Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,8,Mod(11,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.11");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.e (of order \(6\), degree \(2\), 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: | \(11.5582459429\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.3 | ||
Character | \(\chi\) | \(=\) | 37.11 |
Dual form | 37.8.e.a.27.3 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −14.9331 | + | 8.62160i | −1.31991 | + | 0.762049i | −0.983714 | − | 0.179743i | \(-0.942473\pi\) |
−0.336195 | + | 0.941793i | \(0.609140\pi\) | |||||||
\(3\) | 30.8914 | − | 53.5054i | 0.660561 | − | 1.14413i | −0.319908 | − | 0.947449i | \(-0.603652\pi\) |
0.980468 | − | 0.196676i | \(-0.0630148\pi\) | |||||||
\(4\) | 84.6641 | − | 146.643i | 0.661438 | − | 1.14564i | ||||
\(5\) | 237.219 | + | 136.958i | 0.848699 | + | 0.489997i | 0.860212 | − | 0.509937i | \(-0.170331\pi\) |
−0.0115127 | + | 0.999934i | \(0.503665\pi\) | |||||||
\(6\) | 1065.33i | 2.01352i | ||||||||
\(7\) | 106.642 | − | 184.710i | 0.117513 | − | 0.203538i | −0.801269 | − | 0.598305i | \(-0.795841\pi\) |
0.918781 | + | 0.394767i | \(0.129175\pi\) | |||||||
\(8\) | 712.630i | 0.492095i | ||||||||
\(9\) | −815.054 | − | 1411.72i | −0.372681 | − | 0.645503i | ||||
\(10\) | −4723.20 | −1.49361 | ||||||||
\(11\) | −1465.83 | −0.332055 | −0.166028 | − | 0.986121i | \(-0.553094\pi\) | ||||
−0.166028 | + | 0.986121i | \(0.553094\pi\) | |||||||
\(12\) | −5230.78 | − | 9059.98i | −0.873840 | − | 1.51354i | ||||
\(13\) | −2648.87 | − | 1529.32i | −0.334394 | − | 0.193062i | 0.323396 | − | 0.946264i | \(-0.395175\pi\) |
−0.657790 | + | 0.753201i | \(0.728509\pi\) | |||||||
\(14\) | 3677.70i | 0.358202i | ||||||||
\(15\) | 14656.0 | − | 8461.66i | 1.12123 | − | 0.647345i | ||||
\(16\) | 4692.99 | + | 8128.49i | 0.286437 | + | 0.496124i | ||||
\(17\) | 25533.1 | − | 14741.6i | 1.26047 | − | 0.727734i | 0.287306 | − | 0.957839i | \(-0.407240\pi\) |
0.973166 | + | 0.230105i | \(0.0739070\pi\) | |||||||
\(18\) | 24342.5 | + | 14054.1i | 0.983810 | + | 0.568003i | ||||
\(19\) | 13703.7 | + | 7911.85i | 0.458354 | + | 0.264631i | 0.711352 | − | 0.702836i | \(-0.248083\pi\) |
−0.252998 | + | 0.967467i | \(0.581417\pi\) | |||||||
\(20\) | 40167.8 | − | 23190.9i | 1.12272 | − | 0.648205i | ||||
\(21\) | −6588.64 | − | 11411.9i | −0.155249 | − | 0.268899i | ||||
\(22\) | 21889.4 | − | 12637.8i | 0.438282 | − | 0.253043i | ||||
\(23\) | − | 73452.0i | − | 1.25880i | −0.777082 | − | 0.629399i | \(-0.783301\pi\) | ||
0.777082 | − | 0.629399i | \(-0.216699\pi\) | |||||||
\(24\) | 38129.6 | + | 22014.1i | 0.563019 | + | 0.325059i | ||||
\(25\) | −1547.40 | − | 2680.17i | −0.0198067 | − | 0.0343062i | ||||
\(26\) | 52740.9 | 0.588492 | ||||||||
\(27\) | 34406.3 | 0.336407 | ||||||||
\(28\) | −18057.5 | − | 31276.5i | −0.155455 | − | 0.269256i | ||||
\(29\) | − | 60750.1i | − | 0.462545i | −0.972889 | − | 0.231272i | \(-0.925711\pi\) | ||
0.972889 | − | 0.231272i | \(-0.0742889\pi\) | |||||||
\(30\) | −145906. | + | 252717.i | −0.986618 | + | 1.70887i | ||||
\(31\) | − | 121877.i | − | 0.734778i | −0.930067 | − | 0.367389i | \(-0.880252\pi\) | ||
0.930067 | − | 0.367389i | \(-0.119748\pi\) | |||||||
\(32\) | −219157. | − | 126530.i | −1.18231 | − | 0.682606i | ||||
\(33\) | −45281.6 | + | 78430.1i | −0.219343 | + | 0.379913i | ||||
\(34\) | −254192. | + | 440273.i | −1.10914 | + | 1.92108i | ||||
\(35\) | 50595.0 | − | 29211.0i | 0.199466 | − | 0.115162i | ||||
\(36\) | −276023. | −0.986023 | ||||||||
\(37\) | 134510. | − | 277198.i | 0.436566 | − | 0.899672i | ||||
\(38\) | −272851. | −0.806647 | ||||||||
\(39\) | −163654. | + | 94485.8i | −0.441775 | + | 0.255059i | ||||
\(40\) | −97600.6 | + | 169049.i | −0.241125 | + | 0.417641i | ||||
\(41\) | 196435. | − | 340236.i | 0.445119 | − | 0.770968i | −0.552942 | − | 0.833220i | \(-0.686495\pi\) |
0.998060 | + | 0.0622516i | \(0.0198281\pi\) | |||||||
\(42\) | 196777. | + | 113609.i | 0.409828 | + | 0.236615i | ||||
\(43\) | 339523.i | 0.651224i | 0.945504 | + | 0.325612i | \(0.105570\pi\) | ||||
−0.945504 | + | 0.325612i | \(0.894430\pi\) | |||||||
\(44\) | −124104. | + | 214954.i | −0.219634 | + | 0.380417i | ||||
\(45\) | − | 446513.i | − | 0.730450i | ||||||
\(46\) | 633274. | + | 1.09686e6i | 0.959266 | + | 1.66150i | ||||
\(47\) | 324875. | 0.456429 | 0.228214 | − | 0.973611i | \(-0.426711\pi\) | ||||
0.228214 | + | 0.973611i | \(0.426711\pi\) | |||||||
\(48\) | 579891. | 0.756837 | ||||||||
\(49\) | 389026. | + | 673814.i | 0.472381 | + | 0.818189i | ||||
\(50\) | 46214.8 | + | 26682.1i | 0.0522860 | + | 0.0301873i | ||||
\(51\) | − | 1.82155e6i | − | 1.92285i | ||||||
\(52\) | −448528. | + | 258958.i | −0.442362 | + | 0.255398i | ||||
\(53\) | −425460. | − | 736918.i | −0.392548 | − | 0.679913i | 0.600237 | − | 0.799822i | \(-0.295073\pi\) |
−0.992785 | + | 0.119909i | \(0.961740\pi\) | |||||||
\(54\) | −513791. | + | 296637.i | −0.444026 | + | 0.256359i | ||||
\(55\) | −347723. | − | 200758.i | −0.281815 | − | 0.162706i | ||||
\(56\) | 131630. | + | 75996.4i | 0.100160 | + | 0.0578276i | ||||
\(57\) | 846654. | − | 488816.i | 0.605542 | − | 0.349610i | ||||
\(58\) | 523763. | + | 907184.i | 0.352482 | + | 0.610517i | ||||
\(59\) | −2.32671e6 | + | 1.34333e6i | −1.47489 | + | 0.851528i | −0.999599 | − | 0.0283003i | \(-0.990991\pi\) |
−0.475291 | + | 0.879829i | \(0.657657\pi\) | |||||||
\(60\) | − | 2.86559e6i | − | 1.71272i | ||||||
\(61\) | −171680. | − | 99119.3i | −0.0968422 | − | 0.0559119i | 0.450797 | − | 0.892627i | \(-0.351140\pi\) |
−0.547639 | + | 0.836715i | \(0.684473\pi\) | |||||||
\(62\) | 1.05078e6 | + | 1.82000e6i | 0.559937 | + | 0.969840i | ||||
\(63\) | −347676. | −0.175179 | ||||||||
\(64\) | 3.16218e6 | 1.50784 | ||||||||
\(65\) | −418907. | − | 725568.i | −0.189200 | − | 0.327704i | ||||
\(66\) | − | 1.56160e6i | − | 0.668600i | ||||||
\(67\) | −1.80651e6 | + | 3.12896e6i | −0.733800 | + | 1.27098i | 0.221448 | + | 0.975172i | \(0.428922\pi\) |
−0.955248 | + | 0.295807i | \(0.904412\pi\) | |||||||
\(68\) | − | 4.99233e6i | − | 1.92540i | ||||||
\(69\) | −3.93008e6 | − | 2.26903e6i | −1.44022 | − | 0.831513i | ||||
\(70\) | −503692. | + | 872420.i | −0.175518 | + | 0.304006i | ||||
\(71\) | 104184. | − | 180452.i | 0.0345460 | − | 0.0598354i | −0.848235 | − | 0.529619i | \(-0.822335\pi\) |
0.882781 | + | 0.469784i | \(0.155668\pi\) | |||||||
\(72\) | 1.00603e6 | − | 580832.i | 0.317649 | − | 0.183395i | ||||
\(73\) | 3.43373e6 | 1.03308 | 0.516542 | − | 0.856262i | \(-0.327219\pi\) | ||||
0.516542 | + | 0.856262i | \(0.327219\pi\) | |||||||
\(74\) | 381241. | + | 5.29911e6i | 0.109368 | + | 1.52017i | ||||
\(75\) | −191205. | −0.0523341 | ||||||||
\(76\) | 2.32043e6 | − | 1.33970e6i | 0.606346 | − | 0.350074i | ||||
\(77\) | −156320. | + | 270754.i | −0.0390208 | + | 0.0675860i | ||||
\(78\) | 1.62924e6 | − | 2.82192e6i | 0.388735 | − | 0.673309i | ||||
\(79\) | 6.56655e6 | + | 3.79120e6i | 1.49845 | + | 0.865131i | 0.999998 | − | 0.00178619i | \(-0.000568561\pi\) |
0.498452 | + | 0.866917i | \(0.333902\pi\) | |||||||
\(80\) | 2.57097e6i | 0.561413i | ||||||||
\(81\) | 2.84538e6 | − | 4.92834e6i | 0.594899 | − | 1.03039i | ||||
\(82\) | 6.77435e6i | 1.35681i | ||||||||
\(83\) | −1.55537e6 | − | 2.69399e6i | −0.298581 | − | 0.517157i | 0.677231 | − | 0.735771i | \(-0.263180\pi\) |
−0.975811 | + | 0.218614i | \(0.929846\pi\) | |||||||
\(84\) | −2.23129e6 | −0.410750 | ||||||||
\(85\) | 8.07592e6 | 1.42635 | ||||||||
\(86\) | −2.92724e6 | − | 5.07012e6i | −0.496265 | − | 0.859555i | ||||
\(87\) | −3.25046e6 | − | 1.87665e6i | −0.529209 | − | 0.305539i | ||||
\(88\) | − | 1.04460e6i | − | 0.163403i | ||||||
\(89\) | −3.11972e6 | + | 1.80117e6i | −0.469084 | + | 0.270826i | −0.715856 | − | 0.698248i | \(-0.753963\pi\) |
0.246772 | + | 0.969074i | \(0.420630\pi\) | |||||||
\(90\) | 3.84966e6 | + | 6.66781e6i | 0.556639 | + | 0.964127i | ||||
\(91\) | −564961. | + | 326181.i | −0.0785912 | + | 0.0453746i | ||||
\(92\) | −1.07712e7 | − | 6.21875e6i | −1.44214 | − | 0.832617i | ||||
\(93\) | −6.52109e6 | − | 3.76495e6i | −0.840678 | − | 0.485366i | ||||
\(94\) | −4.85137e6 | + | 2.80094e6i | −0.602444 | + | 0.347821i | ||||
\(95\) | 2.16719e6 | + | 3.75368e6i | 0.259336 | + | 0.449184i | ||||
\(96\) | −1.35401e7 | + | 7.81740e6i | −1.56197 | + | 0.901806i | ||||
\(97\) | − | 1.25504e7i | − | 1.39623i | −0.715985 | − | 0.698116i | \(-0.754022\pi\) | ||
0.715985 | − | 0.698116i | \(-0.245978\pi\) | |||||||
\(98\) | −1.16187e7 | − | 6.70806e6i | −1.24700 | − | 0.719956i | ||||
\(99\) | 1.19473e6 | + | 2.06934e6i | 0.123751 | + | 0.214343i | ||||
\(100\) | −524036. | −0.0524036 | ||||||||
\(101\) | 5.63265e6 | 0.543987 | 0.271993 | − | 0.962299i | \(-0.412317\pi\) | ||||
0.271993 | + | 0.962299i | \(0.412317\pi\) | |||||||
\(102\) | 1.57047e7 | + | 2.72013e7i | 1.46531 | + | 2.53799i | ||||
\(103\) | 1.20934e7i | 1.09048i | 0.838279 | + | 0.545241i | \(0.183562\pi\) | ||||
−0.838279 | + | 0.545241i | \(0.816438\pi\) | |||||||
\(104\) | 1.08984e6 | − | 1.88766e6i | 0.0950051 | − | 0.164554i | ||||
\(105\) | − | 3.60947e6i | − | 0.304286i | ||||||
\(106\) | 1.27068e7 | + | 7.33629e6i | 1.03625 | + | 0.598282i | ||||
\(107\) | −6.33075e6 | + | 1.09652e7i | −0.499588 | + | 0.865312i | −1.00000 | 0.000475636i | \(-0.999849\pi\) | |
0.500412 | + | 0.865787i | \(0.333182\pi\) | |||||||
\(108\) | 2.91298e6 | − | 5.04542e6i | 0.222512 | − | 0.385403i | ||||
\(109\) | −1.93315e7 | + | 1.11610e7i | −1.42979 | + | 0.825490i | −0.997104 | − | 0.0760549i | \(-0.975768\pi\) |
−0.432686 | + | 0.901545i | \(0.642434\pi\) | |||||||
\(110\) | 6.92342e6 | 0.495960 | ||||||||
\(111\) | −1.06764e7 | − | 1.57601e7i | −0.740959 | − | 1.09377i | ||||
\(112\) | 2.00188e6 | 0.134640 | ||||||||
\(113\) | 1.00546e6 | − | 580502.i | 0.0655525 | − | 0.0378468i | −0.466866 | − | 0.884328i | \(-0.654617\pi\) |
