Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,60,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 60, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 60);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 60 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(22.0458005510\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots - 23\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{13}\cdot 5^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.54999e7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.42193e9 | −1.87281 | −0.936407 | − | 0.350915i | \(-0.885871\pi\) | ||||
−0.936407 | + | 0.350915i | \(0.885871\pi\) | |||||||
\(3\) | −1.64208e14 | −1.38140 | −0.690698 | − | 0.723144i | \(-0.742696\pi\) | ||||
−0.690698 | + | 0.723144i | \(0.742696\pi\) | |||||||
\(4\) | 1.44544e18 | 2.50744 | ||||||||
\(5\) | 2.46018e20 | 0.590679 | 0.295340 | − | 0.955392i | \(-0.404567\pi\) | ||||
0.295340 | + | 0.955392i | \(0.404567\pi\) | |||||||
\(6\) | 2.33493e23 | 2.58710 | ||||||||
\(7\) | −6.31094e24 | −0.740801 | −0.370401 | − | 0.928872i | \(-0.620780\pi\) | ||||
−0.370401 | + | 0.928872i | \(0.620780\pi\) | |||||||
\(8\) | −1.23563e27 | −2.82315 | ||||||||
\(9\) | 1.28340e28 | 0.908253 | ||||||||
\(10\) | −3.49822e29 | −1.10623 | ||||||||
\(11\) | −1.85237e29 | −0.0352082 | −0.0176041 | − | 0.999845i | \(-0.505604\pi\) | ||||
−0.0176041 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(12\) | −2.37353e32 | −3.46376 | ||||||||
\(13\) | −9.37557e32 | −1.29024 | −0.645118 | − | 0.764083i | \(-0.723192\pi\) | ||||
−0.645118 | + | 0.764083i | \(0.723192\pi\) | |||||||
\(14\) | 8.97374e33 | 1.38738 | ||||||||
\(15\) | −4.03982e34 | −0.815962 | ||||||||
\(16\) | 9.23746e35 | 2.77980 | ||||||||
\(17\) | −2.12710e36 | −1.07040 | −0.535199 | − | 0.844726i | \(-0.679763\pi\) | ||||
−0.535199 | + | 0.844726i | \(0.679763\pi\) | |||||||
\(18\) | −1.82491e37 | −1.70099 | ||||||||
\(19\) | 2.93477e37 | 0.555064 | 0.277532 | − | 0.960716i | \(-0.410484\pi\) | ||||
0.277532 | + | 0.960716i | \(0.410484\pi\) | |||||||
\(20\) | 3.55604e38 | 1.48109 | ||||||||
\(21\) | 1.03631e39 | 1.02334 | ||||||||
\(22\) | 2.63395e38 | 0.0659385 | ||||||||
\(23\) | −1.73933e40 | −1.17330 | −0.586652 | − | 0.809839i | \(-0.699554\pi\) | ||||
−0.586652 | + | 0.809839i | \(0.699554\pi\) | |||||||
\(24\) | 2.02901e41 | 3.89988 | ||||||||
\(25\) | −1.12947e41 | −0.651098 | ||||||||
\(26\) | 1.33315e42 | 2.41637 | ||||||||
\(27\) | 2.12883e41 | 0.126739 | ||||||||
\(28\) | −9.12207e42 | −1.85751 | ||||||||
\(29\) | 2.89914e41 | 0.0209666 | 0.0104833 | − | 0.999945i | \(-0.496663\pi\) | ||||
0.0104833 | + | 0.999945i | \(0.496663\pi\) | |||||||
\(30\) | 5.74436e43 | 1.52815 | ||||||||
\(31\) | −1.46222e44 | −1.47857 | −0.739287 | − | 0.673390i | \(-0.764837\pi\) | ||||
−0.739287 | + | 0.673390i | \(0.764837\pi\) | |||||||
\(32\) | −6.01215e44 | −2.38290 | ||||||||
\(33\) | 3.04175e43 | 0.0486365 | ||||||||
\(34\) | 3.02460e45 | 2.00466 | ||||||||
\(35\) | −1.55260e45 | −0.437576 | ||||||||
\(36\) | 1.85507e46 | 2.27739 | ||||||||
\(37\) | −2.03766e46 | −1.11476 | −0.557379 | − | 0.830258i | \(-0.688193\pi\) | ||||
−0.557379 | + | 0.830258i | \(0.688193\pi\) | |||||||
\(38\) | −4.17306e46 | −1.03953 | ||||||||
\(39\) | 1.53955e47 | 1.78232 | ||||||||
\(40\) | −3.03987e47 | −1.66758 | ||||||||
\(41\) | 2.62740e47 | 0.695669 | 0.347835 | − | 0.937556i | \(-0.386917\pi\) | ||||
0.347835 | + | 0.937556i | \(0.386917\pi\) | |||||||
\(42\) | −1.47356e48 | −1.91653 | ||||||||
\(43\) | 8.93006e47 | 0.580143 | 0.290071 | − | 0.957005i | \(-0.406321\pi\) | ||||
0.290071 | + | 0.957005i | \(0.406321\pi\) | |||||||
\(44\) | −2.67749e47 | −0.0882824 | ||||||||
\(45\) | 3.15739e48 | 0.536486 | ||||||||
\(46\) | 2.47321e49 | 2.19738 | ||||||||
\(47\) | 2.53928e49 | 1.19626 | 0.598128 | − | 0.801401i | \(-0.295911\pi\) | ||||
0.598128 | + | 0.801401i | \(0.295911\pi\) | |||||||
\(48\) | −1.51687e50 | −3.84000 | ||||||||
\(49\) | −3.27466e49 | −0.451213 | ||||||||
\(50\) | 1.60604e50 | 1.21939 | ||||||||
\(51\) | 3.49288e50 | 1.47864 | ||||||||
\(52\) | −1.35518e51 | −3.23518 | ||||||||
\(53\) | 1.22660e51 | 1.66942 | 0.834710 | − | 0.550690i | \(-0.185635\pi\) | ||||
0.834710 | + | 0.550690i | \(0.185635\pi\) | |||||||
\(54\) | −3.02706e50 | −0.237359 | ||||||||
\(55\) | −4.55717e49 | −0.0207968 | ||||||||
\(56\) | 7.79798e51 | 2.09139 | ||||||||
\(57\) | −4.81914e51 | −0.766763 | ||||||||
\(58\) | −4.12239e50 | −0.0392666 | ||||||||
\(59\) | 5.85329e50 | 0.0336717 | 0.0168359 | − | 0.999858i | \(-0.494641\pi\) | ||||
0.0168359 | + | 0.999858i | \(0.494641\pi\) | |||||||
\(60\) | −5.83931e52 | −2.04597 | ||||||||
\(61\) | −6.37747e52 | −1.37220 | −0.686102 | − | 0.727506i | \(-0.740680\pi\) | ||||
−0.686102 | + | 0.727506i | \(0.740680\pi\) | |||||||
\(62\) | 2.07918e53 | 2.76910 | ||||||||
\(63\) | −8.09944e52 | −0.672835 | ||||||||
\(64\) | 3.22385e53 | 1.68293 | ||||||||
\(65\) | −2.30656e53 | −0.762115 | ||||||||
\(66\) | −4.32517e52 | −0.0910871 | ||||||||
\(67\) | 6.46551e53 | 0.873767 | 0.436884 | − | 0.899518i | \(-0.356082\pi\) | ||||
0.436884 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(68\) | −3.07460e54 | −2.68395 | ||||||||
\(69\) | 2.85612e54 | 1.62080 | ||||||||
\(70\) | 2.20770e54 | 0.819499 | ||||||||
\(71\) | −1.44338e54 | −0.352580 | −0.176290 | − | 0.984338i | \(-0.556410\pi\) | ||||
−0.176290 | + | 0.984338i | \(0.556410\pi\) | |||||||
\(72\) | −1.58580e55 | −2.56413 | ||||||||
\(73\) | −2.42309e54 | −0.260822 | −0.130411 | − | 0.991460i | \(-0.541630\pi\) | ||||
−0.130411 | + | 0.991460i | \(0.541630\pi\) | |||||||
\(74\) | 2.89742e55 | 2.08773 | ||||||||
\(75\) | 1.85469e55 | 0.899424 | ||||||||
\(76\) | 4.24203e55 | 1.39179 | ||||||||
\(77\) | 1.16902e54 | 0.0260823 | ||||||||
\(78\) | −2.18913e56 | −3.33796 | ||||||||
\(79\) | 4.97858e54 | 0.0521322 | 0.0260661 | − | 0.999660i | \(-0.491702\pi\) | ||||
0.0260661 | + | 0.999660i | \(0.491702\pi\) | |||||||
\(80\) | 2.27258e56 | 1.64197 | ||||||||
\(81\) | −2.16306e56 | −1.08333 | ||||||||
\(82\) | −3.73599e56 | −1.30286 | ||||||||
\(83\) | 3.44463e56 | 0.840116 | 0.420058 | − | 0.907497i | \(-0.362010\pi\) | ||||
0.420058 | + | 0.907497i | \(0.362010\pi\) | |||||||
\(84\) | 1.49792e57 | 2.56596 | ||||||||
\(85\) | −5.23306e56 | −0.632262 | ||||||||
\(86\) | −1.26980e57 | −1.08650 | ||||||||
\(87\) | −4.76063e55 | −0.0289632 | ||||||||
\(88\) | 2.28885e56 | 0.0993981 | ||||||||
\(89\) | 3.85023e57 | 1.19807 | 0.599034 | − | 0.800724i | \(-0.295551\pi\) | ||||
0.599034 | + | 0.800724i | \(0.295551\pi\) | |||||||
\(90\) | −4.48960e57 | −1.00474 | ||||||||
\(91\) | 5.91687e57 | 0.955808 | ||||||||
\(92\) | −2.51409e58 | −2.94198 | ||||||||
\(93\) | 2.40109e58 | 2.04250 | ||||||||
\(94\) | −3.61069e58 | −2.24037 | ||||||||
\(95\) | 7.22007e57 | 0.327865 | ||||||||
\(96\) | 9.87245e58 | 3.29172 | ||||||||
\(97\) | −2.95516e58 | −0.725797 | −0.362899 | − | 0.931829i | \(-0.618213\pi\) | ||||
−0.362899 | + | 0.931829i | \(0.618213\pi\) | |||||||
\(98\) | 4.65635e58 | 0.845039 | ||||||||
\(99\) | −2.37733e57 | −0.0319780 | ||||||||
\(100\) | −1.63259e59 | −1.63259 | ||||||||
\(101\) | 6.95950e57 | 0.0518916 | 0.0259458 | − | 0.999663i | \(-0.491740\pi\) | ||||
0.0259458 | + | 0.999663i | \(0.491740\pi\) | |||||||
\(102\) | −4.96665e59 | −2.76922 | ||||||||
\(103\) | 9.43331e58 | 0.394426 | 0.197213 | − | 0.980361i | \(-0.436811\pi\) | ||||
0.197213 | + | 0.980361i | \(0.436811\pi\) | |||||||
\(104\) | 1.15847e60 | 3.64252 | ||||||||
\(105\) | 2.54951e59 | 0.604466 | ||||||||
