Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,33,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(25.9466620569\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 72511313626452 x^{12} + \cdots + 62\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{182}\cdot 3^{20}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.7 | ||
Root | \(4.36932e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.33.b.b.3.8 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −15224.0 | − | 63743.2i | −0.232300 | − | 0.972644i | ||||
\(3\) | 6.99091e7i | 1.62403i | 0.583637 | + | 0.812014i | \(0.301629\pi\) | ||||
−0.583637 | + | 0.812014i | \(0.698371\pi\) | |||||||
\(4\) | −3.83143e9 | + | 1.94085e9i | −0.892074 | + | 0.451890i | ||||
\(5\) | −1.46681e11 | −0.961290 | −0.480645 | − | 0.876915i | \(-0.659597\pi\) | ||||
−0.480645 | + | 0.876915i | \(0.659597\pi\) | |||||||
\(6\) | 4.45623e12 | − | 1.06430e12i | 1.57960 | − | 0.377262i | ||||
\(7\) | 5.71644e13i | 1.72011i | 0.510198 | + | 0.860057i | \(0.329572\pi\) | ||||
−0.510198 | + | 0.860057i | \(0.670428\pi\) | |||||||
\(8\) | 1.82046e14 | + | 2.14680e14i | 0.646757 | + | 0.762696i | ||||
\(9\) | −3.03426e15 | −1.63747 | ||||||||
\(10\) | 2.23307e15 | + | 9.34993e15i | 0.223307 | + | 0.934993i | ||||
\(11\) | 6.39967e16i | 1.39276i | 0.717675 | + | 0.696378i | \(0.245206\pi\) | ||||
−0.717675 | + | 0.696378i | \(0.754794\pi\) | |||||||
\(12\) | −1.35683e17 | − | 2.67852e17i | −0.733883 | − | 1.44875i | ||||
\(13\) | 3.82332e17 | 0.574576 | 0.287288 | − | 0.957844i | \(-0.407246\pi\) | ||||
0.287288 | + | 0.957844i | \(0.407246\pi\) | |||||||
\(14\) | 3.64385e18 | − | 8.70272e17i | 1.67306 | − | 0.399582i | ||||
\(15\) | − | 1.02543e19i | − | 1.56116i | ||||||
\(16\) | 1.09129e19 | − | 1.48725e19i | 0.591590 | − | 0.806239i | ||||
\(17\) | −4.07694e19 | −0.837822 | −0.418911 | − | 0.908027i | \(-0.637588\pi\) | ||||
−0.418911 | + | 0.908027i | \(0.637588\pi\) | |||||||
\(18\) | 4.61937e19 | + | 1.93414e20i | 0.380384 | + | 1.59268i | ||||
\(19\) | − | 6.13984e19i | − | 0.212863i | −0.994320 | − | 0.106431i | \(-0.966058\pi\) | ||
0.994320 | − | 0.106431i | \(-0.0339424\pi\) | |||||||
\(20\) | 5.61998e20 | − | 2.84687e20i | 0.857541 | − | 0.434397i | ||||
\(21\) | −3.99632e21 | −2.79352 | ||||||||
\(22\) | 4.07936e21 | − | 9.74287e20i | 1.35466 | − | 0.323537i | ||||
\(23\) | − | 2.81087e20i | − | 0.0458348i | −0.999737 | − | 0.0229174i | \(-0.992705\pi\) | ||
0.999737 | − | 0.0229174i | \(-0.00729548\pi\) | |||||||
\(24\) | −1.50081e22 | + | 1.27267e22i | −1.23864 | + | 1.05035i | ||||
\(25\) | −1.76771e21 | −0.0759224 | ||||||||
\(26\) | −5.82063e21 | − | 2.43711e22i | −0.133474 | − | 0.558858i | ||||
\(27\) | − | 8.25797e22i | − | 1.03527i | ||||||
\(28\) | −1.10948e23 | − | 2.19021e23i | −0.777303 | − | 1.53447i | ||||
\(29\) | 9.24035e22 | 0.369250 | 0.184625 | − | 0.982809i | \(-0.440893\pi\) | ||||
0.184625 | + | 0.982809i | \(0.440893\pi\) | |||||||
\(30\) | −6.53645e23 | + | 1.56112e23i | −1.51846 | + | 0.362658i | ||||
\(31\) | 4.23845e23i | 0.582666i | 0.956622 | + | 0.291333i | \(0.0940987\pi\) | ||||
−0.956622 | + | 0.291333i | \(0.905901\pi\) | |||||||
\(32\) | −1.11416e24 | − | 4.69206e23i | −0.921610 | − | 0.388118i | ||||
\(33\) | −4.47396e24 | −2.26188 | ||||||||
\(34\) | 6.20674e23 | + | 2.59877e24i | 0.194626 | + | 0.814903i | ||||
\(35\) | − | 8.38495e24i | − | 1.65353i | ||||||
\(36\) | 1.16256e25 | − | 5.88906e24i | 1.46074 | − | 0.739957i | ||||
\(37\) | −4.96114e23 | −0.0402118 | −0.0201059 | − | 0.999798i | \(-0.506400\pi\) | ||||
−0.0201059 | + | 0.999798i | \(0.506400\pi\) | |||||||
\(38\) | −3.91373e24 | + | 9.34729e23i | −0.207040 | + | 0.0494480i | ||||
\(39\) | 2.67285e25i | 0.933127i | ||||||||
\(40\) | −2.67027e25 | − | 3.14895e25i | −0.621721 | − | 0.733172i | ||||
\(41\) | 7.78015e25 | 1.22024 | 0.610121 | − | 0.792308i | \(-0.291121\pi\) | ||||
0.610121 | + | 0.792308i | \(0.291121\pi\) | |||||||
\(42\) | 6.08399e25 | + | 2.54738e26i | 0.648933 | + | 2.71710i | ||||
\(43\) | 5.67810e24i | 0.0415631i | 0.999784 | + | 0.0207815i | \(0.00661544\pi\) | ||||
−0.999784 | + | 0.0207815i | \(0.993385\pi\) | |||||||
\(44\) | −1.24208e26 | − | 2.45199e26i | −0.629373 | − | 1.24244i | ||||
\(45\) | 4.45069e26 | 1.57408 | ||||||||
\(46\) | −1.79174e25 | + | 4.27927e24i | −0.0445810 | + | 0.0106474i | ||||
\(47\) | − | 2.70622e26i | − | 0.477307i | −0.971105 | − | 0.238653i | \(-0.923294\pi\) | ||
0.971105 | − | 0.238653i | \(-0.0767059\pi\) | |||||||
\(48\) | 1.03972e27 | + | 7.62912e26i | 1.30935 | + | 0.960760i | ||||
\(49\) | −2.16335e27 | −1.95879 | ||||||||
\(50\) | 2.69116e25 | + | 1.12679e26i | 0.0176368 | + | 0.0738454i | ||||
\(51\) | − | 2.85015e27i | − | 1.36065i | ||||||
\(52\) | −1.46488e27 | + | 7.42051e26i | −0.512564 | + | 0.259645i | ||||
\(53\) | 1.23036e27 | 0.317408 | 0.158704 | − | 0.987326i | \(-0.449268\pi\) | ||||
0.158704 | + | 0.987326i | \(0.449268\pi\) | |||||||
\(54\) | −5.26390e27 | + | 1.25719e27i | −1.00695 | + | 0.240493i | ||||
\(55\) | − | 9.38712e27i | − | 1.33884i | ||||||
\(56\) | −1.22721e28 | + | 1.04066e28i | −1.31192 | + | 1.11250i | ||||
\(57\) | 4.29231e27 | 0.345695 | ||||||||
\(58\) | −1.40675e27 | − | 5.89010e27i | −0.0857768 | − | 0.359149i | ||||
\(59\) | − | 3.43224e27i | − | 0.159201i | −0.996827 | − | 0.0796005i | \(-0.974636\pi\) | ||
0.996827 | − | 0.0796005i | \(-0.0253645\pi\) | |||||||
\(60\) | 1.99022e28 | + | 3.92888e28i | 0.705474 | + | 1.39267i | ||||
\(61\) | 4.92044e28 | 1.33883 | 0.669416 | − | 0.742888i | \(-0.266544\pi\) | ||||
0.669416 | + | 0.742888i | \(0.266544\pi\) | |||||||
\(62\) | 2.70172e28 | − | 6.45261e27i | 0.566726 | − | 0.135353i | ||||
\(63\) | − | 1.73452e29i | − | 2.81663i | ||||||
\(64\) | −1.29467e28 | + | 7.81632e28i | −0.163411 | + | 0.986558i | ||||
\(65\) | −5.60809e28 | −0.552333 | ||||||||
\(66\) | 6.81115e28 | + | 2.85184e29i | 0.525433 | + | 2.20000i | ||||
\(67\) | 1.86282e29i | 1.12973i | 0.825184 | + | 0.564864i | \(0.191071\pi\) | ||||
−0.825184 | + | 0.564864i | \(0.808929\pi\) | |||||||
\(68\) | 1.56205e29 | − | 7.91275e28i | 0.747399 | − | 0.378604i | ||||
\(69\) | 1.96506e28 | 0.0744371 | ||||||||
\(70\) | −5.34483e29 | + | 1.27652e29i | −1.60829 | + | 0.384114i | ||||
\(71\) | − | 7.39887e29i | − | 1.77432i | −0.461463 | − | 0.887159i | \(-0.652675\pi\) | ||
0.461463 | − | 0.887159i | \(-0.347325\pi\) | |||||||
\(72\) | −5.52375e29 | − | 6.51395e29i | −1.05904 | − | 1.24889i | ||||
\(73\) | 1.01270e30 | 1.55710 | 0.778549 | − | 0.627583i | \(-0.215956\pi\) | ||||
0.778549 | + | 0.627583i | \(0.215956\pi\) | |||||||
\(74\) | 7.55284e27 | + | 3.16239e28i | 0.00934120 | + | 0.0391118i | ||||
\(75\) | − | 1.23579e29i | − | 0.123300i | ||||||
\(76\) | 1.19165e29 | + | 2.35243e29i | 0.0961905 | + | 0.189889i | ||||
\(77\) | −3.65834e30 | −2.39570 | ||||||||
\(78\) | 1.70376e30 | − | 4.06915e29i | 0.907601 | − | 0.216765i | ||||
\(79\) | 2.63707e30i | 1.14575i | 0.819644 | + | 0.572874i | \(0.194171\pi\) | ||||
−0.819644 | + | 0.572874i | \(0.805829\pi\) | |||||||
\(80\) | −1.60072e30 | + | 2.18151e30i | −0.568690 | + | 0.775029i | ||||
\(81\) | 1.50522e29 | 0.0438367 | ||||||||
\(82\) | −1.18445e30 | − | 4.95932e30i | −0.283462 | − | 1.18686i | ||||
\(83\) | 5.56904e30i | 1.09782i | 0.835882 | + | 0.548910i | \(0.184957\pi\) | ||||
−0.835882 | + | 0.548910i | \(0.815043\pi\) | |||||||
\(84\) | 1.53116e31 | − | 7.75627e30i | 2.49202 | − | 1.26236i | ||||
\(85\) | 5.98011e30 | 0.805390 | ||||||||
\(86\) | 3.61940e29 | − | 8.64434e28i | 0.0404261 | − | 0.00965510i | ||||
\(87\) | 6.45985e30i | 0.599673i | ||||||||
\(88\) | −1.37388e31 | + | 1.16503e31i | −1.06225 | + | 0.900775i | ||||
\(89\) | 1.36383e31 | 0.880073 | 0.440037 | − | 0.897980i | \(-0.354965\pi\) | ||||
0.440037 | + | 0.897980i | \(0.354965\pi\) | |||||||
\(90\) | −6.77574e30 | − | 2.83701e31i | −0.365659 | − | 1.53102i | ||||
\(91\) | 2.18558e31i | 0.988336i | ||||||||
\(92\) | 5.45549e29 | + | 1.07697e30i | 0.0207123 | + | 0.0408880i | ||||
\(93\) | −2.96306e31 | −0.946266 | ||||||||
\(94\) | −1.72503e31 | + | 4.11995e30i | −0.464249 | + | 0.110878i | ||||
\(95\) | 9.00598e30i | 0.204623i | ||||||||
\(96\) | 3.28017e31 | − | 7.78898e31i | 0.630314 | − | 1.49672i | ||||
\(97\) | −9.37964e31 | −1.52700 | −0.763499 | − | 0.645809i | \(-0.776520\pi\) | ||||
−0.763499 | + | 0.645809i | \(0.776520\pi\) | |||||||
\(98\) | 3.29348e31 | + | 1.37899e32i | 0.455028 | + | 1.90521i | ||||
\(99\) | − | 1.94183e32i | − | 2.28059i | ||||||
\(100\) | 6.77283e30 | − | 3.43086e30i | 0.0677283 | − | 0.0343086i | ||||
\(101\) | 5.72813e30 | 0.0488507 | 0.0244253 | − | 0.999702i | \(-0.492224\pi\) | ||||
0.0244253 | + | 0.999702i | \(0.492224\pi\) | |||||||
\(102\) | −1.81678e32 | + | 4.33908e31i | −1.32343 | + | 0.316078i | ||||
\(103\) | 9.76491e31i | 0.608517i | 0.952590 | + | 0.304258i | \(0.0984087\pi\) | ||||
−0.952590 | + | 0.304258i | \(0.901591\pi\) | |||||||
\(104\) | 6.96020e31 | + | 8.20790e31i | 0.371611 | + | 0.438227i | ||||
\(105\) | 5.86184e32 | 2.68538 | ||||||||
\(106\) | −1.87310e31 | − | 7.84271e31i | −0.0737339 | − | 0.308725i | ||||
\(107\) | − | 2.83419e32i | − | 0.960038i | −0.877258 | − | 0.480019i | \(-0.840630\pi\) | ||
0.877258 | − | 0.480019i | \(-0.159370\pi\) | |||||||
\(108\) | 1.60275e32 | + | 3.16398e32i | 0.467828 | + | 0.923536i | ||||
\(109\) | −2.57765e32 | −0.649232 | −0.324616 | − | 0.945846i | \(-0.605235\pi\) | ||||
−0.324616 | + | 0.945846i | \(0.605235\pi\) | |||||||
\(110\) | −5.98365e32 | + | 1.42910e32i | −1.30222 | + | 0.311013i | ||||
