Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,22,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (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: | \(201.223687887\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.6 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.22.f.a.35.5 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1420.72 | + | 280.555i | −0.981054 | + | 0.193733i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.93973e6 | − | 797180.i | 0.924935 | − | 0.380125i | ||||
\(5\) | 1.26307e7 | 0.578419 | 0.289209 | − | 0.957266i | \(-0.406608\pi\) | ||||
0.289209 | + | 0.957266i | \(0.406608\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.88458e8i | 0.385969i | 0.981202 | + | 0.192985i | \(0.0618168\pi\) | ||||
−0.981202 | + | 0.192985i | \(0.938183\pi\) | |||||||
\(8\) | −2.53216e9 | + | 1.67677e9i | −0.833769 | + | 0.552113i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.79447e10 | + | 3.54361e9i | −0.567460 | + | 0.112059i | ||||
\(11\) | 3.92167e10i | 0.455877i | 0.973676 | + | 0.227938i | \(0.0731985\pi\) | ||||
−0.973676 | + | 0.227938i | \(0.926802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.88488e11i | 0.781578i | 0.920480 | + | 0.390789i | \(0.127798\pi\) | ||||
−0.920480 | + | 0.390789i | \(0.872202\pi\) | |||||||
\(14\) | −8.09283e10 | − | 4.09817e11i | −0.0747749 | − | 0.378657i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.12706e12 | − | 3.09263e12i | 0.711010 | − | 0.703182i | ||||
\(17\) | 1.32533e12i | 0.159445i | 0.996817 | + | 0.0797226i | \(0.0254035\pi\) | ||||
−0.996817 | + | 0.0797226i | \(0.974597\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.57362e13 | −0.963011 | −0.481506 | − | 0.876443i | \(-0.659910\pi\) | ||||
−0.481506 | + | 0.876443i | \(0.659910\pi\) | |||||||
\(20\) | 2.45001e13 | − | 1.00689e13i | 0.535000 | − | 0.219871i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.10024e13 | − | 5.57158e13i | −0.0883183 | − | 0.447240i | ||||
\(23\) | −2.48502e14 | −1.25080 | −0.625400 | − | 0.780304i | \(-0.715064\pi\) | ||||
−0.625400 | + | 0.780304i | \(0.715064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.17303e14 | −0.665432 | ||||||||
\(26\) | −1.08992e14 | − | 5.51932e14i | −0.151417 | − | 0.766771i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.29953e14 | + | 5.59530e14i | 0.146717 | + | 0.356997i | ||||
\(29\) | −9.85080e14 | −0.434803 | −0.217401 | − | 0.976082i | \(-0.569758\pi\) | ||||
−0.217401 | + | 0.976082i | \(0.569758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.59520e15i | − | 0.787817i | −0.919150 | − | 0.393908i | \(-0.871123\pi\) | ||
0.919150 | − | 0.393908i | \(-0.128877\pi\) | |||||||
\(32\) | −3.57501e15 | + | 5.27106e15i | −0.561310 | + | 0.827605i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.71829e14 | − | 1.88293e15i | −0.0308898 | − | 0.156424i | ||||
\(35\) | 3.64342e15i | 0.223252i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.71550e16i | − | 0.586505i | −0.956035 | − | 0.293252i | \(-0.905262\pi\) | ||
0.956035 | − | 0.293252i | \(-0.0947376\pi\) | |||||||
\(38\) | 3.65639e16 | − | 7.22042e15i | 0.944767 | − | 0.186567i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.19829e16 | + | 2.11788e16i | −0.482268 | + | 0.319353i | ||||
\(41\) | − | 9.67643e16i | − | 1.12586i | −0.826504 | − | 0.562930i | \(-0.809674\pi\) | ||
0.826504 | − | 0.562930i | \(-0.190326\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.44106e15 | −0.0383941 | −0.0191971 | − | 0.999816i | \(-0.506111\pi\) | ||||
−0.0191971 | + | 0.999816i | \(0.506111\pi\) | |||||||
\(44\) | 3.12627e16 | + | 7.60697e16i | 0.173290 | + | 0.421657i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.53052e17 | − | 6.97186e16i | 1.22710 | − | 0.242321i | ||||
\(47\) | −1.91059e16 | −0.0529834 | −0.0264917 | − | 0.999649i | \(-0.508434\pi\) | ||||
−0.0264917 | + | 0.999649i | \(0.508434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.75338e17 | 0.851028 | ||||||||
\(50\) | 4.50798e17 | − | 8.90209e16i | 0.652825 | − | 0.128916i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.09695e17 | + | 7.53562e17i | 0.297097 | + | 0.722909i | ||||
\(53\) | 1.08346e18 | 0.850970 | 0.425485 | − | 0.904965i | \(-0.360104\pi\) | ||||
0.425485 | + | 0.904965i | \(0.360104\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.95334e17i | 0.263688i | ||||||||
\(56\) | −4.83677e17 | − | 7.30420e17i | −0.213099 | − | 0.321809i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.39952e18 | − | 2.76369e17i | 0.426565 | − | 0.0842356i | ||||
\(59\) | 1.60073e18i | 0.407729i | 0.978999 | + | 0.203865i | \(0.0653502\pi\) | ||||
−0.978999 | + | 0.203865i | \(0.934650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.20372e18i | − | 1.11350i | −0.830681 | − | 0.556748i | \(-0.812049\pi\) | ||
0.830681 | − | 0.556748i | \(-0.187951\pi\) | |||||||
\(62\) | 1.00865e18 | + | 5.10777e18i | 0.152626 | + | 0.772891i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.60027e18 | − | 8.49168e18i | 0.390342 | − | 0.920670i | ||||
\(65\) | 4.90688e18i | 0.452079i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.15887e19 | 1.44691 | 0.723453 | − | 0.690374i | \(-0.242554\pi\) | ||||
0.723453 | + | 0.690374i | \(0.242554\pi\) | |||||||
\(68\) | 1.05653e18 | + | 2.57079e18i | 0.0606091 | + | 0.147477i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.02218e18 | − | 5.17628e18i | −0.0432512 | − | 0.219022i | ||||
\(71\) | −7.99384e18 | −0.291436 | −0.145718 | − | 0.989326i | \(-0.546549\pi\) | ||||
−0.145718 | + | 0.989326i | \(0.546549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.40042e19 | −0.381389 | −0.190694 | − | 0.981649i | \(-0.561074\pi\) | ||||
−0.190694 | + | 0.981649i | \(0.561074\pi\) | |||||||
\(74\) | 4.81291e18 | + | 2.43724e19i | 0.113625 | + | 0.575393i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.99213e19 | + | 2.05164e19i | −0.890723 | + | 0.366065i | ||||
\(77\) | −1.13124e19 | −0.175955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.09023e20i | − | 1.29548i | −0.761859 | − | 0.647742i | \(-0.775713\pi\) | ||
0.761859 | − | 0.647742i | \(-0.224287\pi\) | |||||||
\(80\) | 3.94969e19 | − | 3.90620e19i | 0.411262 | − | 0.406733i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.71477e19 | + | 1.37475e20i | 0.218116 | + | 1.10453i | ||||
\(83\) | 1.01596e20i | 0.718716i | 0.933200 | + | 0.359358i | \(0.117004\pi\) | ||||
−0.933200 | + | 0.359358i | \(0.882996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.67399e19i | 0.0922261i | ||||||||
\(86\) | 7.73021e18 | − | 1.52652e18i | 0.0376667 | − | 0.00743820i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.57573e19 | − | 9.93028e19i | −0.251696 | − | 0.380096i | ||||
\(89\) | − | 1.04361e20i | − | 0.354767i | −0.984142 | − | 0.177384i | \(-0.943237\pi\) | ||
0.984142 | − | 0.177384i | \(-0.0567633\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.12062e20 | −0.301665 | ||||||||
\(92\) | −4.82027e20 | + | 1.98101e20i | −1.15691 | + | 0.475460i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.71441e19 | − | 5.36025e18i | 0.0519796 | − | 0.0102646i | ||||
\(95\) | −3.25066e20 | −0.557024 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.48553e20 | −0.479917 | −0.239958 | − | 0.970783i | \(-0.577134\pi\) | ||||
−0.239958 | + | 0.970783i | \(0.577134\pi\) | |||||||
\(98\) | −6.75321e20 | + | 1.33358e20i | −0.834904 | + | 0.164872i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.15481e20 | + | 2.52947e20i | −0.615481 | + | 0.252947i | ||||
\(101\) | 6.66650e20 | 0.600515 | 0.300257 | − | 0.953858i | \(-0.402927\pi\) | ||||
0.300257 | + | 0.953858i | \(0.402927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.59809e20i | − | 0.190486i | −0.995454 | − | 0.0952430i | \(-0.969637\pi\) | ||
0.995454 | − | 0.0952430i | \(-0.0303628\pi\) | |||||||
\(104\) | −6.51405e20 | − | 9.83713e20i | −0.431520 | − | 0.651656i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.53928e21 | + | 3.03969e20i | −0.834848 | + | 0.164861i | ||||
\(107\) | − | 2.98809e20i | − | 0.146847i | −0.997301 | − | 0.0734234i | \(-0.976608\pi\) | ||
0.997301 | − | 0.0734234i | \(-0.0233925\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.74224e21i | − | 0.704905i | −0.935830 | − | 0.352453i | \(-0.885348\pi\) | ||
0.935830 | − | 0.352453i | \(-0.114652\pi\) | |||||||
