Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,11,Mod(51,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.51");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.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: | \(63.5357252674\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 199481 x^{18} + 16413464051 x^{16} + 725560177607766 x^{14} + \cdots + 21\!\cdots\!25 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{97}\cdot 3^{4}\cdot 5^{29} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 51.17 | ||
Root | \(-68.5823i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 100.51 |
Dual form | 100.11.b.e.51.18 |
$q$-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 \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 29.9163 | − | 11.3585i | 0.934885 | − | 0.354952i | ||||
\(3\) | − | 137.165i | − | 0.564463i | −0.959346 | − | 0.282232i | \(-0.908925\pi\) | ||
0.959346 | − | 0.282232i | \(-0.0910747\pi\) | |||||||
\(4\) | 765.971 | − | 679.606i | 0.748018 | − | 0.663678i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1557.98 | − | 4103.46i | −0.200357 | − | 0.527708i | ||||
\(7\) | − | 24910.8i | − | 1.48217i | −0.671413 | − | 0.741084i | \(-0.734312\pi\) | ||
0.671413 | − | 0.741084i | \(-0.265688\pi\) | |||||||
\(8\) | 15195.7 | − | 29031.6i | 0.463737 | − | 0.885973i | ||||
\(9\) | 40234.9 | 0.681381 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 11312.4i | − | 0.0702410i | −0.999383 | − | 0.0351205i | \(-0.988818\pi\) | ||
0.999383 | − | 0.0351205i | \(-0.0111815\pi\) | |||||||
\(12\) | −93217.9 | − | 105064.i | −0.374622 | − | 0.422229i | ||||
\(13\) | 407265. | 1.09688 | 0.548442 | − | 0.836189i | \(-0.315221\pi\) | ||||
0.548442 | + | 0.836189i | \(0.315221\pi\) | |||||||
\(14\) | −282948. | − | 745239.i | −0.526098 | − | 1.38566i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 124847. | − | 1.04112e6i | 0.119063 | − | 0.992887i | ||||
\(17\) | 1.49997e6 | 1.05642 | 0.528211 | − | 0.849113i | \(-0.322863\pi\) | ||||
0.528211 | + | 0.849113i | \(0.322863\pi\) | |||||||
\(18\) | 1.20368e6 | − | 457006.i | 0.637013 | − | 0.241857i | ||||
\(19\) | − | 2.09616e6i | − | 0.846557i | −0.906000 | − | 0.423279i | \(-0.860879\pi\) | ||
0.906000 | − | 0.423279i | \(-0.139121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.41688e6 | −0.836629 | ||||||||
\(22\) | −128491. | − | 338425.i | −0.0249322 | − | 0.0656672i | ||||
\(23\) | 1.00854e7i | 1.56695i | 0.621423 | + | 0.783476i | \(0.286555\pi\) | ||||
−0.621423 | + | 0.783476i | \(0.713445\pi\) | |||||||
\(24\) | −3.98210e6 | − | 2.08432e6i | −0.500099 | − | 0.261763i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.21839e7 | − | 4.62590e6i | 1.02546 | − | 0.389341i | ||||
\(27\) | − | 1.36182e7i | − | 0.949078i | ||||||
\(28\) | −1.69295e7 | − | 1.90809e7i | −0.983682 | − | 1.10869i | ||||
\(29\) | −2.68271e7 | −1.30793 | −0.653963 | − | 0.756527i | \(-0.726895\pi\) | ||||
−0.653963 | + | 0.756527i | \(0.726895\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.47015e6i | 0.330787i | 0.986228 | + | 0.165393i | \(0.0528894\pi\) | ||||
−0.986228 | + | 0.165393i | \(0.947111\pi\) | |||||||
\(32\) | −8.09054e6 | − | 3.25644e7i | −0.241117 | − | 0.970496i | ||||
\(33\) | −1.55166e6 | −0.0396485 | ||||||||
\(34\) | 4.48735e7 | − | 1.70373e7i | 0.987633 | − | 0.374979i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.08187e7 | − | 2.73439e7i | 0.509686 | − | 0.452218i | ||||
\(37\) | 6.03238e7 | 0.869922 | 0.434961 | − | 0.900449i | \(-0.356762\pi\) | ||||
0.434961 | + | 0.900449i | \(0.356762\pi\) | |||||||
\(38\) | −2.38091e7 | − | 6.27094e7i | −0.300487 | − | 0.791433i | ||||
\(39\) | − | 5.58623e7i | − | 0.619150i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.12967e7 | −0.270134 | −0.135067 | − | 0.990836i | \(-0.543125\pi\) | ||||
−0.135067 | + | 0.990836i | \(0.543125\pi\) | |||||||
\(42\) | −1.02220e8 | + | 3.88105e7i | −0.782152 | + | 0.296963i | ||||
\(43\) | − | 2.55575e8i | − | 1.73851i | −0.494367 | − | 0.869253i | \(-0.664600\pi\) | ||
0.494367 | − | 0.869253i | \(-0.335400\pi\) | |||||||
\(44\) | −7.68797e6 | − | 8.66496e6i | −0.0466174 | − | 0.0525416i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.14555e8 | + | 3.01719e8i | 0.556192 | + | 1.46492i | ||||
\(47\) | 3.78083e8i | 1.64853i | 0.566202 | + | 0.824267i | \(0.308412\pi\) | ||||
−0.566202 | + | 0.824267i | \(0.691588\pi\) | |||||||
\(48\) | −1.42804e8 | − | 1.71245e7i | −0.560448 | − | 0.0672067i | ||||
\(49\) | −3.38072e8 | −1.19682 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2.05743e8i | − | 0.596312i | ||||||
\(52\) | 3.11953e8 | − | 2.76780e8i | 0.820489 | − | 0.727977i | ||||
\(53\) | −7.29570e6 | −0.0174457 | −0.00872283 | − | 0.999962i | \(-0.502777\pi\) | ||||
−0.00872283 | + | 0.999962i | \(0.502777\pi\) | |||||||
\(54\) | −1.54682e8 | − | 4.07407e8i | −0.336877 | − | 0.887278i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.23199e8 | − | 3.78538e8i | −1.31316 | − | 0.687336i | ||||
\(57\) | −2.87519e8 | −0.477851 | ||||||||
\(58\) | −8.02566e8 | + | 3.04714e8i | −1.22276 | + | 0.464251i | ||||
\(59\) | − | 2.59793e8i | − | 0.363386i | −0.983355 | − | 0.181693i | \(-0.941842\pi\) | ||
0.983355 | − | 0.181693i | \(-0.0581577\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.30862e8 | −0.391740 | −0.195870 | − | 0.980630i | \(-0.562753\pi\) | ||||
−0.195870 | + | 0.980630i | \(0.562753\pi\) | |||||||
\(62\) | 1.07566e8 | + | 2.83312e8i | 0.117413 | + | 0.309248i | ||||
\(63\) | − | 1.00228e9i | − | 1.00992i | ||||||
\(64\) | −6.11921e8 | − | 8.82312e8i | −0.569896 | − | 0.821717i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.64199e7 | + | 1.76244e7i | −0.0370667 | + | 0.0140733i | ||||
\(67\) | − | 7.94046e7i | − | 0.0588128i | −0.999568 | − | 0.0294064i | \(-0.990638\pi\) | ||
0.999568 | − | 0.0294064i | \(-0.00936169\pi\) | |||||||
\(68\) | 1.14893e9 | − | 1.01939e9i | 0.790223 | − | 0.701124i | ||||
\(69\) | 1.38336e9 | 0.884487 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.16126e9i | 0.643630i | 0.946803 | + | 0.321815i | \(0.104293\pi\) | ||||
−0.946803 | + | 0.321815i | \(0.895707\pi\) | |||||||
\(72\) | 6.11399e8 | − | 1.16808e9i | 0.315982 | − | 0.603685i | ||||
\(73\) | −3.86449e9 | −1.86414 | −0.932069 | − | 0.362280i | \(-0.881998\pi\) | ||||
−0.932069 | + | 0.362280i | \(0.881998\pi\) | |||||||
\(74\) | 1.80467e9 | − | 6.85185e8i | 0.813276 | − | 0.308780i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.42456e9 | − | 1.60560e9i | −0.561841 | − | 0.633240i | ||||
\(77\) | −2.81800e8 | −0.104109 | ||||||||
\(78\) | −6.34510e8 | − | 1.67120e9i | −0.219769 | − | 0.578834i | ||||
\(79\) | 3.82600e9i | 1.24340i | 0.783257 | + | 0.621698i | \(0.213557\pi\) | ||||
−0.783257 | + | 0.621698i | \(0.786443\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.07889e8 | 0.145661 | ||||||||
\(82\) | −9.36280e8 | + | 3.55482e8i | −0.252544 | + | 0.0958844i | ||||
\(83\) | 9.01358e8i | 0.228827i | 0.993433 | + | 0.114413i | \(0.0364988\pi\) | ||||
−0.993433 | + | 0.114413i | \(0.963501\pi\) | |||||||
\(84\) | −2.61723e9 | + | 2.32213e9i | −0.625814 | + | 0.555252i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.90294e9 | − | 7.64586e9i | −0.617086 | − | 1.62530i | ||||
\(87\) | 3.67972e9i | 0.738276i | ||||||||
\(88\) | −3.28416e8 | − | 1.71900e8i | −0.0622316 | − | 0.0325734i | ||||
\(89\) | −4.02278e9 | −0.720404 | −0.360202 | − | 0.932874i | \(-0.617292\pi\) | ||||
−0.360202 | + | 0.932874i | \(0.617292\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.01453e10i | − | 1.62576i | ||||||
\(92\) | 6.85412e9 | + | 7.72515e9i | 1.03995 | + | 1.17211i | ||||
\(93\) | 1.29897e9 | 0.186717 | ||||||||
\(94\) | 4.29444e9 | + | 1.13108e10i | 0.585150 | + | 1.54119i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.46669e9 | + | 1.10974e9i | −0.547810 | + | 0.136102i | ||||
\(97\) | 1.37620e10 | 1.60259 | 0.801296 | − | 0.598268i | \(-0.204144\pi\) | ||||
0.801296 | + | 0.598268i | \(0.204144\pi\) | |||||||
\(98\) | −1.01139e10 | + | 3.83998e9i | −1.11889 | + | 0.424813i | ||||
\(99\) | − | 4.55152e8i | − | 0.0478609i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.30862e10 | −1.24511 | −0.622555 | − | 0.782576i | \(-0.713905\pi\) | ||||
−0.622555 | + | 0.782576i | \(0.713905\pi\) | |||||||
\(102\) | −2.33692e9 | − | 6.15506e9i | −0.211662 | − | 0.557482i | ||||
\(103\) | − | 1.33473e10i | − | 1.15135i | −0.817678 | − | 0.575675i | \(-0.804739\pi\) | ||
0.817678 | − | 0.575675i | \(-0.195261\pi\) | |||||||
\(104\) | 6.18869e9 | − | 1.18235e10i | 0.508665 | − | 0.971809i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.18260e8 | + | 8.28679e7i | −0.0163097 | + | 0.00619237i | ||||
\(107\) | 8.37635e9i | 0.597222i | 0.954375 | + | 0.298611i | \(0.0965234\pi\) | ||||
−0.954375 | + | 0.298611i | \(0.903477\pi\) | |||||||
\(108\) | −9.25504e9 | − | 1.04312e10i | −0.629882 | − | 0.709928i | ||||
\(109\) | 2.51755e9 | 0.163623 | 0.0818117 | − | 0.996648i | \(-0.473929\pi\) | ||||
