Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,9,Mod(8,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.8");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.f (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.9976674150\) |
Analytic rank: | \(0\) |
Dimension: | \(138\) |
Relative dimension: | \(23\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 8.14 | ||
Character | \(\chi\) | \(=\) | 81.8 |
Dual form | 81.9.f.a.71.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.66670 | + | 1.35185i | 0.479169 | + | 0.0844904i | 0.408015 | − | 0.912975i | \(-0.366221\pi\) |
0.0711532 | + | 0.997465i | \(0.477332\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −183.611 | − | 66.8288i | −0.717229 | − | 0.261050i | ||||
\(5\) | 24.0534 | + | 28.6657i | 0.0384854 | + | 0.0458652i | 0.784944 | − | 0.619567i | \(-0.212692\pi\) |
−0.746458 | + | 0.665432i | \(0.768247\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2598.90 | + | 945.921i | −1.08242 | + | 0.393970i | −0.820809 | − | 0.571203i | \(-0.806477\pi\) |
−0.261614 | + | 0.965173i | \(0.584255\pi\) | |||||||
\(8\) | −3043.29 | − | 1757.05i | −0.742991 | − | 0.428966i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 145.659 | + | 252.288i | 0.0145659 | + | 0.0252288i | ||||
\(11\) | 4786.80 | − | 5704.68i | 0.326945 | − | 0.389637i | −0.577385 | − | 0.816472i | \(-0.695927\pi\) |
0.904330 | + | 0.426835i | \(0.140371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2684.14 | + | 15222.5i | 0.0939791 | + | 0.532982i | 0.995055 | + | 0.0993213i | \(0.0316672\pi\) |
−0.901076 | + | 0.433661i | \(0.857222\pi\) | |||||||
\(14\) | −21203.7 | + | 3738.78i | −0.551949 | + | 0.0973236i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 17361.5 | + | 14568.0i | 0.264916 | + | 0.222291i | ||||
\(17\) | 124728. | − | 72011.7i | 1.49337 | − | 0.862198i | 0.493400 | − | 0.869802i | \(-0.335754\pi\) |
0.999971 | + | 0.00760413i | \(0.00242049\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −101393. | + | 175618.i | −0.778024 | + | 1.34758i | 0.155054 | + | 0.987906i | \(0.450445\pi\) |
−0.933079 | + | 0.359672i | \(0.882889\pi\) | |||||||
\(20\) | −2500.76 | − | 6870.79i | −0.0156298 | − | 0.0429424i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 44410.8 | − | 37265.1i | 0.189582 | − | 0.159078i | ||||
\(23\) | 39698.1 | − | 109070.i | 0.141860 | − | 0.389756i | −0.848333 | − | 0.529462i | \(-0.822394\pi\) |
0.990193 | + | 0.139707i | \(0.0446159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 67588.2 | − | 383312.i | 0.173026 | − | 0.981277i | ||||
\(26\) | 120335.i | 0.263329i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 540399. | 0.879190 | ||||||||
\(29\) | 609347. | + | 107444.i | 0.861534 | + | 0.151912i | 0.586922 | − | 0.809643i | \(-0.300340\pi\) |
0.274612 | + | 0.961555i | \(0.411451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.01617e6 | + | 369854.i | 1.10032 | + | 0.400483i | 0.827433 | − | 0.561564i | \(-0.189800\pi\) |
0.272884 | + | 0.962047i | \(0.412022\pi\) | |||||||
\(32\) | 691668. | + | 824298.i | 0.659626 | + | 0.786112i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.05360e6 | − | 383479.i | 0.788424 | − | 0.286963i | ||||
\(35\) | −89627.8 | − | 51746.6i | −0.0597270 | − | 0.0344834i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −978631. | − | 1.69504e6i | −0.522170 | − | 0.904426i | −0.999667 | − | 0.0257923i | \(-0.991789\pi\) |
0.477497 | − | 0.878633i | \(-0.341544\pi\) | |||||||
