Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,8,Mod(1,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(3.43623528033\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{15}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 15 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.87298\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 11.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.74597 | 0.331100 | 0.165550 | − | 0.986201i | \(-0.447060\pi\) | ||||
0.165550 | + | 0.986201i | \(0.447060\pi\) | |||||||
\(3\) | −49.4758 | −1.05796 | −0.528979 | − | 0.848635i | \(-0.677425\pi\) | ||||
−0.528979 | + | 0.848635i | \(0.677425\pi\) | |||||||
\(4\) | −113.968 | −0.890373 | ||||||||
\(5\) | −80.0807 | −0.286505 | −0.143253 | − | 0.989686i | \(-0.545756\pi\) | ||||
−0.143253 | + | 0.989686i | \(0.545756\pi\) | |||||||
\(6\) | −185.335 | −0.350290 | ||||||||
\(7\) | 21.1693 | 0.0233272 | 0.0116636 | − | 0.999932i | \(-0.496287\pi\) | ||||
0.0116636 | + | 0.999932i | \(0.496287\pi\) | |||||||
\(8\) | −906.403 | −0.625902 | ||||||||
\(9\) | 260.855 | 0.119275 | ||||||||
\(10\) | −299.980 | −0.0948618 | ||||||||
\(11\) | 1331.00 | 0.301511 | ||||||||
\(12\) | 5638.64 | 0.941977 | ||||||||
\(13\) | 4184.41 | 0.528242 | 0.264121 | − | 0.964490i | \(-0.414918\pi\) | ||||
0.264121 | + | 0.964490i | \(0.414918\pi\) | |||||||
\(14\) | 79.2994 | 0.00772363 | ||||||||
\(15\) | 3962.06 | 0.303111 | ||||||||
\(16\) | 11192.5 | 0.683137 | ||||||||
\(17\) | −32630.7 | −1.61085 | −0.805425 | − | 0.592697i | \(-0.798063\pi\) | ||||
−0.805425 | + | 0.592697i | \(0.798063\pi\) | |||||||
\(18\) | 977.153 | 0.0394920 | ||||||||
\(19\) | −40738.5 | −1.36260 | −0.681298 | − | 0.732006i | \(-0.738584\pi\) | ||||
−0.681298 | + | 0.732006i | \(0.738584\pi\) | |||||||
\(20\) | 9126.61 | 0.255097 | ||||||||
\(21\) | −1047.37 | −0.0246792 | ||||||||
\(22\) | 4985.88 | 0.0998303 | ||||||||
\(23\) | 2487.20 | 0.0426248 | 0.0213124 | − | 0.999773i | \(-0.493216\pi\) | ||||
0.0213124 | + | 0.999773i | \(0.493216\pi\) | |||||||
\(24\) | 44845.0 | 0.662178 | ||||||||
\(25\) | −71712.1 | −0.917915 | ||||||||
\(26\) | 15674.7 | 0.174901 | ||||||||
\(27\) | 95297.6 | 0.931770 | ||||||||
\(28\) | −2412.61 | −0.0207699 | ||||||||
\(29\) | 689.254 | 0.00524791 | 0.00262395 | − | 0.999997i | \(-0.499165\pi\) | ||||
0.00262395 | + | 0.999997i | \(0.499165\pi\) | |||||||
\(30\) | 14841.7 | 0.100360 | ||||||||
\(31\) | 127963. | 0.771469 | 0.385734 | − | 0.922610i | \(-0.373948\pi\) | ||||
0.385734 | + | 0.922610i | \(0.373948\pi\) | |||||||
\(32\) | 157946. | 0.852089 | ||||||||
\(33\) | −65852.3 | −0.318986 | ||||||||
\(34\) | −122234. | −0.533352 | ||||||||
\(35\) | −1695.25 | −0.00668337 | ||||||||
\(36\) | −29729.0 | −0.106199 | ||||||||
\(37\) | −467881. | −1.51855 | −0.759275 | − | 0.650770i | \(-0.774446\pi\) | ||||
−0.759275 | + | 0.650770i | \(0.774446\pi\) | |||||||
\(38\) | −152605. | −0.451155 | ||||||||
\(39\) | −207027. | −0.558857 | ||||||||
\(40\) | 72585.4 | 0.179324 | ||||||||
\(41\) | 391657. | 0.887487 | 0.443744 | − | 0.896154i | \(-0.353650\pi\) | ||||
0.443744 | + | 0.896154i | \(0.353650\pi\) | |||||||
\(42\) | −3923.40 | −0.00817128 | ||||||||
\(43\) | 236581. | 0.453774 | 0.226887 | − | 0.973921i | \(-0.427145\pi\) | ||||
0.226887 | + | 0.973921i | \(0.427145\pi\) | |||||||
\(44\) | −151691. | −0.268458 | ||||||||
\(45\) | −20889.4 | −0.0341730 | ||||||||
\(46\) | 9316.96 | 0.0141131 | ||||||||
\(47\) | 713115. | 1.00188 | 0.500941 | − | 0.865481i | \(-0.332987\pi\) | ||||
0.500941 | + | 0.865481i | \(0.332987\pi\) | |||||||
\(48\) | −553759. | −0.722730 | ||||||||
\(49\) | −823095. | −0.999456 | ||||||||
\(50\) | −268631. | −0.303921 | ||||||||
\(51\) | 1.61443e6 | 1.70421 | ||||||||
\(52\) | −476888. | −0.470332 | ||||||||
\(53\) | 1.32248e6 | 1.22018 | 0.610090 | − | 0.792332i | \(-0.291133\pi\) | ||||
0.610090 | + | 0.792332i | \(0.291133\pi\) | |||||||
\(54\) | 356982. | 0.308509 | ||||||||
\(55\) | −106587. | −0.0863846 | ||||||||
\(56\) | −19187.9 | −0.0146005 | ||||||||
\(57\) | 2.01557e6 | 1.44157 | ||||||||
\(58\) | 2581.92 | 0.00173758 | ||||||||
\(59\) | −2.36633e6 | −1.50000 | −0.750002 | − | 0.661435i | \(-0.769948\pi\) | ||||
−0.750002 | + | 0.661435i | \(0.769948\pi\) | |||||||
\(60\) | −451546. | −0.269881 | ||||||||
\(61\) | −3.23345e6 | −1.82394 | −0.911971 | − | 0.410254i | \(-0.865440\pi\) | ||||
−0.911971 | + | 0.410254i | \(0.865440\pi\) | |||||||
\(62\) | 479345. | 0.255433 | ||||||||
\(63\) | 5522.11 | 0.00278236 | ||||||||
\(64\) | −840980. | −0.401010 | ||||||||
\(65\) | −335090. | −0.151344 | ||||||||
\(66\) | −246680. | −0.105616 | ||||||||
\(67\) | −3.12834e6 | −1.27073 | −0.635363 | − | 0.772214i | \(-0.719149\pi\) | ||||
−0.635363 | + | 0.772214i | \(0.719149\pi\) | |||||||
\(68\) | 3.71885e6 | 1.43426 | ||||||||
\(69\) | −123056. | −0.0450953 | ||||||||
\(70\) | −6350.35 | −0.00221286 | ||||||||
\(71\) | 2.93234e6 | 0.972321 | 0.486161 | − | 0.873869i | \(-0.338397\pi\) | ||||
0.486161 | + | 0.873869i | \(0.338397\pi\) | |||||||
\(72\) | −236440. | −0.0746546 | ||||||||
\(73\) | −1.06930e6 | −0.321715 | −0.160857 | − | 0.986978i | \(-0.551426\pi\) | ||||
−0.160857 | + | 0.986978i | \(0.551426\pi\) | |||||||
\(74\) | −1.75267e6 | −0.502792 | ||||||||
\(75\) | 3.54801e6 | 0.971115 | ||||||||
\(76\) | 4.64287e6 | 1.21322 | ||||||||
\(77\) | 28176.3 | 0.00703342 | ||||||||
\(78\) | −775517. | −0.185038 | ||||||||
\(79\) | 4.40962e6 | 1.00625 | 0.503125 | − | 0.864214i | \(-0.332183\pi\) | ||||
0.503125 | + | 0.864214i | \(0.332183\pi\) | |||||||
\(80\) | −896304. | −0.195722 | ||||||||
\(81\) | −5.28541e6 | −1.10505 | ||||||||
\(82\) | 1.46713e6 | 0.293847 | ||||||||
\(83\) | −2.49753e6 | −0.479443 | −0.239722 | − | 0.970842i | \(-0.577056\pi\) | ||||
−0.239722 | + | 0.970842i | \(0.577056\pi\) | |||||||
\(84\) | 119366. | 0.0219737 | ||||||||
\(85\) | 2.61309e6 | 0.461517 | ||||||||
\(86\) | 886223. | 0.150244 | ||||||||
\(87\) | −34101.4 | −0.00555207 | ||||||||
\(88\) | −1.20642e6 | −0.188717 | ||||||||
\(89\) | −5.17831e6 | −0.778616 | −0.389308 | − | 0.921108i | \(-0.627286\pi\) | ||||
−0.389308 | + | 0.921108i | \(0.627286\pi\) | |||||||
\(90\) | −78251.1 | −0.0113147 | ||||||||
\(91\) | 88580.9 | 0.0123224 | ||||||||
\(92\) | −283460. | −0.0379520 | ||||||||
\(93\) | −6.33107e6 | −0.816182 | ||||||||
\(94\) | 2.67130e6 | 0.331723 | ||||||||
\(95\) | 3.26236e6 | 0.390391 | ||||||||
\(96\) | −7.81452e6 | −0.901474 | ||||||||
\(97\) | 1.32101e6 | 0.146962 | 0.0734810 | − | 0.997297i | \(-0.476589\pi\) | ||||
0.0734810 | + | 0.997297i | \(0.476589\pi\) | |||||||
\(98\) | −3.08329e6 | −0.330920 | ||||||||
\(99\) | 347198. | 0.0359628 | ||||||||
\(100\) | 8.17286e6 | 0.817286 | ||||||||
\(101\) | −1.71975e7 | −1.66089 | −0.830447 | − | 0.557098i | \(-0.811915\pi\) | ||||
−0.830447 | + | 0.557098i | \(0.811915\pi\) | |||||||
\(102\) | 6.04760e6 | 0.564264 | ||||||||
\(103\) | 4.02516e6 | 0.362955 | 0.181477 | − | 0.983395i | \(-0.441912\pi\) | ||||
0.181477 | + | 0.983395i | \(0.441912\pi\) | |||||||
\(104\) | −3.79276e6 | −0.330628 | ||||||||
\(105\) | 83873.8 | 0.00707072 | ||||||||
\(106\) | 4.95397e6 | 0.404001 | ||||||||
\(107\) | 2.17827e7 | 1.71897 | 0.859486 | − | 0.511160i | \(-0.170784\pi\) | ||||
0.859486 | + | 0.511160i | \(0.170784\pi\) | |||||||
\(108\) | −1.08608e7 | −0.829623 | ||||||||
\(109\) | −2.69177e6 | −0.199088 | −0.0995439 | − | 0.995033i | \(-0.531738\pi\) | ||||
−0.0995439 | + | 0.995033i | \(0.531738\pi\) | |||||||