\(111\) | − | 3.46829e31i | − | 0.0653051i | ||||||
\(112\) | 8.50177e32 | + | 6.23831e32i | 1.38682 | + | 1.01760i | ||||
\(113\) | 2.01143e32 | 0.284610 | 0.142305 | − | 0.989823i | \(-0.454549\pi\) | ||||
0.142305 | + | 0.989823i | \(0.454549\pi\) | |||||||
\(114\) | −6.53461e31 | − | 2.73605e32i | −0.0803049 | − | 0.336238i | ||||
\(115\) | 4.12302e31i | 0.0440606i | ||||||||
\(116\) | −3.54037e32 | + | 1.79342e32i | −0.329398 | + | 0.166861i | ||||
\(117\) | −1.16010e33 | −0.940850 | ||||||||
\(118\) | −2.18782e32 | + | 5.22525e31i | −0.154846 | + | 0.0369824i | ||||
\(119\) | − | 2.33056e33i | − | 1.44115i | ||||||
\(120\) | 2.20140e33 | − | 1.86676e33i | 1.19069 | − | 1.00969i | ||||
\(121\) | −1.98421e33 | −0.939768 | ||||||||
\(122\) | −7.49087e32 | − | 3.13644e33i | −0.311011 | − | 1.30221i | ||||
\(123\) | 5.43903e33i | 1.98171i | ||||||||
\(124\) | −8.22620e32 | − | 1.62393e33i | −0.263301 | − | 0.519781i | ||||
\(125\) | 3.67448e33 | 1.03427 | ||||||||
\(126\) | −1.10564e34 | + | 2.64063e33i | −2.73958 | + | 0.654304i | ||||
\(127\) | 7.58615e33i | 1.65639i | 0.560442 | + | 0.828194i | \(0.310631\pi\) | ||||
−0.560442 | + | 0.828194i | \(0.689369\pi\) | |||||||
\(128\) | 5.17947e33 | − | 3.64691e32i | 0.997530 | − | 0.0702370i | ||||
\(129\) | −3.96951e32 | −0.0674996 | ||||||||
\(130\) | 8.53776e32 | + | 3.57478e33i | 0.128307 | + | 0.537224i | ||||
\(131\) | − | 7.08226e33i | − | 0.941523i | −0.882261 | − | 0.470761i | \(-0.843979\pi\) | ||
0.882261 | − | 0.470761i | \(-0.156021\pi\) | |||||||
\(132\) | 1.71416e34 | − | 8.68329e33i | 2.01776 | − | 1.02212i | ||||
\(133\) | 3.50980e33 | 0.366148 | ||||||||
\(134\) | 1.18742e34 | − | 2.83596e33i | 1.09882 | − | 0.262436i | ||||
\(135\) | 1.21129e34i | 0.995193i | ||||||||
\(136\) | −7.42191e33 | − | 8.75238e33i | −0.541868 | − | 0.639004i | ||||
\(137\) | −1.56966e34 | −1.01924 | −0.509620 | − | 0.860399i | \(-0.670214\pi\) | ||||
−0.509620 | + | 0.860399i | \(0.670214\pi\) | |||||||
\(138\) | −2.99160e32 | − | 1.25259e33i | −0.0172917 | − | 0.0724008i | ||||
\(139\) | − | 1.66363e34i | − | 0.856680i | −0.903618 | − | 0.428340i | \(-0.859099\pi\) | ||
0.903618 | − | 0.428340i | \(-0.140901\pi\) | |||||||
\(140\) | 1.62740e34 | + | 3.21263e34i | 0.747213 | + | 1.47507i | ||||
\(141\) | 1.89189e34 | 0.775160 | ||||||||
\(142\) | −4.71628e34 | + | 1.12640e34i | −1.72578 | + | 0.412174i | ||||
\(143\) | 2.44680e34i | 0.800243i | ||||||||
\(144\) | −3.31127e34 | + | 4.51270e34i | −0.968711 | + | 1.32019i | ||||
\(145\) | −1.35539e34 | −0.354956 | ||||||||
\(146\) | −1.54174e34 | − | 6.45529e34i | −0.361714 | − | 1.51450i | ||||
\(147\) | − | 1.51238e35i | − | 3.18114i | ||||||
\(148\) | 1.90082e33 | − | 9.62884e32i | 0.0358719 | − | 0.0181713i | ||||
\(149\) | 3.15083e33 | 0.0533881 | 0.0266941 | − | 0.999644i | \(-0.491502\pi\) | ||||
0.0266941 | + | 0.999644i | \(0.491502\pi\) | |||||||
\(150\) | −7.87730e33 | + | 1.88136e33i | −0.119927 | + | 0.0286426i | ||||
\(151\) | 6.49171e34i | 0.888644i | 0.895867 | + | 0.444322i | \(0.146555\pi\) | ||||
−0.895867 | + | 0.444322i | \(0.853445\pi\) | |||||||
\(152\) | 1.31810e34 | − | 1.11773e34i | 0.162349 | − | 0.137670i | ||||
\(153\) | 1.23705e35 | 1.37191 | ||||||||
\(154\) | 5.56946e34 | + | 2.33194e35i | 0.556521 | + | 2.33016i | ||||
\(155\) | − | 6.21700e34i | − | 0.560111i | ||||||
\(156\) | −5.18761e34 | − | 1.02408e35i | −0.421671 | − | 0.832418i | ||||
\(157\) | −2.59905e35 | −1.90731 | −0.953653 | − | 0.300908i | \(-0.902710\pi\) | ||||
−0.953653 | + | 0.300908i | \(0.902710\pi\) | |||||||
\(158\) | 1.68096e35 | − | 4.01468e34i | 1.11440 | − | 0.266157i | ||||
\(159\) | 8.60134e34i | 0.515480i | ||||||||
\(160\) | 1.63426e35 | + | 6.88236e34i | 0.885934 | + | 0.373093i | ||||
\(161\) | 1.60682e34 | 0.0788412 | ||||||||
\(162\) | −2.29154e33 | − | 9.59472e33i | −0.0101833 | − | 0.0426376i | ||||
\(163\) | − | 1.38465e34i | − | 0.0557619i | −0.999611 | − | 0.0278809i | \(-0.991124\pi\) | ||
0.999611 | − | 0.0278809i | \(-0.00887593\pi\) | |||||||
\(164\) | −2.98091e35 | + | 1.51001e35i | −1.08855 | + | 0.551416i | ||||
\(165\) | 6.56245e35 | 2.17432 | ||||||||
\(166\) | 3.54989e35 | − | 8.47831e34i | 1.06779 | − | 0.255023i | ||||
\(167\) | 6.26917e35i | 1.71296i | 0.516182 | + | 0.856479i | \(0.327353\pi\) | ||||
−0.516182 | + | 0.856479i | \(0.672647\pi\) | |||||||
\(168\) | −7.27513e35 | − | 8.57928e35i | −1.80673 | − | 2.13060i | ||||
\(169\) | −2.96601e35 | −0.669863 | ||||||||
\(170\) | −9.10412e34 | − | 3.81191e35i | −0.187092 | − | 0.783358i | ||||
\(171\) | 1.86299e35i | 0.348556i | ||||||||
\(172\) | −1.10204e34 | − | 2.17552e34i | −0.0187819 | − | 0.0370773i | ||||
\(173\) | −1.09058e36 | −1.69403 | −0.847014 | − | 0.531570i | \(-0.821602\pi\) | ||||
−0.847014 | + | 0.531570i | \(0.821602\pi\) | |||||||
\(174\) | 4.11772e35 | − | 9.83448e34i | 0.583268 | − | 0.139304i | ||||
\(175\) | − | 1.01050e35i | − | 0.130595i | ||||||
\(176\) | 9.51790e35 | + | 6.98391e35i | 1.12289 | + | 0.823941i | ||||
\(177\) | 2.39945e35 | 0.258547 | ||||||||
\(178\) | −2.07629e35 | − | 8.69346e35i | −0.204441 | − | 0.855998i | ||||
\(179\) | − | 1.61896e36i | − | 1.45743i | −0.684815 | − | 0.728717i | \(-0.740117\pi\) | ||
0.684815 | − | 0.728717i | \(-0.259883\pi\) | |||||||
\(180\) | −1.70525e36 | + | 8.63815e35i | −1.40420 | + | 0.711313i | ||||
\(181\) | −8.32130e35 | −0.627096 | −0.313548 | − | 0.949572i | \(-0.601518\pi\) | ||||
−0.313548 | + | 0.949572i | \(0.601518\pi\) | |||||||
\(182\) | 1.39316e36 | − | 3.32733e35i | 0.961299 | − | 0.229590i | ||||
\(183\) | 3.43983e36i | 2.17430i | ||||||||
\(184\) | 6.03438e34 | − | 5.11708e34i | 0.0349581 | − | 0.0296440i | ||||
\(185\) | 7.27705e34 | 0.0386552 | ||||||||
\(186\) | 4.51096e35 | + | 1.88875e36i | 0.219817 | + | 0.920380i | ||||
\(187\) | − | 2.60911e36i | − | 1.16688i | ||||||
\(188\) | 5.25238e35 | + | 1.03687e36i | 0.215690 | + | 0.425793i | ||||
\(189\) | 4.72062e36 | 1.78078 | ||||||||
\(190\) | 5.74070e35 | − | 1.37107e35i | 0.199025 | − | 0.0475338i | ||||
\(191\) | − | 2.12110e36i | − | 0.676127i | −0.941123 | − | 0.338063i | \(-0.890228\pi\) | ||
0.941123 | − | 0.338063i | \(-0.109772\pi\) | |||||||
\(192\) | −5.46432e36 | − | 9.05094e35i | −1.60220 | − | 0.265383i | ||||
\(193\) | 5.32606e36 | 1.43711 | 0.718553 | − | 0.695472i | \(-0.244805\pi\) | ||||
0.718553 | + | 0.695472i | \(0.244805\pi\) | |||||||
\(194\) | 1.42796e36 | + | 5.97888e36i | 0.354721 | + | 1.48523i | ||||
\(195\) | − | 3.92057e36i | − | 0.897005i | ||||||
\(196\) | 8.28870e36 | − | 4.19874e36i | 1.74739 | − | 0.885160i | ||||
\(197\) | −3.57225e36 | −0.694195 | −0.347098 | − | 0.937829i | \(-0.612833\pi\) | ||||
−0.347098 | + | 0.937829i | \(0.612833\pi\) | |||||||
\(198\) | −1.23778e37 | + | 2.95624e36i | −2.21821 | + | 0.529782i | ||||
\(199\) | − | 2.75249e36i | − | 0.455069i | −0.973770 | − | 0.227534i | \(-0.926934\pi\) | ||
0.973770 | − | 0.227534i | \(-0.0730664\pi\) | |||||||
\(200\) | −3.21804e35 | − | 3.79491e35i | −0.0491033 | − | 0.0579057i | ||||
\(201\) | −1.30228e37 | −1.83471 | ||||||||
\(202\) | −8.72050e34 | − | 3.65129e35i | −0.0113480 | − | 0.0475143i | ||||
\(203\) | 5.28220e36i | 0.635152i | ||||||||
\(204\) | 5.53173e36 | + | 1.09202e37i | 0.614863 | + | 1.21380i | ||||
\(205\) | −1.14120e37 | −1.17301 | ||||||||
\(206\) | 6.22447e36 | − | 1.48661e36i | 0.591871 | − | 0.141358i | ||||
\(207\) | 8.52893e35i | 0.0750532i | ||||||||
\(208\) | 4.17236e36 | − | 5.68623e36i | 0.339913 | − | 0.463245i | ||||
\(209\) | 3.92930e36 | 0.296466 | ||||||||
\(210\) | −8.92407e36 | − | 3.73653e37i | −0.623813 | − | 2.61192i | ||||
\(211\) | 2.17197e36i | 0.140713i | 0.997522 | + | 0.0703567i | \(0.0224137\pi\) | ||||
−0.997522 | + | 0.0703567i | \(0.977586\pi\) | |||||||
\(212\) | −4.71403e36 | + | 2.38795e36i | −0.283151 | + | 0.143434i | ||||
\(213\) | 5.17248e37 | 2.88154 | ||||||||
\(214\) | −1.80660e37 | + | 4.31477e36i | −0.933775 | + | 0.223017i | ||||
\(215\) | − | 8.32870e35i | − | 0.0399541i | ||||||
\(216\) | 1.77282e37 | − | 1.50333e37i | 0.789595 | − | 0.669567i | ||||
\(217\) | −2.42288e37 | −1.00225 | ||||||||
\(218\) | 3.92422e36 | + | 1.64308e37i | 0.150817 | + | 0.631472i | ||||
\(219\) | 7.07971e37i | 2.52877i | ||||||||
\(220\) | 1.82190e37 | + | 3.59660e37i | 0.605009 | + | 1.19434i | ||||
\(221\) | −1.55875e37 | −0.481392 | ||||||||
\(222\) | −2.21080e36 | + | 5.28012e35i | −0.0635186 | + | 0.0151704i | ||||
\(223\) | − | 2.64062e36i | − | 0.0706038i | −0.999377 | − | 0.0353019i | \(-0.988761\pi\) | ||
0.999377 | − | 0.0353019i | \(-0.0112393\pi\) | |||||||
\(224\) | 2.68219e37 | − | 6.36902e37i | 0.667607 | − | 1.58527i | ||||
\(225\) | 5.36368e36 | 0.124321 | ||||||||
\(226\) | −3.06220e36 | − | 1.28215e37i | −0.0661148 | − | 0.276824i | ||||
\(227\) | 4.82575e37i | 0.970847i | 0.874279 | + | 0.485423i | \(0.161335\pi\) | ||||
−0.874279 | + | 0.485423i | \(0.838665\pi\) | |||||||
\(228\) | −1.64457e37 | + | 8.33074e36i | −0.308385 | + | 0.156216i | ||||
\(229\) | −6.43637e37 | −1.12531 | −0.562656 | − | 0.826691i | \(-0.690221\pi\) | ||||
−0.562656 | + | 0.826691i | \(0.690221\pi\) | |||||||
\(230\) | 2.62815e36 | − | 6.27689e35i | 0.0428552 | − | 0.0102353i | ||||
\(231\) | − | 2.55751e38i | − | 3.89068i | ||||||
\(232\) | 1.68217e37 | + | 1.98372e37i | 0.238815 | + | 0.281626i | ||||
\(233\) | 9.66736e37 | 1.28119 | 0.640594 | − | 0.767880i | \(-0.278688\pi\) | ||||
0.640594 | + | 0.767880i | \(0.278688\pi\) | |||||||
\(234\) | 1.76613e37 | + | 7.39483e37i | 0.218559 | + | 0.915112i | ||||
\(235\) | 3.96951e37i | 0.458830i | ||||||||