\(106\) | −1.74415e60 | −3.12651 | ||||||||
\(107\) | 4.79536e59 | 0.651627 | 0.325814 | − | 0.945434i | \(-0.394362\pi\) | ||||
0.325814 | + | 0.945434i | \(0.394362\pi\) | |||||||
\(108\) | 3.07710e59 | 0.317790 | ||||||||
\(109\) | 8.62112e59 | 0.678394 | 0.339197 | − | 0.940715i | \(-0.389845\pi\) | ||||
0.339197 | + | 0.940715i | \(0.389845\pi\) | |||||||
\(110\) | 6.48000e58 | 0.0389485 | ||||||||
\(111\) | 3.34600e60 | 1.53992 | ||||||||
\(112\) | −5.82971e60 | −2.05928 | ||||||||
\(113\) | −3.86899e60 | −1.05144 | −0.525719 | − | 0.850658i | \(-0.676204\pi\) | ||||
−0.525719 | + | 0.850658i | \(0.676204\pi\) | |||||||
\(114\) | 6.85250e60 | 1.43601 | ||||||||
\(115\) | −4.27906e60 | −0.693046 | ||||||||
\(116\) | 4.19053e59 | 0.0525725 | ||||||||
\(117\) | −1.20326e61 | −1.17186 | ||||||||
\(118\) | −8.32299e59 | −0.0630609 | ||||||||
\(119\) | 1.34240e61 | 0.792952 | ||||||||
\(120\) | 4.99172e61 | 2.30358 | ||||||||
\(121\) | −2.76458e61 | −0.998760 | ||||||||
\(122\) | 9.06835e61 | 2.56988 | ||||||||
\(123\) | −4.31441e61 | −0.960994 | ||||||||
\(124\) | −2.11355e62 | −3.70743 | ||||||||
\(125\) | −7.04644e61 | −0.975269 | ||||||||
\(126\) | 1.15169e62 | 1.26010 | ||||||||
\(127\) | 2.00091e62 | 1.73388 | 0.866939 | − | 0.498414i | \(-0.166084\pi\) | ||||
0.866939 | + | 0.498414i | \(0.166084\pi\) | |||||||
\(128\) | −1.11834e62 | −0.768918 | ||||||||
\(129\) | −1.46639e62 | −0.801406 | ||||||||
\(130\) | 3.27978e62 | 1.42730 | ||||||||
\(131\) | 1.11788e62 | 0.388053 | 0.194026 | − | 0.980996i | \(-0.437845\pi\) | ||||
0.194026 | + | 0.980996i | \(0.437845\pi\) | |||||||
\(132\) | 4.39666e61 | 0.121953 | ||||||||
\(133\) | −1.85212e62 | −0.411192 | ||||||||
\(134\) | −9.19353e62 | −1.63640 | ||||||||
\(135\) | 5.23731e61 | 0.0748621 | ||||||||
\(136\) | 2.62831e63 | 3.02189 | ||||||||
\(137\) | 2.78939e62 | 0.258376 | 0.129188 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129188 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(138\) | −4.06122e63 | −3.03545 | ||||||||
\(139\) | 2.28698e63 | 1.38142 | 0.690710 | − | 0.723132i | \(-0.257298\pi\) | ||||
0.690710 | + | 0.723132i | \(0.257298\pi\) | |||||||
\(140\) | −2.24419e63 | −1.09719 | ||||||||
\(141\) | −4.16971e63 | −1.65250 | ||||||||
\(142\) | 2.05239e63 | 0.660317 | ||||||||
\(143\) | 1.73671e62 | 0.0454269 | ||||||||
\(144\) | 1.18553e64 | 2.52476 | ||||||||
\(145\) | 7.13242e61 | 0.0123846 | ||||||||
\(146\) | 3.44547e63 | 0.488472 | ||||||||
\(147\) | 5.37726e63 | 0.623304 | ||||||||
\(148\) | −2.94531e64 | −2.79518 | ||||||||
\(149\) | 1.95296e64 | 1.51949 | 0.759745 | − | 0.650221i | \(-0.225324\pi\) | ||||
0.759745 | + | 0.650221i | \(0.225324\pi\) | |||||||
\(150\) | −2.63725e64 | −1.68445 | ||||||||
\(151\) | 3.23263e64 | 1.69721 | 0.848607 | − | 0.529024i | \(-0.177442\pi\) | ||||
0.848607 | + | 0.529024i | \(0.177442\pi\) | |||||||
\(152\) | −3.62629e64 | −1.56703 | ||||||||
\(153\) | −2.72992e64 | −0.972192 | ||||||||
\(154\) | −1.66227e63 | −0.0488473 | ||||||||
\(155\) | −3.59733e64 | −0.873363 | ||||||||
\(156\) | 2.22532e65 | 4.46906 | ||||||||
\(157\) | 1.75281e64 | 0.291538 | 0.145769 | − | 0.989319i | \(-0.453434\pi\) | ||||
0.145769 | + | 0.989319i | \(0.453434\pi\) | |||||||
\(158\) | −7.07922e63 | −0.0976340 | ||||||||
\(159\) | −2.01418e65 | −2.30613 | ||||||||
\(160\) | −1.47910e65 | −1.40753 | ||||||||
\(161\) | 1.09768e65 | 0.869185 | ||||||||
\(162\) | 3.07573e65 | 2.02888 | ||||||||
\(163\) | −3.13298e65 | −1.72355 | −0.861774 | − | 0.507292i | \(-0.830646\pi\) | ||||
−0.861774 | + | 0.507292i | \(0.830646\pi\) | |||||||
\(164\) | 3.79775e65 | 1.74435 | ||||||||
\(165\) | 7.48325e63 | 0.0287286 | ||||||||
\(166\) | −4.89804e65 | −1.57338 | ||||||||
\(167\) | 1.87971e65 | 0.505772 | 0.252886 | − | 0.967496i | \(-0.418620\pi\) | ||||
0.252886 | + | 0.967496i | \(0.418620\pi\) | |||||||
\(168\) | −1.28049e66 | −2.88904 | ||||||||
\(169\) | 3.50984e65 | 0.664706 | ||||||||
\(170\) | 7.44107e65 | 1.18411 | ||||||||
\(171\) | 3.76648e65 | 0.504139 | ||||||||
\(172\) | 1.29078e66 | 1.45467 | ||||||||
\(173\) | −1.53152e65 | −0.145466 | −0.0727330 | − | 0.997351i | \(-0.523172\pi\) | ||||
−0.0727330 | + | 0.997351i | \(0.523172\pi\) | |||||||
\(174\) | 6.76931e64 | 0.0542428 | ||||||||
\(175\) | 7.12805e65 | 0.482334 | ||||||||
\(176\) | −1.71112e65 | −0.0978718 | ||||||||
\(177\) | −9.61158e64 | −0.0465140 | ||||||||
\(178\) | −5.47478e66 | −2.24376 | ||||||||
\(179\) | −4.89309e66 | −1.69988 | −0.849941 | − | 0.526878i | \(-0.823363\pi\) | ||||
−0.849941 | + | 0.526878i | \(0.823363\pi\) | |||||||
\(180\) | 4.56381e66 | 1.34520 | ||||||||
\(181\) | 2.49289e66 | 0.624002 | 0.312001 | − | 0.950082i | \(-0.399001\pi\) | ||||
0.312001 | + | 0.950082i | \(0.399001\pi\) | |||||||
\(182\) | −8.41340e66 | −1.79005 | ||||||||
\(183\) | 1.04723e67 | 1.89556 | ||||||||
\(184\) | 2.14916e67 | 3.31241 | ||||||||
\(185\) | −5.01300e66 | −0.658464 | ||||||||
\(186\) | −3.41419e67 | −3.82522 | ||||||||
\(187\) | 3.94019e65 | 0.0376868 | ||||||||
\(188\) | 3.67037e67 | 2.99953 | ||||||||
\(189\) | −1.34349e66 | −0.0938885 | ||||||||
\(190\) | −1.02665e67 | −0.614030 | ||||||||
\(191\) | 9.18865e66 | 0.470725 | 0.235362 | − | 0.971908i | \(-0.424372\pi\) | ||||
0.235362 | + | 0.971908i | \(0.424372\pi\) | |||||||
\(192\) | −5.29383e67 | −2.32479 | ||||||||
\(193\) | −6.86206e66 | −0.258532 | −0.129266 | − | 0.991610i | \(-0.541262\pi\) | ||||
−0.129266 | + | 0.991610i | \(0.541262\pi\) | |||||||
\(194\) | 4.20205e67 | 1.35928 | ||||||||
\(195\) | 3.78756e67 | 1.05278 | ||||||||
\(196\) | −4.73332e67 | −1.13139 | ||||||||
\(197\) | −2.65331e67 | −0.545800 | −0.272900 | − | 0.962042i | \(-0.587983\pi\) | ||||
−0.272900 | + | 0.962042i | \(0.587983\pi\) | |||||||
\(198\) | 3.38041e66 | 0.0598888 | ||||||||
\(199\) | −4.85073e67 | −0.740699 | −0.370349 | − | 0.928892i | \(-0.620762\pi\) | ||||
−0.370349 | + | 0.928892i | \(0.620762\pi\) | |||||||
\(200\) | 1.39561e68 | 1.83815 | ||||||||
\(201\) | −1.06169e68 | −1.20702 | ||||||||
\(202\) | −9.89595e66 | −0.0971834 | ||||||||
\(203\) | −1.82963e66 | −0.0155321 | ||||||||
\(204\) | 5.04874e68 | 3.70760 | ||||||||
\(205\) | 6.46388e67 | 0.410917 | ||||||||
\(206\) | −1.34136e68 | −0.738687 | ||||||||
\(207\) | −2.23225e68 | −1.06566 | ||||||||
\(208\) | −8.66065e68 | −3.58659 | ||||||||
\(209\) | −5.43629e66 | −0.0195428 | ||||||||
\(210\) | −3.62523e68 | −1.13205 | ||||||||
\(211\) | 1.87935e67 | 0.0510124 | 0.0255062 | − | 0.999675i | \(-0.491880\pi\) | ||||
0.0255062 | + | 0.999675i | \(0.491880\pi\) | |||||||
\(212\) | 1.77298e69 | 4.18596 | ||||||||
\(213\) | 2.37014e68 | 0.487053 | ||||||||
\(214\) | −6.81868e68 | −1.22038 | ||||||||
\(215\) | 2.19695e68 | 0.342678 | ||||||||
\(216\) | −2.63045e68 | −0.357803 | ||||||||
\(217\) | 9.22799e68 | 1.09533 | ||||||||
\(218\) | −1.22587e69 | −1.27051 | ||||||||
\(219\) | 3.97891e68 | 0.360299 | ||||||||
\(220\) | −6.58711e67 | −0.0521466 | ||||||||
\(221\) | 1.99428e69 | 1.38107 | ||||||||
\(222\) | −4.75780e69 | −2.88399 | ||||||||
\(223\) | −9.19286e68 | −0.488042 | −0.244021 | − | 0.969770i | \(-0.578467\pi\) | ||||
−0.244021 | + | 0.969770i | \(0.578467\pi\) | |||||||
\(224\) | 3.79423e69 | 1.76525 | ||||||||
\(225\) | −1.44956e69 | −0.591362 | ||||||||
\(226\) | 5.50146e69 | 1.96915 | ||||||||
\(227\) | −3.67098e69 | −1.15350 | −0.576752 | − | 0.816919i | \(-0.695680\pi\) | ||||
−0.576752 | + | 0.816919i | \(0.695680\pi\) | |||||||
\(228\) | −6.96577e69 | −1.92261 | ||||||||
\(229\) | 4.99969e68 | 0.121282 | 0.0606410 | − | 0.998160i | \(-0.480686\pi\) | ||||