\(110\) | −399273. | −0.0286019 | ||||||||
\(111\) | 2.31488e7 | 1.60656 | ||||||||
\(112\) | 236937. | 0.0159357 | ||||||||
\(113\) | −598776. | −0.0390382 | −0.0195191 | − | 0.999809i | \(-0.506214\pi\) | ||||
−0.0195191 | + | 0.999809i | \(0.506214\pi\) | |||||||
\(114\) | 7.55025e6 | 0.477303 | ||||||||
\(115\) | −199176. | −0.0122122 | ||||||||
\(116\) | −78552.7 | −0.00467260 | ||||||||
\(117\) | 1.09152e6 | 0.0630061 | ||||||||
\(118\) | −8.86418e6 | −0.496651 | ||||||||
\(119\) | −690768. | −0.0375767 | ||||||||
\(120\) | −3.59122e6 | −0.189718 | ||||||||
\(121\) | 1.77156e6 | 0.0909091 | ||||||||
\(122\) | −1.21124e7 | −0.603907 | ||||||||
\(123\) | −1.93775e7 | −0.938924 | ||||||||
\(124\) | −1.45837e7 | −0.686895 | ||||||||
\(125\) | 1.19991e7 | 0.549493 | ||||||||
\(126\) | 20685.6 | 0.000921238 0 | ||||||||
\(127\) | 3.59136e7 | 1.55577 | 0.777886 | − | 0.628405i | \(-0.216292\pi\) | ||||
0.777886 | + | 0.628405i | \(0.216292\pi\) | |||||||
\(128\) | −2.33674e7 | −0.984863 | ||||||||
\(129\) | −1.17050e7 | −0.480074 | ||||||||
\(130\) | −1.25524e6 | −0.0501100 | ||||||||
\(131\) | −1.65324e7 | −0.642521 | −0.321261 | − | 0.946991i | \(-0.604107\pi\) | ||||
−0.321261 | + | 0.946991i | \(0.604107\pi\) | |||||||
\(132\) | 7.50504e6 | 0.284017 | ||||||||
\(133\) | −862404. | −0.0317856 | ||||||||
\(134\) | −1.17187e7 | −0.420737 | ||||||||
\(135\) | −7.63149e6 | −0.266957 | ||||||||
\(136\) | 2.95766e7 | 1.00823 | ||||||||
\(137\) | 2.77432e7 | 0.921797 | 0.460899 | − | 0.887453i | \(-0.347527\pi\) | ||||
0.460899 | + | 0.887453i | \(0.347527\pi\) | |||||||
\(138\) | −460964. | −0.0149310 | ||||||||
\(139\) | −5.04731e7 | −1.59407 | −0.797037 | − | 0.603930i | \(-0.793601\pi\) | ||||
−0.797037 | + | 0.603930i | \(0.793601\pi\) | |||||||
\(140\) | 193204. | 0.00595069 | ||||||||
\(141\) | −3.52819e7 | −1.05995 | ||||||||
\(142\) | 1.09844e7 | 0.321935 | ||||||||
\(143\) | 5.56945e6 | 0.159271 | ||||||||
\(144\) | 2.91962e6 | 0.0814813 | ||||||||
\(145\) | −55195.9 | −0.00150355 | ||||||||
\(146\) | −4.00558e6 | −0.106520 | ||||||||
\(147\) | 4.07233e7 | 1.05738 | ||||||||
\(148\) | 5.33233e7 | 1.35208 | ||||||||
\(149\) | 3.09903e7 | 0.767492 | 0.383746 | − | 0.923439i | \(-0.374634\pi\) | ||||
0.383746 | + | 0.923439i | \(0.374634\pi\) | |||||||
\(150\) | 1.32907e7 | 0.321536 | ||||||||
\(151\) | −6.75757e6 | −0.159724 | −0.0798622 | − | 0.996806i | \(-0.525448\pi\) | ||||
−0.0798622 | + | 0.996806i | \(0.525448\pi\) | |||||||
\(152\) | 3.69255e7 | 0.852852 | ||||||||
\(153\) | −8.51188e6 | −0.192135 | ||||||||
\(154\) | 105547. | 0.00232876 | ||||||||
\(155\) | −1.02474e7 | −0.221030 | ||||||||
\(156\) | 2.35944e7 | 0.497591 | ||||||||
\(157\) | 1.89989e7 | 0.391813 | 0.195907 | − | 0.980623i | \(-0.437235\pi\) | ||||
0.195907 | + | 0.980623i | \(0.437235\pi\) | |||||||
\(158\) | 1.65183e7 | 0.333169 | ||||||||
\(159\) | −6.54308e7 | −1.29090 | ||||||||
\(160\) | −1.26485e7 | −0.244128 | ||||||||
\(161\) | 52652.1 | 0.000994318 0 | ||||||||
\(162\) | −1.97990e7 | −0.365881 | ||||||||
\(163\) | −6.97589e7 | −1.26166 | −0.630831 | − | 0.775921i | \(-0.717286\pi\) | ||||
−0.630831 | + | 0.775921i | \(0.717286\pi\) | |||||||
\(164\) | −4.46362e7 | −0.790195 | ||||||||
\(165\) | 5.27350e6 | 0.0913913 | ||||||||
\(166\) | −9.35566e6 | −0.158744 | ||||||||
\(167\) | −2.42233e7 | −0.402463 | −0.201231 | − | 0.979544i | \(-0.564494\pi\) | ||||
−0.201231 | + | 0.979544i | \(0.564494\pi\) | |||||||
\(168\) | 949336. | 0.0154468 | ||||||||
\(169\) | −4.52392e7 | −0.720961 | ||||||||
\(170\) | 9.78855e6 | 0.152808 | ||||||||
\(171\) | −1.06268e7 | −0.162524 | ||||||||
\(172\) | −2.69625e7 | −0.404028 | ||||||||
\(173\) | 6.00438e7 | 0.881671 | 0.440836 | − | 0.897588i | \(-0.354682\pi\) | ||||
0.440836 | + | 0.897588i | \(0.354682\pi\) | |||||||
\(174\) | −127743. | −0.00183829 | ||||||||
\(175\) | −1.51809e6 | −0.0214124 | ||||||||
\(176\) | 1.48972e7 | 0.205974 | ||||||||
\(177\) | 1.17076e8 | 1.58694 | ||||||||
\(178\) | −1.93978e7 | −0.257800 | ||||||||
\(179\) | 1.82943e6 | 0.0238413 | 0.0119206 | − | 0.999929i | \(-0.496205\pi\) | ||||
0.0119206 | + | 0.999929i | \(0.496205\pi\) | |||||||
\(180\) | 2.38072e6 | 0.0304267 | ||||||||
\(181\) | −1.24476e8 | −1.56030 | −0.780152 | − | 0.625590i | \(-0.784858\pi\) | ||||
−0.780152 | + | 0.625590i | \(0.784858\pi\) | |||||||
\(182\) | 331821. | 0.00407994 | ||||||||
\(183\) | 1.59977e8 | 1.92966 | ||||||||
\(184\) | −2.25440e6 | −0.0266790 | ||||||||
\(185\) | 3.74682e7 | 0.435073 | ||||||||
\(186\) | −2.37160e7 | −0.270238 | ||||||||
\(187\) | −4.34315e7 | −0.485690 | ||||||||
\(188\) | −8.12720e7 | −0.892049 | ||||||||
\(189\) | 2.01738e6 | 0.0217356 | ||||||||
\(190\) | 1.22207e7 | 0.129258 | ||||||||
\(191\) | −7.76142e7 | −0.805980 | −0.402990 | − | 0.915204i | \(-0.632029\pi\) | ||||
−0.402990 | + | 0.915204i | \(0.632029\pi\) | |||||||
\(192\) | 4.16082e7 | 0.424252 | ||||||||
\(193\) | 3.85250e7 | 0.385738 | 0.192869 | − | 0.981225i | \(-0.438221\pi\) | ||||
0.192869 | + | 0.981225i | \(0.438221\pi\) | |||||||
\(194\) | 4.94846e6 | 0.0486591 | ||||||||
\(195\) | 1.65789e7 | 0.160116 | ||||||||
\(196\) | 9.38063e7 | 0.889888 | ||||||||
\(197\) | 1.49067e8 | 1.38915 | 0.694575 | − | 0.719421i | \(-0.255593\pi\) | ||||
0.694575 | + | 0.719421i | \(0.255593\pi\) | |||||||
\(198\) | 1.30059e6 | 0.0119073 | ||||||||
\(199\) | −6.45185e7 | −0.580362 | −0.290181 | − | 0.956972i | \(-0.593715\pi\) | ||||
−0.290181 | + | 0.956972i | \(0.593715\pi\) | |||||||
\(200\) | 6.50001e7 | 0.574525 | ||||||||
\(201\) | 1.54777e8 | 1.34437 | ||||||||
\(202\) | −6.44214e7 | −0.549921 | ||||||||
\(203\) | 14591.0 | 0.000122419 0 | ||||||||
\(204\) | −1.83993e8 | −1.51738 | ||||||||
\(205\) | −3.13641e7 | −0.254270 | ||||||||
\(206\) | 1.50781e7 | 0.120174 | ||||||||
\(207\) | 648797. | 0.00508409 | ||||||||
\(208\) | 4.68341e7 | 0.360861 | ||||||||
\(209\) | −5.42229e7 | −0.410838 | ||||||||
\(210\) | 314188. | 0.00234111 | ||||||||
\(211\) | 3.55799e7 | 0.260745 | 0.130373 | − | 0.991465i | \(-0.458383\pi\) | ||||
0.130373 | + | 0.991465i | \(0.458383\pi\) | |||||||
\(212\) | −1.50720e8 | −1.08642 | ||||||||
\(213\) | −1.45080e8 | −1.02868 | ||||||||
\(214\) | 8.15973e7 | 0.569151 | ||||||||
\(215\) | −1.89455e7 | −0.130009 | ||||||||
\(216\) | −8.63780e7 | −0.583197 | ||||||||
\(217\) | 2.70888e6 | 0.0179962 | ||||||||
\(218\) | −1.00833e7 | −0.0659180 | ||||||||
\(219\) | 5.29047e7 | 0.340361 | ||||||||
\(220\) | 1.21475e7 | 0.0769145 | ||||||||
\(221\) | −1.36540e8 | −0.850918 | ||||||||
\(222\) | 8.67146e7 | 0.531933 | ||||||||
\(223\) | −1.55599e8 | −0.939590 | −0.469795 | − | 0.882776i | \(-0.655672\pi\) | ||||
−0.469795 | + | 0.882776i | \(0.655672\pi\) | |||||||
\(224\) | 3.34361e6 | 0.0198768 | ||||||||
\(225\) | −1.87064e7 | −0.109484 | ||||||||
\(226\) | −2.24300e6 | −0.0129255 | ||||||||
\(227\) | 1.39233e8 | 0.790046 | 0.395023 | − | 0.918671i | \(-0.370737\pi\) | ||||
0.395023 | + | 0.918671i | \(0.370737\pi\) | |||||||
\(228\) | −2.29710e8 | −1.28353 | ||||||||
\(229\) | 2.52955e8 | 1.39193 | 0.695966 | − | 0.718074i | \(-0.254976\pi\) | ||||
0.695966 | + | 0.718074i | \(0.254976\pi\) | |||||||
\(230\) | −746108. | −0.00404347 | ||||||||
\(231\) | −1.39404e6 | −0.00744106 | ||||||||
\(232\) | −624742. | −0.00328468 | ||||||||
\(233\) | 1.00338e8 | 0.519658 | 0.259829 | − | 0.965655i | \(-0.416334\pi\) | ||||
0.259829 | + | 0.965655i | \(0.416334\pi\) | |||||||
\(234\) | 4.08881e6 | 0.0208613 | ||||||||
\(235\) | −5.71067e7 | −0.287045 | ||||||||
