Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,12,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(151.363606570\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −73.7285 | −1.62919 | −0.814593 | − | 0.580033i | \(-0.803040\pi\) | ||||
−0.814593 | + | 0.580033i | \(0.803040\pi\) | |||||||
\(3\) | 331.029 | 0.786500 | 0.393250 | − | 0.919432i | \(-0.371351\pi\) | ||||
0.393250 | + | 0.919432i | \(0.371351\pi\) | |||||||
\(4\) | 3387.90 | 1.65425 | ||||||||
\(5\) | 2290.71 | 0.327820 | 0.163910 | − | 0.986475i | \(-0.447589\pi\) | ||||
0.163910 | + | 0.986475i | \(0.447589\pi\) | |||||||
\(6\) | −24406.3 | −1.28135 | ||||||||
\(7\) | −50357.4 | −1.13246 | −0.566232 | − | 0.824246i | \(-0.691599\pi\) | ||||
−0.566232 | + | 0.824246i | \(0.691599\pi\) | |||||||
\(8\) | −98788.6 | −1.06589 | ||||||||
\(9\) | −67567.1 | −0.381418 | ||||||||
\(10\) | −168891. | −0.534079 | ||||||||
\(11\) | 399282. | 0.747514 | 0.373757 | − | 0.927527i | \(-0.378069\pi\) | ||||
0.373757 | + | 0.927527i | \(0.378069\pi\) | |||||||
\(12\) | 1.12149e6 | 1.30106 | ||||||||
\(13\) | 2.01831e6 | 1.50764 | 0.753822 | − | 0.657079i | \(-0.228208\pi\) | ||||
0.753822 | + | 0.657079i | \(0.228208\pi\) | |||||||
\(14\) | 3.71278e6 | 1.84499 | ||||||||
\(15\) | 758291. | 0.257830 | ||||||||
\(16\) | 345128. | 0.0822850 | ||||||||
\(17\) | 7.93307e6 | 1.35510 | 0.677551 | − | 0.735476i | \(-0.263041\pi\) | ||||
0.677551 | + | 0.735476i | \(0.263041\pi\) | |||||||
\(18\) | 4.98162e6 | 0.621401 | ||||||||
\(19\) | −1.59268e6 | −0.147565 | −0.0737826 | − | 0.997274i | \(-0.523507\pi\) | ||||
−0.0737826 | + | 0.997274i | \(0.523507\pi\) | |||||||
\(20\) | 7.76069e6 | 0.542295 | ||||||||
\(21\) | −1.66698e7 | −0.890683 | ||||||||
\(22\) | −2.94385e7 | −1.21784 | ||||||||
\(23\) | 1.64035e7 | 0.531415 | 0.265707 | − | 0.964054i | \(-0.414395\pi\) | ||||
0.265707 | + | 0.964054i | \(0.414395\pi\) | |||||||
\(24\) | −3.27019e7 | −0.838322 | ||||||||
\(25\) | −4.35808e7 | −0.892534 | ||||||||
\(26\) | −1.48807e8 | −2.45623 | ||||||||
\(27\) | −8.10074e7 | −1.08649 | ||||||||
\(28\) | −1.70606e8 | −1.87337 | ||||||||
\(29\) | 1.26271e8 | 1.14318 | 0.571592 | − | 0.820538i | \(-0.306326\pi\) | ||||
0.571592 | + | 0.820538i | \(0.306326\pi\) | |||||||
\(30\) | −5.59077e7 | −0.420053 | ||||||||
\(31\) | 5.07699e7 | 0.318505 | 0.159253 | − | 0.987238i | \(-0.449092\pi\) | ||||
0.159253 | + | 0.987238i | \(0.449092\pi\) | |||||||
\(32\) | 1.76873e8 | 0.931832 | ||||||||
\(33\) | 1.32174e8 | 0.587920 | ||||||||
\(34\) | −5.84894e8 | −2.20771 | ||||||||
\(35\) | −1.15354e8 | −0.371244 | ||||||||
\(36\) | −2.28910e8 | −0.630960 | ||||||||
\(37\) | −2.64162e8 | −0.626269 | −0.313135 | − | 0.949709i | \(-0.601379\pi\) | ||||
−0.313135 | + | 0.949709i | \(0.601379\pi\) | |||||||
\(38\) | 1.17426e8 | 0.240411 | ||||||||
\(39\) | 6.68117e8 | 1.18576 | ||||||||
\(40\) | −2.26296e8 | −0.349420 | ||||||||
\(41\) | 2.37687e8 | 0.320401 | 0.160201 | − | 0.987084i | \(-0.448786\pi\) | ||||
0.160201 | + | 0.987084i | \(0.448786\pi\) | |||||||
\(42\) | 1.22904e9 | 1.45109 | ||||||||
\(43\) | 5.44415e8 | 0.564747 | 0.282373 | − | 0.959305i | \(-0.408878\pi\) | ||||
0.282373 | + | 0.959305i | \(0.408878\pi\) | |||||||
\(44\) | 1.35273e9 | 1.23657 | ||||||||
\(45\) | −1.54777e8 | −0.125036 | ||||||||
\(46\) | −1.20941e9 | −0.865773 | ||||||||
\(47\) | −9.15873e8 | −0.582501 | −0.291251 | − | 0.956647i | \(-0.594071\pi\) | ||||
−0.291251 | + | 0.956647i | \(0.594071\pi\) | |||||||
\(48\) | 1.14247e8 | 0.0647171 | ||||||||
\(49\) | 5.58546e8 | 0.282475 | ||||||||
\(50\) | 3.21315e9 | 1.45410 | ||||||||
\(51\) | 2.62607e9 | 1.06579 | ||||||||
\(52\) | 6.83782e9 | 2.49401 | ||||||||
\(53\) | 1.92825e9 | 0.633352 | 0.316676 | − | 0.948534i | \(-0.397433\pi\) | ||||
0.316676 | + | 0.948534i | \(0.397433\pi\) | |||||||
\(54\) | 5.97255e9 | 1.77009 | ||||||||
\(55\) | 9.14639e8 | 0.245050 | ||||||||
\(56\) | 4.97474e9 | 1.20708 | ||||||||
\(57\) | −5.27223e8 | −0.116060 | ||||||||
\(58\) | −9.30980e9 | −1.86246 | ||||||||
\(59\) | −3.00106e9 | −0.546498 | −0.273249 | − | 0.961943i | \(-0.588098\pi\) | ||||
−0.273249 | + | 0.961943i | \(0.588098\pi\) | |||||||
\(60\) | 2.56901e9 | 0.426515 | ||||||||
\(61\) | 5.15404e8 | 0.0781329 | 0.0390664 | − | 0.999237i | \(-0.487562\pi\) | ||||
0.0390664 | + | 0.999237i | \(0.487562\pi\) | |||||||
\(62\) | −3.74319e9 | −0.518904 | ||||||||
\(63\) | 3.40251e9 | 0.431942 | ||||||||
\(64\) | −1.37474e10 | −1.60041 | ||||||||
\(65\) | 4.62336e9 | 0.494235 | ||||||||
\(66\) | −9.74497e9 | −0.957831 | ||||||||
\(67\) | −8.98974e9 | −0.813459 | −0.406729 | − | 0.913549i | \(-0.633331\pi\) | ||||
−0.406729 | + | 0.913549i | \(0.633331\pi\) | |||||||
\(68\) | 2.68764e10 | 2.24167 | ||||||||
\(69\) | 5.43003e9 | 0.417958 | ||||||||
\(70\) | 8.50491e9 | 0.604826 | ||||||||
\(71\) | 2.10232e10 | 1.38286 | 0.691429 | − | 0.722445i | \(-0.256982\pi\) | ||||
0.691429 | + | 0.722445i | \(0.256982\pi\) | |||||||
\(72\) | 6.67486e9 | 0.406549 | ||||||||
\(73\) | 9.54887e9 | 0.539108 | 0.269554 | − | 0.962985i | \(-0.413124\pi\) | ||||
0.269554 | + | 0.962985i | \(0.413124\pi\) | |||||||
\(74\) | 1.94763e10 | 1.02031 | ||||||||
\(75\) | −1.44265e10 | −0.701978 | ||||||||
\(76\) | −5.39584e9 | −0.244109 | ||||||||
\(77\) | −2.01068e10 | −0.846533 | ||||||||
\(78\) | −4.92593e10 | −1.93183 | ||||||||
\(79\) | −4.59180e9 | −0.167894 | −0.0839468 | − | 0.996470i | \(-0.526753\pi\) | ||||
−0.0839468 | + | 0.996470i | \(0.526753\pi\) | |||||||
\(80\) | 7.90589e8 | 0.0269747 | ||||||||
\(81\) | −1.48464e10 | −0.473102 | ||||||||
\(82\) | −1.75243e10 | −0.521994 | ||||||||
\(83\) | 1.48825e10 | 0.414713 | 0.207356 | − | 0.978265i | \(-0.433514\pi\) | ||||
0.207356 | + | 0.978265i | \(0.433514\pi\) | |||||||
\(84\) | −5.64754e10 | −1.47341 | ||||||||
\(85\) | 1.81724e10 | 0.444229 | ||||||||
\(86\) | −4.01389e10 | −0.920077 | ||||||||
\(87\) | 4.17994e10 | 0.899113 | ||||||||
\(88\) | −3.94445e10 | −0.796768 | ||||||||
\(89\) | −1.42235e10 | −0.269999 | −0.135000 | − | 0.990846i | \(-0.543103\pi\) | ||||
−0.135000 | + | 0.990846i | \(0.543103\pi\) | |||||||
\(90\) | 1.14115e10 | 0.203708 | ||||||||
\(91\) | −1.01637e11 | −1.70735 | ||||||||
\(92\) | 5.55734e10 | 0.879091 | ||||||||
\(93\) | 1.68063e10 | 0.250504 | ||||||||
\(94\) | 6.75259e10 | 0.949003 | ||||||||
\(95\) | −3.64837e9 | −0.0483748 | ||||||||
\(96\) | 5.85501e10 | 0.732885 | ||||||||
\(97\) | −1.15451e11 | −1.36506 | −0.682532 | − | 0.730855i | \(-0.739121\pi\) | ||||
−0.682532 | + | 0.730855i | \(0.739121\pi\) | |||||||
\(98\) | −4.11808e10 | −0.460204 | ||||||||
\(99\) | −2.69783e10 | −0.285116 | ||||||||
\(100\) | −1.47647e11 | −1.47647 | ||||||||
\(101\) | −9.99493e9 | −0.0946264 | −0.0473132 | − | 0.998880i | \(-0.515066\pi\) | ||||
−0.0473132 | + | 0.998880i | \(0.515066\pi\) | |||||||
\(102\) | −1.93616e11 | −1.73637 | ||||||||
\(103\) | −8.26476e10 | −0.702466 | −0.351233 | − | 0.936288i | \(-0.614238\pi\) | ||||
−0.351233 | + | 0.936288i | \(0.614238\pi\) | |||||||
\(104\) | −1.99386e11 | −1.60698 | ||||||||
\(105\) | −3.81856e10 | −0.291983 | ||||||||
\(106\) | −1.42167e11 | −1.03185 | ||||||||
\(107\) | 6.11104e10 | 0.421215 | 0.210608 | − | 0.977571i | \(-0.432456\pi\) | ||||
0.210608 | + | 0.977571i | \(0.432456\pi\) | |||||||
\(108\) | −2.74445e11 | −1.79731 | ||||||||
\(109\) | 2.25343e11 | 1.40281 | 0.701404 | − | 0.712764i | \(-0.252557\pi\) | ||||
0.701404 | + | 0.712764i | \(0.252557\pi\) | |||||||
