Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,88,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 88, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 88);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 88 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(95.8667262922\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2 x^{3} + \cdots + 13\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 17\cdot 29 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-4.15109e17\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.79609e12 | −0.707107 | ||||||||
\(3\) | 8.97819e20 | 1.57912 | 0.789558 | − | 0.613676i | \(-0.210310\pi\) | ||||
0.789558 | + | 0.613676i | \(0.210310\pi\) | |||||||
\(4\) | 7.73713e25 | 0.500000 | ||||||||
\(5\) | 3.21672e30 | 1.26537 | 0.632685 | − | 0.774409i | \(-0.281953\pi\) | ||||
0.632685 | + | 0.774409i | \(0.281953\pi\) | |||||||
\(6\) | −7.89730e33 | −1.11660 | ||||||||
\(7\) | 8.51076e36 | 1.47300 | 0.736502 | − | 0.676436i | \(-0.236476\pi\) | ||||
0.736502 | + | 0.676436i | \(0.236476\pi\) | |||||||
\(8\) | −6.80565e38 | −0.353553 | ||||||||
\(9\) | 4.82821e41 | 1.49361 | ||||||||
\(10\) | −2.82946e43 | −0.894752 | ||||||||
\(11\) | 1.44187e45 | 0.721679 | 0.360839 | − | 0.932628i | \(-0.382490\pi\) | ||||
0.360839 | + | 0.932628i | \(0.382490\pi\) | |||||||
\(12\) | 6.94654e46 | 0.789558 | ||||||||
\(13\) | 1.58019e48 | 0.552298 | 0.276149 | − | 0.961115i | \(-0.410942\pi\) | ||||
0.276149 | + | 0.961115i | \(0.410942\pi\) | |||||||
\(14\) | −7.48615e49 | −1.04157 | ||||||||
\(15\) | 2.88803e51 | 1.99817 | ||||||||
\(16\) | 5.98631e51 | 0.250000 | ||||||||
\(17\) | −6.18852e53 | −1.84952 | −0.924759 | − | 0.380554i | \(-0.875733\pi\) | ||||
−0.924759 | + | 0.380554i | \(0.875733\pi\) | |||||||
\(18\) | −4.24694e54 | −1.05614 | ||||||||
\(19\) | 6.29366e55 | 1.48978 | 0.744889 | − | 0.667189i | \(-0.232502\pi\) | ||||
0.744889 | + | 0.667189i | \(0.232502\pi\) | |||||||
\(20\) | 2.48882e56 | 0.632685 | ||||||||
\(21\) | 7.64113e57 | 2.32604 | ||||||||
\(22\) | −1.26828e58 | −0.510304 | ||||||||
\(23\) | 2.79664e58 | 0.162733 | 0.0813666 | − | 0.996684i | \(-0.474072\pi\) | ||||
0.0813666 | + | 0.996684i | \(0.474072\pi\) | |||||||
\(24\) | −6.11024e59 | −0.558302 | ||||||||
\(25\) | 3.88493e60 | 0.601164 | ||||||||
\(26\) | −1.38995e61 | −0.390534 | ||||||||
\(27\) | 1.43259e62 | 0.779466 | ||||||||
\(28\) | 6.58489e62 | 0.736502 | ||||||||
\(29\) | 3.72251e63 | 0.904739 | 0.452369 | − | 0.891831i | \(-0.350579\pi\) | ||||
0.452369 | + | 0.891831i | \(0.350579\pi\) | |||||||
\(30\) | −2.54034e64 | −1.41292 | ||||||||
\(31\) | 9.26519e64 | 1.23771 | 0.618857 | − | 0.785503i | \(-0.287596\pi\) | ||||
0.618857 | + | 0.785503i | \(0.287596\pi\) | |||||||
\(32\) | −5.26561e64 | −0.176777 | ||||||||
\(33\) | 1.29454e66 | 1.13962 | ||||||||
\(34\) | 5.44348e66 | 1.30781 | ||||||||
\(35\) | 2.73767e67 | 1.86390 | ||||||||
\(36\) | 3.73565e67 | 0.746804 | ||||||||
\(37\) | 5.17665e67 | 0.314249 | 0.157124 | − | 0.987579i | \(-0.449778\pi\) | ||||
0.157124 | + | 0.987579i | \(0.449778\pi\) | |||||||
\(38\) | −5.53596e68 | −1.05343 | ||||||||
\(39\) | 1.41872e69 | 0.872143 | ||||||||
\(40\) | −2.18919e69 | −0.447376 | ||||||||
\(41\) | −6.26732e69 | −0.437506 | −0.218753 | − | 0.975780i | \(-0.570199\pi\) | ||||
−0.218753 | + | 0.975780i | \(0.570199\pi\) | |||||||
\(42\) | −6.72121e70 | −1.64476 | ||||||||
\(43\) | −1.26820e71 | −1.11509 | −0.557546 | − | 0.830146i | \(-0.688257\pi\) | ||||
−0.557546 | + | 0.830146i | \(0.688257\pi\) | |||||||
\(44\) | 1.11559e71 | 0.360839 | ||||||||
\(45\) | 1.55310e72 | 1.88997 | ||||||||
\(46\) | −2.45995e71 | −0.115070 | ||||||||
\(47\) | −8.18255e72 | −1.50187 | −0.750934 | − | 0.660378i | \(-0.770396\pi\) | ||||
−0.750934 | + | 0.660378i | \(0.770396\pi\) | |||||||
\(48\) | 5.37462e72 | 0.394779 | ||||||||
\(49\) | 3.90498e73 | 1.16974 | ||||||||
\(50\) | −3.41722e73 | −0.425087 | ||||||||
\(51\) | −5.55617e74 | −2.92060 | ||||||||
\(52\) | 1.22261e74 | 0.276149 | ||||||||
\(53\) | −1.68903e75 | −1.66585 | −0.832925 | − | 0.553385i | \(-0.813336\pi\) | ||||
−0.832925 | + | 0.553385i | \(0.813336\pi\) | |||||||
\(54\) | −1.26012e75 | −0.551166 | ||||||||
\(55\) | 4.63809e75 | 0.913192 | ||||||||
\(56\) | −5.79213e75 | −0.520785 | ||||||||
\(57\) | 5.65056e76 | 2.35253 | ||||||||
\(58\) | −3.27436e76 | −0.639747 | ||||||||
\(59\) | −1.48693e77 | −1.38111 | −0.690554 | − | 0.723281i | \(-0.742633\pi\) | ||||
−0.690554 | + | 0.723281i | \(0.742633\pi\) | |||||||
\(60\) | 2.23451e77 | 0.999084 | ||||||||
\(61\) | −3.28414e77 | −0.715442 | −0.357721 | − | 0.933829i | \(-0.616446\pi\) | ||||
−0.357721 | + | 0.933829i | \(0.616446\pi\) | |||||||
\(62\) | −8.14974e77 | −0.875196 | ||||||||
\(63\) | 4.10918e78 | 2.20009 | ||||||||
\(64\) | 4.63168e77 | 0.125000 | ||||||||
\(65\) | 5.08302e78 | 0.698862 | ||||||||
\(66\) | −1.13869e79 | −0.805830 | ||||||||
\(67\) | 3.12202e79 | 1.14863 | 0.574317 | − | 0.818633i | \(-0.305268\pi\) | ||||
0.574317 | + | 0.818633i | \(0.305268\pi\) | |||||||
\(68\) | −4.78813e79 | −0.924759 | ||||||||
\(69\) | 2.51088e79 | 0.256975 | ||||||||
\(70\) | −2.40808e80 | −1.31797 | ||||||||
\(71\) | −2.96376e80 | −0.875194 | −0.437597 | − | 0.899171i | \(-0.644170\pi\) | ||||
−0.437597 | + | 0.899171i | \(0.644170\pi\) | |||||||
\(72\) | −3.28591e80 | −0.528071 | ||||||||
\(73\) | 9.74503e80 | 0.859486 | 0.429743 | − | 0.902951i | \(-0.358604\pi\) | ||||
0.429743 | + | 0.902951i | \(0.358604\pi\) | |||||||
\(74\) | −4.55343e80 | −0.222208 | ||||||||
\(75\) | 3.48796e81 | 0.949307 | ||||||||
\(76\) | 4.86948e81 | 0.744889 | ||||||||
\(77\) | 1.22714e82 | 1.06304 | ||||||||
\(78\) | −1.24792e82 | −0.616698 | ||||||||
\(79\) | −4.07789e82 | −1.15786 | −0.578931 | − | 0.815376i | \(-0.696530\pi\) | ||||
−0.578931 | + | 0.815376i | \(0.696530\pi\) | |||||||
\(80\) | 1.92563e82 | 0.316343 | ||||||||
\(81\) | −2.74553e82 | −0.262741 | ||||||||
\(82\) | 5.51279e82 | 0.309364 | ||||||||
\(83\) | 4.93307e82 | 0.163388 | 0.0816940 | − | 0.996657i | \(-0.473967\pi\) | ||||
0.0816940 | + | 0.996657i | \(0.473967\pi\) | |||||||
\(84\) | 5.91203e83 | 1.16302 | ||||||||
\(85\) | −1.99067e84 | −2.34033 | ||||||||
\(86\) | 1.11552e84 | 0.788490 | ||||||||
\(87\) | 3.34214e84 | 1.42869 | ||||||||
\(88\) | −9.81285e83 | −0.255152 | ||||||||
\(89\) | −4.22584e83 | −0.0672122 | −0.0336061 | − | 0.999435i | \(-0.510699\pi\) | ||||
−0.0336061 | + | 0.999435i | \(0.510699\pi\) | |||||||
\(90\) | −1.36612e85 | −1.33641 | ||||||||
\(91\) | 1.34486e85 | 0.813537 | ||||||||
\(92\) | 2.16380e84 | 0.0813666 | ||||||||
\(93\) | 8.31846e85 | 1.95450 | ||||||||
\(94\) | 7.19744e85 | 1.06198 | ||||||||
\(95\) | 2.02449e86 | 1.88512 | ||||||||
\(96\) | −4.72757e85 | −0.279151 | ||||||||
\(97\) | −3.85645e86 | −1.45083 | −0.725415 | − | 0.688311i | \(-0.758352\pi\) | ||||
−0.725415 | + | 0.688311i | \(0.758352\pi\) | |||||||
\(98\) | −3.43486e86 | −0.827131 | ||||||||
\(99\) | 6.96165e86 | 1.07791 | ||||||||
\(100\) | 3.00582e86 | 0.300582 | ||||||||
\(101\) | 1.18103e87 | 0.766089 | 0.383045 | − | 0.923730i | \(-0.374876\pi\) | ||||
0.383045 | + | 0.923730i | \(0.374876\pi\) | |||||||
\(102\) | 4.88726e87 | 2.06518 | ||||||||
\(103\) | 2.80000e86 | 0.0773997 | 0.0386999 | − | 0.999251i | \(-0.487678\pi\) | ||||
0.0386999 | + | 0.999251i | \(0.487678\pi\) | |||||||
\(104\) | −1.07542e87 | −0.195267 | ||||||||
\(105\) | 2.45793e88 | 2.94331 | ||||||||
\(106\) | 1.48568e88 | 1.17793 | ||||||||
\(107\) | −9.61882e87 | −0.506906 | −0.253453 | − | 0.967348i | \(-0.581566\pi\) | ||||
−0.253453 | + | 0.967348i | \(0.581566\pi\) | |||||||
