Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(81,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.r (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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 737.28 | ||
Character | \(\chi\) | \(=\) | 1148.737 |
Dual form | 1148.2.r.a.81.28 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.89464 | − | 1.67122i | 1.67122 | − | 0.964880i | 0.704266 | − | 0.709936i | \(-0.251276\pi\) |
0.966956 | − | 0.254944i | \(-0.0820570\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.42784 | − | 2.47308i | 0.638548 | − | 1.10600i | −0.347204 | − | 0.937790i | \(-0.612869\pi\) |
0.985752 | − | 0.168207i | \(-0.0537979\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.36322 | + | 2.26752i | 0.515247 | + | 0.857041i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.08596 | − | 7.07710i | 1.36199 | − | 2.35903i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.10288 | + | 0.636749i | −0.332531 | + | 0.191987i | −0.656964 | − | 0.753922i | \(-0.728160\pi\) |
0.324433 | + | 0.945909i | \(0.394826\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41413i | 0.946909i | 0.880818 | + | 0.473454i | \(0.156993\pi\) | ||||
−0.880818 | + | 0.473454i | \(0.843007\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 9.54492i | − | 2.46449i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.97022 | − | 1.13751i | 0.477849 | − | 0.275886i | −0.241671 | − | 0.970358i | \(-0.577695\pi\) |
0.719519 | + | 0.694472i | \(0.244362\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.851130 | + | 0.491400i | 0.195263 | + | 0.112735i | 0.594444 | − | 0.804137i | \(-0.297372\pi\) |
−0.399181 | + | 0.916872i | \(0.630706\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.73555 | + | 4.28541i | 1.68804 | + | 0.935154i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.90559 | + | 6.76468i | −0.814372 | + | 1.41053i | 0.0954064 | + | 0.995438i | \(0.469585\pi\) |
−0.909778 | + | 0.415095i | \(0.863748\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.57743 | − | 2.73219i | −0.315486 | − | 0.546439i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 17.2869i | − | 3.32686i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.0172332i | − | 0.00320012i | −0.999999 | − | 0.00160006i | \(-0.999491\pi\) | ||
0.999999 | − | 0.00160006i | \(-0.000509315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.79997 | − | 8.31379i | −0.862100 | − | 1.49320i | −0.869898 | − | 0.493232i | \(-0.835815\pi\) |
0.00779754 | − | 0.999970i | \(-0.497518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.12830 | + | 3.68632i | −0.370489 | + | 0.641705i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.55422 | − | 0.133706i | 1.27690 | − | 0.0226004i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00389 | + | 6.93495i | −0.658236 | + | 1.14010i | 0.322836 | + | 0.946455i | \(0.395364\pi\) |
−0.981072 | + | 0.193644i | \(0.937969\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.70576 | + | 9.88267i | 0.913653 | + | 1.58249i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.71859 | + | 4.32839i | 0.736920 | + | 0.675980i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.35283 | −0.358802 | −0.179401 | − | 0.983776i | \(-0.557416\pi\) | ||||
−0.179401 | + | 0.983776i | \(0.557416\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.6682 | − | 20.2099i | −1.73939 | − | 3.01271i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.58279 | − | 2.06853i | −0.522604 | − | 0.301726i | 0.215395 | − | 0.976527i | \(-0.430896\pi\) |
−0.737999 | + | 0.674801i | \(0.764229\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.28328 | + | 6.18224i | −0.469040 | + | 0.883177i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.80205 | − | 6.58535i | 0.532394 | − | 0.922133i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.38918 | + | 0.802043i | −0.190819 | + | 0.110169i | −0.592366 | − | 0.805669i | \(-0.701806\pi\) |
0.401547 | + | 0.915838i | \(0.368473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.63669i | 0.490371i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.28495 | 0.435103 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.38451 | − | 5.86214i | −0.440625 | − | 0.763185i | 0.557111 | − | 0.830438i | \(-0.311910\pi\) |
−0.997736 | + | 0.0672529i | \(0.978577\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.36290 | + | 5.82471i | −0.430575 | + | 0.745778i | −0.996923 | − | 0.0783884i | \(-0.975023\pi\) |
0.566348 | + | 0.824166i | \(0.308356\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.6175 | − | 0.382618i | 2.72355 | − | 0.0482054i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.44343 | + | 4.87481i | 1.04728 | + | 0.604646i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.17149 | + | 4.71781i | −0.998306 | + | 0.576372i | −0.907747 | − | 0.419519i | \(-0.862199\pi\) |
−0.0905595 | + | 0.995891i | \(0.528866\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 26.1084i | 3.14308i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.13702i | − | 0.372296i | −0.982522 | − | 0.186148i | \(-0.940400\pi\) | ||
0.982522 | − | 0.186148i | \(-0.0596003\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.62882 | − | 9.74940i | −0.658803 | − | 1.14108i | −0.980926 | − | 0.194382i | \(-0.937730\pi\) |
0.322123 | − | 0.946698i | \(-0.395604\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.13220 | − | 5.27248i | −1.05450 | − | 0.608813i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.94731 | − | 1.63278i | −0.335877 | − | 0.186072i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.10592 | + | 0.638505i | 0.124426 | + | 0.0718375i | 0.560921 | − | 0.827869i | \(-0.310447\pi\) |
−0.436495 | + | 0.899707i | \(0.643780\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −16.6323 | − | 28.8080i | −1.84803 | − | 3.20089i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.83139 | −0.420550 | −0.210275 | − | 0.977642i | \(-0.567436\pi\) | ||||
−0.210275 | + | 0.977642i | \(0.567436\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.49669i | − | 0.704665i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0288004 | − | 0.0498838i | −0.00308773 | − | 0.00534810i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9151 | + | 6.87919i | 1.26300 | + | 0.729193i | 0.973654 | − | 0.228032i | \(-0.0732290\pi\) |
0.289345 | + | 0.957225i | \(0.406562\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.74160 | + | 4.65420i | −0.811540 | + | 0.487892i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −27.7884 | − | 16.0436i | −2.88152 | − | 1.66365i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.43055 | − | 1.40328i | 0.249369 | − | 0.143973i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.5399i | − | 1.07017i | −0.844798 | − | 0.535085i | \(-0.820280\pi\) | ||
0.844798 | − | 0.535085i | \(-0.179720\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.4069i | 1.04594i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.0930 | − | 9.29128i | 1.60131 | − | 0.924517i | 0.610085 | − | 0.792336i | \(-0.291135\pi\) |
0.991226 | − | 0.132181i | \(-0.0421979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.66295 | + | 4.61237i | −0.262389 | + | 0.454470i | −0.966876 | − | 0.255246i | \(-0.917844\pi\) |
0.704488 | + | 0.709716i | \(0.251177\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.6433 | − | 13.0118i | 2.11217 | − | 1.26982i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.41227 | + | 7.64228i | −0.426550 | + | 0.738807i | −0.996564 | − | 0.0828285i | \(-0.973605\pi\) |
0.570013 | + | 0.821635i | \(0.306938\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7691 | + | 7.37222i | −1.22305 | + | 0.706131i | −0.965568 | − | 0.260151i | \(-0.916228\pi\) |