\(110\) | −6.74350e10 | −0.399232 | ||||||||
\(111\) | −8.74452e10 | −0.492561 | ||||||||
\(112\) | −1.73798e10 | −0.0931848 | ||||||||
\(113\) | −1.62232e11 | −0.828332 | −0.414166 | − | 0.910201i | \(-0.635927\pi\) | ||||
−0.414166 | + | 0.910201i | \(0.635927\pi\) | |||||||
\(114\) | 3.88714e10 | 0.189083 | ||||||||
\(115\) | 3.75757e10 | 0.174208 | ||||||||
\(116\) | 4.27794e11 | 1.89111 | ||||||||
\(117\) | −1.36371e11 | −0.575043 | ||||||||
\(118\) | 2.21264e11 | 0.890347 | ||||||||
\(119\) | −3.99489e11 | −1.53461 | ||||||||
\(120\) | −7.49105e10 | −0.274818 | ||||||||
\(121\) | −1.25886e11 | −0.441222 | ||||||||
\(122\) | −3.80000e10 | −0.127293 | ||||||||
\(123\) | 7.86812e10 | 0.251996 | ||||||||
\(124\) | 1.72003e11 | 0.526886 | ||||||||
\(125\) | −2.11682e11 | −0.620410 | ||||||||
\(126\) | −2.50862e11 | −0.703714 | ||||||||
\(127\) | 4.58813e11 | 1.23230 | 0.616149 | − | 0.787630i | \(-0.288692\pi\) | ||||
0.616149 | + | 0.787630i | \(0.288692\pi\) | |||||||
\(128\) | 6.51342e11 | 1.67554 | ||||||||
\(129\) | 1.80217e11 | 0.444173 | ||||||||
\(130\) | −3.40873e11 | −0.805201 | ||||||||
\(131\) | 6.81888e10 | 0.154426 | 0.0772131 | − | 0.997015i | \(-0.475398\pi\) | ||||
0.0772131 | + | 0.997015i | \(0.475398\pi\) | |||||||
\(132\) | 4.47791e11 | 0.972565 | ||||||||
\(133\) | 8.02034e10 | 0.167112 | ||||||||
\(134\) | 6.62800e11 | 1.32528 | ||||||||
\(135\) | −1.85564e11 | −0.356171 | ||||||||
\(136\) | −7.83697e11 | −1.44439 | ||||||||
\(137\) | 1.17320e9 | 0.00207686 | 0.00103843 | − | 0.999999i | \(-0.499669\pi\) | ||||
0.00103843 | + | 0.999999i | \(0.499669\pi\) | |||||||
\(138\) | −4.00348e11 | −0.680931 | ||||||||
\(139\) | −3.45355e11 | −0.564526 | −0.282263 | − | 0.959337i | \(-0.591085\pi\) | ||||
−0.282263 | + | 0.959337i | \(0.591085\pi\) | |||||||
\(140\) | −3.90809e11 | −0.614129 | ||||||||
\(141\) | −3.03180e11 | −0.458137 | ||||||||
\(142\) | −1.55001e12 | −2.25293 | ||||||||
\(143\) | 8.05873e11 | 1.12699 | ||||||||
\(144\) | −2.33193e10 | −0.0313850 | ||||||||
\(145\) | 2.89251e11 | 0.374758 | ||||||||
\(146\) | −7.04024e11 | −0.878308 | ||||||||
\(147\) | 1.84895e11 | 0.222167 | ||||||||
\(148\) | −8.94954e11 | −1.03600 | ||||||||
\(149\) | 1.04364e12 | 1.16419 | 0.582097 | − | 0.813120i | \(-0.302233\pi\) | ||||
0.582097 | + | 0.813120i | \(0.302233\pi\) | |||||||
\(150\) | 1.06364e12 | 1.14365 | ||||||||
\(151\) | 8.16986e11 | 0.846918 | 0.423459 | − | 0.905915i | \(-0.360816\pi\) | ||||
0.423459 | + | 0.905915i | \(0.360816\pi\) | |||||||
\(152\) | 1.57339e11 | 0.157288 | ||||||||
\(153\) | −5.36014e11 | −0.516861 | ||||||||
\(154\) | 1.48245e12 | 1.37916 | ||||||||
\(155\) | 1.16299e11 | 0.104412 | ||||||||
\(156\) | 2.26351e12 | 1.96154 | ||||||||
\(157\) | −1.30094e12 | −1.08845 | −0.544227 | − | 0.838938i | \(-0.683177\pi\) | ||||
−0.544227 | + | 0.838938i | \(0.683177\pi\) | |||||||
\(158\) | 3.38547e11 | 0.273530 | ||||||||
\(159\) | 6.38305e11 | 0.498131 | ||||||||
\(160\) | 4.05166e11 | 0.305473 | ||||||||
\(161\) | −8.26039e11 | −0.601808 | ||||||||
\(162\) | 1.09461e12 | 0.770771 | ||||||||
\(163\) | −8.77386e11 | −0.597254 | −0.298627 | − | 0.954370i | \(-0.596529\pi\) | ||||
−0.298627 | + | 0.954370i | \(0.596529\pi\) | |||||||
\(164\) | 8.05260e11 | 0.530023 | ||||||||
\(165\) | 3.02772e11 | 0.192732 | ||||||||
\(166\) | −1.09727e12 | −0.675644 | ||||||||
\(167\) | 4.13045e11 | 0.246069 | 0.123034 | − | 0.992402i | \(-0.460737\pi\) | ||||
0.123034 | + | 0.992402i | \(0.460737\pi\) | |||||||
\(168\) | 1.64678e12 | 0.949369 | ||||||||
\(169\) | 2.28140e12 | 1.27299 | ||||||||
\(170\) | −1.33982e12 | −0.723732 | ||||||||
\(171\) | 1.07613e11 | 0.0562841 | ||||||||
\(172\) | 1.84442e12 | 0.934230 | ||||||||
\(173\) | −1.01662e12 | −0.498773 | −0.249387 | − | 0.968404i | \(-0.580229\pi\) | ||||
−0.249387 | + | 0.968404i | \(0.580229\pi\) | |||||||
\(174\) | −3.08181e12 | −1.46482 | ||||||||
\(175\) | 2.19462e12 | 1.01076 | ||||||||
\(176\) | 1.37803e11 | 0.0615092 | ||||||||
\(177\) | −9.93437e11 | −0.429821 | ||||||||
\(178\) | 1.04868e12 | 0.439879 | ||||||||
\(179\) | −2.02367e11 | −0.0823090 | −0.0411545 | − | 0.999153i | \(-0.513104\pi\) | ||||
−0.0411545 | + | 0.999153i | \(0.513104\pi\) | |||||||
\(180\) | −5.24367e11 | −0.206841 | ||||||||
\(181\) | 3.58266e12 | 1.37080 | 0.685399 | − | 0.728168i | \(-0.259628\pi\) | ||||
0.685399 | + | 0.728168i | \(0.259628\pi\) | |||||||
\(182\) | 7.49353e12 | 2.78159 | ||||||||
\(183\) | 1.70613e11 | 0.0614515 | ||||||||
\(184\) | −1.62048e12 | −0.566429 | ||||||||
\(185\) | −6.05119e11 | −0.205304 | ||||||||
\(186\) | −1.23910e12 | −0.408118 | ||||||||
\(187\) | 3.16753e12 | 1.01296 | ||||||||
\(188\) | −3.10288e12 | −0.963601 | ||||||||
\(189\) | 4.07932e12 | 1.23041 | ||||||||
\(190\) | 2.68989e11 | 0.0788116 | ||||||||
\(191\) | −1.34066e12 | −0.381622 | −0.190811 | − | 0.981627i | \(-0.561112\pi\) | ||||
−0.190811 | + | 0.981627i | \(0.561112\pi\) | |||||||
\(192\) | −4.55079e12 | −1.25872 | ||||||||
\(193\) | −1.08399e8 | −2.91381e−5 0 | −1.45691e−5 | − | 1.00000i | \(-0.500005\pi\) | ||||
−1.45691e−5 | 1.00000i | \(0.500005\pi\) | ||||||||
\(194\) | 8.51203e12 | 2.22394 | ||||||||
\(195\) | 1.53046e12 | 0.388716 | ||||||||
\(196\) | 1.89230e12 | 0.467284 | ||||||||
\(197\) | −2.96709e11 | −0.0712470 | ||||||||
\(198\) | 1.98907e12 | 0.464506 | ||||||||
\(199\) | 2.20690e12 | 0.501292 | 0.250646 | − | 0.968079i | \(-0.419357\pi\) | ||||
0.250646 | + | 0.968079i | \(0.419357\pi\) | |||||||
\(200\) | 4.30528e12 | 0.951343 | ||||||||
\(201\) | −2.97586e12 | −0.639785 | ||||||||
\(202\) | 7.36911e11 | 0.154164 | ||||||||
\(203\) | −6.35870e12 | −1.29461 | ||||||||
\(204\) | 8.89686e12 | 1.76308 | ||||||||
\(205\) | 5.44472e11 | 0.105034 | ||||||||
\(206\) | 6.09349e12 | 1.14445 | ||||||||
\(207\) | −1.10834e12 | −0.202691 | ||||||||
\(208\) | 6.96575e11 | 0.124056 | ||||||||
\(209\) | −6.35928e11 | −0.110307 | ||||||||
\(210\) | 2.81537e12 | 0.475695 | ||||||||
\(211\) | 4.22161e12 | 0.694904 | 0.347452 | − | 0.937698i | \(-0.387047\pi\) | ||||
0.347452 | + | 0.937698i | \(0.387047\pi\) | |||||||
\(212\) | 6.53270e12 | 1.04772 | ||||||||
\(213\) | 6.95927e12 | 1.08762 | ||||||||
\(214\) | −4.50558e12 | −0.686238 | ||||||||
\(215\) | 1.24710e12 | 0.185135 | ||||||||
\(216\) | 8.00261e12 | 1.15807 | ||||||||
\(217\) | −2.55664e12 | −0.360696 | ||||||||
\(218\) | −1.66142e13 | −2.28543 | ||||||||
\(219\) | 3.16095e12 | 0.424009 | ||||||||
\(220\) | 3.09870e12 | 0.405373 | ||||||||
\(221\) | 1.60114e13 | 2.04301 | ||||||||
\(222\) | 6.44721e12 | 0.802473 | ||||||||
\(223\) | 3.85211e12 | 0.467759 | 0.233880 | − | 0.972266i | \(-0.424858\pi\) | ||||
0.233880 | + | 0.972266i | \(0.424858\pi\) | |||||||
\(224\) | −8.90689e12 | −1.05527 | ||||||||
\(225\) | 2.94463e12 | 0.340429 | ||||||||
\(226\) | 1.19611e13 | 1.34951 | ||||||||
\(227\) | 1.10232e13 | 1.21385 | 0.606927 | − | 0.794758i | \(-0.292402\pi\) | ||||
0.606927 | + | 0.794758i | \(0.292402\pi\) | |||||||
\(228\) | −1.78618e12 | −0.191992 | ||||||||
\(229\) | −7.24160e11 | −0.0759870 | −0.0379935 | − | 0.999278i | \(-0.512097\pi\) | ||||
−0.0379935 | + | 0.999278i | \(0.512097\pi\) | |||||||
\(230\) | −2.77040e12 | −0.283818 | ||||||||
\(231\) | −6.65593e12 | −0.665798 | ||||||||
\(232\) | −1.24742e13 | −1.21851 | ||||||||
\(233\) | −1.39480e12 | −0.133062 | −0.0665309 | − | 0.997784i | \(-0.521193\pi\) | ||||
−0.0665309 | + | 0.997784i | \(0.521193\pi\) | |||||||
\(234\) | 1.00544e13 | 0.936851 | ||||||||