0.0606410 | + | 0.998160i | \(0.480686\pi\) | |||||||
\(230\) | 6.08454e69 | 1.29795 | ||||||||
\(231\) | −1.91963e68 | −0.0360300 | ||||||||
\(232\) | −3.58227e68 | −0.0591919 | ||||||||
\(233\) | −6.24576e69 | −0.909046 | −0.454523 | − | 0.890735i | \(-0.650190\pi\) | ||||
−0.454523 | + | 0.890735i | \(0.650190\pi\) | |||||||
\(234\) | 1.71095e70 | 2.19468 | ||||||||
\(235\) | 6.24709e69 | 0.706603 | ||||||||
\(236\) | 8.46056e68 | 0.0844297 | ||||||||
\(237\) | −8.17524e68 | −0.0720152 | ||||||||
\(238\) | −1.90881e70 | −1.48505 | ||||||||
\(239\) | 7.76076e69 | 0.533539 | 0.266770 | − | 0.963760i | \(-0.414044\pi\) | ||||
0.266770 | + | 0.963760i | \(0.414044\pi\) | |||||||
\(240\) | −3.73177e70 | −2.26821 | ||||||||
\(241\) | −1.26377e70 | −0.679462 | −0.339731 | − | 0.940523i | \(-0.610336\pi\) | ||||
−0.339731 | + | 0.940523i | \(0.610336\pi\) | |||||||
\(242\) | 3.93106e70 | 1.87049 | ||||||||
\(243\) | 3.25111e70 | 1.36977 | ||||||||
\(244\) | −9.21824e70 | −3.44071 | ||||||||
\(245\) | −8.05625e69 | −0.266522 | ||||||||
\(246\) | 6.13481e70 | 1.79976 | ||||||||
\(247\) | −2.75152e70 | −0.716163 | ||||||||
\(248\) | 1.80676e71 | 4.17423 | ||||||||
\(249\) | −5.65637e70 | −1.16053 | ||||||||
\(250\) | 1.00196e71 | 1.82650 | ||||||||
\(251\) | −6.71368e70 | −1.08789 | −0.543946 | − | 0.839120i | \(-0.683070\pi\) | ||||
−0.543946 | + | 0.839120i | \(0.683070\pi\) | |||||||
\(252\) | −1.17072e71 | −1.68709 | ||||||||
\(253\) | 3.22188e69 | 0.0413099 | ||||||||
\(254\) | −2.84517e71 | −3.24723 | ||||||||
\(255\) | 8.59311e70 | 0.873404 | ||||||||
\(256\) | −2.68217e70 | −0.242888 | ||||||||
\(257\) | 1.99205e71 | 1.60795 | 0.803977 | − | 0.594661i | \(-0.202714\pi\) | ||||
0.803977 | + | 0.594661i | \(0.202714\pi\) | |||||||
\(258\) | 2.08511e71 | 1.50089 | ||||||||
\(259\) | 1.28595e71 | 0.825814 | ||||||||
\(260\) | −3.33399e71 | −1.91095 | ||||||||
\(261\) | 3.72075e69 | 0.0190430 | ||||||||
\(262\) | −1.58955e71 | −0.726751 | ||||||||
\(263\) | −9.75645e70 | −0.398655 | −0.199328 | − | 0.979933i | \(-0.563876\pi\) | ||||
−0.199328 | + | 0.979933i | \(0.563876\pi\) | |||||||
\(264\) | −3.75848e70 | −0.137308 | ||||||||
\(265\) | 3.01766e71 | 0.986092 | ||||||||
\(266\) | 2.63359e71 | 0.770087 | ||||||||
\(267\) | −6.32240e71 | −1.65501 | ||||||||
\(268\) | 9.34549e71 | 2.19092 | ||||||||
\(269\) | 5.47919e71 | 1.15086 | 0.575432 | − | 0.817850i | \(-0.304834\pi\) | ||||
0.575432 | + | 0.817850i | \(0.304834\pi\) | |||||||
\(270\) | −7.44711e70 | −0.140203 | ||||||||
\(271\) | 4.44087e71 | 0.749677 | 0.374839 | − | 0.927090i | \(-0.377698\pi\) | ||||
0.374839 | + | 0.927090i | \(0.377698\pi\) | |||||||
\(272\) | −1.96490e72 | −2.97549 | ||||||||
\(273\) | −9.71598e71 | −1.32035 | ||||||||
\(274\) | −3.96634e71 | −0.483891 | ||||||||
\(275\) | 2.09221e70 | 0.0229240 | ||||||||
\(276\) | 4.12834e72 | 4.06404 | ||||||||
\(277\) | −1.63500e72 | −1.44665 | −0.723325 | − | 0.690507i | \(-0.757387\pi\) | ||||
−0.723325 | + | 0.690507i | \(0.757387\pi\) | |||||||
\(278\) | −3.25194e72 | −2.58714 | ||||||||
\(279\) | −1.87661e72 | −1.34292 | ||||||||
\(280\) | 1.91844e72 | 1.23534 | ||||||||
\(281\) | 1.36625e72 | 0.791944 | 0.395972 | − | 0.918263i | \(-0.370408\pi\) | ||||
0.395972 | + | 0.918263i | \(0.370408\pi\) | |||||||
\(282\) | 5.92906e72 | 3.09483 | ||||||||
\(283\) | 2.35491e72 | 1.10732 | 0.553661 | − | 0.832742i | \(-0.313230\pi\) | ||||
0.553661 | + | 0.832742i | \(0.313230\pi\) | |||||||
\(284\) | −2.08631e72 | −0.884072 | ||||||||
\(285\) | −1.18559e72 | −0.452911 | ||||||||
\(286\) | −2.46948e71 | −0.0850762 | ||||||||
\(287\) | −1.65814e72 | −0.515353 | ||||||||
\(288\) | −7.71597e72 | −2.16427 | ||||||||
\(289\) | 5.75573e71 | 0.145752 | ||||||||
\(290\) | −1.01418e71 | −0.0231940 | ||||||||
\(291\) | 4.85262e72 | 1.00261 | ||||||||
\(292\) | −3.50242e72 | −0.653995 | ||||||||
\(293\) | 3.23554e71 | 0.0546200 | 0.0273100 | − | 0.999627i | \(-0.491306\pi\) | ||||
0.0273100 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(294\) | −7.64612e72 | −1.16733 | ||||||||
\(295\) | 1.44001e71 | 0.0198892 | ||||||||
\(296\) | 2.51779e73 | 3.14712 | ||||||||
\(297\) | −3.94339e70 | −0.00446226 | ||||||||
\(298\) | −2.77698e73 | −2.84572 | ||||||||
\(299\) | 1.63072e73 | 1.51384 | ||||||||
\(300\) | 2.68084e73 | 2.25525 | ||||||||
\(301\) | −5.63570e72 | −0.429770 | ||||||||
\(302\) | −4.59659e73 | −3.17857 | ||||||||
\(303\) | −1.14281e72 | −0.0716828 | ||||||||
\(304\) | 2.71099e73 | 1.54297 | ||||||||
\(305\) | −1.56897e73 | −0.810532 | ||||||||
\(306\) | 3.88176e73 | 1.82074 | ||||||||
\(307\) | −7.55894e72 | −0.322017 | −0.161008 | − | 0.986953i | \(-0.551475\pi\) | ||||
−0.161008 | + | 0.986953i | \(0.551475\pi\) | |||||||
\(308\) | 1.68975e72 | 0.0653997 | ||||||||
\(309\) | −1.54903e73 | −0.544859 | ||||||||
\(310\) | 5.11517e73 | 1.63565 | ||||||||
\(311\) | 4.75210e71 | 0.0138183 | 0.00690914 | − | 0.999976i | \(-0.497801\pi\) | ||||
0.00690914 | + | 0.999976i | \(0.497801\pi\) | |||||||
\(312\) | −1.90231e74 | −5.03177 | ||||||||
\(313\) | 4.85436e73 | 1.16835 | 0.584176 | − | 0.811627i | \(-0.301418\pi\) | ||||
0.584176 | + | 0.811627i | \(0.301418\pi\) | |||||||
\(314\) | −2.49239e73 | −0.545997 | ||||||||
\(315\) | −1.99261e73 | −0.397430 | ||||||||
\(316\) | 7.19623e72 | 0.130718 | ||||||||
\(317\) | 5.69481e73 | 0.942391 | 0.471195 | − | 0.882029i | \(-0.343823\pi\) | ||||
0.471195 | + | 0.882029i | \(0.343823\pi\) | |||||||
\(318\) | 2.86404e74 | 4.31895 | ||||||||
\(319\) | −5.37030e70 | −0.000738199 0 | ||||||||
\(320\) | 7.93126e73 | 0.994072 | ||||||||
\(321\) | −7.87437e73 | −0.900155 | ||||||||
\(322\) | −1.56083e74 | −1.62782 | ||||||||
\(323\) | −6.24256e73 | −0.594140 | ||||||||
\(324\) | −3.12657e74 | −2.71638 | ||||||||
\(325\) | 1.05895e74 | 0.840069 | ||||||||
\(326\) | 4.45489e74 | 3.22789 | ||||||||
\(327\) | −1.41566e74 | −0.937131 | ||||||||
\(328\) | −3.24649e74 | −1.96398 | ||||||||
\(329\) | −1.60252e74 | −0.886188 | ||||||||
\(330\) | −1.06407e73 | −0.0538033 | ||||||||
\(331\) | 1.34777e74 | 0.623288 | 0.311644 | − | 0.950199i | \(-0.399120\pi\) | ||||
0.311644 | + | 0.950199i | \(0.399120\pi\) | |||||||
\(332\) | 4.97900e74 | 2.10654 | ||||||||
\(333\) | −2.61512e74 | −1.01248 | ||||||||
\(334\) | −2.67282e74 | −0.947217 | ||||||||
\(335\) | 1.59063e74 | 0.516116 | ||||||||
\(336\) | 9.57286e74 | 2.84468 | ||||||||
\(337\) | −2.02155e74 | −0.550303 | −0.275151 | − | 0.961401i | \(-0.588728\pi\) | ||||
−0.275151 | + | 0.961401i | \(0.588728\pi\) | |||||||
\(338\) | −4.99077e74 | −1.24487 | ||||||||
\(339\) | 6.35320e74 | 1.45245 | ||||||||
\(340\) | −7.56406e74 | −1.58536 | ||||||||
\(341\) | 2.70858e73 | 0.0520580 | ||||||||
\(342\) | −5.35568e74 | −0.944158 | ||||||||
\(343\) | 6.64675e74 | 1.07506 | ||||||||
\(344\) | −1.10342e75 | −1.63783 | ||||||||
\(345\) | 7.02657e74 | 0.957370 | ||||||||
\(346\) | 2.17772e74 | 0.272431 | ||||||||
\(347\) | 1.04939e75 | 1.20564 | 0.602818 | − | 0.797879i | \(-0.294045\pi\) | ||||
0.602818 | + | 0.797879i | \(0.294045\pi\) | |||||||
\(348\) | −6.88120e73 | −0.0726234 | ||||||||
\(349\) | −7.51505e74 | −0.728755 | −0.364378 | − | 0.931251i | \(-0.618718\pi\) | ||||
−0.364378 | + | 0.931251i | \(0.618718\pi\) | |||||||
\(350\) | −1.01356e75 | −0.903323 | ||||||||
\(351\) | −1.99590e74 | −0.163523 | ||||||||
\(352\) | 1.11367e74 | 0.0838977 | ||||||||
\(353\) | −2.22200e75 | −1.53954 | −0.769770 | − | 0.638321i | \(-0.779629\pi\) | ||||
−0.769770 | + | 0.638321i | \(0.779629\pi\) | |||||||
