Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\), degree \(4\), 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: | \(15.1044889615\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 97.5 | ||
Character | \(\chi\) | \(=\) | 256.97 |
Dual form | 256.4.g.b.161.5 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.143768 | + | 0.0595506i | −0.0276682 | + | 0.0114605i | −0.396475 | − | 0.918046i | \(-0.629767\pi\) |
0.368806 | + | 0.929506i | \(0.379767\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.767542 | − | 1.85301i | 0.0686510 | − | 0.165738i | −0.885830 | − | 0.464010i | \(-0.846410\pi\) |
0.954481 | + | 0.298272i | \(0.0964102\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.47741 | − | 5.47741i | −0.295752 | − | 0.295752i | 0.543595 | − | 0.839348i | \(-0.317063\pi\) |
−0.839348 | + | 0.543595i | \(0.817063\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.0748 | + | 19.0748i | −0.706473 | + | 0.706473i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.9342 | + | 15.2986i | 1.01237 | + | 0.419338i | 0.826319 | − | 0.563202i | \(-0.190431\pi\) |
0.186052 | + | 0.982540i | \(0.440431\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.49594 | − | 10.8542i | −0.0959191 | − | 0.231569i | 0.868636 | − | 0.495451i | \(-0.164997\pi\) |
−0.964555 | + | 0.263882i | \(0.914997\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.312111i | 0.00537245i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 53.8999i | 0.768980i | 0.923129 | + | 0.384490i | \(0.125623\pi\) | ||||
−0.923129 | + | 0.384490i | \(0.874377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 31.9796 | + | 77.2056i | 0.386138 | + | 0.932220i | 0.990750 | + | 0.135700i | \(0.0433282\pi\) |
−0.604612 | + | 0.796520i | \(0.706672\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.11366 | + | 0.461293i | 0.0115724 | + | 0.00479344i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 50.0867 | − | 50.0867i | 0.454078 | − | 0.454078i | −0.442628 | − | 0.896706i | \(-0.645954\pi\) |
0.896706 | + | 0.442628i | \(0.145954\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 85.5438 | + | 85.5438i | 0.684351 | + | 0.684351i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.21429 | − | 7.75999i | 0.0229108 | − | 0.0553115i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −156.098 | + | 64.6581i | −0.999543 | + | 0.414024i | −0.821629 | − | 0.570022i | \(-0.806935\pi\) |
−0.177913 | + | 0.984046i | \(0.556935\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 207.668 | 1.20317 | 0.601584 | − | 0.798810i | \(-0.294537\pi\) | ||||
0.601584 | + | 0.798810i | \(0.294537\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.22100 | −0.0328163 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.3538 | + | 5.94555i | −0.0693211 | + | 0.0287138i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −73.7055 | + | 177.941i | −0.327489 | + | 0.790629i | 0.671288 | + | 0.741197i | \(0.265741\pi\) |
−0.998777 | + | 0.0494328i | \(0.984259\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.29274 | + | 1.29274i | 0.00530781 | + | 0.00530781i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −293.943 | + | 293.943i | −1.11966 | + | 1.11966i | −0.127875 | + | 0.991790i | \(0.540815\pi\) |
−0.991790 | + | 0.127875i | \(0.959185\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 342.438 | + | 141.843i | 1.21445 | + | 0.503041i | 0.895641 | − | 0.444778i | \(-0.146717\pi\) |
0.318808 | + | 0.947819i | \(0.396717\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 20.7050 | + | 49.9864i | 0.0685894 | + | 0.165590i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 510.799i | 1.58527i | 0.609697 | + | 0.792635i | \(0.291291\pi\) | ||||
−0.609697 | + | 0.792635i | \(0.708709\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 282.996i | − | 0.825061i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.20978 | − | 7.74908i | −0.00881291 | − | 0.0212762i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 590.228 | + | 244.481i | 1.52970 | + | 0.633622i | 0.979506 | − | 0.201414i | \(-0.0645538\pi\) |
0.550194 | + | 0.835037i | \(0.314554\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.6971 | − | 56.6971i | 0.139001 | − | 0.139001i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.19528 | − | 9.19528i | −0.0213675 | − | 0.0213675i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 257.808 | − | 622.403i | 0.568877 | − | 1.37339i | −0.333626 | − | 0.942706i | \(-0.608272\pi\) |
0.902503 | − | 0.430685i | \(-0.141728\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −424.302 | + | 175.752i | −0.890596 | + | 0.368897i | −0.780597 | − | 0.625035i | \(-0.785085\pi\) |
−0.109999 | + | 0.993932i | \(0.535085\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 208.961 | 0.417882 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −23.5637 | −0.0449648 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −482.813 | + | 199.988i | −0.880373 | + | 0.364663i | −0.776642 | − | 0.629943i | \(-0.783078\pi\) |
−0.103732 | + | 0.994605i | \(0.533078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.21817 | + | 10.1836i | −0.00735953 | + | 0.0177675i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −199.873 | − | 199.873i | −0.334092 | − | 0.334092i | 0.520046 | − | 0.854138i | \(-0.325915\pi\) |
−0.854138 | + | 0.520046i | \(0.825915\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −127.360 | + | 127.360i | −0.204197 | + | 0.204197i | −0.801796 | − | 0.597598i | \(-0.796122\pi\) |
0.597598 | + | 0.801796i | \(0.296122\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.3927 | − | 7.20427i | −0.0267777 | − | 0.0110917i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −118.507 | − | 286.101i | −0.175391 | − | 0.423431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 237.438i | 0.338150i | 0.985603 | + | 0.169075i | \(0.0540780\pi\) | ||||
−0.985603 | + | 0.169075i | \(0.945922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 727.039i | − | 0.997310i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.62194 | − | 23.2294i | −0.0127246 | − | 0.0307200i | 0.917390 | − | 0.397991i | \(-0.130292\pi\) |
−0.930114 | + | 0.367271i | \(0.880292\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 99.8771 | + | 41.3704i | 0.127449 | + | 0.0527912i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.5915 | − | 18.5915i | 0.0229106 | − | 0.0229106i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 329.123 | + | 329.123i | 0.391989 | + | 0.391989i | 0.875396 | − | 0.483407i | \(-0.160601\pi\) |
−0.483407 | + | 0.875396i | \(0.660601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −34.8265 | + | 84.0787i | −0.0401188 | + | 0.0968554i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −29.8560 | + | 12.3667i | −0.0332894 | + | 0.0137889i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 167.608 | 0.181013 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 776.518 | 0.812819 | 0.406410 | − | 0.913691i | \(-0.366781\pi\) | ||||
0.406410 | + | 0.913691i | \(0.366781\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −996.329 | + | 412.693i | −1.01146 | + | 0.418962i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 370.061 | − | 893.405i | 0.364578 | − | 0.880170i | −0.630040 | − | 0.776563i | \(-0.716962\pi\) |
0.994618 | − | 0.103607i | \(-0.0330384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1445.50 | − | 1445.50i | −1.38281 | − | 1.38281i | −0.839595 | − | 0.543212i | \(-0.817208\pi\) |
−0.543212 | − | 0.839595i | \(-0.682792\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.70956 | − | 1.70956i | 0.00158891 | − | 0.00158891i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.88527 | + | 3.68040i | 0.00802777 | + | 0.00332521i | 0.386694 | − | 0.922208i | \(-0.373617\pi\) |
−0.378666 | + | 0.925533i | \(0.623617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −648.092 | − | 1564.63i | −0.569505 | − | 1.37491i | −0.901973 | − | 0.431791i | \(-0.857882\pi\) |