\(235\) | −2.09800e12 | −0.190955 | ||||||||
\(236\) | −1.01673e13 | −0.904043 | ||||||||
\(237\) | −1.52002e12 | −0.132048 | ||||||||
\(238\) | 2.94537e13 | 2.50016 | ||||||||
\(239\) | 3.29448e12 | 0.273274 | 0.136637 | − | 0.990621i | \(-0.456371\pi\) | ||||
0.136637 | + | 0.990621i | \(0.456371\pi\) | |||||||
\(240\) | 2.61708e11 | 0.0212156 | ||||||||
\(241\) | −1.11368e13 | −0.882405 | −0.441202 | − | 0.897408i | \(-0.645448\pi\) | ||||
−0.441202 | + | 0.897408i | \(0.645448\pi\) | |||||||
\(242\) | 9.28138e12 | 0.718833 | ||||||||
\(243\) | 9.43561e12 | 0.714390 | ||||||||
\(244\) | 1.74614e12 | 0.129251 | ||||||||
\(245\) | 1.27947e12 | 0.0926009 | ||||||||
\(246\) | −5.80105e12 | −0.410548 | ||||||||
\(247\) | −3.21452e12 | −0.222476 | ||||||||
\(248\) | −5.01549e12 | −0.339491 | ||||||||
\(249\) | 4.92654e12 | 0.326171 | ||||||||
\(250\) | 1.56070e13 | 1.01076 | ||||||||
\(251\) | 2.17570e13 | 1.37846 | 0.689229 | − | 0.724543i | \(-0.257949\pi\) | ||||
0.689229 | + | 0.724543i | \(0.257949\pi\) | |||||||
\(252\) | 1.15273e13 | 0.714539 | ||||||||
\(253\) | 6.54962e12 | 0.397240 | ||||||||
\(254\) | −3.38276e13 | −2.00764 | ||||||||
\(255\) | 6.01557e12 | 0.349386 | ||||||||
\(256\) | −1.98677e13 | −1.12935 | ||||||||
\(257\) | 1.61133e13 | 0.896503 | 0.448251 | − | 0.893908i | \(-0.352047\pi\) | ||||
0.448251 | + | 0.893908i | \(0.352047\pi\) | |||||||
\(258\) | −1.32871e13 | −0.723640 | ||||||||
\(259\) | 1.33025e13 | 0.709228 | ||||||||
\(260\) | 1.56635e13 | 0.817587 | ||||||||
\(261\) | −8.53179e12 | −0.436031 | ||||||||
\(262\) | −5.02746e12 | −0.251589 | ||||||||
\(263\) | −5.47457e12 | −0.268283 | −0.134142 | − | 0.990962i | \(-0.542828\pi\) | ||||
−0.134142 | + | 0.990962i | \(0.542828\pi\) | |||||||
\(264\) | −1.30573e13 | −0.626657 | ||||||||
\(265\) | 4.41705e12 | 0.207625 | ||||||||
\(266\) | −5.91328e12 | −0.272257 | ||||||||
\(267\) | −4.70840e12 | −0.212354 | ||||||||
\(268\) | −3.04563e13 | −1.34566 | ||||||||
\(269\) | −1.98053e12 | −0.0857320 | −0.0428660 | − | 0.999081i | \(-0.513649\pi\) | ||||
−0.0428660 | + | 0.999081i | \(0.513649\pi\) | |||||||
\(270\) | 1.36814e13 | 0.580269 | ||||||||
\(271\) | 6.50171e12 | 0.270207 | 0.135104 | − | 0.990831i | \(-0.456863\pi\) | ||||
0.135104 | + | 0.990831i | \(0.456863\pi\) | |||||||
\(272\) | 2.73793e12 | 0.111505 | ||||||||
\(273\) | −3.36447e13 | −1.34283 | ||||||||
\(274\) | −8.64981e10 | −0.00338360 | ||||||||
\(275\) | −1.74010e13 | −0.667182 | ||||||||
\(276\) | 1.83964e13 | 0.691405 | ||||||||
\(277\) | −2.36179e13 | −0.870165 | −0.435083 | − | 0.900390i | \(-0.643281\pi\) | ||||
−0.435083 | + | 0.900390i | \(0.643281\pi\) | |||||||
\(278\) | 2.54625e13 | 0.919718 | ||||||||
\(279\) | −3.43037e12 | −0.121484 | ||||||||
\(280\) | 1.13957e13 | 0.395705 | ||||||||
\(281\) | −3.59005e13 | −1.22241 | −0.611203 | − | 0.791474i | \(-0.709314\pi\) | ||||
−0.611203 | + | 0.791474i | \(0.709314\pi\) | |||||||
\(282\) | 2.23530e13 | 0.746390 | ||||||||
\(283\) | 5.22092e13 | 1.70971 | 0.854854 | − | 0.518869i | \(-0.173647\pi\) | ||||
0.854854 | + | 0.518869i | \(0.173647\pi\) | |||||||
\(284\) | 7.12243e13 | 2.28759 | ||||||||
\(285\) | −1.20772e12 | −0.0380468 | ||||||||
\(286\) | −5.94158e13 | −1.83607 | ||||||||
\(287\) | −1.19693e13 | −0.362843 | ||||||||
\(288\) | −1.19508e13 | −0.355417 | ||||||||
\(289\) | 2.86617e13 | 0.836303 | ||||||||
\(290\) | −2.13261e13 | −0.610551 | ||||||||
\(291\) | −3.82176e13 | −1.07362 | ||||||||
\(292\) | 3.23506e13 | 0.891818 | ||||||||
\(293\) | 1.79206e13 | 0.484821 | 0.242411 | − | 0.970174i | \(-0.422062\pi\) | ||||
0.242411 | + | 0.970174i | \(0.422062\pi\) | |||||||
\(294\) | −1.36320e13 | −0.361951 | ||||||||
\(295\) | −6.87456e12 | −0.179153 | ||||||||
\(296\) | 2.60962e13 | 0.667534 | ||||||||
\(297\) | −3.23448e13 | −0.812163 | ||||||||
\(298\) | −7.69458e13 | −1.89669 | ||||||||
\(299\) | 3.31073e13 | 0.801184 | ||||||||
\(300\) | −4.88754e13 | −1.16124 | ||||||||
\(301\) | −2.74154e13 | −0.639555 | ||||||||
\(302\) | −6.02352e13 | −1.37979 | ||||||||
\(303\) | −3.30861e12 | −0.0744236 | ||||||||
\(304\) | −5.49679e11 | −0.0121424 | ||||||||
\(305\) | 1.18064e12 | 0.0256135 | ||||||||
\(306\) | 3.95196e13 | 0.842062 | ||||||||
\(307\) | −4.24972e13 | −0.889405 | −0.444702 | − | 0.895678i | \(-0.646691\pi\) | ||||
−0.444702 | + | 0.895678i | \(0.646691\pi\) | |||||||
\(308\) | −6.81198e13 | −1.40037 | ||||||||
\(309\) | −2.73587e13 | −0.552489 | ||||||||
\(310\) | −8.57456e12 | −0.170107 | ||||||||
\(311\) | −1.88853e13 | −0.368079 | −0.184040 | − | 0.982919i | \(-0.558917\pi\) | ||||
−0.184040 | + | 0.982919i | \(0.558917\pi\) | |||||||
\(312\) | −6.60024e13 | −1.26389 | ||||||||
\(313\) | 1.97471e13 | 0.371543 | 0.185771 | − | 0.982593i | \(-0.440522\pi\) | ||||
0.185771 | + | 0.982593i | \(0.440522\pi\) | |||||||
\(314\) | 9.59166e13 | 1.77329 | ||||||||
\(315\) | 7.79416e12 | 0.141599 | ||||||||
\(316\) | −1.55566e13 | −0.277738 | ||||||||
\(317\) | −4.83693e13 | −0.848680 | −0.424340 | − | 0.905503i | \(-0.639494\pi\) | ||||
−0.424340 | + | 0.905503i | \(0.639494\pi\) | |||||||
\(318\) | −4.70613e13 | −0.811548 | ||||||||
\(319\) | 5.04178e13 | 0.854546 | ||||||||
\(320\) | −3.14914e13 | −0.524647 | ||||||||
\(321\) | 2.02293e13 | 0.331286 | ||||||||
\(322\) | 6.09026e13 | 0.980457 | ||||||||
\(323\) | −1.26349e13 | −0.199966 | ||||||||
\(324\) | −5.02982e13 | −0.782627 | ||||||||
\(325\) | −8.79594e13 | −1.34562 | ||||||||
\(326\) | 6.46884e13 | 0.973037 | ||||||||
\(327\) | 7.45949e13 | 1.10331 | ||||||||
\(328\) | −2.34808e13 | −0.341512 | ||||||||
\(329\) | 4.61210e13 | 0.659662 | ||||||||
\(330\) | −2.23229e13 | −0.313996 | ||||||||
\(331\) | 5.11526e13 | 0.707642 | 0.353821 | − | 0.935313i | \(-0.384882\pi\) | ||||
0.353821 | + | 0.935313i | \(0.384882\pi\) | |||||||
\(332\) | 5.04205e13 | 0.686037 | ||||||||
\(333\) | 1.78487e13 | 0.238871 | ||||||||
\(334\) | −3.04532e13 | −0.400892 | ||||||||
\(335\) | −2.05929e13 | −0.266668 | ||||||||
\(336\) | −5.75320e12 | −0.0732898 | ||||||||
\(337\) | −4.06419e12 | −0.0509342 | −0.0254671 | − | 0.999676i | \(-0.508107\pi\) | ||||
−0.0254671 | + | 0.999676i | \(0.508107\pi\) | |||||||
\(338\) | −1.68204e14 | −2.07394 | ||||||||
\(339\) | −5.37033e13 | −0.651483 | ||||||||
\(340\) | 6.15661e13 | 0.734865 | ||||||||
\(341\) | 2.02715e13 | 0.238087 | ||||||||
\(342\) | −7.93414e12 | −0.0916972 | ||||||||
\(343\) | 7.14462e13 | 0.812571 | ||||||||
\(344\) | −5.37820e13 | −0.601957 | ||||||||
\(345\) | 1.24386e13 | 0.137015 | ||||||||
\(346\) | 7.49536e13 | 0.812595 | ||||||||
\(347\) | 9.12072e13 | 0.973233 | 0.486616 | − | 0.873616i | \(-0.338231\pi\) | ||||
0.486616 | + | 0.873616i | \(0.338231\pi\) | |||||||
\(348\) | 1.41612e14 | 1.48735 | ||||||||
\(349\) | 4.78457e13 | 0.494656 | 0.247328 | − | 0.968932i | \(-0.420447\pi\) | ||||
0.247328 | + | 0.968932i | \(0.420447\pi\) | |||||||
\(350\) | −1.61806e14 | −1.64672 | ||||||||
\(351\) | −1.63498e14 | −1.63803 | ||||||||
\(352\) | 7.06223e13 | 0.696558 | ||||||||
\(353\) | 1.28016e14 | 1.24309 | 0.621547 | − | 0.783377i | \(-0.286505\pi\) | ||||
0.621547 | + | 0.783377i | \(0.286505\pi\) | |||||||
\(354\) | 7.32447e13 | 0.700258 | ||||||||
\(355\) | 4.81580e13 | 0.453328 | ||||||||
\(356\) | −4.81879e13 | −0.446645 | ||||||||
\(357\) | −1.32242e14 | −1.20697 | ||||||||
\(358\) | 1.49202e13 | 0.134097 | ||||||||
\(359\) | 1.37467e14 | 1.21669 | 0.608344 | − | 0.793674i | \(-0.291834\pi\) | ||||
0.608344 | + | 0.793674i | \(0.291834\pi\) | |||||||