0.532418 | + | 0.846482i | \(0.321283\pi\) | |||||||
\(114\) | −8.42876e6 | + | 1.45990e7i | −0.532840 | + | 0.922905i | ||||
\(115\) | 1.00599e7 | − | 1.74242e7i | 0.616807 | − | 1.06834i | ||||
\(116\) | −8.90854e6 | − | 5.14335e6i | −0.529912 | − | 0.305945i | ||||
\(117\) | 4.98593e6i | 0.287803i | ||||||||
\(118\) | 2.31632e7 | − | 4.01199e7i | 1.29781 | − | 2.24788i | ||||
\(119\) | − | 6.28829e6i | − | 0.342072i | ||||||
\(120\) | 6.03003e6 | + | 1.04443e7i | 0.318556 | + | 0.551754i | ||||
\(121\) | −1.73385e7 | −0.889739 | ||||||||
\(122\) | 3.41827e6 | 0.170430 | ||||||||
\(123\) | −1.21363e7 | − | 2.10207e7i | −0.588056 | − | 1.01854i | ||||
\(124\) | −1.78724e7 | − | 1.03186e7i | −0.841795 | − | 0.486011i | ||||
\(125\) | − | 2.22474e7i | − | 1.01881i | ||||||
\(126\) | 5.19187e6 | − | 2.99753e6i | 0.231221 | − | 0.133495i | ||||
\(127\) | 1.85576e7 | + | 3.21427e7i | 0.803912 | + | 1.39242i | 0.917023 | + | 0.398835i | \(0.130585\pi\) |
−0.113111 | + | 0.993582i | \(0.536081\pi\) | |||||||
\(128\) | −1.91689e7 | + | 1.10671e7i | −0.807907 | + | 0.466445i | ||||
\(129\) | 1.81663e7 | + | 1.04883e7i | 0.745081 | + | 0.430173i | ||||
\(130\) | 1.25111e7 | + | 7.22330e6i | 0.499453 | + | 0.288359i | ||||
\(131\) | 1.24988e7 | − | 7.21621e6i | 0.485758 | − | 0.280453i | −0.237055 | − | 0.971496i | \(-0.576182\pi\) |
0.722813 | + | 0.691044i | \(0.242849\pi\) | |||||||
\(132\) | 7.66746e6 | + | 1.32804e7i | 0.290163 | + | 0.502578i | ||||
\(133\) | 2.92279e6 | − | 1.68747e6i | 0.107725 | − | 0.0621951i | ||||
\(134\) | − | 6.22999e7i | − | 2.23677i | ||||||
\(135\) | 8.16181e6 | + | 4.71222e6i | 0.285508 | + | 0.164838i | ||||
\(136\) | 1.05053e7 | + | 1.81957e7i | 0.358114 | + | 0.620272i | ||||
\(137\) | 1.53560e7 | 0.510220 | 0.255110 | − | 0.966912i | \(-0.417888\pi\) | ||||
0.255110 | + | 0.966912i | \(0.417888\pi\) | |||||||
\(138\) | 7.82508e7 | 2.53462 | ||||||||
\(139\) | 1.86963e7 | + | 3.23830e7i | 0.590480 | + | 1.02274i | 0.994168 | + | 0.107844i | \(0.0343947\pi\) |
−0.403688 | + | 0.914897i | \(0.632272\pi\) | |||||||
\(140\) | − | 9.89250e6i | − | 0.304690i | ||||||
\(141\) | 1.00358e7 | − | 1.73826e7i | 0.301499 | − | 0.522212i | ||||
\(142\) | 3.59294e6i | 0.105303i | ||||||||
\(143\) | 3.88280e6 | + | 2.24174e6i | 0.111037 | + | 0.0641074i | ||||
\(144\) | 7.65008e6 | − | 1.32503e7i | 0.213500 | − | 0.369792i | ||||
\(145\) | 8.32022e6 | − | 1.44110e7i | 0.226645 | − | 0.392561i | ||||
\(146\) | −5.12760e7 | + | 2.96042e7i | −1.36358 | + | 0.787261i | ||||
\(147\) | 4.80702e7 | 1.24815 | ||||||||
\(148\) | −2.92608e7 | − | 4.31937e7i | −0.741943 | − | 1.09523i | ||||
\(149\) | −8.33913e6 | −0.206523 | −0.103262 | − | 0.994654i | \(-0.532928\pi\) | ||||
−0.103262 | + | 0.994654i | \(0.532928\pi\) | |||||||
\(150\) | 2.85527e6 | − | 1.64849e6i | 0.0690762 | − | 0.0398812i | ||||
\(151\) | −3.51352e7 | + | 6.08560e7i | −0.830469 | + | 1.43841i | 0.0671980 | + | 0.997740i | \(0.478594\pi\) |
−0.897667 | + | 0.440675i | \(0.854739\pi\) | |||||||
\(152\) | −5.63823e6 | + | 9.76569e6i | −0.130224 | + | 0.225554i | ||||
\(153\) | −4.16218e7 | − | 2.40304e7i | −0.939509 | − | 0.542426i | ||||
\(154\) | − | 5.39090e6i | − | 0.118943i | ||||||
\(155\) | 1.66921e7 | − | 2.89115e7i | 0.360039 | − | 0.623606i | ||||
\(156\) | 3.19982e7i | 0.674823i | ||||||||
\(157\) | 1.94078e7 | + | 3.36153e7i | 0.400246 | + | 0.693247i | 0.993755 | − | 0.111581i | \(-0.0355913\pi\) |
−0.593509 | + | 0.804827i | \(0.702258\pi\) | |||||||
\(158\) | −1.30745e8 | −2.63709 | ||||||||
\(159\) | −5.25721e7 | −1.03721 | ||||||||
\(160\) | −3.46588e7 | − | 6.00308e7i | −0.668949 | − | 1.15865i | ||||
\(161\) | −1.35673e7 | − | 7.83307e6i | −0.256214 | − | 0.147925i | ||||
\(162\) | 9.81270e7i | 1.81337i | ||||||||
\(163\) | −4.47524e7 | + | 2.58378e7i | −0.809393 | + | 0.467304i | −0.846745 | − | 0.531999i | \(-0.821441\pi\) |
0.0373517 | + | 0.999302i | \(0.488108\pi\) | |||||||
\(164\) | −3.32620e7 | − | 5.76115e7i | −0.588837 | − | 1.01990i | ||||
\(165\) | −2.14833e7 | + | 1.24034e7i | −0.372312 | + | 0.214954i | ||||
\(166\) | 4.64530e7 | + | 2.68196e7i | 0.788198 | + | 0.455066i | ||||
\(167\) | −7.23564e6 | − | 4.17750e6i | −0.120218 | − | 0.0694079i | 0.438685 | − | 0.898641i | \(-0.355444\pi\) |
−0.558903 | + | 0.829233i | \(0.688778\pi\) | |||||||
\(168\) | 8.13244e6 | − | 4.69527e6i | 0.132324 | − | 0.0763972i | ||||
\(169\) | −2.66966e7 | − | 4.62399e7i | −0.425454 | − | 0.736908i | ||||
\(170\) | −1.20598e8 | + | 6.96273e7i | −1.88265 | + | 1.08695i | ||||
\(171\) | − | 2.57944e7i | − | 0.394492i | ||||||
\(172\) | 4.97886e7 | + | 2.87454e7i | 0.746071 | + | 0.430744i | ||||
\(173\) | 5.39524e7 | + | 9.34484e7i | 0.792227 | + | 1.37218i | 0.924585 | + | 0.380976i | \(0.124412\pi\) |
−0.132358 | + | 0.991202i | \(0.542255\pi\) | |||||||
\(174\) | 6.47190e7 | 0.931343 | ||||||||
\(175\) | −660071. | −0.00931017 | ||||||||
\(176\) | −6.87914e6 | − | 1.19150e7i | −0.0951130 | − | 0.164741i | ||||
\(177\) | 1.65989e8i | 2.24995i | ||||||||
\(178\) | 3.10580e7 | − | 5.37940e7i | 0.412766 | − | 0.714931i | ||||
\(179\) | − | 1.03451e8i | − | 1.34818i | −0.738648 | − | 0.674092i | \(-0.764535\pi\) | ||
0.738648 | − | 0.674092i | \(-0.235465\pi\) | |||||||
\(180\) | −6.54779e7 | − | 3.78037e7i | −0.836837 | − | 0.483148i | ||||
\(181\) | 5.61281e7 | − | 9.72168e7i | 0.703567 | − | 1.21861i | −0.263639 | − | 0.964621i | \(-0.584923\pi\) |
0.967206 | − | 0.253993i | \(-0.0817440\pi\) | |||||||
\(182\) | 5.62440e6 | − | 9.74175e6i | 0.0691554 | − | 0.119781i | ||||
\(183\) | −1.06068e7 | + | 6.12387e6i | −0.127940 | + | 0.0738664i | ||||
\(184\) | 5.23441e7 | 0.619449 | ||||||||
\(185\) | 6.98729e7 | − | 4.73342e7i | 0.811349 | − | 0.549635i | ||||
\(186\) | 1.29840e8 | 1.47949 | ||||||||
\(187\) | −3.74274e7 | + | 2.16087e7i | −0.418546 | + | 0.241648i | ||||
\(188\) | 2.75052e7 | − | 4.76404e7i | 0.301900 | − | 0.522905i | ||||
\(189\) | 3.66916e6 | − | 6.35517e6i | 0.0395321 | − | 0.0684717i | ||||
\(190\) | −6.47254e7 | − | 3.73692e7i | −0.684601 | − | 0.395254i | ||||
\(191\) | 1.04555e8i | 1.08574i | 0.839817 | + | 0.542870i | \(0.182662\pi\) | ||||
−0.839817 | + | 0.542870i | \(0.817338\pi\) | |||||||
\(192\) | 9.76840e7 | − | 1.69194e8i | 0.996023 | − | 1.72516i | ||||
\(193\) | 9.09378e7i | 0.910529i | 0.890356 | + | 0.455265i | \(0.150455\pi\) | ||||
−0.890356 | + | 0.455265i | \(0.849545\pi\) | |||||||
\(194\) | 1.08205e8 | + | 1.87416e8i | 1.06400 | + | 1.84290i | ||||
\(195\) | −5.17624e7 | −0.499912 | ||||||||
\(196\) | 1.31746e8 | 1.24980 | ||||||||
\(197\) | 1.03527e8 | + | 1.79314e8i | 0.964765 | + | 1.67102i | 0.710244 | + | 0.703956i | \(0.248585\pi\) |
0.254521 | + | 0.967067i | \(0.418082\pi\) | |||||||
\(198\) | −3.56821e7 | − | 2.06011e7i | −0.326679 | − | 0.188608i | ||||
\(199\) | − | 1.64789e8i | − | 1.48233i | −0.671325 | − | 0.741163i | \(-0.734275\pi\) | ||
0.671325 | − | 0.741163i | \(-0.265725\pi\) | |||||||
\(200\) | 1.90997e6 | − | 1.10272e6i | 0.0168819 | − | 0.00974678i | ||||
\(201\) | 1.11611e8 | + | 1.93316e8i | 0.969439 | + | 1.67912i | ||||
\(202\) | −8.41127e7 | + | 4.85625e7i | −0.718012 | + | 0.414545i | ||||
\(203\) | −1.12211e7 | − | 6.47851e6i | −0.0941456 | − | 0.0543550i | ||||
\(204\) | −2.67117e8 | − | 1.54220e8i | −2.20290 | − | 1.27185i | ||||
\(205\) | 9.31962e7 | − | 5.38068e7i | 0.755544 | − | 0.436213i | ||||
\(206\) | −1.04265e8 | − | 1.80592e8i | −0.831002 | − | 1.43934i | ||||
\(207\) | −1.03693e8 | + | 5.98674e7i | −0.812558 | + | 0.469131i | ||||
\(208\) | − | 2.87084e7i | − | 0.221201i | ||||||
\(209\) | −2.00874e7 | − | 1.15975e7i | −0.152199 | − | 0.0878721i | ||||
\(210\) | 3.11195e7 | + | 5.39005e7i | 0.231881 | + | 0.401629i | ||||
\(211\) | −1.43417e8 | −1.05102 | −0.525511 | − | 0.850787i | \(-0.676126\pi\) | ||||
−0.525511 | + | 0.850787i | \(0.676126\pi\) | |||||||
\(212\) | −1.44085e8 | −1.03858 | ||||||||
\(213\) | −6.43679e6 | − | 1.11488e7i | −0.0456395 | − | 0.0790499i | ||||
\(214\) | − | 2.18325e8i | − | 1.52284i | ||||||
\(215\) | −4.65005e7 | + | 8.05413e7i | −0.319097 | + | 0.552693i | ||||
\(216\) | 2.45190e7i | 0.165544i | ||||||||
\(217\) | −2.25119e7 | − | 1.29972e7i | −0.149556 | − | 0.0863459i | ||||
\(218\) | 1.92452e8 | − | 3.33337e8i | 1.25813 | − | 2.17914i | ||||
\(219\) | 1.06073e8 | − | 1.83723e8i | 0.682415 | − | 1.18198i | ||||
\(220\) | −5.88793e7 | + | 3.39940e7i | −0.372806 | + | 0.215240i | ||||
\(221\) | −9.01785e7 | −0.561992 | ||||||||
\(222\) | 2.95308e8 | + | 1.43298e8i | 1.81151 | + | 0.879034i | ||||
\(223\) | −6.52980e7 | −0.394306 | −0.197153 | − | 0.980373i | \(-0.563170\pi\) | ||||
−0.197153 | + | 0.980373i | \(0.563170\pi\) | |||||||
\(224\) | −4.67428e7 | + | 2.69870e7i | −0.277873 | + | 0.160430i | ||||
\(225\) | −2.52243e6 | + | 4.36897e6i | −0.0147632 | + | 0.0255706i | ||||
\(226\) | −1.00097e7 | + | 1.73373e7i | −0.0576822 | + | 0.0999085i | ||||
\(227\) | −1.12083e8 | − | 6.47110e7i | −0.635987 | − | 0.367187i | 0.147080 | − | 0.989125i | \(-0.453013\pi\) |
−0.783067 | + | 0.621937i | \(0.786346\pi\) | |||||||
\(228\) | − | 1.65541e8i | − | 0.924981i | ||||||
\(229\) | −5.62719e7 | + | 9.74657e7i | −0.309647 | + | 0.536325i | −0.978285 | − | 0.207263i | \(-0.933544\pi\) |
0.668638 | + | 0.743588i | \(0.266878\pi\) | |||||||
\(230\) | 3.46928e8i | 1.88015i | ||||||||
\(231\) | 9.65786e6 | + | 1.67279e7i | 0.0515512 | + | 0.0892893i | ||||
\(232\) | 4.32923e7 | 0.227616 | ||||||||
\(233\) | 9.04684e7 | 0.468545 | 0.234272 | − | 0.972171i | \(-0.424729\pi\) | ||||
0.234272 | + | 0.972171i | \(0.424729\pi\) | |||||||
\(234\) | −4.29867e7 | − | 7.44551e7i | −0.219320 | − | 0.379874i | ||||
\(235\) | 7.70663e7 | + | 4.44942e7i | 0.387371 | + | 0.223649i | ||||
\(236\) | 4.54926e8i | 2.25293i | ||||||||
\(237\) | 4.05700e8 | − | 2.34231e8i | 1.97964 | − | 1.14294i | ||||
\(238\) | 5.42151e7 | + | 9.39033e7i | 0.260676 | + | 0.451504i | ||||