\(354\) | 1.36670e74 | 0.0871120 | ||||||||
\(355\) | −3.55096e74 | −0.208262 | ||||||||
\(356\) | 5.56527e75 | 3.00408 | ||||||||
\(357\) | −2.20433e75 | −1.09538 | ||||||||
\(358\) | 6.95766e75 | 3.18356 | ||||||||
\(359\) | −3.15427e74 | −0.132927 | −0.0664635 | − | 0.997789i | \(-0.521172\pi\) | ||||
−0.0664635 | + | 0.997789i | \(0.521172\pi\) | |||||||
\(360\) | −3.90136e75 | −1.51458 | ||||||||
\(361\) | −1.93423e75 | −0.691904 | ||||||||
\(362\) | −3.54473e75 | −1.16864 | ||||||||
\(363\) | 4.53967e75 | 1.37968 | ||||||||
\(364\) | 8.55246e75 | 2.39663 | ||||||||
\(365\) | −5.96123e74 | −0.154062 | ||||||||
\(366\) | −1.48910e76 | −3.55002 | ||||||||
\(367\) | −2.41055e75 | −0.530233 | −0.265116 | − | 0.964216i | \(-0.585410\pi\) | ||||
−0.265116 | + | 0.964216i | \(0.585410\pi\) | |||||||
\(368\) | −1.60670e76 | −3.26155 | ||||||||
\(369\) | 3.37200e75 | 0.631843 | ||||||||
\(370\) | 7.12817e75 | 1.23318 | ||||||||
\(371\) | −7.74101e75 | −1.23671 | ||||||||
\(372\) | 3.47063e76 | 5.12143 | ||||||||
\(373\) | 6.47651e75 | 0.882938 | 0.441469 | − | 0.897276i | \(-0.354457\pi\) | ||||
0.441469 | + | 0.897276i | \(0.354457\pi\) | |||||||
\(374\) | −5.60269e74 | −0.0705804 | ||||||||
\(375\) | 1.15708e76 | 1.34723 | ||||||||
\(376\) | −3.13761e76 | −3.37721 | ||||||||
\(377\) | −2.71811e74 | −0.0270519 | ||||||||
\(378\) | 1.91036e75 | 0.175836 | ||||||||
\(379\) | 3.32994e75 | 0.283517 | 0.141759 | − | 0.989901i | \(-0.454724\pi\) | ||||
0.141759 | + | 0.989901i | \(0.454724\pi\) | |||||||
\(380\) | 1.04362e76 | 0.822100 | ||||||||
\(381\) | −3.28567e76 | −2.39517 | ||||||||
\(382\) | −1.30657e76 | −0.881581 | ||||||||
\(383\) | 2.22332e76 | 1.38880 | 0.694398 | − | 0.719591i | \(-0.255671\pi\) | ||||
0.694398 | + | 0.719591i | \(0.255671\pi\) | |||||||
\(384\) | 1.83641e76 | 1.06218 | ||||||||
\(385\) | 2.87600e74 | 0.0154063 | ||||||||
\(386\) | 9.75740e75 | 0.484182 | ||||||||
\(387\) | 1.14608e76 | 0.526916 | ||||||||
\(388\) | −4.27151e76 | −1.81989 | ||||||||
\(389\) | −1.38935e76 | −0.548653 | −0.274327 | − | 0.961637i | \(-0.588455\pi\) | ||||
−0.274327 | + | 0.961637i | \(0.588455\pi\) | |||||||
\(390\) | −5.38566e76 | −1.97167 | ||||||||
\(391\) | 3.69973e76 | 1.25590 | ||||||||
\(392\) | 4.04627e76 | 1.27384 | ||||||||
\(393\) | −1.83565e76 | −0.536054 | ||||||||
\(394\) | 3.77283e76 | 1.02218 | ||||||||
\(395\) | 1.22482e75 | 0.0307934 | ||||||||
\(396\) | −3.43628e75 | −0.0801827 | ||||||||
\(397\) | −2.17609e76 | −0.471364 | −0.235682 | − | 0.971830i | \(-0.575732\pi\) | ||||
−0.235682 | + | 0.971830i | \(0.575732\pi\) | |||||||
\(398\) | 6.89743e76 | 1.38719 | ||||||||
\(399\) | 3.04133e76 | 0.568019 | ||||||||
\(400\) | −1.04335e77 | −1.80992 | ||||||||
\(401\) | −1.16224e77 | −1.87300 | −0.936499 | − | 0.350671i | \(-0.885954\pi\) | ||||
−0.936499 | + | 0.350671i | \(0.885954\pi\) | |||||||
\(402\) | 1.50965e77 | 2.26052 | ||||||||
\(403\) | 1.37092e77 | 1.90771 | ||||||||
\(404\) | 1.00595e76 | 0.130115 | ||||||||
\(405\) | −5.32152e76 | −0.639900 | ||||||||
\(406\) | 2.60162e75 | 0.0290888 | ||||||||
\(407\) | 3.77450e75 | 0.0392486 | ||||||||
\(408\) | −4.31590e77 | −4.17443 | ||||||||
\(409\) | 4.02114e76 | 0.361836 | 0.180918 | − | 0.983498i | \(-0.442093\pi\) | ||||
0.180918 | + | 0.983498i | \(0.442093\pi\) | |||||||
\(410\) | −9.19122e76 | −0.769572 | ||||||||
\(411\) | −4.58041e76 | −0.356920 | ||||||||
\(412\) | 1.36353e77 | 0.988999 | ||||||||
\(413\) | −3.69397e75 | −0.0249441 | ||||||||
\(414\) | 3.17411e77 | 1.99578 | ||||||||
\(415\) | 8.47442e76 | 0.496239 | ||||||||
\(416\) | 5.63674e77 | 3.07450 | ||||||||
\(417\) | −3.75541e77 | −1.90829 | ||||||||
\(418\) | 7.73006e75 | 0.0366001 | ||||||||
\(419\) | −1.98426e77 | −0.875557 | −0.437778 | − | 0.899083i | \(-0.644235\pi\) | ||||
−0.437778 | + | 0.899083i | \(0.644235\pi\) | |||||||
\(420\) | 3.68515e77 | 1.51566 | ||||||||
\(421\) | −1.57509e77 | −0.603927 | −0.301963 | − | 0.953320i | \(-0.597642\pi\) | ||||
−0.301963 | + | 0.953320i | \(0.597642\pi\) | |||||||
\(422\) | −2.67232e76 | −0.0955368 | ||||||||
\(423\) | 3.25890e77 | 1.08650 | ||||||||
\(424\) | −1.51563e78 | −4.71302 | ||||||||
\(425\) | 2.40251e77 | 0.696934 | ||||||||
\(426\) | −3.37019e77 | −0.912159 | ||||||||
\(427\) | 4.02478e77 | 1.01653 | ||||||||
\(428\) | 6.93139e77 | 1.63391 | ||||||||
\(429\) | −2.85181e76 | −0.0627525 | ||||||||
\(430\) | −3.12393e77 | −0.641773 | ||||||||
\(431\) | −1.55654e77 | −0.298594 | −0.149297 | − | 0.988792i | \(-0.547701\pi\) | ||||
−0.149297 | + | 0.988792i | \(0.547701\pi\) | |||||||
\(432\) | 1.96650e77 | 0.352309 | ||||||||
\(433\) | 1.11740e78 | 1.86989 | 0.934946 | − | 0.354789i | \(-0.115447\pi\) | ||||
0.934946 | + | 0.354789i | \(0.115447\pi\) | |||||||
\(434\) | −1.31216e78 | −2.05135 | ||||||||
\(435\) | −1.17120e76 | −0.0171080 | ||||||||
\(436\) | 1.24613e78 | 1.70103 | ||||||||
\(437\) | −5.10453e77 | −0.651259 | ||||||||
\(438\) | −5.65775e77 | −0.674773 | ||||||||
\(439\) | 3.27856e77 | 0.365578 | 0.182789 | − | 0.983152i | \(-0.441487\pi\) | ||||
0.182789 | + | 0.983152i | \(0.441487\pi\) | |||||||
\(440\) | 5.63098e76 | 0.0587124 | ||||||||
\(441\) | −4.20269e77 | −0.409816 | ||||||||
\(442\) | −2.83574e78 | −2.58648 | ||||||||
\(443\) | 1.54152e78 | 1.31534 | 0.657672 | − | 0.753304i | \(-0.271541\pi\) | ||||
0.657672 | + | 0.753304i | \(0.271541\pi\) | |||||||
\(444\) | 4.83644e78 | 3.86125 | ||||||||
\(445\) | 9.47226e77 | 0.707674 | ||||||||
\(446\) | 1.30716e78 | 0.914012 | ||||||||
\(447\) | −3.20692e78 | −2.09902 | ||||||||
\(448\) | −2.03455e78 | −1.24672 | ||||||||
\(449\) | −2.79348e78 | −1.60280 | −0.801398 | − | 0.598132i | \(-0.795910\pi\) | ||||
−0.801398 | + | 0.598132i | \(0.795910\pi\) | |||||||
\(450\) | 2.06119e78 | 1.10751 | ||||||||
\(451\) | −4.86693e76 | −0.0244933 | ||||||||
\(452\) | −5.59239e78 | −2.63641 | ||||||||
\(453\) | −5.30825e78 | −2.34452 | ||||||||
\(454\) | 5.21989e78 | 2.16030 | ||||||||
\(455\) | 1.45566e78 | 0.564576 | ||||||||
\(456\) | 5.95467e78 | 2.16469 | ||||||||
\(457\) | 5.45392e78 | 1.85858 | 0.929290 | − | 0.369351i | \(-0.120420\pi\) | ||||
0.929290 | + | 0.369351i | \(0.120420\pi\) | |||||||
\(458\) | −7.10924e77 | −0.227139 | ||||||||
\(459\) | −4.52824e77 | −0.135661 | ||||||||
\(460\) | −6.18512e78 | −1.73777 | ||||||||
\(461\) | −1.71684e78 | −0.452430 | −0.226215 | − | 0.974077i | \(-0.572635\pi\) | ||||
−0.226215 | + | 0.974077i | \(0.572635\pi\) | |||||||
\(462\) | 2.72959e77 | 0.0674775 | ||||||||
\(463\) | 5.84613e78 | 1.35590 | 0.677952 | − | 0.735106i | \(-0.262868\pi\) | ||||
0.677952 | + | 0.735106i | \(0.262868\pi\) | |||||||
\(464\) | 2.67807e77 | 0.0582830 | ||||||||
\(465\) | 5.90711e78 | 1.20646 | ||||||||
\(466\) | 8.88107e78 | 1.70247 | ||||||||
\(467\) | −2.20699e78 | −0.397148 | −0.198574 | − | 0.980086i | \(-0.563631\pi\) | ||||
−0.198574 | + | 0.980086i | \(0.563631\pi\) | |||||||
\(468\) | −1.73923e79 | −2.93836 | ||||||||
\(469\) | −4.08034e78 | −0.647288 | ||||||||
\(470\) | −8.88295e78 | −1.32334 | ||||||||
\(471\) | −2.87826e78 | −0.402730 | ||||||||
\(472\) | −7.23249e77 | −0.0950603 | ||||||||
\(473\) | −1.65418e77 | −0.0204258 | ||||||||
\(474\) | 1.16247e78 | 0.134871 | ||||||||
\(475\) | −3.31475e78 | −0.361401 | ||||||||
\(476\) | 1.94036e79 | 1.98828 | ||||||||
\(477\) | 1.57422e79 | 1.51626 | ||||||||
\(478\) | −1.10353e79 | −0.999220 | ||||||||
\(479\) | −1.40796e79 | −1.19865 | −0.599326 | − | 0.800505i | \(-0.704565\pi\) | ||||
−0.599326 | + | 0.800505i | \(0.704565\pi\) | |||||||
\(480\) | 2.42880e79 | 1.94435 | ||||||||
