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 | 35.84 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.22.f.a.35.83 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1443.33 | + | 118.056i | 0.996672 | + | 0.0815213i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.06928e6 | + | 340787.i | 0.986709 | + | 0.162500i | ||||
\(5\) | 2.14944e6 | 0.0984331 | 0.0492166 | − | 0.998788i | \(-0.484328\pi\) | ||||
0.0492166 | + | 0.998788i | \(0.484328\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.68546e8i | 0.359327i | 0.983728 | + | 0.179663i | \(0.0575009\pi\) | ||||
−0.983728 | + | 0.179663i | \(0.942499\pi\) | |||||||
\(8\) | 2.94643e9 | + | 7.36160e8i | 0.970177 | + | 0.242397i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.10237e9 | + | 2.53754e8i | 0.0981055 | + | 0.00802440i | ||||
\(11\) | − | 1.38410e11i | − | 1.60895i | −0.593986 | − | 0.804475i | \(-0.702447\pi\) | ||
0.593986 | − | 0.804475i | \(-0.297553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.50274e11i | 1.10707i | 0.832827 | + | 0.553534i | \(0.186721\pi\) | ||||
−0.832827 | + | 0.553534i | \(0.813279\pi\) | |||||||
\(14\) | −3.17034e10 | + | 3.87602e11i | −0.0292928 | + | 0.358131i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.16577e12 | + | 1.41037e12i | 0.947187 | + | 0.320680i | ||||
\(17\) | 1.14752e13i | 1.38053i | 0.723558 | + | 0.690264i | \(0.242506\pi\) | ||||
−0.723558 | + | 0.690264i | \(0.757494\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.05813e13 | 0.395936 | 0.197968 | − | 0.980208i | \(-0.436566\pi\) | ||||
0.197968 | + | 0.980208i | \(0.436566\pi\) | |||||||
\(20\) | 4.44780e12 | + | 7.32503e11i | 0.0971248 | + | 0.0159954i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.63400e13 | − | 1.99771e14i | 0.131164 | − | 1.60360i | ||||
\(23\) | −3.08144e14 | −1.55100 | −0.775499 | − | 0.631349i | \(-0.782501\pi\) | ||||
−0.775499 | + | 0.631349i | \(0.782501\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.72217e14 | −0.990311 | ||||||||
\(26\) | −6.49629e13 | + | 7.94230e14i | −0.0902496 | + | 1.10338i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.15172e13 | + | 5.55697e14i | −0.0583906 | + | 0.354551i | ||||
\(29\) | 7.39318e14 | 0.326326 | 0.163163 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163163 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.37254e14i | 0.0739026i | 0.999317 | + | 0.0369513i | \(0.0117646\pi\) | ||||
−0.999317 | + | 0.0369513i | \(0.988235\pi\) | |||||||
\(32\) | 5.84611e15 | + | 2.52742e15i | 0.917893 | + | 0.396829i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.35471e15 | + | 1.65625e16i | −0.112542 | + | 1.37593i | ||||
\(35\) | 5.77225e14i | 0.0353697i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.83826e16i | − | 0.628478i | −0.949344 | − | 0.314239i | \(-0.898251\pi\) | ||
0.949344 | − | 0.314239i | \(-0.101749\pi\) | |||||||
\(38\) | 1.52723e16 | + | 1.24918e15i | 0.394619 | + | 0.0322773i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.33318e15 | + | 1.58233e15i | 0.0954975 | + | 0.0238599i | ||||
\(41\) | 1.58363e17i | 1.84257i | 0.388886 | + | 0.921286i | \(0.372860\pi\) | ||||
−0.388886 | + | 0.921286i | \(0.627140\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.11471e17 | 1.49221 | 0.746107 | − | 0.665826i | \(-0.231921\pi\) | ||||
0.746107 | + | 0.665826i | \(0.231921\pi\) | |||||||
\(44\) | 4.71682e16 | − | 2.86408e17i | 0.261455 | − | 1.58757i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.44754e17 | − | 3.63781e16i | −1.54583 | − | 0.126439i | ||||
\(47\) | −6.25398e17 | −1.73432 | −0.867160 | − | 0.498030i | \(-0.834057\pi\) | ||||
−0.867160 | + | 0.498030i | \(0.834057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.86429e17 | 0.870884 | ||||||||
\(50\) | −6.81567e17 | − | 5.57478e16i | −0.987015 | − | 0.0807315i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.87527e17 | + | 1.13867e18i | −0.179899 | + | 1.09235i | ||||
\(53\) | 1.17467e18 | 0.922616 | 0.461308 | − | 0.887240i | \(-0.347380\pi\) | ||||
0.461308 | + | 0.887240i | \(0.347380\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.97504e17i | − | 0.158374i | ||||||
\(56\) | −1.97693e17 | + | 7.91253e17i | −0.0870998 | + | 0.348611i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.06708e18 | + | 8.72805e16i | 0.325240 | + | 0.0266026i | ||||
\(59\) | 5.10779e17i | 0.130103i | 0.997882 | + | 0.0650515i | \(0.0207212\pi\) | ||||
−0.997882 | + | 0.0650515i | \(0.979279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82423e18i | 1.58385i | 0.610620 | + | 0.791924i | \(0.290920\pi\) | ||||
−0.610620 | + | 0.791924i | \(0.709080\pi\) | |||||||
\(62\) | −3.98147e16 | + | 4.86771e17i | −0.00602464 | + | 0.0736566i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.13951e18 | + | 4.33808e18i | 0.882487 | + | 0.470336i | ||||
\(65\) | 1.18278e18i | 0.108972i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.98219e19 | −1.32850 | −0.664248 | − | 0.747512i | \(-0.731248\pi\) | ||||
−0.664248 | + | 0.747512i | \(0.731248\pi\) | |||||||
\(68\) | −3.91059e18 | + | 2.37453e19i | −0.224336 | + | 1.36218i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.81446e16 | + | 8.33129e17i | −0.00288338 | + | 0.0352519i | ||||
\(71\) | −4.98690e19 | −1.81810 | −0.909050 | − | 0.416686i | \(-0.863191\pi\) | ||||
−0.909050 | + | 0.416686i | \(0.863191\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.92144e19 | 0.795622 | 0.397811 | − | 0.917467i | \(-0.369770\pi\) | ||||
0.397811 | + | 0.917467i | \(0.369770\pi\) | |||||||
\(74\) | 2.17017e18 | − | 2.65323e19i | 0.0512344 | − | 0.626386i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.18956e19 | + | 3.60597e18i | 0.390674 | + | 0.0643397i | ||||
\(77\) | 3.71694e19 | 0.578139 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.58629e19i | − | 0.782630i | −0.920257 | − | 0.391315i | \(-0.872020\pi\) | ||
0.920257 | − | 0.391315i | \(-0.127980\pi\) | |||||||
\(80\) | 8.95410e18 | + | 3.03151e18i | 0.0932346 | + | 0.0315656i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.86957e19 | + | 2.28571e20i | −0.150209 | + | 1.83644i | ||||
\(83\) | − | 5.73700e19i | − | 0.405849i | −0.979194 | − | 0.202925i | \(-0.934955\pi\) | ||
0.979194 | − | 0.202925i | \(-0.0650447\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.46652e19i | 0.135890i | ||||||||
\(86\) | 3.05223e20 | + | 2.49653e19i | 1.48725 | + | 0.121647i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.01892e20 | − | 4.07814e20i | 0.390005 | − | 1.56097i | ||||
\(89\) | 2.99565e20i | 1.01835i | 0.860663 | + | 0.509174i | \(0.170049\pi\) | ||||
−0.860663 | + | 0.509174i | \(0.829951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.47774e20 | −0.397799 | ||||||||
\(92\) | −6.37635e20 | − | 1.05011e20i | −1.53038 | − | 0.252037i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.02659e20 | − | 7.38317e19i | −1.72855 | − | 0.141384i | ||||
\(95\) | 2.27439e19 | 0.0389732 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.11276e20 | −0.290902 | −0.145451 | − | 0.989365i | \(-0.546463\pi\) | ||||
−0.145451 | + | 0.989365i | \(0.546463\pi\) | |||||||
\(98\) | 7.02079e20 | + | 5.74256e19i | 0.867985 | + | 0.0709956i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.77148e20 | − | 1.60926e20i | −0.977148 | − | 0.160926i | ||||
\(101\) | 1.79627e21 | 1.61807 | 0.809036 | − | 0.587760i | \(-0.199990\pi\) | ||||
0.809036 | + | 0.587760i | \(0.199990\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.00878e21i | − | 0.739617i | −0.929108 | − | 0.369808i | \(-0.879423\pi\) | ||
0.929108 | − | 0.369808i | \(-0.120577\pi\) | |||||||
\(104\) | −4.05090e20 | + | 1.62134e21i | −0.268350 | + | 1.07405i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.69545e21 | + | 1.38677e20i | 0.919545 | + | 0.0752129i | ||||
\(107\) | 2.53002e21i | 1.24335i | 0.783274 | + | 0.621677i | \(0.213548\pi\) | ||||
−0.783274 | + | 0.621677i | \(0.786452\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.82636e21i | 0.738938i | 0.929243 | + | 0.369469i | \(0.120460\pi\) | ||||
−0.929243 | + | 0.369469i | \(0.879540\pi\) | |||||||
\(110\) | 3.51219e19 | − | 4.29397e20i | 0.0129109 | − | 0.157847i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.78749e20 | + | 1.11870e21i | −0.115229 | + | 0.340350i | ||||
\(113\) | − | 1.62079e21i | − | 0.449163i | −0.974455 | − | 0.224582i | \(-0.927898\pi\) | ||