\(110\) | −1.38968e20 | − | 7.03730e20i | −0.0510850 | − | 0.258692i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.92092e20 | + | 9.02024e20i | 0.271407 | + | 0.274428i | ||||
\(113\) | 5.46109e21i | 1.51341i | 0.653758 | + | 0.756704i | \(0.273192\pi\) | ||||
−0.653758 | + | 0.756704i | \(0.726808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.13876e21 | −0.723486 | ||||||||
\(116\) | −1.91079e21 | + | 7.85286e20i | −0.402165 | + | 0.165279i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.49093e20 | − | 2.27419e21i | −0.0789905 | − | 0.400004i | ||||
\(119\) | −3.82303e20 | −0.0615410 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.86230e21 | 0.792176 | ||||||||
\(122\) | 1.74048e21 | + | 8.81374e21i | 0.215721 | + | 1.09240i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.86602e21 | − | 6.97372e21i | −0.299469 | − | 0.728680i | ||||
\(125\) | −1.00305e22 | −0.963317 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.48468e22i | − | 1.20696i | −0.797376 | − | 0.603482i | \(-0.793779\pi\) | ||
0.797376 | − | 0.603482i | \(-0.206221\pi\) | |||||||
\(128\) | −2.73258e21 | + | 1.30744e22i | −0.204582 | + | 0.978849i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.37665e21 | − | 6.97129e21i | −0.0875826 | − | 0.443514i | ||||
\(131\) | 2.00791e22i | 1.17868i | 0.807885 | + | 0.589340i | \(0.200612\pi\) | ||||
−0.807885 | + | 0.589340i | \(0.799388\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 7.42380e21i | − | 0.371693i | ||||||
\(134\) | −3.06714e22 | + | 6.05681e21i | −1.41949 | + | 0.280313i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.22228e21 | − | 3.35595e21i | −0.0880319 | − | 0.132941i | ||||
\(137\) | 7.69109e21i | 0.282112i | 0.990002 | + | 0.141056i | \(0.0450498\pi\) | ||||
−0.990002 | + | 0.141056i | \(0.954950\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.65844e22 | −0.837474 | −0.418737 | − | 0.908107i | \(-0.637527\pi\) | ||||
−0.418737 | + | 0.908107i | \(0.637527\pi\) | |||||||
\(140\) | 2.90446e21 | + | 7.06726e21i | 0.0848636 | + | 0.206494i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.13570e22 | − | 2.24271e21i | 0.285914 | − | 0.0564607i | ||||
\(143\) | −1.52352e22 | −0.356303 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.24422e22 | −0.251498 | ||||||||
\(146\) | 1.98960e22 | − | 3.92895e21i | 0.374163 | − | 0.0738876i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.36756e22 | − | 3.32760e22i | −0.222945 | − | 0.542479i | ||||
\(149\) | −3.32465e22 | −0.504999 | −0.252500 | − | 0.967597i | \(-0.581253\pi\) | ||||
−0.252500 | + | 0.967597i | \(0.581253\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.33781e22i | 0.572812i | 0.958108 | + | 0.286406i | \(0.0924607\pi\) | ||||
−0.958108 | + | 0.286406i | \(0.907539\pi\) | |||||||
\(152\) | 6.51681e22 | − | 4.31536e22i | 0.802929 | − | 0.531692i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.60717e22 | − | 3.17374e21i | 0.172621 | − | 0.0340882i | ||||
\(155\) | − | 4.54099e22i | − | 0.455688i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.76188e20i | 0.00593091i | 0.999996 | + | 0.00296545i | \(0.000943935\pi\) | ||||
−0.999996 | + | 0.00296545i | \(0.999056\pi\) | |||||||
\(158\) | 3.05869e22 | + | 1.54890e23i | 0.250978 | + | 1.27094i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.51549e22 | + | 6.65772e22i | −0.324672 | + | 0.478702i | ||||
\(161\) | − | 7.16824e22i | − | 0.482771i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.38444e22 | −0.0819037 | −0.0409518 | − | 0.999161i | \(-0.513039\pi\) | ||||
−0.0409518 | + | 0.999161i | \(0.513039\pi\) | |||||||
\(164\) | −7.71385e22 | − | 1.87697e23i | −0.427968 | − | 1.04135i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.85033e22 | − | 1.44340e23i | −0.139239 | − | 0.705099i | ||||
\(167\) | −8.06883e22 | −0.370073 | −0.185037 | − | 0.982732i | \(-0.559240\pi\) | ||||
−0.185037 | + | 0.982732i | \(0.559240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.61416e22 | 0.389135 | ||||||||
\(170\) | −4.69646e21 | − | 2.37827e22i | −0.0178672 | − | 0.0904788i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.05542e22 | + | 4.33750e21i | −0.0355121 | + | 0.0145946i | ||||
\(173\) | 1.74367e23 | 0.552051 | 0.276026 | − | 0.961150i | \(-0.410983\pi\) | ||||
0.276026 | + | 0.961150i | \(0.410983\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 9.15284e22i | − | 0.256836i | ||||||
\(176\) | 1.21282e23 | + | 1.22633e23i | 0.320564 | + | 0.324133i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.92790e22 | + | 1.48268e23i | 0.0687300 | + | 0.348046i | ||||
\(179\) | 4.16072e23i | 0.920897i | 0.887686 | + | 0.460449i | \(0.152311\pi\) | ||||
−0.887686 | + | 0.460449i | \(0.847689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.54507e23i | 0.304314i | 0.988356 | + | 0.152157i | \(0.0486220\pi\) | ||||
−0.988356 | + | 0.152157i | \(0.951378\pi\) | |||||||
\(182\) | 1.59209e23 | − | 3.14397e22i | 0.295950 | − | 0.0584425i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.29247e23 | − | 4.16681e23i | 1.04288 | − | 0.690584i | ||||
\(185\) | − | 2.16679e23i | − | 0.339245i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.19752e22 | −0.0726874 | ||||||||
\(188\) | −3.70602e22 | + | 1.52308e22i | −0.0490062 | + | 0.0201403i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.61827e23 | − | 9.11989e22i | 0.546471 | − | 0.107914i | ||||
\(191\) | 1.25425e24 | 1.40454 | 0.702268 | − | 0.711913i | \(-0.252171\pi\) | ||||
0.702268 | + | 0.711913i | \(0.252171\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.58700e24 | 1.59303 | 0.796516 | − | 0.604618i | \(-0.206674\pi\) | ||||
0.796516 | + | 0.604618i | \(0.206674\pi\) | |||||||
\(194\) | 4.95196e23 | − | 9.77884e22i | 0.470825 | − | 0.0929757i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.22027e23 | − | 3.78930e23i | 0.787145 | − | 0.323497i | ||||
\(197\) | 1.89785e24 | 1.53592 | 0.767958 | − | 0.640500i | \(-0.221273\pi\) | ||||
0.767958 | + | 0.640500i | \(0.221273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.38349e24i | − | 1.00698i | −0.864001 | − | 0.503489i | \(-0.832049\pi\) | ||
0.864001 | − | 0.503489i | \(-0.167951\pi\) | |||||||
\(200\) | 8.03460e23 | − | 5.32043e23i | 0.554816 | − | 0.367394i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.47123e23 | + | 1.87032e23i | −0.589138 | + | 0.116339i | ||||
\(203\) | − | 2.84154e23i | − | 0.167821i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.22220e24i | − | 0.651219i | ||||||
\(206\) | 7.28907e22 | + | 3.69115e23i | 0.0369034 | + | 0.186877i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.20145e24 | + | 1.21482e24i | 0.549592 | + | 0.555710i | ||||
\(209\) | − | 1.00929e24i | − | 0.439015i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.22690e24 | 0.876467 | 0.438234 | − | 0.898861i | \(-0.355604\pi\) | ||||
0.438234 | + | 0.898861i | \(0.355604\pi\) | |||||||
\(212\) | 2.10161e24 | − | 8.63708e23i | 0.787092 | − | 0.323475i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.38325e22 | + | 4.24524e23i | 0.0284491 | + | 0.144065i | ||||
\(215\) | −6.87244e22 | −0.0222079 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.03706e24 | 0.304073 | ||||||||
\(218\) | 4.88795e23 | + | 2.47524e24i | 0.136563 | + | 0.691550i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.94870e23 | + | 9.60814e23i | 0.100234 | + | 0.243894i | ||||
\(221\) | −5.14876e23 | −0.124619 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.62076e23i | − | 0.123764i | −0.998083 | − | 0.0618820i | \(-0.980290\pi\) | ||
0.998083 | − | 0.0618820i | \(-0.0197102\pi\) | |||||||
\(224\) | −1.52048e24 | − | 1.03124e24i | −0.319430 | − | 0.216649i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.53214e24 | − | 7.75868e24i | −0.293197 | − | 1.48474i | ||||
\(227\) | 7.15428e24i | 1.30706i | 0.756902 | + | 0.653528i | \(0.226712\pi\) | ||||
−0.756902 | + | 0.653528i | \(0.773288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.68123e24i | − | 0.946607i | −0.880899 | − | 0.473304i | \(-0.843061\pi\) | ||
0.880899 | − | 0.473304i | \(-0.156939\pi\) | |||||||
\(230\) | 4.45929e24 | − | 8.80594e23i | 0.709780 | − | 0.140163i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.49438e24 | − | 1.65175e24i | 0.362525 | − | 0.240061i | ||||
\(233\) | − | 3.26495e24i | − | 0.453565i | −0.973945 | − | 0.226782i | \(-0.927179\pi\) | ||
0.973945 | − | 0.226782i | \(-0.0728206\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.41321e23 | −0.0306466 | ||||||||