0.0818117 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.27429e9i | − | 0.491039i | ||||||
\(112\) | −2.59350e10 | − | 3.11003e9i | −1.47162 | − | 0.176471i | ||||
\(113\) | −1.47892e9 | −0.0802698 | −0.0401349 | − | 0.999194i | \(-0.512779\pi\) | ||||
−0.0401349 | + | 0.999194i | \(0.512779\pi\) | |||||||
\(114\) | −8.60150e9 | + | 3.26577e9i | −0.446735 | + | 0.169614i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.05487e10 | + | 1.82318e10i | −0.978352 | + | 0.868041i | ||||
\(117\) | 1.63863e10 | 0.747395 | ||||||||
\(118\) | −2.95085e9 | − | 7.77205e9i | −0.128984 | − | 0.339724i | ||||
\(119\) | − | 3.73654e10i | − | 1.56579i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.58095e10 | 0.995066 | ||||||||
\(122\) | −9.89817e9 | + | 3.75808e9i | −0.366232 | + | 0.139049i | ||||
\(123\) | 4.29279e9i | 0.152481i | ||||||||
\(124\) | 6.43597e9 | + | 7.25386e9i | 0.219536 | + | 0.247435i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.13844e10 | − | 2.99846e10i | −0.358473 | − | 0.944159i | ||||
\(127\) | − | 3.20677e10i | − | 0.970621i | −0.874342 | − | 0.485311i | \(-0.838707\pi\) | ||
0.874342 | − | 0.485311i | \(-0.161293\pi\) | |||||||
\(128\) | −2.83281e10 | − | 1.94450e10i | −0.824457 | − | 0.565925i | ||||
\(129\) | −3.50559e10 | −0.981323 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.86920e10i | 1.26212i | 0.775733 | + | 0.631061i | \(0.217380\pi\) | ||||
−0.775733 | + | 0.631061i | \(0.782620\pi\) | |||||||
\(132\) | −1.18853e9 | + | 1.05452e9i | −0.0296578 | + | 0.0263138i | ||||
\(133\) | −5.22170e10 | −1.25474 | ||||||||
\(134\) | −9.01914e8 | − | 2.37549e9i | −0.0208757 | − | 0.0549831i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.27931e10 | − | 4.35464e10i | 0.489902 | − | 0.935961i | ||||
\(137\) | 3.90738e9 | 0.0809623 | 0.0404812 | − | 0.999180i | \(-0.487111\pi\) | ||||
0.0404812 | + | 0.999180i | \(0.487111\pi\) | |||||||
\(138\) | 4.13852e10 | − | 1.57129e10i | 0.826893 | − | 0.313950i | ||||
\(139\) | − | 3.40878e9i | − | 0.0656938i | −0.999460 | − | 0.0328469i | \(-0.989543\pi\) | ||
0.999460 | − | 0.0328469i | \(-0.0104574\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.18596e10 | 0.930537 | ||||||||
\(142\) | 1.31901e10 | + | 3.47405e10i | 0.228458 | + | 0.601720i | ||||
\(143\) | − | 4.60714e9i | − | 0.0770462i | ||||||
\(144\) | 5.02319e9 | − | 4.18892e10i | 0.0811273 | − | 0.676534i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.15611e11 | + | 4.38947e10i | −1.74275 | + | 0.661679i | ||||
\(147\) | 4.63715e10i | 0.675561i | ||||||||
\(148\) | 4.62063e10 | − | 4.09964e10i | 0.650717 | − | 0.577348i | ||||
\(149\) | 2.39565e9 | 0.0326207 | 0.0163103 | − | 0.999867i | \(-0.494808\pi\) | ||||
0.0163103 | + | 0.999867i | \(0.494808\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.19556e10i | 1.04398i | 0.852950 | + | 0.521992i | \(0.174811\pi\) | ||||
−0.852950 | + | 0.521992i | \(0.825189\pi\) | |||||||
\(152\) | −6.08548e10 | − | 3.18527e10i | −0.750027 | − | 0.392580i | ||||
\(153\) | 6.03510e10 | 0.719826 | ||||||||
\(154\) | −8.43042e9 | + | 3.20082e9i | −0.0973298 | + | 0.0369536i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.79644e10 | − | 4.27889e10i | −0.410916 | − | 0.463136i | ||||
\(157\) | 1.18679e11 | 1.24416 | 0.622082 | − | 0.782952i | \(-0.286287\pi\) | ||||
0.622082 | + | 0.782952i | \(0.286287\pi\) | |||||||
\(158\) | 4.34575e10 | + | 1.14460e11i | 0.441346 | + | 1.16243i | ||||
\(159\) | 1.00071e9i | 0.00984744i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.51236e11 | 2.32248 | ||||||||
\(162\) | 1.51942e10 | − | 5.76884e9i | 0.136176 | − | 0.0517027i | ||||
\(163\) | 5.39517e10i | 0.468886i | 0.972130 | + | 0.234443i | \(0.0753266\pi\) | ||||
−0.972130 | + | 0.234443i | \(0.924673\pi\) | |||||||
\(164\) | −2.39723e10 | + | 2.12694e10i | −0.202065 | + | 0.179282i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.02380e10 | + | 2.69653e10i | 0.0812224 | + | 0.213927i | ||||
\(167\) | 8.18493e10i | 0.630133i | 0.949070 | + | 0.315067i | \(0.102027\pi\) | ||||
−0.949070 | + | 0.315067i | \(0.897973\pi\) | |||||||
\(168\) | −5.19220e10 | + | 9.91973e10i | −0.387976 | + | 0.741231i | ||||
\(169\) | 2.80063e10 | 0.203153 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 8.43387e10i | − | 0.576828i | ||||||
\(172\) | −1.73690e11 | − | 1.95763e11i | −1.15381 | − | 1.30043i | ||||
\(173\) | 2.43804e11 | 1.57330 | 0.786649 | − | 0.617400i | \(-0.211814\pi\) | ||||
0.786649 | + | 0.617400i | \(0.211814\pi\) | |||||||
\(174\) | 4.17960e10 | + | 1.10084e11i | 0.262052 | + | 0.690203i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.17775e10 | − | 1.41231e9i | −0.0697414 | − | 0.00836311i | ||||
\(177\) | −3.56344e10 | −0.205118 | ||||||||
\(178\) | −1.20347e11 | + | 4.56926e10i | −0.673495 | + | 0.255709i | ||||
\(179\) | 3.02221e11i | 1.64460i | 0.569056 | + | 0.822299i | \(0.307309\pi\) | ||||
−0.569056 | + | 0.822299i | \(0.692691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.83369e11 | 1.45868 | 0.729340 | − | 0.684152i | \(-0.239827\pi\) | ||||
0.729340 | + | 0.684152i | \(0.239827\pi\) | |||||||
\(182\) | −1.15235e11 | − | 3.03510e11i | −0.577068 | − | 1.51990i | ||||
\(183\) | 4.53826e10i | 0.221123i | ||||||||
\(184\) | 2.92796e11 | + | 1.53256e11i | 1.38828 | + | 0.726653i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.88604e10 | − | 1.47543e10i | 0.174559 | − | 0.0662756i | ||||
\(187\) | − | 1.69682e10i | − | 0.0742041i | ||||||
\(188\) | 2.56948e11 | + | 2.89600e11i | 1.09410 | + | 1.23313i | ||||
\(189\) | −3.39241e11 | −1.40669 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.63631e11i | 1.43052i | 0.698859 | + | 0.715260i | \(0.253692\pi\) | ||||
−0.698859 | + | 0.715260i | \(0.746308\pi\) | |||||||
\(192\) | −1.21022e11 | + | 8.39339e10i | −0.463829 | + | 0.321685i | ||||
\(193\) | 2.05085e11 | 0.765857 | 0.382929 | − | 0.923778i | \(-0.374916\pi\) | ||||
0.382929 | + | 0.923778i | \(0.374916\pi\) | |||||||
\(194\) | 4.11708e11 | − | 1.56315e11i | 1.49824 | − | 0.568843i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.58953e11 | + | 2.29756e11i | −0.895243 | + | 0.794303i | ||||
\(197\) | 4.83954e11 | 1.63107 | 0.815536 | − | 0.578706i | \(-0.196442\pi\) | ||||
0.815536 | + | 0.578706i | \(0.196442\pi\) | |||||||
\(198\) | −5.16983e9 | − | 1.36165e10i | −0.0169883 | − | 0.0447444i | ||||
\(199\) | − | 5.61971e11i | − | 1.80073i | −0.435137 | − | 0.900364i | \(-0.643300\pi\) | ||
0.435137 | − | 0.900364i | \(-0.356700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.08915e10 | −0.0331977 | ||||||||
\(202\) | −3.91492e11 | + | 1.48640e11i | −1.16403 | + | 0.441954i | ||||
\(203\) | 6.68283e11i | 1.93856i | ||||||||
\(204\) | −1.39824e11 | − | 1.57593e11i | −0.395759 | − | 0.446052i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.51605e11 | − | 3.99302e11i | −0.408674 | − | 1.07638i | ||||
\(207\) | 4.05786e11i | 1.06769i | ||||||||
\(208\) | 5.08457e10 | − | 4.24011e11i | 0.130598 | − | 1.08908i | ||||
\(209\) | −2.37126e10 | −0.0594630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.25143e11i | 0.777432i | 0.921358 | + | 0.388716i | \(0.127081\pi\) | ||||
−0.921358 | + | 0.388716i | \(0.872919\pi\) | |||||||
\(212\) | −5.58829e9 | + | 4.95820e9i | −0.0130497 | + | 0.0115783i | ||||
\(213\) | 1.59283e11 | 0.363306 | ||||||||
\(214\) | 9.51425e10 | + | 2.50590e11i | 0.211985 | + | 0.558334i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.95359e11 | − | 2.06939e11i | −0.840857 | − | 0.440123i | ||||
\(217\) | 2.35909e11 | 0.490281 | ||||||||
\(218\) | 7.53158e10 | − | 2.85955e10i | 0.152969 | − | 0.0580784i | ||||
\(219\) | 5.30072e11i | 1.05224i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.10885e11 | 1.15877 | ||||||||
\(222\) | −9.39832e10 | − | 2.47536e11i | −0.174295 | − | 0.459065i | ||||
\(223\) | − | 5.08960e11i | − | 0.922910i | −0.887164 | − | 0.461455i | \(-0.847328\pi\) | ||
0.887164 | − | 0.461455i | \(-0.152672\pi\) | |||||||
\(224\) | −8.11206e11 | + | 2.01542e11i | −1.43844 | + | 0.357375i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.42438e10 | + | 1.67982e10i | −0.0750430 | + | 0.0284919i | ||||
\(227\) | − | 1.00059e11i | − | 0.166008i | −0.996549 | − | 0.0830038i | \(-0.973549\pi\) | ||
0.996549 | − | 0.0830038i | \(-0.0264514\pi\) | |||||||
\(228\) | −2.20231e11 | + | 1.95400e11i | −0.357441 | + | 0.317139i | ||||
\(229\) | −5.09987e10 | −0.0809808 | −0.0404904 | − | 0.999180i | \(-0.512892\pi\) | ||||
−0.0404904 | + | 0.999180i | \(0.512892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.86530e10i | 0.0587657i | ||||||||
\(232\) | −4.07657e11 | + | 7.78831e11i | −0.606534 | + | 1.15879i | ||||
\(233\) | −1.13041e12 | −1.64610 | −0.823051 | − | 0.567968i | \(-0.807730\pi\) | ||||
−0.823051 | + | 0.567968i | \(0.807730\pi\) | |||||||
\(234\) | 4.90216e11 | − | 1.86123e11i | 0.698728 | − | 0.265289i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.76557e11 | − | 1.98994e11i | −0.241171 | − | 0.271819i | ||||
