Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.10 | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.k.2881.10 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.33401 | + | 2.31057i | 0.596587 | + | 1.03332i | 0.993321 | + | 0.115385i | \(0.0368103\pi\) |
−0.396734 | + | 0.917934i | \(0.629856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.581213 | − | 2.58112i | −0.219678 | − | 0.975572i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.682257 | + | 1.18170i | −0.205708 | + | 0.356297i | −0.950358 | − | 0.311158i | \(-0.899283\pi\) |
0.744650 | + | 0.667455i | \(0.232616\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.75597 | + | 4.77348i | −0.764368 | + | 1.32392i | 0.176212 | + | 0.984352i | \(0.443616\pi\) |
−0.940580 | + | 0.339572i | \(0.889718\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.23930 | + | 2.14654i | 0.300575 | + | 0.520611i | 0.976266 | − | 0.216573i | \(-0.0694880\pi\) |
−0.675691 | + | 0.737185i | \(0.736155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19600 | − | 3.80358i | 0.503797 | − | 0.872601i | −0.496194 | − | 0.868212i | \(-0.665269\pi\) |
0.999990 | − | 0.00438950i | \(-0.00139723\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.34501 | + | 4.06167i | 0.488968 | + | 0.846918i | 0.999919 | − | 0.0126921i | \(-0.00404012\pi\) |
−0.510951 | + | 0.859610i | \(0.670707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.05916 | + | 1.83452i | −0.211832 | + | 0.366904i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.94810 | − | 5.10625i | −0.547448 | − | 0.948207i | −0.998448 | − | 0.0556837i | \(-0.982266\pi\) |
0.451001 | − | 0.892524i | \(-0.351067\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.11678 | −0.559789 | −0.279895 | − | 0.960031i | \(-0.590300\pi\) | ||||
−0.279895 | + | 0.960031i | \(0.590300\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.18852 | − | 4.78617i | 0.877021 | − | 0.809011i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.15627 | + | 5.46681i | −0.518887 | + | 0.898739i | 0.480872 | + | 0.876791i | \(0.340320\pi\) |
−0.999759 | + | 0.0219479i | \(0.993013\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.38693 | + | 2.40224i | −0.216603 | + | 0.375167i | −0.953767 | − | 0.300546i | \(-0.902831\pi\) |
0.737164 | + | 0.675713i | \(0.236164\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.87889 | + | 8.45048i | 0.744023 | + | 1.28869i | 0.950650 | + | 0.310267i | \(0.100418\pi\) |
−0.206626 | + | 0.978420i | \(0.566248\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0501 | −1.46596 | −0.732979 | − | 0.680252i | \(-0.761871\pi\) | ||||
−0.732979 | + | 0.680252i | \(0.761871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.32438 | + | 3.00036i | −0.903483 | + | 0.428623i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.47823 | + | 2.56037i | 0.203050 | + | 0.351694i | 0.949510 | − | 0.313737i | \(-0.101581\pi\) |
−0.746459 | + | 0.665431i | \(0.768248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.64055 | −0.490891 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.55617 | 0.462974 | 0.231487 | − | 0.972838i | \(-0.425641\pi\) | ||||
0.231487 | + | 0.972838i | \(0.425641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.32609 | 0.169788 | 0.0848940 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848940 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.7059 | −1.82405 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.29874 | −1.01385 | −0.506926 | − | 0.861990i | \(-0.669218\pi\) | ||||
−0.506926 | + | 0.861990i | \(0.669218\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3069 | 1.46056 | 0.730279 | − | 0.683149i | \(-0.239390\pi\) | ||||
0.730279 | + | 0.683149i | \(0.239390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.11577 | − | 1.93257i | −0.130591 | − | 0.226190i | 0.793314 | − | 0.608813i | \(-0.208354\pi\) |
−0.923905 | + | 0.382623i | \(0.875021\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.44666 | + | 1.07417i | 0.392783 | + | 0.122413i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8307 | −1.44357 | −0.721783 | − | 0.692119i | \(-0.756677\pi\) | ||||
−0.721783 | + | 0.692119i | \(0.756677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.15934 | + | 8.93625i | 0.566312 | + | 0.980881i | 0.996926 | + | 0.0783447i | \(0.0249635\pi\) |
−0.430615 | + | 0.902536i | \(0.641703\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.30648 | + | 5.72700i | −0.358638 | + | 0.621180i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.73159 | + | 13.3915i | −0.819547 | + | 1.41950i | 0.0864698 | + | 0.996254i | \(0.472441\pi\) |
−0.906017 | + | 0.423242i | \(0.860892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9227 | + | 4.33908i | 1.45950 | + | 0.454860i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.7179 | 1.20223 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.55369 | − | 4.42311i | −0.259288 | − | 0.449099i | 0.706764 | − | 0.707450i | \(-0.250154\pi\) |
−0.966051 | + | 0.258351i | \(0.916821\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.34748 | + | 2.33391i | −0.134079 | + | 0.232232i | −0.925245 | − | 0.379369i | \(-0.876141\pi\) |
0.791166 | + | 0.611601i | \(0.209474\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.51071 | − | 11.2769i | −0.641519 | − | 1.11114i | −0.985094 | − | 0.172019i | \(-0.944971\pi\) |
0.343574 | − | 0.939126i | \(-0.388362\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.49753 | + | 2.59379i | −0.144771 | + | 0.250751i | −0.929288 | − | 0.369357i | \(-0.879578\pi\) |
0.784516 | + | 0.620108i | \(0.212911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0132 | + | 17.3434i | 0.959093 | + | 1.66120i | 0.724710 | + | 0.689054i | \(0.241974\pi\) |
0.234383 | + | 0.972144i | \(0.424693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.23211 | − | 10.7943i | 0.586267 | − | 1.01544i | −0.408449 | − | 0.912781i | \(-0.633930\pi\) |
0.994716 | − | 0.102664i | \(-0.0327365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.25652 | + | 10.8366i | −0.583424 | + | 1.01052i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.82017 | − | 4.44639i | 0.441864 | − | 0.407600i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.56905 | + | 7.91383i | 0.415368 | + | 0.719439i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.68837 | 0.687669 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0734 | −1.33754 | −0.668772 | − | 0.743467i | \(-0.733180\pi\) | ||||
−0.668772 | + | 0.743467i | \(0.733180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.42032 | − | 12.8524i | −0.648316 | − | 1.12292i | −0.983525 | − | 0.180773i | \(-0.942140\pi\) |
0.335208 | − | 0.942144i | \(-0.391193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.0938 | − | 3.45745i | −0.961959 | − | 0.299799i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0779 | + | 17.4555i | −0.861017 | + | 1.49132i | 0.00993230 | + | 0.999951i | \(0.496838\pi\) |
−0.870949 | + | 0.491374i | \(0.836495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.91552 | − | 17.1742i | 0.841023 | − | 1.45669i | −0.0480074 | − | 0.998847i | \(-0.515287\pi\) |
0.889031 | − | 0.457848i | \(-0.151380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.76056 | − | 6.51347i | −0.314473 | − | 0.544684i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.86557 | − | 13.6236i | 0.653200 | − | 1.13138i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.65166 | + | 14.9851i | 0.708772 | + | 1.22763i | 0.965313 | + | 0.261096i | \(0.0840838\pi\) |
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.99488 | + | 3.45523i | −0.162341 | + | 0.281183i | −0.935708 | − | 0.352776i | \(-0.885238\pi\) |
0.773367 | + | 0.633959i | \(0.218571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.15781 | − | 7.20153i | −0.333963 | − | 0.578441i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.1988 | −1.93127 | −0.965637 | − | 0.259896i | \(-0.916312\pi\) | ||||
−0.965637 | + | 0.259896i | \(0.916312\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.12073 | − | 8.41345i | 0.718814 | − | 0.663073i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.34498 | + | 4.06162i | −0.183673 | + | 0.318131i | −0.943129 | − | 0.332428i | \(-0.892132\pi\) |
0.759456 | + | 0.650559i | \(0.225465\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.12627 | + | 10.6110i | −0.474065 | + | 0.821104i | −0.999559 | − | 0.0296928i | \(-0.990547\pi\) |
0.525494 | + | 0.850797i | \(0.323880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.69072 | − | 15.0528i | −0.668517 | − | 1.15791i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.11006 | 0.616596 | 0.308298 | − | 0.951290i | \(-0.400241\pi\) | ||||
0.308298 | + | 0.951290i | \(0.400241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.35072 | + | 1.66757i | 0.404476 | + | 0.126057i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.91636 | + | 8.51538i | 0.367466 | + | 0.636469i | 0.989169 | − | 0.146784i | \(-0.0468922\pi\) |
−0.621703 | + | 0.783253i | \(0.713559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8876 | 1.18092 | 0.590458 | − | 0.807068i | \(-0.298947\pi\) | ||||
0.590458 | + | 0.807068i | \(0.298947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.8419 | −1.23824 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.38209 | −0.247323 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.21898 | −0.160560 | −0.0802800 | − | 0.996772i | \(-0.525581\pi\) | ||||
−0.0802800 | + | 0.996772i | \(0.525581\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.84168 | 0.420493 | 0.210247 | − | 0.977648i | \(-0.432573\pi\) | ||||
0.210247 | + | 0.977648i | \(0.432573\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.93695 | −0.138002 | −0.0690010 | − | 0.997617i | \(-0.521981\pi\) | ||||
−0.0690010 | + | 0.997617i | \(0.521981\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.84540 | − | 3.19633i | −0.130817 | − | 0.226582i | 0.793175 | − | 0.608994i | \(-0.208427\pi\) |
−0.923992 | + | 0.382412i | \(0.875093\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.4664 | + | 10.5772i | −0.804783 | + | 0.742375i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.40073 | −0.516889 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.99647 | + | 5.19004i | 0.207270 | + | 0.359002i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.67097 | − | 9.82241i | 0.390406 | − | 0.676202i | −0.602097 | − | 0.798423i | \(-0.705668\pi\) |
0.992503 | + | 0.122220i | \(0.0390014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.0170 | + | 22.5460i | −0.887749 | + | 1.53763i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.81151 | + | 8.04478i | 0.122973 | + | 0.546115i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.6619 | −0.919000 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.965547 | + | 1.67238i | 0.0646578 | + | 0.111991i | 0.896542 | − | 0.442958i | \(-0.146071\pi\) |
−0.831884 | + | 0.554949i | \(0.812738\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.86413 | + | 17.0852i | −0.654705 | + | 1.13398i | 0.327262 | + | 0.944934i | \(0.393874\pi\) |
−0.981968 | + | 0.189049i | \(0.939459\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.2098 | − | 22.8801i | −0.872931 | − | 1.51196i | −0.858951 | − | 0.512058i | \(-0.828883\pi\) |
−0.0139803 | − | 0.999902i | \(-0.504450\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.24071 | − | 7.34513i | 0.277818 | − | 0.481196i | −0.693024 | − | 0.720915i | \(-0.743722\pi\) |
0.970842 | + | 0.239719i | \(0.0770553\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.4069 | − | 23.2215i | −0.874571 | − | 1.51480i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.08023 | + | 13.9954i | −0.522667 | + | 0.905286i | 0.476985 | + | 0.878911i | \(0.341730\pi\) |
−0.999652 | + | 0.0263743i | \(0.991604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.48677 | + | 9.50336i | −0.353434 | + | 0.612165i | −0.986849 | − | 0.161647i | \(-0.948319\pi\) |
0.633415 | + | 0.773812i | \(0.281653\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.3693 | − | 10.6104i | −0.981911 | − | 0.677875i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1042 | + | 20.9651i | 0.770172 | + | 1.33398i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.85873 | 0.180442 | 0.0902208 | − | 0.995922i | \(-0.471243\pi\) | ||||
0.0902208 | + | 0.995922i | \(0.471243\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.39959 | −0.402339 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.2938 | + | 21.2934i | 0.766864 | + | 1.32825i | 0.939256 | + | 0.343218i | \(0.111517\pi\) |
−0.172392 | + | 0.985028i | \(0.555150\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.9450 | + | 4.96933i | 0.990773 | + | 0.308779i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.478986 | + | 0.829628i | −0.0295355 | + | 0.0511570i | −0.880415 | − | 0.474203i | \(-0.842736\pi\) |
0.850880 | + | 0.525360i | \(0.176069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.94394 | + | 6.83111i | −0.242274 | + | 0.419632i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.31005 | − | 14.3934i | −0.506673 | − | 0.877583i | −0.999970 | − | 0.00772245i | \(-0.997542\pi\) |
0.493297 | − | 0.869861i | \(-0.335791\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.21801 | + | 12.5020i | −0.438463 | + | 0.759440i | −0.997571 | − | 0.0696545i | \(-0.977810\pi\) |
0.559108 | + | 0.829095i | \(0.311144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.44524 | − | 2.50323i | −0.0871511 | − | 0.150950i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.23321 | − | 3.86804i | 0.134181 | − | 0.232408i | −0.791103 | − | 0.611682i | \(-0.790493\pi\) |
0.925284 | + | 0.379275i | \(0.123826\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.62617 | − | 4.54867i | −0.156664 | − | 0.271351i | 0.776999 | − | 0.629501i | \(-0.216741\pi\) |
−0.933664 | + | 0.358151i | \(0.883407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.3150 | −0.672608 | −0.336304 | − | 0.941754i | \(-0.609177\pi\) | ||||
−0.336304 | + | 0.941754i | \(0.609177\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.00658 | + | 2.18363i | 0.413585 | + | 0.128896i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.42826 | − | 9.40201i | 0.319309 | − | 0.553060i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.38422 | − | 9.32574i | 0.314549 | − | 0.544815i | −0.664792 | − | 0.747028i | \(-0.731480\pi\) |
0.979342 | + | 0.202213i | \(0.0648133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.74397 | + | 8.21679i | 0.276204 | + | 0.478400i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.8511 | −1.49501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.9761 | − | 17.5045i | 1.09376 | − | 1.00894i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.76901 | + | 3.06402i | 0.101293 | + | 0.175445i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.42151 | −0.537714 | −0.268857 | − | 0.963180i | \(-0.586646\pi\) | ||||
−0.268857 | + | 0.963180i | \(0.586646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3151 | −0.641619 | −0.320809 | − | 0.947144i | \(-0.603955\pi\) | ||||
−0.320809 | + | 0.947144i | \(0.603955\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.6862 | 1.22578 | 0.612889 | − | 0.790169i | \(-0.290007\pi\) | ||||
0.612889 | + | 0.790169i | \(0.290007\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.2174 | 1.41635 | 0.708174 | − | 0.706038i | \(-0.249519\pi\) | ||||
0.708174 | + | 0.706038i | \(0.249519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.04543 | 0.450458 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8860 | 0.605715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.83802 | − | 10.1118i | −0.323835 | − | 0.560899i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.84125 | + | 25.9405i | 0.322038 | + | 1.43015i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0245 | 0.935753 | 0.467876 | − | 0.883794i | \(-0.345019\pi\) | ||||
0.467876 | + | 0.883794i | \(0.345019\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0706 | − | 19.1748i | −0.604851 | − | 1.04763i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.85166 | − | 11.8674i | 0.373233 | − | 0.646459i | −0.616827 | − | 0.787098i | \(-0.711582\pi\) |
0.990061 | + | 0.140639i | \(0.0449157\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.12644 | − | 3.68310i | 0.115153 | − | 0.199451i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4201 | + | 14.5802i | 0.616628 | + | 0.787254i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.4366 | 1.31182 | 0.655912 | − | 0.754837i | \(-0.272284\pi\) | ||||
0.655912 | + | 0.754837i | \(0.272284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4881 | + | 19.8979i | 0.614943 | + | 1.06511i | 0.990394 | + | 0.138271i | \(0.0441544\pi\) |
−0.375451 | + | 0.926842i | \(0.622512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0152 | − | 20.8110i | 0.639507 | − | 1.10766i | −0.346034 | − | 0.938222i | \(-0.612472\pi\) |
0.985541 | − | 0.169437i | \(-0.0541948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.4175 | + | 28.4359i | 0.871349 | + | 1.50922i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.84234 | + | 17.0474i | −0.519459 | + | 0.899729i | 0.480285 | + | 0.877112i | \(0.340533\pi\) |
−0.999744 | + | 0.0226169i | \(0.992800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.144819 | − | 0.250833i | −0.00762204 | − | 0.0132018i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.97690 | − | 5.15613i | 0.155818 | − | 0.269884i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.10028 | + | 12.2980i | −0.370632 | + | 0.641953i | −0.989663 | − | 0.143414i | \(-0.954192\pi\) |
0.619031 | + | 0.785366i | \(0.287525\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.74946 | − | 5.30361i | 0.298497 | − | 0.275350i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2335 | + | 24.6531i | 0.736980 | + | 1.27649i | 0.953849 | + | 0.300287i | \(0.0970823\pi\) |
−0.216869 | + | 0.976201i | \(0.569584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.4994 | 1.67381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.25098 | 0.218358 | 0.109179 | − | 0.994022i | \(-0.465178\pi\) | ||||
0.109179 | + | 0.994022i | \(0.465178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.9214 | + | 31.0407i | 0.915740 | + | 1.58611i | 0.805814 | + | 0.592168i | \(0.201728\pi\) |
0.109926 | + | 0.993940i | \(0.464939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.11593 | + | 9.39669i | 0.107838 | + | 0.478900i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.8972 | + | 27.5348i | −0.806020 | + | 1.39607i | 0.109580 | + | 0.993978i | \(0.465049\pi\) |
−0.915600 | + | 0.402090i | \(0.868284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.81235 | + | 10.0673i | −0.293943 | + | 0.509125i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.1163 | − | 29.6462i | −0.861213 | − | 1.49166i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.07669 | − | 5.32899i | 0.154415 | − | 0.267454i | −0.778431 | − | 0.627730i | \(-0.783984\pi\) |
0.932846 | + | 0.360276i | \(0.117317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.41146 | − | 12.8370i | −0.370111 | − | 0.641051i | 0.619471 | − | 0.785019i | \(-0.287347\pi\) |
−0.989582 | + | 0.143968i | \(0.954014\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.58974 | − | 14.8779i | 0.427885 | − | 0.741119i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.30677 | − | 7.45954i | −0.213479 | − | 0.369756i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.4443 | 1.06035 | 0.530177 | − | 0.847887i | \(-0.322125\pi\) | ||||
0.530177 | + | 0.847887i | \(0.322125\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.06689 | − | 9.17892i | −0.101705 | − | 0.451665i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7652 | + | 23.8421i | −0.675708 | + | 1.17036i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2332 | − | 22.9205i | 0.646483 | − | 1.11974i | −0.337474 | − | 0.941335i | \(-0.609572\pi\) |
0.983957 | − | 0.178406i | \(-0.0570942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.54824 | − | 14.8060i | −0.416616 | − | 0.721600i | 0.578981 | − | 0.815341i | \(-0.303451\pi\) |
−0.995597 | + | 0.0937415i | \(0.970117\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.25048 | −0.254686 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.770739 | − | 3.42279i | −0.0372987 | − | 0.165640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0292 | − | 20.8352i | −0.579425 | − | 1.00359i | −0.995545 | − | 0.0942846i | \(-0.969944\pi\) |
0.416120 | − | 0.909310i | \(-0.363390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.58345 | −0.316380 | −0.158190 | − | 0.987409i | \(-0.550566\pi\) | ||||
−0.158190 | + | 0.987409i | \(0.550566\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.5985 | 0.985362 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.2654 | −1.01494 | −0.507472 | − | 0.861668i | \(-0.669420\pi\) | ||||
−0.507472 | + | 0.861668i | \(0.669420\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.943448 | −0.0448246 | −0.0224123 | − | 0.999749i | \(-0.507135\pi\) | ||||
−0.0224123 | + | 0.999749i | \(0.507135\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.2560 | −1.95572 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.7959 | 0.839842 | 0.419921 | − | 0.907561i | \(-0.362058\pi\) | ||||
0.419921 | + | 0.907561i | \(0.362058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.89249 | − | 3.27789i | −0.0891139 | − | 0.154350i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.54729 | + | 37.9578i | 0.400703 | + | 1.77949i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.7770 | −0.644462 | −0.322231 | − | 0.946661i | \(-0.604433\pi\) | ||||
−0.322231 | + | 0.946661i | \(0.604433\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.97576 | + | 5.15417i | 0.138595 | + | 0.240054i | 0.926965 | − | 0.375148i | \(-0.122408\pi\) |
−0.788370 | + | 0.615201i | \(0.789075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7618 | − | 30.7644i | 0.825463 | − | 1.42974i | −0.0761023 | − | 0.997100i | \(-0.524248\pi\) |
0.901565 | − | 0.432643i | \(-0.142419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2574 | − | 21.2305i | 0.567207 | − | 0.982431i | −0.429634 | − | 0.903003i | \(-0.641357\pi\) |
0.996841 | − | 0.0794277i | \(-0.0253093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.82333 | + | 21.4200i | 0.222721 | + | 0.989086i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.3146 | −0.612207 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.65183 | + | 8.05720i | 0.213440 | + | 0.369690i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.61760 | + | 16.6582i | −0.439439 | + | 0.761131i | −0.997646 | − | 0.0685707i | \(-0.978156\pi\) |
0.558207 | + | 0.829702i | \(0.311489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.3971 | − | 30.1327i | −0.793241 | − | 1.37393i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.81328 | − | 11.8009i | 0.309375 | − | 0.535853i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.3089 | − | 21.3197i | −0.557770 | − | 0.966086i | −0.997682 | − | 0.0680455i | \(-0.978324\pi\) |
0.439912 | − | 0.898041i | \(-0.355010\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.73086 | − | 16.8543i | 0.439147 | − | 0.760626i | −0.558476 | − | 0.829520i | \(-0.688614\pi\) |
0.997624 | + | 0.0688947i | \(0.0219472\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.30717 | − | 12.6564i | 0.329098 | − | 0.570015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.15292 | − | 31.7655i | −0.320852 | − | 1.42488i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.58890 | − | 6.21617i | −0.160661 | − | 0.278274i | 0.774445 | − | 0.632642i | \(-0.218029\pi\) |
−0.935106 | + | 0.354368i | \(0.884696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.1112 | 0.985889 | 0.492945 | − | 0.870061i | \(-0.335921\pi\) | ||||
0.492945 | + | 0.870061i | \(0.335921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.19021 | −0.319960 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.6787 | − | 27.1564i | −0.694947 | − | 1.20368i | −0.970198 | − | 0.242312i | \(-0.922094\pi\) |
0.275251 | − | 0.961372i | \(-0.411239\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.33970 | + | 4.00318i | −0.191977 | + | 0.177090i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.3707 | − | 30.0869i | 0.765444 | − | 1.32579i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.85675 | − | 11.8762i | 0.301559 | − | 0.522316i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.76588 | − | 3.05859i | −0.0773645 | − | 0.133999i | 0.824748 | − | 0.565501i | \(-0.191317\pi\) |
−0.902112 | + | 0.431502i | \(0.857984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.03821 | − | 12.1905i | 0.307759 | − | 0.533055i | −0.670113 | − | 0.742259i | \(-0.733754\pi\) |
0.977872 | + | 0.209205i | \(0.0670875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.86263 | − | 6.69027i | −0.168259 | − | 0.291433i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.501870 | − | 0.869264i | 0.0218204 | − | 0.0377941i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.64469 | − | 13.2410i | −0.331128 | − | 0.573531i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.99086 | −0.345475 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.769313 | − | 9.52056i | 0.0331367 | − | 0.410080i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5799 | − | 20.0569i | 0.497858 | − | 0.862315i | −0.502139 | − | 0.864787i | \(-0.667454\pi\) |
0.999997 | + | 0.00247207i | \(0.000786884\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.7155 | + | 46.2725i | −1.14436 | + | 1.98210i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.76832 | + | 9.99102i | 0.246635 | + | 0.427185i | 0.962590 | − | 0.270962i | \(-0.0873417\pi\) |
−0.715955 | + | 0.698147i | \(0.754008\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.8961 | −1.10321 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.45737 | + | 33.1176i | 0.317120 | + | 1.40830i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.04108 | + | 1.80321i | 0.0441122 | + | 0.0764045i | 0.887238 | − | 0.461311i | \(-0.152621\pi\) |
−0.843126 | + | 0.537716i | \(0.819287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53.7842 | −2.27483 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.70807 | −0.282711 | −0.141356 | − | 0.989959i | \(-0.545146\pi\) | ||||
−0.141356 | + | 0.989959i | \(0.545146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.2548 | 1.39904 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.02223 | 0.336309 | 0.168155 | − | 0.985761i | \(-0.446219\pi\) | ||||
0.168155 | + | 0.985761i | \(0.446219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.68430 | −0.279729 | −0.139865 | − | 0.990171i | \(-0.544667\pi\) | ||||
−0.139865 | + | 0.990171i | \(0.544667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.93496 | −0.414316 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0088 | − | 24.2639i | −0.583193 | − | 1.01012i | −0.995098 | − | 0.0988925i | \(-0.968470\pi\) |
0.411906 | − | 0.911227i | \(-0.364863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.0669 | − | 18.5108i | 0.832514 | − | 0.767956i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.03413 | −0.167076 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.35952 | − | 5.81886i | −0.138662 | − | 0.240170i | 0.788328 | − | 0.615255i | \(-0.210947\pi\) |
−0.926990 | + | 0.375085i | \(0.877614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.84443 | + | 11.8549i | −0.282020 | + | 0.488473i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.19462 | − | 5.53325i | 0.131187 | − | 0.227223i | −0.792947 | − | 0.609290i | \(-0.791454\pi\) |
0.924135 | + | 0.382067i | \(0.124788\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.7038 | + | 5.20583i | 0.684791 | + | 0.213418i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.92196 | −0.241965 | −0.120982 | − | 0.992655i | \(-0.538604\pi\) | ||||
−0.120982 | + | 0.992655i | \(0.538604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.97104 | − | 3.41393i | −0.0804002 | − | 0.139257i | 0.823022 | − | 0.568010i | \(-0.192287\pi\) |
−0.903422 | + | 0.428753i | \(0.858953\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.1903 | + | 21.1142i | −0.495607 | + | 0.858416i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.54775 | − | 6.14489i | −0.143999 | − | 0.249413i | 0.785000 | − | 0.619496i | \(-0.212663\pi\) |
−0.928999 | + | 0.370082i | \(0.879330\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.6978 | − | 47.9739i | 1.12053 | − | 1.94082i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.87000 | + | 11.8992i | 0.277477 | + | 0.480604i | 0.970757 | − | 0.240064i | \(-0.0771685\pi\) |
−0.693280 | + | 0.720668i | \(0.743835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.3605 | − | 28.3372i | 0.658649 | − | 1.14081i | −0.322317 | − | 0.946632i | \(-0.604462\pi\) |
0.980966 | − | 0.194182i | \(-0.0622051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3090 | − | 19.5878i | 0.454547 | − | 0.787299i | −0.544115 | − | 0.839011i | \(-0.683134\pi\) |
0.998662 | + | 0.0517121i | \(0.0164678\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.0588 | + | 12.1729i | 1.56486 | + | 0.487695i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5522 | + | 26.9371i | 0.622086 | + | 1.07749i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.6463 | −0.623858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.9355 | 1.74905 | 0.874523 | − | 0.484984i | \(-0.161175\pi\) | ||||
0.874523 | + | 0.484984i | \(0.161175\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.1080 | − | 34.8281i | −0.797962 | − | 1.38211i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.10763 | − | 38.4582i | 0.123129 | − | 1.52377i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.9297 | − | 34.5193i | 0.787178 | − | 1.36343i | −0.140512 | − | 0.990079i | \(-0.544875\pi\) |
0.927689 | − | 0.373353i | \(-0.121792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.24049 | + | 16.0050i | −0.364410 | + | 0.631176i | −0.988681 | − | 0.150032i | \(-0.952062\pi\) |
0.624272 | + | 0.781207i | \(0.285396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.76068 | + | 15.1739i | 0.344418 | + | 0.596549i | 0.985248 | − | 0.171134i | \(-0.0547430\pi\) |
−0.640830 | + | 0.767683i | \(0.721410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.42622 | + | 4.20234i | −0.0952376 | + | 0.164956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.7027 | + | 23.7338i | 0.536230 | + | 0.928777i | 0.999103 | + | 0.0423525i | \(0.0134852\pi\) |
−0.462873 | + | 0.886425i | \(0.653181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.7975 | − | 34.2904i | 0.773554 | − | 1.33984i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.2580 | − | 28.1597i | −0.633322 | − | 1.09695i | −0.986868 | − | 0.161529i | \(-0.948358\pi\) |
0.353546 | − | 0.935417i | \(-0.384976\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.8671 | 1.51176 | 0.755878 | − | 0.654712i | \(-0.227210\pi\) | ||||
0.755878 | + | 0.654712i | \(0.227210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.81061 | − | 30.2454i | −0.264104 | − | 1.17287i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8266 | − | 23.9484i | 0.535369 | − | 0.927286i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.904731 | + | 1.56704i | −0.0349268 | + | 0.0604949i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.50978 | − | 7.81117i | −0.173839 | − | 0.301099i | 0.765920 | − | 0.642936i | \(-0.222284\pi\) |
−0.939759 | + | 0.341838i | \(0.888951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.8287 | −0.723646 | −0.361823 | − | 0.932247i | \(-0.617845\pi\) | ||||
−0.361823 | + | 0.932247i | \(0.617845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.93236 | + | 9.16215i | −0.381169 | + | 0.351611i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.35476 | + | 9.27471i | 0.204894 | + | 0.354887i | 0.950099 | − | 0.311949i | \(-0.100982\pi\) |
−0.745205 | + | 0.666836i | \(0.767648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −53.7763 | −2.05468 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.2958 | −0.620821 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.04553 | −0.191941 | −0.0959705 | − | 0.995384i | \(-0.530595\pi\) | ||||
−0.0959705 | + | 0.995384i | \(0.530595\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 52.9096 | 2.00697 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.87533 | −0.260422 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.9138 | −1.69637 | −0.848186 | − | 0.529698i | \(-0.822305\pi\) | ||||
−0.848186 | + | 0.529698i | \(0.822305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.8623 | + | 24.0102i | 0.522827 | + | 0.905563i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.80727 | + | 2.12152i | 0.256014 | + | 0.0797879i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.45317 | 0.279910 | 0.139955 | − | 0.990158i | \(-0.455304\pi\) | ||||
0.139955 | + | 0.990158i | \(0.455304\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.30887 | − | 12.6593i | −0.273719 | − | 0.474096i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.0332 | − | 17.3781i | 0.375222 | − | 0.649903i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.5574 | − | 37.3385i | 0.803954 | − | 1.39249i | −0.113040 | − | 0.993590i | \(-0.536059\pi\) |
0.916995 | − | 0.398899i | \(-0.130608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.3229 | + | 23.3592i | −0.943074 | + | 0.869943i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.4900 | 0.463868 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.389926 | + | 0.675372i | 0.0144616 | + | 0.0250482i | 0.873166 | − | 0.487424i | \(-0.162063\pi\) |
−0.858704 | + | 0.512472i | \(0.828730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0928 | + | 20.9454i | −0.447270 | + | 0.774694i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.83859 | + | 13.5768i | 0.289525 | + | 0.501472i | 0.973696 | − | 0.227849i | \(-0.0731694\pi\) |
−0.684171 | + | 0.729321i | \(0.739836\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.66187 | − | 9.80664i | 0.208558 | − | 0.361232i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.87450 | − | 15.3711i | −0.326454 | − | 0.565434i | 0.655352 | − | 0.755324i | \(-0.272520\pi\) |
−0.981805 | + | 0.189889i | \(0.939187\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.74308 | + | 6.48321i | −0.137320 | + | 0.237846i | −0.926481 | − | 0.376340i | \(-0.877182\pi\) |
0.789161 | + | 0.614186i | \(0.210516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.0828 | + | 39.9806i | −0.845688 | + | 1.46477i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.56528 | + | 2.35775i | 0.276429 | + | 0.0861505i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.6800 | + | 20.2303i | 0.426208 | + | 0.738213i | 0.996532 | − | 0.0832060i | \(-0.0265160\pi\) |
−0.570325 | + | 0.821419i | \(0.693183\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.6447 | −0.387402 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2350 | 1.13525 | 0.567627 | − | 0.823286i | \(-0.307862\pi\) | ||||
0.567627 | + | 0.823286i | \(0.307862\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.30735 | + | 14.3887i | 0.301141 | + | 0.521592i | 0.976395 | − | 0.215994i | \(-0.0692992\pi\) |
−0.675254 | + | 0.737586i | \(0.735966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.9457 | − | 35.9256i | 1.40993 | − | 1.30059i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.80070 | + | 16.9753i | −0.353883 | + | 0.612943i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.3794 | − | 31.8340i | 0.662777 | − | 1.14796i | −0.317106 | − | 0.948390i | \(-0.602711\pi\) |
0.979883 | − | 0.199573i | \(-0.0639556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.77690 | − | 8.27382i | −0.171813 | − | 0.297589i | 0.767241 | − | 0.641359i | \(-0.221629\pi\) |
−0.939054 | + | 0.343770i | \(0.888296\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.30116 | − | 5.71778i | 0.118581 | − | 0.205389i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.09141 | + | 10.5506i | 0.218247 | + | 0.378016i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.39645 | + | 14.5431i | −0.300448 | + | 0.520392i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.2814 | − | 55.9130i | −1.15217 | − | 1.99562i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.2677 | 0.722466 | 0.361233 | − | 0.932476i | \(-0.382356\pi\) | ||||
0.361233 | + | 0.932476i | \(0.382356\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.4837 | − | 9.81203i | −1.11943 | − | 0.348876i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.65465 | + | 6.33004i | −0.129780 | + | 0.224786i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.4236 | + | 37.1068i | −0.758863 | + | 1.31439i | 0.184567 | + | 0.982820i | \(0.440912\pi\) |
−0.943431 | + | 0.331570i | \(0.892422\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.4551 | − | 21.5729i | −0.440630 | − | 0.763194i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.04497 | 0.107455 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.6070 | + | 9.85047i | 1.11400 | + | 0.347183i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4750 | + | 18.1432i | 0.368282 | + | 0.637883i | 0.989297 | − | 0.145916i | \(-0.0466129\pi\) |
−0.621015 | + | 0.783798i | \(0.713280\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0129 | 0.667633 | 0.333817 | − | 0.942638i | \(-0.391663\pi\) | ||||
0.333817 | + | 0.942638i | \(0.391663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.5129 | −0.438307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.8561 | 1.49935 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.3905 | 1.16534 | 0.582669 | − | 0.812710i | \(-0.302008\pi\) | ||||
0.582669 | + | 0.812710i | \(0.302008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.04079 | 0.315142 | 0.157571 | − | 0.987508i | \(-0.449634\pi\) | ||||
0.157571 | + | 0.987508i | \(0.449634\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.4071 | 0.779172 | 0.389586 | − | 0.920990i | \(-0.372618\pi\) | ||||
0.389586 | + | 0.920990i | \(0.372618\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.4090 | − | 19.7610i | −0.396252 | − | 0.686328i | 0.597008 | − | 0.802235i | \(-0.296356\pi\) |
−0.993260 | + | 0.115907i | \(0.963023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.2782 | − | 9.85716i | −0.494711 | − | 0.341530i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.6900 | −1.13128 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.05060 | − | 13.9441i | −0.277938 | − | 0.481402i | 0.692934 | − | 0.721001i | \(-0.256318\pi\) |
−0.970872 | + | 0.239598i | \(0.922984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.88254 | + | 4.99271i | −0.0993980 | + | 0.172162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.1870 | − | 40.1611i | 0.797657 | − | 1.38158i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.7710 | − | 16.3929i | 0.610618 | − | 0.563267i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.6059 | −1.01488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7818 | + | 22.1387i | 0.437639 | + | 0.758013i | 0.997507 | − | 0.0705689i | \(-0.0224815\pi\) |
−0.559868 | + | 0.828582i | \(0.689148\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.3278 | + | 45.6011i | −0.899340 | + | 1.55770i | −0.0710001 | + | 0.997476i | \(0.522619\pi\) |
−0.828340 | + | 0.560226i | \(0.810714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.4431 | − | 26.7482i | −0.526912 | − | 0.912638i | −0.999508 | − | 0.0313592i | \(-0.990016\pi\) |
0.472596 | − | 0.881279i | \(-0.343317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.929596 | + | 1.61011i | −0.0316438 | + | 0.0548087i | −0.881414 | − | 0.472345i | \(-0.843408\pi\) |
0.849770 | + | 0.527154i | \(0.176741\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8189 | + | 18.7389i | 0.367853 | + | 0.637141i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.75383 | − | 15.1621i | 0.296953 | − | 0.514338i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.8711 | − | 39.6138i | 0.774956 | − | 1.34226i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.46858 | − | 19.8446i | −0.151066 | − | 0.670871i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.65184 | + | 11.5213i | 0.224617 | + | 0.389048i | 0.956204 | − | 0.292700i | \(-0.0945536\pi\) |
−0.731588 | + | 0.681747i | \(0.761220\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.2210 | −0.714954 | −0.357477 | − | 0.933922i | \(-0.616363\pi\) | ||||
−0.357477 | + | 0.933922i | \(0.616363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.8289 | 1.67687 | 0.838437 | − | 0.544998i | \(-0.183470\pi\) | ||||
0.838437 | + | 0.544998i | \(0.183470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.886358 | + | 1.53522i | 0.0297610 | + | 0.0515475i | 0.880522 | − | 0.474005i | \(-0.157192\pi\) |
−0.850761 | + | 0.525552i | \(0.823859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.76084 | + | 38.9062i | 0.293829 | + | 1.30487i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.0700 | + | 38.2264i | −0.738544 | + | 1.27920i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.1169 | + | 22.7192i | −0.438450 | + | 0.759419i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.18855 | + | 15.9150i | 0.306455 | + | 0.530796i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.66395 | + | 6.34615i | −0.122064 | + | 0.211421i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.1942 | + | 36.7094i | 0.704519 | + | 1.22026i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.28748 | + | 9.15818i | −0.175568 | + | 0.304092i | −0.940358 | − | 0.340188i | \(-0.889509\pi\) |
0.764790 | + | 0.644280i | \(0.222843\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.2693 | + | 26.4473i | 0.505896 | + | 0.876237i | 0.999977 | + | 0.00682127i | \(0.00217130\pi\) |
−0.494081 | + | 0.869416i | \(0.664495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.0800 | −0.465980 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.8608 | + | 26.6227i | −0.953066 | + | 0.879160i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.552490 | − | 0.956940i | 0.0182249 | − | 0.0315665i | −0.856769 | − | 0.515700i | \(-0.827532\pi\) |
0.874994 | + | 0.484134i | \(0.160865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.9174 | + | 58.7466i | −1.11640 | + | 1.93367i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.68598 | − | 11.5805i | −0.219834 | − | 0.380763i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.27458 | 0.173053 | 0.0865266 | − | 0.996250i | \(-0.472423\pi\) | ||||
0.0865266 | + | 0.996250i | \(0.472423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.47621 | + | 30.6441i | −0.0811545 | + | 1.00432i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.51174 | − | 7.81456i | −0.147550 | − | 0.255564i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7481 | 0.579806 | 0.289903 | − | 0.957056i | \(-0.406377\pi\) | ||||
0.289903 | + | 0.957056i | \(0.406377\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.7367 | 0.904192 | 0.452096 | − | 0.891969i | \(-0.350677\pi\) | ||||
0.452096 | + | 0.891969i | \(0.350677\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.0095 | −0.423647 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.2766 | 0.496422 | 0.248211 | − | 0.968706i | \(-0.420157\pi\) | ||||
0.248211 | + | 0.968706i | \(0.420157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.3001 | 0.399279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.3569 | 0.821390 | 0.410695 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410695 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.96014 | − | 5.12712i | −0.0957880 | − | 0.165910i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.9122 | + | 15.8670i | 1.64404 | + | 0.512373i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2857 | −0.686636 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.79286 | + | 13.4976i | 0.250861 | + | 0.434504i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5566 | − | 23.4808i | 0.435952 | − | 0.755090i | −0.561421 | − | 0.827530i | \(-0.689745\pi\) |
0.997373 | + | 0.0724398i | \(0.0230785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.1555 | + | 36.6423i | −0.678911 | + | 1.17591i | 0.296398 | + | 0.955064i | \(0.404214\pi\) |
−0.975309 | + | 0.220844i | \(0.929119\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.0917 | − | 15.6113i | −1.60587 | − | 0.500475i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.37816 | −0.0760841 | −0.0380421 | − | 0.999276i | \(-0.512112\pi\) | ||||
−0.0380421 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5499 | − | 18.2729i | −0.337175 | − | 0.584004i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.64641 | + | 2.85167i | −0.0525124 | + | 0.0909542i | −0.891087 | − | 0.453833i | \(-0.850056\pi\) |
0.838574 | + | 0.544787i | \(0.183390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.58391 | − | 4.47547i | −0.0823303 | − | 0.142600i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.8821 | + | 39.6329i | −0.727607 | + | 1.26025i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5482 | + | 51.1790i | 0.938630 | + | 1.62575i | 0.768030 | + | 0.640414i | \(0.221237\pi\) |
0.170600 | + | 0.985340i | \(0.445429\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.92356 | − | 8.52786i | 0.156087 | − | 0.270351i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.48987 | − | 14.7049i | 0.268877 | − | 0.465708i | −0.699695 | − | 0.714441i | \(-0.746681\pi\) |
0.968572 | + | 0.248733i | \(0.0800142\pi\) | |||||||
\(998\) | 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 | 3024.2.q.k.2305.10 | 22 | ||
3.2 | odd | 2 | 1008.2.q.k.625.6 | 22 | |||
4.3 | odd | 2 | 1512.2.q.c.793.10 | 22 | |||
7.4 | even | 3 | 3024.2.t.l.1873.2 | 22 | |||
9.2 | odd | 6 | 1008.2.t.k.961.3 | 22 | |||
9.7 | even | 3 | 3024.2.t.l.289.2 | 22 | |||
12.11 | even | 2 | 504.2.q.d.121.6 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.t.k.193.3 | 22 | |||
28.11 | odd | 6 | 1512.2.t.d.361.2 | 22 | |||
36.7 | odd | 6 | 1512.2.t.d.289.2 | 22 | |||
36.11 | even | 6 | 504.2.t.d.457.9 | yes | 22 | ||
63.11 | odd | 6 | 1008.2.q.k.529.6 | 22 | |||
63.25 | even | 3 | inner | 3024.2.q.k.2881.10 | 22 | ||
84.11 | even | 6 | 504.2.t.d.193.9 | yes | 22 | ||
252.11 | even | 6 | 504.2.q.d.25.6 | ✓ | 22 | ||
252.151 | odd | 6 | 1512.2.q.c.1369.10 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.6 | ✓ | 22 | 252.11 | even | 6 | ||
504.2.q.d.121.6 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.d.193.9 | yes | 22 | 84.11 | even | 6 | ||
504.2.t.d.457.9 | yes | 22 | 36.11 | even | 6 | ||
1008.2.q.k.529.6 | 22 | 63.11 | odd | 6 | |||
1008.2.q.k.625.6 | 22 | 3.2 | odd | 2 | |||
1008.2.t.k.193.3 | 22 | 21.11 | odd | 6 | |||
1008.2.t.k.961.3 | 22 | 9.2 | odd | 6 | |||
1512.2.q.c.793.10 | 22 | 4.3 | odd | 2 | |||
1512.2.q.c.1369.10 | 22 | 252.151 | odd | 6 | |||
1512.2.t.d.289.2 | 22 | 36.7 | odd | 6 | |||
1512.2.t.d.361.2 | 22 | 28.11 | odd | 6 | |||
3024.2.q.k.2305.10 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.k.2881.10 | 22 | 63.25 | even | 3 | inner | ||
3024.2.t.l.289.2 | 22 | 9.7 | even | 3 | |||
3024.2.t.l.1873.2 | 22 | 7.4 | even | 3 |