Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,6,Mod(177,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.177");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(62.8704573667\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.177 |
Dual form | 392.6.i.e.361.1 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 10.0000 | + | 17.3205i | 0.641500 | + | 1.11111i | 0.985098 | + | 0.171994i | \(0.0550210\pi\) |
−0.343598 | + | 0.939117i | \(0.611646\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −37.0000 | + | 64.0859i | −0.661876 | + | 1.14640i | 0.318246 | + | 0.948008i | \(0.396906\pi\) |
−0.980122 | + | 0.198395i | \(0.936427\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −78.5000 | + | 135.966i | −0.323045 | + | 0.559531i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −62.0000 | − | 107.387i | −0.154493 | − | 0.267590i | 0.778381 | − | 0.627792i | \(-0.216041\pi\) |
−0.932874 | + | 0.360202i | \(0.882708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −478.000 | −0.784458 | −0.392229 | − | 0.919868i | \(-0.628296\pi\) | ||||
−0.392229 | + | 0.919868i | \(0.628296\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1480.00 | −1.69837 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −599.000 | − | 1037.50i | −0.502695 | − | 0.870693i | −0.999995 | − | 0.00311466i | \(-0.999009\pi\) |
0.497300 | − | 0.867579i | \(-0.334325\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1522.00 | − | 2636.18i | 0.967232 | − | 1.67529i | 0.263737 | − | 0.964595i | \(-0.415045\pi\) |
0.703495 | − | 0.710700i | \(-0.251622\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −92.0000 | + | 159.349i | −0.0362634 | + | 0.0628100i | −0.883587 | − | 0.468266i | \(-0.844879\pi\) |
0.847324 | + | 0.531076i | \(0.178212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1175.50 | − | 2036.03i | −0.376160 | − | 0.651528i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1720.00 | 0.454066 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3282.00 | −0.724676 | −0.362338 | − | 0.932047i | \(-0.618021\pi\) | ||||
−0.362338 | + | 0.932047i | \(0.618021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2864.00 | − | 4960.59i | −0.535265 | − | 0.927106i | −0.999150 | − | 0.0412109i | \(-0.986878\pi\) |
0.463886 | − | 0.885895i | \(-0.346455\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1240.00 | − | 2147.74i | 0.198215 | − | 0.343319i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5163.00 | + | 8942.58i | −0.620009 | + | 1.07389i | 0.369475 | + | 0.929241i | \(0.379538\pi\) |
−0.989483 | + | 0.144646i | \(0.953796\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4780.00 | − | 8279.20i | −0.503230 | − | 0.871620i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8886.00 | 0.825556 | 0.412778 | − | 0.910832i | \(-0.364558\pi\) | ||||
0.412778 | + | 0.910832i | \(0.364558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9188.00 | −0.757792 | −0.378896 | − | 0.925439i | \(-0.623696\pi\) | ||||
−0.378896 | + | 0.925439i | \(0.623696\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5809.00 | − | 10061.5i | −0.427632 | − | 0.740680i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11832.0 | − | 20493.6i | 0.781292 | − | 1.35324i | −0.149897 | − | 0.988702i | \(-0.547894\pi\) |
0.931189 | − | 0.364536i | \(-0.118772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11980.0 | − | 20750.0i | 0.644958 | − | 1.11710i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5843.00 | − | 10120.4i | −0.285724 | − | 0.494888i | 0.687061 | − | 0.726600i | \(-0.258901\pi\) |
−0.972784 | + | 0.231712i | \(0.925567\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9176.00 | 0.409022 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 60880.0 | 2.48192 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8438.00 | + | 14615.0i | 0.315580 | + | 0.546601i | 0.979561 | − | 0.201149i | \(-0.0644676\pi\) |
−0.663981 | + | 0.747750i | \(0.731134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9241.00 | + | 16005.9i | −0.317976 | + | 0.550751i | −0.980066 | − | 0.198674i | \(-0.936336\pi\) |
0.662090 | + | 0.749425i | \(0.269670\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17686.0 | − | 30633.1i | 0.519214 | − | 0.899305i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7766.00 | + | 13451.1i | 0.211354 | + | 0.366076i | 0.952139 | − | 0.305667i | \(-0.0988794\pi\) |
−0.740785 | + | 0.671743i | \(0.765546\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3680.00 | −0.0930519 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −31960.0 | −0.752421 | −0.376210 | − | 0.926534i | \(-0.622773\pi\) | ||||
−0.376210 | + | 0.926534i | \(0.622773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2443.00 | − | 4231.40i | −0.0536558 | − | 0.0929345i | 0.837950 | − | 0.545747i | \(-0.183754\pi\) |
−0.891606 | + | 0.452812i | \(0.850421\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 23510.0 | − | 40720.5i | 0.482614 | − | 0.835911i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −22280.0 | + | 38590.1i | −0.401650 | + | 0.695678i | −0.993925 | − | 0.110058i | \(-0.964896\pi\) |
0.592275 | + | 0.805736i | \(0.298230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 36275.5 | + | 62831.0i | 0.614329 | + | 1.06405i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −67364.0 | −1.07333 | −0.536664 | − | 0.843796i | \(-0.680316\pi\) | ||||
−0.536664 | + | 0.843796i | \(0.680316\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 88652.0 | 1.33089 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −32820.0 | − | 56845.9i | −0.464880 | − | 0.805195i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 35997.0 | − | 62348.6i | 0.481716 | − | 0.834357i | −0.518064 | − | 0.855342i | \(-0.673347\pi\) |
0.999780 | + | 0.0209851i | \(0.00668026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 57280.0 | − | 99211.9i | 0.686745 | − | 1.18948i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 112628. | + | 195077.i | 1.28038 | + | 2.21768i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −48866.0 | −0.527324 | −0.263662 | − | 0.964615i | \(-0.584930\pi\) | ||||
−0.263662 | + | 0.964615i | \(0.584930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19468.0 | 0.199633 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 25803.0 | + | 44692.1i | 0.251690 | + | 0.435941i | 0.963991 | − | 0.265934i | \(-0.0856802\pi\) |
−0.712301 | + | 0.701874i | \(0.752347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 90212.0 | − | 156252.i | 0.837860 | − | 1.45122i | −0.0538212 | − | 0.998551i | \(-0.517140\pi\) |
0.891681 | − | 0.452665i | \(-0.149527\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 32850.0 | − | 56897.9i | 0.277381 | − | 0.480437i | −0.693352 | − | 0.720599i | \(-0.743867\pi\) |
0.970733 | + | 0.240162i | \(0.0772004\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 56353.0 | + | 97606.3i | 0.454308 | + | 0.786885i | 0.998648 | − | 0.0519796i | \(-0.0165531\pi\) |
−0.544340 | + | 0.838865i | \(0.683220\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −206520. | −1.59094 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −23502.0 | −0.173145 | −0.0865723 | − | 0.996246i | \(-0.527591\pi\) | ||||
