Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(961,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.i (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: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1537.2 | ||
Root | \(0.809017 - 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1537 |
Dual form | 1568.2.i.v.961.2 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.61803 | − | 2.80252i | 0.934172 | − | 1.61803i | 0.158069 | − | 0.987428i | \(-0.449473\pi\) |
0.776103 | − | 0.630606i | \(-0.217194\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.618034 | + | 1.07047i | 0.276393 | + | 0.478727i | 0.970486 | − | 0.241159i | \(-0.0775275\pi\) |
−0.694092 | + | 0.719886i | \(0.744194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.73607 | − | 6.47106i | −1.24536 | − | 2.15702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23607 | + | 2.14093i | −0.372689 | + | 0.645515i | −0.989978 | − | 0.141221i | \(-0.954897\pi\) |
0.617290 | + | 0.786736i | \(0.288231\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.23607 | 1.45222 | 0.726112 | − | 0.687576i | \(-0.241325\pi\) | ||||
0.726112 | + | 0.687576i | \(0.241325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23607 | − | 3.87298i | 0.542326 | − | 0.939336i | −0.456444 | − | 0.889752i | \(-0.650877\pi\) |
0.998770 | − | 0.0495842i | \(-0.0157896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.61803 | − | 2.80252i | −0.371202 | − | 0.642942i | 0.618548 | − | 0.785747i | \(-0.287721\pi\) |
−0.989751 | + | 0.142805i | \(0.954388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.73607 | − | 3.00696i | 0.347214 | − | 0.601392i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.23607 | + | 5.60503i | −0.581215 | + | 1.00669i | 0.414121 | + | 0.910222i | \(0.364089\pi\) |
−0.995336 | + | 0.0964719i | \(0.969244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.00000 | + | 6.92820i | 0.696311 | + | 1.20605i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.23607 | − | 3.87298i | −0.367607 | − | 0.636715i | 0.621584 | − | 0.783348i | \(-0.286490\pi\) |
−0.989191 | + | 0.146633i | \(0.953156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.47214 | − | 14.6742i | 1.35663 | − | 2.34975i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.472136 | 0.0737352 | 0.0368676 | − | 0.999320i | \(-0.488262\pi\) | ||||
0.0368676 | + | 0.999320i | \(0.488262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.47214 | −0.376997 | −0.188499 | − | 0.982073i | \(-0.560362\pi\) | ||||
−0.188499 | + | 0.982073i | \(0.560362\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.61803 | − | 7.99867i | 0.688416 | − | 1.19237i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.763932 | − | 1.32317i | −0.111431 | − | 0.193004i | 0.804916 | − | 0.593388i | \(-0.202210\pi\) |
−0.916347 | + | 0.400384i | \(0.868877\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.23607 | − | 12.5332i | −1.01325 | − | 1.75500i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.00000 | − | 8.66025i | 0.686803 | − | 1.18958i | −0.286064 | − | 0.958211i | \(-0.592347\pi\) |
0.972867 | − | 0.231367i | \(-0.0743197\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.05573 | −0.412034 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.4721 | −1.38707 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.38197 | − | 4.12569i | 0.310106 | − | 0.537119i | −0.668279 | − | 0.743910i | \(-0.732969\pi\) |
0.978385 | + | 0.206792i | \(0.0663023\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.38197 | − | 5.85774i | −0.433016 | − | 0.750006i | 0.564115 | − | 0.825696i | \(-0.309217\pi\) |
−0.997131 | + | 0.0756898i | \(0.975884\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.23607 | + | 5.60503i | 0.401385 | + | 0.695219i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | + | 3.46410i | −0.244339 | + | 0.423207i | −0.961946 | − | 0.273241i | \(-0.911904\pi\) |
0.717607 | + | 0.696449i | \(0.245238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.9443 | −1.55831 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9443 | 1.53620 | 0.768101 | − | 0.640328i | \(-0.221202\pi\) | ||||
0.768101 | + | 0.640328i | \(0.221202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.47214 | + | 12.9421i | −0.874547 | + | 1.51476i | −0.0173032 | + | 0.999850i | \(0.505508\pi\) |
−0.857244 | + | 0.514910i | \(0.827825\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.61803 | − | 9.73072i | −0.648715 | − | 1.12361i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.47214 | + | 4.28187i | 0.278137 | + | 0.481747i | 0.970922 | − | 0.239397i | \(-0.0769497\pi\) |
−0.692785 | + | 0.721144i | \(0.743616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12.2082 | + | 21.1452i | −1.35647 | + | 2.34947i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.76393 | −0.522909 | −0.261455 | − | 0.965216i | \(-0.584202\pi\) | ||||
−0.261455 | + | 0.965216i | \(0.584202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.52786 | 0.599581 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.23607 | − | 12.5332i | 0.775788 | − | 1.34370i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.4721 | + | 18.1383i | 1.08591 | + | 1.88085i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | − | 3.46410i | 0.205196 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.52786 | 0.358200 | 0.179100 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179100 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.4721 | 1.85652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.85410 | + | 10.1396i | −0.582505 | + | 1.00893i | 0.412677 | + | 0.910878i | \(0.364594\pi\) |
−0.995181 | + | 0.0980505i | \(0.968739\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.23607 | + | 12.5332i | 0.712991 | + | 1.23494i | 0.963729 | + | 0.266882i | \(0.0859933\pi\) |
−0.250738 | + | 0.968055i | \(0.580673\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.47214 | + | 7.74597i | 0.432338 | + | 0.748831i | 0.997074 | − | 0.0764405i | \(-0.0243555\pi\) |
−0.564736 | + | 0.825271i | \(0.691022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.236068 | − | 0.408882i | 0.0226112 | − | 0.0391638i | −0.854498 | − | 0.519454i | \(-0.826135\pi\) |
0.877110 | + | 0.480290i | \(0.159469\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.4721 | −1.37363 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.52786 | −0.331874 | −0.165937 | − | 0.986136i | \(-0.553065\pi\) | ||||
−0.165937 | + | 0.986136i | \(0.553065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.47214 | − | 4.28187i | 0.230528 | − | 0.399286i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.5623 | − | 33.8829i | −1.80854 | − | 3.13248i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.44427 | + | 4.23360i | 0.222207 | + | 0.384873i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.763932 | − | 1.32317i | 0.0688814 | − | 0.119306i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.94427 | −0.793676 | −0.396838 | − | 0.917889i | \(-0.629892\pi\) | ||||
