | 0.504943i | −0.0808557 | + | 0.140046i | −0.903618 | − | 0.428340i | \(-0.859099\pi\) |
0.822762 | + | 0.568386i | \(0.192432\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.61082 | + | 6.25412i | −0.875753 | + | 1.51685i | −0.0197936 | + | 0.999804i | \(0.506301\pi\) |
−0.855959 | + | 0.517044i | \(0.827032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.10268 | − | 3.64194i | −0.482387 | − | 0.835519i | 0.517408 | − | 0.855739i | \(-0.326897\pi\) |
−0.999796 | + | 0.0202194i | \(0.993564\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.27988 | 0.266873 | 0.133437 | − | 0.991057i | \(-0.457399\pi\) | ||||
0.133437 | + | 0.991057i | \(0.457399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.8334 | 2.56668 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.20305 | + | 7.27990i | 0.780487 | + | 1.35184i | 0.931658 | + | 0.363335i | \(0.118362\pi\) |
−0.151171 | + | 0.988508i | \(0.548305\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.476061 | − | 0.824561i | −0.0855030 | − | 0.148096i | 0.820102 | − | 0.572217i | \(-0.193916\pi\) |
−0.905605 | + | 0.424121i | \(0.860583\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.0423 | − | 4.89755i | 1.69746 | − | 0.827837i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.03329 | + | 5.25381i | 0.498669 | + | 0.863721i | 0.999999 | − | 0.00153588i | \(-0.000488885\pi\) |
−0.501330 | + | 0.865256i | \(0.667156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.31299 | + | 2.27416i | −0.205054 | + | 0.355164i | −0.950150 | − | 0.311794i | \(-0.899070\pi\) |
0.745096 | + | 0.666957i | \(0.232404\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.442349 | − | 0.766171i | −0.0674576 | − | 0.116840i | 0.830324 | − | 0.557281i | \(-0.188155\pi\) |
−0.897782 | + | 0.440441i | \(0.854822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.88201 | + | 4.99178i | −0.420384 | + | 0.728126i | −0.995977 | − | 0.0896103i | \(-0.971438\pi\) |
0.575593 | + | 0.817736i | \(0.304771\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.30999 | − | 5.51579i | 0.615713 | − | 0.787970i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.962456 | − | 1.66702i | 0.132204 | − | 0.228983i | −0.792322 | − | 0.610103i | \(-0.791128\pi\) |
0.924526 | + | 0.381120i | \(0.124461\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.14673 | 1.09850 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.27614 | + | 3.94240i | 0.296329 | + | 0.513256i | 0.975293 | − | 0.220915i | \(-0.0709043\pi\) |
−0.678964 | + | 0.734171i | \(0.737571\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.29008 | − | 9.16268i | 0.677325 | − | 1.17316i | −0.298458 | − | 0.954423i | \(-0.596472\pi\) |
0.975783 | − | 0.218739i | \(-0.0701943\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23112 | + | 2.13236i | −0.152701 | + | 0.264486i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.43191 | − | 4.21220i | −0.297106 | − | 0.514602i | 0.678367 | − | 0.734723i | \(-0.262688\pi\) |
−0.975473 | + | 0.220121i | \(0.929355\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5443 | 1.37005 | 0.685027 | − | 0.728518i | \(-0.259791\pi\) | ||||
0.685027 | + | 0.728518i | \(0.259791\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.446138 | − | 0.772734i | 0.0522165 | − | 0.0904417i | −0.838736 | − | 0.544539i | \(-0.816705\pi\) |
0.890952 | + | 0.454097i | \(0.150038\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.58756 | − | 2.23732i | 0.522801 | − | 0.254966i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.93520 | + | 10.2801i | −0.667763 | + | 1.15660i | 0.310766 | + | 0.950487i | \(0.399415\pi\) |
−0.978528 | + | 0.206112i | \(0.933919\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.24250 | − | 9.08028i | −0.575439 | − | 0.996690i | −0.995994 | − | 0.0894227i | \(-0.971498\pi\) |
0.420555 | − | 0.907267i | \(-0.361836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.2484 | + | 26.4109i | −1.65392 | + | 2.86467i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.87906 | − | 6.71874i | −0.411180 | − | 0.712185i | 0.583839 | − | 0.811869i | \(-0.301550\pi\) |
−0.995019 | + | 0.0996849i | \(0.968217\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.107659 | + | 1.53887i | −0.0112857 | + | 0.161317i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.87953 | − | 15.3798i | −0.911020 | − | 1.57793i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.98651 | − | 3.44073i | −0.201699 | − | 0.349353i | 0.747377 | − | 0.664400i | \(-0.231313\pi\) |
−0.949076 | + | 0.315047i | \(0.897980\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.7707 | −1.66874 | −0.834372 | − | 0.551202i | \(-0.814169\pi\) | ||||
−0.834372 | + | 0.551202i | \(0.814169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.6114 | −1.14410 | −0.572052 | − | 0.820218i | \(-0.693852\pi\) | ||||
−0.572052 | + | 0.820218i | \(0.693852\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.2454 | − | 17.7455i | −0.990460 | − | 1.71553i | −0.614570 | − | 0.788862i | \(-0.710671\pi\) |
−0.375890 | − | 0.926664i | \(-0.622663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.46965 | − | 4.27756i | 0.236550 | − | 0.409716i | −0.723172 | − | 0.690668i | \(-0.757317\pi\) |
0.959722 | + | 0.280951i | \(0.0906500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.42131 | − | 12.8541i | 0.698138 | − | 1.20921i | −0.270974 | − | 0.962587i | \(-0.587346\pi\) |
0.969111 | − | 0.246623i | \(-0.0793210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.40488 | 0.504008 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.33344 | + | 19.0601i | −0.122236 | + | 1.74723i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.27838 | −0.661671 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.0802 | 2.95879 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.53648 | 0.757490 | 0.378745 | − | 0.925501i | \(-0.376356\pi\) | ||||
0.378745 | + | 0.925501i | \(0.376356\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.34684 | −0.205045 | −0.102522 | − | 0.994731i | \(-0.532691\pi\) | ||||
−0.102522 | + | 0.994731i | \(0.532691\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.22393 | − | 6.22207i | −0.799817 | − | 0.539522i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.28363 | −0.109668 | −0.0548340 | − | 0.998495i | \(-0.517463\pi\) | ||||
−0.0548340 | + | 0.998495i | \(0.517463\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.610553 | + | 1.05751i | −0.0517865 | + | 0.0896968i | −0.890757 | − | 0.454481i | \(-0.849825\pi\) |
0.838970 | + | 0.544177i | \(0.183158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.562403 | + | 0.974111i | −0.0470305 | + | 0.0814593i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.7493 | + | 30.7427i | 1.47400 | + | 2.55305i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.29459 | −0.515673 | −0.257836 | − | 0.966189i | \(-0.583010\pi\) | ||||
−0.257836 | + | 0.966189i | \(0.583010\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.35453 | −0.191609 | −0.0958044 | − | 0.995400i | \(-0.530542\pi\) | ||||
−0.0958044 | + | 0.995400i | \(0.530542\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.01039 | − | 3.48209i | −0.161478 | − | 0.279688i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.44437 | + | 2.50172i | 0.115273 | + | 0.199659i | 0.917889 | − | 0.396838i | \(-0.129892\pi\) |
−0.802616 | + | 0.596496i | \(0.796559\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.04358 | − | 1.48433i | 0.239868 | − | 0.116982i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.60538 | − | 4.51265i | −0.204069 | − | 0.353458i | 0.745767 | − | 0.666207i | \(-0.232083\pi\) |
−0.949836 | + | 0.312749i | \(0.898750\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5400 | − | 18.2558i | 0.815610 | − | 1.41268i | −0.0932784 | − | 0.995640i | \(-0.529735\pi\) |
0.908889 | − | 0.417039i | \(-0.136932\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.33002 | + | 10.9639i | 0.486925 | + | 0.843378i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.03653 | + | 3.52737i | −0.154834 | + | 0.268181i | −0.932999 | − | 0.359880i | \(-0.882818\pi\) |
0.778164 | + | 0.628061i | \(0.216151\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30.5182 | − | 14.8835i | 2.30696 | − | 1.12508i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.11088 | + | 5.38821i | −0.232518 | + | 0.402733i | −0.958549 | − | 0.284929i | \(-0.908030\pi\) |
0.726030 | + | 0.687663i | \(0.241363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2396 | 1.35574 | 0.677868 | − | 0.735184i | \(-0.262904\pi\) | ||||
0.677868 | + | 0.735184i | \(0.262904\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.8095 | + | 22.1866i | 0.941770 | + | 1.63119i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.96581 | + | 12.0651i | −0.509391 | + | 0.882290i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.69298 | − | 6.39644i | 0.267215 | − | 0.462830i | −0.700927 | − | 0.713233i | \(-0.747230\pi\) |
0.968142 | + | 0.250404i | \(0.0805633\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.75908 | − | 16.9032i | −0.702474 | − | 1.21672i | −0.967595 | − | 0.252506i | \(-0.918745\pi\) |
0.265121 | − | 0.964215i | \(-0.414588\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.77564 | −0.553992 | −0.276996 | − | 0.960871i | \(-0.589339\pi\) | ||||
−0.276996 | + | 0.960871i | \(0.589339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.85734 | − | 6.68110i | 0.273439 | − | 0.473611i | −0.696301 | − | 0.717750i | \(-0.745172\pi\) |
0.969740 | + | 0.244139i | \(0.0785054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.4378 | + | 12.4373i | 1.29408 | + | 0.872928i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.54469 | + | 9.60368i | −0.387258 | + | 0.670750i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.05638 | − | 7.02585i | −0.280586 | − | 0.485989i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7645 | + | 20.3767i | −0.809899 | + | 1.40279i | 0.103034 | + | 0.994678i | \(0.467145\pi\) |
−0.912933 | + | 0.408109i | \(0.866188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.86802 | − | 3.23551i | −0.127398 | − | 0.220660i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.08836 | − | 1.40872i | −0.141767 | − | 0.0956301i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.10532 | − | 3.64652i | −0.141619 | − | 0.245291i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.83093 | + | 8.36742i | 0.323503 | + | 0.560324i | 0.981208 | − | 0.192952i | \(-0.0618061\pi\) |
−0.657705 | + | 0.753275i | \(0.728473\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.9718 | 1.19283 | 0.596417 | − | 0.802675i | \(-0.296591\pi\) | ||||
0.596417 | + | 0.802675i | \(0.296591\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.91668 | −0.523149 | −0.261574 | − | 0.965183i | \(-0.584242\pi\) | ||||
−0.261574 | + | 0.965183i | \(0.584242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.27796 | − | 5.67759i | −0.214746 | − | 0.371951i | 0.738448 | − | 0.674311i | \(-0.235559\pi\) |
−0.953194 | + | 0.302359i | \(0.902226\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1706 | + | 21.0801i | −0.793922 | + | 1.37511i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.01922 | + | 13.8897i | −0.518720 | + | 0.898450i | 0.481043 | + | 0.876697i | \(0.340258\pi\) |
−0.999763 | + | 0.0217529i | \(0.993075\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1791 | 0.720112 | 0.360056 | − | 0.932931i | \(-0.382758\pi\) | ||||
0.360056 | + | 0.932931i | \(0.382758\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.2009 | − | 23.2930i | 1.16282 | − | 1.48813i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.45197 | 0.156015 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6169 | 0.922613 | 0.461307 | − | 0.887241i | \(-0.347381\pi\) | ||||
0.461307 | + | 0.887241i | \(0.347381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.46908 | 0.155230 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9187 | −0.930605 | −0.465302 | − | 0.885152i | \(-0.654054\pi\) | ||||
−0.465302 | + | 0.885152i | \(0.654054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.3063 | + | 8.97585i | 0.826813 | + | 0.557732i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.2114 | −1.36962 | −0.684808 | − | 0.728724i | \(-0.740114\pi\) | ||||
−0.684808 | + | 0.728724i | \(0.740114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.06442 | − | 7.03978i | 0.249675 | − | 0.432450i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.73590 | − | 8.20281i | 0.288753 | − | 0.500134i | −0.684760 | − | 0.728769i | \(-0.740093\pi\) |
0.973512 | + | 0.228635i | \(0.0734261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.78188 | − | 15.2107i | −0.533461 | − | 0.923982i | −0.999236 | − | 0.0390786i | \(-0.987558\pi\) |
0.465775 | − | 0.884903i | \(-0.345776\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.7576 | 1.49294 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5530 | 0.814322 | 0.407161 | − | 0.913356i | \(-0.366519\pi\) | ||||
0.407161 | + | 0.913356i | \(0.366519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.14196 | − | 10.6382i | −0.366398 | − | 0.634621i | 0.622601 | − | 0.782539i | \(-0.286076\pi\) |
−0.989000 | + | 0.147919i | \(0.952743\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.02415 | + | 12.1662i | 0.417542 | + | 0.723204i | 0.995692 | − | 0.0927267i | \(-0.0295583\pi\) |
−0.578149 | + | 0.815931i | \(0.696225\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.484873 | + | 6.93072i | −0.0286212 | + | 0.409108i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.5760 | − | 30.4426i | −1.03388 | − | 1.79074i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.05863 | + | 7.02975i | −0.237108 | + | 0.410682i | −0.959883 | − | 0.280401i | \(-0.909533\pi\) |
0.722776 | + | 0.691083i | \(0.242866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.61207 | + | 16.6486i | 0.559636 | + | 0.969319i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.373122 | + | 0.646266i | −0.0215782 | + | 0.0373746i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.94048 | − | 1.30896i | −0.111847 | − | 0.0754473i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.3398 | − | 38.6937i | 1.27917 | − | 2.21559i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.61556 | −0.377570 | −0.188785 | − | 0.982018i | \(-0.560455\pi\) | ||||
−0.188785 | + | 0.982018i | \(0.560455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.17980 | + | 7.23963i | 0.237015 | + | 0.410522i | 0.959856 | − | 0.280492i | \(-0.0904976\pi\) |
−0.722841 | + | 0.691014i | \(0.757164\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0542 | + | 22.6105i | −0.737864 | + | 1.27802i | 0.215591 | + | 0.976484i | \(0.430832\pi\) |
−0.953455 | + | 0.301535i | \(0.902501\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.60741 | − | 9.71231i | 0.314943 | − | 0.545498i | −0.664482 | − | 0.747304i | \(-0.731348\pi\) |
0.979425 | + | 0.201806i | \(0.0646812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.10831 | + | 14.0440i | 0.453978 | + | 0.786314i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.3696 | 1.68981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.74132 | + | 6.48015i | −0.207531 | + | 0.359454i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.06430 | + | 15.2130i | −0.0586766 | + | 0.838717i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.11645 | + | 15.7902i | −0.501086 | + | 0.867906i | 0.498914 | + | 0.866652i | \(0.333732\pi\) |
−0.999999 | + | 0.00125391i | \(0.999601\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2699 | − | 17.7880i | −0.561104 | − | 0.971860i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.62148 | − | 8.00465i | 0.251748 | − | 0.436041i | −0.712259 | − | 0.701917i | \(-0.752328\pi\) |
0.964007 | + | 0.265876i | \(0.0856612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.918392 | − | 1.59070i | −0.0497337 | − | 0.0861413i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.85237 | − | 18.1152i | 0.208009 | − | 0.978127i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.8325 | + | 27.4226i | 0.849931 | + | 1.47212i | 0.881269 | + | 0.472615i | \(0.156690\pi\) |
−0.0313384 | + | 0.999509i | \(0.509977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.2112 | − | 31.5427i | −0.974821 | − | 1.68844i | −0.680525 | − | 0.732725i | \(-0.738248\pi\) |
−0.294296 | − | 0.955714i | \(-0.595085\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.19777 | −0.383098 | −0.191549 | − | 0.981483i | \(-0.561351\pi\) | ||||
−0.191549 | + | 0.981483i | \(0.561351\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 48.7510 | 2.58744 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.39891 | − | 12.8153i | −0.390499 | − | 0.676365i | 0.602016 | − | 0.798484i | \(-0.294364\pi\) |
−0.992515 | + | 0.122119i | \(0.961031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.657495 | − | 1.13881i | 0.0346050 | − | 0.0599376i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.88402 | − | 3.26323i | 0.0986144 | − | 0.170805i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.19100 | −0.218768 | −0.109384 | − | 0.994000i | \(-0.534888\pi\) | ||||
−0.109384 | + | 0.994000i | \(0.534888\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.355426 | − | 5.08042i | 0.0184528 | − | 0.263762i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.4175 | 0.901844 | 0.450922 | − | 0.892563i | \(-0.351095\pi\) | ||||
0.450922 | + | 0.892563i | \(0.351095\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.90125 | −0.252427 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1732 | 0.573927 | 0.286964 | − | 0.957941i | \(-0.407354\pi\) | ||||
0.286964 | + | 0.957941i | \(0.407354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.1016 | −1.28263 | −0.641316 | − | 0.767276i | \(-0.721611\pi\) | ||||
−0.641316 | + | 0.767276i | \(0.721611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.3731 | − | 9.44811i | 0.987345 | − | 0.481520i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.46402 | −0.0742289 | −0.0371144 | − | 0.999311i | \(-0.511817\pi\) | ||||
−0.0371144 | + | 0.999311i | \(0.511817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.62141 | + | 8.00452i | −0.233715 | + | 0.404806i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.0641 | + | 43.4124i | −1.26111 | + | 2.18431i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.49591 | − | 2.59100i | −0.0750778 | − | 0.130039i | 0.826042 | − | 0.563608i | \(-0.190587\pi\) |
−0.901120 | + | 0.433570i | \(0.857254\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.3371 | 1.31521 | 0.657605 | − | 0.753363i | \(-0.271570\pi\) | ||||
0.657605 | + | 0.753363i | \(0.271570\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.555142 | 0.0276536 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.85166 | + | 10.1354i | 0.290056 | + | 0.502392i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.50392 | − | 2.60487i | −0.0743642 | − | 0.128803i | 0.826445 | − | 0.563017i | \(-0.190359\pi\) |
−0.900810 | + | 0.434214i | \(0.857026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.98489 | + | 6.73537i | 0.491324 | + | 0.331426i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.1389 | − | 38.3457i | −1.08676 | − | 1.88232i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.2414 | + | 29.8630i | −0.842297 | + | 1.45890i | 0.0456508 | + | 0.998957i | \(0.485464\pi\) |
−0.887948 | + | 0.459944i | \(0.847869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.86151 | + | 17.0806i | 0.480620 | + | 0.832459i | 0.999753 | − | 0.0222349i | \(-0.00707818\pi\) |
−0.519132 | + | 0.854694i | \(0.673745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −46.3392 | + | 80.2618i | −2.24778 | + | 3.89327i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.95358 | − | 27.9242i | 0.0945402 | − | 1.35135i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.4257 | − | 18.0578i | 0.502188 | − | 0.869816i | −0.497808 | − | 0.867287i | \(-0.665862\pi\) |
0.999997 | − | 0.00252883i | \(-0.000804953\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.6324 | 0.751247 | 0.375624 | − | 0.926772i | \(-0.377429\pi\) | ||||
0.375624 | + | 0.926772i | \(0.377429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.69117 | − | 4.66125i | −0.128736 | − | 0.222978i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8495 | − | 30.9162i | 0.851909 | − | 1.47555i | −0.0275746 | − | 0.999620i | \(-0.508778\pi\) |
0.879483 | − | 0.475930i | \(-0.157888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.05787 | + | 15.6887i | −0.430352 | + | 0.745392i | −0.996904 | − | 0.0786344i | \(-0.974944\pi\) |
0.566551 | + | 0.824027i | \(0.308277\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.3811 | − | 28.3730i | −0.776541 | − | 1.34501i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.4189 | −0.822051 | −0.411025 | − | 0.911624i | \(-0.634829\pi\) | ||||
−0.411025 | + | 0.911624i | \(0.634829\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.53294 | + | 4.38719i | −0.119272 | + | 0.206585i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.454640 | + | 6.49858i | −0.0213139 | + | 0.304658i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.67918 | + | 13.3007i | −0.359217 | + | 0.622182i | −0.987830 | − | 0.155536i | \(-0.950290\pi\) |
0.628613 | + | 0.777718i | \(0.283623\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.15140 | + | 10.6545i | 0.286499 | + | 0.496231i | 0.972972 | − | 0.230924i | \(-0.0741750\pi\) |
−0.686472 | + | 0.727156i | \(0.740842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.18922 | + | 15.9162i | −0.427059 | + | 0.739688i | −0.996610 | − | 0.0822677i | \(-0.973784\pi\) |
0.569551 | + | 0.821956i | \(0.307117\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.1020 | − | 19.2292i | −0.513738 | − | 0.889820i | −0.999873 | − | 0.0159363i | \(-0.994927\pi\) |
0.486135 | − | 0.873884i | \(-0.338406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6682 | − | 7.19631i | −0.492612 | − | 0.332295i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.853358 | − | 1.47806i | −0.0392374 | − | 0.0679612i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.9845 | − | 46.7386i | −1.23814 | − | 2.14451i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.5938 | −1.58063 | −0.790317 | − | 0.612699i | \(-0.790084\pi\) | ||||
−0.790317 | + | 0.612699i | \(0.790084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.53717 | −0.161281 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.38895 | − | 14.5301i | −0.380922 | − | 0.659777i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.79789 | + | 11.7743i | −0.308042 | + | 0.533544i | −0.977934 | − | 0.208915i | \(-0.933007\pi\) |
0.669892 | + | 0.742458i | \(0.266340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.01841 | + | 12.1563i | −0.316737 | + | 0.548604i | −0.979805 | − | 0.199955i | \(-0.935920\pi\) |
0.663069 | + | 0.748559i | \(0.269254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.7058 | −2.73405 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.4526 | − | 13.3884i | 1.23142 | − | 0.600551i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.2816 | 1.35559 | 0.677794 | − | 0.735251i | \(-0.262936\pi\) | ||||
0.677794 | + | 0.735251i | \(0.262936\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.5942 | −1.58707 | −0.793533 | − | 0.608527i | \(-0.791761\pi\) | ||||
−0.793533 | + | 0.608527i | \(0.791761\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −70.8219 | −3.15153 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.47349 | 0.286932 | 0.143466 | − | 0.989655i | \(-0.454175\pi\) | ||||
0.143466 | + | 0.989655i | \(0.454175\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.164755 | − | 2.35499i | 0.00728832 | − | 0.104178i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −49.0344 | −2.16072 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.55982 | + | 9.62989i | −0.244521 | + | 0.423522i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.18988 | + | 10.7212i | −0.271184 | + | 0.469704i | −0.969165 | − | 0.246412i | \(-0.920748\pi\) |
0.697982 | + | 0.716116i | \(0.254082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.0290 | − | 19.1028i | −0.482265 | − | 0.835308i | 0.517527 | − | 0.855667i | \(-0.326853\pi\) |
−0.999793 | + | 0.0203585i | \(0.993519\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.87588 | 0.299518 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3619 | −0.928779 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.765547 | − | 1.32597i | −0.0331595 | − | 0.0574340i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.2659 | − | 74.9388i | −1.87055 | − | 3.23989i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.31462 | − | 10.6408i | 0.358136 | − | 0.458331i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.24989 | + | 12.5572i | 0.311697 | + | 0.539875i | 0.978730 | − | 0.205153i | \(-0.0657693\pi\) |
−0.667033 | + | 0.745028i | \(0.732436\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.4293 | − | 18.0640i | 0.446740 | − | 0.773777i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.4034 | + | 21.4834i | 0.530332 | + | 0.918562i | 0.999374 | + | 0.0353858i | \(0.0112660\pi\) |
−0.469042 | + | 0.883176i | \(0.655401\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.6753 | − | 30.6146i | 0.752994 | − | 1.30422i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.19182 | + | 31.3296i | −0.0932055 | + | 1.33227i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.02336 | + | 15.6289i | −0.382332 | + | 0.662219i | −0.991395 | − | 0.130903i | \(-0.958212\pi\) |
0.609063 | + | 0.793122i | \(0.291546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.515831 | 0.0218173 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.51748 | − | 16.4848i | −0.401114 | − | 0.694749i | 0.592747 | − | 0.805389i | \(-0.298043\pi\) |
−0.993861 | + | 0.110639i | \(0.964710\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.3399 | − | 54.2823i | 1.31848 | − | 2.28367i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.68018 | − | 8.10631i | 0.196203 | − | 0.339834i | −0.751091 | − | 0.660199i | \(-0.770472\pi\) |
0.947294 | + | 0.320364i | \(0.103805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6805 | + | 30.6236i | 0.739907 | + | 1.28156i | 0.952537 | + | 0.304424i | \(0.0984638\pi\) |
−0.212630 | + | 0.977133i | \(0.568203\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.4252 | 0.684979 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0160 | − | 24.2764i | 0.583493 | − | 1.01064i | −0.411568 | − | 0.911379i | \(-0.635019\pi\) |
0.995061 | − | 0.0992610i | \(-0.0316479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.9976 | − | 15.5132i | −0.954100 | − | 0.643595i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.85672 | − | 3.21594i | 0.0768976 | − | 0.133190i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.7305 | + | 23.7819i | 0.566718 | + | 0.981585i | 0.996888 | + | 0.0788364i | \(0.0251205\pi\) |
−0.430169 | + | 0.902748i | \(0.641546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00200 | + | 3.46757i | −0.0824912 | + | 0.142879i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.1267 | + | 19.2719i | 0.456917 | + | 0.791404i | 0.998796 | − | 0.0490525i | \(-0.0156202\pi\) |
−0.541879 | + | 0.840457i | \(0.682287\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.63108 | + | 80.4900i | −0.230852 | + | 3.29977i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.37059 | − | 5.83804i | −0.137719 | − | 0.238536i | 0.788914 | − | 0.614504i | \(-0.210644\pi\) |
−0.926633 | + | 0.375968i | \(0.877310\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.04153 | + | 7.00013i | 0.164857 | + | 0.285541i | 0.936605 | − | 0.350388i | \(-0.113950\pi\) |
−0.771747 | + | 0.635929i | \(0.780617\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.7363 | −1.24961 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.6039 | −1.28276 | −0.641382 | − | 0.767222i | \(-0.721639\pi\) | ||||
−0.641382 | + | 0.767222i | \(0.721639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.68038 | − | 2.91050i | −0.0679808 | − | 0.117746i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.10601 | + | 5.37977i | −0.125451 | + | 0.217287i | −0.921909 | − | 0.387407i | \(-0.873371\pi\) |
0.796458 | + | 0.604693i | \(0.206704\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.309009 | − | 0.535218i | 0.0124402 | − | 0.0215471i | −0.859738 | − | 0.510735i | \(-0.829373\pi\) |
0.872178 | + | 0.489188i | \(0.162707\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.0206 | −1.60857 | −0.804283 | − | 0.594247i | \(-0.797450\pi\) | ||||
−0.804283 | + | 0.594247i | \(0.797450\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.0165 | − | 11.4786i | −0.681752 | − | 0.459880i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 75.5295 | 3.02118 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.8106 | −1.74684 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.20154 | −0.207070 | −0.103535 | − | 0.994626i | \(-0.533015\pi\) | ||||
−0.103535 | + | 0.994626i | \(0.533015\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.0492 | 1.43057 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.52867 | + | 3.78432i | 0.0605682 | + | 0.149940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.274587 | 0.0108455 | 0.00542277 | − | 0.999985i | \(-0.498274\pi\) | ||||
0.00542277 | + | 0.999985i | \(0.498274\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.2657 | + | 19.5128i | −0.444277 | + | 0.769510i | −0.998002 | − | 0.0631900i | \(-0.979873\pi\) |
0.553725 | + | 0.832700i | \(0.313206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.2737 | − | 21.2586i | 0.482528 | − | 0.835763i | −0.517271 | − | 0.855822i | \(-0.673052\pi\) |
0.999799 | + | 0.0200588i | \(0.00638534\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.39102 | + | 7.60547i | 0.172363 | + | 0.298541i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.0308 | −1.29260 | −0.646298 | − | 0.763085i | \(-0.723684\pi\) | ||||
−0.646298 | + | 0.763085i | \(0.723684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.91064 | −0.387241 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.3813 | + | 37.0335i | 0.832897 | + | 1.44262i | 0.895731 | + | 0.444596i | \(0.146653\pi\) |
−0.0628336 | + | 0.998024i | \(0.520014\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.55416 | + | 16.5483i | 0.371614 | + | 0.643654i | 0.989814 | − | 0.142367i | \(-0.0454713\pi\) |
−0.618200 | + | 0.786021i | \(0.712138\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −38.9523 | − | 26.2756i | −1.51051 | − | 1.01892i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.37940 | + | 9.31739i | 0.208291 | + | 0.360771i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.2054 | − | 17.6762i | 0.393973 | − | 0.682382i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.9345 | − | 22.4032i | −0.498588 | − | 0.863579i | 0.501411 | − | 0.865209i | \(-0.332815\pi\) |
−0.999999 | + | 0.00162995i | \(0.999481\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.946686 | − | 1.63971i | 0.0363841 | − | 0.0630191i | −0.847260 | − | 0.531178i | \(-0.821749\pi\) |
0.883644 | + | 0.468159i | \(0.155083\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.71432 | − | 5.87830i | −0.334425 | − | 0.225589i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.39573 | + | 11.0777i | −0.244726 | + | 0.423878i | −0.962055 | − | 0.272857i | \(-0.912031\pi\) |
0.717329 | + | 0.696735i | \(0.245365\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.42072 | −0.207115 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.561168 | + | 0.971972i | 0.0213788 | + | 0.0370292i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.0349 | + | 31.2373i | −0.686079 | + | 1.18832i | 0.287017 | + | 0.957925i | \(0.407336\pi\) |
−0.973096 | + | 0.230399i | \(0.925997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.57834 | + | 4.46582i | −0.0978022 | + | 0.169398i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.48191 | − | 16.4231i | −0.359153 | − | 0.622071i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.2524 | 0.764922 | 0.382461 | − | 0.923972i | \(-0.375077\pi\) | ||||
0.382461 | + | 0.923972i | \(0.375077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.7560 | − | 22.0941i | 0.481103 | − | 0.833296i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39.8811 | + | 19.4497i | −1.49988 | + | 0.731480i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.38318 | − | 5.85984i | 0.127058 | − | 0.220071i | −0.795478 | − | 0.605983i | \(-0.792780\pi\) |
0.922536 | + | 0.385912i | \(0.126113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.609300 | − | 1.05534i | −0.0228185 | − | 0.0395227i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.37501 | + | 4.11364i | −0.0888203 | + | 0.153841i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.43767 | + | 11.1504i | 0.240084 | + | 0.415839i | 0.960738 | − | 0.277457i | \(-0.0894915\pi\) |
−0.720654 | + | 0.693295i | \(0.756158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.6121 | + | 13.4662i | −1.02833 | + | 0.501508i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 53.9395 | + | 93.4260i | 2.00326 | + | 3.46975i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.3621 | − | 24.8758i | −0.532659 | − | 0.922593i | −0.999273 | − | 0.0381316i | \(-0.987859\pi\) |
0.466613 | − | 0.884461i | \(-0.345474\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.38897 | 0.236305 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.66050 | 0.172139 | 0.0860697 | − | 0.996289i | \(-0.472569\pi\) | ||||
0.0860697 | + | 0.996289i | \(0.472569\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.69153 | − | 8.12596i | −0.172815 | − | 0.299324i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.46395 | + | 16.3920i | −0.348137 | + | 0.602991i | −0.985919 | − | 0.167227i | \(-0.946519\pi\) |
0.637782 | + | 0.770217i | \(0.279852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.64732 | − | 11.5135i | 0.243867 | − | 0.422389i | −0.717946 | − | 0.696099i | \(-0.754917\pi\) |
0.961812 | + | 0.273710i | \(0.0882507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.5818 | −0.973882 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −44.9441 | − | 30.3173i | −1.64222 | − | 1.10777i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2353 | 0.555945 | 0.277972 | − | 0.960589i | \(-0.410338\pi\) | ||||
0.277972 | + | 0.960589i | \(0.410338\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.94308 | −0.361866 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.6279 | 0.568004 | 0.284002 | − | 0.958824i | \(-0.408338\pi\) | ||||
0.284002 | + | 0.958824i | \(0.408338\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.09595 | −0.257228 | −0.128614 | − | 0.991695i | \(-0.541053\pi\) | ||||
−0.128614 | + | 0.991695i | \(0.541053\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.912020 | − | 13.0363i | 0.0330173 | − | 0.471946i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.65425 | −0.0958394 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.71618 | − | 9.90071i | 0.206131 | − | 0.357029i | −0.744362 | − | 0.667777i | \(-0.767246\pi\) |
0.950492 | + | 0.310748i | \(0.100579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.40125 | + | 12.8193i | −0.266204 | + | 0.461080i | −0.967878 | − | 0.251418i | \(-0.919103\pi\) |
0.701674 | + | 0.712498i | \(0.252436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.10949 | − | 10.5819i | −0.219459 | − | 0.380114i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.0431 | 0.395661 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.2706 | 0.796906 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.09951 | + | 10.5647i | 0.217701 | + | 0.377069i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.85887 | − | 17.0761i | −0.351431 | − | 0.608696i | 0.635070 | − | 0.772455i | \(-0.280971\pi\) |
−0.986500 | + | 0.163759i | \(0.947638\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.74062 | − | 39.1741i | 0.0974452 | − | 1.39287i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.08442 | + | 5.34238i | 0.109531 | + | 0.189713i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.2215 | + | 38.4887i | −0.787125 | + | 1.36334i | 0.140597 | + | 0.990067i | \(0.455098\pi\) |
−0.927722 | + | 0.373273i | \(0.878236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.8128 | − | 36.0488i | −0.736304 | − | 1.27532i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.860667 | − | 1.49072i | 0.0303723 | − | 0.0526063i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8529 | − | 6.26827i | 0.453007 | − | 0.220928i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.34657 | − | 9.26053i | 0.187975 | − | 0.325583i | −0.756600 | − | 0.653878i | \(-0.773141\pi\) |
0.944575 | + | 0.328296i | \(0.106474\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.1292 | 0.461030 | 0.230515 | − | 0.973069i | \(-0.425959\pi\) | ||||
0.230515 | + | 0.973069i | \(0.425959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.0024 | − | 19.0567i | −0.385398 | − | 0.667529i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.86024 | + | 3.22202i | −0.0650814 | + | 0.112724i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.31404 | − | 2.27598i | 0.0458602 | − | 0.0794323i | −0.842184 | − | 0.539190i | \(-0.818730\pi\) |
0.888044 | + | 0.459758i | \(0.152064\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.1960 | − | 40.1767i | −0.808563 | − | 1.40047i | −0.913859 | − | 0.406031i | \(-0.866912\pi\) |
0.105296 | − | 0.994441i | \(-0.466421\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.2072 | −0.528807 | −0.264404 | − | 0.964412i | \(-0.585175\pi\) | ||||
−0.264404 | + | 0.964412i | \(0.585175\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0782 | − | 33.0445i | 0.662615 | − | 1.14768i | −0.317311 | − | 0.948322i | \(-0.602780\pi\) |
0.979926 | − | 0.199361i | \(-0.0638867\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.9338 | + | 46.8718i | 0.656018 | + | 1.62401i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.5101 | − | 77.0937i | 1.54033 | − | 2.66794i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.52298 | − | 9.56608i | −0.190674 | − | 0.330258i | 0.754800 | − | 0.655955i | \(-0.227734\pi\) |
−0.945474 | + | 0.325698i | \(0.894401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.8313 | + | 36.0808i | −0.718320 | + | 1.24417i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.7314 | + | 46.3002i | 0.919590 | + | 1.59278i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.3082 | + | 8.44105i | −0.594716 | + | 0.290038i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.88224 | + | 6.72424i | 0.133081 | + | 0.230504i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.4259 | + | 38.8428i | 0.767847 | + | 1.32995i | 0.938728 | + | 0.344659i | \(0.112005\pi\) |
−0.170881 | + | 0.985292i | \(0.554661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.09527 | −0.208211 | −0.104105 | − | 0.994566i | \(-0.533198\pi\) | ||||
−0.104105 | + | 0.994566i | \(0.533198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.2137 | −1.03088 | −0.515438 | − | 0.856927i | \(-0.672371\pi\) | ||||
−0.515438 | + | 0.856927i | \(0.672371\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.3315 | − | 36.9472i | −0.726131 | − | 1.25770i | −0.958507 | − | 0.285070i | \(-0.907983\pi\) |
0.232375 | − | 0.972626i | \(-0.425350\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.60018 | + | 14.8959i | −0.292415 | + | 0.506477i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.4499 | + | 19.8318i | −0.388411 | + | 0.672748i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.83590 | 0.0960907 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 78.6656 | − | 38.3645i | 2.65938 | − | 1.29696i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.6751 | 0.698147 | 0.349074 | − | 0.937095i | \(-0.386496\pi\) | ||||
0.349074 | + | 0.937095i | \(0.386496\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.40674 | −0.182158 | −0.0910789 | − | 0.995844i | \(-0.529032\pi\) | ||||
−0.0910789 | + | 0.995844i | \(0.529032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.16348 | 0.106460 | 0.0532299 | − | 0.998582i | \(-0.483048\pi\) | ||||
0.0532299 | + | 0.998582i | \(0.483048\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.0863 | −0.338666 | −0.169333 | − | 0.985559i | \(-0.554161\pi\) | ||||
−0.169333 | + | 0.985559i | \(0.554161\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.3000 | − | 9.90012i | 0.680839 | − | 0.332039i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.2397 | 0.811151 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.1371 | + | 22.7542i | −0.439126 | + | 0.760589i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00181 | − | 6.93135i | 0.133468 | − | 0.231173i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.95051 | + | 12.0386i | 0.231555 | + | 0.401065i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 77.0249 | 2.56040 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.8637 | 0.792380 | 0.396190 | − | 0.918169i | \(-0.370332\pi\) | ||||
0.396190 | + | 0.918169i | \(0.370332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.67946 | + | 16.7653i | 0.320695 | + | 0.555460i | 0.980632 | − | 0.195862i | \(-0.0627503\pi\) |
−0.659937 | + | 0.751321i | \(0.729417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.1136 | − | 17.5172i | −0.334710 | − | 0.579735i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.58085 | + | 2.72174i | −0.184296 | + | 0.0898796i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.2052 | + | 43.6567i | 0.831444 | + | 1.44010i | 0.896893 | + | 0.442247i | \(0.145818\pi\) |
−0.0654498 | + | 0.997856i | \(0.520848\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.36549 | + | 5.82920i | −0.110777 | + | 0.191871i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.9274 | + | 67.4243i | 1.27993 | + | 2.21690i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.1465 | − | 36.6267i | 0.693793 | − | 1.20168i | −0.276793 | − | 0.960930i | \(-0.589272\pi\) |
0.970586 | − | 0.240755i | \(-0.0773950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.1507 | − | 4.09883i | −0.955377 | − | 0.134334i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.4164 | + | 50.9506i | −0.962018 | + | 1.66626i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6771 | 0.675490 | 0.337745 | − | 0.941238i | \(-0.390336\pi\) | ||||
0.337745 | + | 0.941238i | \(0.390336\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.1646 | − | 29.7300i | −0.559550 | − | 0.969170i | −0.997534 | − | 0.0701867i | \(-0.977640\pi\) |
0.437983 | − | 0.898983i | \(-0.355693\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.68046 | + | 2.91065i | −0.0547234 | + | 0.0947837i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.8650 | − | 24.0149i | 0.450551 | − | 0.780378i | −0.547869 | − | 0.836564i | \(-0.684561\pi\) |
0.998420 | + | 0.0561863i | \(0.0178941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.260125 | + | 0.450549i | 0.00844400 | + | 0.0146254i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.8102 | 0.738894 | 0.369447 | − | 0.929252i | \(-0.379547\pi\) | ||||
0.369447 | + | 0.929252i | \(0.379547\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.5953 | − | 27.0119i | 0.504653 | − | 0.874085i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.05250 | + | 1.48868i | −0.0985705 | + | 0.0480720i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0467 | − | 26.0617i | 0.485378 | − | 0.840700i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −41.2123 | − | 71.3817i | −1.32667 | − | 2.29786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.8697 | + | 18.8269i | −0.349546 | + | 0.605432i | −0.986169 | − | 0.165744i | \(-0.946998\pi\) |
0.636623 | + | 0.771175i | \(0.280331\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.7959 | − | 34.2875i | −0.635281 | − | 1.10034i | −0.986455 | − | 0.164029i | \(-0.947551\pi\) |
0.351174 | − | 0.936310i | \(-0.385782\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.225472 | + | 3.22287i | −0.00722829 | + | 0.103320i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.8724 | − | 39.6161i | −0.731752 | − | 1.26743i | −0.956134 | − | 0.292930i | \(-0.905370\pi\) |
0.224382 | − | 0.974501i | \(-0.427964\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.48329 | − | 12.9614i | −0.239167 | − | 0.414250i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.0498 | 0.480014 | 0.240007 | − | 0.970771i | \(-0.422850\pi\) | ||||
0.240007 | + | 0.970771i | \(0.422850\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.8363 | −1.04625 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.566154 | − | 0.980607i | −0.0180026 | − | 0.0311815i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3516 | − | 19.6616i | 0.360596 | − | 0.624570i | −0.627463 | − | 0.778646i | \(-0.715907\pi\) |
0.988059 | + | 0.154076i | \(0.0492400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.2894 | − | 28.2140i | 0.516408 | − | 0.894445i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.5352 | −1.75882 | −0.879408 | − | 0.476069i | \(-0.842061\pi\) | ||||
−0.879408 | + | 0.476069i | \(0.842061\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3024.2.t.k.1873.11 | 22 | ||
3.2 | odd | 2 | 1008.2.t.l.193.11 | 22 | |||
4.3 | odd | 2 | 1512.2.t.c.361.11 | 22 | |||
7.2 | even | 3 | 3024.2.q.l.2305.1 | 22 | |||
9.2 | odd | 6 | 1008.2.q.l.529.5 | 22 | |||
9.7 | even | 3 | 3024.2.q.l.2881.1 | 22 | |||
12.11 | even | 2 | 504.2.t.c.193.1 | yes | 22 | ||
21.2 | odd | 6 | 1008.2.q.l.625.5 | 22 | |||
28.23 | odd | 6 | 1512.2.q.d.793.1 | 22 | |||
36.7 | odd | 6 | 1512.2.q.d.1369.1 | 22 | |||
36.11 | even | 6 | 504.2.q.c.25.7 | ✓ | 22 | ||
63.2 | odd | 6 | 1008.2.t.l.961.11 | 22 | |||
63.16 | even | 3 | inner | 3024.2.t.k.289.11 | 22 | ||
84.23 | even | 6 | 504.2.q.c.121.7 | yes | 22 | ||
252.79 | odd | 6 | 1512.2.t.c.289.11 | 22 | |||
252.191 | even | 6 | 504.2.t.c.457.1 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.7 | ✓ | 22 | 36.11 | even | 6 | ||
504.2.q.c.121.7 | yes | 22 | 84.23 | even | 6 | ||
504.2.t.c.193.1 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.c.457.1 | yes | 22 | 252.191 | even | 6 | ||
1008.2.q.l.529.5 | 22 | 9.2 | odd | 6 | |||
1008.2.q.l.625.5 | 22 | 21.2 | odd | 6 | |||
1008.2.t.l.193.11 | 22 | 3.2 | odd | 2 | |||
1008.2.t.l.961.11 | 22 | 63.2 | odd | 6 | |||
1512.2.q.d.793.1 | 22 | 28.23 | odd | 6 | |||
1512.2.q.d.1369.1 | 22 | 36.7 | odd | 6 | |||
1512.2.t.c.289.11 | 22 | 252.79 | odd | 6 | |||
1512.2.t.c.361.11 | 22 | 4.3 | odd | 2 | |||
3024.2.q.l.2305.1 | 22 | 7.2 | even | 3 | |||
3024.2.q.l.2881.1 | 22 | 9.7 | even | 3 | |||
3024.2.t.k.289.11 | 22 | 63.16 | even | 3 | inner | ||
3024.2.t.k.1873.11 | 22 | 1.1 | even | 1 | trivial |