Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,12,Mod(28,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.28");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.c (of order \(3\), degree \(2\), not 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: | \(62.2357976253\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 55.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.55 |
Dual form | 81.12.c.e.28.1 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 39.0000 | − | 67.5500i | 0.861786 | − | 1.49266i | −0.00841668 | − | 0.999965i | \(-0.502679\pi\) |
0.870203 | − | 0.492693i | \(-0.163988\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2018.00 | − | 3495.28i | −0.985352 | − | 1.70668i | ||||
\(5\) | −2685.00 | − | 4650.56i | −0.384246 | − | 0.665533i | 0.607418 | − | 0.794382i | \(-0.292205\pi\) |
−0.991664 | + | 0.128849i | \(0.958872\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13880.0 | − | 24040.9i | 0.312141 | − | 0.540643i | −0.666685 | − | 0.745340i | \(-0.732287\pi\) |
0.978826 | + | 0.204696i | \(0.0656207\pi\) | |||||||
\(8\) | −155064. | −1.67308 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −418860. | −1.32455 | ||||||||
\(11\) | 318918. | − | 552382.i | 0.597062 | − | 1.03414i | −0.396191 | − | 0.918168i | \(-0.629668\pi\) |
0.993252 | − | 0.115973i | \(-0.0369986\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −383107. | − | 663561.i | −0.286175 | − | 0.495670i | 0.686718 | − | 0.726923i | \(-0.259051\pi\) |
−0.972893 | + | 0.231254i | \(0.925717\pi\) | |||||||
\(14\) | −1.08264e6 | − | 1.87519e6i | −0.537997 | − | 0.931838i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.91463e6 | + | 3.31624e6i | −0.456484 | + | 0.790653i | ||||
\(17\) | −3.08435e6 | −0.526860 | −0.263430 | − | 0.964679i | \(-0.584854\pi\) | ||||
−0.263430 | + | 0.964679i | \(0.584854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.95114e7 | −1.80777 | −0.903886 | − | 0.427773i | \(-0.859298\pi\) | ||||
−0.903886 | + | 0.427773i | \(0.859298\pi\) | |||||||
\(20\) | −1.08367e7 | + | 1.87696e7i | −0.757235 | + | 1.31157i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.48756e7 | − | 4.30858e7i | −1.02908 | − | 1.78242i | ||||
\(23\) | 7.65618e6 | + | 1.32609e7i | 0.248033 | + | 0.429605i | 0.962980 | − | 0.269573i | \(-0.0868826\pi\) |
−0.714947 | + | 0.699178i | \(0.753549\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.99561e6 | − | 1.73129e7i | 0.204710 | − | 0.354568i | ||||
\(26\) | −5.97647e7 | −0.986487 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.12039e8 | −1.23027 | ||||||||
\(29\) | 5.37563e6 | − | 9.31087e6i | 0.0486677 | − | 0.0842949i | −0.840665 | − | 0.541555i | \(-0.817836\pi\) |
0.889333 | + | 0.457260i | \(0.151169\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.54687e7 | + | 4.41131e7i | 0.159778 | + | 0.276744i | 0.934789 | − | 0.355205i | \(-0.115589\pi\) |
−0.775010 | + | 0.631948i | \(0.782255\pi\) | |||||||
\(32\) | −9.44424e6 | − | 1.63579e7i | −0.0497556 | − | 0.0861793i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.20290e8 | + | 2.08348e8i | −0.454041 | + | 0.786422i | ||||
\(35\) | −1.49071e8 | −0.479755 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.64741e8 | 1.57595 | 0.787976 | − | 0.615706i | \(-0.211129\pi\) | ||||
0.787976 | + | 0.615706i | \(0.211129\pi\) | |||||||
\(38\) | −7.60945e8 | + | 1.31799e9i | −1.55791 | + | 2.69839i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.16347e8 | + | 7.21134e8i | 0.642873 | + | 1.11349i | ||||
\(41\) | 4.49417e8 | + | 7.78413e8i | 0.605812 | + | 1.04930i | 0.991923 | + | 0.126845i | \(0.0404851\pi\) |
−0.386110 | + | 0.922453i | \(0.626182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.78974e8 | − | 8.29607e8i | 0.496861 | − | 0.860589i | −0.503132 | − | 0.864209i | \(-0.667819\pi\) |
0.999993 | + | 0.00362061i | \(0.00115248\pi\) | |||||||
\(44\) | −2.57431e9 | −2.35326 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.19436e9 | 0.855005 | ||||||||
\(47\) | −7.77871e8 | + | 1.34731e9i | −0.494731 | + | 0.856899i | −0.999982 | − | 0.00607340i | \(-0.998067\pi\) |
0.505250 | + | 0.862973i | \(0.331400\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.03355e8 | + | 1.04504e9i | 0.305137 | + | 0.528512i | ||||
\(50\) | −7.79658e8 | − | 1.35041e9i | −0.352833 | − | 0.611124i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.54622e9 | + | 2.67813e9i | −0.563966 | + | 0.976818i | ||||
\(53\) | −3.79242e9 | −1.24566 | −0.622829 | − | 0.782358i | \(-0.714017\pi\) | ||||
−0.622829 | + | 0.782358i | \(0.714017\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.42518e9 | −0.917674 | ||||||||
\(56\) | −2.15229e9 | + | 3.72787e9i | −0.522235 | + | 0.904538i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.19299e8 | − | 7.26248e8i | −0.0838823 | − | 0.145288i | ||||
\(59\) | 2.77653e8 | + | 4.80910e8i | 0.0505612 | + | 0.0875745i | 0.890198 | − | 0.455573i | \(-0.150566\pi\) |
−0.839637 | + | 0.543148i | \(0.817232\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.47521e9 | + | 4.28719e9i | −0.375230 | + | 0.649918i | −0.990361 | − | 0.138507i | \(-0.955770\pi\) |
0.615131 | + | 0.788425i | \(0.289103\pi\) | |||||||
\(62\) | 3.97312e9 | 0.550779 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.31563e9 | −1.08448 | ||||||||
\(65\) | −2.05728e9 | + | 3.56332e9i | −0.219923 | + | 0.380918i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.64620e9 | − | 4.58335e9i | −0.239448 | − | 0.414736i | 0.721108 | − | 0.692823i | \(-0.243633\pi\) |
−0.960556 | + | 0.278087i | \(0.910300\pi\) | |||||||
\(68\) | 6.22423e9 | + | 1.07807e10i | 0.519142 | + | 0.899181i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.81378e9 | + | 1.00698e10i | −0.413446 | + | 0.716110i | ||||
\(71\) | 1.48311e10 | 0.975556 | 0.487778 | − | 0.872968i | \(-0.337808\pi\) | ||||
0.487778 | + | 0.872968i | \(0.337808\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.39710e10 | 0.788773 | 0.394386 | − | 0.918945i | \(-0.370957\pi\) | ||||
0.394386 | + | 0.918945i | \(0.370957\pi\) | |||||||
\(74\) | 2.59249e10 | − | 4.49032e10i | 1.35813 | − | 2.35236i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.93740e10 | + | 6.81978e10i | 1.78129 | + | 3.08529i | ||||
\(77\) | −8.85316e9 | − | 1.53341e10i | −0.372734 | − | 0.645595i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.86027e9 | + | 3.22208e9i | −0.0680185 | + | 0.117812i | −0.898029 | − | 0.439936i | \(-0.855001\pi\) |
0.830010 | + | 0.557748i | \(0.188334\pi\) | |||||||
\(80\) | 2.05631e10 | 0.701608 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.01090e10 | 2.08832 | ||||||||
\(83\) | 4.38423e9 | − | 7.59370e9i | 0.122170 | − | 0.211604i | −0.798453 | − | 0.602057i | \(-0.794348\pi\) |
0.920623 | + | 0.390453i | \(0.127681\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.28149e9 | + | 1.43440e10i | 0.202444 | + | 0.350643i | ||||
\(86\) | −3.73599e10 | − | 6.47093e10i | −0.856376 | − | 1.48329i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.94527e10 | + | 8.56546e10i | −0.998931 | + | 1.73020i | ||||
\(89\) | 2.54728e10 | 0.483539 | 0.241769 | − | 0.970334i | \(-0.422272\pi\) | ||||
0.241769 | + | 0.970334i | \(0.422272\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.12701e10 | −0.357307 | ||||||||
\(92\) | 3.09003e10 | − | 5.35210e10i | 0.488799 | − | 0.846625i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.06739e10 | + | 1.05090e11i | 0.852705 | + | 1.47693i | ||||
\(95\) | 5.23881e10 | + | 9.07389e10i | 0.694629 | + | 1.20313i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.95462e10 | − | 3.38551e10i | 0.231110 | − | 0.400294i | −0.727025 | − | 0.686611i | \(-0.759098\pi\) |
0.958135 | + | 0.286317i | \(0.0924309\pi\) | |||||||
\(98\) | 9.41233e10 | 1.05185 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.06846e10 | −0.806846 | ||||||||
\(101\) | 4.65539e9 | − | 8.06337e9i | 0.0440746 | − | 0.0763395i | −0.843147 | − | 0.537684i | \(-0.819299\pi\) |
0.887221 | + | 0.461344i | \(0.152633\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.42875e10 | − | 4.20672e10i | −0.206433 | − | 0.357552i | 0.744156 | − | 0.668006i | \(-0.232852\pi\) |
−0.950588 | + | 0.310454i | \(0.899519\pi\) | |||||||
\(104\) | 5.94061e10 | + | 1.02894e11i | 0.478793 | + | 0.829294i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.47904e11 | + | 2.56178e11i | −1.07349 | + | 1.85934i | ||||
\(107\) | −2.25596e11 | −1.55496 | −0.777482 | − | 0.628906i | \(-0.783503\pi\) | ||||
−0.777482 | + | 0.628906i | \(0.783503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.94512e10 | −0.432348 | −0.216174 | − | 0.976355i | \(-0.569358\pi\) | ||||
−0.216174 | + | 0.976355i | \(0.569358\pi\) | |||||||
\(110\) | −1.33582e11 | + | 2.31371e11i | −0.790839 | + | 1.36977i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.31502e10 | + | 9.20588e10i | 0.284974 | + | 0.493590i | ||||
