Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(211.244930035\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −135.924 | −1.50176 | −0.750880 | − | 0.660439i | \(-0.770370\pi\) | ||||
−0.750880 | + | 0.660439i | \(0.770370\pi\) | |||||||
\(3\) | −2298.95 | −1.82071 | −0.910355 | − | 0.413829i | \(-0.864191\pi\) | ||||
−0.910355 | + | 0.413829i | \(0.864191\pi\) | |||||||
\(4\) | 10283.3 | 1.25528 | ||||||||
\(5\) | 41046.5 | 1.17482 | 0.587409 | − | 0.809290i | \(-0.300148\pi\) | ||||
0.587409 | + | 0.809290i | \(0.300148\pi\) | |||||||
\(6\) | 312481. | 2.73427 | ||||||||
\(7\) | 283206. | 0.909841 | 0.454921 | − | 0.890532i | \(-0.349668\pi\) | ||||
0.454921 | + | 0.890532i | \(0.349668\pi\) | |||||||
\(8\) | −284251. | −0.383369 | ||||||||
\(9\) | 3.69083e6 | 2.31498 | ||||||||
\(10\) | −5.57919e6 | −1.76429 | ||||||||
\(11\) | 2.50683e6 | 0.426651 | 0.213326 | − | 0.976981i | \(-0.431570\pi\) | ||||
0.213326 | + | 0.976981i | \(0.431570\pi\) | |||||||
\(12\) | −2.36407e7 | −2.28550 | ||||||||
\(13\) | 1.00648e7 | 0.578329 | 0.289165 | − | 0.957279i | \(-0.406623\pi\) | ||||
0.289165 | + | 0.957279i | \(0.406623\pi\) | |||||||
\(14\) | −3.84944e7 | −1.36636 | ||||||||
\(15\) | −9.43636e7 | −2.13900 | ||||||||
\(16\) | −4.56040e7 | −0.679552 | ||||||||
\(17\) | −6.90987e7 | −0.694308 | −0.347154 | − | 0.937808i | \(-0.612852\pi\) | ||||
−0.347154 | + | 0.937808i | \(0.612852\pi\) | |||||||
\(18\) | −5.01672e8 | −3.47655 | ||||||||
\(19\) | −2.54546e8 | −1.24127 | −0.620637 | − | 0.784098i | \(-0.713126\pi\) | ||||
−0.620637 | + | 0.784098i | \(0.713126\pi\) | |||||||
\(20\) | 4.22091e8 | 1.47473 | ||||||||
\(21\) | −6.51076e8 | −1.65656 | ||||||||
\(22\) | −3.40738e8 | −0.640727 | ||||||||
\(23\) | 1.27400e9 | 1.79448 | 0.897238 | − | 0.441548i | \(-0.145570\pi\) | ||||
0.897238 | + | 0.441548i | \(0.145570\pi\) | |||||||
\(24\) | 6.53478e8 | 0.698004 | ||||||||
\(25\) | 4.64108e8 | 0.380197 | ||||||||
\(26\) | −1.36805e9 | −0.868511 | ||||||||
\(27\) | −4.81976e9 | −2.39420 | ||||||||
\(28\) | 2.91228e9 | 1.14211 | ||||||||
\(29\) | 2.31906e9 | 0.723979 | 0.361989 | − | 0.932182i | \(-0.382098\pi\) | ||||
0.361989 | + | 0.932182i | \(0.382098\pi\) | |||||||
\(30\) | 1.28263e10 | 3.21227 | ||||||||
\(31\) | −7.98819e8 | −0.161658 | −0.0808290 | − | 0.996728i | \(-0.525757\pi\) | ||||
−0.0808290 | + | 0.996728i | \(0.525757\pi\) | |||||||
\(32\) | 8.52724e9 | 1.40389 | ||||||||
\(33\) | −5.76308e9 | −0.776808 | ||||||||
\(34\) | 9.39215e9 | 1.04268 | ||||||||
\(35\) | 1.16246e10 | 1.06890 | ||||||||
\(36\) | 3.79538e10 | 2.90595 | ||||||||
\(37\) | −2.18141e10 | −1.39774 | −0.698871 | − | 0.715248i | \(-0.746314\pi\) | ||||
−0.698871 | + | 0.715248i | \(0.746314\pi\) | |||||||
\(38\) | 3.45988e10 | 1.86409 | ||||||||
\(39\) | −2.31385e10 | −1.05297 | ||||||||
\(40\) | −1.16675e10 | −0.450389 | ||||||||
\(41\) | 2.95945e10 | 0.973006 | 0.486503 | − | 0.873679i | \(-0.338272\pi\) | ||||
0.486503 | + | 0.873679i | \(0.338272\pi\) | |||||||
\(42\) | 8.84967e10 | 2.48775 | ||||||||
\(43\) | −3.54603e10 | −0.855455 | −0.427727 | − | 0.903908i | \(-0.640686\pi\) | ||||
−0.427727 | + | 0.903908i | \(0.640686\pi\) | |||||||
\(44\) | 2.57784e10 | 0.535567 | ||||||||
\(45\) | 1.51496e11 | 2.71968 | ||||||||
\(46\) | −1.73166e11 | −2.69487 | ||||||||
\(47\) | 3.45716e10 | 0.467825 | 0.233912 | − | 0.972258i | \(-0.424847\pi\) | ||||
0.233912 | + | 0.972258i | \(0.424847\pi\) | |||||||
\(48\) | 1.04841e11 | 1.23727 | ||||||||
\(49\) | −1.66833e10 | −0.172189 | ||||||||
\(50\) | −6.30833e10 | −0.570965 | ||||||||
\(51\) | 1.58854e11 | 1.26413 | ||||||||
\(52\) | 1.03499e11 | 0.725965 | ||||||||
\(53\) | −2.53893e10 | −0.157347 | −0.0786733 | − | 0.996900i | \(-0.525068\pi\) | ||||
−0.0786733 | + | 0.996900i | \(0.525068\pi\) | |||||||
\(54\) | 6.55120e11 | 3.59552 | ||||||||
\(55\) | 1.02897e11 | 0.501238 | ||||||||
\(56\) | −8.05017e10 | −0.348805 | ||||||||
\(57\) | 5.85187e11 | 2.26000 | ||||||||
\(58\) | −3.15216e11 | −1.08724 | ||||||||
\(59\) | 3.44448e10 | 0.106313 | 0.0531564 | − | 0.998586i | \(-0.483072\pi\) | ||||
0.0531564 | + | 0.998586i | \(0.483072\pi\) | |||||||
\(60\) | −9.70365e11 | −2.68505 | ||||||||
\(61\) | 6.29561e11 | 1.56457 | 0.782283 | − | 0.622923i | \(-0.214055\pi\) | ||||
0.782283 | + | 0.622923i | \(0.214055\pi\) | |||||||
\(62\) | 1.08578e11 | 0.242771 | ||||||||
\(63\) | 1.04527e12 | 2.10627 | ||||||||
\(64\) | −7.85467e11 | −1.42876 | ||||||||
\(65\) | 4.13126e11 | 0.679432 | ||||||||
\(66\) | 7.83339e11 | 1.16658 | ||||||||
\(67\) | −5.29677e11 | −0.715360 | −0.357680 | − | 0.933844i | \(-0.616432\pi\) | ||||
−0.357680 | + | 0.933844i | \(0.616432\pi\) | |||||||
\(68\) | −7.10560e11 | −0.871550 | ||||||||
\(69\) | −2.92885e12 | −3.26722 | ||||||||
\(70\) | −1.58006e12 | −1.60523 | ||||||||
\(71\) | 9.28368e11 | 0.860084 | 0.430042 | − | 0.902809i | \(-0.358499\pi\) | ||||
0.430042 | + | 0.902809i | \(0.358499\pi\) | |||||||
\(72\) | −1.04912e12 | −0.887494 | ||||||||
\(73\) | −2.48962e11 | −0.192546 | −0.0962728 | − | 0.995355i | \(-0.530692\pi\) | ||||
−0.0962728 | + | 0.995355i | \(0.530692\pi\) | |||||||
\(74\) | 2.96506e12 | 2.09907 | ||||||||
\(75\) | −1.06696e12 | −0.692229 | ||||||||
\(76\) | −2.61756e12 | −1.55815 | ||||||||
\(77\) | 7.09951e11 | 0.388185 | ||||||||
\(78\) | 3.14508e12 | 1.58131 | ||||||||
\(79\) | 2.02937e12 | 0.939257 | 0.469628 | − | 0.882864i | \(-0.344388\pi\) | ||||
0.469628 | + | 0.882864i | \(0.344388\pi\) | |||||||
\(80\) | −1.87188e12 | −0.798350 | ||||||||
\(81\) | 5.19600e12 | 2.04417 | ||||||||
\(82\) | −4.02259e12 | −1.46122 | ||||||||
\(83\) | 2.12706e12 | 0.714121 | 0.357060 | − | 0.934081i | \(-0.383779\pi\) | ||||
0.357060 | + | 0.934081i | \(0.383779\pi\) | |||||||
\(84\) | −6.69518e12 | −2.07944 | ||||||||
\(85\) | −2.83626e12 | −0.815685 | ||||||||
\(86\) | 4.81989e12 | 1.28469 | ||||||||
\(87\) | −5.33140e12 | −1.31816 | ||||||||
\(88\) | −7.12570e11 | −0.163565 | ||||||||
\(89\) | −4.73010e12 | −1.00887 | −0.504436 | − | 0.863449i | \(-0.668299\pi\) | ||||
−0.504436 | + | 0.863449i | \(0.668299\pi\) | |||||||
\(90\) | −2.05918e13 | −4.08431 | ||||||||
\(91\) | 2.85043e12 | 0.526188 | ||||||||
\(92\) | 1.31008e13 | 2.25257 | ||||||||
\(93\) | 1.83644e12 | 0.294332 | ||||||||
\(94\) | −4.69910e12 | −0.702560 | ||||||||
\(95\) | −1.04482e13 | −1.45827 | ||||||||
\(96\) | −1.96037e13 | −2.55608 | ||||||||
\(97\) | 1.07707e12 | 0.131289 | 0.0656446 | − | 0.997843i | \(-0.479090\pi\) | ||||
0.0656446 | + | 0.997843i | \(0.479090\pi\) | |||||||
\(98\) | 2.26765e12 | 0.258587 | ||||||||
\(99\) | 9.25230e12 | 0.987691 | ||||||||
\(100\) | 4.77254e12 | 0.477254 | ||||||||
\(101\) | −1.12913e13 | −1.05841 | −0.529206 | − | 0.848494i | \(-0.677510\pi\) | ||||
−0.529206 | + | 0.848494i | \(0.677510\pi\) | |||||||
\(102\) | −2.15921e13 | −1.89842 | ||||||||
\(103\) | −9.34018e12 | −0.770749 | −0.385375 | − | 0.922760i | \(-0.625928\pi\) | ||||
−0.385375 | + | 0.922760i | \(0.625928\pi\) | |||||||
\(104\) | −2.86094e12 | −0.221714 | ||||||||
\(105\) | −2.67244e13 | −1.94615 | ||||||||
\(106\) | 3.45101e12 | 0.236297 | ||||||||
\(107\) | 1.18948e12 | 0.0766235 | 0.0383117 | − | 0.999266i | \(-0.487802\pi\) | ||||
0.0383117 | + | 0.999266i | \(0.487802\pi\) | |||||||
\(108\) | −4.95628e13 | −3.00540 | ||||||||
\(109\) | 1.45695e13 | 0.832091 | 0.416046 | − | 0.909344i | \(-0.363416\pi\) | ||||
0.416046 | + | 0.909344i | \(0.363416\pi\) | |||||||