\(481\) | 1.91042e79 | 1.43830 | ||||||||
\(482\) | 1.79700e79 | 1.27251 | ||||||||
\(483\) | −1.80248e79 | −1.20069 | ||||||||
\(484\) | −3.99603e79 | −2.50433 | ||||||||
\(485\) | −7.27023e78 | −0.428713 | ||||||||
\(486\) | −4.62287e79 | −2.56532 | ||||||||
\(487\) | −2.26249e79 | −1.18163 | −0.590816 | − | 0.806806i | \(-0.701194\pi\) | ||||
−0.590816 | + | 0.806806i | \(0.701194\pi\) | |||||||
\(488\) | 7.88019e79 | 3.87393 | ||||||||
\(489\) | 5.14461e79 | 2.38090 | ||||||||
\(490\) | 1.14555e79 | 0.499147 | ||||||||
\(491\) | 2.61865e78 | 0.107442 | 0.0537210 | − | 0.998556i | \(-0.482892\pi\) | ||||
0.0537210 | + | 0.998556i | \(0.482892\pi\) | |||||||
\(492\) | −6.23621e79 | −2.40963 | ||||||||
\(493\) | −6.16678e77 | −0.0224427 | ||||||||
\(494\) | 3.91248e79 | 1.34124 | ||||||||
\(495\) | −5.84866e77 | −0.0188887 | ||||||||
\(496\) | −1.35072e80 | −4.11014 | ||||||||
\(497\) | 9.10905e78 | 0.261192 | ||||||||
\(498\) | 8.04299e79 | 2.17346 | ||||||||
\(499\) | 2.62064e79 | 0.667485 | 0.333743 | − | 0.942664i | \(-0.391688\pi\) | ||||
0.333743 | + | 0.942664i | \(0.391688\pi\) | |||||||
\(500\) | −1.01852e80 | −2.44543 | ||||||||
\(501\) | −3.08664e79 | −0.698671 | ||||||||
\(502\) | 9.54642e79 | 2.03742 | ||||||||
\(503\) | −5.52525e79 | −1.11198 | −0.555989 | − | 0.831190i | \(-0.687660\pi\) | ||||
−0.555989 | + | 0.831190i | \(0.687660\pi\) | |||||||
\(504\) | 1.00079e80 | 1.89951 | ||||||||
\(505\) | 1.71216e78 | 0.0306513 | ||||||||
\(506\) | −4.58131e78 | −0.0773659 | ||||||||
\(507\) | −5.76345e79 | −0.918222 | ||||||||
\(508\) | 2.89220e80 | 4.34759 | ||||||||
\(509\) | −4.32837e79 | −0.613974 | −0.306987 | − | 0.951714i | \(-0.599321\pi\) | ||||
−0.306987 | + | 0.951714i | \(0.599321\pi\) | |||||||
\(510\) | −1.22188e80 | −1.63572 | ||||||||
\(511\) | 1.52920e79 | 0.193217 | ||||||||
\(512\) | 1.02607e80 | 1.22380 | ||||||||
\(513\) | 6.24764e78 | 0.0703483 | ||||||||
\(514\) | −2.83257e80 | −3.01140 | ||||||||
\(515\) | 2.32076e79 | 0.232979 | ||||||||
\(516\) | −2.11957e80 | −2.00947 | ||||||||
\(517\) | −4.70370e78 | −0.0421181 | ||||||||
\(518\) | −1.82854e80 | −1.54660 | ||||||||
\(519\) | 2.51488e79 | 0.200946 | ||||||||
\(520\) | 2.85005e80 | 2.15156 | ||||||||
\(521\) | 2.41170e80 | 1.72033 | 0.860164 | − | 0.510018i | \(-0.170361\pi\) | ||||
0.860164 | + | 0.510018i | \(0.170361\pi\) | |||||||
\(522\) | −5.29067e78 | −0.0356640 | ||||||||
\(523\) | −2.16416e80 | −1.37876 | −0.689380 | − | 0.724400i | \(-0.742117\pi\) | ||||
−0.689380 | + | 0.724400i | \(0.742117\pi\) | |||||||
\(524\) | 1.61582e80 | 0.973017 | ||||||||
\(525\) | −1.17048e80 | −0.666294 | ||||||||
\(526\) | 1.38730e80 | 0.746607 | ||||||||
\(527\) | 3.11030e80 | 1.58266 | ||||||||
\(528\) | 2.80980e79 | 0.135200 | ||||||||
\(529\) | 8.27693e79 | 0.376640 | ||||||||
\(530\) | −4.29092e80 | −1.84677 | ||||||||
\(531\) | 7.51209e78 | 0.0305824 | ||||||||
\(532\) | −2.67712e80 | −1.03104 | ||||||||
\(533\) | −2.46334e80 | −0.897577 | ||||||||
\(534\) | 8.99004e80 | 3.09952 | ||||||||
\(535\) | 1.17974e80 | 0.384903 | ||||||||
\(536\) | −7.98897e80 | −2.46677 | ||||||||
\(537\) | 8.03486e80 | 2.34821 | ||||||||
\(538\) | −7.79105e80 | −2.15536 | ||||||||
\(539\) | 6.06589e78 | 0.0158864 | ||||||||
\(540\) | 7.57021e79 | 0.187712 | ||||||||
\(541\) | −3.15606e80 | −0.741012 | −0.370506 | − | 0.928830i | \(-0.620816\pi\) | ||||
−0.370506 | + | 0.928830i | \(0.620816\pi\) | |||||||
\(542\) | −6.31463e80 | −1.40401 | ||||||||
\(543\) | −4.09354e80 | −0.861993 | ||||||||
\(544\) | 1.27885e81 | 2.55065 | ||||||||
\(545\) | 2.12095e80 | 0.400713 | ||||||||
\(546\) | 1.38155e81 | 2.47277 | ||||||||
\(547\) | −7.77150e80 | −1.31789 | −0.658945 | − | 0.752191i | \(-0.728997\pi\) | ||||
−0.658945 | + | 0.752191i | \(0.728997\pi\) | |||||||
\(548\) | 4.03190e80 | 0.647862 | ||||||||
\(549\) | −8.18483e80 | −1.24631 | ||||||||
\(550\) | −2.97498e79 | −0.0429324 | ||||||||
\(551\) | 8.50833e78 | 0.0116378 | ||||||||
\(552\) | −3.52911e81 | −4.57575 | ||||||||
\(553\) | −3.14195e79 | −0.0386196 | ||||||||
\(554\) | 2.32486e81 | 2.70931 | ||||||||
\(555\) | 8.23177e80 | 0.909599 | ||||||||
\(556\) | 3.30569e81 | 3.46382 | ||||||||
\(557\) | −1.16000e81 | −1.15274 | −0.576368 | − | 0.817191i | \(-0.695530\pi\) | ||||
−0.576368 | + | 0.817191i | \(0.695530\pi\) | |||||||
\(558\) | 2.66842e81 | 2.51504 | ||||||||
\(559\) | −8.37244e80 | −0.748520 | ||||||||
\(560\) | −1.43421e81 | −1.21637 | ||||||||
\(561\) | −6.47011e79 | −0.0520604 | ||||||||
\(562\) | −1.94272e81 | −1.48316 | ||||||||
\(563\) | 2.67395e81 | 1.93712 | 0.968558 | − | 0.248786i | \(-0.0800316\pi\) | ||||
0.968558 | + | 0.248786i | \(0.0800316\pi\) | |||||||
\(564\) | −6.02706e81 | −4.14354 | ||||||||
\(565\) | −9.51842e80 | −0.621063 | ||||||||
\(566\) | −3.34852e81 | −2.07381 | ||||||||
\(567\) | 1.36509e81 | 0.802532 | ||||||||
\(568\) | 1.78348e81 | 0.995386 | ||||||||
\(569\) | 8.26000e80 | 0.437691 | 0.218846 | − | 0.975759i | \(-0.429771\pi\) | ||||
0.218846 | + | 0.975759i | \(0.429771\pi\) | |||||||
\(570\) | 1.68584e81 | 0.848219 | ||||||||
\(571\) | 1.96473e81 | 0.938722 | 0.469361 | − | 0.883006i | \(-0.344484\pi\) | ||||
0.469361 | + | 0.883006i | \(0.344484\pi\) | |||||||
\(572\) | 2.51030e80 | 0.113905 | ||||||||
\(573\) | −1.50885e81 | −0.650257 | ||||||||
\(574\) | 2.35776e81 | 0.965160 | ||||||||
\(575\) | 1.96453e81 | 0.763935 | ||||||||
\(576\) | 4.13748e81 | 1.52853 | ||||||||
\(577\) | −1.98064e81 | −0.695215 | −0.347607 | − | 0.937640i | \(-0.613006\pi\) | ||||
−0.347607 | + | 0.937640i | \(0.613006\pi\) | |||||||
\(578\) | −8.18428e80 | −0.272966 | ||||||||
\(579\) | 1.12681e81 | 0.357135 | ||||||||
\(580\) | 1.03095e80 | 0.0310535 | ||||||||
\(581\) | −2.17389e81 | −0.622359 | ||||||||
\(582\) | −6.90011e81 | −1.87771 | ||||||||
\(583\) | −2.27212e80 | −0.0587773 | ||||||||
\(584\) | 2.99404e81 | 0.736340 | ||||||||
\(585\) | −2.96023e81 | −0.692193 | ||||||||
\(586\) | −4.60072e80 | −0.102293 | ||||||||
\(587\) | −2.18290e81 | −0.461540 | −0.230770 | − | 0.973008i | \(-0.574124\pi\) | ||||
−0.230770 | + | 0.973008i | \(0.574124\pi\) | |||||||
\(588\) | 7.77250e81 | 1.56289 | ||||||||
\(589\) | −4.29129e81 | −0.820704 | ||||||||
\(590\) | −2.04761e80 | −0.0372488 | ||||||||
\(591\) | 4.35695e81 | 0.753966 | ||||||||
\(592\) | −1.88228e82 | −3.09880 | ||||||||
\(593\) | 8.01746e81 | 1.25581 | 0.627904 | − | 0.778290i | \(-0.283913\pi\) | ||||
0.627904 | + | 0.778290i | \(0.283913\pi\) | |||||||
\(594\) | 5.60725e79 | 0.00835698 | ||||||||
\(595\) | 3.30255e81 | 0.468381 | ||||||||
\(596\) | 2.82288e82 | 3.81002 | ||||||||
\(597\) | 7.96531e81 | 1.02320 | ||||||||
\(598\) | −2.31878e82 | −2.83514 | ||||||||
\(599\) | −3.31265e81 | −0.385553 | −0.192776 | − | 0.981243i | \(-0.561749\pi\) | ||||
−0.192776 | + | 0.981243i | \(0.561749\pi\) | |||||||
\(600\) | −2.29171e82 | −2.53921 | ||||||||
\(601\) | −1.30012e82 | −1.37147 | −0.685733 | − | 0.727853i | \(-0.740518\pi\) | ||||
−0.685733 | + | 0.727853i | \(0.740518\pi\) | |||||||
\(602\) | 8.01360e81 | 0.804880 | ||||||||
\(603\) | 8.29781e81 | 0.793602 | ||||||||
\(604\) | 4.67257e82 | 4.25565 | ||||||||
\(605\) | −6.80137e81 | −0.589947 | ||||||||
\(606\) | 1.62500e81 | 0.134249 | ||||||||
\(607\) | 6.65424e80 | 0.0523639 | 0.0261820 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261820 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(608\) | −1.76443e82 | −1.32266 | ||||||||
\(609\) | 3.00441e80 | 0.0214560 | ||||||||
\(610\) | 2.23098e82 | 1.51798 | ||||||||
\(611\) | −2.38072e82 | −1.54345 | ||||||||
\(612\) | −3.94593e82 | −2.43771 | ||||||||
\(613\) | 1.87920e82 | 1.10634 | 0.553169 | − | 0.833069i | \(-0.313418\pi\) | ||||
0.553169 | + | 0.833069i | \(0.313418\pi\) | |||||||
\(614\) | 1.07483e82 | 0.603078 | ||||||||
\(615\) | −1.06142e82 | −0.567639 | ||||||||
\(616\) | −1.44448e81 | −0.0736342 | ||||||||
\(617\) | −2.20328e80 | −0.0107068 | −0.00535338 | − | 0.999986i | \(-0.501704\pi\) | ||||
−0.00535338 | + | 0.999986i | \(0.501704\pi\) | |||||||
\(618\) | 2.20262e82 | 1.02042 | ||||||||
\(619\) | −1.34870e82 | −0.595719 | −0.297859 | − | 0.954610i | \(-0.596273\pi\) | ||||
−0.297859 | + | 0.954610i | \(0.596273\pi\) | |||||||
\(620\) | −5.19972e82 | −2.18990 | ||||||||
\(621\) | −3.70274e81 | −0.148703 | ||||||||
\(622\) | −6.75717e80 | −0.0258791 | ||||||||
\(623\) | −2.42986e82 | −0.887531 | ||||||||
\(624\) | 1.42215e83 | 4.95450 | ||||||||
\(625\) | 2.25774e81 | 0.0750264 | ||||||||
\(626\) | −6.90258e82 | −2.18811 | ||||||||
\(627\) | 8.92684e80 | 0.0269964 | ||||||||
\(628\) | 2.53358e82 | 0.731014 | ||||||||
\(629\) | 4.33431e82 | 1.19323 | ||||||||
\(630\) | 2.83336e82 | 0.744312 | ||||||||
\(631\) | 7.15154e82 | 1.79281 | 0.896403 | − | 0.443239i | \(-0.146171\pi\) | ||||
0.896403 | + | 0.443239i | \(0.146171\pi\) | |||||||
\(632\) | −6.15168e81 | −0.147177 | ||||||||
\(633\) | −3.08605e81 | −0.0704683 | ||||||||
\(634\) | −8.09765e82 | −1.76492 | ||||||||
\(635\) | 4.92261e82 | 1.02417 | ||||||||
\(636\) | −2.91137e83 | −5.78247 | ||||||||
\(637\) | 3.07018e82 | 0.582171 | ||||||||
\(638\) | 7.63621e79 | 0.00138251 | ||||||||
\(639\) | −1.85242e82 | −0.320232 | ||||||||
\(640\) | −2.75132e82 | −0.454184 | ||||||||
\(641\) | −2.99840e82 | −0.472692 | −0.236346 | − | 0.971669i | \(-0.575950\pi\) | ||||
−0.236346 | + | 0.971669i | \(0.575950\pi\) | |||||||
\(642\) | 1.11968e83 | 1.68582 | ||||||||
\(643\) | 5.90345e81 | 0.0848951 | 0.0424475 | − | 0.999099i | \(-0.486484\pi\) | ||||
0.0424475 | + | 0.999099i | \(0.486484\pi\) | |||||||
\(644\) | 1.58663e83 | 2.17942 | ||||||||
\(645\) | −3.60758e82 | −0.473374 | ||||||||
\(646\) | 8.87652e82 | 1.11271 | ||||||||
\(647\) | −3.93898e82 | −0.471746 | −0.235873 | − | 0.971784i | \(-0.575795\pi\) | ||||
−0.235873 | + | 0.971784i | \(0.575795\pi\) | |||||||
\(648\) | 2.67274e83 | 3.05840 | ||||||||
\(649\) | −1.08425e80 | −0.00118552 | ||||||||
\(650\) | −1.50575e83 | −1.57329 | ||||||||
\(651\) | −1.51531e83 | −1.51308 | ||||||||
\(652\) | −4.52853e83 | −4.32169 | ||||||||
\(653\) | 6.47496e82 | 0.590607 | 0.295303 | − | 0.955404i | \(-0.404579\pi\) | ||||
0.295303 | + | 0.955404i | \(0.404579\pi\) | |||||||
\(654\) | 2.01298e83 | 1.75507 | ||||||||
\(655\) | 2.75018e82 | 0.229215 | ||||||||
\(656\) | 2.42705e83 | 1.93382 | ||||||||
\(657\) | −3.10978e82 | −0.236893 | ||||||||
\(658\) | 2.27869e83 | 1.65967 | ||||||||
\(659\) | −1.27657e83 | −0.889044 | −0.444522 | − | 0.895768i | \(-0.646627\pi\) | ||||
−0.444522 | + | 0.895768i | \(0.646627\pi\) | |||||||
\(660\) | 1.08166e82 | 0.0720350 | ||||||||
\(661\) | 2.81059e83 | 1.79000 | 0.895002 | − | 0.446062i | \(-0.147174\pi\) | ||||
0.895002 | + | 0.446062i | \(0.147174\pi\) | |||||||
\(662\) | −1.91644e83 | −1.16730 | ||||||||
\(663\) | −3.27477e83 | −1.90780 | ||||||||
\(664\) | −4.25629e83 | −2.37177 | ||||||||
\(665\) | −4.55654e82 | −0.242883 | ||||||||
\(666\) | 3.71853e83 | 1.89619 | ||||||||
\(667\) | −5.04256e81 | −0.0246002 | ||||||||
\(668\) | 2.71700e83 | 1.26819 | ||||||||
\(669\) | 1.50954e83 | 0.674179 | ||||||||
\(670\) | −2.26177e83 | −0.966590 | ||||||||
\(671\) | 1.18135e82 | 0.0483129 | ||||||||
\(672\) | −6.23044e83 | −2.43851 | ||||||||
\(673\) | −2.82753e83 | −1.05916 | −0.529581 | − | 0.848260i | \(-0.677651\pi\) | ||||
−0.529581 | + | 0.848260i | \(0.677651\pi\) | |||||||
\(674\) | 2.87451e83 | 1.03062 | ||||||||
\(675\) | −2.40446e82 | −0.0825195 | ||||||||
\(676\) | 5.07326e83 | 1.66671 | ||||||||
\(677\) | 5.84082e83 | 1.83700 | 0.918498 | − | 0.395425i | \(-0.129403\pi\) | ||||
0.918498 | + | 0.395425i | \(0.129403\pi\) | |||||||
\(678\) | −9.03384e83 | −2.72017 | ||||||||
\(679\) | 1.86499e83 | 0.537672 | ||||||||
\(680\) | 6.46612e83 | 1.78497 | ||||||||
\(681\) | 6.02805e83 | 1.59344 | ||||||||
\(682\) | −3.85142e82 | −0.0974950 | ||||||||
\(683\) | −4.16662e83 | −1.01012 | −0.505060 | − | 0.863084i | \(-0.668530\pi\) | ||||
−0.505060 | + | 0.863084i | \(0.668530\pi\) | |||||||
\(684\) | 5.44421e83 | 1.26410 | ||||||||
\(685\) | 6.86241e82 | 0.152618 | ||||||||
\(686\) | −9.45125e83 | −2.01339 | ||||||||
\(687\) | −8.20991e82 | −0.167538 | ||||||||
\(688\) | 8.24910e83 | 1.61268 | ||||||||
\(689\) | −1.15001e84 | −2.15394 | ||||||||
\(690\) | −9.99132e83 | −1.79298 | ||||||||
\(691\) | 6.93132e83 | 1.19183 | 0.595914 | − | 0.803048i | \(-0.296790\pi\) | ||||
0.595914 | + | 0.803048i | \(0.296790\pi\) | |||||||
\(692\) | −2.21371e83 | −0.364747 | ||||||||
\(693\) | 1.50032e82 | 0.0236893 | ||||||||
\(694\) | −1.49216e84 | −2.25793 | ||||||||
\(695\) | 5.62638e83 | 0.815976 | ||||||||
\(696\) | 5.88238e82 | 0.0817675 | ||||||||
\(697\) | −5.58875e83 | −0.744643 | ||||||||
\(698\) | 1.06859e84 | 1.36482 | ||||||||
\(699\) | 1.02561e84 | 1.25575 | ||||||||
\(700\) | 1.03032e84 | 1.20942 | ||||||||
\(701\) | −6.90202e82 | −0.0776774 | −0.0388387 | − | 0.999245i | \(-0.512366\pi\) | ||||
−0.0388387 | + | 0.999245i | \(0.512366\pi\) | |||||||
\(702\) | 2.83804e83 | 0.306249 | ||||||||
\(703\) | −5.98006e83 | −0.618762 | ||||||||
\(704\) | −5.97178e82 | −0.0592530 | ||||||||
\(705\) | −1.02582e84 | −0.976099 | ||||||||
\(706\) | 3.15954e84 | 2.88327 | ||||||||
\(707\) | −4.39210e82 | −0.0384414 | ||||||||
\(708\) | −1.38929e83 | −0.116631 | ||||||||
\(709\) | −1.62009e84 | −1.30460 | −0.652299 | − | 0.757962i | \(-0.726195\pi\) | ||||
−0.652299 | + | 0.757962i | \(0.726195\pi\) | |||||||
\(710\) | 5.04924e83 | 0.390036 | ||||||||
\(711\) | 6.38949e82 | 0.0473492 | ||||||||
\(712\) | −4.75746e84 | −3.38232 | ||||||||
\(713\) | 2.54328e84 | 1.73482 | ||||||||
\(714\) | 3.13442e84 | 2.05145 | ||||||||
\(715\) | 4.27261e82 | 0.0268327 | ||||||||
\(716\) | −7.07266e84 | −4.26235 | ||||||||
\(717\) | −1.27438e84 | −0.737028 | ||||||||
\(718\) | 4.48517e83 | 0.248948 | ||||||||
\(719\) | 2.70431e84 | 1.44064 | 0.720319 | − | 0.693643i | \(-0.243996\pi\) | ||||
0.720319 | + | 0.693643i | \(0.243996\pi\) | |||||||
\(720\) | 2.91662e84 | 1.49132 | ||||||||
\(721\) | −5.95330e83 | −0.292192 | ||||||||
\(722\) | 2.75035e84 | 1.29581 | ||||||||
\(723\) | 2.07521e84 | 0.938606 | ||||||||
\(724\) | 3.60332e84 | 1.56464 | ||||||||
\(725\) | −3.27451e82 | −0.0136513 | ||||||||
\(726\) | −6.45512e84 | −2.58389 | ||||||||
\(727\) | −3.36956e84 | −1.29511 | −0.647557 | − | 0.762017i | \(-0.724209\pi\) | ||||
−0.647557 | + | 0.762017i | \(0.724209\pi\) | |||||||
\(728\) | −7.31105e84 | −2.69839 | ||||||||
\(729\) | −2.28211e84 | −0.808861 | ||||||||
\(730\) | 8.47648e83 | 0.288530 | ||||||||
\(731\) | −1.89951e84 | −0.620983 | ||||||||
\(732\) | 1.51371e85 | 4.75298 | ||||||||
\(733\) | −4.13834e84 | −1.24813 | −0.624063 | − | 0.781374i | \(-0.714519\pi\) | ||||
−0.624063 | + | 0.781374i | \(0.714519\pi\) | |||||||
\(734\) | 3.42764e84 | 0.993028 | ||||||||
\(735\) | 1.32290e84 | 0.368173 | ||||||||
\(736\) | 1.04571e85 | 2.79586 | ||||||||
\(737\) | −1.19765e83 | −0.0307638 | ||||||||
\(738\) | −4.79476e84 | −1.18333 | ||||||||
\(739\) | −1.38714e82 | −0.00328934 | −0.00164467 | − | 0.999999i | \(-0.500524\pi\) | ||||
−0.00164467 | + | 0.999999i | \(0.500524\pi\) | |||||||
\(740\) | −7.24599e84 | −1.65106 | ||||||||
