Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.20 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.4458i | 0.326431i | 0.986590 | + | 0.163216i | \(0.0521866\pi\) | ||||
−0.986590 | + | 0.163216i | \(0.947813\pi\) | |||||||
\(3\) | 477.424i | 1.96471i | 0.187033 | + | 0.982354i | \(0.440113\pi\) | ||||
−0.187033 | + | 0.982354i | \(0.559887\pi\) | |||||||
\(4\) | 914.885 | 0.893443 | ||||||||
\(5\) | 5026.78i | 1.60857i | 0.594244 | + | 0.804285i | \(0.297451\pi\) | ||||
−0.594244 | + | 0.804285i | \(0.702549\pi\) | |||||||
\(6\) | −4987.08 | −0.641342 | ||||||||
\(7\) | − | 7308.14i | − | 0.434827i | −0.976080 | − | 0.217414i | \(-0.930238\pi\) | ||
0.976080 | − | 0.217414i | \(-0.0697620\pi\) | |||||||
\(8\) | 20253.2i | 0.618079i | ||||||||
\(9\) | −168885. | −2.86007 | ||||||||
\(10\) | −52508.8 | −0.525088 | ||||||||
\(11\) | −141725. | −0.879999 | −0.439999 | − | 0.897998i | \(-0.645021\pi\) | ||||
−0.439999 | + | 0.897998i | \(0.645021\pi\) | |||||||
\(12\) | 436788.i | 1.75535i | ||||||||
\(13\) | 566244. | 1.52506 | 0.762530 | − | 0.646952i | \(-0.223957\pi\) | ||||
0.762530 | + | 0.646952i | \(0.223957\pi\) | |||||||
\(14\) | 76339.4 | 0.141941 | ||||||||
\(15\) | −2.39990e6 | −3.16037 | ||||||||
\(16\) | 725281. | 0.691682 | ||||||||
\(17\) | −370530. | −0.260963 | −0.130481 | − | 0.991451i | \(-0.541652\pi\) | ||||
−0.130481 | + | 0.991451i | \(0.541652\pi\) | |||||||
\(18\) | − | 1.76413e6i | − | 0.933618i | ||||||
\(19\) | 1.53235e6i | 0.618856i | 0.950923 | + | 0.309428i | \(0.100138\pi\) | ||||
−0.950923 | + | 0.309428i | \(0.899862\pi\) | |||||||
\(20\) | 4.59893e6i | 1.43716i | ||||||||
\(21\) | 3.48908e6 | 0.854308 | ||||||||
\(22\) | − | 1.48043e6i | − | 0.287259i | ||||||
\(23\) | 9.51431e6 | 1.47822 | 0.739108 | − | 0.673587i | \(-0.235247\pi\) | ||||
0.739108 | + | 0.673587i | \(0.235247\pi\) | |||||||
\(24\) | −9.66937e6 | −1.21434 | ||||||||
\(25\) | −1.55029e7 | −1.58750 | ||||||||
\(26\) | 5.91488e6i | 0.497828i | ||||||||
\(27\) | − | 5.24381e7i | − | 3.65450i | ||||||
\(28\) | − | 6.68611e6i | − | 0.388493i | ||||||
\(29\) | 1.65562e7i | 0.807179i | 0.914940 | + | 0.403590i | \(0.132238\pi\) | ||||
−0.914940 | + | 0.403590i | \(0.867762\pi\) | |||||||
\(30\) | − | 2.50689e7i | − | 1.03164i | ||||||
\(31\) | 2.42402e7 | 0.846696 | 0.423348 | − | 0.905967i | \(-0.360855\pi\) | ||||
0.423348 | + | 0.905967i | \(0.360855\pi\) | |||||||
\(32\) | 2.83154e7i | 0.843866i | ||||||||
\(33\) | − | 6.76627e7i | − | 1.72894i | ||||||
\(34\) | − | 3.87048e6i | − | 0.0851865i | ||||||
\(35\) | 3.67364e7 | 0.699450 | ||||||||
\(36\) | −1.54510e8 | −2.55531 | ||||||||
\(37\) | − | 1.62761e7i | − | 0.234715i | −0.993090 | − | 0.117358i | \(-0.962558\pi\) | ||
0.993090 | − | 0.117358i | \(-0.0374424\pi\) | |||||||
\(38\) | −1.60066e7 | −0.202014 | ||||||||
\(39\) | 2.70339e8i | 2.99630i | ||||||||
\(40\) | −1.01808e8 | −0.994223 | ||||||||
\(41\) | −1.33025e8 | −1.14819 | −0.574097 | − | 0.818787i | \(-0.694647\pi\) | ||||
−0.574097 | + | 0.818787i | \(0.694647\pi\) | |||||||
\(42\) | 3.64462e7i | 0.278873i | ||||||||
\(43\) | 1.01091e8 | − | 1.06734e8i | 0.687655 | − | 0.726038i | ||||
\(44\) | −1.29662e8 | −0.786228 | ||||||||
\(45\) | − | 8.48945e8i | − | 4.60063i | ||||||
\(46\) | 9.93846e7i | 0.482536i | ||||||||
\(47\) | −2.40872e8 | −1.05026 | −0.525130 | − | 0.851022i | \(-0.675983\pi\) | ||||
−0.525130 | + | 0.851022i | \(0.675983\pi\) | |||||||
\(48\) | 3.46267e8i | 1.35895i | ||||||||
\(49\) | 2.29066e8 | 0.810925 | ||||||||
\(50\) | − | 1.61940e8i | − | 0.518209i | ||||||
\(51\) | − | 1.76900e8i | − | 0.512716i | ||||||
\(52\) | 5.18049e8 | 1.36255 | ||||||||
\(53\) | −2.67647e7 | −0.0640004 | −0.0320002 | − | 0.999488i | \(-0.510188\pi\) | ||||
−0.0320002 | + | 0.999488i | \(0.510188\pi\) | |||||||
\(54\) | 5.47758e8 | 1.19294 | ||||||||
\(55\) | − | 7.12419e8i | − | 1.41554i | ||||||
\(56\) | 1.48013e8 | 0.268758 | ||||||||
\(57\) | −7.31579e8 | −1.21587 | ||||||||
\(58\) | −1.72943e8 | −0.263489 | ||||||||
\(59\) | 6.95408e8 | 0.972701 | 0.486351 | − | 0.873764i | \(-0.338328\pi\) | ||||
0.486351 | + | 0.873764i | \(0.338328\pi\) | |||||||
\(60\) | −2.19564e9 | −2.82361 | ||||||||
\(61\) | − | 9.17656e8i | − | 1.08650i | −0.839570 | − | 0.543251i | \(-0.817193\pi\) | ||
0.839570 | − | 0.543251i | \(-0.182807\pi\) | |||||||
\(62\) | 2.53208e8i | 0.276388i | ||||||||
\(63\) | 1.23423e9i | 1.24364i | ||||||||
\(64\) | 4.46911e8 | 0.416218 | ||||||||
\(65\) | 2.84639e9i | 2.45317i | ||||||||
\(66\) | 7.06792e8 | 0.564380 | ||||||||
\(67\) | 1.19151e9 | 0.882522 | 0.441261 | − | 0.897379i | \(-0.354531\pi\) | ||||
0.441261 | + | 0.897379i | \(0.354531\pi\) | |||||||
\(68\) | −3.38993e8 | −0.233155 | ||||||||
\(69\) | 4.54236e9i | 2.90426i | ||||||||
\(70\) | 3.83741e8i | 0.228322i | ||||||||
\(71\) | 4.68128e8i | 0.259462i | 0.991549 | + | 0.129731i | \(0.0414113\pi\) | ||||
−0.991549 | + | 0.129731i | \(0.958589\pi\) | |||||||
\(72\) | − | 3.42045e9i | − | 1.76775i | ||||||
\(73\) | 2.00301e9i | 0.966206i | 0.875564 | + | 0.483103i | \(0.160490\pi\) | ||||
−0.875564 | + | 0.483103i | \(0.839510\pi\) | |||||||
\(74\) | 1.70017e8 | 0.0766184 | ||||||||
\(75\) | − | 7.40145e9i | − | 3.11897i | ||||||
\(76\) | 1.40192e9i | 0.552912i | ||||||||
\(77\) | 1.03574e9i | 0.382647i | ||||||||
\(78\) | −2.82390e9 | −0.978085 | ||||||||
\(79\) | −1.34231e9 | −0.436233 | −0.218116 | − | 0.975923i | \(-0.569991\pi\) | ||||
−0.218116 | + | 0.975923i | \(0.569991\pi\) | |||||||
\(80\) | 3.64583e9i | 1.11262i | ||||||||
\(81\) | 1.50627e10 | 4.31995 | ||||||||
\(82\) | − | 1.38956e9i | − | 0.374807i | ||||||
\(83\) | −1.99067e9 | −0.505369 | −0.252684 | − | 0.967549i | \(-0.581313\pi\) | ||||
−0.252684 | + | 0.967549i | \(0.581313\pi\) | |||||||
\(84\) | 3.19211e9 | 0.763275 | ||||||||
\(85\) | − | 1.86257e9i | − | 0.419777i | ||||||
\(86\) | 1.11492e9 | + | 1.05598e9i | 0.237002 | + | 0.224472i | ||||
\(87\) | −7.90431e9 | −1.58587 | ||||||||
\(88\) | − | 2.87038e9i | − | 0.543909i | ||||||
\(89\) | 2.98276e8i | 0.0534157i | 0.999643 | + | 0.0267079i | \(0.00850238\pi\) | ||||
−0.999643 | + | 0.0267079i | \(0.991498\pi\) | |||||||
\(90\) | 8.86792e9 | 1.50179 | ||||||||
\(91\) | − | 4.13819e9i | − | 0.663138i | ||||||
\(92\) | 8.70450e9 | 1.32070 | ||||||||
\(93\) | 1.15728e10i | 1.66351i | ||||||||
\(94\) | − | 2.51610e9i | − | 0.342838i | ||||||
\(95\) | −7.70278e9 | −0.995473 | ||||||||
\(96\) | −1.35185e10 | −1.65795 | ||||||||
\(97\) | −1.69052e9 | −0.196861 | −0.0984307 | − | 0.995144i | \(-0.531382\pi\) | ||||
−0.0984307 | + | 0.995144i | \(0.531382\pi\) | |||||||
\(98\) | 2.39278e9i | 0.264711i | ||||||||
\(99\) | 2.39351e10 | 2.51686 | ||||||||
\(100\) | −1.41834e10 | −1.41834 | ||||||||
\(101\) | −1.31880e10 | −1.25479 | −0.627397 | − | 0.778700i | \(-0.715880\pi\) | ||||
−0.627397 | + | 0.778700i | \(0.715880\pi\) | |||||||
\(102\) | 1.84786e9 | 0.167367 | ||||||||
\(103\) | −1.56077e10 | −1.34633 | −0.673165 | − | 0.739492i | \(-0.735066\pi\) | ||||
−0.673165 | + | 0.739492i | \(0.735066\pi\) | |||||||
\(104\) | 1.14683e10i | 0.942608i | ||||||||
\(105\) | 1.75388e10i | 1.37421i | ||||||||
\(106\) | − | 2.79578e8i | − | 0.0208917i | ||||||
\(107\) | −6.63611e9 | −0.473145 | −0.236573 | − | 0.971614i | \(-0.576024\pi\) | ||||
−0.236573 | + | 0.971614i | \(0.576024\pi\) | |||||||
\(108\) | − | 4.79748e10i | − | 3.26509i | ||||||
\(109\) | 8.75386e9 | 0.568941 | 0.284470 | − | 0.958685i | \(-0.408182\pi\) | ||||
0.284470 | + | 0.958685i | \(0.408182\pi\) | |||||||
\(110\) | 7.44179e9 | 0.462076 | ||||||||
\(111\) | 7.77059e9 | 0.461147 | ||||||||
\(112\) | − | 5.30046e9i | − | 0.300762i | ||||||
\(113\) | − | 2.39279e10i | − | 1.29871i | −0.760485 | − | 0.649355i | \(-0.775039\pi\) | ||
0.760485 | − | 0.649355i | \(-0.224961\pi\) | |||||||
