Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,14,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(17.1569486323\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{781}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 195 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(14.4732\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2224.57 | −1.76180 | −0.880902 | − | 0.473299i | \(-0.843063\pi\) | ||||
−0.880902 | + | 0.473299i | \(0.843063\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 30700.8 | 0.878709 | 0.439354 | − | 0.898314i | \(-0.355207\pi\) | ||||
0.439354 | + | 0.898314i | \(0.355207\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 341598. | 1.09743 | 0.548717 | − | 0.836008i | \(-0.315117\pi\) | ||||
0.548717 | + | 0.836008i | \(0.315117\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.35438e6 | 2.10395 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.18675e6 | −1.56354 | −0.781771 | − | 0.623566i | \(-0.785683\pi\) | ||||
−0.781771 | + | 0.623566i | \(0.785683\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.32183e6 | −0.535635 | −0.267818 | − | 0.963470i | \(-0.586302\pi\) | ||||
−0.267818 | + | 0.963470i | \(0.586302\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.82961e7 | −1.54811 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.60213e6 | −0.0864347 | −0.0432173 | − | 0.999066i | \(-0.513761\pi\) | ||||
−0.0432173 | + | 0.999066i | \(0.513761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.27175e8 | 1.10780 | 0.553902 | − | 0.832582i | \(-0.313138\pi\) | ||||
0.553902 | + | 0.832582i | \(0.313138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.59908e8 | −1.93346 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.58492e8 | −0.786658 | −0.393329 | − | 0.919398i | \(-0.628677\pi\) | ||||
−0.393329 | + | 0.919398i | \(0.628677\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.78163e8 | −0.227871 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.91537e9 | −1.94495 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.09280e9 | −1.27771 | −0.638857 | − | 0.769326i | \(-0.720592\pi\) | ||||
−0.638857 | + | 0.769326i | \(0.720592\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.31420e8 | −0.0468328 | −0.0234164 | − | 0.999726i | \(-0.507454\pi\) | ||||
−0.0234164 | + | 0.999726i | \(0.507454\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.04366e10 | 2.75465 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.04873e10 | 0.964324 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.41367e10 | −1.54656 | −0.773278 | − | 0.634067i | \(-0.781384\pi\) | ||||
−0.773278 | + | 0.634067i | \(0.781384\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.07370e10 | 0.943685 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.37946e10 | −0.453540 | −0.226770 | − | 0.973948i | \(-0.572817\pi\) | ||||
−0.226770 | + | 0.973948i | \(0.572817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90701e9 | −0.0460052 | −0.0230026 | − | 0.999735i | \(-0.507323\pi\) | ||||
−0.0230026 | + | 0.999735i | \(0.507323\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.02982e11 | 1.84876 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.27170e10 | 0.307408 | 0.153704 | − | 0.988117i | \(-0.450880\pi\) | ||||
0.153704 | + | 0.988117i | \(0.450880\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.98003e10 | 0.204360 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.91360e10 | 0.152281 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.19059e10 | 0.445627 | 0.222813 | − | 0.974861i | \(-0.428476\pi\) | ||||
0.222813 | + | 0.974861i | \(0.428476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82041e11 | −1.37390 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.05367e11 | −1.95173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.71648e11 | −1.14708 | −0.573541 | − | 0.819177i | \(-0.694431\pi\) | ||||
−0.573541 | + | 0.819177i | \(0.694431\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.48930e11 | −0.867151 | −0.433576 | − | 0.901117i | \(-0.642748\pi\) | ||||
−0.433576 | + | 0.901117i | \(0.642748\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.14585e12 | 2.30895 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.86188e11 | −0.470668 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.75836e11 | −1.18287 | −0.591434 | − | 0.806353i | \(-0.701438\pi\) | ||||
−0.591434 | + | 0.806353i | \(0.701438\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.24240e12 | 1.38594 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.10711e11 | −0.102568 | −0.0512838 | − | 0.998684i | \(-0.516331\pi\) | ||||
−0.0512838 | + | 0.998684i | \(0.516331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.15665e12 | 1.66795 | 0.833973 | − | 0.551805i | \(-0.186061\pi\) | ||||
0.833973 | + | 0.551805i | \(0.186061\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.18792e11 | 0.401464 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.13818e12 | −1.71588 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.20959e11 | 0.148550 | 0.0742751 | − | 0.997238i | \(-0.476336\pi\) | ||||
0.0742751 | + | 0.997238i | \(0.476336\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.36204e12 | 1.32266 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.63705e12 | −0.549611 | −0.274805 | − | 0.961500i | \(-0.588613\pi\) | ||||
−0.274805 | + | 0.961500i | \(0.588613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.64092e11 | −0.0759509 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.10471e12 | 2.25108 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.21830e12 | −0.686422 | −0.343211 | − | 0.939258i | \(-0.611515\pi\) | ||||
−0.343211 | + | 0.939258i | \(0.611515\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.18432e12 | −0.587824 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.14810e11 | 0.0825102 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.97447e12 | 0.973437 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.93052e12 | −0.479109 | −0.239554 | − | 0.970883i | \(-0.577001\pi\) | ||||
−0.239554 | + | 0.970883i | \(0.577001\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.08159e13 | −3.28962 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.16615e12 | 0.203049 | 0.101524 | − | 0.994833i | \(-0.467628\pi\) | ||||
0.101524 | + | 0.994833i | \(0.467628\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.09777e13 | −1.73107 | −0.865537 | − | 0.500846i | \(-0.833022\pi\) | ||||
−0.865537 | + | 0.500846i | \(0.833022\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.33298e13 | −1.69895 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.62952e13 | 1.04970 | 0.524850 | − | 0.851194i | \(-0.324121\pi\) | ||||
