Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,24,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(16.7602018673\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 15644845 x^{8} + 79349217360160 x^{6} + \cdots + 34\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{12}\cdot 5^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.6 | ||
Root | \(224.285i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.24.b.a.4.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 448.570i | 0.154876i | 0.996997 | + | 0.0774382i | \(0.0246741\pi\) | ||||
−0.996997 | + | 0.0774382i | \(0.975326\pi\) | |||||||
\(3\) | 302181.i | 0.984855i | 0.870353 | + | 0.492427i | \(0.163890\pi\) | ||||
−0.870353 | + | 0.492427i | \(0.836110\pi\) | |||||||
\(4\) | 8.18739e6 | 0.976013 | ||||||||
\(5\) | 1.05706e8 | − | 2.73336e7i | 0.968156 | − | 0.250346i | ||||
\(6\) | −1.35549e8 | −0.152531 | ||||||||
\(7\) | − | 8.28173e9i | − | 1.58305i | −0.611139 | − | 0.791523i | \(-0.709288\pi\) | ||
0.611139 | − | 0.791523i | \(-0.290712\pi\) | |||||||
\(8\) | 7.43550e9i | 0.306038i | ||||||||
\(9\) | 2.83002e9 | 0.0300609 | ||||||||
\(10\) | 1.22610e10 | + | 4.74167e10i | 0.0387727 | + | 0.149945i | ||||
\(11\) | 1.31538e11 | 0.139007 | 0.0695033 | − | 0.997582i | \(-0.477859\pi\) | ||||
0.0695033 | + | 0.997582i | \(0.477859\pi\) | |||||||
\(12\) | 2.47407e12i | 0.961231i | ||||||||
\(13\) | − | 1.05183e13i | − | 1.62778i | −0.581019 | − | 0.813890i | \(-0.697346\pi\) | ||
0.581019 | − | 0.813890i | \(-0.302654\pi\) | |||||||
\(14\) | 3.71494e12 | 0.245177 | ||||||||
\(15\) | 8.25967e12 | + | 3.19424e13i | 0.246555 | + | 0.953494i | ||||
\(16\) | 6.53455e13 | 0.928615 | ||||||||
\(17\) | 6.97399e13i | 0.493536i | 0.969075 | + | 0.246768i | \(0.0793686\pi\) | ||||
−0.969075 | + | 0.246768i | \(0.920631\pi\) | |||||||
\(18\) | 1.26946e12i | 0.00465572i | ||||||||
\(19\) | 3.53693e14 | 0.696562 | 0.348281 | − | 0.937390i | \(-0.386766\pi\) | ||||
0.348281 | + | 0.937390i | \(0.386766\pi\) | |||||||
\(20\) | 8.65458e14 | − | 2.23791e14i | 0.944933 | − | 0.244341i | ||||
\(21\) | 2.50258e15 | 1.55907 | ||||||||
\(22\) | 5.90041e13i | 0.0215289i | ||||||||
\(23\) | 5.24907e15i | 1.14871i | 0.818605 | + | 0.574357i | \(0.194748\pi\) | ||||
−0.818605 | + | 0.574357i | \(0.805252\pi\) | |||||||
\(24\) | −2.24686e15 | −0.301403 | ||||||||
\(25\) | 1.04267e16 | − | 5.77865e15i | 0.874654 | − | 0.484749i | ||||
\(26\) | 4.71818e15 | 0.252105 | ||||||||
\(27\) | 2.93034e16i | 1.01446i | ||||||||
\(28\) | − | 6.78058e16i | − | 1.54507i | ||||||
\(29\) | −1.00934e17 | −1.53625 | −0.768126 | − | 0.640299i | \(-0.778810\pi\) | ||||
−0.768126 | + | 0.640299i | \(0.778810\pi\) | |||||||
\(30\) | −1.43284e16 | + | 3.70504e15i | −0.147674 | + | 0.0381855i | ||||
\(31\) | −1.02500e17 | −0.724540 | −0.362270 | − | 0.932073i | \(-0.617998\pi\) | ||||
−0.362270 | + | 0.932073i | \(0.617998\pi\) | |||||||
\(32\) | 9.16855e16i | 0.449859i | ||||||||
\(33\) | 3.97483e16i | 0.136901i | ||||||||
\(34\) | −3.12833e16 | −0.0764371 | ||||||||
\(35\) | −2.26369e17 | − | 8.75430e17i | −0.396310 | − | 1.53264i | ||||
\(36\) | 2.31705e16 | 0.0293398 | ||||||||
\(37\) | 1.24538e18i | 1.15075i | 0.817888 | + | 0.575377i | \(0.195145\pi\) | ||||
−0.817888 | + | 0.575377i | \(0.804855\pi\) | |||||||
\(38\) | 1.58656e17i | 0.107881i | ||||||||
\(39\) | 3.17842e18 | 1.60313 | ||||||||
\(40\) | 2.03239e17 | + | 7.85979e17i | 0.0766155 | + | 0.296293i | ||||
\(41\) | 1.51172e18 | 0.429001 | 0.214500 | − | 0.976724i | \(-0.431188\pi\) | ||||
0.214500 | + | 0.976724i | \(0.431188\pi\) | |||||||
\(42\) | 1.12258e18i | 0.241463i | ||||||||
\(43\) | − | 3.61711e18i | − | 0.593573i | −0.954944 | − | 0.296787i | \(-0.904085\pi\) | ||
0.954944 | − | 0.296787i | \(-0.0959150\pi\) | |||||||
\(44\) | 1.07695e18 | 0.135672 | ||||||||
\(45\) | 2.99151e17 | − | 7.73546e16i | 0.0291036 | − | 0.00752562i | ||||
\(46\) | −2.35458e18 | −0.177909 | ||||||||
\(47\) | − | 7.84743e18i | − | 0.463022i | −0.972832 | − | 0.231511i | \(-0.925633\pi\) | ||
0.972832 | − | 0.231511i | \(-0.0743670\pi\) | |||||||
\(48\) | 1.97461e19i | 0.914551i | ||||||||
\(49\) | −4.12183e19 | −1.50604 | ||||||||
\(50\) | 2.59213e18 | + | 4.67710e18i | 0.0750762 | + | 0.135463i | ||||
\(51\) | −2.10741e19 | −0.486061 | ||||||||
\(52\) | − | 8.61172e19i | − | 1.58873i | ||||||
\(53\) | 2.82290e19i | 0.418334i | 0.977880 | + | 0.209167i | \(0.0670753\pi\) | ||||
−0.977880 | + | 0.209167i | \(0.932925\pi\) | |||||||
\(54\) | −1.31446e19 | −0.157116 | ||||||||
\(55\) | 1.39044e19 | − | 3.59540e18i | 0.134580 | − | 0.0347998i | ||||
\(56\) | 6.15788e19 | 0.484472 | ||||||||
\(57\) | 1.06879e20i | 0.686012i | ||||||||
\(58\) | − | 4.52762e19i | − | 0.237929i | ||||||
\(59\) | 2.58305e20 | 1.11516 | 0.557578 | − | 0.830125i | \(-0.311731\pi\) | ||||
0.557578 | + | 0.830125i | \(0.311731\pi\) | |||||||
\(60\) | 6.76252e19 | + | 2.61525e20i | 0.240641 | + | 0.930622i | ||||
\(61\) | −7.40067e19 | −0.217760 | −0.108880 | − | 0.994055i | \(-0.534726\pi\) | ||||
−0.108880 | + | 0.994055i | \(0.534726\pi\) | |||||||
\(62\) | − | 4.59782e19i | − | 0.112214i | ||||||
\(63\) | − | 2.34375e19i | − | 0.0475877i | ||||||
\(64\) | 5.07030e20 | 0.858943 | ||||||||
\(65\) | −2.87502e20 | − | 1.11185e21i | −0.407509 | − | 1.57595i | ||||
\(66\) | −1.78299e19 | −0.0212028 | ||||||||
\(67\) | 9.06429e20i | 0.906721i | 0.891327 | + | 0.453361i | \(0.149775\pi\) | ||||
−0.891327 | + | 0.453361i | \(0.850225\pi\) | |||||||
\(68\) | 5.70988e20i | 0.481698i | ||||||||
\(69\) | −1.58617e21 | −1.13132 | ||||||||
\(70\) | 3.92692e20 | − | 1.01542e20i | 0.237369 | − | 0.0613790i | ||||
\(71\) | −2.88130e21 | −1.47951 | −0.739754 | − | 0.672878i | \(-0.765058\pi\) | ||||
−0.739754 | + | 0.672878i | \(0.765058\pi\) | |||||||
\(72\) | 2.10426e19i | 0.00919976i | ||||||||
\(73\) | − | 3.52488e21i | − | 1.31502i | −0.753447 | − | 0.657508i | \(-0.771610\pi\) | ||
0.753447 | − | 0.657508i | \(-0.228390\pi\) | |||||||
\(74\) | −5.58641e20 | −0.178225 | ||||||||
\(75\) | 1.74620e21 | + | 3.15074e21i | 0.477407 | + | 0.861407i | ||||
\(76\) | 2.89582e21 | 0.679853 | ||||||||
\(77\) | − | 1.08936e21i | − | 0.220054i | ||||||
\(78\) | 1.42574e21i | 0.248287i | ||||||||
\(79\) | 1.32853e21 | 0.199829 | 0.0999145 | − | 0.994996i | \(-0.468143\pi\) | ||||
0.0999145 | + | 0.994996i | \(0.468143\pi\) | |||||||
\(80\) | 6.90742e21 | − | 1.78612e21i | 0.899045 | − | 0.232475i | ||||
\(81\) | −8.58850e21 | −0.969035 | ||||||||
\(82\) | 6.78114e20i | 0.0664421i | ||||||||
\(83\) | 1.00287e22i | 0.854767i | 0.904070 | + | 0.427383i | \(0.140565\pi\) | ||||
−0.904070 | + | 0.427383i | \(0.859435\pi\) | |||||||
\(84\) | 2.04896e22 | 1.52167 | ||||||||
\(85\) | 1.90624e21 | + | 7.37194e21i | 0.123555 | + | 0.477820i | ||||
\(86\) | 1.62253e21 | 0.0919306 | ||||||||
\(87\) | − | 3.05004e22i | − | 1.51298i | ||||||
\(88\) | 9.78051e20i | 0.0425413i | ||||||||
\(89\) | −1.08101e21 | −0.0412899 | −0.0206449 | − | 0.999787i | \(-0.506572\pi\) | ||||
−0.0206449 | + | 0.999787i | \(0.506572\pi\) | |||||||
\(90\) | 3.46990e19 | + | 1.34190e20i | 0.00116554 | + | 0.00450746i | ||||
\(91\) | −8.71095e22 | −2.57685 | ||||||||
\(92\) | 4.29762e22i | 1.12116i | ||||||||
\(93\) | − | 3.09734e22i | − | 0.713567i | ||||||
\(94\) | 3.52012e21 | 0.0717113 | ||||||||
\(95\) | 3.73875e22 | − | 9.66768e21i | 0.674381 | − | 0.174382i | ||||
\(96\) | −2.77056e22 | −0.443045 | ||||||||
\(97\) | 1.74541e22i | 0.247755i | 0.992298 | + | 0.123877i | \(0.0395329\pi\) | ||||
−0.992298 | + | 0.123877i | \(0.960467\pi\) | |||||||
\(98\) | − | 1.84893e22i | − | 0.233249i | ||||||
\(99\) | 3.72256e20 | 0.00417866 | ||||||||
\(100\) | 8.53673e22 | − | 4.73121e22i | 0.853673 | − | 0.473121i | ||||
\(101\) | −1.22364e23 | −1.09134 | −0.545668 | − | 0.838001i | \(-0.683724\pi\) | ||||
−0.545668 | + | 0.838001i | \(0.683724\pi\) | |||||||
\(102\) | − | 9.45320e21i | − | 0.0752795i | ||||||
\(103\) | 6.36214e22i | 0.452872i | 0.974026 | + | 0.226436i | \(0.0727074\pi\) | ||||
−0.974026 | + | 0.226436i | \(0.927293\pi\) | |||||||
\(104\) | 7.82086e22 | 0.498162 | ||||||||
\(105\) | 2.64538e23 | − | 6.84044e22i | 1.50942 | − | 0.390308i | ||||
\(106\) | −1.26627e22 | −0.0647902 | ||||||||
\(107\) | 2.34788e23i | 1.07836i | 0.842191 | + | 0.539179i | \(0.181266\pi\) | ||||
−0.842191 | + | 0.539179i | \(0.818734\pi\) | |||||||
\(108\) | 2.39919e23i | 0.990127i | ||||||||
\(109\) | 2.62018e23 | 0.972583 | 0.486291 | − | 0.873797i | \(-0.338349\pi\) | ||||
0.486291 | + | 0.873797i | \(0.338349\pi\) | |||||||