0.974455 | − | 0.224582i | \(-0.0721015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.62338e20 | −0.152669 | ||||||||
\(116\) | 1.52985e21 | + | 2.51950e20i | 0.321989 | + | 0.0530280i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.03003e19 | + | 7.37225e20i | −0.0106062 | + | 0.129670i | ||||
\(119\) | −3.08161e21 | −0.496061 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.17569e22 | −1.58872 | ||||||||
\(122\) | −1.04175e21 | + | 1.27363e22i | −0.129117 | + | 1.57858i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.14932e20 | + | 6.97873e20i | −0.0120092 | + | 0.0729203i | ||||
\(125\) | −2.03994e21 | −0.195912 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.04227e22i | 0.847312i | 0.905823 | + | 0.423656i | \(0.139253\pi\) | ||||
−0.905823 | + | 0.423656i | \(0.860747\pi\) | |||||||
\(128\) | 1.12359e22 | + | 7.22222e21i | 0.841208 | + | 0.540712i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.39634e20 | + | 1.70715e21i | −0.00888355 | + | 0.108609i | ||||
\(131\) | 1.76627e22i | 1.03683i | 0.855128 | + | 0.518417i | \(0.173479\pi\) | ||||
−0.855128 | + | 0.518417i | \(0.826521\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.84156e21i | 0.142271i | ||||||||
\(134\) | −2.86097e22 | − | 2.34009e21i | −1.32407 | − | 0.108301i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.44755e21 | + | 3.38107e22i | −0.334636 | + | 1.33936i | ||||
\(137\) | 3.78672e22i | 1.38898i | 0.719501 | + | 0.694492i | \(0.244371\pi\) | ||||
−0.719501 | + | 0.694492i | \(0.755629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.81167e22 | 0.570722 | 0.285361 | − | 0.958420i | \(-0.407887\pi\) | ||||
0.285361 | + | 0.958420i | \(0.407887\pi\) | |||||||
\(140\) | −1.96711e20 | + | 1.19444e21i | −0.00574757 | + | 0.0348996i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.19776e22 | − | 5.88731e21i | −1.81205 | − | 0.148214i | ||||
\(143\) | 7.61632e22 | 1.78122 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.58912e21 | 0.0321213 | ||||||||
\(146\) | 4.21662e22 | + | 3.44892e21i | 0.792974 | + | 0.0648602i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.26457e21 | − | 3.80388e22i | 0.102128 | − | 0.620124i | ||||
\(149\) | −9.26618e22 | −1.40749 | −0.703745 | − | 0.710453i | \(-0.748490\pi\) | ||||
−0.703745 | + | 0.710453i | \(0.748490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.73770e22i | 0.625618i | 0.949816 | + | 0.312809i | \(0.101270\pi\) | ||||
−0.949816 | + | 0.312809i | \(0.898730\pi\) | |||||||
\(152\) | 3.11770e22 | + | 7.78951e21i | 0.384128 | + | 0.0959738i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.36478e22 | + | 4.38805e21i | 0.576215 | + | 0.0471307i | ||||
\(155\) | 7.24909e20i | 0.00727446i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.10800e23i | − | 0.971838i | −0.874004 | − | 0.485919i | \(-0.838485\pi\) | ||
0.874004 | − | 0.485919i | \(-0.161515\pi\) | |||||||
\(158\) | 7.77548e21 | − | 9.50622e22i | 0.0638011 | − | 0.780025i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.25659e22 | + | 5.43256e21i | 0.0903510 | + | 0.0390611i | ||||
\(161\) | − | 8.27509e22i | − | 0.557315i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.95808e23 | −1.15840 | −0.579202 | − | 0.815184i | \(-0.696636\pi\) | ||||
−0.579202 | + | 0.815184i | \(0.696636\pi\) | |||||||
\(164\) | −5.39682e22 | + | 3.27698e23i | −0.299418 | + | 1.81808i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.77285e21 | − | 8.28041e22i | 0.0330854 | − | 0.404499i | ||||
\(167\) | −2.40871e23 | −1.10474 | −0.552372 | − | 0.833598i | \(-0.686277\pi\) | ||||
−0.552372 | + | 0.833598i | \(0.686277\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.57375e22 | −0.225599 | ||||||||
\(170\) | −2.91187e21 | + | 3.56002e22i | −0.0110779 | + | 0.135437i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.37591e23 | + | 7.20665e22i | 1.47238 | + | 0.242485i | ||||
\(173\) | 3.82081e23 | 1.20968 | 0.604841 | − | 0.796346i | \(-0.293237\pi\) | ||||
0.604841 | + | 0.796346i | \(0.293237\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.26812e23i | − | 0.355845i | ||||||
\(176\) | 1.95208e23 | − | 5.76583e23i | 0.515959 | − | 1.52398i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.53653e22 | + | 4.32373e23i | −0.0830171 | + | 1.01496i | ||||
\(179\) | − | 2.45839e23i | − | 0.544118i | −0.962281 | − | 0.272059i | \(-0.912295\pi\) | ||
0.962281 | − | 0.272059i | \(-0.0877046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.87717e23i | 1.94539i | 0.232081 | + | 0.972696i | \(0.425446\pi\) | ||||
−0.232081 | + | 0.972696i | \(0.574554\pi\) | |||||||
\(182\) | −2.13288e23 | − | 1.74456e22i | −0.396475 | − | 0.0324291i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.07923e23 | − | 2.26843e23i | −1.50474 | − | 0.375957i | ||||
\(185\) | − | 3.95125e22i | − | 0.0618630i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.58827e24 | 2.22120 | ||||||||
\(188\) | −1.29412e24 | − | 2.13128e23i | −1.71127 | − | 0.281827i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.28270e22 | + | 2.68504e21i | 0.0388435 | + | 0.00317715i | ||||
\(191\) | −1.08437e24 | −1.21430 | −0.607150 | − | 0.794587i | \(-0.707687\pi\) | ||||
−0.607150 | + | 0.794587i | \(0.707687\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.80642e23 | 0.783611 | 0.391805 | − | 0.920048i | \(-0.371851\pi\) | ||||
0.391805 | + | 0.920048i | \(0.371851\pi\) | |||||||
\(194\) | −3.04942e23 | − | 2.49423e22i | −0.289934 | − | 0.0237148i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00656e24 | + | 1.65769e23i | 0.859309 | + | 0.141519i | ||||
\(197\) | −6.60285e23 | −0.534362 | −0.267181 | − | 0.963646i | \(-0.586092\pi\) | ||||
−0.267181 | + | 0.963646i | \(0.586092\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.95218e22i | 0.0724371i | 0.999344 | + | 0.0362185i | \(0.0115312\pi\) | ||||
−0.999344 | + | 0.0362185i | \(0.988469\pi\) | |||||||
\(200\) | −1.39135e24 | − | 3.47627e23i | −0.960777 | − | 0.240048i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.59262e24 | + | 2.12060e23i | 1.61269 | + | 0.131907i | ||||
\(203\) | 1.98541e23i | 0.117258i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.40393e23i | 0.181370i | ||||||||
\(206\) | 1.19092e23 | − | 1.45601e24i | 0.0602945 | − | 0.737155i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.76089e23 | + | 2.29232e24i | −0.355015 | + | 1.04860i | ||||
\(209\) | − | 1.46455e24i | − | 0.637042i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.78924e24 | −0.704212 | −0.352106 | − | 0.935960i | \(-0.614534\pi\) | ||||
−0.352106 | + | 0.935960i | \(0.614534\pi\) | |||||||
\(212\) | 2.43073e24 | + | 4.00314e23i | 0.910353 | + | 0.149925i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.98683e23 | + | 3.65167e24i | −0.101360 | + | 1.23922i | ||||
\(215\) | 4.54544e23 | 0.146883 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.05684e22 | −0.0265552 | ||||||||
\(218\) | −2.15612e23 | + | 2.63605e24i | −0.0602392 | + | 0.736478i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.01385e23 | − | 6.15618e23i | 0.0257358 | − | 0.156269i | ||||
\(221\) | −6.31449e24 | −1.52834 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.66575e24i | 1.68793i | 0.536400 | + | 0.843964i | \(0.319784\pi\) | ||||
−0.536400 | + | 0.843964i | \(0.680216\pi\) | |||||||
\(224\) | −6.78730e23 | + | 1.56995e24i | −0.142591 | + | 0.329824i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.91344e23 | − | 2.33935e24i | 0.0366164 | − | 0.447668i | ||||
\(227\) | − | 3.63328e24i | − | 0.663785i | −0.943317 | − | 0.331892i | \(-0.892313\pi\) | ||
0.943317 | − | 0.331892i | \(-0.107687\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.71331e24i | − | 0.618712i | −0.950946 | − | 0.309356i | \(-0.899887\pi\) | ||
0.950946 | − | 0.309356i | \(-0.100113\pi\) | |||||||
\(230\) | −9.55975e23 | − | 7.81926e22i | −0.152161 | − | 0.0124458i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.17835e24 | + | 5.44256e23i | 0.316594 | + | 0.0791005i | ||||
\(233\) | 8.67117e24i | 1.20459i | 0.798272 | + | 0.602297i | \(0.205748\pi\) | ||||
−0.798272 | + | 0.602297i | \(0.794252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.34426e24 | −0.170714 | ||||||||
\(236\) | −1.74067e23 | + | 1.05694e24i | −0.0211417 | + | 0.128374i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.44780e24 | − | 3.63801e23i | −0.494410 | − | 0.0404395i | ||||
