Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,100,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 100, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 100);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 100 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(62.0676682981\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + \cdots + 23\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{109}\cdot 3^{44}\cdot 5^{13}\cdot 7^{9}\cdot 11^{3}\cdot 13\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(4.33987e12\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.86466e14 | 0.359822 | 0.179911 | − | 0.983683i | \(-0.442419\pi\) | ||||
0.179911 | + | 0.983683i | \(0.442419\pi\) | |||||||
\(3\) | 2.01536e23 | 0.486241 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(4\) | −5.51763e29 | −0.870528 | ||||||||
\(5\) | −4.79915e34 | −1.20823 | −0.604114 | − | 0.796898i | \(-0.706473\pi\) | ||||
−0.604114 | + | 0.796898i | \(0.706473\pi\) | |||||||
\(6\) | 5.77333e37 | 0.174960 | ||||||||
\(7\) | −6.92478e41 | −1.01872 | −0.509358 | − | 0.860555i | \(-0.670117\pi\) | ||||
−0.509358 | + | 0.860555i | \(0.670117\pi\) | |||||||
\(8\) | −3.39630e44 | −0.673057 | ||||||||
\(9\) | −1.31176e47 | −0.763570 | ||||||||
\(10\) | −1.37479e49 | −0.434747 | ||||||||
\(11\) | 1.55674e51 | 0.439823 | 0.219912 | − | 0.975520i | \(-0.429423\pi\) | ||||
0.219912 | + | 0.975520i | \(0.429423\pi\) | |||||||
\(12\) | −1.11200e53 | −0.423286 | ||||||||
\(13\) | −2.14548e55 | −1.55356 | −0.776781 | − | 0.629771i | \(-0.783149\pi\) | ||||
−0.776781 | + | 0.629771i | \(0.783149\pi\) | |||||||
\(14\) | −1.98371e56 | −0.366557 | ||||||||
\(15\) | −9.67203e57 | −0.587490 | ||||||||
\(16\) | 2.52429e59 | 0.628347 | ||||||||
\(17\) | −1.39488e61 | −1.72709 | −0.863545 | − | 0.504272i | \(-0.831761\pi\) | ||||
−0.863545 | + | 0.504272i | \(0.831761\pi\) | |||||||
\(18\) | −3.75773e61 | −0.274749 | ||||||||
\(19\) | 1.51628e63 | 0.762917 | 0.381459 | − | 0.924386i | \(-0.375422\pi\) | ||||
0.381459 | + | 0.924386i | \(0.375422\pi\) | |||||||
\(20\) | 2.64799e64 | 1.05180 | ||||||||
\(21\) | −1.39560e65 | −0.495341 | ||||||||
\(22\) | 4.45952e65 | 0.158258 | ||||||||
\(23\) | 2.55387e67 | 1.00386 | 0.501928 | − | 0.864910i | \(-0.332624\pi\) | ||||
0.501928 | + | 0.864910i | \(0.332624\pi\) | |||||||
\(24\) | −6.84479e67 | −0.327268 | ||||||||
\(25\) | 7.25462e68 | 0.459816 | ||||||||
\(26\) | −6.14606e69 | −0.559006 | ||||||||
\(27\) | −6.10591e70 | −0.857520 | ||||||||
\(28\) | 3.82084e71 | 0.886821 | ||||||||
\(29\) | 1.39180e72 | 0.568692 | 0.284346 | − | 0.958722i | \(-0.408224\pi\) | ||||
0.284346 | + | 0.958722i | \(0.408224\pi\) | |||||||
\(30\) | −2.77071e72 | −0.211392 | ||||||||
\(31\) | −1.44293e73 | −0.217191 | −0.108595 | − | 0.994086i | \(-0.534635\pi\) | ||||
−0.108595 | + | 0.994086i | \(0.534635\pi\) | |||||||
\(32\) | 2.87578e74 | 0.899150 | ||||||||
\(33\) | 3.13740e74 | 0.213860 | ||||||||
\(34\) | −3.99585e75 | −0.621445 | ||||||||
\(35\) | 3.32331e76 | 1.23084 | ||||||||
\(36\) | 7.23778e76 | 0.664709 | ||||||||
\(37\) | −5.19313e77 | −1.22869 | −0.614347 | − | 0.789036i | \(-0.710580\pi\) | ||||
−0.614347 | + | 0.789036i | \(0.710580\pi\) | |||||||
\(38\) | 4.34363e77 | 0.274514 | ||||||||
\(39\) | −4.32392e78 | −0.755405 | ||||||||
\(40\) | 1.62994e79 | 0.813207 | ||||||||
\(41\) | −3.58403e79 | −0.526709 | −0.263354 | − | 0.964699i | \(-0.584829\pi\) | ||||
−0.263354 | + | 0.964699i | \(0.584829\pi\) | |||||||
\(42\) | −3.99790e79 | −0.178235 | ||||||||
\(43\) | 2.84099e80 | 0.395168 | 0.197584 | − | 0.980286i | \(-0.436690\pi\) | ||||
0.197584 | + | 0.980286i | \(0.436690\pi\) | |||||||
\(44\) | −8.58951e80 | −0.382878 | ||||||||
\(45\) | 6.29531e81 | 0.922567 | ||||||||
\(46\) | 7.31597e81 | 0.361209 | ||||||||
\(47\) | −7.73779e82 | −1.31757 | −0.658784 | − | 0.752332i | \(-0.728929\pi\) | ||||
−0.658784 | + | 0.752332i | \(0.728929\pi\) | |||||||
\(48\) | 5.08736e82 | 0.305528 | ||||||||
\(49\) | 1.74580e82 | 0.0377824 | ||||||||
\(50\) | 2.07820e83 | 0.165452 | ||||||||
\(51\) | −2.81119e84 | −0.839782 | ||||||||
\(52\) | 1.18380e85 | 1.35242 | ||||||||
\(53\) | 1.89817e84 | 0.0844655 | 0.0422328 | − | 0.999108i | \(-0.486553\pi\) | ||||
0.0422328 | + | 0.999108i | \(0.486553\pi\) | |||||||
\(54\) | −1.74913e85 | −0.308555 | ||||||||
\(55\) | −7.47103e85 | −0.531407 | ||||||||
\(56\) | 2.35187e86 | 0.685654 | ||||||||
\(57\) | 3.05587e86 | 0.370962 | ||||||||
\(58\) | 3.98704e86 | 0.204628 | ||||||||
\(59\) | −2.13540e87 | −0.470224 | −0.235112 | − | 0.971968i | \(-0.575546\pi\) | ||||
−0.235112 | + | 0.971968i | \(0.575546\pi\) | |||||||
\(60\) | 5.33667e87 | 0.511427 | ||||||||
\(61\) | 4.67707e88 | 1.97764 | 0.988819 | − | 0.149121i | \(-0.0476444\pi\) | ||||
0.988819 | + | 0.149121i | \(0.0476444\pi\) | |||||||
\(62\) | −4.13350e87 | −0.0781501 | ||||||||
\(63\) | 9.08362e88 | 0.777861 | ||||||||
\(64\) | −7.76144e88 | −0.304813 | ||||||||
\(65\) | 1.02965e90 | 1.87706 | ||||||||
\(66\) | 8.98757e88 | 0.0769515 | ||||||||
\(67\) | 3.33536e90 | 1.35656 | 0.678282 | − | 0.734802i | \(-0.262725\pi\) | ||||
0.678282 | + | 0.734802i | \(0.262725\pi\) | |||||||
\(68\) | 7.69642e90 | 1.50348 | ||||||||
\(69\) | 5.14698e90 | 0.488116 | ||||||||
\(70\) | 9.52013e90 | 0.442884 | ||||||||
\(71\) | 2.25284e91 | 0.519328 | 0.259664 | − | 0.965699i | \(-0.416388\pi\) | ||||
0.259664 | + | 0.965699i | \(0.416388\pi\) | |||||||
\(72\) | 4.45512e91 | 0.513926 | ||||||||
\(73\) | 2.47879e90 | 0.0144464 | 0.00722319 | − | 0.999974i | \(-0.497701\pi\) | ||||
0.00722319 | + | 0.999974i | \(0.497701\pi\) | |||||||
\(74\) | −1.48765e92 | −0.442111 | ||||||||
\(75\) | 1.46207e92 | 0.223581 | ||||||||
\(76\) | −8.36629e92 | −0.664141 | ||||||||
\(77\) | −1.07801e93 | −0.448055 | ||||||||
\(78\) | −1.23866e93 | −0.271812 | ||||||||
\(79\) | −1.29965e94 | −1.51805 | −0.759025 | − | 0.651062i | \(-0.774324\pi\) | ||||
−0.759025 | + | 0.651062i | \(0.774324\pi\) | |||||||
\(80\) | −1.21144e94 | −0.759187 | ||||||||
\(81\) | 1.02293e94 | 0.346609 | ||||||||
\(82\) | −1.02670e94 | −0.189521 | ||||||||
\(83\) | −1.54205e95 | −1.56219 | −0.781094 | − | 0.624414i | \(-0.785338\pi\) | ||||
−0.781094 | + | 0.624414i | \(0.785338\pi\) | |||||||
\(84\) | 7.70038e94 | 0.431209 | ||||||||
\(85\) | 6.69423e95 | 2.08672 | ||||||||
\(86\) | 8.13847e94 | 0.142190 | ||||||||
\(87\) | 2.80499e95 | 0.276521 | ||||||||
\(88\) | −5.28716e95 | −0.296026 | ||||||||
\(89\) | 2.29359e96 | 0.734025 | 0.367013 | − | 0.930216i | \(-0.380381\pi\) | ||||
0.367013 | + | 0.930216i | \(0.380381\pi\) | |||||||
\(90\) | 1.80339e96 | 0.331960 | ||||||||
\(91\) | 1.48570e97 | 1.58264 | ||||||||
\(92\) | −1.40913e97 | −0.873884 | ||||||||
\(93\) | −2.90803e96 | −0.105607 | ||||||||
\(94\) | −2.21661e97 | −0.474090 | ||||||||
\(95\) | −7.27688e97 | −0.921778 | ||||||||
\(96\) | 5.79575e97 | 0.437204 | ||||||||
\(97\) | −3.70442e98 | −1.67309 | −0.836545 | − | 0.547898i | \(-0.815428\pi\) | ||||
−0.836545 | + | 0.547898i | \(0.815428\pi\) | |||||||
\(98\) | 5.00113e96 | 0.0135949 | ||||||||
\(99\) | −2.04206e98 | −0.335836 | ||||||||
\(100\) | −4.00283e98 | −0.400283 | ||||||||
\(101\) | 2.07787e99 | 1.26972 | 0.634862 | − | 0.772625i | \(-0.281057\pi\) | ||||
0.634862 | + | 0.772625i | \(0.281057\pi\) | |||||||
\(102\) | −8.05310e98 | −0.302172 | ||||||||
\(103\) | 1.09026e99 | 0.252399 | 0.126200 | − | 0.992005i | \(-0.459722\pi\) | ||||
0.126200 | + | 0.992005i | \(0.459722\pi\) | |||||||
\(104\) | 7.28670e99 | 1.04564 | ||||||||
\(105\) | 6.69767e99 | 0.598486 | ||||||||
\(106\) | 5.43760e98 | 0.0303926 | ||||||||
\(107\) | −1.04962e100 | −0.368583 | −0.184292 | − | 0.982872i | \(-0.558999\pi\) | ||||
