Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.a (trivial) |
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: | yes |
Analytic conductor: | \(28.4270373191\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + \cdots - 7335224320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-6.50047\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.50047 | 0.574566 | 0.287283 | − | 0.957846i | \(-0.407248\pi\) | ||||
0.287283 | + | 0.957846i | \(0.407248\pi\) | |||||||
\(3\) | −52.7234 | −1.12740 | −0.563702 | − | 0.825978i | \(-0.690623\pi\) | ||||
−0.563702 | + | 0.825978i | \(0.690623\pi\) | |||||||
\(4\) | −85.7438 | −0.669874 | ||||||||
\(5\) | 295.835 | 1.05841 | 0.529205 | − | 0.848494i | \(-0.322490\pi\) | ||||
0.529205 | + | 0.848494i | \(0.322490\pi\) | |||||||
\(6\) | −342.727 | −0.647768 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | −1389.44 | −0.959453 | ||||||||
\(9\) | 592.761 | 0.271039 | ||||||||
\(10\) | 1923.06 | 0.608127 | ||||||||
\(11\) | −4167.20 | −0.943996 | −0.471998 | − | 0.881600i | \(-0.656467\pi\) | ||||
−0.471998 | + | 0.881600i | \(0.656467\pi\) | |||||||
\(12\) | 4520.71 | 0.755218 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −2229.66 | −0.217166 | ||||||||
\(15\) | −15597.4 | −1.19325 | ||||||||
\(16\) | 1943.22 | 0.118605 | ||||||||
\(17\) | 31905.1 | 1.57503 | 0.787516 | − | 0.616294i | \(-0.211367\pi\) | ||||
0.787516 | + | 0.616294i | \(0.211367\pi\) | |||||||
\(18\) | 3853.23 | 0.155730 | ||||||||
\(19\) | −16829.1 | −0.562889 | −0.281445 | − | 0.959577i | \(-0.590814\pi\) | ||||
−0.281445 | + | 0.959577i | \(0.590814\pi\) | |||||||
\(20\) | −25366.0 | −0.709001 | ||||||||
\(21\) | 18084.1 | 0.426118 | ||||||||
\(22\) | −27088.8 | −0.542388 | ||||||||
\(23\) | −41368.2 | −0.708957 | −0.354478 | − | 0.935064i | \(-0.615342\pi\) | ||||
−0.354478 | + | 0.935064i | \(0.615342\pi\) | |||||||
\(24\) | 73255.9 | 1.08169 | ||||||||
\(25\) | 9393.08 | 0.120231 | ||||||||
\(26\) | −14281.5 | −0.159356 | ||||||||
\(27\) | 84053.8 | 0.821834 | ||||||||
\(28\) | 29410.1 | 0.253188 | ||||||||
\(29\) | 192426. | 1.46511 | 0.732555 | − | 0.680708i | \(-0.238328\pi\) | ||||
0.732555 | + | 0.680708i | \(0.238328\pi\) | |||||||
\(30\) | −101391. | −0.685604 | ||||||||
\(31\) | 305729. | 1.84319 | 0.921595 | − | 0.388153i | \(-0.126887\pi\) | ||||
0.921595 | + | 0.388153i | \(0.126887\pi\) | |||||||
\(32\) | 190480. | 1.02760 | ||||||||
\(33\) | 219709. | 1.06426 | ||||||||
\(34\) | 207399. | 0.904960 | ||||||||
\(35\) | −101471. | −0.400041 | ||||||||
\(36\) | −50825.6 | −0.181562 | ||||||||
\(37\) | 50734.5 | 0.164664 | 0.0823318 | − | 0.996605i | \(-0.473763\pi\) | ||||
0.0823318 | + | 0.996605i | \(0.473763\pi\) | |||||||
\(38\) | −109397. | −0.323417 | ||||||||
\(39\) | 115833. | 0.312685 | ||||||||
\(40\) | −411043. | −1.01549 | ||||||||
\(41\) | 654222. | 1.48245 | 0.741227 | − | 0.671254i | \(-0.234244\pi\) | ||||
0.741227 | + | 0.671254i | \(0.234244\pi\) | |||||||
\(42\) | 117555. | 0.244833 | ||||||||
\(43\) | −226236. | −0.433932 | −0.216966 | − | 0.976179i | \(-0.569616\pi\) | ||||
−0.216966 | + | 0.976179i | \(0.569616\pi\) | |||||||
\(44\) | 357312. | 0.632358 | ||||||||
\(45\) | 175359. | 0.286870 | ||||||||
\(46\) | −268913. | −0.407343 | ||||||||
\(47\) | −466460. | −0.655348 | −0.327674 | − | 0.944791i | \(-0.606265\pi\) | ||||
−0.327674 | + | 0.944791i | \(0.606265\pi\) | |||||||
\(48\) | −102453. | −0.133715 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 61059.5 | 0.0690809 | ||||||||
\(51\) | −1.68215e6 | −1.77570 | ||||||||
\(52\) | 188379. | 0.185790 | ||||||||
\(53\) | 444270. | 0.409904 | 0.204952 | − | 0.978772i | \(-0.434296\pi\) | ||||
0.204952 | + | 0.978772i | \(0.434296\pi\) | |||||||
\(54\) | 546389. | 0.472198 | ||||||||
\(55\) | −1.23280e6 | −0.999134 | ||||||||
\(56\) | 476577. | 0.362639 | ||||||||
\(57\) | 887288. | 0.634604 | ||||||||
\(58\) | 1.25086e6 | 0.841803 | ||||||||
\(59\) | −652349. | −0.413521 | −0.206761 | − | 0.978392i | \(-0.566292\pi\) | ||||
−0.206761 | + | 0.978392i | \(0.566292\pi\) | |||||||
\(60\) | 1.33738e6 | 0.799330 | ||||||||
\(61\) | −434908. | −0.245326 | −0.122663 | − | 0.992448i | \(-0.539143\pi\) | ||||
−0.122663 | + | 0.992448i | \(0.539143\pi\) | |||||||
\(62\) | 1.98738e6 | 1.05903 | ||||||||
\(63\) | −203317. | −0.102443 | ||||||||
\(64\) | 989476. | 0.471819 | ||||||||
\(65\) | −649949. | −0.293550 | ||||||||
\(66\) | 1.42821e6 | 0.611490 | ||||||||
\(67\) | 3.08414e6 | 1.25277 | 0.626386 | − | 0.779513i | \(-0.284533\pi\) | ||||
0.626386 | + | 0.779513i | \(0.284533\pi\) | |||||||
\(68\) | −2.73567e6 | −1.05507 | ||||||||
\(69\) | 2.18108e6 | 0.799280 | ||||||||
\(70\) | −659611. | −0.229850 | ||||||||
\(71\) | −3.79278e6 | −1.25763 | −0.628816 | − | 0.777554i | \(-0.716460\pi\) | ||||
−0.628816 | + | 0.777554i | \(0.716460\pi\) | |||||||
\(72\) | −823604. | −0.260049 | ||||||||
\(73\) | −168997. | −0.0508450 | −0.0254225 | − | 0.999677i | \(-0.508093\pi\) | ||||
−0.0254225 | + | 0.999677i | \(0.508093\pi\) | |||||||
\(74\) | 329799. | 0.0946101 | ||||||||
\(75\) | −495236. | −0.135549 | ||||||||
\(76\) | 1.44299e6 | 0.377065 | ||||||||
\(77\) | 1.42935e6 | 0.356797 | ||||||||
\(78\) | 752972. | 0.179658 | ||||||||
\(79\) | 1.62128e6 | 0.369966 | 0.184983 | − | 0.982742i | \(-0.440777\pi\) | ||||
0.184983 | + | 0.982742i | \(0.440777\pi\) | |||||||
\(80\) | 574871. | 0.125532 | ||||||||
\(81\) | −5.72797e6 | −1.19758 | ||||||||
\(82\) | 4.25275e6 | 0.851768 | ||||||||
\(83\) | 5.01049e6 | 0.961848 | 0.480924 | − | 0.876762i | \(-0.340301\pi\) | ||||
0.480924 | + | 0.876762i | \(0.340301\pi\) | |||||||
\(84\) | −1.55060e6 | −0.285446 | ||||||||
\(85\) | 9.43864e6 | 1.66703 | ||||||||
\(86\) | −1.47064e6 | −0.249323 | ||||||||
\(87\) | −1.01454e7 | −1.65177 | ||||||||
\(88\) | 5.79006e6 | 0.905719 | ||||||||
\(89\) | −1.21431e7 | −1.82584 | −0.912922 | − | 0.408134i | \(-0.866180\pi\) | ||||
−0.912922 | + | 0.408134i | \(0.866180\pi\) | |||||||
\(90\) | 1.13992e6 | 0.164826 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | 3.54707e6 | 0.474911 | ||||||||
\(93\) | −1.61191e7 | −2.07802 | ||||||||
\(94\) | −3.03221e6 | −0.376541 | ||||||||
\(95\) | −4.97863e6 | −0.595768 | ||||||||
\(96\) | −1.00427e7 | −1.15852 | ||||||||
\(97\) | 9.64770e6 | 1.07330 | 0.536652 | − | 0.843804i | \(-0.319689\pi\) | ||||
0.536652 | + | 0.843804i | \(0.319689\pi\) | |||||||
\(98\) | 764774. | 0.0820809 | ||||||||
\(99\) | −2.47015e6 | −0.255859 | ||||||||
\(100\) | −805399. | −0.0805399 | ||||||||
\(101\) | −2.37966e6 | −0.229821 | −0.114911 | − | 0.993376i | \(-0.536658\pi\) | ||||
−0.114911 | + | 0.993376i | \(0.536658\pi\) | |||||||
\(102\) | −1.09348e7 | −1.02026 | ||||||||
\(103\) | 2.27003e6 | 0.204692 | 0.102346 | − | 0.994749i | \(-0.467365\pi\) | ||||
0.102346 | + | 0.994749i | \(0.467365\pi\) | |||||||
\(104\) | 3.05259e6 | 0.266104 | ||||||||
\(105\) | 5.34991e6 | 0.451008 | ||||||||
\(106\) | 2.88797e6 | 0.235517 | ||||||||
\(107\) | 706516. | 0.0557544 | 0.0278772 | − | 0.999611i | \(-0.491125\pi\) | ||||
0.0278772 | + | 0.999611i | \(0.491125\pi\) | |||||||
\(108\) | −7.20709e6 | −0.550525 | ||||||||
\(109\) | 1.99236e7 | 1.47359 | 0.736794 | − | 0.676117i | \(-0.236339\pi\) | ||||
0.736794 | + | 0.676117i | \(0.236339\pi\) | |||||||
\(110\) | −8.01380e6 | −0.574069 | ||||||||
\(111\) | −2.67490e6 | −0.185642 | ||||||||
