Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(46.8682610909\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4945 x^{11} - 8694 x^{10} + 9009530 x^{9} + 27431200 x^{8} - 7320118704 x^{7} - 28566940352 x^{6} + 2456696387328 x^{5} + \cdots + 20\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-34.7365\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −36.7365 | −1.62354 | −0.811769 | − | 0.583979i | \(-0.801495\pi\) | ||||
−0.811769 | + | 0.583979i | \(0.801495\pi\) | |||||||
\(3\) | −181.146 | −1.29117 | −0.645584 | − | 0.763689i | \(-0.723386\pi\) | ||||
−0.645584 | + | 0.763689i | \(0.723386\pi\) | |||||||
\(4\) | 837.568 | 1.63587 | ||||||||
\(5\) | 2263.64 | 1.61973 | 0.809866 | − | 0.586615i | \(-0.199540\pi\) | ||||
0.809866 | + | 0.586615i | \(0.199540\pi\) | |||||||
\(6\) | 6654.66 | 2.09626 | ||||||||
\(7\) | −2401.00 | −0.377964 | ||||||||
\(8\) | −11960.2 | −1.03237 | ||||||||
\(9\) | 13130.9 | 0.667117 | ||||||||
\(10\) | −83158.3 | −2.62969 | ||||||||
\(11\) | 4940.24 | 0.101737 | 0.0508687 | − | 0.998705i | \(-0.483801\pi\) | ||||
0.0508687 | + | 0.998705i | \(0.483801\pi\) | |||||||
\(12\) | −151722. | −2.11219 | ||||||||
\(13\) | −28561.0 | −0.277350 | ||||||||
\(14\) | 88204.2 | 0.613640 | ||||||||
\(15\) | −410050. | −2.09135 | ||||||||
\(16\) | 10541.0 | 0.0402109 | ||||||||
\(17\) | −178661. | −0.518812 | −0.259406 | − | 0.965768i | \(-0.583527\pi\) | ||||
−0.259406 | + | 0.965768i | \(0.583527\pi\) | |||||||
\(18\) | −482381. | −1.08309 | ||||||||
\(19\) | −471966. | −0.830844 | −0.415422 | − | 0.909629i | \(-0.636366\pi\) | ||||
−0.415422 | + | 0.909629i | \(0.636366\pi\) | |||||||
\(20\) | 1.89595e6 | 2.64968 | ||||||||
\(21\) | 434931. | 0.488016 | ||||||||
\(22\) | −181487. | −0.165175 | ||||||||
\(23\) | 2.11688e6 | 1.57733 | 0.788664 | − | 0.614825i | \(-0.210773\pi\) | ||||
0.788664 | + | 0.614825i | \(0.210773\pi\) | |||||||
\(24\) | 2.16654e6 | 1.33296 | ||||||||
\(25\) | 3.17096e6 | 1.62353 | ||||||||
\(26\) | 1.04923e6 | 0.450288 | ||||||||
\(27\) | 1.18689e6 | 0.429809 | ||||||||
\(28\) | −2.01100e6 | −0.618302 | ||||||||
\(29\) | −4.05803e6 | −1.06543 | −0.532715 | − | 0.846295i | \(-0.678828\pi\) | ||||
−0.532715 | + | 0.846295i | \(0.678828\pi\) | |||||||
\(30\) | 1.50638e7 | 3.39538 | ||||||||
\(31\) | 1.98399e6 | 0.385845 | 0.192922 | − | 0.981214i | \(-0.438203\pi\) | ||||
0.192922 | + | 0.981214i | \(0.438203\pi\) | |||||||
\(32\) | 5.73639e6 | 0.967082 | ||||||||
\(33\) | −894905. | −0.131360 | ||||||||
\(34\) | 6.56338e6 | 0.842311 | ||||||||
\(35\) | −5.43501e6 | −0.612201 | ||||||||
\(36\) | 1.09980e7 | 1.09132 | ||||||||
\(37\) | −9.92848e6 | −0.870913 | −0.435457 | − | 0.900210i | \(-0.643413\pi\) | ||||
−0.435457 | + | 0.900210i | \(0.643413\pi\) | |||||||
\(38\) | 1.73384e7 | 1.34891 | ||||||||
\(39\) | 5.17371e6 | 0.358106 | ||||||||
\(40\) | −2.70736e7 | −1.67216 | ||||||||
\(41\) | 8.06137e6 | 0.445535 | 0.222767 | − | 0.974872i | \(-0.428491\pi\) | ||||
0.222767 | + | 0.974872i | \(0.428491\pi\) | |||||||
\(42\) | −1.59778e7 | −0.792312 | ||||||||
\(43\) | −3.04626e7 | −1.35881 | −0.679405 | − | 0.733763i | \(-0.737762\pi\) | ||||
−0.679405 | + | 0.733763i | \(0.737762\pi\) | |||||||
\(44\) | 4.13779e6 | 0.166430 | ||||||||
\(45\) | 2.97236e7 | 1.08055 | ||||||||
\(46\) | −7.77669e7 | −2.56085 | ||||||||
\(47\) | 5.28351e7 | 1.57936 | 0.789681 | − | 0.613517i | \(-0.210246\pi\) | ||||
0.789681 | + | 0.613517i | \(0.210246\pi\) | |||||||
\(48\) | −1.90947e6 | −0.0519190 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | −1.16490e8 | −2.63586 | ||||||||
\(51\) | 3.23637e7 | 0.669874 | ||||||||
\(52\) | −2.39218e7 | −0.453710 | ||||||||
\(53\) | −6.65323e6 | −0.115822 | −0.0579110 | − | 0.998322i | \(-0.518444\pi\) | ||||
−0.0579110 | + | 0.998322i | \(0.518444\pi\) | |||||||
\(54\) | −4.36023e7 | −0.697810 | ||||||||
\(55\) | 1.11829e7 | 0.164787 | ||||||||
\(56\) | 2.87165e7 | 0.390198 | ||||||||
\(57\) | 8.54947e7 | 1.07276 | ||||||||
\(58\) | 1.49078e8 | 1.72976 | ||||||||
\(59\) | 1.63029e7 | 0.175158 | 0.0875790 | − | 0.996158i | \(-0.472087\pi\) | ||||
0.0875790 | + | 0.996158i | \(0.472087\pi\) | |||||||
\(60\) | −3.43445e8 | −3.42118 | ||||||||
\(61\) | −1.19476e8 | −1.10484 | −0.552418 | − | 0.833567i | \(-0.686295\pi\) | ||||
−0.552418 | + | 0.833567i | \(0.686295\pi\) | |||||||
\(62\) | −7.28849e7 | −0.626434 | ||||||||
\(63\) | −3.15272e7 | −0.252146 | ||||||||
\(64\) | −2.16132e8 | −1.61031 | ||||||||
\(65\) | −6.46519e7 | −0.449233 | ||||||||
\(66\) | 3.28756e7 | 0.213268 | ||||||||
\(67\) | 2.03127e8 | 1.23149 | 0.615746 | − | 0.787944i | \(-0.288855\pi\) | ||||
0.615746 | + | 0.787944i | \(0.288855\pi\) | |||||||
\(68\) | −1.49641e8 | −0.848711 | ||||||||
\(69\) | −3.83465e8 | −2.03660 | ||||||||
\(70\) | 1.99663e8 | 0.993931 | ||||||||
\(71\) | 4.61351e7 | 0.215461 | 0.107731 | − | 0.994180i | \(-0.465642\pi\) | ||||
0.107731 | + | 0.994180i | \(0.465642\pi\) | |||||||
\(72\) | −1.57048e8 | −0.688709 | ||||||||
\(73\) | 1.31899e8 | 0.543610 | 0.271805 | − | 0.962352i | \(-0.412379\pi\) | ||||
0.271805 | + | 0.962352i | \(0.412379\pi\) | |||||||
\(74\) | 3.64737e8 | 1.41396 | ||||||||
\(75\) | −5.74406e8 | −2.09625 | ||||||||
\(76\) | −3.95303e8 | −1.35916 | ||||||||
\(77\) | −1.18615e7 | −0.0384532 | ||||||||
\(78\) | −1.90064e8 | −0.581398 | ||||||||
\(79\) | 4.76417e8 | 1.37615 | 0.688074 | − | 0.725640i | \(-0.258456\pi\) | ||||
0.688074 | + | 0.725640i | \(0.258456\pi\) | |||||||
\(80\) | 2.38611e7 | 0.0651308 | ||||||||
\(81\) | −4.73456e8 | −1.22207 | ||||||||
\(82\) | −2.96146e8 | −0.723342 | ||||||||
\(83\) | −9.05932e7 | −0.209529 | −0.104764 | − | 0.994497i | \(-0.533409\pi\) | ||||
−0.104764 | + | 0.994497i | \(0.533409\pi\) | |||||||
\(84\) | 3.64285e8 | 0.798333 | ||||||||
\(85\) | −4.04425e8 | −0.840336 | ||||||||
\(86\) | 1.11909e9 | 2.20608 | ||||||||
\(87\) | 7.35096e8 | 1.37565 | ||||||||
\(88\) | −5.90863e7 | −0.105030 | ||||||||
\(89\) | −4.07571e7 | −0.0688570 | −0.0344285 | − | 0.999407i | \(-0.510961\pi\) | ||||
−0.0344285 | + | 0.999407i | \(0.510961\pi\) | |||||||
\(90\) | −1.09194e9 | −1.75431 | ||||||||
\(91\) | 6.85750e7 | 0.104828 | ||||||||
\(92\) | 1.77303e9 | 2.58031 | ||||||||
\(93\) | −3.59393e8 | −0.498191 | ||||||||
\(94\) | −1.94097e9 | −2.56415 | ||||||||
\(95\) | −1.06836e9 | −1.34574 | ||||||||
\(96\) | −1.03912e9 | −1.24867 | ||||||||
\(97\) | −6.02654e8 | −0.691187 | −0.345593 | − | 0.938384i | \(-0.612322\pi\) | ||||
−0.345593 | + | 0.938384i | \(0.612322\pi\) | |||||||
\(98\) | −2.11778e8 | −0.231934 | ||||||||
\(99\) | 6.48696e7 | 0.0678708 | ||||||||
\(100\) | 2.65589e9 | 2.65589 | ||||||||
\(101\) | −1.25464e9 | −1.19970 | −0.599849 | − | 0.800114i | \(-0.704773\pi\) | ||||
−0.599849 | + | 0.800114i | \(0.704773\pi\) | |||||||
\(102\) | −1.18893e9 | −1.08757 | ||||||||
\(103\) | −4.08373e8 | −0.357511 | −0.178756 | − | 0.983894i | \(-0.557207\pi\) | ||||
−0.178756 | + | 0.983894i | \(0.557207\pi\) | |||||||
\(104\) | 3.41595e8 | 0.286327 | ||||||||
\(105\) | 9.84530e8 | 0.790455 | ||||||||
\(106\) | 2.44416e8 | 0.188041 | ||||||||
\(107\) | −1.88302e9 | −1.38876 | −0.694380 | − | 0.719609i | \(-0.744321\pi\) | ||||
−0.694380 | + | 0.719609i | \(0.744321\pi\) | |||||||
\(108\) | 9.94104e8 | 0.703113 | ||||||||
\(109\) | 1.46345e9 | 0.993022 | 0.496511 | − | 0.868030i | \(-0.334614\pi\) | ||||
0.496511 | + | 0.868030i | \(0.334614\pi\) | |||||||
\(110\) | −4.10822e8 | −0.267539 | ||||||||