−0.257487 | + | 0.966282i | \(0.582894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.7656i | 2.54048i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.57000 | −0.523982 | −0.261991 | − | 0.965070i | \(-0.584379\pi\) | ||||
−0.261991 | + | 0.965070i | \(0.584379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.1531 | + | 19.3177i | 1.04003 | + | 1.80139i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 24.1621 | + | 13.9500i | 2.23379 | + | 1.28968i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.26516 | + | 2.91684i | 0.482656 | + | 0.267386i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.68910 | + | 8.12176i | −0.426282 | + | 0.738342i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.8923 | + | 4.64332i | 1.88380 | + | 0.418674i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.26910 | 0.471283 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7889 | −1.04610 | −0.523049 | − | 0.852302i | \(-0.675206\pi\) | ||||
−0.523049 | + | 0.852302i | \(0.675206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.81058 | + | 3.93209i | −0.599638 | + | 0.346201i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.27601 | − | 5.67422i | 0.286227 | − | 0.495759i | −0.686679 | − | 0.726960i | \(-0.740932\pi\) |
0.972906 | + | 0.231202i | \(0.0742657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0460158 | + | 2.59984i | 0.00399007 | + | 0.225435i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −42.7519 | − | 24.6828i | −3.67950 | − | 2.12436i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.7173 | − | 6.76496i | 1.00107 | − | 0.577970i | 0.0925076 | − | 0.995712i | \(-0.470512\pi\) |
0.908566 | + | 0.417742i | \(0.137178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1594 | 1.03135 | 0.515673 | − | 0.856785i | \(-0.327542\pi\) | ||||
0.515673 | + | 0.856785i | \(0.327542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.8279 | −1.16452 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.17394 | − | 3.76538i | −0.181794 | − | 0.314877i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0426191 | − | 0.0246061i | −0.00353932 | − | 0.00204343i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.827974 | + | 23.3824i | 0.0682901 | + | 1.92855i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.02593 | − | 0.592323i | −0.0840477 | − | 0.0485250i | 0.457387 | − | 0.889268i | \(-0.348785\pi\) |
−0.541435 | + | 0.840743i | \(0.682119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9980 | − | 9.81380i | 1.38328 | − | 0.798635i | 0.390731 | − | 0.920505i | \(-0.372222\pi\) |
0.992546 | + | 0.121869i | \(0.0388889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 18.5912i | − | 1.50301i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.4143 | −2.20197 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.469171 | − | 0.270876i | 0.0374439 | − | 0.0216183i | −0.481161 | − | 0.876632i | \(-0.659785\pi\) |
0.518605 | + | 0.855014i | \(0.326451\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.68078 | + | 4.64325i | −0.212600 | + | 0.368234i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.6632 | + | 0.365728i | −1.62849 | + | 0.0288234i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7168 | − | 22.0262i | 0.996057 | − | 1.72522i | 0.421201 | − | 0.906967i | \(-0.361609\pi\) |
0.574856 | − | 0.818254i | \(-0.305058\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.07772 | + | 10.5269i | 0.473150 | + | 0.819519i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.26023i | 0.484431i | 0.970222 | + | 0.242216i | \(0.0778742\pi\) | ||||
−0.970222 | + | 0.242216i | \(0.922126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.34373 | 0.103364 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.95537 | − | 4.01569i | 0.531891 | − | 0.307087i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.34229 | − | 16.1813i | 0.710281 | − | 1.23024i | −0.254470 | − | 0.967081i | \(-0.581901\pi\) |
0.964751 | − | 0.263163i | \(-0.0847657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.04492 | − | 7.30143i | 0.305767 | − | 0.551936i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.5939 | − | 11.3125i | −1.47276 | − | 0.850301i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.6712 | + | 7.89306i | −1.02183 | + | 0.589955i | −0.914634 | − | 0.404283i | \(-0.867521\pi\) |
−0.107198 | + | 0.994238i | \(0.534188\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.35013i | 0.323342i | 0.986845 | + | 0.161671i | \(0.0516884\pi\) | ||||
−0.986845 | + | 0.161671i | \(0.948312\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.4806i | 1.66181i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.4338 | + | 19.8039i | 0.840631 | + | 1.45601i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.44861 | + | 2.50907i | −0.105933 | + | 0.183481i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 39.1983 | − | 23.5658i | 2.85126 | − | 1.71416i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9422 | + | 10.9363i | 1.37061 | + | 0.791323i | 0.991005 | − | 0.133825i | \(-0.0427259\pi\) |
0.379607 | + | 0.925148i | \(0.376059\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.9608 | − | 9.21496i | 1.14888 | − | 0.663308i | 0.200268 | − | 0.979741i | \(-0.435819\pi\) |
0.948615 | + | 0.316434i | \(0.102485\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 32.5876 | 2.33365 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4760 | 1.38761 | 0.693803 | − | 0.720165i | \(-0.255934\pi\) | ||||
0.693803 | + | 0.720165i | \(0.255934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.75202 | − | 1.58888i | 0.195085 | − | 0.112633i | −0.399276 | − | 0.916831i | \(-0.630738\pi\) |
0.594361 | + | 0.804198i | \(0.297405\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.7690 | + | 27.3127i | −1.11226 | + | 1.92649i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0390765 | − | 0.0234925i | 0.00274263 | − | 0.00164885i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.4418 | − | 5.48924i | 1.21819 | − | 0.383385i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 31.9162 | + | 55.2805i | 2.21833 | + | 3.84226i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.25159 | −0.0865745 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 20.5647i | − | 1.41573i | −0.706345 | − | 0.707867i | \(-0.749657\pi\) | ||
0.706345 | − | 0.707867i | \(-0.250343\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.24265 | − | 9.08054i | −0.359221 | − | 0.622188i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.35945 | + | 5.81874i | −0.229113 | + | 0.396835i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.3083 | − | 22.2175i | 0.835541 | − | 1.50822i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −32.5868 | − | 18.8140i | −2.20201 | − | 1.27133i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.88359 | + | 6.72658i | 0.261239 | + | 0.452479i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.3009 | −1.49338 | −0.746689 | − | 0.665173i | \(-0.768358\pi\) | ||||
−0.746689 | + | 0.665173i | \(0.768358\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.7813 | −1.71875 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.05944 | − | 5.23047i | 0.601296 | − | 0.347159i | −0.168255 | − | 0.985744i | \(-0.553813\pi\) |
0.769551 | + | 0.638585i | \(0.220480\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.9503 | + | 10.3636i | 1.18619 | + | 0.684847i | 0.957439 | − | 0.288637i | \(-0.0932022\pi\) |
0.228752 | + | 0.973485i | \(0.426535\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.2601 | + | 0.199298i | −0.740862 | + | 0.0131129i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.9415 | − | 11.5132i | −1.30641 | − | 0.754255i | −0.324913 | − | 0.945744i | \(-0.605335\pi\) |