\(112\) | −666523. | −0.0448283 | ||||||||
\(113\) | −3.31200e6 | −0.215931 | −0.107966 | − | 0.994155i | \(-0.534434\pi\) | ||||
−0.107966 | + | 0.994155i | \(0.534434\pi\) | |||||||
\(114\) | 5.76779e6 | 0.364622 | ||||||||
\(115\) | −1.22382e7 | −0.750367 | ||||||||
\(116\) | −1.64993e7 | −0.981439 | ||||||||
\(117\) | −1.30230e6 | −0.0751726 | ||||||||
\(118\) | −4.24058e6 | −0.237595 | ||||||||
\(119\) | −1.09435e7 | −0.595306 | ||||||||
\(120\) | 2.16716e7 | 1.14487 | ||||||||
\(121\) | −2.12161e6 | −0.108872 | ||||||||
\(122\) | −2.82711e6 | −0.140956 | ||||||||
\(123\) | −3.44928e7 | −1.67132 | ||||||||
\(124\) | −2.62143e7 | −1.23470 | ||||||||
\(125\) | −2.03333e7 | −0.931156 | ||||||||
\(126\) | −1.32166e6 | −0.0588602 | ||||||||
\(127\) | 2.01961e7 | 0.874892 | 0.437446 | − | 0.899245i | \(-0.355883\pi\) | ||||
0.437446 | + | 0.899245i | \(0.355883\pi\) | |||||||
\(128\) | −1.79493e7 | −0.756508 | ||||||||
\(129\) | 1.19279e7 | 0.489216 | ||||||||
\(130\) | −4.22497e6 | −0.168664 | ||||||||
\(131\) | 1.87268e7 | 0.727804 | 0.363902 | − | 0.931437i | \(-0.381444\pi\) | ||||
0.363902 | + | 0.931437i | \(0.381444\pi\) | |||||||
\(132\) | −1.88387e7 | −0.712922 | ||||||||
\(133\) | 5.77238e6 | 0.212752 | ||||||||
\(134\) | 2.00484e7 | 0.719800 | ||||||||
\(135\) | 2.48660e7 | 0.869837 | ||||||||
\(136\) | −4.43302e7 | −1.51117 | ||||||||
\(137\) | 3.78003e7 | 1.25595 | 0.627977 | − | 0.778232i | \(-0.283883\pi\) | ||||
0.627977 | + | 0.778232i | \(0.283883\pi\) | |||||||
\(138\) | 1.41780e7 | 0.459239 | ||||||||
\(139\) | −3.65756e7 | −1.15515 | −0.577577 | − | 0.816336i | \(-0.696002\pi\) | ||||
−0.577577 | + | 0.816336i | \(0.696002\pi\) | |||||||
\(140\) | 8.70053e6 | 0.267977 | ||||||||
\(141\) | 2.45934e7 | 0.738842 | ||||||||
\(142\) | −2.46549e7 | −0.722593 | ||||||||
\(143\) | 9.15534e6 | 0.261817 | ||||||||
\(144\) | 1.15186e6 | 0.0321464 | ||||||||
\(145\) | 5.69262e7 | 1.55069 | ||||||||
\(146\) | −1.09856e6 | −0.0292138 | ||||||||
\(147\) | −6.20286e6 | −0.161058 | ||||||||
\(148\) | −4.35017e6 | −0.110304 | ||||||||
\(149\) | 3.97274e7 | 0.983871 | 0.491935 | − | 0.870632i | \(-0.336290\pi\) | ||||
0.491935 | + | 0.870632i | \(0.336290\pi\) | |||||||
\(150\) | −3.21927e6 | −0.0778821 | ||||||||
\(151\) | 6.19695e7 | 1.46473 | 0.732367 | − | 0.680910i | \(-0.238416\pi\) | ||||
0.732367 | + | 0.680910i | \(0.238416\pi\) | |||||||
\(152\) | 2.33830e7 | 0.540066 | ||||||||
\(153\) | 1.89121e7 | 0.426894 | ||||||||
\(154\) | 9.29145e6 | 0.205003 | ||||||||
\(155\) | 9.04451e7 | 1.95085 | ||||||||
\(156\) | −9.93200e6 | −0.209460 | ||||||||
\(157\) | 9.21530e7 | 1.90047 | 0.950234 | − | 0.311536i | \(-0.100843\pi\) | ||||
0.950234 | + | 0.311536i | \(0.100843\pi\) | |||||||
\(158\) | 1.05391e7 | 0.212570 | ||||||||
\(159\) | −2.34235e7 | −0.462127 | ||||||||
\(160\) | 5.63505e7 | 1.08762 | ||||||||
\(161\) | 1.41893e7 | 0.267960 | ||||||||
\(162\) | −3.72345e7 | −0.688087 | ||||||||
\(163\) | −6.01364e7 | −1.08763 | −0.543814 | − | 0.839206i | \(-0.683020\pi\) | ||||
−0.543814 | + | 0.839206i | \(0.683020\pi\) | |||||||
\(164\) | −5.60955e7 | −0.993057 | ||||||||
\(165\) | 6.49976e7 | 1.12643 | ||||||||
\(166\) | 3.25705e7 | 0.552645 | ||||||||
\(167\) | −8.63275e7 | −1.43431 | −0.717153 | − | 0.696916i | \(-0.754555\pi\) | ||||
−0.717153 | + | 0.696916i | \(0.754555\pi\) | |||||||
\(168\) | −2.51268e7 | −0.408841 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 6.13556e7 | 0.957819 | ||||||||
\(171\) | −9.97563e6 | −0.152565 | ||||||||
\(172\) | 1.93983e7 | 0.290680 | ||||||||
\(173\) | −1.09221e8 | −1.60378 | −0.801891 | − | 0.597470i | \(-0.796173\pi\) | ||||
−0.801891 | + | 0.597470i | \(0.796173\pi\) | |||||||
\(174\) | −6.59496e7 | −0.949052 | ||||||||
\(175\) | −3.22183e6 | −0.0454432 | ||||||||
\(176\) | −8.09777e6 | −0.111962 | ||||||||
\(177\) | 3.43941e7 | 0.466205 | ||||||||
\(178\) | −7.89358e7 | −1.04907 | ||||||||
\(179\) | 8.79839e7 | 1.14661 | 0.573307 | − | 0.819340i | \(-0.305660\pi\) | ||||
0.573307 | + | 0.819340i | \(0.305660\pi\) | |||||||
\(180\) | −1.50360e7 | −0.192167 | ||||||||
\(181\) | 9.60304e7 | 1.20374 | 0.601871 | − | 0.798593i | \(-0.294422\pi\) | ||||
0.601871 | + | 0.798593i | \(0.294422\pi\) | |||||||
\(182\) | 4.89857e6 | 0.0602309 | ||||||||
\(183\) | 2.29299e7 | 0.276581 | ||||||||
\(184\) | 5.74785e7 | 0.680211 | ||||||||
\(185\) | 1.50090e7 | 0.174282 | ||||||||
\(186\) | −1.04782e8 | −1.19396 | ||||||||
\(187\) | −1.32955e8 | −1.48682 | ||||||||
\(188\) | 3.99961e7 | 0.439001 | ||||||||
\(189\) | −2.88304e7 | −0.310624 | ||||||||
\(190\) | −3.23634e7 | −0.342308 | ||||||||
\(191\) | 1.28873e8 | 1.33828 | 0.669139 | − | 0.743138i | \(-0.266663\pi\) | ||||
0.669139 | + | 0.743138i | \(0.266663\pi\) | |||||||
\(192\) | −5.21686e7 | −0.531931 | ||||||||
\(193\) | −8.87057e7 | −0.888180 | −0.444090 | − | 0.895982i | \(-0.646473\pi\) | ||||
−0.444090 | + | 0.895982i | \(0.646473\pi\) | |||||||
\(194\) | 6.27146e7 | 0.616684 | ||||||||
\(195\) | 3.42675e7 | 0.330949 | ||||||||
\(196\) | −1.00877e7 | −0.0956962 | ||||||||
\(197\) | 2.17845e6 | 0.0203009 | 0.0101505 | − | 0.999948i | \(-0.496769\pi\) | ||||
0.0101505 | + | 0.999948i | \(0.496769\pi\) | |||||||
\(198\) | −1.60572e7 | −0.147008 | ||||||||
\(199\) | −5.39231e7 | −0.485052 | −0.242526 | − | 0.970145i | \(-0.577976\pi\) | ||||
−0.242526 | + | 0.970145i | \(0.577976\pi\) | |||||||
\(200\) | −1.30511e7 | −0.115356 | ||||||||
\(201\) | −1.62606e8 | −1.41238 | ||||||||
\(202\) | −1.54689e7 | −0.132047 | ||||||||
\(203\) | −6.60021e7 | −0.553760 | ||||||||
\(204\) | 1.44234e8 | 1.18949 | ||||||||
\(205\) | 1.93541e8 | 1.56904 | ||||||||
\(206\) | 1.47563e7 | 0.117609 | ||||||||
\(207\) | −2.45215e7 | −0.192155 | ||||||||
\(208\) | −4.26925e6 | −0.0328950 | ||||||||
\(209\) | 7.01302e7 | 0.531365 | ||||||||
\(210\) | 3.47770e7 | 0.259134 | ||||||||
\(211\) | −1.74383e8 | −1.27795 | −0.638977 | − | 0.769226i | \(-0.720642\pi\) | ||||
−0.638977 | + | 0.769226i | \(0.720642\pi\) | |||||||
\(212\) | −3.80934e7 | −0.274584 | ||||||||
\(213\) | 1.99968e8 | 1.41786 | ||||||||
\(214\) | 4.59269e6 | 0.0320346 | ||||||||
\(215\) | −6.69283e7 | −0.459278 | ||||||||
\(216\) | −1.16787e8 | −0.788511 | ||||||||
\(217\) | −1.04865e8 | −0.696660 | ||||||||
\(218\) | 1.29513e8 | 0.846674 | ||||||||
\(219\) | 8.91009e6 | 0.0573229 | ||||||||
\(220\) | 1.05705e8 | 0.669294 | ||||||||
\(221\) | −7.00956e7 | −0.436835 | ||||||||
\(222\) | −1.73881e7 | −0.106664 | ||||||||
\(223\) | 2.20113e8 | 1.32917 | 0.664583 | − | 0.747215i | \(-0.268609\pi\) | ||||
0.664583 | + | 0.747215i | \(0.268609\pi\) | |||||||
\(224\) | −6.53345e7 | −0.388396 | ||||||||
\(225\) | 5.56786e6 | 0.0325874 | ||||||||
\(226\) | −2.15296e7 | −0.124067 | ||||||||
\(227\) | 2.09224e8 | 1.18719 | 0.593597 | − | 0.804762i | \(-0.297707\pi\) | ||||
0.593597 | + | 0.804762i | \(0.297707\pi\) | |||||||
\(228\) | −7.60795e7 | −0.425104 | ||||||||
\(229\) | −7.00169e6 | −0.0385282 | −0.0192641 | − | 0.999814i | \(-0.506132\pi\) | ||||
−0.0192641 | + | 0.999814i | \(0.506132\pi\) | |||||||
\(230\) | −7.95538e7 | −0.431135 | ||||||||
\(231\) | −7.53602e7 | −0.402254 | ||||||||
\(232\) | −2.67363e8 | −1.40570 | ||||||||
\(233\) | 9.83820e7 | 0.509530 | 0.254765 | − | 0.967003i | \(-0.418002\pi\) | ||||
0.254765 | + | 0.967003i | \(0.418002\pi\) | |||||||
\(234\) | −8.46554e6 | −0.0431916 | ||||||||
\(235\) | −1.37995e8 | −0.693627 | ||||||||