\(239\) | −2.12244e8 | + | 1.22539e8i | −1.00564 | + | 0.580608i | −0.909913 | − | 0.414800i | \(-0.863852\pi\) |
−0.0957291 | + | 0.995407i | \(0.530518\pi\) | |||||||
\(240\) | 1.37561e8 | + | 7.94209e7i | 0.642327 | + | 0.370848i | ||||
\(241\) | −1.19790e8 | − | 6.91608e7i | −0.551266 | − | 0.318274i | 0.198367 | − | 0.980128i | \(-0.436436\pi\) |
−0.749632 | + | 0.661854i | \(0.769770\pi\) | |||||||
\(242\) | 2.58917e8 | − | 1.49486e8i | 1.17437 | − | 0.678025i | ||||
\(243\) | −1.38172e8 | − | 2.39321e8i | −0.617730 | − | 1.06994i | ||||
\(244\) | −2.90702e7 | + | 1.67837e7i | −0.128110 | + | 0.0739645i | ||||
\(245\) | 2.13121e8i | 0.925861i | ||||||||
\(246\) | 3.62464e8 | + | 2.09269e8i | 1.55236 | + | 0.896256i | ||||
\(247\) | −2.41996e7 | − | 4.19149e7i | −0.102181 | − | 0.176982i | ||||
\(248\) | 8.68534e7 | 0.361581 | ||||||||
\(249\) | −1.92191e8 | −0.788922 | ||||||||
\(250\) | 1.91809e8 | + | 3.32222e8i | 0.776386 | + | 1.34474i | ||||
\(251\) | − | 2.93981e8i | − | 1.17344i | −0.809790 | − | 0.586720i | \(-0.800419\pi\) | ||
0.809790 | − | 0.586720i | \(-0.199581\pi\) | |||||||
\(252\) | −2.94357e7 | + | 5.09841e7i | −0.115870 | + | 0.200693i | ||||
\(253\) | 1.07668e8i | 0.417991i | ||||||||
\(254\) | −5.54243e8 | − | 3.19992e8i | −2.12218 | − | 1.22524i | ||||
\(255\) | 2.49476e8 | − | 4.32105e8i | 0.942190 | − | 1.63192i | ||||
\(256\) | −1.15464e7 | + | 1.99989e7i | −0.0430136 | + | 0.0745018i | ||||
\(257\) | −5.23349e7 | + | 3.02156e7i | −0.192320 | + | 0.111036i | −0.593068 | − | 0.805152i | \(-0.702084\pi\) |
0.400748 | + | 0.916188i | \(0.368750\pi\) | |||||||
\(258\) | −3.61705e8 | −1.31125 | ||||||||
\(259\) | −3.68567e7 | − | 5.44063e7i | −0.131816 | − | 0.194581i | ||||
\(260\) | −1.41865e8 | −0.500576 | ||||||||
\(261\) | −8.57618e7 | + | 4.95146e7i | −0.298574 | + | 0.172382i | ||||
\(262\) | −1.24431e8 | + | 2.15520e8i | −0.427438 | + | 0.740344i | ||||
\(263\) | 1.77255e8 | − | 3.07014e8i | 0.600831 | − | 1.04067i | −0.391864 | − | 0.920023i | \(-0.628170\pi\) |
0.992695 | − | 0.120647i | \(-0.0384970\pi\) | |||||||
\(264\) | −5.58917e7 | − | 3.22691e7i | −0.186953 | − | 0.107938i | ||||
\(265\) | − | 2.33081e8i | − | 0.769389i | ||||||
\(266\) | −2.90974e7 | + | 5.03983e7i | −0.0947914 | + | 0.164184i | ||||
\(267\) | 2.22563e8i | 0.715588i | ||||||||
\(268\) | 3.05892e8 | + | 5.29821e8i | 0.970727 | + | 1.68135i | ||||
\(269\) | 3.25870e7 | 0.102073 | 0.0510366 | − | 0.998697i | \(-0.483747\pi\) | ||||
0.0510366 | + | 0.998697i | \(0.483747\pi\) | |||||||
\(270\) | −1.62508e8 | −0.502459 | ||||||||
\(271\) | −3.99910e7 | − | 6.92665e7i | −0.122059 | − | 0.211412i | 0.798520 | − | 0.601968i | \(-0.205616\pi\) |
−0.920580 | + | 0.390555i | \(0.872283\pi\) | |||||||
\(272\) | 2.39654e8 | + | 1.38364e8i | 0.722092 | + | 0.416900i | ||||
\(273\) | 4.03047e7i | 0.119891i | ||||||||
\(274\) | −2.29313e8 | + | 1.32394e8i | −0.673443 | + | 0.388813i | ||||
\(275\) | 2.26823e6 | + | 3.92869e6i | 0.00657692 | + | 0.0113916i | ||||
\(276\) | −6.65473e8 | + | 3.84211e8i | −1.90524 | + | 1.09999i | ||||
\(277\) | 2.83818e8 | + | 1.63862e8i | 0.802344 | + | 0.463233i | 0.844290 | − | 0.535886i | \(-0.180022\pi\) |
−0.0419462 | + | 0.999120i | \(0.513356\pi\) | |||||||
\(278\) | −5.58387e8 | − | 3.22385e8i | −1.55876 | − | 0.899949i | ||||
\(279\) | −1.72056e8 | + | 9.93365e7i | −0.474302 | + | 0.273838i | ||||
\(280\) | 2.08167e7 | + | 3.60555e7i | 0.0566706 | + | 0.0981564i | ||||
\(281\) | 3.66598e8 | − | 2.11655e8i | 0.985639 | − | 0.569059i | 0.0816714 | − | 0.996659i | \(-0.473974\pi\) |
0.903968 | + | 0.427600i | \(0.140641\pi\) | |||||||
\(282\) | 3.46099e8i | 0.919029i | ||||||||
\(283\) | 8.75117e7 | + | 5.05249e7i | 0.229516 | + | 0.132511i | 0.610349 | − | 0.792133i | \(-0.291029\pi\) |
−0.380833 | + | 0.924644i | \(0.624363\pi\) | |||||||
\(284\) | −1.76413e7 | − | 3.05557e7i | −0.0457001 | − | 0.0791549i | ||||
\(285\) | 2.67789e8 | 0.685230 | ||||||||
\(286\) | −7.73094e7 | −0.195412 | ||||||||
\(287\) | −4.18965e7 | − | 7.25669e7i | −0.104614 | − | 0.181197i | ||||
\(288\) | 4.12517e8i | 1.01758i | ||||||||
\(289\) | 2.29458e8 | − | 3.97434e8i | 0.559193 | − | 0.968550i | ||||
\(290\) | 2.86935e8i | 0.690860i | ||||||||
\(291\) | −6.71516e8 | − | 3.87700e8i | −1.59746 | − | 0.922296i | ||||
\(292\) | 2.90713e8 | − | 5.03530e8i | 0.683321 | − | 1.18355i | ||||
\(293\) | 1.54774e8 | − | 2.68076e8i | 0.359468 | − | 0.622617i | −0.628404 | − | 0.777887i | \(-0.716291\pi\) |
0.987872 | + | 0.155270i | \(0.0496248\pi\) | |||||||
\(294\) | −7.17836e8 | + | 4.14443e8i | −1.64744 | + | 0.951149i | ||||
\(295\) | −7.35918e8 | −1.66898 | ||||||||
\(296\) | 1.97540e8 | + | 9.58562e7i | 0.442725 | + | 0.214832i | ||||
\(297\) | −5.04339e7 | −0.111706 | ||||||||
\(298\) | 1.24529e8 | − | 7.18967e7i | 0.272592 | − | 0.157381i | ||||
\(299\) | −1.12332e8 | + | 1.94565e8i | −0.243027 | + | 0.420935i | ||||
\(300\) | −1.61882e7 | + | 2.80388e7i | −0.0346158 | + | 0.0599563i | ||||
\(301\) | 6.27132e7 | + | 3.62075e7i | 0.132549 | + | 0.0765272i | ||||
\(302\) | − | 1.21169e9i | − | 2.53143i | ||||||
\(303\) | 1.74000e8 | − | 3.01378e8i | 0.359336 | − | 0.622389i | ||||
\(304\) | 1.48521e8i | 0.303201i | ||||||||
\(305\) | −2.71504e7 | − | 4.70259e7i | −0.0547933 | − | 0.0949047i | ||||
\(306\) | 8.28721e8 | 1.65342 | ||||||||
\(307\) | 6.95212e8 | 1.37130 | 0.685651 | − | 0.727931i | \(-0.259518\pi\) | ||||
0.685651 | + | 0.727931i | \(0.259518\pi\) | |||||||
\(308\) | 2.64693e7 | + | 4.58462e7i | 0.0516197 | + | 0.0894079i | ||||
\(309\) | 6.47064e8 | + | 3.73582e8i | 1.24765 | + | 0.720330i | ||||
\(310\) | 5.75650e8i | 1.09747i | ||||||||
\(311\) | 2.97795e8 | − | 1.71932e8i | 0.561380 | − | 0.324113i | −0.192319 | − | 0.981332i | \(-0.561601\pi\) |
0.753699 | + | 0.657220i | \(0.228268\pi\) | |||||||
\(312\) | −6.73335e7 | − | 1.16625e8i | −0.125513 | − | 0.217395i | ||||
\(313\) | −1.93505e8 | + | 1.11720e8i | −0.356687 | + | 0.205934i | −0.667627 | − | 0.744496i | \(-0.732690\pi\) |
0.310939 | + | 0.950430i | \(0.399356\pi\) | |||||||
\(314\) | −5.79635e8 | − | 3.34652e8i | −1.05658 | − | 0.610015i | ||||
\(315\) | −8.24753e7 | − | 4.76171e7i | −0.148675 | − | 0.0858373i | ||||
\(316\) | 1.11190e9 | − | 6.41957e8i | 1.98227 | − | 1.14446i | ||||
\(317\) | −2.23998e8 | − | 3.87977e8i | −0.394946 | − | 0.684066i | 0.598148 | − | 0.801385i | \(-0.295903\pi\) |
−0.993094 | + | 0.117319i | \(0.962570\pi\) | |||||||
\(318\) | 7.85062e8 | − | 4.53256e8i | 1.36902 | − | 0.790403i | ||||
\(319\) | 8.90495e7i | 0.153590i | ||||||||
\(320\) | 7.50127e8 | + | 4.33086e8i | 1.27971 | + | 0.738838i | ||||
\(321\) | 3.91131e8 | + | 6.77459e8i | 0.660017 | + | 1.14318i | ||||
\(322\) | 2.70135e8 | 0.450905 | ||||||||
\(323\) | 4.66532e8 | 0.770323 | ||||||||
\(324\) | −4.81803e8 | − | 8.34508e8i | −0.786977 | − | 1.36308i | ||||
\(325\) | 9.46589e6i | 0.0152957i | ||||||||
\(326\) | 4.45527e8 | − | 7.71675e8i | 0.712217 | − | 1.23360i | ||||
\(327\) | 1.37912e9i | 2.18114i | ||||||||
\(328\) | 2.42462e8 | + | 1.39986e8i | 0.379390 | + | 0.219041i | ||||
\(329\) | 3.46453e7 | − | 6.00074e7i | 0.0536363 | − | 0.0929008i | ||||
\(330\) | 2.13874e8 | − | 3.70441e8i | 0.327612 | − | 0.567440i | ||||
\(331\) | −9.20410e8 | + | 5.31399e8i | −1.39503 | + | 0.805420i | −0.993867 | − | 0.110586i | \(-0.964727\pi\) |
−0.401163 | + | 0.916007i | \(0.631394\pi\) | |||||||
\(332\) | −5.26737e8 | −0.789970 | ||||||||
\(333\) | −5.00958e8 | + | 3.60411e7i | −0.743441 | + | 0.0534864i | ||||
\(334\) | 1.44067e8 | 0.211569 | ||||||||
\(335\) | −8.57074e8 | + | 4.94832e8i | −1.24555 | + | 0.719119i | ||||
\(336\) | 6.18408e7 | − | 1.07111e8i | 0.0889381 | − | 0.154045i | ||||
\(337\) | −1.98066e8 | + | 3.43060e8i | −0.281907 | + | 0.488276i | −0.971854 | − | 0.235583i | \(-0.924300\pi\) |
0.689948 | + | 0.723859i | \(0.257633\pi\) | |||||||
\(338\) | 7.97323e8 | + | 4.60335e8i | 1.12312 | + | 0.648434i | ||||
\(339\) | − | 7.17300e7i | − | 0.100000i | ||||||
\(340\) | 6.83740e8 | − | 1.18427e9i | 0.943441 | − | 1.63409i | ||||
\(341\) | 1.78652e8i | 0.243987i | ||||||||
\(342\) | 2.22389e8 | + | 3.85189e8i | 0.300622 | + | 0.520693i | ||||
\(343\) | 3.41595e8 | 0.457069 | ||||||||
\(344\) | −2.41955e8 | −0.320464 | ||||||||
\(345\) | −6.21525e8 | − | 1.07651e9i | −0.814877 | − | 1.41141i | ||||
\(346\) | −1.61135e9 | − | 9.30313e8i | −2.09133 | − | 1.20743i | ||||
\(347\) | − | 1.90283e8i | − | 0.244482i | −0.992500 | − | 0.122241i | \(-0.960992\pi\) | ||
0.992500 | − | 0.122241i | \(-0.0390080\pi\) | |||||||
\(348\) | −5.50394e8 | + | 3.17770e8i | −0.700078 | + | 0.404190i | ||||
\(349\) | 7.13622e7 | + | 1.23603e8i | 0.0898626 | + | 0.155647i | 0.907453 | − | 0.420154i | \(-0.138024\pi\) |
−0.817590 | + | 0.575800i | \(0.804691\pi\) | |||||||
\(350\) | 9.85688e6 | − | 5.69087e6i | 0.0122886 | − | 0.00709481i | ||||
\(351\) | −9.11377e7 | − | 5.26184e7i | −0.112492 | − | 0.0649475i | ||||
\(352\) | 3.21248e8 | + | 1.85473e8i | 0.392592 | + | 0.226663i | ||||
\(353\) | −4.25679e8 | + | 2.45766e8i | −0.515076 | + | 0.297379i | −0.734918 | − | 0.678156i | \(-0.762779\pi\) |
0.219842 | + | 0.975535i | \(0.429446\pi\) | |||||||
\(354\) | −1.43109e9 | − | 2.47872e9i | −1.71457 | − | 2.96972i | ||||
\(355\) | 4.94289e7 | − | 2.85378e7i | 0.0586383 | − | 0.0338548i | ||||
\(356\) | 6.09979e8i | 0.716539i | ||||||||
\(357\) | −3.36458e8 | − | 1.94254e8i | −0.391374 | − | 0.225960i | ||||
\(358\) | 8.91913e8 | + | 1.54484e9i | 1.02738 | + | 1.77948i | ||||
\(359\) | 1.86608e8 | 0.212862 | 0.106431 | − | 0.994320i | \(-0.466058\pi\) | ||||
0.106431 | + | 0.994320i | \(0.466058\pi\) | |||||||
\(360\) | 3.18199e8 | 0.359451 | ||||||||
\(361\) | −3.21741e8 | − | 5.57272e8i | −0.359941 | − | 0.623436i | ||||
\(362\) | 1.93566e9i | 2.14461i | ||||||||
\(363\) | −5.35610e8 | + | 9.27704e8i | −0.587727 | + | 1.01797i | ||||
\(364\) | 1.10463e8i | 0.120050i | ||||||||
\(365\) | 8.14544e8 | + | 4.70277e8i | 0.876778 | + | 0.506208i | ||||
