Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (of order \(4\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1007.1 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1007 |
Dual form | 1600.2.j.b.143.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.93185i | − | 1.11536i | −0.830058 | − | 0.557678i | \(-0.811693\pi\) | ||
0.830058 | − | 0.557678i | \(-0.188307\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.896575 | + | 0.896575i | 0.338874 | + | 0.338874i | 0.855943 | − | 0.517070i | \(-0.172977\pi\) |
−0.517070 | + | 0.855943i | \(0.672977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.732051 | −0.244017 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.09808 | − | 4.09808i | −1.23562 | − | 1.23562i | −0.961775 | − | 0.273842i | \(-0.911706\pi\) |
−0.273842 | − | 0.961775i | \(-0.588294\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.89898 | −1.35873 | −0.679366 | − | 0.733799i | \(-0.737745\pi\) | ||||
−0.679366 | + | 0.733799i | \(0.737745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.707107 | − | 0.707107i | −0.171499 | − | 0.171499i | 0.616139 | − | 0.787638i | \(-0.288696\pi\) |
−0.787638 | + | 0.616139i | \(0.788696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.09808 | + | 3.09808i | 0.710747 | + | 0.710747i | 0.966692 | − | 0.255944i | \(-0.0823863\pi\) |
−0.255944 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73205 | − | 1.73205i | 0.377964 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.96713 | + | 2.96713i | −0.618689 | + | 0.618689i | −0.945195 | − | 0.326506i | \(-0.894129\pi\) |
0.326506 | + | 0.945195i | \(0.394129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.38134i | − | 0.843190i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.26795 | + | 1.26795i | −0.235452 | + | 0.235452i | −0.814964 | − | 0.579512i | \(-0.803243\pi\) |
0.579512 | + | 0.814964i | \(0.303243\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.19615i | 0.753651i | 0.926284 | + | 0.376826i | \(0.122984\pi\) | ||||
−0.926284 | + | 0.376826i | \(0.877016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.91688 | + | 7.91688i | −1.37815 | + | 1.37815i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9348 | −1.79767 | −0.898833 | − | 0.438292i | \(-0.855584\pi\) | ||||
−0.898833 | + | 0.438292i | \(0.855584\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.46410i | 1.51547i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.46410i | − | 1.00952i | −0.863259 | − | 0.504762i | \(-0.831580\pi\) | ||
0.863259 | − | 0.504762i | \(-0.168420\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.14162 | −1.39408 | −0.697042 | − | 0.717030i | \(-0.745501\pi\) | ||||
−0.697042 | + | 0.717030i | \(0.745501\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41421 | − | 1.41421i | 0.206284 | − | 0.206284i | −0.596402 | − | 0.802686i | \(-0.703403\pi\) |
0.802686 | + | 0.596402i | \(0.203403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.39230i | − | 0.770329i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.36603 | + | 1.36603i | −0.191282 | + | 0.191282i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.89949i | − | 1.35980i | −0.733305 | − | 0.679900i | \(-0.762023\pi\) | ||
0.733305 | − | 0.679900i | \(-0.237977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.98502 | − | 5.98502i | 0.792736 | − | 0.792736i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.26795 | + | 4.26795i | −0.555640 | + | 0.555640i | −0.928063 | − | 0.372423i | \(-0.878527\pi\) |
0.372423 | + | 0.928063i | \(0.378527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.19615 | + | 7.19615i | 0.921373 | + | 0.921373i | 0.997127 | − | 0.0757537i | \(-0.0241363\pi\) |
−0.0757537 | + | 0.997127i | \(0.524136\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.656339 | − | 0.656339i | −0.0826909 | − | 0.0826909i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.55291 | −0.189719 | −0.0948593 | − | 0.995491i | \(-0.530240\pi\) | ||||
−0.0948593 | + | 0.995491i | \(0.530240\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.73205 | + | 5.73205i | 0.690058 | + | 0.690058i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9282 | 1.53430 | 0.767148 | − | 0.641470i | \(-0.221675\pi\) | ||||
0.767148 | + | 0.641470i | \(0.221675\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.91447 | + | 3.91447i | 0.458154 | + | 0.458154i | 0.898049 | − | 0.439895i | \(-0.144984\pi\) |
−0.439895 | + | 0.898049i | \(0.644984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 7.34847i | − | 0.837436i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.19615 | −0.922139 | −0.461070 | − | 0.887364i | \(-0.652534\pi\) | ||||
−0.461070 | + | 0.887364i | \(0.652534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6603 | −1.18447 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.65874i | 0.511363i | 0.966761 | + | 0.255682i | \(0.0822999\pi\) | ||||
−0.966761 | + | 0.255682i | \(0.917700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.44949 | + | 2.44949i | 0.262613 | + | 0.262613i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.7321 | −1.45559 | −0.727797 | − | 0.685792i | \(-0.759456\pi\) | ||||
−0.727797 | + | 0.685792i | \(0.759456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.39230 | − | 4.39230i | −0.460439 | − | 0.460439i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.10634 | 0.840589 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.10583 | − | 3.10583i | −0.315349 | − | 0.315349i | 0.531629 | − | 0.846978i | \(-0.321580\pi\) |
−0.846978 | + | 0.531629i | \(0.821580\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.00000 | + | 3.00000i | 0.301511 | + | 0.301511i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.92820 | − | 3.92820i | 0.390871 | − | 0.390871i | −0.484127 | − | 0.874998i | \(-0.660863\pi\) |
0.874998 | + | 0.484127i | \(0.160863\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.44949 | + | 2.44949i | −0.241355 | + | 0.241355i | −0.817411 | − | 0.576055i | \(-0.804591\pi\) |
0.576055 | + | 0.817411i | \(0.304591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.55291i | − | 0.150126i | −0.997179 | − | 0.0750629i | \(-0.976084\pi\) | ||
0.997179 | − | 0.0750629i | \(-0.0239158\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3923 | + | 11.3923i | −1.09118 | + | 1.09118i | −0.0957826 | + | 0.995402i | \(0.530535\pi\) |