\(236\) | 5.59349e7 | 0.277007 | ||||||||
\(237\) | −8.54792e7 | −0.417101 | ||||||||
\(238\) | −7.11377e7 | −0.342043 | ||||||||
\(239\) | −3.50782e8 | −1.66205 | −0.831026 | − | 0.556233i | \(-0.812246\pi\) | ||||
−0.831026 | + | 0.556233i | \(0.812246\pi\) | |||||||
\(240\) | −3.03092e7 | −0.141525 | ||||||||
\(241\) | 2.81267e8 | 1.29437 | 0.647186 | − | 0.762332i | \(-0.275946\pi\) | ||||
0.647186 | + | 0.762332i | \(0.275946\pi\) | |||||||
\(242\) | −1.37915e7 | −0.0625542 | ||||||||
\(243\) | 1.18173e8 | 0.528318 | ||||||||
\(244\) | 3.72907e7 | 0.164337 | ||||||||
\(245\) | 3.48046e7 | 0.151201 | ||||||||
\(246\) | −2.24220e8 | −0.960286 | ||||||||
\(247\) | 3.69735e7 | 0.156117 | ||||||||
\(248\) | −4.24790e8 | −1.76845 | ||||||||
\(249\) | −2.64170e8 | −1.08439 | ||||||||
\(250\) | −1.32176e8 | −0.535011 | ||||||||
\(251\) | −1.90101e8 | −0.758798 | −0.379399 | − | 0.925233i | \(-0.623869\pi\) | ||||
−0.379399 | + | 0.925233i | \(0.623869\pi\) | |||||||
\(252\) | 1.74332e7 | 0.0686238 | ||||||||
\(253\) | 1.72390e8 | 0.669252 | ||||||||
\(254\) | 1.31284e8 | 0.502684 | ||||||||
\(255\) | −4.97638e8 | −1.87941 | ||||||||
\(256\) | −2.43332e8 | −0.906483 | ||||||||
\(257\) | −5.05144e7 | −0.185631 | −0.0928153 | − | 0.995683i | \(-0.529587\pi\) | ||||
−0.0928153 | + | 0.995683i | \(0.529587\pi\) | |||||||
\(258\) | 7.75372e7 | 0.281087 | ||||||||
\(259\) | −1.74019e7 | −0.0622370 | ||||||||
\(260\) | 5.57291e7 | 0.196641 | ||||||||
\(261\) | 1.14063e8 | 0.397101 | ||||||||
\(262\) | 1.21733e8 | 0.418171 | ||||||||
\(263\) | 4.21930e8 | 1.43020 | 0.715098 | − | 0.699024i | \(-0.246382\pi\) | ||||
0.715098 | + | 0.699024i | \(0.246382\pi\) | |||||||
\(264\) | −3.05272e8 | −1.02111 | ||||||||
\(265\) | 1.31430e8 | 0.433846 | ||||||||
\(266\) | 3.75232e7 | 0.122240 | ||||||||
\(267\) | 6.40225e8 | 2.05846 | ||||||||
\(268\) | −2.64446e8 | −0.839199 | ||||||||
\(269\) | 2.50710e8 | 0.785304 | 0.392652 | − | 0.919687i | \(-0.371558\pi\) | ||||
0.392652 | + | 0.919687i | \(0.371558\pi\) | |||||||
\(270\) | 1.61641e8 | 0.499779 | ||||||||
\(271\) | −4.90223e7 | −0.149624 | −0.0748121 | − | 0.997198i | \(-0.523836\pi\) | ||||
−0.0748121 | + | 0.997198i | \(0.523836\pi\) | |||||||
\(272\) | 6.19986e7 | 0.186806 | ||||||||
\(273\) | −3.97309e7 | −0.118184 | ||||||||
\(274\) | 2.45720e8 | 0.721628 | ||||||||
\(275\) | −3.91429e7 | −0.113498 | ||||||||
\(276\) | −1.87014e8 | −0.535417 | ||||||||
\(277\) | −4.88373e8 | −1.38061 | −0.690307 | − | 0.723517i | \(-0.742524\pi\) | ||||
−0.690307 | + | 0.723517i | \(0.742524\pi\) | |||||||
\(278\) | −2.37759e8 | −0.663713 | ||||||||
\(279\) | 1.81224e8 | 0.499576 | ||||||||
\(280\) | 1.40988e8 | 0.383821 | ||||||||
\(281\) | −2.94543e8 | −0.791911 | −0.395956 | − | 0.918270i | \(-0.629587\pi\) | ||||
−0.395956 | + | 0.918270i | \(0.629587\pi\) | |||||||
\(282\) | 1.59869e8 | 0.424514 | ||||||||
\(283\) | −3.25069e8 | −0.852557 | −0.426279 | − | 0.904592i | \(-0.640176\pi\) | ||||
−0.426279 | + | 0.904592i | \(0.640176\pi\) | |||||||
\(284\) | 3.25208e8 | 0.842455 | ||||||||
\(285\) | 2.62490e8 | 0.671671 | ||||||||
\(286\) | 5.95140e7 | 0.150431 | ||||||||
\(287\) | −2.24398e8 | −0.560315 | ||||||||
\(288\) | 1.12909e8 | 0.278519 | ||||||||
\(289\) | 6.07599e8 | 1.48073 | ||||||||
\(290\) | 3.70047e8 | 0.890973 | ||||||||
\(291\) | −5.08660e8 | −1.21005 | ||||||||
\(292\) | 1.44904e7 | 0.0340598 | ||||||||
\(293\) | 2.16739e8 | 0.503385 | 0.251693 | − | 0.967807i | \(-0.419013\pi\) | ||||
0.251693 | + | 0.967807i | \(0.419013\pi\) | |||||||
\(294\) | −4.03215e7 | −0.0925383 | ||||||||
\(295\) | −1.92987e8 | −0.437675 | ||||||||
\(296\) | −7.04924e7 | −0.157987 | ||||||||
\(297\) | −3.50269e8 | −0.775807 | ||||||||
\(298\) | 2.58247e8 | 0.565299 | ||||||||
\(299\) | 9.08860e7 | 0.196629 | ||||||||
\(300\) | 4.24634e7 | 0.0908010 | ||||||||
\(301\) | 7.75988e7 | 0.164011 | ||||||||
\(302\) | 4.02831e8 | 0.841586 | ||||||||
\(303\) | 1.25464e8 | 0.259101 | ||||||||
\(304\) | −3.27026e7 | −0.0667612 | ||||||||
\(305\) | −1.28661e8 | −0.259655 | ||||||||
\(306\) | 1.22938e8 | 0.245279 | ||||||||
\(307\) | 5.01134e8 | 0.988483 | 0.494242 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494242 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(308\) | −1.22558e8 | −0.239009 | ||||||||
\(309\) | −1.19684e8 | −0.230771 | ||||||||
\(310\) | 5.87936e8 | 1.12089 | ||||||||
\(311\) | 3.33730e8 | 0.629120 | 0.314560 | − | 0.949238i | \(-0.398143\pi\) | ||||
0.314560 | + | 0.949238i | \(0.398143\pi\) | |||||||
\(312\) | −1.60943e8 | −0.300007 | ||||||||
\(313\) | 1.00705e9 | 1.85628 | 0.928142 | − | 0.372226i | \(-0.121405\pi\) | ||||
0.928142 | + | 0.372226i | \(0.121405\pi\) | |||||||
\(314\) | 5.99038e8 | 1.09195 | ||||||||
\(315\) | −6.01482e7 | −0.108427 | ||||||||
\(316\) | −1.39014e8 | −0.247831 | ||||||||
\(317\) | 5.51513e8 | 0.972408 | 0.486204 | − | 0.873845i | \(-0.338381\pi\) | ||||
0.486204 | + | 0.873845i | \(0.338381\pi\) | |||||||
\(318\) | −1.52264e8 | −0.265522 | ||||||||
\(319\) | −8.01877e8 | −1.38306 | ||||||||
\(320\) | 2.92721e8 | 0.499378 | ||||||||
\(321\) | −3.72500e7 | −0.0628576 | ||||||||
\(322\) | 9.22372e7 | 0.153961 | ||||||||
\(323\) | −5.36935e8 | −0.886569 | ||||||||
\(324\) | 4.91138e8 | 0.802225 | ||||||||
\(325\) | −2.06366e7 | −0.0333462 | ||||||||
\(326\) | −3.90915e8 | −0.624914 | ||||||||
\(327\) | −1.05044e9 | −1.66133 | ||||||||
\(328\) | −9.08999e8 | −1.42235 | ||||||||
\(329\) | 1.59996e8 | 0.247698 | ||||||||
\(330\) | 4.22515e8 | 0.647207 | ||||||||
\(331\) | 9.73421e8 | 1.47538 | 0.737688 | − | 0.675141i | \(-0.235917\pi\) | ||||
0.737688 | + | 0.675141i | \(0.235917\pi\) | |||||||
\(332\) | −4.29618e8 | −0.644317 | ||||||||
\(333\) | 3.00735e7 | 0.0446302 | ||||||||
\(334\) | −5.61170e8 | −0.824103 | ||||||||
\(335\) | 9.12395e8 | 1.32595 | ||||||||
\(336\) | 3.51414e7 | 0.0505396 | ||||||||
\(337\) | 2.52523e8 | 0.359415 | 0.179708 | − | 0.983720i | \(-0.442485\pi\) | ||||
0.179708 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(338\) | 3.13765e7 | 0.0441974 | ||||||||
\(339\) | 1.74620e8 | 0.243442 | ||||||||
\(340\) | −8.09305e8 | −1.11670 | ||||||||
\(341\) | −1.27403e9 | −1.73996 | ||||||||
\(342\) | −6.48464e7 | −0.0876585 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 3.14340e8 | 0.416337 | ||||||||
\(345\) | 6.45238e8 | 0.845966 | ||||||||
\(346\) | −7.09989e8 | −0.921479 | ||||||||
\(347\) | 6.79989e8 | 0.873673 | 0.436837 | − | 0.899541i | \(-0.356099\pi\) | ||||
0.436837 | + | 0.899541i | \(0.356099\pi\) | |||||||
\(348\) | 8.69901e8 | 1.10648 | ||||||||
\(349\) | 1.02039e7 | 0.0128492 | 0.00642460 | − | 0.999979i | \(-0.497955\pi\) | ||||
0.00642460 | + | 0.999979i | \(0.497955\pi\) | |||||||
\(350\) | −2.09434e7 | −0.0261101 | ||||||||
\(351\) | −1.84666e8 | −0.227936 | ||||||||
\(352\) | −7.93767e8 | −0.970049 | ||||||||
\(353\) | −1.11308e9 | −1.34684 | −0.673420 | − | 0.739260i | \(-0.735175\pi\) | ||||
−0.673420 | + | 0.739260i | \(0.735175\pi\) | |||||||
\(354\) | 2.23578e8 | 0.267866 | ||||||||
\(355\) | −1.12204e9 | −1.33109 | ||||||||
\(356\) | 1.04119e9 | 1.22308 | ||||||||
\(357\) | 5.76977e8 | 0.671150 | ||||||||
\(358\) | 5.71937e8 | 0.658806 | ||||||||
\(359\) | 2.08301e8 | 0.237608 | 0.118804 | − | 0.992918i | \(-0.462094\pi\) | ||||
0.118804 | + | 0.992918i | \(0.462094\pi\) | |||||||
\(360\) | −2.43650e8 | −0.275238 | ||||||||