0.524850 | + | 0.851194i | \(0.324121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.34141e13 | 1.90835 | 0.954174 | − | 0.299252i | \(-0.0967371\pi\) | ||||
0.954174 | + | 0.299252i | \(0.0967371\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.36936e13 | 2.72473 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.92919e12 | 0.177539 | 0.0887693 | − | 0.996052i | \(-0.471707\pi\) | ||||
0.0887693 | + | 0.996052i | \(0.471707\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.71462e13 | −0.691243 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.12690e13 | −1.12695 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.93847e12 | −0.0948563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.98737e13 | 1.44466 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.06871e13 | 0.799048 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.60164e13 | −1.07894 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.18567e13 | 0.673716 | 0.336858 | − | 0.941555i | \(-0.390636\pi\) | ||||
0.336858 | + | 0.941555i | \(0.390636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.24227e12 | 0.0810522 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.05827e13 | −0.874458 | −0.437229 | − | 0.899350i | \(-0.644040\pi\) | ||||
−0.437229 | + | 0.899350i | \(0.644040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.76027e13 | 1.21574 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.20205e14 | −1.70904 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.90097e13 | 1.15015 | 0.575074 | − | 0.818101i | \(-0.304973\pi\) | ||||
0.575074 | + | 0.818101i | \(0.304973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.27644e13 | 0.855703 | 0.427851 | − | 0.903849i | \(-0.359271\pi\) | ||||
0.427851 | + | 0.903849i | \(0.359271\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.05355e13 | −0.541593 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.56373e13 | 0.837488 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.25652e14 | −1.12274 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.40471e13 | −0.360043 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.52533e14 | −1.89063 | −0.945317 | − | 0.326153i | \(-0.894248\pi\) | ||||
−0.945317 | + | 0.326153i | \(0.894248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.28515e14 | −0.882276 | −0.441138 | − | 0.897439i | \(-0.645425\pi\) | ||||
−0.441138 | + | 0.897439i | \(0.645425\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.88548e13 | −0.181854 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.10478e12 | −0.0411524 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.35290e13 | 0.498423 | 0.249212 | − | 0.968449i | \(-0.419829\pi\) | ||||
0.249212 | + | 0.968449i | \(0.419829\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.59960e14 | −0.785107 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.90780e14 | −0.863305 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.06073e14 | 1.69584 | 0.847919 | − | 0.530126i | \(-0.177855\pi\) | ||||
0.847919 | + | 0.530126i | \(0.177855\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.27419e14 | 2.42054 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.27425e14 | −1.52477 | −0.762383 | − | 0.647126i | \(-0.775971\pi\) | ||||
−0.762383 | + | 0.647126i | \(0.775971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.15979e14 | −0.713095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.62033e14 | 2.33077 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.96614e14 | 1.40838 | 0.704189 | − | 0.710013i | \(-0.251311\pi\) | ||||
0.704189 | + | 0.710013i | \(0.251311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.50199e13 | −0.250073 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.26757e14 | 2.02093 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.04957e14 | −1.60184 | −0.800918 | − | 0.598774i | \(-0.795655\pi\) | ||||
−0.800918 | + | 0.598774i | \(0.795655\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.97913e14 | −1.26394 | −0.631971 | − | 0.774992i | \(-0.717754\pi\) | ||||
−0.631971 | + | 0.774992i | \(0.717754\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.76220e14 | 1.52775 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.41015e14 | −1.35897 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.90256e13 | 0.135144 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.33748e15 | −2.13445 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.68786e14 | −0.698647 | −0.349323 | − | 0.937002i | \(-0.613588\pi\) | ||||
−0.349323 | + | 0.937002i | \(0.613588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.66164e14 | 0.649257 | 0.324629 | − | 0.945842i | \(-0.394761\pi\) | ||||
0.324629 | + | 0.945842i | \(0.394761\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.36644e14 | 0.829224 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.99579e14 | 0.243268 | 0.121634 | − | 0.992575i | \(-0.461187\pi\) | ||||
0.121634 | + | 0.992575i | \(0.461187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.01889e14 | 0.344590 | 0.172295 | − | 0.985045i | \(-0.444882\pi\) | ||||
0.172295 | + | 0.985045i | \(0.444882\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.94836e15 | 2.08398 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.39809e15 | −1.40221 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.23507e14 | −0.398529 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.87339e15 | −1.65509 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.08700e15 | −1.73210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.80118e15 | 1.40515 | 0.702573 | − | 0.711611i | \(-0.252034\pi\) | ||||
0.702573 | + | 0.711611i | \(0.252034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.46283e14 | 0.180704 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.85467e13 | −0.0404252 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.90526e13 | −0.0513959 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.79762e15 | −2.93859 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.01876e13 | 0.0462975 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.36916e15 | 1.29007 | 0.645035 | − | 0.764153i | \(-0.276843\pi\) | ||||
0.645035 | + | 0.764153i | \(0.276843\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.33064e14 | −0.479430 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.88352e15 | 0.913697 | 0.456849 | − | 0.889544i | \(-0.348978\pi\) | ||||
0.456849 | + | 0.889544i | \(0.348978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.08258e15 | 1.87070 | 0.935349 | − | 0.353725i | \(-0.115085\pi\) | ||||
0.935349 | + | 0.353725i | \(0.115085\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.98109e15 | 3.02305 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.16749e14 | −0.252520 | −0.126260 | − | 0.991997i | \(-0.540297\pi\) | ||||