−0.0865723 | + | 0.996246i | \(0.527591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6808.00 | − | 11791.8i | −0.0480037 | − | 0.0831449i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 37523.0 | − | 64991.7i | 0.253415 | − | 0.438928i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 72837.5 | − | 126158.i | 0.452264 | − | 0.783343i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 88860.0 | + | 153910.i | 0.529595 | + | 0.917285i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −57276.0 | −0.327867 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −94592.0 | −0.520409 | −0.260205 | − | 0.965553i | \(-0.583790\pi\) | ||||
−0.260205 | + | 0.965553i | \(0.583790\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −91880.0 | − | 159141.i | −0.486124 | − | 0.841991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 35146.0 | − | 60874.7i | 0.178936 | − | 0.309926i | −0.762580 | − | 0.646893i | \(-0.776068\pi\) |
0.941516 | + | 0.336967i | \(0.109401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −63640.0 | + | 110228.i | −0.300535 | + | 0.520543i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −138645. | − | 240140.i | −0.631107 | − | 1.09311i | −0.987326 | − | 0.158706i | \(-0.949268\pi\) |
0.356219 | − | 0.934402i | \(-0.384066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 130308. | 0.572050 | 0.286025 | − | 0.958222i | \(-0.407666\pi\) | ||||
0.286025 | + | 0.958222i | \(0.407666\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 473280. | 2.00480 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29636.0 | + | 51331.1i | 0.121194 | + | 0.209913i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 121434. | − | 210330.i | 0.479645 | − | 0.830770i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 200765. | − | 347735.i | 0.740836 | − | 1.28317i | −0.211278 | − | 0.977426i | \(-0.567763\pi\) |
0.952115 | − | 0.305740i | \(-0.0989040\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 37988.0 | + | 65797.1i | 0.135583 | + | 0.234836i | 0.925820 | − | 0.377965i | \(-0.123376\pi\) |
−0.790237 | + | 0.612801i | \(0.790043\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 188086. | 0.649573 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 423872. | 1.41712 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −197161. | − | 341493.i | −0.638369 | − | 1.10569i | −0.985791 | − | 0.167979i | \(-0.946276\pi\) |
0.347421 | − | 0.937709i | \(-0.387057\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 116860. | − | 202407.i | 0.366584 | − | 0.634941i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5862.00 | − | 10153.3i | 0.0172813 | − | 0.0299321i | −0.857255 | − | 0.514891i | \(-0.827832\pi\) |
0.874537 | + | 0.484959i | \(0.161166\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 91760.0 | + | 158933.i | 0.262388 | + | 0.454469i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 551928. | 1.53141 | 0.765705 | − | 0.643192i | \(-0.222390\pi\) | ||||
0.765705 | + | 0.643192i | \(0.222390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −142809. | −0.384626 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 238954. | + | 413880.i | 0.624919 | + | 1.08239i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 216447. | − | 374897.i | 0.549840 | − | 0.952351i | −0.448445 | − | 0.893810i | \(-0.648022\pi\) |
0.998285 | − | 0.0585404i | \(-0.0186446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −168760. | + | 292301.i | −0.404889 | + | 0.701289i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −279810. | − | 484645.i | −0.652726 | − | 1.13055i | −0.982459 | − | 0.186480i | \(-0.940292\pi\) |
0.329733 | − | 0.944074i | \(-0.393041\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −604710. | −1.37199 | −0.685995 | − | 0.727607i | \(-0.740633\pi\) | ||||
−0.685995 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −369640. | −0.815927 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −382062. | − | 661751.i | −0.820738 | − | 1.42156i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −74276.0 | + | 128650.i | −0.155326 | + | 0.269033i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 204576. | − | 354336.i | 0.405762 | − | 0.702800i | −0.588648 | − | 0.808390i | \(-0.700340\pi\) |
0.994410 | + | 0.105589i | \(0.0336729\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −270433. | − | 468404.i | −0.522596 | − | 0.905164i | −0.999654 | − | 0.0262917i | \(-0.991630\pi\) |
0.477058 | − | 0.878872i | \(-0.341703\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 707440. | 1.33230 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −629898. | −1.15639 | −0.578195 | − | 0.815898i | \(-0.696243\pi\) | ||||
−0.578195 | + | 0.815898i | \(0.696243\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 141524. | + | 245127.i | 0.253336 | + | 0.438791i | 0.964442 | − | 0.264293i | \(-0.0851388\pi\) |
−0.711106 | + | 0.703085i | \(0.751805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −155320. | + | 269022.i | −0.271167 | + | 0.469675i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −328782. | + | 569467.i | −0.546416 | + | 0.946420i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14444.0 | − | 25017.7i | −0.0234294 | − | 0.0405810i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −377456. | −0.597724 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 142756. | 0.220744 | 0.110372 | − | 0.993890i | \(-0.464796\pi\) | ||||
0.110372 | + | 0.993890i | \(0.464796\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −319600. | − | 553563.i | −0.482678 | − | 0.836023i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 339956. | − | 588821.i | 0.501564 | − | 0.868735i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 48860.0 | − | 84628.0i | 0.0688404 | − | 0.119235i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 286322. | + | 495924.i | 0.394343 | + | 0.683022i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −889696. | −1.19806 | −0.599031 | − | 0.800726i | \(-0.704447\pi\) | ||||
−0.599031 | + | 0.800726i | \(0.704447\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 369107. | 0.486067 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 571578. | + | 990002.i | 0.736226 | + | 1.27518i | 0.954184 | + | 0.299222i | \(0.0967271\pi\) |
−0.217958 | + | 0.975958i | \(0.569940\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −347893. | + | 602568.i | −0.438386 | + | 0.759307i | −0.997565 | − | 0.0697396i | \(-0.977783\pi\) |
0.559179 | + | 0.829047i | \(0.311116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 173563. | − | 300620.i | 0.209444 | − | 0.362767i | −0.742096 | − | 0.670294i | \(-0.766168\pi\) |
0.951539 | + | 0.307527i | \(0.0995014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 875568. | + | 1.51653e6i | 1.03424 | + | 1.79135i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −891200. | −1.03063 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.64296e6 | −1.86051 | −0.930255 | − | 0.366912i | \(-0.880415\pi\) | ||||
−0.930255 | + | 0.366912i | \(0.880415\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −583719. | − | 1.01103e6i | −0.647383 | − | 1.12130i | −0.983746 | − | 0.179568i | \(-0.942530\pi\) |