\(237\) | 5.24792e11 | 0.701852 | ||||||||
\(238\) | −4.24413e11 | − | 1.11783e12i | −0.555781 | − | 1.46384i | ||||
\(239\) | − | 6.47347e11i | − | 0.830133i | −0.909791 | − | 0.415067i | \(-0.863758\pi\) | ||
0.909791 | − | 0.415067i | \(-0.136242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.18012e12 | 1.45158 | 0.725788 | − | 0.687919i | \(-0.241475\pi\) | ||||
0.725788 | + | 0.687919i | \(0.241475\pi\) | |||||||
\(242\) | 7.72124e11 | − | 2.93156e11i | 0.930272 | − | 0.353201i | ||||
\(243\) | − | 8.73807e11i | − | 1.03130i | ||||||
\(244\) | −2.53431e11 | + | 2.24856e11i | −0.293029 | + | 0.259989i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.87595e10 | + | 1.28425e11i | 0.0541233 | + | 0.142552i | ||||
\(247\) | − | 8.53693e11i | − | 0.928574i | ||||||
\(248\) | 2.74933e11 | + | 1.43906e11i | 0.293068 | + | 0.153398i | ||||
\(249\) | 1.23634e11 | 0.129164 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.64973e11i | − | 0.667476i | −0.942666 | − | 0.333738i | \(-0.891690\pi\) | ||
0.942666 | − | 0.333738i | \(-0.108310\pi\) | |||||||
\(252\) | −6.81157e11 | − | 7.67719e11i | −0.670262 | − | 0.755439i | ||||
\(253\) | 1.14090e11 | 0.110064 | ||||||||
\(254\) | −3.64240e11 | − | 9.59348e11i | −0.344524 | − | 0.907419i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.06834e12 | − | 2.59960e11i | −0.971648 | − | 0.236432i | ||||
\(257\) | −1.03129e12 | −0.919844 | −0.459922 | − | 0.887959i | \(-0.652123\pi\) | ||||
−0.459922 | + | 0.887959i | \(0.652123\pi\) | |||||||
\(258\) | −1.04874e12 | + | 3.98181e11i | −0.917424 | + | 0.348323i | ||||
\(259\) | − | 1.50271e12i | − | 1.28937i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.07938e12 | −0.891196 | ||||||||
\(262\) | 5.53066e11 | + | 1.45668e12i | 0.447992 | + | 1.17994i | ||||
\(263\) | − | 1.84871e12i | − | 1.46923i | −0.678485 | − | 0.734615i | \(-0.737363\pi\) | ||
0.678485 | − | 0.734615i | \(-0.262637\pi\) | |||||||
\(264\) | −2.35786e10 | + | 4.50471e10i | −0.0183865 | + | 0.0351275i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.56214e12 | + | 5.93104e11i | −1.17304 | + | 0.445372i | ||||
\(267\) | 5.51783e11i | 0.406642i | ||||||||
\(268\) | −5.39639e10 | − | 6.08216e10i | −0.0390327 | − | 0.0439930i | ||||
\(269\) | −5.02760e11 | −0.356943 | −0.178472 | − | 0.983945i | \(-0.557115\pi\) | ||||
−0.178472 | + | 0.983945i | \(0.557115\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.51814e11i | − | 0.309110i | −0.987984 | − | 0.154555i | \(-0.950606\pi\) | ||
0.987984 | − | 0.154555i | \(-0.0493944\pi\) | |||||||
\(272\) | 1.87266e11 | − | 1.56164e12i | 0.125781 | − | 1.04891i | ||||
\(273\) | −1.39157e12 | −0.917684 | ||||||||
\(274\) | 1.16894e11 | − | 4.43818e10i | 0.0756904 | − | 0.0287377i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.05962e12 | − | 9.40143e11i | 0.661612 | − | 0.587014i | ||||
\(277\) | 2.53984e12 | 1.55742 | 0.778712 | − | 0.627381i | \(-0.215873\pi\) | ||||
0.778712 | + | 0.627381i | \(0.215873\pi\) | |||||||
\(278\) | −3.87185e10 | − | 1.01978e11i | −0.0233181 | − | 0.0614161i | ||||
\(279\) | 3.81030e11i | 0.225392i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.11997e11 | −0.406393 | −0.203197 | − | 0.979138i | \(-0.565133\pi\) | ||||
−0.203197 | + | 0.979138i | \(0.565133\pi\) | |||||||
\(282\) | 1.55145e12 | − | 5.89045e11i | 0.869945 | − | 0.330296i | ||||
\(283\) | 2.47422e12i | 1.36303i | 0.731804 | + | 0.681515i | \(0.238678\pi\) | ||||
−0.731804 | + | 0.681515i | \(0.761322\pi\) | |||||||
\(284\) | 7.89197e11 | + | 8.89488e11i | 0.427163 | + | 0.481447i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.23300e10 | − | 1.37829e11i | −0.0273477 | − | 0.0720293i | ||||
\(287\) | 7.79624e11i | 0.400383i | ||||||||
\(288\) | −3.25522e11 | − | 1.31023e12i | −0.164292 | − | 0.661278i | ||||
\(289\) | 2.33911e11 | 0.116027 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.88766e12i | − | 0.904604i | ||||||
\(292\) | −2.96009e12 | + | 2.62633e12i | −1.39441 | + | 1.23719i | ||||
\(293\) | 6.83082e11 | 0.316326 | 0.158163 | − | 0.987413i | \(-0.449443\pi\) | ||||
0.158163 | + | 0.987413i | \(0.449443\pi\) | |||||||
\(294\) | 5.26709e11 | + | 1.38726e12i | 0.239792 | + | 0.631571i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.16665e11 | − | 1.75129e12i | 0.403415 | − | 0.770727i | ||||
\(297\) | −1.54055e11 | −0.0666642 | ||||||||
\(298\) | 7.16691e10 | − | 2.72109e10i | 0.0304965 | − | 0.0115788i | ||||
\(299\) | 4.10744e12i | 1.71876i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.36658e12 | −2.57676 | ||||||||
\(302\) | 9.30889e11 | + | 2.45181e12i | 0.370564 | + | 0.976005i | ||||
\(303\) | 1.79497e12i | 0.702819i | ||||||||
\(304\) | −2.18235e12 | − | 2.61698e11i | −0.840536 | − | 0.100794i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.80548e12 | − | 6.85495e11i | 0.672954 | − | 0.255504i | ||||
\(307\) | 1.64841e12i | 0.604467i | 0.953234 | + | 0.302234i | \(0.0977323\pi\) | ||||
−0.953234 | + | 0.302234i | \(0.902268\pi\) | |||||||
\(308\) | −2.15851e11 | + | 1.91513e11i | −0.0778754 | + | 0.0690948i | ||||
\(309\) | −1.83078e12 | −0.649895 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.37457e12i | 0.816174i | 0.912943 | + | 0.408087i | \(0.133804\pi\) | ||||
−0.912943 | + | 0.408087i | \(0.866196\pi\) | |||||||
\(312\) | −1.62177e12 | − | 8.48870e11i | −0.548550 | − | 0.287123i | ||||
\(313\) | 1.22906e12 | 0.409122 | 0.204561 | − | 0.978854i | \(-0.434423\pi\) | ||||
0.204561 | + | 0.978854i | \(0.434423\pi\) | |||||||
\(314\) | 3.55045e12 | − | 1.34802e12i | 1.16315 | − | 0.441618i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.60018e12 | + | 2.93061e12i | 0.825215 | + | 0.930084i | ||||
\(317\) | −6.24013e12 | −1.94938 | −0.974692 | − | 0.223551i | \(-0.928235\pi\) | ||||
−0.974692 | + | 0.223551i | \(0.928235\pi\) | |||||||
\(318\) | 1.13665e10 | + | 2.99376e10i | 0.00349537 | + | 0.00920622i | ||||
\(319\) | 3.03478e11i | 0.0918700i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.14894e12 | 0.337110 | ||||||||
\(322\) | 7.51606e12 | − | 2.85365e12i | 2.17125 | − | 0.824370i | ||||
\(323\) | − | 3.14417e12i | − | 0.894322i | ||||||
\(324\) | 3.89028e11 | − | 3.45165e11i | 0.108957 | − | 0.0966722i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.12809e11 | + | 1.61404e12i | 0.166432 | + | 0.438354i | ||||
\(327\) | − | 3.45319e11i | − | 0.0923594i | ||||||
\(328\) | −4.75576e11 | + | 9.08591e11i | −0.125271 | + | 0.239331i | ||||
\(329\) | 9.41834e12 | 2.44340 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6.89984e11i | − | 0.173660i | −0.996223 | − | 0.0868299i | \(-0.972326\pi\) | ||
0.996223 | − | 0.0868299i | \(-0.0276737\pi\) | |||||||
\(332\) | 6.12568e11 | + | 6.90414e11i | 0.151867 | + | 0.171167i | ||||
\(333\) | 2.42712e12 | 0.592748 | ||||||||
\(334\) | 9.29682e11 | + | 2.44863e12i | 0.223667 | + | 0.589102i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.26586e11 | + | 3.55737e12i | −0.0996116 | + | 0.830678i | ||||
\(337\) | −1.19316e12 | −0.274503 | −0.137252 | − | 0.990536i | \(-0.543827\pi\) | ||||
−0.137252 | + | 0.990536i | \(0.543827\pi\) | |||||||
\(338\) | 8.37845e11 | − | 3.18108e11i | 0.189924 | − | 0.0721094i | ||||
\(339\) | 2.02855e11i | 0.0453093i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.07130e11 | 0.0232348 | ||||||||
\(342\) | −9.57958e11 | − | 2.52310e12i | −0.204746 | − | 0.539268i | ||||
\(343\) | 1.38496e12i | 0.291719i | ||||||||
\(344\) | −7.41974e12 | − | 3.88365e12i | −1.54027 | − | 0.806210i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.29373e12 | − | 2.76924e12i | 1.47085 | − | 0.558445i | ||||
\(347\) | − | 7.68368e12i | − | 1.52729i | −0.645635 | − | 0.763646i | \(-0.723407\pi\) | ||
0.645635 | − | 0.763646i | \(-0.276593\pi\) | |||||||
\(348\) | 2.50076e12 | + | 2.81856e12i | 0.489978 | + | 0.552244i | ||||
\(349\) | −5.29768e12 | −1.02320 | −0.511598 | − | 0.859225i | \(-0.670946\pi\) | ||||
−0.511598 | + | 0.859225i | \(0.670946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.54623e12i | − | 1.04103i | ||||||
\(352\) | −3.68381e11 | + | 9.15232e10i | −0.0681686 | + | 0.0169363i | ||||
\(353\) | −6.78784e12 | −1.23839 | −0.619196 | − | 0.785237i | \(-0.712541\pi\) | ||||
−0.619196 | + | 0.785237i | \(0.712541\pi\) | |||||||
\(354\) | −1.06605e12 | + | 4.04752e11i | −0.191762 | + | 0.0728070i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.08133e12 | + | 2.73391e12i | −0.538875 | + | 0.478116i | ||||
\(357\) | −5.12521e12 | −0.883833 | ||||||||
\(358\) | 3.43277e12 | + | 9.04134e12i | 0.583753 | + | 1.53751i | ||||
\(359\) | 1.68781e11i | 0.0283042i | 0.999900 | + | 0.0141521i | \(0.00450491\pi\) | ||||
−0.999900 | + | 0.0141521i | \(0.995495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.73718e12 | 0.283341 | ||||||||
\(362\) | 8.47736e12 | − | 3.21864e12i | 1.36370 | − | 0.517761i | ||||
\(363\) | − | 3.54014e12i | − | 0.561678i | ||||||