−0.126260 | + | 0.991997i | \(0.540297\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.97431e14 | 0.270122 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.13995e14 | −0.261716 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.72458e14 | −0.198681 | −0.0993407 | − | 0.995053i | \(-0.531673\pi\) | ||||
−0.0993407 | + | 0.995053i | \(0.531673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.98649e14 | −0.229693 | −0.114847 | − | 0.993383i | \(-0.536638\pi\) | ||||
−0.114847 | + | 0.993383i | \(0.536638\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.23672e15 | −0.385327 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.07884e14 | 0.179573 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.11769e15 | −0.593379 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.64174e15 | 0.968307 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.42788e15 | −1.11768 | −0.558839 | − | 0.829276i | \(-0.688753\pi\) | ||||
−0.558839 | + | 0.829276i | \(0.688753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.13072e15 | 1.22997 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.87491e14 | 0.133811 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.45343e15 | −0.747628 | −0.373814 | − | 0.927504i | \(-0.621950\pi\) | ||||
−0.373814 | + | 0.927504i | \(0.621950\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.24504e15 | −1.69724 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.37288e16 | −2.68825 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.68676e14 | −0.0500629 | −0.0250315 | − | 0.999687i | \(-0.507969\pi\) | ||||
−0.0250315 | + | 0.999687i | \(0.507969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.20757e15 | 0.391576 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.15932e15 | 1.20934 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.84800e15 | −0.780140 | −0.390070 | − | 0.920785i | \(-0.627549\pi\) | ||||
−0.390070 | + | 0.920785i | \(0.627549\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.45435e14 | 0.129652 | 0.0648261 | − | 0.997897i | \(-0.479351\pi\) | ||||
0.0648261 | + | 0.997897i | \(0.479351\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.08373e15 | 1.03563 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.55541e15 | 0.356286 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.23216e15 | 1.22796 | 0.613981 | − | 0.789321i | \(-0.289567\pi\) | ||||
0.613981 | + | 0.789321i | \(0.289567\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.76271e14 | −0.0985340 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.24571e15 | −0.756817 | −0.378408 | − | 0.925639i | \(-0.623529\pi\) | ||||
−0.378408 | + | 0.925639i | \(0.623529\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.27398e15 | 0.263133 | 0.131567 | − | 0.991307i | \(-0.457999\pi\) | ||||
0.131567 | + | 0.991307i | \(0.457999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.55152e16 | −1.71501 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.71222e15 | −0.497730 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.83058e15 | −0.992529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.74371e15 | 0.844095 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.05443e15 | 0.559028 | 0.279514 | − | 0.960142i | \(-0.409827\pi\) | ||||
0.279514 | + | 0.960142i | \(0.409827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.14099e16 | −1.00795 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.59695e16 | 3.04101 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.20616e15 | 0.421362 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.51430e14 | −0.0504877 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.81875e15 | −0.357732 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.07124e16 | −0.761973 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.40774e16 | −0.959671 | −0.479835 | − | 0.877359i | \(-0.659304\pi\) | ||||
−0.479835 | + | 0.877359i | \(0.659304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.66663e16 | 3.04981 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.12928e15 | 0.572129 | 0.286064 | − | 0.958210i | \(-0.407653\pi\) | ||||
0.286064 | + | 0.958210i | \(0.407653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.46408e16 | −1.48121 | −0.740606 | − | 0.671940i | \(-0.765461\pi\) | ||||
−0.740606 | + | 0.671940i | \(0.765461\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.51785e16 | 2.02889 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.17144e16 | 0.648388 | 0.324194 | − | 0.945991i | \(-0.394907\pi\) | ||||
0.324194 | + | 0.945991i | \(0.394907\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.75995e16 | 1.99776 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.62498e16 | −1.84937 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.95419e15 | −0.0957527 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.59299e15 | 0.122056 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.43320e16 | −3.36214 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.76009e15 | 0.337360 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.59924e16 | 0.668392 | 0.334196 | − | 0.942504i | \(-0.391535\pi\) | ||||
0.334196 | + | 0.942504i | \(0.391535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.09635e16 | −3.25388 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.68889e16 | −1.03940 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.65737e15 | 0.210388 | 0.105194 | − | 0.994452i | \(-0.466454\pi\) | ||||
0.105194 | + | 0.994452i | \(0.466454\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.74074e15 | −0.312788 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.12600e15 | 0.0732250 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.63334e16 | −0.873162 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.81428e16 | 1.21783 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.91864e16 | 0.590000 | 0.295000 | − | 0.955497i | \(-0.404680\pi\) | ||||
0.295000 | + | 0.955497i | \(0.404680\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.62333e16 | −0.480885 | −0.240442 | − | 0.970663i | \(-0.577292\pi\) | ||||
−0.240442 | + | 0.970663i | \(0.577292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.64984e16 | 1.04178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.71540e16 | 1.29713 | 0.648564 | − | 0.761160i | \(-0.275370\pi\) | ||||
0.648564 | + | 0.761160i | \(0.275370\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.39891e15 | −0.0901270 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.53683e15 | 0.167118 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.06168e16 | 0.754825 | 0.377413 | − | 0.926045i | \(-0.376814\pi\) | ||||
