Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,7,Mod(13,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(3.22075717068\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.211968.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 30x^{2} + 207 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.3 | ||
Root | \(-4.38664i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.13 |
Dual form | 14.7.b.a.13.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65685 | 0.707107 | ||||||||
\(3\) | − | 29.9539i | − | 1.10940i | −0.832049 | − | 0.554701i | \(-0.812833\pi\) | ||
0.832049 | − | 0.554701i | \(-0.187167\pi\) | |||||||
\(4\) | 32.0000 | 0.500000 | ||||||||
\(5\) | − | 98.3767i | − | 0.787013i | −0.919322 | − | 0.393507i | \(-0.871262\pi\) | ||
0.919322 | − | 0.393507i | \(-0.128738\pi\) | |||||||
\(6\) | − | 169.445i | − | 0.784466i | ||||||
\(7\) | 195.794 | + | 281.627i | 0.570828 | + | 0.821070i | ||||
\(8\) | 181.019 | 0.353553 | ||||||||
\(9\) | −168.235 | −0.230775 | ||||||||
\(10\) | − | 556.502i | − | 0.556502i | ||||||
\(11\) | −1042.12 | −0.782958 | −0.391479 | − | 0.920187i | \(-0.628037\pi\) | ||||
−0.391479 | + | 0.920187i | \(0.628037\pi\) | |||||||
\(12\) | − | 958.524i | − | 0.554701i | ||||||
\(13\) | 3661.70i | 1.66668i | 0.552758 | + | 0.833342i | \(0.313575\pi\) | ||||
−0.552758 | + | 0.833342i | \(0.686425\pi\) | |||||||
\(14\) | 1107.58 | + | 1593.12i | 0.403636 | + | 0.580584i | ||||
\(15\) | −2946.76 | −0.873115 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | 1856.59i | 0.377893i | 0.981987 | + | 0.188946i | \(0.0605072\pi\) | ||||
−0.981987 | + | 0.188946i | \(0.939493\pi\) | |||||||
\(18\) | −951.679 | −0.163182 | ||||||||
\(19\) | − | 7493.18i | − | 1.09246i | −0.837635 | − | 0.546230i | \(-0.816063\pi\) | ||
0.837635 | − | 0.546230i | \(-0.183937\pi\) | |||||||
\(20\) | − | 3148.05i | − | 0.393507i | ||||||
\(21\) | 8435.82 | − | 5864.79i | 0.910897 | − | 0.633278i | ||||
\(22\) | −5895.11 | −0.553635 | ||||||||
\(23\) | 11639.4 | 0.956638 | 0.478319 | − | 0.878186i | \(-0.341246\pi\) | ||||
0.478319 | + | 0.878186i | \(0.341246\pi\) | |||||||
\(24\) | − | 5422.23i | − | 0.392233i | ||||||
\(25\) | 5947.03 | 0.380610 | ||||||||
\(26\) | 20713.7i | 1.17852i | ||||||||
\(27\) | − | 16797.1i | − | 0.853381i | ||||||
\(28\) | 6265.41 | + | 9012.06i | 0.285414 | + | 0.410535i | ||||
\(29\) | −41697.6 | −1.70969 | −0.854844 | − | 0.518885i | \(-0.826347\pi\) | ||||
−0.854844 | + | 0.518885i | \(0.826347\pi\) | |||||||
\(30\) | −16669.4 | −0.617385 | ||||||||
\(31\) | 22040.5i | 0.739838i | 0.929064 | + | 0.369919i | \(0.120614\pi\) | ||||
−0.929064 | + | 0.369919i | \(0.879386\pi\) | |||||||
\(32\) | 5792.62 | 0.176777 | ||||||||
\(33\) | 31215.5i | 0.868616i | ||||||||
\(34\) | 10502.4i | 0.267211i | ||||||||
\(35\) | 27705.5 | − | 19261.6i | 0.646193 | − | 0.449249i | ||||
\(36\) | −5383.51 | −0.115387 | ||||||||
\(37\) | −49174.8 | −0.970816 | −0.485408 | − | 0.874288i | \(-0.661329\pi\) | ||||
−0.485408 | + | 0.874288i | \(0.661329\pi\) | |||||||
\(38\) | − | 42387.8i | − | 0.772486i | ||||||
\(39\) | 109682. | 1.84902 | ||||||||
\(40\) | − | 17808.1i | − | 0.278251i | ||||||
\(41\) | 18029.8i | 0.261601i | 0.991409 | + | 0.130801i | \(0.0417548\pi\) | ||||
−0.991409 | + | 0.130801i | \(0.958245\pi\) | |||||||
\(42\) | 47720.2 | − | 33176.2i | 0.644102 | − | 0.447795i | ||||
\(43\) | −114355. | −1.43830 | −0.719151 | − | 0.694854i | \(-0.755469\pi\) | ||||
−0.719151 | + | 0.694854i | \(0.755469\pi\) | |||||||
\(44\) | −33347.8 | −0.391479 | ||||||||
\(45\) | 16550.4i | 0.181623i | ||||||||
\(46\) | 65842.4 | 0.676445 | ||||||||
\(47\) | − | 139635.i | − | 1.34493i | −0.740129 | − | 0.672465i | \(-0.765235\pi\) | ||
0.740129 | − | 0.672465i | \(-0.234765\pi\) | |||||||
\(48\) | − | 30672.8i | − | 0.277351i | ||||||
\(49\) | −40978.5 | + | 110282.i | −0.348311 | + | 0.937379i | ||||
\(50\) | 33641.5 | 0.269132 | ||||||||
\(51\) | 55612.0 | 0.419235 | ||||||||
\(52\) | 117175.i | 0.833342i | ||||||||
\(53\) | 124198. | 0.834235 | 0.417117 | − | 0.908853i | \(-0.363040\pi\) | ||||
0.417117 | + | 0.908853i | \(0.363040\pi\) | |||||||
\(54\) | − | 95018.7i | − | 0.603431i | ||||||
\(55\) | 102520.i | 0.616199i | ||||||||
\(56\) | 35442.5 | + | 50979.9i | 0.201818 | + | 0.290292i | ||||
\(57\) | −224450. | −1.21198 | ||||||||
\(58\) | −235877. | −1.20893 | ||||||||
\(59\) | − | 271907.i | − | 1.32393i | −0.749537 | − | 0.661963i | \(-0.769724\pi\) | ||
0.749537 | − | 0.661963i | \(-0.230276\pi\) | |||||||
\(60\) | −94296.4 | −0.436557 | ||||||||
\(61\) | 338552.i | 1.49154i | 0.666202 | + | 0.745771i | \(0.267919\pi\) | ||||
−0.666202 | + | 0.745771i | \(0.732081\pi\) | |||||||
\(62\) | 124680.i | 0.523144i | ||||||||
\(63\) | −32939.3 | − | 47379.4i | −0.131733 | − | 0.189482i | ||||
\(64\) | 32768.0 | 0.125000 | ||||||||
\(65\) | 360226. | 1.31170 | ||||||||
\(66\) | 176581.i | 0.614204i | ||||||||
\(67\) | −106386. | −0.353720 | −0.176860 | − | 0.984236i | \(-0.556594\pi\) | ||||
−0.176860 | + | 0.984236i | \(0.556594\pi\) | |||||||
\(68\) | 59410.8i | 0.188946i | ||||||||
\(69\) | − | 348645.i | − | 1.06130i | ||||||
\(70\) | 156726. | − | 108960.i | 0.456927 | − | 0.317667i | ||||
\(71\) | 216021. | 0.603562 | 0.301781 | − | 0.953377i | \(-0.402419\pi\) | ||||
0.301781 | + | 0.953377i | \(0.402419\pi\) | |||||||
\(72\) | −30453.7 | −0.0815911 | ||||||||
\(73\) | − | 111927.i | − | 0.287718i | −0.989598 | − | 0.143859i | \(-0.954049\pi\) | ||
0.989598 | − | 0.143859i | \(-0.0459512\pi\) | |||||||
\(74\) | −278174. | −0.686471 | ||||||||
\(75\) | − | 178137.i | − | 0.422250i | ||||||
\(76\) | − | 239782.i | − | 0.546230i | ||||||
\(77\) | −204040. | − | 293488.i | −0.446934 | − | 0.642864i | ||||
\(78\) | 620456. | 1.30746 | ||||||||
\(79\) | 451441. | 0.915628 | 0.457814 | − | 0.889048i | \(-0.348632\pi\) | ||||
0.457814 | + | 0.889048i | \(0.348632\pi\) | |||||||
\(80\) | − | 100738.i | − | 0.196753i | ||||||
\(81\) | −625781. | −1.17752 | ||||||||
\(82\) | 101992.i | 0.184980i | ||||||||
\(83\) | 225775.i | 0.394859i | 0.980317 | + | 0.197430i | \(0.0632594\pi\) | ||||
−0.980317 | + | 0.197430i | \(0.936741\pi\) | |||||||
\(84\) | 269946. | − | 187673.i | 0.455449 | − | 0.316639i | ||||
\(85\) | 182645. | 0.297407 | ||||||||
\(86\) | −646890. | −1.01703 | ||||||||
\(87\) | 1.24900e6i | 1.89673i | ||||||||
\(88\) | −188643. | −0.276818 | ||||||||
\(89\) | 411409.i | 0.583585i | 0.956482 | + | 0.291792i | \(0.0942516\pi\) | ||||
−0.956482 | + | 0.291792i | \(0.905748\pi\) | |||||||
\(90\) | 93623.0i | 0.128427i | ||||||||
\(91\) | −1.03123e6 | + | 716939.i | −1.36846 | + | 0.951389i | ||||
\(92\) | 372461. | 0.478319 | ||||||||
\(93\) | 660198. | 0.820778 | ||||||||
\(94\) | − | 789893.i | − | 0.951010i | ||||||
\(95\) | −737154. | −0.859780 | ||||||||
\(96\) | − | 173511.i | − | 0.196117i | ||||||
\(97\) | − | 117248.i | − | 0.128467i | −0.997935 | − | 0.0642333i | \(-0.979540\pi\) | ||
0.997935 | − | 0.0642333i | \(-0.0204602\pi\) | |||||||
\(98\) | −231809. | + | 623847.i | −0.246293 | + | 0.662827i | ||||
\(99\) | 175320. | 0.180687 | ||||||||
\(100\) | 190305. | 0.190305 | ||||||||
\(101\) | − | 706191.i | − | 0.685422i | −0.939441 | − | 0.342711i | \(-0.888655\pi\) | ||
0.939441 | − | 0.342711i | \(-0.111345\pi\) | |||||||
\(102\) | 314589. | 0.296444 | ||||||||
\(103\) | − | 1.61841e6i | − | 1.48107i | −0.672016 | − | 0.740536i | \(-0.734572\pi\) | ||
0.672016 | − | 0.740536i | \(-0.265428\pi\) | |||||||
\(104\) | 662839.i | 0.589262i | ||||||||
\(105\) | −576958. | − | 829888.i | −0.498398 | − | 0.716888i | ||||
\(106\) | 702572. | 0.589893 | ||||||||
\(107\) | 439211. | 0.358527 | 0.179264 | − | 0.983801i | \(-0.442629\pi\) | ||||
0.179264 | + | 0.983801i | \(0.442629\pi\) | |||||||
\(108\) | − | 537507.i | − | 0.426690i | ||||||
\(109\) | 1.80395e6 | 1.39298 | 0.696490 | − | 0.717567i | \(-0.254744\pi\) | ||||
0.696490 | + | 0.717567i | \(0.254744\pi\) | |||||||
\(110\) | 579941.i | 0.435718i | ||||||||
\(111\) | 1.47297e6i | 1.07703i | ||||||||
\(112\) | 200493. | + | 288386.i | 0.142707 | + | 0.205267i | ||||
\(113\) | 1.20195e6 | 0.833014 | 0.416507 | − | 0.909133i | \(-0.363254\pi\) | ||||
0.416507 | + | 0.909133i | \(0.363254\pi\) | |||||||
\(114\) | −1.26968e6 | −0.856998 | ||||||||
\(115\) | − | 1.14505e6i | − | 0.752886i | ||||||
\(116\) | −1.33432e6 | −0.854844 | ||||||||
\(117\) | − | 616025.i | − | 0.384628i | ||||||
\(118\) | − | 1.53814e6i | − | 0.936157i | ||||||
\(119\) | −522865. | + | 363508.i | −0.310276 | + | 0.215712i | ||||
\(120\) | −533421. | −0.308693 | ||||||||
\(121\) | −685552. | −0.386976 | ||||||||
\(122\) | 1.91514e6i | 1.05468i | ||||||||
\(123\) | 540063. | 0.290221 | ||||||||
\(124\) | 705296.i | 0.369919i | ||||||||
\(125\) | − | 2.12218e6i | − | 1.08656i | ||||||
\(126\) | −186333. | − | 268018.i | −0.0931490 | − | 0.133984i | ||||
\(127\) | −1.39321e6 | −0.680150 | −0.340075 | − | 0.940398i | \(-0.610452\pi\) | ||||
−0.340075 | + | 0.940398i | \(0.610452\pi\) | |||||||
\(128\) | 185364. | 0.0883883 | ||||||||
\(129\) | 3.42538e6i | 1.59566i | ||||||||
\(130\) | 2.03775e6 | 0.927513 | ||||||||
\(131\) | 2.60277e6i | 1.15777i | 0.815410 | + | 0.578884i | \(0.196511\pi\) | ||||
−0.815410 | + | 0.578884i | \(0.803489\pi\) | |||||||
\(132\) | 998895.i | 0.434308i | ||||||||
\(133\) | 2.11028e6 | − | 1.46712e6i | 0.896986 | − | 0.623606i | ||||
\(134\) | −601810. | −0.250118 | ||||||||
\(135\) | −1.65244e6 | −0.671622 | ||||||||
\(136\) | 336078.i | 0.133605i | ||||||||
\(137\) | −692462. | −0.269299 | −0.134649 | − | 0.990893i | \(-0.542991\pi\) | ||||
−0.134649 | + | 0.990893i | \(0.542991\pi\) | |||||||
\(138\) | − | 1.97224e6i | − | 0.750450i | ||||||
\(139\) | 481984.i | 0.179469i | 0.995966 | + | 0.0897343i | \(0.0286018\pi\) | ||||
−0.995966 | + | 0.0897343i | \(0.971398\pi\) | |||||||
\(140\) | 886576. | − | 616370.i | 0.323096 | − | 0.224625i | ||||
\(141\) | −4.18260e6 | −1.49207 | ||||||||
\(142\) | 1.22200e6 | 0.426783 | ||||||||
\(143\) | − | 3.81593e6i | − | 1.30494i | ||||||
\(144\) | −172272. | −0.0576936 | ||||||||
\(145\) | 4.10207e6i | 1.34555i | ||||||||
\(146\) | − | 633156.i | − | 0.203447i | ||||||
\(147\) | 3.30336e6 | + | 1.22746e6i | 1.03993 | + | 0.386417i | ||||
\(148\) | −1.57359e6 | −0.485408 | ||||||||
\(149\) | −655599. | −0.198189 | −0.0990945 | − | 0.995078i | \(-0.531595\pi\) | ||||
−0.0990945 | + | 0.995078i | \(0.531595\pi\) | |||||||
\(150\) | − | 1.00769e6i | − | 0.298576i | ||||||
\(151\) | 47651.6 | 0.0138403 | 0.00692017 | − | 0.999976i | \(-0.497797\pi\) | ||||
0.00692017 | + | 0.999976i | \(0.497797\pi\) | |||||||
\(152\) | − | 1.35641e6i | − | 0.386243i | ||||||
\(153\) | − | 312342.i | − | 0.0872080i | ||||||
\(154\) | −1.15423e6 | − | 1.66022e6i | −0.316030 | − | 0.454573i | ||||
\(155\) | 2.16827e6 | 0.582262 | ||||||||
\(156\) | 3.50983e6 | 0.924512 | ||||||||
\(157\) | − | 2.08512e6i | − | 0.538806i | −0.963027 | − | 0.269403i | \(-0.913174\pi\) | ||
0.963027 | − | 0.269403i | \(-0.0868264\pi\) | |||||||
\(158\) | 2.55373e6 | 0.647447 | ||||||||
\(159\) | − | 3.72022e6i | − | 0.925502i | ||||||
\(160\) | − | 569858.i | − | 0.139126i | ||||||
\(161\) | 2.27893e6 | + | 3.27797e6i | 0.546075 | + | 0.785466i | ||||
\(162\) | −3.53995e6 | −0.832631 | ||||||||
\(163\) | 1.59326e6 | 0.367894 | 0.183947 | − | 0.982936i | \(-0.441112\pi\) | ||||
0.183947 | + | 0.982936i | \(0.441112\pi\) | |||||||
\(164\) | 576955.i | 0.130801i | ||||||||
\(165\) | 3.07087e6 | 0.683613 | ||||||||
\(166\) | 1.27718e6i | 0.279208i | ||||||||
\(167\) | − | 1.21740e6i | − | 0.261387i | −0.991423 | − | 0.130693i | \(-0.958280\pi\) | ||
0.991423 | − | 0.130693i | \(-0.0417203\pi\) | |||||||
\(168\) | 1.52705e6 | − | 1.06164e6i | 0.322051 | − | 0.223898i | ||||
\(169\) | −8.58126e6 | −1.77783 | ||||||||
\(170\) | 1.03320e6 | 0.210298 | ||||||||
\(171\) | 1.26061e6i | 0.252112i | ||||||||
\(172\) | −3.65936e6 | −0.719151 | ||||||||
\(173\) | − | 4.61804e6i | − | 0.891907i | −0.895056 | − | 0.445953i | \(-0.852865\pi\) | ||
0.895056 | − | 0.445953i | \(-0.147135\pi\) | |||||||
\(174\) | 7.06544e6i | 1.34119i | ||||||||
\(175\) | 1.16439e6 | + | 1.67485e6i | 0.217263 | + | 0.312508i | ||||
\(176\) | −1.06713e6 | −0.195740 | ||||||||
\(177\) | −8.14465e6 | −1.46877 | ||||||||
\(178\) | 2.32728e6i | 0.412657i | ||||||||
\(179\) | −2.87045e6 | −0.500484 | −0.250242 | − | 0.968183i | \(-0.580510\pi\) | ||||
−0.250242 | + | 0.968183i | \(0.580510\pi\) | |||||||
\(180\) | 529612.i | 0.0908113i | ||||||||
\(181\) | 6.81242e6i | 1.14886i | 0.818555 | + | 0.574428i | \(0.194776\pi\) | ||||
−0.818555 | + | 0.574428i | \(0.805224\pi\) | |||||||
\(182\) | −5.83354e6 | + | 4.05562e6i | −0.967650 | + | 0.672734i | ||||
\(183\) | 1.01409e7 | 1.65472 | ||||||||
\(184\) | 2.10696e6 | 0.338222 | ||||||||
\(185\) | 4.83765e6i | 0.764045i | ||||||||
\(186\) | 3.73465e6 | 0.580378 | ||||||||
\(187\) | − | 1.93478e6i | − | 0.295874i | ||||||
\(188\) | − | 4.46831e6i | − | 0.672465i | ||||||
\(189\) | 4.73051e6 | − | 3.28877e6i | 0.700685 | − | 0.487134i | ||||
\(190\) | −4.16997e6 | −0.607956 | ||||||||
\(191\) | −5.00597e6 | −0.718435 | −0.359218 | − | 0.933254i | \(-0.616956\pi\) | ||||
−0.359218 | + | 0.933254i | \(0.616956\pi\) | |||||||
\(192\) | − | 981529.i | − | 0.138675i | ||||||
\(193\) | 1.94995e6 | 0.271238 | 0.135619 | − | 0.990761i | \(-0.456698\pi\) | ||||
0.135619 | + | 0.990761i | \(0.456698\pi\) | |||||||
\(194\) | − | 663255.i | − | 0.0908396i | ||||||
\(195\) | − | 1.07902e7i | − | 1.45521i | ||||||
\(196\) | −1.31131e6 | + | 3.52901e6i | −0.174156 | + | 0.468689i | ||||
\(197\) | 1.16023e7 | 1.51756 | 0.758782 | − | 0.651345i | \(-0.225795\pi\) | ||||
0.758782 | + | 0.651345i | \(0.225795\pi\) | |||||||
\(198\) | 991761. | 0.127765 | ||||||||
\(199\) | − | 727194.i | − | 0.0922765i | −0.998935 | − | 0.0461382i | \(-0.985309\pi\) | ||
0.998935 | − | 0.0461382i | \(-0.0146915\pi\) | |||||||
\(200\) | 1.07653e6 | 0.134566 | ||||||||
\(201\) | 3.18667e6i | 0.392418i | ||||||||
\(202\) | − | 3.99482e6i | − | 0.484666i | ||||||
\(203\) | −8.16414e6 | − | 1.17432e7i | −0.975938 | − | 1.40377i | ||||
\(204\) | 1.77958e6 | 0.209618 | ||||||||
\(205\) | 1.77371e6 | 0.205884 | ||||||||
\(206\) | − | 9.15510e6i | − | 1.04728i | ||||||
\(207\) | −1.95815e6 | −0.220768 | ||||||||
\(208\) | 3.74958e6i | 0.416671i | ||||||||
\(209\) | 7.80878e6i | 0.855350i | ||||||||
\(210\) | −3.26377e6 | − | 4.69455e6i | −0.352421 | − | 0.506916i | ||||
\(211\) | 5.82550e6 | 0.620134 | 0.310067 | − | 0.950715i | \(-0.399648\pi\) | ||||
0.310067 | + | 0.950715i | \(0.399648\pi\) | |||||||
\(212\) | 3.97435e6 | 0.417117 | ||||||||
\(213\) | − | 6.47068e6i | − | 0.669593i | ||||||
\(214\) | 2.48455e6 | 0.253517 | ||||||||
\(215\) | 1.12499e7i | 1.13196i | ||||||||
\(216\) | − | 3.04060e6i | − | 0.301716i | ||||||
\(217\) | −6.20720e6 | + | 4.31540e6i | −0.607458 | + | 0.422320i | ||||
\(218\) | 1.02047e7 | 0.984985 | ||||||||
\(219\) | −3.35265e6 | −0.319195 | ||||||||
\(220\) | 3.28064e6i | 0.308099i | ||||||||
\(221\) | −6.79827e6 | −0.629828 | ||||||||
\(222\) | 8.33240e6i | 0.761573i | ||||||||
\(223\) | 6.05484e6i | 0.545994i | 0.962015 | + | 0.272997i | \(0.0880150\pi\) | ||||
−0.962015 | + | 0.272997i | \(0.911985\pi\) | |||||||
\(224\) | 1.13416e6 | + | 1.63136e6i | 0.100909 | + | 0.145146i | ||||
\(225\) | −1.00050e6 | −0.0878351 | ||||||||
\(226\) | 6.79927e6 | 0.589030 | ||||||||
\(227\) | 1.70220e7i | 1.45524i | 0.685981 | + | 0.727619i | \(0.259373\pi\) | ||||
−0.685981 | + | 0.727619i | \(0.740627\pi\) | |||||||
\(228\) | −7.18239e6 | −0.605989 | ||||||||
\(229\) | − | 8.49217e6i | − | 0.707151i | −0.935406 | − | 0.353576i | \(-0.884966\pi\) | ||
0.935406 | − | 0.353576i | \(-0.115034\pi\) | |||||||
\(230\) | − | 6.47736e6i | − | 0.532371i | ||||||
\(231\) | −8.79112e6 | + | 6.11180e6i | −0.713195 | + | 0.495830i | ||||
\(232\) | −7.54807e6 | −0.604466 | ||||||||
\(233\) | −4.76243e6 | −0.376496 | −0.188248 | − | 0.982122i | \(-0.560281\pi\) | ||||
−0.188248 | + | 0.982122i | \(0.560281\pi\) | |||||||
\(234\) | − | 3.48477e6i | − | 0.271973i | ||||||
\(235\) | −1.37368e7 | −1.05848 | ||||||||
\(236\) | − | 8.70101e6i | − | 0.661963i | ||||||
\(237\) | − | 1.35224e7i | − | 1.01580i | ||||||
\(238\) | −2.95777e6 | + | 2.05631e6i | −0.219398 | + | 0.152531i | ||||
\(239\) | 1.58931e7 | 1.16416 | 0.582082 | − | 0.813130i | \(-0.302238\pi\) | ||||
0.582082 | + | 0.813130i | \(0.302238\pi\) | |||||||
\(240\) | −3.01748e6 | −0.218279 | ||||||||
\(241\) | − | 266157.i | − | 0.0190146i | −0.999955 | − | 0.00950730i | \(-0.996974\pi\) | ||