−0.981495 | + | 0.191489i | \(0.938668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2313 | + | 5.90703i | −0.667415 | + | 0.385332i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.26833 | 0.277258 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.34289i | 0.604341i | 0.953254 | + | 0.302171i | \(0.0977112\pi\) | ||||
−0.953254 | + | 0.302171i | \(0.902289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.94995 | + | 13.7697i | 0.512101 | + | 0.886986i | 0.999902 | + | 0.0140303i | \(0.00446612\pi\) |
−0.487800 | + | 0.872955i | \(0.662201\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −51.3765 | − | 29.6622i | −3.29580 | − | 1.90283i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.6012 | + | 16.9471i | 0.677287 | + | 1.08271i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.67770 | + | 2.90587i | −0.106750 | + | 0.184896i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.0905 | + | 6.40311i | −0.702833 | + | 0.405781i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4444 | 0.659247 | 0.329624 | − | 0.944112i | \(-0.393078\pi\) | ||||
0.329624 | + | 0.944112i | \(0.393078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.94752i | − | 0.625395i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.8574 | − | 18.8056i | −0.679918 | − | 1.17765i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.28526 | − | 1.31940i | −0.142551 | − | 0.0823018i | 0.427028 | − | 0.904238i | \(-0.359560\pi\) |
−0.569579 | + | 0.821936i | \(0.692894\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.1833 | + | 0.374933i | −1.31627 | + | 0.0232972i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.121961 | − | 0.0704141i | −0.00754918 | − | 0.00435852i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7942 | + | 7.38672i | −0.788922 | + | 0.455484i | −0.839583 | − | 0.543232i | \(-0.817201\pi\) |
0.0506608 | + | 0.998716i | \(0.483867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.58075i | 0.281393i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 45.9866 | 2.81434 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.59737 | − | 6.23082i | −0.219335 | − | 0.379900i | 0.735270 | − | 0.677775i | \(-0.237056\pi\) |
−0.954605 | + | 0.297875i | \(0.903722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8734 | + | 22.2973i | −0.782002 | + | 1.35447i | 0.148773 | + | 0.988871i | \(0.452468\pi\) |
−0.930774 | + | 0.365595i | \(0.880866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.6309 | + | 26.4101i | −0.885505 | + | 1.59841i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.47944 | + | 2.00886i | 0.209818 | + | 0.121139i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.04779 | + | 8.74302i | 0.303292 | + | 0.525317i | 0.976880 | − | 0.213790i | \(-0.0685809\pi\) |
−0.673588 | + | 0.739107i | \(0.735248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −78.4500 | −4.69668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.4886i | 1.87845i | 0.343300 | + | 0.939226i | \(0.388455\pi\) | ||||
−0.343300 | + | 0.939226i | \(0.611545\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9374 | − | 18.9441i | −0.650161 | − | 1.12611i | −0.983083 | − | 0.183158i | \(-0.941368\pi\) |
0.332922 | − | 0.942954i | \(-0.391965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.69038 | − | 8.12397i | 0.277834 | − | 0.481223i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.38224 | + | 16.6000i | −0.199647 | + | 0.979868i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.91216 | + | 10.2402i | −0.347774 | + | 0.602362i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.6146 | − | 30.5094i | −1.03259 | − | 1.78849i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.76984i | 0.161816i | 0.996722 | + | 0.0809080i | \(0.0257820\pi\) | ||||
−0.996722 | + | 0.0809080i | \(0.974218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.3301 | −1.12544 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.0074 | + | 19.0654i | 0.638714 | + | 1.10628i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.0955 | − | 13.3342i | −1.33565 | − | 0.771136i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.20741 | − | 5.33507i | −0.184872 | − | 0.307509i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.0556 | − | 53.7898i | 1.78410 | − | 3.09015i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.60334 | + | 16.6335i | 0.549886 | + | 0.952430i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.90088 | −0.393854 | −0.196927 | − | 0.980418i | \(-0.563096\pi\) | ||||
−0.196927 | + | 0.980418i | \(0.563096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.8015i | 1.01269i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.268231 | + | 0.154863i | −0.0152100 | + | 0.00878148i | −0.507586 | − | 0.861601i | \(-0.669462\pi\) |
0.492376 | + | 0.870383i | \(0.336129\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.57240 | − | 3.79458i | −0.371494 | − | 0.214482i | 0.302617 | − | 0.953112i | \(-0.402140\pi\) |
−0.674111 | + | 0.738630i | \(0.735473\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29.9200 | − | 54.0082i | 1.68580 | − | 3.04302i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.0085 | + | 9.24253i | 0.899129 | + | 0.519112i | 0.876918 | − | 0.480641i | \(-0.159596\pi\) |
0.0222115 | + | 0.999753i | \(0.492929\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0109732 | + | 0.0190061i | 0.000614381 | + | 0.00106414i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.4955i | 1.64628i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.23588 | 0.124408 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.32806 | − | 5.38556i | 0.517427 | − | 0.298737i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.6412 | + | 42.6799i | −1.36266 | + | 2.36020i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.193701 | − | 10.9439i | −0.0106791 | − | 0.603357i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.75436 | + | 2.74493i | 0.261323 | + | 0.150875i | 0.624938 | − | 0.780674i | \(-0.285124\pi\) |
−0.363615 | + | 0.931549i | \(0.618458\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.7195 | + | 56.6719i | 1.79302 | + | 3.10560i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.9450i | 1.47217i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4452 | −0.568986 | −0.284493 | − | 0.958678i | \(-0.591825\pi\) | ||||
−0.284493 | + | 0.958678i | \(0.591825\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.1232 | + | 9.30871i | −0.875689 | + | 0.505580i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.5876 | + | 6.11275i | 0.573350 | + | 0.331024i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4942 | + | 0.982832i | −0.998591 | + | 0.0530680i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 64.5683 | + | 37.2786i | 3.47624 | + | 2.00701i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.4144 | + | 12.3636i | −1.14958 | + | 0.663712i | −0.948786 | − | 0.315920i | \(-0.897687\pi\) |
−0.200798 | + | 0.979633i | \(0.564353\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.15478 | −0.168872 | −0.0844359 | − | 0.996429i | \(-0.526909\pi\) | ||||
−0.0844359 | + | 0.996429i | \(0.526909\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 59.0196 | 3.15023 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.697880 | + | 1.20876i | 0.0371444 | + | 0.0643360i | 0.884000 | − | 0.467487i | \(-0.154841\pi\) |
−0.846856 | + | 0.531823i | \(0.821507\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.75811 | − | 4.47915i | −0.411758 | − | 0.237729i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.1154 | − | 0.356032i | 1.06462 | − | 0.0188432i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.470898 | − | 0.815619i | 0.0248530 | − | 0.0430467i | −0.853331 | − | 0.521369i | \(-0.825422\pi\) |