\(361\) | −6.10653e8 | −0.683155 | ||||||||
\(362\) | 6.24243e8 | 0.691630 | ||||||||
\(363\) | 1.11859e8 | 0.122743 | ||||||||
\(364\) | −6.46141e7 | −0.0702218 | ||||||||
\(365\) | −4.99951e7 | −0.0538149 | ||||||||
\(366\) | 1.49055e8 | 0.158914 | ||||||||
\(367\) | −9.63868e8 | −1.01786 | −0.508928 | − | 0.860809i | \(-0.669958\pi\) | ||||
−0.508928 | + | 0.860809i | \(0.669958\pi\) | |||||||
\(368\) | −8.03875e7 | −0.0840855 | ||||||||
\(369\) | 3.87797e8 | 0.401802 | ||||||||
\(370\) | 9.75658e7 | 0.100136 | ||||||||
\(371\) | −1.52385e8 | −0.154929 | ||||||||
\(372\) | 1.38211e9 | 1.39201 | ||||||||
\(373\) | 3.60216e8 | 0.359403 | 0.179701 | − | 0.983721i | \(-0.442487\pi\) | ||||
0.179701 | + | 0.983721i | \(0.442487\pi\) | |||||||
\(374\) | −8.64271e8 | −0.854278 | ||||||||
\(375\) | 1.07204e9 | 1.04979 | ||||||||
\(376\) | 6.48117e8 | 0.628776 | ||||||||
\(377\) | −4.22760e8 | −0.406349 | ||||||||
\(378\) | −1.87412e8 | −0.178474 | ||||||||
\(379\) | 3.66248e8 | 0.345572 | 0.172786 | − | 0.984959i | \(-0.444723\pi\) | ||||
0.172786 | + | 0.984959i | \(0.444723\pi\) | |||||||
\(380\) | 4.26887e8 | 0.399089 | ||||||||
\(381\) | −1.06481e9 | −0.986357 | ||||||||
\(382\) | 8.37737e8 | 0.768929 | ||||||||
\(383\) | −7.49814e8 | −0.681958 | −0.340979 | − | 0.940071i | \(-0.610759\pi\) | ||||
−0.340979 | + | 0.940071i | \(0.610759\pi\) | |||||||
\(384\) | 9.46351e8 | 0.852889 | ||||||||
\(385\) | 4.22851e8 | 0.377637 | ||||||||
\(386\) | −5.76629e8 | −0.510318 | ||||||||
\(387\) | −1.34104e8 | −0.117612 | ||||||||
\(388\) | −8.27231e8 | −0.718978 | ||||||||
\(389\) | −2.72592e8 | −0.234795 | −0.117398 | − | 0.993085i | \(-0.537455\pi\) | ||||
−0.117398 | + | 0.993085i | \(0.537455\pi\) | |||||||
\(390\) | 2.22755e8 | 0.190152 | ||||||||
\(391\) | −1.31986e9 | −1.11663 | ||||||||
\(392\) | −1.63466e8 | −0.137065 | ||||||||
\(393\) | −9.87342e8 | −0.820528 | ||||||||
\(394\) | 1.41610e7 | 0.0116642 | ||||||||
\(395\) | 4.79629e8 | 0.391576 | ||||||||
\(396\) | 2.11801e8 | 0.171393 | ||||||||
\(397\) | −1.80915e9 | −1.45113 | −0.725567 | − | 0.688152i | \(-0.758422\pi\) | ||||
−0.725567 | + | 0.688152i | \(0.758422\pi\) | |||||||
\(398\) | −3.50525e8 | −0.278695 | ||||||||
\(399\) | −3.04340e8 | −0.239858 | ||||||||
\(400\) | 1.82528e7 | 0.0142600 | ||||||||
\(401\) | 2.25412e9 | 1.74571 | 0.872855 | − | 0.487980i | \(-0.162266\pi\) | ||||
0.872855 | + | 0.487980i | \(0.162266\pi\) | |||||||
\(402\) | −1.05702e9 | −0.811505 | ||||||||
\(403\) | −6.71686e8 | −0.511209 | ||||||||
\(404\) | 2.04041e8 | 0.153951 | ||||||||
\(405\) | −1.69453e9 | −1.26753 | ||||||||
\(406\) | −4.29045e8 | −0.318172 | ||||||||
\(407\) | −2.11421e8 | −0.155442 | ||||||||
\(408\) | 2.33724e9 | 1.70370 | ||||||||
\(409\) | −1.99782e8 | −0.144386 | −0.0721930 | − | 0.997391i | \(-0.523000\pi\) | ||||
−0.0721930 | + | 0.997391i | \(0.523000\pi\) | |||||||
\(410\) | 1.25811e9 | 0.901520 | ||||||||
\(411\) | −1.99296e9 | −1.41597 | ||||||||
\(412\) | −1.94641e8 | −0.137118 | ||||||||
\(413\) | 2.23756e8 | 0.156296 | ||||||||
\(414\) | −1.59401e8 | −0.110406 | ||||||||
\(415\) | 1.48227e9 | 1.01803 | ||||||||
\(416\) | −4.18484e8 | −0.285005 | ||||||||
\(417\) | 1.92839e9 | 1.30233 | ||||||||
\(418\) | 4.55880e8 | 0.305304 | ||||||||
\(419\) | 2.88959e9 | 1.91905 | 0.959526 | − | 0.281619i | \(-0.0908713\pi\) | ||||
0.959526 | + | 0.281619i | \(0.0908713\pi\) | |||||||
\(420\) | −4.58722e8 | −0.302118 | ||||||||
\(421\) | −6.08313e8 | −0.397319 | −0.198660 | − | 0.980069i | \(-0.563659\pi\) | ||||
−0.198660 | + | 0.980069i | \(0.563659\pi\) | |||||||
\(422\) | −1.13357e9 | −0.734270 | ||||||||
\(423\) | −2.76500e8 | −0.177625 | ||||||||
\(424\) | −6.17285e8 | −0.393283 | ||||||||
\(425\) | 2.99688e8 | 0.189368 | ||||||||
\(426\) | 1.29989e9 | 0.814654 | ||||||||
\(427\) | 1.49174e8 | 0.0927245 | ||||||||
\(428\) | −6.05794e7 | −0.0373484 | ||||||||
\(429\) | −4.82701e8 | −0.295174 | ||||||||
\(430\) | −4.35066e8 | −0.263885 | ||||||||
\(431\) | 7.49585e7 | 0.0450973 | 0.0225486 | − | 0.999746i | \(-0.492822\pi\) | ||||
0.0225486 | + | 0.999746i | \(0.492822\pi\) | |||||||
\(432\) | 1.63335e8 | 0.0974732 | ||||||||
\(433\) | 1.67605e9 | 0.992153 | 0.496077 | − | 0.868279i | \(-0.334774\pi\) | ||||
0.496077 | + | 0.868279i | \(0.334774\pi\) | |||||||
\(434\) | −6.81672e8 | −0.400278 | ||||||||
\(435\) | −3.00135e9 | −1.74825 | ||||||||
\(436\) | −1.70833e9 | −0.987118 | ||||||||
\(437\) | 6.96190e8 | 0.399064 | ||||||||
\(438\) | 5.79198e7 | 0.0329358 | ||||||||
\(439\) | 1.92663e8 | 0.108686 | 0.0543429 | − | 0.998522i | \(-0.482694\pi\) | ||||
0.0543429 | + | 0.998522i | \(0.482694\pi\) | |||||||
\(440\) | 1.71290e9 | 0.958622 | ||||||||
\(441\) | 6.97378e7 | 0.0387198 | ||||||||
\(442\) | −4.55655e8 | −0.250991 | ||||||||
\(443\) | −1.47972e9 | −0.808662 | −0.404331 | − | 0.914613i | \(-0.632496\pi\) | ||||
−0.404331 | + | 0.914613i | \(0.632496\pi\) | |||||||
\(444\) | 2.29356e8 | 0.124357 | ||||||||
\(445\) | −3.59234e9 | −1.93249 | ||||||||
\(446\) | 1.43084e9 | 0.763694 | ||||||||
\(447\) | −2.09456e9 | −1.10922 | ||||||||
\(448\) | −3.39390e8 | −0.178331 | ||||||||
\(449\) | 2.90185e9 | 1.51291 | 0.756454 | − | 0.654046i | \(-0.226930\pi\) | ||||
0.756454 | + | 0.654046i | \(0.226930\pi\) | |||||||
\(450\) | 3.61937e7 | 0.0187236 | ||||||||
\(451\) | −2.72627e9 | −1.39943 | ||||||||
\(452\) | 2.83984e8 | 0.144647 | ||||||||
\(453\) | −3.26724e9 | −1.65135 | ||||||||
\(454\) | 1.36006e9 | 0.682122 | ||||||||
\(455\) | 2.22932e8 | 0.110952 | ||||||||
\(456\) | −1.23283e9 | −0.608872 | ||||||||
\(457\) | −2.23509e9 | −1.09544 | −0.547720 | − | 0.836661i | \(-0.684504\pi\) | ||||
−0.547720 | + | 0.836661i | \(0.684504\pi\) | |||||||
\(458\) | −4.55143e7 | −0.0221370 | ||||||||
\(459\) | 2.68175e9 | 1.29441 | ||||||||
\(460\) | 1.04935e9 | 0.502651 | ||||||||
\(461\) | −2.50252e9 | −1.18967 | −0.594833 | − | 0.803849i | \(-0.702782\pi\) | ||||
−0.594833 | + | 0.803849i | \(0.702782\pi\) | |||||||
\(462\) | −4.89877e8 | −0.231122 | ||||||||
\(463\) | 1.61344e9 | 0.755475 | 0.377737 | − | 0.925913i | \(-0.376702\pi\) | ||||
0.377737 | + | 0.925913i | \(0.376702\pi\) | |||||||
\(464\) | 3.73925e8 | 0.173769 | ||||||||
\(465\) | −4.76858e9 | −2.19940 | ||||||||
\(466\) | 6.39529e8 | 0.292759 | ||||||||
\(467\) | 5.43251e7 | 0.0246826 | 0.0123413 | − | 0.999924i | \(-0.496072\pi\) | ||||
0.0123413 | + | 0.999924i | \(0.496072\pi\) | |||||||
\(468\) | 1.11664e8 | 0.0503561 | ||||||||
\(469\) | −1.05786e9 | −0.473503 | ||||||||
\(470\) | −8.97034e8 | −0.398535 | ||||||||
\(471\) | −4.85862e9 | −2.14260 | ||||||||
\(472\) | 9.06397e8 | 0.396754 | ||||||||
\(473\) | 9.42769e8 | 0.409630 | ||||||||
\(474\) | −5.55656e8 | −0.239652 | ||||||||
\(475\) | −1.58077e8 | −0.0676770 | ||||||||
\(476\) | 9.38334e8 | 0.398780 | ||||||||
\(477\) | 2.63346e8 | 0.111100 | ||||||||
\(478\) | −2.28025e9 | −0.954959 | ||||||||
\(479\) | 3.25378e9 | 1.35274 | 0.676370 | − | 0.736562i | \(-0.263552\pi\) | ||||
0.676370 | + | 0.736562i | \(0.263552\pi\) | |||||||
\(480\) | −2.97099e9 | −1.22619 | ||||||||
\(481\) | −1.11464e8 | −0.0456695 | ||||||||
\(482\) | 1.82837e9 | 0.743702 | ||||||||
\(483\) | −7.48109e8 | −0.302100 | ||||||||
\(484\) | 1.81915e8 | 0.0729306 | ||||||||
\(485\) | 2.85412e9 | 1.13600 | ||||||||
\(486\) | 7.68179e8 | 0.303554 | ||||||||
\(487\) | −1.98132e9 | −0.777327 | −0.388663 | − | 0.921380i | \(-0.627063\pi\) | ||||