\(38\) | −1.01476e6 | + | 1.20934e6i | −0.486662 | + | 0.579982i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −22834.5 | − | 129501.i | −0.00891974 | − | 0.0505864i | ||||
\(41\) | 1.39463e6 | − | 245911.i | 0.493541 | − | 0.0870247i | 0.0786625 | − | 0.996901i | \(-0.474935\pi\) |
0.414879 | + | 0.909877i | \(0.363824\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.04961e6 | + | 1.71982e6i | 0.599510 | + | 0.503049i | 0.891288 | − | 0.453437i | \(-0.149802\pi\) |
−0.291778 | + | 0.956486i | \(0.594247\pi\) | |||||||
\(44\) | −1.26014e6 | + | 727544.i | −0.336209 | + | 0.194110i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 451799. | − | 782539.i | 0.100905 | − | 0.174773i | ||||
\(47\) | 1.82238e6 | + | 5.00694e6i | 0.373462 | + | 1.02608i | 0.974013 | + | 0.226492i | \(0.0727258\pi\) |
−0.600551 | + | 0.799587i | \(0.705052\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.44340e6 | − | 1.21116e6i | 0.250382 | − | 0.210095i | ||||
\(50\) | 1.03636e6 | − | 2.84736e6i | 0.165817 | − | 0.455578i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 524465. | − | 2.97439e6i | 0.0717304 | − | 0.406803i | ||||
\(53\) | − | 3.45452e6i | − | 0.437809i | −0.975746 | − | 0.218905i | \(-0.929752\pi\) | ||
0.975746 | − | 0.218905i | \(-0.0702483\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 278668. | 0.0304534 | ||||||||
\(56\) | 9.57122e6 | + | 1.68767e6i | 0.973230 | + | 0.171607i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.52643e6 | + | 1.64749e6i | 0.399985 | + | 0.145583i | ||||
\(59\) | 1.16111e7 | + | 1.38375e7i | 0.958217 | + | 1.14196i | 0.989801 | + | 0.142458i | \(0.0455005\pi\) |
−0.0315836 | + | 0.999501i | \(0.510055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.16719e7 | − | 4.24821e6i | 0.842987 | − | 0.306822i | 0.115810 | − | 0.993271i | \(-0.463054\pi\) |
0.727178 | + | 0.686449i | \(0.240832\pi\) | |||||||
\(62\) | 7.29065e6 | + | 4.20926e6i | 0.493401 | + | 0.284865i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.28751e6 | + | 2.23004e6i | 0.0767418 | + | 0.132921i | ||||
\(65\) | −371801. | + | 443096.i | −0.0208285 | + | 0.0248224i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.92937e6 | − | 1.09420e7i | −0.0957452 | − | 0.542998i | −0.994516 | − | 0.104580i | \(-0.966650\pi\) |
0.898771 | − | 0.438418i | \(-0.144461\pi\) | |||||||
\(68\) | −2.77138e7 | + | 4.88669e6i | −1.29617 | + | 0.228549i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −617196. | − | 517889.i | −0.0257058 | − | 0.0215697i | ||||
\(71\) | 2.34487e7 | − | 1.35381e7i | 0.922752 | − | 0.532751i | 0.0382397 | − | 0.999269i | \(-0.487825\pi\) |
0.884512 | + | 0.466518i | \(0.154492\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.28556e7 | + | 2.22665e7i | −0.452690 | + | 0.784082i | −0.998552 | − | 0.0537933i | \(-0.982869\pi\) |
0.545862 | + | 0.837875i | \(0.316202\pi\) | |||||||
\(74\) | −5.21144e6 | − | 1.43183e7i | −0.173792 | − | 0.477491i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.03531e7 | − | 2.54693e7i | 0.909807 | − | 0.763418i | ||||
\(77\) | −7.04421e6 | + | 1.93538e7i | −0.200387 | + | 0.550558i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −981583. | + | 5.56684e6i | −0.0252011 | + | 0.142922i | −0.994812 | − | 0.101729i | \(-0.967562\pi\) |
0.969611 | + | 0.244652i | \(0.0786736\pi\) | |||||||
\(80\) | 848091.i | 0.0207054i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.10246e7 | 0.243842 | ||||||||
\(83\) | −5.90784e6 | − | 1.04171e6i | −0.124485 | − | 0.0219500i | 0.111059 | − | 0.993814i | \(-0.464576\pi\) |