−0.396838 | + | 0.917889i | \(0.629892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00000 | + | 6.92820i | −0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.854102 | + | 1.47935i | 0.0746232 | + | 0.129251i | 0.900922 | − | 0.433980i | \(-0.142891\pi\) |
−0.826299 | + | 0.563232i | \(0.809558\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.94427 | − | 15.4919i | −0.769800 | − | 1.33333i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.47214 | − | 2.54981i | 0.125773 | − | 0.217845i | −0.796262 | − | 0.604952i | \(-0.793192\pi\) |
0.922035 | + | 0.387107i | \(0.126526\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.23607 | −0.274480 | −0.137240 | − | 0.990538i | \(-0.543823\pi\) | ||||
−0.137240 | + | 0.990538i | \(0.543823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.94427 | −0.416383 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.47214 | + | 11.2101i | −0.541227 | + | 0.937433i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.76393 | + | 4.78727i | 0.229532 | + | 0.397561i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.47214 | + | 12.9421i | 0.612141 | + | 1.06026i | 0.990879 | + | 0.134756i | \(0.0430249\pi\) |
−0.378738 | + | 0.925504i | \(0.623642\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.47214 | + | 7.74597i | −0.363937 | + | 0.630358i | −0.988605 | − | 0.150533i | \(-0.951901\pi\) |
0.624668 | + | 0.780891i | \(0.285234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −33.4164 | −2.70156 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.61803 | + | 4.53457i | −0.208942 | + | 0.361898i | −0.951381 | − | 0.308015i | \(-0.900335\pi\) |
0.742440 | + | 0.669913i | \(0.233669\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.1803 | − | 28.0252i | −1.28318 | − | 2.22254i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7082 | − | 20.2792i | −0.917057 | − | 1.58839i | −0.803861 | − | 0.594817i | \(-0.797224\pi\) |
−0.113196 | − | 0.993573i | \(-0.536109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.94427 | + | 8.56373i | −0.384911 | + | 0.666685i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.41641 | −0.264370 | −0.132185 | − | 0.991225i | \(-0.542199\pi\) | ||||
−0.132185 | + | 0.991225i | \(0.542199\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.0902 | + | 20.9408i | −0.924558 | + | 1.60138i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.85410 | + | 6.67550i | 0.293022 | + | 0.507529i | 0.974523 | − | 0.224288i | \(-0.0720058\pi\) |
−0.681501 | + | 0.731817i | \(0.738672\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.70820 | − | 13.3510i | −0.579384 | − | 1.00352i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.4721 | − | 21.6024i | 0.932211 | − | 1.61464i | 0.152678 | − | 0.988276i | \(-0.451210\pi\) |
0.779533 | − | 0.626361i | \(-0.215456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1803 | 0.756699 | 0.378349 | − | 0.925663i | \(-0.376492\pi\) | ||||
0.378349 | + | 0.925663i | \(0.376492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.8885 | −1.61805 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.76393 | − | 4.78727i | 0.203208 | − | 0.351967i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.52786 | + | 9.57454i | 0.404237 | + | 0.700160i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.47214 | + | 11.2101i | 0.468307 | + | 0.811132i | 0.999344 | − | 0.0362168i | \(-0.0115307\pi\) |
−0.531037 | + | 0.847349i | \(0.678197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.23607 | − | 7.33708i | 0.304919 | − | 0.528135i | −0.672324 | − | 0.740257i | \(-0.734704\pi\) |
0.977243 | + | 0.212122i | \(0.0680373\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.9443 | 1.49985 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.94427 | −0.494759 | −0.247379 | − | 0.968919i | \(-0.579569\pi\) | ||||
−0.247379 | + | 0.968919i | \(0.579569\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.70820 | − | 9.88690i | 0.404644 | − | 0.700864i | −0.589636 | − | 0.807669i | \(-0.700729\pi\) |
0.994280 | + | 0.106805i | \(0.0340622\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.47214 | + | 11.2101i | 0.456509 | + | 0.790697i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.291796 | + | 0.505406i | 0.0203799 | + | 0.0352991i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.9443 | + | 25.8842i | −1.03870 | + | 1.79908i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.9443 | − | 36.2765i | 1.43508 | − | 2.48563i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.52786 | − | 2.64634i | −0.104199 | − | 0.180479i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.1803 | + | 41.8816i | 1.63396 | + | 2.83009i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.7082 | − | 20.2792i | 0.787579 | − | 1.36413i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.94427 | −0.331093 | −0.165546 | − | 0.986202i | \(-0.552939\pi\) | ||||
−0.165546 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.9443 | −1.72962 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.38197 | − | 11.0539i | 0.423586 | − | 0.733672i | −0.572701 | − | 0.819764i | \(-0.694104\pi\) |
0.996287 | + | 0.0860918i | \(0.0274378\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7984 | + | 22.1674i | 0.845740 | + | 1.46487i | 0.884977 | + | 0.465635i | \(0.154174\pi\) |
−0.0392364 | + | 0.999230i | \(0.512493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.94427 | − | 17.2240i | −0.651471 | − | 1.12838i | −0.982766 | − | 0.184854i | \(-0.940819\pi\) |
0.331295 | − | 0.943527i | \(-0.392514\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.944272 | − | 1.63553i | 0.0615975 | − | 0.106690i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0000 | 1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.8885 | 1.41585 | 0.707926 | − | 0.706287i | \(-0.249631\pi\) | ||||
0.707926 | + | 0.706287i | \(0.249631\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.76393 | + | 3.05522i | −0.113625 | + | 0.196804i | −0.917229 | − | 0.398360i | \(-0.869580\pi\) |
0.803604 | + | 0.595164i | \(0.202913\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.7984 | + | 30.8277i | 1.14177 | + | 1.97760i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.47214 | − | 14.6742i | −0.539069 | − | 0.933695i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.70820 | + | 13.3510i | −0.488488 | + | 0.846085i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.7082 | 1.11773 | 0.558866 | − | 0.829258i | \(-0.311237\pi\) | ||||