−0.184292 | + | 0.982872i | \(0.558999\pi\) | |||||||
\(108\) | 3.36901e100 | 0.746495 | ||||||||
\(109\) | −5.13800e99 | −0.0721410 | −0.0360705 | − | 0.999349i | \(-0.511484\pi\) | ||||
−0.0360705 | + | 0.999349i | \(0.511484\pi\) | |||||||
\(110\) | −2.14019e100 | −0.191212 | ||||||||
\(111\) | −1.04660e101 | −0.597441 | ||||||||
\(112\) | −1.74801e101 | −0.640107 | ||||||||
\(113\) | −1.99419e101 | −0.470309 | −0.235154 | − | 0.971958i | \(-0.575560\pi\) | ||||
−0.235154 | + | 0.971958i | \(0.575560\pi\) | |||||||
\(114\) | 8.75401e100 | 0.133480 | ||||||||
\(115\) | −1.22564e102 | −1.21289 | ||||||||
\(116\) | −7.67945e101 | −0.495062 | ||||||||
\(117\) | 2.81435e102 | 1.18625 | ||||||||
\(118\) | −6.11719e101 | −0.169197 | ||||||||
\(119\) | 9.65924e102 | 1.75941 | ||||||||
\(120\) | 3.28492e102 | 0.395414 | ||||||||
\(121\) | −1.01044e103 | −0.806556 | ||||||||
\(122\) | 1.33982e103 | 0.711598 | ||||||||
\(123\) | −7.22312e102 | −0.256107 | ||||||||
\(124\) | 7.96155e102 | 0.189071 | ||||||||
\(125\) | 4.09012e103 | 0.652666 | ||||||||
\(126\) | 2.60215e103 | 0.279891 | ||||||||
\(127\) | −2.58406e104 | −1.87940 | −0.939700 | − | 0.342001i | \(-0.888895\pi\) | ||||
−0.939700 | + | 0.342001i | \(0.888895\pi\) | |||||||
\(128\) | −2.04508e104 | −1.00883 | ||||||||
\(129\) | 5.72564e103 | 0.192147 | ||||||||
\(130\) | 2.94959e104 | 0.675407 | ||||||||
\(131\) | −3.18081e104 | −0.498434 | −0.249217 | − | 0.968448i | \(-0.580173\pi\) | ||||
−0.249217 | + | 0.968448i | \(0.580173\pi\) | |||||||
\(132\) | −1.73110e104 | −0.186171 | ||||||||
\(133\) | −1.04999e105 | −0.777196 | ||||||||
\(134\) | 9.55467e104 | 0.488122 | ||||||||
\(135\) | 2.93032e105 | 1.03608 | ||||||||
\(136\) | 4.73743e105 | 1.16243 | ||||||||
\(137\) | −3.08427e105 | −0.526605 | −0.263302 | − | 0.964713i | \(-0.584812\pi\) | ||||
−0.263302 | + | 0.964713i | \(0.584812\pi\) | |||||||
\(138\) | 1.47443e105 | 0.175635 | ||||||||
\(139\) | 1.94625e106 | 1.62168 | 0.810841 | − | 0.585266i | \(-0.199010\pi\) | ||||
0.810841 | + | 0.585266i | \(0.199010\pi\) | |||||||
\(140\) | −1.83368e106 | −1.07148 | ||||||||
\(141\) | −1.55945e106 | −0.640656 | ||||||||
\(142\) | 6.45360e105 | 0.186866 | ||||||||
\(143\) | −3.33995e106 | −0.683292 | ||||||||
\(144\) | −3.31125e106 | −0.479787 | ||||||||
\(145\) | −6.67947e106 | −0.687109 | ||||||||
\(146\) | 7.10089e104 | 0.00519812 | ||||||||
\(147\) | 3.51843e105 | 0.0183713 | ||||||||
\(148\) | 2.86537e107 | 1.06961 | ||||||||
\(149\) | −3.53752e107 | −0.946192 | −0.473096 | − | 0.881011i | \(-0.656864\pi\) | ||||
−0.473096 | + | 0.881011i | \(0.656864\pi\) | |||||||
\(150\) | 4.18833e106 | 0.0804495 | ||||||||
\(151\) | 7.26718e107 | 1.00463 | 0.502316 | − | 0.864684i | \(-0.332481\pi\) | ||||
0.502316 | + | 0.864684i | \(0.332481\pi\) | |||||||
\(152\) | −5.14976e107 | −0.513487 | ||||||||
\(153\) | 1.82974e108 | 1.31875 | ||||||||
\(154\) | −3.08812e107 | −0.161220 | ||||||||
\(155\) | 6.92484e107 | 0.262416 | ||||||||
\(156\) | 2.38578e108 | 0.657602 | ||||||||
\(157\) | −2.65806e108 | −0.533988 | −0.266994 | − | 0.963698i | \(-0.586030\pi\) | ||||
−0.266994 | + | 0.963698i | \(0.586030\pi\) | |||||||
\(158\) | −3.72306e108 | −0.546228 | ||||||||
\(159\) | 3.82550e107 | 0.0410706 | ||||||||
\(160\) | −1.38013e109 | −1.08638 | ||||||||
\(161\) | −1.76850e109 | −1.02264 | ||||||||
\(162\) | 2.93036e108 | 0.124717 | ||||||||
\(163\) | 1.62131e109 | 0.508838 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(164\) | 1.97753e109 | 0.458515 | ||||||||
\(165\) | −1.50568e109 | −0.258392 | ||||||||
\(166\) | −4.41745e109 | −0.562110 | ||||||||
\(167\) | 6.73702e109 | 0.636800 | 0.318400 | − | 0.947957i | \(-0.396855\pi\) | ||||
0.318400 | + | 0.947957i | \(0.396855\pi\) | |||||||
\(168\) | 4.73987e109 | 0.333393 | ||||||||
\(169\) | 2.69591e110 | 1.41356 | ||||||||
\(170\) | 1.91767e110 | 0.750848 | ||||||||
\(171\) | −1.98899e110 | −0.582541 | ||||||||
\(172\) | −1.56755e110 | −0.344005 | ||||||||
\(173\) | −4.92610e110 | −0.811374 | −0.405687 | − | 0.914012i | \(-0.632968\pi\) | ||||
−0.405687 | + | 0.914012i | \(0.632968\pi\) | |||||||
\(174\) | 8.03533e109 | 0.0994984 | ||||||||
\(175\) | −5.02366e110 | −0.468422 | ||||||||
\(176\) | 3.92966e110 | 0.276362 | ||||||||
\(177\) | −4.30361e110 | −0.228642 | ||||||||
\(178\) | 6.57036e110 | 0.264119 | ||||||||
\(179\) | −3.43689e111 | −1.04698 | −0.523492 | − | 0.852030i | \(-0.675371\pi\) | ||||
−0.523492 | + | 0.852030i | \(0.675371\pi\) | |||||||
\(180\) | −3.47352e111 | −0.803120 | ||||||||
\(181\) | 1.56523e111 | 0.275099 | 0.137549 | − | 0.990495i | \(-0.456077\pi\) | ||||
0.137549 | + | 0.990495i | \(0.456077\pi\) | |||||||
\(182\) | 4.25602e111 | 0.569468 | ||||||||
\(183\) | 9.42599e111 | 0.961608 | ||||||||
\(184\) | −8.67372e111 | −0.675652 | ||||||||
\(185\) | 2.49226e112 | 1.48454 | ||||||||
\(186\) | −8.33051e110 | −0.0379998 | ||||||||
\(187\) | −2.17146e112 | −0.759614 | ||||||||
\(188\) | 4.26943e112 | 1.14698 | ||||||||
\(189\) | 4.22821e112 | 0.873569 | ||||||||
\(190\) | −2.08458e112 | −0.331676 | ||||||||
\(191\) | −1.50997e113 | −1.85275 | −0.926377 | − | 0.376598i | \(-0.877094\pi\) | ||||
−0.926377 | + | 0.376598i | \(0.877094\pi\) | |||||||
\(192\) | −1.56421e112 | −0.148213 | ||||||||
\(193\) | −7.52564e112 | −0.551387 | −0.275693 | − | 0.961246i | \(-0.588907\pi\) | ||||
−0.275693 | + | 0.961246i | \(0.588907\pi\) | |||||||
\(194\) | −1.06119e113 | −0.602015 | ||||||||
\(195\) | 2.07512e113 | 0.912702 | ||||||||
\(196\) | −9.63269e111 | −0.0328906 | ||||||||
\(197\) | −2.61400e113 | −0.693789 | −0.346895 | − | 0.937904i | \(-0.612764\pi\) | ||||
−0.346895 | + | 0.937904i | \(0.612764\pi\) | |||||||
\(198\) | −5.84981e112 | −0.120841 | ||||||||
\(199\) | 7.26456e113 | 1.16945 | 0.584725 | − | 0.811231i | \(-0.301202\pi\) | ||||
0.584725 | + | 0.811231i | \(0.301202\pi\) | |||||||
\(200\) | −2.46389e113 | −0.309482 | ||||||||
\(201\) | 6.72197e113 | 0.659617 | ||||||||
\(202\) | 5.95237e113 | 0.456875 | ||||||||
\(203\) | −9.63793e113 | −0.579335 | ||||||||
\(204\) | 1.55111e114 | 0.731054 | ||||||||
\(205\) | 1.72003e114 | 0.636384 | ||||||||
\(206\) | 3.12322e113 | 0.0908188 | ||||||||
\(207\) | −3.35006e114 | −0.766514 | ||||||||
\(208\) | −5.41581e114 | −0.976176 | ||||||||
\(209\) | 2.36046e114 | 0.335549 | ||||||||
\(210\) | 1.91865e114 | 0.215348 | ||||||||
\(211\) | −1.36428e115 | −1.21038 | −0.605190 | − | 0.796081i | \(-0.706903\pi\) | ||||
−0.605190 | + | 0.796081i | \(0.706903\pi\) | |||||||
\(212\) | −1.04734e114 | −0.0735296 | ||||||||
\(213\) | 4.54029e114 | 0.252518 | ||||||||
\(214\) | −3.00680e114 | −0.132624 | ||||||||
\(215\) | −1.36344e115 | −0.477453 | ||||||||
\(216\) | 2.07375e115 | 0.577160 | ||||||||
\(217\) | 9.99198e114 | 0.221256 | ||||||||
\(218\) | −1.47186e114 | −0.0259579 | ||||||||
\(219\) | 4.99567e113 | 0.00702442 | ||||||||
\(220\) | 4.12223e115 | 0.462605 | ||||||||
\(221\) | 2.99269e116 | 2.68314 | ||||||||
\(222\) | −2.99816e115 | −0.214972 | ||||||||
\(223\) | −1.88560e116 | −1.08233 | −0.541164 | − | 0.840917i | \(-0.682016\pi\) | ||||
−0.541164 | + | 0.840917i | \(0.682016\pi\) | |||||||
\(224\) | −1.99142e116 | −0.915979 | ||||||||
\(225\) | −9.51628e115 | −0.351102 | ||||||||
\(226\) | −5.71267e115 | −0.169228 | ||||||||
\(227\) | −1.87429e116 | −0.446228 | −0.223114 | − | 0.974792i | \(-0.571622\pi\) | ||||
−0.223114 | + | 0.974792i | \(0.571622\pi\) | |||||||
\(228\) | −1.68611e116 | −0.322932 | ||||||||
\(229\) | 5.20732e116 | 0.803078 | 0.401539 | − | 0.915842i | \(-0.368475\pi\) | ||||
0.401539 | + | 0.915842i | \(0.368475\pi\) | |||||||
\(230\) | −3.51104e116 | −0.436423 | ||||||||
