Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (of order \(4\), 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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.110166016.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 729.2 | ||
Root | \(1.22833i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.729 |
Dual form | 1148.2.k.a.337.2 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.868559 | + | 0.868559i | −0.501463 | + | 0.501463i | −0.911892 | − | 0.410429i | \(-0.865379\pi\) |
0.410429 | + | 0.911892i | \(0.365379\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.37966i | 1.95864i | 0.202309 | + | 0.979322i | \(0.435156\pi\) | ||||
−0.202309 | + | 0.979322i | \(0.564844\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.49121i | 0.497070i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.10701 | − | 1.10701i | 0.333775 | − | 0.333775i | −0.520243 | − | 0.854018i | \(-0.674159\pi\) |
0.854018 | + | 0.520243i | \(0.174159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.155874 | − | 0.155874i | 0.0432316 | − | 0.0432316i | −0.685161 | − | 0.728392i | \(-0.740268\pi\) |
0.728392 | + | 0.685161i | \(0.240268\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.80399 | − | 3.80399i | −0.982187 | − | 0.982187i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.27265 | + | 5.27265i | 1.27881 | + | 1.27881i | 0.941336 | + | 0.337470i | \(0.109571\pi\) |
0.337470 | + | 0.941336i | \(0.390429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.24822 | + | 5.24822i | 1.20402 | + | 1.20402i | 0.972932 | + | 0.231092i | \(0.0742299\pi\) |
0.231092 | + | 0.972932i | \(0.425770\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.22833i | − | 0.268043i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.28835 | 1.10270 | 0.551349 | − | 0.834275i | \(-0.314113\pi\) | ||||
0.551349 | + | 0.834275i | \(0.314113\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.1814 | −2.83628 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.90088 | − | 3.90088i | −0.750725 | − | 0.750725i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.12690 | + | 4.12690i | −0.766346 | + | 0.766346i | −0.977461 | − | 0.211115i | \(-0.932290\pi\) |
0.211115 | + | 0.977461i | \(0.432290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.03455 | 0.185811 | 0.0929056 | − | 0.995675i | \(-0.470385\pi\) | ||||
0.0929056 | + | 0.995675i | \(0.470385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.92300i | 0.334752i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.09689 | − | 3.09689i | −0.523470 | − | 0.523470i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.58579 | −0.425101 | −0.212550 | − | 0.977150i | \(-0.568177\pi\) | ||||
−0.212550 | + | 0.977150i | \(0.568177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.270771i | 0.0433581i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.93089 | − | 4.08489i | −0.770076 | − | 0.637952i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.71688i | − | 1.32931i | −0.747150 | − | 0.664656i | \(-0.768578\pi\) | ||
0.747150 | − | 0.664656i | \(-0.231422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.53099 | −0.973583 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.00789 | − | 2.00789i | −0.292881 | − | 0.292881i | 0.545336 | − | 0.838217i | \(-0.316402\pi\) |
−0.838217 | + | 0.545336i | \(0.816402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.15922 | −1.28255 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.98800 | − | 5.98800i | 0.822515 | − | 0.822515i | −0.163953 | − | 0.986468i | \(-0.552425\pi\) |
0.986468 | + | 0.163953i | \(0.0524246\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.84832 | + | 4.84832i | 0.653747 | + | 0.653747i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.11678 | −1.20755 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.40829 | 0.834288 | 0.417144 | − | 0.908840i | \(-0.363031\pi\) | ||||
0.417144 | + | 0.908840i | \(0.363031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.4391i | − | 1.59266i | −0.604862 | − | 0.796330i | \(-0.706772\pi\) | ||
0.604862 | − | 0.796330i | \(-0.293228\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.05444 | − | 1.05444i | −0.132848 | − | 0.132848i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.682674 | + | 0.682674i | 0.0846753 | + | 0.0846753i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.54565 | − | 1.54565i | −0.188832 | − | 0.188832i | 0.606359 | − | 0.795191i | \(-0.292629\pi\) |
−0.795191 | + | 0.606359i | \(0.792629\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.59325 | + | 4.59325i | −0.552962 | + | 0.552962i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.123981 | − | 0.123981i | 0.0147138 | − | 0.0147138i | −0.699712 | − | 0.714425i | \(-0.746688\pi\) |
0.714425 | + | 0.699712i | \(0.246688\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.51668i | 0.645679i | 0.946454 | + | 0.322839i | \(0.104637\pi\) | ||||
−0.946454 | + | 0.322839i | \(0.895363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.3174 | − | 12.3174i | 1.42229 | − | 1.42229i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.56555i | 0.178410i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.20809 | + | 8.20809i | −0.923482 | + | 0.923482i | −0.997274 | − | 0.0737917i | \(-0.976490\pi\) |
0.0737917 | + | 0.997274i | \(0.476490\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.30266 | 0.255852 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.8108 | −1.40617 | −0.703087 | − | 0.711104i | \(-0.748195\pi\) | ||||
−0.703087 | + | 0.711104i | \(0.748195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.0924 | + | 23.0924i | −2.50473 | + | 2.50473i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.16891i | − | 0.768588i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9756 | − | 11.9756i | 1.26942 | − | 1.26942i | 0.323026 | − | 0.946390i | \(-0.395300\pi\) |
0.946390 | − | 0.323026i | \(-0.104700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.220439i | 0.0231083i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.898571 | + | 0.898571i | −0.0931775 | + | 0.0931775i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −22.9854 | + | 22.9854i | −2.35825 | + | 2.35825i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.20844 | + | 6.20844i | 0.630371 | + | 0.630371i | 0.948161 | − | 0.317790i | \(-0.102941\pi\) |
−0.317790 | + | 0.948161i | \(0.602941\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.65078 | + | 1.65078i | 0.165910 | + | 0.165910i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.82012 | + | 2.82012i | 0.280613 | + | 0.280613i | 0.833353 | − | 0.552741i | \(-0.186418\pi\) |
−0.552741 | + | 0.833353i | \(0.686418\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.30859i | 0.621604i | 0.950475 | + | 0.310802i | \(0.100598\pi\) | ||||
−0.950475 | + | 0.310802i | \(0.899402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.37966 | 0.525001 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.5426 | 1.69591 | 0.847956 | − | 0.530067i | \(-0.177833\pi\) | ||||
0.847956 | + | 0.530067i | \(0.177833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6850 | − | 10.6850i | −1.02344 | − | 1.02344i | −0.999719 | − | 0.0237172i | \(-0.992450\pi\) |
−0.0237172 | − | 0.999719i | \(-0.507550\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.24591 | − | 2.24591i | 0.213172 | − | 0.213172i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.42733 | −0.322416 | −0.161208 | − | 0.986920i | \(-0.551539\pi\) | ||||