−0.235543 | + | 0.971864i | \(0.575687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.06440e6 | + | 1.84329e6i | 0.0970179 | + | 0.0353116i | ||||
\(86\) | 1.33888e7 | + | 1.59561e7i | 0.244764 | + | 0.291698i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.45910e7 | + | 8.95039e6i | −0.410058 | + | 0.149249i | ||||
\(89\) | −3.29258e7 | − | 1.90097e7i | −0.524779 | − | 0.302981i | 0.214109 | − | 0.976810i | \(-0.431315\pi\) |
−0.738888 | + | 0.673829i | \(0.764649\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.13751e7 | − | 3.70227e7i | −0.311704 | − | 0.539887i | ||||
\(92\) | −1.45780e7 | + | 1.73734e7i | −0.203491 | + | 0.242512i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.20300e6 | + | 4.08503e7i | 0.0922576 | + | 0.523219i | ||||
\(95\) | −7.47305e6 | + | 1.31770e6i | −0.0917495 | + | 0.0161779i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.92181e6 | + | 8.32538e6i | 0.112074 | + | 0.0940410i | 0.697102 | − | 0.716972i | \(-0.254472\pi\) |
−0.585029 | + | 0.811013i | \(0.698917\pi\) | |||||||
\(98\) | 1.27034e7 | − | 7.33433e6i | 0.137726 | − | 0.0795162i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.80261e7 | + | 6.58632e7i | −0.380261 | + | 0.658632i | ||||
\(101\) | −2.54486e7 | − | 6.99195e7i | −0.244556 | − | 0.671912i | −0.999863 | − | 0.0165413i | \(-0.994735\pi\) |
0.755307 | − | 0.655371i | \(-0.227488\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.98778e7 | + | 3.34615e7i | −0.354309 | + | 0.297301i | −0.802518 | − | 0.596628i | \(-0.796507\pi\) |
0.448209 | + | 0.893929i | \(0.352062\pi\) | |||||||
\(104\) | 1.85780e7 | − | 5.10426e7i | 0.158806 | − | 0.436315i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.66998e6 | − | 2.64848e7i | 0.0369906 | − | 0.209784i | ||||
\(107\) | − | 2.19636e8i | − | 1.67559i | −0.545986 | − | 0.837795i | \(-0.683845\pi\) | ||
0.545986 | − | 0.837795i | \(-0.316155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.65997e8 | −1.88439 | −0.942194 | − | 0.335067i | \(-0.891241\pi\) | ||||
−0.942194 | + | 0.335067i | \(0.891241\pi\) | |||||||
\(110\) | 2.13646e6 | + | 376716.i | 0.0145923 | + | 0.00257302i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.89010e7 | − | 2.14382e7i | −0.374326 | − | 0.136244i | ||||
\(113\) | 7.63601e6 | + | 9.10024e6i | 0.0468331 | + | 0.0558135i | 0.788953 | − | 0.614454i | \(-0.210624\pi\) |
−0.742119 | + | 0.670268i | \(0.766179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.08144e6 | − | 1.48552e6i | 0.0233357 | − | 0.00849352i | ||||
\(116\) | −1.04702e8 | − | 6.04498e7i | −0.578260 | − | 0.333859i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.03123e7 | + | 1.21785e8i | 0.362663 | + | 0.628151i | ||||
\(119\) | −2.56037e8 | + | 3.05134e8i | −1.27678 | + | 1.52161i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.75931e7 | + | 1.56488e8i | 0.128724 | + | 0.730028i | ||||
\(122\) | 9.52276e7 | − | 1.67912e7i | 0.429857 | − | 0.0757953i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.61862e8 | − | 1.35818e8i | −0.684633 | − | 0.574476i | ||||
\(125\) | 2.52726e7 | − | 1.45912e7i | 0.103517 | − | 0.0597654i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.66357e7 | + | 2.88139e7i | −0.0639479 | + | 0.110761i | −0.896227 | − | 0.443596i | \(-0.853702\pi\) |
0.832279 | + | 0.554357i | \(0.187036\pi\) | |||||||
\(128\) | −8.73591e7 | − | 2.40017e8i | −0.325438 | − | 0.894133i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.44948e6 | + | 2.89446e6i | −0.0120776 | + | 0.0101343i | ||||
\(131\) | −1.61936e8 | + | 4.44915e8i | −0.549867 | + | 1.51075i | 0.284022 | + | 0.958818i | \(0.408331\pi\) |