0.878184 | + | 0.478322i | \(0.158755\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.01705 | − | 15.6180i | −0.474582 | − | 0.822000i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.3461i | 1.64524i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.1481 | −1.68271 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.9467 | − | 27.6205i | −0.832411 | − | 1.44178i | −0.896121 | − | 0.443809i | \(-0.853627\pi\) |
0.0637108 | − | 0.997968i | \(-0.479706\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 49.9124 | − | 15.7083i | 2.59834 | − | 0.817740i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.71240 | − | 2.05663i | −0.192738 | − | 0.106775i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.36868 | + | 5.83472i | −0.174424 | + | 0.302110i | −0.939962 | − | 0.341280i | \(-0.889140\pi\) |
0.765538 | + | 0.643391i | \(0.222473\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.2522 | − | 8.80584i | 0.787618 | − | 0.454731i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0588362 | 0.00303022 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0763 | 1.08262 | 0.541308 | − | 0.840825i | \(-0.317929\pi\) | ||||
0.541308 | + | 0.840825i | \(0.317929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.1247 | + | 19.7019i | −1.74826 | + | 1.00936i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.45613 | + | 4.88215i | 0.432088 | + | 0.249466i | 0.700236 | − | 0.713912i | \(-0.253078\pi\) |
−0.268148 | + | 0.963378i | \(0.586412\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.24626 | + | 4.95760i | −0.420269 | + | 0.252663i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.61356 | + | 16.6512i | −0.488685 | + | 0.846427i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.89671 | − | 15.4095i | −0.451081 | − | 0.781295i | 0.547372 | − | 0.836889i | \(-0.315628\pi\) |
−0.998453 | + | 0.0555939i | \(0.982295\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.7705i | 0.898695i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 21.8998i | − | 1.10470i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.15816 | − | 1.82336i | 0.158904 | − | 0.0917433i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2634 | + | 12.8538i | 1.11737 | + | 0.645113i | 0.940728 | − | 0.339162i | \(-0.110144\pi\) |
0.176641 | + | 0.984275i | \(0.443477\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.47811 | + | 7.44870i | 0.224186 | + | 0.372901i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6874 | − | 20.2432i | 0.583642 | − | 1.01090i | −0.411401 | − | 0.911455i | \(-0.634960\pi\) |
0.995043 | − | 0.0994438i | \(-0.0317064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.3844 | − | 16.3877i | 1.41393 | − | 0.816330i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −94.9928 | −4.72023 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 10.1979i | − | 0.505491i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.07479 | + | 13.9860i | 0.399273 | + | 0.691561i | 0.993636 | − | 0.112636i | \(-0.0359293\pi\) |
−0.594363 | + | 0.804197i | \(0.702596\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.6115 | − | 39.1643i | 1.11534 | − | 1.93183i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.67869 | − | 15.6658i | 0.427050 | − | 0.770863i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.47060 | + | 9.47536i | −0.268541 | + | 0.465127i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.1971 | − | 20.3211i | 1.72361 | − | 0.995126i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.145809 | −0.00712322 | −0.00356161 | − | 0.999994i | \(-0.501134\pi\) | ||||
−0.00356161 | + | 0.999994i | \(0.501134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 29.9240i | − | 1.45840i | −0.684298 | − | 0.729202i | \(-0.739891\pi\) | ||
0.684298 | − | 0.729202i | \(-0.260109\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.2783 | + | 16.9038i | −1.42356 | + | 0.821893i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.21578 | − | 3.58868i | −0.301509 | − | 0.174077i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.7920 | + | 0.314909i | −0.861015 | + | 0.0152395i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.5856 | − | 7.26627i | −0.607636 | − | 0.350819i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.55062 | − | 4.41781i | −0.122859 | − | 0.212798i | 0.798035 | − | 0.602611i | \(-0.205873\pi\) |
−0.920894 | + | 0.389813i | \(0.872540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4540 | −0.790727 | −0.395363 | − | 0.918525i | \(-0.629381\pi\) | ||||
−0.395363 | + | 0.918525i | \(0.629381\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.164489 | −0.00788665 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.64833 | + | 3.83842i | −0.318033 | + | 0.183616i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.7398 | + | 6.20060i | 0.512581 | + | 0.295939i | 0.733894 | − | 0.679264i | \(-0.237701\pi\) |
−0.221313 | + | 0.975203i | \(0.571034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.3369 | + | 48.4965i | 1.44462 | + | 2.30936i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.08072 | + | 15.7283i | −0.431438 | + | 0.747272i | −0.996997 | − | 0.0774351i | \(-0.975327\pi\) |
0.565559 | + | 0.824708i | \(0.308660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.0257 | − | 19.6447i | 1.61297 | − | 0.931249i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.95961 | −0.187283 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.727275 | −0.0343222 | −0.0171611 | − | 0.999853i | \(-0.505463\pi\) | ||||
−0.0171611 | + | 0.999853i | \(0.505463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.96014 | − | 1.76914i | −0.374828 | − | 0.0833056i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.8021 | − | 56.8148i | 1.54118 | − | 2.66939i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.456488 | + | 25.7911i | 0.0214005 | + | 1.20910i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.1671 | − | 16.2623i | −1.31760 | − | 0.760719i | −0.334261 | − | 0.942481i | \(-0.608487\pi\) |
−0.983343 | + | 0.181762i | \(0.941820\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.6639 | − | 34.0589i | −0.917834 | − | 1.58974i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.5168 | 1.46789 | 0.733943 | − | 0.679211i | \(-0.237678\pi\) | ||||
0.733943 | + | 0.679211i | \(0.237678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.8842i | 1.85358i | 0.375583 | + | 0.926789i | \(0.377442\pi\) | ||||
−0.375583 | + | 0.926789i | \(0.622558\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −79.3545 | + | 45.8154i | −3.67998 | + | 2.12464i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.76790 | − | 16.9185i | 0.452005 | − | 0.782895i | −0.546506 | − | 0.837455i | \(-0.684042\pi\) |
0.998510 | + | 0.0545604i | \(0.0173757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.8372 | − | 12.0976i | −1.00835 | − | 0.558615i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.905388 | − | 1.56818i | 0.0417181 | − | 0.0722578i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.59489 | − | 1.49816i | 0.119313 | − | 0.0688854i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.10060i | − | 0.142265i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.1085i | 0.600196i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.8197 | + | 9.13352i | −0.722822 | + | 0.417321i | −0.815790 | − | 0.578348i | \(-0.803698\pi\) |
0.0929686 | + | 0.995669i | \(0.470364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.6768 | − | 13.6698i | −1.07957 | − | 0.623290i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −59.2013 | + | 35.5914i | −2.69375 | + | 1.61947i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.0662 | − | 15.0493i | −1.18360 | − | 0.683354i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.37745 | − | 4.11786i | −0.107732 | − | 0.186598i | 0.807119 | − | 0.590389i | \(-0.201026\pi\) |