0.336363 | − | 0.941733i | \(-0.390803\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −516530. | + | 894656.i | −0.561151 | + | 0.971942i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −727516. | + | 1.26009e6i | −0.758753 | + | 1.31420i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −673640. | − | 1.16678e6i | −0.688541 | − | 1.19259i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 790612. | 0.792098 | 0.396049 | − | 0.918229i | \(-0.370381\pi\) | ||||
0.396049 | + | 0.918229i | \(0.370381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22816.0 | 0.0224098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 886520. | + | 1.53550e6i | 0.853764 | + | 1.47876i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −64895.0 | + | 112401.i | −0.0612884 | + | 0.106155i | −0.895042 | − | 0.445983i | \(-0.852854\pi\) |
0.833753 | + | 0.552137i | \(0.186188\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 257637. | − | 446240.i | 0.234103 | − | 0.405478i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −35444.0 | − | 61390.8i | −0.0315975 | − | 0.0547286i | 0.849794 | − | 0.527115i | \(-0.176726\pi\) |
−0.881392 | + | 0.472386i | \(0.843393\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 864764. | 0.756455 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.43988e6 | 1.23608 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 895087. | + | 1.55034e6i | 0.754197 | + | 1.30631i | 0.945773 | + | 0.324829i | \(0.105307\pi\) |
−0.191576 | + | 0.981478i | \(0.561360\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −886808. | + | 1.53600e6i | −0.733511 | + | 1.27048i | 0.221863 | + | 0.975078i | \(0.428786\pi\) |
−0.955374 | + | 0.295400i | \(0.904547\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −145762. | + | 252467.i | −0.116228 | + | 0.201314i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 137725. | + | 238547.i | 0.107848 | + | 0.186799i | 0.914898 | − | 0.403684i | \(-0.132271\pi\) |
−0.807050 | + | 0.590483i | \(0.798937\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 899296. | 0.691659 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 594170. | 0.448895 | 0.224448 | − | 0.974486i | \(-0.427942\pi\) | ||||
0.224448 | + | 0.974486i | \(0.427942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 546214. | + | 946070.i | 0.405412 | + | 0.702194i | 0.994369 | − | 0.105970i | \(-0.0337947\pi\) |
−0.588957 | + | 0.808164i | \(0.700461\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.25256e6 | + | 3.90155e6i | −1.64272 | + | 2.84528i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7673.50 | + | 13290.9i | −0.00540442 | + | 0.00936073i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −488660. | − | 846384.i | −0.338278 | − | 0.585915i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −333654. | −0.227053 | −0.113527 | − | 0.993535i | \(-0.536215\pi\) | ||||
−0.113527 | + | 0.993535i | \(0.536215\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.24882e6 | −0.835500 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −106640. | − | 184706.i | −0.0701502 | − | 0.121504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 43976.0 | − | 76168.7i | 0.0284471 | − | 0.0492718i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −516060. | + | 893842.i | −0.322919 | + | 0.559312i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −683834. | − | 1.18444e6i | −0.420921 | − | 0.729057i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.05997e6 | −0.641872 | −0.320936 | − | 0.947101i | \(-0.603997\pi\) | ||||
−0.320936 | + | 0.947101i | \(0.603997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.60848e6 | 2.14995 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −668244. | − | 1.15743e6i | −0.391773 | − | 0.678570i | 0.600911 | − | 0.799316i | \(-0.294805\pi\) |
−0.992683 | + | 0.120746i | \(0.961471\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 822093. | − | 1.42391e6i | 0.474308 | − | 0.821525i | −0.525260 | − | 0.850942i | \(-0.676032\pi\) |
0.999567 | + | 0.0294171i | \(0.00936512\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 861849. | − | 1.49277e6i | 0.481707 | − | 0.834341i | −0.518072 | − | 0.855337i | \(-0.673350\pi\) |
0.999780 | + | 0.0209956i | \(0.00668359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 203484. | + | 352445.i | 0.111958 | + | 0.193916i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.31400e6 | 0.711759 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.64671e6 | −1.94489 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 561889. | + | 973220.i | 0.295082 | + | 0.511096i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.12706e6 | + | 1.95213e6i | −0.582878 | + | 1.00957i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.37481e6 | + | 2.38125e6i | −0.689722 | + | 1.19463i | 0.282206 | + | 0.959354i | \(0.408934\pi\) |
−0.971928 | + | 0.235279i | \(0.924399\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −810591. | − | 1.40398e6i | −0.400582 | − | 0.693828i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.14937e6 | −0.559561 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.41489e6 | −1.63796 | −0.818978 | − | 0.573824i | \(-0.805459\pi\) | ||||
−0.818978 | + | 0.573824i | \(0.805459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −235020. | − | 407067.i | −0.111072 | − | 0.192383i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −355136. | + | 615114.i | −0.165390 | + | 0.286464i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 136160. | − | 235836.i | 0.0615888 | − | 0.106675i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −365382. | − | 632860.i | −0.162901 | − | 0.282153i | 0.773007 | − | 0.634398i | \(-0.218752\pi\) |
−0.935908 | + | 0.352245i | \(0.885418\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.29749e6 | 1.00969 | 0.504847 | − | 0.863209i | \(-0.331549\pi\) | ||||
0.504847 | + | 0.863209i | \(0.331549\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −822160. | −0.356196 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −585359. | − | 1.01387e6i | −0.250026 | − | 0.433058i | 0.713507 | − | 0.700649i | \(-0.247106\pi\) |
−0.963533 | + | 0.267590i | \(0.913773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.18252e6 | − | 2.04818e6i | 0.498009 | − | 0.862578i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.94327e6 | + | 3.36584e6i | −0.795787 | + | 1.37834i | 0.126552 | + | 0.991960i | \(0.459609\pi\) |
−0.922339 | + | 0.386383i | \(0.873724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.39492e6 | − | 5.88017e6i | −1.37108 | − | 2.37477i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.91350e6 | 1.16051 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 361564. | 0.142054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 466520. | + | 808036.i | 0.180803 | + | 0.313160i | 0.942154 | − | 0.335180i | \(-0.108797\pi\) |
−0.761351 | + | 0.648339i | \(0.775464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −697551. | + | 1.20819e6i | −0.266692 | + | 0.461924i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 196109. | − | 339671.i | 0.0729836 | − | 0.126411i | −0.827224 | − | 0.561872i | \(-0.810081\pi\) |
