Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,8,Mod(1,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.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: | \(3.43623528033\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{15}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 15 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.87298\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 11.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.7460 | −1.03821 | −0.519103 | − | 0.854712i | \(-0.673734\pi\) | ||||
−0.519103 | + | 0.854712i | \(0.673734\pi\) | |||||||
\(3\) | 43.4758 | 0.929658 | 0.464829 | − | 0.885400i | \(-0.346116\pi\) | ||||
0.464829 | + | 0.885400i | \(0.346116\pi\) | |||||||
\(4\) | 9.96773 | 0.0778729 | ||||||||
\(5\) | −389.919 | −1.39502 | −0.697509 | − | 0.716576i | \(-0.745708\pi\) | ||||
−0.697509 | + | 0.716576i | \(0.745708\pi\) | |||||||
\(6\) | −510.665 | −0.965177 | ||||||||
\(7\) | −1249.17 | −1.37651 | −0.688253 | − | 0.725471i | \(-0.741622\pi\) | ||||
−0.688253 | + | 0.725471i | \(0.741622\pi\) | |||||||
\(8\) | 1386.40 | 0.957358 | ||||||||
\(9\) | −296.855 | −0.135736 | ||||||||
\(10\) | 4579.98 | 1.44832 | ||||||||
\(11\) | 1331.00 | 0.301511 | ||||||||
\(12\) | 433.355 | 0.0723952 | ||||||||
\(13\) | −3840.41 | −0.484815 | −0.242407 | − | 0.970175i | \(-0.577937\pi\) | ||||
−0.242407 | + | 0.970175i | \(0.577937\pi\) | |||||||
\(14\) | 14672.7 | 1.42910 | ||||||||
\(15\) | −16952.1 | −1.29689 | ||||||||
\(16\) | −17560.5 | −1.07181 | ||||||||
\(17\) | 24162.7 | 1.19282 | 0.596409 | − | 0.802680i | \(-0.296593\pi\) | ||||
0.596409 | + | 0.802680i | \(0.296593\pi\) | |||||||
\(18\) | 3486.85 | 0.140922 | ||||||||
\(19\) | 5458.47 | 0.182572 | 0.0912859 | − | 0.995825i | \(-0.470902\pi\) | ||||
0.0912859 | + | 0.995825i | \(0.470902\pi\) | |||||||
\(20\) | −3886.61 | −0.108634 | ||||||||
\(21\) | −54308.6 | −1.27968 | ||||||||
\(22\) | −15633.9 | −0.313031 | ||||||||
\(23\) | −63973.2 | −1.09635 | −0.548177 | − | 0.836362i | \(-0.684678\pi\) | ||||
−0.548177 | + | 0.836362i | \(0.684678\pi\) | |||||||
\(24\) | 60275.0 | 0.890016 | ||||||||
\(25\) | 73912.1 | 0.946075 | ||||||||
\(26\) | 45109.3 | 0.503338 | ||||||||
\(27\) | −107988. | −1.05585 | ||||||||
\(28\) | −12451.4 | −0.107193 | ||||||||
\(29\) | 178351. | 1.35794 | 0.678972 | − | 0.734164i | \(-0.262426\pi\) | ||||
0.678972 | + | 0.734164i | \(0.262426\pi\) | |||||||
\(30\) | 199118. | 1.34644 | ||||||||
\(31\) | −185129. | −1.11611 | −0.558057 | − | 0.829803i | \(-0.688453\pi\) | ||||
−0.558057 | + | 0.829803i | \(0.688453\pi\) | |||||||
\(32\) | 28805.6 | 0.155400 | ||||||||
\(33\) | 57866.3 | 0.280302 | ||||||||
\(34\) | −283814. | −1.23839 | ||||||||
\(35\) | 487075. | 1.92025 | ||||||||
\(36\) | −2958.97 | −0.0105702 | ||||||||
\(37\) | −409817. | −1.33010 | −0.665050 | − | 0.746799i | \(-0.731590\pi\) | ||||
−0.665050 | + | 0.746799i | \(0.731590\pi\) | |||||||
\(38\) | −64115.0 | −0.189547 | ||||||||
\(39\) | −166965. | −0.450712 | ||||||||
\(40\) | −540585. | −1.33553 | ||||||||
\(41\) | −675273. | −1.53016 | −0.765078 | − | 0.643938i | \(-0.777300\pi\) | ||||
−0.765078 | + | 0.643938i | \(0.777300\pi\) | |||||||
\(42\) | 637907. | 1.32857 | ||||||||
\(43\) | 38903.5 | 0.0746189 | 0.0373094 | − | 0.999304i | \(-0.488121\pi\) | ||||
0.0373094 | + | 0.999304i | \(0.488121\pi\) | |||||||
\(44\) | 13267.1 | 0.0234796 | ||||||||
\(45\) | 115749. | 0.189354 | ||||||||
\(46\) | 751427. | 1.13824 | ||||||||
\(47\) | 949397. | 1.33385 | 0.666923 | − | 0.745127i | \(-0.267611\pi\) | ||||
0.666923 | + | 0.745127i | \(0.267611\pi\) | |||||||
\(48\) | −763457. | −0.996416 | ||||||||
\(49\) | 736881. | 0.894769 | ||||||||
\(50\) | −868169. | −0.982221 | ||||||||
\(51\) | 1.05049e6 | 1.10891 | ||||||||
\(52\) | −38280.2 | −0.0377539 | ||||||||
\(53\) | 294003. | 0.271260 | 0.135630 | − | 0.990760i | \(-0.456694\pi\) | ||||
0.135630 | + | 0.990760i | \(0.456694\pi\) | |||||||
\(54\) | 1.26842e6 | 1.09619 | ||||||||
\(55\) | −518983. | −0.420614 | ||||||||
\(56\) | −1.73185e6 | −1.31781 | ||||||||
\(57\) | 237311. | 0.169729 | ||||||||
\(58\) | −2.09490e6 | −1.40983 | ||||||||
\(59\) | −87803.7 | −0.0556584 | −0.0278292 | − | 0.999613i | \(-0.508859\pi\) | ||||
−0.0278292 | + | 0.999613i | \(0.508859\pi\) | |||||||
\(60\) | −168974. | −0.100993 | ||||||||
\(61\) | −2.78573e6 | −1.57139 | −0.785696 | − | 0.618613i | \(-0.787695\pi\) | ||||
−0.785696 | + | 0.618613i | \(0.787695\pi\) | |||||||
\(62\) | 2.17452e6 | 1.15876 | ||||||||
\(63\) | 370822. | 0.186842 | ||||||||
\(64\) | 1.90940e6 | 0.910471 | ||||||||
\(65\) | 1.49745e6 | 0.676325 | ||||||||
\(66\) | −679696. | −0.291012 | ||||||||
\(67\) | 2.95364e6 | 1.19976 | 0.599882 | − | 0.800089i | \(-0.295214\pi\) | ||||
0.599882 | + | 0.800089i | \(0.295214\pi\) | |||||||
\(68\) | 240847. | 0.0928883 | ||||||||
\(69\) | −2.78129e6 | −1.01923 | ||||||||
\(70\) | −5.72117e6 | −1.99362 | ||||||||
\(71\) | −4.08380e6 | −1.35413 | −0.677065 | − | 0.735923i | \(-0.736749\pi\) | ||||
−0.677065 | + | 0.735923i | \(0.736749\pi\) | |||||||
\(72\) | −411560. | −0.129948 | ||||||||
\(73\) | 1.95525e6 | 0.588263 | 0.294132 | − | 0.955765i | \(-0.404970\pi\) | ||||
0.294132 | + | 0.955765i | \(0.404970\pi\) | |||||||
\(74\) | 4.81370e6 | 1.38092 | ||||||||
\(75\) | 3.21339e6 | 0.879526 | ||||||||
\(76\) | 54408.6 | 0.0142174 | ||||||||
\(77\) | −1.66264e6 | −0.415032 | ||||||||
\(78\) | 1.96116e6 | 0.467932 | ||||||||
\(79\) | −608158. | −0.138778 | −0.0693891 | − | 0.997590i | \(-0.522105\pi\) | ||||
−0.0693891 | + | 0.997590i | \(0.522105\pi\) | |||||||
\(80\) | 6.84718e6 | 1.49519 | ||||||||
\(81\) | −4.04562e6 | −0.845840 | ||||||||
\(82\) | 7.93173e6 | 1.58862 | ||||||||
\(83\) | 214613. | 0.0411986 | 0.0205993 | − | 0.999788i | \(-0.493443\pi\) | ||||
0.0205993 | + | 0.999788i | \(0.493443\pi\) | |||||||
\(84\) | −541334. | −0.0996524 | ||||||||
\(85\) | −9.42151e6 | −1.66400 | ||||||||
\(86\) | −456959. | −0.0774698 | ||||||||
\(87\) | 7.75394e6 | 1.26242 | ||||||||
\(88\) | 1.84530e6 | 0.288654 | ||||||||
\(89\) | −8.30366e6 | −1.24855 | −0.624273 | − | 0.781206i | \(-0.714605\pi\) | ||||
−0.624273 | + | 0.781206i | \(0.714605\pi\) | |||||||
\(90\) | −1.35959e6 | −0.196589 | ||||||||
\(91\) | 4.79732e6 | 0.667351 | ||||||||
\(92\) | −637668. | −0.0853763 | ||||||||
\(93\) | −8.04863e6 | −1.03760 | ||||||||
\(94\) | −1.11516e7 | −1.38481 | ||||||||
\(95\) | −2.12836e6 | −0.254691 | ||||||||
\(96\) | 1.25235e6 | 0.144469 | ||||||||
\(97\) | −1.38909e6 | −0.154536 | −0.0772678 | − | 0.997010i | \(-0.524620\pi\) | ||||
−0.0772678 | + | 0.997010i | \(0.524620\pi\) | |||||||
\(98\) | −8.65538e6 | −0.928955 | ||||||||
\(99\) | −395114. | −0.0409260 | ||||||||
\(100\) | 736736. | 0.0736736 | ||||||||
\(101\) | 1.22974e7 | 1.18765 | 0.593825 | − | 0.804595i | \(-0.297617\pi\) | ||||
0.593825 | + | 0.804595i | \(0.297617\pi\) | |||||||
\(102\) | −1.23391e7 | −1.15128 | ||||||||
\(103\) | 2.14543e7 | 1.93457 | 0.967283 | − | 0.253701i | \(-0.0816481\pi\) | ||||
0.967283 | + | 0.253701i | \(0.0816481\pi\) | |||||||
\(104\) | −5.32436e6 | −0.464142 | ||||||||
\(105\) | 2.11760e7 | 1.78518 | ||||||||
\(106\) | −3.45335e6 | −0.281624 | ||||||||
\(107\) | 4.25610e6 | 0.335868 | 0.167934 | − | 0.985798i | \(-0.446290\pi\) | ||||
0.167934 | + | 0.985798i | \(0.446290\pi\) | |||||||
\(108\) | −1.07639e6 | −0.0822218 | ||||||||
\(109\) | −6.75437e6 | −0.499565 | −0.249783 | − | 0.968302i | \(-0.580359\pi\) | ||||