\(366\) | 1.05595e8 | − | 1.82896e8i | 0.112580 | − | 0.194994i | ||||
\(367\) | −4.98170e8 | + | 8.62856e8i | −0.526073 | + | 0.911186i | 0.473465 | + | 0.880813i | \(0.343003\pi\) |
−0.999539 | + | 0.0303735i | \(0.990330\pi\) | |||||||
\(368\) | 5.97054e8 | − | 3.44709e8i | 0.624520 | − | 0.360567i | ||||
\(369\) | −6.40422e8 | −0.663550 | ||||||||
\(370\) | −6.35319e8 | + | 1.30926e9i | −0.652058 | + | 1.34376i | ||||
\(371\) | −1.81488e8 | −0.184518 | ||||||||
\(372\) | −1.10420e9 | + | 6.37513e8i | −1.11211 | + | 0.642079i | ||||
\(373\) | −6.65692e8 | + | 1.15301e9i | −0.664190 | + | 1.15041i | 0.315314 | + | 0.948987i | \(0.397890\pi\) |
−0.979504 | + | 0.201424i | \(0.935443\pi\) | |||||||
\(374\) | 3.72603e8 | − | 6.45368e8i | 0.368295 | − | 0.637906i | ||||
\(375\) | −1.19036e9 | − | 6.87254e8i | −1.16565 | − | 0.672989i | ||||
\(376\) | 2.31515e8i | 0.224607i | ||||||||
\(377\) | −9.29065e7 | + | 1.60919e8i | −0.0893000 | + | 0.154672i | ||||
\(378\) | 1.26536e8i | 0.120502i | ||||||||
\(379\) | 8.22864e7 | + | 1.42524e8i | 0.0776410 | + | 0.134478i | 0.902232 | − | 0.431252i | \(-0.141928\pi\) |
−0.824591 | + | 0.565730i | \(0.808595\pi\) | |||||||
\(380\) | 7.33931e8 | 0.686140 | ||||||||
\(381\) | 2.29308e9 | 2.12413 | ||||||||
\(382\) | −9.01427e8 | − | 1.56132e9i | −0.827388 | − | 1.43308i | ||||
\(383\) | 1.47340e9 | + | 8.50669e8i | 1.34006 | + | 0.773686i | 0.986816 | − | 0.161843i | \(-0.0517439\pi\) |
0.353248 | + | 0.935530i | \(0.385077\pi\) | |||||||
\(384\) | 1.36752e9i | 1.23246i | ||||||||
\(385\) | −7.41638e7 | + | 4.28185e7i | −0.0662338 | + | 0.0382401i | ||||
\(386\) | −7.84030e8 | − | 1.35798e9i | −0.693868 | − | 1.20181i | ||||
\(387\) | 4.79310e8 | − | 2.76730e8i | 0.420367 | − | 0.242699i | ||||
\(388\) | −1.84043e9 | − | 1.06257e9i | −1.59958 | − | 0.923521i | ||||
\(389\) | 1.65022e9 | + | 9.52757e8i | 1.42141 | + | 0.820651i | 0.996420 | − | 0.0845466i | \(-0.0269442\pi\) |
0.424990 | + | 0.905198i | \(0.360278\pi\) | |||||||
\(390\) | 7.72971e8 | − | 4.46275e8i | 0.659838 | − | 0.380958i | ||||
\(391\) | −1.08280e9 | − | 1.87546e9i | −0.916070 | − | 1.58668i | ||||
\(392\) | −4.80180e8 | + | 2.77232e8i | −0.402627 | + | 0.232457i | ||||
\(393\) | − | 8.91675e8i | − | 0.741025i | ||||||
\(394\) | −3.09195e9 | − | 1.78514e9i | −2.54680 | − | 1.47040i | ||||
\(395\) | 1.03847e9 | + | 1.79869e9i | 0.847822 | + | 1.46847i | ||||
\(396\) | 4.04604e8 | 0.327414 | ||||||||
\(397\) | 1.17408e9 | 0.941742 | 0.470871 | − | 0.882202i | \(-0.343940\pi\) | ||||
0.470871 | + | 0.882202i | \(0.343940\pi\) | |||||||
\(398\) | 1.42075e9 | + | 2.46081e9i | 1.12961 | + | 1.95653i | ||||
\(399\) | − | 2.08513e8i | − | 0.164335i | ||||||
\(400\) | 1.45238e7 | − | 2.51560e7i | 0.0113467 | − | 0.0196531i | ||||
\(401\) | 9.05258e8i | 0.701079i | 0.936548 | + | 0.350539i | \(0.114002\pi\) | ||||
−0.936548 | + | 0.350539i | \(0.885998\pi\) | |||||||
\(402\) | −3.33339e9 | − | 1.92453e9i | −2.55914 | − | 1.47752i | ||||
\(403\) | −1.86390e8 | + | 3.22836e8i | −0.141858 | + | 0.245705i | ||||
\(404\) | 4.76883e8 | − | 8.25986e8i | 0.359814 | − | 0.623215i | ||||
\(405\) | 1.34995e9 | − | 7.79397e8i | 1.00978 | − | 0.582997i | ||||
\(406\) | 2.23421e8 | 0.165685 | ||||||||
\(407\) | −1.97170e8 | + | 4.06327e8i | −0.144964 | + | 0.298741i | ||||
\(408\) | 1.29809e9 | 0.946226 | ||||||||
\(409\) | −1.41939e9 | + | 8.19486e8i | −1.02582 | + | 0.592256i | −0.915784 | − | 0.401671i | \(-0.868429\pi\) |
−0.110034 | + | 0.993928i | \(0.535096\pi\) | |||||||
\(410\) | −9.27803e8 | + | 1.60700e9i | −0.664832 | + | 1.15152i | ||||
\(411\) | 4.74369e8 | − | 8.21632e8i | 0.337031 | − | 0.583755i | ||||
\(412\) | 1.77341e9 | + | 1.02388e9i | 1.24931 | + | 0.721287i | ||||
\(413\) | 5.73020e8i | 0.400262i | ||||||||
\(414\) | 1.03231e9 | − | 1.78801e9i | 0.715002 | − | 1.23842i | ||||
\(415\) | − | 8.52085e8i | − | 0.585214i | ||||||
\(416\) | 3.87012e8 | + | 6.70325e8i | 0.263571 | + | 0.456519i | ||||
\(417\) | 2.31022e9 | 1.56019 | ||||||||
\(418\) | 3.99955e8 | 0.267851 | ||||||||
\(419\) | −6.55418e8 | − | 1.13522e9i | −0.435281 | − | 0.753928i | 0.562038 | − | 0.827111i | \(-0.310018\pi\) |
−0.997319 | + | 0.0731833i | \(0.976684\pi\) | |||||||
\(420\) | −5.29302e8 | − | 3.05593e8i | −0.348603 | − | 0.201266i | ||||
\(421\) | − | 2.21636e9i | − | 1.44762i | −0.690001 | − | 0.723809i | \(-0.742390\pi\) | ||
0.690001 | − | 0.723809i | \(-0.257610\pi\) | |||||||
\(422\) | 2.14165e9 | − | 1.23648e9i | 1.38725 | − | 0.800931i | ||||
\(423\) | −2.64790e8 | − | 4.58630e8i | −0.170103 | − | 0.294626i | ||||
\(424\) | 5.25150e8 | − | 3.03195e8i | 0.334582 | − | 0.193171i | ||||
\(425\) | −7.90199e7 | − | 4.56221e7i | −0.0499316 | − | 0.0288280i | ||||
\(426\) | 1.92242e8 | + | 1.10991e8i | 0.120480 | + | 0.0695591i | ||||
\(427\) | −3.66166e7 | + | 2.11406e7i | −0.0227604 | + | 0.0131407i | ||||
\(428\) | 1.07197e9 | + | 1.85671e9i | 0.660893 | + | 1.14470i | ||||
\(429\) | 2.39890e8 | − | 1.38501e8i | 0.146694 | − | 0.0846937i | ||||
\(430\) | − | 1.60364e9i | − | 0.972672i | ||||||
\(431\) | −1.22849e9 | − | 7.09272e8i | −0.739099 | − | 0.426719i | 0.0826424 | − | 0.996579i | \(-0.473664\pi\) |
−0.821742 | + | 0.569860i | \(0.806997\pi\) | |||||||
\(432\) | 1.61468e8 | + | 2.79671e8i | 0.0963594 | + | 0.166899i | ||||
\(433\) | 1.73939e8 | 0.102965 | 0.0514824 | − | 0.998674i | \(-0.483605\pi\) | ||||
0.0514824 | + | 0.998674i | \(0.483605\pi\) | |||||||
\(434\) | 4.48228e8 | 0.263199 | ||||||||
\(435\) | −5.14046e8 | − | 8.90354e8i | −0.299426 | − | 0.518621i | ||||
\(436\) | 3.77975e9i | 2.18404i | ||||||||
\(437\) | 5.81141e8 | − | 1.00657e9i | 0.333117 | − | 0.576976i | ||||
\(438\) | 3.65806e9i | 2.08014i | ||||||||
\(439\) | 1.20990e9 | + | 6.98537e8i | 0.682534 | + | 0.394061i | 0.800809 | − | 0.598920i | \(-0.204403\pi\) |
−0.118275 | + | 0.992981i | \(0.537736\pi\) | |||||||
\(440\) | 1.43066e8 | − | 2.47798e8i | 0.0800669 | − | 0.138680i | ||||
\(441\) | 6.34155e8 | − | 1.09839e9i | 0.352096 | − | 0.609847i | ||||
\(442\) | 1.34664e9 | − | 7.77484e8i | 0.741778 | − | 0.428266i | ||||
\(443\) | −2.92006e9 | −1.59580 | −0.797899 | − | 0.602791i | \(-0.794055\pi\) | ||||
−0.797899 | + | 0.602791i | \(0.794055\pi\) | |||||||
\(444\) | −3.21500e9 | + | 2.31301e8i | −1.74318 | + | 0.125412i | ||||
\(445\) | −9.86742e8 | −0.530815 | ||||||||
\(446\) | 9.75099e8 | − | 5.62974e8i | 0.520447 | − | 0.300480i | ||||
\(447\) | −2.57607e8 | + | 4.46189e8i | −0.136421 | + | 0.236288i | ||||
\(448\) | 3.37221e8 | − | 5.84084e8i | 0.177191 | − | 0.306904i | ||||
\(449\) | −6.46344e8 | − | 3.73167e8i | −0.336978 | − | 0.194554i | 0.321957 | − | 0.946754i | \(-0.395659\pi\) |
−0.658935 | + | 0.752200i | \(0.728993\pi\) | |||||||
\(450\) | − | 8.69894e7i | − | 0.0450011i | ||||||
\(451\) | −2.87942e8 | + | 4.98729e8i | −0.147804 | + | 0.256004i | ||||
\(452\) | − | 1.96591e8i | − | 0.100133i | ||||||
\(453\) | 2.17075e9 | + | 3.75985e9i | 1.09715 | + | 1.90032i | ||||
\(454\) | 2.23165e9 | 1.11926 | ||||||||
\(455\) | −1.78692e8 | −0.0889337 | ||||||||
\(456\) | 3.48345e8 | + | 6.03351e8i | 0.172041 | + | 0.297984i | ||||
\(457\) | −2.82968e9 | − | 1.63371e9i | −1.38685 | − | 0.800699i | −0.393893 | − | 0.919156i | \(-0.628872\pi\) |
−0.992959 | + | 0.118457i | \(0.962205\pi\) | |||||||
\(458\) | − | 1.94062e9i | − | 0.943866i | ||||||
\(459\) | 8.78501e8 | − | 5.07203e8i | 0.424031 | − | 0.244815i | ||||
\(460\) | −1.70342e9 | − | 2.95040e9i | −0.815959 | − | 1.41328i | ||||
\(461\) | −1.11060e7 | + | 6.41206e6i | −0.00527965 | + | 0.00304821i | −0.502638 | − | 0.864497i | \(-0.667637\pi\) |
0.497358 | + | 0.867545i | \(0.334304\pi\) | |||||||
\(462\) | −2.88443e8 | − | 1.66532e8i | −0.136086 | − | 0.0785691i | ||||
\(463\) | 7.67002e8 | + | 4.42829e8i | 0.359140 | + | 0.207349i | 0.668703 | − | 0.743529i | \(-0.266850\pi\) |
−0.309564 | + | 0.950879i | \(0.600183\pi\) | |||||||
\(464\) | 4.93807e8 | − | 2.85099e8i | 0.229480 | − | 0.132490i | ||||
\(465\) | −1.03128e9 | − | 1.78623e9i | −0.475655 | − | 0.823859i | ||||
\(466\) | −1.35097e9 | + | 7.79983e8i | −0.618436 | + | 0.357054i | ||||
\(467\) | − | 8.06328e8i | − | 0.366355i | −0.983080 | − | 0.183178i | \(-0.941362\pi\) | ||
0.983080 | − | 0.183178i | \(-0.0586384\pi\) | |||||||
\(468\) | 7.31149e8 | + | 4.22129e8i | 0.329720 | + | 0.190364i | ||||
\(469\) | 3.85299e8 | + | 6.67358e8i | 0.172462 | + | 0.298713i | ||||
\(470\) | −1.53445e9 | −0.681725 | ||||||||
\(471\) | 2.39813e9 | 1.05755 | ||||||||
\(472\) | −9.57294e8 | − | 1.65808e9i | −0.419033 | − | 0.725787i | ||||
\(473\) | − | 4.97685e8i | − | 0.216242i | ||||||
\(474\) | −4.03889e9 | + | 6.99556e9i | −1.74196 | + | 3.01716i | ||||
\(475\) | − | 4.89711e7i | − | 0.0209659i | ||||||
\(476\) | −9.22130e8 | − | 5.32392e8i | −0.391893 | − | 0.226260i | ||||
\(477\) | −6.93545e8 | + | 1.20126e9i | −0.292591 | + | 0.506782i | ||||
\(478\) | 2.11297e9 | − | 3.65977e9i | 0.884903 | − | 1.53270i | ||||
\(479\) | −8.59062e8 | + | 4.95980e8i | −0.357150 | + | 0.206200i | −0.667830 | − | 0.744314i | \(-0.732777\pi\) |
0.310680 | + | 0.950515i | \(0.399443\pi\) | |||||||
\(480\) | −4.28263e9 | −1.76753 | ||||||||
\(481\) | −7.80226e8 | + | 5.28551e8i | −0.319678 | + | 0.216560i | ||||
\(482\) | 2.38511e9 | 0.970160 | ||||||||
\(483\) | −8.38224e8 | + | 4.83949e8i | −0.338489 | + | 0.195427i | ||||
\(484\) | −1.46795e9 | + | 2.54256e9i | −0.588508 | + | 1.01932i | ||||
\(485\) | 1.71888e9 | − | 2.97719e9i | 0.684148 | − | 1.18498i | ||||
\(486\) | 4.12667e9 | + | 2.38253e9i | 1.63069 | + | 0.941481i | ||||
\(487\) | − | 2.06029e8i | − | 0.0808307i | −0.999183 | − | 0.0404154i | \(-0.987132\pi\) | ||
0.999183 | − | 0.0404154i | \(-0.0128681\pi\) | |||||||
\(488\) | 7.06355e7 | − | 1.22344e8i | 0.0275140 | − | 0.0476556i | ||||
\(489\) | 3.19266e9i | 1.23473i | ||||||||
\(490\) | −1.83745e9 | − | 3.18255e9i | −0.705552 | − | 1.22205i | ||||