\(114\) | − | 7.64194e9i | − | 0.396898i | ||||||
\(115\) | 4.78263e10i | 2.37781i | ||||||||
\(116\) | 1.51470e10i | 0.721168i | ||||||||
\(117\) | −9.56299e10 | −4.36179 | ||||||||
\(118\) | 7.26409e9i | 0.317520i | ||||||||
\(119\) | 2.70789e9i | 0.113474i | ||||||||
\(120\) | − | 4.86058e10i | − | 1.95336i | ||||||
\(121\) | −5.85155e9 | −0.225602 | ||||||||
\(122\) | 9.58566e9 | 0.354669 | ||||||||
\(123\) | − | 6.35095e10i | − | 2.25587i | ||||||
\(124\) | 2.21770e10 | 0.756474 | ||||||||
\(125\) | − | 2.88400e10i | − | 0.945030i | ||||||
\(126\) | −1.28925e10 | −0.405962 | ||||||||
\(127\) | 1.15940e10 | 0.350924 | 0.175462 | − | 0.984486i | \(-0.443858\pi\) | ||||
0.175462 | + | 0.984486i | \(0.443858\pi\) | |||||||
\(128\) | 3.36633e10i | 0.979732i | ||||||||
\(129\) | 5.09572e10 | + | 4.82633e10i | 1.42645 | + | 1.35104i | ||||
\(130\) | −2.97328e10 | −0.800790 | ||||||||
\(131\) | 1.40406e10i | 0.363941i | 0.983304 | + | 0.181970i | \(0.0582475\pi\) | ||||
−0.983304 | + | 0.181970i | \(0.941753\pi\) | |||||||
\(132\) | − | 6.19036e10i | − | 1.54471i | ||||||
\(133\) | 1.11986e10 | 0.269095 | ||||||||
\(134\) | 1.24463e10i | 0.288083i | ||||||||
\(135\) | 2.63595e11 | 5.87852 | ||||||||
\(136\) | − | 7.50443e9i | − | 0.161296i | ||||||
\(137\) | 6.16181e10i | 1.27675i | 0.769726 | + | 0.638374i | \(0.220393\pi\) | ||||
−0.769726 | + | 0.638374i | \(0.779607\pi\) | |||||||
\(138\) | −4.74486e10 | −0.948042 | ||||||||
\(139\) | −3.92886e10 | −0.757169 | −0.378584 | − | 0.925567i | \(-0.623589\pi\) | ||||
−0.378584 | + | 0.925567i | \(0.623589\pi\) | |||||||
\(140\) | 3.36096e10 | 0.624918 | ||||||||
\(141\) | − | 1.14998e11i | − | 2.06345i | ||||||
\(142\) | −4.88998e9 | −0.0846964 | ||||||||
\(143\) | −8.02508e10 | −1.34205 | ||||||||
\(144\) | −1.22489e11 | −1.97826 | ||||||||
\(145\) | −8.32243e10 | −1.29840 | ||||||||
\(146\) | −2.09231e10 | −0.315400 | ||||||||
\(147\) | 1.09362e11i | 1.59323i | ||||||||
\(148\) | − | 1.48907e10i | − | 0.209705i | ||||||
\(149\) | − | 7.35802e10i | − | 1.00191i | −0.865473 | − | 0.500956i | \(-0.832982\pi\) | ||
0.865473 | − | 0.500956i | \(-0.167018\pi\) | |||||||
\(150\) | 7.73141e10 | 1.01813 | ||||||||
\(151\) | 1.34133e11i | 1.70864i | 0.519745 | + | 0.854321i | \(0.326027\pi\) | ||||
−0.519745 | + | 0.854321i | \(0.673973\pi\) | |||||||
\(152\) | −3.10350e10 | −0.382502 | ||||||||
\(153\) | 6.25768e10 | 0.746374 | ||||||||
\(154\) | −1.08192e10 | −0.124908 | ||||||||
\(155\) | 1.21850e11i | 1.36197i | ||||||||
\(156\) | 2.47329e11i | 2.67702i | ||||||||
\(157\) | − | 4.35018e10i | − | 0.456046i | −0.973656 | − | 0.228023i | \(-0.926774\pi\) | ||
0.973656 | − | 0.228023i | \(-0.0732262\pi\) | |||||||
\(158\) | − | 1.40215e10i | − | 0.142400i | ||||||
\(159\) | − | 1.27781e10i | − | 0.125742i | ||||||
\(160\) | −1.42335e11 | −1.35742 | ||||||||
\(161\) | − | 6.95319e10i | − | 0.642769i | ||||||
\(162\) | 1.57342e11i | 1.41017i | ||||||||
\(163\) | 1.49268e10i | 0.129726i | 0.997894 | + | 0.0648632i | \(0.0206611\pi\) | ||||
−0.997894 | + | 0.0648632i | \(0.979339\pi\) | |||||||
\(164\) | −1.21703e11 | −1.02585 | ||||||||
\(165\) | 3.40126e11 | 2.78112 | ||||||||
\(166\) | − | 2.07941e10i | − | 0.164968i | ||||||
\(167\) | 3.58201e10 | 0.275769 | 0.137884 | − | 0.990448i | \(-0.455970\pi\) | ||||
0.137884 | + | 0.990448i | \(0.455970\pi\) | |||||||
\(168\) | 7.06651e10i | 0.528030i | ||||||||
\(169\) | 1.82774e11 | 1.32581 | ||||||||
\(170\) | 1.94561e10 | 0.137028 | ||||||||
\(171\) | − | 2.58790e11i | − | 1.76997i | ||||||
\(172\) | 9.24867e10 | − | 9.76491e10i | 0.614380 | − | 0.648673i | ||||
\(173\) | 1.78323e11 | 1.15074 | 0.575369 | − | 0.817894i | \(-0.304858\pi\) | ||||
0.575369 | + | 0.817894i | \(0.304858\pi\) | |||||||
\(174\) | − | 8.25669e10i | − | 0.517678i | ||||||
\(175\) | 1.13297e11i | 0.690287i | ||||||||
\(176\) | −1.02790e11 | −0.608679 | ||||||||
\(177\) | 3.32004e11i | 1.91107i | ||||||||
\(178\) | −3.11574e9 | −0.0174366 | ||||||||
\(179\) | − | 2.02752e11i | − | 1.10332i | −0.834070 | − | 0.551658i | \(-0.813995\pi\) | ||
0.834070 | − | 0.551658i | \(-0.186005\pi\) | |||||||
\(180\) | − | 7.76688e11i | − | 4.11040i | ||||||
\(181\) | −1.13688e11 | −0.585223 | −0.292612 | − | 0.956231i | \(-0.594524\pi\) | ||||
−0.292612 | + | 0.956231i | \(0.594524\pi\) | |||||||
\(182\) | 4.32267e10 | 0.216469 | ||||||||
\(183\) | 4.38111e11 | 2.13466 | ||||||||
\(184\) | 1.92695e11i | 0.913655i | ||||||||
\(185\) | 8.18163e10 | 0.377556 | ||||||||
\(186\) | −1.20888e11 | −0.543022 | ||||||||
\(187\) | 5.25133e10 | 0.229647 | ||||||||
\(188\) | −2.20370e11 | −0.938348 | ||||||||
\(189\) | −3.83225e11 | −1.58908 | ||||||||
\(190\) | − | 8.04617e10i | − | 0.324953i | ||||||
\(191\) | 4.88802e11i | 1.92294i | 0.274909 | + | 0.961470i | \(0.411352\pi\) | ||||
−0.274909 | + | 0.961470i | \(0.588648\pi\) | |||||||
\(192\) | 2.13366e11i | 0.817746i | ||||||||
\(193\) | 4.82406e11 | 1.80147 | 0.900734 | − | 0.434372i | \(-0.143030\pi\) | ||||
0.900734 | + | 0.434372i | \(0.143030\pi\) | |||||||
\(194\) | − | 1.76588e10i | − | 0.0642618i | ||||||
\(195\) | −1.35893e12 | −4.81975 | ||||||||
\(196\) | 2.09569e11 | 0.724515 | ||||||||
\(197\) | 2.18452e10 | 0.0736248 | 0.0368124 | − | 0.999322i | \(-0.488280\pi\) | ||||
0.0368124 | + | 0.999322i | \(0.488280\pi\) | |||||||
\(198\) | 2.50021e11i | 0.821582i | ||||||||
\(199\) | − | 4.07116e11i | − | 1.30453i | −0.757993 | − | 0.652263i | \(-0.773820\pi\) | ||
0.757993 | − | 0.652263i | \(-0.226180\pi\) | |||||||
\(200\) | − | 3.13984e11i | − | 0.981199i | ||||||
\(201\) | 5.68858e11i | 1.73390i | ||||||||
\(202\) | − | 1.37759e11i | − | 0.409604i | ||||||
\(203\) | 1.20995e11 | 0.350983 | ||||||||
\(204\) | − | 1.61843e11i | − | 0.458082i | ||||||
\(205\) | − | 6.68690e11i | − | 1.84695i | ||||||
\(206\) | − | 1.63035e11i | − | 0.439484i | ||||||
\(207\) | −1.60682e12 | −4.22781 | ||||||||
\(208\) | 4.10686e11 | 1.05486 | ||||||||
\(209\) | − | 2.17171e11i | − | 0.544592i | ||||||
\(210\) | −1.83207e11 | −0.448587 | ||||||||
\(211\) | 4.28555e11i | 1.02469i | 0.858779 | + | 0.512347i | \(0.171224\pi\) | ||||
−0.858779 | + | 0.512347i | \(0.828776\pi\) | |||||||
\(212\) | −2.44866e10 | −0.0571807 | ||||||||
\(213\) | −2.23496e11 | −0.509766 | ||||||||
\(214\) | − | 6.93195e10i | − | 0.154449i | ||||||
\(215\) | 5.36527e11 | + | 5.08162e11i | 1.16788 | + | 1.10614i | ||||
\(216\) | 1.06204e12 | 2.25877 | ||||||||
\(217\) | − | 1.77151e11i | − | 0.368167i | ||||||
\(218\) | 9.14411e10i | 0.185720i | ||||||||
\(219\) | −9.56286e11 | −1.89831 | ||||||||
\(220\) | − | 6.51781e11i | − | 1.26470i | ||||||
\(221\) | −2.09811e11 | −0.397984 | ||||||||
\(222\) | 8.11701e10i | 0.150533i | ||||||||
\(223\) | 5.05478e11i | 0.916596i | 0.888799 | + | 0.458298i | \(0.151541\pi\) | ||||
−0.888799 | + | 0.458298i | \(0.848459\pi\) | |||||||
\(224\) | 2.06933e11 | 0.366936 | ||||||||
\(225\) | 2.61820e12 | 4.54036 | ||||||||
\(226\) | 2.49946e11 | 0.423940 | ||||||||
\(227\) | − | 9.87423e10i | − | 0.163823i | −0.996640 | − | 0.0819113i | \(-0.973898\pi\) | ||
0.996640 | − | 0.0819113i | \(-0.0261024\pi\) | |||||||
\(228\) | −6.69311e11 | −1.08631 | ||||||||
\(229\) | −1.17644e10 | −0.0186807 | −0.00934034 | − | 0.999956i | \(-0.502973\pi\) | ||||
−0.00934034 | + | 0.999956i | \(0.502973\pi\) | |||||||
\(230\) | −4.99585e11 | −0.776193 | ||||||||
\(231\) | −4.94489e11 | −0.751790 | ||||||||
\(232\) | −3.35316e11 | −0.498901 | ||||||||
\(233\) | − | 1.08585e11i | − | 0.158121i | −0.996870 | − | 0.0790603i | \(-0.974808\pi\) | ||
0.996870 | − | 0.0790603i | \(-0.0251920\pi\) | |||||||
\(234\) | − | 9.98931e11i | − | 1.42382i | ||||||
\(235\) | − | 1.21081e12i | − | 1.68942i | ||||||
\(236\) | 6.36218e11 | 0.869053 | ||||||||
\(237\) | − | 6.40852e11i | − | 0.857069i | ||||||
\(238\) | −2.82860e10 | −0.0370414 | ||||||||
