Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(1,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.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: | \(8.75560921479\) |
Analytic rank: | \(1\) |
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: | \( x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(33.6330\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 26.6330 | 1.17702 | 0.588512 | − | 0.808488i | \(-0.299714\pi\) | ||||
0.588512 | + | 0.808488i | \(0.299714\pi\) | |||||||
\(3\) | −85.9747 | −0.612809 | −0.306404 | − | 0.951901i | \(-0.599126\pi\) | ||||
−0.306404 | + | 0.951901i | \(0.599126\pi\) | |||||||
\(4\) | 197.318 | 0.385386 | ||||||||
\(5\) | −1460.58 | −1.04511 | −0.522553 | − | 0.852607i | \(-0.675020\pi\) | ||||
−0.522553 | + | 0.852607i | \(0.675020\pi\) | |||||||
\(6\) | −2289.77 | −0.721291 | ||||||||
\(7\) | −446.232 | −0.0702456 | −0.0351228 | − | 0.999383i | \(-0.511182\pi\) | ||||
−0.0351228 | + | 0.999383i | \(0.511182\pi\) | |||||||
\(8\) | −8380.94 | −0.723416 | ||||||||
\(9\) | −12291.3 | −0.624465 | ||||||||
\(10\) | −38899.6 | −1.23011 | ||||||||
\(11\) | 2565.20 | 0.0528268 | 0.0264134 | − | 0.999651i | \(-0.491591\pi\) | ||||
0.0264134 | + | 0.999651i | \(0.491591\pi\) | |||||||
\(12\) | −16964.3 | −0.236168 | ||||||||
\(13\) | 70467.9 | 0.684299 | 0.342150 | − | 0.939645i | \(-0.388845\pi\) | ||||
0.342150 | + | 0.939645i | \(0.388845\pi\) | |||||||
\(14\) | −11884.5 | −0.0826808 | ||||||||
\(15\) | 125573. | 0.640450 | ||||||||
\(16\) | −324236. | −1.23686 | ||||||||
\(17\) | −83521.0 | −0.242536 | ||||||||
\(18\) | −327356. | −0.735011 | ||||||||
\(19\) | −474111. | −0.834620 | −0.417310 | − | 0.908764i | \(-0.637027\pi\) | ||||
−0.417310 | + | 0.908764i | \(0.637027\pi\) | |||||||
\(20\) | −288198. | −0.402769 | ||||||||
\(21\) | 38364.6 | 0.0430471 | ||||||||
\(22\) | 68319.0 | 0.0621784 | ||||||||
\(23\) | 1.74586e6 | 1.30087 | 0.650437 | − | 0.759561i | \(-0.274586\pi\) | ||||
0.650437 | + | 0.759561i | \(0.274586\pi\) | |||||||
\(24\) | 720549. | 0.443315 | ||||||||
\(25\) | 180168. | 0.0922461 | ||||||||
\(26\) | 1.87677e6 | 0.805437 | ||||||||
\(27\) | 2.74899e6 | 0.995487 | ||||||||
\(28\) | −88049.4 | −0.0270717 | ||||||||
\(29\) | 501157. | 0.131578 | 0.0657889 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657889 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(30\) | 3.34439e6 | 0.753825 | ||||||||
\(31\) | −510635. | −0.0993077 | −0.0496538 | − | 0.998766i | \(-0.515812\pi\) | ||||
−0.0496538 | + | 0.998766i | \(0.515812\pi\) | |||||||
\(32\) | −4.34435e6 | −0.732403 | ||||||||
\(33\) | −220542. | −0.0323727 | ||||||||
\(34\) | −2.22442e6 | −0.285470 | ||||||||
\(35\) | 651757. | 0.0734141 | ||||||||
\(36\) | −2.42530e6 | −0.240660 | ||||||||
\(37\) | −3.74847e6 | −0.328811 | −0.164406 | − | 0.986393i | \(-0.552571\pi\) | ||||
−0.164406 | + | 0.986393i | \(0.552571\pi\) | |||||||
\(38\) | −1.26270e7 | −0.982368 | ||||||||
\(39\) | −6.05845e6 | −0.419345 | ||||||||
\(40\) | 1.22410e7 | 0.756046 | ||||||||
\(41\) | −3.04327e7 | −1.68195 | −0.840975 | − | 0.541074i | \(-0.818018\pi\) | ||||
−0.840975 | + | 0.541074i | \(0.818018\pi\) | |||||||
\(42\) | 1.02177e6 | 0.0506675 | ||||||||
\(43\) | −2.15222e7 | −0.960017 | −0.480008 | − | 0.877264i | \(-0.659366\pi\) | ||||
−0.480008 | + | 0.877264i | \(0.659366\pi\) | |||||||
\(44\) | 506159. | 0.0203587 | ||||||||
\(45\) | 1.79525e7 | 0.652632 | ||||||||
\(46\) | 4.64976e7 | 1.53116 | ||||||||
\(47\) | 3.43306e6 | 0.102622 | 0.0513111 | − | 0.998683i | \(-0.483660\pi\) | ||||
0.0513111 | + | 0.998683i | \(0.483660\pi\) | |||||||
\(48\) | 2.78761e7 | 0.757961 | ||||||||
\(49\) | −4.01545e7 | −0.995066 | ||||||||
\(50\) | 4.79842e6 | 0.108576 | ||||||||
\(51\) | 7.18069e6 | 0.148628 | ||||||||
\(52\) | 1.39046e7 | 0.263719 | ||||||||
\(53\) | −2.87800e7 | −0.501013 | −0.250506 | − | 0.968115i | \(-0.580597\pi\) | ||||
−0.250506 | + | 0.968115i | \(0.580597\pi\) | |||||||
\(54\) | 7.32138e7 | 1.17171 | ||||||||
\(55\) | −3.74668e6 | −0.0552096 | ||||||||
\(56\) | 3.73984e6 | 0.0508168 | ||||||||
\(57\) | 4.07615e7 | 0.511462 | ||||||||
\(58\) | 1.33473e7 | 0.154870 | ||||||||
\(59\) | −1.37313e8 | −1.47529 | −0.737643 | − | 0.675191i | \(-0.764061\pi\) | ||||
−0.737643 | + | 0.675191i | \(0.764061\pi\) | |||||||
\(60\) | 2.47778e7 | 0.246821 | ||||||||
\(61\) | 1.21854e8 | 1.12682 | 0.563410 | − | 0.826177i | \(-0.309489\pi\) | ||||
0.563410 | + | 0.826177i | \(0.309489\pi\) | |||||||
\(62\) | −1.35997e7 | −0.116888 | ||||||||
\(63\) | 5.48479e6 | 0.0438659 | ||||||||
\(64\) | 5.03058e7 | 0.374808 | ||||||||
\(65\) | −1.02924e8 | −0.715165 | ||||||||
\(66\) | −5.87371e6 | −0.0381035 | ||||||||
\(67\) | −8.31665e7 | −0.504210 | −0.252105 | − | 0.967700i | \(-0.581123\pi\) | ||||
−0.252105 | + | 0.967700i | \(0.581123\pi\) | |||||||
\(68\) | −1.64802e7 | −0.0934698 | ||||||||
\(69\) | −1.50100e8 | −0.797187 | ||||||||
\(70\) | 1.73583e7 | 0.0864102 | ||||||||
\(71\) | 1.48492e8 | 0.693490 | 0.346745 | − | 0.937960i | \(-0.387287\pi\) | ||||
0.346745 | + | 0.937960i | \(0.387287\pi\) | |||||||
\(72\) | 1.03013e8 | 0.451748 | ||||||||
\(73\) | 1.45029e8 | 0.597726 | 0.298863 | − | 0.954296i | \(-0.403393\pi\) | ||||
0.298863 | + | 0.954296i | \(0.403393\pi\) | |||||||
\(74\) | −9.98331e7 | −0.387019 | ||||||||
\(75\) | −1.54899e7 | −0.0565292 | ||||||||
\(76\) | −9.35504e7 | −0.321651 | ||||||||
\(77\) | −1.14467e6 | −0.00371085 | ||||||||
\(78\) | −1.61355e8 | −0.493579 | ||||||||
\(79\) | −4.22172e8 | −1.21946 | −0.609729 | − | 0.792610i | \(-0.708722\pi\) | ||||
−0.609729 | + | 0.792610i | \(0.708722\pi\) | |||||||
\(80\) | 4.73573e8 | 1.29265 | ||||||||
\(81\) | 5.58742e6 | 0.0144221 | ||||||||
\(82\) | −8.10515e8 | −1.97970 | ||||||||
\(83\) | −5.36072e7 | −0.123986 | −0.0619929 | − | 0.998077i | \(-0.519746\pi\) | ||||
−0.0619929 | + | 0.998077i | \(0.519746\pi\) | |||||||
\(84\) | 7.57002e6 | 0.0165898 | ||||||||
\(85\) | 1.21989e8 | 0.253475 | ||||||||
\(86\) | −5.73201e8 | −1.12996 | ||||||||
\(87\) | −4.30868e7 | −0.0806321 | ||||||||
\(88\) | −2.14988e7 | −0.0382157 | ||||||||
\(89\) | 9.26167e8 | 1.56471 | 0.782355 | − | 0.622832i | \(-0.214018\pi\) | ||||
0.782355 | + | 0.622832i | \(0.214018\pi\) | |||||||
\(90\) | 4.78129e8 | 0.768164 | ||||||||
\(91\) | −3.14450e7 | −0.0480690 | ||||||||
\(92\) | 3.44490e8 | 0.501338 | ||||||||
\(93\) | 4.39017e7 | 0.0608566 | ||||||||
\(94\) | 9.14328e7 | 0.120789 | ||||||||
\(95\) | 6.92477e8 | 0.872266 | ||||||||
\(96\) | 3.73504e8 | 0.448823 | ||||||||
\(97\) | 1.44334e9 | 1.65538 | 0.827688 | − | 0.561189i | \(-0.189656\pi\) | ||||
0.827688 | + | 0.561189i | \(0.189656\pi\) | |||||||
\(98\) | −1.06944e9 | −1.17122 | ||||||||
\(99\) | −3.15298e7 | −0.0329885 | ||||||||
\(100\) | 3.55504e7 | 0.0355504 | ||||||||
\(101\) | 1.73497e9 | 1.65900 | 0.829498 | − | 0.558510i | \(-0.188627\pi\) | ||||
0.829498 | + | 0.558510i | \(0.188627\pi\) | |||||||
\(102\) | 1.91244e8 | 0.174939 | ||||||||
\(103\) | −1.15796e9 | −1.01374 | −0.506871 | − | 0.862022i | \(-0.669198\pi\) | ||||
−0.506871 | + | 0.862022i | \(0.669198\pi\) | |||||||
\(104\) | −5.90587e8 | −0.495033 | ||||||||
\(105\) | −5.60346e7 | −0.0449888 | ||||||||
\(106\) | −7.66498e8 | −0.589704 | ||||||||
\(107\) | 6.18767e8 | 0.456352 | 0.228176 | − | 0.973620i | \(-0.426724\pi\) | ||||
0.228176 | + | 0.973620i | \(0.426724\pi\) | |||||||
\(108\) | 5.42423e8 | 0.383647 | ||||||||
\(109\) | −1.81586e9 | −1.23215 | −0.616074 | − | 0.787688i | \(-0.711278\pi\) | ||||
−0.616074 | + | 0.787688i | \(0.711278\pi\) | |||||||
