Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,8,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(70.2866307339\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{19}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 19 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.35890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28220 | 0.113332 | 0.0566659 | − | 0.998393i | \(-0.481953\pi\) | ||||
0.0566659 | + | 0.998393i | \(0.481953\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −126.356 | −0.987156 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 538.197 | 0.593059 | 0.296529 | − | 0.955024i | \(-0.404171\pi\) | ||||
0.296529 | + | 0.955024i | \(0.404171\pi\) | |||||||
\(8\) | −326.136 | −0.225208 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1215.12 | 0.275261 | 0.137630 | − | 0.990484i | \(-0.456051\pi\) | ||||
0.137630 | + | 0.990484i | \(0.456051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7070.42 | −0.892573 | −0.446286 | − | 0.894890i | \(-0.647254\pi\) | ||||
−0.446286 | + | 0.894890i | \(0.647254\pi\) | |||||||
\(14\) | 690.077 | 0.0672124 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15755.4 | 0.961633 | ||||||||
\(17\) | −3348.13 | −0.165284 | −0.0826420 | − | 0.996579i | \(-0.526336\pi\) | ||||
−0.0826420 | + | 0.996579i | \(0.526336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22169.7 | 0.741519 | 0.370759 | − | 0.928729i | \(-0.379097\pi\) | ||||
0.370759 | + | 0.928729i | \(0.379097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1558.03 | 0.0311958 | ||||||||
\(23\) | −58513.1 | −1.00278 | −0.501390 | − | 0.865221i | \(-0.667178\pi\) | ||||
−0.501390 | + | 0.865221i | \(0.667178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9065.71 | −0.101157 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −68004.4 | −0.585442 | ||||||||
\(29\) | 206301. | 1.57076 | 0.785379 | − | 0.619015i | \(-0.212468\pi\) | ||||
0.785379 | + | 0.619015i | \(0.212468\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 177822. | 1.07206 | 0.536030 | − | 0.844199i | \(-0.319923\pi\) | ||||
0.536030 | + | 0.844199i | \(0.319923\pi\) | |||||||
\(32\) | 61947.0 | 0.334191 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4292.98 | −0.0187319 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 284128. | 0.922163 | 0.461081 | − | 0.887358i | \(-0.347462\pi\) | ||||
0.461081 | + | 0.887358i | \(0.347462\pi\) | |||||||
\(38\) | 28426.0 | 0.0840376 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −627353. | −1.42157 | −0.710785 | − | 0.703409i | \(-0.751660\pi\) | ||||
−0.710785 | + | 0.703409i | \(0.751660\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 164889. | 0.316266 | 0.158133 | − | 0.987418i | \(-0.449453\pi\) | ||||
0.158133 | + | 0.987418i | \(0.449453\pi\) | |||||||
\(44\) | −153538. | −0.271725 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −75025.7 | −0.113647 | ||||||||
\(47\) | −449355. | −0.631316 | −0.315658 | − | 0.948873i | \(-0.602225\pi\) | ||||
−0.315658 | + | 0.948873i | \(0.602225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −533887. | −0.648281 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 893390. | 0.881108 | ||||||||
\(53\) | −730190. | −0.673706 | −0.336853 | − | 0.941557i | \(-0.609362\pi\) | ||||
−0.336853 | + | 0.941557i | \(0.609362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −175525. | −0.133562 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 264520. | 0.178017 | ||||||||
\(59\) | −1.42202e6 | −0.901412 | −0.450706 | − | 0.892673i | \(-0.648828\pi\) | ||||
−0.450706 | + | 0.892673i | \(0.648828\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −266326. | −0.150231 | −0.0751153 | − | 0.997175i | \(-0.523932\pi\) | ||||
−0.0751153 | + | 0.997175i | \(0.523932\pi\) | |||||||
\(62\) | 228004. | 0.121498 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.93726e6 | −0.923758 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.95028e6 | −1.19840 | −0.599200 | − | 0.800599i | \(-0.704515\pi\) | ||||
−0.599200 | + | 0.800599i | \(0.704515\pi\) | |||||||
\(68\) | 423056. | 0.163161 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −921138. | −0.305436 | −0.152718 | − | 0.988270i | \(-0.548803\pi\) | ||||
−0.152718 | + | 0.988270i | \(0.548803\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.25657e6 | −1.28065 | −0.640323 | − | 0.768105i | \(-0.721200\pi\) | ||||
−0.640323 | + | 0.768105i | \(0.721200\pi\) | |||||||
\(74\) | 364309. | 0.104510 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.80127e6 | −0.731995 | ||||||||
\(77\) | 653973. | 0.163246 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.28551e6 | 1.43432 | 0.717159 | − | 0.696910i | \(-0.245442\pi\) | ||||
0.717159 | + | 0.696910i | \(0.245442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −804393. | −0.161109 | ||||||||
\(83\) | −9.17165e6 | −1.76065 | −0.880327 | − | 0.474367i | \(-0.842677\pi\) | ||||
−0.880327 | + | 0.474367i | \(0.842677\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 211421. | 0.0358430 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −396294. | −0.0619909 | ||||||||
\(89\) | −242643. | −0.0364840 | −0.0182420 | − | 0.999834i | \(-0.505807\pi\) | ||||
−0.0182420 | + | 0.999834i | \(0.505807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.80528e6 | −0.529348 | ||||||||
\(92\) | 7.39348e6 | 0.989901 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −576164. | −0.0715482 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.59198e6 | 0.288357 | 0.144179 | − | 0.989552i | \(-0.453946\pi\) | ||||
0.144179 | + | 0.989552i | \(0.453946\pi\) | |||||||
\(98\) | −684551. | −0.0734708 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.69169e6 | −0.356534 | −0.178267 | − | 0.983982i | \(-0.557049\pi\) | ||||
−0.178267 | + | 0.983982i | \(0.557049\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.68203e6 | −0.782873 | −0.391436 | − | 0.920205i | \(-0.628022\pi\) | ||||
−0.391436 | + | 0.920205i | \(0.628022\pi\) | |||||||
\(104\) | 2.30592e6 | 0.201014 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −936251. | −0.0763522 | ||||||||
\(107\) | 1.52118e7 | 1.20043 | 0.600216 | − | 0.799838i | \(-0.295081\pi\) | ||||
0.600216 | + | 0.799838i | \(0.295081\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.60843e6 | −0.118963 | −0.0594813 | − | 0.998229i | \(-0.518945\pi\) | ||||