\(239\) | 7.24762e11 | 0.929406 | 0.464703 | − | 0.885467i | \(-0.346161\pi\) | ||||
0.464703 | + | 0.885467i | \(0.346161\pi\) | |||||||
\(240\) | −1.74061e12 | −2.18597 | ||||||||
\(241\) | − | 7.31179e11i | − | 0.899371i | −0.893187 | − | 0.449685i | \(-0.851536\pi\) | ||
0.893187 | − | 0.449685i | \(-0.148464\pi\) | |||||||
\(242\) | − | 6.11241e10i | − | 0.0736437i | ||||||
\(243\) | 4.09489e12i | 4.83294i | ||||||||
\(244\) | − | 8.39550e11i | − | 0.970728i | ||||||
\(245\) | 1.15147e12i | 1.30443i | ||||||||
\(246\) | 6.63408e11 | 0.736386 | ||||||||
\(247\) | 8.67683e11i | 0.943792i | ||||||||
\(248\) | 4.90942e11i | 0.523325i | ||||||||
\(249\) | − | 9.50393e11i | − | 0.992902i | ||||||
\(250\) | 3.01257e11 | 0.308487 | ||||||||
\(251\) | 8.33837e11 | 0.836975 | 0.418488 | − | 0.908222i | \(-0.362560\pi\) | ||||
0.418488 | + | 0.908222i | \(0.362560\pi\) | |||||||
\(252\) | 1.12918e12i | 1.11112i | ||||||||
\(253\) | −1.34841e12 | −1.30083 | ||||||||
\(254\) | 1.21108e11i | 0.114553i | ||||||||
\(255\) | 8.89237e11 | 0.824739 | ||||||||
\(256\) | 1.05996e11 | 0.0964026 | ||||||||
\(257\) | − | 5.20426e11i | − | 0.464187i | −0.972693 | − | 0.232094i | \(-0.925442\pi\) | ||
0.972693 | − | 0.232094i | \(-0.0745576\pi\) | |||||||
\(258\) | −5.04149e11 | + | 5.32289e11i | −0.441022 | + | 0.465639i | ||||
\(259\) | −1.18948e11 | −0.102061 | ||||||||
\(260\) | 2.60412e12i | 2.19176i | ||||||||
\(261\) | − | 2.79608e12i | − | 2.30859i | ||||||
\(262\) | −1.46666e11 | −0.118802 | ||||||||
\(263\) | − | 1.65088e12i | − | 1.31201i | −0.754759 | − | 0.656003i | \(-0.772246\pi\) | ||
0.754759 | − | 0.656003i | \(-0.227754\pi\) | |||||||
\(264\) | 1.37039e12 | 1.06862 | ||||||||
\(265\) | − | 1.34540e11i | − | 0.102949i | ||||||
\(266\) | 1.16979e11i | 0.0878411i | ||||||||
\(267\) | −1.42404e11 | −0.104946 | ||||||||
\(268\) | 1.09010e12 | 0.788482 | ||||||||
\(269\) | 2.76077e11 | 0.196006 | 0.0980029 | − | 0.995186i | \(-0.468755\pi\) | ||||
0.0980029 | + | 0.995186i | \(0.468755\pi\) | |||||||
\(270\) | 2.75346e12i | 1.91893i | ||||||||
\(271\) | −1.40676e12 | −0.962443 | −0.481221 | − | 0.876599i | \(-0.659807\pi\) | ||||
−0.481221 | + | 0.876599i | \(0.659807\pi\) | |||||||
\(272\) | −2.68739e11 | −0.180503 | ||||||||
\(273\) | 1.97567e12 | 1.30287 | ||||||||
\(274\) | −6.43650e11 | −0.416771 | ||||||||
\(275\) | 2.19714e12 | 1.39700 | ||||||||
\(276\) | 4.15574e12i | 2.59479i | ||||||||
\(277\) | − | 7.73200e11i | − | 0.474125i | −0.971494 | − | 0.237063i | \(-0.923815\pi\) | ||
0.971494 | − | 0.237063i | \(-0.0761847\pi\) | |||||||
\(278\) | − | 4.10401e11i | − | 0.247164i | ||||||
\(279\) | −4.09379e12 | −2.42161 | ||||||||
\(280\) | 7.44030e11i | 0.432315i | ||||||||
\(281\) | 1.32834e12 | 0.758191 | 0.379095 | − | 0.925358i | \(-0.376235\pi\) | ||||
0.379095 | + | 0.925358i | \(0.376235\pi\) | |||||||
\(282\) | 1.20125e12 | 0.673576 | ||||||||
\(283\) | 1.24791e12 | 0.687465 | 0.343733 | − | 0.939068i | \(-0.388309\pi\) | ||||
0.343733 | + | 0.939068i | \(0.388309\pi\) | |||||||
\(284\) | 4.28284e11i | 0.231814i | ||||||||
\(285\) | − | 3.67749e12i | − | 1.95581i | ||||||
\(286\) | − | 8.38284e11i | − | 0.438088i | ||||||
\(287\) | 9.72169e11i | 0.499266i | ||||||||
\(288\) | − | 4.78204e12i | − | 2.41352i | ||||||
\(289\) | −1.87870e12 | −0.931898 | ||||||||
\(290\) | − | 8.69344e11i | − | 0.423840i | ||||||
\(291\) | − | 8.07093e11i | − | 0.386775i | ||||||
\(292\) | 1.83253e12i | 0.863249i | ||||||||
\(293\) | −8.68763e11 | −0.402312 | −0.201156 | − | 0.979559i | \(-0.564470\pi\) | ||||
−0.201156 | + | 0.979559i | \(0.564470\pi\) | |||||||
\(294\) | −1.14237e12 | −0.520081 | ||||||||
\(295\) | 3.49566e12i | 1.56466i | ||||||||
\(296\) | 3.29643e11 | 0.145073 | ||||||||
\(297\) | 7.43177e12i | 3.21596i | ||||||||
\(298\) | 7.68605e11 | 0.327056 | ||||||||
\(299\) | 5.38742e12 | 2.25437 | ||||||||
\(300\) | − | 6.77148e12i | − | 2.78662i | ||||||
\(301\) | −7.80025e11 | − | 7.38787e11i | −0.315701 | − | 0.299011i | ||||
\(302\) | −1.40113e12 | −0.557755 | ||||||||
\(303\) | − | 6.29627e12i | − | 2.46530i | ||||||
\(304\) | 1.11138e12i | 0.428051i | ||||||||
\(305\) | 4.61286e12 | 1.74772 | ||||||||
\(306\) | 6.53665e11i | 0.243640i | ||||||||
\(307\) | −2.17669e12 | −0.798187 | −0.399094 | − | 0.916910i | \(-0.630675\pi\) | ||||
−0.399094 | + | 0.916910i | \(0.630675\pi\) | |||||||
\(308\) | 9.47586e11i | 0.341873i | ||||||||
\(309\) | − | 7.45147e12i | − | 2.64514i | ||||||
\(310\) | −1.27282e12 | −0.444590 | ||||||||
\(311\) | −4.62636e12 | −1.59015 | −0.795074 | − | 0.606512i | \(-0.792568\pi\) | ||||
−0.795074 | + | 0.606512i | \(0.792568\pi\) | |||||||
\(312\) | −5.47522e12 | −1.85195 | ||||||||
\(313\) | 9.03142e11i | 0.300631i | 0.988638 | + | 0.150316i | \(0.0480290\pi\) | ||||
−0.988638 | + | 0.150316i | \(0.951971\pi\) | |||||||
\(314\) | 4.54411e11 | 0.148868 | ||||||||
\(315\) | −6.20421e12 | −2.00048 | ||||||||
\(316\) | −1.22806e12 | −0.389749 | ||||||||
\(317\) | −8.37166e11 | −0.261526 | −0.130763 | − | 0.991414i | \(-0.541743\pi\) | ||||
−0.130763 | + | 0.991414i | \(0.541743\pi\) | |||||||
\(318\) | 1.33477e11 | 0.0410461 | ||||||||
\(319\) | − | 2.34642e12i | − | 0.710317i | ||||||
\(320\) | 2.24652e12i | 0.669516i | ||||||||
\(321\) | − | 3.16824e12i | − | 0.929592i | ||||||
\(322\) | 7.26317e11 | 0.209820 | ||||||||
\(323\) | − | 5.67781e11i | − | 0.161498i | ||||||
\(324\) | 1.37807e13 | 3.85963 | ||||||||
\(325\) | −8.77843e12 | −2.42103 | ||||||||
\(326\) | −1.55922e11 | −0.0423468 | ||||||||
\(327\) | 4.17930e12i | 1.11780i | ||||||||
\(328\) | − | 2.69419e12i | − | 0.709675i | ||||||
\(329\) | 1.76033e12i | 0.456682i | ||||||||
\(330\) | 3.55289e12i | 0.907845i | ||||||||
\(331\) | 5.95726e12i | 1.49936i | 0.661800 | + | 0.749681i | \(0.269793\pi\) | ||||
−0.661800 | + | 0.749681i | \(0.730207\pi\) | |||||||
\(332\) | −1.82123e12 | −0.451518 | ||||||||
\(333\) | 2.74878e12i | 0.671303i | ||||||||
\(334\) | 3.74170e11i | 0.0900196i | ||||||||
\(335\) | 5.98948e12i | 1.41960i | ||||||||
\(336\) | 2.53056e12 | 0.590910 | ||||||||
\(337\) | −5.64572e11 | −0.129888 | −0.0649441 | − | 0.997889i | \(-0.520687\pi\) | ||||
−0.0649441 | + | 0.997889i | \(0.520687\pi\) | |||||||
\(338\) | 1.90922e12i | 0.432786i | ||||||||
\(339\) | 1.14238e13 | 2.55159 | ||||||||
\(340\) | − | 1.70404e12i | − | 0.375047i | ||||||
\(341\) | −3.43543e12 | −0.745092 | ||||||||
\(342\) | 2.70327e12 | 0.577775 | ||||||||
\(343\) | − | 3.73842e12i | − | 0.787440i | ||||||
\(344\) | 2.16170e12 | + | 2.04742e12i | 0.448749 | + | 0.425025i | ||||
\(345\) | −2.28334e13 | −4.67171 | ||||||||
\(346\) | 1.86273e12i | 0.375637i | ||||||||
\(347\) | 3.49319e12i | 0.694344i | 0.937801 | + | 0.347172i | \(0.112858\pi\) | ||||
−0.937801 | + | 0.347172i | \(0.887142\pi\) | |||||||
\(348\) | −7.23154e12 | −1.41688 | ||||||||
\(349\) | 2.19585e11i | 0.0424107i | 0.999775 | + | 0.0212054i | \(0.00675038\pi\) | ||||
−0.999775 | + | 0.0212054i | \(0.993250\pi\) | |||||||
\(350\) | −1.18348e12 | −0.225331 | ||||||||
\(351\) | − | 2.96928e13i | − | 5.57334i | ||||||
\(352\) | − | 4.01300e12i | − | 0.742601i | ||||||
\(353\) | 7.26715e12 | 1.32584 | 0.662919 | − | 0.748691i | \(-0.269317\pi\) | ||||
0.662919 | + | 0.748691i | \(0.269317\pi\) | |||||||
\(354\) | −3.46805e12 | −0.623834 | ||||||||
\(355\) | −2.35318e12 | −0.417362 | ||||||||
\(356\) | 2.72889e11i | 0.0477239i | ||||||||
\(357\) | −1.29281e12 | −0.222943 | ||||||||
\(358\) | 2.11791e12 | 0.360157 | ||||||||
\(359\) | 1.90200e12 | 0.318961 | 0.159480 | − | 0.987201i | \(-0.449018\pi\) | ||||
0.159480 | + | 0.987201i | \(0.449018\pi\) | |||||||
\(360\) | 1.71939e13 | 2.84355 | ||||||||
\(361\) | 3.78298e12 | 0.617018 | ||||||||
\(362\) | − | 1.18756e12i | − | 0.191035i | ||||||
\(363\) | − | 2.79367e12i | − | 0.443243i | ||||||
