Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,34,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, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
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: | \(34.4914144405\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 26286285043 x^{14} + \cdots + 16\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{26}\cdot 5^{53}\cdot 7^{4}\cdot 11^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.12 | ||
Root | \(51228.2i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.34.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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 102456.i | 1.10546i | 0.833360 | + | 0.552731i | \(0.186414\pi\) | ||||
−0.833360 | + | 0.552731i | \(0.813586\pi\) | |||||||
\(3\) | 8.77372e7i | 1.17675i | 0.808589 | + | 0.588374i | \(0.200232\pi\) | ||||
−0.808589 | + | 0.588374i | \(0.799768\pi\) | |||||||
\(4\) | −1.90737e9 | −0.222047 | ||||||||
\(5\) | −2.51871e11 | − | 2.30165e11i | −0.738200 | − | 0.674582i | ||||
\(6\) | −8.98924e12 | −1.30085 | ||||||||
\(7\) | 1.11815e14i | 1.27170i | 0.771815 | + | 0.635848i | \(0.219349\pi\) | ||||
−0.771815 | + | 0.635848i | \(0.780651\pi\) | |||||||
\(8\) | 6.84671e14i | 0.859997i | ||||||||
\(9\) | −2.13876e15 | −0.384734 | ||||||||
\(10\) | 2.35819e16 | − | 2.58058e16i | 0.745725 | − | 0.816052i | ||||
\(11\) | −2.24867e17 | −1.47553 | −0.737763 | − | 0.675060i | \(-0.764118\pi\) | ||||
−0.737763 | + | 0.675060i | \(0.764118\pi\) | |||||||
\(12\) | − | 1.67348e17i | − | 0.261294i | ||||||
\(13\) | − | 2.46334e18i | − | 1.02674i | −0.858169 | − | 0.513368i | \(-0.828398\pi\) | ||
0.858169 | − | 0.513368i | \(-0.171602\pi\) | |||||||
\(14\) | −1.14562e19 | −1.40581 | ||||||||
\(15\) | 2.01941e19 | − | 2.20985e19i | 0.793813 | − | 0.868675i | ||||
\(16\) | −8.65331e19 | −1.17274 | ||||||||
\(17\) | − | 3.31898e19i | − | 0.165424i | −0.996574 | − | 0.0827118i | \(-0.973642\pi\) | ||
0.996574 | − | 0.0827118i | \(-0.0263581\pi\) | |||||||
\(18\) | − | 2.19130e20i | − | 0.425309i | ||||||
\(19\) | 7.93484e19 | 0.0631108 | 0.0315554 | − | 0.999502i | \(-0.489954\pi\) | ||||
0.0315554 | + | 0.999502i | \(0.489954\pi\) | |||||||
\(20\) | 4.80413e20 | + | 4.39011e20i | 0.163915 | + | 0.149789i | ||||
\(21\) | −9.81036e21 | −1.49646 | ||||||||
\(22\) | − | 2.30391e22i | − | 1.63114i | ||||||
\(23\) | − | 2.88111e22i | − | 0.979602i | −0.871834 | − | 0.489801i | \(-0.837069\pi\) | ||
0.871834 | − | 0.489801i | \(-0.162931\pi\) | |||||||
\(24\) | −6.00711e22 | −1.01200 | ||||||||
\(25\) | 1.04632e22 | + | 1.15944e23i | 0.0898778 | + | 0.995953i | ||||
\(26\) | 2.52385e23 | 1.13502 | ||||||||
\(27\) | 3.00088e23i | 0.724012i | ||||||||
\(28\) | − | 2.13273e23i | − | 0.282377i | ||||||
\(29\) | 2.32679e24 | 1.72659 | 0.863297 | − | 0.504695i | \(-0.168395\pi\) | ||||
0.863297 | + | 0.504695i | \(0.168395\pi\) | |||||||
\(30\) | 2.26413e24 | + | 2.06901e24i | 0.960287 | + | 0.877530i | ||||
\(31\) | −7.38565e24 | −1.82356 | −0.911781 | − | 0.410676i | \(-0.865293\pi\) | ||||
−0.911781 | + | 0.410676i | \(0.865293\pi\) | |||||||
\(32\) | − | 2.98459e24i | − | 0.436425i | ||||||
\(33\) | − | 1.97292e25i | − | 1.73632i | ||||||
\(34\) | 3.40050e24 | 0.182869 | ||||||||
\(35\) | 2.57360e25 | − | 2.81631e25i | 0.857863 | − | 0.938765i | ||||
\(36\) | 4.07941e24 | 0.0854292 | ||||||||
\(37\) | − | 1.63972e25i | − | 0.218495i | −0.994015 | − | 0.109247i | \(-0.965156\pi\) | ||
0.994015 | − | 0.109247i | \(-0.0348441\pi\) | |||||||
\(38\) | 8.12975e24i | 0.0697666i | ||||||||
\(39\) | 2.16126e26 | 1.20821 | ||||||||
\(40\) | 1.57588e26 | − | 1.72449e26i | 0.580139 | − | 0.634850i | ||||
\(41\) | 4.37241e26 | 1.07100 | 0.535498 | − | 0.844537i | \(-0.320124\pi\) | ||||
0.535498 | + | 0.844537i | \(0.320124\pi\) | |||||||
\(42\) | − | 1.00513e27i | − | 1.65429i | ||||||
\(43\) | 2.93769e26i | 0.327927i | 0.986466 | + | 0.163963i | \(0.0524279\pi\) | ||||
−0.986466 | + | 0.163963i | \(0.947572\pi\) | |||||||
\(44\) | 4.28906e26 | 0.327637 | ||||||||
\(45\) | 5.38693e26 | + | 4.92269e26i | 0.284011 | + | 0.259535i | ||||
\(46\) | 2.95188e27 | 1.08291 | ||||||||
\(47\) | − | 6.15905e26i | − | 0.158452i | −0.996857 | − | 0.0792262i | \(-0.974755\pi\) | ||
0.996857 | − | 0.0792262i | \(-0.0252449\pi\) | |||||||
\(48\) | − | 7.59218e27i | − | 1.38002i | ||||||
\(49\) | −4.77164e27 | −0.617209 | ||||||||
\(50\) | −1.18792e28 | + | 1.07202e27i | −1.10099 | + | 0.0993565i | ||||
\(51\) | 2.91198e27 | 0.194662 | ||||||||
\(52\) | 4.69850e27i | 0.227984i | ||||||||
\(53\) | 1.66687e28i | 0.590678i | 0.955393 | + | 0.295339i | \(0.0954326\pi\) | ||||
−0.955393 | + | 0.295339i | \(0.904567\pi\) | |||||||
\(54\) | −3.07459e28 | −0.800368 | ||||||||
\(55\) | 5.66377e28 | + | 5.17567e28i | 1.08923 | + | 0.995364i | ||||
\(56\) | −7.65566e28 | −1.09365 | ||||||||
\(57\) | 6.96181e27i | 0.0742655i | ||||||||
\(58\) | 2.38395e29i | 1.90869i | ||||||||
\(59\) | 6.84322e28 | 0.413240 | 0.206620 | − | 0.978421i | \(-0.433754\pi\) | ||||
0.206620 | + | 0.978421i | \(0.433754\pi\) | |||||||
\(60\) | −3.85176e28 | + | 4.21501e28i | −0.176264 | + | 0.192887i | ||||
\(61\) | −3.85377e29 | −1.34259 | −0.671295 | − | 0.741191i | \(-0.734261\pi\) | ||||
−0.671295 | + | 0.741191i | \(0.734261\pi\) | |||||||
\(62\) | − | 7.56707e29i | − | 2.01588i | ||||||
\(63\) | − | 2.39146e29i | − | 0.489265i | ||||||
\(64\) | −4.37524e29 | −0.690291 | ||||||||
\(65\) | −5.66975e29 | + | 6.20444e29i | −0.692617 | + | 0.757936i | ||||
\(66\) | 2.02139e30 | 1.91944 | ||||||||
\(67\) | − | 1.10044e30i | − | 0.815327i | −0.913132 | − | 0.407664i | \(-0.866344\pi\) | ||
0.913132 | − | 0.407664i | \(-0.133656\pi\) | |||||||
\(68\) | 6.33053e28i | 0.0367318i | ||||||||
\(69\) | 2.52780e30 | 1.15274 | ||||||||
\(70\) | 2.88548e30 | + | 2.63682e30i | 1.03777 | + | 0.948336i | ||||
\(71\) | 7.46328e29 | 0.212406 | 0.106203 | − | 0.994344i | \(-0.466131\pi\) | ||||
0.106203 | + | 0.994344i | \(0.466131\pi\) | |||||||
\(72\) | − | 1.46435e30i | − | 0.330871i | ||||||
\(73\) | − | 6.29592e30i | − | 1.13301i | −0.824060 | − | 0.566503i | \(-0.808296\pi\) | ||
0.824060 | − | 0.566503i | \(-0.191704\pi\) | |||||||
\(74\) | 1.68000e30 | 0.241538 | ||||||||
\(75\) | −1.01726e31 | + | 9.18008e29i | −1.17198 | + | 0.105763i | ||||
\(76\) | −1.51347e29 | −0.0140136 | ||||||||
\(77\) | − | 2.51436e31i | − | 1.87642i | ||||||
\(78\) | 2.21435e31i | 1.33563i | ||||||||
\(79\) | −1.61054e31 | −0.787273 | −0.393636 | − | 0.919266i | \(-0.628783\pi\) | ||||
−0.393636 | + | 0.919266i | \(0.628783\pi\) | |||||||
\(80\) | 2.17952e31 | + | 1.99169e31i | 0.865718 | + | 0.791111i | ||||
\(81\) | −3.82184e31 | −1.23671 | ||||||||
\(82\) | 4.47982e31i | 1.18394i | ||||||||
\(83\) | − | 2.30501e31i | − | 0.498753i | −0.968407 | − | 0.249376i | \(-0.919774\pi\) | ||
0.968407 | − | 0.249376i | \(-0.0802256\pi\) | |||||||
\(84\) | 1.87120e31 | 0.332286 | ||||||||
\(85\) | −7.63914e30 | + | 8.35956e30i | −0.111592 | + | 0.122116i | ||||
\(86\) | −3.00985e31 | −0.362510 | ||||||||
\(87\) | 2.04146e32i | 2.03177i | ||||||||
\(88\) | − | 1.53960e32i | − | 1.26895i | ||||||
\(89\) | −1.08152e32 | −0.739773 | −0.369886 | − | 0.929077i | \(-0.620603\pi\) | ||||
−0.369886 | + | 0.929077i | \(0.620603\pi\) | |||||||
\(90\) | −5.04361e31 | + | 5.51925e31i | −0.286906 | + | 0.313963i | ||||
\(91\) | 2.75439e32 | 1.30569 | ||||||||
\(92\) | 5.49534e31i | 0.217518i | ||||||||
\(93\) | − | 6.47996e32i | − | 2.14587i | ||||||
\(94\) | 6.31033e31 | 0.175163 | ||||||||
\(95\) | −1.99856e31 | − | 1.82633e31i | −0.0465884 | − | 0.0425734i | ||||
\(96\) | 2.61860e32 | 0.513562 | ||||||||
\(97\) | 2.96871e32i | 0.490721i | 0.969432 | + | 0.245361i | \(0.0789064\pi\) | ||||
−0.969432 | + | 0.245361i | \(0.921094\pi\) | |||||||
\(98\) | − | 4.88885e32i | − | 0.682302i | ||||||
\(99\) | 4.80938e32 | 0.567686 | ||||||||
\(100\) | −1.99571e31 | − | 2.21149e32i | −0.0199571 | − | 0.221149i | ||||
\(101\) | −7.27121e32 | −0.617027 | −0.308513 | − | 0.951220i | \(-0.599831\pi\) | ||||
−0.308513 | + | 0.951220i | \(0.599831\pi\) | |||||||
\(102\) | 2.98351e32i | 0.215191i | ||||||||
\(103\) | − | 1.81397e33i | − | 1.11382i | −0.830572 | − | 0.556912i | \(-0.811986\pi\) | ||
0.830572 | − | 0.556912i | \(-0.188014\pi\) | |||||||
\(104\) | 1.68658e33 | 0.882990 | ||||||||
\(105\) | 2.47095e33 | + | 2.25800e33i | 1.10469 | + | 1.00949i | ||||
\(106\) | −1.70782e33 | −0.652972 | ||||||||
\(107\) | 5.42390e33i | 1.77615i | 0.459701 | + | 0.888074i | \(0.347957\pi\) | ||||