\(491\) | −1.36962e9 | −0.522175 | −0.261087 | − | 0.965315i | \(-0.584081\pi\) | ||||
−0.261087 | + | 0.965315i | \(0.584081\pi\) | |||||||
\(492\) | −4.11004e9 | −1.55585 | ||||||||
\(493\) | −8.95551e8 | − | 1.55114e9i | −0.336609 | − | 0.583025i | ||||
\(494\) | 7.22747e8 | + | 4.17278e8i | 0.269738 | + | 0.155733i | ||||
\(495\) | 6.54515e8i | 0.242550i | ||||||||
\(496\) | 9.90678e8 | − | 5.71968e8i | 0.364541 | − | 0.210468i | ||||
\(497\) | −2.22208e7 | − | 3.84876e7i | −0.00811920 | − | 0.0140629i | ||||
\(498\) | 2.86999e9 | − | 1.65699e9i | 1.04131 | − | 0.601198i | ||||
\(499\) | −4.89339e8 | − | 2.82520e8i | −0.176302 | − | 0.101788i | 0.409252 | − | 0.912421i | \(-0.365790\pi\) |
−0.585554 | + | 0.810633i | \(0.699123\pi\) | |||||||
\(500\) | −3.26242e9 | − | 1.88356e9i | −1.16720 | − | 0.673882i | ||||
\(501\) | −4.47038e8 | + | 2.58097e8i | −0.158823 | + | 0.0916963i | ||||
\(502\) | 2.53459e9 | + | 4.39003e9i | 0.894220 | + | 1.54883i | ||||
\(503\) | 3.92225e9 | − | 2.26451e9i | 1.37419 | − | 0.793390i | 0.382738 | − | 0.923857i | \(-0.374981\pi\) |
0.991453 | + | 0.130467i | \(0.0416477\pi\) | |||||||
\(504\) | − | 2.47765e8i | − | 0.0862050i | ||||||
\(505\) | 1.33617e9 | + | 7.71438e8i | 0.461681 | + | 0.266552i | ||||
\(506\) | −9.28275e8 | − | 1.60782e9i | −0.318530 | − | 0.551709i | ||||
\(507\) | −3.29878e9 | −1.12415 | ||||||||
\(508\) | 6.28465e9 | 2.12695 | ||||||||
\(509\) | 2.39975e9 | + | 4.15649e9i | 0.806593 | + | 1.39706i | 0.915211 | + | 0.402976i | \(0.132024\pi\) |
−0.108618 | + | 0.994084i | \(0.534643\pi\) | |||||||
\(510\) | 8.60354e9i | 2.87198i | ||||||||
\(511\) | 3.66180e8 | − | 6.34242e8i | 0.121401 | − | 0.210272i | ||||
\(512\) | − | 3.23138e9i | − | 1.06400i | ||||||
\(513\) | 4.71495e8 | + | 2.72217e8i | 0.154193 | + | 0.0890236i | ||||
\(514\) | 5.21013e8 | − | 9.02421e8i | 0.169230 | − | 0.293115i | ||||
\(515\) | −1.65629e9 | + | 2.86878e9i | −0.534333 | + | 0.925492i | ||||
\(516\) | 3.07607e9 | − | 1.77597e9i | 0.985650 | − | 0.569066i | ||||
\(517\) | −4.76212e8 | −0.151560 | ||||||||
\(518\) | 1.01945e9 | + | 4.94689e8i | 0.322265 | + | 0.156379i | ||||
\(519\) | 6.66666e9 | 2.09326 | ||||||||
\(520\) | 5.17062e8 | − | 2.98526e8i | 0.161262 | − | 0.0931044i | ||||
\(521\) | −1.96191e9 | + | 3.39813e9i | −0.607782 | + | 1.05271i | 0.383823 | + | 0.923407i | \(0.374607\pi\) |
−0.991605 | + | 0.129303i | \(0.958726\pi\) | |||||||
\(522\) | 8.53791e8 | − | 1.47881e9i | 0.262727 | − | 0.455056i | ||||
\(523\) | −4.96555e8 | − | 2.86686e8i | −0.151779 | − | 0.0876296i | 0.422187 | − | 0.906509i | \(-0.361263\pi\) |
−0.573966 | + | 0.818879i | \(0.694596\pi\) | |||||||
\(524\) | − | 2.44382e9i | − | 0.742009i | ||||||
\(525\) | −2.03905e7 | + | 3.53174e7i | −0.00614993 | + | 0.0106520i | ||||
\(526\) | 6.11288e9i | 1.83145i | ||||||||
\(527\) | −1.79666e9 | − | 3.11191e9i | −0.534723 | − | 0.926167i | ||||
\(528\) | −8.50025e8 | −0.251312 | ||||||||
\(529\) | −1.99037e9 | −0.584573 | ||||||||
\(530\) | 2.00953e9 | + | 3.48061e9i | 0.586312 | + | 1.01552i | ||||
\(531\) | 3.79279e9 | + | 2.18977e9i | 1.09933 | + | 0.634698i | ||||
\(532\) | − | 5.71473e8i | − | 0.164553i | ||||||
\(533\) | −1.04066e9 | + | 6.00826e8i | −0.297690 | + | 0.171871i | ||||
\(534\) | −1.91885e9 | − | 3.32354e9i | −0.545314 | − | 0.944511i | ||||
\(535\) | −3.00354e9 | + | 1.73410e9i | −0.848000 | + | 0.489593i | ||||
\(536\) | −2.22979e9 | − | 1.28737e9i | −0.625443 | − | 0.361100i | ||||
\(537\) | −5.53519e9 | − | 3.19574e9i | −1.54249 | − | 0.890557i | ||||
\(538\) | −4.86624e8 | + | 2.80952e8i | −0.134727 | + | 0.0777848i | ||||
\(539\) | −5.70248e8 | − | 9.87699e8i | −0.156857 | − | 0.271684i | ||||
\(540\) | 1.38202e9 | − | 7.97912e8i | 0.377692 | − | 0.218061i | ||||
\(541\) | 1.10150e9i | 0.299083i | 0.988755 | + | 0.149542i | \(0.0477798\pi\) | ||||
−0.988755 | + | 0.149542i | \(0.952220\pi\) | |||||||
\(542\) | 1.19438e9 | + | 6.89573e8i | 0.322213 | + | 0.186030i | ||||
\(543\) | −3.46775e9 | − | 6.00632e9i | −0.929498 | − | 1.60994i | ||||
\(544\) | −7.46103e9 | −1.98702 | ||||||||
\(545\) | −6.11438e9 | −1.61795 | ||||||||
\(546\) | −3.47491e8 | − | 6.01872e8i | −0.0913627 | − | 0.158245i | ||||
\(547\) | − | 2.50832e8i | − | 0.0655281i | −0.999463 | − | 0.0327640i | \(-0.989569\pi\) | ||
0.999463 | − | 0.0327640i | \(-0.0104310\pi\) | |||||||
\(548\) | 1.30011e9 | − | 2.25185e9i | 0.337479 | − | 0.584531i | ||||
\(549\) | 3.23151e8i | 0.0833493i | ||||||||
\(550\) | −6.77432e7 | − | 3.91115e7i | −0.0173619 | − | 0.0100239i | ||||
\(551\) | 4.80646e8 | − | 8.32503e8i | 0.122404 | − | 0.212009i | ||||
\(552\) | 1.61698e9 | − | 2.80069e9i | 0.409184 | − | 0.708727i | ||||
\(553\) | 1.40054e9 | − | 8.08603e8i | 0.352175 | − | 0.203328i | ||||
\(554\) | −5.65102e9 | −1.41203 | ||||||||
\(555\) | −3.74168e8 | − | 5.20080e9i | −0.0929055 | − | 1.29135i | ||||
\(556\) | 6.33164e9 | 1.56226 | ||||||||
\(557\) | −6.14795e9 | + | 3.54952e9i | −1.50743 | + | 0.870315i | −0.507467 | + | 0.861671i | \(0.669418\pi\) |
−0.999963 | + | 0.00864345i | \(0.997249\pi\) | |||||||
\(558\) | 1.71288e9 | − | 2.96679e9i | 0.417356 | − | 0.722883i | ||||
\(559\) | 5.19241e8 | − | 8.99352e8i | 0.125727 | − | 0.217765i | ||||
\(560\) | 4.74883e8 | + | 2.74174e8i | 0.114269 | + | 0.0659733i | ||||
\(561\) | 2.67009e9i | 0.638493i | ||||||||
\(562\) | −3.64962e9 | + | 6.32133e9i | −0.867302 | + | 1.50221i | ||||
\(563\) | − | 5.14851e9i | − | 1.21591i | −0.793970 | − | 0.607956i | \(-0.791990\pi\) | ||
0.793970 | − | 0.607956i | \(-0.208010\pi\) | |||||||
\(564\) | −1.69935e9 | − | 2.94336e9i | −0.398846 | − | 0.690822i | ||||
\(565\) | 3.18018e8 | 0.0741792 | ||||||||
\(566\) | −1.74242e9 | −0.403921 | ||||||||
\(567\) | −6.06875e8 | − | 1.05114e9i | −0.139816 | − | 0.242169i | ||||
\(568\) | 1.28596e8 | + | 7.42448e7i | 0.0294447 | + | 0.0169999i | ||||
\(569\) | − | 2.07871e9i | − | 0.473043i | −0.971626 | − | 0.236521i | \(-0.923993\pi\) | ||
0.971626 | − | 0.236521i | \(-0.0760073\pi\) | |||||||
\(570\) | −3.99891e9 | + | 2.30877e9i | −0.904441 | + | 0.522179i | ||||
\(571\) | 3.87048e9 | + | 6.70386e9i | 0.870038 | + | 1.50695i | 0.861956 | + | 0.506982i | \(0.169239\pi\) |
0.00808136 | + | 0.999967i | \(0.497428\pi\) | |||||||
\(572\) | 6.57467e8 | − | 3.79589e8i | 0.146889 | − | 0.0848062i | ||||
\(573\) | 5.59423e9 | + | 3.22983e9i | 1.24222 | + | 0.717198i | ||||
\(574\) | 1.25129e9 | + | 7.22431e8i | 0.276163 | + | 0.159443i | ||||
\(575\) | −1.96864e8 | + | 1.13659e8i | −0.0431846 | + | 0.0249326i | ||||
\(576\) | −2.57735e9 | − | 4.46410e9i | −0.561945 | − | 0.973318i | ||||
\(577\) | 7.55192e9 | − | 4.36010e9i | 1.63660 | − | 0.944890i | 0.654605 | − | 0.755971i | \(-0.272835\pi\) |
0.981993 | − | 0.188919i | \(-0.0604985\pi\) | |||||||
\(578\) | 7.91320e9i | 1.70453i | ||||||||
\(579\) | 4.86567e9 | + | 2.80919e9i | 1.04176 | + | 0.601460i | ||||
\(580\) | −1.40885e9 | − | 2.44020e9i | −0.299824 | − | 0.519310i | ||||
\(581\) | −6.63473e8 | −0.140348 | ||||||||
\(582\) | 1.33704e10 | 2.81134 | ||||||||
\(583\) | 6.23653e8 | + | 1.08020e9i | 0.130348 | + | 0.225769i | ||||
\(584\) | 2.44698e9i | 0.508376i | ||||||||
\(585\) | −6.82864e8 | + | 1.18275e9i | −0.141023 | + | 0.244258i | ||||
\(586\) | 5.33759e9i | 1.09573i | ||||||||
\(587\) | −3.83252e8 | − | 2.21270e8i | −0.0782079 | − | 0.0451534i | 0.460386 | − | 0.887719i | \(-0.347711\pi\) |
−0.538594 | + | 0.842565i | \(0.681044\pi\) | |||||||
\(588\) | 4.06982e9 | − | 7.04914e9i | 0.825572 | − | 1.42993i | ||||
\(589\) | 9.64274e8 | − | 1.67017e9i | 0.194445 | − | 0.336789i | ||||
\(590\) | 1.09895e10 | − | 6.34479e9i | 2.20291 | − | 1.27185i | ||||
\(591\) | 1.27924e10 | 2.54915 | ||||||||
\(592\) | 2.88446e9 | − | 2.07520e8i | 0.571398 | − | 0.0411088i | ||||
\(593\) | 6.15611e9 | 1.21231 | 0.606157 | − | 0.795345i | \(-0.292710\pi\) | ||||
0.606157 | + | 0.795345i | \(0.292710\pi\) | |||||||
\(594\) | 7.53132e8 | − | 4.34821e8i | 0.147441 | − | 0.0851252i | ||||
\(595\) | 8.61233e8 | − | 1.49170e9i | 0.167614 | − | 0.290316i | ||||
\(596\) | −7.06025e8 | + | 1.22287e9i | −0.136602 | + | 0.236602i | ||||
\(597\) | −8.81713e9 | − | 5.09057e9i | −1.69597 | − | 0.979166i | ||||
\(598\) | − | 3.87392e9i | − | 0.740793i | ||||||
\(599\) | −2.44335e9 | + | 4.23201e9i | −0.464507 | + | 0.804549i | −0.999179 | − | 0.0405100i | \(-0.987102\pi\) |
0.534672 | + | 0.845060i | \(0.320435\pi\) | |||||||
\(600\) | − | 1.36258e8i | − | 0.0257534i | ||||||
\(601\) | −2.09051e9 | − | 3.62087e9i | −0.392819 | − | 0.680382i | 0.600002 | − | 0.799999i | \(-0.295167\pi\) |
−0.992820 | + | 0.119617i | \(0.961833\pi\) | |||||||
\(602\) | −1.24867e9 | −0.233270 | ||||||||
\(603\) | 5.88960e9 | 1.09389 | ||||||||
\(604\) | 5.94938e9 | + | 1.03046e10i | 1.09861 | + | 1.90284i | ||||
\(605\) | −4.11301e9 | − | 2.37465e9i | −0.755121 | − | 0.435969i | ||||
\(606\) | 6.00065e9i | 1.09533i | ||||||||
\(607\) | 7.12840e9 | − | 4.11558e9i | 1.29369 | − | 0.746915i | 0.314387 | − | 0.949295i | \(-0.398201\pi\) |
0.979307 | + | 0.202380i | \(0.0648677\pi\) | |||||||
\(608\) | −2.00218e9 | − | 3.46788e9i | −0.361277 | − | 0.625751i | ||||
\(609\) | −6.93271e8 | + | 4.00260e8i | −0.124378 | + | 0.0718095i | ||||
\(610\) | 8.10877e8 | + | 4.68160e8i | 0.144644 | + | 0.0835103i | ||||
\(611\) | −8.60549e8 | − | 4.96838e8i | −0.152627 | − | 0.0881193i | ||||
\(612\) | −7.04774e9 | + | 4.06902e9i | −1.24285 | + | 0.717562i | ||||
\(613\) | −8.60410e8 | − | 1.49027e9i | −0.150867 | − | 0.261309i | 0.780680 | − | 0.624932i | \(-0.214873\pi\) |
−0.931546 | + | 0.363623i | \(0.881540\pi\) | |||||||
\(614\) | −1.03816e10 | + | 5.99384e9i | −1.80999 | + | 1.04500i | ||||
\(615\) | − | 6.64867e9i | − | 1.15258i | ||||||
\(616\) | −1.92947e8 | − | 1.11398e8i | −0.0332587 | − | 0.0192019i | ||||
\(617\) | −2.20856e9 | − | 3.82533e9i | −0.378539 | − | 0.655649i | 0.612311 | − | 0.790617i | \(-0.290240\pi\) |
−0.990850 | + | 0.134968i | \(0.956907\pi\) | |||||||