0.558866 | + | 0.829258i | \(0.311237\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.88854 | 0.621687 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.94427 | − | 15.4919i | 0.560112 | − | 0.970143i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.00000 | + | 12.1244i | 0.436648 | + | 0.756297i | 0.997429 | − | 0.0716680i | \(-0.0228322\pi\) |
−0.560781 | + | 0.827964i | \(0.689499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.7082 | − | 28.9395i | −1.03421 | − | 1.79131i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.4721 | + | 25.0665i | −0.892390 | + | 1.54567i | −0.0553884 | + | 0.998465i | \(0.517640\pi\) |
−0.837002 | + | 0.547200i | \(0.815694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.3607 | 0.759311 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.4164 | 1.18826 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.09017 | + | 15.7446i | −0.554237 | + | 0.959967i | 0.443725 | + | 0.896163i | \(0.353657\pi\) |
−0.997962 | + | 0.0638044i | \(0.979677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | + | 20.7846i | 0.728948 | + | 1.26258i | 0.957328 | + | 0.289003i | \(0.0933238\pi\) |
−0.228380 | + | 0.973572i | \(0.573343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.29180 | + | 7.43361i | 0.258805 | + | 0.448263i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9443 | − | 24.1522i | 0.837830 | − | 1.45116i | −0.0538751 | − | 0.998548i | \(-0.517157\pi\) |
0.891705 | − | 0.452617i | \(-0.149509\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 48.3607 | 2.89528 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.09017 | + | 14.0126i | −0.480911 | + | 0.832962i | −0.999760 | − | 0.0219039i | \(-0.993027\pi\) |
0.518849 | + | 0.854866i | \(0.326361\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.47214 | − | 11.2101i | −0.383376 | − | 0.664027i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.50000 | − | 2.59808i | −0.0882353 | − | 0.152828i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.70820 | − | 9.88690i | 0.334621 | − | 0.579580i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.2361 | −1.00694 | −0.503471 | − | 0.864012i | \(-0.667944\pi\) | ||||
−0.503471 | + | 0.864012i | \(0.667944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.88854 | 0.342844 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.8885 | − | 30.9839i | 1.03800 | − | 1.79787i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4721 | − | 18.1383i | −0.605619 | − | 1.04896i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.9443 | + | 32.8124i | 1.08832 | + | 1.88503i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.18034 | − | 7.24056i | 0.239366 | − | 0.414593i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1803 | 1.38004 | 0.690022 | − | 0.723788i | \(-0.257601\pi\) | ||||
0.690022 | + | 0.723788i | \(0.257601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 46.8328 | 2.66423 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.00000 | + | 6.92820i | −0.226819 | + | 0.392862i | −0.956864 | − | 0.290537i | \(-0.906166\pi\) |
0.730044 | + | 0.683400i | \(0.239499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.236068 | − | 0.408882i | −0.0133434 | − | 0.0231114i | 0.859277 | − | 0.511511i | \(-0.170914\pi\) |
−0.872620 | + | 0.488400i | \(0.837581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.4721 | − | 23.3344i | −0.756671 | − | 1.31059i | −0.944540 | − | 0.328398i | \(-0.893491\pi\) |
0.187869 | − | 0.982194i | \(-0.439842\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.52786 | + | 9.57454i | −0.309501 | + | 0.536071i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.9443 | 1.61551 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.4721 | −0.805251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.09017 | − | 15.7446i | 0.504232 | − | 0.873355i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.763932 | − | 1.32317i | −0.0422455 | − | 0.0731714i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.76393 | − | 11.7155i | −0.371779 | − | 0.643941i | 0.618060 | − | 0.786131i | \(-0.287919\pi\) |
−0.989839 | + | 0.142190i | \(0.954586\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.7082 | + | 28.9395i | −0.915604 | + | 1.58587i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.94427 | −0.270134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.3607 | −1.87175 | −0.935873 | − | 0.352338i | \(-0.885387\pi\) | ||||
−0.935873 | + | 0.352338i | \(0.885387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.70820 | + | 9.88690i | −0.310027 | + | 0.536983i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.00000 | − | 13.8564i | −0.433224 | − | 0.750366i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | − | 13.8564i | −0.430706 | − | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.23607 | − | 2.14093i | 0.0663556 | − | 0.114931i | −0.830939 | − | 0.556364i | \(-0.812196\pi\) |
0.897295 | + | 0.441432i | \(0.145529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.65248 | −0.249041 | −0.124521 | − | 0.992217i | \(-0.539739\pi\) | ||||
−0.124521 | + | 0.992217i | \(0.539739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −75.7771 | −4.04468 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.94427 | + | 17.2240i | −0.529280 | + | 0.916740i | 0.470137 | + | 0.882594i | \(0.344205\pi\) |
−0.999417 | + | 0.0341465i | \(0.989129\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | + | 13.8564i | 0.424596 | + | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.472136 | − | 0.817763i | −0.0249184 | − | 0.0431599i | 0.853297 | − | 0.521425i | \(-0.174599\pi\) |
−0.878216 | + | 0.478265i | \(0.841266\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.26393 | − | 7.38535i | 0.224417 | − | 0.388702i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.8197 | 0.830317 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4721 | −0.966876 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.4164 | + | 26.7020i | −0.804730 | + | 1.39383i | 0.111743 | + | 0.993737i | \(0.464357\pi\) |
−0.916473 | + | 0.400096i | \(0.868977\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.76393 | − | 3.05522i | −0.0918266 | − | 0.159048i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.47214 | + | 12.9421i | 0.386893 | + | 0.670118i | 0.992030 | − | 0.126004i | \(-0.0402151\pi\) |
−0.605137 | + | 0.796121i | \(0.706882\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.9443 | − | 29.3483i | 0.874998 | − | 1.51554i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.4164 | 1.20601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.4164 | −1.61375 | −0.806876 | − | 0.590721i | \(-0.798844\pi\) | ||||
−0.806876 | + | 0.590721i | \(0.798844\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.4721 | + | 25.0665i | −0.741430 | + | 1.28419i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.70820 | − | 9.88690i | −0.291676 | − | 0.505197i | 0.682530 | − | 0.730857i | \(-0.260879\pi\) |
