Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,3,Mod(809,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.cs (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(37.2753001645\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 809.19 | ||
Character | \(\chi\) | \(=\) | 1368.809 |
Dual form | 1368.3.cs.a.881.19 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.55555 | + | 4.36220i | 1.51111 | + | 0.872440i | 0.999916 | + | 0.0129755i | \(0.00413035\pi\) |
0.511195 | + | 0.859465i | \(0.329203\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.97290 | 0.996128 | 0.498064 | − | 0.867140i | \(-0.334044\pi\) | ||||
0.498064 | + | 0.867140i | \(0.334044\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.54709i | 0.140645i | 0.997524 | + | 0.0703224i | \(0.0224028\pi\) | ||||
−0.997524 | + | 0.0703224i | \(0.977597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.76688 | + | 4.79238i | 0.212837 | + | 0.368645i | 0.952601 | − | 0.304221i | \(-0.0983963\pi\) |
−0.739764 | + | 0.672866i | \(0.765063\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.4832 | + | 15.2901i | 1.55783 | + | 0.899416i | 0.997464 | + | 0.0711744i | \(0.0226747\pi\) |
0.560371 | + | 0.828242i | \(0.310659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.0307 | − | 13.8275i | −0.685828 | − | 0.727764i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.3299 | + | 8.85070i | −0.666516 | + | 0.384813i | −0.794755 | − | 0.606930i | \(-0.792401\pi\) |
0.128239 | + | 0.991743i | \(0.459067\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.5576 | + | 44.2671i | 1.02230 | + | 1.77068i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.8626 | − | 13.1997i | 0.788365 | − | 0.455163i | −0.0510214 | − | 0.998698i | \(-0.516248\pi\) |
0.839387 | + | 0.543535i | \(0.182914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.6349 | 1.14951 | 0.574757 | − | 0.818324i | \(-0.305097\pi\) | ||||
0.574757 | + | 0.818324i | \(0.305097\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 52.6841 | + | 30.4172i | 1.50526 | + | 0.869062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −25.7157 | −0.695019 | −0.347509 | − | 0.937676i | \(-0.612973\pi\) | ||||
−0.347509 | + | 0.937676i | \(0.612973\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −23.5273 | − | 13.5835i | −0.573837 | − | 0.331305i | 0.184843 | − | 0.982768i | \(-0.440822\pi\) |
−0.758680 | + | 0.651463i | \(0.774156\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.57062 | − | 2.72040i | 0.0365261 | − | 0.0632651i | −0.847184 | − | 0.531299i | \(-0.821704\pi\) |
0.883711 | + | 0.468034i | \(0.155037\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −23.2860 | + | 13.4442i | −0.495447 | + | 0.286047i | −0.726832 | − | 0.686816i | \(-0.759008\pi\) |
0.231384 | + | 0.972862i | \(0.425675\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.378685 | −0.00772827 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 32.9300 | − | 19.0121i | 0.621320 | − | 0.358719i | −0.156063 | − | 0.987747i | \(-0.549880\pi\) |
0.777383 | + | 0.629028i | \(0.216547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.74873 | + | 11.6891i | −0.122704 | + | 0.212530i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.73454 | − | 2.73349i | −0.0802464 | − | 0.0463303i | 0.459340 | − | 0.888261i | \(-0.348086\pi\) |
−0.539586 | + | 0.841930i | \(0.681419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.10711 | − | 15.7740i | −0.149297 | − | 0.258590i | 0.781671 | − | 0.623691i | \(-0.214368\pi\) |
−0.930968 | + | 0.365101i | \(0.881034\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 48.2788i | 0.742751i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −22.9840 | − | 39.8095i | −0.343045 | − | 0.594172i | 0.641952 | − | 0.766745i | \(-0.278125\pi\) |
−0.984997 | + | 0.172574i | \(0.944792\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2880 | − | 7.67183i | −0.187155 | − | 0.108054i | 0.403495 | − | 0.914982i | \(-0.367795\pi\) |
−0.590650 | + | 0.806928i | \(0.701129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28.2274 | + | 48.8913i | −0.386677 | + | 0.669744i | −0.992000 | − | 0.126236i | \(-0.959710\pi\) |
0.605324 | + | 0.795979i | \(0.293044\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.7877i | 0.140100i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −39.4035 | + | 68.2489i | −0.498778 | + | 0.863910i | −0.999999 | − | 0.00140999i | \(-0.999551\pi\) |
0.501221 | + | 0.865320i | \(0.332885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 141.290i | − | 1.70229i | −0.524928 | − | 0.851147i | \(-0.675908\pi\) | ||
0.524928 | − | 0.851147i | \(-0.324092\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 133.397 | + | 231.050i | 1.56937 | + | 2.71824i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 80.0444 | − | 46.2137i | 0.899375 | − | 0.519254i | 0.0223778 | − | 0.999750i | \(-0.492876\pi\) |
0.876997 | + | 0.480495i | \(0.159543\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.2932 | + | 33.4168i | 0.212013 | + | 0.367218i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −38.1360 | − | 161.317i | −0.401431 | − | 1.69808i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −40.5021 | + | 70.1516i | −0.417547 | + | 0.723213i | −0.995692 | − | 0.0927214i | \(-0.970443\pi\) |
0.578145 | + | 0.815934i | \(0.303777\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50.2450 | + | 29.0090i | −0.497475 | + | 0.287217i | −0.727670 | − | 0.685927i | \(-0.759397\pi\) |
0.230195 | + | 0.973145i | \(0.426064\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −139.157 | −1.35104 | −0.675522 | − | 0.737340i | \(-0.736082\pi\) | ||||
−0.675522 | + | 0.737340i | \(0.736082\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 163.414i | − | 1.52723i | −0.645670 | − | 0.763617i | \(-0.723422\pi\) | ||
