Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,11,Mod(21,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.21");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.b (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: | \(13.9778595588\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 135903 x^{8} - 6427236 x^{7} + 6935435151 x^{6} + 631292713590 x^{5} + \cdots + 88\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{2}\cdot 11^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.2 | ||
Root | \(-138.673 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.21 |
Dual form | 22.11.b.a.21.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 22.6274i | − | 0.707107i | ||||||
\(3\) | −251.838 | −1.03637 | −0.518186 | − | 0.855268i | \(-0.673392\pi\) | ||||
−0.518186 | + | 0.855268i | \(0.673392\pi\) | |||||||
\(4\) | −512.000 | −0.500000 | ||||||||
\(5\) | 3507.04 | 1.12225 | 0.561127 | − | 0.827730i | \(-0.310368\pi\) | ||||
0.561127 | + | 0.827730i | \(0.310368\pi\) | |||||||
\(6\) | 5698.45i | 0.732825i | ||||||||
\(7\) | 17033.0i | 1.01345i | 0.862108 | + | 0.506724i | \(0.169144\pi\) | ||||
−0.862108 | + | 0.506724i | \(0.830856\pi\) | |||||||
\(8\) | 11585.2i | 0.353553i | ||||||||
\(9\) | 4373.51 | 0.0740657 | ||||||||
\(10\) | − | 79355.3i | − | 0.793553i | ||||||
\(11\) | 157855. | − | 31925.2i | 0.980155 | − | 0.198230i | ||||
\(12\) | 128941. | 0.518186 | ||||||||
\(13\) | − | 572760.i | − | 1.54261i | −0.636466 | − | 0.771305i | \(-0.719604\pi\) | ||
0.636466 | − | 0.771305i | \(-0.280396\pi\) | |||||||
\(14\) | 385413. | 0.716616 | ||||||||
\(15\) | −883207. | −1.16307 | ||||||||
\(16\) | 262144. | 0.250000 | ||||||||
\(17\) | − | 316651.i | − | 0.223016i | −0.993764 | − | 0.111508i | \(-0.964432\pi\) | ||
0.993764 | − | 0.111508i | \(-0.0355681\pi\) | |||||||
\(18\) | − | 98961.1i | − | 0.0523724i | ||||||
\(19\) | − | 1.70040e6i | − | 0.686724i | −0.939203 | − | 0.343362i | \(-0.888434\pi\) | ||
0.939203 | − | 0.343362i | \(-0.111566\pi\) | |||||||
\(20\) | −1.79561e6 | −0.561127 | ||||||||
\(21\) | − | 4.28957e6i | − | 1.05031i | ||||||
\(22\) | −722384. | − | 3.57185e6i | −0.140170 | − | 0.693075i | ||||
\(23\) | 4.92708e6 | 0.765509 | 0.382755 | − | 0.923850i | \(-0.374975\pi\) | ||||
0.382755 | + | 0.923850i | \(0.374975\pi\) | |||||||
\(24\) | − | 2.91761e6i | − | 0.366413i | ||||||
\(25\) | 2.53372e6 | 0.259452 | ||||||||
\(26\) | −1.29601e7 | −1.09079 | ||||||||
\(27\) | 1.37694e7 | 0.959612 | ||||||||
\(28\) | − | 8.72090e6i | − | 0.506724i | ||||||
\(29\) | − | 1.32575e7i | − | 0.646358i | −0.946338 | − | 0.323179i | \(-0.895248\pi\) | ||
0.946338 | − | 0.323179i | \(-0.104752\pi\) | |||||||
\(30\) | 1.99847e7i | 0.822416i | ||||||||
\(31\) | 4.47396e7 | 1.56273 | 0.781365 | − | 0.624074i | \(-0.214524\pi\) | ||||
0.781365 | + | 0.624074i | \(0.214524\pi\) | |||||||
\(32\) | − | 5.93164e6i | − | 0.176777i | ||||||
\(33\) | −3.97539e7 | + | 8.03998e6i | −1.01581 | + | 0.205440i | ||||
\(34\) | −7.16499e6 | −0.157696 | ||||||||
\(35\) | 5.97355e7i | 1.13735i | ||||||||
\(36\) | −2.23923e6 | −0.0370328 | ||||||||
\(37\) | −1.38623e7 | −0.199906 | −0.0999531 | − | 0.994992i | \(-0.531869\pi\) | ||||
−0.0999531 | + | 0.994992i | \(0.531869\pi\) | |||||||
\(38\) | −3.84756e7 | −0.485587 | ||||||||
\(39\) | 1.44243e8i | 1.59872i | ||||||||
\(40\) | 4.06299e7i | 0.396776i | ||||||||
\(41\) | 1.37050e8i | 1.18294i | 0.806329 | + | 0.591468i | \(0.201451\pi\) | ||||
−0.806329 | + | 0.591468i | \(0.798549\pi\) | |||||||
\(42\) | −9.70618e7 | −0.742680 | ||||||||
\(43\) | − | 2.64207e8i | − | 1.79723i | −0.438742 | − | 0.898613i | \(-0.644576\pi\) | ||
0.438742 | − | 0.898613i | \(-0.355424\pi\) | |||||||
\(44\) | −8.08218e7 | + | 1.63457e7i | −0.490078 | + | 0.0991151i | ||||
\(45\) | 1.53381e7 | 0.0831205 | ||||||||
\(46\) | − | 1.11487e8i | − | 0.541297i | ||||||
\(47\) | 3.51358e8 | 1.53201 | 0.766004 | − | 0.642836i | \(-0.222242\pi\) | ||||
0.766004 | + | 0.642836i | \(0.222242\pi\) | |||||||
\(48\) | −6.60179e7 | −0.259093 | ||||||||
\(49\) | −7.64840e6 | −0.0270764 | ||||||||
\(50\) | − | 5.73314e7i | − | 0.183461i | ||||||
\(51\) | 7.97448e7i | 0.231128i | ||||||||
\(52\) | 2.93253e8i | 0.771305i | ||||||||
\(53\) | −8.58062e7 | −0.205182 | −0.102591 | − | 0.994724i | \(-0.532713\pi\) | ||||
−0.102591 | + | 0.994724i | \(0.532713\pi\) | |||||||
\(54\) | − | 3.11566e8i | − | 0.678548i | ||||||
\(55\) | 5.53604e8 | − | 1.11963e8i | 1.09998 | − | 0.222465i | ||||
\(56\) | −1.97332e8 | −0.358308 | ||||||||
\(57\) | 4.28225e8i | 0.711701i | ||||||||
\(58\) | −2.99984e8 | −0.457044 | ||||||||
\(59\) | 5.57123e7 | 0.0779275 | 0.0389638 | − | 0.999241i | \(-0.487594\pi\) | ||||
0.0389638 | + | 0.999241i | \(0.487594\pi\) | |||||||
\(60\) | 4.52202e8 | 0.581536 | ||||||||
\(61\) | − | 1.30182e9i | − | 1.54135i | −0.637227 | − | 0.770676i | \(-0.719919\pi\) | ||
0.637227 | − | 0.770676i | \(-0.280081\pi\) | |||||||
\(62\) | − | 1.01234e9i | − | 1.10502i | ||||||
\(63\) | 7.44940e7i | 0.0750617i | ||||||||
\(64\) | −1.34218e8 | −0.125000 | ||||||||
\(65\) | − | 2.00869e9i | − | 1.73120i | ||||||
\(66\) | 1.81924e8 | + | 8.99529e8i | 0.145268 | + | 0.718283i | ||||
\(67\) | −5.86911e8 | −0.434709 | −0.217354 | − | 0.976093i | \(-0.569743\pi\) | ||||
−0.217354 | + | 0.976093i | \(0.569743\pi\) | |||||||
\(68\) | 1.62125e8i | 0.111508i | ||||||||
\(69\) | −1.24083e9 | −0.793352 | ||||||||
\(70\) | 1.35166e9 | 0.804224 | ||||||||
\(71\) | −1.48291e9 | −0.821905 | −0.410953 | − | 0.911657i | \(-0.634804\pi\) | ||||
−0.410953 | + | 0.911657i | \(0.634804\pi\) | |||||||
\(72\) | 5.06681e7i | 0.0261862i | ||||||||
\(73\) | 2.61401e9i | 1.26094i | 0.776215 | + | 0.630468i | \(0.217137\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(74\) | 3.13668e8i | 0.141355i | ||||||||
\(75\) | −6.38087e8 | −0.268889 | ||||||||
\(76\) | 8.70603e8i | 0.343362i | ||||||||
\(77\) | 5.43782e8 | + | 2.68875e9i | 0.200896 | + | 0.993336i | ||||
\(78\) | 3.26385e9 | 1.13046 | ||||||||
\(79\) | 3.81282e9i | 1.23911i | 0.784952 | + | 0.619557i | \(0.212688\pi\) | ||||
−0.784952 | + | 0.619557i | \(0.787312\pi\) | |||||||
\(80\) | 9.19350e8 | 0.280563 | ||||||||
\(81\) | −3.72591e9 | −1.06858 | ||||||||
\(82\) | 3.10110e9 | 0.836462 | ||||||||
\(83\) | − | 4.26258e9i | − | 1.08214i | −0.840979 | − | 0.541068i | \(-0.818020\pi\) | ||
0.840979 | − | 0.541068i | \(-0.181980\pi\) | |||||||
\(84\) | 2.19626e9i | 0.525154i | ||||||||
\(85\) | − | 1.11051e9i | − | 0.250281i | ||||||
\(86\) | −5.97833e9 | −1.27083 | ||||||||
\(87\) | 3.33876e9i | 0.669867i | ||||||||
\(88\) | 3.69861e8 | + | 1.82879e9i | 0.0700850 | + | 0.346537i | ||||
\(89\) | 3.96125e9 | 0.709386 | 0.354693 | − | 0.934983i | \(-0.384585\pi\) | ||||
0.354693 | + | 0.934983i | \(0.384585\pi\) | |||||||
\(90\) | − | 3.47061e8i | − | 0.0587750i | ||||||
\(91\) | 9.75584e9 | 1.56335 | ||||||||
\(92\) | −2.52267e9 | −0.382755 | ||||||||
\(93\) | −1.12672e10 | −1.61957 | ||||||||
\(94\) | − | 7.95034e9i | − | 1.08329i | ||||||
\(95\) | − | 5.96336e9i | − | 0.770678i | ||||||
\(96\) | 1.49381e9i | 0.183206i | ||||||||
\(97\) | 2.03909e9 | 0.237453 | 0.118726 | − | 0.992927i | \(-0.462119\pi\) | ||||
0.118726 | + | 0.992927i | \(0.462119\pi\) | |||||||
\(98\) | 1.73064e8i | 0.0191459i | ||||||||
\(99\) | 6.90380e8 | − | 1.39625e8i | 0.0725959 | − | 0.0146821i | ||||
\(100\) | −1.29726e9 | −0.129726 | ||||||||
\(101\) | 3.18411e9i | 0.302957i | 0.988461 | + | 0.151479i | \(0.0484035\pi\) | ||||
−0.988461 | + | 0.151479i | \(0.951597\pi\) | |||||||
\(102\) | 1.80442e9 | 0.163432 | ||||||||
\(103\) | −1.17875e10 | −1.01680 | −0.508402 | − | 0.861120i | \(-0.669763\pi\) | ||||
−0.508402 | + | 0.861120i | \(0.669763\pi\) | |||||||
\(104\) | 6.63556e9 | 0.545395 | ||||||||
\(105\) | − | 1.50437e10i | − | 1.17871i | ||||||
\(106\) | 1.94157e9i | 0.145086i | ||||||||
\(107\) | − | 3.16794e8i | − | 0.0225870i | −0.999936 | − | 0.0112935i | \(-0.996405\pi\) | ||
0.999936 | − | 0.0112935i | \(-0.00359490\pi\) | |||||||
\(108\) | −7.04992e9 | −0.479806 | ||||||||
\(109\) | − | 1.03724e9i | − | 0.0674137i | −0.999432 | − | 0.0337069i | \(-0.989269\pi\) | ||