−0.459701 | + | 0.888074i | \(0.652043\pi\) | |||||||
\(108\) | − | 5.72379e32i | − | 0.160765i | ||||||
\(109\) | −6.01657e33 | −1.45148 | −0.725741 | − | 0.687968i | \(-0.758503\pi\) | ||||
−0.725741 | + | 0.687968i | \(0.758503\pi\) | |||||||
\(110\) | −5.30280e33 | + | 5.80289e33i | −1.10034 | + | 1.20411i | ||||
\(111\) | 1.43864e33 | 0.257113 | ||||||||
\(112\) | − | 9.67572e33i | − | 1.49137i | ||||||
\(113\) | − | 1.07074e34i | − | 1.42524i | −0.701550 | − | 0.712620i | \(-0.747508\pi\) | ||
0.701550 | − | 0.712620i | \(-0.252492\pi\) | |||||||
\(114\) | −7.13282e32 | −0.0820977 | ||||||||
\(115\) | −6.63131e33 | + | 7.25668e33i | −0.660822 | + | 0.723142i | ||||
\(116\) | −4.43806e33 | −0.383386 | ||||||||
\(117\) | 5.26849e33i | 0.395020i | ||||||||
\(118\) | 7.01131e33i | 0.456821i | ||||||||
\(119\) | 3.71112e33 | 0.210368 | ||||||||
\(120\) | 1.51302e34 | + | 1.38263e34i | 0.747058 | + | 0.682677i | ||||
\(121\) | 2.73402e34 | 1.17718 | ||||||||
\(122\) | − | 3.94843e34i | − | 1.48418i | ||||||
\(123\) | 3.83623e34i | 1.26029i | ||||||||
\(124\) | 1.40872e34 | 0.404917 | ||||||||
\(125\) | 2.40510e34 | − | 3.16113e34i | 0.605504 | − | 0.795842i | ||||
\(126\) | 2.45020e34 | 0.540864 | ||||||||
\(127\) | − | 2.11841e33i | − | 0.0410440i | −0.999789 | − | 0.0205220i | \(-0.993467\pi\) | ||
0.999789 | − | 0.0205220i | \(-0.00653281\pi\) | |||||||
\(128\) | − | 7.04645e34i | − | 1.19952i | ||||||
\(129\) | −2.57745e34 | −0.385887 | ||||||||
\(130\) | −6.35685e34 | − | 5.80902e34i | −0.837870 | − | 0.765663i | ||||
\(131\) | −1.12103e35 | −1.30209 | −0.651044 | − | 0.759040i | \(-0.725669\pi\) | ||||
−0.651044 | + | 0.759040i | \(0.725669\pi\) | |||||||
\(132\) | 3.76310e34i | 0.385546i | ||||||||
\(133\) | 8.87236e33i | 0.0802577i | ||||||||
\(134\) | 1.12747e35 | 0.901314 | ||||||||
\(135\) | 6.90698e34 | − | 7.55835e34i | 0.488406 | − | 0.534466i | ||||
\(136\) | 2.27241e34 | 0.142264 | ||||||||
\(137\) | 1.87942e35i | 1.04264i | 0.853361 | + | 0.521320i | \(0.174560\pi\) | ||||
−0.853361 | + | 0.521320i | \(0.825440\pi\) | |||||||
\(138\) | 2.58989e35i | 1.27432i | ||||||||
\(139\) | −2.77030e35 | −1.20999 | −0.604997 | − | 0.796228i | \(-0.706826\pi\) | ||||
−0.604997 | + | 0.796228i | \(0.706826\pi\) | |||||||
\(140\) | −4.90881e34 | + | 5.37174e34i | −0.190486 | + | 0.208450i | ||||
\(141\) | 5.40378e34 | 0.186458 | ||||||||
\(142\) | 7.64661e34i | 0.234807i | ||||||||
\(143\) | 5.53924e35i | 1.51498i | ||||||||
\(144\) | 1.85074e35 | 0.451194 | ||||||||
\(145\) | −5.86052e35 | − | 5.35547e35i | −1.27457 | − | 1.16473i | ||||
\(146\) | 6.45057e35 | 1.25250 | ||||||||
\(147\) | − | 4.18651e35i | − | 0.726300i | ||||||
\(148\) | 3.12755e34i | 0.0485162i | ||||||||
\(149\) | −1.17332e36 | −1.62871 | −0.814354 | − | 0.580369i | \(-0.802908\pi\) | ||||
−0.814354 | + | 0.580369i | \(0.802908\pi\) | |||||||
\(150\) | −9.40558e34 | − | 1.04225e36i | −0.116918 | − | 1.29559i | ||||
\(151\) | −2.03363e35 | −0.226544 | −0.113272 | − | 0.993564i | \(-0.536133\pi\) | ||||
−0.113272 | + | 0.993564i | \(0.536133\pi\) | |||||||
\(152\) | 5.43276e34i | 0.0542751i | ||||||||
\(153\) | 7.09850e34i | 0.0636441i | ||||||||
\(154\) | 2.57612e36 | 2.07431 | ||||||||
\(155\) | 1.86023e36 | + | 1.69992e36i | 1.34615 | + | 1.23014i | ||||
\(156\) | −4.12233e35 | −0.268279 | ||||||||
\(157\) | − | 1.48553e36i | − | 0.870036i | −0.900422 | − | 0.435018i | \(-0.856742\pi\) | ||
0.900422 | − | 0.435018i | \(-0.143258\pi\) | |||||||
\(158\) | − | 1.65010e36i | − | 0.870300i | ||||||
\(159\) | −1.46247e36 | −0.695079 | ||||||||
\(160\) | −6.86949e35 | + | 7.51733e35i | −0.294405 | + | 0.322169i | ||||
\(161\) | 3.22151e36 | 1.24576 | ||||||||
\(162\) | − | 3.91571e36i | − | 1.36714i | ||||||
\(163\) | 2.41405e36i | 0.761466i | 0.924685 | + | 0.380733i | \(0.124328\pi\) | ||||
−0.924685 | + | 0.380733i | \(0.875672\pi\) | |||||||
\(164\) | −8.33982e35 | −0.237812 | ||||||||
\(165\) | −4.54099e36 | + | 4.96923e36i | −1.17129 | + | 1.28175i | ||||
\(166\) | 2.36163e36 | 0.551352 | ||||||||
\(167\) | 6.50430e36i | 1.37524i | 0.726071 | + | 0.687620i | \(0.241345\pi\) | ||||
−0.726071 | + | 0.687620i | \(0.758655\pi\) | |||||||
\(168\) | − | 6.71687e36i | − | 1.28696i | ||||||
\(169\) | −3.11899e35 | −0.0541856 | ||||||||
\(170\) | −8.56490e35 | − | 7.82678e35i | −0.134994 | − | 0.123360i | ||||
\(171\) | −1.69707e35 | −0.0242809 | ||||||||
\(172\) | − | 5.60327e35i | − | 0.0728152i | ||||||
\(173\) | 5.44353e36i | 0.642865i | 0.946933 | + | 0.321432i | \(0.104164\pi\) | ||||
−0.946933 | + | 0.321432i | \(0.895836\pi\) | |||||||
\(174\) | −2.09161e37 | −2.24604 | ||||||||
\(175\) | −1.29643e37 | + | 1.16994e36i | −1.26655 | + | 0.114297i | ||||
\(176\) | 1.94585e37 | 1.73041 | ||||||||
\(177\) | 6.00405e36i | 0.486279i | ||||||||
\(178\) | − | 1.10808e37i | − | 0.817791i | ||||||
\(179\) | 1.55767e37 | 1.04809 | 0.524047 | − | 0.851690i | \(-0.324422\pi\) | ||||
0.524047 | + | 0.851690i | \(0.324422\pi\) | |||||||
\(180\) | −1.02749e36 | − | 9.38940e35i | −0.0630639 | − | 0.0576290i | ||||
\(181\) | −2.16095e37 | −1.21045 | −0.605227 | − | 0.796053i | \(-0.706917\pi\) | ||||
−0.605227 | + | 0.796053i | \(0.706917\pi\) | |||||||
\(182\) | 2.82204e37i | 1.44340i | ||||||||
\(183\) | − | 3.38119e37i | − | 1.57989i | ||||||
\(184\) | 1.97261e37 | 0.842456 | ||||||||
\(185\) | −3.77407e36 | + | 4.12998e36i | −0.147393 | + | 0.161293i | ||||
\(186\) | 6.63914e37 | 2.37218 | ||||||||
\(187\) | 7.46330e36i | 0.244087i | ||||||||
\(188\) | 1.17476e36i | 0.0351839i | ||||||||
\(189\) | −3.35543e37 | −0.920723 | ||||||||
\(190\) | 1.87119e36 | − | 2.04765e36i | 0.0470633 | − | 0.0515017i | ||||
\(191\) | 5.39109e37 | 1.24344 | 0.621722 | − | 0.783238i | \(-0.286433\pi\) | ||||
0.621722 | + | 0.783238i | \(0.286433\pi\) | |||||||
\(192\) | − | 3.83871e37i | − | 0.812298i | ||||||
\(193\) | − | 2.82434e37i | − | 0.548557i | −0.961650 | − | 0.274278i | \(-0.911561\pi\) | ||
0.961650 | − | 0.274278i | \(-0.0884390\pi\) | |||||||
\(194\) | −3.04164e37 | −0.542474 | ||||||||
\(195\) | −5.44361e37 | − | 4.97448e37i | −0.891899 | − | 0.815036i | ||||
\(196\) | 9.10130e36 | 0.137050 | ||||||||
\(197\) | − | 1.24116e37i | − | 0.171844i | −0.996302 | − | 0.0859220i | \(-0.972616\pi\) | ||
0.996302 | − | 0.0859220i | \(-0.0273836\pi\) | |||||||
\(198\) | 4.92751e37i | 0.627555i | ||||||||
\(199\) | −7.16373e37 | −0.839582 | −0.419791 | − | 0.907621i | \(-0.637897\pi\) | ||||
−0.419791 | + | 0.907621i | \(0.637897\pi\) | |||||||
\(200\) | −7.93836e37 | + | 7.16382e36i | −0.856517 | + | 0.0772947i | ||||
\(201\) | 9.65495e37 | 0.959434 | ||||||||
\(202\) | − | 7.44982e37i | − | 0.682100i | ||||||
\(203\) | 2.60171e38i | 2.19570i | ||||||||
\(204\) | −5.55423e36 | −0.0432241 | ||||||||
\(205\) | −1.10129e38 | − | 1.00638e38i | −0.790608 | − | 0.722474i | ||||
\(206\) | 1.85853e38 | 1.23129 | ||||||||
\(207\) | 6.16200e37i | 0.376887i | ||||||||
\(208\) | 2.13160e38i | 1.20410i | ||||||||
\(209\) | −1.78429e37 | −0.0931217 | ||||||||
\(210\) | −2.31347e38 | + | 2.53164e38i | −1.11595 | + | 1.22119i | ||||
\(211\) | 3.78989e38 | 1.69031 | 0.845154 | − | 0.534523i | \(-0.179509\pi\) | ||||
0.845154 | + | 0.534523i | \(0.179509\pi\) | |||||||
\(212\) | − | 3.17935e37i | − | 0.131158i | ||||||
\(213\) | 6.54808e37i | 0.249948i | ||||||||
\(214\) | −5.55713e38 | −1.96346 | ||||||||
\(215\) | 6.76155e37 | − | 7.39921e37i | 0.221213 | − | 0.242075i | ||||
\(216\) | −2.05461e38 | −0.622649 | ||||||||
\(217\) | − | 8.25828e38i | − | 2.31902i | ||||||
\(218\) | − | 6.16436e38i | − | 1.60456i | ||||||
\(219\) | 5.52387e38 | 1.33326 | ||||||||
\(220\) | −1.08029e38 | − | 9.87192e37i | −0.241861 | − | 0.221018i | ||||
\(221\) | −8.17576e37 | −0.169846 | ||||||||
\(222\) | 1.47398e38i | 0.284229i | ||||||||
\(223\) | 4.51907e38i | 0.809131i | 0.914509 | + | 0.404565i | \(0.132577\pi\) | ||||
−0.914509 | + | 0.404565i | \(0.867423\pi\) | |||||||
\(224\) | 3.33722e38 | 0.555000 | ||||||||
\(225\) | −2.23782e37 | − | 2.47977e38i | −0.0345791 | − | 0.383177i | ||||
\(226\) | 1.09704e39 | 1.57555 | ||||||||
\(227\) | 9.98415e38i | 1.33317i | 0.745431 | + | 0.666583i | \(0.232244\pi\) | ||||
−0.745431 | + | 0.666583i | \(0.767756\pi\) | |||||||
\(228\) | − | 1.32788e37i | − | 0.0164905i | ||||||
\(229\) | −5.32577e38 | −0.615314 | −0.307657 | − | 0.951497i | \(-0.599545\pi\) | ||||
−0.307657 | + | 0.951497i | \(0.599545\pi\) | |||||||
\(230\) | −7.43493e38 | − | 6.79419e38i | −0.799407 | − | 0.730514i | ||||
\(231\) | 2.20603e39 | 2.20807 | ||||||||