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.1244i | 2.00504i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.33109 | + | 9.33109i | −0.877795 | + | 0.877795i | −0.993306 | − | 0.115511i | \(-0.963149\pi\) |
0.115511 | + | 0.993306i | \(0.463149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.58630 | 0.331554 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.26795i | − | 0.116233i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.5885i | 2.05350i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.4877 | −1.12598 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.55291 | − | 1.55291i | 0.137799 | − | 0.137799i | −0.634843 | − | 0.772641i | \(-0.718935\pi\) |
0.772641 | + | 0.634843i | \(0.218935\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.6603i | 1.55490i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.92820 | − | 9.92820i | 0.867431 | − | 0.867431i | −0.124756 | − | 0.992187i | \(-0.539815\pi\) |
0.992187 | + | 0.124756i | \(0.0398149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.55532i | 0.481707i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.98262 | + | 1.98262i | −0.169387 | + | 0.169387i | −0.786710 | − | 0.617323i | \(-0.788217\pi\) |
0.617323 | + | 0.786710i | \(0.288217\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.29423 | − | 8.29423i | 0.703507 | − | 0.703507i | −0.261654 | − | 0.965162i | \(-0.584268\pi\) |
0.965162 | + | 0.261654i | \(0.0842680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.73205 | − | 2.73205i | −0.230080 | − | 0.230080i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.0764 | + | 20.0764i | 1.67887 | + | 1.67887i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.4171 | −0.859191 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.12436 | + | 9.12436i | 0.747496 | + | 0.747496i | 0.974008 | − | 0.226512i | \(-0.0727323\pi\) |
−0.226512 | + | 0.974008i | \(0.572732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.196152 | 0.0159627 | 0.00798133 | − | 0.999968i | \(-0.497459\pi\) | ||||
0.00798133 | + | 0.999968i | \(0.497459\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.517638 | + | 0.517638i | 0.0418486 | + | 0.0418486i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.656339i | 0.0523815i | 0.999657 | + | 0.0261908i | \(0.00833773\pi\) | ||||
−0.999657 | + | 0.0261908i | \(0.991662\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.1244 | −1.51666 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.32051 | −0.419315 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.1440i | − | 1.02952i | −0.857334 | − | 0.514760i | \(-0.827881\pi\) | ||
0.857334 | − | 0.514760i | \(-0.172119\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.4195 | − | 14.4195i | −1.11582 | − | 1.11582i | −0.992348 | − | 0.123469i | \(-0.960598\pi\) |
−0.123469 | − | 0.992348i | \(-0.539402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | 0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.26795 | − | 2.26795i | −0.173434 | − | 0.173434i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.76268 | −0.666214 | −0.333107 | − | 0.942889i | \(-0.608097\pi\) | ||||
−0.333107 | + | 0.942889i | \(0.608097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.24504 | + | 8.24504i | 0.619736 | + | 0.619736i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.56218 | − | 4.56218i | −0.340993 | − | 0.340993i | 0.515747 | − | 0.856741i | \(-0.327514\pi\) |
−0.856741 | + | 0.515747i | \(0.827514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1962 | − | 13.1962i | 0.980862 | − | 0.980862i | −0.0189580 | − | 0.999820i | \(-0.506035\pi\) |
0.999820 | + | 0.0189580i | \(0.00603488\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.9019 | − | 13.9019i | 1.02766 | − | 1.02766i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.79555i | 0.423813i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.92820 | − | 3.92820i | 0.285735 | − | 0.285735i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.339746i | − | 0.0245832i | −0.999924 | − | 0.0122916i | \(-0.996087\pi\) | ||
0.999924 | − | 0.0122916i | \(-0.00391263\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.22715 | − | 5.22715i | 0.376258 | − | 0.376258i | −0.493492 | − | 0.869750i | \(-0.664280\pi\) |
0.869750 | + | 0.493492i | \(0.164280\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.9396 | 1.34939 | 0.674695 | − | 0.738097i | \(-0.264275\pi\) | ||||
0.674695 | + | 0.738097i | \(0.264275\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.39230i | − | 0.311362i | −0.987807 | − | 0.155681i | \(-0.950243\pi\) | ||
0.987807 | − | 0.155681i | \(-0.0497572\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.00000i | 0.211604i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.27362 | −0.159577 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.17209 | − | 2.17209i | 0.150971 | − | 0.150971i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 25.3923i | − | 1.75642i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.29423 | − | 4.29423i | 0.295627 | − | 0.295627i | −0.543671 | − | 0.839298i | \(-0.682966\pi\) |
0.839298 | + | 0.543671i | \(0.182966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 24.9754i | − | 1.71128i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.76217 | + | 3.76217i | −0.255393 | + | 0.255393i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.56218 | − | 7.56218i | 0.511005 | − | 0.511005i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.46410 | + | 3.46410i | 0.233021 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.44949 | − | 2.44949i | −0.164030 | − | 0.164030i | 0.620319 | − | 0.784349i | \(-0.287003\pi\) |
−0.784349 | + | 0.620319i | \(0.787003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.4543 | 0.693876 | 0.346938 | − | 0.937888i | \(-0.387221\pi\) | ||||
0.346938 | + | 0.937888i | \(0.387221\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.00000 | − | 4.00000i | −0.264327 | − | 0.264327i | 0.562482 | − | 0.826809i | \(-0.309847\pi\) |
−0.826809 | + | 0.562482i | \(0.809847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.1962 | −0.934038 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.65685 | − | 5.65685i | −0.370593 | − | 0.370593i | 0.497100 | − | 0.867693i | \(-0.334398\pi\) |
−0.867693 | + | 0.497100i | \(0.834398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.8338i | 1.02851i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5359 | 0.940249 | 0.470125 | − | 0.882600i | \(-0.344209\pi\) | ||||