\(364\) | −6.89480e12 | − | 7.77100e12i | −1.07898 | − | 1.21610i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.15476e11 | + | 1.35768e12i | 0.0784879 | + | 0.206724i | ||||
\(367\) | 2.20336e12i | 0.330945i | 0.986214 | + | 0.165472i | \(0.0529148\pi\) | ||||
−0.986214 | + | 0.165472i | \(0.947085\pi\) | |||||||
\(368\) | 1.05001e13 | + | 1.25913e12i | 1.55580 | + | 0.186566i | ||||
\(369\) | −1.25922e12 | −0.184064 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.81742e11i | 0.0258574i | ||||||||
\(372\) | 9.94972e11 | − | 8.82788e11i | 0.139668 | − | 0.123920i | ||||
\(373\) | 5.85726e12 | 0.811241 | 0.405621 | − | 0.914042i | \(-0.367055\pi\) | ||||
0.405621 | + | 0.914042i | \(0.367055\pi\) | |||||||
\(374\) | −1.92733e11 | − | 5.07626e11i | −0.0263389 | − | 0.0693723i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.09763e13 | + | 5.74525e12i | 1.46056 | + | 0.764486i | ||||
\(377\) | −1.09257e13 | −1.43464 | ||||||||
\(378\) | −1.01488e13 | + | 3.85325e12i | −1.31509 | + | 0.499308i | ||||
\(379\) | − | 1.01146e13i | − | 1.29347i | −0.762717 | − | 0.646733i | \(-0.776135\pi\) | ||
0.762717 | − | 0.646733i | \(-0.223865\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.39856e12 | −0.547880 | ||||||||
\(382\) | 4.13029e12 | + | 1.08785e13i | 0.507766 | + | 1.33737i | ||||
\(383\) | 5.61682e12i | 0.681549i | 0.940145 | + | 0.340774i | \(0.110689\pi\) | ||||
−0.940145 | + | 0.340774i | \(0.889311\pi\) | |||||||
\(384\) | −2.66717e12 | + | 3.88561e12i | −0.319444 | + | 0.465376i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.13539e12 | − | 2.32945e12i | 0.715988 | − | 0.271842i | ||||
\(387\) | − | 1.02830e13i | − | 1.18459i | ||||||
\(388\) | 1.05413e13 | − | 9.35274e12i | 1.19877 | − | 1.06361i | ||||
\(389\) | 1.05262e13 | 1.18175 | 0.590875 | − | 0.806763i | \(-0.298783\pi\) | ||||
0.590875 | + | 0.806763i | \(0.298783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.51278e13i | 1.65536i | ||||||||
\(392\) | −5.13725e12 | + | 9.81475e12i | −0.555010 | + | 1.06035i | ||||
\(393\) | 6.67882e12 | 0.712421 | ||||||||
\(394\) | 1.44781e13 | − | 5.49698e12i | 1.52486 | − | 0.578952i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.09324e11 | − | 3.48633e11i | −0.0317642 | − | 0.0358008i | ||||
\(397\) | 1.84913e12 | 0.187506 | 0.0937531 | − | 0.995595i | \(-0.470114\pi\) | ||||
0.0937531 | + | 0.995595i | \(0.470114\pi\) | |||||||
\(398\) | −6.38312e12 | − | 1.68121e13i | −0.639172 | − | 1.68347i | ||||
\(399\) | 7.16232e12i | 0.708254i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.10185e12 | −0.781380 | −0.390690 | − | 0.920522i | \(-0.627764\pi\) | ||||
−0.390690 | + | 0.920522i | \(0.627764\pi\) | |||||||
\(402\) | −3.25833e11 | + | 1.23711e11i | −0.0310360 | + | 0.0117836i | ||||
\(403\) | 3.85686e12i | 0.362835i | ||||||||
\(404\) | −1.00237e13 | + | 8.89349e12i | −0.931366 | + | 0.826353i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.59066e12 | + | 1.99926e13i | 0.688097 | + | 1.81233i | ||||
\(407\) | − | 6.82406e11i | − | 0.0611042i | ||||||
\(408\) | −5.97303e12 | − | 3.12641e12i | −0.528316 | − | 0.276532i | ||||
\(409\) | 9.35378e11 | 0.0817280 | 0.0408640 | − | 0.999165i | \(-0.486989\pi\) | ||||
0.0408640 | + | 0.999165i | \(0.486989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.35954e11i | − | 0.0457003i | ||||||
\(412\) | −9.07091e12 | − | 1.02236e13i | −0.764126 | − | 0.861231i | ||||
\(413\) | −6.47165e12 | −0.538598 | ||||||||
\(414\) | 4.60911e12 | + | 1.21396e13i | 0.378979 | + | 0.998168i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.29499e12 | − | 1.32624e13i | −0.264477 | − | 1.06452i | ||||
\(417\) | −4.67564e11 | −0.0370818 | ||||||||
\(418\) | −7.09392e11 | + | 2.69338e11i | −0.0555911 | + | 0.0211065i | ||||
\(419\) | − | 4.25922e11i | − | 0.0329807i | −0.999864 | − | 0.0164903i | \(-0.994751\pi\) | ||
0.999864 | − | 0.0164903i | \(-0.00524927\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.58379e12 | −0.573424 | −0.286712 | − | 0.958017i | \(-0.592562\pi\) | ||||
−0.286712 | + | 0.958017i | \(0.592562\pi\) | |||||||
\(422\) | 3.69313e12 | + | 9.72709e12i | 0.275951 | + | 0.726810i | ||||
\(423\) | 1.52121e13i | 1.12328i | ||||||||
\(424\) | −1.10864e11 | + | 2.11806e11i | −0.00809020 | + | 0.0154564i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.76517e12 | − | 1.80921e12i | 0.339649 | − | 0.128956i | ||||
\(427\) | 8.24203e12i | 0.580624i | ||||||||
\(428\) | 5.69262e12 | + | 6.41604e12i | 0.396363 | + | 0.446733i | ||||
\(429\) | −6.31936e11 | −0.0434897 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.23217e13i | − | 1.50086i | −0.660949 | − | 0.750431i | \(-0.729846\pi\) | ||
0.660949 | − | 0.750431i | \(-0.270154\pi\) | |||||||
\(432\) | −1.41782e13 | − | 1.70019e12i | −0.942327 | − | 0.113000i | ||||
\(433\) | −2.91087e12 | −0.191242 | −0.0956209 | − | 0.995418i | \(-0.530484\pi\) | ||||
−0.0956209 | + | 0.995418i | \(0.530484\pi\) | |||||||
\(434\) | 7.05752e12 | − | 2.67956e12i | 0.458357 | − | 0.174026i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.92837e12 | − | 1.71094e12i | 0.122393 | − | 0.108593i | ||||
\(437\) | 2.11407e13 | 1.32651 | ||||||||
\(438\) | 6.02080e12 | + | 1.58578e13i | 0.373494 | + | 0.983721i | ||||
\(439\) | 1.34336e13i | 0.823891i | 0.911208 | + | 0.411946i | \(0.135151\pi\) | ||||
−0.911208 | + | 0.411946i | \(0.864849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.36023e13 | −0.815490 | ||||||||
\(442\) | 1.82754e13 | − | 6.93871e12i | 1.08332 | − | 0.411308i | ||||
\(443\) | − | 1.25121e13i | − | 0.733348i | −0.930350 | − | 0.366674i | \(-0.880496\pi\) | ||
0.930350 | − | 0.366674i | \(-0.119504\pi\) | |||||||
\(444\) | −5.62326e12 | − | 6.33787e12i | −0.325892 | − | 0.367306i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.78100e12 | − | 1.52262e13i | −0.327589 | − | 0.862814i | ||||
\(447\) | − | 3.28599e11i | − | 0.0184132i | ||||||
\(448\) | −2.19791e13 | + | 1.52434e13i | −1.21792 | + | 0.844681i | ||||
\(449\) | −1.25344e13 | −0.686865 | −0.343433 | − | 0.939177i | \(-0.611590\pi\) | ||||
−0.343433 | + | 0.939177i | \(0.611590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.54040e11i | 0.0189745i | ||||||||
\(452\) | −1.13281e12 | + | 1.00508e12i | −0.0600433 | + | 0.0532733i | ||||
\(453\) | 1.12414e13 | 0.589291 | ||||||||
\(454\) | −1.13652e12 | − | 2.99340e12i | −0.0589247 | − | 0.155198i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.36906e12 | + | 8.34712e12i | −0.221597 | + | 0.423363i | ||||
\(457\) | −9.29846e12 | −0.466477 | −0.233238 | − | 0.972420i | \(-0.574932\pi\) | ||||
−0.233238 | + | 0.972420i | \(0.574932\pi\) | |||||||
\(458\) | −1.52569e12 | + | 5.79267e11i | −0.0757077 | + | 0.0287443i | ||||
\(459\) | − | 2.04269e13i | − | 1.00263i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.01065e13 | 0.965675 | 0.482837 | − | 0.875710i | \(-0.339606\pi\) | ||||
0.482837 | + | 0.875710i | \(0.339606\pi\) | |||||||
\(462\) | 4.39039e11 | + | 1.15636e12i | 0.0208590 | + | 0.0549391i | ||||
\(463\) | − | 1.04776e13i | − | 0.492442i | −0.969214 | − | 0.246221i | \(-0.920811\pi\) | ||
0.969214 | − | 0.246221i | \(-0.0791889\pi\) | |||||||
\(464\) | −3.34927e12 | + | 2.79301e13i | −0.155726 | + | 1.29862i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.38177e13 | + | 1.28397e13i | −1.53891 | + | 0.584287i | ||||
\(467\) | − | 5.13372e12i | − | 0.231125i | −0.993300 | − | 0.115563i | \(-0.963133\pi\) | ||
0.993300 | − | 0.115563i | \(-0.0368671\pi\) | |||||||
\(468\) | 1.25514e13 | − | 1.11362e13i | 0.559066 | − | 0.496030i | ||||
\(469\) | −1.97803e12 | −0.0871703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.62786e13i | − | 0.702285i | ||||||
\(472\) | −7.54220e12 | − | 3.94775e12i | −0.321950 | − | 0.168515i | ||||
\(473\) | −2.89116e12 | −0.122114 | ||||||||
\(474\) | 1.56998e13 | − | 5.96083e12i | 0.656151 | − | 0.249124i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.53937e13 | − | 2.86208e13i | −1.03918 | − | 1.17124i | ||||
\(477\) | −2.93542e11 | −0.0118871 | ||||||||
\(478\) | −7.35287e12 | − | 1.93662e13i | −0.294657 | − | 0.776079i | ||||
\(479\) | 1.62966e12i | 0.0646279i | 0.999478 | + | 0.0323139i | \(0.0102876\pi\) | ||||
−0.999478 | + | 0.0323139i | \(0.989712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.45678e13 | 0.954202 | ||||||||
\(482\) | 3.53047e13 | − | 1.34043e13i | 1.35706 | − | 0.515239i | ||||
\(483\) | − | 3.44607e13i | − | 1.31096i | ||||||
\(484\) | 1.97693e13 | − | 1.75403e13i | 0.744328 | − | 0.660404i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.92511e12 | − | 2.61411e13i | −0.366061 | − | 0.964145i | ||||
\(487\) | 4.02012e13i | 1.46756i | 0.679390 | + | 0.733778i | \(0.262245\pi\) | ||||
−0.679390 | + | 0.733778i | \(0.737755\pi\) | |||||||
\(488\) | −5.02769e12 | + | 9.60544e12i | −0.181664 | + | 0.347071i | ||||
\(489\) | 7.40027e12 | 0.264669 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.15779e13i | − | 0.756140i | −0.925777 | − | 0.378070i | \(-0.876588\pi\) | ||
0.925777 | − | 0.378070i | \(-0.123412\pi\) | |||||||