0.999955 | − | 0.00950730i | \(-0.00302631\pi\) | |||||||
\(242\) | −3.87807e6 | −0.273633 | ||||||||
\(243\) | 6.49949e6i | 0.452960i | ||||||||
\(244\) | 1.08337e7i | 0.745771i | ||||||||
\(245\) | 1.08491e7 | + | 4.03132e6i | 0.737730 | + | 0.274126i | ||||
\(246\) | 3.05506e6 | 0.205217 | ||||||||
\(247\) | 2.74378e7 | 1.82078 | ||||||||
\(248\) | 3.98976e6i | 0.261572i | ||||||||
\(249\) | 6.76285e6 | 0.438058 | ||||||||
\(250\) | − | 1.20049e7i | − | 0.768313i | ||||||
\(251\) | 1.01995e7i | 0.644999i | 0.946570 | + | 0.322499i | \(0.104523\pi\) | ||||
−0.946570 | + | 0.322499i | \(0.895477\pi\) | |||||||
\(252\) | −1.05406e6 | − | 1.51614e6i | −0.0658663 | − | 0.0947410i | ||||
\(253\) | −1.21296e7 | −0.749008 | ||||||||
\(254\) | −7.88117e6 | −0.480939 | ||||||||
\(255\) | − | 5.47092e6i | − | 0.329944i | ||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | − | 2.68033e7i | − | 1.57902i | −0.613735 | − | 0.789512i | \(-0.710333\pi\) | ||
0.613735 | − | 0.789512i | \(-0.289667\pi\) | |||||||
\(258\) | 1.93769e7i | 1.12830i | ||||||||
\(259\) | −9.62812e6 | − | 1.38489e7i | −0.554169 | − | 0.797108i | ||||
\(260\) | 1.15272e7 | 0.655851 | ||||||||
\(261\) | 7.01498e6 | 0.394553 | ||||||||
\(262\) | 1.47235e7i | 0.818665i | ||||||||
\(263\) | −2.62513e7 | −1.44306 | −0.721529 | − | 0.692385i | \(-0.756560\pi\) | ||||
−0.721529 | + | 0.692385i | \(0.756560\pi\) | |||||||
\(264\) | 5.65060e6i | 0.307102i | ||||||||
\(265\) | − | 1.22182e7i | − | 0.656554i | ||||||
\(266\) | 1.19376e7 | − | 8.29928e6i | 0.634265 | − | 0.440956i | ||||
\(267\) | 1.23233e7 | 0.647431 | ||||||||
\(268\) | −3.40435e6 | −0.176860 | ||||||||
\(269\) | − | 3.58901e7i | − | 1.84382i | −0.387408 | − | 0.921909i | \(-0.626629\pi\) | ||
0.387408 | − | 0.921909i | \(-0.373371\pi\) | |||||||
\(270\) | −9.34762e6 | −0.474908 | ||||||||
\(271\) | − | 1.64221e6i | − | 0.0825127i | −0.999149 | − | 0.0412563i | \(-0.986864\pi\) | ||
0.999149 | − | 0.0412563i | \(-0.0131360\pi\) | |||||||
\(272\) | 1.90115e6i | 0.0944732i | ||||||||
\(273\) | 2.14751e7 | + | 3.08895e7i | 1.05547 | + | 1.51818i | ||||
\(274\) | −3.91715e6 | −0.190423 | ||||||||
\(275\) | −6.19751e6 | −0.298002 | ||||||||
\(276\) | − | 1.11567e7i | − | 0.530648i | ||||||
\(277\) | 3.84263e7 | 1.80796 | 0.903980 | − | 0.427574i | \(-0.140632\pi\) | ||||
0.903980 | + | 0.427574i | \(0.140632\pi\) | |||||||
\(278\) | 2.72652e6i | 0.126904i | ||||||||
\(279\) | − | 3.70798e6i | − | 0.170736i | ||||||
\(280\) | 5.01523e6 | − | 3.48671e6i | 0.228464 | − | 0.158834i | ||||
\(281\) | −3.78655e7 | −1.70657 | −0.853286 | − | 0.521443i | \(-0.825394\pi\) | ||||
−0.853286 | + | 0.521443i | \(0.825394\pi\) | |||||||
\(282\) | −2.36604e7 | −1.05505 | ||||||||
\(283\) | 3.58026e6i | 0.157963i | 0.996876 | + | 0.0789815i | \(0.0251668\pi\) | ||||
−0.996876 | + | 0.0789815i | \(0.974833\pi\) | |||||||
\(284\) | 6.91269e6 | 0.301781 | ||||||||
\(285\) | 2.20806e7i | 0.953842i | ||||||||
\(286\) | − | 2.15861e7i | − | 0.922735i | ||||||
\(287\) | −5.07769e6 | + | 3.53013e6i | −0.214793 | + | 0.149329i | ||||
\(288\) | −974519. | −0.0407956 | ||||||||
\(289\) | 2.06907e7 | 0.857197 | ||||||||
\(290\) | 2.32048e7i | 0.951446i | ||||||||
\(291\) | −3.51203e6 | −0.142521 | ||||||||
\(292\) | − | 3.58167e6i | − | 0.143859i | ||||||
\(293\) | 3.57198e7i | 1.42006i | 0.704172 | + | 0.710030i | \(0.251318\pi\) | ||||
−0.704172 | + | 0.710030i | \(0.748682\pi\) | |||||||
\(294\) | 1.86866e7 | + | 6.94358e6i | 0.735342 | + | 0.273238i | ||||
\(295\) | −2.67493e7 | −1.04195 | ||||||||
\(296\) | −8.90158e6 | −0.343235 | ||||||||
\(297\) | 1.75046e7i | 0.668162i | ||||||||
\(298\) | −3.70863e6 | −0.140141 | ||||||||
\(299\) | 4.26201e7i | 1.59441i | ||||||||
\(300\) | − | 5.70038e6i | − | 0.211125i | ||||||
\(301\) | −2.23900e7 | − | 3.22055e7i | −0.821022 | − | 1.18095i | ||||
\(302\) | 269558. | 0.00978660 | ||||||||
\(303\) | −2.11531e7 | −0.760409 | ||||||||
\(304\) | − | 7.67302e6i | − | 0.273115i | ||||||
\(305\) | 3.33056e7 | 1.17386 | ||||||||
\(306\) | − | 1.76687e6i | − | 0.0616654i | ||||||
\(307\) | − | 3.71810e7i | − | 1.28501i | −0.766282 | − | 0.642504i | \(-0.777895\pi\) | ||
0.766282 | − | 0.642504i | \(-0.222105\pi\) | |||||||
\(308\) | −6.52929e6 | − | 9.39163e6i | −0.223467 | − | 0.321432i | ||||
\(309\) | −4.84776e7 | −1.64311 | ||||||||
\(310\) | 1.22656e7 | 0.411721 | ||||||||
\(311\) | 1.37937e7i | 0.458563i | 0.973360 | + | 0.229281i | \(0.0736376\pi\) | ||||
−0.973360 | + | 0.229281i | \(0.926362\pi\) | |||||||
\(312\) | 1.98546e7 | 0.653728 | ||||||||
\(313\) | 9.13790e6i | 0.297998i | 0.988837 | + | 0.148999i | \(0.0476051\pi\) | ||||
−0.988837 | + | 0.148999i | \(0.952395\pi\) | |||||||
\(314\) | − | 1.17952e7i | − | 0.380994i | ||||||
\(315\) | −4.66103e6 | + | 3.24046e6i | −0.149125 | + | 0.103675i | ||||
\(316\) | 1.44461e7 | 0.457814 | ||||||||
\(317\) | −1.28223e7 | −0.402520 | −0.201260 | − | 0.979538i | \(-0.564504\pi\) | ||||
−0.201260 | + | 0.979538i | \(0.564504\pi\) | |||||||
\(318\) | − | 2.10448e7i | − | 0.654429i | ||||||
\(319\) | 4.34538e7 | 1.33862 | ||||||||
\(320\) | − | 3.22361e6i | − | 0.0983767i | ||||||
\(321\) | − | 1.31561e7i | − | 0.397751i | ||||||
\(322\) | 1.28916e7 | + | 1.85430e7i | 0.386134 | + | 0.555408i | ||||
\(323\) | 1.39117e7 | 0.412833 | ||||||||
\(324\) | −2.00250e7 | −0.588759 | ||||||||
\(325\) | 2.17763e7i | 0.634357i | ||||||||
\(326\) | 9.01282e6 | 0.260141 | ||||||||
\(327\) | − | 5.40353e7i | − | 1.54538i | ||||||
\(328\) | 3.26375e6i | 0.0924901i | ||||||||
\(329\) | 3.93249e7 | − | 2.73396e7i | 1.10428 | − | 0.767724i | ||||
\(330\) | 1.73715e7 | 0.483387 | ||||||||
\(331\) | 6.24496e7 | 1.72205 | 0.861025 | − | 0.508563i | \(-0.169823\pi\) | ||||
0.861025 | + | 0.508563i | \(0.169823\pi\) | |||||||
\(332\) | 7.22481e6i | 0.197430i | ||||||||
\(333\) | 8.27290e6 | 0.224040 | ||||||||
\(334\) | − | 6.88665e6i | − | 0.184828i | ||||||
\(335\) | 1.04659e7i | 0.278383i | ||||||||
\(336\) | 8.63828e6 | − | 6.00554e6i | 0.227724 | − | 0.158319i | ||||
\(337\) | −5.54168e7 | −1.44794 | −0.723972 | − | 0.689829i | \(-0.757686\pi\) | ||||
−0.723972 | + | 0.689829i | \(0.757686\pi\) | |||||||
\(338\) | −4.85430e7 | −1.25712 | ||||||||
\(339\) | − | 3.60031e7i | − | 0.924148i | ||||||
\(340\) | 5.84463e6 | 0.148703 | ||||||||
\(341\) | − | 2.29688e7i | − | 0.579262i | ||||||
\(342\) | 7.13110e6i | 0.178270i | ||||||||
\(343\) | −3.90816e7 | + | 1.00518e7i | −0.968479 | + | 0.249094i | ||||
\(344\) | −2.07005e7 | −0.508516 | ||||||||
\(345\) | −3.42986e7 | −0.835254 | ||||||||
\(346\) | − | 2.61236e7i | − | 0.630673i | ||||||
\(347\) | −1.00493e7 | −0.240518 | −0.120259 | − | 0.992743i | \(-0.538372\pi\) | ||||
−0.120259 | + | 0.992743i | \(0.538372\pi\) | |||||||
\(348\) | 3.99681e7i | 0.948367i | ||||||||
\(349\) | 7.23514e7i | 1.70204i | 0.525130 | + | 0.851022i | \(0.324017\pi\) | ||||
−0.525130 | + | 0.851022i | \(0.675983\pi\) | |||||||
\(350\) | 6.58680e6 | + | 9.47435e6i | 0.153628 | + | 0.220976i | ||||
\(351\) | 6.15060e7 | 1.42232 | ||||||||
\(352\) | −6.03659e6 | −0.138409 | ||||||||
\(353\) | 3.04434e7i | 0.692099i | 0.938216 | + | 0.346050i | \(0.112477\pi\) | ||||
−0.938216 | + | 0.346050i | \(0.887523\pi\) | |||||||
\(354\) | −4.60731e7 | −1.03858 | ||||||||
\(355\) | − | 2.12515e7i | − | 0.475011i | ||||||
\(356\) | 1.31651e7i | 0.291792i | ||||||||
\(357\) | 1.08885e7 | + | 1.56618e7i | 0.239311 | + | 0.344221i | ||||
\(358\) | −1.62377e7 | −0.353896 | ||||||||
\(359\) | 7.98054e6 | 0.172484 | 0.0862420 | − | 0.996274i | \(-0.472514\pi\) | ||||
0.0862420 | + | 0.996274i | \(0.472514\pi\) | |||||||
\(360\) | 2.99594e6i | 0.0642133i | ||||||||
\(361\) | −9.10187e6 | −0.193468 | ||||||||
\(362\) | 3.85369e7i | 0.812364i | ||||||||
\(363\) | 2.05349e7i | 0.429312i | ||||||||
\(364\) | −3.29995e7 | + | 2.29421e7i | −0.684232 | + | 0.475695i | ||||
\(365\) | −1.10110e7 | −0.226438 | ||||||||
\(366\) | 5.73658e7 | 1.17006 | ||||||||
\(367\) | − | 2.06363e7i | − | 0.417478i | −0.977971 | − | 0.208739i | \(-0.933064\pi\) | ||
0.977971 | − | 0.208739i | \(-0.0669360\pi\) | |||||||
\(368\) | 1.19188e7 | 0.239159 | ||||||||
\(369\) | − | 3.03324e6i | − | 0.0603709i | ||||||
\(370\) | 2.73659e7i | 0.540262i | ||||||||
\(371\) | 2.43173e7 | + | 3.49776e7i | 0.476204 | + | 0.684965i | ||||