0.900208 | + | 0.435461i | \(0.143415\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −572760. | − | 992049.i | −0.210327 | − | 0.364297i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.56880e6 | 0.568477 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.72930e6 | −1.69122 | −0.845608 | − | 0.533805i | \(-0.820762\pi\) | ||||
−0.845608 | + | 0.533805i | \(0.820762\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −945920. | − | 1.63838e6i | −0.333843 | − | 0.578233i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 948672. | − | 1.64315e6i | 0.330460 | − | 0.572374i | −0.652142 | − | 0.758097i | \(-0.726129\pi\) |
0.982602 | + | 0.185723i | \(0.0594627\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 721258. | − | 1.24926e6i | 0.244801 | − | 0.424008i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.86148e6 | + | 3.22417e6i | 0.623711 | + | 1.08030i | 0.988789 | + | 0.149323i | \(0.0477093\pi\) |
−0.365077 | + | 0.930977i | \(0.618957\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 220432. | 0.0729177 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.40584e6 | 0.459150 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.64872e6 | − | 2.85567e6i | −0.531685 | − | 0.920905i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.66904e6 | − | 2.89086e6i | 0.531484 | − | 0.920557i | −0.467841 | − | 0.883813i | \(-0.654968\pi\) |
0.999325 | − | 0.0367445i | \(-0.0116988\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.13745e6 | + | 3.70217e6i | −0.663796 | + | 1.14973i | 0.315814 | + | 0.948821i | \(0.397722\pi\) |
−0.979610 | + | 0.200908i | \(0.935611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.36899e6 | + | 2.37116e6i | 0.419893 | + | 0.727275i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.36877e6 | −1.62644 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.28042e6 | 0.383149 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.28660e6 | − | 2.22845e6i | −0.380306 | − | 0.658710i | 0.610800 | − | 0.791785i | \(-0.290848\pi\) |
−0.991106 | + | 0.133075i | \(0.957515\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.77290e6 | − | 4.80280e6i | 0.809710 | − | 1.40246i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.49247e6 | − | 4.31708e6i | 0.710410 | − | 1.23047i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.30308e6 | + | 2.25700e6i | 0.366970 | + | 0.635611i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.26828e6 | −1.46600 | −0.732999 | − | 0.680230i | \(-0.761880\pi\) | ||||
−0.732999 | + | 0.680230i | \(0.761880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −973354. | −0.267649 | −0.133824 | − | 0.991005i | \(-0.542726\pi\) | ||||
−0.133824 | + | 0.991005i | \(0.542726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.85762e6 | + | 3.21750e6i | 0.504786 | + | 0.874314i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.40825e6 | + | 2.43916e6i | −0.378187 | + | 0.655040i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −592720. | + | 1.02662e6i | −0.155491 | + | 0.269319i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.77868e6 | − | 3.08076e6i | −0.461216 | − | 0.798850i | 0.537806 | − | 0.843069i | \(-0.319253\pi\) |
−0.999022 | + | 0.0442188i | \(0.985920\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.95496e6 | 0.501092 | 0.250546 | − | 0.968105i | \(-0.419390\pi\) | ||||
0.250546 | + | 0.968105i | \(0.419390\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.85736e6 | 1.23077 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 280048. | + | 485057.i | 0.0701502 | + | 0.121504i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.64840e6 | + | 2.85512e6i | −0.408228 | + | 0.707071i | −0.994691 | − | 0.102905i | \(-0.967186\pi\) |
0.586464 | + | 0.809976i | \(0.300520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.52910e6 | − | 4.38053e6i | 0.612289 | − | 1.06052i | −0.378565 | − | 0.925575i | \(-0.623582\pi\) |
0.990854 | − | 0.134941i | \(-0.0430844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.66378e6 | + | 4.61380e6i | 0.637673 | + | 1.10448i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.03060e6 | 1.90099 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.12730e6 | 0.497981 | 0.248990 | − | 0.968506i | \(-0.419901\pi\) | ||||
0.248990 | + | 0.968506i | \(0.419901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −550932. | − | 954242.i | −0.127543 | − | 0.220911i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −759760. | + | 1.31594e6i | −0.173953 | + | 0.301295i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −144565. | + | 250394.i | −0.0323797 | + | 0.0560833i | −0.881761 | − | 0.471696i | \(-0.843642\pi\) |
0.849381 | + | 0.527779i | \(0.176975\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.03028e6 | − | 1.78450e6i | −0.228257 | − | 0.395352i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.66870e6 | −0.584854 | −0.292427 | − | 0.956288i | \(-0.594463\pi\) | ||||
−0.292427 | + | 0.956288i | \(0.594463\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.58619e6 | 1.64464 | 0.822321 | − | 0.569024i | \(-0.192679\pi\) | ||||
0.822321 | + | 0.569024i | \(0.192679\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.23872e6 | + | 7.34168e6i | 0.909081 | + | 1.57457i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −709806. | + | 1.22942e6i | −0.150608 | + | 0.260860i | −0.931451 | − | 0.363867i | \(-0.881456\pi\) |
0.780843 | + | 0.624727i | \(0.214790\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.94322e6 | − | 6.82986e6i | 0.819028 | − | 1.41860i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 569656. | + | 986673.i | 0.117074 | + | 0.202778i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.15644e6 | −1.45534 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.83470e6 | 0.369207 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −942032. | − | 1.63165e6i | −0.187597 | − | 0.324928i | 0.756851 | − | 0.653587i | \(-0.226737\pi\) |
−0.944449 | + | 0.328659i | \(0.893403\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.46791e6 | − | 4.27455e6i | 0.486371 | − | 0.842419i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.80804e6 | − | 3.13162e6i | 0.349023 | − | 0.604526i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.00694e6 | + | 5.20817e6i | 0.574516 | + | 0.995091i | 0.996094 | + | 0.0882991i | \(0.0281431\pi\) |
−0.421578 | + | 0.906792i | \(0.638524\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 234480. | 0.0443439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.29232e6 | 0.803504 | 0.401752 | − | 0.915749i | \(-0.368401\pi\) | ||||
0.401752 | + | 0.915749i | \(0.368401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.96592e6 | + | 3.40507e6i | 0.364291 | + | 0.630970i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −720316. | + | 1.24762e6i | −0.132133 | + | 0.228860i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −672546. | + | 1.16488e6i | −0.120912 | + | 0.209426i | −0.920128 | − | 0.391618i | \(-0.871915\pi\) |