−0.249783 | + | 0.968302i | \(0.580359\pi\) | |||||||
\(110\) | 6.09595e6 | 0.436684 | ||||||||
\(111\) | −1.78171e7 | −1.23654 | ||||||||
\(112\) | 2.19361e7 | 1.47535 | ||||||||
\(113\) | 2.26593e6 | 0.147731 | 0.0738656 | − | 0.997268i | \(-0.476466\pi\) | ||||
0.0738656 | + | 0.997268i | \(0.476466\pi\) | |||||||
\(114\) | −2.78745e6 | −0.176214 | ||||||||
\(115\) | 2.49444e7 | 1.52943 | ||||||||
\(116\) | 1.77775e6 | 0.105747 | ||||||||
\(117\) | 1.14004e6 | 0.0658069 | ||||||||
\(118\) | 1.03134e6 | 0.0577849 | ||||||||
\(119\) | −3.01833e7 | −1.64192 | ||||||||
\(120\) | −2.35024e7 | −1.24159 | ||||||||
\(121\) | 1.77156e6 | 0.0909091 | ||||||||
\(122\) | 3.27211e7 | 1.63143 | ||||||||
\(123\) | −2.93580e7 | −1.42252 | ||||||||
\(124\) | −1.84532e6 | −0.0869150 | ||||||||
\(125\) | 1.64270e6 | 0.0752267 | ||||||||
\(126\) | −4.35566e6 | −0.193980 | ||||||||
\(127\) | 1.10495e7 | 0.478661 | 0.239331 | − | 0.970938i | \(-0.423072\pi\) | ||||
0.239331 | + | 0.970938i | \(0.423072\pi\) | |||||||
\(128\) | −2.61148e7 | −1.10066 | ||||||||
\(129\) | 1.69136e6 | 0.0693700 | ||||||||
\(130\) | −1.75890e7 | −0.702165 | ||||||||
\(131\) | −1.05834e7 | −0.411316 | −0.205658 | − | 0.978624i | \(-0.565933\pi\) | ||||
−0.205658 | + | 0.978624i | \(0.565933\pi\) | |||||||
\(132\) | 576796. | 0.0218280 | ||||||||
\(133\) | −6.81856e6 | −0.251311 | ||||||||
\(134\) | −3.46934e7 | −1.24560 | ||||||||
\(135\) | 4.21064e7 | 1.47292 | ||||||||
\(136\) | 3.34993e7 | 1.14196 | ||||||||
\(137\) | −3.39909e7 | −1.12938 | −0.564691 | − | 0.825302i | \(-0.691005\pi\) | ||||
−0.564691 | + | 0.825302i | \(0.691005\pi\) | |||||||
\(138\) | 3.26689e7 | 1.05818 | ||||||||
\(139\) | 2.60529e6 | 0.0822818 | 0.0411409 | − | 0.999153i | \(-0.486901\pi\) | ||||
0.0411409 | + | 0.999153i | \(0.486901\pi\) | |||||||
\(140\) | 4.85504e6 | 0.149536 | ||||||||
\(141\) | 4.12758e7 | 1.24002 | ||||||||
\(142\) | 4.79682e7 | 1.40587 | ||||||||
\(143\) | −5.11159e6 | −0.146177 | ||||||||
\(144\) | 5.21292e6 | 0.145483 | ||||||||
\(145\) | −6.95424e7 | −1.89436 | ||||||||
\(146\) | −2.29663e7 | −0.610739 | ||||||||
\(147\) | 3.20365e7 | 0.831829 | ||||||||
\(148\) | −4.08495e6 | −0.103579 | ||||||||
\(149\) | 9.39464e6 | 0.232663 | 0.116332 | − | 0.993210i | \(-0.462886\pi\) | ||||
0.116332 | + | 0.993210i | \(0.462886\pi\) | |||||||
\(150\) | −3.77443e7 | −0.913130 | ||||||||
\(151\) | −2.58693e7 | −0.611457 | −0.305729 | − | 0.952119i | \(-0.598900\pi\) | ||||
−0.305729 | + | 0.952119i | \(0.598900\pi\) | |||||||
\(152\) | 7.56764e6 | 0.174787 | ||||||||
\(153\) | −7.17282e6 | −0.161909 | ||||||||
\(154\) | 1.95294e7 | 0.430889 | ||||||||
\(155\) | 7.21854e7 | 1.55700 | ||||||||
\(156\) | −1.66426e6 | −0.0350983 | ||||||||
\(157\) | −4.17516e7 | −0.861043 | −0.430521 | − | 0.902580i | \(-0.641670\pi\) | ||||
−0.430521 | + | 0.902580i | \(0.641670\pi\) | |||||||
\(158\) | 7.14340e6 | 0.144080 | ||||||||
\(159\) | 1.27820e7 | 0.252179 | ||||||||
\(160\) | −1.12319e7 | −0.216786 | ||||||||
\(161\) | 7.99134e7 | 1.50914 | ||||||||
\(162\) | 4.75198e7 | 0.878156 | ||||||||
\(163\) | −2.45070e7 | −0.443235 | −0.221618 | − | 0.975134i | \(-0.571134\pi\) | ||||
−0.221618 | + | 0.975134i | \(0.571134\pi\) | |||||||
\(164\) | −6.73094e6 | −0.119158 | ||||||||
\(165\) | −2.25632e7 | −0.391027 | ||||||||
\(166\) | −2.52084e6 | −0.0427727 | ||||||||
\(167\) | −6.73433e7 | −1.11889 | −0.559444 | − | 0.828868i | \(-0.688985\pi\) | ||||
−0.559444 | + | 0.828868i | \(0.688985\pi\) | |||||||
\(168\) | −7.52937e7 | −1.22511 | ||||||||
\(169\) | −4.79998e7 | −0.764955 | ||||||||
\(170\) | 1.10665e8 | 1.72758 | ||||||||
\(171\) | −1.62037e6 | −0.0247816 | ||||||||
\(172\) | 387779. | 0.00581079 | ||||||||
\(173\) | 1.29430e7 | 0.190052 | 0.0950259 | − | 0.995475i | \(-0.469707\pi\) | ||||
0.0950259 | + | 0.995475i | \(0.469707\pi\) | |||||||
\(174\) | −9.10775e7 | −1.31066 | ||||||||
\(175\) | −9.23287e7 | −1.30228 | ||||||||
\(176\) | −2.33730e7 | −0.323162 | ||||||||
\(177\) | −3.81734e6 | −0.0517433 | ||||||||
\(178\) | 9.75345e7 | 1.29625 | ||||||||
\(179\) | 6.35496e6 | 0.0828185 | 0.0414093 | − | 0.999142i | \(-0.486815\pi\) | ||||
0.0414093 | + | 0.999142i | \(0.486815\pi\) | |||||||
\(180\) | 1.15376e6 | 0.0147456 | ||||||||
\(181\) | −3.46385e7 | −0.434194 | −0.217097 | − | 0.976150i | \(-0.569659\pi\) | ||||
−0.217097 | + | 0.976150i | \(0.569659\pi\) | |||||||
\(182\) | −5.63492e7 | −0.692848 | ||||||||
\(183\) | −1.21112e8 | −1.46086 | ||||||||
\(184\) | −8.86926e7 | −1.04960 | ||||||||
\(185\) | 1.59796e8 | 1.85551 | ||||||||
\(186\) | 9.45389e7 | 1.07725 | ||||||||
\(187\) | 3.21606e7 | 0.359648 | ||||||||
\(188\) | 9.46334e6 | 0.103870 | ||||||||
\(189\) | 1.34895e8 | 1.45338 | ||||||||
\(190\) | 2.49997e7 | 0.264422 | ||||||||
\(191\) | 8.18197e7 | 0.849652 | 0.424826 | − | 0.905275i | \(-0.360335\pi\) | ||||
0.424826 | + | 0.905275i | \(0.360335\pi\) | |||||||
\(192\) | 8.30125e7 | 0.846427 | ||||||||
\(193\) | −6.82998e7 | −0.683863 | −0.341931 | − | 0.939725i | \(-0.611081\pi\) | ||||
−0.341931 | + | 0.939725i | \(0.611081\pi\) | |||||||
\(194\) | 1.63162e7 | 0.160440 | ||||||||
\(195\) | 6.51029e7 | 0.628751 | ||||||||
\(196\) | 7.34503e6 | 0.0696783 | ||||||||
\(197\) | 4.70586e7 | 0.438538 | 0.219269 | − | 0.975664i | \(-0.429633\pi\) | ||||
0.219269 | + | 0.975664i | \(0.429633\pi\) | |||||||
\(198\) | 4.64099e6 | 0.0424896 | ||||||||
\(199\) | −9.87712e7 | −0.888474 | −0.444237 | − | 0.895909i | \(-0.646525\pi\) | ||||
−0.444237 | + | 0.895909i | \(0.646525\pi\) | |||||||
\(200\) | 1.02472e8 | 0.905733 | ||||||||
\(201\) | 1.28412e8 | 1.11537 | ||||||||
\(202\) | −1.44445e8 | −1.23303 | ||||||||
\(203\) | −2.22790e8 | −1.86922 | ||||||||
\(204\) | 1.04710e7 | 0.0863543 | ||||||||
\(205\) | 2.63302e8 | 2.13459 | ||||||||
\(206\) | −2.52001e8 | −2.00848 | ||||||||
\(207\) | 1.89908e7 | 0.148815 | ||||||||
\(208\) | 6.74396e7 | 0.519629 | ||||||||
\(209\) | 7.26523e6 | 0.0550474 | ||||||||
\(210\) | −2.48732e8 | −1.85338 | ||||||||
\(211\) | −1.37863e8 | −1.01032 | −0.505160 | − | 0.863026i | \(-0.668566\pi\) | ||||
−0.505160 | + | 0.863026i | \(0.668566\pi\) | |||||||
\(212\) | 2.93054e6 | 0.0211238 | ||||||||
\(213\) | −1.77547e8 | −1.25888 | ||||||||
\(214\) | −4.99920e7 | −0.348700 | ||||||||
\(215\) | −1.51692e7 | −0.104095 | ||||||||
\(216\) | −1.49714e8 | −1.01082 | ||||||||
\(217\) | 2.31257e8 | 1.53634 | ||||||||
\(218\) | 7.93366e7 | 0.518652 | ||||||||
\(219\) | 8.50060e7 | 0.546884 | ||||||||
\(220\) | −5.17308e6 | −0.0327544 | ||||||||
\(221\) | −9.27947e7 | −0.578296 | ||||||||
\(222\) | 2.09279e8 | 1.28378 | ||||||||
\(223\) | 2.67373e8 | 1.61454 | 0.807272 | − | 0.590180i | \(-0.200943\pi\) | ||||
0.807272 | + | 0.590180i | \(0.200943\pi\) | |||||||
\(224\) | −3.59831e7 | −0.213910 | ||||||||
\(225\) | −2.19412e7 | −0.128416 | ||||||||
\(226\) | −2.66155e7 | −0.153375 | ||||||||
\(227\) | −5.68774e7 | −0.322737 | −0.161369 | − | 0.986894i | \(-0.551591\pi\) | ||||
−0.161369 | + | 0.986894i | \(0.551591\pi\) | |||||||
\(228\) | 2.36546e6 | 0.0132173 | ||||||||
\(229\) | −3.00661e8 | −1.65445 | −0.827224 | − | 0.561872i | \(-0.810081\pi\) | ||||
−0.827224 | + | 0.561872i | \(0.810081\pi\) | |||||||
\(230\) | −2.92996e8 | −1.58787 | ||||||||
\(231\) | −7.22848e7 | −0.385838 | ||||||||
\(232\) | 2.47266e8 | 1.30004 | ||||||||
\(233\) | 3.70266e8 | 1.91765 | 0.958823 | − | 0.284006i | \(-0.0916635\pi\) | ||||
0.958823 | + | 0.284006i | \(0.0916635\pi\) | |||||||