\(492\) | 2.91741e12 | + | 3.28815e12i | 0.101198 | + | 0.114058i | ||||
\(493\) | −4.02397e13 | −1.38172 | ||||||||
\(494\) | −9.69663e12 | − | 2.55393e13i | −0.329599 | − | 0.868110i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.85953e12 | + | 1.18232e12i | 0.328434 | + | 0.0393845i | ||||
\(497\) | 2.89278e13 | 0.953967 | ||||||||
\(498\) | 3.69868e12 | − | 1.40430e12i | 0.120754 | − | 0.0458471i | ||||
\(499\) | 4.38721e13i | 1.41803i | 0.705194 | + | 0.709015i | \(0.250860\pi\) | ||||
−0.705194 | + | 0.709015i | \(0.749140\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.12268e13 | 0.355687 | ||||||||
\(502\) | −7.55307e12 | − | 1.98935e13i | −0.236922 | − | 0.624013i | ||||
\(503\) | − | 5.52162e12i | − | 0.171485i | −0.996317 | − | 0.0857426i | \(-0.972674\pi\) | ||
0.996317 | − | 0.0857426i | \(-0.0273263\pi\) | |||||||
\(504\) | −2.90978e13 | − | 1.52304e13i | −0.894762 | − | 0.468338i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.41316e12 | − | 1.29589e12i | 0.102897 | − | 0.0390675i | ||||
\(507\) | − | 3.84147e12i | − | 0.114672i | ||||||
\(508\) | −2.17934e13 | − | 2.45629e13i | −0.644180 | − | 0.726042i | ||||
\(509\) | 1.28339e13 | 0.375639 | 0.187819 | − | 0.982204i | \(-0.439858\pi\) | ||||
0.187819 | + | 0.982204i | \(0.439858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.62675e13i | 2.76296i | ||||||||
\(512\) | −3.49135e13 | + | 4.35763e12i | −0.992301 | + | 0.123851i | ||||
\(513\) | −2.85460e13 | −0.803449 | ||||||||
\(514\) | −3.08523e13 | + | 1.17138e13i | −0.859948 | + | 0.326500i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.68518e13 | + | 2.38242e13i | −0.734048 | + | 0.651283i | ||||
\(517\) | 4.27702e12 | 0.115795 | ||||||||
\(518\) | −1.70685e13 | − | 4.49556e13i | −0.457664 | − | 1.20541i | ||||
\(519\) | − | 3.34413e13i | − | 0.888069i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.10526e13 | −0.287922 | −0.143961 | − | 0.989583i | \(-0.545984\pi\) | ||||
−0.143961 | + | 0.989583i | \(0.545984\pi\) | |||||||
\(522\) | −3.22912e13 | + | 1.22601e13i | −0.833165 | + | 0.316332i | ||||
\(523\) | 2.47975e13i | 0.633723i | 0.948472 | + | 0.316861i | \(0.102629\pi\) | ||||
−0.948472 | + | 0.316861i | \(0.897371\pi\) | |||||||
\(524\) | 3.30914e13 | + | 3.72967e13i | 0.837642 | + | 0.944090i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.09985e13 | − | 5.53065e13i | −0.521506 | − | 1.37356i | ||||
\(527\) | 1.42049e13i | 0.349451i | ||||||||
\(528\) | −1.93719e11 | + | 1.61546e12i | −0.00472067 | + | 0.0393664i | ||||
\(529\) | −6.02895e13 | −1.45534 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.04527e13i | − | 0.247604i | ||||||
\(532\) | −3.99967e13 | + | 3.54870e13i | −0.938568 | + | 0.832743i | ||||
\(533\) | −1.27460e13 | −0.296305 | ||||||||
\(534\) | 6.26740e12 | + | 1.65073e13i | 0.144338 | + | 0.380163i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.30524e12 | − | 1.20661e12i | −0.0521065 | − | 0.0272737i | ||||
\(537\) | 4.14540e13 | 0.928315 | ||||||||
\(538\) | −1.50407e13 | + | 5.71058e12i | −0.333701 | + | 0.126698i | ||||
\(539\) | 3.82440e12i | 0.0840658i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.51994e13 | 1.62266 | 0.811331 | − | 0.584588i | \(-0.198744\pi\) | ||||
0.811331 | + | 0.584588i | \(0.198744\pi\) | |||||||
\(542\) | −5.13191e12 | − | 1.35166e13i | −0.109719 | − | 0.288983i | ||||
\(543\) | − | 3.88682e13i | − | 0.823371i | ||||||
\(544\) | −1.21355e13 | − | 4.88456e13i | −0.254721 | − | 1.02525i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.16308e13 | + | 1.58061e13i | −0.857929 | + | 0.325734i | ||||
\(547\) | 2.15841e13i | 0.440755i | 0.975415 | + | 0.220378i | \(0.0707289\pi\) | ||||
−0.975415 | + | 0.220378i | \(0.929271\pi\) | |||||||
\(548\) | 2.99294e12 | − | 2.65548e12i | 0.0605613 | − | 0.0537329i | ||||
\(549\) | −1.33122e13 | −0.266924 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.62338e13i | 1.10723i | ||||||||
\(552\) | 2.10212e13 | − | 4.01612e13i | 0.410169 | − | 0.783631i | ||||
\(553\) | 9.53087e13 | 1.84292 | ||||||||
\(554\) | 7.59825e13 | − | 2.88486e13i | 1.45601 | − | 0.552811i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.31663e12 | − | 2.61102e12i | −0.0435995 | − | 0.0491402i | ||||
\(557\) | 2.33738e13 | 0.435966 | 0.217983 | − | 0.975953i | \(-0.430052\pi\) | ||||
0.217983 | + | 0.975953i | \(0.430052\pi\) | |||||||
\(558\) | 4.32792e12 | + | 1.13990e13i | 0.0800033 | + | 0.210715i | ||||
\(559\) | − | 1.04087e14i | − | 1.90694i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.32744e12 | −0.0418855 | ||||||||
\(562\) | −2.13003e13 | + | 8.08719e12i | −0.379931 | + | 0.144250i | ||||
\(563\) | 7.94427e13i | 1.40447i | 0.711946 | + | 0.702235i | \(0.247814\pi\) | ||||
−0.711946 | + | 0.702235i | \(0.752186\pi\) | |||||||
\(564\) | 3.97229e13 | − | 3.52441e13i | 0.696059 | − | 0.617577i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.81033e13 | + | 7.40194e13i | 0.483810 | + | 1.27428i | ||||
\(567\) | − | 1.26519e13i | − | 0.215894i | ||||||
\(568\) | 3.37131e13 | + | 1.76461e13i | 0.570239 | + | 0.298475i | ||||
\(569\) | −6.17162e13 | −1.03476 | −0.517378 | − | 0.855757i | \(-0.673092\pi\) | ||||
−0.517378 | + | 0.855757i | \(0.673092\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 7.52115e13i | − | 1.23909i | −0.784960 | − | 0.619546i | \(-0.787317\pi\) | ||
0.784960 | − | 0.619546i | \(-0.212683\pi\) | |||||||
\(572\) | −3.13104e12 | − | 3.52893e12i | −0.0511338 | − | 0.0576319i | ||||
\(573\) | 4.98773e13 | 0.807476 | ||||||||
\(574\) | 8.85533e12 | + | 2.33235e13i | 0.142117 | + | 0.374312i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.46206e13 | − | 3.54997e13i | −0.388316 | − | 0.559902i | ||||
\(577\) | 6.39211e13 | 0.999459 | 0.499730 | − | 0.866182i | \(-0.333433\pi\) | ||||
0.499730 | + | 0.866182i | \(0.333433\pi\) | |||||||
\(578\) | 6.99774e12 | − | 2.65686e12i | 0.108472 | − | 0.0411841i | ||||
\(579\) | − | 2.81304e13i | − | 0.432298i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.24535e13 | 0.339159 | ||||||||
\(582\) | −2.14409e13 | − | 5.64718e13i | −0.321091 | − | 0.845701i | ||||
\(583\) | 8.25317e10i | 0.00122540i | ||||||||
\(584\) | −5.87238e13 | + | 1.12192e14i | −0.864470 | + | 1.65158i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.04353e13 | − | 7.75876e12i | 0.295728 | − | 0.112280i | ||||
\(587\) | − | 2.79751e13i | − | 0.401404i | −0.979652 | − | 0.200702i | \(-0.935678\pi\) | ||
0.979652 | − | 0.200702i | \(-0.0643223\pi\) | |||||||
\(588\) | 3.15144e13 | + | 3.55192e13i | 0.448355 | + | 0.505332i | ||||
\(589\) | 1.98509e13 | 0.280030 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 6.63814e13i | − | 0.920681i | ||||||
\(592\) | 7.53122e12 | − | 6.28042e13i | 0.103576 | − | 0.863734i | ||||
\(593\) | 4.39437e13 | 0.599270 | 0.299635 | − | 0.954054i | \(-0.403135\pi\) | ||||
0.299635 | + | 0.954054i | \(0.403135\pi\) | |||||||
\(594\) | −4.60875e12 | + | 1.74982e12i | −0.0623233 | + | 0.0236626i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.83500e12 | − | 1.62810e12i | 0.0244008 | − | 0.0216496i | ||||
\(597\) | −7.70825e13 | −1.01645 | ||||||||
\(598\) | 4.66542e13 | + | 1.22880e14i | 0.610078 | + | 1.60684i | ||||
\(599\) | 7.69712e13i | 0.998146i | 0.866560 | + | 0.499073i | \(0.166326\pi\) | ||||
−0.866560 | + | 0.499073i | \(0.833674\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.71438e13 | 0.856315 | 0.428157 | − | 0.903704i | \(-0.359163\pi\) | ||||
0.428157 | + | 0.903704i | \(0.359163\pi\) | |||||||
\(602\) | −1.90464e14 | + | 7.23145e13i | −2.40897 | + | 0.914625i | ||||
\(603\) | − | 3.19483e12i | − | 0.0400739i | ||||||
\(604\) | 5.56975e13 | + | 6.27756e13i | 0.692869 | + | 0.780919i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.03881e13 | + | 5.36988e13i | 0.249467 | + | 0.657055i | ||||
\(607\) | − | 7.52005e13i | − | 0.912594i | −0.889828 | − | 0.456297i | \(-0.849176\pi\) | ||
0.889828 | − | 0.456297i | \(-0.150824\pi\) | |||||||
\(608\) | −6.82603e13 | + | 1.69591e13i | −0.821581 | + | 0.204119i | ||||
\(609\) | 9.16648e13 | 1.09425 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.53980e14i | 1.80825i | ||||||||
\(612\) | 4.62271e13 | − | 4.10149e13i | 0.538443 | − | 0.477733i | ||||
\(613\) | −5.79122e13 | −0.669064 | −0.334532 | − | 0.942384i | \(-0.608578\pi\) | ||||
−0.334532 | + | 0.942384i | \(0.608578\pi\) | |||||||
\(614\) | 1.87234e13 | + | 4.93143e13i | 0.214557 | + | 0.565107i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.28216e12 | + | 8.18110e12i | −0.0482792 | + | 0.0922377i | ||||
\(617\) | 1.25223e14 | 1.40042 | 0.700210 | − | 0.713937i | \(-0.253090\pi\) | ||||
0.700210 | + | 0.713937i | \(0.253090\pi\) | |||||||
\(618\) | −5.47701e13 | + | 2.07948e13i | −0.607577 | + | 0.230681i | ||||
\(619\) | 1.33820e14i | 1.47254i | 0.676687 | + | 0.736271i | \(0.263415\pi\) | ||||
−0.676687 | + | 0.736271i | \(0.736585\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.37346e14 | 1.48716 | ||||||||