0.332469 | − | 0.943114i | \(-0.392118\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 29.9714i | − | 0.0256285i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 729.808i | − | 0.607562i | −0.952742 | − | 0.303781i | \(-0.901751\pi\) | ||
0.952742 | − | 0.303781i | \(-0.0982492\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −54.3675 | − | 131.255i | −0.0440852 | − | 0.106431i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 292.799 | + | 121.281i | 0.231362 | + | 0.0958331i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 295.232 | − | 295.232i | 0.227427 | − | 0.227427i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 188.928 | + | 188.928i | 0.141944 | + | 0.141944i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.7551 | − | 59.7642i | 0.0181471 | − | 0.0438110i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 455.798 | − | 188.798i | 0.326143 | − | 0.135093i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1559.09 | −1.08934 | −0.544671 | − | 0.838650i | \(-0.683346\pi\) | ||||
−0.544671 | + | 0.838650i | \(0.683346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −57.6784 | −0.0393667 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −508.328 | + | 210.556i | −0.339029 | + | 0.140431i | −0.545701 | − | 0.837980i | \(-0.683737\pi\) |
0.206672 | + | 0.978410i | \(0.433737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 247.721 | − | 598.052i | 0.161505 | − | 0.389907i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.9122 | − | 11.9122i | −0.00759438 | − | 0.00759438i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −118.150 | + | 118.150i | −0.0736806 | + | 0.0736806i | −0.742987 | − | 0.669306i | \(-0.766591\pi\) |
0.669306 | + | 0.742987i | \(0.266591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.49385 | − | 0.618775i | −0.000911562 | − | 0.000377581i | 0.382228 | − | 0.924068i | \(-0.375157\pi\) |
−0.383139 | + | 0.923691i | \(0.625157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.4184 | − | 73.4365i | −0.0181680 | − | 0.0438615i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 469.671i | − | 0.274657i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 338.880i | 0.194086i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.8526 | + | 40.6858i | 0.00945563 | + | 0.0228279i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 527.451 | + | 218.478i | 0.290003 | + | 0.120123i | 0.522942 | − | 0.852368i | \(-0.324834\pi\) |
−0.232939 | + | 0.972491i | \(0.574834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −893.493 | + | 893.493i | −0.481533 | + | 0.481533i | −0.905621 | − | 0.424088i | \(-0.860595\pi\) |
0.424088 | + | 0.905621i | \(0.360595\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1028.13 | − | 1028.13i | −0.543263 | − | 0.543263i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 159.394 | − | 384.810i | 0.0825987 | − | 0.199411i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 277.684 | − | 115.020i | 0.141157 | − | 0.0584690i | −0.310987 | − | 0.950414i | \(-0.600659\pi\) |
0.452143 | + | 0.891945i | \(0.350659\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −99.4149 | −0.0495856 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −548.690 | −0.268589 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2082.24 | − | 862.493i | 1.00058 | − | 0.414452i | 0.178567 | − | 0.983928i | \(-0.442854\pi\) |
0.822008 | + | 0.569476i | \(0.192854\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.77488 | + | 11.5276i | −0.00225287 | + | 0.00543891i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1423.70 | + | 1423.70i | 0.659697 | + | 0.659697i | 0.955308 | − | 0.295611i | \(-0.0955234\pi\) |
−0.295611 | + | 0.955308i | \(0.595523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1455.91 | − | 1455.91i | 0.662683 | − | 0.662683i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2082.68 | − | 862.675i | −0.931384 | − | 0.385792i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1398.51 | + | 3376.31i | 0.614606 | + | 1.48379i | 0.857889 | + | 0.513835i | \(0.171776\pi\) |
−0.243283 | + | 0.969955i | \(0.578224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 937.117i | − | 0.404796i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 104.834i | 0.0445188i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −664.405 | − | 1604.01i | −0.277430 | − | 0.669775i | 0.722333 | − | 0.691545i | \(-0.243070\pi\) |
−0.999763 | + | 0.0217704i | \(0.993070\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2978.79 | − | 1233.86i | −1.22327 | − | 0.506695i | −0.324822 | − | 0.945775i | \(-0.605304\pi\) |
−0.898448 | + | 0.439080i | \(0.855304\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 50.5350 | − | 50.5350i | 0.0204134 | − | 0.0204134i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 273.154 | + | 273.154i | 0.108555 | + | 0.108555i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −824.596 | + | 1990.75i | −0.322462 | + | 0.778493i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −60.1106 | + | 24.8986i | −0.0231344 | + | 0.00958259i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3559.03 | 1.34829 | 0.674143 | − | 0.738601i | \(-0.264513\pi\) | ||||
0.674143 | + | 0.738601i | \(0.264513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 150.055 | 0.0559648 | 0.0279824 | − | 0.999608i | \(-0.491092\pi\) | ||||
0.0279824 | + | 0.999608i | \(0.491092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.38770 | − | 1.40323i | 0.00124409 | − | 0.000515320i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1519.90 | + | 3669.37i | −0.549689 | + | 1.32707i | 0.368022 | + | 0.929817i | \(0.380035\pi\) |
−0.917711 | + | 0.397249i | \(0.869965\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3083.86 | + | 3083.86i | 1.09854 | + | 1.09854i | 0.994582 | + | 0.103955i | \(0.0331499\pi\) |
0.103955 | + | 0.994582i | \(0.466850\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 57.5037 | − | 57.5037i | 0.0201791 | − | 0.0201791i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1209.17 | + | 500.856i | 0.418066 | + | 0.173168i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 319.066 | + | 770.294i | 0.108705 | + | 0.262437i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1910.78i | 0.641587i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3340.77i | 1.10567i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 868.746 | + | 2097.34i | 0.283445 | + | 0.684297i | 0.999911 | − | 0.0133249i | \(-0.00424156\pi\) |
−0.716466 | + | 0.697622i | \(0.754242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 40.6379 | + | 16.8328i | 0.0130726 | + | 0.00541485i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 525.671 | − | 525.671i | 0.166746 | − | 0.166746i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1137.48 | − | 1137.48i | −0.355840 | − | 0.355840i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.7260 | − | 25.8947i | 0.00330956 | − | 0.00798998i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 585.038 | − | 242.331i | 0.178072 | − | 0.0737599i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3747.63 | −1.12538 | −0.562690 | − | 0.826668i | \(-0.690234\pi\) | ||||
−0.562690 | + | 0.826668i | \(0.690234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3263.46 | −0.966950 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5533.41 | − | 2292.01i | 1.61791 | − | 0.670159i | 0.624107 | − | 0.781339i | \(-0.285463\pi\) |
0.993800 | + | 0.111180i | \(0.0354629\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −719.189 | + | 1736.28i | −0.207534 | + | 0.501032i | −0.993034 | − | 0.117830i | \(-0.962406\pi\) |
0.785500 | + | 0.618862i | \(0.212406\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 34.0750 | + | 34.0750i | 0.00970549 | + | 0.00970549i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −575.901 | + | 575.901i | −0.161925 | + | 0.161925i | −0.783419 | − | 0.621494i | \(-0.786526\pi\) |