0.799215 | + | 0.601045i | \(0.205249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.51928e6 | + | 9.55967e6i | 0.982399 | + | 1.70157i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −202008. | −0.0355999 | −0.0177999 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0177999 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.81884e6 | −0.666352 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.42809e6 | − | 2.47352e6i | −0.246738 | − | 0.427362i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.89172e6 | − | 8.47271e6i | 0.836887 | − | 1.44953i | −0.0555970 | − | 0.998453i | \(-0.517706\pi\) |
0.892484 | − | 0.451078i | \(-0.148960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.61784e6 | − | 4.53423e6i | 0.439187 | − | 0.760695i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.67569e6 | + | 1.15626e7i | 1.10912 | + | 1.92105i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.93434e6 | −0.482818 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.65788e6 | 1.41089 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.24152e6 | − | 9.07857e6i | −0.845985 | − | 1.46529i | −0.884763 | − | 0.466041i | \(-0.845680\pi\) |
0.0387785 | − | 0.999248i | \(-0.487653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.10509e6 | − | 5.37817e6i | 0.496386 | − | 0.859766i | −0.503605 | − | 0.863934i | \(-0.667993\pi\) |
0.999991 | + | 0.00416822i | \(0.00132679\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.43107e6 | + | 5.94279e6i | −0.538150 | + | 0.932103i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.20124e6 | + | 5.54472e6i | 0.497370 | + | 0.861470i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.64953e6 | −0.407787 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24751e6 | −0.647614 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.43090e6 | + | 4.21044e6i | 0.367183 | + | 0.635980i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.59620e6 | − | 9.69290e6i | 0.837447 | − | 1.45050i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.54044e6 | + | 4.40017e6i | −0.373178 | + | 0.646363i | −0.990052 | − | 0.140699i | \(-0.955065\pi\) |
0.616875 | + | 0.787061i | \(0.288398\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.04710e6 | − | 1.04739e7i | −0.880132 | − | 1.52443i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.34024e6 | −1.20278 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.34687e6 | 0.478267 | 0.239133 | − | 0.970987i | \(-0.423137\pi\) | ||||
0.239133 | + | 0.970987i | \(0.423137\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.45084e6 | − | 2.51292e6i | −0.205441 | − | 0.355835i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.99520e6 | + | 8.65195e6i | −0.700929 | + | 1.21405i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.64124e6 | − | 1.32350e7i | 1.05301 | − | 1.82386i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.50189e6 | − | 6.06545e6i | −0.478260 | − | 0.828371i | 0.521429 | − | 0.853295i | \(-0.325399\pi\) |
−0.999689 | + | 0.0249237i | \(0.992066\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.39186e6 | 0.594456 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.97104e6 | −0.398567 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.49094e6 | − | 1.12426e7i | −0.863052 | − | 1.49485i | −0.868969 | − | 0.494867i | \(-0.835217\pi\) |
0.00591737 | − | 0.999982i | \(-0.498116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 869574. | − | 1.50615e6i | 0.114600 | − | 0.198493i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −949709. | + | 1.64494e6i | −0.122973 | + | 0.212996i | −0.920939 | − | 0.389707i | \(-0.872576\pi\) |
0.797966 | + | 0.602703i | \(0.205910\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 831498. | + | 1.44020e6i | 0.106726 | + | 0.184855i | 0.914442 | − | 0.404717i | \(-0.132630\pi\) |
−0.807716 | + | 0.589572i | \(0.799297\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.18304e6 | 1.04119 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 432584. | 0.0545633 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.38672e6 | + | 7.59802e6i | 0.548530 | + | 0.950082i | 0.998376 | + | 0.0569756i | \(0.0181457\pi\) |
−0.449845 | + | 0.893106i | \(0.648521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.40866e6 | − | 9.36807e6i | 0.670491 | − | 1.16133i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −724532. | + | 1.25493e6i | −0.0882849 | + | 0.152914i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.77670e6 | + | 4.80939e6i | 0.335459 | + | 0.581032i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.18393e6 | −0.620961 | −0.310480 | − | 0.950580i | \(-0.600490\pi\) | ||||
−0.310480 | + | 0.950580i | \(0.600490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.74360e7 | −2.07090 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.29898e6 | − | 1.09102e7i | −0.741825 | − | 1.28488i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.24929e6 | − | 7.35998e6i | 0.496226 | − | 0.859489i | −0.503765 | − | 0.863841i | \(-0.668052\pi\) |
0.999991 | + | 0.00435235i | \(0.00138540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.83048e6 | + | 4.90254e6i | −0.325031 | + | 0.562970i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.62355e6 | − | 9.74027e6i | −0.640388 | − | 1.10918i | −0.985346 | − | 0.170567i | \(-0.945440\pi\) |
0.344958 | − | 0.938618i | \(-0.387893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.46439e6 | 0.391238 | 0.195619 | − | 0.980680i | \(-0.437328\pi\) | ||||
0.195619 | + | 0.980680i | \(0.437328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.43852e6 | −0.273108 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.38997e6 | + | 9.33571e6i | 0.598685 | + | 1.03695i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −499856. | + | 865776.i | −0.0550647 | + | 0.0953748i | −0.892244 | − | 0.451554i | \(-0.850870\pi\) |
0.837179 | + | 0.546929i | \(0.184203\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.65570e6 | + | 9.79595e6i | −0.612891 | + | 1.06156i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.90670e6 | − | 8.49865e6i | −0.527398 | − | 0.913480i | −0.999490 | − | 0.0319305i | \(-0.989834\pi\) |
0.472092 | − | 0.881549i | \(-0.343499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.31513e7 | −1.40210 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.34745e6 | −0.565501 | −0.282751 | − | 0.959193i | \(-0.591247\pi\) | ||||
−0.282751 | + | 0.959193i | \(0.591247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.41384e6 | − | 5.91295e6i | −0.358110 | − | 0.620265i | 0.629535 | − | 0.776972i | \(-0.283245\pi\) |
−0.987645 | + | 0.156707i | \(0.949912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −158240. | + | 274080.i | −0.0164660 | + | 0.0285199i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.79265e6 | − | 1.00332e7i | 0.593167 | − | 1.02740i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.77456e6 | − | 6.53773e6i | −0.383440 | − | 0.664138i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.23705e7 | 1.24670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.60970e6 | −0.360909 | −0.180455 | − | 0.983583i | \(-0.557757\pi\) | ||||
−0.180455 | + | 0.983583i | \(0.557757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.42756e6 | + | 2.47261e6i | 0.141607 | + | 0.245271i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.49990e6 | − | 6.06201e6i | 0.344447 | − | 0.596599i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.50886e6 | − | 4.34547e6i | 0.243066 | − | 0.421003i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.69267e6 | + | 1.15920e7i | 0.643361 | + | 1.11433i | 0.984678 | + | 0.174385i | \(0.0557937\pi\) |