\(110\) | 1.61279e21 | + | 6.23710e21i | 0.00538967 | + | 0.0208433i | ||||
\(111\) | −3.76330e23 | −1.13333 | ||||||||
\(112\) | − | 5.41174e23i | − | 1.47004i | ||||||
\(113\) | − | 5.52325e23i | − | 1.35454i | −0.735733 | − | 0.677271i | \(-0.763162\pi\) | ||
0.735733 | − | 0.677271i | \(-0.236838\pi\) | |||||||
\(114\) | −4.79428e22 | −0.106247 | ||||||||
\(115\) | 1.43476e23 | + | 5.54859e23i | 0.287576 | + | 1.11214i | ||||
\(116\) | −8.26390e23 | −1.49940 | ||||||||
\(117\) | − | 2.97670e22i | − | 0.0489324i | ||||||
\(118\) | 1.15868e23i | 0.172711i | ||||||||
\(119\) | 5.77567e23 | 0.781290 | ||||||||
\(120\) | −2.37508e23 | + | 6.14148e22i | −0.291805 | + | 0.0754551i | ||||
\(121\) | −8.78128e23 | −0.980677 | ||||||||
\(122\) | − | 3.31972e22i | − | 0.0337259i | ||||||
\(123\) | 4.56813e23i | 0.422503i | ||||||||
\(124\) | −8.39204e23 | −0.707161 | ||||||||
\(125\) | 9.44214e23 | − | 8.95838e23i | 0.725446 | − | 0.688279i | ||||
\(126\) | 1.05134e22 | 0.00737022 | ||||||||
\(127\) | − | 3.54067e23i | − | 0.226643i | −0.993558 | − | 0.113322i | \(-0.963851\pi\) | ||
0.993558 | − | 0.113322i | \(-0.0361490\pi\) | |||||||
\(128\) | 9.96553e23i | 0.582889i | ||||||||
\(129\) | 1.09302e24 | 0.584584 | ||||||||
\(130\) | 4.98741e23 | − | 1.28965e23i | 0.244077 | − | 0.0631135i | ||||
\(131\) | 3.21116e24 | 1.43894 | 0.719469 | − | 0.694525i | \(-0.244385\pi\) | ||||
0.719469 | + | 0.694525i | \(0.244385\pi\) | |||||||
\(132\) | 3.25435e23i | 0.133618i | ||||||||
\(133\) | − | 2.92919e24i | − | 1.10269i | ||||||
\(134\) | −4.06597e23 | −0.140430 | ||||||||
\(135\) | 8.00967e23 | + | 3.09755e24i | 0.253966 | + | 0.982156i | ||||
\(136\) | −5.18551e23 | −0.151041 | ||||||||
\(137\) | 6.64427e24i | 1.77894i | 0.456995 | + | 0.889469i | \(0.348926\pi\) | ||||
−0.456995 | + | 0.889469i | \(0.651074\pi\) | |||||||
\(138\) | − | 7.11507e23i | − | 0.175214i | ||||||
\(139\) | −2.85476e24 | −0.646993 | −0.323497 | − | 0.946229i | \(-0.604858\pi\) | ||||
−0.323497 | + | 0.946229i | \(0.604858\pi\) | |||||||
\(140\) | −1.85337e24 | − | 7.16749e24i | −0.386804 | − | 1.49587i | ||||
\(141\) | 2.37134e24 | 0.456010 | ||||||||
\(142\) | − | 1.29246e24i | − | 0.229141i | ||||||
\(143\) | − | 1.38355e24i | − | 0.226272i | ||||||
\(144\) | 1.84929e23 | 0.0279150 | ||||||||
\(145\) | −1.06694e25 | + | 2.75890e24i | −1.48733 | + | 0.384595i | ||||
\(146\) | 1.58116e24 | 0.203665 | ||||||||
\(147\) | − | 1.24554e25i | − | 1.48323i | ||||||
\(148\) | 1.01964e25i | 1.12315i | ||||||||
\(149\) | −3.06282e24 | −0.312234 | −0.156117 | − | 0.987739i | \(-0.549898\pi\) | ||||
−0.156117 | + | 0.987739i | \(0.549898\pi\) | |||||||
\(150\) | −1.41333e24 | + | 7.83292e23i | −0.133412 | + | 0.0739391i | ||||
\(151\) | 9.29799e22 | 0.00813119 | 0.00406560 | − | 0.999992i | \(-0.498706\pi\) | ||||
0.00406560 | + | 0.999992i | \(0.498706\pi\) | |||||||
\(152\) | 2.62988e24i | 0.213174i | ||||||||
\(153\) | 1.97366e23i | 0.0148361i | ||||||||
\(154\) | 4.88656e23 | 0.0340812 | ||||||||
\(155\) | −1.08348e25 | + | 2.80168e24i | −0.701468 | + | 0.181386i | ||||
\(156\) | 2.60229e25 | 1.56467 | ||||||||
\(157\) | − | 5.33483e24i | − | 0.298040i | −0.988834 | − | 0.149020i | \(-0.952388\pi\) | ||
0.988834 | − | 0.149020i | \(-0.0476119\pi\) | |||||||
\(158\) | 5.95937e23i | 0.0309488i | ||||||||
\(159\) | −8.53027e24 | −0.411999 | ||||||||
\(160\) | 2.50609e24 | + | 9.69173e24i | 0.112620 | + | 0.435534i | ||||
\(161\) | 4.34714e25 | 1.81847 | ||||||||
\(162\) | − | 3.85255e24i | − | 0.150081i | ||||||
\(163\) | − | 1.58636e25i | − | 0.575765i | −0.957666 | − | 0.287882i | \(-0.907049\pi\) | ||
0.957666 | − | 0.287882i | \(-0.0929513\pi\) | |||||||
\(164\) | 1.23771e25 | 0.418710 | ||||||||
\(165\) | 1.08646e24 | + | 4.20164e24i | 0.0342728 | + | 0.132542i | ||||
\(166\) | −4.49859e24 | −0.132383 | ||||||||
\(167\) | 2.92212e25i | 0.802525i | 0.915963 | + | 0.401263i | \(0.131429\pi\) | ||||
−0.915963 | + | 0.401263i | \(0.868571\pi\) | |||||||
\(168\) | 1.86079e25i | 0.477135i | ||||||||
\(169\) | −6.88801e25 | −1.64967 | ||||||||
\(170\) | −3.30683e24 | + | 8.55083e23i | −0.0740031 | + | 0.0191358i | ||||
\(171\) | 1.00096e24 | 0.0209392 | ||||||||
\(172\) | − | 2.96147e25i | − | 0.579335i | ||||||
\(173\) | − | 1.96813e25i | − | 0.360183i | −0.983650 | − | 0.180092i | \(-0.942361\pi\) | ||
0.983650 | − | 0.180092i | \(-0.0576394\pi\) | |||||||
\(174\) | 1.36816e25 | 0.234326 | ||||||||
\(175\) | −4.78572e25 | − | 8.63510e25i | −0.767379 | − | 1.38462i | ||||
\(176\) | 8.59542e24 | 0.129084 | ||||||||
\(177\) | 7.80549e25i | 1.09827i | ||||||||
\(178\) | − | 4.84908e23i | − | 0.00639483i | ||||||
\(179\) | 4.88685e25 | 0.604253 | 0.302127 | − | 0.953268i | \(-0.402303\pi\) | ||||
0.302127 | + | 0.953268i | \(0.402303\pi\) | |||||||
\(180\) | 2.44927e24 | − | 6.33333e23i | 0.0284055 | − | 0.00734511i | ||||
\(181\) | −1.48889e26 | −1.62016 | −0.810082 | − | 0.586316i | \(-0.800578\pi\) | ||||
−0.810082 | + | 0.586316i | \(0.800578\pi\) | |||||||
\(182\) | − | 3.90747e25i | − | 0.399094i | ||||||
\(183\) | − | 2.23634e25i | − | 0.214462i | ||||||
\(184\) | −3.90295e25 | −0.351550 | ||||||||
\(185\) | 3.40407e25 | + | 1.31645e26i | 0.288087 | + | 1.11411i | ||||
\(186\) | 1.38937e25 | 0.110515 | ||||||||
\(187\) | 9.17346e24i | 0.0686048i | ||||||||
\(188\) | − | 6.42500e25i | − | 0.451916i | ||||||
\(189\) | 2.42683e26 | 1.60594 | ||||||||
\(190\) | 4.33663e24 | + | 1.67709e25i | 0.0270076 | + | 0.104446i | ||||
\(191\) | 1.61479e26 | 0.946742 | 0.473371 | − | 0.880863i | \(-0.343037\pi\) | ||||
0.473371 | + | 0.880863i | \(0.343037\pi\) | |||||||
\(192\) | 1.53215e26i | 0.845934i | ||||||||
\(193\) | 6.35702e25i | 0.330632i | 0.986241 | + | 0.165316i | \(0.0528644\pi\) | ||||
−0.986241 | + | 0.165316i | \(0.947136\pi\) | |||||||
\(194\) | −7.82937e24 | −0.0383713 | ||||||||
\(195\) | 3.35978e26 | − | 8.68774e25i | 1.55208 | − | 0.401337i | ||||
\(196\) | −3.37470e26 | −1.46991 | ||||||||
\(197\) | − | 4.67741e26i | − | 1.92152i | −0.277386 | − | 0.960758i | \(-0.589468\pi\) | ||
0.277386 | − | 0.960758i | \(-0.410532\pi\) | |||||||
\(198\) | 1.66983e23i | 0.000647176i | ||||||||
\(199\) | −5.85962e25 | −0.214318 | −0.107159 | − | 0.994242i | \(-0.534175\pi\) | ||||
−0.107159 | + | 0.994242i | \(0.534175\pi\) | |||||||
\(200\) | 4.29672e25 | + | 7.75276e25i | 0.148351 | + | 0.267677i | ||||
\(201\) | −2.73905e26 | −0.892989 | ||||||||
\(202\) | − | 5.48890e25i | − | 0.169022i | ||||||
\(203\) | 8.35912e26i | 2.43196i | ||||||||
\(204\) | −1.72542e26 | −0.474402 | ||||||||
\(205\) | 1.59799e26 | − | 4.13208e25i | 0.415340 | − | 0.107399i | ||||
\(206\) | −2.85387e25 | −0.0701392 | ||||||||
\(207\) | 1.48550e25i | 0.0345313i | ||||||||
\(208\) | − | 6.87321e26i | − | 1.51158i | ||||||
\(209\) | 4.65241e25 | 0.0968267 | ||||||||
\(210\) | 3.06842e25 | + | 1.18664e26i | 0.0604495 | + | 0.233774i | ||||
\(211\) | −8.76218e26 | −1.63442 | −0.817210 | − | 0.576340i | \(-0.804480\pi\) | ||||
−0.817210 | + | 0.576340i | \(0.804480\pi\) | |||||||
\(212\) | 2.31122e26i | 0.408300i | ||||||||
\(213\) | − | 8.70672e26i | − | 1.45710i | ||||||
\(214\) | −1.05319e26 | −0.167012 | ||||||||
\(215\) | −9.88685e25 | − | 3.82351e26i | −0.148599 | − | 0.574672i | ||||
\(216\) | −2.17886e26 | −0.310463 | ||||||||
\(217\) | 8.48874e26i | 1.14698i | ||||||||
\(218\) | 1.17534e26i | 0.150630i | ||||||||
\(219\) | 1.06515e27 | 1.29510 | ||||||||
\(220\) | 1.13841e26 | − | 2.94370e25i | 0.131352 | − | 0.0339651i | ||||
\(221\) | 7.33543e26 | 0.803368 | ||||||||
\(222\) | − | 1.68811e26i | − | 0.175526i | ||||||
\(223\) | 8.85073e26i | 0.873923i | 0.899480 | + | 0.436961i | \(0.143945\pi\) | ||||
−0.899480 | + | 0.436961i | \(0.856055\pi\) | |||||||
\(224\) | 7.59315e26 | 0.712147 | ||||||||
\(225\) | 2.95078e25 | − | 1.63537e25i | 0.0262928 | − | 0.0145720i | ||||
\(226\) | 2.47757e26 | 0.209787 | ||||||||
\(227\) | 1.25273e26i | 0.100823i | 0.998729 | + | 0.0504117i | \(0.0160534\pi\) | ||||
−0.998729 | + | 0.0504117i | \(0.983947\pi\) | |||||||
\(228\) | 8.75061e26i | 0.669557i | ||||||||
\(229\) | −7.49748e26 | −0.545515 | −0.272758 | − | 0.962083i | \(-0.587936\pi\) | ||||
−0.272758 | + | 0.962083i | \(0.587936\pi\) | |||||||
\(230\) | −2.48893e26 | + | 6.43589e25i | −0.172244 | + | 0.0445388i | ||||
\(231\) | 3.29184e26 | 0.216721 | ||||||||
\(232\) | − | 7.50498e26i | − | 0.470151i | ||||||
\(233\) | − | 1.77705e27i | − | 1.05951i | −0.848150 | − | 0.529757i | \(-0.822283\pi\) | ||
0.848150 | − | 0.529757i | \(-0.177717\pi\) | |||||||
\(234\) | 1.33526e25 | 0.00757849 | ||||||||