−0.161208 | + | 0.986920i | \(0.551539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.1612i | 2.15979i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.232440 | + | 0.232440i | 0.0214891 | + | 0.0214891i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.45666 | −0.683551 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.54907i | 0.777188i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.83074 | − | 0.734808i | 0.706074 | − | 0.0662554i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 40.2115i | − | 3.59663i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.0195 | 1.86518 | 0.932591 | − | 0.360934i | \(-0.117542\pi\) | ||||
0.932591 | + | 0.360934i | \(0.117542\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.57112 | + | 7.57112i | 0.666600 | + | 0.666600i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.79121i | − | 0.418610i | −0.977850 | − | 0.209305i | \(-0.932880\pi\) | ||
0.977850 | − | 0.209305i | \(-0.0671202\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.42210 | −0.643578 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.0845 | − | 17.0845i | 1.47040 | − | 1.47040i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4447 | + | 11.4447i | 0.977783 | + | 0.977783i | 0.999759 | − | 0.0219757i | \(-0.00699563\pi\) |
−0.0219757 | + | 0.999759i | \(0.506996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.7262 | 1.16424 | 0.582122 | − | 0.813101i | \(-0.302223\pi\) | ||||
0.582122 | + | 0.813101i | \(0.302223\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.48794 | 0.293738 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.345107i | − | 0.0288593i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.0744 | − | 18.0744i | −1.50100 | − | 1.50100i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.868559 | + | 0.868559i | 0.0716376 | + | 0.0716376i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.91658 | − | 5.91658i | −0.484705 | − | 0.484705i | 0.421925 | − | 0.906631i | \(-0.361354\pi\) |
−0.906631 | + | 0.421925i | \(0.861354\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.68164 | + | 4.68164i | −0.380986 | + | 0.380986i | −0.871457 | − | 0.490471i | \(-0.836825\pi\) |
0.490471 | + | 0.871457i | \(0.336825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.86263 | + | 7.86263i | −0.635656 | + | 0.635656i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.53099i | 0.363938i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.83898 | + | 6.83898i | −0.545810 | + | 0.545810i | −0.925226 | − | 0.379416i | \(-0.876125\pi\) |
0.379416 | + | 0.925226i | \(0.376125\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4019i | 0.824921i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.73943 | + | 3.73943i | −0.294708 | + | 0.294708i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0562608 | 0.00440669 | 0.00220334 | − | 0.999998i | \(-0.499299\pi\) | ||||
0.00220334 | + | 0.999998i | \(0.499299\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.42210 | −0.655660 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.3830 | − | 17.3830i | 1.34514 | − | 1.34514i | 0.454277 | − | 0.890860i | \(-0.349898\pi\) |
0.890860 | − | 0.454277i | \(-0.150102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9514i | 0.996262i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.82620 | + | 7.82620i | −0.598484 | + | 0.598484i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.1109i | 1.68106i | 0.541767 | + | 0.840528i | \(0.317755\pi\) | ||||
−0.541767 | + | 0.840528i | \(0.682245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0278 | − | 10.0278i | 0.758029 | − | 0.758029i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.56598 | + | 5.56598i | −0.418364 | + | 0.418364i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.88021 | − | 8.88021i | −0.663738 | − | 0.663738i | 0.292521 | − | 0.956259i | \(-0.405506\pi\) |
−0.956259 | + | 0.292521i | \(0.905506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.09192 | + | 2.09192i | 0.155491 | + | 0.155491i | 0.780565 | − | 0.625074i | \(-0.214931\pi\) |
−0.625074 | + | 0.780565i | \(0.714931\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.8041 | + | 10.8041i | 0.798660 | + | 0.798660i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 11.3249i | − | 0.832621i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.6737 | 0.853668 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.51668 | 0.401279 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.26811 | − | 7.26811i | −0.525902 | − | 0.525902i | 0.393446 | − | 0.919348i | \(-0.371283\pi\) |
−0.919348 | + | 0.393446i | \(0.871283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.804344 | + | 0.804344i | −0.0578979 | + | 0.0578979i | −0.735463 | − | 0.677565i | \(-0.763035\pi\) |
0.677565 | + | 0.735463i | \(0.263035\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.18589 | −0.0849230 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.18212i | 0.155470i | 0.996974 | + | 0.0777349i | \(0.0247688\pi\) | ||||
−0.996974 | + | 0.0777349i | \(0.975231\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.70711 | − | 1.70711i | −0.121014 | − | 0.121014i | 0.644006 | − | 0.765020i | \(-0.277271\pi\) |
−0.765020 | + | 0.644006i | \(0.777271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.68498 | 0.189384 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5.83632i | − | 0.409629i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.8904 | − | 21.5956i | 1.24952 | − | 1.50830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.88604i | 0.548118i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.6196 | 0.803747 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.36627 | − | 6.36627i | −0.438272 | − | 0.438272i | 0.453158 | − | 0.891430i | \(-0.350297\pi\) |
−0.891430 | + | 0.453158i | \(0.850297\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.215369i | 0.0147569i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 38.1770 | 2.60365 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.731540 | + | 0.731540i | −0.0496602 | + | 0.0496602i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.79156 | − | 4.79156i | −0.323784 | − | 0.323784i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.64374 | 0.110570 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4795 | 1.10355 | 0.551773 | − | 0.833994i | \(-0.313951\pi\) | ||||
0.551773 | + | 0.833994i | \(0.313951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 21.1475i | − | 1.40983i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.2174 | + | 11.2174i | 0.744523 | + | 0.744523i | 0.973445 | − | 0.228922i | \(-0.0735201\pi\) |
−0.228922 | + | 0.973445i | \(0.573520\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.73009 | − | 8.73009i | −0.576900 | − | 0.576900i | 0.357148 | − | 0.934048i | \(-0.383749\pi\) |
−0.934048 | + | 0.357148i | \(0.883749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.35977 | − | 1.35977i | −0.0894662 | − | 0.0894662i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.3305 | − | 16.3305i | 1.06985 | − | 1.06985i | 0.0724782 | − | 0.997370i | \(-0.476909\pi\) |