−0.833890 | + | 0.551931i | \(0.813891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.73893e7 | − | 5.52322e8i | 0.311246 | − | 1.76517i | ||||
\(134\) | − | 8.64974e7i | − | 0.268277i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.06111e8 | −1.47942 | ||||||||
\(137\) | −2.76763e8 | − | 4.88007e7i | −0.785643 | − | 0.138530i | −0.233586 | − | 0.972336i | \(-0.575046\pi\) |
−0.552057 | + | 0.833806i | \(0.686157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.76410e8 | + | 2.46193e8i | 1.81197 | + | 0.659503i | 0.996769 | + | 0.0803220i | \(0.0255949\pi\) |
0.815199 | + | 0.579180i | \(0.196627\pi\) | |||||||
\(140\) | 1.29984e7 | + | 1.54909e7i | 0.0338360 | + | 0.0403242i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.98075e8 | − | 7.20935e7i | 0.487166 | − | 0.177314i | ||||
\(143\) | 9.96879e7 | + | 5.75548e7i | 0.238396 | + | 0.137638i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.15769e7 | + | 2.00518e7i | 0.0261891 | + | 0.0453608i | ||||
\(146\) | −1.28661e8 | + | 1.53332e8i | −0.283162 | + | 0.337459i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.64097e7 | + | 3.76628e8i | 0.138415 | + | 0.784993i | ||||
\(149\) | 8.91020e8 | − | 1.57111e8i | 1.80777 | − | 0.318758i | 0.834949 | − | 0.550327i | \(-0.185497\pi\) |
0.972819 | + | 0.231569i | \(0.0743859\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.47852e8 | − | 2.07973e8i | −0.476744 | − | 0.400036i | 0.372503 | − | 0.928031i | \(-0.378500\pi\) |
−0.849247 | + | 0.527995i | \(0.822944\pi\) | |||||||
\(152\) | 6.17136e8 | − | 3.56304e8i | 1.15613 | − | 0.667492i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.01692e7 | + | 1.38857e8i | −0.142536 | + | 0.246880i | ||||
\(155\) | 1.38401e7 | + | 3.80254e7i | 0.0239780 | + | 0.0658790i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.95886e8 | − | 5.00008e8i | 0.980764 | − | 0.822959i | −0.00344009 | − | 0.999994i | \(-0.501095\pi\) |
0.984205 | + | 0.177035i | \(0.0566506\pi\) | |||||||
\(158\) | −1.50510e7 | + | 4.13523e7i | −0.0241511 | + | 0.0663546i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.99213e6 | + | 3.96543e7i | −0.0106691 | + | 0.0605077i | ||||
\(161\) | 3.21012e8i | 0.477769i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.09107e9 | 1.54561 | 0.772806 | − | 0.634642i | \(-0.218852\pi\) | ||||
0.772806 | + | 0.634642i | \(0.218852\pi\) | |||||||
\(164\) | −2.72503e8 | − | 4.80496e7i | −0.376700 | − | 0.0664223i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.38854e7 | − | 1.59730e7i | −0.0577947 | − | 0.0210355i | ||||
\(167\) | 8.88832e8 | + | 1.05927e9i | 1.14276 | + | 1.36188i | 0.922294 | + | 0.386488i | \(0.126312\pi\) |
0.220462 | + | 0.975396i | \(0.429243\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.42016e8 | − | 1.97278e8i | 0.664455 | − | 0.241842i | ||||
\(170\) | 3.63354e7 | + | 2.09782e7i | 0.0435045 | + | 0.0251173i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.61396e8 | − | 4.52751e8i | −0.298665 | − | 0.517303i | ||||
\(173\) | −2.53987e7 | + | 3.02690e7i | −0.0283548 | + | 0.0337920i | −0.780035 | − | 0.625735i | \(-0.784799\pi\) |
0.751681 | + | 0.659527i | \(0.229243\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.86928e8 | + | 1.06012e9i | 0.199307 | + | 1.13032i | ||||
\(176\) | 1.66212e8 | − | 2.93077e7i | 0.173225 | − | 0.0305443i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.26734e8 | − | 1.90252e8i | −0.225858 | − | 0.189518i | ||||
\(179\) | 5.49026e8 | − | 3.16980e8i | 0.534787 | − | 0.308759i | −0.208177 | − | 0.978091i | \(-0.566753\pi\) |