0.645670 | − | 0.763617i | \(-0.276578\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −46.4582 | + | 80.4679i | −0.426222 | + | 0.738238i | −0.996534 | − | 0.0831906i | \(-0.973489\pi\) |
0.570312 | + | 0.821428i | \(0.306822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 116.692i | − | 1.03267i | −0.856386 | − | 0.516336i | \(-0.827295\pi\) | ||
0.856386 | − | 0.516336i | \(-0.172705\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −154.434 | −1.34291 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 184.665 | + | 106.616i | 1.55180 | + | 0.895934i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 118.607 | 0.980219 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 227.840i | 1.82272i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 59.4345 | + | 102.944i | 0.467989 | + | 0.810580i | 0.999331 | − | 0.0365773i | \(-0.0116455\pi\) |
−0.531342 | + | 0.847157i | \(0.678312\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 168.162 | + | 97.0885i | 1.28368 | + | 0.741133i | 0.977519 | − | 0.210846i | \(-0.0676220\pi\) |
0.306161 | + | 0.951980i | \(0.400955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −90.8620 | − | 96.4178i | −0.683173 | − | 0.724946i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −117.778 | + | 67.9991i | −0.859692 | + | 0.496344i | −0.863909 | − | 0.503647i | \(-0.831991\pi\) |
0.00421682 | + | 0.999991i | \(0.498658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 104.924 | + | 181.734i | 0.754852 | + | 1.30744i | 0.945448 | + | 0.325773i | \(0.105624\pi\) |
−0.190596 | + | 0.981668i | \(0.561042\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.41426 | + | 4.28062i | −0.0518480 | + | 0.0299344i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 230.319 | 1.58841 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 161.799 | + | 93.4147i | 1.08590 | + | 0.626944i | 0.932482 | − | 0.361217i | \(-0.117639\pi\) |
0.153417 | + | 0.988161i | \(0.450972\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −136.997 | −0.907264 | −0.453632 | − | 0.891189i | \(-0.649872\pi\) | ||||
−0.453632 | + | 0.891189i | \(0.649872\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 269.242 | + | 155.447i | 1.73704 | + | 1.00288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −72.4091 | + | 125.416i | −0.461204 | + | 0.798829i | −0.999021 | − | 0.0442322i | \(-0.985916\pi\) |
0.537817 | + | 0.843062i | \(0.319249\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −106.894 | + | 61.7150i | −0.663935 | + | 0.383323i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 117.323 | 0.719775 | 0.359887 | − | 0.932996i | \(-0.382815\pi\) | ||||
0.359887 | + | 0.932996i | \(0.382815\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 162.015 | − | 93.5392i | 0.970147 | − | 0.560115i | 0.0708661 | − | 0.997486i | \(-0.477424\pi\) |
0.899281 | + | 0.437371i | \(0.144090\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 69.1887 | − | 119.838i | 0.409401 | − | 0.709103i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 163.090 | + | 94.1603i | 0.942719 | + | 0.544279i | 0.890812 | − | 0.454373i | \(-0.150137\pi\) |
0.0519073 | + | 0.998652i | \(0.483470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 178.211 | + | 308.670i | 1.01835 | + | 1.76383i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 233.023i | − | 1.30181i | −0.759161 | − | 0.650903i | \(-0.774391\pi\) | ||
0.759161 | − | 0.650903i | \(-0.225609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 126.922 | + | 219.836i | 0.701227 | + | 1.21456i | 0.968036 | + | 0.250812i | \(0.0806976\pi\) |
−0.266808 | + | 0.963750i | \(0.585969\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −194.296 | − | 112.177i | −1.05025 | − | 0.606362i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.6552 | + | 40.9719i | −0.126498 | + | 0.219101i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 228.873i | − | 1.19829i | −0.800642 | − | 0.599143i | \(-0.795508\pi\) | ||
0.800642 | − | 0.599143i | \(-0.204492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 151.550 | − | 262.493i | 0.785234 | − | 1.36006i | −0.143625 | − | 0.989632i | \(-0.545876\pi\) |
0.928859 | − | 0.370433i | \(-0.120791\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 340.115i | 1.72647i | 0.504802 | + | 0.863235i | \(0.331566\pi\) | ||||
−0.504802 | + | 0.863235i | \(0.668434\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −110.680 | − | 191.703i | −0.556180 | − | 0.963332i | −0.997811 | − | 0.0661350i | \(-0.978933\pi\) |
0.441631 | − | 0.897197i | \(-0.354400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 159.419 | − | 92.0403i | 0.785313 | − | 0.453401i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −118.508 | − | 205.262i | −0.578087 | − | 1.00128i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.3924 | − | 20.1597i | 0.102356 | − | 0.0964581i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1991 | + | 31.5218i | −0.0862518 | + | 0.149393i | −0.905924 | − | 0.423440i | \(-0.860822\pi\) |
0.819672 | + | 0.572833i | \(0.194156\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.7339 | − | 13.7028i | 0.110390 | − | 0.0637337i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 248.479 | 1.14506 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 169.223i | 0.765717i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.87009 | − | 10.1673i | 0.0263233 | − | 0.0455933i | −0.852564 | − | 0.522623i | \(-0.824953\pi\) |
0.878887 | + | 0.477030i | \(0.158287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 308.513i | 1.35909i | 0.733634 | + | 0.679545i | \(0.237823\pi\) | ||||
−0.733634 | + | 0.679545i | \(0.762177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −199.914 | −0.872985 | −0.436493 | − | 0.899708i | \(-0.643780\pi\) | ||||
−0.436493 | + | 0.899708i | \(0.643780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −150.150 | − | 86.6894i | −0.644422 | − | 0.372057i | 0.141894 | − | 0.989882i | \(-0.454681\pi\) |
