Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1241,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.i (of order \(2\), degree \(1\), 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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} - 4 x^{13} - 2 x^{12} + 12 x^{11} + 17 x^{10} + 16 x^{9} - 110 x^{8} + 48 x^{7} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.8 | ||
Root | \(-0.0831550 + 1.73005i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1380.1241 |
Dual form | 1380.2.i.a.1241.7 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0831550 | + | 1.73005i | 0.0480096 | + | 0.998847i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.02092i | 1.51976i | 0.650061 | + | 0.759882i | \(0.274743\pi\) | ||||
−0.650061 | + | 0.759882i | \(0.725257\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98617 | + | 0.287725i | −0.995390 | + | 0.0959084i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.641443 | 0.193402 | 0.0967012 | − | 0.995313i | \(-0.469171\pi\) | ||||
0.0967012 | + | 0.995313i | \(0.469171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.89996 | −0.804305 | −0.402152 | − | 0.915573i | \(-0.631738\pi\) | ||||
−0.402152 | + | 0.915573i | \(0.631738\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0831550 | − | 1.73005i | −0.0214705 | − | 0.446698i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.10358 | −0.752729 | −0.376364 | − | 0.926472i | \(-0.622826\pi\) | ||||
−0.376364 | + | 0.926472i | \(0.622826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.33629i | 0.306567i | 0.988182 | + | 0.153283i | \(0.0489847\pi\) | ||||
−0.988182 | + | 0.153283i | \(0.951015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.95640 | + | 0.334360i | −1.51801 | + | 0.0729633i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.05339 | − | 3.69822i | −0.636676 | − | 0.771132i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.746095 | − | 5.14231i | −0.143586 | − | 0.989638i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.14000i | − | 0.583084i | −0.956558 | − | 0.291542i | \(-0.905832\pi\) | ||
0.956558 | − | 0.291542i | \(-0.0941683\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.11022 | 1.09743 | 0.548714 | − | 0.836010i | \(-0.315118\pi\) | ||||
0.548714 | + | 0.836010i | \(0.315118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0533392 | + | 1.10973i | 0.00928517 | + | 0.193179i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.02092i | − | 0.679659i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.06427i | 1.16136i | 0.814132 | + | 0.580679i | \(0.197213\pi\) | ||||
−0.814132 | + | 0.580679i | \(0.802787\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.241146 | − | 5.01709i | −0.0386143 | − | 0.803377i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.72186i | − | 0.581256i | −0.956836 | − | 0.290628i | \(-0.906136\pi\) | ||
0.956836 | − | 0.290628i | \(-0.0938643\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.20330i | 0.183501i | 0.995782 | + | 0.0917506i | \(0.0292462\pi\) | ||||
−0.995782 | + | 0.0917506i | \(0.970754\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.98617 | − | 0.287725i | 0.445152 | − | 0.0428916i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.57780i | 0.521876i | 0.965356 | + | 0.260938i | \(0.0840318\pi\) | ||||
−0.965356 | + | 0.260938i | \(0.915968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.16778 | −1.30968 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.258078 | − | 5.36936i | −0.0361382 | − | 0.751861i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.12728 | −0.704286 | −0.352143 | − | 0.935946i | \(-0.614547\pi\) | ||||
−0.352143 | + | 0.935946i | \(0.614547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.641443 | −0.0864922 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.31186 | + | 0.111119i | −0.306213 | + | 0.0147181i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.3428i | − | 1.47670i | −0.674415 | − | 0.738352i | \(-0.735604\pi\) | ||
0.674415 | − | 0.738352i | \(-0.264396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.921789i | − | 0.118023i | −0.998257 | − | 0.0590115i | \(-0.981205\pi\) | ||
0.998257 | − | 0.0590115i | \(-0.0187949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.15692 | − | 12.0071i | −0.145758 | − | 1.51276i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.89996 | 0.359696 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.27284i | − | 0.155502i | −0.996973 | − | 0.0777509i | \(-0.975226\pi\) | ||
0.996973 | − | 0.0777509i | \(-0.0247739\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.14421 | − | 5.59005i | 0.739676 | − | 0.672963i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.44420i | 0.171395i | 0.996321 | + | 0.0856976i | \(0.0273119\pi\) | ||||
−0.996321 | + | 0.0856976i | \(0.972688\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9062 | −1.27647 | −0.638235 | − | 0.769841i | \(-0.720335\pi\) | ||||
−0.638235 | + | 0.769841i | \(0.720335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0831550 | + | 1.73005i | 0.00960192 | + | 0.199769i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.57919i | 0.293926i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.08045i | 0.346577i | 0.984871 | + | 0.173289i | \(0.0554393\pi\) | ||||
−0.984871 | + | 0.173289i | \(0.944561\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.83443 | − | 1.71839i | 0.981603 | − | 0.190933i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.6650 | −1.71946 | −0.859728 | − | 0.510752i | \(-0.829367\pi\) | ||||
−0.859728 | + | 0.510752i | \(0.829367\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.10358 | 0.336631 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.43237 | − | 0.261107i | 0.582411 | − | 0.0279936i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.31384 | 0.457266 | 0.228633 | − | 0.973513i | \(-0.426574\pi\) | ||||
0.228633 | + | 0.973513i | \(0.426574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 11.6605i | − | 1.22235i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.508096 | + | 10.5710i | 0.0526871 | + | 1.09616i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1.33629i | − | 0.137101i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1699i | 1.33720i | 0.743620 | + | 0.668602i | \(0.233107\pi\) | ||||
−0.743620 | + | 0.668602i | \(0.766893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.91546 | + | 0.184559i | −0.192511 | + | 0.0185489i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.15864i | 0.712312i | 0.934427 | + | 0.356156i | \(0.115913\pi\) | ||||
−0.934427 | + | 0.356156i | \(0.884087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.510025i | − | 0.0502542i | −0.999684 | − | 0.0251271i | \(-0.992001\pi\) | ||
0.999684 | − | 0.0251271i | \(-0.00799905\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.95640 | − | 0.334360i | 0.678876 | − | 0.0326302i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0806 | −1.36122 | −0.680611 | − | 0.732645i | \(-0.738286\pi\) | ||||
−0.680611 | + | 0.732645i | \(0.738286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.5760i | − | 1.20456i | −0.798283 | − | 0.602282i | \(-0.794258\pi\) | ||