−0.974206 | + | 0.225660i | \(0.927546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.23607 | + | 15.9973i | 0.469496 | + | 0.813190i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.23607 | + | 3.87298i | −0.113373 | + | 0.196368i | −0.917128 | − | 0.398592i | \(-0.869499\pi\) |
0.803755 | + | 0.594960i | \(0.202832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8885 | −0.904663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.52786 | 0.278844 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.05573 | + | 5.29268i | −0.153750 | + | 0.266303i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.38197 | + | 9.32184i | 0.270113 | + | 0.467850i | 0.968891 | − | 0.247489i | \(-0.0796056\pi\) |
−0.698777 | + | 0.715339i | \(0.746272\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.2361 | + | 28.1217i | 0.810791 | + | 1.40433i | 0.912311 | + | 0.409497i | \(0.134296\pi\) |
−0.101521 | + | 0.994833i | \(0.532371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.9443 | + | 29.3483i | −0.844054 | + | 1.46194i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −30.1803 | −1.49967 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0557 | 0.548012 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.70820 | + | 4.69075i | −0.133912 | + | 0.231943i | −0.925181 | − | 0.379525i | \(-0.876087\pi\) |
0.791269 | + | 0.611468i | \(0.209421\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.76393 | − | 8.25137i | −0.234987 | − | 0.407010i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.94427 | − | 5.09963i | −0.144529 | − | 0.250331i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.23607 | + | 9.06914i | −0.256411 | + | 0.444117i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.180340 | −0.00881018 | −0.00440509 | − | 0.999990i | \(-0.501402\pi\) | ||||
−0.00440509 | + | 0.999990i | \(0.501402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.70820 | + | 9.88690i | −0.277542 | + | 0.480717i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.76393 | − | 13.4475i | −0.376606 | − | 0.652301i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.9443 | + | 36.2765i | 1.01120 | + | 1.75145i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0000 | − | 24.2487i | 0.674356 | − | 1.16802i | −0.302300 | − | 0.953213i | \(-0.597755\pi\) |
0.976657 | − | 0.214807i | \(-0.0689121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.4164 | −0.836979 | −0.418490 | − | 0.908222i | \(-0.637440\pi\) | ||||
−0.418490 | + | 0.908222i | \(0.637440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.8885 | 0.857690 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.47214 | + | 11.2101i | −0.309604 | + | 0.536250i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | + | 27.7128i | 0.763638 | + | 1.32266i | 0.940963 | + | 0.338508i | \(0.109922\pi\) |
−0.177325 | + | 0.984152i | \(0.556744\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.9443 | − | 18.9560i | −0.519978 | − | 0.900628i | −0.999730 | − | 0.0232244i | \(-0.992607\pi\) |
0.479752 | − | 0.877404i | \(-0.340727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.70820 | + | 6.42280i | −0.175786 | + | 0.304470i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 48.3607 | 2.28738 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8885 | 1.31614 | 0.658071 | − | 0.752956i | \(-0.271373\pi\) | ||||
0.658071 | + | 0.752956i | \(0.271373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.583592 | + | 1.01081i | −0.0274803 | + | 0.0475972i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.4721 | + | 25.0665i | 0.679960 | + | 1.17773i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.23607 | + | 14.2653i | 0.385267 | + | 0.667302i | 0.991806 | − | 0.127752i | \(-0.0407760\pi\) |
−0.606539 | + | 0.795054i | \(0.707443\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −32.3607 | + | 56.0503i | −1.51047 | + | 2.61621i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.29180 | 0.386187 | 0.193094 | − | 0.981180i | \(-0.438148\pi\) | ||||
0.193094 | + | 0.981180i | \(0.438148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7771 | 1.66270 | 0.831351 | − | 0.555748i | \(-0.187568\pi\) | ||||
0.831351 | + | 0.555748i | \(0.187568\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.9443 | + | 22.4201i | −0.600276 | + | 1.03971i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.0344 | − | 22.5763i | −0.603162 | − | 1.04471i | −0.992339 | − | 0.123544i | \(-0.960574\pi\) |
0.389177 | − | 0.921163i | \(-0.372759\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.47214 | + | 14.6742i | 0.390375 | + | 0.676150i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.05573 | − | 5.29268i | 0.140503 | − | 0.243358i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.2361 | −0.515546 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −74.7214 | −3.42126 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.7082 | − | 30.6715i | 0.809108 | − | 1.40142i | −0.104374 | − | 0.994538i | \(-0.533284\pi\) |
0.913482 | − | 0.406879i | \(-0.133383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.7082 | − | 20.2792i | −0.533848 | − | 0.924652i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.18034 | + | 3.77646i | 0.0990041 | + | 0.171480i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0000 | + | 17.3205i | −0.453143 | + | 0.784867i | −0.998579 | − | 0.0532853i | \(-0.983031\pi\) |
0.545436 | + | 0.838152i | \(0.316364\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −75.7771 | −3.42676 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.11146 | 0.0952887 | 0.0476443 | − | 0.998864i | \(-0.484829\pi\) | ||||
0.0476443 | + | 0.998864i | \(0.484829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0000 | − | 17.3205i | 0.450377 | − | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.4164 | + | 19.7738i | 0.513129 | + | 0.888766i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.94427 | + | 12.0278i | 0.310868 | + | 0.538440i | 0.978551 | − | 0.206007i | \(-0.0660469\pi\) |
−0.667682 | + | 0.744446i | \(0.732714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.52786 | + | 9.57454i | −0.246967 | + | 0.427759i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.9443 | 0.577157 | 0.288578 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288578 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.4721 | −0.644002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.3262 | − | 40.4022i | 1.03595 | − | 1.79433i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.437694 | + | 0.758108i | 0.0194004 | + | 0.0336026i | 0.875563 | − | 0.483105i | \(-0.160491\pi\) |