\(232\) | 1.59309e39i | 1.48487i | ||||||||
\(233\) | − | 1.58065e39i | − | 1.37234i | −0.727440 | − | 0.686171i | \(-0.759290\pi\) | ||
0.727440 | − | 0.686171i | \(-0.240710\pi\) | |||||||
\(234\) | −5.39790e38 | −0.436680 | ||||||||
\(235\) | −1.41760e38 | + | 1.55129e38i | −0.106889 | + | 0.116970i | ||||
\(236\) | −1.30526e38 | −0.0917588 | ||||||||
\(237\) | − | 1.41305e39i | − | 0.926421i | ||||||
\(238\) | 3.80228e38i | 0.232554i | ||||||||
\(239\) | −2.18770e39 | −1.24860 | −0.624300 | − | 0.781185i | \(-0.714616\pi\) | ||||
−0.624300 | + | 0.781185i | \(0.714616\pi\) | |||||||
\(240\) | −1.74746e39 | + | 1.91225e39i | −0.930938 | + | 1.01873i | ||||
\(241\) | −1.34545e39 | −0.669248 | −0.334624 | − | 0.942352i | \(-0.608609\pi\) | ||||
−0.334624 | + | 0.942352i | \(0.608609\pi\) | |||||||
\(242\) | 2.80117e39i | 1.30133i | ||||||||
\(243\) | − | 1.68497e39i | − | 0.731288i | ||||||
\(244\) | 7.35057e38 | 0.298118 | ||||||||
\(245\) | 1.20184e39 | + | 1.09827e39i | 0.455624 | + | 0.416359i | ||||
\(246\) | −3.93047e39 | −1.39320 | ||||||||
\(247\) | − | 1.95462e38i | − | 0.0647981i | ||||||
\(248\) | − | 5.05674e39i | − | 1.56826i | ||||||
\(249\) | 2.02236e39 | 0.586906 | ||||||||
\(250\) | 3.23878e39 | + | 2.46417e39i | 0.879774 | + | 0.669362i | ||||
\(251\) | 1.33521e38 | 0.0339574 | 0.0169787 | − | 0.999856i | \(-0.494595\pi\) | ||||
0.0169787 | + | 0.999856i | \(0.494595\pi\) | |||||||
\(252\) | 4.56141e38i | 0.108640i | ||||||||
\(253\) | 6.47866e39i | 1.44543i | ||||||||
\(254\) | 2.17045e38 | 0.0453726 | ||||||||
\(255\) | −7.33445e38 | − | 6.70237e38i | −0.143699 | − | 0.131315i | ||||
\(256\) | 3.46124e39 | 0.635729 | ||||||||
\(257\) | − | 3.02015e39i | − | 0.520154i | −0.965588 | − | 0.260077i | \(-0.916252\pi\) | ||
0.965588 | − | 0.260077i | \(-0.0837480\pi\) | |||||||
\(258\) | − | 2.64076e39i | − | 0.426583i | ||||||
\(259\) | 1.83346e39 | 0.277859 | ||||||||
\(260\) | 1.08143e39 | − | 1.18342e39i | 0.153794 | − | 0.168298i | ||||
\(261\) | −4.97645e39 | −0.664280 | ||||||||
\(262\) | − | 1.14857e40i | − | 1.43941i | ||||||
\(263\) | 5.25973e39i | 0.619004i | 0.950899 | + | 0.309502i | \(0.100162\pi\) | ||||
−0.950899 | + | 0.309502i | \(0.899838\pi\) | |||||||
\(264\) | 1.35080e40 | 1.49323 | ||||||||
\(265\) | 3.83656e39 | − | 4.19838e39i | 0.398461 | − | 0.436038i | ||||
\(266\) | −9.09029e38 | −0.0887219 | ||||||||
\(267\) | − | 9.48893e39i | − | 0.870526i | ||||||
\(268\) | 2.09895e39i | 0.181041i | ||||||||
\(269\) | −4.00271e39 | −0.324670 | −0.162335 | − | 0.986736i | \(-0.551902\pi\) | ||||
−0.162335 | + | 0.986736i | \(0.551902\pi\) | |||||||
\(270\) | 7.74401e39 | + | 7.07664e39i | 0.590832 | + | 0.539914i | ||||
\(271\) | −1.43945e40 | −1.03325 | −0.516624 | − | 0.856212i | \(-0.672812\pi\) | ||||
−0.516624 | + | 0.856212i | \(0.672812\pi\) | |||||||
\(272\) | 2.87202e39i | 0.193999i | ||||||||
\(273\) | 2.41662e40i | 1.53647i | ||||||||
\(274\) | −1.92559e40 | −1.15260 | ||||||||
\(275\) | −2.35282e39 | − | 2.60721e40i | −0.132617 | − | 1.46955i | ||||
\(276\) | −4.82146e39 | −0.255964 | ||||||||
\(277\) | 1.51033e40i | 0.755364i | 0.925935 | + | 0.377682i | \(0.123279\pi\) | ||||
−0.925935 | + | 0.377682i | \(0.876721\pi\) | |||||||
\(278\) | − | 2.83835e40i | − | 1.33760i | ||||||
\(279\) | 1.57961e40 | 0.701587 | ||||||||
\(280\) | 1.92824e40 | + | 1.76207e40i | 0.807336 | + | 0.737760i | ||||
\(281\) | −2.79172e40 | −1.10209 | −0.551045 | − | 0.834476i | \(-0.685771\pi\) | ||||
−0.551045 | + | 0.834476i | \(0.685771\pi\) | |||||||
\(282\) | 5.53651e39i | 0.206123i | ||||||||
\(283\) | 3.85510e40i | 1.35381i | 0.736069 | + | 0.676907i | \(0.236680\pi\) | ||||
−0.736069 | + | 0.676907i | \(0.763320\pi\) | |||||||
\(284\) | −1.42353e39 | −0.0471642 | ||||||||
\(285\) | 1.60237e39 | − | 1.75348e39i | 0.0500982 | − | 0.0548228i | ||||
\(286\) | −5.67530e40 | −1.67475 | ||||||||
\(287\) | 4.88902e40i | 1.36198i | ||||||||
\(288\) | 6.38332e39i | 0.167908i | ||||||||
\(289\) | 3.91529e40 | 0.972635 | ||||||||
\(290\) | 5.48702e40 | − | 6.00448e40i | 1.28757 | − | 1.40899i | ||||
\(291\) | −2.60467e40 | −0.577455 | ||||||||
\(292\) | 1.20087e40i | 0.251581i | ||||||||
\(293\) | 3.74622e40i | 0.741784i | 0.928676 | + | 0.370892i | \(0.120948\pi\) | ||||
−0.928676 | + | 0.370892i | \(0.879052\pi\) | |||||||
\(294\) | 4.28934e40 | 0.802897 | ||||||||
\(295\) | −1.72361e40 | − | 1.57507e40i | −0.305054 | − | 0.278764i | ||||
\(296\) | 1.12267e40 | 0.187905 | ||||||||
\(297\) | − | 6.74799e40i | − | 1.06830i | ||||||
\(298\) | − | 1.20214e41i | − | 1.80048i | ||||||
\(299\) | −7.09713e40 | −1.00579 | ||||||||
\(300\) | 1.94030e40 | − | 1.75098e39i | 0.260236 | − | 0.0234845i | ||||
\(301\) | −3.28478e40 | −0.417023 | ||||||||
\(302\) | − | 2.08358e40i | − | 0.250436i | ||||||
\(303\) | − | 6.37956e40i | − | 0.726085i | ||||||
\(304\) | −6.86626e39 | −0.0740127 | ||||||||
\(305\) | 9.70654e40 | + | 8.87003e40i | 0.991099 | + | 0.905687i | ||||
\(306\) | −7.27287e39 | −0.0703562 | ||||||||
\(307\) | − | 1.07461e41i | − | 0.985068i | −0.870293 | − | 0.492534i | \(-0.836071\pi\) | ||
0.870293 | − | 0.492534i | \(-0.163929\pi\) | |||||||
\(308\) | 4.79582e40i | 0.416654i | ||||||||
\(309\) | 1.59153e41 | 1.31069 | ||||||||
\(310\) | −1.74168e41 | + | 1.90593e41i | −1.35988 | + | 1.48812i | ||||
\(311\) | 2.27431e41 | 1.68385 | 0.841924 | − | 0.539597i | \(-0.181423\pi\) | ||||
0.841924 | + | 0.539597i | \(0.181423\pi\) | |||||||
\(312\) | 1.47975e41i | 1.03906i | ||||||||
\(313\) | − | 6.49777e40i | − | 0.432796i | −0.976305 | − | 0.216398i | \(-0.930569\pi\) | ||
0.976305 | − | 0.216398i | \(-0.0694308\pi\) | |||||||
\(314\) | 1.52202e41 | 0.961792 | ||||||||
\(315\) | −5.50431e40 | + | 6.02341e40i | −0.330049 | + | 0.361175i | ||||
\(316\) | 3.07190e40 | 0.174812 | ||||||||
\(317\) | − | 5.13146e40i | − | 0.277181i | −0.990350 | − | 0.138590i | \(-0.955743\pi\) | ||
0.990350 | − | 0.138590i | \(-0.0442571\pi\) | |||||||
\(318\) | − | 1.49839e41i | − | 0.768383i | ||||||
\(319\) | −5.23219e41 | −2.54764 | ||||||||
\(320\) | 1.10200e41 | + | 1.00703e41i | 0.509572 | + | 0.465658i | ||||
\(321\) | −4.75878e41 | −2.09008 | ||||||||
\(322\) | 3.30065e41i | 1.37714i | ||||||||
\(323\) | − | 2.63356e39i | − | 0.0104400i | ||||||
\(324\) | 7.28966e40 | 0.274609 | ||||||||
\(325\) | 2.85610e41 | − | 2.57743e40i | 1.02258 | − | 0.0922807i | ||||
\(326\) | −2.47335e41 | −0.841772 | ||||||||
\(327\) | − | 5.27877e41i | − | 1.70803i | ||||||
\(328\) | 2.99366e41i | 0.921053i | ||||||||
\(329\) | 6.88675e40 | 0.201503 | ||||||||
\(330\) | −5.09129e41 | − | 4.65253e41i | −1.41693 | − | 1.29482i | ||||
\(331\) | 3.99589e41 | 1.05792 | 0.528958 | − | 0.848648i | \(-0.322583\pi\) | ||||
0.528958 | + | 0.848648i | \(0.322583\pi\) | |||||||
\(332\) | 4.39652e40i | 0.110747i | ||||||||
\(333\) | 3.50697e40i | 0.0840624i | ||||||||
\(334\) | −6.66407e41 | −1.52028 | ||||||||
\(335\) | −2.53283e41 | + | 2.77169e41i | −0.550005 | + | 0.601874i | ||||
\(336\) | 8.48921e41 | 1.75497 | ||||||||
\(337\) | 5.12879e41i | 1.00954i | 0.863255 | + | 0.504768i | \(0.168422\pi\) | ||||
−0.863255 | + | 0.504768i | \(0.831578\pi\) | |||||||
\(338\) | − | 3.19560e40i | − | 0.0599001i | ||||||
\(339\) | 9.39434e41 | 1.67715 | ||||||||
\(340\) | 1.45707e40 | − | 1.59448e40i | 0.0247786 | − | 0.0271154i | ||||
\(341\) | 1.66079e42 | 2.69072 | ||||||||
\(342\) | − | 1.73876e40i | − | 0.0268416i | ||||||
\(343\) | 3.30900e41i | 0.486793i | ||||||||
\(344\) | −2.01135e41 | −0.282016 | ||||||||
\(345\) | −6.36681e41 | − | 5.81812e41i | −0.850956 | − | 0.777621i | ||||
\(346\) | −5.57724e41 | −0.710663 | ||||||||
\(347\) | − | 4.02876e41i | − | 0.489480i | −0.969589 | − | 0.244740i | \(-0.921297\pi\) | ||
0.969589 | − | 0.244740i | \(-0.0787027\pi\) | |||||||
\(348\) | − | 3.89383e41i | − | 0.451148i | ||||||
\(349\) | −4.84486e41 | −0.535380 | −0.267690 | − | 0.963505i | \(-0.586260\pi\) | ||||
−0.267690 | + | 0.963505i | \(0.586260\pi\) | |||||||
\(350\) | −1.19868e41 | − | 1.32828e42i | −0.126351 | − | 1.40012i | ||||
\(351\) | 7.39217e41 | 0.743369 | ||||||||
\(352\) | 6.71136e41i | 0.643957i | ||||||||
\(353\) | − | 1.01645e42i | − | 0.930687i | −0.885130 | − | 0.465344i | \(-0.845931\pi\) | ||
0.885130 | − | 0.465344i | \(-0.154069\pi\) | |||||||
\(354\) | −6.15153e41 | −0.537563 | ||||||||
\(355\) | −1.87979e41 | − | 1.71779e41i | −0.156798 | − | 0.143285i | ||||
\(356\) | 2.06286e41 | 0.164265 | ||||||||
\(357\) | 3.25604e41i | 0.247550i | ||||||||
\(358\) | 1.59593e42i | 1.15863i | ||||||||
