Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(16,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.16");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.75560921479\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 122690 x^{10} + 5157152560 x^{8} + 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 16.2 | ||
Root | \(119.947i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.16 |
Dual form | 17.10.b.a.16.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −36.0157 | −1.59168 | −0.795842 | − | 0.605504i | \(-0.792971\pi\) | ||||
−0.795842 | + | 0.605504i | \(0.792971\pi\) | |||||||
\(3\) | 119.947i | 0.854955i | 0.904026 | + | 0.427478i | \(0.140598\pi\) | ||||
−0.904026 | + | 0.427478i | \(0.859402\pi\) | |||||||
\(4\) | 785.131 | 1.53346 | ||||||||
\(5\) | − | 917.335i | − | 0.656391i | −0.944610 | − | 0.328196i | \(-0.893559\pi\) | ||
0.944610 | − | 0.328196i | \(-0.106441\pi\) | |||||||
\(6\) | − | 4319.97i | − | 1.36082i | ||||||
\(7\) | − | 4193.73i | − | 0.660175i | −0.943950 | − | 0.330087i | \(-0.892922\pi\) | ||
0.943950 | − | 0.330087i | \(-0.107078\pi\) | |||||||
\(8\) | −9837.00 | −0.849098 | ||||||||
\(9\) | 5295.73 | 0.269051 | ||||||||
\(10\) | 33038.5i | 1.04477i | ||||||||
\(11\) | 56024.5i | 1.15375i | 0.816833 | + | 0.576874i | \(0.195728\pi\) | ||||
−0.816833 | + | 0.576874i | \(0.804272\pi\) | |||||||
\(12\) | 94174.0i | 1.31104i | ||||||||
\(13\) | 1946.10 | 0.0188982 | 0.00944908 | − | 0.999955i | \(-0.496992\pi\) | ||||
0.00944908 | + | 0.999955i | \(0.496992\pi\) | |||||||
\(14\) | 151040.i | 1.05079i | ||||||||
\(15\) | 110032. | 0.561185 | ||||||||
\(16\) | −47700.5 | −0.181963 | ||||||||
\(17\) | 13639.9 | + | 344096.i | 0.0396089 | + | 0.999215i | ||||
\(18\) | −190730. | −0.428244 | ||||||||
\(19\) | −348672. | −0.613798 | −0.306899 | − | 0.951742i | \(-0.599291\pi\) | ||||
−0.306899 | + | 0.951742i | \(0.599291\pi\) | |||||||
\(20\) | − | 720228.i | − | 1.00655i | ||||||
\(21\) | 503025. | 0.564420 | ||||||||
\(22\) | − | 2.01776e6i | − | 1.83640i | ||||||
\(23\) | 287328.i | 0.214093i | 0.994254 | + | 0.107046i | \(0.0341393\pi\) | ||||
−0.994254 | + | 0.107046i | \(0.965861\pi\) | |||||||
\(24\) | − | 1.17992e6i | − | 0.725941i | ||||||
\(25\) | 1.11162e6 | 0.569150 | ||||||||
\(26\) | −70090.0 | −0.0300799 | ||||||||
\(27\) | 2.99612e6i | 1.08498i | ||||||||
\(28\) | − | 3.29262e6i | − | 1.01235i | ||||||
\(29\) | 3.74448e6i | 0.983107i | 0.870847 | + | 0.491554i | \(0.163571\pi\) | ||||
−0.870847 | + | 0.491554i | \(0.836429\pi\) | |||||||
\(30\) | −3.96286e6 | −0.893230 | ||||||||
\(31\) | 3.22892e6i | 0.627956i | 0.949430 | + | 0.313978i | \(0.101662\pi\) | ||||
−0.949430 | + | 0.313978i | \(0.898338\pi\) | |||||||
\(32\) | 6.75451e6 | 1.13873 | ||||||||
\(33\) | −6.71997e6 | −0.986403 | ||||||||
\(34\) | −491252. | − | 1.23928e7i | −0.0630448 | − | 1.59044i | ||||
\(35\) | −3.84705e6 | −0.433333 | ||||||||
\(36\) | 4.15784e6 | 0.412579 | ||||||||
\(37\) | − | 7.92078e6i | − | 0.694801i | −0.937717 | − | 0.347400i | \(-0.887064\pi\) | ||
0.937717 | − | 0.347400i | \(-0.112936\pi\) | |||||||
\(38\) | 1.25576e7 | 0.976972 | ||||||||
\(39\) | 233428.i | 0.0161571i | ||||||||
\(40\) | 9.02382e6i | 0.557341i | ||||||||
\(41\) | 2.96386e7i | 1.63806i | 0.573750 | + | 0.819030i | \(0.305488\pi\) | ||||
−0.573750 | + | 0.819030i | \(0.694512\pi\) | |||||||
\(42\) | −1.81168e7 | −0.898379 | ||||||||
\(43\) | 1.54310e7 | 0.688314 | 0.344157 | − | 0.938912i | \(-0.388165\pi\) | ||||
0.344157 | + | 0.938912i | \(0.388165\pi\) | |||||||
\(44\) | 4.39866e7i | 1.76923i | ||||||||
\(45\) | − | 4.85796e6i | − | 0.176603i | ||||||
\(46\) | − | 1.03483e7i | − | 0.340768i | ||||||
\(47\) | −2.94503e7 | −0.880338 | −0.440169 | − | 0.897915i | \(-0.645081\pi\) | ||||
−0.440169 | + | 0.897915i | \(0.645081\pi\) | |||||||
\(48\) | − | 5.72153e6i | − | 0.155570i | ||||||
\(49\) | 2.27663e7 | 0.564169 | ||||||||
\(50\) | −4.00358e7 | −0.905908 | ||||||||
\(51\) | −4.12732e7 | + | 1.63607e6i | −0.854285 | + | 0.0338638i | ||||
\(52\) | 1.52794e6 | 0.0289795 | ||||||||
\(53\) | 1.12977e8 | 1.96675 | 0.983373 | − | 0.181596i | \(-0.0581263\pi\) | ||||
0.983373 | + | 0.181596i | \(0.0581263\pi\) | |||||||
\(54\) | − | 1.07907e8i | − | 1.72695i | ||||||
\(55\) | 5.13932e7 | 0.757310 | ||||||||
\(56\) | 4.12537e7i | 0.560553i | ||||||||
\(57\) | − | 4.18221e7i | − | 0.524770i | ||||||
\(58\) | − | 1.34860e8i | − | 1.56480i | ||||||
\(59\) | −1.42908e8 | −1.53540 | −0.767700 | − | 0.640809i | \(-0.778599\pi\) | ||||
−0.767700 | + | 0.640809i | \(0.778599\pi\) | |||||||
\(60\) | 8.63891e7 | 0.860555 | ||||||||
\(61\) | 2.77387e7i | 0.256508i | 0.991741 | + | 0.128254i | \(0.0409373\pi\) | ||||
−0.991741 | + | 0.128254i | \(0.959063\pi\) | |||||||
\(62\) | − | 1.16292e8i | − | 0.999508i | ||||||
\(63\) | − | 2.22089e7i | − | 0.177621i | ||||||
\(64\) | −2.18846e8 | −1.63053 | ||||||||
\(65\) | − | 1.78522e6i | − | 0.0124046i | ||||||
\(66\) | 2.42024e8 | 1.57004 | ||||||||
\(67\) | −8.42027e7 | −0.510493 | −0.255246 | − | 0.966876i | \(-0.582157\pi\) | ||||
−0.255246 | + | 0.966876i | \(0.582157\pi\) | |||||||
\(68\) | 1.07091e7 | + | 2.70160e8i | 0.0607386 | + | 1.53226i | ||||
\(69\) | −3.44641e7 | −0.183040 | ||||||||
\(70\) | 1.38554e8 | 0.689730 | ||||||||
\(71\) | 3.54046e8i | 1.65347i | 0.562590 | + | 0.826736i | \(0.309805\pi\) | ||||
−0.562590 | + | 0.826736i | \(0.690195\pi\) | |||||||
\(72\) | −5.20941e7 | −0.228451 | ||||||||
\(73\) | 2.56100e8i | 1.05550i | 0.849401 | + | 0.527748i | \(0.176963\pi\) | ||||
−0.849401 | + | 0.527748i | \(0.823037\pi\) | |||||||
\(74\) | 2.85273e8i | 1.10590i | ||||||||
\(75\) | 1.33336e8i | 0.486598i | ||||||||
\(76\) | −2.73753e8 | −0.941233 | ||||||||
\(77\) | 2.34952e8 | 0.761676 | ||||||||
\(78\) | − | 8.40709e6i | − | 0.0257170i | ||||||
\(79\) | − | 3.39870e8i | − | 0.981728i | −0.871236 | − | 0.490864i | \(-0.836681\pi\) | ||
0.871236 | − | 0.490864i | \(-0.163319\pi\) | |||||||
\(80\) | 4.37573e7i | 0.119439i | ||||||||
\(81\) | −2.55140e8 | −0.658560 | ||||||||
\(82\) | − | 1.06745e9i | − | 2.60727i | ||||||
\(83\) | 5.29228e8 | 1.22403 | 0.612014 | − | 0.790847i | \(-0.290360\pi\) | ||||
0.612014 | + | 0.790847i | \(0.290360\pi\) | |||||||
\(84\) | 3.94940e8 | 0.865515 | ||||||||
\(85\) | 3.15651e8 | − | 1.25124e7i | 0.655876 | − | 0.0259989i | ||||
\(86\) | −5.55759e8 | −1.09558 | ||||||||
\(87\) | −4.49139e8 | −0.840513 | ||||||||
\(88\) | − | 5.51113e8i | − | 0.979645i | ||||||
\(89\) | −6.33877e8 | −1.07090 | −0.535451 | − | 0.844566i | \(-0.679858\pi\) | ||||
−0.535451 | + | 0.844566i | \(0.679858\pi\) | |||||||
\(90\) | 1.74963e8i | 0.281096i | ||||||||
\(91\) | − | 8.16140e6i | − | 0.0124761i | ||||||
\(92\) | 2.25590e8i | 0.328303i | ||||||||
\(93\) | −3.87299e8 | −0.536874 | ||||||||
\(94\) | 1.06067e9 | 1.40122 | ||||||||
\(95\) | 3.19849e8i | 0.402892i | ||||||||
\(96\) | 8.10183e8i | 0.973560i | ||||||||
\(97\) | − | 1.00489e9i | − | 1.15252i | −0.817267 | − | 0.576259i | \(-0.804512\pi\) | ||
0.817267 | − | 0.576259i | \(-0.195488\pi\) | |||||||
\(98\) | −8.19943e8 | −0.897979 | ||||||||
\(99\) | 2.96691e8i | 0.310417i | ||||||||
\(100\) | 8.72768e8 | 0.872768 | ||||||||
\(101\) | 1.52783e9 | 1.46093 | 0.730465 | − | 0.682950i | \(-0.239303\pi\) | ||||
0.730465 | + | 0.682950i | \(0.239303\pi\) | |||||||
\(102\) | 1.48648e9 | − | 5.89242e7i | 1.35975 | − | 0.0539005i | ||||
\(103\) | −1.79886e8 | −0.157482 | −0.0787409 | − | 0.996895i | \(-0.525090\pi\) | ||||
−0.0787409 | + | 0.996895i | \(0.525090\pi\) | |||||||
\(104\) | −1.91438e7 | −0.0160464 | ||||||||
\(105\) | − | 4.61442e8i | − | 0.370481i | ||||||
\(106\) | −4.06894e9 | −3.13044 | ||||||||
\(107\) | − | 2.37895e9i | − | 1.75452i | −0.480019 | − | 0.877258i | \(-0.659370\pi\) | ||
0.480019 | − | 0.877258i | \(-0.340630\pi\) | |||||||
\(108\) | 2.35235e9i | 1.66378i | ||||||||
\(109\) | − | 9.33309e7i | − | 0.0633295i | −0.999499 | − | 0.0316648i | \(-0.989919\pi\) | ||
0.999499 | − | 0.0316648i | \(-0.0100809\pi\) | |||||||