\(108\) | 1.10841e88 | 0.389733 | ||||||||
\(109\) | 2.67965e88 | 0.630995 | 0.315498 | − | 0.948926i | \(-0.397829\pi\) | ||||
0.315498 | + | 0.948926i | \(0.397829\pi\) | |||||||
\(110\) | −4.07970e88 | −0.645724 | ||||||||
\(111\) | 4.64769e88 | 0.496236 | ||||||||
\(112\) | 5.09481e88 | 0.368251 | ||||||||
\(113\) | 3.15948e89 | 1.55132 | 0.775662 | − | 0.631148i | \(-0.217416\pi\) | ||||
0.775662 | + | 0.631148i | \(0.217416\pi\) | |||||||
\(114\) | −4.97029e89 | −1.66349 | ||||||||
\(115\) | 8.99601e88 | 0.205918 | ||||||||
\(116\) | 2.88015e89 | 0.452369 | ||||||||
\(117\) | 7.62949e89 | 0.824917 | ||||||||
\(118\) | 1.30792e90 | 0.976590 | ||||||||
\(119\) | −5.26690e90 | −2.72435 | ||||||||
\(120\) | −1.96549e90 | −0.706459 | ||||||||
\(121\) | −1.91277e90 | −0.479179 | ||||||||
\(122\) | 2.88876e90 | 0.505894 | ||||||||
\(123\) | −5.62692e90 | −0.690873 | ||||||||
\(124\) | 7.16859e90 | 0.618857 | ||||||||
\(125\) | −8.29083e90 | −0.504676 | ||||||||
\(126\) | −3.61447e91 | −1.55570 | ||||||||
\(127\) | −9.29957e89 | −0.0283793 | −0.0141896 | − | 0.999899i | \(-0.504517\pi\) | ||||
−0.0141896 | + | 0.999899i | \(0.504517\pi\) | |||||||
\(128\) | −4.07407e90 | −0.0883883 | ||||||||
\(129\) | −1.13862e92 | −1.76086 | ||||||||
\(130\) | −4.47108e91 | −0.494170 | ||||||||
\(131\) | −8.88835e91 | −0.703914 | −0.351957 | − | 0.936016i | \(-0.614484\pi\) | ||||
−0.351957 | + | 0.936016i | \(0.614484\pi\) | |||||||
\(132\) | 1.00160e92 | 0.569808 | ||||||||
\(133\) | 5.35638e92 | 2.19445 | ||||||||
\(134\) | −2.74616e92 | −0.812208 | ||||||||
\(135\) | 4.60823e92 | 0.986314 | ||||||||
\(136\) | 4.21169e92 | 0.653903 | ||||||||
\(137\) | 5.60345e92 | 0.632573 | 0.316287 | − | 0.948664i | \(-0.397564\pi\) | ||||
0.316287 | + | 0.948664i | \(0.397564\pi\) | |||||||
\(138\) | −2.20859e92 | −0.181708 | ||||||||
\(139\) | 1.14040e93 | 0.685349 | 0.342675 | − | 0.939454i | \(-0.388667\pi\) | ||||
0.342675 | + | 0.939454i | \(0.388667\pi\) | |||||||
\(140\) | 2.11817e93 | 0.931948 | ||||||||
\(141\) | −7.34644e93 | −2.37162 | ||||||||
\(142\) | 2.60695e93 | 0.618856 | ||||||||
\(143\) | 2.27843e93 | 0.398582 | ||||||||
\(144\) | 2.89032e93 | 0.373402 | ||||||||
\(145\) | 1.19743e94 | 1.14483 | ||||||||
\(146\) | −8.57182e93 | −0.607748 | ||||||||
\(147\) | 3.50596e94 | 1.84716 | ||||||||
\(148\) | 4.00524e93 | 0.157124 | ||||||||
\(149\) | 2.30398e93 | 0.0674336 | 0.0337168 | − | 0.999431i | \(-0.489266\pi\) | ||||
0.0337168 | + | 0.999431i | \(0.489266\pi\) | |||||||
\(150\) | −3.06804e94 | −0.671262 | ||||||||
\(151\) | −4.73426e94 | −0.775809 | −0.387905 | − | 0.921699i | \(-0.626801\pi\) | ||||
−0.387905 | + | 0.921699i | \(0.626801\pi\) | |||||||
\(152\) | −4.28324e94 | −0.526716 | ||||||||
\(153\) | −2.98795e95 | −2.76246 | ||||||||
\(154\) | −1.07940e95 | −0.751680 | ||||||||
\(155\) | 2.98035e95 | 1.56617 | ||||||||
\(156\) | 1.09768e95 | 0.436071 | ||||||||
\(157\) | −1.22210e95 | −0.367682 | −0.183841 | − | 0.982956i | \(-0.558853\pi\) | ||||
−0.183841 | + | 0.982956i | \(0.558853\pi\) | |||||||
\(158\) | 3.58695e95 | 0.818733 | ||||||||
\(159\) | −1.51644e96 | −2.63057 | ||||||||
\(160\) | −1.69380e95 | −0.223688 | ||||||||
\(161\) | 2.38016e95 | 0.239706 | ||||||||
\(162\) | 2.41500e95 | 0.185786 | ||||||||
\(163\) | 1.45175e96 | 0.854540 | 0.427270 | − | 0.904124i | \(-0.359475\pi\) | ||||
0.427270 | + | 0.904124i | \(0.359475\pi\) | |||||||
\(164\) | −4.84911e95 | −0.218753 | ||||||||
\(165\) | 4.16416e96 | 1.44204 | ||||||||
\(166\) | −4.33917e95 | −0.115533 | ||||||||
\(167\) | 4.06110e96 | 0.832677 | 0.416339 | − | 0.909210i | \(-0.363313\pi\) | ||||
0.416339 | + | 0.909210i | \(0.363313\pi\) | |||||||
\(168\) | −5.20028e96 | −0.822381 | ||||||||
\(169\) | −5.68900e96 | −0.694967 | ||||||||
\(170\) | 1.75101e97 | 1.65486 | ||||||||
\(171\) | 3.03871e97 | 2.22515 | ||||||||
\(172\) | −9.81225e96 | −0.557546 | ||||||||
\(173\) | −1.43454e97 | −0.633442 | −0.316721 | − | 0.948519i | \(-0.602582\pi\) | ||||
−0.316721 | + | 0.948519i | \(0.602582\pi\) | |||||||
\(174\) | −2.93978e97 | −1.01023 | ||||||||
\(175\) | 3.30637e97 | 0.885516 | ||||||||
\(176\) | 8.63148e96 | 0.180420 | ||||||||
\(177\) | −1.33499e98 | −2.18093 | ||||||||
\(178\) | 3.71709e96 | 0.0475262 | ||||||||
\(179\) | 1.14022e98 | 1.14257 | 0.571285 | − | 0.820752i | \(-0.306445\pi\) | ||||
0.571285 | + | 0.820752i | \(0.306445\pi\) | |||||||
\(180\) | 1.20165e98 | 0.944985 | ||||||||
\(181\) | −1.39959e97 | −0.0864937 | −0.0432468 | − | 0.999064i | \(-0.513770\pi\) | ||||
−0.0432468 | + | 0.999064i | \(0.513770\pi\) | |||||||
\(182\) | −1.18295e98 | −0.575257 | ||||||||
\(183\) | −2.94857e98 | −1.12977 | ||||||||
\(184\) | −1.90330e97 | −0.0575348 | ||||||||
\(185\) | 1.66518e98 | 0.397642 | ||||||||
\(186\) | −7.31699e98 | −1.38204 | ||||||||
\(187\) | −8.92303e98 | −1.33476 | ||||||||
\(188\) | −6.33094e98 | −0.750934 | ||||||||
\(189\) | 1.21924e99 | 1.14816 | ||||||||
\(190\) | −1.78076e99 | −1.33298 | ||||||||
\(191\) | 1.55587e99 | 0.926878 | 0.463439 | − | 0.886129i | \(-0.346615\pi\) | ||||
0.463439 | + | 0.886129i | \(0.346615\pi\) | |||||||
\(192\) | 4.15841e98 | 0.197390 | ||||||||
\(193\) | 3.82299e99 | 1.44764 | 0.723820 | − | 0.689989i | \(-0.242385\pi\) | ||||
0.723820 | + | 0.689989i | \(0.242385\pi\) | |||||||
\(194\) | 3.39217e99 | 1.02589 | ||||||||
\(195\) | 4.56364e99 | 1.10358 | ||||||||
\(196\) | 3.02133e99 | 0.584870 | ||||||||
\(197\) | 3.38893e99 | 0.525753 | 0.262877 | − | 0.964829i | \(-0.415329\pi\) | ||||
0.262877 | + | 0.964829i | \(0.415329\pi\) | |||||||
\(198\) | −6.12353e99 | −0.762195 | ||||||||
\(199\) | −1.68642e100 | −1.68600 | −0.843001 | − | 0.537912i | \(-0.819213\pi\) | ||||
−0.843001 | + | 0.537912i | \(0.819213\pi\) | |||||||
\(200\) | −2.64395e99 | −0.212543 | ||||||||
\(201\) | 2.80301e100 | 1.81383 | ||||||||
\(202\) | −1.03884e100 | −0.541707 | ||||||||
\(203\) | 3.16814e100 | 1.33268 | ||||||||
\(204\) | −4.29888e100 | −1.46030 | ||||||||
\(205\) | −2.01602e100 | −0.553608 | ||||||||
\(206\) | −2.46291e99 | −0.0547299 | ||||||||
\(207\) | 1.35028e100 | 0.243060 | ||||||||
\(208\) | 9.45950e99 | 0.138074 | ||||||||
\(209\) | 9.07463e100 | 1.07514 | ||||||||
\(210\) | −2.16202e101 | −2.08123 | ||||||||
\(211\) | 1.17061e101 | 0.916483 | 0.458242 | − | 0.888828i | \(-0.348479\pi\) | ||||
0.458242 | + | 0.888828i | \(0.348479\pi\) | |||||||
\(212\) | −1.30682e101 | −0.832925 | ||||||||
\(213\) | −2.66092e101 | −1.38203 | ||||||||
\(214\) | 8.46081e100 | 0.358437 | ||||||||
\(215\) | −4.07945e101 | −1.41101 | ||||||||
\(216\) | −9.74968e100 | −0.275583 | ||||||||
\(217\) | 7.88538e101 | 1.82316 | ||||||||
\(218\) | −2.35705e101 | −0.446181 | ||||||||
\(219\) | 8.74927e101 | 1.35723 | ||||||||
\(220\) | 3.58855e101 | 0.456596 | ||||||||
\(221\) | −9.77903e101 | −1.02148 | ||||||||
\(222\) | −4.08816e101 | −0.350892 | ||||||||
\(223\) | 1.83791e102 | 1.29736 | 0.648682 | − | 0.761059i | \(-0.275320\pi\) | ||||
0.648682 | + | 0.761059i | \(0.275320\pi\) | |||||||
\(224\) | −4.48144e101 | −0.260393 | ||||||||
\(225\) | 1.87572e102 | 0.897903 | ||||||||
\(226\) | −2.77910e102 | −1.09695 | ||||||||
\(227\) | −5.10224e101 | −0.166202 | −0.0831009 | − | 0.996541i | \(-0.526482\pi\) | ||||
−0.0831009 | + | 0.996541i | \(0.526482\pi\) | |||||||
\(228\) | 4.37191e102 | 1.17627 | ||||||||
\(229\) | 3.57118e102 | 0.794270 | 0.397135 | − | 0.917760i | \(-0.370005\pi\) | ||||
0.397135 | + | 0.917760i | \(0.370005\pi\) | |||||||
\(230\) | −7.91297e101 | −0.145606 | ||||||||
\(231\) | 1.10175e103 | 1.67866 | ||||||||
\(232\) | −2.53341e102 | −0.319873 | ||||||||