\(622\) | 2.69714e13 | + | 7.10383e13i | 0.289702 | + | 0.763028i | ||||
\(623\) | 1.00211e14i | 1.06776i | ||||||||
\(624\) | −5.81592e13 | − | 6.97423e12i | −0.614746 | − | 0.0737179i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.67691e13 | − | 1.39603e13i | 0.382482 | − | 0.145219i | ||||
\(627\) | 3.25252e12i | 0.0335647i | ||||||||
\(628\) | 9.09050e13 | − | 8.06553e13i | 0.930657 | − | 0.825724i | ||||
\(629\) | 9.04838e13 | 0.919004 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.09639e13i | 0.409501i | 0.978814 | + | 0.204750i | \(0.0656382\pi\) | ||||
−0.978814 | + | 0.204750i | \(0.934362\pi\) | |||||||
\(632\) | 1.11075e14 | + | 5.81389e13i | 1.10162 | + | 0.576609i | ||||
\(633\) | 4.45982e13 | 0.438832 | ||||||||
\(634\) | −1.86682e14 | + | 7.08783e13i | −1.82245 | + | 0.691938i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.80090e11 | + | 7.66516e11i | 0.00653553 | + | 0.00736607i | ||||
\(637\) | −1.37685e14 | −1.31277 | ||||||||
\(638\) | 3.44704e12 | + | 9.07894e12i | 0.0326094 | + | 0.0858878i | ||||
\(639\) | 4.67230e13i | 0.438557i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.26152e13 | −0.486207 | −0.243103 | − | 0.970000i | \(-0.578165\pi\) | ||||
−0.243103 | + | 0.970000i | \(0.578165\pi\) | |||||||
\(642\) | 3.43720e13 | − | 1.30502e13i | 0.315159 | − | 0.119658i | ||||
\(643\) | 1.09830e14i | 0.999228i | 0.866248 | + | 0.499614i | \(0.166525\pi\) | ||||
−0.866248 | + | 0.499614i | \(0.833475\pi\) | |||||||
\(644\) | 1.92440e14 | − | 1.70742e14i | 1.73726 | − | 1.54138i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.57130e13 | − | 9.40620e13i | −0.317441 | − | 0.836088i | ||||
\(647\) | 1.73561e14i | 1.53084i | 0.643532 | + | 0.765420i | \(0.277469\pi\) | ||||
−0.643532 | + | 0.765420i | \(0.722531\pi\) | |||||||
\(648\) | 7.71775e12 | − | 1.47448e13i | 0.0675485 | − | 0.129052i | ||||
\(649\) | −2.93888e12 | −0.0255246 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 3.23583e13i | − | 0.276746i | ||||||
\(652\) | 3.66659e13 | + | 4.13255e13i | 0.311189 | + | 0.350735i | ||||
\(653\) | 6.41305e13 | 0.540131 | 0.270065 | − | 0.962842i | \(-0.412955\pi\) | ||||
0.270065 | + | 0.962842i | \(0.412955\pi\) | |||||||
\(654\) | −3.92229e12 | − | 1.03307e13i | −0.0327831 | − | 0.0863454i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.90728e12 | + | 3.25835e13i | −0.0321629 | + | 0.268212i | ||||
\(657\) | −1.55487e14 | −1.27019 | ||||||||
\(658\) | 2.81762e14 | − | 1.06978e14i | 2.28430 | − | 0.867290i | ||||
\(659\) | − | 4.28929e12i | − | 0.0345111i | −0.999851 | − | 0.0172555i | \(-0.994507\pi\) | ||
0.999851 | − | 0.0172555i | \(-0.00549288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.96698e14 | −1.55881 | −0.779403 | − | 0.626523i | \(-0.784477\pi\) | ||||
−0.779403 | + | 0.626523i | \(0.784477\pi\) | |||||||
\(662\) | −7.83716e12 | − | 2.06418e13i | −0.0616409 | − | 0.162352i | ||||
\(663\) | − | 8.37917e13i | − | 0.654084i | ||||||
\(664\) | 2.61678e13 | + | 1.36968e13i | 0.202734 | + | 0.106115i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.26105e13 | − | 2.75683e13i | 0.554151 | − | 0.210397i | ||||
\(667\) | − | 2.70562e14i | − | 2.04946i | ||||||
\(668\) | 5.56253e13 | + | 6.26942e13i | 0.418206 | + | 0.471351i | ||||
\(669\) | −6.98113e13 | −0.520949 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.74284e12i | 0.0275162i | ||||||||
\(672\) | 2.76444e13 | + | 1.11269e14i | 0.201725 | + | 0.811945i | ||||
\(673\) | −1.92127e14 | −1.39160 | −0.695799 | − | 0.718237i | \(-0.744949\pi\) | ||||
−0.695799 | + | 0.718237i | \(0.744949\pi\) | |||||||
\(674\) | −3.56948e13 | + | 1.35524e13i | −0.256629 | + | 0.0974354i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.14520e13 | − | 1.90333e13i | 0.151962 | − | 0.134828i | ||||
\(677\) | 2.18777e13 | 0.153836 | 0.0769180 | − | 0.997037i | \(-0.475492\pi\) | ||||
0.0769180 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(678\) | 2.30412e12 | + | 6.06868e12i | 0.0160826 | + | 0.0423590i | ||||
\(679\) | − | 3.42822e14i | − | 2.37531i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.37246e13 | −0.0937053 | ||||||||
\(682\) | 3.20493e12 | − | 1.21683e12i | 0.0217219 | − | 0.00824724i | ||||
\(683\) | − | 8.96485e13i | − | 0.603169i | −0.953439 | − | 0.301585i | \(-0.902484\pi\) | ||
0.953439 | − | 0.301585i | \(-0.0975156\pi\) | |||||||
\(684\) | −5.73171e13 | − | 6.46010e13i | −0.382828 | − | 0.431478i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.57310e13 | + | 4.14327e13i | 0.103546 | + | 0.272724i | ||||
\(687\) | 6.99522e12i | 0.0457107i | ||||||||
\(688\) | −2.66084e14 | − | 3.19077e13i | −1.72614 | − | 0.206992i | ||||
\(689\) | −2.97128e12 | −0.0191359 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.22078e14i | − | 0.774905i | −0.921890 | − | 0.387452i | \(-0.873355\pi\) | ||
0.921890 | − | 0.387452i | \(-0.126645\pi\) | |||||||
\(692\) | 1.86747e14 | − | 1.65691e14i | 1.17686 | − | 1.04416i | ||||
\(693\) | −1.13382e13 | −0.0709378 | ||||||||
\(694\) | −8.72748e13 | − | 2.29867e14i | −0.542115 | − | 1.42784i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.06828e14 | + | 5.59161e13i | 0.654092 | + | 0.342366i | ||||
\(697\) | −4.69440e13 | −0.285375 | ||||||||
\(698\) | −1.58487e14 | + | 6.01735e13i | −0.956570 | + | 0.363185i | ||||
\(699\) | 1.55052e14i | 0.929164i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.05940e14 | −0.625847 | −0.312924 | − | 0.949778i | \(-0.601308\pi\) | ||||
−0.312924 | + | 0.949778i | \(0.601308\pi\) | |||||||
\(702\) | −6.29966e13 | − | 1.65923e14i | −0.369515 | − | 0.973241i | ||||
\(703\) | − | 1.26448e14i | − | 0.736439i | ||||||
\(704\) | −9.98105e12 | + | 6.92228e12i | −0.0577182 | + | 0.0400300i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.03067e14 | + | 7.70994e13i | −1.15775 | + | 0.439569i | ||||
\(707\) | 3.25988e14i | 1.84546i | ||||||||
\(708\) | −2.72949e13 | + | 2.42174e13i | −0.153432 | + | 0.136132i | ||||
\(709\) | −4.78197e13 | −0.266916 | −0.133458 | − | 0.991054i | \(-0.542608\pi\) | ||||
−0.133458 | + | 0.991054i | \(0.542608\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.53939e14i | 0.847227i | ||||||||
\(712\) | −6.11291e13 | + | 1.16788e14i | −0.334078 | + | 0.638258i | ||||
\(713\) | −9.55106e13 | −0.518327 | ||||||||
\(714\) | −1.53327e14 | + | 5.82145e13i | −0.826282 | + | 0.313718i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.05391e14 | + | 2.31493e14i | 1.09148 | + | 1.23019i | ||||
\(717\) | −8.87931e13 | −0.468580 | ||||||||
\(718\) | 1.91709e12 | + | 5.04930e12i | 0.0100466 | + | 0.0264612i | ||||
\(719\) | 1.91248e14i | 0.995295i | 0.867379 | + | 0.497648i | \(0.165803\pi\) | ||||
−0.867379 | + | 0.497648i | \(0.834197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.32492e14 | −1.70649 | ||||||||
\(722\) | 5.19700e13 | − | 1.97317e13i | 0.264891 | − | 0.100572i | ||||
\(723\) | − | 1.61870e14i | − | 0.819361i | ||||||
\(724\) | 2.17053e14 | − | 1.92579e14i | 1.09112 | − | 0.968093i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.02106e13 | − | 1.05908e14i | −0.199369 | − | 0.525105i | ||||
\(727\) | − | 1.45816e14i | − | 0.718013i | −0.933335 | − | 0.359006i | \(-0.883116\pi\) | ||
0.933335 | − | 0.359006i | \(-0.116884\pi\) | |||||||
\(728\) | −2.94534e14 | − | 1.54165e14i | −1.44038 | − | 0.753927i | ||||
\(729\) | −8.98651e13 | −0.436469 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.83355e14i | − | 1.83660i | ||||||
\(732\) | 3.08423e13 | + | 3.47617e13i | 0.146754 | + | 0.165404i | ||||
\(733\) | 5.65926e13 | 0.267448 | 0.133724 | − | 0.991019i | \(-0.457306\pi\) | ||||
0.133724 | + | 0.991019i | \(0.457306\pi\) | |||||||
\(734\) | 2.50268e13 | + | 6.59164e13i | 0.117469 | + | 0.309395i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.28427e14 | − | 8.15966e13i | 1.52072 | − | 0.377818i | ||||
\(737\) | −8.98255e11 | −0.00413107 | ||||||||
\(738\) | −3.76711e13 | + | 1.43028e13i | −0.172079 | + | 0.0653338i | ||||
\(739\) | − | 1.97385e14i | − | 0.895552i | −0.894146 | − | 0.447776i | \(-0.852216\pi\) | ||
0.894146 | − | 0.447776i | \(-0.147784\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.17096e14 | −0.524146 | ||||||||
\(742\) | 2.06430e12 | + | 5.43704e12i | 0.00917813 | + | 0.0241737i | ||||
\(743\) | − | 2.26298e14i | − | 0.999392i | −0.866201 | − | 0.499696i | \(-0.833445\pi\) | ||
0.866201 | − | 0.499696i | \(-0.166555\pi\) | |||||||
\(744\) | 1.97388e13 | − | 3.77111e13i | 0.0865877 | − | 0.165426i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.75227e14 | − | 6.65294e13i | 0.758417 | − | 0.287952i | ||||
\(747\) | 3.62660e13i | 0.155918i | ||||||||
\(748\) | −1.15317e13 | − | 1.29972e13i | −0.0492477 | − | 0.0555061i | ||||
\(749\) | 2.08662e14 | 0.885183 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.96141e14i | − | 1.65825i | −0.559063 | − | 0.829125i | \(-0.688839\pi\) | ||
0.559063 | − | 0.829125i | \(-0.311161\pi\) | |||||||
\(752\) | 3.93629e14 | + | 4.72024e13i | 1.63681 | + | 0.196279i | ||||
\(753\) | −9.12108e13 | −0.376766 | ||||||||
