Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 46x^{12} + 126x^{10} + 315x^{8} + 1134x^{6} + 3726x^{4} + 7290x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | no (minimal twist has level 684) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1889.4 | ||
Root | \(-0.654543 + 1.60361i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1889 |
Dual form | 2736.2.dc.d.449.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.406956 | − | 0.234956i | −0.181996 | − | 0.105075i | 0.406234 | − | 0.913769i | \(-0.366842\pi\) |
−0.588230 | + | 0.808694i | \(0.700175\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.49289 | 1.32019 | 0.660094 | − | 0.751183i | \(-0.270517\pi\) | ||||
0.660094 | + | 0.751183i | \(0.270517\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.34919i | − | 0.406795i | −0.979096 | − | 0.203397i | \(-0.934802\pi\) | ||
0.979096 | − | 0.203397i | \(-0.0651983\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.30672 | − | 2.48649i | 1.19447 | − | 0.689627i | 0.235152 | − | 0.971959i | \(-0.424441\pi\) |
0.959317 | + | 0.282332i | \(0.0911078\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.31655 | − | 3.64686i | −1.53199 | − | 0.884494i | −0.999270 | − | 0.0382017i | \(-0.987837\pi\) |
−0.532719 | − | 0.846292i | \(-0.678830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.88959 | + | 3.92803i | −0.433502 | + | 0.901153i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.97653 | − | 4.02790i | 1.45471 | − | 0.839875i | 0.455964 | − | 0.889998i | \(-0.349295\pi\) |
0.998743 | + | 0.0501233i | \(0.0159614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.38959 | − | 4.13889i | −0.477918 | − | 0.827779i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.74117 | − | 8.21194i | −0.880413 | − | 1.52492i | −0.850883 | − | 0.525355i | \(-0.823932\pi\) |
−0.0295296 | − | 0.999564i | \(-0.509401\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.95998i | 0.711234i | 0.934632 | + | 0.355617i | \(0.115729\pi\) | ||||
−0.934632 | + | 0.355617i | \(0.884271\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.42145 | − | 0.820674i | −0.240269 | − | 0.138719i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.581007i | 0.0955169i | 0.998859 | + | 0.0477584i | \(0.0152078\pi\) | ||||
−0.998859 | + | 0.0477584i | \(0.984792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.761473 | + | 1.31891i | −0.118922 | + | 0.205979i | −0.919341 | − | 0.393462i | \(-0.871277\pi\) |
0.800419 | + | 0.599441i | \(0.204611\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.63603 | − | 8.02985i | 0.706989 | − | 1.22454i | −0.258980 | − | 0.965883i | \(-0.583386\pi\) |
0.965969 | − | 0.258658i | \(-0.0832802\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.06693 | − | 0.615993i | 0.155628 | − | 0.0898519i | −0.420164 | − | 0.907448i | \(-0.638027\pi\) |
0.575792 | + | 0.817597i | \(0.304694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.20026 | 0.742894 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.09568 | + | 8.82598i | 0.699946 | + | 1.21234i | 0.968485 | + | 0.249073i | \(0.0801260\pi\) |
−0.268539 | + | 0.963269i | \(0.586541\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.316999 | + | 0.549059i | −0.0427442 | + | 0.0740350i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.09568 | + | 8.82598i | −0.663402 | + | 1.14905i | 0.316314 | + | 0.948654i | \(0.397555\pi\) |
−0.979716 | + | 0.200391i | \(0.935779\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.59618 | − | 6.22877i | −0.460444 | − | 0.797512i | 0.538539 | − | 0.842601i | \(-0.318976\pi\) |
−0.998983 | + | 0.0450883i | \(0.985643\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.33686 | −0.289852 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.23616 | + | 5.33250i | −1.12838 | + | 0.651469i | −0.943526 | − | 0.331298i | \(-0.892514\pi\) |
−0.184851 | + | 0.982767i | \(0.559180\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.67423 | − | 6.36396i | 0.436051 | − | 0.755263i | −0.561329 | − | 0.827592i | \(-0.689710\pi\) |
0.997381 | + | 0.0723293i | \(0.0230432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.703424 | + | 1.21837i | −0.0823296 | + | 0.142599i | −0.904250 | − | 0.427003i | \(-0.859569\pi\) |
0.821921 | + | 0.569602i | \(0.192903\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.71255i | − | 0.537045i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.56422 | + | 0.903104i | 0.175989 | + | 0.101607i | 0.585407 | − | 0.810740i | \(-0.300935\pi\) |
−0.409418 | + | 0.912347i | \(0.634268\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.53518i | − | 0.607565i | −0.952741 | − | 0.303782i | \(-0.901750\pi\) | ||
0.952741 | − | 0.303782i | \(-0.0982496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.71370 | + | 2.96822i | 0.185877 | + | 0.321949i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.73800 | − | 13.4026i | −0.820226 | − | 1.42067i | −0.905513 | − | 0.424317i | \(-0.860514\pi\) |
0.0852870 | − | 0.996356i | \(-0.472819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.0429 | − | 8.68501i | 1.57692 | − | 0.910437i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.69189 | − | 1.15456i | 0.173585 | − | 0.118456i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.66561 | + | 5.58044i | 0.981394 | + | 0.566608i | 0.902691 | − | 0.430290i | \(-0.141589\pi\) |
0.0787031 | + | 0.996898i | \(0.474922\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.75566 | + | 3.32303i | −0.572710 | + | 0.330654i | −0.758231 | − | 0.651986i | \(-0.773936\pi\) |
0.185521 | + | 0.982640i | \(0.440603\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89881i | 0.482694i | 0.970439 | + | 0.241347i | \(0.0775893\pi\) | ||||
−0.970439 | + | 0.241347i | \(0.922411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.28463 | −0.510885 | −0.255442 | − | 0.966824i | \(-0.582221\pi\) | ||||