\(110\) | −1.39861e13 | −0.752738 | ||||||||
\(111\) | 5.01496e13 | 2.54488 | ||||||||
\(112\) | −1.29153e13 | −0.618284 | ||||||||
\(113\) | 1.26616e13 | 0.572111 | 0.286055 | − | 0.958213i | \(-0.407656\pi\) | ||||
0.286055 | + | 0.958213i | \(0.407656\pi\) | |||||||
\(114\) | −7.95408e13 | −3.39397 | ||||||||
\(115\) | 5.22931e13 | 2.10818 | ||||||||
\(116\) | 2.38475e13 | 0.908796 | ||||||||
\(117\) | 3.71476e13 | 1.33882 | ||||||||
\(118\) | −4.68187e12 | −0.159656 | ||||||||
\(119\) | −1.95692e13 | −0.631709 | ||||||||
\(120\) | 2.68230e13 | 0.820028 | ||||||||
\(121\) | −2.82385e13 | −0.817969 | ||||||||
\(122\) | −8.55723e13 | −2.34960 | ||||||||
\(123\) | −6.80361e13 | −1.77156 | ||||||||
\(124\) | −8.21446e12 | −0.202926 | ||||||||
\(125\) | −3.10555e13 | −0.728155 | ||||||||
\(126\) | −1.42077e14 | −3.16311 | ||||||||
\(127\) | 7.15485e13 | 1.51313 | 0.756565 | − | 0.653919i | \(-0.226876\pi\) | ||||
0.756565 | + | 0.653919i | \(0.226876\pi\) | |||||||
\(128\) | 3.69084e13 | 0.741755 | ||||||||
\(129\) | 8.15213e13 | 1.55753 | ||||||||
\(130\) | −5.61536e13 | −1.02034 | ||||||||
\(131\) | 4.94564e13 | 0.854985 | 0.427493 | − | 0.904019i | \(-0.359397\pi\) | ||||
0.427493 | + | 0.904019i | \(0.359397\pi\) | |||||||
\(132\) | −5.92632e13 | −0.975112 | ||||||||
\(133\) | −7.20890e13 | −1.12936 | ||||||||
\(134\) | 7.19957e13 | 1.07430 | ||||||||
\(135\) | −1.97834e14 | −2.81275 | ||||||||
\(136\) | 1.96414e13 | 0.266176 | ||||||||
\(137\) | 3.42598e13 | 0.442691 | 0.221346 | − | 0.975195i | \(-0.428955\pi\) | ||||
0.221346 | + | 0.975195i | \(0.428955\pi\) | |||||||
\(138\) | 3.98100e14 | 4.90658 | ||||||||
\(139\) | 9.32158e13 | 1.09621 | 0.548105 | − | 0.836410i | \(-0.315350\pi\) | ||||
0.548105 | + | 0.836410i | \(0.315350\pi\) | |||||||
\(140\) | 1.19539e14 | 1.34177 | ||||||||
\(141\) | −7.94782e13 | −0.851773 | ||||||||
\(142\) | −1.26187e14 | −1.29164 | ||||||||
\(143\) | 2.52309e13 | 0.246745 | ||||||||
\(144\) | −1.68317e14 | −1.57315 | ||||||||
\(145\) | 9.51894e13 | 0.850543 | ||||||||
\(146\) | 3.38398e13 | 0.289157 | ||||||||
\(147\) | 3.83539e13 | 0.313507 | ||||||||
\(148\) | −2.24320e14 | −1.75456 | ||||||||
\(149\) | −7.90059e13 | −0.591492 | −0.295746 | − | 0.955267i | \(-0.595568\pi\) | ||||
−0.295746 | + | 0.955267i | \(0.595568\pi\) | |||||||
\(150\) | 1.45025e14 | 1.03956 | ||||||||
\(151\) | −5.21913e13 | −0.358301 | −0.179150 | − | 0.983822i | \(-0.557335\pi\) | ||||
−0.179150 | + | 0.983822i | \(0.557335\pi\) | |||||||
\(152\) | 7.23549e13 | 0.475866 | ||||||||
\(153\) | −2.55032e14 | −1.60731 | ||||||||
\(154\) | −9.64991e13 | −0.582960 | ||||||||
\(155\) | −3.27887e13 | −0.189919 | ||||||||
\(156\) | −2.37939e14 | −1.32177 | ||||||||
\(157\) | −9.70806e13 | −0.517350 | −0.258675 | − | 0.965964i | \(-0.583286\pi\) | ||||
−0.258675 | + | 0.965964i | \(0.583286\pi\) | |||||||
\(158\) | −2.75839e14 | −1.41054 | ||||||||
\(159\) | 5.83686e13 | 0.286482 | ||||||||
\(160\) | 3.50013e14 | 1.64932 | ||||||||
\(161\) | 3.60804e14 | 1.63269 | ||||||||
\(162\) | −7.06259e14 | −3.06985 | ||||||||
\(163\) | 1.38754e13 | 0.0579462 | 0.0289731 | − | 0.999580i | \(-0.490776\pi\) | ||||
0.0289731 | + | 0.999580i | \(0.490776\pi\) | |||||||
\(164\) | 3.04327e14 | 1.22139 | ||||||||
\(165\) | −2.36554e14 | −0.912608 | ||||||||
\(166\) | −2.89117e14 | −1.07244 | ||||||||
\(167\) | 2.37760e14 | 0.848167 | 0.424083 | − | 0.905623i | \(-0.360596\pi\) | ||||
0.424083 | + | 0.905623i | \(0.360596\pi\) | |||||||
\(168\) | 1.85069e14 | 0.635073 | ||||||||
\(169\) | −2.01574e14 | −0.665535 | ||||||||
\(170\) | 3.85515e14 | 1.22496 | ||||||||
\(171\) | −9.39486e14 | −2.87353 | ||||||||
\(172\) | −3.64647e14 | −1.07384 | ||||||||
\(173\) | 6.66614e14 | 1.89049 | 0.945246 | − | 0.326358i | \(-0.105821\pi\) | ||||
0.945246 | + | 0.326358i | \(0.105821\pi\) | |||||||
\(174\) | 7.24664e14 | 1.97955 | ||||||||
\(175\) | 1.31438e14 | 0.345919 | ||||||||
\(176\) | −1.14322e14 | −0.289932 | ||||||||
\(177\) | −7.91868e13 | −0.193565 | ||||||||
\(178\) | 6.42933e14 | 1.51508 | ||||||||
\(179\) | 6.28403e14 | 1.42789 | 0.713943 | − | 0.700204i | \(-0.246907\pi\) | ||||
0.713943 | + | 0.700204i | \(0.246907\pi\) | |||||||
\(180\) | 1.55787e15 | 3.41397 | ||||||||
\(181\) | 7.93746e14 | 1.67792 | 0.838959 | − | 0.544195i | \(-0.183165\pi\) | ||||
0.838959 | + | 0.544195i | \(0.183165\pi\) | |||||||
\(182\) | −3.87440e14 | −0.790207 | ||||||||
\(183\) | −1.44733e15 | −2.84862 | ||||||||
\(184\) | −3.62135e14 | −0.687947 | ||||||||
\(185\) | −8.95393e14 | −1.64209 | ||||||||
\(186\) | −2.49616e14 | −0.442016 | ||||||||
\(187\) | −1.73219e14 | −0.296227 | ||||||||
\(188\) | 3.55508e14 | 0.587251 | ||||||||
\(189\) | −1.36499e15 | −2.17834 | ||||||||
\(190\) | 1.42016e15 | 2.18997 | ||||||||
\(191\) | −9.24881e14 | −1.37838 | −0.689190 | − | 0.724581i | \(-0.742033\pi\) | ||||
−0.689190 | + | 0.724581i | \(0.742033\pi\) | |||||||
\(192\) | 1.80575e15 | 2.60135 | ||||||||
\(193\) | 7.57030e14 | 1.05436 | 0.527182 | − | 0.849752i | \(-0.323249\pi\) | ||||
0.527182 | + | 0.849752i | \(0.323249\pi\) | |||||||
\(194\) | −1.46400e14 | −0.197165 | ||||||||
\(195\) | −9.49755e14 | −1.23705 | ||||||||
\(196\) | −1.71558e14 | −0.216146 | ||||||||
\(197\) | 5.84517e13 | 0.0712470 | ||||||||
\(198\) | −1.25761e15 | −1.48327 | ||||||||
\(199\) | −8.06419e13 | −0.0920483 | −0.0460242 | − | 0.998940i | \(-0.514655\pi\) | ||||
−0.0460242 | + | 0.998940i | \(0.514655\pi\) | |||||||
\(200\) | −1.31923e14 | −0.145756 | ||||||||
\(201\) | 1.21770e15 | 1.30246 | ||||||||
\(202\) | 1.53475e15 | 1.58948 | ||||||||
\(203\) | 6.56773e14 | 0.658706 | ||||||||
\(204\) | 1.63354e15 | 1.58684 | ||||||||
\(205\) | 1.21475e15 | 1.14310 | ||||||||
\(206\) | 1.26955e15 | 1.15748 | ||||||||
\(207\) | 4.70211e15 | 4.15418 | ||||||||
\(208\) | −4.58997e14 | −0.393005 | ||||||||
\(209\) | −6.38104e14 | −0.529591 | ||||||||
\(210\) | 3.63247e15 | 2.92265 | ||||||||
\(211\) | 1.53836e15 | 1.20011 | 0.600055 | − | 0.799959i | \(-0.295145\pi\) | ||||
0.600055 | + | 0.799959i | \(0.295145\pi\) | |||||||
\(212\) | −2.61085e14 | −0.197514 | ||||||||
\(213\) | −2.13427e15 | −1.56596 | ||||||||
\(214\) | −1.61678e14 | −0.115070 | ||||||||
\(215\) | −1.45552e15 | −1.00500 | ||||||||
\(216\) | 1.37002e15 | 0.917864 | ||||||||
\(217\) | −2.26230e14 | −0.147083 | ||||||||
\(218\) | −1.98033e15 | −1.24960 | ||||||||
\(219\) | 5.72349e14 | 0.350570 | ||||||||
\(220\) | 1.05811e15 | 0.629194 | ||||||||
\(221\) | −6.95467e14 | −0.401538 | ||||||||
\(222\) | −6.81651e15 | −3.82180 | ||||||||
\(223\) | −2.65136e15 | −1.44374 | −0.721868 | − | 0.692031i | \(-0.756716\pi\) | ||||
−0.721868 | + | 0.692031i | \(0.756716\pi\) | |||||||
\(224\) | 2.41497e15 | 1.27732 | ||||||||
\(225\) | 1.71295e15 | 0.880151 | ||||||||
\(226\) | −1.72102e15 | −0.859173 | ||||||||
\(227\) | 2.78776e15 | 1.35234 | 0.676172 | − | 0.736744i | \(-0.263638\pi\) | ||||
0.676172 | + | 0.736744i | \(0.263638\pi\) | |||||||
\(228\) | 6.01763e15 | 2.83693 | ||||||||
\(229\) | −1.84796e15 | −0.846762 | −0.423381 | − | 0.905952i | \(-0.639157\pi\) | ||||
−0.423381 | + | 0.905952i | \(0.639157\pi\) | |||||||
\(230\) | −7.10787e15 | −3.16598 | ||||||||
\(231\) | −1.63214e15 | −0.706772 | ||||||||
\(232\) | −6.59197e14 | −0.277551 | ||||||||
\(233\) | −3.24217e15 | −1.32746 | −0.663731 | − | 0.747972i | \(-0.731028\pi\) | ||||
−0.663731 | + | 0.747972i | \(0.731028\pi\) | |||||||
\(234\) | −5.04924e15 | −2.01059 | ||||||||