\(236\) | 6.66148e36 | + | 1.31504e37i | 0.0719414 | + | 0.142019i | ||||
\(237\) | −1.84355e38 | −1.86073 | ||||||||
\(238\) | −1.48558e38 | + | 3.54805e37i | −1.40173 | + | 0.334779i | ||||
\(239\) | 9.30138e37i | 0.820694i | 0.911930 | + | 0.410347i | \(0.134592\pi\) | ||||
−0.911930 | + | 0.410347i | \(0.865408\pi\) | |||||||
\(240\) | −1.52508e38 | − | 1.11905e38i | −1.25867 | − | 0.923568i | ||||
\(241\) | 1.83413e38 | 1.41631 | 0.708155 | − | 0.706057i | \(-0.249528\pi\) | ||||
0.708155 | + | 0.706057i | \(0.249528\pi\) | |||||||
\(242\) | 3.02076e37 | + | 1.26480e38i | 0.218308 | + | 0.914060i | ||||
\(243\) | − | 1.42499e38i | − | 0.964077i | ||||||
\(244\) | −1.88523e38 | + | 9.54985e37i | −1.19434 | + | 0.605005i | ||||
\(245\) | 3.17322e38 | 1.88297 | ||||||||
\(246\) | 3.46701e38 | − | 8.28039e37i | 1.92750 | − | 0.460351i | ||||
\(247\) | − | 2.34746e37i | − | 0.122306i | ||||||
\(248\) | −9.09909e37 | + | 7.71592e37i | −0.444397 | + | 0.376843i | ||||
\(249\) | −3.89327e38 | −1.78289 | ||||||||
\(250\) | −5.59402e37 | − | 2.34223e38i | −0.240262 | − | 1.00598i | ||||
\(251\) | − | 1.81978e38i | − | 0.733229i | −0.930373 | − | 0.366614i | \(-0.880517\pi\) | ||
0.930373 | − | 0.366614i | \(-0.119483\pi\) | |||||||
\(252\) | 3.36645e38 | + | 6.64569e38i | 1.27281 | + | 2.51265i | ||||
\(253\) | 1.79887e37 | 0.0638367 | ||||||||
\(254\) | 4.83566e38 | − | 1.15492e38i | 1.61108 | − | 0.384779i | ||||
\(255\) | 4.18064e38i | 1.30798i | ||||||||
\(256\) | −1.02099e38 | − | 3.24604e38i | −0.300042 | − | 0.953926i | ||||
\(257\) | 1.81708e38 | 0.501700 | 0.250850 | − | 0.968026i | \(-0.419290\pi\) | ||||
0.250850 | + | 0.968026i | \(0.419290\pi\) | |||||||
\(258\) | 6.04318e36 | + | 2.53029e37i | 0.0156802 | + | 0.0656531i | ||||
\(259\) | − | 2.83601e37i | − | 0.0691689i | ||||||
\(260\) | 2.14870e38 | − | 1.08845e38i | 0.492722 | − | 0.249594i | ||||
\(261\) | −2.80377e38 | −0.604636 | ||||||||
\(262\) | −4.51446e38 | + | 1.07820e38i | −0.915767 | + | 0.218716i | ||||
\(263\) | 1.03099e38i | 0.196772i | 0.995148 | + | 0.0983859i | \(0.0313680\pi\) | ||||
−0.995148 | + | 0.0983859i | \(0.968632\pi\) | |||||||
\(264\) | −8.14465e38 | − | 9.60468e38i | −1.46288 | − | 1.72512i | ||||
\(265\) | −1.80471e38 | −0.305121 | ||||||||
\(266\) | −5.34333e37 | − | 2.23726e38i | −0.0850561 | − | 0.356132i | ||||
\(267\) | 9.53439e38i | 1.42926i | ||||||||
\(268\) | −3.61546e38 | − | 7.13726e38i | −0.510513 | − | 1.00780i | ||||
\(269\) | 7.79655e38 | 1.03721 | 0.518604 | − | 0.855014i | \(-0.326452\pi\) | ||||
0.518604 | + | 0.855014i | \(0.326452\pi\) | |||||||
\(270\) | 7.72114e38 | − | 1.84407e38i | 0.967969 | − | 0.231183i | ||||
\(271\) | 1.53349e38i | 0.181206i | 0.995887 | + | 0.0906032i | \(0.0288795\pi\) | ||||
−0.995887 | + | 0.0906032i | \(0.971121\pi\) | |||||||
\(272\) | −4.44913e38 | + | 6.06343e38i | −0.495648 | + | 0.675485i | ||||
\(273\) | −1.52792e39 | −1.60509 | ||||||||
\(274\) | 2.38965e38 | + | 1.00055e39i | 0.236770 | + | 0.991359i | ||||
\(275\) | − | 1.13127e38i | − | 0.105741i | ||||||
\(276\) | −7.52897e37 | + | 3.81389e37i | −0.0664034 | + | 0.0336374i | ||||
\(277\) | −4.47583e38 | −0.372561 | −0.186280 | − | 0.982497i | \(-0.559643\pi\) | ||||
−0.186280 | + | 0.982497i | \(0.559643\pi\) | |||||||
\(278\) | −1.06045e39 | + | 2.53270e38i | −0.833245 | + | 0.199007i | ||||
\(279\) | − | 1.28606e39i | − | 0.954097i | ||||||
\(280\) | 1.80008e39 | − | 1.52645e39i | 1.26114 | − | 1.06943i | ||||
\(281\) | 2.40210e39 | 1.58961 | 0.794804 | − | 0.606867i | \(-0.207574\pi\) | ||||
0.794804 | + | 0.606867i | \(0.207574\pi\) | |||||||
\(282\) | −2.88022e38 | − | 1.20595e39i | −0.180069 | − | 0.753954i | ||||
\(283\) | − | 1.34695e39i | − | 0.795736i | −0.917443 | − | 0.397868i | \(-0.869750\pi\) | ||
0.917443 | − | 0.397868i | \(-0.130250\pi\) | |||||||
\(284\) | 1.43601e39 | + | 2.83482e39i | 0.801798 | + | 1.58282i | ||||
\(285\) | −6.29600e38 | −0.332313 | ||||||||
\(286\) | 1.55967e39 | − | 3.72501e38i | 0.778352 | − | 0.185896i | ||||
\(287\) | 4.44748e39i | 2.09896i | ||||||||
\(288\) | 3.38065e39 | + | 1.42369e39i | 1.50911 | + | 0.635531i | ||||
\(289\) | −7.05765e38 | −0.298054 | ||||||||
\(290\) | 2.06344e38 | + | 8.63966e38i | 0.0824563 | + | 0.345246i | ||||
\(291\) | − | 6.55722e39i | − | 2.47989i | ||||||
\(292\) | −3.88010e39 | + | 1.96551e39i | −1.38905 | + | 0.703638i | ||||
\(293\) | 1.19107e39 | 0.403696 | 0.201848 | − | 0.979417i | \(-0.435305\pi\) | ||||
0.201848 | + | 0.979417i | \(0.435305\pi\) | |||||||
\(294\) | −9.64037e39 | + | 2.30244e39i | −3.09411 | + | 0.738978i | ||||
\(295\) | 5.03445e38i | 0.153038i | ||||||||
\(296\) | −9.03155e37 | − | 1.06506e38i | −0.0260073 | − | 0.0306694i | ||||
\(297\) | 5.28483e39 | 1.44188 | ||||||||
\(298\) | −4.79683e37 | − | 2.00844e38i | −0.0124021 | − | 0.0519276i | ||||
\(299\) | − | 1.07469e38i | − | 0.0263356i | ||||||
\(300\) | 2.39848e38 | + | 4.73483e38i | 0.0557181 | + | 0.109993i | ||||
\(301\) | −3.24585e38 | −0.0714932 | ||||||||
\(302\) | 4.13802e39 | − | 9.88298e38i | 0.864335 | − | 0.206432i | ||||
\(303\) | 4.00448e38i | 0.0793349i | ||||||||
\(304\) | −9.13146e38 | − | 6.70035e38i | −0.171618 | − | 0.125927i | ||||
\(305\) | −7.21735e39 | −1.28701 | ||||||||
\(306\) | −1.88329e39 | − | 7.88537e39i | −0.318694 | − | 1.33438i | ||||
\(307\) | − | 9.61787e39i | − | 1.54477i | −0.635152 | − | 0.772387i | \(-0.719063\pi\) | ||
0.635152 | − | 0.772387i | \(-0.280937\pi\) | |||||||
\(308\) | 1.40167e40 | − | 7.10030e39i | 2.13714 | − | 1.08259i | ||||
\(309\) | −6.82656e39 | −0.988249 | ||||||||
\(310\) | −3.96292e39 | + | 9.46477e38i | −0.544788 | + | 0.130114i | ||||
\(311\) | 1.94296e39i | 0.253687i | 0.991923 | + | 0.126844i | \(0.0404846\pi\) | ||||
−0.991923 | + | 0.126844i | \(0.959515\pi\) | |||||||
\(312\) | −5.73807e39 | + | 4.86581e39i | −0.711692 | + | 0.603507i | ||||
\(313\) | −5.24329e39 | −0.617866 | −0.308933 | − | 0.951084i | \(-0.599972\pi\) | ||||
−0.308933 | + | 0.951084i | \(0.599972\pi\) | |||||||
\(314\) | 3.95680e39 | + | 1.65672e40i | 0.443067 | + | 1.85513i | ||||
\(315\) | 2.54421e40i | 2.70760i | ||||||||
\(316\) | −5.11818e39 | − | 1.01038e40i | −0.517752 | − | 1.02209i | ||||
\(317\) | 3.19617e39 | 0.307384 | 0.153692 | − | 0.988119i | \(-0.450884\pi\) | ||||
0.153692 | + | 0.988119i | \(0.450884\pi\) | |||||||
\(318\) | 5.48277e39 | − | 1.30947e39i | 0.501379 | − | 0.119746i | ||||
\(319\) | 5.91353e39i | 0.514275i | ||||||||
\(320\) | 1.89904e39 | − | 1.14651e40i | 0.157085 | − | 0.948368i | ||||
\(321\) | 1.98136e40 | 1.55913 | ||||||||
\(322\) | −2.44622e38 | − | 1.02424e39i | −0.0183148 | − | 0.0766844i | ||||
\(323\) | 2.50318e39i | 0.178341i | ||||||||
\(324\) | −5.76712e38 | + | 2.92140e38i | −0.0391056 | + | 0.0198094i | ||||
\(325\) | −6.75851e38 | −0.0436231 | ||||||||
\(326\) | −8.82619e38 | + | 2.10799e38i | −0.0542365 | + | 0.0129535i | ||||
\(327\) | − | 1.80201e40i | − | 1.05437i | ||||||
\(328\) | 1.41634e40 | + | 1.67024e40i | 0.789201 | + | 0.930674i | ||||
\(329\) | 1.54700e40 | 0.821022 | ||||||||
\(330\) | −9.99068e39 | − | 4.18312e40i | −0.505094 | − | 2.11484i | ||||
\(331\) | 3.13828e40i | 1.51163i | 0.654788 | + | 0.755813i | \(0.272758\pi\) | ||||
−0.654788 | + | 0.755813i | \(0.727242\pi\) | |||||||
\(332\) | −1.08087e40 | − | 2.13374e40i | −0.496094 | − | 0.979336i | ||||
\(333\) | 1.50534e39 | 0.0658456 | ||||||||
\(334\) | 3.99617e40 | − | 9.54419e39i | 1.66610 | − | 0.397920i | ||||
\(335\) | − | 2.73240e40i | − | 1.08600i | ||||||
\(336\) | −4.36115e40 | + | 5.94351e40i | −1.65262 | + | 2.25224i | ||||
\(337\) | −4.25178e40 | −1.53636 | −0.768178 | − | 0.640236i | \(-0.778836\pi\) | ||||
−0.768178 | + | 0.640236i | \(0.778836\pi\) | |||||||
\(338\) | 4.51546e39 | + | 1.89063e40i | 0.155609 | + | 0.651538i | ||||
\(339\) | 1.40617e40i | 0.462214i | ||||||||
\(340\) | −2.29123e40 | + | 1.16065e40i | −0.718467 | + | 0.363948i | ||||
\(341\) | −2.71247e40 | −0.811511 | ||||||||
\(342\) | 1.18753e40 | − | 2.83622e39i | 0.339021 | − | 0.0809695i | ||||
\(343\) | − | 6.05325e40i | − | 1.64923i | ||||||
\(344\) | −1.21897e39 | + | 1.03367e39i | −0.0317000 | + | 0.0268812i | ||||
\(345\) | −2.88237e39 | −0.0715556 | ||||||||
\(346\) | 1.66030e40 | + | 6.95172e40i | 0.393523 | + | 1.64769i | ||||
\(347\) | − | 6.07154e40i | − | 1.37413i | −0.726597 | − | 0.687064i | \(-0.758899\pi\) | ||
0.726597 | − | 0.687064i | \(-0.241101\pi\) | |||||||
\(348\) | −1.25376e40 | − | 2.47504e40i | −0.270986 | − | 0.534952i | ||||
\(349\) | −1.47031e40 | −0.303530 | −0.151765 | − | 0.988417i | \(-0.548496\pi\) | ||||
−0.151765 | + | 0.988417i | \(0.548496\pi\) | |||||||
\(350\) | −6.44124e39 | + | 1.53838e39i | −0.127023 | + | 0.0303372i | ||||
\(351\) | − | 3.15729e40i | − | 0.594840i | ||||||
\(352\) | 3.00276e40 | − | 7.13025e40i | 0.540553 | − | 1.28358i | ||||
\(353\) | 4.72487e40 | 0.812821 | 0.406410 | − | 0.913691i | \(-0.366780\pi\) | ||||
0.406410 | + | 0.913691i | \(0.366780\pi\) | |||||||
\(354\) | −3.65293e39 | − | 1.52949e40i | −0.0600605 | − | 0.251474i | ||||
\(355\) | 1.08527e41i | 1.70563i | ||||||||
\(356\) | −5.22540e40 | + | 2.64699e40i | −0.785090 | + | 0.397697i | ||||
\(357\) | 1.62928e41 | 2.34047 | ||||||||
\(358\) | −1.03198e41 | + | 2.46471e40i | −1.41756 | + | 0.338562i | ||||
\(359\) | 7.34931e40i | 0.965463i | 0.875769 | + | 0.482731i | \(0.160355\pi\) | ||||
−0.875769 | + | 0.482731i | \(0.839645\pi\) | |||||||
\(360\) | 8.10231e40 | + | 9.55474e40i | 1.01805 | + | 1.20055i | ||||
\(361\) | 7.94287e40 | 0.954690 | ||||||||