−0.914851 | + | 0.403791i | \(0.867692\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 85.0104i | − | 3.84430i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.6740 | 1.06839 | 0.534196 | − | 0.845361i | \(-0.320614\pi\) | ||||
0.534196 | + | 0.845361i | \(0.320614\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0196028 | − | 0.0339531i | −0.000882867 | − | 0.00152917i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 25.7372 | + | 14.8594i | 1.15680 | + | 0.667880i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.11325 | − | 4.27644i | 0.319073 | − | 0.191824i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.70632 | + | 3.29454i | 0.255450 | + | 0.147484i | 0.622257 | − | 0.782813i | \(-0.286216\pi\) |
−0.366807 | + | 0.930297i | \(0.619549\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4622 | + | 18.1211i | 0.467418 | + | 0.809592i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.5303i | 0.469522i | 0.972053 | + | 0.234761i | \(0.0754308\pi\) | ||||
−0.972053 | + | 0.234761i | \(0.924569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 53.0657i | − | 2.36139i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.88963 | − | 2.24568i | 0.172744 | − | 0.0997340i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.8073 | − | 18.3640i | −1.40983 | − | 0.813968i | −0.414463 | − | 0.910066i | \(-0.636030\pi\) |
−0.995372 | + | 0.0960979i | \(0.969364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.4336 | − | 26.0540i | 0.638507 | − | 1.15256i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.49477 | − | 14.7134i | 0.375053 | − | 0.649611i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.60452 | + | 13.1714i | 0.335095 | + | 0.580402i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.26852 | 0.231709 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 62.4522i | − | 2.74135i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.3222 | + | 9.42362i | −0.715088 | + | 0.412856i | −0.812942 | − | 0.582344i | \(-0.802136\pi\) |
0.0978540 | + | 0.995201i | \(0.468802\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.62436 | + | 14.9378i | −0.377117 | + | 0.653185i | −0.990641 | − | 0.136490i | \(-0.956418\pi\) |
0.613525 | + | 0.789676i | \(0.289751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.493726 | − | 27.8950i | −0.0215480 | − | 1.21744i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.9140 | − | 10.9200i | −0.823907 | − | 0.475683i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0073 | − | 32.9215i | −0.826403 | − | 1.43137i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −55.3159 | −2.40050 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.7777 | + | 16.1099i | −0.640092 | + | 0.697795i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6000 | + | 21.8238i | 0.544746 | + | 0.943527i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.3821 | + | 45.6951i | −1.13847 | + | 1.97189i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.315465 | − | 8.90890i | −0.0135880 | − | 0.383733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6967 | − | 37.5798i | 0.932814 | − | 1.61568i | 0.154327 | − | 0.988020i | \(-0.450679\pi\) |
0.778487 | − | 0.627661i | \(-0.215988\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.27003 | + | 12.5921i | 0.311987 | + | 0.540377i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 42.1053i | 1.80359i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.8757i | − | 0.550527i | −0.961369 | − | 0.275263i | \(-0.911235\pi\) | ||
0.961369 | − | 0.275263i | \(-0.0887650\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.4814 | + | 47.5991i | 1.17288 | + | 2.03148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.00846838 | − | 0.0146677i | 0.000360765 | − | 0.000624863i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0597910 | + | 3.37812i | 0.00254257 | + | 0.143652i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 66.1936 | + | 38.2169i | 2.80976 | + | 1.62222i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.3677 | − | 17.5328i | 1.28672 | − | 0.742888i | 0.308651 | − | 0.951175i | \(-0.400122\pi\) |
0.978068 | + | 0.208288i | \(0.0667890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.03284i | − | 0.339753i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.68381i | 0.408851i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.6461 | − | 20.0029i | 1.46016 | − | 0.843024i | 0.461142 | − | 0.887326i | \(-0.347440\pi\) |
0.999018 | + | 0.0443026i | \(0.0141066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.95305 | + | 13.7751i | −0.334587 | + | 0.579522i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.6492 | − | 76.9856i | 1.79110 | − | 3.23309i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.60021 | + | 9.69985i | −0.234773 | + | 0.406639i | −0.959207 | − | 0.282706i | \(-0.908768\pi\) |
0.724434 | + | 0.689345i | \(0.242101\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.8072 | + | 14.3224i | −1.03815 | + | 0.599376i | −0.919308 | − | 0.393538i | \(-0.871251\pi\) |
−0.118840 | + | 0.992913i | \(0.537918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 73.1080 | 3.05413 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.6432 | 1.02769 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.53352 | − | 4.34948i | 0.313625 | − | 0.181071i | −0.334923 | − | 0.942246i | \(-0.608710\pi\) |
0.648547 | + | 0.761174i | \(0.275377\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.8005 | − | 53.3480i | 1.28002 | − | 2.21707i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.22302 | − | 8.68776i | −0.216687 | − | 0.360429i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.02140 | − | 1.76912i | 0.0423021 | − | 0.0732693i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 68.9991 | − | 39.8366i | 2.85276 | − | 1.64704i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.55700i | − | 0.353185i | −0.984284 | − | 0.176593i | \(-0.943492\pi\) | ||
0.984284 | − | 0.176593i | \(-0.0565075\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.43483i | − | 0.388755i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 56.3759 | − | 32.5487i | 2.31900 | − | 1.33887i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.5590 | − | 16.4886i | −1.17278 | − | 0.677104i | −0.218446 | − | 0.975849i | \(-0.570099\pi\) |
−0.954333 | + | 0.298745i | \(0.903432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.7314 | − | 8.85640i | 0.603928 | − | 0.363077i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.31073 | − | 9.19846i | 0.217354 | − | 0.376468i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8917 | − | 24.0612i | −0.567600 | − | 0.983113i | −0.996803 | − | 0.0799042i | \(-0.974539\pi\) |
0.429202 | − | 0.903208i | \(-0.358795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.12765i | − | 0.127580i | −0.997963 | − | 0.0637898i | \(-0.979681\pi\) | ||
0.997963 | − | 0.0637898i | \(-0.0203187\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 77.1072i | 3.14005i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.3905 | + | 23.1931i | 0.544403 | + | 0.942933i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.66790 | + | 2.88889i | −0.0676980 | + | 0.117256i | −0.897888 | − | 0.440225i | \(-0.854899\pi\) |
0.830190 | + | 0.557481i | \(0.188232\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0738512 | − | 0.133308i | 0.00299260 | − | 0.00540191i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.06221 | − | 12.2321i | 0.285706 | − | 0.494858i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.7528 | − | 18.6244i | −0.434302 | − | 0.752233i | 0.562936 | − | 0.826500i | \(-0.309672\pi\) |
−0.997238 | + | 0.0742672i | \(0.976338\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 41.3141 | − | 45.0386i | 1.66595 | − | 1.81613i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.5261 | 1.14842 | 0.574210 | − | 0.818708i | \(-0.305309\pi\) | ||||