\(111\) | 1.79850e9 | 1.12450 | ||||||||
\(112\) | −2.53090e7 | −0.0151983 | ||||||||
\(113\) | 2.31179e9 | 1.33381 | 0.666907 | − | 0.745141i | \(-0.267618\pi\) | ||||
0.666907 | + | 0.745141i | \(0.267618\pi\) | |||||||
\(114\) | −3.14077e9 | −1.74167 | ||||||||
\(115\) | 4.79187e9 | 2.55485 | ||||||||
\(116\) | −3.39888e9 | −1.74291 | ||||||||
\(117\) | −3.75030e8 | −0.185025 | ||||||||
\(118\) | −5.98910e8 | −0.284376 | ||||||||
\(119\) | 4.28965e8 | 0.196092 | ||||||||
\(120\) | 4.90428e9 | 2.15904 | ||||||||
\(121\) | −2.33354e9 | −0.989649 | ||||||||
\(122\) | 4.38914e9 | 1.79374 | ||||||||
\(123\) | −1.46028e9 | −0.575261 | ||||||||
\(124\) | 1.66173e9 | 0.631194 | ||||||||
\(125\) | 2.75674e9 | 1.00995 | ||||||||
\(126\) | 1.15820e9 | 0.409369 | ||||||||
\(127\) | 4.98338e9 | 1.69984 | 0.849918 | − | 0.526915i | \(-0.176651\pi\) | ||||
0.849918 | + | 0.526915i | \(0.176651\pi\) | |||||||
\(128\) | 5.00288e9 | 1.64731 | ||||||||
\(129\) | 5.51818e9 | 1.75445 | ||||||||
\(130\) | 2.37508e9 | 0.729346 | ||||||||
\(131\) | −4.28792e9 | −1.27211 | −0.636056 | − | 0.771643i | \(-0.719435\pi\) | ||||
−0.636056 | + | 0.771643i | \(0.719435\pi\) | |||||||
\(132\) | −7.49543e8 | −0.214889 | ||||||||
\(133\) | 1.13319e9 | 0.314029 | ||||||||
\(134\) | −7.46218e9 | −1.99937 | ||||||||
\(135\) | 2.68671e9 | 0.696174 | ||||||||
\(136\) | 2.13682e9 | 0.535604 | ||||||||
\(137\) | −2.17817e9 | −0.528262 | −0.264131 | − | 0.964487i | \(-0.585085\pi\) | ||||
−0.264131 | + | 0.964487i | \(0.585085\pi\) | |||||||
\(138\) | 1.40872e10 | 3.30649 | ||||||||
\(139\) | −3.00478e9 | −0.682726 | −0.341363 | − | 0.939932i | \(-0.610889\pi\) | ||||
−0.341363 | + | 0.939932i | \(0.610889\pi\) | |||||||
\(140\) | −4.55219e9 | −1.00148 | ||||||||
\(141\) | −9.57086e9 | −2.03922 | ||||||||
\(142\) | −1.69484e9 | −0.349809 | ||||||||
\(143\) | −1.41098e8 | −0.0282169 | ||||||||
\(144\) | 1.38413e8 | 0.0268253 | ||||||||
\(145\) | −9.18594e9 | −1.72571 | ||||||||
\(146\) | −4.84549e9 | −0.882572 | ||||||||
\(147\) | −1.04427e9 | −0.184453 | ||||||||
\(148\) | −8.31577e9 | −1.42470 | ||||||||
\(149\) | −1.13565e10 | −1.88758 | −0.943792 | − | 0.330539i | \(-0.892770\pi\) | ||||
−0.943792 | + | 0.330539i | \(0.892770\pi\) | |||||||
\(150\) | 2.11016e10 | 3.40334 | ||||||||
\(151\) | −9.47221e9 | −1.48271 | −0.741353 | − | 0.671115i | \(-0.765816\pi\) | ||||
−0.741353 | + | 0.671115i | \(0.765816\pi\) | |||||||
\(152\) | 5.64481e9 | 0.857735 | ||||||||
\(153\) | −2.34597e9 | −0.346108 | ||||||||
\(154\) | 4.35750e8 | 0.0624301 | ||||||||
\(155\) | 4.49106e9 | 0.624965 | ||||||||
\(156\) | 4.33333e9 | 0.585816 | ||||||||
\(157\) | 6.85342e9 | 0.900241 | 0.450120 | − | 0.892968i | \(-0.351381\pi\) | ||||
0.450120 | + | 0.892968i | \(0.351381\pi\) | |||||||
\(158\) | −1.75019e10 | −2.23423 | ||||||||
\(159\) | 1.20521e9 | 0.149546 | ||||||||
\(160\) | 1.29851e10 | 1.56641 | ||||||||
\(161\) | −5.08264e9 | −0.596174 | ||||||||
\(162\) | 1.73931e10 | 1.98408 | ||||||||
\(163\) | −5.81211e9 | −0.644896 | −0.322448 | − | 0.946587i | \(-0.604506\pi\) | ||||
−0.322448 | + | 0.946587i | \(0.604506\pi\) | |||||||
\(164\) | 6.75195e9 | 0.728839 | ||||||||
\(165\) | −2.02574e9 | −0.212768 | ||||||||
\(166\) | 3.32807e9 | 0.340178 | ||||||||
\(167\) | −1.81398e9 | −0.180471 | −0.0902356 | − | 0.995920i | \(-0.528762\pi\) | ||||
−0.0902356 | + | 0.995920i | \(0.528762\pi\) | |||||||
\(168\) | −5.20187e9 | −0.503811 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | 1.48571e10 | 1.36432 | ||||||||
\(171\) | −6.19731e9 | −0.554270 | ||||||||
\(172\) | −2.55145e10 | −2.22284 | ||||||||
\(173\) | −1.40074e10 | −1.18891 | −0.594456 | − | 0.804128i | \(-0.702633\pi\) | ||||
−0.594456 | + | 0.804128i | \(0.702633\pi\) | |||||||
\(174\) | −2.70048e10 | −2.23342 | ||||||||
\(175\) | −7.61347e9 | −0.613637 | ||||||||
\(176\) | 5.20752e7 | 0.00409095 | ||||||||
\(177\) | −2.95320e9 | −0.226158 | ||||||||
\(178\) | 1.49727e9 | 0.111792 | ||||||||
\(179\) | −9.19182e9 | −0.669210 | −0.334605 | − | 0.942358i | \(-0.608603\pi\) | ||||
−0.334605 | + | 0.942358i | \(0.608603\pi\) | |||||||
\(180\) | 2.48955e10 | 1.76764 | ||||||||
\(181\) | −2.50761e10 | −1.73663 | −0.868313 | − | 0.496017i | \(-0.834795\pi\) | ||||
−0.868313 | + | 0.496017i | \(0.834795\pi\) | |||||||
\(182\) | −2.51920e9 | −0.170193 | ||||||||
\(183\) | 2.16427e10 | 1.42653 | ||||||||
\(184\) | −2.53184e10 | −1.62838 | ||||||||
\(185\) | −2.24745e10 | −1.41065 | ||||||||
\(186\) | 1.32028e10 | 0.808832 | ||||||||
\(187\) | −8.82629e8 | −0.0527826 | ||||||||
\(188\) | 4.42529e10 | 2.58364 | ||||||||
\(189\) | −2.84973e9 | −0.162452 | ||||||||
\(190\) | 3.92478e10 | 2.18487 | ||||||||
\(191\) | 2.60438e10 | 1.41597 | 0.707985 | − | 0.706227i | \(-0.249604\pi\) | ||||
0.707985 | + | 0.706227i | \(0.249604\pi\) | |||||||
\(192\) | 3.91514e10 | 2.07918 | ||||||||
\(193\) | 3.40811e10 | 1.76810 | 0.884049 | − | 0.467394i | \(-0.154807\pi\) | ||||
0.884049 | + | 0.467394i | \(0.154807\pi\) | |||||||
\(194\) | 2.21394e10 | 1.12217 | ||||||||
\(195\) | 1.17114e10 | 0.580035 | ||||||||
\(196\) | 4.82841e9 | 0.233696 | ||||||||
\(197\) | −3.69881e10 | −1.74970 | −0.874851 | − | 0.484392i | \(-0.839041\pi\) | ||||
−0.874851 | + | 0.484392i | \(0.839041\pi\) | |||||||
\(198\) | −2.38308e9 | −0.110191 | ||||||||
\(199\) | −2.61934e10 | −1.18400 | −0.592001 | − | 0.805937i | \(-0.701662\pi\) | ||||
−0.592001 | + | 0.805937i | \(0.701662\pi\) | |||||||
\(200\) | −3.79253e10 | −1.67608 | ||||||||
\(201\) | −3.67957e10 | −1.59006 | ||||||||
\(202\) | 4.60909e10 | 1.94775 | ||||||||
\(203\) | 9.74334e9 | 0.402694 | ||||||||
\(204\) | 2.71068e10 | 1.09583 | ||||||||
\(205\) | 1.82481e10 | 0.721647 | ||||||||
\(206\) | 1.50022e10 | 0.580433 | ||||||||
\(207\) | 2.77965e10 | 1.05226 | ||||||||
\(208\) | −3.01062e8 | −0.0111525 | ||||||||
\(209\) | −2.33162e9 | −0.0845279 | ||||||||
\(210\) | −3.61681e10 | −1.28333 | ||||||||
\(211\) | −1.41870e10 | −0.492743 | −0.246371 | − | 0.969176i | \(-0.579238\pi\) | ||||
−0.246371 | + | 0.969176i | \(0.579238\pi\) | |||||||
\(212\) | −5.57253e9 | −0.189470 | ||||||||
\(213\) | −8.35718e9 | −0.278197 | ||||||||
\(214\) | 6.91754e10 | 2.25470 | ||||||||
\(215\) | −6.89565e10 | −2.20091 | ||||||||
\(216\) | −1.41955e10 | −0.443720 | ||||||||
\(217\) | −4.76357e9 | −0.145836 | ||||||||
\(218\) | −5.37620e10 | −1.61221 | ||||||||
\(219\) | −2.38929e10 | −0.701893 | ||||||||
\(220\) | 9.36647e9 | 0.269572 | ||||||||
\(221\) | 5.10274e9 | 0.143893 | ||||||||
\(222\) | −6.60707e10 | −1.82566 | ||||||||
\(223\) | 4.58529e10 | 1.24164 | 0.620819 | − | 0.783954i | \(-0.286800\pi\) | ||||
0.620819 | + | 0.783954i | \(0.286800\pi\) | |||||||
\(224\) | −1.37731e10 | −0.365523 | ||||||||
\(225\) | 4.16374e10 | 1.08308 | ||||||||
\(226\) | −8.49270e10 | −2.16550 | ||||||||
\(227\) | 3.66125e10 | 0.915194 | 0.457597 | − | 0.889160i | \(-0.348710\pi\) | ||||
0.457597 | + | 0.889160i | \(0.348710\pi\) | |||||||
\(228\) | 7.16076e10 | 1.75490 | ||||||||
\(229\) | −4.61194e10 | −1.10821 | −0.554107 | − | 0.832445i | \(-0.686940\pi\) | ||||
−0.554107 | + | 0.832445i | \(0.686940\pi\) | |||||||
\(230\) | −1.76036e11 | −4.14789 | ||||||||
\(231\) | 2.14867e9 | 0.0496495 | ||||||||
\(232\) | 4.85349e10 | 1.09991 | ||||||||
\(233\) | −7.71305e10 | −1.71445 | −0.857224 | − | 0.514943i | \(-0.827813\pi\) | ||||
−0.857224 | + | 0.514943i | \(0.827813\pi\) | |||||||
\(234\) | 1.37773e10 | 0.300395 | ||||||||
\(235\) | 1.19600e11 | 2.55814 | ||||||||