−0.0594813 | + | 0.998229i | \(0.518945\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.47950e6 | 0.570305 | ||||||||
\(113\) | −2.62766e7 | −1.71315 | −0.856574 | − | 0.516024i | \(-0.827411\pi\) | ||||
−0.856574 | + | 0.516024i | \(0.827411\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.60674e7 | −1.55058 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.82332e6 | −0.102159 | ||||||||
\(119\) | −1.80195e6 | −0.0980231 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.80107e7 | −0.924231 | ||||||||
\(122\) | −341483. | −0.0170259 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.24688e7 | −1.05829 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.91864e7 | 0.831152 | 0.415576 | − | 0.909559i | \(-0.363580\pi\) | ||||
0.415576 | + | 0.909559i | \(0.363580\pi\) | |||||||
\(128\) | −1.04132e7 | −0.438882 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.07018e7 | −1.19320 | −0.596602 | − | 0.802537i | \(-0.703483\pi\) | ||||
−0.596602 | + | 0.802537i | \(0.703483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.19317e7 | 0.439764 | ||||||||
\(134\) | −3.78286e6 | −0.135817 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.09194e6 | 0.0372232 | ||||||||
\(137\) | −3.16847e7 | −1.05276 | −0.526378 | − | 0.850251i | \(-0.676450\pi\) | ||||
−0.526378 | + | 0.850251i | \(0.676450\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.07581e7 | 0.655596 | 0.327798 | − | 0.944748i | \(-0.393693\pi\) | ||||
0.327798 | + | 0.944748i | \(0.393693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.18108e6 | −0.0346156 | ||||||||
\(143\) | −8.59140e6 | −0.245690 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.45778e6 | −0.145138 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.59012e7 | −0.910318 | ||||||||
\(149\) | −2.94607e7 | −0.729611 | −0.364806 | − | 0.931084i | \(-0.618865\pi\) | ||||
−0.364806 | + | 0.931084i | \(0.618865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.60002e7 | 1.08728 | 0.543638 | − | 0.839320i | \(-0.317046\pi\) | ||||
0.543638 | + | 0.839320i | \(0.317046\pi\) | |||||||
\(152\) | −7.23033e6 | −0.166996 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 838526. | 0.0185009 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.92998e7 | −0.398019 | −0.199010 | − | 0.979998i | \(-0.563773\pi\) | ||||
−0.199010 | + | 0.979998i | \(0.563773\pi\) | |||||||
\(158\) | 8.05929e6 | 0.162554 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.14916e7 | −0.594708 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.35624e7 | −0.426151 | −0.213076 | − | 0.977036i | \(-0.568348\pi\) | ||||
−0.213076 | + | 0.977036i | \(0.568348\pi\) | |||||||
\(164\) | 7.92698e7 | 1.40331 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.17599e7 | −0.199538 | ||||||||
\(167\) | 2.18824e7 | 0.363570 | 0.181785 | − | 0.983338i | \(-0.441813\pi\) | ||||
0.181785 | + | 0.983338i | \(0.441813\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.27577e7 | −0.203314 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.08347e7 | −0.312204 | ||||||||
\(173\) | −9.62312e7 | −1.41304 | −0.706520 | − | 0.707693i | \(-0.749736\pi\) | ||||
−0.706520 | + | 0.707693i | \(0.749736\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.91447e7 | 0.264700 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −311117. | −0.00413479 | ||||||||
\(179\) | −8.46776e7 | −1.10353 | −0.551763 | − | 0.834001i | \(-0.686045\pi\) | ||||
−0.551763 | + | 0.834001i | \(0.686045\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.65249e7 | −1.20994 | −0.604971 | − | 0.796248i | \(-0.706815\pi\) | ||||
−0.604971 | + | 0.796248i | \(0.706815\pi\) | |||||||
\(182\) | −4.87913e6 | −0.0599919 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.90832e7 | 0.225834 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.06837e6 | −0.0454962 | ||||||||
\(188\) | 5.67787e7 | 0.623208 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.46467e8 | 1.52098 | 0.760491 | − | 0.649348i | \(-0.224958\pi\) | ||||
0.760491 | + | 0.649348i | \(0.224958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.53275e7 | 0.854355 | 0.427177 | − | 0.904168i | \(-0.359508\pi\) | ||||
0.427177 | + | 0.904168i | \(0.359508\pi\) | |||||||
\(194\) | 3.32345e6 | 0.0326800 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.74598e7 | 0.639954 | ||||||||
\(197\) | 1.44802e8 | 1.34941 | 0.674705 | − | 0.738087i | \(-0.264271\pi\) | ||||
0.674705 | + | 0.738087i | \(0.264271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.26870e7 | 0.114123 | 0.0570617 | − | 0.998371i | \(-0.481827\pi\) | ||||
0.0570617 | + | 0.998371i | \(0.481827\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.73349e6 | −0.0404066 | ||||||||
\(203\) | 1.11031e8 | 0.931552 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.11321e7 | −0.0887243 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.11397e8 | −0.858327 | ||||||||
\(209\) | 2.69388e7 | 0.204111 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.47331e7 | −0.694246 | −0.347123 | − | 0.937820i | \(-0.612841\pi\) | ||||
−0.347123 | + | 0.937820i | \(0.612841\pi\) | |||||||
\(212\) | 9.22638e7 | 0.665053 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.95046e7 | 0.136047 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.57031e7 | 0.635795 | ||||||||
\(218\) | −2.06234e6 | −0.0134822 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.36727e7 | 0.147528 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.28554e8 | 1.38014 | 0.690069 | − | 0.723744i | \(-0.257580\pi\) | ||||
0.690069 | + | 0.723744i | \(0.257580\pi\) | |||||||
\(224\) | 3.33397e7 | 0.198195 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.36919e7 | −0.194154 | ||||||||
\(227\) | −3.00587e8 | −1.70561 | −0.852806 | − | 0.522229i | \(-0.825101\pi\) | ||||
−0.852806 | + | 0.522229i | \(0.825101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.05343e8 | −0.579669 | −0.289835 | − | 0.957077i | \(-0.593600\pi\) | ||||
−0.289835 | + | 0.957077i | \(0.593600\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.72823e7 | −0.353747 | ||||||||
\(233\) | 3.27196e8 | 1.69458 | 0.847291 | − | 0.531130i | \(-0.178232\pi\) | ||||