\(359\) | 3.81937e41 | 0.264809 | 0.132405 | − | 0.991196i | \(-0.457730\pi\) | ||||
0.132405 | + | 0.991196i | \(0.457730\pi\) | |||||||
\(360\) | −3.37042e41 | + | 3.68828e41i | −0.223199 | + | 0.244249i | ||||
\(361\) | −1.57447e42 | −0.996017 | ||||||||
\(362\) | − | 2.21403e42i | − | 1.33811i | ||||||
\(363\) | 2.39875e42i | 1.38524i | ||||||||
\(364\) | −5.25364e41 | −0.289926 | ||||||||
\(365\) | −1.44910e42 | + | 1.58576e42i | −0.764306 | + | 0.836385i | ||||
\(366\) | 3.46424e42 | 1.74651 | ||||||||
\(367\) | 1.28100e41i | 0.0617391i | 0.999523 | + | 0.0308695i | \(0.00982764\pi\) | ||||
−0.999523 | + | 0.0308695i | \(0.990172\pi\) | |||||||
\(368\) | 2.49311e42i | 1.14882i | ||||||||
\(369\) | −9.35155e41 | −0.412049 | ||||||||
\(370\) | −4.23143e41 | − | 3.86677e41i | −0.178303 | − | 0.162937i | ||||
\(371\) | −1.86382e42 | −0.751162 | ||||||||
\(372\) | 1.23597e42i | 0.476485i | ||||||||
\(373\) | − | 4.95556e41i | − | 0.182767i | −0.995816 | − | 0.0913834i | \(-0.970871\pi\) | ||
0.995816 | − | 0.0913834i | \(-0.0291289\pi\) | |||||||
\(374\) | −7.64662e41 | −0.269829 | ||||||||
\(375\) | 2.77349e42 | + | 2.11016e42i | 0.936505 | + | 0.712526i | ||||
\(376\) | 4.21692e41 | 0.136269 | ||||||||
\(377\) | − | 5.73167e42i | − | 1.77276i | ||||||
\(378\) | − | 3.43786e42i | − | 1.01782i | ||||||
\(379\) | −2.01391e42 | −0.570813 | −0.285406 | − | 0.958407i | \(-0.592129\pi\) | ||||
−0.285406 | + | 0.958407i | \(0.592129\pi\) | |||||||
\(380\) | 3.81200e40 | + | 3.48348e40i | 0.0103448 | + | 0.00945332i | ||||
\(381\) | 1.85864e41 | 0.0482984 | ||||||||
\(382\) | 5.52352e42i | 1.37458i | ||||||||
\(383\) | − | 6.11625e42i | − | 1.45782i | −0.684607 | − | 0.728912i | \(-0.740026\pi\) | ||
0.684607 | − | 0.728912i | \(-0.259974\pi\) | |||||||
\(384\) | 6.18236e42 | 1.41153 | ||||||||
\(385\) | −5.78718e42 | + | 6.33295e42i | −1.26580 | + | 1.38517i | ||||
\(386\) | 2.89372e42 | 0.606409 | ||||||||
\(387\) | − | 6.28302e41i | − | 0.126165i | ||||||
\(388\) | − | 5.66244e41i | − | 0.108963i | ||||||
\(389\) | −8.01591e41 | −0.147837 | −0.0739187 | − | 0.997264i | \(-0.523551\pi\) | ||||
−0.0739187 | + | 0.997264i | \(0.523551\pi\) | |||||||
\(390\) | 5.09667e42 | − | 5.57732e42i | 0.900991 | − | 0.985961i | ||||
\(391\) | −9.56233e41 | −0.162049 | ||||||||
\(392\) | − | 3.26701e42i | − | 0.530799i | ||||||
\(393\) | − | 9.83560e42i | − | 1.53223i | ||||||
\(394\) | 1.27165e42 | 0.189967 | ||||||||
\(395\) | 4.05650e42 | + | 3.70691e42i | 0.581164 | + | 0.531080i | ||||
\(396\) | −9.17327e41 | −0.126053 | ||||||||
\(397\) | 6.77326e42i | 0.892800i | 0.894834 | + | 0.446400i | \(0.147294\pi\) | ||||
−0.894834 | + | 0.446400i | \(0.852706\pi\) | |||||||
\(398\) | − | 7.33969e42i | − | 0.928127i | ||||||
\(399\) | −7.78436e41 | −0.0944431 | ||||||||
\(400\) | −9.05409e41 | − | 1.00330e43i | −0.105403 | − | 1.16800i | ||||
\(401\) | −1.14344e42 | −0.127741 | −0.0638707 | − | 0.997958i | \(-0.520345\pi\) | ||||
−0.0638707 | + | 0.997958i | \(0.520345\pi\) | |||||||
\(402\) | 9.89212e42i | 1.06062i | ||||||||
\(403\) | 1.81933e43i | 1.87232i | ||||||||
\(404\) | 1.38689e42 | 0.137009 | ||||||||
\(405\) | 9.62611e42 | + | 8.79654e42i | 0.912942 | + | 0.834265i | ||||
\(406\) | −2.66561e43 | −2.42727 | ||||||||
\(407\) | 3.68719e42i | 0.322395i | ||||||||
\(408\) | 1.99375e42i | 0.167409i | ||||||||
\(409\) | 1.58336e43 | 1.27687 | 0.638434 | − | 0.769677i | \(-0.279583\pi\) | ||||
0.638434 | + | 0.769677i | \(0.279583\pi\) | |||||||
\(410\) | 1.03110e43 | − | 1.12834e43i | 0.798668 | − | 0.873988i | ||||
\(411\) | −1.64895e43 | −1.22692 | ||||||||
\(412\) | 3.45992e42i | 0.247321i | ||||||||
\(413\) | 7.65176e42i | 0.525515i | ||||||||
\(414\) | −6.31336e42 | −0.416634 | ||||||||
\(415\) | −5.30535e42 | + | 5.80568e42i | −0.336450 | + | 0.368179i | ||||
\(416\) | −7.35205e42 | −0.448093 | ||||||||
\(417\) | − | 2.43059e43i | − | 1.42386i | ||||||
\(418\) | − | 1.82811e42i | − | 0.102943i | ||||||
\(419\) | 5.87784e42 | 0.318190 | 0.159095 | − | 0.987263i | \(-0.449142\pi\) | ||||
0.159095 | + | 0.987263i | \(0.449142\pi\) | |||||||
\(420\) | −4.71302e42 | − | 4.30685e42i | −0.245293 | − | 0.224154i | ||||
\(421\) | −7.76874e41 | −0.0388773 | −0.0194386 | − | 0.999811i | \(-0.506188\pi\) | ||||
−0.0194386 | + | 0.999811i | \(0.506188\pi\) | |||||||
\(422\) | 3.88298e43i | 1.86857i | ||||||||
\(423\) | 1.31727e42i | 0.0609621i | ||||||||
\(424\) | −1.14126e43 | −0.507982 | ||||||||
\(425\) | 3.84816e42 | − | 3.47270e41i | 0.164754 | − | 0.0148679i | ||||
\(426\) | −6.70892e42 | −0.276309 | ||||||||
\(427\) | − | 4.30910e43i | − | 1.70736i | ||||||
\(428\) | − | 1.03454e43i | − | 0.394389i | ||||||
\(429\) | −4.85998e43 | −1.78274 | ||||||||
\(430\) | 7.58096e42 | + | 6.92763e42i | 0.267605 | + | 0.244543i | ||||
\(431\) | 2.29433e43 | 0.779438 | 0.389719 | − | 0.920934i | \(-0.372572\pi\) | ||||
0.389719 | + | 0.920934i | \(0.372572\pi\) | |||||||
\(432\) | − | 2.59675e43i | − | 0.849080i | ||||||
\(433\) | 1.80460e43i | 0.567977i | 0.958828 | + | 0.283988i | \(0.0916577\pi\) | ||||
−0.958828 | + | 0.283988i | \(0.908342\pi\) | |||||||
\(434\) | 8.46113e43 | 2.56359 | ||||||||
\(435\) | 4.69874e43 | − | 5.14186e43i | 1.37059 | − | 1.49985i | ||||
\(436\) | 1.14758e43 | 0.322298 | ||||||||
\(437\) | − | 2.28611e42i | − | 0.0618235i | ||||||
\(438\) | 5.65956e43i | 1.47387i | ||||||||
\(439\) | 1.60697e43 | 0.403035 | 0.201517 | − | 0.979485i | \(-0.435413\pi\) | ||||
0.201517 | + | 0.979485i | \(0.435413\pi\) | |||||||
\(440\) | −3.54363e43 | + | 3.87782e43i | −0.856010 | + | 0.936738i | ||||
\(441\) | 1.02054e43 | 0.237462 | ||||||||
\(442\) | − | 8.37659e42i | − | 0.187759i | ||||||
\(443\) | 4.88560e43i | 1.05501i | 0.849552 | + | 0.527504i | \(0.176872\pi\) | ||||
−0.849552 | + | 0.527504i | \(0.823128\pi\) | |||||||
\(444\) | −2.74403e42 | −0.0570913 | ||||||||
\(445\) | 2.72403e43 | + | 2.48928e43i | 0.546100 | + | 0.499038i | ||||
\(446\) | −4.63007e43 | −0.894464 | ||||||||
\(447\) | − | 1.02944e44i | − | 1.91658i | ||||||
\(448\) | − | 4.89218e43i | − | 0.877840i | ||||||
\(449\) | 4.45262e43 | 0.770106 | 0.385053 | − | 0.922894i | \(-0.374183\pi\) | ||||
0.385053 | + | 0.922894i | \(0.374183\pi\) | |||||||
\(450\) | 2.54068e43 | − | 2.29279e42i | 0.423588 | − | 0.0382259i | ||||
\(451\) | −9.83213e43 | −1.58028 | ||||||||
\(452\) | 2.04229e43i | 0.316471i | ||||||||
\(453\) | − | 1.78425e43i | − | 0.266585i | ||||||
\(454\) | −1.02294e44 | −1.47377 | ||||||||
\(455\) | −6.93751e43 | − | 6.33964e43i | −0.963864 | − | 0.880798i | ||||
\(456\) | −4.76655e42 | −0.0638681 | ||||||||
\(457\) | 5.52879e43i | 0.714517i | 0.934006 | + | 0.357259i | \(0.116289\pi\) | ||||
−0.934006 | + | 0.357259i | \(0.883711\pi\) | |||||||
\(458\) | − | 5.45659e43i | − | 0.680207i | ||||||
\(459\) | 9.95984e42 | 0.119769 | ||||||||
\(460\) | 1.26484e43 | − | 1.38412e43i | 0.146734 | − | 0.160572i | ||||
\(461\) | 1.08910e44 | 1.21900 | 0.609501 | − | 0.792785i | \(-0.291370\pi\) | ||||
0.609501 | + | 0.792785i | \(0.291370\pi\) | |||||||
\(462\) | 2.26022e44i | 2.44094i | ||||||||
\(463\) | − | 7.34911e43i | − | 0.765858i | −0.923778 | − | 0.382929i | \(-0.874915\pi\) | ||
0.923778 | − | 0.382929i | \(-0.125085\pi\) | |||||||
\(464\) | −2.01344e44 | −2.02485 | ||||||||
\(465\) | −1.49146e44 | + | 1.63212e44i | −1.44757 | + | 1.58408i | ||||
\(466\) | 1.61947e44 | 1.51707 | ||||||||
\(467\) | 1.16367e44i | 1.05220i | 0.850421 | + | 0.526102i | \(0.176347\pi\) | ||||
−0.850421 | + | 0.526102i | \(0.823653\pi\) | |||||||
\(468\) | − | 1.00490e43i | − | 0.0877132i | ||||||
\(469\) | 1.23046e44 | 1.03685 | ||||||||
\(470\) | −1.58939e43 | − | 1.45242e43i | −0.129305 | − | 0.118162i | ||||
\(471\) | 1.30336e44 | 1.02381 | ||||||||
\(472\) | 4.68535e43i | 0.355385i | ||||||||
\(473\) | − | 6.60591e43i | − | 0.483864i | ||||||
\(474\) | 1.44775e44 | 1.02412 | ||||||||
\(475\) | 8.30234e41 | + | 9.19998e42i | 0.00567226 | + | 0.0628554i | ||||
\(476\) | −7.07849e42 | −0.0467117 | ||||||||
\(477\) | − | 3.56504e43i | − | 0.227254i | ||||||
\(478\) | − | 2.24144e44i | − | 1.38028i | ||||||
\(479\) | −1.45527e44 | −0.865783 | −0.432891 | − | 0.901446i | \(-0.642507\pi\) | ||||
−0.432891 | + | 0.901446i | \(0.642507\pi\) | |||||||
\(480\) | −6.59549e43 | − | 6.02710e43i | −0.379111 | − | 0.346440i | ||||
\(481\) | −4.03918e43 | −0.224336 | ||||||||
\(482\) | − | 1.37850e44i | − | 0.739828i | ||||||
\(483\) | 2.82647e44i | 1.46594i | ||||||||
\(484\) | −5.21479e43 | −0.261389 | ||||||||
\(485\) | 6.83295e43 | − | 7.47734e43i | 0.331032 | − | 0.362250i | ||||
\(486\) | 1.72636e44 | 0.808411 | ||||||||
\(487\) | − | 2.82151e44i | − | 1.27718i | −0.769546 | − | 0.638591i | \(-0.779517\pi\) | ||
0.769546 | − | 0.638591i | \(-0.220483\pi\) | |||||||
\(488\) | − | 2.63856e44i | − | 1.15462i | ||||||
\(489\) | −2.11802e44 | −0.896053 | ||||||||
\(490\) | −1.12524e44 | + | 1.23136e44i | −0.460269 | + | 0.503675i | ||||
\(491\) | 2.10330e44 | 0.831874 | 0.415937 | − | 0.909393i | \(-0.363454\pi\) | ||||
0.415937 | + | 0.909393i | \(0.363454\pi\) | |||||||
\(492\) | − | 7.31713e43i | − | 0.279844i | ||||||
\(493\) | − | 7.72257e43i | − | 0.285619i | ||||||
\(494\) | 2.00263e43 | 0.0716319 | ||||||||
\(495\) | −1.21134e44 | − | 1.10695e44i | −0.419066 | − | 0.382951i | ||||
\(496\) | 6.39103e44 | 2.13857 | ||||||||
\(497\) | 8.34508e43i | 0.270116i | ||||||||
\(498\) | 2.07203e44i | 0.648802i | ||||||||
\(499\) | 3.94604e44 | 1.19537 | 0.597686 | − | 0.801730i | \(-0.296087\pi\) | ||||
0.597686 | + | 0.801730i | \(0.296087\pi\) | |||||||
\(500\) | −4.58741e43 | + | 6.02945e43i | −0.134451 | + | 0.176715i | ||||
\(501\) | −5.70669e44 | −1.61831 | ||||||||
\(502\) | 1.36801e43i | 0.0375386i | ||||||||
\(503\) | 7.12742e44i | 1.89261i | 0.323279 | + | 0.946304i | \(0.395215\pi\) | ||||
−0.323279 | + | 0.946304i | \(0.604785\pi\) | |||||||
\(504\) | 1.63736e44 | 0.420767 | ||||||||
\(505\) | 1.83141e44 | + | 1.67358e44i | 0.455489 | + | 0.416235i | ||||
\(506\) | −6.63780e44 | −1.59787 | ||||||||
\(507\) | − | 2.73652e43i | − | 0.0637627i | ||||||
\(508\) | 4.04060e42i | 0.00911370i | ||||||||
\(509\) | −9.04650e44 | −1.97532 | −0.987659 | − | 0.156618i | \(-0.949941\pi\) | ||||
−0.987659 | + | 0.156618i | \(0.949941\pi\) | |||||||
\(510\) | 6.86700e43 | − | 7.51461e43i | 0.145164 | − | 0.158854i | ||||
\(511\) | 7.03980e44 | 1.44084 | ||||||||
\(512\) | − | 2.50660e44i | − | 0.496741i | ||||||
\(513\) | 2.38115e43i | 0.0456930i | ||||||||
\(514\) | 3.09434e44 | 0.575011 | ||||||||
\(515\) | −4.17513e44 | + | 4.56888e44i | −0.751365 | + | 0.822224i | ||||
\(516\) | 4.91615e43 | 0.0856851 | ||||||||
\(517\) | 1.38497e44i | 0.233801i | ||||||||
\(518\) | 1.87849e44i | 0.307162i | ||||||||
\(519\) | −4.77600e44 | −0.756490 | ||||||||
\(520\) | −4.24800e44 | − | 3.88191e44i | −0.651823 | − | 0.595649i | ||||
\(521\) | 5.72183e43 | 0.0850575 | 0.0425288 | − | 0.999095i | \(-0.486459\pi\) | ||||
0.0425288 | + | 0.999095i | \(0.486459\pi\) | |||||||
\(522\) | − | 5.09869e44i | − | 0.734337i | ||||||
\(523\) | − | 6.60401e43i | − | 0.0921573i | −0.998938 | − | 0.0460787i | \(-0.985328\pi\) | ||
0.998938 | − | 0.0460787i | \(-0.0146725\pi\) | |||||||
\(524\) | 2.13822e44 | 0.289125 | ||||||||
\(525\) | −1.02647e44 | − | 1.13745e45i | −0.134499 | − | 1.49041i | ||||
\(526\) | −5.38893e44 | −0.684286 | ||||||||
\(527\) | 2.45128e44i | 0.301660i | ||||||||
\(528\) | 1.70723e45i | 2.03626i | ||||||||
\(529\) | 3.49283e43 | 0.0403793 | ||||||||
\(530\) | 4.30151e44 | + | 3.93080e44i | 0.482024 | + | 0.440483i | ||||
\(531\) | −1.46360e44 | −0.158988 | ||||||||
\(532\) | − | 1.69229e43i | − | 0.0178210i | ||||||
\(533\) | − | 1.07707e45i | − | 1.09963i | ||||||
\(534\) | 9.72202e44 | 0.962334 | ||||||||
\(535\) | 1.24839e45 | − | 1.36612e45i | 1.19816 | − | 1.31115i | ||||
\(536\) | 7.53439e44 | 0.701180 | ||||||||
\(537\) | 1.36665e45i | 1.23334i | ||||||||
\(538\) | − | 4.10103e44i | − | 0.358910i | ||||||
\(539\) | 1.07299e45 | 0.910709 | ||||||||
\(540\) | −1.31742e44 | + | 1.44166e44i | −0.108449 | + | 0.118677i | ||||
\(541\) | −1.77379e45 | −1.41628 | −0.708138 | − | 0.706074i | \(-0.750464\pi\) | ||||
−0.708138 | + | 0.706074i | \(0.750464\pi\) | |||||||
\(542\) | − | 1.47481e45i | − | 1.14222i | ||||||
\(543\) | − | 1.89596e45i | − | 1.42440i | ||||||
\(544\) | −9.90578e43 | −0.0721950 | ||||||||
\(545\) | 1.51540e45 | + | 1.38481e45i | 1.07148 | + | 0.979144i | ||||
\(546\) | −2.47598e45 | −1.69851 | ||||||||
\(547\) | 1.16728e45i | 0.776937i | 0.921462 | + | 0.388468i | \(0.126996\pi\) | ||||
−0.921462 | + | 0.388468i | \(0.873004\pi\) | |||||||
\(548\) | − | 3.58475e44i | − | 0.231515i | ||||||
\(549\) | 8.24229e44 | 0.516540 | ||||||||
\(550\) | 2.67125e45 | − | 2.41061e44i | 1.62454 | − | 0.146603i | ||||
\(551\) | 1.84627e44 | 0.108967 | ||||||||
\(552\) | 1.73071e45i | 0.991357i | ||||||||
\(553\) | − | 1.80083e45i | − | 1.00117i | ||||||
\(554\) | −1.54743e45 | −0.835027 | ||||||||
\(555\) | −3.62353e44 | − | 3.31126e44i | −0.189801 | − | 0.173444i | ||||
\(556\) | 5.28400e44 | 0.268676 | ||||||||
\(557\) | 3.04688e45i | 1.50399i | 0.659170 | + | 0.751994i | \(0.270908\pi\) | ||||
−0.659170 | + | 0.751994i | \(0.729092\pi\) | |||||||
\(558\) | 1.61842e45i | 0.775579i | ||||||||
\(559\) | 7.23652e44 | 0.336694 | ||||||||
\(560\) | −2.22701e45 | + | 2.43704e45i | −1.00605 | + | 1.10093i | ||||
\(561\) | −6.54809e44 | −0.287228 | ||||||||
\(562\) | − | 2.86029e45i | − | 1.21832i | ||||||
\(563\) | − | 3.49063e45i | − | 1.44383i | −0.691982 | − | 0.721914i | \(-0.743262\pi\) | ||
0.691982 | − | 0.721914i | \(-0.256738\pi\) | |||||||
\(564\) | −1.03070e44 | −0.0414026 | ||||||||
\(565\) | −2.46446e45 | + | 2.69688e45i | −0.961442 | + | 1.05211i | ||||
\(566\) | −3.94979e45 | −1.49659 | ||||||||
\(567\) | − | 4.27339e45i | − | 1.57272i | ||||||
\(568\) | 5.10989e44i | 0.182669i | ||||||||
\(569\) | 1.15922e45 | 0.402543 | 0.201272 | − | 0.979535i | \(-0.435493\pi\) | ||||
0.201272 | + | 0.979535i | \(0.435493\pi\) | |||||||
\(570\) | 1.79655e44 | + | 1.64173e44i | 0.0606045 | + | 0.0553816i | ||||
\(571\) | −3.31452e44 | −0.108624 | −0.0543119 | − | 0.998524i | \(-0.517297\pi\) | ||||
−0.0543119 | + | 0.998524i | \(0.517297\pi\) | |||||||
\(572\) | − | 1.05654e45i | − | 0.336396i | ||||||
\(573\) | 4.72999e45i | 1.46322i | ||||||||
\(574\) | −5.00911e45 | −1.50562 | ||||||||
\(575\) | 3.34047e45 | − | 3.01454e44i | 0.975638 | − | 0.0880445i | ||||
\(576\) | 9.35759e44 | 0.265579 | ||||||||
\(577\) | 1.81007e45i | 0.499224i | 0.968346 | + | 0.249612i | \(0.0803031\pi\) | ||||
−0.968346 | + | 0.249612i | \(0.919697\pi\) | |||||||
\(578\) | 4.01147e45i | 1.07521i | ||||||||
\(579\) | 2.47800e45 | 0.645513 | ||||||||
\(580\) | 1.11782e45 | + | 1.02149e45i | 0.283015 | + | 0.258625i | ||||
\(581\) | 2.57736e45 | 0.634262 | ||||||||
\(582\) | − | 2.66865e45i | − | 0.638355i | ||||||
\(583\) | − | 3.74825e45i | − | 0.871561i | ||||||
\(584\) | 4.31064e45 | 0.974382 | ||||||||
\(585\) | 1.21262e45 | − | 1.32698e45i | 0.266474 | − | 0.291604i | ||||
\(586\) | −3.83824e45 | −0.820014 | ||||||||
\(587\) | 4.38043e45i | 0.909887i | 0.890520 | + | 0.454944i | \(0.150341\pi\) | ||||
−0.890520 | + | 0.454944i | \(0.849659\pi\) | |||||||
\(588\) | 7.98523e44i | 0.161273i | ||||||||
\(589\) | −5.86039e44 | −0.115087 | ||||||||
\(590\) | 1.61376e45 | − | 1.76595e45i | 0.308164 | − | 0.337225i | ||||
\(591\) | 1.08896e45 | 0.202217 | ||||||||
\(592\) | 1.41890e45i | 0.256238i | ||||||||
\(593\) | − | 4.28135e44i | − | 0.0751932i | −0.999293 | − | 0.0375966i | \(-0.988030\pi\) | ||
0.999293 | − | 0.0375966i | \(-0.0119702\pi\) | |||||||
\(594\) | 6.91374e45 | 1.18096 | ||||||||
\(595\) | −9.34726e44 | − | 8.54172e44i | −0.155294 | − | 0.141911i | ||||
\(596\) | 2.23796e45 | 0.361650 | ||||||||
\(597\) | − | 6.28526e45i | − | 0.987976i | ||||||
\(598\) | − | 7.27146e45i | − | 1.11187i | ||||||
\(599\) | −3.79121e45 | −0.563944 | −0.281972 | − | 0.959423i | \(-0.590988\pi\) | ||||
−0.281972 | + | 0.959423i | \(0.590988\pi\) | |||||||
\(600\) | −6.28533e44 | − | 6.96490e45i | −0.0909563 | − | 1.00790i | ||||
\(601\) | 9.56105e44 | 0.134610 | 0.0673049 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673049 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(602\) | − | 3.36547e45i | − | 0.461003i | ||||||
\(603\) | 2.35358e45i | 0.313685i | ||||||||
\(604\) | 3.87889e44 | 0.0503035 | ||||||||
\(605\) | −6.88621e45 | − | 6.29276e45i | −0.868993 | − | 0.794104i | ||||
\(606\) | 6.53626e45 | 0.802659 | ||||||||
\(607\) | 3.04630e45i | 0.364049i | 0.983294 | + | 0.182025i | \(0.0582650\pi\) | ||||
−0.983294 | + | 0.182025i | \(0.941735\pi\) | |||||||
\(608\) | − | 2.36822e44i | − | 0.0275431i | ||||||
\(609\) | −2.28266e46 | −2.58379 | ||||||||
\(610\) | −9.08792e45 | + | 9.94497e45i | −1.00120 | + | 1.09562i | ||||
\(611\) | −1.51718e45 | −0.162689 | ||||||||
\(612\) | − | 1.35395e44i | − | 0.0141320i | ||||||
\(613\) | 1.50267e46i | 1.52674i | 0.645959 | + | 0.763372i | \(0.276458\pi\) | ||||
−0.645959 | + | 0.763372i | \(0.723542\pi\) | |||||||
\(614\) | 1.10100e46 | 1.08896 | ||||||||
\(615\) | 8.82968e45 | − | 9.66238e45i | 0.850170 | − | 0.930346i | ||||
\(616\) | 1.72151e46 | 1.61372 | ||||||||
\(617\) | 3.76624e45i | 0.343718i | 0.985122 | + | 0.171859i | \(0.0549774\pi\) | ||||
−0.985122 | + | 0.171859i | \(0.945023\pi\) | |||||||
\(618\) | 1.63062e46i | 1.44892i | ||||||||
\(619\) | 3.61256e45 | 0.312549 | 0.156275 | − | 0.987714i | \(-0.450051\pi\) | ||||
0.156275 | + | 0.987714i | \(0.450051\pi\) | |||||||
\(620\) | −3.54816e45 | − | 3.24238e45i | −0.298910 | − | 0.273150i | ||||
\(621\) | 8.64584e45 | 0.709244 | ||||||||
\(622\) | 2.33017e46i | 1.86143i | ||||||||
\(623\) | − | 1.20930e46i | − | 0.940766i | ||||||
\(624\) | −1.87021e46 | −1.41692 | ||||||||
\(625\) | −1.33336e46 | + | 2.42628e45i | −0.983844 | + | 0.179028i | ||||
\(626\) | 6.65738e45 | 0.478440 | ||||||||
\(627\) | − | 1.56548e45i | − | 0.109581i | ||||||
\(628\) | 2.83346e45i | 0.193189i | ||||||||
\(629\) | −5.44219e44 | −0.0361442 | ||||||||
\(630\) | −6.17136e45 | − | 5.63952e45i | −0.399266 | − | 0.364857i | ||||
\(631\) | −1.19160e46 | −0.751008 | −0.375504 | − | 0.926821i | \(-0.622530\pi\) | ||||
−0.375504 | + | 0.926821i | \(0.622530\pi\) | |||||||
\(632\) | − | 1.10269e46i | − | 0.677052i | ||||||
\(633\) | 3.32514e46i | 1.98907i | ||||||||
\(634\) | 5.25750e45 | 0.306413 | ||||||||
\(635\) | −4.87585e44 | + | 5.33568e44i | −0.0276875 | + | 0.0302986i | ||||
\(636\) | 2.78947e45 | 0.154340 | ||||||||
\(637\) | 1.17542e46i | 0.633711i | ||||||||
\(638\) | − | 5.36071e46i | − | 2.81632i | ||||||
\(639\) | −1.59622e45 | −0.0817200 | ||||||||
\(640\) | −1.62185e46 | + | 1.77480e46i | −0.809172 | + | 0.885482i | ||||
\(641\) | 1.22124e45 | 0.0593806 | 0.0296903 | − | 0.999559i | \(-0.490548\pi\) | ||||
0.0296903 | + | 0.999559i | \(0.490548\pi\) | |||||||
\(642\) | − | 4.87567e46i | − | 2.31050i | ||||||
\(643\) | − | 2.16557e46i | − | 1.00021i | −0.865965 | − | 0.500105i | \(-0.833295\pi\) | ||
0.865965 | − | 0.500105i | \(-0.166705\pi\) | |||||||
\(644\) | −6.14462e45 | −0.276617 | ||||||||
\(645\) | 6.49186e45 | + | 5.93239e45i | 0.284861 | + | 0.260312i | ||||
\(646\) | 2.69825e44 | 0.0115410 | ||||||||
\(647\) | − | 1.30233e45i | − | 0.0543002i | −0.999631 | − | 0.0271501i | \(-0.991357\pi\) | ||
0.999631 | − | 0.0271501i | \(-0.00864321\pi\) | |||||||
\(648\) | − | 2.61670e46i | − | 1.06357i | ||||||
\(649\) | −1.53882e46 | −0.609747 | ||||||||
\(650\) | 2.64074e45 | + | 2.92625e46i | 0.102013 | + | 1.13042i | ||||
\(651\) | 7.24559e46 | 2.72890 | ||||||||
\(652\) | − | 4.60449e45i | − | 0.169081i | ||||||
\(653\) | 1.93235e46i | 0.691861i | 0.938260 | + | 0.345930i | \(0.112437\pi\) | ||||
−0.938260 | + | 0.345930i | \(0.887563\pi\) | |||||||
\(654\) | 5.40844e46 | 1.88816 | ||||||||
\(655\) | 2.82355e46 | + | 2.58022e46i | 0.961201 | + | 0.878366i | ||||
\(656\) | −3.78358e46 | −1.25600 | ||||||||
\(657\) | 1.34655e46i | 0.435906i | ||||||||
\(658\) | 7.05591e45i | 0.222754i | ||||||||
\(659\) | 1.11486e46 | 0.343249 | 0.171625 | − | 0.985162i | \(-0.445098\pi\) | ||||
0.171625 | + | 0.985162i | \(0.445098\pi\) | |||||||
\(660\) | 8.66135e45 | − | 9.47817e45i | 0.260082 | − | 0.284610i | ||||
\(661\) | −5.28685e46 | −1.54836 | −0.774182 | − | 0.632963i | \(-0.781839\pi\) | ||||
−0.774182 | + | 0.632963i | \(0.781839\pi\) | |||||||
\(662\) | 4.09404e46i | 1.16949i | ||||||||
\(663\) | − | 7.17319e45i | − | 0.199866i | ||||||
\(664\) | 1.57818e46 | 0.428926 | ||||||||
\(665\) | 2.04211e45 | − | 2.23469e45i | 0.0541404 | − | 0.0592462i | ||||
\(666\) | −3.59311e45 | −0.0929279 | ||||||||
\(667\) | − | 6.70373e46i | − | 1.69138i | ||||||
\(668\) | − | 1.24061e46i | − | 0.305368i | ||||||
\(669\) | −3.96491e46 | −0.952143 | ||||||||
\(670\) | −2.83978e46 | − | 2.59505e46i | −0.665350 | − | 0.608010i | ||||
\(671\) | 8.66586e46 | 1.98103 | ||||||||
\(672\) | 2.92799e46i | 0.653095i | ||||||||
\(673\) | − | 3.85972e46i | − | 0.840054i | −0.907512 | − | 0.420027i | \(-0.862021\pi\) | ||
0.907512 | − | 0.420027i | \(-0.137979\pi\) | |||||||
\(674\) | −5.25478e46 | −1.11600 | ||||||||
\(675\) | −3.47934e46 | + | 3.13986e45i | −0.721082 | + | 0.0650726i | ||||
\(676\) | 5.94908e44 | 0.0120318 | ||||||||
\(677\) | − | 2.19045e46i | − | 0.432335i | −0.976356 | − | 0.216167i | \(-0.930644\pi\) | ||
0.976356 | − | 0.216167i | \(-0.0693557\pi\) | |||||||
\(678\) | 9.62510e46i | 1.85402i | ||||||||
\(679\) | −3.31947e46 | −0.624048 | ||||||||
\(680\) | −5.72355e45 | − | 5.23030e45i | −0.105019 | − | 0.0959686i | ||||
\(681\) | −8.75981e46 | −1.56880 | ||||||||
\(682\) | 1.70159e47i | 2.97449i | ||||||||
\(683\) | − | 8.23915e44i | − | 0.0140586i | −0.999975 | − | 0.00702928i | \(-0.997762\pi\) | ||
0.999975 | − | 0.00702928i | \(-0.00223751\pi\) | |||||||
\(684\) | 3.23695e44 | 0.00539151 | ||||||||
\(685\) | 4.32577e46 | − | 4.73372e46i | 0.703346 | − | 0.769677i | ||||
\(686\) | −3.39029e46 | −0.538131 | ||||||||
\(687\) | − | 4.67268e46i | − | 0.724069i | ||||||
\(688\) | − | 2.54208e46i | − | 0.384573i | ||||||
\(689\) | 4.10607e46 | 0.606470 | ||||||||
\(690\) | 5.96104e46 | − | 6.52320e46i | 0.859631 | − | 0.940700i | ||||
\(691\) | −6.11797e46 | −0.861430 | −0.430715 | − | 0.902488i | \(-0.641739\pi\) | ||||
−0.430715 | + | 0.902488i | \(0.641739\pi\) | |||||||
\(692\) | − | 1.03828e46i | − | 0.142746i | ||||||
\(693\) | 5.37761e46i | 0.721924i | ||||||||
\(694\) | 4.12772e46 | 0.541102 | ||||||||
\(695\) | 6.97761e46 | + | 6.37628e46i | 0.893218 | + | 0.816241i | ||||
\(696\) | −1.39773e47 | −1.74731 | ||||||||
\(697\) | − | 1.45119e46i | − | 0.177168i | ||||||
\(698\) | − | 4.96387e46i | − | 0.591842i | ||||||
\(699\) | 1.38682e47 | 1.61490 | ||||||||
\(700\) | 2.47278e46 | − | 2.23151e45i | 0.281234 | − | 0.0253794i | ||||
\(701\) | −9.95653e46 | −1.10601 | −0.553007 | − | 0.833177i | \(-0.686520\pi\) | ||||
−0.553007 | + | 0.833177i | \(0.686520\pi\) | |||||||
\(702\) | 7.57375e46i | 0.821766i | ||||||||
\(703\) | − | 1.30109e45i | − | 0.0137894i | ||||||
\(704\) | 9.83848e46 | 1.01854 | ||||||||
\(705\) | −1.36106e46 | − | 1.24376e46i | −0.137644 | − | 0.125782i | ||||
\(706\) | 1.04142e47 | 1.02884 | ||||||||
\(707\) | − | 8.13032e46i | − | 0.784670i | ||||||
\(708\) | − | 1.14520e46i | − | 0.107977i | ||||||
\(709\) | −1.13327e47 | −1.04393 | −0.521964 | − | 0.852967i | \(-0.674801\pi\) | ||||
−0.521964 | + | 0.852967i | \(0.674801\pi\) | |||||||
\(710\) | 1.75998e46 | − | 1.92596e46i | 0.158397 | − | 0.173335i | ||||
\(711\) | 3.44457e46 | 0.302891 | ||||||||
\(712\) | − | 7.40484e46i | − | 0.636203i | ||||||
\(713\) | 2.12788e47i | 1.78637i | ||||||||
\(714\) | −3.33602e46 | −0.273658 | ||||||||
\(715\) | 1.27494e47 | − | 1.39518e47i | 1.02198 | − | 1.11835i | ||||
\(716\) | −2.97105e46 | −0.232726 | ||||||||
\(717\) | − | 1.91943e47i | − | 1.46929i | ||||||
\(718\) | 3.91319e46i | 0.292737i | ||||||||
\(719\) | 5.42492e46 | 0.396613 | 0.198306 | − | 0.980140i | \(-0.436456\pi\) | ||||
0.198306 | + | 0.980140i | \(0.436456\pi\) | |||||||
\(720\) | −4.66148e46 | − | 4.25976e46i | −0.333072 | − | 0.304368i | ||||
\(721\) | 2.02830e47 | 1.41644 | ||||||||
\(722\) | − | 1.61315e47i | − | 1.10106i | ||||||
\(723\) | − | 1.18046e47i | − | 0.787536i | ||||||
\(724\) | 4.12173e46 | 0.268778 | ||||||||
\(725\) | 2.43456e46 | + | 2.69778e47i | 0.155183 | + | 1.71961i | ||||
\(726\) | −2.45767e47 | −1.53133 | ||||||||
\(727\) | 1.08635e47i | 0.661687i | 0.943686 | + | 0.330843i | \(0.107333\pi\) | ||||
−0.943686 | + | 0.330843i | \(0.892667\pi\) | |||||||
\(728\) | 1.88585e47i | 1.12289i | ||||||||
\(729\) | −6.46237e46 | −0.376173 | ||||||||
\(730\) | −1.62472e47 | − | 1.48470e47i | −0.924592 | − | 0.844911i | ||||
\(731\) | 9.75013e45 | 0.0542468 | ||||||||
\(732\) | 6.44918e46i | 0.350810i | ||||||||
\(733\) | − | 1.51370e47i | − | 0.805054i | −0.915408 | − | 0.402527i | \(-0.868132\pi\) | ||
0.915408 | − | 0.402527i | \(-0.131868\pi\) | |||||||
\(734\) | −1.31247e46 | −0.0682502 | ||||||||
\(735\) | −9.63589e46 | + | 1.05446e47i | −0.489949 | + | 0.536154i | ||||
\(736\) | −8.59891e46 | −0.427523 | ||||||||
\(737\) | 2.47453e47i | 1.20304i | ||||||||
\(738\) | − | 9.58126e46i | − | 0.455504i | ||||||
\(739\) | −2.57207e47 | −1.19578 | −0.597888 | − | 0.801580i | \(-0.703993\pi\) | ||||
−0.597888 | + | 0.801580i | \(0.703993\pi\) | |||||||
\(740\) | 7.19855e45 | − | 7.87742e45i | 0.0327281 | − | 0.0358146i | ||||
\(741\) | 1.71493e46 | 0.0762510 | ||||||||
\(742\) | − | 1.90960e47i | − | 0.830382i | ||||||
\(743\) | − | 1.84386e46i | − | 0.0784173i | −0.999231 | − | 0.0392087i | \(-0.987516\pi\) | ||
0.999231 | − | 0.0392087i | \(-0.0124837\pi\) | |||||||
\(744\) | 4.43664e47 | 1.84545 | ||||||||
\(745\) | 2.95526e47 | + | 2.70058e47i | 1.20231 | + | 1.09870i | ||||
\(746\) | 5.07729e46 | 0.202042 | ||||||||
\(747\) | 4.92988e46i | 0.191887i | ||||||||
\(748\) | − | 1.42353e46i | − | 0.0541988i | ||||||
\(749\) | −6.06474e47 | −2.25872 | ||||||||
\(750\) | −2.16200e47 | + | 2.84161e47i | −0.787670 | + | 1.03527i | ||||
\(751\) | −4.41078e46 | −0.157201 | −0.0786007 | − | 0.996906i | \(-0.525045\pi\) | ||||
−0.0786007 | + | 0.996906i | \(0.525045\pi\) | |||||||
\(752\) | 5.32961e46i | 0.185824i | ||||||||
\(753\) | 1.17148e46i | 0.0399593i | ||||||||
\(754\) | 5.87246e47 | 1.95972 | ||||||||
\(755\) | 5.12213e46 | + | 4.68071e46i | 0.167235 | + | 0.152822i | ||||
\(756\) | 6.40006e46 | 0.204444 | ||||||||
\(757\) | 4.65678e47i | 1.45547i | 0.685857 | + | 0.727736i | \(0.259427\pi\) | ||||
−0.685857 | + | 0.727736i | \(0.740573\pi\) | |||||||
\(758\) | − | 2.06338e47i | − | 0.631012i | ||||||
\(759\) | −5.68420e47 | −1.70091 | ||||||||
\(760\) | 1.25043e46 | − | 1.36836e46i | 0.0366130 | − | 0.0400659i | ||||
\(761\) | 1.32920e47 | 0.380841 | 0.190420 | − | 0.981703i | \(-0.439015\pi\) | ||||
0.190420 | + | 0.981703i | \(0.439015\pi\) | |||||||
\(762\) | 1.90429e46i | 0.0533920i | ||||||||
\(763\) | − | 6.72744e47i | − | 1.84584i | ||||||
\(764\) | −1.02828e47 | −0.276103 | ||||||||
\(765\) | 1.63383e46 | − | 1.78791e46i | 0.0429332 | − | 0.0469821i | ||||
\(766\) | 6.26648e47 | 1.61157 | ||||||||
\(767\) | − | 1.68572e47i | − | 0.424288i | ||||||
\(768\) | 3.03679e47i | 0.748092i | ||||||||
\(769\) | 2.70521e47 | 0.652253 | 0.326127 | − | 0.945326i | \(-0.394256\pi\) | ||||
0.326127 | + | 0.945326i | \(0.394256\pi\) | |||||||
\(770\) | −6.48851e47 | − | 5.92934e47i | −1.53126 | − | 1.39929i | ||||
\(771\) | 2.64980e47 | 0.612090 | ||||||||
\(772\) | 5.38707e46i | 0.121806i | ||||||||
\(773\) | − | 6.16100e47i | − | 1.36361i | −0.731535 | − | 0.681804i | \(-0.761196\pi\) | ||
0.731535 | − | 0.681804i | \(-0.238804\pi\) | |||||||
\(774\) | 6.43736e46 | 0.139470 | ||||||||
\(775\) | −7.72772e46 | − | 8.56323e47i | −0.163898 | − | 1.81618i | ||||
\(776\) | −2.03259e47 | −0.422019 | ||||||||
\(777\) | 1.60862e47i | 0.326970i | ||||||||
\(778\) | − | 8.21281e46i | − | 0.163429i | ||||||
\(779\) | 3.46944e46 | 0.0675914 | ||||||||
\(780\) | 1.03830e47 | + | 9.48818e46i | 0.198044 | + | 0.180977i | ||||
\(781\) | −1.67825e47 | −0.313411 | ||||||||
\(782\) | − | 9.79721e46i | − | 0.179139i | ||||||
\(783\) | 6.98241e47i | 1.25008i | ||||||||
\(784\) | 4.12905e47 | 0.723828 | ||||||||
\(785\) | −3.41918e47 | + | 3.74163e47i | −0.586911 | + | 0.642261i | ||||
\(786\) | 1.00772e48 | 1.69382 | ||||||||
\(787\) | 9.09975e46i | 0.149777i | 0.997192 | + | 0.0748887i | \(0.0238602\pi\) | ||||
−0.997192 | + | 0.0748887i | \(0.976140\pi\) | |||||||
\(788\) | 2.36735e46i | 0.0381575i | ||||||||
\(789\) | −4.61474e47 | −0.728412 | ||||||||
\(790\) | −3.79797e47 | + | 4.15614e47i | −0.587089 | + | 0.642455i | ||||
\(791\) | 1.19725e48 | 1.81247 | ||||||||
\(792\) | 3.29284e47i | 0.488208i | ||||||||
\(793\) | 9.49313e47i | 1.37848i | ||||||||
\(794\) | −6.93963e47 | −0.986957 | ||||||||
\(795\) | 3.68354e47 | + | 3.36610e47i | 0.513107 | + | 0.468888i | ||||
\(796\) | 1.36639e47 | 0.186427 | ||||||||
\(797\) | − | 9.51335e47i | − | 1.27137i | −0.771950 | − | 0.635684i | \(-0.780718\pi\) | ||
0.771950 | − | 0.635684i | \(-0.219282\pi\) | |||||||
\(798\) | − | 7.97557e46i | − | 0.104403i | ||||||
\(799\) | −2.04417e46 | −0.0262117 | ||||||||
\(800\) | 3.46046e47 | − | 3.12282e46i | 0.434659 | − | 0.0392249i | ||||
\(801\) | 2.31311e47 | 0.284616 | ||||||||
\(802\) | − | 1.17153e47i | − | 0.141213i | ||||||
\(803\) | 1.41575e48i | 1.67178i | ||||||||
\(804\) | −1.84156e47 | −0.213040 | ||||||||
\(805\) | −8.11407e47 | − | 7.41481e47i | −0.919617 | − | 0.840365i | ||||
\(806\) | −1.86402e48 | −2.06978 | ||||||||
\(807\) | − | 3.51187e47i | − | 0.382054i | ||||||
\(808\) | − | 4.97839e47i | − | 0.530642i | ||||||
\(809\) | −6.61127e46 | −0.0690453 | −0.0345227 | − | 0.999404i | \(-0.510991\pi\) | ||||
−0.0345227 | + | 0.999404i | \(0.510991\pi\) | |||||||
\(810\) | −9.01262e47 | + | 9.86257e47i | −0.922249 | + | 1.00922i | ||||
\(811\) | −1.12294e48 | −1.12593 | −0.562966 | − | 0.826480i | \(-0.690340\pi\) | ||||
−0.562966 | + | 0.826480i | \(0.690340\pi\) | |||||||
\(812\) | − | 4.96242e47i | − | 0.487550i | ||||||
\(813\) | − | 1.26294e48i | − | 1.21587i | ||||||
\(814\) | −3.77776e47 | −0.356395 | ||||||||
\(815\) | 5.55630e47 | − | 6.08030e47i | 0.513671 | − | 0.562114i | ||||
\(816\) | −2.51983e47 | −0.228288 | ||||||||
\(817\) | 2.33101e46i | 0.0206957i | ||||||||
\(818\) | 1.62226e48i | 1.41153i | ||||||||
\(819\) | −5.89097e47 | −0.502346 | ||||||||
\(820\) | 2.10056e47 | + | 1.91954e47i | 0.175552 | + | 0.160423i | ||||
\(821\) | 1.43390e48 | 1.17451 | 0.587257 | − | 0.809401i | \(-0.300208\pi\) | ||||
0.587257 | + | 0.809401i | \(0.300208\pi\) | |||||||
\(822\) | − | 1.68946e48i | − | 1.35632i | ||||||
\(823\) | 1.07892e48i | 0.848970i | 0.905435 | + | 0.424485i | \(0.139545\pi\) | ||||
−0.905435 | + | 0.424485i | \(0.860455\pi\) | |||||||
\(824\) | 1.24197e48 | 0.957885 | ||||||||
\(825\) | 2.28749e48 | − | 2.06430e47i | 1.72929 | − | 0.156057i | ||||
\(826\) | −7.83971e47 | −0.580938 | ||||||||
\(827\) | 1.67232e48i | 1.21473i | 0.794424 | + | 0.607364i | \(0.207773\pi\) | ||||
−0.794424 | + | 0.607364i | \(0.792227\pi\) | |||||||
\(828\) | − | 1.17532e47i | − | 0.0836867i | ||||||
\(829\) | −3.48680e47 | −0.243376 | −0.121688 | − | 0.992568i | \(-0.538831\pi\) | ||||
−0.121688 | + | 0.992568i | \(0.538831\pi\) | |||||||
\(830\) | −5.94828e47 | − | 5.43566e47i | −0.407008 | − | 0.371932i | ||||
\(831\) | −1.32512e48 | −0.888873 | ||||||||
\(832\) | 1.07777e48i | 0.708746i | ||||||||
\(833\) | 1.58370e47i | 0.102101i | ||||||||
\(834\) | 2.49029e48 | 1.57402 | ||||||||
\(835\) | 1.49706e48 | − | 1.63825e48i | 0.927713 | − | 1.01520i | ||||
\(836\) | 3.40330e46 | 0.0206774 | ||||||||
\(837\) | − | 2.21634e48i | − | 1.32028i | ||||||
\(838\) | 6.02222e47i | 0.351747i | ||||||||
\(839\) | 1.43688e48 | 0.822900 | 0.411450 | − | 0.911432i | \(-0.365022\pi\) | ||||
0.411450 | + | 0.911432i | \(0.365022\pi\) | |||||||
\(840\) | −1.54599e48 | + | 1.69179e48i | −0.868157 | + | 0.950030i | ||||
\(841\) | 3.59788e48 | 1.98113 | ||||||||
\(842\) | − | 7.95957e46i | − | 0.0429774i | ||||||
\(843\) | − | 2.44937e48i | − | 1.29688i | ||||||
\(844\) | −7.22873e47 | −0.375328 | ||||||||
\(845\) | 7.85585e46 | + | 7.17884e46i | 0.0399998 | + | 0.0365526i | ||||
\(846\) | −1.34963e47 | −0.0673913 | ||||||||
\(847\) | 3.05704e48i | 1.49701i | ||||||||
\(848\) | − | 1.44240e48i | − | 0.692713i | ||||||
\(849\) | −3.38235e48 | −1.59310 | ||||||||
\(850\) | 3.55800e46 | + | 3.94269e47i | 0.0164359 | + | 0.182129i | ||||
\(851\) | −4.72420e47 | −0.214038 | ||||||||
\(852\) | − | 1.24896e47i | − | 0.0555004i | ||||||
\(853\) | − | 3.06470e48i | − | 1.33576i | −0.744269 | − | 0.667880i | \(-0.767202\pi\) | ||
0.744269 | − | 0.667880i | \(-0.232798\pi\) | |||||||
\(854\) | 4.41494e48 | 1.88743 | ||||||||
\(855\) | 4.27444e46 | + | 3.90607e46i | 0.0179242 | + | 0.0163795i | ||||
\(856\) | −3.71358e48 | −1.52748 | ||||||||
\(857\) | 3.52656e47i | 0.142288i | 0.997466 | + | 0.0711439i | \(0.0226650\pi\) | ||||
−0.997466 | + | 0.0711439i | \(0.977335\pi\) | |||||||
\(858\) | − | 4.97935e48i | − | 1.97076i | ||||||
\(859\) | −3.49821e48 | −1.35819 | −0.679093 | − | 0.734052i | \(-0.737627\pi\) | ||||
−0.679093 | + | 0.734052i | \(0.737627\pi\) | |||||||
\(860\) | −1.28968e47 | + | 1.41130e47i | −0.0491198 | + | 0.0537522i | ||||
\(861\) | −4.28949e48 | −1.60271 | ||||||||
\(862\) | 2.35069e48i | 0.861639i | ||||||||
\(863\) | 2.18223e48i | 0.784733i | 0.919809 | + | 0.392366i | \(0.128343\pi\) | ||||
−0.919809 | + | 0.392366i | \(0.871657\pi\) | |||||||
\(864\) | 8.95638e47 | 0.315977 | ||||||||
\(865\) | 1.25291e48 | − | 1.37107e48i | 0.433665 | − | 0.474563i | ||||
\(866\) | −1.84893e48 | −0.627877 | ||||||||
\(867\) | 3.43517e48i | 1.14455i | ||||||||
\(868\) | 1.57516e48i | 0.514932i | ||||||||
\(869\) | 3.62158e48 | 1.16164 | ||||||||
\(870\) | 5.26816e48 | + | 4.81416e48i | 1.65803 | + | 1.51514i | ||||
\(871\) | −2.71075e48 | −0.837125 | ||||||||
\(872\) | − | 4.11937e48i | − | 1.24827i | ||||||
\(873\) | − | 6.34937e47i | − | 0.188797i | ||||||
\(874\) | 2.34227e47 | 0.0683436 | ||||||||
\(875\) | 3.53462e48 | + | 2.68926e48i | 1.01207 | + | 0.770017i | ||||
\(876\) | −1.05361e48 | −0.296047 | ||||||||
\(877\) | 5.47361e48i | 1.50932i | 0.656117 | + | 0.754659i | \(0.272198\pi\) | ||||
−0.656117 | + | 0.754659i | \(0.727802\pi\) | |||||||
\(878\) | 1.64644e48i | 0.445540i | ||||||||
\(879\) | −3.28683e48 | −0.872892 | ||||||||
\(880\) | −4.90103e48 | − | 4.47867e48i | −1.27739 | − | 1.16731i | ||||
\(881\) | −1.58161e48 | −0.404572 | −0.202286 | − | 0.979326i | \(-0.564837\pi\) | ||||
−0.202286 | + | 0.979326i | \(0.564837\pi\) | |||||||
\(882\) | 1.04561e48i | 0.262505i | ||||||||
\(883\) | 2.91205e48i | 0.717542i | 0.933426 | + | 0.358771i | \(0.116804\pi\) | ||||
−0.933426 | + | 0.358771i | \(0.883196\pi\) | |||||||
\(884\) | 1.55942e47 | 0.0377139 | ||||||||
\(885\) | 1.38192e48 | − | 1.51225e48i | 0.328035 | − | 0.358971i | ||||
\(886\) | −5.00561e48 | −1.16627 | ||||||||
\(887\) | − | 5.31827e48i | − | 1.21627i | −0.793833 | − | 0.608136i | \(-0.791918\pi\) | ||
0.793833 | − | 0.608136i | \(-0.208082\pi\) | |||||||
\(888\) | 9.84998e47i | 0.221117i | ||||||||
\(889\) | 2.36871e47 | 0.0521954 | ||||||||
\(890\) | −2.55042e48 | + | 2.79095e48i | −0.551667 | + | 0.603693i | ||||
\(891\) | 8.59406e48 | 1.82480 | ||||||||
\(892\) | − | 8.61955e47i | − | 0.179665i | ||||||
\(893\) | − | 4.88710e46i | − | 0.0100001i | ||||||
\(894\) | 1.05473e49 | 2.11870 | ||||||||
\(895\) | −3.92332e48 | − | 3.58521e48i | −0.773702 | − | 0.707025i | ||||
\(896\) | 7.87900e48 | 1.52542 | ||||||||
\(897\) | − | 6.22683e48i | − | 1.18356i | ||||||
\(898\) | 4.56199e48i | 0.851324i | ||||||||
\(899\) | −1.71849e49 | −3.14855 | ||||||||
\(900\) | 4.26835e46 | + | 4.72984e47i | 0.00767819 | + | 0.0850835i | ||||
\(901\) | 5.53232e47 | 0.0977120 | ||||||||
\(902\) | − | 1.00736e49i | − | 1.74694i | ||||||
\(903\) | − | 2.88198e48i | − | 0.490730i | ||||||
\(904\) | 7.33102e48 | 1.22570 | ||||||||
\(905\) | 5.44281e48 | + | 4.97375e48i | 0.893556 | + | 0.816550i | ||||
\(906\) | 1.82808e48 | 0.294700 | ||||||||
\(907\) | 3.23851e48i | 0.512654i | 0.966590 | + | 0.256327i | \(0.0825124\pi\) | ||||
−0.966590 | + | 0.256327i | \(0.917488\pi\) | |||||||
\(908\) | − | 1.90435e48i | − | 0.296026i | ||||||
\(909\) | 1.55514e48 | 0.237391 | ||||||||
\(910\) | 6.49536e48 | − | 7.10792e48i | 0.973690 | − | 1.06552i | ||||
\(911\) | −5.41124e48 | −0.796605 | −0.398303 | − | 0.917254i | \(-0.630401\pi\) | ||||
−0.398303 | + | 0.917254i | \(0.630401\pi\) | |||||||
\(912\) | − | 6.02427e47i | − | 0.0870943i | ||||||
\(913\) | 5.18323e48i | 0.735923i | ||||||||
\(914\) | −5.66460e48 | −0.789872 | ||||||||
\(915\) | −7.78232e48 | + | 8.51625e48i | −1.06576 | + | 1.16627i | ||||
\(916\) | 1.01582e48 | 0.136629 | ||||||||
\(917\) | − | 1.25348e49i | − | 1.65586i | ||||||
\(918\) | 1.02045e48i | 0.132400i | ||||||||
\(919\) | 4.23316e48 | 0.539459 | 0.269730 | − | 0.962936i | \(-0.413066\pi\) | ||||
0.269730 | + | 0.962936i | \(0.413066\pi\) | |||||||
\(920\) | −4.96844e48 | − | 4.54026e48i | −0.621900 | − | 0.568305i | ||||
\(921\) | 9.42830e48 | 1.15918 | ||||||||
\(922\) | 1.11586e49i | 1.34756i | ||||||||
\(923\) | − | 1.83846e48i | − | 0.218085i | ||||||
\(924\) | −4.20772e48 | −0.490297 | ||||||||
\(925\) | 1.90116e48 | − | 1.71566e47i | 0.217610 | − | 0.0196378i | ||||
\(926\) | 7.52963e48 | 0.846627 | ||||||||
\(927\) | 3.87965e48i | 0.428526i | ||||||||
\(928\) | − | 6.94451e48i | − | 0.753529i | ||||||
\(929\) | 1.09693e49 | 1.16929 | 0.584644 | − | 0.811290i | \(-0.301234\pi\) | ||||
0.584644 | + | 0.811290i | \(0.301234\pi\) | |||||||
\(930\) | −1.67221e49 | − | 1.52810e49i | −1.75114 | − | 1.60023i | ||||
\(931\) | −3.78622e47 | −0.0389526 | ||||||||
\(932\) | 3.01488e48i | 0.304725i | ||||||||
\(933\) | 1.99541e49i | 1.98146i | ||||||||
\(934\) | −1.19225e49 | −1.16317 | ||||||||
\(935\) | 1.71779e48 | − | 1.87979e48i | 0.164657 | − | 0.180185i | ||||
\(936\) | −3.60718e48 | −0.339717 | ||||||||
\(937\) | 8.82160e48i | 0.816289i | 0.912917 | + | 0.408145i | \(0.133824\pi\) | ||||
−0.912917 | + | 0.408145i | \(0.866176\pi\) | |||||||
\(938\) | 1.26068e49i | 1.14620i | ||||||||
\(939\) | 5.70097e48 | 0.509291 | ||||||||
\(940\) | 2.70389e47 | − | 2.95888e47i | 0.0237345 | − | 0.0259728i | ||||
\(941\) | −7.63482e48 | −0.658522 | −0.329261 | − | 0.944239i | \(-0.606800\pi\) | ||||
−0.329261 | + | 0.944239i | \(0.606800\pi\) | |||||||
\(942\) | 1.33538e49i | 1.13179i | ||||||||
\(943\) | − | 1.25974e49i | − | 1.04915i | ||||||
\(944\) | −5.92165e48 | −0.484624 | ||||||||
\(945\) | 8.45138e48 | + | 7.72305e48i | 0.679678 | + | 0.621103i | ||||
\(946\) | 6.76817e48 | 0.534894 | ||||||||
\(947\) | 1.62448e49i | 1.26165i | 0.775924 | + | 0.630827i | \(0.217284\pi\) | ||||
−0.775924 | + | 0.630827i | \(0.782716\pi\) | |||||||
\(948\) | 2.69520e48i | 0.205709i | ||||||||
\(949\) | −1.55090e49 | −1.16330 | ||||||||
\(950\) | −9.42597e47 | + | 8.50628e46i | −0.0694843 | + | 0.00627047i | ||||
\(951\) | 4.50220e48 | 0.326172 | ||||||||
\(952\) | 2.54090e48i | 0.180916i | ||||||||
\(953\) | − | 9.94250e48i | − | 0.695766i | −0.937538 | − | 0.347883i | \(-0.886901\pi\) | ||
0.937538 | − | 0.347883i | \(-0.113099\pi\) | |||||||
\(954\) | 3.65262e48 | 0.251221 | ||||||||
\(955\) | −1.35786e49 | − | 1.24084e49i | −0.917910 | − | 0.838805i | ||||
\(956\) | 4.17277e48 | 0.277248 | ||||||||
\(957\) | − | 4.59058e49i | − | 2.99792i | ||||||
\(958\) | − | 1.49102e49i | − | 0.957090i | ||||||
\(959\) | −2.10148e49 | −1.32592 | ||||||||
\(960\) | −8.83538e48 | + | 9.66862e48i | −0.547962 | + | 0.599638i | ||||
\(961\) | 3.81443e49 | 2.32538 | ||||||||
\(962\) | − | 4.13840e48i | − | 0.247995i | ||||||
\(963\) | − | 1.16004e49i | − | 0.683345i | ||||||
\(964\) | 2.56628e48 | 0.148605 | ||||||||
\(965\) | −6.50065e48 | + | 7.11371e48i | −0.370047 | + | 0.404944i | ||||
\(966\) | −2.89589e49 | −1.62054 | ||||||||
\(967\) | 2.72293e49i | 1.49796i | 0.662593 | + | 0.748980i | \(0.269456\pi\) | ||||
−0.662593 | + | 0.748980i | \(0.730544\pi\) | |||||||
\(968\) | 1.87190e49i | 1.01237i | ||||||||
\(969\) | 2.31061e47 | 0.0122853 | ||||||||
\(970\) | 7.66101e48 | + | 7.00079e48i | 0.400454 | + | 0.365943i | ||||
\(971\) | 3.20196e48 | 0.164550 | 0.0822751 | − | 0.996610i | \(-0.473781\pi\) | ||||
0.0822751 | + | 0.996610i | \(0.473781\pi\) | |||||||
\(972\) | 3.21386e48i | 0.162380i | ||||||||
\(973\) | − | 3.09762e49i | − | 1.53874i | ||||||
\(974\) | 2.89081e49 | 1.41188 | ||||||||
\(975\) | 2.26136e48 | + | 2.50586e49i | 0.108591 | + | 1.20332i | ||||
\(976\) | 3.33478e49 | 1.57451 | ||||||||
\(977\) | − | 2.56729e49i | − | 1.19183i | −0.803047 | − | 0.595915i | \(-0.796789\pi\) | ||
0.803047 | − | 0.595915i | \(-0.203211\pi\) | |||||||
\(978\) | − | 2.17005e49i | − | 0.990553i | ||||||
\(979\) | 2.43198e49 | 1.09155 | ||||||||
\(980\) | −2.29236e48 | − | 2.09480e48i | −0.101170 | − | 0.0924513i | ||||
\(981\) | 1.28680e49 | 0.558435 | ||||||||
\(982\) | 2.15497e49i | 0.919606i | ||||||||
\(983\) | − | 2.12937e49i | − | 0.893548i | −0.894647 | − | 0.446774i | \(-0.852573\pi\) | ||
0.894647 | − | 0.446774i | \(-0.147427\pi\) | |||||||
\(984\) | −2.62656e49 | −1.08385 | ||||||||
\(985\) | −2.85672e48 | + | 3.12612e48i | −0.115923 | + | 0.126855i | ||||
\(986\) | 7.91226e48 | 0.315742 | ||||||||
\(987\) | 6.04224e48i | 0.237118i | ||||||||
\(988\) | 3.72818e47i | 0.0143882i | ||||||||
\(989\) | 8.46380e48 | 0.321238 | ||||||||
\(990\) | 1.13414e49 | − | 1.24110e49i | 0.423338 | − | 0.463261i | ||||
\(991\) | −1.22972e49 | −0.451432 | −0.225716 | − | 0.974193i | \(-0.572472\pi\) | ||||
−0.225716 | + | 0.974193i | \(0.572472\pi\) | |||||||
\(992\) | 2.20431e49i | 0.795849i | ||||||||
\(993\) | 3.50588e49i | 1.24490i | ||||||||
\(994\) | −8.55007e48 | −0.298603 | ||||||||
\(995\) | 1.80434e49 | + | 1.64884e49i | 0.619779 | + | 0.566367i | ||||
\(996\) | −3.85739e48 | −0.130321 | ||||||||
\(997\) | − | 4.53447e49i | − | 1.50680i | −0.657562 | − | 0.753401i | \(-0.728412\pi\) | ||
0.657562 | − | 0.753401i | \(-0.271588\pi\) | |||||||
\(998\) | 4.04297e49i | 1.32144i | ||||||||
\(999\) | 4.92059e48 | 0.158193 |
(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 | 5.34.b.a.4.12 | yes | 16 | |
5.2 | odd | 4 | 25.34.a.f.1.5 | 16 | |||
5.3 | odd | 4 | 25.34.a.f.1.12 | 16 | |||
5.4 | even | 2 | inner | 5.34.b.a.4.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.b.a.4.5 | ✓ | 16 | 5.4 | even | 2 | inner | |
5.34.b.a.4.12 | yes | 16 | 1.1 | even | 1 | trivial | |
25.34.a.f.1.5 | 16 | 5.2 | odd | 4 | |||
25.34.a.f.1.12 | 16 | 5.3 | odd | 4 |