−0.786316 | + | 0.617825i | \(0.788014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −234.585 | −0.998234 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 92.3221i | 0.386285i | 0.981171 | + | 0.193142i | \(0.0618679\pi\) | ||||
−0.981171 | + | 0.193142i | \(0.938132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −73.8527 | − | 127.917i | −0.306443 | − | 0.530775i | 0.671139 | − | 0.741332i | \(-0.265806\pi\) |
−0.977582 | + | 0.210557i | \(0.932472\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.86118 | − | 1.65190i | −0.0116783 | − | 0.00674246i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.2122 | − | 100.707i | 0.122317 | − | 0.407722i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 72.3166 | − | 41.7520i | 0.288114 | − | 0.166343i | −0.348977 | − | 0.937131i | \(-0.613471\pi\) |
0.637091 | + | 0.770789i | \(0.280138\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.6928 | − | 23.7167i | −0.0541219 | − | 0.0937419i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −237.979 | + | 137.397i | −0.925990 | + | 0.534620i | −0.885541 | − | 0.464561i | \(-0.846212\pi\) |
−0.0404487 | + | 0.999182i | \(0.512879\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −179.313 | −0.692328 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −155.944 | − | 90.0343i | −0.592943 | − | 0.342336i | 0.173318 | − | 0.984866i | \(-0.444551\pi\) |
−0.766260 | + | 0.642530i | \(0.777885\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 331.739 | 1.25185 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 131.944 | + | 76.1780i | 0.490499 | + | 0.283190i | 0.724781 | − | 0.688979i | \(-0.241941\pi\) |
−0.234283 | + | 0.972169i | \(0.575274\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.27548 | + | 5.67330i | −0.0120867 | + | 0.0209347i | −0.872005 | − | 0.489496i | \(-0.837181\pi\) |
0.859919 | + | 0.510431i | \(0.170514\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −68.4852 | + | 39.5400i | −0.249037 | + | 0.143782i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −486.332 | −1.75571 | −0.877856 | − | 0.478924i | \(-0.841027\pi\) | ||||
−0.877856 | + | 0.478924i | \(0.841027\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −235.113 | + | 135.743i | −0.836703 | + | 0.483070i | −0.856142 | − | 0.516741i | \(-0.827145\pi\) |
0.0194394 | + | 0.999811i | \(0.493812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 196.799 | − | 340.866i | 0.695404 | − | 1.20448i | −0.274640 | − | 0.961547i | \(-0.588559\pi\) |
0.970044 | − | 0.242928i | \(-0.0781079\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −164.054 | − | 94.7164i | −0.571615 | − | 0.330022i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 323.073 | + | 559.579i | 1.11790 | + | 1.93626i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 529.445i | − | 1.80698i | −0.428610 | − | 0.903489i | \(-0.640997\pi\) | ||
0.428610 | − | 0.903489i | \(-0.359003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.8480 | − | 41.3060i | −0.0808408 | − | 0.140020i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −84.8319 | − | 48.9777i | −0.283719 | − | 0.163805i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.9518 | − | 18.9691i | 0.0363847 | − | 0.0630202i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 158.908i | − | 0.521010i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 192.412 | − | 333.267i | 0.626749 | − | 1.08556i | −0.361451 | − | 0.932391i | \(-0.617718\pi\) |
0.988200 | − | 0.153170i | \(-0.0489483\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 329.752i | 1.06030i | 0.847905 | + | 0.530148i | \(0.177864\pi\) | ||||
−0.847905 | + | 0.530148i | \(0.822136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.8195 | − | 25.6681i | −0.0473467 | − | 0.0820068i | 0.841381 | − | 0.540443i | \(-0.181743\pi\) |
−0.888728 | + | 0.458436i | \(0.848410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 541.900 | − | 312.866i | 1.70946 | − | 0.986959i | 0.774247 | − | 0.632884i | \(-0.218129\pi\) |
0.935217 | − | 0.354076i | \(-0.115204\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.4212 | + | 35.3705i | 0.0640163 | + | 0.110879i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −133.672 | − | 565.437i | −0.413844 | − | 1.75058i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −141.430 | + | 244.964i | −0.435169 | + | 0.753734i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −162.371 | + | 93.7450i | −0.493529 | + | 0.284939i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −504.353 | −1.52373 | −0.761863 | − | 0.647738i | \(-0.775715\pi\) | ||||
−0.761863 | + | 0.647738i | \(0.775715\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 401.044i | − | 1.19715i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −118.223 | + | 204.769i | −0.350811 | + | 0.607622i | −0.986392 | − | 0.164412i | \(-0.947427\pi\) |
0.635581 | + | 0.772034i | \(0.280761\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 55.1305i | 0.161673i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −344.313 | −1.00383 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −534.925 | − | 308.839i | −1.54157 | − | 0.890027i | −0.998740 | − | 0.0501853i | \(-0.984019\pi\) |
−0.542832 | − | 0.839842i | \(-0.682648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 123.801 | 0.354730 | 0.177365 | − | 0.984145i | \(-0.443243\pi\) | ||||
0.177365 | + | 0.984145i | \(0.443243\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 153.890i | 0.435949i | 0.975954 | + | 0.217975i | \(0.0699450\pi\) | ||||
−0.975954 | + | 0.217975i | \(0.930055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −66.9321 | − | 115.930i | −0.188541 | − | 0.326563i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −405.104 | − | 233.887i | −1.12842 | − | 0.651495i | −0.184885 | − | 0.982760i | \(-0.559191\pi\) |