\(110\) | −9.97854e7 | −0.0649830 | ||||||||
\(111\) | 3.22274e8 | 0.201498 | ||||||||
\(112\) | 1.44685e8 | 0.0868842 | ||||||||
\(113\) | −2.89208e9 | −1.66862 | −0.834310 | − | 0.551296i | \(-0.814134\pi\) | ||||
−0.834310 | + | 0.551296i | \(0.814134\pi\) | |||||||
\(114\) | 1.08560e9 | 0.602004 | ||||||||
\(115\) | −2.54997e9 | −1.35955 | ||||||||
\(116\) | 9.88871e7 | 0.0507083 | ||||||||
\(117\) | −8.66145e8 | −0.427321 | ||||||||
\(118\) | −3.65705e9 | −1.73645 | ||||||||
\(119\) | 3.72697e7 | 0.0170371 | ||||||||
\(120\) | −1.05242e9 | −0.463312 | ||||||||
\(121\) | −2.35137e9 | −0.997209 | ||||||||
\(122\) | 3.24533e9 | 1.32629 | ||||||||
\(123\) | 2.61644e9 | 1.03071 | ||||||||
\(124\) | −1.00757e8 | −0.0382718 | ||||||||
\(125\) | 2.58954e9 | 0.948699 | ||||||||
\(126\) | 1.46076e8 | 0.0516313 | ||||||||
\(127\) | 1.38692e9 | 0.473081 | 0.236540 | − | 0.971622i | \(-0.423986\pi\) | ||||
0.236540 | + | 0.971622i | \(0.423986\pi\) | |||||||
\(128\) | 3.56410e9 | 1.17356 | ||||||||
\(129\) | 1.85037e9 | 0.588307 | ||||||||
\(130\) | −2.74118e9 | −0.841767 | ||||||||
\(131\) | 5.87855e9 | 1.74401 | 0.872006 | − | 0.489496i | \(-0.162819\pi\) | ||||
0.872006 | + | 0.489496i | \(0.162819\pi\) | |||||||
\(132\) | −4.35169e7 | −0.0124760 | ||||||||
\(133\) | 2.11563e8 | 0.0586284 | ||||||||
\(134\) | −2.21497e9 | −0.593468 | ||||||||
\(135\) | −4.01511e9 | −1.04039 | ||||||||
\(136\) | 6.99985e8 | 0.175454 | ||||||||
\(137\) | 2.25574e9 | 0.547075 | 0.273538 | − | 0.961861i | \(-0.411806\pi\) | ||||
0.273538 | + | 0.961861i | \(0.411806\pi\) | |||||||
\(138\) | −3.99762e9 | −0.938308 | ||||||||
\(139\) | −2.06541e9 | −0.469289 | −0.234645 | − | 0.972081i | \(-0.575393\pi\) | ||||
−0.234645 | + | 0.972081i | \(0.575393\pi\) | |||||||
\(140\) | 1.28603e8 | 0.0282928 | ||||||||
\(141\) | −2.95156e8 | −0.0628878 | ||||||||
\(142\) | 3.95479e9 | 0.816254 | ||||||||
\(143\) | 1.80764e8 | 0.0361493 | ||||||||
\(144\) | 3.98530e9 | 0.772378 | ||||||||
\(145\) | −7.31980e8 | −0.137513 | ||||||||
\(146\) | 3.86256e9 | 0.703538 | ||||||||
\(147\) | 3.45227e9 | 0.609785 | ||||||||
\(148\) | −7.39640e8 | −0.126719 | ||||||||
\(149\) | −3.00126e9 | −0.498845 | −0.249422 | − | 0.968395i | \(-0.580241\pi\) | ||||
−0.249422 | + | 0.968395i | \(0.580241\pi\) | |||||||
\(150\) | −4.12543e8 | −0.0665363 | ||||||||
\(151\) | −1.05501e10 | −1.65143 | −0.825714 | − | 0.564089i | \(-0.809227\pi\) | ||||
−0.825714 | + | 0.564089i | \(0.809227\pi\) | |||||||
\(152\) | 3.97349e9 | 0.603777 | ||||||||
\(153\) | 1.02659e9 | 0.151455 | ||||||||
\(154\) | −3.04861e7 | −0.00436776 | ||||||||
\(155\) | 7.45823e8 | 0.103787 | ||||||||
\(156\) | −1.19544e9 | −0.161610 | ||||||||
\(157\) | 8.51695e9 | 1.11876 | 0.559378 | − | 0.828912i | \(-0.311040\pi\) | ||||
0.559378 | + | 0.828912i | \(0.311040\pi\) | |||||||
\(158\) | −1.12437e10 | −1.43533 | ||||||||
\(159\) | 2.47435e9 | 0.307025 | ||||||||
\(160\) | 6.34527e9 | 0.765439 | ||||||||
\(161\) | −7.79059e8 | −0.0913806 | ||||||||
\(162\) | 1.48810e8 | 0.0169752 | ||||||||
\(163\) | −6.90475e9 | −0.766133 | −0.383066 | − | 0.923721i | \(-0.625132\pi\) | ||||
−0.383066 | + | 0.923721i | \(0.625132\pi\) | |||||||
\(164\) | −6.00491e9 | −0.648200 | ||||||||
\(165\) | 3.22120e8 | 0.0338329 | ||||||||
\(166\) | −1.42772e9 | −0.145934 | ||||||||
\(167\) | −8.18088e9 | −0.813909 | −0.406954 | − | 0.913448i | \(-0.633409\pi\) | ||||
−0.406954 | + | 0.913448i | \(0.633409\pi\) | |||||||
\(168\) | −3.21532e8 | −0.0311410 | ||||||||
\(169\) | −5.63878e9 | −0.531735 | ||||||||
\(170\) | 3.24894e9 | 0.298347 | ||||||||
\(171\) | 5.82746e9 | 0.521191 | ||||||||
\(172\) | −4.24671e9 | −0.369977 | ||||||||
\(173\) | 1.96517e9 | 0.166799 | 0.0833995 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0833995 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(174\) | −1.14753e9 | −0.0949059 | ||||||||
\(175\) | −8.03968e7 | −0.00647988 | ||||||||
\(176\) | −8.31731e8 | −0.0653395 | ||||||||
\(177\) | 1.18054e10 | 0.904069 | ||||||||
\(178\) | 2.46666e10 | 1.84170 | ||||||||
\(179\) | −2.51083e10 | −1.82801 | −0.914006 | − | 0.405701i | \(-0.867028\pi\) | ||||
−0.914006 | + | 0.405701i | \(0.867028\pi\) | |||||||
\(180\) | 3.54234e9 | 0.251515 | ||||||||
\(181\) | −3.03563e9 | −0.210230 | −0.105115 | − | 0.994460i | \(-0.533521\pi\) | ||||
−0.105115 | + | 0.994460i | \(0.533521\pi\) | |||||||
\(182\) | −8.37475e8 | −0.0565784 | ||||||||
\(183\) | −1.04763e10 | −0.690526 | ||||||||
\(184\) | −1.46320e10 | −0.941072 | ||||||||
\(185\) | 5.47494e9 | 0.343642 | ||||||||
\(186\) | 1.16923e9 | 0.0716297 | ||||||||
\(187\) | −2.14248e8 | −0.0128124 | ||||||||
\(188\) | 6.77404e8 | 0.0395491 | ||||||||
\(189\) | −1.22668e9 | −0.0699286 | ||||||||
\(190\) | 1.84427e10 | 1.02668 | ||||||||
\(191\) | −3.15580e10 | −1.71577 | −0.857885 | − | 0.513841i | \(-0.828222\pi\) | ||||
−0.857885 | + | 0.513841i | \(0.828222\pi\) | |||||||
\(192\) | −4.32503e9 | −0.229685 | ||||||||
\(193\) | 2.29526e9 | 0.119076 | 0.0595379 | − | 0.998226i | \(-0.481037\pi\) | ||||
0.0595379 | + | 0.998226i | \(0.481037\pi\) | |||||||
\(194\) | 3.84406e10 | 1.94842 | ||||||||
\(195\) | 8.84886e9 | 0.438260 | ||||||||
\(196\) | −7.92319e9 | −0.383484 | ||||||||
\(197\) | 2.65359e10 | 1.25527 | 0.627633 | − | 0.778509i | \(-0.284024\pi\) | ||||
0.627633 | + | 0.778509i | \(0.284024\pi\) | |||||||
\(198\) | −8.39733e8 | −0.0388283 | ||||||||
\(199\) | −1.45778e10 | −0.658949 | −0.329475 | − | 0.944164i | \(-0.606872\pi\) | ||||
−0.329475 | + | 0.944164i | \(0.606872\pi\) | |||||||
\(200\) | −1.50998e9 | −0.0667323 | ||||||||
\(201\) | 7.15021e9 | 0.308985 | ||||||||
\(202\) | 4.62074e10 | 1.95268 | ||||||||
\(203\) | −2.23632e8 | −0.00924276 | ||||||||
\(204\) | 1.41688e9 | 0.0572792 | ||||||||
\(205\) | 4.44494e10 | 1.75782 | ||||||||
\(206\) | −3.08401e10 | −1.19320 | ||||||||
\(207\) | −2.14590e10 | −0.812350 | ||||||||
\(208\) | −2.28482e10 | −0.846385 | ||||||||
\(209\) | −1.21619e9 | −0.0440903 | ||||||||
\(210\) | −1.49237e9 | −0.0529529 | ||||||||
\(211\) | 4.31184e10 | 1.49759 | 0.748793 | − | 0.662804i | \(-0.230634\pi\) | ||||
0.748793 | + | 0.662804i | \(0.230634\pi\) | |||||||
\(212\) | −5.67880e9 | −0.193083 | ||||||||
\(213\) | −1.27665e10 | −0.424977 | ||||||||
\(214\) | 1.64796e10 | 0.537137 | ||||||||
\(215\) | 3.14349e10 | 1.00332 | ||||||||
\(216\) | −2.30391e10 | −0.720151 | ||||||||
\(217\) | 2.27861e8 | 0.00697593 | ||||||||
\(218\) | −4.83618e10 | −1.45027 | ||||||||
\(219\) | −1.24688e10 | −0.366292 | ||||||||
\(220\) | −7.39286e8 | −0.0212770 | ||||||||
\(221\) | −5.88555e9 | −0.165967 | ||||||||
\(222\) | 8.58312e9 | 0.237169 | ||||||||
\(223\) | −3.81093e10 | −1.03195 | −0.515975 | − | 0.856604i | \(-0.672570\pi\) | ||||
−0.515975 | + | 0.856604i | \(0.672570\pi\) | |||||||
\(224\) | 1.93859e9 | 0.0514481 | ||||||||
\(225\) | −2.21451e9 | −0.0576045 | ||||||||
\(226\) | −7.70248e10 | −1.96401 | ||||||||
\(227\) | −2.78123e10 | −0.695216 | −0.347608 | − | 0.937640i | \(-0.613006\pi\) | ||||
−0.347608 | + | 0.937640i | \(0.613006\pi\) | |||||||
\(228\) | 8.04297e9 | 0.197110 | ||||||||
\(229\) | 3.54756e10 | 0.852452 | 0.426226 | − | 0.904617i | \(-0.359843\pi\) | ||||
0.426226 | + | 0.904617i | \(0.359843\pi\) | |||||||
\(230\) | −6.79135e10 | −1.60022 | ||||||||
\(231\) | 9.84130e7 | 0.00227404 | ||||||||
\(232\) | −4.20017e9 | −0.0951854 | ||||||||
\(233\) | 4.62674e10 | 1.02843 | 0.514213 | − | 0.857662i | \(-0.328084\pi\) | ||||
0.514213 | + | 0.857662i | \(0.328084\pi\) | |||||||
\(234\) | −2.30681e10 | −0.502967 | ||||||||