0.377413 | + | 0.926045i | \(0.376814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.55572e15 | 0.227231 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.10947e17 | −2.54521 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.62110e16 | 1.46564 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.05053e15 | 0.193350 | 0.0966751 | − | 0.995316i | \(-0.469179\pi\) | ||||
0.0966751 | + | 0.995316i | \(0.469179\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.62725e16 | −0.954226 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.45629e16 | 0.489046 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.96602e16 | −1.14704 | −0.573519 | − | 0.819192i | \(-0.694422\pi\) | ||||
−0.573519 | + | 0.819192i | \(0.694422\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.02367e17 | 1.90088 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.81524e16 | 0.684389 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.59746e16 | 0.623507 | 0.311753 | − | 0.950163i | \(-0.399084\pi\) | ||||
0.311753 | + | 0.950163i | \(0.399084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.08675e16 | −1.18696 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.65533e16 | 0.591745 | 0.295872 | − | 0.955227i | \(-0.404390\pi\) | ||||
0.295872 | + | 0.955227i | \(0.404390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.63446e16 | −1.50776 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.39683e15 | −0.0967929 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.30128e17 | 1.90414 | 0.952072 | − | 0.305873i | \(-0.0989483\pi\) | ||||
0.952072 | + | 0.305873i | \(0.0989483\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.80422e15 | 0.0679945 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.12525e17 | 1.54062 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.85371e15 | 0.130532 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.04022e16 | 0.517924 | 0.258962 | − | 0.965887i | \(-0.416619\pi\) | ||||
0.258962 | + | 0.965887i | \(0.416619\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.72633e17 | −2.14190 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.10742e17 | −1.33007 | −0.665037 | − | 0.746811i | \(-0.731584\pi\) | ||||
−0.665037 | + | 0.746811i | \(0.731584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.15726e15 | 0.0250853 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.03217e17 | 1.16224 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.21737e17 | 2.41811 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.65227e16 | 0.280166 | 0.140083 | − | 0.990140i | \(-0.455263\pi\) | ||||
0.140083 | + | 0.990140i | \(0.455263\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.98008e17 | −2.02634 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.26954e17 | −1.25885 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.02589e16 | −0.482948 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.61869e17 | −1.50758 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.41472e17 | −1.27726 | −0.638631 | − | 0.769513i | \(-0.720499\pi\) | ||||
−0.638631 | + | 0.769513i | \(0.720499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.28484e17 | 1.12465 | 0.562323 | − | 0.826918i | \(-0.309908\pi\) | ||||
0.562323 | + | 0.826918i | \(0.309908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.62015e16 | 0.646772 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.39279e15 | 0.0196960 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.19194e17 | −0.951641 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.90506e17 | −1.47549 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.43879e17 | −1.08117 | −0.540587 | − | 0.841288i | \(-0.681798\pi\) | ||||
−0.540587 | + | 0.841288i | \(0.681798\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.64520e15 | −0.0192880 | −0.00964402 | − | 0.999953i | \(-0.503070\pi\) | ||||
−0.00964402 | + | 0.999953i | \(0.503070\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.79522e17 | 1.97804 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.26876e17 | −0.871463 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.34376e17 | −0.895989 | −0.447994 | − | 0.894036i | \(-0.647862\pi\) | ||||
−0.447994 | + | 0.894036i | \(0.647862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.64176e16 | 0.429965 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.81369e16 | 0.554030 | 0.277015 | − | 0.960866i | \(-0.410655\pi\) | ||||
0.277015 | + | 0.960866i | \(0.410655\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.88044e16 | −0.603165 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.61777e17 | 3.33093 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.36300e17 | 0.785044 | 0.392522 | − | 0.919743i | \(-0.371603\pi\) | ||||
0.392522 | + | 0.919743i | \(0.371603\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.26728e17 | 0.709128 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.85891e17 | 1.55440 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.77612e16 | −0.516526 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.64371e17 | 1.87106 | 0.935532 | − | 0.353243i | \(-0.114921\pi\) | ||||
0.935532 | + | 0.353243i | \(0.114921\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.36805e16 | 0.168111 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.15694e16 | −0.201706 | −0.100853 | − | 0.994901i | \(-0.532157\pi\) | ||||
−0.100853 | + | 0.994901i | \(0.532157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.15266e17 | −1.95907 | −0.979534 | − | 0.201279i | \(-0.935490\pi\) | ||||
−0.979534 | + | 0.201279i | \(0.935490\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.58051e16 | 0.0725024 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.46646e17 | −0.654202 | −0.327101 | − | 0.944989i | \(-0.606072\pi\) | ||||
−0.327101 | + | 0.944989i | \(0.606072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.99184e17 | −1.29812 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.08062e17 | −0.878124 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.75192e16 | 0.0719311 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.31918e16 | −0.252437 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.41200e17 | 0.937578 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.66742e17 | 0.630758 | 0.315379 | − | 0.948966i | \(-0.397868\pi\) | ||||
0.315379 | + | 0.948966i | \(0.397868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.24998e17 | 0.828391 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.24403e17 | 1.52097 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.20670e17 | −0.420997 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.02648e17 | 0.348667 | 0.174334 | − | 0.984687i | \(-0.444223\pi\) | ||||
0.174334 | + | 0.984687i | \(0.444223\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.03336e17 | −2.98773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.03049e17 | 0.976073 | 0.488037 | − | 0.872823i | \(-0.337713\pi\) | ||||
0.488037 | + | 0.872823i | \(0.337713\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.52068e16 | 0.110439 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.46072e17 | −2.89062 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.78185e16 | −0.112561 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.25532e17 | 0.364001 | 0.182001 | − | 0.983298i | \(-0.441743\pi\) | ||||
0.182001 | + | 0.983298i | \(0.441743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.50837e17 | 2.68634 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.18681e16 | 0.0602032 | 0.0301016 | − | 0.999547i | \(-0.490417\pi\) | ||||
0.0301016 | + | 0.999547i | \(0.490417\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.65027e16 | 0.178421 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.80459e17 | 1.25633 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.98743e17 | −1.52607 | −0.763035 | − | 0.646357i | \(-0.776292\pi\) | ||||
−0.763035 | + | 0.646357i | \(0.776292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.36709e17 | 1.83046 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.89476e17 | −2.15462 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.44032e17 | −1.52111 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.08696e17 | −0.480645 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.10475e18 | −2.48128 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.32756e15 | −0.0182420 | −0.00912100 | − | 0.999958i | \(-0.502903\pi\) | ||||
−0.00912100 | + | 0.999958i | \(0.502903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.41495e17 | 0.302328 | 0.151164 | − | 0.988509i | \(-0.451698\pi\) | ||||
0.151164 | + | 0.988509i | \(0.451698\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.11378e17 | 0.440580 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.99070e15 | 0.00404797 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.92123e17 | −0.381169 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.24665e18 | −2.41341 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.28591e17 | 0.242932 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.00276e17 | 0.922381 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.56823e18 | 2.82212 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.81900e17 | −0.319526 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.45803e17 | 0.764471 | 0.382236 | − | 0.924065i | \(-0.375154\pi\) | ||||
0.382236 | + | 0.924065i | \(0.375154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.33010e18 | 2.22682 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.02584e18 | 1.67688 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.13831e17 | 1.45864 | 0.729320 | − | 0.684172i | \(-0.239836\pi\) | ||||
0.729320 | + | 0.684172i | \(0.239836\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.17045e18 | −1.82445 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.29784e17 | −1.41546 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.09639e17 | 0.163024 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.64844e18 | 2.39424 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.27602e17 | −0.890482 | −0.445241 | − | 0.895411i | \(-0.646882\pi\) | ||||
−0.445241 | + | 0.895411i | \(0.646882\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.77768e16 | 0.0246420 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.75798e17 | −0.238098 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.33220e17 | −0.838011 | −0.419006 | − | 0.907984i | \(-0.637621\pi\) | ||||
−0.419006 | + | 0.907984i | \(0.637621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.20629e17 | 0.156005 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.14847e18 | 1.45154 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.18457e17 | −0.640446 | −0.320223 | − | 0.947342i | \(-0.603758\pi\) | ||||
−0.320223 | + | 0.947342i | \(0.603758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.98029e17 | −0.239108 | −0.119554 | − | 0.992828i | \(-0.538146\pi\) | ||||
−0.119554 | + | 0.992828i | \(0.538146\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.04285e18 | 1.23088 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.55352e17 | 0.179257 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.09548e16 | −0.0462021 | −0.0231011 | − | 0.999733i | \(-0.507354\pi\) | ||||
−0.0231011 | + | 0.999733i | \(0.507354\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.03701e18 | −1.14386 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.59215e17 | −0.603161 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.60581e17 | −0.696756 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.59983e17 | −0.990262 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.00006e18 | −1.00897 | −0.504485 | − | 0.863420i | \(-0.668318\pi\) | ||||
−0.504485 | + | 0.863420i | \(0.668318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.25730e16 | −0.0518816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.43977e17 | −0.428590 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.62146e17 | 0.153126 | 0.0765631 | − | 0.997065i | \(-0.475605\pi\) | ||||
0.0765631 | + | 0.997065i | \(0.475605\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.02135e16 | −0.0833510 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.71573e17 | −0.607100 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.85462e18 | 1.64052 | 0.820260 | − | 0.571992i | \(-0.193829\pi\) | ||||
0.820260 | + | 0.571992i | \(0.193829\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.05677e18 | −0.914737 | −0.457369 | − | 0.889277i | \(-0.651208\pi\) | ||||
−0.457369 | + | 0.889277i | \(0.651208\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.93789e18 | −2.48870 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.53116e18 | 1.26944 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.72501e17 | 0.626863 | 0.313431 | − | 0.949611i | \(-0.398521\pi\) | ||||
0.313431 | + | 0.949611i | \(0.398521\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.11015e18 | 2.47041 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.11764e17 | −0.164659 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.15792e18 | −0.881428 | −0.440714 | − | 0.897648i | \(-0.645275\pi\) | ||||
−0.440714 | + | 0.897648i | \(0.645275\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.42120e17 | 0.702131 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.42912e18 | −1.04283 | −0.521416 | − | 0.853303i | \(-0.674596\pi\) | ||||
−0.521416 | + | 0.853303i | \(0.674596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.90926e18 | −1.36420 | −0.682098 | − | 0.731261i | \(-0.738932\pi\) | ||||
−0.682098 | + | 0.731261i | \(0.738932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.18670e18 | 1.53001 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.09936e18 | −0.753303 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.07319e18 | −0.720204 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.64268e18 | 3.05162 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.07627e17 | 0.133676 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.10754e18 | −0.698501 | −0.349251 | − | 0.937029i | \(-0.613564\pi\) | ||||
−0.349251 | + | 0.937029i | \(0.613564\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.00685e18 | −2.47559 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.78028e17 | 0.592000 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.84575e17 | −0.109463 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.71365e17 | −0.215797 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.03185e18 | −1.72636 | −0.863178 | − | 0.504900i | \(-0.831529\pi\) | ||||
−0.863178 | + | 0.504900i | \(0.831529\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.83914e17 | 0.102622 | 0.0513112 | − | 0.998683i | \(-0.483660\pi\) | ||||
0.0513112 | + | 0.998683i | \(0.483660\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.30241e17 | 0.0712213 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.82632e18 | 0.978810 | 0.489405 | − | 0.872057i | \(-0.337214\pi\) | ||||
0.489405 | + | 0.872057i | \(0.337214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.41424e18 | 1.79351 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.75858e17 | 0.0905494 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.09505e16 | 0.0408587 | 0.0204293 | − | 0.999791i | \(-0.493497\pi\) | ||||
0.0204293 | + | 0.999791i | \(0.493497\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.55293e18 | −0.768394 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.23424e18 | 3.50928 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.86521e17 | −0.326512 | −0.163256 | − | 0.986584i | \(-0.552200\pi\) | ||||
−0.163256 | + | 0.986584i | \(0.552200\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.88664e17 | 0.367775 | 0.183888 | − | 0.982947i | \(-0.441132\pi\) | ||||
0.183888 | + | 0.982947i | \(0.441132\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.78383e17 | −0.0815671 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.38247e18 | 1.06828 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.28580e18 | 1.00512 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.27036e18 | −2.27285 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.20554e18 | 1.35583 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.18239e18 | 0.905388 | 0.452694 | − | 0.891666i | \(-0.350463\pi\) | ||||
0.452694 | + | 0.891666i | \(0.350463\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.08911e18 | 0.443197 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.05717e18 | 1.22038 | 0.610188 | − | 0.792256i | \(-0.291094\pi\) | ||||
0.610188 | + | 0.792256i | \(0.291094\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.34266e18 | −0.525790 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.19002e18 | −1.60976 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.48644e18 | −0.560290 | −0.280145 | − | 0.959958i | \(-0.590383\pi\) | ||||
−0.280145 | + | 0.959958i | \(0.590383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.73267e18 | 1.01064 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.08197e18 | −3.29580 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.70294e17 | −0.238693 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.56014e16 | 0.00894655 | 0.00447328 | − | 0.999990i | \(-0.498576\pi\) | ||||
0.00447328 | + | 0.999990i | \(0.498576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.05266e19 | −3.61014 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.23393e18 | 0.751914 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.18663e17 | 0.0392016 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.37200e18 | 0.444890 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.23789e18 | 0.712313 | 0.356156 | − | 0.934426i | \(-0.384087\pi\) | ||||
0.356156 | + | 0.934426i | \(0.384087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.48326e18 | −1.71328 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.55148e18 | −0.475902 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.39954e17 | 0.222832 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.45363e18 | −0.429786 | −0.214893 | − | 0.976638i | \(-0.568940\pi\) | ||||
−0.214893 | + | 0.976638i | \(0.568940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.07662e18 | 0.312543 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.29246e17 | 0.0368414 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.62914e18 | 0.735908 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.27347e18 | 0.350038 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.32656e18 | 1.70777 | 0.853885 | − | 0.520461i | \(-0.174240\pi\) | ||||
0.853885 | + | 0.520461i | \(0.174240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.16593e18 | −1.89974 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.55419e18 | 0.404675 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.13847e18 | 0.291154 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.41363e18 | −0.857517 | −0.428758 | − | 0.903419i | \(-0.641049\pi\) | ||||
−0.428758 | + | 0.903419i | \(0.641049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.60901e18 | −0.643793 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.64043e16 | 0.00397645 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.93022e18 | 1.88847 | 0.944234 | − | 0.329276i | \(-0.106805\pi\) | ||||
0.944234 | + | 0.329276i | \(0.106805\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.35228e18 | −0.316373 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.04608e18 | 1.84946 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.86152e17 | −0.132380 | −0.0661898 | − | 0.997807i | \(-0.521084\pi\) | ||||
−0.0661898 | + | 0.997807i | \(0.521084\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.71095e18 | 1.04542 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.31469e17 | 0.115891 | 0.0579456 | − | 0.998320i | \(-0.481545\pi\) | ||||
0.0579456 | + | 0.998320i | \(0.481545\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.75297e18 | −1.66132 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.49130e18 | −1.15636 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.56642e18 | 1.15198 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.47766e18 | 0.910734 | 0.455367 | − | 0.890304i | \(-0.349508\pi\) | ||||
0.455367 | + | 0.890304i | \(0.349508\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.85013e18 | 1.96913 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.94552e18 | −0.775264 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.54650e18 | −0.878120 | −0.439060 | − | 0.898458i | \(-0.644689\pi\) | ||||
−0.439060 | + | 0.898458i | \(0.644689\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.14136e19 | −2.16697 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.91093e18 | −1.47648 | −0.738239 | − | 0.674539i | \(-0.764342\pi\) | ||||
−0.738239 | + | 0.674539i | \(0.764342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.14142e19 | 2.09429 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.85866e17 | −0.159797 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.46444e18 | 0.614418 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.56634e18 | −1.14499 | −0.572495 | − | 0.819908i | \(-0.694024\pi\) | ||||
−0.572495 | + | 0.819908i | \(0.694024\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.68239e18 | 1.31717 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.09277e18 | −1.02718 | −0.513592 | − | 0.858035i | \(-0.671685\pi\) | ||||
−0.513592 | + | 0.858035i | \(0.671685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.43725e16 | 0.0106718 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.83416e19 | 2.99021 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.13381e18 | −0.502433 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.01707e18 | 0.160369 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.60248e19 | 2.48509 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.87142e18 | 0.437969 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.62269e18 | −0.843545 | −0.421773 | − | 0.906702i | \(-0.638592\pi\) | ||||
−0.421773 | + | 0.906702i | \(0.638592\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.97688e17 | 0.0882010 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.34220e18 | 0.194837 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.25267e18 | 0.464477 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.91089e18 | −0.689880 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.28588e19 | −1.77713 | −0.888567 | − | 0.458746i | \(-0.848299\pi\) | ||||
−0.888567 | + | 0.458746i | \(0.848299\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.95415e17 | −0.0265707 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.07954e19 | −1.44420 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.98126e19 | −2.60790 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.85709e18 | −0.758593 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.07847e19 | 1.37445 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.07548e18 | 0.636520 | 0.318260 | − | 0.948003i | \(-0.396902\pi\) | ||||
0.318260 | + | 0.948003i | \(0.396902\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.26888e18 | 0.897082 | 0.448541 | − | 0.893762i | \(-0.351944\pi\) | ||||
0.448541 | + | 0.893762i | \(0.351944\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.88073e18 | −0.228422 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.24668e19 | 1.49015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.33225e17 | −0.0509648 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.06814e19 | −1.23675 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.50633e19 | 1.71668 | 0.858339 | − | 0.513083i | \(-0.171497\pi\) | ||||
0.858339 | + | 0.513083i | \(0.171497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.23976e19 | −1.39072 | −0.695359 | − | 0.718662i | \(-0.744755\pi\) | ||||
−0.695359 | + | 0.718662i | \(0.744755\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.68469e18 | −0.627706 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.01774e19 | −1.10625 | −0.553124 | − | 0.833099i | \(-0.686564\pi\) | ||||
−0.553124 | + | 0.833099i | \(0.686564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.57706e18 | −1.02477 | −0.512386 | − | 0.858755i | \(-0.671238\pi\) | ||||
−0.512386 | + | 0.858755i | \(0.671238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.05376e19 | −2.16343 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.70324e17 | −0.0176638 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.31223e19 | −1.33982 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.06094e17 | 0.0910873 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.29416e19 | −1.28095 | −0.640477 | − | 0.767977i | \(-0.721263\pi\) | ||||
−0.640477 | + | 0.767977i | \(0.721263\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.49038e18 | 0.632552 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.38940e19 | 1.33336 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.63072e18 | −0.626602 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.70367e19 | 1.58542 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.05863e18 | −0.463589 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.34801e19 | 1.21661 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.74188e19 | 1.54828 | 0.774138 | − | 0.633016i | \(-0.218183\pi\) | ||||
0.774138 | + | 0.633016i | \(0.218183\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.33950e19 | 2.04807 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.71644e18 | −0.406667 | −0.203334 | − | 0.979110i | \(-0.565178\pi\) | ||||
−0.203334 | + | 0.979110i | \(0.565178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.14265e19 | 0.970414 | 0.485207 | − | 0.874399i | \(-0.338744\pi\) | ||||
0.485207 | + | 0.874399i | \(0.338744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.04827e19 | 0.876902 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.59537e18 | −0.378661 | −0.189330 | − | 0.981913i | \(-0.560632\pi\) | ||||
−0.189330 | + | 0.981913i | \(0.560632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.52464e19 | 1.23755 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.18688e19 | 1.74864 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.94857e18 | −0.232265 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.16439e18 | 0.633586 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.31845e19 | −1.00802 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.57191e19 | −1.18407 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.03578e19 | −0.768726 | −0.384363 | − | 0.923182i | \(-0.625579\pi\) | ||||
−0.384363 | + | 0.923182i | \(0.625579\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.34685e19 | −0.984898 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.80889e19 | −1.30337 | −0.651686 | − | 0.758489i | \(-0.725938\pi\) | ||||
−0.651686 | + | 0.758489i | \(0.725938\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.36653e18 | 0.594019 | 0.297010 | − | 0.954874i | \(-0.404011\pi\) | ||||
0.297010 | + | 0.954874i | \(0.404011\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.53821e19 | 1.77581 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.65265e19 | 1.13941 | 0.569703 | − | 0.821851i | \(-0.307058\pi\) | ||||
0.569703 | + | 0.821851i | \(0.307058\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.08822e19 | 0.739359 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.08862e19 | −2.06804 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.16075e18 | 0.340548 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.16428e19 | −1.40755 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.15815e19 | −0.742357 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.47156e17 | 0.0598389 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.18544e17 | −0.0385176 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.44915e18 | 0.0889494 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.83564e19 | −1.11064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.48578e18 | −0.0886147 | −0.0443074 | − | 0.999018i | \(-0.514108\pi\) | ||||
−0.0443074 | + | 0.999018i | \(0.514108\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.26610e18 | 0.427205 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.98362e19 | 1.14971 | 0.574855 | − | 0.818256i | \(-0.305059\pi\) | ||||
0.574855 | + | 0.818256i | \(0.305059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.50392e19 | 0.859340 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.38306e19 | 1.34245 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.72790e19 | −0.959659 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.49392e19 | −0.818044 | −0.409022 | − | 0.912524i | \(-0.634130\pi\) | ||||
−0.409022 | + | 0.912524i | \(0.634130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.13161e19 | 1.69075 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.03202e18 | 0.0549388 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.71392e18 | 0.352416 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.03671e19 | −3.64210 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.18869e19 | 0.606692 | 0.303346 | − | 0.952881i | \(-0.401896\pi\) | ||||
0.303346 | + | 0.952881i | \(0.401896\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.49814e18 | 0.226391 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.03087e19 | −1.00798 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.42615e18 | 0.118752 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.64517e19 | 1.27687 | 0.638434 | − | 0.769677i | \(-0.279583\pi\) | ||||
0.638434 | + | 0.769677i | \(0.279583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.48152e19 | 2.60960 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.39169e19 | −1.12298 | −0.561489 | − | 0.827484i | \(-0.689771\pi\) | ||||
−0.561489 | + | 0.827484i | \(0.689771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.70420e18 | 0.356781 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.10618e19 | −1.87556 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.42855e19 | −1.54467 | −0.772336 | − | 0.635214i | \(-0.780912\pi\) | ||||
−0.772336 | + | 0.635214i | \(0.780912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.01040e19 | −0.893411 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.60595e19 | −1.14233 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.90816e19 | 1.25752 | 0.628760 | − | 0.777599i | \(-0.283563\pi\) | ||||
0.628760 | + | 0.777599i | \(0.283563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.43921e19 | −0.613907 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.36427e19 | −3.51966 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.04056e19 | 1.26221 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.43640e19 | −0.997807 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.46604e19 | 2.20852 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.43116e19 | 0.570508 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.38894e17 | 0.0369270 | 0.0184635 | − | 0.999830i | \(-0.494123\pi\) | ||||
0.0184635 | + | 0.999830i | \(0.494123\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.34723e18 | 0.168697 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.07232e19 | −1.55925 | −0.779626 | − | 0.626245i | \(-0.784591\pi\) | ||||
−0.779626 | + | 0.626245i | \(0.784591\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.48562e19 | 0.939077 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.76828e18 | −0.215038 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.18079e19 | −0.434370 | −0.217185 | − | 0.976131i | \(-0.569687\pi\) | ||||
−0.217185 | + | 0.976131i | \(0.569687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.95657e19 | 1.07325 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.12084e20 | 4.01507 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.30186e19 | −1.16724 | −0.583621 | − | 0.812026i | \(-0.698365\pi\) | ||||
−0.583621 | + | 0.812026i | \(0.698365\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.12724e18 | 0.213761 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.72628e19 | −0.594362 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.06505e18 | 0.0361904 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.46516e19 | −0.491367 | −0.245684 | − | 0.969350i | \(-0.579012\pi\) | ||||
−0.245684 | + | 0.969350i | \(0.579012\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.55761e19 | −1.17758 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.26825e18 | 0.302794 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.12523e19 | 0.685312 | 0.342656 | − | 0.939461i | \(-0.388674\pi\) | ||||
0.342656 | + | 0.939461i | \(0.388674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.45039e19 | 3.00797 |
(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 | 16.14.a.e.1.1 | 2 | ||
3.2 | odd | 2 | 144.14.a.n.1.1 | 2 | |||
4.3 | odd | 2 | 8.14.a.b.1.2 | ✓ | 2 | ||
8.3 | odd | 2 | 64.14.a.j.1.1 | 2 | |||
8.5 | even | 2 | 64.14.a.l.1.2 | 2 | |||
12.11 | even | 2 | 72.14.a.c.1.1 | 2 | |||
20.3 | even | 4 | 200.14.c.b.49.4 | 4 | |||
20.7 | even | 4 | 200.14.c.b.49.1 | 4 | |||
20.19 | odd | 2 | 200.14.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.14.a.b.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
16.14.a.e.1.1 | 2 | 1.1 | even | 1 | trivial | ||
64.14.a.j.1.1 | 2 | 8.3 | odd | 2 | |||
64.14.a.l.1.2 | 2 | 8.5 | even | 2 | |||
72.14.a.c.1.1 | 2 | 12.11 | even | 2 | |||
144.14.a.n.1.1 | 2 | 3.2 | odd | 2 | |||
200.14.a.b.1.1 | 2 | 20.19 | odd | 2 | |||
200.14.c.b.49.1 | 4 | 20.7 | even | 4 | |||
200.14.c.b.49.4 | 4 | 20.3 | even | 4 |