0.999432 | − | 0.0337069i | \(-0.0107313\pi\) | |||||||
\(110\) | −2.53343e9 | − | 1.25266e10i | −0.157306 | − | 0.777805i | ||||
\(111\) | 3.49105e9 | 0.207177 | ||||||||
\(112\) | 4.46510e9i | 0.253362i | ||||||||
\(113\) | 1.87245e10 | 1.01629 | 0.508144 | − | 0.861272i | \(-0.330332\pi\) | ||||
0.508144 | + | 0.861272i | \(0.330332\pi\) | |||||||
\(114\) | 9.68962e9 | 0.503248 | ||||||||
\(115\) | 1.72795e10 | 0.859096 | ||||||||
\(116\) | 6.78786e9i | 0.323179i | ||||||||
\(117\) | − | 2.50497e9i | − | 0.114254i | ||||||
\(118\) | − | 1.26063e9i | − | 0.0551031i | ||||||
\(119\) | 5.39352e9 | 0.226015 | ||||||||
\(120\) | − | 1.02322e10i | − | 0.411208i | ||||||
\(121\) | 2.38990e10 | − | 1.00791e10i | 0.921410 | − | 0.388593i | ||||
\(122\) | −2.94568e10 | −1.08990 | ||||||||
\(123\) | − | 3.45145e10i | − | 1.22596i | ||||||
\(124\) | −2.29067e10 | −0.781365 | ||||||||
\(125\) | −2.53626e10 | −0.831082 | ||||||||
\(126\) | 1.68561e9 | 0.0530766 | ||||||||
\(127\) | 5.83927e10i | 1.76742i | 0.468035 | + | 0.883710i | \(0.344962\pi\) | ||||
−0.468035 | + | 0.883710i | \(0.655038\pi\) | |||||||
\(128\) | 3.03700e9i | 0.0883883i | ||||||||
\(129\) | 6.65375e10i | 1.86259i | ||||||||
\(130\) | −4.54516e10 | −1.22414 | ||||||||
\(131\) | 2.61686e10i | 0.678304i | 0.940732 | + | 0.339152i | \(0.110140\pi\) | ||||
−0.940732 | + | 0.339152i | \(0.889860\pi\) | |||||||
\(132\) | 2.03540e10 | − | 4.11647e9i | 0.507903 | − | 0.102720i | ||||
\(133\) | 2.89629e10 | 0.695959 | ||||||||
\(134\) | 1.32803e10i | 0.307386i | ||||||||
\(135\) | 4.82898e10 | 1.07693 | ||||||||
\(136\) | 3.66848e9 | 0.0788481 | ||||||||
\(137\) | −5.47181e10 | −1.13378 | −0.566889 | − | 0.823794i | \(-0.691853\pi\) | ||||
−0.566889 | + | 0.823794i | \(0.691853\pi\) | |||||||
\(138\) | 2.80767e10i | 0.560985i | ||||||||
\(139\) | 6.67916e10i | 1.28721i | 0.765360 | + | 0.643603i | \(0.222561\pi\) | ||||
−0.765360 | + | 0.643603i | \(0.777439\pi\) | |||||||
\(140\) | − | 3.05846e10i | − | 0.568673i | ||||||
\(141\) | −8.84855e10 | −1.58773 | ||||||||
\(142\) | 3.35543e10i | 0.581175i | ||||||||
\(143\) | −1.82855e10 | − | 9.04131e10i | −0.305792 | − | 1.51200i | ||||
\(144\) | 1.14649e9 | 0.0185164 | ||||||||
\(145\) | − | 4.64948e10i | − | 0.725377i | ||||||
\(146\) | 5.91483e10 | 0.891616 | ||||||||
\(147\) | 1.92616e9 | 0.0280612 | ||||||||
\(148\) | 7.09749e9 | 0.0999531 | ||||||||
\(149\) | − | 8.77588e10i | − | 1.19498i | −0.801878 | − | 0.597488i | \(-0.796166\pi\) | ||
0.801878 | − | 0.597488i | \(-0.203834\pi\) | |||||||
\(150\) | 1.44383e10i | 0.190133i | ||||||||
\(151\) | 1.72260e10i | 0.219432i | 0.993963 | + | 0.109716i | \(0.0349942\pi\) | ||||
−0.993963 | + | 0.109716i | \(0.965006\pi\) | |||||||
\(152\) | 1.96995e10 | 0.242794 | ||||||||
\(153\) | − | 1.38487e9i | − | 0.0165178i | ||||||
\(154\) | 6.08394e10 | − | 1.23044e10i | 0.702395 | − | 0.142055i | ||||
\(155\) | 1.56904e11 | 1.75378 | ||||||||
\(156\) | − | 7.38524e10i | − | 0.799359i | ||||||
\(157\) | −1.77458e11 | −1.86036 | −0.930178 | − | 0.367108i | \(-0.880348\pi\) | ||||
−0.930178 | + | 0.367108i | \(0.880348\pi\) | |||||||
\(158\) | 8.62744e10 | 0.876186 | ||||||||
\(159\) | 2.16093e10 | 0.212645 | ||||||||
\(160\) | − | 2.08025e10i | − | 0.198388i | ||||||
\(161\) | 8.39231e10i | 0.775804i | ||||||||
\(162\) | 8.43077e10i | 0.755600i | ||||||||
\(163\) | 1.65972e11 | 1.44244 | 0.721218 | − | 0.692709i | \(-0.243583\pi\) | ||||
0.721218 | + | 0.692709i | \(0.243583\pi\) | |||||||
\(164\) | − | 7.01698e10i | − | 0.591468i | ||||||
\(165\) | −1.39419e11 | + | 2.81966e10i | −1.13999 | + | 0.230556i | ||||
\(166\) | −9.64512e10 | −0.765186 | ||||||||
\(167\) | − | 1.99990e11i | − | 1.53966i | −0.638249 | − | 0.769830i | \(-0.720341\pi\) | ||
0.638249 | − | 0.769830i | \(-0.279659\pi\) | |||||||
\(168\) | 4.96956e10 | 0.371340 | ||||||||
\(169\) | −1.90196e11 | −1.37965 | ||||||||
\(170\) | −2.51279e10 | −0.176975 | ||||||||
\(171\) | − | 7.43669e9i | − | 0.0508627i | ||||||
\(172\) | 1.35274e11i | 0.898613i | ||||||||
\(173\) | − | 2.56274e11i | − | 1.65377i | −0.562375 | − | 0.826883i | \(-0.690112\pi\) | ||
0.562375 | − | 0.826883i | \(-0.309888\pi\) | |||||||
\(174\) | 7.55474e10 | 0.473667 | ||||||||
\(175\) | 4.31568e10i | 0.262942i | ||||||||
\(176\) | 4.13807e10 | − | 8.36899e9i | 0.245039 | − | 0.0495576i | ||||
\(177\) | −1.40305e10 | −0.0807619 | ||||||||
\(178\) | − | 8.96330e10i | − | 0.501612i | ||||||
\(179\) | 8.20427e10 | 0.446452 | 0.223226 | − | 0.974767i | \(-0.428341\pi\) | ||||
0.223226 | + | 0.974767i | \(0.428341\pi\) | |||||||
\(180\) | −7.85309e9 | −0.0415602 | ||||||||
\(181\) | −4.46390e9 | −0.0229785 | −0.0114892 | − | 0.999934i | \(-0.503657\pi\) | ||||
−0.0114892 | + | 0.999934i | \(0.503657\pi\) | |||||||
\(182\) | − | 2.20749e11i | − | 1.10546i | ||||||
\(183\) | 3.27848e11i | 1.59741i | ||||||||
\(184\) | 5.70814e10i | 0.270648i | ||||||||
\(185\) | −4.86156e10 | −0.224345 | ||||||||
\(186\) | 2.54947e11i | 1.14521i | ||||||||
\(187\) | −1.01091e10 | − | 4.99849e10i | −0.0442085 | − | 0.218590i | ||||
\(188\) | −1.79896e11 | −0.766004 | ||||||||
\(189\) | 2.34534e11i | 0.972516i | ||||||||
\(190\) | −1.34935e11 | −0.544952 | ||||||||
\(191\) | 1.06444e11 | 0.418748 | 0.209374 | − | 0.977836i | \(-0.432857\pi\) | ||||
0.209374 | + | 0.977836i | \(0.432857\pi\) | |||||||
\(192\) | 3.38012e10 | 0.129546 | ||||||||
\(193\) | − | 4.43331e11i | − | 1.65555i | −0.561062 | − | 0.827774i | \(-0.689607\pi\) | ||
0.561062 | − | 0.827774i | \(-0.310393\pi\) | |||||||
\(194\) | − | 4.61393e10i | − | 0.167904i | ||||||
\(195\) | 5.05866e11i | 1.79417i | ||||||||
\(196\) | 3.91598e9 | 0.0135382 | ||||||||
\(197\) | 1.58152e11i | 0.533019i | 0.963832 | + | 0.266510i | \(0.0858704\pi\) | ||||
−0.963832 | + | 0.266510i | \(0.914130\pi\) | |||||||
\(198\) | −3.15935e9 | − | 1.56215e10i | −0.0103818 | − | 0.0513330i | ||||
\(199\) | 2.57831e10 | 0.0826170 | 0.0413085 | − | 0.999146i | \(-0.486847\pi\) | ||||
0.0413085 | + | 0.999146i | \(0.486847\pi\) | |||||||
\(200\) | 2.93537e10i | 0.0917303i | ||||||||
\(201\) | 1.47807e11 | 0.450520 | ||||||||
\(202\) | 7.20482e10 | 0.214223 | ||||||||
\(203\) | 2.25816e11 | 0.655050 | ||||||||
\(204\) | − | 4.08294e10i | − | 0.115564i | ||||||
\(205\) | 4.80641e11i | 1.32755i | ||||||||
\(206\) | 2.66721e11i | 0.718988i | ||||||||
\(207\) | 2.15486e10 | 0.0566980 | ||||||||
\(208\) | − | 1.50146e11i | − | 0.385653i | ||||||
\(209\) | −5.42855e10 | − | 2.68416e11i | −0.136129 | − | 0.673096i | ||||
\(210\) | −3.40400e11 | −0.833475 | ||||||||
\(211\) | 3.49699e11i | 0.836145i | 0.908414 | + | 0.418072i | \(0.137294\pi\) | ||||
−0.908414 | + | 0.418072i | \(0.862706\pi\) | |||||||
\(212\) | 4.39328e10 | 0.102591 | ||||||||
\(213\) | 3.73452e11 | 0.851799 | ||||||||
\(214\) | −7.16822e9 | −0.0159714 | ||||||||
\(215\) | − | 9.26586e11i | − | 2.01694i | ||||||
\(216\) | 1.59522e11i | 0.339274i | ||||||||
\(217\) | 7.62051e11i | 1.58375i | ||||||||
\(218\) | −2.34702e10 | −0.0476687 | ||||||||
\(219\) | − | 6.58308e11i | − | 1.30680i | ||||||
\(220\) | −2.83445e11 | + | 5.73250e10i | −0.549991 | + | 0.111232i | ||||
\(221\) | −1.81365e11 | −0.344027 | ||||||||
\(222\) | − | 7.89935e10i | − | 0.146496i | ||||||
\(223\) | −1.02566e12 | −1.85986 | −0.929930 | − | 0.367737i | \(-0.880133\pi\) | ||||
−0.929930 | + | 0.367737i | \(0.880133\pi\) | |||||||
\(224\) | 1.01034e11 | 0.179154 | ||||||||
\(225\) | 1.10812e10 | 0.0192165 | ||||||||
\(226\) | − | 4.23686e11i | − | 0.718625i | ||||||
\(227\) | 1.33950e10i | 0.0222235i | 0.999938 | + | 0.0111118i | \(0.00353706\pi\) | ||||
−0.999938 | + | 0.0111118i | \(0.996463\pi\) | |||||||
\(228\) | − | 2.19251e11i | − | 0.355850i | ||||||
\(229\) | 8.31243e11 | 1.31993 | 0.659965 | − | 0.751297i | \(-0.270571\pi\) | ||||
0.659965 | + | 0.751297i | \(0.270571\pi\) | |||||||
\(230\) | − | 3.90990e11i | − | 0.607472i | ||||||
\(231\) | −1.36945e11 | − | 6.77129e11i | −0.208203 | − | 1.02947i | ||||
\(232\) | 1.53592e11 | 0.228522 | ||||||||
\(233\) | − | 1.07974e12i | − | 1.57232i | −0.618022 | − | 0.786160i | \(-0.712066\pi\) | ||
0.618022 | − | 0.786160i | \(-0.287934\pi\) | |||||||
\(234\) | −5.66810e10 | −0.0807901 | ||||||||