\(113\) | −1.79832e11 | − | 3.11479e11i | −0.918198 | − | 1.59037i | −0.802151 | − | 0.597121i | \(-0.796311\pi\) |
−0.116047 | − | 0.993244i | \(-0.537022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.11137e10 | − | 7.12110e10i | 0.190611 | − | 0.330148i | ||||
\(116\) | −4.33921e10 | −0.191819 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.33139e10 | 0.174292 | ||||||||
\(119\) | −4.28108e10 | + | 7.41505e10i | −0.164454 | + | 0.284843i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.07615e10 | − | 1.05242e11i | −0.212966 | − | 0.368867i | ||||
\(122\) | 1.93066e11 | + | 3.34401e11i | 0.646737 | + | 1.12018i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.02792e11 | − | 1.78040e11i | 0.314875 | − | 0.545380i | ||||
\(125\) | −3.69560e11 | −1.08313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.50273e11 | 0.672192 | 0.336096 | − | 0.941828i | \(-0.390893\pi\) | ||||
0.336096 | + | 0.941828i | \(0.390893\pi\) | |||||||
\(128\) | −3.43968e11 | + | 5.95770e11i | −0.884837 | + | 1.53258i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.60468e11 | + | 2.77939e11i | 0.379054 | + | 0.656540i | ||||
\(131\) | −4.89459e10 | − | 8.47768e10i | −0.110847 | − | 0.191993i | 0.805265 | − | 0.592915i | \(-0.202023\pi\) |
−0.916112 | + | 0.400922i | \(0.868690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.70818e11 | + | 4.69071e11i | −0.564279 | + | 0.977360i | ||||
\(134\) | −4.12807e11 | −0.825412 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.78272e11 | 0.881477 | ||||||||
\(137\) | −7.75074e10 | + | 1.34247e11i | −0.137208 | + | 0.237651i | −0.926439 | − | 0.376445i | \(-0.877146\pi\) |
0.789231 | + | 0.614097i | \(0.210480\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.63133e11 | + | 9.75374e11i | 0.920512 | + | 1.59437i | 0.798625 | + | 0.601829i | \(0.205561\pi\) |
0.121887 | + | 0.992544i | \(0.461105\pi\) | |||||||
\(140\) | 3.00826e11 | + | 5.21045e11i | 0.472727 | + | 0.818788i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.78412e11 | − | 1.00184e12i | 0.840721 | − | 1.45617i | ||||
\(143\) | −4.88719e11 | −0.683457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.77343e10 | −0.0748014 | ||||||||
\(146\) | 5.44869e11 | − | 9.43741e11i | 0.679754 | − | 1.17737i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.34145e12 | − | 2.32345e12i | −1.55287 | − | 2.68964i | ||||
\(149\) | −6.92290e11 | − | 1.19908e12i | −0.772261 | − | 1.33759i | −0.936321 | − | 0.351144i | \(-0.885793\pi\) |
0.164061 | − | 0.986450i | \(-0.447541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.49301e11 | − | 6.05007e11i | 0.362098 | − | 0.627172i | −0.626208 | − | 0.779656i | \(-0.715394\pi\) |
0.988306 | + | 0.152484i | \(0.0487272\pi\) | |||||||
\(152\) | 3.02552e12 | 3.02454 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.38109e12 | −1.28487 | ||||||||
\(155\) | 1.36767e11 | − | 2.36887e11i | 0.122788 | − | 0.212675i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.06563e12 | − | 1.84573e12i | −0.891580 | − | 1.54426i | −0.837981 | − | 0.545699i | \(-0.816264\pi\) |
−0.0535991 | − | 0.998563i | \(-0.517069\pi\) | |||||||
\(158\) | 1.45101e11 | + | 2.51323e11i | 0.117235 | + | 0.203057i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.07156e10 | + | 8.78419e10i | −0.0382368 | + | 0.0662281i | ||||
\(161\) | 4.25071e11 | 0.309684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.63564e11 | −0.111342 | −0.0556708 | − | 0.998449i | \(-0.517730\pi\) | ||||
−0.0556708 | + | 0.998449i | \(0.517730\pi\) | |||||||
\(164\) | 1.81385e12 | − | 3.14167e12i | 1.19388 | − | 2.06785i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.41970e11 | − | 5.92309e11i | −0.210568 | − | 0.364715i | ||||
\(167\) | −4.40471e9 | − | 7.62919e9i | −0.00262408 | − | 0.00454504i | 0.864710 | − | 0.502271i | \(-0.167502\pi\) |
−0.867334 | + | 0.497726i | \(0.834169\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.02538e11 | − | 1.04363e12i | 0.336208 | − | 0.582329i | ||||
\(170\) | 1.29191e12 | 0.697853 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.86627e12 | −1.95833 | ||||||||
\(173\) | −3.65426e11 | + | 6.32936e11i | −0.179286 | + | 0.310532i | −0.941636 | − | 0.336633i | \(-0.890712\pi\) |
0.762350 | + | 0.647164i | \(0.224045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.77478e11 | − | 4.80606e11i | −0.127797 | − | 0.221350i | ||||
\(176\) | 1.22122e12 | + | 2.11522e12i | 0.545098 | + | 0.944138i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.93438e11 | − | 1.72069e12i | 0.416707 | − | 0.721758i | ||||
\(179\) | −3.92371e12 | −1.59590 | −0.797950 | − | 0.602724i | \(-0.794082\pi\) | ||||
−0.797950 | + | 0.602724i | \(0.794082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.27931e12 | 0.872110 | 0.436055 | − | 0.899920i | \(-0.356375\pi\) | ||||
0.436055 | + | 0.899920i | \(0.356375\pi\) | |||||||
\(182\) | −8.29534e11 | + | 1.43679e12i | −0.307923 | + | 0.533338i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.18720e12 | − | 2.05629e12i | −0.414978 | − | 0.718763i | ||||
\(185\) | −1.78483e12 | − | 3.09141e12i | −0.605553 | − | 1.04885i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.83656e11 | + | 1.70374e12i | −0.314568 | + | 0.544848i | ||||
\(188\) | 6.27897e12 | 1.94994 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.17255e12 | 2.39449 | ||||||||
\(191\) | 1.69354e12 | − | 2.93330e12i | 0.482073 | − | 0.834975i | −0.517715 | − | 0.855553i | \(-0.673217\pi\) |
0.999788 | + | 0.0205777i | \(0.00655056\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.46460e12 | + | 4.26882e12i | 0.662494 | + | 1.14747i | 0.979958 | + | 0.199203i | \(0.0638353\pi\) |
−0.317464 | + | 0.948270i | \(0.602831\pi\) | |||||||
\(194\) | −1.52461e12 | − | 2.64070e12i | −0.398335 | − | 0.689936i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.43514e12 | − | 4.21778e12i | 0.601333 | − | 1.04154i | ||||
\(197\) | −6.35785e12 | −1.52667 | −0.763337 | − | 0.646001i | \(-0.776440\pi\) | ||||
−0.763337 | + | 0.646001i | \(0.776440\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.78554e12 | −0.859875 | −0.429938 | − | 0.902859i | \(-0.641464\pi\) | ||||
−0.429938 | + | 0.902859i | \(0.641464\pi\) | |||||||
\(200\) | −1.54996e12 | + | 2.68461e12i | −0.342496 | + | 0.593220i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.63120e11 | − | 6.28943e11i | −0.0759658 | − | 0.131577i | ||||
\(203\) | −1.49228e11 | − | 2.58470e11i | −0.0303823 | − | 0.0526237i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.41337e12 | − | 4.18008e12i | 0.465562 | − | 0.806377i | ||||
\(206\) | −3.78885e12 | −0.711604 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.93404e12 | 0.522537 | ||||||||
\(209\) | −6.22254e12 | + | 1.07778e13i | −1.07935 | + | 1.86949i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.97469e10 | − | 1.55446e11i | −0.0147729 | − | 0.0255874i | 0.858544 | − | 0.512739i | \(-0.171369\pi\) |
−0.873317 | + | 0.487152i | \(0.838036\pi\) | |||||||
\(212\) | 7.65310e12 | + | 1.32556e13i | 1.22741 | + | 2.12594i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.79823e12 | + | 1.52390e13i | −1.34005 | + | 2.32103i | ||||
\(215\) | −5.14418e12 | −0.763668 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.41402e12 | 0.199493 | ||||||||
\(218\) | −2.70860e12 | + | 4.69143e12i | −0.372592 | + | 0.645348i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.91201e12 | + | 1.19720e13i | 0.904232 | + | 1.56618i | ||||
\(221\) | 1.18164e12 | + | 2.04666e12i | 0.150774 | + | 0.261148i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.11284e12 | + | 1.92750e12i | −0.135132 | + | 0.234055i | −0.925648 | − | 0.378386i | \(-0.876479\pi\) |
0.790516 | + | 0.612441i | \(0.209812\pi\) | |||||||
\(224\) | −5.24344e11 | −0.0621230 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.80538e13 | −3.16516 | ||||||||
\(227\) | −2.07924e11 | + | 3.60135e11i | −0.0228961 | + | 0.0396573i | −0.877246 | − | 0.480040i | \(-0.840622\pi\) |
0.854350 | + | 0.519698i | \(0.173955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.06239e12 | − | 1.56965e13i | −0.950928 | − | 1.64705i | −0.743424 | − | 0.668821i | \(-0.766799\pi\) |
−0.207504 | − | 0.978234i | \(-0.566534\pi\) | |||||||
\(230\) | −3.20687e12 | − | 5.55446e12i | −0.328532 | − | 0.569034i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.33567e11 | + | 1.44378e12i | −0.0814248 | + | 0.141032i | ||||
\(233\) | 1.87641e10 | 0.00179007 | 0.000895033 | − | 1.00000i | \(-0.499715\pi\) | ||||
0.000895033 | 1.00000i | \(0.499715\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.35433e12 | 0.760394 | ||||||||
\(236\) | 1.12061e12 | − | 1.94095e12i | 0.0996410 | − | 0.172583i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.33925e12 | + | 5.78374e12i | 0.283449 | + | 0.490948i | ||||