\(235\) | −5.01426e9 | −0.107251 | ||||||||
\(236\) | −2.70942e10 | −0.568555 | ||||||||
\(237\) | 3.62961e10 | 0.747295 | ||||||||
\(238\) | 9.92605e8 | 0.0200530 | ||||||||
\(239\) | 8.33772e10 | 1.65294 | 0.826469 | − | 0.562982i | \(-0.190346\pi\) | ||||
0.826469 | + | 0.562982i | \(0.190346\pi\) | |||||||
\(240\) | −4.07153e10 | −0.792149 | ||||||||
\(241\) | −7.31412e9 | −0.139664 | −0.0698321 | − | 0.997559i | \(-0.522246\pi\) | ||||
−0.0698321 | + | 0.997559i | \(0.522246\pi\) | |||||||
\(242\) | −6.26240e10 | −1.17374 | ||||||||
\(243\) | −5.45887e10 | −1.00432 | ||||||||
\(244\) | 2.40439e10 | 0.434261 | ||||||||
\(245\) | 5.86488e10 | 1.03995 | ||||||||
\(246\) | 6.96838e10 | 1.21318 | ||||||||
\(247\) | −3.34096e10 | −0.571130 | ||||||||
\(248\) | 4.27960e9 | 0.0718407 | ||||||||
\(249\) | 4.60886e9 | 0.0759795 | ||||||||
\(250\) | 6.89674e10 | 1.11664 | ||||||||
\(251\) | 9.50519e10 | 1.51157 | 0.755786 | − | 0.654818i | \(-0.227255\pi\) | ||||
0.755786 | + | 0.654818i | \(0.227255\pi\) | |||||||
\(252\) | 1.08225e9 | 0.0169053 | ||||||||
\(253\) | 4.47849e9 | 0.0687210 | ||||||||
\(254\) | 3.69379e10 | 0.556827 | ||||||||
\(255\) | −1.04880e10 | −0.155332 | ||||||||
\(256\) | 6.91663e10 | 1.00650 | ||||||||
\(257\) | −7.20648e10 | −1.03044 | −0.515222 | − | 0.857057i | \(-0.672290\pi\) | ||||
−0.515222 | + | 0.857057i | \(0.672290\pi\) | |||||||
\(258\) | 4.92808e10 | 0.692451 | ||||||||
\(259\) | 1.67269e9 | 0.0230975 | ||||||||
\(260\) | −2.03087e10 | −0.275615 | ||||||||
\(261\) | −6.15989e9 | −0.0821658 | ||||||||
\(262\) | 1.56564e11 | 2.05274 | ||||||||
\(263\) | −1.71832e10 | −0.221464 | −0.110732 | − | 0.993850i | \(-0.535320\pi\) | ||||
−0.110732 | + | 0.993850i | \(0.535320\pi\) | |||||||
\(264\) | 1.84835e9 | 0.0234189 | ||||||||
\(265\) | 4.20354e10 | 0.523612 | ||||||||
\(266\) | 5.63457e9 | 0.0690070 | ||||||||
\(267\) | −7.96269e10 | −0.958869 | ||||||||
\(268\) | −1.64102e10 | −0.194316 | ||||||||
\(269\) | 1.10544e10 | 0.128721 | 0.0643605 | − | 0.997927i | \(-0.479499\pi\) | ||||
0.0643605 | + | 0.997927i | \(0.479499\pi\) | |||||||
\(270\) | −1.06935e11 | −1.22456 | ||||||||
\(271\) | −1.41142e11 | −1.58963 | −0.794813 | − | 0.606855i | \(-0.792431\pi\) | ||||
−0.794813 | + | 0.606855i | \(0.792431\pi\) | |||||||
\(272\) | 2.70805e10 | 0.299983 | ||||||||
\(273\) | 2.70347e9 | 0.0294571 | ||||||||
\(274\) | 6.00773e10 | 0.643921 | ||||||||
\(275\) | 4.62168e8 | 0.00487307 | ||||||||
\(276\) | −2.96174e10 | −0.307225 | ||||||||
\(277\) | −1.12712e11 | −1.15030 | −0.575151 | − | 0.818047i | \(-0.695057\pi\) | ||||
−0.575151 | + | 0.818047i | \(0.695057\pi\) | |||||||
\(278\) | −5.50082e10 | −0.552365 | ||||||||
\(279\) | 6.27639e9 | 0.0620142 | ||||||||
\(280\) | −5.46234e9 | −0.0531089 | ||||||||
\(281\) | 4.86687e10 | 0.465662 | 0.232831 | − | 0.972517i | \(-0.425201\pi\) | ||||
0.232831 | + | 0.972517i | \(0.425201\pi\) | |||||||
\(282\) | −7.86091e9 | −0.0740204 | ||||||||
\(283\) | −1.21207e11 | −1.12328 | −0.561640 | − | 0.827382i | \(-0.689829\pi\) | ||||
−0.561640 | + | 0.827382i | \(0.689829\pi\) | |||||||
\(284\) | 2.93001e10 | 0.267261 | ||||||||
\(285\) | −5.95355e10 | −0.534532 | ||||||||
\(286\) | 4.81430e9 | 0.0425486 | ||||||||
\(287\) | 1.35800e10 | 0.118150 | ||||||||
\(288\) | 5.33979e10 | 0.457360 | ||||||||
\(289\) | 6.97576e9 | 0.0588235 | ||||||||
\(290\) | −1.94948e10 | −0.161856 | ||||||||
\(291\) | −1.24091e11 | −1.01443 | ||||||||
\(292\) | 2.86168e10 | 0.230355 | ||||||||
\(293\) | 9.65141e10 | 0.765044 | 0.382522 | − | 0.923946i | \(-0.375056\pi\) | ||||
0.382522 | + | 0.923946i | \(0.375056\pi\) | |||||||
\(294\) | 9.19444e10 | 0.717732 | ||||||||
\(295\) | 2.00556e11 | 1.54183 | ||||||||
\(296\) | 3.14157e10 | 0.237867 | ||||||||
\(297\) | 7.05170e9 | 0.0525884 | ||||||||
\(298\) | −7.99326e10 | −0.587153 | ||||||||
\(299\) | 1.23027e11 | 0.890187 | ||||||||
\(300\) | −3.05643e9 | −0.0217856 | ||||||||
\(301\) | 9.60389e9 | 0.0674370 | ||||||||
\(302\) | −2.80981e11 | −1.94377 | ||||||||
\(303\) | −1.49163e11 | −1.01665 | ||||||||
\(304\) | 1.53724e11 | 1.03231 | ||||||||
\(305\) | −1.77977e11 | −1.17765 | ||||||||
\(306\) | 2.73411e10 | 0.178266 | ||||||||
\(307\) | −1.31572e11 | −0.845360 | −0.422680 | − | 0.906279i | \(-0.638911\pi\) | ||||
−0.422680 | + | 0.906279i | \(0.638911\pi\) | |||||||
\(308\) | −2.25864e8 | −0.00143011 | ||||||||
\(309\) | 9.95556e10 | 0.621230 | ||||||||
\(310\) | 1.98635e10 | 0.122160 | ||||||||
\(311\) | 3.19848e9 | 0.0193875 | 0.00969376 | − | 0.999953i | \(-0.496914\pi\) | ||||
0.00969376 | + | 0.999953i | \(0.496914\pi\) | |||||||
\(312\) | 5.07755e10 | 0.303360 | ||||||||
\(313\) | −1.59936e11 | −0.941882 | −0.470941 | − | 0.882165i | \(-0.656086\pi\) | ||||
−0.470941 | + | 0.882165i | \(0.656086\pi\) | |||||||
\(314\) | 2.26832e11 | 1.31680 | ||||||||
\(315\) | −8.01097e9 | −0.0458445 | ||||||||
\(316\) | −8.33019e10 | −0.469962 | ||||||||
\(317\) | 6.77437e10 | 0.376792 | 0.188396 | − | 0.982093i | \(-0.439671\pi\) | ||||
0.188396 | + | 0.982093i | \(0.439671\pi\) | |||||||
\(318\) | 6.58994e10 | 0.361376 | ||||||||
\(319\) | 1.28557e9 | 0.00695083 | ||||||||
\(320\) | −7.34757e10 | −0.391714 | ||||||||
\(321\) | −5.31983e10 | −0.279657 | ||||||||
\(322\) | −2.07487e10 | −0.107557 | ||||||||
\(323\) | 3.95982e10 | 0.202425 | ||||||||
\(324\) | 1.10250e9 | 0.00555808 | ||||||||
\(325\) | 1.26961e10 | 0.0631239 | ||||||||
\(326\) | −1.83894e11 | −0.901757 | ||||||||
\(327\) | 1.56118e11 | 0.755071 | ||||||||
\(328\) | 2.55055e11 | 1.21675 | ||||||||
\(329\) | −1.53194e9 | −0.00720876 | ||||||||
\(330\) | 8.57902e9 | 0.0398222 | ||||||||
\(331\) | 1.23890e11 | 0.567295 | 0.283647 | − | 0.958929i | \(-0.408456\pi\) | ||||
0.283647 | + | 0.958929i | \(0.408456\pi\) | |||||||
\(332\) | −1.05776e10 | −0.0477824 | ||||||||
\(333\) | 4.60738e10 | 0.205331 | ||||||||
\(334\) | −2.17881e11 | −0.957990 | ||||||||
\(335\) | 1.21471e11 | 0.526953 | ||||||||
\(336\) | −1.24392e10 | −0.0532434 | ||||||||
\(337\) | −1.66091e11 | −0.701476 | −0.350738 | − | 0.936474i | \(-0.614069\pi\) | ||||
−0.350738 | + | 0.936474i | \(0.614069\pi\) | |||||||
\(338\) | −1.50178e11 | −0.625865 | ||||||||
\(339\) | 2.48646e11 | 1.02254 | ||||||||
\(340\) | 2.40706e10 | 0.0976859 | ||||||||
\(341\) | −1.30988e9 | −0.00524611 | ||||||||
\(342\) | 1.55203e11 | 0.613454 | ||||||||
\(343\) | 3.59253e10 | 0.140145 | ||||||||
\(344\) | 1.80376e11 | 0.694491 | ||||||||
\(345\) | 2.19233e11 | 0.833144 | ||||||||
\(346\) | 5.23385e10 | 0.196327 | ||||||||
\(347\) | −3.59340e11 | −1.33052 | −0.665262 | − | 0.746610i | \(-0.731680\pi\) | ||||
−0.665262 | + | 0.746610i | \(0.731680\pi\) | |||||||
\(348\) | −8.50179e9 | −0.0310745 | ||||||||
\(349\) | 4.55698e11 | 1.64423 | 0.822116 | − | 0.569321i | \(-0.192794\pi\) | ||||
0.822116 | + | 0.569321i | \(0.192794\pi\) | |||||||
\(350\) | −2.14121e9 | −0.00762698 | ||||||||
\(351\) | 1.93715e11 | 0.681211 | ||||||||
\(352\) | −1.11441e10 | −0.0386905 | ||||||||
\(353\) | −2.35070e11 | −0.805772 | −0.402886 | − | 0.915250i | \(-0.631993\pi\) | ||||
−0.402886 | + | 0.915250i | \(0.631993\pi\) | |||||||
\(354\) | 3.14414e11 | 1.06411 | ||||||||
\(355\) | −2.16884e11 | −0.724770 | ||||||||
\(356\) | 1.82749e11 | 0.603018 | ||||||||
\(357\) | −3.20425e9 | −0.0104405 | ||||||||
\(358\) | −6.68710e11 | −2.15161 | ||||||||
\(359\) | 8.46696e10 | 0.269031 | 0.134516 | − | 0.990911i | \(-0.457052\pi\) | ||||
0.134516 | + | 0.990911i | \(0.457052\pi\) | |||||||
\(360\) | −1.50459e11 | −0.472124 | ||||||||
\(361\) | −9.79067e10 | −0.303410 | ||||||||