\(362\) | 1.26684e40 | + | 5.30427e40i | 0.145674 | + | 0.609941i | ||||
\(363\) | − | 1.38714e41i | − | 1.52621i | ||||||
\(364\) | −4.24189e40 | − | 8.37389e40i | −0.446619 | − | 0.881668i | ||||
\(365\) | −1.48544e41 | −1.49682 | ||||||||
\(366\) | 2.19266e41 | − | 5.23680e40i | 2.11482 | − | 0.505090i | ||||
\(367\) | 2.06487e40i | 0.190649i | 0.995446 | + | 0.0953245i | \(0.0303889\pi\) | ||||
−0.995446 | + | 0.0953245i | \(0.969611\pi\) | |||||||
\(368\) | −4.18046e39 | − | 3.06748e39i | −0.0369538 | − | 0.0271154i | ||||
\(369\) | −2.36070e41 | −1.99811 | ||||||||
\(370\) | −1.10786e39 | − | 4.63863e39i | −0.00897959 | − | 0.0375977i | ||||
\(371\) | 7.03328e40i | 0.545979i | ||||||||
\(372\) | 1.13527e41 | − | 5.75087e40i | 0.844139 | − | 0.427608i | ||||
\(373\) | 1.13423e41 | 0.807907 | 0.403954 | − | 0.914780i | \(-0.367636\pi\) | ||||
0.403954 | + | 0.914780i | \(0.367636\pi\) | |||||||
\(374\) | −1.66313e41 | + | 3.97211e40i | −1.13496 | + | 0.271067i | ||||
\(375\) | 2.56879e41i | 1.67969i | ||||||||
\(376\) | 5.80971e40 | − | 4.92656e40i | 0.364040 | − | 0.308701i | ||||
\(377\) | 3.53288e40 | 0.212162 | ||||||||
\(378\) | −7.18668e40 | − | 3.00908e41i | −0.413675 | − | 1.73207i | ||||
\(379\) | − | 3.63335e40i | − | 0.200484i | −0.994963 | − | 0.100242i | \(-0.968038\pi\) | ||
0.994963 | − | 0.100242i | \(-0.0319617\pi\) | |||||||
\(380\) | −1.74793e40 | − | 3.45058e40i | −0.0924670 | − | 0.182538i | ||||
\(381\) | −5.30341e41 | −2.69002 | ||||||||
\(382\) | −1.35206e41 | + | 3.22917e40i | −0.657631 | + | 0.157064i | ||||
\(383\) | − | 1.98232e40i | − | 0.0924686i | −0.998931 | − | 0.0462343i | \(-0.985278\pi\) | ||
0.998931 | − | 0.0462343i | \(-0.0147221\pi\) | |||||||
\(384\) | 2.54953e40 | + | 3.62092e41i | 0.114067 | + | 1.62002i | ||||
\(385\) | 5.36609e41 | 2.30296 | ||||||||
\(386\) | −8.10839e40 | − | 3.39500e41i | −0.333840 | − | 1.39779i | ||||
\(387\) | − | 1.72288e40i | − | 0.0680583i | ||||||
\(388\) | 3.59374e41 | − | 1.82045e41i | 1.36219 | − | 0.690035i | ||||
\(389\) | −1.68951e41 | −0.614563 | −0.307282 | − | 0.951619i | \(-0.599419\pi\) | ||||
−0.307282 | + | 0.951619i | \(0.599419\pi\) | |||||||
\(390\) | −2.49910e41 | + | 5.96867e40i | −0.872467 | + | 0.208374i | ||||
\(391\) | 1.14598e40i | 0.0384015i | ||||||||
\(392\) | −3.93828e41 | − | 4.64427e41i | −1.26686 | − | 1.49396i | ||||
\(393\) | 4.95114e41 | 1.52906 | ||||||||
\(394\) | 5.43839e40 | + | 2.27706e41i | 0.161262 | + | 0.675205i | ||||
\(395\) | − | 3.86809e41i | − | 1.10139i | ||||||
\(396\) | 3.76881e41 | + | 7.43998e41i | 1.03058 | + | 2.03446i | ||||
\(397\) | 2.48937e40 | 0.0653794 | 0.0326897 | − | 0.999466i | \(-0.489593\pi\) | ||||
0.0326897 | + | 0.999466i | \(0.489593\pi\) | |||||||
\(398\) | −1.75453e41 | + | 4.19040e40i | −0.442620 | + | 0.105712i | ||||
\(399\) | 2.45367e41i | 0.594635i | ||||||||
\(400\) | −1.92908e40 | + | 2.62902e40i | −0.0449149 | + | 0.0612116i | ||||
\(401\) | −1.93121e41 | −0.432035 | −0.216017 | − | 0.976389i | \(-0.569307\pi\) | ||||
−0.216017 | + | 0.976389i | \(0.569307\pi\) | |||||||
\(402\) | 1.98259e41 | + | 8.30115e41i | 0.426203 | + | 1.78452i | ||||
\(403\) | 1.62049e41i | 0.334786i | ||||||||
\(404\) | −2.19469e40 | + | 1.11175e40i | −0.0435784 | + | 0.0220751i | ||||
\(405\) | −2.20787e40 | −0.0421398 | ||||||||
\(406\) | 3.36704e41 | − | 8.04162e40i | 0.617777 | − | 0.147546i | ||||
\(407\) | − | 3.17496e40i | − | 0.0560052i | ||||||
\(408\) | 6.11871e41 | − | 5.18859e41i | 1.03776 | − | 0.880008i | ||||
\(409\) | −6.28224e41 | −1.02457 | −0.512285 | − | 0.858816i | \(-0.671201\pi\) | ||||
−0.512285 | + | 0.858816i | \(0.671201\pi\) | |||||||
\(410\) | 1.73737e41 | + | 7.27438e41i | 0.272489 | + | 1.14092i | ||||
\(411\) | − | 1.09734e42i | − | 1.65528i | ||||||
\(412\) | −1.89523e41 | − | 3.74135e41i | −0.274983 | − | 0.542842i | ||||
\(413\) | 1.96202e41 | 0.273844 | ||||||||
\(414\) | 5.43661e40 | − | 1.29844e40i | 0.0730000 | − | 0.0174348i | ||||
\(415\) | − | 8.16874e41i | − | 1.05532i | ||||||
\(416\) | −4.25978e41 | − | 1.79392e41i | −0.529534 | − | 0.223003i | ||||
\(417\) | 1.16303e42 | 1.39127 | ||||||||
\(418\) | −5.98196e40 | − | 2.50466e41i | −0.0688689 | − | 0.288355i | ||||
\(419\) | − | 5.12219e41i | − | 0.567586i | −0.958886 | − | 0.283793i | \(-0.908407\pi\) | ||
0.958886 | − | 0.283793i | \(-0.0915928\pi\) | |||||||
\(420\) | −2.24592e42 | + | 1.13770e42i | −2.39555 | + | 1.21350i | ||||
\(421\) | 1.70891e41 | 0.175471 | 0.0877355 | − | 0.996144i | \(-0.472037\pi\) | ||||
0.0877355 | + | 0.996144i | \(0.472037\pi\) | |||||||
\(422\) | 1.38449e41 | − | 3.30661e40i | 0.136864 | − | 0.0326877i | ||||
\(423\) | 8.21139e41i | 0.781575i | ||||||||
\(424\) | 2.23982e41 | + | 2.64133e41i | 0.205286 | + | 0.242086i | ||||
\(425\) | 7.20683e40 | 0.0636095 | ||||||||
\(426\) | −7.87459e41 | − | 3.29711e42i | −0.669383 | − | 2.80272i | ||||
\(427\) | 2.81274e42i | 2.30294i | ||||||||
\(428\) | 5.50075e41 | + | 1.08590e42i | 0.433832 | + | 0.856424i | ||||
\(429\) | −1.71054e42 | −1.29962 | ||||||||
\(430\) | −5.30898e40 | + | 1.26796e40i | −0.0388612 | + | 0.00928134i | ||||
\(431\) | 2.81567e41i | 0.198584i | 0.995058 | + | 0.0992922i | \(0.0316579\pi\) | ||||
−0.995058 | + | 0.0992922i | \(0.968342\pi\) | |||||||
\(432\) | −1.22816e42 | − | 9.01185e41i | −0.834674 | − | 0.612455i | ||||
\(433\) | −2.65364e42 | −1.73795 | −0.868973 | − | 0.494859i | \(-0.835220\pi\) | ||||
−0.868973 | + | 0.494859i | \(0.835220\pi\) | |||||||
\(434\) | 3.68860e41 | + | 1.54442e42i | 0.232823 | + | 0.974834i | ||||
\(435\) | − | 9.47538e41i | − | 0.576459i | ||||||
\(436\) | 9.87608e41 | − | 5.00284e41i | 0.579163 | − | 0.293382i | ||||
\(437\) | −1.72583e40 | −0.00975652 | ||||||||
\(438\) | 4.51284e42 | − | 1.07782e42i | 2.45960 | − | 0.587434i | ||||
\(439\) | 1.28733e42i | 0.676482i | 0.941059 | + | 0.338241i | \(0.109832\pi\) | ||||
−0.941059 | + | 0.338241i | \(0.890168\pi\) | |||||||
\(440\) | 2.01522e42 | − | 1.70889e42i | 1.02113 | − | 0.865905i | ||||
\(441\) | 6.56416e42 | 3.20746 | ||||||||
\(442\) | 2.37304e41 | + | 9.93595e41i | 0.111827 | + | 0.468223i | ||||
\(443\) | − | 1.10165e42i | − | 0.500708i | −0.968154 | − | 0.250354i | \(-0.919453\pi\) | ||
0.968154 | − | 0.250354i | \(-0.0805471\pi\) | |||||||
\(444\) | 6.73144e40 | + | 1.32885e41i | 0.0295107 | + | 0.0582570i | ||||
\(445\) | −2.00048e42 | −0.846005 | ||||||||
\(446\) | −1.68322e41 | + | 4.02008e40i | −0.0686724 | + | 0.0164013i | ||||
\(447\) | 2.20272e41i | 0.0867038i | ||||||||
\(448\) | −4.46816e42 | − | 7.40092e41i | −1.69699 | − | 0.281085i | ||||
\(449\) | −1.09716e42 | −0.402093 | −0.201047 | − | 0.979582i | \(-0.564434\pi\) | ||||
−0.201047 | + | 0.979582i | \(0.564434\pi\) | |||||||
\(450\) | −8.16568e40 | − | 3.41898e41i | −0.0288797 | − | 0.120920i | ||||
\(451\) | 4.97904e42i | 1.69950i | ||||||||
\(452\) | −7.70664e41 | + | 3.90389e41i | −0.253893 | + | 0.128612i | ||||
\(453\) | −4.53830e42 | −1.44318 | ||||||||
\(454\) | 3.07609e42 | − | 7.34672e41i | 0.944289 | − | 0.225528i | ||||
\(455\) | − | 3.20583e42i | − | 0.950077i | ||||||
\(456\) | 7.81397e41 | + | 9.21472e41i | 0.223581 | + | 0.263660i | ||||
\(457\) | 6.91623e42 | 1.91078 | 0.955389 | − | 0.295351i | \(-0.0954364\pi\) | ||||
0.955389 | + | 0.295351i | \(0.0954364\pi\) | |||||||
\(458\) | 9.79873e41 | + | 4.10275e42i | 0.261410 | + | 1.09453i | ||||
\(459\) | 3.36673e42i | 0.867371i | ||||||||
\(460\) | −8.00218e40 | − | 1.57970e41i | −0.0199105 | − | 0.0393053i | ||||
\(461\) | 2.42051e40 | 0.00581690 | 0.00290845 | − | 0.999996i | \(-0.499074\pi\) | ||||
0.00290845 | + | 0.999996i | \(0.499074\pi\) | |||||||
\(462\) | −1.63024e43 | + | 3.89356e42i | −3.78425 | + | 0.903806i | ||||
\(463\) | − | 7.32467e42i | − | 1.64245i | −0.570604 | − | 0.821225i | \(-0.693291\pi\) | ||
0.570604 | − | 0.821225i | \(-0.306709\pi\) | |||||||
\(464\) | 1.00839e42 | − | 1.37427e42i | 0.218445 | − | 0.297704i | ||||
\(465\) | 4.34625e42 | 0.909636 | ||||||||
\(466\) | −1.47176e42 | − | 6.16228e42i | −0.297620 | − | 1.24614i | ||||
\(467\) | 5.77631e41i | 0.112870i | 0.998406 | + | 0.0564352i | \(0.0179734\pi\) | ||||
−0.998406 | + | 0.0564352i | \(0.982027\pi\) | |||||||
\(468\) | 4.44482e42 | − | 2.25158e42i | 0.839307 | − | 0.425161i | ||||
\(469\) | −1.06487e43 | −1.94326 | ||||||||
\(470\) | 2.53030e42 | − | 6.04319e41i | 0.446278 | − | 0.106586i | ||||
\(471\) | − | 1.81697e43i | − | 3.09752i | ||||||
\(472\) | 7.36834e41 | − | 6.24826e41i | 0.121422 | − | 0.102964i | ||||
\(473\) | −3.63380e41 | −0.0578872 | ||||||||
\(474\) | 2.80663e42 | + | 1.17514e43i | 0.432247 | + | 1.80982i | ||||
\(475\) | 1.08534e41i | 0.0161610i | ||||||||
\(476\) | 4.52328e42 | + | 8.92938e42i | 0.651242 | + | 1.28561i | ||||
\(477\) | −3.73324e42 | −0.519746 | ||||||||
\(478\) | 5.92900e42 | − | 1.41604e42i | 0.798243 | − | 0.190647i | ||||
\(479\) | 9.75812e42i | 1.27057i | 0.772278 | + | 0.635284i | \(0.219117\pi\) | ||||
−0.772278 | + | 0.635284i | \(0.780883\pi\) | |||||||
\(480\) | −4.81140e42 | + | 1.14250e43i | −0.605915 | + | 1.43878i | ||||
\(481\) | −1.89680e41 | −0.0231047 | ||||||||
\(482\) | −2.79229e42 | − | 1.16914e43i | −0.329009 | − | 1.37757i | ||||
\(483\) | 1.12331e42i | 0.128040i | ||||||||
\(484\) | 7.60234e42 | − | 3.85105e42i | 0.838342 | − | 0.424672i | ||||
\(485\) | 1.37582e43 | 1.46789 | ||||||||
\(486\) | −9.08335e42 | + | 2.16941e42i | −0.937704 | + | 0.223955i | ||||
\(487\) | 8.73926e42i | 0.872994i | 0.899706 | + | 0.436497i | \(0.143781\pi\) | ||||
−0.899706 | + | 0.436497i | \(0.856219\pi\) | |||||||
\(488\) | 8.95745e42 | + | 1.05632e43i | 0.865899 | + | 1.02112i | ||||
\(489\) | 9.67995e41 | 0.0905589 | ||||||||
\(490\) | −4.83091e42 | − | 2.02271e43i | −0.437413 | − | 1.83146i | ||||
\(491\) | − | 6.41960e42i | − | 0.562606i | −0.959619 | − | 0.281303i | \(-0.909233\pi\) | ||
0.959619 | − | 0.281303i | \(-0.0907665\pi\) | |||||||
\(492\) | −1.05564e43 | − | 2.08393e43i | −0.895515 | − | 1.76783i | ||||
\(493\) | −3.76724e42 | −0.309366 | ||||||||
\(494\) | −1.49634e42 | + | 3.57377e41i | −0.118960 | + | 0.0284116i | ||||
\(495\) | 2.84830e43i | 2.19231i | ||||||||
\(496\) | 6.30362e42 | + | 4.62538e42i | 0.469768 | + | 0.344699i | ||||
\(497\) | 4.22952e43 | 3.05203 | ||||||||
\(498\) | 5.92711e42 | + | 2.48169e43i | 0.414165 | + | 1.73412i | ||||
\(499\) | − | 1.60910e43i | − | 1.08886i | −0.838805 | − | 0.544432i | \(-0.816745\pi\) | ||
0.838805 | − | 0.544432i | \(-0.183255\pi\) | |||||||
\(500\) | −1.40785e43 | + | 7.13162e42i | −0.922647 | + | 0.467378i | ||||
\(501\) | −4.38272e43 | −2.78189 | ||||||||
\(502\) | −1.15999e43 | + | 2.77043e42i | −0.713171 | + | 0.170329i | ||||
\(503\) | 9.65906e42i | 0.575238i | 0.957745 | + | 0.287619i | \(0.0928636\pi\) | ||||
−0.957745 | + | 0.287619i | \(0.907136\pi\) | |||||||
\(504\) | 3.72367e43 | − | 3.15762e43i | 2.14824 | − | 1.82168i | ||||
\(505\) | −8.40208e41 | −0.0469597 | ||||||||
\(506\) | −2.73860e41 | − | 1.14666e42i | −0.0148293 | − | 0.0620904i | ||||
\(507\) | − | 2.07351e43i | − | 1.08788i | ||||||
\(508\) | −1.47236e43 | − | 2.90658e43i | −0.748506 | − | 1.47762i | ||||
\(509\) | −3.22003e43 | −1.58626 | −0.793132 | − | 0.609050i | \(-0.791551\pi\) | ||||
−0.793132 | + | 0.609050i | \(0.791551\pi\) | |||||||
\(510\) | 2.66487e43 | − | 6.36461e42i | 1.27220 | − | 0.303843i | ||||
\(511\) | 5.78906e43i | 2.67839i | ||||||||
\(512\) | −1.91370e43 | + | 1.14499e43i | −0.858131 | + | 0.513431i | ||||
\(513\) | −5.07026e42 | −0.220370 | ||||||||
\(514\) | −2.76633e42 | − | 1.15827e43i | −0.116545 | − | 0.487976i | ||||
\(515\) | − | 1.43233e43i | − | 0.584961i | ||||||
\(516\) | 1.52089e42 | − | 7.70424e41i | 0.0602146 | − | 0.0305024i | ||||
\(517\) | 1.73189e43 | 0.664771 | ||||||||
\(518\) | −1.80776e42 | + | 4.31754e41i | −0.0672767 | + | 0.0160679i | ||||
\(519\) | − | 7.62416e43i | − | 2.75115i | ||||||
\(520\) | −1.02093e43 | − | 1.20394e43i | −0.357226 | − | 0.421263i | ||||
\(521\) | −2.63327e43 | −0.893494 | −0.446747 | − | 0.894660i | \(-0.647418\pi\) | ||||
−0.446747 | + | 0.894660i | \(0.647418\pi\) | |||||||
\(522\) | 4.26846e42 | + | 1.78721e43i | 0.140457 | + | 0.588096i | ||||
\(523\) | 5.37407e43i | 1.71505i | 0.514444 | + | 0.857524i | \(0.327998\pi\) | ||||
−0.514444 | + | 0.857524i | \(0.672002\pi\) | |||||||
\(524\) | 1.37456e43 | + | 2.71351e43i | 0.425465 | + | 0.839908i | ||||
\(525\) | 7.06431e42 | 0.212090 | ||||||||
\(526\) | 6.57187e42 | − | 1.56958e42i | 0.191389 | − | 0.0457101i | ||||
\(527\) | − | 1.72799e43i | − | 0.488170i | ||||||
\(528\) | −4.88239e43 | + | 6.65388e43i | −1.33810 | + | 1.82361i | ||||
\(529\) | 3.75299e43 | 0.997899 | ||||||||
\(530\) | 2.74749e42 | + | 1.15038e43i | 0.0708796 | + | 0.296774i | ||||
\(531\) | 1.04143e43i | 0.260687i | ||||||||
\(532\) | −1.34476e43 | + | 6.81202e42i | −0.326631 | + | 0.165459i | ||||
\(533\) | 2.97460e43 | 0.701122 | ||||||||
\(534\) | 6.07752e43 | − | 1.45152e43i | 1.39017 | − | 0.332018i | ||||
\(535\) | 4.15722e43i | 0.922874i | ||||||||
\(536\) | −3.99910e43 | + | 3.39119e43i | −0.861639 | + | 0.730660i | ||||
\(537\) | 1.13180e44 | 2.36691 | ||||||||
\(538\) | −1.18695e43 | − | 4.96977e43i | −0.240943 | − | 1.00883i | ||||
\(539\) | − | 1.38447e44i | − | 2.72812i | ||||||
\(540\) | −2.35093e43 | − | 4.64096e43i | −0.449718 | − | 0.887785i | ||||
\(541\) | −4.14984e43 | −0.770682 | −0.385341 | − | 0.922774i | \(-0.625916\pi\) | ||||
−0.385341 | + | 0.922774i | \(0.625916\pi\) | |||||||
\(542\) | 9.77498e42 | − | 2.33459e42i | 0.176249 | − | 0.0420942i | ||||
\(543\) | − | 5.81735e43i | − | 1.01842i | ||||||
\(544\) | 4.54236e43 | + | 1.91292e43i | 0.772145 | + | 0.325174i | ||||
\(545\) | 3.78093e43 | 0.624100 | ||||||||
\(546\) | 2.32611e43 | + | 9.73945e43i | 0.372861 | + | 1.56118i | ||||
\(547\) | 8.89957e43i | 1.38539i | 0.721231 | + | 0.692694i | \(0.243576\pi\) | ||||
−0.721231 | + | 0.692694i | \(0.756424\pi\) | |||||||
\(548\) | 6.01404e43 | − | 3.04648e43i | 0.909238 | − | 0.460585i | ||||
\(549\) | −1.49299e44 | −2.19230 | ||||||||
\(550\) | −7.21110e42 | + | 1.72225e42i | −0.102849 | + | 0.0245637i | ||||
\(551\) | − | 5.67343e42i | − | 0.0785995i | ||||||
\(552\) | 3.57730e42 | + | 4.21858e42i | 0.0481427 | + | 0.0567729i | ||||
\(553\) | −1.50747e44 | −1.97082 | ||||||||
\(554\) | 6.81401e42 | + | 2.85304e43i | 0.0865459 | + | 0.362369i | ||||
\(555\) | 5.08732e42i | 0.0627771i | ||||||||
\(556\) | 3.22885e43 | + | 6.37406e43i | 0.387125 | + | 0.764222i | ||||
\(557\) | −4.03548e43 | −0.470123 | −0.235062 | − | 0.971980i | \(-0.575529\pi\) | ||||
−0.235062 | + | 0.971980i | \(0.575529\pi\) | |||||||
\(558\) | −8.19774e43 | + | 1.95789e43i | −0.927997 | + | 0.221637i | ||||
\(559\) | 2.17092e42i | 0.0238811i | ||||||||
\(560\) | −1.24705e44 | − | 9.15042e43i | −1.33314 | − | 0.978211i | ||||
\(561\) | 1.82401e44 | 1.89505 | ||||||||
\(562\) | −3.65696e43 | − | 1.53118e44i | −0.369266 | − | 1.54612i | ||||
\(563\) | 5.34292e43i | 0.524378i | 0.965017 | + | 0.262189i | \(0.0844444\pi\) | ||||
−0.965017 | + | 0.262189i | \(0.915556\pi\) | |||||||
\(564\) | −7.24865e43 | + | 3.67189e43i | −0.691499 | + | 0.350287i | ||||
\(565\) | −2.95039e43 | −0.273592 | ||||||||
\(566\) | −8.58590e43 | + | 2.05060e43i | −0.773968 | + | 0.184849i | ||||
\(567\) | 8.60448e42i | 0.0754042i | ||||||||
\(568\) | 1.58839e44 | − | 1.34693e44i | 1.35327 | − | 1.14755i | ||||
\(569\) | 9.27836e42 | 0.0768555 | 0.0384277 | − | 0.999261i | \(-0.487765\pi\) | ||||
0.0384277 | + | 0.999261i | \(0.487765\pi\) | |||||||
\(570\) | 9.58504e42 | + | 4.01328e43i | 0.0771963 | + | 0.323222i | ||||
\(571\) | 2.36677e43i | 0.185344i | 0.995697 | + | 0.0926719i | \(0.0295408\pi\) | ||||
−0.995697 | + | 0.0926719i | \(0.970459\pi\) | |||||||
\(572\) | −4.74888e43 | − | 9.37474e43i | −0.361622 | − | 0.713876i | ||||
\(573\) | 1.48285e44 | 1.09805 | ||||||||
\(574\) | 2.83497e44 | − | 6.77084e43i | 2.04154 | − | 0.487588i | ||||
\(575\) | 4.96879e41i | 0.00347989i | ||||||||
\(576\) | 3.92838e43 | − | 2.37168e44i | 0.267580 | − | 1.61546i | ||||
\(577\) | 1.03883e44 | 0.688225 | 0.344113 | − | 0.938928i | \(-0.388180\pi\) | ||||
0.344113 | + | 0.938928i | \(0.388180\pi\) | |||||||
\(578\) | 1.07446e43 | + | 4.49877e43i | 0.0692379 | + | 0.289900i | ||||
\(579\) | 3.72340e44i | 2.33390i | ||||||||
\(580\) | 5.19306e43 | − | 2.63061e43i | 0.316647 | − | 0.160401i | ||||
\(581\) | −3.18351e44 | −1.88838 | ||||||||
\(582\) | −4.17978e44 | + | 9.98272e43i | −2.41205 | + | 0.576078i | ||||
\(583\) | 7.87390e43i | 0.442072i | ||||||||
\(584\) | 1.84358e44 | + | 2.17407e44i | 1.00706 | + | 1.18759i | ||||
\(585\) | 1.70164e44 | 0.904429 | ||||||||
\(586\) | −1.81328e43 | − | 7.59224e43i | −0.0937785 | − | 0.392652i | ||||
\(587\) | − | 2.34372e44i | − | 1.17949i | −0.807588 | − | 0.589747i | \(-0.799228\pi\) | ||
0.807588 | − | 0.589747i | \(-0.200772\pi\) | |||||||
\(588\) | 2.93530e44 | + | 5.79456e44i | 1.43753 | + | 2.83781i | ||||
\(589\) | 2.60234e43 | 0.124028 | ||||||||
\(590\) | 3.20912e43 | − | 7.66446e42i | 0.148852 | − | 0.0355508i | ||||
\(591\) | − | 2.49733e44i | − | 1.12739i | ||||||
\(592\) | −5.41404e42 | + | 7.37844e42i | −0.0237889 | + | 0.0324203i | ||||
\(593\) | −3.76769e44 | −1.61139 | −0.805695 | − | 0.592331i | \(-0.798208\pi\) | ||||
−0.805695 | + | 0.592331i | \(0.798208\pi\) | |||||||
\(594\) | −8.04563e43 | − | 3.36872e44i | −0.334948 | − | 1.40243i | ||||
\(595\) | 3.41850e44i | 1.38536i | ||||||||
\(596\) | −1.20722e43 | + | 6.11530e42i | −0.0476261 | + | 0.0241256i | ||||
\(597\) | 1.92424e44 | 0.739045 | ||||||||
\(598\) | −6.85040e42 | + | 1.63610e42i | −0.0256151 | + | 0.00611775i | ||||
\(599\) | − | 3.22426e44i | − | 1.17382i | −0.809652 | − | 0.586910i | \(-0.800344\pi\) | ||
0.809652 | − | 0.586910i | \(-0.199656\pi\) | |||||||
\(600\) | 2.65299e43 | − | 2.24970e43i | 0.0940405 | − | 0.0797452i | ||||
\(601\) | −2.80517e43 | −0.0968206 | −0.0484103 | − | 0.998828i | \(-0.515416\pi\) | ||||
−0.0484103 | + | 0.998828i | \(0.515416\pi\) | |||||||
\(602\) | 4.94149e42 | + | 2.06901e43i | 0.0166079 | + | 0.0695375i | ||||
\(603\) | − | 5.65229e44i | − | 1.84990i | ||||||
\(604\) | −1.25995e44 | − | 2.48725e44i | −0.401570 | − | 0.792736i | ||||
\(605\) | 2.91046e44 | 0.903389 | ||||||||
\(606\) | 2.55259e43 | − | 6.09643e42i | 0.0771646 | − | 0.0184295i | ||||
\(607\) | 3.35287e44i | 0.987184i | 0.869694 | + | 0.493592i | \(0.164316\pi\) | ||||
−0.869694 | + | 0.493592i | \(0.835684\pi\) | |||||||
\(608\) | −2.88085e43 | + | 6.84075e43i | −0.0826157 | + | 0.196176i | ||||
\(609\) | −3.69274e44 | −1.03151 | ||||||||
\(610\) | 1.09877e44 | + | 4.60057e44i | 0.298971 | + | 1.25180i | ||||
\(611\) | − | 1.03467e44i | − | 0.274249i | ||||||
\(612\) | −4.73967e44 | + | 2.40094e44i | −1.22384 | + | 0.619952i | ||||
\(613\) | 5.01061e44 | 1.26044 | 0.630221 | − | 0.776416i | \(-0.282964\pi\) | ||||
0.630221 | + | 0.776416i | \(0.282964\pi\) | |||||||
\(614\) | −6.13074e44 | + | 1.46423e44i | −1.50252 | + | 0.358851i | ||||
\(615\) | − | 7.97804e44i | − | 1.90500i | ||||||
\(616\) | −6.65986e44 | − | 7.85372e44i | −1.54944 | − | 1.82719i | ||||
\(617\) | 9.93241e43 | 0.225161 | 0.112580 | − | 0.993643i | \(-0.464088\pi\) | ||||
0.112580 | + | 0.993643i | \(0.464088\pi\) | |||||||
\(618\) | 1.03928e44 | + | 4.35147e44i | 0.229570 | + | 0.961215i | ||||
\(619\) | 1.77023e44i | 0.381048i | 0.981683 | + | 0.190524i | \(0.0610187\pi\) | ||||
−0.981683 | + | 0.190524i | \(0.938981\pi\) | |||||||
\(620\) | 1.20663e44 | + | 2.38200e44i | 0.253109 | + | 0.499660i | ||||
\(621\) | −2.32121e43 | −0.0474514 | ||||||||
\(622\) | 1.23851e44 | − | 2.95797e43i | 0.246747 | − | 0.0589315i | ||||
\(623\) | 7.79624e44i | 1.51383i | ||||||||
\(624\) | 3.97519e44 | + | 2.91686e44i | 0.752323 | + | 0.552029i | ||||
\(625\) | −4.97819e44 | −0.918313 | ||||||||
\(626\) | 7.98239e43 | + | 3.34224e44i | 0.143530 | + | 0.600964i | ||||
\(627\) | 2.74694e44i | 0.481469i | ||||||||
\(628\) | 9.95808e44 | − | 5.04438e44i | 1.70146 | − | 0.861893i | ||||
\(629\) | 2.02263e43 | 0.0336903 | ||||||||
\(630\) | 1.62176e45 | − | 3.87331e44i | 2.63353 | − | 0.628976i | ||||
\(631\) | − | 4.90233e44i | − | 0.776128i | −0.921633 | − | 0.388064i | \(-0.873144\pi\) | ||
0.921633 | − | 0.388064i | \(-0.126856\pi\) | |||||||
\(632\) | −5.66127e44 | + | 4.80069e44i | −0.873857 | + | 0.741020i | ||||
\(633\) | −1.51841e44 | −0.228523 | ||||||||
\(634\) | −4.86585e43 | − | 2.03734e44i | −0.0714054 | − | 0.298976i | ||||
\(635\) | − | 1.11275e45i | − | 1.59227i | ||||||
\(636\) | −1.66939e44 | − | 3.29554e44i | −0.232940 | − | 0.459846i | ||||
\(637\) | −8.27117e44 | −1.12548 | ||||||||
\(638\) | 3.76947e44 | − | 9.00276e43i | 0.500207 | − | 0.119466i | ||||
\(639\) | 2.24501e45i | 2.90539i | ||||||||
\(640\) | −7.59731e44 | + | 5.34934e43i | −0.958916 | + | 0.0675181i | ||||
\(641\) | 1.44698e45 | 1.78128 | 0.890641 | − | 0.454706i | \(-0.150256\pi\) | ||||
0.890641 | + | 0.454706i | \(0.150256\pi\) | |||||||
\(642\) | −3.01642e44 | − | 1.26298e45i | −0.362186 | − | 1.51648i | ||||
\(643\) | 1.18107e45i | 1.38325i | 0.722258 | + | 0.691623i | \(0.243104\pi\) | ||||
−0.722258 | + | 0.691623i | \(0.756896\pi\) | |||||||
\(644\) | −6.15641e43 | + | 3.11860e43i | −0.0703321 | + | 0.0356276i | ||||
\(645\) | 5.82252e43 | 0.0648867 | ||||||||
\(646\) | 1.59561e44 | − | 3.81084e43i | 0.173462 | − | 0.0414286i | ||||
\(647\) | 4.17210e44i | 0.442472i | 0.975220 | + | 0.221236i | \(0.0710091\pi\) | ||||
−0.975220 | + | 0.221236i | \(0.928991\pi\) | |||||||
\(648\) | 2.74018e43 | + | 3.23139e43i | 0.0283517 | + | 0.0334341i | ||||
\(649\) | 2.19652e44 | 0.221728 | ||||||||
\(650\) | 1.02892e43 | + | 4.30809e43i | 0.0101336 | + | 0.0424298i | ||||
\(651\) | − | 1.69382e45i | − | 1.62769i | ||||||
\(652\) | 2.68740e43 | + | 5.30517e43i | 0.0251983 | + | 0.0497437i | ||||
\(653\) | 1.61773e45 | 1.48011 | 0.740057 | − | 0.672544i | \(-0.234799\pi\) | ||||
0.740057 | + | 0.672544i | \(0.234799\pi\) | |||||||
\(654\) | −1.14866e45 | + | 2.74339e44i | −1.02553 | + | 0.244930i | ||||
\(655\) | 1.03883e45i | 0.905076i | ||||||||
\(656\) | 8.49041e44 | − | 1.15710e45i | 0.721884 | − | 0.983807i | ||||
\(657\) | −3.07281e45 | −2.54970 | ||||||||
\(658\) | −2.35515e44 | − | 9.86105e44i | −0.190723 | − | 0.798562i | ||||
\(659\) | − | 9.04904e44i | − | 0.715214i | −0.933872 | − | 0.357607i | \(-0.883593\pi\) | ||
0.933872 | − | 0.357607i | \(-0.116407\pi\) | |||||||
\(660\) | −2.51435e45 | + | 1.27368e45i | −1.93965 | + | 0.982553i | ||||
\(661\) | −5.46004e44 | −0.411124 | −0.205562 | − | 0.978644i | \(-0.565902\pi\) | ||||
−0.205562 | + | 0.978644i | \(0.565902\pi\) | |||||||
\(662\) | 2.00044e45 | − | 4.77772e44i | 1.47027 | − | 0.351150i | ||||
\(663\) | − | 1.08971e45i | − | 0.781795i | ||||||
\(664\) | −1.19556e45 | + | 1.01382e45i | −0.837303 | + | 0.710023i | ||||
\(665\) | −5.14822e44 | −0.351974 | ||||||||
\(666\) | −2.29173e43 | − | 9.59552e43i | −0.0152959 | − | 0.0640443i | ||||
\(667\) | − | 2.59735e43i | − | 0.0169245i | ||||||
\(668\) | −1.21675e45 | − | 2.40199e45i | −0.774069 | − | 1.52808i | ||||
\(669\) | 1.84603e44 | 0.114663 | ||||||||
\(670\) | −1.74172e45 | + | 4.15981e44i | −1.05629 | + | 0.252277i | ||||
\(671\) | 3.14892e45i | 1.86467i | ||||||||
\(672\) | 4.45253e45 | + | 1.87509e45i | 2.57453 | + | 1.08421i | ||||
\(673\) | 6.50078e44 | 0.367050 | 0.183525 | − | 0.983015i | \(-0.441249\pi\) | ||||
0.183525 | + | 0.983015i | \(0.441249\pi\) | |||||||
\(674\) | 6.47291e44 | + | 2.71022e45i | 0.356895 | + | 1.49433i | ||||
\(675\) | 1.45977e44i | 0.0786000i | ||||||||
\(676\) | 1.13641e45 | − | 5.75660e44i | 0.597567 | − | 0.302705i | ||||
\(677\) | 1.51141e45 | 0.776181 | 0.388091 | − | 0.921621i | \(-0.373135\pi\) | ||||
0.388091 | + | 0.921621i | \(0.373135\pi\) | |||||||
\(678\) | 8.96339e44 | − | 2.14076e44i | 0.449570 | − | 0.107372i | ||||
\(679\) | − | 5.36182e45i | − | 2.62661i | ||||||
\(680\) | 1.08865e45 | + | 1.28381e45i | 0.520892 | + | 0.614268i | ||||
\(681\) | −3.37364e45 | −1.57668 | ||||||||
\(682\) | 4.12946e44 | + | 1.72901e45i | 0.188514 | + | 0.789311i | ||||
\(683\) | − | 1.57870e45i | − | 0.703992i | −0.936001 | − | 0.351996i | \(-0.885503\pi\) | ||
0.936001 | − | 0.351996i | \(-0.114497\pi\) | |||||||
\(684\) | −3.61579e44 | − | 7.13791e44i | −0.157509 | − | 0.310938i | ||||
\(685\) | 2.30240e45 | 0.979786 | ||||||||
\(686\) | −3.85853e45 | + | 9.21547e44i | −1.60412 | + | 0.383117i | ||||
\(687\) | − | 4.49961e45i | − | 1.82754i | ||||||
\(688\) | 8.44474e43 | + | 6.19646e43i | 0.0335098 | + | 0.0245883i | ||||
\(689\) | 4.70406e44 | 0.182375 | ||||||||
\(690\) | 4.38812e43 | + | 1.83731e44i | 0.0166224 | + | 0.0695981i | ||||
\(691\) | 2.81812e45i | 1.04306i | 0.853232 | + | 0.521532i | \(0.174639\pi\) | ||||
−0.853232 | + | 0.521532i | \(0.825361\pi\) | |||||||
\(692\) | 4.17848e45 | − | 2.11666e45i | 1.51120 | − | 0.765515i | ||||
\(693\) | 1.11004e46 | 3.92288 | ||||||||
\(694\) | −3.87019e45 | + | 9.24332e44i | −1.33654 | + | 0.319210i | ||||
\(695\) | 2.44022e45i | 0.823518i | ||||||||
\(696\) | −1.38680e45 | + | 1.17599e45i | −0.457368 | + | 0.387843i | ||||
\(697\) | −3.17192e45 | −1.02235 | ||||||||
\(698\) | 2.23840e44 | + | 9.37223e44i | 0.0705101 | + | 0.295227i | ||||
\(699\) | 6.75836e45i | 2.08069i | ||||||||
\(700\) | 1.96123e44 | + | 3.87165e44i | 0.0590147 | + | 0.116500i | ||||
\(701\) | −5.77620e45 | −1.69884 | −0.849422 | − | 0.527714i | \(-0.823049\pi\) | ||||
−0.849422 | + | 0.527714i | \(0.823049\pi\) | |||||||
\(702\) | −2.01256e45 | + | 4.80666e44i | −0.578568 | + | 0.138181i | ||||
\(703\) | 3.04606e43i | 0.00855959i | ||||||||
\(704\) | −5.00219e45 | − | 8.28548e44i | −1.37403 | − | 0.227591i | ||||
\(705\) | −2.77505e45 | −0.745153 | ||||||||
\(706\) | −7.19315e44 | − | 3.01179e45i | −0.188818 | − | 0.790585i | ||||
\(707\) | 3.27445e44i | 0.0840288i | ||||||||
\(708\) | −9.19332e44 | + | 4.65698e44i | −0.230643 | + | 0.116835i | ||||
\(709\) | 3.05399e44 | 0.0749080 | 0.0374540 | − | 0.999298i | \(-0.488075\pi\) | ||||
0.0374540 | + | 0.999298i | \(0.488075\pi\) | |||||||
\(710\) | 6.91789e45 | − | 1.65222e45i | 1.65898 | − | 0.396219i | ||||
\(711\) | − | 8.00158e45i | − | 1.87613i | ||||||
\(712\) | 2.48279e45 | + | 2.92786e45i | 0.569194 | + | 0.671228i | ||||
\(713\) | 1.19137e44 | 0.0267064 | ||||||||
\(714\) | −2.48041e45 | − | 1.03855e46i | −0.543691 | − | 2.27644i | ||||
\(715\) | − | 3.58900e45i | − | 0.769266i | ||||||
\(716\) | 3.14217e45 | + | 6.20294e45i | 0.658600 | + | 1.30014i | ||||
\(717\) | −6.50251e45 | −1.33283 | ||||||||
\(718\) | 4.68469e45 | − | 1.11886e45i | 0.939052 | − | 0.224277i | ||||
\(719\) | 2.10378e45i | 0.412418i | 0.978508 | + | 0.206209i | \(0.0661127\pi\) | ||||
−0.978508 | + | 0.206209i | \(0.933887\pi\) | |||||||
\(720\) | 4.85700e45 | − | 6.61928e45i | 0.931212 | − | 1.26909i | ||||
\(721\) | −5.58206e45 | −1.04672 | ||||||||
\(722\) | −1.20922e45 | − | 5.06304e45i | −0.221774 | − | 0.928573i | ||||
\(723\) | 1.28223e46i | 2.30013i | ||||||||
\(724\) | 3.18825e45 | − | 1.61504e45i | 0.559416 | − | 0.283379i | ||||
\(725\) | −1.63342e44 | −0.0280343 | ||||||||
\(726\) | −8.84208e45 | + | 2.11178e45i | −1.48446 | + | 0.354539i | ||||
\(727\) | − | 5.93359e45i | − | 0.974466i | −0.873272 | − | 0.487233i | \(-0.838006\pi\) | ||
0.873272 | − | 0.487233i | \(-0.161994\pi\) | |||||||
\(728\) | −4.69200e45 | + | 3.97876e45i | −0.753800 | + | 0.639213i | ||||
\(729\) | 1.02409e46 | 1.60952 | ||||||||
\(730\) | 2.26144e45 | + | 9.46869e45i | 0.347712 | + | 1.45588i | ||||
\(731\) | − | 2.31493e44i | − | 0.0348225i | ||||||
\(732\) | −6.67621e45 | − | 1.31795e46i | −0.982546 | − | 1.93964i | ||||
\(733\) | 1.14451e46 | 1.64800 | 0.824000 | − | 0.566590i | \(-0.191738\pi\) | ||||
0.824000 | + | 0.566590i | \(0.191738\pi\) | |||||||
\(734\) | 1.31621e45 | − | 3.14355e44i | 0.185434 | − | 0.0442878i | ||||
\(735\) | 2.21837e46i | 3.05799i | ||||||||
\(736\) | −1.31888e44 | + | 3.13176e44i | −0.0177893 | + | 0.0422418i | ||||
\(737\) | −1.19214e46 | −1.57343 | ||||||||
\(738\) | 3.59394e45 | + | 1.50479e46i | 0.464161 | + | 1.94345i | ||||
\(739\) | − | 2.33426e45i | − | 0.295011i | −0.989061 | − | 0.147505i | \(-0.952876\pi\) | ||
0.989061 | − | 0.147505i | \(-0.0471244\pi\) | |||||||
\(740\) | −2.78815e44 | + | 1.41237e44i | −0.0344833 | + | 0.0174679i | ||||
\(741\) | 1.64109e45 | 0.198628 | ||||||||
\(742\) | 4.48324e45 | − | 1.07075e45i | 0.531043 | − | 0.126831i | ||||
\(743\) | 2.99487e45i | 0.347182i | 0.984818 | + | 0.173591i | \(0.0555371\pi\) | ||||
−0.984818 | + | 0.173591i | \(0.944463\pi\) | |||||||
\(744\) | −5.39413e45 | − | 6.36109e45i | −0.612004 | − | 0.721713i | ||||
\(745\) | −4.62167e44 | −0.0513214 | ||||||||
\(746\) | −1.72676e45 | − | 7.22997e45i | −0.187677 | − | 0.785806i | ||||
\(747\) | − | 1.68979e46i | − | 1.79765i | ||||||
\(748\) | 5.06390e45 | + | 9.99662e45i | 0.527303 | + | 1.04094i | ||||
\(749\) | 1.62015e46 | 1.65138 | ||||||||
\(750\) | 1.63743e46 | − | 3.91073e45i | 1.63374 | − | 0.390192i | ||||
\(751\) | − | 1.07059e46i | − | 1.04564i | −0.852442 | − | 0.522822i | \(-0.824879\pi\) | ||
0.852442 | − | 0.522822i | \(-0.175121\pi\) | |||||||
\(752\) | −4.02482e45 | − | 2.95327e45i | −0.384823 | − | 0.282370i | ||||
\(753\) | 1.27219e46 | 1.19078 | ||||||||
\(754\) | −5.37847e44 | − | 2.25197e45i | −0.0492852 | − | 0.206358i | ||||
\(755\) | − | 9.52211e45i | − | 0.854244i | ||||||
\(756\) | −1.80867e46 | + | 9.16204e45i | −1.58859 | + | 0.804718i | ||||
\(757\) | −9.65089e45 | −0.829915 | −0.414957 | − | 0.909841i | \(-0.636203\pi\) | ||||
−0.414957 | + | 0.909841i | \(0.636203\pi\) | |||||||
\(758\) | −2.31601e45 | + | 5.53141e44i | −0.195000 | + | 0.0465724i | ||||
\(759\) | 1.25757e45i | 0.103673i | ||||||||
\(760\) | −1.93340e45 | + | 1.63950e45i | −0.156065 | + | 0.132341i | ||||
\(761\) | −1.39608e46 | −1.10346 | −0.551729 | − | 0.834023i | \(-0.686032\pi\) | ||||
−0.551729 | + | 0.834023i | \(0.686032\pi\) | |||||||
\(762\) | 8.07392e45 | + | 3.38057e46i | 0.624892 | + | 2.61643i | ||||
\(763\) | − | 1.47350e46i | − | 1.11675i | ||||||
\(764\) | 4.11675e45 | + | 8.12686e45i | 0.305535 | + | 0.603155i | ||||
\(765\) | −1.81452e46 | −1.31880 | ||||||||
\(766\) | −1.26360e45 | + | 3.01789e44i | −0.0899391 | + | 0.0214804i | ||||
\(767\) | − | 1.31226e45i | − | 0.0914730i | ||||||
\(768\) | 2.26928e46 | − | 7.13765e45i | 1.54920 | − | 0.487277i | ||||
\(769\) | −1.40709e45 | −0.0940808 | −0.0470404 | − | 0.998893i | \(-0.514979\pi\) | ||||
−0.0470404 | + | 0.998893i | \(0.514979\pi\) | |||||||
\(770\) | −8.16934e45 | − | 3.42052e46i | −0.534977 | − | 2.23996i | ||||
\(771\) | 1.27031e46i | 0.814776i | ||||||||
\(772\) | −2.04064e46 | + | 1.03371e46i | −1.28200 | + | 0.649414i | ||||
\(773\) | −2.99265e46 | −1.84155 | −0.920775 | − | 0.390093i | \(-0.872443\pi\) | ||||
−0.920775 | + | 0.390093i | \(0.872443\pi\) | |||||||
\(774\) | −1.09822e45 | + | 2.62292e44i | −0.0661965 | + | 0.0158099i | ||||
\(775\) | − | 7.49232e44i | − | 0.0442374i | ||||||
\(776\) | −1.70752e46 | − | 2.01362e46i | −0.987596 | − | 1.16463i | ||||
\(777\) | 1.98263e45 | 0.112332 | ||||||||
\(778\) | 2.57211e45 | + | 1.07695e46i | 0.142763 | + | 0.597751i | ||||
\(779\) | − | 4.77689e45i | − | 0.259744i | ||||||
\(780\) | 7.60925e45 | + | 1.50214e46i | 0.405348 | + | 0.800195i | ||||
\(781\) | 4.73503e46 | 2.47119 | ||||||||
\(782\) | 7.30482e44 | − | 1.74464e44i | 0.0373510 | − | 0.00892065i | ||||
\(783\) | − | 7.63066e45i | − | 0.382273i | ||||||
\(784\) | −2.36084e46 | + | 3.21743e46i | −1.15880 | + | 1.57926i | ||||
\(785\) | 3.81232e46 | 1.83347 | ||||||||
\(786\) | −7.53762e45 | − | 3.15602e46i | −0.355201 | − | 1.48723i | ||||
\(787\) | 1.65954e46i | 0.766290i | 0.923688 | + | 0.383145i | \(0.125159\pi\) | ||||
−0.923688 | + | 0.383145i | \(0.874841\pi\) | |||||||
\(788\) | 1.36868e46 | − | 6.93321e45i | 0.619273 | − | 0.313700i | ||||
\(789\) | −7.20757e45 | −0.319563 | ||||||||
\(790\) | −2.46564e46 | + | 5.88878e45i | −1.07127 | + | 0.255854i | ||||
\(791\) | 1.14982e46i | 0.489561i | ||||||||
\(792\) | 4.16872e46 | − | 3.53502e46i | 1.73940 | − | 1.47499i | ||||
\(793\) | 1.88124e46 | 0.769260 | ||||||||
\(794\) | −3.78981e44 | − | 1.58680e45i | −0.0151876 | − | 0.0635909i | ||||
\(795\) | − | 1.26165e46i | − | 0.495526i | ||||||
\(796\) | 5.34219e45 | + | 1.05460e46i | 0.205641 | + | 0.405955i | ||||
\(797\) | −2.40047e46 | −0.905655 | −0.452827 | − | 0.891598i | \(-0.649585\pi\) | ||||
−0.452827 | + | 0.891598i | \(0.649585\pi\) | |||||||
\(798\) | 1.56405e46 | − | 3.73547e45i | 0.578368 | − | 0.138134i | ||||
\(799\) | 1.10331e46i | 0.399898i | ||||||||
\(800\) | 1.96950e45 | + | 8.29417e44i | 0.0699708 | + | 0.0294668i | ||||
\(801\) | −4.13821e46 | −1.44109 | ||||||||
\(802\) | 2.94007e45 | + | 1.23101e46i | 0.100362 | + | 0.420216i | ||||
\(803\) | 6.48097e46i | 2.16866i | ||||||||
\(804\) | 4.98959e46 | − | 2.52754e46i | 1.63670 | − | 0.829088i | ||||
\(805\) | −2.35690e45 | −0.0757892 | ||||||||
\(806\) | 1.03295e46 | − | 2.46704e45i | 0.325627 | − | 0.0777706i | ||||
\(807\) | 5.45050e46i | 1.68446i | ||||||||
\(808\) | 1.04278e45 | + | 1.22971e45i | 0.0315945 | + | 0.0372582i | ||||
\(809\) | −1.46290e45 | −0.0434549 | −0.0217275 | − | 0.999764i | \(-0.506917\pi\) | ||||
−0.0217275 | + | 0.999764i | \(0.506917\pi\) | |||||||
\(810\) | 3.36126e44 | + | 1.40737e45i | 0.00978907 | + | 0.0409870i | ||||
\(811\) | − | 6.60062e46i | − | 1.88474i | −0.334574 | − | 0.942369i | \(-0.608592\pi\) | ||
0.334574 | − | 0.942369i | \(-0.391408\pi\) | |||||||
\(812\) | −1.02520e46 | − | 2.02384e46i | −0.287019 | − | 0.566603i | ||||
\(813\) | −1.07205e46 | −0.294284 | ||||||||
\(814\) | −2.02382e45 | + | 4.83357e44i | −0.0544731 | + | 0.0130100i | ||||
\(815\) | 2.03102e45i | 0.0536033i | ||||||||
\(816\) | −4.23889e46 | − | 3.11035e46i | −1.09701 | − | 0.804946i | ||||
\(817\) | 3.48626e44 | 0.00884722 | ||||||||
\(818\) | 9.56409e45 | + | 4.00450e46i | 0.238008 | + | 0.996542i | ||||
\(819\) | − | 6.63163e46i | − | 1.61837i | ||||||
\(820\) | 4.37243e46 | − | 2.21490e46i | 1.04641 | − | 0.530070i | ||||
\(821\) | −8.81734e45 | −0.206941 | −0.103471 | − | 0.994633i | \(-0.532995\pi\) | ||||
−0.103471 | + | 0.994633i | \(0.532995\pi\) | |||||||
\(822\) | −6.99477e46 | + | 1.67059e46i | −1.61000 | + | 0.384521i | ||||
\(823\) | 3.84058e46i | 0.866961i | 0.901163 | + | 0.433480i | \(0.142715\pi\) | ||||
−0.901163 | + | 0.433480i | \(0.857285\pi\) | |||||||
\(824\) | −2.09633e46 | + | 1.77766e46i | −0.464113 | + | 0.393563i | ||||
\(825\) | 7.90863e45 | 0.171727 | ||||||||
\(826\) | −2.98698e45 | − | 1.25066e46i | −0.0636139 | − | 0.266353i | ||||
\(827\) | 5.40170e46i | 1.12835i | 0.825656 | + | 0.564174i | \(0.190805\pi\) | ||||
−0.825656 | + | 0.564174i | \(0.809195\pi\) | |||||||
\(828\) | −1.65534e45 | − | 3.26780e45i | −0.0339158 | − | 0.0669529i | ||||
\(829\) | −5.31805e46 | −1.06876 | −0.534380 | − | 0.845244i | \(-0.679455\pi\) | ||||
−0.534380 | + | 0.845244i | \(0.679455\pi\) | |||||||
\(830\) | −5.20701e46 | + | 1.24361e46i | −1.02645 | + | 0.245151i | ||||
\(831\) | − | 3.12901e46i | − | 0.605050i | ||||||
\(832\) | −4.94995e45 | + | 2.98843e46i | −0.0938917 | + | 0.566852i | ||||
\(833\) | 8.81984e46 | 1.64112 | ||||||||
\(834\) | −1.77059e46 | − | 7.41350e46i | −0.323193 | − | 1.35321i | ||||
\(835\) | − | 9.19569e46i | − | 1.64665i | ||||||
\(836\) | −1.50548e46 | + | 7.62619e45i | −0.264469 | + | 0.133970i | ||||
\(837\) | 3.50010e46 | 0.603216 | ||||||||
\(838\) | −3.26505e46 | + | 7.79803e45i | −0.552059 | + | 0.131850i | ||||
\(839\) | − | 1.08388e47i | − | 1.79801i | −0.437943 | − | 0.899003i | \(-0.644293\pi\) | ||
0.437943 | − | 0.899003i | \(-0.355707\pi\) | |||||||
\(840\) | 1.06712e47 | + | 1.25842e47i | 1.73679 | + | 2.04813i | ||||
\(841\) | −5.40849e46 | −0.863654 | ||||||||
\(842\) | −2.60164e45 | − | 1.08931e46i | −0.0407619 | − | 0.170671i | ||||
\(843\) | 1.67929e47i | 2.58157i | ||||||||
\(844\) | −4.21548e45 | − | 8.32176e45i | −0.0635870 | − | 0.125527i | ||||
\(845\) | 4.35058e46 | 0.643932 | ||||||||
\(846\) | 5.23420e46 | − | 1.25010e46i | 0.760194 | − | 0.181560i | ||||
\(847\) | − | 1.13426e47i | − | 1.61651i | ||||||
\(848\) | 1.34268e46 | − | 1.82985e46i | 0.187776 | − | 0.255907i | ||||
\(849\) | 9.41642e46 | 1.29230 | ||||||||
\(850\) | −1.09717e45 | − | 4.59387e45i | −0.0147765 | − | 0.0618694i | ||||
\(851\) | 1.39451e44i | 0.00184310i | ||||||||
\(852\) | −1.98180e47 | + | 1.00390e47i | −2.57055 | + | 1.30214i | ||||
\(853\) | −3.06780e46 | −0.390520 | −0.195260 | − | 0.980752i | \(-0.562555\pi\) | ||||
−0.195260 | + | 0.980752i | \(0.562555\pi\) | |||||||
\(854\) | 1.79293e47 | − | 4.28212e46i | 2.23995 | − | 0.534974i | ||||
\(855\) | − | 2.73265e46i | − | 0.335063i | ||||||
\(856\) | 6.08443e46 | − | 5.15953e46i | 0.732217 | − | 0.620911i | ||||
\(857\) | 1.81471e46 | 0.214345 | 0.107172 | − | 0.994240i | \(-0.465820\pi\) | ||||
0.107172 | + | 0.994240i | \(0.465820\pi\) | |||||||
\(858\) | 2.60412e46 | + | 1.09035e47i | 0.301901 | + | 1.26407i | ||||
\(859\) | 1.25824e47i | 1.43177i | 0.698216 | + | 0.715887i | \(0.253977\pi\) | ||||
−0.698216 | + | 0.715887i | \(0.746023\pi\) | |||||||
\(860\) | 1.61648e45 | + | 3.19108e45i | 0.0180549 | + | 0.0356420i | ||||
\(861\) | −3.10919e47 | −3.40877 | ||||||||
\(862\) | 1.79480e46 | − | 4.28658e45i | 0.193152 | − | 0.0461311i | ||||
\(863\) | − | 1.26832e47i | − | 1.33984i | −0.742431 | − | 0.669922i | \(-0.766327\pi\) | ||
0.742431 | − | 0.669922i | \(-0.233673\pi\) | |||||||
\(864\) | −3.87469e46 | + | 9.20068e46i | −0.401806 | + | 0.954114i | ||||
\(865\) | 1.59968e47 | 1.62845 | ||||||||
\(866\) | 4.03991e46 | + | 1.69152e47i | 0.403725 | + | 1.69040i | ||||
\(867\) | − | 4.93394e46i | − | 0.484048i | ||||||
\(868\) | 9.28310e46 | − | 4.70246e46i | 0.894082 | − | 0.452908i | ||||
\(869\) | −1.68764e47 | −1.59575 | ||||||||
\(870\) | −6.03991e46 | + | 1.44253e46i | −0.560690 | + | 0.133911i | ||||
\(871\) | 7.12216e46i | 0.649114i | ||||||||
\(872\) | −4.69251e46 | − | 5.53370e46i | −0.419896 | − | 0.495167i | ||||
\(873\) | 2.84603e47 | 2.50041 | ||||||||
\(874\) | 2.62740e44 | + | 1.10010e45i | 0.00226644 | + | 0.00948962i | ||||
\(875\) | 2.10049e47i | 1.77907i | ||||||||
\(876\) | −1.37407e47 | − | 2.71254e47i | −1.14273 | − | 2.25585i | ||||
\(877\) | 1.96939e47 | 1.60820 | 0.804098 | − | 0.594497i | \(-0.202649\pi\) | ||||
0.804098 | + | 0.594497i | \(0.202649\pi\) | |||||||
\(878\) | 8.20584e46 | − | 1.95983e46i | 0.657977 | − | 0.157147i | ||||
\(879\) | 8.32664e46i | 0.655613i | ||||||||
\(880\) | −1.39610e47 | − | 1.02441e47i | −1.07943 | − | 0.792046i | ||||
\(881\) | −2.44488e46 | −0.185628 | −0.0928141 | − | 0.995683i | \(-0.529586\pi\) | ||||
−0.0928141 | + | 0.995683i | \(0.529586\pi\) | |||||||
\(882\) | −9.99329e46 | − | 4.18421e47i | −0.745094 | − | 3.11972i | ||||
\(883\) | − | 2.15626e47i | − | 1.57881i | −0.613874 | − | 0.789404i | \(-0.710390\pi\) | ||
0.613874 | − | 0.789404i | \(-0.289610\pi\) | |||||||
\(884\) | 5.97222e46 | − | 3.02530e46i | 0.429437 | − | 0.217536i | ||||
\(885\) | −3.51954e46 | −0.248539 | ||||||||
\(886\) | −7.02228e46 | + | 1.67716e46i | −0.487011 | + | 0.116315i | ||||
\(887\) | 3.56722e46i | 0.242970i | 0.992593 | + | 0.121485i | \(0.0387656\pi\) | ||||
−0.992593 | + | 0.121485i | \(0.961234\pi\) | |||||||
\(888\) | 7.44571e45 | − | 6.31387e45i | 0.0498080 | − | 0.0422365i | ||||
\(889\) | −4.33658e47 | −2.84918 | ||||||||
\(890\) | 3.04553e46 | + | 1.27517e47i | 0.196527 | + | 0.822862i | ||||
\(891\) | 9.63289e45i | 0.0610539i | ||||||||
\(892\) | 5.12506e45 | + | 1.01173e46i | 0.0319052 | + | 0.0629838i | ||||
\(893\) | −1.66158e46 | −0.101601 | ||||||||
\(894\) | 1.40408e46 | − | 3.35342e45i | 0.0843320 | − | 0.0201413i | ||||
\(895\) | 2.37471e47i | 1.40102i | ||||||||
\(896\) | 2.08474e46 | + | 2.96082e47i | 0.120816 | + | 1.71587i | ||||
\(897\) | 7.51304e45 | 0.0427697 | ||||||||
\(898\) | 1.67031e46 | + | 6.99362e46i | 0.0934062 | + | 0.391094i | ||||
\(899\) | 3.91647e46i | 0.215149i | ||||||||
\(900\) | −2.05506e46 | + | 1.04101e46i | −0.110903 | + | 0.0561793i | ||||
\(901\) | −5.01611e46 | −0.265932 | ||||||||
\(902\) | 3.17380e47 | − | 7.58010e46i | 1.65301 | − | 0.394794i | ||||
\(903\) | − | 2.26915e46i | − | 0.116107i | ||||||
\(904\) | 3.66172e46 | + | 4.31813e46i | 0.184073 | + | 0.217071i | ||||
\(905\) | 1.22058e47 | 0.602821 | ||||||||
\(906\) | 6.90910e46 | + | 2.89286e47i | 0.335251 | + | 1.40370i | ||||
\(907\) | 1.18540e47i | 0.565129i | 0.959248 | + | 0.282565i | \(0.0911851\pi\) | ||||
−0.959248 | + | 0.282565i | \(0.908815\pi\) | |||||||
\(908\) | −9.36607e46 | − | 1.84895e47i | −0.438716 | − | 0.866067i | ||||
\(909\) | −1.73806e46 | −0.0799915 | ||||||||
\(910\) | −2.04350e47 | + | 4.88056e46i | −0.924087 | + | 0.220703i | ||||
\(911\) | − | 2.37322e46i | − | 0.105450i | −0.998609 | − | 0.0527248i | \(-0.983209\pi\) | ||
0.998609 | − | 0.0527248i | \(-0.0167906\pi\) | |||||||
\(912\) | 4.68416e46 | − | 6.38372e46i | 0.204510 | − | 0.278713i | ||||
\(913\) | −3.56401e47 | −1.52899 | ||||||||
\(914\) | −1.05293e47 | − | 4.40863e47i | −0.443874 | − | 1.85851i | ||||
\(915\) | − | 5.04559e47i | − | 2.09013i | ||||||
\(916\) | 2.46605e47 | − | 1.24921e47i | 1.00386 | − | 0.508518i | ||||
\(917\) | 4.04853e47 | 1.61953 | ||||||||
\(918\) | 2.14606e47 | − | 5.12551e46i | 0.843644 | − | 0.201490i | ||||
\(919\) | 3.14225e47i | 1.21393i | 0.794730 | + | 0.606963i | \(0.207612\pi\) | ||||
−0.794730 | + | 0.606963i | \(0.792388\pi\) | |||||||
\(920\) | −8.85129e45 | + | 7.50579e45i | −0.0336048 | + | 0.0284965i | ||||
\(921\) | 6.72377e47 | 2.50876 | ||||||||
\(922\) | −3.68498e44 | − | 1.54291e45i | −0.00135127 | − | 0.00565777i | ||||
\(923\) | − | 2.82882e47i | − | 1.01948i | ||||||
\(924\) | 4.96376e47 | + | 9.79892e47i | 1.75816 | + | 3.47078i | ||||
\(925\) | 8.76983e44 | 0.00305297 | ||||||||
\(926\) | −4.66898e47 | + | 1.11511e47i | −1.59752 | + | 0.381541i | ||||
\(927\) | − | 2.96293e47i | − | 0.996428i | ||||||
\(928\) | −1.02952e47 | − | 4.33563e46i | −0.340305 | − | 0.143313i | ||||
\(929\) | −2.38969e46 | −0.0776409 | −0.0388205 | − | 0.999246i | \(-0.512360\pi\) | ||||
−0.0388205 | + | 0.999246i | \(0.512360\pi\) | |||||||
\(930\) | −6.61673e46 | − | 2.77044e47i | −0.211308 | − | 0.884752i | ||||
\(931\) | 1.32826e47i | 0.416954i | ||||||||
\(932\) | −3.70398e47 | + | 1.87629e47i | −1.14291 | + | 0.578957i | ||||
\(933\) | −1.35831e47 | −0.411995 | ||||||||
\(934\) | 3.68200e46 | − | 8.79385e45i | 0.109783 | − | 0.0262198i | ||||
\(935\) | 3.82707e47i | 1.12171i | ||||||||
\(936\) | −2.11191e47 | − | 2.49049e47i | −0.608501 | − | 0.717583i | ||||
\(937\) | 5.26937e46 | 0.149254 | 0.0746268 | − | 0.997212i | \(-0.476223\pi\) | ||||
0.0746268 | + | 0.997212i | \(0.476223\pi\) | |||||||
\(938\) | 1.62116e47 | + | 6.78783e47i | 0.451419 | + | 1.89010i | ||||
\(939\) | − | 3.66554e47i | − | 1.00343i | ||||||
\(940\) | −7.70425e46 | − | 1.52089e47i | −0.207341 | − | 0.409310i | ||||
\(941\) | −1.10297e47 | −0.291829 | −0.145915 | − | 0.989297i | \(-0.546612\pi\) | ||||
−0.145915 | + | 0.989297i | \(0.546612\pi\) | |||||||
\(942\) | −1.15820e48 | + | 2.76616e47i | −3.01279 | + | 0.719554i | ||||
\(943\) | − | 2.18690e46i | − | 0.0559296i | ||||||
\(944\) | −5.10460e46 | − | 3.74558e46i | −0.128354 | − | 0.0941818i | ||||
\(945\) | −6.92426e47 | −1.71185 | ||||||||
\(946\) | 5.53210e45 | + | 2.31630e46i | 0.0134472 | + | 0.0563036i | ||||
\(947\) | − | 7.59630e47i | − | 1.81552i | −0.419485 | − | 0.907762i | \(-0.637789\pi\) | ||
0.419485 | − | 0.907762i | \(-0.362211\pi\) | |||||||
\(948\) | 7.06345e47 | − | 3.57807e47i | 1.65990 | − | 0.840844i | ||||
\(949\) | 3.87189e47 | 0.894671 | ||||||||
\(950\) | 6.91832e45 | − | 1.65233e45i | 0.0157189 | − | 0.00375421i | ||||
\(951\) | 2.23442e47i | 0.499201i | ||||||||
\(952\) | 5.00325e47 | − | 4.24269e47i | 1.09916 | − | 0.932074i | ||||
\(953\) | −2.69647e47 | −0.582517 | −0.291259 | − | 0.956644i | \(-0.594074\pi\) | ||||
−0.291259 | + | 0.956644i | \(0.594074\pi\) | |||||||
\(954\) | 5.68348e46 | + | 2.37968e47i | 0.120737 | + | 0.505528i | ||||
\(955\) | 3.11126e47i | 0.649954i | ||||||||
\(956\) | −1.80526e47 | − | 3.56376e47i | −0.370863 | − | 0.732119i | ||||
\(957\) | −4.13409e47 | −0.835198 | ||||||||
\(958\) | 6.22014e47 | − | 1.48558e47i | 1.23581 | − | 0.295153i | ||||
\(959\) | − | 8.97288e47i | − | 1.75321i | ||||||
\(960\) | 8.01513e47 | + | 1.32760e47i | 1.54018 | + | 0.255110i | ||||
\(961\) | 3.49500e47 | 0.660501 | ||||||||
\(962\) | 2.88769e45 | + | 1.20908e46i | 0.00536722 | + | 0.0224727i | ||||
\(963\) | 8.59968e47i | 1.57203i | ||||||||
\(964\) | −7.02735e47 | + | 3.55979e47i | −1.26345 | + | 0.640017i | ||||
\(965\) | −7.81232e47 | −1.38148 | ||||||||
\(966\) | 7.16036e46 | − | 1.71013e46i | 0.124538 | − | 0.0297438i | ||||
\(967\) | 8.68662e47i | 1.48603i | 0.669276 | + | 0.743014i | \(0.266604\pi\) | ||||
−0.669276 | + | 0.743014i | \(0.733396\pi\) | |||||||
\(968\) | −3.61217e47 | − | 4.25969e47i | −0.607802 | − | 0.716757i | ||||
\(969\) | −1.74995e47 | −0.289631 | ||||||||
\(970\) | −2.09454e47 | − | 8.76989e47i | −0.340990 | − | 1.42773i | ||||
\(971\) | 3.07628e47i | 0.492627i | 0.969190 | + | 0.246314i | \(0.0792193\pi\) | ||||
−0.969190 | + | 0.246314i | \(0.920781\pi\) | |||||||
\(972\) | 2.76570e47 | + | 5.45975e47i | 0.435657 | + | 0.860027i | ||||
\(973\) | 9.51002e47 | 1.47359 | ||||||||
\(974\) | 5.57069e47 | − | 1.33047e47i | 0.849113 | − | 0.202797i | ||||
\(975\) | − | 4.72481e46i | − | 0.0708452i | ||||||
\(976\) | 5.36963e47 | − | 7.31791e47i | 0.792040 | − | 1.07942i | ||||
\(977\) | 1.00138e48 | 1.45306 | 0.726531 | − | 0.687134i | \(-0.241131\pi\) | ||||
0.726531 | + | 0.687134i | \(0.241131\pi\) | |||||||
\(978\) | −1.47368e46 | − | 6.17031e46i | −0.0210368 | − | 0.0880816i | ||||
\(979\) | 8.72804e47i | 1.22573i | ||||||||
\(980\) | −1.21580e48 | + | 6.15876e47i | −1.67975 | + | 0.850895i | ||||
\(981\) | 7.82127e47 | 1.06310 | ||||||||
\(982\) | −4.09206e47 | + | 9.77320e46i | −0.547215 | + | 0.130693i | ||||
\(983\) | − | 5.92610e47i | − | 0.779674i | −0.920884 | − | 0.389837i | \(-0.872531\pi\) | ||
0.920884 | − | 0.389837i | \(-0.127469\pi\) | |||||||
\(984\) | −1.16765e48 | + | 9.90154e47i | −1.51144 | + | 1.28168i | ||||
\(985\) | 5.23981e47 | 0.667323 | ||||||||
\(986\) | 5.73525e46 | + | 2.40136e47i | 0.0718657 | + | 0.300903i | ||||
\(987\) | 1.08149e48i | 1.33336i | ||||||||
\(988\) | 4.55607e46 | + | 8.99411e46i | 0.0552687 | + | 0.109106i | ||||
\(989\) | 1.59604e45 | 0.00190504 | ||||||||
\(990\) | 1.81560e48 | − | 4.33625e47i | 2.13234 | − | 0.509274i | ||||
\(991\) | − | 7.60458e47i | − | 0.878813i | −0.898288 | − | 0.439407i | \(-0.855189\pi\) | ||
0.898288 | − | 0.439407i | \(-0.144811\pi\) | |||||||
\(992\) | 1.98870e47 | − | 4.72230e47i | 0.226143 | − | 0.536991i | ||||
\(993\) | −2.19395e48 | −2.45492 | ||||||||
\(994\) | −6.43903e47 | − | 2.69603e48i | −0.708987 | − | 2.96854i | ||||
\(995\) | 4.03739e47i | 0.437453i | ||||||||
\(996\) | 1.49168e48 | − | 7.55627e47i | 1.59047 | − | 0.805671i | ||||
\(997\) | −4.12064e47 | −0.432356 | −0.216178 | − | 0.976354i | \(-0.569359\pi\) | ||||
−0.216178 | + | 0.976354i | \(0.569359\pi\) | |||||||
\(998\) | −1.02569e48 | + | 2.44969e47i | −1.05908 | + | 0.252943i | ||||
\(999\) | 4.09689e46i | 0.0416300i |
(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 | 4.33.b.b.3.7 | ✓ | 14 | |
3.2 | odd | 2 | 36.33.d.b.19.8 | 14 | |||
4.3 | odd | 2 | inner | 4.33.b.b.3.8 | yes | 14 | |
12.11 | even | 2 | 36.33.d.b.19.7 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.33.b.b.3.7 | ✓ | 14 | 1.1 | even | 1 | trivial | |
4.33.b.b.3.8 | yes | 14 | 4.3 | odd | 2 | inner | |
36.33.d.b.19.7 | 14 | 12.11 | even | 2 | |||
36.33.d.b.19.8 | 14 | 3.2 | odd | 2 |