\(233\) | 3.49149e102 | 0.365618 | 0.182809 | − | 0.983148i | \(-0.441481\pi\) | ||||
0.182809 | + | 0.983148i | \(0.441481\pi\) | |||||||
\(234\) | −6.71097e102 | −0.583304 | ||||||||
\(235\) | −2.63209e103 | −1.90042 | ||||||||
\(236\) | −1.15045e103 | −0.690554 | ||||||||
\(237\) | −3.66121e103 | −1.82840 | ||||||||
\(238\) | 4.63281e103 | 1.92640 | ||||||||
\(239\) | −4.31374e103 | −1.49467 | −0.747334 | − | 0.664448i | \(-0.768667\pi\) | ||||
−0.747334 | + | 0.664448i | \(0.768667\pi\) | |||||||
\(240\) | 1.72886e103 | 0.499542 | ||||||||
\(241\) | −2.40361e103 | −0.579592 | −0.289796 | − | 0.957088i | \(-0.593587\pi\) | ||||
−0.289796 | + | 0.957088i | \(0.593587\pi\) | |||||||
\(242\) | 1.68249e103 | 0.338831 | ||||||||
\(243\) | −7.09594e103 | −1.19437 | ||||||||
\(244\) | −2.54098e103 | −0.357721 | ||||||||
\(245\) | 1.25612e104 | 1.48015 | ||||||||
\(246\) | 4.94949e103 | 0.488521 | ||||||||
\(247\) | 9.94517e103 | 0.822801 | ||||||||
\(248\) | −6.30556e103 | −0.437598 | ||||||||
\(249\) | 4.42900e103 | 0.258009 | ||||||||
\(250\) | 7.29269e103 | 0.356860 | ||||||||
\(251\) | 3.64103e103 | 0.149768 | 0.0748838 | − | 0.997192i | \(-0.476141\pi\) | ||||
0.0748838 | + | 0.997192i | \(0.476141\pi\) | |||||||
\(252\) | 3.17932e104 | 1.10005 | ||||||||
\(253\) | 4.03239e103 | 0.117441 | ||||||||
\(254\) | 8.17999e102 | 0.0200672 | ||||||||
\(255\) | −1.78726e105 | −3.69565 | ||||||||
\(256\) | 3.58359e103 | 0.0625000 | ||||||||
\(257\) | 1.10285e105 | 1.62339 | 0.811697 | − | 0.584079i | \(-0.198544\pi\) | ||||
0.811697 | + | 0.584079i | \(0.198544\pi\) | |||||||
\(258\) | 1.00154e105 | 1.24512 | ||||||||
\(259\) | 4.40573e104 | 0.462890 | ||||||||
\(260\) | 3.93280e104 | 0.349431 | ||||||||
\(261\) | 1.79731e105 | 1.35133 | ||||||||
\(262\) | 7.81828e104 | 0.497743 | ||||||||
\(263\) | −1.64613e105 | −0.887952 | −0.443976 | − | 0.896039i | \(-0.646432\pi\) | ||||
−0.443976 | + | 0.896039i | \(0.646432\pi\) | |||||||
\(264\) | −8.81017e104 | −0.402915 | ||||||||
\(265\) | −5.43312e105 | −2.10792 | ||||||||
\(266\) | −4.71152e105 | −1.55171 | ||||||||
\(267\) | −3.79404e104 | −0.106136 | ||||||||
\(268\) | 2.41555e105 | 0.574317 | ||||||||
\(269\) | 4.37506e105 | 0.884626 | 0.442313 | − | 0.896861i | \(-0.354158\pi\) | ||||
0.442313 | + | 0.896861i | \(0.354158\pi\) | |||||||
\(270\) | −4.05344e105 | −0.697429 | ||||||||
\(271\) | −9.18571e105 | −1.34570 | −0.672850 | − | 0.739779i | \(-0.734930\pi\) | ||||
−0.672850 | + | 0.739779i | \(0.734930\pi\) | |||||||
\(272\) | −3.70464e105 | −0.462379 | ||||||||
\(273\) | 1.20744e106 | 1.28467 | ||||||||
\(274\) | −4.92885e105 | −0.447297 | ||||||||
\(275\) | 5.60156e105 | 0.433847 | ||||||||
\(276\) | 1.94270e105 | 0.128487 | ||||||||
\(277\) | 1.36462e106 | 0.771156 | 0.385578 | − | 0.922675i | \(-0.374002\pi\) | ||||
0.385578 | + | 0.922675i | \(0.374002\pi\) | |||||||
\(278\) | −1.00310e106 | −0.484615 | ||||||||
\(279\) | 4.47343e106 | 1.84866 | ||||||||
\(280\) | −1.86316e106 | −0.658987 | ||||||||
\(281\) | −2.89936e106 | −0.878167 | −0.439084 | − | 0.898446i | \(-0.644697\pi\) | ||||
−0.439084 | + | 0.898446i | \(0.644697\pi\) | |||||||
\(282\) | 6.46200e106 | 1.67699 | ||||||||
\(283\) | −6.04289e106 | −1.34442 | −0.672210 | − | 0.740361i | \(-0.734655\pi\) | ||||
−0.672210 | + | 0.740361i | \(0.734655\pi\) | |||||||
\(284\) | −2.29310e106 | −0.437597 | ||||||||
\(285\) | 1.81763e107 | 2.97683 | ||||||||
\(286\) | −2.00413e106 | −0.281840 | ||||||||
\(287\) | −5.33397e106 | −0.644448 | ||||||||
\(288\) | −2.54235e106 | −0.264035 | ||||||||
\(289\) | 2.71019e107 | 2.42072 | ||||||||
\(290\) | −1.05327e107 | −0.809517 | ||||||||
\(291\) | −3.46239e107 | −2.29103 | ||||||||
\(292\) | 7.53985e106 | 0.429743 | ||||||||
\(293\) | 1.29720e107 | 0.637187 | 0.318594 | − | 0.947891i | \(-0.396790\pi\) | ||||
0.318594 | + | 0.947891i | \(0.396790\pi\) | |||||||
\(294\) | −3.08388e107 | −1.30614 | ||||||||
\(295\) | −4.78303e107 | −1.74761 | ||||||||
\(296\) | −3.52305e106 | −0.111104 | ||||||||
\(297\) | 2.06560e107 | 0.562524 | ||||||||
\(298\) | −2.02660e106 | −0.0476828 | ||||||||
\(299\) | 4.41922e106 | 0.0898771 | ||||||||
\(300\) | 2.69868e107 | 0.474654 | ||||||||
\(301\) | −1.07934e108 | −1.64254 | ||||||||
\(302\) | 4.16430e107 | 0.548580 | ||||||||
\(303\) | 1.06035e108 | 1.20974 | ||||||||
\(304\) | 3.76758e107 | 0.372444 | ||||||||
\(305\) | −1.05642e108 | −0.905299 | ||||||||
\(306\) | 2.62822e108 | 1.95335 | ||||||||
\(307\) | −1.51511e108 | −0.977066 | −0.488533 | − | 0.872545i | \(-0.662468\pi\) | ||||
−0.488533 | + | 0.872545i | \(0.662468\pi\) | |||||||
\(308\) | 9.49454e107 | 0.531518 | ||||||||
\(309\) | 2.51390e107 | 0.122223 | ||||||||
\(310\) | −2.62154e108 | −1.10745 | ||||||||
\(311\) | −1.58827e108 | −0.583242 | −0.291621 | − | 0.956534i | \(-0.594195\pi\) | ||||
−0.291621 | + | 0.956534i | \(0.594195\pi\) | |||||||
\(312\) | −9.65534e107 | −0.308349 | ||||||||
\(313\) | 3.50787e107 | 0.0974687 | 0.0487343 | − | 0.998812i | \(-0.484481\pi\) | ||||
0.0487343 | + | 0.998812i | \(0.484481\pi\) | |||||||
\(314\) | 1.07497e108 | 0.259990 | ||||||||
\(315\) | 1.32181e109 | 2.78393 | ||||||||
\(316\) | −3.15511e108 | −0.578931 | ||||||||
\(317\) | −2.87115e108 | −0.459175 | −0.229587 | − | 0.973288i | \(-0.573738\pi\) | ||||
−0.229587 | + | 0.973288i | \(0.573738\pi\) | |||||||
\(318\) | 1.33387e109 | 1.86010 | ||||||||
\(319\) | 5.36737e108 | 0.652931 | ||||||||
\(320\) | 1.48988e108 | 0.158171 | ||||||||
\(321\) | −8.63596e108 | −0.800464 | ||||||||
\(322\) | −2.09361e108 | −0.169498 | ||||||||
\(323\) | −3.89484e109 | −2.75537 | ||||||||
\(324\) | −2.12425e108 | −0.131371 | ||||||||
\(325\) | 6.13892e108 | 0.332021 | ||||||||
\(326\) | −1.27698e109 | −0.604251 | ||||||||
\(327\) | 2.40584e109 | 0.996415 | ||||||||
\(328\) | 4.26532e108 | 0.154682 | ||||||||
\(329\) | −6.96397e109 | −2.21226 | ||||||||
\(330\) | −3.66284e109 | −1.01967 | ||||||||
\(331\) | 1.66095e109 | 0.405358 | 0.202679 | − | 0.979245i | \(-0.435035\pi\) | ||||
0.202679 | + | 0.979245i | \(0.435035\pi\) | |||||||
\(332\) | 3.81678e108 | 0.0816940 | ||||||||
\(333\) | 2.49940e109 | 0.469365 | ||||||||
\(334\) | −3.57218e109 | −0.588792 | ||||||||
\(335\) | 1.00427e110 | 1.45345 | ||||||||
\(336\) | 4.57422e109 | 0.581511 | ||||||||
\(337\) | −4.60181e109 | −0.514077 | −0.257038 | − | 0.966401i | \(-0.582747\pi\) | ||||
−0.257038 | + | 0.966401i | \(0.582747\pi\) | |||||||
\(338\) | 5.00410e109 | 0.491416 | ||||||||
\(339\) | 2.83664e110 | 2.44972 | ||||||||
\(340\) | −1.54021e110 | −1.17016 | ||||||||
\(341\) | 1.33592e110 | 0.893232 | ||||||||
\(342\) | −2.67288e110 | −1.57342 | ||||||||
\(343\) | 4.82261e109 | 0.250027 | ||||||||
\(344\) | 8.63094e109 | 0.394245 | ||||||||
\(345\) | 8.07679e109 | 0.325168 | ||||||||
\(346\) | 1.26183e110 | 0.447911 | ||||||||
\(347\) | −4.71404e110 | −1.47591 | −0.737957 | − | 0.674848i | \(-0.764209\pi\) | ||||
−0.737957 | + | 0.674848i | \(0.764209\pi\) | |||||||
\(348\) | 2.58586e110 | 0.714344 | ||||||||
\(349\) | 7.55353e108 | 0.0184180 | 0.00920902 | − | 0.999958i | \(-0.497069\pi\) | ||||
0.00920902 | + | 0.999958i | \(0.497069\pi\) | |||||||
\(350\) | −2.90832e110 | −0.626155 | ||||||||
\(351\) | 2.26376e110 | 0.430497 | ||||||||
\(352\) | −7.59233e109 | −0.127576 | ||||||||
\(353\) | 8.97229e110 | 1.33261 | 0.666306 | − | 0.745679i | \(-0.267875\pi\) | ||||
0.666306 | + | 0.745679i | \(0.267875\pi\) | |||||||
\(354\) | 1.17427e111 | 1.54215 | ||||||||
\(355\) | −9.53357e110 | −1.10745 | ||||||||
\(356\) | −3.26959e109 | −0.0336061 | ||||||||
\(357\) | −4.72872e111 | −4.30206 | ||||||||
\(358\) | −1.00295e111 | −0.807919 | ||||||||