−0.341317 | + | 0.939948i | \(0.610873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.91115e6 | 0.945358 | 0.472679 | − | 0.881235i | \(-0.343287\pi\) | ||||
0.472679 | + | 0.881235i | \(0.343287\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.35982e7 | 1.28701 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.91796e6 | − | 1.54464e7i | −0.837539 | − | 1.45066i | −0.891946 | − | 0.452141i | \(-0.850660\pi\) |
0.0544074 | − | 0.998519i | \(-0.482673\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.04631e6 | − | 1.81227e6i | 0.0975101 | − | 0.168892i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.16162e6 | − | 3.74403e6i | 0.198379 | − | 0.343603i | −0.749624 | − | 0.661864i | \(-0.769766\pi\) |
0.948003 | + | 0.318261i | \(0.103099\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.60080e6 | + | 4.50472e6i | 0.236867 | + | 0.410266i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 767102. | 0.0693330 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.97858e7 | 1.77476 | 0.887382 | − | 0.461035i | \(-0.152522\pi\) | ||||
0.887382 | + | 0.461035i | \(0.152522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.88858e6 | + | 1.36634e7i | 0.702255 | + | 1.21634i | 0.967673 | + | 0.252209i | \(0.0811569\pi\) |
−0.265417 | + | 0.964134i | \(0.585510\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.72644e6 | + | 9.91849e6i | −0.505942 | + | 0.876318i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 301944. | − | 522982.i | 0.0262792 | − | 0.0455169i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.89696e6 | − | 1.54100e7i | −0.768557 | − | 1.33118i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.29177e6 | 0.196501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.78762e6 | 0.577670 | 0.288835 | − | 0.957379i | \(-0.406732\pi\) | ||||
0.288835 | + | 0.957379i | \(0.406732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.02186e6 | − | 3.50196e6i | −0.170801 | − | 0.295837i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.49711e6 | + | 1.29854e7i | −0.628669 | + | 1.08889i | 0.359150 | + | 0.933280i | \(0.383067\pi\) |
−0.987819 | + | 0.155607i | \(0.950267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.14316e7 | + | 1.98000e7i | −0.944578 | + | 1.63606i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.77902e6 | − | 1.00096e7i | −0.474026 | − | 0.821038i | 0.525531 | − | 0.850774i | \(-0.323867\pi\) |
−0.999558 | + | 0.0297363i | \(0.990533\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.05195e7 | 1.67086 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.39157e7 | −1.12490 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.79295e6 | + | 4.83754e6i | 0.224138 | + | 0.388219i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −110078. | + | 190661.i | −0.00877012 | + | 0.0151903i | −0.870377 | − | 0.492386i | \(-0.836125\pi\) |
0.861607 | + | 0.507576i | \(0.169458\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.82140e6 | + | 8.35090e6i | −0.378626 | + | 0.655800i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.32271e6 | − | 9.21921e6i | −0.415003 | − | 0.718806i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.94252e6 | 0.537433 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.78933e6 | 0.368111 | 0.184056 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184056 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.57162e7 | + | 2.72212e7i | 1.19938 | + | 2.07740i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.75114e7 | + | 3.03306e7i | −1.32693 | + | 2.29831i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.13446e6 | + | 3.69699e6i | −0.159468 | + | 0.276206i | −0.934677 | − | 0.355499i | \(-0.884311\pi\) |
0.775209 | + | 0.631705i | \(0.217644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.49796e6 | − | 6.05864e6i | −0.259502 | − | 0.449471i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.05395e6 | 0.0776421 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.38613e6 | −0.320860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.64296e7 | − | 2.84569e7i | −1.19352 | − | 2.06723i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.09798e6 | + | 1.40261e7i | −0.584190 | + | 1.01185i | 0.410786 | + | 0.911732i | \(0.365254\pi\) |
−0.994976 | + | 0.100115i | \(0.968079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.16744e7 | − | 2.02206e7i | 0.830593 | − | 1.43863i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.85799e6 | + | 6.68224e6i | 0.272594 | + | 0.472147i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.53426e6 | −0.458522 | −0.229261 | − | 0.973365i | \(-0.573631\pi\) | ||||
−0.229261 | + | 0.973365i | \(0.573631\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.03131e6 | −0.211257 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.50361e6 | + | 9.53254e6i | 0.380938 | + | 0.659804i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.58086e6 | − | 1.13984e7i | 0.452400 | − | 0.783579i | −0.546135 | − | 0.837697i | \(-0.683901\pi\) |
0.998535 | + | 0.0541179i | \(0.0172347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 962984. | − | 1.66794e6i | 0.0653056 | − | 0.113113i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.11738e6 | + | 1.23277e7i | 0.479412 | + | 0.830366i | 0.999721 | − | 0.0236117i | \(-0.00751652\pi\) |
−0.520309 | + | 0.853978i | \(0.674183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.91006e7 | −1.94696 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.15835e7 | −1.43434 | −0.717168 | − | 0.696901i | \(-0.754562\pi\) | ||||
−0.717168 | + | 0.696901i | \(0.754562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.48566e7 | + | 2.57324e7i | 0.980684 | + | 1.69859i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.28807e6 | − | 9.15921e6i | 0.346734 | − | 0.600560i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.32969e6 | + | 1.61595e7i | −0.603625 | + | 1.04551i | 0.388642 | + | 0.921389i | \(0.372944\pi\) |
−0.992267 | + | 0.124121i | \(0.960389\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.90612e6 | + | 1.36938e7i | 0.508131 | + | 0.880109i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.62222e6 | −0.358956 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.56681e6 | −0.162800 | −0.0813999 | − | 0.996682i | \(-0.525939\pi\) | ||||
−0.0813999 | + | 0.996682i | \(0.525939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 228160. | + | 395185.i | 0.0143759 | + | 0.0248998i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.29793e7 | + | 2.24808e7i | −0.812436 | + | 1.40718i | 0.0987188 | + | 0.995115i | \(0.468526\pi\) |
−0.911155 | + | 0.412065i | \(0.864808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.95918e6 | + | 1.20537e7i | −0.429937 | + | 0.744672i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.03336e6 | − | 6.98599e6i | −0.247559 | − | 0.428785i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.53267e6 | −0.337380 | −0.168690 | − | 0.985669i | \(-0.553954\pi\) | ||||