0.798283 | − | 0.602282i | \(-0.205742\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.2216 | + | 0.587430i | −1.16002 | + | 0.0557563i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.170942 | −0.0160809 | −0.00804045 | − | 0.999968i | \(-0.502559\pi\) | ||||
−0.00804045 | + | 0.999968i | \(0.502559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.05339 | + | 3.69822i | 0.284730 | + | 0.344861i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.65978 | − | 0.834393i | 0.800597 | − | 0.0771396i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 12.4792i | − | 1.14397i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5886 | −0.962596 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.43901 | − | 0.309491i | 0.580586 | − | 0.0279059i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8686 | 1.40811 | 0.704056 | − | 0.710145i | \(-0.251371\pi\) | ||||
0.704056 | + | 0.710145i | \(0.251371\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.08177 | + | 0.100060i | −0.183290 | + | 0.00880981i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.60285i | 0.751634i | 0.926694 | + | 0.375817i | \(0.122638\pi\) | ||||
−0.926694 | + | 0.375817i | \(0.877362\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.37312 | −0.465909 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.746095 | + | 5.14231i | 0.0642137 | + | 0.442579i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.74794 | 0.661951 | 0.330975 | − | 0.943639i | \(-0.392622\pi\) | ||||
0.330975 | + | 0.943639i | \(0.392622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.2656 | −0.870715 | −0.435358 | − | 0.900258i | \(-0.643378\pi\) | ||||
−0.435358 | + | 0.900258i | \(0.643378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.18979 | + | 0.297512i | −0.521274 | + | 0.0250551i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.86016 | −0.155554 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.14000i | 0.260763i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.762347 | − | 15.8608i | −0.0628774 | − | 1.30817i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.47232 | 0.776003 | 0.388001 | − | 0.921659i | \(-0.373166\pi\) | ||||
0.388001 | + | 0.921659i | \(0.373166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8802 | −1.12956 | −0.564779 | − | 0.825242i | \(-0.691038\pi\) | ||||
−0.564779 | + | 0.825242i | \(0.691038\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.26782 | − | 0.892979i | 0.749259 | − | 0.0721931i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.11022 | −0.490785 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.9188i | − | 1.03103i | −0.856880 | − | 0.515516i | \(-0.827600\pi\) | ||
0.856880 | − | 0.515516i | \(-0.172400\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.426359 | − | 8.87047i | −0.0338125 | − | 0.703474i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.8702 | − | 12.2774i | 1.17194 | − | 0.967597i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.6758 | 1.69778 | 0.848892 | − | 0.528567i | \(-0.177270\pi\) | ||||
0.848892 | + | 0.528567i | \(0.177270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0533392 | − | 1.10973i | −0.00415245 | − | 0.0863924i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.64677i | − | 0.282196i | −0.989996 | − | 0.141098i | \(-0.954937\pi\) | ||
0.989996 | − | 0.141098i | \(-0.0450632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.59022 | −0.353094 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.384485 | − | 3.99040i | −0.0294023 | − | 0.305153i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.85550i | 0.749300i | 0.927166 | + | 0.374650i | \(0.122237\pi\) | ||||
−0.927166 | + | 0.374650i | \(0.877763\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.02092i | 0.303953i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.6236 | − | 0.943210i | 1.47500 | − | 0.0708960i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.9605i | 1.26769i | 0.773460 | + | 0.633845i | \(0.218524\pi\) | ||||
−0.773460 | + | 0.633845i | \(0.781476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.5650i | 1.90023i | 0.311893 | + | 0.950117i | \(0.399037\pi\) | ||||
−0.311893 | + | 0.950117i | \(0.600963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.59474 | − | 0.0766514i | 0.117887 | − | 0.00566624i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 7.06427i | − | 0.519375i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.99077 | −0.145580 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.6768 | − | 2.99999i | 1.50402 | − | 0.218217i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4794 | −0.902981 | −0.451491 | − | 0.892276i | \(-0.649108\pi\) | ||||
−0.451491 | + | 0.892276i | \(0.649108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.0097 | −1.51231 | −0.756155 | − | 0.654392i | \(-0.772924\pi\) | ||||
−0.756155 | + | 0.654392i | \(0.772924\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.241146 | + | 5.01709i | 0.0172689 | + | 0.359281i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.84641i | 0.701528i | 0.936464 | + | 0.350764i | \(0.114078\pi\) | ||||
−0.936464 | + | 0.350764i | \(0.885922\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.69855i | 0.616624i | 0.951285 | + | 0.308312i | \(0.0997640\pi\) | ||||
−0.951285 | + | 0.308312i | \(0.900236\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.20208 | − | 0.105843i | 0.155323 | − | 0.00746558i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.6257 | 0.886150 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.72186i | 0.259946i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.1820 | + | 10.1650i | 0.707699 | + | 0.706514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.857156i | 0.0592907i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.8422 | −1.36600 | −0.682998 | − | 0.730420i | \(-0.739324\pi\) | ||||
−0.682998 | + | 0.730420i | \(0.739324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.49855 | + | 0.120093i | −0.171197 | + | 0.00822861i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.20330i | − | 0.0820642i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.5687i | 1.66783i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.906903 | − | 18.8683i | −0.0612828 | − | 1.27500i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.00027 | 0.605423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.99786 | −0.133786 | −0.0668932 | − | 0.997760i | \(-0.521309\pi\) | ||||
−0.0668932 | + | 0.997760i | \(0.521309\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.98617 | + | 0.287725i | −0.199078 | + | 0.0191817i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.61196 | 0.106990 | 0.0534949 | − | 0.998568i | \(-0.482964\pi\) | ||||
0.0534949 | + | 0.998568i | \(0.482964\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.7830i | − | 0.778641i | −0.921102 | − | 0.389321i | \(-0.872710\pi\) | ||
0.921102 | − | 0.389321i | \(-0.127290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.46214 | + | 0.214473i | −0.293587 | + | 0.0141113i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.04517i | − | 0.592569i | −0.955100 | − | 0.296285i | \(-0.904252\pi\) | ||