\(359\) | 1.40978e111 | 1.00587 | 0.502935 | − | 0.864324i | \(-0.332254\pi\) | ||||
0.502935 | + | 0.864324i | \(0.332254\pi\) | |||||||
\(360\) | −1.05698e111 | −0.668205 | ||||||||
\(361\) | 2.17632e111 | 1.21944 | ||||||||
\(362\) | 1.23110e110 | 0.0611602 | ||||||||
\(363\) | −1.71732e111 | −0.756680 | ||||||||
\(364\) | 1.04054e111 | 0.406768 | ||||||||
\(365\) | 3.13470e111 | 1.08757 | ||||||||
\(366\) | 2.59359e111 | 0.798865 | ||||||||
\(367\) | 1.94715e111 | 0.532629 | 0.266315 | − | 0.963886i | \(-0.414194\pi\) | ||||
0.266315 | + | 0.963886i | \(0.414194\pi\) | |||||||
\(368\) | 1.67416e110 | 0.0406833 | ||||||||
\(369\) | −3.02599e111 | −0.653463 | ||||||||
\(370\) | −1.46471e111 | −0.281175 | ||||||||
\(371\) | −1.43749e112 | −2.45380 | ||||||||
\(372\) | 6.43610e111 | 0.977248 | ||||||||
\(373\) | 1.03968e112 | 1.40464 | 0.702320 | − | 0.711862i | \(-0.252148\pi\) | ||||
0.702320 | + | 0.711862i | \(0.252148\pi\) | |||||||
\(374\) | 7.84878e111 | 0.943816 | ||||||||
\(375\) | −7.44367e111 | −0.796942 | ||||||||
\(376\) | 5.56875e111 | 0.530990 | ||||||||
\(377\) | 5.88227e111 | 0.499685 | ||||||||
\(378\) | −1.07246e112 | −0.811869 | ||||||||
\(379\) | 1.66352e112 | 1.12259 | 0.561296 | − | 0.827615i | \(-0.310303\pi\) | ||||
0.561296 | + | 0.827615i | \(0.310303\pi\) | |||||||
\(380\) | 1.56638e112 | 0.942561 | ||||||||
\(381\) | −8.34933e110 | −0.0448141 | ||||||||
\(382\) | −1.36856e112 | −0.655401 | ||||||||
\(383\) | 2.10808e111 | 0.0901034 | 0.0450517 | − | 0.998985i | \(-0.485655\pi\) | ||||
0.0450517 | + | 0.998985i | \(0.485655\pi\) | |||||||
\(384\) | −3.65778e111 | −0.139576 | ||||||||
\(385\) | 3.94737e112 | 1.34513 | ||||||||
\(386\) | −3.36274e112 | −1.02364 | ||||||||
\(387\) | −6.12315e112 | −1.66551 | ||||||||
\(388\) | −2.98378e112 | −0.725415 | ||||||||
\(389\) | 3.31733e112 | 0.721076 | 0.360538 | − | 0.932744i | \(-0.382593\pi\) | ||||
0.360538 | + | 0.932744i | \(0.382593\pi\) | |||||||
\(390\) | −4.01422e112 | −0.780352 | ||||||||
\(391\) | −1.73071e112 | −0.300978 | ||||||||
\(392\) | −2.65759e112 | −0.413565 | ||||||||
\(393\) | −7.98013e112 | −1.11156 | ||||||||
\(394\) | −2.98094e112 | −0.371764 | ||||||||
\(395\) | −1.31174e113 | −1.46513 | ||||||||
\(396\) | 5.38631e112 | 0.538953 | ||||||||
\(397\) | 6.59828e112 | 0.591622 | 0.295811 | − | 0.955247i | \(-0.404410\pi\) | ||||
0.295811 | + | 0.955247i | \(0.404410\pi\) | |||||||
\(398\) | 1.48339e113 | 1.19218 | ||||||||
\(399\) | 4.80906e113 | 3.46529 | ||||||||
\(400\) | 2.32564e112 | 0.150291 | ||||||||
\(401\) | −2.95181e112 | −0.171123 | −0.0855614 | − | 0.996333i | \(-0.527268\pi\) | ||||
−0.0855614 | + | 0.996333i | \(0.527268\pi\) | |||||||
\(402\) | −2.46555e113 | −1.28257 | ||||||||
\(403\) | 1.46407e113 | 0.683587 | ||||||||
\(404\) | 9.13774e112 | 0.383045 | ||||||||
\(405\) | −8.83160e112 | −0.332465 | ||||||||
\(406\) | −2.78673e113 | −0.942349 | ||||||||
\(407\) | 7.46405e112 | 0.226787 | ||||||||
\(408\) | 3.78133e113 | 1.03259 | ||||||||
\(409\) | −3.18283e113 | −0.781357 | −0.390678 | − | 0.920527i | \(-0.627760\pi\) | ||||
−0.390678 | + | 0.920527i | \(0.627760\pi\) | |||||||
\(410\) | 1.77331e113 | 0.391460 | ||||||||
\(411\) | 5.03088e113 | 0.998907 | ||||||||
\(412\) | 2.16640e112 | 0.0386999 | ||||||||
\(413\) | −1.26549e114 | −2.03438 | ||||||||
\(414\) | −1.18772e113 | −0.171869 | ||||||||
\(415\) | 1.58683e113 | 0.206746 | ||||||||
\(416\) | −8.32067e112 | −0.0976334 | ||||||||
\(417\) | 1.02387e114 | 1.08225 | ||||||||
\(418\) | −7.98213e113 | −0.760240 | ||||||||
\(419\) | 1.46754e114 | 1.25973 | 0.629867 | − | 0.776703i | \(-0.283109\pi\) | ||||
0.629867 | + | 0.776703i | \(0.283109\pi\) | |||||||
\(420\) | 1.90174e114 | 1.47165 | ||||||||
\(421\) | −1.99988e114 | −1.39551 | −0.697754 | − | 0.716337i | \(-0.745817\pi\) | ||||
−0.697754 | + | 0.716337i | \(0.745817\pi\) | |||||||
\(422\) | −1.02968e114 | −0.648052 | ||||||||
\(423\) | −3.95070e114 | −2.24320 | ||||||||
\(424\) | 1.14949e114 | 0.588967 | ||||||||
\(425\) | −2.40419e114 | −1.11186 | ||||||||
\(426\) | 2.34057e114 | 0.977246 | ||||||||
\(427\) | −2.79506e114 | −1.05385 | ||||||||
\(428\) | −7.44220e113 | −0.253453 | ||||||||
\(429\) | 2.04561e114 | 0.629407 | ||||||||
\(430\) | 3.58832e114 | 0.997732 | ||||||||
\(431\) | −4.46887e114 | −1.12315 | −0.561573 | − | 0.827427i | \(-0.689804\pi\) | ||||
−0.561573 | + | 0.827427i | \(0.689804\pi\) | |||||||
\(432\) | 8.57591e113 | 0.194867 | ||||||||
\(433\) | 5.90128e114 | 1.21261 | 0.606307 | − | 0.795231i | \(-0.292650\pi\) | ||||
0.606307 | + | 0.795231i | \(0.292650\pi\) | |||||||
\(434\) | −6.93605e114 | −1.28917 | ||||||||
\(435\) | 1.07507e115 | 1.80782 | ||||||||
\(436\) | 2.07328e114 | 0.315498 | ||||||||
\(437\) | 1.76011e114 | 0.242436 | ||||||||
\(438\) | −7.69594e114 | −0.959706 | ||||||||
\(439\) | 2.72880e113 | 0.0308153 | 0.0154076 | − | 0.999881i | \(-0.495095\pi\) | ||||
0.0154076 | + | 0.999881i | \(0.495095\pi\) | |||||||
\(440\) | −3.15652e114 | −0.322862 | ||||||||
\(441\) | 1.88541e115 | 1.74713 | ||||||||
\(442\) | 8.60172e114 | 0.722299 | ||||||||
\(443\) | −1.53437e113 | −0.0116780 | −0.00583898 | − | 0.999983i | \(-0.501859\pi\) | ||||
−0.00583898 | + | 0.999983i | \(0.501859\pi\) | |||||||
\(444\) | 3.59598e114 | 0.248118 | ||||||||
\(445\) | −1.35933e114 | −0.0850483 | ||||||||
\(446\) | −1.61664e115 | −0.917375 | ||||||||
\(447\) | 2.06856e114 | 0.106486 | ||||||||
\(448\) | 3.94192e114 | 0.184125 | ||||||||
\(449\) | −1.10481e115 | −0.468350 | −0.234175 | − | 0.972195i | \(-0.575239\pi\) | ||||
−0.234175 | + | 0.972195i | \(0.575239\pi\) | |||||||
\(450\) | −1.64991e115 | −0.634914 | ||||||||
\(451\) | −9.03666e114 | −0.315739 | ||||||||
\(452\) | 2.44453e115 | 0.775662 | ||||||||
\(453\) | −4.25051e115 | −1.22509 | ||||||||
\(454\) | 4.48797e114 | 0.117522 | ||||||||
\(455\) | 4.32604e115 | 1.02943 | ||||||||
\(456\) | −3.84558e115 | −0.831746 | ||||||||
\(457\) | 5.68270e115 | 1.11738 | 0.558689 | − | 0.829377i | \(-0.311305\pi\) | ||||
0.558689 | + | 0.829377i | \(0.311305\pi\) | |||||||
\(458\) | −3.14124e115 | −0.561633 | ||||||||
\(459\) | −8.86559e115 | −1.44164 | ||||||||
\(460\) | 6.96032e114 | 0.102959 | ||||||||
\(461\) | −6.76860e115 | −0.910980 | −0.455490 | − | 0.890241i | \(-0.650536\pi\) | ||||
−0.455490 | + | 0.890241i | \(0.650536\pi\) | |||||||
\(462\) | −9.69110e115 | −1.18699 | ||||||||
\(463\) | −1.43609e116 | −1.60106 | −0.800531 | − | 0.599291i | \(-0.795449\pi\) | ||||
−0.800531 | + | 0.599291i | \(0.795449\pi\) | |||||||
\(464\) | 2.22841e115 | 0.226185 | ||||||||
\(465\) | 2.67581e116 | 2.47316 | ||||||||
\(466\) | −3.07114e115 | −0.258531 | ||||||||
\(467\) | 1.23456e116 | 0.946735 | 0.473368 | − | 0.880865i | \(-0.343038\pi\) | ||||
0.473368 | + | 0.880865i | \(0.343038\pi\) | |||||||
\(468\) | 5.90303e115 | 0.412458 | ||||||||
\(469\) | 2.65708e116 | 1.69194 | ||||||||
\(470\) | 2.31521e116 | 1.34380 | ||||||||
\(471\) | −1.09722e116 | −0.580612 | ||||||||
\(472\) | 1.01195e116 | 0.488295 | ||||||||
\(473\) | −1.82858e116 | −0.804739 | ||||||||
\(474\) | 3.22043e116 | 1.29287 | ||||||||
\(475\) | 2.44504e116 | 0.895600 | ||||||||
\(476\) | −4.07507e116 | −1.36217 | ||||||||
\(477\) | −8.15497e116 | −2.48813 | ||||||||
\(478\) | 3.79440e116 | 1.05689 | ||||||||
\(479\) | −3.03388e116 | −0.771621 | −0.385810 | − | 0.922578i | \(-0.626078\pi\) | ||||
−0.385810 | + | 0.922578i | \(0.626078\pi\) | |||||||
\(480\) | −1.52073e116 | −0.353230 | ||||||||
\(481\) | 8.18009e115 | 0.173559 | ||||||||
\(482\) | 2.11424e116 | 0.409833 | ||||||||
\(483\) | 2.13695e116 | 0.378524 | ||||||||
\(484\) | −1.47993e116 | −0.239590 | ||||||||