−0.168690 | + | 0.985669i | \(0.553954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.59580e6 | −0.157266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.16470e6 | + | 7.21347e6i | 0.250689 | + | 0.434206i | 0.963716 | − | 0.266931i | \(-0.0860096\pi\) |
−0.713027 | + | 0.701137i | \(0.752676\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.73326e6 | + | 1.16624e7i | −0.402691 | + | 0.697480i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.35245e7 | − | 2.34251e7i | 0.798504 | − | 1.38305i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.98152e6 | + | 3.43209e6i | 0.116244 | + | 0.201341i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.64504e6 | −0.329051 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.91798e7 | 1.69009 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.82613e6 | − | 1.18232e7i | −0.392860 | − | 0.680453i | 0.599966 | − | 0.800026i | \(-0.295181\pi\) |
−0.992825 | + | 0.119573i | \(0.961848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 708880. | − | 1.22782e6i | 0.0405397 | − | 0.0702168i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.41720e6 | − | 7.65081e6i | 0.249439 | − | 0.432041i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.64764e6 | + | 1.49782e7i | 0.485266 | + | 0.840505i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.54626e6 | 0.476574 | 0.238287 | − | 0.971195i | \(-0.423414\pi\) | ||||
0.238287 | + | 0.971195i | \(0.423414\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.83495e7 | −1.57101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.65153e6 | + | 9.78874e6i | 0.311232 | + | 0.539070i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −302932. | + | 524694.i | −0.0165789 | + | 0.0287155i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.79017e7 | + | 3.10067e7i | −0.967635 | + | 1.67599i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.79242e6 | − | 6.56867e6i | −0.203725 | − | 0.352863i | 0.746000 | − | 0.665945i | \(-0.231972\pi\) |
−0.949726 | + | 0.313083i | \(0.898638\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.18473e6 | −0.330194 | −0.165097 | − | 0.986277i | \(-0.552794\pi\) | ||||
−0.165097 | + | 0.986277i | \(0.552794\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.54723e7 | −1.88219 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 433788. | + | 751343.i | 0.0228762 | + | 0.0396227i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.39841e7 | + | 2.42212e7i | −0.732960 | + | 1.26952i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.39051e6 | − | 2.40843e6i | 0.0719973 | − | 0.124703i | −0.827779 | − | 0.561054i | \(-0.810396\pi\) |
0.899777 | + | 0.436351i | \(0.143729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.19473e6 | − | 1.41937e7i | −0.421731 | − | 0.730459i | 0.574378 | − | 0.818590i | \(-0.305244\pi\) |
−0.996109 | + | 0.0881311i | \(0.971911\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.83048e6 | −0.298242 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.29511e7 | 1.16692 | 0.583459 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583459 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.75068e6 | − | 3.03227e6i | −0.0884750 | − | 0.153243i | 0.818392 | − | 0.574661i | \(-0.194866\pi\) |
−0.906867 | + | 0.421418i | \(0.861533\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.75450e6 | + | 4.77093e6i | −0.138369 | + | 0.239663i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.04213e7 | + | 3.53708e7i | −1.01360 | + | 1.75561i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.92608e6 | − | 8.53222e6i | −0.243046 | − | 0.420967i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.29668e6 | −0.259776 | −0.129888 | − | 0.991529i | \(-0.541462\pi\) | ||||
−0.129888 | + | 0.991529i | \(0.541462\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.73962e6 | −0.474845 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.94170e6 | + | 1.02913e7i | 0.287966 | + | 0.498772i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.28393e6 | − | 9.15204e6i | 0.254575 | − | 0.440937i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.09243e7 | + | 1.89214e7i | −0.520144 | + | 0.900916i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −949992. | − | 1.64543e6i | −0.0449672 | − | 0.0778855i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.02948e7 | 0.955021 | 0.477511 | − | 0.878626i | \(-0.341539\pi\) | ||||
0.477511 | + | 0.878626i | \(0.341539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.53652e7 | −1.65448 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.41392e6 | − | 4.18104e6i | −0.112272 | − | 0.194461i | 0.804414 | − | 0.594069i | \(-0.202479\pi\) |
−0.916686 | + | 0.399608i | \(0.869146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.51052e6 | + | 1.12766e7i | −0.301046 | + | 0.521427i | −0.976373 | − | 0.216091i | \(-0.930669\pi\) |
0.675327 | + | 0.737518i | \(0.264002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.96193e7 | − | 3.39817e7i | 0.896721 | − | 1.55317i | 0.0650616 | − | 0.997881i | \(-0.479276\pi\) |
0.831660 | − | 0.555286i | \(-0.187391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.60171e7 | + | 2.77424e7i | 0.727852 | + | 1.26068i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −306940. | −0.0138677 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.52544e6 | 0.248209 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.71215e6 | − | 6.42963e6i | −0.165798 | − | 0.287171i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.83598e6 | − | 6.64411e6i | 0.170349 | − | 0.295054i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.73110e6 | + | 1.16586e7i | −0.295520 | + | 0.511856i | −0.975106 | − | 0.221740i | \(-0.928826\pi\) |
0.679586 | + | 0.733596i | \(0.262160\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.33654e6 | − | 5.77906e6i | −0.145655 | − | 0.252281i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 917710. | 0.0398351 | 0.0199175 | − | 0.999802i | \(-0.493660\pi\) | ||||
0.0199175 | + | 0.999802i | \(0.493660\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.45488e7 | 1.05957 | 0.529784 | − | 0.848133i | \(-0.322273\pi\) | ||||
0.529784 | + | 0.848133i | \(0.322273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.24882e7 | − | 2.16303e7i | −0.535973 | − | 0.928333i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.07314e6 | + | 1.39831e7i | −0.344535 | + | 0.596752i | −0.985269 | − | 0.171011i | \(-0.945297\pi\) |
0.640734 | + | 0.767763i | \(0.278630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.49816e6 | − | 7.79105e6i | 0.189820 | − | 0.328777i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.60166e7 | − | 6.23826e7i | −1.51138 | − | 2.61779i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.14119e7 | 1.72809 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.75904e6 | 0.0729953 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.39965e6 | + | 1.62807e7i | 0.387893 | + | 0.671851i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.99991e6 | + | 1.21242e7i | −0.287264 | + | 0.497555i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.23743e7 | − | 3.87534e7i | 0.908087 | − | 1.57285i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.01681e7 | + | 1.76116e7i | 0.410412 | + | 0.710855i | 0.994935 | − | 0.100523i | \(-0.0320515\pi\) |