\(362\) | −8.08479e10 | −0.247446 | ||||||||
\(363\) | 2.02158e11 | 0.611099 | ||||||||
\(364\) | −6.20465e9 | −0.0185251 | ||||||||
\(365\) | −2.11827e11 | −0.624687 | ||||||||
\(366\) | −2.79017e11 | −0.812765 | ||||||||
\(367\) | 3.10781e10 | 0.0894246 | 0.0447123 | − | 0.999000i | \(-0.485763\pi\) | ||||
0.0447123 | + | 0.999000i | \(0.485763\pi\) | |||||||
\(368\) | −5.66072e11 | −1.60900 | ||||||||
\(369\) | 3.74059e11 | 1.05032 | ||||||||
\(370\) | 1.45814e11 | 0.404476 | ||||||||
\(371\) | 1.28425e10 | 0.0351940 | ||||||||
\(372\) | 8.66258e9 | 0.0234533 | ||||||||
\(373\) | −6.64364e11 | −1.77712 | −0.888559 | − | 0.458763i | \(-0.848293\pi\) | ||||
−0.888559 | + | 0.458763i | \(0.848293\pi\) | |||||||
\(374\) | −5.70607e9 | −0.0150805 | ||||||||
\(375\) | −2.22635e11 | −0.581371 | ||||||||
\(376\) | −2.87723e10 | −0.0742385 | ||||||||
\(377\) | 3.53155e10 | 0.0900386 | ||||||||
\(378\) | −3.26703e10 | −0.0823076 | ||||||||
\(379\) | −1.05029e11 | −0.261475 | −0.130738 | − | 0.991417i | \(-0.541735\pi\) | ||||
−0.130738 | + | 0.991417i | \(0.541735\pi\) | |||||||
\(380\) | 1.36638e11 | 0.336159 | ||||||||
\(381\) | −1.19240e11 | −0.289908 | ||||||||
\(382\) | −8.40485e11 | −2.01950 | ||||||||
\(383\) | 6.90072e11 | 1.63870 | 0.819351 | − | 0.573293i | \(-0.194334\pi\) | ||||
0.819351 | + | 0.573293i | \(0.194334\pi\) | |||||||
\(384\) | −3.06423e11 | −0.719168 | ||||||||
\(385\) | 1.67189e9 | 0.00387823 | ||||||||
\(386\) | 6.11297e10 | 0.140155 | ||||||||
\(387\) | 2.64537e11 | 0.599497 | ||||||||
\(388\) | 2.84797e11 | 0.637959 | ||||||||
\(389\) | 1.43485e11 | 0.317712 | 0.158856 | − | 0.987302i | \(-0.449219\pi\) | ||||
0.158856 | + | 0.987302i | \(0.449219\pi\) | |||||||
\(390\) | 2.35672e11 | 0.515842 | ||||||||
\(391\) | −1.45816e11 | −0.315508 | ||||||||
\(392\) | 3.36532e11 | 0.719846 | ||||||||
\(393\) | −5.05407e11 | −1.06875 | ||||||||
\(394\) | 7.06731e11 | 1.47748 | ||||||||
\(395\) | 6.16615e11 | 1.27446 | ||||||||
\(396\) | −6.22138e9 | −0.0127133 | ||||||||
\(397\) | −4.59121e11 | −0.927620 | −0.463810 | − | 0.885935i | \(-0.653518\pi\) | ||||
−0.463810 | + | 0.885935i | \(0.653518\pi\) | |||||||
\(398\) | −3.88250e11 | −0.775599 | ||||||||
\(399\) | −1.81891e10 | −0.0359280 | ||||||||
\(400\) | −5.84171e10 | −0.114096 | ||||||||
\(401\) | −1.18477e11 | −0.228815 | −0.114408 | − | 0.993434i | \(-0.536497\pi\) | ||||
−0.114408 | + | 0.993434i | \(0.536497\pi\) | |||||||
\(402\) | 1.90432e11 | 0.363682 | ||||||||
\(403\) | −3.59834e10 | −0.0679562 | ||||||||
\(404\) | 3.42340e11 | 0.639354 | ||||||||
\(405\) | −8.16088e9 | −0.0150726 | ||||||||
\(406\) | −5.95600e9 | −0.0108790 | ||||||||
\(407\) | −9.61558e9 | −0.0173700 | ||||||||
\(408\) | −6.01810e10 | −0.107520 | ||||||||
\(409\) | 3.44816e11 | 0.609301 | 0.304651 | − | 0.952464i | \(-0.401460\pi\) | ||||
0.304651 | + | 0.952464i | \(0.401460\pi\) | |||||||
\(410\) | 1.18382e12 | 2.06899 | ||||||||
\(411\) | −1.93937e11 | −0.335253 | ||||||||
\(412\) | −2.28487e11 | −0.390682 | ||||||||
\(413\) | 6.12732e10 | 0.103632 | ||||||||
\(414\) | −5.71518e11 | −0.956156 | ||||||||
\(415\) | 7.82976e10 | 0.129578 | ||||||||
\(416\) | −3.06137e11 | −0.501183 | ||||||||
\(417\) | 1.77573e11 | 0.287585 | ||||||||
\(418\) | −3.23908e10 | −0.0518953 | ||||||||
\(419\) | 1.06432e12 | 1.68697 | 0.843487 | − | 0.537150i | \(-0.180499\pi\) | ||||
0.843487 | + | 0.537150i | \(0.180499\pi\) | |||||||
\(420\) | −1.10566e10 | −0.0173381 | ||||||||
\(421\) | 8.40482e11 | 1.30394 | 0.651972 | − | 0.758243i | \(-0.273942\pi\) | ||||
0.651972 | + | 0.758243i | \(0.273942\pi\) | |||||||
\(422\) | 1.14837e12 | 1.76269 | ||||||||
\(423\) | −4.21970e10 | −0.0640840 | ||||||||
\(424\) | 2.41203e11 | 0.362441 | ||||||||
\(425\) | −1.50478e10 | −0.0223730 | ||||||||
\(426\) | −3.40012e11 | −0.500208 | ||||||||
\(427\) | −5.43750e10 | −0.0791542 | ||||||||
\(428\) | 1.22094e11 | 0.175872 | ||||||||
\(429\) | −1.55411e10 | −0.0221526 | ||||||||
\(430\) | 8.37206e11 | 1.18093 | ||||||||
\(431\) | −7.86921e11 | −1.09846 | −0.549229 | − | 0.835672i | \(-0.685078\pi\) | ||||
−0.549229 | + | 0.835672i | \(0.685078\pi\) | |||||||
\(432\) | −8.91321e11 | −1.23128 | ||||||||
\(433\) | −7.27832e11 | −0.995029 | −0.497514 | − | 0.867456i | \(-0.665754\pi\) | ||||
−0.497514 | + | 0.867456i | \(0.665754\pi\) | |||||||
\(434\) | 6.06864e9 | 0.00821084 | ||||||||
\(435\) | 6.29317e10 | 0.0842690 | ||||||||
\(436\) | −3.58301e11 | −0.474853 | ||||||||
\(437\) | −8.27733e11 | −1.08573 | ||||||||
\(438\) | −3.32083e11 | −0.431135 | ||||||||
\(439\) | −5.63619e11 | −0.724261 | −0.362130 | − | 0.932127i | \(-0.617950\pi\) | ||||
−0.362130 | + | 0.932127i | \(0.617950\pi\) | |||||||
\(440\) | 3.14007e10 | 0.0399395 | ||||||||
\(441\) | 4.93553e11 | 0.621384 | ||||||||
\(442\) | −1.56750e11 | −0.195347 | ||||||||
\(443\) | 2.48083e11 | 0.306041 | 0.153021 | − | 0.988223i | \(-0.451100\pi\) | ||||
0.153021 | + | 0.988223i | \(0.451100\pi\) | |||||||
\(444\) | 6.35903e10 | 0.0776547 | ||||||||
\(445\) | −1.35274e12 | −1.63529 | ||||||||
\(446\) | −1.01496e12 | −1.21463 | ||||||||
\(447\) | 2.58033e11 | 0.305697 | ||||||||
\(448\) | −2.24481e10 | −0.0263286 | ||||||||
\(449\) | −1.36225e12 | −1.58178 | −0.790891 | − | 0.611957i | \(-0.790383\pi\) | ||||
−0.790891 | + | 0.611957i | \(0.790383\pi\) | |||||||
\(450\) | −5.89791e10 | −0.0678019 | ||||||||
\(451\) | −7.80660e10 | −0.0888520 | ||||||||
\(452\) | −5.70658e11 | −0.643063 | ||||||||
\(453\) | 9.07040e11 | 1.01201 | ||||||||
\(454\) | −7.40724e11 | −0.818286 | ||||||||
\(455\) | 4.59279e10 | 0.0502372 | ||||||||
\(456\) | −3.41620e11 | −0.370000 | ||||||||
\(457\) | 9.81977e11 | 1.05312 | 0.526560 | − | 0.850138i | \(-0.323481\pi\) | ||||
0.526560 | + | 0.850138i | \(0.323481\pi\) | |||||||
\(458\) | 9.44822e11 | 1.00336 | ||||||||
\(459\) | −2.29598e11 | −0.241441 | ||||||||
\(460\) | −5.03155e11 | −0.523952 | ||||||||
\(461\) | 7.36336e11 | 0.759314 | 0.379657 | − | 0.925127i | \(-0.376042\pi\) | ||||
0.379657 | + | 0.925127i | \(0.376042\pi\) | |||||||
\(462\) | 2.62103e9 | 0.00267660 | ||||||||
\(463\) | 1.79548e11 | 0.181579 | 0.0907894 | − | 0.995870i | \(-0.471061\pi\) | ||||
0.0907894 | + | 0.995870i | \(0.471061\pi\) | |||||||
\(464\) | −1.62493e11 | −0.162744 | ||||||||
\(465\) | −6.41219e10 | −0.0636016 | ||||||||
\(466\) | 1.23224e12 | 1.21048 | ||||||||
\(467\) | 1.13676e11 | 0.110596 | 0.0552982 | − | 0.998470i | \(-0.482389\pi\) | ||||
0.0552982 | + | 0.998470i | \(0.482389\pi\) | |||||||
\(468\) | −1.70906e11 | −0.164684 | ||||||||
\(469\) | 3.71115e10 | 0.0354186 | ||||||||
\(470\) | −1.33545e11 | −0.126237 | ||||||||
\(471\) | −7.32242e11 | −0.685584 | ||||||||
\(472\) | 1.15081e12 | 1.06724 | ||||||||
\(473\) | −5.52088e10 | −0.0507146 | ||||||||
\(474\) | 9.66674e11 | 0.879584 | ||||||||
\(475\) | −8.54197e10 | −0.0769904 | ||||||||
\(476\) | 7.35397e9 | 0.00656585 | ||||||||
\(477\) | 3.53745e11 | 0.312865 | ||||||||
\(478\) | 2.22059e12 | 1.94555 | ||||||||
\(479\) | −5.35347e11 | −0.464649 | −0.232325 | − | 0.972638i | \(-0.574633\pi\) | ||||
−0.232325 | + | 0.972638i | \(0.574633\pi\) | |||||||
\(480\) | −5.45533e11 | −0.469068 | ||||||||
\(481\) | −2.64147e11 | −0.225005 | ||||||||
\(482\) | −1.94797e11 | −0.164388 | ||||||||
\(483\) | 6.69794e10 | 0.0559989 | ||||||||
\(484\) | −4.63966e11 | −0.384311 | ||||||||
\(485\) | −2.10812e12 | −1.73004 | ||||||||
\(486\) | −1.45386e12 | −1.18211 | ||||||||
\(487\) | 9.30784e11 | 0.749840 | 0.374920 | − | 0.927057i | \(-0.377670\pi\) | ||||
0.374920 | + | 0.927057i | \(0.377670\pi\) | |||||||