\(236\) | 1.27607e24 | + | 3.10498e24i | 0.154988 | + | 0.377123i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.43145e23 | − | 1.07257e23i | 0.0603751 | − | 0.0119225i | ||||
\(239\) | 3.04072e24 | 0.323443 | 0.161722 | − | 0.986836i | \(-0.448295\pi\) | ||||
0.161722 | + | 0.986836i | \(0.448295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.22649e24 | −0.119532 | −0.0597662 | − | 0.998212i | \(-0.519036\pi\) | ||||
−0.0597662 | + | 0.998212i | \(0.519036\pi\) | |||||||
\(242\) | −8.32868e24 | + | 1.64470e24i | −0.777168 | + | 0.153471i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.94548e24 | − | 1.20335e25i | −0.423268 | − | 1.02991i | ||||
\(245\) | 6.00385e24 | 0.492250 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 9.99820e24i | − | 0.752669i | ||||||
\(248\) | 6.02832e24 | + | 9.10361e24i | 0.434964 | + | 0.656857i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.42506e25 | − | 2.81412e24i | 0.945066 | − | 0.186626i | ||||
\(251\) | 1.39356e25i | 0.886241i | 0.896462 | + | 0.443120i | \(0.146129\pi\) | ||||
−0.896462 | + | 0.443120i | \(0.853871\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.74543e24i | − | 0.570211i | ||||||
\(254\) | 4.16535e24 | + | 2.10932e25i | 0.233829 | + | 1.18410i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.14146e23 | − | 1.93416e25i | 0.0110711 | − | 0.999939i | ||||
\(257\) | 1.72167e25i | 0.854384i | 0.904161 | + | 0.427192i | \(0.140497\pi\) | ||||
−0.904161 | + | 0.427192i | \(0.859503\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.94848e24 | 0.226373 | ||||||||
\(260\) | 3.91166e24 | + | 9.51801e24i | 0.171847 | + | 0.418144i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.63330e24 | − | 2.85268e25i | −0.228349 | − | 1.15635i | ||||
\(263\) | 5.12014e24 | 0.199410 | 0.0997049 | − | 0.995017i | \(-0.468210\pi\) | ||||
0.0997049 | + | 0.995017i | \(0.468210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.36848e25 | 0.492217 | ||||||||
\(266\) | 2.08279e24 | + | 1.05471e25i | 0.0720091 | + | 0.364651i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.18762e25 | − | 1.72100e25i | 1.33829 | − | 0.550005i | ||||
\(269\) | −1.05897e25 | −0.325451 | −0.162725 | − | 0.986671i | \(-0.552028\pi\) | ||||
−0.162725 | + | 0.986671i | \(0.552028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.39486e25i | − | 1.24959i | −0.780789 | − | 0.624795i | \(-0.785183\pi\) | ||
0.780789 | − | 0.624795i | \(-0.214817\pi\) | |||||||
\(272\) | 4.09876e24 | + | 4.14439e24i | 0.112119 | + | 0.113367i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.15777e24 | − | 1.09269e25i | −0.0546544 | − | 0.276767i | ||||
\(275\) | − | 1.24436e25i | − | 0.303355i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.71712e25i | − | 0.613863i | −0.951732 | − | 0.306931i | \(-0.900698\pi\) | ||
0.951732 | − | 0.306931i | \(-0.0993022\pi\) | |||||||
\(278\) | 3.77689e25 | − | 7.45839e24i | 0.821608 | − | 0.162246i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.10918e24 | − | 9.22572e24i | −0.123260 | − | 0.186141i | ||||
\(281\) | 6.15193e25i | 1.19562i | 0.801636 | + | 0.597812i | \(0.203963\pi\) | ||||
−0.801636 | + | 0.597812i | \(0.796037\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.30974e25 | 0.777488 | 0.388744 | − | 0.921346i | \(-0.372909\pi\) | ||||
0.388744 | + | 0.921346i | \(0.372909\pi\) | |||||||
\(284\) | −1.55059e25 | + | 6.37253e24i | −0.269559 | + | 0.110782i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.16449e25 | − | 4.27432e24i | 0.349553 | − | 0.0690277i | ||||
\(287\) | 2.79124e25 | 0.434548 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.73354e25 | 0.974577 | ||||||||
\(290\) | 1.76769e25 | − | 3.49074e24i | 0.246733 | − | 0.0487234i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.71644e25 | + | 1.11639e25i | −0.352760 | + | 0.144975i | ||||
\(293\) | 1.21717e26 | 1.52489 | 0.762447 | − | 0.647051i | \(-0.223998\pi\) | ||||
0.762447 | + | 0.647051i | \(0.223998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.02183e25i | 0.235838i | ||||||||
\(296\) | 2.87649e25 | + | 4.34390e25i | 0.323817 | + | 0.489009i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.72340e25 | − | 9.32749e24i | 0.495432 | − | 0.0978349i | ||||
\(299\) | − | 9.65402e25i | − | 0.977599i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.56952e24i | − | 0.0148190i | ||||||
\(302\) | −1.21699e25 | − | 6.16280e25i | −0.110973 | − | 0.561960i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.04785e25 | + | 7.95924e25i | −0.684711 | + | 0.677172i | ||||
\(305\) | − | 7.83573e25i | − | 0.644067i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.84747e25 | −0.372016 | −0.186008 | − | 0.982548i | \(-0.559555\pi\) | ||||
−0.186008 | + | 0.982548i | \(0.559555\pi\) | |||||||
\(308\) | −2.19429e25 | + | 9.01798e24i | −0.162747 | + | 0.0668847i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.27400e25 | + | 6.45147e25i | 0.0882817 | + | 0.447055i | ||||
\(311\) | 6.07657e25 | 0.407075 | 0.203537 | − | 0.979067i | \(-0.434756\pi\) | ||||
0.203537 | + | 0.979067i | \(0.434756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.97751e25 | −0.374373 | −0.187187 | − | 0.982324i | \(-0.559937\pi\) | ||||
−0.187187 | + | 0.982324i | \(0.559937\pi\) | |||||||
\(314\) | −1.89708e23 | − | 9.60673e23i | −0.00114901 | − | 0.00581854i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.69106e25 | − | 2.11474e26i | −0.492446 | − | 1.19824i | ||||
\(317\) | −1.16509e26 | −0.638611 | −0.319306 | − | 0.947652i | \(-0.603450\pi\) | ||||
−0.319306 | + | 0.947652i | \(0.603450\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.86316e25i | − | 0.198217i | ||||||
\(320\) | 4.54739e25 | − | 1.07256e26i | 0.225781 | − | 0.532533i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.01109e25 | + | 1.01841e26i | 0.0935285 | + | 0.473624i | ||||
\(323\) | − | 3.41090e25i | − | 0.153548i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.23268e26i | − | 0.520087i | ||||||
\(326\) | 1.96690e25 | − | 3.88411e24i | 0.0803519 | − | 0.0158674i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.62251e26 | + | 2.45022e26i | 0.621603 | + | 0.938708i | ||||
\(329\) | − | 5.51124e24i | − | 0.0204500i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.92930e26 | 1.71629 | 0.858147 | − | 0.513405i | \(-0.171616\pi\) | ||||
0.858147 | + | 0.513405i | \(0.171616\pi\) | |||||||
\(332\) | 8.09904e25 | + | 1.97069e26i | 0.273202 | + | 0.664766i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.14635e26 | − | 2.26375e25i | 0.363062 | − | 0.0716954i | ||||
\(335\) | 2.72680e26 | 0.836918 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.49650e24 | 0.00719808 | 0.00359904 | − | 0.999994i | \(-0.498854\pi\) | ||||
0.00359904 | + | 0.999994i | \(0.498854\pi\) | |||||||
\(338\) | −1.36590e26 | + | 2.69730e25i | −0.381763 | + | 0.0753883i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.33447e25 | + | 3.24709e25i | 0.0350574 | + | 0.0853032i | ||||
\(341\) | 1.40992e26 | 0.359148 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.98232e26i | 0.714440i | ||||||||
\(344\) | 1.37776e25 | − | 9.12340e24i | 0.0320118 | − | 0.0211979i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.47726e26 | + | 4.89195e25i | −0.541592 | + | 0.106950i | ||||
\(347\) | − | 4.25076e26i | − | 0.901586i | −0.892628 | − | 0.450793i | \(-0.851141\pi\) | ||
0.892628 | − | 0.450793i | \(-0.148859\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.53504e26i | 1.50459i | 0.658826 | + | 0.752295i | \(0.271053\pi\) | ||||
−0.658826 | + | 0.752295i | \(0.728947\pi\) | |||||||
\(350\) | 2.56788e25 | + | 1.30036e26i | 0.0497576 | + | 0.251970i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.06713e26 | − | 1.40200e26i | −0.377286 | − | 0.255888i | ||||
\(353\) | − | 3.73358e26i | − | 0.661441i | −0.943729 | − | 0.330720i | \(-0.892708\pi\) | ||
0.943729 | − | 0.330720i | \(-0.107292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.00968e26 | −0.168572 | ||||||||
\(356\) | −8.31945e25 | − | 2.02432e26i | −0.134856 | − | 0.328137i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.16731e26 | − | 5.91121e26i | −0.178408 | − | 0.903450i | ||||
\(359\) | −3.26249e26 | −0.484237 | −0.242119 | − | 0.970247i | \(-0.577842\pi\) | ||||
−0.242119 | + | 0.970247i | \(0.577842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.18580e25 | −0.0726090 | ||||||||
