Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,17,Mod(6,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.6");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(11.3627180700\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5365384x^{6} + 10449491370210x^{4} + 8743024230718881600x^{2} + 2655236149032650377194000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{5}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 6.1 | ||
Root | \(-1246.39i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.6 |
Dual form | 7.17.b.b.6.2 |
$q$-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 \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −408.297 | −1.59491 | −0.797456 | − | 0.603377i | \(-0.793821\pi\) | ||||
−0.797456 | + | 0.603377i | \(0.793821\pi\) | |||||||
\(3\) | − | 7478.36i | − | 1.13982i | −0.821707 | − | 0.569910i | \(-0.806978\pi\) | ||
0.821707 | − | 0.569910i | \(-0.193022\pi\) | |||||||
\(4\) | 101171. | 1.54374 | ||||||||
\(5\) | 25884.6i | 0.0662645i | 0.999451 | + | 0.0331322i | \(0.0105483\pi\) | ||||
−0.999451 | + | 0.0331322i | \(0.989452\pi\) | |||||||
\(6\) | 3.05340e6i | 1.81791i | ||||||||
\(7\) | 879246. | + | 5.69736e6i | 0.152520 | + | 0.988300i | ||||
\(8\) | −1.45496e7 | −0.867223 | ||||||||
\(9\) | −1.28792e7 | −0.299191 | ||||||||
\(10\) | − | 1.05686e7i | − | 0.105686i | ||||||
\(11\) | 2.58740e8 | 1.20704 | 0.603521 | − | 0.797347i | \(-0.293764\pi\) | ||||
0.603521 | + | 0.797347i | \(0.293764\pi\) | |||||||
\(12\) | − | 7.56592e8i | − | 1.75959i | ||||||
\(13\) | − | 7.88399e8i | − | 0.966495i | −0.875484 | − | 0.483247i | \(-0.839457\pi\) | ||
0.875484 | − | 0.483247i | \(-0.160543\pi\) | |||||||
\(14\) | −3.58994e8 | − | 2.32622e9i | −0.243256 | − | 1.57625i | ||||
\(15\) | 1.93574e8 | 0.0755296 | ||||||||
\(16\) | −6.89767e8 | −0.160599 | ||||||||
\(17\) | 8.43625e9i | 1.20937i | 0.796466 | + | 0.604683i | \(0.206700\pi\) | ||||
−0.796466 | + | 0.604683i | \(0.793300\pi\) | |||||||
\(18\) | 5.25853e9 | 0.477183 | ||||||||
\(19\) | − | 2.52026e10i | − | 1.48394i | −0.670432 | − | 0.741971i | \(-0.733891\pi\) | ||
0.670432 | − | 0.741971i | \(-0.266109\pi\) | |||||||
\(20\) | 2.61876e9i | 0.102295i | ||||||||
\(21\) | 4.26069e10 | − | 6.57532e9i | 1.12649 | − | 0.173845i | ||||
\(22\) | −1.05643e11 | −1.92512 | ||||||||
\(23\) | −9.65568e9 | −0.123299 | −0.0616496 | − | 0.998098i | \(-0.519636\pi\) | ||||
−0.0616496 | + | 0.998098i | \(0.519636\pi\) | |||||||
\(24\) | 1.08807e11i | 0.988479i | ||||||||
\(25\) | 1.51918e11 | 0.995609 | ||||||||
\(26\) | 3.21901e11i | 1.54147i | ||||||||
\(27\) | − | 2.25604e11i | − | 0.798797i | ||||||
\(28\) | 8.89540e10 | + | 5.76406e11i | 0.235451 | + | 1.52568i | ||||
\(29\) | −6.70946e11 | −1.34123 | −0.670616 | − | 0.741805i | \(-0.733970\pi\) | ||||
−0.670616 | + | 0.741805i | \(0.733970\pi\) | |||||||
\(30\) | −7.90358e10 | −0.120463 | ||||||||
\(31\) | − | 7.88414e11i | − | 0.924401i | −0.886775 | − | 0.462201i | \(-0.847060\pi\) | ||
0.886775 | − | 0.462201i | \(-0.152940\pi\) | |||||||
\(32\) | 1.23515e12 | 1.12336 | ||||||||
\(33\) | − | 1.93495e12i | − | 1.37581i | ||||||
\(34\) | − | 3.44450e12i | − | 1.92883i | ||||||
\(35\) | −1.47474e11 | + | 2.27589e10i | −0.0654892 | + | 0.0101066i | ||||
\(36\) | −1.30300e12 | −0.461874 | ||||||||
\(37\) | 4.88762e12 | 1.39150 | 0.695750 | − | 0.718284i | \(-0.255072\pi\) | ||||
0.695750 | + | 0.718284i | \(0.255072\pi\) | |||||||
\(38\) | 1.02902e13i | 2.36676i | ||||||||
\(39\) | −5.89594e12 | −1.10163 | ||||||||
\(40\) | − | 3.76610e11i | − | 0.0574661i | ||||||
\(41\) | 2.16776e11i | 0.0271481i | 0.999908 | + | 0.0135740i | \(0.00432089\pi\) | ||||
−0.999908 | + | 0.0135740i | \(0.995679\pi\) | |||||||
\(42\) | −1.73963e13 | + | 2.68469e12i | −1.79664 | + | 0.277268i | ||||
\(43\) | 5.58592e12 | 0.477911 | 0.238956 | − | 0.971030i | \(-0.423195\pi\) | ||||
0.238956 | + | 0.971030i | \(0.423195\pi\) | |||||||
\(44\) | 2.61769e13 | 1.86336 | ||||||||
\(45\) | − | 3.33372e11i | − | 0.0198257i | ||||||
\(46\) | 3.94239e12 | 0.196651 | ||||||||
\(47\) | − | 4.97420e11i | − | 0.0208901i | −0.999945 | − | 0.0104450i | \(-0.996675\pi\) | ||
0.999945 | − | 0.0104450i | \(-0.00332482\pi\) | |||||||
\(48\) | 5.15833e12i | 0.183054i | ||||||||
\(49\) | −3.16868e13 | + | 1.00188e13i | −0.953475 | + | 0.301471i | ||||
\(50\) | −6.20277e13 | −1.58791 | ||||||||
\(51\) | 6.30893e13 | 1.37846 | ||||||||
\(52\) | − | 7.97630e13i | − | 1.49202i | ||||||
\(53\) | 4.55472e13 | 0.731569 | 0.365784 | − | 0.930700i | \(-0.380801\pi\) | ||||
0.365784 | + | 0.930700i | \(0.380801\pi\) | |||||||
\(54\) | 9.21135e13i | 1.27401i | ||||||||
\(55\) | 6.69738e12i | 0.0799840i | ||||||||
\(56\) | −1.27927e13 | − | 8.28942e13i | −0.132269 | − | 0.857077i | ||||
\(57\) | −1.88474e14 | −1.69143 | ||||||||
\(58\) | 2.73946e14 | 2.13915 | ||||||||
\(59\) | − | 1.09329e14i | − | 0.744594i | −0.928114 | − | 0.372297i | \(-0.878570\pi\) | ||
0.928114 | − | 0.372297i | \(-0.121430\pi\) | |||||||
\(60\) | 1.95841e13 | 0.116598 | ||||||||
\(61\) | − | 3.61273e14i | − | 1.88450i | −0.334907 | − | 0.942251i | \(-0.608705\pi\) | ||
0.334907 | − | 0.942251i | \(-0.391295\pi\) | |||||||
\(62\) | 3.21907e14i | 1.47434i | ||||||||
\(63\) | −1.13240e13 | − | 7.33772e13i | −0.0456325 | − | 0.295690i | ||||
\(64\) | −4.59105e14 | −1.63107 | ||||||||
\(65\) | 2.04074e13 | 0.0640443 | ||||||||
\(66\) | 7.90036e14i | 2.19430i | ||||||||
\(67\) | 2.27208e14 | 0.559531 | 0.279766 | − | 0.960068i | \(-0.409743\pi\) | ||||
0.279766 | + | 0.960068i | \(0.409743\pi\) | |||||||
\(68\) | 8.53502e14i | 1.86695i | ||||||||
\(69\) | 7.22087e13i | 0.140539i | ||||||||
\(70\) | 6.02131e13 | − | 9.29240e12i | 0.104450 | − | 0.0161192i | ||||
\(71\) | 6.95480e14 | 1.07700 | 0.538502 | − | 0.842624i | \(-0.318990\pi\) | ||||
0.538502 | + | 0.842624i | \(0.318990\pi\) | |||||||
\(72\) | 1.87387e14 | 0.259465 | ||||||||
\(73\) | − | 1.27766e15i | − | 1.58428i | −0.610338 | − | 0.792141i | \(-0.708967\pi\) | ||
0.610338 | − | 0.792141i | \(-0.291033\pi\) | |||||||
\(74\) | −1.99560e15 | −2.21932 | ||||||||
\(75\) | − | 1.13610e15i | − | 1.13482i | ||||||
\(76\) | − | 2.54977e15i | − | 2.29082i | ||||||
\(77\) | 2.27496e14 | + | 1.47413e15i | 0.184098 | + | 1.19292i | ||||
\(78\) | 2.40730e15 | 1.75700 | ||||||||
\(79\) | −1.01425e14 | −0.0668544 | −0.0334272 | − | 0.999441i | \(-0.510642\pi\) | ||||
−0.0334272 | + | 0.999441i | \(0.510642\pi\) | |||||||
\(80\) | − | 1.78543e13i | − | 0.0106420i | ||||||
\(81\) | −2.24155e15 | −1.20968 | ||||||||
\(82\) | − | 8.85089e13i | − | 0.0432988i | ||||||
\(83\) | 9.27081e14i | 0.411617i | 0.978592 | + | 0.205808i | \(0.0659823\pi\) | ||||
−0.978592 | + | 0.205808i | \(0.934018\pi\) | |||||||
\(84\) | 4.31057e15 | − | 6.65230e14i | 1.73900 | − | 0.268372i | ||||
\(85\) | −2.18369e14 | −0.0801381 | ||||||||
\(86\) | −2.28072e15 | −0.762227 | ||||||||
\(87\) | 5.01758e15i | 1.52876i | ||||||||
\(88\) | −3.76456e15 | −1.04677 | ||||||||
\(89\) | 2.66921e15i | 0.678051i | 0.940777 | + | 0.339026i | \(0.110097\pi\) | ||||
−0.940777 | + | 0.339026i | \(0.889903\pi\) | |||||||
\(90\) | 1.36115e14i | 0.0316203i | ||||||||
\(91\) | 4.49179e15 | − | 6.93197e14i | 0.955187 | − | 0.147410i | ||||
\(92\) | −9.76873e14 | −0.190342 | ||||||||
\(93\) | −5.89604e15 | −1.05365 | ||||||||
\(94\) | 2.03095e14i | 0.0333178i | ||||||||
\(95\) | 6.52359e14 | 0.0983326 | ||||||||
\(96\) | − | 9.23692e15i | − | 1.28043i | ||||||
\(97\) | 6.68122e15i | 0.852476i | 0.904611 | + | 0.426238i | \(0.140161\pi\) | ||||
−0.904611 | + | 0.426238i | \(0.859839\pi\) | |||||||
\(98\) | 1.29376e16 | − | 4.09063e15i | 1.52071 | − | 0.480819i | ||||
\(99\) | −3.33236e15 | −0.361136 | ||||||||
\(100\) | 1.53697e16 | 1.53697 | ||||||||
\(101\) | − | 1.23999e16i | − | 1.14511i | −0.819865 | − | 0.572557i | \(-0.805952\pi\) | ||
0.819865 | − | 0.572557i | \(-0.194048\pi\) | |||||||
\(102\) | −2.57592e16 | −2.19852 | ||||||||
\(103\) | 1.67784e16i | 1.32450i | 0.749283 | + | 0.662250i | \(0.230399\pi\) | ||||
−0.749283 | + | 0.662250i | \(0.769601\pi\) | |||||||
\(104\) | 1.14709e16i | 0.838167i | ||||||||
\(105\) | 1.70199e14 | + | 1.10286e15i | 0.0115198 | + | 0.0746460i | ||||
\(106\) | −1.85968e16 | −1.16679 | ||||||||
\(107\) | 1.80063e16 | 1.04799 | 0.523993 | − | 0.851723i | \(-0.324442\pi\) | ||||
0.523993 | + | 0.851723i | \(0.324442\pi\) | |||||||