\(239\) | −8.81262e12 | − | 1.52639e13i | −0.730999 | − | 1.26613i | −0.956457 | − | 0.291874i | \(-0.905721\pi\) |
0.225458 | − | 0.974253i | \(-0.427612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.45058e11 | − | 7.70864e11i | 0.0352633 | − | 0.0610779i | −0.847855 | − | 0.530228i | \(-0.822106\pi\) |
0.883118 | + | 0.469150i | \(0.155440\pi\) | |||||||
\(242\) | −9.47880e12 | −0.734123 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.99799e13 | 1.47894 | ||||||||
\(245\) | 3.24001e12 | − | 5.61187e12i | 0.234495 | − | 0.406157i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.47496e12 | + | 1.29470e13i | 0.517339 | + | 0.896058i | ||||
\(248\) | −3.94928e12 | − | 6.84035e12i | −0.267321 | − | 0.463014i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.44128e13 | + | 2.49638e13i | −0.933425 | + | 1.61674i | ||||
\(251\) | 2.42280e13 | 1.53502 | 0.767508 | − | 0.641040i | \(-0.221497\pi\) | ||||
0.767508 | + | 0.641040i | \(0.221497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.76677e12 | 0.592364 | ||||||||
\(254\) | 9.76065e12 | − | 1.69059e13i | 0.579286 | − | 1.00335i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.72903e13 | + | 2.99477e13i | 0.982839 | + | 1.70233i | ||||
\(257\) | 3.90246e12 | + | 6.75926e12i | 0.217123 | + | 0.376068i | 0.953927 | − | 0.300038i | \(-0.0969993\pi\) |
−0.736804 | + | 0.676106i | \(0.763666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.22660e12 | − | 1.59809e13i | 0.491918 | − | 0.852028i | ||||
\(260\) | 1.66064e13 | 0.866806 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.63556e12 | −0.382106 | ||||||||
\(263\) | 8.29779e12 | − | 1.43722e13i | 0.406636 | − | 0.704314i | −0.587874 | − | 0.808952i | \(-0.700035\pi\) |
0.994510 | + | 0.104638i | \(0.0333684\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.01826e13 | + | 1.76368e13i | 0.478639 | + | 0.829027i | ||||
\(266\) | 2.11238e13 | + | 3.65875e13i | 0.972576 | + | 1.68455i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.06801e13 | + | 1.84984e13i | −0.471881 | + | 0.817322i | ||||
\(269\) | −2.85236e13 | −1.23471 | −0.617357 | − | 0.786683i | \(-0.711797\pi\) | ||||
−0.617357 | + | 0.786683i | \(0.711797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.33800e13 | 0.971658 | 0.485829 | − | 0.874054i | \(-0.338518\pi\) | ||||
0.485829 | + | 0.874054i | \(0.338518\pi\) | |||||||
\(272\) | 5.90540e12 | − | 1.02285e13i | 0.240503 | − | 0.416563i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.04557e12 | + | 1.04712e13i | 0.236488 | + | 0.409610i | ||||
\(275\) | −6.37556e12 | − | 1.10428e13i | −0.244449 | − | 0.423398i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.51821e13 | − | 2.62961e13i | 0.559361 | − | 0.968841i | −0.438189 | − | 0.898883i | \(-0.644380\pi\) |
0.997550 | − | 0.0699584i | \(-0.0222867\pi\) | |||||||
\(278\) | 8.78487e13 | 3.17314 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.31156e13 | 0.802667 | ||||||||
\(281\) | 7.98743e12 | − | 1.38346e13i | 0.271971 | − | 0.471067i | −0.697396 | − | 0.716686i | \(-0.745658\pi\) |
0.969366 | + | 0.245619i | \(0.0789912\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.43523e13 | − | 2.48588e13i | −0.469997 | − | 0.814058i | 0.529415 | − | 0.848363i | \(-0.322412\pi\) |
−0.999411 | + | 0.0343051i | \(0.989078\pi\) | |||||||
\(284\) | −2.99291e13 | − | 5.18388e13i | −0.961265 | − | 1.66496i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.90600e13 | + | 3.30130e13i | −0.588994 | + | 1.02017i | ||||
\(287\) | 2.49516e13 | 0.756394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.47587e13 | −0.722419 | ||||||||
\(290\) | −2.25164e12 | + | 3.89995e12i | −0.0644628 | + | 0.111653i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.81935e13 | − | 4.88326e13i | −0.777219 | − | 1.34618i | ||||
\(293\) | 2.40877e13 | + | 4.17211e13i | 0.651663 | + | 1.12871i | 0.982719 | + | 0.185103i | \(0.0592619\pi\) |
−0.331056 | + | 0.943611i | \(0.607405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.49100e12 | − | 2.58249e12i | 0.0388558 | − | 0.0673003i | ||||
\(296\) | −1.03077e14 | −2.63669 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.07997e14 | −2.66209 | ||||||||
\(299\) | 5.86627e12 | − | 1.01607e13i | 0.141962 | − | 0.245885i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.32963e13 | − | 2.30299e13i | −0.310181 | − | 0.537249i | ||||
\(302\) | −2.72455e13 | − | 4.71905e13i | −0.624102 | − | 1.08098i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.73572e13 | − | 6.47045e13i | 0.825219 | − | 1.42932i | ||||
\(305\) | 2.65838e13 | 0.576723 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.57350e13 | 0.538597 | 0.269298 | − | 0.963057i | \(-0.413208\pi\) | ||||
0.269298 | + | 0.963057i | \(0.413208\pi\) | |||||||
\(308\) | −3.57314e13 | + | 6.18885e13i | −0.734549 | + | 1.27228i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.06678e13 | − | 1.84772e13i | −0.211634 | − | 0.366562i | ||||
\(311\) | 1.73021e13 | + | 2.99682e13i | 0.337223 | + | 0.584088i | 0.983909 | − | 0.178668i | \(-0.0571789\pi\) |
−0.646686 | + | 0.762756i | \(0.723846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.30329e12 | + | 1.09176e13i | −0.118597 | + | 0.205416i | −0.919212 | − | 0.393763i | \(-0.871173\pi\) |
0.800615 | + | 0.599179i | \(0.204506\pi\) | |||||||
\(314\) | −1.66239e14 | −3.07341 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.50161e13 | 0.268089 | ||||||||
\(317\) | −4.09121e13 | + | 7.08619e13i | −0.717838 | + | 1.24333i | 0.244017 | + | 0.969771i | \(0.421535\pi\) |
−0.961855 | + | 0.273561i | \(0.911799\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.42877e12 | − | 5.93881e12i | −0.0581152 | − | 0.100658i | ||||
\(320\) | 2.50125e13 | + | 4.33229e13i | 0.416708 | + | 0.721759i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.65778e13 | − | 2.87135e13i | 0.266882 | − | 0.462253i | ||||
\(323\) | 6.01801e13 | 0.952443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.53176e13 | −0.234332 | ||||||||
\(326\) | −6.37901e12 | + | 1.10488e13i | −0.0959526 | + | 0.166195i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.96884e13 | − | 1.20704e14i | −1.01357 | − | 1.75556i | ||||
\(329\) | 2.15937e13 | + | 3.74014e13i | 0.308851 | + | 0.534946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.70057e13 | − | 2.94548e13i | 0.235256 | − | 0.407476i | −0.724091 | − | 0.689705i | \(-0.757740\pi\) |
0.959347 | + | 0.282229i | \(0.0910737\pi\) | |||||||
\(332\) | −3.53895e13 | −0.481520 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.87135e11 | −0.00904558 | ||||||||
\(335\) | −1.42101e13 | + | 2.46126e13i | −0.184014 | + | 0.318721i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.99720e13 | + | 5.19130e13i | 0.375622 | + | 0.650596i | 0.990420 | − | 0.138088i | \(-0.0440958\pi\) |
−0.614798 | + | 0.788685i | \(0.710762\pi\) | |||||||
\(338\) | −4.69980e13 | − | 8.14029e13i | −0.579479 | − | 1.00369i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.34241e13 | − | 5.78922e13i | 0.398957 | − | 0.691013i | ||||
\(341\) | 3.24897e13 | 0.381590 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.83888e13 | 1.00526 | ||||||||
\(344\) | −7.42716e13 | + | 1.28642e14i | −0.831287 | + | 1.43983i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.85032e13 | + | 4.93690e13i | 0.309012 | + | 0.535224i | ||||
\(347\) | 4.89343e13 | + | 8.47566e13i | 0.522157 | + | 0.904402i | 0.999668 | + | 0.0257762i | \(0.00820572\pi\) |
−0.477511 | + | 0.878626i | \(0.658461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.13948e13 | − | 1.23659e14i | 0.738120 | − | 1.27846i | −0.215221 | − | 0.976565i | \(-0.569047\pi\) |
0.953341 | − | 0.301895i | \(-0.0976193\pi\) | |||||||
\(350\) | −4.32866e13 | −0.440534 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.20478e13 | −0.118829 | ||||||||
\(353\) | 7.21230e13 | − | 1.24921e14i | 0.700346 | − | 1.21303i | −0.267999 | − | 0.963419i | \(-0.586362\pi\) |
0.968345 | − | 0.249616i | \(-0.0803043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.98215e13 | − | 6.89728e13i | −0.374853 | − | 0.649265i | ||||
\(356\) | −5.14040e13 | − | 8.90344e13i | −0.476455 | − | 0.825245i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.53025e14 | + | 2.65047e14i | −1.37533 | + | 2.38213i | ||||
\(359\) | 1.24349e14 | 1.10059 | 0.550293 | − | 0.834972i | \(-0.314516\pi\) | ||||
0.550293 | + | 0.834972i | \(0.314516\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.64205e14 | 2.26804 | ||||||||
\(362\) | 8.88930e13 | − | 1.53967e14i | 0.751572 | − | 1.30176i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.29231e13 | + | 7.43449e13i | 0.352073 | + | 0.609809i | ||||
\(365\) | −3.75121e13 | − | 6.49729e13i | −0.303083 | − | 0.524955i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00548e13 | − | 1.38659e14i | 0.627659 | − | 1.08714i | −0.360361 | − | 0.932813i | \(-0.617347\pi\) |