\(234\) | −1.33909e7 | −0.0683211 | ||||||||
\(235\) | −3.70188e8 | −1.86074 | ||||||||
\(236\) | −875204. | −0.00433428 | ||||||||
\(237\) | −2.64401e7 | −0.129016 | ||||||||
\(238\) | 3.54532e8 | 1.70465 | ||||||||
\(239\) | 3.00432e8 | 1.42349 | 0.711743 | − | 0.702440i | \(-0.247906\pi\) | ||||
0.711743 | + | 0.702440i | \(0.247906\pi\) | |||||||
\(240\) | 2.97687e8 | 1.39002 | ||||||||
\(241\) | 2.75534e7 | 0.126799 | 0.0633994 | − | 0.997988i | \(-0.479806\pi\) | ||||
0.0633994 | + | 0.997988i | \(0.479806\pi\) | |||||||
\(242\) | −2.08087e7 | −0.0943824 | ||||||||
\(243\) | 6.02821e7 | 0.269505 | ||||||||
\(244\) | −2.77674e7 | −0.122369 | ||||||||
\(245\) | −2.87324e8 | −1.24822 | ||||||||
\(246\) | 3.44838e8 | 1.47687 | ||||||||
\(247\) | −2.09628e7 | −0.0885135 | ||||||||
\(248\) | −2.56663e8 | −1.06852 | ||||||||
\(249\) | 9.33047e6 | 0.0383006 | ||||||||
\(250\) | −1.92951e7 | −0.0781009 | ||||||||
\(251\) | −1.17084e8 | −0.467347 | −0.233673 | − | 0.972315i | \(-0.575075\pi\) | ||||
−0.233673 | + | 0.972315i | \(0.575075\pi\) | |||||||
\(252\) | 3.69625e6 | 0.0145499 | ||||||||
\(253\) | −8.51483e7 | −0.330563 | ||||||||
\(254\) | −1.29787e8 | −0.496949 | ||||||||
\(255\) | −4.09608e8 | −1.54695 | ||||||||
\(256\) | 6.23411e7 | 0.232239 | ||||||||
\(257\) | −1.05899e8 | −0.389157 | −0.194579 | − | 0.980887i | \(-0.562334\pi\) | ||||
−0.194579 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(258\) | −1.98666e7 | −0.0720204 | ||||||||
\(259\) | 5.11931e8 | 1.83089 | ||||||||
\(260\) | 1.49262e7 | 0.0526674 | ||||||||
\(261\) | −5.29443e7 | −0.184322 | ||||||||
\(262\) | 1.24312e8 | 0.427031 | ||||||||
\(263\) | 2.69446e8 | 0.913328 | 0.456664 | − | 0.889639i | \(-0.349044\pi\) | ||||
0.456664 | + | 0.889639i | \(0.349044\pi\) | |||||||
\(264\) | 8.02260e7 | 0.268350 | ||||||||
\(265\) | −1.14637e8 | −0.378413 | ||||||||
\(266\) | 8.00905e7 | 0.260913 | ||||||||
\(267\) | −3.61008e8 | −1.16072 | ||||||||
\(268\) | 2.94411e7 | 0.0934291 | ||||||||
\(269\) | −6.89849e7 | −0.216083 | −0.108042 | − | 0.994146i | \(-0.534458\pi\) | ||||
−0.108042 | + | 0.994146i | \(0.534458\pi\) | |||||||
\(270\) | −4.94581e8 | −1.52920 | ||||||||
\(271\) | 6.86311e7 | 0.209473 | 0.104737 | − | 0.994500i | \(-0.466600\pi\) | ||||
0.104737 | + | 0.994500i | \(0.466600\pi\) | |||||||
\(272\) | −4.24310e8 | −1.27847 | ||||||||
\(273\) | 2.08567e8 | 0.620408 | ||||||||
\(274\) | 3.99256e8 | 1.17253 | ||||||||
\(275\) | 9.83770e7 | 0.285252 | ||||||||
\(276\) | −2.77231e7 | −0.0793707 | ||||||||
\(277\) | −6.22102e8 | −1.75866 | −0.879330 | − | 0.476212i | \(-0.842009\pi\) | ||||
−0.879330 | + | 0.476212i | \(0.842009\pi\) | |||||||
\(278\) | −3.06016e7 | −0.0854255 | ||||||||
\(279\) | 5.49564e7 | 0.151497 | ||||||||
\(280\) | 6.75283e8 | 1.83837 | ||||||||
\(281\) | −8.07383e7 | −0.217074 | −0.108537 | − | 0.994092i | \(-0.534617\pi\) | ||||
−0.108537 | + | 0.994092i | \(0.534617\pi\) | |||||||
\(282\) | −4.84824e8 | −1.28740 | ||||||||
\(283\) | −3.19850e8 | −0.838868 | −0.419434 | − | 0.907786i | \(-0.637771\pi\) | ||||
−0.419434 | + | 0.907786i | \(0.637771\pi\) | |||||||
\(284\) | −4.07063e7 | −0.105450 | ||||||||
\(285\) | −9.25323e7 | −0.236775 | ||||||||
\(286\) | 6.00405e7 | 0.151762 | ||||||||
\(287\) | 8.43530e8 | 2.10627 | ||||||||
\(288\) | −8.55109e6 | −0.0210935 | ||||||||
\(289\) | 1.73498e8 | 0.422817 | ||||||||
\(290\) | 8.16843e8 | 1.96673 | ||||||||
\(291\) | −6.03917e7 | −0.143665 | ||||||||
\(292\) | 1.94894e7 | 0.0458098 | ||||||||
\(293\) | −4.26992e8 | −0.991707 | −0.495854 | − | 0.868406i | \(-0.665145\pi\) | ||||
−0.495854 | + | 0.868406i | \(0.665145\pi\) | |||||||
\(294\) | −3.76299e8 | −0.863611 | ||||||||
\(295\) | 3.42364e7 | 0.0776445 | ||||||||
\(296\) | −5.68172e8 | −1.27338 | ||||||||
\(297\) | −1.43731e8 | −0.318350 | ||||||||
\(298\) | −1.10349e8 | −0.241553 | ||||||||
\(299\) | 2.45683e8 | 0.531529 | ||||||||
\(300\) | 3.20302e7 | 0.0684912 | ||||||||
\(301\) | −4.85970e7 | −0.102713 | ||||||||
\(302\) | 3.03860e8 | 0.634819 | ||||||||
\(303\) | 5.34639e8 | 1.10411 | ||||||||
\(304\) | −9.58536e7 | −0.195682 | ||||||||
\(305\) | 1.08621e9 | 2.19212 | ||||||||
\(306\) | 8.42517e7 | 0.168095 | ||||||||
\(307\) | 1.63077e8 | 0.321669 | 0.160834 | − | 0.986981i | \(-0.448582\pi\) | ||||
0.160834 | + | 0.986981i | \(0.448582\pi\) | |||||||
\(308\) | −1.65728e7 | −0.0323198 | ||||||||
\(309\) | 9.32741e8 | 1.79848 | ||||||||
\(310\) | −8.47887e8 | −1.61649 | ||||||||
\(311\) | 1.22234e8 | 0.230426 | 0.115213 | − | 0.993341i | \(-0.463245\pi\) | ||||
0.115213 | + | 0.993341i | \(0.463245\pi\) | |||||||
\(312\) | −2.31481e8 | −0.431493 | ||||||||
\(313\) | 7.58549e7 | 0.139823 | 0.0699115 | − | 0.997553i | \(-0.477728\pi\) | ||||
0.0699115 | + | 0.997553i | \(0.477728\pi\) | |||||||
\(314\) | 4.90413e8 | 0.893940 | ||||||||
\(315\) | −1.44591e8 | −0.260647 | ||||||||
\(316\) | −6.06195e6 | −0.0108071 | ||||||||
\(317\) | −9.48844e8 | −1.67297 | −0.836483 | − | 0.547992i | \(-0.815392\pi\) | ||||
−0.836483 | + | 0.547992i | \(0.815392\pi\) | |||||||
\(318\) | −1.50137e8 | −0.261814 | ||||||||
\(319\) | 2.37385e8 | 0.409436 | ||||||||
\(320\) | −7.44510e8 | −1.27012 | ||||||||
\(321\) | 1.85037e8 | 0.312242 | ||||||||
\(322\) | −9.38660e8 | −1.56680 | ||||||||
\(323\) | 1.31892e8 | 0.217775 | ||||||||
\(324\) | −4.03257e7 | −0.0658680 | ||||||||
\(325\) | −2.83853e8 | −0.458671 | ||||||||
\(326\) | 2.87859e8 | 0.460170 | ||||||||
\(327\) | −2.93652e8 | −0.464425 | ||||||||
\(328\) | −9.36200e8 | −1.46491 | ||||||||
\(329\) | −1.18596e9 | −1.83605 | ||||||||
\(330\) | 2.65026e8 | 0.405967 | ||||||||
\(331\) | −5.20078e8 | −0.788262 | −0.394131 | − | 0.919054i | \(-0.628954\pi\) | ||||
−0.394131 | + | 0.919054i | \(0.628954\pi\) | |||||||
\(332\) | 2.13920e6 | 0.00320826 | ||||||||
\(333\) | 1.21656e8 | 0.180542 | ||||||||
\(334\) | 7.91013e8 | 1.16164 | ||||||||
\(335\) | −1.15168e9 | −1.67369 | ||||||||
\(336\) | 9.53688e8 | 1.37157 | ||||||||
\(337\) | 6.53022e8 | 0.929443 | 0.464722 | − | 0.885457i | \(-0.346154\pi\) | ||||
0.464722 | + | 0.885457i | \(0.346154\pi\) | |||||||
\(338\) | 5.63804e8 | 0.794181 | ||||||||
\(339\) | 9.85131e7 | 0.137339 | ||||||||
\(340\) | −9.39111e7 | −0.129581 | ||||||||
\(341\) | −2.46407e8 | −0.336521 | ||||||||
\(342\) | 1.90329e7 | 0.0257284 | ||||||||
\(343\) | 1.08256e8 | 0.144851 | ||||||||
\(344\) | 5.39359e7 | 0.0714370 | ||||||||
\(345\) | 1.08448e9 | 1.42185 | ||||||||
\(346\) | −1.52028e8 | −0.197313 | ||||||||
\(347\) | 4.63419e8 | 0.595416 | 0.297708 | − | 0.954657i | \(-0.403778\pi\) | ||||
0.297708 | + | 0.954657i | \(0.403778\pi\) | |||||||
\(348\) | 7.72892e7 | 0.0983086 | ||||||||
\(349\) | 2.76638e8 | 0.348355 | 0.174178 | − | 0.984714i | \(-0.444273\pi\) | ||||
0.174178 | + | 0.984714i | \(0.444273\pi\) | |||||||
\(350\) | 1.08449e9 | 1.35203 | ||||||||
\(351\) | 4.14717e8 | 0.511890 | ||||||||
\(352\) | 3.83403e7 | 0.0468550 | ||||||||
\(353\) | −5.47428e8 | −0.662393 | −0.331197 | − | 0.943562i | \(-0.607452\pi\) | ||||
−0.331197 | + | 0.943562i | \(0.607452\pi\) | |||||||
\(354\) | 4.48383e7 | 0.0537202 | ||||||||
\(355\) | 1.59235e9 | 1.88904 | ||||||||
\(356\) | −8.27686e7 | −0.0972279 | ||||||||
\(357\) | −1.31224e9 | −1.52643 | ||||||||
\(358\) | −7.46452e7 | −0.0859827 | ||||||||
\(359\) | −4.51664e8 | −0.515211 | −0.257605 | − | 0.966250i | \(-0.582933\pi\) | ||||
−0.257605 | + | 0.966250i | \(0.582933\pi\) | |||||||
\(360\) | 1.60475e8 | 0.181280 | ||||||||