\(235\) | −2.14498e26 | − | 8.29522e26i | −0.115916 | − | 0.448278i | ||||
\(236\) | 2.11485e27 | 1.08841 | ||||||||
\(237\) | 4.01455e26i | 0.196803i | ||||||||
\(238\) | 2.59079e26i | 0.121004i | ||||||||
\(239\) | −3.55752e27 | −1.58333 | −0.791666 | − | 0.610954i | \(-0.790786\pi\) | ||||
−0.791666 | + | 0.610954i | \(0.790786\pi\) | |||||||
\(240\) | 5.39732e26 | + | 2.08729e27i | 0.228954 | + | 0.885429i | ||||
\(241\) | −4.31970e26 | −0.174686 | −0.0873429 | − | 0.996178i | \(-0.527838\pi\) | ||||
−0.0873429 | + | 0.996178i | \(0.527838\pi\) | |||||||
\(242\) | − | 3.93902e26i | − | 0.151884i | ||||||
\(243\) | 1.63439e26i | 0.0601011i | ||||||||
\(244\) | −6.05922e26 | −0.212537 | ||||||||
\(245\) | −4.35703e27 | + | 1.12664e27i | −1.45808 | + | 0.377030i | ||||
\(246\) | −2.04913e26 | −0.0654358 | ||||||||
\(247\) | − | 3.72023e27i | − | 1.13385i | ||||||
\(248\) | − | 7.62135e26i | − | 0.221737i | ||||||
\(249\) | −3.03049e27 | −0.841821 | ||||||||
\(250\) | 4.01846e26 | + | 4.23546e26i | 0.106598 | + | 0.112355i | ||||
\(251\) | 5.77138e27 | 1.46229 | 0.731143 | − | 0.682224i | \(-0.238987\pi\) | ||||
0.731143 | + | 0.682224i | \(0.238987\pi\) | |||||||
\(252\) | − | 1.91892e26i | − | 0.0464462i | ||||||
\(253\) | 6.90452e26i | 0.159679i | ||||||||
\(254\) | 1.58824e26 | 0.0351017 | ||||||||
\(255\) | −2.22766e27 | + | 5.76029e26i | −0.470583 | + | 0.121684i | ||||
\(256\) | 3.80625e27 | 0.768667 | ||||||||
\(257\) | 4.52366e27i | 0.873492i | 0.899585 | + | 0.436746i | \(0.143869\pi\) | ||||
−0.899585 | + | 0.436746i | \(0.856131\pi\) | |||||||
\(258\) | 4.90296e26i | 0.0905383i | ||||||||
\(259\) | 1.03139e28 | 1.82170 | ||||||||
\(260\) | −2.35389e27 | − | 9.10312e27i | −0.397734 | − | 1.53814i | ||||
\(261\) | −2.85647e26 | −0.0461810 | ||||||||
\(262\) | 1.44043e27i | 0.222858i | ||||||||
\(263\) | 4.90619e27i | 0.726530i | 0.931686 | + | 0.363265i | \(0.118338\pi\) | ||||
−0.931686 | + | 0.363265i | \(0.881662\pi\) | |||||||
\(264\) | −2.95548e26 | −0.0418970 | ||||||||
\(265\) | 7.71600e26 | + | 2.98399e27i | 0.104728 | + | 0.405013i | ||||
\(266\) | 1.31395e27 | 0.170781 | ||||||||
\(267\) | − | 3.26660e26i | − | 0.0406645i | ||||||
\(268\) | 7.42129e27i | 0.884972i | ||||||||
\(269\) | −4.42638e27 | −0.505705 | −0.252853 | − | 0.967505i | \(-0.581369\pi\) | ||||
−0.252853 | + | 0.967505i | \(0.581369\pi\) | |||||||
\(270\) | −1.38947e27 | + | 3.59290e26i | −0.152113 | + | 0.0393334i | ||||
\(271\) | 9.10090e27 | 0.954855 | 0.477427 | − | 0.878671i | \(-0.341569\pi\) | ||||
0.477427 | + | 0.878671i | \(0.341569\pi\) | |||||||
\(272\) | 4.55719e27i | 0.458305i | ||||||||
\(273\) | − | 2.63228e28i | − | 2.53782i | ||||||
\(274\) | −2.98042e27 | −0.275516 | ||||||||
\(275\) | 1.37151e27 | − | 7.60113e26i | 0.121583 | − | 0.0673833i | ||||
\(276\) | −1.29866e28 | −1.10418 | ||||||||
\(277\) | 3.21248e27i | 0.262013i | 0.991381 | + | 0.131007i | \(0.0418209\pi\) | ||||
−0.991381 | + | 0.131007i | \(0.958179\pi\) | |||||||
\(278\) | − | 1.28056e27i | − | 0.100204i | ||||||
\(279\) | −2.90076e26 | −0.0217803 | ||||||||
\(280\) | 6.50926e27 | − | 1.68317e27i | 0.469045 | − | 0.121286i | ||||
\(281\) | −1.62849e28 | −1.12632 | −0.563162 | − | 0.826347i | \(-0.690415\pi\) | ||||
−0.563162 | + | 0.826347i | \(0.690415\pi\) | |||||||
\(282\) | 1.06371e27i | 0.0706252i | ||||||||
\(283\) | 1.42599e28i | 0.909015i | 0.890743 | + | 0.454507i | \(0.150185\pi\) | ||||
−0.890743 | + | 0.454507i | \(0.849815\pi\) | |||||||
\(284\) | −2.35903e28 | −1.44402 | ||||||||
\(285\) | 2.92139e27 | + | 1.12978e28i | 0.171741 | + | 0.664167i | ||||
\(286\) | 6.20621e26 | 0.0350443 | ||||||||
\(287\) | − | 1.25197e28i | − | 0.679128i | ||||||
\(288\) | 2.59472e26i | 0.0135231i | ||||||||
\(289\) | 1.51039e28 | 0.756422 | ||||||||
\(290\) | −1.23756e27 | − | 4.78597e27i | −0.0595647 | − | 0.230353i | ||||
\(291\) | −5.27428e27 | −0.244002 | ||||||||
\(292\) | − | 2.88596e28i | − | 1.28347i | ||||||
\(293\) | 2.58150e28i | 1.10381i | 0.833906 | + | 0.551906i | \(0.186099\pi\) | ||||
−0.833906 | + | 0.551906i | \(0.813901\pi\) | |||||||
\(294\) | 5.58711e27 | 0.229717 | ||||||||
\(295\) | 2.73045e28 | − | 7.06041e27i | 1.07964 | − | 0.279175i | ||||
\(296\) | −9.26004e27 | −0.352175 | ||||||||
\(297\) | 3.85452e27i | 0.141017i | ||||||||
\(298\) | − | 1.37389e27i | − | 0.0483577i | ||||||
\(299\) | 5.52111e28 | 1.86985 | ||||||||
\(300\) | 1.42968e28 | + | 2.57964e28i | 0.465956 | + | 0.840744i | ||||
\(301\) | −2.99559e28 | −0.939654 | ||||||||
\(302\) | 4.17080e25i | 0.00125933i | ||||||||
\(303\) | − | 3.69761e28i | − | 1.07481i | ||||||
\(304\) | 2.31122e28 | 0.646838 | ||||||||
\(305\) | −7.82297e27 | + | 2.02287e27i | −0.210826 | + | 0.0545154i | ||||
\(306\) | −8.85324e25 | −0.00229777 | ||||||||
\(307\) | 6.24975e28i | 1.56233i | 0.624327 | + | 0.781163i | \(0.285373\pi\) | ||||
−0.624327 | + | 0.781163i | \(0.714627\pi\) | |||||||
\(308\) | − | 8.91904e27i | − | 0.214776i | ||||||
\(309\) | −1.92252e28 | −0.446013 | ||||||||
\(310\) | −1.25675e27 | − | 4.86019e27i | −0.0280924 | − | 0.108641i | ||||
\(311\) | −3.68771e28 | −0.794350 | −0.397175 | − | 0.917743i | \(-0.630009\pi\) | ||||
−0.397175 | + | 0.917743i | \(0.630009\pi\) | |||||||
\(312\) | 2.36331e28i | 0.490618i | ||||||||
\(313\) | 3.94526e27i | 0.0789434i | 0.999221 | + | 0.0394717i | \(0.0125675\pi\) | ||||
−0.999221 | + | 0.0394717i | \(0.987432\pi\) | |||||||
\(314\) | 2.39305e27 | 0.0461594 | ||||||||
\(315\) | −6.40630e26 | − | 2.47749e27i | −0.0119134 | − | 0.0460724i | ||||
\(316\) | 1.08772e28 | 0.195036 | ||||||||
\(317\) | − | 1.02232e29i | − | 1.76768i | −0.467789 | − | 0.883840i | \(-0.654949\pi\) | ||
0.467789 | − | 0.883840i | \(-0.345051\pi\) | |||||||
\(318\) | − | 3.82642e27i | − | 0.0638089i | ||||||
\(319\) | −1.32767e28 | −0.213549 | ||||||||
\(320\) | 5.35963e28 | − | 1.38589e28i | 0.831591 | − | 0.215033i | ||||
\(321\) | −7.09485e28 | −1.06203 | ||||||||
\(322\) | 1.95000e28i | 0.281638i | ||||||||
\(323\) | 2.46665e28i | 0.343778i | ||||||||
\(324\) | −7.03174e28 | −0.945792 | ||||||||
\(325\) | −6.07814e28 | − | 1.09671e29i | −0.789064 | − | 1.42374i | ||||
\(326\) | 7.11595e27 | 0.0891725 | ||||||||
\(327\) | 7.91768e28i | 0.957853i | ||||||||
\(328\) | 1.12404e28i | 0.131290i | ||||||||
\(329\) | −6.49903e28 | −0.732986 | ||||||||
\(330\) | −1.88473e27 | + | 4.87354e26i | −0.0205276 | + | 0.00530804i | ||||
\(331\) | 9.05001e28 | 0.951978 | 0.475989 | − | 0.879451i | \(-0.342090\pi\) | ||||
0.475989 | + | 0.879451i | \(0.342090\pi\) | |||||||
\(332\) | 8.21091e28i | 0.834264i | ||||||||
\(333\) | 3.52446e27i | 0.0345927i | ||||||||
\(334\) | −1.31078e28 | −0.124292 | ||||||||
\(335\) | 2.47759e28 | + | 9.58152e28i | 0.226994 | + | 0.877848i | ||||
\(336\) | 1.63532e29 | 1.44778 | ||||||||
\(337\) | − | 1.45621e29i | − | 1.24589i | −0.782267 | − | 0.622944i | \(-0.785937\pi\) | ||
0.782267 | − | 0.622944i | \(-0.214063\pi\) | |||||||
\(338\) | − | 3.08975e28i | − | 0.255495i | ||||||
\(339\) | 1.66902e29 | 1.33403 | ||||||||
\(340\) | 1.56071e28 | + | 6.03570e28i | 0.120591 | + | 0.466359i | ||||
\(341\) | −1.34826e28 | −0.100716 | ||||||||
\(342\) | 4.49000e26i | 0.00324300i | ||||||||
\(343\) | 1.14698e29i | 0.801077i | ||||||||
\(344\) | 2.68950e28 | 0.181656 | ||||||||
\(345\) | −1.67668e29 | + | 4.33556e28i | −1.09529 | + | 0.283221i | ||||
\(346\) | 8.82844e27 | 0.0557839 | ||||||||
\(347\) | − | 1.64255e29i | − | 1.00399i | −0.864871 | − | 0.501994i | \(-0.832600\pi\) | ||
0.864871 | − | 0.501994i | \(-0.167400\pi\) | |||||||
\(348\) | − | 2.49719e29i | − | 1.47669i | ||||||
\(349\) | −9.00037e28 | −0.514953 | −0.257477 | − | 0.966285i | \(-0.582891\pi\) | ||||
−0.257477 | + | 0.966285i | \(0.582891\pi\) | |||||||
\(350\) | 3.87345e28 | − | 2.14673e28i | 0.214445 | − | 0.118849i | ||||
\(351\) | 3.08221e29 | 1.65132 | ||||||||
\(352\) | 1.20601e28i | 0.0625334i | ||||||||
\(353\) | 2.76696e29i | 1.38865i | 0.719660 | + | 0.694327i | \(0.244298\pi\) | ||||
−0.719660 | + | 0.694327i | \(0.755702\pi\) | |||||||
\(354\) | −3.50131e28 | −0.170096 | ||||||||
\(355\) | −3.04571e29 | + | 7.87561e28i | −1.43239 | + | 0.370389i | ||||
\(356\) | −8.85063e27 | −0.0402995 | ||||||||
\(357\) | 1.74530e29i | 0.769458i | ||||||||
\(358\) | 2.19209e28i | 0.0935846i | ||||||||
\(359\) | 2.41821e29 | 0.999789 | 0.499895 | − | 0.866086i | \(-0.333372\pi\) | ||||
0.499895 | + | 0.866086i | \(0.333372\pi\) | |||||||
\(360\) | 5.75170e26 | + | 2.22434e27i | 0.00230313 | + | 0.00890681i | ||||
\(361\) | −1.32731e29 | −0.514802 | ||||||||