\(360\) | 1.52902e13 | 0.133275 | ||||||||
\(361\) | −1.13954e14 | −0.978224 | ||||||||
\(362\) | −2.64144e14 | −2.23328 | ||||||||
\(363\) | −4.16718e13 | −0.347021 | ||||||||
\(364\) | −3.44335e14 | −2.82438 | ||||||||
\(365\) | 2.18737e13 | 0.176730 | ||||||||
\(366\) | −1.25791e13 | −0.100116 | ||||||||
\(367\) | 1.70128e14 | 1.33386 | 0.666932 | − | 0.745119i | \(-0.267607\pi\) | ||||
0.666932 | + | 0.745119i | \(0.267607\pi\) | |||||||
\(368\) | 5.66131e12 | 0.0437275 | ||||||||
\(369\) | −1.60598e13 | −0.122207 | ||||||||
\(370\) | 4.46145e13 | 0.334478 | ||||||||
\(371\) | −9.71016e13 | −0.717249 | ||||||||
\(372\) | 5.69379e13 | 0.414396 | ||||||||
\(373\) | 1.42254e14 | 1.02016 | 0.510079 | − | 0.860128i | \(-0.329616\pi\) | ||||
0.510079 | + | 0.860128i | \(0.329616\pi\) | |||||||
\(374\) | −2.33537e14 | −1.65030 | ||||||||
\(375\) | −7.00728e13 | −0.487952 | ||||||||
\(376\) | 9.04778e13 | 0.620882 | ||||||||
\(377\) | 2.54854e14 | 1.72351 | ||||||||
\(378\) | −3.00763e14 | −2.00456 | ||||||||
\(379\) | 4.38157e13 | 0.287815 | 0.143908 | − | 0.989591i | \(-0.454033\pi\) | ||||
0.143908 | + | 0.989591i | \(0.454033\pi\) | |||||||
\(380\) | −1.23603e13 | −0.0800239 | ||||||||
\(381\) | 1.51880e14 | 0.969202 | ||||||||
\(382\) | 9.88445e13 | 0.621733 | ||||||||
\(383\) | 1.88156e14 | 1.16661 | 0.583303 | − | 0.812255i | \(-0.301760\pi\) | ||||
0.583303 | + | 0.812255i | \(0.301760\pi\) | |||||||
\(384\) | 2.15613e14 | 1.31781 | ||||||||
\(385\) | −4.60589e13 | −0.277510 | ||||||||
\(386\) | 7.99213e9 | 4.74715e−5 0 | ||||||||
\(387\) | −3.67845e13 | −0.215405 | ||||||||
\(388\) | −3.91136e14 | −2.25815 | ||||||||
\(389\) | 1.24223e14 | 0.707095 | 0.353548 | − | 0.935417i | \(-0.384975\pi\) | ||||
0.353548 | + | 0.935417i | \(0.384975\pi\) | |||||||
\(390\) | −1.12839e14 | −0.633291 | ||||||||
\(391\) | 1.30130e14 | 0.720121 | ||||||||
\(392\) | −5.51780e13 | −0.301087 | ||||||||
\(393\) | 2.25724e13 | 0.121456 | ||||||||
\(394\) | 2.18759e13 | 0.116075 | ||||||||
\(395\) | −1.05185e13 | −0.0550389 | ||||||||
\(396\) | −9.13997e13 | −0.471651 | ||||||||
\(397\) | 3.33821e14 | 1.69889 | 0.849445 | − | 0.527676i | \(-0.176937\pi\) | ||||
0.849445 | + | 0.527676i | \(0.176937\pi\) | |||||||
\(398\) | −1.62711e14 | −0.816698 | ||||||||
\(399\) | 2.65496e13 | 0.131434 | ||||||||
\(400\) | −1.50410e13 | −0.0734422 | ||||||||
\(401\) | 1.61490e14 | 0.777772 | 0.388886 | − | 0.921286i | \(-0.372860\pi\) | ||||
0.388886 | + | 0.921286i | \(0.372860\pi\) | |||||||
\(402\) | 2.19406e14 | 1.04233 | ||||||||
\(403\) | 1.02469e14 | 0.480193 | ||||||||
\(404\) | −3.38618e13 | −0.156535 | ||||||||
\(405\) | −3.40089e13 | −0.155092 | ||||||||
\(406\) | 4.68818e14 | 2.10917 | ||||||||
\(407\) | −1.05475e14 | −0.468145 | ||||||||
\(408\) | −2.59426e14 | −1.13601 | ||||||||
\(409\) | 3.11378e14 | 1.34527 | 0.672636 | − | 0.739973i | \(-0.265162\pi\) | ||||
0.672636 | + | 0.739973i | \(0.265162\pi\) | |||||||
\(410\) | −4.01432e13 | −0.171120 | ||||||||
\(411\) | 3.88362e11 | 0.00163345 | ||||||||
\(412\) | −2.80001e14 | −1.16205 | ||||||||
\(413\) | 1.51126e14 | 0.618890 | ||||||||
\(414\) | 8.17161e13 | 0.330222 | ||||||||
\(415\) | 3.40916e13 | 0.135951 | ||||||||
\(416\) | 3.56985e14 | 1.40487 | ||||||||
\(417\) | −1.14322e14 | −0.444000 | ||||||||
\(418\) | 4.68861e13 | 0.179711 | ||||||||
\(419\) | 3.23883e14 | 1.22521 | 0.612607 | − | 0.790388i | \(-0.290121\pi\) | ||||
0.612607 | + | 0.790388i | \(0.290121\pi\) | |||||||
\(420\) | −1.29369e14 | −0.483013 | ||||||||
\(421\) | 2.72604e14 | 1.00457 | 0.502285 | − | 0.864702i | \(-0.332493\pi\) | ||||
0.502285 | + | 0.864702i | \(0.332493\pi\) | |||||||
\(422\) | −3.11253e14 | −1.13213 | ||||||||
\(423\) | 6.18828e13 | 0.222177 | ||||||||
\(424\) | −1.90489e14 | −0.675083 | ||||||||
\(425\) | −3.45729e14 | −1.20948 | ||||||||
\(426\) | −5.13097e14 | −1.77193 | ||||||||
\(427\) | −2.59544e13 | −0.0884827 | ||||||||
\(428\) | 2.07036e14 | 0.696794 | ||||||||
\(429\) | 2.66767e14 | 0.886374 | ||||||||
\(430\) | −9.19467e13 | −0.301620 | ||||||||
\(431\) | −3.41043e14 | −1.10455 | −0.552273 | − | 0.833664i | \(-0.686239\pi\) | ||||
−0.552273 | + | 0.833664i | \(0.686239\pi\) | |||||||
\(432\) | −2.79579e13 | −0.0894014 | ||||||||
\(433\) | 2.01034e14 | 0.634724 | 0.317362 | − | 0.948304i | \(-0.397203\pi\) | ||||
0.317362 | + | 0.948304i | \(0.397203\pi\) | |||||||
\(434\) | 1.88497e14 | 0.587641 | ||||||||
\(435\) | 9.57504e13 | 0.294747 | ||||||||
\(436\) | 7.63438e14 | 2.32059 | ||||||||
\(437\) | −2.61256e13 | −0.0784183 | ||||||||
\(438\) | −2.33052e14 | −0.690789 | ||||||||
\(439\) | −3.96585e14 | −1.16086 | −0.580432 | − | 0.814309i | \(-0.697116\pi\) | ||||
−0.580432 | + | 0.814309i | \(0.697116\pi\) | |||||||
\(440\) | −9.03559e13 | −0.261196 | ||||||||
\(441\) | −3.77393e13 | −0.107741 | ||||||||
\(442\) | −1.18049e15 | −3.32845 | ||||||||
\(443\) | 3.34805e14 | 0.932334 | 0.466167 | − | 0.884697i | \(-0.345635\pi\) | ||||
0.466167 | + | 0.884697i | \(0.345635\pi\) | |||||||
\(444\) | −2.96255e14 | −0.814817 | ||||||||
\(445\) | −3.25820e13 | −0.0885111 | ||||||||
\(446\) | −2.84011e14 | −0.762066 | ||||||||
\(447\) | 3.45474e14 | 0.915638 | ||||||||
\(448\) | 6.92286e14 | 1.81241 | ||||||||
\(449\) | 6.12342e13 | 0.158358 | 0.0791788 | − | 0.996860i | \(-0.474770\pi\) | ||||
0.0791788 | + | 0.996860i | \(0.474770\pi\) | |||||||
\(450\) | −2.17103e14 | −0.554622 | ||||||||
\(451\) | 9.49041e13 | 0.239505 | ||||||||
\(452\) | −5.49624e14 | −1.37027 | ||||||||
\(453\) | 2.70446e14 | 0.666101 | ||||||||
\(454\) | −8.12726e14 | −1.97759 | ||||||||
\(455\) | −2.32820e14 | −0.559704 | ||||||||
\(456\) | 5.20836e13 | 0.123707 | ||||||||
\(457\) | −5.14743e14 | −1.20796 | −0.603978 | − | 0.797001i | \(-0.706418\pi\) | ||||
−0.603978 | + | 0.797001i | \(0.706418\pi\) | |||||||
\(458\) | 5.33913e13 | 0.123797 | ||||||||
\(459\) | −6.42637e14 | −1.47230 | ||||||||
\(460\) | 1.27303e14 | 0.288183 | ||||||||
\(461\) | 2.87114e14 | 0.642242 | 0.321121 | − | 0.947038i | \(-0.395940\pi\) | ||||
0.321121 | + | 0.947038i | \(0.395940\pi\) | |||||||
\(462\) | 4.90732e14 | 1.08471 | ||||||||
\(463\) | −1.72267e14 | −0.376276 | −0.188138 | − | 0.982143i | \(-0.560245\pi\) | ||||
−0.188138 | + | 0.982143i | \(0.560245\pi\) | |||||||
\(464\) | 4.35798e13 | 0.0940668 | ||||||||
\(465\) | 3.84983e13 | 0.0821203 | ||||||||
\(466\) | 1.02836e14 | 0.216782 | ||||||||
\(467\) | −6.00139e14 | −1.25029 | −0.625143 | − | 0.780510i | \(-0.714959\pi\) | ||||
−0.625143 | + | 0.780510i | \(0.714959\pi\) | |||||||
\(468\) | −4.62011e14 | −0.951262 | ||||||||
\(469\) | 4.52700e14 | 0.921213 | ||||||||
\(470\) | 1.54682e14 | 0.311102 | ||||||||
\(471\) | −4.30649e14 | −0.856069 | ||||||||
\(472\) | 2.96471e14 | 0.582507 | ||||||||
\(473\) | 2.17375e14 | 0.422156 | ||||||||
\(474\) | 1.12069e14 | 0.215131 | ||||||||
\(475\) | 6.94103e13 | 0.131707 | ||||||||
\(476\) | −1.35343e15 | −2.53862 | ||||||||
\(477\) | −1.30286e14 | −0.241572 | ||||||||
\(478\) | −2.42897e14 | −0.445214 | ||||||||
\(479\) | 4.83658e14 | 0.876381 | 0.438190 | − | 0.898882i | \(-0.355620\pi\) | ||||
0.438190 | + | 0.898882i | \(0.355620\pi\) | |||||||
\(480\) | 1.34121e14 | 0.240254 | ||||||||
\(481\) | −5.33160e14 | −0.944191 | ||||||||
\(482\) | 8.21102e14 | 1.43760 | ||||||||
\(483\) | −2.73442e14 | −0.473322 | ||||||||
\(484\) | −4.26488e14 | −0.729890 | ||||||||
\(485\) | −2.64465e14 | −0.447495 | ||||||||
\(486\) | −6.95674e14 | −1.16387 | ||||||||