\(239\) | 9.36551e23 | 0.0996215 | 0.0498108 | − | 0.998759i | \(-0.484138\pi\) | ||||
0.0498108 | + | 0.998759i | \(0.484138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.99621e24 | 0.486924 | 0.243462 | − | 0.969910i | \(-0.421717\pi\) | ||||
0.243462 | + | 0.969910i | \(0.421717\pi\) | |||||||
\(242\) | −1.69692e25 | − | 1.38797e24i | −1.58343 | − | 0.129515i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.00719e24 | + | 1.82598e25i | −0.257375 | + | 1.56280i | ||||
\(245\) | 1.04555e24 | 0.0857238 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.82261e24i | 0.438328i | ||||||||
\(248\) | −2.48273e23 | + | 9.93696e23i | −0.0179138 | + | 0.0716986i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.94432e24 | − | 2.40826e23i | −0.195260 | − | 0.0159710i | ||||
\(251\) | 7.15897e24i | 0.455278i | 0.973746 | + | 0.227639i | \(0.0731006\pi\) | ||||
−0.973746 | + | 0.227639i | \(0.926899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.26500e25i | 2.49548i | ||||||||
\(254\) | −1.23046e24 | + | 1.50435e25i | −0.0690740 | + | 0.844491i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.53645e25 | + | 1.17505e25i | 0.794328 | + | 0.607489i | ||||
\(257\) | 1.68026e25i | 0.833833i | 0.908945 | + | 0.416916i | \(0.136889\pi\) | ||||
−0.908945 | + | 0.416916i | \(0.863111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.93659e24 | 0.225829 | ||||||||
\(260\) | −4.03078e23 | + | 2.44751e24i | −0.0177080 | + | 0.107524i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.08518e24 | + | 2.54933e25i | −0.0845242 | + | 1.03338i | ||||
\(263\) | −3.23185e25 | −1.25868 | −0.629341 | − | 0.777129i | \(-0.716675\pi\) | ||||
−0.629341 | + | 0.777129i | \(0.716675\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.52490e24 | 0.0908159 | ||||||||
\(266\) | −3.35462e23 | + | 4.10133e24i | −0.0115981 | + | 0.141797i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.10170e25 | − | 6.75505e24i | −1.31084 | − | 0.215881i | ||||
\(269\) | −1.97262e25 | −0.606238 | −0.303119 | − | 0.952953i | \(-0.598028\pi\) | ||||
−0.303119 | + | 0.952953i | \(0.598028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.71618e25i | 1.05662i | 0.849051 | + | 0.528311i | \(0.177174\pi\) | ||||
−0.849051 | + | 0.528311i | \(0.822826\pi\) | |||||||
\(272\) | −1.61842e25 | + | 4.78029e25i | −0.442708 | + | 1.30762i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.47043e24 | + | 5.46550e25i | −0.113232 | + | 1.38436i | ||||
\(275\) | 6.53593e25i | 1.59336i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00635e25i | 0.227358i | 0.993518 | + | 0.113679i | \(0.0362635\pi\) | ||||
−0.993518 | + | 0.113679i | \(0.963736\pi\) | |||||||
\(278\) | 2.61485e25 | + | 2.13878e24i | 0.568822 | + | 0.0465260i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.24930e23 | + | 1.70075e24i | −0.00857350 | + | 0.0343148i | ||||
\(281\) | − | 6.50611e25i | − | 1.26446i | −0.774781 | − | 0.632230i | \(-0.782140\pi\) | ||
0.774781 | − | 0.632230i | \(-0.217860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.72762e25 | 0.311667 | 0.155833 | − | 0.987783i | \(-0.450194\pi\) | ||||
0.155833 | + | 0.987783i | \(0.450194\pi\) | |||||||
\(284\) | −1.03193e26 | − | 1.69947e25i | −1.79394 | − | 0.295441i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.09929e26 | + | 8.99149e24i | 1.77529 | + | 0.145207i | ||||
\(287\) | −4.25279e25 | −0.662086 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.25874e25 | −0.905857 | ||||||||
\(290\) | 2.29364e24 | + | 1.87605e23i | 0.0320144 | + | 0.00261857i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.04527e25 | + | 9.95590e24i | 0.785047 | + | 0.129289i | ||||
\(293\) | 2.41738e25 | 0.302855 | 0.151427 | − | 0.988468i | \(-0.451613\pi\) | ||||
0.151427 | + | 0.988468i | \(0.451613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.09789e24i | 0.0128064i | ||||||||
\(296\) | 1.35326e25 | − | 5.41632e25i | 0.152341 | − | 0.609735i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.33742e26 | − | 1.09392e25i | −1.40280 | − | 0.114740i | ||||
\(299\) | − | 1.69564e26i | − | 1.71706i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.67896e25i | 0.536193i | ||||||||
\(302\) | −5.59311e24 | + | 6.83808e25i | −0.0510012 | + | 0.623536i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.40792e25 | + | 1.49235e25i | 0.375026 | + | 0.126969i | ||||
\(305\) | 1.89672e25i | 0.155903i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.15414e26 | 0.885737 | 0.442869 | − | 0.896586i | \(-0.353961\pi\) | ||||
0.442869 | + | 0.896586i | \(0.353961\pi\) | |||||||
\(308\) | 7.69137e25 | + | 1.26668e25i | 0.570455 | + | 0.0939477i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.55795e22 | + | 1.04629e24i | −0.000593024 | + | 0.00725025i | ||||
\(311\) | 4.72558e25 | 0.316571 | 0.158286 | − | 0.987393i | \(-0.449403\pi\) | ||||
0.158286 | + | 0.987393i | \(0.449403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.01420e26 | 1.26150 | 0.630750 | − | 0.775986i | \(-0.282747\pi\) | ||||
0.630750 | + | 0.775986i | \(0.282747\pi\) | |||||||
\(314\) | 1.30806e25 | − | 1.59922e26i | 0.0792255 | − | 0.968603i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.24452e25 | − | 1.36289e26i | 0.127177 | − | 0.772228i | ||||
\(317\) | −1.74834e26 | −0.958304 | −0.479152 | − | 0.877732i | \(-0.659056\pi\) | ||||
−0.479152 | + | 0.877732i | \(0.659056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.02329e26i | − | 0.525043i | ||||||
\(320\) | 1.74954e25 | + | 9.32447e24i | 0.0868660 | + | 0.0462966i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.76920e24 | − | 1.19437e26i | 0.0454331 | − | 0.555460i | ||||
\(323\) | 1.21422e26i | 0.546601i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.59849e26i | − | 1.09634i | ||||||
\(326\) | −2.82616e26 | − | 2.31162e25i | −1.15455 | − | 0.0944346i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.16581e26 | + | 4.66607e26i | −0.446634 | + | 1.78762i | ||||
\(329\) | − | 1.67948e26i | − | 0.623188i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.78837e25 | −0.340813 | −0.170407 | − | 0.985374i | \(-0.554508\pi\) | ||||
−0.170407 | + | 0.985374i | \(0.554508\pi\) | |||||||
\(332\) | 1.95510e25 | − | 1.18714e26i | 0.0659505 | − | 0.400455i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.47658e26 | − | 2.84362e25i | −1.10107 | − | 0.0900602i | ||||
\(335\) | −4.26061e25 | −0.130768 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.99180e26 | 0.862619 | 0.431309 | − | 0.902204i | \(-0.358052\pi\) | ||||
0.431309 | + | 0.902204i | \(0.358052\pi\) | |||||||
\(338\) | −8.04478e25 | − | 6.58012e24i | −0.224848 | − | 0.0183911i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.40559e24 | + | 5.10392e25i | −0.0220821 | + | 0.134083i | ||||
\(341\) | 4.66792e25 | 0.118906 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.80624e26i | 0.672259i | ||||||||
\(344\) | 6.23083e26 | + | 1.55676e26i | 1.44771 | + | 0.361708i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.51470e26 | + | 4.51067e25i | 1.20566 | + | 0.0986149i | ||||
\(347\) | − | 7.05424e26i | − | 1.49620i | −0.663584 | − | 0.748102i | \(-0.730965\pi\) | ||
0.663584 | − | 0.748102i | \(-0.269035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.64936e26i | 0.329343i | 0.986348 | + | 0.164671i | \(0.0526564\pi\) | ||||
−0.986348 | + | 0.164671i | \(0.947344\pi\) | |||||||
\(350\) | 1.49709e25 | − | 1.83032e26i | 0.0290090 | − | 0.354661i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.49820e26 | − | 8.09157e26i | 0.638478 | − | 1.47684i | ||||
\(353\) | − | 3.12318e26i | − | 0.553302i | −0.960970 | − | 0.276651i | \(-0.910775\pi\) | ||
0.960970 | − | 0.276651i | \(-0.0892246\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.07191e26 | −0.178961 | ||||||||
\(356\) | −1.02088e26 | + | 6.19884e26i | −0.165482 | + | 1.00481i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.90226e25 | − | 3.54827e26i | 0.0443573 | − | 0.542307i | ||||
\(359\) | 5.50617e26 | 0.817256 | 0.408628 | − | 0.912701i | \(-0.366007\pi\) | ||||
0.408628 | + | 0.912701i | \(0.366007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.02246e26 | −0.843234 | ||||||||
\(362\) | −1.16605e26 | + | 1.42561e27i | −0.158591 | + | 1.93892i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.05786e26 | − | 5.03596e25i | −0.392512 | − | 0.0646424i | ||||
\(365\) | 6.27947e25 | 0.0783156 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.48708e26i | − | 0.410647i | −0.978694 | − | 0.205323i | \(-0.934175\pi\) | ||
0.978694 | − | 0.205323i | \(-0.0658246\pi\) | |||||||
\(368\) | −1.28366e27 | − | 4.34596e26i | −1.46909 | − | 0.497374i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.66467e24 | − | 5.70297e25i | 0.00504316 | − | 0.0616571i | ||||
\(371\) | 3.15454e26i | 0.331521i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.09781e27i | − | 1.09040i | −0.838307 | − | 0.545199i | \(-0.816454\pi\) | ||
0.838307 | − | 0.545199i | \(-0.183546\pi\) | |||||||
\(374\) | 2.29241e27 | + | 1.87504e26i | 2.21381 | + | 0.181075i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.84269e27 | − | 4.60393e26i | −1.68260 | − | 0.420394i | ||||
\(377\) | 4.06828e26i | 0.361265i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.37440e26 | 0.619462 | 0.309731 | − | 0.950824i | \(-0.399761\pi\) | ||||
0.309731 | + | 0.950824i | \(0.399761\pi\) | |||||||
\(380\) | 4.70634e25 | + | 7.75082e24i | 0.0384552 | + | 0.00633315i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.56510e27 | − | 1.28016e26i | −1.21026 | − | 0.0989914i | ||||
\(383\) | 3.67081e26 | 0.276169 | 0.138085 | − | 0.990420i | \(-0.455905\pi\) | ||||
0.138085 | + | 0.990420i | \(0.455905\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.98935e25 | 0.0569081 | ||||||||
\(386\) | 1.12673e27 | + | 9.21592e25i | 0.781003 | + | 0.0638810i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.37189e26 | − | 7.20002e25i | −0.287036 | − | 0.0472716i | ||||
\(389\) | 2.61039e27 | 1.66815 | 0.834074 | − | 0.551652i | \(-0.186002\pi\) | ||||
0.834074 | + | 0.551652i | \(0.186002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.53600e27i | − | 2.14119i | ||||||
\(392\) | 1.43323e27 | + | 3.58089e26i | 0.844912 | + | 0.211100i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.53012e26 | − | 7.79502e25i | −0.532584 | − | 0.0435619i | ||||
\(395\) | − | 1.41569e26i | − | 0.0770367i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.25300e26i | 0.116268i | 0.998309 | + | 0.0581340i | \(0.0185151\pi\) | ||||
−0.998309 | + | 0.0581340i | \(0.981485\pi\) | |||||||
\(398\) | −1.17491e25 | + | 1.43643e26i | −0.00590517 | + | 0.0721960i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.96715e27 | − | 6.65999e26i | −0.938010 | − | 0.317573i | ||||
\(401\) | − | 1.39358e27i | − | 0.647315i | −0.946174 | − | 0.323657i | \(-0.895087\pi\) | ||
0.946174 | − | 0.323657i | \(-0.104913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.85582e26 | −0.0818152 | ||||||||
\(404\) | 3.71699e27 | + | 6.12147e26i | 1.59656 | + | 0.262937i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.34389e25 | + | 2.86561e26i | −0.00955902 | + | 0.116868i | ||||
\(407\) | −2.54433e27 | −1.01119 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.49403e27 | 0.563980 | 0.281990 | − | 0.959417i | \(-0.409005\pi\) | ||||
0.281990 | + | 0.959417i | \(0.409005\pi\) | |||||||
\(410\) | −4.01853e25 | + | 4.91302e26i | −0.0147855 | + | 0.180766i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.43780e26 | − | 2.08745e27i | 0.120188 | − | 0.729786i | ||||
\(413\) | −1.37168e26 | −0.0467495 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.23314e26i | − | 0.0399490i | ||||||
\(416\) | −1.39078e27 | + | 3.21696e27i | −0.439317 | + | 1.01617i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.72898e26 | − | 2.11384e27i | 0.0519325 | − | 0.634922i | ||||
\(419\) | − | 3.82004e27i | − | 1.11897i | −0.828839 | − | 0.559487i | \(-0.810998\pi\) | ||
0.828839 | − | 0.559487i | \(-0.189002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.81115e27i | − | 0.783289i | −0.920117 | − | 0.391644i | \(-0.871906\pi\) | ||
0.920117 | − | 0.391644i | \(-0.128094\pi\) | |||||||
\(422\) | −2.58248e27 | − | 2.11230e26i | −0.701868 | − | 0.0574083i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.46109e27 | + | 8.64748e26i | 0.895101 | + | 0.223639i | ||||
\(425\) | − | 5.41877e27i | − | 1.36715i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.36971e27 | −0.569119 | ||||||||
\(428\) | −8.62199e26 | + | 5.23532e27i | −0.202045 | + | 1.22683i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.56059e26 | + | 5.36615e25i | 0.146394 | + | 0.0119741i | ||||
\(431\) | 6.00753e27 | 1.30823 | 0.654116 | − | 0.756395i | \(-0.273041\pi\) | ||||
0.654116 | + | 0.756395i | \(0.273041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.45812e27 | 0.302461 | 0.151231 | − | 0.988498i | \(-0.451676\pi\) | ||||
0.151231 | + | 0.988498i | \(0.451676\pi\) | |||||||
\(434\) | −1.30720e26 | − | 1.06921e25i | −0.0264668 | − | 0.00216481i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.22400e26 | + | 3.77924e27i | −0.120077 | + | 0.729116i | ||||
\(437\) | −3.26055e27 | −0.614096 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.43022e27i | 0.795331i | 0.917531 | + | 0.397665i | \(0.130179\pi\) | ||||
−0.917531 | + | 0.397665i | \(0.869821\pi\) | |||||||
\(440\) | 2.19010e26 | − | 8.76573e26i | 0.0383894 | − | 0.153651i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.11392e27 | − | 7.45460e26i | −1.52325 | − | 0.124592i | ||||
\(443\) | − | 1.00665e28i | − | 1.64301i | −0.570200 | − | 0.821506i | \(-0.693134\pi\) | ||
0.570200 | − | 0.821506i | \(-0.306866\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.43899e26i | 0.100239i | ||||||||
\(446\) | −9.04985e26 | + | 1.10642e28i | −0.137602 | + | 1.68231i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.16498e27 | + | 2.18584e27i | −0.169004 | + | 0.317102i | ||||
\(449\) | 1.35340e27i | 0.191796i | 0.995391 | + | 0.0958978i | \(0.0305722\pi\) | ||||
−0.995391 | + | 0.0958978i | \(0.969428\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.19190e28 | 2.96461 | ||||||||
\(452\) | 5.52346e26 | − | 3.35387e27i | 0.0729890 | − | 0.443193i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.28929e26 | − | 5.24404e27i | 0.0541126 | − | 0.661575i | ||||
\(455\) | −3.17632e26 | −0.0391566 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.49017e27 | 0.999531 | 0.499766 | − | 0.866161i | \(-0.333419\pi\) | ||||
0.499766 | + | 0.866161i | \(0.333419\pi\) | |||||||
\(458\) | 4.38376e26 | − | 5.35955e27i | 0.0504382 | − | 0.616652i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.37056e27 | − | 2.25716e26i | −0.150640 | − | 0.0248088i | ||||
\(461\) | −1.27978e28 | −1.37492 | −0.687458 | − | 0.726224i | \(-0.741273\pi\) | ||||
−0.687458 | + | 0.726224i | \(0.741273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.04347e27i | 0.107122i | 0.998565 | + | 0.0535609i | \(0.0170571\pi\) | ||||
−0.998565 | + | 0.0535609i | \(0.982943\pi\) | |||||||
\(464\) | 3.07983e27 | + | 1.04271e27i | 0.309092 | + | 0.104646i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.02368e27 | + | 1.25154e28i | −0.0982001 | + | 1.20058i | ||||
\(467\) | − | 1.66252e27i | − | 0.155933i | −0.996956 | − | 0.0779666i | \(-0.975157\pi\) | ||
0.996956 | − | 0.0779666i | \(-0.0248427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.32310e27i | − | 0.477364i | ||||||
\(470\) | −1.94022e27 | − | 1.58697e26i | −0.170146 | − | 0.0139169i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.76015e26 | + | 1.50497e27i | −0.0315366 | + | 0.126223i | ||||
\(473\) | − | 2.92695e28i | − | 2.40090i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.99666e27 | −0.392100 | ||||||||
\(476\) | −6.37671e27 | − | 1.05017e27i | −0.489467 | − | 0.0806099i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.35176e27 | + | 1.10565e26i | 0.0992900 | + | 0.00812128i | ||||
\(479\) | −8.99237e27 | −0.646177 | −0.323088 | − | 0.946369i | \(-0.604721\pi\) | ||||
−0.323088 | + | 0.946369i | \(0.604721\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.01155e28 | 0.695767 | ||||||||
\(482\) | 7.21120e27 | + | 5.89830e26i | 0.485304 | + | 0.0396947i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.43284e28 | − | 4.00662e27i | −1.56761 | − | 0.258167i | ||||
\(485\) | −4.54126e26 | −0.0286344 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.48673e27i | − | 0.452104i | −0.974115 | − | 0.226052i | \(-0.927418\pi\) | ||
0.974115 | − | 0.226052i | \(-0.0725819\pi\) | |||||||
\(488\) | −6.49604e27 | + | 2.60000e28i | −0.383920 | + | 1.53661i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.50908e27 | + | 1.23433e26i | 0.0854385 | + | 0.00698832i | ||||
\(491\) | − | 1.74661e28i | − | 0.967922i | −0.875090 | − | 0.483961i | \(-0.839198\pi\) | ||
0.875090 | − | 0.483961i | \(-0.160802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.48379e27i | 0.450503i | ||||||||
\(494\) | −6.87391e26 | + | 8.40397e27i | −0.0357331 | + | 0.436869i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.75652e26 | + | 1.40493e27i | −0.0236991 | + | 0.0699996i | ||||
\(497\) | − | 1.33921e28i | − | 0.653293i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.03858e28 | 1.42107 | 0.710533 | − | 0.703663i | \(-0.248454\pi\) | ||||
0.710533 | + | 0.703663i | \(0.248454\pi\) | |||||||
\(500\) | −4.22120e27 | − | 6.95185e26i | −0.193309 | − | 0.0318358i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.45156e26 | + | 1.03328e28i | −0.0371149 | + | 0.453763i | ||||
\(503\) | −3.68322e28 | −1.58403 | −0.792015 | − | 0.610501i | \(-0.790968\pi\) | ||||
−0.792015 | + | 0.610501i | \(0.790968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.86099e27 | 0.159272 | ||||||||
\(506\) | −5.03507e27 | + | 6.15582e28i | −0.203435 | + | 2.48717i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.55194e27 | + | 2.15676e28i | −0.137688 | + | 0.836050i | ||||
\(509\) | 3.74929e28 | 1.42368 | 0.711840 | − | 0.702342i | \(-0.247862\pi\) | ||||
0.711840 | + | 0.702342i | \(0.247862\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.84542e27i | 0.285889i | ||||||||
\(512\) | 2.07890e28 | + | 1.87738e28i | 0.742161 | + | 0.670222i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.98364e27 | + | 2.42518e28i | −0.0679752 | + | 0.831058i | ||||
\(515\) | − | 2.16832e27i | − | 0.0728028i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.65611e28i | 2.79044i | ||||||||
\(518\) | 7.12515e27 | + | 5.82792e26i | 0.225077 | + | 0.0184099i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.70718e26 | + | 3.48499e27i | −0.0264145 | + | 0.105722i | ||||
\(521\) | 9.22865e27i | 0.274373i | 0.990545 | + | 0.137187i | \(0.0438060\pi\) | ||||
−0.990545 | + | 0.137187i | \(0.956194\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.80552e28 | −1.08679 | −0.543395 | − | 0.839477i | \(-0.682862\pi\) | ||||
−0.543395 | + | 0.839477i | \(0.682862\pi\) | |||||||
\(524\) | −6.01924e27 | + | 3.65491e28i | −0.168486 | + | 1.02305i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.66464e28 | − | 3.81538e27i | −1.25449 | − | 0.102609i | ||||
\(527\) | −3.87005e27 | −0.102025 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.54810e28 | 1.40559 | ||||||||
\(530\) | 3.64427e27 | + | 2.98078e26i | 0.0905136 | + | 0.00740344i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.68369e26 | + | 5.87999e27i | −0.0231190 | + | 0.140380i | ||||
\(533\) | −8.71434e28 | −2.03985 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.43814e27i | 0.122387i | ||||||||
\(536\) | −5.84038e28 | − | 1.45921e28i | −1.28888 | − | 0.322023i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.84714e28 | − | 2.32878e27i | −0.604221 | − | 0.0494214i | ||||
\(539\) | − | 6.73264e28i | − | 1.40121i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 8.54488e28i | − | 1.71055i | −0.518177 | − | 0.855273i | \(-0.673389\pi\) | ||
0.518177 | − | 0.855273i | \(-0.326611\pi\) | |||||||
\(542\) | −4.38716e27 | + | 5.36369e28i | −0.0861372 | + | 1.05310i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.90026e28 | + | 6.70850e28i | −0.547833 | + | 1.26718i | ||||
\(545\) | 3.92566e27i | 0.0727359i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.54490e28 | 1.16691 | 0.583453 | − | 0.812147i | \(-0.301701\pi\) | ||||
0.583453 | + | 0.812147i | \(0.301701\pi\) | |||||||
\(548\) | −1.29047e28 | + | 7.83577e28i | −0.225710 | + | 1.37052i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.71603e27 | + | 9.43354e28i | −0.129893 | + | 1.58806i | ||||
\(551\) | 7.82293e27 | 0.129204 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.76872e28 | 0.281220 | ||||||||
\(554\) | −1.18805e27 | + | 1.45250e28i | −0.0185345 | + | 0.226601i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.74886e28 | + | 6.17395e27i | 0.563136 | + | 0.0927423i | ||||
\(557\) | −2.43076e28 | −0.358312 | −0.179156 | − | 0.983821i | \(-0.557337\pi\) | ||||
−0.179156 | + | 0.983821i | \(0.557337\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.16367e29i | 1.65198i | ||||||||
\(560\) | −8.14100e26 | + | 2.40459e27i | −0.0113424 | + | 0.0335017i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.68082e27 | − | 9.39049e28i | 0.103080 | − | 1.26025i | ||||
\(563\) | − | 1.33175e28i | − | 0.175422i | −0.996146 | − | 0.0877111i | \(-0.972045\pi\) | ||
0.996146 | − | 0.0877111i | \(-0.0279552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.48381e27i | − | 0.0442125i | ||||||
\(566\) | 2.49353e28 | + | 2.03955e27i | 0.310630 | + | 0.0254075i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.46935e29 | − | 3.67115e28i | −1.76388 | − | 0.440702i | ||||
\(569\) | − | 1.02329e29i | − | 1.20593i | −0.797768 | − | 0.602964i | \(-0.793986\pi\) | ||
0.797768 | − | 0.602964i | \(-0.206014\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.10541e28 | 0.579898 | 0.289949 | − | 0.957042i | \(-0.406362\pi\) | ||||
0.289949 | + | 0.957042i | \(0.406362\pi\) | |||||||
\(572\) | 1.57603e29 | + | 2.59555e28i | 1.75754 | + | 0.289448i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.13820e28 | − | 5.02066e27i | −0.659882 | − | 0.0539741i | ||||
\(575\) | 1.45511e29 | 1.53597 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.99202e28 | 1.01697 | 0.508484 | − | 0.861072i | \(-0.330206\pi\) | ||||
0.508484 | + | 0.861072i | \(0.330206\pi\) | |||||||
\(578\) | −9.03346e28 | − | 7.38879e27i | −0.902842 | − | 0.0738467i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.28834e27 | + | 5.41553e26i | 0.0316944 | + | 0.00521971i | ||||
\(581\) | 1.54065e28 | 0.145833 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.62586e29i | − | 1.48444i | ||||||
\(584\) | 8.60782e28 | + | 2.15065e28i | 0.771895 | + | 0.192856i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.48908e28 | + | 2.85385e27i | 0.301847 | + | 0.0246891i | ||||
\(587\) | 5.08606e27i | 0.0432197i | 0.999766 | + | 0.0216098i | \(0.00687916\pi\) | ||||
−0.999766 | + | 0.0216098i | \(0.993121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.56858e27i | 0.0292607i | ||||||||
\(590\) | −1.29612e26 | + | 1.58462e27i | −0.00104400 | + | 0.0127638i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.59263e28 | − | 7.65780e28i | 0.201540 | − | 0.595286i | ||||
\(593\) | − | 1.46496e29i | − | 1.11880i | −0.828898 | − | 0.559400i | \(-0.811032\pi\) | ||
0.828898 | − | 0.559400i | \(-0.188968\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.62376e27 | −0.0488288 | ||||||||
\(596\) | −1.91743e29 | − | 3.15780e28i | −1.38878 | − | 0.228717i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.00179e28 | − | 2.44737e29i | 0.139977 | − | 1.71134i | ||||
\(599\) | −8.86133e28 | −0.608859 | −0.304430 | − | 0.952535i | \(-0.598466\pi\) | ||||
−0.304430 | + | 0.952535i | \(0.598466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.50826e29 | −1.66414 | −0.832070 | − | 0.554670i | \(-0.812845\pi\) | ||||
−0.832070 | + | 0.554670i | \(0.812845\pi\) | |||||||
\(602\) | −6.70433e27 | + | 8.19665e28i | −0.0437112 | + | 0.534408i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.61455e28 | + | 9.80361e28i | −0.101663 | + | 0.617303i | ||||
\(605\) | −2.52709e28 | −0.156383 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.02859e29i | − | 1.21259i | −0.795240 | − | 0.606295i | \(-0.792655\pi\) | ||
0.795240 | − | 0.606295i | \(-0.207345\pi\) | |||||||
\(608\) | 6.18593e28 | + | 2.67434e28i | 0.363427 | + | 0.157119i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.23918e27 | + | 2.73760e28i | −0.0127094 | + | 0.155384i | ||||
\(611\) | − | 3.44141e29i | − | 1.92001i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.19775e29i | − | 0.645699i | −0.946450 | − | 0.322849i | \(-0.895359\pi\) | ||
0.946450 | − | 0.322849i | \(-0.104641\pi\) | |||||||
\(614\) | 1.66581e29 | + | 1.36252e28i | 0.882789 | + | 0.0722065i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.09517e29 | + | 2.73626e28i | 0.560898 | + | 0.140139i | ||||
\(617\) | − | 2.02124e29i | − | 1.01771i | −0.860853 | − | 0.508854i | \(-0.830069\pi\) | ||
0.860853 | − | 0.508854i | \(-0.169931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.98741e29 | 1.45393 | 0.726964 | − | 0.686676i | \(-0.240931\pi\) | ||||
0.726964 | + | 0.686676i | \(0.240931\pi\) | |||||||
\(620\) | −2.47040e26 | + | 1.50004e27i | −0.00118210 | + | 0.00717777i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.82060e28 | + | 5.57881e27i | 0.315517 | + | 0.0258073i | ||||
\(623\) | −8.04472e28 | −0.365920 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.20786e29 | 0.971027 | ||||||||
\(626\) | 2.90717e29 | + | 2.37788e28i | 1.25730 | + | 0.102839i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.77593e28 | − | 2.29276e29i | 0.157924 | − | 0.958921i | ||||
\(629\) | 2.10944e29 | 0.867631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.40188e29i | − | 0.955528i | −0.878488 | − | 0.477764i | \(-0.841447\pi\) | ||
0.878488 | − | 0.477764i | \(-0.158553\pi\) | |||||||
\(632\) | 4.84856e28 | − | 1.94060e29i | 0.189707 | − | 0.759290i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.52344e29 | − | 2.06401e28i | −0.955115 | − | 0.0781223i | ||||
\(635\) | 2.24031e28i | 0.0834035i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.67669e29i | 0.964128i | ||||||||
\(638\) | 1.20805e28 | − | 1.47694e29i | 0.0428022 | − | 0.523295i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.41509e28 | + | 1.55238e28i | 0.0828027 | + | 0.0532240i | ||||
\(641\) | 2.96425e29i | 0.999782i | 0.866088 | + | 0.499891i | \(0.166627\pi\) | ||||
−0.866088 | + | 0.499891i | \(0.833373\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.15607e29 | −0.703797 | −0.351898 | − | 0.936038i | \(-0.614464\pi\) | ||||
−0.351898 | + | 0.936038i | \(0.614464\pi\) | |||||||
\(644\) | 2.82004e28 | − | 1.71235e29i | 0.0905637 | − | 0.549908i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.43345e28 | + | 1.75252e29i | −0.0445597 | + | 0.544782i | ||||
\(647\) | −1.90384e29 | −0.582286 | −0.291143 | − | 0.956680i | \(-0.594036\pi\) | ||||
−0.291143 | + | 0.956680i | \(0.594036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.06967e28 | 0.209329 | ||||||||
\(650\) | 3.06766e28 | − | 3.75049e29i | 0.0893752 | − | 1.09269i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.05181e29 | − | 6.67288e28i | −1.14301 | − | 0.188241i | ||||
\(653\) | 3.76760e27 | 0.0104587 | 0.00522933 | − | 0.999986i | \(-0.498335\pi\) | ||||
0.00522933 | + | 0.999986i | \(0.498335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.79651e28i | 0.102059i | ||||||||
\(656\) | −2.23351e29 | + | 6.59706e29i | −0.590877 | + | 1.74526i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.98272e28 | − | 2.42406e29i | 0.0508031 | − | 0.621114i | ||||
\(659\) | 5.72298e29i | 1.44320i | 0.692312 | + | 0.721598i | \(0.256592\pi\) | ||||
−0.692312 | + | 0.721598i | \(0.743408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.93410e29i | − | 0.961015i | −0.876991 | − | 0.480507i | \(-0.840453\pi\) | ||
0.876991 | − | 0.480507i | \(-0.159547\pi\) | |||||||
\(662\) | −1.41279e29 | − | 1.15557e28i | −0.339679 | − | 0.0277836i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.22335e28 | − | 1.69037e29i | 0.0983767 | − | 0.393746i | ||||
\(665\) | 6.10778e27i | 0.0140041i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.27816e29 | −0.506131 | ||||||||
\(668\) | −4.98429e29 | − | 8.20858e28i | −1.09006 | − | 0.179521i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.14949e28 | − | 5.02989e27i | −0.130333 | − | 0.0106604i | ||||
\(671\) | 1.22136e30 | 2.54833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.90178e29 | 0.789050 | 0.394525 | − | 0.918885i | \(-0.370909\pi\) | ||||
0.394525 | + | 0.918885i | \(0.370909\pi\) | |||||||
\(674\) | 4.31817e29 | + | 3.53199e28i | 0.859748 | + | 0.0703218i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.15336e29 | − | 1.89946e28i | −0.222600 | − | 0.0366598i | ||||
\(677\) | 6.71548e28 | 0.127613 | 0.0638067 | − | 0.997962i | \(-0.479676\pi\) | ||||
0.0638067 | + | 0.997962i | \(0.479676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.67374e28i | − | 0.104529i | ||||||
\(680\) | −1.81575e28 | + | 7.26743e28i | −0.0329392 | + | 0.131837i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.73737e28 | + | 5.51074e27i | 0.118510 | + | 0.00969335i | ||||
\(683\) | − | 5.76744e29i | − | 0.999000i | −0.866314 | − | 0.499500i | \(-0.833517\pi\) | ||
0.866314 | − | 0.499500i | \(-0.166483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.13934e28i | 0.136722i | ||||||||
\(686\) | −3.31292e28 | + | 4.05034e29i | −0.0548035 | + | 0.670022i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.80939e29 | + | 2.98251e29i | 1.41341 | + | 0.478524i | ||||
\(689\) | 6.46393e29i | 1.02140i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.04807e30 | −1.60646 | −0.803232 | − | 0.595667i | \(-0.796888\pi\) | ||||
−0.803232 | + | 0.595667i | \(0.796888\pi\) | |||||||
\(692\) | 7.90631e29 | + | 1.30208e29i | 1.19360 | + | 0.196573i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.32792e28 | − | 1.01816e30i | 0.121973 | − | 1.49122i | ||||
\(695\) | 3.89409e28 | 0.0561779 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.81725e30 | −2.54372 | ||||||||
\(698\) | −1.94716e28 | + | 2.38058e29i | −0.0268485 | + | 0.328247i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.32160e28 | − | 2.62410e29i | 0.0578249 | − | 0.351116i | ||||
\(701\) | −5.52002e29 | −0.727615 | −0.363807 | − | 0.931474i | \(-0.618523\pi\) | ||||
−0.363807 | + | 0.931474i | \(0.618523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.94512e29i | − | 0.248837i | ||||||
\(704\) | 6.00432e29 | − | 1.12659e30i | 0.756747 | − | 1.41988i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.68708e28 | − | 4.50779e29i | 0.0451059 | − | 0.551461i | ||||
\(707\) | 4.82382e29i | 0.581417i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.98932e29i | 1.16883i | 0.811456 | + | 0.584414i | \(0.198676\pi\) | ||||
−0.811456 | + | 0.584414i | \(0.801324\pi\) | |||||||
\(710\) | −1.54712e29 | − | 1.26544e28i | −0.178366 | − | 0.0145892i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.20528e29 | + | 8.82648e29i | −0.246845 | + | 0.987978i | ||||
\(713\) | − | 1.03923e29i | − | 0.114623i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63709e29 | 0.175331 | ||||||||
\(716\) | 8.37787e28 | − | 5.08708e29i | 0.0884192 | − | 0.536886i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.94725e29 | + | 6.50034e28i | 0.814536 | + | 0.0666238i | ||||
\(719\) | 2.92611e29 | 0.295554 | 0.147777 | − | 0.989021i | \(-0.452788\pi\) | ||||
0.147777 | + | 0.989021i | \(0.452788\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.70905e29 | 0.265764 | ||||||||
\(722\) | −8.69243e29 | − | 7.10985e28i | −0.840428 | − | 0.0687416i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.36601e29 | + | 2.04386e30i | −0.316126 | + | 1.91954i | ||||
\(725\) | −3.49118e29 | −0.323164 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.27358e30i | − | 1.14529i | −0.819803 | − | 0.572645i | \(-0.805917\pi\) | ||
0.819803 | − | 0.572645i | \(-0.194083\pi\) | |||||||
\(728\) | −4.35406e29 | − | 1.08785e29i | −0.385936 | − | 0.0964253i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.06338e28 | + | 7.41327e27i | 0.0780549 | + | 0.00638439i | ||||
\(731\) | 2.42666e30i | 2.06004i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.50891e28i | − | 0.0289454i | −0.999895 | − | 0.0144727i | \(-0.995393\pi\) | ||
0.999895 | − | 0.0144727i | \(-0.00460697\pi\) | |||||||
\(734\) | 4.11669e28 | − | 5.03303e29i | 0.0334765 | − | 0.409280i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.80144e30 | − | 7.78810e29i | −1.42365 | − | 0.615481i | ||||
\(737\) | 2.74354e30i | 2.13748i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.61183e29 | 0.424950 | 0.212475 | − | 0.977167i | \(-0.431848\pi\) | ||||
0.212475 | + | 0.977167i | \(0.431848\pi\) | |||||||
\(740\) | 1.34653e28 | − | 8.17623e28i | 0.0100527 | − | 0.0610408i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.72411e28 | + | 4.55306e29i | −0.0270260 | + | 0.330417i | ||||
\(743\) | −4.81542e29 | −0.344550 | −0.172275 | − | 0.985049i | \(-0.555112\pi\) | ||||
−0.172275 | + | 0.985049i | \(0.555112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.99171e29 | −0.138544 | ||||||||
\(746\) | 1.29603e29 | − | 1.58451e30i | 0.0888906 | − | 1.08677i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.28658e30 | + | 5.41263e29i | 2.19168 | + | 0.360945i | ||||
\(749\) | −6.79428e29 | −0.446770 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.84564e30i | 1.81954i | 0.415114 | + | 0.909769i | \(0.363742\pi\) | ||||
−0.415114 | + | 0.909769i | \(0.636258\pi\) | |||||||
\(752\) | −2.60527e30 | − | 8.82041e29i | −1.64273 | − | 0.556162i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.80282e28 | + | 5.87188e29i | −0.0294508 | + | 0.360063i | ||||
\(755\) | 1.01834e29i | 0.0615815i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.34966e30i | 0.793814i | 0.917859 | + | 0.396907i | \(0.129916\pi\) | ||||
−0.917859 | + | 0.396907i | \(0.870084\pi\) | |||||||
\(758\) | 1.06437e30 | + | 8.70588e28i | 0.617400 | + | 0.0504994i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.70132e28 | + | 1.67431e28i | 0.0378110 | + | 0.00944700i | ||||
\(761\) | − | 1.38344e30i | − | 0.769880i | −0.922942 | − | 0.384940i | \(-0.874222\pi\) | ||
0.922942 | − | 0.384940i | \(-0.125778\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.90462e29 | −0.265520 | ||||||||
\(764\) | −2.24386e30 | − | 3.69538e29i | −1.19816 | − | 0.197324i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.29821e29 | + | 4.33360e28i | 0.275250 | + | 0.0225137i | ||||
\(767\) | −2.81069e29 | −0.144033 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.23078e30 | 1.11232 | 0.556161 | − | 0.831074i | \(-0.312274\pi\) | ||||
0.556161 | + | 0.831074i | \(0.312274\pi\) | |||||||
\(770\) | 1.15313e29 | + | 9.43187e27i | 0.0567186 | + | 0.00463922i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.61537e30 | + | 2.66033e29i | 0.773196 | + | 0.127337i | ||||
\(773\) | −9.81452e29 | −0.463430 | −0.231715 | − | 0.972784i | \(-0.574434\pi\) | ||||
−0.231715 | + | 0.972784i | \(0.574434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.59257e29i | − | 0.0731865i | ||||||
\(776\) | −6.22510e29 | − | 1.55533e29i | −0.282227 | − | 0.0705139i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.76767e30 | + | 3.08171e29i | 1.66260 | + | 0.135990i | ||||
\(779\) | 1.67569e30i | 0.729541i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.90234e30i | 2.92523i | ||||||||
\(782\) | 4.17444e29 | − | 5.10363e30i | 0.174553 | − | 2.13407i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.02635e30 | + | 6.86043e29i | 0.824891 | + | 0.279275i | ||||
\(785\) | − | 2.38159e29i | − | 0.0956610i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.24592e30 | −1.26941 | −0.634706 | − | 0.772753i | \(-0.718879\pi\) | ||||
−0.634706 | + | 0.772753i | \(0.718879\pi\) | |||||||
\(788\) | −1.36631e30 | − | 2.25017e29i | −0.527260 | − | 0.0868339i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.67130e28 | − | 2.04331e29i | 0.00628014 | − | 0.0767803i | ||||
\(791\) | 4.35258e29 | 0.161396 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.85575e30 | −1.75343 | ||||||||
\(794\) | −2.65979e28 | + | 3.25183e29i | −0.00947833 | + | 0.115881i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.39158e28 | + | 2.05938e29i | −0.0117710 | + | 0.0714743i | ||||
\(797\) | −2.66837e30 | −0.913973 | −0.456986 | − | 0.889474i | \(-0.651071\pi\) | ||||
−0.456986 | + | 0.889474i | \(0.651071\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.17655e30i | − | 2.39428i | ||||||
\(800\) | −2.76063e30 | − | 1.19349e30i | −0.908999 | − | 0.392984i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.64520e29 | − | 2.01140e30i | 0.0527700 | − | 0.645160i | ||||
\(803\) | − | 4.04355e30i | − | 1.28012i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.77868e29i | − | 0.0548583i | ||||||
\(806\) | −2.67858e29 | − | 2.19090e28i | −0.0815429 | − | 0.00666968i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.29259e30 | + | 1.32234e30i | 1.56982 | + | 0.392216i | ||||
\(809\) | 4.96815e30i | 1.45457i | 0.686334 | + | 0.727286i | \(0.259219\pi\) | ||||
−0.686334 | + | 0.727286i | \(0.740781\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.25320e30 | 0.357521 | 0.178761 | − | 0.983893i | \(-0.442791\pi\) | ||||
0.178761 | + | 0.983893i | \(0.442791\pi\) | |||||||
\(812\) | −6.76603e28 | + | 4.10837e29i | −0.0190544 | + | 0.115699i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.67232e30 | − | 3.00373e29i | −1.00782 | − | 0.0824336i | ||||
\(815\) | −4.20878e29 | −0.114025 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.23763e30 | 0.590822 | ||||||||
\(818\) | 2.15638e30 | + | 1.76378e29i | 0.562103 | + | 0.0459764i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.16002e29 | + | 7.04369e29i | −0.0294726 | + | 0.178959i | ||||
\(821\) | 9.53926e29 | 0.239283 | 0.119641 | − | 0.992817i | \(-0.461826\pi\) | ||||
0.119641 | + | 0.992817i | \(0.461826\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.17566e30i | 0.776489i | 0.921556 | + | 0.388245i | \(0.126918\pi\) | ||||
−0.921556 | + | 0.388245i | \(0.873082\pi\) | |||||||
\(824\) | 7.42625e29 | − | 2.97231e30i | 0.179281 | − | 0.717559i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.97979e29 | − | 1.61934e28i | −0.0465939 | − | 0.00381108i | ||||
\(827\) | 6.26257e30i | 1.45527i | 0.685963 | + | 0.727636i | \(0.259381\pi\) | ||||
−0.685963 | + | 0.727636i | \(0.740619\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.71383e29i | − | 0.152107i | −0.997104 | − | 0.0760533i | \(-0.975768\pi\) | ||
0.997104 | − | 0.0760533i | \(-0.0242319\pi\) | |||||||
\(830\) | 1.45579e28 | − | 1.77983e29i | 0.00325670 | − | 0.0398161i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.38714e30 | + | 4.47896e30i | −0.520694 | + | 0.976973i | ||||
\(833\) | 5.58185e30i | 1.20228i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.17739e29 | −0.108743 | ||||||||
\(836\) | 4.99100e29 | − | 3.03056e30i | 0.103519 | − | 0.628575i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.50976e29 | − | 5.51359e30i | 0.0912203 | − | 1.11525i | ||||
\(839\) | 7.92009e30 | 1.58208 | 0.791042 | − | 0.611762i | \(-0.209539\pi\) | ||||
0.791042 | + | 0.611762i | \(0.209539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.58625e30 | −0.893511 | ||||||||
\(842\) | 3.31872e29 | − | 4.05743e30i | 0.0638548 | − | 0.780682i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.70244e30 | − | 6.09751e29i | −0.694852 | − | 0.114434i | ||||
\(845\) | −1.19805e29 | −0.0222064 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.15728e30i | − | 0.570871i | ||||||
\(848\) | 4.89343e30 | + | 1.65672e30i | 0.873890 | + | 0.295865i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.39715e29 | − | 7.82109e30i | 0.111452 | − | 1.36260i | ||||
\(851\) | 5.66450e30i | 0.974767i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.52144e30i | 1.59859i | 0.600938 | + | 0.799296i | \(0.294794\pi\) | ||||
−0.600938 | + | 0.799296i | \(0.705206\pi\) | |||||||
\(854\) | −3.42029e30 | − | 2.79758e29i | −0.567225 | − | 0.0463954i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.86250e30 | + | 7.45453e30i | −0.301385 | + | 1.20627i | ||||
\(857\) | − | 8.34978e30i | − | 1.33468i | −0.744754 | − | 0.667339i | \(-0.767433\pi\) | ||
0.744754 | − | 0.667339i | \(-0.232567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.46393e30 | −0.540308 | −0.270154 | − | 0.962817i | \(-0.587075\pi\) | ||||
−0.270154 | + | 0.962817i | \(0.587075\pi\) | |||||||
\(860\) | 9.40578e29 | + | 1.54903e29i | 0.144931 | + | 0.0238685i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.67087e30 | + | 7.09222e29i | 1.30388 | + | 0.106649i | ||||
\(863\) | 5.50275e30 | 0.817460 | 0.408730 | − | 0.912655i | \(-0.365972\pi\) | ||||
0.408730 | + | 0.912655i | \(0.365972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.21261e29 | 0.119073 | ||||||||
\(866\) | 2.10455e30 | + | 1.72139e29i | 0.301455 | + | 0.0246571i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.87411e29 | − | 3.08646e28i | −0.0262022 | − | 0.00431522i | ||||
\(869\) | −9.11605e30 | −1.25921 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.09075e31i | − | 1.47073i | ||||||
\(872\) | −1.34449e30 | + | 5.38123e30i | −0.179116 | + | 0.716900i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.70607e30 | − | 3.84926e29i | −0.612052 | − | 0.0500619i | ||||
\(875\) | − | 5.47818e29i | − | 0.0703966i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 8.33046e30i | − | 1.04514i | −0.852597 | − | 0.522569i | \(-0.824974\pi\) | ||
0.852597 | − | 0.522569i | \(-0.175026\pi\) | |||||||
\(878\) | −5.23012e29 | + | 6.39429e30i | −0.0648364 | + | 0.792683i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.19589e29 | − | 1.23933e30i | 0.0507874 | − | 0.150010i | ||||
\(881\) | 9.27206e30i | 1.10899i | 0.832186 | + | 0.554497i | \(0.187089\pi\) | ||||
−0.832186 | + | 0.554497i | \(0.812911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.07358e28 | 0.00475761 | 0.00237880 | − | 0.999997i | \(-0.499243\pi\) | ||||
0.00237880 | + | 0.999997i | \(0.499243\pi\) | |||||||
\(884\) | −1.30664e31 | − | 2.15190e30i | −1.50802 | − | 0.248355i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.18841e30 | − | 1.45294e31i | 0.133941 | − | 1.63754i | ||||
\(887\) | 1.04464e31 | 1.16350 | 0.581750 | − | 0.813367i | \(-0.302368\pi\) | ||||
0.581750 | + | 0.813367i | \(0.302368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.79899e30 | −0.304462 | ||||||||
\(890\) | −7.60158e28 | + | 9.29362e29i | −0.00817163 | + | 0.0999056i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.61239e30 | + | 1.58626e31i | −0.274288 | + | 1.66549i | ||||
\(893\) | −6.61751e30 | −0.686680 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.28416e29i | − | 0.0535592i | ||||||
\(896\) | −1.93950e30 | + | 3.01736e30i | −0.194292 | + | 0.302269i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.59776e29 | + | 1.95341e30i | −0.0156354 | + | 0.191157i | ||||
\(899\) | 2.49338e29i | 0.0241164i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.34796e31i | 1.27370i | ||||||||
\(902\) | 3.16365e31 | + | 2.58766e30i | 2.95474 | + | 0.241679i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.19316e30 | − | 4.77555e30i | 0.108876 | − | 0.435768i | ||||
\(905\) | 2.12304e30i | 0.191491i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.06013e31 | −0.934293 | −0.467146 | − | 0.884180i | \(-0.654718\pi\) | ||||
−0.467146 | + | 0.884180i | \(0.654718\pi\) | |||||||
\(908\) | 1.23818e30 | − | 7.51826e30i | 0.107865 | − | 0.654962i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.58450e29 | − | 3.74983e28i | −0.0390263 | − | 0.00319210i | ||||
\(911\) | 8.91151e30 | 0.749908 | 0.374954 | − | 0.927043i | \(-0.377658\pi\) | ||||
0.374954 | + | 0.927043i | \(0.377658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.94055e30 | −0.652992 | ||||||||
\(914\) | 1.22542e31 | + | 1.00231e30i | 0.996204 | + | 0.0814831i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.26545e30 | − | 7.68387e30i | 0.100541 | − | 0.610488i | ||||
\(917\) | −4.74327e30 | −0.372563 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.07064e31i | − | 1.58961i | −0.606862 | − | 0.794807i | \(-0.707572\pi\) | ||
0.606862 | − | 0.794807i | \(-0.292428\pi\) | |||||||
\(920\) | −1.95153e30 | − | 4.87586e29i | −0.148116 | − | 0.0370066i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.84715e31 | − | 1.51085e30i | −1.37034 | − | 0.112085i | ||||
\(923\) | − | 2.74416e31i | − | 2.01276i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.68060e30i | 0.622388i | ||||||||
\(926\) | −1.23187e29 | + | 1.50607e30i | −0.00873272 | + | 0.106765i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.32213e30 | + | 1.86857e30i | 0.299532 | + | 0.129496i | ||||
\(929\) | 3.09174e30i | 0.211855i | 0.994374 | + | 0.105927i | \(0.0337811\pi\) | ||||
−0.994374 | + | 0.105927i | \(0.966219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.14704e30 | 0.344815 | ||||||||
\(932\) | −2.95502e30 | + | 1.79431e31i | −0.195746 | + | 1.18858i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.96269e29 | − | 2.39957e30i | 0.0127119 | − | 0.155414i | ||||
\(935\) | 3.41390e30 | 0.218640 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.78477e31 | 1.74391 | 0.871954 | − | 0.489587i | \(-0.162853\pi\) | ||||
0.871954 | + | 0.489587i | \(0.162853\pi\) | |||||||
\(938\) | 6.28422e29 | − | 7.68302e30i | 0.0389154 | − | 0.475775i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.78165e30 | − | 4.58106e29i | −0.168445 | − | 0.0277411i | ||||
\(941\) | 2.09581e31 | 1.25505 | 0.627526 | − | 0.778596i | \(-0.284068\pi\) | ||||
0.627526 | + | 0.778596i | \(0.284068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.87987e31i | − | 2.85782i | ||||||
\(944\) | −7.20386e29 | + | 2.12779e30i | −0.0417214 | + | 0.123232i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.45543e30 | − | 4.22457e31i | 0.195725 | − | 2.39291i | ||||
\(947\) | 7.31568e30i | 0.409807i | 0.978782 | + | 0.204904i | \(0.0656881\pi\) | ||||
−0.978782 | + | 0.204904i | \(0.934312\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.60759e31i | 0.880808i | ||||||||
\(950\) | −7.21185e30 | − | 5.89883e29i | −0.390795 | − | 0.0319645i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.07975e30 | − | 2.26856e30i | −0.481267 | − | 0.120244i | ||||
\(953\) | − | 3.20223e31i | − | 1.67871i | −0.543580 | − | 0.839357i | \(-0.682932\pi\) | ||
0.543580 | − | 0.839357i | \(-0.317068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.33079e30 | −0.119527 | ||||||||
\(956\) | 1.93798e30 | + | 3.19164e29i | 0.0982974 | + | 0.0161885i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.29790e31 | − | 1.06160e30i | −0.644026 | − | 0.0526772i | ||||
\(959\) | −1.01691e31 | −0.499099 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.07118e31 | 0.994538 | ||||||||
\(962\) | 1.46001e31 | + | 1.19419e30i | 0.693452 | + | 0.0567199i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.03385e31 | + | 1.70264e30i | 0.480452 | + | 0.0791252i | ||||
\(965\) | 1.67795e30 | 0.0771332 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.18490e30i | − | 0.323179i | −0.986858 | − | 0.161589i | \(-0.948338\pi\) | ||
0.986858 | − | 0.161589i | \(-0.0516620\pi\) | |||||||
\(968\) | −3.46410e31 | − | 8.65499e30i | −1.54134 | − | 0.385101i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.55456e29 | − | 5.36121e28i | −0.0285391 | − | 0.00233432i | ||||
\(971\) | − | 2.50153e31i | − | 1.07747i | −0.842476 | − | 0.538734i | \(-0.818903\pi\) | ||
0.842476 | − | 0.538734i | \(-0.181097\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.86518e30i | 0.205076i | ||||||||
\(974\) | 8.83850e29 | − | 1.08059e31i | 0.0368561 | − | 0.450599i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.24454e31 | + | 3.67598e31i | −0.507909 | + | 1.50020i | ||||
\(977\) | − | 3.65570e31i | − | 1.47597i | −0.674818 | − | 0.737985i | \(-0.735778\pi\) | ||
0.674818 | − | 0.737985i | \(-0.264222\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.14627e31 | 1.63847 | ||||||||
\(980\) | 2.16354e30 | + | 3.56311e29i | 0.0845844 | + | 0.0139301i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.06197e30 | − | 2.52094e31i | 0.0789063 | − | 0.964701i | ||||
\(983\) | 3.77934e31 | 1.43088 | 0.715442 | − | 0.698672i | \(-0.246225\pi\) | ||||
0.715442 | + | 0.698672i | \(0.246225\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.41925e30 | −0.0525989 | ||||||||
\(986\) | −1.00156e30 | + | 1.22449e31i | −0.0367256 | + | 0.449003i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.98427e30 | + | 1.20486e31i | −0.0712284 | + | 0.432502i | ||||
\(989\) | −6.51633e31 | −2.31442 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.81645e31i | − | 0.631613i | −0.948824 | − | 0.315806i | \(-0.897725\pi\) | ||
0.948824 | − | 0.315806i | \(-0.102275\pi\) | |||||||
\(992\) | −8.52385e29 | + | 1.97162e30i | −0.0293267 | + | 0.0678346i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.58102e30 | − | 1.93293e31i | 0.0532573 | − | 0.651118i | ||||
\(995\) | 2.13917e29i | 0.00713021i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.71498e31i | 0.886068i | 0.896505 | + | 0.443034i | \(0.146098\pi\) | ||||
−0.896505 | + | 0.443034i | \(0.853902\pi\) | |||||||
\(998\) | 4.38568e31 | + | 3.58721e30i | 1.41634 | + | 0.115847i | ||||
\(999\) | 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.35.84 | yes | 84 | |
3.2 | odd | 2 | inner | 72.22.f.a.35.1 | ✓ | 84 | |
8.3 | odd | 2 | inner | 72.22.f.a.35.2 | yes | 84 | |
24.11 | even | 2 | inner | 72.22.f.a.35.83 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.22.f.a.35.1 | ✓ | 84 | 3.2 | odd | 2 | inner | |
72.22.f.a.35.2 | yes | 84 | 8.3 | odd | 2 | inner | |
72.22.f.a.35.83 | yes | 84 | 24.11 | even | 2 | inner | |
72.22.f.a.35.84 | yes | 84 | 1.1 | even | 1 | trivial |