Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,10,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.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: | \(87.0410563117\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 1602x^{2} + 1544x + 342272 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-36.8028\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −28.8028 | −1.27292 | −0.636459 | − | 0.771311i | \(-0.719601\pi\) | ||||
−0.636459 | + | 0.771311i | \(0.719601\pi\) | |||||||
\(3\) | −204.594 | −1.45830 | −0.729150 | − | 0.684354i | \(-0.760084\pi\) | ||||
−0.729150 | + | 0.684354i | \(0.760084\pi\) | |||||||
\(4\) | 317.603 | 0.620318 | ||||||||
\(5\) | 258.914 | 0.185264 | 0.0926319 | − | 0.995700i | \(-0.470472\pi\) | ||||
0.0926319 | + | 0.995700i | \(0.470472\pi\) | |||||||
\(6\) | 5892.88 | 1.85629 | ||||||||
\(7\) | 8862.28 | 1.39510 | 0.697548 | − | 0.716538i | \(-0.254274\pi\) | ||||
0.697548 | + | 0.716538i | \(0.254274\pi\) | |||||||
\(8\) | 5599.18 | 0.483303 | ||||||||
\(9\) | 22175.6 | 1.12664 | ||||||||
\(10\) | −7457.46 | −0.235825 | ||||||||
\(11\) | −36087.9 | −0.743181 | −0.371591 | − | 0.928397i | \(-0.621188\pi\) | ||||
−0.371591 | + | 0.928397i | \(0.621188\pi\) | |||||||
\(12\) | −64979.6 | −0.904610 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −255259. | −1.77584 | ||||||||
\(15\) | −52972.2 | −0.270170 | ||||||||
\(16\) | −323885. | −1.23552 | ||||||||
\(17\) | 327405. | 0.950747 | 0.475373 | − | 0.879784i | \(-0.342313\pi\) | ||||
0.475373 | + | 0.879784i | \(0.342313\pi\) | |||||||
\(18\) | −638720. | −1.43412 | ||||||||
\(19\) | −265525. | −0.467428 | −0.233714 | − | 0.972305i | \(-0.575088\pi\) | ||||
−0.233714 | + | 0.972305i | \(0.575088\pi\) | |||||||
\(20\) | 82231.9 | 0.114923 | ||||||||
\(21\) | −1.81317e6 | −2.03447 | ||||||||
\(22\) | 1.03943e6 | 0.946008 | ||||||||
\(23\) | −2.42458e6 | −1.80660 | −0.903299 | − | 0.429012i | \(-0.858862\pi\) | ||||
−0.903299 | + | 0.429012i | \(0.858862\pi\) | |||||||
\(24\) | −1.14556e6 | −0.704801 | ||||||||
\(25\) | −1.88609e6 | −0.965677 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −509973. | −0.184676 | ||||||||
\(28\) | 2.81469e6 | 0.865404 | ||||||||
\(29\) | 3.99178e6 | 1.04803 | 0.524017 | − | 0.851708i | \(-0.324433\pi\) | ||||
0.524017 | + | 0.851708i | \(0.324433\pi\) | |||||||
\(30\) | 1.52575e6 | 0.343904 | ||||||||
\(31\) | 6.45220e6 | 1.25482 | 0.627408 | − | 0.778691i | \(-0.284116\pi\) | ||||
0.627408 | + | 0.778691i | \(0.284116\pi\) | |||||||
\(32\) | 6.46202e6 | 1.08942 | ||||||||
\(33\) | 7.38336e6 | 1.08378 | ||||||||
\(34\) | −9.43018e6 | −1.21022 | ||||||||
\(35\) | 2.29457e6 | 0.258461 | ||||||||
\(36\) | 7.04304e6 | 0.698874 | ||||||||
\(37\) | 8.15498e6 | 0.715344 | 0.357672 | − | 0.933847i | \(-0.383571\pi\) | ||||
0.357672 | + | 0.933847i | \(0.383571\pi\) | |||||||
\(38\) | 7.64787e6 | 0.594997 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.44971e6 | 0.0895386 | ||||||||
\(41\) | 720241. | 0.0398062 | 0.0199031 | − | 0.999802i | \(-0.493664\pi\) | ||||
0.0199031 | + | 0.999802i | \(0.493664\pi\) | |||||||
\(42\) | 5.22244e7 | 2.58971 | ||||||||
\(43\) | −4.13245e7 | −1.84332 | −0.921658 | − | 0.388004i | \(-0.873165\pi\) | ||||
−0.921658 | + | 0.388004i | \(0.873165\pi\) | |||||||
\(44\) | −1.14616e7 | −0.461009 | ||||||||
\(45\) | 5.74158e6 | 0.208725 | ||||||||
\(46\) | 6.98348e7 | 2.29965 | ||||||||
\(47\) | −3.67369e7 | −1.09815 | −0.549076 | − | 0.835772i | \(-0.685020\pi\) | ||||
−0.549076 | + | 0.835772i | \(0.685020\pi\) | |||||||
\(48\) | 6.62649e7 | 1.80176 | ||||||||
\(49\) | 3.81864e7 | 0.946295 | ||||||||
\(50\) | 5.43247e7 | 1.22923 | ||||||||
\(51\) | −6.69850e7 | −1.38647 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.67334e7 | 0.291302 | 0.145651 | − | 0.989336i | \(-0.453472\pi\) | ||||
0.145651 | + | 0.989336i | \(0.453472\pi\) | |||||||
\(54\) | 1.46887e7 | 0.235077 | ||||||||
\(55\) | −9.34367e6 | −0.137685 | ||||||||
\(56\) | 4.96215e7 | 0.674255 | ||||||||
\(57\) | 5.43248e7 | 0.681649 | ||||||||
\(58\) | −1.14975e8 | −1.33406 | ||||||||
\(59\) | 5.89865e7 | 0.633751 | 0.316875 | − | 0.948467i | \(-0.397366\pi\) | ||||
0.316875 | + | 0.948467i | \(0.397366\pi\) | |||||||
\(60\) | −1.68241e7 | −0.167591 | ||||||||
\(61\) | 1.28785e8 | 1.19091 | 0.595456 | − | 0.803388i | \(-0.296971\pi\) | ||||
0.595456 | + | 0.803388i | \(0.296971\pi\) | |||||||
\(62\) | −1.85842e8 | −1.59728 | ||||||||
\(63\) | 1.96527e8 | 1.57177 | ||||||||
\(64\) | −2.02955e7 | −0.151213 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.12662e8 | −1.37956 | ||||||||
\(67\) | 1.91470e8 | 1.16082 | 0.580410 | − | 0.814324i | \(-0.302892\pi\) | ||||
0.580410 | + | 0.814324i | \(0.302892\pi\) | |||||||
\(68\) | 1.03985e8 | 0.589766 | ||||||||
\(69\) | 4.96054e8 | 2.63456 | ||||||||
\(70\) | −6.60901e7 | −0.328999 | ||||||||
\(71\) | −3.40865e8 | −1.59192 | −0.795958 | − | 0.605351i | \(-0.793033\pi\) | ||||
−0.795958 | + | 0.605351i | \(0.793033\pi\) | |||||||
\(72\) | 1.24165e8 | 0.544508 | ||||||||
\(73\) | −3.19890e8 | −1.31840 | −0.659200 | − | 0.751968i | \(-0.729105\pi\) | ||||
−0.659200 | + | 0.751968i | \(0.729105\pi\) | |||||||
\(74\) | −2.34887e8 | −0.910574 | ||||||||
\(75\) | 3.85882e8 | 1.40825 | ||||||||
\(76\) | −8.43316e7 | −0.289954 | ||||||||
\(77\) | −3.19821e8 | −1.03681 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44328e8 | 0.705751 | 0.352876 | − | 0.935670i | \(-0.385204\pi\) | ||||
0.352876 | + | 0.935670i | \(0.385204\pi\) | |||||||
\(80\) | −8.38584e7 | −0.228898 | ||||||||
\(81\) | −3.32145e8 | −0.857325 | ||||||||
\(82\) | −2.07450e7 | −0.0506700 | ||||||||
\(83\) | 4.38630e8 | 1.01449 | 0.507244 | − | 0.861802i | \(-0.330664\pi\) | ||||
0.507244 | + | 0.861802i | \(0.330664\pi\) | |||||||
\(84\) | −5.75868e8 | −1.26202 | ||||||||
\(85\) | 8.47697e7 | 0.176139 | ||||||||
\(86\) | 1.19026e9 | 2.34639 | ||||||||
\(87\) | −8.16693e8 | −1.52835 | ||||||||
\(88\) | −2.02063e8 | −0.359182 | ||||||||
\(89\) | 7.90342e8 | 1.33524 | 0.667621 | − | 0.744501i | \(-0.267312\pi\) | ||||
0.667621 | + | 0.744501i | \(0.267312\pi\) | |||||||
\(90\) | −1.65374e8 | −0.265690 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.70054e8 | −1.12067 | ||||||||
\(93\) | −1.32008e9 | −1.82990 | ||||||||
\(94\) | 1.05813e9 | 1.39786 | ||||||||
\(95\) | −6.87481e7 | −0.0865974 | ||||||||
\(96\) | −1.32209e9 | −1.58869 | ||||||||
\(97\) | 1.65696e8 | 0.190037 | 0.0950185 | − | 0.995476i | \(-0.469709\pi\) | ||||
0.0950185 | + | 0.995476i | \(0.469709\pi\) | |||||||
\(98\) | −1.09988e9 | −1.20456 | ||||||||
\(99\) | −8.00272e8 | −0.837296 | ||||||||
\(100\) | −5.99027e8 | −0.599027 | ||||||||
\(101\) | −7.41636e8 | −0.709161 | −0.354580 | − | 0.935026i | \(-0.615376\pi\) | ||||
−0.354580 | + | 0.935026i | \(0.615376\pi\) | |||||||
\(102\) | 1.92936e9 | 1.76487 | ||||||||
\(103\) | 1.42175e9 | 1.24467 | 0.622336 | − | 0.782750i | \(-0.286184\pi\) | ||||
0.622336 | + | 0.782750i | \(0.286184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.69454e8 | −0.376913 | ||||||||
\(106\) | −4.81970e8 | −0.370803 | ||||||||
\(107\) | −1.44196e9 | −1.06347 | −0.531736 | − | 0.846910i | \(-0.678460\pi\) | ||||
−0.531736 | + | 0.846910i | \(0.678460\pi\) | |||||||
\(108\) | −1.61969e8 | −0.114558 | ||||||||
\(109\) | 8.42758e7 | 0.0571852 | 0.0285926 | − | 0.999591i | \(-0.490897\pi\) | ||||
0.0285926 | + | 0.999591i | \(0.490897\pi\) | |||||||
\(110\) | 2.69124e8 | 0.175261 | ||||||||
\(111\) | −1.66846e9 | −1.04319 | ||||||||
\(112\) | −2.87036e9 | −1.72367 | ||||||||
\(113\) | 8.60241e8 | 0.496326 | 0.248163 | − | 0.968718i | \(-0.420173\pi\) | ||||
0.248163 | + | 0.968718i | \(0.420173\pi\) | |||||||
\(114\) | −1.56471e9 | −0.867683 | ||||||||
\(115\) | −6.27758e8 | −0.334697 | ||||||||
\(116\) | 1.26780e9 | 0.650115 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.69898e9 | −0.806712 | ||||||||
\(119\) | 2.90155e9 | 1.32638 | ||||||||
\(120\) | −2.96601e8 | −0.130574 | ||||||||
\(121\) | −1.05561e9 | −0.447681 | ||||||||
\(122\) | −3.70936e9 | −1.51593 | ||||||||
\(123\) | −1.47357e8 | −0.0580494 | ||||||||
\(124\) | 2.04924e9 | 0.778386 | ||||||||
\(125\) | −9.94026e8 | −0.364169 | ||||||||
\(126\) | −5.66052e9 | −2.00073 | ||||||||
\(127\) | −1.44120e9 | −0.491596 | −0.245798 | − | 0.969321i | \(-0.579050\pi\) | ||||
−0.245798 | + | 0.969321i | \(0.579050\pi\) | |||||||
\(128\) | −2.72399e9 | −0.896934 | ||||||||
\(129\) | 8.45474e9 | 2.68811 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.54928e9 | −1.34965 | −0.674827 | − | 0.737976i | \(-0.735782\pi\) | ||||
−0.674827 | + | 0.737976i | \(0.735782\pi\) | |||||||
\(132\) | 2.34498e9 | 0.672289 | ||||||||
\(133\) | −2.35316e9 | −0.652107 | ||||||||
\(134\) | −5.51489e9 | −1.47763 | ||||||||
\(135\) | −1.32039e8 | −0.0342138 | ||||||||
\(136\) | 1.83320e9 | 0.459499 | ||||||||
\(137\) | 1.99742e9 | 0.484426 | 0.242213 | − | 0.970223i | \(-0.422127\pi\) | ||||
0.242213 | + | 0.970223i | \(0.422127\pi\) | |||||||
\(138\) | −1.42878e10 | −3.35358 | ||||||||
\(139\) | 3.55325e8 | 0.0807345 | 0.0403672 | − | 0.999185i | \(-0.487147\pi\) | ||||
0.0403672 | + | 0.999185i | \(0.487147\pi\) | |||||||
\(140\) | 7.28762e8 | 0.160328 | ||||||||
\(141\) | 7.51615e9 | 1.60143 | ||||||||
\(142\) | 9.81789e9 | 2.02638 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.18235e9 | −1.39199 | ||||||||
\(145\) | 1.03353e9 | 0.194163 | ||||||||
\(146\) | 9.21372e9 | 1.67821 | ||||||||
\(147\) | −7.81270e9 | −1.37998 | ||||||||
\(148\) | 2.59005e9 | 0.443741 | ||||||||
\(149\) | −5.92546e9 | −0.984881 | −0.492440 | − | 0.870346i | \(-0.663895\pi\) | ||||
−0.492440 | + | 0.870346i | \(0.663895\pi\) | |||||||
\(150\) | −1.11145e10 | −1.79258 | ||||||||
\(151\) | 1.07568e10 | 1.68378 | 0.841891 | − | 0.539647i | \(-0.181442\pi\) | ||||
0.841891 | + | 0.539647i | \(0.181442\pi\) | |||||||
\(152\) | −1.48672e9 | −0.225909 | ||||||||
\(153\) | 7.26040e9 | 1.07115 | ||||||||
\(154\) | 9.21176e9 | 1.31977 | ||||||||
\(155\) | 1.67056e9 | 0.232472 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.87634e9 | 1.16597 | 0.582983 | − | 0.812485i | \(-0.301886\pi\) | ||||
0.582983 | + | 0.812485i | \(0.301886\pi\) | |||||||
\(158\) | −7.03734e9 | −0.898363 | ||||||||
\(159\) | −3.42355e9 | −0.424805 | ||||||||
\(160\) | 1.67311e9 | 0.201829 | ||||||||
\(161\) | −2.14873e10 | −2.52038 | ||||||||
\(162\) | 9.56672e9 | 1.09130 | ||||||||
\(163\) | −2.75052e9 | −0.305190 | −0.152595 | − | 0.988289i | \(-0.548763\pi\) | ||||
−0.152595 | + | 0.988289i | \(0.548763\pi\) | |||||||
\(164\) | 2.28751e8 | 0.0246925 | ||||||||
\(165\) | 1.91166e9 | 0.200785 | ||||||||
\(166\) | −1.26338e10 | −1.29136 | ||||||||
\(167\) | 9.17849e9 | 0.913160 | 0.456580 | − | 0.889682i | \(-0.349074\pi\) | ||||
0.456580 | + | 0.889682i | \(0.349074\pi\) | |||||||
\(168\) | −1.01523e10 | −0.983266 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.44161e9 | −0.224210 | ||||||||
\(171\) | −5.88818e9 | −0.526622 | ||||||||
\(172\) | −1.31248e10 | −1.14344 | ||||||||
\(173\) | 9.75049e8 | 0.0827598 | 0.0413799 | − | 0.999143i | \(-0.486825\pi\) | ||||
0.0413799 | + | 0.999143i | \(0.486825\pi\) | |||||||
\(174\) | 2.35231e10 | 1.94546 | ||||||||
\(175\) | −1.67150e10 | −1.34721 | ||||||||
\(176\) | 1.16883e10 | 0.918218 | ||||||||
\(177\) | −1.20683e10 | −0.924198 | ||||||||
\(178\) | −2.27641e10 | −1.69965 | ||||||||
\(179\) | −8.88356e9 | −0.646768 | −0.323384 | − | 0.946268i | \(-0.604820\pi\) | ||||
−0.323384 | + | 0.946268i | \(0.604820\pi\) | |||||||
\(180\) | 1.82354e9 | 0.129476 | ||||||||
\(181\) | −5.22791e9 | −0.362055 | −0.181028 | − | 0.983478i | \(-0.557942\pi\) | ||||
−0.181028 | + | 0.983478i | \(0.557942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.63485e10 | −1.73671 | ||||||||
\(184\) | −1.35757e10 | −0.873134 | ||||||||
\(185\) | 2.11144e9 | 0.132527 | ||||||||
\(186\) | 3.80220e10 | 2.32931 | ||||||||
\(187\) | −1.18154e10 | −0.706577 | ||||||||
\(188\) | −1.16678e10 | −0.681204 | ||||||||
\(189\) | −4.51952e9 | −0.257641 | ||||||||
\(190\) | 1.98014e9 | 0.110231 | ||||||||
\(191\) | 9.23471e9 | 0.502080 | 0.251040 | − | 0.967977i | \(-0.419227\pi\) | ||||
0.251040 | + | 0.967977i | \(0.419227\pi\) | |||||||
\(192\) | 4.15232e9 | 0.220514 | ||||||||
\(193\) | −1.07065e10 | −0.555441 | −0.277720 | − | 0.960662i | \(-0.589579\pi\) | ||||
−0.277720 | + | 0.960662i | \(0.589579\pi\) | |||||||
\(194\) | −4.77250e9 | −0.241901 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.21281e10 | 0.587004 | ||||||||
\(197\) | 2.77001e10 | 1.31034 | 0.655169 | − | 0.755482i | \(-0.272597\pi\) | ||||
0.655169 | + | 0.755482i | \(0.272597\pi\) | |||||||
\(198\) | 2.30501e10 | 1.06581 | ||||||||
\(199\) | 3.32299e10 | 1.50207 | 0.751035 | − | 0.660262i | \(-0.229555\pi\) | ||||
0.751035 | + | 0.660262i | \(0.229555\pi\) | |||||||
\(200\) | −1.05606e10 | −0.466715 | ||||||||
\(201\) | −3.91737e10 | −1.69282 | ||||||||
\(202\) | 2.13612e10 | 0.902703 | ||||||||
\(203\) | 3.53763e10 | 1.46211 | ||||||||
\(204\) | −2.12746e10 | −0.860055 | ||||||||
\(205\) | 1.86481e8 | 0.00737465 | ||||||||
\(206\) | −4.09503e10 | −1.58436 | ||||||||
\(207\) | −5.37666e10 | −2.03538 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.58225e9 | 0.347383 | ||||||||
\(210\) | 1.35216e10 | 0.479780 | ||||||||
\(211\) | −1.49261e10 | −0.518411 | −0.259205 | − | 0.965822i | \(-0.583461\pi\) | ||||
−0.259205 | + | 0.965822i | \(0.583461\pi\) | |||||||
\(212\) | 5.31458e9 | 0.180700 | ||||||||
\(213\) | 6.97389e10 | 2.32149 | ||||||||
\(214\) | 4.15325e10 | 1.35371 | ||||||||
\(215\) | −1.06995e10 | −0.341500 | ||||||||
\(216\) | −2.85543e9 | −0.0892545 | ||||||||
\(217\) | 5.71812e10 | 1.75059 | ||||||||
\(218\) | −2.42738e9 | −0.0727920 | ||||||||
\(219\) | 6.54474e10 | 1.92262 | ||||||||
\(220\) | −2.96758e9 | −0.0854083 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.80563e10 | 1.32789 | ||||||||
\(223\) | −2.23373e10 | −0.604865 | −0.302433 | − | 0.953171i | \(-0.597799\pi\) | ||||
−0.302433 | + | 0.953171i | \(0.597799\pi\) | |||||||
\(224\) | 5.72683e10 | 1.51984 | ||||||||
\(225\) | −4.18252e10 | −1.08797 | ||||||||
\(226\) | −2.47774e10 | −0.631782 | ||||||||
\(227\) | −5.20726e9 | −0.130165 | −0.0650824 | − | 0.997880i | \(-0.520731\pi\) | ||||
−0.0650824 | + | 0.997880i | \(0.520731\pi\) | |||||||
\(228\) | 1.72537e10 | 0.422840 | ||||||||
\(229\) | −1.35573e10 | −0.325773 | −0.162887 | − | 0.986645i | \(-0.552080\pi\) | ||||
−0.162887 | + | 0.986645i | \(0.552080\pi\) | |||||||
\(230\) | 1.80812e10 | 0.426042 | ||||||||
\(231\) | 6.54335e10 | 1.51198 | ||||||||
\(232\) | 2.23507e10 | 0.506518 | ||||||||
\(233\) | 2.06224e8 | 0.00458393 | 0.00229196 | − | 0.999997i | \(-0.499270\pi\) | ||||
0.00229196 | + | 0.999997i | \(0.499270\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.51170e9 | −0.203448 | ||||||||
\(236\) | 1.87343e10 | 0.393127 | ||||||||
\(237\) | −4.99880e10 | −1.02920 | ||||||||
\(238\) | −8.35729e10 | −1.68838 | ||||||||
\(239\) | −1.89887e10 | −0.376448 | −0.188224 | − | 0.982126i | \(-0.560273\pi\) | ||||
−0.188224 | + | 0.982126i | \(0.560273\pi\) | |||||||
\(240\) | 1.71569e10 | 0.333801 | ||||||||
\(241\) | 6.11533e10 | 1.16773 | 0.583866 | − | 0.811850i | \(-0.301539\pi\) | ||||
0.583866 | + | 0.811850i | \(0.301539\pi\) | |||||||
\(242\) | 3.04045e10 | 0.569861 | ||||||||
\(243\) | 7.79927e10 | 1.43491 | ||||||||
\(244\) | 4.09024e10 | 0.738745 | ||||||||
\(245\) | 9.88700e9 | 0.175314 | ||||||||
\(246\) | 4.24430e9 | 0.0738920 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.61270e10 | 0.606457 | ||||||||
\(249\) | −8.97410e10 | −1.47943 | ||||||||
\(250\) | 2.86308e10 | 0.463557 | ||||||||
\(251\) | −3.20685e9 | −0.0509973 | −0.0254986 | − | 0.999675i | \(-0.508117\pi\) | ||||
−0.0254986 | + | 0.999675i | \(0.508117\pi\) | |||||||
\(252\) | 6.24174e10 | 0.974997 | ||||||||
\(253\) | 8.74981e10 | 1.34263 | ||||||||
\(254\) | 4.15107e10 | 0.625761 | ||||||||
\(255\) | −1.73433e10 | −0.256863 | ||||||||
\(256\) | 8.88499e10 | 1.29294 | ||||||||
\(257\) | −2.80963e10 | −0.401744 | −0.200872 | − | 0.979617i | \(-0.564378\pi\) | ||||
−0.200872 | + | 0.979617i | \(0.564378\pi\) | |||||||
\(258\) | −2.43520e11 | −3.42174 | ||||||||
\(259\) | 7.22717e10 | 0.997975 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.85201e10 | 1.18076 | ||||||||
\(262\) | 1.31032e11 | 1.71800 | ||||||||
\(263\) | −1.25524e11 | −1.61780 | −0.808902 | − | 0.587944i | \(-0.799938\pi\) | ||||
−0.808902 | + | 0.587944i | \(0.799938\pi\) | |||||||
\(264\) | 4.13408e10 | 0.523795 | ||||||||
\(265\) | 4.33252e9 | 0.0539677 | ||||||||
\(266\) | 6.77776e10 | 0.830078 | ||||||||
\(267\) | −1.61699e11 | −1.94718 | ||||||||
\(268\) | 6.08116e10 | 0.720078 | ||||||||
\(269\) | −1.78558e10 | −0.207918 | −0.103959 | − | 0.994582i | \(-0.533151\pi\) | ||||
−0.103959 | + | 0.994582i | \(0.533151\pi\) | |||||||
\(270\) | 3.80310e9 | 0.0435513 | ||||||||
\(271\) | −1.25204e11 | −1.41013 | −0.705063 | − | 0.709144i | \(-0.749081\pi\) | ||||
−0.705063 | + | 0.709144i | \(0.749081\pi\) | |||||||
\(272\) | −1.06041e11 | −1.17467 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.75314e10 | −0.616634 | ||||||||
\(275\) | 6.80650e10 | 0.717673 | ||||||||
\(276\) | 1.57548e11 | 1.63427 | ||||||||
\(277\) | −5.55594e10 | −0.567020 | −0.283510 | − | 0.958969i | \(-0.591499\pi\) | ||||
−0.283510 | + | 0.958969i | \(0.591499\pi\) | |||||||
\(278\) | −1.02344e10 | −0.102768 | ||||||||
\(279\) | 1.43081e11 | 1.41372 | ||||||||
\(280\) | 1.28477e10 | 0.124915 | ||||||||
\(281\) | −1.01237e11 | −0.968635 | −0.484317 | − | 0.874892i | \(-0.660932\pi\) | ||||
−0.484317 | + | 0.874892i | \(0.660932\pi\) | |||||||
\(282\) | −2.16486e11 | −2.03849 | ||||||||
\(283\) | −1.08041e11 | −1.00127 | −0.500635 | − | 0.865658i | \(-0.666900\pi\) | ||||
−0.500635 | + | 0.865658i | \(0.666900\pi\) | |||||||
\(284\) | −1.08260e11 | −0.987495 | ||||||||
\(285\) | 1.40654e10 | 0.126285 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.38298e9 | 0.0555335 | ||||||||
\(288\) | 1.43299e11 | 1.22738 | ||||||||
\(289\) | −1.13940e10 | −0.0960810 | ||||||||
\(290\) | −2.97685e10 | −0.247153 | ||||||||
\(291\) | −3.39003e10 | −0.277131 | ||||||||
\(292\) | −1.01598e11 | −0.817828 | ||||||||
\(293\) | −3.53224e9 | −0.0279992 | −0.0139996 | − | 0.999902i | \(-0.504456\pi\) | ||||
−0.0139996 | + | 0.999902i | \(0.504456\pi\) | |||||||
\(294\) | 2.25028e11 | 1.75660 | ||||||||
\(295\) | 1.52724e10 | 0.117411 | ||||||||
\(296\) | 4.56612e10 | 0.345728 | ||||||||
\(297\) | 1.84039e10 | 0.137248 | ||||||||
\(298\) | 1.70670e11 | 1.25367 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.22557e11 | 0.873562 | ||||||||
\(301\) | −3.66229e11 | −2.57160 | ||||||||
\(302\) | −3.09826e11 | −2.14332 | ||||||||
\(303\) | 1.51734e11 | 1.03417 | ||||||||
\(304\) | 8.59996e10 | 0.577518 | ||||||||
\(305\) | 3.33441e10 | 0.220633 | ||||||||
\(306\) | −2.09120e11 | −1.36348 | ||||||||
\(307\) | 1.82031e11 | 1.16956 | 0.584781 | − | 0.811191i | \(-0.301180\pi\) | ||||
0.584781 | + | 0.811191i | \(0.301180\pi\) | |||||||
\(308\) | −1.01576e11 | −0.643152 | ||||||||
\(309\) | −2.90881e11 | −1.81510 | ||||||||
\(310\) | −4.81170e10 | −0.295918 | ||||||||
\(311\) | −1.51907e11 | −0.920781 | −0.460390 | − | 0.887717i | \(-0.652291\pi\) | ||||
−0.460390 | + | 0.887717i | \(0.652291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.10194e10 | 0.359351 | 0.179675 | − | 0.983726i | \(-0.442495\pi\) | ||||
0.179675 | + | 0.983726i | \(0.442495\pi\) | |||||||
\(314\) | −2.55664e11 | −1.48418 | ||||||||
\(315\) | 5.08835e10 | 0.291192 | ||||||||
\(316\) | 7.75994e10 | 0.437790 | ||||||||
\(317\) | −6.89227e10 | −0.383350 | −0.191675 | − | 0.981458i | \(-0.561392\pi\) | ||||
−0.191675 | + | 0.981458i | \(0.561392\pi\) | |||||||
\(318\) | 9.86080e10 | 0.540742 | ||||||||
\(319\) | −1.44055e11 | −0.778880 | ||||||||
\(320\) | −5.25478e9 | −0.0280143 | ||||||||
\(321\) | 2.95016e11 | 1.55086 | ||||||||
\(322\) | 6.18896e11 | 3.20823 | ||||||||
\(323\) | −8.69341e10 | −0.444405 | ||||||||
\(324\) | −1.05490e11 | −0.531814 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.92227e10 | 0.388481 | ||||||||
\(327\) | −1.72423e10 | −0.0833931 | ||||||||
\(328\) | 4.03276e9 | 0.0192385 | ||||||||
\(329\) | −3.25573e11 | −1.53203 | ||||||||
\(330\) | −5.50611e10 | −0.255583 | ||||||||
\(331\) | −4.70422e10 | −0.215408 | −0.107704 | − | 0.994183i | \(-0.534350\pi\) | ||||
−0.107704 | + | 0.994183i | \(0.534350\pi\) | |||||||
\(332\) | 1.39310e11 | 0.629306 | ||||||||
\(333\) | 1.80842e11 | 0.805934 | ||||||||
\(334\) | −2.64366e11 | −1.16238 | ||||||||
\(335\) | 4.95744e10 | 0.215058 | ||||||||
\(336\) | 5.87258e11 | 2.51363 | ||||||||
\(337\) | −3.76711e11 | −1.59101 | −0.795507 | − | 0.605944i | \(-0.792795\pi\) | ||||
−0.795507 | + | 0.605944i | \(0.792795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.76000e11 | −0.723792 | ||||||||
\(340\) | 2.69231e10 | 0.109262 | ||||||||
\(341\) | −2.32846e11 | −0.932556 | ||||||||
\(342\) | 1.69596e11 | 0.670346 | ||||||||
\(343\) | −1.92062e10 | −0.0749235 | ||||||||
\(344\) | −2.31383e11 | −0.890880 | ||||||||
\(345\) | 1.28435e11 | 0.488089 | ||||||||
\(346\) | −2.80842e10 | −0.105346 | ||||||||
\(347\) | 1.68331e11 | 0.623278 | 0.311639 | − | 0.950201i | \(-0.399122\pi\) | ||||
0.311639 | + | 0.950201i | \(0.399122\pi\) | |||||||
\(348\) | −2.59384e11 | −0.948062 | ||||||||
\(349\) | 9.36126e10 | 0.337769 | 0.168884 | − | 0.985636i | \(-0.445984\pi\) | ||||
0.168884 | + | 0.985636i | \(0.445984\pi\) | |||||||
\(350\) | 4.81441e11 | 1.71489 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.33201e11 | −0.809634 | ||||||||
\(353\) | 3.49043e11 | 1.19644 | 0.598222 | − | 0.801330i | \(-0.295874\pi\) | ||||
0.598222 | + | 0.801330i | \(0.295874\pi\) | |||||||
\(354\) | 3.47600e11 | 1.17643 | ||||||||
\(355\) | −8.82548e10 | −0.294924 | ||||||||
\(356\) | 2.51015e11 | 0.828276 | ||||||||
\(357\) | −5.93640e11 | −1.93426 | ||||||||
\(358\) | 2.55872e11 | 0.823282 | ||||||||
\(359\) | −5.83173e11 | −1.85299 | −0.926493 | − | 0.376312i | \(-0.877192\pi\) | ||||
−0.926493 | + | 0.376312i | \(0.877192\pi\) | |||||||
\(360\) | 3.21481e10 | 0.100878 | ||||||||
\(361\) | −2.52184e11 | −0.781512 | ||||||||
\(362\) | 1.50579e11 | 0.460866 | ||||||||
\(363\) | 2.15971e11 | 0.652854 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.28239e10 | −0.244252 | ||||||||
\(366\) | 7.58912e11 | 2.21068 | ||||||||
\(367\) | 5.28604e11 | 1.52101 | 0.760507 | − | 0.649329i | \(-0.224950\pi\) | ||||
0.760507 | + | 0.649329i | \(0.224950\pi\) | |||||||
\(368\) | 7.85286e11 | 2.23209 | ||||||||
\(369\) | 1.59718e10 | 0.0448472 | ||||||||
\(370\) | −6.08154e10 | −0.168696 | ||||||||
\(371\) | 1.48296e11 | 0.406394 | ||||||||
\(372\) | −4.19261e11 | −1.13512 | ||||||||
\(373\) | −4.19405e11 | −1.12187 | −0.560937 | − | 0.827858i | \(-0.689559\pi\) | ||||
−0.560937 | + | 0.827858i | \(0.689559\pi\) | |||||||
\(374\) | 3.40316e11 | 0.899414 | ||||||||
\(375\) | 2.03372e11 | 0.531067 | ||||||||
\(376\) | −2.05697e11 | −0.530740 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.30175e11 | 0.327955 | ||||||||
\(379\) | −4.24128e11 | −1.05590 | −0.527948 | − | 0.849277i | \(-0.677038\pi\) | ||||
−0.527948 | + | 0.849277i | \(0.677038\pi\) | |||||||
\(380\) | −2.18346e10 | −0.0537180 | ||||||||
\(381\) | 2.94861e11 | 0.716894 | ||||||||
\(382\) | −2.65986e11 | −0.639107 | ||||||||
\(383\) | −6.52696e10 | −0.154995 | −0.0774973 | − | 0.996993i | \(-0.524693\pi\) | ||||
−0.0774973 | + | 0.996993i | \(0.524693\pi\) | |||||||
\(384\) | 5.57311e11 | 1.30800 | ||||||||
\(385\) | −8.28062e10 | −0.192083 | ||||||||
\(386\) | 3.08376e11 | 0.707030 | ||||||||
\(387\) | −9.16396e11 | −2.07675 | ||||||||
\(388\) | 5.26254e10 | 0.117883 | ||||||||
\(389\) | −5.91803e11 | −1.31040 | −0.655200 | − | 0.755455i | \(-0.727416\pi\) | ||||
−0.655200 | + | 0.755455i | \(0.727416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.93819e11 | −1.71762 | ||||||||
\(392\) | 2.13813e11 | 0.457347 | ||||||||
\(393\) | 9.30755e11 | 1.96820 | ||||||||
\(394\) | −7.97842e11 | −1.66795 | ||||||||
\(395\) | 6.32600e10 | 0.130750 | ||||||||
\(396\) | −2.54169e11 | −0.519390 | ||||||||
\(397\) | 3.05131e11 | 0.616495 | 0.308248 | − | 0.951306i | \(-0.400257\pi\) | ||||
0.308248 | + | 0.951306i | \(0.400257\pi\) | |||||||
\(398\) | −9.57115e11 | −1.91201 | ||||||||
\(399\) | 4.81441e11 | 0.950967 | ||||||||
\(400\) | 6.10876e11 | 1.19312 | ||||||||
\(401\) | −2.56722e11 | −0.495808 | −0.247904 | − | 0.968785i | \(-0.579742\pi\) | ||||
−0.247904 | + | 0.968785i | \(0.579742\pi\) | |||||||
\(402\) | 1.12831e12 | 2.15483 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.35546e11 | −0.439906 | ||||||||
\(405\) | −8.59971e10 | −0.158831 | ||||||||
\(406\) | −1.01894e12 | −1.86114 | ||||||||
\(407\) | −2.94296e11 | −0.531631 | ||||||||
\(408\) | −3.75061e11 | −0.670087 | ||||||||
\(409\) | 4.57003e11 | 0.807540 | 0.403770 | − | 0.914860i | \(-0.367700\pi\) | ||||
0.403770 | + | 0.914860i | \(0.367700\pi\) | |||||||
\(410\) | −5.37117e9 | −0.00938732 | ||||||||
\(411\) | −4.08660e11 | −0.706438 | ||||||||
\(412\) | 4.51551e11 | 0.772093 | ||||||||
\(413\) | 5.22755e11 | 0.884144 | ||||||||
\(414\) | 1.54863e12 | 2.59087 | ||||||||
\(415\) | 1.13567e11 | 0.187948 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.26973e10 | −0.117735 | ||||||||
\(418\) | −2.75996e11 | −0.442190 | ||||||||
\(419\) | −1.65068e11 | −0.261637 | −0.130818 | − | 0.991406i | \(-0.541760\pi\) | ||||
−0.130818 | + | 0.991406i | \(0.541760\pi\) | |||||||
\(420\) | −1.49100e11 | −0.233806 | ||||||||
\(421\) | 9.10255e10 | 0.141219 | 0.0706096 | − | 0.997504i | \(-0.477506\pi\) | ||||
0.0706096 | + | 0.997504i | \(0.477506\pi\) | |||||||
\(422\) | 4.29913e11 | 0.659894 | ||||||||
\(423\) | −8.14664e11 | −1.23722 | ||||||||
\(424\) | 9.36935e10 | 0.140787 | ||||||||
\(425\) | −6.17514e11 | −0.918114 | ||||||||
\(426\) | −2.00868e12 | −2.95507 | ||||||||
\(427\) | 1.14133e12 | 1.66144 | ||||||||
\(428\) | −4.57971e11 | −0.659691 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.08176e11 | 0.434701 | ||||||||
\(431\) | −7.94605e11 | −1.10918 | −0.554592 | − | 0.832122i | \(-0.687126\pi\) | ||||
−0.554592 | + | 0.832122i | \(0.687126\pi\) | |||||||
\(432\) | 1.65173e11 | 0.228171 | ||||||||
\(433\) | −8.26325e11 | −1.12968 | −0.564840 | − | 0.825200i | \(-0.691062\pi\) | ||||
−0.564840 | + | 0.825200i | \(0.691062\pi\) | |||||||
\(434\) | −1.64698e12 | −2.22836 | ||||||||
\(435\) | −2.11453e11 | −0.283148 | ||||||||
\(436\) | 2.67662e10 | 0.0354730 | ||||||||
\(437\) | 6.43787e11 | 0.844453 | ||||||||
\(438\) | −1.88507e12 | −2.44734 | ||||||||
\(439\) | 1.21562e12 | 1.56210 | 0.781050 | − | 0.624469i | \(-0.214684\pi\) | ||||
0.781050 | + | 0.624469i | \(0.214684\pi\) | |||||||
\(440\) | −5.23169e10 | −0.0665434 | ||||||||
\(441\) | 8.46807e11 | 1.06613 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.73136e11 | −1.07712 | −0.538561 | − | 0.842586i | \(-0.681032\pi\) | ||||
−0.538561 | + | 0.842586i | \(0.681032\pi\) | |||||||
\(444\) | −5.29907e11 | −0.647108 | ||||||||
\(445\) | 2.04631e11 | 0.247372 | ||||||||
\(446\) | 6.43377e11 | 0.769943 | ||||||||
\(447\) | 1.21231e12 | 1.43625 | ||||||||
\(448\) | −1.79864e11 | −0.210957 | ||||||||
\(449\) | −1.22107e12 | −1.41785 | −0.708927 | − | 0.705282i | \(-0.750821\pi\) | ||||
−0.708927 | + | 0.705282i | \(0.750821\pi\) | |||||||
\(450\) | 1.20468e12 | 1.38489 | ||||||||
\(451\) | −2.59920e10 | −0.0295832 | ||||||||
\(452\) | 2.73215e11 | 0.307880 | ||||||||
\(453\) | −2.20077e12 | −2.45546 | ||||||||
\(454\) | 1.49984e11 | 0.165689 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.04174e11 | 0.329443 | ||||||||
\(457\) | −6.32643e11 | −0.678478 | −0.339239 | − | 0.940700i | \(-0.610170\pi\) | ||||
−0.339239 | + | 0.940700i | \(0.610170\pi\) | |||||||
\(458\) | 3.90490e11 | 0.414682 | ||||||||
\(459\) | −1.66968e11 | −0.175580 | ||||||||
\(460\) | −1.99378e11 | −0.207619 | ||||||||
\(461\) | −8.09117e11 | −0.834367 | −0.417184 | − | 0.908822i | \(-0.636983\pi\) | ||||
−0.417184 | + | 0.908822i | \(0.636983\pi\) | |||||||
\(462\) | −1.88467e12 | −1.92463 | ||||||||
\(463\) | −7.69685e11 | −0.778393 | −0.389196 | − | 0.921155i | \(-0.627247\pi\) | ||||
−0.389196 | + | 0.921155i | \(0.627247\pi\) | |||||||
\(464\) | −1.29288e12 | −1.29487 | ||||||||
\(465\) | −3.41787e11 | −0.339014 | ||||||||
\(466\) | −5.93984e9 | −0.00583496 | ||||||||
\(467\) | 1.59708e12 | 1.55382 | 0.776909 | − | 0.629613i | \(-0.216787\pi\) | ||||
0.776909 | + | 0.629613i | \(0.216787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.69686e12 | 1.61946 | ||||||||
\(470\) | 2.73964e11 | 0.258972 | ||||||||
\(471\) | −1.81604e12 | −1.70033 | ||||||||
\(472\) | 3.30276e11 | 0.306294 | ||||||||
\(473\) | 1.49132e12 | 1.36992 | ||||||||
\(474\) | 1.43980e12 | 1.31008 | ||||||||
\(475\) | 5.00804e11 | 0.451384 | ||||||||
\(476\) | 9.21542e11 | 0.822780 | ||||||||
\(477\) | 3.71074e11 | 0.328192 | ||||||||
\(478\) | 5.46929e11 | 0.479187 | ||||||||
\(479\) | −1.61308e12 | −1.40006 | −0.700028 | − | 0.714115i | \(-0.746829\pi\) | ||||
−0.700028 | + | 0.714115i | \(0.746829\pi\) | |||||||
\(480\) | −3.42308e11 | −0.294328 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.76139e12 | −1.48643 | ||||||||
\(483\) | 4.39617e12 | 3.67547 | ||||||||
\(484\) | −3.35265e11 | −0.277705 | ||||||||
\(485\) | 4.29009e10 | 0.0352070 | ||||||||
\(486\) | −2.24641e12 | −1.82653 | ||||||||
\(487\) | −9.29058e11 | −0.748449 | −0.374225 | − | 0.927338i | \(-0.622091\pi\) | ||||
−0.374225 | + | 0.927338i | \(0.622091\pi\) | |||||||
\(488\) | 7.21089e11 | 0.575572 | ||||||||
\(489\) | 5.62739e11 | 0.445058 | ||||||||
\(490\) | −2.84774e11 | −0.223160 | ||||||||
\(491\) | −2.30662e12 | −1.79106 | −0.895528 | − | 0.445005i | \(-0.853202\pi\) | ||||
−0.895528 | + | 0.445005i | \(0.853202\pi\) | |||||||
\(492\) | −4.68010e10 | −0.0360091 | ||||||||
\(493\) | 1.30693e12 | 0.996415 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.07202e11 | −0.155121 | ||||||||
\(496\) | −2.08977e12 | −1.55036 | ||||||||
\(497\) | −3.02084e12 | −2.22088 | ||||||||
\(498\) | 2.58480e12 | 1.88319 | ||||||||
\(499\) | 1.31410e11 | 0.0948800 | 0.0474400 | − | 0.998874i | \(-0.484894\pi\) | ||||
0.0474400 | + | 0.998874i | \(0.484894\pi\) | |||||||
\(500\) | −3.15706e11 | −0.225901 | ||||||||
\(501\) | −1.87786e12 | −1.33166 | ||||||||
\(502\) | 9.23664e10 | 0.0649153 | ||||||||
\(503\) | −1.88419e12 | −1.31241 | −0.656203 | − | 0.754584i | \(-0.727838\pi\) | ||||
−0.656203 | + | 0.754584i | \(0.727838\pi\) | |||||||
\(504\) | 1.10039e12 | 0.759641 | ||||||||
\(505\) | −1.92020e11 | −0.131382 | ||||||||
\(506\) | −2.52019e12 | −1.70906 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.57730e11 | −0.304946 | ||||||||
\(509\) | 1.00390e11 | 0.0662919 | 0.0331459 | − | 0.999451i | \(-0.489447\pi\) | ||||
0.0331459 | + | 0.999451i | \(0.489447\pi\) | |||||||
\(510\) | 4.99537e11 | 0.326966 | ||||||||
\(511\) | −2.83495e12 | −1.83930 | ||||||||
\(512\) | −1.16445e12 | −0.748866 | ||||||||
\(513\) | 1.35411e11 | 0.0863226 | ||||||||
\(514\) | 8.09252e11 | 0.511387 | ||||||||
\(515\) | 3.68110e11 | 0.230593 | ||||||||
\(516\) | 2.68525e12 | 1.66748 | ||||||||
\(517\) | 1.32576e12 | 0.816126 | ||||||||
\(518\) | −2.08163e12 | −1.27034 | ||||||||
\(519\) | −1.99489e11 | −0.120689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.04516e11 | −0.0621462 | −0.0310731 | − | 0.999517i | \(-0.509892\pi\) | ||||
−0.0310731 | + | 0.999517i | \(0.509892\pi\) | |||||||
\(522\) | −2.54963e12 | −1.50300 | ||||||||
\(523\) | 1.17694e12 | 0.687855 | 0.343927 | − | 0.938996i | \(-0.388243\pi\) | ||||
0.343927 | + | 0.938996i | \(0.388243\pi\) | |||||||
\(524\) | −1.44487e12 | −0.837215 | ||||||||
\(525\) | 3.41979e12 | 1.96464 | ||||||||
\(526\) | 3.61544e12 | 2.05933 | ||||||||
\(527\) | 2.11248e12 | 1.19301 | ||||||||
\(528\) | −2.39136e12 | −1.33904 | ||||||||
\(529\) | 4.07744e12 | 2.26379 | ||||||||
\(530\) | −1.24789e11 | −0.0686964 | ||||||||
\(531\) | 1.30806e12 | 0.714008 | ||||||||
\(532\) | −7.47370e11 | −0.404514 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.65739e12 | 2.47860 | ||||||||
\(535\) | −3.73343e11 | −0.197023 | ||||||||
\(536\) | 1.07208e12 | 0.561028 | ||||||||
\(537\) | 1.81752e12 | 0.943181 | ||||||||
\(538\) | 5.14296e11 | 0.264663 | ||||||||
\(539\) | −1.37807e12 | −0.703269 | ||||||||
\(540\) | −4.19360e10 | −0.0212234 | ||||||||
\(541\) | 2.98502e12 | 1.49817 | 0.749083 | − | 0.662476i | \(-0.230494\pi\) | ||||
0.749083 | + | 0.662476i | \(0.230494\pi\) | |||||||
\(542\) | 3.60624e12 | 1.79497 | ||||||||
\(543\) | 1.06960e12 | 0.527985 | ||||||||
\(544\) | 2.11570e12 | 1.03576 | ||||||||
\(545\) | 2.18202e10 | 0.0105943 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.78628e12 | 1.80830 | 0.904148 | − | 0.427219i | \(-0.140507\pi\) | ||||
0.904148 | + | 0.427219i | \(0.140507\pi\) | |||||||
\(548\) | 6.34387e11 | 0.300498 | ||||||||
\(549\) | 2.85588e12 | 1.34173 | ||||||||
\(550\) | −1.96047e12 | −0.913539 | ||||||||
\(551\) | −1.05992e12 | −0.489880 | ||||||||
\(552\) | 2.77750e12 | 1.27329 | ||||||||
\(553\) | 2.16530e12 | 0.984591 | ||||||||
\(554\) | 1.60027e12 | 0.721770 | ||||||||
\(555\) | −4.31987e11 | −0.193265 | ||||||||
\(556\) | 1.12852e11 | 0.0500811 | ||||||||
\(557\) | −1.00551e12 | −0.442627 | −0.221313 | − | 0.975203i | \(-0.571034\pi\) | ||||
−0.221313 | + | 0.975203i | \(0.571034\pi\) | |||||||
\(558\) | −4.12115e12 | −1.79955 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.43177e11 | −0.319335 | ||||||||
\(561\) | 2.41735e12 | 1.03040 | ||||||||
\(562\) | 2.91591e12 | 1.23299 | ||||||||
\(563\) | 2.76515e11 | 0.115993 | 0.0579964 | − | 0.998317i | \(-0.481529\pi\) | ||||
0.0579964 | + | 0.998317i | \(0.481529\pi\) | |||||||
\(564\) | 2.38715e12 | 0.993399 | ||||||||
\(565\) | 2.22728e11 | 0.0919512 | ||||||||
\(566\) | 3.11190e12 | 1.27453 | ||||||||
\(567\) | −2.94356e12 | −1.19605 | ||||||||
\(568\) | −1.90857e12 | −0.769378 | ||||||||
\(569\) | 8.39220e11 | 0.335638 | 0.167819 | − | 0.985818i | \(-0.446328\pi\) | ||||
0.167819 | + | 0.985818i | \(0.446328\pi\) | |||||||
\(570\) | −4.05125e11 | −0.160750 | ||||||||
\(571\) | −1.02285e11 | −0.0402672 | −0.0201336 | − | 0.999797i | \(-0.506409\pi\) | ||||
−0.0201336 | + | 0.999797i | \(0.506409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.88936e12 | −0.732184 | ||||||||
\(574\) | −1.83848e11 | −0.0706896 | ||||||||
\(575\) | 4.57297e12 | 1.74459 | ||||||||
\(576\) | −4.50064e11 | −0.170362 | ||||||||
\(577\) | 1.44021e12 | 0.540921 | 0.270461 | − | 0.962731i | \(-0.412824\pi\) | ||||
0.270461 | + | 0.962731i | \(0.412824\pi\) | |||||||
\(578\) | 3.28181e11 | 0.122303 | ||||||||
\(579\) | 2.19047e12 | 0.809999 | ||||||||
\(580\) | 3.28251e11 | 0.120443 | ||||||||
\(581\) | 3.88726e12 | 1.41531 | ||||||||
\(582\) | 9.76424e11 | 0.352765 | ||||||||
\(583\) | −6.03874e11 | −0.216490 | ||||||||
\(584\) | −1.79112e12 | −0.637187 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.01738e11 | 0.0356407 | ||||||||
\(587\) | 2.13185e11 | 0.0741116 | 0.0370558 | − | 0.999313i | \(-0.488202\pi\) | ||||
0.0370558 | + | 0.999313i | \(0.488202\pi\) | |||||||
\(588\) | −2.48134e12 | −0.856028 | ||||||||
\(589\) | −1.71322e12 | −0.586536 | ||||||||
\(590\) | −4.39889e11 | −0.149455 | ||||||||
\(591\) | −5.66727e12 | −1.91087 | ||||||||
\(592\) | −2.64128e12 | −0.883825 | ||||||||
\(593\) | 1.76049e12 | 0.584640 | 0.292320 | − | 0.956321i | \(-0.405573\pi\) | ||||
0.292320 | + | 0.956321i | \(0.405573\pi\) | |||||||
\(594\) | −5.30084e11 | −0.174705 | ||||||||
\(595\) | 7.51253e11 | 0.245731 | ||||||||
\(596\) | −1.88194e12 | −0.610940 | ||||||||
\(597\) | −6.79863e12 | −2.19047 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.06753e12 | −0.656191 | −0.328096 | − | 0.944644i | \(-0.606407\pi\) | ||||
−0.328096 | + | 0.944644i | \(0.606407\pi\) | |||||||
\(600\) | 2.16062e12 | 0.680610 | ||||||||
\(601\) | −1.24403e12 | −0.388951 | −0.194476 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194476 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(602\) | 1.05484e13 | 3.27344 | ||||||||
\(603\) | 4.24597e12 | 1.30782 | ||||||||
\(604\) | 3.41639e12 | 1.04448 | ||||||||
\(605\) | −2.73312e11 | −0.0829391 | ||||||||
\(606\) | −4.37037e12 | −1.31641 | ||||||||
\(607\) | −1.31511e12 | −0.393200 | −0.196600 | − | 0.980484i | \(-0.562990\pi\) | ||||
−0.196600 | + | 0.980484i | \(0.562990\pi\) | |||||||
\(608\) | −1.71583e12 | −0.509223 | ||||||||
\(609\) | −7.23776e12 | −2.13219 | ||||||||
\(610\) | −9.60406e11 | −0.280847 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.30593e12 | 0.664452 | ||||||||
\(613\) | 3.08252e12 | 0.881726 | 0.440863 | − | 0.897574i | \(-0.354672\pi\) | ||||
0.440863 | + | 0.897574i | \(0.354672\pi\) | |||||||
\(614\) | −5.24301e12 | −1.48876 | ||||||||
\(615\) | −3.81528e10 | −0.0107544 | ||||||||
\(616\) | −1.79074e12 | −0.501094 | ||||||||
\(617\) | 2.29075e10 | 0.00636348 | 0.00318174 | − | 0.999995i | \(-0.498987\pi\) | ||||
0.00318174 | + | 0.999995i | \(0.498987\pi\) | |||||||
\(618\) | 8.37818e12 | 2.31048 | ||||||||
\(619\) | 4.45350e12 | 1.21925 | 0.609626 | − | 0.792689i | \(-0.291320\pi\) | ||||
0.609626 | + | 0.792689i | \(0.291320\pi\) | |||||||
\(620\) | 5.30576e11 | 0.144207 | ||||||||
\(621\) | 1.23647e12 | 0.333635 | ||||||||
\(622\) | 4.37535e12 | 1.17208 | ||||||||
\(623\) | 7.00424e12 | 1.86279 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.42640e12 | 0.898210 | ||||||||
\(626\) | −1.75753e12 | −0.457423 | ||||||||
\(627\) | −1.96047e12 | −0.506589 | ||||||||
\(628\) | 2.81915e12 | 0.723270 | ||||||||
\(629\) | 2.66998e12 | 0.680111 | ||||||||
\(630\) | −1.46559e12 | −0.370663 | ||||||||
\(631\) | −3.83831e12 | −0.963847 | −0.481923 | − | 0.876213i | \(-0.660062\pi\) | ||||
−0.481923 | + | 0.876213i | \(0.660062\pi\) | |||||||
\(632\) | 1.36804e12 | 0.341092 | ||||||||
\(633\) | 3.05378e12 | 0.755998 | ||||||||
\(634\) | 1.98517e12 | 0.487973 | ||||||||
\(635\) | −3.73148e11 | −0.0910749 | ||||||||
\(636\) | −1.08733e12 | −0.263515 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.14919e12 | 0.991449 | ||||||||
\(639\) | −7.55890e12 | −1.79351 | ||||||||
\(640\) | −7.05279e11 | −0.166169 | ||||||||
\(641\) | 9.09238e11 | 0.212724 | 0.106362 | − | 0.994327i | \(-0.466080\pi\) | ||||
0.106362 | + | 0.994327i | \(0.466080\pi\) | |||||||
\(642\) | −8.49729e12 | −1.97412 | ||||||||
\(643\) | −8.23839e12 | −1.90061 | −0.950305 | − | 0.311321i | \(-0.899229\pi\) | ||||
−0.950305 | + | 0.311321i | \(0.899229\pi\) | |||||||
\(644\) | −6.82444e12 | −1.56344 | ||||||||
\(645\) | 2.18905e12 | 0.498009 | ||||||||
\(646\) | 2.50395e12 | 0.565691 | ||||||||
\(647\) | −8.73559e12 | −1.95985 | −0.979925 | − | 0.199365i | \(-0.936112\pi\) | ||||
−0.979925 | + | 0.199365i | \(0.936112\pi\) | |||||||
\(648\) | −1.85974e12 | −0.414348 | ||||||||
\(649\) | −2.12870e12 | −0.470992 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.16989e13 | −2.55289 | ||||||||
\(652\) | −8.73573e11 | −0.189315 | ||||||||
\(653\) | −6.13232e11 | −0.131982 | −0.0659911 | − | 0.997820i | \(-0.521021\pi\) | ||||
−0.0659911 | + | 0.997820i | \(0.521021\pi\) | |||||||
\(654\) | 4.96627e11 | 0.106153 | ||||||||
\(655\) | −1.17787e12 | −0.250042 | ||||||||
\(656\) | −2.33275e11 | −0.0491815 | ||||||||
\(657\) | −7.09375e12 | −1.48536 | ||||||||
\(658\) | 9.37742e12 | 1.95015 | ||||||||
\(659\) | −8.83233e12 | −1.82428 | −0.912139 | − | 0.409882i | \(-0.865570\pi\) | ||||
−0.912139 | + | 0.409882i | \(0.865570\pi\) | |||||||
\(660\) | 6.07148e11 | 0.124551 | ||||||||
\(661\) | 5.61801e12 | 1.14466 | 0.572329 | − | 0.820024i | \(-0.306040\pi\) | ||||
0.572329 | + | 0.820024i | \(0.306040\pi\) | |||||||
\(662\) | 1.35495e12 | 0.274196 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.45597e12 | 0.490306 | ||||||||
\(665\) | −6.09265e11 | −0.120812 | ||||||||
\(666\) | −5.20875e12 | −1.02589 | ||||||||
\(667\) | −9.67839e12 | −1.89338 | ||||||||
\(668\) | 2.91511e12 | 0.566450 | ||||||||
\(669\) | 4.57007e12 | 0.882075 | ||||||||
\(670\) | −1.42788e12 | −0.273751 | ||||||||
\(671\) | −4.64757e12 | −0.885064 | ||||||||
\(672\) | −1.17167e13 | −2.21638 | ||||||||
\(673\) | 4.50151e12 | 0.845844 | 0.422922 | − | 0.906166i | \(-0.361004\pi\) | ||||
0.422922 | + | 0.906166i | \(0.361004\pi\) | |||||||
\(674\) | 1.08503e13 | 2.02523 | ||||||||
\(675\) | 9.61854e11 | 0.178337 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.33098e12 | 0.792387 | 0.396193 | − | 0.918167i | \(-0.370331\pi\) | ||||
0.396193 | + | 0.918167i | \(0.370331\pi\) | |||||||
\(678\) | 5.06929e12 | 0.921327 | ||||||||
\(679\) | 1.46844e12 | 0.265120 | ||||||||
\(680\) | 4.74641e11 | 0.0851285 | ||||||||
\(681\) | 1.06537e12 | 0.189819 | ||||||||
\(682\) | 6.70664e12 | 1.18707 | ||||||||
\(683\) | −6.25107e12 | −1.09916 | −0.549580 | − | 0.835441i | \(-0.685212\pi\) | ||||
−0.549580 | + | 0.835441i | \(0.685212\pi\) | |||||||
\(684\) | −1.87010e12 | −0.326673 | ||||||||
\(685\) | 5.17161e11 | 0.0897466 | ||||||||
\(686\) | 5.53193e11 | 0.0953715 | ||||||||
\(687\) | 2.77375e12 | 0.475075 | ||||||||
\(688\) | 1.33844e13 | 2.27746 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.69930e12 | −0.621296 | ||||||||
\(691\) | −7.34082e12 | −1.22488 | −0.612440 | − | 0.790517i | \(-0.709812\pi\) | ||||
−0.612440 | + | 0.790517i | \(0.709812\pi\) | |||||||
\(692\) | 3.09679e11 | 0.0513374 | ||||||||
\(693\) | −7.09223e12 | −1.16811 | ||||||||
\(694\) | −4.84841e12 | −0.793381 | ||||||||
\(695\) | 9.19986e10 | 0.0149572 | ||||||||
\(696\) | −4.57281e12 | −0.738656 | ||||||||
\(697\) | 2.35810e11 | 0.0378456 | ||||||||
\(698\) | −2.69631e12 | −0.429952 | ||||||||
\(699\) | −4.21922e10 | −0.00668474 | ||||||||
\(700\) | −5.30875e12 | −0.835701 | ||||||||
\(701\) | −1.71509e11 | −0.0268259 | −0.0134130 | − | 0.999910i | \(-0.504270\pi\) | ||||
−0.0134130 | + | 0.999910i | \(0.504270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.16535e12 | −0.334372 | ||||||||
\(704\) | 7.32421e11 | 0.112379 | ||||||||
\(705\) | 1.94604e12 | 0.296688 | ||||||||
\(706\) | −1.00534e13 | −1.52297 | ||||||||
\(707\) | −6.57259e12 | −0.989348 | ||||||||
\(708\) | −3.83292e12 | −0.573297 | ||||||||
\(709\) | 1.00896e13 | 1.49956 | 0.749780 | − | 0.661687i | \(-0.230159\pi\) | ||||
0.749780 | + | 0.661687i | \(0.230159\pi\) | |||||||
\(710\) | 2.54199e12 | 0.375414 | ||||||||
\(711\) | 5.41813e12 | 0.795126 | ||||||||
\(712\) | 4.42527e12 | 0.645327 | ||||||||
\(713\) | −1.56439e13 | −2.26695 | ||||||||
\(714\) | 1.70985e13 | 2.46216 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.82145e12 | −0.401202 | ||||||||
\(717\) | 3.88497e12 | 0.548974 | ||||||||
\(718\) | 1.67970e13 | 2.35870 | ||||||||
\(719\) | 8.18068e12 | 1.14159 | 0.570794 | − | 0.821093i | \(-0.306635\pi\) | ||||
0.570794 | + | 0.821093i | \(0.306635\pi\) | |||||||
\(720\) | −1.85961e12 | −0.257885 | ||||||||
\(721\) | 1.25999e13 | 1.73644 | ||||||||
\(722\) | 7.26362e12 | 0.994800 | ||||||||
\(723\) | −1.25116e13 | −1.70290 | ||||||||
\(724\) | −1.66040e12 | −0.224589 | ||||||||
\(725\) | −7.52885e12 | −1.01206 | ||||||||
\(726\) | −6.22058e12 | −0.831029 | ||||||||
\(727\) | −9.98421e11 | −0.132559 | −0.0662795 | − | 0.997801i | \(-0.521113\pi\) | ||||
−0.0662795 | + | 0.997801i | \(0.521113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.41920e12 | −1.23521 | ||||||||
\(730\) | 2.38556e12 | 0.310912 | ||||||||
\(731\) | −1.35298e13 | −1.75253 | ||||||||
\(732\) | −8.36837e12 | −1.07731 | ||||||||
\(733\) | 2.10457e12 | 0.269274 | 0.134637 | − | 0.990895i | \(-0.457013\pi\) | ||||
0.134637 | + | 0.990895i | \(0.457013\pi\) | |||||||
\(734\) | −1.52253e13 | −1.93613 | ||||||||
\(735\) | −2.02282e12 | −0.255661 | ||||||||
\(736\) | −1.56677e13 | −1.96814 | ||||||||
\(737\) | −6.90977e12 | −0.862700 | ||||||||
\(738\) | −4.60033e11 | −0.0570867 | ||||||||
\(739\) | 1.28931e13 | 1.59023 | 0.795113 | − | 0.606461i | \(-0.207412\pi\) | ||||
0.795113 | + | 0.606461i | \(0.207412\pi\) | |||||||
\(740\) | 6.70599e11 | 0.0822092 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.27135e12 | −0.517306 | ||||||||
\(743\) | −2.72357e11 | −0.0327861 | −0.0163930 | − | 0.999866i | \(-0.505218\pi\) | ||||
−0.0163930 | + | 0.999866i | \(0.505218\pi\) | |||||||
\(744\) | −7.39137e12 | −0.884396 | ||||||||
\(745\) | −1.53418e12 | −0.182463 | ||||||||
\(746\) | 1.20801e13 | 1.42805 | ||||||||
\(747\) | 9.72689e12 | 1.14296 | ||||||||
\(748\) | −3.75259e12 | −0.438303 | ||||||||
\(749\) | −1.27790e13 | −1.48365 | ||||||||
\(750\) | −5.85768e12 | −0.676005 | ||||||||
\(751\) | −1.40530e13 | −1.61209 | −0.806045 | − | 0.591855i | \(-0.798396\pi\) | ||||
−0.806045 | + | 0.591855i | \(0.798396\pi\) | |||||||
\(752\) | 1.18985e13 | 1.35679 | ||||||||
\(753\) | 6.56102e11 | 0.0743693 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.78508e12 | 0.311944 | ||||||||
\(756\) | −1.43541e12 | −0.159819 | ||||||||
\(757\) | 8.53220e12 | 0.944342 | 0.472171 | − | 0.881507i | \(-0.343470\pi\) | ||||
0.472171 | + | 0.881507i | \(0.343470\pi\) | |||||||
\(758\) | 1.22161e13 | 1.34407 | ||||||||
\(759\) | −1.79016e13 | −1.95796 | ||||||||
\(760\) | −3.84933e11 | −0.0418528 | ||||||||
\(761\) | −1.13835e13 | −1.23039 | −0.615197 | − | 0.788373i | \(-0.710924\pi\) | ||||
−0.615197 | + | 0.788373i | \(0.710924\pi\) | |||||||
\(762\) | −8.49283e12 | −0.912547 | ||||||||
\(763\) | 7.46876e11 | 0.0797789 | ||||||||
\(764\) | 2.93297e12 | 0.311450 | ||||||||
\(765\) | 1.87982e12 | 0.198445 | ||||||||
\(766\) | 1.87995e12 | 0.197295 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.81781e13 | −1.88549 | ||||||||
\(769\) | −1.94858e12 | −0.200933 | −0.100466 | − | 0.994940i | \(-0.532033\pi\) | ||||
−0.100466 | + | 0.994940i | \(0.532033\pi\) | |||||||
\(770\) | 2.38505e12 | 0.244506 | ||||||||
\(771\) | 5.74832e12 | 0.585864 | ||||||||
\(772\) | −3.40040e12 | −0.344550 | ||||||||
\(773\) | 1.09355e13 | 1.10161 | 0.550807 | − | 0.834633i | \(-0.314320\pi\) | ||||
0.550807 | + | 0.834633i | \(0.314320\pi\) | |||||||
\(774\) | 2.63948e13 | 2.64353 | ||||||||
\(775\) | −1.21694e13 | −1.21175 | ||||||||
\(776\) | 9.27760e11 | 0.0918455 | ||||||||
\(777\) | −1.47863e13 | −1.45535 | ||||||||
\(778\) | 1.70456e13 | 1.66803 | ||||||||
\(779\) | −1.91242e11 | −0.0186065 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.23011e13 | 1.18308 | ||||||||
\(782\) | 2.28642e13 | 2.18638 | ||||||||
\(783\) | −2.03570e12 | −0.193547 | ||||||||
\(784\) | −1.23680e13 | −1.16917 | ||||||||
\(785\) | 2.29821e12 | 0.216011 | ||||||||
\(786\) | −2.68084e13 | −2.50535 | ||||||||
\(787\) | −7.50366e12 | −0.697247 | −0.348623 | − | 0.937263i | \(-0.613351\pi\) | ||||
−0.348623 | + | 0.937263i | \(0.613351\pi\) | |||||||
\(788\) | 8.79764e12 | 0.812827 | ||||||||
\(789\) | 2.56814e13 | 2.35924 | ||||||||
\(790\) | −1.82207e12 | −0.166434 | ||||||||
\(791\) | 7.62369e12 | 0.692423 | ||||||||
\(792\) | −4.48087e12 | −0.404668 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −8.78865e12 | −0.784747 | ||||||||
\(795\) | −8.86406e11 | −0.0787011 | ||||||||
\(796\) | 1.05539e13 | 0.931762 | ||||||||
\(797\) | 1.65844e12 | 0.145592 | 0.0727962 | − | 0.997347i | \(-0.476808\pi\) | ||||
0.0727962 | + | 0.997347i | \(0.476808\pi\) | |||||||
\(798\) | −1.38669e13 | −1.21050 | ||||||||
\(799\) | −1.20278e13 | −1.04406 | ||||||||
\(800\) | −1.21880e13 | −1.05202 | ||||||||
\(801\) | 1.75263e13 | 1.50434 | ||||||||
\(802\) | 7.39433e12 | 0.631123 | ||||||||
\(803\) | 1.15441e13 | 0.979810 | ||||||||
\(804\) | −1.24417e13 | −1.05009 | ||||||||
\(805\) | −5.56337e12 | −0.466935 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.65318e12 | 0.303207 | ||||||||
\(808\) | −4.15256e12 | −0.342740 | ||||||||
\(809\) | −7.07921e12 | −0.581054 | −0.290527 | − | 0.956867i | \(-0.593831\pi\) | ||||
−0.290527 | + | 0.956867i | \(0.593831\pi\) | |||||||
\(810\) | 2.47696e12 | 0.202179 | ||||||||
\(811\) | 1.84596e13 | 1.49840 | 0.749201 | − | 0.662343i | \(-0.230438\pi\) | ||||
0.749201 | + | 0.662343i | \(0.230438\pi\) | |||||||
\(812\) | 1.12356e13 | 0.906973 | ||||||||
\(813\) | 2.56161e13 | 2.05639 | ||||||||
\(814\) | 8.47657e12 | 0.676722 | ||||||||
\(815\) | −7.12147e11 | −0.0565406 | ||||||||
\(816\) | 2.16954e13 | 1.71302 | ||||||||
\(817\) | 1.09727e13 | 0.861616 | ||||||||
\(818\) | −1.31630e13 | −1.02793 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.92268e10 | 0.00457463 | ||||||||
\(821\) | −2.40377e13 | −1.84650 | −0.923250 | − | 0.384200i | \(-0.874477\pi\) | ||||
−0.923250 | + | 0.384200i | \(0.874477\pi\) | |||||||
\(822\) | 1.17706e13 | 0.899237 | ||||||||
\(823\) | −1.26494e12 | −0.0961104 | −0.0480552 | − | 0.998845i | \(-0.515302\pi\) | ||||
−0.0480552 | + | 0.998845i | \(0.515302\pi\) | |||||||
\(824\) | 7.96062e12 | 0.601554 | ||||||||
\(825\) | −1.39257e13 | −1.04658 | ||||||||
\(826\) | −1.50568e13 | −1.12544 | ||||||||
\(827\) | 9.81229e12 | 0.729450 | 0.364725 | − | 0.931115i | \(-0.381163\pi\) | ||||
0.364725 | + | 0.931115i | \(0.381163\pi\) | |||||||
\(828\) | −1.70764e13 | −1.26258 | ||||||||
\(829\) | 1.26128e13 | 0.927504 | 0.463752 | − | 0.885965i | \(-0.346503\pi\) | ||||
0.463752 | + | 0.885965i | \(0.346503\pi\) | |||||||
\(830\) | −3.27107e12 | −0.239242 | ||||||||
\(831\) | 1.13671e13 | 0.826886 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.25024e13 | 0.899687 | ||||||||
\(834\) | 2.09389e12 | 0.149867 | ||||||||
\(835\) | 2.37644e12 | 0.169175 | ||||||||
\(836\) | 3.04335e12 | 0.215488 | ||||||||
\(837\) | −3.29045e12 | −0.231734 | ||||||||
\(838\) | 4.75441e12 | 0.333042 | ||||||||
\(839\) | 8.53632e12 | 0.594760 | 0.297380 | − | 0.954759i | \(-0.403887\pi\) | ||||
0.297380 | + | 0.954759i | \(0.403887\pi\) | |||||||
\(840\) | −2.62856e12 | −0.182163 | ||||||||
\(841\) | 1.42715e12 | 0.0983759 | ||||||||
\(842\) | −2.62179e12 | −0.179760 | ||||||||
\(843\) | 2.07124e13 | 1.41256 | ||||||||
\(844\) | −4.74056e12 | −0.321580 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.34646e13 | 1.57488 | ||||||||
\(847\) | −9.35511e12 | −0.624559 | ||||||||
\(848\) | −5.41970e12 | −0.359910 | ||||||||
\(849\) | 2.21046e13 | 1.46015 | ||||||||
\(850\) | 1.77862e13 | 1.16868 | ||||||||
\(851\) | −1.97724e13 | −1.29234 | ||||||||
\(852\) | 2.21493e13 | 1.44006 | ||||||||
\(853\) | 1.12025e13 | 0.724507 | 0.362254 | − | 0.932080i | \(-0.382007\pi\) | ||||
0.362254 | + | 0.932080i | \(0.382007\pi\) | |||||||
\(854\) | −3.28734e13 | −2.11487 | ||||||||
\(855\) | −1.52453e12 | −0.0975639 | ||||||||
\(856\) | −8.07379e12 | −0.513979 | ||||||||
\(857\) | −2.23241e13 | −1.41371 | −0.706856 | − | 0.707357i | \(-0.749887\pi\) | ||||
−0.706856 | + | 0.707357i | \(0.749887\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.11323e13 | −1.32428 | −0.662138 | − | 0.749382i | \(-0.730351\pi\) | ||||
−0.662138 | + | 0.749382i | \(0.730351\pi\) | |||||||
\(860\) | −3.39819e12 | −0.211838 | ||||||||
\(861\) | −1.30592e12 | −0.0809845 | ||||||||
\(862\) | 2.28869e13 | 1.41190 | ||||||||
\(863\) | −1.17061e13 | −0.718395 | −0.359197 | − | 0.933262i | \(-0.616950\pi\) | ||||
−0.359197 | + | 0.933262i | \(0.616950\pi\) | |||||||
\(864\) | −3.29546e12 | −0.201189 | ||||||||
\(865\) | 2.52454e11 | 0.0153324 | ||||||||
\(866\) | 2.38005e13 | 1.43799 | ||||||||
\(867\) | 2.33115e12 | 0.140115 | ||||||||
\(868\) | 1.81609e13 | 1.08592 | ||||||||
\(869\) | −8.81730e12 | −0.524501 | ||||||||
\(870\) | 6.09045e12 | 0.360423 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.71876e11 | 0.0276378 | ||||||||
\(873\) | 3.67440e12 | 0.214103 | ||||||||
\(874\) | −1.85429e13 | −1.07492 | ||||||||
\(875\) | −8.80934e12 | −0.508051 | ||||||||
\(876\) | 2.07863e13 | 1.19264 | ||||||||
\(877\) | −1.17836e13 | −0.672638 | −0.336319 | − | 0.941748i | \(-0.609182\pi\) | ||||
−0.336319 | + | 0.941748i | \(0.609182\pi\) | |||||||
\(878\) | −3.50134e13 | −1.98842 | ||||||||
\(879\) | 7.22674e11 | 0.0408312 | ||||||||
\(880\) | 3.02627e12 | 0.170113 | ||||||||
\(881\) | −1.93741e13 | −1.08350 | −0.541751 | − | 0.840539i | \(-0.682238\pi\) | ||||
−0.541751 | + | 0.840539i | \(0.682238\pi\) | |||||||
\(882\) | −2.43904e13 | −1.35710 | ||||||||
\(883\) | −1.50199e13 | −0.831466 | −0.415733 | − | 0.909487i | \(-0.636475\pi\) | ||||
−0.415733 | + | 0.909487i | \(0.636475\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.12464e12 | −0.171220 | ||||||||
\(886\) | 2.51488e13 | 1.37109 | ||||||||
\(887\) | 1.23661e13 | 0.670776 | 0.335388 | − | 0.942080i | \(-0.391133\pi\) | ||||
0.335388 | + | 0.942080i | \(0.391133\pi\) | |||||||
\(888\) | −9.34200e12 | −0.504175 | ||||||||
\(889\) | −1.27723e13 | −0.685824 | ||||||||
\(890\) | −5.89394e12 | −0.314884 | ||||||||
\(891\) | 1.19864e13 | 0.637148 | ||||||||
\(892\) | −7.09439e12 | −0.375209 | ||||||||
\(893\) | 9.75457e12 | 0.513306 | ||||||||
\(894\) | −3.49180e13 | −1.82823 | ||||||||
\(895\) | −2.30008e12 | −0.119823 | ||||||||
\(896\) | −2.41408e13 | −1.25131 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.51702e13 | 1.80481 | ||||||||
\(899\) | 2.57558e13 | 1.31509 | ||||||||
\(900\) | −1.32838e13 | −0.674887 | ||||||||
\(901\) | 5.47860e12 | 0.276954 | ||||||||
\(902\) | 7.48644e11 | 0.0376570 | ||||||||
\(903\) | 7.49283e13 | 3.75017 | ||||||||
\(904\) | 4.81664e12 | 0.239876 | ||||||||
\(905\) | −1.35358e12 | −0.0670757 | ||||||||
\(906\) | 6.33884e13 | 3.12560 | ||||||||
\(907\) | 9.76708e12 | 0.479217 | 0.239608 | − | 0.970870i | \(-0.422981\pi\) | ||||
0.239608 | + | 0.970870i | \(0.422981\pi\) | |||||||
\(908\) | −1.65384e12 | −0.0807436 | ||||||||
\(909\) | −1.64462e13 | −0.798967 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.91556e13 | −0.921430 | −0.460715 | − | 0.887548i | \(-0.652407\pi\) | ||||
−0.460715 | + | 0.887548i | \(0.652407\pi\) | |||||||
\(912\) | −1.75950e13 | −0.842194 | ||||||||
\(913\) | −1.58293e13 | −0.753949 | ||||||||
\(914\) | 1.82219e13 | 0.863647 | ||||||||
\(915\) | −6.82200e12 | −0.321749 | ||||||||
\(916\) | −4.30586e12 | −0.202083 | ||||||||
\(917\) | −4.03170e13 | −1.88290 | ||||||||
\(918\) | 4.80914e12 | 0.223499 | ||||||||
\(919\) | −2.82464e13 | −1.30630 | −0.653150 | − | 0.757229i | \(-0.726553\pi\) | ||||
−0.653150 | + | 0.757229i | \(0.726553\pi\) | |||||||
\(920\) | −3.51493e12 | −0.161760 | ||||||||
\(921\) | −3.72425e13 | −1.70557 | ||||||||
\(922\) | 2.33049e13 | 1.06208 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.07819e13 | 0.937909 | ||||||||
\(925\) | −1.53810e13 | −0.690792 | ||||||||
\(926\) | 2.21691e13 | 0.990830 | ||||||||
\(927\) | 3.15281e13 | 1.40229 | ||||||||
\(928\) | 2.57950e13 | 1.14175 | ||||||||
\(929\) | −1.81017e13 | −0.797348 | −0.398674 | − | 0.917093i | \(-0.630529\pi\) | ||||
−0.398674 | + | 0.917093i | \(0.630529\pi\) | |||||||
\(930\) | 9.84444e12 | 0.431537 | ||||||||
\(931\) | −1.01395e13 | −0.442324 | ||||||||
\(932\) | 6.54974e10 | 0.00284350 | ||||||||
\(933\) | 3.10792e13 | 1.34277 | ||||||||
\(934\) | −4.60004e13 | −1.97788 | ||||||||
\(935\) | −3.05916e12 | −0.130903 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.51202e13 | 1.06462 | 0.532310 | − | 0.846550i | \(-0.321324\pi\) | ||||
0.532310 | + | 0.846550i | \(0.321324\pi\) | |||||||
\(938\) | −4.88745e13 | −2.06143 | ||||||||
\(939\) | −1.24842e13 | −0.524041 | ||||||||
\(940\) | −3.02095e12 | −0.126202 | ||||||||
\(941\) | −8.09156e11 | −0.0336418 | −0.0168209 | − | 0.999859i | \(-0.505355\pi\) | ||||
−0.0168209 | + | 0.999859i | \(0.505355\pi\) | |||||||
\(942\) | 5.23072e13 | 2.16438 | ||||||||
\(943\) | −1.74628e12 | −0.0719138 | ||||||||
\(944\) | −1.91048e13 | −0.783014 | ||||||||
\(945\) | −1.17017e12 | −0.0477315 | ||||||||
\(946\) | −4.29541e13 | −1.74379 | ||||||||
\(947\) | 1.25569e13 | 0.507349 | 0.253675 | − | 0.967290i | \(-0.418361\pi\) | ||||
0.253675 | + | 0.967290i | \(0.418361\pi\) | |||||||
\(948\) | −1.58763e13 | −0.638430 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.44246e13 | −0.574575 | ||||||||
\(951\) | 1.41012e13 | 0.559040 | ||||||||
\(952\) | 1.62463e13 | 0.641045 | ||||||||
\(953\) | −3.64201e13 | −1.43029 | −0.715144 | − | 0.698977i | \(-0.753639\pi\) | ||||
−0.715144 | + | 0.698977i | \(0.753639\pi\) | |||||||
\(954\) | −1.06880e13 | −0.417761 | ||||||||
\(955\) | 2.39100e12 | 0.0930173 | ||||||||
\(956\) | −6.03087e12 | −0.233518 | ||||||||
\(957\) | 2.94728e13 | 1.13584 | ||||||||
\(958\) | 4.64612e13 | 1.78216 | ||||||||
\(959\) | 1.77017e13 | 0.675821 | ||||||||
\(960\) | 1.07509e12 | 0.0408532 | ||||||||
\(961\) | 1.51913e13 | 0.574564 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.19763e13 | −1.19815 | ||||||||
\(964\) | 1.94225e13 | 0.724366 | ||||||||
\(965\) | −2.77205e12 | −0.102903 | ||||||||
\(966\) | −1.26622e14 | −4.67857 | ||||||||
\(967\) | −2.96691e13 | −1.09115 | −0.545575 | − | 0.838062i | \(-0.683689\pi\) | ||||
−0.545575 | + | 0.838062i | \(0.683689\pi\) | |||||||
\(968\) | −5.91055e12 | −0.216366 | ||||||||
\(969\) | 1.77862e13 | 0.648076 | ||||||||
\(970\) | −1.23567e12 | −0.0448156 | ||||||||
\(971\) | −1.05417e13 | −0.380563 | −0.190281 | − | 0.981730i | \(-0.560940\pi\) | ||||
−0.190281 | + | 0.981730i | \(0.560940\pi\) | |||||||
\(972\) | 2.47707e13 | 0.890103 | ||||||||
\(973\) | 3.14899e12 | 0.112632 | ||||||||
\(974\) | 2.67595e13 | 0.952714 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.17114e13 | −1.47140 | ||||||||
\(977\) | 2.40729e13 | 0.845285 | 0.422643 | − | 0.906296i | \(-0.361103\pi\) | ||||
0.422643 | + | 0.906296i | \(0.361103\pi\) | |||||||
\(978\) | −1.62085e13 | −0.566522 | ||||||||
\(979\) | −2.85218e13 | −0.992328 | ||||||||
\(980\) | 3.14014e12 | 0.108751 | ||||||||
\(981\) | 1.86887e12 | 0.0644270 | ||||||||
\(982\) | 6.64372e13 | 2.27987 | ||||||||
\(983\) | 3.57135e13 | 1.21995 | 0.609974 | − | 0.792421i | \(-0.291180\pi\) | ||||
0.609974 | + | 0.792421i | \(0.291180\pi\) | |||||||
\(984\) | −8.25078e11 | −0.0280555 | ||||||||
\(985\) | 7.17195e12 | 0.242758 | ||||||||
\(986\) | −3.76432e13 | −1.26835 | ||||||||
\(987\) | 6.66102e13 | 2.23416 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.00195e14 | 3.33013 | ||||||||
\(990\) | 5.96799e12 | 0.197456 | ||||||||
\(991\) | 2.48780e13 | 0.819376 | 0.409688 | − | 0.912226i | \(-0.365638\pi\) | ||||
0.409688 | + | 0.912226i | \(0.365638\pi\) | |||||||
\(992\) | 4.16943e13 | 1.36702 | ||||||||
\(993\) | 9.62454e12 | 0.314129 | ||||||||
\(994\) | 8.70089e13 | 2.82699 | ||||||||
\(995\) | 8.60369e12 | 0.278279 | ||||||||
\(996\) | −2.85020e13 | −0.917717 | ||||||||
\(997\) | −3.31717e13 | −1.06326 | −0.531630 | − | 0.846977i | \(-0.678420\pi\) | ||||
−0.531630 | + | 0.846977i | \(0.678420\pi\) | |||||||
\(998\) | −3.78497e12 | −0.120774 | ||||||||
\(999\) | −4.15882e12 | −0.132107 |
(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 | 169.10.a.a.1.1 | 4 | ||
13.12 | even | 2 | 13.10.a.a.1.4 | ✓ | 4 | ||
39.38 | odd | 2 | 117.10.a.c.1.1 | 4 | |||
52.51 | odd | 2 | 208.10.a.g.1.4 | 4 | |||
65.64 | even | 2 | 325.10.a.a.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.10.a.a.1.4 | ✓ | 4 | 13.12 | even | 2 | ||
117.10.a.c.1.1 | 4 | 39.38 | odd | 2 | |||
169.10.a.a.1.1 | 4 | 1.1 | even | 1 | trivial | ||
208.10.a.g.1.4 | 4 | 52.51 | odd | 2 | |||
325.10.a.a.1.1 | 4 | 65.64 | even | 2 |