0.574210 | + | 0.818708i | \(0.305309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.4267 | − | 23.2556i | −0.539663 | − | 0.934723i | −0.998922 | − | 0.0464209i | \(-0.985218\pi\) |
0.459259 | − | 0.888302i | \(-0.348115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 116.940 | + | 67.5154i | 4.69265 | + | 2.70930i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.644182 | + | 36.3956i | 0.0258086 | + | 1.45816i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.4106 | − | 26.6919i | 0.616423 | − | 1.06768i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.62291 | + | 2.09169i | −0.144685 | + | 0.0835341i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.2178i | 0.726393i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7854 | 0.907072 | 0.453536 | − | 0.891238i | \(-0.350162\pi\) | ||||
0.453536 | + | 0.891238i | \(0.350162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −34.3682 | − | 59.5275i | −1.36601 | − | 2.36601i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.8327 | + | 29.1550i | −0.667984 | + | 1.15698i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.1069 | − | 11.2095i | −0.836288 | − | 0.444138i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.2010 | − | 12.8177i | −0.878257 | − | 0.507062i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.90828 | + | 1.67910i | −0.114870 | + | 0.0663203i | −0.556334 | − | 0.830959i | \(-0.687793\pi\) |
0.441464 | + | 0.897279i | \(0.354459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.07260i | − | 0.121171i | −0.998163 | − | 0.0605857i | \(-0.980703\pi\) | ||
0.998163 | − | 0.0605857i | \(-0.0192968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.4575i | 0.884265i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.2697 | + | 31.6440i | 0.718255 | + | 1.24405i | 0.961691 | + | 0.274136i | \(0.0883920\pi\) |
−0.243436 | + | 0.969917i | \(0.578275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.46542 | + | 4.31016i | 0.293043 | + | 0.169189i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.50236 | − | 84.8816i | −0.0588822 | − | 3.32677i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.6308 | + | 17.6847i | 1.19868 | + | 0.692056i | 0.960260 | − | 0.279107i | \(-0.0900384\pi\) |
0.238416 | + | 0.971163i | \(0.423372\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.35522 | − | 16.2037i | −0.365539 | − | 0.633132i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −91.9965 | −3.58913 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.9277i | 1.55536i | 0.628659 | + | 0.777681i | \(0.283604\pi\) | ||||
−0.628659 | + | 0.777681i | \(0.716396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.01545 | − | 15.6152i | −0.350660 | − | 0.607362i | 0.635705 | − | 0.771932i | \(-0.280709\pi\) |
−0.986365 | + | 0.164571i | \(0.947376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.4832 | + | 12.9807i | 0.873176 | + | 0.504128i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.49532 | + | 3.59834i | 0.251878 | + | 0.139538i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.116577 | + | 0.0673056i | 0.00451387 | + | 0.00260608i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −64.5531 | + | 37.2697i | −2.49577 | + | 1.44093i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.56529i | − | 0.330659i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.02214i | − | 0.116495i | −0.998302 | − | 0.0582476i | \(-0.981449\pi\) | ||
0.998302 | − | 0.0582476i | \(-0.0185513\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −47.2311 | + | 27.2689i | −1.81792 | + | 1.04958i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.2286 | − | 29.8409i | 0.662151 | − | 1.14688i | −0.317899 | − | 0.948125i | \(-0.602977\pi\) |
0.980049 | − | 0.198754i | \(-0.0636895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.8995 | − | 14.3682i | 0.917180 | − | 0.551402i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.4826 | − | 30.2807i | 0.669933 | − | 1.16036i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.61335 | − | 5.55027i | 0.367844 | − | 0.212375i | −0.304672 | − | 0.952457i | \(-0.598547\pi\) |
0.672516 | + | 0.740082i | \(0.265213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 38.6370i | − | 1.47625i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 69.2796 | 2.64318 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.73828 | − | 4.74284i | −0.104320 | − | 0.180688i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1725 | − | 14.5333i | −0.957607 | − | 0.552875i | −0.0621711 | − | 0.998066i | \(-0.519802\pi\) |
−0.895436 | + | 0.445191i | \(0.853136\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23.5979 | + | 14.1869i | −0.896410 | + | 0.538916i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.3616 | − | 30.0712i | 0.658564 | − | 1.14067i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.2202 | + | 3.16045i | 0.538629 | + | 0.119710i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −76.9645 | −2.91106 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.8934 | −1.28014 | −0.640068 | − | 0.768319i | \(-0.721094\pi\) | ||||
−0.640068 | + | 0.768319i | \(0.721094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.81567 | + | 3.93503i | −0.257058 | + | 0.148412i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.7439 | + | 34.1975i | −0.743599 | + | 1.28795i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43.0064 | + | 23.8251i | 1.61742 | + | 0.896034i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.3457 | + | 12.9013i | 0.839209 | + | 0.484518i | 0.856995 | − | 0.515324i | \(-0.172329\pi\) |
−0.0177863 | + | 0.999842i | \(0.505662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.03753 | − | 5.21782i | 0.338934 | − | 0.195683i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 74.9869 | 2.80828 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.4161 | −0.464337 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.6140 | + | 27.0443i | 0.583117 | + | 1.00999i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.8802 | − | 21.2928i | −1.37540 | − | 0.794086i | −0.383796 | − | 0.923418i | \(-0.625383\pi\) |
−0.991601 | + | 0.129332i | \(0.958717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0888 | + | 0.249365i | −0.524695 | + | 0.00928683i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.0245 | + | 26.5723i | 1.71167 | + | 0.988233i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0470843 | + | 0.0271841i | −0.00174867 | + | 0.00100959i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 18.7582i | − | 0.695704i | −0.937549 | − | 0.347852i | \(-0.886911\pi\) | ||
0.937549 | − | 0.347852i | \(-0.113089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −98.4948 | −3.64795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.63558 | + | 2.67636i | −0.171453 | + | 0.0989886i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.63365 | − | 13.2219i | 0.281955 | − | 0.488361i | −0.689911 | − | 0.723894i | \(-0.742350\pi\) |
0.971866 | + | 0.235533i | \(0.0756837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 59.0090 | + | 31.3387i | 2.17658 | + | 1.15594i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00812 | − | 10.4064i | 0.221312 | − | 0.383324i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4654 | + | 23.3227i | 0.495331 | + | 0.857939i | 0.999986 | − | 0.00538236i | \(-0.00171327\pi\) |
−0.504654 | + | 0.863322i | \(0.668380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.2153i | 0.412003i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.2812 | −1.40440 | −0.702201 | − | 0.711979i | \(-0.747799\pi\) | ||||