\(618\) | −1.28835e10 | −2.19571 | ||||||||
\(619\) | −1.75797e9 | −0.297916 | −0.148958 | − | 0.988844i | \(-0.547592\pi\) | ||||
−0.148958 | + | 0.988844i | \(0.547592\pi\) | |||||||
\(620\) | −2.82644e9 | − | 4.89554e9i | −0.476287 | − | 0.824953i | ||||
\(621\) | − | 2.52721e9i | − | 0.423468i | ||||||
\(622\) | −2.96466e9 | + | 5.13495e9i | −0.493980 | + | 0.855598i | ||||
\(623\) | 7.68323e8i | 0.127302i | ||||||||
\(624\) | −1.53605e9 | − | 8.86842e8i | −0.253082 | − | 0.146117i | ||||
\(625\) | 2.92608e9 | − | 5.06812e9i | 0.479409 | − | 0.830360i | ||||
\(626\) | 1.92642e9 | − | 3.33665e9i | 0.313863 | − | 0.543627i | ||||
\(627\) | −1.24105e9 | + | 7.16523e8i | −0.201073 | + | 0.116090i | ||||
\(628\) | 6.57257e9 | 1.05895 | ||||||||
\(629\) | −6.51861e8 | − | 9.06064e9i | −0.104443 | − | 1.45172i | ||||
\(630\) | 1.64214e9 | 0.261649 | ||||||||
\(631\) | −5.23579e9 | + | 3.02289e9i | −0.829621 | + | 0.478982i | −0.853723 | − | 0.520728i | \(-0.825661\pi\) |
0.0241021 | + | 0.999710i | \(0.492327\pi\) | |||||||
\(632\) | −2.70172e9 | + | 4.67952e9i | −0.425727 | + | 0.737381i | ||||
\(633\) | −4.43035e9 | + | 7.67359e9i | −0.694264 | + | 1.20250i | ||||
\(634\) | 6.68996e9 | + | 3.86245e9i | 1.04258 | + | 0.601936i | ||||
\(635\) | 1.01665e10i | 1.57566i | ||||||||
\(636\) | −4.45097e9 | + | 7.70931e9i | −0.686049 | + | 1.18827i | ||||
\(637\) | − | 2.37979e9i | − | 0.364796i | ||||||
\(638\) | −7.67750e8 | − | 1.32978e9i | −0.117043 | − | 0.202725i | ||||
\(639\) | −3.39663e8 | −0.0514986 | ||||||||
\(640\) | −6.06294e9 | −0.914226 | ||||||||
\(641\) | 5.47868e9 | + | 9.48934e9i | 0.821623 | + | 1.42309i | 0.904473 | + | 0.426530i | \(0.140264\pi\) |
−0.0828505 | + | 0.996562i | \(0.526402\pi\) | |||||||
\(642\) | −1.16816e10 | − | 6.74436e9i | −1.74232 | − | 1.00593i | ||||
\(643\) | 1.20642e10i | 1.78961i | 0.446453 | + | 0.894807i | \(0.352687\pi\) | ||||
−0.446453 | + | 0.894807i | \(0.647313\pi\) | |||||||
\(644\) | −2.29732e9 | + | 1.32636e9i | −0.338939 | + | 0.195687i | ||||
\(645\) | 2.87293e9 | + | 4.97606e9i | 0.421566 | + | 0.730175i | ||||
\(646\) | −6.96676e9 | + | 4.02226e9i | −1.01676 | + | 0.587024i | ||||
\(647\) | −3.84562e9 | − | 2.22027e9i | −0.558215 | − | 0.322286i | 0.194214 | − | 0.980959i | \(-0.437784\pi\) |
−0.752429 | + | 0.658674i | \(0.771118\pi\) | |||||||
\(648\) | 3.51209e9 | + | 2.02770e9i | 0.507052 | + | 0.292747i | ||||
\(649\) | 3.41057e9 | − | 1.96909e9i | 0.489745 | − | 0.282755i | ||||
\(650\) | −8.16111e7 | − | 1.41355e8i | −0.0116561 | − | 0.0201889i | ||||
\(651\) | −1.39085e9 | + | 8.03005e8i | −0.197581 | + | 0.114073i | ||||
\(652\) | 8.75014e9i | 1.23637i | ||||||||
\(653\) | −1.12327e10 | − | 6.48520e9i | −1.57866 | − | 0.911438i | −0.995047 | − | 0.0994028i | \(-0.968307\pi\) |
−0.583609 | − | 0.812035i | \(-0.698360\pi\) | |||||||
\(654\) | −1.18902e10 | − | 2.05945e10i | −1.66214 | − | 2.87891i | ||||
\(655\) | 3.95328e9 | 0.549684 | ||||||||
\(656\) | 3.68747e9 | 0.509994 | ||||||||
\(657\) | −2.79867e9 | − | 4.84745e9i | −0.385011 | − | 0.666859i | ||||
\(658\) | 1.19479e9i | 0.163494i | ||||||||
\(659\) | −5.44024e9 | + | 9.42276e9i | −0.740489 | + | 1.28256i | 0.211784 | + | 0.977317i | \(0.432073\pi\) |
−0.952273 | + | 0.305248i | \(0.901261\pi\) | |||||||
\(660\) | 4.20048e9i | 0.568716i | ||||||||
\(661\) | 5.49289e9 | + | 3.17132e9i | 0.739769 | + | 0.427106i | 0.821985 | − | 0.569509i | \(-0.192867\pi\) |
−0.0822164 | + | 0.996614i | \(0.526200\pi\) | |||||||
\(662\) | 9.16302e9 | − | 1.58708e10i | 1.22754 | − | 2.12616i | ||||
\(663\) | −2.78574e9 | + | 4.82504e9i | −0.371230 | + | 0.642989i | ||||
\(664\) | 1.91982e9 | − | 1.10841e9i | 0.254490 | − | 0.146930i | ||||
\(665\) | 9.24453e8 | 0.121902 | ||||||||
\(666\) | 7.17010e9 | − | 4.85727e9i | 0.940515 | − | 0.637136i | ||||
\(667\) | −4.46221e9 | −0.582251 | ||||||||
\(668\) | −1.22520e9 | + | 7.07368e8i | −0.159034 | + | 0.0918180i | ||||
\(669\) | −2.01715e9 | + | 3.49380e9i | −0.260463 | + | 0.451135i | ||||
\(670\) | 8.53249e9 | − | 1.47787e10i | 1.09601 | − | 1.89834i | ||||
\(671\) | 2.51654e8 | + | 1.45293e8i | 0.0321570 | + | 0.0185658i | ||||
\(672\) | 3.33466e9i | 0.423895i | ||||||||
\(673\) | −3.71908e9 | + | 6.44164e9i | −0.470309 | + | 0.814599i | −0.999423 | − | 0.0339514i | \(-0.989191\pi\) |
0.529115 | + | 0.848550i | \(0.322524\pi\) | |||||||
\(674\) | − | 6.83058e9i | − | 0.859307i | ||||||
\(675\) | −5.32402e7 | − | 9.22148e7i | −0.00666310 | − | 0.0115408i | ||||
\(676\) | −9.04097e9 | −1.12565 | ||||||||
\(677\) | −1.68870e9 | −0.209167 | −0.104583 | − | 0.994516i | \(-0.533351\pi\) | ||||
−0.104583 | + | 0.994516i | \(0.533351\pi\) | |||||||
\(678\) | 6.18427e8 | + | 1.07115e9i | 0.0762052 | + | 0.131991i | ||||
\(679\) | −2.31818e9 | − | 1.33840e9i | −0.284186 | − | 0.164075i | ||||
\(680\) | 5.75514e9i | 0.701899i | ||||||||
\(681\) | −6.92478e9 | + | 3.99802e9i | −0.840216 | + | 0.485099i | ||||
\(682\) | −1.54026e9 | − | 2.66782e9i | −0.185930 | − | 0.322041i | ||||
\(683\) | 3.27319e9 | − | 1.88978e9i | 0.393096 | − | 0.226954i | −0.290405 | − | 0.956904i | \(-0.593790\pi\) |
0.683501 | + | 0.729950i | \(0.260457\pi\) | |||||||
\(684\) | −3.78255e9 | − | 2.18386e9i | −0.451948 | − | 0.260932i | ||||
\(685\) | 3.64274e9 | + | 2.10314e9i | 0.433023 | + | 0.250006i | ||||
\(686\) | −5.10106e9 | + | 2.94510e9i | −0.603290 | + | 0.348309i | ||||
\(687\) | 3.47663e9 | + | 6.02170e9i | 0.409082 | + | 0.708550i | ||||
\(688\) | −2.75981e9 | + | 1.59338e9i | −0.323088 | + | 0.186535i | ||||
\(689\) | 2.60266e9i | 0.303145i | ||||||||
\(690\) | 1.85625e10 | + | 1.07171e10i | 2.15113 | + | 1.24195i | ||||
\(691\) | 1.66363e9 | + | 2.88149e9i | 0.191815 | + | 0.332234i | 0.945852 | − | 0.324599i | \(-0.105229\pi\) |
−0.754037 | + | 0.656832i | \(0.771896\pi\) | |||||||
\(692\) | 1.82713e10 | 2.09604 | ||||||||
\(693\) | 5.09636e8 | 0.0581693 | ||||||||
\(694\) | 1.64054e9 | + | 2.84150e9i | 0.186307 | + | 0.322693i | ||||
\(695\) | 1.02425e10i | 1.15733i | ||||||||
\(696\) | 1.33736e9 | − | 2.31638e9i | 0.150354 | − | 0.260421i | ||||
\(697\) | − | 1.15831e10i | − | 1.29571i | ||||||
\(698\) | −2.13131e9 | − | 1.23051e9i | −0.237221 | − | 0.136960i | ||||
\(699\) | 2.79469e9 | − | 4.84055e9i | 0.309502 | − | 0.536074i | ||||
\(700\) | −5.58843e7 | + | 9.67945e7i | −0.00615810 | + | 0.0106661i | ||||
\(701\) | 7.63170e9 | − | 4.40617e9i | 0.836774 | − | 0.483112i | −0.0193921 | − | 0.999812i | \(-0.506173\pi\) |
0.856167 | + | 0.516700i | \(0.172840\pi\) | |||||||
\(702\) | 1.81462e9 | 0.197973 | ||||||||
\(703\) | 4.03645e9 | − | 2.73442e9i | 0.438183 | − | 0.296840i | ||||
\(704\) | −4.63523e9 | −0.500688 | ||||||||
\(705\) | 4.76137e9 | − | 2.74898e9i | 0.511764 | − | 0.295467i | ||||
\(706\) | 4.23779e9 | − | 7.34007e9i | 0.453235 | − | 0.785026i | ||||
\(707\) | 6.00678e8 | − | 1.04040e9i | 0.0639254 | − | 0.110722i | ||||
\(708\) | 2.43410e10 | + | 1.40533e10i | 2.57764 | + | 1.48820i | ||||
\(709\) | − | 6.64473e9i | − | 0.700189i | −0.936714 | − | 0.350095i | \(-0.886149\pi\) | ||
0.936714 | − | 0.350095i | \(-0.113851\pi\) | |||||||
\(710\) | −4.92083e8 | + | 8.52312e8i | −0.0515981 | + | 0.0893706i | ||||
\(711\) | − | 1.23601e10i | − | 1.28967i | ||||||
\(712\) | −1.28357e9 | − | 2.22321e9i | −0.133272 | − | 0.230834i | ||||
\(713\) | −8.95212e9 | −0.924938 | ||||||||
\(714\) | 6.69912e9 | 0.688770 | ||||||||
\(715\) | 6.14048e8 | + | 1.06356e9i | 0.0628248 | + | 0.108816i | ||||
\(716\) | −1.51703e10 | − | 8.75858e9i | −1.54454 | − | 0.891740i | ||||
\(717\) | 1.51416e10i | 1.53411i | ||||||||
\(718\) | −2.78662e9 | + | 1.60886e9i | −0.280959 | + | 0.162212i | ||||
\(719\) | −4.79589e9 | − | 8.30673e9i | −0.481192 | − | 0.833449i | 0.518575 | − | 0.855032i | \(-0.326463\pi\) |
−0.999767 | + | 0.0215833i | \(0.993129\pi\) | |||||||
\(720\) | 3.62948e9 | − | 2.09548e9i | 0.362394 | − | 0.209228i | ||||
\(721\) | 2.23377e9 | + | 1.28967e9i | 0.221955 | + | 0.128146i | ||||
\(722\) | 9.60915e9 | + | 5.54785e9i | 0.950178 | + | 0.548586i | ||||
\(723\) | −7.40096e9 | + | 4.27295e9i | −0.728289 | + | 0.420478i | ||||
\(724\) | −9.50408e9 | − | 1.64615e10i | −0.930733 | − | 1.61208i | ||||
\(725\) | −1.62821e8 | + | 9.40045e7i | −0.0158682 | + | 0.00916148i | ||||
\(726\) | − | 1.84713e10i | − | 1.79151i | ||||||
\(727\) | 1.00353e10 | + | 5.79390e9i | 0.968638 | + | 0.559243i | 0.898821 | − | 0.438317i | \(-0.144425\pi\) |
0.0698171 | + | 0.997560i | \(0.477758\pi\) | |||||||
\(728\) | −2.32446e8 | − | 4.02609e8i | −0.0223287 | − | 0.0386744i | ||||
\(729\) | −4.62762e9 | −0.442396 | ||||||||
\(730\) | −1.62182e10 | −1.54302 | ||||||||
\(731\) | 5.00511e9 | + | 8.66910e9i | 0.473917 | + | 0.820849i | ||||
\(732\) | 2.07389e9i | 0.195432i | ||||||||
\(733\) | 4.74741e9 | − | 8.22276e9i | 0.445239 | − | 0.771177i | −0.552830 | − | 0.833294i | \(-0.686452\pi\) |
0.998069 | + | 0.0621176i | \(0.0197854\pi\) | |||||||
\(734\) | − | 1.71801e10i | − | 1.60358i | ||||||
\(735\) | 1.14032e10 | + | 6.58361e9i | 1.05930 | + | 0.611588i | ||||
\(736\) | −9.29392e9 | + | 1.60975e10i | −0.859264 | + | 1.48829i | ||||
\(737\) | 2.64804e9 | − | 4.58654e9i | 0.243662 | − | 0.422035i | ||||
\(738\) | 9.56345e9 | − | 5.52146e9i | 0.875825 | − | 0.505658i | ||||
\(739\) | 1.87768e10 | 1.71146 | 0.855728 | − | 0.517427i | \(-0.173110\pi\) | ||||
0.855728 | + | 0.517427i | \(0.173110\pi\) | |||||||
\(740\) | −1.02548e9 | − | 1.42539e10i | −0.0930289 | − | 1.29307i | ||||
\(741\) | −2.99023e9 | −0.269986 | ||||||||
\(742\) | 2.71016e9 | − | 1.56471e9i | 0.243547 | − | 0.140612i | ||||
\(743\) | −6.46413e9 | + | 1.11962e10i | −0.578161 | + | 1.00140i | 0.417529 | + | 0.908664i | \(0.362896\pi\) |
−0.995690 | + | 0.0927411i | \(0.970437\pi\) | |||||||
\(744\) | 2.68302e9 | − | 4.64713e9i | 0.238846 | − | 0.413694i | ||||
\(745\) | −1.97820e9 | − | 1.14211e9i | −0.175276 | − | 0.101196i | ||||