\(364\) | − | 3.78597e12i | − | 0.592476i | ||||||
\(365\) | −1.00687e13 | −1.55421 | ||||||||
\(366\) | 4.57642e12i | 0.696820i | ||||||||
\(367\) | 7.89705e12 | 1.18614 | 0.593068 | − | 0.805153i | \(-0.297917\pi\) | ||||
0.593068 | + | 0.805153i | \(0.297917\pi\) | |||||||
\(368\) | 6.90055e12 | 1.02246 | ||||||||
\(369\) | 2.24659e13 | 3.28392 | ||||||||
\(370\) | 8.54637e11i | 0.123246i | ||||||||
\(371\) | 1.95600e11i | 0.0278291i | ||||||||
\(372\) | 1.05878e13i | 1.48625i | ||||||||
\(373\) | 9.69913e12i | 1.34335i | 0.740847 | + | 0.671674i | \(0.234425\pi\) | ||||
−0.740847 | + | 0.671674i | \(0.765575\pi\) | |||||||
\(374\) | 5.48543e11i | 0.0749640i | ||||||||
\(375\) | 1.37689e13 | 1.85671 | ||||||||
\(376\) | − | 4.87843e12i | − | 0.649144i | ||||||
\(377\) | 9.37484e12i | 1.23100i | ||||||||
\(378\) | − | 4.00309e12i | − | 0.518724i | ||||||
\(379\) | 9.41452e12 | 1.20393 | 0.601966 | − | 0.798522i | \(-0.294384\pi\) | ||||
0.601966 | + | 0.798522i | \(0.294384\pi\) | |||||||
\(380\) | −7.04716e12 | −0.889398 | ||||||||
\(381\) | 5.53524e12i | 0.689464i | ||||||||
\(382\) | −5.10593e12 | −0.627708 | ||||||||
\(383\) | − | 6.22024e12i | − | 0.754767i | −0.926057 | − | 0.377384i | \(-0.876824\pi\) | ||
0.926057 | − | 0.377384i | \(-0.123176\pi\) | |||||||
\(384\) | −1.60717e13 | −1.92489 | ||||||||
\(385\) | −5.20646e12 | −0.615515 | ||||||||
\(386\) | 5.03912e12i | 0.588055i | ||||||||
\(387\) | −1.70727e13 | + | 1.80257e13i | −1.96674 | + | 2.07652i | ||||
\(388\) | −1.54663e12 | −0.175884 | ||||||||
\(389\) | 1.64883e12i | 0.185109i | 0.995708 | + | 0.0925547i | \(0.0295033\pi\) | ||||
−0.995708 | + | 0.0925547i | \(0.970497\pi\) | |||||||
\(390\) | − | 1.41951e13i | − | 1.57332i | ||||||
\(391\) | −3.52534e12 | −0.385760 | ||||||||
\(392\) | 4.63933e12i | 0.501216i | ||||||||
\(393\) | −6.70334e12 | −0.715037 | ||||||||
\(394\) | 2.28190e11i | 0.0240334i | ||||||||
\(395\) | − | 6.74751e12i | − | 0.701711i | ||||||
\(396\) | 2.18979e13 | 2.24867 | ||||||||
\(397\) | −2.98785e12 | −0.302974 | −0.151487 | − | 0.988459i | \(-0.548406\pi\) | ||||
−0.151487 | + | 0.988459i | \(0.548406\pi\) | |||||||
\(398\) | 4.25265e12 | 0.425838 | ||||||||
\(399\) | 5.34649e12i | 0.528693i | ||||||||
\(400\) | −1.12440e13 | −1.09804 | ||||||||
\(401\) | 1.38543e13 | 1.33617 | 0.668085 | − | 0.744085i | \(-0.267114\pi\) | ||||
0.668085 | + | 0.744085i | \(0.267114\pi\) | |||||||
\(402\) | −5.94217e12 | −0.565998 | ||||||||
\(403\) | 1.37259e13 | 1.29126 | ||||||||
\(404\) | −1.20655e13 | −1.12109 | ||||||||
\(405\) | 7.57171e13i | 6.94894i | ||||||||
\(406\) | 1.26389e12i | 0.114572i | ||||||||
\(407\) | 2.30672e12i | 0.206549i | ||||||||
\(408\) | 3.58279e12 | 0.316899 | ||||||||
\(409\) | − | 2.08622e13i | − | 1.82282i | −0.411502 | − | 0.911409i | \(-0.634996\pi\) | ||
0.411502 | − | 0.911409i | \(-0.365004\pi\) | |||||||
\(410\) | 6.98500e12 | 0.602903 | ||||||||
\(411\) | −2.94179e13 | −2.50844 | ||||||||
\(412\) | −1.42792e13 | −1.20287 | ||||||||
\(413\) | − | 5.08214e12i | − | 0.422957i | ||||||
\(414\) | − | 1.67845e13i | − | 1.38009i | ||||||
\(415\) | − | 1.00067e13i | − | 0.812921i | ||||||
\(416\) | 1.60335e13i | 1.28695i | ||||||||
\(417\) | − | 1.87573e13i | − | 1.48761i | ||||||
\(418\) | 2.26853e12 | 0.177772 | ||||||||
\(419\) | 3.56689e11i | 0.0276198i | 0.999905 | + | 0.0138099i | \(0.00439596\pi\) | ||||
−0.999905 | + | 0.0138099i | \(0.995604\pi\) | |||||||
\(420\) | 1.60460e13i | 1.22778i | ||||||||
\(421\) | − | 1.13802e13i | − | 0.860480i | −0.902714 | − | 0.430240i | \(-0.858429\pi\) | ||
0.902714 | − | 0.430240i | \(-0.141571\pi\) | |||||||
\(422\) | −4.47660e12 | −0.334492 | ||||||||
\(423\) | 4.06796e13 | 3.00382 | ||||||||
\(424\) | − | 5.42071e11i | − | 0.0395573i | ||||||
\(425\) | 5.74429e12 | 0.414278 | ||||||||
\(426\) | − | 2.33459e12i | − | 0.166404i | ||||||
\(427\) | −6.70636e12 | −0.472441 | ||||||||
\(428\) | −6.07128e12 | −0.422728 | ||||||||
\(429\) | − | 3.83136e13i | − | 2.63674i | ||||||
\(430\) | −5.30816e12 | + | 5.60446e12i | −0.361079 | + | 0.381234i | ||||
\(431\) | 1.90208e13 | 1.27892 | 0.639458 | − | 0.768826i | \(-0.279159\pi\) | ||||
0.639458 | + | 0.768826i | \(0.279159\pi\) | |||||||
\(432\) | − | 3.80324e13i | − | 2.52775i | ||||||
\(433\) | 5.41588e12i | 0.355820i | 0.984047 | + | 0.177910i | \(0.0569335\pi\) | ||||
−0.984047 | + | 0.177910i | \(0.943066\pi\) | |||||||
\(434\) | 1.85048e12 | 0.120181 | ||||||||
\(435\) | − | 3.97332e13i | − | 2.55098i | ||||||
\(436\) | 8.00878e12 | 0.508316 | ||||||||
\(437\) | 1.45792e13i | 0.914803i | ||||||||
\(438\) | − | 9.98918e12i | − | 0.619668i | ||||||
\(439\) | −1.61738e13 | −0.991951 | −0.495976 | − | 0.868336i | \(-0.665189\pi\) | ||||
−0.495976 | + | 0.868336i | \(0.665189\pi\) | |||||||
\(440\) | 1.44288e13 | 0.874915 | ||||||||
\(441\) | −3.86858e13 | −2.31931 | ||||||||
\(442\) | − | 2.19164e12i | − | 0.129915i | ||||||
\(443\) | 2.44931e12 | 0.143557 | 0.0717786 | − | 0.997421i | \(-0.477133\pi\) | ||||
0.0717786 | + | 0.997421i | \(0.477133\pi\) | |||||||
\(444\) | 7.10920e12 | 0.412008 | ||||||||
\(445\) | −1.49937e12 | −0.0859229 | ||||||||
\(446\) | −5.28012e12 | −0.299206 | ||||||||
\(447\) | 3.51290e13 | 1.96847 | ||||||||
\(448\) | − | 3.26609e12i | − | 0.180983i | ||||||
\(449\) | − | 5.17378e12i | − | 0.283515i | −0.989901 | − | 0.141758i | \(-0.954725\pi\) | ||
0.989901 | − | 0.141758i | \(-0.0452753\pi\) | |||||||
\(450\) | 2.73492e13i | 1.48212i | ||||||||
\(451\) | 1.88530e13 | 1.01041 | ||||||||
\(452\) | − | 2.18913e13i | − | 1.16032i | ||||||
\(453\) | −6.40384e13 | −3.35698 | ||||||||
\(454\) | 1.03144e12 | 0.0534768 | ||||||||
\(455\) | 2.08018e13 | 1.06670 | ||||||||
\(456\) | − | 1.48168e13i | − | 0.751504i | ||||||
\(457\) | − | 2.19511e13i | − | 1.10122i | −0.834761 | − | 0.550612i | \(-0.814394\pi\) | ||
0.834761 | − | 0.550612i | \(-0.185606\pi\) | |||||||
\(458\) | − | 1.22889e11i | − | 0.00609796i | ||||||
\(459\) | 1.94299e13i | 0.953690i | ||||||||
\(460\) | 4.37556e13i | 2.12444i | ||||||||
\(461\) | 4.11135e13 | 1.97460 | 0.987300 | − | 0.158864i | \(-0.0507833\pi\) | ||||
0.987300 | + | 0.158864i | \(0.0507833\pi\) | |||||||
\(462\) | − | 5.16533e12i | − | 0.245408i | ||||||
\(463\) | 2.72180e13i | 1.27924i | 0.768693 | + | 0.639618i | \(0.220908\pi\) | ||||
−0.768693 | + | 0.639618i | \(0.779092\pi\) | |||||||
\(464\) | 1.20079e13i | 0.558311i | ||||||||
\(465\) | −5.81742e13 | −2.67587 | ||||||||
\(466\) | 1.13425e12 | 0.0516155 | ||||||||
\(467\) | 2.92917e13i | 1.31874i | 0.751818 | + | 0.659371i | \(0.229177\pi\) | ||||
−0.751818 | + | 0.659371i | \(0.770823\pi\) | |||||||
\(468\) | −8.74904e13 | −3.89701 | ||||||||
\(469\) | − | 8.70776e12i | − | 0.383744i | ||||||
\(470\) | 1.26479e13 | 0.551479 | ||||||||
\(471\) | 2.07688e13 | 0.895998 | ||||||||
\(472\) | 1.40842e13i | 0.601206i | ||||||||
\(473\) | −1.43271e13 | + | 1.51268e13i | −0.605135 | + | 0.638912i | ||||
\(474\) | 6.69421e12 | 0.279774 | ||||||||
\(475\) | − | 2.37558e13i | − | 0.982432i | ||||||
\(476\) | 2.47740e12i | 0.101382i | ||||||||
\(477\) | 4.52014e12 | 0.183046 | ||||||||
\(478\) | 7.57072e12i | 0.303387i | ||||||||
\(479\) | 5.43350e12 | 0.215477 | 0.107739 | − | 0.994179i | \(-0.465639\pi\) | ||||
0.107739 | + | 0.994179i | \(0.465639\pi\) | |||||||
\(480\) | − | 6.79544e13i | − | 2.66693i | ||||||
\(481\) | − | 9.21624e12i | − | 0.357955i | ||||||
\(482\) | 7.63776e12 | 0.293583 | ||||||||
\(483\) | 3.31962e13 | 1.26285 | ||||||||
\(484\) | −5.35349e12 | −0.201563 | ||||||||
\(485\) | − | 8.49785e12i | − | 0.316665i | ||||||
\(486\) | −4.27744e13 | −1.57762 | ||||||||
\(487\) | −2.85945e13 | −1.04385 | −0.521925 | − | 0.852992i | \(-0.674786\pi\) | ||||
−0.521925 | + | 0.852992i | \(0.674786\pi\) | |||||||
\(488\) | 1.85855e13 | 0.671544 | ||||||||