−0.584523 | + | 0.811377i | \(0.698718\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.10214e6 | −0.325230 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.07726e7 | 0.430054 | 0.215027 | − | 0.976608i | \(-0.431016\pi\) | ||||
0.215027 | + | 0.976608i | \(0.431016\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.17657e6 | + | 7.23403e6i | 0.165822 | + | 0.287212i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.36767e7 | − | 2.36887e7i | 0.540043 | − | 0.935381i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.09283e7 | + | 3.62489e7i | −0.817419 | + | 1.41581i | 0.0901585 | + | 0.995927i | \(0.471263\pi\) |
−0.907578 | + | 0.419884i | \(0.862071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.05997e7 | − | 1.83593e7i | −0.411761 | − | 0.713191i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.52769e7 | 0.590242 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.42764e7 | 0.932890 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.41633e7 | + | 2.45315e7i | 0.541333 | + | 0.937617i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.49923e7 | − | 2.59674e7i | 0.569939 | − | 0.987163i | −0.426633 | − | 0.904425i | \(-0.640300\pi\) |
0.996571 | − | 0.0827379i | \(-0.0263664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.33649e7 | − | 2.31487e7i | 0.502645 | − | 0.870606i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.49642e6 | − | 9.52009e6i | −0.205613 | − | 0.356133i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.42402e7 | −0.529867 | −0.264934 | − | 0.964267i | \(-0.585350\pi\) | ||||
−0.264934 | + | 0.964267i | \(0.585350\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.28837e7 | 1.21707 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.07273e7 | − | 3.59007e7i | −0.763077 | − | 1.32169i | −0.941257 | − | 0.337691i | \(-0.890354\pi\) |
0.178180 | − | 0.983998i | \(-0.442979\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −817512. | + | 1.41597e6i | −0.0299375 | + | 0.0518532i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.70393e6 | − | 1.33436e7i | 0.279150 | − | 0.483502i | −0.692024 | − | 0.721875i | \(-0.743281\pi\) |
0.971174 | + | 0.238373i | \(0.0766140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.16775e6 | + | 2.02261e6i | 0.0420907 | + | 0.0729032i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.44740e7 | 1.23606 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.06328e7 | −0.735912 | −0.367956 | − | 0.929843i | \(-0.619942\pi\) | ||||
−0.367956 | + | 0.929843i | \(0.619942\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.51386e7 | + | 2.62209e7i | 0.537128 | + | 0.930333i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.06968e6 | + | 7.04889e6i | −0.143642 | + | 0.248795i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09042e6 | + | 3.62071e6i | −0.0730171 | + | 0.126469i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.15745e6 | + | 8.93297e6i | 0.179213 | + | 0.310406i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.00241e7 | 1.38358 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.18724e7 | 0.408294 | 0.204147 | − | 0.978940i | \(-0.434558\pi\) | ||||
0.204147 | + | 0.978940i | \(0.434558\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.64671e7 | − | 6.31629e7i | −1.24765 | − | 2.16099i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 766110. | − | 1.32694e6i | 0.0260761 | − | 0.0451652i | −0.852693 | − | 0.522413i | \(-0.825032\pi\) |
0.878769 | + | 0.477247i | \(0.158365\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.12378e7 | + | 1.94644e7i | −0.378590 | + | 0.655737i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.71604e6 | − | 1.50966e7i | −0.292135 | − | 0.505992i | 0.682180 | − | 0.731185i | \(-0.261032\pi\) |
−0.974314 | + | 0.225193i | \(0.927699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.92726e6 | −0.297688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.76948e7 | −0.587049 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.11635e6 | + | 1.93357e6i | 0.0368482 | + | 0.0638229i | 0.883861 | − | 0.467749i | \(-0.154935\pi\) |
−0.847013 | + | 0.531572i | \(0.821602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.33062e7 | − | 4.03676e7i | 0.765388 | − | 1.32569i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 845296. | − | 1.46410e6i | 0.0274801 | − | 0.0475969i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.11250e7 | − | 1.92691e7i | −0.359847 | − | 0.623273i | 0.628088 | − | 0.778142i | \(-0.283838\pi\) |
−0.987935 | + | 0.154869i | \(0.950504\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.49926e7 | −1.76983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.09456e7 | −0.670709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.66331e7 | + | 4.61299e7i | 0.848562 | + | 1.46975i | 0.882491 | + | 0.470329i | \(0.155865\pi\) |
−0.0339287 | + | 0.999424i | \(0.510802\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.88036e6 | + | 1.53812e7i | −0.281525 | + | 0.487615i |
(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 | 392.6.i.e.177.1 | 2 | ||
7.2 | even | 3 | 392.6.a.b.1.1 | 1 | |||
7.3 | odd | 6 | 392.6.i.b.361.1 | 2 | |||
7.4 | even | 3 | inner | 392.6.i.e.361.1 | 2 | ||
7.5 | odd | 6 | 8.6.a.a.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 392.6.i.b.177.1 | 2 | |||
21.5 | even | 6 | 72.6.a.f.1.1 | 1 | |||
28.19 | even | 6 | 16.6.a.a.1.1 | 1 | |||
28.23 | odd | 6 | 784.6.a.l.1.1 | 1 | |||
35.12 | even | 12 | 200.6.c.a.49.1 | 2 | |||
35.19 | odd | 6 | 200.6.a.a.1.1 | 1 | |||
35.33 | even | 12 | 200.6.c.a.49.2 | 2 | |||
56.5 | odd | 6 | 64.6.a.a.1.1 | 1 | |||
56.19 | even | 6 | 64.6.a.g.1.1 | 1 | |||
77.54 | even | 6 | 968.6.a.a.1.1 | 1 | |||
84.47 | odd | 6 | 144.6.a.k.1.1 | 1 | |||
112.5 | odd | 12 | 256.6.b.f.129.1 | 2 | |||
112.19 | even | 12 | 256.6.b.d.129.1 | 2 | |||
112.61 | odd | 12 | 256.6.b.f.129.2 | 2 | |||
112.75 | even | 12 | 256.6.b.d.129.2 | 2 | |||
140.19 | even | 6 | 400.6.a.l.1.1 | 1 | |||
140.47 | odd | 12 | 400.6.c.d.49.2 | 2 | |||
140.103 | odd | 12 | 400.6.c.d.49.1 | 2 | |||
168.5 | even | 6 | 576.6.a.g.1.1 | 1 | |||
168.131 | odd | 6 | 576.6.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.6.a.a.1.1 | ✓ | 1 | 7.5 | odd | 6 | ||
16.6.a.a.1.1 | 1 | 28.19 | even | 6 | |||
64.6.a.a.1.1 | 1 | 56.5 | odd | 6 | |||
64.6.a.g.1.1 | 1 | 56.19 | even | 6 | |||
72.6.a.f.1.1 | 1 | 21.5 | even | 6 | |||
144.6.a.k.1.1 | 1 | 84.47 | odd | 6 | |||
200.6.a.a.1.1 | 1 | 35.19 | odd | 6 | |||
200.6.c.a.49.1 | 2 | 35.12 | even | 12 | |||
200.6.c.a.49.2 | 2 | 35.33 | even | 12 | |||
256.6.b.d.129.1 | 2 | 112.19 | even | 12 | |||
256.6.b.d.129.2 | 2 | 112.75 | even | 12 | |||
256.6.b.f.129.1 | 2 | 112.5 | odd | 12 | |||
256.6.b.f.129.2 | 2 | 112.61 | odd | 12 | |||
392.6.a.b.1.1 | 1 | 7.2 | even | 3 | |||
392.6.i.b.177.1 | 2 | 7.6 | odd | 2 | |||
392.6.i.b.361.1 | 2 | 7.3 | odd | 6 | |||
392.6.i.e.177.1 | 2 | 1.1 | even | 1 | trivial | ||
392.6.i.e.361.1 | 2 | 7.4 | even | 3 | inner | ||
400.6.a.l.1.1 | 1 | 140.19 | even | 6 | |||
400.6.c.d.49.1 | 2 | 140.103 | odd | 12 | |||
400.6.c.d.49.2 | 2 | 140.47 | odd | 12 | |||
576.6.a.g.1.1 | 1 | 168.5 | even | 6 | |||
576.6.a.h.1.1 | 1 | 168.131 | odd | 6 | |||
784.6.a.l.1.1 | 1 | 28.23 | odd | 6 | |||
968.6.a.a.1.1 | 1 | 77.54 | even | 6 |