\(362\) | − | 6.67872e28i | − | 0.250925i | ||||||
\(363\) | − | 2.65353e29i | − | 0.965825i | ||||||
\(364\) | −7.13199e29 | −2.51504 | ||||||||
\(365\) | −9.63475e28 | − | 3.72602e29i | −0.329209 | − | 1.27314i | ||||
\(366\) | 1.00316e28 | 0.0332151 | ||||||||
\(367\) | − | 1.07500e29i | − | 0.344945i | −0.985014 | − | 0.172472i | \(-0.944824\pi\) | ||
0.985014 | − | 0.172472i | \(-0.0551755\pi\) | |||||||
\(368\) | 3.43003e29i | 1.06671i | ||||||||
\(369\) | 4.27821e27 | 0.0128961 | ||||||||
\(370\) | −5.90519e28 | + | 1.52697e28i | −0.172549 | + | 0.0446179i | ||||
\(371\) | 2.33785e29 | 0.662243 | ||||||||
\(372\) | − | 2.53591e29i | − | 0.696451i | ||||||
\(373\) | − | 3.98056e29i | − | 1.05997i | −0.848008 | − | 0.529984i | \(-0.822198\pi\) | ||
0.848008 | − | 0.529984i | \(-0.177802\pi\) | |||||||
\(374\) | −4.11494e27 | −0.0106253 | ||||||||
\(375\) | 2.70705e29 | + | 2.85323e29i | 0.677855 | + | 0.714459i | ||||
\(376\) | 5.83495e28 | 0.141702 | ||||||||
\(377\) | 1.06166e30i | 2.50068i | ||||||||
\(378\) | 1.08860e29i | 0.248722i | ||||||||
\(379\) | 3.47509e29 | 0.770220 | 0.385110 | − | 0.922871i | \(-0.374163\pi\) | ||||
0.385110 | + | 0.922871i | \(0.374163\pi\) | |||||||
\(380\) | 3.06106e29 | − | 7.91531e28i | 0.658204 | − | 0.170199i | ||||
\(381\) | 1.06992e29 | 0.223211 | ||||||||
\(382\) | 7.24345e28i | 0.146628i | ||||||||
\(383\) | − | 7.01936e29i | − | 1.37883i | −0.724365 | − | 0.689417i | \(-0.757867\pi\) | ||
0.724365 | − | 0.689417i | \(-0.242133\pi\) | |||||||
\(384\) | −3.01139e29 | −0.574061 | ||||||||
\(385\) | −2.97762e28 | − | 1.15152e29i | −0.0550897 | − | 0.213047i | ||||
\(386\) | −2.85157e28 | −0.0512071 | ||||||||
\(387\) | − | 1.02365e28i | − | 0.0178433i | ||||||
\(388\) | 1.42903e29i | 0.241812i | ||||||||
\(389\) | 6.11916e29 | 1.00524 | 0.502622 | − | 0.864506i | \(-0.332369\pi\) | ||||
0.502622 | + | 0.864506i | \(0.332369\pi\) | |||||||
\(390\) | 3.89706e28 | + | 1.50710e29i | 0.0621576 | + | 0.240380i | ||||
\(391\) | −3.66070e29 | −0.566932 | ||||||||
\(392\) | − | 3.06479e29i | − | 0.460904i | ||||||
\(393\) | 9.70350e29i | 1.41714i | ||||||||
\(394\) | 2.09815e29 | 0.297598 | ||||||||
\(395\) | 1.40433e29 | − | 3.63133e28i | 0.193466 | − | 0.0500264i | ||||
\(396\) | 3.04781e27 | 0.00407843 | ||||||||
\(397\) | − | 1.10711e30i | − | 1.43913i | −0.694426 | − | 0.719564i | \(-0.744342\pi\) | ||
0.694426 | − | 0.719564i | \(-0.255658\pi\) | |||||||
\(398\) | − | 2.62845e28i | − | 0.0331929i | ||||||
\(399\) | 8.85144e29 | 1.08599 | ||||||||
\(400\) | 6.81337e29 | − | 3.77609e29i | 0.812217 | − | 0.450145i | ||||
\(401\) | −1.50507e30 | −1.74340 | −0.871700 | − | 0.490039i | \(-0.836982\pi\) | ||||
−0.871700 | + | 0.490039i | \(0.836982\pi\) | |||||||
\(402\) | − | 1.22866e29i | − | 0.138303i | ||||||
\(403\) | 1.07812e30i | 1.17939i | ||||||||
\(404\) | −1.00184e30 | −1.06516 | ||||||||
\(405\) | −9.07858e29 | + | 2.34754e29i | −0.938178 | + | 0.242594i | ||||
\(406\) | −3.74965e29 | −0.376653 | ||||||||
\(407\) | 1.63815e29i | 0.159963i | ||||||||
\(408\) | − | 1.56696e29i | − | 0.148753i | ||||||
\(409\) | 3.99507e29 | 0.368729 | 0.184364 | − | 0.982858i | \(-0.440977\pi\) | ||||
0.184364 | + | 0.982858i | \(0.440977\pi\) | |||||||
\(410\) | 1.85353e28 | + | 7.16809e28i | 0.0166335 | + | 0.0643263i | ||||
\(411\) | −2.00777e30 | −1.75200 | ||||||||
\(412\) | 5.20893e29i | 0.442009i | ||||||||
\(413\) | − | 2.13922e30i | − | 1.76534i | ||||||
\(414\) | −6.66351e27 | −0.00534809 | ||||||||
\(415\) | 2.74121e29 | + | 1.06010e30i | 0.213988 | + | 0.827548i | ||||
\(416\) | 9.64373e29 | 0.732271 | ||||||||
\(417\) | − | 8.62654e29i | − | 0.637194i | ||||||
\(418\) | 2.08693e28i | 0.0149962i | ||||||||
\(419\) | 3.22107e28 | 0.0225185 | 0.0112592 | − | 0.999937i | \(-0.496416\pi\) | ||||
0.0112592 | + | 0.999937i | \(0.496416\pi\) | |||||||
\(420\) | 2.16588e30 | − | 5.60053e29i | 1.47322 | − | 0.380945i | ||||
\(421\) | −5.89545e29 | −0.390187 | −0.195093 | − | 0.980785i | \(-0.562501\pi\) | ||||
−0.195093 | + | 0.980785i | \(0.562501\pi\) | |||||||
\(422\) | − | 3.93045e29i | − | 0.253133i | ||||||
\(423\) | − | 2.22084e28i | − | 0.0139188i | ||||||
\(424\) | −2.09897e29 | −0.128026 | ||||||||
\(425\) | 4.03003e29 | + | 7.27156e29i | 0.239241 | + | 0.431673i | ||||
\(426\) | 3.90558e29 | 0.225671 | ||||||||
\(427\) | 6.12903e29i | 0.344724i | ||||||||
\(428\) | 1.92231e30i | 1.05249i | ||||||||
\(429\) | 4.18083e29 | 0.222845 | ||||||||
\(430\) | 1.71511e29 | − | 4.43494e28i | 0.0890032 | − | 0.0230145i | ||||
\(431\) | 5.69231e29 | 0.287607 | 0.143804 | − | 0.989606i | \(-0.454067\pi\) | ||||
0.143804 | + | 0.989606i | \(0.454067\pi\) | |||||||
\(432\) | 1.91485e30i | 0.942043i | ||||||||
\(433\) | − | 8.60930e29i | − | 0.412437i | −0.978506 | − | 0.206218i | \(-0.933884\pi\) | ||
0.978506 | − | 0.206218i | \(-0.0661157\pi\) | |||||||
\(434\) | −3.80779e29 | −0.177640 | ||||||||
\(435\) | −8.33685e29 | − | 3.22409e30i | −0.378770 | − | 1.46481i | ||||
\(436\) | 2.14524e30 | 0.949254 | ||||||||
\(437\) | 1.85656e30i | 0.800151i | ||||||||
\(438\) | 4.77795e29i | 0.200581i | ||||||||
\(439\) | 2.12796e30 | 0.870207 | 0.435103 | − | 0.900381i | \(-0.356712\pi\) | ||||
0.435103 | + | 0.900381i | \(0.356712\pi\) | |||||||
\(440\) | 2.67336e28 | + | 1.03386e29i | 0.0106501 | + | 0.0411867i | ||||
\(441\) | −1.16649e29 | −0.0452727 | ||||||||
\(442\) | 3.29046e29i | 0.124423i | ||||||||
\(443\) | 8.39480e29i | 0.309291i | 0.987970 | + | 0.154646i | \(0.0494236\pi\) | ||||
−0.987970 | + | 0.154646i | \(0.950576\pi\) | |||||||
\(444\) | −3.08116e30 | −1.10614 | ||||||||
\(445\) | −1.14269e29 | + | 2.95478e28i | −0.0399751 | + | 0.0103368i | ||||
\(446\) | −3.97017e29 | −0.135350 | ||||||||
\(447\) | − | 9.25526e29i | − | 0.307505i | ||||||
\(448\) | − | 4.19909e30i | − | 1.35975i | ||||||
\(449\) | 1.44706e30 | 0.456724 | 0.228362 | − | 0.973576i | \(-0.426663\pi\) | ||||
0.228362 | + | 0.973576i | \(0.426663\pi\) | |||||||
\(450\) | 7.33580e27 | + | 1.32363e28i | 0.00225685 | + | 0.00407214i | ||||
\(451\) | 1.98849e29 | 0.0596339 | ||||||||
\(452\) | − | 4.52210e30i | − | 1.32205i | ||||||
\(453\) | 2.80967e28i | 0.00800804i | ||||||||
\(454\) | −5.61939e28 | −0.0156152 | ||||||||
\(455\) | −9.20801e30 | + | 2.38101e30i | −2.49479 | + | 0.645105i | ||||
\(456\) | −7.94699e29 | −0.209946 | ||||||||
\(457\) | 3.32229e30i | 0.855857i | 0.903813 | + | 0.427928i | \(0.140756\pi\) | ||||
−0.903813 | + | 0.427928i | \(0.859244\pi\) | |||||||
\(458\) | − | 3.36314e29i | − | 0.0844875i | ||||||
\(459\) | −2.04362e30 | −0.500673 | ||||||||
\(460\) | 1.17469e30 | + | 4.54285e30i | 0.280678 | + | 1.08546i | ||||
\(461\) | 4.28913e30 | 0.999559 | 0.499780 | − | 0.866153i | \(-0.333414\pi\) | ||||
0.499780 | + | 0.866153i | \(0.333414\pi\) | |||||||
\(462\) | 1.47662e29i | 0.0335650i | ||||||||
\(463\) | 3.74937e30i | 0.831337i | 0.909516 | + | 0.415668i | \(0.136452\pi\) | ||||
−0.909516 | + | 0.415668i | \(0.863548\pi\) | |||||||
\(464\) | −6.59561e30 | −1.42659 | ||||||||
\(465\) | −8.46613e29 | − | 3.27408e30i | −0.178639 | − | 0.690844i | ||||
\(466\) | 7.97131e29 | 0.164094 | ||||||||
\(467\) | − | 6.06791e30i | − | 1.21870i | −0.792903 | − | 0.609348i | \(-0.791431\pi\) | ||
0.792903 | − | 0.609348i | \(-0.208569\pi\) | |||||||
\(468\) | − | 2.43714e29i | − | 0.0477587i | ||||||
\(469\) | 7.50680e30 | 1.43538 | ||||||||
\(470\) | 3.72099e29 | − | 9.62174e28i | 0.0694277 | − | 0.0179526i | ||||
\(471\) | 1.61208e30 | 0.293526 | ||||||||
\(472\) | 1.92063e30i | 0.341280i | ||||||||
\(473\) | − | 4.75788e29i | − | 0.0825107i | ||||||
\(474\) | −1.80081e29 | −0.0304801 | ||||||||
\(475\) | 3.68784e30 | − | 2.04387e30i | 0.609250 | − | 0.337657i | ||||
\(476\) | 4.72877e30 | 0.762550 | ||||||||
\(477\) | 7.98889e28i | 0.0125755i | ||||||||
\(478\) | − | 1.59580e30i | − | 0.245221i | ||||||
\(479\) | −3.01378e30 | −0.452120 | −0.226060 | − | 0.974113i | \(-0.572585\pi\) | ||||
−0.226060 | + | 0.974113i | \(0.572585\pi\) | |||||||
\(480\) | −2.92865e30 | + | 7.57292e29i | −0.428937 | + | 0.110915i | ||||
\(481\) | 1.30993e31 | 1.87318 | ||||||||
\(482\) | − | 1.93769e29i | − | 0.0270547i | ||||||
\(483\) | 1.31362e31i | 1.79093i | ||||||||
\(484\) | −7.18958e30 | −0.957154 | ||||||||
\(485\) | 4.77082e29 | + | 1.84500e30i | 0.0620244 | + | 0.239865i | ||||
\(486\) | −7.33137e28 | −0.00930825 | ||||||||
\(487\) | − | 8.39432e30i | − | 1.04088i | −0.853897 | − | 0.520442i | \(-0.825767\pi\) | ||
0.853897 | − | 0.520442i | \(-0.174233\pi\) | |||||||
\(488\) | − | 5.50277e29i | − | 0.0666428i | ||||||