\(231\) | −2.17258e116 | −0.217863 | ||||||||
\(232\) | −4.72698e116 | −0.382762 | ||||||||
\(233\) | −7.31940e116 | −0.479024 | −0.239512 | − | 0.970893i | \(-0.576987\pi\) | ||||
−0.239512 | + | 0.970893i | \(0.576987\pi\) | |||||||
\(234\) | 8.06214e116 | 0.426840 | ||||||||
\(235\) | 3.71348e117 | 1.59192 | ||||||||
\(236\) | 1.17824e117 | 0.409344 | ||||||||
\(237\) | −2.61927e117 | −0.738138 | ||||||||
\(238\) | 2.76704e117 | 0.633076 | ||||||||
\(239\) | −4.11127e116 | −0.0764329 | −0.0382165 | − | 0.999269i | \(-0.512168\pi\) | ||||
−0.0382165 | + | 0.999269i | \(0.512168\pi\) | |||||||
\(240\) | −2.44150e117 | −0.369148 | ||||||||
\(241\) | 6.44827e117 | 0.793596 | 0.396798 | − | 0.917906i | \(-0.370121\pi\) | ||||
0.396798 | + | 0.917906i | \(0.370121\pi\) | |||||||
\(242\) | −2.89456e117 | −0.290217 | ||||||||
\(243\) | 1.25511e118 | 1.02606 | ||||||||
\(244\) | −2.58063e118 | −1.72159 | ||||||||
\(245\) | −8.37837e116 | −0.0456498 | ||||||||
\(246\) | −2.06918e117 | −0.0921530 | ||||||||
\(247\) | −3.25316e118 | −1.18524 | ||||||||
\(248\) | 4.90063e117 | 0.146182 | ||||||||
\(249\) | −3.10780e118 | −0.759600 | ||||||||
\(250\) | 1.17168e118 | 0.234844 | ||||||||
\(251\) | 1.09110e119 | 1.79479 | 0.897396 | − | 0.441226i | \(-0.145456\pi\) | ||||
0.897396 | + | 0.441226i | \(0.145456\pi\) | |||||||
\(252\) | −5.01200e118 | −0.677150 | ||||||||
\(253\) | 3.97571e118 | 0.441519 | ||||||||
\(254\) | −7.40246e118 | −0.676249 | ||||||||
\(255\) | 1.34913e119 | 1.01465 | ||||||||
\(256\) | −9.39066e117 | −0.0581859 | ||||||||
\(257\) | 1.79659e119 | 0.917823 | 0.458911 | − | 0.888482i | \(-0.348240\pi\) | ||||
0.458911 | + | 0.888482i | \(0.348240\pi\) | |||||||
\(258\) | 1.64020e118 | 0.0691387 | ||||||||
\(259\) | 3.59613e119 | 1.25169 | ||||||||
\(260\) | −5.68121e119 | −1.63403 | ||||||||
\(261\) | −1.82570e119 | −0.434236 | ||||||||
\(262\) | −9.11192e118 | −0.179348 | ||||||||
\(263\) | −4.33923e119 | −0.707299 | −0.353650 | − | 0.935378i | \(-0.615059\pi\) | ||||
−0.353650 | + | 0.935378i | \(0.615059\pi\) | |||||||
\(264\) | −1.06556e119 | −0.143940 | ||||||||
\(265\) | −9.10960e118 | −0.102054 | ||||||||
\(266\) | −3.00787e119 | −0.279652 | ||||||||
\(267\) | 4.62243e119 | 0.356913 | ||||||||
\(268\) | −1.84033e120 | −1.18093 | ||||||||
\(269\) | 2.31687e120 | 1.23642 | 0.618208 | − | 0.786015i | \(-0.287859\pi\) | ||||
0.618208 | + | 0.786015i | \(0.287859\pi\) | |||||||
\(270\) | 8.39435e119 | 0.372804 | ||||||||
\(271\) | 2.02469e120 | 0.748821 | 0.374410 | − | 0.927263i | \(-0.377845\pi\) | ||||
0.374410 | + | 0.927263i | \(0.377845\pi\) | |||||||
\(272\) | −3.52108e120 | −1.08521 | ||||||||
\(273\) | 2.99422e120 | 0.769544 | ||||||||
\(274\) | −8.83538e119 | −0.189484 | ||||||||
\(275\) | 1.12935e120 | 0.202238 | ||||||||
\(276\) | −2.83991e120 | −0.424918 | ||||||||
\(277\) | 1.08848e121 | 1.36167 | 0.680836 | − | 0.732436i | \(-0.261617\pi\) | ||||
0.680836 | + | 0.732436i | \(0.261617\pi\) | |||||||
\(278\) | 5.57534e120 | 0.583517 | ||||||||
\(279\) | 1.89277e120 | 0.165840 | ||||||||
\(280\) | −1.12870e121 | −0.828427 | ||||||||
\(281\) | −1.65497e121 | −1.01819 | −0.509094 | − | 0.860711i | \(-0.670020\pi\) | ||||
−0.509094 | + | 0.860711i | \(0.670020\pi\) | |||||||
\(282\) | −4.46728e120 | −0.230522 | ||||||||
\(283\) | −4.53692e120 | −0.196486 | −0.0982432 | − | 0.995162i | \(-0.531322\pi\) | ||||
−0.0982432 | + | 0.995162i | \(0.531322\pi\) | |||||||
\(284\) | −1.24303e121 | −0.452089 | ||||||||
\(285\) | −1.46656e121 | −0.448206 | ||||||||
\(286\) | −9.56782e120 | −0.245864 | ||||||||
\(287\) | 2.48186e121 | 0.536566 | ||||||||
\(288\) | −3.77233e121 | −0.686564 | ||||||||
\(289\) | 1.29339e122 | 1.98284 | ||||||||
\(290\) | −1.91344e121 | −0.247237 | ||||||||
\(291\) | −7.46576e121 | −0.813525 | ||||||||
\(292\) | −1.36771e120 | −0.0125760 | ||||||||
\(293\) | 1.79667e122 | 1.39483 | 0.697415 | − | 0.716668i | \(-0.254334\pi\) | ||||
0.697415 | + | 0.716668i | \(0.254334\pi\) | |||||||
\(294\) | 1.00791e120 | 0.00661041 | ||||||||
\(295\) | 1.02481e122 | 0.568138 | ||||||||
\(296\) | 1.76374e122 | 0.826981 | ||||||||
\(297\) | −9.50531e121 | −0.377157 | ||||||||
\(298\) | −1.01338e122 | −0.340461 | ||||||||
\(299\) | −5.47928e122 | −1.55955 | ||||||||
\(300\) | −8.06715e121 | −0.194634 | ||||||||
\(301\) | −1.96733e122 | −0.402564 | ||||||||
\(302\) | 2.08180e122 | 0.361489 | ||||||||
\(303\) | 4.18766e122 | 0.617392 | ||||||||
\(304\) | 3.82754e122 | 0.479377 | ||||||||
\(305\) | −2.24459e123 | −2.38944 | ||||||||
\(306\) | 5.24158e122 | 0.474517 | ||||||||
\(307\) | 3.36933e119 | 0.000259534 0 | 0.000129767 | − | 1.00000i | \(-0.499959\pi\) | ||||
0.000129767 | 1.00000i | \(0.499959\pi\) | ||||||||
\(308\) | 5.94805e122 | 0.390044 | ||||||||
\(309\) | 2.19727e122 | 0.122727 | ||||||||
\(310\) | 1.98373e122 | 0.0944232 | ||||||||
\(311\) | 2.85284e123 | 1.15781 | 0.578907 | − | 0.815394i | \(-0.303479\pi\) | ||||
0.578907 | + | 0.815394i | \(0.303479\pi\) | |||||||
\(312\) | 1.46854e123 | 0.508431 | ||||||||
\(313\) | 9.19803e121 | 0.0271800 | 0.0135900 | − | 0.999908i | \(-0.495674\pi\) | ||||
0.0135900 | + | 0.999908i | \(0.495674\pi\) | |||||||
\(314\) | −7.61442e122 | −0.192141 | ||||||||
\(315\) | −4.35937e123 | −0.939834 | ||||||||
\(316\) | 7.17099e123 | 1.32150 | ||||||||
\(317\) | −4.99463e123 | −0.787172 | −0.393586 | − | 0.919288i | \(-0.628766\pi\) | ||||
−0.393586 | + | 0.919288i | \(0.628766\pi\) | |||||||
\(318\) | 1.09588e122 | 0.0147781 | ||||||||
\(319\) | 2.16667e123 | 0.250124 | ||||||||
\(320\) | 3.72483e123 | 0.368284 | ||||||||
\(321\) | −2.11537e123 | −0.179220 | ||||||||
\(322\) | −5.06615e123 | −0.367970 | ||||||||
\(323\) | −2.11503e124 | −1.31763 | ||||||||
\(324\) | −5.64417e123 | −0.301733 | ||||||||
\(325\) | −1.55646e124 | −0.714353 | ||||||||
\(326\) | 4.64449e123 | 0.183091 | ||||||||
\(327\) | −1.03549e123 | −0.0350779 | ||||||||
\(328\) | 1.21724e124 | 0.354505 | ||||||||
\(329\) | 5.35825e124 | 1.34223 | ||||||||
\(330\) | −4.31327e123 | −0.0929750 | ||||||||
\(331\) | −2.71673e124 | −0.504152 | −0.252076 | − | 0.967707i | \(-0.581113\pi\) | ||||
−0.252076 | + | 0.967707i | \(0.581113\pi\) | |||||||
\(332\) | 8.50846e124 | 1.35993 | ||||||||
\(333\) | 6.81211e124 | 0.938193 | ||||||||
\(334\) | 1.92993e124 | 0.229135 | ||||||||
\(335\) | −1.60069e125 | −1.63904 | ||||||||
\(336\) | −3.52289e124 | −0.311246 | ||||||||
\(337\) | 1.28573e125 | 0.980550 | 0.490275 | − | 0.871568i | \(-0.336896\pi\) | ||||
0.490275 | + | 0.871568i | \(0.336896\pi\) | |||||||
\(338\) | 7.72284e124 | 0.508628 | ||||||||
\(339\) | −4.01902e124 | −0.228683 | ||||||||
\(340\) | −3.69363e125 | −1.81655 | ||||||||
\(341\) | −2.24627e124 | −0.0955256 | ||||||||
\(342\) | −5.69779e124 | −0.209611 | ||||||||
\(343\) | 3.07883e125 | 0.980227 | ||||||||
\(344\) | −9.64887e124 | −0.265971 | ||||||||
\(345\) | −2.47011e125 | −0.589755 | ||||||||
\(346\) | −1.41116e125 | −0.291950 | ||||||||
\(347\) | −1.50266e125 | −0.269496 | −0.134748 | − | 0.990880i | \(-0.543022\pi\) | ||||
−0.134748 | + | 0.990880i | \(0.543022\pi\) | |||||||
\(348\) | −1.54769e125 | −0.240719 | ||||||||
\(349\) | 5.17125e125 | 0.697809 | 0.348905 | − | 0.937158i | \(-0.386554\pi\) | ||||
0.348905 | + | 0.937158i | \(0.386554\pi\) | |||||||
\(350\) | −1.43911e125 | −0.168549 | ||||||||
\(351\) | 1.31001e126 | 1.33221 | ||||||||
\(352\) | 4.47685e125 | 0.395467 | ||||||||
\(353\) | 7.00287e125 | 0.537561 | 0.268781 | − | 0.963201i | \(-0.413379\pi\) | ||||
0.268781 | + | 0.963201i | \(0.413379\pi\) | |||||||
\(354\) | −1.23284e125 | −0.0822706 | ||||||||
\(355\) | −1.08117e126 | −0.627467 | ||||||||
\(356\) | −1.26552e126 | −0.638990 | ||||||||
\(357\) | 1.94669e126 | 0.855499 | ||||||||
\(358\) | −9.84550e125 | −0.376728 | ||||||||
\(359\) | 3.38663e126 | 1.12874 | 0.564368 | − | 0.825523i | \(-0.309120\pi\) | ||||
0.564368 | + | 0.825523i | \(0.309120\pi\) | |||||||
\(360\) | −2.13808e126 | −0.620940 | ||||||||
\(361\) | −1.65097e126 | −0.417957 | ||||||||
\(362\) | 4.48385e125 | 0.0989867 | ||||||||
\(363\) | −2.03640e126 | −0.392180 | ||||||||
\(364\) | −8.19753e126 | −1.37773 | ||||||||
\(365\) | −1.18961e125 | −0.0174545 | ||||||||
\(366\) | 2.70022e126 | 0.346008 | ||||||||
\(367\) | −9.71020e126 | −1.08707 | −0.543536 | − | 0.839386i | \(-0.682915\pi\) | ||||
−0.543536 | + | 0.839386i | \(0.682915\pi\) | |||||||
\(368\) | 6.44671e126 | 0.630770 | ||||||||
\(369\) | 4.70137e126 | 0.402179 | ||||||||
\(370\) | 7.13947e126 | 0.534171 | ||||||||
\(371\) | −1.31444e126 | −0.0860464 | ||||||||
\(372\) | 1.60454e126 | 0.0919339 | ||||||||
\(373\) | 2.06903e127 | 1.03796 | 0.518980 | − | 0.854786i | \(-0.326312\pi\) | ||||
0.518980 | + | 0.854786i | \(0.326312\pi\) | |||||||
\(374\) | −6.22050e126 | −0.273326 | ||||||||
\(375\) | 8.24309e126 | 0.317353 | ||||||||
\(376\) | 2.62799e127 | 0.886799 | ||||||||
\(377\) | −2.98609e127 | −0.883498 | ||||||||
\(378\) | 1.21124e127 | 0.314329 | ||||||||
\(379\) | 7.13227e126 | 0.162400 | 0.0812002 | − | 0.996698i | \(-0.474125\pi\) | ||||
0.0812002 | + | 0.996698i | \(0.474125\pi\) | |||||||
\(380\) | 4.01511e127 | 0.802434 | ||||||||
\(381\) | −5.20783e127 | −0.913841 | ||||||||
\(382\) | −4.32556e127 | −0.666662 | ||||||||
\(383\) | −1.17016e128 | −1.58456 | −0.792278 | − | 0.610160i | \(-0.791105\pi\) | ||||
−0.792278 | + | 0.610160i | \(0.791105\pi\) | |||||||
\(384\) | −4.12159e127 | −0.490534 | ||||||||
\(385\) | 5.17352e127 | 0.541353 | ||||||||
\(386\) | −2.15584e127 | −0.198401 | ||||||||
\(387\) | −3.72669e127 | −0.301738 | ||||||||
\(388\) | 2.04396e128 | 1.45647 | ||||||||
\(389\) | 1.08825e128 | 0.682691 | 0.341345 | − | 0.939938i | \(-0.389117\pi\) | ||||
0.341345 | + | 0.939938i | \(0.389117\pi\) | |||||||
\(390\) | 5.94450e127 | 0.328410 | ||||||||
\(391\) | −3.56234e128 | −1.73375 | ||||||||
\(392\) | −5.92928e126 | −0.0254297 | ||||||||
\(393\) | −6.41048e127 | −0.242359 | ||||||||
\(394\) | −7.48821e127 | −0.249641 | ||||||||
\(395\) | 6.23722e128 | 1.83415 | ||||||||
\(396\) | 1.12673e128 | 0.292354 | ||||||||
\(397\) | 1.78683e128 | 0.409216 | 0.204608 | − | 0.978844i | \(-0.434408\pi\) | ||||
0.204608 | + | 0.978844i | \(0.434408\pi\) | |||||||
\(398\) | 2.08105e128 | 0.420794 | ||||||||
\(399\) | −2.11612e128 | −0.377905 | ||||||||
\(400\) | 1.83127e128 | 0.288924 | ||||||||
\(401\) | −6.41533e128 | −0.894484 | −0.447242 | − | 0.894413i | \(-0.647594\pi\) | ||||
−0.447242 | + | 0.894413i | \(0.647594\pi\) | |||||||
\(402\) | 1.92561e128 | 0.237345 | ||||||||
\(403\) | 3.09578e128 | 0.337420 | ||||||||
\(404\) | −1.14649e129 | −1.10533 | ||||||||
\(405\) | −4.90922e128 | −0.418782 | ||||||||
\(406\) | −2.76094e128 | −0.208458 | ||||||||
\(407\) | −8.08435e128 | −0.540408 | ||||||||
\(408\) | 9.54765e128 | 0.565221 | ||||||||
\(409\) | −9.06187e128 | −0.475241 | −0.237621 | − | 0.971358i | \(-0.576367\pi\) | ||||
−0.237621 | + | 0.971358i | \(0.576367\pi\) | |||||||
\(410\) | 4.92729e128 | 0.228985 | ||||||||
\(411\) | −6.21593e128 | −0.256057 | ||||||||
\(412\) | −6.01565e128 | −0.219721 | ||||||||
\(413\) | 1.47872e129 | 0.479025 | ||||||||
\(414\) | −9.59676e128 | −0.275809 | ||||||||
\(415\) | 7.40053e129 | 1.88748 | ||||||||
\(416\) | −6.16994e129 | −1.39689 | ||||||||
\(417\) | 3.92240e129 | 0.788529 | ||||||||
\(418\) | 6.76191e128 | 0.120738 | ||||||||
\(419\) | 1.07548e130 | 1.70611 | 0.853055 | − | 0.521821i | \(-0.174747\pi\) | ||||
0.853055 | + | 0.521821i | \(0.174747\pi\) | |||||||
\(420\) | −3.69553e129 | −0.520998 | ||||||||
\(421\) | −4.44148e129 | −0.556626 | −0.278313 | − | 0.960490i | \(-0.589775\pi\) | ||||
−0.278313 | + | 0.960490i | \(0.589775\pi\) | |||||||
\(422\) | −3.90819e129 | −0.435522 | ||||||||
\(423\) | 1.01501e130 | 1.00606 | ||||||||
\(424\) | −6.44676e128 | −0.0568501 | ||||||||
\(425\) | −1.01193e130 | −0.794144 | ||||||||
\(426\) | 1.30064e129 | 0.0908617 | ||||||||
\(427\) | −3.23877e130 | −2.01465 | ||||||||
\(428\) | 5.79142e129 | 0.320862 | ||||||||
\(429\) | −6.73122e129 | −0.332245 | ||||||||
\(430\) | −3.90577e129 | −0.171798 | ||||||||
\(431\) | 1.43411e130 | 0.562285 | 0.281142 | − | 0.959666i | \(-0.409287\pi\) | ||||
0.281142 | + | 0.959666i | \(0.409287\pi\) | |||||||
\(432\) | −1.54131e130 | −0.538820 | ||||||||
\(433\) | 3.50235e130 | 1.09196 | 0.545982 | − | 0.837797i | \(-0.316157\pi\) | ||||
0.545982 | + | 0.837797i | \(0.316157\pi\) | |||||||
\(434\) | 2.86236e129 | 0.0796127 | ||||||||
\(435\) | −1.34616e130 | −0.334101 | ||||||||
\(436\) | 2.83495e129 | 0.0628008 | ||||||||
\(437\) | 3.87240e130 | 0.765859 | ||||||||
\(438\) | 1.43109e128 | 0.00252754 | ||||||||
\(439\) | −3.20537e130 | −0.505690 | −0.252845 | − | 0.967507i | \(-0.581366\pi\) | ||||
−0.252845 | + | 0.967507i | \(0.581366\pi\) | |||||||
\(440\) | 2.53739e130 | 0.357667 | ||||||||
\(441\) | −2.29007e129 | −0.0288495 | ||||||||
\(442\) | 8.57302e130 | 0.965454 | ||||||||
\(443\) | 3.56275e130 | 0.358757 | 0.179379 | − | 0.983780i | \(-0.442591\pi\) | ||||
0.179379 | + | 0.983780i | \(0.442591\pi\) | |||||||
\(444\) | 5.77477e130 | 0.520089 | ||||||||
\(445\) | −1.10073e131 | −0.886870 | ||||||||
\(446\) | −5.40160e130 | −0.389446 | ||||||||
\(447\) | −7.12940e130 | −0.460077 | ||||||||
\(448\) | 5.37463e130 | 0.310518 | ||||||||
\(449\) | −1.31807e131 | −0.681936 | −0.340968 | − | 0.940075i | \(-0.610755\pi\) | ||||
−0.340968 | + | 0.940075i | \(0.610755\pi\) | |||||||
\(450\) | −2.72609e130 | −0.126334 | ||||||||
\(451\) | −5.57940e130 | −0.231659 | ||||||||
\(452\) | 1.10032e131 | 0.409417 | ||||||||
\(453\) | 1.46460e131 | 0.488493 | ||||||||
\(454\) | −5.36919e130 | −0.160563 | ||||||||
\(455\) | −7.13009e131 | −1.91219 | ||||||||
\(456\) | −1.03786e131 | −0.249678 | ||||||||
\(457\) | −2.21686e131 | −0.478505 | −0.239252 | − | 0.970957i | \(-0.576902\pi\) | ||||
−0.239252 | + | 0.970957i | \(0.576902\pi\) | |||||||
\(458\) | 1.49172e131 | 0.288965 | ||||||||
\(459\) | 8.51701e131 | 1.48101 | ||||||||
\(460\) | 6.76263e131 | 1.05585 | ||||||||
\(461\) | 2.50995e131 | 0.351940 | 0.175970 | − | 0.984396i | \(-0.443694\pi\) | ||||
0.175970 | + | 0.984396i | \(0.443694\pi\) | |||||||
\(462\) | −6.22369e130 | −0.0783918 | ||||||||
\(463\) | 2.98626e131 | 0.337962 | 0.168981 | − | 0.985619i | \(-0.445952\pi\) | ||||
0.168981 | + | 0.985619i | \(0.445952\pi\) | |||||||
\(464\) | 3.51331e131 | 0.357336 | ||||||||
\(465\) | 1.39561e131 | 0.127598 | ||||||||
\(466\) | −2.09676e131 | −0.172363 | ||||||||
\(467\) | 8.36468e131 | 0.618392 | 0.309196 | − | 0.950998i | \(-0.399940\pi\) | ||||
0.309196 | + | 0.950998i | \(0.399940\pi\) | |||||||
\(468\) | −1.55285e132 | −1.03267 | ||||||||
\(469\) | −2.30967e132 | −1.38195 | ||||||||
\(470\) | 1.06379e132 | 0.572809 | ||||||||
\(471\) | −5.35695e131 | −0.259647 | ||||||||
\(472\) | 7.25247e131 | 0.316488 | ||||||||
\(473\) | 4.42269e131 | 0.173804 | ||||||||
\(474\) | −7.50331e131 | −0.265598 | ||||||||
\(475\) | 1.10001e132 | 0.350802 | ||||||||
\(476\) | −5.32961e132 | −1.53162 | ||||||||
\(477\) | −2.48993e131 | −0.0644953 | ||||||||
\(478\) | −1.17774e131 | −0.0275022 | ||||||||
\(479\) | −3.09756e132 | −0.652247 | −0.326123 | − | 0.945327i | \(-0.605743\pi\) | ||||
−0.326123 | + | 0.945327i | \(0.605743\pi\) | |||||||
\(480\) | −2.78147e132 | −0.528242 | ||||||||
\(481\) | 1.11418e133 | 1.90885 | ||||||||
\(482\) | 1.84721e132 | 0.285553 | ||||||||
\(483\) | −3.56417e132 | −0.497251 | ||||||||
\(484\) | 5.57523e132 | 0.702129 | ||||||||
\(485\) | 1.77781e133 | 2.02148 | ||||||||
\(486\) | 3.59545e132 | 0.369197 | ||||||||
\(487\) | −1.43917e133 | −1.33484 | −0.667418 | − | 0.744683i | \(-0.732601\pi\) | ||||
−0.667418 | + | 0.744683i | \(0.732601\pi\) | |||||||
\(488\) | −1.58847e133 | −1.33106 | ||||||||
\(489\) | 3.26753e132 | 0.247418 | ||||||||
\(490\) | −2.40012e131 | −0.0164258 | ||||||||
\(491\) | 2.27807e133 | 1.40940 | 0.704699 | − | 0.709507i | \(-0.251082\pi\) | ||||
0.704699 | + | 0.709507i | \(0.251082\pi\) | |||||||
\(492\) | 3.98545e132 | 0.222949 | ||||||||
\(493\) | −1.94140e133 | −0.982182 | ||||||||
\(494\) | −9.31918e132 | −0.426475 | ||||||||
\(495\) | 9.80016e132 | 0.405766 | ||||||||
\(496\) | −3.64237e132 | −0.136471 | ||||||||
\(497\) | −1.56004e133 | −0.529048 | ||||||||
\(498\) | −8.90277e132 | −0.273321 | ||||||||
\(499\) | −1.75564e133 | −0.488044 | −0.244022 | − | 0.969770i | \(-0.578467\pi\) | ||||
−0.244022 | + | 0.969770i | \(0.578467\pi\) | |||||||
\(500\) | −2.25678e133 | −0.568164 | ||||||||
\(501\) | 1.35776e133 | 0.309638 | ||||||||
\(502\) | 3.12562e133 | 0.645806 | ||||||||
\(503\) | 2.26721e133 | 0.424498 | 0.212249 | − | 0.977216i | \(-0.431921\pi\) | ||||
0.212249 | + | 0.977216i | \(0.431921\pi\) | |||||||
\(504\) | −3.08507e133 | −0.523545 | ||||||||
\(505\) | −9.97199e133 | −1.53412 | ||||||||
\(506\) | 1.13891e133 | 0.158868 | ||||||||
\(507\) | 5.43323e133 | 0.687328 | ||||||||
\(508\) | 1.42579e134 | 1.63607 | ||||||||
\(509\) | 1.50518e133 | 0.156696 | 0.0783481 | − | 0.996926i | \(-0.475035\pi\) | ||||
0.0783481 | + | 0.996926i | \(0.475035\pi\) | |||||||
\(510\) | 3.86480e133 | 0.365093 | ||||||||
\(511\) | −1.71651e132 | −0.0147167 | ||||||||
\(512\) | 1.26932e134 | 0.987892 | ||||||||
\(513\) | −9.25830e133 | −0.654217 | ||||||||
\(514\) | 5.14661e133 | 0.330253 | ||||||||
\(515\) | −5.23233e133 | −0.304956 | ||||||||
\(516\) | −3.15919e133 | −0.167269 | ||||||||
\(517\) | −1.20457e134 | −0.579497 | ||||||||
\(518\) | 1.03017e134 | 0.450386 | ||||||||
\(519\) | −9.92789e133 | −0.394523 | ||||||||
\(520\) | −3.49700e134 | −1.26337 | ||||||||
\(521\) | 2.78816e133 | 0.0915905 | 0.0457952 | − | 0.998951i | \(-0.485418\pi\) | ||||
0.0457952 | + | 0.998951i | \(0.485418\pi\) | |||||||
\(522\) | −5.23002e133 | −0.156248 | ||||||||
\(523\) | −1.88184e134 | −0.511387 | −0.255694 | − | 0.966758i | \(-0.582304\pi\) | ||||
−0.255694 | + | 0.966758i | \(0.582304\pi\) | |||||||
\(524\) | 1.75505e134 | 0.433901 | ||||||||
\(525\) | −1.01245e134 | −0.227766 | ||||||||
\(526\) | −1.24304e134 | −0.254502 | ||||||||
\(527\) | 2.01271e134 | 0.375108 | ||||||||
\(528\) | 7.91969e133 | 0.134378 | ||||||||
\(529\) | 5.00049e132 | 0.00772603 | ||||||||
\(530\) | −2.60959e133 | −0.0367211 | ||||||||
\(531\) | 2.80113e134 | 0.359049 | ||||||||
\(532\) | 5.79348e134 | 0.676571 | ||||||||
\(533\) | 7.68946e134 | 0.818274 | ||||||||
\(534\) | 1.32417e134 | 0.128425 | ||||||||
\(535\) | 5.03729e134 | 0.445333 | ||||||||
\(536\) | −1.13279e135 | −0.913046 | ||||||||
\(537\) | −6.92658e134 | −0.509087 | ||||||||
\(538\) | 6.63705e134 | 0.444890 | ||||||||
\(539\) | 2.71776e133 | 0.0166176 | ||||||||
\(540\) | −1.61684e135 | −0.901936 | ||||||||
\(541\) | 2.89315e135 | 1.47267 | 0.736337 | − | 0.676615i | \(-0.236554\pi\) | ||||
0.736337 | + | 0.676615i | \(0.236554\pi\) | |||||||
\(542\) | 5.80003e134 | 0.269442 | ||||||||
\(543\) | 3.15451e134 | 0.133764 | ||||||||
\(544\) | −4.01137e135 | −1.55291 | ||||||||
\(545\) | 2.46580e134 | 0.0871628 | ||||||||
\(546\) | 8.57742e134 | 0.276899 | ||||||||
\(547\) | −4.76347e135 | −1.40459 | −0.702297 | − | 0.711884i | \(-0.747842\pi\) | ||||
−0.702297 | + | 0.711884i | \(0.747842\pi\) | |||||||
\(548\) | 1.70179e135 | 0.458424 | ||||||||
\(549\) | −6.13517e135 | −1.51006 | ||||||||
\(550\) | 3.23521e134 | 0.0727696 | ||||||||
\(551\) | 2.11037e135 | 0.433865 | ||||||||
\(552\) | −1.74807e135 | −0.328530 | ||||||||
\(553\) | 8.99980e135 | 1.54646 | ||||||||
\(554\) | 3.11813e135 | 0.489960 | ||||||||
\(555\) | 5.02281e135 | 0.721845 | ||||||||
\(556\) | −1.07387e136 | −1.41172 | ||||||||
\(557\) | 6.56024e135 | 0.789019 | 0.394510 | − | 0.918892i | \(-0.370914\pi\) | ||||
0.394510 | + | 0.918892i | \(0.370914\pi\) | |||||||
\(558\) | 5.42214e134 | 0.0596730 | ||||||||
\(559\) | −6.09530e135 | −0.613918 | ||||||||
\(560\) | 8.38898e135 | 0.773396 | ||||||||
\(561\) | −4.37629e135 | −0.369355 | ||||||||
\(562\) | −4.74093e135 | −0.366367 | ||||||||
\(563\) | 1.74627e136 | 1.23579 | 0.617896 | − | 0.786260i | \(-0.287985\pi\) | ||||
0.617896 | + | 0.786260i | \(0.287985\pi\) | |||||||
\(564\) | 8.60445e135 | 0.557709 | ||||||||
\(565\) | 9.57041e135 | 0.568241 | ||||||||
\(566\) | −1.29967e135 | −0.0707001 | ||||||||
\(567\) | −7.08360e135 | −0.353096 | ||||||||
\(568\) | −7.65132e135 | −0.349537 | ||||||||
\(569\) | −2.60131e136 | −1.08927 | −0.544635 | − | 0.838673i | \(-0.683332\pi\) | ||||
−0.544635 | + | 0.838673i | \(0.683332\pi\) | |||||||
\(570\) | −4.20118e135 | −0.161275 | ||||||||
\(571\) | −4.79163e136 | −1.68654 | −0.843268 | − | 0.537493i | \(-0.819371\pi\) | ||||
−0.843268 | + | 0.537493i | \(0.819371\pi\) | |||||||
\(572\) | 1.84286e136 | 0.594825 | ||||||||
\(573\) | −3.04315e136 | −0.900884 | ||||||||
\(574\) | 7.10968e135 | 0.193068 | ||||||||
\(575\) | 1.85274e136 | 0.461589 | ||||||||
\(576\) | 1.01811e136 | 0.232746 | ||||||||
\(577\) | −2.53022e136 | −0.530831 | −0.265415 | − | 0.964134i | \(-0.585509\pi\) | ||||
−0.265415 | + | 0.964134i | \(0.585509\pi\) | |||||||
\(578\) | 3.70513e136 | 0.713470 | ||||||||
\(579\) | −1.51669e136 | −0.268107 | ||||||||
\(580\) | 3.68548e136 | 0.598148 | ||||||||
\(581\) | 1.06784e137 | 1.59143 | ||||||||
\(582\) | −2.13868e136 | −0.292724 | ||||||||
\(583\) | 2.95496e135 | 0.0371499 | ||||||||
\(584\) | −8.41873e134 | −0.00972324 | ||||||||
\(585\) | −1.35065e137 | −1.43326 | ||||||||
\(586\) | 5.14684e136 | 0.501891 | ||||||||
\(587\) | 1.70706e137 | 1.52990 | 0.764948 | − | 0.644092i | \(-0.222765\pi\) | ||||
0.764948 | + | 0.644092i | \(0.222765\pi\) | |||||||
\(588\) | −1.94134e135 | −0.0159928 | ||||||||
\(589\) | −2.18789e136 | −0.165699 | ||||||||
\(590\) | 2.93573e136 | 0.204429 | ||||||||
\(591\) | −5.26816e136 | −0.337349 | ||||||||
\(592\) | −1.31089e137 | −0.772046 | ||||||||
\(593\) | 7.61876e136 | 0.412740 | 0.206370 | − | 0.978474i | \(-0.433835\pi\) | ||||
0.206370 | + | 0.978474i | \(0.433835\pi\) | |||||||
\(594\) | −2.72295e136 | −0.135709 | ||||||||
\(595\) | −4.63561e137 | −2.12577 | ||||||||
\(596\) | 1.95187e137 | 0.823687 | ||||||||
\(597\) | 1.46407e137 | 0.568635 | ||||||||
\(598\) | −1.56963e137 | −0.561161 | ||||||||
\(599\) | 1.91129e137 | 0.629071 | 0.314535 | − | 0.949246i | \(-0.398151\pi\) | ||||
0.314535 | + | 0.949246i | \(0.398151\pi\) | |||||||
\(600\) | −4.96563e136 | −0.150483 | ||||||||
\(601\) | −6.32287e136 | −0.176452 | −0.0882262 | − | 0.996100i | \(-0.528120\pi\) | ||||
−0.0882262 | + | 0.996100i | \(0.528120\pi\) | |||||||
\(602\) | −5.63571e136 | −0.144851 | ||||||||
\(603\) | −4.37518e137 | −1.03583 | ||||||||
\(604\) | −4.00976e137 | −0.874560 | ||||||||
\(605\) | 4.84925e137 | 0.974503 | ||||||||
\(606\) | 1.19962e137 | 0.222151 | ||||||||
\(607\) | 8.01601e137 | 1.36810 | 0.684051 | − | 0.729434i | \(-0.260217\pi\) | ||||
0.684051 | + | 0.729434i | \(0.260217\pi\) | |||||||
\(608\) | 4.36051e137 | 0.685977 | ||||||||
\(609\) | −1.94239e137 | −0.281696 | ||||||||
\(610\) | −6.42999e137 | −0.859773 | ||||||||
\(611\) | 1.66013e138 | 2.04692 | ||||||||
\(612\) | −1.00958e138 | −1.14801 | ||||||||
\(613\) | 3.02896e137 | 0.317687 | 0.158844 | − | 0.987304i | \(-0.449223\pi\) | ||||
0.158844 | + | 0.987304i | \(0.449223\pi\) | |||||||
\(614\) | 9.65198e133 | 9.33861e−5 0 | ||||||||
\(615\) | 3.46648e137 | 0.309436 | ||||||||
\(616\) | 3.66124e137 | 0.301567 | ||||||||
\(617\) | −7.78262e137 | −0.591575 | −0.295788 | − | 0.955254i | \(-0.595582\pi\) | ||||
−0.295788 | + | 0.955254i | \(0.595582\pi\) | |||||||
\(618\) | 6.29443e136 | 0.0441598 | ||||||||
\(619\) | 1.49252e137 | 0.0966572 | 0.0483286 | − | 0.998831i | \(-0.484611\pi\) | ||||
0.0483286 | + | 0.998831i | \(0.484611\pi\) | |||||||
\(620\) | −3.82087e137 | −0.228441 | ||||||||
\(621\) | −1.55937e138 | −0.860826 | ||||||||
\(622\) | 8.17242e137 | 0.416607 | ||||||||
\(623\) | −1.58826e138 | −0.747763 | ||||||||
\(624\) | −1.09148e138 | −0.474657 | ||||||||
\(625\) | −3.10749e138 | −1.24839 | ||||||||
\(626\) | 2.63492e136 | 0.00977998 | ||||||||
\(627\) | 4.75719e137 | 0.163157 | ||||||||
\(628\) | 1.46662e138 | 0.464851 | ||||||||
\(629\) | 7.24379e138 | 2.12206 | ||||||||
\(630\) | −1.24881e138 | −0.338173 | ||||||||
\(631\) | −7.38843e138 | −1.84969 | −0.924844 | − | 0.380346i | \(-0.875805\pi\) | ||||
−0.924844 | + | 0.380346i | \(0.875805\pi\) | |||||||
\(632\) | 4.41401e138 | 1.02173 | ||||||||
\(633\) | −2.74952e138 | −0.588537 | ||||||||
\(634\) | −1.43079e138 | −0.283242 | ||||||||
\(635\) | 1.24013e139 | 2.27074 | ||||||||
\(636\) | −2.11077e137 | −0.0357531 | ||||||||
\(637\) | −3.74559e137 | −0.0586973 | ||||||||
\(638\) | 6.20678e137 | 0.0900000 | ||||||||
\(639\) | −2.95517e138 | −0.396543 | ||||||||
\(640\) | 9.81466e138 | 1.21890 | ||||||||
\(641\) | 2.38758e138 | 0.274464 | 0.137232 | − | 0.990539i | \(-0.456179\pi\) | ||||
0.137232 | + | 0.990539i | \(0.456179\pi\) | |||||||
\(642\) | −6.05981e137 | −0.0644874 | ||||||||
\(643\) | −1.42797e139 | −1.40694 | −0.703471 | − | 0.710724i | \(-0.748368\pi\) | ||||
−0.703471 | + | 0.710724i | \(0.748368\pi\) | |||||||
\(644\) | 9.75793e138 | 0.890240 | ||||||||
\(645\) | −2.74782e138 | −0.232157 | ||||||||
\(646\) | −6.05885e138 | −0.474111 | ||||||||
\(647\) | −2.03156e139 | −1.47254 | −0.736272 | − | 0.676686i | \(-0.763416\pi\) | ||||
−0.736272 | + | 0.676686i | \(0.763416\pi\) | |||||||
\(648\) | −3.47420e138 | −0.233287 | ||||||||
\(649\) | −3.32427e138 | −0.206816 | ||||||||
\(650\) | −4.45873e138 | −0.257040 | ||||||||
\(651\) | 2.01375e138 | 0.107584 | ||||||||
\(652\) | −8.94578e138 | −0.442957 | ||||||||
\(653\) | 3.32057e139 | 1.52409 | 0.762044 | − | 0.647526i | \(-0.224196\pi\) | ||||
0.762044 | + | 0.647526i | \(0.224196\pi\) | |||||||
\(654\) | −2.96633e137 | −0.0126218 | ||||||||
\(655\) | 1.52652e139 | 0.602223 | ||||||||
\(656\) | −9.04711e138 | −0.330956 | ||||||||
\(657\) | −3.25157e137 | −0.0110308 | ||||||||
\(658\) | 1.53496e139 | 0.482963 | ||||||||
\(659\) | −5.05125e139 | −1.47425 | −0.737124 | − | 0.675757i | \(-0.763817\pi\) | ||||
−0.737124 | + | 0.675757i | \(0.763817\pi\) | |||||||
\(660\) | 8.30780e138 | 0.224937 | ||||||||
\(661\) | −3.47031e139 | −0.871757 | −0.435879 | − | 0.900005i | \(-0.643562\pi\) | ||||
−0.435879 | + | 0.900005i | \(0.643562\pi\) | |||||||
\(662\) | −7.78251e138 | −0.181405 | ||||||||
\(663\) | 6.03135e139 | 1.30465 | ||||||||
\(664\) | 5.23727e139 | 1.05144 | ||||||||
\(665\) | 5.03908e139 | 0.939030 | ||||||||
\(666\) | 1.95144e139 | 0.337583 | ||||||||
\(667\) | 3.55449e139 | 0.570884 | ||||||||
\(668\) | −3.71724e139 | −0.554352 | ||||||||
\(669\) | −3.80017e139 | −0.526272 | ||||||||
\(670\) | −4.58543e139 | −0.589763 | ||||||||
\(671\) | 7.28097e139 | 0.869811 | ||||||||
\(672\) | −4.01343e139 | −0.445386 | ||||||||
\(673\) | −1.04366e140 | −1.07600 | −0.538001 | − | 0.842944i | \(-0.680820\pi\) | ||||
−0.538001 | + | 0.842944i | \(0.680820\pi\) | |||||||
\(674\) | 3.68318e139 | 0.352824 | ||||||||
\(675\) | −4.42960e139 | −0.394301 | ||||||||
\(676\) | −1.48750e140 | −1.23054 | ||||||||
\(677\) | 1.63497e139 | 0.125710 | 0.0628552 | − | 0.998023i | \(-0.479979\pi\) | ||||
0.0628552 | + | 0.998023i | \(0.479979\pi\) | |||||||
\(678\) | −1.15131e139 | −0.0822854 | ||||||||
\(679\) | 2.56523e140 | 1.70440 | ||||||||
\(680\) | −2.27356e140 | −1.40448 | ||||||||
\(681\) | −3.77738e139 | −0.216974 | ||||||||
\(682\) | −6.43478e138 | −0.0343722 | ||||||||
\(683\) | −1.91884e140 | −0.953265 | −0.476633 | − | 0.879103i | \(-0.658143\pi\) | ||||
−0.476633 | + | 0.879103i | \(0.658143\pi\) | |||||||
\(684\) | 1.09745e140 | 0.507118 | ||||||||
\(685\) | 1.48019e140 | 0.636259 | ||||||||
\(686\) | 8.81978e139 | 0.352707 | ||||||||
\(687\) | 1.04946e140 | 0.390490 | ||||||||
\(688\) | 7.17149e139 | 0.248303 | ||||||||
\(689\) | −4.07249e139 | −0.131222 | ||||||||
\(690\) | −7.07603e139 | −0.212207 | ||||||||
\(691\) | 5.50389e140 | 1.53641 | 0.768203 | − | 0.640206i | \(-0.221151\pi\) | ||||
0.768203 | + | 0.640206i | \(0.221151\pi\) | |||||||
\(692\) | 2.71804e140 | 0.706324 | ||||||||
\(693\) | 1.41408e140 | 0.342121 | ||||||||
\(694\) | −4.30461e139 | −0.0969706 | ||||||||
\(695\) | −9.34034e140 | −1.95936 | ||||||||
\(696\) | −9.52659e139 | −0.186115 | ||||||||
\(697\) | 4.99929e140 | 0.909673 | ||||||||
\(698\) | 1.48138e140 | 0.251087 | ||||||||
\(699\) | −1.47513e140 | −0.232921 | ||||||||
\(700\) | 2.77187e140 | 0.407774 | ||||||||
\(701\) | −1.30656e141 | −1.79096 | −0.895482 | − | 0.445098i | \(-0.853169\pi\) | ||||
−0.895482 | + | 0.445098i | \(0.853169\pi\) | |||||||
\(702\) | 3.75273e140 | 0.479359 | ||||||||
\(703\) | −7.87426e140 | −0.937392 | ||||||||
\(704\) | −1.20825e140 | −0.134064 | ||||||||
\(705\) | 7.48402e140 | 0.774058 | ||||||||
\(706\) | 2.00608e140 | 0.193426 | ||||||||
\(707\) | −1.43888e141 | −1.29349 | ||||||||
\(708\) | 2.37457e140 | 0.199040 | ||||||||
\(709\) | −3.58096e140 | −0.279905 | −0.139952 | − | 0.990158i | \(-0.544695\pi\) | ||||
−0.139952 | + | 0.990158i | \(0.544695\pi\) | |||||||
\(710\) | −3.09718e140 | −0.225776 | ||||||||
\(711\) | 1.70483e141 | 1.15914 | ||||||||
\(712\) | −7.78974e140 | −0.494041 | ||||||||
\(713\) | −3.68506e140 | −0.218028 | ||||||||
\(714\) | 5.57659e140 | 0.307828 | ||||||||
\(715\) | 1.60289e141 | 0.825573 | ||||||||
\(716\) | 1.89635e141 | 0.911430 | ||||||||
\(717\) | −8.28572e139 | −0.0371648 | ||||||||
\(718\) | 9.70153e140 | 0.406144 | ||||||||
\(719\) | −2.27670e141 | −0.889665 | −0.444832 | − | 0.895614i | \(-0.646737\pi\) | ||||
−0.444832 | + | 0.895614i | \(0.646737\pi\) | |||||||
\(720\) | 1.58912e141 | 0.579692 | ||||||||
\(721\) | −7.54982e140 | −0.257123 | ||||||||
\(722\) | −4.72945e140 | −0.150390 | ||||||||
\(723\) | 1.29956e141 | 0.385879 | ||||||||
\(724\) | −8.63636e140 | −0.239481 | ||||||||
\(725\) | 1.00970e141 | 0.261493 | ||||||||
\(726\) | −5.83360e140 | −0.141115 | ||||||||
\(727\) | 3.97311e141 | 0.897796 | 0.448898 | − | 0.893583i | \(-0.351817\pi\) | ||||
0.448898 | + | 0.893583i | \(0.351817\pi\) | |||||||
\(728\) | −5.04588e141 | −1.06521 | ||||||||
\(729\) | 7.72176e140 | 0.152301 | ||||||||
\(730\) | −3.40782e139 | −0.00628052 | ||||||||
\(731\) | −3.96284e141 | −0.682491 | ||||||||
\(732\) | −5.20091e141 | −0.837107 | ||||||||
\(733\) | −1.69430e141 | −0.254884 | −0.127442 | − | 0.991846i | \(-0.540677\pi\) | ||||
−0.127442 | + | 0.991846i | \(0.540677\pi\) | |||||||
\(734\) | −2.78164e141 | −0.391152 | ||||||||
\(735\) | −1.68855e140 | −0.0221968 | ||||||||
\(736\) | 7.34438e141 | 0.902617 | ||||||||
\(737\) | 5.19229e141 | 0.596648 | ||||||||
\(738\) | 1.34678e141 | 0.144713 | ||||||||
\(739\) | −6.64582e141 | −0.667804 | −0.333902 | − | 0.942608i | \(-0.608365\pi\) | ||||
−0.333902 | + | 0.942608i | \(0.608365\pi\) | |||||||
\(740\) | −1.37514e142 | −1.29234 | ||||||||
\(741\) | −6.55630e141 | −0.576312 | ||||||||
\(742\) | −3.76542e140 | −0.0309614 | ||||||||
\(743\) | 1.43356e142 | 1.10273 | 0.551364 | − | 0.834265i | \(-0.314108\pi\) | ||||
0.551364 | + | 0.834265i | \(0.314108\pi\) | |||||||
\(744\) | 9.87655e140 | 0.0710796 | ||||||||
\(745\) | 1.69771e142 | 1.14322 | ||||||||
\(746\) | 5.92707e141 | 0.373481 | ||||||||
\(747\) | 2.02279e142 | 1.19284 | ||||||||
\(748\) | 1.19813e142 | 0.661265 | ||||||||
\(749\) | 7.26840e141 | 0.375482 | ||||||||
\(750\) | 2.36136e141 | 0.114191 | ||||||||
\(751\) | −2.22287e142 | −1.00632 | −0.503161 | − | 0.864193i | \(-0.667830\pi\) | ||||
−0.503161 | + | 0.864193i | \(0.667830\pi\) | |||||||
\(752\) | −1.95324e142 | −0.827890 | ||||||||
\(753\) | 2.19896e142 | 0.872701 | ||||||||
\(754\) | −8.55411e141 | −0.317902 | ||||||||
\(755\) | −3.48763e142 | −1.21382 | ||||||||
\(756\) | −2.33297e142 | −0.760466 | ||||||||
\(757\) | −3.03014e141 | −0.0925160 | −0.0462580 | − | 0.998930i | \(-0.514730\pi\) | ||||
−0.0462580 | + | 0.998930i | \(0.514730\pi\) | |||||||
\(758\) | 2.04315e141 | 0.0584352 | ||||||||
\(759\) | 8.01251e141 | 0.214685 | ||||||||
\(760\) | 2.47145e142 | 0.620410 | ||||||||
\(761\) | −3.72039e142 | −0.875079 | −0.437540 | − | 0.899199i | \(-0.644150\pi\) | ||||
−0.437540 | + | 0.899199i | \(0.644150\pi\) | |||||||
\(762\) | −1.49186e142 | −0.328820 | ||||||||
\(763\) | 3.55795e141 | 0.0734912 | ||||||||
\(764\) | 8.33147e142 | 1.61287 | ||||||||
\(765\) | −8.78120e142 | −1.59336 | ||||||||
\(766\) | −3.35212e142 | −0.570158 | ||||||||
\(767\) | 4.58146e142 | 0.730523 | ||||||||
\(768\) | −1.89256e141 | −0.0282924 | ||||||||
\(769\) | −6.63743e142 | −0.930349 | −0.465174 | − | 0.885219i | \(-0.654008\pi\) | ||||
−0.465174 | + | 0.885219i | \(0.654008\pi\) | |||||||
\(770\) | 1.48204e142 | 0.194791 | ||||||||
\(771\) | 3.62078e142 | 0.446283 | ||||||||
\(772\) | 4.15237e142 | 0.479998 | ||||||||
\(773\) | 8.24179e142 | 0.893587 | 0.446793 | − | 0.894637i | \(-0.352566\pi\) | ||||
0.446793 | + | 0.894637i | \(0.352566\pi\) | |||||||
\(774\) | −1.06757e142 | −0.108572 | ||||||||
\(775\) | −1.04679e142 | −0.0998678 | ||||||||
\(776\) | 1.25813e143 | 1.12609 | ||||||||
\(777\) | 7.24751e142 | 0.608623 | ||||||||
\(778\) | 3.11747e142 | 0.245647 | ||||||||
\(779\) | −5.43440e142 | −0.401835 | ||||||||
\(780\) | −1.14497e143 | −0.794533 | ||||||||
\(781\) | 3.50708e142 | 0.228412 | ||||||||
\(782\) | −1.02049e143 | −0.623841 | ||||||||
\(783\) | −8.49822e142 | −0.487664 | ||||||||
\(784\) | 4.40691e141 | 0.0237405 | ||||||||
\(785\) | 1.27564e143 | 0.645179 | ||||||||
\(786\) | −1.83638e142 | −0.0872062 | ||||||||
\(787\) | −2.45354e143 | −1.09407 | −0.547034 | − | 0.837111i | \(-0.684243\pi\) | ||||
−0.547034 | + | 0.837111i | \(0.684243\pi\) | |||||||
\(788\) | 1.44231e143 | 0.603963 | ||||||||
\(789\) | −8.74513e142 | −0.343918 | ||||||||
\(790\) | 1.78675e143 | 0.659968 | ||||||||
\(791\) | 1.38093e143 | 0.479111 | ||||||||
\(792\) | 6.93546e142 | 0.226037 | ||||||||
\(793\) | −1.00346e144 | −3.07238 | ||||||||
\(794\) | 5.11864e142 | 0.147245 | ||||||||
\(795\) | −1.83592e142 | −0.0496226 | ||||||||
\(796\) | −4.00831e143 | −1.01804 | ||||||||
\(797\) | 4.52195e143 | 1.07929 | 0.539646 | − | 0.841892i | \(-0.318558\pi\) | ||||
0.539646 | + | 0.841892i | \(0.318558\pi\) | |||||||
\(798\) | −6.06196e142 | −0.135978 | ||||||||
\(799\) | 1.07933e144 | 2.27556 | ||||||||
\(800\) | 2.08627e143 | 0.413444 | ||||||||
\(801\) | −3.00863e143 | −0.560480 | ||||||||
\(802\) | −1.83777e143 | −0.321855 | ||||||||
\(803\) | 3.85884e141 | 0.00635385 | ||||||||
\(804\) | −3.70893e143 | −0.574215 | ||||||||
\(805\) | 8.48730e143 | 1.23559 | ||||||||
\(806\) | 8.86835e142 | 0.121411 | ||||||||
\(807\) | 4.66935e143 | 0.601196 | ||||||||
\(808\) | −7.05706e143 | −0.854598 | ||||||||
\(809\) | 1.26235e144 | 1.43789 | 0.718946 | − | 0.695066i | \(-0.244625\pi\) | ||||
0.718946 | + | 0.695066i | \(0.244625\pi\) | |||||||
\(810\) | −1.40632e143 | −0.150687 | ||||||||
\(811\) | −9.23607e143 | −0.931011 | −0.465506 | − | 0.885045i | \(-0.654128\pi\) | ||||
−0.465506 | + | 0.885045i | \(0.654128\pi\) | |||||||
\(812\) | 5.31785e143 | 0.504328 | ||||||||
\(813\) | 4.08048e143 | 0.364107 | ||||||||
\(814\) | −2.31589e143 | −0.194451 | ||||||||
\(815\) | −7.78090e143 | −0.614792 | ||||||||
\(816\) | −7.09625e143 | −0.527675 | ||||||||
\(817\) | 4.30776e143 | 0.301480 | ||||||||
\(818\) | −2.59591e143 | −0.171002 | ||||||||
\(819\) | −1.94887e144 | −1.20846 | ||||||||
\(820\) | −9.49047e143 | −0.553990 | ||||||||
\(821\) | −4.63326e143 | −0.254625 | −0.127312 | − | 0.991863i | \(-0.540635\pi\) | ||||
−0.127312 | + | 0.991863i | \(0.540635\pi\) | |||||||
\(822\) | −1.78065e143 | −0.0921348 | ||||||||
\(823\) | 3.30495e143 | 0.161018 | 0.0805088 | − | 0.996754i | \(-0.474345\pi\) | ||||
0.0805088 | + | 0.996754i | \(0.474345\pi\) | |||||||
\(824\) | −3.70286e143 | −0.169879 | ||||||||
\(825\) | 2.27606e143 | 0.0983362 | ||||||||
\(826\) | 4.23602e143 | 0.172364 | ||||||||
\(827\) | 6.42093e142 | 0.0246079 | 0.0123040 | − | 0.999924i | \(-0.496083\pi\) | ||||
0.0123040 | + | 0.999924i | \(0.496083\pi\) | |||||||
\(828\) | 1.84844e144 | 0.667272 | ||||||||
\(829\) | −1.76717e143 | −0.0600939 | −0.0300469 | − | 0.999548i | \(-0.509566\pi\) | ||||
−0.0300469 | + | 0.999548i | \(0.509566\pi\) | |||||||
\(830\) | 2.12000e144 | 0.679157 | ||||||||
\(831\) | 2.19369e144 | 0.662101 | ||||||||
\(832\) | 1.66520e144 | 0.473546 | ||||||||
\(833\) | −2.43519e143 | −0.0652536 | ||||||||
\(834\) | 1.12363e144 | 0.283730 | ||||||||
\(835\) | −3.23320e144 | −0.769399 | ||||||||
\(836\) | −1.30241e144 | −0.292105 | ||||||||
\(837\) | 8.81041e143 | 0.186245 | ||||||||
\(838\) | 3.08087e144 | 0.613896 | ||||||||
\(839\) | 4.47862e144 | 0.841254 | 0.420627 | − | 0.907234i | \(-0.361810\pi\) | ||||
0.420627 | + | 0.907234i | \(0.361810\pi\) | |||||||
\(840\) | −2.27473e144 | −0.402815 | ||||||||
\(841\) | −4.05254e144 | −0.676590 | ||||||||
\(842\) | −1.27233e144 | −0.200286 | ||||||||
\(843\) | −3.33538e144 | −0.495085 | ||||||||
\(844\) | 7.52759e144 | 1.05367 | ||||||||
\(845\) | −1.29381e145 | −1.70790 | ||||||||
\(846\) | 2.90765e144 | 0.362001 | ||||||||
\(847\) | 6.99707e144 | 0.821651 | ||||||||
\(848\) | 4.79153e143 | 0.0530737 | ||||||||
\(849\) | −9.14354e143 | −0.0955397 | ||||||||
\(850\) | −2.89884e144 | −0.285750 | ||||||||
\(851\) | −1.32626e145 | −1.23343 | ||||||||
\(852\) | −2.50516e144 | −0.219824 | ||||||||
\(853\) | 5.43353e144 | 0.449889 | 0.224945 | − | 0.974372i | \(-0.427780\pi\) | ||||
0.224945 | + | 0.974372i | \(0.427780\pi\) | |||||||
\(854\) | −9.27796e144 | −0.724916 | ||||||||
\(855\) | 9.54548e144 | 0.703842 | ||||||||
\(856\) | 3.56483e144 | 0.248078 | ||||||||
\(857\) | −1.93165e145 | −1.26876 | −0.634378 | − | 0.773023i | \(-0.718744\pi\) | ||||
−0.634378 | + | 0.773023i | \(0.718744\pi\) | |||||||
\(858\) | −1.92826e144 | −0.119549 | ||||||||
\(859\) | 6.16032e144 | 0.360530 | 0.180265 | − | 0.983618i | \(-0.442304\pi\) | ||||
0.180265 | + | 0.983618i | \(0.442304\pi\) | |||||||
\(860\) | 7.52293e144 | 0.415636 | ||||||||
\(861\) | 5.00185e144 | 0.260901 | ||||||||
\(862\) | 4.10822e144 | 0.202322 | ||||||||
\(863\) | 3.34826e145 | 1.55699 | 0.778493 | − | 0.627653i | \(-0.215984\pi\) | ||||
0.778493 | + | 0.627653i | \(0.215984\pi\) | |||||||
\(864\) | −1.75593e145 | −0.771039 | ||||||||
\(865\) | 2.36411e145 | 0.980325 | ||||||||
\(866\) | 1.00330e145 | 0.392913 | ||||||||
\(867\) | 2.60666e145 | 0.964138 | ||||||||
\(868\) | −5.51320e144 | −0.192609 | ||||||||
\(869\) | −2.02322e145 | −0.667673 | ||||||||
\(870\) | −3.85628e144 | −0.120217 | ||||||||
\(871\) | −7.15596e145 | −2.10751 | ||||||||
\(872\) | 1.74502e144 | 0.0485550 | ||||||||
\(873\) | 4.85930e145 | 1.27752 | ||||||||
\(874\) | 1.10931e145 | 0.275573 | ||||||||
\(875\) | −2.83232e145 | −0.664881 | ||||||||
\(876\) | −2.75643e143 | −0.00611495 | ||||||||
\(877\) | 1.75895e145 | 0.368785 | 0.184393 | − | 0.982853i | \(-0.440968\pi\) | ||||
0.184393 | + | 0.982853i | \(0.440968\pi\) | |||||||
\(878\) | −9.18228e144 | −0.181958 | ||||||||
\(879\) | 3.62095e145 | 0.678223 | ||||||||
\(880\) | −1.88590e145 | −0.333908 | ||||||||
\(881\) | −4.32841e145 | −0.724470 | −0.362235 | − | 0.932087i | \(-0.617986\pi\) | ||||
−0.362235 | + | 0.932087i | \(0.617986\pi\) | |||||||
\(882\) | −6.56026e143 | −0.0103807 | ||||||||
\(883\) | −7.42579e145 | −1.11093 | −0.555467 | − | 0.831539i | \(-0.687460\pi\) | ||||
−0.555467 | + | 0.831539i | \(0.687460\pi\) | |||||||
\(884\) | −1.65125e146 | −2.33575 | ||||||||
\(885\) | 2.06537e145 | 0.276252 | ||||||||
\(886\) | 1.02060e145 | 0.129089 | ||||||||
\(887\) | 6.27848e145 | 0.750991 | 0.375496 | − | 0.926824i | \(-0.377472\pi\) | ||||
0.375496 | + | 0.926824i | \(0.377472\pi\) | |||||||
\(888\) | 3.55459e145 | 0.402112 | ||||||||
\(889\) | 1.78941e146 | 1.91457 | ||||||||
\(890\) | −3.15321e145 | −0.319116 | ||||||||
\(891\) | 1.59244e145 | 0.152446 | ||||||||
\(892\) | 1.04040e146 | 0.942198 | ||||||||
\(893\) | −1.17327e146 | −1.00520 | ||||||||
\(894\) | −2.04233e145 | −0.165546 | ||||||||
\(895\) | 1.64941e146 | 1.26500 | ||||||||
\(896\) | 1.41618e146 | 1.02771 | ||||||||
\(897\) | −1.10428e146 | −0.758318 | ||||||||
\(898\) | −3.77581e145 | −0.245376 | ||||||||
\(899\) | −2.00827e145 | −0.123515 | ||||||||
\(900\) | 5.25073e145 | 0.305644 | ||||||||
\(901\) | −2.64772e145 | −0.145880 | ||||||||
\(902\) | −1.59831e145 | −0.0833559 | ||||||||
\(903\) | −3.96488e145 | −0.195743 | ||||||||
\(904\) | 6.77287e145 | 0.316545 | ||||||||
\(905\) | −7.51177e145 | −0.332382 | ||||||||
\(906\) | 4.19558e145 | 0.175771 | ||||||||
\(907\) | −2.30882e146 | −0.915862 | −0.457931 | − | 0.888988i | \(-0.651409\pi\) | ||||
−0.457931 | + | 0.888988i | \(0.651409\pi\) | |||||||
\(908\) | 1.03416e146 | 0.388454 | ||||||||
\(909\) | −2.72565e146 | −0.969524 | ||||||||
\(910\) | −2.04253e146 | −0.688048 | ||||||||
\(911\) | 3.63913e146 | 1.16102 | 0.580508 | − | 0.814255i | \(-0.302854\pi\) | ||||
0.580508 | + | 0.814255i | \(0.302854\pi\) | |||||||
\(912\) | 7.71388e145 | 0.233093 | ||||||||
\(913\) | −2.40057e146 | −0.687086 | ||||||||
\(914\) | −6.35054e145 | −0.172177 | ||||||||
\(915\) | −4.52368e146 | −1.16184 | ||||||||
\(916\) | −2.87321e146 | −0.699102 | ||||||||
\(917\) | 2.20264e146 | 0.507763 | ||||||||
\(918\) | 2.43983e146 | 0.532902 | ||||||||
\(919\) | 6.10053e146 | 1.26255 | 0.631277 | − | 0.775557i | \(-0.282531\pi\) | ||||
0.631277 | + | 0.775557i | \(0.282531\pi\) | |||||||
\(920\) | 4.16265e146 | 0.816342 | ||||||||
\(921\) | 6.79043e142 | 0.000126196 0 | ||||||||
\(922\) | 7.19013e145 | 0.126636 | ||||||||
\(923\) | −4.83342e146 | −0.806808 | ||||||||
\(924\) | 1.19875e146 | 0.189655 | ||||||||
\(925\) | −3.76741e146 | −0.564973 | ||||||||
\(926\) | 8.55460e145 | 0.121606 | ||||||||
\(927\) | −1.43016e146 | −0.192724 | ||||||||
\(928\) | 4.00252e146 | 0.511339 | ||||||||
\(929\) | 4.77493e146 | 0.578347 | 0.289174 | − | 0.957277i | \(-0.406619\pi\) | ||||
0.289174 | + | 0.957277i | \(0.406619\pi\) | |||||||
\(930\) | 3.99794e145 | 0.0459124 | ||||||||
\(931\) | 2.64714e145 | 0.0288248 | ||||||||
\(932\) | 4.03857e146 | 0.417004 | ||||||||
\(933\) | 5.74952e146 | 0.562977 | ||||||||
\(934\) | 2.39619e146 | 0.222511 | ||||||||
\(935\) | 1.04212e147 | 0.917787 | ||||||||
\(936\) | −9.55837e146 | −0.798416 | ||||||||
\(937\) | −5.64932e146 | −0.447596 | −0.223798 | − | 0.974636i | \(-0.571846\pi\) | ||||
−0.223798 | + | 0.974636i | \(0.571846\pi\) | |||||||
\(938\) | −6.61640e146 | −0.497257 | ||||||||
\(939\) | 1.85374e145 | 0.0132160 | ||||||||
\(940\) | −2.04896e147 | −1.38581 | ||||||||
\(941\) | 1.66307e146 | 0.106715 | 0.0533575 | − | 0.998575i | \(-0.483008\pi\) | ||||
0.0533575 | + | 0.998575i | \(0.483008\pi\) | |||||||
\(942\) | −1.53458e146 | −0.0934266 | ||||||||
\(943\) | −9.15315e146 | −0.528739 | ||||||||
\(944\) | −5.39037e146 | −0.295464 | ||||||||
\(945\) | −2.02918e147 | −1.05547 | ||||||||
\(946\) | 1.26695e146 | 0.0625385 | ||||||||
\(947\) | 1.95971e147 | 0.918051 | 0.459026 | − | 0.888423i | \(-0.348199\pi\) | ||||
0.459026 | + | 0.888423i | \(0.348199\pi\) | |||||||
\(948\) | 1.44522e147 | 0.642570 | ||||||||
\(949\) | −5.31820e145 | −0.0224433 | ||||||||
\(950\) | 3.15114e146 | 0.126226 | ||||||||
\(951\) | −1.00660e147 | −0.382755 | ||||||||
\(952\) | −3.28057e147 | −1.18419 | ||||||||
\(953\) | 1.82910e147 | 0.626816 | 0.313408 | − | 0.949619i | \(-0.398529\pi\) | ||||
0.313408 | + | 0.949619i | \(0.398529\pi\) | |||||||
\(954\) | −7.13281e145 | −0.0232068 | ||||||||
\(955\) | 7.24659e147 | 2.23855 | ||||||||
\(956\) | 2.26845e146 | 0.0665370 | ||||||||
\(957\) | 4.36664e146 | 0.121620 | ||||||||
\(958\) | −8.87345e146 | −0.234693 | ||||||||
\(959\) | 2.13579e147 | 0.536460 | ||||||||
\(960\) | 7.50689e146 | 0.179075 | ||||||||
\(961\) | −4.20554e147 | −0.952828 | ||||||||
\(962\) | 3.19173e147 | 0.686847 | ||||||||
\(963\) | 1.37685e147 | 0.281439 | ||||||||
\(964\) | −3.55791e147 | −0.690847 | ||||||||
\(965\) | 3.61167e147 | 0.666201 | ||||||||
\(966\) | −1.02101e147 | −0.178922 | ||||||||
\(967\) | −4.78838e147 | −0.797221 | −0.398610 | − | 0.917120i | \(-0.630507\pi\) | ||||
−0.398610 | + | 0.917120i | \(0.630507\pi\) | |||||||
\(968\) | 3.43176e147 | 0.542858 | ||||||||
\(969\) | −4.26256e147 | −0.640684 | ||||||||
\(970\) | 5.09281e147 | 0.727372 | ||||||||
\(971\) | 6.24694e147 | 0.847843 | 0.423922 | − | 0.905699i | \(-0.360653\pi\) | ||||
0.423922 | + | 0.905699i | \(0.360653\pi\) | |||||||
\(972\) | −6.92522e147 | −0.893210 | ||||||||
\(973\) | −1.34774e148 | −1.65203 | ||||||||
\(974\) | −4.12272e147 | −0.480303 | ||||||||
\(975\) | −3.13684e147 | −0.347347 | ||||||||
\(976\) | 1.18063e148 | 1.24264 | ||||||||
\(977\) | −1.55966e148 | −1.56045 | −0.780224 | − | 0.625500i | \(-0.784895\pi\) | ||||
−0.780224 | + | 0.625500i | \(0.784895\pi\) | |||||||
\(978\) | 9.36034e146 | 0.0890263 | ||||||||
\(979\) | 3.57053e147 | 0.322841 | ||||||||
\(980\) | 4.62287e146 | 0.0397394 | ||||||||
\(981\) | 6.73980e146 | 0.0550847 | ||||||||
\(982\) | 6.52589e147 | 0.507132 | ||||||||
\(983\) | −8.87816e147 | −0.656031 | −0.328015 | − | 0.944672i | \(-0.606380\pi\) | ||||
−0.328015 | + | 0.944672i | \(0.606380\pi\) | |||||||
\(984\) | 2.45319e147 | 0.172375 | ||||||||
\(985\) | 1.25450e148 | 0.838256 | ||||||||
\(986\) | −5.56144e147 | −0.353411 | ||||||||
\(987\) | 1.07988e148 | 0.652646 | ||||||||
\(988\) | 1.79497e148 | 1.03178 | ||||||||
\(989\) | 7.25553e147 | 0.396692 | ||||||||
\(990\) | 2.80741e147 | 0.146004 | ||||||||
\(991\) | −1.06594e147 | −0.0527336 | −0.0263668 | − | 0.999652i | \(-0.508394\pi\) | ||||
−0.0263668 | + | 0.999652i | \(0.508394\pi\) | |||||||
\(992\) | −4.14956e147 | −0.195287 | ||||||||
\(993\) | −5.47521e147 | −0.245139 | ||||||||
\(994\) | −4.46898e147 | −0.190363 | ||||||||
\(995\) | −3.48637e148 | −1.41296 | ||||||||
\(996\) | 1.71477e148 | 0.661253 | ||||||||
\(997\) | 6.57506e147 | 0.241262 | 0.120631 | − | 0.992697i | \(-0.461508\pi\) | ||||
0.120631 | + | 0.992697i | \(0.461508\pi\) | |||||||
\(998\) | −5.02931e147 | −0.175609 | ||||||||
\(999\) | 3.17088e148 | 1.05363 |
(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 | 1.100.a.a.1.5 | ✓ | 8 | |
3.2 | odd | 2 | 9.100.a.d.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.100.a.a.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
9.100.a.d.1.4 | 8 | 3.2 | odd | 2 |