\(489\) | −7.12641e12 | −0.254874 | ||||||||
\(490\) | −1.20280e13 | −0.425807 | ||||||||
\(491\) | − | 2.23033e13i | − | 0.781560i | −0.920484 | − | 0.390780i | \(-0.872205\pi\) | ||
0.920484 | − | 0.390780i | \(-0.127795\pi\) | |||||||
\(492\) | − | 5.81039e13i | − | 2.01549i | ||||||
\(493\) | − | 6.13456e12i | − | 0.210644i | ||||||
\(494\) | −9.06365e12 | −0.308083 | ||||||||
\(495\) | 1.20317e14i | 4.04855i | ||||||||
\(496\) | 1.75810e13 | 0.585645 | ||||||||
\(497\) | 3.42115e12 | 0.112821 | ||||||||
\(498\) | 9.92762e12 | 0.324114 | ||||||||
\(499\) | 8.65964e12i | 0.279896i | 0.990159 | + | 0.139948i | \(0.0446936\pi\) | ||||
−0.990159 | + | 0.139948i | \(0.955306\pi\) | |||||||
\(500\) | − | 2.63853e13i | − | 0.844330i | ||||||
\(501\) | 1.71014e13i | 0.541805i | ||||||||
\(502\) | 8.71010e12i | 0.273215i | ||||||||
\(503\) | 5.57072e13i | 1.73010i | 0.501685 | + | 0.865050i | \(0.332714\pi\) | ||||
−0.501685 | + | 0.865050i | \(0.667286\pi\) | |||||||
\(504\) | −2.49972e13 | −0.768667 | ||||||||
\(505\) | − | 6.62932e13i | − | 2.01842i | ||||||
\(506\) | − | 1.40852e13i | − | 0.424631i | ||||||
\(507\) | 8.72607e13i | 2.60483i | ||||||||
\(508\) | 1.06072e13 | 0.313531 | ||||||||
\(509\) | 4.10921e13 | 1.20273 | 0.601367 | − | 0.798973i | \(-0.294623\pi\) | ||||
0.601367 | + | 0.798973i | \(0.294623\pi\) | |||||||
\(510\) | 9.28880e12i | 0.269221i | ||||||||
\(511\) | 1.46383e13 | 0.420132 | ||||||||
\(512\) | 3.55785e13i | 1.01120i | ||||||||
\(513\) | 8.03534e13 | 2.26161 | ||||||||
\(514\) | 5.43627e12 | 0.151525 | ||||||||
\(515\) | − | 7.84563e13i | − | 2.16567i | ||||||
\(516\) | 4.66200e13 | + | 4.41553e13i | 1.27445 | + | 1.20708i | ||||
\(517\) | 3.41375e13 | 0.924228 | ||||||||
\(518\) | − | 1.24251e12i | − | 0.0333158i | ||||||
\(519\) | 8.51356e13i | 2.26086i | ||||||||
\(520\) | −5.76485e13 | −1.51625 | ||||||||
\(521\) | − | 6.96468e13i | − | 1.81431i | −0.420792 | − | 0.907157i | \(-0.638248\pi\) | ||
0.420792 | − | 0.907157i | \(-0.361752\pi\) | |||||||
\(522\) | 2.92073e13 | 0.753597 | ||||||||
\(523\) | − | 5.84635e13i | − | 1.49409i | −0.664775 | − | 0.747044i | \(-0.731472\pi\) | ||
0.664775 | − | 0.747044i | \(-0.268528\pi\) | |||||||
\(524\) | 1.28456e13i | 0.325160i | ||||||||
\(525\) | −5.40909e13 | −1.35621 | ||||||||
\(526\) | 1.72447e13 | 0.428280 | ||||||||
\(527\) | −8.98172e12 | −0.220956 | ||||||||
\(528\) | − | 4.90745e13i | − | 1.19588i | ||||||
\(529\) | 4.90956e13 | 1.18512 | ||||||||
\(530\) | 1.40538e12 | 0.0336058 | ||||||||
\(531\) | −1.17444e14 | −2.78200 | ||||||||
\(532\) | 1.02454e13 | 0.240421 | ||||||||
\(533\) | −7.53249e13 | −1.75107 | ||||||||
\(534\) | − | 1.48753e12i | − | 0.0342577i | ||||||
\(535\) | − | 3.33582e13i | − | 0.761087i | ||||||
\(536\) | 2.41320e13i | 0.545468i | ||||||||
\(537\) | 9.67986e13 | 2.16769 | ||||||||
\(538\) | 2.88385e12i | 0.0639824i | ||||||||
\(539\) | −3.24643e13 | −0.713613 | ||||||||
\(540\) | 2.41159e14 | 5.25212 | ||||||||
\(541\) | −2.63024e13 | −0.567556 | −0.283778 | − | 0.958890i | \(-0.591588\pi\) | ||||
−0.283778 | + | 0.958890i | \(0.591588\pi\) | |||||||
\(542\) | − | 1.46948e13i | − | 0.314172i | ||||||
\(543\) | − | 5.42774e13i | − | 1.14979i | ||||||
\(544\) | − | 1.04917e13i | − | 0.220218i | ||||||
\(545\) | 4.40037e13i | 0.915181i | ||||||||
\(546\) | 2.06375e13i | 0.425298i | ||||||||
\(547\) | 2.10805e13 | 0.430471 | 0.215235 | − | 0.976562i | \(-0.430948\pi\) | ||||
0.215235 | + | 0.976562i | \(0.430948\pi\) | |||||||
\(548\) | 5.63735e13i | 1.14070i | ||||||||
\(549\) | 1.54978e14i | 3.10748i | ||||||||
\(550\) | 2.29509e13i | 0.456023i | ||||||||
\(551\) | −2.53698e13 | −0.499527 | ||||||||
\(552\) | −9.19973e13 | −1.79506 | ||||||||
\(553\) | 9.80981e12i | 0.189686i | ||||||||
\(554\) | 8.07670e12 | 0.154769 | ||||||||
\(555\) | 3.90611e13i | 0.741787i | ||||||||
\(556\) | −3.59446e13 | −0.676487 | ||||||||
\(557\) | 1.96259e13 | 0.366062 | 0.183031 | − | 0.983107i | \(-0.441409\pi\) | ||||
0.183031 | + | 0.983107i | \(0.441409\pi\) | |||||||
\(558\) | − | 4.27630e13i | − | 0.790491i | ||||||
\(559\) | 5.72422e13 | − | 6.04374e13i | 1.04871 | − | 1.10725i | ||||
\(560\) | 2.66442e13 | 0.483797 | ||||||||
\(561\) | 2.50711e13i | 0.451189i | ||||||||
\(562\) | 1.38756e13i | 0.247497i | ||||||||
\(563\) | 6.45640e13 | 1.14143 | 0.570714 | − | 0.821149i | \(-0.306667\pi\) | ||||
0.570714 | + | 0.821149i | \(0.306667\pi\) | |||||||
\(564\) | − | 1.05210e14i | − | 1.84358i | ||||||
\(565\) | 1.20280e14 | 2.08907 | ||||||||
\(566\) | 1.30354e13i | 0.224410i | ||||||||
\(567\) | − | 1.10081e14i | − | 1.87843i | ||||||
\(568\) | −9.48110e12 | −0.160368 | ||||||||
\(569\) | −4.65334e11 | −0.00780195 | −0.00390097 | − | 0.999992i | \(-0.501242\pi\) | ||||
−0.00390097 | + | 0.999992i | \(0.501242\pi\) | |||||||
\(570\) | 3.84143e13 | 0.638438 | ||||||||
\(571\) | 6.79642e13i | 1.11970i | 0.828596 | + | 0.559848i | \(0.189140\pi\) | ||||
−0.828596 | + | 0.559848i | \(0.810860\pi\) | |||||||
\(572\) | −7.34203e13 | −1.19905 | ||||||||
\(573\) | −2.33366e14 | −3.77801 | ||||||||
\(574\) | −1.01551e13 | −0.162976 | ||||||||
\(575\) | −1.47499e14 | −2.34666 | ||||||||
\(576\) | −7.54763e13 | −1.19041 | ||||||||
\(577\) | 8.47586e13i | 1.32527i | 0.748942 | + | 0.662636i | \(0.230562\pi\) | ||||
−0.748942 | + | 0.662636i | \(0.769438\pi\) | |||||||
\(578\) | − | 1.96245e13i | − | 0.304201i | ||||||
\(579\) | 2.30312e14i | 3.53936i | ||||||||
\(580\) | −7.61406e13 | −1.16005 | ||||||||
\(581\) | 1.45481e13i | 0.219748i | ||||||||
\(582\) | 8.43073e12 | 0.126256 | ||||||||
\(583\) | 3.79321e12 | 0.0563202 | ||||||||
\(584\) | −4.05675e13 | −0.597191 | ||||||||
\(585\) | − | 4.80711e14i | − | 7.01624i | ||||||
\(586\) | − | 9.07493e12i | − | 0.131327i | ||||||
\(587\) | − | 1.42421e13i | − | 0.204354i | −0.994766 | − | 0.102177i | \(-0.967419\pi\) | ||
0.994766 | − | 0.102177i | \(-0.0325808\pi\) | |||||||
\(588\) | 1.00053e14i | 1.42346i | ||||||||
\(589\) | 3.71444e13i | 0.523983i | ||||||||
\(590\) | −3.65150e13 | −0.510754 | ||||||||
\(591\) | 1.04294e13i | 0.144651i | ||||||||
\(592\) | − | 1.18047e13i | − | 0.162348i | ||||||
\(593\) | − | 4.45083e13i | − | 0.606971i | −0.952836 | − | 0.303485i | \(-0.901850\pi\) | ||
0.952836 | − | 0.303485i | \(-0.0981503\pi\) | |||||||
\(594\) | −7.76308e13 | −1.04979 | ||||||||
\(595\) | −1.36119e13 | −0.182531 | ||||||||
\(596\) | − | 6.73175e13i | − | 0.895152i | ||||||
\(597\) | 1.94367e14 | 2.56301 | ||||||||
\(598\) | 5.62760e13i | 0.735897i | ||||||||
\(599\) | 1.13656e13 | 0.147387 | 0.0736936 | − | 0.997281i | \(-0.476521\pi\) | ||||
0.0736936 | + | 0.997281i | \(0.476521\pi\) | |||||||
\(600\) | 1.49903e14 | 1.92777 | ||||||||
\(601\) | 2.65428e13i | 0.338513i | 0.985572 | + | 0.169256i | \(0.0541366\pi\) | ||||
−0.985572 | + | 0.169256i | \(0.945863\pi\) | |||||||
\(602\) | 7.71723e12 | − | 8.14799e12i | 0.0976065 | − | 0.103055i | ||||
\(603\) | −2.01228e14 | −2.52408 | ||||||||
\(604\) | 1.22716e14i | 1.52657i | ||||||||
\(605\) | − | 2.94144e13i | − | 0.362897i | ||||||
\(606\) | 6.57696e13 | 0.804752 | ||||||||
\(607\) | − | 1.05162e14i | − | 1.27619i | −0.769959 | − | 0.638094i | \(-0.779723\pi\) | ||
0.769959 | − | 0.638094i | \(-0.220277\pi\) | |||||||
\(608\) | −4.33891e13 | −0.522231 | ||||||||
\(609\) | 5.77658e13i | 0.689580i | ||||||||
\(610\) | 4.81850e13i | 0.570509i | ||||||||
\(611\) | −1.36392e14 | −1.60171 | ||||||||
\(612\) | 5.72506e13 | 0.666842 | ||||||||
\(613\) | 1.04062e14 | 1.20223 | 0.601116 | − | 0.799162i | \(-0.294723\pi\) | ||||
0.601116 | + | 0.799162i | \(0.294723\pi\) | |||||||
\(614\) | − | 2.27373e13i | − | 0.260553i | ||||||
\(615\) | 3.19249e14 | 3.62872 | ||||||||
\(616\) | −2.09771e13 | −0.236506 | ||||||||
\(617\) | −1.03295e14 | −1.15519 | −0.577596 | − | 0.816323i | \(-0.696009\pi\) | ||||