\(489\) | 4.79368e30 | 0.567045 | ||||||||
\(490\) | −5.05378e29 | − | 1.95443e30i | −0.0583931 | − | 0.225822i | ||||
\(491\) | −2.64316e30 | −0.298323 | −0.149161 | − | 0.988813i | \(-0.547657\pi\) | ||||
−0.149161 | + | 0.988813i | \(0.547657\pi\) | |||||||
\(492\) | 3.74011e30i | 0.412369i | ||||||||
\(493\) | − | 7.03916e30i | − | 0.758196i | ||||||
\(494\) | 1.66879e30 | 0.175607 | ||||||||
\(495\) | 3.93498e28 | − | 1.01751e28i | 0.00404560 | − | 0.00104611i | ||||
\(496\) | −6.69788e30 | −0.672819 | ||||||||
\(497\) | 2.38621e31i | 2.34213i | ||||||||
\(498\) | − | 1.35939e30i | − | 0.130378i | ||||||
\(499\) | −3.04753e30 | −0.285622 | −0.142811 | − | 0.989750i | \(-0.545614\pi\) | ||||
−0.142811 | + | 0.989750i | \(0.545614\pi\) | |||||||
\(500\) | 7.73065e30 | − | 7.33458e30i | 0.708045 | − | 0.671769i | ||||
\(501\) | −8.83008e30 | −0.790371 | ||||||||
\(502\) | 2.58887e30i | 0.226474i | ||||||||
\(503\) | − | 2.02438e31i | − | 1.73086i | −0.501034 | − | 0.865428i | \(-0.667047\pi\) | ||
0.501034 | − | 0.865428i | \(-0.332953\pi\) | |||||||
\(504\) | 1.74269e29 | 0.0145636 | ||||||||
\(505\) | −1.29347e31 | + | 3.34465e30i | −1.05658 | + | 0.273212i | ||||
\(506\) | −3.09716e29 | −0.0247305 | ||||||||
\(507\) | − | 2.08142e31i | − | 1.62468i | ||||||
\(508\) | − | 2.89889e30i | − | 0.221207i | ||||||
\(509\) | 6.74069e30 | 0.502863 | 0.251431 | − | 0.967875i | \(-0.419099\pi\) | ||||
0.251431 | + | 0.967875i | \(0.419099\pi\) | |||||||
\(510\) | −2.58389e29 | − | 9.99262e29i | −0.0188459 | − | 0.0728823i | ||||
\(511\) | −2.91921e31 | −2.08173 | ||||||||
\(512\) | 1.00671e31i | 0.701937i | ||||||||
\(513\) | 1.03644e31i | 0.706634i | ||||||||
\(514\) | −2.02918e30 | −0.135283 | ||||||||
\(515\) | 1.73900e30 | + | 6.72518e30i | 0.113375 | + | 0.438451i | ||||
\(516\) | 8.94899e30 | 0.570561 | ||||||||
\(517\) | − | 1.03224e30i | − | 0.0643632i | ||||||
\(518\) | 4.62652e30i | 0.282138i | ||||||||
\(519\) | 5.94730e30 | 0.354728 | ||||||||
\(520\) | 8.26713e30 | − | 2.13772e30i | 0.482299 | − | 0.124713i | ||||
\(521\) | −8.68856e30 | −0.495808 | −0.247904 | − | 0.968785i | \(-0.579742\pi\) | ||||
−0.247904 | + | 0.968785i | \(0.579742\pi\) | |||||||
\(522\) | − | 1.28133e29i | − | 0.00715236i | ||||||
\(523\) | 2.50430e31i | 1.36747i | 0.729731 | + | 0.683734i | \(0.239645\pi\) | ||||
−0.729731 | + | 0.683734i | \(0.760355\pi\) | |||||||
\(524\) | 2.62910e31 | 1.40442 | ||||||||
\(525\) | 2.60936e31 | − | 1.44615e31i | 1.36365 | − | 0.755757i | ||||
\(526\) | −2.20077e30 | −0.112522 | ||||||||
\(527\) | − | 7.14831e30i | − | 0.357587i | ||||||
\(528\) | 2.59737e30i | 0.127129i | ||||||||
\(529\) | −6.67226e30 | −0.319545 | ||||||||
\(530\) | −1.33853e30 | + | 3.46117e29i | −0.0627270 | + | 0.0162200i | ||||
\(531\) | 7.31011e29 | 0.0335225 | ||||||||
\(532\) | − | 2.39824e31i | − | 1.07624i | ||||||
\(533\) | − | 1.59007e31i | − | 0.698319i | ||||||
\(534\) | 1.46530e29 | 0.00629798 | ||||||||
\(535\) | 6.41760e30 | + | 2.48186e31i | 0.269963 | + | 1.04402i | ||||
\(536\) | −6.73976e30 | −0.277491 | ||||||||
\(537\) | 1.47671e31i | 0.595102i | ||||||||
\(538\) | − | 1.98554e30i | − | 0.0783218i | ||||||
\(539\) | −5.42178e30 | −0.209349 | ||||||||
\(540\) | 6.55783e30 | + | 2.53609e31i | 0.247875 | + | 0.958598i | ||||
\(541\) | 1.42855e30 | 0.0528598 | 0.0264299 | − | 0.999651i | \(-0.491586\pi\) | ||||
0.0264299 | + | 0.999651i | \(0.491586\pi\) | |||||||
\(542\) | 4.08239e30i | 0.147885i | ||||||||
\(543\) | − | 4.49914e31i | − | 1.59563i | ||||||
\(544\) | −6.39414e30 | −0.222021 | ||||||||
\(545\) | 2.76969e31 | − | 7.16189e30i | 0.941612 | − | 0.243482i | ||||
\(546\) | 1.18076e31 | 0.393049 | ||||||||
\(547\) | − | 1.36802e30i | − | 0.0445902i | −0.999751 | − | 0.0222951i | \(-0.992903\pi\) | ||
0.999751 | − | 0.0222951i | \(-0.00709734\pi\) | |||||||
\(548\) | 5.43993e31i | 1.73627i | ||||||||
\(549\) | −2.09441e29 | −0.00654605 | ||||||||
\(550\) | 3.40964e29 | + | 6.15217e29i | 0.0104361 | + | 0.0188303i | ||||
\(551\) | −3.56998e31 | −1.07009 | ||||||||
\(552\) | − | 1.17939e31i | − | 0.346226i | ||||||
\(553\) | − | 1.10025e31i | − | 0.316338i | ||||||
\(554\) | −1.44102e30 | −0.0405797 | ||||||||
\(555\) | −3.97805e31 | + | 1.02864e31i | −1.09724 | + | 0.283724i | ||||
\(556\) | −2.33731e31 | −0.631474 | ||||||||
\(557\) | − | 3.27739e30i | − | 0.0867348i | −0.999059 | − | 0.0433674i | \(-0.986191\pi\) | ||
0.999059 | − | 0.0433674i | \(-0.0138086\pi\) | |||||||
\(558\) | − | 1.30120e29i | − | 0.00337326i | ||||||
\(559\) | −3.80457e31 | −0.966207 | ||||||||
\(560\) | −1.47922e31 | − | 5.72054e31i | −0.368019 | − | 1.42323i | ||||
\(561\) | −2.77204e30 | −0.0675658 | ||||||||
\(562\) | − | 7.30494e30i | − | 0.174441i | ||||||
\(563\) | − | 1.96163e30i | − | 0.0458955i | −0.999737 | − | 0.0229478i | \(-0.992695\pi\) | ||
0.999737 | − | 0.0229478i | \(-0.00730514\pi\) | |||||||
\(564\) | 1.94151e31 | 0.445072 | ||||||||
\(565\) | −1.50970e31 | − | 5.83842e31i | −0.339105 | − | 1.31141i | ||||
\(566\) | −6.39654e30 | −0.140785 | ||||||||
\(567\) | 7.11276e31i | 1.53403i | ||||||||
\(568\) | − | 2.14239e31i | − | 0.452785i | ||||||
\(569\) | 3.45236e31 | 0.715032 | 0.357516 | − | 0.933907i | \(-0.383624\pi\) | ||||
0.357516 | + | 0.933907i | \(0.383624\pi\) | |||||||
\(570\) | −5.06785e30 | + | 1.31045e30i | −0.102864 | + | 0.0265986i | ||||
\(571\) | 6.79955e31 | 1.35259 | 0.676293 | − | 0.736633i | \(-0.263585\pi\) | ||||
0.676293 | + | 0.736633i | \(0.263585\pi\) | |||||||
\(572\) | − | 1.13277e31i | − | 0.220845i | ||||||
\(573\) | 4.87957e31i | 0.932403i | ||||||||
\(574\) | 5.61596e30 | 0.105181 | ||||||||
\(575\) | 3.03326e31 | + | 5.47304e31i | 0.556838 | + | 1.00473i | ||||
\(576\) | 1.43491e30 | 0.0258205 | ||||||||
\(577\) | 1.16391e31i | 0.205304i | 0.994717 | + | 0.102652i | \(0.0327327\pi\) | ||||
−0.994717 | + | 0.102652i | \(0.967267\pi\) | |||||||
\(578\) | 6.77516e30i | 0.117152i | ||||||||
\(579\) | −1.92097e31 | −0.325624 | ||||||||
\(580\) | −8.73546e31 | + | 2.25882e31i | −1.45166 | + | 0.375370i | ||||
\(581\) | 8.30552e31 | 1.35314 | ||||||||
\(582\) | − | 2.36588e30i | − | 0.0377902i | ||||||
\(583\) | 3.71319e30i | 0.0581513i | ||||||||
\(584\) | 2.62092e31 | 0.402445 | ||||||||
\(585\) | −8.13637e29 | − | 3.14655e30i | −0.0122501 | − | 0.0473743i | ||||
\(586\) | −1.15799e31 | −0.170955 | ||||||||
\(587\) | − | 5.91729e31i | − | 0.856613i | −0.903634 | − | 0.428306i | \(-0.859110\pi\) | ||
0.903634 | − | 0.428306i | \(-0.140890\pi\) | |||||||
\(588\) | − | 1.01977e32i | − | 1.44765i | ||||||
\(589\) | −3.62533e31 | −0.504687 | ||||||||
\(590\) | 3.16709e30 | + | 1.22480e31i | 0.0432376 | + | 0.167212i | ||||
\(591\) | 1.41342e32 | 1.89242 | ||||||||
\(592\) | 8.13801e31i | 1.06861i | ||||||||
\(593\) | 1.23535e31i | 0.159096i | 0.996831 | + | 0.0795482i | \(0.0253478\pi\) | ||||
−0.996831 | + | 0.0795482i | \(0.974652\pi\) | |||||||
\(594\) | −1.72902e30 | −0.0218402 | ||||||||
\(595\) | 6.10525e31 | − | 1.57870e31i | 0.756411 | − | 0.195593i | ||||
\(596\) | −2.50766e31 | −0.304744 | ||||||||
\(597\) | − | 1.77066e31i | − | 0.211072i | ||||||
\(598\) | 2.47661e31i | 0.289596i | ||||||||
\(599\) | −3.67204e31 | −0.421210 | −0.210605 | − | 0.977571i | \(-0.567543\pi\) | ||||
−0.210605 | + | 0.977571i | \(0.567543\pi\) | |||||||
\(600\) | −2.34273e31 | + | 1.29839e31i | −0.263623 | + | 0.146105i | ||||
\(601\) | 6.53454e31 | 0.721371 | 0.360686 | − | 0.932687i | \(-0.382543\pi\) | ||||
0.360686 | + | 0.932687i | \(0.382543\pi\) | |||||||
\(602\) | − | 1.34373e31i | − | 0.145530i | ||||||
\(603\) | 2.56522e30i | 0.0272568i | ||||||||
\(604\) | 7.61263e29 | 0.00793615 | ||||||||
\(605\) | −9.28236e31 | + | 2.40024e31i | −0.949449 | + | 0.245509i | ||||
\(606\) | 1.65864e31 | 0.166463 | ||||||||
\(607\) | − | 1.25990e32i | − | 1.24070i | −0.784326 | − | 0.620349i | \(-0.786991\pi\) | ||
0.784326 | − | 0.620349i | \(-0.213009\pi\) | |||||||
\(608\) | 3.24285e31i | 0.313354i | ||||||||
\(609\) | −2.52596e32 | −2.39513 | ||||||||
\(610\) | −9.07397e29 | − | 3.50915e30i | −0.00844315 | − | 0.0326519i | ||||
\(611\) | −8.25413e31 | −0.753698 | ||||||||
\(612\) | 1.61591e30i | 0.0144802i | ||||||||
\(613\) | 8.59467e31i | 0.755847i | 0.925837 | + | 0.377923i | \(0.123362\pi\) | ||||
−0.925837 | + | 0.377923i | \(0.876638\pi\) | |||||||
\(614\) | −2.80345e31 | −0.241967 | ||||||||
\(615\) | 1.24863e31 | + | 4.82880e31i | 0.105772 | + | 0.409049i | ||||
\(616\) | 8.09996e30 | 0.0673449 | ||||||||
\(617\) | − | 4.44519e31i | − | 0.362753i | −0.983414 | − | 0.181377i | \(-0.941945\pi\) | ||
