Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1279,3024)]
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([3, 0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1279");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.cz (of order \(6\), 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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1279.4 | ||
Character | \(\chi\) | \(=\) | 3024.1279 |
Dual form | 3024.2.cz.g.2719.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | −1.73177 | + | 0.999840i | −0.774472 | + | 0.447142i | −0.834468 | − | 0.551057i | \(-0.814225\pi\) |
0.0599953 | + | 0.998199i | \(0.480891\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.38101 | + | 1.15360i | −0.899937 | + | 0.436019i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17995 | + | 0.681244i | 0.355768 | + | 0.205403i | 0.667223 | − | 0.744858i | \(-0.267483\pi\) |
−0.311455 | + | 0.950261i | \(0.600816\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.71030 | + | 0.987444i | 0.474353 | + | 0.273868i | 0.718060 | − | 0.695981i | \(-0.245030\pi\) |
−0.243707 | + | 0.969849i | \(0.578364\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.868852 | + | 0.501632i | −0.210728 | + | 0.121664i | −0.601649 | − | 0.798760i | \(-0.705490\pi\) |
0.390922 | + | 0.920424i | \(0.372156\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.774396 | − | 1.34129i | 0.177659 | − | 0.307714i | −0.763420 | − | 0.645903i | \(-0.776481\pi\) |
0.941078 | + | 0.338189i | \(0.109814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.59639 | + | 4.38578i | −1.58396 | + | 0.914498i | −0.589682 | + | 0.807635i | \(0.700747\pi\) |
−0.994274 | + | 0.106862i | \(0.965920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500642 | + | 0.867137i | −0.100128 | + | 0.173427i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.854529 | − | 1.48009i | −0.158682 | − | 0.274846i | 0.775712 | − | 0.631088i | \(-0.217391\pi\) |
−0.934394 | + | 0.356242i | \(0.884058\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.522244 | 0.0937979 | 0.0468989 | − | 0.998900i | \(-0.485066\pi\) | ||||
0.0468989 | + | 0.998900i | \(0.485066\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.96996 | − | 4.37840i | 0.502014 | − | 0.740085i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.53855 | − | 2.66485i | 0.252936 | − | 0.438099i | −0.711397 | − | 0.702791i | \(-0.751937\pi\) |
0.964333 | + | 0.264692i | \(0.0852703\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.386794 | + | 0.223316i | 0.0604071 | + | 0.0348761i | 0.529899 | − | 0.848061i | \(-0.322230\pi\) |
−0.469492 | + | 0.882937i | \(0.655563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.49888 | − | 3.17478i | 0.838572 | − | 0.484150i | −0.0182067 | − | 0.999834i | \(-0.505796\pi\) |
0.856779 | + | 0.515685i | \(0.172462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.63949 | −0.239144 | −0.119572 | − | 0.992826i | \(-0.538152\pi\) | ||||
−0.119572 | + | 0.992826i | \(0.538152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.33842 | − | 5.49346i | 0.619774 | − | 0.784780i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.24313 | − | 2.15316i | −0.170757 | − | 0.295760i | 0.767928 | − | 0.640537i | \(-0.221288\pi\) |
−0.938685 | + | 0.344777i | \(0.887955\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.72454 | −0.367377 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.6284 | −1.64408 | −0.822040 | − | 0.569430i | \(-0.807164\pi\) | ||||
−0.822040 | + | 0.569430i | \(0.807164\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5433i | 1.34994i | 0.737847 | + | 0.674968i | \(0.235843\pi\) | ||||
−0.737847 | + | 0.674968i | \(0.764157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.94914 | −0.489831 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50486i | 0.794695i | 0.917668 | + | 0.397347i | \(0.130069\pi\) | ||||
−0.917668 | + | 0.397347i | \(0.869931\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.57299i | − | 0.186679i | −0.995634 | − | 0.0933396i | \(-0.970246\pi\) | ||
0.995634 | − | 0.0933396i | \(-0.0297542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6347 | − | 7.87199i | 1.59582 | − | 0.921346i | 0.603538 | − | 0.797334i | \(-0.293757\pi\) |
0.992281 | − | 0.124012i | \(-0.0395760\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.59535 | − | 0.260861i | −0.409728 | − | 0.0297279i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.95935i | − | 0.670479i | −0.942133 | − | 0.335240i | \(-0.891183\pi\) | ||
0.942133 | − | 0.335240i | \(-0.108817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.80565 | − | 8.32363i | −0.527489 | − | 0.913637i | −0.999487 | − | 0.0320377i | \(-0.989800\pi\) |
0.471998 | − | 0.881600i | \(-0.343533\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00310 | − | 1.73743i | 0.108802 | − | 0.188450i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.10887 | + | 0.640207i | 0.117540 | + | 0.0678618i | 0.557617 | − | 0.830098i | \(-0.311716\pi\) |
−0.440077 | + | 0.897960i | \(0.645049\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.21136 | − | 0.378111i | −0.546299 | − | 0.0396368i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.09709i | 0.317754i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.31781 | − | 4.80229i | 0.844546 | − | 0.487599i | −0.0142608 | − | 0.999898i | \(-0.504540\pi\) |
0.858807 | + | 0.512299i | \(0.171206\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.76069 | − | 5.63534i | −0.971225 | − | 0.560737i | −0.0716156 | − | 0.997432i | \(-0.522815\pi\) |
−0.899610 | + | 0.436695i | \(0.856149\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.80600 | − | 8.32424i | −0.473550 | − | 0.820212i | 0.525992 | − | 0.850490i | \(-0.323694\pi\) |
−0.999542 | + | 0.0302775i | \(0.990361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.0876 | − | 6.40144i | −1.07188 | − | 0.618850i | −0.143186 | − | 0.989696i | \(-0.545735\pi\) |