0.955100 | − | 0.296285i | \(-0.0957477\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.57780i | − | 0.233390i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.32934 | + | 0.256155i | −0.346178 | + | 0.0166390i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.0937i | 0.846962i | 0.905905 | + | 0.423481i | \(0.139192\pi\) | ||||
−0.905905 | + | 0.423481i | \(0.860808\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.5418i | 1.38763i | 0.720155 | + | 0.693813i | \(0.244071\pi\) | ||||
−0.720155 | + | 0.693813i | \(0.755929\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.70754 | + | 15.1411i | 0.237839 | + | 0.971305i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.16778 | 0.585708 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.87520i | − | 0.246573i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.30262 | − | 27.1013i | −0.0825504 | − | 1.71747i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.74004 | 0.172950 | 0.0864750 | − | 0.996254i | \(-0.472440\pi\) | ||||
0.0864750 | + | 0.996254i | \(0.472440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.95858 | − | 2.37220i | −0.123135 | − | 0.149139i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.258078 | + | 5.36936i | 0.0161615 | + | 0.336242i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.5539i | 1.65639i | 0.560442 | + | 0.828194i | \(0.310631\pi\) | ||||
−0.560442 | + | 0.828194i | \(0.689369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.4048 | −1.76499 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.903458 | + | 9.37658i | 0.0559227 | + | 0.580396i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.09330 | −0.252404 | −0.126202 | − | 0.992005i | \(-0.540279\pi\) | ||||
−0.126202 | + | 0.992005i | \(0.540279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.12728 | 0.314966 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.358718 | + | 7.46317i | 0.0219532 | + | 0.456739i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.94400i | 0.362412i | 0.983445 | + | 0.181206i | \(0.0580001\pi\) | ||||
−0.983445 | + | 0.181206i | \(0.942000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.18049 | 0.132456 | 0.0662278 | − | 0.997805i | \(-0.478904\pi\) | ||||
0.0662278 | + | 0.997805i | \(0.478904\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.1733 | − | 0.969630i | 1.22094 | − | 0.0586847i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.641443 | 0.0386805 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.4414 | 1.52862 | 0.764312 | − | 0.644846i | \(-0.223079\pi\) | ||||
0.764312 | + | 0.644846i | \(0.223079\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.2462 | + | 1.75807i | −1.09237 | + | 0.105253i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.1951 | 1.56267 | 0.781335 | − | 0.624112i | \(-0.214539\pi\) | ||||
0.781335 | + | 0.624112i | \(0.214539\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.9054i | 0.648261i | 0.946012 | + | 0.324130i | \(0.105072\pi\) | ||||
−0.946012 | + | 0.324130i | \(0.894928\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.31186 | − | 0.111119i | 0.136943 | − | 0.00658215i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.9653 | 0.883373 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.36779 | −0.433399 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.7847 | + | 1.09515i | −1.33566 | + | 0.0641986i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.0813 | −1.58211 | −0.791054 | − | 0.611746i | \(-0.790468\pi\) | ||||
−0.791054 | + | 0.611746i | \(0.790468\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.3428i | 0.660402i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.478578 | − | 3.29850i | −0.0277699 | − | 0.191398i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.85471 | + | 10.7247i | 0.512081 | + | 0.620225i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.83836 | −0.278878 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.3848 | + | 0.595277i | −0.711490 | + | 0.0341978i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.921789i | 0.0527815i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8147 | 0.845517 | 0.422759 | − | 0.906242i | \(-0.361062\pi\) | ||||
0.422759 | + | 0.906242i | \(0.361062\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.882370 | − | 0.0424111i | 0.0501963 | − | 0.00241269i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.729791i | 0.0413826i | 0.999786 | + | 0.0206913i | \(0.00658672\pi\) | ||||
−0.999786 | + | 0.0206913i | \(0.993413\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.2658i | 0.975921i | 0.872866 | + | 0.487960i | \(0.162259\pi\) | ||||
−0.872866 | + | 0.487960i | \(0.837741\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.15692 | + | 12.0071i | 0.0651851 | + | 0.676526i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.1142i | 1.46672i | 0.679841 | + | 0.733360i | \(0.262049\pi\) | ||||
−0.679841 | + | 0.733360i | \(0.737951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.01413i | − | 0.112770i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.17087 | − | 24.3602i | −0.0653517 | − | 1.35965i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.14729i | − | 0.230762i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.89996 | −0.160861 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.7572 | − | 1.04576i | 1.20318 | − | 0.0578306i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.3860 | −0.793129 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.80035 | 0.208886 | 0.104443 | − | 0.994531i | \(-0.466694\pi\) | ||||
0.104443 | + | 0.994531i | \(0.466694\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.03257 | − | 21.0951i | −0.111384 | − | 1.15601i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.27284i | 0.0695426i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.5995i | 1.72133i | 0.509169 | + | 0.860667i | \(0.329953\pi\) | ||||
−0.509169 | + | 0.860667i | \(0.670047\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0142147 | − | 0.295740i | −0.000772038 | − | 0.0160624i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.91936 | 0.212245 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.71648i | − | 0.470646i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.14421 | + | 5.59005i | −0.330793 | + | 0.300958i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 35.4098i | − | 1.90090i | −0.310879 | − | 0.950449i | \(-0.600624\pi\) | ||
0.310879 | − | 0.950449i | \(-0.399376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.70111 | −0.358702 | −0.179351 | − | 0.983785i | \(-0.557400\pi\) | ||||
−0.179351 | + | 0.983785i | \(0.557400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.16365 | + | 14.9125i | 0.115487 | + | 0.795970i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.1005i | 0.856942i | 0.903556 | + | 0.428471i | \(0.140948\pi\) | ||||
−0.903556 | + | 0.428471i | \(0.859052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.44420i | − | 0.0766502i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.5898 | − | 1.03771i | 1.14265 | − | 0.0549215i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.18835 | −0.221053 | −0.110526 | − | 0.993873i | \(-0.535254\pi\) | ||||