0.983414 | − | 0.181377i | \(-0.0580553\pi\) | |||||||
\(618\) | − | 8.62383e30i | − | 0.0690769i | ||||||
\(619\) | 1.46179e32 | 1.14933 | 0.574664 | − | 0.818389i | \(-0.305133\pi\) | ||||
0.574664 | + | 0.818389i | \(0.305133\pi\) | |||||||
\(620\) | −8.87091e31 | + | 2.29384e31i | −0.684642 | + | 0.177035i | ||||
\(621\) | −1.53816e32 | −1.16533 | ||||||||
\(622\) | − | 1.65420e31i | − | 0.123026i | ||||||
\(623\) | 8.95261e30i | 0.0653638i | ||||||||
\(624\) | 2.07695e32 | 1.48869 | ||||||||
\(625\) | 7.53229e31 | − | 1.20504e32i | 0.530038 | − | 0.847974i | ||||
\(626\) | −1.76973e30 | −0.0122265 | ||||||||
\(627\) | 1.40587e31i | 0.0953603i | ||||||||
\(628\) | − | 4.36783e31i | − | 0.290891i | ||||||
\(629\) | −8.68528e31 | −0.567939 | ||||||||
\(630\) | 1.11133e30 | − | 2.87368e29i | 0.00713552 | − | 0.00184511i | ||||
\(631\) | 2.21285e32 | 1.39513 | 0.697564 | − | 0.716523i | \(-0.254267\pi\) | ||||
0.697564 | + | 0.716523i | \(0.254267\pi\) | |||||||
\(632\) | 9.87825e30i | 0.0611552i | ||||||||
\(633\) | − | 2.64776e32i | − | 1.60967i | ||||||
\(634\) | 4.58580e31 | 0.273772 | ||||||||
\(635\) | −9.67791e30 | − | 3.74271e31i | −0.0567393 | − | 0.219426i | ||||
\(636\) | −6.98407e31 | −0.402116 | ||||||||
\(637\) | 4.33545e32i | 2.45149i | ||||||||
\(638\) | − | 5.95554e30i | − | 0.0330738i | ||||||
\(639\) | −8.15414e30 | −0.0444752 | ||||||||
\(640\) | 2.72393e31 | + | 1.05342e32i | 0.145924 | + | 0.564327i | ||||
\(641\) | −1.47537e32 | −0.776308 | −0.388154 | − | 0.921595i | \(-0.626887\pi\) | ||||
−0.388154 | + | 0.921595i | \(0.626887\pi\) | |||||||
\(642\) | − | 3.18254e31i | − | 0.164483i | ||||||
\(643\) | 2.39840e32i | 1.21757i | 0.793334 | + | 0.608786i | \(0.208343\pi\) | ||||
−0.793334 | + | 0.608786i | \(0.791657\pi\) | |||||||
\(644\) | 3.55917e32 | 1.77485 | ||||||||
\(645\) | 1.15539e32 | − | 2.98761e31i | 0.565968 | − | 0.146348i | ||||
\(646\) | −1.10647e31 | −0.0532432 | ||||||||
\(647\) | 6.15724e30i | 0.0291063i | 0.999894 | + | 0.0145532i | \(0.00463258\pi\) | ||||
−0.999894 | + | 0.0145532i | \(0.995367\pi\) | |||||||
\(648\) | − | 6.38598e31i | − | 0.296562i | ||||||
\(649\) | 3.39770e31 | 0.155014 | ||||||||
\(650\) | 4.91950e31 | − | 2.72647e31i | 0.220504 | − | 0.122207i | ||||
\(651\) | −2.56513e32 | −1.12961 | ||||||||
\(652\) | − | 1.29882e32i | − | 0.561954i | ||||||
\(653\) | − | 1.31379e31i | − | 0.0558500i | −0.999610 | − | 0.0279250i | \(-0.991110\pi\) | ||
0.999610 | − | 0.0279250i | \(-0.00888996\pi\) | |||||||
\(654\) | −3.55164e31 | −0.148349 | ||||||||
\(655\) | 3.39439e32 | − | 8.77724e31i | 1.39312 | − | 0.360233i | ||||
\(656\) | 9.87843e31 | 0.398376 | ||||||||
\(657\) | − | 9.97549e30i | − | 0.0395305i | ||||||
\(658\) | − | 2.91527e31i | − | 0.113522i | ||||||
\(659\) | −2.54141e32 | −0.972506 | −0.486253 | − | 0.873818i | \(-0.661637\pi\) | ||||
−0.486253 | + | 0.873818i | \(0.661637\pi\) | |||||||
\(660\) | 8.89529e30 | + | 3.44005e31i | 0.0334507 | + | 0.129363i | ||||
\(661\) | −3.16549e32 | −1.16983 | −0.584917 | − | 0.811093i | \(-0.698873\pi\) | ||||
−0.584917 | + | 0.811093i | \(0.698873\pi\) | |||||||
\(662\) | 4.05956e31i | 0.147439i | ||||||||
\(663\) | 2.21663e32i | 0.791201i | ||||||||
\(664\) | −7.45686e31 | −0.261591 | ||||||||
\(665\) | −8.00651e31 | − | 3.09633e32i | −0.276054 | − | 1.06758i | ||||
\(666\) | −1.58097e30 | −0.00535759 | ||||||||
\(667\) | − | 5.29812e32i | − | 1.76471i | ||||||
\(668\) | 2.39245e32i | 0.783275i | ||||||||
\(669\) | −2.67452e32 | −0.860687 | ||||||||
\(670\) | −4.29799e31 | + | 1.11137e31i | −0.135958 | + | 0.0351561i | ||||
\(671\) | −9.73470e30 | −0.0302701 | ||||||||
\(672\) | 2.29450e32i | 0.701361i | ||||||||
\(673\) | − | 2.36325e32i | − | 0.710127i | −0.934842 | − | 0.355063i | \(-0.884459\pi\) | ||
0.934842 | − | 0.355063i | \(-0.115541\pi\) | |||||||
\(674\) | 6.53210e31 | 0.192959 | ||||||||
\(675\) | 1.69334e32 | + | 3.05538e32i | 0.491758 | + | 0.887301i | ||||
\(676\) | −5.63948e32 | −1.61010 | ||||||||
\(677\) | 1.16353e31i | 0.0326595i | 0.999867 | + | 0.0163297i | \(0.00519815\pi\) | ||||
−0.999867 | + | 0.0163297i | \(0.994802\pi\) | |||||||
\(678\) | 7.48672e31i | 0.206610i | ||||||||
\(679\) | 1.44550e32 | 0.392207 | ||||||||
\(680\) | −5.48141e31 | + | 1.41739e31i | −0.146231 | + | 0.0378125i | ||||
\(681\) | −3.78552e31 | −0.0992965 | ||||||||
\(682\) | − | 6.04789e30i | − | 0.0155985i | ||||||
\(683\) | − | 2.63629e32i | − | 0.668582i | −0.942470 | − | 0.334291i | \(-0.891503\pi\) | ||
0.942470 | − | 0.334291i | \(-0.108497\pi\) | |||||||
\(684\) | 8.19524e30 | 0.0204370 | ||||||||
\(685\) | 1.81612e32 | + | 7.02341e32i | 0.445350 | + | 1.72229i | ||||
\(686\) | −5.14502e31 | −0.124068 | ||||||||
\(687\) | − | 2.26559e32i | − | 0.537253i | ||||||
\(688\) | − | 2.36362e32i | − | 0.551201i | ||||||
\(689\) | 2.96921e32 | 0.680956 | ||||||||
\(690\) | −1.94480e31 | − | 7.52108e31i | −0.0438643 | − | 0.169635i | ||||
\(691\) | 5.50229e32 | 1.22052 | 0.610262 | − | 0.792200i | \(-0.291064\pi\) | ||||
0.610262 | + | 0.792200i | \(0.291064\pi\) | |||||||
\(692\) | − | 1.61138e32i | − | 0.351543i | ||||||
\(693\) | − | 3.08292e30i | − | 0.00661501i | ||||||
\(694\) | 7.36798e31 | 0.155494 | ||||||||
\(695\) | −3.01766e32 | + | 7.80308e31i | −0.626391 | + | 0.161972i | ||||
\(696\) | 2.26786e32 | 0.463031 | ||||||||
\(697\) | 1.05427e32i | 0.211727i | ||||||||
\(698\) | − | 4.03730e31i | − | 0.0797541i | ||||||
\(699\) | 5.36990e32 | 1.04347 | ||||||||
\(700\) | −3.91826e32 | − | 7.06989e32i | −0.748973 | − | 1.35140i | ||||
\(701\) | 3.64948e32 | 0.686236 | 0.343118 | − | 0.939292i | \(-0.388517\pi\) | ||||
0.343118 | + | 0.939292i | \(0.388517\pi\) | |||||||
\(702\) | 1.38259e32i | 0.255750i | ||||||||
\(703\) | 4.40482e32i | 0.801572i | ||||||||
\(704\) | 6.66938e31 | 0.119399 | ||||||||
\(705\) | 2.50665e32 | − | 6.48172e31i | 0.441489 | − | 0.114160i | ||||
\(706\) | −1.24118e32 | −0.215070 | ||||||||
\(707\) | 1.01339e33i | 1.72764i | ||||||||
\(708\) | 6.39066e32i | 1.07192i | ||||||||
\(709\) | −3.85906e32 | −0.636869 | −0.318434 | − | 0.947945i | \(-0.603157\pi\) | ||||
−0.318434 | + | 0.947945i | \(0.603157\pi\) | |||||||
\(710\) | −3.53276e31 | − | 1.36622e32i | −0.0573646 | − | 0.221844i | ||||
\(711\) | 3.75976e30 | 0.00600703 | ||||||||
\(712\) | − | 8.03783e30i | − | 0.0126363i | ||||||
\(713\) | − | 5.38027e32i | − | 0.832290i | ||||||
\(714\) | −7.82888e31 | −0.119171 | ||||||||
\(715\) | −3.78174e31 | − | 1.46250e32i | −0.0566464 | − | 0.219067i | ||||
\(716\) | 4.00105e32 | 0.589759 | ||||||||
\(717\) | − | 1.07501e33i | − | 1.55935i | ||||||
\(718\) | 1.08474e32i | 0.154844i | ||||||||
\(719\) | 1.78348e32 | 0.250545 | 0.125273 | − | 0.992122i | \(-0.460019\pi\) | ||||
0.125273 | + | 0.992122i | \(0.460019\pi\) | |||||||
\(720\) | 1.95482e31 | − | 5.05478e30i | 0.0270260 | − | 0.00698841i | ||||
\(721\) | 5.26895e32 | 0.716917 | ||||||||
\(722\) | − | 5.95392e31i | − | 0.0797307i | ||||||
\(723\) | − | 1.30533e32i | − | 0.172040i | ||||||
\(724\) | −1.21901e33 | −1.58130 | ||||||||
\(725\) | −1.05241e33 | + | 5.83265e32i | −1.34369 | + | 0.744696i | ||||
\(726\) | 1.19030e32 | 0.149584 | ||||||||
\(727\) | 1.17673e33i | 1.45556i | 0.685810 | + | 0.727781i | \(0.259448\pi\) | ||||
−0.685810 | + | 0.727781i | \(0.740552\pi\) | |||||||
\(728\) | − | 6.47702e32i | − | 0.788614i | ||||||
\(729\) | −8.57937e32 | −1.02823 | ||||||||
\(730\) | 1.67138e32 | − | 4.32186e31i | 0.197180 | − | 0.0509868i | ||||
\(731\) | 2.52257e32 | 0.292950 | ||||||||
\(732\) | − | 1.83098e32i | − | 0.209318i | ||||||
\(733\) | − | 9.99183e32i | − | 1.12447i | −0.826976 | − | 0.562237i | \(-0.809941\pi\) | ||
0.826976 | − | 0.562237i | \(-0.190059\pi\) | |||||||
\(734\) | 4.82214e31 | 0.0534238 | ||||||||
\(735\) | −3.40450e32 | − | 1.31661e33i | −0.371320 | − | 1.43599i | ||||
\(736\) | −4.81264e32 | −0.516759 | ||||||||
\(737\) | 1.19230e32i | 0.126040i | ||||||||
\(738\) | 1.91908e30i | 0.00199731i | ||||||||
\(739\) | −1.30194e33 | −1.33408 | −0.667039 | − | 0.745022i | \(-0.732439\pi\) | ||||
−0.667039 | + | 0.745022i | \(0.732439\pi\) | |||||||
\(740\) | 2.78705e32 | + | 1.07783e33i | 0.281177 | + | 1.08739i | ||||
\(741\) | 1.12418e33 | 1.11668 | ||||||||
\(742\) | 1.04869e32i | 0.102566i | ||||||||
\(743\) | 9.92153e32i | 0.955449i | 0.878510 | + | 0.477724i | \(0.158538\pi\) | ||||
−0.878510 | + | 0.477724i | \(0.841462\pi\) | |||||||
\(744\) | 2.30303e32 | 0.218379 | ||||||||
\(745\) | −3.23760e32 | + | 8.37179e31i | −0.302291 | + | 0.0781666i | ||||
\(746\) | 1.78556e32 | 0.164164 | ||||||||