\(361\) | −8.64077e8 | −0.966668 | ||||||||
\(362\) | 4.06863e8 | 0.450783 | ||||||||
\(363\) | 7.70200e7 | 0.0845144 | ||||||||
\(364\) | 4.78184e7 | 0.0519685 | ||||||||
\(365\) | −7.62389e8 | −0.820638 | ||||||||
\(366\) | 1.42258e9 | 1.51667 | ||||||||
\(367\) | −8.85429e8 | −0.935024 | −0.467512 | − | 0.883987i | \(-0.654849\pi\) | ||||
−0.467512 | + | 0.883987i | \(0.654849\pi\) | |||||||
\(368\) | 1.12340e9 | 1.17508 | ||||||||
\(369\) | 2.00458e8 | 0.207697 | ||||||||
\(370\) | −1.87695e9 | −1.92640 | ||||||||
\(371\) | −3.67259e8 | −0.373391 | ||||||||
\(372\) | −8.02266e7 | −0.0808013 | ||||||||
\(373\) | 8.02566e7 | 0.0800755 | 0.0400377 | − | 0.999198i | \(-0.487252\pi\) | ||||
0.0400377 | + | 0.999198i | \(0.487252\pi\) | |||||||
\(374\) | −3.77757e8 | −0.373389 | ||||||||
\(375\) | 7.14175e7 | 0.0699351 | ||||||||
\(376\) | 1.31625e9 | 1.27697 | ||||||||
\(377\) | −6.84940e8 | −0.658352 | ||||||||
\(378\) | −1.58447e9 | −1.50891 | ||||||||
\(379\) | 1.14669e9 | 1.08196 | 0.540978 | − | 0.841036i | \(-0.318054\pi\) | ||||
0.540978 | + | 0.841036i | \(0.318054\pi\) | |||||||
\(380\) | −2.12150e7 | −0.0198335 | ||||||||
\(381\) | 4.80384e8 | 0.444991 | ||||||||
\(382\) | −9.61051e8 | −0.882114 | ||||||||
\(383\) | 5.01359e8 | 0.455987 | 0.227994 | − | 0.973663i | \(-0.426783\pi\) | ||||
0.227994 | + | 0.973663i | \(0.426783\pi\) | |||||||
\(384\) | −1.13536e9 | −1.02323 | ||||||||
\(385\) | 6.48297e8 | 0.578977 | ||||||||
\(386\) | 8.02247e8 | 0.709991 | ||||||||
\(387\) | −1.15487e7 | −0.0101285 | ||||||||
\(388\) | −1.38461e7 | −0.0120341 | ||||||||
\(389\) | 6.92770e8 | 0.596713 | 0.298357 | − | 0.954454i | \(-0.403562\pi\) | ||||
0.298357 | + | 0.954454i | \(0.403562\pi\) | |||||||
\(390\) | −7.64696e8 | −0.652774 | ||||||||
\(391\) | −1.54577e9 | −1.30775 | ||||||||
\(392\) | 1.02161e9 | 0.856615 | ||||||||
\(393\) | −4.60121e8 | −0.382383 | ||||||||
\(394\) | −5.52748e8 | −0.455293 | ||||||||
\(395\) | 2.37132e8 | 0.193598 | ||||||||
\(396\) | −3.93839e6 | −0.00318702 | ||||||||
\(397\) | −1.51646e9 | −1.21637 | −0.608184 | − | 0.793796i | \(-0.708102\pi\) | ||||
−0.608184 | + | 0.793796i | \(0.708102\pi\) | |||||||
\(398\) | 1.16016e9 | 0.922419 | ||||||||
\(399\) | −2.96442e8 | −0.233633 | ||||||||
\(400\) | −1.29793e9 | −1.01401 | ||||||||
\(401\) | 1.51899e9 | 1.17639 | 0.588193 | − | 0.808721i | \(-0.299840\pi\) | ||||
0.588193 | + | 0.808721i | \(0.299840\pi\) | |||||||
\(402\) | −1.50832e9 | −1.15798 | ||||||||
\(403\) | 7.10971e8 | 0.541109 | ||||||||
\(404\) | 1.22577e8 | 0.0924857 | ||||||||
\(405\) | 1.57747e9 | 1.17996 | ||||||||
\(406\) | 2.61689e9 | 1.94064 | ||||||||
\(407\) | −5.45467e8 | −0.401040 | ||||||||
\(408\) | 1.45641e9 | 1.06163 | ||||||||
\(409\) | −6.06955e7 | −0.0438657 | −0.0219329 | − | 0.999759i | \(-0.506982\pi\) | ||||
−0.0219329 | + | 0.999759i | \(0.506982\pi\) | |||||||
\(410\) | −3.09274e9 | −2.21615 | ||||||||
\(411\) | −1.47778e9 | −1.04994 | ||||||||
\(412\) | 2.13850e8 | 0.150650 | ||||||||
\(413\) | 1.09682e8 | 0.0766141 | ||||||||
\(414\) | −2.23065e8 | −0.154500 | ||||||||
\(415\) | −8.36817e7 | −0.0574728 | ||||||||
\(416\) | −1.10625e8 | −0.0753405 | ||||||||
\(417\) | 1.13267e8 | 0.0764939 | ||||||||
\(418\) | −8.53371e7 | −0.0571506 | ||||||||
\(419\) | −4.38581e8 | −0.291274 | −0.145637 | − | 0.989338i | \(-0.546523\pi\) | ||||
−0.145637 | + | 0.989338i | \(0.546523\pi\) | |||||||
\(420\) | 2.11077e8 | 0.139017 | ||||||||
\(421\) | −1.88412e9 | −1.23061 | −0.615305 | − | 0.788289i | \(-0.710967\pi\) | ||||
−0.615305 | + | 0.788289i | \(0.710967\pi\) | |||||||
\(422\) | 1.61933e9 | 1.04892 | ||||||||
\(423\) | −2.81833e8 | −0.181051 | ||||||||
\(424\) | 4.07606e8 | 0.259693 | ||||||||
\(425\) | 1.78592e9 | 1.12850 | ||||||||
\(426\) | 2.08546e9 | 1.30698 | ||||||||
\(427\) | 3.47985e9 | 2.16303 | ||||||||
\(428\) | 4.24237e7 | 0.0261550 | ||||||||
\(429\) | −2.22230e8 | −0.135895 | ||||||||
\(430\) | 1.78177e8 | 0.108072 | ||||||||
\(431\) | 7.36561e8 | 0.443137 | 0.221569 | − | 0.975145i | \(-0.428882\pi\) | ||||
0.221569 | + | 0.975145i | \(0.428882\pi\) | |||||||
\(432\) | 1.89632e9 | 1.13167 | ||||||||
\(433\) | 7.99028e8 | 0.472992 | 0.236496 | − | 0.971632i | \(-0.424001\pi\) | ||||
0.236496 | + | 0.971632i | \(0.424001\pi\) | |||||||
\(434\) | −2.71634e9 | −1.59504 | ||||||||
\(435\) | −3.02341e9 | −1.76110 | ||||||||
\(436\) | −6.73258e7 | −0.0389026 | ||||||||
\(437\) | −3.49196e8 | −0.200163 | ||||||||
\(438\) | −9.98477e8 | −0.567778 | ||||||||
\(439\) | 9.89554e8 | 0.558230 | 0.279115 | − | 0.960258i | \(-0.409959\pi\) | ||||
0.279115 | + | 0.960258i | \(0.409959\pi\) | |||||||
\(440\) | −7.19519e8 | −0.402678 | ||||||||
\(441\) | −2.18747e8 | −0.121452 | ||||||||
\(442\) | 1.08996e9 | 0.600391 | ||||||||
\(443\) | −7.19768e8 | −0.393350 | −0.196675 | − | 0.980469i | \(-0.563014\pi\) | ||||
−0.196675 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(444\) | −1.77596e8 | −0.0962928 | ||||||||
\(445\) | 3.23776e9 | 1.74174 | ||||||||
\(446\) | −3.14055e9 | −1.67623 | ||||||||
\(447\) | 4.08439e8 | 0.216297 | ||||||||
\(448\) | −2.38516e9 | −1.25327 | ||||||||
\(449\) | 1.35412e8 | 0.0705987 | 0.0352993 | − | 0.999377i | \(-0.488762\pi\) | ||||
0.0352993 | + | 0.999377i | \(0.488762\pi\) | |||||||
\(450\) | 2.57720e8 | 0.133323 | ||||||||
\(451\) | −8.98788e8 | −0.461359 | ||||||||
\(452\) | 2.25862e7 | 0.0115043 | ||||||||
\(453\) | −1.12469e9 | −0.568446 | ||||||||
\(454\) | 6.68080e8 | 0.335068 | ||||||||
\(455\) | −1.87057e9 | −0.930966 | ||||||||
\(456\) | 3.29009e8 | 0.162492 | ||||||||
\(457\) | 3.03772e9 | 1.48882 | 0.744409 | − | 0.667724i | \(-0.232731\pi\) | ||||
0.744409 | + | 0.667724i | \(0.232731\pi\) | |||||||
\(458\) | 3.53156e9 | 1.71766 | ||||||||
\(459\) | −2.60927e9 | −1.25943 | ||||||||
\(460\) | 2.48639e8 | 0.119101 | ||||||||
\(461\) | −1.35818e9 | −0.645660 | −0.322830 | − | 0.946457i | \(-0.604634\pi\) | ||||
−0.322830 | + | 0.946457i | \(0.604634\pi\) | |||||||
\(462\) | 8.49055e8 | 0.400580 | ||||||||
\(463\) | −1.31208e9 | −0.614366 | −0.307183 | − | 0.951650i | \(-0.599386\pi\) | ||||
−0.307183 | + | 0.951650i | \(0.599386\pi\) | |||||||
\(464\) | −3.13193e9 | −1.45546 | ||||||||
\(465\) | 3.13832e9 | 1.44748 | ||||||||
\(466\) | −4.34913e9 | −1.99091 | ||||||||
\(467\) | 1.37898e8 | 0.0626542 | 0.0313271 | − | 0.999509i | \(-0.490027\pi\) | ||||
0.0313271 | + | 0.999509i | \(0.490027\pi\) | |||||||
\(468\) | 1.13637e7 | 0.00512457 | ||||||||
\(469\) | −3.68960e9 | −1.65148 | ||||||||
\(470\) | 4.34822e9 | 1.93183 | ||||||||
\(471\) | −1.81519e9 | −0.800475 | ||||||||
\(472\) | −1.21731e8 | −0.0532851 | ||||||||
\(473\) | 5.17805e7 | 0.0224984 | ||||||||
\(474\) | 3.10565e8 | 0.133946 | ||||||||
\(475\) | 4.03447e8 | 0.172726 | ||||||||
\(476\) | −3.00859e8 | −0.127861 | ||||||||
\(477\) | −8.72761e7 | −0.0368198 | ||||||||
\(478\) | −3.52886e9 | −1.47787 | ||||||||
\(479\) | 2.23257e9 | 0.928178 | 0.464089 | − | 0.885788i | \(-0.346382\pi\) | ||||
0.464089 | + | 0.885788i | \(0.346382\pi\) | |||||||
\(480\) | −4.88314e8 | −0.201537 | ||||||||
\(481\) | 1.57387e9 | 0.644852 | ||||||||
\(482\) | −3.23641e8 | −0.131643 | ||||||||
\(483\) | 3.47430e9 | 1.40298 | ||||||||
\(484\) | 1.76584e7 | 0.00707936 | ||||||||
\(485\) | 5.41632e8 | 0.215580 | ||||||||
\(486\) | −7.08071e8 | −0.279801 | ||||||||
\(487\) | 3.51454e9 | 1.37885 | 0.689425 | − | 0.724357i | \(-0.257863\pi\) | ||||
0.689425 | + | 0.724357i | \(0.257863\pi\) | |||||||
\(488\) | −3.86214e9 | −1.50439 | ||||||||
\(489\) | −1.06546e9 | −0.412057 | ||||||||
\(490\) | 3.37490e9 | 1.29591 | ||||||||
\(491\) | −1.57552e9 | −0.600672 | −0.300336 | − | 0.953833i | \(-0.597099\pi\) | ||||
−0.300336 | + | 0.953833i | \(0.597099\pi\) | |||||||
\(492\) | −2.92633e8 | −0.110776 | ||||||||
\(493\) | 4.30944e9 | 1.61978 | ||||||||
\(494\) | 2.46228e8 | 0.0918953 | ||||||||
\(495\) | 1.54062e8 | 0.0570925 | ||||||||
\(496\) | 3.25096e9 | 1.19626 | ||||||||
\(497\) | 5.10136e9 | 1.86397 | ||||||||
\(498\) | −1.09595e8 | −0.0397639 | ||||||||
\(499\) | 4.77854e9 | 1.72164 | 0.860822 | − | 0.508907i | \(-0.169950\pi\) | ||||
0.860822 | + | 0.508907i | \(0.169950\pi\) | |||||||
\(500\) | 1.63740e7 | 0.00585813 | ||||||||
\(501\) | −2.92781e9 | −1.04018 | ||||||||
\(502\) | 1.37526e9 | 0.485202 | ||||||||
\(503\) | 1.99980e8 | 0.0700646 | 0.0350323 | − | 0.999386i | \(-0.488847\pi\) | ||||
0.0350323 | + | 0.999386i | \(0.488847\pi\) | |||||||
\(504\) | 5.14109e8 | 0.178874 | ||||||||
\(505\) | −4.79499e9 | −1.65679 | ||||||||
\(506\) | 1.00015e9 | 0.343193 | ||||||||
\(507\) | −2.08683e9 | −0.711146 | ||||||||
\(508\) | 1.10138e8 | 0.0372747 | ||||||||
\(509\) | −5.40122e9 | −1.81543 | −0.907715 | − | 0.419587i | \(-0.862175\pi\) | ||||
−0.907715 | + | 0.419587i | \(0.862175\pi\) | |||||||
\(510\) | 4.81124e9 | 1.60606 | ||||||||
\(511\) | −2.44244e9 | −0.809748 | ||||||||
\(512\) | 2.61044e9 | 0.859546 | ||||||||
\(513\) | −5.89447e8 | −0.192768 | ||||||||
\(514\) | 1.24388e9 | 0.404026 | ||||||||
\(515\) | −8.36543e9 | −2.69875 | ||||||||
\(516\) | 1.68590e7 | 0.00540205 | ||||||||
\(517\) | 1.26365e9 | 0.402170 | ||||||||
\(518\) | −6.01312e9 | −1.90084 | ||||||||
\(519\) | 5.62705e8 | 0.176683 | ||||||||
\(520\) | 2.07607e9 | 0.647486 | ||||||||
\(521\) | 4.76502e9 | 1.47616 | 0.738079 | − | 0.674715i | \(-0.235733\pi\) | ||||
0.738079 | + | 0.674715i | \(0.235733\pi\) | |||||||
\(522\) | 6.21882e8 | 0.191364 | ||||||||
\(523\) | −4.61783e9 | −1.41151 | −0.705753 | − | 0.708458i | \(-0.749391\pi\) | ||||
−0.705753 | + | 0.708458i | \(0.749391\pi\) | |||||||
\(524\) | −1.05492e8 | −0.0320304 | ||||||||
\(525\) | −4.01406e9 | −1.21067 | ||||||||
\(526\) | −3.16490e9 | −0.948223 | ||||||||
\(527\) | −4.47322e9 | −1.33132 | ||||||||
\(528\) | −1.01616e9 | −0.300431 | ||||||||
\(529\) | 6.87745e8 | 0.201991 | ||||||||
\(530\) | 1.34653e9 | 0.392870 | ||||||||
\(531\) | 2.60650e7 | 0.00755485 | ||||||||
\(532\) | −6.79656e7 | −0.0195703 | ||||||||
\(533\) | 2.59332e9 | 0.741842 | ||||||||
\(534\) | 4.24039e9 | 1.20507 | ||||||||
\(535\) | −1.65954e9 | −0.468542 | ||||||||
\(536\) | 4.09494e9 | 1.14860 | ||||||||
\(537\) | 2.76287e8 | 0.0769929 | ||||||||
\(538\) | 8.10294e8 | 0.224339 | ||||||||
\(539\) | 9.80788e8 | 0.269783 | ||||||||
\(540\) | 4.19706e8 | 0.114701 | ||||||||
\(541\) | −4.03282e9 | −1.09501 | −0.547506 | − | 0.836802i | \(-0.684423\pi\) | ||||
−0.547506 | + | 0.836802i | \(0.684423\pi\) | |||||||
\(542\) | −8.06139e8 | −0.217476 | ||||||||
\(543\) | −1.50594e9 | −0.403652 | ||||||||
\(544\) | 6.96022e8 | 0.185365 | ||||||||
\(545\) | 2.63366e9 | 0.696902 | ||||||||
\(546\) | −2.44983e9 | −0.644112 | ||||||||
\(547\) | −3.23762e9 | −0.845804 | −0.422902 | − | 0.906175i | \(-0.638989\pi\) | ||||
−0.422902 | + | 0.906175i | \(0.638989\pi\) | |||||||
\(548\) | −3.38813e8 | −0.0879483 | ||||||||
\(549\) | 8.26957e8 | 0.213295 | ||||||||
\(550\) | −1.15553e9 | −0.296151 | ||||||||
\(551\) | 9.73523e8 | 0.247922 | ||||||||
\(552\) | −3.85598e9 | −0.975772 | ||||||||
\(553\) | 7.59692e8 | 0.191029 | ||||||||
\(554\) | 7.30718e9 | 1.82585 | ||||||||
\(555\) | 6.94724e9 | 1.72499 | ||||||||
\(556\) | 2.59688e7 | 0.00640752 | ||||||||
\(557\) | 6.03647e9 | 1.48009 | 0.740047 | − | 0.672555i | \(-0.234803\pi\) | ||||
0.740047 | + | 0.672555i | \(0.234803\pi\) | |||||||
\(558\) | −6.45516e8 | −0.157285 | ||||||||
\(559\) | −1.49405e8 | −0.0361763 | ||||||||
\(560\) | −8.55329e9 | −2.05814 | ||||||||
\(561\) | 1.39821e9 | 0.334350 | ||||||||
\(562\) | 9.48349e8 | 0.225367 | ||||||||
\(563\) | 7.03032e9 | 1.66033 | 0.830167 | − | 0.557515i | \(-0.188245\pi\) | ||||
0.830167 | + | 0.557515i | \(0.188245\pi\) | |||||||
\(564\) | 4.11426e8 | 0.0965640 | ||||||||
\(565\) | −8.83530e8 | −0.206088 | ||||||||
\(566\) | 3.75695e9 | 0.870918 | ||||||||
\(567\) | 5.05367e9 | 1.16430 | ||||||||
\(568\) | −5.66180e9 | −1.29639 | ||||||||
\(569\) | −4.25341e9 | −0.967930 | −0.483965 | − | 0.875087i | \(-0.660804\pi\) | ||||
−0.483965 | + | 0.875087i | \(0.660804\pi\) | |||||||
\(570\) | 1.08688e9 | 0.245822 | ||||||||
\(571\) | 3.26097e9 | 0.733029 | 0.366514 | − | 0.930412i | \(-0.380551\pi\) | ||||
0.366514 | + | 0.930412i | \(0.380551\pi\) | |||||||
\(572\) | −5.09509e7 | −0.0113832 | ||||||||
\(573\) | 3.55718e9 | 0.789886 | ||||||||
\(574\) | −9.90807e9 | −2.18674 | ||||||||
\(575\) | −4.72839e9 | −1.03723 | ||||||||
\(576\) | −5.66813e8 | −0.123584 | ||||||||
\(577\) | −7.44043e9 | −1.61244 | −0.806219 | − | 0.591617i | \(-0.798490\pi\) | ||||
−0.806219 | + | 0.591617i | \(0.798490\pi\) | |||||||
\(578\) | −2.03790e9 | −0.438971 | ||||||||
\(579\) | −2.96939e9 | −0.635758 | ||||||||
\(580\) | −6.93180e8 | −0.147519 | ||||||||
\(581\) | −2.68088e8 | −0.0567101 | ||||||||
\(582\) | 7.09359e8 | 0.149154 | ||||||||
\(583\) | 3.91318e8 | 0.0817880 | ||||||||
\(584\) | 2.71076e9 | 0.563179 | ||||||||
\(585\) | −4.44525e8 | −0.0918018 | ||||||||
\(586\) | 5.01544e9 | 1.02960 | ||||||||
\(587\) | 4.66637e9 | 0.952238 | 0.476119 | − | 0.879381i | \(-0.342043\pi\) | ||||
0.476119 | + | 0.879381i | \(0.342043\pi\) | |||||||
\(588\) | 3.19331e8 | 0.0647770 | ||||||||
\(589\) | −1.01052e9 | −0.203771 | ||||||||
\(590\) | −4.02139e8 | −0.0806110 | ||||||||
\(591\) | 2.04591e9 | 0.407690 | ||||||||
\(592\) | 7.19660e9 | 1.42561 | ||||||||
\(593\) | 5.22317e9 | 1.02859 | 0.514296 | − | 0.857613i | \(-0.328053\pi\) | ||||
0.514296 | + | 0.857613i | \(0.328053\pi\) | |||||||
\(594\) | 1.68826e9 | 0.330513 | ||||||||
\(595\) | 1.17691e10 | 2.29051 | ||||||||
\(596\) | 9.36433e7 | 0.0181182 | ||||||||
\(597\) | −4.29416e9 | −0.825977 | ||||||||
\(598\) | −2.88579e9 | −0.551836 | ||||||||
\(599\) | 3.32573e9 | 0.632257 | 0.316128 | − | 0.948716i | \(-0.397617\pi\) | ||||
0.316128 | + | 0.948716i | \(0.397617\pi\) | |||||||
\(600\) | 4.45505e9 | 0.842022 | ||||||||
\(601\) | −9.44629e9 | −1.77501 | −0.887504 | − | 0.460799i | \(-0.847563\pi\) | ||||
−0.887504 | + | 0.460799i | \(0.847563\pi\) | |||||||
\(602\) | 5.70819e8 | 0.106638 | ||||||||
\(603\) | −8.76802e8 | −0.162851 | ||||||||
\(604\) | −2.57859e8 | −0.0476160 | ||||||||
\(605\) | −6.90766e8 | −0.126820 | ||||||||
\(606\) | −6.27985e9 | −1.14629 | ||||||||
\(607\) | −4.62671e9 | −0.839676 | −0.419838 | − | 0.907599i | \(-0.637913\pi\) | ||||
−0.419838 | + | 0.907599i | \(0.637913\pi\) | |||||||
\(608\) | 1.57235e8 | 0.0283717 | ||||||||
\(609\) | −9.68599e9 | −1.73773 | ||||||||
\(610\) | −1.27586e10 | −2.27587 | ||||||||
\(611\) | −3.64608e9 | −0.646668 | ||||||||
\(612\) | −7.14967e7 | −0.0126083 | ||||||||
\(613\) | 8.77518e9 | 1.53867 | 0.769333 | − | 0.638848i | \(-0.220589\pi\) | ||||
0.769333 | + | 0.638848i | \(0.220589\pi\) | |||||||
\(614\) | −1.91550e9 | −0.333959 | ||||||||
\(615\) | 1.14473e10 | 1.98444 | ||||||||
\(616\) | −2.30510e9 | −0.397335 | ||||||||
\(617\) | −3.17693e9 | −0.544514 | −0.272257 | − | 0.962225i | \(-0.587770\pi\) | ||||
−0.272257 | + | 0.962225i | \(0.587770\pi\) | |||||||
\(618\) | −1.09559e10 | −1.86720 | ||||||||
\(619\) | −5.77076e9 | −0.977948 | −0.488974 | − | 0.872298i | \(-0.662629\pi\) | ||||
−0.488974 | + | 0.872298i | \(0.662629\pi\) | |||||||
\(620\) | 7.19525e8 | 0.121248 | ||||||||
\(621\) | 6.90831e9 | 1.15758 | ||||||||
\(622\) | −1.43576e9 | −0.239230 | ||||||||
\(623\) | 1.03727e10 | 1.71863 | ||||||||
\(624\) | 2.93199e9 | 0.483077 | ||||||||
\(625\) | −6.41490e9 | −1.05102 | ||||||||
\(626\) | −8.90989e8 | −0.145165 | ||||||||
\(627\) | 3.15862e8 | 0.0511753 | ||||||||
\(628\) | −4.16169e8 | −0.0670519 | ||||||||
\(629\) | −9.90229e9 | −1.58657 | ||||||||
\(630\) | 1.69836e9 | 0.270606 | ||||||||
\(631\) | 9.29360e9 | 1.47259 | 0.736294 | − | 0.676662i | \(-0.236574\pi\) | ||||
0.736294 | + | 0.676662i | \(0.236574\pi\) | |||||||
\(632\) | −8.43152e8 | −0.132861 | ||||||||
\(633\) | −5.99370e9 | −0.939251 | ||||||||
\(634\) | 1.11451e10 | 1.73689 | ||||||||
\(635\) | −4.30840e9 | −0.667741 | ||||||||
\(636\) | 1.27408e8 | 0.0196379 | ||||||||
\(637\) | −2.82993e9 | −0.433797 | ||||||||
\(638\) | −2.78831e9 | −0.425079 | ||||||||
\(639\) | 1.21230e9 | 0.183804 | ||||||||
\(640\) | 1.01827e10 | 1.53544 | ||||||||
\(641\) | 6.12597e9 | 0.918696 | 0.459348 | − | 0.888256i | \(-0.348083\pi\) | ||||
0.459348 | + | 0.888256i | \(0.348083\pi\) | |||||||
\(642\) | −2.17344e9 | −0.324172 | ||||||||
\(643\) | 7.62998e8 | 0.113184 | 0.0565920 | − | 0.998397i | \(-0.481977\pi\) | ||||
0.0565920 | + | 0.998397i | \(0.481977\pi\) | |||||||
\(644\) | 7.96555e8 | 0.117521 | ||||||||
\(645\) | −6.59494e8 | −0.0967724 | ||||||||
\(646\) | −1.54919e9 | −0.226095 | ||||||||
\(647\) | −1.50623e9 | −0.218638 | −0.109319 | − | 0.994007i | \(-0.534867\pi\) | ||||
−0.109319 | + | 0.994007i | \(0.534867\pi\) | |||||||
\(648\) | −5.60887e9 | −0.809772 | ||||||||
\(649\) | −1.16867e8 | −0.0167816 | ||||||||
\(650\) | 3.33413e9 | 0.476195 | ||||||||
\(651\) | 1.00541e10 | 1.42827 | ||||||||
\(652\) | −2.44280e8 | −0.0345160 | ||||||||
\(653\) | −3.12302e9 | −0.438913 | −0.219456 | − | 0.975622i | \(-0.570428\pi\) | ||||
−0.219456 | + | 0.975622i | \(0.570428\pi\) | |||||||
\(654\) | 3.44922e9 | 0.482169 | ||||||||
\(655\) | 4.12667e9 | 0.573793 | ||||||||
\(656\) | 1.18581e10 | 1.64003 | ||||||||
\(657\) | −5.80425e8 | −0.0798486 | ||||||||
\(658\) | 1.39302e10 | 1.90620 | ||||||||
\(659\) | −1.41329e10 | −1.92368 | −0.961840 | − | 0.273613i | \(-0.911781\pi\) | ||||
−0.961840 | + | 0.273613i | \(0.911781\pi\) | |||||||
\(660\) | −2.24904e8 | −0.0304504 | ||||||||
\(661\) | −5.09870e9 | −0.686680 | −0.343340 | − | 0.939211i | \(-0.611558\pi\) | ||||
−0.343340 | + | 0.939211i | \(0.611558\pi\) | |||||||
\(662\) | 6.10882e9 | 0.818379 | ||||||||
\(663\) | −4.03433e9 | −0.537618 | ||||||||
\(664\) | 2.97540e8 | 0.0394418 | ||||||||
\(665\) | 2.65869e9 | 0.350583 | ||||||||
\(666\) | −1.42897e9 | −0.187440 | ||||||||
\(667\) | −1.14097e10 | −1.48879 | ||||||||
\(668\) | −6.71260e8 | −0.0871312 | ||||||||
\(669\) | 1.16242e10 | 1.50097 | ||||||||
\(670\) | 1.35276e10 | 1.73764 | ||||||||
\(671\) | −3.70781e9 | −0.473793 | ||||||||
\(672\) | −1.56439e9 | −0.198863 | ||||||||
\(673\) | 1.45170e10 | 1.83580 | 0.917901 | − | 0.396811i | \(-0.129883\pi\) | ||||
0.917901 | + | 0.396811i | \(0.129883\pi\) | |||||||
\(674\) | −7.67037e9 | −0.964954 | ||||||||
\(675\) | −7.98159e9 | −0.998909 | ||||||||
\(676\) | −4.78449e8 | −0.0595692 | ||||||||
\(677\) | −7.52045e9 | −0.931501 | −0.465751 | − | 0.884916i | \(-0.654216\pi\) | ||||
−0.465751 | + | 0.884916i | \(0.654216\pi\) | |||||||
\(678\) | −1.15713e9 | −0.142587 | ||||||||
\(679\) | 1.73521e9 | 0.212719 | ||||||||
\(680\) | −1.30620e10 | −1.59305 | ||||||||
\(681\) | −2.47279e9 | −0.300035 | ||||||||
\(682\) | 2.89428e9 | 0.349378 | ||||||||
\(683\) | −2.67143e9 | −0.320828 | −0.160414 | − | 0.987050i | \(-0.551283\pi\) | ||||
−0.160414 | + | 0.987050i | \(0.551283\pi\) | |||||||
\(684\) | −1.61515e7 | −0.00192981 | ||||||||
\(685\) | 1.32537e10 | 1.57551 | ||||||||
\(686\) | −1.27157e9 | −0.150385 | ||||||||
\(687\) | −1.30715e10 | −1.53807 | ||||||||
\(688\) | −6.83165e8 | −0.0799772 | ||||||||
\(689\) | −1.12909e9 | −0.131511 | ||||||||
\(690\) | −1.27382e10 | −1.47617 | ||||||||
\(691\) | −8.80524e8 | −0.101524 | −0.0507619 | − | 0.998711i | \(-0.516165\pi\) | ||||
−0.0507619 | + | 0.998711i | \(0.516165\pi\) | |||||||
\(692\) | 1.29012e8 | 0.0147999 | ||||||||
\(693\) | 4.93564e8 | 0.0563348 | ||||||||
\(694\) | −5.44330e9 | −0.618165 | ||||||||
\(695\) | −1.01585e9 | −0.114785 | ||||||||
\(696\) | 1.07501e10 | 1.20859 | ||||||||
\(697\) | −1.63164e10 | −1.82520 | ||||||||
\(698\) | −3.24938e9 | −0.361665 | ||||||||
\(699\) | 1.60976e10 | 1.78275 | ||||||||
\(700\) | −9.20308e8 | −0.101412 | ||||||||
\(701\) | 1.16510e10 | 1.27747 | 0.638733 | − | 0.769429i | \(-0.279459\pi\) | ||||
0.638733 | + | 0.769429i | \(0.279459\pi\) | |||||||
\(702\) | −4.87125e9 | −0.531447 | ||||||||
\(703\) | −2.23698e9 | −0.242839 | ||||||||
\(704\) | 2.54141e9 | 0.274517 | ||||||||
\(705\) | −1.60942e10 | −1.72985 | ||||||||
\(706\) | 6.43007e9 | 0.687701 | ||||||||
\(707\) | −1.53615e10 | −1.63481 | ||||||||
\(708\) | −3.80502e7 | −0.00402940 | ||||||||
\(709\) | 1.07976e10 | 1.13779 | 0.568897 | − | 0.822409i | \(-0.307370\pi\) | ||||
0.568897 | + | 0.822409i | \(0.307370\pi\) | |||||||
\(710\) | −1.87037e10 | −1.96121 | ||||||||
\(711\) | 1.80535e8 | 0.0188372 | ||||||||
\(712\) | −1.15122e10 | −1.19531 | ||||||||
\(713\) | 1.18433e10 | 1.22366 | ||||||||
\(714\) | 1.54136e10 | 1.58475 | ||||||||
\(715\) | 1.99311e9 | 0.203920 | ||||||||
\(716\) | 6.33446e7 | 0.00644932 | ||||||||
\(717\) | 1.30615e10 | 1.32335 | ||||||||
\(718\) | 5.30523e9 | 0.534895 | ||||||||
\(719\) | −2.39680e9 | −0.240481 | −0.120241 | − | 0.992745i | \(-0.538367\pi\) | ||||
−0.120241 | + | 0.992745i | \(0.538367\pi\) | |||||||
\(720\) | −2.03262e9 | −0.202952 | ||||||||
\(721\) | −2.68000e10 | −2.66294 | ||||||||
\(722\) | 1.01494e10 | 1.00360 | ||||||||
\(723\) | 1.19791e9 | 0.117880 | ||||||||
\(724\) | −3.45267e8 | −0.0338120 | ||||||||
\(725\) | 1.31823e10 | 1.28472 | ||||||||
\(726\) | −9.04675e8 | −0.0877434 | ||||||||
\(727\) | 7.10027e9 | 0.685337 | 0.342669 | − | 0.939456i | \(-0.388669\pi\) | ||||
0.342669 | + | 0.939456i | \(0.388669\pi\) | |||||||
\(728\) | 6.65102e9 | 0.638894 | ||||||||
\(729\) | 1.14686e10 | 1.09639 | ||||||||
\(730\) | 8.95500e9 | 0.851992 | ||||||||
\(731\) | 9.40013e8 | 0.0890068 | ||||||||
\(732\) | −1.20721e9 | −0.113761 | ||||||||
\(733\) | −1.02464e10 | −0.960964 | −0.480482 | − | 0.877005i | \(-0.659538\pi\) | ||||
−0.480482 | + | 0.877005i | \(0.659538\pi\) | |||||||
\(734\) | 1.04002e10 | 0.970748 | ||||||||
\(735\) | −1.24916e10 | −1.16042 | ||||||||
\(736\) | −1.84279e9 | −0.170374 | ||||||||
\(737\) | 3.93129e9 | 0.361742 | ||||||||
\(738\) | −2.35457e9 | −0.215633 | ||||||||
\(739\) | 1.01080e10 | 0.921318 | 0.460659 | − | 0.887577i | \(-0.347613\pi\) | ||||
0.460659 | + | 0.887577i | \(0.347613\pi\) | |||||||
\(740\) | 1.59280e9 | 0.144494 | ||||||||
\(741\) | −9.11374e8 | −0.0822873 | ||||||||
\(742\) | 4.31381e9 | 0.387657 | ||||||||
\(743\) | 1.79087e10 | 1.60178 | 0.800892 | − | 0.598809i | \(-0.204359\pi\) | ||||
0.800892 | + | 0.598809i | \(0.204359\pi\) | |||||||
\(744\) | −1.11586e10 | −0.993359 | ||||||||
\(745\) | −3.66315e9 | −0.324570 | ||||||||
\(746\) | −9.42691e8 | −0.0831349 | ||||||||
\(747\) | −6.37089e7 | −0.00559214 | ||||||||
\(748\) | 3.20568e8 | 0.0280069 | ||||||||
\(749\) | −5.31659e9 | −0.462324 | ||||||||
\(750\) | −8.38868e8 | −0.0726071 | ||||||||
\(751\) | 1.14603e10 | 0.987313 | 0.493657 | − | 0.869657i | \(-0.335660\pi\) | ||||
0.493657 | + | 0.869657i | \(0.335660\pi\) | |||||||
\(752\) | −1.66719e10 | −1.42963 | ||||||||
\(753\) | −5.09032e9 | −0.434473 | ||||||||
\(754\) | 8.04528e9 | 0.683505 | ||||||||
\(755\) | 1.00870e10 | 0.852994 | ||||||||
\(756\) | 1.34460e9 | 0.113179 | ||||||||
\(757\) | 1.69859e10 | 1.42315 | 0.711577 | − | 0.702608i | \(-0.247981\pi\) | ||||
0.711577 | + | 0.702608i | \(0.247981\pi\) | |||||||
\(758\) | −1.34690e10 | −1.12329 | ||||||||
\(759\) | −3.70189e9 | −0.307311 | ||||||||
\(760\) | −2.95077e9 | −0.243830 | ||||||||
\(761\) | −1.67046e10 | −1.37401 | −0.687004 | − | 0.726654i | \(-0.741074\pi\) | ||||
−0.687004 | + | 0.726654i | \(0.741074\pi\) | |||||||
\(762\) | −5.64258e9 | −0.461993 | ||||||||
\(763\) | 8.43735e9 | 0.687655 | ||||||||
\(764\) | 8.15557e8 | 0.0661649 | ||||||||
\(765\) | 2.79682e9 | 0.225865 | ||||||||
\(766\) | −5.88894e9 | −0.473409 | ||||||||
\(767\) | 3.37202e8 | 0.0269840 | ||||||||
\(768\) | 2.71033e9 | 0.215903 | ||||||||
\(769\) | −1.27067e10 | −1.00761 | −0.503803 | − | 0.863818i | \(-0.668066\pi\) | ||||
−0.503803 | + | 0.863818i | \(0.668066\pi\) | |||||||
\(770\) | −7.61488e9 | −0.601098 | ||||||||
\(771\) | −4.60404e9 | −0.361783 | ||||||||
\(772\) | −6.80794e8 | −0.0532544 | ||||||||
\(773\) | −8.89505e9 | −0.692660 | −0.346330 | − | 0.938113i | \(-0.612572\pi\) | ||||
−0.346330 | + | 0.938113i | \(0.612572\pi\) | |||||||
\(774\) | 1.35650e8 | 0.0105154 | ||||||||
\(775\) | −1.36833e10 | −1.05593 | ||||||||
\(776\) | −1.92584e9 | −0.147946 | ||||||||
\(777\) | 2.22566e10 | 1.70210 | ||||||||
\(778\) | −8.13726e9 | −0.619512 | ||||||||
\(779\) | −3.68596e9 | −0.279363 | ||||||||
\(780\) | 6.48928e8 | 0.0489627 | ||||||||
\(781\) | −5.43554e9 | −0.408286 | ||||||||
\(782\) | 1.81565e10 | 1.35772 | ||||||||
\(783\) | −1.92597e10 | −1.43378 | ||||||||
\(784\) | −1.29400e10 | −0.959021 | ||||||||
\(785\) | 1.62798e10 | 1.20117 | ||||||||
\(786\) | 5.40457e9 | 0.396992 | ||||||||
\(787\) | 6.24086e9 | 0.456386 | 0.228193 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228193 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(788\) | 4.69067e8 | 0.0341502 | ||||||||
\(789\) | 1.17144e10 | 0.849082 | ||||||||
\(790\) | −2.78535e9 | −0.200995 | ||||||||
\(791\) | −2.83053e9 | −0.203353 | ||||||||
\(792\) | −5.47787e8 | −0.0391808 | ||||||||
\(793\) | 1.06983e10 | 0.761834 | ||||||||
\(794\) | 1.78123e10 | 1.26284 | ||||||||
\(795\) | −4.98395e9 | −0.351794 | ||||||||
\(796\) | −9.84525e8 | −0.0691880 | ||||||||
\(797\) | −7.50982e9 | −0.525442 | −0.262721 | − | 0.964872i | \(-0.584620\pi\) | ||||
−0.262721 | + | 0.964872i | \(0.584620\pi\) | |||||||
\(798\) | 3.48200e9 | 0.242560 | ||||||||
\(799\) | 2.29400e10 | 1.59104 | ||||||||
\(800\) | 2.12908e9 | 0.147020 | ||||||||
\(801\) | 2.46498e9 | 0.169473 | ||||||||
\(802\) | −1.78420e10 | −1.22133 | ||||||||
\(803\) | 2.60244e9 | 0.177368 | ||||||||
\(804\) | 1.27998e9 | 0.0868571 | ||||||||
\(805\) | −3.11598e10 | −2.10527 | ||||||||
\(806\) | −8.35105e9 | −0.561783 | ||||||||
\(807\) | −2.99917e9 | −0.200883 | ||||||||
\(808\) | 1.70491e10 | 1.13701 | ||||||||
\(809\) | 5.76686e9 | 0.382930 | 0.191465 | − | 0.981499i | \(-0.438676\pi\) | ||||
0.191465 | + | 0.981499i | \(0.438676\pi\) | |||||||
\(810\) | −1.85289e10 | −1.22504 | ||||||||
\(811\) | −1.72046e10 | −1.13259 | −0.566293 | − | 0.824204i | \(-0.691623\pi\) | ||||
−0.566293 | + | 0.824204i | \(0.691623\pi\) | |||||||
\(812\) | −2.22071e9 | −0.145562 | ||||||||
\(813\) | 2.98379e9 | 0.194738 | ||||||||
\(814\) | 6.40703e9 | 0.416362 | ||||||||
\(815\) | 9.55577e9 | 0.618321 | ||||||||
\(816\) | −1.84472e10 | −1.18854 | ||||||||
\(817\) | 2.12354e8 | 0.0136233 | ||||||||
\(818\) | 7.12928e8 | 0.0455417 | ||||||||
\(819\) | −1.42411e9 | −0.0905836 | ||||||||
\(820\) | 2.62452e9 | 0.166227 | ||||||||
\(821\) | −5.07112e9 | −0.319818 | −0.159909 | − | 0.987132i | \(-0.551120\pi\) | ||||
−0.159909 | + | 0.987132i | \(0.551120\pi\) | |||||||
\(822\) | 1.73580e10 | 1.09005 | ||||||||
\(823\) | −2.75808e10 | −1.72467 | −0.862337 | − | 0.506335i | \(-0.831000\pi\) | ||||
−0.862337 | + | 0.506335i | \(0.831000\pi\) | |||||||
\(824\) | 2.97443e10 | 1.85207 | ||||||||
\(825\) | 4.27702e9 | 0.265187 | ||||||||
\(826\) | −1.28832e9 | −0.0795413 | ||||||||
\(827\) | −1.37072e10 | −0.842710 | −0.421355 | − | 0.906896i | \(-0.638445\pi\) | ||||
−0.421355 | + | 0.906896i | \(0.638445\pi\) | |||||||
\(828\) | 1.89295e8 | 0.0115886 | ||||||||
\(829\) | −5.39751e9 | −0.329043 | −0.164521 | − | 0.986374i | \(-0.552608\pi\) | ||||
−0.164521 | + | 0.986374i | \(0.552608\pi\) | |||||||
\(830\) | 9.82923e8 | 0.0596686 | ||||||||
\(831\) | −2.70464e10 | −1.63495 | ||||||||
\(832\) | −7.33286e9 | −0.441410 | ||||||||
\(833\) | 1.78050e10 | 1.06730 | ||||||||
\(834\) | −1.33043e9 | −0.0794165 | ||||||||
\(835\) | 2.62585e10 | 1.56087 | ||||||||
\(836\) | 7.24178e7 | 0.00428671 | ||||||||
\(837\) | 1.99916e10 | 1.17844 | ||||||||
\(838\) | 5.15156e9 | 0.302402 | ||||||||
\(839\) | 7.66291e9 | 0.447948 | 0.223974 | − | 0.974595i | \(-0.428097\pi\) | ||||
0.223974 | + | 0.974595i | \(0.428097\pi\) | |||||||
\(840\) | 2.93585e10 | 1.70905 | ||||||||
\(841\) | 1.45591e10 | 0.844013 | ||||||||
\(842\) | 2.21308e10 | 1.27763 | ||||||||
\(843\) | −3.51016e9 | −0.201804 | ||||||||
\(844\) | −1.37418e9 | −0.0786765 | ||||||||
\(845\) | 1.87160e10 | 1.06713 | ||||||||
\(846\) | 3.31040e9 | 0.187968 | ||||||||
\(847\) | −2.21298e9 | −0.125137 | ||||||||
\(848\) | −5.16284e9 | −0.290739 | ||||||||
\(849\) | −1.39057e10 | −0.779860 | ||||||||
\(850\) | −2.09773e10 | −1.17161 | ||||||||
\(851\) | 2.62173e10 | 1.45826 | ||||||||
\(852\) | −1.76974e9 | −0.0980325 | ||||||||
\(853\) | 9.11744e9 | 0.502981 | 0.251490 | − | 0.967860i | \(-0.419079\pi\) | ||||
0.251490 | + | 0.967860i | \(0.419079\pi\) | |||||||
\(854\) | −4.08742e10 | −2.24567 | ||||||||
\(855\) | 6.31815e8 | 0.0345707 | ||||||||
\(856\) | 5.90067e9 | 0.321546 | ||||||||
\(857\) | −2.27356e10 | −1.23388 | −0.616942 | − | 0.787009i | \(-0.711629\pi\) | ||||
−0.616942 | + | 0.787009i | \(0.711629\pi\) | |||||||
\(858\) | 2.61031e9 | 0.141087 | ||||||||
\(859\) | −4.15338e9 | −0.223576 | −0.111788 | − | 0.993732i | \(-0.535658\pi\) | ||||
−0.111788 | + | 0.993732i | \(0.535658\pi\) | |||||||
\(860\) | −1.51203e8 | −0.00810615 | ||||||||
\(861\) | 3.66731e10 | 1.95811 | ||||||||
\(862\) | −8.65162e9 | −0.460068 | ||||||||
\(863\) | −1.94331e10 | −1.02921 | −0.514606 | − | 0.857427i | \(-0.672062\pi\) | ||||
−0.514606 | + | 0.857427i | \(0.672062\pi\) | |||||||
\(864\) | −3.11065e9 | −0.164079 | ||||||||
\(865\) | −5.04671e9 | −0.265126 | ||||||||
\(866\) | −9.38535e9 | −0.491064 | ||||||||
\(867\) | 7.54297e9 | 0.393075 | ||||||||
\(868\) | 2.30511e9 | 0.119639 | ||||||||
\(869\) | −8.09458e8 | −0.0418432 | ||||||||
\(870\) | 3.55129e10 | 1.82839 | ||||||||
\(871\) | −1.13432e10 | −0.581663 | ||||||||
\(872\) | −9.36428e9 | −0.478263 | ||||||||
\(873\) | 4.12357e8 | 0.0209761 | ||||||||
\(874\) | 4.10164e9 | 0.207811 | ||||||||
\(875\) | −2.05201e9 | −0.103550 | ||||||||
\(876\) | 8.47317e8 | 0.0425874 | ||||||||
\(877\) | −1.61113e10 | −0.806550 | −0.403275 | − | 0.915079i | \(-0.632128\pi\) | ||||
−0.403275 | + | 0.915079i | \(0.632128\pi\) | |||||||
\(878\) | −1.16233e10 | −0.579559 | ||||||||