0.997370 | − | 0.0724782i | \(-0.0230908\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.79387 | − | 8.79387i | 0.573649 | − | 0.573649i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 14.2584i | − | 0.926184i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.12956 | + | 4.12956i | −0.267119 | + | 0.267119i | −0.827938 | − | 0.560819i | \(-0.810486\pi\) |
0.560819 | + | 0.827938i | \(0.310486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2473i | 0.660084i | 0.943966 | + | 0.330042i | \(0.107063\pi\) | ||||
−0.943966 | + | 0.330042i | \(0.892937\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.70264 | − | 9.70264i | 0.622425 | − | 0.622425i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.37966 | 0.279806 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.63612 | 0.104104 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.1270 | − | 11.1270i | 0.705144 | − | 0.705144i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1273i | 0.891709i | 0.895105 | + | 0.445855i | \(0.147100\pi\) | ||||
−0.895105 | + | 0.445855i | \(0.852900\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.85425 | − | 5.85425i | 0.368053 | − | 0.368053i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 40.1143i | − | 2.51205i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.25507 | + | 7.25507i | −0.452559 | + | 0.452559i | −0.896203 | − | 0.443644i | \(-0.853685\pi\) |
0.443644 | + | 0.896203i | \(0.353685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.82843 | − | 1.82843i | 0.113613 | − | 0.113613i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.15407 | − | 6.15407i | −0.380928 | − | 0.380928i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4488 | − | 10.4488i | −0.644303 | − | 0.644303i | 0.307307 | − | 0.951610i | \(-0.400572\pi\) |
−0.951610 | + | 0.307307i | \(0.900572\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.2254 | + | 26.2254i | 1.61101 | + | 1.61101i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.8031i | 1.27313i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.9583 | −1.15591 | −0.577955 | − | 0.816069i | \(-0.696149\pi\) | ||||
−0.577955 | + | 0.816069i | \(0.696149\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.58116 | 0.0960489 | 0.0480245 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480245 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.191464 | − | 0.191464i | −0.0115879 | − | 0.0115879i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.6989 | + | 15.6989i | −0.946682 | + | 0.946682i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00642 | 0.240723 | 0.120361 | − | 0.992730i | \(-0.461595\pi\) | ||||
0.120361 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.54274i | 0.0923612i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.60198 | − | 6.60198i | −0.393841 | − | 0.393841i | 0.482213 | − | 0.876054i | \(-0.339833\pi\) |
−0.876054 | + | 0.482213i | \(0.839833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.4135 | −1.51068 | −0.755338 | − | 0.655335i | \(-0.772527\pi\) | ||||
−0.755338 | + | 0.655335i | \(0.772527\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 39.9284i | − | 2.36515i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.37512 | − | 0.598218i | 0.376311 | − | 0.0353117i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.6017i | 2.27069i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.7848 | −0.632216 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.58587 | − | 1.58587i | −0.0926473 | − | 0.0926473i | 0.659264 | − | 0.751911i | \(-0.270868\pi\) |
−0.751911 | + | 0.659264i | \(0.770868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.0661i | 1.63407i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.63661 | −0.501147 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.824315 | − | 0.824315i | 0.0476714 | − | 0.0476714i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.16376 | + | 6.16376i | 0.355273 | + | 0.355273i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.89889 | −0.281434 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 54.4789 | 3.11945 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.98715i | − | 0.569997i | −0.958528 | − | 0.284998i | \(-0.908007\pi\) | ||
0.958528 | − | 0.284998i | \(-0.0919931\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.47939 | − | 5.47939i | −0.311711 | − | 0.311711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.19335 | − | 8.19335i | −0.464602 | − | 0.464602i | 0.435558 | − | 0.900160i | \(-0.356551\pi\) |
−0.900160 | + | 0.435558i | \(0.856551\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.8900 | + | 15.8900i | 0.898156 | + | 0.898156i | 0.995273 | − | 0.0971172i | \(-0.0309622\pi\) |
−0.0971172 | + | 0.995273i | \(0.530962\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.61811 | − | 4.61811i | 0.260201 | − | 0.260201i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.85893 | + | 6.85893i | −0.385236 | + | 0.385236i | −0.872984 | − | 0.487748i | \(-0.837818\pi\) |
0.487748 | + | 0.872984i | \(0.337818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.13702i | 0.511575i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.2368 | + | 15.2368i | −0.850437 | + | 0.850437i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 55.3441i | 3.07943i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.21051 | + | 2.21051i | −0.122617 | + | 0.122617i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.5611 | 1.02643 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.83958 | 0.156551 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1612 | − | 10.1612i | 0.558509 | − | 0.558509i | −0.370374 | − | 0.928883i | \(-0.620770\pi\) |
0.928883 | + | 0.370374i | \(0.120770\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.85595i | − | 0.211305i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.76944 | − | 6.76944i | 0.369854 | − | 0.369854i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.07470i | 0.167490i | 0.996487 | + | 0.0837448i | \(0.0266881\pi\) | ||||
−0.996487 | + | 0.0837448i | \(0.973312\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.97684 | − | 2.97684i | 0.161680 | − | 0.161680i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.14526 | − | 1.14526i | 0.0620192 | − | 0.0620192i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.1169 | − | 20.1169i | −1.08306 | − | 1.08306i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.7853 | − | 19.7853i | −1.06213 | − | 1.06213i | −0.997938 | − | 0.0641922i | \(-0.979553\pi\) |
−0.0641922 | − | 0.997938i | \(-0.520447\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.92170i | − | 0.531096i | −0.964098 | − | 0.265548i | \(-0.914447\pi\) | ||
0.964098 | − | 0.265548i | \(-0.0855529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.21609 | −0.0649101 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.01578 | 0.426637 | 0.213318 | − | 0.976983i | \(-0.431573\pi\) | ||||
0.213318 | + | 0.976983i | \(0.431573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.542994 | + | 0.542994i | 0.0288191 | + | 0.0288191i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.47655 | − | 6.47655i | 0.342775 | − | 0.342775i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.4833 | −0.817178 | −0.408589 | − | 0.912718i | \(-0.633979\pi\) | ||||
−0.408589 | + | 0.912718i | \(0.633979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.0876i | 1.89935i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.42537 | − | 7.42537i | −0.389731 | − | 0.389731i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.1612 | −1.26465 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 17.5727i | − | 0.917289i | −0.888620 | − | 0.458645i | \(-0.848335\pi\) | ||
0.888620 | − | 0.458645i | \(-0.151665\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.09142 | − | 7.35300i | 0.317107 | − | 0.382782i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.46831i | 0.439653i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.1630 | 0.577997 | 0.288999 | − | 0.957329i | \(-0.406678\pi\) | ||||
0.288999 | + | 0.957329i | \(0.406678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 34.9261 | + | 34.9261i | 1.80358 | + | 1.80358i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.28655i | 0.0662607i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.3324 | 1.30124 | 0.650620 | − | 0.759404i | \(-0.274509\pi\) | ||||
0.650620 | + | 0.759404i | \(0.274509\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.2567 | + | 18.2567i | −0.935320 | + | 0.935320i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3746 | − | 10.3746i | −0.530119 | − | 0.530119i | 0.390489 | − | 0.920608i | \(-0.372306\pi\) |
−0.920608 | + | 0.390489i | \(0.872306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.85656 | −0.349443 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.9987 | 0.660761 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9.08901i | − | 0.460831i | −0.973092 | − | 0.230416i | \(-0.925991\pi\) | ||
0.973092 | − | 0.230416i | \(-0.0740086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.8836 | + | 27.8836i | 1.41014 | + | 1.41014i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.16145 | + | 4.16145i | 0.209918 | + | 0.209918i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.9486 | − | 35.9486i | −1.80877 | − | 1.80877i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.8991 | + | 16.8991i | −0.848144 | + | 0.848144i | −0.989901 | − | 0.141758i | \(-0.954725\pi\) |
0.141758 | + | 0.989901i | \(0.454725\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.44654 | − | 6.44654i | 0.322730 | − | 0.322730i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 17.2355i | − | 0.860701i | −0.902662 | − | 0.430350i | \(-0.858390\pi\) | ||
0.902662 | − | 0.430350i | \(-0.141610\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.161260 | − | 0.161260i | 0.00803292 | − | 0.00803292i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0849i | 0.501122i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.86249 | + | 2.86249i | −0.141888 | + | 0.141888i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.14926 | 0.304061 | 0.152031 | − | 0.988376i | \(-0.451419\pi\) | ||||
0.152031 | + | 0.988376i | \(0.451419\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.8807 | −0.980644 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.53134 | + | 4.53134i | −0.222973 | + | 0.222973i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 56.1072i | − | 2.75419i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.9220 | + | 11.9220i | −0.583825 | + | 0.583825i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 18.6826i | − | 0.912705i | −0.889799 | − | 0.456352i | \(-0.849156\pi\) | ||
0.889799 | − | 0.456352i | \(-0.150844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0459 | + | 14.0459i | −0.684554 | + | 0.684554i | −0.961023 | − | 0.276469i | \(-0.910836\pi\) |
0.276469 | + | 0.961023i | \(0.410836\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.99418 | − | 2.99418i | 0.145582 | − | 0.145582i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −74.7737 | − | 74.7737i | −3.62706 | − | 3.62706i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.79576 | + | 8.79576i | 0.425656 | + | 0.425656i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.299746 | + | 0.299746i | 0.0144719 | + | 0.0144719i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8378i | 0.618374i | 0.951001 | + | 0.309187i | \(0.100057\pi\) | ||||
−0.951001 | + | 0.309187i | \(0.899943\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.64434 | −0.271250 | −0.135625 | − | 0.990760i | \(-0.543304\pi\) | ||||
−0.135625 | + | 0.990760i | \(0.543304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.3974 | 1.50539 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.7544 | + | 27.7544i | 1.32767 | + | 1.32767i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.47844 | + | 9.47844i | −0.452381 | + | 0.452381i | −0.896144 | − | 0.443763i | \(-0.853643\pi\) |
0.443763 | + | 0.896144i | \(0.353643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.49121 | 0.0710100 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.52930i | 0.452751i | 0.974040 | + | 0.226375i | \(0.0726876\pi\) | ||||
−0.974040 | + | 0.226375i | \(0.927312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 52.4493 | + | 52.4493i | 2.48633 | + | 2.48633i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.2778 | 0.486123 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.0528i | 1.04074i | 0.853942 | + | 0.520368i | \(0.174205\pi\) | ||||
−0.853942 | + | 0.520368i | \(0.825795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.98054 | + | 0.936537i | −0.469965 | + | 0.0440998i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 8.13256i | − | 0.382101i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.965447 | −0.0452608 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.2147 | + | 18.2147i | 0.852048 | + | 0.852048i | 0.990385 | − | 0.138337i | \(-0.0441758\pi\) |
−0.138337 | + | 0.990385i | \(0.544176\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 41.1360i | − | 1.92006i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.79545 | −0.316496 | −0.158248 | − | 0.987399i | \(-0.550585\pi\) | ||||
−0.158248 | + | 0.987399i | \(0.550585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.57774 | + | 5.57774i | −0.259220 | + | 0.259220i | −0.824737 | − | 0.565517i | \(-0.808677\pi\) |
0.565517 | + | 0.824737i | \(0.308677\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.93543 | − | 3.93543i | −0.182501 | − | 0.182501i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.3150 | 1.68046 | 0.840228 | − | 0.542234i | \(-0.182421\pi\) | ||||
0.840228 | + | 0.542234i | \(0.182421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.18589 | 0.100935 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 11.8801i | − | 0.547407i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.64965 | − | 9.64965i | −0.443691 | − | 0.443691i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −74.4272 | − | 74.4272i | −3.41496 | − | 3.41496i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.92936 | + | 8.92936i | 0.408847 | + | 0.408847i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.30292 | + | 5.30292i | −0.242297 | + | 0.242297i | −0.817800 | − | 0.575503i | \(-0.804806\pi\) |
0.575503 | + | 0.817800i | \(0.304806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.403056 | + | 0.403056i | −0.0183778 | + | 0.0183778i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 6.49583i | − | 0.295571i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −27.1908 | + | 27.1908i | −1.23467 | + | 1.23467i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3.16695i | − | 0.143508i | −0.997422 | − | 0.0717541i | \(-0.977140\pi\) | ||
0.997422 | − | 0.0717541i | \(-0.0228597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0488658 | + | 0.0488658i | −0.00220979 | + | 0.00220979i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.86591 | −0.309854 | −0.154927 | − | 0.987926i | \(-0.549514\pi\) | ||||
−0.154927 | + | 0.987926i | \(0.549514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.5194 | −1.96002 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.22986 | + | 7.22986i | −0.324958 | + | 0.324958i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.175335i | 0.00786487i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.01551 | − | 2.01551i | 0.0902265 | − | 0.0902265i | −0.660553 | − | 0.750779i | \(-0.729678\pi\) |
0.750779 | + | 0.660553i | \(0.229678\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.1963i | 1.34907i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2797 | − | 12.2797i | 0.547525 | − | 0.547525i | −0.378199 | − | 0.925724i | \(-0.623457\pi\) |
0.925724 | + | 0.378199i | \(0.123457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.3512 | + | 12.3512i | −0.549620 | + | 0.549620i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.2491 | − | 11.2491i | −0.499588 | − | 0.499588i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.586823 | − | 0.586823i | −0.0260105 | − | 0.0260105i | 0.693982 | − | 0.719992i | \(-0.255855\pi\) |
−0.719992 | + | 0.693982i | \(0.755855\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.90088 | − | 3.90088i | −0.172565 | − | 0.172565i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 40.9454i | − | 1.80778i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.6295 | −1.21750 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.44550 | −0.195513 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.2046 | − | 19.2046i | −0.842988 | − | 0.842988i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.58336 | − | 1.58336i | 0.0693684 | − | 0.0693684i | −0.671571 | − | 0.740940i | \(-0.734380\pi\) |
0.740940 | + | 0.671571i | \(0.234380\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.4893 | 1.33320 | 0.666602 | − | 0.745414i | \(-0.267748\pi\) | ||||
0.666602 | + | 0.745414i | \(0.267748\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.4194i | 0.760247i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.45484 | + | 5.45484i | 0.237617 | + | 0.237617i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.96666 | 0.215942 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.55610i | 0.414699i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.40532 | + | 0.131870i | −0.0608713 | + | 0.00571194i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 76.8308i | 3.32169i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.4260 | 0.665680 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.10701 | − | 1.10701i | −0.0476822 | − | 0.0476822i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.4848i | − | 0.966696i | −0.875428 | − | 0.483348i | \(-0.839420\pi\) | ||
0.875428 | − | 0.483348i | \(-0.160580\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.63391 | −0.155946 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 46.7966 | − | 46.7966i | 2.00455 | − | 2.00455i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2934 | − | 11.2934i | −0.482870 | − | 0.482870i | 0.423177 | − | 0.906047i | \(-0.360915\pi\) |
−0.906047 | + | 0.423177i | \(0.860915\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.5493 | 0.791664 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −43.3177 | −1.84540 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 11.6080i | − | 0.493622i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.83632 | + | 9.83632i | 0.417528 | + | 0.417528i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.04517 | − | 2.04517i | −0.0866566 | − | 0.0866566i | 0.662450 | − | 0.749106i | \(-0.269517\pi\) |
−0.749106 | + | 0.662450i | \(0.769517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.35873 | − | 1.35873i | −0.0574682 | − | 0.0574682i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.1393 | + | 10.1393i | −0.428083 | + | 0.428083i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.39793 | − | 5.39793i | 0.227496 | − | 0.227496i | −0.584150 | − | 0.811646i | \(-0.698572\pi\) |
0.811646 | + | 0.584150i | \(0.198572\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 15.0105i | − | 0.631499i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.62823 | + | 1.62823i | −0.0683792 | + | 0.0683792i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.2256i | 0.973666i | 0.873495 | + | 0.486833i | \(0.161848\pi\) | ||||
−0.873495 | + | 0.486833i | \(0.838152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.4191 | + | 26.4191i | −1.10561 | + | 1.10561i | −0.111884 | + | 0.993721i | \(0.535688\pi\) |
−0.993721 | + | 0.111884i | \(0.964312\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.6256 | 0.527441 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −74.9964 | −3.12756 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0881 | − | 20.0881i | 0.836279 | − | 0.836279i | −0.152088 | − | 0.988367i | \(-0.548600\pi\) |
0.988367 | + | 0.152088i | \(0.0485996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1.39724i | − | 0.0580673i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.05864 | − | 9.05864i | 0.375816 | − | 0.375816i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 13.2575i | − | 0.549070i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.01801 | + | 1.01801i | −0.0420895 | + | 0.0420895i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.7778 | − | 24.7778i | 1.02269 | − | 1.02269i | 0.0229544 | − | 0.999737i | \(-0.492693\pi\) |
0.999737 | − | 0.0229544i | \(-0.00730725\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.42956 | + | 5.42956i | 0.223721 | + | 0.223721i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.89530 | − | 1.89530i | −0.0779623 | − | 0.0779623i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.33118 | + | 9.33118i | 0.383185 | + | 0.383185i | 0.872248 | − | 0.489063i | \(-0.162661\pi\) |
−0.489063 | + | 0.872248i | \(0.662661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 32.6576i | − | 1.33883i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.96545 | 0.121368 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.48082 | −0.264799 | −0.132400 | − | 0.991196i | \(-0.542268\pi\) | ||||
−0.132400 | + | 0.991196i | \(0.542268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0624 | + | 19.0624i | 0.777572 | + | 0.777572i | 0.979417 | − | 0.201845i | \(-0.0646938\pi\) |
−0.201845 | + | 0.979417i | \(0.564694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.30489 | − | 2.30489i | 0.0938626 | − | 0.0938626i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.4420 | −1.52223 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 10.7243i | − | 0.435285i | −0.976029 | − | 0.217642i | \(-0.930163\pi\) | ||
0.976029 | − | 0.217642i | \(-0.0698367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.06919 | + | 5.06919i | 0.205414 | + | 0.205414i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.625954 | −0.0253234 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 32.8034i | − | 1.32492i | −0.749099 | − | 0.662458i | \(-0.769513\pi\) | ||
0.749099 | − | 0.662458i | \(-0.230487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.21821 | + | 34.2960i | 0.129771 | + | 1.38295i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6634i | 0.952654i | 0.879268 | + | 0.476327i | \(0.158032\pi\) | ||||
−0.879268 | + | 0.476327i | \(0.841968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.18699 | 0.329063 | 0.164531 | − | 0.986372i | \(-0.447389\pi\) | ||||
0.164531 | + | 0.986372i | \(0.447389\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.6292 | − | 20.6292i | −0.827823 | − | 0.827823i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9361i | 0.678531i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 105.206 | 4.20823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.0923 | + | 10.0923i | −0.403049 | + | 0.403049i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.6340 | − | 13.6340i | −0.543621 | − | 0.543621i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.5192 | 1.01590 | 0.507952 | − | 0.861385i | \(-0.330403\pi\) | ||||
0.507952 | + | 0.861385i | \(0.330403\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.0590 | 0.439555 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 92.0584i | 3.65323i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.155874 | − | 0.155874i | −0.00617594 | − | 0.00617594i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.184881 | + | 0.184881i | 0.00731380 | + | 0.00731380i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.8663 | − | 16.8663i | −0.666180 | − | 0.666180i | 0.290650 | − | 0.956830i | \(-0.406129\pi\) |
−0.956830 | + | 0.290650i | \(0.906129\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.2517 | + | 31.2517i | −1.23245 | + | 1.23245i | −0.269427 | + | 0.963021i | \(0.586834\pi\) |
−0.963021 | + | 0.269427i | \(0.913166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.1590 | + | 33.1590i | −1.30563 | + | 1.30563i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.3661i | 1.15450i | 0.816567 | + | 0.577250i | \(0.195874\pi\) | ||||
−0.816567 | + | 0.577250i | \(0.804126\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.09402 | − | 7.09402i | 0.278465 | − | 0.278465i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.27077i | − | 0.0498054i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.0154 | + | 22.0154i | −0.861530 | + | 0.861530i | −0.991516 | − | 0.129986i | \(-0.958507\pi\) |
0.129986 | + | 0.991516i | \(0.458507\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.9839 | 0.819908 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.22653 | −0.320947 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.7540 | − | 10.7540i | 0.418917 | − | 0.418917i | −0.465913 | − | 0.884830i | \(-0.654274\pi\) |
0.884830 | + | 0.465913i | \(0.154274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0314i | 1.20698i | 0.797369 | + | 0.603492i | \(0.206224\pi\) | ||||
−0.797369 | + | 0.603492i | \(0.793776\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.42768 | + | 1.42768i | −0.0554466 | + | 0.0554466i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 32.5063i | − | 1.26054i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.8245 | + | 21.8245i | −0.845048 | + | 0.845048i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.3134 | + | 14.3134i | −0.553388 | + | 0.553388i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.7702 | − | 13.7702i | −0.531591 | − | 0.531591i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.8292 | − | 13.8292i | −0.533077 | − | 0.533077i | 0.388410 | − | 0.921487i | \(-0.373024\pi\) |
−0.921487 | + | 0.388410i | \(0.873024\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 55.3201 | + | 55.3201i | 2.12927 | + | 2.12927i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.7263i | 1.60367i | 0.597544 | + | 0.801836i | \(0.296143\pi\) | ||||
−0.597544 | + | 0.801836i | \(0.703857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.78006 | −0.336948 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.4859 | −0.746701 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.539996 | + | 0.539996i | 0.0206624 | + | 0.0206624i | 0.717362 | − | 0.696700i | \(-0.245349\pi\) |
−0.696700 | + | 0.717362i | \(0.745349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50.1237 | + | 50.1237i | −1.91513 | + | 1.91513i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.1652 | 0.578588 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.86674i | − | 0.0711172i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.7208 | − | 26.7208i | −1.01651 | − | 1.01651i | −0.999861 | − | 0.0166475i | \(-0.994701\pi\) |
−0.0166475 | − | 0.999861i | \(-0.505299\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.33456 | −0.0886825 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 60.1162i | 2.28034i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.46070 | − | 47.5371i | −0.168961 | − | 1.80059i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.3681i | 1.07298i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.3918 | −1.07234 | −0.536172 | − | 0.844109i | \(-0.680130\pi\) | ||||
−0.536172 | + | 0.844109i | \(0.680130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.5708 | − | 13.5708i | −0.511831 | − | 0.511831i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.2760i | 0.575327i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.98826 | −0.149994 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.16891 | + | 7.16891i | −0.269234 | + | 0.269234i | −0.828792 | − | 0.559557i | \(-0.810971\pi\) |
0.559557 | + | 0.828792i | \(0.310971\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.2400 | − | 12.2400i | −0.459035 | − | 0.459035i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.47108 | 0.204894 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.51145 | 0.0565251 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 7.17353i | − | 0.267901i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.38409 | − | 8.38409i | −0.312674 | − | 0.312674i | 0.533271 | − | 0.845945i | \(-0.320963\pi\) |
−0.845945 | + | 0.533271i | \(0.820963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.46085 | − | 4.46085i | −0.166131 | − | 0.166131i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.90035 | − | 8.90035i | −0.331008 | − | 0.331008i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 58.5253 | − | 58.5253i | 2.17358 | − | 2.17358i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.1718 | + | 26.1718i | −0.970658 | + | 0.970658i | −0.999582 | − | 0.0289234i | \(-0.990792\pi\) |
0.0289234 | + | 0.999582i | \(0.490792\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.7626i | 0.880098i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.9611 | − | 45.9611i | 1.69993 | − | 1.69993i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.1504i | 1.51992i | 0.649967 | + | 0.759962i | \(0.274783\pi\) | ||||
−0.649967 | + | 0.759962i | \(0.725217\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.80399 | + | 3.80399i | −0.140312 | + | 0.140312i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.42210 | −0.126055 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.37977 | 0.308255 | 0.154127 | − | 0.988051i | \(-0.450743\pi\) | ||||
0.154127 | + | 0.988051i | \(0.450743\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.42107 | + | 1.42107i | −0.0522042 | + | 0.0522042i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.7799i | − | 0.615596i | −0.951452 | − | 0.307798i | \(-0.900408\pi\) | ||
0.951452 | − | 0.307798i | \(-0.0995922\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.9126 | − | 25.9126i | 0.949365 | − | 0.949365i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 19.1037i | − | 0.698966i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.4045 | + | 12.4045i | −0.453251 | + | 0.453251i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1427 | + | 12.1427i | −0.443092 | + | 0.443092i | −0.893050 | − | 0.449958i | \(-0.851439\pi\) |
0.449958 | + | 0.893050i | \(0.351439\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.2704 | − | 12.2704i | −0.447159 | − | 0.447159i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.5040 | − | 20.5040i | −0.746216 | − | 0.746216i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.89100 | − | 5.89100i | −0.214112 | − | 0.214112i | 0.591900 | − | 0.806012i | \(-0.298378\pi\) |
−0.806012 | + | 0.591900i | \(0.798378\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.1695i | 0.369130i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.8289 | 1.37130 | 0.685648 | − | 0.727934i | \(-0.259519\pi\) | ||||
0.685648 | + | 0.727934i | \(0.259519\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.1109 | 0.547050 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −34.4357 | − | 34.4357i | −1.24502 | − | 1.24502i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.998883 | − | 0.998883i | 0.0360676 | − | 0.0360676i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.4226 | −0.772519 | −0.386259 | − | 0.922390i | \(-0.626233\pi\) | ||||
−0.386259 | + | 0.922390i | \(0.626233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 12.6029i | − | 0.453883i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.4236 | + | 18.4236i | 0.662653 | + | 0.662653i | 0.956005 | − | 0.293352i | \(-0.0947708\pi\) |
−0.293352 | + | 0.956005i | \(0.594771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.6714 | −0.527014 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.17619i | 0.113945i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.44003 | − | 47.3168i | −0.159081 | − | 1.69530i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 0.274495i | − | 0.00982222i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.1971 | 1.15063 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.9524 | − | 29.9524i | −1.06905 | − | 1.06905i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.81107i | − | 0.0645578i | −0.999479 | − | 0.0322789i | \(-0.989724\pi\) | ||
0.999479 | − | 0.0322789i | \(-0.0102765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.1509 | 0.646189 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.42349 | − | 2.42349i | 0.0861694 | − | 0.0861694i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.93892 | − | 1.93892i | −0.0688532 | − | 0.0688532i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −45.5566 | −1.61573 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.9410 | 1.16683 | 0.583415 | − | 0.812174i | \(-0.301716\pi\) | ||||
0.583415 | + | 0.812174i | \(0.301716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 21.1738i | − | 0.749075i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.8582 | + | 17.8582i | 0.630989 | + | 0.630989i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.10701 | + | 6.10701i | 0.215512 | + | 0.215512i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.3774 | − | 16.3774i | −0.577229 | − | 0.577229i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.4664 | − | 16.4664i | 0.579646 | − | 0.579646i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.4128 | − | 28.4128i | 0.998942 | − | 0.998942i | −0.00105755 | − | 0.999999i | \(-0.500337\pi\) |
0.999999 | + | 0.00105755i | \(0.000336628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.5163i | 1.42272i | 0.702829 | + | 0.711359i | \(0.251920\pi\) | ||||
−0.702829 | + | 0.711359i | \(0.748080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.37334 | + | 1.37334i | −0.0481650 | + | 0.0481650i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.246403i | 0.00863113i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.7481 | − | 45.7481i | 1.60052 | − | 1.60052i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.328720 | −0.0114864 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5128 | 0.436700 | 0.218350 | − | 0.975871i | \(-0.429933\pi\) | ||||
0.218350 | + | 0.975871i | \(0.429933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.7502 | + | 16.7502i | −0.583874 | + | 0.583874i | −0.935966 | − | 0.352091i | \(-0.885471\pi\) |
0.352091 | + | 0.935966i | \(0.385471\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 27.2709i | − | 0.949452i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.64710 | − | 1.64710i | 0.0572754 | − | 0.0572754i | −0.677889 | − | 0.735164i | \(-0.737105\pi\) |
0.735164 | + | 0.677889i | \(0.237105\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.13120i | 0.0392883i | 0.999807 | + | 0.0196442i | \(0.00625334\pi\) | ||||
−0.999807 | + | 0.0196442i | \(0.993747\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.47982 | + | 3.47982i | −0.120713 | + | 0.120713i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.27265 | − | 5.27265i | 0.182687 | − | 0.182687i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 76.1317 | + | 76.1317i | 2.63465 | + | 2.63465i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.03567 | − | 4.03567i | −0.139493 | − | 0.139493i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.30070 | + | 1.30070i | 0.0449053 | + | 0.0449053i | 0.729203 | − | 0.684298i | \(-0.239891\pi\) |
−0.684298 | + | 0.729203i | \(0.739891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 5.06259i | − | 0.174572i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.4684 | 0.394993 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −56.7228 | −1.95132 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.04510 | − | 6.04510i | −0.207712 | − | 0.207712i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.0731 | − | 22.0731i | 0.757548 | − | 0.757548i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.6745 | −0.468757 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.7835i | 0.506177i | 0.967443 | + | 0.253088i | \(0.0814464\pi\) | ||||
−0.967443 | + | 0.253088i | \(0.918554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −34.2761 | − | 34.2761i | −1.17222 | − | 1.17222i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.788037 | 0.0269188 | 0.0134594 | − | 0.999909i | \(-0.495716\pi\) | ||||
0.0134594 | + | 0.999909i | \(0.495716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14.9245i | − | 0.509217i | −0.967044 | − | 0.254609i | \(-0.918053\pi\) | ||
0.967044 | − | 0.254609i | \(-0.0819466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.01758 | + | 6.05676i | −0.170999 | + | 0.206414i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 36.5079i | − | 1.24274i | −0.783516 | − | 0.621371i | \(-0.786576\pi\) | ||
0.783516 | − | 0.621371i | \(-0.213424\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −96.8380 | −3.29259 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.5279 | − | 33.5279i | −1.13867 | − | 1.13867i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.1728i | 0.616471i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.481854 | −0.0163270 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.25808 | + | 9.25808i | −0.313339 | + | 0.313339i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.4338 | + | 28.4338i | 0.961239 | + | 0.961239i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.2806 | 0.684829 | 0.342414 | − | 0.939549i | \(-0.388755\pi\) | ||||
0.342414 | + | 0.939549i | \(0.388755\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.75484 | 0.0929184 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 55.5345i | − | 1.87101i | −0.353318 | − | 0.935503i | \(-0.614947\pi\) | ||
0.353318 | − | 0.935503i | \(-0.385053\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6799 | + | 11.6799i | 0.393060 | + | 0.393060i | 0.875777 | − | 0.482717i | \(-0.160350\pi\) |
−0.482717 | + | 0.875777i | \(0.660350\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.3771 | − | 24.3771i | −0.819427 | − | 0.819427i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.12683 | + | 7.12683i | 0.239296 | + | 0.239296i | 0.816558 | − | 0.577263i | \(-0.195879\pi\) |
−0.577263 | + | 0.816558i | \(0.695879\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.8631 | + | 14.8631i | −0.498491 | + | 0.498491i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.54907 | − | 2.54907i | 0.0853970 | − | 0.0853970i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 21.0757i | − | 0.705271i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.8923 | − | 38.8923i | 1.30003 | − | 1.30003i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.43193i | 0.0478108i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.26950 | + | 4.26950i | −0.142396 | + | 0.142396i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.1453 | 2.10367 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.7072 | −0.356313 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.16188 | + | 9.16188i | −0.304551 | + | 0.304551i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.2975i | 0.441538i | 0.975326 | + | 0.220769i | \(0.0708567\pi\) | ||||
−0.975326 | + | 0.220769i | \(0.929143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.20539 | + | 4.20539i | −0.139484 | + | 0.139484i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.3284i | − | 0.607247i | −0.952792 | − | 0.303623i | \(-0.901804\pi\) | ||
0.952792 | − | 0.303623i | \(-0.0981964\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.1817 | + | 14.1817i | −0.469346 | + | 0.469346i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −47.3182 | + | 47.3182i | −1.56429 | + | 1.56429i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.38790 | + | 3.38790i | 0.111878 | + | 0.111878i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.9667 | + | 10.9667i | 0.361759 | + | 0.361759i | 0.864460 | − | 0.502701i | \(-0.167660\pi\) |
−0.502701 | + | 0.864460i | \(0.667660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.67443 | + | 8.67443i | 0.285832 | + | 0.285832i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 0.0386507i | − | 0.00127220i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.6701 | 1.20571 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.40743 | −0.308981 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.36774 | − | 3.36774i | −0.110492 | − | 0.110492i | 0.649699 | − | 0.760191i | \(-0.274895\pi\) |
−0.760191 | + | 0.649699i | \(0.774895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.24822 | − | 5.24822i | 0.172003 | − | 0.172003i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.2328 | 0.465961 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51.1270i | 1.67203i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.36515 | + | 4.36515i | 0.142603 | + | 0.142603i | 0.774804 | − | 0.632201i | \(-0.217848\pi\) |
−0.632201 | + | 0.774804i | \(0.717848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.6028 | −0.900784 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.1833i | 0.592758i | 0.955070 | + | 0.296379i | \(0.0957791\pi\) | ||||
−0.955070 | + | 0.296379i | \(0.904221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.0763 | − | 21.6023i | −0.849161 | − | 0.703468i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.1612i | 0.785963i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.60761 | −0.312205 | −0.156103 | − | 0.987741i | \(-0.549893\pi\) | ||||
−0.156103 | + | 0.987741i | \(0.549893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.859905 | + | 0.859905i | 0.0279137 | + | 0.0279137i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 11.9148i | − | 0.386363i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.1635 | 1.43060 | 0.715299 | − | 0.698819i | \(-0.246291\pi\) | ||||
0.715299 | + | 0.698819i | \(0.246291\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.8319 | − | 31.8319i | 1.03005 | − | 1.03005i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.93604 | − | 7.93604i | −0.256536 | − | 0.256536i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.1852 | −0.522647 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9297 | −0.965474 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.1598i | 0.842987i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.52275 | − | 3.52275i | −0.113401 | − | 0.113401i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.2127 | − | 17.2127i | −0.553523 | − | 0.553523i | 0.373933 | − | 0.927456i | \(-0.378009\pi\) |
−0.927456 | + | 0.373933i | \(0.878009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −48.0696 | − | 48.0696i | −1.54422 | − | 1.54422i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.80811 | − | 8.80811i | 0.282666 | − | 0.282666i | −0.551506 | − | 0.834171i | \(-0.685946\pi\) |
0.834171 | + | 0.551506i | \(0.185946\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.70591 | + | 9.70591i | −0.311157 | + | 0.311157i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 3.83992i | − | 0.122976i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.6771 | − | 38.6771i | 1.23739 | − | 1.23739i | 0.276326 | − | 0.961064i | \(-0.410883\pi\) |
0.961064 | − | 0.276326i | \(-0.0891170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 26.5143i | − | 0.847400i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.9336 | − | 15.9336i | 0.508719 | − | 0.508719i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.8838 | 1.08072 | 0.540362 | − | 0.841433i | \(-0.318287\pi\) | ||||
0.540362 | + | 0.841433i | \(0.318287\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.55696 | −0.304510 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.46635 | + | 2.46635i | −0.0785047 | + | 0.0785047i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 46.0979i | − | 1.46583i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.42169 | + | 9.42169i | −0.299290 | + | 0.299290i | −0.840736 | − | 0.541446i | \(-0.817877\pi\) |
0.541446 | + | 0.840736i | \(0.317877\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6512i | 0.560143i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.47655 | − | 7.47655i | 0.237022 | − | 0.237022i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.6502 | − | 31.6502i | 1.00237 | − | 1.00237i | 0.00237415 | − | 0.999997i | \(-0.499244\pi\) |
0.999997 | − | 0.00237415i | \(-0.000755717\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.0868 | + | 10.0868i | 0.319134 | + | 0.319134i |
(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.k.a.729.2 | yes | 8 | |
41.9 | even | 4 | inner | 1148.2.k.a.337.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.a.337.2 | ✓ | 8 | 41.9 | even | 4 | inner | |
1148.2.k.a.729.2 | yes | 8 | 1.1 | even | 1 | trivial |