−0.110526 | + | 0.993873i | \(0.535254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.2143 | 0.906017 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.880491 | − | 18.3188i | −0.0462138 | − | 0.961486i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.9062 | 0.570855 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.2504i | 1.10926i | 0.832097 | + | 0.554630i | \(0.187140\pi\) | ||||
−0.832097 | + | 0.554630i | \(0.812860\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.07087 | + | 11.1141i | 0.0557474 | + | 0.578577i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 20.6164i | − | 1.07035i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 30.7001i | − | 1.58959i | −0.606877 | − | 0.794796i | \(-0.707578\pi\) | ||
0.606877 | − | 0.794796i | \(-0.292422\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.0831550 | − | 1.73005i | −0.00429411 | − | 0.0893396i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.10589i | 0.468977i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 30.0529i | − | 1.54371i | −0.635797 | − | 0.771857i | \(-0.719328\pi\) | ||
0.635797 | − | 0.771857i | \(-0.280672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.31955 | + | 27.4535i | 0.0676028 | + | 1.40649i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.4414 | 1.35109 | 0.675546 | − | 0.737318i | \(-0.263908\pi\) | ||||
0.675546 | + | 0.737318i | \(0.263908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 2.57919i | − | 0.131448i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.346219 | − | 3.59325i | −0.0175993 | − | 0.182655i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.8089 | −0.801542 | −0.400771 | − | 0.916178i | \(-0.631258\pi\) | ||||
−0.400771 | + | 0.916178i | \(0.631258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.47644 | + | 11.4777i | 0.479244 | + | 0.580453i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.8834 | + | 0.715370i | −0.750767 | + | 0.0360856i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.08045i | − | 0.154994i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5795 | 0.631348 | 0.315674 | − | 0.948868i | \(-0.397769\pi\) | ||||
0.315674 | + | 0.948868i | \(0.397769\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.446802 | − | 9.29579i | −0.0223681 | − | 0.465372i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.7830 | 1.73698 | 0.868489 | − | 0.495708i | \(-0.165091\pi\) | ||||
0.868489 | + | 0.495708i | \(0.165091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.7194 | −0.882667 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.83443 | + | 1.71839i | −0.438986 | + | 0.0853877i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.53133i | 0.224610i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.98209 | −0.295795 | −0.147898 | − | 0.989003i | \(-0.547251\pi\) | ||||
−0.147898 | + | 0.989003i | \(0.547251\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.644280 | + | 13.4043i | 0.0317800 | + | 0.661188i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.6084 | 2.24424 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.6650 | 0.768964 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.853635 | − | 17.7600i | −0.0418027 | − | 0.869711i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.04481 | −0.393015 | −0.196507 | − | 0.980502i | \(-0.562960\pi\) | ||||
−0.196507 | + | 0.980502i | \(0.562960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 13.4364i | − | 0.654849i | −0.944877 | − | 0.327425i | \(-0.893819\pi\) | ||
0.944877 | − | 0.327425i | \(-0.106181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.02942 | − | 10.6839i | −0.0500523 | − | 0.519470i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.10358 | −0.150546 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.70644 | 0.179367 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.154682 | − | 3.21818i | −0.00746811 | − | 0.155375i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.73846 | −0.131907 | −0.0659534 | − | 0.997823i | \(-0.521009\pi\) | ||||
−0.0659534 | + | 0.997823i | \(0.521009\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.0187i | − | 0.913979i | −0.889472 | − | 0.456989i | \(-0.848928\pi\) | ||
0.889472 | − | 0.456989i | \(-0.151072\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.43237 | + | 0.261107i | −0.260462 | + | 0.0125191i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.94190 | − | 4.08022i | 0.236403 | − | 0.195183i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0581 | 1.14823 | 0.574114 | − | 0.818775i | \(-0.305346\pi\) | ||||
0.574114 | + | 0.818775i | \(0.305346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 27.3766 | − | 2.63780i | 1.30365 | − | 0.125610i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.5450i | − | 0.786074i | −0.919523 | − | 0.393037i | \(-0.871424\pi\) | ||
0.919523 | − | 0.393037i | \(-0.128576\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.31384 | −0.204496 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.787671 | + | 16.3876i | 0.0372556 | + | 0.775108i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9142i | 0.892617i | 0.894879 | + | 0.446309i | \(0.147262\pi\) | ||||
−0.894879 | + | 0.446309i | \(0.852738\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.38736i | − | 0.112416i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.15421 | − | 24.0135i | −0.0542296 | − | 1.12825i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.6605i | 0.546653i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.91674i | 0.183217i | 0.995795 | + | 0.0916087i | \(0.0292009\pi\) | ||||
−0.995795 | + | 0.0916087i | \(0.970799\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.31557 | + | 15.9596i | 0.108081 | + | 0.744929i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 21.7358i | − | 1.01234i | −0.862435 | − | 0.506168i | \(-0.831062\pi\) | ||
0.862435 | − | 0.506168i | \(-0.168938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.15417 | −0.332483 | −0.166241 | − | 0.986085i | \(-0.553163\pi\) | ||||
−0.166241 | + | 0.986085i | \(0.553163\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.508096 | − | 10.5710i | −0.0235624 | − | 0.490219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.0147 | −1.62029 | −0.810143 | − | 0.586232i | \(-0.800611\pi\) | ||||
−0.810143 | + | 0.586232i | \(0.800611\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.11798 | 0.236326 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.3502 | − | 1.07426i | 1.02984 | − | 0.0494994i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.771847i | 0.0354896i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.33629i | 0.0613133i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.3109 | − | 1.47525i | 0.701039 | − | 0.0675470i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.5386 | 0.572903 | 0.286451 | − | 0.958095i | \(-0.407524\pi\) | ||||
0.286451 | + | 0.958095i | \(0.407524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 20.4861i | − | 0.934086i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.4771 | + | 24.7054i | 1.02275 | + | 1.12413i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 13.1699i | − | 0.598016i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3582 | 0.741262 | 0.370631 | − | 0.928780i | \(-0.379141\pi\) | ||||