\(108\) | − | 2.28245e16i | − | 1.23314i | ||||||
\(109\) | −9.07598e14 | −0.0455493 | −0.0227746 | − | 0.999741i | \(-0.507250\pi\) | ||||
−0.0227746 | + | 0.999741i | \(0.507250\pi\) | |||||||
\(110\) | − | 2.73452e15i | − | 0.127567i | ||||||
\(111\) | − | 3.65514e16i | − | 1.58606i | ||||||
\(112\) | −6.06475e14 | − | 3.92985e15i | −0.0244945 | − | 0.158720i | ||||
\(113\) | 7.26810e15 | 0.273397 | 0.136698 | − | 0.990613i | \(-0.456351\pi\) | ||||
0.136698 | + | 0.990613i | \(0.456351\pi\) | |||||||
\(114\) | 7.69535e16 | 2.69768 | ||||||||
\(115\) | − | 2.49933e14i | − | 0.00817036i | ||||||
\(116\) | −6.78802e16 | −2.07052 | ||||||||
\(117\) | 1.01539e16i | 0.289166i | ||||||||
\(118\) | 4.46388e16i | 1.18756i | ||||||||
\(119\) | −4.80643e16 | + | 7.41754e15i | −1.19522 | + | 0.184452i | ||||
\(120\) | −2.81643e15 | −0.0655011 | ||||||||
\(121\) | 2.09967e16 | 0.456949 | ||||||||
\(122\) | 1.47507e17i | 3.00562i | ||||||||
\(123\) | 1.62113e15 | 0.0309440 | ||||||||
\(124\) | − | 7.97644e16i | − | 1.42704i | ||||||
\(125\) | 7.88200e15i | 0.132238i | ||||||||
\(126\) | 4.62355e15 | + | 2.99597e16i | 0.0727798 | + | 0.471600i | ||||
\(127\) | −9.59192e16 | −1.41735 | −0.708673 | − | 0.705537i | \(-0.750706\pi\) | ||||
−0.708673 | + | 0.705537i | \(0.750706\pi\) | |||||||
\(128\) | 1.06504e17 | 1.47805 | ||||||||
\(129\) | − | 4.17736e16i | − | 0.544733i | ||||||
\(130\) | −8.33228e15 | −0.102145 | ||||||||
\(131\) | 7.13773e16i | 0.822981i | 0.911414 | + | 0.411490i | \(0.134992\pi\) | ||||
−0.911414 | + | 0.411490i | \(0.865008\pi\) | |||||||
\(132\) | − | 1.95761e17i | − | 2.12390i | ||||||
\(133\) | 1.43588e17 | − | 2.21593e16i | 1.46658 | − | 0.226330i | ||||
\(134\) | −9.27683e16 | −0.892403 | ||||||||
\(135\) | 5.83966e15 | 0.0529319 | ||||||||
\(136\) | − | 1.22744e17i | − | 1.04879i | ||||||
\(137\) | 5.85495e16 | 0.471801 | 0.235900 | − | 0.971777i | \(-0.424196\pi\) | ||||
0.235900 | + | 0.971777i | \(0.424196\pi\) | |||||||
\(138\) | − | 2.94826e16i | − | 0.224147i | ||||||
\(139\) | − | 6.49021e16i | − | 0.465737i | −0.972508 | − | 0.232868i | \(-0.925189\pi\) | ||
0.972508 | − | 0.232868i | \(-0.0748111\pi\) | |||||||
\(140\) | −1.49200e16 | + | 2.30254e15i | −0.101099 | + | 0.0156021i | ||||
\(141\) | −3.71989e15 | −0.0238109 | ||||||||
\(142\) | −2.83963e17 | −1.71773 | ||||||||
\(143\) | − | 2.03990e17i | − | 1.16660i | ||||||
\(144\) | 8.88363e15 | 0.0480497 | ||||||||
\(145\) | − | 1.73672e16i | − | 0.0888760i | ||||||
\(146\) | 5.21665e17i | 2.52679i | ||||||||
\(147\) | 7.49239e16 | + | 2.36965e17i | 0.343622 | + | 1.08679i | ||||
\(148\) | 4.94484e17 | 2.14812 | ||||||||
\(149\) | −2.20489e17 | −0.907605 | −0.453802 | − | 0.891102i | \(-0.649933\pi\) | ||||
−0.453802 | + | 0.891102i | \(0.649933\pi\) | |||||||
\(150\) | 4.63865e17i | 1.80993i | ||||||||
\(151\) | 4.42629e16 | 0.163766 | 0.0818831 | − | 0.996642i | \(-0.473907\pi\) | ||||
0.0818831 | + | 0.996642i | \(0.473907\pi\) | |||||||
\(152\) | 3.66688e17i | 1.28691i | ||||||||
\(153\) | − | 1.08652e17i | − | 0.361831i | ||||||
\(154\) | −9.28861e16 | − | 6.01885e17i | −0.293620 | − | 1.90260i | ||||
\(155\) | 2.04077e16 | 0.0612550 | ||||||||
\(156\) | −5.96496e17 | −1.70063 | ||||||||
\(157\) | − | 3.29112e17i | − | 0.891550i | −0.895145 | − | 0.445775i | \(-0.852928\pi\) | ||
0.895145 | − | 0.445775i | \(-0.147072\pi\) | |||||||
\(158\) | 4.14117e16 | 0.106627 | ||||||||
\(159\) | − | 3.40619e17i | − | 0.833857i | ||||||
\(160\) | 3.19714e16i | 0.0744392i | ||||||||
\(161\) | −8.48972e15 | − | 5.50119e16i | −0.0188056 | − | 0.121857i | ||||
\(162\) | 9.15220e17 | 1.92933 | ||||||||
\(163\) | −2.26747e17 | −0.455030 | −0.227515 | − | 0.973775i | \(-0.573060\pi\) | ||||
−0.227515 | + | 0.973775i | \(0.573060\pi\) | |||||||
\(164\) | 2.19314e16i | 0.0419097i | ||||||||
\(165\) | 5.00854e16 | 0.0911674 | ||||||||
\(166\) | − | 3.78525e17i | − | 0.656492i | ||||||
\(167\) | 7.85584e17i | 1.29856i | 0.760551 | + | 0.649278i | \(0.224929\pi\) | ||||
−0.760551 | + | 0.649278i | \(0.775071\pi\) | |||||||
\(168\) | −6.19913e17 | + | 9.56682e16i | −0.976914 | + | 0.150763i | ||||
\(169\) | 4.38432e16 | 0.0658883 | ||||||||
\(170\) | 8.91594e16 | 0.127813 | ||||||||
\(171\) | 3.24589e17i | 0.443981i | ||||||||
\(172\) | 5.65132e17 | 0.737773 | ||||||||
\(173\) | 2.44552e17i | 0.304791i | 0.988320 | + | 0.152395i | \(0.0486987\pi\) | ||||
−0.988320 | + | 0.152395i | \(0.951301\pi\) | |||||||
\(174\) | − | 2.04866e18i | − | 2.43824i | ||||||
\(175\) | 1.33573e17 | + | 8.65530e17i | 0.151850 | + | 0.983961i | ||||
\(176\) | −1.78470e17 | −0.193850 | ||||||||
\(177\) | −8.17603e17 | −0.848704 | ||||||||
\(178\) | − | 1.08983e18i | − | 1.08143i | ||||||
\(179\) | 2.04826e18 | 1.94340 | 0.971698 | − | 0.236227i | \(-0.0759110\pi\) | ||||
0.971698 | + | 0.236227i | \(0.0759110\pi\) | |||||||
\(180\) | − | 3.37275e16i | − | 0.0306058i | ||||||
\(181\) | − | 2.67477e16i | − | 0.0232198i | −0.999933 | − | 0.0116099i | \(-0.996304\pi\) | ||
0.999933 | − | 0.0116099i | \(-0.00369563\pi\) | |||||||
\(182\) | −1.83399e18 | + | 2.83031e17i | −1.52344 | + | 0.235105i | ||||
\(183\) | −2.70173e18 | −2.14799 | ||||||||
\(184\) | 1.40486e17 | 0.106928 | ||||||||
\(185\) | 1.26514e17i | 0.0922071i | ||||||||
\(186\) | 2.40734e18 | 1.68048 | ||||||||
\(187\) | 2.18280e18i | 1.45976i | ||||||||
\(188\) | − | 5.03244e16i | − | 0.0322489i | ||||||
\(189\) | 1.28535e18 | − | 1.98361e17i | 0.789451 | − | 0.121832i | ||||
\(190\) | −2.66356e17 | −0.156832 | ||||||||
\(191\) | 2.28035e18 | 1.28746 | 0.643731 | − | 0.765252i | \(-0.277386\pi\) | ||||
0.643731 | + | 0.765252i | \(0.277386\pi\) | |||||||
\(192\) | 3.43335e18i | 1.85913i | ||||||||
\(193\) | 1.10363e17 | 0.0573278 | 0.0286639 | − | 0.999589i | \(-0.490875\pi\) | ||||
0.0286639 | + | 0.999589i | \(0.490875\pi\) | |||||||
\(194\) | − | 2.72793e18i | − | 1.35962i | ||||||
\(195\) | − | 1.52614e17i | − | 0.0729990i | ||||||
\(196\) | −3.20578e18 | + | 1.01361e18i | −1.47192 | + | 0.465394i | ||||
\(197\) | −3.51439e18 | −1.54925 | −0.774624 | − | 0.632422i | \(-0.782061\pi\) | ||||
−0.774624 | + | 0.632422i | \(0.782061\pi\) | |||||||
\(198\) | 1.36059e18 | 0.575979 | ||||||||
\(199\) | 2.37297e18i | 0.964868i | 0.875932 | + | 0.482434i | \(0.160247\pi\) | ||||
−0.875932 | + | 0.482434i | \(0.839753\pi\) | |||||||
\(200\) | −2.21034e18 | −0.863415 | ||||||||
\(201\) | − | 1.69914e18i | − | 0.637765i | ||||||
\(202\) | 5.06286e18i | 1.82636i | ||||||||
\(203\) | −5.89927e17 | − | 3.82262e18i | −0.204564 | − | 1.32554i | ||||
\(204\) | 6.38280e18 | 2.12799 | ||||||||
\(205\) | −5.61114e15 | −0.00179895 | ||||||||
\(206\) | − | 6.85057e18i | − | 2.11246i | ||||||
\(207\) | 1.24357e17 | 0.0368900 | ||||||||
\(208\) | 5.43812e17i | 0.155218i | ||||||||
\(209\) | − | 6.52092e18i | − | 1.79118i | ||||||
\(210\) | −6.94920e16 | − | 4.50295e17i | −0.0183730 | − | 0.119054i | ||||
\(211\) | 1.78169e18 | 0.453494 | 0.226747 | − | 0.973954i | \(-0.427191\pi\) | ||||
0.226747 | + | 0.973954i | \(0.427191\pi\) | |||||||
\(212\) | 4.60805e18 | 1.12935 | ||||||||
\(213\) | − | 5.20105e18i | − | 1.22759i | ||||||
\(214\) | −7.35194e18 | −1.67144 | ||||||||
\(215\) | 1.44589e17i | 0.0316686i | ||||||||
\(216\) | 3.28244e18i | 0.692735i | ||||||||
\(217\) | 4.49187e18 | − | 6.93210e17i | 0.913586 | − | 0.140989i | ||||
\(218\) | 3.70570e17 | 0.0726471 | ||||||||
\(219\) | −9.55480e18 | −1.80580 | ||||||||
\(220\) | 6.77579e17i | 0.123475i | ||||||||
\(221\) | 6.65113e18 | 1.16885 | ||||||||
\(222\) | 1.49238e19i | 2.52963i | ||||||||
\(223\) | 7.19769e18i | 1.17694i | 0.808519 | + | 0.588470i | \(0.200269\pi\) | ||||
−0.808519 | + | 0.588470i | \(0.799731\pi\) | |||||||
\(224\) | 1.08600e18 | + | 7.03710e18i | 0.171335 | + | 1.11022i | ||||
\(225\) | −1.95658e18 | −0.297877 | ||||||||
\(226\) | −2.96755e18 | −0.436044 | ||||||||
\(227\) | 6.89000e18i | 0.977265i | 0.872490 | + | 0.488633i | \(0.162504\pi\) | ||||
−0.872490 | + | 0.488633i | \(0.837496\pi\) | |||||||
\(228\) | −1.90681e19 | −2.61113 | ||||||||
\(229\) | − | 1.04660e19i | − | 1.38387i | −0.721960 | − | 0.691934i | \(-0.756759\pi\) | ||
0.721960 | − | 0.691934i | \(-0.243241\pi\) | |||||||
\(230\) | 1.02047e17i | 0.0130310i | ||||||||
\(231\) | 1.10241e19 | − | 1.70130e18i | 1.35971 | − | 0.209838i | ||||
\(232\) | 9.76200e18 | 1.16315 | ||||||||
\(233\) | 5.39492e18 | 0.621066 | 0.310533 | − | 0.950563i | \(-0.399492\pi\) | ||||
0.310533 | + | 0.950563i | \(0.399492\pi\) | |||||||
\(234\) | − | 4.14583e18i | − | 0.461195i | ||||||
\(235\) | 1.28755e16 | 0.00138427 | ||||||||
\(236\) | − | 1.10609e19i | − | 1.14946i | ||||||
\(237\) | 7.58495e17i | 0.0762020i | ||||||||
\(238\) | 1.96245e19 | − | 3.02856e18i | 1.90627 | − | 0.294185i | ||||
\(239\) | −1.56767e19 | −1.47256 | −0.736279 | − | 0.676678i | \(-0.763419\pi\) | ||||
−0.736279 | + | 0.676678i | \(0.763419\pi\) | |||||||
\(240\) | −1.33521e17 | −0.0121300 | ||||||||
\(241\) | 1.10188e19i | 0.968270i | 0.874993 | + | 0.484135i | \(0.160866\pi\) | ||||
−0.874993 | + | 0.484135i | \(0.839134\pi\) | |||||||
\(242\) | −8.57290e18 | −0.728794 | ||||||||
\(243\) | 7.05164e18i | 0.580016i | ||||||||
\(244\) | − | 3.65503e19i | − | 2.90919i | ||||||
\(245\) | −2.59331e17 | − | 8.20199e17i | −0.0199768 | − | 0.0631816i | ||||
\(246\) | −6.61902e17 | −0.0493529 | ||||||||
\(247\) | −1.98697e19 | −1.43422 | ||||||||
\(248\) | 1.14711e19i | 0.801662i | ||||||||
\(249\) | 6.93305e18 | 0.469169 | ||||||||
\(250\) | − | 3.21820e18i | − | 0.210908i | ||||||
\(251\) | 8.64238e18i | 0.548584i | 0.961646 | + | 0.274292i | \(0.0884435\pi\) | ||||
−0.961646 | + | 0.274292i | \(0.911556\pi\) | |||||||
\(252\) | −1.14565e18 | − | 7.42363e18i | −0.0704449 | − | 0.456470i | ||||
\(253\) | −2.49831e18 | −0.148827 | ||||||||
\(254\) | 3.91636e19 | 2.26054 | ||||||||
\(255\) | 1.63304e18i | 0.0913430i | ||||||||
\(256\) | −1.33976e19 | −0.726284 | ||||||||
\(257\) | − | 2.02542e19i | − | 1.06427i | −0.846661 | − | 0.532133i | \(-0.821391\pi\) | ||
0.846661 | − | 0.532133i | \(-0.178609\pi\) | |||||||
\(258\) | 1.70560e19i | 0.868801i | ||||||||
\(259\) | 4.29742e18 | + | 2.78465e19i | 0.212231 | + | 1.37522i | ||||
\(260\) | 2.06463e18 | 0.0988680 | ||||||||
\(261\) | 8.64124e18 | 0.401284 | ||||||||
\(262\) | − | 2.91432e19i | − | 1.31258i | ||||||
\(263\) | −1.07807e19 | −0.470977 | −0.235488 | − | 0.971877i | \(-0.575669\pi\) | ||||
−0.235488 | + | 0.971877i | \(0.575669\pi\) | |||||||
\(264\) | 2.81528e19i | 1.19314i | ||||||||
\(265\) | 1.17897e18i | 0.0484770i | ||||||||
\(266\) | −5.86267e19 | + | 9.04758e18i | −2.33907 | + | 0.360977i | ||||
\(267\) | 1.99613e19 | 0.772856 | ||||||||
\(268\) | 2.29868e19 | 0.863773 | ||||||||
\(269\) | − | 2.06012e19i | − | 0.751404i | −0.926741 | − | 0.375702i | \(-0.877402\pi\) | ||
0.926741 | − | 0.375702i | \(-0.122598\pi\) | |||||||
\(270\) | −2.38432e18 | −0.0844217 | ||||||||
\(271\) | 1.74826e19i | 0.600970i | 0.953787 | + | 0.300485i | \(0.0971485\pi\) | ||||
−0.953787 | + | 0.300485i | \(0.902852\pi\) | |||||||
\(272\) | − | 5.81904e18i | − | 0.194223i | ||||||
\(273\) | −5.18398e18 | − | 3.35912e19i | −0.168020 | − | 1.08874i | ||||
\(274\) | −2.39056e19 | −0.752481 | ||||||||
\(275\) | 3.93072e19 | 1.20174 | ||||||||
\(276\) | 7.30541e18i | 0.216956i | ||||||||
\(277\) | −1.37674e19 | −0.397204 | −0.198602 | − | 0.980080i | \(-0.563640\pi\) | ||||
−0.198602 | + | 0.980080i | \(0.563640\pi\) | |||||||
\(278\) | 2.64994e19i | 0.742809i | ||||||||
\(279\) | 1.01541e19i | 0.276572i | ||||||||
\(280\) | 2.14568e18 | − | 3.31133e17i | 0.0567938 | − | 0.00876472i | ||||
\(281\) | −3.60798e19 | −0.928141 | −0.464071 | − | 0.885798i | \(-0.653612\pi\) | ||||
−0.464071 | + | 0.885798i | \(0.653612\pi\) | |||||||
\(282\) | 1.51882e18 | 0.0379764 | ||||||||
\(283\) | 3.17753e19i | 0.772323i | 0.922431 | + | 0.386161i | \(0.126199\pi\) | ||||
−0.922431 | + | 0.386161i | \(0.873801\pi\) | |||||||
\(284\) | 7.03622e19 | 1.66262 | ||||||||
\(285\) | − | 4.87857e18i | − | 0.112082i | ||||||
\(286\) | 8.32888e19i | 1.86062i | ||||||||
\(287\) | −1.23505e18 | + | 1.90599e17i | −0.0268305 | + | 0.00414062i | ||||
\(288\) | −1.59077e19 | −0.336100 | ||||||||
\(289\) | −2.25091e19 | −0.462567 | ||||||||
\(290\) | 7.09097e18i | 0.141749i | ||||||||
\(291\) | 4.99646e19 | 0.971669 | ||||||||
\(292\) | − | 1.29262e20i | − | 2.44572i | ||||||
\(293\) | − | 6.40161e18i | − | 0.117855i | −0.998262 | − | 0.0589275i | \(-0.981232\pi\) | ||
0.998262 | − | 0.0589275i | \(-0.0187681\pi\) | |||||||
\(294\) | −3.05912e19 | − | 9.67523e19i | −0.548048 | − | 1.73334i | ||||
\(295\) | 2.82994e18 | 0.0493402 | ||||||||
\(296\) | −7.11129e19 | −1.20674 | ||||||||
\(297\) | − | 5.83727e19i | − | 0.964181i | ||||||
\(298\) | 9.00251e19 | 1.44755 | ||||||||
\(299\) | 7.61253e18i | 0.119168i | ||||||||
\(300\) | − | 1.14940e20i | − | 1.75186i | ||||||
\(301\) | 4.91140e18 | + | 3.18250e19i | 0.0728909 | + | 0.472320i | ||||
\(302\) | −1.80724e19 | −0.261193 | ||||||||
\(303\) | −9.27312e19 | −1.30522 | ||||||||
\(304\) | 1.73839e19i | 0.238319i | ||||||||
\(305\) | 9.35139e18 | 0.124876 | ||||||||
\(306\) | 4.43623e19i | 0.577089i | ||||||||
\(307\) | − | 5.38516e19i | − | 0.682483i | −0.939976 | − | 0.341241i | \(-0.889153\pi\) | ||
0.939976 | − | 0.341241i | \(-0.110847\pi\) | |||||||
\(308\) | 2.30160e19 | + | 1.49139e20i | 0.284200 | + | 1.84156i | ||||
\(309\) | 1.25475e20 | 1.50969 | ||||||||
\(310\) | −8.33243e18 | −0.0976963 | ||||||||
\(311\) | 2.58213e18i | 0.0295049i | 0.999891 | + | 0.0147525i | \(0.00469603\pi\) | ||||
−0.999891 | + | 0.0147525i | \(0.995304\pi\) | |||||||
\(312\) | 8.57835e19 | 0.955360 | ||||||||
\(313\) | 1.59989e20i | 1.73674i | 0.495916 | + | 0.868371i | \(0.334832\pi\) | ||||
−0.495916 | + | 0.868371i | \(0.665168\pi\) | |||||||
\(314\) | 1.34375e20i | 1.42194i | ||||||||
\(315\) | 1.89934e18 | − | 2.93116e17i | 0.0195938 | − | 0.00302381i | ||||
\(316\) | −1.02613e19 | −0.103206 | ||||||||
\(317\) | −1.54925e20 | −1.51931 | −0.759654 | − | 0.650327i | \(-0.774632\pi\) | ||||
−0.759654 | + | 0.650327i | \(0.774632\pi\) | |||||||
\(318\) | 1.39074e20i | 1.32993i | ||||||||
\(319\) | −1.73601e20 | −1.61892 | ||||||||
\(320\) | − | 1.18837e19i | − | 0.108082i | ||||||
\(321\) | − | 1.34658e20i | − | 1.19452i | ||||||
\(322\) | 3.46633e18 | + | 2.24612e19i | 0.0299932 | + | 0.194351i | ||||
\(323\) | 2.12615e20 | 1.79463 | ||||||||
\(324\) | −2.26780e20 | −1.86743 | ||||||||
\(325\) | − | 1.19772e20i | − | 0.962251i | ||||||
\(326\) | 9.25801e19 | 0.725733 | ||||||||
\(327\) | 6.78734e18i | 0.0519180i | ||||||||
\(328\) | − | 3.15400e18i | − | 0.0235435i | ||||||
\(329\) | 2.83398e18 | − | 4.37354e17i | 0.0206457 | − | 0.00318615i | ||||
\(330\) | −2.04497e19 | −0.145404 | ||||||||
\(331\) | 1.34757e20 | 0.935250 | 0.467625 | − | 0.883927i | \(-0.345110\pi\) | ||||
0.467625 | + | 0.883927i | \(0.345110\pi\) | |||||||
\(332\) | 9.37935e19i | 0.635431i | ||||||||
\(333\) | −6.29485e19 | −0.416324 | ||||||||
\(334\) | − | 3.20752e20i | − | 2.07108i | ||||||
\(335\) | 5.88117e18i | 0.0370771i | ||||||||
\(336\) | −2.93888e19 | + | 4.53544e18i | −0.180912 | + | 0.0279193i | ||||
\(337\) | 3.14834e20 | 1.89253 | 0.946263 | − | 0.323397i | \(-0.104825\pi\) | ||||
0.946263 | + | 0.323397i | \(0.104825\pi\) | |||||||
\(338\) | −1.79011e19 | −0.105086 | ||||||||
\(339\) | − | 5.43535e19i | − | 0.311623i | ||||||
\(340\) | −2.20925e19 | −0.123713 | ||||||||
\(341\) | − | 2.03994e20i | − | 1.11579i | ||||||
\(342\) | − | 1.32529e20i | − | 0.708111i | ||||||
\(343\) | −8.49409e19 | − | 1.71722e20i | −0.443367 | − | 0.896340i | ||||
\(344\) | −8.12729e19 | −0.414456 | ||||||||
\(345\) | −1.86909e18 | −0.00931275 | ||||||||
\(346\) | − | 9.98499e19i | − | 0.486115i | ||||||
\(347\) | −5.16019e19 | −0.245488 | −0.122744 | − | 0.992438i | \(-0.539169\pi\) | ||||
−0.122744 | + | 0.992438i | \(0.539169\pi\) | |||||||
\(348\) | 5.07633e20i | 2.36002i | ||||||||
\(349\) | 3.15723e20i | 1.43451i | 0.696813 | + | 0.717253i | \(0.254601\pi\) | ||||
−0.696813 | + | 0.717253i | \(0.745399\pi\) | |||||||
\(350\) | −5.45376e19 | − | 3.53394e20i | −0.242187 | − | 1.56933i | ||||
\(351\) | −1.77866e20 | −0.772033 | ||||||||
\(352\) | 3.19583e20 | 1.35595 | ||||||||
\(353\) | 1.58851e20i | 0.658859i | 0.944180 | + | 0.329430i | \(0.106856\pi\) | ||||
−0.944180 | + | 0.329430i | \(0.893144\pi\) | |||||||
\(354\) | 3.33825e20 | 1.35361 | ||||||||
\(355\) | 1.80022e19i | 0.0713672i | ||||||||
\(356\) | 2.70046e20i | 1.04674i | ||||||||
\(357\) | 5.54710e19 | + | 3.59442e20i | 0.210242 | + | 1.36233i | ||||
\(358\) | −8.36300e20 | −3.09954 | ||||||||
\(359\) | −2.20331e20 | −0.798584 | −0.399292 | − | 0.916824i | \(-0.630744\pi\) | ||||
−0.399292 | + | 0.916824i | \(0.630744\pi\) | |||||||
\(360\) | 4.85043e18i | 0.0171933i | ||||||||
\(361\) | −3.46730e20 | −1.20208 | ||||||||
\(362\) | 1.09210e19i | 0.0370335i | ||||||||
\(363\) | − | 1.57021e20i | − | 0.520840i | ||||||
\(364\) | 4.54438e20 | − | 7.01313e19i | 1.47456 | − | 0.227563i | ||||
\(365\) | 3.30717e19 | 0.104982 | ||||||||
\(366\) | 1.10311e21 | 3.42586 | ||||||||
\(367\) | − | 2.42153e20i | − | 0.735804i | −0.929865 | − | 0.367902i | \(-0.880076\pi\) | ||
0.929865 | − | 0.367902i | \(-0.119924\pi\) | |||||||
\(368\) | 6.66017e18 | 0.0198017 | ||||||||
\(369\) | − | 2.79189e18i | − | 0.00812246i | ||||||
\(370\) | − | 5.16553e19i | − | 0.147062i | ||||||
\(371\) | 4.00472e19 | + | 2.59499e20i | 0.111579 | + | 0.723010i | ||||
\(372\) | −5.96507e20 | −1.62657 | ||||||||
\(373\) | 1.57395e20 | 0.420070 | 0.210035 | − | 0.977694i | \(-0.432642\pi\) | ||||
0.210035 | + | 0.977694i | \(0.432642\pi\) | |||||||
\(374\) | − | 8.91230e20i | − | 2.32818i | ||||||
\(375\) | 5.89445e19 | 0.150728 | ||||||||
\(376\) | 7.23726e18i | 0.0181164i | ||||||||
\(377\) | 5.28974e20i | 1.29629i | ||||||||
\(378\) | −5.24803e20 | + | 8.09904e19i | −1.25911 | + | 0.194312i | ||||
\(379\) | 3.11365e20 | 0.731402 | 0.365701 | − | 0.930732i | \(-0.380829\pi\) | ||||
0.365701 | + | 0.930732i | \(0.380829\pi\) | |||||||
\(380\) | 6.59996e19 | 0.151800 | ||||||||
\(381\) | 7.17319e20i | 1.61552i | ||||||||
\(382\) | −9.31061e20 | −2.05339 | ||||||||
\(383\) | 1.87875e20i | 0.405770i | 0.979203 | + | 0.202885i | \(0.0650318\pi\) | ||||
−0.979203 | + | 0.202885i | \(0.934968\pi\) | |||||||
\(384\) | − | 7.96479e20i | − | 1.68471i | ||||||
\(385\) | −3.81573e19 | + | 5.88864e18i | −0.0790482 | + | 0.0121991i | ||||
\(386\) | −4.50610e19 | −0.0914328 | ||||||||
\(387\) | −7.19421e19 | −0.142987 | ||||||||
\(388\) | 6.75945e20i | 1.31600i | ||||||||
\(389\) | 1.12070e20 | 0.213744 | 0.106872 | − | 0.994273i | \(-0.465917\pi\) | ||||
0.106872 | + | 0.994273i | \(0.465917\pi\) | |||||||
\(390\) | 6.23118e19i | 0.116427i | ||||||||
\(391\) | − | 8.14577e19i | − | 0.149114i | ||||||
\(392\) | 4.61030e20 | − | 1.45769e20i | 0.826876 | − | 0.261442i | ||||
\(393\) | 5.33785e20 | 0.938050 | ||||||||
\(394\) | 1.43492e21 | 2.47091 | ||||||||
\(395\) | − | 2.62535e18i | − | 0.00443007i | ||||||
\(396\) | −3.37137e20 | −0.557501 | ||||||||
\(397\) | − | 6.53675e20i | − | 1.05935i | −0.848202 | − | 0.529673i | \(-0.822315\pi\) | ||
0.848202 | − | 0.529673i | \(-0.177685\pi\) | |||||||
\(398\) | − | 9.68878e20i | − | 1.53888i | ||||||
\(399\) | −1.65715e20 | − | 1.07380e21i | −0.257976 | − | 1.67164i | ||||
\(400\) | −1.04788e20 | −0.159894 | ||||||||
\(401\) | −1.04007e21 | −1.55564 | −0.777818 | − | 0.628489i | \(-0.783674\pi\) | ||||
−0.777818 | + | 0.628489i | \(0.783674\pi\) | |||||||
\(402\) | 6.93755e20i | 1.01718i | ||||||||
\(403\) | −6.21585e20 | −0.893429 | ||||||||
\(404\) | − | 1.25451e21i | − | 1.76776i | ||||||
\(405\) | − | 5.80216e19i | − | 0.0801585i | ||||||
\(406\) | 2.40866e20 | + | 1.56077e21i | 0.326262 | + | 2.11412i | ||||
\(407\) | 1.26462e21 | 1.67960 | ||||||||
\(408\) | −9.17924e20 | −1.19543 | ||||||||
\(409\) | − | 6.01406e19i | − | 0.0768036i | −0.999262 | − | 0.0384018i | \(-0.987773\pi\) | ||
0.999262 | − | 0.0384018i | \(-0.0122267\pi\) | |||||||
\(410\) | 2.29101e18 | 0.00286917 | ||||||||
\(411\) | − | 4.37855e20i | − | 0.537768i | ||||||
\(412\) | 1.69748e21i | 2.04469i | ||||||||
\(413\) | 6.22887e20 | − | 9.61272e19i | 0.735883 | − | 0.113565i | ||||
\(414\) | −5.07748e19 | −0.0588363 | ||||||||
\(415\) | −2.39971e19 | −0.0272756 | ||||||||
\(416\) | − | 9.73793e20i | − | 1.08573i | ||||||
\(417\) | −4.85361e20 | −0.530856 | ||||||||
\(418\) | 2.66248e21i | 2.85677i | ||||||||
\(419\) | − | 1.48142e21i | − | 1.55943i | −0.626132 | − | 0.779717i | \(-0.715363\pi\) | ||
0.626132 | − | 0.779717i | \(-0.284637\pi\) | |||||||
\(420\) | 1.72192e19 | + | 1.11577e20i | 0.0177836 | + | 0.115234i | ||||
\(421\) | −8.00717e20 | −0.811377 | −0.405688 | − | 0.914011i | \(-0.632968\pi\) | ||||
−0.405688 | + | 0.914011i | \(0.632968\pi\) | |||||||
\(422\) | −7.27458e20 | −0.723283 | ||||||||
\(423\) | 6.40636e18i | 0.00625012i | ||||||||
\(424\) | −6.62694e20 | −0.634433 | ||||||||
\(425\) | 1.28162e21i | 1.20406i | ||||||||
\(426\) | 2.12358e21i | 1.95790i | ||||||||
\(427\) | 2.05830e21 | − | 3.17648e20i | 1.86245 | − | 0.287424i | ||||
\(428\) | 1.82172e21 | 1.61782 | ||||||||
\(429\) | −1.52551e21 | −1.32971 | ||||||||
\(430\) | − | 5.90354e19i | − | 0.0505086i | ||||||
\(431\) | 9.39265e20 | 0.788805 | 0.394403 | − | 0.918938i | \(-0.370952\pi\) | ||||
0.394403 | + | 0.918938i | \(0.370952\pi\) | |||||||
\(432\) | 1.55614e20i | 0.128286i | ||||||||
\(433\) | − | 8.56977e20i | − | 0.693531i | −0.937952 | − | 0.346766i | \(-0.887280\pi\) | ||
0.937952 | − | 0.346766i | \(-0.112720\pi\) | |||||||
\(434\) | −1.83402e21 | + | 2.83036e20i | −1.45709 | + | 0.224866i | ||||
\(435\) | −1.29878e20 | −0.101303 | ||||||||
\(436\) | −9.18224e19 | −0.0703164 | ||||||||
\(437\) | 2.43348e20i | 0.182969i | ||||||||
\(438\) | 3.90120e21 | 2.88009 | ||||||||
\(439\) | − | 9.40472e20i | − | 0.681757i | −0.940107 | − | 0.340879i | \(-0.889275\pi\) | ||
0.940107 | − | 0.340879i | \(-0.110725\pi\) | |||||||
\(440\) | − | 9.74441e19i | − | 0.0693640i | ||||||
\(441\) | 4.08100e20 | − | 1.29033e20i | 0.285271 | − | 0.0901972i | ||||
\(442\) | −2.71564e21 | −1.86421 | ||||||||
\(443\) | −2.61949e21 | −1.76598 | −0.882991 | − | 0.469390i | \(-0.844474\pi\) | ||||
−0.882991 | + | 0.469390i | \(0.844474\pi\) | |||||||
\(444\) | − | 3.69793e21i | − | 2.44847i | ||||||
\(445\) | −6.90913e19 | −0.0449307 | ||||||||
\(446\) | − | 2.93880e21i | − | 1.87712i | ||||||
\(447\) | 1.64890e21i | 1.03451i | ||||||||
\(448\) | −4.03666e20 | − | 2.61568e21i | −0.248770 | − | 1.61199i | ||||
\(449\) | −2.75819e20 | −0.166976 | −0.0834879 | − | 0.996509i | \(-0.526606\pi\) | ||||
−0.0834879 | + | 0.996509i | \(0.526606\pi\) | |||||||
\(450\) | 7.98865e20 | 0.475087 | ||||||||
\(451\) | 5.60885e19i | 0.0327689i | ||||||||
\(452\) | 7.35319e20 | 0.422054 | ||||||||
\(453\) | − | 3.31014e20i | − | 0.186664i | ||||||
\(454\) | − | 2.81317e21i | − | 1.55865i | ||||||
\(455\) | 1.79431e19 | + | 1.16268e20i | 0.00976802 | + | 0.0632950i | ||||
\(456\) | 2.74222e21 | 1.46684 | ||||||||
\(457\) | 2.49048e21 | 1.30904 | 0.654520 | − | 0.756044i | \(-0.272871\pi\) | ||||
0.654520 | + | 0.756044i | \(0.272871\pi\) | |||||||
\(458\) | 4.27322e21i | 2.20715i | ||||||||
\(459\) | 1.90325e21 | 0.966038 | ||||||||
\(460\) | − | 2.52859e19i | − | 0.0126129i | ||||||
\(461\) | 3.69003e21i | 1.80893i | 0.426545 | + | 0.904466i | \(0.359730\pi\) | ||||
−0.426545 | + | 0.904466i | \(0.640270\pi\) | |||||||
\(462\) | −4.50112e21 | + | 6.94636e20i | −2.16862 | + | 0.334674i | ||||
\(463\) | −3.06537e20 | −0.145156 | −0.0725780 | − | 0.997363i | \(-0.523123\pi\) | ||||
−0.0725780 | + | 0.997363i | \(0.523123\pi\) | |||||||
\(464\) | 4.62797e20 | 0.215400 | ||||||||
\(465\) | − | 1.52617e20i | − | 0.0698197i | ||||||
\(466\) | −2.20273e21 | −0.990546 | ||||||||
\(467\) | 3.86462e21i | 1.70833i | 0.520002 | + | 0.854165i | \(0.325931\pi\) | ||||
−0.520002 | + | 0.854165i | \(0.674069\pi\) | |||||||
\(468\) | 1.02728e21i | 0.446398i | ||||||||
\(469\) | 1.99771e20 | + | 1.29448e21i | 0.0853396 | + | 0.552985i | ||||
\(470\) | −5.25703e18 | −0.00220779 | ||||||||
\(471\) | −2.46122e21 | −1.01621 | ||||||||
\(472\) | 1.59069e21i | 0.645730i | ||||||||
\(473\) | 1.44530e21 | 0.576859 | ||||||||
\(474\) | − | 3.09692e20i | − | 0.121535i | ||||||
\(475\) | − | 3.82873e21i | − | 1.47743i | ||||||
\(476\) | −4.86270e21 | + | 7.50438e20i | −1.84511 | + | 0.284747i | ||||
\(477\) | −5.86611e20 | −0.218879 | ||||||||
\(478\) | 6.40077e21 | 2.34860 | ||||||||
\(479\) | 2.80191e21i | 1.01105i | 0.862813 | + | 0.505523i | \(0.168700\pi\) | ||||
−0.862813 | + | 0.505523i | \(0.831300\pi\) | |||||||
\(480\) | 2.39094e20 | 0.0848473 | ||||||||
\(481\) | − | 3.85339e21i | − | 1.34488i | ||||||
\(482\) | − | 4.49893e21i | − | 1.54431i | ||||||
\(483\) | −4.11399e20 | + | 6.34892e19i | −0.138895 | + | 0.0214350i | ||||
\(484\) | 2.12425e21 | 0.705413 | ||||||||
\(485\) | −1.72941e20 | −0.0564889 | ||||||||
\(486\) | − | 2.87917e21i | − | 0.925075i | ||||||
\(487\) | −2.42694e21 | −0.767058 | −0.383529 | − | 0.923529i | \(-0.625291\pi\) | ||||
−0.383529 | + | 0.923529i | \(0.625291\pi\) | |||||||
\(488\) | 5.25637e21i | 1.63428i | ||||||||
\(489\) | 1.69569e21i | 0.518652i | ||||||||
\(490\) | 1.05884e20 | + | 3.34885e20i | 0.0318612 | + | 0.100769i | ||||
\(491\) | −3.73522e21 | −1.10577 | −0.552884 | − | 0.833258i | \(-0.686473\pi\) | ||||
−0.552884 | + | 0.833258i | \(0.686473\pi\) | |||||||
\(492\) | 1.64011e20 | 0.0477695 | ||||||||
\(493\) | − | 5.66027e21i | − | 1.62204i | ||||||
\(494\) | 8.11275e21 | 2.28746 | ||||||||
\(495\) | − | 8.62567e19i | − | 0.0239305i | ||||||
\(496\) | 5.43822e20i | 0.148458i | ||||||||
\(497\) | 6.11498e20 | + | 3.96240e21i | 0.164265 | + | 1.06440i | ||||
\(498\) | −2.83074e21 | −0.748283 | ||||||||
\(499\) | −2.75957e21 | −0.717855 | −0.358928 | − | 0.933365i | \(-0.616857\pi\) | ||||
−0.358928 | + | 0.933365i | \(0.616857\pi\) | |||||||
\(500\) | 7.97428e20i | 0.204142i | ||||||||
\(501\) | 5.87488e21 | 1.48012 | ||||||||
\(502\) | − | 3.52866e21i | − | 0.874944i | ||||||
\(503\) | − | 1.16453e21i | − | 0.284190i | −0.989853 | − | 0.142095i | \(-0.954616\pi\) | ||
0.989853 | − | 0.142095i | \(-0.0453838\pi\) | |||||||
\(504\) | 1.64759e20 | + | 1.06761e21i | 0.0395736 | + | 0.256430i | ||||
\(505\) | 3.20967e20 | 0.0758804 | ||||||||
\(506\) | 1.02005e21 | 0.237366 | ||||||||
\(507\) | − | 3.27875e20i | − | 0.0751008i | ||||||
\(508\) | −9.70422e21 | −2.18802 | ||||||||
\(509\) | − | 1.91798e21i | − | 0.425697i | −0.977085 | − | 0.212849i | \(-0.931726\pi\) | ||
0.977085 | − | 0.212849i | \(-0.0682742\pi\) | |||||||
\(510\) | − | 6.66766e20i | − | 0.145684i | ||||||
\(511\) | 7.27928e21 | − | 1.12338e21i | 1.56575 | − | 0.241634i | ||||
\(512\) | −1.50968e21 | −0.319686 | ||||||||
\(513\) | −5.68580e21 | −1.18537 | ||||||||
\(514\) | 8.26974e21i | 1.69741i | ||||||||
\(515\) | −4.34301e20 | −0.0877674 | ||||||||
\(516\) | − | 4.22626e21i | − | 0.840928i | ||||||
\(517\) | − | 1.28702e20i | − | 0.0252152i | ||||||
\(518\) | −1.75463e21 | − | 1.13697e22i | −0.338490 | − | 2.19336i | ||||
\(519\) | 1.82885e21 | 0.347407 | ||||||||
\(520\) | −2.96919e20 | −0.0555407 | ||||||||
\(521\) | − | 4.45565e21i | − | 0.820747i | −0.911918 | − | 0.410373i | \(-0.865398\pi\) | ||
0.911918 | − | 0.410373i | \(-0.134602\pi\) | |||||||
\(522\) | −3.52819e21 | −0.640013 | ||||||||
\(523\) | 1.08881e22i | 1.94509i | 0.232708 | + | 0.972547i | \(0.425241\pi\) | ||||
−0.232708 | + | 0.972547i | \(0.574759\pi\) | |||||||
\(524\) | 7.22130e21i | 1.27047i | ||||||||
\(525\) | 6.47275e21 | − | 9.98909e20i | 1.12154 | − | 0.173082i | ||||
\(526\) | 4.40172e21 | 0.751166 | ||||||||
\(527\) | 6.65125e21 | 1.11794 | ||||||||
\(528\) | 1.33467e21i | 0.220954i | ||||||||
\(529\) | −6.03938e21 | −0.984797 | ||||||||
\(530\) | − | 4.81371e20i | − | 0.0773166i | ||||||
\(531\) | 1.40807e21i | 0.222776i | ||||||||
\(532\) | 1.45269e22 | − | 2.24187e21i | 2.26402 | − | 0.349396i | ||||
\(533\) | 1.70906e20 | 0.0262385 | ||||||||
\(534\) | −8.15015e21 | −1.23264 | ||||||||
\(535\) | 4.66086e20i | 0.0694442i | ||||||||
\(536\) | −3.30578e21 | −0.485239 | ||||||||
\(537\) | − | 1.53176e22i | − | 2.21512i | ||||||
\(538\) | 8.41140e21i | 1.19842i | ||||||||
\(539\) | −8.19864e21 | + | 2.59225e21i | −1.15088 | + | 0.363888i | ||||
\(540\) | 5.90803e20 | 0.0817132 | ||||||||
\(541\) | −7.31461e21 | −0.996812 | −0.498406 | − | 0.866944i | \(-0.666081\pi\) | ||||
−0.498406 | + | 0.866944i | \(0.666081\pi\) | |||||||
\(542\) | − | 7.13811e21i | − | 0.958494i | ||||||
\(543\) | −2.00029e20 | −0.0264664 | ||||||||
\(544\) | 1.04201e22i | 1.35856i | ||||||||
\(545\) | − | 2.34928e19i | − | 0.00301830i | ||||||
\(546\) | 2.11660e21 | + | 1.37152e22i | 0.267978 | + | 1.73645i | ||||
\(547\) | 2.34362e21 | 0.292408 | 0.146204 | − | 0.989254i | \(-0.453294\pi\) | ||||
0.146204 | + | 0.989254i | \(0.453294\pi\) | |||||||
\(548\) | 5.92350e21 | 0.728340 | ||||||||
\(549\) | 4.65290e21i | 0.563826i | ||||||||
\(550\) | −1.60490e22 | −1.91667 | ||||||||
\(551\) | 1.69096e22i | 1.99031i | ||||||||
\(552\) | − | 1.05061e21i | − | 0.121879i | ||||||
\(553\) | −8.91778e19 | − | 5.77856e20i | −0.0101966 | − | 0.0660722i | ||||
\(554\) | 5.62120e21 | 0.633506 | ||||||||
\(555\) | 9.46117e20 | 0.105100 | ||||||||
\(556\) | − | 6.56620e21i | − | 0.718978i | ||||||
\(557\) | −6.84087e21 | −0.738362 | −0.369181 | − | 0.929357i | \(-0.620362\pi\) | ||||
−0.369181 | + | 0.929357i | \(0.620362\pi\) | |||||||
\(558\) | − | 4.14590e21i | − | 0.441108i | ||||||
\(559\) | − | 4.40394e21i | − | 0.461899i | ||||||
\(560\) | 1.01722e20 | − | 1.56983e19i | 0.0105175 | − | 0.00162312i | ||||
\(561\) | 1.63237e22 | 1.66386 | ||||||||
\(562\) | 1.47313e22 | 1.48030 | ||||||||
\(563\) | − | 7.20778e21i | − | 0.714059i | −0.934093 | − | 0.357030i | \(-0.883789\pi\) | ||
0.934093 | − | 0.357030i | \(-0.116211\pi\) | |||||||
\(564\) | −3.76344e20 | −0.0367580 | ||||||||
\(565\) | 1.88132e20i | 0.0181165i | ||||||||
\(566\) | − | 1.29738e22i | − | 1.23179i | ||||||
\(567\) | −1.97088e21 | − | 1.27709e22i | −0.184499 | − | 1.19552i | ||||
\(568\) | −1.01189e22 | −0.934004 | ||||||||
\(569\) | 6.81288e20 | 0.0620058 | 0.0310029 | − | 0.999519i | \(-0.490130\pi\) | ||||
0.0310029 | + | 0.999519i | \(0.490130\pi\) | |||||||
\(570\) | 1.99191e21i | 0.178760i | ||||||||
\(571\) | −2.77732e21 | −0.245774 | −0.122887 | − | 0.992421i | \(-0.539215\pi\) | ||||
−0.122887 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(572\) | − | 2.06379e22i | − | 1.80093i | ||||||
\(573\) | − | 1.70533e22i | − | 1.46748i | ||||||
\(574\) | 5.04267e20 | − | 7.78211e19i | 0.0427922 | − | 0.00660393i | ||||
\(575\) | −1.46687e21 | −0.122758 | ||||||||
\(576\) | 5.91289e21 | 0.488000 | ||||||||
\(577\) | − | 1.80819e20i | − | 0.0147176i | −0.999973 | − | 0.00735880i | \(-0.997658\pi\) | ||
0.999973 | − | 0.00735880i | \(-0.00234240\pi\) | |||||||
\(578\) | 9.19040e21 | 0.737754 | ||||||||
\(579\) | − | 8.25335e20i | − | 0.0653434i | ||||||
\(580\) | − | 1.75705e21i | − | 0.137202i | ||||||
\(581\) | −5.28191e21 | + | 8.15132e20i | −0.406801 | + | 0.0627797i | ||||
\(582\) | −2.04004e22 | −1.54973 | ||||||||
\(583\) | 1.17849e22 | 0.883034 | ||||||||
\(584\) | 1.85894e22i | 1.37393i | ||||||||
\(585\) | −2.62830e20 | −0.0191614 | ||||||||
\(586\) | 2.61376e21i | 0.187968i | ||||||||
\(587\) | 6.30905e21i | 0.447568i | 0.974639 | + | 0.223784i | \(0.0718410\pi\) | ||||
−0.974639 | + | 0.223784i | \(0.928159\pi\) | |||||||
\(588\) | 7.58011e21 | + | 2.39740e22i | 0.530465 | + | 1.67773i | ||||
\(589\) | −1.98701e22 | −1.37176 | ||||||||
\(590\) | −1.15546e21 | −0.0786932 | ||||||||
\(591\) | 2.62819e22i | 1.76586i | ||||||||
\(592\) | −3.37132e21 | −0.223473 | ||||||||
\(593\) | − | 1.60991e22i | − | 1.05284i | −0.850224 | − | 0.526421i | \(-0.823534\pi\) | ||
0.850224 | − | 0.526421i | \(-0.176466\pi\) | |||||||
\(594\) | 2.38334e22i | 1.53778i | ||||||||
\(595\) | −1.92000e20 | − | 1.24412e21i | −0.0122226 | − | 0.0792005i | ||||
\(596\) | −2.23070e22 | −1.40111 | ||||||||
\(597\) | 1.77459e22 | 1.09978 | ||||||||
\(598\) | − | 3.10818e21i | − | 0.190063i | ||||||
\(599\) | 1.71308e22 | 1.03362 | 0.516812 | − | 0.856099i | \(-0.327119\pi\) | ||||
0.516812 | + | 0.856099i | \(0.327119\pi\) | |||||||
\(600\) | 1.65297e22i | 0.984139i | ||||||||
\(601\) | 1.53192e22i | 0.899993i | 0.893030 | + | 0.449997i | \(0.148575\pi\) | ||||
−0.893030 | + | 0.449997i | \(0.851425\pi\) | |||||||
\(602\) | −2.00531e21 | − | 1.29941e22i | −0.116255 | − | 0.753309i | ||||
\(603\) | −2.92625e21 | −0.167407 | ||||||||
\(604\) | 4.47811e21 | 0.252813 | ||||||||
\(605\) | 5.43490e20i | 0.0302795i | ||||||||
\(606\) | 3.78619e22 | 2.08172 | ||||||||
\(607\) | 5.15548e21i | 0.279743i | 0.990170 | + | 0.139872i | \(0.0446690\pi\) | ||||
−0.990170 | + | 0.139872i | \(0.955331\pi\) | |||||||
\(608\) | − | 3.11291e22i | − | 1.66701i | ||||||
\(609\) | −2.85869e22 | + | 4.41169e21i | −1.51088 | + | 0.233167i | ||||
\(610\) | −3.81815e21 | −0.199166 | ||||||||
\(611\) | −3.92165e20 | −0.0201902 | ||||||||
\(612\) | − | 1.09924e22i | − | 0.558575i | ||||||
\(613\) | 1.13034e22 | 0.566923 | 0.283462 | − | 0.958984i | \(-0.408517\pi\) | ||||
0.283462 | + | 0.958984i | \(0.408517\pi\) | |||||||
\(614\) | 2.19875e22i | 1.08850i | ||||||||
\(615\) | 4.19621e19i | 0.00205049i | ||||||||
\(616\) | −3.30998e21 | − | 2.14481e22i | −0.159654 | − | 1.03453i | ||||
\(617\) | 2.39769e22 | 1.14159 | 0.570797 | − | 0.821091i | \(-0.306634\pi\) | ||||
0.570797 | + | 0.821091i | \(0.306634\pi\) | |||||||
\(618\) | −5.12310e22 | −2.40783 | ||||||||
\(619\) | − | 3.21184e21i | − | 0.149015i | −0.997220 | − | 0.0745073i | \(-0.976262\pi\) | ||
0.997220 | − | 0.0745073i | \(-0.0237384\pi\) | |||||||
\(620\) | 2.06467e21 | 0.0945620 | ||||||||
\(621\) | 2.17836e21i | 0.0984910i | ||||||||
\(622\) | − | 1.05428e21i | − | 0.0470578i | ||||||
\(623\) | −1.52074e22 | + | 2.34689e21i | −0.670118 | + | 0.103416i | ||||
\(624\) | 4.06682e21 | 0.176921 | ||||||||
\(625\) | 2.29768e22 | 0.986846 | ||||||||
\(626\) | − | 6.53230e22i | − | 2.76995i | ||||||
\(627\) | −4.87658e22 | −2.04162 | ||||||||
\(628\) | − | 3.32965e22i | − | 1.37633i | ||||||
\(629\) | 4.12332e22i | 1.68283i | ||||||||
\(630\) | −7.75495e20 | + | 1.19679e20i | −0.0312503 | + | 0.00482272i | ||||
\(631\) | 9.93900e21 | 0.395465 | 0.197732 | − | 0.980256i | \(-0.436642\pi\) | ||||
0.197732 | + | 0.980256i | \(0.436642\pi\) | |||||||
\(632\) | 1.47570e21 | 0.0579777 | ||||||||
\(633\) | − | 1.33241e22i | − | 0.516902i | ||||||
\(634\) | 6.32553e22 | 2.42316 | ||||||||
\(635\) | − | 2.48283e21i | − | 0.0939197i | ||||||
\(636\) | − | 3.44607e22i | − | 1.28726i | ||||||
\(637\) | 7.89878e21 | + | 2.49818e22i | 0.291370 | + | 0.921529i | ||||
\(638\) | 7.08807e22 | 2.58204 | ||||||||
\(639\) | −8.95721e21 | −0.322230 | ||||||||
\(640\) | 2.75682e21i | 0.0979420i | ||||||||
\(641\) | −3.43710e22 | −1.20594 | −0.602972 | − | 0.797762i | \(-0.706017\pi\) | ||||
−0.602972 | + | 0.797762i | \(0.706017\pi\) | |||||||
\(642\) | 5.49805e22i | 1.90515i | ||||||||
\(643\) | 3.40151e20i | 0.0116408i | 0.999983 | + | 0.00582042i | \(0.00185271\pi\) | ||||
−0.999983 | + | 0.00582042i | \(0.998147\pi\) | |||||||
\(644\) | −8.58912e20 | − | 5.56559e21i | −0.0290310 | − | 0.188115i | ||||
\(645\) | 1.08129e21 | 0.0360965 | ||||||||
\(646\) | −8.68103e22 | −2.86227 | ||||||||
\(647\) | 3.80798e22i | 1.24011i | 0.784558 | + | 0.620055i | \(0.212890\pi\) | ||||
−0.784558 | + | 0.620055i | \(0.787110\pi\) | |||||||
\(648\) | 3.26137e22 | 1.04906 | ||||||||
\(649\) | − | 2.82878e22i | − | 0.898756i | ||||||
\(650\) | 4.89026e22i | 1.53471i | ||||||||
\(651\) | −5.18407e21 | − | 3.35918e22i | −0.160703 | − | 1.04132i | ||||
\(652\) | −2.29401e22 | −0.702450 | ||||||||
\(653\) | −1.17440e22 | −0.355230 | −0.177615 | − | 0.984100i | \(-0.556838\pi\) | ||||
−0.177615 | + | 0.984100i | \(0.556838\pi\) | |||||||
\(654\) | − | 2.77126e21i | − | 0.0828046i | ||||||
\(655\) | −1.84757e21 | −0.0545344 | ||||||||
\(656\) | − | 1.49525e20i | − | 0.00435995i | ||||||
\(657\) | 1.64552e22i | 0.474002i | ||||||||
\(658\) | −1.15711e21 | + | 1.78571e20i | −0.0329280 | + | 0.00508163i | ||||
\(659\) | 4.51030e22 | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(660\) | 5.06718e21 | 0.140739 | ||||||||
\(661\) | 1.43753e22i | 0.394463i | 0.980357 | + | 0.197231i | \(0.0631950\pi\) | ||||
−0.980357 | + | 0.197231i | \(0.936805\pi\) | |||||||
\(662\) | −5.50210e22 | −1.49164 | ||||||||
\(663\) | − | 4.97396e22i | − | 1.33227i | ||||||
\(664\) | − | 1.34887e22i | − | 0.356964i | ||||||
\(665\) | 5.73584e20 | + | 3.71672e21i | 0.0149977 | + | 0.0971822i | ||||
\(666\) | 2.57017e22 | 0.664000 | ||||||||
\(667\) | 6.47845e21 | 0.165373 | ||||||||
\(668\) | 7.94782e22i | 2.00464i | ||||||||
\(669\) | 5.38269e22 | 1.34150 | ||||||||
\(670\) | − | 2.40127e21i | − | 0.0591346i | ||||||
\(671\) | − | 9.34758e22i | − | 2.27467i | ||||||
\(672\) | 5.26260e22 | − | 8.12152e21i | 1.26545 | − | 0.195291i | ||||
\(673\) | −4.89270e21 | −0.116259 | −0.0581297 | − | 0.998309i | \(-0.518514\pi\) | ||||
−0.0581297 | + | 0.998309i | \(0.518514\pi\) | |||||||
\(674\) | −1.28546e23 | −3.01841 | ||||||||
\(675\) | − | 3.42733e22i | − | 0.795289i | ||||||
\(676\) | 4.43565e21 | 0.101715 | ||||||||
\(677\) | 1.54232e22i | 0.349514i | 0.984612 | + | 0.174757i | \(0.0559139\pi\) | ||||
−0.984612 | + | 0.174757i | \(0.944086\pi\) | |||||||
\(678\) | 2.21924e22i | 0.497011i | ||||||||
\(679\) | −3.80653e22 | + | 5.87444e21i | −0.842502 | + | 0.130019i | ||||
\(680\) | 3.17718e21 | 0.0694976 | ||||||||
\(681\) | 5.15259e22 | 1.11391 | ||||||||
\(682\) | 8.32903e22i | 1.77959i | ||||||||
\(683\) | 6.61604e22 | 1.39712 | 0.698558 | − | 0.715554i | \(-0.253826\pi\) | ||||
0.698558 | + | 0.715554i | \(0.253826\pi\) | |||||||
\(684\) | 3.28389e22i | 0.685393i | ||||||||
\(685\) | 1.51553e21i | 0.0312637i | ||||||||
\(686\) | 3.46811e22 | + | 7.01136e22i | 0.707132 | + | 1.42958i | ||||
\(687\) | −7.82682e22 | −1.57736 | ||||||||
\(688\) | −3.85299e21 | −0.0767520 | ||||||||
\(689\) | − | 3.59094e22i | − | 0.707057i | ||||||
\(690\) | 7.63145e20 | 0.0148530 | ||||||||
\(691\) | 8.37600e22i | 1.61143i | 0.592302 | + | 0.805716i | \(0.298219\pi\) | ||||
−0.592302 | + | 0.805716i | \(0.701781\pi\) | |||||||
\(692\) | 2.47415e22i | 0.470519i | ||||||||
\(693\) | −2.92996e21 | − | 1.89856e22i | −0.0550803 | − | 0.356910i | ||||
\(694\) | 2.10689e22 | 0.391531 | ||||||||
\(695\) | 1.67996e21 | 0.0308618 | ||||||||
\(696\) | − | 7.30038e22i | − | 1.32578i | ||||||
\(697\) | −1.82877e21 | −0.0328320 | ||||||||
\(698\) | − | 1.28909e23i | − | 2.28791i | ||||||
\(699\) | − | 4.03452e22i | − | 0.707904i | ||||||
\(700\) | 1.35137e22 | + | 8.75664e22i | 0.234418 | + | 1.51898i | ||||
\(701\) | −8.86161e22 | −1.51974 | −0.759869 | − | 0.650077i | \(-0.774737\pi\) | ||||
−0.759869 | + | 0.650077i | \(0.774737\pi\) | |||||||
\(702\) | 7.26222e22 | 1.23132 | ||||||||
\(703\) | − | 1.23181e23i | − | 2.06491i | ||||||
\(704\) | −1.18789e23 | −1.96877 | ||||||||
\(705\) | − | 9.62876e19i | − | 0.00157782i | ||||||
\(706\) | − | 6.48585e22i | − | 1.05082i | ||||||
\(707\) | 7.06469e22 | − | 1.09026e22i | 1.13172 | − | 0.174652i | ||||
\(708\) | −8.27175e22 | −1.31018 | ||||||||
\(709\) | 7.77992e21 | 0.121844 | 0.0609221 | − | 0.998143i | \(-0.480596\pi\) | ||||
0.0609221 | + | 0.998143i | \(0.480596\pi\) | |||||||
\(710\) | − | 7.35025e21i | − | 0.113824i | ||||||
\(711\) | 1.30627e21 | 0.0200022 | ||||||||
\(712\) | − | 3.88359e22i | − | 0.588022i | ||||||
\(713\) | 7.61267e21i | 0.113978i | ||||||||
\(714\) | −2.26487e22 | − | 1.46759e23i | −0.335318 | − | 2.17280i | ||||
\(715\) | 5.28021e21 | 0.0773041 | ||||||||
\(716\) | 2.07224e23 | 3.00010 | ||||||||
\(717\) | 1.17236e23i | 1.67845i | ||||||||
\(718\) | 8.99607e22 | 1.27367 | ||||||||
\(719\) | 6.60721e22i | 0.925097i | 0.886594 | + | 0.462548i | \(0.153065\pi\) | ||||
−0.886594 | + | 0.462548i | \(0.846935\pi\) | |||||||
\(720\) | 2.29949e20i | 0.00318399i | ||||||||
\(721\) | −9.55924e22 | + | 1.47523e22i | −1.30900 | + | 0.202013i | ||||
\(722\) | 1.41569e23 | 1.91721 | ||||||||
\(723\) | 8.24023e22 | 1.10365 | ||||||||
\(724\) | − | 2.70609e21i | − | 0.0358454i | ||||||
\(725\) | −1.01929e23 | −1.33534 | ||||||||
\(726\) | 6.41112e22i | 0.830694i | ||||||||
\(727\) | 3.85624e21i | 0.0494184i | 0.999695 | + | 0.0247092i | \(0.00786599\pi\) | ||||
−0.999695 | + | 0.0247092i | \(0.992134\pi\) | |||||||
\(728\) | −6.53537e22 | + | 1.00857e22i | −0.828361 | + | 0.127837i | ||||
\(729\) | −4.37568e22 | −0.548561 | ||||||||
\(730\) | −1.35031e22 | −0.167436 | ||||||||
\(731\) | 4.71242e22i | 0.577970i | ||||||||
\(732\) | −2.73336e23 | −3.31595 | ||||||||
\(733\) | − | 2.57776e20i | − | 0.00309322i | −0.999999 | − | 0.00154661i | \(-0.999508\pi\) | ||
0.999999 | − | 0.00154661i | \(-0.000492302\pi\) | |||||||
\(734\) | 9.88706e22i | 1.17354i | ||||||||
\(735\) | −6.13374e21 | + | 1.93937e21i | −0.0720156 | + | 0.0227700i | ||||
\(736\) | −1.19262e22 | −0.138510 | ||||||||
\(737\) | 5.87877e22 | 0.675377 | ||||||||
\(738\) | 1.13992e21i | 0.0129546i | ||||||||
\(739\) | 1.11396e23 | 1.25232 | 0.626160 | − | 0.779695i | \(-0.284626\pi\) | ||||
0.626160 | + | 0.779695i | \(0.284626\pi\) | |||||||
\(740\) | 1.27995e22i | 0.142344i | ||||||||
\(741\) | 1.48593e23i | 1.63475i | ||||||||
\(742\) | −1.63512e22 | − | 1.05953e23i | −0.177958 | − | 1.15314i | ||||
\(743\) | −6.66485e22 | −0.717596 | −0.358798 | − | 0.933415i | \(-0.616813\pi\) | ||||
−0.358798 | + | 0.933415i | \(0.616813\pi\) | |||||||
\(744\) | 8.57850e22 | 0.913751 | ||||||||
\(745\) | − | 5.70726e21i | − | 0.0601420i | ||||||
\(746\) | −6.42641e22 | −0.669974 | ||||||||
\(747\) | − | 1.19400e22i | − | 0.123152i | ||||||
\(748\) | 2.20835e23i | 2.25349i | ||||||||
\(749\) | 1.58320e22 | + | 1.02589e23i | 0.159838 | + | 1.03572i | ||||
\(750\) | −2.40669e22 | −0.240397 | ||||||||
\(751\) | 5.43412e22 | 0.537044 | 0.268522 | − | 0.963274i | \(-0.413465\pi\) | ||||
0.268522 | + | 0.963274i | \(0.413465\pi\) | |||||||
\(752\) | 3.43104e20i | 0.00335492i | ||||||||
\(753\) | 6.46308e22 | 0.625288 | ||||||||
\(754\) | − | 2.15979e23i | − | 2.06747i | ||||||
\(755\) | 1.14573e21i | 0.0108519i | ||||||||
\(756\) | 1.30039e23 | − | 2.00684e22i | 1.21871 | − | 0.188078i | ||||
\(757\) | −7.67803e22 | −0.712004 | −0.356002 | − | 0.934485i | \(-0.615860\pi\) | ||||
−0.356002 | + | 0.934485i | \(0.615860\pi\) | |||||||
\(758\) | −1.27130e23 | −1.16652 | ||||||||
\(759\) | 1.86833e22i | 0.169636i | ||||||||
\(760\) | −9.49155e21 | −0.0852763 | ||||||||
\(761\) | 1.23846e23i | 1.10104i | 0.834822 | + | 0.550520i | \(0.185571\pi\) | ||||
−0.834822 | + | 0.550520i | \(0.814429\pi\) | |||||||
\(762\) | − | 2.92879e23i | − | 2.57661i | ||||||
\(763\) | −7.98002e20 | − | 5.17091e21i | −0.00694716 | − | 0.0450164i | ||||
\(764\) | 2.30705e23 | 1.98751 | ||||||||
\(765\) | 2.81241e21 | 0.0239766 | ||||||||
\(766\) | − | 7.67091e22i | − | 0.647167i | ||||||
\(767\) | −8.61950e22 | −0.719646 | ||||||||
\(768\) | 1.00192e23i | 0.827834i | ||||||||
\(769\) | − | 2.33391e23i | − | 1.90841i | −0.299148 | − | 0.954207i | \(-0.596702\pi\) | ||
0.299148 | − | 0.954207i | \(-0.403298\pi\) | |||||||
\(770\) | 1.55795e22 | − | 2.40432e21i | 0.126075 | − | 0.0194566i | ||||
\(771\) | −1.51468e23 | −1.21307 | ||||||||
\(772\) | 1.11655e22 | 0.0884994 | ||||||||
\(773\) | − | 1.65084e23i | − | 1.29500i | −0.762067 | − | 0.647498i | \(-0.775816\pi\) | ||
0.762067 | − | 0.647498i | \(-0.224184\pi\) | |||||||
\(774\) | 2.93738e22 | 0.228051 | ||||||||
\(775\) | − | 1.19774e23i | − | 0.920342i | ||||||
\(776\) | − | 9.72091e22i | − | 0.739287i | ||||||
\(777\) | 2.08246e23 | − | 3.21377e22i | 1.56750 | − | 0.241906i | ||||
\(778\) | −4.57579e22 | −0.340902 | ||||||||
\(779\) | 5.46331e21 | 0.0402862 | ||||||||
\(780\) | − | 1.54401e22i | − | 0.112692i | ||||||
\(781\) | 1.79948e23 | 1.29999 | ||||||||
\(782\) | 3.32590e22i | 0.237824i | ||||||||
\(783\) | 1.51368e23i | 1.07137i | ||||||||
\(784\) | 2.18565e22 | − | 6.91061e21i | 0.153127 | − | 0.0484159i | ||||
\(785\) | 8.51891e21 | 0.0590781 | ||||||||
\(786\) | −2.17943e23 | −1.49611 | ||||||||
\(787\) | − | 3.33541e22i | − | 0.226648i | −0.993558 | − | 0.113324i | \(-0.963850\pi\) | ||
0.993558 | − | 0.113324i | \(-0.0361498\pi\) | |||||||
\(788\) | −3.55554e23 | −2.39164 | ||||||||
\(789\) | 8.06217e22i | 0.536829i | ||||||||
\(790\) | 1.07192e21i | 0.00706557i | ||||||||
\(791\) | 6.39045e21 | + | 4.14089e22i | 0.0416984 | + | 0.270198i | ||||
\(792\) | 4.84845e22 | 0.313185 | ||||||||
\(793\) | −2.84827e23 | −1.82136 | ||||||||
\(794\) | 2.66894e23i | 1.68956i | ||||||||
\(795\) | 8.81677e21 | 0.0552551 | ||||||||
\(796\) | 2.40075e23i | 1.48951i | ||||||||
\(797\) | 5.63199e22i | 0.345936i | 0.984927 | + | 0.172968i | \(0.0553357\pi\) | ||||
−0.984927 | + | 0.172968i | \(0.944664\pi\) | |||||||
\(798\) | 6.76611e22 | + | 4.38432e23i | 0.411449 | + | 2.66611i | ||||
\(799\) | 4.19636e21 | 0.0252638 | ||||||||
\(800\) | 1.87642e23 | 1.11843 | ||||||||
\(801\) | − | 3.43772e22i | − | 0.202867i | ||||||
\(802\) | 4.24658e23 | 2.48110 | ||||||||
\(803\) | − | 3.30582e23i | − | 1.91229i | ||||||
\(804\) | − | 1.71903e23i | − | 0.984546i | ||||||
\(805\) | 1.42396e21 | − | 2.19753e20i | 0.00807477 | − | 0.00124614i | ||||
\(806\) | 2.53791e23 | 1.42494 | ||||||||
\(807\) | −1.54063e23 | −0.856465 | ||||||||
\(808\) | 1.80414e23i | 0.993069i | ||||||||
\(809\) | 5.47445e22 | 0.298368 | 0.149184 | − | 0.988809i | \(-0.452335\pi\) | ||||
0.149184 | + | 0.988809i | \(0.452335\pi\) | |||||||
\(810\) | 2.36901e22i | 0.127846i | ||||||||
\(811\) | 1.44446e23i | 0.771863i | 0.922528 | + | 0.385931i | \(0.126120\pi\) | ||||
−0.922528 | + | 0.385931i | \(0.873880\pi\) | |||||||
\(812\) | −5.96834e22 | − | 3.86737e23i | −0.315795 | − | 2.04629i | ||||
\(813\) | 1.30741e23 | 0.684998 | ||||||||
\(814\) | −5.16342e23 | −2.67881 | ||||||||
\(815\) | − | 5.86924e21i | − | 0.0301523i | ||||||
\(816\) | −4.35169e22 | −0.221379 | ||||||||
\(817\) | − | 1.40780e23i | − | 0.709192i | ||||||
\(818\) | 2.45553e22i | 0.122495i | ||||||||
\(819\) | −5.78506e22 | + | 8.92781e21i | −0.285783 | + | 0.0441036i | ||||
\(820\) | −5.67684e20 | −0.00277713 | ||||||||
\(821\) | 7.11622e22 | 0.344750 | 0.172375 | − | 0.985031i | \(-0.444856\pi\) | ||||
0.172375 | + | 0.985031i | \(0.444856\pi\) | |||||||
\(822\) | 1.78775e23i | 0.857693i | ||||||||
\(823\) | 8.58942e22 | 0.408098 | 0.204049 | − | 0.978961i | \(-0.434590\pi\) | ||||
0.204049 | + | 0.978961i | \(0.434590\pi\) | |||||||
\(824\) | − | 2.44119e23i | − | 1.14864i | ||||||
\(825\) | − | 2.93954e23i | − | 1.36977i | ||||||
\(826\) | −2.54323e23 | + | 3.92485e22i | −1.17367 | + | 0.181127i | ||||
\(827\) | −4.41577e22 | −0.201819 | −0.100910 | − | 0.994896i | \(-0.532175\pi\) | ||||
−0.100910 | + | 0.994896i | \(0.532175\pi\) | |||||||
\(828\) | 1.25813e22 | 0.0569487 | ||||||||
\(829\) | 3.71226e23i | 1.66419i | 0.554635 | + | 0.832094i | \(0.312858\pi\) | ||||
−0.554635 | + | 0.832094i | \(0.687142\pi\) | |||||||
\(830\) | 9.79795e21 | 0.0435021 | ||||||||
\(831\) | 1.02958e23i | 0.452742i | ||||||||
\(832\) | 3.61958e23i | 1.57642i | ||||||||
\(833\) | −8.45207e22 | − | 2.67318e23i | −0.364589 | − | 1.15310i | ||||
\(834\) | 1.98172e23 | 0.846669 | ||||||||
\(835\) | −2.03345e22 | −0.0860482 | ||||||||
\(836\) | − | 6.59727e23i | − | 2.76512i | ||||||
\(837\) | −1.77869e23 | −0.738409 | ||||||||
\(838\) | 6.04861e23i | 2.48716i | ||||||||
\(839\) | 8.56516e22i | 0.348851i | 0.984670 | + | 0.174425i | \(0.0558068\pi\) | ||||
−0.984670 | + | 0.174425i | \(0.944193\pi\) | |||||||
\(840\) | −2.47633e21 | − | 1.60462e22i | −0.00999021 | − | 0.0647347i | ||||
\(841\) | 1.99923e23 | 0.798903 | ||||||||
\(842\) | 3.26931e23 | 1.29407 | ||||||||
\(843\) | 2.69818e23i | 1.05791i | ||||||||
\(844\) | 1.80255e23 | 0.700079 | ||||||||
\(845\) | 1.13486e21i | 0.00436605i | ||||||||
\(846\) | − | 2.61570e21i | − | 0.00996839i | ||||||
\(847\) | 1.84613e22 | + | 1.19626e23i | 0.0696938 | + | 0.451603i | ||||
\(848\) | −3.14170e22 | −0.117489 | ||||||||
\(849\) | 2.37628e23 | 0.880309 | ||||||||
\(850\) | − | 5.23281e23i | − | 1.92036i | ||||||
\(851\) | −4.71933e22 | −0.171571 | ||||||||
\(852\) | − | 5.26194e23i | − | 1.89509i | ||||||
\(853\) | 4.29816e21i | 0.0153352i | 0.999971 | + | 0.00766761i | \(0.00244070\pi\) | ||||
−0.999971 | + | 0.00766761i | \(0.997559\pi\) | |||||||
\(854\) | −8.40399e23 | + | 1.29695e23i | −2.97045 | + | 0.458416i | ||||
\(855\) | −8.40184e21 | −0.0294202 | ||||||||
\(856\) | −2.61985e23 | −0.908837 | ||||||||
\(857\) | − | 2.97073e23i | − | 1.02098i | −0.859884 | − | 0.510490i | \(-0.829464\pi\) | ||
0.859884 | − | 0.510490i | \(-0.170536\pi\) | |||||||
\(858\) | 6.22864e23 | 2.12078 | ||||||||
\(859\) | 6.90793e22i | 0.233025i | 0.993189 | + | 0.116513i | \(0.0371715\pi\) | ||||
−0.993189 | + | 0.116513i | \(0.962828\pi\) | |||||||
\(860\) | 1.46282e22i | 0.0488881i | ||||||||
\(861\) | 1.42537e21 | + | 9.23613e21i | 0.00471956 | + | 0.0305819i | ||||
\(862\) | −3.83499e23 | −1.25807 | ||||||||
\(863\) | 3.93816e23 | 1.27999 | 0.639995 | − | 0.768379i | \(-0.278936\pi\) | ||||
0.639995 | + | 0.768379i | \(0.278936\pi\) | |||||||
\(864\) | − | 2.78655e23i | − | 0.897340i | ||||||
\(865\) | −6.33012e21 | −0.0201968 | ||||||||
\(866\) | 3.49902e23i | 1.10612i | ||||||||
\(867\) | 1.68331e23i | 0.527244i | ||||||||
\(868\) | 4.54446e23 | − | 7.01326e22i | 1.41034 | − | 0.217652i | ||||
\(869\) | −2.62428e22 | −0.0806960 | ||||||||
\(870\) | 5.30288e22 | 0.161569 | ||||||||
\(871\) | − | 1.79130e23i | − | 0.540784i | ||||||
\(872\) | 1.32052e22 | 0.0395014 | ||||||||
\(873\) | − | 8.60486e22i | − | 0.255053i | ||||||
\(874\) | − | 9.93585e22i | − | 0.291819i | ||||||
\(875\) | −4.49066e22 | + | 6.93022e21i | −0.130691 | + | 0.0201689i | ||||
\(876\) | −9.66667e23 | −2.78769 | ||||||||
\(877\) | −2.92693e23 | −0.836403 | −0.418201 | − | 0.908354i | \(-0.637339\pi\) | ||||
−0.418201 | + | 0.908354i | \(0.637339\pi\) | |||||||
\(878\) | 3.83992e23i | 1.08734i | ||||||||
\(879\) | −4.78735e22 | −0.134334 | ||||||||
\(880\) | − | 4.61963e21i | − | 0.0128453i | ||||||
\(881\) | − | 3.48409e23i | − | 0.960024i | −0.877262 | − | 0.480012i | \(-0.840632\pi\) | ||
0.877262 | − | 0.480012i | \(-0.159368\pi\) | |||||||
\(882\) | −1.66626e23 | + | 5.26840e22i | −0.454982 | + | 0.143857i | ||||
\(883\) | −1.09594e23 | −0.296552 | −0.148276 | − | 0.988946i | \(-0.547372\pi\) | ||||
−0.148276 | + | 0.988946i | \(0.547372\pi\) | |||||||
\(884\) | 6.72900e23 | 1.80440 | ||||||||
\(885\) | − | 2.11633e22i | − | 0.0562389i | ||||||
\(886\) | 1.06953e24 | 2.81659 | ||||||||
\(887\) | 2.59226e23i | 0.676534i | 0.941050 | + | 0.338267i | \(0.109841\pi\) | ||||
−0.941050 | + | 0.338267i | \(0.890159\pi\) | |||||||
\(888\) | 5.31808e23i | 1.37547i | ||||||||
\(889\) | −8.43366e22 | − | 5.46486e23i | −0.216173 | − | 1.40076i | ||||
\(890\) | 2.82098e22 | 0.0716605 | ||||||||
\(891\) | −5.79980e23 | −1.46013 | ||||||||
\(892\) | 7.28196e23i | 1.81689i | ||||||||
\(893\) | −1.25363e22 | −0.0309997 | ||||||||
\(894\) | − | 6.73240e23i | − | 1.64995i | ||||||
\(895\) | 5.30184e22i | 0.128778i | ||||||||
\(896\) | 9.36436e22 | + | 6.06794e23i | 0.225431 | + | 1.46075i | ||||
\(897\) | 5.69293e22 | 0.135830 | ||||||||
\(898\) | 1.12616e23 | 0.266312 | ||||||||
\(899\) | 5.28983e23i | 1.23984i | ||||||||
\(900\) | −1.97948e23 | −0.459846 | ||||||||
\(901\) | 3.84248e23i | 0.884735i | ||||||||
\(902\) | − | 2.29008e22i | − | 0.0522635i | ||||||
\(903\) | 2.37999e23 | − | 3.67292e22i | 0.538360 | − | 0.0830826i | ||||
\(904\) | −1.05748e23 | −0.237096 | ||||||||
\(905\) | 6.92353e20 | 0.00153865 | ||||||||
\(906\) | 1.35152e23i | 0.297713i | ||||||||
\(907\) | −2.87326e23 | −0.627360 | −0.313680 | − | 0.949529i | \(-0.601562\pi\) | ||||
−0.313680 | + | 0.949529i | \(0.601562\pi\) | |||||||
\(908\) | 6.97067e23i | 1.50865i | ||||||||
\(909\) | 1.59701e23i | 0.342607i | ||||||||
\(910\) | −7.32612e21 | − | 4.74720e22i | −0.0155791 | − | 0.100950i | ||||
\(911\) | 7.32222e23 | 1.54346 | 0.771731 | − | 0.635949i | \(-0.219391\pi\) | ||||
0.771731 | + | 0.635949i | \(0.219391\pi\) | |||||||
\(912\) | 1.30003e23 | 0.271641 | ||||||||
\(913\) | 2.39873e23i | 0.496838i | ||||||||
\(914\) | −1.01686e24 | −2.08780 | ||||||||
\(915\) | − | 6.99331e22i | − | 0.142336i | ||||||
\(916\) | − | 1.05885e24i | − | 2.13634i | ||||||
\(917\) | −4.06662e23 | + | 6.27582e22i | −0.813352 | + | 0.125521i | ||||
\(918\) | −7.77092e23 | −1.54075 | ||||||||
\(919\) | 1.29155e23 | 0.253856 | 0.126928 | − | 0.991912i | \(-0.459488\pi\) | ||||
0.126928 | + | 0.991912i | \(0.459488\pi\) | |||||||
\(920\) | 3.63643e21i | 0.00708553i | ||||||||
\(921\) | −4.02722e23 | −0.777908 | ||||||||
\(922\) | − | 1.50663e24i | − | 2.88509i | ||||||
\(923\) | − | 5.48316e23i | − | 1.04092i | ||||||
\(924\) | 1.11532e24 | − | 1.72122e23i | 2.09905 | − | 0.323937i | ||||
\(925\) | 7.42517e23 | 1.38539 | ||||||||
\(926\) | 1.25158e23 | 0.231511 | ||||||||
\(927\) | − | 2.16092e23i | − | 0.396278i | ||||||
\(928\) | −8.28721e23 | −1.50669 | ||||||||
\(929\) | − | 5.12792e23i | − | 0.924306i | −0.886800 | − | 0.462153i | \(-0.847077\pi\) | ||
0.886800 | − | 0.462153i | \(-0.152923\pi\) | |||||||
\(930\) | 6.23129e22i | 0.111356i | ||||||||
\(931\) | 2.52499e23 | + | 7.98590e23i | 0.447365 | + | 1.41490i | ||||
\(932\) | 5.45809e23 | 0.958767 | ||||||||
\(933\) | 1.93101e22 | 0.0336303 | ||||||||
\(934\) | − | 1.57792e24i | − | 2.72464i | ||||||
\(935\) | −5.65007e22 | −0.0967300 | ||||||||
\(936\) | − | 1.47736e23i | − | 0.250772i | ||||||
\(937\) | 8.68179e22i | 0.146114i | 0.997328 | + | 0.0730571i | \(0.0232755\pi\) | ||||
−0.997328 | + | 0.0730571i | \(0.976724\pi\) | |||||||
\(938\) | −8.15661e22 | − | 5.28534e23i | −0.136109 | − | 0.881962i | ||||
\(939\) | 1.19645e24 | 1.97957 | ||||||||
\(940\) | 1.30262e21 | 0.00213696 | ||||||||
\(941\) | 1.04223e23i | 0.169531i | 0.996401 | + | 0.0847653i | \(0.0270140\pi\) | ||||
−0.996401 | + | 0.0847653i | \(0.972986\pi\) | |||||||
\(942\) | 1.00491e24 | 1.62076 | ||||||||
\(943\) | − | 2.09312e21i | − | 0.00334734i | ||||||
\(944\) | 7.54116e22i | 0.119581i | ||||||||
\(945\) | 5.13450e21 | + | 3.32706e22i | 0.00807316 | + | 0.0523126i | ||||
\(946\) | −5.90113e23 | −0.920039 | ||||||||
\(947\) | −1.05845e24 | −1.63633 | −0.818166 | − | 0.574982i | \(-0.805009\pi\) | ||||
−0.818166 | + | 0.574982i | \(0.805009\pi\) | |||||||
\(948\) | 7.67376e22i | 0.117636i | ||||||||
\(949\) | −1.00731e24 | −1.53120 | ||||||||
\(950\) | 1.56326e24i | 2.35636i | ||||||||
\(951\) | 1.15858e24i | 1.73174i | ||||||||
\(952\) | 6.99316e23 | − | 1.07922e23i | 1.03652 | − | 0.159961i | ||||
\(953\) | 1.95863e23 | 0.287878 | 0.143939 | − | 0.989587i | \(-0.454023\pi\) | ||||
0.143939 | + | 0.989587i | \(0.454023\pi\) | |||||||
\(954\) | 2.39512e23 | 0.349092 | ||||||||
\(955\) | 5.90258e22i | 0.0853130i | ||||||||
\(956\) | −1.58603e24 | −2.27325 | ||||||||
\(957\) | 1.29825e24i | 1.84528i | ||||||||
\(958\) | − | 1.14401e24i | − | 1.61253i | ||||||
\(959\) | 5.14794e22 | + | 3.33577e23i | 0.0719590 | + | 0.466281i | ||||
\(960\) | −8.88709e22 | −0.123194 | ||||||||
\(961\) | 1.05827e23 | 0.145482 | ||||||||
\(962\) | 1.57333e24i | 2.14496i | ||||||||
\(963\) | −2.31907e23 | −0.313547 | ||||||||
\(964\) | 1.11478e24i | 1.49476i | ||||||||
\(965\) | 2.85670e21i | 0.00379880i | ||||||||
\(966\) | 1.67973e23 | − | 2.59225e22i | 0.221525 | − | 0.0341869i | ||||
\(967\) | −1.73315e23 | −0.226685 | −0.113343 | − | 0.993556i | \(-0.536156\pi\) | ||||
−0.113343 | + | 0.993556i | \(0.536156\pi\) | |||||||
\(968\) | −3.05493e23 | −0.396277 | ||||||||
\(969\) | − | 1.59002e24i | − | 2.04555i | ||||||
\(970\) | 7.06112e22 | 0.0900948 | ||||||||
\(971\) | − | 1.48269e24i | − | 1.87627i | −0.346268 | − | 0.938136i | \(-0.612551\pi\) | ||
0.346268 | − | 0.938136i | \(-0.387449\pi\) | |||||||
\(972\) | 7.13420e23i | 0.895396i | ||||||||
\(973\) | 3.69770e23 | − | 5.70649e22i | 0.460288 | − | 0.0710340i | ||||
\(974\) | 9.90915e23 | 1.22339 | ||||||||
\(975\) | −8.95698e23 | −1.09679 | ||||||||
\(976\) | 2.49194e23i | 0.302649i | ||||||||
\(977\) | 4.94529e23 | 0.595710 | 0.297855 | − | 0.954611i | \(-0.403729\pi\) | ||||
0.297855 | + | 0.954611i | \(0.403729\pi\) | |||||||
\(978\) | − | 6.92347e23i | − | 0.827205i | ||||||
\(979\) | 6.90631e23i | 0.818436i | ||||||||
\(980\) | −2.62367e22 | − | 8.29802e22i | −0.0308391 | − | 0.0975362i | ||||
\(981\) | 1.16891e22 | 0.0136279 | ||||||||
\(982\) | 1.52508e24 | 1.76360 | ||||||||
\(983\) | − | 6.39086e23i | − | 0.733046i | −0.930409 | − | 0.366523i | \(-0.880548\pi\) | ||
0.930409 | − | 0.366523i | \(-0.119452\pi\) | |||||||
\(984\) | −2.35867e22 | −0.0268353 | ||||||||
\(985\) | − | 9.09686e22i | − | 0.102660i | ||||||
\(986\) | 2.31107e24i | 2.58701i | ||||||||
\(987\) | −3.27069e21 | − | 2.11935e22i | −0.00363164 | − | 0.0235324i | ||||
\(988\) | −2.01024e24 | −2.21407 | ||||||||
\(989\) | −5.39359e22 | −0.0589261 | ||||||||
\(990\) | 3.52184e22i | 0.0381670i | ||||||||
\(991\) | 3.14566e23 | 0.338160 | 0.169080 | − | 0.985602i | \(-0.445920\pi\) | ||||
0.169080 | + | 0.985602i | \(0.445920\pi\) | |||||||
\(992\) | − | 9.73811e23i | − | 1.03844i | ||||||
\(993\) | − | 1.00776e24i | − | 1.06602i | ||||||
\(994\) | −2.49673e23 | − | 1.61784e24i | −0.261987 | − | 1.69763i | ||||
\(995\) | −6.14233e22 | −0.0639365 | ||||||||
\(996\) | 7.01422e23 | 0.724277 | ||||||||
\(997\) | 1.42667e24i | 1.46138i | 0.682711 | + | 0.730688i | \(0.260801\pi\) | ||||
−0.682711 | + | 0.730688i | \(0.739199\pi\) | |||||||
\(998\) | 1.12672e24 | 1.14492 | ||||||||
\(999\) | − | 1.10267e24i | − | 1.11153i |
(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 | 7.17.b.b.6.1 | ✓ | 8 | |
3.2 | odd | 2 | 63.17.d.c.55.7 | 8 | |||
4.3 | odd | 2 | 112.17.c.b.97.7 | 8 | |||
7.6 | odd | 2 | inner | 7.17.b.b.6.2 | yes | 8 | |
21.20 | even | 2 | 63.17.d.c.55.8 | 8 | |||
28.27 | even | 2 | 112.17.c.b.97.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.17.b.b.6.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
7.17.b.b.6.2 | yes | 8 | 7.6 | odd | 2 | inner | |
63.17.d.c.55.7 | 8 | 3.2 | odd | 2 | |||
63.17.d.c.55.8 | 8 | 21.20 | even | 2 | |||
112.17.c.b.97.2 | 8 | 28.27 | even | 2 | |||
112.17.c.b.97.7 | 8 | 4.3 | odd | 2 |