\(110\) | −1.85096e9 | −1.20540 | ||||||||
\(111\) | 9.50073e8 | 0.594024 | ||||||||
\(112\) | 2.00043e8i | 0.120127i | ||||||||
\(113\) | − | 1.71780e9i | − | 0.991104i | −0.868578 | − | 0.495552i | \(-0.834966\pi\) | ||
0.868578 | − | 0.495552i | \(-0.165034\pi\) | |||||||
\(114\) | 1.50625e9i | 0.835268i | ||||||||
\(115\) | 2.63576e8 | 0.140529 | ||||||||
\(116\) | 2.93991e9i | 1.50755i | ||||||||
\(117\) | 1.03060e7 | 0.00508457 | ||||||||
\(118\) | 5.14692e9 | 2.44387 | ||||||||
\(119\) | 1.44304e9 | − | 5.72022e7i | 0.659657 | − | 0.0261488i | ||||
\(120\) | −1.08238e9 | −0.476501 | ||||||||
\(121\) | −7.80799e8 | −0.331135 | ||||||||
\(122\) | − | 9.99028e8i | − | 0.408280i | ||||||
\(123\) | −3.55506e9 | −1.40047 | ||||||||
\(124\) | 2.53512e9i | 0.962945i | ||||||||
\(125\) | − | 2.81140e9i | − | 1.02998i | ||||||
\(126\) | 7.99868e8i | 0.282716i | ||||||||
\(127\) | −2.30615e9 | −0.786629 | −0.393315 | − | 0.919404i | \(-0.628672\pi\) | ||||
−0.393315 | + | 0.919404i | \(0.628672\pi\) | |||||||
\(128\) | 4.42358e9 | 1.45656 | ||||||||
\(129\) | 1.85090e9i | 0.588478i | ||||||||
\(130\) | 6.42960e7i | 0.0197442i | ||||||||
\(131\) | 2.35000e9i | 0.697183i | 0.937275 | + | 0.348591i | \(0.113340\pi\) | ||||
−0.937275 | + | 0.348591i | \(0.886660\pi\) | |||||||
\(132\) | −5.27606e9 | −1.51261 | ||||||||
\(133\) | 1.46223e9i | 0.405214i | ||||||||
\(134\) | 3.03262e9 | 0.812543 | ||||||||
\(135\) | 2.74845e9 | 0.712173 | ||||||||
\(136\) | −1.34176e8 | − | 3.38487e9i | −0.0336318 | − | 0.848432i | ||||
\(137\) | −2.35491e9 | −0.571127 | −0.285563 | − | 0.958360i | \(-0.592181\pi\) | ||||
−0.285563 | + | 0.958360i | \(0.592181\pi\) | |||||||
\(138\) | 1.24125e9 | 0.291342 | ||||||||
\(139\) | 5.15857e9i | 1.17209i | 0.810277 | + | 0.586047i | \(0.199317\pi\) | ||||
−0.810277 | + | 0.586047i | \(0.800683\pi\) | |||||||
\(140\) | −3.02044e9 | −0.664499 | ||||||||
\(141\) | − | 3.53247e9i | − | 0.752649i | ||||||
\(142\) | − | 1.27512e10i | − | 2.63181i | ||||||
\(143\) | 1.09029e8i | 0.0218037i | ||||||||
\(144\) | −2.52609e8 | −0.0489573 | ||||||||
\(145\) | 3.43495e9 | 0.645303 | ||||||||
\(146\) | − | 9.22361e9i | − | 1.68002i | ||||||
\(147\) | 2.73074e9i | 0.482339i | ||||||||
\(148\) | − | 6.21885e9i | − | 1.06545i | ||||||
\(149\) | −6.04226e9 | −1.00429 | −0.502147 | − | 0.864782i | \(-0.667457\pi\) | ||||
−0.502147 | + | 0.864782i | \(0.667457\pi\) | |||||||
\(150\) | − | 4.80218e9i | − | 0.774511i | ||||||
\(151\) | 7.56844e9 | 1.18471 | 0.592353 | − | 0.805679i | \(-0.298199\pi\) | ||||
0.592353 | + | 0.805679i | \(0.298199\pi\) | |||||||
\(152\) | 3.42988e9 | 0.521174 | ||||||||
\(153\) | 7.22335e7 | + | 1.82224e9i | 0.0106568 | + | 0.268840i | ||||
\(154\) | −8.46195e9 | −1.21235 | ||||||||
\(155\) | 2.96200e9 | 0.412185 | ||||||||
\(156\) | 1.83272e8i | 0.0247762i | ||||||||
\(157\) | 3.59797e9 | 0.472616 | 0.236308 | − | 0.971678i | \(-0.424062\pi\) | ||||
0.236308 | + | 0.971678i | \(0.424062\pi\) | |||||||
\(158\) | 1.22407e10i | 1.56260i | ||||||||
\(159\) | 1.35512e10i | 1.68148i | ||||||||
\(160\) | − | 6.19615e9i | − | 0.747450i | ||||||
\(161\) | 1.20497e9 | 0.141339 | ||||||||
\(162\) | 9.18904e9 | 1.04822 | ||||||||
\(163\) | 2.46020e9i | 0.272977i | 0.990642 | + | 0.136488i | \(0.0435816\pi\) | ||||
−0.990642 | + | 0.136488i | \(0.956418\pi\) | |||||||
\(164\) | 2.32702e10i | 2.51190i | ||||||||
\(165\) | 6.16446e9i | 0.647467i | ||||||||
\(166\) | −1.90605e10 | −1.94827 | ||||||||
\(167\) | 6.06431e9i | 0.603333i | 0.953414 | + | 0.301667i | \(0.0975429\pi\) | ||||
−0.953414 | + | 0.301667i | \(0.902457\pi\) | |||||||
\(168\) | −4.94825e9 | −0.479248 | ||||||||
\(169\) | −1.06007e10 | −0.999643 | ||||||||
\(170\) | −1.13684e10 | + | 4.50643e8i | −1.04395 | + | 0.0413821i | ||||
\(171\) | −1.84647e9 | −0.165143 | ||||||||
\(172\) | 1.21154e10 | 1.05550 | ||||||||
\(173\) | 7.56160e9i | 0.641810i | 0.947111 | + | 0.320905i | \(0.103987\pi\) | ||||
−0.947111 | + | 0.320905i | \(0.896013\pi\) | |||||||
\(174\) | 1.61761e10 | 1.33783 | ||||||||
\(175\) | − | 4.66184e9i | − | 0.375739i | ||||||
\(176\) | − | 2.67240e9i | − | 0.209939i | ||||||
\(177\) | − | 1.71413e10i | − | 1.31270i | ||||||
\(178\) | 2.28295e10 | 1.70454 | ||||||||
\(179\) | −1.98968e9 | −0.144859 | −0.0724293 | − | 0.997374i | \(-0.523075\pi\) | ||||
−0.0724293 | + | 0.997374i | \(0.523075\pi\) | |||||||
\(180\) | − | 3.81414e9i | − | 0.270813i | ||||||
\(181\) | − | 2.17900e10i | − | 1.50905i | −0.656272 | − | 0.754525i | \(-0.727867\pi\) | ||
0.656272 | − | 0.754525i | \(-0.272133\pi\) | |||||||
\(182\) | 2.93939e8i | 0.0198580i | ||||||||
\(183\) | −3.32717e9 | −0.219303 | ||||||||
\(184\) | − | 2.82644e9i | − | 0.181786i | ||||||
\(185\) | −7.26601e9 | −0.456061 | ||||||||
\(186\) | 1.39488e10 | 0.854535 | ||||||||
\(187\) | −1.92778e10 | + | 7.64172e8i | −1.15284 | + | 0.0456987i | ||||
\(188\) | −2.31223e10 | −1.34996 | ||||||||
\(189\) | 1.25649e10 | 0.716278 | ||||||||
\(190\) | − | 1.15196e10i | − | 0.641276i | ||||||
\(191\) | 1.55821e10 | 0.847180 | 0.423590 | − | 0.905854i | \(-0.360770\pi\) | ||||
0.423590 | + | 0.905854i | \(0.360770\pi\) | |||||||
\(192\) | − | 2.62499e10i | − | 1.39403i | ||||||
\(193\) | 3.56806e9i | 0.185108i | 0.995708 | + | 0.0925538i | \(0.0295030\pi\) | ||||
−0.995708 | + | 0.0925538i | \(0.970497\pi\) | |||||||
\(194\) | 3.61920e10i | 1.83444i | ||||||||
\(195\) | 2.14132e8 | 0.0106054 | ||||||||
\(196\) | 1.78745e10 | 0.865130 | ||||||||
\(197\) | − | 3.07563e10i | − | 1.45491i | −0.686155 | − | 0.727456i | \(-0.740703\pi\) | ||
0.686155 | − | 0.727456i | \(-0.259297\pi\) | |||||||
\(198\) | − | 1.06855e10i | − | 0.494086i | ||||||
\(199\) | 1.48762e10i | 0.672441i | 0.941783 | + | 0.336220i | \(0.109149\pi\) | ||||
−0.941783 | + | 0.336220i | \(0.890851\pi\) | |||||||
\(200\) | −1.09350e10 | −0.483264 | ||||||||
\(201\) | − | 1.00999e10i | − | 0.436449i | ||||||
\(202\) | −5.50260e10 | −2.32534 | ||||||||
\(203\) | 1.57033e10 | 0.649023 | ||||||||
\(204\) | −3.24049e10 | + | 1.28453e9i | −1.31001 | + | 0.0519288i | ||||
\(205\) | 2.71885e10 | 1.07521 | ||||||||
\(206\) | 6.47873e9 | 0.250661 | ||||||||
\(207\) | 1.52161e9i | 0.0576019i | ||||||||
\(208\) | −9.28298e7 | −0.00343876 | ||||||||
\(209\) | − | 1.95342e10i | − | 0.708168i | ||||||
\(210\) | 1.66192e10i | 0.589688i | ||||||||
\(211\) | 3.47123e10i | 1.20562i | 0.797883 | + | 0.602812i | \(0.205953\pi\) | ||||
−0.797883 | + | 0.602812i | \(0.794047\pi\) | |||||||
\(212\) | 8.87017e10 | 3.01592 | ||||||||
\(213\) | −4.24667e10 | −1.41364 | ||||||||
\(214\) | 8.56794e10i | 2.79264i | ||||||||
\(215\) | − | 1.41554e10i | − | 0.451803i | ||||||
\(216\) | − | 2.94729e10i | − | 0.921256i | ||||||
\(217\) | 1.35412e10 | 0.414561 | ||||||||
\(218\) | 3.36138e9i | 0.100801i | ||||||||
\(219\) | −3.07184e10 | −0.902401 | ||||||||
\(220\) | 4.03504e10 | 1.16130 | ||||||||
\(221\) | 2.65447e7 | + | 6.69643e8i | 0.000748535 | + | 0.0188833i | ||||
\(222\) | −3.42176e10 | −0.945498 | ||||||||
\(223\) | −3.59058e10 | −0.972283 | −0.486142 | − | 0.873880i | \(-0.661596\pi\) | ||||
−0.486142 | + | 0.873880i | \(0.661596\pi\) | |||||||
\(224\) | − | 2.83266e10i | − | 0.751758i | ||||||
\(225\) | 5.88685e9 | 0.153131 | ||||||||
\(226\) | 6.18677e10i | 1.57753i | ||||||||
\(227\) | − | 5.61479e9i | − | 0.140352i | −0.997535 | − | 0.0701758i | \(-0.977644\pi\) | ||
0.997535 | − | 0.0701758i | \(-0.0223560\pi\) | |||||||
\(228\) | − | 3.28358e10i | − | 0.804713i | ||||||
\(229\) | 7.90733e10 | 1.90007 | 0.950036 | − | 0.312139i | \(-0.101046\pi\) | ||||
0.950036 | + | 0.312139i | \(0.101046\pi\) | |||||||
\(230\) | −9.49286e9 | −0.223677 | ||||||||
\(231\) | 2.81817e10i | 0.651199i | ||||||||
\(232\) | − | 3.68345e10i | − | 0.834754i | ||||||
\(233\) | − | 6.81753e10i | − | 1.51539i | −0.652607 | − | 0.757697i | \(-0.726325\pi\) | ||
0.652607 | − | 0.757697i | \(-0.273675\pi\) | |||||||
\(234\) | −3.71178e8 | −0.00809303 | ||||||||
\(235\) | 2.70158e10i | 0.577846i | ||||||||
\(236\) | −1.12201e11 | −2.35447 | ||||||||
\(237\) | 4.07664e10 | 0.839334 | ||||||||
\(238\) | −5.19722e10 | + | 2.06018e9i | −1.04997 | + | 0.0416206i | ||||
\(239\) | −3.19952e10 | −0.634300 | −0.317150 | − | 0.948375i | \(-0.602726\pi\) | ||||
−0.317150 | + | 0.948375i | \(0.602726\pi\) | |||||||
\(240\) | −5.24856e9 | −0.102115 | ||||||||
\(241\) | 4.21107e9i | 0.0804111i | 0.999191 | + | 0.0402056i | \(0.0128013\pi\) | ||||
−0.999191 | + | 0.0402056i | \(0.987199\pi\) | |||||||
\(242\) | 2.81210e10 | 0.527062 | ||||||||
\(243\) | 2.83694e10i | 0.521942i | ||||||||
\(244\) | 2.17785e10i | 0.393345i | ||||||||
\(245\) | − | 2.08843e10i | − | 0.370316i | ||||||
\(246\) | 1.28038e11 | 2.22910 | ||||||||
\(247\) | −6.78548e8 | −0.0115996 | ||||||||
\(248\) | − | 3.17629e10i | − | 0.533196i | ||||||
\(249\) | 6.34793e10i | 1.04649i | ||||||||
\(250\) | 1.01255e11i | 1.63940i | ||||||||
\(251\) | 1.26806e10 | 0.201654 | 0.100827 | − | 0.994904i | \(-0.467851\pi\) | ||||
0.100827 | + | 0.994904i | \(0.467851\pi\) | |||||||
\(252\) | − | 1.74369e10i | − | 0.272374i | ||||||
\(253\) | −1.60974e10 | −0.247009 | ||||||||
\(254\) | 8.30575e10 | 1.25207 | ||||||||
\(255\) | 1.50082e9 | + | 3.78614e10i | 0.0222279 | + | 0.560745i | ||||
\(256\) | −4.72692e10 | −0.687857 | ||||||||
\(257\) | −8.11867e10 | −1.16088 | −0.580438 | − | 0.814304i | \(-0.697119\pi\) | ||||
−0.580438 | + | 0.814304i | \(0.697119\pi\) | |||||||
\(258\) | − | 6.66616e10i | − | 0.936671i | ||||||
\(259\) | −3.32176e10 | −0.458690 | ||||||||
\(260\) | − | 1.40163e9i | − | 0.0190219i | ||||||
\(261\) | 1.98298e10i | 0.264506i | ||||||||
\(262\) | − | 8.46368e10i | − | 1.10969i | ||||||
\(263\) | 4.36957e10 | 0.563168 | 0.281584 | − | 0.959537i | \(-0.409140\pi\) | ||||
0.281584 | + | 0.959537i | \(0.409140\pi\) | |||||||
\(264\) | 6.61043e10 | 0.837553 | ||||||||
\(265\) | − | 1.03638e11i | − | 1.29096i | ||||||
\(266\) | − | 5.26634e10i | − | 0.644972i | ||||||
\(267\) | − | 7.60316e10i | − | 0.915574i | ||||||
\(268\) | −6.61102e10 | −0.782819 | ||||||||
\(269\) | − | 1.52414e11i | − | 1.77476i | −0.461042 | − | 0.887378i | \(-0.652524\pi\) | ||
0.461042 | − | 0.887378i | \(-0.347476\pi\) | |||||||
\(270\) | −9.89873e10 | −1.13355 | ||||||||
\(271\) | 1.41824e10 | 0.159731 | 0.0798655 | − | 0.996806i | \(-0.474551\pi\) | ||||
0.0798655 | + | 0.996806i | \(0.474551\pi\) | |||||||
\(272\) | −6.50632e8 | − | 1.64135e10i | −0.00720735 | − | 0.181820i | ||||
\(273\) | 9.78935e8 | 0.0106665 | ||||||||
\(274\) | 8.48139e10 | 0.909053 | ||||||||
\(275\) | 6.22781e10i | 0.656656i | ||||||||
\(276\) | −2.70588e10 | −0.280684 | ||||||||
\(277\) | 7.86224e10i | 0.802394i | 0.915992 | + | 0.401197i | \(0.131406\pi\) | ||||
−0.915992 | + | 0.401197i | \(0.868594\pi\) | |||||||
\(278\) | − | 1.85789e11i | − | 1.86560i | ||||||
\(279\) | 1.70995e10i | 0.168952i | ||||||||
\(280\) | 3.78435e10 | 0.367942 | ||||||||
\(281\) | −3.72134e10 | −0.356058 | −0.178029 | − | 0.984025i | \(-0.556972\pi\) | ||||
−0.178029 | + | 0.984025i | \(0.556972\pi\) | |||||||
\(282\) | 1.27224e11i | 1.19798i | ||||||||
\(283\) | − | 7.37798e9i | − | 0.0683752i | −0.999415 | − | 0.0341876i | \(-0.989116\pi\) | ||
0.999415 | − | 0.0341876i | \(-0.0108844\pi\) | |||||||
\(284\) | 2.77972e11i | 2.53553i | ||||||||
\(285\) | −3.83649e10 | −0.344454 | ||||||||
\(286\) | − | 3.92676e9i | − | 0.0347046i | ||||||
\(287\) | 1.24296e11 | 1.08141 | ||||||||
\(288\) | 3.57701e10 | 0.306375 | ||||||||
\(289\) | −1.18216e11 | + | 9.38689e9i | −0.996862 | + | 0.0791556i | ||||
\(290\) | −1.23712e11 | −1.02712 | ||||||||
\(291\) | 1.20534e11 | 0.985351 | ||||||||
\(292\) | 2.01072e11i | 1.61856i | ||||||||
\(293\) | 9.58955e10 | 0.760140 | 0.380070 | − | 0.924958i | \(-0.375900\pi\) | ||||
0.380070 | + | 0.924958i | \(0.375900\pi\) | |||||||
\(294\) | − | 9.83496e10i | − | 0.767732i | ||||||
\(295\) | 1.31094e11i | 1.00782i | ||||||||
\(296\) | 7.79167e10i | 0.589954i | ||||||||
\(297\) | −1.67856e11 | −1.25180 | ||||||||
\(298\) | 2.17616e11 | 1.59852 | ||||||||
\(299\) | 5.59167e8i | 0.00404596i | ||||||||
\(300\) | 1.04686e11i | 0.746178i | ||||||||
\(301\) | − | 6.47135e10i | − | 0.454407i | ||||||
\(302\) | −2.72583e11 | −1.88568 | ||||||||
\(303\) | 1.83259e11i | 1.24903i | ||||||||
\(304\) | 1.66318e10 | 0.111688 | ||||||||
\(305\) | 2.54457e10 | 0.168370 | ||||||||
\(306\) | −2.60154e9 | − | 6.56292e10i | −0.0169623 | − | 0.427908i | ||||
\(307\) | 1.36312e11 | 0.875814 | 0.437907 | − | 0.899020i | \(-0.355720\pi\) | ||||
0.437907 | + | 0.899020i | \(0.355720\pi\) | |||||||
\(308\) | 1.84468e11 | 1.16800 | ||||||||
\(309\) | − | 2.15768e10i | − | 0.134640i | ||||||
\(310\) | −1.06678e11 | −0.656068 | ||||||||
\(311\) | − | 1.33880e11i | − | 0.811507i | −0.913983 | − | 0.405754i | \(-0.867009\pi\) | ||
0.913983 | − | 0.405754i | \(-0.132991\pi\) | |||||||
\(312\) | − | 2.29623e9i | − | 0.0137189i | ||||||
\(313\) | 8.69004e10i | 0.511767i | 0.966708 | + | 0.255883i | \(0.0823663\pi\) | ||||
−0.966708 | + | 0.255883i | \(0.917634\pi\) | |||||||
\(314\) | −1.29583e11 | −0.752256 | ||||||||
\(315\) | −2.03730e10 | −0.116589 | ||||||||
\(316\) | − | 2.66843e11i | − | 1.50544i | ||||||
\(317\) | 2.48261e11i | 1.38083i | 0.723412 | + | 0.690417i | \(0.242573\pi\) | ||||
−0.723412 | + | 0.690417i | \(0.757427\pi\) | |||||||
\(318\) | − | 4.88057e11i | − | 2.67639i | ||||||
\(319\) | −2.09783e11 | −1.13426 | ||||||||
\(320\) | 2.00755e11i | 1.07026i | ||||||||
\(321\) | 2.85347e11 | 1.50003 | ||||||||
\(322\) | −4.33980e10 | −0.224967 | ||||||||
\(323\) | −4.75586e9 | − | 1.19976e11i | −0.0243118 | − | 0.613316i | ||||
\(324\) | −2.00318e11 | −1.00988 | ||||||||
\(325\) | 2.16332e9 | 0.0107559 | ||||||||
\(326\) | − | 8.86057e10i | − | 0.434493i | ||||||
\(327\) | 1.11948e10 | 0.0541439 | ||||||||
\(328\) | − | 2.91555e11i | − | 1.39087i | ||||||
\(329\) | 1.23506e11i | 0.581177i | ||||||||
\(330\) | − | 2.22017e11i | − | 1.03056i | ||||||
\(331\) | −2.88811e11 | −1.32248 | −0.661239 | − | 0.750175i | \(-0.729969\pi\) | ||||
−0.661239 | + | 0.750175i | \(0.729969\pi\) | |||||||
\(332\) | 4.15513e11 | 1.87700 | ||||||||
\(333\) | − | 4.19463e10i | − | 0.186937i | ||||||
\(334\) | − | 2.18410e11i | − | 0.960316i | ||||||
\(335\) | 7.72421e10i | 0.335083i | ||||||||
\(336\) | −2.39945e10 | −0.102704 | ||||||||
\(337\) | − | 9.17448e10i | − | 0.387478i | −0.981053 | − | 0.193739i | \(-0.937939\pi\) | ||
0.981053 | − | 0.193739i | \(-0.0620615\pi\) | |||||||
\(338\) | 3.81792e11 | 1.59112 | ||||||||
\(339\) | 2.06045e11 | 0.847350 | ||||||||
\(340\) | 2.47827e11 | − | 9.82387e9i | 1.00576 | − | 0.0398683i | ||||
\(341\) | −1.80898e11 | −0.724503 | ||||||||
\(342\) | 6.65020e10 | 0.262855 | ||||||||
\(343\) | − | 2.64708e11i | − | 1.03263i | ||||||
\(344\) | −1.51795e11 | −0.584446 | ||||||||
\(345\) | 3.16151e10i | 0.120146i | ||||||||
\(346\) | − | 2.72336e11i | − | 1.02156i | ||||||
\(347\) | 4.84910e11i | 1.79547i | 0.440534 | + | 0.897736i | \(0.354789\pi\) | ||||
−0.440534 | + | 0.897736i | \(0.645211\pi\) | |||||||
\(348\) | −3.52633e11 | −1.28889 | ||||||||
\(349\) | −6.43524e9 | −0.0232194 | −0.0116097 | − | 0.999933i | \(-0.503696\pi\) | ||||
−0.0116097 | + | 0.999933i | \(0.503696\pi\) | |||||||
\(350\) | 1.67899e11i | 0.598057i | ||||||||
\(351\) | 5.83074e9i | 0.0205042i | ||||||||
\(352\) | 3.78418e11i | 1.31380i | ||||||||
\(353\) | −1.83629e11 | −0.629440 | −0.314720 | − | 0.949185i | \(-0.601911\pi\) | ||||
−0.314720 | + | 0.949185i | \(0.601911\pi\) | |||||||
\(354\) | 6.17357e11i | 2.08940i | ||||||||
\(355\) | 3.24779e11 | 1.08532 | ||||||||
\(356\) | −4.97676e11 | −1.64218 | ||||||||
\(357\) | 6.86123e9 | + | 1.73089e11i | 0.0223561 | + | 0.563977i | ||||
\(358\) | 7.16596e10 | 0.230569 | ||||||||
\(359\) | −4.45051e11 | −1.41412 | −0.707058 | − | 0.707155i | \(-0.749978\pi\) | ||||
−0.707058 | + | 0.707155i | \(0.749978\pi\) | |||||||
\(360\) | 4.77878e10i | 0.149953i | ||||||||
\(361\) | −2.01116e11 | −0.623252 | ||||||||
\(362\) | 7.84782e11i | 2.40193i | ||||||||
\(363\) | − | 9.36544e10i | − | 0.283106i | ||||||
\(364\) | − | 6.40777e9i | − | 0.0191316i | ||||||
\(365\) | 2.34929e11 | 0.692818 | ||||||||
\(366\) | 1.19830e11 | 0.349061 | ||||||||
\(367\) | − | 4.05760e11i | − | 1.16754i | −0.811919 | − | 0.583770i | \(-0.801577\pi\) | ||
0.811919 | − | 0.583770i | \(-0.198423\pi\) | |||||||
\(368\) | − | 1.37057e10i | − | 0.0389570i | ||||||
\(369\) | 1.56958e11i | 0.440722i | ||||||||
\(370\) | 2.61690e11 | 0.725906 | ||||||||
\(371\) | − | 4.73794e11i | − | 1.29840i | ||||||
\(372\) | −3.04080e11 | −0.823275 | ||||||||
\(373\) | 4.07694e11 | 1.09055 | 0.545274 | − | 0.838258i | \(-0.316426\pi\) | ||||
0.545274 | + | 0.838258i | \(0.316426\pi\) | |||||||
\(374\) | 6.94303e11 | − | 2.75222e10i | 1.83496 | − | 0.0727379i | ||||
\(375\) | 3.37219e11 | 0.880584 | ||||||||
\(376\) | 2.89703e11 | 0.747493 | ||||||||
\(377\) | 7.28713e9i | 0.0185789i | ||||||||
\(378\) | −4.52534e11 | −1.14009 | ||||||||
\(379\) | − | 6.72982e11i | − | 1.67543i | −0.546105 | − | 0.837717i | \(-0.683890\pi\) | ||
0.546105 | − | 0.837717i | \(-0.316110\pi\) | |||||||
\(380\) | 2.51123e11i | 0.617818i | ||||||||
\(381\) | − | 2.76615e11i | − | 0.672533i | ||||||
\(382\) | −5.61200e11 | −1.34844 | ||||||||
\(383\) | −3.49592e11 | −0.830170 | −0.415085 | − | 0.909783i | \(-0.636248\pi\) | ||||
−0.415085 | + | 0.909783i | \(0.636248\pi\) | |||||||
\(384\) | 5.30594e11i | 1.24529i | ||||||||
\(385\) | − | 2.15529e11i | − | 0.499957i | ||||||
\(386\) | − | 1.28506e11i | − | 0.294633i | ||||||
\(387\) | 8.17185e10 | 0.185192 | ||||||||
\(388\) | − | 7.88973e11i | − | 1.76734i | ||||||
\(389\) | 4.97423e11 | 1.10142 | 0.550709 | − | 0.834697i | \(-0.314357\pi\) | ||||
0.550709 | + | 0.834697i | \(0.314357\pi\) | |||||||
\(390\) | −7.71211e9 | −0.0168804 | ||||||||
\(391\) | −9.88682e10 | + | 3.91913e9i | −0.213925 | + | 0.00847998i | ||||
\(392\) | −2.23952e11 | −0.479035 | ||||||||
\(393\) | −2.81875e11 | −0.596060 | ||||||||
\(394\) | 1.10771e12i | 2.31576i | ||||||||
\(395\) | −3.11775e11 | −0.644398 | ||||||||
\(396\) | 2.32941e11i | 0.476012i | ||||||||
\(397\) | − | 1.58244e11i | − | 0.319721i | −0.987140 | − | 0.159860i | \(-0.948896\pi\) | ||
0.987140 | − | 0.159860i | \(-0.0511044\pi\) | |||||||
\(398\) | − | 5.35778e11i | − | 1.07031i | ||||||
\(399\) | −1.75390e11 | −0.346440 | ||||||||
\(400\) | −5.30249e10 | −0.103564 | ||||||||
\(401\) | 9.10311e10i | 0.175809i | 0.996129 | + | 0.0879043i | \(0.0280170\pi\) | ||||
−0.996129 | + | 0.0879043i | \(0.971983\pi\) | |||||||
\(402\) | 3.63754e11i | 0.694688i | ||||||||
\(403\) | 6.28378e9i | 0.0118672i | ||||||||
\(404\) | 1.19955e12 | 2.24028 | ||||||||
\(405\) | 2.34049e11i | 0.432273i | ||||||||
\(406\) | −5.65567e11 | −1.03304 | ||||||||
\(407\) | 4.43758e11 | 0.801625 | ||||||||
\(408\) | 4.06005e11 | − | 1.60940e10i | 0.725371 | − | 0.0287537i | ||||
\(409\) | 4.23339e11 | 0.748055 | 0.374027 | − | 0.927418i | \(-0.377977\pi\) | ||||
0.374027 | + | 0.927418i | \(0.377977\pi\) | |||||||
\(410\) | −9.79213e11 | −1.71139 | ||||||||
\(411\) | − | 2.82465e11i | − | 0.488288i | ||||||
\(412\) | −1.41234e11 | −0.241492 | ||||||||
\(413\) | 5.99316e11i | 1.01363i | ||||||||
\(414\) | − | 5.48019e10i | − | 0.0916841i | ||||||
\(415\) | − | 4.85479e11i | − | 0.803442i | ||||||
\(416\) | 1.31449e10 | 0.0215198 | ||||||||
\(417\) | −6.18754e11 | −1.00209 | ||||||||
\(418\) | 7.03536e11i | 1.12718i | ||||||||
\(419\) | − | 6.22425e11i | − | 0.986561i | −0.869870 | − | 0.493280i | \(-0.835798\pi\) | ||
0.869870 | − | 0.493280i | \(-0.164202\pi\) | |||||||
\(420\) | − | 3.62292e11i | − | 0.568117i | ||||||
\(421\) | 4.67294e11 | 0.724971 | 0.362486 | − | 0.931989i | \(-0.381928\pi\) | ||||
0.362486 | + | 0.931989i | \(0.381928\pi\) | |||||||
\(422\) | − | 1.25019e12i | − | 1.91897i | ||||||
\(423\) | −1.55961e11 | −0.236856 | ||||||||
\(424\) | −1.11135e12 | −1.66996 | ||||||||
\(425\) | 1.51625e10 | + | 3.82504e11i | 0.0225434 | + | 0.568704i | ||||
\(426\) | 1.52947e12 | 2.25008 | ||||||||
\(427\) | 1.16328e11 | 0.169340 | ||||||||
\(428\) | − | 1.86778e12i | − | 2.69048i | ||||||
\(429\) | −1.30777e10 | −0.0186412 | ||||||||
\(430\) | 5.09817e11i | 0.719128i | ||||||||
\(431\) | 2.57969e11i | 0.360097i | 0.983658 | + | 0.180049i | \(0.0576255\pi\) | ||||
−0.983658 | + | 0.180049i | \(0.942374\pi\) | |||||||
\(432\) | − | 1.42917e11i | − | 0.197427i | ||||||
\(433\) | −2.74180e11 | −0.374836 | −0.187418 | − | 0.982280i | \(-0.560012\pi\) | ||||
−0.187418 | + | 0.982280i | \(0.560012\pi\) | |||||||
\(434\) | −4.87696e11 | −0.659850 | ||||||||
\(435\) | 4.12011e11i | 0.551705i | ||||||||
\(436\) | − | 7.32770e10i | − | 0.0971132i | ||||||
\(437\) | − | 1.00183e11i | − | 0.131410i | ||||||
\(438\) | 1.10634e12 | 1.43634 | ||||||||
\(439\) | 7.90421e11i | 1.01571i | 0.861444 | + | 0.507853i | \(0.169561\pi\) | ||||
−0.861444 | + | 0.507853i | \(0.830439\pi\) | |||||||
\(440\) | −5.05555e11 | −0.643031 | ||||||||
\(441\) | 1.20564e11 | 0.151790 | ||||||||
\(442\) | −9.56024e8 | − | 2.41177e10i | −0.00119143 | − | 0.0300563i | ||||
\(443\) | −6.58883e10 | −0.0812815 | −0.0406407 | − | 0.999174i | \(-0.512940\pi\) | ||||
−0.0406407 | + | 0.999174i | \(0.512940\pi\) | |||||||
\(444\) | 7.45932e11 | 0.910911 | ||||||||
\(445\) | 5.81477e11i | 0.702931i | ||||||||
\(446\) | 1.29317e12 | 1.54757 | ||||||||
\(447\) | − | 7.24751e11i | − | 0.858627i | ||||||
\(448\) | 9.17780e11i | 1.07643i | ||||||||
\(449\) | 8.66534e11i | 1.00618i | 0.864233 | + | 0.503092i | \(0.167804\pi\) | ||||
−0.864233 | + | 0.503092i | \(0.832196\pi\) | |||||||
\(450\) | −2.12019e11 | −0.243735 | ||||||||
\(451\) | −1.66049e12 | −1.88991 | ||||||||
\(452\) | − | 1.34870e12i | − | 1.51982i | ||||||
\(453\) | 9.07811e11i | 1.01287i | ||||||||
\(454\) | 2.02221e11i | 0.223395i | ||||||||
\(455\) | −7.48674e9 | −0.00818920 | ||||||||
\(456\) | 4.11404e11i | 0.445581i | ||||||||
\(457\) | 6.25354e11 | 0.670661 | 0.335330 | − | 0.942101i | \(-0.391152\pi\) | ||||
0.335330 | + | 0.942101i | \(0.391152\pi\) | |||||||
\(458\) | −2.84788e12 | −3.02432 | ||||||||
\(459\) | −1.03095e12 | + | 4.08670e10i | −1.08413 | + | 0.0429749i | ||||
\(460\) | 2.06941e11 | 0.215495 | ||||||||
\(461\) | −1.45870e12 | −1.50422 | −0.752110 | − | 0.659038i | \(-0.770964\pi\) | ||||
−0.752110 | + | 0.659038i | \(0.770964\pi\) | |||||||
\(462\) | − | 1.01498e12i | − | 1.03650i | ||||||
\(463\) | 1.55507e12 | 1.57266 | 0.786330 | − | 0.617807i | \(-0.211979\pi\) | ||||
0.786330 | + | 0.617807i | \(0.211979\pi\) | |||||||
\(464\) | − | 1.78614e11i | − | 0.178889i | ||||||
\(465\) | 3.55283e11i | 0.352400i | ||||||||
\(466\) | 2.45538e12i | 2.41203i | ||||||||
\(467\) | 1.93889e12 | 1.88638 | 0.943188 | − | 0.332260i | \(-0.107811\pi\) | ||||
0.943188 | + | 0.332260i | \(0.107811\pi\) | |||||||
\(468\) | 8.09157e9 | 0.00779698 | ||||||||
\(469\) | 3.53123e11i | 0.337014i | ||||||||
\(470\) | − | 9.72992e11i | − | 0.919748i | ||||||
\(471\) | 4.31565e11i | 0.404066i | ||||||||
\(472\) | 1.40578e12 | 1.30370 | ||||||||
\(473\) | 8.64515e11i | 0.794141i | ||||||||
\(474\) | −1.46823e12 | −1.33595 | ||||||||
\(475\) | −3.87591e11 | −0.349343 | ||||||||
\(476\) | 1.13298e12 | − | 4.49112e10i | 1.01156 | − | 0.0400981i | ||||
\(477\) | 5.98296e11 | 0.529155 | ||||||||
\(478\) | 1.15233e12 | 1.00960 | ||||||||
\(479\) | 1.79275e12i | 1.55600i | 0.628266 | + | 0.777998i | \(0.283765\pi\) | ||||
−0.628266 | + | 0.777998i | \(0.716235\pi\) | |||||||
\(480\) | 7.43209e11 | 0.639036 | ||||||||
\(481\) | − | 1.54146e10i | − | 0.0131304i | ||||||
\(482\) | − | 1.51665e11i | − | 0.127989i | ||||||
\(483\) | 1.44533e11i | 0.120838i | ||||||||
\(484\) | −6.13029e11 | −0.507782 | ||||||||
\(485\) | −9.21824e11 | −0.756502 | ||||||||
\(486\) | − | 1.02175e12i | − | 0.830768i | ||||||
\(487\) | − | 1.88154e12i | − | 1.51577i | −0.652386 | − | 0.757887i | \(-0.726232\pi\) | ||
0.652386 | − | 0.757887i | \(-0.273768\pi\) | |||||||
\(488\) | − | 2.72865e11i | − | 0.217801i | ||||||
\(489\) | −2.95093e11 | −0.233383 | ||||||||
\(490\) | 7.52162e11i | 0.589426i | ||||||||
\(491\) | 2.04604e12 | 1.58872 | 0.794359 | − | 0.607448i | \(-0.207807\pi\) | ||||
0.794359 | + | 0.607448i | \(0.207807\pi\) | |||||||
\(492\) | −2.79118e12 | −2.14756 | ||||||||
\(493\) | −1.28846e12 | + | 5.10746e10i | −0.982336 | + | 0.0389398i | ||||
\(494\) | 2.44384e10 | 0.0184630 | ||||||||
\(495\) | 2.72165e11 | 0.203755 | ||||||||
\(496\) | − | 1.54021e11i | − | 0.114265i | ||||||
\(497\) | 1.48477e12 | 1.09158 | ||||||||
\(498\) | − | 2.28625e12i | − | 1.66568i | ||||||
\(499\) | − | 2.49934e12i | − | 1.80457i | −0.431141 | − | 0.902284i | \(-0.641889\pi\) | ||
0.431141 | − | 0.902284i | \(-0.358111\pi\) | |||||||
\(500\) | − | 2.20732e12i | − | 1.57943i | ||||||
\(501\) | −7.27395e11 | −0.515823 | ||||||||
\(502\) | −4.56701e11 | −0.320970 | ||||||||
\(503\) | 1.26660e12i | 0.882231i | 0.897450 | + | 0.441115i | \(0.145417\pi\) | ||||
−0.897450 | + | 0.441115i | \(0.854583\pi\) | |||||||
\(504\) | 2.18469e11i | 0.150817i | ||||||||
\(505\) | − | 1.40153e12i | − | 0.958942i | ||||||
\(506\) | 5.79759e11 | 0.393161 | ||||||||
\(507\) | − | 1.27152e12i | − | 0.854650i | ||||||
\(508\) | −1.81063e12 | −1.20626 | ||||||||
\(509\) | −9.24061e11 | −0.610198 | −0.305099 | − | 0.952321i | \(-0.598690\pi\) | ||||
−0.305099 | + | 0.952321i | \(0.598690\pi\) | |||||||
\(510\) | −5.40532e10 | − | 1.36360e12i | −0.0353798 | − | 0.892529i | ||||
\(511\) | 1.07401e12 | 0.696811 | ||||||||
\(512\) | −5.62439e11 | −0.361710 | ||||||||
\(513\) | − | 1.04466e12i | − | 0.665960i | ||||||
\(514\) | 2.92400e12 | 1.84775 | ||||||||
\(515\) | 1.65016e11i | 0.103370i | ||||||||
\(516\) | 1.45320e12i | 0.902406i | ||||||||
\(517\) | − | 1.64994e12i | − | 1.01569i | ||||||
\(518\) | 1.19636e12 | 0.730090 | ||||||||
\(519\) | −9.06991e11 | −0.548719 | ||||||||
\(520\) | 1.75612e10i | 0.0105327i | ||||||||
\(521\) | 1.78556e12i | 1.06171i | 0.847464 | + | 0.530853i | \(0.178128\pi\) | ||||
−0.847464 | + | 0.530853i | \(0.821872\pi\) | |||||||
\(522\) | − | 7.14184e11i | − | 0.421010i | ||||||
\(523\) | 1.92158e11 | 0.112306 | 0.0561528 | − | 0.998422i | \(-0.482117\pi\) | ||||
0.0561528 | + | 0.998422i | \(0.482117\pi\) | |||||||
\(524\) | 1.84506e12i | 1.06910i | ||||||||
\(525\) | 5.59173e11 | 0.321240 | ||||||||
\(526\) | −1.57373e12 | −0.896386 | ||||||||
\(527\) | −1.11106e12 | + | 4.40423e10i | −0.627463 | + | 0.0248726i | ||||
\(528\) | 3.20546e11 | 0.179489 | ||||||||
\(529\) | 1.71860e12 | 0.954164 | ||||||||
\(530\) | 3.73258e12i | 2.05479i | ||||||||
\(531\) | −7.56801e11 | −0.413101 | ||||||||
\(532\) | 1.14804e12i | 0.621379i | ||||||||
\(533\) | 5.76795e10i | 0.0309563i | ||||||||
\(534\) | 2.73833e12i | 1.45730i | ||||||||
\(535\) | −2.18229e12 | −1.15165 | ||||||||
\(536\) | 8.28302e11 | 0.433458 | ||||||||
\(537\) | − | 2.38656e11i | − | 0.123848i | ||||||
\(538\) | 5.48929e12i | 2.82485i | ||||||||
\(539\) | 1.27547e12i | 0.650909i | ||||||||
\(540\) | 2.15789e12 | 1.09209 | ||||||||
\(541\) | − | 1.86552e12i | − | 0.936294i | −0.883651 | − | 0.468147i | \(-0.844922\pi\) | ||
0.883651 | − | 0.468147i | \(-0.155078\pi\) | |||||||
\(542\) | −5.10791e11 | −0.254241 | ||||||||
\(543\) | 2.61364e12 | 1.29017 | ||||||||
\(544\) | 9.21312e10 | + | 2.32420e12i | 0.0451036 | + | 1.13783i | ||||
\(545\) | −8.56157e10 | −0.0415690 | ||||||||
\(546\) | −3.52570e10 | −0.0169777 | ||||||||
\(547\) | 7.99617e11i | 0.381891i | 0.981601 | + | 0.190945i | \(0.0611554\pi\) | ||||
−0.981601 | + | 0.190945i | \(0.938845\pi\) | |||||||
\(548\) | −1.84892e12 | −0.875799 | ||||||||
\(549\) | 1.46897e11i | 0.0690138i | ||||||||
\(550\) | − | 2.24299e12i | − | 1.04519i | ||||||
\(551\) | − | 1.30559e12i | − | 0.603429i | ||||||
\(552\) | 3.39023e11 | 0.155419 | ||||||||
\(553\) | −1.42532e12 | −0.648112 | ||||||||
\(554\) | − | 2.83164e12i | − | 1.27716i | ||||||
\(555\) | − | 8.71536e11i | − | 0.389912i | ||||||
\(556\) | 4.05015e12i | 1.79736i | ||||||||
\(557\) | −9.85166e11 | −0.433672 | −0.216836 | − | 0.976208i | \(-0.569574\pi\) | ||||
−0.216836 | + | 0.976208i | \(0.569574\pi\) | |||||||
\(558\) | − | 6.15850e11i | − | 0.268919i | ||||||
\(559\) | 3.00302e10 | 0.0130079 | ||||||||
\(560\) | 1.83506e11 | 0.0788506 | ||||||||
\(561\) | −9.16600e10 | − | 2.31231e12i | −0.0390703 | − | 0.985629i | ||||
\(562\) | 1.34027e12 | 0.566733 | ||||||||
\(563\) | −2.98482e12 | −1.25207 | −0.626037 | − | 0.779793i | \(-0.715324\pi\) | ||||
−0.626037 | + | 0.779793i | \(0.715324\pi\) | |||||||
\(564\) | − | 2.77345e12i | − | 1.15416i | ||||||
\(565\) | −1.57580e12 | −0.650552 | ||||||||
\(566\) | 2.65723e11i | 0.108832i | ||||||||
\(567\) | 1.06999e12i | 0.434765i | ||||||||
\(568\) | − | 3.48275e12i | − | 1.40396i | ||||||
\(569\) | 2.16083e12 | 0.864202 | 0.432101 | − | 0.901825i | \(-0.357772\pi\) | ||||
0.432101 | + | 0.901825i | \(0.357772\pi\) | |||||||
\(570\) | 1.38174e12 | 0.548263 | ||||||||
\(571\) | − | 2.50099e12i | − | 0.984576i | −0.870432 | − | 0.492288i | \(-0.836161\pi\) | ||
0.870432 | − | 0.492288i | \(-0.163839\pi\) | |||||||
\(572\) | 8.56021e10i | 0.0334351i | ||||||||
\(573\) | 1.86902e12i | 0.724301i | ||||||||
\(574\) | −4.47661e12 | −1.72126 | ||||||||
\(575\) | 3.19400e11i | 0.121851i | ||||||||
\(576\) | −1.15895e12 | −0.438696 | ||||||||
\(577\) | 3.98607e12 | 1.49711 | 0.748556 | − | 0.663072i | \(-0.230748\pi\) | ||||
0.748556 | + | 0.663072i | \(0.230748\pi\) | |||||||
\(578\) | 4.25762e12 | − | 3.38076e11i | 1.58669 | − | 0.125991i | ||||
\(579\) | −4.27978e11 | −0.158259 | ||||||||
\(580\) | 2.69688e12 | 0.989546 | ||||||||
\(581\) | − | 2.21944e12i | − | 0.808073i | ||||||
\(582\) | −4.34111e12 | −1.56837 | ||||||||
\(583\) | 6.32948e12i | 2.26913i | ||||||||
\(584\) | − | 2.51925e12i | − | 0.896219i | ||||||
\(585\) | − | 9.45406e9i | − | 0.00333747i | ||||||
\(586\) | −3.45374e12 | −1.20990 | ||||||||
\(587\) | 3.85772e11 | 0.134110 | 0.0670548 | − | 0.997749i | \(-0.478640\pi\) | ||||
0.0670548 | + | 0.997749i | \(0.478640\pi\) | |||||||
\(588\) | 2.14399e12i | 0.739648i | ||||||||
\(589\) | − | 1.12583e12i | − | 0.385438i | ||||||
\(590\) | − | 4.72145e12i | − | 1.60414i | ||||||
\(591\) | 3.68913e12 | 1.24388 | ||||||||
\(592\) | 3.77825e11i | 0.126428i | ||||||||
\(593\) | 3.33499e12 | 1.10751 | 0.553755 | − | 0.832679i | \(-0.313194\pi\) | ||||
0.553755 | + | 0.832679i | \(0.313194\pi\) | |||||||
\(594\) | 6.04546e12 | 1.99246 | ||||||||
\(595\) | −5.24736e10 | − | 1.32375e12i | −0.0171638 | − | 0.432993i | ||||
\(596\) | −4.74397e12 | −1.54004 | ||||||||
\(597\) | −1.78436e12 | −0.574907 | ||||||||
\(598\) | − | 2.01388e10i | − | 0.00643989i | ||||||
\(599\) | −3.02329e12 | −0.959531 | −0.479766 | − | 0.877397i | \(-0.659278\pi\) | ||||
−0.479766 | + | 0.877397i | \(0.659278\pi\) | |||||||
\(600\) | − | 1.31162e12i | − | 0.413169i | ||||||
\(601\) | 1.33418e12i | 0.417137i | 0.978008 | + | 0.208568i | \(0.0668804\pi\) | ||||
−0.978008 | + | 0.208568i | \(0.933120\pi\) | |||||||
\(602\) | 2.33070e12i | 0.723273i | ||||||||
\(603\) | −4.45915e11 | −0.137349 | ||||||||
\(604\) | 5.94222e12 | 1.81670 | ||||||||
\(605\) | 7.16254e11i | 0.217354i | ||||||||
\(606\) | − | 6.60020e12i | − | 1.98806i | ||||||
\(607\) | 8.24460e11i | 0.246502i | 0.992376 | + | 0.123251i | \(0.0393320\pi\) | ||||
−0.992376 | + | 0.123251i | \(0.960668\pi\) | |||||||
\(608\) | −2.35511e12 | −0.698947 | ||||||||
\(609\) | 1.88357e12i | 0.554886i | ||||||||
\(610\) | −9.16443e11 | −0.267992 | ||||||||
\(611\) | −5.73131e10 | −0.0166368 | ||||||||
\(612\) | 5.67128e10 | + | 1.43070e12i | 0.0163418 | + | 0.412255i | ||||
\(613\) | −2.33330e12 | −0.667419 | −0.333709 | − | 0.942676i | \(-0.608300\pi\) | ||||
−0.333709 | + | 0.942676i | \(0.608300\pi\) | |||||||
\(614\) | −4.90938e12 | −1.39402 | ||||||||
\(615\) | 3.26118e12i | 0.919256i | ||||||||
\(616\) | −2.31122e12 | −0.646737 | ||||||||
\(617\) | − | 3.34499e12i | − | 0.929206i | −0.885519 | − | 0.464603i | \(-0.846197\pi\) | ||
0.885519 | − | 0.464603i | \(-0.153803\pi\) | |||||||
\(618\) | 7.77104e11i | 0.214304i | ||||||||
\(619\) | − | 3.20260e12i | − | 0.876788i | −0.898783 | − | 0.438394i | \(-0.855547\pi\) | ||
0.898783 | − | 0.438394i | \(-0.144453\pi\) | |||||||
\(620\) | 2.32556e12 | 0.632069 | ||||||||
\(621\) | −8.60869e11 | −0.232287 | ||||||||
\(622\) | 4.82176e12i | 1.29166i | ||||||||
\(623\) | 2.65831e12i | 0.706983i | ||||||||
\(624\) | − | 1.11346e10i | − | 0.00293999i | ||||||
\(625\) | −4.07859e11 | −0.106918 | ||||||||
\(626\) | − | 3.12978e12i | − | 0.814571i | ||||||
\(627\) | 2.34306e12 | 0.605452 | ||||||||
\(628\) | 2.82488e12 | 0.724738 | ||||||||
\(629\) | 2.72551e12 | − | 1.08039e11i | 0.694255 | − | 0.0275203i | ||||
\(630\) | 7.33747e11 | 0.185573 | ||||||||
\(631\) | 1.11507e12 | 0.280007 | 0.140004 | − | 0.990151i | \(-0.455289\pi\) | ||||
0.140004 | + | 0.990151i | \(0.455289\pi\) | |||||||
\(632\) | 3.34330e12i | 0.833583i | ||||||||
\(633\) | −4.16363e12 | −1.03076 | ||||||||
\(634\) | − | 8.94129e12i | − | 2.19785i | ||||||
\(635\) | 2.11551e12i | 0.516337i | ||||||||
\(636\) | 1.06395e13i | 2.57848i | ||||||||
\(637\) | 4.43053e10 | 0.0106618 | ||||||||
\(638\) | 7.55548e12 | 1.80538 | ||||||||
\(639\) | 1.87493e12i | 0.444868i | ||||||||
\(640\) | − | 4.05790e12i | − | 0.956074i | ||||||
\(641\) | − | 4.56993e12i | − | 1.06917i | −0.845113 | − | 0.534587i | \(-0.820467\pi\) | ||
0.845113 | − | 0.534587i | \(-0.179533\pi\) | |||||||
\(642\) | −1.02770e13 | −2.38758 | ||||||||
\(643\) | 2.30320e12i | 0.531351i | 0.964062 | + | 0.265676i | \(0.0855950\pi\) | ||||
−0.964062 | + | 0.265676i | \(0.914405\pi\) | |||||||
\(644\) | 9.46062e11 | 0.216737 | ||||||||
\(645\) | 1.69790e12 | 0.386272 | ||||||||
\(646\) | 1.71286e11 | + | 4.32103e12i | 0.0386968 | + | 0.976205i | ||||
\(647\) | −5.60809e12 | −1.25819 | −0.629094 | − | 0.777329i | \(-0.716574\pi\) | ||||
−0.629094 | + | 0.777329i | \(0.716574\pi\) | |||||||
\(648\) | 2.50981e12 | 0.559182 | ||||||||
\(649\) | − | 8.00633e12i | − | 1.77146i | ||||||
\(650\) | −7.79136e10 | −0.0171200 | ||||||||
\(651\) | 1.62422e12i | 0.354431i | ||||||||
\(652\) | 1.93158e12i | 0.418598i | ||||||||
\(653\) | − | 1.27396e12i | − | 0.274186i | −0.990558 | − | 0.137093i | \(-0.956224\pi\) | ||
0.990558 | − | 0.137093i | \(-0.0437759\pi\) | |||||||
\(654\) | −4.03187e11 | −0.0861800 | ||||||||
\(655\) | 2.15574e12 | 0.457625 | ||||||||
\(656\) | − | 1.41377e12i | − | 0.298066i | ||||||
\(657\) | 1.35624e12i | 0.283982i | ||||||||
\(658\) | − | 4.44817e12i | − | 0.925050i | ||||||
\(659\) | −2.22728e12 | −0.460035 | −0.230017 | − | 0.973187i | \(-0.573878\pi\) | ||||
−0.230017 | + | 0.973187i | \(0.573878\pi\) | |||||||
\(660\) | 4.83991e12i | 0.992864i | ||||||||
\(661\) | 5.98094e12 | 1.21860 | 0.609302 | − | 0.792938i | \(-0.291450\pi\) | ||||
0.609302 | + | 0.792938i | \(0.291450\pi\) | |||||||
\(662\) | 1.04017e13 | 2.10497 | ||||||||
\(663\) | −8.03217e10 | + | 3.18395e9i | −0.0161444 | + | 0.000639964i | ||||
\(664\) | −5.20602e12 | −1.03932 | ||||||||
\(665\) | 1.34136e12 | 0.265979 | ||||||||
\(666\) | 1.51073e12i | 0.297545i | ||||||||
\(667\) | −1.07589e12 | −0.210476 | ||||||||
\(668\) | 4.76128e12i | 0.925186i | ||||||||
\(669\) | − | 4.30679e12i | − | 0.831259i | ||||||
\(670\) | − | 2.78193e12i | − | 0.533346i | ||||||
\(671\) | −1.55405e12 | −0.295946 | ||||||||
\(672\) | 3.39769e12 | 0.642720 | ||||||||
\(673\) | 6.43719e12i | 1.20956i | 0.796392 | + | 0.604781i | \(0.206739\pi\) | ||||
−0.796392 | + | 0.604781i | \(0.793261\pi\) | |||||||
\(674\) | 3.30425e12i | 0.616742i | ||||||||
\(675\) | 3.33055e12i | 0.617518i | ||||||||
\(676\) | −8.32295e12 | −1.53291 | ||||||||
\(677\) | 7.34022e11i | 0.134295i | 0.997743 | + | 0.0671476i | \(0.0213898\pi\) | ||||
−0.997743 | + | 0.0671476i | \(0.978610\pi\) | |||||||
\(678\) | −7.42085e12 | −1.34871 | ||||||||
\(679\) | −4.21425e12 | −0.760863 | ||||||||
\(680\) | −3.10506e12 | + | 1.23085e11i | −0.556903 | + | 0.0220756i | ||||
\(681\) | 6.73477e11 | 0.119994 | ||||||||
\(682\) | 6.51519e12 | 1.15318 | ||||||||
\(683\) | − | 4.45334e12i | − | 0.783057i | −0.920166 | − | 0.391528i | \(-0.871947\pi\) | ||
0.920166 | − | 0.391528i | \(-0.128053\pi\) | |||||||
\(684\) | −1.44972e12 | −0.253240 | ||||||||
\(685\) | 2.16024e12i | 0.374883i | ||||||||
\(686\) | 9.53363e12i | 1.64361i | ||||||||
\(687\) | 9.48460e12i | 1.62448i | ||||||||
\(688\) | −7.36067e11 | −0.125248 | ||||||||
\(689\) | 2.19864e11 | 0.0371679 | ||||||||
\(690\) | − | 1.13864e12i | − | 0.191234i | ||||||
\(691\) | − | 1.18066e12i | − | 0.197004i | −0.995137 | − | 0.0985019i | \(-0.968595\pi\) | ||
0.995137 | − | 0.0985019i | \(-0.0314051\pi\) | |||||||
\(692\) | 5.93685e12i | 0.984189i | ||||||||
\(693\) | 1.24424e12 | 0.204930 | ||||||||
\(694\) | − | 1.74644e13i | − | 2.85782i | ||||||
\(695\) | 4.73213e12 | 0.769352 | ||||||||
\(696\) | 4.41818e12 | 0.713678 | ||||||||
\(697\) | −1.01985e13 | + | 4.04269e11i | −1.63677 | + | 0.0648817i | ||||
\(698\) | 2.31770e11 | 0.0369579 | ||||||||
\(699\) | 8.17742e12 | 1.29559 | ||||||||
\(700\) | − | 3.66015e12i | − | 0.576180i | ||||||
\(701\) | 5.00732e11 | 0.0783202 | 0.0391601 | − | 0.999233i | \(-0.487532\pi\) | ||||
0.0391601 | + | 0.999233i | \(0.487532\pi\) | |||||||
\(702\) | − | 2.09998e11i | − | 0.0326361i | ||||||
\(703\) | 2.76175e12i | 0.426467i | ||||||||
\(704\) | − | 1.22607e13i | − | 1.88122i | ||||||
\(705\) | −3.24046e12 | −0.494033 | ||||||||
\(706\) | 6.61352e12 | 1.00187 | ||||||||
\(707\) | − | 6.40731e12i | − | 0.964470i | ||||||
\(708\) | − | 1.34582e13i | − | 2.01297i | ||||||
\(709\) | − | 4.45528e12i | − | 0.662166i | −0.943602 | − | 0.331083i | \(-0.892586\pi\) | ||
0.943602 | − | 0.331083i | \(-0.107414\pi\) | |||||||
\(710\) | −1.16971e13 | −1.72749 | ||||||||
\(711\) | − | 1.79986e12i | − | 0.264135i | ||||||
\(712\) | 6.23545e12 | 0.909301 | ||||||||
\(713\) | −9.27757e11 | −0.134441 | ||||||||
\(714\) | −2.47112e11 | − | 6.23391e12i | −0.0355838 | − | 0.897674i | ||||
\(715\) | 1.00016e11 | 0.0143118 | ||||||||
\(716\) | −1.56216e12 | −0.222135 | ||||||||
\(717\) | − | 3.83773e12i | − | 0.542298i | ||||||
\(718\) | 1.60288e13 | 2.25083 | ||||||||
\(719\) | 2.07009e12i | 0.288874i | 0.989514 | + | 0.144437i | \(0.0461372\pi\) | ||||
−0.989514 | + | 0.144437i | \(0.953863\pi\) | |||||||
\(720\) | 2.31727e11i | 0.0321352i | ||||||||
\(721\) | 7.54394e11i | 0.103966i | ||||||||
\(722\) | 7.24333e12 | 0.992021 | ||||||||
\(723\) | −5.05105e11 | −0.0687479 | ||||||||
\(724\) | − | 1.71080e13i | − | 2.31407i | ||||||
\(725\) | 4.16245e12i | 0.559536i | ||||||||
\(726\) | 3.37303e12i | 0.450615i | ||||||||
\(727\) | −5.41864e12 | −0.719425 | −0.359713 | − | 0.933063i | \(-0.617125\pi\) | ||||
−0.359713 | + | 0.933063i | \(0.617125\pi\) | |||||||
\(728\) | 8.02837e10i | 0.0105934i | ||||||||
\(729\) | −8.42474e12 | −1.10480 | ||||||||
\(730\) | −8.46114e12 | −1.10275 | ||||||||
\(731\) | 2.10478e11 | + | 5.30975e12i | 0.0272633 | + | 0.687774i | ||||
\(732\) | −2.61226e12 | −0.336292 | ||||||||
\(733\) | 1.11750e13 | 1.42982 | 0.714909 | − | 0.699218i | \(-0.246468\pi\) | ||||
0.714909 | + | 0.699218i | \(0.246468\pi\) | |||||||
\(734\) | 1.46137e13i | 1.85836i | ||||||||
\(735\) | 2.50501e12 | 0.316603 | ||||||||
\(736\) | 1.94076e12i | 0.243793i | ||||||||
\(737\) | − | 4.71742e12i | − | 0.588980i | ||||||
\(738\) | − | 5.65295e12i | − | 0.701490i | ||||||
\(739\) | 5.17452e12 | 0.638219 | 0.319110 | − | 0.947718i | \(-0.396616\pi\) | ||||
0.319110 | + | 0.947718i | \(0.396616\pi\) | |||||||
\(740\) | −5.70477e12 | −0.699351 | ||||||||
\(741\) | − | 8.13898e10i | − | 0.00991718i | ||||||
\(742\) | 1.70640e13i | 2.06664i | ||||||||
\(743\) | 6.63620e12i | 0.798859i | 0.916764 | + | 0.399429i | \(0.130792\pi\) | ||||
−0.916764 | + | 0.399429i | \(0.869208\pi\) | |||||||
\(744\) | 3.80986e12 | 0.455859 | ||||||||
\(745\) | 5.54278e12i | 0.659211i | ||||||||
\(746\) | −1.46834e13 | −1.73581 | ||||||||
\(747\) | 2.80265e12 | 0.329326 | ||||||||
\(748\) | −1.51356e13 | + | 5.99975e11i | −1.76784 | + | 0.0700770i | ||||
\(749\) | −9.97665e12 | −1.15829 | ||||||||
\(750\) | −1.21452e13 | −1.40161 | ||||||||
\(751\) | 1.50960e13i | 1.73173i | 0.500275 | + | 0.865866i | \(0.333232\pi\) | ||||
−0.500275 | + | 0.865866i | \(0.666768\pi\) | |||||||
\(752\) | 1.40479e12 | 0.160189 | ||||||||
\(753\) | 1.52100e12i | 0.172406i | ||||||||
\(754\) | − | 2.62451e11i | − | 0.0295718i | ||||||
\(755\) | − | 6.94280e12i | − | 0.777630i | ||||||
\(756\) | 9.86511e12 | 1.09838 | ||||||||
\(757\) | 3.33377e12 | 0.368981 | 0.184491 | − | 0.982834i | \(-0.440936\pi\) | ||||
0.184491 | + | 0.982834i | \(0.440936\pi\) | |||||||
\(758\) | 2.42379e13i | 2.66676i | ||||||||
\(759\) | − | 1.93083e12i | − | 0.211182i | ||||||
\(760\) | − | 3.14635e12i | − | 0.342094i | ||||||
\(761\) | 1.76503e13 | 1.90774 | 0.953872 | − | 0.300213i | \(-0.0970579\pi\) | ||||
0.953872 | + | 0.300213i | \(0.0970579\pi\) | |||||||
\(762\) | 9.96249e12i | 1.07046i | ||||||||
\(763\) | −3.91404e11 | −0.0418086 | ||||||||
\(764\) | 1.22340e13 | 1.29912 | ||||||||
\(765\) | 1.67160e12 | − | 6.62623e10i | 0.176464 | − | 0.00699504i | ||||
\(766\) | 1.25908e13 | 1.32137 | ||||||||
\(767\) | −2.78112e11 | −0.0290162 | ||||||||
\(768\) | − | 5.66979e12i | − | 0.588087i | ||||||
\(769\) | 1.65629e12 | 0.170793 | 0.0853963 | − | 0.996347i | \(-0.472784\pi\) | ||||
0.0853963 | + | 0.996347i | \(0.472784\pi\) | |||||||
\(770\) | 7.76244e12i | 0.795774i | ||||||||
\(771\) | − | 9.73810e12i | − | 0.992497i | ||||||
\(772\) | 2.80139e12i | 0.283855i | ||||||||
\(773\) | 9.98087e12 | 1.00545 | 0.502725 | − | 0.864446i | \(-0.332331\pi\) | ||||
0.502725 | + | 0.864446i | \(0.332331\pi\) | |||||||
\(774\) | −2.94315e12 | −0.294767 | ||||||||
\(775\) | 3.58933e12i | 0.357401i | ||||||||
\(776\) | 9.88514e12i | 0.978600i | ||||||||
\(777\) | − | 3.98435e12i | − | 0.392160i | ||||||
\(778\) | −1.79150e13 | −1.75311 | ||||||||
\(779\) | − | 1.03341e13i | − | 1.00544i | ||||||
\(780\) | 1.68122e11 | 0.0162629 | ||||||||
\(781\) | −1.98352e13 | −1.90769 | ||||||||
\(782\) | 3.56081e12 | − | 1.41150e11i | 0.340501 | − | 0.0134974i | ||||
\(783\) | −1.12189e13 | −1.06665 | ||||||||
\(784\) | −1.08596e12 | −0.102658 | ||||||||
\(785\) | − | 3.30054e12i | − | 0.310221i | ||||||
\(786\) | 1.01519e13 | 0.948740 | ||||||||
\(787\) | − | 8.71656e12i | − | 0.809951i | −0.914328 | − | 0.404975i | \(-0.867280\pi\) | ||
0.914328 | − | 0.404975i | \(-0.132720\pi\) | |||||||
\(788\) | − | 2.41478e13i | − | 2.23105i | ||||||
\(789\) | 5.24117e12i | 0.481484i | ||||||||
\(790\) | 1.12288e13 | 1.02568 | ||||||||
\(791\) | −7.20398e12 | −0.654302 | ||||||||
\(792\) | − | 2.91855e12i | − | 0.263575i | ||||||
\(793\) | 5.39821e10i | 0.00484753i | ||||||||
\(794\) | 5.69928e12i | 0.508895i | ||||||||
\(795\) | 1.24310e13 | 1.10371 | ||||||||
\(796\) | 1.16798e13i | 1.03116i | ||||||||
\(797\) | −1.27804e13 | −1.12197 | −0.560987 | − | 0.827825i | \(-0.689578\pi\) | ||||
−0.560987 | + | 0.827825i | \(0.689578\pi\) | |||||||
\(798\) | 6.31681e12 | 0.551423 | ||||||||
\(799\) | −4.01700e11 | − | 1.01337e13i | −0.0348692 | − | 0.879647i | ||||
\(800\) | 7.50846e12 | 0.648106 | ||||||||
\(801\) | −3.35684e12 | −0.288127 | ||||||||
\(802\) | − | 3.27855e12i | − | 0.279832i | ||||||
\(803\) | −1.43479e13 | −1.21778 | ||||||||
\(804\) | − | 7.92971e12i | − | 0.669276i | ||||||
\(805\) | − | 1.10536e12i | − | 0.0927735i | ||||||
\(806\) | − | 2.26315e11i | − | 0.0188888i | ||||||
\(807\) | 1.82816e13 | 1.51734 | ||||||||
\(808\) | −1.50293e13 | −1.24047 | ||||||||
\(809\) | − | 3.13377e12i | − | 0.257216i | −0.991695 | − | 0.128608i | \(-0.958949\pi\) | ||
0.991695 | − | 0.128608i | \(-0.0410509\pi\) | |||||||
\(810\) | − | 8.42943e12i | − | 0.688043i | ||||||
\(811\) | − | 9.63303e12i | − | 0.781932i | −0.920405 | − | 0.390966i | \(-0.872141\pi\) | ||
0.920405 | − | 0.390966i | \(-0.127859\pi\) | |||||||
\(812\) | 1.23292e13 | 0.995250 | ||||||||
\(813\) | 1.70114e12i | 0.136563i | ||||||||
\(814\) | −1.59823e13 | −1.27593 | ||||||||
\(815\) | 2.25682e12 | 0.179180 | ||||||||
\(816\) | 1.96875e12 | − | 7.80413e10i | 0.155448 | − | 0.00616196i | ||||
\(817\) | −5.38036e12 | −0.422485 | ||||||||
\(818\) | −1.52469e13 | −1.19067 | ||||||||
\(819\) | − | 4.32206e10i | − | 0.00335670i | ||||||
\(820\) | 2.13465e13 | 1.64879 | ||||||||
\(821\) | − | 2.49670e13i | − | 1.91788i | −0.283602 | − | 0.958942i | \(-0.591529\pi\) | ||
0.283602 | − | 0.958942i | \(-0.408471\pi\) | |||||||
\(822\) | 1.01732e13i | 0.777200i | ||||||||
\(823\) | 4.54640e12i | 0.345437i | 0.984971 | + | 0.172718i | \(0.0552551\pi\) | ||||
−0.984971 | + | 0.172718i | \(0.944745\pi\) | |||||||
\(824\) | 1.76954e12 | 0.133718 | ||||||||
\(825\) | −7.47006e12 | −0.561412 | ||||||||
\(826\) | − | 2.15848e13i | − | 1.61338i | ||||||
\(827\) | − | 2.42269e13i | − | 1.80104i | −0.434819 | − | 0.900518i | \(-0.643188\pi\) | ||
0.434819 | − | 0.900518i | \(-0.356812\pi\) | |||||||
\(828\) | 1.19466e12i | 0.0883302i | ||||||||
\(829\) | 1.77633e13 | 1.30626 | 0.653130 | − | 0.757246i | \(-0.273456\pi\) | ||||
0.653130 | + | 0.757246i | \(0.273456\pi\) | |||||||
\(830\) | 1.74849e13i | 1.27883i | ||||||||
\(831\) | −9.43052e12 | −0.686011 | ||||||||
\(832\) | −4.25895e11 | −0.0308140 | ||||||||
\(833\) | 3.10531e11 | + | 7.83377e12i | 0.0223461 | + | 0.563726i | ||||
\(834\) | 2.22849e13 | 1.59501 | ||||||||
\(835\) | 5.56300e12 | 0.396023 | ||||||||
\(836\) | − | 1.53369e13i | − | 1.08595i | ||||||
\(837\) | −9.67423e12 | −0.681321 | ||||||||
\(838\) | 2.24171e13i | 1.57029i | ||||||||
\(839\) | 1.27875e13i | 0.890955i | 0.895293 | + | 0.445477i | \(0.146966\pi\) | ||||
−0.895293 | + | 0.445477i | \(0.853034\pi\) | |||||||
\(840\) | 4.53921e12i | 0.314574i | ||||||||
\(841\) | 4.85991e11 | 0.0335001 | ||||||||
\(842\) | −1.68299e13 | −1.15393 | ||||||||
\(843\) | − | 4.46364e12i | − | 0.304414i | ||||||
\(844\) | 2.72537e13i | 1.84878i | ||||||||
\(845\) | 9.72440e12i | 0.656157i | ||||||||
\(846\) | 5.61704e12 | 0.377000 | ||||||||
\(847\) | 3.27446e12i | 0.218607i | ||||||||
\(848\) | −5.38906e12 | −0.357875 | ||||||||
\(849\) | 8.84966e11 | 0.0584577 | ||||||||
\(850\) | −5.46087e11 | − | 1.37762e13i | −0.0358820 | − | 0.905197i | ||||
\(851\) | 2.27586e12 | 0.148752 | ||||||||
\(852\) | −3.33419e13 | −2.16777 | ||||||||
\(853\) | 1.39538e13i | 0.902450i | 0.892410 | + | 0.451225i | \(0.149013\pi\) | ||||
−0.892410 | + | 0.451225i | \(0.850987\pi\) | |||||||
\(854\) | −4.18965e12 | −0.269536 | ||||||||
\(855\) | 1.69383e12i | 0.108398i | ||||||||
\(856\) | 2.34017e13i | 1.48976i | ||||||||
\(857\) | 1.46381e13i | 0.926984i | 0.886101 | + | 0.463492i | \(0.153404\pi\) | ||||
−0.886101 | + | 0.463492i | \(0.846596\pi\) | |||||||
\(858\) | 4.71003e11 | 0.0296709 | ||||||||
\(859\) | 1.39610e13 | 0.874876 | 0.437438 | − | 0.899249i | \(-0.355886\pi\) | ||||
0.437438 | + | 0.899249i | \(0.355886\pi\) | |||||||
\(860\) | − | 1.11138e13i | − | 0.692822i | ||||||
\(861\) | 1.49089e13i | 0.924554i | ||||||||
\(862\) | − | 9.29093e12i | − | 0.573161i | ||||||
\(863\) | 3.05848e13 | 1.87697 | 0.938485 | − | 0.345321i | \(-0.112230\pi\) | ||||
0.938485 | + | 0.345321i | \(0.112230\pi\) | |||||||
\(864\) | 2.02373e13i | 1.23550i | ||||||||
\(865\) | 6.93652e12 | 0.421278 | ||||||||
\(866\) | 9.87480e12 | 0.596620 | ||||||||
\(867\) | −1.12593e12 | − | 1.41796e13i | −0.0676745 | − | 0.852273i | ||||
\(868\) | 1.06316e13 | 0.635712 | ||||||||
\(869\) | 1.90411e13 | 1.13267 | ||||||||
\(870\) | − | 1.48389e13i | − | 0.878141i | ||||||
\(871\) | −1.63867e11 | −0.00964737 | ||||||||
\(872\) | 9.18096e11i | 0.0537730i | ||||||||
\(873\) | − | 5.32165e12i | − | 0.310086i | ||||||
\(874\) | 3.60816e12i | 0.209163i | ||||||||
\(875\) | −1.17902e13 | −0.679965 | ||||||||
\(876\) | −2.41179e13 | −1.38380 | ||||||||
\(877\) | 1.08401e13i | 0.618781i | 0.950935 | + | 0.309391i | \(0.100125\pi\) | ||||
−0.950935 | + | 0.309391i | \(0.899875\pi\) | |||||||
\(878\) | − | 2.84676e13i | − | 1.61668i | ||||||
\(879\) | 1.15024e13i | 0.649886i | ||||||||
\(880\) | −2.45148e12 | −0.137802 | ||||||||
\(881\) | − | 2.25641e13i | − | 1.26190i | −0.775822 | − | 0.630952i | \(-0.782665\pi\) | ||
0.775822 | − | 0.630952i | \(-0.217335\pi\) | |||||||
\(882\) | −4.34220e12 | −0.241602 | ||||||||
\(883\) | −2.69045e13 | −1.48937 | −0.744684 | − | 0.667417i | \(-0.767400\pi\) | ||||
−0.744684 | + | 0.667417i | \(0.767400\pi\) | |||||||
\(884\) | 2.08410e10 | + | 5.25758e11i | 0.00114785 | + | 0.0289568i | ||||
\(885\) | −1.57243e13 | −0.861644 | ||||||||
\(886\) | 2.37301e12 | 0.129374 | ||||||||
\(887\) | 1.58992e12i | 0.0862422i | 0.999070 | + | 0.0431211i | \(0.0137301\pi\) | ||||
−0.999070 | + | 0.0431211i | \(0.986270\pi\) | |||||||
\(888\) | −9.34587e12 | −0.504384 | ||||||||
\(889\) | 9.67135e12i | 0.519313i | ||||||||
\(890\) | − | 2.09423e13i | − | 1.11884i | ||||||
\(891\) | − | 1.42941e13i | − | 0.759813i | ||||||
\(892\) | −2.81908e13 | −1.49096 | ||||||||
\(893\) | 1.02685e13 | 0.540349 | ||||||||
\(894\) | 2.61024e13i | 1.36666i | ||||||||
\(895\) | 1.82520e12i | 0.0950839i | ||||||||
\(896\) | − | 1.85513e13i | − | 0.961585i | ||||||
\(897\) | −6.70704e10 | −0.00345911 | ||||||||
\(898\) | − | 3.12088e13i | − | 1.60153i | ||||||
\(899\) | −1.20906e13 | −0.617348 | ||||||||
\(900\) | 4.62195e12 | 0.234819 | ||||||||
\(901\) | 1.54100e12 | + | 3.88749e13i | 0.0779006 | + | 1.96520i | ||||
\(902\) | 5.98036e13 | 3.00814 | ||||||||
\(903\) | 7.76218e12 | 0.388498 | ||||||||
\(904\) | 1.68980e13i | 0.841545i | ||||||||
\(905\) | −1.99887e13 | −0.990527 | ||||||||
\(906\) | − | 3.26955e13i | − | 1.61217i | ||||||
\(907\) | 1.69740e13i | 0.832821i | 0.909177 | + | 0.416411i | \(0.136712\pi\) | ||||
−0.909177 | + | 0.416411i | \(0.863288\pi\) | |||||||
\(908\) | − | 4.40834e12i | − | 0.215223i | ||||||
\(909\) | 8.09099e12 | 0.393065 | ||||||||
\(910\) | 2.69640e11 | 0.0130346 | ||||||||
\(911\) | − | 7.56497e12i | − | 0.363894i | −0.983308 | − | 0.181947i | \(-0.941760\pi\) | ||
0.983308 | − | 0.181947i | \(-0.0582399\pi\) | |||||||
\(912\) | 1.99493e12i | 0.0954886i | ||||||||
\(913\) | 2.96497e13i | 1.41222i | ||||||||
\(914\) | −2.25226e13 | −1.06748 | ||||||||
\(915\) | 3.05213e12i | 0.143949i | ||||||||
\(916\) | 6.20829e13 | 2.91368 | ||||||||
\(917\) | 9.85525e12 | 0.460263 | ||||||||
\(918\) | 3.71305e13 | − | 1.47185e12i | 1.72559 | − | 0.0684025i | ||||
\(919\) | −3.81894e13 | −1.76613 | −0.883065 | − | 0.469251i | \(-0.844524\pi\) | ||||
−0.883065 | + | 0.469251i | \(0.844524\pi\) | |||||||
\(920\) | −2.59279e12 | −0.119323 | ||||||||
\(921\) | 1.63502e13i | 0.748782i | ||||||||
\(922\) | 5.25360e13 | 2.39424 | ||||||||
\(923\) | 6.89007e11i | 0.0312476i | ||||||||
\(924\) | 2.21263e13i | 0.998586i | ||||||||
\(925\) | − | 8.80491e12i | − | 0.395446i | ||||||
\(926\) | −5.60068e13 | −2.50318 | ||||||||
\(927\) | −9.52630e11 | −0.0423707 | ||||||||
\(928\) | 2.52922e13i | 1.11949i | ||||||||
\(929\) | 3.31874e13i | 1.46185i | 0.682457 | + | 0.730925i | \(0.260911\pi\) | ||||
−0.682457 | + | 0.730925i | \(0.739089\pi\) | |||||||
\(930\) | − | 1.27958e13i | − | 0.560909i | ||||||
\(931\) | −7.93795e12 | −0.346286 | ||||||||
\(932\) | − | 5.35265e13i | − | 2.32379i | ||||||
\(933\) | 1.60584e13 | 0.693803 | ||||||||
\(934\) | −6.98306e13 | −3.00251 | ||||||||
\(935\) | 7.01001e11 | + | 1.76842e13i | 0.0299962 | + | 0.756716i | ||||
\(936\) | −1.01380e11 | −0.00431730 | ||||||||
\(937\) | 1.99592e13 | 0.845891 | 0.422945 | − | 0.906155i | \(-0.360996\pi\) | ||||
0.422945 | + | 0.906155i | \(0.360996\pi\) | |||||||
\(938\) | − | 1.27180e13i | − | 0.536421i | ||||||
\(939\) | −1.04234e13 | −0.437538 | ||||||||
\(940\) | 2.12109e13i | 0.886103i | ||||||||
\(941\) | 9.88180e12i | 0.410849i | 0.978673 | + | 0.205425i | \(0.0658576\pi\) | ||||
−0.978673 | + | 0.205425i | \(0.934142\pi\) | |||||||
\(942\) | − | 1.55431e13i | − | 0.643146i | ||||||
\(943\) | −8.51598e12 | −0.350697 | ||||||||
\(944\) | 6.81677e12 | 0.279386 | ||||||||
\(945\) | − | 1.15262e13i | − | 0.470159i | ||||||
\(946\) | − | 3.11361e13i | − | 1.26402i | ||||||
\(947\) | − | 4.35997e13i | − | 1.76161i | −0.473482 | − | 0.880803i | \(-0.657003\pi\) | ||
0.473482 | − | 0.880803i | \(-0.342997\pi\) | |||||||
\(948\) | 3.20069e13 | 1.28708 | ||||||||
\(949\) | 4.98395e11i | 0.0199469i | ||||||||
\(950\) | 1.39594e13 | 0.556044 | ||||||||
\(951\) | −2.97781e13 | −1.18055 | ||||||||
\(952\) | −1.41952e13 | + | 5.62698e11i | −0.560113 | + | 0.0222029i | ||||
\(953\) | −8.78631e12 | −0.345055 | −0.172528 | − | 0.985005i | \(-0.555193\pi\) | ||||
−0.172528 | + | 0.985005i | \(0.555193\pi\) | |||||||
\(954\) | −2.15480e13 | −0.842248 | ||||||||
\(955\) | − | 1.42940e13i | − | 0.556082i | ||||||
\(956\) | −2.51204e13 | −0.972672 | ||||||||
\(957\) | − | 2.51628e13i | − | 0.969740i | ||||||
\(958\) | − | 6.45670e13i | − | 2.47666i | ||||||
\(959\) | 9.87587e12i | 0.377043i | ||||||||
\(960\) | −2.40799e13 | −0.915029 | ||||||||
\(961\) | 1.60137e13 | 0.605671 | ||||||||
\(962\) | 5.55168e11i | 0.0208995i | ||||||||
\(963\) | − | 1.25983e13i | − | 0.472055i | ||||||
\(964\) | 3.30624e12i | 0.123307i | ||||||||
\(965\) | 3.27310e12 | 0.121503 | ||||||||
\(966\) | − | 5.20545e12i | − | 0.192336i | ||||||
\(967\) | 5.16213e13 | 1.89850 | 0.949249 | − | 0.314525i | \(-0.101845\pi\) | ||||
0.949249 | + | 0.314525i | \(0.101845\pi\) | |||||||
\(968\) | 7.68072e12 | 0.281166 | ||||||||
\(969\) | 1.43908e13 | − | 5.70451e11i | 0.524358 | − | 0.0207855i | ||||
\(970\) | 3.32001e13 | 1.20411 | ||||||||
\(971\) | 2.90086e13 | 1.04722 | 0.523612 | − | 0.851957i | \(-0.324584\pi\) | ||||
0.523612 | + | 0.851957i | \(0.324584\pi\) | |||||||
\(972\) | 2.22737e13i | 0.800377i | ||||||||
\(973\) | 2.16336e13 | 0.773787 | ||||||||
\(974\) | 6.77651e13i | 2.41263i | ||||||||
\(975\) | 2.59484e11i | 0.00919581i | ||||||||
\(976\) | − | 1.32315e12i | − | 0.0466750i | ||||||
\(977\) | −3.35721e13 | −1.17883 | −0.589417 | − | 0.807829i | \(-0.700642\pi\) | ||||
−0.589417 | + | 0.807829i | \(0.700642\pi\) | |||||||
\(978\) | 1.06280e13 | 0.371472 | ||||||||
\(979\) | − | 3.55126e13i | − | 1.23555i | ||||||
\(980\) | − | 1.63969e13i | − | 0.567864i | ||||||
\(981\) | − | 4.94256e11i | − | 0.0170389i | ||||||
\(982\) | −7.36895e13 | −2.52874 | ||||||||
\(983\) | 3.00685e13i | 1.02712i | 0.858054 | + | 0.513559i | \(0.171673\pi\) | ||||
−0.858054 | + | 0.513559i | \(0.828327\pi\) | |||||||
\(984\) | 3.49711e13 | 1.18914 | ||||||||
\(985\) | −2.82139e13 | −0.954991 | ||||||||
\(986\) | 4.64048e13 | − | 1.83949e12i | 1.56357 | − | 0.0619798i | ||||
\(987\) | −1.48142e13 | −0.496880 | ||||||||
\(988\) | −5.32749e11 | −0.0177876 | ||||||||
\(989\) | 4.43376e12i | 0.147363i | ||||||||
\(990\) | −9.80221e12 | −0.324314 | ||||||||
\(991\) | 2.45476e13i | 0.808494i | 0.914650 | + | 0.404247i | \(0.132466\pi\) | ||||
−0.914650 | + | 0.404247i | \(0.867534\pi\) | |||||||
\(992\) | 2.18098e13i | 0.715069i | ||||||||
\(993\) | − | 3.46420e13i | − | 1.13066i | ||||||
\(994\) | −5.34751e13 | −1.73745 | ||||||||
\(995\) | 1.36465e13 | 0.441384 | ||||||||
\(996\) | 4.98395e13i | 1.60475i | ||||||||
\(997\) | − | 4.26106e13i | − | 1.36581i | −0.730509 | − | 0.682904i | \(-0.760717\pi\) | ||
0.730509 | − | 0.682904i | \(-0.239283\pi\) | |||||||
\(998\) | 9.00156e13i | 2.87230i | ||||||||
\(999\) | 2.37316e13 | 0.753846 |
(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 | 17.10.b.a.16.2 | yes | 12 | |
3.2 | odd | 2 | 153.10.d.b.118.12 | 12 | |||
4.3 | odd | 2 | 272.10.b.c.33.3 | 12 | |||
17.4 | even | 4 | 289.10.a.c.1.12 | 12 | |||
17.13 | even | 4 | 289.10.a.c.1.11 | 12 | |||
17.16 | even | 2 | inner | 17.10.b.a.16.1 | ✓ | 12 | |
51.50 | odd | 2 | 153.10.d.b.118.11 | 12 | |||
68.67 | odd | 2 | 272.10.b.c.33.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.b.a.16.1 | ✓ | 12 | 17.16 | even | 2 | inner | |
17.10.b.a.16.2 | yes | 12 | 1.1 | even | 1 | trivial | |
153.10.d.b.118.11 | 12 | 51.50 | odd | 2 | |||
153.10.d.b.118.12 | 12 | 3.2 | odd | 2 | |||
272.10.b.c.33.3 | 12 | 4.3 | odd | 2 | |||
272.10.b.c.33.10 | 12 | 68.67 | odd | 2 | |||
289.10.a.c.1.11 | 12 | 17.13 | even | 4 | |||
289.10.a.c.1.12 | 12 | 17.4 | even | 4 |