\(746\) | − | 2.29573e10i | − | 2.02458i | ||||||
\(747\) | −2.53543e9 | + | 4.39149e9i | −0.222551 | + | 0.385469i | ||||
\(748\) | 7.31792e9i | 0.639340i | ||||||||
\(749\) | 1.35025e9 | + | 2.33870e9i | 0.117416 | + | 0.203371i | ||||
\(750\) | 2.37009e10 | 2.05140 | ||||||||
\(751\) | 6.69889e9 | 0.577116 | 0.288558 | − | 0.957462i | \(-0.406824\pi\) | ||||
0.288558 | + | 0.957462i | \(0.406824\pi\) | |||||||
\(752\) | 1.52463e9 | + | 2.64074e9i | 0.130738 | + | 0.226445i | ||||
\(753\) | −1.57296e10 | − | 9.08147e9i | −1.34256 | − | 0.775129i | ||||
\(754\) | − | 3.20401e9i | − | 0.272204i | ||||||
\(755\) | −1.66695e10 | + | 9.62411e9i | −1.40964 | + | 0.813854i | ||||
\(756\) | −6.21292e8 | − | 1.07611e9i | −0.0522961 | − | 0.0905795i | ||||
\(757\) | 7.69609e8 | − | 4.44334e8i | 0.0644814 | − | 0.0372283i | −0.467413 | − | 0.884039i | \(-0.654814\pi\) |
0.531894 | + | 0.846811i | \(0.321480\pi\) | |||||||
\(758\) | −2.45758e9 | − | 1.41888e9i | −0.204958 | − | 0.118333i | ||||
\(759\) | 5.76085e9 | + | 3.32603e9i | 0.478234 | + | 0.276108i | ||||
\(760\) | −2.67498e9 | + | 1.54440e9i | −0.221041 | + | 0.127618i | ||||
\(761\) | 2.68882e9 | + | 4.65717e9i | 0.221165 | + | 0.383068i | 0.955162 | − | 0.296084i | \(-0.0956809\pi\) |
−0.733997 | + | 0.679152i | \(0.762348\pi\) | |||||||
\(762\) | −3.42427e10 | + | 1.97700e10i | −2.80366 | + | 1.61869i | ||||
\(763\) | 4.76094e9i | 0.388023i | ||||||||
\(764\) | 1.53321e10 | + | 8.85201e9i | 1.24387 | + | 0.718150i | ||||
\(765\) | −6.58231e9 | − | 1.14009e10i | −0.531573 | − | 0.920712i | ||||
\(766\) | −2.93365e10 | −2.35835 | ||||||||
\(767\) | 8.21752e9 | 0.657592 | ||||||||
\(768\) | 7.13367e8 | + | 1.23559e9i | 0.0568262 | + | 0.0984259i | ||||
\(769\) | − | 1.71658e10i | − | 1.36120i | −0.732656 | − | 0.680599i | \(-0.761720\pi\) | ||
0.732656 | − | 0.680599i | \(-0.238280\pi\) | |||||||
\(770\) | 7.38328e8 | − | 1.27882e9i | 0.0582817 | − | 0.100947i | ||||
\(771\) | 3.73360e9i | 0.293385i | ||||||||
\(772\) | 1.33353e10 | + | 7.69916e9i | 1.04314 | + | 0.602259i | ||||
\(773\) | −7.66536e9 | + | 1.32768e10i | −0.596904 | + | 1.03387i | 0.396371 | + | 0.918090i | \(0.370269\pi\) |
−0.993275 | + | 0.115778i | \(0.963064\pi\) | |||||||
\(774\) | −4.77171e9 | + | 8.26485e9i | −0.369897 | + | 0.640681i | ||||
\(775\) | −3.26652e8 | + | 1.88592e8i | −0.0252075 | + | 0.0145535i | ||||
\(776\) | 8.94381e9 | 0.687079 | ||||||||
\(777\) | −4.04959e9 | + | 2.91345e8i | −0.309697 | + | 0.0222810i | ||||
\(778\) | −3.28572e10 | −2.50151 | ||||||||
\(779\) | 5.38379e9 | − | 3.10833e9i | 0.408044 | − | 0.235584i | ||||
\(780\) | −4.38242e9 | + | 7.59057e9i | −0.330661 | + | 0.572722i | ||||
\(781\) | −1.52717e8 | + | 2.64513e8i | −0.0114712 | + | 0.0198687i | ||||
\(782\) | 3.23390e10 | + | 1.86709e10i | 2.41826 | + | 1.39618i | ||||
\(783\) | − | 2.09018e9i | − | 0.155603i | ||||||
\(784\) | −3.65139e9 | + | 6.32440e9i | −0.270615 | + | 0.468719i | ||||
\(785\) | 1.06322e10i | 0.784477i | ||||||||
\(786\) | 7.68767e9 | + | 1.33154e10i | 0.564697 | + | 0.978084i | ||||
\(787\) | 9.16756e9 | 0.670412 | 0.335206 | − | 0.942145i | \(-0.391194\pi\) | ||||
0.335206 | + | 0.942145i | \(0.391194\pi\) | |||||||
\(788\) | 3.50601e10 | 2.55253 | ||||||||
\(789\) | −1.09513e10 | − | 1.89682e10i | −0.793771 | − | 1.37485i | ||||
\(790\) | −3.10151e10 | − | 1.79066e10i | −2.23810 | − | 1.29216i | ||||
\(791\) | − | 2.47624e8i | − | 0.0177899i | ||||||
\(792\) | −1.47467e9 | + | 8.51404e8i | −0.105477 | + | 0.0608972i | ||||
\(793\) | 3.03171e8 | + | 5.25108e8i | 0.0215890 | + | 0.0373932i | ||||
\(794\) | −1.75326e10 | + | 1.01225e10i | −1.24301 | + | 0.717654i | ||||
\(795\) | −1.24711e10 | − | 7.20018e9i | −0.880277 | − | 0.508228i | ||||
\(796\) | −2.41651e10 | − | 1.39517e10i | −1.69822 | − | 0.980467i | ||||
\(797\) | −1.70160e10 | + | 9.82417e9i | −1.19056 | + | 0.687372i | −0.958434 | − | 0.285314i | \(-0.907902\pi\) |
−0.232128 | + | 0.972685i | \(0.574569\pi\) | |||||||
\(798\) | 1.79772e9 | + | 3.11374e9i | 0.125231 | + | 0.216907i | ||||
\(799\) | 8.29507e9 | − | 4.78916e9i | 0.575316 | − | 0.332159i | ||||
\(800\) | 7.83172e8i | 0.0540807i | ||||||||
\(801\) | 5.08549e9 | + | 2.93611e9i | 0.349638 | + | 0.201864i | ||||
\(802\) | −7.80477e9 | − | 1.35183e10i | −0.534257 | − | 0.925360i | ||||
\(803\) | −5.03328e9 | −0.343041 | ||||||||
\(804\) | 3.77978e10 | 2.56490 | ||||||||
\(805\) | −2.14561e9 | − | 3.71630e9i | −0.144966 | − | 0.251088i | ||||
\(806\) | − | 6.42791e9i | − | 0.432411i | ||||||
\(807\) | 1.00666e9 | − | 1.74358e9i | 0.0674256 | − | 0.116785i | ||||
\(808\) | 4.01400e9i | 0.267693i | ||||||||
\(809\) | 1.86757e10 | + | 1.07824e10i | 1.24010 | + | 0.715974i | 0.969115 | − | 0.246608i | \(-0.0793161\pi\) |
0.270989 | + | 0.962583i | \(0.412649\pi\) | |||||||
\(810\) | −1.34393e10 | + | 2.32775e10i | −0.888544 | + | 1.53900i | ||||
\(811\) | 5.06719e9 | − | 8.77663e9i | 0.333575 | − | 0.577770i | −0.649635 | − | 0.760246i | \(-0.725078\pi\) |
0.983210 | + | 0.182477i | \(0.0584115\pi\) | |||||||
\(812\) | −1.90005e9 | + | 1.09700e9i | −0.124543 | + | 0.0719049i | ||||
\(813\) | −4.94151e9 | −0.322510 | ||||||||
\(814\) | −5.58836e8 | − | 7.76762e9i | −0.0363161 | − | 0.504780i | ||||
\(815\) | −1.41548e10 | −0.915909 | ||||||||
\(816\) | 1.48065e10 | − | 8.54851e9i | 0.953972 | − | 0.550776i | ||||
\(817\) | −2.68626e9 | + | 4.65274e9i | −0.172334 | + | 0.298491i | ||||
\(818\) | 1.41306e10 | − | 2.44748e10i | 0.902657 | − | 1.56345i | ||||
\(819\) | 9.20948e8 | + | 5.31710e8i | 0.0585789 | + | 0.0338206i | ||||
\(820\) | − | 1.82220e10i | − | 1.15411i | ||||||
\(821\) | 4.09627e9 | − | 7.09495e9i | 0.258338 | − | 0.447454i | −0.707459 | − | 0.706754i | \(-0.750159\pi\) |
0.965797 | + | 0.259300i | \(0.0834920\pi\) | |||||||
\(822\) | 1.63593e10i | 1.02734i | ||||||||
\(823\) | −7.63880e9 | − | 1.32308e10i | −0.477668 | − | 0.827345i | 0.522005 | − | 0.852943i | \(-0.325184\pi\) |
−0.999672 | + | 0.0255980i | \(0.991851\pi\) | |||||||
\(824\) | −8.61814e9 | −0.536622 | ||||||||
\(825\) | 2.80275e8 | 0.0173778 | ||||||||
\(826\) | −4.94035e9 | − | 8.55694e9i | −0.305020 | − | 0.528309i | ||||
\(827\) | 3.37651e9 | + | 1.94943e9i | 0.207587 | + | 0.119850i | 0.600189 | − | 0.799858i | \(-0.295092\pi\) |
−0.392603 | + | 0.919708i | \(0.628425\pi\) | |||||||
\(828\) | 2.02745e10i | 1.24120i | ||||||||
\(829\) | −2.04295e10 | + | 1.17950e10i | −1.24542 | + | 0.719044i | −0.970193 | − | 0.242335i | \(-0.922087\pi\) |
−0.275228 | + | 0.961379i | \(0.588753\pi\) | |||||||
\(830\) | 7.34634e9 | + | 1.27242e10i | 0.445962 | + | 0.772428i | ||||
\(831\) | 1.75350e10 | − | 1.01239e10i | 1.05999 | − | 0.611988i | ||||
\(832\) | −8.37619e9 | − | 4.83599e9i | −0.504214 | − | 0.291108i | ||||
\(833\) | 1.98661e10 | + | 1.14697e10i | 1.19085 | + | 0.687536i | ||||
\(834\) | −3.44987e10 | + | 1.99178e10i | −2.05931 | + | 1.18894i | ||||
\(835\) | −1.14429e9 | − | 1.98196e9i | −0.0680192 | − | 0.117813i | ||||
\(836\) | −3.40136e9 | + | 1.96378e9i | −0.201340 | + | 0.116244i | ||||
\(837\) | − | 4.19334e9i | − | 0.247184i | ||||||
\(838\) | 1.95748e10 | + | 1.13015e10i | 1.14906 | + | 0.663411i | ||||
\(839\) | 1.08784e10 | + | 1.88420e10i | 0.635916 | + | 1.10144i | 0.986320 | + | 0.164840i | \(0.0527109\pi\) |
−0.350404 | + | 0.936599i | \(0.613956\pi\) | |||||||
\(840\) | 2.57222e9 | 0.149738 | ||||||||
\(841\) | 1.35593e10 | 0.786052 | ||||||||
\(842\) | 1.91086e10 | + | 3.30971e10i | 1.10316 | + | 1.91072i | ||||
\(843\) | − | 2.61533e10i | − | 1.50359i | ||||||
\(844\) | −1.21423e10 | + | 2.10310e10i | −0.695186 | + | 1.20410i | ||||
\(845\) | − | 1.46253e10i | − | 0.833884i | ||||||
\(846\) | 7.90826e9 | + | 4.56583e9i | 0.449039 | + | 0.259253i | ||||
\(847\) | −1.84901e9 | + | 3.20259e9i | −0.104556 | + | 0.181096i | ||||
\(848\) | 3.99335e9 | − | 6.91669e9i | 0.224881 | − | 0.389505i | ||||
\(849\) | 5.40672e9 | − | 3.12157e9i | 0.303219 | − | 0.175064i | ||||
\(850\) | 1.57334e9 | 0.0878734 | ||||||||
\(851\) | −2.03608e10 | − | 9.88006e9i | −1.13251 | − | 0.549549i | ||||
\(852\) | −2.17986e9 | −0.120751 | ||||||||
\(853\) | 8.68134e9 | − | 5.01218e9i | 0.478923 | − | 0.276506i | −0.241045 | − | 0.970514i | \(-0.577490\pi\) |
0.719967 | + | 0.694008i | \(0.244157\pi\) | |||||||
\(854\) | 3.64532e8 | − | 6.31387e8i | 0.0200278 | − | 0.0346891i | ||||
\(855\) | 3.53275e9 | − | 6.11890e9i | 0.193300 | − | 0.334805i | ||||
\(856\) | −7.81412e9 | − | 4.51149e9i | −0.425816 | − | 0.245845i | ||||
\(857\) | − | 9.42193e9i | − | 0.511337i | −0.966765 | − | 0.255668i | \(-0.917704\pi\) | ||
0.966765 | − | 0.255668i | \(-0.0822955\pi\) | |||||||
\(858\) | −2.38819e9 | + | 4.13647e9i | −0.129082 | + | 0.223576i | ||||
\(859\) | − | 1.34497e10i | − | 0.723995i | −0.932179 | − | 0.361998i | \(-0.882095\pi\) | ||
0.932179 | − | 0.361998i | \(-0.117905\pi\) | |||||||
\(860\) | 7.87385e9 | + | 1.36379e10i | 0.422126 | + | 0.731144i | ||||
\(861\) | −5.17697e9 | −0.276417 | ||||||||
\(862\) | 2.44602e10 | 1.30072 | ||||||||
\(863\) | −1.00543e9 | − | 1.74145e9i | −0.0532491 | − | 0.0922302i | 0.838172 | − | 0.545406i | \(-0.183624\pi\) |
−0.891421 | + | 0.453176i | \(0.850291\pi\) | |||||||
\(864\) | −7.54039e9 | − | 4.35345e9i | −0.397737 | − | 0.229633i | ||||
\(865\) | 2.95569e10i | 1.55275i | ||||||||
\(866\) | −2.59744e9 | + | 1.49963e9i | −0.135904 | + | 0.0784643i | ||||
\(867\) | −1.41766e10 | − | 2.45545e10i | −0.738762 | − | 1.27957i | ||||
\(868\) | −3.81189e9 | + | 2.20080e9i | −0.197844 | + | 0.114225i | ||||
\(869\) | −9.62547e9 | − | 5.55727e9i | −0.497569 | − | 0.287271i | ||||
\(870\) | 1.53526e10 | + | 8.86380e9i | 0.790430 | + | 0.456355i | ||||
\(871\) | 9.57039e9 | − | 5.52547e9i | 0.490757 | − | 0.283338i | ||||
\(872\) | −7.95369e9 | − | 1.37762e10i | −0.406220 | − | 0.703593i | ||||
\(873\) | −1.77176e10 | + | 1.02293e10i | −0.901271 | + | 0.520349i | ||||
\(874\) | 2.00415e10i | 1.01541i | ||||||||