\(879\) | −1.85638e10 | −0.921948 | ||||||||
\(880\) | 9.11360e9 | 0.450817 | ||||||||
\(881\) | −1.85288e10 | −0.912916 | −0.456458 | − | 0.889745i | \(-0.650882\pi\) | ||||
−0.456458 | + | 0.889745i | \(0.650882\pi\) | |||||||
\(882\) | 2.56939e9 | 0.126093 | ||||||||
\(883\) | −1.99740e10 | −0.976345 | −0.488172 | − | 0.872747i | \(-0.662336\pi\) | ||||
−0.488172 | + | 0.872747i | \(0.662336\pi\) | |||||||
\(884\) | −9.24953e8 | −0.0450336 | ||||||||
\(885\) | 1.48845e9 | 0.0721828 | ||||||||
\(886\) | 8.45437e9 | 0.408379 | ||||||||
\(887\) | −5.34255e9 | −0.257049 | −0.128525 | − | 0.991706i | \(-0.541024\pi\) | ||||
−0.128525 | + | 0.991706i | \(0.541024\pi\) | |||||||
\(888\) | −2.47017e10 | −1.18381 | ||||||||
\(889\) | −1.38026e10 | −0.658880 | ||||||||
\(890\) | −3.80306e10 | −1.80829 | ||||||||
\(891\) | −5.38473e9 | −0.255030 | ||||||||
\(892\) | 2.66510e9 | 0.125729 | ||||||||
\(893\) | 5.18226e9 | 0.243523 | ||||||||
\(894\) | −4.79752e9 | −0.224561 | ||||||||
\(895\) | −2.47792e9 | −0.115533 | ||||||||
\(896\) | 3.26218e10 | 1.51506 | ||||||||
\(897\) | 1.06813e10 | 0.494140 | ||||||||
\(898\) | −1.59055e9 | −0.0732960 | ||||||||
\(899\) | −3.30179e10 | −1.51562 | ||||||||
\(900\) | −2.18704e8 | −0.0100002 | ||||||||
\(901\) | 7.10390e9 | 0.323564 | ||||||||
\(902\) | 1.05571e10 | 0.478986 | ||||||||
\(903\) | −2.11279e9 | −0.0954883 | ||||||||
\(904\) | 3.14149e9 | 0.141432 | ||||||||
\(905\) | 1.35062e10 | 0.605709 | ||||||||
\(906\) | 1.32106e10 | 0.590165 | ||||||||
\(907\) | 7.80696e9 | 0.347421 | 0.173711 | − | 0.984797i | \(-0.444424\pi\) | ||||
0.173711 | + | 0.984797i | \(0.444424\pi\) | |||||||
\(908\) | −5.66939e8 | −0.0251325 | ||||||||
\(909\) | −3.65054e9 | −0.161207 | ||||||||
\(910\) | 2.19716e10 | 0.966535 | ||||||||
\(911\) | −2.92975e10 | −1.28386 | −0.641928 | − | 0.766765i | \(-0.721865\pi\) | ||||
−0.641928 | + | 0.766765i | \(0.721865\pi\) | |||||||
\(912\) | −4.16731e9 | −0.181917 | ||||||||
\(913\) | 2.85650e8 | 0.0124218 | ||||||||
\(914\) | −3.56810e10 | −1.54570 | ||||||||
\(915\) | 4.72238e10 | 2.03792 | ||||||||
\(916\) | −2.99691e9 | −0.128837 | ||||||||
\(917\) | 1.32204e10 | 0.566179 | ||||||||
\(918\) | 3.06484e10 | 1.30755 | ||||||||
\(919\) | 4.50916e10 | 1.91642 | 0.958212 | − | 0.286061i | \(-0.0923459\pi\) | ||||
0.958212 | + | 0.286061i | \(0.0923459\pi\) | |||||||
\(920\) | 3.45830e10 | 1.46422 | ||||||||
\(921\) | 7.08991e9 | 0.299042 | ||||||||
\(922\) | 1.59531e10 | 0.670328 | ||||||||
\(923\) | 1.56835e10 | 0.656503 | ||||||||
\(924\) | −7.20516e8 | −0.0300463 | ||||||||
\(925\) | −3.02904e10 | −1.25837 | ||||||||
\(926\) | 1.54117e10 | 0.637839 | ||||||||
\(927\) | −6.36880e9 | −0.262590 | ||||||||
\(928\) | 5.13750e9 | 0.211025 | ||||||||
\(929\) | −3.94849e10 | −1.61576 | −0.807878 | − | 0.589350i | \(-0.799384\pi\) | ||||
−0.807878 | + | 0.589350i | \(0.799384\pi\) | |||||||
\(930\) | −3.68626e10 | −1.50278 | ||||||||
\(931\) | 4.02224e9 | 0.163360 | ||||||||
\(932\) | 3.69071e9 | 0.149333 | ||||||||
\(933\) | 5.31424e9 | 0.214218 | ||||||||
\(934\) | −1.61975e9 | −0.0650480 | ||||||||
\(935\) | −1.25400e10 | −0.501716 | ||||||||
\(936\) | 1.58056e9 | 0.0630008 | ||||||||
\(937\) | −2.59072e10 | −1.02880 | −0.514402 | − | 0.857549i | \(-0.671986\pi\) | ||||
−0.514402 | + | 0.857549i | \(0.671986\pi\) | |||||||
\(938\) | 4.33379e10 | 1.71458 | ||||||||
\(939\) | 3.29785e9 | 0.129987 | ||||||||
\(940\) | −3.68994e9 | −0.144901 | ||||||||
\(941\) | 4.37803e10 | 1.71283 | 0.856417 | − | 0.516285i | \(-0.172685\pi\) | ||||
0.856417 | + | 0.516285i | \(0.172685\pi\) | |||||||
\(942\) | 2.13211e10 | 0.831059 | ||||||||
\(943\) | 4.31994e10 | 1.67759 | ||||||||
\(944\) | 1.54188e9 | 0.0596552 | ||||||||
\(945\) | −5.25981e10 | −2.02749 | ||||||||
\(946\) | −6.08212e8 | −0.0233580 | ||||||||
\(947\) | 2.38242e10 | 0.911578 | 0.455789 | − | 0.890088i | \(-0.349357\pi\) | ||||
0.455789 | + | 0.890088i | \(0.349357\pi\) | |||||||
\(948\) | −2.63548e8 | −0.0100469 | ||||||||
\(949\) | −7.50896e9 | −0.285199 | ||||||||
\(950\) | −4.73888e9 | −0.179326 | ||||||||
\(951\) | −4.12517e10 | −1.55529 | ||||||||
\(952\) | −4.18462e10 | −1.57191 | ||||||||
\(953\) | −3.79309e9 | −0.141961 | −0.0709803 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709803 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(954\) | 1.02514e9 | 0.0382265 | ||||||||
\(955\) | −3.19031e10 | −1.18528 | ||||||||
\(956\) | 2.99462e9 | 0.110851 | ||||||||
\(957\) | 1.03205e10 | 0.380635 | ||||||||
\(958\) | −2.62237e10 | −0.963641 | ||||||||
\(959\) | 4.24604e10 | 1.55460 | ||||||||
\(960\) | −3.23682e10 | −1.18078 | ||||||||
\(961\) | 6.76013e9 | 0.245710 | ||||||||
\(962\) | −1.84866e10 | −0.669490 | ||||||||
\(963\) | −1.26344e9 | −0.0455894 | ||||||||
\(964\) | 2.74645e8 | 0.00987419 | ||||||||
\(965\) | 2.66314e10 | 0.954000 | ||||||||
\(966\) | −4.08090e10 | −1.45658 | ||||||||
\(967\) | 5.24034e10 | 1.86366 | 0.931830 | − | 0.362895i | \(-0.118212\pi\) | ||||
0.931830 | + | 0.362895i | \(0.118212\pi\) | |||||||
\(968\) | 2.45610e9 | 0.0870326 | ||||||||
\(969\) | 5.73409e9 | 0.202456 | ||||||||
\(970\) | −6.36199e9 | −0.223816 | ||||||||
\(971\) | 2.89908e10 | 1.01623 | 0.508116 | − | 0.861288i | \(-0.330342\pi\) | ||||
0.508116 | + | 0.861288i | \(0.330342\pi\) | |||||||
\(972\) | 6.00875e8 | 0.0209871 | ||||||||
\(973\) | −3.25444e9 | −0.113261 | ||||||||
\(974\) | −4.12817e10 | −1.43153 | ||||||||
\(975\) | −1.23407e10 | −0.426407 | ||||||||
\(976\) | 4.89188e10 | 1.68423 | ||||||||
\(977\) | 5.13449e10 | 1.76143 | 0.880717 | − | 0.473643i | \(-0.157061\pi\) | ||||
0.880717 | + | 0.473643i | \(0.157061\pi\) | |||||||
\(978\) | 1.25149e10 | 0.427800 | ||||||||
\(979\) | −1.10522e10 | −0.376451 | ||||||||
\(980\) | −2.86397e9 | −0.0972024 | ||||||||
\(981\) | 2.00507e9 | 0.0678090 | ||||||||
\(982\) | 1.85060e10 | 0.623622 | ||||||||
\(983\) | −4.63039e10 | −1.55482 | −0.777410 | − | 0.628994i | \(-0.783467\pi\) | ||||
−0.777410 | + | 0.628994i | \(0.783467\pi\) | |||||||
\(984\) | −4.07021e10 | −1.36186 | ||||||||
\(985\) | −1.83490e10 | −0.611768 | ||||||||
\(986\) | −5.06185e10 | −1.68167 | ||||||||
\(987\) | −5.15605e10 | −1.70690 | ||||||||
\(988\) | −2.08951e8 | −0.00689280 | ||||||||
\(989\) | −2.48878e9 | −0.0818087 | ||||||||
\(990\) | −1.80961e9 | −0.0592738 | ||||||||
\(991\) | 1.61581e10 | 0.527389 | 0.263695 | − | 0.964606i | \(-0.415059\pi\) | ||||
0.263695 | + | 0.964606i | \(0.415059\pi\) | |||||||
\(992\) | −5.33276e9 | −0.173445 | ||||||||
\(993\) | −2.26108e10 | −0.732814 | ||||||||
\(994\) | −5.99204e10 | −1.93519 | ||||||||
\(995\) | 3.85128e10 | 1.23944 | ||||||||
\(996\) | 9.30036e7 | 0.00298258 | ||||||||
\(997\) | 5.17011e10 | 1.65222 | 0.826108 | − | 0.563512i | \(-0.190550\pi\) | ||||
0.826108 | + | 0.563512i | \(0.190550\pi\) | |||||||
\(998\) | −5.61285e10 | −1.78742 | ||||||||
\(999\) | 4.42552e10 | 1.40438 |
(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 | 11.8.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 99.8.a.c.1.2 | 2 | |||
4.3 | odd | 2 | 176.8.a.d.1.1 | 2 | |||
5.4 | even | 2 | 275.8.a.a.1.2 | 2 | |||
7.6 | odd | 2 | 539.8.a.a.1.1 | 2 | |||
11.10 | odd | 2 | 121.8.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.8.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.8.a.c.1.2 | 2 | 3.2 | odd | 2 | |||
121.8.a.b.1.2 | 2 | 11.10 | odd | 2 | |||
176.8.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
275.8.a.a.1.2 | 2 | 5.4 | even | 2 | |||
539.8.a.a.1.1 | 2 | 7.6 | odd | 2 |