0.370631 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.80246 | + | 37.5004i | 0.0815099 | + | 1.69583i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.4930i | − | 0.563803i | −0.959443 | − | 0.281902i | \(-0.909035\pi\) | ||
0.959443 | − | 0.281902i | \(-0.0909651\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.74525i | 0.438904i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.91546 | − | 0.184559i | 0.0860935 | − | 0.00829533i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.80701 | −0.260480 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.5989 | −1.14596 | −0.572981 | − | 0.819568i | \(-0.694213\pi\) | ||||
−0.572981 | + | 0.819568i | \(0.694213\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.30911 | − | 0.303247i | 0.281870 | − | 0.0135481i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.4303 | 1.71352 | 0.856762 | − | 0.515712i | \(-0.172472\pi\) | ||||
0.856762 | + | 0.515712i | \(0.172472\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.15864i | − | 0.318556i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.381700 | − | 7.94132i | −0.0169519 | − | 0.352687i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.0597i | 0.933455i | 0.884401 | + | 0.466728i | \(0.154567\pi\) | ||||
−0.884401 | + | 0.466728i | \(0.845433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 43.8528i | − | 1.93993i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.87163 | − | 0.997002i | 0.303390 | − | 0.0440187i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.510025i | 0.0224744i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.29496i | 0.100932i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.0505 | + | 0.819534i | −0.748436 | + | 0.0359736i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.4599 | −1.29066 | −0.645331 | − | 0.763903i | \(-0.723280\pi\) | ||||
−0.645331 | + | 0.763903i | \(0.723280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.3365i | − | 1.06416i | −0.846694 | − | 0.532080i | \(-0.821411\pi\) | ||
0.846694 | − | 0.532080i | \(-0.178589\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.95640 | + | 0.334360i | −0.303602 | + | 0.0145927i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.9636 | −0.826066 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.35364 | + | 22.5842i | −0.189289 | + | 0.981921i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.26361 | + | 33.8715i | 0.141628 | + | 1.46990i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.7932i | 0.467507i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0806 | 0.608757 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.3427 | + | 1.41035i | −1.26623 | + | 0.0608613i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.88061 | −0.253296 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0056 | 0.559157 | 0.279578 | − | 0.960123i | \(-0.409805\pi\) | ||||
0.279578 | + | 0.960123i | \(0.409805\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −44.2289 | + | 2.12586i | −1.89804 | + | 0.0912295i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5760i | 0.538698i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.2330 | −0.694073 | −0.347037 | − | 0.937852i | \(-0.612812\pi\) | ||||
−0.347037 | + | 0.937852i | \(0.612812\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.265222 | + | 2.75262i | 0.0113194 | + | 0.117479i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.19596 | 0.178754 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.3862 | −0.526716 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.2216 | − | 0.587430i | 0.518776 | − | 0.0249350i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.76745 | −0.117261 | −0.0586303 | − | 0.998280i | \(-0.518673\pi\) | ||||
−0.0586303 | + | 0.998280i | \(0.518673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.48952i | − | 0.147591i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.165543 | − | 3.44414i | −0.00698921 | − | 0.145412i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.3086 | −1.36165 | −0.680823 | − | 0.732448i | \(-0.738378\pi\) | ||||
−0.680823 | + | 0.732448i | \(0.738378\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.170942 | 0.00719160 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.90952 | + | 35.5225i | 0.290173 | + | 1.49181i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.6500 | −1.82990 | −0.914952 | − | 0.403563i | \(-0.867772\pi\) | ||||
−0.914952 | + | 0.403563i | \(0.867772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 19.2922i | − | 0.807352i | −0.914902 | − | 0.403676i | \(-0.867732\pi\) | ||
0.914902 | − | 0.403676i | \(-0.132268\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.03773 | − | 21.5901i | −0.0433517 | − | 0.901940i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.05339 | − | 3.69822i | −0.127335 | − | 0.154226i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.1157 | −1.33700 | −0.668498 | − | 0.743714i | \(-0.733062\pi\) | ||||
−0.668498 | + | 0.743714i | \(0.733062\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.74706 | − | 36.3479i | −0.0726054 | − | 1.51057i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 62.9877i | − | 2.61317i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.28886 | −0.136211 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.65978 | + | 0.834393i | −0.358038 | + | 0.0344979i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.67739i | 0.316880i | 0.987369 | + | 0.158440i | \(0.0506464\pi\) | ||||
−0.987369 | + | 0.158440i | \(0.949354\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.16505i | 0.336435i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.0348 | + | 0.818779i | −0.700719 | + | 0.0336800i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.82648i | − | 0.198200i | −0.995077 | − | 0.0990998i | \(-0.968404\pi\) | ||
0.995077 | − | 0.0990998i | \(-0.0315963\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.4792i | 0.511599i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.0490 | + | 0.723328i | −0.615913 | + | 0.0296039i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.9192i | 1.34504i | 0.740078 | + | 0.672521i | \(0.234789\pi\) | ||||
−0.740078 | + | 0.672521i | \(0.765211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.84513 | 0.156846 | 0.0784231 | − | 0.996920i | \(-0.475011\pi\) | ||||
0.0784231 | + | 0.996920i | \(0.475011\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.366228 | + | 3.80091i | 0.0149139 | + | 0.154785i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.5886 | 0.430486 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.90559 | 0.239700 | 0.119850 | − | 0.992792i | \(-0.461759\pi\) | ||||
0.119850 | + | 0.992792i | \(0.461759\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.04989 | + | 21.8431i | 0.0425437 | + | 0.885128i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 10.3755i | − | 0.419747i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.79086i | − | 0.233890i | −0.993138 | − | 0.116945i | \(-0.962690\pi\) | ||
0.993138 | − | 0.116945i | \(-0.0373102\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.43901 | + | 0.309491i | −0.259646 | + | 0.0124799i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.1573 | −0.892018 | −0.446009 | − | 0.895028i | \(-0.647155\pi\) | ||||