−0.255442 | + | 0.966824i | \(0.582221\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.19011 | − | 2.41916i | −0.401340 | − | 0.231714i | 0.285722 | − | 0.958313i | \(-0.407767\pi\) |
−0.687062 | + | 0.726599i | \(0.741100\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.7955 | 1.95627 | 0.978137 | − | 0.207960i | \(-0.0666825\pi\) | ||||
0.978137 | + | 0.207960i | \(0.0666825\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.78552 | −0.353001 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22.0630 | − | 12.7381i | −2.02251 | − | 1.16770i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.17970 | 0.834518 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.59535i | 0.411021i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6103 | − | 7.28054i | 1.11898 | − | 0.646044i | 0.177840 | − | 0.984059i | \(-0.443089\pi\) |
0.941141 | + | 0.338016i | \(0.109756\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.06693 | − | 0.615993i | −0.0932183 | − | 0.0538196i | 0.452666 | − | 0.891680i | \(-0.350473\pi\) |
−0.545884 | + | 0.837860i | \(0.683806\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.60013 | + | 13.7202i | −0.572304 | + | 1.18969i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.1566 | − | 7.59595i | 1.12404 | − | 0.648966i | 0.181612 | − | 0.983370i | \(-0.441869\pi\) |
0.942430 | + | 0.334405i | \(0.108535\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.34657 | − | 7.52848i | −0.368671 | − | 0.638558i | 0.620687 | − | 0.784059i | \(-0.286854\pi\) |
−0.989358 | + | 0.145501i | \(0.953521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.35473 | − | 5.81056i | −0.280537 | − | 0.485904i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.45586i | 0.370039i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1911 | − | 7.03855i | −0.998737 | − | 0.576621i | −0.0908623 | − | 0.995863i | \(-0.528962\pi\) |
−0.907874 | + | 0.419243i | \(0.862296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.4128i | − | 1.17289i | −0.809987 | − | 0.586447i | \(-0.800526\pi\) | ||
0.809987 | − | 0.586447i | \(-0.199474\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.930421 | − | 1.61154i | 0.0747332 | − | 0.129442i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.27918 | − | 3.94766i | 0.181899 | − | 0.315058i | −0.760628 | − | 0.649187i | \(-0.775109\pi\) |
0.942527 | + | 0.334130i | \(0.108442\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.3682 | − | 14.0690i | 1.92048 | − | 1.10879i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.3066 | 1.59053 | 0.795267 | − | 0.606259i | \(-0.207331\pi\) | ||||
0.795267 | + | 0.606259i | \(0.207331\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.75542 | − | 13.4328i | −0.600133 | − | 1.03946i | −0.992800 | − | 0.119780i | \(-0.961781\pi\) |
0.392668 | − | 0.919680i | \(-0.371552\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.86522 | − | 10.1589i | 0.451171 | − | 0.781451i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.813911 | + | 1.40974i | −0.0618805 | + | 0.107180i | −0.895306 | − | 0.445452i | \(-0.853043\pi\) |
0.833425 | + | 0.552632i | \(0.186376\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.34657 | − | 14.4567i | −0.630942 | − | 1.09282i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8023 | 0.807401 | 0.403700 | − | 0.914891i | \(-0.367724\pi\) | ||||
0.403700 | + | 0.914891i | \(0.367724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.19328 | − | 1.84364i | 0.237355 | − | 0.137037i | −0.376606 | − | 0.926374i | \(-0.622909\pi\) |
0.613960 | + | 0.789337i | \(0.289575\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.136511 | − | 0.236444i | 0.0100365 | − | 0.0173837i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.92029 | + | 8.52220i | −0.359808 | + | 0.623205i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2996i | 1.32411i | 0.749453 | + | 0.662057i | \(0.230316\pi\) | ||||
−0.749453 | + | 0.662057i | \(0.769684\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.17194 | − | 3.56337i | −0.444266 | − | 0.256497i | 0.261139 | − | 0.965301i | \(-0.415902\pi\) |
−0.705406 | + | 0.708804i | \(0.749235\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.88677i | 0.419415i | 0.977764 | + | 0.209708i | \(0.0672512\pi\) | ||||
−0.977764 | + | 0.209708i | \(0.932749\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.22602 | − | 2.12353i | −0.0869103 | − | 0.150533i | 0.819293 | − | 0.573375i | \(-0.194366\pi\) |
−0.906204 | + | 0.422842i | \(0.861033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.5604 | − | 28.6834i | −1.16231 | − | 2.01318i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.619772 | − | 0.357825i | 0.0432867 | − | 0.0249916i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.29965 | + | 2.54941i | 0.366584 | + | 0.176346i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1777 | − | 7.60813i | −0.907188 | − | 0.523765i | −0.0276624 | − | 0.999617i | \(-0.508806\pi\) |
−0.879525 | + | 0.475852i | \(0.842140\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.77332 | + | 2.17853i | −0.257338 | + | 0.148574i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8318i | 0.938961i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −36.2715 | −2.43988 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.1808 | + | 12.2288i | 1.41837 | + | 0.818898i | 0.996156 | − | 0.0875966i | \(-0.0279186\pi\) |
0.422217 | + | 0.906495i | \(0.361252\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.84290 | 0.188690 | 0.0943449 | − | 0.995540i | \(-0.469924\pi\) | ||||
0.0943449 | + | 0.995540i | \(0.469924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.64189 | 0.438909 | 0.219454 | − | 0.975623i | \(-0.429572\pi\) | ||||
0.219454 | + | 0.975623i | \(0.429572\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.14836 | − | 1.81771i | −0.206256 | − | 0.119082i | 0.393314 | − | 0.919404i | \(-0.371328\pi\) |
−0.599570 | + | 0.800322i | \(0.704662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.578925 | −0.0377649 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.762075i | − | 0.0492945i | −0.999696 | − | 0.0246473i | \(-0.992154\pi\) | ||
0.999696 | − | 0.0246473i | \(-0.00784626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.97549 | − | 4.02730i | 0.449331 | − | 0.259421i | −0.258217 | − | 0.966087i | \(-0.583135\pi\) |
0.707548 | + | 0.706666i | \(0.249801\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.11627 | − | 1.22183i | −0.135204 | − | 0.0780599i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.62906 | + | 21.6154i | 0.103654 | + | 1.37535i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.2665 | + | 12.2782i | −1.34233 | + | 0.774995i | −0.987149 | − | 0.159803i | \(-0.948914\pi\) |
−0.355181 | + | 0.934797i | \(0.615581\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.43438 | − | 9.41263i | −0.341657 | − | 0.591767i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.33081 | − | 16.1614i | −0.582040 | − | 1.00812i | −0.995237 | − | 0.0974812i | \(-0.968921\pi\) |
0.413197 | − | 0.910641i | \(-0.364412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.02939i | 0.126100i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.9821 | + | 10.9593i | 1.17049 | + | 0.675780i | 0.953794 | − | 0.300460i | \(-0.0971401\pi\) |
0.216691 | + | 0.976240i | \(0.430473\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.78904i | − | 0.294189i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.97653 | + | 12.0837i | −0.425366 | + | 0.736756i | −0.996455 | − | 0.0841325i | \(-0.973188\pi\) |
0.571088 | + | 0.820889i | \(0.306521\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.00000 | − | 1.73205i | 0.0607457 | − | 0.105215i | −0.834053 | − | 0.551684i | \(-0.813985\pi\) |
0.894799 | + | 0.446469i | \(0.147319\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.58414 | + | 3.22400i | −0.336736 | + | 0.194415i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.35811 | −0.502190 | −0.251095 | − | 0.967962i | \(-0.580791\pi\) | ||||
−0.251095 | + | 0.967962i | \(0.580791\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.87768 | − | 8.44839i | −0.290978 | − | 0.503988i | 0.683063 | − | 0.730359i | \(-0.260647\pi\) |
−0.974041 | + | 0.226371i | \(0.927314\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.41318 | − | 7.64385i | 0.262336 | − | 0.454380i | −0.704526 | − | 0.709678i | \(-0.748840\pi\) |
0.966862 | + | 0.255298i | \(0.0821737\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.65974 | + | 4.60681i | −0.157000 | + | 0.271931i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.0992 | + | 31.3488i | 1.06466 | + | 1.84404i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.3358 | 1.12961 | 0.564805 | − | 0.825224i | \(-0.308951\pi\) | ||||
0.564805 | + | 0.825224i | \(0.308951\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.14743 | − | 2.39452i | 0.241473 | − | 0.139414i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.0306 | − | 34.6941i | 1.15840 | − | 2.00641i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.1931 | − | 28.0473i | 0.933357 | − | 1.61662i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.37978i | 0.193525i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.04900 | + | 4.64709i | 0.459381 | + | 0.265224i | 0.711784 | − | 0.702399i | \(-0.247888\pi\) |
−0.252403 | + | 0.967622i | \(0.581221\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.7734i | 1.06454i | 0.846573 | + | 0.532272i | \(0.178662\pi\) | ||||
−0.846573 | + | 0.532272i | \(0.821338\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5891 | + | 25.2690i | 0.824623 | + | 1.42829i | 0.902207 | + | 0.431303i | \(0.141946\pi\) |
−0.0775842 | + | 0.996986i | \(0.524721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.43254 | + | 12.8735i | 0.417453 | + | 0.723050i | 0.995683 | − | 0.0928242i | \(-0.0295894\pi\) |
−0.578229 | + | 0.815874i | \(0.696256\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.0794 | + | 6.39671i | −0.620329 | + | 0.358147i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.2607 | − | 17.9205i | 1.46118 | − | 0.997126i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.5826 | − | 11.8834i | −1.14172 | − | 0.659171i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.72667 | − | 2.15160i | 0.205458 | − | 0.118621i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.5415i | 1.23899i | 0.784999 | + | 0.619497i | \(0.212664\pi\) | ||||
−0.784999 | + | 0.619497i | \(0.787336\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.01161 | 0.273814 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.17511 | − | 4.71990i | −0.445326 | − | 0.257109i | 0.260528 | − | 0.965466i | \(-0.416103\pi\) |
−0.705854 | + | 0.708357i | \(0.749437\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.34275 | 0.289326 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.28630 | −0.339428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.8418 | + | 14.3424i | 1.33358 | + | 0.769942i | 0.985846 | − | 0.167651i | \(-0.0536183\pi\) |
0.347733 | + | 0.937594i | \(0.386952\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.1576 | −1.77488 | −0.887442 | − | 0.460919i | \(-0.847520\pi\) | ||||
−0.887442 | + | 0.460919i | \(0.847520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 0.993688i | − | 0.0528887i | −0.999650 | − | 0.0264443i | \(-0.991582\pi\) | ||
0.999650 | − | 0.0264443i | \(-0.00841848\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.99050 | + | 1.72657i | −0.158719 | + | 0.0916366i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.8513 | + | 9.15177i | 0.836601 | + | 0.483012i | 0.856107 | − | 0.516798i | \(-0.172876\pi\) |
−0.0195066 | + | 0.999810i | \(0.506210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.8589 | − | 14.8448i | −0.624152 | − | 0.781303i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.572525 | − | 0.330547i | 0.0299673 | − | 0.0173016i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0460 | − | 17.4003i | −0.524400 | − | 0.908287i | −0.999596 | − | 0.0284071i | \(-0.990957\pi\) |
0.475197 | − | 0.879879i | \(-0.342377\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.7986 | + | 30.8282i | 0.924060 | + | 1.60052i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 32.6611i | − | 1.69113i | −0.533873 | − | 0.845565i | \(-0.679264\pi\) | ||
0.533873 | − | 0.845565i | \(-0.320736\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.8377 | − | 23.5777i | −2.10325 | − | 1.21431i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.9346i | 0.869874i | 0.900461 | + | 0.434937i | \(0.143229\pi\) | ||||
−0.900461 | + | 0.434937i | \(0.856771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.912997 | + | 1.58136i | −0.0466520 | + | 0.0808036i | −0.888408 | − | 0.459054i | \(-0.848189\pi\) |
0.841756 | + | 0.539857i | \(0.181522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.10724 | + | 1.91780i | −0.0564303 | + | 0.0977401i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.336928 | − | 0.194525i | 0.0170829 | − | 0.00986283i | −0.491434 | − | 0.870915i | \(-0.663527\pi\) |
0.508517 | + | 0.861052i | \(0.330194\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −58.7568 | −2.97146 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.424379 | − | 0.735047i | −0.0213528 | − | 0.0369842i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.4415 | − | 18.0852i | 0.524044 | − | 0.907670i | −0.475564 | − | 0.879681i | \(-0.657756\pi\) |
0.999608 | − | 0.0279895i | \(-0.00891051\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.11018 | + | 10.5831i | −0.305128 | + | 0.528497i | −0.977290 | − | 0.211907i | \(-0.932033\pi\) |
0.672162 | + | 0.740404i | \(0.265366\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.84644 | + | 17.0545i | 0.490486 | + | 0.849547i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.783886 | 0.0388558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.4233 | − | 9.48201i | 0.812081 | − | 0.468855i | −0.0355969 | − | 0.999366i | \(-0.511333\pi\) |
0.847678 | + | 0.530511i | \(0.178000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.7986 | + | 30.8282i | −0.875814 | + | 1.51695i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.30052 | + | 2.25257i | −0.0638401 | + | 0.110574i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3264i | 0.748745i | 0.927278 | + | 0.374373i | \(0.122142\pi\) | ||||
−0.927278 | + | 0.374373i | \(0.877858\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6624 | + | 6.15596i | 0.519656 | + | 0.300023i | 0.736794 | − | 0.676118i | \(-0.236339\pi\) |
−0.217138 | + | 0.976141i | \(0.569672\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.8580i | 1.69086i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.5611 | − | 21.7564i | −0.607872 | − | 1.05287i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.69475 | + | 4.66745i | 0.129802 | + | 0.224823i | 0.923600 | − | 0.383358i | \(-0.125233\pi\) |
−0.793798 | + | 0.608182i | \(0.791899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.5304 | + | 16.4721i | −1.37108 | + | 0.791596i | −0.991065 | − | 0.133382i | \(-0.957416\pi\) |
−0.380020 | + | 0.924978i | \(0.624083\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.63894 | + | 35.0151i | 0.126238 | + | 1.67500i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.6658 | + | 17.7049i | 1.46360 | + | 0.845009i | 0.999175 | − | 0.0406035i | \(-0.0129281\pi\) |
0.464424 | + | 0.885613i | \(0.346261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.4202 | + | 11.7896i | −0.970191 | + | 0.560140i | −0.899295 | − | 0.437344i | \(-0.855919\pi\) |
−0.0708967 | + | 0.997484i | \(0.522586\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.27236i | 0.344743i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.9061 | 1.31697 | 0.658485 | − | 0.752594i | \(-0.271197\pi\) | ||||
0.658485 | + | 0.752594i | \(0.271197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.77946 | + | 1.02737i | 0.0837913 | + | 0.0483769i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.16238 | −0.382658 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.38023 | 0.0645644 | 0.0322822 | − | 0.999479i | \(-0.489722\pi\) | ||||
0.0322822 | + | 0.999479i | \(0.489722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.29648 | − | 4.78998i | −0.386406 | − | 0.223091i | 0.294196 | − | 0.955745i | \(-0.404948\pi\) |
−0.680602 | + | 0.732654i | \(0.738281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3114 | −0.804527 | −0.402263 | − | 0.915524i | \(-0.631776\pi\) | ||||
−0.402263 | + | 0.915524i | \(0.631776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7691i | 0.683432i | 0.939803 | + | 0.341716i | \(0.111008\pi\) | ||||
−0.939803 | + | 0.341716i | \(0.888992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.2609 | + | 18.6258i | −1.48967 | + | 0.860061i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.8338 | − | 6.25487i | −0.498137 | − | 0.287599i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.7731 | − | 1.56558i | 0.953134 | − | 0.0718336i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.8909 | + | 16.1028i | −1.27437 | + | 0.735757i | −0.975807 | − | 0.218633i | \(-0.929840\pi\) |
−0.298562 | + | 0.954390i | \(0.596507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.44466 | + | 2.50223i | 0.0658710 | + | 0.114092i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.62232 | − | 4.54198i | −0.119073 | − | 0.206241i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.60690i | 0.254073i | 0.991898 | + | 0.127037i | \(0.0405466\pi\) | ||||