\(754\) | −3.26857e14 | + | 1.24099e14i | −1.34122 | + | 0.509229i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.59849e14 | + | 2.30550e14i | −1.05223 | + | 0.933591i | ||||
\(757\) | −3.60698e13 | −0.145099 | −0.0725495 | − | 0.997365i | \(-0.523114\pi\) | ||||
−0.0725495 | + | 0.997365i | \(0.523114\pi\) | |||||||
\(758\) | −1.14887e14 | − | 3.02593e14i | −0.459118 | − | 1.20924i | ||||
\(759\) | − | 1.56492e13i | − | 0.0621272i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.12974e14 | −1.22627 | −0.613133 | − | 0.789980i | \(-0.710091\pi\) | ||||
−0.613133 | + | 0.789980i | \(0.710091\pi\) | |||||||
\(762\) | −1.31589e14 | + | 4.99608e13i | −0.512205 | + | 0.194471i | ||||
\(763\) | − | 6.27141e13i | − | 0.242517i | ||||||
\(764\) | 2.47126e14 | + | 2.78531e14i | 0.949404 | + | 1.07005i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.37985e13 | + | 1.68035e14i | 0.241917 | + | 0.637170i | ||||
\(767\) | − | 1.05805e14i | − | 0.398592i | ||||||
\(768\) | −3.56573e13 | + | 1.46538e14i | −0.133457 | + | 0.548460i | ||||
\(769\) | 1.81483e14 | 0.674847 | 0.337423 | − | 0.941353i | \(-0.390445\pi\) | ||||
0.337423 | + | 0.941353i | \(0.390445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.41456e14i | 0.519218i | ||||||||
\(772\) | 1.57089e14 | − | 1.39377e14i | 0.572875 | − | 0.508283i | ||||
\(773\) | 3.11418e13 | 0.112835 | 0.0564177 | − | 0.998407i | \(-0.482032\pi\) | ||||
0.0564177 | + | 0.998407i | \(0.482032\pi\) | |||||||
\(774\) | −1.16799e14 | − | 3.07630e14i | −0.420471 | − | 1.10745i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.09124e14 | − | 3.99532e14i | 0.743181 | − | 1.41985i | ||||
\(777\) | −2.06119e14 | −0.727802 | ||||||||
\(778\) | 3.14907e14 | − | 1.19562e14i | 1.10480 | − | 0.419464i | ||||
\(779\) | 6.56028e13i | 0.228684i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.31366e13 | 0.0452092 | ||||||||
\(782\) | 1.71829e14 | + | 4.52569e14i | 0.587574 | + | 1.54757i | ||||
\(783\) | 3.65337e14i | 1.24132i | ||||||||
\(784\) | −4.22071e13 | + | 3.51972e14i | −0.142497 | + | 1.18831i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.99806e14 | − | 7.58611e13i | 0.666032 | − | 0.252875i | ||||
\(787\) | − | 1.00057e14i | − | 0.331417i | −0.986175 | − | 0.165709i | \(-0.947009\pi\) | ||
0.986175 | − | 0.165709i | \(-0.0529911\pi\) | |||||||
\(788\) | 3.70695e14 | − | 3.28898e14i | 1.22007 | − | 1.08251i | ||||
\(789\) | −2.53577e14 | −0.829326 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.68410e13i | 0.118973i | ||||||||
\(792\) | −1.32138e13 | − | 6.91637e12i | −0.0424034 | − | 0.0221949i | ||||
\(793\) | −1.34749e14 | −0.429693 | ||||||||
\(794\) | 5.53193e13 | − | 2.10033e13i | 0.175297 | − | 0.0665557i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.81919e14 | − | 4.30453e14i | −1.19510 | − | 1.34698i | ||||
\(797\) | 3.48016e14 | 1.08220 | 0.541100 | − | 0.840958i | \(-0.318008\pi\) | ||||
0.541100 | + | 0.840958i | \(0.318008\pi\) | |||||||
\(798\) | 8.13529e13 | + | 2.14270e14i | 0.251396 | + | 0.662136i | ||||
\(799\) | 5.67112e14i | 1.74155i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.61856e14 | −0.490870 | ||||||||
\(802\) | −2.42378e14 | + | 9.20246e13i | −0.730501 | + | 0.277352i | ||||
\(803\) | 4.37166e13i | 0.130939i | ||||||||
\(804\) | −8.34257e12 | + | 7.40193e12i | −0.0248325 | + | 0.0220326i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.38080e13 | + | 1.15383e14i | 0.128789 | + | 0.339208i | ||||
\(807\) | 6.89609e13i | 0.201481i | ||||||||
\(808\) | −1.98855e14 | + | 3.79914e14i | −0.577404 | + | 1.10313i | ||||
\(809\) | 3.13921e14 | 0.905896 | 0.452948 | − | 0.891537i | \(-0.350372\pi\) | ||||
0.452948 | + | 0.891537i | \(0.350372\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.70608e14i | 0.771323i | 0.922640 | + | 0.385662i | \(0.126027\pi\) | ||||
−0.922640 | + | 0.385662i | \(0.873973\pi\) | |||||||
\(812\) | 4.54169e14 | + | 5.11885e14i | 1.28658 | + | 1.45008i | ||||
\(813\) | −6.19729e13 | −0.174481 | ||||||||
\(814\) | −7.75108e12 | − | 2.04151e13i | −0.0216890 | − | 0.0571253i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.14202e14 | − | 2.56863e13i | −0.592070 | − | 0.0709987i | ||||
\(817\) | −5.35726e14 | −1.47175 | ||||||||
\(818\) | 2.79831e13 | − | 1.06245e13i | 0.0764062 | − | 0.0290095i | ||||
\(819\) | − | 4.08194e14i | − | 1.10776i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.85577e13 | 0.264225 | 0.132113 | − | 0.991235i | \(-0.457824\pi\) | ||||
0.132113 | + | 0.991235i | \(0.457824\pi\) | |||||||
\(822\) | −6.08762e12 | − | 1.60338e13i | −0.0162214 | − | 0.0427245i | ||||
\(823\) | 6.43156e14i | 1.70340i | 0.524027 | + | 0.851701i | \(0.324429\pi\) | ||||
−0.524027 | + | 0.851701i | \(0.675571\pi\) | |||||||
\(824\) | −3.87493e14 | − | 2.02822e14i | −1.02007 | − | 0.533924i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.93608e14 | + | 7.35080e13i | −0.503527 | + | 0.191176i | ||||
\(827\) | − | 1.77707e14i | − | 0.459386i | −0.973263 | − | 0.229693i | \(-0.926228\pi\) | ||
0.973263 | − | 0.229693i | \(-0.0737722\pi\) | |||||||
\(828\) | 2.75775e14 | + | 3.10820e14i | 0.708603 | + | 0.798652i | ||||
\(829\) | 1.33310e14 | 0.340478 | 0.170239 | − | 0.985403i | \(-0.445546\pi\) | ||||
0.170239 | + | 0.985403i | \(0.445546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 3.48376e14i | − | 0.879109i | ||||||
\(832\) | −2.49214e14 | − | 3.59335e14i | −0.625109 | − | 0.901328i | ||||
\(833\) | −5.07097e14 | −1.26435 | ||||||||
\(834\) | −1.39878e13 | + | 5.31080e12i | −0.0346672 | + | 0.0131622i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.81631e13 | + | 1.61152e13i | −0.0444794 | + | 0.0394643i | ||||
\(837\) | 1.28967e14 | 0.313943 | ||||||||
\(838\) | −4.83781e12 | − | 1.27420e13i | −0.0117065 | − | 0.0308331i | ||||
\(839\) | 1.39938e14i | 0.336608i | 0.985735 | + | 0.168304i | \(0.0538290\pi\) | ||||
−0.985735 | + | 0.168304i | \(0.946171\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.98984e14 | 0.710669 | ||||||||
\(842\) | −2.26879e14 | + | 8.61401e13i | −0.536085 | + | 0.203538i | ||||
\(843\) | 9.76608e13i | 0.229394i | ||||||||
\(844\) | 2.20969e14 | + | 2.49050e14i | 0.515965 | + | 0.581534i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.72786e14 | + | 4.55090e14i | 0.398710 | + | 1.05014i | ||||
\(847\) | − | 6.42934e14i | − | 1.47485i | ||||||
\(848\) | −9.10844e11 | + | 7.59568e12i | −0.00207713 | + | 0.0173216i | ||||
\(849\) | 3.39375e14 | 0.769380 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.08392e14i | 1.36312i | ||||||||
\(852\) | 1.22006e14 | − | 1.08250e14i | 0.271759 | − | 0.241118i | ||||
\(853\) | 5.04867e14 | 1.11797 | 0.558987 | − | 0.829176i | \(-0.311190\pi\) | ||||
0.558987 | + | 0.829176i | \(0.311190\pi\) | |||||||
\(854\) | 9.36168e13 | + | 2.46571e14i | 0.206094 | + | 0.542816i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.43179e14 | + | 1.27285e14i | 0.529123 | + | 0.276954i | ||||
\(857\) | 1.38544e14 | 0.299697 | 0.149848 | − | 0.988709i | \(-0.452121\pi\) | ||||
0.149848 | + | 0.988709i | \(0.452121\pi\) | |||||||
\(858\) | −1.89052e13 | + | 7.17782e12i | −0.0406579 | + | 0.0154368i | ||||
\(859\) | − | 3.87563e14i | − | 0.828661i | −0.910126 | − | 0.414331i | \(-0.864016\pi\) | ||
0.910126 | − | 0.414331i | \(-0.135984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.06937e14 | 0.226002 | ||||||||
\(862\) | −2.53540e14 | − | 6.67782e14i | −0.532733 | − | 1.40313i | ||||
\(863\) | − | 7.16581e14i | − | 1.49696i | −0.663155 | − | 0.748482i | \(-0.730783\pi\) | ||
0.663155 | − | 0.748482i | \(-0.269217\pi\) | |||||||
\(864\) | −4.43470e14 | + | 1.10179e14i | −0.921077 | + | 0.228839i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.70824e13 | + | 3.30630e13i | −0.178789 | + | 0.0678816i | ||||
\(867\) | − | 3.20843e13i | − | 0.0654932i | ||||||
\(868\) | 1.80699e14 | − | 1.60325e14i | 0.366740 | − | 0.325389i | ||||
\(869\) | 4.32812e13 | 0.0873374 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.23387e13i | − | 0.0645107i | ||||||
\(872\) | 3.82560e13 | − | 7.30884e13i | 0.0758782 | − | 0.144966i | ||||
\(873\) | 5.53712e14 | 1.09198 | ||||||||
\(874\) | 6.32451e14 | − | 2.40126e14i | 1.24014 | − | 0.470849i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.60240e14 | + | 4.06019e14i | 0.698347 | + | 0.787093i | ||||
\(877\) | −7.36516e14 | −1.41966 | −0.709830 | − | 0.704373i | \(-0.751228\pi\) | ||||
−0.709830 | + | 0.704373i | \(0.751228\pi\) | |||||||
\(878\) | 1.52585e14 | + | 4.01884e14i | 0.292442 | + | 0.770243i | ||||
\(879\) | − | 9.36947e13i | − | 0.178554i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.86757e14 | 1.67080 | 0.835401 | − | 0.549641i | \(-0.185236\pi\) | ||||
0.835401 | + | 0.549641i | \(0.185236\pi\) | |||||||
\(882\) | −4.06930e14 | + | 1.54501e14i | −0.762389 | + | 0.289460i | ||||
\(883\) | − | 5.90422e14i | − | 1.09991i | −0.835193 | − | 0.549957i | \(-0.814644\pi\) | ||
0.835193 | − | 0.549957i | \(-0.185356\pi\) | |||||||
\(884\) | 4.67920e14 | − | 4.15161e14i | 0.866782 | − | 0.769051i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.42118e14 | − | 3.74314e14i | −0.260303 | − | 0.685596i | ||||
\(887\) | 9.79412e14i | 1.78381i | 0.452227 | + | 0.891903i | \(0.350630\pi\) | ||||
−0.452227 | + | 0.891903i | \(0.649370\pi\) | |||||||
\(888\) | −2.40216e14 | − | 1.25734e14i | −0.435047 | − | 0.227713i | ||||
\(889\) | −7.98832e14 | −1.43862 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5.74544e12i | − | 0.0102314i | ||||||
\(892\) | −3.45892e14 | − | 3.89848e14i | −0.612515 | − | 0.690353i | ||||
\(893\) | 7.92522e14 | 1.39558 | ||||||||
\(894\) | −3.73238e12 | − | 9.83046e12i | −0.00653579 | − | 0.0172142i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.84391e14 | + | 7.05676e14i | −0.838796 | + | 1.22198i | ||||
\(897\) | 5.63396e14 | 0.970178 | ||||||||
\(898\) | −3.74983e14 | + | 1.42371e14i | −0.642140 | + | 0.243804i | ||||
\(899\) | − | 2.54056e14i | − | 0.432645i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09433e13 | −0.0184300 | ||||||||
\(902\) | 4.02135e12 | + | 1.05916e13i | 0.00673502 | + | 0.0177389i | ||||
\(903\) | 8.73269e14i | 1.45449i | ||||||||
\(904\) | −2.24733e13 | + | 4.29353e13i | −0.0372241 | + | 0.0711168i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.36301e14 | − | 1.27685e14i | 0.550919 | − | 0.209170i | ||||
\(907\) | 5.03887e14i | 0.820912i | 0.911880 | + | 0.410456i | \(0.134631\pi\) | ||||
−0.911880 | + | 0.410456i | \(0.865369\pi\) | |||||||
\(908\) | −6.80009e13 | − | 7.66425e13i | −0.110176 | − | 0.124177i | ||||
\(909\) | −5.26523e14 | −0.848395 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.24734e14i | − | 0.198789i | −0.995048 | − | 0.0993946i | \(-0.968309\pi\) | ||
0.995048 | − | 0.0993946i | \(-0.0316906\pi\) | |||||||
\(912\) | −3.58958e13 | + | 2.99341e14i | −0.0568943 | + | 0.474452i | ||||
\(913\) | 1.01965e13 | 0.0160730 | ||||||||
\(914\) | −2.78176e14 | + | 1.05616e14i | −0.436102 | + | 0.165577i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.90636e13 | + | 3.46591e13i | −0.0605751 | + | 0.0537452i | ||||
\(917\) | 1.21296e15 | 1.87067 | ||||||||
\(918\) | −2.32018e14 | − | 6.11098e14i | −0.355884 | − | 0.937340i | ||||
\(919\) | 5.28572e14i | 0.806356i | 0.915122 | + | 0.403178i | \(0.132095\pi\) | ||||
−0.915122 | + | 0.403178i | \(0.867905\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.26103e14 | 0.341200 | ||||||||
\(922\) | 6.01511e14 | − | 2.28378e14i | 0.902794 | − | 0.342768i | ||||
\(923\) | 4.72939e14i | 0.705987i | ||||||||
\(924\) | 2.62688e13 | + | 2.96071e13i | 0.0390015 | + | 0.0439578i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.19009e14 | − | 3.13450e14i | −0.174793 | − | 0.460376i | ||||
\(927\) | − | 5.37027e14i | − | 0.784508i | ||||||
\(928\) | 2.17045e14 | + | 8.73608e14i | 0.315363 | + | 1.26934i | ||||
\(929\) | 2.34323e14 | 0.338639 | 0.169319 | − | 0.985561i | \(-0.445843\pi\) | ||||
0.169319 | + | 0.985561i | \(0.445843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.08653e14i | 1.01318i | ||||||||
\(932\) | −8.65861e14 | + | 7.68234e14i | −1.23131 | + | 1.09248i | ||||
\(933\) | 3.25707e14 | 0.460700 | ||||||||
\(934\) | −5.83111e13 | − | 1.53582e14i | −0.0820383 | − | 0.216075i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.49001e14 | − | 4.75719e14i | 0.346595 | − | 0.662172i | ||||
\(937\) | 6.49421e14 | 0.899142 | 0.449571 | − | 0.893245i | \(-0.351577\pi\) | ||||
0.449571 | + | 0.893245i | \(0.351577\pi\) | |||||||
\(938\) | −5.91754e13 | + | 2.24674e13i | −0.0814942 | + | 0.0309413i | ||||
\(939\) | − | 1.68584e14i | − | 0.230934i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.81546e14 | 0.788199 | 0.394099 | − | 0.919068i | \(-0.371057\pi\) | ||||
0.394099 | + | 0.919068i | \(0.371057\pi\) | |||||||
\(942\) | −1.84900e14 | − | 4.86996e14i | −0.249277 | − | 0.656555i | ||||
\(943\) | − | 3.15640e14i | − | 0.423286i | ||||||
\(944\) | −2.70475e14 | − | 3.24343e13i | −0.360801 | − | 0.0432658i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.64929e13 | + | 3.28392e13i | −0.114163 | + | 0.0433447i | ||||
\(947\) | 8.31766e14i | 1.09207i | 0.837762 | + | 0.546036i | \(0.183864\pi\) | ||||
−0.837762 | + | 0.546036i | \(0.816136\pi\) | |||||||
\(948\) | 4.01975e14 | − | 3.56652e14i | 0.524998 | − | 0.465804i | ||||
\(949\) | −1.57387e15 | −2.04474 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.55925e14i | 1.10036i | ||||||||
\(952\) | −1.08478e15 | − | 5.67795e14i | −1.38725 | − | 0.726117i | ||||
\(953\) | −1.06960e15 | −1.36068 | −0.680338 | − | 0.732898i | \(-0.738167\pi\) | ||||
−0.680338 | + | 0.732898i | \(0.738167\pi\) | |||||||
\(954\) | −8.78168e12 | + | 3.33418e12i | −0.0111131 | + | 0.00421937i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.39941e14 | − | 4.95849e14i | −0.550941 | − | 0.620955i | ||||
\(957\) | 4.16264e13 | 0.0518572 | ||||||||
\(958\) | 1.85105e13 | + | 4.87535e13i | 0.0229398 | + | 0.0604196i | ||||
\(959\) | − | 9.73359e13i | − | 0.120000i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.29945e14 | 0.890580 | ||||||||
\(962\) | 7.34977e14 | − | 2.79052e14i | 0.892069 | − | 0.338696i | ||||
\(963\) | 3.37021e14i | 0.406936i | ||||||||
\(964\) | 9.03935e14 | − | 8.02015e14i | 1.08581 | − | 0.963379i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.91420e14 | − | 1.03094e15i | −0.465327 | − | 1.22559i | ||||
\(967\) | 6.55048e13i | 0.0774713i | 0.999249 | + | 0.0387356i | \(0.0123330\pi\) | ||||
−0.999249 | + | 0.0387356i | \(0.987667\pi\) | |||||||
\(968\) | 3.92194e14 | − | 7.49289e14i | 0.461449 | − | 0.881602i | ||||
\(969\) | −4.31269e14 | −0.504812 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.63694e14i | 0.189643i | 0.995494 | + | 0.0948213i | \(0.0302280\pi\) | ||||
−0.995494 | + | 0.0948213i | \(0.969772\pi\) | |||||||
\(972\) | −5.93845e14 | − | 6.69311e14i | −0.684450 | − | 0.771430i | ||||
\(973\) | −8.49153e13 | −0.0973692 | ||||||||
\(974\) | 4.56624e14 | + | 1.20267e15i | 0.520911 | + | 1.37199i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.13070e13 | + | 3.44466e14i | −0.0466417 | + | 0.388953i | ||||
\(977\) | −4.43613e14 | −0.498347 | −0.249173 | − | 0.968459i | \(-0.580159\pi\) | ||||
−0.249173 | + | 0.968459i | \(0.580159\pi\) | |||||||
\(978\) | 2.21389e14 | − | 8.40556e13i | 0.247435 | − | 0.0939448i | ||||
\(979\) | 4.55072e13i | 0.0506019i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.01293e14 | 0.111490 | ||||||||
\(982\) | −2.45092e14 | − | 6.45532e14i | −0.268393 | − | 0.706904i | ||||
\(983\) | − | 1.06351e14i | − | 0.115870i | −0.998320 | − | 0.0579352i | \(-0.981548\pi\) | ||
0.998320 | − | 0.0579352i | \(-0.0184517\pi\) | |||||||
\(984\) | 1.24626e14 | + | 6.52322e13i | 0.135094 | + | 0.0707109i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.20382e15 | + | 4.57061e14i | −1.29175 | + | 0.490444i | ||||
\(987\) | − | 1.29186e15i | − | 1.37921i | ||||||
\(988\) | −5.80175e14 | − | 6.53904e14i | −0.616274 | − | 0.694591i | ||||
\(989\) | 2.57759e15 | 2.72415 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6.83253e14i | − | 0.714847i | −0.933942 | − | 0.357424i | \(-0.883655\pi\) | ||
0.933942 | − | 0.357424i | \(-0.116345\pi\) | |||||||
\(992\) | 3.08390e14 | − | 7.66186e13i | 0.321027 | − | 0.0797583i | ||||
\(993\) | −9.46414e13 | −0.0980246 | ||||||||
\(994\) | 8.65413e14 | − | 3.28575e14i | 0.891849 | − | 0.338612i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.47003e13 | − | 8.40227e13i | 0.0966173 | − | 0.0857235i | ||||
\(997\) | 1.83065e14 | 0.185836 | 0.0929180 | − | 0.995674i | \(-0.470381\pi\) | ||||
0.0929180 | + | 0.995674i | \(0.470381\pi\) | |||||||
\(998\) | 4.98319e14 | + | 1.31249e15i | 0.503332 | + | 1.32569i | ||||
\(999\) | − | 8.21504e14i | − | 0.825624i |
(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 | 100.11.b.e.51.17 | 20 | ||
4.3 | odd | 2 | inner | 100.11.b.e.51.18 | 20 | ||
5.2 | odd | 4 | 100.11.d.c.99.28 | 40 | |||
5.3 | odd | 4 | 100.11.d.c.99.13 | 40 | |||
5.4 | even | 2 | 20.11.b.a.11.4 | yes | 20 | ||
15.14 | odd | 2 | 180.11.c.a.91.17 | 20 | |||
20.3 | even | 4 | 100.11.d.c.99.27 | 40 | |||
20.7 | even | 4 | 100.11.d.c.99.14 | 40 | |||
20.19 | odd | 2 | 20.11.b.a.11.3 | ✓ | 20 | ||
40.19 | odd | 2 | 320.11.b.d.191.13 | 20 | |||
40.29 | even | 2 | 320.11.b.d.191.8 | 20 | |||
60.59 | even | 2 | 180.11.c.a.91.18 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.b.a.11.3 | ✓ | 20 | 20.19 | odd | 2 | ||
20.11.b.a.11.4 | yes | 20 | 5.4 | even | 2 | ||
100.11.b.e.51.17 | 20 | 1.1 | even | 1 | trivial | ||
100.11.b.e.51.18 | 20 | 4.3 | odd | 2 | inner | ||
100.11.d.c.99.13 | 40 | 5.3 | odd | 4 | |||
100.11.d.c.99.14 | 40 | 20.7 | even | 4 | |||
100.11.d.c.99.27 | 40 | 20.3 | even | 4 | |||
100.11.d.c.99.28 | 40 | 5.2 | odd | 4 | |||
180.11.c.a.91.17 | 20 | 15.14 | odd | 2 | |||
180.11.c.a.91.18 | 20 | 60.59 | even | 2 | |||
320.11.b.d.191.8 | 20 | 40.29 | even | 2 | |||
320.11.b.d.191.13 | 20 | 40.19 | odd | 2 |