\(747\) | 2.83815e31i | 0.0256950i | ||||||||
\(748\) | 7.51067e31i | 0.0669592i | ||||||||
\(749\) | 1.94445e33 | 1.70709 | ||||||||
\(750\) | −1.27988e32 | + | 1.21430e32i | −0.110653 | + | 0.104984i | ||||
\(751\) | −4.69843e31 | −0.0400030 | −0.0200015 | − | 0.999800i | \(-0.506367\pi\) | ||||
−0.0200015 | + | 0.999800i | \(0.506367\pi\) | |||||||
\(752\) | − | 5.12794e32i | − | 0.429970i | ||||||
\(753\) | 1.74400e33i | 1.44014i | ||||||||
\(754\) | −4.76227e32 | −0.387296 | ||||||||
\(755\) | 9.82856e30 | − | 2.54147e30i | 0.00787227 | − | 0.00203561i | ||||
\(756\) | 1.98694e33 | 1.56742 | ||||||||
\(757\) | − | 1.32997e33i | − | 1.03333i | −0.856187 | − | 0.516666i | \(-0.827173\pi\) | ||
0.856187 | − | 0.516666i | \(-0.172827\pi\) | |||||||
\(758\) | 1.55882e32i | 0.119289i | ||||||||
\(759\) | −2.08641e32 | −0.157261 | ||||||||
\(760\) | 7.18840e31 | + | 2.77995e32i | 0.0533674 | + | 0.206386i | ||||
\(761\) | −1.37543e33 | −1.00581 | −0.502903 | − | 0.864343i | \(-0.667735\pi\) | ||||
−0.502903 | + | 0.864343i | \(0.667735\pi\) | |||||||
\(762\) | 4.79935e31i | 0.0345701i | ||||||||
\(763\) | − | 2.16996e33i | − | 1.53964i | ||||||
\(764\) | 1.32209e33 | 0.924033 | ||||||||
\(765\) | 5.39471e30 | + | 2.08628e31i | 0.00371417 | + | 0.0143637i | ||||
\(766\) | 3.14868e32 | 0.213549 | ||||||||
\(767\) | − | 2.71693e33i | − | 1.81523i | ||||||
\(768\) | 1.15018e33i | 0.757025i | ||||||||
\(769\) | 1.99445e33 | 1.29321 | 0.646606 | − | 0.762824i | \(-0.276188\pi\) | ||||
0.646606 | + | 0.762824i | \(0.276188\pi\) | |||||||
\(770\) | 5.16540e31 | − | 1.33567e31i | 0.0329959 | − | 0.00853210i | ||||
\(771\) | −1.36696e33 | −0.860263 | ||||||||
\(772\) | 5.20474e32i | 0.322701i | ||||||||
\(773\) | 2.90186e33i | 1.77261i | 0.463103 | + | 0.886305i | \(0.346736\pi\) | ||||
−0.463103 | + | 0.886305i | \(0.653264\pi\) | |||||||
\(774\) | 4.59179e30 | 0.00276351 | ||||||||
\(775\) | −1.06873e33 | + | 5.92309e32i | −0.633722 | + | 0.351220i | ||||
\(776\) | −1.29780e32 | −0.0758223 | ||||||||
\(777\) | 3.11667e33i | 1.79411i | ||||||||
\(778\) | 2.74487e32i | 0.155689i | ||||||||
\(779\) | 5.34685e32 | 0.298825 | ||||||||
\(780\) | 2.75079e33 | − | 7.11300e32i | 1.51485 | − | 0.391710i | ||||
\(781\) | −3.79000e32 | −0.205661 | ||||||||
\(782\) | − | 1.64208e32i | − | 0.0878045i | ||||||
\(783\) | − | 2.95772e33i | − | 1.55847i | ||||||
\(784\) | −2.69343e33 | −1.39853 | ||||||||
\(785\) | −1.45820e32 | − | 5.63925e32i | −0.0746132 | − | 0.288549i | ||||
\(786\) | −4.35270e32 | −0.219482 | ||||||||
\(787\) | 2.39501e33i | 1.19014i | 0.803674 | + | 0.595070i | \(0.202876\pi\) | ||||
−0.803674 | + | 0.595070i | \(0.797124\pi\) | |||||||
\(788\) | − | 3.82958e33i | − | 1.87543i | ||||||
\(789\) | −1.48256e33 | −0.715526 | ||||||||
\(790\) | 1.62891e31 | + | 6.29943e31i | 0.00774792 | + | 0.0299633i | ||||
\(791\) | −4.57421e33 | −2.14430 | ||||||||
\(792\) | 2.76791e30i | 0.00127883i | ||||||||
\(793\) | 7.78422e32i | 0.354465i | ||||||||
\(794\) | 4.96616e32 | 0.222887 | ||||||||
\(795\) | −9.01703e32 | + | 2.33163e32i | −0.398879 | + | 0.103142i | ||||
\(796\) | −4.79750e32 | −0.209177 | ||||||||
\(797\) | − | 2.15419e33i | − | 0.925793i | −0.886412 | − | 0.462896i | \(-0.846810\pi\) | ||
0.886412 | − | 0.462896i | \(-0.153190\pi\) | |||||||
\(798\) | 3.97049e32i | 0.168194i | ||||||||
\(799\) | 5.47279e32 | 0.228518 | ||||||||
\(800\) | 5.29819e32 | + | 9.55976e32i | 0.218068 | + | 0.393470i | ||||
\(801\) | −3.05928e30 | −0.00124121 | ||||||||
\(802\) | − | 6.75131e32i | − | 0.270012i | ||||||
\(803\) | − | 4.63656e32i | − | 0.182796i | ||||||
\(804\) | −2.24257e33 | −0.871569 | ||||||||
\(805\) | 4.59519e33 | − | 1.18823e33i | 1.76056 | − | 0.455247i | ||||
\(806\) | −4.83612e32 | −0.182660 | ||||||||
\(807\) | − | 1.33757e33i | − | 0.498046i | ||||||
\(808\) | − | 9.09840e32i | − | 0.333991i | ||||||
\(809\) | 3.40486e33 | 1.23223 | 0.616114 | − | 0.787657i | \(-0.288706\pi\) | ||||
0.616114 | + | 0.787657i | \(0.288706\pi\) | |||||||
\(810\) | −1.05304e32 | − | 4.07238e32i | −0.0375722 | − | 0.145302i | ||||
\(811\) | 1.95755e33 | 0.688608 | 0.344304 | − | 0.938858i | \(-0.388115\pi\) | ||||
0.344304 | + | 0.938858i | \(0.388115\pi\) | |||||||
\(812\) | 6.84394e33i | 2.37362i | ||||||||
\(813\) | 2.75011e33i | 0.940393i | ||||||||
\(814\) | −7.34826e31 | −0.0247744 | ||||||||
\(815\) | −4.33610e32 | − | 1.67688e33i | −0.144141 | − | 0.557431i | ||||
\(816\) | −1.37709e33 | −0.451364 | ||||||||
\(817\) | − | 1.27934e33i | − | 0.413460i | ||||||
\(818\) | 1.79207e32i | 0.0571074i | ||||||||
\(819\) | −2.46522e32 | −0.0774623 | ||||||||
\(820\) | 1.30833e33 | − | 3.38309e32i | 0.405377 | − | 0.104823i | ||||
\(821\) | −2.75076e33 | −0.840438 | −0.420219 | − | 0.907423i | \(-0.638047\pi\) | ||||
−0.420219 | + | 0.907423i | \(0.638047\pi\) | |||||||
\(822\) | − | 9.00626e32i | − | 0.271343i | ||||||
\(823\) | 4.11882e33i | 1.22370i | 0.790974 | + | 0.611849i | \(0.209574\pi\) | ||||
−0.790974 | + | 0.611849i | \(0.790426\pi\) | |||||||
\(824\) | −4.73057e32 | −0.138596 | ||||||||
\(825\) | 2.29691e32 | + | 4.14443e32i | 0.0663628 | + | 0.119741i | ||||
\(826\) | 9.59588e32 | 0.273410 | ||||||||
\(827\) | 1.35807e33i | 0.381600i | 0.981629 | + | 0.190800i | \(0.0611082\pi\) | ||||
−0.981629 | + | 0.190800i | \(0.938892\pi\) | |||||||
\(828\) | 1.21624e32i | 0.0337030i | ||||||||
\(829\) | 6.52663e33 | 1.78366 | 0.891830 | − | 0.452371i | \(-0.149422\pi\) | ||||
0.891830 | + | 0.452371i | \(0.149422\pi\) | |||||||
\(830\) | −4.75529e32 | + | 1.22962e32i | −0.128168 | + | 0.0331417i | ||||
\(831\) | −9.70750e32 | −0.258045 | ||||||||
\(832\) | − | 5.33308e33i | − | 1.39817i | ||||||
\(833\) | − | 2.87456e33i | − | 0.743283i | ||||||
\(834\) | 3.86961e32 | 0.0986864 | ||||||||
\(835\) | 7.98719e32 | + | 3.08886e33i | 0.200909 | + | 0.776970i | ||||
\(836\) | 3.80911e32 | 0.0945042 | ||||||||
\(837\) | − | 3.00359e33i | − | 0.735017i | ||||||
\(838\) | 1.44488e31i | 0.00348758i | ||||||||
\(839\) | 6.44324e33 | 1.53406 | 0.767029 | − | 0.641612i | \(-0.221734\pi\) | ||||
0.767029 | + | 0.641612i | \(0.221734\pi\) | |||||||
\(840\) | 5.08621e32 | + | 1.96697e33i | 0.119449 | + | 0.461941i | ||||
\(841\) | 5.87104e33 | 1.36007 | ||||||||
\(842\) | − | 2.64452e32i | − | 0.0604307i | ||||||
\(843\) | − | 4.92099e33i | − | 1.10927i | ||||||
\(844\) | −7.17394e33 | −1.59522 | ||||||||
\(845\) | −7.28105e33 | + | 1.88274e33i | −1.59714 | + | 0.412988i | ||||
\(846\) | 9.96203e30 | 0.00215570 | ||||||||
\(847\) | 7.27242e33i | 1.55246i | ||||||||
\(848\) | 1.84464e33i | 0.388472i | ||||||||
\(849\) | −4.30905e33 | −0.895248 | ||||||||
\(850\) | −3.26181e32 | + | 1.80775e32i | −0.0668560 | + | 0.0370528i | ||||
\(851\) | −6.53709e33 | −1.32189 | ||||||||
\(852\) | − | 7.12854e33i | − | 1.42215i | ||||||
\(853\) | 8.01201e32i | 0.157699i | 0.996887 | + | 0.0788493i | \(0.0251246\pi\) | ||||
−0.996887 | + | 0.0788493i | \(0.974875\pi\) | |||||||
\(854\) | −2.74930e32 | −0.0533896 | ||||||||
\(855\) | 1.05808e32 | − | 2.73598e31i | 0.0202725 | − | 0.00524206i | ||||
\(856\) | −1.74577e33 | −0.330019 | ||||||||
\(857\) | − | 1.18824e33i | − | 0.221628i | −0.993841 | − | 0.110814i | \(-0.964654\pi\) | ||
0.993841 | − | 0.110814i | \(-0.0353457\pi\) | |||||||
\(858\) | 1.87540e32i | 0.0345135i | ||||||||
\(859\) | −4.00333e33 | −0.726943 | −0.363471 | − | 0.931605i | \(-0.618409\pi\) | ||||
−0.363471 | + | 0.931605i | \(0.618409\pi\) | |||||||
\(860\) | −8.09475e32 | − | 3.13046e33i | −0.145034 | − | 0.560887i | ||||
\(861\) | 3.78321e33 | 0.668842 | ||||||||
\(862\) | 2.55340e32i | 0.0445436i | ||||||||
\(863\) | 8.84592e32i | 0.152272i | 0.997097 | + | 0.0761358i | \(0.0242582\pi\) | ||||
−0.997097 | + | 0.0761358i | \(0.975742\pi\) | |||||||
\(864\) | −2.68670e33 | −0.456364 | ||||||||
\(865\) | −5.37959e32 | − | 2.08043e33i | −0.0901705 | − | 0.348713i | ||||
\(866\) | 3.86188e32 | 0.0638767 | ||||||||
\(867\) | 4.56411e33i | 0.744966i | ||||||||
\(868\) | 6.95006e33i | 1.11947i | ||||||||
\(869\) | 1.74752e32 | 0.0277776 | ||||||||
\(870\) | 1.44623e33 | − | 3.73966e32i | 0.226864 | − | 0.0586626i | ||||
\(871\) | 9.53407e33 | 1.47594 | ||||||||
\(872\) | 1.94824e33i | 0.297647i | ||||||||
\(873\) | 4.93954e31i | 0.00744771i | ||||||||
\(874\) | −8.32796e32 | −0.123925 | ||||||||
\(875\) | −7.41909e33 | − | 7.81973e33i | −1.08958 | − | 1.14842i | ||||
\(876\) | 8.72080e33 | 1.26404 | ||||||||
\(877\) | − | 8.56753e33i | − | 1.22563i | −0.790225 | − | 0.612817i | \(-0.790036\pi\) | ||
0.790225 | − | 0.612817i | \(-0.209964\pi\) | |||||||