−0.991898 | + | 0.127037i | \(0.959453\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.87723 | + | 2.23852i | 0.174977 | + | 0.101023i | 0.584930 | − | 0.811083i | \(-0.301122\pi\) |
−0.409954 | + | 0.912106i | \(0.634455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 69.1615i | 3.11488i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.8337 | − | 22.2286i | 0.575669 | − | 0.997089i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.05013 | − | 10.4791i | 0.270841 | − | 0.469111i | −0.698236 | − | 0.715867i | \(-0.746032\pi\) |
0.969077 | + | 0.246757i | \(0.0793649\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.4265 | + | 8.32914i | −0.643246 | + | 0.371378i | −0.785864 | − | 0.618400i | \(-0.787781\pi\) |
0.142618 | + | 0.989778i | \(0.454448\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.12306 | 0.138975 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.5662 | + | 20.0332i | 0.512661 | + | 0.887956i | 0.999892 | + | 0.0146825i | \(0.00467374\pi\) |
−0.487231 | + | 0.873273i | \(0.661993\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.45698 | + | 4.25562i | −0.108690 | + | 0.188257i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.15101 | − | 1.99360i | 0.0507193 | − | 0.0878485i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.831089 | − | 1.43949i | −0.0365513 | − | 0.0633087i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.3189 | 1.24067 | 0.620336 | − | 0.784336i | \(-0.286996\pi\) | ||||
0.620336 | + | 0.784336i | \(0.286996\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.2457 | + | 12.2662i | −0.929008 | + | 0.536363i | −0.886498 | − | 0.462733i | \(-0.846869\pi\) |
−0.0425103 | + | 0.999096i | \(0.513536\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.4415 | − | 25.0134i | 0.629082 | − | 1.08960i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.9480 | − | 36.2829i | 0.910781 | − | 1.57752i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.57357i | 0.328048i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.15061 | + | 1.24166i | 0.0929790 | + | 0.0536815i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 7.01611i | − | 0.302205i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.97233 | − | 15.5405i | −0.385750 | − | 0.668139i | 0.606123 | − | 0.795371i | \(-0.292724\pi\) |
−0.991873 | + | 0.127232i | \(0.959391\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.13679 | + | 1.96898i | 0.0486949 | + | 0.0843420i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.51521 | + | 5.49361i | −0.406841 | + | 0.234890i | −0.689432 | − | 0.724351i | \(-0.742140\pi\) |
0.282591 | + | 0.959241i | \(0.408806\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.2156 | − | 3.10625i | 1.75585 | − | 0.132330i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.46365 | + | 3.15444i | 0.232338 | + | 0.134141i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.00262 | + | 1.73357i | −0.127225 | + | 0.0734535i | −0.562262 | − | 0.826959i | \(-0.690069\pi\) |
0.435037 | + | 0.900413i | \(0.356735\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 46.1097i | − | 1.95023i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.55779 | 0.0656532 | 0.0328266 | − | 0.999461i | \(-0.489549\pi\) | ||||
0.0328266 | + | 0.999461i | \(0.489549\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.46284 | − | 4.88602i | −0.356034 | − | 0.205556i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.3886 | 0.770890 | 0.385445 | − | 0.922731i | \(-0.374048\pi\) | ||||
0.385445 | + | 0.922731i | \(0.374048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4660 | −1.19126 | −0.595632 | − | 0.803257i | \(-0.703098\pi\) | ||||
−0.595632 | + | 0.803257i | \(0.703098\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.3421 | − | 19.2501i | −1.39046 | − | 0.802783i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.6213 | −0.775216 | −0.387608 | − | 0.921824i | \(-0.626699\pi\) | ||||
−0.387608 | + | 0.921824i | \(0.626699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 19.3337i | − | 0.802099i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.9079 | − | 6.87502i | 0.493174 | − | 0.284734i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.35787 | − | 3.09337i | −0.221143 | − | 0.127677i | 0.385336 | − | 0.922776i | \(-0.374085\pi\) |
−0.606479 | + | 0.795099i | \(0.707419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.5549 | − | 7.48275i | −0.640930 | − | 0.308321i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.5420 | − | 9.55051i | 0.679297 | − | 0.392192i | −0.120293 | − | 0.992738i | \(-0.538383\pi\) |
0.799590 | + | 0.600546i | \(0.205050\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.98577 | + | 10.3677i | 0.245393 | + | 0.425033i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.9789 | + | 38.0686i | 0.898035 | + | 1.55544i | 0.830003 | + | 0.557758i | \(0.188338\pi\) |
0.0680310 | + | 0.997683i | \(0.478328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.3002i | 1.03202i | 0.856583 | + | 0.516009i | \(0.172583\pi\) | ||||
−0.856583 | + | 0.516009i | \(0.827417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.73573 | − | 2.15682i | −0.151879 | − | 0.0876874i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.2880i | 0.498754i | 0.968406 | + | 0.249377i | \(0.0802259\pi\) | ||||
−0.968406 | + | 0.249377i | \(0.919774\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.06332 | − | 5.30582i | 0.123929 | − | 0.214651i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.52042 | − | 9.56165i | 0.222968 | − | 0.386192i | −0.732740 | − | 0.680509i | \(-0.761759\pi\) |
0.955708 | + | 0.294317i | \(0.0950922\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.4315 | − | 15.8376i | 1.10435 | − | 0.637598i | 0.166991 | − | 0.985958i | \(-0.446595\pi\) |
0.937361 | + | 0.348360i | \(0.113261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.0244 | 1.36755 | 0.683777 | − | 0.729691i | \(-0.260336\pi\) | ||||
0.683777 | + | 0.729691i | \(0.260336\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.0280 | − | 46.8138i | −1.08285 | − | 1.87556i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.8683 | + | 18.8244i | −0.434730 | + | 0.752975i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.11885 | − | 3.66996i | 0.0844841 | − | 0.146331i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9530 | − | 24.1674i | −0.555462 | − | 0.962088i | −0.997867 | − | 0.0652727i | \(-0.979208\pi\) |
0.442406 | − | 0.896815i | \(-0.354125\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.84243 | −0.271533 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3961 | − | 12.9304i | 0.887364 | − | 0.512320i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.0350138 | − | 0.0606458i | 0.00138296 | − | 0.00239536i | −0.865333 | − | 0.501197i | \(-0.832893\pi\) |
0.866716 | + | 0.498802i | \(0.166226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.0562 | − | 27.8101i | 0.633194 | − | 1.09672i | −0.353700 | − | 0.935359i | \(-0.615077\pi\) |
0.986895 | − | 0.161366i | \(-0.0515900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.51784i | 0.216929i | 0.994100 | + | 0.108464i | \(0.0345933\pi\) | ||||
−0.994100 | + | 0.108464i | \(0.965407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.9079 | + | 6.87502i | 0.467426 | + | 0.269868i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.9898i | 0.977928i | 0.872304 | + | 0.488964i | \(0.162625\pi\) | ||||
−0.872304 | + | 0.488964i | \(0.837375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.289463 | + | 0.501364i | 0.0113102 | + | 0.0195899i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.43887 | − | 2.49220i | −0.0560506 | − | 0.0970824i | 0.836639 | − | 0.547755i | \(-0.184517\pi\) |
−0.892689 | + | 0.450673i | \(0.851184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9510 | + | 16.7149i | −1.12606 | + | 0.650133i | −0.942942 | − | 0.332958i | \(-0.891953\pi\) |
−0.183121 | + | 0.983090i | \(0.558620\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.90960 | − | 4.03276i | 0.229164 | − | 0.156384i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −66.1538 | − | 38.1939i | −2.56148 | − | 1.47887i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.40377 | + | 4.85192i | −0.324424 | + | 0.187306i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.66815i | − | 0.0643026i | −0.999483 | − | 0.0321513i | \(-0.989764\pi\) | ||
0.999483 | − | 0.0321513i | \(-0.0102358\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.30258 | −0.165361 | −0.0826807 | − | 0.996576i | \(-0.526348\pi\) | ||||
−0.0826807 | + | 0.996576i | \(0.526348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.7609 | + | 19.4918i | 1.29562 | + | 0.748029i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.412745 | 0.0157933 | 0.00789663 | − | 0.999969i | \(-0.497486\pi\) | ||||
0.00789663 | + | 0.999969i | \(0.497486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.13885 | −0.272762 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.8914 | + | 25.3407i | 1.67213 | + | 0.965403i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.9573 | 0.492920 | 0.246460 | − | 0.969153i | \(-0.420733\pi\) | ||||
0.246460 | + | 0.969153i | \(0.420733\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.08501i | 0.154953i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.61977 | − | 5.55398i | 0.364375 | − | 0.210372i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.1208 | − | 9.30735i | −0.608874 | − | 0.351534i | 0.163651 | − | 0.986518i | \(-0.447673\pi\) |
−0.772525 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.28221 | − | 1.09787i | −0.0860753 | − | 0.0414068i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.1039 | + | 11.6070i | −0.756084 | + | 0.436525i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7822 | + | 30.7997i | 0.667825 | + | 1.15671i | 0.978511 | + | 0.206194i | \(0.0661079\pi\) |
−0.310686 | + | 0.950513i | \(0.600559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.9504 | + | 27.6269i | 0.597347 | + | 1.03464i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.15286i | 0.117910i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.6858 | − | 6.16944i | −0.398512 | − | 0.230081i | 0.287330 | − | 0.957832i | \(-0.407232\pi\) |
−0.685842 | + | 0.727751i | \(0.740566\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.1110i | 0.637247i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.6589 | + | 39.2464i | −0.841530 | + | 1.45757i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.42944 | + | 9.40407i | −0.201367 | + | 0.348778i | −0.948969 | − | 0.315369i | \(-0.897872\pi\) |
0.747602 | + | 0.664147i | \(0.231205\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −58.5675 | + | 33.8140i | −2.16620 | + | 1.25065i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.5581 | −1.05482 | −0.527409 | − | 0.849612i | \(-0.676836\pi\) | ||||
−0.527409 | + | 0.849612i | \(0.676836\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.19453 | + | 12.4613i | 0.265014 | + | 0.459018i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.0090 | + | 31.1925i | −0.662472 | + | 1.14744i | 0.317492 | + | 0.948261i | \(0.397159\pi\) |
−0.979964 | + | 0.199175i | \(0.936174\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.65055 | + | 13.2511i | −0.280671 | + | 0.486137i | −0.971550 | − | 0.236833i | \(-0.923890\pi\) |
0.690879 | + | 0.722971i | \(0.257224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.30750 | + | 5.72876i | 0.121177 | + | 0.209885i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.4586 | −0.674463 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.48161 | + | 0.855410i | −0.0540648 | + | 0.0312143i | −0.526789 | − | 0.849996i | \(-0.676604\pi\) |
0.472724 | + | 0.881211i | \(0.343271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.38637 | + | 5.86536i | −0.123242 | + | 0.213462i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.74519 | − | 11.6830i | 0.245158 | − | 0.424626i | −0.717018 | − | 0.697055i | \(-0.754493\pi\) |
0.962176 | + | 0.272429i | \(0.0878268\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32.3374i | − | 1.17223i | −0.810228 | − | 0.586115i | \(-0.800657\pi\) | ||
0.810228 | − | 0.586115i | \(-0.199343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.6356 | − | 8.44986i | −0.529844 | − | 0.305906i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.6814i | 1.83000i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.87233 | + | 15.3673i | 0.319945 | + | 0.554160i | 0.980476 | − | 0.196638i | \(-0.0630024\pi\) |
−0.660532 | + | 0.750798i | \(0.729669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.4209 | + | 38.8341i | 0.806424 | + | 1.39677i | 0.915326 | + | 0.402714i | \(0.131933\pi\) |
−0.108902 | + | 0.994052i | \(0.534734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.3899 | − | 9.46274i | 0.588744 | − | 0.339912i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.74185 | − | 5.48330i | −0.134066 | − | 0.196459i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.58616 | − | 4.95722i | −0.307237 | − | 0.177383i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.85505 | + | 1.07102i | −0.0662097 | + | 0.0382262i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.31647i | − | 0.0825731i | −0.999147 | − | 0.0412866i | \(-0.986854\pi\) | ||
0.999147 | − | 0.0412866i | \(-0.0131457\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 72.6363 | 2.58265 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.9755 | − | 17.8837i | −1.09997 | − | 0.635069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.2067 | 1.67215 | 0.836074 | − | 0.548616i | \(-0.184845\pi\) | ||||
0.836074 | + | 0.548616i | \(0.184845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.98577 | −0.317894 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.64380 | + | 0.949050i | 0.0580085 | + | 0.0334912i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.2224 | −0.466028 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.6610i | 0.937352i | 0.883370 | + | 0.468676i | \(0.155269\pi\) | ||||
−0.883370 | + | 0.468676i | \(0.844731\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.9478 | + | 6.89808i | −0.419545 | + | 0.242224i | −0.694883 | − | 0.719123i | \(-0.744544\pi\) |
0.275338 | + | 0.961348i | \(0.411210\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.26388 | − | 4.77115i | −0.289471 | − | 0.167126i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.7813 | + | 33.3836i | 0.797017 | + | 1.16795i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.3464 | + | 23.8713i | −1.44300 | + | 0.833115i | −0.998049 | − | 0.0624403i | \(-0.980112\pi\) |
−0.444949 | + | 0.895556i | \(0.646778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.3097 | + | 33.4455i | 0.673096 | + | 1.16584i | 0.977022 | + | 0.213140i | \(0.0683691\pi\) |
−0.303926 | + | 0.952696i | \(0.598298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.4671 | + | 37.1821i | 0.746484 | + | 1.29295i | 0.949498 | + | 0.313772i | \(0.101593\pi\) |
−0.203014 | + | 0.979176i | \(0.565074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.0605i | 0.418877i | 0.977822 | + | 0.209439i | \(0.0671636\pi\) | ||||
−0.977822 | + | 0.209439i | \(0.932836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.8477 | − | 18.9646i | −1.13811 | − | 0.657085i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.28873i | 0.252237i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.4589 | − | 28.5076i | 0.568223 | − | 0.984191i | −0.428519 | − | 0.903533i | \(-0.640964\pi\) |
0.996742 | − | 0.0806582i | \(-0.0257022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.4573 | + | 52.7536i | −1.05025 | + | 1.81909i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.77377 | + | 2.75614i | −0.164223 | + | 0.0948140i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.0636 | 1.10172 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.34024 | + | 4.05341i | 0.0802223 | + | 0.138949i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.9818 | − | 32.8775i | 0.649925 | − | 1.12570i | −0.333215 | − | 0.942851i | \(-0.608133\pi\) |
0.983140 | − | 0.182853i | \(-0.0585332\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.3194 | − | 29.9981i | 0.591620 | − | 1.02472i | −0.402394 | − | 0.915466i | \(-0.631822\pi\) |
0.994014 | − | 0.109250i | \(-0.0348448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.7044 | − | 18.5406i | −0.365230 | − | 0.632597i | 0.623583 | − | 0.781757i | \(-0.285676\pi\) |
−0.988813 | + | 0.149160i | \(0.952343\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.2030 | 0.517515 | 0.258758 | − | 0.965942i | \(-0.416687\pi\) | ||||
0.258758 | + | 0.965942i | \(0.416687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.662451 | − | 0.382466i | 0.0225240 | − | 0.0130043i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.21846 | − | 2.11043i | 0.0413333 | − | 0.0715913i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.5184 | + | 45.9312i | −0.898541 | + | 1.55632i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.0511i | 0.542625i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.6506 | − | 27.5111i | −1.60905 | − | 0.928983i | −0.989584 | − | 0.143957i | \(-0.954017\pi\) |
−0.619462 | − | 0.785027i | \(-0.712649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.6052i | 1.16588i | 0.812516 | + | 0.582939i | \(0.198097\pi\) | ||||
−0.812516 | + | 0.582939i | \(0.801903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.1634 | − | 29.7279i | −0.577596 | − | 1.00042i | −0.995754 | − | 0.0920509i | \(-0.970658\pi\) |
0.418159 | − | 0.908374i | \(-0.362676\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0978 | + | 41.7386i | 0.809124 | + | 1.40144i | 0.913471 | + | 0.406903i | \(0.133391\pi\) |
−0.104347 | + | 0.994541i | \(0.533275\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.0463 | − | 25.4301i | 1.47726 | − | 0.852899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.403577 | + | 5.35492i | 0.0135052 | + | 0.179196i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.39605 | − | 2.53806i | −0.146944 | − | 0.0848380i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.5191 | − | 18.7749i | 1.08457 | − | 0.626179i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 74.3330i | − | 2.47639i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.73270 | −0.0575968 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.7241 | + | 8.50097i | 0.488906 | + | 0.282270i | 0.724121 | − | 0.689673i | \(-0.242246\pi\) |
−0.235214 | + | 0.971943i | \(0.575579\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0110 | −0.928045 | −0.464023 | − | 0.885823i | \(-0.653594\pi\) | ||||
−0.464023 | + | 0.885823i | \(0.653594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.46798 | −0.247154 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.72667 | − | 2.15160i | −0.123066 | − | 0.0710519i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.1408 | −1.52205 | −0.761023 | − | 0.648725i | \(-0.775303\pi\) | ||||
−0.761023 | + | 0.648725i | \(0.775303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 36.5437i | − | 1.20285i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.40472 | − | 1.38837i | 0.0790669 | − | 0.0456493i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.6526 | − | 24.0482i | −1.36658 | − | 0.788994i | −0.376089 | − | 0.926584i | \(-0.622731\pi\) |
−0.990489 | + | 0.137589i | \(0.956065\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.82636 | + | 20.4268i | −0.322046 | + | 0.669461i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00468 | − | 2.31210i | 0.130967 | − | 0.0756139i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.17194 | − | 2.02986i | −0.0382856 | − | 0.0663127i | 0.846248 | − | 0.532790i | \(-0.178856\pi\) |
−0.884533 | + | 0.466477i | \(0.845523\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.24721 | + | 9.08843i | 0.171054 | + | 0.296274i | 0.938789 | − | 0.344494i | \(-0.111949\pi\) |
−0.767735 | + | 0.640768i | \(0.778616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.2686i | 0.399519i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.6357 | + | 9.02729i | 0.508093 | + | 0.293348i | 0.732049 | − | 0.681252i | \(-0.238564\pi\) |
−0.223957 | + | 0.974599i | \(0.571897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.99622i | 0.227107i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.1592 | − | 19.3283i | 0.361482 | − | 0.626106i | −0.626723 | − | 0.779242i | \(-0.715604\pi\) |
0.988205 | + | 0.153136i | \(0.0489374\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.29961 | − | 7.44714i | 0.139132 | − | 0.240984i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.9544 | − | 26.5318i | 1.48394 | − | 0.856756i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3185 | 0.494147 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.67447 | + | 2.90027i | 0.0539031 | + | 0.0933629i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.6439 | − | 18.4358i | 0.342286 | − | 0.592856i | −0.642571 | − | 0.766226i | \(-0.722132\pi\) |
0.984857 | + | 0.173370i | \(0.0554656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.1329 | + | 38.3352i | −0.710277 | + | 1.23024i | 0.254476 | + | 0.967079i | \(0.418097\pi\) |
−0.964753 | + | 0.263157i | \(0.915236\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.1821 | − | 26.2961i | −0.486715 | − | 0.843016i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.8291 | −1.81812 | −0.909062 | − | 0.416660i | \(-0.863201\pi\) | ||||
−0.909062 | + | 0.416660i | \(0.863201\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.0826 | + | 10.4400i | −0.577923 | + | 0.333664i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.7404 | − | 39.3875i | 0.725306 | − | 1.25627i | −0.233542 | − | 0.972347i | \(-0.575032\pi\) |
0.958848 | − | 0.283920i | \(-0.0916351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.38313 | − | 2.39566i | 0.0440703 | − | 0.0763319i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 74.6939i | − | 2.37513i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.64805 | + | 4.99295i | 0.274714 | + | 0.158606i | 0.631028 | − | 0.775760i | \(-0.282633\pi\) |
−0.356314 | + | 0.934366i | \(0.615967\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.15224i | 0.0365285i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.2792 | + | 19.5361i | 0.357215 | + | 0.618715i | 0.987494 | − | 0.157654i | \(-0.0503929\pi\) |
−0.630279 | + | 0.776369i | \(0.717060\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.dc.d.1889.4 | 16 | ||
3.2 | odd | 2 | inner | 2736.2.dc.d.1889.5 | 16 | ||
4.3 | odd | 2 | 684.2.bk.a.521.4 | yes | 16 | ||
12.11 | even | 2 | 684.2.bk.a.521.5 | yes | 16 | ||
19.12 | odd | 6 | inner | 2736.2.dc.d.449.5 | 16 | ||
57.50 | even | 6 | inner | 2736.2.dc.d.449.4 | 16 | ||
76.31 | even | 6 | 684.2.bk.a.449.5 | yes | 16 | ||
228.107 | odd | 6 | 684.2.bk.a.449.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.bk.a.449.4 | ✓ | 16 | 228.107 | odd | 6 | ||
684.2.bk.a.449.5 | yes | 16 | 76.31 | even | 6 | ||
684.2.bk.a.521.4 | yes | 16 | 4.3 | odd | 2 | ||
684.2.bk.a.521.5 | yes | 16 | 12.11 | even | 2 | ||
2736.2.dc.d.449.4 | 16 | 57.50 | even | 6 | inner | ||
2736.2.dc.d.449.5 | 16 | 19.12 | odd | 6 | inner | ||
2736.2.dc.d.1889.4 | 16 | 1.1 | even | 1 | trivial | ||
2736.2.dc.d.1889.5 | 16 | 3.2 | odd | 2 | inner |