\(235\) | 1.23223e12 | 1.71930 | ||||||||
\(236\) | −2.85247e10 | −0.0389638 | ||||||||
\(237\) | − | 9.60215e11i | − | 1.28418i | ||||||
\(238\) | − | 1.22041e11i | − | 0.159817i | ||||||
\(239\) | 1.27584e12i | 1.63608i | 0.575160 | + | 0.818041i | \(0.304940\pi\) | ||||
−0.575160 | + | 0.818041i | \(0.695060\pi\) | |||||||
\(240\) | −2.31527e11 | −0.290768 | ||||||||
\(241\) | 4.12875e11i | 0.507848i | 0.967224 | + | 0.253924i | \(0.0817213\pi\) | ||||
−0.967224 | + | 0.253924i | \(0.918279\pi\) | |||||||
\(242\) | −2.28064e11 | − | 5.40772e11i | −0.274777 | − | 0.651535i | ||||
\(243\) | 1.25258e11 | 0.147834 | ||||||||
\(244\) | 6.66532e11i | 0.770676i | ||||||||
\(245\) | −2.68233e10 | −0.0303865 | ||||||||
\(246\) | −7.80975e11 | −0.866885 | ||||||||
\(247\) | −9.73919e11 | −1.05935 | ||||||||
\(248\) | 5.18319e11i | 0.552509i | ||||||||
\(249\) | 1.07348e12i | 1.12150i | ||||||||
\(250\) | 5.73890e11i | 0.587664i | ||||||||
\(251\) | 6.81635e11 | 0.684200 | 0.342100 | − | 0.939663i | \(-0.388862\pi\) | ||||
0.342100 | + | 0.939663i | \(0.388862\pi\) | |||||||
\(252\) | − | 3.81409e10i | − | 0.0375309i | ||||||
\(253\) | 7.77765e11 | − | 1.57298e11i | 0.750318 | − | 0.151747i | ||||
\(254\) | 1.32128e12 | 1.24975 | ||||||||
\(255\) | 2.79668e11i | 0.259384i | ||||||||
\(256\) | 6.87195e10 | 0.0625000 | ||||||||
\(257\) | −1.90164e12 | −1.69615 | −0.848074 | − | 0.529878i | \(-0.822238\pi\) | ||||
−0.848074 | + | 0.529878i | \(0.822238\pi\) | |||||||
\(258\) | 1.50557e12 | 1.31705 | ||||||||
\(259\) | − | 2.36117e11i | − | 0.202595i | ||||||
\(260\) | 1.02845e12i | 0.865600i | ||||||||
\(261\) | − | 5.79819e10i | − | 0.0478729i | ||||||
\(262\) | 5.92128e11 | 0.479633 | ||||||||
\(263\) | 4.55728e11i | 0.362182i | 0.983466 | + | 0.181091i | \(0.0579629\pi\) | ||||
−0.983466 | + | 0.181091i | \(0.942037\pi\) | |||||||
\(264\) | −9.31451e10 | − | 4.60559e11i | −0.0726341 | − | 0.359141i | ||||
\(265\) | −3.00926e11 | −0.230266 | ||||||||
\(266\) | − | 6.55355e11i | − | 0.492117i | ||||||
\(267\) | −9.97595e11 | −0.735187 | ||||||||
\(268\) | 3.00499e11 | 0.217354 | ||||||||
\(269\) | −8.28392e11 | −0.588131 | −0.294066 | − | 0.955785i | \(-0.595008\pi\) | ||||
−0.294066 | + | 0.955785i | \(0.595008\pi\) | |||||||
\(270\) | − | 1.09267e12i | − | 0.761503i | ||||||
\(271\) | 5.63086e11i | 0.385237i | 0.981274 | + | 0.192619i | \(0.0616980\pi\) | ||||
−0.981274 | + | 0.192619i | \(0.938302\pi\) | |||||||
\(272\) | − | 8.30082e10i | − | 0.0557540i | ||||||
\(273\) | −2.45689e12 | −1.62022 | ||||||||
\(274\) | 1.23813e12i | 0.801702i | ||||||||
\(275\) | 3.99960e11 | − | 8.08893e10i | 0.254304 | − | 0.0514313i | ||||
\(276\) | 6.35304e11 | 0.396676 | ||||||||
\(277\) | − | 2.02830e12i | − | 1.24375i | −0.783116 | − | 0.621876i | \(-0.786371\pi\) | ||
0.783116 | − | 0.621876i | \(-0.213629\pi\) | |||||||
\(278\) | 1.51132e12 | 0.910192 | ||||||||
\(279\) | 1.95669e11 | 0.115745 | ||||||||
\(280\) | −6.92050e11 | −0.402112 | ||||||||
\(281\) | 7.37475e11i | 0.420936i | 0.977601 | + | 0.210468i | \(0.0674987\pi\) | ||||
−0.977601 | + | 0.210468i | \(0.932501\pi\) | |||||||
\(282\) | 2.00220e12i | 1.12269i | ||||||||
\(283\) | 8.65033e11i | 0.476541i | 0.971199 | + | 0.238271i | \(0.0765805\pi\) | ||||
−0.971199 | + | 0.238271i | \(0.923419\pi\) | |||||||
\(284\) | 7.59248e11 | 0.410953 | ||||||||
\(285\) | 1.50180e12i | 0.798709i | ||||||||
\(286\) | −2.04581e12 | + | 4.13753e11i | −1.06914 | + | 0.216228i | ||||
\(287\) | −2.33438e12 | −1.19884 | ||||||||
\(288\) | − | 2.59421e10i | − | 0.0130931i | ||||||
\(289\) | 1.91573e12 | 0.950264 | ||||||||
\(290\) | −1.05206e12 | −0.512919 | ||||||||
\(291\) | −5.13520e11 | −0.246089 | ||||||||
\(292\) | − | 1.33837e12i | − | 0.630468i | ||||||
\(293\) | 3.62491e12i | 1.67865i | 0.543632 | + | 0.839324i | \(0.317049\pi\) | ||||
−0.543632 | + | 0.839324i | \(0.682951\pi\) | |||||||
\(294\) | − | 4.35840e10i | − | 0.0198422i | ||||||
\(295\) | 1.95385e11 | 0.0874544 | ||||||||
\(296\) | − | 1.60598e11i | − | 0.0706775i | ||||||
\(297\) | 2.17357e12 | − | 4.39590e11i | 0.940569 | − | 0.190224i | ||||
\(298\) | −1.98575e12 | −0.844976 | ||||||||
\(299\) | − | 2.82204e12i | − | 1.18088i | ||||||
\(300\) | 3.26700e11 | 0.134445 | ||||||||
\(301\) | 4.50025e12 | 1.82139 | ||||||||
\(302\) | 3.89781e11 | 0.155162 | ||||||||
\(303\) | − | 8.01881e11i | − | 0.313976i | ||||||
\(304\) | − | 4.45749e11i | − | 0.171681i | ||||||
\(305\) | − | 4.56554e12i | − | 1.72979i | ||||||
\(306\) | −3.13361e10 | −0.0116799 | ||||||||
\(307\) | − | 1.38783e12i | − | 0.508914i | −0.967084 | − | 0.254457i | \(-0.918103\pi\) | ||
0.967084 | − | 0.254457i | \(-0.0818967\pi\) | |||||||
\(308\) | −2.78416e11 | − | 1.37664e12i | −0.100448 | − | 0.496668i | ||||
\(309\) | 2.96855e12 | 1.05379 | ||||||||
\(310\) | − | 3.55033e12i | − | 1.24011i | ||||||
\(311\) | −4.20610e11 | −0.144570 | −0.0722849 | − | 0.997384i | \(-0.523029\pi\) | ||||
−0.0722849 | + | 0.997384i | \(0.523029\pi\) | |||||||
\(312\) | −1.67109e12 | −0.565232 | ||||||||
\(313\) | 3.50926e12 | 1.16814 | 0.584068 | − | 0.811705i | \(-0.301460\pi\) | ||||
0.584068 | + | 0.811705i | \(0.301460\pi\) | |||||||
\(314\) | 4.01541e12i | 1.31547i | ||||||||
\(315\) | 2.61253e11i | 0.0842383i | ||||||||
\(316\) | − | 1.95217e12i | − | 0.619557i | ||||||
\(317\) | −3.64129e12 | −1.13752 | −0.568760 | − | 0.822504i | \(-0.692577\pi\) | ||||
−0.568760 | + | 0.822504i | \(0.692577\pi\) | |||||||
\(318\) | − | 4.88962e11i | − | 0.150363i | ||||||
\(319\) | −4.23249e11 | − | 2.09277e12i | −0.128128 | − | 0.633531i | ||||
\(320\) | −4.70707e11 | −0.140282 | ||||||||
\(321\) | 7.97808e10i | 0.0234085i | ||||||||
\(322\) | 1.89896e12 | 0.548576 | ||||||||
\(323\) | −5.38432e11 | −0.153150 | ||||||||
\(324\) | 1.90766e12 | 0.534290 | ||||||||
\(325\) | − | 1.45121e12i | − | 0.400234i | ||||||
\(326\) | − | 3.75551e12i | − | 1.01996i | ||||||
\(327\) | 2.61218e11i | 0.0698657i | ||||||||
\(328\) | −1.58776e12 | −0.418231 | ||||||||
\(329\) | 5.98470e12i | 1.55261i | ||||||||
\(330\) | 6.38015e11 | + | 3.15468e12i | 0.163028 | + | 0.806095i | ||||
\(331\) | −1.46115e11 | −0.0367751 | −0.0183875 | − | 0.999831i | \(-0.505853\pi\) | ||||
−0.0183875 | + | 0.999831i | \(0.505853\pi\) | |||||||
\(332\) | 2.18244e12i | 0.541068i | ||||||||
\(333\) | −6.06268e10 | −0.0148062 | ||||||||
\(334\) | −4.52525e12 | −1.08870 | ||||||||
\(335\) | −2.05832e12 | −0.487853 | ||||||||
\(336\) | − | 1.12448e12i | − | 0.262577i | ||||||
\(337\) | − | 2.78713e12i | − | 0.641222i | −0.947211 | − | 0.320611i | \(-0.896112\pi\) | ||
0.947211 | − | 0.320611i | \(-0.103888\pi\) | |||||||
\(338\) | 4.30364e12i | 0.975557i | ||||||||
\(339\) | −4.71554e12 | −1.05325 | ||||||||
\(340\) | 5.68580e11i | 0.125140i | ||||||||
\(341\) | 7.06238e12 | − | 1.42832e12i | 1.53172 | − | 0.309780i | ||||
\(342\) | −1.68273e11 | −0.0359653 | ||||||||
\(343\) | 4.68113e12i | 0.986007i | ||||||||
\(344\) | 3.06091e12 | 0.635415 | ||||||||
\(345\) | −4.35163e12 | −0.890342 | ||||||||
\(346\) | −5.79882e12 | −1.16939 | ||||||||
\(347\) | 6.14272e12i | 1.22099i | 0.792019 | + | 0.610497i | \(0.209030\pi\) | ||||
−0.792019 | + | 0.610497i | \(0.790970\pi\) | |||||||
\(348\) | − | 1.70944e12i | − | 0.334933i | ||||||
\(349\) | 7.20268e12i | 1.39113i | 0.718464 | + | 0.695564i | \(0.244845\pi\) | ||||
−0.718464 | + | 0.695564i | \(0.755155\pi\) | |||||||
\(350\) | 9.76527e11 | 0.185928 | ||||||||
\(351\) | − | 7.88656e12i | − | 1.48031i | ||||||
\(352\) | −1.89369e11 | − | 9.36339e11i | −0.0350425 | − | 0.173269i | ||||
\(353\) | 1.08313e13 | 1.97610 | 0.988050 | − | 0.154133i | \(-0.0492585\pi\) | ||||
0.988050 | + | 0.154133i | \(0.0492585\pi\) | |||||||
\(354\) | 3.17474e11i | 0.0571073i | ||||||||
\(355\) | −5.20061e12 | −0.922386 | ||||||||
\(356\) | −2.02816e12 | −0.354693 | ||||||||
\(357\) | −1.35830e12 | −0.234236 | ||||||||
\(358\) | − | 1.85641e12i | − | 0.315689i | ||||||
\(359\) | 2.24946e12i | 0.377230i | 0.982051 | + | 0.188615i | \(0.0603998\pi\) | ||||
−0.982051 | + | 0.188615i | \(0.939600\pi\) | |||||||
\(360\) | 1.77695e11i | 0.0293875i | ||||||||
\(361\) | 3.23972e12 | 0.528411 | ||||||||
\(362\) | 1.01006e11i | 0.0162482i | ||||||||
\(363\) | −6.01868e12 | + | 2.53830e12i | −0.954922 | + | 0.402727i | ||||
\(364\) | −4.99499e12 | −0.781677 | ||||||||
\(365\) | 9.16744e12i | 1.41509i | ||||||||
\(366\) | 7.41836e12 | 1.12954 | ||||||||
\(367\) | 5.56623e12 | 0.836048 | 0.418024 | − | 0.908436i | \(-0.362723\pi\) | ||||
0.418024 | + | 0.908436i | \(0.362723\pi\) | |||||||
\(368\) | 1.29160e12 | 0.191377 | ||||||||
\(369\) | 5.99391e11i | 0.0876149i | ||||||||
\(370\) | 1.10005e12i | 0.158636i | ||||||||
\(371\) | − | 1.46154e12i | − | 0.207941i | ||||||
\(372\) | 5.76878e12 | 0.809784 | ||||||||
\(373\) | − | 1.04265e13i | − | 1.44409i | −0.691848 | − | 0.722043i | \(-0.743203\pi\) | ||
0.691848 | − | 0.722043i | \(-0.256797\pi\) | |||||||
\(374\) | −1.13103e12 | + | 2.28744e11i | −0.154567 | + | 0.0312602i | ||||
\(375\) | 6.38727e12 | 0.861310 | ||||||||
\(376\) | 4.07057e12i | 0.541647i | ||||||||
\(377\) | −7.59339e12 | −0.997078 | ||||||||
\(378\) | 5.30690e12 | 0.687673 | ||||||||
\(379\) | −4.96319e12 | −0.634695 | −0.317347 | − | 0.948309i | \(-0.602792\pi\) | ||||
−0.317347 | + | 0.948309i | \(0.602792\pi\) | |||||||
\(380\) | 3.05324e12i | 0.385339i | ||||||||
\(381\) | − | 1.47055e13i | − | 1.83170i | ||||||
\(382\) | − | 2.40854e12i | − | 0.296100i | ||||||
\(383\) | 1.63528e12 | 0.198426 | 0.0992128 | − | 0.995066i | \(-0.468368\pi\) | ||||
0.0992128 | + | 0.995066i | \(0.468368\pi\) | |||||||
\(384\) | − | 7.64833e11i | − | 0.0916032i | ||||||
\(385\) | 1.90707e12 | + | 9.42955e12i | 0.225456 | + | 1.11478i | ||||
\(386\) | −1.00314e13 | −1.17065 | ||||||||
\(387\) | − | 1.15551e12i | − | 0.133113i | ||||||
\(388\) | −1.04401e12 | −0.118726 | ||||||||
\(389\) | −6.16183e12 | −0.691769 | −0.345885 | − | 0.938277i | \(-0.612421\pi\) | ||||
−0.345885 | + | 0.938277i | \(0.612421\pi\) | |||||||
\(390\) | 1.14464e13 | 1.26867 | ||||||||
\(391\) | − | 1.56017e12i | − | 0.170721i | ||||||
\(392\) | − | 8.86086e10i | − | 0.00957294i | ||||||
\(393\) | − | 6.59026e12i | − | 0.702975i | ||||||
\(394\) | 3.57857e12 | 0.376902 | ||||||||
\(395\) | 1.33717e13i | 1.39060i | ||||||||
\(396\) | −3.53474e11 | + | 7.14880e10i | −0.0362979 | + | 0.00734103i | ||||
\(397\) | 2.98076e12 | 0.302255 | 0.151128 | − | 0.988514i | \(-0.451710\pi\) | ||||
0.151128 | + | 0.988514i | \(0.451710\pi\) | |||||||
\(398\) | − | 5.83405e11i | − | 0.0584191i | ||||||
\(399\) | −7.29396e12 | −0.721272 | ||||||||
\(400\) | 6.64198e11 | 0.0648631 | ||||||||
\(401\) | −1.19198e13 | −1.14960 | −0.574801 | − | 0.818293i | \(-0.694921\pi\) | ||||
−0.574801 | + | 0.818293i | \(0.694921\pi\) | |||||||
\(402\) | − | 3.34448e12i | − | 0.318566i | ||||||
\(403\) | − | 2.56251e13i | − | 2.41068i | ||||||
\(404\) | − | 1.63026e12i | − | 0.151479i | ||||||
\(405\) | −1.30669e13 | −1.19922 | ||||||||
\(406\) | − | 5.10963e12i | − | 0.463190i | ||||||
\(407\) | −2.18823e12 | + | 4.42556e11i | −0.195939 | + | 0.0396275i | ||||
\(408\) | −9.23863e11 | −0.0817159 | ||||||||
\(409\) | 1.01841e13i | 0.889825i | 0.895574 | + | 0.444913i | \(0.146765\pi\) | ||||
−0.895574 | + | 0.444913i | \(0.853235\pi\) | |||||||
\(410\) | 1.08757e13 | 0.938722 | ||||||||
\(411\) | 1.37801e13 | 1.17501 | ||||||||
\(412\) | 6.03522e12 | 0.508402 | ||||||||
\(413\) | 9.48948e11i | 0.0789755i | ||||||||
\(414\) | − | 4.87590e11i | − | 0.0400915i | ||||||
\(415\) | − | 1.49490e13i | − | 1.21443i | ||||||
\(416\) | −3.39741e12 | −0.272698 | ||||||||
\(417\) | − | 1.68207e13i | − | 1.33402i | ||||||
\(418\) | −6.07356e12 | + | 1.22834e12i | −0.475951 | + | 0.0962580i | ||||
\(419\) | −3.03014e12 | −0.234635 | −0.117317 | − | 0.993094i | \(-0.537429\pi\) | ||||
−0.117317 | + | 0.993094i | \(0.537429\pi\) | |||||||
\(420\) | 7.70237e12i | 0.589356i | ||||||||
\(421\) | 4.16824e12 | 0.315168 | 0.157584 | − | 0.987506i | \(-0.449630\pi\) | ||||
0.157584 | + | 0.987506i | \(0.449630\pi\) | |||||||
\(422\) | 7.91277e12 | 0.591244 | ||||||||
\(423\) | 1.53667e12 | 0.113469 | ||||||||
\(424\) | − | 9.94085e11i | − | 0.0725428i | ||||||
\(425\) | − | 8.02304e11i | − | 0.0578621i | ||||||
\(426\) | − | 8.45026e12i | − | 0.602313i | ||||||
\(427\) | 2.21739e13 | 1.56208 | ||||||||
\(428\) | 1.62198e11i | 0.0112935i | ||||||||
\(429\) | 4.60498e12 | + | 2.27695e13i | 0.316914 | + | 1.56699i | ||||
\(430\) | −2.09663e13 | −1.42619 | ||||||||
\(431\) | − | 4.31809e12i | − | 0.290339i | −0.989407 | − | 0.145169i | \(-0.953627\pi\) | ||
0.989407 | − | 0.145169i | \(-0.0463727\pi\) | |||||||
\(432\) | 3.60956e12 | 0.239903 | ||||||||
\(433\) | −2.01077e13 | −1.32106 | −0.660532 | − | 0.750798i | \(-0.729669\pi\) | ||||
−0.660532 | + | 0.750798i | \(0.729669\pi\) | |||||||
\(434\) | 1.72432e13 | 1.11988 | ||||||||
\(435\) | 1.17092e13i | 0.751760i | ||||||||
\(436\) | 5.31069e11i | 0.0337069i | ||||||||
\(437\) | − | 8.37799e12i | − | 0.525694i | ||||||
\(438\) | −1.48958e13 | −0.924045 | ||||||||
\(439\) | 2.02565e13i | 1.24234i | 0.783675 | + | 0.621172i | \(0.213343\pi\) | ||||
−0.783675 | + | 0.621172i | \(0.786657\pi\) | |||||||
\(440\) | 1.29712e12 | + | 6.41364e12i | 0.0786531 | + | 0.388903i | ||||
\(441\) | −3.34503e10 | −0.00200543 | ||||||||
\(442\) | 4.10382e12i | 0.243264i | ||||||||
\(443\) | −1.68372e13 | −0.986849 | −0.493424 | − | 0.869789i | \(-0.664255\pi\) | ||||
−0.493424 | + | 0.869789i | \(0.664255\pi\) | |||||||
\(444\) | −1.78742e12 | −0.103589 | ||||||||
\(445\) | 1.38923e13 | 0.796111 | ||||||||
\(446\) | 2.32081e13i | 1.31512i | ||||||||
\(447\) | 2.21010e13i | 1.23844i | ||||||||
\(448\) | − | 2.28613e12i | − | 0.126681i | ||||||
\(449\) | 1.27938e13 | 0.701080 | 0.350540 | − | 0.936548i | \(-0.385998\pi\) | ||||
0.350540 | + | 0.936548i | \(0.385998\pi\) | |||||||
\(450\) | − | 2.50739e11i | − | 0.0135881i | ||||||
\(451\) | 4.37536e12 | + | 2.16341e13i | 0.234494 | + | 1.15946i | ||||
\(452\) | −9.58692e12 | −0.508144 | ||||||||
\(453\) | − | 4.33817e12i | − | 0.227413i | ||||||
\(454\) | 3.03094e11 | 0.0157144 | ||||||||
\(455\) | 3.42141e13 | 1.75448 | ||||||||
\(456\) | −4.96109e12 | −0.251624 | ||||||||
\(457\) | 1.88575e13i | 0.946027i | 0.881055 | + | 0.473013i | \(0.156834\pi\) | ||||
−0.881055 | + | 0.473013i | \(0.843166\pi\) | |||||||
\(458\) | − | 1.88089e13i | − | 0.933331i | ||||||
\(459\) | − | 4.36009e12i | − | 0.214009i | ||||||
\(460\) | −8.84709e12 | −0.429548 | ||||||||
\(461\) | 2.51422e12i | 0.120753i | 0.998176 | + | 0.0603765i | \(0.0192301\pi\) | ||||
−0.998176 | + | 0.0603765i | \(0.980770\pi\) | |||||||
\(462\) | −1.53217e13 | + | 3.09871e12i | −0.727942 | + | 0.147222i | ||||
\(463\) | 2.99795e13 | 1.40903 | 0.704514 | − | 0.709690i | \(-0.251165\pi\) | ||||
0.704514 | + | 0.709690i | \(0.251165\pi\) | |||||||
\(464\) | − | 3.47539e12i | − | 0.161589i | ||||||
\(465\) | −3.95144e13 | −1.81757 | ||||||||
\(466\) | −2.44318e13 | −1.11180 | ||||||||
\(467\) | −3.48289e13 | −1.56803 | −0.784016 | − | 0.620740i | \(-0.786832\pi\) | ||||
−0.784016 | + | 0.620740i | \(0.786832\pi\) | |||||||
\(468\) | 1.28254e12i | 0.0571272i | ||||||||
\(469\) | − | 9.99687e12i | − | 0.440555i | ||||||
\(470\) | − | 2.78822e13i | − | 1.21573i | ||||||
\(471\) | 4.46906e13 | 1.92802 | ||||||||
\(472\) | 6.45440e11i | 0.0275515i | ||||||||
\(473\) | −8.43487e12 | − | 4.17065e13i | −0.356265 | − | 1.76156i | ||||
\(474\) | −2.17272e13 | −0.908054 | ||||||||
\(475\) | − | 4.30832e12i | − | 0.178172i | ||||||
\(476\) | −2.76148e12 | −0.113008 | ||||||||
\(477\) | −3.75274e11 | −0.0151970 | ||||||||
\(478\) | 2.88689e13 | 1.15688 | ||||||||
\(479\) | 3.01723e13i | 1.19655i | 0.801291 | + | 0.598275i | \(0.204147\pi\) | ||||
−0.801291 | + | 0.598275i | \(0.795853\pi\) | |||||||
\(480\) | 5.23887e12i | 0.205604i | ||||||||
\(481\) | 7.93977e12i | 0.308377i | ||||||||
\(482\) | 9.34230e12 | 0.359103 | ||||||||
\(483\) | − | 2.11350e13i | − | 0.804021i | ||||||
\(484\) | −1.22363e13 | + | 5.16050e12i | −0.460705 | + | 0.194296i | ||||
\(485\) | 7.15116e12 | 0.266482 | ||||||||
\(486\) | − | 2.83426e12i | − | 0.104534i | ||||||
\(487\) | 6.42921e12 | 0.234700 | 0.117350 | − | 0.993091i | \(-0.462560\pi\) | ||||
0.117350 | + | 0.993091i | \(0.462560\pi\) | |||||||
\(488\) | 1.50819e13 | 0.544950 | ||||||||
\(489\) | −4.17980e13 | −1.49490 | ||||||||
\(490\) | 6.06941e11i | 0.0214865i | ||||||||
\(491\) | − | 3.83365e13i | − | 1.34340i | −0.740823 | − | 0.671700i | \(-0.765564\pi\) | ||
0.740823 | − | 0.671700i | \(-0.234436\pi\) | |||||||
\(492\) | 1.76714e13i | 0.612980i | ||||||||
\(493\) | −4.19801e12 | −0.144148 | ||||||||
\(494\) | 2.20373e13i | 0.749071i | ||||||||
\(495\) | 2.42119e12 | − | 4.89670e11i | 0.0814710 | − | 0.0164770i | ||||
\(496\) | 1.17282e13 | 0.390683 | ||||||||
\(497\) | − | 2.52584e13i | − | 0.832958i | ||||||
\(498\) | 2.42901e13 | 0.793017 | ||||||||
\(499\) | 2.31289e13 | 0.747571 | 0.373785 | − | 0.927515i | \(-0.378060\pi\) | ||||
0.373785 | + | 0.927515i | \(0.378060\pi\) | |||||||
\(500\) | 1.29857e13 | 0.415541 | ||||||||
\(501\) | 5.03650e13i | 1.59566i | ||||||||
\(502\) | − | 1.54236e13i | − | 0.483803i | ||||||
\(503\) | − | 4.99365e13i | − | 1.55088i | −0.631421 | − | 0.775440i | \(-0.717528\pi\) | ||
0.631421 | − | 0.775440i | \(-0.282472\pi\) | |||||||
\(504\) | −8.63030e11 | −0.0265383 | ||||||||
\(505\) | 1.11668e13i | 0.339995i | ||||||||
\(506\) | −3.55925e12 | − | 1.75988e13i | −0.107301 | − | 0.530555i | ||||
\(507\) | 4.78986e13 | 1.42983 | ||||||||
\(508\) | − | 2.98970e13i | − | 0.883710i | ||||||
\(509\) | −4.05426e12 | −0.118665 | −0.0593325 | − | 0.998238i | \(-0.518897\pi\) | ||||
−0.0593325 | + | 0.998238i | \(0.518897\pi\) | |||||||
\(510\) | 6.32817e12 | 0.183412 | ||||||||
\(511\) | −4.45245e13 | −1.27789 | ||||||||
\(512\) | − | 1.55494e12i | − | 0.0441942i | ||||||
\(513\) | − | 2.34134e13i | − | 0.658988i | ||||||
\(514\) | 4.30293e13i | 1.19936i | ||||||||
\(515\) | −4.13394e13 | −1.14111 | ||||||||
\(516\) | − | 3.40672e13i | − | 0.931297i | ||||||
\(517\) | 5.54637e13 | − | 1.12172e13i | 1.50161 | − | 0.303690i | ||||
\(518\) | −5.34271e12 | −0.143256 | ||||||||
\(519\) | 6.45396e13i | 1.71391i | ||||||||
\(520\) | 2.32712e13 | 0.612071 | ||||||||
\(521\) | −4.97675e13 | −1.29645 | −0.648227 | − | 0.761447i | \(-0.724489\pi\) | ||||
−0.648227 | + | 0.761447i | \(0.724489\pi\) | |||||||
\(522\) | −1.31198e12 | −0.0338513 | ||||||||
\(523\) | − | 2.39051e13i | − | 0.610916i | −0.952206 | − | 0.305458i | \(-0.901190\pi\) | ||
0.952206 | − | 0.305458i | \(-0.0988095\pi\) | |||||||
\(524\) | − | 1.33983e13i | − | 0.339152i | ||||||
\(525\) | − | 1.08685e13i | − | 0.272505i | ||||||
\(526\) | 1.03119e13 | 0.256101 | ||||||||
\(527\) | − | 1.41669e13i | − | 0.348514i | ||||||
\(528\) | −1.04213e13 | + | 2.10763e12i | −0.253951 | + | 0.0513600i | ||||
\(529\) | −1.71504e13 | −0.413995 | ||||||||
\(530\) | 6.80918e12i | 0.162823i | ||||||||
\(531\) | 2.43658e11 | 0.00577176 | ||||||||
\(532\) | −1.48290e13 | −0.347979 | ||||||||
\(533\) | 7.84970e13 | 1.82481 | ||||||||
\(534\) | 2.25730e13i | 0.519856i | ||||||||
\(535\) | − | 1.11101e12i | − | 0.0253483i | ||||||
\(536\) | − | 6.79951e12i | − | 0.153693i | ||||||
\(537\) | −2.06615e13 | −0.462690 | ||||||||
\(538\) | 1.87444e13i | 0.415872i | ||||||||
\(539\) | −1.20734e12 | + | 2.44177e11i | −0.0265390 | + | 0.00536736i | ||||
\(540\) | −2.47244e13 | −0.538464 | ||||||||
\(541\) | 1.18234e13i | 0.255126i | 0.991830 | + | 0.127563i | \(0.0407155\pi\) | ||||
−0.991830 | + | 0.127563i | \(0.959285\pi\) | |||||||
\(542\) | 1.27412e13 | 0.272404 | ||||||||
\(543\) | 1.12418e12 | 0.0238142 | ||||||||
\(544\) | −1.87826e12 | −0.0394241 | ||||||||
\(545\) | − | 3.63766e12i | − | 0.0756553i | ||||||
\(546\) | 5.55931e13i | 1.14567i | ||||||||
\(547\) | 5.62806e13i | 1.14927i | 0.818410 | + | 0.574635i | \(0.194856\pi\) | ||||
−0.818410 | + | 0.574635i | \(0.805144\pi\) | |||||||
\(548\) | 2.80156e13 | 0.566889 | ||||||||
\(549\) | − | 5.69352e12i | − | 0.114161i | ||||||
\(550\) | −1.83032e12 | − | 9.05006e12i | −0.0363674 | − | 0.179820i | ||||
\(551\) | −2.25431e13 | −0.443869 | ||||||||
\(552\) | − | 1.43753e13i | − | 0.280492i | ||||||
\(553\) | −6.49439e13 | −1.25578 | ||||||||
\(554\) | −4.58953e13 | −0.879466 | ||||||||
\(555\) | 1.22433e13 | 0.232505 | ||||||||
\(556\) | − | 3.41973e13i | − | 0.643603i | ||||||
\(557\) | 3.46645e13i | 0.646561i | 0.946303 | + | 0.323280i | \(0.104786\pi\) | ||||
−0.946303 | + | 0.323280i | \(0.895214\pi\) | |||||||
\(558\) | − | 4.42749e12i | − | 0.0818439i | ||||||
\(559\) | −1.51328e14 | −2.77242 | ||||||||
\(560\) | 1.56593e13i | 0.284336i | ||||||||
\(561\) | 2.54587e12 | + | 1.25881e13i | 0.0458165 | + | 0.226541i | ||||
\(562\) | 1.66872e13 | 0.297647 | ||||||||
\(563\) | − | 3.45958e13i | − | 0.611619i | −0.952093 | − | 0.305810i | \(-0.901073\pi\) | ||
0.952093 | − | 0.305810i | \(-0.0989271\pi\) | |||||||
\(564\) | 4.53046e13 | 0.793865 | ||||||||
\(565\) | 6.56675e13 | 1.14053 | ||||||||
\(566\) | 1.95735e13 | 0.336966 | ||||||||
\(567\) | − | 6.34635e13i | − | 1.08295i | ||||||
\(568\) | − | 1.71798e13i | − | 0.290587i | ||||||
\(569\) | 6.14224e13i | 1.02983i | 0.857241 | + | 0.514915i | \(0.172177\pi\) | ||||
−0.857241 | + | 0.514915i | \(0.827823\pi\) | |||||||
\(570\) | 3.39819e13 | 0.564772 | ||||||||
\(571\) | 6.89157e13i | 1.13537i | 0.823246 | + | 0.567685i | \(0.192161\pi\) | ||||
−0.823246 | + | 0.567685i | \(0.807839\pi\) | |||||||
\(572\) | 9.36217e12 | + | 4.62915e13i | 0.152896 | + | 0.755999i | ||||
\(573\) | −2.68066e13 | −0.433978 | ||||||||
\(574\) | 5.28210e13i | 0.847710i | ||||||||
\(575\) | 1.24838e13 | 0.198613 | ||||||||
\(576\) | −5.87002e11 | −0.00925821 | ||||||||
\(577\) | −1.81704e13 | −0.284110 | −0.142055 | − | 0.989859i | \(-0.545371\pi\) | ||||
−0.142055 | + | 0.989859i | \(0.545371\pi\) | |||||||
\(578\) | − | 4.33479e13i | − | 0.671938i | ||||||
\(579\) | 1.11648e14i | 1.71576i | ||||||||
\(580\) | 2.38053e13i | 0.362689i | ||||||||
\(581\) | 7.26046e13 | 1.09669 | ||||||||
\(582\) | 1.16196e13i | 0.174011i | ||||||||
\(583\) | −1.35449e13 | + | 2.73938e12i | −0.201110 | + | 0.0406733i | ||||
\(584\) | −3.02839e13 | −0.445808 | ||||||||
\(585\) | − | 8.78504e12i | − | 0.128222i | ||||||
\(586\) | 8.20224e13 | 1.18698 | ||||||||
\(587\) | 4.08503e13 | 0.586145 | 0.293072 | − | 0.956090i | \(-0.405322\pi\) | ||||
0.293072 | + | 0.956090i | \(0.405322\pi\) | |||||||
\(588\) | −9.86194e11 | −0.0140306 | ||||||||
\(589\) | − | 7.60751e13i | − | 1.07316i | ||||||
\(590\) | − | 4.42106e12i | − | 0.0618396i | ||||||
\(591\) | − | 3.98287e13i | − | 0.552406i | ||||||
\(592\) | −3.63392e12 | −0.0499766 | ||||||||
\(593\) | 1.38480e13i | 0.188848i | 0.995532 | + | 0.0944241i | \(0.0301010\pi\) | ||||
−0.995532 | + | 0.0944241i | \(0.969899\pi\) | |||||||
\(594\) | −9.94679e12 | − | 4.91822e13i | −0.134509 | − | 0.665083i | ||||
\(595\) | 1.89153e13 | 0.253646 | ||||||||
\(596\) | 4.49325e13i | 0.597488i | ||||||||
\(597\) | −6.49317e12 | −0.0856219 | ||||||||
\(598\) | −6.38554e13 | −0.835010 | ||||||||
\(599\) | 6.05813e12 | 0.0785606 | 0.0392803 | − | 0.999228i | \(-0.487493\pi\) | ||||
0.0392803 | + | 0.999228i | \(0.487493\pi\) | |||||||
\(600\) | − | 7.39238e12i | − | 0.0950667i | ||||||
\(601\) | − | 4.32973e13i | − | 0.552190i | −0.961130 | − | 0.276095i | \(-0.910960\pi\) | ||
0.961130 | − | 0.276095i | \(-0.0890405\pi\) | |||||||
\(602\) | − | 1.01829e14i | − | 1.28792i | ||||||
\(603\) | −2.56686e12 | −0.0321970 | ||||||||
\(604\) | − | 8.81973e12i | − | 0.109716i | ||||||
\(605\) | 8.38148e13 | − | 3.53478e13i | 1.03405 | − | 0.436100i | ||||
\(606\) | −1.81445e13 | −0.222015 | ||||||||
\(607\) | − | 1.27913e13i | − | 0.155229i | −0.996983 | − | 0.0776144i | \(-0.975270\pi\) | ||
0.996983 | − | 0.0776144i | \(-0.0247303\pi\) | |||||||
\(608\) | −1.00861e13 | −0.121397 | ||||||||
\(609\) | −5.68691e13 | −0.678875 | ||||||||
\(610\) | −1.03306e14 | −1.22314 | ||||||||
\(611\) | − | 2.01244e14i | − | 2.36329i | ||||||
\(612\) | 7.09056e11i | 0.00825892i | ||||||||
\(613\) | 1.04340e13i | 0.120545i | 0.998182 | + | 0.0602726i | \(0.0191970\pi\) | ||||
−0.998182 | + | 0.0602726i | \(0.980803\pi\) | |||||||
\(614\) | −3.14030e13 | −0.359856 | ||||||||
\(615\) | − | 1.21044e14i | − | 1.37584i | ||||||
\(616\) | −3.11498e13 | + | 6.29985e12i | −0.351197 | + | 0.0710275i | ||||
\(617\) | 1.43404e14 | 1.60374 | 0.801870 | − | 0.597498i | \(-0.203838\pi\) | ||||