\(485\) | −1.24051e117 | −1.83584 | ||||||||
\(486\) | 6.24166e116 | 0.844544 | ||||||||
\(487\) | 1.06153e117 | 1.31348 | 0.656739 | − | 0.754118i | \(-0.271935\pi\) | ||||
0.656739 | + | 0.754118i | \(0.271935\pi\) | |||||||
\(488\) | 2.23507e116 | 0.252947 | ||||||||
\(489\) | 1.30341e117 | 1.34942 | ||||||||
\(490\) | −1.10490e117 | −1.04663 | ||||||||
\(491\) | −5.80317e116 | −0.503061 | −0.251530 | − | 0.967849i | \(-0.580934\pi\) | ||||
−0.251530 | + | 0.967849i | \(0.580934\pi\) | |||||||
\(492\) | −4.35362e116 | −0.345437 | ||||||||
\(493\) | −2.30368e117 | −1.67333 | ||||||||
\(494\) | −8.74786e116 | −0.581808 | ||||||||
\(495\) | 2.23937e117 | 1.36395 | ||||||||
\(496\) | 5.54643e116 | 0.309429 | ||||||||
\(497\) | −2.52238e117 | −1.28916 | ||||||||
\(498\) | −3.89579e116 | −0.182440 | ||||||||
\(499\) | −1.49861e117 | −0.643154 | −0.321577 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321577 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(500\) | −6.41472e116 | −0.252338 | ||||||||
\(501\) | 3.64613e117 | 1.31489 | ||||||||
\(502\) | −3.20269e116 | −0.105902 | ||||||||
\(503\) | 3.43905e117 | 1.04287 | 0.521436 | − | 0.853290i | \(-0.325396\pi\) | ||||
0.521436 | + | 0.853290i | \(0.325396\pi\) | |||||||
\(504\) | −2.79656e117 | −0.777850 | ||||||||
\(505\) | 3.79902e117 | 0.969387 | ||||||||
\(506\) | −3.54693e116 | −0.0830434 | ||||||||
\(507\) | −5.10769e117 | −1.09743 | ||||||||
\(508\) | −7.19519e115 | −0.0141896 | ||||||||
\(509\) | 2.54328e117 | 0.460438 | 0.230219 | − | 0.973139i | \(-0.426056\pi\) | ||||
0.230219 | + | 0.973139i | \(0.426056\pi\) | |||||||
\(510\) | 1.57209e118 | 2.61322 | ||||||||
\(511\) | 8.29377e117 | 1.26603 | ||||||||
\(512\) | −3.15216e116 | −0.0441942 | ||||||||
\(513\) | 9.01621e117 | 1.16123 | ||||||||
\(514\) | −9.70073e117 | −1.14791 | ||||||||
\(515\) | 9.00683e116 | 0.0979394 | ||||||||
\(516\) | −8.80962e117 | −0.880431 | ||||||||
\(517\) | −1.17982e118 | −1.08387 | ||||||||
\(518\) | −3.87532e117 | −0.327313 | ||||||||
\(519\) | −1.28796e118 | −1.00028 | ||||||||
\(520\) | −3.45933e117 | −0.247085 | ||||||||
\(521\) | −6.00755e116 | −0.0394691 | −0.0197345 | − | 0.999805i | \(-0.506282\pi\) | ||||
−0.0197345 | + | 0.999805i | \(0.506282\pi\) | |||||||
\(522\) | −1.58093e118 | −0.955531 | ||||||||
\(523\) | 1.87265e118 | 1.04144 | 0.520720 | − | 0.853728i | \(-0.325664\pi\) | ||||
0.520720 | + | 0.853728i | \(0.325664\pi\) | |||||||
\(524\) | −6.87703e117 | −0.351957 | ||||||||
\(525\) | 2.96852e118 | 1.39833 | ||||||||
\(526\) | 1.44795e118 | 0.627877 | ||||||||
\(527\) | −5.73378e118 | −2.28917 | ||||||||
\(528\) | 7.74950e117 | 0.284904 | ||||||||
\(529\) | −2.87518e118 | −0.973518 | ||||||||
\(530\) | 4.77902e118 | 1.49052 | ||||||||
\(531\) | −7.17920e118 | −2.06283 | ||||||||
\(532\) | 4.14430e118 | 1.09722 | ||||||||
\(533\) | −9.90356e117 | −0.241634 | ||||||||
\(534\) | 3.33727e117 | 0.0750494 | ||||||||
\(535\) | −3.09410e118 | −0.641424 | ||||||||
\(536\) | −2.12474e118 | −0.406104 | ||||||||
\(537\) | 1.02371e119 | 1.80425 | ||||||||
\(538\) | −3.84834e118 | −0.625525 | ||||||||
\(539\) | 5.63047e118 | 0.844177 | ||||||||
\(540\) | 3.56544e118 | 0.493157 | ||||||||
\(541\) | −3.21989e118 | −0.410923 | −0.205462 | − | 0.978665i | \(-0.565870\pi\) | ||||
−0.205462 | + | 0.978665i | \(0.565870\pi\) | |||||||
\(542\) | 8.07983e118 | 0.951554 | ||||||||
\(543\) | −1.25658e118 | −0.136584 | ||||||||
\(544\) | 3.25863e118 | 0.326952 | ||||||||
\(545\) | 8.61969e118 | 0.798443 | ||||||||
\(546\) | −1.06208e119 | −0.908398 | ||||||||
\(547\) | 1.71992e119 | 1.35850 | 0.679251 | − | 0.733906i | \(-0.262305\pi\) | ||||
0.679251 | + | 0.733906i | \(0.262305\pi\) | |||||||
\(548\) | 4.33546e118 | 0.316287 | ||||||||
\(549\) | −1.58565e119 | −1.06859 | ||||||||
\(550\) | −4.92718e118 | −0.306776 | ||||||||
\(551\) | 2.34282e119 | 1.34786 | ||||||||
\(552\) | −1.70881e118 | −0.0908542 | ||||||||
\(553\) | −3.47060e119 | −1.70554 | ||||||||
\(554\) | −1.20033e119 | −0.545289 | ||||||||
\(555\) | 1.49503e119 | 0.627922 | ||||||||
\(556\) | 8.82339e118 | 0.342675 | ||||||||
\(557\) | 2.60860e117 | 0.00936930 | 0.00468465 | − | 0.999989i | \(-0.498509\pi\) | ||||
0.00468465 | + | 0.999989i | \(0.498509\pi\) | |||||||
\(558\) | −3.93487e119 | −1.30720 | ||||||||
\(559\) | −2.00400e119 | −0.615863 | ||||||||
\(560\) | 1.63886e119 | 0.465974 | ||||||||
\(561\) | −8.01127e119 | −2.10774 | ||||||||
\(562\) | 2.55030e119 | 0.620958 | ||||||||
\(563\) | 4.80695e119 | 1.08331 | 0.541657 | − | 0.840599i | \(-0.317797\pi\) | ||||
0.541657 | + | 0.840599i | \(0.317797\pi\) | |||||||
\(564\) | −5.68404e119 | −1.18581 | ||||||||
\(565\) | 1.01631e120 | 1.96300 | ||||||||
\(566\) | 5.31538e119 | 0.950648 | ||||||||
\(567\) | −2.33666e119 | −0.387019 | ||||||||
\(568\) | 2.01703e119 | 0.309428 | ||||||||
\(569\) | 1.04059e118 | 0.0147876 | 0.00739381 | − | 0.999973i | \(-0.497646\pi\) | ||||
0.00739381 | + | 0.999973i | \(0.497646\pi\) | |||||||
\(570\) | −1.59880e120 | −2.10493 | ||||||||
\(571\) | −8.21661e119 | −1.00236 | −0.501178 | − | 0.865344i | \(-0.667100\pi\) | ||||
−0.501178 | + | 0.865344i | \(0.667100\pi\) | |||||||
\(572\) | 1.76285e119 | 0.199291 | ||||||||
\(573\) | 1.39689e120 | 1.46365 | ||||||||
\(574\) | 4.69181e119 | 0.455694 | ||||||||
\(575\) | 1.08648e119 | 0.0978292 | ||||||||
\(576\) | 2.23627e119 | 0.186701 | ||||||||
\(577\) | −2.15475e120 | −1.66820 | −0.834100 | − | 0.551613i | \(-0.814012\pi\) | ||||
−0.834100 | + | 0.551613i | \(0.814012\pi\) | |||||||
\(578\) | −2.38391e120 | −1.71170 | ||||||||
\(579\) | 3.43235e120 | 2.28599 | ||||||||
\(580\) | 9.26464e119 | 0.572415 | ||||||||
\(581\) | 4.19842e119 | 0.240671 | ||||||||
\(582\) | 3.04555e120 | 1.62000 | ||||||||
\(583\) | −2.43535e120 | −1.20221 | ||||||||
\(584\) | −6.63212e119 | −0.303874 | ||||||||
\(585\) | 2.45419e120 | 1.04383 | ||||||||
\(586\) | −1.14103e120 | −0.450559 | ||||||||
\(587\) | −6.39895e119 | −0.234613 | −0.117306 | − | 0.993096i | \(-0.537426\pi\) | ||||
−0.117306 | + | 0.993096i | \(0.537426\pi\) | |||||||
\(588\) | 2.71261e120 | 0.923578 | ||||||||
\(589\) | 5.83119e120 | 1.84392 | ||||||||
\(590\) | 4.20720e120 | 1.23575 | ||||||||
\(591\) | 3.04265e120 | 0.830226 | ||||||||
\(592\) | 3.09890e119 | 0.0785622 | ||||||||
\(593\) | −7.21074e120 | −1.69864 | −0.849319 | − | 0.527880i | \(-0.822987\pi\) | ||||
−0.849319 | + | 0.527880i | \(0.822987\pi\) | |||||||
\(594\) | −1.81692e120 | −0.397765 | ||||||||
\(595\) | −1.69421e121 | −3.44731 | ||||||||
\(596\) | 1.78262e119 | 0.0337168 | ||||||||
\(597\) | −1.51410e121 | −2.66239 | ||||||||
\(598\) | −3.88719e119 | −0.0635527 | ||||||||
\(599\) | −3.97745e120 | −0.604696 | −0.302348 | − | 0.953198i | \(-0.597771\pi\) | ||||
−0.302348 | + | 0.953198i | \(0.597771\pi\) | |||||||
\(600\) | −2.37378e120 | −0.335631 | ||||||||
\(601\) | 7.35051e120 | 0.966669 | 0.483335 | − | 0.875436i | \(-0.339425\pi\) | ||||
0.483335 | + | 0.875436i | \(0.339425\pi\) | |||||||
\(602\) | 9.49396e120 | 1.16145 | ||||||||
\(603\) | 1.50738e121 | 1.71561 | ||||||||
\(604\) | −3.66296e120 | −0.387905 | ||||||||
\(605\) | −6.15283e120 | −0.606340 | ||||||||
\(606\) | −9.32691e120 | −0.855418 | ||||||||
\(607\) | 6.72390e120 | 0.574002 | 0.287001 | − | 0.957930i | \(-0.407342\pi\) | ||||
0.287001 | + | 0.957930i | \(0.407342\pi\) | |||||||
\(608\) | −3.31400e120 | −0.263358 | ||||||||
\(609\) | 2.84442e121 | 2.10446 | ||||||||
\(610\) | 9.29234e120 | 0.640143 | ||||||||
\(611\) | −1.29300e121 | −0.829478 | ||||||||
\(612\) | −2.31181e121 | −1.38123 | ||||||||
\(613\) | 1.67656e121 | 0.933015 | 0.466507 | − | 0.884517i | \(-0.345512\pi\) | ||||