\(372\) | 2.11264e7 | 0.410389 | ||||||||
\(373\) | −9.06283e6 | −0.174637 | −0.0873187 | − | 0.996180i | \(-0.527830\pi\) | ||||
−0.0873187 | + | 0.996180i | \(0.527830\pi\) | |||||||
\(374\) | − | 1.09448e7i | − | 0.209215i | ||||||
\(375\) | −6.35676e7 | −1.20543 | ||||||||
\(376\) | − | 2.52766e7i | − | 0.475505i | ||||||
\(377\) | − | 1.52684e8i | − | 2.84951i | ||||||
\(378\) | 2.67598e7 | − | 1.86041e7i | 0.495459 | − | 0.344455i | ||||
\(379\) | 3.92591e7 | 0.721146 | 0.360573 | − | 0.932731i | \(-0.382581\pi\) | ||||
0.360573 | + | 0.932731i | \(0.382581\pi\) | |||||||
\(380\) | −2.35889e7 | −0.429890 | ||||||||
\(381\) | 4.17320e7i | 0.754560i | ||||||||
\(382\) | −2.83180e7 | −0.508011 | ||||||||
\(383\) | − | 4.25901e7i | − | 0.758075i | −0.925381 | − | 0.379037i | \(-0.876255\pi\) | ||
0.925381 | − | 0.379037i | \(-0.123745\pi\) | |||||||
\(384\) | − | 5.55236e6i | − | 0.0980583i | ||||||
\(385\) | −2.88724e7 | + | 2.00728e7i | −0.505942 | + | 0.351743i | ||||
\(386\) | 1.10306e7 | 0.191795 | ||||||||
\(387\) | 1.92385e7 | 0.331923 | ||||||||
\(388\) | − | 3.75194e6i | − | 0.0642333i | ||||||
\(389\) | −3.23230e7 | −0.549114 | −0.274557 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274557 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(390\) | − | 6.10384e7i | − | 1.02899i | ||||||
\(391\) | 2.16096e7i | 0.361506i | ||||||||
\(392\) | −7.41789e6 | + | 1.99631e7i | −0.123147 | + | 0.331414i | ||||
\(393\) | 7.79629e7 | 1.28443 | ||||||||
\(394\) | 6.56327e7 | 1.07308 | ||||||||
\(395\) | − | 4.44112e7i | − | 0.720612i | ||||||
\(396\) | 5.61025e6 | 0.0903434 | ||||||||
\(397\) | 1.21097e8i | 1.93536i | 0.252186 | + | 0.967679i | \(0.418851\pi\) | ||||
−0.252186 | + | 0.967679i | \(0.581149\pi\) | |||||||
\(398\) | − | 4.11363e6i | − | 0.0652493i | ||||||
\(399\) | −4.39459e7 | − | 6.32111e7i | −0.691831 | − | 0.995118i | ||||
\(400\) | 6.08976e6 | 0.0951526 | ||||||||
\(401\) | 4.98925e7 | 0.773753 | 0.386876 | − | 0.922132i | \(-0.373554\pi\) | ||||
0.386876 | + | 0.922132i | \(0.373554\pi\) | |||||||
\(402\) | 1.80265e7i | 0.277482i | ||||||||
\(403\) | −8.07058e7 | −1.23308 | ||||||||
\(404\) | − | 2.25981e7i | − | 0.342711i | ||||||
\(405\) | 6.15623e7i | 0.926722i | ||||||||
\(406\) | −4.61833e7 | − | 6.64294e7i | −0.690092 | − | 0.992618i | ||||
\(407\) | 5.12459e7 | 0.760109 | ||||||||
\(408\) | 1.00668e7 | 0.148222 | ||||||||
\(409\) | 1.08411e7i | 0.158454i | 0.996857 | + | 0.0792269i | \(0.0252452\pi\) | ||||
−0.996857 | + | 0.0792269i | \(0.974755\pi\) | |||||||
\(410\) | 1.00336e7 | 0.145582 | ||||||||
\(411\) | 2.07419e7i | 0.298761i | ||||||||
\(412\) | − | 5.17891e7i | − | 0.740536i | ||||||
\(413\) | 7.65762e7 | − | 5.32377e7i | 1.08704 | − | 0.755734i | ||||
\(414\) | −1.10770e7 | −0.156106 | ||||||||
\(415\) | 2.22110e7 | 0.310759 | ||||||||
\(416\) | 2.12109e7i | 0.294631i | ||||||||
\(417\) | 1.44373e7 | 0.199103 | ||||||||
\(418\) | 4.41731e7i | 0.604824i | ||||||||
\(419\) | 3.85015e7i | 0.523402i | 0.965149 | + | 0.261701i | \(0.0842834\pi\) | ||||
−0.965149 | + | 0.261701i | \(0.915717\pi\) | |||||||
\(420\) | −1.84627e7 | − | 2.65564e7i | −0.249199 | − | 0.358444i | ||||
\(421\) | −6.80531e7 | −0.912014 | −0.456007 | − | 0.889976i | \(-0.650721\pi\) | ||||
−0.456007 | + | 0.889976i | \(0.650721\pi\) | |||||||
\(422\) | 3.29540e7 | 0.438501 | ||||||||
\(423\) | 2.34914e7i | 0.310376i | ||||||||
\(424\) | 2.24823e7 | 0.294947 | ||||||||
\(425\) | 1.10412e7i | 0.143830i | ||||||||
\(426\) | − | 3.66037e7i | − | 0.473474i | ||||||
\(427\) | −9.53453e7 | + | 6.62864e7i | −1.22466 | + | 0.851414i | ||||
\(428\) | 1.40548e7 | 0.179264 | ||||||||
\(429\) | −1.14302e8 | −1.44771 | ||||||||
\(430\) | 6.36388e7i | 0.800418i | ||||||||
\(431\) | −5.94074e7 | −0.742008 | −0.371004 | − | 0.928631i | \(-0.620986\pi\) | ||||
−0.371004 | + | 0.928631i | \(0.620986\pi\) | |||||||
\(432\) | − | 1.72002e7i | − | 0.213345i | ||||||
\(433\) | − | 6.40026e7i | − | 0.788377i | −0.919030 | − | 0.394189i | \(-0.871026\pi\) | ||
0.919030 | − | 0.394189i | \(-0.128974\pi\) | |||||||
\(434\) | −3.51132e7 | + | 2.44116e7i | −0.429538 | + | 0.298625i | ||||
\(435\) | 1.22873e8 | 1.49275 | ||||||||
\(436\) | 5.77264e7 | 0.696490 | ||||||||
\(437\) | − | 8.72162e7i | − | 1.04509i | ||||||
\(438\) | −1.89655e7 | −0.225705 | ||||||||
\(439\) | 5.84728e7i | 0.691131i | 0.938395 | + | 0.345565i | \(0.112313\pi\) | ||||
−0.938395 | + | 0.345565i | \(0.887687\pi\) | |||||||
\(440\) | 1.85581e7i | 0.217859i | ||||||||
\(441\) | 6.89400e6 | − | 1.85532e7i | 0.0803814 | − | 0.216323i | ||||
\(442\) | −3.84568e7 | −0.445355 | ||||||||
\(443\) | −1.54616e8 | −1.77845 | −0.889227 | − | 0.457467i | \(-0.848757\pi\) | ||||
−0.889227 | + | 0.457467i | \(0.848757\pi\) | |||||||
\(444\) | 4.71352e7i | 0.538513i | ||||||||
\(445\) | 4.04731e7 | 0.459289 | ||||||||
\(446\) | 3.42513e7i | 0.386076i | ||||||||
\(447\) | 1.96377e7i | 0.219871i | ||||||||
\(448\) | 6.41578e6 | + | 9.22835e6i | 0.0713535 | + | 0.102634i | ||||
\(449\) | 8.30902e7 | 0.917933 | 0.458966 | − | 0.888454i | \(-0.348220\pi\) | ||||
0.458966 | + | 0.888454i | \(0.348220\pi\) | |||||||
\(450\) | −5.65967e6 | −0.0621088 | ||||||||
\(451\) | − | 1.87892e7i | − | 0.204823i | ||||||
\(452\) | 3.84625e7 | 0.416507 | ||||||||
\(453\) | − | 1.42735e6i | − | 0.0153545i | ||||||
\(454\) | 9.62913e7i | 1.02901i | ||||||||
\(455\) | 7.05301e7 | + | 1.01449e8i | 0.748756 | + | 1.07700i | ||||
\(456\) | −4.06298e7 | −0.428499 | ||||||||
\(457\) | 3.71422e7 | 0.389152 | 0.194576 | − | 0.980887i | \(-0.437667\pi\) | ||||
0.194576 | + | 0.980887i | \(0.437667\pi\) | |||||||
\(458\) | − | 4.80390e7i | − | 0.500031i | ||||||
\(459\) | 3.11853e7 | 0.322486 | ||||||||
\(460\) | − | 3.66415e7i | − | 0.376443i | ||||||
\(461\) | 3.38118e6i | 0.0345116i | 0.999851 | + | 0.0172558i | \(0.00549296\pi\) | ||||
−0.999851 | + | 0.0172558i | \(0.994507\pi\) | |||||||
\(462\) | −4.97301e7 | + | 3.45736e7i | −0.504305 | + | 0.350605i | ||||
\(463\) | 6.63410e7 | 0.668404 | 0.334202 | − | 0.942502i | \(-0.391533\pi\) | ||||
0.334202 | + | 0.942502i | \(0.391533\pi\) | |||||||
\(464\) | −4.26983e7 | −0.427422 | ||||||||
\(465\) | − | 6.49481e7i | − | 0.645963i | ||||||
\(466\) | −2.69404e7 | −0.266223 | ||||||||
\(467\) | − | 9.97322e7i | − | 0.979230i | −0.871939 | − | 0.489615i | \(-0.837137\pi\) | ||
0.871939 | − | 0.489615i | \(-0.162863\pi\) | |||||||
\(468\) | − | 1.97128e7i | − | 0.192314i | ||||||
\(469\) | −2.08297e7 | − | 2.99612e7i | −0.201913 | − | 0.290429i | ||||
\(470\) | −7.77071e7 | −0.748457 | ||||||||
\(471\) | −6.24575e7 | −0.597753 | ||||||||
\(472\) | − | 4.92203e7i | − | 0.468078i | ||||||
\(473\) | 1.19171e8 | 1.12613 | ||||||||
\(474\) | − | 7.64942e7i | − | 0.718280i | ||||||
\(475\) | − | 4.45622e7i | − | 0.415801i | ||||||
\(476\) | −1.67317e7 | + | 1.16323e7i | −0.155138 | + | 0.107856i | ||||
\(477\) | −2.08945e7 | −0.192520 | ||||||||
\(478\) | 8.99048e7 | 0.823188 | ||||||||
\(479\) | 8.50867e7i | 0.774203i | 0.922037 | + | 0.387102i | \(0.126524\pi\) | ||||
−0.922037 | + | 0.387102i | \(0.873476\pi\) | |||||||
\(480\) | −1.70695e7 | −0.154346 | ||||||||
\(481\) | − | 1.80063e8i | − | 1.61804i | ||||||
\(482\) | − | 1.50561e6i | − | 0.0134453i | ||||||
\(483\) | 9.81879e7 | − | 6.82627e7i | 0.871398 | − | 0.605818i | ||||
\(484\) | −2.19377e7 | −0.193488 | ||||||||
\(485\) | −1.15345e7 | −0.101105 | ||||||||
\(486\) | 3.67667e7i | 0.320291i | ||||||||
\(487\) | 1.19789e8 | 1.03712 | 0.518560 | − | 0.855041i | \(-0.326468\pi\) | ||||
0.518560 | + | 0.855041i | \(0.326468\pi\) | |||||||
\(488\) | 6.12844e7i | 0.527340i | ||||||||
\(489\) | − | 4.77242e7i | − | 0.408143i | ||||||
\(490\) | 6.13720e7 | + | 2.28046e7i | 0.521654 | + | 0.193836i | ||||
\(491\) | −2.24857e8 | −1.89960 | −0.949800 | − | 0.312859i | \(-0.898713\pi\) | ||||
−0.949800 | + | 0.312859i | \(0.898713\pi\) | |||||||
\(492\) | 1.72820e7 | 0.145111 | ||||||||
\(493\) | − | 7.74152e7i | − | 0.646079i | ||||||
\(494\) | 1.55212e8 | 1.28749 | ||||||||
\(495\) | − | 1.72474e7i | − | 0.142203i | ||||||
\(496\) | 2.25695e7i | 0.184959i | ||||||||
\(497\) | 4.22957e7 | + | 6.08375e7i | 0.344530 | + | 0.495566i | ||||
\(498\) | 3.82564e7 | 0.309754 | ||||||||
\(499\) | 5.80019e7 | 0.466810 | 0.233405 | − | 0.972380i | \(-0.425013\pi\) | ||||
0.233405 | + | 0.972380i | \(0.425013\pi\) | |||||||
\(500\) | − | 6.79099e7i | − | 0.543279i | ||||||
\(501\) | −3.64658e7 | −0.289983 | ||||||||
\(502\) | 5.76972e7i | 0.456083i | ||||||||
\(503\) | 9.94846e7i | 0.781721i | 0.920450 | + | 0.390860i | \(0.127823\pi\) | ||||
−0.920450 | + | 0.390860i | \(0.872177\pi\) | |||||||
\(504\) | −5.96265e6 | − | 8.57659e6i | −0.0465745 | − | 0.0669920i | ||||
\(505\) | −6.94727e7 | −0.539436 | ||||||||
\(506\) | −6.86156e7 | −0.529628 | ||||||||
\(507\) | 2.57042e8i | 1.97233i | ||||||||
\(508\) | −4.45826e7 | −0.340075 | ||||||||
\(509\) | 1.51579e8i | 1.14944i | 0.818350 | + | 0.574721i | \(0.194889\pi\) | ||||
−0.818350 | + | 0.574721i | \(0.805111\pi\) | |||||||
\(510\) | − | 3.09482e7i | − | 0.233305i | ||||||
\(511\) | 3.15217e7 | − | 2.19147e7i | 0.236237 | − | 0.164237i | ||||
\(512\) | 5.93164e6 | 0.0441942 | ||||||||
\(513\) | −1.25864e8 | −0.932284 | ||||||||
\(514\) | − | 1.51622e8i | − | 1.11654i | ||||||
\(515\) | −1.59214e8 | −1.16562 | ||||||||
\(516\) | 1.09612e8i | 0.797828i | ||||||||
\(517\) | 1.45516e8i | 1.05302i | ||||||||
\(518\) | −5.44649e7 | − | 7.83414e7i | −0.391857 | − | 0.563640i | ||||
\(519\) | −1.38328e8 | −0.989484 | ||||||||
\(520\) | 6.52079e7 | 0.463757 | ||||||||
\(521\) | 1.36113e8i | 0.962469i | 0.876592 | + | 0.481234i | \(0.159811\pi\) | ||||
−0.876592 | + | 0.481234i | \(0.840189\pi\) | |||||||
\(522\) | 3.96827e7 | 0.278991 | ||||||||
\(523\) | − | 1.02678e8i | − | 0.717749i | −0.933386 | − | 0.358874i | \(-0.883161\pi\) | ||
0.933386 | − | 0.358874i | \(-0.116839\pi\) | |||||||
\(524\) | 8.32885e7i | 0.578884i | ||||||||
\(525\) | 5.01681e7 | − | 3.48781e7i | 0.346697 | − | 0.241032i | ||||
\(526\) | −1.48500e8 | −1.02040 | ||||||||
\(527\) | −4.09201e7 | −0.279579 | ||||||||
\(528\) | 3.19646e7i | 0.217154i | ||||||||
\(529\) | −1.25600e7 | −0.0848445 | ||||||||
\(530\) | − | 6.91167e7i | − | 0.464254i | ||||||
\(531\) | 4.57441e7i | 0.305528i | ||||||||
\(532\) | 6.75290e7 | − | 4.69478e7i | 0.448493 | − | 0.311803i | ||||
\(533\) | −6.60199e7 | −0.436007 | ||||||||
\(534\) | 6.97111e7 | 0.457803 | ||||||||
\(535\) | − | 4.32081e7i | − | 0.282166i | ||||||
\(536\) | −1.92579e7 | −0.125059 | ||||||||
\(537\) | 8.59810e7i | 0.555239i | ||||||||
\(538\) | − | 2.03025e8i | − | 1.30378i | ||||||
\(539\) | 4.27044e7 | − | 1.14927e8i | 0.272713 | − | 0.733929i | ||||
\(540\) | −5.28781e7 | −0.335811 | ||||||||
\(541\) | 1.71991e8 | 1.08621 | 0.543104 | − | 0.839665i | \(-0.317249\pi\) | ||||
0.543104 | + | 0.839665i | \(0.317249\pi\) | |||||||
\(542\) | − | 9.28974e6i | − | 0.0583453i | ||||||
\(543\) | 2.04058e8 | 1.27454 | ||||||||
\(544\) | 1.07545e7i | 0.0668026i | ||||||||
\(545\) | − | 1.77466e8i | − | 1.09629i | ||||||
\(546\) | 1.21482e8 | + | 1.74737e8i | 0.746333 | + | 1.07351i | ||||
\(547\) | −3.57048e7 | −0.218154 | −0.109077 | − | 0.994033i | \(-0.534790\pi\) | ||||
−0.109077 | + | 0.994033i | \(0.534790\pi\) | |||||||
\(548\) | −2.21588e7 | −0.134649 | ||||||||
\(549\) | − | 5.69561e7i | − | 0.344210i | ||||||
\(550\) | −3.50584e7 | −0.210719 | ||||||||
\(551\) | 3.12448e8i | 1.86777i | ||||||||
\(552\) | − | 6.31116e7i | − | 0.375225i | ||||||
\(553\) | 8.83893e7 | + | 1.27138e8i | 0.522666 | + | 0.751795i | ||||
\(554\) | 2.17372e8 | 1.27842 | ||||||||
\(555\) | 1.44906e8 | 0.847634 | ||||||||
\(556\) | 1.54235e7i | 0.0897343i | ||||||||
\(557\) | −7.51706e7 | −0.434993 | −0.217497 | − | 0.976061i | \(-0.569789\pi\) | ||||
−0.217497 | + | 0.976061i | \(0.569789\pi\) | |||||||
\(558\) | − | 2.09755e7i | − | 0.120728i | ||||||
\(559\) | − | 4.18734e8i | − | 2.39719i | ||||||
\(560\) | 2.83704e7 | − | 1.97238e7i | 0.161548 | − | 0.112312i | ||||
\(561\) | −5.79542e7 | −0.328244 | ||||||||
\(562\) | −2.14200e8 | −1.20673 | ||||||||
\(563\) | − | 2.09618e8i | − | 1.17464i | −0.809356 | − | 0.587318i | \(-0.800184\pi\) | ||
0.809356 | − | 0.587318i | \(-0.199816\pi\) | |||||||
\(564\) | −1.33843e8 | −0.746035 | ||||||||
\(565\) | − | 1.18244e8i | − | 0.655593i | ||||||
\(566\) | 2.02530e7i | 0.111697i | ||||||||
\(567\) | −1.22524e8 | − | 1.76237e8i | −0.672160 | − | 0.966824i | ||||
\(568\) | 3.91041e7 | 0.213391 | ||||||||
\(569\) | 3.85572e7 | 0.209300 | 0.104650 | − | 0.994509i | \(-0.466628\pi\) | ||||
0.104650 | + | 0.994509i | \(0.466628\pi\) | |||||||
\(570\) | 1.24907e8i | 0.674468i | ||||||||
\(571\) | 6.50282e7 | 0.349296 | 0.174648 | − | 0.984631i | \(-0.444121\pi\) | ||||
0.174648 | + | 0.984631i | \(0.444121\pi\) | |||||||
\(572\) | − | 1.22110e8i | − | 0.652472i | ||||||
\(573\) | 1.49948e8i | 0.797034i | ||||||||
\(574\) | −2.87237e7 | + | 1.99694e7i | −0.151882 | + | 0.105592i | ||||
\(575\) | 6.92200e7 | 0.364106 | ||||||||
\(576\) | −5.51271e6 | −0.0288468 | ||||||||
\(577\) | 1.17548e8i | 0.611909i | 0.952046 | + | 0.305954i | \(0.0989755\pi\) | ||||
−0.952046 | + | 0.305954i | \(0.901025\pi\) | |||||||
\(578\) | 1.17044e8 | 0.606130 | ||||||||
\(579\) | − | 5.84085e7i | − | 0.300913i | ||||||
\(580\) | 1.31266e8i | 0.672774i | ||||||||
\(581\) | −6.35844e7 | + | 4.42055e7i | −0.324207 | + | 0.225397i | ||||
\(582\) | −1.98671e7 | −0.100778 | ||||||||
\(583\) | −1.29429e8 | −0.653171 | ||||||||
\(584\) | − | 2.02610e7i | − | 0.101724i | ||||||
\(585\) | −6.06025e7 | −0.302707 | ||||||||
\(586\) | 2.02062e8i | 1.00413i | ||||||||
\(587\) | 2.41814e8i | 1.19555i | 0.801664 | + | 0.597775i | \(0.203948\pi\) | ||||
−0.801664 | + | 0.597775i | \(0.796052\pi\) | |||||||
\(588\) | 1.05708e8 | + | 3.92788e7i | 0.519965 | + | 0.193209i | ||||
\(589\) | 1.65153e8 | 0.808243 | ||||||||
\(590\) | −1.51317e8 | −0.736768 | ||||||||
\(591\) | − | 3.47535e8i | − | 1.68359i | ||||||
\(592\) | −5.03550e7 | −0.242704 | ||||||||
\(593\) | − | 2.31180e8i | − | 1.10863i | −0.832307 | − | 0.554314i | \(-0.812981\pi\) | ||
0.832307 | − | 0.554314i | \(-0.187019\pi\) | |||||||
\(594\) | 9.90207e7i | 0.472462i | ||||||||
\(595\) | 3.57607e7 | + | 5.14377e7i | 0.169768 | + | 0.244192i | ||||
\(596\) | −2.09792e7 | −0.0990945 | ||||||||
\(597\) | −2.17823e7 | −0.102372 | ||||||||
\(598\) | 2.41096e8i | 1.12742i | ||||||||
\(599\) | −3.84910e7 | −0.179093 | −0.0895464 | − | 0.995983i | \(-0.528542\pi\) | ||||
−0.0895464 | + | 0.995983i | \(0.528542\pi\) | |||||||
\(600\) | − | 3.22462e7i | − | 0.149288i | ||||||
\(601\) | 3.32931e8i | 1.53367i | 0.641847 | + | 0.766833i | \(0.278168\pi\) | ||||
−0.641847 | + | 0.766833i | \(0.721832\pi\) | |||||||
\(602\) | −1.26657e8 | − | 1.82182e8i | −0.580550 | − | 0.835055i | ||||
\(603\) | 1.78978e7 | 0.0816297 | ||||||||
\(604\) | 1.52485e6 | 0.00692017 | ||||||||
\(605\) | 6.74423e7i | 0.304555i | ||||||||
\(606\) | −1.19660e8 | −0.537690 | ||||||||
\(607\) | 5.87633e7i | 0.262749i | 0.991333 | + | 0.131374i | \(0.0419390\pi\) | ||||
−0.991333 | + | 0.131374i | \(0.958061\pi\) | |||||||
\(608\) | − | 4.34051e7i | − | 0.193121i | ||||||
\(609\) | −3.51753e8 | + | 2.44547e8i | −1.55735 | + | 1.08271i | ||||
\(610\) | 1.88405e8 | 0.830047 | ||||||||
\(611\) | 5.11301e8 | 2.24157 | ||||||||
\(612\) | − | 9.99495e6i | − | 0.0436040i | ||||||
\(613\) | −1.11411e7 | −0.0483665 | −0.0241833 | − | 0.999708i | \(-0.507699\pi\) | ||||
−0.0241833 | + | 0.999708i | \(0.507699\pi\) | |||||||
\(614\) | − | 2.10328e8i | − | 0.908639i | ||||||
\(615\) | − | 5.31296e7i | − | 0.228408i | ||||||
\(616\) | −3.69352e7 | − | 5.31271e7i | −0.158015 | − | 0.227287i | ||||
\(617\) | 6.61360e7 | 0.281567 | 0.140784 | − | 0.990040i | \(-0.455038\pi\) | ||||
0.140784 | + | 0.990040i | \(0.455038\pi\) | |||||||
\(618\) | −2.74231e8 | −1.16185 | ||||||||
\(619\) | 1.81247e8i | 0.764185i | 0.924124 | + | 0.382093i | \(0.124796\pi\) | ||||
−0.924124 | + | 0.382093i | \(0.875204\pi\) | |||||||
\(620\) | 6.93847e7 | 0.291131 | ||||||||
\(621\) | − | 1.95508e8i | − | 0.816376i | ||||||
\(622\) | 7.80288e7i | 0.324253i | ||||||||
\(623\) | −1.15864e8 | + | 8.05514e7i | −0.479164 | + | 0.333126i | ||||
\(624\) | 1.12315e8 | 0.462256 | ||||||||
\(625\) | −1.15851e8 | −0.474526 | ||||||||
\(626\) | 5.16918e7i | 0.210716i | ||||||||
\(627\) | 2.33903e8 | 0.948928 | ||||||||
\(628\) | − | 6.67239e7i | − | 0.269403i | ||||||
\(629\) | − | 9.12972e7i | − | 0.366864i | ||||||
\(630\) | −2.63668e7 | + | 1.83308e7i | −0.105447 | + | 0.0733095i | ||||
\(631\) | −1.25706e8 | −0.500344 | −0.250172 | − | 0.968201i | \(-0.580487\pi\) | ||||
−0.250172 | + | 0.968201i | \(0.580487\pi\) | |||||||
\(632\) | 8.17195e7 | 0.323724 | ||||||||
\(633\) | − | 1.74496e8i | − | 0.687979i | ||||||
\(634\) | −7.25338e7 | −0.284625 | ||||||||
\(635\) | 1.37059e8i | 0.535287i | ||||||||
\(636\) | − | 1.19047e8i | − | 0.462751i | ||||||
\(637\) | −4.03819e8 | − | 1.50051e8i | −1.56231 | − | 0.580525i | ||||
\(638\) | 2.45812e8 | 0.946544 | ||||||||
\(639\) | −3.63423e7 | −0.139287 | ||||||||
\(640\) | − | 1.82355e7i | − | 0.0695628i | ||||||
\(641\) | −5.14744e8 | −1.95442 | −0.977209 | − | 0.212281i | \(-0.931911\pi\) | ||||
−0.977209 | + | 0.212281i | \(0.931911\pi\) | |||||||
\(642\) | − | 7.44220e7i | − | 0.281252i | ||||||
\(643\) | − | 2.77852e8i | − | 1.04515i | −0.852592 | − | 0.522577i | \(-0.824971\pi\) | ||
0.852592 | − | 0.522577i | \(-0.175029\pi\) | |||||||
\(644\) | 7.29256e7 | + | 1.04895e8i | 0.273038 | + | 0.392733i | ||||
\(645\) | 3.36977e8 | 1.25580 | ||||||||
\(646\) | 7.86967e7 | 0.291917 | ||||||||
\(647\) | 1.33880e8i | 0.494315i | 0.968975 | + | 0.247157i | \(0.0794965\pi\) | ||||
−0.968975 | + | 0.247157i | \(0.920504\pi\) | |||||||
\(648\) | −1.13278e8 | −0.416315 | ||||||||
\(649\) | 2.83359e8i | 1.03658i | ||||||||
\(650\) | 1.23185e8i | 0.448558i | ||||||||
\(651\) | 1.29263e8 | + | 1.85930e8i | 0.468523 | + | 0.673916i | ||||
\(652\) | 5.09842e7 | 0.183947 | ||||||||
\(653\) | 3.72064e8 | 1.33622 | 0.668110 | − | 0.744062i | \(-0.267103\pi\) | ||||
0.668110 | + | 0.744062i | \(0.267103\pi\) | |||||||
\(654\) | − | 3.05670e8i | − | 1.09275i | ||||||
\(655\) | 2.56051e8 | 0.911178 | ||||||||
\(656\) | 1.84625e7i | 0.0654003i | ||||||||
\(657\) | 1.88300e7i | 0.0663980i | ||||||||
\(658\) | 2.22455e8 | − | 1.54656e8i | 0.780845 | − | 0.542863i | ||||
\(659\) | −4.95336e7 | −0.173079 | −0.0865394 | − | 0.996248i | \(-0.527581\pi\) | ||||
−0.0865394 | + | 0.996248i | \(0.527581\pi\) | |||||||
\(660\) | 9.82679e7 | 0.341806 | ||||||||
\(661\) | − | 6.94997e7i | − | 0.240646i | −0.992735 | − | 0.120323i | \(-0.961607\pi\) | ||
0.992735 | − | 0.120323i | \(-0.0383930\pi\) | |||||||
\(662\) | 3.53268e8 | 1.21767 | ||||||||
\(663\) | 2.03635e8i | 0.698732i | ||||||||
\(664\) | 4.08697e7i | 0.139604i | ||||||||
\(665\) | −1.44330e8 | − | 2.07602e8i | −0.490786 | − | 0.705939i | ||||
\(666\) | 4.67986e7 | 0.158420 | ||||||||
\(667\) | −4.85335e8 | −1.63555 | ||||||||
\(668\) | − | 3.89568e7i | − | 0.130693i | ||||||
\(669\) | 1.81366e8 | 0.605728 | ||||||||
\(670\) | 5.92041e7i | 0.196846i | ||||||||
\(671\) | − | 3.52811e8i | − | 1.16782i | ||||||
\(672\) | 4.88655e7 | − | 3.39725e7i | 0.161025 | − | 0.111949i | ||||
\(673\) | 1.80776e8 | 0.593056 | 0.296528 | − | 0.955024i | \(-0.404171\pi\) | ||||
0.296528 | + | 0.955024i | \(0.404171\pi\) | |||||||
\(674\) | −3.13485e8 | −1.02385 | ||||||||
\(675\) | − | 9.98929e7i | − | 0.324805i | ||||||
\(676\) | −2.74600e8 | −0.888917 | ||||||||
\(677\) | − | 2.40792e8i | − | 0.776024i | −0.921654 | − | 0.388012i | \(-0.873162\pi\) | ||
0.921654 | − | 0.388012i | \(-0.126838\pi\) | |||||||
\(678\) | − | 2.03665e8i | − | 0.653471i | ||||||
\(679\) | 3.30202e7 | − | 2.29564e7i | 0.105480 | − | 0.0733323i | ||||
\(680\) | 3.30622e7 | 0.105149 | ||||||||
\(681\) | 5.09876e8 | 1.61445 | ||||||||
\(682\) | − | 1.29931e8i | − | 0.409600i | ||||||
\(683\) | −5.06433e8 | −1.58950 | −0.794749 | − | 0.606939i | \(-0.792397\pi\) | ||||
−0.794749 | + | 0.606939i | \(0.792397\pi\) | |||||||
\(684\) | 4.03396e7i | 0.126056i | ||||||||
\(685\) | 6.81221e7i | 0.211942i | ||||||||
\(686\) | −2.21079e8 | + | 5.68618e7i | −0.684818 | + | 0.176136i | ||||
\(687\) | −2.54373e8 | −0.784515 | ||||||||
\(688\) | −1.17100e8 | −0.359575 | ||||||||
\(689\) | 4.54778e8i | 1.39041i | ||||||||
\(690\) | −1.94022e8 | −0.590614 | ||||||||
\(691\) | 3.85108e7i | 0.116721i | 0.998296 | + | 0.0583604i | \(0.0185873\pi\) | ||||
−0.998296 | + | 0.0583604i | \(0.981413\pi\) | |||||||
\(692\) | − | 1.47777e8i | − | 0.445953i | ||||||
\(693\) | 3.43267e7 | + | 4.93749e7i | 0.103141 | + | 0.148357i | ||||
\(694\) | −5.68474e7 | −0.170072 | ||||||||
\(695\) | 4.74160e7 | 0.141244 | ||||||||
\(696\) | 2.26094e8i | 0.670596i | ||||||||
\(697\) | −3.34739e7 | −0.0988573 | ||||||||
\(698\) | 4.09281e8i | 1.20353i | ||||||||
\(699\) | 1.42653e8i | 0.417686i | ||||||||
\(700\) | 3.72606e7 | + | 5.35950e7i | 0.108631 | + | 0.156254i | ||||
\(701\) | 3.57882e8 | 1.03893 | 0.519464 | − | 0.854492i | \(-0.326132\pi\) | ||||
0.519464 | + | 0.854492i | \(0.326132\pi\) | |||||||
\(702\) | 3.47930e8 | 1.00573 | ||||||||
\(703\) | 3.68475e8i | 1.06058i | ||||||||
\(704\) | −3.41481e7 | −0.0978698 | ||||||||
\(705\) | 4.11470e8i | 1.17428i | ||||||||
\(706\) | 1.72214e8i | 0.489388i | ||||||||
\(707\) | 1.98882e8 | − | 1.38268e8i | 0.562779 | − | 0.391258i | ||||
\(708\) | −2.60629e8 | −0.734383 | ||||||||
\(709\) | −2.84537e8 | −0.798361 | −0.399181 | − | 0.916872i | \(-0.630705\pi\) | ||||
−0.399181 | + | 0.916872i | \(0.630705\pi\) | |||||||
\(710\) | − | 1.20216e8i | − | 0.335884i | ||||||
\(711\) | −7.59479e7 | −0.211304 | ||||||||
\(712\) | 7.44730e7i | 0.206328i | ||||||||
\(713\) | 2.56538e8i | 0.707756i | ||||||||
\(714\) | 6.15946e7 | + | 8.85967e7i | 0.169219 | + | 0.243401i | ||||
\(715\) | −3.75398e8 | −1.02701 | ||||||||
\(716\) | −9.18543e7 | −0.250242 | ||||||||
\(717\) | − | 4.76059e8i | − | 1.29153i | ||||||
\(718\) | 4.51447e7 | 0.121965 | ||||||||
\(719\) | − | 3.52700e8i | − | 0.948896i | −0.880283 | − | 0.474448i | \(-0.842648\pi\) | ||
0.880283 | − | 0.474448i | \(-0.157352\pi\) | |||||||
\(720\) | 1.69476e7i | 0.0454057i | ||||||||
\(721\) | 4.55787e8 | − | 3.16874e8i | 1.21606 | − | 0.845437i | ||||
\(722\) | −5.14879e7 | −0.136802 | ||||||||
\(723\) | −7.97244e6 | −0.0210948 | ||||||||
\(724\) | 2.17997e8i | 0.574428i | ||||||||
\(725\) | −2.47977e8 | −0.650725 | ||||||||
\(726\) | 1.16163e8i | 0.303570i | ||||||||
\(727\) | 7.48885e8i | 1.94900i | 0.224387 | + | 0.974500i | \(0.427962\pi\) | ||||
−0.224387 | + | 0.974500i | \(0.572038\pi\) | |||||||
\(728\) | −1.86673e8 | + | 1.29780e8i | −0.483825 | + | 0.336367i | ||||
\(729\) | −2.61510e8 | −0.675002 | ||||||||
\(730\) | −6.22877e7 | −0.160116 | ||||||||
\(731\) | − | 2.12310e8i | − | 0.543524i | ||||||
\(732\) | 3.24510e8 | 0.827361 | ||||||||
\(733\) | − | 6.35196e8i | − | 1.61286i | −0.591331 | − | 0.806429i | \(-0.701398\pi\) | ||
0.591331 | − | 0.806429i | \(-0.298602\pi\) | |||||||
\(734\) | − | 1.16737e8i | − | 0.295202i | ||||||
\(735\) | 1.20754e8 | − | 3.24974e8i | 0.304116 | − | 0.818439i | ||||
\(736\) | 6.74227e7 | 0.169111 | ||||||||
\(737\) | 1.10867e8 | 0.276948 | ||||||||
\(738\) | − | 1.71586e7i | − | 0.0426887i | ||||||
\(739\) | 3.65308e8 | 0.905161 | 0.452580 | − | 0.891724i | \(-0.350504\pi\) | ||||
0.452580 | + | 0.891724i | \(0.350504\pi\) | |||||||
\(740\) | 1.54805e8i | 0.382023i | ||||||||
\(741\) | − | 8.21869e8i | − | 2.01998i | ||||||
\(742\) | 1.37559e8 | + | 1.97863e8i | 0.336727 | + | 0.484343i | ||||
\(743\) | −2.84817e8 | −0.694384 | −0.347192 | − | 0.937794i | \(-0.612865\pi\) | ||||
−0.347192 | + | 0.937794i | \(0.612865\pi\) | |||||||
\(744\) | 1.19509e8 | 0.290189 | ||||||||
\(745\) | 6.44956e7i | 0.155977i | ||||||||
\(746\) | −5.12671e7 | −0.123487 | ||||||||
\(747\) | − | 3.79832e7i | − | 0.0911235i | ||||||
\(748\) | − | 6.19130e7i | − | 0.147937i | ||||||
\(749\) | 8.59949e7 | + | 1.23694e8i | 0.204657 | + | 0.294376i | ||||
\(750\) | −3.59593e8 | −0.852368 | ||||||||
\(751\) | −1.41864e8 | −0.334929 | −0.167465 | − | 0.985878i | \(-0.553558\pi\) | ||||
−0.167465 | + | 0.985878i | \(0.553558\pi\) | |||||||
\(752\) | − | 1.42986e8i | − | 0.336233i | ||||||
\(753\) | 3.05515e8 | 0.715563 | ||||||||
\(754\) | − | 8.63712e8i | − | 2.01491i | ||||||
\(755\) | − | 4.68781e6i | − | 0.0108925i | ||||||
\(756\) | 1.51376e8 | − | 1.05241e8i | 0.350343 | − | 0.243567i | ||||
\(757\) | 4.81270e8 | 1.10943 | 0.554716 | − | 0.832040i | \(-0.312827\pi\) | ||||
0.554716 | + | 0.832040i | \(0.312827\pi\) | |||||||
\(758\) | 2.22083e8 | 0.509927 | ||||||||
\(759\) | 3.63330e8i | 0.830951i | ||||||||
\(760\) | −1.33439e8 | −0.303978 | ||||||||
\(761\) | − | 4.55601e8i | − | 1.03379i | −0.856050 | − | 0.516893i | \(-0.827088\pi\) | ||
0.856050 | − | 0.516893i | \(-0.172912\pi\) | |||||||
\(762\) | 2.36072e8i | 0.533555i | ||||||||
\(763\) | 3.53202e8 | + | 5.08041e8i | 0.795151 | + | 1.14373i | ||||
\(764\) | −1.60191e8 | −0.359218 | ||||||||
\(765\) | −3.07272e7 | −0.0686339 | ||||||||
\(766\) | − | 2.40926e8i | − | 0.536040i | ||||||
\(767\) | 9.95641e8 | 2.20657 | ||||||||
\(768\) | − | 3.14089e7i | − | 0.0693377i | ||||||
\(769\) | − | 3.23170e8i | − | 0.710643i | −0.934744 | − | 0.355322i | \(-0.884371\pi\) | ||
0.934744 | − | 0.355322i | \(-0.115629\pi\) | |||||||
\(770\) | −1.63327e8 | + | 1.13549e8i | −0.357755 | + | 0.248720i | ||||
\(771\) | −8.02863e8 | −1.75177 | ||||||||
\(772\) | 6.23984e7 | 0.135619 | ||||||||
\(773\) | 2.14005e8i | 0.463324i | 0.972796 | + | 0.231662i | \(0.0744164\pi\) | ||||
−0.972796 | + | 0.231662i | \(0.925584\pi\) | |||||||
\(774\) | 1.08829e8 | 0.234705 | ||||||||
\(775\) | 1.31076e8i | 0.281590i | ||||||||
\(776\) | − | 2.12242e7i | − | 0.0454198i | ||||||
\(777\) | −4.14829e8 | + | 2.88399e8i | −0.884314 | + | 0.614797i | ||||
\(778\) | −1.82846e8 | −0.388282 | ||||||||
\(779\) | 1.35101e8 | 0.285789 | ||||||||
\(780\) | − | 3.45285e8i | − | 0.727603i | ||||||
\(781\) | −2.25120e8 | −0.472564 | ||||||||
\(782\) | 1.22242e8i | 0.255624i | ||||||||
\(783\) | 7.00398e8i | 1.45902i | ||||||||
\(784\) | −4.19619e7 | + | 1.12928e8i | −0.0870778 | + | 0.234345i | ||||
\(785\) | −2.05127e8 | −0.424048 | ||||||||
\(786\) | 4.41025e8 | 0.908229 | ||||||||
\(787\) | − | 6.93076e8i | − | 1.42186i | −0.703263 | − | 0.710930i | \(-0.748274\pi\) | ||
0.703263 | − | 0.710930i | \(-0.251726\pi\) | |||||||
\(788\) | 3.71275e8 | 0.758782 | ||||||||
\(789\) | 7.86328e8i | 1.60093i | ||||||||
\(790\) | − | 2.51228e8i | − | 0.509549i | ||||||
\(791\) | 2.35335e8 | + | 3.38502e8i | 0.475507 | + | 0.683962i | ||||
\(792\) | 3.17364e7 | 0.0638825 | ||||||||
\(793\) | −1.23968e9 | −2.48593 | ||||||||
\(794\) | 6.85027e8i | 1.36850i | ||||||||
\(795\) | −3.65983e8 | −0.728383 | ||||||||
\(796\) | − | 2.32702e7i | − | 0.0461382i | ||||||
\(797\) | 1.42327e8i | 0.281134i | 0.990071 | + | 0.140567i | \(0.0448926\pi\) | ||||
−0.990071 | + | 0.140567i | \(0.955107\pi\) | |||||||
\(798\) | −2.48596e8 | − | 3.57576e8i | −0.489198 | − | 0.703655i | ||||
\(799\) | 2.59244e8 | 0.508240 | ||||||||
\(800\) | 3.44489e7 | 0.0672830 | ||||||||
\(801\) | − | 6.92133e7i | − | 0.134676i | ||||||
\(802\) | 2.82235e8 | 0.547126 | ||||||||
\(803\) | 1.16641e8i | 0.225271i | ||||||||
\(804\) | 1.01974e8i | 0.196209i | ||||||||
\(805\) | 3.22476e8 | − | 2.24193e8i | 0.618172 | − | 0.429769i | ||||
\(806\) | −4.56541e8 | −0.871916 | ||||||||
\(807\) | −1.07505e9 | −2.04554 | ||||||||
\(808\) | − | 1.27834e8i | − | 0.242333i | ||||||
\(809\) | −2.01624e8 | −0.380800 | −0.190400 | − | 0.981707i | \(-0.560979\pi\) | ||||
−0.190400 | + | 0.981707i | \(0.560979\pi\) | |||||||
\(810\) | 3.48249e8i | 0.655291i | ||||||||
\(811\) | 1.69349e7i | 0.0317483i | 0.999874 | + | 0.0158741i | \(0.00505311\pi\) | ||||
−0.999874 | + | 0.0158741i | \(0.994947\pi\) | |||||||
\(812\) | −2.61252e8 | − | 3.75781e8i | −0.487969 | − | 0.701887i | ||||
\(813\) | −4.91905e7 | −0.0915398 | ||||||||
\(814\) | 2.89891e8 | 0.537478 | ||||||||
\(815\) | − | 1.56739e8i | − | 0.289538i | ||||||
\(816\) | 5.69467e7 | 0.104809 | ||||||||
\(817\) | 8.56883e8i | 1.57129i | ||||||||
\(818\) | 6.13264e7i | 0.112044i | ||||||||
\(819\) | 1.73489e8 | − | 1.20614e8i | 0.315806 | − | 0.219556i | ||||
\(820\) | 5.67589e7 | 0.102942 | ||||||||
\(821\) | 3.77973e8 | 0.683018 | 0.341509 | − | 0.939879i | \(-0.389062\pi\) | ||||
0.341509 | + | 0.939879i | \(0.389062\pi\) | |||||||
\(822\) | 1.17334e8i | 0.211256i | ||||||||
\(823\) | 5.19539e8 | 0.932006 | 0.466003 | − | 0.884783i | \(-0.345694\pi\) | ||||
0.466003 | + | 0.884783i | \(0.345694\pi\) | |||||||
\(824\) | − | 2.92963e8i | − | 0.523638i | ||||||
\(825\) | 1.85639e8i | 0.330604i | ||||||||
\(826\) | 4.33180e8 | − | 3.01158e8i | 0.768650 | − | 0.534384i | ||||
\(827\) | 5.17270e7 | 0.0914536 | 0.0457268 | − | 0.998954i | \(-0.485440\pi\) | ||||
0.0457268 | + | 0.998954i | \(0.485440\pi\) | |||||||
\(828\) | −6.26609e7 | −0.110384 | ||||||||
\(829\) | 7.51588e7i | 0.131922i | 0.997822 | + | 0.0659609i | \(0.0210113\pi\) | ||||
−0.997822 | + | 0.0659609i | \(0.978989\pi\) | |||||||
\(830\) | 1.25645e8 | 0.219740 | ||||||||
\(831\) | − | 1.15102e9i | − | 2.00576i | ||||||
\(832\) | 1.19987e8i | 0.208335i | ||||||||
\(833\) | −2.04748e8 | − | 7.60801e7i | −0.354229 | − | 0.131624i | ||||
\(834\) | 8.16697e7 | 0.140787 | ||||||||
\(835\) | −1.19764e8 | −0.205715 | ||||||||
\(836\) | 2.49881e8i | 0.427675i | ||||||||
\(837\) | 3.70216e8 | 0.631363 | ||||||||
\(838\) | 2.17797e8i | 0.370101i | ||||||||
\(839\) | − | 8.14179e8i | − | 1.37859i | −0.724483 | − | 0.689293i | \(-0.757921\pi\) | ||
0.724483 | − | 0.689293i | \(-0.242079\pi\) | |||||||
\(840\) | −1.04441e8 | − | 1.50226e8i | −0.176210 | − | 0.253458i | ||||
\(841\) | 1.14387e9 | 1.92303 | ||||||||
\(842\) | −3.84966e8 | −0.644891 | ||||||||
\(843\) | 1.13422e9i | 1.89328i | ||||||||
\(844\) | 1.86416e8 | 0.310067 | ||||||||
\(845\) | 8.44196e8i | 1.39918i | ||||||||
\(846\) | 1.32887e8i | 0.219469i | ||||||||
\(847\) | −1.34227e8 | − | 1.93070e8i | −0.220897 | − | 0.317734i | ||||
\(848\) | 1.27179e8 | 0.208559 | ||||||||
\(849\) | 1.07243e8 | 0.175245 | ||||||||
\(850\) | 6.24584e7i | 0.101703i | ||||||||
\(851\) | −5.72365e8 | −0.928719 | ||||||||
\(852\) | − | 2.07062e8i | − | 0.334797i | ||||||
\(853\) | − | 9.81909e8i | − | 1.58206i | −0.611774 | − | 0.791032i | \(-0.709544\pi\) | ||
0.611774 | − | 0.791032i | \(-0.290456\pi\) | |||||||
\(854\) | −5.39354e8 | + | 3.74972e8i | −0.865966 | + | 0.602040i | ||||
\(855\) | 1.24015e8 | 0.198415 | ||||||||
\(856\) | 7.95057e7 | 0.126759 | ||||||||
\(857\) | − | 1.05751e9i | − | 1.68013i | −0.542487 | − | 0.840064i | \(-0.682517\pi\) | ||
0.542487 | − | 0.840064i | \(-0.317483\pi\) | |||||||
\(858\) | −6.46588e8 | −1.02368 | ||||||||
\(859\) | − | 1.43809e8i | − | 0.226886i | −0.993545 | − | 0.113443i | \(-0.963812\pi\) | ||
0.993545 | − | 0.113443i | \(-0.0361879\pi\) | |||||||
\(860\) | 3.59996e8i | 0.565981i | ||||||||
\(861\) | 1.05741e8 | + | 1.52096e8i | 0.165666 | + | 0.238292i | ||||
\(862\) | −3.36059e8 | −0.524679 | ||||||||
\(863\) | 3.42007e8 | 0.532111 | 0.266056 | − | 0.963958i | \(-0.414280\pi\) | ||||
0.266056 | + | 0.963958i | \(0.414280\pi\) | |||||||
\(864\) | − | 9.72992e7i | − | 0.150858i | ||||||
\(865\) | −4.54307e8 | −0.701942 | ||||||||
\(866\) | − | 3.62054e8i | − | 0.557467i | ||||||
\(867\) | − | 6.19765e8i | − | 0.950977i | ||||||
\(868\) | −1.98630e8 | + | 1.38093e8i | −0.303729 | + | 0.211160i | ||||
\(869\) | −4.70454e8 | −0.716899 | ||||||||
\(870\) | 6.95074e8 | 1.05554 | ||||||||
\(871\) | − | 3.89554e8i | − | 0.589540i | ||||||
\(872\) | 3.26550e8 | 0.492493 | ||||||||
\(873\) | 1.97252e7i | 0.0296468i | ||||||||
\(874\) | − | 4.93369e8i | − | 0.738989i | ||||||
\(875\) | 5.97664e8 | − | 4.15511e8i | 0.892140 | − | 0.620238i | ||||
\(876\) | −1.07285e8 | −0.159598 | ||||||||
\(877\) | −2.00898e8 | −0.297836 | −0.148918 | − | 0.988850i | \(-0.547579\pi\) | ||||
−0.148918 | + | 0.988850i | \(0.547579\pi\) | |||||||
\(878\) | 3.30772e8i | 0.488703i | ||||||||
\(879\) | 1.06995e9 | 1.57542 | ||||||||
\(880\) | 1.04981e8i | 0.154050i | ||||||||
\(881\) | 1.00494e9i | 1.46964i | 0.678262 | + | 0.734820i | \(0.262733\pi\) | ||||
−0.678262 | + | 0.734820i | \(0.737267\pi\) | |||||||
\(882\) | 3.89983e7 | − | 1.04953e8i | 0.0568382 | − | 0.152964i | ||||
\(883\) | 5.37005e8 | 0.780003 | 0.390001 | − | 0.920814i | \(-0.372475\pi\) | ||||
0.390001 | + | 0.920814i | \(0.372475\pi\) | |||||||
\(884\) | −2.17545e8 | −0.314914 | ||||||||
\(885\) | 8.01244e8i | 1.15594i | ||||||||
\(886\) | −8.74639e8 | −1.25756 | ||||||||
\(887\) | − | 1.31599e8i | − | 0.188574i | −0.995545 | − | 0.0942871i | \(-0.969943\pi\) | ||
0.995545 | − | 0.0942871i | \(-0.0300572\pi\) | |||||||
\(888\) | 2.66637e8i | 0.380786i | ||||||||
\(889\) | −2.72782e8 | − | 3.92365e8i | −0.388249 | − | 0.558451i | ||||
\(890\) | 2.28950e8 | 0.324766 | ||||||||
\(891\) | 6.52138e8 | 0.921947 | ||||||||
\(892\) | 1.93755e8i | 0.272997i | ||||||||
\(893\) | −1.04631e9 | −1.46928 | ||||||||
\(894\) | 1.11088e8i | 0.155473i | ||||||||
\(895\) | 2.82385e8i | 0.393888i | ||||||||
\(896\) | 3.62931e7 | + | 5.22034e7i | 0.0504545 | + | 0.0725730i | ||||
\(897\) | 1.27664e9 | 1.76885 | ||||||||
\(898\) | 4.70029e8 | 0.649076 | ||||||||
\(899\) | − | 9.19036e8i | − | 1.26489i | ||||||
\(900\) | −3.20159e7 | −0.0439176 | ||||||||
\(901\) | 2.30585e8i | 0.315251i | ||||||||
\(902\) | − | 1.06288e8i | − | 0.144832i | ||||||
\(903\) | −9.64678e8 | + | 6.70668e8i | −1.31014 | + | 0.910845i | ||||
\(904\) | 2.17577e8 | 0.294515 | ||||||||
\(905\) | 6.70183e8 | 0.904165 | ||||||||
\(906\) | − | 8.07432e6i | − | 0.0108573i | ||||||
\(907\) | −1.20778e9 | −1.61870 | −0.809349 | − | 0.587328i | \(-0.800180\pi\) | ||||
−0.809349 | + | 0.587328i | \(0.800180\pi\) | |||||||
\(908\) | 5.44706e8i | 0.727619i | ||||||||
\(909\) | 1.18806e8i | 0.158178i | ||||||||
\(910\) | 3.98978e8 | + | 5.73884e8i | 0.529450 | + | 0.761553i | ||||
\(911\) | −1.08236e8 | −0.143158 | −0.0715792 | − | 0.997435i | \(-0.522804\pi\) | ||||
−0.0715792 | + | 0.997435i | \(0.522804\pi\) | |||||||
\(912\) | −2.29837e8 | −0.302994 | ||||||||
\(913\) | − | 2.35285e8i | − | 0.309158i | ||||||
\(914\) | 2.10108e8 | 0.275172 | ||||||||
\(915\) | − | 9.97631e8i | − | 1.30229i | ||||||
\(916\) | − | 2.71749e8i | − | 0.353576i | ||||||
\(917\) | −7.33009e8 | + | 5.09606e8i | −0.950608 | + | 0.660886i | ||||
\(918\) | 1.76411e8 | 0.228032 | ||||||||
\(919\) | −8.87506e8 | −1.14347 | −0.571735 | − | 0.820438i | \(-0.693729\pi\) | ||||
−0.571735 | + | 0.820438i | \(0.693729\pi\) | |||||||
\(920\) | − | 2.07275e8i | − | 0.266186i | ||||||
\(921\) | −1.11372e9 | −1.42559 | ||||||||
\(922\) | 1.91268e7i | 0.0244034i | ||||||||
\(923\) | 7.91006e8i | 1.00595i | ||||||||
\(924\) | −2.81316e8 | + | 1.95578e8i | −0.356597 | + | 0.247915i | ||||
\(925\) | −2.92444e8 | −0.369503 | ||||||||
\(926\) | 3.75281e8 | 0.472633 | ||||||||
\(927\) | 2.72272e8i | 0.341794i | ||||||||
\(928\) | −2.41538e8 | −0.302233 | ||||||||
\(929\) | − | 5.79061e7i | − | 0.0722233i | −0.999348 | − | 0.0361116i | \(-0.988503\pi\) | ||
0.999348 | − | 0.0361116i | \(-0.0114972\pi\) | |||||||
\(930\) | − | 3.67402e8i | − | 0.456765i | ||||||
\(931\) | 8.26361e8 | + | 3.07059e8i | 1.02405 | + | 0.380516i | ||||
\(932\) | −1.52398e8 | −0.188248 | ||||||||
\(933\) | 4.13174e8 | 0.508731 | ||||||||
\(934\) | − | 5.64171e8i | − | 0.692420i | ||||||
\(935\) | −1.90337e8 | −0.232857 | ||||||||
\(936\) | − | 1.11512e8i | − | 0.135987i | ||||||
\(937\) | 1.01207e9i | 1.23024i | 0.788432 | + | 0.615122i | \(0.210893\pi\) | ||||
−0.788432 | + | 0.615122i | \(0.789107\pi\) | |||||||
\(938\) | −1.17831e8 | − | 1.69486e8i | −0.142774 | − | 0.205364i | ||||
\(939\) | 2.73715e8 | 0.330600 | ||||||||
\(940\) | −4.39578e8 | −0.529239 | ||||||||
\(941\) | 9.96415e8i | 1.19584i | 0.801557 | + | 0.597918i | \(0.204005\pi\) | ||||
−0.801557 | + | 0.597918i | \(0.795995\pi\) | |||||||
\(942\) | −3.53313e8 | −0.422675 | ||||||||
\(943\) | 2.09857e8i | 0.250258i | ||||||||
\(944\) | − | 2.78432e8i | − | 0.330981i | ||||||
\(945\) | −3.23538e8 | − | 4.65372e8i | −0.383381 | − | 0.551449i | ||||
\(946\) | 6.74135e8 | 0.796294 | ||||||||
\(947\) | 8.94254e8 | 1.05296 | 0.526479 | − | 0.850188i | \(-0.323512\pi\) | ||||
0.526479 | + | 0.850188i | \(0.323512\pi\) | |||||||
\(948\) | − | 4.32717e8i | − | 0.507900i | ||||||
\(949\) | 4.09844e8 | 0.479535 | ||||||||
\(950\) | − | 2.52082e8i | − | 0.294016i | ||||||
\(951\) | 3.84077e8i | 0.446557i | ||||||||
\(952\) | −9.46487e7 | + | 6.58021e7i | −0.109699 | + | 0.0762656i | ||||
\(953\) | −7.60395e8 | −0.878538 | −0.439269 | − | 0.898355i | \(-0.644763\pi\) | ||||
−0.439269 | + | 0.898355i | \(0.644763\pi\) | |||||||
\(954\) | −1.18197e8 | −0.136132 | ||||||||
\(955\) | 4.92470e8i | 0.565418i | ||||||||
\(956\) | 5.08578e8 | 0.582082 | ||||||||
\(957\) | − | 1.30161e9i | − | 1.48506i | ||||||
\(958\) | 4.81323e8i | 0.547444i | ||||||||
\(959\) | −1.35580e8 | − | 1.95016e8i | −0.153723 | − | 0.221113i | ||||
\(960\) | −9.65595e7 | −0.109139 | ||||||||
\(961\) | 4.01720e8 | 0.452640 | ||||||||
\(962\) | − | 1.01859e9i | − | 1.14413i | ||||||
\(963\) | −7.38905e7 | −0.0827389 | ||||||||
\(964\) | − | 8.51703e6i | − | 0.00950730i | ||||||
\(965\) | − | 1.91829e8i | − | 0.213468i | ||||||
\(966\) | 5.55435e8 | − | 3.86152e8i | 0.616172 | − | 0.428378i | ||||
\(967\) | 9.71735e8 | 1.07465 | 0.537327 | − | 0.843374i | \(-0.319434\pi\) | ||||
0.537327 | + | 0.843374i | \(0.319434\pi\) | |||||||
\(968\) | −1.24098e8 | −0.136817 | ||||||||
\(969\) | − | 4.16711e8i | − | 0.457998i | ||||||
\(970\) | −6.52488e7 | −0.0714920 | ||||||||
\(971\) | 1.27689e9i | 1.39475i | 0.716708 | + | 0.697374i | \(0.245648\pi\) | ||||
−0.716708 | + | 0.697374i | \(0.754352\pi\) | |||||||
\(972\) | 2.07984e8i | 0.226480i | ||||||||
\(973\) | −1.35740e8 | + | 9.43696e7i | −0.147356 | + | 0.102446i | ||||
\(974\) | 6.77628e8 | 0.733355 | ||||||||
\(975\) | 6.52284e8 | 0.703757 | ||||||||
\(976\) | 3.46677e8i | 0.372886i | ||||||||
\(977\) | 1.53509e9 | 1.64608 | 0.823040 | − | 0.567984i | \(-0.192276\pi\) | ||||
0.823040 | + | 0.567984i | \(0.192276\pi\) | |||||||
\(978\) | − | 2.69969e8i | − | 0.288601i | ||||||
\(979\) | − | 4.28737e8i | − | 0.456923i | ||||||
\(980\) | 3.47173e8 | + | 1.29002e8i | 0.368865 | + | 0.137063i | ||||
\(981\) | −3.03487e8 | −0.321464 | ||||||||
\(982\) | −1.27198e9 | −1.34322 | ||||||||
\(983\) | − | 9.46892e8i | − | 0.996873i | −0.866926 | − | 0.498436i | \(-0.833908\pi\) | ||
0.866926 | − | 0.498436i | \(-0.166092\pi\) | |||||||
\(984\) | 9.77619e7 | 0.102609 | ||||||||
\(985\) | − | 1.14140e9i | − | 1.19434i | ||||||
\(986\) | − | 4.37927e8i | − | 0.456847i | ||||||
\(987\) | −8.18928e8 | − | 1.17793e9i | −0.851715 | − | 1.22509i | ||||
\(988\) | 8.78010e8 | 0.910392 | ||||||||
\(989\) | −1.33102e9 | −1.37593 | ||||||||
\(990\) | − | 9.75662e7i | − | 0.100553i | ||||||
\(991\) | −1.27731e9 | −1.31242 | −0.656211 | − | 0.754577i | \(-0.727842\pi\) | ||||
−0.656211 | + | 0.754577i | \(0.727842\pi\) | |||||||
\(992\) | 1.27672e8i | 0.130786i | ||||||||
\(993\) | − | 1.87061e9i | − | 1.91045i | ||||||
\(994\) | 2.39261e8 | + | 3.44149e8i | 0.243619 | + | 0.350418i | ||||
\(995\) | −7.15389e7 | −0.0726228 | ||||||||
\(996\) | 2.16411e8 | 0.219029 | ||||||||
\(997\) | 1.51510e9i | 1.52882i | 0.644731 | + | 0.764409i | \(0.276969\pi\) | ||||
−0.644731 | + | 0.764409i | \(0.723031\pi\) | |||||||
\(998\) | 3.28108e8 | 0.330085 | ||||||||
\(999\) | 8.25993e8i | 0.828476i |
(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 | 14.7.b.a.13.3 | ✓ | 4 | |
3.2 | odd | 2 | 126.7.c.a.55.2 | 4 | |||
4.3 | odd | 2 | 112.7.c.c.97.4 | 4 | |||
5.2 | odd | 4 | 350.7.d.a.349.5 | 8 | |||
5.3 | odd | 4 | 350.7.d.a.349.4 | 8 | |||
5.4 | even | 2 | 350.7.b.a.251.2 | 4 | |||
7.2 | even | 3 | 98.7.d.b.31.2 | 8 | |||
7.3 | odd | 6 | 98.7.d.b.19.2 | 8 | |||
7.4 | even | 3 | 98.7.d.b.19.1 | 8 | |||
7.5 | odd | 6 | 98.7.d.b.31.1 | 8 | |||
7.6 | odd | 2 | inner | 14.7.b.a.13.4 | yes | 4 | |
8.3 | odd | 2 | 448.7.c.e.321.1 | 4 | |||
8.5 | even | 2 | 448.7.c.h.321.4 | 4 | |||
21.20 | even | 2 | 126.7.c.a.55.1 | 4 | |||
28.27 | even | 2 | 112.7.c.c.97.1 | 4 | |||
35.13 | even | 4 | 350.7.d.a.349.1 | 8 | |||
35.27 | even | 4 | 350.7.d.a.349.8 | 8 | |||
35.34 | odd | 2 | 350.7.b.a.251.1 | 4 | |||
56.13 | odd | 2 | 448.7.c.h.321.1 | 4 | |||
56.27 | even | 2 | 448.7.c.e.321.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.7.b.a.13.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
14.7.b.a.13.4 | yes | 4 | 7.6 | odd | 2 | inner | |
98.7.d.b.19.1 | 8 | 7.4 | even | 3 | |||
98.7.d.b.19.2 | 8 | 7.3 | odd | 6 | |||
98.7.d.b.31.1 | 8 | 7.5 | odd | 6 | |||
98.7.d.b.31.2 | 8 | 7.2 | even | 3 | |||
112.7.c.c.97.1 | 4 | 28.27 | even | 2 | |||
112.7.c.c.97.4 | 4 | 4.3 | odd | 2 | |||
126.7.c.a.55.1 | 4 | 21.20 | even | 2 | |||
126.7.c.a.55.2 | 4 | 3.2 | odd | 2 | |||
350.7.b.a.251.1 | 4 | 35.34 | odd | 2 | |||
350.7.b.a.251.2 | 4 | 5.4 | even | 2 | |||
350.7.d.a.349.1 | 8 | 35.13 | even | 4 | |||
350.7.d.a.349.4 | 8 | 5.3 | odd | 4 | |||
350.7.d.a.349.5 | 8 | 5.2 | odd | 4 | |||
350.7.d.a.349.8 | 8 | 35.27 | even | 4 | |||
448.7.c.e.321.1 | 4 | 8.3 | odd | 2 | |||
448.7.c.e.321.4 | 4 | 56.27 | even | 2 | |||
448.7.c.h.321.1 | 4 | 56.13 | odd | 2 | |||
448.7.c.h.321.4 | 4 | 8.5 | even | 2 |