Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,17,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (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: | \(19.4789452628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 37115 x^{14} + 433616 x^{13} + 965822723 x^{12} + 11579264195 x^{11} + \cdots + 43\!\cdots\!49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{106}\cdot 3^{51} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.9 | ||
Root | \(-66.3279 + 114.883i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.17.d.a.7.10 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.3734 | − | 255.747i | 0.0444273 | − | 0.999013i | ||||
\(3\) | 3788.00i | 0.577350i | ||||||||
\(4\) | −65277.3 | − | 5817.42i | −0.996052 | − | 0.0887668i | ||||
\(5\) | 86591.3 | 0.221674 | 0.110837 | − | 0.993839i | \(-0.464647\pi\) | ||||
0.110837 | + | 0.993839i | \(0.464647\pi\) | |||||||
\(6\) | 968769. | + | 43082.3i | 0.576780 | + | 0.0256501i | ||||
\(7\) | − | 1.07917e7i | − | 1.87200i | −0.352005 | − | 0.935998i | \(-0.614500\pi\) | ||
0.352005 | − | 0.935998i | \(-0.385500\pi\) | |||||||
\(8\) | −2.23021e6 | + | 1.66283e7i | −0.132931 | + | 0.991125i | ||||
\(9\) | −1.43489e7 | −0.333333 | ||||||||
\(10\) | 984836. | − | 2.21455e7i | 0.00984836 | − | 0.221455i | ||||
\(11\) | 3.08747e8i | 1.44033i | 0.693804 | + | 0.720163i | \(0.255933\pi\) | ||||
−0.693804 | + | 0.720163i | \(0.744067\pi\) | |||||||
\(12\) | 2.20364e7 | − | 2.47270e8i | 0.0512495 | − | 0.575071i | ||||
\(13\) | −9.27660e8 | −1.13721 | −0.568607 | − | 0.822609i | \(-0.692517\pi\) | ||||
−0.568607 | + | 0.822609i | \(0.692517\pi\) | |||||||
\(14\) | −2.75994e9 | − | 1.22738e8i | −1.87015 | − | 0.0831677i | ||||
\(15\) | 3.28007e8i | 0.127983i | ||||||||
\(16\) | 4.22728e9 | + | 7.59491e8i | 0.984241 | + | 0.176833i | ||||
\(17\) | 1.04989e9 | 0.150505 | 0.0752525 | − | 0.997165i | \(-0.476024\pi\) | ||||
0.0752525 | + | 0.997165i | \(0.476024\pi\) | |||||||
\(18\) | −1.63196e8 | + | 3.66969e9i | −0.0148091 | + | 0.333004i | ||||
\(19\) | 2.14400e10i | 1.26240i | 0.775620 | + | 0.631200i | \(0.217437\pi\) | ||||
−0.775620 | + | 0.631200i | \(0.782563\pi\) | |||||||
\(20\) | −5.65245e9 | − | 5.03738e8i | −0.220799 | − | 0.0196773i | ||||
\(21\) | 4.08789e10 | 1.08080 | ||||||||
\(22\) | 7.89612e10 | + | 3.51149e9i | 1.43890 | + | 0.0639898i | ||||
\(23\) | 8.03506e10i | 1.02605i | 0.858375 | + | 0.513023i | \(0.171474\pi\) | ||||
−0.858375 | + | 0.513023i | \(0.828526\pi\) | |||||||
\(24\) | −6.29880e10 | − | 8.44803e9i | −0.572226 | − | 0.0767478i | ||||
\(25\) | −1.45090e11 | −0.950861 | ||||||||
\(26\) | −1.05506e10 | + | 2.37247e11i | −0.0505233 | + | 1.13609i | ||||
\(27\) | − | 5.43536e10i | − | 0.192450i | ||||||
\(28\) | −6.27798e10 | + | 7.04452e11i | −0.166171 | + | 1.86461i | ||||
\(29\) | 6.46948e10 | 0.129326 | 0.0646630 | − | 0.997907i | \(-0.479403\pi\) | ||||
0.0646630 | + | 0.997907i | \(0.479403\pi\) | |||||||
\(30\) | 8.38870e10 | + | 3.73055e9i | 0.127857 | + | 0.00568595i | ||||
\(31\) | 1.00444e12i | 1.17769i | 0.808245 | + | 0.588846i | \(0.200418\pi\) | ||||
−0.808245 | + | 0.588846i | \(0.799582\pi\) | |||||||
\(32\) | 2.42316e11 | − | 1.07248e12i | 0.220385 | − | 0.975413i | ||||
\(33\) | −1.16953e12 | −0.831573 | ||||||||
\(34\) | 1.19408e10 | − | 2.68506e11i | 0.00668653 | − | 0.150356i | ||||
\(35\) | − | 9.34466e11i | − | 0.414972i | ||||||
\(36\) | 9.36658e11 | + | 8.34736e10i | 0.332017 | + | 0.0295889i | ||||
\(37\) | 1.20118e12 | 0.341975 | 0.170988 | − | 0.985273i | \(-0.445304\pi\) | ||||
0.170988 | + | 0.985273i | \(0.445304\pi\) | |||||||
\(38\) | 5.48323e12 | + | 2.43846e11i | 1.26115 | + | 0.0560849i | ||||
\(39\) | − | 3.51397e12i | − | 0.656571i | ||||||
\(40\) | −1.93117e11 | + | 1.43987e12i | −0.0294673 | + | 0.219706i | ||||
\(41\) | −1.21222e13 | −1.51814 | −0.759068 | − | 0.651011i | \(-0.774345\pi\) | ||||
−0.759068 | + | 0.651011i | \(0.774345\pi\) | |||||||
\(42\) | 4.64931e11 | − | 1.04547e13i | 0.0480169 | − | 1.07973i | ||||
\(43\) | 2.28614e12i | 0.195594i | 0.995206 | + | 0.0977968i | \(0.0311795\pi\) | ||||
−0.995206 | + | 0.0977968i | \(0.968820\pi\) | |||||||
\(44\) | 1.79611e12 | − | 2.01542e13i | 0.127853 | − | 1.43464i | ||||
\(45\) | −1.24249e12 | −0.0738912 | ||||||||
\(46\) | 2.05494e13 | + | 9.13858e11i | 1.02503 | + | 0.0455844i | ||||
\(47\) | − | 2.13186e13i | − | 0.895317i | −0.894205 | − | 0.447658i | \(-0.852258\pi\) | ||
0.894205 | − | 0.447658i | \(-0.147742\pi\) | |||||||
\(48\) | −2.87695e12 | + | 1.60129e13i | −0.102094 | + | 0.568252i | ||||
\(49\) | −8.32276e13 | −2.50437 | ||||||||
\(50\) | −1.65016e12 | + | 3.71063e13i | −0.0422441 | + | 0.949922i | ||||
\(51\) | 3.97697e12i | 0.0868942i | ||||||||
\(52\) | 6.05551e13 | + | 5.39659e12i | 1.13272 | + | 0.100947i | ||||
\(53\) | 1.37605e13 | 0.221018 | 0.110509 | − | 0.993875i | \(-0.464752\pi\) | ||||
0.110509 | + | 0.993875i | \(0.464752\pi\) | |||||||
\(54\) | −1.39008e13 | − | 6.18184e11i | −0.192260 | − | 0.00855003i | ||||
\(55\) | 2.67348e13i | 0.319283i | ||||||||
\(56\) | 1.79448e14 | + | 2.40678e13i | 1.85538 | + | 0.248846i | ||||
\(57\) | −8.12148e13 | −0.728847 | ||||||||
\(58\) | 7.35799e11 | − | 1.65455e13i | 0.00574560 | − | 0.129198i | ||||
\(59\) | 1.78862e14i | 1.21815i | 0.793112 | + | 0.609076i | \(0.208460\pi\) | ||||
−0.793112 | + | 0.609076i | \(0.791540\pi\) | |||||||
\(60\) | 1.90816e12 | − | 2.14114e13i | 0.0113607 | − | 0.127478i | ||||
\(61\) | −5.51686e13 | −0.287775 | −0.143888 | − | 0.989594i | \(-0.545960\pi\) | ||||
−0.143888 | + | 0.989594i | \(0.545960\pi\) | |||||||
\(62\) | 2.56884e14 | + | 1.14239e13i | 1.17653 | + | 0.0523216i | ||||
\(63\) | 1.54849e14i | 0.623999i | ||||||||
\(64\) | −2.71527e14 | − | 7.41694e13i | −0.964659 | − | 0.263503i | ||||
\(65\) | −8.03273e13 | −0.252090 | ||||||||
\(66\) | −1.33015e13 | + | 2.99104e14i | −0.0369445 | + | 0.830752i | ||||
\(67\) | − | 2.57456e14i | − | 0.634021i | −0.948422 | − | 0.317011i | \(-0.897321\pi\) | ||
0.948422 | − | 0.317011i | \(-0.102679\pi\) | |||||||
\(68\) | −6.85338e13 | − | 6.10763e12i | −0.149911 | − | 0.0133599i | ||||
\(69\) | −3.04368e14 | −0.592387 | ||||||||
\(70\) | −2.38987e14 | − | 1.06280e13i | −0.414563 | − | 0.0184361i | ||||
\(71\) | − | 4.05525e14i | − | 0.627987i | −0.949425 | − | 0.313993i | \(-0.898333\pi\) | ||
0.949425 | − | 0.313993i | \(-0.101667\pi\) | |||||||
\(72\) | 3.20011e13 | − | 2.38598e14i | 0.0443103 | − | 0.330375i | ||||
\(73\) | −2.94670e14 | −0.365387 | −0.182693 | − | 0.983170i | \(-0.558482\pi\) | ||||
−0.182693 | + | 0.983170i | \(0.558482\pi\) | |||||||
\(74\) | 1.36615e13 | − | 3.07199e14i | 0.0151930 | − | 0.341638i | ||||
\(75\) | − | 5.49600e14i | − | 0.548980i | ||||||
\(76\) | 1.24726e14 | − | 1.39955e15i | 0.112059 | − | 1.25742i | ||||
\(77\) | 3.33190e15 | 2.69629 | ||||||||
\(78\) | −8.98689e14 | − | 3.99657e13i | −0.655922 | − | 0.0291696i | ||||
\(79\) | − | 1.81169e14i | − | 0.119417i | −0.998216 | − | 0.0597085i | \(-0.980983\pi\) | ||
0.998216 | − | 0.0597085i | \(-0.0190171\pi\) | |||||||
\(80\) | 3.66046e14 | + | 6.57653e13i | 0.218180 | + | 0.0391992i | ||||
\(81\) | 2.05891e14 | 0.111111 | ||||||||
\(82\) | −1.37870e14 | + | 3.10022e15i | −0.0674466 | + | 1.51664i | ||||
\(83\) | − | 1.39106e15i | − | 0.617620i | −0.951124 | − | 0.308810i | \(-0.900069\pi\) | ||
0.951124 | − | 0.308810i | \(-0.0999308\pi\) | |||||||
\(84\) | −2.66846e15 | − | 2.37809e14i | −1.07653 | − | 0.0959389i | ||||
\(85\) | 9.09111e13 | 0.0333630 | ||||||||
\(86\) | 5.84673e14 | + | 2.60011e13i | 0.195400 | + | 0.00868969i | ||||
\(87\) | 2.45064e14i | 0.0746664i | ||||||||
\(88\) | −5.13394e15 | − | 6.88571e14i | −1.42754 | − | 0.191464i | ||||
\(89\) | 3.78150e15 | 0.960604 | 0.480302 | − | 0.877103i | \(-0.340527\pi\) | ||||
0.480302 | + | 0.877103i | \(0.340527\pi\) | |||||||
\(90\) | −1.41313e13 | + | 3.17764e14i | −0.00328279 | + | 0.0738183i | ||||
\(91\) | 1.00110e16i | 2.12886i | ||||||||
\(92\) | 4.67433e14 | − | 5.24507e15i | 0.0910787 | − | 1.02199i | ||||
\(93\) | −3.80483e15 | −0.679941 | ||||||||
\(94\) | −5.45219e15 | − | 2.42465e14i | −0.894433 | − | 0.0397765i | ||||
\(95\) | 1.85652e15i | 0.279841i | ||||||||
\(96\) | 4.06254e15 | + | 9.17892e14i | 0.563155 | + | 0.127239i | ||||
\(97\) | 8.34786e15 | 1.06513 | 0.532564 | − | 0.846390i | \(-0.321229\pi\) | ||||
0.532564 | + | 0.846390i | \(0.321229\pi\) | |||||||
\(98\) | −9.46579e14 | + | 2.12852e16i | −0.111262 | + | 2.50190i | ||||
\(99\) | − | 4.43018e15i | − | 0.480109i | ||||||
\(100\) | 9.47107e15 | + | 8.44048e14i | 0.947107 | + | 0.0844048i | ||||
\(101\) | −2.02699e15 | −0.187189 | −0.0935947 | − | 0.995610i | \(-0.529836\pi\) | ||||
−0.0935947 | + | 0.995610i | \(0.529836\pi\) | |||||||
\(102\) | 1.01710e15 | + | 4.52315e13i | 0.0868084 | + | 0.00386047i | ||||
\(103\) | − | 1.04678e16i | − | 0.826342i | −0.910654 | − | 0.413171i | \(-0.864421\pi\) | ||
0.910654 | − | 0.413171i | \(-0.135579\pi\) | |||||||
\(104\) | 2.06888e15 | − | 1.54254e16i | 0.151171 | − | 1.12712i | ||||
\(105\) | 3.53975e15 | 0.239584 | ||||||||
\(106\) | 1.56504e14 | − | 3.51922e15i | 0.00981923 | − | 0.220800i | ||||
\(107\) | − | 8.34371e15i | − | 0.485612i | −0.970075 | − | 0.242806i | \(-0.921932\pi\) | ||
0.970075 | − | 0.242806i | \(-0.0780678\pi\) | |||||||
\(108\) | −3.16198e14 | + | 3.54806e15i | −0.0170832 | + | 0.191690i | ||||
\(109\) | −2.25395e16 | −1.13118 | −0.565591 | − | 0.824686i | \(-0.691352\pi\) | ||||
−0.565591 | + | 0.824686i | \(0.691352\pi\) | |||||||
\(110\) | 6.83735e15 | + | 3.04065e14i | 0.318967 | + | 0.0141849i | ||||
\(111\) | 4.55007e15i | 0.197439i | ||||||||
\(112\) | 8.19619e15 | − | 4.56195e16i | 0.331030 | − | 1.84250i | ||||
\(113\) | −3.96494e16 | −1.49145 | −0.745726 | − | 0.666253i | \(-0.767897\pi\) | ||||
−0.745726 | + | 0.666253i | \(0.767897\pi\) | |||||||
\(114\) | −9.23686e14 | + | 2.07705e16i | −0.0323807 | + | 0.728127i | ||||
\(115\) | 6.95766e15i | 0.227447i | ||||||||
\(116\) | −4.22310e15 | − | 3.76357e14i | −0.128815 | − | 0.0114798i | ||||
\(117\) | 1.33109e16 | 0.379071 | ||||||||
\(118\) | 4.57434e16 | + | 2.03426e15i | 1.21695 | + | 0.0541191i | ||||
\(119\) | − | 1.13301e16i | − | 0.281745i | ||||||
\(120\) | −5.45421e15 | − | 7.31526e14i | −0.126848 | − | 0.0170130i | ||||
\(121\) | −4.93749e16 | −1.07454 | ||||||||
\(122\) | −6.27453e14 | + | 1.41092e16i | −0.0127851 | + | 0.287491i | ||||
\(123\) | − | 4.59188e16i | − | 0.876496i | ||||||
\(124\) | 5.84327e15 | − | 6.55673e16i | 0.104540 | − | 1.17304i | ||||
\(125\) | −2.57763e16 | −0.432455 | ||||||||
\(126\) | 3.96022e16 | + | 1.76116e15i | 0.623383 | + | 0.0277226i | ||||
\(127\) | 9.50930e16i | 1.40514i | 0.711616 | + | 0.702569i | \(0.247964\pi\) | ||||
−0.711616 | + | 0.702569i | \(0.752036\pi\) | |||||||
\(128\) | −2.20568e16 | + | 6.85988e16i | −0.306100 | + | 0.952000i | ||||
\(129\) | −8.65988e15 | −0.112926 | ||||||||
\(130\) | −9.13593e14 | + | 2.05435e16i | −0.0111997 | + | 0.251841i | ||||
\(131\) | 1.40724e16i | 0.162254i | 0.996704 | + | 0.0811272i | \(0.0258520\pi\) | ||||
−0.996704 | + | 0.0811272i | \(0.974148\pi\) | |||||||
\(132\) | 7.63439e16 | + | 6.80366e15i | 0.828290 | + | 0.0738161i | ||||
\(133\) | 2.31374e17 | 2.36321 | ||||||||
\(134\) | −6.58436e16 | − | 2.92814e15i | −0.633395 | − | 0.0281678i | ||||
\(135\) | − | 4.70655e15i | − | 0.0426611i | ||||||
\(136\) | −2.34147e15 | + | 1.74579e16i | −0.0200068 | + | 0.149169i | ||||
\(137\) | −1.77783e17 | −1.43260 | −0.716300 | − | 0.697793i | \(-0.754166\pi\) | ||||
−0.716300 | + | 0.697793i | \(0.754166\pi\) | |||||||
\(138\) | −3.46169e15 | + | 7.78412e16i | −0.0263181 | + | 0.591802i | ||||
\(139\) | 2.20734e17i | 1.58398i | 0.610532 | + | 0.791992i | \(0.290956\pi\) | ||||
−0.610532 | + | 0.791992i | \(0.709044\pi\) | |||||||
\(140\) | −5.43618e15 | + | 6.09994e16i | −0.0368358 | + | 0.413334i | ||||
\(141\) | 8.07549e16 | 0.516911 | ||||||||
\(142\) | −1.03712e17 | − | 4.61219e15i | −0.627367 | − | 0.0278997i | ||||
\(143\) | − | 2.86412e17i | − | 1.63796i | ||||||
\(144\) | −6.06569e16 | − | 1.08979e16i | −0.328080 | − | 0.0589442i | ||||
\(145\) | 5.60201e15 | 0.0286682 | ||||||||
\(146\) | −3.35139e15 | + | 7.53610e16i | −0.0162331 | + | 0.365026i | ||||
\(147\) | − | 3.15266e17i | − | 1.44590i | ||||||
\(148\) | −7.84098e16 | − | 6.98777e15i | −0.340625 | − | 0.0303560i | ||||
\(149\) | 3.42196e17 | 1.40859 | 0.704296 | − | 0.709906i | \(-0.251263\pi\) | ||||
0.704296 | + | 0.709906i | \(0.251263\pi\) | |||||||
\(150\) | −1.40559e17 | − | 6.25080e15i | −0.548438 | − | 0.0243897i | ||||
\(151\) | 3.61914e17i | 1.33903i | 0.742799 | + | 0.669514i | \(0.233498\pi\) | ||||
−0.742799 | + | 0.669514i | \(0.766502\pi\) | |||||||
\(152\) | −3.56512e17 | − | 4.78158e16i | −1.25120 | − | 0.167812i | ||||
\(153\) | −1.50647e16 | −0.0501684 | ||||||||
\(154\) | 3.78950e16 | − | 8.52124e17i | 0.119789 | − | 2.69362i | ||||
\(155\) | 8.69761e16i | 0.261064i | ||||||||
\(156\) | −2.04422e16 | + | 2.29383e17i | −0.0582817 | + | 0.653979i | ||||
\(157\) | −1.92467e17 | −0.521386 | −0.260693 | − | 0.965422i | \(-0.583951\pi\) | ||||
−0.260693 | + | 0.965422i | \(0.583951\pi\) | |||||||
\(158\) | −4.63334e16 | − | 2.06050e15i | −0.119299 | − | 0.00530537i | ||||
\(159\) | 5.21248e16i | 0.127605i | ||||||||
\(160\) | 2.09825e16 | − | 9.28673e16i | 0.0488536 | − | 0.216223i | ||||
\(161\) | 8.67119e17 | 1.92075 | ||||||||
\(162\) | 2.34168e15 | − | 5.26561e16i | 0.00493636 | − | 0.111001i | ||||
\(163\) | − | 3.03025e17i | − | 0.608103i | −0.952656 | − | 0.304051i | \(-0.901661\pi\) | ||
0.952656 | − | 0.304051i | \(-0.0983395\pi\) | |||||||
\(164\) | 7.91305e17 | + | 7.05199e16i | 1.51214 | + | 0.134760i | ||||
\(165\) | −1.01271e17 | −0.184338 | ||||||||
\(166\) | −3.55760e17 | − | 1.58211e16i | −0.617011 | − | 0.0274392i | ||||
\(167\) | − | 9.25468e17i | − | 1.52978i | −0.644159 | − | 0.764891i | \(-0.722793\pi\) | ||
0.644159 | − | 0.764891i | \(-0.277207\pi\) | |||||||
\(168\) | −9.11685e16 | + | 6.79747e17i | −0.143672 | + | 1.07121i | ||||
\(169\) | 1.95137e17 | 0.293255 | ||||||||
\(170\) | 1.03397e15 | − | 2.32503e16i | 0.00148223 | − | 0.0333301i | ||||
\(171\) | − | 3.07641e17i | − | 0.420800i | ||||||
\(172\) | 1.32994e16 | − | 1.49233e17i | 0.0173622 | − | 0.194821i | ||||
\(173\) | −1.28458e18 | −1.60100 | −0.800502 | − | 0.599330i | \(-0.795434\pi\) | ||||
−0.800502 | + | 0.599330i | \(0.795434\pi\) | |||||||
\(174\) | 6.26744e16 | + | 2.78720e15i | 0.0745926 | + | 0.00331722i | ||||
\(175\) | 1.56576e18i | 1.78001i | ||||||||
\(176\) | −2.34490e17 | + | 1.30516e18i | −0.254697 | + | 1.41763i | ||||
\(177\) | −6.77527e17 | −0.703300 | ||||||||
\(178\) | 4.30084e16 | − | 9.67108e17i | 0.0426770 | − | 0.959655i | ||||
\(179\) | 1.51930e18i | 1.44152i | 0.693187 | + | 0.720758i | \(0.256206\pi\) | ||||
−0.693187 | + | 0.720758i | \(0.743794\pi\) | |||||||
\(180\) | 8.11064e16 | + | 7.22809e15i | 0.0735996 | + | 0.00655909i | ||||
\(181\) | −5.20028e17 | −0.451438 | −0.225719 | − | 0.974192i | \(-0.572473\pi\) | ||||
−0.225719 | + | 0.974192i | \(0.572473\pi\) | |||||||
\(182\) | 2.56029e18 | + | 1.13859e17i | 2.12676 | + | 0.0945794i | ||||
\(183\) | − | 2.08978e17i | − | 0.166147i | ||||||
\(184\) | −1.33610e18 | − | 1.79199e17i | −1.01694 | − | 0.136393i | ||||
\(185\) | 1.04012e17 | 0.0758069 | ||||||||
\(186\) | −4.32737e16 | + | 9.73074e17i | −0.0302079 | + | 0.679270i | ||||
\(187\) | 3.24149e17i | 0.216777i | ||||||||
\(188\) | −1.24020e17 | + | 1.39162e18i | −0.0794744 | + | 0.891783i | ||||
\(189\) | −5.86567e17 | −0.360266 | ||||||||
\(190\) | 4.74800e17 | + | 2.11149e16i | 0.279565 | + | 0.0124326i | ||||
\(191\) | − | 2.42860e18i | − | 1.37116i | −0.727996 | − | 0.685582i | \(-0.759548\pi\) | ||
0.727996 | − | 0.685582i | \(-0.240452\pi\) | |||||||
\(192\) | 2.80953e17 | − | 1.02854e18i | 0.152133 | − | 0.556946i | ||||
\(193\) | −2.42269e18 | −1.25846 | −0.629230 | − | 0.777219i | \(-0.716630\pi\) | ||||
−0.629230 | + | 0.777219i | \(0.716630\pi\) | |||||||
\(194\) | 9.49434e16 | − | 2.13494e18i | 0.0473207 | − | 1.06408i | ||||
\(195\) | − | 3.04279e17i | − | 0.145544i | ||||||
\(196\) | 5.43287e18 | + | 4.84170e17i | 2.49448 | + | 0.222305i | ||||
\(197\) | 3.03655e18 | 1.33860 | 0.669300 | − | 0.742992i | \(-0.266594\pi\) | ||||
0.669300 | + | 0.742992i | \(0.266594\pi\) | |||||||
\(198\) | −1.13301e18 | − | 5.03861e16i | −0.479635 | − | 0.0213299i | ||||
\(199\) | 2.93148e18i | 1.19196i | 0.802998 | + | 0.595981i | \(0.203237\pi\) | ||||
−0.802998 | + | 0.595981i | \(0.796763\pi\) | |||||||
\(200\) | 3.23581e17 | − | 2.41260e18i | 0.126399 | − | 0.942422i | ||||
\(201\) | 9.75241e17 | 0.366052 | ||||||||
\(202\) | −2.30538e16 | + | 5.18398e17i | −0.00831632 | + | 0.187005i | ||||
\(203\) | − | 6.98166e17i | − | 0.242098i | ||||||
\(204\) | 2.31357e16 | − | 2.59606e17i | 0.00771331 | − | 0.0865511i | ||||
\(205\) | −1.04968e18 | −0.336531 | ||||||||
\(206\) | −2.67712e18 | − | 1.19055e17i | −0.825526 | − | 0.0367121i | ||||
\(207\) | − | 1.15294e18i | − | 0.342015i | ||||||
\(208\) | −3.92148e18 | − | 7.04549e17i | −1.11929 | − | 0.201097i | ||||
\(209\) | −6.61955e18 | −1.81827 | ||||||||
\(210\) | 4.02590e16 | − | 9.05282e17i | 0.0106441 | − | 0.239348i | ||||
\(211\) | − | 4.81806e18i | − | 1.22634i | −0.789950 | − | 0.613172i | \(-0.789893\pi\) | ||
0.789950 | − | 0.613172i | \(-0.210107\pi\) | |||||||
\(212\) | −8.98250e17 | − | 8.00508e16i | −0.220146 | − | 0.0196191i | ||||
\(213\) | 1.53613e18 | 0.362568 | ||||||||
\(214\) | −2.13388e18 | − | 9.48962e16i | −0.485132 | − | 0.0215744i | ||||
\(215\) | 1.97960e17i | 0.0433580i | ||||||||
\(216\) | 9.03809e17 | + | 1.21220e17i | 0.190742 | + | 0.0255826i | ||||
\(217\) | 1.08396e19 | 2.20464 | ||||||||
\(218\) | −2.56350e17 | + | 5.76442e18i | −0.0502553 | + | 1.13006i | ||||
\(219\) | − | 1.11621e18i | − | 0.210956i | ||||||
\(220\) | 1.55528e17 | − | 1.74517e18i | 0.0283417 | − | 0.318022i | ||||
\(221\) | −9.73938e17 | −0.171156 | ||||||||
\(222\) | 1.16367e18 | + | 5.17496e16i | 0.197245 | + | 0.00877169i | ||||
\(223\) | − | 4.28116e18i | − | 0.700039i | −0.936742 | − | 0.350020i | \(-0.886175\pi\) | ||
0.936742 | − | 0.350020i | \(-0.113825\pi\) | |||||||
\(224\) | −1.15738e19 | − | 2.61500e18i | −1.82597 | − | 0.412560i | ||||
\(225\) | 2.08188e18 | 0.316954 | ||||||||
\(226\) | −4.50948e17 | + | 1.01402e19i | −0.0662611 | + | 1.48998i | ||||
\(227\) | 7.61610e18i | 1.08025i | 0.841583 | + | 0.540127i | \(0.181624\pi\) | ||||
−0.841583 | + | 0.540127i | \(0.818376\pi\) | |||||||
\(228\) | 5.30148e18 | + | 4.72460e17i | 0.725970 | + | 0.0646974i | ||||
\(229\) | 5.72737e18 | 0.757307 | 0.378653 | − | 0.925539i | \(-0.376387\pi\) | ||||
0.378653 | + | 0.925539i | \(0.376387\pi\) | |||||||
\(230\) | 1.77940e18 | + | 7.91321e16i | 0.227223 | + | 0.0101049i | ||||
\(231\) | 1.26212e19i | 1.55670i | ||||||||
\(232\) | −1.44283e17 | + | 1.07577e18i | −0.0171914 | + | 0.128178i | ||||
\(233\) | 9.31720e18 | 1.07260 | 0.536300 | − | 0.844027i | \(-0.319822\pi\) | ||||
0.536300 | + | 0.844027i | \(0.319822\pi\) | |||||||
\(234\) | 1.51390e17 | − | 3.40423e18i | 0.0168411 | − | 0.378697i | ||||
\(235\) | − | 1.84601e18i | − | 0.198468i | ||||||
\(236\) | 1.04051e18 | − | 1.16756e19i | 0.108131 | − | 1.21334i | ||||
\(237\) | 6.86266e17 | 0.0689454 | ||||||||
\(238\) | −2.89763e18 | − | 1.28861e17i | −0.281467 | − | 0.0125172i | ||||
\(239\) | 1.10615e19i | 1.03903i | 0.854460 | + | 0.519517i | \(0.173888\pi\) | ||||
−0.854460 | + | 0.519517i | \(0.826112\pi\) | |||||||
\(240\) | −2.49119e17 | + | 1.38658e18i | −0.0226317 | + | 0.125966i | ||||
\(241\) | −3.38785e18 | −0.297707 | −0.148853 | − | 0.988859i | \(-0.547558\pi\) | ||||
−0.148853 | + | 0.988859i | \(0.547558\pi\) | |||||||
\(242\) | −5.61559e17 | + | 1.26275e19i | −0.0477389 | + | 1.07348i | ||||
\(243\) | 7.79915e17i | 0.0641500i | ||||||||
\(244\) | 3.60126e18 | + | 3.20939e17i | 0.286639 | + | 0.0255449i | ||||
\(245\) | −7.20679e18 | −0.555153 | ||||||||
\(246\) | −1.17436e19 | − | 5.22252e17i | −0.875631 | − | 0.0389403i | ||||
\(247\) | − | 1.98891e19i | − | 1.43562i | ||||||
\(248\) | −1.67022e19 | − | 2.24012e18i | −1.16724 | − | 0.156552i | ||||
\(249\) | 5.26934e18 | 0.356583 | ||||||||
\(250\) | −2.93164e17 | + | 6.59222e18i | −0.0192128 | + | 0.432028i | ||||
\(251\) | − | 8.87067e18i | − | 0.563076i | −0.959550 | − | 0.281538i | \(-0.909156\pi\) | ||
0.959550 | − | 0.281538i | \(-0.0908445\pi\) | |||||||
\(252\) | 9.00821e17 | − | 1.01081e19i | 0.0553904 | − | 0.621536i | ||||
\(253\) | −2.48080e19 | −1.47784 | ||||||||
\(254\) | 2.43198e19 | + | 1.08153e18i | 1.40375 | + | 0.0624264i | ||||
\(255\) | 3.44371e17i | 0.0192622i | ||||||||
\(256\) | 1.72931e19 | + | 6.42116e18i | 0.937460 | + | 0.348092i | ||||
\(257\) | −2.60354e18 | −0.136804 | −0.0684021 | − | 0.997658i | \(-0.521790\pi\) | ||||
−0.0684021 | + | 0.997658i | \(0.521790\pi\) | |||||||
\(258\) | −9.84920e16 | + | 2.21474e18i | −0.00501699 | + | 0.112815i | ||||
\(259\) | − | 1.29628e19i | − | 0.640176i | ||||||
\(260\) | 5.24355e18 | + | 4.67298e17i | 0.251095 | + | 0.0223773i | ||||
\(261\) | −9.28300e17 | −0.0431086 | ||||||||
\(262\) | 3.59897e18 | + | 1.60050e17i | 0.162094 | + | 0.00720852i | ||||
\(263\) | 1.18064e19i | 0.515788i | 0.966173 | + | 0.257894i | \(0.0830285\pi\) | ||||
−0.966173 | + | 0.257894i | \(0.916971\pi\) | |||||||
\(264\) | 2.60830e18 | − | 1.94473e19i | 0.110542 | − | 0.824193i | ||||
\(265\) | 1.19154e18 | 0.0489939 | ||||||||
\(266\) | 2.63151e18 | − | 5.91733e19i | 0.104991 | − | 2.36087i | ||||
\(267\) | 1.43243e19i | 0.554605i | ||||||||
\(268\) | −1.49773e18 | + | 1.68060e19i | −0.0562800 | + | 0.631519i | ||||
\(269\) | −1.50417e19 | −0.548628 | −0.274314 | − | 0.961640i | \(-0.588451\pi\) | ||||
−0.274314 | + | 0.961640i | \(0.588451\pi\) | |||||||
\(270\) | −1.20369e18 | − | 5.35293e16i | −0.0426190 | − | 0.00189532i | ||||
\(271\) | − | 1.48927e19i | − | 0.511941i | −0.966685 | − | 0.255970i | \(-0.917605\pi\) | ||
0.966685 | − | 0.255970i | \(-0.0823950\pi\) | |||||||
\(272\) | 4.43817e18 | + | 7.97380e17i | 0.148133 | + | 0.0266142i | ||||
\(273\) | −3.79217e19 | −1.22910 | ||||||||
\(274\) | −2.02199e18 | + | 4.54674e19i | −0.0636465 | + | 1.43118i | ||||
\(275\) | − | 4.47960e19i | − | 1.36955i | ||||||
\(276\) | 1.98683e19 | + | 1.77063e18i | 0.590049 | + | 0.0525843i | ||||
\(277\) | 5.25867e18 | 0.151718 | 0.0758592 | − | 0.997119i | \(-0.475830\pi\) | ||||
0.0758592 | + | 0.997119i | \(0.475830\pi\) | |||||||
\(278\) | 5.64521e19 | + | 2.51049e18i | 1.58242 | + | 0.0703720i | ||||
\(279\) | − | 1.44127e19i | − | 0.392564i | ||||||
\(280\) | 1.55386e19 | + | 2.08406e18i | 0.411290 | + | 0.0551627i | ||||
\(281\) | 2.72271e19 | 0.700409 | 0.350204 | − | 0.936673i | \(-0.386112\pi\) | ||||
0.350204 | + | 0.936673i | \(0.386112\pi\) | |||||||
\(282\) | 9.18456e17 | − | 2.06529e19i | 0.0229650 | − | 0.516401i | ||||
\(283\) | 2.29628e19i | 0.558128i | 0.960273 | + | 0.279064i | \(0.0900241\pi\) | ||||
−0.960273 | + | 0.279064i | \(0.909976\pi\) | |||||||
\(284\) | −2.35911e18 | + | 2.64716e19i | −0.0557444 | + | 0.625508i | ||||
\(285\) | −7.03249e18 | −0.161566 | ||||||||
\(286\) | −7.32491e19 | − | 3.25747e18i | −1.63634 | − | 0.0727700i | ||||
\(287\) | 1.30819e20i | 2.84195i | ||||||||
\(288\) | −3.47697e18 | + | 1.53889e19i | −0.0734618 | + | 0.325138i | ||||
\(289\) | −4.75589e19 | −0.977348 | ||||||||
\(290\) | 6.37138e16 | − | 1.43270e18i | 0.00127365 | − | 0.0286399i | ||||
\(291\) | 3.16217e19i | 0.614951i | ||||||||
\(292\) | 1.92353e19 | + | 1.71422e18i | 0.363945 | + | 0.0324342i | ||||
\(293\) | 4.58027e19 | 0.843239 | 0.421619 | − | 0.906773i | \(-0.361462\pi\) | ||||
0.421619 | + | 0.906773i | \(0.361462\pi\) | |||||||
\(294\) | −8.06283e19 | − | 3.58564e18i | −1.44447 | − | 0.0642373i | ||||
\(295\) | 1.54879e19i | 0.270032i | ||||||||
\(296\) | −2.67889e18 | + | 1.99736e19i | −0.0454591 | + | 0.338940i | ||||
\(297\) | 1.67815e19 | 0.277191 | ||||||||
\(298\) | 3.89193e18 | − | 8.75158e19i | 0.0625799 | − | 1.40720i | ||||
\(299\) | − | 7.45380e19i | − | 1.16683i | ||||||
\(300\) | −3.19725e18 | + | 3.58764e19i | −0.0487312 | + | 0.546813i | ||||
\(301\) | 2.46713e19 | 0.366150 | ||||||||
\(302\) | 9.25585e19 | + | 4.11619e18i | 1.33771 | + | 0.0594894i | ||||
\(303\) | − | 7.67824e18i | − | 0.108074i | ||||||
\(304\) | −1.62835e19 | + | 9.06331e19i | −0.223234 | + | 1.24251i | ||||
\(305\) | −4.77712e18 | −0.0637922 | ||||||||
\(306\) | −1.71337e17 | + | 3.85276e18i | −0.00222884 | + | 0.0501188i | ||||
\(307\) | − | 7.08212e19i | − | 0.897545i | −0.893646 | − | 0.448773i | \(-0.851861\pi\) | ||
0.893646 | − | 0.448773i | \(-0.148139\pi\) | |||||||
\(308\) | −2.17497e20 | − | 1.93831e19i | −2.68564 | − | 0.239341i | ||||
\(309\) | 3.96522e19 | 0.477089 | ||||||||
\(310\) | 2.22439e19 | + | 9.89212e17i | 0.260806 | + | 0.0115983i | ||||
\(311\) | − | 6.64720e19i | − | 0.759549i | −0.925079 | − | 0.379774i | \(-0.876002\pi\) | ||
0.925079 | − | 0.379774i | \(-0.123998\pi\) | |||||||
\(312\) | 5.84315e19 | + | 7.83690e18i | 0.650744 | + | 0.0872786i | ||||
\(313\) | 2.79684e19 | 0.303608 | 0.151804 | − | 0.988411i | \(-0.451492\pi\) | ||||
0.151804 | + | 0.988411i | \(0.451492\pi\) | |||||||
\(314\) | −2.18900e18 | + | 4.92229e19i | −0.0231638 | + | 0.520871i | ||||
\(315\) | 1.34086e19i | 0.138324i | ||||||||
\(316\) | −1.05393e18 | + | 1.18262e19i | −0.0106003 | + | 0.118946i | ||||
\(317\) | 1.53397e20 | 1.50433 | 0.752165 | − | 0.658975i | \(-0.229010\pi\) | ||||
0.752165 | + | 0.658975i | \(0.229010\pi\) | |||||||
\(318\) | 1.33308e19 | + | 5.92835e17i | 0.127479 | + | 0.00566914i | ||||
\(319\) | 1.99743e19i | 0.186272i | ||||||||
\(320\) | −2.35119e19 | − | 6.42242e18i | −0.213840 | − | 0.0584116i | ||||
\(321\) | 3.16060e19 | 0.280368 | ||||||||
\(322\) | 9.86207e18 | − | 2.21763e20i | 0.0853338 | − | 1.91886i | ||||
\(323\) | 2.25096e19i | 0.189998i | ||||||||
\(324\) | −1.34400e19 | − | 1.19776e18i | −0.110672 | − | 0.00986298i | ||||
\(325\) | 1.34594e20 | 1.08133 | ||||||||
\(326\) | −7.74977e19 | − | 3.44641e18i | −0.607502 | − | 0.0270163i | ||||
\(327\) | − | 8.53795e19i | − | 0.653088i | ||||||
\(328\) | 2.70351e19 | − | 2.01572e20i | 0.201807 | − | 1.50466i | ||||
\(329\) | −2.30064e20 | −1.67603 | ||||||||
\(330\) | −1.15180e18 | + | 2.58998e19i | −0.00818963 | + | 0.184156i | ||||
\(331\) | 2.20271e19i | 0.152874i | 0.997074 | + | 0.0764371i | \(0.0243544\pi\) | ||||
−0.997074 | + | 0.0764371i | \(0.975646\pi\) | |||||||
\(332\) | −8.09239e18 | + | 9.08047e19i | −0.0548242 | + | 0.615182i | ||||
\(333\) | −1.72356e19 | −0.113992 | ||||||||
\(334\) | −2.36686e20 | − | 1.05257e19i | −1.52827 | − | 0.0679641i | ||||
\(335\) | − | 2.22934e19i | − | 0.140546i | ||||||
\(336\) | 1.72806e20 | + | 3.10471e19i | 1.06377 | + | 0.191120i | ||||
\(337\) | 1.11783e20 | 0.671948 | 0.335974 | − | 0.941871i | \(-0.390935\pi\) | ||||
0.335974 | + | 0.941871i | \(0.390935\pi\) | |||||||
\(338\) | 2.21936e18 | − | 4.99057e19i | 0.0130285 | − | 0.292965i | ||||
\(339\) | − | 1.50192e20i | − | 0.861090i | ||||||
\(340\) | −5.93443e18 | − | 5.28868e17i | −0.0332313 | − | 0.00296153i | ||||
\(341\) | −3.10119e20 | −1.69626 | ||||||||
\(342\) | −7.86784e19 | − | 3.49892e18i | −0.420384 | − | 0.0186950i | ||||
\(343\) | 5.39527e20i | 2.81618i | ||||||||
\(344\) | −3.80146e19 | − | 5.09857e18i | −0.193858 | − | 0.0260005i | ||||
\(345\) | −2.63556e19 | −0.131317 | ||||||||
\(346\) | −1.46100e19 | + | 3.28528e20i | −0.0711282 | + | 1.59942i | ||||
\(347\) | − | 2.52380e20i | − | 1.20066i | −0.799754 | − | 0.600328i | \(-0.795037\pi\) | ||
0.799754 | − | 0.600328i | \(-0.204963\pi\) | |||||||
\(348\) | 1.42564e18 | − | 1.59971e19i | 0.00662789 | − | 0.0743716i | ||||
\(349\) | −1.31132e20 | −0.595805 | −0.297903 | − | 0.954596i | \(-0.596287\pi\) | ||||
−0.297903 | + | 0.954596i | \(0.596287\pi\) | |||||||
\(350\) | 4.00440e20 | + | 1.78080e19i | 1.77825 | + | 0.0790809i | ||||
\(351\) | 5.04217e19i | 0.218857i | ||||||||
\(352\) | 3.31124e20 | + | 7.48143e19i | 1.40491 | + | 0.317427i | ||||
\(353\) | 1.27633e20 | 0.529379 | 0.264690 | − | 0.964334i | \(-0.414731\pi\) | ||||
0.264690 | + | 0.964334i | \(0.414731\pi\) | |||||||
\(354\) | −7.70578e18 | + | 1.73276e20i | −0.0312457 | + | 0.702606i | ||||
\(355\) | − | 3.51149e19i | − | 0.139208i | ||||||
\(356\) | −2.46846e20 | − | 2.19986e19i | −0.956811 | − | 0.0852697i | ||||
\(357\) | 4.29182e19 | 0.162666 | ||||||||
\(358\) | 3.88557e20 | + | 1.72796e19i | 1.44009 | + | 0.0640426i | ||||
\(359\) | 2.34814e20i | 0.851075i | 0.904941 | + | 0.425537i | \(0.139915\pi\) | ||||
−0.904941 | + | 0.425537i | \(0.860085\pi\) | |||||||
\(360\) | 2.77102e18 | − | 2.06605e19i | 0.00982244 | − | 0.0732355i | ||||
\(361\) | −1.71234e20 | −0.593653 | ||||||||
\(362\) | −5.91448e18 | + | 1.32996e20i | −0.0200562 | + | 0.450992i | ||||
\(363\) | − | 1.87032e20i | − | 0.620387i | ||||||
\(364\) | 5.82383e19 | − | 6.53492e20i | 0.188972 | − | 2.12046i | ||||
\(365\) | −2.55159e19 | −0.0809967 | ||||||||
\(366\) | −5.34456e19 | − | 2.37679e18i | −0.165983 | − | 0.00738145i | ||||
\(367\) | 3.65051e20i | 1.10924i | 0.832104 | + | 0.554619i | \(0.187136\pi\) | ||||
−0.832104 | + | 0.554619i | \(0.812864\pi\) | |||||||
\(368\) | −6.10255e19 | + | 3.39665e20i | −0.181438 | + | 1.00988i | ||||
\(369\) | 1.73940e20 | 0.506045 | ||||||||
\(370\) | 1.18297e18 | − | 2.66007e19i | 0.00336789 | − | 0.0757321i | ||||
\(371\) | − | 1.48499e20i | − | 0.413745i | ||||||
\(372\) | 2.48369e20 | + | 2.21343e19i | 0.677257 | + | 0.0603562i | ||||
\(373\) | −4.99356e20 | −1.33272 | −0.666362 | − | 0.745629i | \(-0.732149\pi\) | ||||
−0.666362 | + | 0.745629i | \(0.732149\pi\) | |||||||
\(374\) | 8.29003e19 | + | 3.68667e18i | 0.216562 | + | 0.00963079i | ||||
\(375\) | − | 9.76405e19i | − | 0.249678i | ||||||
\(376\) | 3.54493e20 | + | 4.75451e19i | 0.887371 | + | 0.119015i | ||||
\(377\) | −6.00148e19 | −0.147071 | ||||||||
\(378\) | −6.67125e18 | + | 1.50013e20i | −0.0160056 | + | 0.359910i | ||||
\(379\) | − | 2.81240e20i | − | 0.660639i | −0.943869 | − | 0.330319i | \(-0.892844\pi\) | ||
0.943869 | − | 0.330319i | \(-0.107156\pi\) | |||||||
\(380\) | 1.08002e19 | − | 1.21189e20i | 0.0248406 | − | 0.278736i | ||||
\(381\) | −3.60212e20 | −0.811256 | ||||||||
\(382\) | −6.21108e20 | − | 2.76214e19i | −1.36981 | − | 0.0609170i | ||||
\(383\) | − | 2.75719e20i | − | 0.595492i | −0.954645 | − | 0.297746i | \(-0.903765\pi\) | ||
0.954645 | − | 0.297746i | \(-0.0962348\pi\) | |||||||
\(384\) | −2.59852e20 | − | 8.35510e19i | −0.549637 | − | 0.176727i | ||||
\(385\) | 2.88514e20 | 0.597696 | ||||||||
\(386\) | −2.75542e19 | + | 6.19597e20i | −0.0559099 | + | 1.25722i | ||||
\(387\) | − | 3.28036e19i | − | 0.0651979i | ||||||
\(388\) | −5.44926e20 | − | 4.85630e19i | −1.06092 | − | 0.0945479i | ||||
\(389\) | −2.91955e20 | −0.556826 | −0.278413 | − | 0.960461i | \(-0.589808\pi\) | ||||
−0.278413 | + | 0.960461i | \(0.589808\pi\) | |||||||
\(390\) | −7.78186e19 | − | 3.46068e18i | −0.145401 | − | 0.00646614i | ||||
\(391\) | 8.43590e19i | 0.154425i | ||||||||
\(392\) | 1.85615e20 | − | 1.38394e21i | 0.332909 | − | 2.48215i | ||||
\(393\) | −5.33060e19 | −0.0936776 | ||||||||
\(394\) | 3.45358e19 | − | 7.76589e20i | 0.0594703 | − | 1.33728i | ||||
\(395\) | − | 1.56876e19i | − | 0.0264716i | ||||||
\(396\) | −2.57722e19 | + | 2.89190e20i | −0.0426177 | + | 0.478214i | ||||
\(397\) | 6.92196e20 | 1.12177 | 0.560886 | − | 0.827893i | \(-0.310460\pi\) | ||||
0.560886 | + | 0.827893i | \(0.310460\pi\) | |||||||
\(398\) | 7.49719e20 | + | 3.33409e19i | 1.19079 | + | 0.0529556i | ||||
\(399\) | 8.76445e20i | 1.36440i | ||||||||
\(400\) | −6.13336e20 | − | 1.10194e20i | −0.935876 | − | 0.168143i | ||||
\(401\) | 1.00851e21 | 1.50844 | 0.754219 | − | 0.656623i | \(-0.228016\pi\) | ||||
0.754219 | + | 0.656623i | \(0.228016\pi\) | |||||||
\(402\) | 1.10918e19 | − | 2.49415e20i | 0.0162627 | − | 0.365691i | ||||
\(403\) | − | 9.31782e20i | − | 1.33929i | ||||||
\(404\) | 1.32317e20 | + | 1.17919e19i | 0.186451 | + | 0.0166162i | ||||
\(405\) | 1.78284e19 | 0.0246304 | ||||||||
\(406\) | −1.78554e20 | − | 7.94051e18i | −0.241859 | − | 0.0107557i | ||||
\(407\) | 3.70861e20i | 0.492556i | ||||||||
\(408\) | −6.61303e19 | − | 8.86948e18i | −0.0861230 | − | 0.0115509i | ||||
\(409\) | −1.90540e20 | −0.243333 | −0.121666 | − | 0.992571i | \(-0.538824\pi\) | ||||
−0.121666 | + | 0.992571i | \(0.538824\pi\) | |||||||
\(410\) | −1.19384e19 | + | 2.68452e20i | −0.0149511 | + | 0.336199i | ||||
\(411\) | − | 6.73440e20i | − | 0.827112i | ||||||
\(412\) | −6.08959e19 | + | 6.83313e20i | −0.0733517 | + | 0.823080i | ||||
\(413\) | 1.93022e21 | 2.28038 | ||||||||
\(414\) | −2.94862e20 | − | 1.31129e19i | −0.341677 | − | 0.0151948i | ||||
\(415\) | − | 1.20454e20i | − | 0.136910i | ||||||
\(416\) | −2.24787e20 | + | 9.94895e20i | −0.250625 | + | 1.10925i | ||||
\(417\) | −8.36139e20 | −0.914513 | ||||||||
\(418\) | −7.52866e19 | + | 1.69293e21i | −0.0807807 | + | 1.81647i | ||||
\(419\) | − | 6.02298e19i | − | 0.0634015i | −0.999497 | − | 0.0317007i | \(-0.989908\pi\) | ||
0.999497 | − | 0.0317007i | \(-0.0100923\pi\) | |||||||
\(420\) | −2.31066e20 | − | 2.05922e19i | −0.238639 | − | 0.0212671i | ||||
\(421\) | 3.25175e20 | 0.329504 | 0.164752 | − | 0.986335i | \(-0.447318\pi\) | ||||
0.164752 | + | 0.986335i | \(0.447318\pi\) | |||||||
\(422\) | −1.23220e21 | − | 5.47976e19i | −1.22513 | − | 0.0544831i | ||||
\(423\) | 3.05899e20i | 0.298439i | ||||||||
\(424\) | −3.06889e19 | + | 2.28814e20i | −0.0293802 | + | 0.219057i | ||||
\(425\) | −1.52328e20 | −0.143109 | ||||||||
\(426\) | 1.74709e19 | − | 3.92860e20i | 0.0161079 | − | 0.362210i | ||||
\(427\) | 5.95362e20i | 0.538714i | ||||||||
\(428\) | −4.85389e19 | + | 5.44655e20i | −0.0431062 | + | 0.483695i | ||||
\(429\) | 1.08493e21 | 0.945676 | ||||||||
\(430\) | 5.06276e19 | + | 2.25147e18i | 0.0433151 | + | 0.00192628i | ||||
\(431\) | 1.23048e21i | 1.03337i | 0.856174 | + | 0.516687i | \(0.172835\pi\) | ||||
−0.856174 | + | 0.516687i | \(0.827165\pi\) | |||||||
\(432\) | 4.12811e19 | − | 2.29768e20i | 0.0340315 | − | 0.189417i | ||||
\(433\) | −1.61953e21 | −1.31065 | −0.655324 | − | 0.755348i | \(-0.727468\pi\) | ||||
−0.655324 | + | 0.755348i | \(0.727468\pi\) | |||||||
\(434\) | 1.23283e20 | − | 2.77221e21i | 0.0979459 | − | 2.20246i | ||||
\(435\) | 2.12204e19i | 0.0165516i | ||||||||
\(436\) | 1.47132e21 | + | 1.31122e20i | 1.12672 | + | 0.100411i | ||||
\(437\) | −1.72272e21 | −1.29528 | ||||||||
\(438\) | −2.85467e20 | − | 1.26951e19i | −0.210748 | − | 0.00937221i | ||||
\(439\) | 7.38096e20i | 0.535053i | 0.963551 | + | 0.267526i | \(0.0862063\pi\) | ||||
−0.963551 | + | 0.267526i | \(0.913794\pi\) | |||||||
\(440\) | −4.44555e20 | − | 5.96243e19i | −0.316449 | − | 0.0424426i | ||||
\(441\) | 1.19422e21 | 0.834790 | ||||||||
\(442\) | −1.10770e19 | + | 2.49082e20i | −0.00760401 | + | 0.170987i | ||||
\(443\) | − | 5.24293e20i | − | 0.353463i | −0.984259 | − | 0.176732i | \(-0.943448\pi\) | ||
0.984259 | − | 0.176732i | \(-0.0565525\pi\) | |||||||
\(444\) | 2.64696e19 | − | 2.97016e20i | 0.0175261 | − | 0.196660i | ||||
\(445\) | 3.27445e20 | 0.212941 | ||||||||
\(446\) | −1.09489e21 | − | 4.86912e19i | −0.699348 | − | 0.0311008i | ||||
\(447\) | 1.29624e21i | 0.813251i | ||||||||
\(448\) | −8.00413e20 | + | 2.93024e21i | −0.493276 | + | 1.80584i | ||||
\(449\) | −3.38302e20 | −0.204802 | −0.102401 | − | 0.994743i | \(-0.532652\pi\) | ||||
−0.102401 | + | 0.994743i | \(0.532652\pi\) | |||||||
\(450\) | 2.36780e19 | − | 5.32435e20i | 0.0140814 | − | 0.316641i | ||||
\(451\) | − | 3.74269e21i | − | 2.18661i | ||||||
\(452\) | 2.58821e21 | + | 2.30657e20i | 1.48556 | + | 0.132391i | ||||
\(453\) | −1.37093e21 | −0.773089 | ||||||||
\(454\) | 1.94780e21 | + | 8.66208e19i | 1.07919 | + | 0.0479927i | ||||
\(455\) | 8.66867e20i | 0.471912i | ||||||||
\(456\) | 1.81126e20 | − | 1.35047e21i | 0.0968863 | − | 0.722378i | ||||
\(457\) | 2.94882e21 | 1.54995 | 0.774976 | − | 0.631991i | \(-0.217762\pi\) | ||||
0.774976 | + | 0.631991i | \(0.217762\pi\) | |||||||
\(458\) | 6.51396e19 | − | 1.46476e21i | 0.0336451 | − | 0.756559i | ||||
\(459\) | − | 5.70651e19i | − | 0.0289647i | ||||||
\(460\) | 4.04756e19 | − | 4.54177e20i | 0.0201898 | − | 0.226549i | ||||
\(461\) | −3.14872e21 | −1.54357 | −0.771785 | − | 0.635883i | \(-0.780636\pi\) | ||||
−0.771785 | + | 0.635883i | \(0.780636\pi\) | |||||||
\(462\) | 3.22784e21 | + | 1.43546e20i | 1.55516 | + | 0.0691600i | ||||
\(463\) | − | 7.56882e20i | − | 0.358410i | −0.983812 | − | 0.179205i | \(-0.942647\pi\) | ||
0.983812 | − | 0.179205i | \(-0.0573526\pi\) | |||||||
\(464\) | 2.73483e20 | + | 4.91351e19i | 0.127288 | + | 0.0228691i | ||||
\(465\) | −3.29465e20 | −0.150725 | ||||||||
\(466\) | 1.05968e20 | − | 2.38285e21i | 0.0476527 | − | 1.07154i | ||||
\(467\) | − | 3.65068e20i | − | 0.161376i | −0.996739 | − | 0.0806880i | \(-0.974288\pi\) | ||
0.996739 | − | 0.0806880i | \(-0.0257117\pi\) | |||||||
\(468\) | −8.68900e20 | − | 7.74351e19i | −0.377575 | − | 0.0336489i | ||||
\(469\) | −2.77838e21 | −1.18689 | ||||||||
\(470\) | −4.72112e20 | − | 2.09954e19i | −0.198272 | − | 0.00881740i | ||||
\(471\) | − | 7.29065e20i | − | 0.301022i | ||||||
\(472\) | −2.97417e21 | − | 3.98900e20i | −1.20734 | − | 0.161930i | ||||
\(473\) | −7.05838e20 | −0.281719 | ||||||||
\(474\) | 7.80516e18 | − | 1.75511e20i | 0.00306306 | − | 0.0688774i | ||||
\(475\) | − | 3.11073e21i | − | 1.20037i | ||||||
\(476\) | −6.59117e19 | + | 7.39595e20i | −0.0250096 | + | 0.280633i | ||||
\(477\) | −1.97449e20 | −0.0736727 | ||||||||
\(478\) | 2.82894e21 | + | 1.25806e20i | 1.03801 | + | 0.0461614i | ||||
\(479\) | 1.16860e21i | 0.421678i | 0.977521 | + | 0.210839i | \(0.0676196\pi\) | ||||
−0.977521 | + | 0.210839i | \(0.932380\pi\) | |||||||
\(480\) | 3.51781e20 | + | 7.94815e19i | 0.124837 | + | 0.0282057i | ||||
\(481\) | −1.11429e21 | −0.388899 | ||||||||
\(482\) | −3.85313e19 | + | 8.66434e20i | −0.0132263 | + | 0.297413i | ||||
\(483\) | 3.28464e21i | 1.10895i | ||||||||
\(484\) | 3.22306e21 | + | 2.87234e20i | 1.07030 | + | 0.0953836i | ||||
\(485\) | 7.22852e20 | 0.236111 | ||||||||
\(486\) | 1.99461e20 | + | 8.87026e18i | 0.0640867 | + | 0.00285001i | ||||
\(487\) | 1.89144e21i | 0.597808i | 0.954283 | + | 0.298904i | \(0.0966210\pi\) | ||||
−0.954283 | + | 0.298904i | \(0.903379\pi\) | |||||||
\(488\) | 1.23038e20 | − | 9.17361e20i | 0.0382542 | − | 0.285221i | ||||
\(489\) | 1.14786e21 | 0.351088 | ||||||||
\(490\) | −8.19655e19 | + | 1.84312e21i | −0.0246639 | + | 0.554605i | ||||
\(491\) | − | 1.22609e21i | − | 0.362969i | −0.983394 | − | 0.181484i | \(-0.941910\pi\) | ||
0.983394 | − | 0.181484i | \(-0.0580902\pi\) | |||||||
\(492\) | −2.67129e20 | + | 2.99746e21i | −0.0778037 | + | 0.873036i | ||||
\(493\) | 6.79223e19 | 0.0194642 | ||||||||
\(494\) | −5.08658e21 | − | 2.26206e20i | −1.43420 | − | 0.0637806i | ||||
\(495\) | − | 3.83615e20i | − | 0.106428i | ||||||
\(496\) | −7.62866e20 | + | 4.24607e21i | −0.208255 | + | 1.15913i | ||||
\(497\) | −4.37630e21 | −1.17559 | ||||||||
\(498\) | 5.99301e19 | − | 1.34762e21i | 0.0158420 | − | 0.356231i | ||||
\(499\) | − | 2.70150e21i | − | 0.702750i | −0.936235 | − | 0.351375i | \(-0.885714\pi\) | ||
0.936235 | − | 0.351375i | \(-0.114286\pi\) | |||||||
\(500\) | 1.68261e21 | + | 1.49952e20i | 0.430747 | + | 0.0383876i | ||||
\(501\) | 3.50567e21 | 0.883221 | ||||||||
\(502\) | −2.26865e21 | − | 1.00889e20i | −0.562520 | − | 0.0250159i | ||||
\(503\) | 5.65754e21i | 1.38065i | 0.723499 | + | 0.690325i | \(0.242532\pi\) | ||||
−0.723499 | + | 0.690325i | \(0.757468\pi\) | |||||||
\(504\) | −2.57488e21 | − | 3.45346e20i | −0.618461 | − | 0.0829488i | ||||
\(505\) | −1.75520e20 | −0.0414950 | ||||||||
\(506\) | −2.82151e20 | + | 6.34458e21i | −0.0656564 | + | 1.47638i | ||||
\(507\) | 7.39177e20i | 0.169311i | ||||||||
\(508\) | 5.53196e20 | − | 6.20741e21i | 0.124730 | − | 1.39959i | ||||
\(509\) | 7.61503e21 | 1.69017 | 0.845083 | − | 0.534635i | \(-0.179551\pi\) | ||||
0.845083 | + | 0.534635i | \(0.179551\pi\) | |||||||
\(510\) | 8.80719e19 | + | 3.91666e18i | 0.0192431 | + | 0.000855765i | ||||
\(511\) | 3.17999e21i | 0.684003i | ||||||||
\(512\) | 1.83888e21 | − | 4.34963e21i | 0.389397 | − | 0.921070i | ||||
\(513\) | 1.16534e21 | 0.242949 | ||||||||
\(514\) | −2.96110e19 | + | 6.65848e20i | −0.00607783 | + | 0.136669i | ||||
\(515\) | − | 9.06425e20i | − | 0.183178i | ||||||
\(516\) | 5.65293e20 | + | 5.03781e19i | 0.112480 | + | 0.0100241i | ||||
\(517\) | 6.58207e21 | 1.28955 | ||||||||
\(518\) | −3.31519e21 | − | 1.47430e20i | −0.639544 | − | 0.0284413i | ||||
\(519\) | − | 4.86598e21i | − | 0.924340i | ||||||
\(520\) | 1.79147e20 | − | 1.33571e21i | 0.0335106 | − | 0.249853i | ||||
\(521\) | 2.49450e21 | 0.459495 | 0.229748 | − | 0.973250i | \(-0.426210\pi\) | ||||
0.229748 | + | 0.973250i | \(0.426210\pi\) | |||||||
\(522\) | −1.05579e19 | + | 2.37410e20i | −0.00191520 | + | 0.0430661i | ||||
\(523\) | 9.64800e21i | 1.72355i | 0.507291 | + | 0.861775i | \(0.330647\pi\) | ||||
−0.507291 | + | 0.861775i | \(0.669353\pi\) | |||||||
\(524\) | 8.18648e19 | − | 9.18605e20i | 0.0144028 | − | 0.161614i | ||||
\(525\) | −5.93111e21 | −1.02769 | ||||||||
\(526\) | 3.01945e21 | + | 1.34279e20i | 0.515279 | + | 0.0229150i | ||||
\(527\) | 1.05455e21i | 0.177249i | ||||||||
\(528\) | −4.94394e21 | − | 8.88248e20i | −0.818468 | − | 0.147049i | ||||
\(529\) | −3.23608e20 | −0.0527684 | ||||||||
\(530\) | 1.35519e19 | − | 3.04734e20i | 0.00217667 | − | 0.0489456i | ||||
\(531\) | − | 2.56647e21i | − | 0.406051i | ||||||
\(532\) | −1.51035e22 | − | 1.34600e21i | −2.35388 | − | 0.209774i | ||||
\(533\) | 1.12453e22 | 1.72644 | ||||||||
\(534\) | 3.66340e21 | + | 1.62916e20i | 0.554057 | + | 0.0246396i | ||||
\(535\) | − | 7.22493e20i | − | 0.107647i | ||||||
\(536\) | 4.28106e21 | + | 5.74181e20i | 0.628395 | + | 0.0842811i | ||||
\(537\) | −5.75510e21 | −0.832259 | ||||||||
\(538\) | −1.71075e20 | + | 3.84687e21i | −0.0243740 | + | 0.548086i | ||||
\(539\) | − | 2.56963e22i | − | 3.60711i | ||||||
\(540\) | −2.73800e19 | + | 3.07231e20i | −0.00378689 | + | 0.0424927i | ||||
\(541\) | −1.85308e20 | −0.0252532 | −0.0126266 | − | 0.999920i | \(-0.504019\pi\) | ||||
−0.0126266 | + | 0.999920i | \(0.504019\pi\) | |||||||
\(542\) | −3.80877e21 | − | 1.69381e20i | −0.511435 | − | 0.0227441i | ||||
\(543\) | − | 1.96986e21i | − | 0.260638i | ||||||
\(544\) | 2.54405e20 | − | 1.12598e21i | 0.0331691 | − | 0.146805i | ||||
\(545\) | −1.95173e21 | −0.250753 | ||||||||
\(546\) | −4.31298e20 | + | 9.69837e21i | −0.0546054 | + | 1.22788i | ||||
\(547\) | 3.32896e21i | 0.415346i | 0.978198 | + | 0.207673i | \(0.0665890\pi\) | ||||
−0.978198 | + | 0.207673i | \(0.933411\pi\) | |||||||
\(548\) | 1.16052e22 | + | 1.03424e21i | 1.42694 | + | 0.127167i | ||||
\(549\) | 7.91609e20 | 0.0959250 | ||||||||
\(550\) | −1.14565e22 | − | 5.09482e20i | −1.36820 | − | 0.0608454i | ||||
\(551\) | 1.38706e21i | 0.163261i | ||||||||
\(552\) | 6.78804e20 | − | 5.06112e21i | 0.0787466 | − | 0.587130i | ||||
\(553\) | −1.95511e21 | −0.223548 | ||||||||
\(554\) | 5.98089e19 | − | 1.34489e21i | 0.00674043 | − | 0.151569i | ||||
\(555\) | 3.93996e20i | 0.0437671i | ||||||||
\(556\) | 1.28410e21 | − | 1.44089e22i | 0.140605 | − | 1.57773i | ||||
\(557\) | −1.43792e22 | −1.55201 | −0.776003 | − | 0.630730i | \(-0.782756\pi\) | ||||
−0.776003 | + | 0.630730i | \(0.782756\pi\) | |||||||
\(558\) | −3.68600e21 | − | 1.63921e20i | −0.392177 | − | 0.0174405i | ||||
\(559\) | − | 2.12076e21i | − | 0.222432i | ||||||
\(560\) | 7.09719e20 | − | 3.95025e21i | 0.0733807 | − | 0.408433i | ||||
\(561\) | −1.22788e21 | −0.125156 | ||||||||
\(562\) | 3.09665e20 | − | 6.96327e21i | 0.0311172 | − | 0.699717i | ||||
\(563\) | 1.86531e22i | 1.84793i | 0.382483 | + | 0.923963i | \(0.375069\pi\) | ||||
−0.382483 | + | 0.923963i | \(0.624931\pi\) | |||||||
\(564\) | −5.27146e21 | − | 4.69785e20i | −0.514871 | − | 0.0458846i | ||||
\(565\) | −3.43329e21 | −0.330616 | ||||||||
\(566\) | 5.87268e21 | + | 2.61165e20i | 0.557577 | + | 0.0247961i | ||||
\(567\) | − | 2.22191e21i | − | 0.208000i | ||||||
\(568\) | 6.74320e21 | + | 9.04406e20i | 0.622414 | + | 0.0834789i | ||||
\(569\) | 1.93429e22 | 1.76045 | 0.880224 | − | 0.474558i | \(-0.157392\pi\) | ||||
0.880224 | + | 0.474558i | \(0.157392\pi\) | |||||||
\(570\) | −7.99832e19 | + | 1.79854e21i | −0.00717794 | + | 0.161407i | ||||
\(571\) | 1.79385e22i | 1.58744i | 0.608281 | + | 0.793721i | \(0.291859\pi\) | ||||
−0.608281 | + | 0.793721i | \(0.708141\pi\) | |||||||
\(572\) | −1.66618e21 | + | 1.86962e22i | −0.145396 | + | 1.63149i | ||||
\(573\) | 9.19953e21 | 0.791642 | ||||||||
\(574\) | 3.34566e22 | + | 1.48785e21i | 2.83914 | + | 0.126260i | ||||
\(575\) | − | 1.16581e22i | − | 0.975626i | ||||||
\(576\) | 3.89612e21 | + | 1.06425e21i | 0.321553 | + | 0.0878342i | ||||
\(577\) | −9.13899e21 | −0.743861 | −0.371930 | − | 0.928261i | \(-0.621304\pi\) | ||||
−0.371930 | + | 0.928261i | \(0.621304\pi\) | |||||||
\(578\) | −5.40906e20 | + | 1.21631e22i | −0.0434209 | + | 0.976383i | ||||
\(579\) | − | 9.17714e21i | − | 0.726572i | ||||||
\(580\) | −3.65684e20 | − | 3.25892e19i | −0.0285550 | − | 0.00254478i | ||||
\(581\) | −1.50119e22 | −1.15618 | ||||||||
\(582\) | 8.08715e21 | + | 3.59645e20i | 0.614344 | + | 0.0273206i | ||||
\(583\) | 4.24852e21i | 0.318339i | ||||||||
\(584\) | 6.57177e20 | − | 4.89987e21i | 0.0485712 | − | 0.362144i | ||||
\(585\) | 1.15261e21 | 0.0840301 | ||||||||
\(586\) | 5.20932e20 | − | 1.17139e22i | 0.0374628 | − | 0.842406i | ||||
\(587\) | 6.18065e21i | 0.438459i | 0.975673 | + | 0.219230i | \(0.0703544\pi\) | ||||
−0.975673 | + | 0.219230i | \(0.929646\pi\) | |||||||
\(588\) | −1.83403e21 | + | 2.05797e22i | −0.128348 | + | 1.44019i | ||||
\(589\) | −2.15353e22 | −1.48672 | ||||||||
\(590\) | 3.96098e21 | + | 1.76149e20i | 0.269766 | + | 0.0119968i | ||||
\(591\) | 1.15024e22i | 0.772841i | ||||||||
\(592\) | 5.07773e21 | + | 9.12286e20i | 0.336586 | + | 0.0604724i | ||||
\(593\) | −1.54453e22 | −1.01009 | −0.505045 | − | 0.863093i | \(-0.668524\pi\) | ||||
−0.505045 | + | 0.863093i | \(0.668524\pi\) | |||||||
\(594\) | 1.90862e20 | − | 4.29182e21i | 0.0123148 | − | 0.276917i | ||||
\(595\) | − | 9.81084e20i | − | 0.0624555i | ||||||
\(596\) | −2.23377e22 | − | 1.99070e21i | −1.40303 | − | 0.125036i | ||||
\(597\) | −1.11044e22 | −0.688180 | ||||||||
\(598\) | −1.90629e22 | − | 8.47749e20i | −1.16568 | − | 0.0518392i | ||||
\(599\) | − | 2.88339e21i | − | 0.173976i | −0.996209 | − | 0.0869880i | \(-0.972276\pi\) | ||
0.996209 | − | 0.0869880i | \(-0.0277242\pi\) | |||||||
\(600\) | 9.13892e21 | + | 1.22572e21i | 0.544108 | + | 0.0729764i | ||||
\(601\) | 3.09120e22 | 1.81607 | 0.908033 | − | 0.418899i | \(-0.137584\pi\) | ||||
0.908033 | + | 0.418899i | \(0.137584\pi\) | |||||||
\(602\) | 2.80596e20 | − | 6.30961e21i | 0.0162671 | − | 0.365789i | ||||
\(603\) | 3.69421e21i | 0.211340i | ||||||||
\(604\) | 2.10541e21 | − | 2.36248e22i | 0.118861 | − | 1.33374i | ||||
\(605\) | −4.27544e21 | −0.238198 | ||||||||
\(606\) | −1.96369e21 | − | 8.73276e19i | −0.107967 | − | 0.00480143i | ||||
\(607\) | − | 5.21560e21i | − | 0.283005i | −0.989938 | − | 0.141503i | \(-0.954807\pi\) | ||
0.989938 | − | 0.141503i | \(-0.0451934\pi\) | |||||||
\(608\) | 2.29940e22 | + | 5.19527e21i | 1.23136 | + | 0.278214i | ||||
\(609\) | 2.64465e21 | 0.139775 | ||||||||
\(610\) | −5.43320e19 | + | 1.22174e21i | −0.00283411 | + | 0.0637292i | ||||
\(611\) | 1.97765e22i | 1.01817i | ||||||||
\(612\) | 9.83385e20 | + | 8.76379e19i | 0.0499703 | + | 0.00445328i | ||||
\(613\) | −1.12100e22 | −0.562239 | −0.281119 | − | 0.959673i | \(-0.590706\pi\) | ||||
−0.281119 | + | 0.959673i | \(0.590706\pi\) | |||||||
\(614\) | −1.81123e22 | − | 8.05476e20i | −0.896659 | − | 0.0398755i | ||||
\(615\) | − | 3.97617e21i | − | 0.194296i | ||||||
\(616\) | −7.43084e21 | + | 5.54039e22i | −0.358420 | + | 2.67236i | ||||
\(617\) | −7.59471e21 | −0.361601 | −0.180801 | − | 0.983520i | \(-0.557869\pi\) | ||||
−0.180801 | + | 0.983520i | \(0.557869\pi\) | |||||||
\(618\) | 4.50979e20 | − | 1.01409e22i | 0.0211957 | − | 0.476617i | ||||
\(619\) | − | 1.37221e22i | − | 0.636642i | −0.947983 | − | 0.318321i | \(-0.896881\pi\) | ||
0.947983 | − | 0.318321i | \(-0.103119\pi\) | |||||||
\(620\) | 5.05976e20 | − | 5.67756e21i | 0.0231738 | − | 0.260033i | ||||
\(621\) | 4.36734e21 | 0.197462 | ||||||||
\(622\) | −1.70000e22 | − | 7.56011e20i | −0.758799 | − | 0.0337447i | ||||
\(623\) | − | 4.08088e22i | − | 1.79825i | ||||||
\(624\) | 2.66883e21 | − | 1.48546e22i | 0.116103 | − | 0.646224i | ||||
\(625\) | 1.99069e22 | 0.854997 | ||||||||
\(626\) | 3.18096e20 | − | 7.15285e21i | 0.0134885 | − | 0.303308i | ||||
\(627\) | − | 2.50748e22i | − | 1.04978i | ||||||
\(628\) | 1.25637e22 | + | 1.11966e21i | 0.519328 | + | 0.0462818i | ||||
\(629\) | 1.26110e21 | 0.0514690 | ||||||||
\(630\) | 3.42920e21 | + | 1.52501e20i | 0.138188 | + | 0.00614536i | ||||
\(631\) | − | 1.18843e22i | − | 0.472865i | −0.971648 | − | 0.236433i | \(-0.924022\pi\) | ||
0.971648 | − | 0.236433i | \(-0.0759782\pi\) | |||||||
\(632\) | 3.01253e21 | + | 4.04044e20i | 0.118357 | + | 0.0158742i | ||||
\(633\) | 1.82508e22 | 0.708030 | ||||||||
\(634\) | 1.74464e21 | − | 3.92309e22i | 0.0668333 | − | 1.50284i | ||||
\(635\) | 8.23423e21i | 0.311482i | ||||||||
\(636\) | 3.03232e20 | − | 3.40257e21i | 0.0113271 | − | 0.127101i | ||||
\(637\) | 7.72069e22 | 2.84800 | ||||||||
\(638\) | 5.10838e21 | + | 2.27176e20i | 0.186088 | + | 0.00827554i | ||||
\(639\) | 5.81884e21i | 0.209329i | ||||||||
\(640\) | −1.90993e21 | + | 5.94006e21i | −0.0678542 | + | 0.211033i | ||||
\(641\) | −1.01345e22 | −0.355582 | −0.177791 | − | 0.984068i | \(-0.556895\pi\) | ||||
−0.177791 | + | 0.984068i | \(0.556895\pi\) | |||||||
\(642\) | 3.59466e20 | − | 8.08313e21i | 0.0124560 | − | 0.280091i | ||||
\(643\) | 1.20343e22i | 0.411845i | 0.978568 | + | 0.205922i | \(0.0660194\pi\) | ||||
−0.978568 | + | 0.205922i | \(0.933981\pi\) | |||||||
\(644\) | −5.66031e22 | − | 5.04439e21i | −1.91317 | − | 0.170499i | ||||
\(645\) | −7.49870e20 | −0.0250327 | ||||||||
\(646\) | 5.75677e21 | + | 2.56010e20i | 0.189810 | + | 0.00844107i | ||||
\(647\) | − | 2.59972e21i | − | 0.0846628i | −0.999104 | − | 0.0423314i | \(-0.986521\pi\) | ||
0.999104 | − | 0.0423314i | \(-0.0134785\pi\) | |||||||
\(648\) | −4.59181e20 | + | 3.42362e21i | −0.0147701 | + | 0.110125i | ||||
\(649\) | −5.52230e22 | −1.75454 | ||||||||
\(650\) | 1.53079e21 | − | 3.44221e22i | 0.0480406 | − | 1.08026i | ||||
\(651\) | 4.10605e22i | 1.27285i | ||||||||
\(652\) | −1.76282e21 | + | 1.97806e22i | −0.0539793 | + | 0.605702i | ||||
\(653\) | 4.59610e22 | 1.39022 | 0.695111 | − | 0.718903i | \(-0.255355\pi\) | ||||
0.695111 | + | 0.718903i | \(0.255355\pi\) | |||||||
\(654\) | −2.18356e22 | − | 9.71054e20i | −0.652443 | − | 0.0290149i | ||||
\(655\) | 1.21854e21i | 0.0359675i | ||||||||
\(656\) | −5.12440e22 | − | 9.20670e21i | −1.49421 | − | 0.268456i | ||||
\(657\) | 4.22819e21 | 0.121796 | ||||||||
\(658\) | −2.61661e21 | + | 5.88383e22i | −0.0744614 | + | 1.67438i | ||||
\(659\) | 4.92808e22i | 1.38546i | 0.721196 | + | 0.692731i | \(0.243593\pi\) | ||||
−0.721196 | + | 0.692731i | \(0.756407\pi\) | |||||||
\(660\) | 6.61071e21 | + | 5.89137e20i | 0.183610 | + | 0.0163631i | ||||
\(661\) | −5.05160e22 | −1.38617 | −0.693086 | − | 0.720855i | \(-0.743749\pi\) | ||||
−0.693086 | + | 0.720855i | \(0.743749\pi\) | |||||||
\(662\) | 5.63338e21 | + | 2.50523e20i | 0.152723 | + | 0.00679178i | ||||
\(663\) | − | 3.68927e21i | − | 0.0988172i | ||||||
\(664\) | 2.31310e22 | + | 3.10236e21i | 0.612139 | + | 0.0821009i | ||||
\(665\) | 2.00350e22 | 0.523861 | ||||||||
\(666\) | −1.96027e20 | + | 4.40797e21i | −0.00506434 | + | 0.113879i | ||||
\(667\) | 5.19827e21i | 0.132694i | ||||||||
\(668\) | −5.38384e21 | + | 6.04121e22i | −0.135794 | + | 1.52374i | ||||
\(669\) | 1.62170e22 | 0.404168 | ||||||||
\(670\) | −5.70148e21 | − | 2.53551e20i | −0.140407 | − | 0.00624407i | ||||
\(671\) | − | 1.70331e22i | − | 0.414490i | ||||||
\(672\) | 9.90561e21 | − | 4.38417e22i | 0.238192 | − | 1.05422i | ||||
\(673\) | 3.85828e22 | 0.916797 | 0.458398 | − | 0.888747i | \(-0.348423\pi\) | ||||
0.458398 | + | 0.888747i | \(0.348423\pi\) | |||||||
\(674\) | 1.27135e21 | − | 2.85881e22i | 0.0298528 | − | 0.671284i | ||||
\(675\) | 7.88615e21i | 0.182993i | ||||||||
\(676\) | −1.27380e22 | − | 1.13519e21i | −0.292097 | − | 0.0260313i | ||||
\(677\) | 1.69357e21 | 0.0383790 | 0.0191895 | − | 0.999816i | \(-0.493891\pi\) | ||||
0.0191895 | + | 0.999816i | \(0.493891\pi\) | |||||||
\(678\) | −3.84111e22 | − | 1.70819e21i | −0.860240 | − | 0.0382559i | ||||
\(679\) | − | 9.00875e22i | − | 1.99391i | ||||||
\(680\) | −2.02751e20 | + | 1.51170e21i | −0.00443498 | + | 0.0330669i | ||||
\(681\) | −2.88498e22 | −0.623685 | ||||||||
\(682\) | −3.52710e21 | + | 7.93120e22i | −0.0753603 | + | 1.69459i | ||||
\(683\) | 5.11935e22i | 1.08106i | 0.841326 | + | 0.540529i | \(0.181776\pi\) | ||||
−0.841326 | + | 0.540529i | \(0.818224\pi\) | |||||||
\(684\) | −1.78968e21 | + | 2.00820e22i | −0.0373530 | + | 0.419139i | ||||
\(685\) | −1.53944e22 | −0.317570 | ||||||||
\(686\) | 1.37982e23 | + | 6.13624e21i | 2.81340 | + | 0.125115i | ||||
\(687\) | 2.16953e22i | 0.437231i | ||||||||
\(688\) | −1.73630e21 | + | 9.66415e21i | −0.0345873 | + | 0.192511i | ||||
\(689\) | −1.27651e22 | −0.251345 | ||||||||
\(690\) | −2.99752e20 | + | 6.74037e21i | −0.00583404 | + | 0.131187i | ||||
\(691\) | − | 5.80131e22i | − | 1.11610i | −0.829809 | − | 0.558048i | \(-0.811551\pi\) | ||
0.829809 | − | 0.558048i | \(-0.188449\pi\) | |||||||
\(692\) | 8.38539e22 | + | 7.47294e21i | 1.59468 | + | 0.142116i | ||||
\(693\) | −4.78091e22 | −0.898762 | ||||||||
\(694\) | −6.45454e22 | − | 2.87041e21i | −1.19947 | − | 0.0533418i | ||||
\(695\) | 1.91136e22i | 0.351127i | ||||||||
\(696\) | −4.07500e21 | − | 5.46544e20i | −0.0740037 | − | 0.00992547i | ||||
\(697\) | −1.27269e22 | −0.228487 | ||||||||
\(698\) | −1.49141e21 | + | 3.35366e22i | −0.0264700 | + | 0.595217i | ||||
\(699\) | 3.52935e22i | 0.619266i | ||||||||
\(700\) | 9.10871e21 | − | 1.02209e23i | 0.158006 | − | 1.77298i | ||||
\(701\) | 4.57259e22 | 0.784184 | 0.392092 | − | 0.919926i | \(-0.371752\pi\) | ||||
0.392092 | + | 0.919926i | \(0.371752\pi\) | |||||||
\(702\) | 1.28952e22 | + | 5.73465e20i | 0.218641 | + | 0.00972321i | ||||
\(703\) | 2.57534e22i | 0.431709i | ||||||||
\(704\) | 2.28996e22 | − | 8.38332e22i | 0.379530 | − | 1.38942i | ||||
\(705\) | 6.99268e21 | 0.114586 | ||||||||
\(706\) | 1.45162e21 | − | 3.26419e22i | 0.0235189 | − | 0.528856i | ||||
\(707\) | 2.18747e22i | 0.350418i | ||||||||
\(708\) | 4.42272e22 | + | 3.94146e21i | 0.700524 | + | 0.0624297i | ||||
\(709\) | 1.97438e21 | 0.0309215 | 0.0154607 | − | 0.999880i | \(-0.495078\pi\) | ||||
0.0154607 | + | 0.999880i | \(0.495078\pi\) | |||||||
\(710\) | −8.98054e21 | − | 3.99375e20i | −0.139071 | − | 0.00618464i | ||||
\(711\) | 2.59957e21i | 0.0398057i | ||||||||
\(712\) | −8.43355e21 | + | 6.28800e22i | −0.127694 | + | 0.952078i | ||||
\(713\) | −8.07076e22 | −1.20837 | ||||||||
\(714\) | 4.88125e20 | − | 1.09762e22i | 0.00722678 | − | 0.162505i | ||||
\(715\) | − | 2.48008e22i | − | 0.363093i | ||||||
\(716\) | 8.83840e21 | − | 9.91758e22i | 0.127959 | − | 1.43582i | ||||
\(717\) | −4.19008e22 | −0.599886 | ||||||||
\(718\) | 6.00529e22 | + | 2.67062e21i | 0.850234 | + | 0.0378109i | ||||
\(719\) | − | 1.09202e23i | − | 1.52897i | −0.644642 | − | 0.764485i | \(-0.722993\pi\) | ||
0.644642 | − | 0.764485i | \(-0.277007\pi\) | |||||||
\(720\) | −5.25236e21 | − | 9.43660e20i | −0.0727268 | − | 0.0130664i | ||||
\(721\) | −1.12966e23 | −1.54691 | ||||||||
\(722\) | −1.94751e21 | + | 4.37926e22i | −0.0263744 | + | 0.593067i | ||||
\(723\) | − | 1.28332e22i | − | 0.171881i | ||||||
\(724\) | 3.39460e22 | + | 3.02522e21i | 0.449656 | + | 0.0400727i | ||||
\(725\) | −9.38656e21 | −0.122971 | ||||||||
\(726\) | −4.78329e22 | − | 2.12718e21i | −0.619774 | − | 0.0275621i | ||||
\(727\) | − | 6.91664e22i | − | 0.886380i | −0.896428 | − | 0.443190i | \(-0.853847\pi\) | ||
0.896428 | − | 0.443190i | \(-0.146153\pi\) | |||||||
\(728\) | −1.66466e23 | − | 2.23267e22i | −2.10997 | − | 0.282992i | ||||
\(729\) | −2.95431e21 | −0.0370370 | ||||||||
\(730\) | −2.90201e20 | + | 6.52561e21i | −0.00359846 | + | 0.0809167i | ||||
\(731\) | 2.40019e21i | 0.0294378i | ||||||||
\(732\) | −1.21571e21 | + | 1.36415e22i | −0.0147483 | + | 0.165491i | ||||
\(733\) | −2.16381e22 | −0.259649 | −0.129825 | − | 0.991537i | \(-0.541441\pi\) | ||||
−0.129825 | + | 0.991537i | \(0.541441\pi\) | |||||||
\(734\) | 9.33608e22 | + | 4.15186e21i | 1.10814 | + | 0.0492804i | ||||
\(735\) | − | 2.72993e22i | − | 0.320518i | ||||||
\(736\) | 8.61742e22 | + | 1.94702e22i | 1.00082 | + | 0.226125i | ||||
\(737\) | 7.94886e22 | 0.913198 | ||||||||
\(738\) | 1.97829e21 | − | 4.44848e22i | 0.0224822 | − | 0.505546i | ||||
\(739\) | 6.07196e22i | 0.682612i | 0.939952 | + | 0.341306i | \(0.110869\pi\) | ||||
−0.939952 | + | 0.341306i | \(0.889131\pi\) | |||||||
\(740\) | −6.78961e21 | − | 6.05080e20i | −0.0755077 | − | 0.00672914i | ||||
\(741\) | 7.53397e22 | 0.828854 | ||||||||
\(742\) | −3.79783e22 | − | 1.68894e21i | −0.413337 | − | 0.0183816i | ||||
\(743\) | 8.98422e22i | 0.967319i | 0.875256 | + | 0.483660i | \(0.160693\pi\) | ||||
−0.875256 | + | 0.483660i | \(0.839307\pi\) | |||||||
\(744\) | 8.48557e21 | − | 6.32679e22i | 0.0903853 | − | 0.673907i | ||||
\(745\) | 2.96312e22 | 0.312248 | ||||||||
\(746\) | −5.67937e21 | + | 1.27709e23i | −0.0592092 | + | 1.33141i | ||||
\(747\) | 1.99602e22i | 0.205873i | ||||||||
\(748\) | 1.88571e21 | − | 2.11596e22i | 0.0192426 | − | 0.215921i | ||||
\(749\) | −9.00428e22 | −0.909064 | ||||||||
\(750\) | −2.49713e22 | − | 1.11050e21i | −0.249431 | − | 0.0110925i | ||||
\(751\) | 8.45223e22i | 0.835318i | 0.908604 | + | 0.417659i | \(0.137149\pi\) | ||||
−0.908604 | + | 0.417659i | \(0.862851\pi\) | |||||||
\(752\) | 1.61913e22 | − | 9.01200e22i | 0.158321 | − | 0.881208i | ||||
\(753\) | 3.36021e22 | 0.325092 | ||||||||
\(754\) | −6.82571e20 | + | 1.53486e22i | −0.00653397 | + | 0.146926i | ||||
\(755\) | 3.13386e22i | 0.296828i | ||||||||
\(756\) | 3.82895e22 | + | 3.41231e21i | 0.358844 | + | 0.0319796i | ||||
\(757\) | 5.06405e21 | 0.0469603 | 0.0234802 | − | 0.999724i | \(-0.492525\pi\) | ||||
0.0234802 | + | 0.999724i | \(0.492525\pi\) | |||||||
\(758\) | −7.19265e22 | − | 3.19865e21i | −0.659986 | − | 0.0293504i | ||||
\(759\) | − | 9.39726e22i | − | 0.853231i | ||||||
\(760\) | −3.08708e22 | − | 4.14044e21i | −0.277357 | − | 0.0371995i | ||||
\(761\) | 2.94175e22 | 0.261534 | 0.130767 | − | 0.991413i | \(-0.458256\pi\) | ||||
0.130767 | + | 0.991413i | \(0.458256\pi\) | |||||||
\(762\) | −4.09683e21 | + | 9.21232e22i | −0.0360419 | + | 0.810455i | ||||
\(763\) | 2.43239e23i | 2.11757i | ||||||||
\(764\) | −1.41282e22 | + | 1.58532e23i | −0.121714 | + | 1.36575i | ||||
\(765\) | −1.30447e21 | −0.0111210 | ||||||||
\(766\) | −7.05143e22 | − | 3.13585e21i | −0.594904 | − | 0.0264561i | ||||
\(767\) | − | 1.65923e23i | − | 1.38530i | ||||||
\(768\) | −2.43233e22 | + | 6.55061e22i | −0.200971 | + | 0.541243i | ||||
\(769\) | 1.97968e23 | 1.61877 | 0.809384 | − | 0.587280i | \(-0.199801\pi\) | ||||
0.809384 | + | 0.587280i | \(0.199801\pi\) | |||||||
\(770\) | 3.28137e21 | − | 7.37865e22i | 0.0265540 | − | 0.597106i | ||||
\(771\) | − | 9.86220e21i | − | 0.0789839i | ||||||
\(772\) | 1.58147e23 | + | 1.40938e22i | 1.25349 | + | 0.111709i | ||||
\(773\) | 6.25457e22 | 0.490638 | 0.245319 | − | 0.969442i | \(-0.421107\pi\) | ||||
0.245319 | + | 0.969442i | \(0.421107\pi\) | |||||||
\(774\) | −8.38942e21 | − | 3.73087e20i | −0.0651335 | − | 0.00289656i | ||||
\(775\) | − | 1.45735e23i | − | 1.11982i | ||||||
\(776\) | −1.86175e22 | + | 1.38811e23i | −0.141588 | + | 1.05567i | ||||
\(777\) | 4.91029e22 | 0.369606 | ||||||||
\(778\) | −3.32052e21 | + | 7.46668e22i | −0.0247383 | + | 0.556276i | ||||
\(779\) | − | 2.59901e23i | − | 1.91649i | ||||||
\(780\) | −1.77012e21 | + | 1.98625e22i | −0.0129195 | + | 0.144970i | ||||
\(781\) | 1.25204e23 | 0.904506 | ||||||||
\(782\) | 2.15746e22 | + | 9.59447e20i | 0.154273 | + | 0.00686068i | ||||
\(783\) | − | 3.51640e21i | − | 0.0248888i | ||||||
\(784\) | −3.51827e23 | − | 6.32106e22i | −2.46490 | − | 0.442855i | ||||
\(785\) | −1.66660e22 | −0.115578 | ||||||||
\(786\) | −6.06269e20 | + | 1.36329e22i | −0.00416184 | + | 0.0935851i | ||||
\(787\) | 2.18866e23i | 1.48724i | 0.668603 | + | 0.743619i | \(0.266893\pi\) | ||||
−0.668603 | + | 0.743619i | \(0.733107\pi\) | |||||||
\(788\) | −1.98218e23 | − | 1.76649e22i | −1.33332 | − | 0.118823i | ||||
\(789\) | −4.47226e22 | −0.297790 | ||||||||
\(790\) | −4.01207e21 | − | 1.78421e20i | −0.0264455 | − | 0.00117606i | ||||
\(791\) | 4.27884e23i | 2.79199i | ||||||||
\(792\) | 7.36665e22 | + | 9.88024e21i | 0.475848 | + | 0.0638214i | ||||
\(793\) | 5.11777e22 | 0.327262 | ||||||||
\(794\) | 7.87260e21 | − | 1.77027e23i | 0.0498373 | − | 1.12067i | ||||
\(795\) | 4.51356e21i | 0.0282867i | ||||||||
\(796\) | 1.70537e22 | − | 1.91359e23i | 0.105807 | − | 1.18726i | ||||
\(797\) | −4.97106e22 | −0.305339 | −0.152669 | − | 0.988277i | \(-0.548787\pi\) | ||||
−0.152669 | + | 0.988277i | \(0.548787\pi\) | |||||||
\(798\) | 2.24148e23 | + | 9.96813e21i | 1.36305 | + | 0.0606165i | ||||
\(799\) | − | 2.23822e22i | − | 0.134750i | ||||||
\(800\) | −3.51576e22 | + | 1.55606e23i | −0.209556 | + | 0.927482i | ||||
\(801\) | −5.42604e22 | −0.320201 | ||||||||
\(802\) | 1.14702e22 | − | 2.57925e23i | 0.0670157 | − | 1.50695i | ||||
\(803\) | − | 9.09784e22i | − | 0.526277i | ||||||
\(804\) | −6.36611e22 | − | 5.67338e21i | −0.364607 | − | 0.0324933i | ||||
\(805\) | 7.50849e22 | 0.425780 | ||||||||
\(806\) | −2.38301e23 | − | 1.05975e22i | −1.33797 | − | 0.0595009i | ||||
\(807\) | − | 5.69778e22i | − | 0.316751i | ||||||
\(808\) | 4.52063e21 | − | 3.37055e22i | 0.0248833 | − | 0.185528i | ||||
\(809\) | −2.58507e23 | −1.40891 | −0.704455 | − | 0.709748i | \(-0.748809\pi\) | ||||
−0.704455 | + | 0.709748i | \(0.748809\pi\) | |||||||
\(810\) | 2.02769e20 | − | 4.55956e21i | 0.00109426 | − | 0.0246061i | ||||
\(811\) | − | 9.75187e22i | − | 0.521100i | −0.965460 | − | 0.260550i | \(-0.916096\pi\) | ||
0.965460 | − | 0.260550i | \(-0.0839039\pi\) | |||||||
\(812\) | −4.06153e21 | + | 4.55744e22i | −0.0214902 | + | 0.241142i | ||||
\(813\) | 5.64136e22 | 0.295569 | ||||||||
\(814\) | 9.48466e22 | + | 4.21794e21i | 0.492070 | + | 0.0218829i | ||||
\(815\) | − | 2.62393e22i | − | 0.134800i | ||||||
\(816\) | −3.02047e21 | + | 1.68118e22i | −0.0153657 | + | 0.0855248i | ||||
\(817\) | −4.90149e22 | −0.246917 | ||||||||
\(818\) | −2.16709e21 | + | 4.87302e22i | −0.0108106 | + | 0.243092i | ||||
\(819\) | − | 1.43647e23i | − | 0.709620i | ||||||
\(820\) | 6.85201e22 | + | 6.10641e21i | 0.335202 | + | 0.0298728i | ||||
\(821\) | 1.80543e23 | 0.874653 | 0.437327 | − | 0.899303i | \(-0.355925\pi\) | ||||
0.437327 | + | 0.899303i | \(0.355925\pi\) | |||||||
\(822\) | −1.72230e23 | − | 7.65928e21i | −0.826295 | − | 0.0367463i | ||||
\(823\) | − | 5.84547e22i | − | 0.277729i | −0.990311 | − | 0.138864i | \(-0.955655\pi\) | ||
0.990311 | − | 0.138864i | \(-0.0443452\pi\) | |||||||
\(824\) | 1.74063e23 | + | 2.33455e22i | 0.819008 | + | 0.109846i | ||||
\(825\) | 1.69687e23 | 0.790710 | ||||||||
\(826\) | 2.19531e22 | − | 4.93648e23i | 0.101311 | − | 2.27812i | ||||
\(827\) | − | 2.70285e23i | − | 1.23532i | −0.786446 | − | 0.617658i | \(-0.788081\pi\) | ||
0.786446 | − | 0.617658i | \(-0.211919\pi\) | |||||||
\(828\) | −6.70715e21 | + | 7.52610e22i | −0.0303596 | + | 0.340665i | ||||
\(829\) | −3.13380e23 | −1.40487 | −0.702433 | − | 0.711749i | \(-0.747903\pi\) | ||||
−0.702433 | + | 0.711749i | \(0.747903\pi\) | |||||||
\(830\) | −3.08057e22 | − | 1.36997e21i | −0.136775 | − | 0.00608255i | ||||
\(831\) | 1.99198e22i | 0.0875946i | ||||||||
\(832\) | 2.51885e23 | + | 6.88040e22i | 1.09702 | + | 0.299659i | ||||
\(833\) | −8.73796e22 | −0.376921 | ||||||||
\(834\) | −9.50972e21 | + | 2.13840e23i | −0.0406293 | + | 0.913610i | ||||
\(835\) | − | 8.01375e22i | − | 0.339113i | ||||||
\(836\) | 4.32106e23 | + | 3.85087e22i | 1.81109 | + | 0.161402i | ||||
\(837\) | 5.45951e22 | 0.226647 | ||||||||
\(838\) | −1.54036e22 | − | 6.85016e20i | −0.0633389 | − | 0.00281675i | ||||
\(839\) | − | 1.22175e23i | − | 0.497608i | −0.968554 | − | 0.248804i | \(-0.919963\pi\) | ||
0.968554 | − | 0.248804i | \(-0.0800375\pi\) | |||||||
\(840\) | −7.89440e21 | + | 5.88602e22i | −0.0318482 | + | 0.237458i | ||||
\(841\) | −2.46061e23 | −0.983275 | ||||||||
\(842\) | 3.69834e21 | − | 8.31627e22i | 0.0146390 | − | 0.329179i | ||||
\(843\) | 1.03136e23i | 0.404381i | ||||||||
\(844\) | −2.80287e22 | + | 3.14510e23i | −0.108859 | + | 1.22150i | ||||
\(845\) | 1.68971e22 | 0.0650069 | ||||||||
\(846\) | 7.82329e22 | + | 3.47911e21i | 0.298144 | + | 0.0132588i | ||||
\(847\) | 5.32838e23i | 2.01154i | ||||||||
\(848\) | 5.81696e22 | + | 1.04510e22i | 0.217535 | + | 0.0390833i | ||||
\(849\) | −8.69830e22 | −0.322235 | ||||||||
\(850\) | −1.73248e21 | + | 3.89574e22i | −0.00635796 | + | 0.142968i | ||||
\(851\) | 9.65156e22i | 0.350882i | ||||||||
\(852\) | −1.00274e23 | − | 8.93629e21i | −0.361137 | − | 0.0321840i | ||||
\(853\) | 1.08159e23 | 0.385896 | 0.192948 | − | 0.981209i | \(-0.438195\pi\) | ||||
0.192948 | + | 0.981209i | \(0.438195\pi\) | |||||||
\(854\) | 1.52262e23 | + | 6.77128e21i | 0.538182 | + | 0.0239336i | ||||
\(855\) | − | 2.66391e22i | − | 0.0932803i | ||||||
\(856\) | 1.38742e23 | + | 1.86083e22i | 0.481302 | + | 0.0645529i | ||||
\(857\) | 2.22560e23 | 0.764894 | 0.382447 | − | 0.923977i | \(-0.375081\pi\) | ||||
0.382447 | + | 0.923977i | \(0.375081\pi\) | |||||||
\(858\) | 1.23393e22 | − | 2.77467e23i | 0.0420138 | − | 0.944743i | ||||
\(859\) | 6.15550e22i | 0.207643i | 0.994596 | + | 0.103822i | \(0.0331071\pi\) | ||||
−0.994596 | + | 0.103822i | \(0.966893\pi\) | |||||||
\(860\) | 1.15161e21 | − | 1.29223e22i | 0.00384875 | − | 0.0431868i | ||||
\(861\) | −4.95542e23 | −1.64080 | ||||||||
\(862\) | 3.14693e23 | + | 1.39947e22i | 1.03235 | + | 0.0459100i | ||||
\(863\) | 3.86238e22i | 0.125536i | 0.998028 | + | 0.0627681i | \(0.0199928\pi\) | ||||
−0.998028 | + | 0.0627681i | \(0.980007\pi\) | |||||||
\(864\) | −5.82930e22 | − | 1.31708e22i | −0.187718 | − | 0.0424132i | ||||
\(865\) | −1.11233e23 | −0.354900 | ||||||||
\(866\) | −1.84195e22 | + | 4.14190e23i | −0.0582285 | + | 1.30935i | ||||
\(867\) | − | 1.80153e23i | − | 0.564272i | ||||||
\(868\) | −7.07582e23 | − | 6.30587e22i | −2.19593 | − | 0.195698i | ||||
\(869\) | 5.59352e22 | 0.171999 | ||||||||
\(870\) | 5.42705e21 | + | 2.41347e20i | 0.0165352 | + | 0.000735341i | ||||
\(871\) | 2.38831e23i | 0.721018i | ||||||||
\(872\) | 5.02679e22 | − | 3.74794e23i | 0.150369 | − | 1.12114i | ||||
\(873\) | −1.19783e23 | −0.355042 | ||||||||
\(874\) | −1.95931e22 | + | 4.40581e23i | −0.0575457 | + | 1.29400i | ||||
\(875\) | 2.78170e23i | 0.809554i | ||||||||
\(876\) | −6.49345e21 | + | 7.28631e22i | −0.0187259 | + | 0.210123i | ||||
\(877\) | −6.96394e23 | −1.99002 | −0.995011 | − | 0.0997617i | \(-0.968192\pi\) | ||||
−0.995011 | + | 0.0997617i | \(0.968192\pi\) | |||||||
\(878\) | 1.88766e23 | + | 8.39465e21i | 0.534525 | + | 0.0237709i | ||||
\(879\) | 1.73501e23i | 0.486844i | ||||||||
\(880\) | −2.03048e22 | + | 1.13016e23i | −0.0564596 | + | 0.314251i | ||||
\(881\) | −3.36202e23 | −0.926388 | −0.463194 | − | 0.886257i | \(-0.653297\pi\) | ||||
−0.463194 | + | 0.886257i | \(0.653297\pi\) | |||||||
\(882\) | 1.35824e22 | − | 3.05420e23i | 0.0370874 | − | 0.833966i | ||||
\(883\) | − | 4.48123e23i | − | 1.21258i | −0.795242 | − | 0.606292i | \(-0.792656\pi\) | ||
0.795242 | − | 0.606292i | \(-0.207344\pi\) | |||||||
\(884\) | 6.35761e22 | + | 5.66581e21i | 0.170481 | + | 0.0151930i | ||||
\(885\) | −5.86680e22 | −0.155903 | ||||||||
\(886\) | −1.34086e23 | − | 5.96298e21i | −0.353114 | − | 0.0157034i | ||||
\(887\) | 6.64749e21i | 0.0173488i | 0.999962 | + | 0.00867439i | \(0.00276118\pi\) | ||||
−0.999962 | + | 0.00867439i | \(0.997239\pi\) | |||||||
\(888\) | −7.56600e22 | − | 1.01476e22i | −0.195687 | − | 0.0262458i | ||||
\(889\) | 1.02621e24 | 2.63041 | ||||||||
\(890\) | 3.72416e21 | − | 8.37432e22i | 0.00946037 | − | 0.212730i | ||||
\(891\) | 6.35682e22i | 0.160036i | ||||||||
\(892\) | −2.49053e22 | + | 2.79462e23i | −0.0621402 | + | 0.697276i | ||||
\(893\) | 4.57073e23 | 1.13025 | ||||||||
\(894\) | 3.31509e23 | + | 1.47426e22i | 0.812448 | + | 0.0361305i | ||||
\(895\) | 1.31558e23i | 0.319546i | ||||||||
\(896\) | 7.40297e23 | + | 2.38030e23i | 1.78214 | + | 0.573017i | ||||
\(897\) | 2.82350e23 | 0.673671 | ||||||||
\(898\) | −3.84764e21 | + | 8.65198e22i | −0.00909878 | + | 0.204600i | ||||
\(899\) | 6.49823e22i | 0.152306i | ||||||||
\(900\) | −1.35900e23 | − | 1.21112e22i | −0.315702 | − | 0.0281349i | ||||
\(901\) | 1.44470e22 | 0.0332644 | ||||||||
\(902\) | −9.57183e23 | − | 4.25670e22i | −2.18445 | − | 0.0971452i | ||||
\(903\) | 9.34547e22i | 0.211397i | ||||||||
\(904\) | 8.84266e22 | − | 6.59303e23i | 0.198260 | − | 1.47822i | ||||
\(905\) | −4.50299e22 | −0.100072 | ||||||||
\(906\) | −1.55921e22 | + | 3.50611e23i | −0.0343462 | + | 0.772325i | ||||
\(907\) | − | 4.63696e23i | − | 1.01245i | −0.862400 | − | 0.506227i | \(-0.831040\pi\) | ||
0.862400 | − | 0.506227i | \(-0.168960\pi\) | |||||||
\(908\) | 4.43061e22 | − | 4.97159e23i | 0.0958907 | − | 1.07599i | ||||
\(909\) | 2.90851e22 | 0.0623965 | ||||||||
\(910\) | 2.21699e23 | + | 9.85921e21i | 0.471446 | + | 0.0209658i | ||||
\(911\) | − | 5.45620e23i | − | 1.15012i | −0.818111 | − | 0.575060i | \(-0.804979\pi\) | ||
0.818111 | − | 0.575060i | \(-0.195021\pi\) | |||||||
\(912\) | −3.43318e23 | − | 6.16819e22i | −0.717361 | − | 0.128884i | ||||
\(913\) | 4.29486e23 | 0.889575 | ||||||||
\(914\) | 3.35380e22 | − | 7.54152e23i | 0.0688601 | − | 1.54842i | ||||
\(915\) | − | 1.80957e22i | − | 0.0368304i | ||||||
\(916\) | −3.73867e23 | − | 3.33185e22i | −0.754317 | − | 0.0672237i | ||||
\(917\) | 1.51864e23 | 0.303740 | ||||||||
\(918\) | −1.45942e22 | − | 6.49023e20i | −0.0289361 | − | 0.00128682i | ||||
\(919\) | 3.81492e23i | 0.749827i | 0.927060 | + | 0.374913i | \(0.122328\pi\) | ||||
−0.927060 | + | 0.374913i | \(0.877672\pi\) | |||||||
\(920\) | −1.15694e23 | − | 1.55171e22i | −0.225429 | − | 0.0302348i | ||||
\(921\) | 2.68270e23 | 0.518198 | ||||||||
\(922\) | −3.58116e22 | + | 8.05276e23i | −0.0685766 | + | 1.54205i | ||||
\(923\) | 3.76189e23i | 0.714155i | ||||||||
\(924\) | 7.34229e22 | − | 8.23879e23i | 0.138183 | − | 1.55056i | ||||
\(925\) | −1.74279e23 | −0.325171 | ||||||||
\(926\) | −1.93571e23 | − | 8.60831e21i | −0.358056 | − | 0.0159232i | ||||
\(927\) | 1.50202e23i | 0.275447i | ||||||||
\(928\) | 1.56766e22 | − | 6.93838e22i | 0.0285015 | − | 0.126146i | ||||
\(929\) | 2.87790e23 | 0.518740 | 0.259370 | − | 0.965778i | \(-0.416485\pi\) | ||||
0.259370 | + | 0.965778i | \(0.416485\pi\) | |||||||
\(930\) | −3.74713e21 | + | 8.42597e22i | −0.00669630 | + | 0.150576i | ||||
\(931\) | − | 1.78440e24i | − | 3.16152i | ||||||
\(932\) | −6.08201e23 | − | 5.42020e22i | −1.06837 | − | 0.0952113i | ||||
\(933\) | 2.51796e23 | 0.438526 | ||||||||
\(934\) | −9.33651e22 | − | 4.15206e21i | −0.161217 | − | 0.00716949i | ||||
\(935\) | 2.80685e22i | 0.0480537i | ||||||||
\(936\) | −2.96862e22 | + | 2.21338e23i | −0.0503903 | + | 0.375707i | ||||
\(937\) | −9.03324e23 | −1.52029 | −0.760146 | − | 0.649753i | \(-0.774872\pi\) | ||||
−0.760146 | + | 0.649753i | \(0.774872\pi\) | |||||||
\(938\) | −3.15996e22 | + | 7.10563e23i | −0.0527301 | + | 1.18571i | ||||
\(939\) | 1.05944e23i | 0.175288i | ||||||||
\(940\) | −1.07390e22 | + | 1.20503e23i | −0.0176174 | + | 0.197685i | ||||
\(941\) | 3.62505e23 | 0.589653 | 0.294826 | − | 0.955551i | \(-0.404738\pi\) | ||||
0.294826 | + | 0.955551i | \(0.404738\pi\) | |||||||
\(942\) | −1.86456e23 | − | 8.29193e21i | −0.300725 | − | 0.0133736i | ||||
\(943\) | − | 9.74026e23i | − | 1.55768i | ||||||
\(944\) | −1.35844e23 | + | 7.56099e23i | −0.215409 | + | 1.19895i | ||||
\(945\) | −5.07916e22 | −0.0798615 | ||||||||
\(946\) | −8.02776e21 | + | 1.80516e23i | −0.0125160 | + | 0.281441i | ||||
\(947\) | 2.76095e23i | 0.426834i | 0.976961 | + | 0.213417i | \(0.0684593\pi\) | ||||
−0.976961 | + | 0.213417i | \(0.931541\pi\) | |||||||
\(948\) | −4.47976e22 | − | 3.99229e21i | −0.0686733 | − | 0.00612006i | ||||
\(949\) | 2.73354e23 | 0.415523 | ||||||||
\(950\) | −7.95561e23 | − | 3.53795e22i | −1.19918 | − | 0.0533290i | ||||
\(951\) | 5.81068e23i | 0.868525i | ||||||||
\(952\) | 1.88400e23 | + | 2.52684e22i | 0.279245 | + | 0.0374526i | ||||
\(953\) | −2.33311e23 | −0.342919 | −0.171459 | − | 0.985191i | \(-0.554848\pi\) | ||||
−0.171459 | + | 0.985191i | \(0.554848\pi\) | |||||||
\(954\) | −2.24566e21 | + | 5.04969e22i | −0.00327308 | + | 0.0736000i | ||||
\(955\) | − | 2.10296e23i | − | 0.303951i | ||||||
\(956\) | 6.43492e22 | − | 7.22063e23i | 0.0922316 | − | 1.03493i | ||||
\(957\) | −7.56626e22 | −0.107544 | ||||||||
\(958\) | 2.98866e23 | + | 1.32909e22i | 0.421262 | + | 0.0187340i | ||||
\(959\) | 1.91857e24i | 2.68182i | ||||||||
\(960\) | 2.43281e22 | − | 8.90630e22i | 0.0337240 | − | 0.123460i | ||||
\(961\) | −2.81483e23 | −0.386960 | ||||||||
\(962\) | −1.26732e22 | + | 2.84976e23i | −0.0172777 | + | 0.388515i | ||||
\(963\) | 1.19723e23i | 0.161871i | ||||||||
\(964\) | 2.21150e23 | + | 1.97086e22i | 0.296531 | + | 0.0264264i | ||||
\(965\) | −2.09784e23 | −0.278968 | ||||||||
\(966\) | 8.40038e23 | + | 3.73575e22i | 1.10785 | + | 0.0492675i | ||||
\(967\) | 1.41945e24i | 1.85656i | 0.371879 | + | 0.928281i | \(0.378714\pi\) | ||||
−0.371879 | + | 0.928281i | \(0.621286\pi\) | |||||||
\(968\) | 1.10116e23 | − | 8.21022e23i | 0.142840 | − | 1.06501i | ||||
\(969\) | −8.52663e22 | −0.109695 | ||||||||
\(970\) | 8.22127e21 | − | 1.84867e23i | 0.0104898 | − | 0.235878i | ||||
\(971\) | − | 1.02803e24i | − | 1.30092i | −0.759539 | − | 0.650462i | \(-0.774575\pi\) | ||
0.759539 | − | 0.650462i | \(-0.225425\pi\) | |||||||
\(972\) | 4.53709e21 | − | 5.09107e22i | 0.00569439 | − | 0.0638968i | ||||
\(973\) | 2.38209e24 | 2.96521 | ||||||||
\(974\) | 4.83731e23 | + | 2.15121e22i | 0.597218 | + | 0.0265590i | ||||
\(975\) | 5.09842e23i | 0.624307i | ||||||||
\(976\) | −2.33213e23 | − | 4.19000e22i | −0.283240 | − | 0.0508880i | ||||
\(977\) | −1.25942e24 | −1.51710 | −0.758549 | − | 0.651615i | \(-0.774092\pi\) | ||||
−0.758549 | + | 0.651615i | \(0.774092\pi\) | |||||||
\(978\) | 1.30550e22 | − | 2.93561e23i | 0.0155979 | − | 0.350742i | ||||
\(979\) | 1.16753e24i | 1.38358i | ||||||||
\(980\) | 4.70439e23 | + | 4.19249e22i | 0.552962 | + | 0.0492792i | ||||
\(981\) | 3.23417e23 | 0.377061 | ||||||||
\(982\) | −3.13568e23 | − | 1.39448e22i | −0.362610 | − | 0.0161257i | ||||
\(983\) | − | 5.44196e23i | − | 0.624205i | −0.950048 | − | 0.312103i | \(-0.898967\pi\) | ||
0.950048 | − | 0.312103i | \(-0.101033\pi\) | |||||||
\(984\) | 7.63553e23 | + | 1.02409e23i | 0.868718 | + | 0.116514i | ||||
\(985\) | 2.62939e23 | 0.296732 | ||||||||
\(986\) | 7.72505e20 | − | 1.73709e22i | 0.000864741 | − | 0.0194450i | ||||
\(987\) | − | 8.71482e23i | − | 0.967656i | ||||||
\(988\) | −1.15703e23 | + | 1.29830e24i | −0.127435 | + | 1.42995i | ||||
\(989\) | −1.83692e23 | −0.200688 | ||||||||
\(990\) | −9.81085e22 | − | 4.36300e21i | −0.106322 | − | 0.00472828i | ||||
\(991\) | − | 1.42399e24i | − | 1.53080i | −0.643553 | − | 0.765401i | \(-0.722541\pi\) | ||
0.643553 | − | 0.765401i | \(-0.277459\pi\) | |||||||
\(992\) | 1.07724e24 | + | 2.43393e23i | 1.14874 | + | 0.259546i | ||||
\(993\) | −8.34387e22 | −0.0882620 | ||||||||
\(994\) | −4.97733e22 | + | 1.11923e24i | −0.0522282 | + | 1.17443i | ||||
\(995\) | 2.53841e23i | 0.264227i | ||||||||
\(996\) | −3.43968e23 | − | 3.06539e22i | −0.355176 | − | 0.0316528i | ||||
\(997\) | −1.83119e24 | −1.87574 | −0.937869 | − | 0.346989i | \(-0.887204\pi\) | ||||
−0.937869 | + | 0.346989i | \(0.887204\pi\) | |||||||
\(998\) | −6.90902e23 | − | 3.07252e22i | −0.702056 | − | 0.0312213i | ||||
\(999\) | − | 6.52885e22i | − | 0.0658132i |
(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 | 12.17.d.a.7.9 | ✓ | 16 | |
3.2 | odd | 2 | 36.17.d.d.19.8 | 16 | |||
4.3 | odd | 2 | inner | 12.17.d.a.7.10 | yes | 16 | |
12.11 | even | 2 | 36.17.d.d.19.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.17.d.a.7.9 | ✓ | 16 | 1.1 | even | 1 | trivial | |
12.17.d.a.7.10 | yes | 16 | 4.3 | odd | 2 | inner | |
36.17.d.d.19.7 | 16 | 12.11 | even | 2 | |||
36.17.d.d.19.8 | 16 | 3.2 | odd | 2 |