0.466507 | + | 0.884517i | \(0.345512\pi\) | |||||||
\(614\) | 1.33270e121 | 0.690890 | ||||||||
\(615\) | −1.81002e121 | −0.874211 | ||||||||
\(616\) | −8.35149e120 | −0.375840 | ||||||||
\(617\) | 1.03203e121 | 0.432800 | 0.216400 | − | 0.976305i | \(-0.430568\pi\) | ||||
0.216400 | + | 0.976305i | \(0.430568\pi\) | |||||||
\(618\) | −2.21125e120 | −0.0864249 | ||||||||
\(619\) | 2.31175e121 | 0.842167 | 0.421083 | − | 0.907022i | \(-0.361650\pi\) | ||||
0.421083 | + | 0.907022i | \(0.361650\pi\) | |||||||
\(620\) | 2.30593e121 | 0.783084 | ||||||||
\(621\) | 4.00643e120 | 0.126845 | ||||||||
\(622\) | 1.39706e121 | 0.412414 | ||||||||
\(623\) | −3.59651e120 | −0.0990038 | ||||||||
\(624\) | 8.49292e120 | 0.218036 | ||||||||
\(625\) | −5.17750e121 | −1.23977 | ||||||||
\(626\) | −3.08556e120 | −0.0689207 | ||||||||
\(627\) | 8.14737e121 | 1.69777 | ||||||||
\(628\) | −9.45554e120 | −0.183841 | ||||||||
\(629\) | −3.20358e121 | −0.581209 | ||||||||
\(630\) | −1.16267e122 | −1.96854 | ||||||||
\(631\) | −2.45238e121 | −0.387535 | −0.193768 | − | 0.981047i | \(-0.562071\pi\) | ||||
−0.193768 | + | 0.981047i | \(0.562071\pi\) | |||||||
\(632\) | 2.77527e121 | 0.409366 | ||||||||
\(633\) | 1.05099e122 | 1.44723 | ||||||||
\(634\) | 2.52549e121 | 0.324686 | ||||||||
\(635\) | −2.99141e120 | −0.0359103 | ||||||||
\(636\) | −1.17329e122 | −1.31529 | ||||||||
\(637\) | 6.17061e121 | 0.646045 | ||||||||
\(638\) | −4.72119e121 | −0.461692 | ||||||||
\(639\) | −1.43096e122 | −1.30720 | ||||||||
\(640\) | −1.31051e121 | −0.111844 | ||||||||
\(641\) | −2.05207e122 | −1.63632 | −0.818160 | − | 0.574991i | \(-0.805006\pi\) | ||||
−0.818160 | + | 0.574991i | \(0.805006\pi\) | |||||||
\(642\) | 7.59627e121 | 0.566014 | ||||||||
\(643\) | 2.00713e122 | 1.39765 | 0.698826 | − | 0.715292i | \(-0.253706\pi\) | ||||
0.698826 | + | 0.715292i | \(0.253706\pi\) | |||||||
\(644\) | 1.84156e121 | 0.119853 | ||||||||
\(645\) | −3.66261e122 | −2.22814 | ||||||||
\(646\) | 3.42594e122 | 1.94834 | ||||||||
\(647\) | 5.77265e121 | 0.306930 | 0.153465 | − | 0.988154i | \(-0.450957\pi\) | ||||
0.153465 | + | 0.988154i | \(0.450957\pi\) | |||||||
\(648\) | 1.86851e121 | 0.0928930 | ||||||||
\(649\) | −2.14396e122 | −0.996716 | ||||||||
\(650\) | −5.39985e121 | −0.234775 | ||||||||
\(651\) | 7.07964e122 | 2.87898 | ||||||||
\(652\) | 1.12324e122 | 0.427270 | ||||||||
\(653\) | −1.84671e122 | −0.657168 | −0.328584 | − | 0.944475i | \(-0.606571\pi\) | ||||
−0.328584 | + | 0.944475i | \(0.606571\pi\) | |||||||
\(654\) | −2.11620e122 | −0.704572 | ||||||||
\(655\) | −2.85913e122 | −0.890713 | ||||||||
\(656\) | −3.75181e121 | −0.109377 | ||||||||
\(657\) | 4.70511e122 | 1.28374 | ||||||||
\(658\) | 6.12557e122 | 1.56430 | ||||||||
\(659\) | −4.00419e122 | −0.957193 | −0.478596 | − | 0.878035i | \(-0.658854\pi\) | ||||
−0.478596 | + | 0.878035i | \(0.658854\pi\) | |||||||
\(660\) | 3.22186e122 | 0.721018 | ||||||||
\(661\) | −4.91223e122 | −1.02924 | −0.514618 | − | 0.857420i | \(-0.672066\pi\) | ||||
−0.514618 | + | 0.857420i | \(0.672066\pi\) | |||||||
\(662\) | −1.46099e122 | −0.286632 | ||||||||
\(663\) | −8.77980e122 | −1.61304 | ||||||||
\(664\) | −3.35727e121 | −0.0577664 | ||||||||
\(665\) | 1.72300e123 | 2.77679 | ||||||||
\(666\) | −2.19849e122 | −0.331891 | ||||||||
\(667\) | 1.04105e122 | 0.147231 | ||||||||
\(668\) | 3.14212e122 | 0.416339 | ||||||||
\(669\) | 1.65011e123 | 2.04869 | ||||||||
\(670\) | −8.83362e122 | −1.02774 | ||||||||
\(671\) | −4.73531e122 | −0.516319 | ||||||||
\(672\) | −4.02352e122 | −0.411190 | ||||||||
\(673\) | −9.36043e122 | −0.896686 | −0.448343 | − | 0.893862i | \(-0.647986\pi\) | ||||
−0.448343 | + | 0.893862i | \(0.647986\pi\) | |||||||
\(674\) | 4.04779e122 | 0.363507 | ||||||||
\(675\) | 5.56550e122 | 0.468587 | ||||||||
\(676\) | −4.40165e122 | −0.347484 | ||||||||
\(677\) | −1.31829e123 | −0.975895 | −0.487947 | − | 0.872873i | \(-0.662254\pi\) | ||||
−0.487947 | + | 0.872873i | \(0.662254\pi\) | |||||||
\(678\) | −2.49513e123 | −1.73222 | ||||||||
\(679\) | −3.28213e123 | −2.13708 | ||||||||
\(680\) | 1.35478e123 | 0.827430 | ||||||||
\(681\) | −4.58088e122 | −0.262452 | ||||||||
\(682\) | −1.17509e123 | −0.631611 | ||||||||
\(683\) | 3.59072e122 | 0.181085 | 0.0905423 | − | 0.995893i | \(-0.471140\pi\) | ||||
0.0905423 | + | 0.995893i | \(0.471140\pi\) | |||||||
\(684\) | 2.35109e123 | 1.11257 | ||||||||
\(685\) | 1.80247e123 | 0.800440 | ||||||||
\(686\) | −4.24201e122 | −0.176796 | ||||||||
\(687\) | 3.20627e123 | 1.25424 | ||||||||
\(688\) | −7.59186e122 | −0.278773 | ||||||||
\(689\) | −2.66898e123 | −0.920046 | ||||||||
\(690\) | −7.10442e122 | −0.229929 | ||||||||
\(691\) | 1.59983e123 | 0.486161 | 0.243081 | − | 0.970006i | \(-0.421842\pi\) | ||||
0.243081 | + | 0.970006i | \(0.421842\pi\) | |||||||
\(692\) | −1.10992e123 | −0.316721 | ||||||||
\(693\) | 5.92489e123 | 1.58776 | ||||||||
\(694\) | 4.14651e123 | 1.04363 | ||||||||
\(695\) | 3.66833e123 | 0.867221 | ||||||||
\(696\) | −2.27454e123 | −0.505117 | ||||||||
\(697\) | 3.87854e123 | 0.809175 | ||||||||
\(698\) | −6.64415e121 | −0.0130235 | ||||||||
\(699\) | 3.13472e123 | 0.577354 | ||||||||
\(700\) | 2.55818e123 | 0.442758 | ||||||||
\(701\) | −4.73824e123 | −0.770697 | −0.385348 | − | 0.922771i | \(-0.625919\pi\) | ||||
−0.385348 | + | 0.922771i | \(0.625919\pi\) | |||||||
\(702\) | −1.99122e123 | −0.304408 | ||||||||
\(703\) | 3.25801e123 | 0.468161 | ||||||||
\(704\) | 6.67828e122 | 0.0902099 | ||||||||
\(705\) | −2.36314e124 | −3.00098 | ||||||||
\(706\) | −7.89211e123 | −0.942299 | ||||||||
\(707\) | 1.00514e124 | 1.12845 | ||||||||
\(708\) | −1.03290e124 | −1.09046 | ||||||||
\(709\) | 5.80124e123 | 0.575983 | 0.287992 | − | 0.957633i | \(-0.407012\pi\) | ||||
0.287992 | + | 0.957633i | \(0.407012\pi\) | |||||||
\(710\) | 8.38582e123 | 0.783082 | ||||||||
\(711\) | −1.96889e124 | −1.72939 | ||||||||
\(712\) | 2.87596e122 | 0.0237631 | ||||||||
\(713\) | 2.59114e123 | 0.201417 | ||||||||
\(714\) | 4.15943e124 | 3.04202 | ||||||||
\(715\) | 7.32906e123 | 0.504354 | ||||||||
\(716\) | 8.82205e123 | 0.571285 | ||||||||
\(717\) | −3.87295e124 | −2.36026 | ||||||||
\(718\) | −1.24005e124 | −0.711257 | ||||||||
\(719\) | −7.63623e122 | −0.0412261 | −0.0206131 | − | 0.999788i | \(-0.506562\pi\) | ||||
−0.0206131 | + | 0.999788i | \(0.506562\pi\) | |||||||
\(720\) | 9.29733e123 | 0.472492 | ||||||||
\(721\) | 2.38302e123 | 0.114010 | ||||||||
\(722\) | −1.91431e124 | −0.862272 | ||||||||
\(723\) | −2.15800e124 | −0.915243 | ||||||||
\(724\) | −1.08288e123 | −0.0432468 | ||||||||
\(725\) | 1.44617e124 | 0.543896 | ||||||||
\(726\) | 1.51057e124 | 0.535054 | ||||||||
\(727\) | −4.58002e123 | −0.152799 | −0.0763995 | − | 0.997077i | \(-0.524342\pi\) | ||||
−0.0763995 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(728\) | −9.15266e123 | −0.287629 | ||||||||
\(729\) | −5.48336e124 | −1.62330 | ||||||||
\(730\) | −2.75731e124 | −0.769027 | ||||||||
\(731\) | 7.84830e124 | 2.06238 | ||||||||
\(732\) | −2.28134e124 | −0.564883 | ||||||||
\(733\) | 9.12974e123 | 0.213027 | 0.106514 | − | 0.994311i | \(-0.466031\pi\) | ||||
0.106514 | + | 0.994311i | \(0.466031\pi\) | |||||||
\(734\) | −1.71273e124 | −0.376626 | ||||||||
\(735\) | 1.12777e125 | 2.33734 | ||||||||
\(736\) | −1.47260e123 | −0.0287674 | ||||||||
\(737\) | 4.50155e124 | 0.828946 | ||||||||
\(738\) | 2.66169e124 | 0.462068 | ||||||||
\(739\) | −4.63834e124 | −0.759154 | −0.379577 | − | 0.925160i | \(-0.623930\pi\) | ||||
−0.379577 | + | 0.925160i | \(0.623930\pi\) | |||||||
\(740\) | 1.28837e124 | 0.198821 | ||||||||
\(741\) | 8.92896e124 | 1.29930 | ||||||||