0.801870 | + | 0.597498i | \(0.203838\pi\) | |||||||
\(618\) | − | 6.71707e13i | − | 0.745139i | ||||||
\(619\) | 1.43785e14 | 1.58219 | 0.791097 | − | 0.611690i | \(-0.209510\pi\) | ||||
0.791097 | + | 0.611690i | \(0.209510\pi\) | |||||||
\(620\) | −8.03347e13 | −0.876890 | ||||||||
\(621\) | 6.78429e13 | 0.734592 | ||||||||
\(622\) | 9.51731e12i | 0.102226i | ||||||||
\(623\) | 6.74721e13i | 0.718926i | ||||||||
\(624\) | 3.78124e13i | 0.399679i | ||||||||
\(625\) | −1.13691e14 | −1.19214 | ||||||||
\(626\) | − | 7.94054e13i | − | 0.825997i | ||||||
\(627\) | 1.36712e13 | + | 6.75974e13i | 0.141081 | + | 0.697577i | ||||
\(628\) | 9.08583e13 | 0.930178 | ||||||||
\(629\) | 4.38951e12i | 0.0445823i | ||||||||
\(630\) | 5.91149e12 | 0.0595654 | ||||||||
\(631\) | 2.99445e13 | 0.299344 | 0.149672 | − | 0.988736i | \(-0.452178\pi\) | ||||
0.149672 | + | 0.988736i | \(0.452178\pi\) | |||||||
\(632\) | −4.41725e13 | −0.438093 | ||||||||
\(633\) | − | 8.80675e13i | − | 0.866557i | ||||||
\(634\) | 8.23930e13i | 0.804348i | ||||||||
\(635\) | 2.04786e14i | 1.98349i | ||||||||
\(636\) | −1.10640e13 | −0.106322 | ||||||||
\(637\) | 4.38070e12i | 0.0417683i | ||||||||
\(638\) | −4.73540e13 | + | 9.57704e12i | −0.447974 | + | 0.0906000i | ||||
\(639\) | −6.48550e12 | −0.0608750 | ||||||||
\(640\) | 1.06509e13i | 0.0991941i | ||||||||
\(641\) | −1.08076e14 | −0.998710 | −0.499355 | − | 0.866398i | \(-0.666430\pi\) | ||||
−0.499355 | + | 0.866398i | \(0.666430\pi\) | |||||||
\(642\) | 1.80523e12 | 0.0165523 | ||||||||
\(643\) | −1.19429e14 | −1.08656 | −0.543279 | − | 0.839552i | \(-0.682818\pi\) | ||||
−0.543279 | + | 0.839552i | \(0.682818\pi\) | |||||||
\(644\) | − | 4.29686e13i | − | 0.387902i | ||||||
\(645\) | 2.33350e14i | 2.09030i | ||||||||
\(646\) | 1.21833e13i | 0.108294i | ||||||||
\(647\) | −4.96569e13 | −0.437984 | −0.218992 | − | 0.975727i | \(-0.570277\pi\) | ||||
−0.218992 | + | 0.975727i | \(0.570277\pi\) | |||||||
\(648\) | − | 4.31655e13i | − | 0.377800i | ||||||
\(649\) | 8.79446e12 | − | 1.77862e12i | 0.0763811 | − | 0.0154476i | ||||
\(650\) | −3.28372e13 | −0.283008 | ||||||||
\(651\) | − | 1.91914e14i | − | 1.64135i | ||||||
\(652\) | −8.49776e13 | −0.721218 | ||||||||
\(653\) | 3.61478e11 | 0.00304450 | 0.00152225 | − | 0.999999i | \(-0.499515\pi\) | ||||
0.00152225 | + | 0.999999i | \(0.499515\pi\) | |||||||
\(654\) | 5.91068e12 | 0.0494025 | ||||||||
\(655\) | 9.17744e13i | 0.761229i | ||||||||
\(656\) | 3.59269e13i | 0.295734i | ||||||||
\(657\) | 1.14324e13i | 0.0933921i | ||||||||
\(658\) | 1.35418e14 | 1.09786 | ||||||||
\(659\) | 7.12158e13i | 0.572993i | 0.958081 | + | 0.286497i | \(0.0924907\pi\) | ||||
−0.958081 | + | 0.286497i | \(0.907509\pi\) | |||||||
\(660\) | 7.13824e13 | − | 1.44366e13i | 0.569995 | − | 0.115278i | ||||
\(661\) | 9.17572e12 | 0.0727165 | 0.0363583 | − | 0.999339i | \(-0.488424\pi\) | ||||
0.0363583 | + | 0.999339i | \(0.488424\pi\) | |||||||
\(662\) | 3.30619e12i | 0.0260039i | ||||||||
\(663\) | 4.56747e13 | 0.356540 | ||||||||
\(664\) | 4.93830e13 | 0.382593 | ||||||||
\(665\) | 1.01574e14 | 0.781042 | ||||||||
\(666\) | 1.37183e12i | 0.0104696i | ||||||||
\(667\) | − | 6.53210e13i | − | 0.494793i | ||||||
\(668\) | 1.02395e14i | 0.769830i | ||||||||
\(669\) | 2.58301e14 | 1.92751 | ||||||||
\(670\) | 4.65745e13i | 0.344964i | ||||||||
\(671\) | −4.15609e13 | − | 2.05499e14i | −0.305543 | − | 1.51077i | ||||
\(672\) | −2.54442e13 | −0.185670 | ||||||||
\(673\) | 5.08704e12i | 0.0368460i | 0.999830 | + | 0.0184230i | \(0.00586455\pi\) | ||||
−0.999830 | + | 0.0184230i | \(0.994135\pi\) | |||||||
\(674\) | −6.30656e13 | −0.453412 | ||||||||
\(675\) | 3.48877e13 | 0.248974 | ||||||||
\(676\) | 9.73803e13 | 0.689823 | ||||||||
\(677\) | 2.43029e13i | 0.170890i | 0.996343 | + | 0.0854448i | \(0.0272311\pi\) | ||||
−0.996343 | + | 0.0854448i | \(0.972769\pi\) | |||||||
\(678\) | 1.06700e14i | 0.744762i | ||||||||
\(679\) | 3.47318e13i | 0.240646i | ||||||||
\(680\) | 1.28655e13 | 0.0884875 | ||||||||
\(681\) | − | 3.37337e12i | − | 0.0230318i | ||||||
\(682\) | −3.23192e13 | − | 1.59803e14i | −0.219048 | − | 1.08309i | ||||
\(683\) | −9.28320e13 | −0.624589 | −0.312294 | − | 0.949985i | \(-0.601098\pi\) | ||||
−0.312294 | + | 0.949985i | \(0.601098\pi\) | |||||||
\(684\) | 3.80759e12i | 0.0254313i | ||||||||
\(685\) | −1.91898e14 | −1.27239 | ||||||||
\(686\) | 1.05922e14 | 0.697212 | ||||||||
\(687\) | −2.09339e14 | −1.36794 | ||||||||
\(688\) | − | 6.92604e13i | − | 0.449306i | ||||||
\(689\) | 4.91464e13i | 0.316516i | ||||||||
\(690\) | 9.84662e13i | 0.629567i | ||||||||
\(691\) | −1.42903e14 | −0.907092 | −0.453546 | − | 0.891233i | \(-0.649841\pi\) | ||||
−0.453546 | + | 0.891233i | \(0.649841\pi\) | |||||||
\(692\) | 1.31212e14i | 0.826883i | ||||||||
\(693\) | 2.37823e12 | + | 1.17592e13i | 0.0148795 | + | 0.0735721i | ||||
\(694\) | 1.38994e14 | 0.863373 | ||||||||
\(695\) | 2.34241e14i | 1.44457i | ||||||||
\(696\) | −3.86803e13 | −0.236834 | ||||||||
\(697\) | 4.33971e13 | 0.263814 | ||||||||
\(698\) | 1.62978e14 | 0.983676 | ||||||||
\(699\) | 2.71921e14i | 1.62951i | ||||||||
\(700\) | − | 2.20963e13i | − | 0.131471i | ||||||
\(701\) | 1.56090e14i | 0.922114i | 0.887371 | + | 0.461057i | \(0.152530\pi\) | ||||
−0.887371 | + | 0.461057i | \(0.847470\pi\) | |||||||
\(702\) | −1.78452e14 | −1.04674 | ||||||||
\(703\) | 2.35714e13i | 0.137280i | ||||||||
\(704\) | −2.11869e13 | + | 4.28493e12i | −0.122519 | + | 0.0247788i | ||||
\(705\) | −3.10322e14 | −1.78183 | ||||||||
\(706\) | − | 2.45085e14i | − | 1.39731i | ||||||
\(707\) | −5.42350e13 | −0.307031 | ||||||||
\(708\) | 7.18361e12 | 0.0403809 | ||||||||
\(709\) | 2.49375e14 | 1.39195 | 0.695973 | − | 0.718068i | \(-0.254973\pi\) | ||||
0.695973 | + | 0.718068i | \(0.254973\pi\) | |||||||
\(710\) | 1.17676e14i | 0.652225i | ||||||||
\(711\) | 1.66754e13i | 0.0917759i | ||||||||
\(712\) | 4.58921e13i | 0.250806i | ||||||||
\(713\) | 2.20436e14 | 1.19628 | ||||||||
\(714\) | 3.07347e13i | 0.165630i | ||||||||
\(715\) | −6.41279e13 | − | 3.17083e14i | −0.343176 | − | 1.69684i | ||||
\(716\) | −4.20059e13 | −0.223226 | ||||||||
\(717\) | − | 3.21304e14i | − | 1.69559i | ||||||
\(718\) | 5.08995e13 | 0.266742 | ||||||||
\(719\) | −2.40822e14 | −1.25329 | −0.626645 | − | 0.779305i | \(-0.715572\pi\) | ||||
−0.626645 | + | 0.779305i | \(0.715572\pi\) | |||||||
\(720\) | 4.02078e12 | 0.0207801 | ||||||||
\(721\) | − | 2.00777e14i | − | 1.03048i | ||||||
\(722\) | − | 7.33065e13i | − | 0.373643i | ||||||
\(723\) | − | 1.03978e14i | − | 0.526319i | ||||||
\(724\) | 2.28552e12 | 0.0114892 | ||||||||
\(725\) | − | 3.35908e13i | − | 0.167699i | ||||||
\(726\) | 5.74352e13 | + | 1.36187e14i | 0.284771 | + | 0.675232i | ||||
\(727\) | −1.27130e14 | −0.626003 | −0.313001 | − | 0.949753i | \(-0.601334\pi\) | ||||
−0.313001 | + | 0.949753i | \(0.601334\pi\) | |||||||
\(728\) | 1.13024e14i | 0.552729i | ||||||||
\(729\) | 1.88466e14 | 0.915369 | ||||||||
\(730\) | 2.07436e14 | 1.00062 | ||||||||
\(731\) | −8.36615e13 | −0.400810 | ||||||||
\(732\) | − | 1.67858e14i | − | 0.798707i | ||||||
\(733\) | 8.33489e13i | 0.393895i | 0.980414 | + | 0.196947i | \(0.0631028\pi\) | ||||
−0.980414 | + | 0.196947i | \(0.936897\pi\) | |||||||
\(734\) | − | 1.25949e14i | − | 0.591175i | ||||||
\(735\) | 6.75512e12 | 0.0314917 | ||||||||
\(736\) | − | 2.92257e13i | − | 0.135324i | ||||||
\(737\) | −9.26469e13 | + | 1.87373e13i | −0.426082 | + | 0.0861724i | ||||
\(738\) | 1.35627e13 | 0.0619531 | ||||||||
\(739\) | − | 2.51503e14i | − | 1.14109i | −0.821265 | − | 0.570547i | \(-0.806731\pi\) | ||
0.821265 | − | 0.570547i | \(-0.193269\pi\) | |||||||
\(740\) | 2.48912e13 | 0.112173 | ||||||||
\(741\) | 2.45270e14 | 1.09788 | ||||||||
\(742\) | −3.30708e13 | −0.147037 | ||||||||
\(743\) | − | 1.36480e14i | − | 0.602733i | −0.953508 | − | 0.301366i | \(-0.902557\pi\) | ||
0.953508 | − | 0.301366i | \(-0.0974427\pi\) | |||||||
\(744\) | − | 1.30533e14i | − | 0.572604i | ||||||
\(745\) | − | 3.07774e14i | − | 1.34107i | ||||||
\(746\) | −2.35924e14 | −1.02112 | ||||||||
\(747\) | − | 1.86424e13i | − | 0.0801492i | ||||||