\(487\) | 8.09121e14 | 1.33846 | 0.669229 | − | 0.743057i | \(-0.266625\pi\) | ||||
0.669229 | + | 0.743057i | \(0.266625\pi\) | |||||||
\(488\) | −5.09161e13 | −0.0832810 | ||||||||
\(489\) | −2.90440e14 | −0.469740 | ||||||||
\(490\) | −9.43332e13 | −0.150864 | ||||||||
\(491\) | −5.64967e14 | −0.893460 | −0.446730 | − | 0.894669i | \(-0.647412\pi\) | ||||
−0.446730 | + | 0.894669i | \(0.647412\pi\) | |||||||
\(492\) | 2.66564e14 | 0.416863 | ||||||||
\(493\) | 1.00172e15 | 1.54913 | ||||||||
\(494\) | 2.37002e14 | 0.362454 | ||||||||
\(495\) | −6.17995e13 | −0.0934665 | ||||||||
\(496\) | 1.75221e13 | 0.0262082 | ||||||||
\(497\) | −1.05867e15 | −1.56604 | ||||||||
\(498\) | −3.63227e14 | −0.531394 | ||||||||
\(499\) | 8.81666e14 | 1.27571 | 0.637853 | − | 0.770158i | \(-0.279823\pi\) | ||||
0.637853 | + | 0.770158i | \(0.279823\pi\) | |||||||
\(500\) | −7.17157e14 | −1.02631 | ||||||||
\(501\) | 1.36730e14 | 0.193533 | ||||||||
\(502\) | −1.60411e15 | −2.24577 | ||||||||
\(503\) | 2.53182e14 | 0.350597 | 0.175298 | − | 0.984515i | \(-0.443911\pi\) | ||||
0.175298 | + | 0.984515i | \(0.443911\pi\) | |||||||
\(504\) | −3.36129e14 | −0.460403 | ||||||||
\(505\) | −2.28955e13 | −0.0310204 | ||||||||
\(506\) | −4.82894e14 | −0.647178 | ||||||||
\(507\) | 7.55209e14 | 1.00121 | ||||||||
\(508\) | 1.55441e15 | 2.03852 | ||||||||
\(509\) | −5.59138e13 | −0.0725390 | −0.0362695 | − | 0.999342i | \(-0.511547\pi\) | ||||
−0.0362695 | + | 0.999342i | \(0.511547\pi\) | |||||||
\(510\) | −4.43519e14 | −0.569215 | ||||||||
\(511\) | −4.80857e14 | −0.610521 | ||||||||
\(512\) | 1.30870e14 | 0.164382 | ||||||||
\(513\) | 1.29019e14 | 0.160327 | ||||||||
\(514\) | −1.18801e15 | −1.46057 | ||||||||
\(515\) | −1.89322e14 | −0.230282 | ||||||||
\(516\) | 6.10556e14 | 0.734772 | ||||||||
\(517\) | −3.65691e14 | −0.435428 | ||||||||
\(518\) | −9.80776e14 | −1.15546 | ||||||||
\(519\) | −3.36529e14 | −0.392285 | ||||||||
\(520\) | −4.56735e14 | −0.526800 | ||||||||
\(521\) | −1.50269e15 | −1.71500 | −0.857498 | − | 0.514487i | \(-0.827982\pi\) | ||||
−0.857498 | + | 0.514487i | \(0.827982\pi\) | |||||||
\(522\) | 6.29036e14 | 0.710375 | ||||||||
\(523\) | 1.49288e15 | 1.66827 | 0.834134 | − | 0.551562i | \(-0.185968\pi\) | ||||
0.834134 | + | 0.551562i | \(0.185968\pi\) | |||||||
\(524\) | 2.31017e14 | 0.255459 | ||||||||
\(525\) | 7.26481e14 | 0.794965 | ||||||||
\(526\) | 4.03632e14 | 0.437083 | ||||||||
\(527\) | 4.02761e14 | 0.431607 | ||||||||
\(528\) | 4.56169e13 | 0.0483770 | ||||||||
\(529\) | −6.83735e14 | −0.717598 | ||||||||
\(530\) | −3.25663e14 | −0.338260 | ||||||||
\(531\) | 2.02773e14 | 0.208444 | ||||||||
\(532\) | 2.71721e14 | 0.276445 | ||||||||
\(533\) | 4.79726e14 | 0.483051 | ||||||||
\(534\) | 3.47143e14 | 0.345965 | ||||||||
\(535\) | 1.39986e14 | 0.138083 | ||||||||
\(536\) | 8.88084e14 | 0.867057 | ||||||||
\(537\) | −6.69891e13 | −0.0647360 | ||||||||
\(538\) | 1.46021e14 | 0.139673 | ||||||||
\(539\) | 2.23017e14 | 0.211154 | ||||||||
\(540\) | −6.28673e14 | −0.589195 | ||||||||
\(541\) | −3.42334e14 | −0.317589 | −0.158794 | − | 0.987312i | \(-0.550761\pi\) | ||||
−0.158794 | + | 0.987312i | \(0.550761\pi\) | |||||||
\(542\) | −4.79362e14 | −0.440218 | ||||||||
\(543\) | 1.18596e15 | 1.07813 | ||||||||
\(544\) | 1.40315e15 | 1.26273 | ||||||||
\(545\) | 5.16195e14 | 0.459868 | ||||||||
\(546\) | 2.48057e15 | 2.18772 | ||||||||
\(547\) | 2.06884e15 | 1.80633 | 0.903165 | − | 0.429294i | \(-0.141238\pi\) | ||||
0.903165 | + | 0.429294i | \(0.141238\pi\) | |||||||
\(548\) | 3.97467e12 | 0.00343564 | ||||||||
\(549\) | −3.48243e13 | −0.0298013 | ||||||||
\(550\) | 1.28295e15 | 1.08696 | ||||||||
\(551\) | −2.01110e14 | −0.168694 | ||||||||
\(552\) | −5.36425e14 | −0.445496 | ||||||||
\(553\) | 2.31231e14 | 0.190134 | ||||||||
\(554\) | 1.74131e15 | 1.41766 | ||||||||
\(555\) | −2.00312e14 | −0.161471 | ||||||||
\(556\) | −1.17003e15 | −0.933865 | ||||||||
\(557\) | −1.93311e15 | −1.52775 | −0.763875 | − | 0.645364i | \(-0.776706\pi\) | ||||
−0.763875 | + | 0.645364i | \(0.776706\pi\) | |||||||
\(558\) | 2.52916e14 | 0.197920 | ||||||||
\(559\) | 1.09880e15 | 0.851437 | ||||||||
\(560\) | −3.98120e13 | −0.0305478 | ||||||||
\(561\) | 1.04854e15 | 0.796692 | ||||||||
\(562\) | 2.64689e15 | 1.99153 | ||||||||
\(563\) | −4.76413e14 | −0.354966 | −0.177483 | − | 0.984124i | \(-0.556796\pi\) | ||||
−0.177483 | + | 0.984124i | \(0.556796\pi\) | |||||||
\(564\) | −1.02714e15 | −0.757872 | ||||||||
\(565\) | −3.71626e14 | −0.271544 | ||||||||
\(566\) | −3.84931e15 | −2.78543 | ||||||||
\(567\) | 7.47629e14 | 0.535771 | ||||||||
\(568\) | −2.07685e15 | −1.47397 | ||||||||
\(569\) | −1.92878e14 | −0.135571 | −0.0677854 | − | 0.997700i | \(-0.521593\pi\) | ||||
−0.0677854 | + | 0.997700i | \(0.521593\pi\) | |||||||
\(570\) | 8.90431e13 | 0.0619853 | ||||||||
\(571\) | 7.17628e14 | 0.494767 | 0.247384 | − | 0.968918i | \(-0.420429\pi\) | ||||
0.247384 | + | 0.968918i | \(0.420429\pi\) | |||||||
\(572\) | 2.73021e15 | 1.86431 | ||||||||
\(573\) | −4.43795e14 | −0.300146 | ||||||||
\(574\) | 8.82480e14 | 0.591139 | ||||||||
\(575\) | −7.14877e14 | −0.474306 | ||||||||
\(576\) | 9.28874e14 | 0.610426 | ||||||||
\(577\) | −4.07758e14 | −0.265421 | −0.132710 | − | 0.991155i | \(-0.542368\pi\) | ||||
−0.132710 | + | 0.991155i | \(0.542368\pi\) | |||||||
\(578\) | −2.11318e15 | −1.36249 | ||||||||
\(579\) | −3.58833e10 | −2.29171e−5 0 | ||||||||
\(580\) | 9.79953e14 | 0.619942 | ||||||||
\(581\) | −7.49446e14 | −0.469647 | ||||||||
\(582\) | 2.81773e15 | 1.74913 | ||||||||
\(583\) | 7.69913e14 | 0.473440 | ||||||||
\(584\) | −9.43320e14 | −0.574630 | ||||||||
\(585\) | −3.12387e14 | −0.188510 | ||||||||
\(586\) | −1.32126e15 | −0.789864 | ||||||||
\(587\) | 2.14190e15 | 1.26850 | 0.634248 | − | 0.773130i | \(-0.281310\pi\) | ||||
0.634248 | + | 0.773130i | \(0.281310\pi\) | |||||||
\(588\) | 6.26404e14 | 0.367518 | ||||||||
\(589\) | −8.08602e13 | −0.0470003 | ||||||||
\(590\) | 5.06852e14 | 0.291874 | ||||||||
\(591\) | −9.82193e13 | −0.0560358 | ||||||||
\(592\) | −9.11699e13 | −0.0515326 | ||||||||
\(593\) | −2.99983e15 | −1.67995 | −0.839974 | − | 0.542627i | \(-0.817430\pi\) | ||||
−0.839974 | + | 0.542627i | \(0.817430\pi\) | |||||||
\(594\) | 2.38473e15 | 1.32316 | ||||||||
\(595\) | −9.15114e14 | −0.503074 | ||||||||
\(596\) | 3.53573e15 | 1.92586 | ||||||||
\(597\) | 7.30547e14 | 0.394266 | ||||||||
\(598\) | −2.44095e15 | −1.30528 | ||||||||
\(599\) | 1.17931e15 | 0.624855 | 0.312427 | − | 0.949942i | \(-0.398858\pi\) | ||||
0.312427 | + | 0.949942i | \(0.398858\pi\) | |||||||
\(600\) | 1.42517e15 | 0.748231 | ||||||||
\(601\) | 2.22042e15 | 1.15512 | 0.577558 | − | 0.816349i | \(-0.304006\pi\) | ||||
0.577558 | + | 0.816349i | \(0.304006\pi\) | |||||||
\(602\) | 2.02129e15 | 1.04195 | ||||||||
\(603\) | 6.07410e14 | 0.310268 | ||||||||
\(604\) | 2.76786e15 | 1.40101 | ||||||||
\(605\) | −2.88368e14 | −0.144641 | ||||||||
\(606\) | 2.43939e14 | 0.121250 | ||||||||
\(607\) | −9.57108e14 | −0.471437 | −0.235718 | − | 0.971821i | \(-0.575744\pi\) | ||||
−0.235718 | + | 0.971821i | \(0.575744\pi\) | |||||||
\(608\) | −2.81703e14 | −0.137506 | ||||||||
\(609\) | −2.10491e15 | −1.01821 | ||||||||
\(610\) | −8.70470e13 | −0.0417292 | ||||||||
\(611\) | −1.84851e15 | −0.878204 | ||||||||
\(612\) | −1.81596e15 | −0.855015 | ||||||||
\(613\) | 2.26404e15 | 1.05646 | 0.528229 | − | 0.849102i | \(-0.322856\pi\) | ||||
0.528229 | + | 0.849102i | \(0.322856\pi\) | |||||||
\(614\) | 3.13326e15 | 1.44901 | ||||||||
\(615\) | 1.80236e14 | 0.0826092 | ||||||||
\(616\) | 1.98632e15 | 0.902311 | ||||||||
\(617\) | −2.19161e15 | −0.986724 | −0.493362 | − | 0.869824i | \(-0.664232\pi\) | ||||
−0.493362 | + | 0.869824i | \(0.664232\pi\) | |||||||
\(618\) | 2.01712e15 | 0.900108 | ||||||||
\(619\) | −3.40666e15 | −1.50671 | −0.753355 | − | 0.657614i | \(-0.771566\pi\) | ||||
−0.753355 | + | 0.657614i | \(0.771566\pi\) | |||||||
\(620\) | 3.94009e14 | 0.172724 | ||||||||
\(621\) | −1.32880e15 | −0.577374 | ||||||||
\(622\) | 1.39238e15 | 0.599669 | ||||||||
\(623\) | 7.16261e14 | 0.305765 | ||||||||
\(624\) | 2.30586e14 | 0.0975704 | ||||||||
\(625\) | 1.64307e15 | 0.689151 | ||||||||
\(626\) | −1.45592e15 | −0.605313 | ||||||||
\(627\) | −2.10510e14 | −0.0867565 | ||||||||
\(628\) | −4.40746e15 | −1.80057 | ||||||||
\(629\) | −2.09562e15 | −0.848659 | ||||||||
\(630\) | −5.74652e14 | −0.230692 | ||||||||
\(631\) | −2.25820e15 | −0.898672 | −0.449336 | − | 0.893363i | \(-0.648339\pi\) | ||||
−0.449336 | + | 0.893363i | \(0.648339\pi\) | |||||||
\(632\) | 4.53618e14 | 0.178956 | ||||||||
\(633\) | 1.39748e15 | 0.546542 | ||||||||
\(634\) | 3.56620e15 | 1.38266 | ||||||||
\(635\) | 1.05101e15 | 0.403972 | ||||||||
\(636\) | 2.16251e15 | 0.824032 | ||||||||
\(637\) | 1.12732e15 | 0.425872 | ||||||||
\(638\) | −3.71723e15 | −1.39221 | ||||||||
\(639\) | −1.42047e15 | −0.527447 | ||||||||
\(640\) | 1.49203e15 | 0.549274 | ||||||||
\(641\) | −3.54602e15 | −1.29426 | −0.647130 | − | 0.762380i | \(-0.724031\pi\) | ||||
−0.647130 | + | 0.762380i | \(0.724031\pi\) | |||||||
\(642\) | −1.49148e15 | −0.539726 | ||||||||
\(643\) | 1.96644e15 | 0.705539 | 0.352770 | − | 0.935710i | \(-0.385240\pi\) | ||||
0.352770 | + | 0.935710i | \(0.385240\pi\) | |||||||
\(644\) | −2.79853e15 | −0.995539 | ||||||||
\(645\) | 4.12825e14 | 0.145609 | ||||||||
\(646\) | 9.31549e14 | 0.325782 | ||||||||
\(647\) | 5.18068e15 | 1.79644 | 0.898221 | − | 0.439544i | \(-0.144860\pi\) | ||||
0.898221 | + | 0.439544i | \(0.144860\pi\) | |||||||
\(648\) | 1.46666e15 | 0.504274 | ||||||||
\(649\) | −1.19827e15 | −0.408515 | ||||||||
\(650\) | 6.48512e15 | 2.19227 | ||||||||
\(651\) | −8.46321e14 | −0.283687 | ||||||||
\(652\) | −2.97249e15 | −0.988005 | ||||||||
\(653\) | −1.91238e14 | −0.0630305 | −0.0315153 | − | 0.999503i | \(-0.510033\pi\) | ||||
−0.0315153 | + | 0.999503i | \(0.510033\pi\) | |||||||
\(654\) | −5.49977e15 | −1.79749 | ||||||||
\(655\) | 1.56201e14 | 0.0506240 | ||||||||
\(656\) | 8.20326e13 | 0.0263642 | ||||||||
\(657\) | −6.45189e14 | −0.205626 | ||||||||
\(658\) | −3.40043e15 | −1.07471 | ||||||||
\(659\) | −4.48314e15 | −1.40512 | −0.702559 | − | 0.711625i | \(-0.747959\pi\) | ||||
−0.702559 | + | 0.711625i | \(0.747959\pi\) | |||||||
\(660\) | 1.02576e15 | 0.318826 | ||||||||
\(661\) | 5.33081e15 | 1.64318 | 0.821590 | − | 0.570079i | \(-0.193087\pi\) | ||||
0.821590 | + | 0.570079i | \(0.193087\pi\) | |||||||
\(662\) | −3.77141e15 | −1.15288 | ||||||||
\(663\) | 5.30022e15 | 1.60683 | ||||||||
\(664\) | −1.47022e15 | −0.442038 | ||||||||
\(665\) | 1.83723e14 | 0.0547827 | ||||||||
\(666\) | −1.31596e15 | −0.389164 | ||||||||
\(667\) | 2.07129e15 | 0.607504 | ||||||||
\(668\) | 1.39935e15 | 0.407058 | ||||||||
\(669\) | 1.27516e15 | 0.367892 | ||||||||
\(670\) | 1.51828e15 | 0.434452 | ||||||||
\(671\) | 2.05791e14 | 0.0584054 | ||||||||
\(672\) | −2.94843e15 | −0.829966 | ||||||||
\(673\) | −8.39608e13 | −0.0234419 | −0.0117210 | − | 0.999931i | \(-0.503731\pi\) | ||||
−0.0117210 | + | 0.999931i | \(0.503731\pi\) | |||||||
\(674\) | 2.99647e14 | 0.0829813 | ||||||||
\(675\) | 3.53036e15 | 0.969725 | ||||||||
\(676\) | 7.72915e15 | 2.10584 | ||||||||
\(677\) | −6.79837e15 | −1.83724 | −0.918622 | − | 0.395137i | \(-0.870697\pi\) | ||||
−0.918622 | + | 0.395137i | \(0.870697\pi\) | |||||||
\(678\) | 3.95947e15 | 1.06139 | ||||||||
\(679\) | 5.81382e15 | 1.54589 | ||||||||
\(680\) | −1.79522e15 | −0.473499 | ||||||||
\(681\) | 3.64900e15 | 0.954696 | ||||||||
\(682\) | −1.49459e15 | −0.387889 | ||||||||
\(683\) | 2.14600e15 | 0.552478 | 0.276239 | − | 0.961089i | \(-0.410912\pi\) | ||||
0.276239 | + | 0.961089i | \(0.410912\pi\) | |||||||
\(684\) | 3.64581e14 | 0.0931077 | ||||||||
\(685\) | 2.68746e12 | 0.000680837 0 | ||||||||
\(686\) | −5.26762e15 | −1.32383 | ||||||||
\(687\) | −2.39718e14 | −0.0597638 | ||||||||
\(688\) | 1.87893e14 | 0.0464702 | ||||||||
\(689\) | 3.89179e15 | 0.954869 | ||||||||
\(690\) | −9.17082e14 | −0.223223 | ||||||||
\(691\) | −4.37783e15 | −1.05713 | −0.528566 | − | 0.848892i | \(-0.677270\pi\) | ||||
−0.528566 | + | 0.848892i | \(0.677270\pi\) | |||||||
\(692\) | −3.44419e15 | −0.825094 | ||||||||
\(693\) | 1.35856e15 | 0.322883 | ||||||||
\(694\) | −6.72457e15 | −1.58558 | ||||||||
\(695\) | −7.91108e14 | −0.185063 | ||||||||
\(696\) | −4.12931e15 | −0.958355 | ||||||||
\(697\) | 1.88559e15 | 0.434177 | ||||||||
\(698\) | −3.52760e15 | −0.805887 | ||||||||
\(699\) | −4.61718e14 | −0.104653 | ||||||||
\(700\) | 7.43513e15 | 1.67205 | ||||||||
\(701\) | 6.04215e15 | 1.34816 | 0.674081 | − | 0.738657i | \(-0.264540\pi\) | ||||
0.674081 | + | 0.738657i | \(0.264540\pi\) | |||||||
\(702\) | 1.20544e16 | 2.66866 | ||||||||
\(703\) | 4.20726e14 | 0.0924156 | ||||||||
\(704\) | −5.48910e15 | −1.19633 | ||||||||
\(705\) | −6.94498e14 | −0.150186 | ||||||||
\(706\) | −9.43844e15 | −2.02523 | ||||||||
\(707\) | 5.03319e14 | 0.107161 | ||||||||
\(708\) | −3.36566e15 | −0.711030 | ||||||||
\(709\) | 3.12868e15 | 0.655853 | 0.327926 | − | 0.944703i | \(-0.393650\pi\) | ||||
0.327926 | + | 0.944703i | \(0.393650\pi\) | |||||||
\(710\) | −3.55062e15 | −0.738555 | ||||||||
\(711\) | 3.10255e14 | 0.0640377 | ||||||||
\(712\) | 1.40512e15 | 0.287789 | ||||||||
\(713\) | 8.32804e14 | 0.169258 | ||||||||
\(714\) | 9.75003e15 | 1.96637 | ||||||||
\(715\) | 1.84602e15 | 0.369448 | ||||||||
\(716\) | −6.85597e14 | −0.136159 | ||||||||
\(717\) | 1.09057e15 | 0.214930 | ||||||||
\(718\) | −1.01352e16 | −1.98221 | ||||||||
\(719\) | −4.67906e15 | −0.908133 | −0.454067 | − | 0.890968i | \(-0.650027\pi\) | ||||
−0.454067 | + | 0.890968i | \(0.650027\pi\) | |||||||
\(720\) | −5.34178e13 | −0.0102886 | ||||||||
\(721\) | 4.16192e15 | 0.795518 | ||||||||
\(722\) | 8.40163e15 | 1.59371 | ||||||||
\(723\) | −3.68661e15 | −0.694011 | ||||||||
\(724\) | 1.21377e16 | 2.26764 | ||||||||
\(725\) | −5.50300e15 | −1.02033 | ||||||||
\(726\) | 3.07240e15 | 0.565362 | ||||||||
\(727\) | 6.26366e14 | 0.114390 | 0.0571951 | − | 0.998363i | \(-0.481784\pi\) | ||||
0.0571951 | + | 0.998363i | \(0.481784\pi\) | |||||||
\(728\) | 1.00406e16 | 1.81985 | ||||||||
\(729\) | 5.75346e15 | 1.03497 | ||||||||
\(730\) | −1.61272e15 | −0.287927 | ||||||||
\(731\) | 4.31888e15 | 0.765290 | ||||||||
\(732\) | 5.78021e14 | 0.101656 | ||||||||
\(733\) | −1.75098e15 | −0.305639 | −0.152820 | − | 0.988254i | \(-0.548835\pi\) | ||||
−0.152820 | + | 0.988254i | \(0.548835\pi\) | |||||||
\(734\) | −1.25433e16 | −2.17311 | ||||||||
\(735\) | 4.23540e14 | 0.0728306 | ||||||||
\(736\) | 2.90134e15 | 0.495189 | ||||||||
\(737\) | −3.58944e15 | −0.608072 | ||||||||
\(738\) | 1.18407e15 | 0.199098 | ||||||||
\(739\) | 8.05370e14 | 0.134416 | 0.0672080 | − | 0.997739i | \(-0.478591\pi\) | ||||
0.0672080 | + | 0.997739i | \(0.478591\pi\) | |||||||
\(740\) | −2.05008e15 | −0.339623 | ||||||||
\(741\) | −1.06410e15 | −0.174977 | ||||||||
\(742\) | 7.15916e15 | 1.16853 | ||||||||
\(743\) | 7.19998e15 | 1.16652 | 0.583261 | − | 0.812285i | \(-0.301777\pi\) | ||||
0.583261 | + | 0.812285i | \(0.301777\pi\) | |||||||
\(744\) | −1.66027e15 | −0.267010 | ||||||||
\(745\) | 2.39067e15 | 0.381646 | ||||||||
\(746\) | −1.04882e16 | −1.66203 | ||||||||
\(747\) | −1.00557e15 | −0.158179 | ||||||||
\(748\) | 1.07313e16 | 1.67568 | ||||||||
\(749\) | −3.07736e15 | −0.477011 | ||||||||
\(750\) | 5.16636e15 | 0.794965 | ||||||||
\(751\) | −7.94398e15 | −1.21344 | −0.606720 | − | 0.794915i | \(-0.707515\pi\) | ||||
−0.606720 | + | 0.794915i | \(0.707515\pi\) | |||||||
\(752\) | −3.16094e14 | −0.0479311 | ||||||||
\(753\) | 7.20219e15 | 1.08416 | ||||||||
\(754\) | −1.87900e16 | −2.80792 | ||||||||
\(755\) | 1.87148e15 | 0.277636 | ||||||||
\(756\) | 1.38203e16 | 2.03539 | ||||||||
\(757\) | 1.80773e15 | 0.264305 | 0.132153 | − | 0.991229i | \(-0.457811\pi\) | ||||
0.132153 | + | 0.991229i | \(0.457811\pi\) | |||||||
\(758\) | −3.23047e15 | −0.468905 | ||||||||
\(759\) | 2.16811e15 | 0.312429 | ||||||||
\(760\) | 3.60418e14 | 0.0515622 | ||||||||
\(761\) | −9.95318e15 | −1.41366 | −0.706832 | − | 0.707382i | \(-0.749876\pi\) | ||||
−0.706832 | + | 0.707382i | \(0.749876\pi\) | |||||||
\(762\) | −1.11979e16 | −1.57901 | ||||||||
\(763\) | −1.13477e16 | −1.58863 | ||||||||
\(764\) | −4.54200e15 | −0.631297 | ||||||||
\(765\) | −1.22785e15 | −0.169437 | ||||||||
\(766\) | −1.38724e16 | −1.90062 | ||||||||
\(767\) | −6.05706e15 | −0.823925 | ||||||||
\(768\) | −6.57678e15 | −0.888233 | ||||||||
\(769\) | −1.61413e15 | −0.216443 | −0.108221 | − | 0.994127i | \(-0.534516\pi\) | ||||
−0.108221 | + | 0.994127i | \(0.534516\pi\) | |||||||
\(770\) | 3.39585e15 | 0.452116 | ||||||||
\(771\) | 5.33395e15 | 0.705099 | ||||||||
\(772\) | −3.67246e11 | −4.82017e−5 0 | ||||||||
\(773\) | 9.02775e15 | 1.17650 | 0.588251 | − | 0.808679i | \(-0.299817\pi\) | ||||
0.588251 | + | 0.808679i | \(0.299817\pi\) | |||||||
\(774\) | 2.71207e15 | 0.350934 | ||||||||
\(775\) | −2.21259e15 | −0.284277 | ||||||||
\(776\) | 1.14052e16 | 1.45501 | ||||||||
\(777\) | 4.40352e15 | 0.557807 | ||||||||
\(778\) | −9.15875e15 | −1.15199 | ||||||||
\(779\) | −3.78560e14 | −0.0472801 | ||||||||
\(780\) | 5.18505e15 | 0.643032 | ||||||||
\(781\) | 8.39417e15 | 1.03371 | ||||||||
\(782\) | −9.59431e15 | −1.17321 | ||||||||
\(783\) | −1.02289e16 | −1.24205 | ||||||||
\(784\) | 1.92770e14 | 0.0232435 | ||||||||
\(785\) | −2.98008e15 | −0.356817 | ||||||||
\(786\) | −1.66423e15 | −0.197875 | ||||||||
\(787\) | 1.46678e16 | 1.73182 | 0.865909 | − | 0.500201i | \(-0.166740\pi\) | ||||
0.865909 | + | 0.500201i | \(0.166740\pi\) | |||||||
\(788\) | −1.00522e15 | −0.117860 | ||||||||
\(789\) | −1.81224e15 | −0.211005 | ||||||||
\(790\) | 7.75513e14 | 0.0896685 | ||||||||
\(791\) | 8.16958e15 | 0.938056 | ||||||||
\(792\) | 2.66515e15 | 0.303902 | ||||||||
\(793\) | 1.04024e15 | 0.117797 | ||||||||
\(794\) | −2.46121e16 | −2.76781 | ||||||||
\(795\) | 1.46217e15 | 0.163297 | ||||||||
\(796\) | 7.47675e15 | 0.829260 | ||||||||
\(797\) | −1.53657e16 | −1.69252 | −0.846258 | − | 0.532773i | \(-0.821150\pi\) | ||||
−0.846258 | + | 0.532773i | \(0.821150\pi\) | |||||||
\(798\) | −1.95746e15 | −0.214130 | ||||||||
\(799\) | −7.26568e15 | −0.789349 | ||||||||
\(800\) | −7.70828e15 | −0.831692 | ||||||||
\(801\) | 9.61043e14 | 0.102983 | ||||||||
\(802\) | −1.19064e16 | −1.26713 | ||||||||
\(803\) | 3.81269e15 | 0.402991 | ||||||||
\(804\) | −1.00819e16 | −1.05836 | ||||||||
\(805\) | −1.89222e15 | −0.197285 | ||||||||
\(806\) | −7.55490e15 | −0.782323 | ||||||||
\(807\) | −6.55611e14 | −0.0674282 | ||||||||
\(808\) | 9.87385e14 | 0.100861 | ||||||||
\(809\) | 2.05032e15 | 0.208020 | 0.104010 | − | 0.994576i | \(-0.466833\pi\) | ||||
0.104010 | + | 0.994576i | \(0.466833\pi\) | |||||||
\(810\) | 2.50743e15 | 0.252674 | ||||||||
\(811\) | −1.78243e16 | −1.78401 | −0.892005 | − | 0.452025i | \(-0.850702\pi\) | ||||
−0.892005 | + | 0.452025i | \(0.850702\pi\) | |||||||
\(812\) | −2.15426e16 | −2.14161 | ||||||||
\(813\) | 2.15225e15 | 0.212518 | ||||||||
\(814\) | 7.77653e15 | 0.762696 | ||||||||
\(815\) | −2.00984e15 | −0.195792 | ||||||||
\(816\) | 9.06332e14 | 0.0876984 | ||||||||
\(817\) | −8.67080e14 | −0.0833370 | ||||||||
\(818\) | −2.29575e16 | −2.19170 | ||||||||
\(819\) | 6.86730e15 | 0.651215 | ||||||||
\(820\) | 1.84462e15 | 0.173752 | ||||||||
\(821\) | −9.30037e15 | −0.870188 | −0.435094 | − | 0.900385i | \(-0.643285\pi\) | ||||
−0.435094 | + | 0.900385i | \(0.643285\pi\) | |||||||
\(822\) | −2.86333e13 | −0.00266120 | ||||||||
\(823\) | −7.97756e15 | −0.736497 | −0.368249 | − | 0.929727i | \(-0.620042\pi\) | ||||
−0.368249 | + | 0.929727i | \(0.620042\pi\) | |||||||
\(824\) | 8.16464e15 | 0.748751 | ||||||||
\(825\) | −5.76023e15 | −0.524739 | ||||||||
\(826\) | −1.11423e16 | −1.00829 | ||||||||
\(827\) | −2.22714e15 | −0.200201 | −0.100101 | − | 0.994977i | \(-0.531916\pi\) | ||||
−0.100101 | + | 0.994977i | \(0.531916\pi\) | |||||||
\(828\) | −3.75493e15 | −0.335301 | ||||||||
\(829\) | −1.30117e16 | −1.15421 | −0.577106 | − | 0.816669i | \(-0.695818\pi\) | ||||
−0.577106 | + | 0.816669i | \(0.695818\pi\) | |||||||
\(830\) | −2.51352e15 | −0.221489 | ||||||||
\(831\) | −7.81819e15 | −0.684385 | ||||||||
\(832\) | −2.77465e16 | −2.41285 | ||||||||
\(833\) | 4.43098e15 | 0.382783 | ||||||||
\(834\) | 8.42882e15 | 0.723358 | ||||||||
\(835\) | 9.46166e14 | 0.0806662 | ||||||||
\(836\) | −2.15446e15 | −0.182475 | ||||||||
\(837\) | −4.11273e15 | −0.346051 | ||||||||
\(838\) | −2.38795e16 | −1.99610 | ||||||||
\(839\) | −6.51934e15 | −0.541394 | −0.270697 | − | 0.962665i | \(-0.587254\pi\) | ||||
−0.270697 | + | 0.962665i | \(0.587254\pi\) | |||||||
\(840\) | 3.77230e15 | 0.311222 | ||||||||
\(841\) | 3.74394e15 | 0.306868 | ||||||||
\(842\) | −2.00987e16 | −1.63663 | ||||||||
\(843\) | −1.18841e16 | −0.961422 | ||||||||
\(844\) | 1.43024e16 | 1.14954 | ||||||||
\(845\) | 5.22603e15 | 0.417311 | ||||||||
\(846\) | −4.56253e15 | −0.361967 | ||||||||
\(847\) | 6.33929e15 | 0.499668 | ||||||||
\(848\) | 6.65493e14 | 0.0521154 | ||||||||
\(849\) | 1.72827e16 | 1.34468 | ||||||||
\(850\) | 2.54901e16 | 1.97046 | ||||||||
\(851\) | −4.33319e15 | −0.332809 | ||||||||
\(852\) | 2.35773e16 | 1.79919 | ||||||||
\(853\) | −2.49420e16 | −1.89108 | −0.945542 | − | 0.325500i | \(-0.894467\pi\) | ||||
−0.945542 | + | 0.325500i | \(0.894467\pi\) | |||||||
\(854\) | 1.91358e15 | 0.144155 | ||||||||
\(855\) | 2.46510e14 | 0.0184510 | ||||||||
\(856\) | −6.03701e15 | −0.448969 | ||||||||
\(857\) | 1.18643e16 | 0.876692 | 0.438346 | − | 0.898806i | \(-0.355564\pi\) | ||||
0.438346 | + | 0.898806i | \(0.355564\pi\) | |||||||
\(858\) | −1.96683e16 | −1.44407 | ||||||||
\(859\) | −3.39126e15 | −0.247399 | −0.123700 | − | 0.992320i | \(-0.539476\pi\) | ||||
−0.123700 | + | 0.992320i | \(0.539476\pi\) | |||||||
\(860\) | 4.22504e15 | 0.306259 | ||||||||
\(861\) | −3.96219e15 | −0.285376 | ||||||||
\(862\) | 2.51446e16 | 1.79951 | ||||||||
\(863\) | 5.01659e14 | 0.0356738 | 0.0178369 | − | 0.999841i | \(-0.494322\pi\) | ||||
0.0178369 | + | 0.999841i | \(0.494322\pi\) | |||||||
\(864\) | −1.43280e16 | −1.01242 | ||||||||
\(865\) | −2.32877e15 | −0.163508 | ||||||||
\(866\) | −1.48219e16 | −1.03408 | ||||||||
\(867\) | 9.48784e15 | 0.657752 | ||||||||
\(868\) | −8.66164e15 | −0.596680 | ||||||||
\(869\) | −1.83342e15 | −0.125503 | ||||||||
\(870\) | −7.05953e15 | −0.480198 | ||||||||
\(871\) | −1.81440e16 | −1.22641 | ||||||||
\(872\) | −2.22613e16 | −1.49524 | ||||||||
\(873\) | 7.80069e15 | 0.520660 | ||||||||
\(874\) | 1.92620e15 | 0.127758 | ||||||||
\(875\) | 1.06598e16 | 0.702592 | ||||||||
\(876\) | 1.07090e16 | 0.701415 | ||||||||
\(877\) | 2.06847e16 | 1.34633 | 0.673164 | − | 0.739493i | \(-0.264935\pi\) | ||||
0.673164 | + | 0.739493i | \(0.264935\pi\) | |||||||
\(878\) | 2.92396e16 | 1.89126 | ||||||||
\(879\) | 5.93225e15 | 0.381312 | ||||||||
\(880\) | 3.15668e14 | 0.0201639 | ||||||||
\(881\) | 1.42453e16 | 0.904280 | 0.452140 | − | 0.891947i | \(-0.350661\pi\) | ||||
0.452140 | + | 0.891947i | \(0.350661\pi\) | |||||||
\(882\) | 2.78246e15 | 0.175530 | ||||||||
\(883\) | −7.17959e14 | −0.0450107 | −0.0225054 | − | 0.999747i | \(-0.507164\pi\) | ||||
−0.0225054 | + | 0.999747i | \(0.507164\pi\) | |||||||
\(884\) | 5.42449e16 | 3.37965 | ||||||||
\(885\) | −2.27568e15 | −0.140904 | ||||||||
\(886\) | −2.46847e16 | −1.51895 | ||||||||
\(887\) | 1.71047e16 | 1.04601 | 0.523005 | − | 0.852329i | \(-0.324811\pi\) | ||||
0.523005 | + | 0.852329i | \(0.324811\pi\) | |||||||
\(888\) | 8.63860e15 | 0.525015 | ||||||||
\(889\) | −2.31047e16 | −1.39553 | ||||||||
\(890\) | 2.40222e15 | 0.144201 | ||||||||
\(891\) | −5.92791e15 | −0.353651 | ||||||||
\(892\) | 1.30506e16 | 0.773789 | ||||||||
\(893\) | 1.45869e15 | 0.0859569 | ||||||||
\(894\) | −2.54713e16 | −1.49174 | ||||||||
\(895\) | −4.63563e14 | −0.0269825 | ||||||||
\(896\) | −3.27999e16 | −1.89749 | ||||||||
\(897\) | 1.09595e16 | 0.630131 | ||||||||
\(898\) | −4.51471e15 | −0.257994 | ||||||||
\(899\) | 6.41078e15 | 0.364110 | ||||||||
\(900\) | 9.97609e15 | 0.563153 | ||||||||
\(901\) | 1.52969e16 | 0.858257 | ||||||||
\(902\) | −6.99714e15 | −0.390198 | ||||||||
\(903\) | −9.07527e15 | −0.503010 | ||||||||
\(904\) | 1.60267e16 | 0.882910 | ||||||||
\(905\) | 8.20683e15 | 0.449375 | ||||||||
\(906\) | −1.99396e16 | −1.08520 | ||||||||
\(907\) | −1.89857e16 | −1.02704 | −0.513519 | − | 0.858078i | \(-0.671658\pi\) | ||||
−0.513519 | + | 0.858078i | \(0.671658\pi\) | |||||||
\(908\) | 3.73455e16 | 2.00801 | ||||||||
\(909\) | 6.75328e14 | 0.0360922 | ||||||||
\(910\) | 1.71655e16 | 0.911862 | ||||||||
\(911\) | −3.33554e16 | −1.76123 | −0.880613 | − | 0.473836i | \(-0.842869\pi\) | ||||
−0.880613 | + | 0.473836i | \(0.842869\pi\) | |||||||
\(912\) | −1.81960e14 | −0.00955000 | ||||||||
\(913\) | 5.94232e15 | 0.310004 | ||||||||
\(914\) | 3.79512e16 | 1.96798 | ||||||||
\(915\) | 3.90826e14 | 0.0201450 | ||||||||
\(916\) | −2.45338e15 | −0.125701 | ||||||||
\(917\) | −3.43381e15 | −0.174882 | ||||||||
\(918\) | 4.73807e16 | 2.39865 | ||||||||
\(919\) | −1.26006e15 | −0.0634098 | −0.0317049 | − | 0.999497i | \(-0.510094\pi\) | ||||
−0.0317049 | + | 0.999497i | \(0.510094\pi\) | |||||||
\(920\) | −3.71205e15 | −0.185687 | ||||||||
\(921\) | −1.40678e16 | −0.699516 | ||||||||
\(922\) | −2.11685e16 | −1.04633 | ||||||||
\(923\) | 4.24312e16 | 2.08486 | ||||||||
\(924\) | −2.25496e16 | −1.10139 | ||||||||
\(925\) | 1.15124e16 | 0.558967 | ||||||||
\(926\) | 1.27010e16 | 0.613024 | ||||||||
\(927\) | 5.58426e15 | 0.267933 | ||||||||
\(928\) | 2.23340e16 | 1.06525 | ||||||||
\(929\) | 2.58888e16 | 1.22751 | 0.613756 | − | 0.789496i | \(-0.289658\pi\) | ||||
0.613756 | + | 0.789496i | \(0.289658\pi\) | |||||||
\(930\) | −2.83842e15 | −0.133789 | ||||||||
\(931\) | −8.89585e14 | −0.0416835 | ||||||||
\(932\) | −4.72543e15 | −0.220117 | ||||||||
\(933\) | −6.25157e15 | −0.289494 | ||||||||
\(934\) | 4.42474e16 | 2.03695 | ||||||||
\(935\) | 7.25589e15 | 0.332068 | ||||||||
\(936\) | 1.34719e16 | 0.612932 | ||||||||
\(937\) | −1.04329e16 | −0.471887 | −0.235943 | − | 0.971767i | \(-0.575818\pi\) | ||||
−0.235943 | + | 0.971767i | \(0.575818\pi\) | |||||||
\(938\) | −3.33769e16 | −1.50083 | ||||||||
\(939\) | 6.53685e15 | 0.292218 | ||||||||
\(940\) | −7.10780e15 | −0.315887 | ||||||||
\(941\) | 2.54394e16 | 1.12400 | 0.561998 | − | 0.827139i | \(-0.310033\pi\) | ||||
0.561998 | + | 0.827139i | \(0.310033\pi\) | |||||||
\(942\) | 3.17511e16 | 1.39470 | ||||||||
\(943\) | 3.89890e15 | 0.170266 | ||||||||
\(944\) | −1.03575e15 | −0.0449686 | ||||||||
\(945\) | 9.34455e15 | 0.403351 | ||||||||
\(946\) | −1.60267e16 | −0.687771 | ||||||||
\(947\) | 1.28374e16 | 0.547712 | 0.273856 | − | 0.961771i | \(-0.411701\pi\) | ||||
0.273856 | + | 0.961771i | \(0.411701\pi\) | |||||||
\(948\) | −5.14966e15 | −0.218440 | ||||||||
\(949\) | 1.92725e16 | 0.812784 | ||||||||
\(950\) | −5.11752e15 | −0.214575 | ||||||||
\(951\) | −1.60116e16 | −0.667486 | ||||||||
\(952\) | 3.94650e16 | 1.63572 | ||||||||
\(953\) | 2.82424e16 | 1.16383 | 0.581917 | − | 0.813248i | \(-0.302303\pi\) | ||||
0.581917 | + | 0.813248i | \(0.302303\pi\) | |||||||
\(954\) | 9.60579e15 | 0.393566 | ||||||||
\(955\) | −3.07105e15 | −0.125103 | ||||||||
\(956\) | 1.11614e16 | 0.452062 | ||||||||
\(957\) | 1.66897e16 | 0.672100 | ||||||||
\(958\) | −3.56594e16 | −1.42779 | ||||||||
\(959\) | −5.90792e13 | −0.00235197 | ||||||||
\(960\) | −1.04245e16 | −0.412634 | ||||||||
\(961\) | −2.28309e16 | −0.898554 | ||||||||
\(962\) | 3.93091e16 | 1.53826 | ||||||||
\(963\) | −4.12905e15 | −0.160659 | ||||||||
\(964\) | −3.77304e16 | −1.45971 | ||||||||
\(965\) | −2.48312e11 | −9.55206e−6 0 | ||||||||
\(966\) | 2.01605e16 | 0.771129 | ||||||||
\(967\) | 1.74832e16 | 0.664929 | 0.332465 | − | 0.943116i | \(-0.392120\pi\) | ||||
0.332465 | + | 0.943116i | \(0.392120\pi\) | |||||||
\(968\) | 1.24361e16 | 0.470294 | ||||||||
\(969\) | −4.18250e15 | −0.157273 | ||||||||
\(970\) | 1.94986e16 | 0.729053 | ||||||||
\(971\) | 2.35331e15 | 0.0874931 | 0.0437466 | − | 0.999043i | \(-0.486071\pi\) | ||||
0.0437466 | + | 0.999043i | \(0.486071\pi\) | |||||||
\(972\) | 3.19669e16 | 1.18178 | ||||||||
\(973\) | 1.73912e16 | 0.639306 | ||||||||
\(974\) | −5.96553e16 | −2.18060 | ||||||||
\(975\) | −2.91171e16 | −1.05833 | ||||||||
\(976\) | 1.77881e14 | 0.00642916 | ||||||||
\(977\) | 1.83471e16 | 0.659397 | 0.329698 | − | 0.944086i | \(-0.393053\pi\) | ||||
0.329698 | + | 0.944086i | \(0.393053\pi\) | |||||||
\(978\) | 2.14137e16 | 0.765294 | ||||||||
\(979\) | −5.67920e15 | −0.201828 | ||||||||
\(980\) | 4.33470e15 | 0.153185 | ||||||||
\(981\) | −1.52258e16 | −0.535056 | ||||||||
\(982\) | 4.16542e16 | 1.45561 | ||||||||
\(983\) | 1.35715e16 | 0.471611 | 0.235805 | − | 0.971800i | \(-0.424227\pi\) | ||||
0.235805 | + | 0.971800i | \(0.424227\pi\) | |||||||
\(984\) | −7.77281e15 | −0.268599 | ||||||||
\(985\) | −6.79675e14 | −0.0233562 | ||||||||
\(986\) | −7.38553e16 | −2.52382 | ||||||||
\(987\) | 1.52674e16 | 0.518824 | ||||||||
\(988\) | −1.08905e16 | −0.368030 | ||||||||
\(989\) | 8.93032e15 | 0.300115 | ||||||||
\(990\) | 4.55638e15 | 0.152274 | ||||||||
\(991\) | 7.33626e15 | 0.243820 | 0.121910 | − | 0.992541i | \(-0.461098\pi\) | ||||
0.121910 | + | 0.992541i | \(0.461098\pi\) | |||||||
\(992\) | 8.97984e15 | 0.296793 | ||||||||
\(993\) | 1.69330e16 | 0.556560 | ||||||||
\(994\) | 7.80544e16 | 2.55136 | ||||||||
\(995\) | 5.05537e15 | 0.164333 | ||||||||
\(996\) | 1.66906e16 | 0.539568 | ||||||||
\(997\) | 2.93527e16 | 0.943679 | 0.471840 | − | 0.881684i | \(-0.343590\pi\) | ||||
0.471840 | + | 0.881684i | \(0.343590\pi\) | |||||||
\(998\) | −6.50039e16 | −2.07836 | ||||||||
\(999\) | 2.13991e16 | 0.680432 |
(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 | 197.12.a.b.1.11 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.12.a.b.1.11 | ✓ | 92 | 1.1 | even | 1 | trivial |