\(742\) | 1.26443e125 | 1.73510 | ||||||||
\(743\) | −1.05547e125 | −1.36595 | −0.682974 | − | 0.730442i | \(-0.739314\pi\) | ||||
−0.682974 | + | 0.730442i | \(0.739314\pi\) | |||||||
\(744\) | −5.66125e124 | −0.691018 | ||||||||
\(745\) | 7.41126e123 | 0.0853285 | ||||||||
\(746\) | −9.14511e124 | −0.993230 | ||||||||
\(747\) | 2.38179e124 | 0.244038 | ||||||||
\(748\) | −6.90386e124 | −0.667379 | ||||||||
\(749\) | −8.18635e124 | −0.746675 | ||||||||
\(750\) | 6.54752e124 | 0.563523 | ||||||||
\(751\) | 1.50180e124 | 0.121976 | 0.0609880 | − | 0.998138i | \(-0.480575\pi\) | ||||
0.0609880 | + | 0.998138i | \(0.480575\pi\) | |||||||
\(752\) | −4.89833e124 | −0.375467 | ||||||||
\(753\) | 3.26899e124 | 0.236500 | ||||||||
\(754\) | −5.17410e124 | −0.353331 | ||||||||
\(755\) | −1.52288e125 | −0.981687 | ||||||||
\(756\) | 9.43342e124 | 0.574078 | ||||||||
\(757\) | 2.22005e125 | 1.27553 | 0.637766 | − | 0.770230i | \(-0.279859\pi\) | ||||
0.637766 | + | 0.770230i | \(0.279859\pi\) | |||||||
\(758\) | −1.46325e125 | −0.793793 | ||||||||
\(759\) | 3.62036e124 | 0.185453 | ||||||||
\(760\) | −1.37780e125 | −0.666491 | ||||||||
\(761\) | 1.86018e124 | 0.0849811 | 0.0424905 | − | 0.999097i | \(-0.486471\pi\) | ||||
0.0424905 | + | 0.999097i | \(0.486471\pi\) | |||||||
\(762\) | 7.34415e123 | 0.0316884 | ||||||||
\(763\) | 2.28059e125 | 0.929458 | ||||||||
\(764\) | 1.20380e125 | 0.463439 | ||||||||
\(765\) | −9.61138e125 | −3.49553 | ||||||||
\(766\) | −1.85429e124 | −0.0637127 | ||||||||
\(767\) | −2.34963e125 | −0.762783 | ||||||||
\(768\) | 3.21742e124 | 0.0986948 | ||||||||
\(769\) | −2.32072e125 | −0.672707 | −0.336354 | − | 0.941736i | \(-0.609194\pi\) | ||||
−0.336354 | + | 0.941736i | \(0.609194\pi\) | |||||||
\(770\) | −3.47214e125 | −0.951154 | ||||||||
\(771\) | 9.90156e125 | 2.56353 | ||||||||
\(772\) | 2.95790e125 | 0.723820 | ||||||||
\(773\) | 5.23576e124 | 0.121108 | 0.0605538 | − | 0.998165i | \(-0.480713\pi\) | ||||
0.0605538 | + | 0.998165i | \(0.480713\pi\) | |||||||
\(774\) | 5.38598e125 | 1.17770 | ||||||||
\(775\) | 3.59946e125 | 0.744069 | ||||||||
\(776\) | 2.62456e125 | 0.512946 | ||||||||
\(777\) | 3.95554e125 | 0.730957 | ||||||||
\(778\) | −2.91796e125 | −0.509878 | ||||||||
\(779\) | −3.94444e125 | −0.651787 | ||||||||
\(780\) | 3.53094e125 | 0.551792 | ||||||||
\(781\) | −4.27335e125 | −0.631609 | ||||||||
\(782\) | 1.52235e125 | 0.212823 | ||||||||
\(783\) | 5.33282e125 | 0.705213 | ||||||||
\(784\) | 2.33764e125 | 0.292435 | ||||||||
\(785\) | −3.93115e125 | −0.465253 | ||||||||
\(786\) | 7.01940e125 | 0.785994 | ||||||||
\(787\) | −5.66853e125 | −0.600578 | −0.300289 | − | 0.953848i | \(-0.597083\pi\) | ||||
−0.300289 | + | 0.953848i | \(0.597083\pi\) | |||||||
\(788\) | 2.62206e125 | 0.262877 | ||||||||
\(789\) | −1.47793e126 | −1.40218 | ||||||||
\(790\) | 1.15382e126 | 1.03600 | ||||||||
\(791\) | 2.68896e126 | 2.28511 | ||||||||
\(792\) | −4.73785e125 | −0.381097 | ||||||||
\(793\) | −5.18957e125 | −0.395137 | ||||||||
\(794\) | −5.80391e125 | −0.418340 | ||||||||
\(795\) | −4.87796e126 | −3.32865 | ||||||||
\(796\) | −1.30481e126 | −0.843001 | ||||||||
\(797\) | −1.32779e126 | −0.812254 | −0.406127 | − | 0.913817i | \(-0.633121\pi\) | ||||
−0.406127 | + | 0.913817i | \(0.633121\pi\) | |||||||
\(798\) | −4.23010e126 | −2.45033 | ||||||||
\(799\) | 5.06378e126 | 2.77773 | ||||||||
\(800\) | −2.04565e125 | −0.106272 | ||||||||
\(801\) | −2.04032e125 | −0.100389 | ||||||||
\(802\) | 2.59644e125 | 0.121002 | ||||||||
\(803\) | 1.40511e126 | 0.620273 | ||||||||
\(804\) | 2.16872e126 | 0.906914 | ||||||||
\(805\) | 7.65629e125 | 0.303318 | ||||||||
\(806\) | −1.28781e126 | −0.483369 | ||||||||
\(807\) | 3.92801e126 | 1.39693 | ||||||||
\(808\) | −8.03764e125 | −0.270853 | ||||||||
\(809\) | −1.95970e126 | −0.625789 | −0.312894 | − | 0.949788i | \(-0.601299\pi\) | ||||
−0.312894 | + | 0.949788i | \(0.601299\pi\) | |||||||
\(810\) | 7.76836e125 | 0.235088 | ||||||||
\(811\) | 3.24597e126 | 0.930974 | 0.465487 | − | 0.885055i | \(-0.345879\pi\) | ||||
0.465487 | + | 0.885055i | \(0.345879\pi\) | |||||||
\(812\) | 2.45123e126 | 0.666342 | ||||||||
\(813\) | −8.24710e126 | −2.12502 | ||||||||
\(814\) | −6.56545e125 | −0.160363 | ||||||||
\(815\) | 4.66988e126 | 1.08131 | ||||||||
\(816\) | −3.32609e126 | −0.730151 | ||||||||
\(817\) | −7.98164e126 | −1.66124 | ||||||||
\(818\) | 2.79965e126 | 0.552503 | ||||||||
\(819\) | 6.49328e126 | 1.21511 | ||||||||
\(820\) | −1.55982e126 | −0.276804 | ||||||||
\(821\) | 5.75776e126 | 0.969006 | 0.484503 | − | 0.874790i | \(-0.339001\pi\) | ||||
0.484503 | + | 0.874790i | \(0.339001\pi\) | |||||||
\(822\) | −4.42521e126 | −0.706334 | ||||||||
\(823\) | −8.10145e126 | −1.22651 | −0.613253 | − | 0.789886i | \(-0.710140\pi\) | ||||
−0.613253 | + | 0.789886i | \(0.710140\pi\) | |||||||
\(824\) | −1.90558e125 | −0.0273649 | ||||||||
\(825\) | 5.02919e126 | 0.685095 | ||||||||
\(826\) | 1.11314e127 | 1.43852 | ||||||||
\(827\) | −5.55803e125 | −0.0681446 | −0.0340723 | − | 0.999419i | \(-0.510848\pi\) | ||||
−0.0340723 | + | 0.999419i | \(0.510848\pi\) | |||||||
\(828\) | 1.04473e126 | 0.121530 | ||||||||
\(829\) | 1.76276e127 | 1.94567 | 0.972837 | − | 0.231493i | \(-0.0743610\pi\) | ||||
0.972837 | + | 0.231493i | \(0.0743610\pi\) | |||||||
\(830\) | −1.39579e126 | −0.146192 | ||||||||
\(831\) | 1.22518e127 | 1.21774 | ||||||||
\(832\) | 7.31894e125 | 0.0690372 | ||||||||
\(833\) | −2.41660e127 | −2.16345 | ||||||||
\(834\) | −9.00605e126 | −0.765264 | ||||||||
\(835\) | 1.30634e127 | 1.05365 | ||||||||
\(836\) | 7.02116e126 | 0.537571 | ||||||||
\(837\) | 1.32732e127 | 0.964756 | ||||||||
\(838\) | −1.29086e127 | −0.890767 | ||||||||
\(839\) | −2.97966e127 | −1.95219 | −0.976094 | − | 0.217347i | \(-0.930260\pi\) | ||||
−0.976094 | + | 0.217347i | \(0.930260\pi\) | |||||||
\(840\) | −1.67278e127 | −1.04062 | ||||||||
\(841\) | −3.07170e126 | −0.181448 | ||||||||
\(842\) | 1.75911e127 | 0.986773 | ||||||||
\(843\) | −2.60310e127 | −1.38673 | ||||||||
\(844\) | 9.05714e126 | 0.458242 | ||||||||
\(845\) | −1.82999e127 | −0.879391 | ||||||||
\(846\) | 3.47508e127 | 1.58618 | ||||||||
\(847\) | −1.62791e127 | −0.705833 | ||||||||
\(848\) | −1.01110e127 | −0.416463 | ||||||||
\(849\) | −5.42542e127 | −2.12300 | ||||||||
\(850\) | 2.11475e127 | 0.786206 | ||||||||
\(851\) | 1.44772e126 | 0.0511387 | ||||||||
\(852\) | −2.05879e127 | −0.691017 | ||||||||
\(853\) | −4.88236e127 | −1.55721 | −0.778605 | − | 0.627514i | \(-0.784072\pi\) | ||||
−0.778605 | + | 0.627514i | \(0.784072\pi\) | |||||||
\(854\) | 2.45856e127 | 0.745183 | ||||||||
\(855\) | 9.77467e127 | 2.81563 | ||||||||
\(856\) | 6.54623e126 | 0.179218 | ||||||||
\(857\) | 6.19965e127 | 1.61325 | 0.806625 | − | 0.591064i | \(-0.201292\pi\) | ||||
0.806625 | + | 0.591064i | \(0.201292\pi\) | |||||||
\(858\) | −1.79934e127 | −0.445058 | ||||||||
\(859\) | 4.88783e127 | 1.14925 | 0.574624 | − | 0.818418i | \(-0.305148\pi\) | ||||
0.574624 | + | 0.818418i | \(0.305148\pi\) | |||||||
\(860\) | −3.15632e127 | −0.705503 | ||||||||
\(861\) | −4.78894e127 | −1.01766 | ||||||||
\(862\) | 3.93086e127 | 0.794184 | ||||||||
\(863\) | 3.27692e126 | 0.0629500 | 0.0314750 | − | 0.999505i | \(-0.489980\pi\) | ||||
0.0314750 | + | 0.999505i | \(0.489980\pi\) | |||||||
\(864\) | −7.54345e126 | −0.137791 | ||||||||
\(865\) | −4.61450e127 | −0.801539 | ||||||||
\(866\) | −5.19082e127 | −0.857447 | ||||||||
\(867\) | 2.43326e128 | 3.82259 | ||||||||
\(868\) | 6.10102e127 | 0.911579 | ||||||||
\(869\) | −5.87978e127 | −0.835605 | ||||||||
\(870\) | −9.45644e127 | −1.27832 | ||||||||
\(871\) | 4.93339e127 | 0.634389 | ||||||||