0.470125 | + | 0.882600i | \(0.344209\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1962 | −1.49420 | −0.747098 | − | 0.664714i | \(-0.768553\pi\) | ||||
−0.747098 | + | 0.664714i | \(0.768553\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.45001i | 0.477918i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.1774 | − | 15.1774i | −0.965716 | − | 0.965716i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.00000 | 0.570352 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.169873 | − | 0.169873i | −0.0107223 | − | 0.0107223i | 0.701725 | − | 0.712448i | \(-0.252413\pi\) |
−0.712448 | + | 0.701725i | \(0.752413\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.3190 | 1.52892 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1769 | + | 10.1769i | 0.634817 | + | 0.634817i | 0.949272 | − | 0.314455i | \(-0.101822\pi\) |
−0.314455 | + | 0.949272i | \(0.601822\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.80385 | − | 9.80385i | −0.609181 | − | 0.609181i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.928203 | − | 0.928203i | 0.0574543 | − | 0.0574543i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.27551 | − | 1.27551i | 0.0786515 | − | 0.0786515i | −0.666687 | − | 0.745338i | \(-0.732288\pi\) |
0.745338 | + | 0.666687i | \(0.232288\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.5283i | 1.62350i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.7321 | − | 10.7321i | 0.654345 | − | 0.654345i | −0.299691 | − | 0.954036i | \(-0.596884\pi\) |
0.954036 | + | 0.299691i | \(0.0968837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 30.5885i | − | 1.85812i | −0.369934 | − | 0.929058i | \(-0.620620\pi\) | ||
0.369934 | − | 0.929058i | \(-0.379380\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.48528 | + | 8.48528i | −0.513553 | + | 0.513553i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.07180i | − | 0.183904i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.53590i | − | 0.509209i | −0.967045 | − | 0.254605i | \(-0.918055\pi\) | ||
0.967045 | − | 0.254605i | \(-0.0819453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.9730 | −1.24671 | −0.623357 | − | 0.781938i | \(-0.714232\pi\) | ||||
−0.623357 | + | 0.781938i | \(0.714232\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.79555 | − | 5.79555i | 0.342101 | − | 0.342101i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.0000i | − | 0.941176i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | + | 6.00000i | −0.351726 | + | 0.351726i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.89949i | 0.578335i | 0.957279 | + | 0.289167i | \(0.0933784\pi\) | ||||
−0.957279 | + | 0.289167i | \(0.906622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.9551 | + | 17.9551i | −1.04186 | + | 1.04186i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.5359 | − | 14.5359i | 0.840633 | − | 0.840633i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.19615 | − | 8.19615i | −0.472418 | − | 0.472418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.58871 | − | 7.58871i | −0.435960 | − | 0.435960i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.27603 | 0.358192 | 0.179096 | − | 0.983832i | \(-0.442683\pi\) | ||||
0.179096 | + | 0.983832i | \(0.442683\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.73205 | + | 4.73205i | 0.269197 | + | 0.269197i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.66025 | −0.320964 | −0.160482 | − | 0.987039i | \(-0.551305\pi\) | ||||
−0.160482 | + | 0.987039i | \(0.551305\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.14162 | + | 9.14162i | 0.516715 | + | 0.516715i | 0.916576 | − | 0.399861i | \(-0.130942\pi\) |
−0.399861 | + | 0.916576i | \(0.630942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 20.0764i | − | 1.12760i | −0.825911 | − | 0.563801i | \(-0.809338\pi\) | ||
0.825911 | − | 0.563801i | \(-0.190662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.3923 | 0.581857 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | −0.167444 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.38134i | − | 0.243784i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.0082 | + | 22.0082i | 1.21706 | + | 1.21706i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.53590 | 0.139809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.49038 | − | 6.49038i | −0.356744 | − | 0.356744i | 0.505868 | − | 0.862611i | \(-0.331172\pi\) |
−0.862611 | + | 0.505868i | \(0.831172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00481 | 0.438661 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.71003 | − | 9.71003i | −0.528939 | − | 0.528939i | 0.391317 | − | 0.920256i | \(-0.372020\pi\) |
−0.920256 | + | 0.391317i | \(0.872020\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.0263 | + | 18.0263i | 0.979053 | + | 0.979053i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.1962 | − | 17.1962i | 0.931224 | − | 0.931224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1106 | − | 11.1106i | 0.599918 | − | 0.599918i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4.38134i | − | 0.235203i | −0.993061 | − | 0.117601i | \(-0.962479\pi\) | ||
0.993061 | − | 0.117601i | \(-0.0375205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.58846 | + | 7.58846i | −0.406201 | + | 0.406201i | −0.880411 | − | 0.474211i | \(-0.842734\pi\) |
0.474211 | + | 0.880411i | \(0.342734\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.4641i | 1.14567i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.5964 | − | 24.5964i | 1.30914 | − | 1.30914i | 0.387097 | − | 0.922039i | \(-0.373478\pi\) |
0.922039 | − | 0.387097i | \(-0.126522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.44949 | −0.129641 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.58846i | 0.347725i | 0.984770 | + | 0.173863i | \(0.0556249\pi\) | ||||
−0.984770 | + | 0.173863i | \(0.944375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.196152i | 0.0103238i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 43.6375 | 2.29038 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.5259 | + | 22.5259i | −1.17584 | + | 1.17584i | −0.195048 | + | 0.980794i | \(0.562486\pi\) |