−0.856162 | + | 0.516707i | \(0.827158\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.4164 | + | 40.5584i | 1.03386 | + | 1.79070i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.94427 | + | 15.4919i | −0.394132 | + | 0.682656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.77709 | 0.166116 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.9443 | 1.09493 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.7082 | − | 28.9395i | 0.732000 | − | 1.26786i | −0.224028 | − | 0.974583i | \(-0.571921\pi\) |
0.956027 | − | 0.293278i | \(-0.0947461\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.85410 | + | 15.3358i | 0.387163 | + | 0.670586i | 0.992067 | − | 0.125713i | \(-0.0401218\pi\) |
−0.604904 | + | 0.796299i | \(0.706788\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.4721 | + | 25.0665i | 0.630416 | + | 1.09191i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.5967 | −1.54477 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.47214 | 0.107080 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.52786 | + | 9.57454i | −0.238990 | + | 0.413944i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −40.3607 | − | 69.9067i | −1.74169 | − | 3.01670i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.4721 | + | 19.8703i | 0.493226 | + | 0.854292i | 0.999970 | − | 0.00780476i | \(-0.00248436\pi\) |
−0.506744 | + | 0.862097i | \(0.669151\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.4721 | − | 28.5306i | 0.706887 | − | 1.22436i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.583592 | 0.0249983 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4164 | −1.34327 | −0.671634 | − | 0.740883i | \(-0.734407\pi\) | ||||
−0.671634 | + | 0.740883i | \(0.734407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.2705 | + | 43.7698i | −1.07852 | + | 1.86805i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.23607 | − | 12.5332i | −0.308267 | − | 0.533934i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.94427 | − | 15.4919i | −0.379663 | − | 0.657596i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.4721 | + | 23.3344i | −0.570833 | + | 0.988711i | 0.425648 | + | 0.904889i | \(0.360046\pi\) |
−0.996481 | + | 0.0838224i | \(0.973287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.9443 | −0.547484 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.7771 | 1.51051 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.0902 | − | 34.7972i | 0.846700 | − | 1.46653i | −0.0374372 | − | 0.999299i | \(-0.511919\pi\) |
0.884137 | − | 0.467228i | \(-0.154747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.18034 | − | 3.77646i | −0.0917276 | − | 0.158877i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.18034 | + | 15.9008i | 0.384860 | + | 0.666597i | 0.991750 | − | 0.128189i | \(-0.0409164\pi\) |
−0.606890 | + | 0.794786i | \(0.707583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.76393 | − | 4.78727i | 0.115667 | − | 0.200341i | −0.802379 | − | 0.596815i | \(-0.796433\pi\) |
0.918046 | + | 0.396474i | \(0.129766\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 41.8885 | 1.74992 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8885 | −0.579192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00000 | − | 5.19615i | 0.124892 | − | 0.216319i | −0.796799 | − | 0.604245i | \(-0.793475\pi\) |
0.921691 | + | 0.387926i | \(0.126808\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.7082 | − | 23.7433i | −0.569694 | − | 0.986738i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.3607 | + | 21.4093i | 0.511927 | + | 0.886684i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.1803 | − | 41.8816i | 0.999734 | − | 1.73159i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.70820 | 0.400700 | 0.200350 | − | 0.979724i | \(-0.435792\pi\) | ||||
0.200350 | + | 0.979724i | \(0.435792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.9443 | 0.862994 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.2361 | + | 19.4614i | −0.462190 | + | 0.800537i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.4164 | + | 18.0417i | 0.427751 | + | 0.740886i | 0.996673 | − | 0.0815055i | \(-0.0259728\pi\) |
−0.568922 | + | 0.822391i | \(0.692639\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.4721 | − | 31.9947i | −0.756014 | − | 1.30945i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.94427 | − | 15.4919i | 0.365453 | − | 0.632983i | −0.623396 | − | 0.781907i | \(-0.714247\pi\) |
0.988849 | + | 0.148923i | \(0.0475807\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.7771 | −1.70412 | −0.852061 | − | 0.523442i | \(-0.824648\pi\) | ||||
−0.852061 | + | 0.523442i | \(0.824648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.8885 | 1.21716 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.02129 | + | 5.23302i | −0.122833 | + | 0.212753i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9443 | + | 22.4201i | 0.525392 | + | 0.910005i | 0.999563 | + | 0.0295724i | \(0.00941457\pi\) |
−0.474171 | + | 0.880433i | \(0.657252\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | − | 6.92820i | −0.161823 | − | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.29180 | + | 2.23746i | −0.0521752 | + | 0.0903700i | −0.890933 | − | 0.454134i | \(-0.849949\pi\) |
0.838758 | + | 0.544504i | \(0.183282\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.88854 | 0.0761534 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.3607 | −0.417105 | −0.208553 | − | 0.978011i | \(-0.566875\pi\) | ||||
−0.208553 | + | 0.978011i | \(0.566875\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.03444 | + | 8.71991i | −0.202351 | + | 0.350483i | −0.949286 | − | 0.314415i | \(-0.898192\pi\) |
0.746934 | + | 0.664898i | \(0.231525\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.9443 | + | 50.1329i | 1.16149 | + | 2.01177i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.20820 | − | 3.82472i | −0.0883282 | − | 0.152989i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.9443 | − | 22.4201i | 0.516944 | − | 0.895374i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.0557 | −1.07707 | −0.538536 | − | 0.842603i | \(-0.681022\pi\) | ||||
−0.538536 | + | 0.842603i | \(0.681022\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.4164 | + | 33.6302i | −0.771733 | + | 1.33668i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.52786 | − | 9.57454i | −0.219367 | − | 0.379954i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −48.3607 | − | 83.7632i | −1.91312 | − | 3.31362i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.7082 | + | 35.8677i | −0.817925 | + | 1.41669i | 0.0892837 | + | 0.996006i | \(0.471542\pi\) |
−0.907209 | + | 0.420681i | \(0.861791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.2918 | −1.19459 | −0.597296 | − | 0.802021i | \(-0.703758\pi\) | ||||
−0.597296 | + | 0.802021i | \(0.703758\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.88854 | −0.389361 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.1803 | + | 21.0970i | −0.478859 | + | 0.829407i | −0.999706 | − | 0.0242423i | \(-0.992283\pi\) |
0.520848 | + | 0.853650i | \(0.325616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.88854 | + | 10.1993i | 0.231146 | + | 0.400356i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.70820 | − | 15.0831i | −0.340778 | − | 0.590245i | 0.643799 | − | 0.765195i | \(-0.277357\pi\) |
−0.984577 | + | 0.174949i | \(0.944024\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.05573 | + | 1.82857i | −0.0412507 | + | 0.0714483i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 111.666 | 4.35649 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.3050 | −0.985741 | −0.492870 | − | 0.870103i | \(-0.664052\pi\) | ||||
−0.492870 | + | 0.870103i | \(0.664052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.32624 | + | 7.49326i | −0.168271 | + | 0.291454i | −0.937812 | − | 0.347143i | \(-0.887152\pi\) |
0.769541 | + | 0.638597i | \(0.220485\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −37.8885 | − | 65.6249i | −1.47147 | − | 2.54866i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.94427 | − | 15.4919i | −0.346324 | − | 0.599850i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.7214 | 0.645521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.9443 | 0.576059 | 0.288030 | − | 0.957621i | \(-0.407000\pi\) | ||||
0.288030 | + | 0.957621i | \(0.407000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.1246 | + | 43.5171i | −0.967047 | + | 1.67497i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.0902 | − | 36.5292i | −0.810561 | − | 1.40393i | −0.912472 | − | 0.409139i | \(-0.865829\pi\) |
0.101911 | − | 0.994794i | \(-0.467504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.6525 | − | 35.7711i | −0.791405 | − | 1.37075i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.8885 | − | 41.3762i | 0.914070 | − | 1.58322i | 0.105812 | − | 0.994386i | \(-0.466256\pi\) |
0.808258 | − | 0.588829i | \(-0.200411\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.63932 | 0.139051 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 82.8328 | 3.16027 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.1803 | − | 45.3457i | 0.997392 | − | 1.72753i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.09017 | − | 7.08438i | −0.155597 | − | 0.269503i | 0.777679 | − | 0.628662i | \(-0.216397\pi\) |
−0.933276 | + | 0.359159i | \(0.883064\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.00000 | − | 3.46410i | −0.0758643 | − | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.05573 | − | 1.82857i | 0.0399886 | − | 0.0692622i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −64.3607 | −2.43434 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5836 | −0.550815 | −0.275407 | − | 0.961328i | \(-0.588813\pi\) | ||||
−0.275407 | + | 0.961328i | \(0.588813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.23607 | + | 12.5332i | −0.272913 | + | 0.472700i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.05573 | − | 5.29268i | −0.115085 | − | 0.199334i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1803 | − | 40.1495i | −0.870556 | − | 1.50785i | −0.861423 | − | 0.507889i | \(-0.830426\pi\) |
−0.00913331 | − | 0.999958i | \(-0.502907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.4721 | − | 31.9947i | 0.692759 | − | 1.19989i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.8885 | 0.969534 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0000 | −0.598366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 35.4164 | − | 61.3430i | 1.32265 | − | 2.29090i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.5967 | + | 40.8708i | 0.880010 | + | 1.52422i | 0.851328 | + | 0.524634i | \(0.175798\pi\) |
0.0286822 | + | 0.999589i | \(0.490869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.70820 | + | 9.88690i | 0.212290 | + | 0.367698i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.76393 | − | 13.4475i | 0.288345 | − | 0.499429i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.3607 | −1.20019 | −0.600096 | − | 0.799928i | \(-0.704871\pi\) | ||||
−0.600096 | + | 0.799928i | \(0.704871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.52786 | + | 9.57454i | −0.204455 | + | 0.354127i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.61803 | + | 7.99867i | 0.170571 | + | 0.295438i | 0.938620 | − | 0.344954i | \(-0.112105\pi\) |
−0.768049 | + | 0.640391i | \(0.778772\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.94427 | − | 8.56373i | −0.182125 | − | 0.315449i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.7082 | + | 20.2792i | −0.430693 | + | 0.745983i | −0.996933 | − | 0.0782579i | \(-0.975064\pi\) |
0.566240 | + | 0.824240i | \(0.308398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −54.8328 | −2.01433 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.05573 | 0.258850 | 0.129425 | − | 0.991589i | \(-0.458687\pi\) | ||||
0.129425 | + | 0.991589i | \(0.458687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.23607 | + | 15.9973i | −0.338383 | + | 0.586097i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.7984 | + | 30.8277i | 0.651208 | + | 1.12793i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0000 | − | 31.1769i | −0.656829 | − | 1.13766i | −0.981432 | − | 0.191811i | \(-0.938564\pi\) |
0.324603 | − | 0.945851i | \(-0.394769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.6525 | − | 49.6275i | 1.04415 | − | 1.80853i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.0557 | −0.402359 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.3050 | −0.847033 | −0.423516 | − | 0.905888i | \(-0.639204\pi\) | ||||
−0.423516 | + | 0.905888i | \(0.639204\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.0000 | − | 27.7128i | 0.580763 | − | 1.00591i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.23607 | + | 10.8012i | 0.226057 | + | 0.391543i | 0.956636 | − | 0.291286i | \(-0.0940830\pi\) |
−0.730579 | + | 0.682828i | \(0.760750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.6525 | − | 35.7711i | −0.746692 | − | 1.29331i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.4721 | − | 21.6024i | 0.450343 | − | 0.780016i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.3607 | 0.950590 | 0.475295 | − | 0.879826i | \(-0.342341\pi\) | ||||
0.475295 | + | 0.879826i | \(0.342341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.3050 | 1.63162 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.90983 | + | 15.4323i | −0.320464 | + | 0.555060i | −0.980584 | − | 0.196100i | \(-0.937172\pi\) |
0.660120 | + | 0.751161i | \(0.270506\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.2361 | + | 19.4614i | 0.403611 | + | 0.699076i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.763932 | − | 1.32317i | −0.0273707 | − | 0.0474075i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | + | 27.7128i | −0.572525 | + | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −64.7214 | −2.31295 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.47214 | −0.231000 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.8541 | − | 22.2640i | 0.458199 | − | 0.793624i | −0.540667 | − | 0.841237i | \(-0.681828\pi\) |
0.998866 | + | 0.0476126i | \(0.0151613\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 46.8328 | + | 81.1168i | 1.66729 | + | 2.88784i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.7082 | − | 30.6715i | −0.628837 | − | 1.08918i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.0000 | − | 34.6410i | 0.709327 | − | 1.22859i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.8197 | −1.05627 | −0.528133 | − | 0.849161i | \(-0.677108\pi\) | ||||
−0.528133 | + | 0.849161i | \(0.677108\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.83282 | −0.241728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.4164 | − | 38.8264i | 0.792045 | − | 1.37186i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.4721 | − | 31.9947i | −0.651868 | − | 1.12907i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.4164 | + | 50.9507i | 1.03551 | + | 1.79355i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.70820 | + | 8.15485i | −0.165532 | + | 0.286709i | −0.936844 | − | 0.349748i | \(-0.886267\pi\) |
0.771312 | + | 0.636457i | \(0.219601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.0132 | 0.808101 | 0.404051 | − | 0.914737i | \(-0.367602\pi\) | ||||
0.404051 | + | 0.914737i | \(0.367602\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 77.6656 | 2.72385 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.4721 | − | 25.0665i | 0.506937 | − | 0.878040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | + | 6.92820i | 0.139942 | + | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.9443 | − | 34.5445i | −0.696060 | − | 1.20561i | −0.969822 | − | 0.243814i | \(-0.921601\pi\) |
0.273762 | − | 0.961797i | \(-0.411732\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.8885 | + | 44.8403i | −0.902418 | + | 1.56303i | −0.0780717 | + | 0.996948i | \(0.524876\pi\) |
−0.824346 | + | 0.566086i | \(0.808457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 27.7771 | 0.967074 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.9443 | 1.14558 | 0.572792 | − | 0.819701i | \(-0.305860\pi\) | ||||
0.572792 | + | 0.819701i | \(0.305860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.38197 | + | 5.85774i | −0.117461 | + | 0.203448i | −0.918761 | − | 0.394815i | \(-0.870809\pi\) |
0.801300 | + | 0.598263i | \(0.204142\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −45.1246 | − | 78.1581i | −1.56536 | − | 2.71128i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.11146 | − | 3.65715i | −0.0730700 | − | 0.126561i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 46.8328 | − | 81.1168i | 1.61878 | − | 2.80381i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.4721 | −1.05201 | −0.526007 | − | 0.850480i | \(-0.676312\pi\) | ||||
−0.526007 | + | 0.850480i | \(0.676312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.0689 | − | 72.8654i | 1.44893 | − | 2.50962i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.90983 | + | 15.4323i | 0.306507 | + | 0.530887i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.1803 | + | 45.3457i | 0.898507 | + | 1.55626i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.94427 | + | 15.4919i | −0.306606 | + | 0.531057i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.291796 | 0.00999091 | 0.00499545 | − | 0.999988i | \(-0.498410\pi\) | ||||
0.00499545 | + | 0.999988i | \(0.498410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.8885 | −1.02217 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.2361 | − | 31.5858i | 0.622932 | − | 1.07895i | −0.366005 | − | 0.930613i | \(-0.619275\pi\) |
0.988937 | − | 0.148337i | \(-0.0473921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0902 | + | 48.6536i | 0.958424 | + | 1.66004i | 0.726330 | + | 0.687346i | \(0.241224\pi\) |
0.232094 | + | 0.972693i | \(0.425442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.52786 | + | 2.64634i | 0.0520091 | + | 0.0900824i | 0.890858 | − | 0.454282i | \(-0.150104\pi\) |
−0.838849 | + | 0.544365i | \(0.816771\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.76393 | + | 8.25137i | −0.161979 | + | 0.280555i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.70820 | −0.329708 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.2229 | −0.414634 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4721 | + | 18.1383i | −0.354835 | + | 0.614592i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.1803 | − | 22.8290i | −0.446087 | − | 0.772645i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.70820 | + | 11.6190i | 0.226520 | + | 0.392344i | 0.956774 | − | 0.290831i | \(-0.0939318\pi\) |
−0.730254 | + | 0.683175i | \(0.760598\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.8885 | + | 48.3044i | −0.940657 | + | 1.62927i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.8328 | −0.971402 | −0.485701 | − | 0.874125i | \(-0.661436\pi\) | ||||
−0.485701 | + | 0.874125i | \(0.661436\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.9443 | 1.37788 | 0.688942 | − | 0.724816i | \(-0.258075\pi\) | ||||
0.688942 | + | 0.724816i | \(0.258075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.52786 | − | 16.5027i | 0.320276 | − | 0.554734i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.6525 | − | 25.3788i | −0.491982 | − | 0.852138i | 0.507975 | − | 0.861372i | \(-0.330394\pi\) |
−0.999957 | + | 0.00923379i | \(0.997061\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.1803 | − | 52.2739i | −1.01108 | − | 1.75124i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.47214 | + | 4.28187i | −0.0827269 | + | 0.143287i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.8328 | 1.03063 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −67.7771 | −2.26301 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.4721 | + | 25.0665i | −0.482673 | + | 0.836014i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.3607 | − | 38.7298i | −0.744942 | − | 1.29028i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.29180 | + | 10.8977i | 0.209146 | + | 0.362252i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.47214 | − | 14.6742i | 0.281313 | − | 0.487248i | −0.690396 | − | 0.723432i | \(-0.742564\pi\) |
0.971708 | + | 0.236184i | \(0.0758969\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 87.4853 | 2.90170 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.8328 | 0.623959 | 0.311980 | − | 0.950089i | \(-0.399008\pi\) | ||||
0.311980 | + | 0.950089i | \(0.399008\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.88854 | − | 10.1993i | 0.194882 | − | 0.337546i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.5279 | − | 23.4309i | −0.447217 | − | 0.774603i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.8885 | − | 30.9839i | −0.590089 | − | 1.02206i | −0.994220 | − | 0.107362i | \(-0.965759\pi\) |
0.404131 | − | 0.914701i | \(-0.367574\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.1246 | − | 67.7658i | 1.28920 | − | 2.23296i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.7771 | 2.23091 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.5279 | −0.510553 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 54.0689 | − | 93.6501i | 1.77586 | − | 3.07587i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.65248 | − | 13.2545i | −0.251070 | − | 0.434865i | 0.712751 | − | 0.701417i | \(-0.247449\pi\) |
−0.963821 | + | 0.266552i | \(0.914116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.9443 | + | 22.4201i | 0.423776 | + | 0.734002i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.83282 | + | 11.8348i | −0.223457 | + | 0.387039i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.9443 | −0.880231 | −0.440115 | − | 0.897941i | \(-0.645063\pi\) | ||||
−0.440115 | + | 0.897941i | \(0.645063\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.52786 | −0.0498600 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.79837 | + | 11.7751i | −0.221621 | + | 0.383858i | −0.955300 | − | 0.295637i | \(-0.904468\pi\) |
0.733680 | + | 0.679496i | \(0.237801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.944272 | − | 1.63553i | −0.0307497 | − | 0.0532601i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.7082 | + | 27.2074i | 0.510448 | + | 0.884122i | 0.999927 | + | 0.0121067i | \(0.00385377\pi\) |
−0.489479 | + | 0.872015i | \(0.662813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.1246 | + | 67.7658i | −1.27004 | + | 2.19977i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −87.1935 | −2.82744 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.1115 | 0.521901 | 0.260951 | − | 0.965352i | \(-0.415964\pi\) | ||||
0.260951 | + | 0.965352i | \(0.415964\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | + | 13.8564i | −0.258874 | + | 0.448383i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.8885 | + | 30.9839i | 0.578254 | + | 1.00157i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.44427 | − | 9.42976i | −0.175622 | − | 0.304186i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33.4164 | − | 57.8789i | 1.07683 | − | 1.86512i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.4721 | 0.337110 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.88854 | −0.189363 | −0.0946814 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946814 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.4164 | + | 40.5584i | −0.752243 | + | 1.30292i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.6180 | − | 23.5871i | −0.437024 | − | 0.756947i | 0.560435 | − | 0.828199i | \(-0.310634\pi\) |
−0.997458 | + | 0.0712516i | \(0.977301\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29.4164 | − | 50.9507i | −0.942079 | − | 1.63173i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.4164 | + | 35.3623i | −0.653179 | + | 1.13134i | 0.329168 | + | 0.944271i | \(0.393232\pi\) |
−0.982347 | + | 0.187068i | \(0.940102\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.8328 | −0.474059 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.52786 | −0.112636 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.23607 | − | 12.5332i | 0.230795 | − | 0.399748i | −0.727247 | − | 0.686375i | \(-0.759201\pi\) |
0.958042 | + | 0.286627i | \(0.0925341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.29180 | − | 7.43361i | −0.136748 | − | 0.236854i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.94427 | + | 8.56373i | 0.157219 | + | 0.272311i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.0000 | − | 20.7846i | 0.381193 | − | 0.660245i | −0.610040 | − | 0.792370i | \(-0.708847\pi\) |
0.991233 | + | 0.132125i | \(0.0421802\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.7771 | −1.38922 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.1115 | 0.447363 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.0344 | − | 34.7007i | 0.634497 | − | 1.09898i | −0.352124 | − | 0.935953i | \(-0.614541\pi\) |
0.986621 | − | 0.163028i | \(-0.0521261\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.3607 | + | 56.0503i | 1.02385 | + | 1.77335i |
(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 | 1568.2.i.v.1537.2 | 4 | ||
4.3 | odd | 2 | 1568.2.i.m.1537.1 | 4 | |||
7.2 | even | 3 | inner | 1568.2.i.v.961.2 | 4 | ||
7.3 | odd | 6 | 1568.2.a.v.1.2 | 2 | |||
7.4 | even | 3 | 224.2.a.c.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | 1568.2.i.n.961.1 | 4 | |||
7.6 | odd | 2 | 1568.2.i.n.1537.1 | 4 | |||
21.11 | odd | 6 | 2016.2.a.r.1.2 | 2 | |||
28.3 | even | 6 | 1568.2.a.k.1.1 | 2 | |||
28.11 | odd | 6 | 224.2.a.d.1.2 | yes | 2 | ||
28.19 | even | 6 | 1568.2.i.w.961.2 | 4 | |||
28.23 | odd | 6 | 1568.2.i.m.961.1 | 4 | |||
28.27 | even | 2 | 1568.2.i.w.1537.2 | 4 | |||
35.4 | even | 6 | 5600.2.a.bk.1.2 | 2 | |||
56.3 | even | 6 | 3136.2.a.by.1.2 | 2 | |||
56.11 | odd | 6 | 448.2.a.i.1.1 | 2 | |||
56.45 | odd | 6 | 3136.2.a.bf.1.1 | 2 | |||
56.53 | even | 6 | 448.2.a.j.1.2 | 2 | |||
84.11 | even | 6 | 2016.2.a.o.1.2 | 2 | |||
112.11 | odd | 12 | 1792.2.b.m.897.1 | 4 | |||
112.53 | even | 12 | 1792.2.b.k.897.4 | 4 | |||
112.67 | odd | 12 | 1792.2.b.m.897.4 | 4 | |||
112.109 | even | 12 | 1792.2.b.k.897.1 | 4 | |||
140.39 | odd | 6 | 5600.2.a.z.1.1 | 2 | |||
168.11 | even | 6 | 4032.2.a.bv.1.1 | 2 | |||
168.53 | odd | 6 | 4032.2.a.bw.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.a.c.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
224.2.a.d.1.2 | yes | 2 | 28.11 | odd | 6 | ||
448.2.a.i.1.1 | 2 | 56.11 | odd | 6 | |||
448.2.a.j.1.2 | 2 | 56.53 | even | 6 | |||
1568.2.a.k.1.1 | 2 | 28.3 | even | 6 | |||
1568.2.a.v.1.2 | 2 | 7.3 | odd | 6 | |||
1568.2.i.m.961.1 | 4 | 28.23 | odd | 6 | |||
1568.2.i.m.1537.1 | 4 | 4.3 | odd | 2 | |||
1568.2.i.n.961.1 | 4 | 7.5 | odd | 6 | |||
1568.2.i.n.1537.1 | 4 | 7.6 | odd | 2 | |||
1568.2.i.v.961.2 | 4 | 7.2 | even | 3 | inner | ||
1568.2.i.v.1537.2 | 4 | 1.1 | even | 1 | trivial | ||
1568.2.i.w.961.2 | 4 | 28.19 | even | 6 | |||
1568.2.i.w.1537.2 | 4 | 28.27 | even | 2 | |||
1792.2.b.k.897.1 | 4 | 112.109 | even | 12 | |||
1792.2.b.k.897.4 | 4 | 112.53 | even | 12 | |||
1792.2.b.m.897.1 | 4 | 112.11 | odd | 12 | |||
1792.2.b.m.897.4 | 4 | 112.67 | odd | 12 | |||
2016.2.a.o.1.2 | 2 | 84.11 | even | 6 | |||
2016.2.a.r.1.2 | 2 | 21.11 | odd | 6 | |||
3136.2.a.bf.1.1 | 2 | 56.45 | odd | 6 | |||
3136.2.a.by.1.2 | 2 | 56.3 | even | 6 | |||
4032.2.a.bv.1.1 | 2 | 168.11 | even | 6 | |||
4032.2.a.bw.1.1 | 2 | 168.53 | odd | 6 | |||
5600.2.a.z.1.1 | 2 | 140.39 | odd | 6 | |||
5600.2.a.bk.1.2 | 2 | 35.4 | even | 6 |