−0.928695 | + | 0.370845i | \(0.879068\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.28182 | − | 12.6125i | −0.697472 | − | 1.20806i | −0.969340 | − | 0.245722i | \(-0.920975\pi\) |
0.271869 | − | 0.962334i | \(-0.412358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.07922 | − | 15.7257i | 0.854101 | − | 1.47935i | −0.0233754 | − | 0.999727i | \(-0.507441\pi\) |
0.877476 | − | 0.479620i | \(-0.159225\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.77014 | − | 15.1903i | 0.817820 | − | 1.41651i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.49006 | − | 2.19670i | 0.136594 | − | 0.201371i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.57181 | − | 7.91861i | −0.415619 | − | 0.719874i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0006i | − | 1.07337i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.2304i | − | 1.17401i | −0.809585 | − | 0.587003i | \(-0.800308\pi\) | ||
0.809585 | − | 0.587003i | \(-0.199692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.27126 | − | 7.39804i | −0.373182 | − | 0.646370i | 0.616871 | − | 0.787064i | \(-0.288400\pi\) |
−0.990053 | + | 0.140694i | \(0.955067\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.296530 | + | 4.08697i | −0.0257125 | + | 0.354386i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.92756 | + | 3.33864i | −0.164683 | + | 0.285239i | −0.936543 | − | 0.350554i | \(-0.885993\pi\) |
0.771860 | + | 0.635793i | \(0.219327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.59749 | + | 13.1592i | −0.644410 | + | 1.11615i | 0.340027 | + | 0.940416i | \(0.389564\pi\) |
−0.984437 | + | 0.175736i | \(0.943770\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.34538 | + | 2.33027i | 0.112506 | + | 0.194867i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.95970 | + | 1.70878i | 0.245790 | + | 0.141907i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.77752 | + | 10.0070i | 0.473313 | + | 0.819802i | 0.999533 | − | 0.0305463i | \(-0.00972470\pi\) |
−0.526221 | + | 0.850348i | \(0.676391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.6224 | − | 11.3290i | −1.59685 | − | 0.921941i | −0.992089 | − | 0.125533i | \(-0.959936\pi\) |
−0.604759 | − | 0.796408i | \(-0.706731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.904409 | + | 0.522161i | −0.0726439 | + | 0.0419409i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6276i | 1.16741i | 0.811965 | + | 0.583706i | \(0.198398\pi\) | ||||
−0.811965 | + | 0.583706i | \(0.801602\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.0276 | − | 19.2058i | 1.02672 | − | 1.51363i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4437 | − | 6.02970i | −0.818017 | − | 0.472282i | 0.0317152 | − | 0.999497i | \(-0.489903\pi\) |
−0.849732 | + | 0.527215i | \(0.823236\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0887 | + | 19.2062i | −0.858069 | + | 1.48622i | 0.0156998 | + | 0.999877i | \(0.495002\pi\) |
−0.873769 | + | 0.486342i | \(0.838331\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.54991 | − | 7.88067i | −0.349993 | − | 0.606206i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.9706i | 1.13819i | 0.822270 | + | 0.569097i | \(0.192707\pi\) | ||||
−0.822270 | + | 0.569097i | \(0.807293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.191705 | − | 2.64220i | 0.0144915 | − | 0.199732i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1951 | − | 7.04084i | 0.911505 | − | 0.526257i | 0.0305897 | − | 0.999532i | \(-0.490261\pi\) |
0.880915 | + | 0.473275i | \(0.156928\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.70875i | 0.349999i | 0.984569 | + | 0.174999i | \(0.0559924\pi\) | ||||
−0.984569 | + | 0.174999i | \(0.944008\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.15322i | 0.452394i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.36693 | −0.0999601 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.63432i | − | 0.624758i | −0.949958 | − | 0.312379i | \(-0.898874\pi\) | ||
0.949958 | − | 0.312379i | \(-0.101126\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9280 | 0.786613 | 0.393307 | − | 0.919407i | \(-0.371331\pi\) | ||||
0.393307 | + | 0.919407i | \(0.371331\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7147 | 1.40461 | 0.702305 | − | 0.711876i | \(-0.252154\pi\) | ||||
0.702305 | + | 0.711876i | \(0.252154\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.3575 | − | 23.1359i | −0.946889 | − | 1.64006i | −0.751924 | − | 0.659249i | \(-0.770874\pi\) |
−0.194965 | − | 0.980810i | \(-0.562459\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.74207 | + | 2.53832i | 0.262642 | + | 0.178155i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.893120 | −0.0623782 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.82749 | − | 1.05510i | 0.126410 | − | 0.0729831i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.27293 | − | 3.62168i | −0.431846 | − | 0.249327i | 0.268286 | − | 0.963339i | \(-0.413543\pi\) |
−0.700133 | + | 0.714012i | \(0.746876\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.34854 | + | 10.9960i | −0.432967 | + | 0.749921i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.24347 | + | 0.602460i | −0.0844122 | + | 0.0408977i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.98133 | −0.133279 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.80779 | + | 16.9876i | 0.656778 | + | 1.13757i | 0.981445 | + | 0.191744i | \(0.0614145\pi\) |
−0.324667 | + | 0.945828i | \(0.605252\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3892 | + | 17.9947i | −0.689557 | + | 1.19435i | 0.282424 | + | 0.959290i | \(0.408861\pi\) |
−0.971981 | + | 0.235058i | \(0.924472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.1630 | + | 11.0638i | −1.26633 | + | 0.731113i | −0.974291 | − | 0.225294i | \(-0.927666\pi\) |
−0.292035 | + | 0.956408i | \(0.594332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.95965 | − | 3.39421i | 0.128381 | − | 0.222362i | −0.794669 | − | 0.607043i | \(-0.792355\pi\) |