\(748\) | 5.17588e12 | + | 2.55923e13i | 0.0221043 | + | 0.109295i | ||||
\(749\) | 5.39595e12 | 0.0228907 | ||||||||
\(750\) | − | 1.44528e14i | − | 0.609038i | ||||||
\(751\) | 2.73472e14 | 1.14476 | 0.572378 | − | 0.819990i | \(-0.306021\pi\) | ||||
0.572378 | + | 0.819990i | \(0.306021\pi\) | |||||||
\(752\) | 9.21065e13 | 0.383002 | ||||||||
\(753\) | −1.71662e14 | −0.709086 | ||||||||
\(754\) | 1.71819e14i | 0.705041i | ||||||||
\(755\) | 6.04124e13i | 0.246259i | ||||||||
\(756\) | − | 1.20081e14i | − | 0.486258i | ||||||
\(757\) | 3.59616e14 | 1.44664 | 0.723319 | − | 0.690514i | \(-0.242616\pi\) | ||||
0.723319 | + | 0.690514i | \(0.242616\pi\) | |||||||
\(758\) | 1.12304e14i | 0.448797i | ||||||||
\(759\) | −1.95871e14 | + | 3.96136e13i | −0.777608 | + | 0.157266i | ||||
\(760\) | 6.90869e13 | 0.272476 | ||||||||
\(761\) | 3.97670e14i | 1.55812i | 0.626952 | + | 0.779058i | \(0.284302\pi\) | ||||
−0.626952 | + | 0.779058i | \(0.715698\pi\) | |||||||
\(762\) | −3.32748e14 | −1.29521 | ||||||||
\(763\) | 1.76674e13 | 0.0683203 | ||||||||
\(764\) | −5.44991e13 | −0.209374 | ||||||||
\(765\) | − | 4.85681e12i | − | 0.0185372i | ||||||
\(766\) | − | 3.70021e13i | − | 0.140308i | ||||||
\(767\) | − | 3.19098e13i | − | 0.120212i | ||||||
\(768\) | −1.73062e13 | −0.0647732 | ||||||||
\(769\) | 3.87504e14i | 1.44093i | 0.693489 | + | 0.720467i | \(0.256072\pi\) | ||||
−0.693489 | + | 0.720467i | \(0.743928\pi\) | |||||||
\(770\) | 2.13366e14 | − | 4.31520e13i | 0.788265 | − | 0.159422i | ||||
\(771\) | 4.78907e14 | 1.75784 | ||||||||
\(772\) | 2.26985e14i | 0.827774i | ||||||||
\(773\) | 1.63408e13 | 0.0592072 | 0.0296036 | − | 0.999562i | \(-0.490576\pi\) | ||||
0.0296036 | + | 0.999562i | \(0.490576\pi\) | |||||||
\(774\) | −2.61463e13 | −0.0941249 | ||||||||
\(775\) | 1.13358e14 | 0.405454 | ||||||||
\(776\) | 2.36233e13i | 0.0839522i | ||||||||
\(777\) | 5.94632e13i | 0.209963i | ||||||||
\(778\) | 1.39426e14i | 0.489155i | ||||||||
\(779\) | 2.33040e14 | 0.812350 | ||||||||
\(780\) | − | 2.59003e14i | − | 0.897083i | ||||||
\(781\) | −2.34084e14 | + | 4.73420e13i | −0.805595 | + | 0.162926i | ||||
\(782\) | −3.53025e13 | −0.120718 | ||||||||
\(783\) | − | 1.82548e14i | − | 0.620253i | ||||||
\(784\) | −2.00498e12 | −0.00676909 | ||||||||
\(785\) | −6.22351e14 | −2.08779 | ||||||||
\(786\) | −1.49121e14 | −0.497078 | ||||||||
\(787\) | 1.35627e14i | 0.449233i | 0.974447 | + | 0.224616i | \(0.0721129\pi\) | ||||
−0.974447 | + | 0.224616i | \(0.927887\pi\) | |||||||
\(788\) | − | 8.09737e13i | − | 0.266510i | ||||||
\(789\) | − | 1.14770e14i | − | 0.375355i | ||||||
\(790\) | 3.02568e14 | 0.983303 | ||||||||
\(791\) | 3.18934e14i | 1.02996i | ||||||||
\(792\) | 1.61759e12 | + | 7.99821e12i | 0.00519089 | + | 0.0256665i | ||||
\(793\) | −7.45631e14 | −2.37771 | ||||||||
\(794\) | − | 6.74468e13i | − | 0.213727i | ||||||
\(795\) | 7.57847e13 | 0.238641 | ||||||||
\(796\) | −1.32009e13 | −0.0413085 | ||||||||
\(797\) | 2.16092e14 | 0.671965 | 0.335983 | − | 0.941868i | \(-0.390932\pi\) | ||||
0.335983 | + | 0.941868i | \(0.390932\pi\) | |||||||
\(798\) | 1.65043e14i | 0.510016i | ||||||||
\(799\) | − | 1.11258e14i | − | 0.341663i | ||||||
\(800\) | − | 1.50291e13i | − | 0.0458652i | ||||||
\(801\) | 1.73246e13 | 0.0525412 | ||||||||
\(802\) | 2.69715e14i | 0.812892i | ||||||||
\(803\) | 8.34527e13 | + | 4.12635e14i | 0.249956 | + | 1.23591i | ||||
\(804\) | −7.56770e13 | −0.225260 | ||||||||
\(805\) | 2.94322e14i | 0.870648i | ||||||||
\(806\) | −5.79830e14 | −1.70461 | ||||||||
\(807\) | 2.08621e14 | 0.609522 | ||||||||
\(808\) | −3.68887e13 | −0.107112 | ||||||||
\(809\) | − | 4.08529e14i | − | 1.17891i | −0.807802 | − | 0.589455i | \(-0.799343\pi\) | ||
0.807802 | − | 0.589455i | \(-0.200657\pi\) | |||||||
\(810\) | 2.95671e14i | 0.847975i | ||||||||
\(811\) | 2.05159e14i | 0.584773i | 0.956300 | + | 0.292386i | \(0.0944493\pi\) | ||||
−0.956300 | + | 0.292386i | \(0.905551\pi\) | |||||||
\(812\) | −1.15618e14 | −0.327525 | ||||||||
\(813\) | − | 1.41807e14i | − | 0.399249i | ||||||
\(814\) | 1.00139e13 | + | 4.95140e13i | 0.0280208 | + | 0.138550i | ||||
\(815\) | 5.82070e14 | 1.61878 | ||||||||
\(816\) | 2.09046e13i | 0.0577819i | ||||||||
\(817\) | −4.49257e14 | −1.23420 | ||||||||
\(818\) | 2.30439e14 | 0.629201 | ||||||||
\(819\) | 4.26672e13 | 0.115791 | ||||||||
\(820\) | − | 2.46088e14i | − | 0.663777i | ||||||
\(821\) | − | 3.42794e14i | − | 0.919004i | −0.888177 | − | 0.459502i | \(-0.848028\pi\) | ||
0.888177 | − | 0.459502i | \(-0.151972\pi\) | |||||||
\(822\) | − | 3.11808e14i | − | 0.830861i | ||||||
\(823\) | 1.71647e14 | 0.454607 | 0.227304 | − | 0.973824i | \(-0.427009\pi\) | ||||
0.227304 | + | 0.973824i | \(0.427009\pi\) | |||||||
\(824\) | − | 1.36561e14i | − | 0.359494i | ||||||
\(825\) | −1.00725e14 | + | 2.03710e13i | −0.263553 | + | 0.0533020i | ||||
\(826\) | 2.14722e13 | 0.0558441 | ||||||||
\(827\) | 4.14254e14i | 1.07088i | 0.844574 | + | 0.535438i | \(0.179853\pi\) | ||||
−0.844574 | + | 0.535438i | \(0.820147\pi\) | |||||||
\(828\) | −1.10329e13 | −0.0283490 | ||||||||
\(829\) | −2.65366e14 | −0.677754 | −0.338877 | − | 0.940831i | \(-0.610047\pi\) | ||||
−0.338877 | + | 0.940831i | \(0.610047\pi\) | |||||||
\(830\) | −3.38258e14 | −0.858733 | ||||||||
\(831\) | 5.10804e14i | 1.28899i | ||||||||
\(832\) | 7.68746e13i | 0.192826i | ||||||||
\(833\) | 2.42187e12i | 0.00603847i | ||||||||
\(834\) | −3.80608e14 | −0.943296 | ||||||||
\(835\) | − | 7.01372e14i | − | 1.72789i | ||||||
\(836\) | 2.77942e13 | + | 1.37429e14i | 0.0680647 | + | 0.336548i | ||||
\(837\) | 6.16037e14 | 1.49961 | ||||||||
\(838\) | 6.85642e13i | 0.165912i | ||||||||
\(839\) | 7.27443e14 | 1.74980 | 0.874902 | − | 0.484301i | \(-0.160926\pi\) | ||||
0.874902 | + | 0.484301i | \(0.160926\pi\) | |||||||
\(840\) | 1.74285e14 | 0.416738 | ||||||||
\(841\) | 2.44945e14 | 0.582222 | ||||||||
\(842\) | − | 9.43164e13i | − | 0.222857i | ||||||
\(843\) | − | 1.85724e14i | − | 0.436246i | ||||||
\(844\) | − | 1.79046e14i | − | 0.418072i | ||||||
\(845\) | −6.67025e14 | −1.54831 | ||||||||
\(846\) | − | 3.47708e13i | − | 0.0802349i | ||||||
\(847\) | 1.71677e14 | + | 4.07072e14i | 0.393819 | + | 0.933800i | ||||
\(848\) | −2.24936e13 | −0.0512955 | ||||||||
\(849\) | − | 2.17848e14i | − | 0.493874i | ||||||
\(850\) | −1.81541e13 | −0.0409147 | ||||||||
\(851\) | −6.83006e13 | −0.153030 | ||||||||
\(852\) | −1.91208e14 | −0.425900 | ||||||||
\(853\) | 6.89970e14i | 1.52786i | 0.645297 | + | 0.763932i | \(0.276734\pi\) | ||||
−0.645297 | + | 0.763932i | \(0.723266\pi\) | |||||||
\(854\) | − | 5.01739e14i | − | 1.10456i | ||||||
\(855\) | − | 2.60808e13i | − | 0.0570808i | ||||||
\(856\) | 3.67013e12 | 0.00798569 | ||||||||
\(857\) | − | 3.82753e14i | − | 0.827970i | −0.910284 | − | 0.413985i | \(-0.864137\pi\) | ||
0.910284 | − | 0.413985i | \(-0.135863\pi\) | |||||||
\(858\) | 5.15214e14 | − | 1.04199e14i | 1.10803 | − | 0.224092i | ||||
\(859\) | −3.58849e14 | −0.767267 | −0.383633 | − | 0.923485i | \(-0.625327\pi\) | ||||
−0.383633 | + | 0.923485i | \(0.625327\pi\) | |||||||
\(860\) | 4.74412e14i | 1.00847i | ||||||||
\(861\) | 5.87887e14 | 1.24245 | ||||||||
\(862\) | −9.77072e13 | −0.205301 | ||||||||
\(863\) | 3.80616e14 | 0.795121 | 0.397560 | − | 0.917576i | \(-0.369857\pi\) | ||||
0.397560 | + | 0.917576i | \(0.369857\pi\) | |||||||
\(864\) | − | 8.16750e13i | − | 0.169637i | ||||||
\(865\) | − | 8.98763e14i | − | 1.85594i | ||||||
\(866\) | 4.54986e14i | 0.934133i | ||||||||
\(867\) | −4.82453e14 | −0.984826 | ||||||||
\(868\) | − | 3.90170e14i | − | 0.791873i | ||||||
\(869\) | 1.21725e14 | + | 6.01873e14i | 0.245630 | + | 1.21452i | ||||
\(870\) | 2.64948e14 | 0.531575 | ||||||||
\(871\) | 3.36160e14i | 0.670586i | ||||||||
\(872\) | 1.20167e13 | 0.0238344 | ||||||||
\(873\) | 8.91796e12 | 0.0175871 | ||||||||
\(874\) | −1.89572e14 | −0.371721 | ||||||||
\(875\) | − | 4.32002e14i | − | 0.842258i | ||||||
\(876\) | 3.37054e14i | 0.653399i | ||||||||
\(877\) | − | 2.05434e14i | − | 0.395980i | −0.980204 | − | 0.197990i | \(-0.936559\pi\) | ||
0.980204 | − | 0.197990i | \(-0.0634414\pi\) | |||||||
\(878\) | 4.58352e14 | 0.878469 | ||||||||