\(872\) | −1.82368e127 | −0.223090 | ||||||||
\(873\) | −1.86197e128 | −2.16697 | ||||||||
\(874\) | −1.54821e127 | −0.171428 | ||||||||
\(875\) | −7.05613e127 | −0.743390 | ||||||||
\(876\) | 6.76942e127 | 0.678614 | ||||||||
\(877\) | 1.60850e128 | 1.53440 | 0.767200 | − | 0.641408i | \(-0.221649\pi\) | ||||
0.767200 | + | 0.641408i | \(0.221649\pi\) | |||||||
\(878\) | −2.40028e126 | −0.0217897 | ||||||||
\(879\) | 1.16465e128 | 1.00619 | ||||||||
\(880\) | 2.77650e127 | 0.228298 | ||||||||
\(881\) | 1.71862e128 | 1.34502 | 0.672509 | − | 0.740089i | \(-0.265217\pi\) | ||||
0.672509 | + | 0.740089i | \(0.265217\pi\) | |||||||
\(882\) | −1.65842e128 | −1.23541 | ||||||||
\(883\) | 1.46950e128 | 1.04202 | 0.521012 | − | 0.853549i | \(-0.325555\pi\) | ||||
0.521012 | + | 0.853549i | \(0.325555\pi\) | |||||||
\(884\) | −7.56616e127 | −0.510742 | ||||||||
\(885\) | −4.29429e128 | −2.75968 | ||||||||
\(886\) | 1.34964e126 | 0.00825756 | ||||||||
\(887\) | −3.18960e128 | −1.85806 | −0.929028 | − | 0.370009i | \(-0.879355\pi\) | ||||
−0.929028 | + | 0.370009i | \(0.879355\pi\) | |||||||
\(888\) | −3.16306e127 | −0.175446 | ||||||||
\(889\) | −7.91464e126 | −0.0418027 | ||||||||
\(890\) | 1.19568e127 | 0.0601382 | ||||||||
\(891\) | −3.95870e127 | −0.189615 | ||||||||
\(892\) | 1.42201e128 | 0.648682 | ||||||||
\(893\) | −5.14981e128 | −2.23745 | ||||||||
\(894\) | −1.81952e127 | −0.0752966 | ||||||||
\(895\) | 3.66778e128 | 1.44577 | ||||||||
\(896\) | −3.46735e127 | −0.130196 | ||||||||
\(897\) | 3.96766e127 | 0.141926 | ||||||||
\(898\) | 9.71798e127 | 0.331173 | ||||||||
\(899\) | 3.44898e128 | 1.11981 | ||||||||
\(900\) | 1.45127e128 | 0.448952 | ||||||||
\(901\) | 1.04526e129 | 3.08102 | ||||||||
\(902\) | 7.94873e127 | 0.223261 | ||||||||
\(903\) | −9.69050e128 | −2.59376 | ||||||||
\(904\) | −2.15023e128 | −0.548476 | ||||||||
\(905\) | −4.50210e127 | −0.109447 | ||||||||
\(906\) | 3.73879e128 | 0.866272 | ||||||||
\(907\) | −1.17471e128 | −0.259426 | −0.129713 | − | 0.991552i | \(-0.541406\pi\) | ||||
−0.129713 | + | 0.991552i | \(0.541406\pi\) | |||||||
\(908\) | −3.94766e127 | −0.0831009 | ||||||||
\(909\) | 5.70224e128 | 1.14424 | ||||||||
\(910\) | −3.80523e128 | −0.727914 | ||||||||
\(911\) | 4.24958e128 | 0.774990 | 0.387495 | − | 0.921872i | \(-0.373340\pi\) | ||||
0.387495 | + | 0.921872i | \(0.373340\pi\) | |||||||
\(912\) | 3.38260e128 | 0.588133 | ||||||||
\(913\) | 7.11284e127 | 0.117914 | ||||||||
\(914\) | −4.99856e128 | −0.790105 | ||||||||
\(915\) | −9.48471e128 | −1.42957 | ||||||||
\(916\) | 2.76306e128 | 0.397135 | ||||||||
\(917\) | −7.56467e128 | −1.03687 | ||||||||
\(918\) | 7.79825e128 | 1.01939 | ||||||||
\(919\) | 7.60961e128 | 0.948719 | 0.474360 | − | 0.880331i | \(-0.342680\pi\) | ||||
0.474360 | + | 0.880331i | \(0.342680\pi\) | |||||||
\(920\) | −6.12237e127 | −0.0728029 | ||||||||
\(921\) | −1.36029e129 | −1.54290 | ||||||||
\(922\) | 5.95373e128 | 0.644160 | ||||||||
\(923\) | −4.68330e128 | −0.483368 | ||||||||
\(924\) | 8.52438e128 | 0.839329 | ||||||||
\(925\) | 2.01109e128 | 0.188915 | ||||||||
\(926\) | 1.26320e129 | 1.13212 | ||||||||
\(927\) | 1.35190e128 | 0.115605 | ||||||||
\(928\) | −1.96013e128 | −0.159937 | ||||||||
\(929\) | 4.43080e128 | 0.344984 | 0.172492 | − | 0.985011i | \(-0.444818\pi\) | ||||
0.172492 | + | 0.985011i | \(0.444818\pi\) | |||||||
\(930\) | −2.35367e129 | −1.74879 | ||||||||
\(931\) | 2.45766e129 | 1.74265 | ||||||||
\(932\) | 2.70141e128 | 0.182809 | ||||||||
\(933\) | −1.42598e129 | −0.921007 | ||||||||
\(934\) | −1.08593e129 | −0.669443 | ||||||||
\(935\) | −2.87029e129 | −1.68896 | ||||||||
\(936\) | −5.19236e128 | −0.291652 | ||||||||
\(937\) | 8.57093e128 | 0.459574 | 0.229787 | − | 0.973241i | \(-0.426197\pi\) | ||||
0.229787 | + | 0.973241i | \(0.426197\pi\) | |||||||
\(938\) | −2.33719e129 | −1.19638 | ||||||||
\(939\) | 3.14943e128 | 0.153914 | ||||||||
\(940\) | −2.03648e129 | −0.950210 | ||||||||
\(941\) | −3.09635e128 | −0.137943 | −0.0689717 | − | 0.997619i | \(-0.521972\pi\) | ||||
−0.0689717 | + | 0.997619i | \(0.521972\pi\) | |||||||
\(942\) | 9.65129e128 | 0.410555 | ||||||||
\(943\) | −1.75275e128 | −0.0711967 | ||||||||
\(944\) | −8.90121e128 | −0.345277 | ||||||||
\(945\) | 3.92195e129 | 1.45284 | ||||||||
\(946\) | 1.60844e129 | 0.569036 | ||||||||
\(947\) | 1.66144e129 | 0.561383 | 0.280692 | − | 0.959798i | \(-0.409436\pi\) | ||||
0.280692 | + | 0.959798i | \(0.409436\pi\) | |||||||
\(948\) | −2.83272e129 | −0.914200 | ||||||||
\(949\) | 1.53990e129 | 0.474692 | ||||||||
\(950\) | −2.15068e129 | −0.633285 | ||||||||
\(951\) | −2.57777e129 | −0.725091 | ||||||||
\(952\) | 3.58447e129 | 0.963202 | ||||||||
\(953\) | −2.81155e129 | −0.721779 | −0.360890 | − | 0.932608i | \(-0.617527\pi\) | ||||
−0.360890 | + | 0.932608i | \(0.617527\pi\) | |||||||
\(954\) | 7.17319e129 | 1.75937 | ||||||||
\(955\) | 5.00480e129 | 1.17284 | ||||||||
\(956\) | −3.33759e129 | −0.747334 | ||||||||
\(957\) | 4.81893e129 | 1.03105 | ||||||||
\(958\) | 2.66863e129 | 0.545618 | ||||||||
\(959\) | 4.76896e129 | 0.931782 | ||||||||
\(960\) | 1.33764e129 | 0.249771 | ||||||||
\(961\) | 2.98076e129 | 0.531937 | ||||||||
\(962\) | −7.19528e128 | −0.122725 | ||||||||
\(963\) | −4.64417e129 | −0.757120 | ||||||||
\(964\) | −1.85970e129 | −0.289796 | ||||||||
\(965\) | 1.22975e130 | 1.83180 | ||||||||
\(966\) | −1.87968e129 | −0.267657 | ||||||||
\(967\) | −6.12643e129 | −0.833980 | −0.416990 | − | 0.908911i | \(-0.636915\pi\) | ||||
−0.416990 | + | 0.908911i | \(0.636915\pi\) | |||||||
\(968\) | 1.30176e129 | 0.169416 | ||||||||
\(969\) | −3.49686e130 | −4.35105 | ||||||||
\(970\) | 1.09116e130 | 1.29813 | ||||||||
\(971\) | −1.30319e130 | −1.48241 | −0.741207 | − | 0.671276i | \(-0.765746\pi\) | ||||
−0.741207 | + | 0.671276i | \(0.765746\pi\) | |||||||
\(972\) | −5.49022e129 | −0.597183 | ||||||||
\(973\) | 9.70564e129 | 1.00952 | ||||||||
\(974\) | −9.33733e129 | −0.928769 | ||||||||
\(975\) | 5.51164e129 | 0.524300 | ||||||||
\(976\) | −1.96599e129 | −0.178860 | ||||||||
\(977\) | 2.62874e129 | 0.228736 | 0.114368 | − | 0.993438i | \(-0.463516\pi\) | ||||
0.114368 | + | 0.993438i | \(0.463516\pi\) | |||||||
\(978\) | −1.14649e130 | −0.954182 | ||||||||
\(979\) | −6.09311e128 | −0.0485056 | ||||||||
\(980\) | 9.71877e129 | 0.740077 | ||||||||
\(981\) | 1.29379e130 | 0.942460 | ||||||||
\(982\) | 5.10452e129 | 0.355718 | ||||||||
\(983\) | 5.46064e129 | 0.364054 | 0.182027 | − | 0.983294i | \(-0.441734\pi\) | ||||
0.182027 | + | 0.983294i | \(0.441734\pi\) | |||||||
\(984\) | 3.82948e129 | 0.244261 | ||||||||
\(985\) | 1.09012e130 | 0.665273 | ||||||||
\(986\) | 2.02634e130 | 1.18322 | ||||||||
\(987\) | −6.25239e130 | −3.49341 | ||||||||
\(988\) | 7.69470e129 | 0.411400 | ||||||||
\(989\) | −3.54671e129 | −0.181463 | ||||||||
\(990\) | −1.96977e130 | −0.964459 | ||||||||
\(991\) | 3.33654e129 | 0.156348 | 0.0781741 | − | 0.996940i | \(-0.475091\pi\) | ||||
0.0781741 | + | 0.996940i | \(0.475091\pi\) | |||||||
\(992\) | −4.87869e129 | −0.218799 | ||||||||
\(993\) | 1.49123e130 | 0.640108 | ||||||||
\(994\) | 2.21871e130 | 0.911577 | ||||||||
\(995\) | −5.42475e130 | −2.13342 | ||||||||
\(996\) | 3.42677e129 | 0.129004 | ||||||||
\(997\) | 3.85557e130 | 1.38947 | 0.694736 | − | 0.719265i | \(-0.255521\pi\) | ||||
0.694736 | + | 0.719265i | \(0.255521\pi\) | |||||||
\(998\) | 1.31819e130 | 0.454778 | ||||||||
\(999\) | 7.41600e129 | 0.244946 |
(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 | 2.88.a.b.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.88.a.b.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |