Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.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: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.961 |
Dual form | 1960.2.q.s.361.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.780776 | + | 1.35234i | 0.450781 | + | 0.780776i | 0.998435 | − | 0.0559290i | \(-0.0178120\pi\) |
−0.547653 | + | 0.836705i | \(0.684479\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.280776 | − | 0.486319i | 0.0935921 | − | 0.162106i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.780776 | − | 1.35234i | −0.235413 | − | 0.407747i | 0.723980 | − | 0.689821i | \(-0.242311\pi\) |
−0.959393 | + | 0.282074i | \(0.908978\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.68466 | 1.85399 | 0.926995 | − | 0.375073i | \(-0.122382\pi\) | ||||
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.78078 | − | 6.54850i | −0.916973 | − | 1.58824i | −0.803987 | − | 0.594647i | \(-0.797292\pi\) |
−0.112986 | − | 0.993597i | \(-0.536042\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.56155 | − | 6.16879i | 0.817076 | − | 1.41522i | −0.0907512 | − | 0.995874i | \(-0.528927\pi\) |
0.907827 | − | 0.419344i | \(-0.137740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.56155 | + | 2.70469i | −0.325606 | + | 0.563967i | −0.981635 | − | 0.190769i | \(-0.938902\pi\) |
0.656029 | + | 0.754736i | \(0.272235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.438447 | 0.0814176 | 0.0407088 | − | 0.999171i | \(-0.487038\pi\) | ||||
0.0407088 | + | 0.999171i | \(0.487038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.12311 | − | 5.40938i | −0.560926 | − | 0.971553i | −0.997416 | − | 0.0718436i | \(-0.977112\pi\) |
0.436490 | − | 0.899709i | \(-0.356222\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.21922 | − | 2.11176i | 0.212240 | − | 0.367610i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.12311 | − | 7.14143i | 0.677834 | − | 1.17404i | −0.297797 | − | 0.954629i | \(-0.596252\pi\) |
0.975632 | − | 0.219414i | \(-0.0704147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.21922 | + | 9.03996i | 0.835745 | + | 1.44755i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.12311 | −0.175400 | −0.0876998 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0876998 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.12311 | −1.08626 | −0.543132 | − | 0.839648i | \(-0.682762\pi\) | ||||
−0.543132 | + | 0.839648i | \(0.682762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.280776 | + | 0.486319i | 0.0418557 | + | 0.0724962i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.21922 | + | 2.11176i | −0.177842 | + | 0.308031i | −0.941141 | − | 0.338014i | \(-0.890245\pi\) |
0.763299 | + | 0.646045i | \(0.223578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.90388 | − | 10.2258i | 0.826709 | − | 1.43190i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.56155 | + | 11.3649i | 0.901299 | + | 1.56109i | 0.825810 | + | 0.563948i | \(0.190718\pi\) |
0.0754885 | + | 0.997147i | \(0.475948\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.56155 | 0.210560 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1231 | 1.47329 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | + | 3.46410i | 0.260378 | + | 0.450988i | 0.966342 | − | 0.257260i | \(-0.0828195\pi\) |
−0.705965 | + | 0.708247i | \(0.749486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.43845 | − | 5.95557i | 0.440248 | − | 0.762532i | −0.557460 | − | 0.830204i | \(-0.688224\pi\) |
0.997708 | + | 0.0676721i | \(0.0215572\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.34233 | + | 5.78908i | −0.414565 | + | 0.718048i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.12311 | − | 1.94528i | −0.137209 | − | 0.237653i | 0.789230 | − | 0.614098i | \(-0.210480\pi\) |
−0.926439 | + | 0.376444i | \(0.877147\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.87689 | −0.587109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.12311 | + | 3.67733i | 0.248491 | + | 0.430399i | 0.963107 | − | 0.269118i | \(-0.0867321\pi\) |
−0.714617 | + | 0.699516i | \(0.753399\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.780776 | − | 1.35234i | 0.0901563 | − | 0.156155i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.342329 | + | 0.592932i | −0.0385150 | + | 0.0667100i | −0.884640 | − | 0.466274i | \(-0.845596\pi\) |
0.846125 | + | 0.532984i | \(0.178929\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50000 | + | 6.06218i | 0.388889 | + | 0.673575i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.56155 | 0.820166 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.342329 | + | 0.592932i | 0.0367015 | + | 0.0635689i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.56155 | + | 4.43674i | −0.271524 | + | 0.470293i | −0.969252 | − | 0.246069i | \(-0.920861\pi\) |
0.697728 | + | 0.716363i | \(0.254194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.87689 | − | 8.44703i | 0.505710 | − | 0.875916i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.56155 | + | 6.16879i | 0.365408 | + | 0.632905i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.31534 | 0.133553 | 0.0667764 | − | 0.997768i | \(-0.478729\pi\) | ||||
0.0667764 | + | 0.997768i | \(0.478729\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.876894 | −0.0881312 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.90388 | − | 10.2258i | 0.581727 | − | 1.00758i | −0.413548 | − | 0.910482i | \(-0.635711\pi\) |
0.995275 | − | 0.0970980i | \(-0.0309560\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.56155 | + | 13.0970i | −0.731003 | + | 1.26613i | 0.225452 | + | 0.974254i | \(0.427614\pi\) |
−0.956455 | + | 0.291880i | \(0.905719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.21922 | + | 3.84381i | 0.212563 | + | 0.368170i | 0.952516 | − | 0.304489i | \(-0.0984856\pi\) |
−0.739953 | + | 0.672659i | \(0.765152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.8769 | 1.22222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.24621 | 0.775738 | 0.387869 | − | 0.921714i | \(-0.373211\pi\) | ||||
0.387869 | + | 0.921714i | \(0.373211\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.56155 | − | 2.70469i | −0.145616 | − | 0.252214i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.87689 | − | 3.25088i | 0.173519 | − | 0.300544i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.28078 | − | 7.41452i | 0.389161 | − | 0.674047i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.876894 | − | 1.51883i | −0.0790669 | − | 0.136948i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.24621 | −0.554262 | −0.277131 | − | 0.960832i | \(-0.589384\pi\) | ||||
−0.277131 | + | 0.960832i | \(0.589384\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.56155 | − | 9.63289i | −0.489667 | − | 0.848129i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.56155 | + | 13.0970i | −0.660656 | + | 1.14429i | 0.319788 | + | 0.947489i | \(0.396388\pi\) |
−0.980444 | + | 0.196800i | \(0.936945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.78078 | + | 4.81645i | −0.239331 | + | 0.414534i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.68466 | + | 6.38202i | 0.314802 | + | 0.545252i | 0.979395 | − | 0.201953i | \(-0.0647287\pi\) |
−0.664594 | + | 0.747205i | \(0.731395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.3693 | −1.81252 | −0.906261 | − | 0.422719i | \(-0.861076\pi\) | ||||
−0.906261 | + | 0.422719i | \(0.861076\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.80776 | −0.320672 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.21922 | − | 9.03996i | −0.436453 | − | 0.755959i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.219224 | + | 0.379706i | −0.0182055 | + | 0.0315329i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.123106 | − | 0.213225i | 0.0100852 | − | 0.0174681i | −0.860939 | − | 0.508709i | \(-0.830123\pi\) |
0.871024 | + | 0.491241i | \(0.163456\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.90388 | + | 17.1540i | 0.805966 | + | 1.39597i | 0.915637 | + | 0.402007i | \(0.131687\pi\) |
−0.109670 | + | 0.993968i | \(0.534979\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.24621 | −0.343286 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.24621 | 0.501708 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.12311 | − | 3.67733i | −0.169442 | − | 0.293483i | 0.768782 | − | 0.639511i | \(-0.220863\pi\) |
−0.938224 | + | 0.346029i | \(0.887530\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.2462 | + | 17.7470i | −0.812577 | + | 1.40743i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.80776 | + | 16.9875i | −0.768203 | + | 1.33057i | 0.170333 | + | 0.985387i | \(0.445516\pi\) |
−0.938536 | + | 0.345181i | \(0.887818\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.21922 | + | 2.11176i | 0.0949164 | + | 0.164400i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.19224 | 0.324405 | 0.162202 | − | 0.986757i | \(-0.448140\pi\) | ||||
0.162202 | + | 0.986757i | \(0.448140\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.6847 | 2.43728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | − | 3.46410i | −0.152944 | − | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5885 | − | 20.0719i | 0.881060 | − | 1.52604i | 0.0308969 | − | 0.999523i | \(-0.490164\pi\) |
0.850163 | − | 0.526519i | \(-0.176503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.12311 | + | 5.40938i | −0.234747 | + | 0.406594i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000 | + | 3.46410i | 0.149487 | + | 0.258919i | 0.931038 | − | 0.364922i | \(-0.118904\pi\) |
−0.781551 | + | 0.623841i | \(0.785571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.12311 | −0.380797 | −0.190399 | − | 0.981707i | \(-0.560978\pi\) | ||||
−0.190399 | + | 0.981707i | \(0.560978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.7386 | 0.793823 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.12311 | + | 7.14143i | 0.303137 | + | 0.525048i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.90388 | + | 10.2258i | −0.431735 | + | 0.747786i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.342329 | − | 0.592932i | 0.0247701 | − | 0.0429030i | −0.853375 | − | 0.521298i | \(-0.825448\pi\) |
0.878145 | + | 0.478395i | \(0.158781\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.56155 | − | 11.3649i | −0.472311 | − | 0.818066i | 0.527187 | − | 0.849749i | \(-0.323247\pi\) |
−0.999498 | + | 0.0316828i | \(0.989913\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.4384 | −0.747513 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.1231 | −0.934983 | −0.467491 | − | 0.883998i | \(-0.654842\pi\) | ||||
−0.467491 | + | 0.883998i | \(0.654842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.12311 | + | 12.3376i | 0.504944 | + | 0.874588i | 0.999984 | + | 0.00571778i | \(0.00182004\pi\) |
−0.495040 | + | 0.868870i | \(0.664847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.75379 | − | 3.03765i | 0.123703 | − | 0.214259i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.561553 | − | 0.972638i | 0.0392205 | − | 0.0679320i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.876894 | + | 1.51883i | 0.0609484 | + | 0.105566i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.1231 | −0.769401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.5616 | −1.20899 | −0.604494 | − | 0.796610i | \(-0.706624\pi\) | ||||
−0.604494 | + | 0.796610i | \(0.706624\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.56155 | − | 6.16879i | 0.242896 | − | 0.420708i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.31534 | + | 5.74234i | −0.224030 | + | 0.388031i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.2732 | − | 43.7745i | −1.70006 | − | 2.94459i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.6847 | 1.65301 | 0.826503 | − | 0.562932i | \(-0.190327\pi\) | ||||
0.826503 | + | 0.562932i | \(0.190327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.65767 | + | 9.79937i | 0.375513 | + | 0.650407i | 0.990404 | − | 0.138205i | \(-0.0441333\pi\) |
−0.614891 | + | 0.788612i | \(0.710800\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.68466 | − | 9.84612i | 0.375653 | − | 0.650650i | −0.614772 | − | 0.788705i | \(-0.710752\pi\) |
0.990425 | + | 0.138055i | \(0.0440852\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.43845 | − | 9.41967i | 0.356285 | − | 0.617103i | −0.631052 | − | 0.775740i | \(-0.717377\pi\) |
0.987337 | + | 0.158637i | \(0.0507101\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.21922 | − | 2.11176i | −0.0795334 | − | 0.137756i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.06913 | −0.0694475 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0540 | −1.16781 | −0.583907 | − | 0.811820i | \(-0.698477\pi\) | ||||
−0.583907 | + | 0.811820i | \(0.698477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | − | 1.73205i | −0.0644157 | − | 0.111571i | 0.832019 | − | 0.554747i | \(-0.187185\pi\) |
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.87689 | − | 4.98293i | 0.184553 | − | 0.319655i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.8078 | − | 41.2363i | 1.51485 | − | 2.62380i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.36932 | + | 16.2281i | 0.593756 | + | 1.02842i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3693 | 0.843864 | 0.421932 | − | 0.906628i | \(-0.361352\pi\) | ||||