\(875\) | −4.10931e9 | − | 2.37251e9i | −0.207368 | − | 0.119724i | ||||
\(876\) | −1.79611e10 | − | 3.11095e10i | −0.902751 | − | 1.56361i | ||||
\(877\) | 1.98100e10 | 0.991711 | 0.495855 | − | 0.868405i | \(-0.334855\pi\) | ||||
0.495855 | + | 0.868405i | \(0.334855\pi\) | |||||||
\(878\) | −2.40900e10 | −1.20118 | ||||||||
\(879\) | −9.56234e9 | − | 1.65625e10i | −0.474901 | − | 0.822553i | ||||
\(880\) | − | 3.76862e9i | − | 0.186420i | ||||||
\(881\) | 1.51256e10 | − | 2.61983e10i | 0.745240 | − | 1.29079i | −0.204842 | − | 0.978795i | \(-0.565668\pi\) |
0.950082 | − | 0.311999i | \(-0.100998\pi\) | |||||||
\(882\) | 2.18697e10i | 1.07326i | ||||||||
\(883\) | −2.58471e10 | − | 1.49228e10i | −1.26342 | − | 0.729438i | −0.289688 | − | 0.957121i | \(-0.593552\pi\) |
−0.973735 | + | 0.227683i | \(0.926885\pi\) | |||||||
\(884\) | −7.63488e9 | + | 1.32240e10i | −0.371723 | + | 0.643843i | ||||
\(885\) | −2.27335e10 | + | 3.93756e10i | −1.10247 | + | 1.90953i | ||||
\(886\) | 4.36054e10 | − | 2.51756e10i | 2.10631 | − | 1.21608i | ||||
\(887\) | 5.36043e9 | 0.257909 | 0.128955 | − | 0.991650i | \(-0.458838\pi\) | ||||
0.128955 | + | 0.991650i | \(0.458838\pi\) | |||||||
\(888\) | 1.12311e10 | − | 7.60832e9i | 0.538241 | − | 0.364623i | ||||
\(889\) | 7.91608e9 | 0.377880 | ||||||||
\(890\) | 1.47351e10 | − | 8.50730e9i | 0.700627 | − | 0.404507i | ||||
\(891\) | −4.17086e9 | + | 7.22414e9i | −0.197539 | + | 0.342148i | ||||
\(892\) | −5.52840e9 | + | 9.57547e9i | −0.260809 | + | 0.451734i | ||||
\(893\) | 4.45199e9 | + | 2.57036e9i | 0.209206 | + | 0.120785i | ||||
\(894\) | − | 8.88395e9i | − | 0.415838i | ||||||
\(895\) | 1.41685e10 | − | 2.45405e10i | 0.660605 | − | 1.14420i | ||||
\(896\) | 4.72089e9i | 0.219253i | ||||||||
\(897\) | 6.94017e9 | + | 1.20207e10i | 0.321068 | + | 0.556106i | ||||
\(898\) | 1.28692e10 | 0.593040 | ||||||||
\(899\) | −7.40405e9 | −0.339868 | ||||||||
\(900\) | 4.27118e8 | + | 7.39790e8i | 0.0195299 | + | 0.0338267i | ||||
\(901\) | −2.17266e10 | − | 1.25439e10i | −0.989591 | − | 0.571341i | ||||
\(902\) | − | 9.93007e9i | − | 0.450536i | ||||||
\(903\) | 3.87459e9 | − | 2.23700e9i | 0.175113 | − | 0.101102i | ||||
\(904\) | 4.13683e8 | + | 7.16520e8i | 0.0186242 | + | 0.0322581i | ||||
\(905\) | 2.66293e10 | − | 1.53744e10i | 1.19423 | − | 0.689491i | ||||
\(906\) | −6.48319e10 | − | 3.74307e10i | −2.89628 | − | 1.67217i | ||||
\(907\) | 1.69284e10 | + | 9.77360e9i | 0.753338 | + | 0.434940i | 0.826899 | − | 0.562351i | \(-0.190103\pi\) |
−0.0735611 | + | 0.997291i | \(0.523436\pi\) | |||||||
\(908\) | −1.89788e10 | + | 1.09574e10i | −0.841332 | + | 0.485743i | ||||
\(909\) | −4.59092e9 | − | 7.95170e9i | −0.202734 | − | 0.351145i | ||||
\(910\) | 2.66842e9 | − | 1.54062e9i | 0.117384 | − | 0.0677718i | ||||
\(911\) | 2.55835e10i | 1.12110i | 0.828119 | + | 0.560552i | \(0.189411\pi\) | ||||
−0.828119 | + | 0.560552i | \(0.810589\pi\) | |||||||
\(912\) | 7.94667e9 | + | 4.58801e9i | 0.346899 | + | 0.200282i | ||||
\(913\) | 2.27992e9 | + | 3.94894e9i | 0.0991452 | + | 0.171725i | ||||
\(914\) | 5.63409e10 | 2.44069 | ||||||||
\(915\) | −3.35486e9 | −0.144777 | ||||||||
\(916\) | 9.52841e9 | + | 1.65037e10i | 0.409625 | + | 0.709491i | ||||
\(917\) | − | 3.07821e9i | − | 0.131827i | ||||||
\(918\) | −8.74580e9 | + | 1.51482e10i | −0.373121 | + | 0.646265i | ||||
\(919\) | 1.64599e10i | 0.699556i | 0.936833 | + | 0.349778i | \(0.113743\pi\) | ||||
−0.936833 | + | 0.349778i | \(0.886257\pi\) | |||||||
\(920\) | 1.24170e10 | + | 7.16896e9i | 0.525726 | + | 0.303528i | ||||
\(921\) | 2.14761e10 | − | 3.71976e10i | 0.905828 | − | 1.56894i | ||||
\(922\) | 1.10565e8 | − | 1.91503e8i | 0.00464577 | − | 0.00804671i | ||||
\(923\) | −5.51940e8 | + | 3.18663e8i | −0.0231039 | + | 0.0133391i | ||||
\(924\) | 3.27069e9 | 0.136392 | ||||||||
\(925\) | −9.51080e8 | + | 6.84248e7i | −0.0395113 | + | 0.00284261i | ||||
\(926\) | −1.52716e10 | −0.632042 | ||||||||
\(927\) | 1.70725e10 | − | 9.85679e9i | 0.703910 | − | 0.406403i | ||||
\(928\) | −7.68674e9 | + | 1.33138e10i | −0.315736 | + | 0.546871i | ||||
\(929\) | −1.92079e10 | + | 3.32691e10i | −0.786006 | + | 1.36140i | 0.142391 | + | 0.989811i | \(0.454521\pi\) |
−0.928396 | + | 0.371591i | \(0.878812\pi\) | |||||||
\(930\) | 3.08004e10 | + | 1.77826e10i | 1.25564 | + | 0.724945i | ||||
\(931\) | 1.23117e10i | 0.500027i | ||||||||
\(932\) | 7.65942e9 | − | 1.32665e10i | 0.309913 | − | 0.536786i | ||||
\(933\) | − | 2.12449e10i | − | 0.856385i | ||||||
\(934\) | 6.95184e9 | + | 1.20409e10i | 0.279181 | + | 0.483555i | ||||
\(935\) | −1.18380e10 | −0.473627 | ||||||||
\(936\) | −3.55312e9 | −0.141627 | ||||||||
\(937\) | 1.97000e10 | + | 3.41214e10i | 0.782308 | + | 1.35500i | 0.930594 | + | 0.366053i | \(0.119291\pi\) |
−0.148286 | + | 0.988945i | \(0.547376\pi\) | |||||||
\(938\) | −1.15074e10 | − | 6.64380e9i | −0.455268 | − | 0.262849i | ||||
\(939\) | 1.38048e10i | 0.544127i | ||||||||
\(940\) | 1.30495e10 | − | 7.53413e9i | 0.512444 | − | 0.295859i | ||||
\(941\) | 1.78842e9 | + | 3.09764e9i | 0.0699692 | + | 0.121190i | 0.898887 | − | 0.438180i | \(-0.144377\pi\) |
−0.828918 | + | 0.559370i | \(0.811043\pi\) | |||||||
\(942\) | −3.58114e10 | + | 2.06757e10i | −1.39587 | + | 0.805903i | ||||
\(943\) | −2.49910e10 | − | 1.44286e10i | −0.970494 | − | 0.560315i | ||||
\(944\) | −2.18384e10 | − | 1.26084e10i | −0.844927 | − | 0.487819i | ||||
\(945\) | 1.74079e9 | − | 1.00504e9i | 0.0671018 | − | 0.0387412i | ||||
\(946\) | 4.29084e9 | + | 7.43196e9i | 0.164787 | + | 0.285420i | ||||
\(947\) | 2.38331e10 | − | 1.37601e10i | 0.911919 | − | 0.526496i | 0.0308707 | − | 0.999523i | \(-0.490172\pi\) |
0.881048 | + | 0.473027i | \(0.156839\pi\) | |||||||
\(948\) | − | 7.93237e10i | − | 3.02395i | ||||||
\(949\) | −9.09549e9 | − | 5.25128e9i | −0.345457 | − | 0.199450i | ||||
\(950\) | 4.22210e8 | + | 7.31289e8i | 0.0159770 | + | 0.0276730i | ||||
\(951\) | −2.76785e10 | −1.04354 | ||||||||
\(952\) | 4.48122e9 | 0.168332 | ||||||||
\(953\) | −2.34718e10 | − | 4.06543e10i | −0.878458 | − | 1.52153i | −0.853033 | − | 0.521858i | \(-0.825239\pi\) |
−0.0254256 | − | 0.999677i | \(-0.508094\pi\) | |||||||
\(954\) | − | 2.39179e10i | − | 0.891874i | ||||||
\(955\) | −1.43196e10 | + | 2.48023e10i | −0.532009 | + | 0.921467i | ||||
\(956\) | 4.14987e10i | 1.53614i | ||||||||
\(957\) | 4.76463e9 | + | 2.75086e9i | 0.175727 | + | 0.101456i | ||||
\(958\) | 8.55228e9 | − | 1.48130e10i | 0.314270 | − | 0.544331i | ||||
\(959\) | 1.63760e9 | − | 2.83641e9i | 0.0599574 | − | 0.103849i | ||||
\(960\) | 4.63449e10 | − | 2.67573e10i | 1.69065 | − | 0.976096i | ||||
\(961\) | 1.26586e10 | 0.460101 | ||||||||
\(962\) | 7.09420e9 | − | 1.46197e10i | 0.256916 | − | 0.529450i | ||||
\(963\) | 2.06396e10 | 0.744749 | ||||||||
\(964\) | −2.02838e10 | + | 1.17109e10i | −0.729257 | + | 0.421037i | ||||
\(965\) | −1.24547e10 | + | 2.15721e10i | −0.446156 | + | 0.772765i | ||||
\(966\) | 8.34483e9 | − | 1.44537e10i | 0.297850 | − | 0.515891i | ||||
\(967\) | −1.48946e10 | − | 8.59941e9i | −0.529708 | − | 0.305827i | 0.211190 | − | 0.977445i | \(-0.432266\pi\) |
−0.740898 | + | 0.671618i | \(0.765600\pi\) | |||||||
\(968\) | − | 1.23559e10i | − | 0.437837i | ||||||
\(969\) | 1.44118e10 | − | 2.49620e10i | 0.508845 | − | 0.881346i | ||||
\(970\) | 5.92781e10i | 2.08542i | ||||||||
\(971\) | −1.76577e10 | − | 3.05840e10i | −0.618964 | − | 1.07208i | −0.989675 | − | 0.143329i | \(-0.954219\pi\) |
0.370711 | − | 0.928748i | \(-0.379114\pi\) | |||||||
\(972\) | −4.67929e10 | −1.63436 | ||||||||
\(973\) | 7.97527e9 | 0.277556 | ||||||||
\(974\) | 1.77630e9 | + | 3.07664e9i | 0.0615970 | + | 0.106689i | ||||
\(975\) | 5.06476e8 | + | 2.92414e8i | 0.0175002 | + | 0.0101037i | ||||
\(976\) | − | 1.86066e9i | − | 0.0640610i | ||||||
\(977\) | −4.88881e9 | + | 2.82256e9i | −0.167715 | + | 0.0968304i | −0.581508 | − | 0.813541i | \(-0.697537\pi\) |
0.413793 | + | 0.910371i | \(0.364204\pi\) | |||||||
\(978\) | −2.75259e10 | − | 4.76762e10i | −0.940925 | − | 1.62973i | ||||
\(979\) | 4.57300e9 | − | 2.64022e9i | 0.155762 | − | 0.0899292i | ||||
\(980\) | 3.12527e10 | + | 1.80437e10i | 1.06071 | + | 0.612400i | ||||
\(981\) | 3.15124e10 | + | 1.81937e10i | 1.06571 | + | 0.615289i | ||||
\(982\) | 2.04527e10 | − | 1.18083e10i | 0.689223 | − | 0.397923i | ||||
\(983\) | 1.14523e10 | + | 1.98360e10i | 0.384554 | + | 0.666067i | 0.991707 | − | 0.128518i | \(-0.0410220\pi\) |
−0.607153 | + | 0.794585i | \(0.707689\pi\) | |||||||
\(984\) | 1.49800e10 | − | 8.64870e9i | 0.501220 | − | 0.289380i | ||||
\(985\) | 5.67155e10i | 1.89093i | ||||||||
\(986\) | 2.67466e10 | + | 1.54422e10i | 0.888587 | + | 0.513026i | ||||
\(987\) | −2.14048e9 | − | 3.70742e9i | −0.0708601 | − | 0.122733i | ||||
\(988\) | −8.19534e9 | −0.270344 | ||||||||
\(989\) | 2.49387e10 | 0.819759 | ||||||||
\(990\) | −5.64297e9 | − | 9.77390e9i | −0.184835 | − | 0.320144i | ||||
\(991\) | 1.97176e10i | 0.643570i | 0.946813 | + | 0.321785i | \(0.104283\pi\) | ||||
−0.946813 | + | 0.321785i | \(0.895717\pi\) | |||||||
\(992\) | −1.54212e10 | + | 2.67103e10i | −0.501564 | + | 0.868735i | ||||
\(993\) | 6.56626e10i | 2.12812i | ||||||||
\(994\) | 6.63650e8 | + | 3.83159e8i | 0.0214332 | + | 0.0123745i | ||||
\(995\) | 2.25693e10 | − | 3.90911e10i | 0.726335 | − | 1.25805i | ||||
\(996\) | −1.62716e10 | + | 2.81833e10i | −0.521823 | + | 0.903825i | ||||
\(997\) | −7.06714e9 | + | 4.08022e9i | −0.225845 | + | 0.130392i | −0.608654 | − | 0.793436i | \(-0.708290\pi\) |
0.382809 | + | 0.923828i | \(0.374957\pi\) | |||||||
\(998\) | 9.74310e9 | 0.310270 | ||||||||
\(999\) | 4.62801e9 | − | 9.53736e9i | 0.146864 | − | 0.302656i |
(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 | 37.8.e.a.11.3 | ✓ | 40 | |
37.27 | even | 6 | inner | 37.8.e.a.27.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.8.e.a.11.3 | ✓ | 40 | 1.1 | even | 1 | trivial | |
37.8.e.a.27.3 | yes | 40 | 37.27 | even | 6 | inner |