−0.943538 | + | 0.331265i | \(0.892524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.4002 | + | 360.365i | −0.0592803 | + | 0.998241i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −426.547 | + | 246.267i | −1.16862 | + | 0.674704i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −65.3268 | − | 113.149i | −0.178002 | − | 0.308309i | 0.763194 | − | 0.646169i | \(-0.223630\pi\) |
−0.941196 | + | 0.337861i | \(0.890297\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 229.617 | − | 132.570i | 0.618915 | − | 0.357331i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.77753 | 0.0208513 | 0.0104256 | − | 0.999946i | \(-0.496681\pi\) | ||||
0.0104256 | + | 0.999946i | \(0.496681\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 126.516 | + | 73.0442i | 0.335587 | + | 0.193751i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −77.1360 | −0.203525 | −0.101763 | − | 0.994809i | \(-0.532448\pi\) | ||||
−0.101763 | + | 0.994809i | \(0.532448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 379.325 | + | 219.003i | 0.990404 | + | 0.571810i | 0.905395 | − | 0.424570i | \(-0.139575\pi\) |
0.0850086 | + | 0.996380i | \(0.472908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −47.0582 | + | 81.5072i | −0.122229 | + | 0.211707i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −145.895 | + | 84.2326i | −0.375052 | + | 0.216536i | −0.675663 | − | 0.737210i | \(-0.736143\pi\) |
0.300611 | + | 0.953747i | \(0.402809\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −541.311 | −1.38443 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −595.430 | + | 343.772i | −1.50742 | + | 0.870309i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 342.696 | − | 593.567i | 0.863214 | − | 1.49513i | −0.00559518 | − | 0.999984i | \(-0.501781\pi\) |
0.868809 | − | 0.495147i | \(-0.164886\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −502.251 | − | 289.975i | −1.25250 | − | 0.723129i | −0.280892 | − | 0.959739i | \(-0.590630\pi\) |
−0.971605 | + | 0.236610i | \(0.923964\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 98.5977 | + | 170.776i | 0.244659 | + | 0.423762i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 39.7845i | − | 0.0977507i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −230.293 | − | 398.878i | −0.563062 | − | 0.975253i | −0.997227 | − | 0.0744192i | \(-0.976290\pi\) |
0.434165 | − | 0.900834i | \(-0.357044\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.0135 | − | 19.0603i | −0.0799357 | − | 0.0461509i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 616.337 | − | 1067.53i | 1.48515 | − | 2.57235i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 231.953i | 0.553587i | 0.960929 | + | 0.276793i | \(0.0892717\pi\) | ||||
−0.960929 | + | 0.276793i | \(0.910728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 235.613 | − | 408.094i | 0.559651 | − | 0.969345i | −0.437874 | − | 0.899036i | \(-0.644268\pi\) |
0.997525 | − | 0.0703082i | \(-0.0223983\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1563.11i | 3.67791i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −63.5030 | − | 109.990i | −0.148719 | − | 0.257589i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 709.700 | − | 409.745i | 1.64664 | − | 0.950685i | 0.668239 | − | 0.743947i | \(-0.267048\pi\) |
0.978396 | − | 0.206738i | \(-0.0662849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −68.9423 | − | 119.412i | −0.159220 | − | 0.275777i | 0.775368 | − | 0.631510i | \(-0.217565\pi\) |
−0.934588 | + | 0.355733i | \(0.884231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 322.142 | + | 96.6428i | 0.737168 | + | 0.221150i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 107.874 | − | 186.843i | 0.245727 | − | 0.425611i | −0.716609 | − | 0.697475i | \(-0.754307\pi\) |
0.962336 | + | 0.271864i | \(0.0876402\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −156.973 | + | 90.6285i | −0.354341 | + | 0.204579i | −0.666596 | − | 0.745420i | \(-0.732249\pi\) |
0.312254 | + | 0.949998i | \(0.398916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 806.373 | 1.81207 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 748.052i | − | 1.66604i | −0.553244 | − | 0.833019i | \(-0.686610\pi\) | ||
0.553244 | − | 0.833019i | \(-0.313390\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0149 | − | 36.3989i | 0.0465963 | − | 0.0807071i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 336.643i | 0.739875i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −227.449 | −0.497701 | −0.248850 | − | 0.968542i | \(-0.580053\pi\) | ||||
−0.248850 | + | 0.968542i | \(0.580053\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 362.235 | + | 209.136i | 0.785759 | + | 0.453658i | 0.838467 | − | 0.544952i | \(-0.183452\pi\) |
−0.0527086 | + | 0.998610i | \(0.516785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 689.238 | 1.48864 | 0.744318 | − | 0.667826i | \(-0.232775\pi\) | ||||
0.744318 | + | 0.667826i | \(0.232775\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 336.790i | − | 0.721178i | −0.932725 | − | 0.360589i | \(-0.882576\pi\) | ||
0.932725 | − | 0.360589i | \(-0.117424\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −160.265 | − | 277.588i | −0.341717 | − | 0.591871i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.20871 | + | 2.42990i | 0.00889790 | + | 0.00513721i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 279.069 | − | 930.230i | 0.587514 | − | 1.95838i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −382.931 | + | 221.085i | −0.799438 | + | 0.461556i | −0.843275 | − | 0.537483i | \(-0.819375\pi\) |
0.0438364 | + | 0.999039i | \(0.486042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −71.1524 | − | 123.239i | −0.147926 | − | 0.256215i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −612.031 | + | 353.356i | −1.26192 | + | 0.728570i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −933.143 | −1.91610 | −0.958052 | − | 0.286593i | \(-0.907477\pi\) | ||||