−0.577596 | + | 0.816323i | \(0.696009\pi\) | |||||||
\(618\) | 7.78366e13 | 0.863458 | ||||||||
\(619\) | −1.62504e13 | −0.178817 | −0.0894087 | − | 0.995995i | \(-0.528498\pi\) | ||||
−0.0894087 | + | 0.995995i | \(0.528498\pi\) | |||||||
\(620\) | 1.11479e14i | 1.21684i | ||||||||
\(621\) | − | 4.98912e14i | − | 5.40214i | ||||||
\(622\) | − | 4.83261e13i | − | 0.519074i | ||||||
\(623\) | 2.17985e12 | 0.0232266 | ||||||||
\(624\) | 1.96072e14i | 2.07249i | ||||||||
\(625\) | −6.42304e12 | −0.0673504 | ||||||||
\(626\) | −9.43405e12 | −0.0981355 | ||||||||
\(627\) | 1.03683e14 | 1.06996 | ||||||||
\(628\) | − | 3.97992e13i | − | 0.407451i | ||||||
\(629\) | 6.03078e12i | 0.0612520i | ||||||||
\(630\) | − | 6.48080e13i | − | 0.653019i | ||||||
\(631\) | − | 1.21127e13i | − | 0.121086i | −0.998166 | − | 0.0605432i | \(-0.980717\pi\) | ||
0.998166 | − | 0.0605432i | \(-0.0192833\pi\) | |||||||
\(632\) | − | 2.71861e13i | − | 0.269626i | ||||||
\(633\) | −2.04602e14 | −2.01322 | ||||||||
\(634\) | − | 8.74488e12i | − | 0.0853704i | ||||||
\(635\) | 5.82804e13i | 0.564486i | ||||||||
\(636\) | − | 1.16905e13i | − | 0.112343i | ||||||
\(637\) | 1.29708e14 | 1.23671 | ||||||||
\(638\) | 2.45102e13 | 0.231870 | ||||||||
\(639\) | − | 7.90596e13i | − | 0.742080i | ||||||
\(640\) | −1.69218e14 | −1.57597 | ||||||||
\(641\) | − | 1.35807e14i | − | 1.25496i | −0.778631 | − | 0.627482i | \(-0.784086\pi\) | ||
0.778631 | − | 0.627482i | \(-0.215914\pi\) | |||||||
\(642\) | 3.30948e13 | 0.303448 | ||||||||
\(643\) | −1.89535e13 | −0.172438 | −0.0862191 | − | 0.996276i | \(-0.527479\pi\) | ||||
−0.0862191 | + | 0.996276i | \(0.527479\pi\) | |||||||
\(644\) | − | 6.36137e13i | − | 0.574277i | ||||||
\(645\) | −2.42609e14 | + | 2.56151e14i | −2.17324 | + | 2.29455i | ||||
\(646\) | 5.93093e12 | 0.0527182 | ||||||||
\(647\) | − | 8.06429e13i | − | 0.711287i | −0.934622 | − | 0.355643i | \(-0.884262\pi\) | ||
0.934622 | − | 0.355643i | \(-0.115738\pi\) | |||||||
\(648\) | 3.05069e14i | 2.67007i | ||||||||
\(649\) | −9.85564e13 | −0.855976 | ||||||||
\(650\) | − | 9.16977e13i | − | 0.790300i | ||||||
\(651\) | 8.45760e13 | 0.723339 | ||||||||
\(652\) | 1.36563e13i | 0.115903i | ||||||||
\(653\) | 1.21280e14i | 1.02147i | 0.859739 | + | 0.510733i | \(0.170626\pi\) | ||||
−0.859739 | + | 0.510733i | \(0.829374\pi\) | |||||||
\(654\) | −4.36562e13 | −0.364886 | ||||||||
\(655\) | −7.05792e13 | −0.585424 | ||||||||
\(656\) | −9.64809e13 | −0.794186 | ||||||||
\(657\) | − | 3.38278e14i | − | 2.76342i | ||||||
\(658\) | −1.83880e13 | −0.149075 | ||||||||
\(659\) | 2.00699e14 | 1.61480 | 0.807398 | − | 0.590008i | \(-0.200875\pi\) | ||||
0.807398 | + | 0.590008i | \(0.200875\pi\) | |||||||
\(660\) | 3.11176e14 | 2.48477 | ||||||||
\(661\) | 2.33784e13 | 0.185271 | 0.0926353 | − | 0.995700i | \(-0.470471\pi\) | ||||
0.0926353 | + | 0.995700i | \(0.470471\pi\) | |||||||
\(662\) | −6.22283e13 | −0.489438 | ||||||||
\(663\) | − | 1.00169e14i | − | 0.781923i | ||||||
\(664\) | − | 4.03174e13i | − | 0.312358i | ||||||
\(665\) | 5.62930e13i | 0.432859i | ||||||||
\(666\) | −2.87132e13 | −0.219134 | ||||||||
\(667\) | 1.57521e14i | 1.19319i | ||||||||
\(668\) | 3.27713e13 | 0.246384 | ||||||||
\(669\) | −2.41327e14 | −1.80084 | ||||||||
\(670\) | −6.25650e13 | −0.463401 | ||||||||
\(671\) | 1.30054e14i | 0.956121i | ||||||||
\(672\) | 9.87948e13i | 0.720921i | ||||||||
\(673\) | 1.68095e14i | 1.21753i | 0.793351 | + | 0.608765i | \(0.208335\pi\) | ||||
−0.793351 | + | 0.608765i | \(0.791665\pi\) | |||||||
\(674\) | − | 5.89741e12i | − | 0.0423996i | ||||||
\(675\) | 8.12943e14i | 5.80151i | ||||||||
\(676\) | 1.67217e14 | 1.18453 | ||||||||
\(677\) | − | 1.26890e14i | − | 0.892242i | −0.894973 | − | 0.446121i | \(-0.852805\pi\) | ||
0.894973 | − | 0.446121i | \(-0.147195\pi\) | |||||||
\(678\) | 1.19330e14i | 0.832918i | ||||||||
\(679\) | 1.23545e13i | 0.0856007i | ||||||||
\(680\) | 3.77231e13 | 0.259455 | ||||||||
\(681\) | 4.71419e13 | 0.321863 | ||||||||
\(682\) | − | 3.58859e13i | − | 0.243221i | ||||||
\(683\) | −7.77449e12 | −0.0523080 | −0.0261540 | − | 0.999658i | \(-0.508326\pi\) | ||||
−0.0261540 | + | 0.999658i | \(0.508326\pi\) | |||||||
\(684\) | − | 2.36763e14i | − | 1.58137i | ||||||
\(685\) | −3.09741e14 | −2.05374 | ||||||||
\(686\) | 3.90508e13 | 0.257045 | ||||||||
\(687\) | − | 5.61661e12i | − | 0.0367021i | ||||||
\(688\) | 7.33194e13 | − | 7.74120e13i | 0.475638 | − | 0.502188i | ||||
\(689\) | −1.51553e13 | −0.0976044 | ||||||||
\(690\) | − | 2.38514e14i | − | 1.52499i | ||||||
\(691\) | 2.72610e14i | 1.73042i | 0.501410 | + | 0.865210i | \(0.332815\pi\) | ||||
−0.501410 | + | 0.865210i | \(0.667185\pi\) | |||||||
\(692\) | 1.63145e14 | 1.02812 | ||||||||
\(693\) | − | 1.74921e14i | − | 1.09440i | ||||||
\(694\) | −3.64892e13 | −0.226656 | ||||||||
\(695\) | − | 1.97495e14i | − | 1.21796i | ||||||
\(696\) | − | 1.60088e14i | − | 0.980193i | ||||||
\(697\) | 4.92900e13 | 0.299636 | ||||||||
\(698\) | −2.29374e12 | −0.0138442 | ||||||||
\(699\) | 5.18409e13 | 0.310661 | ||||||||
\(700\) | 1.03654e14i | 0.616732i | ||||||||
\(701\) | −2.61157e14 | −1.54281 | −0.771404 | − | 0.636346i | \(-0.780445\pi\) | ||||
−0.771404 | + | 0.636346i | \(0.780445\pi\) | |||||||
\(702\) | 3.10165e14 | 1.81931 | ||||||||
\(703\) | 2.49406e13 | 0.145255 | ||||||||
\(704\) | −6.33383e13 | −0.366271 | ||||||||
\(705\) | 5.78070e14 | 3.31921 | ||||||||
\(706\) | 7.59112e13i | 0.432795i | ||||||||
\(707\) | 9.63798e13i | 0.545619i | ||||||||
\(708\) | 3.03746e14i | 1.70743i | ||||||||
\(709\) | 1.73483e14 | 0.968335 | 0.484167 | − | 0.874975i | \(-0.339123\pi\) | ||||
0.484167 | + | 0.874975i | \(0.339123\pi\) | |||||||
\(710\) | − | 2.45808e13i | − | 0.136240i | ||||||
\(711\) | 2.26696e14 | 1.24766 | ||||||||
\(712\) | −6.04106e12 | −0.0330151 | ||||||||
\(713\) | 2.30629e14 | 1.25160 | ||||||||
\(714\) | − | 1.35044e13i | − | 0.0727755i | ||||||
\(715\) | − | 4.03403e14i | − | 2.15878i | ||||||
\(716\) | − | 1.85495e14i | − | 0.985749i | ||||||
\(717\) | 3.46018e14i | 1.82601i | ||||||||
\(718\) | 1.98679e13i | 0.104119i | ||||||||
\(719\) | 1.87163e14 | 0.974037 | 0.487019 | − | 0.873392i | \(-0.338084\pi\) | ||||
0.487019 | + | 0.873392i | \(0.338084\pi\) | |||||||
\(720\) | − | 6.15724e14i | − | 3.18217i | ||||||
\(721\) | 1.14063e14i | 0.585421i | ||||||||
\(722\) | 3.95162e13i | 0.201414i | ||||||||
\(723\) | 3.49083e14 | 1.76700 | ||||||||
\(724\) | −1.04011e14 | −0.522864 | ||||||||
\(725\) | − | 2.56669e14i | − | 1.28139i | ||||||
\(726\) | 2.91821e13 | 0.144688 | ||||||||
\(727\) | 3.95170e14i | 1.94586i | 0.231094 | + | 0.972931i | \(0.425769\pi\) | ||||
−0.231094 | + | 0.972931i | \(0.574231\pi\) | |||||||
\(728\) | 8.38117e13 | 0.409872 | ||||||||
\(729\) | −1.06556e15 | −5.17536 | ||||||||
\(730\) | − | 1.05176e14i | − | 0.507343i | ||||||
\(731\) | −3.74573e13 | + | 3.95481e13i | −0.179452 | + | 0.189469i | ||||
\(732\) | 4.00821e14 | 1.90720 | ||||||||
\(733\) | 9.69391e12i | 0.0458120i | 0.999738 | + | 0.0229060i | \(0.00729184\pi\) | ||||
−0.999738 | + | 0.0229060i | \(0.992708\pi\) | |||||||
\(734\) | 8.24910e13i | 0.387192i | ||||||||
\(735\) | −5.49737e14 | −2.56282 | ||||||||
\(736\) | 2.69402e14i | 1.24742i | ||||||||
\(737\) | −1.68867e14 | −0.776618 | ||||||||
\(738\) | 2.34675e14i | 1.07198i | ||||||||
\(739\) | − | 2.97871e14i | − | 1.35147i | −0.737145 | − | 0.675734i | \(-0.763827\pi\) | ||
0.737145 | − | 0.675734i | \(-0.236173\pi\) | |||||||
\(740\) | 7.48525e13 | 0.337324 | ||||||||
\(741\) | −4.14253e14 | −1.85428 | ||||||||
\(742\) | −2.04320e12 | −0.00908429 | ||||||||
\(743\) | − | 2.86394e14i | − | 1.26480i | −0.774644 | − | 0.632398i | \(-0.782071\pi\) | ||
0.774644 | − | 0.632398i | \(-0.217929\pi\) | |||||||
\(744\) | −2.34387e14 | −1.02818 | ||||||||
\(745\) | 3.69872e14 | 1.61165 | ||||||||
\(746\) | −1.01315e14 | −0.438511 | ||||||||
\(747\) | 3.36193e14 | 1.44539 | ||||||||
\(748\) | 4.80436e13 | 0.205176 | ||||||||
\(749\) | 4.84976e13i | 0.205736i | ||||||||
\(750\) | 1.43827e14i | 0.606087i | ||||||||
\(751\) | 3.73464e14i | 1.56333i | 0.623701 | + | 0.781663i | \(0.285628\pi\) | ||||
−0.623701 | + | 0.781663i | \(0.714372\pi\) | |||||||
\(752\) | −1.74700e14 | −0.726447 | ||||||||
\(753\) | 3.98094e14i | 1.64441i | ||||||||
\(754\) | −9.79277e13 | −0.401836 | ||||||||
\(755\) | −6.74258e14 | −2.74847 | ||||||||
\(756\) | −3.50607e14 | −1.41975 | ||||||||
\(757\) | − | 1.06247e14i | − | 0.427401i | −0.976899 | − | 0.213701i | \(-0.931448\pi\) | ||
0.976899 | − | 0.213701i | \(-0.0685517\pi\) | |||||||
\(758\) | 9.83422e13i | 0.393001i | ||||||||
\(759\) | − | 6.43764e14i | − | 2.55575i | ||||||
\(760\) | − | 1.56006e14i | − | 0.615281i | ||||||
\(761\) | − | 4.08008e14i | − | 1.59862i | −0.600919 | − | 0.799310i | \(-0.705199\pi\) | ||
0.600919 | − | 0.799310i | \(-0.294801\pi\) | |||||||
\(762\) | −5.78200e13 | −0.225063 | ||||||||
\(763\) | − | 6.39745e13i | − | 0.247391i | ||||||
\(764\) | 4.47197e14i | 1.71804i | ||||||||
\(765\) | 3.14560e14i | 1.20059i | ||||||||
\(766\) | 6.49754e13 | 0.246380 | ||||||||
\(767\) | 3.93771e14 | 1.48343 | ||||||||
\(768\) | 5.06049e13i | 0.189403i | ||||||||
\(769\) | −9.49805e13 | −0.353185 | −0.176593 | − | 0.984284i | \(-0.556508\pi\) | ||||
−0.176593 | + | 0.984284i | \(0.556508\pi\) | |||||||
\(770\) | − | 5.43856e13i | − | 0.200923i | ||||||
\(771\) | 2.48464e14 | 0.911992 | ||||||||
\(772\) | 4.41346e14 | 1.60951 | ||||||||
\(773\) | 1.72137e14i | 0.623700i | 0.950131 | + | 0.311850i | \(0.100949\pi\) | ||||
−0.950131 | + | 0.311850i | \(0.899051\pi\) | |||||||
\(774\) | −1.88293e14 | − | 1.78338e14i | −0.677842 | − | 0.642007i | ||||
\(775\) | −3.75793e14 | −1.34413 | ||||||||
\(776\) | − | 3.42384e13i | − | 0.121676i | ||||||
\(777\) | − | 5.67886e13i | − | 0.200519i | ||||||
\(778\) | −1.72234e13 | −0.0604255 | ||||||||
\(779\) | − | 2.03841e14i | − | 0.710567i | ||||||
\(780\) | −1.24327e15 | −4.30617 | ||||||||
\(781\) | − | 6.63453e13i | − | 0.228326i | ||||||
\(782\) | − | 3.68250e13i | − | 0.125924i | ||||||
\(783\) | 8.68174e14 | 2.94984 | ||||||||
\(784\) | 1.66138e14 | 0.560903 | ||||||||
\(785\) | 2.18674e14 | 0.733582 | ||||||||
\(786\) | − | 7.00217e13i | − | 0.233410i | ||||||
\(787\) | −3.02927e14 | −1.00338 | −0.501689 | − | 0.865048i | \(-0.667288\pi\) | ||||
−0.501689 | + | 0.865048i | \(0.667288\pi\) | |||||||
\(788\) | 1.99858e13 | 0.0657795 | ||||||||
\(789\) | 7.88167e14 | 2.57771 | ||||||||
\(790\) | 7.04832e13 | 0.229060 | ||||||||
\(791\) | −1.74868e14 | −0.564715 | ||||||||
\(792\) | 4.84763e14i | 1.55562i | ||||||||
\(793\) | − | 5.19618e14i | − | 1.65698i | ||||||
\(794\) | − | 3.12104e13i | − | 0.0989003i | ||||||
\(795\) | 6.42327e13 | 0.202265 | ||||||||
\(796\) | − | 3.72464e14i | − | 1.16552i | ||||||
\(797\) | −5.57510e13 | −0.173365 | −0.0866824 | − | 0.996236i | \(-0.527627\pi\) | ||||
−0.0866824 | + | 0.996236i | \(0.527627\pi\) | |||||||
\(798\) | −5.58483e13 | −0.172582 | ||||||||
\(799\) | 8.92504e13 | 0.274079 | ||||||||
\(800\) | − | 4.38971e14i | − | 1.33963i | ||||||
\(801\) | − | 5.03743e13i | − | 0.152773i | ||||||
\(802\) | 1.44719e14i | 0.436168i | ||||||||
\(803\) | − | 2.83876e14i | − | 0.850260i | ||||||
\(804\) | 5.20439e14i | 1.54914i | ||||||||
\(805\) | 3.49522e14 | 1.03394 | ||||||||
\(806\) | 1.43378e14i | 0.421509i | ||||||||
\(807\) | 1.31806e14i | 0.385094i | ||||||||
\(808\) | − | 2.67100e14i | − | 0.775562i | ||||||
\(809\) | 1.53146e14 | 0.441941 | 0.220970 | − | 0.975281i | \(-0.429078\pi\) | ||||
0.220970 | + | 0.975281i | \(0.429078\pi\) | |||||||
\(810\) | −7.90926e14 | −2.26835 | ||||||||
\(811\) | − | 2.51948e14i | − | 0.718137i | −0.933311 | − | 0.359068i | \(-0.883095\pi\) | ||
0.933311 | − | 0.359068i | \(-0.116905\pi\) | |||||||
\(812\) | 1.10696e14 | 0.313584 | ||||||||
\(813\) | − | 6.71623e14i | − | 1.89092i | ||||||
\(814\) | −2.40956e13 | −0.0674241 | ||||||||
\(815\) | −7.50337e13 | −0.208674 | ||||||||
\(816\) | − | 1.28302e14i | − | 0.354636i | ||||||
\(817\) | 1.63553e14 | + | 1.54907e14i | 0.449313 | + | 0.425559i | ||||
\(818\) | 2.17922e14 | 0.595025 | ||||||||
\(819\) | 6.98877e14i | 1.89662i | ||||||||
\(820\) | − | 6.11775e14i | − | 1.65015i | ||||||
\(821\) | 2.19969e14 | 0.589721 | 0.294860 | − | 0.955540i | \(-0.404727\pi\) | ||||
0.294860 | + | 0.955540i | \(0.404727\pi\) | |||||||
\(822\) | − | 3.07294e14i | − | 0.818832i | ||||||
\(823\) | 1.48542e14 | 0.393414 | 0.196707 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196707 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(824\) | − | 3.16105e14i | − | 0.832139i | ||||||
\(825\) | 1.04897e15i | 2.74469i | ||||||||
\(826\) | 5.30870e13 | 0.138066 | ||||||||
\(827\) | −5.24355e14 | −1.35549 | −0.677747 | − | 0.735295i | \(-0.737044\pi\) | ||||
−0.677747 | + | 0.735295i | \(0.737044\pi\) | |||||||
\(828\) | −1.47006e15 | −3.77730 | ||||||||
\(829\) | − | 3.98925e14i | − | 1.01887i | −0.860510 | − | 0.509434i | \(-0.829855\pi\) | ||
0.860510 | − | 0.509434i | \(-0.170145\pi\) | |||||||
\(830\) | 1.04528e14 | 0.265363 | ||||||||
\(831\) | 3.69144e14 | 0.931518 | ||||||||
\(832\) | 2.53061e14 | 0.634758 | ||||||||
\(833\) | −8.48760e13 | −0.211622 | ||||||||
\(834\) | 1.95935e14 | 0.485604 | ||||||||
\(835\) | 1.80060e14i | 0.443593i | ||||||||
\(836\) | − | 1.98687e14i | − | 0.486562i | ||||||
\(837\) | − | 1.27111e15i | − | 3.09425i | ||||||
\(838\) | −3.72591e12 | −0.00901596 | ||||||||
\(839\) | − | 4.03413e11i | − | 0.000970377i | −1.00000 | 0.000485189i | \(-0.999846\pi\) | |||
1.00000 | 0.000485189i | \(-0.000154440\pi\) | ||||||||
\(840\) | −3.55218e14 | −0.849373 | ||||||||
\(841\) | 1.46600e14 | 0.348462 | ||||||||
\(842\) | 1.18876e14 | 0.280888 | ||||||||
\(843\) | 6.34182e14i | 1.48962i | ||||||||
\(844\) | 3.92078e14i | 0.915505i | ||||||||
\(845\) | 9.18766e14i | 2.13266i | ||||||||
\(846\) | 4.24931e14i | 0.980542i | ||||||||
\(847\) | 4.27639e13i | 0.0980981i | ||||||||
\(848\) | −1.94119e13 | −0.0442679 | ||||||||
\(849\) | 5.95782e14i | 1.35067i | ||||||||
\(850\) | 6.00037e13i | 0.135233i | ||||||||
\(851\) | − | 1.54856e14i | − | 0.346960i | ||||||
\(852\) | −2.04473e14 | −0.455447 | ||||||||
\(853\) | −2.53025e14 | −0.560297 | −0.280148 | − | 0.959957i | \(-0.590384\pi\) | ||||
−0.280148 | + | 0.959957i | \(0.590384\pi\) | |||||||
\(854\) | − | 7.00533e13i | − | 0.154220i | ||||||
\(855\) | 1.30088e15 | 2.84713 | ||||||||
\(856\) | − | 1.34402e14i | − | 0.292441i | ||||||
\(857\) | −5.75843e14 | −1.24566 | −0.622831 | − | 0.782356i | \(-0.714018\pi\) | ||||
−0.622831 | + | 0.782356i | \(0.714018\pi\) | |||||||
\(858\) | 4.00217e14 | 0.860714 | ||||||||
\(859\) | 4.23797e14i | 0.906134i | 0.891476 | + | 0.453067i | \(0.149670\pi\) | ||||
−0.891476 | + | 0.453067i | \(0.850330\pi\) | |||||||
\(860\) | 4.90861e14 | + | 4.64910e14i | 1.04344 | + | 0.988273i | ||||
\(861\) | −4.64137e14 | −0.980912 | ||||||||
\(862\) | 1.98687e14i | 0.417478i | ||||||||
\(863\) | 6.55776e13i | 0.136994i | 0.997651 | + | 0.0684970i | \(0.0218204\pi\) | ||||
−0.997651 | + | 0.0684970i | \(0.978180\pi\) | |||||||
\(864\) | 1.48481e15 | 3.08391 | ||||||||
\(865\) | 8.96391e14i | 1.85104i | ||||||||
\(866\) | −5.65733e13 | −0.116151 | ||||||||
\(867\) | − | 8.96937e14i | − | 1.83091i | ||||||
\(868\) | − | 1.62073e14i | − | 0.328936i | ||||||
\(869\) | 1.90239e14 | 0.383884 | ||||||||
\(870\) | 4.15046e14 | 0.832721 | ||||||||
\(871\) | 6.74688e14 | 1.34590 | ||||||||
\(872\) | 1.77294e14i | 0.351650i | ||||||||
\(873\) | 2.85502e14 | 0.563038 | ||||||||
\(874\) | −1.52292e14 | −0.298620 | ||||||||
\(875\) | −2.10767e14 | −0.410925 | ||||||||
\(876\) | −8.74892e14 | −1.69603 | ||||||||
\(877\) | −9.37856e14 | −1.80775 | −0.903875 | − | 0.427797i | \(-0.859290\pi\) | ||||
−0.903875 | + | 0.427797i | \(0.859290\pi\) | |||||||
\(878\) | − | 1.68949e14i | − | 0.323804i | ||||||
\(879\) | − | 4.14768e14i | − | 0.790426i | ||||||
\(880\) | − | 5.16704e14i | − | 0.979103i | ||||||
\(881\) | −4.94059e14 | −0.930892 | −0.465446 | − | 0.885076i | \(-0.654106\pi\) | ||||
−0.465446 | + | 0.885076i | \(0.654106\pi\) | |||||||
\(882\) | − | 4.04104e14i | − | 0.757094i | ||||||
\(883\) | 3.93749e14 | 0.733528 | 0.366764 | − | 0.930314i | \(-0.380466\pi\) | ||||
0.366764 | + | 0.930314i | \(0.380466\pi\) | |||||||
\(884\) | −1.91953e14 | −0.355576 | ||||||||
\(885\) | −1.66891e15 | −3.07410 | ||||||||
\(886\) | 2.55850e13i | 0.0468615i | ||||||||
\(887\) | 4.28664e14i | 0.780726i | 0.920661 | + | 0.390363i | \(0.127651\pi\) | ||||
−0.920661 | + | 0.390363i | \(0.872349\pi\) | |||||||
\(888\) | 1.57379e14i | 0.285025i | ||||||||
\(889\) | − | 8.47304e13i | − | 0.152591i | ||||||
\(890\) | − | 1.56621e13i | − | 0.0280479i | ||||||
\(891\) | −2.13476e15 | −3.80155 | ||||||||
\(892\) | 4.62454e14i | 0.818926i | ||||||||
\(893\) | − | 3.69100e14i | − | 0.649960i | ||||||
\(894\) | 3.66950e14i | 0.642569i | ||||||||
\(895\) | 1.01919e15 | 1.77476 | ||||||||
\(896\) | 2.46016e14 | 0.426014 | ||||||||
\(897\) | 2.57208e15i | 4.42918i | ||||||||
\(898\) | 5.40443e13 | 0.0925482 | ||||||||
\(899\) | 4.01325e14i | 0.683436i | ||||||||
\(900\) | 2.39535e15 | 4.05655 | ||||||||
\(901\) | 9.91712e12 | 0.0167017 | ||||||||
\(902\) | 1.96935e14i | 0.329829i | ||||||||
\(903\) | 3.52715e14 | − | 3.72403e14i | 0.587469 | − | 0.620260i | ||||
\(904\) | 4.84617e14 | 0.802706 | ||||||||
\(905\) | − | 5.71485e14i | − | 0.941373i | ||||||
\(906\) | − | 6.68932e14i | − | 1.09582i | ||||||
\(907\) | −7.79544e14 | −1.27000 | −0.635001 | − | 0.772511i | \(-0.719000\pi\) | ||||
−0.635001 | + | 0.772511i | \(0.719000\pi\) | |||||||
\(908\) | − | 9.03378e13i | − | 0.146366i | ||||||
\(909\) | 2.22725e15 | 3.58880 | ||||||||
\(910\) | 2.17291e14i | 0.348205i | ||||||||
\(911\) | − | 6.18865e14i | − | 0.986289i | −0.869947 | − | 0.493144i | \(-0.835847\pi\) | ||
0.869947 | − | 0.493144i | \(-0.164153\pi\) | |||||||
\(912\) | −5.30601e14 | −0.840996 | ||||||||
\(913\) | 2.82127e14 | 0.444724 | ||||||||
\(914\) | 2.29297e14 | 0.359474 | ||||||||
\(915\) | 2.20229e15i | 3.43375i | ||||||||
\(916\) | −1.07631e13 | −0.0166901 | ||||||||
\(917\) | 1.02611e14 | 0.158251 | ||||||||
\(918\) | −2.02961e14 | −0.311314 | ||||||||
\(919\) | 2.38502e14 | 0.363843 | 0.181922 | − | 0.983313i | \(-0.441768\pi\) | ||||
0.181922 | + | 0.983313i | \(0.441768\pi\) | |||||||
\(920\) | −9.68637e14 | −1.46968 | ||||||||
\(921\) | − | 1.03920e15i | − | 1.56820i | ||||||
\(922\) | 4.29463e14i | 0.644572i | ||||||||
\(923\) | 2.65075e14i | 0.395695i | ||||||||
\(924\) | −4.52400e14 | −0.671681 | ||||||||
\(925\) | 2.52326e14i | 0.372610i | ||||||||
\(926\) | −2.84314e14 | −0.417583 | ||||||||
\(927\) | 2.63589e15 | 3.85060 | ||||||||
\(928\) | −4.68795e14 | −0.681151 | ||||||||
\(929\) | − | 5.41939e14i | − | 0.783198i | −0.920136 | − | 0.391599i | \(-0.871922\pi\) | ||
0.920136 | − | 0.391599i | \(-0.128078\pi\) | |||||||
\(930\) | − | 6.07676e14i | − | 0.873489i | ||||||
\(931\) | 3.51009e14i | 0.501846i | ||||||||
\(932\) | − | 9.93424e13i | − | 0.141272i | ||||||
\(933\) | − | 2.20874e15i | − | 3.12418i | ||||||
\(934\) | −3.05975e14 | −0.430479 | ||||||||
\(935\) | 2.63973e14i | 0.369403i | ||||||||
\(936\) | − | 1.93681e15i | − | 2.69593i | ||||||
\(937\) | − | 5.10159e13i | − | 0.0706330i | −0.999376 | − | 0.0353165i | \(-0.988756\pi\) | ||
0.999376 | − | 0.0353165i | \(-0.0112439\pi\) | |||||||
\(938\) | 9.09595e13 | 0.125266 | ||||||||
\(939\) | −4.31182e14 | −0.590653 | ||||||||
\(940\) | − | 1.10775e15i | − | 1.50940i | ||||||
\(941\) | −8.18491e14 | −1.10934 | −0.554671 | − | 0.832070i | \(-0.687156\pi\) | ||||
−0.554671 | + | 0.832070i | \(0.687156\pi\) | |||||||
\(942\) | 2.16947e14i | 0.292482i | ||||||||
\(943\) | −1.26565e15 | −1.69728 | ||||||||
\(944\) | 5.04366e14 | 0.672800 | ||||||||
\(945\) | − | 1.92639e15i | − | 2.55614i | ||||||
\(946\) | −1.58012e14 | − | 1.49658e14i | −0.208561 | − | 0.197535i | ||||
\(947\) | 4.87484e13 | 0.0640045 | 0.0320022 | − | 0.999488i | \(-0.489812\pi\) | ||||
0.0320022 | + | 0.999488i | \(0.489812\pi\) | |||||||
\(948\) | − | 5.86306e14i | − | 0.765742i | ||||||
\(949\) | 1.13420e15i | 1.47352i | ||||||||
\(950\) | 2.48149e14 | 0.320696 | ||||||||
\(951\) | − | 3.99683e14i | − | 0.513823i | ||||||
\(952\) | −5.48434e13 | −0.0701358 | ||||||||
\(953\) | 4.66740e14i | 0.593759i | 0.954915 | + | 0.296879i | \(0.0959459\pi\) | ||||
−0.954915 | + | 0.296879i | \(0.904054\pi\) | |||||||
\(954\) | 4.72165e13i | 0.0597519i | ||||||||
\(955\) | −2.45710e15 | −3.09318 | ||||||||
\(956\) | 6.63074e14 | 0.830371 | ||||||||
\(957\) | 1.12024e15 | 1.39556 | ||||||||
\(958\) | 5.67572e13i | 0.0703386i | ||||||||
\(959\) | 4.50314e14 | 0.555165 | ||||||||
\(960\) | −1.07254e15 | −1.31540 | ||||||||
\(961\) | −2.32041e14 | −0.283105 | ||||||||
\(962\) | 9.62710e13 | 0.116848 | ||||||||
\(963\) | 1.12074e15 | 1.35323 | ||||||||
\(964\) | − | 6.68945e14i | − | 0.803536i | ||||||
\(965\) | 2.42495e15i | 2.89779i | ||||||||
\(966\) | 3.46761e14i | 0.412235i | ||||||||
\(967\) | −1.03127e15 | −1.21967 | −0.609833 | − | 0.792530i | \(-0.708764\pi\) | ||||
−0.609833 | + | 0.792530i | \(0.708764\pi\) | |||||||
\(968\) | − | 1.18513e14i | − | 0.139440i | ||||||
\(969\) | 2.71072e14 | 0.317297 | ||||||||
\(970\) | 8.87669e13 | 0.103370 | ||||||||
\(971\) | 1.49524e15 | 1.73227 | 0.866134 | − | 0.499813i | \(-0.166598\pi\) | ||||
0.866134 | + | 0.499813i | \(0.166598\pi\) | |||||||
\(972\) | 3.74636e15i | 4.31795i | ||||||||
\(973\) | 2.87127e14i | 0.329237i | ||||||||
\(974\) | − | 2.98693e14i | − | 0.340745i | ||||||
\(975\) | − | 4.19103e15i | − | 4.75661i | ||||||
\(976\) | − | 6.65559e14i | − | 0.751515i | ||||||
\(977\) | −1.06638e15 | −1.19795 | −0.598975 | − | 0.800767i | \(-0.704425\pi\) | ||||
−0.598975 | + | 0.800767i | \(0.704425\pi\) | |||||||
\(978\) | − | 7.44410e13i | − | 0.0831990i | ||||||
\(979\) | − | 4.22731e13i | − | 0.0470057i | ||||||
\(980\) | 1.05346e15i | 1.16543i | ||||||||
\(981\) | −1.47839e15 | −1.62721 | ||||||||
\(982\) | 2.32976e14 | 0.255126 | ||||||||
\(983\) | 1.21100e15i | 1.31940i | 0.751528 | + | 0.659701i | \(0.229317\pi\) | ||||
−0.751528 | + | 0.659701i | \(0.770683\pi\) | |||||||
\(984\) | 1.28627e15 | 1.39430 | ||||||||
\(985\) | 1.09811e14i | 0.118431i | ||||||||
\(986\) | 6.40804e13 | 0.0687608 | ||||||||
\(987\) | −8.40422e14 | −0.897246 | ||||||||
\(988\) | 7.93831e14i | 0.843224i | ||||||||
\(989\) | 9.61811e14 | − | 1.01550e15i | 1.01650 | − | 1.07324i | ||||
\(990\) | −1.25680e15 | −1.32157 | ||||||||
\(991\) | 8.83809e14i | 0.924677i | 0.886703 | + | 0.462339i | \(0.152990\pi\) | ||||
−0.886703 | + | 0.462339i | \(0.847010\pi\) | |||||||
\(992\) | 6.86372e14i | 0.714498i | ||||||||
\(993\) | −2.84414e15 | −2.94581 | ||||||||
\(994\) | 3.57366e13i | 0.0368283i | ||||||||
\(995\) | 2.04648e15 | 2.09842 | ||||||||
\(996\) | − | 8.69500e14i | − | 0.887101i | ||||||
\(997\) | − | 1.02035e15i | − | 1.03580i | −0.855442 | − | 0.517898i | \(-0.826715\pi\) | ||
0.855442 | − | 0.517898i | \(-0.173285\pi\) | |||||||
\(998\) | −9.04569e13 | −0.0913669 | ||||||||
\(999\) | −8.53487e14 | −0.857767 |
(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 | 43.11.b.b.42.20 | yes | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.15 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.15 | ✓ | 34 | 43.42 | odd | 2 | inner | |
43.11.b.b.42.20 | yes | 34 | 1.1 | even | 1 | trivial |