\(878\) | 9.54541e32i | 0.134775i | ||||||||
\(879\) | −7.80081e33 | −1.08710 | ||||||||
\(880\) | 9.08589e32 | − | 2.34943e32i | 0.124973 | − | 0.0323156i | ||||
\(881\) | 4.76522e33 | 0.646934 | 0.323467 | − | 0.946239i | \(-0.395152\pi\) | ||||
0.323467 | + | 0.946239i | \(0.395152\pi\) | |||||||
\(882\) | − | 5.23252e31i | − | 0.00701168i | ||||||
\(883\) | − | 5.97151e33i | − | 0.789835i | −0.918717 | − | 0.394917i | \(-0.870773\pi\) | ||
0.918717 | − | 0.394917i | \(-0.129227\pi\) | |||||||
\(884\) | 6.00581e33 | 0.784098 | ||||||||
\(885\) | 2.13352e33 | + | 8.25089e33i | 0.274947 | + | 1.06329i | ||||
\(886\) | −3.76566e32 | −0.0479019 | ||||||||
\(887\) | 7.37111e33i | 0.925574i | 0.886470 | + | 0.462787i | \(0.153150\pi\) | ||||
−0.886470 | + | 0.462787i | \(0.846850\pi\) | |||||||
\(888\) | − | 2.79820e33i | − | 0.346841i | ||||||
\(889\) | −2.93229e33 | −0.358787 | ||||||||
\(890\) | −1.32543e31 | − | 5.12578e31i | −0.00160092 | − | 0.00619120i | ||||
\(891\) | −1.12972e33 | −0.134702 | ||||||||
\(892\) | 7.24644e33i | 0.852960i | ||||||||
\(893\) | − | 2.77558e33i | − | 0.322524i | ||||||
\(894\) | 4.15164e32 | 0.0476253 | ||||||||
\(895\) | 5.16570e33 | − | 1.33575e33i | 0.585011 | − | 0.151272i | ||||
\(896\) | 8.25318e33 | 0.922740 | ||||||||
\(897\) | 1.66837e34i | 1.84154i | ||||||||
\(898\) | 6.49108e32i | 0.0707358i | ||||||||
\(899\) | 1.03457e34 | 1.11308 | ||||||||
\(900\) | 2.41592e32 | − | 1.33894e32i | 0.0256622 | − | 0.0142224i | ||||
\(901\) | −1.96869e33 | −0.206463 | ||||||||
\(902\) | 8.91978e31i | 0.00923590i | ||||||||
\(903\) | − | 9.05210e33i | − | 0.925423i | ||||||
\(904\) | 4.10681e33 | 0.414541 | ||||||||
\(905\) | −1.57385e34 | + | 4.06967e33i | −1.56857 | + | 0.405602i | ||||
\(906\) | −1.26034e31 | −0.00124026 | ||||||||
\(907\) | − | 1.64019e34i | − | 1.59372i | −0.604166 | − | 0.796859i | \(-0.706493\pi\) | ||
0.604166 | − | 0.796859i | \(-0.293507\pi\) | |||||||
\(908\) | 1.02566e33i | 0.0984051i | ||||||||
\(909\) | −3.46294e32 | −0.0328065 | ||||||||
\(910\) | −1.06805e33 | − | 4.13044e33i | −0.0999116 | − | 0.386385i | ||||
\(911\) | 8.41201e33 | 0.777031 | 0.388515 | − | 0.921442i | \(-0.372988\pi\) | ||||
0.388515 | + | 0.921442i | \(0.372988\pi\) | |||||||
\(912\) | 6.98406e33i | 0.637041i | ||||||||
\(913\) | 1.31916e33i | 0.118818i | ||||||||
\(914\) | −1.49028e33 | −0.132552 | ||||||||
\(915\) | −6.11271e32 | − | 2.36395e33i | −0.0536897 | − | 0.207633i | ||||
\(916\) | −6.13848e33 | −0.532430 | ||||||||
\(917\) | − | 2.65940e34i | − | 2.27790i | ||||||
\(918\) | − | 9.16707e32i | − | 0.0775425i | ||||||
\(919\) | −1.29076e34 | −1.07824 | −0.539122 | − | 0.842227i | \(-0.681244\pi\) | ||||
−0.539122 | + | 0.842227i | \(0.681244\pi\) | |||||||
\(920\) | −4.12566e33 | + | 1.06681e33i | −0.340356 | + | 0.0880093i | ||||
\(921\) | −1.88855e34 | −1.53866 | ||||||||
\(922\) | 1.92398e33i | 0.154808i | ||||||||
\(923\) | 3.03063e34i | 2.40831i | ||||||||
\(924\) | 2.69516e33 | 0.211523 | ||||||||
\(925\) | 7.19663e33 | + | 1.29852e34i | 0.557827 | + | 1.00651i | ||||
\(926\) | −1.68186e33 | −0.128755 | ||||||||
\(927\) | 1.80050e32i | 0.0136137i | ||||||||
\(928\) | − | 9.25423e33i | − | 0.691096i | ||||||
\(929\) | 1.74424e33 | 0.128655 | 0.0643274 | − | 0.997929i | \(-0.479510\pi\) | ||||
0.0643274 | + | 0.997929i | \(0.479510\pi\) | |||||||
\(930\) | 1.46865e33 | − | 3.79765e32i | 0.106996 | − | 0.0276670i | ||||
\(931\) | −1.45786e34 | −1.04905 | ||||||||
\(932\) | − | 1.45494e34i | − | 1.03410i | ||||||
\(933\) | − | 1.11435e34i | − | 0.782319i | ||||||
\(934\) | 2.72189e33 | 0.188747 | ||||||||
\(935\) | 2.50743e32 | + | 9.69692e32i | 0.0171750 | + | 0.0664202i | ||||
\(936\) | 2.21332e32 | 0.0149752 | ||||||||
\(937\) | 1.34695e34i | 0.900216i | 0.892974 | + | 0.450108i | \(0.148615\pi\) | ||||
−0.892974 | + | 0.450108i | \(0.851385\pi\) | |||||||
\(938\) | 3.36733e33i | 0.222307i | ||||||||
\(939\) | −1.19218e33 | −0.0777478 | ||||||||
\(940\) | −1.75618e33 | − | 6.79162e33i | −0.113135 | − | 0.437525i | ||||
\(941\) | −6.18067e33 | −0.393328 | −0.196664 | − | 0.980471i | \(-0.563011\pi\) | ||||
−0.196664 | + | 0.980471i | \(0.563011\pi\) | |||||||
\(942\) | 7.23132e32i | 0.0454603i | ||||||||
\(943\) | 7.93514e33i | 0.492799i | ||||||||
\(944\) | 1.68791e34 | 1.03555 | ||||||||
\(945\) | 2.56531e34 | − | 6.63339e33i | 1.55480 | − | 0.402040i | ||||
\(946\) | 2.13424e32 | 0.0127790 | ||||||||
\(947\) | 2.85928e33i | 0.169135i | 0.996418 | + | 0.0845673i | \(0.0269508\pi\) | ||||
−0.996418 | + | 0.0845673i | \(0.973049\pi\) | |||||||
\(948\) | 3.28687e33i | 0.192082i | ||||||||
\(949\) | −3.70756e34 | −2.14056 | ||||||||
\(950\) | 9.16818e32 | + | 1.65426e33i | 0.0522952 | + | 0.0943585i | ||||
\(951\) | 3.08924e34 | 1.74091 | ||||||||
\(952\) | 4.29450e33i | 0.239105i | ||||||||
\(953\) | − | 1.98643e34i | − | 1.09271i | −0.837554 | − | 0.546355i | \(-0.816015\pi\) | ||
0.837554 | − | 0.546355i | \(-0.183985\pi\) | |||||||
\(954\) | −3.58358e31 | −0.00194765 | ||||||||
\(955\) | 1.70693e34 | − | 4.41379e33i | 0.916594 | − | 0.237013i | ||||
\(956\) | −2.91268e34 | −1.54535 | ||||||||
\(957\) | − | 4.01197e33i | − | 0.210315i | ||||||
\(958\) | − | 1.35189e33i | − | 0.0700228i | ||||||
\(959\) | 5.50261e34 | 2.81614 | ||||||||
\(960\) | 4.18790e33 | + | 1.61958e34i | 0.211776 | + | 0.818996i | ||||
\(961\) | −9.50715e33 | −0.475041 | ||||||||
\(962\) | 5.87594e33i | 0.290111i | ||||||||
\(963\) | 6.64457e32i | 0.0324164i | ||||||||
\(964\) | −3.53671e33 | −0.170496 | ||||||||
\(965\) | 1.73760e33 | + | 6.71977e33i | 0.0827724 | + | 0.320103i | ||||
\(966\) | −5.89251e33 | −0.277373 | ||||||||
\(967\) | − | 2.37516e33i | − | 0.110481i | −0.998473 | − | 0.0552407i | \(-0.982407\pi\) | ||
0.998473 | − | 0.0552407i | \(-0.0175926\pi\) | |||||||
\(968\) | − | 6.52932e33i | − | 0.300124i | ||||||
\(969\) | −7.45374e33 | −0.338572 | ||||||||
\(970\) | −8.27613e32 | + | 2.14005e32i | −0.0371495 | + | 0.00960612i | ||||
\(971\) | −5.00274e33 | −0.221915 | −0.110957 | − | 0.993825i | \(-0.535392\pi\) | ||||
−0.110957 | + | 0.993825i | \(0.535392\pi\) | |||||||
\(972\) | 1.33814e33i | 0.0586595i | ||||||||
\(973\) | 2.36424e34i | 1.02422i | ||||||||
\(974\) | 3.76544e33 | 0.161209 | ||||||||
\(975\) | 3.31403e34 | − | 1.83670e34i | 1.40218 | − | 0.777114i | ||||
\(976\) | −4.83600e33 | −0.202215 | ||||||||
\(977\) | 4.46851e34i | 1.84661i | 0.384066 | + | 0.923306i | \(0.374524\pi\) | ||||
−0.384066 | + | 0.923306i | \(0.625476\pi\) | |||||||
\(978\) | 2.15030e33i | 0.0878219i | ||||||||
\(979\) | −1.42194e32 | −0.00573957 | ||||||||
\(980\) | −3.56727e34 | + | 9.22427e33i | −1.42310 | + | 0.367987i | ||||
\(981\) | 7.41517e32 | 0.0292367 | ||||||||
\(982\) | − | 1.18564e33i | − | 0.0462032i | ||||||
\(983\) | − | 5.04005e33i | − | 0.194120i | −0.995279 | − | 0.0970598i | \(-0.969056\pi\) | ||
0.995279 | − | 0.0970598i | \(-0.0309438\pi\) | |||||||
\(984\) | −3.39664e33 | −0.129302 | ||||||||
\(985\) | −1.27850e34 | − | 4.94432e34i | −0.481045 | − | 1.86033i | ||||
\(986\) | 3.15756e33 | 0.117427 | ||||||||
\(987\) | − | 1.96388e34i | − | 0.721885i | ||||||
\(988\) | − | 3.04590e34i | − | 1.10665i | ||||||
\(989\) | 1.89865e34 | 0.681846 | ||||||||
\(990\) | 4.56424e30 | + | 1.76511e31i | 0.000162018 | + | 0.000626568i | ||||
\(991\) | −2.67998e34 | −0.940338 | −0.470169 | − | 0.882576i | \(-0.655807\pi\) | ||||
−0.470169 | + | 0.882576i | \(0.655807\pi\) | |||||||
\(992\) | − | 9.39773e33i | − | 0.325941i | ||||||
\(993\) | 2.73474e34i | 0.937560i | ||||||||
\(994\) | −1.07038e34 | −0.362741 | ||||||||
\(995\) | −6.19398e33 | + | 1.60164e33i | −0.207494 | + | 0.0536538i | ||||
\(996\) | −2.48118e34 | −0.821629 | ||||||||
\(997\) | − | 2.07338e34i | − | 0.678710i | −0.940658 | − | 0.339355i | \(-0.889791\pi\) | ||
0.940658 | − | 0.339355i | \(-0.110209\pi\) | |||||||
\(998\) | − | 1.36703e33i | − | 0.0442362i | ||||||
\(999\) | −3.64940e34 | −1.16739 |
(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 | 5.24.b.a.4.6 | yes | 10 | |
3.2 | odd | 2 | 45.24.b.b.19.5 | 10 | |||
5.2 | odd | 4 | 25.24.a.f.1.5 | 10 | |||
5.3 | odd | 4 | 25.24.a.f.1.6 | 10 | |||
5.4 | even | 2 | inner | 5.24.b.a.4.5 | ✓ | 10 | |
15.14 | odd | 2 | 45.24.b.b.19.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.24.b.a.4.5 | ✓ | 10 | 5.4 | even | 2 | inner | |
5.24.b.a.4.6 | yes | 10 | 1.1 | even | 1 | trivial | |
25.24.a.f.1.5 | 10 | 5.2 | odd | 4 | |||
25.24.a.f.1.6 | 10 | 5.3 | odd | 4 | |||
45.24.b.b.19.5 | 10 | 3.2 | odd | 2 | |||
45.24.b.b.19.6 | 10 | 15.14 | odd | 2 |