\(236\) | 1.36548e10 | 0.286536 | ||||||||
\(237\) | −8.63010e10 | −1.77684 | ||||||||
\(238\) | −1.57587e10 | −0.318363 | ||||||||
\(239\) | −6.91404e10 | −1.37070 | −0.685348 | − | 0.728216i | \(-0.740350\pi\) | ||||
−0.685348 | + | 0.728216i | \(0.740350\pi\) | |||||||
\(240\) | −4.32235e9 | −0.0840948 | ||||||||
\(241\) | 4.18522e10 | 0.799174 | 0.399587 | − | 0.916695i | \(-0.369154\pi\) | ||||
0.399587 | + | 0.916695i | \(0.369154\pi\) | |||||||
\(242\) | 8.57261e10 | 1.60673 | ||||||||
\(243\) | 6.24030e10 | 1.14809 | ||||||||
\(244\) | −1.00070e11 | −1.80737 | ||||||||
\(245\) | 1.30495e10 | 0.231390 | ||||||||
\(246\) | 5.36457e10 | 0.933957 | ||||||||
\(247\) | 1.34798e10 | 0.230435 | ||||||||
\(248\) | −2.37290e10 | −0.398333 | ||||||||
\(249\) | 1.64106e10 | 0.270537 | ||||||||
\(250\) | −1.01273e11 | −1.63969 | ||||||||
\(251\) | 8.40440e10 | 1.33652 | 0.668260 | − | 0.743928i | \(-0.267040\pi\) | ||||
0.668260 | + | 0.743928i | \(0.267040\pi\) | |||||||
\(252\) | −2.64062e10 | −0.412480 | ||||||||
\(253\) | 1.04579e10 | 0.160473 | ||||||||
\(254\) | −1.83072e11 | −2.75975 | ||||||||
\(255\) | 7.32600e10 | 1.08502 | ||||||||
\(256\) | −7.31287e10 | −1.06416 | ||||||||
\(257\) | −1.15453e11 | −1.65084 | −0.825419 | − | 0.564521i | \(-0.809061\pi\) | ||||
−0.825419 | + | 0.564521i | \(0.809061\pi\) | |||||||
\(258\) | −2.02718e11 | −2.84842 | ||||||||
\(259\) | 2.38383e10 | 0.329174 | ||||||||
\(260\) | −5.41504e10 | −0.734888 | ||||||||
\(261\) | −5.32855e10 | −0.710766 | ||||||||
\(262\) | 1.57523e11 | 2.06532 | ||||||||
\(263\) | −5.72660e10 | −0.738068 | −0.369034 | − | 0.929416i | \(-0.620311\pi\) | ||||
−0.369034 | + | 0.929416i | \(0.620311\pi\) | |||||||
\(264\) | 1.07032e10 | 0.135612 | ||||||||
\(265\) | −1.50605e10 | −0.187601 | ||||||||
\(266\) | −4.16294e10 | −0.509838 | ||||||||
\(267\) | 7.38298e9 | 0.0889060 | ||||||||
\(268\) | 1.70133e11 | 2.01457 | ||||||||
\(269\) | 5.92578e10 | 0.690018 | 0.345009 | − | 0.938599i | \(-0.387876\pi\) | ||||
0.345009 | + | 0.938599i | \(0.387876\pi\) | |||||||
\(270\) | −9.87001e10 | −1.13027 | ||||||||
\(271\) | −1.29346e10 | −0.145677 | −0.0728386 | − | 0.997344i | \(-0.523206\pi\) | ||||
−0.0728386 | + | 0.997344i | \(0.523206\pi\) | |||||||
\(272\) | −1.88327e9 | −0.0208619 | ||||||||
\(273\) | −1.24221e10 | −0.135351 | ||||||||
\(274\) | 8.00183e10 | 0.857654 | ||||||||
\(275\) | 1.56653e10 | 0.165174 | ||||||||
\(276\) | −3.21178e11 | −3.33162 | ||||||||
\(277\) | 8.86317e10 | 0.904545 | 0.452272 | − | 0.891880i | \(-0.350614\pi\) | ||||
0.452272 | + | 0.891880i | \(0.350614\pi\) | |||||||
\(278\) | 1.10385e11 | 1.10843 | ||||||||
\(279\) | 2.60515e10 | 0.257404 | ||||||||
\(280\) | 6.50038e10 | 0.632016 | ||||||||
\(281\) | 4.17541e10 | 0.399503 | 0.199752 | − | 0.979847i | \(-0.435986\pi\) | ||||
0.199752 | + | 0.979847i | \(0.435986\pi\) | |||||||
\(282\) | 3.51599e11 | 3.31076 | ||||||||
\(283\) | −8.52161e10 | −0.789737 | −0.394869 | − | 0.918738i | \(-0.629210\pi\) | ||||
−0.394869 | + | 0.918738i | \(0.629210\pi\) | |||||||
\(284\) | 3.86413e10 | 0.352467 | ||||||||
\(285\) | 1.93529e11 | 1.73758 | ||||||||
\(286\) | 5.18345e9 | 0.0458112 | ||||||||
\(287\) | −1.93554e10 | −0.168396 | ||||||||
\(288\) | 7.53237e10 | 0.645157 | ||||||||
\(289\) | −8.66681e10 | −0.730834 | ||||||||
\(290\) | 3.37459e11 | 2.80175 | ||||||||
\(291\) | 1.09168e11 | 0.892439 | ||||||||
\(292\) | 1.10474e11 | 0.889278 | ||||||||
\(293\) | −1.32163e10 | −0.104763 | −0.0523813 | − | 0.998627i | \(-0.516681\pi\) | ||||
−0.0523813 | + | 0.998627i | \(0.516681\pi\) | |||||||
\(294\) | 3.83628e10 | 0.299466 | ||||||||
\(295\) | 3.69039e10 | 0.283709 | ||||||||
\(296\) | 1.18747e11 | 0.899101 | ||||||||
\(297\) | 5.86354e9 | 0.0437276 | ||||||||
\(298\) | 4.17198e11 | 3.06456 | ||||||||
\(299\) | −6.04603e10 | −0.437472 | ||||||||
\(300\) | −4.81104e11 | −3.42920 | ||||||||
\(301\) | 7.31407e10 | 0.513582 | ||||||||
\(302\) | 3.47975e11 | 2.40723 | ||||||||
\(303\) | 2.27272e11 | 1.54901 | ||||||||
\(304\) | −4.97501e9 | −0.0334089 | ||||||||
\(305\) | −2.70452e11 | −1.78954 | ||||||||
\(306\) | 8.61828e10 | 0.561919 | ||||||||
\(307\) | −1.28224e11 | −0.823849 | −0.411925 | − | 0.911218i | \(-0.635143\pi\) | ||||
−0.411925 | + | 0.911218i | \(0.635143\pi\) | |||||||
\(308\) | −9.93482e9 | −0.0629045 | ||||||||
\(309\) | 7.39751e10 | 0.461607 | ||||||||
\(310\) | −1.64985e11 | −1.01465 | ||||||||
\(311\) | 1.32478e11 | 0.803011 | 0.401505 | − | 0.915857i | \(-0.368487\pi\) | ||||
0.401505 | + | 0.915857i | \(0.368487\pi\) | |||||||
\(312\) | −6.18786e10 | −0.369696 | ||||||||
\(313\) | 7.23487e10 | 0.426070 | 0.213035 | − | 0.977045i | \(-0.431665\pi\) | ||||
0.213035 | + | 0.977045i | \(0.431665\pi\) | |||||||
\(314\) | −2.51770e11 | −1.46157 | ||||||||
\(315\) | −7.13663e10 | −0.408409 | ||||||||
\(316\) | 3.99031e11 | 2.25121 | ||||||||
\(317\) | −1.28788e11 | −0.716320 | −0.358160 | − | 0.933660i | \(-0.616596\pi\) | ||||
−0.358160 | + | 0.933660i | \(0.616596\pi\) | |||||||
\(318\) | −4.42750e10 | −0.242793 | ||||||||
\(319\) | −2.00477e10 | −0.108394 | ||||||||
\(320\) | −4.89245e11 | −2.60826 | ||||||||
\(321\) | 3.41101e11 | 1.79312 | ||||||||
\(322\) | 1.86718e11 | 0.967911 | ||||||||
\(323\) | 8.43219e10 | 0.431052 | ||||||||
\(324\) | −3.96551e11 | −1.99916 | ||||||||
\(325\) | −9.05657e10 | −0.450286 | ||||||||
\(326\) | 2.13516e11 | 1.04701 | ||||||||
\(327\) | −2.65098e11 | −1.28216 | ||||||||
\(328\) | −9.64157e10 | −0.459955 | ||||||||
\(329\) | −1.26857e11 | −0.596943 | ||||||||
\(330\) | 7.44187e10 | 0.345437 | ||||||||
\(331\) | 8.71662e10 | 0.399137 | 0.199569 | − | 0.979884i | \(-0.436046\pi\) | ||||
0.199569 | + | 0.979884i | \(0.436046\pi\) | |||||||
\(332\) | −7.58779e10 | −0.342763 | ||||||||
\(333\) | −1.30369e11 | −0.581001 | ||||||||
\(334\) | 6.66391e10 | 0.293002 | ||||||||
\(335\) | 4.59808e11 | 1.99469 | ||||||||
\(336\) | 4.58463e9 | 0.0196235 | ||||||||
\(337\) | 2.73441e10 | 0.115486 | 0.0577430 | − | 0.998331i | \(-0.481610\pi\) | ||||
0.0577430 | + | 0.998331i | \(0.481610\pi\) | |||||||
\(338\) | −2.99671e10 | −0.124888 | ||||||||
\(339\) | −4.18771e11 | −1.72218 | ||||||||
\(340\) | −3.38733e11 | −1.37468 | ||||||||
\(341\) | 9.80141e9 | 0.0392549 | ||||||||
\(342\) | 2.27667e11 | 0.899878 | ||||||||
\(343\) | −1.38413e10 | −0.0539949 | ||||||||
\(344\) | 3.64339e11 | 1.40279 | ||||||||
\(345\) | −8.68028e11 | −3.29874 | ||||||||
\(346\) | 5.14582e11 | 1.93024 | ||||||||
\(347\) | 4.21270e11 | 1.55983 | 0.779916 | − | 0.625884i | \(-0.215262\pi\) | ||||
0.779916 | + | 0.625884i | \(0.215262\pi\) | |||||||
\(348\) | 6.15693e11 | 2.25039 | ||||||||
\(349\) | 6.84953e10 | 0.247142 | 0.123571 | − | 0.992336i | \(-0.460565\pi\) | ||||
0.123571 | + | 0.992336i | \(0.460565\pi\) | |||||||
\(350\) | 2.79692e11 | 0.996262 | ||||||||
\(351\) | −3.38989e10 | −0.119207 | ||||||||
\(352\) | 2.83391e10 | 0.0983885 | ||||||||
\(353\) | −3.33099e11 | −1.14179 | −0.570897 | − | 0.821022i | \(-0.693404\pi\) | ||||
−0.570897 | + | 0.821022i | \(0.693404\pi\) | |||||||
\(354\) | 1.08490e11 | 0.367177 | ||||||||
\(355\) | 1.04433e11 | 0.348989 | ||||||||
\(356\) | −3.41368e10 | −0.112641 | ||||||||
\(357\) | −7.77053e10 | −0.253188 | ||||||||
\(358\) | 3.37675e11 | 1.08649 | ||||||||
\(359\) | −4.87654e11 | −1.54948 | −0.774741 | − | 0.632279i | \(-0.782120\pi\) | ||||
−0.774741 | + | 0.632279i | \(0.782120\pi\) | |||||||
\(360\) | −3.55500e11 | −1.11552 | ||||||||
\(361\) | −9.99360e10 | −0.309699 | ||||||||
\(362\) | 9.21207e11 | 2.81948 | ||||||||
\(363\) | 4.22712e11 | 1.27780 | ||||||||
\(364\) | 5.74362e10 | 0.171486 | ||||||||
\(365\) | 2.98572e11 | 0.880503 | ||||||||
\(366\) | −7.95075e11 | −2.31603 | ||||||||
\(367\) | −3.97139e11 | −1.14273 | −0.571367 | − | 0.820694i | \(-0.693587\pi\) | ||||
−0.571367 | + | 0.820694i | \(0.693587\pi\) | |||||||
\(368\) | 2.23142e10 | 0.0634257 | ||||||||
\(369\) | 1.05853e11 | 0.297224 | ||||||||
\(370\) | 8.25635e11 | 2.29024 | ||||||||
\(371\) | 1.59744e10 | 0.0437766 | ||||||||
\(372\) | −3.01016e11 | −0.814978 | ||||||||
\(373\) | −2.70965e11 | −0.724810 | −0.362405 | − | 0.932021i | \(-0.618044\pi\) | ||||
−0.362405 | + | 0.932021i | \(0.618044\pi\) | |||||||
\(374\) | 3.24247e10 | 0.0856946 | ||||||||
\(375\) | −4.99372e11 | −1.30402 | ||||||||
\(376\) | −6.31918e11 | −1.63048 | ||||||||
\(377\) | 1.15901e11 | 0.295497 | ||||||||
\(378\) | 1.04689e11 | 0.263748 | ||||||||
\(379\) | −3.62277e11 | −0.901913 | −0.450957 | − | 0.892546i | \(-0.648917\pi\) | ||||
−0.450957 | + | 0.892546i | \(0.648917\pi\) | |||||||
\(380\) | −8.94826e11 | −2.20147 | ||||||||
\(381\) | −9.02719e11 | −2.19478 | ||||||||
\(382\) | −9.56757e11 | −2.29888 | ||||||||
\(383\) | −1.63326e11 | −0.387848 | −0.193924 | − | 0.981017i | \(-0.562121\pi\) | ||||
−0.193924 | + | 0.981017i | \(0.562121\pi\) | |||||||
\(384\) | −9.06251e11 | −2.12695 | ||||||||
\(385\) | −2.68502e10 | −0.0622838 | ||||||||
\(386\) | −1.25202e12 | −2.87057 | ||||||||
\(387\) | −4.00000e11 | −0.906485 | ||||||||
\(388\) | −5.04764e11 | −1.13069 | ||||||||
\(389\) | 4.37595e11 | 0.968945 | 0.484473 | − | 0.874806i | \(-0.339012\pi\) | ||||
0.484473 | + | 0.874806i | \(0.339012\pi\) | |||||||
\(390\) | −4.30237e11 | −0.941709 | ||||||||
\(391\) | −3.78205e11 | −0.818336 | ||||||||
\(392\) | −6.89482e10 | −0.147481 | ||||||||
\(393\) | 7.76739e11 | 1.64251 | ||||||||
\(394\) | 1.35881e12 | 2.84071 | ||||||||
\(395\) | 1.07844e12 | 2.22899 | ||||||||
\(396\) | 5.43327e10 | 0.111028 | ||||||||
\(397\) | −1.67915e11 | −0.339261 | −0.169630 | − | 0.985508i | \(-0.554257\pi\) | ||||
−0.169630 | + | 0.985508i | \(0.554257\pi\) | |||||||
\(398\) | 9.62251e11 | 1.92227 | ||||||||
\(399\) | −2.05273e11 | −0.405465 | ||||||||
\(400\) | 3.34252e10 | 0.0652835 | ||||||||
\(401\) | −4.53747e11 | −0.876322 | −0.438161 | − | 0.898897i | \(-0.644370\pi\) | ||||
−0.438161 | + | 0.898897i | \(0.644370\pi\) | |||||||
\(402\) | 1.35174e12 | 2.58153 | ||||||||
\(403\) | −5.66649e10 | −0.107014 | ||||||||
\(404\) | −1.05084e12 | −1.96255 | ||||||||
\(405\) | −1.07174e12 | −1.97943 | ||||||||
\(406\) | −3.57936e11 | −0.653790 | ||||||||
\(407\) | −4.90491e10 | −0.0886045 | ||||||||
\(408\) | −3.87077e11 | −0.691555 | ||||||||
\(409\) | 5.07750e11 | 0.897212 | 0.448606 | − | 0.893730i | \(-0.351921\pi\) | ||||
0.448606 | + | 0.893730i | \(0.351921\pi\) | |||||||
\(410\) | −6.70370e11 | −1.17162 | ||||||||
\(411\) | 3.94567e11 | 0.682076 | ||||||||
\(412\) | −3.42040e11 | −0.584843 | ||||||||
\(413\) | −3.91432e10 | −0.0662035 | ||||||||
\(414\) | −1.02115e12 | −1.70839 | ||||||||
\(415\) | −2.05071e11 | −0.339381 | ||||||||
\(416\) | −1.63837e11 | −0.268220 | ||||||||
\(417\) | 5.44304e11 | 0.881514 | ||||||||
\(418\) | 8.56556e10 | 0.137234 | ||||||||
\(419\) | 9.94618e11 | 1.57650 | 0.788249 | − | 0.615357i | \(-0.210988\pi\) | ||||
0.788249 | + | 0.615357i | \(0.210988\pi\) | |||||||
\(420\) | 8.24610e11 | 1.29308 | ||||||||
\(421\) | −4.38374e11 | −0.680104 | −0.340052 | − | 0.940407i | \(-0.610445\pi\) | ||||
−0.340052 | + | 0.940407i | \(0.610445\pi\) | |||||||
\(422\) | 5.21181e11 | 0.799986 | ||||||||
\(423\) | 6.93770e11 | 1.05362 | ||||||||
\(424\) | 7.95740e10 | 0.119571 | ||||||||
\(425\) | −5.66527e11 | −0.842307 | ||||||||
\(426\) | 3.07013e11 | 0.451663 | ||||||||
\(427\) | 2.86863e11 | 0.417589 | ||||||||
\(428\) | −1.57715e12 | −2.27184 | ||||||||
\(429\) | 2.55594e10 | 0.0364328 | ||||||||
\(430\) | 2.53322e12 | 3.57326 | ||||||||
\(431\) | −1.19861e12 | −1.67313 | −0.836566 | − | 0.547866i | \(-0.815440\pi\) | ||||
−0.836566 | + | 0.547866i | \(0.815440\pi\) | |||||||
\(432\) | 1.25111e10 | 0.0172830 | ||||||||
\(433\) | −6.29247e11 | −0.860251 | −0.430126 | − | 0.902769i | \(-0.641531\pi\) | ||||
−0.430126 | + | 0.902769i | \(0.641531\pi\) | |||||||
\(434\) | 1.74997e11 | 0.236770 | ||||||||
\(435\) | 1.66400e12 | 2.22818 | ||||||||
\(436\) | 1.22574e12 | 1.62446 | ||||||||
\(437\) | −9.99097e11 | −1.31051 | ||||||||
\(438\) | 8.77741e11 | 1.13955 | ||||||||
\(439\) | 8.66984e11 | 1.11409 | 0.557046 | − | 0.830482i | \(-0.311935\pi\) | ||||
0.557046 | + | 0.830482i | \(0.311935\pi\) | |||||||
\(440\) | −1.33750e11 | −0.170121 | ||||||||
\(441\) | 7.56968e10 | 0.0953024 | ||||||||
\(442\) | −1.87457e11 | −0.233615 | ||||||||
\(443\) | −2.63092e11 | −0.324557 | −0.162278 | − | 0.986745i | \(-0.551884\pi\) | ||||
−0.162278 | + | 0.986745i | \(0.551884\pi\) | |||||||
\(444\) | 1.50637e12 | 1.83953 | ||||||||
\(445\) | −9.22595e10 | −0.111530 | ||||||||
\(446\) | −1.68447e12 | −2.01585 | ||||||||
\(447\) | 2.05718e12 | 2.43719 | ||||||||
\(448\) | 5.18932e11 | 0.608638 | ||||||||
\(449\) | −5.64159e10 | −0.0655078 | −0.0327539 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327539 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(450\) | −1.52961e12 | −1.75843 | ||||||||
\(451\) | 3.98251e10 | 0.0453276 | ||||||||
\(452\) | 1.93628e12 | 2.18195 | ||||||||
\(453\) | 1.71585e12 | 1.91442 | ||||||||
\(454\) | −1.34501e12 | −1.48585 | ||||||||
\(455\) | 1.55229e11 | 0.169794 | ||||||||
\(456\) | −1.02253e12 | −1.10748 | ||||||||
\(457\) | 1.12328e12 | 1.20466 | 0.602331 | − | 0.798246i | \(-0.294239\pi\) | ||||
0.602331 | + | 0.798246i | \(0.294239\pi\) | |||||||
\(458\) | 1.69426e12 | 1.79923 | ||||||||
\(459\) | −2.12052e11 | −0.222990 | ||||||||
\(460\) | 4.01352e12 | 4.17941 | ||||||||
\(461\) | 2.95941e11 | 0.305177 | 0.152588 | − | 0.988290i | \(-0.451239\pi\) | ||||
0.152588 | + | 0.988290i | \(0.451239\pi\) | |||||||
\(462\) | −7.89344e10 | −0.0806078 | ||||||||
\(463\) | −1.64043e12 | −1.65899 | −0.829494 | − | 0.558516i | \(-0.811371\pi\) | ||||
−0.829494 | + | 0.558516i | \(0.811371\pi\) | |||||||
\(464\) | −4.27759e10 | −0.0428418 | ||||||||
\(465\) | −8.13537e11 | −0.806935 | ||||||||
\(466\) | 2.83350e12 | 2.78347 | ||||||||
\(467\) | −1.15569e12 | −1.12438 | −0.562192 | − | 0.827007i | \(-0.690042\pi\) | ||||
−0.562192 | + | 0.827007i | \(0.690042\pi\) | |||||||
\(468\) | −3.14113e11 | −0.302677 | ||||||||
\(469\) | −4.87709e11 | −0.465460 | ||||||||
\(470\) | −4.39367e12 | −4.15324 | ||||||||
\(471\) | −1.24147e12 | −1.16236 | ||||||||
\(472\) | −1.94986e11 | −0.180827 | ||||||||
\(473\) | −1.50493e11 | −0.138242 | ||||||||
\(474\) | 3.17039e12 | 2.88477 | ||||||||
\(475\) | −1.49658e12 | −1.34890 | ||||||||
\(476\) | 3.59288e11 | 0.320783 | ||||||||
\(477\) | −8.73626e10 | −0.0772668 | ||||||||
\(478\) | 2.53997e12 | 2.22538 | ||||||||
\(479\) | −1.87129e12 | −1.62417 | −0.812083 | − | 0.583542i | \(-0.801666\pi\) | ||||
−0.812083 | + | 0.583542i | \(0.801666\pi\) | |||||||
\(480\) | −2.35220e12 | −2.02250 | ||||||||
\(481\) | 2.83567e11 | 0.241548 | ||||||||
\(482\) | −1.53750e12 | −1.29749 | ||||||||
\(483\) | 9.20700e11 | 0.769761 | ||||||||
\(484\) | −1.95450e12 | −1.61894 | ||||||||
\(485\) | −1.36419e12 | −1.11954 | ||||||||
\(486\) | −2.29246e12 | −1.86397 | ||||||||
\(487\) | −9.21564e11 | −0.742412 | −0.371206 | − | 0.928551i | \(-0.621056\pi\) | ||||
−0.371206 | + | 0.928551i | \(0.621056\pi\) | |||||||
\(488\) | 1.42896e12 | 1.14060 | ||||||||
\(489\) | 1.05284e12 | 0.832670 | ||||||||
\(490\) | −4.79391e11 | −0.375671 | ||||||||
\(491\) | −1.40709e12 | −1.09259 | −0.546294 | − | 0.837593i | \(-0.683962\pi\) | ||||
−0.546294 | + | 0.837593i | \(0.683962\pi\) | |||||||
\(492\) | −1.22309e12 | −0.941054 | ||||||||
\(493\) | 7.25013e11 | 0.552757 | ||||||||
\(494\) | −4.95201e11 | −0.374119 | ||||||||
\(495\) | 1.46842e11 | 0.109932 | ||||||||
\(496\) | 2.09133e10 | 0.0155152 | ||||||||
\(497\) | −1.10770e11 | −0.0814366 | ||||||||
\(498\) | −6.02867e11 | −0.439227 | ||||||||
\(499\) | 4.85195e11 | 0.350319 | 0.175160 | − | 0.984540i | \(-0.443956\pi\) | ||||
0.175160 | + | 0.984540i | \(0.443956\pi\) | |||||||
\(500\) | 2.30895e12 | 1.65215 | ||||||||
\(501\) | 3.28595e11 | 0.233019 | ||||||||
\(502\) | −3.08748e12 | −2.16989 | ||||||||
\(503\) | 2.20742e12 | 1.53755 | 0.768776 | − | 0.639518i | \(-0.220866\pi\) | ||||
0.768776 | + | 0.639518i | \(0.220866\pi\) | |||||||
\(504\) | 3.77072e11 | 0.260307 | ||||||||
\(505\) | −2.84005e12 | −1.94319 | ||||||||
\(506\) | −3.84187e11 | −0.260535 | ||||||||
\(507\) | −1.47766e11 | −0.0993207 | ||||||||
\(508\) | 4.17392e12 | 2.78072 | ||||||||
\(509\) | −8.18353e11 | −0.540394 | −0.270197 | − | 0.962805i | \(-0.587089\pi\) | ||||
−0.270197 | + | 0.962805i | \(0.587089\pi\) | |||||||
\(510\) | −2.69131e12 | −1.76156 | ||||||||
\(511\) | −3.16689e11 | −0.205465 | ||||||||
\(512\) | 1.25017e11 | 0.0803995 | ||||||||
\(513\) | −5.60173e11 | −0.357104 | ||||||||
\(514\) | 4.24132e12 | 2.68020 | ||||||||
\(515\) | −9.24411e11 | −0.579072 | ||||||||
\(516\) | 4.62185e12 | 2.87007 | ||||||||
\(517\) | 2.61018e11 | 0.160680 | ||||||||
\(518\) | −8.75734e11 | −0.534427 | ||||||||
\(519\) | 2.53738e12 | 1.53509 | ||||||||
\(520\) | 7.73250e11 | 0.463773 | ||||||||
\(521\) | 7.25289e10 | 0.0431262 | 0.0215631 | − | 0.999767i | \(-0.493136\pi\) | ||||
0.0215631 | + | 0.999767i | \(0.493136\pi\) | |||||||
\(522\) | 1.95752e12 | 1.15395 | ||||||||
\(523\) | 5.08349e11 | 0.297101 | 0.148551 | − | 0.988905i | \(-0.452539\pi\) | ||||
0.148551 | + | 0.988905i | \(0.452539\pi\) | |||||||
\(524\) | −3.59142e12 | −2.08102 | ||||||||
\(525\) | 1.37915e12 | 0.792308 | ||||||||
\(526\) | 2.10375e12 | 1.19828 | ||||||||
\(527\) | −3.54463e11 | −0.200181 | ||||||||
\(528\) | −9.43322e9 | −0.00528211 | ||||||||
\(529\) | 2.68005e12 | 1.48796 | ||||||||
\(530\) | 5.53271e11 | 0.304577 | ||||||||
\(531\) | 2.14071e11 | 0.116851 | ||||||||
\(532\) | 9.49123e11 | 0.513713 | ||||||||
\(533\) | −2.30241e11 | −0.123569 | ||||||||
\(534\) | −2.71225e11 | −0.144342 | ||||||||
\(535\) | −4.26248e12 | −2.24942 | ||||||||
\(536\) | −2.42945e12 | −1.27135 | ||||||||
\(537\) | 1.66506e12 | 0.864064 | ||||||||
\(538\) | −2.17692e12 | −1.12027 | ||||||||
\(539\) | 2.84795e10 | 0.0145339 | ||||||||
\(540\) | 2.25030e12 | 1.13885 | ||||||||
\(541\) | 1.12944e12 | 0.566860 | 0.283430 | − | 0.958993i | \(-0.408528\pi\) | ||||
0.283430 | + | 0.958993i | \(0.408528\pi\) | |||||||
\(542\) | 4.75172e11 | 0.236512 | ||||||||
\(543\) | 4.54243e12 | 2.24228 | ||||||||
\(544\) | −1.02487e12 | −0.501734 | ||||||||
\(545\) | 3.31273e12 | 1.60843 | ||||||||
\(546\) | 4.56343e11 | 0.219748 | ||||||||
\(547\) | −1.88876e12 | −0.902056 | −0.451028 | − | 0.892510i | \(-0.648942\pi\) | ||||
−0.451028 | + | 0.892510i | \(0.648942\pi\) | |||||||
\(548\) | −1.82437e12 | −0.864171 | ||||||||
\(549\) | −1.56883e12 | −0.737055 | ||||||||
\(550\) | −5.75487e11 | −0.268166 | ||||||||
\(551\) | 1.91525e12 | 0.885205 | ||||||||
\(552\) | 4.58632e12 | 2.10251 | ||||||||
\(553\) | −1.14388e12 | −0.520135 | ||||||||
\(554\) | −3.25601e12 | −1.46856 | ||||||||
\(555\) | 4.07117e12 | 1.82138 | ||||||||
\(556\) | −2.51671e12 | −1.11685 | ||||||||
\(557\) | 4.55848e11 | 0.200665 | 0.100333 | − | 0.994954i | \(-0.468009\pi\) | ||||
0.100333 | + | 0.994954i | \(0.468009\pi\) | |||||||
\(558\) | −9.57042e11 | −0.417904 | ||||||||
\(559\) | 8.70042e11 | 0.376866 | ||||||||
\(560\) | −5.72906e10 | −0.0246171 | ||||||||
\(561\) | 1.59885e11 | 0.0681513 | ||||||||
\(562\) | −1.53390e12 | −0.648609 | ||||||||
\(563\) | 4.13409e12 | 1.73417 | 0.867085 | − | 0.498160i | \(-0.165991\pi\) | ||||
0.867085 | + | 0.498160i | \(0.165991\pi\) | |||||||
\(564\) | −8.01624e12 | −3.33591 | ||||||||
\(565\) | 5.23307e12 | 2.16042 | ||||||||
\(566\) | 3.13054e12 | 1.28217 | ||||||||
\(567\) | 1.13677e12 | 0.461900 | ||||||||
\(568\) | −5.51785e11 | −0.222435 | ||||||||
\(569\) | 4.08880e12 | 1.63528 | 0.817638 | − | 0.575733i | \(-0.195283\pi\) | ||||
0.817638 | + | 0.575733i | \(0.195283\pi\) | |||||||
\(570\) | −7.10959e12 | −2.82103 | ||||||||
\(571\) | −4.29824e12 | −1.69211 | −0.846055 | − | 0.533096i | \(-0.821028\pi\) | ||||
−0.846055 | + | 0.533096i | \(0.821028\pi\) | |||||||
\(572\) | −1.18179e11 | −0.0461593 | ||||||||
\(573\) | −4.71773e12 | −1.82826 | ||||||||
\(574\) | 7.11047e11 | 0.273398 | ||||||||
\(575\) | 6.71255e12 | 2.56084 | ||||||||
\(576\) | −2.83799e12 | −1.07426 | ||||||||
\(577\) | −1.59653e12 | −0.599634 | −0.299817 | − | 0.953997i | \(-0.596926\pi\) | ||||
−0.299817 | + | 0.953997i | \(0.596926\pi\) | |||||||
\(578\) | 3.18388e12 | 1.18654 | ||||||||
\(579\) | −6.17366e12 | −2.28291 | ||||||||
\(580\) | −7.69385e12 | −2.82304 | ||||||||
\(581\) | 2.17514e11 | 0.0791945 | ||||||||
\(582\) | −4.01046e12 | −1.44891 | ||||||||
\(583\) | −3.28685e10 | −0.0117834 | ||||||||
\(584\) | −1.57754e12 | −0.561205 | ||||||||
\(585\) | −8.48935e11 | −0.299691 | ||||||||
\(586\) | 4.85521e11 | 0.170086 | ||||||||
\(587\) | −3.18350e11 | −0.110671 | −0.0553354 | − | 0.998468i | \(-0.517623\pi\) | ||||
−0.0553354 | + | 0.998468i | \(0.517623\pi\) | |||||||
\(588\) | −8.74647e11 | −0.301741 | ||||||||
\(589\) | −9.36377e11 | −0.320577 | ||||||||
\(590\) | −1.35572e12 | −0.460612 | ||||||||
\(591\) | 6.70025e12 | 2.25916 | ||||||||
\(592\) | −1.04656e11 | −0.0350202 | ||||||||
\(593\) | 5.02708e12 | 1.66944 | 0.834718 | − | 0.550678i | \(-0.185631\pi\) | ||||
0.834718 | + | 0.550678i | \(0.185631\pi\) | |||||||
\(594\) | −2.15406e11 | −0.0709935 | ||||||||
\(595\) | 9.71025e11 | 0.317617 | ||||||||
\(596\) | −9.51184e12 | −3.08785 | ||||||||
\(597\) | 4.74482e12 | 1.52875 | ||||||||
\(598\) | 2.22110e12 | 0.710252 | ||||||||
\(599\) | −3.37361e11 | −0.107072 | −0.0535358 | − | 0.998566i | \(-0.517049\pi\) | ||||
−0.0535358 | + | 0.998566i | \(0.517049\pi\) | |||||||
\(600\) | 6.87002e12 | 2.16410 | ||||||||
\(601\) | −1.88701e12 | −0.589984 | −0.294992 | − | 0.955500i | \(-0.595317\pi\) | ||||
−0.294992 | + | 0.955500i | \(0.595317\pi\) | |||||||
\(602\) | −2.68693e12 | −0.833820 | ||||||||
\(603\) | 2.66724e12 | 0.821549 | ||||||||
\(604\) | −7.93362e12 | −2.42552 | ||||||||
\(605\) | −5.28231e12 | −1.60297 | ||||||||
\(606\) | −8.34918e12 | −2.51488 | ||||||||
\(607\) | −6.92739e11 | −0.207119 | −0.103560 | − | 0.994623i | \(-0.533023\pi\) | ||||
−0.103560 | + | 0.994623i | \(0.533023\pi\) | |||||||
\(608\) | −2.70738e12 | −0.803494 | ||||||||
\(609\) | −1.76497e12 | −0.519946 | ||||||||
\(610\) | 9.93545e12 | 2.90538 | ||||||||
\(611\) | −1.50902e12 | −0.438036 | ||||||||
\(612\) | −1.96491e12 | −0.566189 | ||||||||
\(613\) | 3.82623e12 | 1.09446 | 0.547229 | − | 0.836983i | \(-0.315683\pi\) | ||||
0.547229 | + | 0.836983i | \(0.315683\pi\) | |||||||
\(614\) | 4.71051e12 | 1.33755 | ||||||||
\(615\) | −3.30556e12 | −0.931768 | ||||||||
\(616\) | 1.41866e11 | 0.0396977 | ||||||||
\(617\) | −4.74746e12 | −1.31880 | −0.659399 | − | 0.751793i | \(-0.729189\pi\) | ||||
−0.659399 | + | 0.751793i | \(0.729189\pi\) | |||||||
\(618\) | −2.71759e12 | −0.749437 | ||||||||
\(619\) | 4.54492e12 | 1.24428 | 0.622140 | − | 0.782906i | \(-0.286264\pi\) | ||||
0.622140 | + | 0.782906i | \(0.286264\pi\) | |||||||
\(620\) | 3.76156e12 | 1.02236 | ||||||||
\(621\) | 2.51252e12 | 0.677949 | ||||||||
\(622\) | −4.86677e12 | −1.30372 | ||||||||
\(623\) | 9.78578e10 | 0.0260255 | ||||||||
\(624\) | 5.45362e10 | 0.0143997 | ||||||||
\(625\) | 4.69957e10 | 0.0123197 | ||||||||
\(626\) | −2.65784e12 | −0.691741 | ||||||||
\(627\) | 4.22364e11 | 0.109140 | ||||||||
\(628\) | 5.74020e12 | 1.47268 | ||||||||
\(629\) | 1.77383e12 | 0.451840 | ||||||||
\(630\) | 2.62175e12 | 0.663068 | ||||||||
\(631\) | 2.30717e12 | 0.579358 | 0.289679 | − | 0.957124i | \(-0.406452\pi\) | ||||
0.289679 | + | 0.957124i | \(0.406452\pi\) | |||||||
\(632\) | −5.69805e12 | −1.42069 | ||||||||
\(633\) | 2.56992e12 | 0.636214 | ||||||||
\(634\) | 4.73120e12 | 1.16297 | ||||||||
\(635\) | 1.12806e13 | 2.75328 | ||||||||
\(636\) | 1.00944e12 | 0.244638 | ||||||||
\(637\) | −1.64648e11 | −0.0396214 | ||||||||
\(638\) | 7.36480e11 | 0.175982 | ||||||||
\(639\) | 6.05793e11 | 0.143738 | ||||||||
\(640\) | 1.13247e13 | 2.66820 | ||||||||
\(641\) | −4.20974e12 | −0.984904 | −0.492452 | − | 0.870340i | \(-0.663899\pi\) | ||||
−0.492452 | + | 0.870340i | \(0.663899\pi\) | |||||||
\(642\) | −1.25308e13 | −2.91120 | ||||||||
\(643\) | −5.26829e12 | −1.21540 | −0.607702 | − | 0.794165i | \(-0.707908\pi\) | ||||
−0.607702 | + | 0.794165i | \(0.707908\pi\) | |||||||
\(644\) | −4.25706e12 | −0.975266 | ||||||||
\(645\) | 1.24912e13 | 2.84174 | ||||||||
\(646\) | −3.09769e12 | −0.699828 | ||||||||
\(647\) | 4.94062e12 | 1.10844 | 0.554220 | − | 0.832370i | \(-0.313017\pi\) | ||||
0.554220 | + | 0.832370i | \(0.313017\pi\) | |||||||
\(648\) | 5.66263e12 | 1.26163 | ||||||||
\(649\) | 8.05401e10 | 0.0178201 | ||||||||
\(650\) | 3.32706e12 | 0.731057 | ||||||||
\(651\) | 8.62901e11 | 0.188298 | ||||||||
\(652\) | −4.86804e12 | −1.05497 | ||||||||
\(653\) | −1.05701e12 | −0.227494 | −0.113747 | − | 0.993510i | \(-0.536285\pi\) | ||||
−0.113747 | + | 0.993510i | \(0.536285\pi\) | |||||||
\(654\) | 9.73877e12 | 2.08163 | ||||||||
\(655\) | −9.70631e12 | −2.06048 | ||||||||
\(656\) | 8.49752e10 | 0.0179153 | ||||||||
\(657\) | 1.73194e12 | 0.362652 | ||||||||
\(658\) | 4.66028e12 | 0.969159 | ||||||||
\(659\) | −6.19800e12 | −1.28017 | −0.640084 | − | 0.768305i | \(-0.721100\pi\) | ||||
−0.640084 | + | 0.768305i | \(0.721100\pi\) | |||||||
\(660\) | −1.69670e12 | −0.348062 | ||||||||
\(661\) | −3.53191e12 | −0.719619 | −0.359810 | − | 0.933026i | \(-0.617158\pi\) | ||||
−0.359810 | + | 0.933026i | \(0.617158\pi\) | |||||||
\(662\) | −3.20218e12 | −0.648014 | ||||||||
\(663\) | −9.24341e11 | −0.185790 | ||||||||
\(664\) | 1.08351e12 | 0.216311 | ||||||||
\(665\) | 2.56514e12 | 0.508643 | ||||||||
\(666\) | 4.78931e12 | 0.943277 | ||||||||
\(667\) | −8.59039e12 | −1.68053 | ||||||||
\(668\) | −1.51933e12 | −0.295228 | ||||||||
\(669\) | −8.30607e12 | −1.60316 | ||||||||
\(670\) | −1.68917e13 | −3.23845 | ||||||||
\(671\) | −5.90242e11 | −0.112403 | ||||||||
\(672\) | 2.49493e12 | 0.471952 | ||||||||
\(673\) | −1.03450e12 | −0.194384 | −0.0971922 | − | 0.995266i | \(-0.530986\pi\) | ||||
−0.0971922 | + | 0.995266i | \(0.530986\pi\) | |||||||
\(674\) | −1.00453e12 | −0.187496 | ||||||||
\(675\) | 3.76359e12 | 0.697807 | ||||||||
\(676\) | 6.83230e11 | 0.125836 | ||||||||
\(677\) | 3.37289e12 | 0.617097 | 0.308548 | − | 0.951209i | \(-0.400157\pi\) | ||||
0.308548 | + | 0.951209i | \(0.400157\pi\) | |||||||
\(678\) | 1.53842e13 | 2.79602 | ||||||||
\(679\) | 1.44697e12 | 0.261244 | ||||||||
\(680\) | 4.83701e12 | 0.867534 | ||||||||
\(681\) | −6.63221e12 | −1.18167 | ||||||||
\(682\) | −3.60069e11 | −0.0637318 | ||||||||
\(683\) | −8.33511e12 | −1.46561 | −0.732804 | − | 0.680439i | \(-0.761789\pi\) | ||||
−0.732804 | + | 0.680439i | \(0.761789\pi\) | |||||||
\(684\) | −5.19067e12 | −0.906715 | ||||||||
\(685\) | −4.93060e12 | −0.855643 | ||||||||
\(686\) | 5.08480e11 | 0.0876628 | ||||||||
\(687\) | 8.35434e12 | 1.43089 | ||||||||
\(688\) | −3.21107e11 | −0.0546389 | ||||||||
\(689\) | 1.90023e11 | 0.0321232 | ||||||||
\(690\) | 3.18883e13 | 5.35563 | ||||||||
\(691\) | −7.68704e12 | −1.28265 | −0.641325 | − | 0.767270i | \(-0.721615\pi\) | ||||
−0.641325 | + | 0.767270i | \(0.721615\pi\) | |||||||
\(692\) | −1.17321e13 | −1.94491 | ||||||||
\(693\) | −1.55752e11 | −0.0256527 | ||||||||
\(694\) | −1.54760e13 | −2.53245 | ||||||||
\(695\) | −6.80176e12 | −1.10583 | ||||||||
\(696\) | −8.79191e12 | −1.42017 | ||||||||
\(697\) | −1.44025e12 | −0.231149 | ||||||||
\(698\) | −2.51628e12 | −0.401244 | ||||||||
\(699\) | 1.39719e13 | 2.21364 | ||||||||
\(700\) | −6.37680e12 | −1.00383 | ||||||||
\(701\) | −5.32226e12 | −0.832463 | −0.416231 | − | 0.909259i | \(-0.636649\pi\) | ||||
−0.416231 | + | 0.909259i | \(0.636649\pi\) | |||||||
\(702\) | 1.24533e12 | 0.193538 | ||||||||
\(703\) | 4.68590e12 | 0.723593 | ||||||||
\(704\) | −1.06774e12 | −0.163828 | ||||||||
\(705\) | −2.16650e13 | −3.30299 | ||||||||
\(706\) | 1.22369e13 | 1.85374 | ||||||||
\(707\) | 3.01238e12 | 0.453443 | ||||||||
\(708\) | −2.47350e12 | −0.369967 | ||||||||
\(709\) | 2.56286e11 | 0.0380906 | 0.0190453 | − | 0.999819i | \(-0.493937\pi\) | ||||
0.0190453 | + | 0.999819i | \(0.493937\pi\) | |||||||
\(710\) | −3.83651e12 | −0.566597 | ||||||||
\(711\) | 6.25576e12 | 0.918052 | ||||||||
\(712\) | 4.87463e11 | 0.0710857 | ||||||||
\(713\) | 4.19989e12 | 0.608604 | ||||||||
\(714\) | 2.85462e12 | 0.411061 | ||||||||
\(715\) | −3.19396e11 | −0.0457038 | ||||||||
\(716\) | −7.69877e12 | −1.09474 | ||||||||
\(717\) | 1.25245e13 | 1.76980 | ||||||||
\(718\) | 1.79147e13 | 2.51564 | ||||||||
\(719\) | −6.49502e11 | −0.0906360 | −0.0453180 | − | 0.998973i | \(-0.514430\pi\) | ||||
−0.0453180 | + | 0.998973i | \(0.514430\pi\) | |||||||
\(720\) | 3.13317e11 | 0.0434498 | ||||||||
\(721\) | 9.80504e11 | 0.135127 | ||||||||
\(722\) | 3.67130e12 | 0.502808 | ||||||||
\(723\) | −7.58135e12 | −1.03187 | ||||||||
\(724\) | −2.10029e13 | −2.84090 | ||||||||
\(725\) | −1.28679e13 | −1.72976 | ||||||||
\(726\) | −1.55289e13 | −2.07456 | ||||||||
\(727\) | 7.29457e12 | 0.968490 | 0.484245 | − | 0.874933i | \(-0.339094\pi\) | ||||
0.484245 | + | 0.874933i | \(0.339094\pi\) | |||||||
\(728\) | −8.20171e11 | −0.108221 | ||||||||
\(729\) | −1.98501e12 | −0.260309 | ||||||||
\(730\) | −1.09685e13 | −1.42953 | ||||||||
\(731\) | 5.44248e12 | 0.704967 | ||||||||
\(732\) | 1.81272e13 | 2.33362 | ||||||||
\(733\) | −1.04087e13 | −1.33176 | −0.665882 | − | 0.746057i | \(-0.731945\pi\) | ||||
−0.665882 | + | 0.746057i | \(0.731945\pi\) | |||||||
\(734\) | 1.45895e13 | 1.85527 | ||||||||
\(735\) | −2.36386e12 | −0.298764 | ||||||||
\(736\) | 1.21433e13 | 1.52541 | ||||||||
\(737\) | 1.00350e12 | 0.125289 | ||||||||
\(738\) | −3.88865e12 | −0.482554 | ||||||||
\(739\) | −5.49183e12 | −0.677356 | −0.338678 | − | 0.940902i | \(-0.609980\pi\) | ||||
−0.338678 | + | 0.940902i | \(0.609980\pi\) | |||||||
\(740\) | −1.88239e13 | −2.30764 | ||||||||
\(741\) | −2.44181e12 | −0.297530 | ||||||||
\(742\) | −5.86843e11 | −0.0710730 | ||||||||
\(743\) | 3.40388e12 | 0.409755 | 0.204878 | − | 0.978788i | \(-0.434320\pi\) | ||||
0.204878 | + | 0.978788i | \(0.434320\pi\) | |||||||
\(744\) | 4.29841e12 | 0.514315 | ||||||||
\(745\) | −2.57071e13 | −3.05738 | ||||||||
\(746\) | 9.95431e12 | 1.17676 | ||||||||
\(747\) | −1.18957e12 | −0.139780 | ||||||||
\(748\) | −7.39261e11 | −0.0863457 | ||||||||
\(749\) | 4.52112e12 | 0.524902 | ||||||||
\(750\) | 1.83452e13 | 2.11712 | ||||||||
\(751\) | 1.41818e13 | 1.62687 | 0.813435 | − | 0.581656i | \(-0.197595\pi\) | ||||
0.813435 | + | 0.581656i | \(0.197595\pi\) | |||||||
\(752\) | 5.56936e11 | 0.0635075 | ||||||||
\(753\) | −1.52242e13 | −1.72567 | ||||||||
\(754\) | −4.25781e12 | −0.479750 | ||||||||
\(755\) | −2.14417e13 | −2.40159 | ||||||||
\(756\) | −2.38684e12 | −0.265752 | ||||||||
\(757\) | 1.30639e13 | 1.44591 | 0.722953 | − | 0.690897i | \(-0.242784\pi\) | ||||
0.722953 | + | 0.690897i | \(0.242784\pi\) | |||||||
\(758\) | 1.33088e13 | 1.46429 | ||||||||
\(759\) | −1.89441e12 | −0.207198 | ||||||||
\(760\) | 1.27778e13 | 1.38930 | ||||||||
\(761\) | −3.27918e12 | −0.354433 | −0.177216 | − | 0.984172i | \(-0.556709\pi\) | ||||
−0.177216 | + | 0.984172i | \(0.556709\pi\) | |||||||
\(762\) | 3.31627e13 | 3.56330 | ||||||||
\(763\) | −3.51375e12 | −0.375327 | ||||||||
\(764\) | 2.18134e13 | 2.31635 | ||||||||
\(765\) | −5.31045e12 | −0.560602 | ||||||||
\(766\) | 6.00003e12 | 0.629685 | ||||||||
\(767\) | −4.65626e11 | −0.0485801 | ||||||||
\(768\) | 1.32470e13 | 1.37401 | ||||||||
\(769\) | −1.98573e12 | −0.204763 | −0.102382 | − | 0.994745i | \(-0.532646\pi\) | ||||
−0.102382 | + | 0.994745i | \(0.532646\pi\) | |||||||
\(770\) | 9.86383e11 | 0.101120 | ||||||||
\(771\) | 2.09138e13 | 2.13151 | ||||||||
\(772\) | 2.85453e13 | 2.89239 | ||||||||
\(773\) | 1.71094e13 | 1.72357 | 0.861783 | − | 0.507277i | \(-0.169348\pi\) | ||||
0.861783 | + | 0.507277i | \(0.169348\pi\) | |||||||
\(774\) | 1.46946e13 | 1.47171 | ||||||||
\(775\) | 6.29116e12 | 0.626431 | ||||||||
\(776\) | 7.20787e12 | 0.713558 | ||||||||
\(777\) | −4.31821e12 | −0.425020 | ||||||||
\(778\) | −1.60757e13 | −1.57312 | ||||||||
\(779\) | −3.80469e12 | −0.370170 | ||||||||
\(780\) | 9.80912e12 | 0.948865 | ||||||||
\(781\) | 2.27918e11 | 0.0219205 | ||||||||
\(782\) | 1.38939e13 | 1.32860 | ||||||||
\(783\) | −4.81646e12 | −0.457931 | ||||||||
\(784\) | 6.07670e10 | 0.00574441 | ||||||||
\(785\) | 1.55137e13 | 1.45815 | ||||||||
\(786\) | −2.85346e13 | −2.66668 | ||||||||
\(787\) | 8.64917e12 | 0.803689 | 0.401845 | − | 0.915708i | \(-0.368369\pi\) | ||||
0.401845 | + | 0.915708i | \(0.368369\pi\) | |||||||
\(788\) | −3.09800e13 | −2.86229 | ||||||||
\(789\) | 1.03735e13 | 0.952970 | ||||||||
\(790\) | −3.96180e13 | −3.61885 | ||||||||
\(791\) | −5.55061e12 | −0.504135 | ||||||||
\(792\) | −7.75854e11 | −0.0700675 | ||||||||
\(793\) | 3.41237e12 | 0.306427 | ||||||||
\(794\) | 6.16862e12 | 0.550802 | ||||||||
\(795\) | 2.72816e12 | 0.242224 | ||||||||
\(796\) | −2.19387e13 | −1.93688 | ||||||||
\(797\) | 5.72954e12 | 0.502988 | 0.251494 | − | 0.967859i | \(-0.419078\pi\) | ||||
0.251494 | + | 0.967859i | \(0.419078\pi\) | |||||||
\(798\) | 7.54099e12 | 0.658288 | ||||||||
\(799\) | −9.43957e12 | −0.819392 | ||||||||
\(800\) | 1.81898e13 | 1.57009 | ||||||||
\(801\) | −5.35176e11 | −0.0459357 | ||||||||
\(802\) | 1.66690e13 | 1.42274 | ||||||||
\(803\) | 6.51611e11 | 0.0553056 | ||||||||
\(804\) | −3.08189e13 | −2.60115 | ||||||||
\(805\) | −1.15053e13 | −0.965642 | ||||||||
\(806\) | 2.08167e12 | 0.173741 | ||||||||
\(807\) | −1.07343e13 | −0.890930 | ||||||||
\(808\) | 1.50057e13 | 1.23853 | ||||||||
\(809\) | −3.18891e12 | −0.261743 | −0.130871 | − | 0.991399i | \(-0.541777\pi\) | ||||
−0.130871 | + | 0.991399i | \(0.541777\pi\) | |||||||
\(810\) | 3.93718e13 | 3.21368 | ||||||||
\(811\) | 7.19763e12 | 0.584246 | 0.292123 | − | 0.956381i | \(-0.405638\pi\) | ||||
0.292123 | + | 0.956381i | \(0.405638\pi\) | |||||||
\(812\) | 8.16071e12 | 0.658758 | ||||||||
\(813\) | 2.34305e12 | 0.188094 | ||||||||
\(814\) | 1.80189e12 | 0.143853 | ||||||||
\(815\) | −1.31566e13 | −1.04456 | ||||||||
\(816\) | 3.41147e11 | 0.0269362 | ||||||||
\(817\) | 1.43773e13 | 1.12896 | ||||||||
\(818\) | −1.86529e13 | −1.45666 | ||||||||
\(819\) | 9.00448e11 | 0.0699328 | ||||||||
\(820\) | 1.52840e13 | 1.18052 | ||||||||
\(821\) | 1.43670e13 | 1.10362 | 0.551812 | − | 0.833968i | \(-0.313937\pi\) | ||||
0.551812 | + | 0.833968i | \(0.313937\pi\) | |||||||
\(822\) | −1.44950e13 | −1.10738 | ||||||||
\(823\) | −4.72106e12 | −0.358707 | −0.179354 | − | 0.983785i | \(-0.557401\pi\) | ||||
−0.179354 | + | 0.983785i | \(0.557401\pi\) | |||||||
\(824\) | 4.88423e12 | 0.369082 | ||||||||
\(825\) | −2.83770e12 | −0.213267 | ||||||||
\(826\) | 1.43798e12 | 0.107484 | ||||||||
\(827\) | 6.76103e12 | 0.502618 | 0.251309 | − | 0.967907i | \(-0.419139\pi\) | ||||
0.251309 | + | 0.967907i | \(0.419139\pi\) | |||||||
\(828\) | 2.32815e13 | 1.72137 | ||||||||
\(829\) | 2.09255e13 | 1.53880 | 0.769398 | − | 0.638770i | \(-0.220556\pi\) | ||||
0.769398 | + | 0.638770i | \(0.220556\pi\) | |||||||
\(830\) | 7.53357e12 | 0.550997 | ||||||||
\(831\) | −1.60553e13 | −1.16792 | ||||||||
\(832\) | 6.17293e12 | 0.446618 | ||||||||
\(833\) | −1.02995e12 | −0.0741160 | ||||||||
\(834\) | −1.99958e13 | −1.43117 | ||||||||
\(835\) | −4.10620e12 | −0.292315 | ||||||||
\(836\) | −1.95289e12 | −0.138277 | ||||||||
\(837\) | 2.35479e12 | 0.165839 | ||||||||
\(838\) | −3.65388e13 | −2.55950 | ||||||||
\(839\) | −8.97849e12 | −0.625568 | −0.312784 | − | 0.949824i | \(-0.601262\pi\) | ||||
−0.312784 | + | 0.949824i | \(0.601262\pi\) | |||||||
\(840\) | −1.17752e13 | −0.816039 | ||||||||
\(841\) | 1.96049e12 | 0.135140 | ||||||||
\(842\) | 1.61043e13 | 1.10417 | ||||||||
\(843\) | −7.56358e12 | −0.515826 | ||||||||
\(844\) | −1.18826e13 | −0.806065 | ||||||||
\(845\) | 1.84652e12 | 0.124595 | ||||||||
\(846\) | −2.54866e13 | −1.71059 | ||||||||
\(847\) | 5.60283e12 | 0.374052 | ||||||||
\(848\) | −7.01319e10 | −0.00465730 | ||||||||
\(849\) | 1.54365e13 | 1.01968 | ||||||||
\(850\) | 2.08122e13 | 1.36752 | ||||||||
\(851\) | −2.10174e13 | −1.37372 | ||||||||
\(852\) | −6.99971e12 | −0.455095 | ||||||||
\(853\) | 3.05360e13 | 1.97489 | 0.987443 | − | 0.157974i | \(-0.0504962\pi\) | ||||
0.987443 | + | 0.157974i | \(0.0504962\pi\) | |||||||
\(854\) | −1.05383e13 | −0.677971 | ||||||||
\(855\) | −1.40285e13 | −0.897768 | ||||||||
\(856\) | 2.25213e13 | 1.43371 | ||||||||
\(857\) | −7.68700e12 | −0.486792 | −0.243396 | − | 0.969927i | \(-0.578261\pi\) | ||||
−0.243396 | + | 0.969927i | \(0.578261\pi\) | |||||||
\(858\) | −9.38961e11 | −0.0591500 | ||||||||
\(859\) | 2.39704e13 | 1.50212 | 0.751062 | − | 0.660232i | \(-0.229542\pi\) | ||||
0.751062 | + | 0.660232i | \(0.229542\pi\) | |||||||
\(860\) | −5.77557e13 | −3.60041 | ||||||||
\(861\) | 3.50614e12 | 0.217428 | ||||||||
\(862\) | 4.40327e13 | 2.71639 | ||||||||
\(863\) | −1.85204e12 | −0.113658 | −0.0568292 | − | 0.998384i | \(-0.518099\pi\) | ||||
−0.0568292 | + | 0.998384i | \(0.518099\pi\) | |||||||
\(864\) | 6.80848e12 | 0.415660 | ||||||||
\(865\) | −3.17077e13 | −1.92572 | ||||||||
\(866\) | 2.31163e13 | 1.39665 | ||||||||
\(867\) | 1.56996e13 | 0.943630 | ||||||||
\(868\) | −3.98981e12 | −0.238569 | ||||||||
\(869\) | 2.35361e12 | 0.140006 | ||||||||
\(870\) | −6.11293e13 | −3.61754 | ||||||||
\(871\) | −5.80152e12 | −0.341555 | ||||||||
\(872\) | −1.75032e13 | −1.02516 | ||||||||
\(873\) | −7.91337e12 | −0.461102 | ||||||||
\(874\) | 3.67033e13 | 2.12767 | ||||||||
\(875\) | −6.61893e12 | −0.381726 | ||||||||
\(876\) | −2.00119e13 | −1.14821 | ||||||||
\(877\) | 1.17900e13 | 0.673001 | 0.336501 | − | 0.941683i | \(-0.390757\pi\) | ||||
0.336501 | + | 0.941683i | \(0.390757\pi\) | |||||||
\(878\) | −3.18499e13 | −1.80877 | ||||||||
\(879\) | 2.39408e12 | 0.135266 | ||||||||
\(880\) | 1.17880e11 | 0.00662624 | ||||||||
\(881\) | −2.04680e13 | −1.14468 | −0.572339 | − | 0.820017i | \(-0.693964\pi\) | ||||
−0.572339 | + | 0.820017i | \(0.693964\pi\) | |||||||
\(882\) | −2.78083e12 | −0.154727 | ||||||||
\(883\) | −2.67886e13 | −1.48295 | −0.741475 | − | 0.670981i | \(-0.765873\pi\) | ||||
−0.741475 | + | 0.670981i | \(0.765873\pi\) | |||||||
\(884\) | 4.27389e12 | 0.235390 | ||||||||
\(885\) | −6.68499e12 | −0.366316 | ||||||||
\(886\) | 9.66507e12 | 0.526930 | ||||||||
\(887\) | 1.60633e13 | 0.871320 | 0.435660 | − | 0.900111i | \(-0.356515\pi\) | ||||
0.435660 | + | 0.900111i | \(0.356515\pi\) | |||||||
\(888\) | −2.15105e13 | −1.16089 | ||||||||
\(889\) | −1.19651e13 | −0.642478 | ||||||||
\(890\) | 3.38929e12 | 0.181073 | ||||||||
\(891\) | −2.33899e12 | −0.124331 | ||||||||
\(892\) | 3.84049e13 | 2.03116 | ||||||||
\(893\) | −2.49363e13 | −1.31220 | ||||||||
\(894\) | −7.55737e13 | −3.95687 | ||||||||
\(895\) | −2.08070e13 | −1.08394 | ||||||||
\(896\) | −1.20119e13 | −0.622624 | ||||||||
\(897\) | 1.09521e13 | 0.564850 | ||||||||
\(898\) | 2.07252e12 | 0.106354 | ||||||||
\(899\) | −8.05111e12 | −0.411090 | ||||||||
\(900\) | 3.48741e13 | 1.77179 | ||||||||
\(901\) | 1.18867e12 | 0.0600898 | ||||||||
\(902\) | −1.46303e12 | −0.0735910 | ||||||||
\(903\) | −1.32491e13 | −0.663121 | ||||||||
\(904\) | −2.76495e13 | −1.37699 | ||||||||
\(905\) | −5.67633e13 | −2.81287 | ||||||||
\(906\) | −6.30343e13 | −3.10814 | ||||||||
\(907\) | 6.32202e12 | 0.310186 | 0.155093 | − | 0.987900i | \(-0.450432\pi\) | ||||
0.155093 | + | 0.987900i | \(0.450432\pi\) | |||||||
\(908\) | 3.06655e13 | 1.49714 | ||||||||
\(909\) | −1.64744e13 | −0.800338 | ||||||||
\(910\) | −5.70257e12 | −0.275667 | ||||||||
\(911\) | −2.44911e13 | −1.17808 | −0.589041 | − | 0.808103i | \(-0.700494\pi\) | ||||
−0.589041 | + | 0.808103i | \(0.700494\pi\) | |||||||
\(912\) | 9.01202e11 | 0.0431366 | ||||||||
\(913\) | −4.47552e11 | −0.0213169 | ||||||||
\(914\) | −4.12654e13 | −1.95582 | ||||||||
\(915\) | 4.89913e13 | 2.31060 | ||||||||
\(916\) | −3.86281e13 | −1.81290 | ||||||||
\(917\) | 1.02953e13 | 0.480813 | ||||||||
\(918\) | 7.79004e12 | 0.362032 | ||||||||
\(919\) | 1.06492e13 | 0.492491 | 0.246245 | − | 0.969208i | \(-0.420803\pi\) | ||||
0.246245 | + | 0.969208i | \(0.420803\pi\) | |||||||
\(920\) | −5.73118e13 | −2.63754 | ||||||||
\(921\) | 2.32273e13 | 1.06373 | ||||||||
\(922\) | −1.08718e13 | −0.495466 | ||||||||
\(923\) | −1.31766e12 | −0.0597581 | ||||||||
\(924\) | 1.79965e12 | 0.0812204 | ||||||||
\(925\) | −3.14828e13 | −1.41395 | ||||||||
\(926\) | 6.02636e13 | 2.69343 | ||||||||
\(927\) | −5.36229e12 | −0.238502 | ||||||||
\(928\) | −2.32784e13 | −1.03036 | ||||||||
\(929\) | 3.06163e13 | 1.34860 | 0.674299 | − | 0.738458i | \(-0.264446\pi\) | ||||
0.674299 | + | 0.738458i | \(0.264446\pi\) | |||||||
\(930\) | 2.98865e13 | 1.31009 | ||||||||
\(931\) | −2.72079e12 | −0.118692 | ||||||||
\(932\) | −6.46020e13 | −2.80462 | ||||||||
\(933\) | −2.39978e13 | −1.03682 | ||||||||
\(934\) | 4.24559e13 | 1.82548 | ||||||||
\(935\) | −1.99796e12 | −0.0854937 | ||||||||
\(936\) | 4.48544e12 | 0.191013 | ||||||||
\(937\) | 2.74612e13 | 1.16384 | 0.581918 | − | 0.813247i | \(-0.302302\pi\) | ||||
0.581918 | + | 0.813247i | \(0.302302\pi\) | |||||||
\(938\) | 1.79167e13 | 0.755693 | ||||||||
\(939\) | −1.31057e13 | −0.550129 | ||||||||
\(940\) | 1.00173e14 | 4.18480 | ||||||||
\(941\) | 7.57137e12 | 0.314790 | 0.157395 | − | 0.987536i | \(-0.449690\pi\) | ||||
0.157395 | + | 0.987536i | \(0.449690\pi\) | |||||||
\(942\) | 4.56072e13 | 1.88714 | ||||||||
\(943\) | 1.70650e13 | 0.702754 | ||||||||
\(944\) | 1.71849e11 | 0.00704325 | ||||||||
\(945\) | −6.45078e12 | −0.263129 | ||||||||
\(946\) | 5.52856e12 | 0.224441 | ||||||||
\(947\) | −1.16957e12 | −0.0472552 | −0.0236276 | − | 0.999721i | \(-0.507522\pi\) | ||||
−0.0236276 | + | 0.999721i | \(0.507522\pi\) | |||||||
\(948\) | −7.22829e13 | −2.90669 | ||||||||
\(949\) | −3.76716e12 | −0.150770 | ||||||||
\(950\) | 5.49792e13 | 2.18999 | ||||||||
\(951\) | 2.33293e13 | 0.924890 | ||||||||
\(952\) | −5.13051e12 | −0.202439 | ||||||||
\(953\) | −3.67280e13 | −1.44238 | −0.721190 | − | 0.692737i | \(-0.756404\pi\) | ||||
−0.721190 | + | 0.692737i | \(0.756404\pi\) | |||||||
\(954\) | 3.20939e12 | 0.125446 | ||||||||
\(955\) | 5.89539e13 | 2.29349 | ||||||||
\(956\) | −5.79097e13 | −2.24229 | ||||||||
\(957\) | 3.63155e12 | 0.139955 | ||||||||
\(958\) | 6.87444e13 | 2.63689 | ||||||||
\(959\) | 5.22979e12 | 0.199664 | ||||||||
\(960\) | 8.86247e13 | 3.36771 | ||||||||
\(961\) | −2.25034e13 | −0.851124 | ||||||||
\(962\) | −1.04173e13 | −0.392162 | ||||||||
\(963\) | −2.47256e13 | −0.926465 | ||||||||
\(964\) | 3.50540e13 | 1.30735 | ||||||||
\(965\) | 7.71476e13 | 2.86384 | ||||||||
\(966\) | −3.38233e13 | −1.24974 | ||||||||
\(967\) | 3.20474e13 | 1.17862 | 0.589310 | − | 0.807907i | \(-0.299400\pi\) | ||||
0.589310 | + | 0.807907i | \(0.299400\pi\) | |||||||
\(968\) | 2.79096e13 | 1.02168 | ||||||||
\(969\) | −1.52746e13 | −0.556560 | ||||||||
\(970\) | 5.01157e13 | 1.81761 | ||||||||
\(971\) | −3.55791e13 | −1.28442 | −0.642211 | − | 0.766528i | \(-0.721983\pi\) | ||||
−0.642211 | + | 0.766528i | \(0.721983\pi\) | |||||||
\(972\) | 5.22667e13 | 1.87814 | ||||||||
\(973\) | 7.21448e12 | 0.258046 | ||||||||
\(974\) | 3.38550e13 | 1.20533 | ||||||||
\(975\) | 1.64056e13 | 0.581395 | ||||||||
\(976\) | −1.25941e12 | −0.0444264 | ||||||||
\(977\) | 1.87873e13 | 0.659688 | 0.329844 | − | 0.944036i | \(-0.393004\pi\) | ||||
0.329844 | + | 0.944036i | \(0.393004\pi\) | |||||||
\(978\) | −3.86776e13 | −1.35187 | ||||||||
\(979\) | −2.01350e11 | −0.00700534 | ||||||||
\(980\) | 1.09298e13 | 0.378525 | ||||||||
\(981\) | 1.92164e13 | 0.662462 | ||||||||
\(982\) | 5.16917e13 | 1.77386 | ||||||||
\(983\) | −2.46921e13 | −0.843466 | −0.421733 | − | 0.906720i | \(-0.638578\pi\) | ||||
−0.421733 | + | 0.906720i | \(0.638578\pi\) | |||||||
\(984\) | 1.74653e13 | 0.593880 | ||||||||
\(985\) | −8.37279e13 | −2.83405 | ||||||||
\(986\) | −2.66344e13 | −0.897422 | ||||||||
\(987\) | 2.29796e13 | 0.770754 | ||||||||
\(988\) | 1.12903e13 | 0.376962 | ||||||||
\(989\) | −6.44858e13 | −2.14329 | ||||||||
\(990\) | −5.39444e12 | −0.178479 | ||||||||
\(991\) | 4.81567e13 | 1.58608 | 0.793040 | − | 0.609170i | \(-0.208497\pi\) | ||||
0.793040 | + | 0.609170i | \(0.208497\pi\) | |||||||
\(992\) | 1.13810e13 | 0.373144 | ||||||||
\(993\) | −1.57898e13 | −0.515353 | ||||||||
\(994\) | 4.06931e12 | 0.132215 | ||||||||
\(995\) | −5.92924e13 | −1.91776 | ||||||||
\(996\) | 1.37450e13 | 0.442565 | ||||||||
\(997\) | −2.46353e13 | −0.789641 | −0.394820 | − | 0.918758i | \(-0.629193\pi\) | ||||
−0.394820 | + | 0.918758i | \(0.629193\pi\) | |||||||
\(998\) | −1.78244e13 | −0.568757 | ||||||||
\(999\) | −1.17841e13 | −0.374326 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 91.10.a.b.1.2 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.b.1.2 | ✓ | 13 | 1.1 | even | 1 | trivial |