\(741\) | 4.51822e84 | 0.989305 | ||||||||
\(742\) | 1.10072e85 | 2.31613 | ||||||||
\(743\) | 1.47222e84 | 0.297716 | 0.148858 | − | 0.988859i | \(-0.452440\pi\) | ||||
0.148858 | + | 0.988859i | \(0.452440\pi\) | |||||||
\(744\) | −2.96686e85 | −5.76627 | ||||||||
\(745\) | 4.80463e84 | 0.897531 | ||||||||
\(746\) | −9.20917e84 | −1.65358 | ||||||||
\(747\) | 4.42083e84 | 0.763038 | ||||||||
\(748\) | 5.69530e83 | 0.0944973 | ||||||||
\(749\) | −3.02632e84 | −0.482727 | ||||||||
\(750\) | −1.64530e85 | −2.52312 | ||||||||
\(751\) | 2.68915e84 | 0.396494 | 0.198247 | − | 0.980152i | \(-0.436475\pi\) | ||||
0.198247 | + | 0.980152i | \(0.436475\pi\) | |||||||
\(752\) | 2.34565e85 | 3.32535 | ||||||||
\(753\) | 1.10244e85 | 1.50281 | ||||||||
\(754\) | 3.86498e83 | 0.0506632 | ||||||||
\(755\) | 7.95286e84 | 1.00251 | ||||||||
\(756\) | −1.94194e84 | −0.235419 | ||||||||
\(757\) | −1.64478e85 | −1.91770 | −0.958850 | − | 0.283915i | \(-0.908367\pi\) | ||||
−0.958850 | + | 0.283915i | \(0.908367\pi\) | |||||||
\(758\) | −4.73495e84 | −0.530975 | ||||||||
\(759\) | −5.29060e83 | −0.0570653 | ||||||||
\(760\) | −8.92133e84 | −0.925611 | ||||||||
\(761\) | 7.57979e84 | 0.756502 | 0.378251 | − | 0.925703i | \(-0.376526\pi\) | ||||
0.378251 | + | 0.925703i | \(0.376526\pi\) | |||||||
\(762\) | 4.67200e85 | 4.48571 | ||||||||
\(763\) | −5.44074e84 | −0.502555 | ||||||||
\(764\) | 1.32816e85 | 1.18031 | ||||||||
\(765\) | −6.71609e84 | −0.574254 | ||||||||
\(766\) | −3.16142e85 | −2.60096 | ||||||||
\(767\) | −5.48779e83 | −0.0434444 | ||||||||
\(768\) | 4.40434e84 | 0.335525 | ||||||||
\(769\) | −2.70374e84 | −0.198216 | −0.0991078 | − | 0.995077i | \(-0.531599\pi\) | ||||
−0.0991078 | + | 0.995077i | \(0.531599\pi\) | |||||||
\(770\) | −4.08949e83 | −0.0288531 | ||||||||
\(771\) | −3.27111e85 | −2.22122 | ||||||||
\(772\) | −9.91868e84 | −0.648252 | ||||||||
\(773\) | −6.61906e84 | −0.416391 | −0.208195 | − | 0.978087i | \(-0.566759\pi\) | ||||
−0.208195 | + | 0.978087i | \(0.566759\pi\) | |||||||
\(774\) | −1.62965e85 | −0.986816 | ||||||||
\(775\) | 1.65154e85 | 0.962697 | ||||||||
\(776\) | 3.65149e85 | 2.04903 | ||||||||
\(777\) | −2.11164e85 | −1.14078 | ||||||||
\(778\) | 1.97556e85 | 1.02753 | ||||||||
\(779\) | 7.71083e84 | 0.386141 | ||||||||
\(780\) | 5.47468e85 | 2.63978 | ||||||||
\(781\) | 2.67367e83 | 0.0124137 | ||||||||
\(782\) | −5.26077e85 | −2.35207 | ||||||||
\(783\) | 6.17179e82 | 0.00265729 | ||||||||
\(784\) | −3.02495e85 | −1.25428 | ||||||||
\(785\) | 4.31223e84 | 0.172206 | ||||||||
\(786\) | 2.61017e85 | 1.00393 | ||||||||
\(787\) | 3.14052e84 | 0.116345 | 0.0581724 | − | 0.998307i | \(-0.481473\pi\) | ||||
0.0581724 | + | 0.998307i | \(0.481473\pi\) | |||||||
\(788\) | −3.83519e85 | −1.36856 | ||||||||
\(789\) | 1.60209e85 | 0.550700 | ||||||||
\(790\) | −1.74161e84 | −0.0576704 | ||||||||
\(791\) | 2.44170e85 | 0.778907 | ||||||||
\(792\) | 2.93750e84 | 0.0902786 | ||||||||
\(793\) | 5.97924e85 | 1.77046 | ||||||||
\(794\) | 3.09426e85 | 0.882778 | ||||||||
\(795\) | −4.95525e85 | −1.36218 | ||||||||
\(796\) | −7.01144e85 | −1.85726 | ||||||||
\(797\) | 2.74800e85 | 0.701449 | 0.350725 | − | 0.936479i | \(-0.385935\pi\) | ||||
0.350725 | + | 0.936479i | \(0.385935\pi\) | |||||||
\(798\) | −4.32457e85 | −1.06379 | ||||||||
\(799\) | −5.40131e85 | −1.28047 | ||||||||
\(800\) | 6.79057e85 | 1.55150 | ||||||||
\(801\) | 4.94137e85 | 1.08815 | ||||||||
\(802\) | 1.65263e86 | 3.50778 | ||||||||
\(803\) | 4.48846e83 | 0.00918309 | ||||||||
\(804\) | −1.53461e86 | −3.02652 | ||||||||
\(805\) | 2.70049e85 | 0.513409 | ||||||||
\(806\) | −1.94935e86 | −3.57279 | ||||||||
\(807\) | −8.99728e85 | −1.58980 | ||||||||
\(808\) | −8.59936e84 | −0.146498 | ||||||||
\(809\) | 1.02903e85 | 0.169024 | 0.0845119 | − | 0.996422i | \(-0.473067\pi\) | ||||
0.0845119 | + | 0.996422i | \(0.473067\pi\) | |||||||
\(810\) | 7.56685e85 | 1.19841 | ||||||||
\(811\) | 9.82250e85 | 1.50005 | 0.750027 | − | 0.661407i | \(-0.230041\pi\) | ||||
0.750027 | + | 0.661407i | \(0.230041\pi\) | |||||||
\(812\) | −2.64462e84 | −0.0389458 | ||||||||
\(813\) | −7.29228e85 | −1.03560 | ||||||||
\(814\) | −5.36710e84 | −0.0735054 | ||||||||
\(815\) | −7.70770e85 | −1.01806 | ||||||||
\(816\) | 3.22653e86 | 4.11033 | ||||||||
\(817\) | 2.62077e85 | 0.322016 | ||||||||
\(818\) | −5.71781e85 | −0.677652 | ||||||||
\(819\) | 7.59368e85 | 0.868115 | ||||||||
\(820\) | 9.34314e85 | 1.03035 | ||||||||
\(821\) | 1.25320e86 | 1.33321 | 0.666603 | − | 0.745413i | \(-0.267748\pi\) | ||||
0.666603 | + | 0.745413i | \(0.267748\pi\) | |||||||
\(822\) | 6.51305e85 | 0.668445 | ||||||||
\(823\) | −1.58233e86 | −1.56676 | −0.783378 | − | 0.621546i | \(-0.786505\pi\) | ||||
−0.783378 | + | 0.621546i | \(0.786505\pi\) | |||||||
\(824\) | −1.16561e86 | −1.11352 | ||||||||
\(825\) | −3.43558e84 | −0.0316671 | ||||||||
\(826\) | 5.25259e84 | 0.0467156 | ||||||||
\(827\) | −2.03076e86 | −1.74280 | −0.871398 | − | 0.490576i | \(-0.836786\pi\) | ||||
−0.871398 | + | 0.490576i | \(0.836786\pi\) | |||||||
\(828\) | −3.22657e86 | −2.67206 | ||||||||
\(829\) | −6.59368e85 | −0.526950 | −0.263475 | − | 0.964666i | \(-0.584869\pi\) | ||||
−0.263475 | + | 0.964666i | \(0.584869\pi\) | |||||||
\(830\) | −1.20501e86 | −0.929364 | ||||||||
\(831\) | 2.68480e86 | 1.99840 | ||||||||
\(832\) | −3.02255e86 | −2.17138 | ||||||||
\(833\) | 6.96554e85 | 0.482978 | ||||||||
\(834\) | 5.33995e86 | 3.57387 | ||||||||
\(835\) | 4.62442e85 | 0.298749 | ||||||||
\(836\) | −7.85783e84 | −0.0490024 | ||||||||
\(837\) | −3.11282e85 | −0.187393 | ||||||||
\(838\) | 2.82148e86 | 1.63976 | ||||||||
\(839\) | 3.14600e85 | 0.176515 | 0.0882573 | − | 0.996098i | \(-0.471870\pi\) | ||||
0.0882573 | + | 0.996098i | \(0.471870\pi\) | |||||||
\(840\) | −3.15024e86 | −1.70650 | ||||||||
\(841\) | −1.91113e86 | −0.999560 | ||||||||
\(842\) | 2.23968e86 | 1.13104 | ||||||||
\(843\) | −2.24350e86 | −1.09399 | ||||||||
\(844\) | 2.71649e85 | 0.127910 | ||||||||
\(845\) | 8.63484e85 | 0.392628 | ||||||||
\(846\) | −4.63395e86 | −2.03482 | ||||||||
\(847\) | 1.74471e86 | 0.739883 | ||||||||
\(848\) | 1.13307e87 | 4.64065 | ||||||||
\(849\) | −3.86695e86 | −1.52965 | ||||||||
\(850\) | −3.41621e86 | −1.30523 | ||||||||
\(851\) | 3.54415e86 | 1.30795 | ||||||||
\(852\) | 3.42589e86 | 1.22125 | ||||||||
\(853\) | −8.87150e85 | −0.305492 | −0.152746 | − | 0.988265i | \(-0.548812\pi\) | ||||
−0.152746 | + | 0.988265i | \(0.548812\pi\) | |||||||
\(854\) | −5.72298e86 | −1.90377 | ||||||||
\(855\) | 9.26621e85 | 0.297784 | ||||||||
\(856\) | −5.92528e86 | −1.83964 | ||||||||
\(857\) | −3.27258e86 | −0.981648 | −0.490824 | − | 0.871259i | \(-0.663304\pi\) | ||||
−0.490824 | + | 0.871259i | \(0.663304\pi\) | |||||||
\(858\) | 4.05509e85 | 0.117524 | ||||||||
\(859\) | 1.26296e86 | 0.353664 | 0.176832 | − | 0.984241i | \(-0.443415\pi\) | ||||
0.176832 | + | 0.984241i | \(0.443415\pi\) | |||||||
\(860\) | 3.17556e86 | 0.859244 | ||||||||
\(861\) | 2.72280e86 | 0.711906 | ||||||||
\(862\) | 2.21330e86 | 0.559211 | ||||||||
\(863\) | 4.16687e86 | 1.01740 | 0.508700 | − | 0.860944i | \(-0.330126\pi\) | ||||
0.508700 | + | 0.860944i | \(0.330126\pi\) | |||||||
\(864\) | −1.27989e86 | −0.302006 | ||||||||
\(865\) | −3.76781e85 | −0.0859238 | ||||||||
\(866\) | −1.58887e87 | −3.50196 | ||||||||
\(867\) | −9.45139e85 | −0.201341 | ||||||||
\(868\) | 1.33385e87 | 2.74647 | ||||||||
\(869\) | −9.22219e83 | −0.00183548 | ||||||||
\(870\) | 1.66537e85 | 0.0320401 | ||||||||
\(871\) | −6.06178e86 | −1.12737 | ||||||||
\(872\) | −1.06525e87 | −1.91521 | ||||||||
\(873\) | −3.79265e86 | −0.659207 | ||||||||
\(874\) | 7.25831e86 | 1.21969 | ||||||||
\(875\) | 4.44697e86 | 0.722481 | ||||||||
\(876\) | 5.75127e86 | 0.903425 | ||||||||
\(877\) | 1.19187e87 | 1.81026 | 0.905128 | − | 0.425139i | \(-0.139775\pi\) | ||||
0.905128 | + | 0.425139i | \(0.139775\pi\) | |||||||
\(878\) | −4.66191e86 | −0.684660 | ||||||||
\(879\) | −5.31302e85 | −0.0754517 | ||||||||
\(880\) | −4.20967e85 | −0.0578108 | ||||||||
\(881\) | 5.33978e86 | 0.709143 | 0.354572 | − | 0.935029i | \(-0.384627\pi\) | ||||
0.354572 | + | 0.935029i | \(0.384627\pi\) | |||||||
\(882\) | 5.97595e86 | 0.767509 | ||||||||
\(883\) | −3.28934e85 | −0.0408571 | −0.0204286 | − | 0.999791i | \(-0.506503\pi\) | ||||
−0.0204286 | + | 0.999791i | \(0.506503\pi\) | |||||||
\(884\) | 2.88261e87 | 3.46293 | ||||||||
\(885\) | −2.36462e85 | −0.0274748 | ||||||||
\(886\) | −2.19194e87 | −2.46340 | ||||||||
\(887\) | 6.82023e86 | 0.741400 | 0.370700 | − | 0.928753i | \(-0.379118\pi\) | ||||
0.370700 | + | 0.928753i | \(0.379118\pi\) | |||||||
\(888\) | −4.13442e87 | −4.34742 | ||||||||
\(889\) | −1.26276e87 | −1.28446 | ||||||||
\(890\) | −1.34689e87 | −1.32534 | ||||||||
\(891\) | 4.00680e85 | 0.0381421 | ||||||||
\(892\) | −1.32877e87 | −1.22373 | ||||||||
\(893\) | 7.45221e86 | 0.663999 | ||||||||
\(894\) | 4.56003e87 | 3.93107 | ||||||||
\(895\) | −1.20379e87 | −1.00409 | ||||||||
\(896\) | 7.05778e86 | 0.569616 | ||||||||
\(897\) | −2.67778e87 | −2.09121 | ||||||||
\(898\) | 3.97214e87 | 3.00174 | ||||||||
\(899\) | −4.23919e85 | −0.0310007 | ||||||||
\(900\) | −2.09526e87 | −1.48280 | ||||||||
\(901\) | −2.60911e87 | −1.78694 | ||||||||
\(902\) | 6.92045e85 | 0.0458714 | ||||||||
\(903\) | 9.25429e86 | 0.593683 | ||||||||
\(904\) | 4.78064e87 | 2.96837 | ||||||||
\(905\) | 6.13297e86 | 0.368585 | ||||||||
\(906\) | 7.54799e87 | 4.39086 | ||||||||
\(907\) | −1.50909e87 | −0.849767 | −0.424883 | − | 0.905248i | \(-0.639685\pi\) | ||||
−0.424883 | + | 0.905248i | \(0.639685\pi\) | |||||||
\(908\) | −5.30617e87 | −2.89234 | ||||||||
\(909\) | 8.93179e85 | 0.0471307 | ||||||||
\(910\) | −2.06985e87 | −1.05735 | ||||||||
\(911\) | 3.87850e87 | 1.91810 | 0.959051 | − | 0.283234i | \(-0.0914073\pi\) | ||||
0.959051 | + | 0.283234i | \(0.0914073\pi\) | |||||||
\(912\) | −4.45166e87 | −2.13145 | ||||||||
\(913\) | −6.38075e85 | −0.0295790 | ||||||||
\(914\) | −7.75513e87 | −3.48078 | ||||||||
\(915\) | 2.57638e87 | 1.11967 | ||||||||
\(916\) | 7.22674e86 | 0.304107 | ||||||||
\(917\) | −7.05485e86 | −0.287470 | ||||||||
\(918\) | 6.43887e86 | 0.254068 | ||||||||
\(919\) | −2.15450e87 | −0.823263 | −0.411632 | − | 0.911350i | \(-0.635041\pi\) | ||||
−0.411632 | + | 0.911350i | \(0.635041\pi\) | |||||||
\(920\) | 5.28733e87 | 1.95657 | ||||||||
\(921\) | 1.24124e87 | 0.444833 | ||||||||
\(922\) | 2.44123e87 | 0.847319 | ||||||||
\(923\) | 1.35325e87 | 0.454911 | ||||||||
\(924\) | −2.77471e86 | −0.0903429 | ||||||||
\(925\) | 2.30148e87 | 0.725816 | ||||||||
\(926\) | −8.31282e87 | −2.53936 | ||||||||
\(927\) | 1.21067e87 | 0.358239 | ||||||||
\(928\) | −1.74301e86 | −0.0499614 | ||||||||
\(929\) | 5.54912e87 | 1.54085 | 0.770426 | − | 0.637530i | \(-0.220044\pi\) | ||||
0.770426 | + | 0.637530i | \(0.220044\pi\) | |||||||
\(930\) | −8.39953e87 | −2.25948 | ||||||||
\(931\) | −9.61038e86 | −0.250452 | ||||||||
\(932\) | −9.02786e87 | −2.27937 | ||||||||
\(933\) | −7.80334e85 | −0.0190885 | ||||||||
\(934\) | 3.13819e87 | 0.743784 | ||||||||
\(935\) | 9.69357e85 | 0.0222608 | ||||||||
\(936\) | 1.48678e88 | 3.30833 | ||||||||
\(937\) | 3.57990e86 | 0.0771885 | 0.0385942 | − | 0.999255i | \(-0.487712\pi\) | ||||
0.0385942 | + | 0.999255i | \(0.487712\pi\) | |||||||
\(938\) | 5.80198e87 | 1.21225 | ||||||||
\(939\) | −7.97125e87 | −1.61396 | ||||||||
\(940\) | 9.02978e87 | 1.77176 | ||||||||
\(941\) | −4.47034e87 | −0.850054 | −0.425027 | − | 0.905181i | \(-0.639735\pi\) | ||||
−0.425027 | + | 0.905181i | \(0.639735\pi\) | |||||||
\(942\) | 4.09270e87 | 0.754238 | ||||||||
\(943\) | −4.56991e87 | −0.816231 | ||||||||
\(944\) | 5.40695e86 | 0.0936006 | ||||||||
\(945\) | −3.30523e86 | −0.0554580 | ||||||||
\(946\) | 2.35214e86 | 0.0382537 | ||||||||
\(947\) | −9.93580e86 | −0.156631 | −0.0783156 | − | 0.996929i | \(-0.524954\pi\) | ||||
−0.0783156 | + | 0.996929i | \(0.524954\pi\) | |||||||
\(948\) | −1.18168e87 | −0.180573 | ||||||||
\(949\) | 2.27178e87 | 0.336522 | ||||||||
\(950\) | 4.71336e87 | 0.676837 | ||||||||
\(951\) | −9.35135e87 | −1.30181 | ||||||||
\(952\) | −1.65871e88 | −2.23862 | ||||||||
\(953\) | 1.00705e88 | 1.31768 | 0.658842 | − | 0.752281i | \(-0.271047\pi\) | ||||
0.658842 | + | 0.752281i | \(0.271047\pi\) | |||||||
\(954\) | −2.23843e88 | −2.83967 | ||||||||
\(955\) | 2.26057e87 | 0.278047 | ||||||||
\(956\) | 1.12177e88 | 1.33782 | ||||||||
\(957\) | 8.81847e84 | 0.00101974 | ||||||||
\(958\) | 2.00203e88 | 2.24485 | ||||||||
\(959\) | −1.76037e87 | −0.191406 | ||||||||
\(960\) | −1.30238e88 | −1.37321 | ||||||||
\(961\) | 1.16009e88 | 1.18618 | ||||||||
\(962\) | −2.71649e88 | −2.69367 | ||||||||
\(963\) | 6.15434e87 | 0.591843 | ||||||||
\(964\) | −1.82670e88 | −1.70371 | ||||||||
\(965\) | −1.68819e87 | −0.152709 | ||||||||
\(966\) | 2.56301e88 | 2.24867 | ||||||||
\(967\) | −3.35222e87 | −0.285267 | −0.142633 | − | 0.989776i | \(-0.545557\pi\) | ||||
−0.142633 | + | 0.989776i | \(0.545557\pi\) | |||||||
\(968\) | 3.41600e88 | 2.81965 | ||||||||
\(969\) | 1.02508e88 | 0.820742 | ||||||||
\(970\) | 1.03378e88 | 0.802901 | ||||||||
\(971\) | −1.60573e88 | −1.20978 | −0.604889 | − | 0.796309i | \(-0.706783\pi\) | ||||
−0.604889 | + | 0.796309i | \(0.706783\pi\) | |||||||
\(972\) | 4.69928e88 | 3.43460 | ||||||||
\(973\) | −1.44330e88 | −1.02336 | ||||||||
\(974\) | 3.21711e88 | 2.21298 | ||||||||
\(975\) | −1.73888e88 | −1.16047 | ||||||||
\(976\) | −5.89117e88 | −3.81445 | ||||||||
\(977\) | 6.18037e87 | 0.388262 | 0.194131 | − | 0.980976i | \(-0.437811\pi\) | ||||
0.194131 | + | 0.980976i | \(0.437811\pi\) | |||||||
\(978\) | −7.31530e88 | −4.45899 | ||||||||
\(979\) | −7.13206e86 | −0.0421819 | ||||||||
\(980\) | −1.16448e88 | −0.668288 | ||||||||
\(981\) | 1.10643e88 | 0.616154 | ||||||||
\(982\) | −3.72355e87 | −0.201219 | ||||||||
\(983\) | 4.68900e87 | 0.245896 | 0.122948 | − | 0.992413i | \(-0.460765\pi\) | ||||
0.122948 | + | 0.992413i | \(0.460765\pi\) | |||||||
\(984\) | 5.33101e88 | 2.71303 | ||||||||
\(985\) | −6.52761e87 | −0.322393 | ||||||||
\(986\) | 8.76876e86 | 0.0420309 | ||||||||
\(987\) | 2.63148e88 | 1.22418 | ||||||||
\(988\) | −3.97715e88 | −1.79573 | ||||||||
\(989\) | −1.55323e88 | −0.680683 | ||||||||
\(990\) | 8.31641e86 | 0.0353751 | ||||||||
\(991\) | 3.12613e88 | 1.29073 | 0.645363 | − | 0.763876i | \(-0.276706\pi\) | ||||
0.645363 | + | 0.763876i | \(0.276706\pi\) | |||||||
\(992\) | 8.79110e88 | 3.52329 | ||||||||
\(993\) | −2.21314e88 | −0.861007 | ||||||||
\(994\) | −1.29525e88 | −0.489164 | ||||||||
\(995\) | −1.19337e88 | −0.437516 | ||||||||
\(996\) | −8.17594e88 | −2.90996 | ||||||||
\(997\) | 2.03910e88 | 0.704581 | 0.352290 | − | 0.935891i | \(-0.385403\pi\) | ||||
0.352290 | + | 0.935891i | \(0.385403\pi\) | |||||||
\(998\) | −3.72638e88 | −1.25008 | ||||||||
\(999\) | −4.33783e87 | −0.141283 |
(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 | 1.60.a.a.1.1 | ✓ | 5 | |
3.2 | odd | 2 | 9.60.a.c.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.60.a.a.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.60.a.c.1.5 | 5 | 3.2 | odd | 2 |