−0.980794 | + | 0.195048i | \(0.937514\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.73205i | 0.246341i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.87564 | − | 8.87564i | 0.460800 | − | 0.460800i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.13681i | 0.0588619i | 0.999567 | + | 0.0294310i | \(0.00936952\pi\) | ||||
−0.999567 | + | 0.0294310i | \(0.990630\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.21166 | − | 6.21166i | 0.319917 | − | 0.319917i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.29423 | + | 5.29423i | −0.271946 | + | 0.271946i | −0.829883 | − | 0.557937i | \(-0.811593\pi\) |
0.557937 | + | 0.829883i | \(0.311593\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | − | 3.00000i | −0.153695 | − | 0.153695i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.20977 | + | 7.20977i | 0.368402 | + | 0.368402i | 0.866894 | − | 0.498492i | \(-0.166113\pi\) |
−0.498492 | + | 0.866894i | \(0.666113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.69213 | 0.340180 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.3205 | − | 26.3205i | −1.33450 | − | 1.33450i | −0.901293 | − | 0.433209i | \(-0.857381\pi\) |
−0.433209 | − | 0.901293i | \(-0.642619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.19615 | 0.212209 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.1798 | − | 19.1798i | −0.967494 | − | 0.967494i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3843i | 0.671737i | 0.941909 | + | 0.335868i | \(0.109030\pi\) | ||||
−0.941909 | + | 0.335868i | \(0.890970\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.7321 | 0.537275 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.1244 | 0.605461 | 0.302731 | − | 0.953076i | \(-0.402102\pi\) | ||||
0.302731 | + | 0.953076i | \(0.402102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.5569i | − | 1.02401i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.8115 | + | 44.8115i | 2.22122 | + | 2.22122i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.60770 | −0.227836 | −0.113918 | − | 0.993490i | \(-0.536340\pi\) | ||||
−0.113918 | + | 0.993490i | \(0.536340\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.83013 | + | 3.83013i | 0.188926 | + | 0.188926i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.65308 | −0.376583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0232 | − | 16.0232i | −0.784660 | − | 0.784660i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5622 | − | 16.5622i | −0.809115 | − | 0.809115i | 0.175385 | − | 0.984500i | \(-0.443883\pi\) |
−0.984500 | + | 0.175385i | \(0.943883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.3923 | + | 26.3923i | −1.28628 | + | 1.28628i | −0.349254 | + | 0.937028i | \(0.613565\pi\) |
−0.937028 | + | 0.349254i | \(0.886435\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.03528 | + | 1.03528i | −0.0503369 | + | 0.0503369i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9038i | 0.624458i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 38.7846 | − | 38.7846i | 1.87254 | − | 1.87254i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.58846i | 0.317355i | 0.987330 | + | 0.158677i | \(0.0507230\pi\) | ||||
−0.987330 | + | 0.158677i | \(0.949277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.57081 | − | 4.57081i | 0.219659 | − | 0.219659i | −0.588696 | − | 0.808355i | \(-0.700358\pi\) |
0.808355 | + | 0.588696i | \(0.200358\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.3848 | −0.879463 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 40.3923i | − | 1.92782i | −0.266229 | − | 0.963910i | \(-0.585778\pi\) | ||
0.266229 | − | 0.963910i | \(-0.414222\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.94744i | 0.187973i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5545 | 0.786526 | 0.393263 | − | 0.919426i | \(-0.371346\pi\) | ||||
0.393263 | + | 0.919426i | \(0.371346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.6269 | − | 17.6269i | 0.833724 | − | 0.833724i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.12436i | − | 0.289026i | −0.989503 | − | 0.144513i | \(-0.953838\pi\) | ||
0.989503 | − | 0.144513i | \(-0.0461616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.4904 | + | 26.4904i | −1.24738 | + | 1.24738i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 0.378937i | − | 0.0178040i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1953 | − | 18.1953i | 0.851141 | − | 0.851141i | −0.139133 | − | 0.990274i | \(-0.544432\pi\) |
0.990274 | + | 0.139133i | \(0.0444316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.09808 | + | 3.09808i | −0.144606 | + | 0.144606i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.2679 | − | 13.2679i | −0.617950 | − | 0.617950i | 0.327055 | − | 0.945005i | \(-0.393944\pi\) |
−0.945005 | + | 0.327055i | \(0.893944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00481 | + | 8.00481i | 0.372015 | + | 0.372015i | 0.868211 | − | 0.496196i | \(-0.165270\pi\) |
−0.496196 | + | 0.868211i | \(0.665270\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.41421 | 0.0654420 | 0.0327210 | − | 0.999465i | \(-0.489583\pi\) | ||||
0.0327210 | + | 0.999465i | \(0.489583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.39230 | − | 1.39230i | −0.0642907 | − | 0.0642907i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.26795 | 0.0584240 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.4631 | + | 37.4631i | 1.72255 | + | 1.72255i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.24693i | 0.331814i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.3397 | −1.11211 | −0.556056 | − | 0.831145i | \(-0.687686\pi\) | ||||
−0.556056 | + | 0.831145i | \(0.687686\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 53.5692 | 2.44255 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.2784i | 0.467685i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.4225 | − | 23.4225i | −1.06137 | − | 1.06137i | −0.997989 | − | 0.0633836i | \(-0.979811\pi\) |
−0.0633836 | − | 0.997989i | \(-0.520189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.3923 | −1.14828 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.3205 | + | 14.3205i | 0.646275 | + | 0.646275i | 0.952091 | − | 0.305815i | \(-0.0989290\pi\) |
−0.305815 | + | 0.952091i | \(0.598929\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.79315 | 0.0807595 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.5911 | + | 11.5911i | 0.519932 | + | 0.519932i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0000 | + | 23.0000i | 1.02962 | + | 1.02962i | 0.999548 | + | 0.0300737i | \(0.00957421\pi\) |