−0.388663 | + | 0.921380i | \(0.627063\pi\) | |||||||
\(488\) | 6.04278e8 | 0.235379 | ||||||||
\(489\) | 3.17060e9 | 1.22620 | ||||||||
\(490\) | 2.26247e8 | 0.0868752 | ||||||||
\(491\) | 4.58463e8 | 0.174791 | 0.0873954 | − | 0.996174i | \(-0.472146\pi\) | ||||
0.0873954 | + | 0.996174i | \(0.472146\pi\) | |||||||
\(492\) | 2.95755e9 | 1.11958 | ||||||||
\(493\) | 6.13937e9 | 2.30760 | ||||||||
\(494\) | 2.40345e8 | 0.0896998 | ||||||||
\(495\) | −7.30757e8 | −0.270804 | ||||||||
\(496\) | 5.94097e8 | 0.218611 | ||||||||
\(497\) | 1.30092e9 | 0.475340 | ||||||||
\(498\) | −1.71723e9 | −0.623054 | ||||||||
\(499\) | −2.67502e9 | −0.963773 | −0.481887 | − | 0.876234i | \(-0.660048\pi\) | ||||
−0.481887 | + | 0.876234i | \(0.660048\pi\) | |||||||
\(500\) | 1.74345e9 | 0.623757 | ||||||||
\(501\) | 4.55148e9 | 1.61704 | ||||||||
\(502\) | −1.23575e9 | −0.435980 | ||||||||
\(503\) | −3.20863e9 | −1.12417 | −0.562084 | − | 0.827080i | \(-0.690000\pi\) | ||||
−0.562084 | + | 0.827080i | \(0.690000\pi\) | |||||||
\(504\) | 2.82496e8 | 0.0982892 | ||||||||
\(505\) | −7.03985e8 | −0.243245 | ||||||||
\(506\) | 1.12062e9 | 0.384530 | ||||||||
\(507\) | −2.54486e8 | −0.0867233 | ||||||||
\(508\) | −1.73169e9 | −0.586067 | ||||||||
\(509\) | 5.69298e9 | 1.91349 | 0.956747 | − | 0.290921i | \(-0.0939616\pi\) | ||||
0.956747 | + | 0.290921i | \(0.0939616\pi\) | |||||||
\(510\) | −3.23488e9 | −1.07985 | ||||||||
\(511\) | 5.79659e7 | 0.0192176 | ||||||||
\(512\) | 7.15740e8 | 0.235673 | ||||||||
\(513\) | −1.41455e9 | −0.462602 | ||||||||
\(514\) | −3.28368e8 | −0.106657 | ||||||||
\(515\) | 6.71553e8 | 0.216648 | ||||||||
\(516\) | −1.02275e9 | −0.327713 | ||||||||
\(517\) | 1.94383e9 | 0.618646 | ||||||||
\(518\) | −1.13121e8 | −0.0357593 | ||||||||
\(519\) | 5.75852e9 | 1.80811 | ||||||||
\(520\) | 9.03062e8 | 0.281647 | ||||||||
\(521\) | 4.01360e9 | 1.24338 | 0.621688 | − | 0.783265i | \(-0.286447\pi\) | ||||
0.621688 | + | 0.783265i | \(0.286447\pi\) | |||||||
\(522\) | 7.41461e8 | 0.228161 | ||||||||
\(523\) | 3.14718e9 | 0.961980 | 0.480990 | − | 0.876726i | \(-0.340277\pi\) | ||||
0.480990 | + | 0.876726i | \(0.340277\pi\) | |||||||
\(524\) | −1.60571e9 | −0.487536 | ||||||||
\(525\) | 1.69866e8 | 0.0512328 | ||||||||
\(526\) | 2.74275e9 | 0.821743 | ||||||||
\(527\) | 9.75431e9 | 2.90308 | ||||||||
\(528\) | 4.26943e8 | 0.126227 | ||||||||
\(529\) | −1.69349e9 | −0.497380 | ||||||||
\(530\) | 8.54361e8 | 0.249273 | ||||||||
\(531\) | −3.86687e8 | −0.112080 | ||||||||
\(532\) | −4.94946e8 | −0.142517 | ||||||||
\(533\) | −1.43732e9 | −0.411159 | ||||||||
\(534\) | 4.16176e9 | 1.18272 | ||||||||
\(535\) | 2.09012e8 | 0.0590110 | ||||||||
\(536\) | −4.28521e9 | −1.20198 | ||||||||
\(537\) | −4.63881e9 | −1.29270 | ||||||||
\(538\) | 1.62973e9 | 0.451209 | ||||||||
\(539\) | −4.90267e8 | −0.134857 | ||||||||
\(540\) | −2.13211e9 | −0.582681 | ||||||||
\(541\) | 1.40011e9 | 0.380165 | 0.190082 | − | 0.981768i | \(-0.439124\pi\) | ||||
0.190082 | + | 0.981768i | \(0.439124\pi\) | |||||||
\(542\) | −3.18669e8 | −0.0859690 | ||||||||
\(543\) | −5.06305e9 | −1.35710 | ||||||||
\(544\) | 6.07728e9 | 1.61850 | ||||||||
\(545\) | 5.89410e9 | 1.55966 | ||||||||
\(546\) | −2.58269e8 | −0.0679045 | ||||||||
\(547\) | 6.13945e8 | 0.160389 | 0.0801944 | − | 0.996779i | \(-0.474446\pi\) | ||||
0.0801944 | + | 0.996779i | \(0.474446\pi\) | |||||||
\(548\) | −3.24114e9 | −0.841330 | ||||||||
\(549\) | −2.57797e8 | −0.0664928 | ||||||||
\(550\) | −2.54447e8 | −0.0652121 | ||||||||
\(551\) | −3.23835e9 | −0.824695 | ||||||||
\(552\) | −3.03047e9 | −0.766872 | ||||||||
\(553\) | −5.56098e8 | −0.139834 | ||||||||
\(554\) | −3.17465e9 | −0.793254 | ||||||||
\(555\) | −7.91328e8 | −0.196486 | ||||||||
\(556\) | 3.13614e9 | 0.773808 | ||||||||
\(557\) | 2.17564e9 | 0.533451 | 0.266725 | − | 0.963773i | \(-0.414058\pi\) | ||||
0.266725 | + | 0.963773i | \(0.414058\pi\) | |||||||
\(558\) | 1.17804e9 | 0.287039 | ||||||||
\(559\) | 4.97040e8 | 0.120351 | ||||||||
\(560\) | −1.97181e8 | −0.0474467 | ||||||||
\(561\) | 7.00985e9 | 1.67625 | ||||||||
\(562\) | −1.91467e9 | −0.455006 | ||||||||
\(563\) | 2.66923e9 | 0.630385 | 0.315193 | − | 0.949028i | \(-0.397931\pi\) | ||||
0.315193 | + | 0.949028i | \(0.397931\pi\) | |||||||
\(564\) | −2.10873e9 | −0.494931 | ||||||||
\(565\) | −9.79804e8 | −0.228544 | ||||||||
\(566\) | −2.11311e9 | −0.489851 | ||||||||
\(567\) | 1.96469e9 | 0.452641 | ||||||||
\(568\) | 5.26983e9 | 1.20664 | ||||||||
\(569\) | 3.22353e9 | 0.733565 | 0.366782 | − | 0.930307i | \(-0.380459\pi\) | ||||
0.366782 | + | 0.930307i | \(0.380459\pi\) | |||||||
\(570\) | 1.70631e9 | 0.385919 | ||||||||
\(571\) | −2.77463e9 | −0.623704 | −0.311852 | − | 0.950131i | \(-0.600949\pi\) | ||||
−0.311852 | + | 0.950131i | \(0.600949\pi\) | |||||||
\(572\) | −7.85014e8 | −0.175385 | ||||||||
\(573\) | −6.79464e9 | −1.50878 | ||||||||
\(574\) | −1.45869e9 | −0.321938 | ||||||||
\(575\) | −3.88575e8 | −0.0852389 | ||||||||
\(576\) | 5.86523e8 | 0.127881 | ||||||||
\(577\) | 1.90843e9 | 0.413581 | 0.206791 | − | 0.978385i | \(-0.433698\pi\) | ||||
0.206791 | + | 0.978385i | \(0.433698\pi\) | |||||||
\(578\) | 3.94968e9 | 0.850775 | ||||||||
\(579\) | 4.67687e9 | 1.00134 | ||||||||
\(580\) | −4.88107e9 | −1.03876 | ||||||||
\(581\) | −1.71860e9 | −0.363544 | ||||||||
\(582\) | −3.30653e9 | −0.695252 | ||||||||
\(583\) | −1.85136e9 | −0.386947 | ||||||||
\(584\) | 2.34810e8 | 0.0487834 | ||||||||
\(585\) | −3.85264e8 | −0.0795634 | ||||||||
\(586\) | 1.40891e9 | 0.289228 | ||||||||
\(587\) | −3.28107e9 | −0.669549 | −0.334774 | − | 0.942298i | \(-0.608660\pi\) | ||||
−0.334774 | + | 0.942298i | \(0.608660\pi\) | |||||||
\(588\) | 5.31857e8 | 0.107888 | ||||||||
\(589\) | −5.14514e9 | −1.03751 | ||||||||
\(590\) | −1.25451e9 | −0.251473 | ||||||||
\(591\) | −1.14856e8 | −0.0228874 | ||||||||
\(592\) | 9.85882e7 | 0.0195299 | ||||||||
\(593\) | −6.58808e9 | −1.29738 | −0.648690 | − | 0.761053i | \(-0.724683\pi\) | ||||
−0.648690 | + | 0.761053i | \(0.724683\pi\) | |||||||
\(594\) | −2.27691e9 | −0.445753 | ||||||||
\(595\) | −3.23745e9 | −0.630078 | ||||||||
\(596\) | −3.40638e9 | −0.659069 | ||||||||
\(597\) | 2.84301e9 | 0.546850 | ||||||||
\(598\) | 5.90802e8 | 0.112976 | ||||||||
\(599\) | 3.71767e9 | 0.706769 | 0.353384 | − | 0.935478i | \(-0.385031\pi\) | ||||
0.353384 | + | 0.935478i | \(0.385031\pi\) | |||||||
\(600\) | 6.88098e8 | 0.130053 | ||||||||
\(601\) | 2.62109e9 | 0.492518 | 0.246259 | − | 0.969204i | \(-0.420799\pi\) | ||||
0.246259 | + | 0.969204i | \(0.420799\pi\) | |||||||
\(602\) | 5.04429e8 | 0.0942351 | ||||||||
\(603\) | 1.82816e9 | 0.339549 | ||||||||
\(604\) | −5.31350e9 | −0.981186 | ||||||||
\(605\) | −6.27646e8 | −0.115231 | ||||||||
\(606\) | 8.15574e8 | 0.148871 | ||||||||
\(607\) | −1.04965e10 | −1.90494 | −0.952472 | − | 0.304627i | \(-0.901468\pi\) | ||||
−0.952472 | + | 0.304627i | \(0.901468\pi\) | |||||||
\(608\) | −3.20560e9 | −0.578425 | ||||||||
\(609\) | 3.47986e9 | 0.624311 | ||||||||
\(610\) | −8.36357e8 | −0.149189 | ||||||||
\(611\) | 1.02481e9 | 0.181761 | ||||||||
\(612\) | −1.62160e9 | −0.285965 | ||||||||
\(613\) | 2.60944e9 | 0.457547 | 0.228774 | − | 0.973480i | \(-0.426528\pi\) | ||||
0.228774 | + | 0.973480i | \(0.426528\pi\) | |||||||
\(614\) | 3.25761e9 | 0.567949 | ||||||||
\(615\) | −1.02042e10 | −1.76895 | ||||||||