−0.958052 | + | 0.286593i | \(0.907477\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 736.877 | + | 425.436i | 1.50077 | + | 0.866469i | 1.00000 | 0.000887369i | \(0.000282458\pi\) | |
0.500768 | + | 0.865581i | \(0.333051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 807.299 | 1.63752 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −92.6559 | − | 53.4949i | −0.186430 | − | 0.107636i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −68.6506 | + | 118.906i | −0.137576 | + | 0.238289i | −0.926579 | − | 0.376101i | \(-0.877265\pi\) |
0.789002 | + | 0.614390i | \(0.210598\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −526.517 | + | 303.985i | −1.04675 | + | 0.604344i | −0.921739 | − | 0.387811i | \(-0.873231\pi\) |
−0.125015 | + | 0.992155i | \(0.539898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −506.172 | −1.00232 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 53.0407 | − | 30.6231i | 0.104206 | − | 0.0601632i | −0.446991 | − | 0.894538i | \(-0.647505\pi\) |
0.551197 | + | 0.834375i | \(0.314171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −196.827 | + | 340.914i | −0.385180 | + | 0.667151i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1051.41 | − | 607.033i | −2.04158 | − | 1.17870i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.7994 | − | 36.0256i | −0.0402309 | − | 0.0696820i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 210.458i | − | 0.403950i | −0.979391 | − | 0.201975i | \(-0.935264\pi\) | ||
0.979391 | − | 0.201975i | \(-0.0647359\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −389.363 | − | 674.397i | −0.744480 | − | 1.28948i | −0.950437 | − | 0.310917i | \(-0.899364\pi\) |
0.205957 | − | 0.978561i | \(-0.433969\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 943.726 | + | 544.861i | 1.79075 | + | 1.03389i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −107.830 | + | 186.768i | −0.203838 | + | 0.353058i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 150.336i | − | 0.282056i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 712.845 | − | 1234.68i | 1.33242 | − | 2.30782i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 0.585861i | − | 0.00108694i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −287.444 | − | 497.868i | −0.531320 | − | 0.920273i | −0.999332 | − | 0.0365507i | \(-0.988363\pi\) |
0.468012 | − | 0.883722i | \(-0.344970\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −702.034 | + | 405.320i | −1.28814 | + | 0.743706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 338.221 | + | 585.817i | 0.618321 | + | 1.07096i | 0.989792 | + | 0.142518i | \(0.0455200\pi\) |
−0.371472 | + | 0.928444i | \(0.621147\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −480.436 | − | 144.131i | −0.871934 | − | 0.261580i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −274.757 | + | 475.892i | −0.496847 | + | 0.860565i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.6883 | − | 15.4085i | 0.0479144 | − | 0.0276634i | −0.475851 | − | 0.879526i | \(-0.657860\pi\) |
0.523766 | + | 0.851862i | \(0.324527\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.3829 | 0.0310965 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 566.760i | 1.00668i | 0.864089 | + | 0.503339i | \(0.167895\pi\) | ||||
−0.864089 | + | 0.503339i | \(0.832105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 509.034 | − | 881.673i | 0.900945 | − | 1.56048i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 490.796i | 0.862559i | 0.902218 | + | 0.431280i | \(0.141938\pi\) | ||||
−0.902218 | + | 0.431280i | \(0.858062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −446.171 | −0.781385 | −0.390692 | − | 0.920521i | \(-0.627764\pi\) | ||||
−0.390692 | + | 0.920521i | \(0.627764\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −783.589 | − | 452.405i | −1.36276 | − | 0.786792i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −309.678 | −0.536704 | −0.268352 | − | 0.963321i | \(-0.586479\pi\) | ||||
−0.268352 | + | 0.963321i | \(0.586479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 985.204i | − | 1.69570i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.4135 | + | 50.9457i | 0.0504520 | + | 0.0873854i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 267.910 | + | 154.678i | 0.456406 | + | 0.263506i | 0.710532 | − | 0.703665i | \(-0.248454\pi\) |
−0.254126 | + | 0.967171i | \(0.581788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −464.349 | − | 492.742i | −0.788368 | − | 0.836574i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −301.852 | + | 174.275i | −0.509026 | + | 0.293886i | −0.732433 | − | 0.680839i | \(-0.761615\pi\) |
0.223407 | + | 0.974725i | \(0.428282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 930.162 | + | 1611.09i | 1.56330 | + | 2.70771i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 370.252 | − | 213.765i | 0.618117 | − | 0.356870i | −0.158019 | − | 0.987436i | \(-0.550511\pi\) |
0.776136 | + | 0.630566i | \(0.217177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 697.294 | 1.16022 | 0.580111 | − | 0.814537i | \(-0.303009\pi\) | ||||
0.580111 | + | 0.814537i | \(0.303009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 896.138 | + | 517.385i | 1.48122 | + | 0.855183i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −521.986 | −0.859944 | −0.429972 | − | 0.902842i | \(-0.641476\pi\) | ||||
−0.429972 | + | 0.902842i | \(0.641476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −128.859 | − | 74.3970i | −0.210899 | − | 0.121763i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 357.609 | − | 619.398i | 0.583376 | − | 1.01044i | −0.411700 | − | 0.911320i | \(-0.635065\pi\) |
0.995076 | − | 0.0991173i | \(-0.0316019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 810.906 | − | 468.177i | 1.31427 | − | 0.758795i | 0.331471 | − | 0.943465i | \(-0.392455\pi\) |
0.982801 | + | 0.184670i | \(0.0591216\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 93.3680 | 0.150837 | 0.0754184 | − | 0.997152i | \(-0.475971\pi\) | ||||
0.0754184 | + | 0.997152i | \(0.475971\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 558.141 | − | 322.243i | 0.895893 | − | 0.517244i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −354.942 | + | 614.777i | −0.567907 | + | 0.983644i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −681.034 | − | 393.195i | −1.08272 | − | 0.625111i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −267.657 | − | 463.595i | −0.424178 | − | 0.734698i | 0.572165 | − | 0.820139i | \(-0.306104\pi\) |
−0.996343 | + | 0.0854402i | \(0.972770\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1037.06i | 1.63317i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.04778 | − | 1.81481i | −0.00164486 | − | 0.00284899i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −586.854 | − | 338.820i | −0.915528 | − | 0.528580i | −0.0333225 | − | 0.999445i | \(-0.510609\pi\) |
−0.882206 | + | 0.470864i | \(0.843942\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −433.732 | + | 751.246i | −0.674545 | + | 1.16835i | 0.302057 | + | 0.953290i | \(0.402327\pi\) |
−0.976602 | + | 0.215056i | \(0.931007\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 599.147i | − | 0.926039i | −0.886348 | − | 0.463020i | \(-0.846766\pi\) | ||
0.886348 | − | 0.463020i | \(-0.153234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.22896 | − | 7.32477i | 0.00651611 | − | 0.0112862i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 83.4862i | − | 0.127850i | −0.997955 | − | 0.0639251i | \(-0.979638\pi\) | ||
0.997955 | − | 0.0639251i | \(-0.0203619\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 847.039 | + | 1467.11i | 1.29319 | + | 2.23987i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 811.780 | − | 468.681i | 1.23184 | − | 0.711201i | 0.264423 | − | 0.964407i | \(-0.414818\pi\) |
0.967412 | + | 0.253206i | \(0.0814851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 175.330 | + | 303.680i | 0.265250 | + | 0.459426i | 0.967629 | − | 0.252377i | \(-0.0812123\pi\) |
−0.702379 | + | 0.711803i | \(0.747879\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −265.918 | − | 1124.85i | −0.399877 | − | 1.69150i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −233.654 | + | 404.700i | −0.350305 | + | 0.606746i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.4038 | − | 14.0895i | 0.0363693 | − | 0.0209978i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −843.178 | −1.25287 | −0.626433 | − | 0.779476i | \(-0.715486\pi\) | ||||
−0.626433 | + | 0.779476i | \(0.715486\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 923.246i | − | 1.36373i | −0.731478 | − | 0.681865i | \(-0.761169\pi\) | ||
0.731478 | − | 0.681865i | \(-0.238831\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −282.417 | + | 489.160i | −0.415930 | + | 0.720413i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 86.0356i | − | 0.125967i | −0.998015 | − | 0.0629836i | \(-0.979938\pi\) | ||
0.998015 | − | 0.0629836i | \(-0.0200616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1186.50 | −1.73212 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 182.227 | + | 105.209i | 0.264480 | + | 0.152698i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1240.37 | 1.79504 | 0.897518 | − | 0.440977i | \(-0.145368\pi\) | ||||
0.897518 | + | 0.440977i | \(0.145368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1830.80i | 2.63425i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −415.385 | − | 719.469i | −0.595962 | − | 1.03224i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −412.894 | − | 238.384i | −0.589007 | − | 0.340063i | 0.175698 | − | 0.984444i | \(-0.443782\pi\) |
−0.764705 | + | 0.644381i | \(0.777115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 335.094 | + | 355.584i | 0.476663 | + | 0.505810i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −350.353 | + | 202.277i | −0.495549 | + | 0.286105i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −662.983 | − | 1148.32i | −0.935096 | − | 1.61963i | −0.774463 | − | 0.632619i | \(-0.781980\pi\) |
−0.160633 | − | 0.987014i | \(-0.551353\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −546.278 | + | 315.394i | −0.766169 | + | 0.442348i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −74.6918 | −0.104464 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 216.967 | + | 125.266i | 0.301762 | + | 0.174222i | 0.643234 | − | 0.765670i | \(-0.277592\pi\) |
−0.341472 | + | 0.939892i | \(0.610926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −970.331 | −1.34581 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1168.63 | + | 674.707i | 1.61190 | + | 0.930630i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −369.591 | + | 640.150i | −0.508378 | + | 0.880536i | 0.491575 | + | 0.870835i | \(0.336421\pi\) |
−0.999953 | + | 0.00970078i | \(0.996912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 83.1902 | − | 48.0299i | 0.113803 | − | 0.0657044i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 575.654 | 0.785340 | 0.392670 | − | 0.919680i | \(-0.371552\pi\) | ||||
0.392670 | + | 0.919680i | \(0.371552\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 61.5889 | − | 35.5584i | 0.0835671 | − | 0.0482475i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 296.205 | − | 513.043i | 0.400819 | − | 0.694239i | −0.593006 | − | 0.805198i | \(-0.702059\pi\) |
0.993825 | + | 0.110959i | \(0.0353923\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −296.361 | − | 171.104i | −0.398871 | − | 0.230289i | 0.287125 | − | 0.957893i | \(-0.407300\pi\) |
−0.685997 | + | 0.727604i | \(0.740634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 814.987 | + | 1411.60i | 1.09394 | + | 1.89476i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1139.47i | − | 1.52132i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −366.642 | − | 635.042i | −0.488204 | − | 0.845595i | 0.511704 | − | 0.859162i | \(-0.329015\pi\) |
−0.999908 | + | 0.0135672i | \(0.995681\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1035.09 | − | 597.608i | −1.37098 | − | 0.791534i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −151.497 | + | 262.400i | −0.200128 | + | 0.346631i | −0.948569 | − | 0.316569i | \(-0.897469\pi\) |
0.748442 | + | 0.663200i | \(0.230802\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 876.517i | − | 1.15180i | −0.817521 | − | 0.575898i | \(-0.804652\pi\) | ||
0.817521 | − | 0.575898i | \(-0.195348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −323.948 | + | 561.094i | −0.424571 | + | 0.735379i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 30.2530i | − | 0.0394432i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 196.099 | + | 339.653i | 0.255005 | + | 0.441681i | 0.964897 | − | 0.262629i | \(-0.0845896\pi\) |
−0.709892 | + | 0.704310i | \(0.751256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 490.012 | − | 282.908i | 0.633909 | − | 0.365988i | −0.148355 | − | 0.988934i | \(-0.547398\pi\) |
0.782264 | + | 0.622946i | \(0.214065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 910.743 | + | 1577.45i | 1.17515 | + | 2.03542i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 118.752 | + | 502.327i | 0.152442 | + | 0.644836i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.8690 | − | 20.5578i | 0.0151972 | − | 0.0263224i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1094.18 | + | 631.726i | −1.39386 | + | 0.804747i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −432.589 | −0.549668 | −0.274834 | − | 0.961492i | \(-0.588623\pi\) | ||||
−0.274834 | + | 0.961492i | \(0.588623\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 813.681i | − | 1.02867i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.3966 | − | 87.2895i | 0.0635519 | − | 0.110075i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 62.7709i | − | 0.0787590i | −0.999224 | − | 0.0393795i | \(-0.987462\pi\) | ||
0.999224 | − | 0.0393795i | \(-0.0125381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −822.251 | −1.02910 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −75.6393 | − | 43.6704i | −0.0941959 | − | 0.0543840i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1076.85 | −1.33771 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 246.241i | − | 0.304377i | −0.988351 | − | 0.152189i | \(-0.951368\pi\) | ||
0.988351 | − | 0.152189i | \(-0.0486321\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −147.909 | − | 256.186i | −0.182378 | − | 0.315889i | 0.760312 | − | 0.649559i | \(-0.225046\pi\) |
−0.942690 | + | 0.333670i | \(0.891713\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 886.442 | + | 511.788i | 1.08766 | + | 0.627960i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −58.0827 | + | 13.7310i | −0.0710927 | + | 0.0168066i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1211.82 | − | 699.644i | 1.47603 | − | 0.852185i | 0.476393 | − | 0.879233i | \(-0.341944\pi\) |
0.999634 | + | 0.0270480i | \(0.00861070\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.3206 | + | 24.8039i | 0.0174004 | + | 0.0301384i | 0.874595 | − | 0.484855i | \(-0.161128\pi\) |
−0.857194 | + | 0.514994i | \(0.827794\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −943.226 | + | 544.572i | −1.14054 | + | 0.658491i | −0.946564 | − | 0.322516i | \(-0.895471\pi\) |
−0.193975 | + | 0.981006i | \(0.562138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 243.575 | 0.293817 | 0.146909 | − | 0.989150i | \(-0.453068\pi\) | ||||
0.146909 | + | 0.989150i | \(0.453068\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.0288 | − | 5.79013i | −0.0120394 | − | 0.00695093i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1632.15 | 1.95467 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 363.154 | + | 209.667i | 0.432842 | + | 0.249901i | 0.700557 | − | 0.713597i | \(-0.252935\pi\) |
−0.267715 | + | 0.963498i | \(0.586268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −72.0345 | + | 124.767i | −0.0856534 | + | 0.148356i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1045.52 | − | 603.630i | 1.23730 | − | 0.714355i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 827.031 | 0.976424 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 394.218 | − | 227.602i | 0.463241 | − | 0.267452i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 199.991 | − | 346.394i | 0.234456 | − | 0.406089i | −0.724659 | − | 0.689108i | \(-0.758003\pi\) |
0.959114 | + | 0.283019i | \(0.0913359\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1158.17 | + | 668.667i | 1.35142 | + | 0.780241i | 0.988448 | − | 0.151559i | \(-0.0484295\pi\) |
0.362970 | + | 0.931801i | \(0.381763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −523.987 | − | 907.572i | −0.609996 | − | 1.05654i | −0.991240 | − | 0.132070i | \(-0.957838\pi\) |
0.381244 | − | 0.924474i | \(-0.375496\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 588.373i | − | 0.681777i | −0.940104 | − | 0.340888i | \(-0.889272\pi\) | ||
0.940104 | − | 0.340888i | \(-0.110728\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 821.492 | + | 1422.87i | 0.949702 | + | 1.64493i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −105.587 | − | 60.9608i | −0.121504 | − | 0.0701505i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 127.188 | − | 220.297i | 0.146026 | − | 0.252924i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1588.70i | 1.81566i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.13264 | + | 5.42590i | −0.00357200 | + | 0.00618689i | −0.867806 | − | 0.496903i | \(-0.834470\pi\) |
0.864234 | + | 0.503090i | \(0.167804\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 428.968i | 0.486910i | 0.969912 | + | 0.243455i | \(0.0782809\pi\) | ||||
−0.969912 | + | 0.243455i | \(0.921719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 130.002 | + | 225.170i | 0.147227 | + | 0.255005i | 0.930202 | − | 0.367049i | \(-0.119632\pi\) |
−0.782974 | + | 0.622054i | \(0.786298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1231.71 | + | 711.128i | −1.38862 | + | 0.801723i | −0.993160 | − | 0.116759i | \(-0.962750\pi\) |
−0.395464 | + | 0.918481i | \(0.629416\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 414.431 | + | 717.816i | 0.466177 | + | 0.807442i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 489.334 | + | 146.800i | 0.547966 | + | 0.164390i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1016.49 | − | 1760.62i | 1.13575 | − | 1.96717i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 814.707 | − | 470.371i | 0.906237 | − | 0.523216i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1162.79 | 1.29055 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2214.64i | 2.44712i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −828.365 | + | 1434.77i | −0.913302 | + | 1.58189i | −0.103933 | + | 0.994584i | \(0.533143\pi\) |
−0.809369 | + | 0.587301i | \(0.800191\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 893.788i | 0.981106i | 0.871411 | + | 0.490553i | \(0.163205\pi\) | ||||
−0.871411 | + | 0.490553i | \(0.836795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 218.589 | 0.239419 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1172.58 | + | 676.988i | 1.27871 | + | 0.738264i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −343.060 | −0.373297 | −0.186648 | − | 0.982427i | \(-0.559763\pi\) | ||||
−0.186648 | + | 0.982427i | \(0.559763\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 84.9083i | − | 0.0919916i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −657.231 | − | 1138.36i | −0.710520 | − | 1.23066i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 709.290 | + | 409.509i | 0.763498 | + | 0.440806i | 0.830550 | − | 0.556944i | \(-0.188026\pi\) |
−0.0670522 | + | 0.997749i | \(0.521359\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.93455 | + | 5.23628i | 0.00530026 | + | 0.00562436i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −357.456 | + | 206.377i | −0.382305 | + | 0.220724i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −222.612 | − | 385.576i | −0.237580 | − | 0.411500i | 0.722440 | − | 0.691434i | \(-0.243021\pi\) |
−0.960019 | + | 0.279934i | \(0.909687\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 122.681 | − | 70.8301i | 0.130373 | − | 0.0752711i | −0.433395 | − | 0.901204i | \(-0.642684\pi\) |
0.563768 | + | 0.825933i | \(0.309351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 480.894 | 0.509962 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1406.28 | + | 811.919i | 1.48499 | + | 0.857359i | 0.999854 | − | 0.0170810i | \(-0.00543732\pi\) |
0.485134 | + | 0.874440i | \(0.338771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −312.408 | −0.329197 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −602.610 | − | 347.917i | −0.632330 | − | 0.365076i | 0.149324 | − | 0.988788i | \(-0.452290\pi\) |
−0.781654 | + | 0.623713i | \(0.785624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 998.388 | − | 1729.26i | 1.04543 | − | 1.81074i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −821.253 | + | 474.151i | −0.856364 | + | 0.494422i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 308.848 | 0.321381 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2290.09 | − | 1322.18i | 2.37315 | − | 1.37014i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −584.211 | + | 1011.88i | −0.604147 | + | 1.04641i | 0.388038 | + | 0.921643i | \(0.373153\pi\) |
−0.992186 | + | 0.124771i | \(0.960180\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 113.347 | + | 65.4408i | 0.116732 | + | 0.0673953i | 0.557229 | − | 0.830359i | \(-0.311864\pi\) |
−0.440497 | + | 0.897754i | \(0.645198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 731.627 | + | 1267.22i | 0.751929 | + | 1.30238i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1191.76i | − | 1.21982i | −0.792472 | − | 0.609908i | \(-0.791206\pi\) | ||
0.792472 | − | 0.609908i | \(-0.208794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 71.4968 | + | 123.836i | 0.0730304 | + | 0.126492i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1383.54 | + | 798.789i | 1.40747 | + | 0.812603i | 0.995144 | − | 0.0984338i | \(-0.0313833\pi\) |
0.412326 | + | 0.911037i | \(0.364717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1483.65 | + | 2569.76i | −1.50624 | + | 2.60889i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.6045i | 0.0562229i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 311.165 | − | 538.954i | 0.313991 | − | 0.543848i | −0.665232 | − | 0.746637i | \(-0.731667\pi\) |
0.979222 | + | 0.202789i | \(0.0650005\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1931.23i | − | 1.94094i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 793.782 | + | 1374.87i | 0.796171 | + | 1.37901i | 0.922093 | + | 0.386968i | \(0.126478\pi\) |
−0.125922 | + | 0.992040i | \(0.540189\pi\) | |||||||
\(998\) | 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 | 1368.3.cs.a.809.19 | yes | 40 | |
3.2 | odd | 2 | inner | 1368.3.cs.a.809.2 | ✓ | 40 | |
19.7 | even | 3 | inner | 1368.3.cs.a.881.2 | yes | 40 | |
57.26 | odd | 6 | inner | 1368.3.cs.a.881.19 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.3.cs.a.809.2 | ✓ | 40 | 3.2 | odd | 2 | inner | |
1368.3.cs.a.809.19 | yes | 40 | 1.1 | even | 1 | trivial | |
1368.3.cs.a.881.2 | yes | 40 | 19.7 | even | 3 | inner | |
1368.3.cs.a.881.19 | yes | 40 | 57.26 | odd | 6 | inner |