0.988020 | − | 0.154325i | \(-0.0493202\pi\) | |||||||
\(368\) | −5.86351e13 | −0.452892 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.78433e14 | −2.08743 | ||||||||
\(371\) | −5.26387e13 | + | 9.11730e13i | −0.388820 | + | 0.673457i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.73629e13 | + | 3.00734e13i | 0.124516 | + | 0.215667i | 0.921544 | − | 0.388275i | \(-0.126929\pi\) |
−0.797028 | + | 0.603943i | \(0.793596\pi\) | |||||||
\(374\) | 7.67252e13 | + | 1.32892e14i | 0.542181 | + | 0.939084i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.20620e14 | − | 2.08920e14i | 0.827723 | − | 1.43366i | ||||
\(377\) | −8.23777e12 | −0.0557099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.46500e14 | −0.962327 | −0.481163 | − | 0.876631i | \(-0.659786\pi\) | ||||
−0.481163 | + | 0.876631i | \(0.659786\pi\) | |||||||
\(380\) | 2.11438e14 | − | 3.66222e14i | 1.36891 | − | 2.37102i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.32096e14 | − | 2.28798e14i | −0.830888 | − | 1.43914i | ||||
\(383\) | 3.21709e13 | + | 5.57217e13i | 0.199467 | + | 0.345486i | 0.948356 | − | 0.317209i | \(-0.102746\pi\) |
−0.748889 | + | 0.662695i | \(0.769412\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.75415e13 | + | 8.23443e13i | −0.286443 | + | 0.496134i | ||||
\(386\) | 3.84478e14 | 2.28371 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.57777e14 | −0.910899 | ||||||||
\(389\) | −1.99450e13 | + | 3.45458e13i | −0.113530 | + | 0.196640i | −0.917191 | − | 0.398447i | \(-0.869549\pi\) |
0.803661 | + | 0.595087i | \(0.202883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.36144e13 | − | 4.09013e13i | −0.130679 | − | 0.226342i | ||||
\(392\) | −9.35586e13 | − | 1.62048e14i | −0.510517 | − | 0.884241i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.47956e14 | + | 4.29473e14i | −1.31567 | + | 2.27880i | ||||
\(395\) | 1.99793e13 | 0.104543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.06552e14 | 0.542268 | 0.271134 | − | 0.962542i | \(-0.412601\pi\) | ||||
0.271134 | + | 0.962542i | \(0.412601\pi\) | |||||||
\(398\) | −1.47636e14 | + | 2.55713e14i | −0.741029 | + | 1.28350i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.82758e13 | + | 6.62957e13i | 0.186894 | + | 0.323709i | ||||
\(401\) | 1.70722e13 | + | 2.95700e13i | 0.0822236 | + | 0.142415i | 0.904205 | − | 0.427099i | \(-0.140464\pi\) |
−0.821981 | + | 0.569515i | \(0.807131\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.95145e13 | − | 3.38001e13i | 0.0914490 | − | 0.158394i | ||||
\(404\) | −3.75783e13 | −0.173716 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.32795e13 | −0.104732 | ||||||||
\(407\) | 2.11998e14 | − | 3.67191e14i | 0.940940 | − | 1.62976i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.66675e13 | − | 4.61894e13i | −0.115213 | − | 0.199556i | 0.802652 | − | 0.596448i | \(-0.203422\pi\) |
−0.917865 | + | 0.396893i | \(0.870089\pi\) | |||||||
\(410\) | −1.88243e14 | − | 3.26046e14i | −0.802430 | − | 1.38985i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.80245e13 | + | 1.69783e14i | −0.406818 | + | 0.704629i | ||||
\(413\) | 1.54153e13 | 0.0631288 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.70866e13 | −0.187773 | ||||||||
\(416\) | −7.23631e12 | + | 1.25337e13i | −0.0284776 | + | 0.0493247i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.85358e14 | + | 8.40665e14i | 1.86034 | + | 3.22221i | ||||
\(419\) | −5.06438e13 | − | 8.77177e13i | −0.191580 | − | 0.331826i | 0.754194 | − | 0.656651i | \(-0.228028\pi\) |
−0.945774 | + | 0.324826i | \(0.894694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.89642e13 | − | 1.36770e14i | 0.290991 | − | 0.504010i | −0.683054 | − | 0.730368i | \(-0.739349\pi\) |
0.974044 | + | 0.226358i | \(0.0726818\pi\) | |||||||
\(422\) | −1.40005e13 | −0.0509244 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.88067e14 | 2.08408 | ||||||||
\(425\) | −3.08300e13 | + | 5.33991e13i | −0.107854 | + | 0.186808i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.87118e13 | + | 1.19012e14i | 0.234249 | + | 0.405732i | ||||
\(428\) | 4.55252e14 | + | 7.88520e14i | 1.53219 | + | 2.65382i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.00623e14 | + | 3.47489e14i | −0.658118 | + | 1.13989i | ||||
\(431\) | −5.13171e14 | −1.66202 | −0.831012 | − | 0.556254i | \(-0.812238\pi\) | ||||
−0.831012 | + | 0.556254i | \(0.812238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.49248e13 | −0.236560 | −0.118280 | − | 0.992980i | \(-0.537738\pi\) | ||||
−0.118280 | + | 0.992980i | \(0.537738\pi\) | |||||||
\(434\) | 5.51469e13 | − | 9.55172e13i | 0.171920 | − | 0.297775i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.40152e14 | + | 2.42751e14i | 0.426015 | + | 0.737880i | ||||
\(437\) | −1.49383e14 | − | 2.58739e14i | −0.448387 | − | 0.776629i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.84168e14 | − | 3.18988e14i | 0.539086 | − | 0.933725i | −0.459867 | − | 0.887988i | \(-0.652103\pi\) |
0.998954 | − | 0.0457373i | \(-0.0145637\pi\) | |||||||
\(440\) | 5.31122e14 | 1.53534 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.84335e14 | 0.519740 | ||||||||
\(443\) | −5.56239e13 | + | 9.63434e13i | −0.154896 | + | 0.268288i | −0.933021 | − | 0.359821i | \(-0.882838\pi\) |
0.778125 | + | 0.628110i | \(0.216171\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.83944e13 | − | 1.18463e14i | −0.185798 | − | 0.321811i | ||||
\(446\) | 8.68017e13 | + | 1.50345e14i | 0.232909 | + | 0.403410i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.29301e14 | + | 2.23956e14i | −0.338511 | + | 0.586318i | ||||
\(449\) | 8.83314e13 | 0.228434 | 0.114217 | − | 0.993456i | \(-0.463564\pi\) | ||||
0.114217 | + | 0.993456i | \(0.463564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.73308e14 | 1.44683 | ||||||||
\(452\) | −7.25803e14 | + | 1.25713e15i | −1.80950 | + | 3.13414i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.62181e13 | + | 2.80905e13i | 0.0394632 | + | 0.0683522i | ||||
\(455\) | 5.71102e13 | + | 9.89178e13i | 0.137294 | + | 0.237800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.71047e12 | − | 8.15877e12i | 0.0110541 | − | 0.0191463i | −0.860445 | − | 0.509543i | \(-0.829815\pi\) |
0.871500 | + | 0.490396i | \(0.163148\pi\) | |||||||
\(458\) | −1.41373e15 | −3.27799 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.31870e14 | −0.751276 | ||||||||
\(461\) | −3.48567e14 | + | 6.03735e14i | −0.779706 | + | 1.35049i | 0.152405 | + | 0.988318i | \(0.451298\pi\) |
−0.932111 | + | 0.362172i | \(0.882035\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.39706e13 | + | 1.62762e14i | 0.205256 | + | 0.355515i | 0.950214 | − | 0.311597i | \(-0.100864\pi\) |
−0.744958 | + | 0.667111i | \(0.767531\pi\) | |||||||
\(464\) | 2.05847e13 | + | 3.56538e13i | 0.0444320 | + | 0.0769585i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.31798e11 | − | 1.26751e12i | 0.00154266 | − | 0.00267196i | ||||
\(467\) | −3.20007e14 | −0.666678 | −0.333339 | − | 0.942807i | \(-0.608175\pi\) | ||||
−0.333339 | + | 0.942807i | \(0.608175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.46917e14 | −0.298966 | ||||||||
\(470\) | 3.25819e14 | − | 5.64335e14i | 0.655297 | − | 1.13501i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.30541e13 | − | 7.45718e13i | −0.0845927 | − | 0.146519i | ||||
\(473\) | −3.05507e14 | − | 5.29153e14i | −0.593314 | − | 1.02765i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.95028e14 | + | 3.37799e14i | −0.370069 | + | 0.640979i | ||||
\(476\) | 3.45569e14 | 0.648181 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.37477e15 | −2.51986 | ||||||||
\(479\) | −7.51912e13 | + | 1.30235e14i | −0.136245 | + | 0.235984i | −0.926072 | − | 0.377346i | \(-0.876837\pi\) |
0.789827 | + | 0.613329i | \(0.210170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.54667e14 | − | 4.41096e14i | −0.450998 | − | 0.781151i | ||||
\(482\) | −3.47146e13 | − | 6.01274e13i | −0.0607789 | − | 0.105272i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.45234e14 | + | 4.24757e14i | −0.419692 | + | 0.726928i | ||||
\(485\) | −2.09927e14 | −0.355212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.76546e14 | 0.292045 | 0.146022 | − | 0.989281i | \(-0.453353\pi\) | ||||
0.146022 | + | 0.989281i | \(0.453353\pi\) | |||||||
\(488\) | 3.83816e14 | − | 6.64789e14i | 0.627790 | − | 1.08736i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.52721e14 | − | 4.37726e14i | −0.404169 | − | 0.700041i | ||||
\(491\) | −4.30479e14 | − | 7.45612e14i | −0.680775 | − | 1.17914i | −0.974745 | − | 0.223323i | \(-0.928310\pi\) |
0.293969 | − | 0.955815i | \(-0.405024\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.65803e13 | + | 2.87180e13i | −0.0256410 | + | 0.0444116i | ||||
\(494\) | 1.16609e15 | 1.78334 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.95053e14 | −0.291745 | ||||||||
\(497\) | 2.05855e14 | − | 3.56552e14i | 0.304511 | − | 0.527428i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.00605e14 | − | 5.20663e14i | −0.434953 | − | 0.753362i | 0.562338 | − | 0.826907i | \(-0.309902\pi\) |
−0.997292 | + | 0.0735457i | \(0.976569\pi\) | |||||||
\(500\) | 7.45772e14 | + | 1.29171e15i | 1.06726 | + | 1.84855i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.44894e14 | − | 1.63660e15i | 1.32286 | − | 2.29125i | ||||
\(503\) | −1.09203e15 | −1.51221 | −0.756103 | − | 0.654453i | \(-0.772899\pi\) | ||||
−0.756103 | + | 0.654453i | \(0.772899\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.99989e13 | −0.0677420 | ||||||||
\(506\) | 3.80904e14 | − | 6.59745e14i | 0.510491 | − | 0.884196i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.05051e14 | − | 8.74774e14i | −0.662346 | − | 1.14722i | ||||
\(509\) | 4.38186e14 | + | 7.58960e14i | 0.568474 | + | 0.984625i | 0.996717 | + | 0.0809617i | \(0.0257992\pi\) |
−0.428244 | + | 0.903663i | \(0.640868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.93918e14 | − | 3.35875e14i | 0.246208 | − | 0.426445i | ||||
\(512\) | 1.28839e15 | 1.61832 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.08784e14 | 0.748455 | ||||||||
\(515\) | −1.30424e14 | + | 2.25901e14i | −0.158642 | + | 0.274776i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.96154e14 | + | 8.59364e14i | 0.590770 | + | 1.02324i | ||||
\(518\) | −7.19675e14 | − | 1.24651e15i | −0.847857 | − | 1.46853i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.19011e14 | − | 5.52543e14i | 0.367948 | − | 0.637305i | ||||
\(521\) | 3.71989e14 | 0.424544 | 0.212272 | − | 0.977211i | \(-0.431914\pi\) | ||||
0.212272 | + | 0.977211i | \(0.431914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.73507e14 | −1.08788 | −0.543939 | − | 0.839125i | \(-0.683068\pi\) | ||||
−0.543939 | + | 0.839125i | \(0.683068\pi\) | |||||||
\(524\) | −1.97546e14 | + | 3.42159e14i | −0.218447 | + | 0.378361i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.47227e14 | − | 1.12103e15i | −0.700867 | − | 1.21394i | ||||
\(527\) | −7.85545e13 | − | 1.36060e14i | −0.0841807 | − | 0.145805i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.59171e14 | − | 6.22102e14i | 0.376960 | − | 0.652913i | ||||
\(530\) | 1.58849e15 | 1.64994 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.18605e15 | 2.22405 | ||||||||
\(533\) | 3.44349e14 | − | 5.96431e14i | 0.346737 | − | 0.600565i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.05724e14 | + | 1.04915e15i | 0.597488 | + | 1.03488i | ||||
\(536\) | 4.10330e14 | + | 7.10713e14i | 0.400615 | + | 0.693886i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.11242e15 | + | 1.92677e15i | −1.06406 | + | 1.84301i | ||||
\(539\) | 7.69683e14 | 0.728741 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.74606e15 | 1.61985 | 0.809925 | − | 0.586533i | \(-0.199508\pi\) | ||||
0.809925 | + | 0.586533i | \(0.199508\pi\) | |||||||
\(542\) | 9.11820e14 | − | 1.57932e15i | 0.837361 | − | 1.45035i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.91294e13 | + | 5.04536e13i | 0.0262142 | + | 0.0454044i | ||||
\(545\) | 1.86476e14 | + | 3.22987e14i | 0.166128 | + | 0.287742i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.73122e13 | + | 1.51229e14i | −0.0762333 | + | 0.132040i | −0.901622 | − | 0.432525i | \(-0.857623\pi\) |
0.825389 | + | 0.564565i | \(0.190956\pi\) | |||||||
\(548\) | 6.25639e14 | 0.540793 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.94588e14 | −0.842652 | ||||||||
\(551\) | −1.04886e14 | + | 1.81668e14i | −0.0879800 | + | 0.152386i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.16411e13 | + | 8.94451e13i | 0.0424627 | + | 0.0735475i | ||||
\(554\) | −1.18420e15 | − | 2.05110e15i | −0.964099 | − | 1.66987i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.27280e15 | − | 3.93661e15i | 1.81406 | − | 3.14204i | ||||
\(557\) | −1.58365e15 | −1.25157 | −0.625785 | − | 0.779995i | \(-0.715221\pi\) | ||||
−0.625785 | + | 0.779995i | \(0.715221\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.33993e14 | −0.568757 | ||||||||
\(560\) | 2.85416e14 | − | 4.94356e14i | 0.219000 | − | 0.379320i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.23020e14 | − | 1.07910e15i | −0.468761 | − | 0.811919i | ||||
\(563\) | −4.87899e14 | − | 8.45066e14i | −0.363525 | − | 0.629643i | 0.625014 | − | 0.780614i | \(-0.285093\pi\) |
−0.988538 | + | 0.150971i | \(0.951760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.65699e14 | + | 1.67264e15i | −0.705627 | + | 1.22218i | ||||
\(566\) | −2.23895e15 | −1.62015 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.29977e15 | −1.63218 | ||||||||
\(569\) | 9.62137e14 | − | 1.66647e15i | 0.676269 | − | 1.17133i | −0.299827 | − | 0.953994i | \(-0.596929\pi\) |
0.976096 | − | 0.217339i | \(-0.0697377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.05660e14 | − | 1.39544e15i | −0.555461 | − | 0.962086i | −0.997868 | − | 0.0652716i | \(-0.979209\pi\) |
0.442407 | − | 0.896814i | \(-0.354125\pi\) | |||||||
\(572\) | 9.86235e14 | + | 1.70821e15i | 0.673445 | + | 1.16644i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.73113e14 | − | 1.68548e15i | 0.651850 | − | 1.12904i | ||||
\(575\) | 3.06113e14 | 0.203099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.53250e15 | −1.64848 | −0.824239 | − | 0.566242i | \(-0.808397\pi\) | ||||
−0.824239 | + | 0.566242i | \(0.808397\pi\) | |||||||
\(578\) | −9.65588e14 | + | 1.67245e15i | −0.622571 | + | 1.07832i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.16508e14 | + | 2.01797e14i | 0.0737057 | + | 0.127662i | ||||
\(581\) | −1.21706e14 | − | 2.10801e14i | −0.0762682 | − | 0.132100i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.20947e15 | + | 2.09486e15i | −0.743735 | + | 1.28819i | ||||
\(584\) | −2.16640e15 | −1.31968 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.75768e15 | 2.24638 | ||||||||
\(587\) | −1.55754e15 | + | 2.69773e15i | −0.922421 | + | 1.59768i | −0.126763 | + | 0.991933i | \(0.540459\pi\) |
−0.795658 | + | 0.605747i | \(0.792875\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.96930e14 | − | 8.60708e14i | −0.288843 | − | 0.500290i | ||||
\(590\) | −1.16298e14 | − | 2.01434e14i | −0.0669709 | − | 0.115997i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.27273e15 | + | 2.20444e15i | −0.719396 | + | 1.24603i | ||||
\(593\) | 2.20723e15 | 1.23608 | 0.618040 | − | 0.786146i | \(-0.287927\pi\) | ||||
0.618040 | + | 0.786146i | \(0.287927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.59788e14 | 0.252764 | ||||||||
\(596\) | −2.79408e15 | + | 4.83950e15i | −1.52190 | + | 2.63600i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.57569e14 | − | 7.92533e14i | −0.244681 | − | 0.423800i | ||||
\(599\) | 1.70579e15 | + | 2.95452e15i | 0.903813 | + | 1.56545i | 0.822502 | + | 0.568762i | \(0.192577\pi\) |
0.0813112 | + | 0.996689i | \(0.474089\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.87726e14 | − | 1.36438e15i | 0.409794 | − | 0.709784i | −0.585072 | − | 0.810981i | \(-0.698934\pi\) |
0.994866 | + | 0.101197i | \(0.0322672\pi\) | |||||||
\(602\) | −2.07422e15 | −1.06924 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.81956e15 | −1.42718 | ||||||||
\(605\) | −3.26290e14 | + | 5.65150e14i | −0.163662 | + | 0.283471i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.52796e14 | + | 4.37856e14i | 0.124518 | + | 0.215672i | 0.921544 | − | 0.388273i | \(-0.126928\pi\) |
−0.797026 | + | 0.603945i | \(0.793595\pi\) | |||||||
\(608\) | 1.84270e14 | + | 3.19166e14i | 0.0899468 | + | 0.155792i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.03677e15 | − | 1.79573e15i | 0.497012 | − | 0.860850i | ||||
\(611\) | 1.19203e15 | 0.566319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.98375e15 | −0.925665 | −0.462832 | − | 0.886446i | \(-0.653167\pi\) | ||||
−0.462832 | + | 0.886446i | \(0.653167\pi\) | |||||||
\(614\) | 1.00367e15 | − | 1.73840e15i | 0.464155 | − | 0.803940i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.37281e15 | + | 2.37777e15i | 0.623614 | + | 1.08013i | ||||
\(617\) | −9.65493e14 | − | 1.67228e15i | −0.434691 | − | 0.752907i | 0.562579 | − | 0.826743i | \(-0.309809\pi\) |
−0.997270 | + | 0.0738362i | \(0.976476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.73844e14 | + | 8.20722e14i | −0.209574 | + | 0.362993i | −0.951580 | − | 0.307400i | \(-0.900541\pi\) |
0.742006 | + | 0.670393i | \(0.233874\pi\) | |||||||
\(620\) | −1.10398e15 | −0.483958 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.69913e15 | 1.16246 | ||||||||
\(623\) | 3.53562e14 | − | 6.12387e14i | 0.150932 | − | 0.261422i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.04201e14 | + | 8.73302e14i | 0.211477 | + | 0.366290i | ||||
\(626\) | 4.91657e14 | + | 8.51575e14i | 0.204411 | + | 0.354050i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.30090e15 | + | 7.44938e15i | −1.75704 | + | 3.04328i | ||||
\(629\) | −2.05030e15 | −0.830306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00593e15 | 0.400318 | 0.200159 | − | 0.979763i | \(-0.435854\pi\) | ||||
0.200159 | + | 0.979763i | \(0.435854\pi\) | |||||||
\(632\) | 2.88461e14 | − | 4.99629e14i | 0.113800 | − | 0.197108i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.19115e15 | + | 5.52723e15i | 1.23725 | + | 2.14297i | ||||
\(635\) | −6.71983e14 | − | 1.16391e15i | −0.258287 | − | 0.447367i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.62299e14 | − | 8.00725e14i | 0.174645 | − | 0.302494i | ||||
\(638\) | −5.34888e14 | −0.200332 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.69422e15 | 1.35998 | ||||||||
\(641\) | 5.65722e14 | − | 9.79859e14i | 0.206483 | − | 0.357639i | −0.744121 | − | 0.668044i | \(-0.767132\pi\) |
0.950604 | + | 0.310406i | \(0.100465\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.34153e14 | + | 7.51975e14i | 0.155769 | + | 0.269801i | 0.933339 | − | 0.358996i | \(-0.116881\pi\) |
−0.777569 | + | 0.628797i | \(0.783548\pi\) | |||||||
\(644\) | −8.57794e14 | − | 1.48574e15i | −0.305148 | − | 0.528532i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.34702e15 | − | 4.06516e15i | 0.820802 | − | 1.42167i | ||||
\(647\) | 1.37636e15 | 0.477265 | 0.238633 | − | 0.971110i | \(-0.423301\pi\) | ||||
0.238633 | + | 0.971110i | \(0.423301\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.54195e14 | 0.120753 | ||||||||
\(650\) | −5.97385e14 | + | 1.03470e15i | −0.201944 | + | 0.349777i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.30073e14 | + | 5.71703e14i | 0.109711 | + | 0.190024i | ||||
\(653\) | 1.27638e15 | + | 2.21075e15i | 0.420685 | + | 0.728648i | 0.996007 | − | 0.0892793i | \(-0.0284564\pi\) |
−0.575321 | + | 0.817927i | \(0.695123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.62839e14 | + | 4.55251e14i | −0.0851850 | + | 0.147545i | ||||
\(656\) | −3.44187e15 | −1.10617 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.36862e15 | 1.06466 | ||||||||
\(659\) | 4.63396e14 | − | 8.02626e14i | 0.145239 | − | 0.251561i | −0.784223 | − | 0.620479i | \(-0.786938\pi\) |
0.929462 | + | 0.368918i | \(0.120272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.51659e14 | + | 1.64832e15i | 0.293342 | + | 0.508082i | 0.974598 | − | 0.223963i | \(-0.0718994\pi\) |
−0.681256 | + | 0.732045i | \(0.738566\pi\) | |||||||
\(662\) | −1.32645e15 | − | 2.29747e15i | −0.405482 | − | 0.702315i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.79836e14 | + | 1.17751e15i | −0.204399 | + | 0.354030i | ||||
\(665\) | 2.90859e15 | 0.867288 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.64627e14 | 0.0482847 | ||||||||
\(668\) | −1.77774e13 | + | 3.07914e13i | −0.00517128 | + | 0.00895692i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.10839e15 | + | 1.91978e15i | 0.317161 | + | 0.549339i | ||||
\(671\) | 1.57878e15 | + | 2.73452e15i | 0.448071 | + | 0.776083i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.46495e15 | + | 4.26942e15i | −0.688217 | + | 1.19203i | 0.284197 | + | 0.958766i | \(0.408273\pi\) |
−0.972414 | + | 0.233261i | \(0.925060\pi\) | |||||||
\(674\) | 4.67563e15 | 1.29482 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.86369e15 | −1.32513 | ||||||||
\(677\) | 2.15147e14 | − | 3.72645e14i | 0.0581429 | − | 0.100707i | −0.835489 | − | 0.549507i | \(-0.814815\pi\) |
0.893632 | + | 0.448801i | \(0.148149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.42604e14 | − | 9.39817e14i | −0.144278 | − | 0.249896i | ||||
\(680\) | −1.28416e15 | − | 2.22423e15i | −0.338704 | − | 0.586653i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.26710e15 | − | 2.19468e15i | 0.328849 | − | 0.569583i | ||||
\(683\) | 3.81244e15 | 0.981498 | 0.490749 | − | 0.871301i | \(-0.336723\pi\) | ||||
0.490749 | + | 0.871301i | \(0.336723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.32429e14 | 0.210887 | ||||||||
\(686\) | 3.44716e15 | − | 5.97066e15i | 0.866322 | − | 1.50051i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.83412e15 | + | 3.17678e15i | 0.453618 | + | 0.785690i | ||||
\(689\) | 1.45290e15 | + | 2.51650e15i | 0.356476 | + | 0.617435i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.01864e15 | + | 3.49639e15i | −0.487450 | + | 0.844289i | −0.999896 | − | 0.0144309i | \(-0.995406\pi\) |
0.512445 | + | 0.858720i | \(0.328740\pi\) | |||||||
\(692\) | 2.94972e15 | 0.706638 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.63374e15 | 1.79995 | ||||||||
\(695\) | 3.02402e15 | − | 5.23776e15i | 0.707406 | − | 1.22526i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.38616e15 | − | 2.40090e15i | −0.319178 | − | 0.552833i | ||||
\(698\) | −5.56879e15 | − | 9.64544e15i | −1.27220 | − | 2.20352i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.11990e15 | + | 1.93973e15i | −0.251849 | + | 0.436216i | ||||
\(701\) | 4.71267e15 | 1.05152 | 0.525761 | − | 0.850632i | \(-0.323781\pi\) | ||||
0.525761 | + | 0.850632i | \(0.323781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.29700e16 | −2.84896 | ||||||||
\(704\) | −2.97092e15 | + | 5.14579e15i | −0.647503 | + | 1.12151i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.62559e15 | − | 9.74381e15i | −1.20710 | − | 2.09075i | ||||
\(707\) | −1.29234e14 | − | 2.23839e14i | −0.0275150 | − | 0.0476573i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.33353e14 | + | 7.50589e14i | −0.0908422 | + | 0.157343i | −0.907866 | − | 0.419261i | \(-0.862289\pi\) |
0.817024 | + | 0.576604i | \(0.195623\pi\) | |||||||
\(710\) | −6.21215e15 | −1.29217 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.94991e15 | −0.808997 | ||||||||
\(713\) | −3.89986e14 | + | 6.75475e14i | −0.0792604 | + | 0.137283i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.31221e15 | + | 2.27281e15i | 0.262615 | + | 0.454863i | ||||
\(716\) | 7.91806e15 | + | 1.37145e16i | 1.57252 | + | 2.72369i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.84962e15 | − | 8.39979e15i | 0.948470 | − | 1.64280i | ||||
\(719\) | −2.62666e13 | −0.00509795 | −0.00254897 | − | 0.999997i | \(-0.500811\pi\) | ||||
−0.00254897 | + | 0.999997i | \(0.500811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.34844e15 | −0.257744 | ||||||||
\(722\) | 1.03040e16 | − | 1.78470e16i | 1.95457 | − | 3.38541i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.59965e15 | − | 7.96682e15i | −0.859335 | − | 1.48841i | ||||
\(725\) | −1.07465e14 | − | 1.86136e14i | −0.0199255 | − | 0.0345120i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.84009e15 | − | 4.91918e15i | 0.518672 | − | 0.898367i | −0.481092 | − | 0.876670i | \(-0.659760\pi\) |
0.999765 | − | 0.0216967i | \(-0.00690683\pi\) | |||||||
\(728\) | 3.29823e15 | 0.597803 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.85190e15 | −1.04477 | ||||||||
\(731\) | −1.47732e15 | + | 2.55880e15i | −0.261776 | + | 0.453410i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.11558e14 | + | 1.40566e15i | 0.141660 | + | 0.245363i | 0.928122 | − | 0.372276i | \(-0.121423\pi\) |
−0.786462 | + | 0.617639i | \(0.788089\pi\) | |||||||
\(734\) | −6.24427e15 | − | 1.08154e16i | −1.08182 | − | 1.87376i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.44614e14 | − | 2.50478e14i | 0.0246820 | − | 0.0427506i | ||||
\(737\) | −3.37568e15 | −0.571861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.64794e15 | 0.608840 | 0.304420 | − | 0.952538i | \(-0.401537\pi\) | ||||
0.304420 | + | 0.952538i | \(0.401537\pi\) | |||||||
\(740\) | −7.20357e15 | + | 1.24769e16i | −1.19337 | + | 2.06697i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.10582e15 | + | 7.11149e15i | 0.670160 | + | 1.16075i | ||||
\(743\) | 3.38022e15 | + | 5.85472e15i | 0.547655 | + | 0.948566i | 0.998435 | + | 0.0559310i | \(0.0178127\pi\) |
−0.450780 | + | 0.892635i | \(0.648854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.71760e15 | + | 6.43907e15i | −0.593476 | + | 1.02793i | ||||
\(746\) | 2.70861e15 | 0.429224 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.94007e15 | 1.23984 | ||||||||
\(749\) | −3.13127e15 | + | 5.42352e15i | −0.485367 | + | 0.840680i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.32417e13 | − | 2.29352e13i | −0.00202266 | − | 0.00350335i | 0.865012 | − | 0.501751i | \(-0.167311\pi\) |
−0.867035 | + | 0.498247i | \(0.833977\pi\) | |||||||
\(752\) | −2.97867e15 | − | 5.15921e15i | −0.451673 | − | 0.782321i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.21273e14 | + | 5.56461e14i | −0.0480100 | + | 0.0831558i | ||||
\(755\) | −3.75149e15 | −0.556539 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.37364e15 | 1.07809 | 0.539045 | − | 0.842277i | \(-0.318785\pi\) | ||||
0.539045 | + | 0.842277i | \(0.318785\pi\) | |||||||
\(758\) | −5.71351e15 | + | 9.89609e15i | −0.829320 | + | 1.43642i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.12351e15 | − | 1.40703e16i | −1.16217 | − | 2.01293i | ||||
\(761\) | 3.10492e15 | + | 5.37787e15i | 0.440996 | + | 0.763827i | 0.997764 | − | 0.0668412i | \(-0.0212921\pi\) |
−0.556768 | + | 0.830668i | \(0.687959\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.63982e14 | + | 1.66967e15i | −0.134953 | + | 0.233746i | ||||
\(764\) | −1.36703e16 | −1.90005 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.01866e15 | 0.687591 | ||||||||
\(767\) | 2.12742e14 | − | 3.68480e14i | 0.0289387 | − | 0.0501233i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.43098e15 | + | 7.67468e15i | 0.594162 | + | 1.02912i | 0.993665 | + | 0.112386i | \(0.0358494\pi\) |
−0.399503 | + | 0.916732i | \(0.630817\pi\) | |||||||
\(770\) | 3.70824e15 | + | 6.42285e15i | 0.493706 | + | 0.855124i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.94714e15 | − | 1.72290e16i | 1.30558 | − | 2.26133i | ||||
\(773\) | 2.95047e15 | 0.384507 | 0.192254 | − | 0.981345i | \(-0.438420\pi\) | ||||
0.192254 | + | 0.981345i | \(0.438420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.01830e15 | 0.130833 | ||||||||
\(776\) | −3.03092e15 | + | 5.24971e15i | −0.386665 | + | 0.669723i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.55571e15 | + | 2.69457e15i | 0.195678 | + | 0.338924i | ||||
\(779\) | −8.76875e15 | − | 1.51879e16i | −1.09517 | − | 1.89689i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.72990e15 | − | 8.19243e15i | 0.582467 | − | 1.00886i | ||||
\(782\) | −3.68384e15 | −0.450468 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.62081e15 | −0.557160 | ||||||||
\(785\) | −5.72246e15 | + | 9.91159e15i | −0.685172 | + | 1.18675i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.77726e15 | − | 1.17386e16i | −0.800190 | − | 1.38597i | −0.919491 | − | 0.393112i | \(-0.871399\pi\) |
0.119301 | − | 0.992858i | \(-0.461935\pi\) | |||||||
\(788\) | 1.28301e16 | + | 2.22225e16i | 1.50431 | + | 2.60554i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.79193e14 | − | 1.34960e15i | 0.0900941 | − | 0.156047i | ||||
\(791\) | −9.98429e15 | −1.14643 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.79308e15 | 0.429526 | ||||||||
\(794\) | 4.15553e15 | − | 7.19758e15i | 0.467319 | − | 0.809420i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.63921e15 | + | 1.32315e16i | 0.847279 | + | 1.46753i | ||||
\(797\) | −7.99612e15 | − | 1.38497e16i | −0.880762 | − | 1.52553i | −0.850495 | − | 0.525983i | \(-0.823697\pi\) |
−0.0302677 | − | 0.999542i | \(-0.509636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.39923e15 | − | 4.15559e15i | 0.260654 | − | 0.451466i | ||||
\(800\) | −3.77604e14 | −0.0407419 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.66327e15 | 0.283437 | ||||||||
\(803\) | 4.45561e15 | − | 7.71733e15i | 0.470946 | − | 0.815703i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.14132e15 | − | 1.97682e15i | −0.118995 | − | 0.206105i | ||||
\(806\) | −1.52213e15 | − | 2.63640e15i | −0.157619 | − | 0.273004i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.21884e14 | + | 1.25034e15i | −0.0737403 | + | 0.127722i | ||||
\(809\) | −9.45859e15 | −0.959643 | −0.479821 | − | 0.877366i | \(-0.659299\pi\) | ||||
−0.479821 | + | 0.877366i | \(0.659299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.07996e16 | −1.08092 | −0.540461 | − | 0.841369i | \(-0.681750\pi\) | ||||
−0.540461 | + | 0.841369i | \(0.681750\pi\) | |||||||
\(812\) | −6.02282e14 | + | 1.04318e15i | −0.0598745 | + | 0.103706i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.65358e16 | − | 2.86409e16i | −1.62178 | − | 2.80900i | ||||
\(815\) | 4.39171e14 | + | 7.60666e14i | 0.0427825 | + | 0.0741015i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.34545e15 | + | 1.61868e16i | −0.898212 | + | 1.55575i | ||||
\(818\) | −4.16012e15 | −0.397158 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.94807e16 | −1.83497 | ||||||||
\(821\) | −5.52054e15 | + | 9.56186e15i | −0.516529 | + | 0.894654i | 0.483287 | + | 0.875462i | \(0.339443\pi\) |
−0.999816 | + | 0.0191922i | \(0.993891\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.30518e15 | − | 1.09209e16i | −0.582101 | − | 1.00823i | −0.995230 | − | 0.0975557i | \(-0.968898\pi\) |
0.413129 | − | 0.910672i | \(-0.364436\pi\) | |||||||
\(824\) | 3.76612e15 | + | 6.52311e15i | 0.345378 | + | 0.598212i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.01197e14 | − | 1.04130e15i | 0.0544035 | − | 0.0942296i | ||||
\(827\) | 7.86172e14 | 0.0706704 | 0.0353352 | − | 0.999376i | \(-0.488750\pi\) | ||||
0.0353352 | + | 0.999376i | \(0.488750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.92589e15 | −0.525659 | −0.262829 | − | 0.964842i | \(-0.584656\pi\) | ||||
−0.262829 | + | 0.964842i | \(0.584656\pi\) | |||||||
\(830\) | −1.83638e15 | + | 3.18070e15i | −0.161820 | + | 0.280281i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.56888e15 | + | 6.18149e15i | 0.310352 | + | 0.537545i | ||||
\(833\) | −1.86096e15 | − | 3.22328e15i | −0.160764 | − | 0.278452i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.36533e13 | + | 4.09687e13i | −0.00201658 | + | 0.00349283i | ||||
\(836\) | 5.02283e16 | 4.25416 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.90044e15 | −0.660403 | ||||||||
\(839\) | 1.05104e16 | − | 1.82046e16i | 0.872831 | − | 1.51179i | 0.0137758 | − | 0.999905i | \(-0.495615\pi\) |
0.859055 | − | 0.511883i | \(-0.171052\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.04246e15 | + | 1.04658e16i | 0.495263 | + | 0.857821i | ||||
\(842\) | −6.15921e15 | − | 1.06681e16i | −0.501543 | − | 0.868699i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.62219e14 | + | 6.27381e14i | −0.0291130 | + | 0.0504252i | ||||
\(845\) | −6.47126e15 | −0.516746 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.37348e15 | −0.265901 | ||||||||
\(848\) | 7.26108e15 | − | 1.25766e16i | 0.568623 | − | 0.984883i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.40474e15 | + | 4.16513e15i | 0.185893 | + | 0.321977i | ||||
\(851\) | 5.08938e15 | + | 8.81506e15i | 0.390888 | + | 0.677037i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.91891e15 | − | 1.71801e16i | 0.752046 | − | 1.30258i | −0.194783 | − | 0.980846i | \(-0.562400\pi\) |
0.946829 | − | 0.321736i | \(-0.104266\pi\) | |||||||
\(854\) | 1.07190e16 | 0.807491 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.49818e16 | 2.60157 | ||||||||
\(857\) | 3.98319e15 | − | 6.89909e15i | 0.294332 | − | 0.509797i | −0.680498 | − | 0.732750i | \(-0.738236\pi\) |
0.974829 | + | 0.222953i | \(0.0715696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.98745e15 | + | 1.38347e16i | 0.582701 | + | 1.00927i | 0.995158 | + | 0.0982902i | \(0.0313373\pi\) |
−0.412457 | + | 0.910977i | \(0.635329\pi\) | |||||||
\(860\) | 1.03809e16 | + | 1.79803e16i | 0.752481 | + | 1.30334i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.00137e16 | + | 3.46647e16i | −1.43231 | + | 2.48083i | ||||
\(863\) | 4.02926e15 | 0.286527 | 0.143264 | − | 0.989685i | \(-0.454240\pi\) | ||||
0.143264 | + | 0.989685i | \(0.454240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.92467e15 | 0.275559 | ||||||||
\(866\) | −2.92207e15 | + | 5.06117e15i | −0.203865 | + | 0.353104i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.85350e15 | − | 4.94240e15i | −0.196571 | − | 0.340471i | ||||
\(869\) | 1.18655e15 | + | 2.05516e15i | 0.0812225 | + | 0.140682i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.02756e15 | + | 3.51183e15i | −0.137048 | + | 0.237374i | ||||
\(872\) | 1.07694e16 | 0.723352 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.33037e16 | −1.54565 | ||||||||
\(875\) | −5.12949e15 | + | 8.88454e15i | −0.338088 | + | 0.585586i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.88479e15 | − | 8.46070e15i | −0.317942 | − | 0.550692i | 0.662116 | − | 0.749401i | \(-0.269658\pi\) |
−0.980058 | + | 0.198709i | \(0.936325\pi\) | |||||||
\(878\) | −1.43651e16 | − | 2.48810e16i | −0.929155 | − | 1.60934i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.55796e15 | − | 1.13587e16i | 0.418903 | − | 0.725562i | ||||
\(881\) | −1.62583e16 | −1.03207 | −0.516033 | − | 0.856569i | \(-0.672592\pi\) | ||||
−0.516033 | + | 0.856569i | \(0.672592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.66061e16 | 1.04108 | 0.520540 | − | 0.853837i | \(-0.325731\pi\) | ||||
0.520540 | + | 0.853837i | \(0.325731\pi\) | |||||||
\(884\) | 4.76909e15 | − | 8.26031e15i | 0.297131 | − | 0.514646i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.33867e15 | + | 7.51479e15i | 0.266975 | + | 0.462414i | ||||
\(887\) | −9.56571e15 | − | 1.65683e16i | −0.584975 | − | 1.01321i | −0.994879 | − | 0.101077i | \(-0.967771\pi\) |
0.409904 | − | 0.912129i | \(-0.365562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.47379e15 | − | 6.01678e15i | 0.209819 | − | 0.363416i | ||||
\(890\) | −1.06695e16 | −0.640472 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.98286e15 | 0.532608 | ||||||||
\(893\) | 1.51773e16 | − | 2.62879e16i | 0.894361 | − | 1.54908i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.05352e16 | + | 1.82475e16i | 0.613218 | + | 1.06212i | ||||
\(896\) | 9.54855e15 | + | 1.65386e16i | 0.552387 | + | 0.956762i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.44493e15 | − | 5.96679e15i | 0.196861 | − | 0.340973i | ||||
\(899\) | 5.47641e14 | 0.0311041 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.16972e16 | 0.656287 | ||||||||
\(902\) | 2.23590e16 | − | 3.87270e16i | 1.24686 | − | 2.15962i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.78855e16 | + | 4.82991e16i | 1.53622 | + | 2.66080i | ||||
\(905\) | −6.11994e15 | − | 1.06001e16i | −0.335105 | − | 0.580418i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.36258e15 | − | 9.28827e15i | 0.290091 | − | 0.502452i | −0.683740 | − | 0.729726i | \(-0.739648\pi\) |
0.973831 | + | 0.227274i | \(0.0729812\pi\) | |||||||
\(908\) | 1.67836e15 | 0.0902430 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.90919e15 | 0.473272 | ||||||||
\(911\) | −1.41124e16 | + | 2.44435e16i | −0.745162 | + | 1.29066i | 0.204957 | + | 0.978771i | \(0.434295\pi\) |
−0.950119 | + | 0.311888i | \(0.899039\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.79642e15 | − | 4.84354e15i | −0.145886 | − | 0.252681i | ||||
\(914\) | −3.67417e14 | − | 6.36384e14i | −0.0190526 | − | 0.0330001i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.65758e16 | + | 6.33511e16i | −1.87400 | + | 3.24586i | ||||
\(917\) | −2.71748e15 | −0.138399 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.83551e16 | 0.923679 | 0.461839 | − | 0.886964i | \(-0.347190\pi\) | ||||
0.461839 | + | 0.886964i | \(0.347190\pi\) | |||||||
\(920\) | −6.37525e15 | + | 1.10423e16i | −0.318907 | + | 0.552364i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.71882e16 | + | 4.70914e16i | 1.34388 | + | 2.32767i | ||||
\(923\) | −5.68189e15 | − | 9.84133e15i | −0.279180 | − | 0.483553i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.64449e15 | − | 1.15086e16i | 0.322613 | − | 0.558783i | ||||
\(926\) | 1.46594e16 | 0.707549 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.03075e14 | −0.00968596 | ||||||||
\(929\) | −5.50625e15 | + | 9.53711e15i | −0.261078 | + | 0.452200i | −0.966529 | − | 0.256559i | \(-0.917411\pi\) |
0.705451 | + | 0.708759i | \(0.250745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.17723e16 | − | 2.03902e16i | −0.551617 | − | 0.955429i | ||||
\(932\) | −3.78659e13 | − | 6.55856e13i | −0.00176385 | − | 0.00305507i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.24803e16 | + | 2.16164e16i | −0.574534 | + | 0.995122i | ||||
\(935\) | 1.05645e16 | 0.483486 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.36357e15 | 0.378289 | 0.189145 | − | 0.981949i | \(-0.439429\pi\) | ||||
0.189145 | + | 0.981949i | \(0.439429\pi\) | |||||||
\(938\) | −5.72976e15 | + | 9.92424e15i | −0.257645 | + | 0.446254i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.68590e16 | − | 2.92007e16i | −0.749255 | − | 1.29775i | ||||
\(941\) | 1.11471e16 | + | 1.93073e16i | 0.492514 | + | 0.853059i | 0.999963 | − | 0.00862287i | \(-0.00274478\pi\) |
−0.507449 | + | 0.861682i | \(0.669411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.88163e15 | + | 1.19193e16i | −0.300523 | + | 0.520520i | ||||
\(944\) | −2.12642e15 | −0.0923214 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.76590e16 | −2.04524 | ||||||||
\(947\) | −1.89019e16 | + | 3.27391e16i | −0.806457 | + | 1.39682i | 0.108847 | + | 0.994059i | \(0.465284\pi\) |
−0.915303 | + | 0.402765i | \(0.868049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.35239e15 | − | 9.27061e15i | −0.225727 | − | 0.390971i | ||||
\(950\) | 1.52122e16 | + | 2.63483e16i | 0.637841 | + | 1.10477i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.63842e15 | − | 1.14981e16i | 0.275145 | − | 0.476565i | ||||
\(953\) | −4.79568e15 | −0.197624 | −0.0988119 | − | 0.995106i | \(-0.531504\pi\) | ||||
−0.0988119 | + | 0.995106i | \(0.531504\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.81887e16 | −0.740939 | ||||||||
\(956\) | −3.55677e16 | + | 6.16051e16i | −1.44058 | + | 2.49516i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.86491e15 | + | 1.01583e16i | 0.234829 | + | 0.406735i | ||||
\(959\) | 2.15160e15 | + | 3.72669e15i | 0.0856564 | + | 0.148361i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.14069e16 | − | 1.97574e16i | 0.448942 | − | 0.777590i | ||||
\(962\) | −3.97280e16 | −1.55466 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.59251e15 | −0.138987 | ||||||||
\(965\) | 1.32349e16 | − | 2.29236e16i | 0.509121 | − | 0.881824i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.68710e16 | − | 2.92214e16i | −0.641645 | − | 1.11136i | −0.985066 | − | 0.172180i | \(-0.944919\pi\) |
0.343421 | − | 0.939182i | \(-0.388414\pi\) | |||||||
\(968\) | 9.42193e15 | + | 1.63193e16i | 0.356308 | + | 0.617143i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.18714e15 | + | 1.41805e16i | −0.306117 | + | 0.530211i | ||||
\(971\) | −3.58587e16 | −1.33318 | −0.666590 | − | 0.745425i | \(-0.732247\pi\) | ||||
−0.666590 | + | 0.745425i | \(0.732247\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.12651e16 | 1.14932 | ||||||||
\(974\) | 6.88530e15 | − | 1.19257e16i | 0.251680 | − | 0.435923i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.47823e15 | − | 1.64168e16i | −0.342573 | − | 0.593354i | ||||
\(977\) | −6.00117e15 | − | 1.03943e16i | −0.215683 | − | 0.373574i | 0.737801 | − | 0.675019i | \(-0.235864\pi\) |
−0.953484 | + | 0.301445i | \(0.902531\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.12372e15 | − | 1.40707e16i | 0.288702 | − | 0.500047i | ||||
\(980\) | −2.61534e16 | −0.924240 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.71547e16 | −2.34673 | ||||||||
\(983\) | −2.21343e15 | + | 3.83378e15i | −0.0769170 | + | 0.133224i | −0.901918 | − | 0.431907i | \(-0.857841\pi\) |
0.825001 | + | 0.565131i | \(0.191174\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.70708e16 | + | 2.95675e16i | 0.586618 | + | 1.01605i | ||||
\(986\) | 1.29327e15 | + | 2.24000e15i | 0.0441942 | + | 0.0765466i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.01689e16 | − | 5.22541e16i | 1.01952 | − | 1.76586i | ||||
\(989\) | 1.46684e16 | 0.492951 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.79167e16 | −1.26016 | −0.630080 | − | 0.776530i | \(-0.716978\pi\) | ||||
−0.630080 | + | 0.776530i | \(0.716978\pi\) | |||||||
\(992\) | 4.81065e14 | − | 8.33229e14i | 0.0158997 | − | 0.0275391i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.60567e16 | − | 2.78111e16i | −0.524846 | − | 0.909060i | ||||
\(995\) | 1.01642e16 | + | 1.76048e16i | 0.330404 | + | 0.572276i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.88001e13 | + | 4.98833e13i | −0.000925915 | + | 0.00160373i | −0.866488 | − | 0.499198i | \(-0.833628\pi\) |
0.865562 | + | 0.500802i | \(0.166961\pi\) | |||||||
\(998\) | −4.68943e16 | −1.49935 | ||||||||
\(999\) | 0 | 0 |
(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 | 81.12.c.e.55.1 | 2 | ||
3.2 | odd | 2 | 81.12.c.a.55.1 | 2 | |||
9.2 | odd | 6 | 3.12.a.a.1.1 | ✓ | 1 | ||
9.4 | even | 3 | inner | 81.12.c.e.28.1 | 2 | ||
9.5 | odd | 6 | 81.12.c.a.28.1 | 2 | |||
9.7 | even | 3 | 9.12.a.a.1.1 | 1 | |||
36.7 | odd | 6 | 144.12.a.l.1.1 | 1 | |||
36.11 | even | 6 | 48.12.a.f.1.1 | 1 | |||
45.2 | even | 12 | 75.12.b.a.49.2 | 2 | |||
45.7 | odd | 12 | 225.12.b.a.199.1 | 2 | |||
45.29 | odd | 6 | 75.12.a.a.1.1 | 1 | |||
45.34 | even | 6 | 225.12.a.f.1.1 | 1 | |||
45.38 | even | 12 | 75.12.b.a.49.1 | 2 | |||
45.43 | odd | 12 | 225.12.b.a.199.2 | 2 | |||
63.20 | even | 6 | 147.12.a.c.1.1 | 1 | |||
72.11 | even | 6 | 192.12.a.g.1.1 | 1 | |||
72.29 | odd | 6 | 192.12.a.q.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.12.a.a.1.1 | ✓ | 1 | 9.2 | odd | 6 | ||
9.12.a.a.1.1 | 1 | 9.7 | even | 3 | |||
48.12.a.f.1.1 | 1 | 36.11 | even | 6 | |||
75.12.a.a.1.1 | 1 | 45.29 | odd | 6 | |||
75.12.b.a.49.1 | 2 | 45.38 | even | 12 | |||
75.12.b.a.49.2 | 2 | 45.2 | even | 12 | |||
81.12.c.a.28.1 | 2 | 9.5 | odd | 6 | |||
81.12.c.a.55.1 | 2 | 3.2 | odd | 2 | |||
81.12.c.e.28.1 | 2 | 9.4 | even | 3 | inner | ||
81.12.c.e.55.1 | 2 | 1.1 | even | 1 | trivial | ||
144.12.a.l.1.1 | 1 | 36.7 | odd | 6 | |||
147.12.a.c.1.1 | 1 | 63.20 | even | 6 | |||
192.12.a.g.1.1 | 1 | 72.11 | even | 6 | |||
192.12.a.q.1.1 | 1 | 72.29 | odd | 6 | |||
225.12.a.f.1.1 | 1 | 45.34 | even | 6 | |||
225.12.b.a.199.1 | 2 | 45.7 | odd | 12 | |||
225.12.b.a.199.2 | 2 | 45.43 | odd | 12 |