−0.446009 | + | 0.895028i | \(0.647155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 44.6942i | − | 1.79641i | −0.439574 | − | 0.898206i | \(-0.644871\pi\) | ||
0.439574 | − | 0.898206i | \(-0.355129\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.7393 | + | 18.4607i | −0.671723 | + | 0.740802i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.3456i | 0.694937i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.48293 | + | 0.0712768i | −0.0592223 | + | 0.00284652i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 21.9245i | − | 0.874188i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.96253i | − | 0.356793i | −0.983959 | − | 0.178396i | \(-0.942909\pi\) | ||
0.983959 | − | 0.178396i | \(-0.0570909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.64998 | − | 34.3282i | −0.0655809 | − | 1.36442i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.8686 | −0.629727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.5862 | 1.05338 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.415533 | − | 4.31263i | −0.0164382 | − | 0.170605i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.2004 | −1.39033 | −0.695166 | − | 0.718849i | \(-0.744669\pi\) | ||||
−0.695166 | + | 0.718849i | \(0.744669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.1653i | 1.50509i | 0.658538 | + | 0.752547i | \(0.271175\pi\) | ||||
−0.658538 | + | 0.752547i | \(0.728825\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.08177 | − | 0.100060i | 0.0819696 | − | 0.00393987i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 16.4962i | − | 0.648533i | −0.945966 | − | 0.324266i | \(-0.894883\pi\) | ||
0.945966 | − | 0.324266i | \(-0.105117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.27575i | − | 0.285598i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.5052 | + | 2.04301i | −1.66591 | + | 0.0800719i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.1280i | 0.865934i | 0.901410 | + | 0.432967i | \(0.142533\pi\) | ||||
−0.901410 | + | 0.432967i | \(0.857467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8.60285i | − | 0.336141i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.5677 | − | 3.13798i | 1.27059 | − | 0.122424i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.8854 | −1.67058 | −0.835288 | − | 0.549813i | \(-0.814699\pi\) | ||||
−0.835288 | + | 0.549813i | \(0.814699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0140i | 0.778455i | 0.921142 | + | 0.389228i | \(0.127258\pi\) | ||||
−0.921142 | + | 0.389228i | \(0.872742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.748418 | + | 15.5709i | 0.0290661 | + | 0.604725i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.37312 | 0.208361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.6124 | + | 9.58764i | −0.449634 | + | 0.371235i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.166132 | − | 3.45640i | −0.00642303 | − | 0.133632i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 0.591275i | − | 0.0228259i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.8502 | 0.456793 | 0.228396 | − | 0.973568i | \(-0.426652\pi\) | ||||
0.228396 | + | 0.973568i | \(0.426652\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.746095 | − | 5.14231i | −0.0287172 | − | 0.197928i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.1072 | 1.08025 | 0.540123 | − | 0.841586i | \(-0.318378\pi\) | ||||
0.540123 | + | 0.841586i | \(0.318378\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −52.9553 | −2.03224 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.134043 | + | 2.78878i | 0.00513653 | + | 0.106866i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 41.5454i | − | 1.58969i | −0.606813 | − | 0.794844i | \(-0.707552\pi\) | ||
0.606813 | − | 0.794844i | \(-0.292448\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.74794 | −0.296033 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.3852 | − | 0.979814i | 0.777744 | − | 0.0373823i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.8689 | 0.566461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.0681 | −0.497133 | −0.248566 | − | 0.968615i | \(-0.579959\pi\) | ||||
−0.248566 | + | 0.968615i | \(0.579959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.742098 | − | 7.70190i | −0.0281900 | − | 0.292571i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.2656 | 0.389396 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.5511i | 0.437529i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.6486 | − | 0.752152i | 0.591886 | − | 0.0284490i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.3220 | 0.918629 | 0.459314 | − | 0.888274i | \(-0.348095\pi\) | ||||
0.459314 | + | 0.888274i | \(0.348095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.43993 | −0.356034 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.18979 | − | 0.297512i | 0.233121 | − | 0.0112050i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.7843 | −1.08255 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 19.2745i | − | 0.723870i | −0.932203 | − | 0.361935i | \(-0.882116\pi\) | ||
0.932203 | − | 0.361935i | \(-0.117884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.886322 | − | 9.19874i | −0.0332397 | − | 0.344980i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.6569 | − | 22.5969i | −0.698706 | − | 0.846262i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.86016 | 0.0695661 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.6528 | + | 1.08881i | −0.845985 | + | 0.0406623i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2588i | 0.419883i | 0.977714 | + | 0.209942i | \(0.0673274\pi\) | ||||
−0.977714 | + | 0.209942i | \(0.932673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.05077 | 0.0763746 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −37.2684 | + | 1.79131i | −1.38603 | + | 0.0666194i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 3.14000i | − | 0.116617i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.9001i | 0.552614i | 0.961069 | + | 0.276307i | \(0.0891107\pi\) | ||||
−0.961069 | + | 0.276307i | \(0.910889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.8867 | + | 7.67331i | −0.958766 | + | 0.284197i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.73453i | − | 0.138127i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.6998i | 0.838435i | 0.907886 | + | 0.419217i | \(0.137696\pi\) | ||||
−0.907886 | + | 0.419217i | \(0.862304\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.762347 | + | 15.8608i | 0.0281196 | + | 0.585033i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.816453i | − | 0.0300744i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.0904 | 1.73225 | 0.866124 | − | 0.499829i | \(-0.166604\pi\) | ||||
0.866124 | + | 0.499829i | \(0.166604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.70430 | − | 0.322242i | 0.246289 | − | 0.0118379i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.1428 | 1.69282 | 0.846408 | − | 0.532536i | \(-0.178761\pi\) | ||||