\(616\) | −1.98599e9 | −0.342330 | ||||||||
\(617\) | −6.60062e9 | −1.13132 | −0.565662 | − | 0.824637i | \(-0.691379\pi\) | ||||
−0.565662 | + | 0.824637i | \(0.691379\pi\) | |||||||
\(618\) | −7.78001e8 | −0.132593 | ||||||||
\(619\) | 7.56093e9 | 1.28132 | 0.640661 | − | 0.767824i | \(-0.278661\pi\) | ||||
0.640661 | + | 0.767824i | \(0.278661\pi\) | |||||||
\(620\) | −7.75511e9 | −1.30682 | ||||||||
\(621\) | −3.47716e9 | −0.582644 | ||||||||
\(622\) | 2.16940e9 | 0.361471 | ||||||||
\(623\) | 4.16508e9 | 0.690104 | ||||||||
\(624\) | 2.25089e8 | 0.0370859 | ||||||||
\(625\) | −6.74912e9 | −1.10578 | ||||||||
\(626\) | 6.54628e9 | 1.06656 | ||||||||
\(627\) | −3.69751e9 | −0.599063 | ||||||||
\(628\) | −7.90155e9 | −1.27307 | ||||||||
\(629\) | 1.61869e9 | 0.259350 | ||||||||
\(630\) | −3.90992e8 | −0.0622983 | ||||||||
\(631\) | 3.56014e9 | 0.564111 | 0.282056 | − | 0.959398i | \(-0.408984\pi\) | ||||
0.282056 | + | 0.959398i | \(0.408984\pi\) | |||||||
\(632\) | −2.25266e9 | −0.354965 | ||||||||
\(633\) | 9.19407e9 | 1.44077 | ||||||||
\(634\) | 3.58510e9 | 0.558712 | ||||||||
\(635\) | 5.97471e9 | 0.925995 | ||||||||
\(636\) | 2.00842e9 | 0.309567 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −5.21258e9 | −0.794658 | ||||||||
\(639\) | −2.24821e9 | −0.340867 | ||||||||
\(640\) | −5.31003e9 | −0.800695 | ||||||||
\(641\) | −3.70708e9 | −0.555941 | −0.277971 | − | 0.960590i | \(-0.589662\pi\) | ||||
−0.277971 | + | 0.960590i | \(0.589662\pi\) | |||||||
\(642\) | −2.42142e8 | −0.0361159 | ||||||||
\(643\) | −4.37448e9 | −0.648915 | −0.324458 | − | 0.945900i | \(-0.605182\pi\) | ||||
−0.324458 | + | 0.945900i | \(0.605182\pi\) | |||||||
\(644\) | −1.21665e9 | −0.179500 | ||||||||
\(645\) | 3.52869e9 | 0.517791 | ||||||||
\(646\) | −3.49033e9 | −0.509393 | ||||||||
\(647\) | −8.40749e9 | −1.22040 | −0.610199 | − | 0.792248i | \(-0.708911\pi\) | ||||
−0.610199 | + | 0.792248i | \(0.708911\pi\) | |||||||
\(648\) | 7.95865e9 | 1.14902 | ||||||||
\(649\) | 2.71847e9 | 0.390362 | ||||||||
\(650\) | −1.34148e8 | −0.0191596 | ||||||||
\(651\) | 5.52884e9 | 0.785417 | ||||||||
\(652\) | 5.15632e9 | 0.728574 | ||||||||
\(653\) | −4.62631e9 | −0.650188 | −0.325094 | − | 0.945682i | \(-0.605396\pi\) | ||||
−0.325094 | + | 0.945682i | \(0.605396\pi\) | |||||||
\(654\) | −6.82838e9 | −0.954543 | ||||||||
\(655\) | 5.54004e9 | 0.770315 | ||||||||
\(656\) | 1.27129e9 | 0.175826 | ||||||||
\(657\) | −1.00175e8 | −0.0137810 | ||||||||
\(658\) | 1.04005e9 | 0.142319 | ||||||||
\(659\) | 8.59881e9 | 1.17041 | 0.585207 | − | 0.810884i | \(-0.301013\pi\) | ||||
0.585207 | + | 0.810884i | \(0.301013\pi\) | |||||||
\(660\) | −5.57314e9 | −0.754564 | ||||||||
\(661\) | −3.09178e9 | −0.416393 | −0.208197 | − | 0.978087i | \(-0.566759\pi\) | ||||
−0.208197 | + | 0.978087i | \(0.566759\pi\) | |||||||
\(662\) | 6.32770e9 | 0.847702 | ||||||||
\(663\) | 3.69568e9 | 0.492490 | ||||||||
\(664\) | −6.96175e9 | −0.922848 | ||||||||
\(665\) | 1.70767e9 | 0.225179 | ||||||||
\(666\) | 1.95492e8 | 0.0256430 | ||||||||
\(667\) | −7.96032e9 | −1.03870 | ||||||||
\(668\) | 7.40205e9 | 0.960804 | ||||||||
\(669\) | −1.16051e10 | −1.49851 | ||||||||
\(670\) | 5.93100e9 | 0.761844 | ||||||||
\(671\) | 1.81235e9 | 0.231587 | ||||||||
\(672\) | 3.44466e9 | 0.437879 | ||||||||
\(673\) | 3.53335e9 | 0.446821 | 0.223411 | − | 0.974724i | \(-0.428281\pi\) | ||||
0.223411 | + | 0.974724i | \(0.428281\pi\) | |||||||
\(674\) | 1.64152e9 | 0.206508 | ||||||||
\(675\) | 7.89524e8 | 0.0988103 | ||||||||
\(676\) | −4.13869e8 | −0.0515287 | ||||||||
\(677\) | 7.28572e9 | 0.902427 | 0.451213 | − | 0.892416i | \(-0.350991\pi\) | ||||
0.451213 | + | 0.892416i | \(0.350991\pi\) | |||||||
\(678\) | 1.13511e9 | 0.139873 | ||||||||
\(679\) | −3.30916e9 | −0.405671 | ||||||||
\(680\) | −1.31144e10 | −1.59944 | ||||||||
\(681\) | −1.10310e10 | −1.33845 | ||||||||
\(682\) | −8.28182e9 | −0.999724 | ||||||||
\(683\) | 4.58761e9 | 0.550952 | 0.275476 | − | 0.961308i | \(-0.411165\pi\) | ||||
0.275476 | + | 0.961308i | \(0.411165\pi\) | |||||||
\(684\) | 8.55349e8 | 0.102199 | ||||||||
\(685\) | 1.11826e10 | 1.32931 | ||||||||
\(686\) | −2.62318e8 | −0.0310237 | ||||||||
\(687\) | 3.69153e8 | 0.0434368 | ||||||||
\(688\) | −4.39625e8 | −0.0514663 | ||||||||
\(689\) | −9.76062e8 | −0.113687 | ||||||||
\(690\) | 4.19435e9 | 0.486063 | ||||||||
\(691\) | −4.79400e9 | −0.552745 | −0.276373 | − | 0.961051i | \(-0.589132\pi\) | ||||
−0.276373 | + | 0.961051i | \(0.589132\pi\) | |||||||
\(692\) | 9.36504e9 | 1.07433 | ||||||||
\(693\) | 8.47263e8 | 0.0967057 | ||||||||
\(694\) | 4.42025e9 | 0.501983 | ||||||||
\(695\) | −1.08203e10 | −1.22263 | ||||||||
\(696\) | 1.40963e10 | 1.58480 | ||||||||
\(697\) | 2.08730e10 | 2.33491 | ||||||||
\(698\) | 6.63301e7 | 0.00738272 | ||||||||
\(699\) | −5.18704e9 | −0.574446 | ||||||||
\(700\) | 2.76252e8 | 0.0304412 | ||||||||
\(701\) | −1.30910e10 | −1.43535 | −0.717676 | − | 0.696377i | \(-0.754794\pi\) | ||||
−0.717676 | + | 0.696377i | \(0.754794\pi\) | |||||||
\(702\) | −1.20042e9 | −0.130964 | ||||||||
\(703\) | −8.53816e8 | −0.0926874 | ||||||||
\(704\) | −4.12335e9 | −0.445395 | ||||||||
\(705\) | 7.27558e9 | 0.781998 | ||||||||
\(706\) | −7.23556e9 | −0.773848 | ||||||||
\(707\) | 8.16223e8 | 0.0868642 | ||||||||
\(708\) | −2.94908e9 | −0.312299 | ||||||||
\(709\) | −3.90402e7 | −0.00411386 | −0.00205693 | − | 0.999998i | \(-0.500655\pi\) | ||||
−0.00205693 | + | 0.999998i | \(0.500655\pi\) | |||||||
\(710\) | −7.29376e9 | −0.764799 | ||||||||
\(711\) | 9.61029e8 | 0.100275 | ||||||||
\(712\) | 1.68720e10 | 1.75181 | ||||||||
\(713\) | −1.26475e10 | −1.30674 | ||||||||
\(714\) | 3.75062e9 | 0.385620 | ||||||||
\(715\) | 2.70847e9 | 0.277110 | ||||||||
\(716\) | −7.54408e9 | −0.768087 | ||||||||
\(717\) | 1.84944e10 | 1.87380 | ||||||||
\(718\) | 1.35406e9 | 0.136521 | ||||||||
\(719\) | −1.42934e10 | −1.43412 | −0.717059 | − | 0.697013i | \(-0.754512\pi\) | ||||
−0.717059 | + | 0.697013i | \(0.754512\pi\) | |||||||
\(720\) | 3.40761e8 | 0.0340241 | ||||||||
\(721\) | −7.78620e8 | −0.0773663 | ||||||||
\(722\) | −3.96954e9 | −0.392518 | ||||||||
\(723\) | −1.48294e10 | −1.45928 | ||||||||
\(724\) | −8.23401e9 | −0.806355 | ||||||||
\(725\) | 1.80747e9 | 0.176152 | ||||||||
\(726\) | 7.27134e8 | 0.0705239 | ||||||||
\(727\) | 7.90232e9 | 0.762753 | 0.381377 | − | 0.924420i | \(-0.375450\pi\) | ||||
0.381377 | + | 0.924420i | \(0.375450\pi\) | |||||||
\(728\) | −1.04704e9 | −0.100578 | ||||||||
\(729\) | 6.29660e9 | 0.601949 | ||||||||
\(730\) | −3.24992e8 | −0.0309202 | ||||||||
\(731\) | −7.21808e9 | −0.683457 | ||||||||
\(732\) | −1.96610e9 | −0.185275 | ||||||||
\(733\) | 8.00899e9 | 0.751128 | 0.375564 | − | 0.926797i | \(-0.377449\pi\) | ||||
0.375564 | + | 0.926797i | \(0.377449\pi\) | |||||||
\(734\) | −6.26560e9 | −0.584825 | ||||||||
\(735\) | −1.83502e9 | −0.170465 | ||||||||
\(736\) | −7.87981e9 | −0.728523 | ||||||||
\(737\) | −1.28522e10 | −1.18261 | ||||||||
\(738\) | 2.52087e9 | 0.230862 | ||||||||
\(739\) | −7.30652e9 | −0.665971 | −0.332985 | − | 0.942932i | \(-0.608056\pi\) | ||||
−0.332985 | + | 0.942932i | \(0.608056\pi\) | |||||||
\(740\) | −1.28693e9 | −0.116747 | ||||||||
\(741\) | −1.94937e9 | −0.176007 | ||||||||
\(742\) | −9.90573e8 | −0.0890170 | ||||||||
\(743\) | 7.68027e9 | 0.686935 | 0.343468 | − | 0.939165i | \(-0.388398\pi\) | ||||