0.847291 | + | 0.531130i | \(0.178232\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.79681e8 | 0.889834 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.31047e6 | −0.0111091 | ||||||||
\(239\) | 5.72888e7 | 0.271442 | 0.135721 | − | 0.990747i | \(-0.456665\pi\) | ||||
0.135721 | + | 0.990747i | \(0.456665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.84287e8 | 1.30827 | 0.654134 | − | 0.756379i | \(-0.273033\pi\) | ||||
0.654134 | + | 0.756379i | \(0.273033\pi\) | |||||||
\(242\) | −2.30933e7 | −0.104745 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.36518e7 | 0.148301 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.56749e8 | −0.661859 | ||||||||
\(248\) | −5.79941e7 | −0.241436 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.69178e7 | 0.107444 | 0.0537220 | − | 0.998556i | \(-0.482892\pi\) | ||||
0.0537220 | + | 0.998556i | \(0.482892\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.11004e7 | −0.276026 | ||||||||
\(254\) | 2.46008e7 | 0.0941959 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.34618e8 | 0.874019 | ||||||||
\(257\) | −3.28749e8 | −1.20809 | −0.604044 | − | 0.796951i | \(-0.706445\pi\) | ||||
−0.604044 | + | 0.796951i | \(0.706445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.52917e8 | 0.546897 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.93660e7 | −0.135228 | ||||||||
\(263\) | 1.85590e8 | 0.629084 | 0.314542 | − | 0.949244i | \(-0.398149\pi\) | ||||
0.314542 | + | 0.949244i | \(0.398149\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.52988e7 | 0.0498393 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.72786e8 | 1.18301 | ||||||||
\(269\) | −2.70876e8 | −0.848471 | −0.424236 | − | 0.905552i | \(-0.639457\pi\) | ||||
−0.424236 | + | 0.905552i | \(0.639457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.30743e8 | 0.704263 | 0.352132 | − | 0.935950i | \(-0.385457\pi\) | ||||
0.352132 | + | 0.935950i | \(0.385457\pi\) | |||||||
\(272\) | −5.27511e7 | −0.158942 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.06262e7 | −0.119311 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.42059e8 | −0.401595 | −0.200798 | − | 0.979633i | \(-0.564353\pi\) | ||||
−0.200798 | + | 0.979633i | \(0.564353\pi\) | |||||||
\(278\) | 2.66161e7 | 0.0742998 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.15362e8 | 0.310164 | 0.155082 | − | 0.987902i | \(-0.450436\pi\) | ||||
0.155082 | + | 0.987902i | \(0.450436\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.18080e8 | −0.571958 | −0.285979 | − | 0.958236i | \(-0.592319\pi\) | ||||
−0.285979 | + | 0.958236i | \(0.592319\pi\) | |||||||
\(284\) | 1.16391e8 | 0.301513 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.10159e7 | −0.0278445 | ||||||||
\(287\) | −3.37639e8 | −0.843075 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.99129e8 | −0.972681 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.37842e8 | 1.26420 | ||||||||
\(293\) | 4.12384e8 | 0.957778 | 0.478889 | − | 0.877875i | \(-0.341040\pi\) | ||||
0.478889 | + | 0.877875i | \(0.341040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.26642e7 | −0.207678 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.77746e7 | −0.0826881 | ||||||||
\(299\) | 4.13713e8 | 0.895055 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.87428e7 | 0.187564 | ||||||||
\(302\) | 5.89815e7 | 0.123223 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.49292e8 | 0.713069 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.57983e8 | −0.311621 | −0.155810 | − | 0.987787i | \(-0.549799\pi\) | ||||
−0.155810 | + | 0.987787i | \(0.549799\pi\) | |||||||
\(308\) | −8.26334e7 | −0.161149 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.69169e8 | 0.318904 | 0.159452 | − | 0.987206i | \(-0.449027\pi\) | ||||
0.159452 | + | 0.987206i | \(0.449027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.22117e8 | 0.962415 | 0.481208 | − | 0.876607i | \(-0.340198\pi\) | ||||
0.481208 | + | 0.876607i | \(0.340198\pi\) | |||||||
\(314\) | −2.47463e7 | −0.0451082 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.94211e8 | −1.41590 | ||||||||
\(317\) | 4.73280e8 | 0.834470 | 0.417235 | − | 0.908799i | \(-0.362999\pi\) | ||||
0.417235 | + | 0.908799i | \(0.362999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50681e8 | 0.432368 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.03786e7 | −0.0673993 | ||||||||
\(323\) | −7.42270e7 | −0.122561 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.02118e7 | −0.0482965 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.04602e8 | 0.320149 | ||||||||
\(329\) | −2.41841e8 | −0.374408 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.75892e7 | −0.132756 | −0.0663778 | − | 0.997795i | \(-0.521144\pi\) | ||||
−0.0663778 | + | 0.997795i | \(0.521144\pi\) | |||||||
\(332\) | 1.15889e9 | 1.73804 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.80577e7 | 0.0412040 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.04119e8 | 0.432851 | 0.216426 | − | 0.976299i | \(-0.430560\pi\) | ||||
0.216426 | + | 0.976299i | \(0.430560\pi\) | |||||||
\(338\) | −1.63579e7 | −0.0230419 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.16075e8 | 0.295096 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.30565e8 | −0.977528 | ||||||||
\(344\) | −5.37762e7 | −0.0712256 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.23388e8 | −0.160142 | ||||||||
\(347\) | 3.15347e8 | 0.405169 | 0.202584 | − | 0.979265i | \(-0.435066\pi\) | ||||
0.202584 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.23418e8 | −0.659112 | −0.329556 | − | 0.944136i | \(-0.606899\pi\) | ||||
−0.329556 | + | 0.944136i | \(0.606899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.52730e7 | 0.0919898 | ||||||||
\(353\) | −4.13964e8 | −0.500900 | −0.250450 | − | 0.968130i | \(-0.580579\pi\) | ||||
−0.250450 | + | 0.968130i | \(0.580579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.06593e7 | 0.0360154 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.08574e8 | −0.125065 | ||||||||
\(359\) | 2.48768e8 | 0.283768 | 0.141884 | − | 0.989883i | \(-0.454684\pi\) | ||||
0.141884 | + | 0.989883i | \(0.454684\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.02376e8 | −0.450150 | ||||||||
\(362\) | −1.23764e8 | −0.137125 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.80819e8 | 0.522549 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.45884e9 | −1.54056 | −0.770278 | − | 0.637708i | \(-0.779883\pi\) | ||||
−0.770278 | + | 0.637708i | \(0.779883\pi\) | |||||||
\(368\) | −9.21897e8 | −0.964307 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.92986e8 | −0.399547 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.29125e8 | −0.627706 | −0.313853 | − | 0.949472i | \(-0.601620\pi\) | ||||
−0.313853 | + | 0.949472i | \(0.601620\pi\) | |||||||
\(374\) | −5.21648e6 | −0.00515616 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.46551e8 | 0.142177 | ||||||||
\(377\) | −1.45864e9 | −1.40202 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.54658e7 | 0.0806409 | 0.0403204 | − | 0.999187i | \(-0.487162\pi\) | ||||
0.0403204 | + | 0.999187i | \(0.487162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.87801e8 | 0.172376 | ||||||||
\(383\) | −7.56340e8 | −0.687893 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.09407e8 | 0.0968255 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.27512e8 | −0.284654 | ||||||||
\(389\) | −1.42837e9 | −1.23032 | −0.615160 | − | 0.788402i | \(-0.710908\pi\) | ||||
−0.615160 | + | 0.788402i | \(0.710908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.95909e8 | 0.165744 | ||||||||
\(392\) | 1.74120e8 | 0.145998 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.85666e8 | 0.152931 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.67152e8 | 0.134074 | 0.0670372 | − | 0.997750i | \(-0.478645\pi\) | ||||
0.0670372 | + | 0.997750i | \(0.478645\pi\) | |||||||
\(398\) | 1.62673e7 | 0.0129338 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.32051e9 | −1.79712 | −0.898561 | − | 0.438848i | \(-0.855387\pi\) | ||||
−0.898561 | + | 0.438848i | \(0.855387\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.25728e9 | −0.956892 | ||||||||
\(404\) | 4.66467e8 | 0.351954 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.42364e8 | 0.105574 | ||||||||
\(407\) | 3.45249e8 | 0.253835 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.24735e8 | −0.596050 | −0.298025 | − | 0.954558i | \(-0.596328\pi\) | ||||
−0.298025 | + | 0.954558i | \(0.596328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.09703e9 | 0.772817 | ||||||||
\(413\) | −7.65326e8 | −0.534590 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.37991e8 | −0.298290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.45410e7 | 0.0231323 | ||||||||
\(419\) | −8.23968e8 | −0.547219 | −0.273610 | − | 0.961841i | \(-0.588218\pi\) | ||||
−0.273610 | + | 0.961841i | \(0.588218\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.12046e8 | −0.138498 | −0.0692488 | − | 0.997599i | \(-0.522060\pi\) | ||||
−0.0692488 | + | 0.997599i | \(0.522060\pi\) | |||||||
\(422\) | −1.21467e8 | −0.0786801 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.38141e8 | 0.151724 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.43336e8 | −0.0890956 | ||||||||
\(428\) | −1.92210e9 | −1.18501 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.44023e8 | −0.447627 | −0.223813 | − | 0.974632i | \(-0.571851\pi\) | ||||
−0.223813 | + | 0.974632i | \(0.571851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.93573e9 | 1.14588 | 0.572938 | − | 0.819598i | \(-0.305803\pi\) | ||||
0.572938 | + | 0.819598i | \(0.305803\pi\) | |||||||
\(434\) | 1.22711e8 | 0.0720557 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.03235e8 | 0.117435 | ||||||||
\(437\) | −1.29722e9 | −0.743581 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.35485e9 | −0.764300 | −0.382150 | − | 0.924100i | \(-0.624816\pi\) | ||||
−0.382150 | + | 0.924100i | \(0.624816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.03531e7 | 0.0167196 | ||||||||
\(443\) | 1.05985e9 | 0.579203 | 0.289601 | − | 0.957147i | \(-0.406477\pi\) | ||||
0.289601 | + | 0.957147i | \(0.406477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.93053e8 | 0.156413 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.04263e9 | −0.547843 | ||||||||
\(449\) | 1.70272e9 | 0.887730 | 0.443865 | − | 0.896094i | \(-0.353607\pi\) | ||||
0.443865 | + | 0.896094i | \(0.353607\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.62309e8 | −0.391303 | ||||||||
\(452\) | 3.32021e9 | 1.69114 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.85414e8 | −0.193300 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.76431e9 | 1.84493 | 0.922463 | − | 0.386085i | \(-0.126173\pi\) | ||||
0.922463 | + | 0.386085i | \(0.126173\pi\) | |||||||
\(458\) | −1.35071e8 | −0.0656949 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.59084e9 | −1.70704 | −0.853519 | − | 0.521062i | \(-0.825536\pi\) | ||||
−0.853519 | + | 0.521062i | \(0.825536\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.45649e8 | 0.115022 | 0.0575111 | − | 0.998345i | \(-0.481684\pi\) | ||||
0.0575111 | + | 0.998345i | \(0.481684\pi\) | |||||||
\(464\) | 3.25036e9 | 1.51049 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.19532e8 | 0.192050 | ||||||||
\(467\) | −4.04985e8 | −0.184005 | −0.0920025 | − | 0.995759i | \(-0.529327\pi\) | ||||
−0.0920025 | + | 0.995759i | \(0.529327\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.58783e9 | −0.710722 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.63771e8 | 0.203005 | ||||||||
\(473\) | 2.00360e8 | 0.0870556 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.27687e8 | 0.0967641 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.34559e7 | 0.0307630 | ||||||||
\(479\) | −4.18334e9 | −1.73920 | −0.869598 | − | 0.493760i | \(-0.835622\pi\) | ||||
−0.869598 | + | 0.493760i | \(0.835622\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00890e9 | −0.823097 | ||||||||
\(482\) | 3.64513e8 | 0.148268 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.27575e9 | 0.912361 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.25089e9 | −1.27541 | −0.637706 | − | 0.770280i | \(-0.720117\pi\) | ||||
−0.637706 | + | 0.770280i | \(0.720117\pi\) | |||||||
\(488\) | 8.68583e7 | 0.0338331 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.37360e9 | 1.28620 | 0.643100 | − | 0.765782i | \(-0.277648\pi\) | ||||
0.643100 | + | 0.765782i | \(0.277648\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.90723e8 | −0.259621 | ||||||||
\(494\) | −2.00984e8 | −0.0750097 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.80165e9 | 1.03093 | ||||||||
\(497\) | −4.95753e8 | −0.181142 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.74951e9 | 1.35090 | 0.675449 | − | 0.737406i | \(-0.263950\pi\) | ||||
0.675449 | + | 0.737406i | \(0.263950\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.45141e7 | 0.0121768 | ||||||||
\(503\) | −3.09301e9 | −1.08366 | −0.541830 | − | 0.840488i | \(-0.682268\pi\) | ||||
−0.541830 | + | 0.840488i | \(0.682268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.11651e7 | −0.0312825 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.42432e9 | −0.820476 | ||||||||
\(509\) | −1.36862e9 | −0.460015 | −0.230007 | − | 0.973189i | \(-0.573875\pi\) | ||||
−0.230007 | + | 0.973189i | \(0.573875\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.29087e9 | −0.759499 | ||||||||
\(512\) | 1.63371e9 | 0.537937 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.21523e8 | −0.136915 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.46020e8 | −0.173777 | ||||||||
\(518\) | 1.96070e8 | 0.0619808 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.47414e9 | 1.38604 | 0.693022 | − | 0.720916i | \(-0.256279\pi\) | ||||
0.693022 | + | 0.720916i | \(0.256279\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.01993e9 | 0.923085 | 0.461542 | − | 0.887118i | \(-0.347296\pi\) | ||||
0.461542 | + | 0.887118i | \(0.347296\pi\) | |||||||
\(524\) | 3.87936e9 | 1.17788 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.37963e8 | 0.0712952 | ||||||||
\(527\) | −5.95370e8 | −0.177194 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.89619e7 | 0.00556913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.50764e9 | −0.434116 | ||||||||
\(533\) | 4.43565e9 | 1.26885 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.62193e8 | 0.269889 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.47318e8 | −0.0961587 | ||||||||
\(539\) | −6.48737e8 | −0.178446 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.23946e9 | 0.879593 | 0.439796 | − | 0.898097i | \(-0.355051\pi\) | ||||
0.439796 | + | 0.898097i | \(0.355051\pi\) | |||||||
\(542\) | 2.95859e8 | 0.0798154 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.07406e8 | −0.0552365 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.25742e9 | −1.11222 | −0.556111 | − | 0.831108i | \(-0.687707\pi\) | ||||
−0.556111 | + | 0.831108i | \(0.687707\pi\) | |||||||
\(548\) | 4.00355e9 | 1.03923 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.57364e9 | 1.16475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.38284e9 | 0.850635 | ||||||||
\(554\) | −1.82148e8 | −0.0455135 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.62291e9 | −0.647175 | ||||||||
\(557\) | −5.65828e9 | −1.38737 | −0.693684 | − | 0.720280i | \(-0.744013\pi\) | ||||
−0.693684 | + | 0.720280i | \(0.744013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.16584e9 | −0.282290 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.47918e8 | 0.0351515 | ||||||||
\(563\) | 4.37511e9 | 1.03326 | 0.516630 | − | 0.856209i | \(-0.327186\pi\) | ||||
0.516630 | + | 0.856209i | \(0.327186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.79623e8 | −0.0648210 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.00416e8 | 0.0687866 | ||||||||
\(569\) | −1.67226e9 | −0.380550 | −0.190275 | − | 0.981731i | \(-0.560938\pi\) | ||||
−0.190275 | + | 0.981731i | \(0.560938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.39802e8 | 0.143820 | 0.0719100 | − | 0.997411i | \(-0.477091\pi\) | ||||
0.0719100 | + | 0.997411i | \(0.477091\pi\) | |||||||
\(572\) | 1.08558e9 | 0.242535 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.32922e8 | −0.0955472 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.87101e9 | −1.05561 | −0.527805 | − | 0.849366i | \(-0.676985\pi\) | ||||
−0.527805 | + | 0.849366i | \(0.676985\pi\) | |||||||
\(578\) | −5.11764e8 | −0.110236 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.93615e9 | −1.04417 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.87268e8 | −0.185445 | ||||||||
\(584\) | 1.38822e9 | 0.288412 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.28760e8 | 0.108547 | ||||||||
\(587\) | −2.32406e9 | −0.474258 | −0.237129 | − | 0.971478i | \(-0.576206\pi\) | ||||
−0.237129 | + | 0.971478i | \(0.576206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.94226e9 | 0.794953 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.47654e9 | 0.886782 | ||||||||
\(593\) | 4.27080e9 | 0.841043 | 0.420522 | − | 0.907283i | \(-0.361847\pi\) | ||||
0.420522 | + | 0.907283i | \(0.361847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.72254e9 | 0.720240 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.30463e8 | 0.101438 | ||||||||
\(599\) | −3.50335e9 | −0.666023 | −0.333012 | − | 0.942923i | \(-0.608065\pi\) | ||||
−0.333012 | + | 0.942923i | \(0.608065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.98866e9 | 0.561585 | 0.280792 | − | 0.959769i | \(-0.409403\pi\) | ||||
0.280792 | + | 0.959769i | \(0.409403\pi\) | |||||||
\(602\) | 1.13786e8 | 0.0212570 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.81240e9 | −1.07331 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.31901e9 | 1.32829 | 0.664143 | − | 0.747605i | \(-0.268797\pi\) | ||||
0.664143 | + | 0.747605i | \(0.268797\pi\) | |||||||
\(608\) | 1.37335e9 | 0.247809 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.17713e9 | 0.563496 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.32799e9 | 1.46026 | 0.730128 | − | 0.683311i | \(-0.239461\pi\) | ||||
0.730128 | + | 0.683311i | \(0.239461\pi\) | |||||||
\(614\) | −2.02566e8 | −0.0353165 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.13284e8 | −0.0367643 | ||||||||
\(617\) | −2.88456e9 | −0.494403 | −0.247201 | − | 0.968964i | \(-0.579511\pi\) | ||||
−0.247201 | + | 0.968964i | \(0.579511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.27213e9 | −0.385049 | −0.192525 | − | 0.981292i | \(-0.561668\pi\) | ||||
−0.192525 | + | 0.981292i | \(0.561668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.16909e8 | 0.0361420 | ||||||||
\(623\) | −1.30589e8 | −0.0216371 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.69459e8 | 0.109072 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.43865e9 | 0.392907 | ||||||||
\(629\) | −9.51296e8 | −0.152419 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.90856e7 | −0.00460867 | −0.00230434 | − | 0.999997i | \(-0.500733\pi\) | ||||
−0.00230434 | + | 0.999997i | \(0.500733\pi\) | |||||||
\(632\) | −2.04993e9 | −0.323020 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.06841e8 | 0.0945719 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.77481e9 | 0.578638 | ||||||||
\(638\) | 3.21423e8 | 0.0490010 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.12634e9 | 0.468849 | 0.234424 | − | 0.972134i | \(-0.424680\pi\) | ||||
0.234424 | + | 0.972134i | \(0.424680\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.48120e9 | −0.368064 | −0.184032 | − | 0.982920i | \(-0.558915\pi\) | ||||
−0.184032 | + | 0.982920i | \(0.558915\pi\) | |||||||
\(644\) | 3.97915e9 | 0.587070 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.51740e7 | −0.0138901 | ||||||||
\(647\) | 3.10080e9 | 0.450100 | 0.225050 | − | 0.974347i | \(-0.427746\pi\) | ||||
0.225050 | + | 0.974347i | \(0.427746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.72792e9 | −0.248123 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.97726e9 | 0.420678 | ||||||||
\(653\) | 9.64911e8 | 0.135610 | 0.0678049 | − | 0.997699i | \(-0.478400\pi\) | ||||
0.0678049 | + | 0.997699i | \(0.478400\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.88419e9 | −1.36703 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.10089e8 | −0.0424323 | ||||||||
\(659\) | 7.70039e9 | 1.04813 | 0.524063 | − | 0.851679i | \(-0.324416\pi\) | ||||
0.524063 | + | 0.851679i | \(0.324416\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.30650e10 | 1.75956 | 0.879779 | − | 0.475382i | \(-0.157690\pi\) | ||||
0.879779 | + | 0.475382i | \(0.157690\pi\) | |||||||
\(662\) | −1.12307e8 | −0.0150454 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.99120e9 | 0.396513 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.20713e10 | −1.57513 | ||||||||
\(668\) | −2.76498e9 | −0.358900 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.23617e8 | −0.0413526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.31771e10 | −1.66636 | −0.833179 | − | 0.553003i | \(-0.813482\pi\) | ||||
−0.833179 | + | 0.553003i | \(0.813482\pi\) | |||||||
\(674\) | 3.89942e8 | 0.0490558 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.61201e9 | 0.200703 | ||||||||
\(677\) | −3.18151e9 | −0.394069 | −0.197035 | − | 0.980397i | \(-0.563131\pi\) | ||||
−0.197035 | + | 0.980397i | \(0.563131\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.39500e9 | 0.171013 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.77051e8 | 0.0334438 | ||||||||
\(683\) | −3.33139e8 | −0.0400086 | −0.0200043 | − | 0.999800i | \(-0.506368\pi\) | ||||
−0.0200043 | + | 0.999800i | \(0.506368\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.36731e8 | −0.110785 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.59789e9 | 0.304132 | ||||||||
\(689\) | 5.16275e9 | 0.601331 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.45248e9 | −0.513368 | −0.256684 | − | 0.966495i | \(-0.582630\pi\) | ||||
−0.256684 | + | 0.966495i | \(0.582630\pi\) | |||||||
\(692\) | 1.21594e10 | 1.39489 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.04339e8 | 0.0459185 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.10046e9 | 0.234963 | ||||||||
\(698\) | −6.71127e8 | −0.0746983 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.91380e9 | 0.209838 | 0.104919 | − | 0.994481i | \(-0.466542\pi\) | ||||
0.104919 | + | 0.994481i | \(0.466542\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.29902e9 | 0.683801 | ||||||||
\(704\) | −2.35400e9 | −0.254274 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.30785e8 | −0.0567679 | ||||||||
\(707\) | −1.98686e9 | −0.211445 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.38704e9 | 0.146160 | 0.0730799 | − | 0.997326i | \(-0.476717\pi\) | ||||
0.0730799 | + | 0.997326i | \(0.476717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.91344e7 | 0.00821647 | ||||||||
\(713\) | −1.04049e10 | −1.07504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.06995e10 | 1.08935 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.18970e8 | 0.0321599 | ||||||||
\(719\) | −9.42958e9 | −0.946109 | −0.473055 | − | 0.881033i | \(-0.656849\pi\) | ||||
−0.473055 | + | 0.881033i | \(0.656849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.67264e9 | −0.464290 | ||||||||
\(722\) | −5.15928e8 | −0.0510163 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.21965e10 | 1.19440 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.99387e9 | 0.288976 | 0.144488 | − | 0.989507i | \(-0.453846\pi\) | ||||
0.144488 | + | 0.989507i | \(0.453846\pi\) | |||||||
\(728\) | 1.24104e9 | 0.119213 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.52070e8 | −0.0522737 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.11711e10 | −1.04768 | −0.523842 | − | 0.851815i | \(-0.675502\pi\) | ||||
−0.523842 | + | 0.851815i | \(0.675502\pi\) | |||||||
\(734\) | −1.87053e9 | −0.174594 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.62471e9 | −0.335121 | ||||||||
\(737\) | −3.58495e9 | −0.329873 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.96449e9 | −0.634796 | −0.317398 | − | 0.948292i | \(-0.602809\pi\) | ||||
−0.317398 | + | 0.948292i | \(0.602809\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.03887e8 | −0.0452814 | ||||||||
\(743\) | 1.27161e9 | 0.113734 | 0.0568672 | − | 0.998382i | \(-0.481889\pi\) | ||||
0.0568672 | + | 0.998382i | \(0.481889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.06666e8 | −0.0711390 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.14063e8 | 0.0449119 | ||||||||
\(749\) | 8.18695e9 | 0.711927 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.70771e10 | −1.47121 | −0.735603 | − | 0.677413i | \(-0.763101\pi\) | ||||
−0.735603 | + | 0.677413i | \(0.763101\pi\) | |||||||
\(752\) | −7.07976e9 | −0.607094 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.87027e9 | −0.158893 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.37933e10 | −1.15567 | −0.577833 | − | 0.816155i | \(-0.696101\pi\) | ||||
−0.577833 | + | 0.816155i | \(0.696101\pi\) | |||||||
\(758\) | 1.09584e8 | 0.00913917 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.71364e10 | −1.40953 | −0.704765 | − | 0.709441i | \(-0.748947\pi\) | ||||
−0.704765 | + | 0.709441i | \(0.748947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.65654e8 | −0.0705518 | ||||||||
\(764\) | −1.85070e10 | −1.50145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.69780e8 | −0.0779602 | ||||||||
\(767\) | 1.00543e10 | 0.804575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.41529e9 | −0.350120 | −0.175060 | − | 0.984558i | \(-0.556012\pi\) | ||||
−0.175060 | + | 0.984558i | \(0.556012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.07816e10 | −0.843381 | ||||||||
\(773\) | −5.87300e8 | −0.0457332 | −0.0228666 | − | 0.999739i | \(-0.507279\pi\) | ||||
−0.0228666 | + | 0.999739i | \(0.507279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.45338e8 | −0.0649403 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.83146e9 | −0.139434 | ||||||||
\(779\) | −1.39082e10 | −1.05412 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.11929e9 | −0.0840746 | ||||||||
\(782\) | 2.51195e8 | 0.0187840 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.41160e9 | −0.623408 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.30069e10 | 1.68247 | 0.841235 | − | 0.540670i | \(-0.181829\pi\) | ||||
0.841235 | + | 0.540670i | \(0.181829\pi\) | |||||||
\(788\) | −1.82967e10 | −1.33208 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.41420e10 | −1.01600 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.88303e9 | 0.134092 | ||||||||
\(794\) | 2.14323e8 | 0.0151949 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.60308e9 | −0.112658 | ||||||||
\(797\) | 2.49526e10 | 1.74587 | 0.872935 | − | 0.487836i | \(-0.162213\pi\) | ||||
0.872935 | + | 0.487836i | \(0.162213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.50450e9 | 0.104346 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.97536e9 | −0.203671 | ||||||||
\(803\) | −5.17223e9 | −0.352512 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.61208e9 | −0.108446 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.20399e9 | 0.0802942 | ||||||||
\(809\) | 1.29758e10 | 0.861616 | 0.430808 | − | 0.902443i | \(-0.358229\pi\) | ||||
0.430808 | + | 0.902443i | \(0.358229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.04887e10 | −1.34878 | −0.674391 | − | 0.738374i | \(-0.735594\pi\) | ||||
−0.674391 | + | 0.738374i | \(0.735594\pi\) | |||||||
\(812\) | −1.40294e10 | −0.919587 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.42679e8 | 0.0287676 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.65554e9 | 0.234517 | ||||||||
\(818\) | −1.05748e9 | −0.0675514 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.97556e9 | 0.502991 | 0.251495 | − | 0.967858i | \(-0.419078\pi\) | ||||
0.251495 | + | 0.967858i | \(0.419078\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.64462e9 | −0.352968 | −0.176484 | − | 0.984304i | \(-0.556472\pi\) | ||||
−0.176484 | + | 0.984304i | \(0.556472\pi\) | |||||||
\(824\) | 2.83152e9 | 0.176309 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.81302e8 | −0.0605860 | ||||||||
\(827\) | 1.22946e10 | 0.755866 | 0.377933 | − | 0.925833i | \(-0.376635\pi\) | ||||
0.377933 | + | 0.925833i | \(0.376635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.72844e10 | −1.05369 | −0.526845 | − | 0.849962i | \(-0.676625\pi\) | ||||
−0.526845 | + | 0.849962i | \(0.676625\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.36973e10 | 0.824521 | ||||||||
\(833\) | 1.78752e9 | 0.107150 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.40388e9 | −0.201489 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.05649e9 | −0.0620173 | ||||||||
\(839\) | 4.87580e9 | 0.285023 | 0.142511 | − | 0.989793i | \(-0.454482\pi\) | ||||
0.142511 | + | 0.989793i | \(0.454482\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.53104e10 | 1.46728 | ||||||||
\(842\) | −2.71885e8 | −0.0156962 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.19701e10 | 0.685329 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.69328e9 | −0.548124 | ||||||||
\(848\) | −1.15044e10 | −0.647857 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.66252e10 | −0.924727 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.67542e10 | 0.924277 | 0.462138 | − | 0.886808i | \(-0.347082\pi\) | ||||
0.462138 | + | 0.886808i | \(0.347082\pi\) | |||||||
\(854\) | −1.83785e8 | −0.0100974 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.96112e9 | −0.270347 | ||||||||
\(857\) | −1.45198e10 | −0.788001 | −0.394001 | − | 0.919110i | \(-0.628909\pi\) | ||||
−0.394001 | + | 0.919110i | \(0.628909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.44108e10 | 1.31403 | 0.657016 | − | 0.753877i | \(-0.271819\pi\) | ||||
0.657016 | + | 0.753877i | \(0.271819\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.53988e8 | −0.0507303 | ||||||||
\(863\) | −2.03914e10 | −1.07996 | −0.539981 | − | 0.841677i | \(-0.681569\pi\) | ||||
−0.539981 | + | 0.841677i | \(0.681569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.48200e9 | 0.129864 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.20927e10 | −0.627629 | ||||||||
\(869\) | 7.63764e9 | 0.394812 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.08597e10 | 1.06966 | ||||||||
\(872\) | 5.24568e8 | 0.0267913 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.66330e9 | −0.0842713 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.75418e10 | 1.87939 | 0.939693 | − | 0.342018i | \(-0.111110\pi\) | ||||
0.939693 | + | 0.342018i | \(0.111110\pi\) | |||||||
\(878\) | −1.73719e9 | −0.0866194 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.05852e10 | −0.521533 | −0.260767 | − | 0.965402i | \(-0.583975\pi\) | ||||
−0.260767 | + | 0.965402i | \(0.583975\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.45129e10 | −1.68702 | −0.843509 | − | 0.537116i | \(-0.819514\pi\) | ||||
−0.843509 | + | 0.537116i | \(0.819514\pi\) | |||||||
\(884\) | −2.99118e9 | −0.145633 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.35894e9 | 0.0656420 | ||||||||
\(887\) | 1.68685e10 | 0.811602 | 0.405801 | − | 0.913961i | \(-0.366993\pi\) | ||||
0.405801 | + | 0.913961i | \(0.366993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.03261e10 | 0.492922 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.88792e10 | −1.36241 | ||||||||
\(893\) | −9.96206e9 | −0.468133 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.60434e9 | −0.260283 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.18323e9 | 0.100608 | ||||||||
\(899\) | 3.66849e10 | 1.68395 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.44477e9 | 0.111353 | ||||||||
\(902\) | −9.77434e8 | −0.0443470 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.56974e9 | 0.385814 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.14713e10 | 0.510492 | 0.255246 | − | 0.966876i | \(-0.417844\pi\) | ||||
0.255246 | + | 0.966876i | \(0.417844\pi\) | |||||||
\(908\) | 3.79810e10 | 1.68370 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.62306e10 | −0.711248 | −0.355624 | − | 0.934629i | \(-0.615732\pi\) | ||||
−0.355624 | + | 0.934629i | \(0.615732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.11446e10 | −0.484639 | ||||||||
\(914\) | 4.82661e9 | 0.209089 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.33107e10 | 0.572224 | ||||||||
\(917\) | −1.65236e10 | −0.707641 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.36259e10 | −1.85413 | −0.927065 | − | 0.374900i | \(-0.877677\pi\) | ||||
−0.927065 | + | 0.374900i | \(0.877677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.60419e9 | −0.193462 | ||||||||
\(923\) | 6.51283e9 | 0.272624 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.14972e8 | 0.0130357 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.27797e10 | 0.524934 | ||||||||
\(929\) | −1.67801e10 | −0.686656 | −0.343328 | − | 0.939216i | \(-0.611554\pi\) | ||||
−0.343328 | + | 0.939216i | \(0.611554\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.18361e10 | −0.480713 | ||||||||
\(932\) | −4.13432e10 | −1.67282 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.19273e8 | −0.0208536 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.94934e10 | −0.774105 | −0.387053 | − | 0.922058i | \(-0.626507\pi\) | ||||
−0.387053 | + | 0.922058i | \(0.626507\pi\) | |||||||
\(938\) | −2.03592e9 | −0.0805474 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.91523e10 | 1.92300 | 0.961502 | − | 0.274797i | \(-0.0886108\pi\) | ||||
0.961502 | + | 0.274797i | \(0.0886108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.67084e10 | 1.42552 | ||||||||
\(944\) | −2.24045e10 | −0.866827 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.56902e8 | 0.00986617 | ||||||||
\(947\) | 3.01570e10 | 1.15389 | 0.576944 | − | 0.816784i | \(-0.304245\pi\) | ||||
0.576944 | + | 0.816784i | \(0.304245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.00957e10 | 1.14307 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.87681e8 | 0.0220756 | ||||||||
\(953\) | −1.86916e10 | −0.699554 | −0.349777 | − | 0.936833i | \(-0.613743\pi\) | ||||
−0.349777 | + | 0.936833i | \(0.613743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.23879e9 | −0.267956 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.36388e9 | −0.197106 | ||||||||
\(959\) | −1.70526e10 | −0.624346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.10799e9 | 0.149313 | ||||||||
\(962\) | −2.57582e9 | −0.0932830 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.59213e10 | −1.29146 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.61328e9 | 0.270757 | 0.135378 | − | 0.990794i | \(-0.456775\pi\) | ||||
0.135378 | + | 0.990794i | \(0.456775\pi\) | |||||||
\(968\) | 5.87392e9 | 0.208144 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.83242e10 | 1.69394 | 0.846969 | − | 0.531643i | \(-0.178425\pi\) | ||||
0.846969 | + | 0.531643i | \(0.178425\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.11720e10 | 0.388807 | ||||||||
\(974\) | −4.16829e9 | −0.144545 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.19606e9 | −0.144467 | ||||||||
\(977\) | 1.42491e9 | 0.0488829 | 0.0244414 | − | 0.999701i | \(-0.492219\pi\) | ||||
0.0244414 | + | 0.999701i | \(0.492219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.94840e8 | −0.0100426 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.32564e9 | 0.145767 | ||||||||
\(983\) | 4.85675e10 | 1.63083 | 0.815415 | − | 0.578877i | \(-0.196509\pi\) | ||||
0.815415 | + | 0.578877i | \(0.196509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.85647e8 | −0.0294233 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.98062e10 | 0.653358 | ||||||||
\(989\) | −9.64818e9 | −0.317145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.69341e10 | −0.552719 | −0.276360 | − | 0.961054i | \(-0.589128\pi\) | ||||
−0.276360 | + | 0.961054i | \(0.589128\pi\) | |||||||
\(992\) | 1.10155e10 | 0.358273 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.35656e8 | −0.0205291 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.36849e10 | −0.756900 | −0.378450 | − | 0.925622i | \(-0.623543\pi\) | ||||
−0.378450 | + | 0.925622i | \(0.623543\pi\) | |||||||
\(998\) | 4.80763e9 | 0.153100 | ||||||||
\(999\) | 0 | 0 |
(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 | 225.8.a.w.1.1 | 2 | ||
3.2 | odd | 2 | 25.8.a.b.1.2 | 2 | |||
5.2 | odd | 4 | 225.8.b.m.199.3 | 4 | |||
5.3 | odd | 4 | 225.8.b.m.199.2 | 4 | |||
5.4 | even | 2 | 45.8.a.h.1.2 | 2 | |||
12.11 | even | 2 | 400.8.a.bb.1.2 | 2 | |||
15.2 | even | 4 | 25.8.b.c.24.2 | 4 | |||
15.8 | even | 4 | 25.8.b.c.24.3 | 4 | |||
15.14 | odd | 2 | 5.8.a.b.1.1 | ✓ | 2 | ||
60.23 | odd | 4 | 400.8.c.m.49.4 | 4 | |||
60.47 | odd | 4 | 400.8.c.m.49.1 | 4 | |||
60.59 | even | 2 | 80.8.a.g.1.1 | 2 | |||
105.104 | even | 2 | 245.8.a.c.1.1 | 2 | |||
120.29 | odd | 2 | 320.8.a.l.1.1 | 2 | |||
120.59 | even | 2 | 320.8.a.u.1.2 | 2 | |||
165.164 | even | 2 | 605.8.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.8.a.b.1.1 | ✓ | 2 | 15.14 | odd | 2 | ||
25.8.a.b.1.2 | 2 | 3.2 | odd | 2 | |||
25.8.b.c.24.2 | 4 | 15.2 | even | 4 | |||
25.8.b.c.24.3 | 4 | 15.8 | even | 4 | |||
45.8.a.h.1.2 | 2 | 5.4 | even | 2 | |||
80.8.a.g.1.1 | 2 | 60.59 | even | 2 | |||
225.8.a.w.1.1 | 2 | 1.1 | even | 1 | trivial | ||
225.8.b.m.199.2 | 4 | 5.3 | odd | 4 | |||
225.8.b.m.199.3 | 4 | 5.2 | odd | 4 | |||
245.8.a.c.1.1 | 2 | 105.104 | even | 2 | |||
320.8.a.l.1.1 | 2 | 120.29 | odd | 2 | |||
320.8.a.u.1.2 | 2 | 120.59 | even | 2 | |||
400.8.a.bb.1.2 | 2 | 12.11 | even | 2 | |||
400.8.c.m.49.1 | 4 | 60.47 | odd | 4 | |||
400.8.c.m.49.4 | 4 | 60.23 | odd | 4 | |||
605.8.a.d.1.2 | 2 | 165.164 | even | 2 |