\(235\) | 1.41904e15 | 0.549609 | ||||||||
\(236\) | 3.54205e14 | 0.133452 | ||||||||
\(237\) | −4.66540e15 | −1.71011 | ||||||||
\(238\) | 2.65992e15 | 0.948675 | ||||||||
\(239\) | −3.88510e15 | −1.34839 | −0.674196 | − | 0.738553i | \(-0.735510\pi\) | ||||
−0.674196 | + | 0.738553i | \(0.735510\pi\) | |||||||
\(240\) | 4.30335e15 | 1.45356 | ||||||||
\(241\) | −5.65616e15 | −1.85956 | −0.929781 | − | 0.368113i | \(-0.880004\pi\) | ||||
−0.929781 | + | 0.368113i | \(0.880004\pi\) | |||||||
\(242\) | 3.83828e15 | 1.22839 | ||||||||
\(243\) | −4.26106e15 | −1.32763 | ||||||||
\(244\) | 6.47394e15 | 1.96397 | ||||||||
\(245\) | −6.84788e14 | −0.202291 | ||||||||
\(246\) | 9.24772e15 | 2.66046 | ||||||||
\(247\) | −2.56196e15 | −0.717865 | ||||||||
\(248\) | 2.27065e14 | 0.0619747 | ||||||||
\(249\) | −4.88999e15 | −1.30021 | ||||||||
\(250\) | 4.22118e15 | 1.09351 | ||||||||
\(251\) | 3.32292e14 | 0.0838766 | 0.0419383 | − | 0.999120i | \(-0.486647\pi\) | ||||
0.0419383 | + | 0.999120i | \(0.486647\pi\) | |||||||
\(252\) | 1.07487e16 | 2.64396 | ||||||||
\(253\) | 3.19370e15 | 0.765615 | ||||||||
\(254\) | −9.72513e15 | −2.27236 | ||||||||
\(255\) | 6.52040e15 | 1.48513 | ||||||||
\(256\) | 1.41782e15 | 0.314819 | ||||||||
\(257\) | 7.18806e15 | 1.55613 | 0.778065 | − | 0.628183i | \(-0.216201\pi\) | ||||
0.778065 | + | 0.628183i | \(0.216201\pi\) | |||||||
\(258\) | −1.10807e16 | −2.33904 | ||||||||
\(259\) | −6.17790e15 | −1.27172 | ||||||||
\(260\) | 4.24828e15 | 0.852877 | ||||||||
\(261\) | 8.55928e15 | 1.67600 | ||||||||
\(262\) | −6.72229e15 | −1.28398 | ||||||||
\(263\) | 6.86451e14 | 0.127908 | 0.0639539 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639539 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(264\) | 1.63816e15 | 0.297804 | ||||||||
\(265\) | −1.04214e15 | −0.184854 | ||||||||
\(266\) | 9.79860e15 | 1.69603 | ||||||||
\(267\) | 1.08743e16 | 1.83686 | ||||||||
\(268\) | −5.44680e15 | −0.897978 | ||||||||
\(269\) | 3.23839e14 | 0.0521122 | 0.0260561 | − | 0.999660i | \(-0.491705\pi\) | ||||
0.0260561 | + | 0.999660i | \(0.491705\pi\) | |||||||
\(270\) | 2.68903e16 | 4.22408 | ||||||||
\(271\) | 1.99742e14 | 0.0306315 | 0.0153158 | − | 0.999883i | \(-0.495125\pi\) | ||||
0.0153158 | + | 0.999883i | \(0.495125\pi\) | |||||||
\(272\) | 3.15117e15 | 0.471818 | ||||||||
\(273\) | −6.55298e15 | −0.958035 | ||||||||
\(274\) | −4.65672e15 | −0.664816 | ||||||||
\(275\) | 1.16344e15 | 0.162212 | ||||||||
\(276\) | −3.01181e16 | −4.10127 | ||||||||
\(277\) | 6.21216e15 | 0.826274 | 0.413137 | − | 0.910669i | \(-0.364433\pi\) | ||||
0.413137 | + | 0.910669i | \(0.364433\pi\) | |||||||
\(278\) | −1.26702e16 | −1.64624 | ||||||||
\(279\) | −2.94831e15 | −0.374236 | ||||||||
\(280\) | −3.30431e15 | −0.409782 | ||||||||
\(281\) | 1.66008e15 | 0.201159 | 0.100579 | − | 0.994929i | \(-0.467930\pi\) | ||||
0.100579 | + | 0.994929i | \(0.467930\pi\) | |||||||
\(282\) | 1.08030e16 | 1.27916 | ||||||||
\(283\) | 8.26471e15 | 0.956348 | 0.478174 | − | 0.878265i | \(-0.341299\pi\) | ||||
0.478174 | + | 0.878265i | \(0.341299\pi\) | |||||||
\(284\) | 9.54665e15 | 1.07965 | ||||||||
\(285\) | 2.40199e16 | 2.65509 | ||||||||
\(286\) | −3.42947e15 | −0.370551 | ||||||||
\(287\) | 8.38134e15 | 0.885281 | ||||||||
\(288\) | 3.14726e16 | 3.24999 | ||||||||
\(289\) | −5.12995e15 | −0.517937 | ||||||||
\(290\) | −1.29385e16 | −1.27731 | ||||||||
\(291\) | −2.47614e15 | −0.239040 | ||||||||
\(292\) | −2.56014e15 | −0.241699 | ||||||||
\(293\) | 4.93579e15 | 0.455740 | 0.227870 | − | 0.973692i | \(-0.426824\pi\) | ||||
0.227870 | + | 0.973692i | \(0.426824\pi\) | |||||||
\(294\) | −5.21320e15 | −0.470812 | ||||||||
\(295\) | 1.41384e15 | 0.124898 | ||||||||
\(296\) | 6.20070e15 | 0.535851 | ||||||||
\(297\) | −1.20823e16 | −1.02149 | ||||||||
\(298\) | 1.07388e16 | 0.888278 | ||||||||
\(299\) | 1.28226e16 | 1.03780 | ||||||||
\(300\) | −1.09718e16 | −0.868942 | ||||||||
\(301\) | −1.00426e16 | −0.778328 | ||||||||
\(302\) | 7.09403e15 | 0.538081 | ||||||||
\(303\) | 2.59581e16 | 1.92706 | ||||||||
\(304\) | 1.16083e16 | 0.843510 | ||||||||
\(305\) | 2.58413e16 | 1.83808 | ||||||||
\(306\) | 3.46649e16 | 2.41379 | ||||||||
\(307\) | 9.84951e15 | 0.671452 | 0.335726 | − | 0.941960i | \(-0.391018\pi\) | ||||
0.335726 | + | 0.941960i | \(0.391018\pi\) | |||||||
\(308\) | 7.30060e15 | 0.487281 | ||||||||
\(309\) | 2.14726e16 | 1.40331 | ||||||||
\(310\) | 4.45676e15 | 0.285212 | ||||||||
\(311\) | −8.08379e15 | −0.506609 | −0.253304 | − | 0.967387i | \(-0.581517\pi\) | ||||
−0.253304 | + | 0.967387i | \(0.581517\pi\) | |||||||
\(312\) | 6.57715e15 | 0.403676 | ||||||||
\(313\) | −4.41406e15 | −0.265338 | −0.132669 | − | 0.991160i | \(-0.542355\pi\) | ||||
−0.132669 | + | 0.991160i | \(0.542355\pi\) | |||||||
\(314\) | 1.31956e16 | 0.776935 | ||||||||
\(315\) | 4.29045e16 | 2.47448 | ||||||||
\(316\) | 2.08685e16 | 1.17903 | ||||||||
\(317\) | 1.09266e14 | 0.00604781 | 0.00302391 | − | 0.999995i | \(-0.499037\pi\) | ||||
0.00302391 | + | 0.999995i | \(0.499037\pi\) | |||||||
\(318\) | −7.93368e15 | −0.430228 | ||||||||
\(319\) | 5.81351e15 | 0.308886 | ||||||||
\(320\) | −3.22406e16 | −1.67853 | ||||||||
\(321\) | −2.73455e15 | −0.139509 | ||||||||
\(322\) | −4.90418e16 | −2.45190 | ||||||||
\(323\) | 1.75888e16 | 0.861826 | ||||||||
\(324\) | 5.34318e16 | 2.56600 | ||||||||
\(325\) | 4.67118e15 | 0.219879 | ||||||||
\(326\) | −1.88599e15 | −0.0870212 | ||||||||
\(327\) | −3.34944e16 | −1.51500 | ||||||||
\(328\) | −8.41226e15 | −0.373021 | ||||||||
\(329\) | 9.79088e15 | 0.425646 | ||||||||
\(330\) | 3.21533e16 | 1.37052 | ||||||||
\(331\) | −2.94502e16 | −1.23086 | −0.615428 | − | 0.788193i | \(-0.711017\pi\) | ||||
−0.615428 | + | 0.788193i | \(0.711017\pi\) | |||||||
\(332\) | 2.18731e16 | 0.896421 | ||||||||
\(333\) | −8.05123e16 | −3.23575 | ||||||||
\(334\) | −3.23172e16 | −1.27374 | ||||||||
\(335\) | −2.17414e16 | −0.840418 | ||||||||
\(336\) | 2.96916e16 | 1.12572 | ||||||||
\(337\) | 5.42519e15 | 0.201753 | 0.100877 | − | 0.994899i | \(-0.467835\pi\) | ||||
0.100877 | + | 0.994899i | \(0.467835\pi\) | |||||||
\(338\) | 2.73987e16 | 0.999474 | ||||||||
\(339\) | −2.91084e16 | −1.04165 | ||||||||
\(340\) | −2.91659e16 | −1.02391 | ||||||||
\(341\) | −2.00251e15 | −0.0689716 | ||||||||
\(342\) | 1.27698e17 | 4.31535 | ||||||||
\(343\) | −3.21644e16 | −1.06651 | ||||||||
\(344\) | 1.00796e16 | 0.327955 | ||||||||
\(345\) | −1.20219e17 | −3.83839 | ||||||||
\(346\) | −9.06087e16 | −2.83906 | ||||||||
\(347\) | 6.02544e16 | 1.85288 | 0.926440 | − | 0.376442i | \(-0.122853\pi\) | ||||
0.926440 | + | 0.376442i | \(0.122853\pi\) | |||||||
\(348\) | −5.48242e16 | −1.65465 | ||||||||
\(349\) | 5.56245e16 | 1.64779 | 0.823894 | − | 0.566744i | \(-0.191797\pi\) | ||||
0.823894 | + | 0.566744i | \(0.191797\pi\) | |||||||
\(350\) | −1.78656e16 | −0.519487 | ||||||||
\(351\) | −4.85101e16 | −1.38464 | ||||||||
\(352\) | 2.13764e16 | 0.598972 | ||||||||
\(353\) | −6.91470e16 | −1.90212 | −0.951060 | − | 0.309006i | \(-0.900004\pi\) | ||||
−0.951060 | + | 0.309006i | \(0.900004\pi\) | |||||||
\(354\) | 1.07634e16 | 0.290688 | ||||||||
\(355\) | 3.81062e16 | 1.01044 | ||||||||
\(356\) | −4.86409e16 | −1.26642 | ||||||||
\(357\) | 4.49885e16 | 1.15016 | ||||||||
\(358\) | −8.54149e16 | −2.14434 | ||||||||
\(359\) | 4.60010e16 | 1.13411 | 0.567053 | − | 0.823682i | \(-0.308084\pi\) | ||||
0.567053 | + | 0.823682i | \(0.308084\pi\) | |||||||
\(360\) | −4.30628e16 | −1.04264 | ||||||||
\(361\) | 2.27406e16 | 0.540761 | ||||||||
\(362\) | −1.07889e17 | −2.51983 | ||||||||
\(363\) | 6.49188e16 | 1.48928 | ||||||||
\(364\) | 2.93117e16 | 0.660513 | ||||||||
\(365\) | −1.02190e16 | −0.226206 | ||||||||
\(366\) | 1.96726e17 | 4.27794 | ||||||||
\(367\) | −5.41385e16 | −1.15658 | −0.578292 | − | 0.815830i | \(-0.696281\pi\) | ||||
−0.578292 | + | 0.815830i | \(0.696281\pi\) | |||||||
\(368\) | −5.80993e16 | −1.21944 | ||||||||
\(369\) | 1.09228e17 | 2.25249 | ||||||||
\(370\) | 1.21705e17 | 2.46603 | ||||||||
\(371\) | −7.19040e15 | −0.143160 | ||||||||
\(372\) | 1.88846e16 | 0.369470 | ||||||||
\(373\) | −5.87869e16 | −1.13025 | −0.565123 | − | 0.825007i | \(-0.691171\pi\) | ||||
−0.565123 | + | 0.825007i | \(0.691171\pi\) | |||||||
\(374\) | 2.35446e16 | 0.444862 | ||||||||
\(375\) | 7.13950e16 | 1.32576 | ||||||||
\(376\) | −9.82701e15 | −0.179350 | ||||||||
\(377\) | 2.33410e16 | 0.418698 | ||||||||
\(378\) | 1.85534e17 | 3.27135 | ||||||||
\(379\) | −8.51513e16 | −1.47583 | −0.737915 | − | 0.674894i | \(-0.764190\pi\) | ||||
−0.737915 | + | 0.674894i | \(0.764190\pi\) | |||||||
\(380\) | −1.07442e17 | −1.83054 | ||||||||
\(381\) | −1.64486e17 | −2.75497 | ||||||||
\(382\) | 1.25713e17 | 2.06999 | ||||||||
\(383\) | 8.76814e16 | 1.41943 | 0.709717 | − | 0.704487i | \(-0.248823\pi\) | ||||
0.709717 | + | 0.704487i | \(0.248823\pi\) | |||||||
\(384\) | −8.48505e16 | −1.35052 | ||||||||
\(385\) | 2.91410e16 | 0.456046 | ||||||||
\(386\) | −1.02898e17 | −1.58340 | ||||||||
\(387\) | −1.30878e17 | −1.98036 | ||||||||
\(388\) | 1.10758e16 | 0.164805 | ||||||||
\(389\) | −3.93493e16 | −0.575790 | −0.287895 | − | 0.957662i | \(-0.592955\pi\) | ||||
−0.287895 | + | 0.957662i | \(0.592955\pi\) | |||||||
\(390\) | 1.29094e17 | 1.85775 | ||||||||
\(391\) | −8.80315e16 | −1.24592 | ||||||||
\(392\) | 4.74223e15 | 0.0660121 | ||||||||
\(393\) | −1.13698e17 | −1.55668 | ||||||||
\(394\) | −7.94498e15 | −0.106996 | ||||||||
\(395\) | 8.32983e16 | 1.10346 | ||||||||
\(396\) | 9.51438e16 | 1.23983 | ||||||||
\(397\) | −5.24413e16 | −0.672256 | −0.336128 | − | 0.941816i | \(-0.609118\pi\) | ||||
−0.336128 | + | 0.941816i | \(0.609118\pi\) | |||||||
\(398\) | 1.09611e16 | 0.138234 | ||||||||
\(399\) | 1.65729e17 | 2.05624 | ||||||||
\(400\) | −2.11652e16 | −0.258364 | ||||||||
\(401\) | −1.36499e17 | −1.63942 | −0.819712 | − | 0.572776i | \(-0.805867\pi\) | ||||
−0.819712 | + | 0.572776i | \(0.805867\pi\) | |||||||
\(402\) | −1.65514e17 | −1.95599 | ||||||||
\(403\) | −8.03999e15 | −0.0934916 | ||||||||
\(404\) | −1.16111e17 | −1.32860 | ||||||||
\(405\) | 2.13277e17 | 2.40152 | ||||||||
\(406\) | −8.92711e16 | −0.989217 | ||||||||
\(407\) | −5.46844e16 | −0.596348 | ||||||||
\(408\) | −4.51545e16 | −0.484629 | ||||||||
\(409\) | 3.58350e15 | 0.0378535 | 0.0189267 | − | 0.999821i | \(-0.493975\pi\) | ||||
0.0189267 | + | 0.999821i | \(0.493975\pi\) | |||||||
\(410\) | −1.65113e17 | −1.71667 | ||||||||
\(411\) | −7.87614e16 | −0.806012 | ||||||||
\(412\) | −9.60474e16 | −0.967506 | ||||||||
\(413\) | 9.75499e15 | 0.0967278 | ||||||||
\(414\) | −6.39128e17 | −6.23858 | ||||||||
\(415\) | 8.73081e16 | 0.838962 | ||||||||
\(416\) | 8.58254e16 | 0.811912 | ||||||||
\(417\) | −2.14298e17 | −1.99588 | ||||||||
\(418\) | 8.67335e16 | 0.795318 | ||||||||
\(419\) | −9.84652e16 | −0.888979 | −0.444489 | − | 0.895784i | \(-0.646615\pi\) | ||||
−0.444489 | + | 0.895784i | \(0.646615\pi\) | |||||||
\(420\) | −2.74813e17 | −2.44297 | ||||||||
\(421\) | 6.86393e16 | 0.600813 | 0.300406 | − | 0.953811i | \(-0.402878\pi\) | ||||
0.300406 | + | 0.953811i | \(0.402878\pi\) | |||||||
\(422\) | −2.09099e17 | −1.80228 | ||||||||
\(423\) | 1.27598e17 | 1.08301 | ||||||||
\(424\) | 7.21693e15 | 0.0603218 | ||||||||
\(425\) | −3.20693e16 | −0.263974 | ||||||||
\(426\) | 2.90098e17 | 2.35170 | ||||||||
\(427\) | 1.78296e17 | 1.42351 | ||||||||
\(428\) | 1.22317e16 | 0.0961840 | ||||||||
\(429\) | −5.80044e16 | −0.449251 | ||||||||
\(430\) | 1.97839e17 | 1.50927 | ||||||||
\(431\) | −6.98347e16 | −0.524770 | −0.262385 | − | 0.964963i | \(-0.584509\pi\) | ||||
−0.262385 | + | 0.964963i | \(0.584509\pi\) | |||||||
\(432\) | 2.19800e17 | 1.62699 | ||||||||
\(433\) | −1.17000e17 | −0.853125 | −0.426563 | − | 0.904458i | \(-0.640276\pi\) | ||||
−0.426563 | + | 0.904458i | \(0.640276\pi\) | |||||||
\(434\) | 3.07501e16 | 0.220883 | ||||||||
\(435\) | −2.18835e17 | −1.54859 | ||||||||
\(436\) | 1.49821e17 | 1.04451 | ||||||||
\(437\) | −3.24291e17 | −2.22744 | ||||||||
\(438\) | −7.77959e16 | −0.526471 | ||||||||
\(439\) | 2.34231e17 | 1.56180 | 0.780898 | − | 0.624658i | \(-0.214762\pi\) | ||||
0.780898 | + | 0.624658i | \(0.214762\pi\) | |||||||
\(440\) | −2.92485e16 | −0.192159 | ||||||||
\(441\) | −6.15751e16 | −0.398615 | ||||||||
\(442\) | 9.45305e16 | 0.603014 | ||||||||
\(443\) | −5.03349e16 | −0.316406 | −0.158203 | − | 0.987407i | \(-0.550570\pi\) | ||||
−0.158203 | + | 0.987407i | \(0.550570\pi\) | |||||||
\(444\) | 5.15701e17 | 3.19454 | ||||||||
\(445\) | −1.94154e17 | −1.18524 | ||||||||
\(446\) | 3.60383e17 | 2.16814 | ||||||||
\(447\) | 1.81630e17 | 1.07693 | ||||||||
\(448\) | −2.22449e17 | −1.29994 | ||||||||
\(449\) | 9.14986e16 | 0.527003 | 0.263502 | − | 0.964659i | \(-0.415123\pi\) | ||||
0.263502 | + | 0.964659i | \(0.415123\pi\) | |||||||
\(450\) | −2.32830e17 | −1.32177 | ||||||||
\(451\) | 7.41884e16 | 0.415134 | ||||||||
\(452\) | 1.30203e17 | 0.718159 | ||||||||
\(453\) | 1.19985e17 | 0.652361 | ||||||||
\(454\) | −3.78922e17 | −2.03089 | ||||||||
\(455\) | 1.17000e17 | 0.618175 | ||||||||
\(456\) | −1.66340e17 | −0.866414 | ||||||||
\(457\) | 1.61041e17 | 0.826953 | 0.413477 | − | 0.910515i | \(-0.364314\pi\) | ||||
0.413477 | + | 0.910515i | \(0.364314\pi\) | |||||||
\(458\) | 2.51181e17 | 1.27163 | ||||||||
\(459\) | 3.33039e17 | 1.66231 | ||||||||
\(460\) | 5.37743e17 | 2.64636 | ||||||||
\(461\) | −1.67392e17 | −0.812228 | −0.406114 | − | 0.913823i | \(-0.633116\pi\) | ||||
−0.406114 | + | 0.913823i | \(0.633116\pi\) | |||||||
\(462\) | 2.21846e17 | 1.06140 | ||||||||
\(463\) | 2.38660e17 | 1.12591 | 0.562955 | − | 0.826487i | \(-0.309664\pi\) | ||||
0.562955 | + | 0.826487i | \(0.309664\pi\) | |||||||
\(464\) | −1.05759e17 | −0.491981 | ||||||||
\(465\) | 7.53794e16 | 0.345787 | ||||||||
\(466\) | 4.40687e17 | 1.99353 | ||||||||
\(467\) | −3.59768e17 | −1.60495 | −0.802477 | − | 0.596684i | \(-0.796485\pi\) | ||||
−0.802477 | + | 0.596684i | \(0.796485\pi\) | |||||||
\(468\) | 3.81999e17 | 1.68060 | ||||||||
\(469\) | −1.50008e17 | −0.650864 | ||||||||
\(470\) | −1.92881e17 | −0.825380 | ||||||||
\(471\) | 2.23183e17 | 0.941945 | ||||||||
\(472\) | −9.79098e15 | −0.0407571 | ||||||||
\(473\) | −8.88930e16 | −0.364981 | ||||||||
\(474\) | 6.34139e17 | 2.56818 | ||||||||
\(475\) | −1.18137e17 | −0.471929 | ||||||||
\(476\) | −2.01235e17 | −0.792972 | ||||||||
\(477\) | −9.37076e16 | −0.364255 | ||||||||
\(478\) | 5.28077e17 | 2.02496 | ||||||||
\(479\) | −3.21916e17 | −1.21776 | −0.608880 | − | 0.793262i | \(-0.708381\pi\) | ||||
−0.608880 | + | 0.793262i | \(0.708381\pi\) | |||||||
\(480\) | −8.04661e17 | −3.00293 | ||||||||
\(481\) | −2.19556e17 | −0.808355 | ||||||||
\(482\) | 7.68806e17 | 2.79261 | ||||||||
\(483\) | −8.29469e17 | −2.97265 | ||||||||
\(484\) | −2.90384e17 | −1.02678 | ||||||||
\(485\) | 4.42101e16 | 0.154241 | ||||||||
\(486\) | 5.79179e17 | 1.99378 | ||||||||
\(487\) | 3.09460e17 | 1.05115 | 0.525577 | − | 0.850746i | \(-0.323850\pi\) | ||||
0.525577 | + | 0.850746i | \(0.323850\pi\) | |||||||
\(488\) | −1.78953e17 | −0.599807 | ||||||||
\(489\) | −3.18987e16 | −0.105503 | ||||||||
\(490\) | 9.30790e16 | 0.303792 | ||||||||
\(491\) | 4.75038e17 | 1.53003 | 0.765013 | − | 0.644015i | \(-0.222733\pi\) | ||||
0.765013 | + | 0.644015i | \(0.222733\pi\) | |||||||
\(492\) | −6.99633e17 | −2.22381 | ||||||||
\(493\) | −1.60244e17 | −0.502664 | ||||||||
\(494\) | 3.48232e17 | 1.07806 | ||||||||
\(495\) | 3.79774e17 | 1.16036 | ||||||||
\(496\) | 3.64293e16 | 0.109855 | ||||||||
\(497\) | 2.62920e17 | 0.782540 | ||||||||
\(498\) | 6.64666e17 | 1.95260 | ||||||||
\(499\) | −1.96792e17 | −0.570628 | −0.285314 | − | 0.958434i | \(-0.592098\pi\) | ||||
−0.285314 | + | 0.958434i | \(0.592098\pi\) | |||||||
\(500\) | −3.19352e17 | −0.914039 | ||||||||
\(501\) | −5.46597e17 | −1.54427 | ||||||||
\(502\) | −4.51664e16 | −0.125962 | ||||||||
\(503\) | 5.05386e17 | 1.39133 | 0.695667 | − | 0.718365i | \(-0.255109\pi\) | ||||
0.695667 | + | 0.718365i | \(0.255109\pi\) | |||||||
\(504\) | −2.97118e17 | −0.807478 | ||||||||
\(505\) | −4.63467e17 | −1.24344 | ||||||||
\(506\) | −4.34099e17 | −1.14977 | ||||||||
\(507\) | 4.63408e17 | 1.21175 | ||||||||
\(508\) | 7.35751e17 | 1.89940 | ||||||||
\(509\) | −2.34421e17 | −0.597491 | −0.298746 | − | 0.954333i | \(-0.596568\pi\) | ||||
−0.298746 | + | 0.954333i | \(0.596568\pi\) | |||||||
\(510\) | −8.86277e17 | −2.23030 | ||||||||
\(511\) | −7.05075e16 | −0.175186 | ||||||||
\(512\) | −4.95069e17 | −1.21454 | ||||||||
\(513\) | 1.22685e18 | 2.97186 | ||||||||
\(514\) | −9.77027e17 | −2.33693 | ||||||||
\(515\) | −3.83381e17 | −0.905490 | ||||||||
\(516\) | 8.38304e17 | 1.95514 | ||||||||
\(517\) | 8.66652e16 | 0.199598 | ||||||||
\(518\) | 8.39723e17 | 1.90982 | ||||||||
\(519\) | −1.53251e18 | −3.44204 | ||||||||
\(520\) | −1.17432e17 | −0.260473 | ||||||||
\(521\) | 4.94593e17 | 1.08343 | 0.541717 | − | 0.840561i | \(-0.317774\pi\) | ||||
0.541717 | + | 0.840561i | \(0.317774\pi\) | |||||||
\(522\) | −1.16341e18 | −2.51695 | ||||||||
\(523\) | 1.99376e17 | 0.426003 | 0.213002 | − | 0.977052i | \(-0.431676\pi\) | ||||
0.213002 | + | 0.977052i | \(0.431676\pi\) | |||||||
\(524\) | 5.08572e17 | 1.07325 | ||||||||
\(525\) | −3.02170e17 | −0.629819 | ||||||||
\(526\) | −9.33050e16 | −0.192087 | ||||||||
\(527\) | 5.51973e16 | 0.112240 | ||||||||
\(528\) | 2.62819e17 | 0.527881 | ||||||||
\(529\) | 1.11903e18 | 2.22014 | ||||||||
\(530\) | 1.41652e17 | 0.277606 | ||||||||
\(531\) | 1.27130e17 | 0.246113 | ||||||||
\(532\) | −7.41309e17 | −1.41767 | ||||||||
\(533\) | 2.97864e17 | 0.562718 | ||||||||
\(534\) | −1.47807e18 | −2.75852 | ||||||||
\(535\) | 4.88239e16 | 0.0900187 | ||||||||
\(536\) | 1.50561e17 | 0.274247 | ||||||||
\(537\) | −1.44467e18 | −2.59977 | ||||||||
\(538\) | −4.40174e16 | −0.0782600 | ||||||||
\(539\) | −4.18221e16 | −0.0734648 | ||||||||
\(540\) | −2.03438e18 | −3.53079 | ||||||||
\(541\) | −6.86151e17 | −1.17662 | −0.588311 | − | 0.808634i | \(-0.700207\pi\) | ||||
−0.588311 | + | 0.808634i | \(0.700207\pi\) | |||||||
\(542\) | −2.71496e16 | −0.0460011 | ||||||||
\(543\) | −1.82478e18 | −3.05500 | ||||||||
\(544\) | −5.89221e17 | −0.974733 | ||||||||
\(545\) | 5.98024e17 | 0.977556 | ||||||||
\(546\) | 8.90705e17 | 1.43874 | ||||||||
\(547\) | 7.92060e17 | 1.26427 | 0.632136 | − | 0.774858i | \(-0.282178\pi\) | ||||
0.632136 | + | 0.774858i | \(0.282178\pi\) | |||||||
\(548\) | 3.52302e17 | 0.555702 | ||||||||
\(549\) | 2.32360e18 | 3.62195 | ||||||||
\(550\) | −1.58139e17 | −0.243603 | ||||||||
\(551\) | −5.90308e17 | −0.898656 | ||||||||
\(552\) | 8.32529e17 | 1.25255 | ||||||||
\(553\) | 5.74729e17 | 0.854574 | ||||||||
\(554\) | −8.44380e17 | −1.24086 | ||||||||
\(555\) | 2.05846e18 | 2.98977 | ||||||||
\(556\) | 9.58562e17 | 1.37605 | ||||||||
\(557\) | 1.05547e18 | 1.49758 | 0.748788 | − | 0.662809i | \(-0.230636\pi\) | ||||
0.748788 | + | 0.662809i | \(0.230636\pi\) | |||||||
\(558\) | 4.00745e17 | 0.562012 | ||||||||
\(559\) | −3.56902e17 | −0.494734 | ||||||||
\(560\) | −5.30128e17 | −0.726371 | ||||||||
\(561\) | 3.98221e17 | 0.539344 | ||||||||
\(562\) | −2.25645e17 | −0.302092 | ||||||||
\(563\) | −6.65481e17 | −0.880707 | −0.440353 | − | 0.897825i | \(-0.645147\pi\) | ||||
−0.440353 | + | 0.897825i | \(0.645147\pi\) | |||||||
\(564\) | −8.17295e17 | −1.06921 | ||||||||
\(565\) | 5.19716e17 | 0.672126 | ||||||||
\(566\) | −1.12337e18 | −1.43620 | ||||||||
\(567\) | 1.47154e18 | 1.85987 | ||||||||
\(568\) | −2.63890e17 | −0.329730 | ||||||||
\(569\) | 4.49546e16 | 0.0555321 | 0.0277660 | − | 0.999614i | \(-0.491161\pi\) | ||||
0.0277660 | + | 0.999614i | \(0.491161\pi\) | |||||||
\(570\) | −3.26487e18 | −3.98730 | ||||||||
\(571\) | 1.05238e17 | 0.127069 | 0.0635344 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635344 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(572\) | 2.59456e17 | 0.309734 | ||||||||
\(573\) | 2.12625e18 | 2.50963 | ||||||||
\(574\) | −1.13922e18 | −1.32948 | ||||||||
\(575\) | 5.91273e17 | 0.682255 | ||||||||
\(576\) | −2.89903e18 | −3.30755 | ||||||||
\(577\) | 1.43150e18 | 1.61491 | 0.807455 | − | 0.589929i | \(-0.200844\pi\) | ||||
0.807455 | + | 0.589929i | \(0.200844\pi\) | |||||||
\(578\) | 6.97282e17 | 0.777817 | ||||||||
\(579\) | −1.74037e18 | −1.91969 | ||||||||
\(580\) | 9.78856e17 | 1.06767 | ||||||||
\(581\) | 6.02396e17 | 0.649736 | ||||||||
\(582\) | 3.36565e17 | 0.358980 | ||||||||
\(583\) | −6.36467e16 | −0.0671321 | ||||||||
\(584\) | 7.07676e16 | 0.0738161 | ||||||||
\(585\) | 1.52478e18 | 1.57287 | ||||||||
\(586\) | −6.70891e17 | −0.684412 | ||||||||
\(587\) | 1.54283e18 | 1.55657 | 0.778287 | − | 0.627909i | \(-0.216089\pi\) | ||||
0.778287 | + | 0.627909i | \(0.216089\pi\) | |||||||
\(588\) | 3.94403e17 | 0.393539 | ||||||||
\(589\) | 2.03336e17 | 0.200662 | ||||||||
\(590\) | −1.92174e17 | −0.187567 | ||||||||
\(591\) | −1.34377e17 | −0.129720 | ||||||||
\(592\) | 9.94811e17 | 0.949838 | ||||||||
\(593\) | 5.65418e17 | 0.533967 | 0.266983 | − | 0.963701i | \(-0.413973\pi\) | ||||
0.266983 | + | 0.963701i | \(0.413973\pi\) | |||||||
\(594\) | 1.64228e18 | 1.53403 | ||||||||
\(595\) | −8.03245e17 | −0.742144 | ||||||||
\(596\) | −8.12437e17 | −0.742488 | ||||||||
\(597\) | 1.85391e17 | 0.167593 | ||||||||
\(598\) | −1.74289e18 | −1.55852 | ||||||||
\(599\) | −1.07258e18 | −0.948757 | −0.474379 | − | 0.880321i | \(-0.657327\pi\) | ||||
−0.474379 | + | 0.880321i | \(0.657327\pi\) | |||||||
\(600\) | 3.03285e17 | 0.265379 | ||||||||
\(601\) | −1.26289e18 | −1.09316 | −0.546578 | − | 0.837408i | \(-0.684070\pi\) | ||||
−0.546578 | + | 0.837408i | \(0.684070\pi\) | |||||||
\(602\) | 1.36502e18 | 1.16886 | ||||||||
\(603\) | −1.95495e18 | −1.65605 | ||||||||
\(604\) | −5.36696e17 | −0.449768 | ||||||||
\(605\) | −1.15909e18 | −0.960964 | ||||||||
\(606\) | −3.52832e18 | −2.89398 | ||||||||
\(607\) | 2.53882e17 | 0.206018 | 0.103009 | − | 0.994680i | \(-0.467153\pi\) | ||||
0.103009 | + | 0.994680i | \(0.467153\pi\) | |||||||
\(608\) | −2.17057e18 | −1.74262 | ||||||||
\(609\) | −1.50989e18 | −1.19931 | ||||||||
\(610\) | −3.51244e18 | −2.76036 | ||||||||
\(611\) | 3.47957e17 | 0.270557 | ||||||||
\(612\) | −2.62256e18 | −2.01763 | ||||||||
\(613\) | 2.35374e18 | 1.79170 | 0.895851 | − | 0.444355i | \(-0.146567\pi\) | ||||
0.895851 | + | 0.444355i | \(0.146567\pi\) | |||||||
\(614\) | −1.33878e18 | −1.00836 | ||||||||
\(615\) | −2.79264e18 | −2.08126 | ||||||||
\(616\) | −2.01804e17 | −0.148818 | ||||||||
\(617\) | 2.31855e18 | 1.69186 | 0.845928 | − | 0.533297i | \(-0.179047\pi\) | ||||
0.845928 | + | 0.533297i | \(0.179047\pi\) | |||||||
\(618\) | −2.91863e18 | −2.10743 | ||||||||
\(619\) | −1.00027e18 | −0.714706 | −0.357353 | − | 0.933969i | \(-0.616321\pi\) | ||||
−0.357353 | + | 0.933969i | \(0.616321\pi\) | |||||||
\(620\) | −3.37174e17 | −0.238401 | ||||||||
\(621\) | −6.14036e18 | −4.29634 | ||||||||
\(622\) | 1.09878e18 | 0.760804 | ||||||||
\(623\) | −1.33959e18 | −0.917912 | ||||||||
\(624\) | 1.05521e18 | 0.715548 | ||||||||
\(625\) | −1.84126e18 | −1.23565 | ||||||||
\(626\) | 5.99975e17 | 0.398474 | ||||||||
\(627\) | 1.46697e18 | 0.964232 | ||||||||
\(628\) | −9.98304e17 | −0.649419 | ||||||||
\(629\) | 1.50733e18 | 0.970463 | ||||||||
\(630\) | −5.83174e18 | −3.71607 | ||||||||
\(631\) | 1.33539e18 | 0.842203 | 0.421101 | − | 0.907014i | \(-0.361644\pi\) | ||||
0.421101 | + | 0.907014i | \(0.361644\pi\) | |||||||
\(632\) | −5.76849e17 | −0.360082 | ||||||||
\(633\) | −3.53660e18 | −2.18505 | ||||||||
\(634\) | −1.48518e16 | −0.00908236 | ||||||||
\(635\) | 2.93681e18 | 1.77765 | ||||||||
\(636\) | 6.00219e17 | 0.359616 | ||||||||
\(637\) | −1.67914e17 | −0.0995821 | ||||||||
\(638\) | −7.90193e17 | −0.463873 | ||||||||
\(639\) | 3.42645e18 | 1.99108 | ||||||||
\(640\) | 1.51496e18 | 0.871427 | ||||||||
\(641\) | −1.31404e18 | −0.748226 | −0.374113 | − | 0.927383i | \(-0.622053\pi\) | ||||
−0.374113 | + | 0.927383i | \(0.622053\pi\) | |||||||
\(642\) | 3.71690e17 | 0.209509 | ||||||||
\(643\) | 6.04768e17 | 0.337456 | 0.168728 | − | 0.985663i | \(-0.446034\pi\) | ||||
0.168728 | + | 0.985663i | \(0.446034\pi\) | |||||||
\(644\) | 3.71024e18 | 2.04948 | ||||||||
\(645\) | 3.34616e18 | 1.82982 | ||||||||
\(646\) | −2.39073e18 | −1.29425 | ||||||||
\(647\) | −1.14773e18 | −0.615125 | −0.307562 | − | 0.951528i | \(-0.599513\pi\) | ||||
−0.307562 | + | 0.951528i | \(0.599513\pi\) | |||||||
\(648\) | −1.47697e18 | −0.783670 | ||||||||
\(649\) | 8.63474e16 | 0.0453585 | ||||||||
\(650\) | −6.34924e17 | −0.330206 | ||||||||
\(651\) | 5.20092e17 | 0.267796 | ||||||||
\(652\) | 1.42684e17 | 0.0727387 | ||||||||
\(653\) | −2.64283e18 | −1.33393 | −0.666966 | − | 0.745088i | \(-0.732407\pi\) | ||||
−0.666966 | + | 0.745088i | \(0.732407\pi\) | |||||||
\(654\) | 4.55268e18 | 2.27516 | ||||||||
\(655\) | 2.03001e18 | 1.00445 | ||||||||
\(656\) | −1.34962e18 | −0.661208 | ||||||||
\(657\) | −9.18876e17 | −0.445740 | ||||||||
\(658\) | −1.33081e18 | −0.639218 | ||||||||
\(659\) | 2.76702e18 | 1.31601 | 0.658003 | − | 0.753015i | \(-0.271401\pi\) | ||||
0.658003 | + | 0.753015i | \(0.271401\pi\) | |||||||
\(660\) | −2.43254e18 | −1.14558 | ||||||||
\(661\) | 2.66733e18 | 1.24385 | 0.621925 | − | 0.783077i | \(-0.286351\pi\) | ||||
0.621925 | + | 0.783077i | \(0.286351\pi\) | |||||||
\(662\) | 4.00299e18 | 1.84845 | ||||||||
\(663\) | 1.59884e18 | 0.731085 | ||||||||
\(664\) | −6.04618e17 | −0.273772 | ||||||||
\(665\) | −2.95900e18 | −1.32679 | ||||||||
\(666\) | 1.09435e19 | 4.85932 | ||||||||
\(667\) | 2.95448e18 | 1.29916 | ||||||||
\(668\) | 2.44494e18 | 1.06469 | ||||||||
\(669\) | 6.09535e18 | 2.62862 | ||||||||
\(670\) | 2.95517e18 | 1.26211 | ||||||||
\(671\) | 1.57821e18 | 0.667524 | ||||||||
\(672\) | −5.55188e18 | −2.32563 | ||||||||
\(673\) | −2.43373e18 | −1.00966 | −0.504828 | − | 0.863220i | \(-0.668444\pi\) | ||||
−0.504828 | + | 0.863220i | \(0.668444\pi\) | |||||||
\(674\) | −7.37412e17 | −0.302985 | ||||||||
\(675\) | −2.23689e18 | −0.910270 | ||||||||
\(676\) | −2.07284e18 | −0.835433 | ||||||||
\(677\) | 1.14719e18 | 0.457940 | 0.228970 | − | 0.973434i | \(-0.426464\pi\) | ||||
0.228970 | + | 0.973434i | \(0.426464\pi\) | |||||||
\(678\) | 3.95653e18 | 1.56430 | ||||||||
\(679\) | 3.05034e17 | 0.119452 | ||||||||
\(680\) | 8.06209e17 | 0.312709 | ||||||||
\(681\) | −6.40891e18 | −2.46222 | ||||||||
\(682\) | 2.72188e17 | 0.103579 | ||||||||
\(683\) | 2.97064e18 | 1.11973 | 0.559867 | − | 0.828582i | \(-0.310852\pi\) | ||||
0.559867 | + | 0.828582i | \(0.310852\pi\) | |||||||
\(684\) | −9.66097e18 | −3.60708 | ||||||||
\(685\) | 1.40624e18 | 0.520082 | ||||||||
\(686\) | 4.37190e18 | 1.60163 | ||||||||
\(687\) | 4.24836e18 | 1.54171 | ||||||||
\(688\) | 1.61713e18 | 0.581326 | ||||||||
\(689\) | −2.55539e17 | −0.0909981 | ||||||||
\(690\) | 1.63406e19 | 5.76433 | ||||||||
\(691\) | 5.48581e18 | 1.91705 | 0.958525 | − | 0.285007i | \(-0.0919961\pi\) | ||||
0.958525 | + | 0.285007i | \(0.0919961\pi\) | |||||||
\(692\) | 6.85497e18 | 2.37310 | ||||||||
\(693\) | 2.62031e18 | 0.898642 | ||||||||
\(694\) | −8.19001e18 | −2.78258 | ||||||||
\(695\) | 3.82618e18 | 1.28785 | ||||||||
\(696\) | 1.51546e18 | 0.505340 | ||||||||
\(697\) | −2.04494e18 | −0.675565 | ||||||||
\(698\) | −7.56069e18 | −2.47458 | ||||||||
\(699\) | 7.45357e18 | 2.41692 | ||||||||
\(700\) | 1.35161e18 | 0.434226 | ||||||||
\(701\) | −2.08495e18 | −0.663632 | −0.331816 | − | 0.943344i | \(-0.607661\pi\) | ||||
−0.331816 | + | 0.943344i | \(0.607661\pi\) | |||||||
\(702\) | 6.59368e18 | 2.07939 | ||||||||
\(703\) | 5.55270e18 | 1.73498 | ||||||||
\(704\) | −1.96903e18 | −0.609581 | ||||||||
\(705\) | −3.26230e18 | −1.00068 | ||||||||
\(706\) | 9.39872e18 | 2.85653 | ||||||||
\(707\) | −3.19776e18 | −0.962986 | ||||||||
\(708\) | −8.14298e17 | −0.242978 | ||||||||
\(709\) | −6.35912e18 | −1.88017 | −0.940084 | − | 0.340942i | \(-0.889254\pi\) | ||||
−0.940084 | + | 0.340942i | \(0.889254\pi\) | |||||||
\(710\) | −5.17954e18 | −1.51744 | ||||||||
\(711\) | 7.49005e18 | 2.17436 | ||||||||
\(712\) | 1.34454e18 | 0.386770 | ||||||||
\(713\) | −1.01769e18 | −0.290091 | ||||||||
\(714\) | −6.11500e18 | −1.72726 | ||||||||
\(715\) | 1.03564e18 | 0.289880 | ||||||||
\(716\) | 6.46203e18 | 1.79240 | ||||||||
\(717\) | 8.93164e18 | 2.45503 | ||||||||
\(718\) | −6.25263e18 | −1.70315 | ||||||||
\(719\) | −2.39740e18 | −0.647148 | −0.323574 | − | 0.946203i | \(-0.604884\pi\) | ||||
−0.323574 | + | 0.946203i | \(0.604884\pi\) | |||||||
\(720\) | −6.90880e18 | −1.84817 | ||||||||
\(721\) | −2.64520e18 | −0.701259 | ||||||||
\(722\) | −3.09099e18 | −0.812093 | ||||||||
\(723\) | 1.30032e19 | 3.38572 | ||||||||
\(724\) | 8.16229e18 | 2.10626 | ||||||||
\(725\) | 1.07630e18 | 0.275255 | ||||||||
\(726\) | −8.82400e18 | −2.23655 | ||||||||
\(727\) | −1.78163e18 | −0.447553 | −0.223777 | − | 0.974640i | \(-0.571839\pi\) | ||||
−0.223777 | + | 0.974640i | \(0.571839\pi\) | |||||||
\(728\) | −8.10237e17 | −0.201724 | ||||||||
\(729\) | 1.51185e18 | 0.373062 | ||||||||
\(730\) | 1.38900e18 | 0.339707 | ||||||||
\(731\) | 2.45026e18 | 0.593949 | ||||||||
\(732\) | −1.48832e19 | −3.57582 | ||||||||
\(733\) | 4.36996e18 | 1.04064 | 0.520321 | − | 0.853971i | \(-0.325812\pi\) | ||||
0.520321 | + | 0.853971i | \(0.325812\pi\) | |||||||
\(734\) | 7.35871e18 | 1.73691 | ||||||||
\(735\) | 1.57429e18 | 0.368313 | ||||||||
\(736\) | 1.08637e19 | 2.51925 | ||||||||
\(737\) | −1.32781e18 | −0.305209 | ||||||||
\(738\) | −1.48467e19 | −3.38270 | ||||||||
\(739\) | −5.10948e18 | −1.15395 | −0.576976 | − | 0.816761i | \(-0.695768\pi\) | ||||
−0.576976 | + | 0.816761i | \(0.695768\pi\) | |||||||
\(740\) | −9.20756e18 | −2.06129 | ||||||||
\(741\) | 5.88982e18 | 1.30702 | ||||||||
\(742\) | 9.77346e17 | 0.214992 | ||||||||
\(743\) | −4.03931e18 | −0.880806 | −0.440403 | − | 0.897800i | \(-0.645164\pi\) | ||||
−0.440403 | + | 0.897800i | \(0.645164\pi\) | |||||||
\(744\) | −5.22011e17 | −0.112838 | ||||||||
\(745\) | −3.24291e18 | −0.694895 | ||||||||
\(746\) | 7.99053e18 | 1.69736 | ||||||||
\(747\) | 7.85061e18 | 1.65318 | ||||||||
\(748\) | −1.78125e18 | −0.371848 | ||||||||
\(749\) | 3.36868e17 | 0.0697152 | ||||||||
\(750\) | −9.70428e18 | −1.99097 | ||||||||
\(751\) | 7.63199e18 | 1.55231 | 0.776154 | − | 0.630543i | \(-0.217168\pi\) | ||||
0.776154 | + | 0.630543i | \(0.217168\pi\) | |||||||
\(752\) | −1.57660e18 | −0.317911 | ||||||||
\(753\) | −7.63922e17 | −0.152715 | ||||||||
\(754\) | −3.17260e18 | −0.628784 | ||||||||
\(755\) | −2.14227e18 | −0.420938 | ||||||||
\(756\) | −1.40365e19 | −2.73443 | ||||||||
\(757\) | 6.10723e18 | 1.17956 | 0.589781 | − | 0.807563i | \(-0.299214\pi\) | ||||
0.589781 | + | 0.807563i | \(0.299214\pi\) | |||||||
\(758\) | 1.15741e19 | 2.21634 | ||||||||
\(759\) | −7.34214e18 | −1.39396 | ||||||||
\(760\) | 2.96991e18 | 0.559056 | ||||||||
\(761\) | 9.05524e18 | 1.69005 | 0.845025 | − | 0.534726i | \(-0.179585\pi\) | ||||
0.845025 | + | 0.534726i | \(0.179585\pi\) | |||||||
\(762\) | 2.23576e19 | 4.13730 | ||||||||
\(763\) | 4.12616e18 | 0.757071 | ||||||||
\(764\) | −9.51078e18 | −1.73025 | ||||||||
\(765\) | −1.04681e19 | −1.88830 | ||||||||
\(766\) | −1.19180e19 | −2.13165 | ||||||||
\(767\) | 3.46682e17 | 0.0614839 | ||||||||
\(768\) | −3.25949e18 | −0.573194 | ||||||||
\(769\) | 9.89304e17 | 0.172508 | 0.0862539 | − | 0.996273i | \(-0.472510\pi\) | ||||
0.0862539 | + | 0.996273i | \(0.472510\pi\) | |||||||
\(770\) | −3.96095e18 | −0.684872 | ||||||||
\(771\) | −1.65250e19 | −2.83326 | ||||||||
\(772\) | 7.78473e18 | 1.32352 | ||||||||
\(773\) | 8.42772e18 | 1.42083 | 0.710417 | − | 0.703781i | \(-0.248506\pi\) | ||||
0.710417 | + | 0.703781i | \(0.248506\pi\) | |||||||
\(774\) | 1.77894e19 | 2.97403 | ||||||||
\(775\) | −3.70738e17 | −0.0614620 | ||||||||
\(776\) | −3.06159e17 | −0.0503323 | ||||||||
\(777\) | 1.42027e19 | 2.31544 | ||||||||
\(778\) | 5.34850e18 | 0.864698 | ||||||||
\(779\) | −7.53315e18 | −1.20777 | ||||||||
\(780\) | −9.76657e18 | −1.55284 | ||||||||
\(781\) | 2.32726e18 | 0.366956 | ||||||||
\(782\) | 1.19656e19 | 1.87107 | ||||||||
\(783\) | −1.11773e19 | −1.73335 | ||||||||
\(784\) | 7.60822e17 | 0.117012 | ||||||||
\(785\) | −3.98481e18 | −0.607792 | ||||||||
\(786\) | 1.54542e19 | 2.33776 | ||||||||
\(787\) | −2.05174e18 | −0.307812 | −0.153906 | − | 0.988085i | \(-0.549185\pi\) | ||||
−0.153906 | + | 0.988085i | \(0.549185\pi\) | |||||||
\(788\) | 6.01074e17 | 0.0894350 | ||||||||
\(789\) | −1.57811e18 | −0.232883 | ||||||||
\(790\) | −1.13222e19 | −1.65712 | ||||||||
\(791\) | 3.58586e18 | 0.520530 | ||||||||
\(792\) | −2.62998e18 | −0.378650 | ||||||||
\(793\) | 6.33643e18 | 0.904835 | ||||||||
\(794\) | 7.12801e18 | 1.00957 | ||||||||
\(795\) | 2.39582e18 | 0.336565 | ||||||||
\(796\) | −8.29261e17 | −0.115546 | ||||||||
\(797\) | −1.27644e18 | −0.176409 | −0.0882043 | − | 0.996102i | \(-0.528113\pi\) | ||||
−0.0882043 | + | 0.996102i | \(0.528113\pi\) | |||||||
\(798\) | −2.25265e19 | −3.08798 | ||||||||
\(799\) | −2.38885e18 | −0.324814 | ||||||||
\(800\) | 3.95756e18 | 0.533756 | ||||||||
\(801\) | −1.74580e19 | −2.33552 | ||||||||
\(802\) | 1.85535e19 | 2.46202 | ||||||||
\(803\) | −6.24105e17 | −0.0821499 | ||||||||
\(804\) | 1.25219e19 | 1.63496 | ||||||||
\(805\) | 1.48097e19 | 1.91811 | ||||||||
\(806\) | 1.09282e18 | 0.140402 | ||||||||
\(807\) | −7.44489e17 | −0.0948812 | ||||||||
\(808\) | 3.20956e18 | 0.405762 | ||||||||
\(809\) | −1.17915e19 | −1.47878 | −0.739392 | − | 0.673275i | \(-0.764887\pi\) | ||||
−0.739392 | + | 0.673275i | \(0.764887\pi\) | |||||||
\(810\) | −2.89894e19 | −3.60651 | ||||||||
\(811\) | −8.89407e18 | −1.09765 | −0.548826 | − | 0.835937i | \(-0.684925\pi\) | ||||
−0.548826 | + | 0.835937i | \(0.684925\pi\) | |||||||
\(812\) | 6.75377e18 | 0.826860 | ||||||||
\(813\) | −4.59196e17 | −0.0557711 | ||||||||
\(814\) | 7.43291e18 | 0.895571 | ||||||||
\(815\) | 5.69534e17 | 0.0680762 | ||||||||
\(816\) | −7.24438e18 | −0.859044 | ||||||||
\(817\) | 9.02626e18 | 1.06185 | ||||||||
\(818\) | −4.87082e17 | −0.0568468 | ||||||||
\(819\) | 1.05204e19 | 1.21812 | ||||||||
\(820\) | 1.24916e19 | 1.43492 | ||||||||
\(821\) | −6.60331e18 | −0.752543 | −0.376272 | − | 0.926509i | \(-0.622794\pi\) | ||||
−0.376272 | + | 0.926509i | \(0.622794\pi\) | |||||||
\(822\) | 1.07055e19 | 1.21044 | ||||||||
\(823\) | 7.28751e18 | 0.817486 | 0.408743 | − | 0.912650i | \(-0.365967\pi\) | ||||
0.408743 | + | 0.912650i | \(0.365967\pi\) | |||||||
\(824\) | 2.65496e18 | 0.295482 | ||||||||
\(825\) | −2.67469e18 | −0.295340 | ||||||||
\(826\) | −1.32593e18 | −0.145262 | ||||||||
\(827\) | 8.78024e18 | 0.954379 | 0.477189 | − | 0.878800i | \(-0.341656\pi\) | ||||
0.477189 | + | 0.878800i | \(0.341656\pi\) | |||||||
\(828\) | 4.83530e19 | 5.21466 | ||||||||
\(829\) | 6.95471e18 | 0.744174 | 0.372087 | − | 0.928198i | \(-0.378642\pi\) | ||||
0.372087 | + | 0.928198i | \(0.378642\pi\) | |||||||
\(830\) | −1.18672e19 | −1.25992 | ||||||||
\(831\) | −1.42814e19 | −1.50440 | ||||||||
\(832\) | −7.90560e18 | −0.826292 | ||||||||
\(833\) | 1.15279e18 | 0.119552 | ||||||||
\(834\) | 2.91282e19 | 2.99733 | ||||||||
\(835\) | 9.75920e18 | 0.996442 | ||||||||
\(836\) | −6.56179e18 | −0.664785 | ||||||||
\(837\) | 3.85012e18 | 0.387042 | ||||||||
\(838\) | 1.33837e19 | 1.33503 | ||||||||
\(839\) | 6.80740e18 | 0.673796 | 0.336898 | − | 0.941541i | \(-0.390622\pi\) | ||||
0.336898 | + | 0.941541i | \(0.390622\pi\) | |||||||
\(840\) | 7.59643e18 | 0.746095 | ||||||||
\(841\) | −4.88257e18 | −0.475855 | ||||||||
\(842\) | −9.32971e18 | −0.902276 | ||||||||
\(843\) | −3.81644e18 | −0.366252 | ||||||||
\(844\) | 1.58193e19 | 1.50647 | ||||||||
\(845\) | −8.27390e18 | −0.781883 | ||||||||
\(846\) | −1.73436e19 | −1.62641 | ||||||||
\(847\) | −7.99732e18 | −0.744222 | ||||||||
\(848\) | 1.15785e18 | 0.106925 | ||||||||
\(849\) | −1.90001e19 | −1.74123 | ||||||||
\(850\) | 4.35897e18 | 0.396425 | ||||||||
\(851\) | −2.77912e19 | −2.50821 | ||||||||
\(852\) | −2.19472e19 | −1.96572 | ||||||||
\(853\) | −7.32734e18 | −0.651295 | −0.325647 | − | 0.945491i | \(-0.605582\pi\) | ||||
−0.325647 | + | 0.945491i | \(0.605582\pi\) | |||||||
\(854\) | −2.42346e19 | −2.13776 | ||||||||
\(855\) | −3.85626e19 | −3.37587 | ||||||||
\(856\) | −3.38111e17 | −0.0293751 | ||||||||
\(857\) | −1.47181e19 | −1.26905 | −0.634523 | − | 0.772904i | \(-0.718803\pi\) | ||||
−0.634523 | + | 0.772904i | \(0.718803\pi\) | |||||||
\(858\) | 7.88418e18 | 0.674666 | ||||||||
\(859\) | −1.13234e19 | −0.961663 | −0.480831 | − | 0.876813i | \(-0.659665\pi\) | ||||
−0.480831 | + | 0.876813i | \(0.659665\pi\) | |||||||
\(860\) | −1.49675e19 | −1.26156 | ||||||||
\(861\) | −1.92682e19 | −1.61184 | ||||||||
\(862\) | 9.49219e18 | 0.788078 | ||||||||
\(863\) | 6.25098e18 | 0.515084 | 0.257542 | − | 0.966267i | \(-0.417087\pi\) | ||||
0.257542 | + | 0.966267i | \(0.417087\pi\) | |||||||
\(864\) | −4.10993e19 | −3.36120 | ||||||||
\(865\) | 2.73622e19 | 2.22098 | ||||||||
\(866\) | 1.59030e19 | 1.28119 | ||||||||
\(867\) | 1.17935e19 | 0.943013 | ||||||||
\(868\) | −2.32639e18 | −0.184631 | ||||||||
\(869\) | 5.08728e18 | 0.400735 | ||||||||
\(870\) | 2.97449e19 | 2.32561 | ||||||||
\(871\) | −5.33111e18 | −0.413714 | ||||||||
\(872\) | −4.14138e18 | −0.318998 | ||||||||
\(873\) | 3.97530e18 | 0.303933 | ||||||||
\(874\) | 4.40788e19 | 3.34507 | ||||||||
\(875\) | −8.79512e18 | −0.662505 | ||||||||
\(876\) | 5.88562e18 | 0.440063 | ||||||||
\(877\) | −2.98789e17 | −0.0221752 | −0.0110876 | − | 0.999939i | \(-0.503529\pi\) | ||||
−0.0110876 | + | 0.999939i | \(0.503529\pi\) | |||||||
\(878\) | −3.18375e19 | −2.34544 | ||||||||
\(879\) | −1.13471e19 | −0.829771 | ||||||||
\(880\) | −4.69249e18 | −0.340617 | ||||||||
\(881\) | 2.12640e19 | 1.53215 | 0.766074 | − | 0.642752i | \(-0.222207\pi\) | ||||
0.766074 | + | 0.642752i | \(0.222207\pi\) | |||||||
\(882\) | 8.36951e18 | 0.598624 | ||||||||
\(883\) | 2.28861e19 | 1.62490 | 0.812452 | − | 0.583028i | \(-0.198132\pi\) | ||||
0.812452 | + | 0.583028i | \(0.198132\pi\) | |||||||
\(884\) | −7.15167e18 | −0.504043 | ||||||||
\(885\) | −3.25034e18 | −0.227404 | ||||||||
\(886\) | 6.84171e18 | 0.475166 | ||||||||
\(887\) | −1.68688e18 | −0.116300 | −0.0581501 | − | 0.998308i | \(-0.518520\pi\) | ||||
−0.0581501 | + | 0.998308i | \(0.518520\pi\) | |||||||
\(888\) | −1.42551e19 | −0.975630 | ||||||||
\(889\) | 2.02630e19 | 1.37671 | ||||||||
\(890\) | 2.63901e19 | 1.77994 | ||||||||
\(891\) | 1.30255e19 | 0.872146 | ||||||||
\(892\) | −2.72647e19 | −1.81229 | ||||||||
\(893\) | −8.80005e18 | −0.580699 | ||||||||
\(894\) | −2.46879e19 | −1.61730 | ||||||||
\(895\) | 2.57937e19 | 1.67751 | ||||||||
\(896\) | 1.04527e19 | 0.674879 | ||||||||
\(897\) | −2.94784e19 | −1.88953 | ||||||||
\(898\) | −1.24368e19 | −0.791432 | ||||||||
\(899\) | −1.85251e18 | −0.117037 | ||||||||
\(900\) | 1.76147e19 | 1.10484 | ||||||||
\(901\) | 1.75437e18 | 0.109247 | ||||||||
\(902\) | −1.00840e19 | −0.623431 | ||||||||
\(903\) | 2.30873e19 | 1.41711 | ||||||||
\(904\) | −3.59909e18 | −0.219330 | ||||||||
\(905\) | 3.25804e19 | 1.97125 | ||||||||
\(906\) | −1.63088e19 | −0.979690 | ||||||||
\(907\) | 9.26728e18 | 0.552719 | 0.276360 | − | 0.961054i | \(-0.410872\pi\) | ||||
0.276360 | + | 0.961054i | \(0.410872\pi\) | |||||||
\(908\) | 2.86672e19 | 1.69757 | ||||||||
\(909\) | −4.16742e19 | −2.45021 | ||||||||
\(910\) | −1.59031e19 | −0.928350 | ||||||||
\(911\) | −2.08939e19 | −1.21102 | −0.605508 | − | 0.795839i | \(-0.707030\pi\) | ||||
−0.605508 | + | 0.795839i | \(0.707030\pi\) | |||||||
\(912\) | −2.66869e19 | −1.53579 | ||||||||
\(913\) | 5.33218e18 | 0.304680 | ||||||||
\(914\) | −2.18893e19 | −1.24188 | ||||||||
\(915\) | −5.94077e19 | −3.34661 | ||||||||
\(916\) | −1.90030e19 | −1.06292 | ||||||||
\(917\) | 1.40063e19 | 0.777901 | ||||||||
\(918\) | −4.52679e19 | −2.49639 | ||||||||
\(919\) | −6.57630e18 | −0.360106 | −0.180053 | − | 0.983657i | \(-0.557627\pi\) | ||||
−0.180053 | + | 0.983657i | \(0.557627\pi\) | |||||||
\(920\) | −1.48644e19 | −0.808212 | ||||||||
\(921\) | −2.26435e19 | −1.22252 | ||||||||
\(922\) | 2.27525e19 | 1.21977 | ||||||||
\(923\) | 9.34388e18 | 0.497412 | ||||||||
\(924\) | −1.67837e19 | −0.887197 | ||||||||
\(925\) | −1.01241e19 | −0.531418 | ||||||||
\(926\) | −3.24396e19 | −1.69085 | ||||||||
\(927\) | −3.44730e19 | −1.78427 | ||||||||
\(928\) | 1.97752e19 | 1.01639 | ||||||||
\(929\) | −1.70376e19 | −0.869572 | −0.434786 | − | 0.900534i | \(-0.643176\pi\) | ||||
−0.434786 | + | 0.900534i | \(0.643176\pi\) | |||||||
\(930\) | −1.02459e19 | −0.519289 | ||||||||
\(931\) | 4.24665e18 | 0.213734 | ||||||||
\(932\) | −3.33400e19 | −1.66634 | ||||||||
\(933\) | 1.85842e19 | 0.922387 | ||||||||
\(934\) | 4.89010e19 | 2.41025 | ||||||||
\(935\) | −7.11002e18 | −0.348013 | ||||||||
\(936\) | −1.05593e19 | −0.513263 | ||||||||
\(937\) | −1.08181e18 | −0.0522210 | −0.0261105 | − | 0.999659i | \(-0.508312\pi\) | ||||
−0.0261105 | + | 0.999659i | \(0.508312\pi\) | |||||||
\(938\) | 2.03896e19 | 0.977441 | ||||||||
\(939\) | 1.01477e19 | 0.483104 | ||||||||
\(940\) | 1.45924e19 | 0.689913 | ||||||||
\(941\) | −1.19027e19 | −0.558871 | −0.279435 | − | 0.960165i | \(-0.590147\pi\) | ||||
−0.279435 | + | 0.960165i | \(0.590147\pi\) | |||||||
\(942\) | −3.03359e19 | −1.41457 | ||||||||
\(943\) | 3.77033e19 | 1.74604 | ||||||||
\(944\) | −1.57082e18 | −0.0722451 | ||||||||
\(945\) | −5.60279e19 | −2.55916 | ||||||||
\(946\) | 1.20827e19 | 0.548113 | ||||||||
\(947\) | −5.44646e18 | −0.245380 | −0.122690 | − | 0.992445i | \(-0.539152\pi\) | ||||
−0.122690 | + | 0.992445i | \(0.539152\pi\) | |||||||
\(948\) | −4.79755e19 | −2.14667 | ||||||||
\(949\) | −2.50576e18 | −0.111355 | ||||||||
\(950\) | 1.60576e19 | 0.708724 | ||||||||
\(951\) | −2.51196e17 | −0.0110113 | ||||||||
\(952\) | 5.56256e18 | 0.242178 | ||||||||
\(953\) | 3.25548e18 | 0.140770 | 0.0703851 | − | 0.997520i | \(-0.477577\pi\) | ||||
0.0703851 | + | 0.997520i | \(0.477577\pi\) | |||||||
\(954\) | 1.27371e19 | 0.547023 | ||||||||
\(955\) | −3.79631e19 | −1.61934 | ||||||||
\(956\) | −3.99515e19 | −1.69261 | ||||||||
\(957\) | −1.33649e19 | −0.562392 | ||||||||
\(958\) | 4.37560e19 | 1.82878 | ||||||||
\(959\) | 9.70258e18 | 0.402779 | ||||||||
\(960\) | 7.41195e19 | 3.05611 | ||||||||
\(961\) | −2.37794e19 | −0.973867 | ||||||||
\(962\) | 2.98429e19 | 1.21395 | ||||||||
\(963\) | 4.39016e18 | 0.177382 | ||||||||
\(964\) | −5.81637e19 | −2.33427 | ||||||||
\(965\) | 3.10734e19 | 1.23869 | ||||||||
\(966\) | 1.12744e20 | 4.46420 | ||||||||
\(967\) | −8.33167e17 | −0.0327688 | −0.0163844 | − | 0.999866i | \(-0.505216\pi\) | ||||
−0.0163844 | + | 0.999866i | \(0.505216\pi\) | |||||||
\(968\) | 8.02682e18 | 0.313584 | ||||||||
\(969\) | −4.04357e19 | −1.56913 | ||||||||
\(970\) | −6.00920e18 | −0.231633 | ||||||||
\(971\) | −1.47868e19 | −0.566172 | −0.283086 | − | 0.959095i | \(-0.591358\pi\) | ||||
−0.283086 | + | 0.959095i | \(0.591358\pi\) | |||||||
\(972\) | −4.38176e19 | −1.66655 | ||||||||
\(973\) | 2.63993e19 | 0.997376 | ||||||||
\(974\) | −4.20629e19 | −1.57858 | ||||||||
\(975\) | −1.07388e19 | −0.400336 | ||||||||
\(976\) | −2.87105e19 | −1.06320 | ||||||||
\(977\) | −1.67964e19 | −0.617876 | −0.308938 | − | 0.951082i | \(-0.599974\pi\) | ||||
−0.308938 | + | 0.951082i | \(0.599974\pi\) | |||||||
\(978\) | 4.33579e18 | 0.158440 | ||||||||
\(979\) | −1.18576e19 | −0.430436 | ||||||||
\(980\) | −7.04185e18 | −0.253932 | ||||||||
\(981\) | 5.37734e19 | 1.92628 | ||||||||
\(982\) | −6.45689e19 | −2.29773 | ||||||||
\(983\) | 1.15643e19 | 0.408809 | 0.204404 | − | 0.978887i | \(-0.434474\pi\) | ||||
0.204404 | + | 0.978887i | \(0.434474\pi\) | |||||||
\(984\) | 1.93393e19 | 0.679162 | ||||||||
\(985\) | 2.39924e18 | 0.0837023 | ||||||||
\(986\) | 2.17810e19 | 0.754880 | ||||||||
\(987\) | −2.25087e19 | −0.774978 | ||||||||
\(988\) | −2.63453e19 | −0.901122 | ||||||||
\(989\) | −4.51763e19 | −1.53509 | ||||||||
\(990\) | −5.16203e19 | −1.74258 | ||||||||
\(991\) | 4.48782e18 | 0.150507 | 0.0752535 | − | 0.997164i | \(-0.476023\pi\) | ||||
0.0752535 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(992\) | −6.81172e18 | −0.226951 | ||||||||
\(993\) | 6.77045e19 | 2.24103 | ||||||||
\(994\) | −3.57370e19 | −1.17519 | ||||||||
\(995\) | −3.31006e18 | −0.108140 | ||||||||
\(996\) | −5.02850e19 | −1.63212 | ||||||||
\(997\) | −1.98245e19 | −0.639268 | −0.319634 | − | 0.947541i | \(-0.603560\pi\) | ||||
−0.319634 | + | 0.947541i | \(0.603560\pi\) | |||||||
\(998\) | 2.67486e19 | 0.856945 | ||||||||
\(999\) | 1.05139e20 | 3.34648 |
(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 | 197.14.a.b.1.15 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.b.1.15 | ✓ | 109 | 1.1 | even | 1 | trivial |