0.421932 | + | 0.906628i | \(0.361352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.87689 | 0.306608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.90388 | + | 10.2258i | 0.369715 | + | 0.640366i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.24621 | − | 16.0149i | 0.576763 | − | 0.998982i | −0.419085 | − | 0.907947i | \(-0.637649\pi\) |
0.995848 | − | 0.0910354i | \(-0.0290176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.123106 | − | 0.213225i | 0.00762005 | − | 0.0131983i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.68466 | − | 8.11407i | −0.288868 | − | 0.500335i | 0.684672 | − | 0.728852i | \(-0.259946\pi\) |
−0.973540 | + | 0.228517i | \(0.926612\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.1231 | −0.806146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.00000 | −0.489592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.12311 | − | 3.67733i | −0.129448 | − | 0.224211i | 0.794015 | − | 0.607898i | \(-0.207987\pi\) |
−0.923463 | + | 0.383688i | \(0.874654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.12311 | − | 5.40938i | 0.189715 | − | 0.328596i | −0.755440 | − | 0.655218i | \(-0.772577\pi\) |
0.945155 | + | 0.326621i | \(0.105910\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.780776 | + | 1.35234i | −0.0470826 | + | 0.0815494i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.12311 | + | 7.14143i | 0.247733 | + | 0.429087i | 0.962897 | − | 0.269871i | \(-0.0869810\pi\) |
−0.715163 | + | 0.698958i | \(0.753648\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.50758 | −0.209993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.5616 | −1.16694 | −0.583472 | − | 0.812133i | \(-0.698306\pi\) | ||||
−0.583472 | + | 0.812133i | \(0.698306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.34233 | + | 4.05703i | 0.139237 | + | 0.241166i | 0.927208 | − | 0.374547i | \(-0.122202\pi\) |
−0.787971 | + | 0.615712i | \(0.788868\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.56155 | + | 9.63289i | −0.329438 | + | 0.570603i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.0885 | + | 34.7944i | −1.18168 | + | 2.04673i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.02699 | + | 1.77879i | 0.0602031 | + | 0.104275i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.0540 | 1.87261 | 0.936307 | − | 0.351184i | \(-0.114221\pi\) | ||||
0.936307 | + | 0.351184i | \(0.114221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.34233 | − | 7.52113i | −0.251967 | − | 0.436421i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4384 | + | 18.0799i | −0.603671 | + | 1.04559i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.68466 | − | 8.11407i | 0.269127 | − | 0.466141i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.43845 | + | 5.95557i | 0.196885 | + | 0.341015i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.6847 | −1.63712 | −0.818560 | − | 0.574421i | \(-0.805227\pi\) | ||||
−0.818560 | + | 0.574421i | \(0.805227\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.4384 | 1.04893 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.43845 | + | 11.1517i | 0.365091 | + | 0.632356i | 0.988791 | − | 0.149308i | \(-0.0477046\pi\) |
−0.623700 | + | 0.781664i | \(0.714371\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.3423 | + | 23.1096i | −0.754153 | + | 1.30623i | 0.191641 | + | 0.981465i | \(0.438619\pi\) |
−0.945794 | + | 0.324766i | \(0.894714\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.00000 | − | 8.66025i | 0.280828 | − | 0.486408i | −0.690761 | − | 0.723083i | \(-0.742724\pi\) |
0.971589 | + | 0.236675i | \(0.0760576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.342329 | − | 0.592932i | −0.0191668 | − | 0.0331978i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.6155 | −1.31809 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −53.8617 | −2.99695 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.34233 | − | 5.78908i | −0.185399 | − | 0.321121i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.46543 | + | 6.00231i | −0.191639 | + | 0.331928i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000 | − | 10.3923i | 0.329790 | − | 0.571213i | −0.652680 | − | 0.757634i | \(-0.726355\pi\) |
0.982470 | + | 0.186421i | \(0.0596888\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.31534 | − | 4.01029i | −0.126880 | − | 0.219762i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.24621 | 0.122724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.43845 | + | 11.1517i | 0.349688 | + | 0.605678i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.87689 | + | 8.44703i | −0.264099 | + | 0.457432i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.43845 | − | 4.22351i | 0.131282 | − | 0.227386i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.56155 | − | 13.0970i | −0.405925 | − | 0.703083i | 0.588503 | − | 0.808495i | \(-0.299717\pi\) |
−0.994429 | + | 0.105411i | \(0.966384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.7538 | −0.629166 | −0.314583 | − | 0.949230i | \(-0.601865\pi\) | ||||
−0.314583 | + | 0.949230i | \(0.601865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.1771 | 1.98437 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.09612 | + | 1.89853i | 0.0583405 | + | 0.101049i | 0.893721 | − | 0.448624i | \(-0.148086\pi\) |
−0.835380 | + | 0.549673i | \(0.814752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.0000 | + | 27.7128i | −0.844448 | + | 1.46263i | 0.0416523 | + | 0.999132i | \(0.486738\pi\) |
−0.886100 | + | 0.463494i | \(0.846596\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8693 | − | 27.4865i | −0.835227 | − | 1.44666i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.3693 | 0.701707 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.24621 | −0.222257 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.46543 | − | 12.9305i | −0.389693 | − | 0.674967i | 0.602716 | − | 0.797956i | \(-0.294085\pi\) |
−0.992408 | + | 0.122989i | \(0.960752\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.315342 | + | 0.546188i | −0.0164160 | + | 0.0284334i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.68466 | + | 13.3102i | −0.397897 | + | 0.689177i | −0.993466 | − | 0.114127i | \(-0.963593\pi\) |
0.595570 | + | 0.803304i | \(0.296926\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.780776 | + | 1.35234i | 0.0403191 | + | 0.0698348i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.93087 | 0.150947 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.4924 | 1.66902 | 0.834512 | − | 0.550990i | \(-0.185750\pi\) | ||||
0.834512 | + | 0.550990i | \(0.185750\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.87689 | − | 8.44703i | −0.249851 | − | 0.432754i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.87689 | − | 8.44703i | 0.249198 | − | 0.431623i | −0.714106 | − | 0.700038i | \(-0.753166\pi\) |
0.963303 | + | 0.268415i | \(0.0864998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.00000 | + | 3.46410i | −0.101666 | + | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.1501 | − | 19.3125i | −0.565332 | − | 0.979184i | −0.997019 | − | 0.0771603i | \(-0.975415\pi\) |
0.431687 | − | 0.902024i | \(-0.357919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.6155 | 1.19429 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.6155 | −1.19125 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.342329 | − | 0.592932i | −0.0172245 | − | 0.0298336i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.5885 | − | 20.0719i | 0.581612 | − | 1.00738i | −0.413676 | − | 0.910424i | \(-0.635755\pi\) |
0.995288 | − | 0.0969578i | \(-0.0309112\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.46543 | − | 11.1985i | 0.322868 | − | 0.559224i | −0.658210 | − | 0.752834i | \(-0.728686\pi\) |
0.981079 | + | 0.193610i | \(0.0620195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.8769 | − | 36.1598i | −1.03995 | − | 1.80125i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.8769 | −0.638284 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.24621 | + | 16.0149i | 0.457196 | + | 0.791886i | 0.998812 | − | 0.0487399i | \(-0.0155206\pi\) |
−0.541616 | + | 0.840626i | \(0.682187\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.75379 | + | 9.96585i | −0.283813 | + | 0.491579i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | + | 10.3923i | −0.294528 | + | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.6847 | − | 28.8987i | −0.817051 | − | 1.41517i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.2462 | −0.891386 | −0.445693 | − | 0.895186i | \(-0.647043\pi\) | ||||
−0.445693 | + | 0.895186i | \(0.647043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.56155 | 0.173579 | 0.0867897 | − | 0.996227i | \(-0.472339\pi\) | ||||
0.0867897 | + | 0.996227i | \(0.472339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.684658 | + | 1.18586i | 0.0332892 | + | 0.0576586i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.78078 | + | 6.54850i | −0.183395 | + | 0.317649i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.15009 | − | 14.1164i | 0.393490 | − | 0.681545i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4654 | + | 19.8587i | 0.552271 | + | 0.956561i | 0.998110 | + | 0.0614479i | \(0.0195718\pi\) |
−0.445840 | + | 0.895113i | \(0.647095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7538 | 0.949307 | 0.474653 | − | 0.880173i | \(-0.342573\pi\) | ||||
0.474653 | + | 0.880173i | \(0.342573\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.684658 | −0.0328269 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.1231 | + | 19.2658i | 0.532090 | + | 0.921607i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.56155 | + | 16.5611i | −0.456348 | + | 0.790418i | −0.998765 | − | 0.0496917i | \(-0.984176\pi\) |
0.542417 | + | 0.840110i | \(0.317509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.80776 | − | 16.9875i | 0.465981 | − | 0.807103i | −0.533264 | − | 0.845949i | \(-0.679035\pi\) |
0.999245 | + | 0.0388461i | \(0.0123682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.56155 | − | 4.43674i | −0.121429 | − | 0.210322i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.384472 | 0.0181849 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.3153 | −1.00593 | −0.502967 | − | 0.864306i | \(-0.667758\pi\) | ||||
−0.502967 | + | 0.864306i | \(0.667758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.876894 | + | 1.51883i | 0.0412913 | + | 0.0715187i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.4654 | + | 26.7869i | −0.726630 | + | 1.25856i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.31534 | + | 7.47439i | −0.201863 | + | 0.349637i | −0.949129 | − | 0.314888i | \(-0.898033\pi\) |
0.747266 | + | 0.664525i | \(0.231366\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.0270 | − | 36.4198i | −0.981456 | − | 1.69993i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8769 | 0.879185 | 0.439592 | − | 0.898197i | \(-0.355123\pi\) | ||||
0.439592 | + | 0.898197i | \(0.355123\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.24621 | −0.290286 | −0.145143 | − | 0.989411i | \(-0.546364\pi\) | ||||
−0.145143 | + | 0.989411i | \(0.546364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.87689 | + | 8.44703i | 0.226161 | + | 0.391722i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.7808 | + | 22.1370i | −0.591424 | + | 1.02438i | 0.402617 | + | 0.915368i | \(0.368101\pi\) |
−0.994041 | + | 0.109008i | \(0.965233\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.31534 | − | 5.74234i | 0.152763 | − | 0.264593i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.56155 | + | 9.63289i | 0.255720 | + | 0.442921i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.12311 | −0.326831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.36932 | 0.337418 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.68466 | − | 15.0423i | −0.396812 | − | 0.687299i | 0.596518 | − | 0.802599i | \(-0.296550\pi\) |
−0.993331 | + | 0.115300i | \(0.963217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.5616 | − | 47.7380i | 1.25670 | − | 2.17667i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.657671 | + | 1.13912i | −0.0298633 | + | 0.0517247i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.56155 | − | 2.70469i | −0.0707607 | − | 0.122561i | 0.828474 | − | 0.560027i | \(-0.189209\pi\) |
−0.899235 | + | 0.437466i | \(0.855876\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.6307 | −1.38517 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.31534 | −0.149619 | −0.0748096 | − | 0.997198i | \(-0.523835\pi\) | ||||
−0.0748096 | + | 0.997198i | \(0.523835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.65767 | − | 2.87117i | −0.0746577 | − | 0.129311i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.438447 | − | 0.759413i | 0.0197067 | − | 0.0341331i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.0961180 | − | 0.166481i | 0.00430283 | − | 0.00745272i | −0.863866 | − | 0.503722i | \(-0.831964\pi\) |
0.868169 | + | 0.496269i | \(0.165297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.27320 | + | 5.66935i | 0.146236 | + | 0.253288i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.1771 | −1.30094 | −0.650471 | − | 0.759531i | \(-0.725428\pi\) | ||||
−0.650471 | + | 0.759531i | \(0.725428\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.7386 | + | 42.8486i | 1.09868 | + | 1.90297i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.3693 | + | 28.3525i | −0.725557 | + | 1.25670i | 0.233187 | + | 0.972432i | \(0.425085\pi\) |
−0.958744 | + | 0.284270i | \(0.908249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.8078 | − | 34.3081i | 0.874534 | − | 1.51474i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.90388 | + | 10.2258i | 0.260156 | + | 0.450604i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.80776 | 0.167465 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.1922 | 1.58866 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.12311 | + | 10.6055i | 0.268258 | + | 0.464637i | 0.968412 | − | 0.249355i | \(-0.0802187\pi\) |
−0.700154 | + | 0.713992i | \(0.746885\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.00000 | − | 10.3923i | 0.262362 | − | 0.454424i | −0.704507 | − | 0.709697i | \(-0.748832\pi\) |
0.966869 | + | 0.255273i | \(0.0821653\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.6155 | + | 40.9033i | −1.02871 | + | 1.78178i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.62311 | + | 11.4716i | 0.287961 | + | 0.498763i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.24621 | 0.0974773 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.50758 | −0.325189 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.56155 | − | 13.0970i | −0.326914 | − | 0.566232i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.12311 | + | 5.40938i | −0.134772 | + | 0.233432i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.7116 | + | 35.8736i | −0.890463 | + | 1.54233i | −0.0511422 | + | 0.998691i | \(0.516286\pi\) |
−0.839321 | + | 0.543636i | \(0.817047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.00000 | − | 6.92820i | −0.171656 | − | 0.297318i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.43845 | −0.190122 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.93087 | − | 3.34436i | −0.0824075 | − | 0.142734i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.56155 | − | 2.70469i | 0.0665244 | − | 0.115224i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.43845 | + | 11.1517i | −0.273297 | + | 0.473364i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.80776 | + | 15.2555i | 0.373197 | + | 0.646396i | 0.990055 | − | 0.140678i | \(-0.0449282\pi\) |
−0.616858 | + | 0.787074i | \(0.711595\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.6155 | −2.01392 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.4384 | −0.778472 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.75379 | + | 6.50175i | 0.158203 | + | 0.274016i | 0.934221 | − | 0.356695i | \(-0.116097\pi\) |
−0.776017 | + | 0.630711i | \(0.782763\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.12311 | + | 7.14143i | −0.173460 | + | 0.300442i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.49242 | + | 16.4414i | −0.397943 | + | 0.689258i | −0.993472 | − | 0.114076i | \(-0.963609\pi\) |
0.595529 | + | 0.803334i | \(0.296943\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.06913 | 0.0446636 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.12311 | 0.130243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.78078 | + | 3.08440i | 0.0741347 | + | 0.128405i | 0.900710 | − | 0.434422i | \(-0.143047\pi\) |
−0.826575 | + | 0.562827i | \(0.809714\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.2462 | − | 17.7470i | 0.425818 | − | 0.737538i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2462 | − | 17.7470i | 0.424355 | − | 0.735004i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.87689 | + | 3.25088i | 0.0776000 | + | 0.134407i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.2462 | 0.422906 | 0.211453 | − | 0.977388i | \(-0.432180\pi\) | ||||
0.211453 | + | 0.977388i | \(0.432180\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.4924 | −1.83328 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.2462 | − | 17.7470i | −0.421473 | − | 0.730012i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.7116 | + | 32.4095i | −0.768395 | + | 1.33090i | 0.170038 | + | 0.985438i | \(0.445611\pi\) |
−0.938433 | + | 0.345462i | \(0.887722\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.1231 | + | 19.2658i | −0.455238 | + | 0.788496i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.4654 | + | 40.6433i | 0.958772 | + | 1.66064i | 0.725491 | + | 0.688232i | \(0.241613\pi\) |
0.233281 | + | 0.972409i | \(0.425054\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.26137 | −0.0513668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.28078 | + | 7.41452i | 0.174038 | + | 0.301443i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.34233 | − | 7.52113i | 0.176250 | − | 0.305273i | −0.764343 | − | 0.644809i | \(-0.776937\pi\) |
0.940593 | + | 0.339536i | \(0.110270\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.15009 | + | 14.1164i | −0.329717 | + | 0.571087i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.36932 | − | 14.4961i | −0.338034 | − | 0.585491i | 0.646029 | − | 0.763313i | \(-0.276428\pi\) |
−0.984063 | + | 0.177821i | \(0.943095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.75379 | 0.0707196 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.7538 | −0.634224 | −0.317112 | − | 0.948388i | \(-0.602713\pi\) | ||||
−0.317112 | + | 0.948388i | \(0.602713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.31534 | − | 9.20644i | −0.213642 | − | 0.370038i | 0.739210 | − | 0.673475i | \(-0.235199\pi\) |
−0.952852 | + | 0.303437i | \(0.901866\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.68466 | + | 15.0423i | −0.348503 | + | 0.603625i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.68466 | − | 15.0423i | −0.346832 | − | 0.600730i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −62.3542 | −2.48622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4233 | −1.09170 | −0.545852 | − | 0.837882i | \(-0.683794\pi\) | ||||
−0.545852 | + | 0.837882i | \(0.683794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.7116 | − | 23.7493i | −0.544989 | − | 0.943949i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.12311 | − | 5.40938i | 0.123937 | − | 0.214665i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.4924 | + | 19.9055i | 0.453923 | + | 0.786218i | 0.998626 | − | 0.0524112i | \(-0.0166906\pi\) |
−0.544702 | + | 0.838630i | \(0.683357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.0540 | −1.18521 | −0.592607 | − | 0.805492i | \(-0.701901\pi\) | ||||
−0.592607 | + | 0.805492i | \(0.701901\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.1231 | 0.437972 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.00000 | − | 6.92820i | −0.157256 | − | 0.272376i | 0.776622 | − | 0.629967i | \(-0.216932\pi\) |
−0.933878 | + | 0.357591i | \(0.883598\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.12311 | − | 5.40938i | 0.122593 | − | 0.212337i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.2462 | − | 33.3354i | 0.753162 | − | 1.30452i | −0.193120 | − | 0.981175i | \(-0.561861\pi\) |
0.946283 | − | 0.323341i | \(-0.104806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.56155 | − | 13.0970i | −0.295454 | − | 0.511742i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.38447 | 0.0930271 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.192236 | −0.00748845 | −0.00374422 | − | 0.999993i | \(-0.501192\pi\) | ||||
−0.00374422 | + | 0.999993i | \(0.501192\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.80776 | + | 15.2555i | 0.342582 | + | 0.593370i | 0.984911 | − | 0.173059i | \(-0.0553651\pi\) |
−0.642329 | + | 0.766429i | \(0.722032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 39.4654 | − | 68.3561i | 1.53271 | − | 2.65473i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.684658 | + | 1.18586i | −0.0265101 | + | 0.0459168i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.2732 | + | 33.3822i | 0.745145 | + | 1.29063i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.7386 | −0.414560 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.6155 | 1.60416 | 0.802080 | − | 0.597216i | \(-0.203727\pi\) | ||||
0.802080 | + | 0.597216i | \(0.203727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.78078 | − | 4.81645i | −0.107032 | − | 0.185385i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.657671 | − | 1.13912i | 0.0252763 | − | 0.0437799i | −0.853111 | − | 0.521730i | \(-0.825287\pi\) |
0.878387 | + | 0.477950i | \(0.158620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.83475 | + | 15.3022i | −0.338548 | + | 0.586383i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.4924 | − | 38.9580i | −0.860649 | − | 1.49069i | −0.871304 | − | 0.490744i | \(-0.836725\pi\) |
0.0106552 | − | 0.999943i | \(-0.496608\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.36932 | −0.281567 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.7538 | 0.677349 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.8617 | + | 75.9708i | 1.67100 | + | 2.89426i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.24621 | + | 14.2829i | −0.313701 | + | 0.543345i | −0.979160 | − | 0.203088i | \(-0.934902\pi\) |
0.665460 | + | 0.746434i | \(0.268236\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.6847 | − | 18.5064i | 0.405292 | − | 0.701987i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.24621 | + | 7.35465i | 0.160837 | + | 0.278577i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.9848 | 0.642426 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.31534 | −0.351836 | −0.175918 | − | 0.984405i | \(-0.556289\pi\) | ||||
−0.175918 | + | 0.984405i | \(0.556289\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.3693 | − | 50.8691i | −1.10768 | − | 1.91857i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.90388 | − | 3.29762i | 0.0717043 | − | 0.124196i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.02699 | − | 3.51085i | 0.0761251 | − | 0.131853i | −0.825450 | − | 0.564475i | \(-0.809078\pi\) |
0.901575 | + | 0.432623i | \(0.142412\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.192236 | + | 0.332962i | 0.00720941 | + | 0.0124871i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.5076 | 0.730565 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.4384 | 0.390376 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.0961 | − | 24.4152i | −0.526429 | − | 0.911802i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.8078 | − | 20.4516i | 0.440355 | − | 0.762718i | −0.557360 | − | 0.830271i | \(-0.688186\pi\) |
0.997716 | + | 0.0675529i | \(0.0215192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.56155 | − | 2.70469i | 0.0580748 | − | 0.100588i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.219224 | − | 0.379706i | −0.00814176 | − | 0.0141019i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.9848 | 1.81675 | 0.908374 | − | 0.418159i | \(-0.137325\pi\) | ||||
0.908374 | + | 0.418159i | \(0.137325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.9309 | + | 46.6456i | 0.996074 | + | 1.72525i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.21922 | + | 14.2361i | −0.303584 | + | 0.525823i | −0.976945 | − | 0.213491i | \(-0.931517\pi\) |
0.673361 | + | 0.739314i | \(0.264850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.75379 | + | 3.03765i | −0.0646016 | + | 0.111893i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.21922 | + | 5.57586i | 0.118421 | + | 0.205111i | 0.919142 | − | 0.393926i | \(-0.128883\pi\) |
−0.800721 | + | 0.599037i | \(0.795550\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 74.3542 | 2.73147 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.123106 | + | 0.213225i | 0.00451024 | + | 0.00781197i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.36932 | − | 5.83583i | 0.123277 | − | 0.213522i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6577 | − | 27.1199i | 0.571357 | − | 0.989619i | −0.425070 | − | 0.905160i | \(-0.639751\pi\) |
0.996427 | − | 0.0844583i | \(-0.0269160\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.4384 | + | 18.0799i | 0.380398 | + | 0.658869i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.8078 | −0.720878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.3693 | 0.558607 | 0.279304 | − | 0.960203i | \(-0.409896\pi\) | ||||
0.279304 | + | 0.960203i | \(0.409896\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.80776 | + | 6.59524i | 0.138213 | + | 0.239392i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.0000 | + | 22.5167i | −0.471250 | + | 0.816228i | −0.999459 | − | 0.0328858i | \(-0.989530\pi\) |
0.528209 | + | 0.849114i | \(0.322864\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.12311 | − | 3.67733i | 0.0767610 | − | 0.132954i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.3693 | + | 23.1563i | 0.482738 | + | 0.836127i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.9848 | 1.55007 | 0.775037 | − | 0.631916i | \(-0.217731\pi\) | ||||
0.775037 | + | 0.631916i | \(0.217731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.8769 | 1.03998 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.9039 | + | 25.8143i | 0.536055 | + | 0.928475i | 0.999111 | + | 0.0421462i | \(0.0134195\pi\) |
−0.463056 | + | 0.886329i | \(0.653247\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.12311 | + | 5.40938i | −0.112185 | + | 0.194311i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.00000 | + | 6.92820i | −0.143315 | + | 0.248229i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.43845 | 0.0871430 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.24621 | 0.151554 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.5885 | − | 28.7322i | −0.591318 | − | 1.02419i | −0.994055 | − | 0.108877i | \(-0.965275\pi\) |
0.402738 | − | 0.915315i | \(-0.368059\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.31534 | − | 12.6705i | 0.260433 | − | 0.451083i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.9848 | − | 39.8109i | 0.816216 | − | 1.41373i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.2462 | − | 17.7470i | −0.363396 | − | 0.629420i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.8078 | 0.630783 | 0.315392 | − | 0.948962i | \(-0.397864\pi\) | ||||
0.315392 | + | 0.948962i | \(0.397864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.4384 | 0.652305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.43845 | + | 2.49146i | 0.0508250 | + | 0.0880315i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.31534 | − | 5.74234i | 0.116996 | − | 0.202643i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.31534 | − | 5.74234i | 0.116706 | − | 0.202140i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.02699 | − | 3.51085i | −0.0712651 | − | 0.123435i | 0.828191 | − | 0.560446i | \(-0.189370\pi\) |
−0.899456 | + | 0.437011i | \(0.856037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.6155 | −0.969712 | −0.484856 | − | 0.874594i | \(-0.661128\pi\) | ||||
−0.484856 | + | 0.874594i | \(0.661128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.75379 | 0.342080 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.80776 | − | 16.9875i | −0.343551 | − | 0.595048i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.3693 | + | 43.9409i | −0.887560 | + | 1.53730i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.1501 | + | 47.0253i | −0.947545 | + | 1.64120i | −0.196971 | + | 0.980409i | \(0.563110\pi\) |
−0.750574 | + | 0.660786i | \(0.770223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.87689 | + | 15.3752i | 0.309429 | + | 0.535947i | 0.978238 | − | 0.207488i | \(-0.0665287\pi\) |
−0.668809 | + | 0.743435i | \(0.733195\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.43845 | −0.0848958 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.8769 | 0.865054 | 0.432527 | − | 0.901621i | \(-0.357622\pi\) | ||||
0.432527 | + | 0.901621i | \(0.357622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.80776 | − | 4.86319i | −0.0975177 | − | 0.168906i | 0.813139 | − | 0.582070i | \(-0.197757\pi\) |
−0.910657 | + | 0.413164i | \(0.864424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.43845 | + | 11.1517i | −0.223347 | + | 0.386849i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.09612 | + | 3.63058i | −0.0725392 | + | 0.125641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.3693 | − | 30.0845i | −0.600371 | − | 1.03987i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.1231 | 0.660203 | 0.330101 | − | 0.943945i | \(-0.392917\pi\) | ||||
0.330101 | + | 0.943945i | \(0.392917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8078 | −0.993371 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.2732 | − | 26.4540i | −0.526037 | − | 0.911123i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.8423 | + | 27.4397i | −0.544993 | + | 0.943955i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.65767 | + | 6.33527i | −0.125531 | + | 0.217426i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.8769 | + | 22.3034i | 0.441414 | + | 0.764552i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.7538 | 0.539399 | 0.269700 | − | 0.962944i | \(-0.413076\pi\) | ||||
0.269700 | + | 0.962944i | \(0.413076\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.3693 | − | 45.6730i | −0.900759 | − | 1.56016i | −0.826511 | − | 0.562920i | \(-0.809678\pi\) |
−0.0742473 | − | 0.997240i | \(-0.523655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.4924 | + | 32.0298i | −0.630953 | + | 1.09284i | 0.356404 | + | 0.934332i | \(0.384003\pi\) |
−0.987357 | + | 0.158511i | \(0.949331\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.2462 | + | 24.6752i | −0.484947 | + | 0.839952i | −0.999850 | − | 0.0172957i | \(-0.994494\pi\) |
0.514904 | + | 0.857248i | \(0.327828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5885 | + | 20.0719i | 0.394022 | + | 0.682466i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −62.7386 | −2.13072 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.06913 | 0.0362678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.50758 | − | 13.0035i | −0.254385 | − | 0.440607i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.369317 | − | 0.639676i | 0.0124995 | − | 0.0216497i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.75379 | − | 11.6979i | 0.228059 | − | 0.395010i | −0.729174 | − | 0.684329i | \(-0.760095\pi\) |
0.957233 | + | 0.289319i | \(0.0934287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.0270 | + | 43.3480i | 0.844139 | + | 1.46209i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.1080 | 1.82294 | 0.911472 | − | 0.411363i | \(-0.134947\pi\) | ||||
0.911472 | + | 0.411363i | \(0.134947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.7538 | 0.732073 | 0.366037 | − | 0.930600i | \(-0.380714\pi\) | ||||
0.366037 | + | 0.930600i | \(0.380714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.12311 | − | 5.40938i | −0.104982 | − | 0.181834i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.2462 | − | 31.6034i | 0.612648 | − | 1.06114i | −0.378144 | − | 0.925747i | \(-0.623438\pi\) |
0.990792 | − | 0.135391i | \(-0.0432289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.46543 | − | 9.46641i | 0.183099 | − | 0.317137i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.68466 | + | 15.0423i | 0.290621 | + | 0.503370i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | −0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.6004 | −1.08849 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.36932 | − | 2.37173i | −0.0456693 | − | 0.0791015i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.6155 | − | 85.9366i | 1.65293 | − | 2.86296i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.56155 | − | 4.43674i | 0.0851489 | − | 0.147482i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0540 | + | 41.6627i | 0.798699 | + | 1.38339i | 0.920464 | + | 0.390828i | \(0.127811\pi\) |
−0.121764 | + | 0.992559i | \(0.538855\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.36932 | −0.111753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.36932 | − | 16.2281i | −0.310079 | − | 0.537073i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.36932 | + | 9.29993i | −0.177504 | + | 0.307446i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.21922 | + | 2.11176i | −0.0402185 | + | 0.0696604i | −0.885434 | − | 0.464765i | \(-0.846139\pi\) |
0.845215 | + | 0.534426i | \(0.179472\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.3963 | − | 38.7915i | −0.737983 | − | 1.27822i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.24621 | −0.271134 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.31534 | − | 5.74234i | −0.108890 | − | 0.188603i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.43845 | − | 2.49146i | 0.0471939 | − | 0.0817423i | −0.841463 | − | 0.540314i | \(-0.818305\pi\) |
0.888657 | + | 0.458572i | \(0.151639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.0540 | + | 17.4140i | −0.329152 | + | 0.570109i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.90388 | − | 10.2258i | −0.193078 | − | 0.334420i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.8078 | 1.23513 | 0.617563 | − | 0.786521i | \(-0.288120\pi\) | ||||
0.617563 | + | 0.786521i | \(0.288120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.6695 | −1.35983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.3153 | − | 24.7949i | −0.466667 | − | 0.808291i | 0.532608 | − | 0.846362i | \(-0.321212\pi\) |
−0.999275 | + | 0.0380713i | \(0.987879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.75379 | − | 3.03765i | 0.0571112 | − | 0.0989195i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.6155 | − | 30.5110i | 0.572428 | − | 0.991474i | −0.423888 | − | 0.905715i | \(-0.639335\pi\) |
0.996316 | − | 0.0857594i | \(-0.0273316\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.1922 | + | 24.5817i | 0.460699 | + | 0.797955i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.6155 | 0.506368 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.8617 | −1.67997 | −0.839983 | − | 0.542612i | \(-0.817435\pi\) | ||||
−0.839983 | + | 0.542612i | \(0.817435\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.342329 | + | 0.592932i | 0.0110775 | + | 0.0191868i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.534565 | − | 0.925894i | 0.0172800 | − | 0.0299299i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.00758 | + | 6.94133i | −0.129277 | + | 0.223914i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.24621 | + | 7.35465i | 0.136832 | + | 0.237000i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.1231 | 0.422448 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.1080 | 1.41842 | 0.709208 | − | 0.704999i | \(-0.249053\pi\) | ||||
0.709208 | + | 0.704999i | \(0.249053\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −42.0540 | − | 72.8396i | −1.35097 | − | 2.33995i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3693 | − | 19.6922i | 0.364859 | − | 0.631954i | −0.623895 | − | 0.781508i | \(-0.714451\pi\) |
0.988753 | + | 0.149555i | \(0.0477839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.21922 | − | 9.03996i | 0.167149 | − | 0.289510i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.49242 | − | 9.51315i | −0.175718 | − | 0.304353i | 0.764691 | − | 0.644397i | \(-0.222891\pi\) |
−0.940410 | + | 0.340044i | \(0.889558\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | 0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.49242 | 0.0795769 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.5885 | + | 25.2681i | 0.465302 | + | 0.805927i | 0.999215 | − | 0.0396124i | \(-0.0126123\pi\) |
−0.533913 | + | 0.845539i | \(0.679279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.56155 | − | 11.3649i | 0.209068 | − | 0.362117i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.1231 | − | 19.2658i | 0.353694 | − | 0.612616i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.2462 | + | 17.7470i | 0.325482 | + | 0.563751i | 0.981610 | − | 0.190899i | \(-0.0611402\pi\) |
−0.656128 | + | 0.754650i | \(0.727807\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7386 | 0.594653 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.2462 | −0.451635 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.4654 | + | 49.3036i | 0.901509 | + | 1.56146i | 0.825535 | + | 0.564350i | \(0.190873\pi\) |
0.0759739 | + | 0.997110i | \(0.475793\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.9309 | − | 39.7174i | 0.725501 | − | 1.25660i |
(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 | 1960.2.q.s.961.2 | 4 | ||
7.2 | even | 3 | 280.2.a.d.1.1 | ✓ | 2 | ||
7.3 | odd | 6 | 1960.2.q.u.361.1 | 4 | |||
7.4 | even | 3 | inner | 1960.2.q.s.361.2 | 4 | ||
7.5 | odd | 6 | 1960.2.a.r.1.2 | 2 | |||
7.6 | odd | 2 | 1960.2.q.u.961.1 | 4 | |||
21.2 | odd | 6 | 2520.2.a.w.1.1 | 2 | |||
28.19 | even | 6 | 3920.2.a.bu.1.1 | 2 | |||
28.23 | odd | 6 | 560.2.a.g.1.2 | 2 | |||
35.2 | odd | 12 | 1400.2.g.k.449.3 | 4 | |||
35.9 | even | 6 | 1400.2.a.p.1.2 | 2 | |||
35.19 | odd | 6 | 9800.2.a.by.1.1 | 2 | |||
35.23 | odd | 12 | 1400.2.g.k.449.2 | 4 | |||
56.37 | even | 6 | 2240.2.a.be.1.2 | 2 | |||
56.51 | odd | 6 | 2240.2.a.bi.1.1 | 2 | |||
84.23 | even | 6 | 5040.2.a.bq.1.2 | 2 | |||
140.23 | even | 12 | 2800.2.g.u.449.3 | 4 | |||
140.79 | odd | 6 | 2800.2.a.bn.1.1 | 2 | |||
140.107 | even | 12 | 2800.2.g.u.449.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.d.1.1 | ✓ | 2 | 7.2 | even | 3 | ||
560.2.a.g.1.2 | 2 | 28.23 | odd | 6 | |||
1400.2.a.p.1.2 | 2 | 35.9 | even | 6 | |||
1400.2.g.k.449.2 | 4 | 35.23 | odd | 12 | |||
1400.2.g.k.449.3 | 4 | 35.2 | odd | 12 | |||
1960.2.a.r.1.2 | 2 | 7.5 | odd | 6 | |||
1960.2.q.s.361.2 | 4 | 7.4 | even | 3 | inner | ||
1960.2.q.s.961.2 | 4 | 1.1 | even | 1 | trivial | ||
1960.2.q.u.361.1 | 4 | 7.3 | odd | 6 | |||
1960.2.q.u.961.1 | 4 | 7.6 | odd | 2 | |||
2240.2.a.be.1.2 | 2 | 56.37 | even | 6 | |||
2240.2.a.bi.1.1 | 2 | 56.51 | odd | 6 | |||
2520.2.a.w.1.1 | 2 | 21.2 | odd | 6 | |||
2800.2.a.bn.1.1 | 2 | 140.79 | odd | 6 | |||
2800.2.g.u.449.2 | 4 | 140.107 | even | 12 | |||
2800.2.g.u.449.3 | 4 | 140.23 | even | 12 | |||
3920.2.a.bu.1.1 | 2 | 28.19 | even | 6 | |||
5040.2.a.bq.1.2 | 2 | 84.23 | even | 6 | |||
9800.2.a.by.1.1 | 2 | 35.19 | odd | 6 |