\(488\) | −1.02125e12 | −0.815159 | ||||||||
\(489\) | 5.93634e11 | 0.469493 | ||||||||
\(490\) | 1.56200e12 | 1.22404 | ||||||||
\(491\) | 1.40150e12 | 1.08824 | 0.544122 | − | 0.839006i | \(-0.316863\pi\) | ||||
0.544122 | + | 0.839006i | \(0.316863\pi\) | |||||||
\(492\) | 5.16270e11 | 0.397223 | ||||||||
\(493\) | −4.18571e10 | −0.0319123 | ||||||||
\(494\) | −8.89798e11 | −0.672233 | ||||||||
\(495\) | 4.60517e10 | 0.0344765 | ||||||||
\(496\) | 1.65566e11 | 0.122830 | ||||||||
\(497\) | −6.62617e10 | −0.0487146 | ||||||||
\(498\) | 1.22748e11 | 0.0894298 | ||||||||
\(499\) | 9.65319e11 | 0.696977 | 0.348488 | − | 0.937313i | \(-0.386695\pi\) | ||||
0.348488 | + | 0.937313i | \(0.386695\pi\) | |||||||
\(500\) | 5.10963e11 | 0.365615 | ||||||||
\(501\) | 7.03348e11 | 0.498771 | ||||||||
\(502\) | 2.53152e12 | 1.77916 | ||||||||
\(503\) | −1.35251e12 | −0.942076 | −0.471038 | − | 0.882113i | \(-0.656121\pi\) | ||||
−0.471038 | + | 0.882113i | \(0.656121\pi\) | |||||||
\(504\) | −4.59677e10 | −0.0317333 | ||||||||
\(505\) | −2.53406e12 | −1.73383 | ||||||||
\(506\) | 1.19276e11 | 0.0808862 | ||||||||
\(507\) | 4.84792e11 | 0.325852 | ||||||||
\(508\) | 2.73664e11 | 0.182319 | ||||||||
\(509\) | −1.24943e12 | −0.825053 | −0.412527 | − | 0.910946i | \(-0.635354\pi\) | ||||
−0.412527 | + | 0.910946i | \(0.635354\pi\) | |||||||
\(510\) | −2.79326e11 | −0.182829 | ||||||||
\(511\) | −6.47166e10 | −0.0419876 | ||||||||
\(512\) | 1.72851e10 | 0.0111162 | ||||||||
\(513\) | −1.30332e12 | −0.830853 | ||||||||
\(514\) | −1.91930e12 | −1.21286 | ||||||||
\(515\) | 1.69130e12 | 1.05947 | ||||||||
\(516\) | 3.65110e11 | 0.226725 | ||||||||
\(517\) | 8.80649e9 | 0.00542120 | ||||||||
\(518\) | 4.45487e10 | 0.0271864 | ||||||||
\(519\) | −1.68955e11 | −0.102216 | ||||||||
\(520\) | 8.62599e11 | 0.517361 | ||||||||
\(521\) | 2.83113e11 | 0.168341 | 0.0841706 | − | 0.996451i | \(-0.473176\pi\) | ||||
0.0841706 | + | 0.996451i | \(0.473176\pi\) | |||||||
\(522\) | −1.64057e11 | −0.0967111 | ||||||||
\(523\) | 6.03608e11 | 0.352774 | 0.176387 | − | 0.984321i | \(-0.443559\pi\) | ||||
0.176387 | + | 0.984321i | \(0.443559\pi\) | |||||||
\(524\) | 1.15994e12 | 0.672118 | ||||||||
\(525\) | 6.91209e9 | 0.00397093 | ||||||||
\(526\) | −4.57640e11 | −0.260668 | ||||||||
\(527\) | 4.26487e10 | 0.0240857 | ||||||||
\(528\) | 7.15078e10 | 0.0400406 | ||||||||
\(529\) | 1.24689e12 | 0.692271 | ||||||||
\(530\) | 1.11953e12 | 0.616303 | ||||||||
\(531\) | 1.68776e12 | 0.921265 | ||||||||
\(532\) | 4.17452e10 | 0.0225946 | ||||||||
\(533\) | −2.14453e12 | −1.15096 | ||||||||
\(534\) | −2.12070e12 | −1.12861 | ||||||||
\(535\) | −9.03758e11 | −0.476936 | ||||||||
\(536\) | 6.97013e11 | 0.364754 | ||||||||
\(537\) | 2.15868e12 | 1.12022 | ||||||||
\(538\) | 2.94412e11 | 0.151508 | ||||||||
\(539\) | −1.03004e11 | −0.0525661 | ||||||||
\(540\) | −7.92253e11 | −0.400951 | ||||||||
\(541\) | −7.92682e11 | −0.397843 | −0.198921 | − | 0.980015i | \(-0.563744\pi\) | ||||
−0.198921 | + | 0.980015i | \(0.563744\pi\) | |||||||
\(542\) | −3.75904e12 | −1.87103 | ||||||||
\(543\) | 2.60987e11 | 0.128831 | ||||||||
\(544\) | 3.62845e11 | 0.177634 | ||||||||
\(545\) | 2.65221e12 | 1.28773 | ||||||||
\(546\) | 7.20017e10 | 0.0346717 | ||||||||
\(547\) | 5.81013e10 | 0.0277487 | 0.0138744 | − | 0.999904i | \(-0.495584\pi\) | ||||
0.0138744 | + | 0.999904i | \(0.495584\pi\) | |||||||
\(548\) | 4.45098e11 | 0.210835 | ||||||||
\(549\) | −1.49775e12 | −0.703660 | ||||||||
\(550\) | 1.23089e10 | 0.00573572 | ||||||||
\(551\) | −2.37604e11 | −0.109817 | ||||||||
\(552\) | 1.25798e12 | 0.576697 | ||||||||
\(553\) | 1.88386e11 | 0.0856616 | ||||||||
\(554\) | −3.00187e12 | −1.35393 | ||||||||
\(555\) | −4.70707e11 | −0.210587 | ||||||||
\(556\) | −4.07543e11 | −0.180857 | ||||||||
\(557\) | −8.04975e11 | −0.354351 | −0.177176 | − | 0.984179i | \(-0.556696\pi\) | ||||
−0.177176 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(558\) | 1.67159e11 | 0.0729922 | ||||||||
\(559\) | −1.51662e12 | −0.656939 | ||||||||
\(560\) | −2.11323e11 | −0.0908032 | ||||||||
\(561\) | 1.84199e10 | 0.00785154 | ||||||||
\(562\) | 1.29619e12 | 0.548096 | ||||||||
\(563\) | −3.22746e12 | −1.35386 | −0.676929 | − | 0.736048i | \(-0.736690\pi\) | ||||
−0.676929 | + | 0.736048i | \(0.736690\pi\) | |||||||
\(564\) | −5.82396e10 | −0.0242361 | ||||||||
\(565\) | 4.22411e12 | 1.74388 | ||||||||
\(566\) | −3.22810e12 | −1.32213 | ||||||||
\(567\) | −2.49329e9 | −0.00101309 | ||||||||
\(568\) | −1.24450e12 | −0.501681 | ||||||||
\(569\) | −2.00792e12 | −0.803048 | −0.401524 | − | 0.915848i | \(-0.631519\pi\) | ||||
−0.401524 | + | 0.915848i | \(0.631519\pi\) | |||||||
\(570\) | −1.58561e12 | −0.629157 | ||||||||
\(571\) | 3.16004e11 | 0.124403 | 0.0622013 | − | 0.998064i | \(-0.480188\pi\) | ||||
0.0622013 | + | 0.998064i | \(0.480188\pi\) | |||||||
\(572\) | 3.56680e10 | 0.0139314 | ||||||||
\(573\) | 2.71319e12 | 1.05144 | ||||||||
\(574\) | 3.61677e11 | 0.139065 | ||||||||
\(575\) | 3.14549e11 | 0.120001 | ||||||||
\(576\) | −6.18327e11 | −0.234054 | ||||||||
\(577\) | −1.81033e12 | −0.679932 | −0.339966 | − | 0.940438i | \(-0.610416\pi\) | ||||
−0.339966 | + | 0.940438i | \(0.610416\pi\) | |||||||
\(578\) | 1.85785e11 | 0.0692367 | ||||||||
\(579\) | −1.97334e11 | −0.0729707 | ||||||||
\(580\) | −1.44432e11 | −0.0529955 | ||||||||
\(581\) | 2.39212e10 | 0.00870945 | ||||||||
\(582\) | −3.30492e12 | −1.19401 | ||||||||
\(583\) | −7.38264e10 | −0.0264669 | ||||||||
\(584\) | −1.21548e12 | −0.432404 | ||||||||
\(585\) | 1.26507e12 | 0.446596 | ||||||||
\(586\) | 2.57046e12 | 0.900475 | ||||||||
\(587\) | 2.94820e12 | 1.02491 | 0.512455 | − | 0.858714i | \(-0.328736\pi\) | ||||
0.512455 | + | 0.858714i | \(0.328736\pi\) | |||||||
\(588\) | 6.81194e11 | 0.235003 | ||||||||
\(589\) | 2.42098e11 | 0.0828842 | ||||||||
\(590\) | 5.34141e12 | 1.81477 | ||||||||
\(591\) | −2.28142e12 | −0.769238 | ||||||||
\(592\) | 1.21539e12 | 0.406695 | ||||||||
\(593\) | 4.46478e12 | 1.48270 | 0.741350 | − | 0.671118i | \(-0.234186\pi\) | ||||
0.741350 | + | 0.671118i | \(0.234186\pi\) | |||||||
\(594\) | 1.87808e11 | 0.0618978 | ||||||||
\(595\) | −5.44354e10 | −0.0178055 | ||||||||
\(596\) | −5.92202e11 | −0.192248 | ||||||||
\(597\) | 1.25332e12 | 0.403810 | ||||||||
\(598\) | 3.27659e12 | 1.04777 | ||||||||
\(599\) | 3.15817e12 | 1.00234 | 0.501170 | − | 0.865349i | \(-0.332903\pi\) | ||||
0.501170 | + | 0.865349i | \(0.332903\pi\) | |||||||
\(600\) | 1.29820e11 | 0.0408941 | ||||||||
\(601\) | 5.98536e12 | 1.87135 | 0.935675 | − | 0.352863i | \(-0.114792\pi\) | ||||
0.935675 | + | 0.352863i | \(0.114792\pi\) | |||||||
\(602\) | 2.55781e11 | 0.0793749 | ||||||||
\(603\) | 1.02223e12 | 0.314862 | ||||||||
\(604\) | −2.08172e12 | −0.636437 | ||||||||
\(605\) | 3.43436e12 | 1.04219 | ||||||||
\(606\) | −3.97267e12 | −1.19662 | ||||||||
\(607\) | 1.60857e11 | 0.0480939 | 0.0240469 | − | 0.999711i | \(-0.492345\pi\) | ||||
0.0240469 | + | 0.999711i | \(0.492345\pi\) | |||||||
\(608\) | 2.05970e12 | 0.611278 | ||||||||
\(609\) | 1.92267e10 | 0.00566405 | ||||||||
\(610\) | −4.74007e12 | −1.38612 | ||||||||
\(611\) | 2.41920e11 | 0.0702243 | ||||||||
\(612\) | 2.02564e11 | 0.0583687 | ||||||||
\(613\) | −4.87119e12 | −1.39336 | −0.696679 | − | 0.717383i | \(-0.745340\pi\) | ||||
−0.696679 | + | 0.717383i | \(0.745340\pi\) | |||||||
\(614\) | −3.50417e12 | −0.995009 | ||||||||
\(615\) | −3.82152e12 | −1.07721 | ||||||||
\(616\) | 9.59344e9 | 0.00268449 | ||||||||
\(617\) | 3.48094e12 | 0.966970 | 0.483485 | − | 0.875353i | \(-0.339371\pi\) | ||||
0.483485 | + | 0.875353i | \(0.339371\pi\) | |||||||
\(618\) | 2.65147e12 | 0.731203 | ||||||||
\(619\) | 2.25847e12 | 0.618310 | 0.309155 | − | 0.951012i | \(-0.399954\pi\) | ||||
0.309155 | + | 0.951012i | \(0.399954\pi\) | |||||||
\(620\) | 1.47164e11 | 0.0399981 | ||||||||
\(621\) | 4.79935e12 | 1.29500 | ||||||||
\(622\) | 8.51852e10 | 0.0228196 | ||||||||
\(623\) | −4.13285e11 | −0.109914 | ||||||||
\(624\) | 1.96437e12 | 0.518672 | ||||||||
\(625\) | −4.13413e12 | −1.08374 | ||||||||
\(626\) | −4.25958e12 | −1.10862 | ||||||||
\(627\) | 1.04561e11 | 0.0270189 | ||||||||
\(628\) | 1.68054e12 | 0.431153 | ||||||||
\(629\) | 3.13076e11 | 0.0797484 | ||||||||
\(630\) | −2.13356e11 | −0.0539601 | ||||||||
\(631\) | −6.76730e12 | −1.69935 | −0.849676 | − | 0.527305i | \(-0.823203\pi\) | ||||
−0.849676 | + | 0.527305i | \(0.823203\pi\) | |||||||
\(632\) | 3.53819e12 | 0.882175 | ||||||||
\(633\) | −3.70709e12 | −0.917734 | ||||||||
\(634\) | 1.80422e12 | 0.443494 | ||||||||
\(635\) | −2.02571e12 | −0.494419 | ||||||||
\(636\) | 4.88233e11 | 0.118323 | ||||||||
\(637\) | −2.82960e12 | −0.680923 | ||||||||
\(638\) | 3.42385e10 | 0.00818130 | ||||||||
\(639\) | −1.82516e12 | −0.433060 | ||||||||
\(640\) | −5.20566e12 | −1.22649 | ||||||||
\(641\) | 7.28070e12 | 1.70338 | 0.851691 | − | 0.524045i | \(-0.175578\pi\) | ||||
0.851691 | + | 0.524045i | \(0.175578\pi\) | |||||||
\(642\) | −1.41683e12 | −0.329163 | ||||||||
\(643\) | −6.62565e12 | −1.52855 | −0.764274 | − | 0.644892i | \(-0.776902\pi\) | ||||
−0.764274 | + | 0.644892i | \(0.776902\pi\) | |||||||
\(644\) | −1.53722e11 | −0.0352168 | ||||||||
\(645\) | −2.70261e12 | −0.614843 | ||||||||
\(646\) | 1.05462e12 | 0.238259 | ||||||||
\(647\) | −6.36313e12 | −1.42758 | −0.713792 | − | 0.700358i | \(-0.753024\pi\) | ||||
−0.713792 | + | 0.700358i | \(0.753024\pi\) | |||||||
\(648\) | −4.68279e10 | −0.0104332 | ||||||||
\(649\) | −3.52234e11 | −0.0779346 | ||||||||
\(650\) | 3.38135e11 | 0.0742984 | ||||||||
\(651\) | −1.95903e10 | −0.00427491 | ||||||||
\(652\) | −1.36243e12 | −0.295257 | ||||||||
\(653\) | 5.95209e12 | 1.28103 | 0.640516 | − | 0.767945i | \(-0.278720\pi\) | ||||
0.640516 | + | 0.767945i | \(0.278720\pi\) | |||||||
\(654\) | 4.15789e12 | 0.888737 | ||||||||
\(655\) | −8.58609e12 | −1.82268 | ||||||||
\(656\) | 9.86739e12 | 2.08034 | ||||||||
\(657\) | −1.78260e12 | −0.373259 | ||||||||
\(658\) | −4.08002e10 | −0.00848488 | ||||||||
\(659\) | −5.45445e12 | −1.12659 | −0.563296 | − | 0.826255i | \(-0.690467\pi\) | ||||
−0.563296 | + | 0.826255i | \(0.690467\pi\) | |||||||
\(660\) | 6.35599e10 | 0.0130387 | ||||||||
\(661\) | −2.82523e12 | −0.575634 | −0.287817 | − | 0.957685i | \(-0.592930\pi\) | ||||
−0.287817 | + | 0.957685i | \(0.592930\pi\) | |||||||
\(662\) | 3.29955e12 | 0.667720 | ||||||||
\(663\) | 5.06008e11 | 0.101706 | ||||||||
\(664\) | 4.49279e11 | 0.0896932 | ||||||||
\(665\) | −3.09005e11 | −0.0612728 | ||||||||
\(666\) | 1.22708e12 | 0.241680 | ||||||||
\(667\) | 8.74951e11 | 0.171166 | ||||||||
\(668\) | −1.61423e12 | −0.313669 | ||||||||
\(669\) | 3.27643e12 | 0.632388 | ||||||||
\(670\) | 3.23515e12 | 0.620237 | ||||||||
\(671\) | 3.12579e11 | 0.0595263 | ||||||||
\(672\) | −1.66669e11 | −0.0315278 | ||||||||
\(673\) | −2.66233e12 | −0.500259 | −0.250129 | − | 0.968212i | \(-0.580473\pi\) | ||||
−0.250129 | + | 0.968212i | \(0.580473\pi\) | |||||||
\(674\) | −4.42352e12 | −0.825654 | ||||||||
\(675\) | 4.95280e11 | 0.0918298 | ||||||||
\(676\) | −1.11263e12 | −0.204923 | ||||||||
\(677\) | −6.37169e12 | −1.16575 | −0.582875 | − | 0.812562i | \(-0.698072\pi\) | ||||
−0.582875 | + | 0.812562i | \(0.698072\pi\) | |||||||
\(678\) | 6.62219e12 | 1.20356 | ||||||||
\(679\) | −6.44065e11 | −0.116283 | ||||||||
\(680\) | −1.02238e12 | −0.183368 | ||||||||
\(681\) | 2.39115e12 | 0.426035 | ||||||||
\(682\) | −3.48861e10 | −0.00617479 | ||||||||
\(683\) | 7.29274e12 | 1.28232 | 0.641161 | − | 0.767406i | \(-0.278453\pi\) | ||||
0.641161 | + | 0.767406i | \(0.278453\pi\) | |||||||
\(684\) | 1.14986e12 | 0.200860 | ||||||||
\(685\) | −3.29469e12 | −0.571752 | ||||||||
\(686\) | 9.56798e11 | 0.164954 | ||||||||
\(687\) | −3.05000e12 | −0.522390 | ||||||||
\(688\) | 6.97828e12 | 1.18741 | ||||||||
\(689\) | −2.02806e12 | −0.342843 | ||||||||
\(690\) | 5.83884e12 | 0.980631 | ||||||||
\(691\) | 8.91264e12 | 1.48715 | 0.743576 | − | 0.668652i | \(-0.233128\pi\) | ||||
0.743576 | + | 0.668652i | \(0.233128\pi\) | |||||||
\(692\) | 3.87764e11 | 0.0642820 | ||||||||
\(693\) | 1.40696e10 | 0.00231730 | ||||||||
\(694\) | −9.57030e12 | −1.56606 | ||||||||
\(695\) | 3.01670e12 | 0.490457 | ||||||||
\(696\) | 3.61108e11 | 0.0583305 | ||||||||
\(697\) | 2.54177e12 | 0.407933 | ||||||||
\(698\) | 1.21366e13 | 1.93530 | ||||||||
\(699\) | −3.97782e12 | −0.630229 | ||||||||
\(700\) | −1.58637e10 | −0.00249726 | ||||||||
\(701\) | 3.09782e12 | 0.484534 | 0.242267 | − | 0.970210i | \(-0.422109\pi\) | ||||
0.242267 | + | 0.970210i | \(0.422109\pi\) | |||||||
\(702\) | 5.15922e12 | 0.801802 | ||||||||
\(703\) | 1.77719e12 | 0.274432 | ||||||||
\(704\) | 1.29045e11 | 0.0197999 | ||||||||
\(705\) | 4.31099e11 | 0.0657244 | ||||||||
\(706\) | −6.26064e12 | −0.948413 | ||||||||
\(707\) | −7.74197e11 | −0.116537 | ||||||||
\(708\) | 2.32942e12 | 0.348415 | ||||||||
\(709\) | 5.42374e12 | 0.806104 | 0.403052 | − | 0.915177i | \(-0.367949\pi\) | ||||
0.403052 | + | 0.915177i | \(0.367949\pi\) | |||||||
\(710\) | −5.77628e12 | −0.853072 | ||||||||
\(711\) | 5.18906e12 | 0.761509 | ||||||||
\(712\) | −7.76215e12 | −1.13194 | ||||||||
\(713\) | −8.91499e11 | −0.129187 | ||||||||
\(714\) | −8.53389e10 | −0.0122887 | ||||||||
\(715\) | −2.64020e11 | −0.0377799 | ||||||||
\(716\) | −4.95432e12 | −0.704490 | ||||||||
\(717\) | −7.16833e12 | −1.01294 | ||||||||
\(718\) | 2.25501e12 | 0.316656 | ||||||||
\(719\) | −5.08993e12 | −0.710284 | −0.355142 | − | 0.934812i | \(-0.615567\pi\) | ||||
−0.355142 | + | 0.934812i | \(0.615567\pi\) | |||||||
\(720\) | −5.82085e12 | −0.807217 | ||||||||
\(721\) | 5.16720e11 | 0.0712109 | ||||||||
\(722\) | −2.60755e12 | −0.357121 | ||||||||
\(723\) | 6.28829e11 | 0.0855875 | ||||||||
\(724\) | −5.98982e11 | −0.0810197 | ||||||||
\(725\) | 9.02925e10 | 0.0121375 | ||||||||
\(726\) | 5.38408e12 | 0.719278 | ||||||||
\(727\) | 8.07173e12 | 1.07167 | 0.535836 | − | 0.844322i | \(-0.319997\pi\) | ||||
0.535836 | + | 0.844322i | \(0.319997\pi\) | |||||||
\(728\) | 2.63539e11 | 0.0347739 | ||||||||
\(729\) | 4.58327e12 | 0.601037 | ||||||||
\(730\) | −5.64158e12 | −0.735272 | ||||||||
\(731\) | 1.79756e12 | 0.232838 | ||||||||
\(732\) | −2.06717e12 | −0.266119 | ||||||||
\(733\) | 6.29376e12 | 0.805272 | 0.402636 | − | 0.915360i | \(-0.368094\pi\) | ||||
0.402636 | + | 0.915360i | \(0.368094\pi\) | |||||||
\(734\) | 8.27703e11 | 0.105255 | ||||||||
\(735\) | −5.04232e12 | −0.637290 | ||||||||
\(736\) | −7.58464e12 | −0.952763 | ||||||||
\(737\) | −2.13339e11 | −0.0266358 | ||||||||
\(738\) | 9.96232e12 | 1.23625 | ||||||||
\(739\) | −9.33473e11 | −0.115134 | −0.0575668 | − | 0.998342i | \(-0.518334\pi\) | ||||
−0.0575668 | + | 0.998342i | \(0.518334\pi\) | |||||||
\(740\) | 1.08030e12 | 0.132435 | ||||||||
\(741\) | 2.87238e12 | 0.349993 | ||||||||
\(742\) | 3.42035e11 | 0.0414241 | ||||||||
\(743\) | −1.42665e13 | −1.71739 | −0.858694 | − | 0.512489i | \(-0.828724\pi\) | ||||
−0.858694 | + | 0.512489i | \(0.828724\pi\) | |||||||
\(744\) | −3.67937e11 | −0.0440246 | ||||||||
\(745\) | 4.38358e12 | 0.521346 | ||||||||
\(746\) | −1.76940e13 | −2.09171 | ||||||||
\(747\) | 6.58905e11 | 0.0774248 | ||||||||
\(748\) | −4.22749e10 | −0.00493771 | ||||||||
\(749\) | −2.76113e11 | −0.0320567 | ||||||||
\(750\) | −5.92945e12 | −0.684288 | ||||||||
\(751\) | 1.42997e13 | 1.64039 | 0.820197 | − | 0.572081i | \(-0.193864\pi\) | ||||
0.820197 | + | 0.572081i | \(0.193864\pi\) | |||||||
\(752\) | −1.11312e12 | −0.126930 | ||||||||
\(753\) | −8.17206e12 | −0.926305 | ||||||||
\(754\) | 9.40557e11 | 0.105978 | ||||||||
\(755\) | 1.54092e13 | 1.72592 | ||||||||
\(756\) | −2.42046e11 | −0.0269495 | ||||||||
\(757\) | −6.04819e12 | −0.669413 | −0.334706 | − | 0.942322i | \(-0.608637\pi\) | ||||
−0.334706 | + | 0.942322i | \(0.608637\pi\) | |||||||
\(758\) | −2.79723e12 | −0.307763 | ||||||||
\(759\) | −3.85037e11 | −0.0421128 | ||||||||
\(760\) | −5.80361e12 | −0.631011 | ||||||||
\(761\) | 5.22191e12 | 0.564414 | 0.282207 | − | 0.959353i | \(-0.408933\pi\) | ||||
0.282207 | + | 0.959353i | \(0.408933\pi\) | |||||||
\(762\) | −3.17573e12 | −0.341229 | ||||||||
\(763\) | 8.10294e11 | 0.0865530 | ||||||||
\(764\) | −6.22695e12 | −0.661234 | ||||||||
\(765\) | −1.49941e12 | −0.158287 | ||||||||
\(766\) | 1.83787e13 | 1.92879 | ||||||||
\(767\) | −9.67612e12 | −1.00954 | ||||||||
\(768\) | −5.94655e12 | −0.616793 | ||||||||
\(769\) | −8.85529e12 | −0.913134 | −0.456567 | − | 0.889689i | \(-0.650921\pi\) | ||||
−0.456567 | + | 0.889689i | \(0.650921\pi\) | |||||||
\(770\) | 4.45274e10 | 0.00456477 | ||||||||
\(771\) | 6.19575e12 | 0.631465 | ||||||||
\(772\) | 4.52895e11 | 0.0458902 | ||||||||
\(773\) | 5.21750e12 | 0.525599 | 0.262799 | − | 0.964850i | \(-0.415354\pi\) | ||||
0.262799 | + | 0.964850i | \(0.415354\pi\) | |||||||
\(774\) | 7.04542e12 | 0.705623 | ||||||||
\(775\) | −9.20002e10 | −0.00916075 | ||||||||
\(776\) | −1.20966e13 | −1.19752 | ||||||||
\(777\) | −1.43809e11 | −0.0141544 | ||||||||
\(778\) | 3.82144e12 | 0.373955 | ||||||||
\(779\) | 1.44285e13 | 1.40379 | ||||||||
\(780\) | 1.74604e12 | 0.168899 | ||||||||
\(781\) | 3.80911e11 | 0.0366348 | ||||||||
\(782\) | −3.88353e12 | −0.371361 | ||||||||
\(783\) | 1.37767e12 | 0.130984 | ||||||||
\(784\) | 1.30195e13 | 1.23076 | ||||||||
\(785\) | −1.24397e13 | −1.16922 | ||||||||
\(786\) | −1.34605e13 | −1.25794 | ||||||||
\(787\) | −1.22879e13 | −1.14181 | −0.570903 | − | 0.821017i | \(-0.693407\pi\) | ||||
−0.570903 | + | 0.821017i | \(0.693407\pi\) | |||||||
\(788\) | 5.23600e12 | 0.483762 | ||||||||
\(789\) | 1.47732e12 | 0.135715 | ||||||||
\(790\) | 1.64223e13 | 1.50007 | ||||||||
\(791\) | 1.29054e12 | 0.117213 | ||||||||
\(792\) | 2.64249e11 | 0.0238644 | ||||||||
\(793\) | 8.58678e12 | 0.771082 | ||||||||
\(794\) | −1.22278e13 | −1.09183 | ||||||||
\(795\) | −3.61399e12 | −0.320874 | ||||||||
\(796\) | −2.87645e12 | −0.253950 | ||||||||
\(797\) | 1.04691e13 | 0.919063 | 0.459532 | − | 0.888161i | \(-0.348017\pi\) | ||||
0.459532 | + | 0.888161i | \(0.348017\pi\) | |||||||
\(798\) | −4.84430e11 | −0.0422881 | ||||||||
\(799\) | −2.86733e11 | −0.0248895 | ||||||||
\(800\) | −7.82714e11 | −0.0675613 | ||||||||
\(801\) | −1.13838e13 | −0.977107 | ||||||||
\(802\) | −3.15540e12 | −0.269321 | ||||||||
\(803\) | 3.72029e11 | 0.0315760 | ||||||||
\(804\) | 1.41086e12 | 0.119078 | ||||||||
\(805\) | 1.13788e12 | 0.0955024 | ||||||||
\(806\) | −9.58345e11 | −0.0799861 | ||||||||
\(807\) | −9.50398e11 | −0.0788814 | ||||||||
\(808\) | −1.45407e13 | −1.20014 | ||||||||
\(809\) | −1.43675e13 | −1.17927 | −0.589634 | − | 0.807671i | \(-0.700728\pi\) | ||||
−0.589634 | + | 0.807671i | \(0.700728\pi\) | |||||||
\(810\) | −2.17349e11 | −0.0177409 | ||||||||
\(811\) | −1.55011e12 | −0.125825 | −0.0629127 | − | 0.998019i | \(-0.520039\pi\) | ||||
−0.0629127 | + | 0.998019i | \(0.520039\pi\) | |||||||
\(812\) | −4.41265e10 | −0.00356203 | ||||||||
\(813\) | 1.21347e13 | 0.974137 | ||||||||
\(814\) | −2.56092e11 | −0.0204450 | ||||||||
\(815\) | 1.00849e13 | 0.800690 | ||||||||
\(816\) | −2.32824e12 | −0.183833 | ||||||||
\(817\) | 1.02039e13 | 0.801249 | ||||||||
\(818\) | 9.18348e12 | 0.717163 | ||||||||
\(819\) | 3.86501e11 | 0.0300174 | ||||||||
\(820\) | 8.77065e12 | 0.677438 | ||||||||
\(821\) | −1.37949e13 | −1.05968 | −0.529839 | − | 0.848098i | \(-0.677748\pi\) | ||||
−0.529839 | + | 0.848098i | \(0.677748\pi\) | |||||||
\(822\) | −5.16513e12 | −0.394601 | ||||||||
\(823\) | −1.07251e13 | −0.814899 | −0.407449 | − | 0.913228i | \(-0.633582\pi\) | ||||
−0.407449 | + | 0.913228i | \(0.633582\pi\) | |||||||
\(824\) | 9.70482e12 | 0.733357 | ||||||||
\(825\) | −3.97347e10 | −0.00298626 | ||||||||
\(826\) | 1.63189e12 | 0.121978 | ||||||||
\(827\) | 1.65480e13 | 1.23019 | 0.615093 | − | 0.788454i | \(-0.289118\pi\) | ||||
0.615093 | + | 0.788454i | \(0.289118\pi\) | |||||||
\(828\) | −4.23424e12 | −0.313068 | ||||||||
\(829\) | 1.03812e13 | 0.763398 | 0.381699 | − | 0.924287i | \(-0.375339\pi\) | ||||
0.381699 | + | 0.924287i | \(0.375339\pi\) | |||||||
\(830\) | 2.08530e12 | 0.152517 | ||||||||
\(831\) | 9.69040e12 | 0.704916 | ||||||||
\(832\) | 3.54494e12 | 0.256481 | ||||||||
\(833\) | 3.35374e12 | 0.241339 | ||||||||
\(834\) | 4.72931e12 | 0.338494 | ||||||||
\(835\) | 1.19488e13 | 0.850621 | ||||||||
\(836\) | −2.39976e11 | −0.0169918 | ||||||||
\(837\) | −1.40373e12 | −0.0988595 | ||||||||
\(838\) | 2.83460e13 | 1.98561 | ||||||||
\(839\) | −6.25038e12 | −0.435489 | −0.217745 | − | 0.976006i | \(-0.569870\pi\) | ||||
−0.217745 | + | 0.976006i | \(0.569870\pi\) | |||||||
\(840\) | 4.69623e11 | 0.0325456 | ||||||||
\(841\) | −1.42560e13 | −0.982687 | ||||||||
\(842\) | 2.23846e13 | 1.53477 | ||||||||
\(843\) | −4.18428e12 | −0.285362 | ||||||||
\(844\) | 8.50802e12 | 0.577149 | ||||||||
\(845\) | 8.23589e12 | 0.555719 | ||||||||
\(846\) | −1.12383e12 | −0.0754284 | ||||||||
\(847\) | 1.04925e12 | 0.0700496 | ||||||||
\(848\) | 9.33151e12 | 0.619685 | ||||||||
\(849\) | 1.04207e13 | 0.688356 | ||||||||
\(850\) | −4.00769e11 | −0.0263335 | ||||||||
\(851\) | −6.54432e12 | −0.427742 | ||||||||
\(852\) | −2.51906e12 | −0.163780 | ||||||||
\(853\) | −2.08264e13 | −1.34693 | −0.673464 | − | 0.739220i | \(-0.735194\pi\) | ||||
−0.673464 | + | 0.739220i | \(0.735194\pi\) | |||||||
\(854\) | −1.44817e12 | −0.0931664 | ||||||||
\(855\) | −8.51147e12 | −0.544700 | ||||||||
\(856\) | −5.18585e12 | −0.330132 | ||||||||
\(857\) | 2.34103e12 | 0.148249 | 0.0741246 | − | 0.997249i | \(-0.476384\pi\) | ||||
0.0741246 | + | 0.997249i | \(0.476384\pi\) | |||||||
\(858\) | −4.13908e11 | −0.0260742 | ||||||||
\(859\) | −1.14439e13 | −0.717139 | −0.358569 | − | 0.933503i | \(-0.616735\pi\) | ||||
−0.358569 | + | 0.933503i | \(0.616735\pi\) | |||||||
\(860\) | 6.20266e12 | 0.386665 | ||||||||
\(861\) | −1.16754e12 | −0.0724031 | ||||||||
\(862\) | −2.09581e13 | −1.29291 | ||||||||
\(863\) | −1.65044e13 | −1.01286 | −0.506431 | − | 0.862281i | \(-0.669035\pi\) | ||||
−0.506431 | + | 0.862281i | \(0.669035\pi\) | |||||||
\(864\) | −1.19426e13 | −0.729097 | ||||||||
\(865\) | −2.87029e12 | −0.174323 | ||||||||
\(866\) | −1.93844e13 | −1.17117 | ||||||||
\(867\) | −5.99739e11 | −0.0360476 | ||||||||
\(868\) | 4.49611e10 | 0.00268843 | ||||||||
\(869\) | −1.08295e12 | −0.0644201 | ||||||||
\(870\) | 1.67606e12 | 0.0991867 | ||||||||
\(871\) | −5.86056e12 | −0.345031 | ||||||||
\(872\) | 1.52186e13 | 0.891355 | ||||||||
\(873\) | −1.77406e13 | −1.03372 | ||||||||
\(874\) | −2.20450e13 | −1.27794 | ||||||||
\(875\) | −1.15554e12 | −0.0666419 | ||||||||
\(876\) | −2.46032e12 | −0.141164 | ||||||||
\(877\) | −1.42710e11 | −0.00814620 | −0.00407310 | − | 0.999992i | \(-0.501297\pi\) | ||||
−0.00407310 | + | 0.999992i | \(0.501297\pi\) | |||||||
\(878\) | −1.50109e13 | −0.852473 | ||||||||
\(879\) | −8.29777e12 | −0.468826 | ||||||||
\(880\) | 1.21481e12 | 0.0682867 | ||||||||
\(881\) | 2.11785e13 | 1.18441 | 0.592206 | − | 0.805786i | \(-0.298257\pi\) | ||||
0.592206 | + | 0.805786i | \(0.298257\pi\) | |||||||
\(882\) | 1.31448e13 | 0.731384 | ||||||||
\(883\) | 1.83970e13 | 1.01841 | 0.509207 | − | 0.860644i | \(-0.329939\pi\) | ||||
0.509207 | + | 0.860644i | \(0.329939\pi\) | |||||||
\(884\) | −1.16132e12 | −0.0639613 | ||||||||
\(885\) | −1.72427e13 | −0.944847 | ||||||||
\(886\) | 6.60720e12 | 0.360218 | ||||||||
\(887\) | −1.18951e13 | −0.645225 | −0.322613 | − | 0.946531i | \(-0.604561\pi\) | ||||
−0.322613 | + | 0.946531i | \(0.604561\pi\) | |||||||
\(888\) | −2.70096e12 | −0.145767 | ||||||||
\(889\) | −6.18888e11 | −0.0332318 | ||||||||
\(890\) | −3.60276e13 | −1.92477 | ||||||||
\(891\) | 1.43329e10 | 0.000761874 0 | ||||||||
\(892\) | −7.51963e12 | −0.397699 | ||||||||
\(893\) | −1.62765e12 | −0.0856505 | ||||||||
\(894\) | 6.87219e12 | 0.359812 | ||||||||
\(895\) | 3.66727e13 | 1.91047 | ||||||||
\(896\) | −1.59042e12 | −0.0824375 | ||||||||
\(897\) | −1.05772e13 | −0.545514 | ||||||||
\(898\) | −3.62807e13 | −1.86180 | ||||||||
\(899\) | −2.55908e11 | −0.0130667 | ||||||||
\(900\) | −4.36962e11 | −0.0222000 | ||||||||
\(901\) | 2.40373e12 | 0.121513 | ||||||||
\(902\) | −2.07913e12 | −0.104581 | ||||||||
\(903\) | −8.25692e11 | −0.0413260 | ||||||||
\(904\) | 2.42384e13 | 1.20711 | ||||||||
\(905\) | 4.43377e12 | 0.219713 | ||||||||
\(906\) | 2.41572e13 | 1.19116 | ||||||||
\(907\) | 3.91571e13 | 1.92122 | 0.960612 | − | 0.277893i | \(-0.0896361\pi\) | ||||
0.960612 | + | 0.277893i | \(0.0896361\pi\) | |||||||
\(908\) | −5.48785e12 | −0.267927 | ||||||||
\(909\) | −2.13251e13 | −1.03599 | ||||||||
\(910\) | 1.22320e12 | 0.0591304 | ||||||||
\(911\) | −2.83393e13 | −1.36319 | −0.681595 | − | 0.731730i | \(-0.738713\pi\) | ||||
−0.681595 | + | 0.731730i | \(0.738713\pi\) | |||||||
\(912\) | −1.32164e13 | −0.632609 | ||||||||
\(913\) | −1.37513e11 | −0.00654977 | ||||||||
\(914\) | 2.61530e13 | 1.23955 | ||||||||
\(915\) | 1.53015e13 | 0.721672 | ||||||||
\(916\) | 6.99996e12 | 0.328523 | ||||||||
\(917\) | −2.62319e12 | −0.122509 | ||||||||
\(918\) | −6.11489e12 | −0.284182 | ||||||||
\(919\) | −1.73995e13 | −0.804668 | −0.402334 | − | 0.915493i | \(-0.631801\pi\) | ||||
−0.402334 | + | 0.915493i | \(0.631801\pi\) | |||||||
\(920\) | 2.13712e13 | 0.983520 | ||||||||
\(921\) | 1.13119e13 | 0.518044 | ||||||||
\(922\) | 1.96108e13 | 0.893731 | ||||||||
\(923\) | 1.04639e13 | 0.474554 | ||||||||
\(924\) | 1.94186e10 | 0.000876384 0 | ||||||||
\(925\) | −6.75356e11 | −0.0303316 | ||||||||
\(926\) | 4.78189e12 | 0.213723 | ||||||||
\(927\) | 1.42329e13 | 0.633047 | ||||||||
\(928\) | −2.17720e12 | −0.0963680 | ||||||||
\(929\) | −3.95509e13 | −1.74215 | −0.871074 | − | 0.491151i | \(-0.836576\pi\) | ||||
−0.871074 | + | 0.491151i | \(0.836576\pi\) | |||||||
\(930\) | −1.70776e12 | −0.0748607 | ||||||||
\(931\) | 1.90377e13 | 0.830501 | ||||||||
\(932\) | 9.12937e12 | 0.396341 | ||||||||
\(933\) | −2.74988e11 | −0.0118808 | ||||||||
\(934\) | 3.02752e12 | 0.130175 | ||||||||
\(935\) | 3.12926e11 | 0.0133903 | ||||||||
\(936\) | 7.25911e12 | 0.309131 | ||||||||
\(937\) | 4.31185e13 | 1.82741 | 0.913704 | − | 0.406381i | \(-0.133210\pi\) | ||||
0.913704 | + | 0.406381i | \(0.133210\pi\) | |||||||
\(938\) | 9.88392e11 | 0.0416885 | ||||||||
\(939\) | 1.37504e13 | 0.577194 | ||||||||
\(940\) | −9.89402e11 | −0.0413330 | ||||||||
\(941\) | 1.23028e13 | 0.511505 | 0.255753 | − | 0.966742i | \(-0.417677\pi\) | ||||
0.255753 | + | 0.966742i | \(0.417677\pi\) | |||||||
\(942\) | −1.95018e13 | −0.806949 | ||||||||
\(943\) | −5.31313e13 | −2.18800 | ||||||||
\(944\) | 4.45217e13 | 1.82473 | ||||||||
\(945\) | 1.79167e12 | 0.0730828 | ||||||||
\(946\) | −1.47038e12 | −0.0596923 | ||||||||
\(947\) | 3.99251e13 | 1.61314 | 0.806568 | − | 0.591142i | \(-0.201323\pi\) | ||||
0.806568 | + | 0.591142i | \(0.201323\pi\) | |||||||
\(948\) | 7.16186e12 | 0.287997 | ||||||||
\(949\) | 1.02199e13 | 0.409024 | ||||||||
\(950\) | −2.27498e12 | −0.0906196 | ||||||||
\(951\) | −5.82424e12 | −0.230902 | ||||||||
\(952\) | −3.12355e11 | −0.0123249 | ||||||||
\(953\) | −4.12885e13 | −1.62148 | −0.810739 | − | 0.585408i | \(-0.800934\pi\) | ||||
−0.810739 | + | 0.585408i | \(0.800934\pi\) | |||||||
\(954\) | 9.42129e12 | 0.368250 | ||||||||
\(955\) | 4.60930e13 | 1.79316 | ||||||||
\(956\) | 1.64518e13 | 0.637019 | ||||||||
\(957\) | −1.10526e11 | −0.00425953 | ||||||||
\(958\) | −1.42579e13 | −0.546904 | ||||||||
\(959\) | −1.00658e12 | −0.0384296 | ||||||||
\(960\) | 6.31705e12 | 0.240046 | ||||||||
\(961\) | −2.61789e13 | −0.990138 | ||||||||
\(962\) | −7.03503e12 | −0.264837 | ||||||||
\(963\) | −7.60548e12 | −0.284976 | ||||||||
\(964\) | −1.44320e12 | −0.0538246 | ||||||||
\(965\) | −3.35241e12 | −0.124447 | ||||||||
\(966\) | 1.78386e12 | 0.0659120 | ||||||||
\(967\) | −3.74952e13 | −1.37898 | −0.689488 | − | 0.724297i | \(-0.742164\pi\) | ||||
−0.689488 | + | 0.724297i | \(0.742164\pi\) | |||||||
\(968\) | 1.97067e13 | 0.721397 | ||||||||
\(969\) | −3.40444e12 | −0.124048 | ||||||||
\(970\) | −5.61455e13 | −2.03630 | ||||||||
\(971\) | −1.85734e13 | −0.670508 | −0.335254 | − | 0.942128i | \(-0.608822\pi\) | ||||
−0.335254 | + | 0.942128i | \(0.608822\pi\) | |||||||
\(972\) | −1.07713e13 | −0.387053 | ||||||||
\(973\) | 9.21653e11 | 0.0329655 | ||||||||
\(974\) | 2.47896e13 | 0.882580 | ||||||||
\(975\) | −1.09154e12 | −0.0386829 | ||||||||
\(976\) | −3.95094e13 | −1.39372 | ||||||||
\(977\) | −5.09643e13 | −1.78954 | −0.894769 | − | 0.446530i | \(-0.852660\pi\) | ||||
−0.894769 | + | 0.446530i | \(0.852660\pi\) | |||||||
\(978\) | 1.58103e13 | 0.552604 | ||||||||
\(979\) | 2.37580e12 | 0.0826586 | ||||||||
\(980\) | 1.15724e13 | 0.400782 | ||||||||
\(981\) | 2.23194e13 | 0.769434 | ||||||||
\(982\) | 3.73262e13 | 1.28089 | ||||||||
\(983\) | 1.27845e12 | 0.0436710 | 0.0218355 | − | 0.999762i | \(-0.493049\pi\) | ||||
0.0218355 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(984\) | −2.19283e13 | −0.745635 | ||||||||
\(985\) | −3.87578e13 | −1.31189 | ||||||||
\(986\) | −1.11478e12 | −0.0375616 | ||||||||
\(987\) | 1.31708e11 | 0.00441759 | ||||||||
\(988\) | −6.59230e12 | −0.220105 | ||||||||
\(989\) | −3.75748e13 | −1.24886 | ||||||||
\(990\) | 1.22650e12 | 0.0405796 | ||||||||
\(991\) | 1.53850e13 | 0.506719 | 0.253360 | − | 0.967372i | \(-0.418464\pi\) | ||||
0.253360 | + | 0.967372i | \(0.418464\pi\) | |||||||
\(992\) | 2.21838e12 | 0.0727332 | ||||||||
\(993\) | −1.06514e13 | −0.347643 | ||||||||
\(994\) | −1.76475e12 | −0.0573383 | ||||||||
\(995\) | 2.12920e13 | 0.688672 | ||||||||
\(996\) | 9.09410e11 | 0.0292815 | ||||||||
\(997\) | 3.56093e13 | 1.14139 | 0.570696 | − | 0.821162i | \(-0.306674\pi\) | ||||
0.570696 | + | 0.821162i | \(0.306674\pi\) | |||||||
\(998\) | 2.57094e13 | 0.820359 | ||||||||
\(999\) | −1.03045e13 | −0.327327 |
(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 | 17.10.a.a.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 153.10.a.c.1.1 | 5 | |||
4.3 | odd | 2 | 272.10.a.f.1.4 | 5 | |||
17.16 | even | 2 | 289.10.a.a.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.a.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
153.10.a.c.1.1 | 5 | 3.2 | odd | 2 | |||
272.10.a.f.1.4 | 5 | 4.3 | odd | 2 | |||
289.10.a.a.1.5 | 5 | 17.16 | even | 2 |