0.621494 | + | 0.783419i | \(0.286526\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 946.515 | + | 392.059i | 0.262740 | + | 0.108830i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.1396 | − | 34.1360i | −0.00387538 | − | 0.00935599i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3712.45i | − | 1.00476i | −0.864646 | − | 0.502381i | \(-0.832457\pi\) | ||
0.864646 | − | 0.502381i | \(-0.167543\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6285.59i | 1.68004i | 0.542553 | + | 0.840021i | \(0.317458\pi\) | ||||
−0.542553 | + | 0.840021i | \(0.682542\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 130.082 | + | 314.045i | 0.0343405 | + | 0.0829052i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −524.394 | − | 217.211i | −0.136744 | − | 0.0566413i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 694.223 | − | 694.223i | 0.178835 | − | 0.178835i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.76665 | + | 2.76665i | 0.000704135 | + | 0.000704135i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −639.477 | + | 1543.83i | −0.160810 | + | 0.388231i | −0.983662 | − | 0.180026i | \(-0.942382\pi\) |
0.822852 | + | 0.568256i | \(0.192382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2616.17 | − | 1083.65i | 0.650108 | − | 0.269283i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.8228 | −0.00413130 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 42.7546 | 0.0103773 | 0.00518864 | − | 0.999987i | \(-0.498348\pi\) | ||||
0.00518864 | + | 0.999987i | \(0.498348\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1378.37 | − | 570.939i | 0.330686 | − | 0.136975i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1744.20 | − | 4210.88i | 0.413653 | − | 0.998646i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2360.67 | + | 2360.67i | 0.553479 | + | 0.553479i | 0.927443 | − | 0.373964i | \(-0.122002\pi\) |
−0.373964 | + | 0.927443i | \(0.622002\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 906.050 | − | 906.050i | 0.210031 | − | 0.210031i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −66.9169 | − | 27.7179i | −0.0153380 | − | 0.00635321i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1665.10 | + | 4019.90i | 0.377408 | + | 0.911143i | 0.992450 | + | 0.122649i | \(0.0391389\pi\) |
−0.615042 | + | 0.788494i | \(0.710861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4547.41i | − | 1.01932i | −0.860376 | − | 0.509660i | \(-0.829771\pi\) | ||
0.860376 | − | 0.509660i | \(-0.170229\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 14.1618i | − | 0.00313959i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1850.79 | + | 4468.20i | 0.405843 | + | 0.979791i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6747.39 | − | 2794.86i | −1.46358 | − | 0.606234i | −0.498194 | − | 0.867065i | \(-0.666003\pi\) |
−0.965384 | + | 0.260831i | \(0.916003\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3961.21 | + | 3961.21i | −0.850005 | + | 0.850005i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3178.42 | + | 3178.42i | 0.674764 | + | 0.674764i | 0.958811 | − | 0.284046i | \(-0.0916770\pi\) |
−0.284046 | + | 0.958811i | \(0.591677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1868.13 | + | 4510.06i | −0.392399 | + | 0.947334i | 0.597018 | + | 0.802228i | \(0.296352\pi\) |
−0.989416 | + | 0.145106i | \(0.953648\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.0967 | + | 9.98118i | −0.00500830 | + | 0.00207451i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3220.10 | 0.662287 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2007.80 | 0.408670 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −111.638 | + | 46.2421i | −0.0224892 | + | 0.00931533i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −509.398 | + | 1229.79i | −0.101568 | + | 0.245206i | −0.966492 | − | 0.256696i | \(-0.917366\pi\) |
0.864925 | + | 0.501902i | \(0.167366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −955.441 | − | 955.441i | −0.188569 | − | 0.188569i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 237.435 | − | 237.435i | 0.0463884 | − | 0.0463884i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −768.835 | − | 318.462i | −0.148705 | − | 0.0615957i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1098.74 | − | 2652.60i | −0.210401 | − | 0.507952i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 150.480i | 0.0285309i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 921.133i | 0.172931i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2519.05 | − | 6081.52i | −0.468305 | − | 1.13059i | −0.964903 | − | 0.262607i | \(-0.915418\pi\) |
0.496598 | − | 0.867981i | \(-0.334582\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 293.897 | + | 121.736i | 0.0541074 | + | 0.0224120i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5470.06 | − | 5470.06i | 0.997358 | − | 0.997358i | −0.00263825 | − | 0.999997i | \(-0.500840\pi\) |
0.999997 | + | 0.00263825i | \(0.000839783\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4168.95 | − | 4168.95i | −0.752853 | − | 0.752853i | 0.222158 | − | 0.975011i | \(-0.428690\pi\) |
−0.975011 | + | 0.222158i | \(0.928690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 160.386 | − | 387.206i | 0.0286880 | − | 0.0692590i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3013.16 | + | 1248.09i | −0.533868 | + | 0.221135i | −0.633296 | − | 0.773909i | \(-0.718299\pi\) |
0.0994284 | + | 0.995045i | \(0.468299\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6754.55 | −1.18552 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.49659 | −0.000260222 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4161.38 | + | 1723.70i | −0.716858 | + | 0.296932i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 543.906 | − | 1313.11i | 0.0928322 | − | 0.224117i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 186.350 | + | 186.350i | 0.0315143 | + | 0.0315143i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2797.85 | − | 2797.85i | 0.468847 | − | 0.468847i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5175.95 | − | 2143.95i | −0.859504 | − | 0.356018i | −0.0909902 | − | 0.995852i | \(-0.529003\pi\) |
−0.768513 | + | 0.639834i | \(0.779003\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1988.26 | − | 4800.09i | −0.327196 | − | 0.789920i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1048.16i | 0.170946i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6275.84i | − | 1.01444i | −0.861816 | − | 0.507220i | \(-0.830673\pi\) | ||
0.861816 | − | 0.507220i | \(-0.169327\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.4605 | + | 104.923i | 0.00696298 | + | 0.0168101i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7670.04 | + | 3177.03i | 1.21805 | + | 0.504534i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3428.84 | + | 3428.84i | −0.539766 | + | 0.539766i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.6326 | + | 15.6326i | 0.00243951 | + | 0.00243951i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2873.53 | − | 6937.32i | 0.444551 | − | 1.07324i | −0.529782 | − | 0.848134i | \(-0.677726\pi\) |
0.974334 | − | 0.225108i | \(-0.0722736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4992.75 | − | 2068.06i | 0.765775 | − | 0.317194i | 0.0346154 | − | 0.999401i | \(-0.488979\pi\) |
0.731160 | + | 0.682206i | \(0.238979\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −98.6794 | −0.0150060 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1773.18 | 0.267356 | 0.133678 | − | 0.991025i | \(-0.457321\pi\) | ||||
0.133678 | + | 0.991025i | \(0.457321\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −523.777 | + | 216.956i | −0.0783076 | + | 0.0324361i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.8636 | + | 60.0261i | −0.00368606 | + | 0.00889894i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7338.52 | − | 7338.52i | −1.07886 | − | 1.07886i | −0.996612 | − | 0.0822522i | \(-0.973789\pi\) |
−0.0822522 | − | 0.996612i | \(-0.526211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −87.9631 | + | 87.9631i | −0.0128245 | + | 0.0128245i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −38.4125 | − | 15.9110i | −0.00555409 | − | 0.00230058i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 138.246 | + | 333.754i | 0.0198249 | + | 0.0478617i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8883.05i | 1.26346i | 0.775187 | + | 0.631732i | \(0.217656\pi\) | ||||
−0.775187 | + | 0.631732i | \(0.782344\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 11213.8i | − | 1.58203i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1893.80 | − | 4572.04i | −0.265017 | − | 0.639808i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3736.23 | + | 1547.60i | 0.518645 | + | 0.214830i | 0.626622 | − | 0.779323i | \(-0.284437\pi\) |
−0.107976 | + | 0.994153i | \(0.534437\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −54.2861 | + | 54.2861i | −0.00747553 | + | 0.00747553i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1403.62 | + | 1403.62i | 0.191751 | + | 0.191751i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 619.566 | − | 1495.76i | 0.0839708 | − | 0.202724i | −0.876317 | − | 0.481735i | \(-0.840007\pi\) |
0.960288 | + | 0.279012i | \(0.0900068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 224.147 | − | 92.8445i | 0.0301401 | − | 0.0124844i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2505.69 | 0.334294 | 0.167147 | − | 0.985932i | \(-0.446545\pi\) | ||||
0.167147 | + | 0.985932i | \(0.446545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −621.106 | −0.0822195 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9237.54 | + | 3826.31i | −1.21336 | + | 0.502590i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1376.18 | − | 3322.40i | 0.179371 | − | 0.433039i | −0.808464 | − | 0.588545i | \(-0.799701\pi\) |
0.987835 | + | 0.155506i | \(0.0497009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2699.67 | + | 2699.67i | 0.349177 | + | 0.349177i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 60.5425 | − | 60.5425i | 0.00777091 | − | 0.00777091i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 439.975 | + | 182.244i | 0.0560444 | + | 0.0232143i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −134.074 | − | 323.683i | −0.0169495 | − | 0.0409198i | 0.915178 | − | 0.403049i | \(-0.132050\pi\) |
−0.932128 | + | 0.362130i | \(0.882050\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 100.733i | 0.0126389i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1126.07i | − | 0.140233i | −0.997539 | − | 0.0701166i | \(-0.977663\pi\) | ||
0.997539 | − | 0.0701166i | \(-0.0223371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −933.661 | − | 2254.06i | −0.115407 | − | 0.278617i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1347.21 | − | 558.033i | −0.165292 | − | 0.0684663i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5444.51 | + | 5444.51i | −0.663082 | + | 0.663082i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5373.28 | − | 5373.28i | −0.649612 | − | 0.649612i | 0.303287 | − | 0.952899i | \(-0.401916\pi\) |
−0.952899 | + | 0.303287i | \(0.901916\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.95029 | − | 24.0221i | 0.00119419 | − | 0.00288303i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4821.28 | + | 1997.04i | −0.574430 | + | 0.237937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −50.4296 | −0.00596504 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.251617 | 2.95485e−5 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6114.35 | − | 2532.65i | 0.712901 | − | 0.295293i | 0.00339649 | − | 0.999994i | \(-0.498919\pi\) |
0.709504 | + | 0.704701i | \(0.248919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1033.34 | − | 2494.70i | 0.119624 | − | 0.288799i | −0.852713 | − | 0.522380i | \(-0.825044\pi\) |
0.972337 | + | 0.233581i | \(0.0750444\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9743.36 | − | 9743.36i | −1.11995 | − | 1.11995i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4610.81 | + | 4610.81i | −0.526252 | + | 0.526252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3286.74 | + | 1361.41i | 0.372498 | + | 0.154294i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.9692 | + | 67.5237i | 0.00314771 | + | 0.00759924i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1487.87i | 0.166283i | 0.996538 | + | 0.0831417i | \(0.0264954\pi\) | ||||
−0.996538 | + | 0.0831417i | \(0.973505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3672.70i | − | 0.407618i | −0.979011 | − | 0.203809i | \(-0.934668\pi\) | ||
0.979011 | − | 0.203809i | \(-0.0653321\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.1805 | − | 48.7200i | −0.00222432 | − | 0.00536999i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5468.72 | + | 2265.22i | 0.598637 | + | 0.247964i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7362.81 | − | 7362.81i | 0.800473 | − | 0.800473i | −0.182696 | − | 0.983169i | \(-0.558482\pi\) |
0.983169 | + | 0.182696i | \(0.0584825\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5398.08 | + | 5398.08i | 0.582883 | + | 0.582883i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4893.54 | − | 11814.0i | 0.524828 | − | 1.26705i | −0.410044 | − | 0.912066i | \(-0.634487\pi\) |
0.934873 | − | 0.354983i | \(-0.115513\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 862.485 | − | 357.253i | 0.0918780 | − | 0.0380571i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −88.8411 | −0.00940054 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4998.86 | 0.525414 | 0.262707 | − | 0.964876i | \(-0.415385\pi\) | ||||
0.262707 | + | 0.964876i | \(0.415385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15353.5 | + | 6359.63i | −1.60303 | + | 0.663999i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 75.2476 | − | 181.664i | 0.00780450 | − | 0.0188417i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 129.068 | + | 129.068i | 0.0132984 | + | 0.0132984i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4394.36 | + | 4394.36i | −0.449801 | + | 0.449801i | −0.895288 | − | 0.445487i | \(-0.853031\pi\) |
0.445487 | + | 0.895288i | \(0.353031\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 418.263 | + | 173.250i | 0.0425334 | + | 0.0176179i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3050.81 | − | 7365.31i | −0.308222 | − | 0.744115i | −0.999763 | − | 0.0217769i | \(-0.993068\pi\) |
0.691540 | − | 0.722338i | \(-0.256932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 616.179i | 0.0618493i | 0.999522 | + | 0.0309247i | \(0.00984520\pi\) | ||||
−0.999522 | + | 0.0309247i | \(0.990155\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 64.8153i | 0.00646396i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7113.42 | + | 17173.3i | 0.704860 | + | 1.70168i | 0.712461 | + | 0.701712i | \(0.247580\pi\) |
−0.00760112 | + | 0.999971i | \(0.502420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3739.98 | + | 1549.15i | 0.368222 | + | 0.152523i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.0725 | + | 33.0725i | −0.00323546 | + | 0.00323546i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10477.7 | + | 10477.7i | 1.01853 | + | 1.01853i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3868.80 | + | 9340.12i | −0.373711 | + | 0.902219i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15921.9 | + | 6595.06i | −1.52833 | + | 0.633054i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10609.5 | 1.01203 | 0.506014 | − | 0.862525i | \(-0.331118\pi\) | ||||
0.506014 | + | 0.862525i | \(0.331118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2262.77 | 0.214498 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 78.8841 | − | 32.6749i | 0.00743137 | − | 0.00307817i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 596.010 | − | 1438.89i | 0.0558008 | − | 0.134715i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2513.20 | + | 2513.20i | 0.233848 | + | 0.233848i | 0.814297 | − | 0.580449i | \(-0.197123\pi\) |
−0.580449 | + | 0.814297i | \(0.697123\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −247.998 | + | 247.998i | −0.0229342 | + | 0.0229342i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14882.3 | + | 6164.44i | 1.36788 | + | 0.566593i | 0.941212 | − | 0.337817i | \(-0.109688\pi\) |
0.426665 | + | 0.904410i | \(0.359688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3485.07 | − | 8413.69i | −0.318376 | − | 0.768628i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2162.97i | 0.196400i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2189.57i | 0.197617i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4424.27 | − | 10681.1i | −0.396909 | − | 0.958222i | −0.988395 | − | 0.151907i | \(-0.951459\pi\) |
0.591486 | − | 0.806315i | \(-0.298541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −289.465 | − | 119.900i | −0.0258131 | − | 0.0106921i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9855.92 | − | 9855.92i | 0.873666 | − | 0.873666i | −0.119204 | − | 0.992870i | \(-0.538034\pi\) |
0.992870 | + | 0.119204i | \(0.0380342\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1371.45 | − | 1371.45i | −0.120849 | − | 0.120849i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −122.613 | + | 296.014i | −0.0107405 | + | 0.0259299i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6891.66 | + | 2854.62i | −0.600132 | + | 0.248583i | −0.662003 | − | 0.749501i | \(-0.730293\pi\) |
0.0618706 | + | 0.998084i | \(0.480293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1395.21 | 0.120784 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 701.906 | 0.0604092 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3788.00 | + | 1569.04i | −0.324115 | + | 0.134253i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7814.53 | + | 18865.9i | −0.664763 | + | 1.60488i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −402.122 | − | 402.122i | −0.0340100 | − | 0.0340100i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14514.6 | + | 14514.6i | −1.22053 | + | 1.22053i | −0.253088 | + | 0.967443i | \(0.581446\pi\) |
−0.967443 | + | 0.253088i | \(0.918554\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5451.43 | + | 2258.06i | 0.455783 | + | 0.188791i | 0.598750 | − | 0.800936i | \(-0.295664\pi\) |
−0.142967 | + | 0.989727i | \(0.545664\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 55.8059 | + | 134.727i | 0.00463918 | + | 0.0112000i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11193.3i | 0.925212i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7149.65i | 0.587626i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6954.57 | + | 16789.8i | 0.568367 | + | 1.37216i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4512.06 | + | 1868.96i | 0.366677 | + | 0.151883i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6396 | − | 13.6396i | 0.00110223 | − | 0.00110223i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 191.040 | + | 191.040i | 0.0153519 | + | 0.0153519i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4329.46 | − | 10452.2i | 0.345979 | − | 0.835268i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10798.7 | − | 4472.96i | 0.858172 | − | 0.355466i | 0.0901796 | − | 0.995926i | \(-0.471256\pi\) |
0.767992 | + | 0.640459i | \(0.221256\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 501.732 | 0.0396526 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3396.72 | −0.266971 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19366.3 | − | 8021.78i | 1.51379 | − | 0.627032i | 0.537453 | − | 0.843294i | \(-0.319386\pi\) |
0.976335 | + | 0.216262i | \(0.0693865\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4741.04 | − | 11445.9i | 0.368566 | − | 0.889797i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9983.93 | − | 9983.93i | −0.771923 | − | 0.771923i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1300.54 | − | 1300.54i | 0.100009 | − | 0.100009i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −55.5373 | − | 23.0043i | −0.00424761 | − | 0.00175942i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4652.66 | + | 11232.5i | 0.353931 | + | 0.854466i | 0.996127 | + | 0.0879250i | \(0.0280236\pi\) |
−0.642196 | + | 0.766541i | \(0.721976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4354.59i | − | 0.329480i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 335.311i | − | 0.0252350i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3815.91 | − | 9212.42i | −0.285651 | − | 0.689622i | 0.714297 | − | 0.699843i | \(-0.246747\pi\) |
−0.999948 | + | 0.0102205i | \(0.996747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1352.34 | − | 560.158i | −0.100696 | − | 0.0417098i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3982.29 | + | 3982.29i | −0.294957 | + | 0.294957i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7598.85 | + | 7598.85i | 0.559860 | + | 0.559860i | 0.929268 | − | 0.369407i | \(-0.120439\pi\) |
−0.369407 | + | 0.929268i | \(0.620439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5406.36 | + | 13052.1i | −0.396233 | + | 0.956591i | 0.592318 | + | 0.805704i | \(0.298213\pi\) |
−0.988551 | + | 0.150887i | \(0.951787\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −511.675 | + | 211.943i | −0.0373046 | + | 0.0154521i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8569.21 | 0.621497 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13340.9 | −0.962548 | −0.481274 | − | 0.876570i | \(-0.659826\pi\) | ||||
−0.481274 | + | 0.876570i | \(0.659826\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.5731 | + | 8.93589i | −0.00154844 | + | 0.000641386i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −74.5337 | + | 179.940i | −0.00532217 | + | 0.0128489i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18059.4 | + | 18059.4i | 1.28292 | + | 1.28292i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 449.471 | − | 449.471i | 0.0317664 | − | 0.0317664i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8254.52 | + | 3419.14i | 0.580410 | + | 0.240414i | 0.653519 | − | 0.756910i | \(-0.273292\pi\) |
−0.0731089 | + | 0.997324i | \(0.523292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6641.13 | + | 16033.1i | 0.464589 | + | 1.12162i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 618.050i | − | 0.0430172i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3054.91i | − | 0.211552i | −0.994390 | − | 0.105776i | \(-0.966267\pi\) | ||
0.994390 | − | 0.105776i | \(-0.0337326\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −320.465 | − | 773.670i | −0.0220803 | − | 0.0533065i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −627.006 | − | 259.714i | −0.0429843 | − | 0.0178047i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17187.4 | + | 17187.4i | −1.17239 | + | 1.17239i | −0.190748 | + | 0.981639i | \(0.561091\pi\) |
−0.981639 | + | 0.190748i | \(0.938909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16155.9 | − | 16155.9i | −1.09653 | − | 1.09653i | −0.994814 | − | 0.101716i | \(-0.967567\pi\) |
−0.101716 | − | 0.994814i | \(-0.532433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5394.83 | − | 13024.3i | 0.364336 | − | 0.879584i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 495.095 | − | 205.075i | 0.0332702 | − | 0.0137810i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5713.13 | −0.382025 | −0.191012 | − | 0.981588i | \(-0.561177\pi\) | ||||
−0.191012 | + | 0.981588i | \(0.561177\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −203.667 | −0.0135517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5544.29 | − | 2296.52i | 0.367100 | − | 0.152058i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6320.21 | + | 15258.3i | −0.416429 | + | 1.00535i | 0.566945 | + | 0.823755i | \(0.308125\pi\) |
−0.983374 | + | 0.181592i | \(0.941875\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −91.7430 | − | 91.7430i | −0.00601534 | − | 0.00601534i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4724.98 | − | 4724.98i | 0.308299 | − | 0.308299i | −0.535951 | − | 0.844249i | \(-0.680047\pi\) |
0.844249 | + | 0.535951i | \(0.180047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24539.1 | − | 10164.4i | −1.59339 | − | 0.660006i | −0.602933 | − | 0.797792i | \(-0.706001\pi\) |
−0.990462 | + | 0.137786i | \(0.956001\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −227.679 | − | 549.665i | −0.0147125 | − | 0.0355190i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3605.49i | − | 0.231863i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14132.6i | 0.904489i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −198.945 | − | 480.296i | −0.0126716 | − | 0.0305920i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9591.00 | − | 3972.72i | −0.607978 | − | 0.251833i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15837.8 | − | 15837.8i | 0.999194 | − | 0.999194i | −0.000805461 | − | 1.00000i | \(-0.500256\pi\) |
1.00000 | 0.000805461i | \(0.000256386\pi\) | ||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −249.796 | − | 249.796i | −0.0156848 | − | 0.0156848i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1196.66 | + | 2889.00i | −0.0747844 | + | 0.180546i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3071.68 | + | 1272.33i | −0.191059 | + | 0.0791391i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7625.06 | 0.472054 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.03221 | 0.000248460 | 0.000124230 | − | 1.00000i | \(-0.499960\pi\) | ||||
0.000124230 | 1.00000i | \(0.499960\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6758.04 | + | 2799.27i | −0.414481 | + | 0.171683i | −0.580172 | − | 0.814494i | \(-0.697015\pi\) |
0.165691 | + | 0.986178i | \(0.447015\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −44.2706 | + | 106.879i | −0.00270256 | + | 0.00652456i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17744.9 | + | 17744.9i | 1.07824 | + | 1.07824i | 0.996667 | + | 0.0815765i | \(0.0259955\pi\) |
0.0815765 | + | 0.996667i | \(0.474005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19043.9 | − | 19043.9i | 1.15183 | − | 1.15183i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 231.271 | + | 95.7956i | 0.0139235 | + | 0.00576732i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1174.68 | − | 2835.93i | −0.0703963 | − | 0.169952i | 0.884765 | − | 0.466037i | \(-0.154319\pi\) |
−0.955161 | + | 0.296085i | \(0.904319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1103.55i | 0.0658308i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4858.74i | − | 0.288520i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1291.33 | + | 3117.55i | 0.0763325 | + | 0.184283i | 0.957440 | − | 0.288634i | \(-0.0932011\pi\) |
−0.881107 | + | 0.472917i | \(0.843201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5796.90 | − | 2401.15i | −0.341109 | − | 0.141292i | 0.205551 | − | 0.978646i | \(-0.434101\pi\) |
−0.546661 | + | 0.837354i | \(0.684101\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −69.6788 | + | 69.6788i | −0.00408160 | + | 0.00408160i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −918.059 | − | 918.059i | −0.0535351 | − | 0.0535351i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4579.94 | + | 11057.0i | −0.265871 | + | 0.641870i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 538.789 | − | 223.174i | 0.0311372 | − | 0.0128974i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18360.0 | −1.05631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19927.1 | 1.14135 | 0.570677 | − | 0.821174i | \(-0.306681\pi\) | ||||
0.570677 | + | 0.821174i | \(0.306681\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 938.782 | − | 388.856i | 0.0535315 | − | 0.0221735i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1135.03 | − | 2740.21i | 0.0644356 | − | 0.155561i | −0.888382 | − | 0.459105i | \(-0.848170\pi\) |
0.952817 | + | 0.303544i | \(0.0981700\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4253.31 | − | 4253.31i | −0.240393 | − | 0.240393i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −659.036 | + | 659.036i | −0.0370841 | + | 0.0370841i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14514.9 | − | 6012.25i | −0.813171 | − | 0.336826i | −0.0629526 | − | 0.998017i | \(-0.520052\pi\) |
−0.750218 | + | 0.661190i | \(0.770052\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 128.248 | + | 309.618i | 0.00715344 | + | 0.0172699i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 292.449i | − | 0.0162411i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 7505.60i | − | 0.415008i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10219.6 | − | 24672.3i | −0.562621 | − | 1.35829i | −0.907663 | − | 0.419701i | \(-0.862135\pi\) |
0.345041 | − | 0.938588i | \(-0.387865\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7717.79 | + | 3196.81i | 0.423051 | + | 0.175234i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.29319 | + | 2.29319i | −0.000125159 | + | 0.000125159i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15843.5 | − | 15843.5i | −0.860999 | − | 0.860999i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.5008 | − | 117.091i | 0.00262442 | − | 0.00633591i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18637.8 | − | 7720.05i | 1.00420 | − | 0.415952i | 0.180862 | − | 0.983508i | \(-0.442111\pi\) |
0.823334 | + | 0.567557i | \(0.192111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16095.1 | −0.863497 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −159.426 | −0.00851677 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6920.52 | + | 2866.57i | −0.368137 | + | 0.152487i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7105.65 | − | 17154.6i | 0.376387 | − | 0.908678i | −0.616250 | − | 0.787550i | \(-0.711349\pi\) |
0.992637 | − | 0.121128i | \(-0.0386510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4529.07 | − | 4529.07i | −0.238894 | − | 0.238894i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10401.4 | − | 10401.4i | 0.546332 | − | 0.546332i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −870.305 | − | 360.492i | −0.0455211 | − | 0.0188554i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 221.079 | + | 533.731i | 0.0115151 | + | 0.0277999i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 26810.6i | − | 1.39064i | −0.718702 | − | 0.695318i | \(-0.755264\pi\) | ||
0.718702 | − | 0.695318i | \(-0.244736\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15835.2i | 0.817937i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −374.311 | − | 903.666i | −0.0192542 | − | 0.0464837i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18884.4 | − | 7822.16i | −0.967376 | − | 0.400700i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17418.8 | + | 17418.8i | −0.888623 | + | 0.888623i | −0.994391 | − | 0.105768i | \(-0.966270\pi\) |
0.105768 | + | 0.994391i | \(0.466270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13843.1 | + | 13843.1i | 0.703305 | + | 0.703305i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7645.30 | + | 18457.4i | −0.386829 | + | 0.933887i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34809.3 | − | 14418.5i | 1.75404 | − | 0.726547i | 0.756690 | − | 0.653774i | \(-0.226815\pi\) |
0.997349 | − | 0.0727727i | \(-0.0231848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 88.3261 | 0.00443260 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20891.9 | −1.04418 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35885.8 | − | 14864.4i | 1.78630 | − | 0.739911i | 0.795278 | − | 0.606245i | \(-0.207325\pi\) |
0.991026 | − | 0.133666i | \(-0.0426749\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −58.4656 | + | 141.148i | −0.00289850 | + | 0.00699759i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19477.4 | − | 19477.4i | −0.961718 | − | 0.961718i | 0.0375762 | − | 0.999294i | \(-0.488036\pi\) |
−0.999294 | + | 0.0375762i | \(0.988036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 809.682 | − | 809.682i | 0.0398180 | − | 0.0398180i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 626.632 | + | 259.559i | 0.0306925 | + | 0.0127132i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.5092 | − | 68.8273i | −0.00139079 | − | 0.00335767i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 26371.3i | − | 1.28136i | −0.767807 | − | 0.640681i | \(-0.778652\pi\) | ||
0.767807 | − | 0.640681i | \(-0.221348\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 260.035i | − | 0.0125846i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 969.857 | + | 2341.44i | 0.0467506 | + | 0.112866i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26271.7 | − | 10882.1i | −1.26137 | − | 0.522478i | −0.351043 | − | 0.936359i | \(-0.614173\pi\) |
−0.910331 | + | 0.413881i | \(0.864173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −311.589 | + | 311.589i | −0.0149012 | + | 0.0149012i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7394.46 | − | 7394.46i | −0.352233 | − | 0.352233i | 0.508707 | − | 0.860940i | \(-0.330124\pi\) |
−0.860940 | + | 0.508707i | \(0.830124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5020.27 | + | 12120.0i | −0.238199 | + | 0.575064i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2694.26 | + | 1116.00i | −0.127335 | + | 0.0527439i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7914.75 | −0.372601 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4771.82 | 0.223766 | 0.111883 | − | 0.993721i | \(-0.464312\pi\) | ||||
0.111883 | + | 0.993721i | \(0.464312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.14675 | + | 2.54607i | −0.000287120 | + | 0.000118929i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8895.17 | − | 21474.8i | 0.413890 | − | 0.999219i | −0.570193 | − | 0.821511i | \(-0.693132\pi\) |
0.984083 | − | 0.177709i | \(-0.0568684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17764.7 | + | 17764.7i | 0.823389 | + | 0.823389i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −164.166 | + | 164.166i | −0.00757967 | + | 0.00757967i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32094.3 | − | 13293.9i | −1.47612 | − | 0.611429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4324.36 | − | 10439.9i | −0.198128 | − | 0.478323i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1419.15i | 0.0647718i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 602.834i | − | 0.0274090i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7111.73 | + | 17169.2i | 0.322117 | + | 0.777659i | 0.999131 | + | 0.0416884i | \(0.0132737\pi\) |
−0.677014 | + | 0.735970i | \(0.736726\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −479.968 | − | 198.809i | −0.0216569 | − | 0.00897059i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3997.46 | + | 3997.46i | −0.179688 | + | 0.179688i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3815.27 | + | 3815.27i | 0.170850 | + | 0.170850i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −76.3051 | + | 184.217i | −0.00340410 | + | 0.00821823i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24661.7 | + | 10215.2i | −1.09606 | + | 0.454004i | −0.856117 | − | 0.516782i | \(-0.827130\pi\) |
−0.239946 | + | 0.970786i | \(0.577130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27532.0 | −1.21904 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12555.9 | −0.553859 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6652.40 | + | 2755.51i | −0.292351 | + | 0.121096i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −421.143 | + | 1016.73i | −0.0184389 | + | 0.0445155i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −478.775 | − | 478.775i | −0.0208844 | − | 0.0208844i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22540.9 | − | 22540.9i | 0.979600 | − | 0.979600i | −0.0201963 | − | 0.999796i | \(-0.506429\pi\) |
0.999796 | + | 0.0201963i | \(0.00642911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12287.9 | + | 5089.83i | 0.532044 | + | 0.220380i | 0.632498 | − | 0.774562i | \(-0.282030\pi\) |
−0.100454 | + | 0.994942i | \(0.532030\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 270.801 | + | 653.772i | 0.0116819 | + | 0.0282027i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 4520.41i | − | 0.194286i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30974.2i | 1.32638i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −939.473 | − | 2268.09i | −0.0400829 | − | 0.0967686i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15862.2 | + | 6570.34i | 0.674293 | + | 0.279301i | 0.693439 | − | 0.720515i | \(-0.256095\pi\) |
−0.0191460 | + | 0.999817i | \(0.506095\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11289.1 | − | 11289.1i | 0.478146 | − | 0.478146i | −0.426392 | − | 0.904538i | \(-0.640216\pi\) |
0.904538 | + | 0.426392i | \(0.140216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −532.168 | − | 532.168i | −0.0224578 | − | 0.0224578i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2548.49 | + | 6152.59i | −0.107158 | + | 0.258702i | −0.968359 | − | 0.249563i | \(-0.919713\pi\) |
0.861201 | + | 0.508265i | \(0.169713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40448.6 | − | 16754.4i | 1.69462 | − | 0.701934i | 0.694768 | − | 0.719234i | \(-0.255507\pi\) |
0.999850 | + | 0.0173006i | \(0.00550723\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1136.49 | 0.0474423 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15253.5 | 0.634455 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3730.88 | − | 1545.38i | 0.154626 | − | 0.0640481i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 667.504 | − | 1611.50i | 0.0275655 | − | 0.0665490i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2282.23 | + | 2282.23i | 0.0939108 | + | 0.0939108i | 0.752501 | − | 0.658591i | \(-0.228847\pi\) |
−0.658591 | + | 0.752501i | \(0.728847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2940.42 | − | 2940.42i | 0.120563 | − | 0.120563i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −646.232 | − | 267.678i | −0.0264026 | − | 0.0109363i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1580.35 | − | 3815.30i | −0.0643380 | − | 0.155326i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2069.67i | − | 0.0839607i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 759.651i | − | 0.0307081i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5220.80 | + | 12604.1i | 0.210302 | + | 0.507713i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8660.34 | − | 3587.23i | −0.347625 | − | 0.143991i | 0.202037 | − | 0.979378i | \(-0.435244\pi\) |
−0.549663 | + | 0.835387i | \(0.685244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3197.09 | + | 3197.09i | −0.127881 | + | 0.127881i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10879.0 | − | 10879.0i | −0.433630 | − | 0.433630i | 0.456231 | − | 0.889861i | \(-0.349199\pi\) |
−0.889861 | + | 0.456231i | \(0.849199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 816.021 | − | 1970.05i | 0.0324124 | − | 0.0782506i | −0.906844 | − | 0.421465i | \(-0.861516\pi\) |
0.939257 | + | 0.343215i | \(0.111516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −462.947 | + | 191.759i | −0.0183243 | + | 0.00759016i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17532.1 | 0.691541 | 0.345771 | − | 0.938319i | \(-0.387617\pi\) | ||||
0.345771 | + | 0.938319i | \(0.387617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7329.74 | 0.288114 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −288.657 | + | 119.566i | −0.0113072 | + | 0.00468358i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3632.48 | + | 8769.58i | −0.141799 | + | 0.342333i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4341.40 | + | 4341.40i | 0.168889 | + | 0.168889i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14811.9 | + | 14811.9i | −0.574234 | + | 0.574234i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3530.71 | − | 1462.47i | −0.136411 | − | 0.0565034i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1857.78 | + | 4485.09i | 0.0715313 | + | 0.172692i | 0.955601 | − | 0.294663i | \(-0.0952072\pi\) |
−0.884070 | + | 0.467354i | \(0.845207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 207.140i | − | 0.00794842i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 24865.4i | − | 0.950894i | −0.879744 | − | 0.475447i | \(-0.842286\pi\) | ||
0.879744 | − | 0.475447i | \(-0.157714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14018.3 | − | 33843.3i | −0.534264 | − | 1.28983i | −0.928676 | − | 0.370893i | \(-0.879052\pi\) |
0.394412 | − | 0.918934i | \(-0.370948\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 194.259 | + | 80.4647i | 0.00737847 | + | 0.00305626i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4048.92 | − | 4048.92i | 0.153269 | − | 0.153269i | −0.626307 | − | 0.779576i | \(-0.715435\pi\) |
0.779576 | + | 0.626307i | \(0.215435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8539.75 | + | 8539.75i | 0.322175 | + | 0.322175i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11122.7 | − | 26852.6i | 0.418210 | − | 1.00965i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39436.5 | + | 16335.1i | −1.47782 | + | 0.612133i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3482.21 | −0.130053 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 129.498 | 0.00482032 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32416.6 | + | 13427.4i | −1.20262 | + | 0.498141i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13177.5 | + | 31813.3i | −0.487243 | + | 1.17631i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 315.928 | + | 315.928i | 0.0116428 | + | 0.0116428i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4572.69 | + | 4572.69i | −0.167957 | + | 0.167957i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30120.4 | + | 12476.3i | 1.10268 | + | 0.456745i | 0.858411 | − | 0.512963i | \(-0.171452\pi\) |
0.244268 | + | 0.969708i | \(0.421452\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9982.67 | + | 24100.3i | 0.364251 | + | 0.879380i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26490.1i | 0.963400i | 0.876336 | + | 0.481700i | \(0.159980\pi\) | ||||
−0.876336 | + | 0.481700i | \(0.840020\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1005.16i | − | 0.0364360i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −54.8541 | − | 132.429i | −0.00198188 | − | 0.00478468i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3937.62 | + | 1631.02i | 0.141801 | + | 0.0587360i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2467.15 | − | 2467.15i | 0.0885570 | − | 0.0885570i | −0.661441 | − | 0.749998i | \(-0.730055\pi\) |
0.749998 | + | 0.661441i | \(0.230055\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 724.316 | + | 724.316i | 0.0259143 | + | 0.0259143i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1270.84 | + | 3068.07i | −0.0453197 | + | 0.109411i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21526.8 | + | 8916.69i | −0.765185 | + | 0.316950i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 55145.1 | 1.95383 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13097.0 | −0.462537 | −0.231269 | − | 0.972890i | \(-0.574288\pi\) | ||||
−0.231269 | + | 0.972890i | \(0.574288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21848.9 | − | 9050.10i | 0.769138 | − | 0.318588i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −460.673 | + | 1112.16i | −0.0161648 | + | 0.0390253i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3055.97 | + | 3055.97i | 0.106889 | + | 0.106889i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24748.7 | + | 24748.7i | −0.862864 | + | 0.862864i | −0.991670 | − | 0.128806i | \(-0.958886\pi\) |
0.128806 | + | 0.991670i | \(0.458886\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 847.625 | + | 351.098i | 0.0294581 | + | 0.0122020i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3168.01 | + | 7648.26i | 0.109749 | + | 0.264959i | 0.969207 | − | 0.246249i | \(-0.0791982\pi\) |
−0.859457 | + | 0.511208i | \(0.829198\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29445.3i | 1.01683i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 130.496i | 0.00449211i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4403.80 | + | 10631.7i | 0.151113 | + | 0.364820i | 0.981250 | − | 0.192741i | \(-0.0617376\pi\) |
−0.830137 | + | 0.557560i | \(0.811738\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1954.99 | + | 809.785i | 0.0668723 | + | 0.0276994i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 358.872 | − | 358.872i | 0.0122368 | − | 0.0122368i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4833.37 | − | 4833.37i | −0.164290 | − | 0.164290i | 0.620174 | − | 0.784464i | \(-0.287062\pi\) |
−0.784464 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2731.71 | − | 6594.92i | 0.0925612 | − | 0.223462i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 971.088 | − | 402.238i | 0.0328013 | − | 0.0135867i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1294.31 | 0.0435824 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13334.8 | 0.447613 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −239.687 | + | 99.2817i | −0.00802057 | + | 0.00332223i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 115.174 | − | 278.054i | 0.00384204 | − | 0.00927551i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11429.8 | + | 11429.8i | 0.380101 | + | 0.380101i | 0.871138 | − | 0.491037i | \(-0.163382\pi\) |
−0.491037 | + | 0.871138i | \(0.663382\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 495.625 | − | 495.625i | 0.0164311 | − | 0.0164311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6489.63 | − | 2688.09i | −0.214482 | − | 0.0888414i | 0.272856 | − | 0.962055i | \(-0.412032\pi\) |
−0.487338 | + | 0.873214i | \(0.662032\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.79317 | + | 11.5717i | 0.000157926 | + | 0.000381267i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 221.172i | 0.00726481i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 19891.1i | − | 0.651354i | −0.945481 | − | 0.325677i | \(-0.894408\pi\) | ||
0.945481 | − | 0.325677i | \(-0.105592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7120.77 | + | 17191.1i | 0.232462 | + | 0.561214i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42207.2 | + | 17482.8i | 1.37367 | + | 0.568994i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 606.701 | − | 606.701i | 0.0196854 | − | 0.0196854i | −0.697196 | − | 0.716881i | \(-0.745569\pi\) |
0.716881 | + | 0.697196i | \(0.245569\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5632.79 | + | 5632.79i | 0.182209 | + | 0.182209i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −235.628 | + | 568.856i | −0.00759890 | + | 0.0183454i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24256.0 | − | 10047.2i | 0.779875 | − | 0.323035i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2306.07 | 0.0739201 | 0.0369600 | − | 0.999317i | \(-0.488233\pi\) | ||||
0.0369600 | + | 0.999317i | \(0.488233\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 871.808 | 0.0278610 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8081.41 | − | 3347.43i | 0.257485 | − | 0.106654i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11827.8 | + | 28554.9i | −0.375718 | + | 0.907064i | 0.617040 | + | 0.786932i | \(0.288332\pi\) |
−0.992758 | + | 0.120132i | \(0.961668\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1143.91 | + | 1143.91i | 0.0362279 | + | 0.0362279i |
(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 | 256.4.g.b.97.5 | 44 | ||
4.3 | odd | 2 | 256.4.g.a.97.7 | 44 | |||
8.3 | odd | 2 | 128.4.g.a.49.5 | 44 | |||
8.5 | even | 2 | 32.4.g.a.21.11 | ✓ | 44 | ||
32.3 | odd | 8 | 256.4.g.a.161.7 | 44 | |||
32.13 | even | 8 | 32.4.g.a.29.11 | yes | 44 | ||
32.19 | odd | 8 | 128.4.g.a.81.5 | 44 | |||
32.29 | even | 8 | inner | 256.4.g.b.161.5 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.21.11 | ✓ | 44 | 8.5 | even | 2 | ||
32.4.g.a.29.11 | yes | 44 | 32.13 | even | 8 | ||
128.4.g.a.49.5 | 44 | 8.3 | odd | 2 | |||
128.4.g.a.81.5 | 44 | 32.19 | odd | 8 | |||
256.4.g.a.97.7 | 44 | 4.3 | odd | 2 | |||
256.4.g.a.161.7 | 44 | 32.3 | odd | 8 | |||
256.4.g.b.97.5 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.b.161.5 | 44 | 32.29 | even | 8 | inner |