0.846408 | + | 0.532536i | \(0.178761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.47232 | −0.347039 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46.7783 | − | 4.50722i | 1.71153 | − | 0.164910i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 56.6169i | − | 2.06874i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.8659i | 1.08982i | 0.838494 | + | 0.544911i | \(0.183437\pi\) | ||||
−0.838494 | + | 0.544911i | \(0.816563\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.227849 | + | 4.74042i | 0.00830326 | + | 0.172751i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.8802 | 0.505153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 39.1104i | − | 1.42149i | −0.703449 | − | 0.710746i | \(-0.748358\pi\) | ||
0.703449 | − | 0.710746i | \(-0.251642\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.94116 | − | 3.58570i | 0.143055 | − | 0.130153i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0699634i | 0.00253617i | 0.999999 | + | 0.00126809i | \(0.000403644\pi\) | ||||
−0.999999 | + | 0.00126809i | \(0.999596\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50.5672 | 1.83065 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.26782 | + | 0.892979i | −0.335079 | + | 0.0322857i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.8936i | 1.18772i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.1180i | 0.797596i | 0.917039 | + | 0.398798i | \(0.130573\pi\) | ||||
−0.917039 | + | 0.398798i | \(0.869427\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.9397 | + | 2.20809i | −1.65448 | + | 0.0795225i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.8192 | −1.18043 | −0.590213 | − | 0.807248i | \(-0.700956\pi\) | ||||
−0.590213 | + | 0.807248i | \(0.700956\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.11022 | 0.219486 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.36201 | − | 49.1419i | −0.0847365 | − | 1.76296i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.97349 | 0.178194 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.926373i | 0.0331482i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.1469 | + | 2.34274i | −0.577042 | + | 0.0837227i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.9188i | 0.461091i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 34.8223i | − | 1.24128i | −0.784096 | − | 0.620640i | \(-0.786873\pi\) | ||
0.784096 | − | 0.620640i | \(-0.213127\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.340379 | − | 7.08163i | −0.0121178 | − | 0.252113i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.687345i | − | 0.0244392i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.67315i | 0.0949265i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.426359 | + | 8.87047i | 0.0151214 | + | 0.314603i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.6425 | −0.872882 | −0.436441 | − | 0.899733i | \(-0.643761\pi\) | ||||
−0.436441 | + | 0.899733i | \(0.643761\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.1040i | − | 0.392831i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.8819 | + | 1.24120i | −0.455158 | + | 0.0438557i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.99569 | −0.246872 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.8702 | + | 12.2774i | −0.524107 | + | 0.432722i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.2834 | + | 0.494274i | −0.361994 | + | 0.0173993i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17.7305i | − | 0.623372i | −0.950185 | − | 0.311686i | \(-0.899106\pi\) | ||
0.950185 | − | 0.311686i | \(-0.100894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.1173 | −0.390380 | −0.195190 | − | 0.980765i | \(-0.562532\pi\) | ||||
−0.195190 | + | 0.980765i | \(0.562532\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.181319 | + | 3.77237i | 0.00635913 | + | 0.132303i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.6758 | −0.759272 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.60796 | −0.0562553 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.35502 | + | 34.8203i | 0.117234 | + | 1.21672i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 35.5549i | − | 1.24088i | −0.784256 | − | 0.620438i | \(-0.786955\pi\) | ||
0.784256 | − | 0.620438i | \(-0.213045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.0792 | 1.71079 | 0.855397 | − | 0.517973i | \(-0.173313\pi\) | ||||
0.855397 | + | 0.517973i | \(0.173313\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0533392 | + | 1.10973i | 0.00185703 | + | 0.0386359i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.2238 | −0.425062 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.73797 | −0.303482 | −0.151741 | − | 0.988420i | \(-0.548488\pi\) | ||||
−0.151741 | + | 0.988420i | \(0.548488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.11558 | + | 44.0150i | 0.0733886 | + | 1.52686i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.4530 | 0.985837 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.64677i | 0.126202i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.55881 | − | 31.4206i | −0.157575 | − | 1.08606i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.22017 | 0.0421250 | 0.0210625 | − | 0.999778i | \(-0.493295\pi\) | ||||
0.0210625 | + | 0.999778i | \(0.493295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.1404 | 0.660013 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.17826 | + | 45.3190i | 0.0750231 | + | 1.56087i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.59022 | 0.157908 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 42.5757i | − | 1.46292i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.8670 | + | 0.906842i | −0.647513 | + | 0.0311227i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.1252 | − | 21.5700i | 0.895561 | − | 0.739409i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.6114 | −0.739959 | −0.369980 | − | 0.929040i | \(-0.620635\pi\) | ||||
−0.369980 | + | 0.929040i | \(0.620635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.384485 | + | 3.99040i | 0.0131491 | + | 0.136469i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.5300i | 1.11120i | 0.831448 | + | 0.555602i | \(0.187512\pi\) | ||||
−0.831448 | + | 0.555602i | \(0.812488\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.7309 | 1.79916 | 0.899578 | − | 0.436760i | \(-0.143874\pi\) | ||||
0.899578 | + | 0.436760i | \(0.143874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.24444 | + | 25.8907i | 0.0424104 | + | 0.882354i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.1954i | 1.50443i | 0.658918 | + | 0.752214i | \(0.271014\pi\) | ||||
−0.658918 | + | 0.752214i | \(0.728986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 9.85550i | − | 0.335097i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.612669 | − | 12.7467i | −0.0208073 | − | 0.432899i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.97593i | 0.0670289i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.69118i | 0.125071i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.78933 | − | 39.3277i | −0.128249 | − | 1.33104i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.02092i | − | 0.135932i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.0543 | 1.92659 | 0.963293 | − | 0.268454i | \(-0.0865126\pi\) | ||||
0.963293 | + | 0.268454i | \(0.0865126\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.25195 | − | 46.8522i | −0.0759564 | − | 1.58028i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.7818 | −1.23921 | −0.619605 | − | 0.784914i | \(-0.712707\pi\) | ||||
−0.619605 | + | 0.784914i | \(0.712707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.4704 | 1.56385 | 0.781926 | − | 0.623371i | \(-0.214237\pi\) | ||||
0.781926 | + | 0.623371i | \(0.214237\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.6236 | + | 0.943210i | −0.659641 | + | 0.0317056i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 21.1776i | − | 0.711074i | −0.934662 | − | 0.355537i | \(-0.884298\pi\) | ||
0.934662 | − | 0.355537i | \(-0.115702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 63.8064i | 2.14000i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.66678 | − | 1.10225i | 0.189844 | − | 0.0369268i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.78099 | −0.159990 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 16.9605i | − | 0.566929i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.8180 | + | 16.2109i | −0.594925 | + | 0.541267i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 19.1861i | − | 0.639892i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.9129 | 0.530136 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.402334 | − | 8.37062i | −0.0133888 | − | 0.278557i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 25.5650i | − | 0.849811i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 45.8979i | − | 1.52402i | −0.647567 | − | 0.762008i | \(-0.724214\pi\) | ||
0.647567 | − | 0.762008i | \(-0.275786\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.05972 | − | 21.3769i | −0.0683167 | − | 0.709028i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.9640 | 1.29093 | 0.645467 | − | 0.763788i | \(-0.276663\pi\) | ||||
0.645467 | + | 0.763788i | \(0.276663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0482 | −0.332547 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.59474 | + | 0.0766514i | −0.0527206 | + | 0.00253402i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.5913 | −1.14231 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 41.4674i | − | 1.36788i | −0.729537 | − | 0.683941i | \(-0.760265\pi\) | ||
0.729537 | − | 0.683941i | \(-0.239735\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.23191 | + | 25.6302i | 0.0405929 | + | 0.844542i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 4.18813i | − | 0.137854i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.06427i | 0.232272i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.146747 | + | 1.52302i | 0.00481981 | + | 0.0500226i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0813i | 0.790082i | 0.918663 | + | 0.395041i | \(0.129270\pi\) | ||||
−0.918663 | + | 0.395041i | \(0.870730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 12.2508i | − | 0.401505i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.26258 | + | 0.0606858i | −0.0413349 | + | 0.00198676i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.99077 | 0.0651052 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.45592i | − | 0.112900i | −0.998405 | − | 0.0564499i | \(-0.982022\pi\) | ||
0.998405 | − | 0.0564499i | \(-0.0179781\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.8708 | + | 1.43574i | −0.974795 | + | 0.0468535i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.70843 | −0.316486 | −0.158243 | − | 0.987400i | \(-0.550583\pi\) | ||||
−0.158243 | + | 0.987400i | \(0.550583\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.7642 | + | 11.3643i | −0.448225 | + | 0.370072i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.6768 | + | 2.99999i | −0.672616 | + | 0.0975896i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.2341i | 0.819998i | 0.912086 | + | 0.409999i | \(0.134471\pi\) | ||||
−0.912086 | + | 0.409999i | \(0.865529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.6275 | 1.02667 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.1790 | + | 2.17153i | −1.46503 | + | 0.0704166i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.6762 | −1.83592 | −0.917960 | − | 0.396672i | \(-0.870165\pi\) | ||||
−0.917960 | + | 0.396672i | \(0.870165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.4794 | 0.403825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.48456 | − | 0.167485i | 0.112640 | − | 0.00541403i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.1538i | 1.00601i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.33481 | 0.204349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.0470 | − | 4.05134i | 1.35495 | − | 0.130553i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.0097 | 0.676326 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.76298 | 0.0888513 | 0.0444257 | − | 0.999013i | \(-0.485854\pi\) | ||||
0.0444257 | + | 0.999013i | \(0.485854\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.17504 | − | 0.344868i | 0.230495 | − | 0.0110788i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.8285 | −0.379594 | −0.189797 | − | 0.981823i | \(-0.560783\pi\) | ||||
−0.189797 | + | 0.981823i | \(0.560783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 41.2771i | − | 1.32328i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.241146 | − | 5.01709i | −0.00772287 | − | 0.160675i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.2315 | −1.38310 | −0.691549 | − | 0.722330i | \(-0.743071\pi\) | ||||
−0.691549 | + | 0.722330i | \(0.743071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.76708 | 0.0884364 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.61844 | + | 37.5541i | 0.115528 | + | 1.19901i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.4684 | −0.844211 | −0.422105 | − | 0.906547i | \(-0.638709\pi\) | ||||
−0.422105 | + | 0.906547i | \(0.638709\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.84641i | − | 0.313733i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.19627 | − | 24.8886i | −0.0380778 | − | 0.792214i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.45006 | − | 3.67413i | 0.141504 | − | 0.116831i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1890 | 0.323664 | 0.161832 | − | 0.986818i | \(-0.448260\pi\) | ||||
0.161832 | + | 0.986818i | \(0.448260\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.316018 | + | 6.57480i | 0.0100285 | + | 0.208645i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8.69855i | − | 0.275763i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60.4205 | −1.91354 | −0.956769 | − | 0.290849i | \(-0.906062\pi\) | ||||
−0.956769 | + | 0.290849i | \(0.906062\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.3267 | − | 5.27062i | 1.14932 | − | 0.166755i |
(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 | 1380.2.i.a.1241.8 | yes | 16 | |
3.2 | odd | 2 | 1380.2.i.b.1241.7 | yes | 16 | ||
23.22 | odd | 2 | 1380.2.i.b.1241.8 | yes | 16 | ||
69.68 | even | 2 | inner | 1380.2.i.a.1241.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.i.a.1241.7 | ✓ | 16 | 69.68 | even | 2 | inner | |
1380.2.i.a.1241.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1380.2.i.b.1241.7 | yes | 16 | 3.2 | odd | 2 | ||
1380.2.i.b.1241.8 | yes | 16 | 23.22 | odd | 2 |