0.923049 | + | 0.384681i | \(0.125689\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.83922 | − | 1.63922i | 0.185210 | − | 0.106931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.38657 | − | 4.26464i | −0.477798 | − | 0.275857i | 0.241701 | − | 0.970351i | \(-0.422295\pi\) |
−0.719498 | + | 0.694494i | \(0.755628\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.09775 | + | 1.21114i | 0.135128 | + | 0.0780161i | 0.566040 | − | 0.824378i | \(-0.308475\pi\) |
−0.430912 | + | 0.902394i | \(0.641808\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.02058 | + | 13.8512i | −0.129090 | + | 0.884918i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.64890 | − | 1.52934i | 0.168546 | − | 0.0973099i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.09792 | −0.0693002 | −0.0346501 | − | 0.999400i | \(-0.511032\pi\) | ||||
−0.0346501 | + | 0.999400i | \(0.511032\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.9511 | −0.751361 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2289 | − | 10.5245i | 1.13709 | − | 0.656498i | 0.191380 | − | 0.981516i | \(-0.438704\pi\) |
0.945708 | + | 0.325018i | \(0.105371\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.589140 | + | 8.11991i | −0.0366074 | + | 0.504547i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.1850 | + | 12.2312i | 1.30632 | + | 0.754206i | 0.981481 | − | 0.191562i | \(-0.0613552\pi\) |
0.324843 | + | 0.945768i | \(0.394689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.30564 | + | 2.48586i | 0.264493 | + | 0.152705i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.79690 | − | 5.65624i | 0.597327 | − | 0.344867i | −0.170662 | − | 0.985330i | \(-0.554591\pi\) |
0.767989 | + | 0.640462i | \(0.221257\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.480849 | + | 0.832856i | −0.0292095 | + | 0.0505924i | −0.880261 | − | 0.474490i | \(-0.842632\pi\) |
0.851051 | + | 0.525083i | \(0.175966\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.18146 | + | 0.682118i | −0.0712449 | + | 0.0411333i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5249 | − | 21.6938i | 0.752549 | − | 1.30345i | −0.194034 | − | 0.980995i | \(-0.562157\pi\) |
0.946583 | − | 0.322459i | \(-0.104509\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0324 | − | 19.1087i | −0.658139 | − | 1.13993i | −0.981097 | − | 0.193517i | \(-0.938010\pi\) |
0.322958 | − | 0.946413i | \(-0.395323\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.26865 | 0.313189 | 0.156594 | − | 0.987663i | \(-0.449948\pi\) | ||||
0.156594 | + | 0.987663i | \(0.449948\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.17858 | − | 0.0855118i | −0.0695693 | − | 0.00504760i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.99673 | + | 13.8507i | −0.470396 | + | 0.814750i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1084 | + | 6.99080i | 0.707381 | + | 0.408407i | 0.810091 | − | 0.586305i | \(-0.199418\pi\) |
−0.102709 | + | 0.994711i | \(0.532751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.8696 | − | 12.6264i | 1.27329 | − | 0.735137i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.3228 | −1.00181 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.43047 | + | 13.9027i | −0.543563 | + | 0.801338i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.5416 | − | 18.2587i | −0.603613 | − | 1.04549i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2755 | 0.928893 | 0.464446 | − | 0.885601i | \(-0.346253\pi\) | ||||
0.464446 | + | 0.885601i | \(0.346253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.38973 | −0.362329 | −0.181164 | − | 0.983453i | \(-0.557987\pi\) | ||||
−0.181164 | + | 0.983453i | \(0.557987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.6429i | 1.44942i | 0.689053 | + | 0.724711i | \(0.258027\pi\) | ||||
−0.689053 | + | 0.724711i | \(0.741973\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.3042 | −1.64589 | −0.822945 | − | 0.568122i | \(-0.807670\pi\) | ||||
−0.822945 | + | 0.568122i | \(0.807670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.32857i | − | 0.130375i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.55385i | 0.0864583i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.71250 | + | 0.988711i | −0.0949923 | + | 0.0548438i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.90363 | − | 1.89131i | 0.215214 | − | 0.104271i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 0.133691i | − | 0.00734833i | −0.999993 | − | 0.00367417i | \(-0.998830\pi\) | ||
0.999993 | − | 0.00367417i | \(-0.00116953\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.50381 | − | 11.2649i | −0.355341 | − | 0.615469i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.96606 | − | 17.2617i | 0.542886 | − | 0.940306i | −0.455851 | − | 0.890056i | \(-0.650665\pi\) |
0.998737 | − | 0.0502498i | \(-0.0160017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.616222 | + | 0.355776i | 0.0333703 | + | 0.0192663i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.99257 | + | 18.0848i | −0.215579 | + | 0.976486i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.55582i | 0.298252i | 0.988818 | + | 0.149126i | \(0.0476460\pi\) | ||||
−0.988818 | + | 0.149126i | \(0.952354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.710293 | − | 0.410088i | 0.0380211 | − | 0.0219515i | −0.480869 | − | 0.876792i | \(-0.659679\pi\) |
0.518890 | + | 0.854841i | \(0.326345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.5479 | − | 10.7086i | −0.987203 | − | 0.569962i | −0.0827662 | − | 0.996569i | \(-0.526375\pi\) |
−0.904437 | + | 0.426607i | \(0.859709\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.57273 | + | 2.72406i | 0.0834721 | + | 0.144578i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.64573 | + | 3.25956i | 0.297970 | + | 0.172033i | 0.641531 | − | 0.767097i | \(-0.278300\pi\) |
−0.343560 | + | 0.939131i | \(0.611633\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.30062 | + | 14.3771i | 0.436875 | + | 0.756689i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.7414 | + | 27.2650i | −0.823945 | + | 1.42711i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.58460 | + | 11.4049i | −0.343713 | + | 0.595329i | −0.985119 | − | 0.171873i | \(-0.945018\pi\) |
0.641406 | + | 0.767202i | \(0.278351\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.44379 | + | 3.69263i | 0.282628 | + | 0.191712i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7435 | − | 25.5364i | −0.763388 | − | 1.32223i | −0.941095 | − | 0.338143i | \(-0.890201\pi\) |
0.177707 | − | 0.984083i | \(-0.443132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.37520i | − | 0.173832i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2566i | 1.29735i | 0.761067 | + | 0.648673i | \(0.224676\pi\) | ||||
−0.761067 | + | 0.648673i | \(0.775324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.61272 | − | 4.52537i | −0.133504 | − | 0.231236i | 0.791521 | − | 0.611142i | \(-0.209290\pi\) |
−0.925025 | + | 0.379906i | \(0.875956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.48715 | − | 3.14302i | 0.330616 | − | 0.160183i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.9830 | + | 22.4872i | −0.658264 | + | 1.14015i | 0.322801 | + | 0.946467i | \(0.395375\pi\) |
−0.981065 | + | 0.193679i | \(0.937958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.40009 | − | 7.62118i | 0.222522 | − | 0.385420i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.95839 | + | 10.3202i | 0.299799 | + | 0.519268i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5913 | + | 7.26961i | 0.631941 | + | 0.364851i | 0.781503 | − | 0.623901i | \(-0.214453\pi\) |
−0.149562 | + | 0.988752i | \(0.547786\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.86138 | + | 11.8843i | 0.342641 | + | 0.593471i | 0.984922 | − | 0.172998i | \(-0.0553453\pi\) |
−0.642281 | + | 0.766469i | \(0.722012\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.893196 | + | 0.515687i | 0.0444933 | + | 0.0256882i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.63082 | − | 2.09626i | 0.179973 | − | 0.103908i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.0019i | − | 0.494561i | −0.968944 | − | 0.247281i | \(-0.920463\pi\) | ||
0.968944 | − | 0.247281i | \(-0.0795370\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.0684 | − | 14.5681i | 1.47957 | − | 0.716851i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.6446 | + | 9.60976i | 0.817051 | + | 0.471725i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.51452 | − | 6.08732i | 0.171695 | − | 0.297385i | −0.767317 | − | 0.641268i | \(-0.778409\pi\) |
0.939013 | + | 0.343882i | \(0.111742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.01107 | − | 5.21533i | −0.146751 | − | 0.254179i | 0.783274 | − | 0.621676i | \(-0.213548\pi\) |
−0.930025 | + | 0.367497i | \(0.880215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.00455i | − | 0.0487279i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.1628 | − | 25.1038i | −0.588598 | − | 1.21486i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.3683 | − | 8.29555i | 0.692097 | − | 0.399582i | −0.112300 | − | 0.993674i | \(-0.535822\pi\) |
0.804397 | + | 0.594092i | \(0.202488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.42380i | − | 0.308708i | −0.988016 | − | 0.154354i | \(-0.950670\pi\) | ||
0.988016 | − | 0.154354i | \(-0.0493297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.5853i | 0.649873i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.46311 | 0.213013 | 0.106506 | − | 0.994312i | \(-0.466034\pi\) | ||||
0.106506 | + | 0.994312i | \(0.466034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 27.5435i | − | 1.30863i | −0.756222 | − | 0.654315i | \(-0.772957\pi\) | ||
0.756222 | − | 0.654315i | \(-0.227043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.56042 | −0.121375 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.3329 | −1.80904 | −0.904520 | − | 0.426432i | \(-0.859771\pi\) | ||||
−0.904520 | + | 0.426432i | \(0.859771\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.304265 | + | 0.527003i | 0.0143273 | + | 0.0248156i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.40295 | − | 4.55573i | 0.440817 | − | 0.213576i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.3165 | −1.60526 | −0.802629 | − | 0.596478i | \(-0.796566\pi\) | ||||
−0.802629 | + | 0.596478i | \(0.796566\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.9331 | − | 8.04429i | 0.648930 | − | 0.374660i | −0.139116 | − | 0.990276i | \(-0.544426\pi\) |
0.788046 | + | 0.615616i | \(0.211093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.7583 | + | 9.09805i | 0.732349 | + | 0.422822i | 0.819281 | − | 0.573392i | \(-0.194373\pi\) |
−0.0869318 | + | 0.996214i | \(0.527706\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.08122 | + | 12.2650i | −0.327680 | + | 0.567558i | −0.982051 | − | 0.188615i | \(-0.939600\pi\) |
0.654371 | + | 0.756173i | \(0.272933\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.50399 | − | 15.4881i | −0.346502 | − | 0.715175i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.65120 | 0.397783 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.775389 | + | 1.34301i | 0.0355773 | + | 0.0616217i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.8982 | − | 29.2685i | 0.772096 | − | 1.33731i | −0.164316 | − | 0.986408i | \(-0.552542\pi\) |
0.936412 | − | 0.350902i | \(-0.114125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.26278 | − | 3.03847i | 0.239962 | − | 0.138542i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.60304 | + | 16.6330i | −0.436052 | + | 0.755264i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.41218 | + | 5.43412i | −0.426506 | + | 0.246244i | −0.697857 | − | 0.716237i | \(-0.745863\pi\) |
0.271351 | + | 0.962481i | \(0.412530\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3930 | + | 16.9701i | 1.32649 | + | 0.765848i | 0.984755 | − | 0.173949i | \(-0.0556529\pi\) |
0.341733 | + | 0.939797i | \(0.388986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.48492 | + | 0.857318i | 0.0668774 | + | 0.0386117i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.81460 | + | 3.74530i | 0.0813958 | + | 0.168000i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.57367 | − | 1.48591i | 0.115213 | − | 0.0665185i | −0.441286 | − | 0.897367i | \(-0.645478\pi\) |
0.556499 | + | 0.830848i | \(0.312144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.0651 | 1.16219 | 0.581093 | − | 0.813837i | \(-0.302625\pi\) | ||||
0.581093 | + | 0.813837i | \(0.302625\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.5377 | 1.00292 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.3806 | + | 8.87997i | −0.681731 | + | 0.393598i | −0.800507 | − | 0.599323i | \(-0.795436\pi\) |
0.118776 | + | 0.992921i | \(0.462103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.3832 | + | 34.4722i | −1.03441 | + | 1.52496i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.6458 | + | 9.61047i | 0.733502 | + | 0.423488i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.93451 | − | 1.11689i | −0.0850796 | − | 0.0491207i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.9679 | + | 14.4152i | −1.09387 | + | 0.631543i | −0.934603 | − | 0.355693i | \(-0.884245\pi\) |
−0.159262 | + | 0.987236i | \(0.550912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.32766 | + | 10.9598i | −0.276689 | + | 0.479240i | −0.970560 | − | 0.240860i | \(-0.922571\pi\) |
0.693871 | + | 0.720100i | \(0.255904\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.453753 | + | 0.261974i | −0.0197658 | + | 0.0114118i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.9701 | − | 46.7135i | 1.17261 | − | 2.03102i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.441024 | + | 0.763876i | 0.0191029 | + | 0.0330871i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.6016 | 1.10686 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.86150 | − | 3.52648i | 0.381692 | − | 0.151896i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.29665 | + | 12.6382i | −0.313708 | + | 0.543358i | −0.979162 | − | 0.203081i | \(-0.934905\pi\) |
0.665454 | + | 0.746439i | \(0.268238\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.2209 | + | 14.5613i | 1.08035 | + | 0.623738i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.61933 | + | 3.24432i | −0.240265 | + | 0.138717i | −0.615299 | − | 0.788294i | \(-0.710965\pi\) |
0.375033 | + | 0.927011i | \(0.377631\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.64698 | −0.112765 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.87470 | + | 14.1893i | 0.292342 | + | 0.603389i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.2102 | − | 31.5410i | −0.771590 | − | 1.33643i | −0.936691 | − | 0.350157i | \(-0.886128\pi\) |
0.165101 | − | 0.986277i | \(-0.447205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5397 | 0.530372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.55398 | −0.318362 | −0.159181 | − | 0.987249i | \(-0.550885\pi\) | ||||
−0.159181 | + | 0.987249i | \(0.550885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.3110i | 1.52762i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.8329 | −0.999127 | −0.499564 | − | 0.866277i | \(-0.666506\pi\) | ||||
−0.499564 | + | 0.866277i | \(0.666506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.1328i | 0.800682i | 0.916366 | + | 0.400341i | \(0.131108\pi\) | ||||
−0.916366 | + | 0.400341i | \(0.868892\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.78281i | − | 0.366268i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.278675 | − | 0.160893i | 0.0116014 | − | 0.00669808i | −0.494188 | − | 0.869355i | \(-0.664535\pi\) |
0.505789 | + | 0.862657i | \(0.331201\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.0444 | + | 14.2749i | 0.873070 | + | 0.592221i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.38750i | − | 0.140296i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.9285 | − | 39.7134i | −0.946362 | − | 1.63915i | −0.753001 | − | 0.658019i | \(-0.771395\pi\) |
−0.193360 | − | 0.981128i | \(-0.561939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.404424 | − | 0.700483i | 0.0166640 | − | 0.0288629i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.8195 | + | 14.3295i | 1.01921 | + | 0.588443i | 0.913876 | − | 0.405993i | \(-0.133074\pi\) |
0.105338 | + | 0.994437i | \(0.466408\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.384107 | + | 5.29401i | −0.0157468 | + | 0.217033i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 24.4551i | − | 0.999208i | −0.866254 | − | 0.499604i | \(-0.833479\pi\) | ||
0.866254 | − | 0.499604i | \(-0.166521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.86788 | + | 3.96517i | −0.280147 | + | 0.161743i | −0.633490 | − | 0.773751i | \(-0.718378\pi\) |
0.353343 | + | 0.935494i | \(0.385045\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.8347 | + | 9.14216i | 0.643772 | + | 0.371682i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.45236 | − | 4.24762i | −0.0995384 | − | 0.172406i | 0.811955 | − | 0.583720i | \(-0.198403\pi\) |
−0.911494 | + | 0.411314i | \(0.865070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.80402 | − | 1.61890i | −0.113438 | − | 0.0654937i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.53276 | + | 16.5112i | 0.385025 | + | 0.666882i | 0.991773 | − | 0.128012i | \(-0.0408596\pi\) |
−0.606748 | + | 0.794894i | \(0.707526\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2636 | + | 36.8296i | −0.856040 | + | 1.48270i | 0.0196377 | + | 0.999807i | \(0.493749\pi\) |
−0.875677 | + | 0.482897i | \(0.839585\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.26243 | + | 10.8468i | −0.251708 | + | 0.435971i | −0.963996 | − | 0.265916i | \(-0.914326\pi\) |
0.712288 | + | 0.701887i | \(0.247659\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.37877 | − | 0.245147i | −0.135368 | − | 0.00982161i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.49551 | + | 16.4467i | 0.379820 | + | 0.657868i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.08715i | 0.123093i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8526i | 0.710700i | 0.934733 | + | 0.355350i | \(0.115638\pi\) | ||||
−0.934733 | + | 0.355350i | \(0.884362\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.2283 | + | 22.9120i | 0.524947 | + | 0.909235i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.8445 | − | 5.11154i | 0.508918 | − | 0.202526i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5722 | − | 33.9000i | 0.773054 | − | 1.33897i | −0.162827 | − | 0.986655i | \(-0.552061\pi\) |
0.935882 | − | 0.352315i | \(-0.114605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.93372 | − | 5.08136i | 0.115695 | − | 0.200389i | −0.802363 | − | 0.596837i | \(-0.796424\pi\) |
0.918057 | + | 0.396448i | \(0.129757\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5795 | + | 33.9127i | 0.769750 | + | 1.33325i | 0.937699 | + | 0.347450i | \(0.112952\pi\) |
−0.167949 | + | 0.985796i | \(0.553714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.9009 | − | 8.60303i | −0.584911 | − | 0.337698i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.6261 | + | 23.6011i | 0.533231 | + | 0.923584i | 0.999247 | + | 0.0388072i | \(0.0123558\pi\) |
−0.466015 | + | 0.884777i | \(0.654311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.7937 | + | 8.54115i | 0.578038 | + | 0.333730i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.1766 | + | 10.4943i | −0.708061 | + | 0.408799i | −0.810343 | − | 0.585956i | \(-0.800719\pi\) |
0.102282 | + | 0.994755i | \(0.467386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.10749i | 0.0819720i | 0.999160 | + | 0.0409860i | \(0.0130499\pi\) | ||||
−0.999160 | + | 0.0409860i | \(0.986950\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.57279 | − | 7.37419i | −0.138547 | − | 0.285959i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.9827 | + | 7.49555i | 0.502691 | + | 0.290229i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.18258 | + | 12.4406i | −0.277281 | + | 0.480264i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.40292 | + | 5.89403i | 0.131173 | + | 0.227198i | 0.924129 | − | 0.382081i | \(-0.124792\pi\) |
−0.792956 | + | 0.609279i | \(0.791459\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.3463i | 1.66593i | 0.553323 | + | 0.832967i | \(0.313360\pi\) | ||||
−0.553323 | + | 0.832967i | \(0.686640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.2649 | + | 21.0297i | −0.547436 | + | 0.807047i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.2674 | − | 14.5882i | 0.966832 | − | 0.558201i | 0.0685629 | − | 0.997647i | \(-0.478159\pi\) |
0.898269 | + | 0.439446i | \(0.144825\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.70901i | − | 0.294546i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4.91008i | − | 0.187059i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.1974 | −1.79547 | −0.897736 | − | 0.440533i | \(-0.854790\pi\) | ||||
−0.897736 | + | 0.440533i | \(0.854790\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 30.3851i | − | 1.15257i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.448089 | −0.0169726 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.7459 | −0.556946 | −0.278473 | − | 0.960444i | \(-0.589828\pi\) | ||||
−0.278473 | + | 0.960444i | \(0.589828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.38290 | − | 4.12730i | −0.0898726 | − | 0.155664i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.7412 | + | 2.15788i | 1.11853 | + | 0.0811553i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.3420 | −1.10196 | −0.550981 | − | 0.834518i | \(-0.685746\pi\) | ||||
−0.550981 | + | 0.834518i | \(0.685746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.96717 | + | 2.29045i | −0.148572 | + | 0.0857779i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.65978 | − | 2.69033i | −0.174266 | − | 0.100613i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.0100 | + | 32.9262i | −0.708952 | + | 1.22794i | 0.256294 | + | 0.966599i | \(0.417498\pi\) |
−0.965246 | + | 0.261342i | \(0.915835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.0460 | + | 14.2759i | 0.783793 | + | 0.531663i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.71125 | 0.0635543 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.33619 | + | 2.31435i | 0.0495565 | + | 0.0858343i | 0.889740 | − | 0.456469i | \(-0.150886\pi\) |
−0.840183 | + | 0.542303i | \(0.817553\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.18514 | + | 5.51683i | −0.117807 | + | 0.204047i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.84392 | + | 1.64194i | −0.105042 | + | 0.0606463i | −0.551601 | − | 0.834108i | \(-0.685983\pi\) |
0.446558 | + | 0.894754i | \(0.352650\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.43139 | + | 7.67540i | −0.163232 | + | 0.282727i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.7991 | − | 13.1631i | 0.838680 | − | 0.484212i | −0.0181356 | − | 0.999836i | \(-0.505773\pi\) |
0.856815 | + | 0.515624i | \(0.172440\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.0356 | − | 12.1449i | −0.771720 | − | 0.445553i | 0.0617681 | − | 0.998091i | \(-0.480326\pi\) |
−0.833488 | + | 0.552538i | \(0.813659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0107 | − | 11.5532i | −0.733135 | − | 0.423276i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.7844 | + | 2.45123i | 1.23446 | + | 0.0895660i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.11887 | − | 4.68743i | 0.296262 | − | 0.171047i | −0.344501 | − | 0.938786i | \(-0.611952\pi\) |
0.640762 | + | 0.767739i | \(0.278618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.3087 | 1.64895 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.8723 | −1.84899 | −0.924493 | − | 0.381200i | \(-0.875511\pi\) | ||||
−0.924493 | + | 0.381200i | \(0.875511\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.6769 | − | 21.1754i | 1.32954 | − | 0.767608i | 0.344308 | − | 0.938857i | \(-0.388114\pi\) |
0.985228 | + | 0.171249i | \(0.0547803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.8878 | + | 21.6301i | 1.15442 | + | 0.783064i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.5984 | − | 12.4699i | −0.779874 | − | 0.450260i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.61419 | − | 2.08665i | −0.130331 | − | 0.0752467i | 0.433417 | − | 0.901194i | \(-0.357308\pi\) |
−0.563748 | + | 0.825947i | \(0.690641\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.51890 | − | 2.60899i | 0.162534 | − | 0.0938389i | −0.416527 | − | 0.909123i | \(-0.636753\pi\) |
0.579061 | + | 0.815285i | \(0.303419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.261457 | + | 0.452857i | −0.00939182 | + | 0.0162671i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.599064 | − | 0.345870i | 0.0214637 | − | 0.0123921i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07159 | − | 1.85604i | 0.0383444 | − | 0.0664145i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.6253 | − | 25.3317i | −0.521998 | − | 0.904128i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.5860 | 1.05463 | 0.527314 | − | 0.849670i | \(-0.323199\pi\) | ||||
0.527314 | + | 0.849670i | \(0.323199\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.47660 | + | 47.9168i | −0.123614 | + | 1.70372i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.4110 | + | 18.0323i | −0.369704 | + | 0.640346i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.7053 | − | 24.0785i | −1.47728 | − | 0.852906i | −0.477606 | − | 0.878574i | \(-0.658495\pi\) |
−0.999671 | + | 0.0256682i | \(0.991829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.42447 | − | 0.822418i | 0.0503941 | − | 0.0290951i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.4510 | 0.756988 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.35825 | + | 46.2856i | −0.118363 | + | 1.63135i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.61482 | + | 4.52900i | 0.0919321 | + | 0.159231i | 0.908324 | − | 0.418267i | \(-0.137362\pi\) |
−0.816392 | + | 0.577498i | \(0.804029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.4364 | 0.998538 | 0.499269 | − | 0.866447i | \(-0.333602\pi\) | ||||
0.499269 | + | 0.866447i | \(0.333602\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.1149 | 0.844709 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.83415i | − | 0.344053i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.16817 | −0.180370 | −0.0901851 | − | 0.995925i | \(-0.528746\pi\) | ||||
−0.0901851 | + | 0.995925i | \(0.528746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1504i | 0.597825i | 0.954281 | + | 0.298912i | \(0.0966238\pi\) | ||||
−0.954281 | + | 0.298912i | \(0.903376\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 46.7499i | − | 1.62565i | −0.582505 | − | 0.812827i | \(-0.697927\pi\) | ||
0.582505 | − | 0.812827i | \(-0.302073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5449 | + | 18.2124i | −1.09560 | + | 0.632544i | −0.935062 | − | 0.354485i | \(-0.884656\pi\) |
−0.160538 | + | 0.987030i | \(0.551323\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.01375 | + | 6.94929i | −0.0351243 | + | 0.240779i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 44.3477i | − | 1.53471i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.36691 | + | 9.29577i | 0.185286 | + | 0.320925i | 0.943673 | − | 0.330880i | \(-0.107345\pi\) |
−0.758387 | + | 0.651805i | \(0.774012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0396 | − | 22.5852i | 0.449640 | − | 0.778799i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.7588 | + | 9.09836i | 0.542120 | + | 0.312993i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.0204 | + | 13.5803i | 0.687910 | + | 0.466623i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.9910i | 0.925239i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.2849 | + | 16.9076i | −1.00269 | + | 0.578906i | −0.909044 | − | 0.416699i | \(-0.863187\pi\) |
−0.0936502 | + | 0.995605i | \(0.529854\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.5914 | − | 15.3526i | −0.908347 | − | 0.524434i | −0.0284478 | − | 0.999595i | \(-0.509056\pi\) |
−0.879899 | + | 0.475161i | \(0.842390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9394 | − | 22.4117i | −0.441487 | − | 0.764679i | 0.556313 | − | 0.830973i | \(-0.312216\pi\) |
−0.997800 | + | 0.0662945i | \(0.978882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.1208 | + | 13.9262i | 0.821083 | + | 0.474052i | 0.850790 | − | 0.525506i | \(-0.176124\pi\) |
−0.0297071 | + | 0.999559i | \(0.509457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.9682 | − | 25.9257i | −0.508935 | − | 0.881500i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.05977 | − | 7.03173i | 0.137718 | − | 0.238535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.42318 | + | 11.1253i | −0.217641 | + | 0.376966i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.8439 | + | 28.5736i | 0.468010 | + | 0.965966i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.25496 | − | 16.0301i | −0.312518 | − | 0.541297i | 0.666389 | − | 0.745604i | \(-0.267839\pi\) |
−0.978907 | + | 0.204307i | \(0.934506\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 37.6194i | − | 1.26743i | −0.773567 | − | 0.633714i | \(-0.781530\pi\) | ||
0.773567 | − | 0.633714i | \(-0.218470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.2541i | 0.513340i | 0.966499 | + | 0.256670i | \(0.0826254\pi\) | ||||
−0.966499 | + | 0.256670i | \(0.917375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.98340 | − | 15.5597i | −0.301633 | − | 0.522444i | 0.674873 | − | 0.737934i | \(-0.264198\pi\) |
−0.976506 | + | 0.215490i | \(0.930865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.2625 | + | 31.5017i | 0.511889 | + | 1.05653i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.26961 | + | 2.19903i | −0.0424859 | + | 0.0735877i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.0794 | + | 24.3863i | −0.470623 | + | 0.815144i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.446273 | − | 0.772968i | −0.0148840 | − | 0.0257799i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.16019 | + | 1.24719i | 0.0719664 | + | 0.0415498i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.70800 | − | 8.15449i | −0.156499 | − | 0.271064i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.6153 | + | 9.01551i | 0.518498 | + | 0.299355i | 0.736320 | − | 0.676633i | \(-0.236562\pi\) |