0.343468 | + | 0.939165i | \(0.388398\pi\) | |||||||
\(744\) | 2.23964e10 | 1.99376 | ||||||||
\(745\) | 1.17527e10 | 1.04134 | ||||||||
\(746\) | 2.34157e9 | 0.206501 | ||||||||
\(747\) | 2.97002e9 | 0.260698 | ||||||||
\(748\) | 1.14001e10 | 0.995984 | ||||||||
\(749\) | −2.42335e8 | −0.0210732 | ||||||||
\(750\) | 6.96877e9 | 0.603173 | ||||||||
\(751\) | 1.28085e10 | 1.10347 | 0.551734 | − | 0.834020i | \(-0.313966\pi\) | ||||
0.551734 | + | 0.834020i | \(0.313966\pi\) | |||||||
\(752\) | −9.06434e8 | −0.0777273 | ||||||||
\(753\) | 1.00228e10 | 0.855472 | ||||||||
\(754\) | −2.74814e9 | −0.233474 | ||||||||
\(755\) | 1.83327e10 | 1.55029 | ||||||||
\(756\) | 2.47203e9 | 0.208079 | ||||||||
\(757\) | −1.53569e10 | −1.28667 | −0.643336 | − | 0.765584i | \(-0.722450\pi\) | ||||
−0.643336 | + | 0.765584i | \(0.722450\pi\) | |||||||
\(758\) | 2.38079e9 | 0.198554 | ||||||||
\(759\) | −9.08898e9 | −0.754517 | ||||||||
\(760\) | 6.91749e9 | 0.571611 | ||||||||
\(761\) | 1.70998e10 | 1.40651 | 0.703257 | − | 0.710935i | \(-0.251728\pi\) | ||||
0.703257 | + | 0.710935i | \(0.251728\pi\) | |||||||
\(762\) | −6.92176e9 | −0.566727 | ||||||||
\(763\) | −6.83381e9 | −0.556964 | ||||||||
\(764\) | −1.10501e10 | −0.896477 | ||||||||
\(765\) | 5.59486e9 | 0.451829 | ||||||||
\(766\) | −4.87415e9 | −0.391830 | ||||||||
\(767\) | 1.43321e9 | 0.114690 | ||||||||
\(768\) | 1.28293e10 | 1.02197 | ||||||||
\(769\) | −2.35139e9 | −0.186459 | −0.0932294 | − | 0.995645i | \(-0.529719\pi\) | ||||
−0.0932294 | + | 0.995645i | \(0.529719\pi\) | |||||||
\(770\) | 2.74873e9 | 0.216978 | ||||||||
\(771\) | 2.66329e9 | 0.209281 | ||||||||
\(772\) | 7.60597e9 | 0.594968 | ||||||||
\(773\) | −2.34257e9 | −0.182417 | −0.0912083 | − | 0.995832i | \(-0.529073\pi\) | ||||
−0.0912083 | + | 0.995832i | \(0.529073\pi\) | |||||||
\(774\) | −8.71738e8 | −0.0675760 | ||||||||
\(775\) | 2.87173e9 | 0.221609 | ||||||||
\(776\) | −1.34049e10 | −1.02978 | ||||||||
\(777\) | 9.17490e8 | 0.0701662 | ||||||||
\(778\) | −1.77198e9 | −0.134906 | ||||||||
\(779\) | −1.10100e10 | −0.834458 | ||||||||
\(780\) | −2.93823e9 | −0.221694 | ||||||||
\(781\) | 1.58053e10 | 1.18720 | ||||||||
\(782\) | −8.57971e9 | −0.641578 | ||||||||
\(783\) | 1.61741e10 | 1.20408 | ||||||||
\(784\) | 2.28618e8 | 0.0169435 | ||||||||
\(785\) | 2.72620e10 | 2.01148 | ||||||||
\(786\) | −6.41819e9 | −0.471448 | ||||||||
\(787\) | 7.91498e9 | 0.578813 | 0.289406 | − | 0.957206i | \(-0.406542\pi\) | ||||
0.289406 | + | 0.957206i | \(0.406542\pi\) | |||||||
\(788\) | −1.86789e8 | −0.0135991 | ||||||||
\(789\) | −2.22456e10 | −1.61241 | ||||||||
\(790\) | 3.11782e9 | 0.224986 | ||||||||
\(791\) | 1.13602e9 | 0.0816144 | ||||||||
\(792\) | 3.43212e9 | 0.245485 | ||||||||
\(793\) | 9.55494e8 | 0.0680412 | ||||||||
\(794\) | −1.17603e10 | −0.833772 | ||||||||
\(795\) | −6.92947e9 | −0.489119 | ||||||||
\(796\) | 4.62357e9 | 0.324924 | ||||||||
\(797\) | 1.19781e10 | 0.838075 | 0.419038 | − | 0.907969i | \(-0.362368\pi\) | ||||
0.419038 | + | 0.907969i | \(0.362368\pi\) | |||||||
\(798\) | −1.97835e9 | −0.137814 | ||||||||
\(799\) | −1.48825e10 | −1.03219 | ||||||||
\(800\) | 1.78919e9 | 0.123550 | ||||||||
\(801\) | −7.19794e9 | −0.494874 | ||||||||
\(802\) | 1.46529e10 | 1.00303 | ||||||||
\(803\) | 7.04244e8 | 0.0479975 | ||||||||
\(804\) | 1.39425e10 | 0.946116 | ||||||||
\(805\) | 4.19769e9 | 0.283612 | ||||||||
\(806\) | −4.36628e9 | −0.293723 | ||||||||
\(807\) | −1.32183e10 | −0.885355 | ||||||||
\(808\) | 3.30638e9 | 0.220503 | ||||||||
\(809\) | 1.85053e10 | 1.22879 | 0.614394 | − | 0.789000i | \(-0.289401\pi\) | ||||
0.614394 | + | 0.789000i | \(0.289401\pi\) | |||||||
\(810\) | −1.10153e10 | −0.728278 | ||||||||
\(811\) | −8.34631e9 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588585\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588585\pi\) | |||||||
\(812\) | 5.65927e9 | 0.370949 | ||||||||
\(813\) | 2.58463e9 | 0.168687 | ||||||||
\(814\) | −1.37434e9 | −0.0893116 | ||||||||
\(815\) | −1.77904e10 | −1.15116 | ||||||||
\(816\) | −3.26878e9 | −0.210606 | ||||||||
\(817\) | 3.80734e9 | 0.244256 | ||||||||
\(818\) | −1.29868e9 | −0.0829593 | ||||||||
\(819\) | 4.46688e8 | 0.0284126 | ||||||||
\(820\) | −1.65950e10 | −1.05106 | ||||||||
\(821\) | −1.52462e10 | −0.961525 | −0.480762 | − | 0.876851i | \(-0.659640\pi\) | ||||
−0.480762 | + | 0.876851i | \(0.659640\pi\) | |||||||
\(822\) | −1.29552e10 | −0.813566 | ||||||||
\(823\) | −2.79970e10 | −1.75070 | −0.875352 | − | 0.483486i | \(-0.839370\pi\) | ||||
−0.875352 | + | 0.483486i | \(0.839370\pi\) | |||||||
\(824\) | −3.15406e9 | −0.196392 | ||||||||
\(825\) | 2.06375e9 | 0.127958 | ||||||||
\(826\) | 1.45452e9 | 0.0898026 | ||||||||
\(827\) | −1.18156e10 | −0.726418 | −0.363209 | − | 0.931708i | \(-0.618319\pi\) | ||||
−0.363209 | + | 0.931708i | \(0.618319\pi\) | |||||||
\(828\) | 2.10257e9 | 0.128719 | ||||||||
\(829\) | 1.38969e10 | 0.847185 | 0.423592 | − | 0.905853i | \(-0.360769\pi\) | ||||
0.423592 | + | 0.905853i | \(0.360769\pi\) | |||||||
\(830\) | 9.63549e9 | 0.584925 | ||||||||
\(831\) | 2.57487e10 | 1.55651 | ||||||||
\(832\) | −2.17388e9 | −0.130859 | ||||||||
\(833\) | 3.75361e9 | 0.225005 | ||||||||
\(834\) | 1.25355e10 | 0.748272 | ||||||||
\(835\) | −2.55387e10 | −1.51808 | ||||||||
\(836\) | −6.01323e9 | −0.355948 | ||||||||
\(837\) | 2.56976e10 | 1.51480 | ||||||||
\(838\) | 1.87837e10 | 1.10262 | ||||||||
\(839\) | −2.03877e9 | −0.119180 | −0.0595898 | − | 0.998223i | \(-0.518979\pi\) | ||||
−0.0595898 | + | 0.998223i | \(0.518979\pi\) | |||||||
\(840\) | −7.43336e9 | −0.432721 | ||||||||
\(841\) | 1.97778e10 | 1.14655 | ||||||||
\(842\) | −3.95432e9 | −0.228286 | ||||||||
\(843\) | 1.55293e10 | 0.892804 | ||||||||
\(844\) | 1.49523e10 | 0.856068 | ||||||||
\(845\) | 1.42794e9 | 0.0814161 | ||||||||
\(846\) | −1.79738e9 | −0.102057 | ||||||||
\(847\) | 7.27712e8 | 0.0411498 | ||||||||
\(848\) | 8.63313e8 | 0.0486164 | ||||||||
\(849\) | 1.71388e10 | 0.961176 | ||||||||
\(850\) | 1.94811e9 | 0.108805 | ||||||||
\(851\) | −2.09880e9 | −0.116739 | ||||||||
\(852\) | −1.71461e10 | −0.949786 | ||||||||
\(853\) | −2.35848e10 | −1.30110 | −0.650550 | − | 0.759464i | \(-0.725461\pi\) | ||||
−0.650550 | + | 0.759464i | \(0.725461\pi\) | |||||||
\(854\) | 9.69699e8 | 0.0532763 | ||||||||
\(855\) | −2.95114e9 | −0.161476 | ||||||||
\(856\) | −9.81659e8 | −0.0534937 | ||||||||
\(857\) | −5.84270e9 | −0.317089 | −0.158544 | − | 0.987352i | \(-0.550680\pi\) | ||||
−0.158544 | + | 0.987352i | \(0.550680\pi\) | |||||||
\(858\) | −3.13779e9 | −0.169597 | ||||||||
\(859\) | 1.89371e10 | 1.01938 | 0.509691 | − | 0.860358i | \(-0.329760\pi\) | ||||
0.509691 | + | 0.860358i | \(0.329760\pi\) | |||||||
\(860\) | 5.73869e9 | 0.307658 | ||||||||
\(861\) | 1.18310e10 | 0.631701 | ||||||||
\(862\) | 4.87266e8 | 0.0259114 | ||||||||
\(863\) | −1.94559e9 | −0.103042 | −0.0515208 | − | 0.998672i | \(-0.516407\pi\) | ||||
−0.0515208 | + | 0.998672i | \(0.516407\pi\) | |||||||
\(864\) | 1.60105e10 | 0.844516 | ||||||||
\(865\) | −3.23114e10 | −1.69746 | ||||||||
\(866\) | 1.08951e10 | 0.570058 | ||||||||
\(867\) | −3.20347e10 | −1.66938 | ||||||||
\(868\) | 8.99152e9 | 0.466675 | ||||||||
\(869\) | −6.75618e9 | −0.349247 | ||||||||
\(870\) | −1.95102e10 | −1.00449 | ||||||||
\(871\) | −6.77585e9 | −0.347456 | ||||||||
\(872\) | −2.76826e10 | −1.41384 | ||||||||
\(873\) | 5.71878e9 | 0.290907 | ||||||||
\(874\) | 4.52557e9 | 0.229289 | ||||||||
\(875\) | 6.97431e9 | 0.351944 | ||||||||
\(876\) | −7.63986e8 | −0.0383991 | ||||||||
\(877\) | −2.89874e9 | −0.145115 | −0.0725574 | − | 0.997364i | \(-0.523116\pi\) | ||||
−0.0725574 | + | 0.997364i | \(0.523116\pi\) | |||||||
\(878\) | 1.25240e9 | 0.0624472 | ||||||||
\(879\) | −1.14272e10 | −0.567518 | ||||||||
\(880\) | −2.39560e9 | −0.118502 | ||||||||
\(881\) | 1.73032e10 | 0.852534 | 0.426267 | − | 0.904598i | \(-0.359828\pi\) | ||||
0.426267 | + | 0.904598i | \(0.359828\pi\) | |||||||
\(882\) | 4.53329e8 | 0.0222471 | ||||||||
\(883\) | 2.28544e10 | 1.11714 | 0.558570 | − | 0.829457i | \(-0.311350\pi\) | ||||
0.558570 | + | 0.829457i | \(0.311350\pi\) | |||||||
\(884\) | 6.01026e9 | 0.292624 | ||||||||
\(885\) | 1.01750e10 | 0.493436 | ||||||||
\(886\) | −9.61890e9 | −0.464630 | ||||||||
\(887\) | −1.52330e10 | −0.732913 | −0.366457 | − | 0.930435i | \(-0.619429\pi\) | ||||
−0.366457 | + | 0.930435i | \(0.619429\pi\) | |||||||
\(888\) | 3.71660e9 | 0.178115 | ||||||||
\(889\) | −6.92726e9 | −0.330678 | ||||||||
\(890\) | −2.33519e10 | −1.11034 | ||||||||
\(891\) | 2.38696e10 | 1.13051 | ||||||||
\(892\) | −1.88734e10 | −0.890373 | ||||||||
\(893\) | 7.85011e9 | 0.368889 | ||||||||
\(894\) | −1.36157e10 | −0.637320 | ||||||||
\(895\) | 2.60287e10 | 1.21359 | ||||||||
\(896\) | 6.15662e9 | 0.285933 | ||||||||
\(897\) | −4.79182e9 | −0.221680 | ||||||||
\(898\) | 1.88634e10 | 0.869266 | ||||||||
\(899\) | 5.88301e10 | 2.70048 | ||||||||
\(900\) | −4.77409e8 | −0.0218294 | ||||||||
\(901\) | 1.41745e10 | 0.645611 | ||||||||
\(902\) | −1.77221e10 | −0.804065 | ||||||||
\(903\) | −4.09128e9 | −0.184906 | ||||||||
\(904\) | 4.60181e9 | 0.207176 | ||||||||
\(905\) | 2.84091e10 | 1.27405 | ||||||||
\(906\) | −2.12386e10 | −0.948807 | ||||||||
\(907\) | −2.39482e10 | −1.06573 | −0.532865 | − | 0.846200i | \(-0.678885\pi\) | ||||
−0.532865 | + | 0.846200i | \(0.678885\pi\) | |||||||
\(908\) | −1.79397e10 | −0.795271 | ||||||||
\(909\) | −1.41057e9 | −0.0622904 | ||||||||
\(910\) | 1.44917e9 | 0.0637490 | ||||||||
\(911\) | −2.95933e10 | −1.29682 | −0.648409 | − | 0.761292i | \(-0.724565\pi\) | ||||
−0.648409 | + | 0.761292i | \(0.724565\pi\) | |||||||
\(912\) | 1.72419e9 | 0.0752669 | ||||||||
\(913\) | −2.08797e10 | −0.907981 | ||||||||
\(914\) | −1.45292e10 | −0.629403 | ||||||||
\(915\) | 6.78345e9 | 0.292736 | ||||||||
\(916\) | 6.00351e8 | 0.0258090 | ||||||||
\(917\) | −6.42329e9 | −0.275084 | ||||||||
\(918\) | 1.74326e10 | 0.743727 | ||||||||
\(919\) | −1.40021e10 | −0.595097 | −0.297548 | − | 0.954707i | \(-0.596169\pi\) | ||||
−0.297548 | + | 0.954707i | \(0.596169\pi\) | |||||||
\(920\) | 1.70041e10 | 0.719942 | ||||||||
\(921\) | −2.64215e10 | −1.11442 | ||||||||
\(922\) | −1.62676e10 | −0.683542 | ||||||||
\(923\) | 8.33274e9 | 0.348804 | ||||||||
\(924\) | 6.46168e9 | 0.269459 | ||||||||
\(925\) | 4.76554e8 | 0.0197977 | ||||||||
\(926\) | 1.04881e10 | 0.434070 | ||||||||
\(927\) | 1.34558e9 | 0.0554794 | ||||||||
\(928\) | 3.66532e10 | 1.50555 | ||||||||
\(929\) | −4.47459e10 | −1.83104 | −0.915520 | − | 0.402272i | \(-0.868221\pi\) | ||||
−0.915520 | + | 0.402272i | \(0.868221\pi\) | |||||||
\(930\) | −3.09980e10 | −1.26370 | ||||||||
\(931\) | −1.97993e9 | −0.0804128 | ||||||||
\(932\) | −8.43565e9 | −0.341321 | ||||||||
\(933\) | −1.75954e10 | −0.709272 | ||||||||
\(934\) | 3.53139e8 | 0.0141818 | ||||||||
\(935\) | −3.93327e10 | −1.57367 | ||||||||
\(936\) | 1.80946e9 | 0.0721245 | ||||||||
\(937\) | −3.99242e10 | −1.58543 | −0.792716 | − | 0.609591i | \(-0.791334\pi\) | ||||
−0.792716 | + | 0.609591i | \(0.791334\pi\) | |||||||
\(938\) | −6.87659e9 | −0.272059 | ||||||||
\(939\) | −5.30950e10 | −2.09278 | ||||||||
\(940\) | 1.18322e10 | 0.464643 | ||||||||
\(941\) | −7.73309e9 | −0.302544 | −0.151272 | − | 0.988492i | \(-0.548337\pi\) | ||||
−0.151272 | + | 0.988492i | \(0.548337\pi\) | |||||||
\(942\) | −3.15834e10 | −1.23106 | ||||||||
\(943\) | −2.70640e10 | −1.05100 | ||||||||
\(944\) | −1.26766e9 | −0.0490455 | ||||||||
\(945\) | −8.52904e9 | −0.328767 | ||||||||
\(946\) | 6.12845e9 | 0.235359 | ||||||||
\(947\) | −2.90345e10 | −1.11094 | −0.555468 | − | 0.831538i | \(-0.687461\pi\) | ||||
−0.555468 | + | 0.831538i | \(0.687461\pi\) | |||||||
\(948\) | 7.32932e9 | 0.279405 | ||||||||
\(949\) | 3.71286e8 | 0.0141019 | ||||||||
\(950\) | −1.02758e9 | −0.0388849 | ||||||||
\(951\) | −2.90777e10 | −1.09630 | ||||||||
\(952\) | 1.52052e10 | 0.571168 | ||||||||
\(953\) | 3.39685e10 | 1.27131 | 0.635655 | − | 0.771973i | \(-0.280730\pi\) | ||||
0.635655 | + | 0.771973i | \(0.280730\pi\) | |||||||
\(954\) | 1.71188e9 | 0.0638341 | ||||||||
\(955\) | 3.81252e10 | 1.41645 | ||||||||
\(956\) | 3.00774e10 | 1.11337 | ||||||||
\(957\) | 4.22777e10 | 1.55926 | ||||||||
\(958\) | 2.11511e10 | 0.777239 | ||||||||
\(959\) | −1.29655e10 | −0.474706 | ||||||||
\(960\) | −1.54333e10 | −0.563001 | ||||||||
\(961\) | 6.59574e10 | 2.39735 | ||||||||
\(962\) | −7.24567e8 | −0.0262401 | ||||||||
\(963\) | 4.18795e8 | 0.0151116 | ||||||||
\(964\) | −2.41169e10 | −0.867065 | ||||||||
\(965\) | −2.62422e10 | −0.940059 | ||||||||
\(966\) | −4.86306e9 | −0.173576 | ||||||||
\(967\) | −2.42149e10 | −0.861173 | −0.430587 | − | 0.902549i | \(-0.641693\pi\) | ||||
−0.430587 | + | 0.902549i | \(0.641693\pi\) | |||||||
\(968\) | 2.94784e9 | 0.104458 | ||||||||
\(969\) | 2.83090e10 | 0.999521 | ||||||||
\(970\) | 1.85532e10 | 0.652705 | ||||||||
\(971\) | 4.08684e9 | 0.143259 | 0.0716293 | − | 0.997431i | \(-0.477180\pi\) | ||||
0.0716293 | + | 0.997431i | \(0.477180\pi\) | |||||||
\(972\) | −1.01326e10 | −0.353907 | ||||||||
\(973\) | 1.25454e10 | 0.436608 | ||||||||
\(974\) | −1.28795e10 | −0.446626 | ||||||||
\(975\) | 1.08803e9 | 0.0375946 | ||||||||
\(976\) | −8.45121e8 | −0.0290968 | ||||||||
\(977\) | −2.94781e10 | −1.01127 | −0.505636 | − | 0.862747i | \(-0.668742\pi\) | ||||
−0.505636 | + | 0.862747i | \(0.668742\pi\) | |||||||
\(978\) | 2.06104e10 | 0.704531 | ||||||||
\(979\) | 5.06026e10 | 1.72359 | ||||||||
\(980\) | −2.98428e9 | −0.101286 | ||||||||
\(981\) | 1.18100e10 | 0.399399 | ||||||||
\(982\) | 2.98022e9 | 0.100429 | ||||||||
\(983\) | −2.06234e10 | −0.692504 | −0.346252 | − | 0.938142i | \(-0.612546\pi\) | ||||
−0.346252 | + | 0.938142i | \(0.612546\pi\) | |||||||
\(984\) | 4.79256e10 | 1.60356 | ||||||||
\(985\) | 6.44462e8 | 0.0214867 | ||||||||
\(986\) | 3.99088e10 | 1.32587 | ||||||||
\(987\) | −8.43554e9 | −0.279256 | ||||||||
\(988\) | −3.17025e9 | −0.104579 | ||||||||
\(989\) | 9.35897e9 | 0.307639 | ||||||||
\(990\) | −4.75027e9 | −0.155595 | ||||||||
\(991\) | −4.08599e10 | −1.33364 | −0.666821 | − | 0.745218i | \(-0.732345\pi\) | ||||
−0.666821 | + | 0.745218i | \(0.732345\pi\) | |||||||
\(992\) | 5.82351e10 | 1.89406 | ||||||||
\(993\) | −5.13221e10 | −1.66334 | ||||||||
\(994\) | 8.45662e9 | 0.273114 | ||||||||
\(995\) | −1.59523e10 | −0.513384 | ||||||||
\(996\) | 2.26510e10 | 0.726405 | ||||||||
\(997\) | −6.62022e7 | −0.00211563 | −0.00105781 | − | 0.999999i | \(-0.500337\pi\) | ||||
−0.00105781 | + | 0.999999i | \(0.500337\pi\) | |||||||
\(998\) | −1.73889e10 | −0.553751 | ||||||||
\(999\) | 4.26443e9 | 0.135326 |
(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 | 91.8.a.d.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.d.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial |