Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,22,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(201.223687887\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.78 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.22.f.a.35.77 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1383.40 | + | 428.211i | 0.955283 | + | 0.295694i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73042e6 | + | 1.18477e6i | 0.825130 | + | 0.564943i | ||||
\(5\) | −4.14728e7 | −1.89923 | −0.949616 | − | 0.313416i | \(-0.898527\pi\) | ||||
−0.949616 | + | 0.313416i | \(0.898527\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.70660e8i | 0.362155i | 0.983469 | + | 0.181077i | \(0.0579585\pi\) | ||||
−0.983469 | + | 0.181077i | \(0.942042\pi\) | |||||||
\(8\) | 1.88653e9 | + | 2.38000e9i | 0.621182 | + | 0.783667i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.73733e10 | − | 1.77591e10i | −1.81430 | − | 0.561592i | ||||
\(11\) | 1.22616e11i | 1.42536i | 0.701490 | + | 0.712680i | \(0.252519\pi\) | ||||
−0.701490 | + | 0.712680i | \(0.747481\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 9.13395e10i | − | 0.183761i | −0.995770 | − | 0.0918805i | \(-0.970712\pi\) | ||
0.995770 | − | 0.0918805i | \(-0.0292878\pi\) | |||||||
\(14\) | −1.15899e11 | + | 3.74430e11i | −0.107087 | + | 0.345960i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.59068e12 | + | 4.10031e12i | 0.361678 | + | 0.932303i | ||||
\(17\) | 1.30428e13i | 1.56913i | 0.620048 | + | 0.784564i | \(0.287113\pi\) | ||||
−0.620048 | + | 0.784564i | \(0.712887\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.42830e13 | 1.65701 | 0.828503 | − | 0.559985i | \(-0.189193\pi\) | ||||
0.828503 | + | 0.559985i | \(0.189193\pi\) | |||||||
\(20\) | −7.17654e13 | − | 4.91358e13i | −1.56711 | − | 1.07296i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.25056e13 | + | 1.69627e14i | −0.421471 | + | 1.36162i | ||||
\(23\) | 1.64232e14 | 0.826636 | 0.413318 | − | 0.910587i | \(-0.364370\pi\) | ||||
0.413318 | + | 0.910587i | \(0.364370\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.24315e15 | 2.60708 | ||||||||
\(26\) | 3.91126e13 | − | 1.26359e14i | 0.0543371 | − | 0.175544i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.20670e14 | + | 4.68356e14i | −0.204597 | + | 0.298825i | ||||
\(29\) | −2.31284e15 | −1.02086 | −0.510431 | − | 0.859919i | \(-0.670514\pi\) | ||||
−0.510431 | + | 0.859919i | \(0.670514\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.58177e15i | 0.346612i | 0.984868 | + | 0.173306i | \(0.0554450\pi\) | ||||
−0.984868 | + | 0.173306i | \(0.944555\pi\) | |||||||
\(32\) | 4.44741e14 | + | 6.35350e15i | 0.0698285 | + | 0.997559i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.58508e15 | + | 1.80434e16i | −0.463982 | + | 1.49896i | ||||
\(35\) | − | 1.12250e16i | − | 0.687816i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.81093e16i | − | 1.30291i | −0.758689 | − | 0.651453i | \(-0.774160\pi\) | ||
0.758689 | − | 0.651453i | \(-0.225840\pi\) | |||||||
\(38\) | 6.12609e16 | + | 1.89625e16i | 1.58291 | + | 0.489967i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.82396e16 | − | 9.87050e16i | −1.17977 | − | 1.48836i | ||||
\(41\) | 1.05875e17i | 1.23186i | 0.787799 | + | 0.615932i | \(0.211221\pi\) | ||||
−0.787799 | + | 0.615932i | \(0.788779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.64492e16 | 0.186635 | 0.0933176 | − | 0.995636i | \(-0.470253\pi\) | ||||
0.0933176 | + | 0.995636i | \(0.470253\pi\) | |||||||
\(44\) | −1.45272e17 | + | 2.12178e17i | −0.805247 | + | 1.17611i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.27197e17 | + | 7.03258e16i | 0.789671 | + | 0.244432i | ||||
\(47\) | 3.60142e17 | 0.998725 | 0.499362 | − | 0.866393i | \(-0.333568\pi\) | ||||
0.499362 | + | 0.866393i | \(0.333568\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.85289e17 | 0.868844 | ||||||||
\(50\) | 1.71977e18 | + | 5.32332e17i | 2.49050 | + | 0.770899i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.08216e17 | − | 1.58056e17i | 0.103815 | − | 0.151627i | ||||
\(53\) | 7.43815e17 | 0.584209 | 0.292104 | − | 0.956386i | \(-0.405645\pi\) | ||||
0.292104 | + | 0.956386i | \(0.405645\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.08523e18i | − | 2.70709i | ||||||
\(56\) | −6.44169e17 | + | 5.10608e17i | −0.283809 | + | 0.224964i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.19958e18 | − | 9.90385e17i | −0.975212 | − | 0.301863i | ||||
\(59\) | 3.96701e18i | 1.01046i | 0.862986 | + | 0.505228i | \(0.168592\pi\) | ||||
−0.862986 | + | 0.505228i | \(0.831408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.70909e18i | 0.845228i | 0.906310 | + | 0.422614i | \(0.138887\pi\) | ||||
−0.906310 | + | 0.422614i | \(0.861113\pi\) | |||||||
\(62\) | −6.77329e17 | + | 2.18821e18i | −0.102491 | + | 0.331113i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.10539e18 | + | 8.97986e18i | −0.228267 | + | 0.973599i | ||||
\(65\) | 3.78810e18i | 0.349005i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.46007e19 | −1.64878 | −0.824390 | − | 0.566022i | \(-0.808482\pi\) | ||||
−0.824390 | + | 0.566022i | \(0.808482\pi\) | |||||||
\(68\) | −1.54528e19 | + | 2.25696e19i | −0.886468 | + | 1.29473i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.80667e18 | − | 1.55286e19i | 0.203383 | − | 0.657059i | ||||
\(71\) | −1.80477e19 | −0.657974 | −0.328987 | − | 0.944334i | \(-0.606707\pi\) | ||||
−0.328987 | + | 0.944334i | \(0.606707\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.21935e19 | −1.69377 | −0.846885 | − | 0.531775i | \(-0.821525\pi\) | ||||
−0.846885 | + | 0.531775i | \(0.821525\pi\) | |||||||
\(74\) | 1.63188e19 | − | 5.27203e19i | 0.385262 | − | 1.24464i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.66282e19 | + | 5.24652e19i | 1.36724 | + | 0.936114i | ||||
\(77\) | −3.31872e19 | −0.516201 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.17050e20i | 1.39087i | 0.718590 | + | 0.695434i | \(0.244788\pi\) | ||||
−0.718590 | + | 0.695434i | \(0.755212\pi\) | |||||||
\(80\) | −6.59698e19 | − | 1.70051e20i | −0.686911 | − | 1.77066i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.53369e19 | + | 1.46467e20i | −0.364255 | + | 1.17678i | ||||
\(83\) | 2.71098e19i | 0.191781i | 0.995392 | + | 0.0958907i | \(0.0305699\pi\) | ||||
−0.995392 | + | 0.0958907i | \(0.969430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.40922e20i | − | 2.98014i | ||||||
\(86\) | 3.65897e19 | + | 1.13258e19i | 0.178289 | + | 0.0551870i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.91826e20 | + | 2.31319e20i | −1.11701 | + | 0.885407i | ||||
\(89\) | − | 1.51004e20i | − | 0.513326i | −0.966501 | − | 0.256663i | \(-0.917377\pi\) | ||
0.966501 | − | 0.256663i | \(-0.0826231\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.47219e19 | 0.0665500 | ||||||||
\(92\) | 2.84190e20 | + | 1.94577e20i | 0.682082 | + | 0.467002i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.98219e20 | + | 1.54217e20i | 0.954064 | + | 0.295317i | ||||
\(95\) | −1.83654e21 | −3.14704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.99303e19 | −0.0549793 | −0.0274897 | − | 0.999622i | \(-0.508751\pi\) | ||||
−0.0274897 | + | 0.999622i | \(0.508751\pi\) | |||||||
\(98\) | 6.71348e20 | + | 2.07806e20i | 0.829991 | + | 0.256912i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.15118e21 | + | 1.47285e21i | 2.15118 | + | 1.47285i | ||||
\(101\) | 6.46427e20 | 0.582298 | 0.291149 | − | 0.956678i | \(-0.405963\pi\) | ||||
0.291149 | + | 0.956678i | \(0.405963\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.63829e21i | − | 1.20116i | −0.799564 | − | 0.600581i | \(-0.794936\pi\) | ||
0.799564 | − | 0.600581i | \(-0.205064\pi\) | |||||||
\(104\) | 2.17388e20 | − | 1.72315e20i | 0.144007 | − | 0.114149i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.02899e21 | + | 3.18510e20i | 0.558085 | + | 0.172747i | ||||
\(107\) | 2.14616e21i | 1.05471i | 0.849645 | + | 0.527355i | \(0.176816\pi\) | ||||
−0.849645 | + | 0.527355i | \(0.823184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.23991e20i | − | 0.0906260i | −0.998973 | − | 0.0453130i | \(-0.985571\pi\) | ||
0.998973 | − | 0.0453130i | \(-0.0144285\pi\) | |||||||
\(110\) | 2.17755e21 | − | 7.03489e21i | 0.800470 | − | 2.58603i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.10979e21 | + | 4.30533e20i | −0.337638 | + | 0.130984i | ||||
\(113\) | 2.30205e21i | 0.637957i | 0.947762 | + | 0.318978i | \(0.103340\pi\) | ||||
−0.947762 | + | 0.318978i | \(0.896660\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.81114e21 | −1.56997 | ||||||||
\(116\) | −4.00220e21 | − | 2.74019e21i | −0.842344 | − | 0.576729i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.69872e21 | + | 5.48796e21i | −0.298786 | + | 0.965272i | ||||
\(119\) | −3.53017e21 | −0.568267 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.63446e21 | −1.03165 | ||||||||
\(122\) | −2.01648e21 | + | 6.51454e21i | −0.249929 | + | 0.807432i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.87403e21 | + | 2.73712e21i | −0.195816 | + | 0.286000i | ||||
\(125\) | −3.17813e22 | −3.05222 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.13165e22i | 0.919965i | 0.887928 | + | 0.459982i | \(0.152144\pi\) | ||||
−0.887928 | + | 0.459982i | \(0.847856\pi\) | |||||||
\(128\) | −6.75786e21 | + | 1.15212e22i | −0.505947 | + | 0.862565i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.62211e21 | + | 5.24045e21i | −0.103199 | + | 0.333398i | ||||
\(131\) | − | 2.41878e22i | − | 1.41987i | −0.704267 | − | 0.709935i | \(-0.748724\pi\) | ||
0.704267 | − | 0.709935i | \(-0.251276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.19856e22i | 0.600092i | ||||||||
\(134\) | −3.40326e22 | − | 1.05343e22i | −1.57505 | − | 0.487535i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.10419e22 | + | 2.46057e22i | −1.22967 | + | 0.974713i | ||||
\(137\) | 6.73944e20i | 0.0247205i | 0.999924 | + | 0.0123603i | \(0.00393450\pi\) | ||||
−0.999924 | + | 0.0123603i | \(0.996066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.20391e22 | −0.694287 | −0.347144 | − | 0.937812i | \(-0.612848\pi\) | ||||
−0.347144 | + | 0.937812i | \(0.612848\pi\) | |||||||
\(140\) | 1.32991e22 | − | 1.94240e22i | 0.388577 | − | 0.567538i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.49671e22 | − | 7.72822e21i | −0.628551 | − | 0.194559i | ||||
\(143\) | 1.11997e22 | 0.261926 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.59200e22 | 1.93885 | ||||||||
\(146\) | −8.60382e22 | − | 2.66319e22i | −1.61803 | − | 0.500838i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.51509e22 | − | 6.59452e22i | 0.736068 | − | 1.07507i | ||||
\(149\) | 1.02771e23 | 1.56104 | 0.780519 | − | 0.625132i | \(-0.214955\pi\) | ||||
0.780519 | + | 0.625132i | \(0.214955\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.07511e22i | 0.406072i | 0.979171 | + | 0.203036i | \(0.0650809\pi\) | ||||
−0.979171 | + | 0.203036i | \(0.934919\pi\) | |||||||
\(152\) | 8.35411e22 | + | 1.05393e23i | 1.02930 | + | 1.29854i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.59111e22 | − | 1.42111e22i | −0.493118 | − | 0.152638i | ||||
\(155\) | − | 6.56002e22i | − | 0.658297i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.32560e22i | 0.817957i | 0.912544 | + | 0.408978i | \(0.134115\pi\) | ||||
−0.912544 | + | 0.408978i | \(0.865885\pi\) | |||||||
\(158\) | −5.01219e22 | + | 1.61926e23i | −0.411271 | + | 1.32867i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.84447e22 | − | 2.63497e23i | −0.132621 | − | 1.89460i | ||||
\(161\) | 4.44509e22i | 0.299370i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.96490e22 | −0.175404 | −0.0877021 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0877021 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(164\) | −1.25438e23 | + | 1.83209e23i | −0.695934 | + | 1.01645i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.16087e22 | + | 3.75036e22i | −0.0567086 | + | 0.183205i | ||||
\(167\) | 2.62512e22 | 0.120400 | 0.0601999 | − | 0.998186i | \(-0.480826\pi\) | ||||
0.0601999 | + | 0.998186i | \(0.480826\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.38722e23 | 0.966232 | ||||||||
\(170\) | 2.31629e23 | − | 7.48310e23i | 0.881209 | − | 2.84687i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.57683e22 | + | 3.13363e22i | 0.153998 | + | 0.105438i | ||||
\(173\) | 5.81627e22 | 0.184145 | 0.0920726 | − | 0.995752i | \(-0.470651\pi\) | ||||
0.0920726 | + | 0.995752i | \(0.470651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.36472e23i | 0.944167i | ||||||||
\(176\) | −5.02764e23 | + | 1.95043e23i | −1.32887 | + | 0.515522i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.46616e22 | − | 2.08899e23i | 0.151788 | − | 0.490372i | ||||
\(179\) | − | 5.75206e23i | − | 1.27311i | −0.771231 | − | 0.636556i | \(-0.780358\pi\) | ||
0.771231 | − | 0.636556i | \(-0.219642\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.95825e23i | − | 1.37049i | −0.728314 | − | 0.685243i | \(-0.759696\pi\) | ||
0.728314 | − | 0.685243i | \(-0.240304\pi\) | |||||||
\(182\) | 3.42002e22 | + | 1.05862e22i | 0.0635740 | + | 0.0196784i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.09828e23 | + | 3.90870e23i | 0.513491 | + | 0.647807i | ||||
\(185\) | 1.58050e24i | 2.47452i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.59926e24 | −2.23657 | ||||||||
\(188\) | 6.23197e23 | + | 4.26686e23i | 0.824077 | + | 0.564223i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.54066e24 | − | 7.86425e23i | −3.00631 | − | 0.930561i | ||||
\(191\) | −1.32712e24 | −1.48614 | −0.743070 | − | 0.669214i | \(-0.766631\pi\) | ||||
−0.743070 | + | 0.669214i | \(0.766631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.40826e22 | 0.0241742 | 0.0120871 | − | 0.999927i | \(-0.496152\pi\) | ||||
0.0120871 | + | 0.999927i | \(0.496152\pi\) | |||||||
\(194\) | −5.52395e22 | − | 1.70986e22i | −0.0525208 | − | 0.0162571i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.39755e23 | + | 5.74957e23i | 0.716909 | + | 0.490847i | ||||
\(197\) | 9.07905e23 | 0.734760 | 0.367380 | − | 0.930071i | \(-0.380255\pi\) | ||||
0.367380 | + | 0.930071i | \(0.380255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.32341e24i | − | 1.69110i | −0.533899 | − | 0.845548i | \(-0.679274\pi\) | ||
0.533899 | − | 0.845548i | \(-0.320726\pi\) | |||||||
\(200\) | 2.34525e24 | + | 2.95870e24i | 1.61947 | + | 2.04308i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.94265e23 | + | 2.76807e23i | 0.556259 | + | 0.172182i | ||||
\(203\) | − | 6.25993e23i | − | 0.369710i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.39093e24i | − | 2.33960i | ||||||
\(206\) | 7.01536e23 | − | 2.26641e24i | 0.355176 | − | 1.14745i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.74520e23 | − | 1.45292e23i | 0.171321 | − | 0.0664624i | ||||
\(209\) | 5.42981e24i | 2.36183i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.18515e24 | −0.860033 | −0.430017 | − | 0.902821i | \(-0.641492\pi\) | ||||
−0.430017 | + | 0.902821i | \(0.641492\pi\) | |||||||
\(212\) | 1.28711e24 | + | 8.81251e23i | 0.482048 | + | 0.330045i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.19011e23 | + | 2.96900e24i | −0.311872 | + | 1.00755i | ||||
\(215\) | −1.09692e24 | −0.354464 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.28120e23 | −0.125527 | ||||||||
\(218\) | 9.59155e22 | − | 3.09869e23i | 0.0267976 | − | 0.0865734i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.02484e24 | − | 8.79960e24i | 1.52935 | − | 2.23370i | ||||
\(221\) | 1.19133e24 | 0.288344 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.96264e23i | − | 0.175330i | −0.996150 | − | 0.0876650i | \(-0.972060\pi\) | ||
0.996150 | − | 0.0876650i | \(-0.0279405\pi\) | |||||||
\(224\) | −1.71964e24 | + | 1.20374e23i | −0.361271 | + | 0.0252887i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.85764e23 | + | 3.18465e24i | −0.188640 | + | 0.609429i | ||||
\(227\) | − | 4.28227e24i | − | 0.782353i | −0.920316 | − | 0.391176i | \(-0.872068\pi\) | ||
0.920316 | − | 0.391176i | \(-0.127932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.71312e24i | 0.285440i | 0.989763 | + | 0.142720i | \(0.0455848\pi\) | ||||
−0.989763 | + | 0.142720i | \(0.954415\pi\) | |||||||
\(230\) | −9.42251e24 | − | 2.91660e24i | −1.49977 | − | 0.464232i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.36325e24 | − | 5.50456e24i | −0.634141 | − | 0.800016i | ||||
\(233\) | 9.50214e24i | 1.32003i | 0.751252 | + | 0.660016i | \(0.229450\pi\) | ||||
−0.751252 | + | 0.660016i | \(0.770550\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.49361e25 | −1.89681 | ||||||||
\(236\) | −4.70001e24 | + | 6.86461e24i | −0.570851 | + | 0.833758i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.88363e24 | − | 1.51166e24i | −0.542856 | − | 0.168033i | ||||
\(239\) | −3.34184e24 | −0.355474 | −0.177737 | − | 0.984078i | \(-0.556878\pi\) | ||||
−0.177737 | + | 0.984078i | \(0.556878\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.78257e24 | 0.661021 | 0.330511 | − | 0.943802i | \(-0.392779\pi\) | ||||
0.330511 | + | 0.943802i | \(0.392779\pi\) | |||||||
\(242\) | −1.05615e25 | − | 3.26916e24i | −0.985517 | − | 0.305053i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.57920e24 | + | 8.14872e24i | −0.477506 | + | 0.697423i | ||||
\(245\) | −2.01263e25 | −1.65014 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.04478e24i | − | 0.304493i | ||||||
\(248\) | −3.76459e24 | + | 2.98405e24i | −0.271629 | + | 0.215309i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.39661e25 | − | 1.36091e25i | −2.91573 | − | 0.902524i | ||||
\(251\) | − | 2.69968e25i | − | 1.71687i | −0.512919 | − | 0.858437i | \(-0.671436\pi\) | ||
0.512919 | − | 0.858437i | \(-0.328564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.01374e25i | 1.17825i | ||||||||
\(254\) | −4.84583e24 | + | 1.56551e25i | −0.272028 | + | 0.878826i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.42823e25 | + | 1.30446e25i | −0.738377 | + | 0.674388i | ||||
\(257\) | − | 5.63292e24i | − | 0.279535i | −0.990184 | − | 0.139767i | \(-0.955365\pi\) | ||
0.990184 | − | 0.139767i | \(-0.0446355\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.03147e25 | 0.471854 | ||||||||
\(260\) | −4.48804e24 | + | 6.55502e24i | −0.197168 | + | 0.287974i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.03575e25 | − | 3.34614e25i | 0.419847 | − | 1.35638i | ||||
\(263\) | −8.78848e24 | −0.342278 | −0.171139 | − | 0.985247i | \(-0.554745\pi\) | ||||
−0.171139 | + | 0.985247i | \(0.554745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.08481e25 | −1.10955 | ||||||||
\(266\) | −5.13237e24 | + | 1.65809e25i | −0.177444 | + | 0.573258i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.25697e25 | − | 2.91463e25i | −1.36046 | − | 0.931467i | ||||
\(269\) | 6.12733e24 | 0.188310 | 0.0941548 | − | 0.995558i | \(-0.469985\pi\) | ||||
0.0941548 | + | 0.995558i | \(0.469985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.42193e25i | 1.25729i | 0.777694 | + | 0.628643i | \(0.216389\pi\) | ||||
−0.777694 | + | 0.628643i | \(0.783611\pi\) | |||||||
\(272\) | −5.34797e25 | + | 2.07469e25i | −1.46290 | + | 0.567519i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.88590e23 | + | 9.32332e23i | −0.00730972 | + | 0.0236151i | ||||
\(275\) | 1.52431e26i | 3.71603i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.60294e25i | − | 1.94361i | −0.235784 | − | 0.971806i | \(-0.575766\pi\) | ||
0.235784 | − | 0.971806i | \(-0.424234\pi\) | |||||||
\(278\) | −3.04889e25 | − | 9.43740e24i | −0.663241 | − | 0.205297i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.67155e25 | − | 2.11763e25i | 0.539018 | − | 0.427259i | ||||
\(281\) | 5.51814e24i | 0.107245i | 0.998561 | + | 0.0536224i | \(0.0170767\pi\) | ||||
−0.998561 | + | 0.0536224i | \(0.982923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.73234e25 | −0.492920 | −0.246460 | − | 0.969153i | \(-0.579267\pi\) | ||||
−0.246460 | + | 0.969153i | \(0.579267\pi\) | |||||||
\(284\) | −3.12301e25 | − | 2.13824e25i | −0.542914 | − | 0.371718i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.54936e25 | + | 4.79583e24i | 0.250213 | + | 0.0774499i | ||||
\(287\) | −2.86561e25 | −0.446126 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.01023e26 | −1.46216 | ||||||||
\(290\) | 1.32695e26 | + | 4.10740e25i | 1.85215 | + | 0.573308i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.07621e26 | − | 7.36850e25i | −1.39758 | − | 0.956884i | ||||
\(293\) | 6.05146e25 | 0.758141 | 0.379070 | − | 0.925368i | \(-0.376244\pi\) | ||||
0.379070 | + | 0.925368i | \(0.376244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.64523e26i | − | 1.91909i | ||||||
\(296\) | 9.07000e25 | − | 7.18944e25i | 1.02104 | − | 0.809342i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.42173e26 | + | 4.40076e25i | 1.49123 | + | 0.461590i | ||||
\(299\) | − | 1.50008e25i | − | 0.151904i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.15873e24i | 0.0675909i | ||||||||
\(302\) | −1.31680e25 | + | 4.25410e25i | −0.120073 | + | 0.387914i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.04400e25 | + | 1.81574e26i | 0.599303 | + | 1.54483i | ||||
\(305\) | − | 1.95299e26i | − | 1.60528i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.93773e25 | 0.609177 | 0.304588 | − | 0.952484i | \(-0.401481\pi\) | ||||
0.304588 | + | 0.952484i | \(0.401481\pi\) | |||||||
\(308\) | −5.74280e25 | − | 3.93193e25i | −0.425933 | − | 0.291624i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.80907e25 | − | 9.07511e25i | 0.194655 | − | 0.628860i | ||||
\(311\) | −4.67376e25 | −0.313099 | −0.156550 | − | 0.987670i | \(-0.550037\pi\) | ||||
−0.156550 | + | 0.987670i | \(0.550037\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.43657e24 | 0.0277864 | 0.0138932 | − | 0.999903i | \(-0.495578\pi\) | ||||
0.0138932 | + | 0.999903i | \(0.495578\pi\) | |||||||
\(314\) | −3.99332e25 | + | 1.29010e26i | −0.241865 | + | 0.781380i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.38677e26 | + | 2.02545e26i | −0.785761 | + | 1.14765i | ||||
\(317\) | −3.09298e26 | −1.69533 | −0.847665 | − | 0.530532i | \(-0.821992\pi\) | ||||
−0.847665 | + | 0.530532i | \(0.821992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.83592e26i | − | 1.45510i | ||||||
\(320\) | 8.73162e25 | − | 3.72420e26i | 0.433531 | − | 1.84909i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.90344e25 | + | 6.14932e25i | −0.0885221 | + | 0.285983i | ||||
\(323\) | 5.77575e26i | 2.60005i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.13549e26i | − | 0.479080i | ||||||
\(326\) | −4.10163e25 | − | 1.26960e25i | −0.167561 | − | 0.0518660i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.51982e26 | + | 1.99736e26i | −0.965371 | + | 0.765212i | ||||
\(329\) | 9.74758e25i | 0.361693i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.56291e26 | 0.544177 | 0.272089 | − | 0.962272i | \(-0.412286\pi\) | ||||
0.272089 | + | 0.962272i | \(0.412286\pi\) | |||||||
\(332\) | −3.21189e25 | + | 4.69114e25i | −0.108346 | + | 0.158245i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.63158e25 | + | 1.12410e25i | 0.115016 | + | 0.0356015i | ||||
\(335\) | 1.02026e27 | 3.13141 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.22884e26 | −0.930962 | −0.465481 | − | 0.885058i | \(-0.654119\pi\) | ||||
−0.465481 | + | 0.885058i | \(0.654119\pi\) | |||||||
\(338\) | 3.30247e26 | + | 1.02223e26i | 0.923025 | + | 0.285709i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.40869e26 | − | 9.36024e26i | 1.68361 | − | 2.45900i | ||||
\(341\) | −1.93950e26 | −0.494047 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.82524e26i | 0.676811i | ||||||||
\(344\) | 4.98972e25 | + | 6.29490e25i | 0.115934 | + | 0.146260i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.04621e25 | + | 2.49059e25i | 0.175911 | + | 0.0544507i | ||||
\(347\) | − | 4.52778e26i | − | 0.960342i | −0.877175 | − | 0.480171i | \(-0.840575\pi\) | ||
0.877175 | − | 0.480171i | \(-0.159425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.27832e26i | 0.654612i | 0.944918 | + | 0.327306i | \(0.106141\pi\) | ||||
−0.944918 | + | 0.327306i | \(0.893859\pi\) | |||||||
\(350\) | −1.44081e26 | + | 4.65474e26i | −0.279185 | + | 0.901947i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.79042e26 | + | 5.45325e25i | −1.42188 | + | 0.0995307i | ||||
\(353\) | 5.61843e25i | 0.0995362i | 0.998761 | + | 0.0497681i | \(0.0158482\pi\) | ||||
−0.998761 | + | 0.0497681i | \(0.984152\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.48488e26 | 1.24965 | ||||||||
\(356\) | 1.78905e26 | − | 2.61301e26i | 0.290000 | − | 0.423561i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.46310e26 | − | 7.95738e26i | 0.376452 | − | 1.21618i | ||||
\(359\) | −3.25539e26 | −0.483182 | −0.241591 | − | 0.970378i | \(-0.577669\pi\) | ||||
−0.241591 | + | 0.970378i | \(0.577669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.24677e27 | 1.74567 | ||||||||
\(362\) | 2.97960e26 | − | 9.62602e26i | 0.405245 | − | 1.30920i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.27794e25 | + | 2.92898e25i | 0.0549124 | + | 0.0375969i | ||||
\(365\) | 2.57933e27 | 3.21686 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.84892e26i | 0.806545i | 0.915080 | + | 0.403272i | \(0.132127\pi\) | ||||
−0.915080 | + | 0.403272i | \(0.867873\pi\) | |||||||
\(368\) | 2.61240e26 | + | 6.73401e26i | 0.298976 | + | 0.770675i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.76787e26 | + | 2.18646e27i | −0.731702 | + | 2.36387i | ||||
\(371\) | 2.01321e26i | 0.211574i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.33427e27i | 1.32526i | 0.748945 | + | 0.662632i | \(0.230560\pi\) | ||||
−0.748945 | + | 0.662632i | \(0.769440\pi\) | |||||||
\(374\) | −2.21241e27 | − | 6.84821e26i | −2.13656 | − | 0.661341i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.79418e26 | + | 8.57135e26i | 0.620389 | + | 0.782667i | ||||
\(377\) | 2.11254e26i | 0.187595i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.99825e26 | 0.419862 | 0.209931 | − | 0.977716i | \(-0.432676\pi\) | ||||
0.209931 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(380\) | −3.17799e27 | − | 2.17588e27i | −2.59671 | − | 1.77790i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.83593e27 | − | 5.68287e26i | −1.41968 | − | 0.439443i | ||||
\(383\) | −2.52990e27 | −1.90334 | −0.951671 | − | 0.307121i | \(-0.900634\pi\) | ||||
−0.951671 | + | 0.307121i | \(0.900634\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.37637e27 | 0.980385 | ||||||||
\(386\) | 3.33158e25 | + | 1.03124e25i | 0.0230932 | + | 0.00714817i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.90963e25 | − | 4.73083e25i | −0.0453651 | − | 0.0310602i | ||||
\(389\) | −5.83925e26 | −0.373153 | −0.186576 | − | 0.982440i | \(-0.559739\pi\) | ||||
−0.186576 | + | 0.982440i | \(0.559739\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.14204e27i | 1.29710i | ||||||||
\(392\) | 9.15512e26 | + | 1.15499e27i | 0.539710 | + | 0.680884i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.25599e27 | + | 3.88775e26i | 0.701903 | + | 0.217264i | ||||
\(395\) | − | 4.85437e27i | − | 2.64158i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.05478e27i | − | 0.544331i | −0.962251 | − | 0.272165i | \(-0.912260\pi\) | ||
0.962251 | − | 0.272165i | \(-0.0877398\pi\) | |||||||
\(398\) | 9.94910e26 | − | 3.21420e27i | 0.500048 | − | 1.61548i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.97746e27 | + | 5.09732e27i | 0.942925 | + | 2.43059i | ||||
\(401\) | − | 4.82816e26i | − | 0.224267i | −0.993693 | − | 0.112134i | \(-0.964232\pi\) | ||
0.993693 | − | 0.112134i | \(-0.0357685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.44478e26 | 0.0636939 | ||||||||
\(404\) | 1.11859e27 | + | 7.65868e26i | 0.480471 | + | 0.328965i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.68057e26 | − | 8.65998e26i | 0.109321 | − | 0.353178i | ||||
\(407\) | 4.67282e27 | 1.85711 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.67932e27 | 1.38891 | 0.694453 | − | 0.719538i | \(-0.255646\pi\) | ||||
0.694453 | + | 0.719538i | \(0.255646\pi\) | |||||||
\(410\) | 1.88024e27 | − | 6.07440e27i | 0.691805 | − | 2.23498i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.94101e27 | − | 2.83494e27i | 0.678588 | − | 0.991114i | ||||
\(413\) | −1.07371e27 | −0.365942 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.12432e27i | − | 0.364237i | ||||||
\(416\) | 5.80326e26 | − | 4.06225e25i | 0.183313 | − | 0.0128318i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.32510e27 | + | 7.51158e27i | −0.698379 | + | 2.25621i | ||||
\(419\) | 2.73787e27i | 0.801984i | 0.916082 | + | 0.400992i | \(0.131334\pi\) | ||||
−0.916082 | + | 0.400992i | \(0.868666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 6.93173e27i | − | 1.93143i | −0.259600 | − | 0.965716i | \(-0.583591\pi\) | ||
0.259600 | − | 0.965716i | \(-0.416409\pi\) | |||||||
\(422\) | −3.02293e27 | − | 9.35705e26i | −0.821575 | − | 0.254307i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.40323e27 | + | 1.77028e27i | 0.362900 | + | 0.457825i | ||||
\(425\) | 1.62142e28i | 4.09084i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.27456e27 | −0.306103 | ||||||||
\(428\) | −2.54271e27 | + | 3.71377e27i | −0.595852 | + | 0.870273i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.51748e27 | − | 4.69714e26i | −0.338613 | − | 0.104813i | ||||
\(431\) | 1.63202e27 | 0.355398 | 0.177699 | − | 0.984085i | \(-0.443135\pi\) | ||||
0.177699 | + | 0.984085i | \(0.443135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.46078e27 | 0.303013 | 0.151506 | − | 0.988456i | \(-0.451588\pi\) | ||||
0.151506 | + | 0.988456i | \(0.451588\pi\) | |||||||
\(434\) | −5.92260e26 | − | 1.83326e26i | −0.119914 | − | 0.0371177i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.65378e26 | − | 3.87599e26i | 0.0511985 | − | 0.0747782i | ||||
\(437\) | 7.27266e27 | 1.36974 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.87252e27i | − | 1.59283i | −0.604750 | − | 0.796415i | \(-0.706727\pi\) | ||
0.604750 | − | 0.796415i | \(-0.293273\pi\) | |||||||
\(440\) | 1.21028e28 | − | 9.59343e27i | 2.12145 | − | 1.68159i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.64808e27 | + | 5.10139e26i | 0.275450 | + | 0.0852618i | ||||
\(443\) | 9.45932e27i | 1.54391i | 0.635680 | + | 0.771953i | \(0.280720\pi\) | ||||
−0.635680 | + | 0.771953i | \(0.719280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.26256e27i | 0.974926i | ||||||||
\(446\) | 3.40969e26 | − | 1.10155e27i | 0.0518441 | − | 0.167490i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.43049e27 | − | 5.69844e26i | −0.352593 | − | 0.0826678i | ||||
\(449\) | − | 4.72742e27i | − | 0.669943i | −0.942228 | − | 0.334971i | \(-0.891273\pi\) | ||
0.942228 | − | 0.334971i | \(-0.108727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.29820e28 | −1.75585 | ||||||||
\(452\) | −2.72740e27 | + | 3.98352e27i | −0.360409 | + | 0.526397i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.83372e27 | − | 5.92408e27i | 0.231337 | − | 0.747368i | ||||
\(455\) | −1.02529e27 | −0.126394 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.77342e27 | 1.15061 | 0.575303 | − | 0.817941i | \(-0.304884\pi\) | ||||
0.575303 | + | 0.817941i | \(0.304884\pi\) | |||||||
\(458\) | −7.33576e26 | + | 2.36992e27i | −0.0844029 | + | 0.272676i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.17861e28 | − | 8.06964e27i | −1.29543 | − | 0.886946i | ||||
\(461\) | 3.52212e27 | 0.378394 | 0.189197 | − | 0.981939i | \(-0.439412\pi\) | ||||
0.189197 | + | 0.981939i | \(0.439412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.64319e27i | − | 0.681987i | −0.940066 | − | 0.340993i | \(-0.889237\pi\) | ||
0.940066 | − | 0.340993i | \(-0.110763\pi\) | |||||||
\(464\) | −3.67899e27 | − | 9.48338e27i | −0.369224 | − | 0.951753i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.06892e27 | + | 1.31452e28i | −0.390326 | + | 1.26100i | ||||
\(467\) | − | 7.01354e25i | − | 0.00657825i | −0.999995 | − | 0.00328912i | \(-0.998953\pi\) | ||
0.999995 | − | 0.00328912i | \(-0.00104696\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.65843e27i | − | 0.597114i | ||||||
\(470\) | −2.06625e28 | − | 6.39579e27i | −1.81199 | − | 0.560876i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.44148e27 | + | 7.48389e27i | −0.791861 | + | 0.627677i | ||||
\(473\) | 3.24310e27i | 0.266022i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.50505e28 | 4.31995 | ||||||||
\(476\) | −6.10868e27 | − | 4.18244e27i | −0.468894 | − | 0.321039i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.62310e27 | − | 1.43101e27i | −0.339578 | − | 0.105112i | ||||
\(479\) | 1.80345e28 | 1.29593 | 0.647966 | − | 0.761669i | \(-0.275620\pi\) | ||||
0.647966 | + | 0.761669i | \(0.275620\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.48089e27 | −0.239423 | ||||||||
\(482\) | 9.38299e27 | + | 2.90437e27i | 0.631462 | + | 0.195460i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.32108e28 | − | 9.04509e27i | −0.851244 | − | 0.582823i | ||||
\(485\) | 1.65602e27 | 0.104418 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.64624e28i | 0.994123i | 0.867715 | + | 0.497062i | \(0.165588\pi\) | ||||
−0.867715 | + | 0.497062i | \(0.834412\pi\) | |||||||
\(488\) | −1.12076e28 | + | 8.88384e27i | −0.662377 | + | 0.525040i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.78426e28 | − | 8.61830e27i | −1.57635 | − | 0.487936i | ||||
\(491\) | 3.10560e28i | 1.72104i | 0.509421 | + | 0.860518i | \(0.329860\pi\) | ||||
−0.509421 | + | 0.860518i | \(0.670140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.01660e28i | − | 1.60186i | ||||||
\(494\) | 1.73202e27 | − | 5.59554e27i | 0.0900368 | − | 0.290877i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.48573e27 | + | 2.51608e27i | −0.323148 | + | 0.125362i | ||||
\(497\) | − | 4.88478e27i | − | 0.238289i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.35720e28 | −1.10240 | −0.551201 | − | 0.834372i | \(-0.685830\pi\) | ||||
−0.551201 | + | 0.834372i | \(0.685830\pi\) | |||||||
\(500\) | −5.49950e28 | − | 3.76535e28i | −2.51848 | − | 1.72433i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.15603e28 | − | 3.73473e28i | 0.507670 | − | 1.64010i | ||||
\(503\) | 3.02255e28 | 1.29990 | 0.649950 | − | 0.759977i | \(-0.274790\pi\) | ||||
0.649950 | + | 0.759977i | \(0.274790\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.68091e28 | −1.10592 | ||||||||
\(506\) | −8.62307e27 | + | 2.78581e28i | −0.348403 | + | 1.12557i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.34074e28 | + | 1.95822e28i | −0.519728 | + | 0.759090i | ||||
\(509\) | 1.04573e28 | 0.397085 | 0.198542 | − | 0.980092i | \(-0.436379\pi\) | ||||
0.198542 | + | 0.980092i | \(0.436379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.68333e28i | − | 0.613407i | ||||||
\(512\) | −2.53439e28 | + | 1.19300e28i | −0.904772 | + | 0.425897i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.41208e27 | − | 7.79257e27i | 0.0826568 | − | 0.267035i | ||||
\(515\) | 6.79446e28i | 2.28128i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.41592e28i | 1.42354i | ||||||||
\(518\) | 1.42693e28 | + | 4.41685e27i | 0.450754 | + | 0.139524i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.01567e27 | + | 7.14637e27i | −0.273503 | + | 0.216795i | ||||
\(521\) | 2.96507e28i | 0.881535i | 0.897621 | + | 0.440767i | \(0.145294\pi\) | ||||
−0.897621 | + | 0.440767i | \(0.854706\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.38670e28 | 1.53835 | 0.769174 | − | 0.639039i | \(-0.220668\pi\) | ||||
0.769174 | + | 0.639039i | \(0.220668\pi\) | |||||||
\(524\) | 2.86571e28 | − | 4.18552e28i | 0.802146 | − | 1.17158i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.21580e28 | − | 3.76333e27i | −0.326972 | − | 0.101210i | ||||
\(527\) | −2.06307e28 | −0.543879 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.24996e28 | −0.316673 | ||||||||
\(530\) | −4.26751e28 | − | 1.32095e28i | −1.05993 | − | 0.328087i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.42002e28 | + | 2.07402e28i | −0.339018 | + | 0.495154i | ||||
\(533\) | 9.67057e27 | 0.226369 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.90074e28i | − | 2.00314i | ||||||
\(536\) | −4.64100e28 | − | 5.85496e28i | −1.02419 | − | 1.29209i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.47653e27 | + | 2.62379e27i | 0.179889 | + | 0.0556821i | ||||
\(539\) | 5.95043e28i | 1.23841i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 6.85616e28i | − | 1.37249i | −0.727370 | − | 0.686246i | \(-0.759258\pi\) | ||
0.727370 | − | 0.686246i | \(-0.240742\pi\) | |||||||
\(542\) | −1.89352e28 | + | 6.11729e28i | −0.371772 | + | 1.20106i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.28677e28 | + | 5.80069e27i | −1.56530 | + | 0.109570i | ||||
\(545\) | 9.28954e27i | 0.172120i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.75520e28 | −0.669523 | −0.334762 | − | 0.942303i | \(-0.608656\pi\) | ||||
−0.334762 | + | 0.942303i | \(0.608656\pi\) | |||||||
\(548\) | −7.98470e26 | + | 1.16621e27i | −0.0139657 | + | 0.0203976i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.52725e28 | + | 2.10872e29i | −1.09881 | + | 3.54986i | ||||
\(551\) | −1.02420e29 | −1.69157 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.16806e28 | −0.503709 | ||||||||
\(554\) | 3.68387e28 | − | 1.19013e29i | 0.574715 | − | 1.85670i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.81370e28 | − | 2.61114e28i | −0.572877 | − | 0.392233i | ||||
\(557\) | −9.35504e28 | −1.37901 | −0.689503 | − | 0.724283i | \(-0.742171\pi\) | ||||
−0.689503 | + | 0.724283i | \(0.742171\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.41586e27i | − | 0.0342963i | ||||||
\(560\) | 4.60260e28 | − | 1.78554e28i | 0.641253 | − | 0.248768i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.36293e27 | + | 7.63378e27i | −0.0317117 | + | 0.102449i | ||||
\(563\) | 7.72669e27i | 0.101778i | 0.998704 | + | 0.0508892i | \(0.0162055\pi\) | ||||
−0.998704 | + | 0.0508892i | \(0.983794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 9.54724e28i | − | 1.21163i | ||||||
\(566\) | −3.77991e28 | − | 1.17002e28i | −0.470878 | − | 0.145754i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.40475e28 | − | 4.29534e28i | −0.408722 | − | 0.515632i | ||||
\(569\) | 8.80243e28i | 1.03735i | 0.854973 | + | 0.518673i | \(0.173574\pi\) | ||||
−0.854973 | + | 0.518673i | \(0.826426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00665e27 | −0.0909436 | −0.0454718 | − | 0.998966i | \(-0.514479\pi\) | ||||
−0.0454718 | + | 0.998966i | \(0.514479\pi\) | |||||||
\(572\) | 1.93802e28 | + | 1.32691e28i | 0.216123 | + | 0.147973i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.96428e28 | − | 1.22709e28i | −0.426176 | − | 0.131917i | ||||
\(575\) | 2.04165e29 | 2.15511 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.20011e29 | 1.22145 | 0.610723 | − | 0.791844i | \(-0.290879\pi\) | ||||
0.610723 | + | 0.791844i | \(0.290879\pi\) | |||||||
\(578\) | −1.39756e29 | − | 4.32593e28i | −1.39678 | − | 0.432352i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.65982e29 | + | 1.13643e29i | 1.59981 | + | 1.09534i | ||||
\(581\) | −7.33753e27 | −0.0694545 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.12037e28i | 0.832708i | ||||||||
\(584\) | −1.17330e29 | − | 1.48020e29i | −1.05214 | − | 1.32735i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.37157e28 | + | 2.59130e28i | 0.724239 | + | 0.224178i | ||||
\(587\) | − | 8.61883e28i | − | 0.732400i | −0.930536 | − | 0.366200i | \(-0.880659\pi\) | ||
0.930536 | − | 0.366200i | \(-0.119341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00452e28i | 0.574339i | ||||||||
\(590\) | 7.04506e28 | − | 2.27601e29i | 0.567464 | − | 1.83327i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.56260e29 | − | 6.06197e28i | 1.21470 | − | 0.471233i | ||||
\(593\) | 1.67847e29i | 1.28185i | 0.767602 | + | 0.640926i | \(0.221450\pi\) | ||||
−0.767602 | + | 0.640926i | \(0.778550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.46406e29 | 1.07927 | ||||||||
\(596\) | 1.77837e29 | + | 1.21760e29i | 1.28806 | + | 0.881898i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.42352e27 | − | 2.07521e28i | 0.0449170 | − | 0.145111i | ||||
\(599\) | 1.96423e29 | 1.34961 | 0.674807 | − | 0.737994i | \(-0.264227\pi\) | ||||
0.674807 | + | 0.737994i | \(0.264227\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.35958e29 | 0.902036 | 0.451018 | − | 0.892515i | \(-0.351061\pi\) | ||||
0.451018 | + | 0.892515i | \(0.351061\pi\) | |||||||
\(602\) | −3.06545e27 | + | 9.90337e27i | −0.0199862 | + | 0.0645684i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.64331e28 | + | 5.32125e28i | −0.229408 | + | 0.335062i | ||||
\(605\) | 3.16622e29 | 1.95934 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.83550e28i | − | 0.528141i | −0.964503 | − | 0.264071i | \(-0.914935\pi\) | ||
0.964503 | − | 0.264071i | \(-0.0850652\pi\) | |||||||
\(608\) | 1.96945e28 | + | 2.81352e29i | 0.115706 | + | 1.65296i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.36292e28 | − | 2.70176e29i | 0.474673 | − | 1.53350i | ||||
\(611\) | − | 3.28952e28i | − | 0.183527i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.84775e28i | − | 0.315249i | −0.987499 | − | 0.157625i | \(-0.949616\pi\) | ||
0.987499 | − | 0.157625i | \(-0.0503836\pi\) | |||||||
\(614\) | 1.09810e29 | + | 3.39902e28i | 0.581936 | + | 0.180130i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.26087e28 | − | 7.89855e28i | −0.320654 | − | 0.404529i | ||||
\(617\) | 1.01413e29i | 0.510622i | 0.966859 | + | 0.255311i | \(0.0821779\pi\) | ||||
−0.966859 | + | 0.255311i | \(0.917822\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.75640e29 | −0.854812 | −0.427406 | − | 0.904060i | \(-0.640572\pi\) | ||||
−0.427406 | + | 0.904060i | \(0.640572\pi\) | |||||||
\(620\) | 7.77212e28 | − | 1.13516e29i | 0.371901 | − | 0.543181i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.46566e28 | − | 2.00135e28i | −0.299098 | − | 0.0925817i | ||||
\(623\) | 4.08707e28 | 0.185904 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.25275e29 | 3.18979 | ||||||||
\(626\) | 6.13754e27 | + | 1.89979e27i | 0.0265438 | + | 0.00821627i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.10487e29 | + | 1.61372e29i | −0.462099 | + | 0.674921i | ||||
\(629\) | 4.97053e29 | 2.04443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.72251e29i | 0.685259i | 0.939471 | + | 0.342629i | \(0.111318\pi\) | ||||
−0.939471 | + | 0.342629i | \(0.888682\pi\) | |||||||
\(632\) | −2.78578e29 | + | 2.20818e29i | −1.08998 | + | 0.863981i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.27881e29 | − | 1.32445e29i | −1.61952 | − | 0.501299i | ||||
\(635\) | − | 4.69325e29i | − | 1.74723i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.43261e28i | − | 0.159660i | ||||||
\(638\) | 1.21437e29 | − | 3.92320e29i | 0.430263 | − | 1.39003i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.80267e29 | − | 4.77815e29i | 0.960910 | − | 1.63821i | ||||
\(641\) | 3.56547e28i | 0.120256i | 0.998191 | + | 0.0601282i | \(0.0191509\pi\) | ||||
−0.998191 | + | 0.0601282i | \(0.980849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.85976e29 | 1.25993 | 0.629963 | − | 0.776625i | \(-0.283070\pi\) | ||||
0.629963 | + | 0.776625i | \(0.283070\pi\) | |||||||
\(644\) | −5.26642e28 | + | 7.69188e28i | −0.169127 | + | 0.247019i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.47324e29 | + | 7.99016e29i | −0.768820 | + | 2.48378i | ||||
\(647\) | −1.60078e29 | −0.489594 | −0.244797 | − | 0.969574i | \(-0.578721\pi\) | ||||
−0.244797 | + | 0.969574i | \(0.578721\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.86420e29 | −1.44026 | ||||||||
\(650\) | 4.86229e28 | − | 1.57083e29i | 0.141661 | − | 0.457657i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.13053e28 | − | 3.51273e28i | −0.144731 | − | 0.0990934i | ||||
\(653\) | −2.00046e29 | −0.555318 | −0.277659 | − | 0.960680i | \(-0.589559\pi\) | ||||
−0.277659 | + | 0.960680i | \(0.589559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00314e30i | 2.69666i | ||||||||
\(656\) | −4.34121e29 | + | 1.68413e29i | −1.14847 | + | 0.445539i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.17402e28 | + | 1.34848e29i | −0.106951 | + | 0.345519i | ||||
\(659\) | 7.02306e28i | 0.177105i | 0.996072 | + | 0.0885523i | \(0.0282240\pi\) | ||||
−0.996072 | + | 0.0885523i | \(0.971776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.38617e28i | 0.131572i | 0.997834 | + | 0.0657862i | \(0.0209555\pi\) | ||||
−0.997834 | + | 0.0657862i | \(0.979044\pi\) | |||||||
\(662\) | 2.16213e29 | + | 6.69256e28i | 0.519843 | + | 0.160910i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.45212e28 | + | 5.11434e28i | −0.150293 | + | 0.119131i | ||||
\(665\) | − | 4.97077e29i | − | 1.13971i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.79842e29 | −0.843882 | ||||||||
\(668\) | 4.54256e28 | + | 3.11016e28i | 0.0993454 | + | 0.0680190i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.41143e30 | + | 4.36887e29i | 2.99139 | + | 0.925941i | ||||
\(671\) | −5.77410e29 | −1.20475 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.06107e28 | 0.0416806 | 0.0208403 | − | 0.999783i | \(-0.493366\pi\) | ||||
0.0208403 | + | 0.999783i | \(0.493366\pi\) | |||||||
\(674\) | −4.46676e29 | − | 1.38262e29i | −0.889332 | − | 0.275280i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.13089e29 | + | 2.82831e29i | 0.797267 | + | 0.545866i | ||||
\(677\) | −9.69834e29 | −1.84296 | −0.921481 | − | 0.388424i | \(-0.873020\pi\) | ||||
−0.921481 | + | 0.388424i | \(0.873020\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.08075e28i | − | 0.0199110i | ||||||
\(680\) | 1.28739e30 | − | 1.02047e30i | 2.33543 | − | 1.85121i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.68310e29 | − | 8.30515e28i | −0.471955 | − | 0.146087i | ||||
\(683\) | − | 1.07877e29i | − | 0.186858i | −0.995626 | − | 0.0934292i | \(-0.970217\pi\) | ||
0.995626 | − | 0.0934292i | \(-0.0297829\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.79503e28i | − | 0.0469500i | ||||||
\(686\) | −1.20980e29 | + | 3.90843e29i | −0.200129 | + | 0.646546i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.20722e28 | + | 1.08450e29i | 0.0675019 | + | 0.174001i | ||||
\(689\) | − | 6.79397e28i | − | 0.107355i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.29139e29 | 0.811054 | 0.405527 | − | 0.914083i | \(-0.367088\pi\) | ||||
0.405527 | + | 0.914083i | \(0.367088\pi\) | |||||||
\(692\) | 1.00646e29 | + | 6.89095e28i | 0.151944 | + | 0.104032i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.93885e29 | − | 6.26372e29i | 0.283968 | − | 0.917398i | ||||
\(695\) | 9.14024e29 | 1.31861 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.38091e30 | −1.93295 | ||||||||
\(698\) | −1.40381e29 | + | 4.53521e29i | −0.193565 | + | 0.625339i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.98642e29 | + | 5.82238e29i | −0.533401 | + | 0.779061i | ||||
\(701\) | −2.70843e29 | −0.357008 | −0.178504 | − | 0.983939i | \(-0.557126\pi\) | ||||
−0.178504 | + | 0.983939i | \(0.557126\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.68759e30i | − | 2.15892i | ||||||
\(704\) | −1.10108e30 | − | 2.58154e29i | −1.38773 | − | 0.325362i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.40588e28 | + | 7.77252e28i | −0.0294323 | + | 0.0950852i | ||||
\(707\) | 1.74962e29i | 0.210882i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.81867e28i | − | 0.0446813i | −0.999750 | − | 0.0223407i | \(-0.992888\pi\) | ||
0.999750 | − | 0.0223407i | \(-0.00711185\pi\) | |||||||
\(710\) | 1.03546e30 | + | 3.20511e29i | 1.19376 | + | 0.369513i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.59389e29 | − | 2.84874e29i | 0.402277 | − | 0.318869i | ||||
\(713\) | 2.59776e29i | 0.286522i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.64482e29 | −0.497457 | ||||||||
\(716\) | 6.81488e29 | − | 9.95349e29i | 0.719236 | − | 1.05048i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.50349e29 | − | 1.39399e29i | −0.461576 | − | 0.142874i | ||||
\(719\) | 3.85193e29 | 0.389068 | 0.194534 | − | 0.980896i | \(-0.437681\pi\) | ||||
0.194534 | + | 0.980896i | \(0.437681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.43421e29 | 0.435006 | ||||||||
\(722\) | 1.72478e30 | + | 5.33881e29i | 1.66760 | + | 0.516184i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.24394e29 | − | 1.20407e30i | 0.774247 | − | 1.13083i | ||||
\(725\) | −2.87522e30 | −2.66147 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17649e30i | 1.05798i | 0.848629 | + | 0.528988i | \(0.177428\pi\) | ||||
−0.848629 | + | 0.528988i | \(0.822572\pi\) | |||||||
\(728\) | 4.66387e28 | + | 5.88381e28i | 0.0413396 | + | 0.0521530i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.56824e30 | + | 1.10450e30i | 3.07301 | + | 0.951208i | ||||
\(731\) | 3.44972e29i | 0.292854i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.09025e29i | 0.172427i | 0.996277 | + | 0.0862136i | \(0.0274768\pi\) | ||||
−0.996277 | + | 0.0862136i | \(0.972523\pi\) | |||||||
\(734\) | −2.93278e29 | + | 9.47478e29i | −0.238491 | + | 0.770478i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.30406e28 | + | 1.04345e30i | 0.0577228 | + | 0.824618i | ||||
\(737\) | − | 3.01645e30i | − | 2.35010i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.16141e29 | 0.163670 | 0.0818352 | − | 0.996646i | \(-0.473922\pi\) | ||||
0.0818352 | + | 0.996646i | \(0.473922\pi\) | |||||||
\(740\) | −1.87253e30 | + | 2.73493e30i | −1.39796 | + | 2.04180i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.62078e28 | + | 2.78506e29i | −0.0625612 | + | 0.202113i | ||||
\(743\) | −1.11801e30 | −0.799953 | −0.399977 | − | 0.916525i | \(-0.630982\pi\) | ||||
−0.399977 | + | 0.916525i | \(0.630982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.26219e30 | −2.96477 | ||||||||
\(746\) | −5.71351e29 | + | 1.84583e30i | −0.391873 | + | 1.26600i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.76740e30 | − | 1.89476e30i | −1.84546 | − | 1.26353i | ||||
\(749\) | −5.80880e29 | −0.381969 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.71110e29i | 0.620939i | 0.950583 | + | 0.310470i | \(0.100486\pi\) | ||||
−0.950583 | + | 0.310470i | \(0.899514\pi\) | |||||||
\(752\) | 5.72869e29 | + | 1.47669e30i | 0.361217 | + | 0.931114i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.04613e28 | + | 2.92248e29i | −0.0554707 | + | 0.179206i | ||||
\(755\) | − | 1.27534e30i | − | 0.771225i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.71480e29i | − | 0.512567i | −0.966602 | − | 0.256284i | \(-0.917502\pi\) | ||
0.966602 | − | 0.256284i | \(-0.0824981\pi\) | |||||||
\(758\) | 6.91457e29 | + | 2.14031e29i | 0.401087 | + | 0.124151i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.46468e30 | − | 4.37095e30i | −1.95488 | − | 2.46623i | ||||
\(761\) | − | 5.58699e27i | − | 0.00310913i | −0.999999 | − | 0.00155457i | \(-0.999505\pi\) | ||
0.999999 | − | 0.00155457i | \(-0.000494834\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.06254e28 | 0.0328206 | ||||||||
\(764\) | −2.29648e30 | − | 1.57233e30i | −1.22626 | − | 0.839584i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.49986e30 | − | 1.08333e30i | −1.81823 | − | 0.562807i | ||||
\(767\) | 3.62345e29 | 0.185683 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.80205e29 | −0.438892 | −0.219446 | − | 0.975625i | \(-0.570425\pi\) | ||||
−0.219446 | + | 0.975625i | \(0.570425\pi\) | |||||||
\(770\) | 1.90406e30 | + | 5.89376e29i | 0.936545 | + | 0.289894i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.16731e28 | + | 2.85324e28i | 0.0199468 | + | 0.0136570i | ||||
\(773\) | 3.12368e30 | 1.47496 | 0.737482 | − | 0.675366i | \(-0.236014\pi\) | ||||
0.737482 | + | 0.675366i | \(0.236014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.96638e30i | 0.903647i | ||||||||
\(776\) | −7.53297e28 | − | 9.50339e28i | −0.0341522 | − | 0.0430855i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.07801e29 | − | 2.50043e29i | −0.356466 | − | 0.110339i | ||||
\(779\) | 4.68846e30i | 2.04121i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.21294e30i | − | 0.937850i | ||||||
\(782\) | −9.17247e29 | + | 2.96330e30i | −0.383544 | + | 1.23909i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.71939e29 | + | 1.98984e30i | 0.314242 | + | 0.810026i | ||||
\(785\) | − | 3.86758e30i | − | 1.55349i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.57921e30 | −0.617596 | −0.308798 | − | 0.951128i | \(-0.599927\pi\) | ||||
−0.308798 | + | 0.951128i | \(0.599927\pi\) | |||||||
\(788\) | 1.57106e30 | + | 1.07566e30i | 0.606272 | + | 0.415097i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.07870e30 | − | 6.71552e30i | 0.781100 | − | 2.52345i | ||||
\(791\) | −6.23073e29 | −0.231039 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.30126e29 | 0.155320 | ||||||||
\(794\) | 4.51670e29 | − | 1.45918e30i | 0.160955 | − | 0.519990i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.75271e30 | − | 4.02048e30i | 0.955374 | − | 1.39537i | ||||
\(797\) | −2.55126e30 | −0.873862 | −0.436931 | − | 0.899495i | \(-0.643935\pi\) | ||||
−0.436931 | + | 0.899495i | \(0.643935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.69726e30i | 1.56713i | ||||||||
\(800\) | 5.52882e29 | + | 7.89838e30i | 0.182049 | + | 2.60072i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.06747e29 | − | 6.67927e29i | 0.0663146 | − | 0.214239i | ||||
\(803\) | − | 7.62592e30i | − | 2.41423i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.84350e30i | − | 0.568574i | ||||||
\(806\) | 1.99870e29 | + | 6.18669e28i | 0.0608457 | + | 0.0188339i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.21950e30 | + | 1.53849e30i | 0.361713 | + | 0.456327i | ||||
\(809\) | 5.27500e30i | 1.54441i | 0.635372 | + | 0.772206i | \(0.280847\pi\) | ||||
−0.635372 | + | 0.772206i | \(0.719153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.74255e30 | −0.782412 | −0.391206 | − | 0.920303i | \(-0.627942\pi\) | ||||
−0.391206 | + | 0.920303i | \(0.627942\pi\) | |||||||
\(812\) | 7.41659e29 | − | 1.08323e30i | 0.208865 | − | 0.305059i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.46436e30 | + | 2.00095e30i | 1.77406 | + | 0.549137i | ||||
\(815\) | 1.22963e30 | 0.333133 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.17125e30 | 0.309256 | ||||||||
\(818\) | 5.08996e30 | + | 1.57553e30i | 1.32680 | + | 0.410692i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.20225e30 | − | 7.59817e30i | 1.32174 | − | 1.93047i | ||||
\(821\) | −2.49651e30 | −0.626225 | −0.313113 | − | 0.949716i | \(-0.601372\pi\) | ||||
−0.313113 | + | 0.949716i | \(0.601372\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.84477e30i | 0.451071i | 0.974235 | + | 0.225536i | \(0.0724132\pi\) | ||||
−0.974235 | + | 0.225536i | \(0.927587\pi\) | |||||||
\(824\) | 3.89914e30 | − | 3.09069e30i | 0.941310 | − | 0.746139i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.48537e30 | − | 4.59775e29i | −0.349578 | − | 0.108207i | ||||
\(827\) | − | 4.67681e30i | − | 1.08678i | −0.839480 | − | 0.543391i | \(-0.817140\pi\) | ||
0.839480 | − | 0.543391i | \(-0.182860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.02108e30i | − | 0.457889i | −0.973439 | − | 0.228945i | \(-0.926472\pi\) | ||
0.973439 | − | 0.228945i | \(-0.0735275\pi\) | |||||||
\(830\) | 4.81446e29 | − | 1.55538e30i | 0.107703 | − | 0.347950i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.20216e29 | + | 1.92305e29i | 0.178910 | + | 0.0419465i | ||||
\(833\) | 6.32954e30i | 1.36333i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.08871e30 | −0.228667 | ||||||||
\(836\) | −6.43308e30 | + | 9.39586e30i | −1.33430 | + | 1.94881i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.17239e30 | + | 3.78756e30i | −0.237142 | + | 0.766121i | ||||
\(839\) | 3.05059e30 | 0.609373 | 0.304686 | − | 0.952453i | \(-0.401448\pi\) | ||||
0.304686 | + | 0.952453i | \(0.401448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.16399e29 | 0.0421596 | ||||||||
\(842\) | 2.96824e30 | − | 9.58933e30i | 0.571113 | − | 1.84506i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.78123e30 | − | 2.58890e30i | −0.709639 | − | 0.485870i | ||||
\(845\) | −9.90045e30 | −1.83510 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.06634e30i | − | 0.373617i | ||||||
\(848\) | 1.18317e30 | + | 3.04987e30i | 0.211296 | + | 0.544660i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.94311e30 | + | 2.24307e31i | −1.20964 | + | 3.90791i | ||||
\(851\) | − | 6.25876e30i | − | 1.07703i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.19544e30i | − | 1.37597i | −0.725727 | − | 0.687983i | \(-0.758496\pi\) | ||
0.725727 | − | 0.687983i | \(-0.241504\pi\) | |||||||
\(854\) | −1.76322e30 | − | 5.45781e29i | −0.292415 | − | 0.0905130i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.10786e30 | + | 4.04880e30i | −0.826541 | + | 0.655167i | ||||
\(857\) | 2.15319e29i | 0.0344179i | 0.999852 | + | 0.0172089i | \(0.00547804\pi\) | ||||
−0.999852 | + | 0.0172089i | \(0.994522\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.37529e30 | −0.370500 | −0.185250 | − | 0.982691i | \(-0.559310\pi\) | ||||
−0.185250 | + | 0.982691i | \(0.559310\pi\) | |||||||
\(860\) | −1.89814e30 | − | 1.29960e30i | −0.292478 | − | 0.200252i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.25773e30 | + | 6.98850e29i | 0.339505 | + | 0.105089i | ||||
\(863\) | 9.44602e29 | 0.140325 | 0.0701626 | − | 0.997536i | \(-0.477648\pi\) | ||||
0.0701626 | + | 0.997536i | \(0.477648\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.41217e30 | −0.349734 | ||||||||
\(866\) | 2.02083e30 | + | 6.25520e29i | 0.289463 | + | 0.0895991i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.40829e29 | − | 5.07225e29i | −0.103576 | − | 0.0709158i | ||||
\(869\) | −1.43522e31 | −1.98249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.24702e30i | 0.302982i | ||||||||
\(872\) | 5.33098e29 | − | 4.22566e29i | 0.0710206 | − | 0.0562952i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.00610e31 | + | 3.11423e30i | 1.30849 | + | 0.405024i | ||||
\(875\) | − | 8.60191e30i | − | 1.10538i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.69320e30i | 0.337888i | 0.985626 | + | 0.168944i | \(0.0540357\pi\) | ||||
−0.985626 | + | 0.168944i | \(0.945964\pi\) | |||||||
\(878\) | 3.79931e30 | − | 1.22742e31i | 0.470991 | − | 1.52160i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.08510e31 | − | 8.08897e30i | 2.52383 | − | 0.979095i | ||||
\(881\) | − | 1.07042e31i | − | 1.28029i | −0.768253 | − | 0.640146i | \(-0.778874\pi\) | ||
0.768253 | − | 0.640146i | \(-0.221126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.08446e31 | −1.26656 | −0.633280 | − | 0.773923i | \(-0.718292\pi\) | ||||
−0.633280 | + | 0.773923i | \(0.718292\pi\) | |||||||
\(884\) | 2.06150e30 | + | 1.41145e30i | 0.237922 | + | 0.162898i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.05058e30 | + | 1.30860e31i | −0.456524 | + | 1.47487i | ||||
\(887\) | −1.33132e31 | −1.48280 | −0.741400 | − | 0.671063i | \(-0.765838\pi\) | ||||
−0.741400 | + | 0.671063i | \(0.765838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.06291e30 | −0.333170 | ||||||||
\(890\) | −2.68170e30 | + | 8.66360e30i | −0.288280 | + | 0.931330i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.43391e29 | − | 1.37787e30i | 0.0990514 | − | 0.144670i | ||||
\(893\) | 1.59481e31 | 1.65489 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.38554e31i | 2.41793i | ||||||||
\(896\) | −3.11832e30 | − | 1.82908e30i | −0.312382 | − | 0.183231i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.02433e30 | − | 6.53990e30i | 0.198098 | − | 0.639985i | ||||
\(899\) | − | 3.65837e30i | − | 0.353844i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.70145e30i | 0.916698i | ||||||||
\(902\) | −1.79592e31 | − | 5.55903e30i | −1.67733 | − | 0.519195i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.47887e30 | + | 4.34289e30i | −0.499945 | + | 0.396287i | ||||
\(905\) | 2.88578e31i | 2.60287i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.08414e31 | 1.83675 | 0.918377 | − | 0.395708i | \(-0.129501\pi\) | ||||
0.918377 | + | 0.395708i | \(0.129501\pi\) | |||||||
\(908\) | 5.07351e30 | − | 7.41014e30i | 0.441985 | − | 0.645543i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.41838e30 | − | 4.39039e29i | −0.120742 | − | 0.0373739i | ||||
\(911\) | 7.18004e30 | 0.604204 | 0.302102 | − | 0.953276i | \(-0.402312\pi\) | ||||
0.302102 | + | 0.953276i | \(0.402312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.32410e30 | −0.273357 | ||||||||
\(914\) | 1.35205e31 | + | 4.18508e30i | 1.09915 | + | 0.340227i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.02965e30 | + | 2.96442e30i | −0.161257 | + | 0.235525i | ||||
\(917\) | 6.54668e30 | 0.514213 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.09169e31i | 1.60578i | 0.596129 | + | 0.802889i | \(0.296705\pi\) | ||||
−0.596129 | + | 0.802889i | \(0.703295\pi\) | |||||||
\(920\) | −1.28494e31 | − | 1.62105e31i | −0.975239 | − | 1.23034i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.87249e30 | + | 1.50821e30i | 0.361473 | + | 0.111889i | ||||
\(923\) | 1.64847e30i | 0.120910i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.73757e31i | − | 3.39678i | ||||||
\(926\) | 2.84469e30 | − | 9.19016e30i | 0.201660 | − | 0.651490i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.02862e30 | − | 1.46947e31i | −0.0712853 | − | 1.01837i | ||||
\(929\) | − | 1.41504e31i | − | 0.969624i | −0.874618 | − | 0.484812i | \(-0.838888\pi\) | ||
0.874618 | − | 0.484812i | \(-0.161112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.14900e31 | 1.43968 | ||||||||
\(932\) | −1.12579e31 | + | 1.64427e31i | −0.745743 | + | 1.08920i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.00328e28 | − | 9.70251e28i | 0.00194515 | − | 0.00628409i | ||||
\(935\) | 6.63258e31 | 4.24776 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.74303e31 | 1.09154 | 0.545768 | − | 0.837936i | \(-0.316238\pi\) | ||||
0.545768 | + | 0.837936i | \(0.316238\pi\) | |||||||
\(938\) | 2.85121e30 | − | 9.21125e30i | 0.176563 | − | 0.570412i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.58457e31 | − | 1.76958e31i | −1.56511 | − | 1.07159i | ||||
\(941\) | −1.54614e31 | −0.925886 | −0.462943 | − | 0.886388i | \(-0.653207\pi\) | ||||
−0.462943 | + | 0.886388i | \(0.653207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.73880e31i | 1.01830i | ||||||||
\(944\) | −1.62660e31 | + | 6.31024e30i | −0.942052 | + | 0.365460i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.38873e30 | + | 4.48649e30i | −0.0786613 | + | 0.254126i | ||||
\(947\) | 3.02895e31i | 1.69675i | 0.529397 | + | 0.848374i | \(0.322418\pi\) | ||||
−0.529397 | + | 0.848374i | \(0.677582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.68072e30i | 0.311249i | ||||||||
\(950\) | 7.61567e31 | + | 2.35732e31i | 4.12677 | + | 1.27738i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.65977e30 | − | 8.40179e30i | −0.352997 | − | 0.445332i | ||||
\(953\) | − | 2.88987e31i | − | 1.51497i | −0.652855 | − | 0.757483i | \(-0.726429\pi\) | ||
0.652855 | − | 0.757483i | \(-0.273571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.50393e31 | 2.82252 | ||||||||
\(956\) | −5.78280e30 | − | 3.95932e30i | −0.293312 | − | 0.200823i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.49489e31 | + | 7.72259e30i | 1.23798 | + | 0.383200i | ||||
\(959\) | −1.82410e29 | −0.00895266 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.83235e31 | 0.879860 | ||||||||
\(962\) | −4.81545e30 | − | 1.49055e30i | −0.228717 | − | 0.0707961i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.17367e31 | + | 8.03580e30i | 0.545428 | + | 0.373440i | ||||
\(965\) | −9.98773e29 | −0.0459124 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.05511e31i | 0.474590i | 0.971438 | + | 0.237295i | \(0.0762609\pi\) | ||||
−0.971438 | + | 0.237295i | \(0.923739\pi\) | |||||||
\(968\) | −1.44026e31 | − | 1.81700e31i | −0.640842 | − | 0.808469i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.29093e30 | + | 7.09126e29i | 0.0997492 | + | 0.0308759i | ||||
\(971\) | − | 2.73385e31i | − | 1.17753i | −0.808304 | − | 0.588765i | \(-0.799614\pi\) | ||
0.808304 | − | 0.588765i | \(-0.200386\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.96511e30i | − | 0.251440i | ||||||
\(974\) | −7.04940e30 | + | 2.27741e31i | −0.293956 | + | 0.949668i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.93087e31 | + | 7.49065e30i | −0.788008 | + | 0.305701i | ||||
\(977\) | 4.04409e28i | 0.00163278i | 1.00000 | 0.000816390i | \(0.000259865\pi\) | |||||
−1.00000 | 0.000816390i | \(0.999740\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.85155e31 | 0.731674 | ||||||||
\(980\) | −3.48270e31 | − | 2.38451e31i | −1.36158 | − | 0.932233i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.32985e31 | + | 4.29628e31i | −0.508900 | + | 1.64408i | ||||
\(983\) | 3.08040e31 | 1.16626 | 0.583130 | − | 0.812378i | \(-0.301828\pi\) | ||||
0.583130 | + | 0.812378i | \(0.301828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.76533e31 | −1.39548 | ||||||||
\(986\) | 1.29174e31 | − | 4.17316e31i | 0.473662 | − | 1.53023i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.79215e30 | − | 6.99919e30i | 0.172021 | − | 0.251246i | ||||
\(989\) | 4.34379e30 | 0.154279 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.21458e31i | − | 1.46548i | −0.680507 | − | 0.732741i | \(-0.738241\pi\) | ||
0.680507 | − | 0.732741i | \(-0.261759\pi\) | |||||||
\(992\) | −1.00498e31 | + | 7.03476e29i | −0.345766 | + | 0.0242034i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.09172e30 | − | 6.75759e30i | 0.0704606 | − | 0.227633i | ||||
\(995\) | 9.63582e31i | 3.21179i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 3.53074e31i | − | 1.15230i | −0.817343 | − | 0.576151i | \(-0.804554\pi\) | ||
0.817343 | − | 0.576151i | \(-0.195446\pi\) | |||||||
\(998\) | −3.26094e31 | − | 1.00938e31i | −1.05311 | − | 0.325974i | ||||
\(999\) | 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 | 72.22.f.a.35.78 | yes | 84 | |
3.2 | odd | 2 | inner | 72.22.f.a.35.7 | ✓ | 84 | |
8.3 | odd | 2 | inner | 72.22.f.a.35.8 | yes | 84 | |
24.11 | even | 2 | inner | 72.22.f.a.35.77 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.22.f.a.35.7 | ✓ | 84 | 3.2 | odd | 2 | inner | |
72.22.f.a.35.8 | yes | 84 | 8.3 | odd | 2 | inner | |
72.22.f.a.35.77 | yes | 84 | 24.11 | even | 2 | inner | |
72.22.f.a.35.78 | yes | 84 | 1.1 | even | 1 | trivial |