−0.702201 | + | 0.711979i | \(0.747799\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.92973 | + | 1.69148i | −0.107337 | + | 0.0619710i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.6549 | + | 27.1151i | −0.572784 | + | 0.992091i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.3439 | + | 0.413175i | −0.852967 | + | 0.0150971i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.9073 | + | 13.8029i | 0.872389 | + | 0.503674i | 0.868142 | − | 0.496317i | \(-0.165315\pi\) |
0.00424786 | + | 0.999991i | \(0.498648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.2329 | − | 17.4550i | 1.10175 | − | 0.636095i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 56.0500i | − | 2.03987i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 23.3325i | − | 0.848035i | −0.905654 | − | 0.424017i | \(-0.860620\pi\) | ||
0.905654 | − | 0.424017i | \(-0.139380\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.6245 | − | 28.7945i | −0.603431 | − | 1.04517i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.3816 | − | 24.9097i | 0.521332 | − | 0.902974i | −0.478360 | − | 0.878164i | \(-0.658769\pi\) |
0.999692 | − | 0.0248103i | \(-0.00789816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.1237 | − | 18.9042i | −1.23536 | − | 0.684376i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −45.9777 | − | 26.5453i | −1.66233 | − | 0.959746i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.0141 | − | 11.5551i | 0.722667 | − | 0.417232i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.1204 | 0.581318 | 0.290659 | − | 0.956827i | \(-0.406126\pi\) | ||||
0.290659 | + | 0.956827i | \(0.406126\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.82003 | −0.317645 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.4003 | + | 25.0572i | −1.56100 | + | 0.901244i | −0.563844 | + | 0.825881i | \(0.690678\pi\) |
−0.997156 | + | 0.0753630i | \(0.975988\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1433 | + | 26.2289i | −0.543962 | + | 0.942170i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −60.6915 | + | 36.4873i | −2.17729 | + | 1.30897i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.88916 | + | 6.00274i | 0.0676863 | + | 0.215070i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.99749 | + | 3.45976i | 0.0714759 | + | 0.123800i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.297907 | −0.0106463 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.54707i | − | 0.0552172i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.7910 | + | 23.8867i | 0.491596 | + | 0.851470i | 0.999953 | − | 0.00967687i | \(-0.00308029\pi\) |
−0.508357 | + | 0.861146i | \(0.669747\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.6897 | + | 42.7638i | −0.878976 | + | 1.52243i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.59312 | − | 12.6301i | −0.269980 | − | 0.449074i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.8863 | − | 11.4814i | −0.706184 | − | 0.407715i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.65544 | + | 13.2596i | 0.271511 | + | 0.470270i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.4626 | −1.32699 | −0.663496 | − | 0.748180i | \(-0.730928\pi\) | ||||
−0.663496 | + | 0.748180i | \(0.730928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.41185 | −0.332967 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 97.3694 | − | 56.2163i | 3.44038 | − | 1.98630i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.4158 | + | 7.16828i | 0.438145 | + | 0.252963i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.5992 | + | 51.6241i | −1.00799 | + | 1.81951i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.8262 | − | 12.0240i | −0.733116 | − | 0.423265i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.1564 | − | 12.7920i | 0.778977 | − | 0.449743i | −0.0570906 | − | 0.998369i | \(-0.518182\pi\) |
0.836068 | + | 0.548626i | \(0.184849\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.33968 | 0.222616 | 0.111308 | − | 0.993786i | \(-0.464496\pi\) | ||||
0.111308 | + | 0.993786i | \(0.464496\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 86.0570i | 3.01815i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.3150 | − | 62.8995i | −1.27206 | − | 2.20327i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00256 | − | 1.15618i | −0.0700607 | − | 0.0404496i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.30631 | + | 73.8049i | 0.0456461 | + | 2.57895i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.9064 | − | 25.8187i | 0.520238 | − | 0.901079i | −0.479485 | − | 0.877550i | \(-0.659177\pi\) |
0.999723 | − | 0.0235286i | \(-0.00749009\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.5749 | + | 11.8789i | −0.717195 | + | 0.414073i | −0.813719 | − | 0.581258i | \(-0.802561\pi\) |
0.0965245 | + | 0.995331i | \(0.469227\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.4290 | 0.467537 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.7429i | − | 0.547434i | −0.961810 | − | 0.273717i | \(-0.911747\pi\) | ||
0.961810 | − | 0.273717i | \(-0.0882531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6466 | + | 23.6366i | 0.473965 | + | 0.820932i | 0.999556 | − | 0.0298060i | \(-0.00948896\pi\) |
−0.525591 | + | 0.850738i | \(0.676156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.2231 | + | 16.8719i | 1.01374 | + | 0.585281i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.563555 | + | 15.9151i | 0.0195260 | + | 0.551426i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.4821 | + | 8.93859i | 0.535780 | + | 0.309333i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −143.719 | + | 82.9765i | −4.96767 | + | 2.86809i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.3952i | 1.56722i | 0.621255 | + | 0.783609i | \(0.286623\pi\) | ||||
−0.621255 | + | 0.783609i | \(0.713377\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9997 | 0.999990 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 52.6244 | + | 91.1481i | 1.81248 | + | 3.13931i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.91863 | − | 3.32317i | 0.0660029 | − | 0.114320i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.8085 | + | 0.439098i | −0.852431 | + | 0.0150876i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −63.3197 | − | 36.5577i | −2.17313 | − | 1.25466i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.2751 | − | 54.1701i | −1.07210 | − | 1.85693i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.9508 | −0.683102 | −0.341551 | − | 0.939863i | \(-0.610952\pi\) | ||||
−0.341551 | + | 0.939863i | \(0.610952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 22.9350i | − | 0.784359i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.97078 | − | 8.60964i | −0.169798 | − | 0.294100i | 0.768550 | − | 0.639789i | \(-0.220978\pi\) |
−0.938349 | + | 0.345690i | \(0.887645\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.58450 | + | 7.94059i | −0.156421 | + | 0.270929i | −0.933576 | − | 0.358381i | \(-0.883329\pi\) |
0.777154 | + | 0.629310i | \(0.216662\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.9519 | + | 53.7035i | 0.611800 | + | 1.83021i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.1781 | − | 34.9495i | 0.686871 | − | 1.18970i | −0.285974 | − | 0.958237i | \(-0.592317\pi\) |
0.972845 | − | 0.231458i | \(-0.0743496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.6785 | − | 46.2086i | −0.907097 | − | 1.57114i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.5221i | 1.34224i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.62627 | −0.0551674 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.1072 | − | 27.8985i | −0.545772 | − | 0.945305i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −74.5922 | − | 43.0658i | −2.52456 | − | 1.45756i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.18293 | + | 11.9478i | 0.242827 | + | 0.403909i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.63603 | + | 13.2260i | −0.257850 | + | 0.446610i | −0.965666 | − | 0.259787i | \(-0.916348\pi\) |
0.707815 | + | 0.706397i | \(0.249681\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.62902 | + | 8.01770i | 0.156133 | + | 0.270430i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.0412 | −0.809967 | −0.404984 | − | 0.914324i | \(-0.632723\pi\) | ||||
−0.404984 | + | 0.914324i | \(0.632723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.11357i | 0.172085i | 0.996291 | + | 0.0860426i | \(0.0274221\pi\) | ||||
−0.996291 | + | 0.0860426i | \(0.972578\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −55.9537 | + | 32.3049i | −1.88086 | + | 1.08592i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.2220 | + | 7.05638i | 0.410375 | + | 0.236930i | 0.690951 | − | 0.722902i | \(-0.257192\pi\) |
−0.280576 | + | 0.959832i | \(0.590525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0709 | − | 26.7316i | −0.539000 | − | 0.896550i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.6869 | + | 21.1812i | 1.22906 | + | 0.709597i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.03295 | − | 3.52117i | −0.0680300 | − | 0.117831i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.0800i | 1.50686i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −89.1375 | −2.97621 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.143273 | + | 0.0827187i | −0.00477842 | + | 0.00275882i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.82466 | + | 3.16040i | −0.0607882 | + | 0.105288i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.2004 | − | 10.0828i | −0.605671 | − | 0.335536i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.7582 | + | 6.21127i | 0.357616 | + | 0.206470i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.9635 | − | 22.4534i | −0.430445 | − | 0.745552i | 0.566467 | − | 0.824085i | \(-0.308310\pi\) |
−0.996912 | + | 0.0785324i | \(0.974977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 151.855i | − | 5.03672i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.1565 | −0.402763 | −0.201382 | − | 0.979513i | \(-0.564543\pi\) | ||||
−0.201382 | + | 0.979513i | \(0.564543\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.22557 | − | 2.43964i | 0.139846 | − | 0.0807401i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 55.5964 | + | 32.0986i | 1.83796 | + | 1.06115i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.3323 | − | 0.306773i | 0.572363 | − | 0.0101305i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.2671 | − | 16.3200i | −0.932445 | − | 0.538347i | −0.0448608 | − | 0.998993i | \(-0.514284\pi\) |
−0.887584 | + | 0.460646i | \(0.847618\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.9756 | + | 11.5329i | −0.658217 | + | 0.380022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.7102 | 0.352530 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.2635 | 0.830659 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.7615 | + | 37.6920i | 0.714740 | + | 1.23797i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.0610 | + | 14.4690i | 0.822224 | + | 0.474711i | 0.851183 | − | 0.524870i | \(-0.175886\pi\) |
−0.0289590 | + | 0.999581i | \(0.509219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.83245 | + | 3.64848i | −0.191151 | + | 0.119574i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.517621 | + | 0.896546i | −0.0169461 | + | 0.0293516i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.13676 | + | 7.16508i | 0.135287 | + | 0.234323i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.1555i | 0.658452i | 0.944251 | + | 0.329226i | \(0.106788\pi\) | ||||
−0.944251 | + | 0.329226i | \(0.893212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.3663 | −0.827799 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.3519 | + | 52.5710i | 0.989443 | + | 1.71376i | 0.620230 | + | 0.784420i | \(0.287039\pi\) |
0.369213 | + | 0.929345i | \(0.379627\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.7090 | + | 15.0148i | −1.55362 | + | 0.488950i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.31135 | − | 130.589i | −0.0751883 | − | 4.24805i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.92380 | − | 6.79623i | 0.127506 | − | 0.220848i | −0.795203 | − | 0.606343i | \(-0.792636\pi\) |
0.922710 | + | 0.385495i | \(0.125969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.2857 | − | 19.2175i | 1.08050 | − | 0.623826i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 61.7853 | 2.00353 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.6709 | −0.507631 | −0.253815 | − | 0.967253i | \(-0.581686\pi\) | ||||
−0.253815 | + | 0.967253i | \(0.581686\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.0928 | − | 31.2305i | 1.75040 | − | 1.01060i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0635269 | + | 0.0366773i | 0.00205353 | + | 0.00118561i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.3129 | + | 17.3470i | 1.01114 | + | 0.560164i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5794 | + | 52.9652i | −0.986434 | + | 1.70855i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.0568 | + | 62.4521i | 1.16191 | + | 2.01249i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 52.6298i | − | 1.69421i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.7669i | 0.474870i | 0.971403 | + | 0.237435i | \(0.0763067\pi\) | ||||
−0.971403 | + | 0.237435i | \(0.923693\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.47208 | − | 3.73666i | 0.207913 | − | 0.120039i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.46712 | − | 4.88849i | −0.271723 | − | 0.156879i | 0.357947 | − | 0.933742i | \(-0.383477\pi\) |
−0.629670 | + | 0.776862i | \(0.716810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.5759 | + | 27.5717i | 0.531399 | + | 0.883907i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.0009 | − | 31.1785i | 0.576491 | − | 0.998511i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.95563 | + | 3.43848i | −0.190537 | + | 0.110007i | −0.592234 | − | 0.805766i | \(-0.701754\pi\) |
0.401697 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5213 | −0.559982 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 120.491i | 3.84697i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.3611 | − | 28.3382i | −0.521837 | − | 0.903848i | −0.999677 | − | 0.0254015i | \(-0.991914\pi\) |
0.477840 | − | 0.878447i | \(-0.341420\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.8085 | − | 48.1657i | 0.886052 | − | 1.53469i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.8504 | − | 31.3549i | −0.600014 | − | 0.998038i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.18917 | − | 15.9161i | 0.292199 | − | 0.506103i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.8188 | + | 21.2573i | −1.16959 | + | 0.675262i | −0.953583 | − | 0.301131i | \(-0.902636\pi\) |
−0.216004 | + | 0.976392i | \(0.569303\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.3496 | 0.582306 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 9.07463i | − | 0.287685i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.9108 | + | 17.8463i | −0.978954 | + | 0.565199i | −0.901954 | − | 0.431832i | \(-0.857867\pi\) |
−0.0769995 | + | 0.997031i | \(0.524534\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 119.884 | + | 69.2148i | 3.79295 | + | 2.18986i |
(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 | 1148.2.r.a.737.28 | yes | 56 | |
7.4 | even | 3 | inner | 1148.2.r.a.81.1 | ✓ | 56 | |
41.40 | even | 2 | inner | 1148.2.r.a.737.1 | yes | 56 | |
287.81 | even | 6 | inner | 1148.2.r.a.81.28 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.r.a.81.1 | ✓ | 56 | 7.4 | even | 3 | inner | |
1148.2.r.a.81.28 | yes | 56 | 287.81 | even | 6 | inner | |
1148.2.r.a.737.1 | yes | 56 | 41.40 | even | 2 | inner | |
1148.2.r.a.737.28 | yes | 56 | 1.1 | even | 1 | trivial |