\(362\) | −4.33476e25 | − | 2.19511e26i | −0.0589557 | − | 0.298549i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.17371e26 | + | 8.93339e25i | −0.279021 | + | 0.114670i | ||||
\(365\) | −1.76883e26 | −0.220603 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.68923e26i | 1.02326i | 0.859205 | + | 0.511632i | \(0.170959\pi\) | ||||
−0.859205 | + | 0.511632i | \(0.829041\pi\) | |||||||
\(368\) | −7.77081e26 | + | 7.68525e26i | −0.889332 | + | 0.879540i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.07904e25 | + | 3.07840e26i | 0.0657229 | + | 0.332818i | ||||
\(371\) | 3.12531e26i | 0.328448i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.31159e26i | − | 0.428247i | −0.976807 | − | 0.214124i | \(-0.931310\pi\) | ||
0.976807 | − | 0.214124i | \(-0.0686895\pi\) | |||||||
\(374\) | 7.38421e25 | − | 1.45819e25i | 0.0713103 | − | 0.0140819i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.83791e25 | − | 3.20361e25i | 0.0441759 | − | 0.0292528i | ||||
\(377\) | − | 3.82692e26i | − | 0.339833i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.85931e27 | −1.56186 | −0.780928 | − | 0.624621i | \(-0.785254\pi\) | ||||
−0.780928 | + | 0.624621i | \(0.785254\pi\) | |||||||
\(380\) | −6.30540e26 | + | 2.59136e26i | −0.515211 | + | 0.211739i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.78193e27 | + | 3.51885e26i | −1.37793 | + | 0.272105i | ||||
\(383\) | −2.15760e27 | −1.62324 | −0.811621 | − | 0.584184i | \(-0.801415\pi\) | ||||
−0.811621 | + | 0.584184i | \(0.801415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.42883e26 | −0.101775 | ||||||||
\(386\) | −2.25468e27 | + | 4.45240e26i | −1.56285 | + | 0.308623i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.76099e26 | + | 2.77860e26i | −0.443892 | + | 0.182428i | ||||
\(389\) | −1.11177e27 | −0.710464 | −0.355232 | − | 0.934778i | \(-0.615598\pi\) | ||||
−0.355232 | + | 0.934778i | \(0.615598\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.29348e26i | − | 0.199434i | ||||||
\(392\) | −1.20363e27 | + | 7.97032e26i | −0.709560 | + | 0.469864i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.69632e27 | + | 5.32453e26i | −1.50682 | + | 0.297557i | ||||
\(395\) | − | 1.37703e27i | − | 0.749333i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.82207e27i | 1.45636i | 0.685388 | + | 0.728178i | \(0.259633\pi\) | ||||
−0.685388 | + | 0.728178i | \(0.740367\pi\) | |||||||
\(398\) | 3.88147e26 | + | 1.96556e27i | 0.195085 | + | 0.987901i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.92223e26 | + | 9.81298e26i | −0.473129 | + | 0.467919i | ||||
\(401\) | − | 3.27950e27i | − | 1.52332i | −0.647975 | − | 0.761662i | \(-0.724384\pi\) | ||
0.647975 | − | 0.761662i | \(-0.275616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.39669e27 | 0.615741 | ||||||||
\(404\) | 1.29312e27 | − | 5.31440e26i | 0.555437 | − | 0.228271i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.97208e25 | + | 4.03703e26i | 0.0325124 | + | 0.164641i | ||||
\(407\) | 6.72760e26 | 0.267374 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.04414e26 | −0.341407 | −0.170703 | − | 0.985322i | \(-0.554604\pi\) | ||||
−0.170703 | + | 0.985322i | \(0.554604\pi\) | |||||||
\(410\) | 3.42895e26 | + | 1.73640e27i | 0.126162 | + | 0.638881i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.07114e26 | − | 5.03959e26i | −0.0724085 | − | 0.176187i | ||||
\(413\) | −4.61743e26 | −0.157371 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.28323e27i | 0.415719i | ||||||||
\(416\) | −2.04774e27 | − | 1.38885e27i | −0.646838 | − | 0.438708i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.83161e26 | + | 1.43391e27i | 0.0850515 | + | 0.430697i | ||||
\(419\) | − | 1.74108e27i | − | 0.510003i | −0.966941 | − | 0.255001i | \(-0.917924\pi\) | ||
0.966941 | − | 0.255001i | \(-0.0820760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.10879e25i | − | 0.0225940i | −0.999936 | − | 0.0112970i | \(-0.996404\pi\) | ||
0.999936 | − | 0.0112970i | \(-0.00359603\pi\) | |||||||
\(422\) | −3.16380e27 | + | 6.24769e26i | −0.859862 | + | 0.169800i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.74348e27 | + | 1.81670e27i | −0.709513 | + | 0.469832i | ||||
\(425\) | − | 4.20532e26i | − | 0.106100i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.78951e27 | 0.429776 | ||||||||
\(428\) | −2.38205e26 | − | 5.79610e26i | −0.0558201 | − | 0.135824i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.76380e25 | − | 1.92810e25i | 0.0217871 | − | 0.00430239i | ||||
\(431\) | 5.77021e27 | 1.25655 | 0.628276 | − | 0.777991i | \(-0.283761\pi\) | ||||
0.628276 | + | 0.777991i | \(0.283761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.70274e27 | 1.80523 | 0.902617 | − | 0.430446i | \(-0.141644\pi\) | ||||
0.902617 | + | 0.430446i | \(0.141644\pi\) | |||||||
\(434\) | −1.47338e27 | + | 2.90953e26i | −0.298312 | + | 0.0589090i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.38888e27 | − | 3.37948e27i | −0.267952 | − | 0.651991i | ||||
\(437\) | 6.39550e27 | 1.20454 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.00137e27i | 0.359294i | 0.983731 | + | 0.179647i | \(0.0574956\pi\) | ||||
−0.983731 | + | 0.179647i | \(0.942504\pi\) | |||||||
\(440\) | −8.30560e26 | − | 1.25426e27i | −0.145585 | − | 0.219855i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.31494e26 | − | 1.44451e26i | 0.122258 | − | 0.0241428i | ||||
\(443\) | − | 8.50340e26i | − | 0.138789i | −0.997589 | − | 0.0693943i | \(-0.977893\pi\) | ||
0.997589 | − | 0.0693943i | \(-0.0221067\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1.31815e27i | − | 0.205204i | ||||||
\(446\) | 1.57693e26 | + | 7.98552e26i | 0.0239771 | + | 0.121419i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.44949e27 | + | 1.03852e27i | 0.355350 | + | 0.150660i | ||||
\(449\) | − | 1.28689e28i | − | 1.82371i | −0.410514 | − | 0.911854i | \(-0.634651\pi\) | ||
0.410514 | − | 0.911854i | \(-0.365349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.79477e27 | 0.513254 | ||||||||
\(452\) | 4.35347e27 | + | 1.05930e28i | 0.575284 | + | 1.39980i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.00717e27 | − | 1.01642e28i | −0.253220 | − | 1.28229i | ||||
\(455\) | −1.41543e27 | −0.174489 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.83702e27 | 0.687181 | 0.343590 | − | 0.939120i | \(-0.388357\pi\) | ||||
0.343590 | + | 0.939120i | \(0.388357\pi\) | |||||||
\(458\) | 1.59390e27 | + | 8.07143e27i | 0.183389 | + | 0.928673i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.08834e27 | + | 2.50215e27i | −0.669178 | + | 0.275015i | ||||
\(461\) | 6.86810e27 | 0.737865 | 0.368933 | − | 0.929456i | \(-0.379723\pi\) | ||||
0.368933 | + | 0.929456i | \(0.379723\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.14213e27i | 0.733208i | 0.930377 | + | 0.366604i | \(0.119480\pi\) | ||||
−0.930377 | + | 0.366604i | \(0.880520\pi\) | |||||||
\(464\) | −3.08040e27 | + | 3.04648e27i | −0.309149 | + | 0.305745i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.15998e26 | + | 4.63857e27i | 0.0878703 | + | 0.444972i | ||||
\(467\) | − | 1.84942e28i | − | 1.73463i | −0.497757 | − | 0.867317i | \(-0.665843\pi\) | ||
0.497757 | − | 0.867317i | \(-0.334157\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.22742e27i | 0.558462i | ||||||||
\(470\) | 3.42849e26 | − | 6.77037e25i | 0.0300659 | − | 0.00593724i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.68405e27 | − | 4.05330e27i | −0.225113 | − | 0.339952i | ||||
\(473\) | − | 2.13380e26i | − | 0.0175030i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.16616e27 | 0.640819 | ||||||||
\(476\) | −7.41564e26 | + | 3.04764e26i | −0.0569214 | + | 0.0233933i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.32000e27 | + | 8.53088e26i | −0.317315 | + | 0.0626615i | ||||
\(479\) | 1.64383e28 | 1.18123 | 0.590615 | − | 0.806954i | \(-0.298885\pi\) | ||||
0.590615 | + | 0.806954i | \(0.298885\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.66450e27 | 0.458399 | ||||||||
\(482\) | 1.74250e27 | − | 3.44098e26i | 0.117268 | − | 0.0231573i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.13713e28 | − | 4.67331e27i | 0.732712 | − | 0.301126i | ||||
\(485\) | −4.40247e27 | −0.277593 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.01367e28i | − | 0.612128i | −0.952011 | − | 0.306064i | \(-0.900988\pi\) | ||
0.952011 | − | 0.306064i | \(-0.0990121\pi\) | |||||||
\(488\) | 1.04022e28 | + | 1.57088e28i | 0.614776 | + | 0.928399i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.52978e27 | + | 1.68441e27i | −0.482924 | + | 0.0953650i | ||||
\(491\) | − | 2.34662e28i | − | 1.30043i | −0.759750 | − | 0.650216i | \(-0.774679\pi\) | ||
0.759750 | − | 0.650216i | \(-0.225321\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.30556e27i | − | 0.0693273i | ||||||
\(494\) | 2.80505e27 | + | 1.42046e28i | 0.145817 | + | 0.738409i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.11186e28 | − | 1.12424e28i | −0.553978 | − | 0.560146i | ||||
\(497\) | − | 2.30589e27i | − | 0.112485i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.03408e28 | 0.951286 | 0.475643 | − | 0.879638i | \(-0.342215\pi\) | ||||
0.475643 | + | 0.879638i | \(0.342215\pi\) | |||||||
\(500\) | −1.94565e28 | + | 7.99614e27i | −0.891006 | + | 0.366181i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.90970e27 | − | 1.97986e28i | −0.171694 | − | 0.869450i | ||||
\(503\) | 1.95226e27 | 0.0839601 | 0.0419801 | − | 0.999118i | \(-0.486633\pi\) | ||||
0.0419801 | + | 0.999118i | \(0.486633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.42026e27 | 0.347349 | ||||||||
\(506\) | 2.73413e27 | + | 1.38455e28i | 0.110469 | + | 0.559408i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.18356e28 | − | 2.87988e28i | −0.458797 | − | 1.11636i | ||||
\(509\) | 2.01801e28 | 0.766277 | 0.383138 | − | 0.923691i | \(-0.374843\pi\) | ||||
0.383138 | + | 0.923691i | \(0.374843\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.03962e27i | − | 0.147204i | ||||||
\(512\) | 5.12215e27 | + | 2.75391e28i | 0.182860 | + | 0.983139i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.83025e27 | − | 2.44602e28i | −0.165522 | − | 0.838198i | ||||
\(515\) | − | 3.28157e27i | − | 0.110181i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7.49269e26i | − | 0.0241539i | ||||||
\(518\) | −7.03040e27 | + | 1.38832e27i | −0.222084 | + | 0.0438558i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.22769e27 | − | 1.24250e28i | −0.249599 | − | 0.376930i | ||||
\(521\) | − | 2.27717e28i | − | 0.677016i | −0.940964 | − | 0.338508i | \(-0.890078\pi\) | ||
0.940964 | − | 0.338508i | \(-0.109922\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.85211e28 | 1.38568 | 0.692840 | − | 0.721091i | \(-0.256359\pi\) | ||||
0.692840 | + | 0.721091i | \(0.256359\pi\) | |||||||
\(524\) | 1.60067e28 | + | 3.89481e28i | 0.448046 | + | 1.09020i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.27428e27 | + | 1.43648e27i | −0.195632 | + | 0.0386322i | ||||
\(527\) | 4.76484e27 | 0.125614 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.22818e28 | 0.564502 | ||||||||
\(530\) | −1.94422e28 | + | 3.83934e27i | −0.482892 | + | 0.0953586i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.91811e27 | − | 1.44002e28i | −0.141290 | − | 0.343792i | ||||
\(533\) | 3.75918e28 | 0.879948 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.77417e27i | − | 0.0849390i | ||||||
\(536\) | −5.46659e28 | + | 3.61992e28i | −1.20639 | + | 0.798856i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.50450e28 | − | 2.97100e27i | 0.319285 | − | 0.0630505i | ||||
\(539\) | 1.86412e28i | 0.387964i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 9.83271e28i | − | 1.96835i | −0.177206 | − | 0.984174i | \(-0.556706\pi\) | ||
0.177206 | − | 0.984174i | \(-0.443294\pi\) | |||||||
\(542\) | 1.23300e28 | + | 6.24386e28i | 0.242086 | + | 1.22592i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.98592e27 | − | 4.73809e27i | −0.131958 | − | 0.0894983i | ||||
\(545\) | − | 2.20057e28i | − | 0.407730i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.53513e28 | 0.986872 | 0.493436 | − | 0.869782i | \(-0.335741\pi\) | ||||
0.493436 | + | 0.869782i | \(0.335741\pi\) | |||||||
\(548\) | 6.13118e27 | + | 1.49186e28i | 0.107238 | + | 0.260936i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.49110e27 | + | 1.76788e28i | 0.0587698 | + | 0.297608i | ||||
\(551\) | 2.53522e28 | 0.418720 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.14484e28 | 0.500017 | ||||||||
\(554\) | 7.62302e27 | + | 3.86026e28i | 0.118925 | + | 0.602233i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.15666e28 | + | 2.11925e28i | −0.774609 | + | 0.318345i | ||||
\(557\) | 1.75916e28 | 0.259314 | 0.129657 | − | 0.991559i | \(-0.458612\pi\) | ||||
0.129657 | + | 0.991559i | \(0.458612\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.11379e27i | − | 0.0300080i | ||||||
\(560\) | 1.12677e28 | + | 1.13932e28i | 0.156987 | + | 0.158734i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.72595e28 | − | 8.74015e28i | −0.231632 | − | 1.17297i | ||||
\(563\) | − | 7.72492e28i | − | 1.01755i | −0.860900 | − | 0.508775i | \(-0.830098\pi\) | ||
0.860900 | − | 0.508775i | \(-0.169902\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.89774e28i | 0.875383i | ||||||||
\(566\) | −6.12293e28 | + | 1.20912e28i | −0.762758 | + | 0.150625i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.02417e28 | − | 1.34038e28i | 0.242990 | − | 0.160906i | ||||
\(569\) | 1.70073e28i | 0.200427i | 0.994966 | + | 0.100213i | \(0.0319525\pi\) | ||||
−0.994966 | + | 0.100213i | \(0.968047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.06815e28 | −0.462081 | −0.231041 | − | 0.972944i | \(-0.574213\pi\) | ||||
−0.231041 | + | 0.972944i | \(0.574213\pi\) | |||||||
\(572\) | −2.95522e28 | + | 1.21452e28i | −0.329558 | + | 0.135440i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.96557e28 | + | 7.83097e27i | −0.426315 | + | 0.0841862i | ||||
\(575\) | 7.88504e28 | 0.832323 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.33998e28 | −0.136380 | −0.0681902 | − | 0.997672i | \(-0.521722\pi\) | ||||
−0.0681902 | + | 0.997672i | \(0.521722\pi\) | |||||||
\(578\) | −9.56647e28 | + | 1.88913e28i | −0.956113 | + | 0.188808i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.41346e28 | + | 9.91870e27i | −0.232619 | + | 0.0956007i | ||||
\(581\) | −2.93062e28 | −0.277402 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.24895e28i | 0.387938i | ||||||||
\(584\) | 3.54608e28 | − | 2.34818e28i | 0.317990 | − | 0.210570i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.72925e29 | + | 3.41482e28i | −1.49600 | + | 0.295422i | ||||
\(587\) | − | 1.35443e29i | − | 1.15095i | −0.817820 | − | 0.575474i | \(-0.804818\pi\) | ||
0.817820 | − | 0.575474i | \(-0.195182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.25268e28i | 0.758677i | ||||||||
\(590\) | −5.67235e27 | − | 2.87245e28i | −0.0456896 | − | 0.231370i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.30539e28 | − | 5.36445e28i | −0.412419 | − | 0.417011i | ||||
\(593\) | − | 1.98032e29i | − | 1.51238i | −0.654354 | − | 0.756189i | \(-0.727059\pi\) | ||
0.654354 | − | 0.756189i | \(-0.272941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.82875e27 | −0.0355965 | ||||||||
\(596\) | −6.44893e28 | + | 2.65035e28i | −0.467092 | + | 0.191963i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.70848e28 | + | 1.37156e29i | 0.189393 | + | 0.959077i | ||||
\(599\) | −9.63667e28 | −0.662133 | −0.331067 | − | 0.943607i | \(-0.607408\pi\) | ||||
−0.331067 | + | 0.943607i | \(0.607408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.25757e29 | 1.49782 | 0.748909 | − | 0.662672i | \(-0.230578\pi\) | ||||
0.748909 | + | 0.662672i | \(0.230578\pi\) | |||||||
\(602\) | 4.40336e26 | + | 2.22984e27i | 0.00287092 | + | 0.0145382i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.45801e28 | + | 8.41418e28i | 0.217740 | + | 0.529814i | ||||
\(605\) | 7.40450e28 | 0.458210 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.32358e29i | 1.38892i | 0.719532 | + | 0.694460i | \(0.244357\pi\) | ||||
−0.719532 | + | 0.694460i | \(0.755643\pi\) | |||||||
\(608\) | 9.20072e28 | − | 1.35657e29i | 0.540548 | − | 0.796993i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.19835e28 | + | 1.11324e29i | 0.124777 | + | 0.631865i | ||||
\(611\) | − | 7.42241e27i | − | 0.0414106i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.79578e28i | 0.420266i | 0.977673 | + | 0.210133i | \(0.0673897\pi\) | ||||
−0.977673 | + | 0.210133i | \(0.932610\pi\) | |||||||
\(614\) | 6.88689e28 | − | 1.35998e28i | 0.364968 | − | 0.0720718i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.86447e28 | − | 1.89682e28i | 0.146705 | − | 0.0971468i | ||||
\(617\) | − | 2.85401e29i | − | 1.43702i | −0.695518 | − | 0.718509i | \(-0.744825\pi\) | ||
0.695518 | − | 0.718509i | \(-0.255175\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.14885e29 | −0.559130 | −0.279565 | − | 0.960127i | \(-0.590190\pi\) | ||||
−0.279565 | + | 0.960127i | \(0.590190\pi\) | |||||||
\(620\) | −3.61998e28 | − | 8.80829e28i | −0.173218 | − | 0.421482i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.63309e28 | + | 1.70481e28i | −0.399363 | + | 0.0788638i | ||||
\(623\) | 3.01038e28 | 0.136929 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.46090e28 | 0.108231 | ||||||||
\(626\) | 8.49236e28 | − | 1.67702e28i | 0.367280 | − | 0.0725284i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.39043e26 | + | 1.31162e27i | 0.00225449 | + | 0.00548571i | ||||
\(629\) | 2.27360e28 | 0.0935154 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.05866e28i | 0.241028i | 0.992712 | + | 0.120514i | \(0.0384543\pi\) | ||||
−0.992712 | + | 0.120514i | \(0.961546\pi\) | |||||||
\(632\) | 1.82806e29 | + | 2.76062e29i | 0.715254 | + | 1.08014i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.65526e29 | − | 3.26871e28i | 0.626512 | − | 0.123720i | ||||
\(635\) | − | 1.87526e29i | − | 0.698131i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.84663e29i | 0.665145i | ||||||||
\(638\) | 1.08383e28 | + | 5.48846e28i | 0.0384011 | + | 0.194461i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.45144e28 | + | 1.65138e29i | −0.118334 | + | 0.566185i | ||||
\(641\) | 2.32482e29i | 0.784115i | 0.919941 | + | 0.392058i | \(0.128237\pi\) | ||||
−0.919941 | + | 0.392058i | \(0.871763\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.15244e29 | −0.376186 | −0.188093 | − | 0.982151i | \(-0.560231\pi\) | ||||
−0.188093 | + | 0.982151i | \(0.560231\pi\) | |||||||
\(644\) | −5.71438e28 | − | 1.39045e29i | −0.183513 | − | 0.446532i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.56947e27 | + | 4.84593e28i | 0.0297472 | + | 0.150639i | ||||
\(647\) | −5.52470e29 | −1.68971 | −0.844857 | − | 0.534992i | \(-0.820315\pi\) | ||||
−0.844857 | + | 0.534992i | \(0.820315\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.27753e28 | −0.185874 | ||||||||
\(650\) | 3.45835e28 | + | 1.75130e29i | 0.100758 | + | 0.510234i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.68543e28 | + | 1.10364e28i | −0.0757556 | + | 0.0311336i | ||||
\(653\) | −1.24212e28 | −0.0344805 | −0.0172402 | − | 0.999851i | \(-0.505488\pi\) | ||||
−0.0172402 | + | 0.999851i | \(0.505488\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.53613e29i | 0.681771i | ||||||||
\(656\) | −2.99256e29 | − | 3.02587e29i | −0.791685 | − | 0.800499i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.54621e27 | + | 7.82992e27i | 0.00396183 | + | 0.0200625i | ||||
\(659\) | 2.13249e29i | 0.537763i | 0.963173 | + | 0.268881i | \(0.0866539\pi\) | ||||
−0.963173 | + | 0.268881i | \(0.913346\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.64733e29i | − | 0.890963i | −0.895291 | − | 0.445481i | \(-0.853033\pi\) | ||
0.895291 | − | 0.445481i | \(-0.146967\pi\) | |||||||
\(662\) | −7.00315e29 | + | 1.38294e29i | −1.68378 | + | 0.332502i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.70353e29 | − | 2.57257e29i | −0.396813 | − | 0.599243i | ||||
\(665\) | − | 9.37678e28i | − | 0.214994i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.44795e29 | 0.543852 | ||||||||
\(668\) | −1.56514e29 | + | 6.43231e28i | −0.342294 | + | 0.140674i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.87401e29 | + | 7.65017e28i | −0.821062 | + | 0.162138i | ||||
\(671\) | 2.43289e29 | 0.507617 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.71986e29 | −1.76340 | −0.881701 | − | 0.471809i | \(-0.843601\pi\) | ||||
−0.881701 | + | 0.471809i | \(0.843601\pi\) | |||||||
\(674\) | −3.54682e27 | + | 7.00404e26i | −0.00706171 | + | 0.00139450i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.86489e29 | − | 7.66421e28i | 0.359925 | − | 0.147920i | ||||
\(677\) | −3.37073e28 | −0.0640535 | −0.0320268 | − | 0.999487i | \(-0.510196\pi\) | ||||
−0.0320268 | + | 0.999487i | \(0.510196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.00543e29i | − | 0.185233i | ||||||
\(680\) | −2.80689e28 | − | 4.23880e28i | −0.0509193 | − | 0.0768953i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00310e29 | + | 3.95560e28i | −0.352343 | + | 0.0695787i | ||||
\(683\) | 5.16670e29i | 0.894943i | 0.894298 | + | 0.447472i | \(0.147675\pi\) | ||||
−0.894298 | + | 0.447472i | \(0.852325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.71438e28i | 0.163179i | ||||||||
\(686\) | −8.36705e28 | − | 4.23703e29i | −0.138410 | − | 0.700904i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.70145e28 | + | 1.68272e28i | −0.0272986 | + | 0.0269980i | ||||
\(689\) | 4.20909e29i | 0.665100i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.54018e29 | −1.00247 | −0.501233 | − | 0.865312i | \(-0.667120\pi\) | ||||
−0.501233 | + | 0.865312i | \(0.667120\pi\) | |||||||
\(692\) | 3.38224e29 | − | 1.39002e29i | 0.510612 | − | 0.209848i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.19257e29 | + | 6.03914e29i | 0.174667 | + | 0.884505i | ||||
\(695\) | −3.35780e29 | −0.484411 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.28245e29 | 0.179513 | ||||||||
\(698\) | −2.11399e29 | − | 1.07052e30i | −0.291489 | − | 1.47609i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.29646e28 | − | 1.77540e29i | −0.0976299 | − | 0.237557i | ||||
\(701\) | −4.61494e29 | −0.608312 | −0.304156 | − | 0.952622i | \(-0.598374\pi\) | ||||
−0.304156 | + | 0.952622i | \(0.598374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.41503e29i | 0.564811i | ||||||||
\(704\) | 3.33016e29 | + | 1.41190e29i | 0.419712 | + | 0.177948i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.04747e29 | + | 5.30437e29i | 0.128143 | + | 0.648909i | ||||
\(707\) | 1.92301e29i | 0.231780i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 9.25637e29i | − | 1.08307i | −0.840679 | − | 0.541533i | \(-0.817844\pi\) | ||
0.840679 | − | 0.541533i | \(-0.182156\pi\) | |||||||
\(710\) | 1.43447e29 | − | 2.83270e28i | 0.165378 | − | 0.0326579i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.74989e29 | + | 2.64258e29i | 0.195872 | + | 0.295794i | ||||
\(713\) | 8.93416e29i | 0.985402i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.92431e29 | −0.206093 | ||||||||
\(716\) | 3.31684e29 | + | 8.07066e29i | 0.350056 | + | 0.851770i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.63509e29 | − | 9.15309e28i | 0.475063 | − | 0.0938126i | ||||
\(719\) | −8.05335e29 | −0.813435 | −0.406718 | − | 0.913554i | \(-0.633327\pi\) | ||||
−0.406718 | + | 0.913554i | \(0.633327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.49439e28 | 0.0735218 | ||||||||
\(722\) | 7.36756e28 | − | 1.45490e28i | 0.0712333 | − | 0.0140667i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.23170e29 | + | 2.99701e29i | 0.115677 | + | 0.281471i | ||||
\(725\) | 3.12568e29 | 0.289332 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.04103e29i | − | 0.633177i | −0.948563 | − | 0.316588i | \(-0.897463\pi\) | ||
0.948563 | − | 0.316588i | \(-0.102537\pi\) | |||||||
\(728\) | 2.83760e29 | − | 1.87903e29i | 0.251519 | − | 0.166553i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.51301e29 | − | 4.96254e28i | 0.216423 | − | 0.0427379i | ||||
\(731\) | − | 7.21122e27i | − | 0.00612176i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.59242e30i | − | 1.31361i | −0.754061 | − | 0.656804i | \(-0.771908\pi\) | ||
0.754061 | − | 0.656804i | \(-0.228092\pi\) | |||||||
\(734\) | −2.43781e29 | − | 1.23450e30i | −0.198240 | − | 1.00388i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.88399e29 | − | 1.30987e30i | 0.702087 | − | 1.03517i | ||||
\(737\) | 8.46636e29i | 0.659611i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.85144e29 | −0.215923 | −0.107961 | − | 0.994155i | \(-0.534432\pi\) | ||||
−0.107961 | + | 0.994155i | \(0.534432\pi\) | |||||||
\(740\) | −1.72732e29 | − | 4.20299e29i | −0.128956 | − | 0.313780i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.76822e28 | − | 4.44019e29i | −0.0636312 | − | 0.322226i | ||||
\(743\) | 3.45973e29 | 0.247548 | 0.123774 | − | 0.992310i | \(-0.460500\pi\) | ||||
0.123774 | + | 0.992310i | \(0.460500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.19927e29 | −0.292101 | ||||||||
\(746\) | 1.20964e29 | + | 6.12555e29i | 0.0829655 | + | 0.420134i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.00818e29 | + | 4.14335e28i | −0.0672311 | + | 0.0276303i | ||||
\(749\) | 8.61939e28 | 0.0566784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.33112e29i | 0.0851131i | 0.999094 | + | 0.0425565i | \(0.0135503\pi\) | ||||
−0.999094 | + | 0.0425565i | \(0.986450\pi\) | |||||||
\(752\) | −5.97451e28 | + | 5.90873e28i | −0.0376717 | + | 0.0372569i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.07366e29 | + | 5.43697e29i | 0.0658367 | + | 0.333394i | ||||
\(755\) | 5.47895e29i | 0.331325i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.79693e30i | − | 1.05688i | −0.848972 | − | 0.528438i | \(-0.822778\pi\) | ||
0.848972 | − | 0.528438i | \(-0.177222\pi\) | |||||||
\(758\) | 2.64156e30 | − | 5.21640e29i | 1.53227 | − | 0.302583i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.23118e29 | − | 5.45061e29i | 0.464429 | − | 0.307540i | ||||
\(761\) | 3.39198e30i | 1.88762i | 0.330493 | + | 0.943809i | \(0.392785\pi\) | ||||
−0.330493 | + | 0.943809i | \(0.607215\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.02564e29 | 0.272072 | ||||||||
\(764\) | 2.43290e30 | − | 9.99860e29i | 1.29910 | − | 0.533899i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.06534e30 | − | 6.05325e29i | 1.59249 | − | 0.314475i | ||||
\(767\) | −6.21864e29 | −0.318672 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.06042e30 | −0.528749 | −0.264374 | − | 0.964420i | \(-0.585165\pi\) | ||||
−0.264374 | + | 0.964420i | \(0.585165\pi\) | |||||||
\(770\) | 2.02996e29 | − | 4.00865e28i | 0.0998472 | − | 0.0197172i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.07835e30 | − | 1.26512e30i | 1.47345 | − | 0.605551i | ||||
\(773\) | 3.18532e30 | 1.50407 | 0.752034 | − | 0.659124i | \(-0.229073\pi\) | ||||
0.752034 | + | 0.659124i | \(0.229073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.14077e30i | 0.524239i | ||||||||
\(776\) | 8.82592e29 | − | 5.84443e29i | 0.400140 | − | 0.264969i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.57951e30 | − | 3.11911e29i | 0.697004 | − | 0.137640i | ||||
\(779\) | 2.49034e30i | 1.08422i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 3.13492e29i | − | 0.132859i | ||||||
\(782\) | 9.24004e28 | + | 4.67911e29i | 0.0386370 | + | 0.195656i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.48641e30 | − | 1.47004e30i | 0.605089 | − | 0.598427i | ||||
\(785\) | 8.54073e27i | 0.00343055i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.70851e29 | 0.145032 | 0.0725162 | − | 0.997367i | \(-0.476897\pi\) | ||||
0.0725162 | + | 0.997367i | \(0.476897\pi\) | |||||||
\(788\) | 3.68133e30 | − | 1.51293e30i | 1.42062 | − | 0.583840i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.86333e29 | + | 1.95637e30i | 0.145170 | + | 0.735136i | ||||
\(791\) | −1.57530e30 | −0.584129 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.41007e30 | 0.870285 | ||||||||
\(794\) | −7.91746e29 | − | 4.00937e30i | −0.282144 | − | 1.42876i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.10289e30 | − | 2.68361e30i | −0.382778 | − | 0.931390i | ||||
\(797\) | 1.07896e30 | 0.369568 | 0.184784 | − | 0.982779i | \(-0.440842\pi\) | ||||
0.184784 | + | 0.982779i | \(0.440842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.53217e28i | − | 0.00844794i | ||||||
\(800\) | 1.13436e30 | − | 1.67252e30i | 0.373514 | − | 0.550715i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.20081e29 | + | 4.65925e30i | 0.295118 | + | 1.49446i | ||||
\(803\) | − | 5.49198e29i | − | 0.173866i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 9.05399e29i | − | 0.279244i | ||||||
\(806\) | −1.98431e30 | + | 3.91849e29i | −0.604075 | + | 0.119289i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.68806e30 | + | 1.11782e30i | −0.500691 | + | 0.331552i | ||||
\(809\) | − | 2.83812e29i | − | 0.0830944i | −0.999137 | − | 0.0415472i | \(-0.986771\pi\) | ||
0.999137 | − | 0.0415472i | \(-0.0132287\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.46506e30 | −1.27382 | −0.636910 | − | 0.770938i | \(-0.719788\pi\) | ||||
−0.636910 | + | 0.770938i | \(0.719788\pi\) | |||||||
\(812\) | −2.26522e29 | − | 5.51182e29i | −0.0637928 | − | 0.155223i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.55803e29 | + | 1.88746e29i | −0.262308 | + | 0.0517991i | ||||
\(815\) | −1.74864e29 | −0.0473746 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.40032e29 | 0.0369740 | ||||||||
\(818\) | 1.28492e30 | − | 2.53738e29i | 0.334939 | − | 0.0661417i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.74313e29 | − | 2.37074e30i | −0.247544 | − | 0.602335i | ||||
\(821\) | −9.72752e29 | −0.244005 | −0.122003 | − | 0.992530i | \(-0.538932\pi\) | ||||
−0.122003 | + | 0.992530i | \(0.538932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.50469e30i | 0.612430i | 0.951962 | + | 0.306215i | \(0.0990626\pi\) | ||||
−0.951962 | + | 0.306215i | \(0.900937\pi\) | |||||||
\(824\) | 4.35639e29 | + | 6.57877e29i | 0.105170 | + | 0.158821i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.56007e29 | − | 1.29544e29i | 0.154389 | − | 0.0304879i | ||||
\(827\) | 3.09889e30i | 0.720110i | 0.932931 | + | 0.360055i | \(0.117242\pi\) | ||||
−0.932931 | + | 0.360055i | \(0.882758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.77675e30i | − | 1.53532i | −0.640857 | − | 0.767660i | \(-0.721421\pi\) | ||
0.640857 | − | 0.767660i | \(-0.278579\pi\) | |||||||
\(830\) | −3.60017e29 | − | 1.82311e30i | −0.0805383 | − | 0.407843i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.29892e30 | + | 1.39866e30i | 0.719576 | + | 0.305083i | ||||
\(833\) | 6.29981e29i | 0.135692i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.01915e30 | −0.214057 | ||||||||
\(836\) | −8.04584e29 | − | 1.95775e30i | −0.166880 | − | 0.406060i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.88470e29 | + | 2.47359e30i | 0.0988043 | + | 0.500341i | ||||
\(839\) | −4.72269e30 | −0.943385 | −0.471693 | − | 0.881763i | \(-0.656357\pi\) | ||||
−0.471693 | + | 0.881763i | \(0.656357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.16246e30 | −0.810946 | ||||||||
\(842\) | 2.27496e28 | + | 1.15203e29i | 0.00437721 | + | 0.0221660i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.31959e30 | − | 1.77524e30i | 0.810675 | − | 0.333167i | ||||
\(845\) | 1.21433e30 | 0.225083 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.69103e30i | 0.305756i | ||||||||
\(848\) | 3.38803e30 | − | 3.35072e30i | 0.605048 | − | 0.598387i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.17982e29 | + | 5.97457e29i | 0.0205550 | + | 0.104090i | ||||
\(851\) | 4.26305e30i | 0.733600i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.99566e30i | − | 0.335059i | −0.985867 | − | 0.167530i | \(-0.946421\pi\) | ||
0.985867 | − | 0.167530i | \(-0.0535790\pi\) | |||||||
\(854\) | −2.54239e30 | + | 5.02056e29i | −0.421633 | + | 0.0832616i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.01034e29 | + | 7.56632e29i | 0.0810761 | + | 0.122436i | ||||
\(857\) | 6.68470e30i | 1.06852i | 0.845320 | + | 0.534261i | \(0.179410\pi\) | ||||
−0.845320 | + | 0.534261i | \(0.820590\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.11717e30 | −1.26612 | −0.633062 | − | 0.774101i | \(-0.718202\pi\) | ||||
−0.633062 | + | 0.774101i | \(0.718202\pi\) | |||||||
\(860\) | −1.33307e29 | + | 5.47857e28i | −0.0205408 | + | 0.00844176i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.19784e30 | + | 1.61886e30i | −1.23274 | + | 0.243435i | ||||
\(863\) | −5.82775e30 | −0.865741 | −0.432870 | − | 0.901456i | \(-0.642499\pi\) | ||||
−0.432870 | + | 0.901456i | \(0.642499\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.20237e30 | 0.319317 | ||||||||
\(866\) | −1.23641e31 | + | 2.44160e30i | −1.77103 | + | 0.349733i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.01162e30 | − | 8.26726e29i | 0.281248 | − | 0.115586i | ||||
\(869\) | 4.27551e30 | 0.590581 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.38694e30i | 1.13087i | ||||||||
\(872\) | 2.92134e30 | + | 4.41163e30i | 0.389188 | + | 0.587728i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.08621e30 | + | 1.79429e30i | −1.18171 | + | 0.233358i | ||||
\(875\) | − | 2.89339e30i | − | 0.371811i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.49736e31i | − | 1.87858i | −0.343126 | − | 0.939289i | \(-0.611486\pi\) | ||
0.343126 | − | 0.939289i | \(-0.388514\pi\) | |||||||
\(878\) | −5.61495e29 | − | 2.84338e30i | −0.0696071 | − | 0.352487i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.53188e30 | + | 1.54894e30i | 0.185420 | + | 0.187485i | ||||
\(881\) | − | 1.75535e30i | − | 0.209951i | −0.994475 | − | 0.104975i | \(-0.966524\pi\) | ||
0.994475 | − | 0.104975i | \(-0.0334764\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.66963e30 | −0.195000 | −0.0974999 | − | 0.995236i | \(-0.531085\pi\) | ||||
−0.0974999 | + | 0.995236i | \(0.531085\pi\) | |||||||
\(884\) | −9.98721e29 | + | 4.10449e29i | −0.115264 | + | 0.0473708i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.38567e29 | + | 1.20809e30i | 0.0268879 | + | 0.136159i | ||||
\(887\) | −5.21045e30 | −0.580333 | −0.290167 | − | 0.956976i | \(-0.593711\pi\) | ||||
−0.290167 | + | 0.956976i | \(0.593711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.28268e30 | 0.465851 | ||||||||
\(890\) | 3.69814e29 | + | 1.87272e30i | 0.0397547 | + | 0.201316i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.48076e29 | − | 1.09028e30i | −0.0470457 | − | 0.114474i | ||||
\(893\) | 4.91712e29 | 0.0510236 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.25527e30i | 0.532664i | ||||||||
\(896\) | −3.77140e30 | − | 7.88234e29i | −0.377806 | − | 0.0789625i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.61044e30 | + | 1.82831e31i | 0.353312 | + | 1.78916i | ||||
\(899\) | 3.54156e30i | 0.342545i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.43594e30i | 0.135683i | ||||||||
\(902\) | −5.39131e30 | + | 1.06464e30i | −0.503530 | + | 0.0994341i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.15699e30 | − | 1.38283e31i | −0.835573 | − | 1.26183i | ||||
\(905\) | 1.95153e30i | 0.176021i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.99978e30 | 0.616890 | 0.308445 | − | 0.951242i | \(-0.400191\pi\) | ||||
0.308445 | + | 0.951242i | \(0.400191\pi\) | |||||||
\(908\) | 5.70324e30 | + | 1.38774e31i | 0.496845 | + | 1.20894i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.01092e30 | − | 3.97105e29i | 0.171183 | − | 0.0338042i | ||||
\(911\) | −2.09804e31 | −1.76551 | −0.882755 | − | 0.469833i | \(-0.844314\pi\) | ||||
−0.882755 | + | 0.469833i | \(0.844314\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.98426e30 | −0.327646 | ||||||||
\(914\) | −8.29276e30 | + | 1.63761e30i | −0.674162 | + | 0.133129i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.52896e30 | − | 1.10200e31i | −0.359829 | − | 0.875550i | ||||
\(917\) | −5.79198e30 | −0.454935 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.93321e31i | 1.48411i | 0.670341 | + | 0.742053i | \(0.266148\pi\) | ||||
−0.670341 | + | 0.742053i | \(0.733852\pi\) | |||||||
\(920\) | 7.94783e30 | − | 5.26297e30i | 0.603221 | − | 0.399447i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.75764e30 | + | 1.92688e30i | −0.723886 | + | 0.142949i | ||||
\(923\) | − | 3.10551e30i | − | 0.227780i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.44331e30i | 0.390279i | ||||||||
\(926\) | −2.00376e30 | − | 1.01470e31i | −0.142047 | − | 0.719317i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.52167e30 | − | 5.19242e30i | 0.244059 | − | 0.359845i | ||||
\(929\) | − | 2.03508e31i | − | 1.39449i | −0.716831 | − | 0.697247i | \(-0.754408\pi\) | ||
0.716831 | − | 0.697247i | \(-0.245592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.22334e31 | −0.819549 | ||||||||
\(932\) | −2.60275e30 | − | 6.33312e30i | −0.172411 | − | 0.419518i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.18863e30 | + | 2.62750e31i | 0.336055 | + | 1.70177i | ||||
\(935\) | −6.56483e29 | −0.0420437 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.14056e31 | −0.714252 | −0.357126 | − | 0.934056i | \(-0.616243\pi\) | ||||
−0.357126 | + | 0.934056i | \(0.616243\pi\) | |||||||
\(938\) | −1.74713e30 | − | 8.84741e30i | −0.108192 | − | 0.547881i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.68097e29 | + | 1.92376e29i | −0.0283461 | + | 0.0116495i | ||||
\(941\) | 3.14376e31 | 1.88260 | 0.941300 | − | 0.337571i | \(-0.109605\pi\) | ||||
0.941300 | + | 0.337571i | \(0.109605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.40462e31i | 1.40823i | ||||||||
\(944\) | 4.95046e30 | + | 5.00557e30i | 0.286708 | + | 0.289900i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.98649e28 | + | 3.03153e29i | 0.00339090 | + | 0.0171714i | ||||
\(947\) | − | 2.80622e31i | − | 1.57198i | −0.618240 | − | 0.785990i | \(-0.712154\pi\) | ||
0.618240 | − | 0.785990i | \(-0.287846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 5.44046e30i | − | 0.298085i | ||||||
\(950\) | −1.16018e31 | + | 2.29106e30i | −0.628678 | + | 0.124148i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.68051e29 | − | 6.41033e29i | 0.0513110 | − | 0.0339776i | ||||
\(953\) | − | 1.14106e31i | − | 0.598181i | −0.954225 | − | 0.299090i | \(-0.903317\pi\) | ||
0.954225 | − | 0.299090i | \(-0.0966832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.58420e31 | 0.812410 | ||||||||
\(956\) | 5.89817e30 | − | 2.42400e30i | 0.299164 | − | 0.122949i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.33542e31 | + | 4.61185e30i | −1.15885 | + | 0.228843i | ||||
\(959\) | −2.21855e30 | −0.108887 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.90004e30 | 0.379344 | ||||||||
\(962\) | −9.46837e30 | + | 1.86976e30i | −0.449715 | + | 0.0888070i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.37906e30 | + | 9.77733e29i | −0.110560 | + | 0.0454372i | ||||
\(965\) | 2.00449e31 | 0.921439 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.65650e31i | 1.64470i | 0.568981 | + | 0.822351i | \(0.307338\pi\) | ||||
−0.568981 | + | 0.822351i | \(0.692662\pi\) | |||||||
\(968\) | −1.48443e31 | + | 9.82973e30i | −0.660492 | + | 0.437371i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.25467e30 | − | 1.23514e30i | 0.272334 | − | 0.0537789i | ||||
\(971\) | − | 4.32015e31i | − | 1.86079i | −0.366562 | − | 0.930394i | \(-0.619465\pi\) | ||
0.366562 | − | 0.930394i | \(-0.380535\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 7.66848e30i | − | 0.323239i | ||||||
\(974\) | 2.84390e30 | + | 1.44014e31i | 0.118589 | + | 0.600530i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.91858e31 | − | 1.93994e31i | −0.782990 | − | 0.791707i | ||||
\(977\) | 1.19922e31i | 0.484180i | 0.970254 | + | 0.242090i | \(0.0778329\pi\) | ||||
−0.970254 | + | 0.242090i | \(0.922167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.09269e30 | 0.161730 | ||||||||
\(980\) | 1.16458e31 | − | 4.78615e30i | 0.455300 | − | 0.187117i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.58357e30 | + | 3.33389e31i | 0.251936 | + | 1.27579i | ||||
\(983\) | −8.52609e29 | −0.0322803 | −0.0161402 | − | 0.999870i | \(-0.505138\pi\) | ||||
−0.0161402 | + | 0.999870i | \(0.505138\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.39712e31 | 0.888403 | ||||||||
\(986\) | 3.66281e29 | + | 1.85483e30i | 0.0134310 | + | 0.0680138i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.97036e30 | − | 1.93938e31i | −0.286108 | − | 0.696170i | ||||
\(989\) | 1.35212e30 | 0.0480234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.35165e31i | 1.51315i | 0.653910 | + | 0.756573i | \(0.273128\pi\) | ||||
−0.653910 | + | 0.756573i | \(0.726872\pi\) | |||||||
\(992\) | 1.89505e31 | + | 1.28529e31i | 0.652002 | + | 0.442210i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.46928e29 | + | 3.27601e30i | 0.0217921 | + | 0.110354i | ||||
\(995\) | − | 1.74745e31i | − | 0.582455i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4.74655e31i | − | 1.54910i | −0.632514 | − | 0.774549i | \(-0.717977\pi\) | ||
0.632514 | − | 0.774549i | \(-0.282023\pi\) | |||||||
\(998\) | −2.88985e31 | + | 5.70670e30i | −0.933264 | + | 0.184295i | ||||
\(999\) | 0 | 0 |
(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 | 72.22.f.a.35.6 | yes | 84 | |
3.2 | odd | 2 | inner | 72.22.f.a.35.79 | yes | 84 | |
8.3 | odd | 2 | inner | 72.22.f.a.35.80 | yes | 84 | |
24.11 | even | 2 | inner | 72.22.f.a.35.5 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.22.f.a.35.5 | ✓ | 84 | 24.11 | even | 2 | inner | |
72.22.f.a.35.6 | yes | 84 | 1.1 | even | 1 | trivial | |
72.22.f.a.35.79 | yes | 84 | 3.2 | odd | 2 | inner | |
72.22.f.a.35.80 | yes | 84 | 8.3 | odd | 2 | inner |