\(236\) | 2.69685e8 | 1.33556 | ||||||||
\(237\) | −2.18169e8 | −1.06457 | ||||||||
\(238\) | −2.58760e6 | −0.0124416 | ||||||||
\(239\) | 7.53046e7 | 0.356803 | 0.178402 | − | 0.983958i | \(-0.442907\pi\) | ||||
0.178402 | + | 0.983958i | \(0.442907\pi\) | |||||||
\(240\) | 4.43454e7 | 0.207066 | ||||||||
\(241\) | 1.25802e8 | 0.578934 | 0.289467 | − | 0.957188i | \(-0.406522\pi\) | ||||
0.289467 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(242\) | 6.63621e6 | 0.0301000 | ||||||||
\(243\) | 5.30843e7 | 0.237325 | ||||||||
\(244\) | 3.68509e8 | 1.62399 | ||||||||
\(245\) | 6.59140e7 | 0.286349 | ||||||||
\(246\) | −7.25876e7 | −0.310878 | ||||||||
\(247\) | −1.70467e8 | −0.719780 | ||||||||
\(248\) | −1.15986e8 | −0.482864 | ||||||||
\(249\) | 1.23567e8 | 0.507231 | ||||||||
\(250\) | 4.49481e7 | 0.181937 | ||||||||
\(251\) | −1.64527e8 | −0.656718 | −0.328359 | − | 0.944553i | \(-0.606496\pi\) | ||||
−0.328359 | + | 0.944553i | \(0.606496\pi\) | |||||||
\(252\) | −629342. | −0.00247733 | ||||||||
\(253\) | 3.31046e6 | 0.0128519 | ||||||||
\(254\) | 1.34531e8 | 0.515116 | ||||||||
\(255\) | −1.29285e8 | −0.488266 | ||||||||
\(256\) | 2.01119e7 | 0.0749225 | ||||||||
\(257\) | −1.10435e8 | −0.405828 | −0.202914 | − | 0.979197i | \(-0.565041\pi\) | ||||
−0.202914 | + | 0.979197i | \(0.565041\pi\) | |||||||
\(258\) | −4.38466e7 | −0.158952 | ||||||||
\(259\) | −9.90470e6 | −0.0354235 | ||||||||
\(260\) | 3.81895e7 | 0.134753 | ||||||||
\(261\) | 179795. | 0.000625945 0 | ||||||||
\(262\) | −6.19300e7 | −0.212739 | ||||||||
\(263\) | −3.98541e8 | −1.35091 | −0.675457 | − | 0.737400i | \(-0.736053\pi\) | ||||
−0.675457 | + | 0.737400i | \(0.736053\pi\) | |||||||
\(264\) | 5.96887e7 | 0.199654 | ||||||||
\(265\) | −1.05905e8 | −0.349588 | ||||||||
\(266\) | −3.23054e6 | −0.0105242 | ||||||||
\(267\) | 2.56201e8 | 0.823743 | ||||||||
\(268\) | 3.56530e8 | 1.13142 | ||||||||
\(269\) | −2.99250e8 | −0.937350 | −0.468675 | − | 0.883371i | \(-0.655268\pi\) | ||||
−0.468675 | + | 0.883371i | \(0.655268\pi\) | |||||||
\(270\) | −2.85873e7 | −0.0883894 | ||||||||
\(271\) | −1.37158e7 | −0.0418628 | −0.0209314 | − | 0.999781i | \(-0.506663\pi\) | ||||
−0.0209314 | + | 0.999781i | \(0.506663\pi\) | |||||||
\(272\) | −3.65220e8 | −1.10043 | ||||||||
\(273\) | −4.38261e6 | −0.0130366 | ||||||||
\(274\) | 1.03925e8 | 0.305207 | ||||||||
\(275\) | −9.54488e7 | −0.276762 | ||||||||
\(276\) | 1.40244e7 | 0.0401516 | ||||||||
\(277\) | −6.73807e8 | −1.90483 | −0.952415 | − | 0.304804i | \(-0.901409\pi\) | ||||
−0.952415 | + | 0.304804i | \(0.901409\pi\) | |||||||
\(278\) | −1.89071e8 | −0.527798 | ||||||||
\(279\) | 3.33798e7 | 0.0920171 | ||||||||
\(280\) | 1.53658e6 | 0.00418313 | ||||||||
\(281\) | 5.66275e8 | 1.52249 | 0.761246 | − | 0.648463i | \(-0.224588\pi\) | ||||
0.761246 | + | 0.648463i | \(0.224588\pi\) | |||||||
\(282\) | −1.32165e8 | −0.350949 | ||||||||
\(283\) | 6.29800e8 | 1.65177 | 0.825886 | − | 0.563837i | \(-0.190675\pi\) | ||||
0.825886 | + | 0.563837i | \(0.190675\pi\) | |||||||
\(284\) | −3.34192e8 | −0.865729 | ||||||||
\(285\) | −1.61408e8 | −0.413017 | ||||||||
\(286\) | 2.08630e7 | 0.0527345 | ||||||||
\(287\) | 8.29109e6 | 0.0207026 | ||||||||
\(288\) | 4.12011e7 | 0.101633 | ||||||||
\(289\) | 6.54425e8 | 1.59484 | ||||||||
\(290\) | −206762. | −0.000497826 0 | ||||||||
\(291\) | −6.53580e7 | −0.155480 | ||||||||
\(292\) | 1.21866e8 | 0.286446 | ||||||||
\(293\) | −1.23830e6 | −0.00287600 | −0.00143800 | − | 0.999999i | \(-0.500458\pi\) | ||||
−0.00143800 | + | 0.999999i | \(0.500458\pi\) | |||||||
\(294\) | 1.52548e8 | 0.350099 | ||||||||
\(295\) | 1.89497e8 | 0.429759 | ||||||||
\(296\) | 4.24089e8 | 0.950464 | ||||||||
\(297\) | 1.26841e8 | 0.280939 | ||||||||
\(298\) | 1.16089e8 | 0.254116 | ||||||||
\(299\) | 1.04075e7 | 0.0225162 | ||||||||
\(300\) | −4.04359e8 | −0.864655 | ||||||||
\(301\) | 5.00824e6 | 0.0105853 | ||||||||
\(302\) | −2.53136e7 | −0.0528847 | ||||||||
\(303\) | 8.50862e8 | 1.75716 | ||||||||
\(304\) | −4.55966e8 | −0.930840 | ||||||||
\(305\) | 2.58937e8 | 0.522569 | ||||||||
\(306\) | −3.18852e7 | −0.0636157 | ||||||||
\(307\) | −4.88441e8 | −0.963447 | −0.481723 | − | 0.876323i | \(-0.659989\pi\) | ||||
−0.481723 | + | 0.876323i | \(0.659989\pi\) | |||||||
\(308\) | −3.21119e6 | −0.00626236 | ||||||||
\(309\) | −1.99148e8 | −0.383991 | ||||||||
\(310\) | −3.83863e7 | −0.0731830 | ||||||||
\(311\) | −4.81123e8 | −0.906974 | −0.453487 | − | 0.891263i | \(-0.649820\pi\) | ||||
−0.453487 | + | 0.891263i | \(0.649820\pi\) | |||||||
\(312\) | 1.87650e8 | 0.349790 | ||||||||
\(313\) | 5.17645e7 | 0.0954172 | 0.0477086 | − | 0.998861i | \(-0.484808\pi\) | ||||
0.0477086 | + | 0.998861i | \(0.484808\pi\) | |||||||
\(314\) | 7.11691e7 | 0.129729 | ||||||||
\(315\) | −442214. | −0.000797160 0 | ||||||||
\(316\) | −5.02554e8 | −0.895938 | ||||||||
\(317\) | −4.71412e8 | −0.831177 | −0.415588 | − | 0.909553i | \(-0.636424\pi\) | ||||
−0.415588 | + | 0.909553i | \(0.636424\pi\) | |||||||
\(318\) | −2.45102e8 | −0.427417 | ||||||||
\(319\) | 917397. | 0.00158230 | ||||||||
\(320\) | 6.73462e7 | 0.114892 | ||||||||
\(321\) | −1.07772e9 | −1.81860 | ||||||||
\(322\) | 197233. | 0.000329219 0 | ||||||||
\(323\) | 1.32933e9 | 2.19494 | ||||||||
\(324\) | 6.02367e8 | 0.983905 | ||||||||
\(325\) | −3.00073e8 | −0.484881 | ||||||||
\(326\) | −2.61314e8 | −0.417736 | ||||||||
\(327\) | 1.33177e8 | 0.210627 | ||||||||
\(328\) | −3.54999e8 | −0.555480 | ||||||||
\(329\) | 1.50961e7 | 0.0233711 | ||||||||
\(330\) | 1.97543e7 | 0.0302596 | ||||||||
\(331\) | 5.97269e8 | 0.905258 | 0.452629 | − | 0.891699i | \(-0.350486\pi\) | ||||
0.452629 | + | 0.891699i | \(0.350486\pi\) | |||||||
\(332\) | 2.84638e8 | 0.426883 | ||||||||
\(333\) | −1.22049e8 | −0.181125 | ||||||||
\(334\) | −9.07397e7 | −0.133255 | ||||||||
\(335\) | 2.50519e8 | 0.364070 | ||||||||
\(336\) | −1.17227e7 | −0.0168593 | ||||||||
\(337\) | −8.11952e8 | −1.15565 | −0.577824 | − | 0.816161i | \(-0.696098\pi\) | ||||
−0.577824 | + | 0.816161i | \(0.696098\pi\) | |||||||
\(338\) | −1.69465e8 | −0.238710 | ||||||||
\(339\) | 2.96249e7 | 0.0413008 | ||||||||
\(340\) | −2.97808e8 | −0.410923 | ||||||||
\(341\) | 1.70319e8 | 0.232607 | ||||||||
\(342\) | −3.98077e7 | −0.0538116 | ||||||||
\(343\) | −3.48581e7 | −0.0466417 | ||||||||
\(344\) | −2.14437e8 | −0.284018 | ||||||||
\(345\) | 9.85441e6 | 0.0129200 | ||||||||
\(346\) | 2.24922e8 | 0.291921 | ||||||||
\(347\) | −4.61385e8 | −0.592803 | −0.296401 | − | 0.955063i | \(-0.595787\pi\) | ||||
−0.296401 | + | 0.955063i | \(0.595787\pi\) | |||||||
\(348\) | 3.88646e6 | 0.00494341 | ||||||||
\(349\) | −9.00068e8 | −1.13341 | −0.566704 | − | 0.823922i | \(-0.691782\pi\) | ||||
−0.566704 | + | 0.823922i | \(0.691782\pi\) | |||||||
\(350\) | −5.68672e6 | −0.00708964 | ||||||||
\(351\) | 3.98764e8 | 0.492200 | ||||||||
\(352\) | 2.10227e8 | 0.256914 | ||||||||
\(353\) | 7.73849e8 | 0.936364 | 0.468182 | − | 0.883632i | \(-0.344909\pi\) | ||||
0.468182 | + | 0.883632i | \(0.344909\pi\) | |||||||
\(354\) | 4.38562e8 | 0.525436 | ||||||||
\(355\) | −2.34824e8 | −0.278575 | ||||||||
\(356\) | 5.90161e8 | 0.693259 | ||||||||
\(357\) | 3.41763e7 | 0.0397545 | ||||||||
\(358\) | 6.85298e6 | 0.00789384 | ||||||||
\(359\) | 1.71828e9 | 1.96003 | 0.980016 | − | 0.198918i | \(-0.0637427\pi\) | ||||
0.980016 | + | 0.198918i | \(0.0637427\pi\) | |||||||
\(360\) | 1.89342e7 | 0.0213889 | ||||||||
\(361\) | 7.65751e8 | 0.856668 | ||||||||
\(362\) | −4.66281e8 | −0.516616 | ||||||||
\(363\) | −8.76494e7 | −0.0961780 | ||||||||
\(364\) | −1.00954e7 | −0.0109715 | ||||||||
\(365\) | 8.56306e7 | 0.0921730 | ||||||||
\(366\) | 5.99270e8 | 0.638908 | ||||||||
\(367\) | −3.00191e8 | −0.317005 | −0.158503 | − | 0.987359i | \(-0.550667\pi\) | ||||
−0.158503 | + | 0.987359i | \(0.550667\pi\) | |||||||
\(368\) | 2.78380e7 | 0.0291186 | ||||||||
\(369\) | 1.02166e8 | 0.105855 | ||||||||
\(370\) | 1.40355e8 | 0.144053 | ||||||||
\(371\) | 2.79960e7 | 0.0284634 | ||||||||
\(372\) | 7.21538e8 | 0.726706 | ||||||||
\(373\) | −9.39634e7 | −0.0937514 | −0.0468757 | − | 0.998901i | \(-0.514926\pi\) | ||||
−0.0468757 | + | 0.998901i | \(0.514926\pi\) | |||||||
\(374\) | −1.62693e8 | −0.160812 | ||||||||
\(375\) | −5.93663e8 | −0.581340 | ||||||||
\(376\) | −6.46369e8 | −0.627080 | ||||||||
\(377\) | 2.88412e6 | 0.00277216 | ||||||||
\(378\) | 7.55704e6 | 0.00719665 | ||||||||
\(379\) | −7.85315e8 | −0.740980 | −0.370490 | − | 0.928836i | \(-0.620810\pi\) | ||||
−0.370490 | + | 0.928836i | \(0.620810\pi\) | |||||||
\(380\) | −3.71804e8 | −0.347594 | ||||||||
\(381\) | −1.77685e9 | −1.64594 | ||||||||
\(382\) | −2.90740e8 | −0.266860 | ||||||||
\(383\) | −1.56792e9 | −1.42603 | −0.713014 | − | 0.701149i | \(-0.752671\pi\) | ||||
−0.713014 | + | 0.701149i | \(0.752671\pi\) | |||||||
\(384\) | 1.15612e9 | 1.04194 | ||||||||
\(385\) | −2.25638e6 | −0.00201511 | ||||||||
\(386\) | 1.44313e8 | 0.127718 | ||||||||
\(387\) | 6.17132e7 | 0.0541239 | ||||||||
\(388\) | −1.50552e8 | −0.130851 | ||||||||
\(389\) | −1.59542e9 | −1.37420 | −0.687101 | − | 0.726562i | \(-0.741117\pi\) | ||||
−0.687101 | + | 0.726562i | \(0.741117\pi\) | |||||||
\(390\) | 6.21039e7 | 0.0530142 | ||||||||
\(391\) | −8.11590e7 | −0.0686623 | ||||||||
\(392\) | 7.46056e8 | 0.625562 | ||||||||
\(393\) | 8.17956e8 | 0.679761 | ||||||||
\(394\) | 5.58399e8 | 0.459947 | ||||||||
\(395\) | −3.53125e8 | −0.288296 | ||||||||
\(396\) | −3.95693e7 | −0.0320203 | ||||||||
\(397\) | 1.23380e8 | 0.0989645 | 0.0494822 | − | 0.998775i | \(-0.484243\pi\) | ||||
0.0494822 | + | 0.998775i | \(0.484243\pi\) | |||||||
\(398\) | −2.41684e8 | −0.192158 | ||||||||
\(399\) | 4.26681e7 | 0.0336278 | ||||||||
\(400\) | −8.02639e8 | −0.627061 | ||||||||
\(401\) | −7.80784e8 | −0.604680 | −0.302340 | − | 0.953200i | \(-0.597768\pi\) | ||||
−0.302340 | + | 0.953200i | \(0.597768\pi\) | |||||||
\(402\) | 5.79790e8 | 0.445122 | ||||||||
\(403\) | 5.35450e8 | 0.407522 | ||||||||
\(404\) | 1.95997e9 | 1.47881 | ||||||||
\(405\) | 4.23259e8 | 0.316602 | ||||||||
\(406\) | 54657.4 | 4.05329e−5 0 | ||||||||
\(407\) | −6.22749e8 | −0.457860 | ||||||||
\(408\) | −1.46332e9 | −1.06667 | ||||||||
\(409\) | 1.78733e9 | 1.29174 | 0.645868 | − | 0.763449i | \(-0.276495\pi\) | ||||
0.645868 | + | 0.763449i | \(0.276495\pi\) | |||||||
\(410\) | −1.17489e8 | −0.0841887 | ||||||||
\(411\) | −1.37262e9 | −0.975223 | ||||||||
\(412\) | −4.58738e8 | −0.323165 | ||||||||
\(413\) | −5.00934e7 | −0.0349909 | ||||||||
\(414\) | 2.43037e6 | 0.00168334 | ||||||||
\(415\) | 2.00004e8 | 0.137363 | ||||||||
\(416\) | 6.60913e8 | 0.450109 | ||||||||
\(417\) | 2.49720e9 | 1.68646 | ||||||||
\(418\) | −2.03117e8 | −0.136028 | ||||||||
\(419\) | −1.51640e9 | −1.00708 | −0.503542 | − | 0.863971i | \(-0.667970\pi\) | ||||
−0.503542 | + | 0.863971i | \(0.667970\pi\) | |||||||
\(420\) | −9.55891e6 | −0.00629558 | ||||||||
\(421\) | 2.24522e9 | 1.46646 | 0.733231 | − | 0.679980i | \(-0.238011\pi\) | ||||
0.733231 | + | 0.679980i | \(0.238011\pi\) | |||||||
\(422\) | 1.33281e8 | 0.0863326 | ||||||||
\(423\) | 1.86019e8 | 0.119500 | ||||||||
\(424\) | −1.19870e9 | −0.763713 | ||||||||
\(425\) | 2.34002e9 | 1.47862 | ||||||||
\(426\) | −5.43464e8 | −0.340594 | ||||||||
\(427\) | −6.84497e7 | −0.0425475 | ||||||||
\(428\) | −2.48253e9 | −1.53053 | ||||||||
\(429\) | −2.75553e8 | −0.168502 | ||||||||
\(430\) | −7.09693e7 | −0.0430458 | ||||||||
\(431\) | 2.62807e9 | 1.58113 | 0.790564 | − | 0.612380i | \(-0.209788\pi\) | ||||
0.790564 | + | 0.612380i | \(0.209788\pi\) | |||||||
\(432\) | 1.06662e9 | 0.636526 | ||||||||
\(433\) | 3.73140e8 | 0.220884 | 0.110442 | − | 0.993883i | \(-0.464773\pi\) | ||||
0.110442 | + | 0.993883i | \(0.464773\pi\) | |||||||
\(434\) | 1.01474e7 | 0.00595854 | ||||||||
\(435\) | 2.73086e6 | 0.00159070 | ||||||||
\(436\) | 3.06775e8 | 0.177262 | ||||||||
\(437\) | −1.01325e8 | −0.0580804 | ||||||||
\(438\) | 1.98179e8 | 0.112693 | ||||||||
\(439\) | 2.04384e9 | 1.15298 | 0.576488 | − | 0.817105i | \(-0.304423\pi\) | ||||
0.576488 | + | 0.817105i | \(0.304423\pi\) | |||||||
\(440\) | 9.66111e7 | 0.0540683 | ||||||||
\(441\) | −2.14708e8 | −0.119210 | ||||||||
\(442\) | −5.11475e8 | −0.281739 | ||||||||
\(443\) | −3.44729e9 | −1.88393 | −0.941965 | − | 0.335712i | \(-0.891023\pi\) | ||||
−0.941965 | + | 0.335712i | \(0.891023\pi\) | |||||||
\(444\) | −2.63821e9 | −1.43044 | ||||||||
\(445\) | 4.14683e8 | 0.223078 | ||||||||
\(446\) | −5.82867e8 | −0.311098 | ||||||||
\(447\) | −1.53327e9 | −0.811974 | ||||||||
\(448\) | −1.78029e7 | −0.00935445 | ||||||||
\(449\) | 1.53897e9 | 0.802357 | 0.401178 | − | 0.916000i | \(-0.368601\pi\) | ||||
0.401178 | + | 0.916000i | \(0.368601\pi\) | |||||||
\(450\) | −7.00737e7 | −0.0362503 | ||||||||
\(451\) | 5.21295e8 | 0.267587 | ||||||||
\(452\) | 6.82412e7 | 0.0347586 | ||||||||
\(453\) | 3.34336e8 | 0.168982 | ||||||||
\(454\) | 5.21563e8 | 0.261584 | ||||||||
\(455\) | −7.09362e6 | −0.00353043 | ||||||||
\(456\) | −1.82692e9 | −0.902281 | ||||||||
\(457\) | −1.48389e9 | −0.727268 | −0.363634 | − | 0.931542i | \(-0.618464\pi\) | ||||
−0.363634 | + | 0.931542i | \(0.618464\pi\) | |||||||
\(458\) | 9.47559e8 | 0.460869 | ||||||||
\(459\) | −3.10963e9 | −1.50094 | ||||||||
\(460\) | 2.26997e7 | 0.0108735 | ||||||||
\(461\) | −2.44680e9 | −1.16317 | −0.581587 | − | 0.813484i | \(-0.697568\pi\) | ||||
−0.581587 | + | 0.813484i | \(0.697568\pi\) | |||||||
\(462\) | −5.22205e6 | −0.00246373 | ||||||||
\(463\) | 1.45022e9 | 0.679049 | 0.339524 | − | 0.940597i | \(-0.389734\pi\) | ||||
0.339524 | + | 0.940597i | \(0.389734\pi\) | |||||||
\(464\) | 7.71448e6 | 0.00358504 | ||||||||
\(465\) | 5.06996e8 | 0.233840 | ||||||||
\(466\) | 3.75861e8 | 0.172059 | ||||||||
\(467\) | 1.48083e9 | 0.672814 | 0.336407 | − | 0.941717i | \(-0.390788\pi\) | ||||
0.336407 | + | 0.941717i | \(0.390788\pi\) | |||||||
\(468\) | −1.24398e8 | −0.0560989 | ||||||||
\(469\) | −6.62246e7 | −0.0296425 | ||||||||
\(470\) | −2.13920e8 | −0.0950404 | ||||||||
\(471\) | −9.39984e8 | −0.414522 | ||||||||
\(472\) | 2.14485e9 | 0.938856 | ||||||||
\(473\) | 3.14889e8 | 0.136818 | ||||||||
\(474\) | −8.17255e8 | −0.352479 | ||||||||
\(475\) | 2.92144e9 | 1.25075 | ||||||||
\(476\) | 7.87253e7 | 0.0334572 | ||||||||
\(477\) | 3.44976e8 | 0.145537 | ||||||||
\(478\) | 2.82089e8 | 0.118138 | ||||||||
\(479\) | −3.76893e9 | −1.56691 | −0.783455 | − | 0.621449i | \(-0.786544\pi\) | ||||
−0.783455 | + | 0.621449i | \(0.786544\pi\) | |||||||
\(480\) | 6.25792e8 | 0.258277 | ||||||||
\(481\) | −1.95781e9 | −0.802162 | ||||||||
\(482\) | 4.71251e8 | 0.191685 | ||||||||
\(483\) | −2.60501e6 | −0.00105195 | ||||||||
\(484\) | −2.01901e8 | −0.0809430 | ||||||||
\(485\) | −1.05787e8 | −0.0421054 | ||||||||
\(486\) | 1.98852e8 | 0.0785783 | ||||||||
\(487\) | 9.84963e8 | 0.386428 | 0.193214 | − | 0.981157i | \(-0.438109\pi\) | ||||
0.193214 | + | 0.981157i | \(0.438109\pi\) | |||||||
\(488\) | 2.93081e9 | 1.14161 | ||||||||
\(489\) | 3.45138e9 | 1.33478 | ||||||||
\(490\) | 2.46912e8 | 0.0948102 | ||||||||
\(491\) | −3.56853e8 | −0.136052 | −0.0680259 | − | 0.997684i | \(-0.521670\pi\) | ||||
−0.0680259 | + | 0.997684i | \(0.521670\pi\) | |||||||
\(492\) | 2.20841e9 | 0.835993 | ||||||||
\(493\) | −2.24908e7 | −0.00845360 | ||||||||
\(494\) | −6.38562e8 | −0.238319 | ||||||||
\(495\) | −2.78038e7 | −0.0103035 | ||||||||
\(496\) | 1.43223e9 | 0.527019 | ||||||||
\(497\) | 6.20754e7 | 0.0226815 | ||||||||
\(498\) | 4.62879e8 | 0.167944 | ||||||||
\(499\) | −2.25684e9 | −0.813111 | −0.406555 | − | 0.913626i | \(-0.633270\pi\) | ||||
−0.406555 | + | 0.913626i | \(0.633270\pi\) | |||||||
\(500\) | −1.36750e9 | −0.489253 | ||||||||
\(501\) | 1.19847e9 | 0.425789 | ||||||||
\(502\) | −6.16312e8 | −0.217439 | ||||||||
\(503\) | 1.74836e9 | 0.612553 | 0.306277 | − | 0.951943i | \(-0.400917\pi\) | ||||
0.306277 | + | 0.951943i | \(0.400917\pi\) | |||||||
\(504\) | −5.00525e6 | −0.00174148 | ||||||||
\(505\) | 1.37719e9 | 0.475855 | ||||||||
\(506\) | 1.24009e7 | 0.00425525 | ||||||||
\(507\) | 2.23825e9 | 0.762746 | ||||||||
\(508\) | −4.09299e9 | −1.38522 | ||||||||
\(509\) | −4.30470e9 | −1.44687 | −0.723437 | − | 0.690391i | \(-0.757439\pi\) | ||||
−0.723437 | + | 0.690391i | \(0.757439\pi\) | |||||||
\(510\) | −4.84296e8 | −0.161665 | ||||||||
\(511\) | −2.26364e7 | −0.00750471 | ||||||||
\(512\) | 3.06637e9 | 1.00967 | ||||||||
\(513\) | −3.88228e9 | −1.26963 | ||||||||
\(514\) | −4.13687e8 | −0.134370 | ||||||||
\(515\) | −3.22337e8 | −0.103989 | ||||||||
\(516\) | 1.33399e9 | 0.427445 | ||||||||
\(517\) | 9.49155e8 | 0.302079 | ||||||||
\(518\) | −3.71027e7 | −0.0117287 | ||||||||
\(519\) | −2.97071e9 | −0.932771 | ||||||||
\(520\) | 3.03727e8 | 0.0947265 | ||||||||
\(521\) | 3.38119e9 | 1.04746 | 0.523730 | − | 0.851885i | \(-0.324540\pi\) | ||||
0.523730 | + | 0.851885i | \(0.324540\pi\) | |||||||
\(522\) | 673507. | 0.000207250 0 | ||||||||
\(523\) | 4.20231e9 | 1.28449 | 0.642247 | − | 0.766497i | \(-0.278002\pi\) | ||||
0.642247 | + | 0.766497i | \(0.278002\pi\) | |||||||
\(524\) | 1.88417e9 | 0.572084 | ||||||||
\(525\) | 7.51088e7 | 0.0226534 | ||||||||
\(526\) | −1.49292e9 | −0.447287 | ||||||||
\(527\) | −4.17552e9 | −1.24272 | ||||||||
\(528\) | −7.37053e8 | −0.217911 | ||||||||
\(529\) | −3.39864e9 | −0.998183 | ||||||||
\(530\) | −3.96717e8 | −0.115749 | ||||||||
\(531\) | −6.17268e8 | −0.178913 | ||||||||
\(532\) | 9.82862e7 | 0.0283010 | ||||||||
\(533\) | 1.63885e9 | 0.468808 | ||||||||
\(534\) | 9.59721e8 | 0.272741 | ||||||||
\(535\) | −1.74437e9 | −0.492495 | ||||||||
\(536\) | 2.83554e9 | 0.795350 | ||||||||
\(537\) | −9.05124e7 | −0.0252231 | ||||||||
\(538\) | −1.12098e9 | −0.310356 | ||||||||
\(539\) | −1.09554e9 | −0.301347 | ||||||||
\(540\) | 8.69744e8 | 0.237691 | ||||||||
\(541\) | −6.90757e9 | −1.87558 | −0.937788 | − | 0.347208i | \(-0.887130\pi\) | ||||
−0.937788 | + | 0.347208i | \(0.887130\pi\) | |||||||
\(542\) | −5.13789e7 | −0.0138608 | ||||||||
\(543\) | 6.15853e9 | 1.65074 | ||||||||
\(544\) | −5.15390e9 | −1.37259 | ||||||||
\(545\) | 2.15559e8 | 0.0570397 | ||||||||
\(546\) | −1.64171e7 | −0.00431641 | ||||||||
\(547\) | −1.87201e9 | −0.489049 | −0.244525 | − | 0.969643i | \(-0.578632\pi\) | ||||
−0.244525 | + | 0.969643i | \(0.578632\pi\) | |||||||
\(548\) | −3.16184e9 | −0.820743 | ||||||||
\(549\) | −8.43460e8 | −0.217551 | ||||||||
\(550\) | −3.57548e8 | −0.0916357 | ||||||||
\(551\) | −2.80792e7 | −0.00715078 | ||||||||
\(552\) | 1.11538e8 | 0.0282252 | ||||||||
\(553\) | 9.33484e7 | 0.0234730 | ||||||||
\(554\) | −2.52406e9 | −0.630689 | ||||||||
\(555\) | −1.85377e9 | −0.460289 | ||||||||
\(556\) | 5.75231e9 | 1.41932 | ||||||||
\(557\) | 2.57944e9 | 0.632458 | 0.316229 | − | 0.948683i | \(-0.397583\pi\) | ||||
0.316229 | + | 0.948683i | \(0.397583\pi\) | |||||||
\(558\) | 1.25039e8 | 0.0304668 | ||||||||
\(559\) | 9.89950e8 | 0.239702 | ||||||||
\(560\) | −1.89741e7 | −0.00456566 | ||||||||
\(561\) | 2.14881e9 | 0.513839 | ||||||||
\(562\) | 2.12125e9 | 0.504097 | ||||||||
\(563\) | −2.44826e7 | −0.00578199 | −0.00289100 | − | 0.999996i | \(-0.500920\pi\) | ||||
−0.00289100 | + | 0.999996i | \(0.500920\pi\) | |||||||
\(564\) | 4.02100e9 | 0.943750 | ||||||||
\(565\) | 4.79504e7 | 0.0111847 | ||||||||
\(566\) | 2.35921e9 | 0.546902 | ||||||||
\(567\) | −1.11888e8 | −0.0257777 | ||||||||
\(568\) | −2.65788e9 | −0.608578 | ||||||||
\(569\) | 6.24602e9 | 1.42138 | 0.710690 | − | 0.703505i | \(-0.248383\pi\) | ||||
0.710690 | + | 0.703505i | \(0.248383\pi\) | |||||||
\(570\) | −6.04629e8 | −0.136750 | ||||||||
\(571\) | 2.67106e9 | 0.600423 | 0.300211 | − | 0.953873i | \(-0.402943\pi\) | ||||
0.300211 | + | 0.953873i | \(0.402943\pi\) | |||||||
\(572\) | −6.34738e8 | −0.141810 | ||||||||
\(573\) | 3.84002e9 | 0.852693 | ||||||||
\(574\) | 3.10581e7 | 0.00685463 | ||||||||
\(575\) | −1.78362e8 | −0.0391260 | ||||||||
\(576\) | −2.19374e8 | −0.0478306 | ||||||||
\(577\) | 2.92211e9 | 0.633258 | 0.316629 | − | 0.948549i | \(-0.397449\pi\) | ||||
0.316629 | + | 0.948549i | \(0.397449\pi\) | |||||||
\(578\) | 2.45145e9 | 0.528051 | ||||||||
\(579\) | −1.90606e9 | −0.408094 | ||||||||
\(580\) | 6.29055e6 | 0.00133872 | ||||||||
\(581\) | −5.28709e7 | −0.0111841 | ||||||||
\(582\) | −2.44829e8 | −0.0514792 | ||||||||
\(583\) | 1.76022e9 | 0.367898 | ||||||||
\(584\) | 9.69220e8 | 0.201362 | ||||||||
\(585\) | −8.74099e7 | −0.0180516 | ||||||||
\(586\) | −4.63863e6 | −0.000952245 0 | ||||||||
\(587\) | 8.18950e9 | 1.67118 | 0.835592 | − | 0.549351i | \(-0.185125\pi\) | ||||
0.835592 | + | 0.549351i | \(0.185125\pi\) | |||||||
\(588\) | −4.64114e9 | −0.941465 | ||||||||
\(589\) | −5.21302e9 | −1.05120 | ||||||||
\(590\) | 7.09849e8 | 0.142293 | ||||||||
\(591\) | −7.37520e9 | −1.46966 | ||||||||
\(592\) | −5.23676e9 | −1.03738 | ||||||||
\(593\) | −9.08514e9 | −1.78912 | −0.894562 | − | 0.446944i | \(-0.852512\pi\) | ||||
−0.894562 | + | 0.446944i | \(0.852512\pi\) | |||||||
\(594\) | 4.75142e8 | 0.0930189 | ||||||||
\(595\) | 5.53172e7 | 0.0107659 | ||||||||
\(596\) | −3.53189e9 | −0.683354 | ||||||||
\(597\) | 3.19211e9 | 0.613998 | ||||||||
\(598\) | 3.89860e7 | 0.00745511 | ||||||||
\(599\) | 3.46726e9 | 0.659162 | 0.329581 | − | 0.944127i | \(-0.393093\pi\) | ||||
0.329581 | + | 0.944127i | \(0.393093\pi\) | |||||||
\(600\) | −3.21593e9 | −0.607823 | ||||||||
\(601\) | −2.56544e9 | −0.482060 | −0.241030 | − | 0.970518i | \(-0.577485\pi\) | ||||
−0.241030 | + | 0.970518i | \(0.577485\pi\) | |||||||
\(602\) | 1.87607e7 | 0.00350478 | ||||||||
\(603\) | −8.16042e8 | −0.151566 | ||||||||
\(604\) | 7.70145e8 | 0.142214 | ||||||||
\(605\) | −1.41868e8 | −0.0260459 | ||||||||
\(606\) | 3.18730e9 | 0.581794 | ||||||||
\(607\) | 1.86107e9 | 0.337755 | 0.168877 | − | 0.985637i | \(-0.445986\pi\) | ||||
0.168877 | + | 0.985637i | \(0.445986\pi\) | |||||||
\(608\) | −6.43449e9 | −1.16105 | ||||||||
\(609\) | −721902. | −0.000129514 0 | ||||||||
\(610\) | 9.69968e8 | 0.173023 | ||||||||
\(611\) | 2.98396e9 | 0.529236 | ||||||||
\(612\) | 9.70079e8 | 0.171071 | ||||||||
\(613\) | −2.35285e9 | −0.412556 | −0.206278 | − | 0.978493i | \(-0.566135\pi\) | ||||
−0.206278 | + | 0.978493i | \(0.566135\pi\) | |||||||
\(614\) | −1.82968e9 | −0.318997 | ||||||||
\(615\) | 1.55177e9 | 0.269007 | ||||||||
\(616\) | −2.55391e7 | −0.00440223 | ||||||||
\(617\) | −5.81579e9 | −0.996806 | −0.498403 | − | 0.866946i | \(-0.666080\pi\) | ||||
−0.498403 | + | 0.866946i | \(0.666080\pi\) | |||||||
\(618\) | −7.46002e8 | −0.127139 | ||||||||
\(619\) | 3.71473e9 | 0.629520 | 0.314760 | − | 0.949171i | \(-0.398076\pi\) | ||||
0.314760 | + | 0.949171i | \(0.398076\pi\) | |||||||
\(620\) | 1.16787e9 | 0.196799 | ||||||||
\(621\) | 2.37024e8 | 0.0397165 | ||||||||
\(622\) | −1.80227e9 | −0.300299 | ||||||||
\(623\) | −1.09621e8 | −0.0181629 | ||||||||
\(624\) | −2.31715e9 | −0.381776 | ||||||||
\(625\) | 4.64161e9 | 0.760482 | ||||||||
\(626\) | 1.93908e8 | 0.0315926 | ||||||||
\(627\) | 2.68272e9 | 0.434650 | ||||||||
\(628\) | −2.16526e9 | −0.348860 | ||||||||
\(629\) | 1.52673e10 | 2.44616 | ||||||||
\(630\) | −1.65652e6 | −0.000263939 0 | ||||||||
\(631\) | −6.61199e9 | −1.04768 | −0.523841 | − | 0.851816i | \(-0.675501\pi\) | ||||
−0.523841 | + | 0.851816i | \(0.675501\pi\) | |||||||
\(632\) | −3.99689e9 | −0.629814 | ||||||||
\(633\) | −1.76034e9 | −0.275857 | ||||||||
\(634\) | −1.76589e9 | −0.275202 | ||||||||
\(635\) | −2.87599e9 | −0.445737 | ||||||||
\(636\) | 7.45700e9 | 1.14938 | ||||||||
\(637\) | −3.44417e9 | −0.527954 | ||||||||
\(638\) | 3.43654e6 | 0.000523901 0 | ||||||||
\(639\) | 7.64914e8 | 0.115974 | ||||||||
\(640\) | 1.87128e9 | 0.282168 | ||||||||
\(641\) | −1.31108e10 | −1.96619 | −0.983093 | − | 0.183106i | \(-0.941385\pi\) | ||||
−0.983093 | + | 0.183106i | \(0.941385\pi\) | |||||||
\(642\) | −4.03709e9 | −0.602138 | ||||||||
\(643\) | 8.73321e9 | 1.29549 | 0.647747 | − | 0.761856i | \(-0.275711\pi\) | ||||
0.647747 | + | 0.761856i | \(0.275711\pi\) | |||||||
\(644\) | −6.00065e6 | −0.000885314 0 | ||||||||
\(645\) | 9.37345e8 | 0.137544 | ||||||||
\(646\) | 4.97961e9 | 0.726744 | ||||||||
\(647\) | −4.05488e9 | −0.588590 | −0.294295 | − | 0.955715i | \(-0.595085\pi\) | ||||
−0.294295 | + | 0.955715i | \(0.595085\pi\) | |||||||
\(648\) | 4.79071e9 | 0.691652 | ||||||||
\(649\) | −3.14958e9 | −0.452268 | ||||||||
\(650\) | −1.12406e9 | −0.160544 | ||||||||
\(651\) | −1.34024e8 | −0.0190392 | ||||||||
\(652\) | 7.95026e9 | 1.12335 | ||||||||
\(653\) | 2.96057e9 | 0.416082 | 0.208041 | − | 0.978120i | \(-0.433291\pi\) | ||||
0.208041 | + | 0.978120i | \(0.433291\pi\) | |||||||
\(654\) | 4.98878e8 | 0.0697384 | ||||||||
\(655\) | 1.32393e9 | 0.184086 | ||||||||
\(656\) | 4.38362e9 | 0.606275 | ||||||||
\(657\) | −2.78933e8 | −0.0383726 | ||||||||
\(658\) | 5.65495e7 | 0.00773817 | ||||||||
\(659\) | 1.25563e10 | 1.70908 | 0.854540 | − | 0.519386i | \(-0.173839\pi\) | ||||
0.854540 | + | 0.519386i | \(0.173839\pi\) | |||||||
\(660\) | −6.01008e8 | −0.0813723 | ||||||||
\(661\) | −8.54786e9 | −1.15120 | −0.575602 | − | 0.817730i | \(-0.695232\pi\) | ||||
−0.575602 | + | 0.817730i | \(0.695232\pi\) | |||||||
\(662\) | 2.23735e9 | 0.299731 | ||||||||
\(663\) | 6.75544e9 | 0.900236 | ||||||||
\(664\) | 2.26377e9 | 0.300085 | ||||||||
\(665\) | 6.90619e7 | 0.00910673 | ||||||||
\(666\) | −4.57191e8 | −0.0599706 | ||||||||
\(667\) | 1.71431e6 | 0.000223691 0 | ||||||||
\(668\) | 2.76068e9 | 0.358342 | ||||||||
\(669\) | 7.69836e9 | 0.994047 | ||||||||
\(670\) | 9.38437e8 | 0.120543 | ||||||||
\(671\) | −4.30372e9 | −0.549939 | ||||||||
\(672\) | −1.65428e8 | −0.0210289 | ||||||||
\(673\) | −7.90222e9 | −0.999301 | −0.499650 | − | 0.866227i | \(-0.666538\pi\) | ||||
−0.499650 | + | 0.866227i | \(0.666538\pi\) | |||||||
\(674\) | −3.04154e9 | −0.382635 | ||||||||
\(675\) | −6.83399e9 | −0.855285 | ||||||||
\(676\) | 5.15581e9 | 0.641924 | ||||||||
\(677\) | −8.15033e9 | −1.00952 | −0.504760 | − | 0.863260i | \(-0.668419\pi\) | ||||
−0.504760 | + | 0.863260i | \(0.668419\pi\) | |||||||
\(678\) | 1.10974e8 | 0.0136747 | ||||||||
\(679\) | 2.79648e7 | 0.00342821 | ||||||||
\(680\) | −2.36851e9 | −0.288865 | ||||||||
\(681\) | −6.88867e9 | −0.835835 | ||||||||
\(682\) | 6.38008e8 | 0.0770160 | ||||||||
\(683\) | −6.93643e8 | −0.0833036 | −0.0416518 | − | 0.999132i | \(-0.513262\pi\) | ||||
−0.0416518 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(684\) | 1.21112e9 | 0.144707 | ||||||||
\(685\) | −2.22170e9 | −0.264100 | ||||||||
\(686\) | −1.30577e8 | −0.0154431 | ||||||||
\(687\) | −1.25151e10 | −1.47261 | ||||||||
\(688\) | 2.64793e9 | 0.309990 | ||||||||
\(689\) | 5.53380e9 | 0.644550 | ||||||||
\(690\) | 3.69143e7 | 0.00427782 | ||||||||
\(691\) | 3.17516e7 | 0.00366094 | 0.00183047 | − | 0.999998i | \(-0.499417\pi\) | ||||
0.00183047 | + | 0.999998i | \(0.499417\pi\) | |||||||
\(692\) | −6.84305e9 | −0.785016 | ||||||||
\(693\) | 7.34992e6 | 0.000838912 0 | ||||||||
\(694\) | −1.72833e9 | −0.196277 | ||||||||
\(695\) | 4.04192e9 | 0.456711 | ||||||||
\(696\) | 3.09096e7 | 0.00347505 | ||||||||
\(697\) | −1.27800e10 | −1.42961 | ||||||||
\(698\) | −3.37162e9 | −0.375271 | ||||||||
\(699\) | −4.96428e9 | −0.549777 | ||||||||
\(700\) | 1.73014e8 | 0.0190650 | ||||||||
\(701\) | 7.68876e9 | 0.843030 | 0.421515 | − | 0.906821i | \(-0.361498\pi\) | ||||
0.421515 | + | 0.906821i | \(0.361498\pi\) | |||||||
\(702\) | 1.49376e9 | 0.162967 | ||||||||
\(703\) | 1.90608e10 | 2.06917 | ||||||||
\(704\) | −1.11934e9 | −0.120909 | ||||||||
\(705\) | 2.82540e9 | 0.303681 | ||||||||
\(706\) | 2.89881e9 | 0.310030 | ||||||||
\(707\) | −3.64059e8 | −0.0387440 | ||||||||
\(708\) | −1.33429e10 | −1.41297 | ||||||||
\(709\) | −4.65053e9 | −0.490051 | −0.245025 | − | 0.969517i | \(-0.578796\pi\) | ||||
−0.245025 | + | 0.969517i | \(0.578796\pi\) | |||||||
\(710\) | −8.79641e8 | −0.0922362 | ||||||||
\(711\) | 1.15027e9 | 0.120021 | ||||||||
\(712\) | 4.69364e9 | 0.487337 | ||||||||
\(713\) | 3.18269e8 | 0.0328837 | ||||||||
\(714\) | 1.28023e8 | 0.0131627 | ||||||||
\(715\) | −4.46005e8 | −0.0456319 | ||||||||
\(716\) | −2.08496e8 | −0.0212276 | ||||||||
\(717\) | −3.72576e9 | −0.377483 | ||||||||
\(718\) | 6.43662e9 | 0.648966 | ||||||||
\(719\) | −9.19022e9 | −0.922093 | −0.461047 | − | 0.887376i | \(-0.652526\pi\) | ||||
−0.461047 | + | 0.887376i | \(0.652526\pi\) | |||||||
\(720\) | −2.33805e8 | −0.0233448 | ||||||||
\(721\) | 8.52097e7 | 0.00846672 | ||||||||
\(722\) | 2.86848e9 | 0.283643 | ||||||||
\(723\) | −6.22417e9 | −0.612488 | ||||||||
\(724\) | 1.41862e10 | 1.38925 | ||||||||
\(725\) | −4.94278e7 | −0.00481713 | ||||||||
\(726\) | −3.28332e8 | −0.0318445 | ||||||||
\(727\) | 9.36688e9 | 0.904117 | 0.452059 | − | 0.891988i | \(-0.350690\pi\) | ||||
0.452059 | + | 0.891988i | \(0.350690\pi\) | |||||||
\(728\) | −8.02900e7 | −0.00771262 | ||||||||
\(729\) | 8.93281e9 | 0.853969 | ||||||||
\(730\) | 3.20769e8 | 0.0305185 | ||||||||
\(731\) | −7.71979e9 | −0.730962 | ||||||||
\(732\) | −1.82323e10 | −1.71811 | ||||||||
\(733\) | 1.29034e10 | 1.21015 | 0.605076 | − | 0.796168i | \(-0.293143\pi\) | ||||
0.605076 | + | 0.796168i | \(0.293143\pi\) | |||||||
\(734\) | −1.12451e9 | −0.104960 | ||||||||
\(735\) | −3.26115e9 | −0.302946 | ||||||||
\(736\) | 3.92844e8 | 0.0363201 | ||||||||
\(737\) | −4.16382e9 | −0.383138 | ||||||||
\(738\) | 3.82709e8 | 0.0350486 | ||||||||
\(739\) | 6.13118e9 | 0.558841 | 0.279421 | − | 0.960169i | \(-0.409858\pi\) | ||||
0.279421 | + | 0.960169i | \(0.409858\pi\) | |||||||
\(740\) | −4.27017e9 | −0.387377 | ||||||||
\(741\) | 8.43397e9 | 0.761497 | ||||||||
\(742\) | 1.04872e8 | 0.00942422 | ||||||||
\(743\) | 9.12544e9 | 0.816193 | 0.408096 | − | 0.912939i | \(-0.366193\pi\) | ||||
0.408096 | + | 0.912939i | \(0.366193\pi\) | |||||||
\(744\) | 5.73850e9 | 0.510850 | ||||||||
\(745\) | −2.48172e9 | −0.219891 | ||||||||
\(746\) | −3.51984e8 | −0.0310411 | ||||||||
\(747\) | −6.51492e8 | −0.0571857 | ||||||||
\(748\) | 4.94979e9 | 0.432445 | ||||||||
\(749\) | 4.61124e8 | 0.0400988 | ||||||||
\(750\) | −2.22384e9 | −0.192482 | ||||||||
\(751\) | −1.80702e9 | −0.155676 | −0.0778381 | − | 0.996966i | \(-0.524802\pi\) | ||||
−0.0778381 | + | 0.996966i | \(0.524802\pi\) | |||||||
\(752\) | 7.98154e9 | 0.684423 | ||||||||
\(753\) | 8.14010e9 | 0.694780 | ||||||||
\(754\) | 1.08038e7 | 0.000917863 0 | ||||||||
\(755\) | 5.41151e8 | 0.0457619 | ||||||||
\(756\) | −2.29916e8 | −0.0193528 | ||||||||
\(757\) | 4.78438e9 | 0.400858 | 0.200429 | − | 0.979708i | \(-0.435766\pi\) | ||||
0.200429 | + | 0.979708i | \(0.435766\pi\) | |||||||
\(758\) | −2.94176e9 | −0.245338 | ||||||||
\(759\) | −1.63788e8 | −0.0135967 | ||||||||
\(760\) | −2.95702e9 | −0.244347 | ||||||||
\(761\) | 8.11100e9 | 0.667157 | 0.333578 | − | 0.942722i | \(-0.391744\pi\) | ||||
0.333578 | + | 0.942722i | \(0.391744\pi\) | |||||||
\(762\) | −6.65604e9 | −0.544971 | ||||||||
\(763\) | −5.69828e7 | −0.00464416 | ||||||||
\(764\) | 8.84551e9 | 0.717623 | ||||||||
\(765\) | 6.81637e8 | 0.0550476 | ||||||||
\(766\) | −5.87338e9 | −0.472158 | ||||||||
\(767\) | −9.90168e9 | −0.792365 | ||||||||
\(768\) | −9.95050e8 | −0.0792649 | ||||||||
\(769\) | −4.03304e9 | −0.319809 | −0.159904 | − | 0.987133i | \(-0.551119\pi\) | ||||
−0.159904 | + | 0.987133i | \(0.551119\pi\) | |||||||
\(770\) | −8.45231e6 | −0.000667203 0 | ||||||||
\(771\) | 5.46388e9 | 0.429349 | ||||||||
\(772\) | −4.39061e9 | −0.343451 | ||||||||
\(773\) | 3.46346e9 | 0.269701 | 0.134850 | − | 0.990866i | \(-0.456945\pi\) | ||||
0.134850 | + | 0.990866i | \(0.456945\pi\) | |||||||
\(774\) | 2.31175e8 | 0.0179204 | ||||||||
\(775\) | −9.17649e9 | −0.708143 | ||||||||
\(776\) | −1.19737e9 | −0.0919838 | ||||||||
\(777\) | 4.90043e8 | 0.0374766 | ||||||||
\(778\) | −5.97638e9 | −0.454998 | ||||||||
\(779\) | −1.59555e10 | −1.20929 | ||||||||
\(780\) | −1.88946e9 | −0.142563 | ||||||||
\(781\) | 3.90294e9 | 0.293166 | ||||||||
\(782\) | −3.04019e8 | −0.0227341 | ||||||||
\(783\) | 6.56842e7 | 0.00488984 | ||||||||
\(784\) | −9.21250e9 | −0.682765 | ||||||||
\(785\) | −1.52144e9 | −0.112257 | ||||||||
\(786\) | 3.06404e9 | 0.225069 | ||||||||
\(787\) | −7.81853e9 | −0.571760 | −0.285880 | − | 0.958265i | \(-0.592286\pi\) | ||||
−0.285880 | + | 0.958265i | \(0.592286\pi\) | |||||||
\(788\) | −1.69888e10 | −1.23686 | ||||||||
\(789\) | 1.97181e10 | 1.42921 | ||||||||
\(790\) | −1.32279e9 | −0.0954548 | ||||||||
\(791\) | −1.26757e7 | −0.000910652 0 | ||||||||
\(792\) | −3.14701e8 | −0.0225092 | ||||||||
\(793\) | −1.35301e10 | −0.963482 | ||||||||
\(794\) | 4.62179e8 | 0.0327671 | ||||||||
\(795\) | 5.23974e9 | 0.369850 | ||||||||
\(796\) | 7.35303e9 | 0.516738 | ||||||||
\(797\) | 1.19003e10 | 0.832635 | 0.416318 | − | 0.909219i | \(-0.363320\pi\) | ||||
0.416318 | + | 0.909219i | \(0.363320\pi\) | |||||||
\(798\) | 1.59833e8 | 0.0111342 | ||||||||
\(799\) | −2.32694e10 | −1.61388 | ||||||||
\(800\) | −1.13267e10 | −0.782145 | ||||||||
\(801\) | −1.35079e9 | −0.0928696 | ||||||||
\(802\) | −2.92479e9 | −0.200209 | ||||||||
\(803\) | −1.42324e9 | −0.0970007 | ||||||||
\(804\) | −1.76396e10 | −1.19699 | ||||||||
\(805\) | −4.21642e6 | −0.000284878 0 | ||||||||
\(806\) | 2.00578e9 | 0.134930 | ||||||||
\(807\) | 1.48057e10 | 0.991677 | ||||||||
\(808\) | 1.55879e10 | 1.03956 | ||||||||
\(809\) | 1.04001e10 | 0.690584 | 0.345292 | − | 0.938495i | \(-0.387780\pi\) | ||||
0.345292 | + | 0.938495i | \(0.387780\pi\) | |||||||
\(810\) | 1.58552e9 | 0.104827 | ||||||||
\(811\) | −1.00469e10 | −0.661392 | −0.330696 | − | 0.943737i | \(-0.607283\pi\) | ||||
−0.330696 | + | 0.943737i | \(0.607283\pi\) | |||||||
\(812\) | −1.66290e6 | −0.000108999 0 | ||||||||
\(813\) | 6.78600e8 | 0.0442891 | ||||||||
\(814\) | −2.33280e9 | −0.151597 | ||||||||
\(815\) | 5.58634e9 | 0.361473 | ||||||||
\(816\) | 1.80695e10 | 1.16421 | ||||||||
\(817\) | −9.63793e9 | −0.618310 | ||||||||
\(818\) | 6.69529e9 | 0.427694 | ||||||||
\(819\) | 2.31068e7 | 0.00146976 | ||||||||
\(820\) | 3.57450e9 | 0.226395 | ||||||||
\(821\) | 2.01156e10 | 1.26862 | 0.634309 | − | 0.773079i | \(-0.281285\pi\) | ||||
0.634309 | + | 0.773079i | \(0.281285\pi\) | |||||||
\(822\) | −5.14179e9 | −0.322896 | ||||||||
\(823\) | −4.01271e9 | −0.250922 | −0.125461 | − | 0.992099i | \(-0.540041\pi\) | ||||
−0.125461 | + | 0.992099i | \(0.540041\pi\) | |||||||
\(824\) | −3.64842e9 | −0.227174 | ||||||||
\(825\) | 4.72241e9 | 0.292802 | ||||||||
\(826\) | −1.87648e8 | −0.0115855 | ||||||||
\(827\) | −1.18312e10 | −0.727378 | −0.363689 | − | 0.931520i | \(-0.618483\pi\) | ||||
−0.363689 | + | 0.931520i | \(0.618483\pi\) | |||||||
\(828\) | −7.39420e7 | −0.00452673 | ||||||||
\(829\) | 7.67662e9 | 0.467982 | 0.233991 | − | 0.972239i | \(-0.424821\pi\) | ||||
0.233991 | + | 0.972239i | \(0.424821\pi\) | |||||||
\(830\) | 7.49207e8 | 0.0454809 | ||||||||
\(831\) | 3.33371e10 | 2.01523 | ||||||||
\(832\) | −3.51901e9 | −0.211830 | ||||||||
\(833\) | 2.68582e10 | 1.60997 | ||||||||
\(834\) | 9.35443e9 | 0.558388 | ||||||||
\(835\) | 1.93982e9 | 0.115308 | ||||||||
\(836\) | 6.17966e9 | 0.365799 | ||||||||
\(837\) | 1.21946e10 | 0.718832 | ||||||||
\(838\) | −5.68039e9 | −0.333445 | ||||||||
\(839\) | −9.41603e9 | −0.550429 | −0.275214 | − | 0.961383i | \(-0.588749\pi\) | ||||
−0.275214 | + | 0.961383i | \(0.588749\pi\) | |||||||
\(840\) | −7.60235e7 | −0.00442558 | ||||||||
\(841\) | −1.72494e10 | −0.999972 | ||||||||
\(842\) | 8.41050e9 | 0.485545 | ||||||||
\(843\) | −2.80169e10 | −1.61073 | ||||||||
\(844\) | −4.05496e9 | −0.232160 | ||||||||
\(845\) | 3.62279e9 | 0.206559 | ||||||||
\(846\) | 6.96822e8 | 0.0395663 | ||||||||
\(847\) | 3.75027e7 | 0.00212066 | ||||||||
\(848\) | 1.48019e10 | 0.833550 | ||||||||
\(849\) | −3.11599e10 | −1.74751 | ||||||||
\(850\) | 8.76562e9 | 0.489572 | ||||||||
\(851\) | −1.16371e9 | −0.0647280 | ||||||||
\(852\) | 1.65344e10 | 0.915904 | ||||||||
\(853\) | −1.58189e9 | −0.0872680 | −0.0436340 | − | 0.999048i | \(-0.513894\pi\) | ||||
−0.0436340 | + | 0.999048i | \(0.513894\pi\) | |||||||
\(854\) | −2.56410e8 | −0.0140875 | ||||||||
\(855\) | 8.51003e8 | 0.0465640 | ||||||||
\(856\) | −1.97439e10 | −1.07591 | ||||||||
\(857\) | −1.73709e10 | −0.942734 | −0.471367 | − | 0.881937i | \(-0.656239\pi\) | ||||
−0.471367 | + | 0.881937i | \(0.656239\pi\) | |||||||
\(858\) | −1.03221e9 | −0.0557909 | ||||||||
\(859\) | 8.52987e9 | 0.459163 | 0.229581 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229581 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(860\) | 2.15918e9 | 0.115756 | ||||||||
\(861\) | −4.10208e8 | −0.0219025 | ||||||||
\(862\) | 9.84467e9 | 0.523511 | ||||||||
\(863\) | −2.50924e10 | −1.32894 | −0.664470 | − | 0.747315i | \(-0.731343\pi\) | ||||
−0.664470 | + | 0.747315i | \(0.731343\pi\) | |||||||
\(864\) | 1.50519e10 | 0.793950 | ||||||||
\(865\) | −4.80834e9 | −0.252603 | ||||||||
\(866\) | 1.39777e9 | 0.0731346 | ||||||||
\(867\) | −3.23782e10 | −1.68727 | ||||||||
\(868\) | −3.08725e8 | −0.0160233 | ||||||||
\(869\) | 5.86920e9 | 0.303396 | ||||||||
\(870\) | 1.02297e7 | 0.000526679 0 | ||||||||
\(871\) | −1.30903e10 | −0.671250 | ||||||||
\(872\) | 2.43983e9 | 0.124610 | ||||||||
\(873\) | 3.44592e8 | 0.0175289 | ||||||||
\(874\) | −3.79559e8 | −0.0192304 | ||||||||
\(875\) | 2.54011e8 | 0.0128181 | ||||||||
\(876\) | −6.02943e9 | −0.303048 | ||||||||
\(877\) | 1.68456e10 | 0.843314 | 0.421657 | − | 0.906756i | \(-0.361449\pi\) | ||||
0.421657 | + | 0.906756i | \(0.361449\pi\) | |||||||
\(878\) | 7.65615e9 | 0.381750 | ||||||||
\(879\) | 6.12659e7 | 0.00304269 | ||||||||
\(880\) | −1.19298e9 | −0.0590125 | ||||||||
\(881\) | −1.17288e10 | −0.577881 | −0.288941 | − | 0.957347i | \(-0.593303\pi\) | ||||
−0.288941 | + | 0.957347i | \(0.593303\pi\) | |||||||
\(882\) | −8.04290e8 | −0.0394705 | ||||||||
\(883\) | 3.11743e10 | 1.52382 | 0.761911 | − | 0.647682i | \(-0.224261\pi\) | ||||
0.761911 | + | 0.647682i | \(0.224261\pi\) | |||||||
\(884\) | 1.55612e10 | 0.757635 | ||||||||
\(885\) | −9.37551e9 | −0.454667 | ||||||||
\(886\) | −1.29134e10 | −0.623769 | ||||||||
\(887\) | 2.88046e10 | 1.38589 | 0.692944 | − | 0.720991i | \(-0.256313\pi\) | ||||
0.692944 | + | 0.720991i | \(0.256313\pi\) | |||||||
\(888\) | −2.09821e10 | −1.00555 | ||||||||
\(889\) | 7.60265e8 | 0.0362918 | ||||||||
\(890\) | 1.55339e9 | 0.0738610 | ||||||||
\(891\) | −7.03488e9 | −0.333185 | ||||||||
\(892\) | 1.77332e10 | 0.836586 | ||||||||
\(893\) | −2.90512e10 | −1.36516 | ||||||||
\(894\) | −5.74358e9 | −0.268845 | ||||||||
\(895\) | −1.46502e8 | −0.00683065 | ||||||||
\(896\) | −4.94671e8 | −0.0229741 | ||||||||
\(897\) | −5.14917e8 | −0.0238212 | ||||||||
\(898\) | 5.76492e9 | 0.265660 | ||||||||
\(899\) | 8.81990e7 | 0.00404860 | ||||||||
\(900\) | 2.13193e9 | 0.0974820 | ||||||||
\(901\) | −4.31535e10 | −1.96553 | ||||||||
\(902\) | 1.95275e9 | 0.0885982 | ||||||||
\(903\) | −2.47787e8 | −0.0111988 | ||||||||
\(904\) | 5.42733e8 | 0.0244341 | ||||||||
\(905\) | 9.96809e9 | 0.447035 | ||||||||
\(906\) | 1.25241e9 | 0.0559498 | ||||||||
\(907\) | −1.47721e10 | −0.657381 | −0.328690 | − | 0.944438i | \(-0.606607\pi\) | ||||
−0.328690 | + | 0.944438i | \(0.606607\pi\) | |||||||
\(908\) | −1.58681e10 | −0.703435 | ||||||||
\(909\) | −4.48606e9 | −0.198103 | ||||||||
\(910\) | −2.65725e7 | −0.00116893 | ||||||||
\(911\) | 1.23248e10 | 0.540089 | 0.270044 | − | 0.962848i | \(-0.412962\pi\) | ||||
0.270044 | + | 0.962848i | \(0.412962\pi\) | |||||||
\(912\) | 2.25593e10 | 0.984789 | ||||||||
\(913\) | −3.32421e9 | −0.144558 | ||||||||
\(914\) | −5.55859e9 | −0.240798 | ||||||||
\(915\) | −1.28111e10 | −0.552856 | ||||||||
\(916\) | −2.88287e10 | −1.23934 | ||||||||
\(917\) | −3.49980e8 | −0.0149882 | ||||||||
\(918\) | −1.16486e10 | −0.496962 | ||||||||
\(919\) | 2.59401e10 | 1.10247 | 0.551235 | − | 0.834350i | \(-0.314157\pi\) | ||||
0.551235 | + | 0.834350i | \(0.314157\pi\) | |||||||
\(920\) | 1.80534e8 | 0.00764367 | ||||||||
\(921\) | 2.41660e10 | 1.01929 | ||||||||
\(922\) | −9.16562e9 | −0.385127 | ||||||||
\(923\) | 1.22701e10 | 0.513621 | ||||||||
\(924\) | 1.58876e8 | 0.00662532 | ||||||||
\(925\) | 3.35527e10 | 1.39390 | ||||||||
\(926\) | 5.43248e9 | 0.224833 | ||||||||
\(927\) | 1.04998e9 | 0.0432915 | ||||||||
\(928\) | 1.08865e8 | 0.00447168 | ||||||||
\(929\) | 2.78900e10 | 1.14128 | 0.570642 | − | 0.821199i | \(-0.306694\pi\) | ||||
0.570642 | + | 0.821199i | \(0.306694\pi\) | |||||||
\(930\) | 1.89919e9 | 0.0774245 | ||||||||
\(931\) | 3.35316e10 | 1.36185 | ||||||||
\(932\) | −1.14352e10 | −0.462690 | ||||||||
\(933\) | 2.38039e10 | 0.959540 | ||||||||
\(934\) | 5.54713e9 | 0.222769 | ||||||||
\(935\) | 3.47802e9 | 0.139153 | ||||||||
\(936\) | −9.89360e8 | −0.0394357 | ||||||||
\(937\) | 9.94837e9 | 0.395060 | 0.197530 | − | 0.980297i | \(-0.436708\pi\) | ||||
0.197530 | + | 0.980297i | \(0.436708\pi\) | |||||||
\(938\) | −2.48075e8 | −0.00981462 | ||||||||
\(939\) | −2.56109e9 | −0.100947 | ||||||||
\(940\) | 6.50832e9 | 0.255577 | ||||||||
\(941\) | −2.18049e10 | −0.853082 | −0.426541 | − | 0.904468i | \(-0.640268\pi\) | ||||
−0.426541 | + | 0.904468i | \(0.640268\pi\) | |||||||
\(942\) | −3.52115e9 | −0.137248 | ||||||||
\(943\) | 9.74127e8 | 0.0378290 | ||||||||
\(944\) | −2.64851e10 | −1.02471 | ||||||||
\(945\) | −1.61553e8 | −0.00622736 | ||||||||
\(946\) | 1.17956e9 | 0.0453004 | ||||||||
\(947\) | 1.74659e10 | 0.668290 | 0.334145 | − | 0.942522i | \(-0.391552\pi\) | ||||
0.334145 | + | 0.942522i | \(0.391552\pi\) | |||||||
\(948\) | 2.48643e10 | 0.947865 | ||||||||
\(949\) | −4.47441e9 | −0.169943 | ||||||||
\(950\) | 1.09436e10 | 0.414122 | ||||||||
\(951\) | 2.33235e10 | 0.879350 | ||||||||
\(952\) | 6.26115e8 | 0.0235193 | ||||||||
\(953\) | −4.46489e10 | −1.67104 | −0.835518 | − | 0.549464i | \(-0.814832\pi\) | ||||
−0.835518 | + | 0.549464i | \(0.814832\pi\) | |||||||
\(954\) | 1.29227e9 | 0.0481873 | ||||||||
\(955\) | 6.21539e9 | 0.230917 | ||||||||
\(956\) | −8.58230e9 | −0.317688 | ||||||||
\(957\) | −4.53890e7 | −0.00167401 | ||||||||
\(958\) | −1.41183e10 | −0.518804 | ||||||||
\(959\) | 5.87304e8 | 0.0215030 | ||||||||
\(960\) | −3.33201e9 | −0.121551 | ||||||||
\(961\) | −1.11381e10 | −0.404836 | ||||||||
\(962\) | −7.33388e9 | −0.265596 | ||||||||
\(963\) | 5.68213e9 | 0.205031 | ||||||||
\(964\) | −1.43374e10 | −0.515467 | ||||||||
\(965\) | −3.08511e9 | −0.110516 | ||||||||
\(966\) | −9.75827e6 | −0.000348300 0 | ||||||||
\(967\) | 2.46485e10 | 0.876594 | 0.438297 | − | 0.898830i | \(-0.355582\pi\) | ||||
0.438297 | + | 0.898830i | \(0.355582\pi\) | |||||||
\(968\) | −1.60575e9 | −0.0569002 | ||||||||
\(969\) | −6.57694e10 | −2.32215 | ||||||||
\(970\) | −3.96276e8 | −0.0139411 | ||||||||
\(971\) | −1.77832e10 | −0.623365 | −0.311682 | − | 0.950186i | \(-0.600892\pi\) | ||||
−0.311682 | + | 0.950186i | \(0.600892\pi\) | |||||||
\(972\) | −6.04989e9 | −0.211308 | ||||||||
\(973\) | −1.06848e9 | −0.0371853 | ||||||||
\(974\) | 3.68964e9 | 0.127946 | ||||||||
\(975\) | 1.48463e10 | 0.512983 | ||||||||
\(976\) | −3.61904e10 | −1.24600 | ||||||||
\(977\) | 4.72834e10 | 1.62210 | 0.811051 | − | 0.584976i | \(-0.198896\pi\) | ||||
0.811051 | + | 0.584976i | \(0.198896\pi\) | |||||||
\(978\) | 1.29287e10 | 0.441947 | ||||||||
\(979\) | −6.89234e9 | −0.234762 | ||||||||
\(980\) | −7.51207e9 | −0.254958 | ||||||||
\(981\) | −7.02161e8 | −0.0237462 | ||||||||
\(982\) | −1.33676e9 | −0.0450468 | ||||||||
\(983\) | −4.34353e10 | −1.45850 | −0.729249 | − | 0.684249i | \(-0.760130\pi\) | ||||
−0.729249 | + | 0.684249i | \(0.760130\pi\) | |||||||
\(984\) | 1.75639e10 | 0.587675 | ||||||||
\(985\) | −1.19374e10 | −0.397999 | ||||||||
\(986\) | −8.42500e7 | −0.00279898 | ||||||||
\(987\) | −7.46892e8 | −0.0247257 | ||||||||
\(988\) | 1.94277e10 | 0.640873 | ||||||||
\(989\) | 5.88422e8 | 0.0193420 | ||||||||
\(990\) | −1.04152e8 | −0.00341150 | ||||||||
\(991\) | 3.94776e9 | 0.128853 | 0.0644263 | − | 0.997922i | \(-0.479478\pi\) | ||||
0.0644263 | + | 0.997922i | \(0.479478\pi\) | |||||||
\(992\) | 2.02113e10 | 0.657360 | ||||||||
\(993\) | −2.95504e10 | −0.957725 | ||||||||
\(994\) | 2.32533e8 | 0.00750985 | ||||||||
\(995\) | 5.16669e9 | 0.166277 | ||||||||
\(996\) | −1.40827e10 | −0.451625 | ||||||||
\(997\) | 1.90391e10 | 0.608434 | 0.304217 | − | 0.952603i | \(-0.401605\pi\) | ||||
0.304217 | + | 0.952603i | \(0.401605\pi\) | |||||||
\(998\) | −8.45406e9 | −0.269221 | ||||||||
\(999\) | −4.45879e10 | −1.41494 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 11.8.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 99.8.a.c.1.1 | 2 | |||
4.3 | odd | 2 | 176.8.a.d.1.2 | 2 | |||
5.4 | even | 2 | 275.8.a.a.1.1 | 2 | |||
7.6 | odd | 2 | 539.8.a.a.1.2 | 2 | |||
11.10 | odd | 2 | 121.8.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.8.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.8.a.c.1.1 | 2 | 3.2 | odd | 2 | |||
121.8.a.b.1.1 | 2 | 11.10 | odd | 2 | |||
176.8.a.d.1.2 | 2 | 4.3 | odd | 2 | |||
275.8.a.a.1.1 | 2 | 5.4 | even | 2 | |||
539.8.a.a.1.2 | 2 | 7.6 | odd | 2 |