\(879\) | − | 9.12892e14i | − | 1.73970i | ||||||
\(880\) | 1.45124e14 | − | 2.93504e13i | 0.274996 | − | 0.0556161i | ||||
\(881\) | −5.81723e14 | −1.09607 | −0.548033 | − | 0.836457i | \(-0.684623\pi\) | ||||
−0.548033 | + | 0.836457i | \(0.684623\pi\) | |||||||
\(882\) | 7.56895e11i | 0.00141805i | ||||||||
\(883\) | 9.09212e13 | 0.169380 | 0.0846899 | − | 0.996407i | \(-0.473010\pi\) | ||||
0.0846899 | + | 0.996407i | \(0.473010\pi\) | |||||||
\(884\) | 9.28590e13 | 0.172013 | ||||||||
\(885\) | −4.92055e13 | −0.0906353 | ||||||||
\(886\) | 3.80982e14i | 0.697807i | ||||||||
\(887\) | − | 6.57821e14i | − | 1.19809i | −0.800715 | − | 0.599045i | \(-0.795547\pi\) | ||
0.800715 | − | 0.599045i | \(-0.204453\pi\) | |||||||
\(888\) | 4.04447e13i | 0.0732482i | ||||||||
\(889\) | −9.94603e14 | −1.79119 | ||||||||
\(890\) | − | 3.14346e14i | − | 0.562935i | ||||||
\(891\) | −5.88153e14 | + | 1.18950e14i | −1.04737 | + | 0.211825i | ||||
\(892\) | 5.25139e14 | 0.929930 | ||||||||
\(893\) | − | 5.97449e14i | − | 1.05207i | ||||||
\(894\) | 5.00089e14 | 0.875708 | ||||||||
\(895\) | 2.87727e14 | 0.501032 | ||||||||
\(896\) | −5.17293e13 | −0.0895770 | ||||||||
\(897\) | 7.10697e14i | 1.22383i | ||||||||
\(898\) | − | 2.89491e14i | − | 0.495739i | ||||||
\(899\) | − | 5.93138e14i | − | 1.01008i | ||||||
\(900\) | −5.67358e12 | −0.00960826 | ||||||||
\(901\) | 2.71706e13i | 0.0457589i | ||||||||
\(902\) | 4.89524e14 | − | 9.90031e13i | 0.819862 | − | 0.165812i | ||||
\(903\) | −1.13333e15 | −1.88764 | ||||||||
\(904\) | 2.16927e14i | 0.359312i | ||||||||
\(905\) | −1.56551e13 | −0.0257877 | ||||||||
\(906\) | −9.81617e13 | −0.160806 | ||||||||
\(907\) | −1.02388e12 | −0.00166806 | −0.000834032 | − | 1.00000i | \(-0.500265\pi\) | ||||
−0.000834032 | 1.00000i | \(0.500265\pi\) | ||||||||
\(908\) | − | 6.85824e12i | − | 0.0111118i | ||||||
\(909\) | 1.39257e13i | 0.0224387i | ||||||||
\(910\) | − | 7.74177e14i | − | 1.24060i | ||||||
\(911\) | 5.93081e14 | 0.945196 | 0.472598 | − | 0.881278i | \(-0.343316\pi\) | ||||
0.472598 | + | 0.881278i | \(0.343316\pi\) | |||||||
\(912\) | 1.12257e14i | 0.177925i | ||||||||
\(913\) | −1.36084e14 | − | 6.72870e14i | −0.214512 | − | 1.06066i | ||||
\(914\) | 4.26697e14 | 0.668942 | ||||||||
\(915\) | 1.14978e15i | 1.79270i | ||||||||
\(916\) | −4.25597e14 | −0.659965 | ||||||||
\(917\) | −4.45731e14 | −0.687426 | ||||||||
\(918\) | −9.86575e13 | −0.151327 | ||||||||
\(919\) | − | 1.69820e14i | − | 0.259067i | −0.991575 | − | 0.129533i | \(-0.958652\pi\) | ||
0.991575 | − | 0.129533i | \(-0.0413479\pi\) | |||||||
\(920\) | 2.00187e14i | 0.303736i | ||||||||
\(921\) | 3.49508e14i | 0.527424i | ||||||||
\(922\) | 5.68903e13 | 0.0853853 | ||||||||
\(923\) | 8.49350e14i | 1.26788i | ||||||||
\(924\) | 7.01159e13 | + | 3.46690e14i | 0.104101 | + | 0.514733i | ||||
\(925\) | −3.51231e13 | −0.0518662 | ||||||||
\(926\) | − | 6.78359e14i | − | 0.996334i | ||||||
\(927\) | −5.15528e13 | −0.0753102 | ||||||||
\(928\) | −7.86390e13 | −0.114261 | ||||||||
\(929\) | 4.28073e14 | 0.618642 | 0.309321 | − | 0.950958i | \(-0.399898\pi\) | ||||
0.309321 | + | 0.950958i | \(0.399898\pi\) | |||||||
\(930\) | 8.94108e14i | 1.28521i | ||||||||
\(931\) | 1.30053e13i | 0.0185940i | ||||||||
\(932\) | 5.52829e14i | 0.786160i | ||||||||
\(933\) | 1.05926e14 | 0.149828 | ||||||||
\(934\) | 7.88088e14i | 1.10877i | ||||||||
\(935\) | −3.54532e13 | − | 1.75299e14i | −0.0496132 | − | 0.245314i | ||||
\(936\) | 2.90207e13 | 0.0403951 | ||||||||
\(937\) | 4.66801e14i | 0.646299i | 0.946348 | + | 0.323150i | \(0.104742\pi\) | ||||
−0.946348 | + | 0.323150i | \(0.895258\pi\) | |||||||
\(938\) | −2.26203e14 | −0.311519 | ||||||||
\(939\) | −8.83765e14 | −1.21062 | ||||||||
\(940\) | −6.30901e14 | −0.859651 | ||||||||
\(941\) | 8.81140e14i | 1.19425i | 0.802147 | + | 0.597127i | \(0.203691\pi\) | ||||
−0.802147 | + | 0.597127i | \(0.796309\pi\) | |||||||
\(942\) | − | 1.01123e15i | − | 1.36332i | ||||||
\(943\) | 6.75258e14i | 0.905548i | ||||||||
\(944\) | 1.46046e13 | 0.0194819 | ||||||||
\(945\) | 8.22521e14i | 1.09141i | ||||||||
\(946\) | −9.43710e14 | + | 1.90859e14i | −1.24561 | + | 0.251917i | ||||
\(947\) | −7.52110e13 | −0.0987487 | −0.0493743 | − | 0.998780i | \(-0.515723\pi\) | ||||
−0.0493743 | + | 0.998780i | \(0.515723\pi\) | |||||||
\(948\) | 4.91630e14i | 0.642091i | ||||||||
\(949\) | 1.49720e15 | 1.94513 | ||||||||
\(950\) | −9.74862e13 | −0.125987 | ||||||||
\(951\) | 9.17016e14 | 1.17889 | ||||||||
\(952\) | 6.24852e13i | 0.0799084i | ||||||||
\(953\) | − | 5.01720e12i | − | 0.00638259i | −0.999995 | − | 0.00319129i | \(-0.998984\pi\) | ||
0.999995 | − | 0.00319129i | \(-0.00101582\pi\) | |||||||
\(954\) | 8.49148e12i | 0.0107459i | ||||||||
\(955\) | 3.73302e14 | 0.469941 | ||||||||
\(956\) | − | 6.53228e14i | − | 0.818041i | ||||||
\(957\) | 1.06590e14 | + | 5.27039e14i | 0.132788 | + | 0.656574i | ||||
\(958\) | 6.82721e14 | 0.846089 | ||||||||
\(959\) | − | 9.32014e14i | − | 1.14902i | ||||||
\(960\) | 1.18542e14 | 0.145384 | ||||||||
\(961\) | 1.18201e15 | 1.44213 | ||||||||
\(962\) | 1.79656e14 | 0.218056 | ||||||||
\(963\) | − | 1.38550e12i | − | 0.00167292i | ||||||
\(964\) | − | 2.11392e14i | − | 0.253924i | ||||||
\(965\) | − | 1.55478e15i | − | 1.85794i | ||||||
\(966\) | −4.78231e14 | −0.568529 | ||||||||
\(967\) | 8.51010e14i | 1.00647i | 0.864149 | + | 0.503237i | \(0.167858\pi\) | ||||
−0.864149 | + | 0.503237i | \(0.832142\pi\) | |||||||
\(968\) | 1.16769e14 | + | 2.76875e14i | 0.137388 | + | 0.325767i | ||||
\(969\) | 1.35598e14 | 0.158721 | ||||||||
\(970\) | − | 1.61812e14i | − | 0.188431i | ||||||
\(971\) | −4.07930e14 | −0.472595 | −0.236298 | − | 0.971681i | \(-0.575934\pi\) | ||||
−0.236298 | + | 0.971681i | \(0.575934\pi\) | |||||||
\(972\) | −6.41321e13 | −0.0739169 | ||||||||
\(973\) | −1.13766e15 | −1.30452 | ||||||||
\(974\) | − | 1.45476e14i | − | 0.165958i | ||||||
\(975\) | 3.65471e14i | 0.414791i | ||||||||
\(976\) | − | 3.41264e14i | − | 0.385338i | ||||||
\(977\) | −5.75540e13 | −0.0646551 | −0.0323275 | − | 0.999477i | \(-0.510292\pi\) | ||||
−0.0323275 | + | 0.999477i | \(0.510292\pi\) | |||||||
\(978\) | 9.45782e14i | 1.05705i | ||||||||
\(979\) | 6.25304e14 | − | 1.26464e14i | 0.695309 | − | 0.140622i | ||||
\(980\) | 1.37335e13 | 0.0151933 | ||||||||
\(981\) | − | 4.53639e12i | − | 0.00499305i | ||||||
\(982\) | −8.67457e14 | −0.949927 | ||||||||
\(983\) | −1.78324e15 | −1.94286 | −0.971429 | − | 0.237329i | \(-0.923728\pi\) | ||||
−0.971429 | + | 0.237329i | \(0.923728\pi\) | |||||||
\(984\) | 3.99859e14 | 0.433442 | ||||||||
\(985\) | 5.54645e14i | 0.598183i | ||||||||
\(986\) | 9.49902e13i | 0.101928i | ||||||||
\(987\) | − | 1.50718e15i | − | 1.60908i | ||||||
\(988\) | 4.98647e14 | 0.529674 | ||||||||
\(989\) | − | 1.30177e15i | − | 1.37579i | ||||||
\(990\) | −1.10800e13 | − | 5.47853e13i | −0.0116510 | − | 0.0576087i | ||||
\(991\) | 1.91671e14 | 0.200534 | 0.100267 | − | 0.994961i | \(-0.468030\pi\) | ||||
0.100267 | + | 0.994961i | \(0.468030\pi\) | |||||||
\(992\) | − | 2.65380e14i | − | 0.276254i | ||||||
\(993\) | 3.67972e13 | 0.0381126 | ||||||||
\(994\) | −5.71531e14 | −0.588990 | ||||||||
\(995\) | 9.04224e13 | 0.0927172 | ||||||||
\(996\) | − | 5.49622e14i | − | 0.560748i | ||||||
\(997\) | 6.76413e14i | 0.686651i | 0.939217 | + | 0.343325i | \(0.111553\pi\) | ||||
−0.939217 | + | 0.343325i | \(0.888447\pi\) | |||||||
\(998\) | − | 5.23347e14i | − | 0.528612i | ||||||
\(999\) | −1.90875e14 | −0.191832 |
(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 | 22.11.b.a.21.2 | ✓ | 10 | |
3.2 | odd | 2 | 198.11.d.a.109.6 | 10 | |||
4.3 | odd | 2 | 176.11.h.e.65.7 | 10 | |||
11.10 | odd | 2 | inner | 22.11.b.a.21.7 | yes | 10 | |
33.32 | even | 2 | 198.11.d.a.109.1 | 10 | |||
44.43 | even | 2 | 176.11.h.e.65.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.11.b.a.21.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
22.11.b.a.21.7 | yes | 10 | 11.10 | odd | 2 | inner | |
176.11.h.e.65.7 | 10 | 4.3 | odd | 2 | |||
176.11.h.e.65.8 | 10 | 44.43 | even | 2 | |||
198.11.d.a.109.1 | 10 | 33.32 | even | 2 | |||
198.11.d.a.109.6 | 10 | 3.2 | odd | 2 |