0.0300737 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.8564 | + | 27.8564i | −1.24453 | + | 1.24453i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.62587 | − | 7.62587i | 0.340021 | − | 0.340021i | −0.516354 | − | 0.856375i | \(-0.672711\pi\) |
0.856375 | + | 0.516354i | \(0.172711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 21.2504i | − | 0.943762i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0000 | + | 15.0000i | −0.664863 | + | 0.664863i | −0.956522 | − | 0.291659i | \(-0.905793\pi\) |
0.291659 | + | 0.956522i | \(0.405793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.01924i | 0.310513i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.5737 | − | 13.5737i | 0.599295 | − | 0.599295i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.5911 | −0.509776 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.9282i | 0.743066i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 45.2487i | − | 1.98238i | −0.132440 | − | 0.991191i | \(-0.542281\pi\) | ||
0.132440 | − | 0.991191i | \(-0.457719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0478 | 1.13899 | 0.569496 | − | 0.821994i | \(-0.307139\pi\) | ||||
0.569496 | + | 0.821994i | \(0.307139\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.96713 | − | 2.96713i | 0.129250 | − | 0.129250i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.39230i | 0.234448i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.12436 | − | 3.12436i | 0.135585 | − | 0.135585i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.6675i | 1.37167i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.81345 | + | 8.81345i | −0.380328 | + | 0.380328i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.0981 | + | 22.0981i | −0.951832 | + | 0.951832i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.1962 | + | 30.1962i | 1.29823 | + | 1.29823i | 0.929558 | + | 0.368676i | \(0.120189\pi\) |
0.368676 | + | 0.929558i | \(0.379811\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.4930 | − | 25.4930i | −1.09401 | − | 1.09401i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2808 | 0.610604 | 0.305302 | − | 0.952256i | \(-0.401243\pi\) | ||||
0.305302 | + | 0.952256i | \(0.401243\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.26795 | − | 5.26795i | −0.224831 | − | 0.224831i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.85641 | −0.334694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.34847 | − | 7.34847i | −0.312489 | − | 0.312489i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.38323i | 0.143352i | 0.997428 | + | 0.0716760i | \(0.0228348\pi\) | ||||
−0.997428 | + | 0.0716760i | \(0.977165\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.7846 | 1.89419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.1962 | 0.472702 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.4612i | 1.62094i | 0.585777 | + | 0.810472i | \(0.300790\pi\) | ||||
−0.585777 | + | 0.810472i | \(0.699210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.55772 | − | 9.55772i | −0.401387 | − | 0.401387i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.0718 | 0.589920 | 0.294960 | − | 0.955510i | \(-0.404694\pi\) | ||||
0.294960 | + | 0.955510i | \(0.404694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.607695 | − | 0.607695i | −0.0254313 | − | 0.0254313i | 0.694277 | − | 0.719708i | \(-0.255724\pi\) |
−0.719708 | + | 0.694277i | \(0.755724\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.656339 | −0.0274189 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.4722 | + | 13.4722i | 0.560855 | + | 0.560855i | 0.929550 | − | 0.368695i | \(-0.120195\pi\) |
−0.368695 | + | 0.929550i | \(0.620195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.0981 | − | 10.0981i | −0.419662 | − | 0.419662i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.17691 | + | 4.17691i | −0.173288 | + | 0.173288i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40.5689 | + | 40.5689i | −1.68019 | + | 1.68019i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 45.9483i | − | 1.89649i | −0.317538 | − | 0.948245i | \(-0.602856\pi\) | ||
0.317538 | − | 0.948245i | \(-0.397144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.0000 | + | 13.0000i | −0.535656 | + | 0.535656i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 36.5885i | − | 1.50505i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.3001 | + | 11.3001i | −0.464040 | + | 0.464040i | −0.899977 | − | 0.435937i | \(-0.856417\pi\) |
0.435937 | + | 0.899977i | \(0.356417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.48528 | −0.347279 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.1962i | 1.07035i | 0.844743 | + | 0.535173i | \(0.179754\pi\) | ||||
−0.844743 | + | 0.535173i | \(0.820246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.1962i | 0.946191i | 0.881011 | + | 0.473095i | \(0.156863\pi\) | ||||
−0.881011 | + | 0.473095i | \(0.843137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.13681 | 0.0462946 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.3190 | + | 24.3190i | −0.987079 | + | 0.987079i | −0.999918 | − | 0.0128385i | \(-0.995913\pi\) |
0.0128385 | + | 0.999918i | \(0.495913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.39230i | 0.177985i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.92820 | + | 6.92820i | −0.280285 | + | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13.5601i | − | 0.547688i | −0.961774 | − | 0.273844i | \(-0.911705\pi\) | ||
0.961774 | − | 0.273844i | \(-0.0882953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.9048 | − | 22.9048i | 0.922113 | − | 0.922113i | −0.0750653 | − | 0.997179i | \(-0.523917\pi\) |
0.997179 | + | 0.0750653i | \(0.0239165\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.7846 | + | 15.7846i | −0.634437 | + | 0.634437i | −0.949178 | − | 0.314741i | \(-0.898082\pi\) |
0.314741 | + | 0.949178i | \(0.398082\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.0000 | + | 13.0000i | 0.521672 | + | 0.521672i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.3118 | − | 12.3118i | −0.493263 | − | 0.493263i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −49.0542 | −1.95903 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.73205 | + | 7.73205i | 0.308297 | + | 0.308297i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.5885 | 0.739995 | 0.369997 | − | 0.929033i | \(-0.379359\pi\) | ||||