−0.217822 | + | 0.975989i | \(0.569895\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.79715 | + | 4.50169i | −0.258331 | + | 0.149148i | −0.623573 | − | 0.781765i | \(-0.714320\pi\) |
0.365242 | + | 0.930913i | \(0.380986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.0953i | − | 0.433390i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.7043 | + | 12.6875i | 0.617670 | + | 0.418978i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9938 | + | 12.1208i | 0.692522 | + | 0.399828i | 0.804556 | − | 0.593876i | \(-0.202403\pi\) |
−0.112034 | + | 0.993704i | \(0.535737\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.55324 | − | 2.69028i | 0.0511254 | − | 0.0885518i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.54053 | + | 2.66827i | 0.0506522 | + | 0.0877322i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.8160i | 1.50317i | 0.659635 | + | 0.751586i | \(0.270711\pi\) | ||||
−0.659635 | + | 0.751586i | \(0.729289\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00869 | − | 10.0732i | −0.131379 | − | 0.330136i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.36722 | − | 1.36671i | 0.0774164 | − | 0.0446964i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.0236i | 0.523467i | 0.965140 | + | 0.261733i | \(0.0842941\pi\) | ||||
−0.965140 | + | 0.261733i | \(0.915706\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 7.92698i | − | 0.258412i | −0.991618 | − | 0.129206i | \(-0.958757\pi\) | ||
0.991618 | − | 0.129206i | \(-0.0412428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.91765 | −0.127576 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.3073i | 0.497421i | 0.968578 | + | 0.248711i | \(0.0800068\pi\) | ||||
−0.968578 | + | 0.248711i | \(0.919993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.0926 | 1.00931 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.5759 | 1.18481 | 0.592405 | − | 0.805640i | \(-0.298179\pi\) | ||||
0.592405 | + | 0.805640i | \(0.298179\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.63294 | + | 14.9527i | 0.279355 | + | 0.483858i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.738099 | − | 10.1730i | 0.0238345 | − | 0.328502i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7273 | −0.991202 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.9248 | + | 10.9262i | −0.609210 | + | 0.351728i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.8653 | − | 16.0880i | −0.896088 | − | 0.517357i | −0.0201591 | − | 0.999797i | \(-0.506417\pi\) |
−0.875929 | + | 0.482440i | \(0.839751\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.1287 | + | 41.7921i | −0.774326 | + | 1.34117i | 0.160846 | + | 0.986979i | \(0.448578\pi\) |
−0.935172 | + | 0.354193i | \(0.884756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.90922 | − | 40.0967i | 0.0932653 | − | 1.28544i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.60494 | −0.0833394 | −0.0416697 | − | 0.999131i | \(-0.513268\pi\) | ||||
−0.0416697 | + | 0.999131i | \(0.513268\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.872274 | + | 1.51082i | 0.0278780 | + | 0.0482861i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.9000 | − | 34.4678i | 0.634711 | − | 1.09935i | −0.351865 | − | 0.936051i | \(-0.614453\pi\) |
0.986576 | − | 0.163301i | \(-0.0522141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.1413 | + | 19.7115i | −1.08783 | + | 0.628060i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.8478 | + | 48.2337i | −0.885507 | + | 1.53374i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.30303 | − | 5.37111i | 0.295521 | − | 0.170619i | −0.344908 | − | 0.938636i | \(-0.612090\pi\) |
0.640429 | + | 0.768018i | \(0.278757\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.2644 | + | 26.7107i | 1.46668 | + | 0.846787i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.6620 | − | 11.9292i | −0.654373 | − | 0.377803i | 0.135756 | − | 0.990742i | \(-0.456654\pi\) |
−0.790130 | + | 0.612940i | \(0.789987\pi\) | |||||||
\(998\) | 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.cz.g.1279.4 | 24 | ||
3.2 | odd | 2 | 1008.2.cz.h.607.3 | yes | 24 | ||
4.3 | odd | 2 | 3024.2.cz.h.1279.4 | 24 | |||
7.3 | odd | 6 | 3024.2.bf.g.1711.9 | 24 | |||
9.2 | odd | 6 | 1008.2.bf.g.943.11 | yes | 24 | ||
9.7 | even | 3 | 3024.2.bf.h.2287.4 | 24 | |||
12.11 | even | 2 | 1008.2.cz.g.607.10 | yes | 24 | ||
21.17 | even | 6 | 1008.2.bf.h.31.2 | yes | 24 | ||
28.3 | even | 6 | 3024.2.bf.h.1711.9 | 24 | |||
36.7 | odd | 6 | 3024.2.bf.g.2287.4 | 24 | |||
36.11 | even | 6 | 1008.2.bf.h.943.2 | yes | 24 | ||
63.38 | even | 6 | 1008.2.cz.g.367.10 | yes | 24 | ||
63.52 | odd | 6 | 3024.2.cz.h.2719.4 | 24 | |||
84.59 | odd | 6 | 1008.2.bf.g.31.11 | ✓ | 24 | ||
252.115 | even | 6 | inner | 3024.2.cz.g.2719.4 | 24 | ||
252.227 | odd | 6 | 1008.2.cz.h.367.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.bf.g.31.11 | ✓ | 24 | 84.59 | odd | 6 | ||
1008.2.bf.g.943.11 | yes | 24 | 9.2 | odd | 6 | ||
1008.2.bf.h.31.2 | yes | 24 | 21.17 | even | 6 | ||
1008.2.bf.h.943.2 | yes | 24 | 36.11 | even | 6 | ||
1008.2.cz.g.367.10 | yes | 24 | 63.38 | even | 6 | ||
1008.2.cz.g.607.10 | yes | 24 | 12.11 | even | 2 | ||
1008.2.cz.h.367.3 | yes | 24 | 252.227 | odd | 6 | ||
1008.2.cz.h.607.3 | yes | 24 | 3.2 | odd | 2 | ||
3024.2.bf.g.1711.9 | 24 | 7.3 | odd | 6 | |||
3024.2.bf.g.2287.4 | 24 | 36.7 | odd | 6 | |||
3024.2.bf.h.1711.9 | 24 | 28.3 | even | 6 | |||
3024.2.bf.h.2287.4 | 24 | 9.7 | even | 3 | |||
3024.2.cz.g.1279.4 | 24 | 1.1 | even | 1 | trivial | ||
3024.2.cz.g.2719.4 | 24 | 252.115 | even | 6 | inner | ||
3024.2.cz.h.1279.4 | 24 | 4.3 | odd | 2 | |||
3024.2.cz.h.2719.4 | 24 | 63.52 | odd | 6 |