0.369997 | + | 0.929033i | \(0.379359\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.29581 | − | 8.29581i | −0.329729 | − | 0.329729i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.4168i | 1.04667i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.46410 | −0.374394 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.928203 | 0.0366618 | 0.0183309 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183309 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 32.3238i | − | 1.27473i | −0.770563 | − | 0.637364i | \(-0.780025\pi\) | ||
0.770563 | − | 0.637364i | \(-0.219975\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.96524 | + | 3.96524i | 0.155890 | + | 0.155890i | 0.780743 | − | 0.624853i | \(-0.214841\pi\) |
−0.624853 | + | 0.780743i | \(0.714841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.9808 | 1.37312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.26795 | + | 7.26795i | 0.284853 | + | 0.284853i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.62587 | −0.298423 | −0.149212 | − | 0.988805i | \(-0.547674\pi\) | ||||
−0.149212 | + | 0.988805i | \(0.547674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.86559 | − | 2.86559i | −0.111797 | − | 0.111797i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.4904 | − | 26.4904i | −1.03192 | − | 1.03192i | −0.999474 | − | 0.0324452i | \(-0.989671\pi\) |
−0.0324452 | − | 0.999474i | \(-0.510329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.00000 | + | 8.00000i | −0.311164 | + | 0.311164i | −0.845360 | − | 0.534196i | \(-0.820614\pi\) |
0.534196 | + | 0.845360i | \(0.320614\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.69213 | − | 6.69213i | 0.259901 | − | 0.259901i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.52433i | − | 0.291343i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.73205 | + | 4.73205i | −0.182952 | + | 0.182952i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 58.9808i | − | 2.27693i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.17260 | − | 7.17260i | 0.276484 | − | 0.276484i | −0.555220 | − | 0.831704i | \(-0.687366\pi\) |
0.831704 | + | 0.555220i | \(0.187366\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.1127 | 1.19576 | 0.597879 | − | 0.801586i | \(-0.296010\pi\) | ||||
0.597879 | + | 0.801586i | \(0.296010\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.56922i | − | 0.213727i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 20.1962i | − | 0.773918i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.7314 | 1.02285 | 0.511423 | − | 0.859329i | \(-0.329118\pi\) | ||||
0.511423 | + | 0.859329i | \(0.329118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.72741 | + | 7.72741i | −0.294819 | + | 0.294819i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48.4974i | 1.84760i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.8827 | + | 25.8827i | −0.984624 | + | 0.984624i | −0.999884 | − | 0.0152598i | \(-0.995142\pi\) |
0.0152598 | + | 0.999884i | \(0.495142\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.37945i | 0.204349i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.57081 | + | 4.57081i | −0.173132 | + | 0.173132i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.9282 | + | 10.9282i | −0.413343 | + | 0.413343i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.5885 | − | 12.5885i | −0.475459 | − | 0.475459i | 0.428217 | − | 0.903676i | \(-0.359142\pi\) |
−0.903676 | + | 0.428217i | \(0.859142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.8768 | − | 33.8768i | −1.27769 | − | 1.27769i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.04386 | 0.264912 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.00000 | − | 2.00000i | −0.0751116 | − | 0.0751116i | 0.668553 | − | 0.743665i | \(-0.266914\pi\) |
−0.743665 | + | 0.668553i | \(0.766914\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.00000 | 0.225018 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.4505 | − | 12.4505i | −0.466276 | − | 0.466276i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 28.0812i | − | 1.04871i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.73205 | 0.176476 | 0.0882379 | − | 0.996099i | \(-0.471876\pi\) | ||||
0.0882379 | + | 0.996099i | \(0.471876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.39230 | −0.163578 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 44.8115i | 1.66656i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.34847 | + | 7.34847i | 0.272540 | + | 0.272540i | 0.830122 | − | 0.557582i | \(-0.188271\pi\) |
−0.557582 | + | 0.830122i | \(0.688271\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.5885 | −0.651424 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.46410 | + | 6.46410i | 0.239083 | + | 0.239083i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.6771 | −1.76099 | −0.880497 | − | 0.474051i | \(-0.842791\pi\) | ||||
−0.880497 | + | 0.474051i | \(0.842791\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.36396 | + | 6.36396i | 0.234420 | + | 0.234420i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.607695 | − | 0.607695i | −0.0223544 | − | 0.0223544i | 0.695841 | − | 0.718196i | \(-0.255032\pi\) |
−0.718196 | + | 0.695841i | \(0.755032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29.3205 | + | 29.3205i | −1.07712 | + | 1.07712i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.4267 | + | 26.4267i | −0.969503 | + | 0.969503i | −0.999549 | − | 0.0300451i | \(-0.990435\pi\) |
0.0300451 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3.41044i | − | 0.124781i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.39230 | − | 1.39230i | 0.0508737 | − | 0.0508737i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6077i | 0.861457i | 0.902482 | + | 0.430729i | \(0.141743\pi\) | ||||
−0.902482 | + | 0.430729i | \(0.858257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.328169 | + | 0.328169i | −0.0119592 | + | 0.0119592i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.37945 | 0.195520 | 0.0977598 | − | 0.995210i | \(-0.468832\pi\) | ||||
0.0977598 | + | 0.995210i | \(0.468832\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 46.9808i | − | 1.70529i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25.3923i | − | 0.920470i | −0.887797 | − | 0.460235i | \(-0.847765\pi\) | ||
0.887797 | − | 0.460235i | \(-0.152235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.4281 | −0.739548 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.9086 | − | 20.9086i | 0.754966 | − | 0.754966i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.8038i | 0.894450i | 0.894422 | + | 0.447225i | \(0.147588\pi\) | ||||
−0.894422 | + | 0.447225i | \(0.852412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6603 | − | 19.6603i | 0.708047 | − | 0.708047i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.9850i | 1.47413i | 0.675823 | + | 0.737064i | \(0.263788\pi\) | ||||
−0.675823 | + | 0.737064i | \(0.736212\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.9396 | + | 18.9396i | −0.679454 | + | 0.679454i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0263 | − | 20.0263i | 0.717516 | − | 0.717516i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.9808 | − | 52.9808i | −1.89580 | − | 1.89580i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.55532 | + | 5.55532i | 0.198531 | + | 0.198531i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.1026 | 0.360118 | 0.180059 | − | 0.983656i | \(-0.442371\pi\) | ||||
0.180059 | + | 0.983656i | \(0.442371\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.46410 | − | 2.46410i | −0.0877243 | − | 0.0877243i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.7321 | −0.594923 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.2538 | − | 35.2538i | −1.25190 | − | 1.25190i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 22.0454i | − | 0.780888i | −0.920627 | − | 0.390444i | \(-0.872321\pi\) | ||
0.920627 | − | 0.390444i | \(-0.127679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.00000 | −0.0707549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0526 | 0.355190 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 32.0836i | − | 1.13221i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.7327 | − | 20.7327i | −0.729827 | − | 0.729827i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.24871 | 0.219693 | 0.109846 | − | 0.993949i | \(-0.464964\pi\) | ||||
0.109846 | + | 0.993949i | \(0.464964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.78461 | + | 3.78461i | 0.132896 | + | 0.132896i | 0.770426 | − | 0.637530i | \(-0.220044\pi\) |
−0.637530 | + | 0.770426i | \(0.720044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −59.0924 | −2.07246 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.3214 | − | 28.3214i | −0.990842 | − | 0.990842i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.21539 | + | 3.21539i | 0.112355 | + | 0.112355i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.4641 | − | 18.4641i | 0.644402 | − | 0.644402i | −0.307233 | − | 0.951634i | \(-0.599403\pi\) |
0.951634 | + | 0.307233i | \(0.0994030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5911 | + | 11.5911i | −0.404041 | + | 0.404041i | −0.879654 | − | 0.475614i | \(-0.842226\pi\) |
0.475614 | + | 0.879654i | \(0.342226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.4524i | − | 0.398239i | −0.979975 | − | 0.199120i | \(-0.936192\pi\) | ||
0.979975 | − | 0.199120i | \(-0.0638082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.5885 | + | 14.5885i | −0.506678 | + | 0.506678i | −0.913505 | − | 0.406827i | \(-0.866635\pi\) |
0.406827 | + | 0.913505i | \(0.366635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.81294 | + | 3.81294i | −0.132110 | + | 0.132110i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.3848 | 0.635471 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.4641i | 0.948166i | 0.880480 | + | 0.474083i | \(0.157220\pi\) | ||||
−0.880480 | + | 0.474083i | \(0.842780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.7846i | 0.889124i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.4901 | −0.567949 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.2523 | + | 20.2523i | −0.695876 | + | 0.695876i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.5167i | 1.39053i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.4449 | − | 32.4449i | 1.11220 | − | 1.11220i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.6937i | 0.742777i | 0.928477 | + | 0.371389i | \(0.121118\pi\) | ||||
−0.928477 | + | 0.371389i | \(0.878882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.53365 | + | 4.53365i | −0.154866 | + | 0.154866i | −0.780287 | − | 0.625421i | \(-0.784927\pi\) |
0.625421 | + | 0.780287i | \(0.284927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.9019 | + | 27.9019i | −0.952001 | + | 0.952001i | −0.998900 | − | 0.0468983i | \(-0.985066\pi\) |
0.0468983 | + | 0.998900i | \(0.485066\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.1962 | − | 11.1962i | −0.381564 | − | 0.381564i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.8685 | − | 11.8685i | −0.404009 | − | 0.404009i | 0.475634 | − | 0.879643i | \(-0.342219\pi\) |
−0.879643 | + | 0.475634i | \(0.842219\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.9096 | −1.04975 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.5885 | + | 33.5885i | 1.13941 | + | 1.13941i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.60770 | 0.257777 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.27362 | + | 2.27362i | 0.0769505 | + | 0.0769505i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 0.480473i | − | 0.0162244i | −0.999967 | − | 0.00811222i | \(-0.997418\pi\) | ||
0.999967 | − | 0.00811222i | \(-0.00258223\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.1244 | 0.645049 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8564 | 0.466834 | 0.233417 | − | 0.972377i | \(-0.425009\pi\) | ||||
0.233417 | + | 0.972377i | \(0.425009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.8768i | 1.14004i | 0.821630 | + | 0.570022i | \(0.193065\pi\) | ||||
−0.821630 | + | 0.570022i | \(0.806935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.6932 | − | 16.6932i | −0.560502 | − | 0.560502i | 0.368948 | − | 0.929450i | \(-0.379718\pi\) |
−0.929450 | + | 0.368948i | \(0.879718\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.78461 | 0.0933928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.6865 | + | 43.6865i | 1.46355 | + | 1.46355i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.76268 | 0.293232 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.0812 | − | 28.0812i | −0.937604 | − | 0.937604i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.32051 | − | 5.32051i | −0.177449 | − | 0.177449i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.00000 | + | 7.00000i | −0.233204 | + | 0.233204i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.8338 | + | 15.8338i | −0.526914 | + | 0.526914i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.8807i | 1.75587i | 0.478775 | + | 0.877937i | \(0.341081\pi\) | ||||
−0.478775 | + | 0.877937i | \(0.658919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.87564 | + | 2.87564i | −0.0953791 | + | 0.0953791i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.2487i | − | 0.803396i | −0.915772 | − | 0.401698i | \(-0.868420\pi\) | ||
0.915772 | − | 0.401698i | \(-0.131580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.0919 | − | 19.0919i | 0.631849 | − | 0.631849i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.8028 | 0.587899 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.19615i | − | 0.138418i | −0.997602 | − | 0.0692091i | \(-0.977952\pi\) | ||
0.997602 | − | 0.0692091i | \(-0.0220476\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 12.1244i | − | 0.399511i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −63.3350 | −2.08470 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.79315 | − | 1.79315i | 0.0588948 | − | 0.0588948i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.0000i | 1.18112i | 0.806993 | + | 0.590561i | \(0.201093\pi\) | ||||
−0.806993 | + | 0.590561i | \(0.798907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.7058 | − | 16.7058i | 0.547510 | − | 0.547510i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.9348i | 0.357988i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.7482 | − | 19.7482i | 0.645146 | − | 0.645146i | −0.306670 | − | 0.951816i | \(-0.599215\pi\) |
0.951816 | + | 0.306670i | \(0.0992147\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.6603 | − | 17.6603i | 0.576321 | − | 0.576321i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.7846 | + | 26.7846i | 0.873153 | + | 0.873153i | 0.992815 | − | 0.119661i | \(-0.0381809\pi\) |
−0.119661 | + | 0.992815i | \(0.538181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.1798 | + | 19.1798i | 0.624581 | + | 0.624581i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.8338 | 0.514528 | 0.257264 | − | 0.966341i | \(-0.417179\pi\) | ||||
0.257264 | + | 0.966341i | \(0.417179\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.1769 | − | 19.1769i | −0.622509 | − | 0.622509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.7846 | −1.25768 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.12321 | − | 1.12321i | −0.0363843 | − | 0.0363843i | 0.688681 | − | 0.725065i | \(-0.258190\pi\) |
−0.725065 | + | 0.688681i | \(0.758190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 20.0764i | − | 0.648978i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.55514 | −0.114801 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.3923 | 0.432010 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.13681i | 0.0366333i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.9053 | − | 27.9053i | −0.897375 | − | 0.897375i | 0.0978283 | − | 0.995203i | \(-0.468810\pi\) |
−0.995203 | + | 0.0978283i | \(0.968810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.46410 | −0.271906 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.633975 | − | 0.633975i | −0.0203452 | − | 0.0203452i | 0.696861 | − | 0.717206i | \(-0.254579\pi\) |
−0.717206 | + | 0.696861i | \(0.754579\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.8728 | 0.476800 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.3292 | + | 10.3292i | 0.330460 | + | 0.330460i | 0.852761 | − | 0.522301i | \(-0.174926\pi\) |
−0.522301 | + | 0.852761i | \(0.674926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.2750 | + | 56.2750i | 1.79856 | + | 1.79856i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.33975 | − | 8.33975i | 0.266268 | − | 0.266268i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.48717 | − | 7.48717i | 0.238804 | − | 0.238804i | −0.577551 | − | 0.816355i | \(-0.695992\pi\) |
0.816355 | + | 0.577551i | \(0.195992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 4.89898i | − | 0.155936i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.1244 | − | 27.1244i | 0.862504 | − | 0.862504i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.5885i | − | 0.590482i | −0.955423 | − | 0.295241i | \(-0.904600\pi\) | ||
0.955423 | − | 0.295241i | \(-0.0953999\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.5385 | + | 12.5385i | −0.397896 | + | 0.397896i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.3692 | −1.72189 | −0.860946 | − | 0.508697i | \(-0.830127\pi\) | ||||
−0.860946 | + | 0.508697i | \(0.830127\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 47.9090i | 1.51577i |
(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 | 1600.2.j.b.1007.1 | 8 | ||
4.3 | odd | 2 | 400.2.j.b.307.4 | yes | 8 | ||
5.2 | odd | 4 | 1600.2.s.b.943.1 | 8 | |||
5.3 | odd | 4 | 1600.2.s.b.943.4 | 8 | |||
5.4 | even | 2 | inner | 1600.2.j.b.1007.4 | 8 | ||
16.5 | even | 4 | 400.2.s.b.107.3 | yes | 8 | ||
16.11 | odd | 4 | 1600.2.s.b.207.4 | 8 | |||
20.3 | even | 4 | 400.2.s.b.243.1 | yes | 8 | ||
20.7 | even | 4 | 400.2.s.b.243.4 | yes | 8 | ||
20.19 | odd | 2 | 400.2.j.b.307.1 | yes | 8 | ||
80.27 | even | 4 | inner | 1600.2.j.b.143.1 | 8 | ||
80.37 | odd | 4 | 400.2.j.b.43.2 | ✓ | 8 | ||
80.43 | even | 4 | inner | 1600.2.j.b.143.4 | 8 | ||
80.53 | odd | 4 | 400.2.j.b.43.3 | yes | 8 | ||
80.59 | odd | 4 | 1600.2.s.b.207.1 | 8 | |||
80.69 | even | 4 | 400.2.s.b.107.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.b.43.2 | ✓ | 8 | 80.37 | odd | 4 | ||
400.2.j.b.43.3 | yes | 8 | 80.53 | odd | 4 | ||
400.2.j.b.307.1 | yes | 8 | 20.19 | odd | 2 | ||
400.2.j.b.307.4 | yes | 8 | 4.3 | odd | 2 | ||
400.2.s.b.107.2 | yes | 8 | 80.69 | even | 4 | ||
400.2.s.b.107.3 | yes | 8 | 16.5 | even | 4 | ||
400.2.s.b.243.1 | yes | 8 | 20.3 | even | 4 | ||
400.2.s.b.243.4 | yes | 8 | 20.7 | even | 4 | ||
1600.2.j.b.143.1 | 8 | 80.27 | even | 4 | inner | ||
1600.2.j.b.143.4 | 8 | 80.43 | even | 4 | inner | ||
1600.2.j.b.1007.1 | 8 | 1.1 | even | 1 | trivial | ||
1600.2.j.b.1007.4 | 8 | 5.4 | even | 2 | inner | ||
1600.2.s.b.207.1 | 8 | 80.59 | odd | 4 | |||
1600.2.s.b.207.4 | 8 | 16.11 | odd | 4 | |||
1600.2.s.b.943.1 | 8 | 5.2 | odd | 4 | |||
1600.2.s.b.943.4 | 8 | 5.3 | odd | 4 |