0.742963 | + | 0.669332i | \(0.233420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.29163e8 | + | 7.43332e8i | −0.399860 | + | 0.692578i | −0.993708 | − | 0.111999i | \(-0.964275\pi\) |
0.593848 | + | 0.804577i | \(0.297608\pi\) | |||||||
\(182\) | −1.13827e8 | − | 3.12738e8i | −0.103743 | − | 0.285033i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.12453e8 | + | 2.62179e8i | −0.272592 | + | 0.228732i | ||||
\(185\) | 2.50501e7 | − | 6.88246e7i | 0.0213857 | − | 0.0587567i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.86243e8 | − | 1.05624e9i | 0.152305 | − | 0.863764i | ||||
\(188\) | − | 1.04111e9i | − | 0.833425i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.90750e7 | −0.0453304 | ||||||||
\(191\) | −6.61152e8 | − | 1.16579e8i | −0.496784 | − | 0.0875965i | −0.0803582 | − | 0.996766i | \(-0.525606\pi\) |
−0.416426 | + | 0.909170i | \(0.636718\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.97918e7 | − | 1.08433e7i | −0.0214718 | − | 0.00781508i | 0.331262 | − | 0.943539i | \(-0.392526\pi\) |
−0.352734 | + | 0.935724i | \(0.614748\pi\) | |||||||
\(194\) | 6.48129e7 | + | 7.72410e7i | 0.0457567 | + | 0.0545307i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.45964e8 | + | 1.25921e8i | −0.234426 | + | 0.0853242i | ||||
\(197\) | 8.67018e8 | + | 5.00573e8i | 0.575656 | + | 0.332355i | 0.759405 | − | 0.650618i | \(-0.225490\pi\) |
−0.183749 | + | 0.982973i | \(0.558823\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.45511e8 | + | 2.52033e8i | 0.0927865 | + | 0.160711i | 0.908683 | − | 0.417488i | \(-0.137089\pi\) |
−0.815896 | + | 0.578198i | \(0.803756\pi\) | |||||||
\(200\) | −8.79186e8 | + | 1.04777e9i | −0.549491 | + | 0.654858i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.00586e8 | − | 5.70454e8i | −0.0604135 | − | 0.342622i | ||||
\(203\) | −1.68526e9 | + | 2.97157e8i | −0.992392 | + | 0.174986i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.05948e7 | + | 3.40631e7i | 0.0229856 | + | 0.0192872i | ||||
\(206\) | −3.50966e8 | + | 2.02630e8i | −0.194893 | + | 0.112521i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.75161e8 | + | 3.03388e8i | −0.0935803 | + | 0.162086i | ||||
\(209\) | 5.16496e8 | + | 1.41906e9i | 0.270696 | + | 0.743731i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.57792e9 | − | 2.16313e9i | 1.30059 | − | 1.09132i | 0.310543 | − | 0.950559i | \(-0.399489\pi\) |
0.990043 | − | 0.140762i | \(-0.0449553\pi\) | |||||||
\(212\) | −2.30862e8 | + | 6.34287e8i | −0.114290 | + | 0.314009i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.96913e8 | − | 1.68388e9i | 0.141571 | − | 0.802890i | ||||
\(215\) | 1.00121e8i | 0.0468567i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.99076e9 | −1.34879 | ||||||||
\(218\) | −2.03932e9 | − | 3.59587e8i | −0.902940 | − | 0.159213i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.11663e7 | − | 1.86230e7i | −0.0218420 | − | 0.00794985i | ||||
\(221\) | 1.43098e9 | + | 1.70538e9i | 0.599882 | + | 0.714911i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.84150e8 | + | 1.39819e8i | −0.155339 | + | 0.0565388i | −0.418519 | − | 0.908208i | \(-0.637451\pi\) |
0.263180 | + | 0.964747i | \(0.415229\pi\) | |||||||
\(224\) | −2.57729e9 | − | 1.48800e9i | −1.02370 | − | 0.591032i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.62409e7 | + | 8.00915e7i | 0.0177252 | + | 0.0307010i | ||||
\(227\) | 1.70797e9 | − | 2.03548e9i | 0.643246 | − | 0.766591i | −0.341633 | − | 0.939833i | \(-0.610980\pi\) |
0.984879 | + | 0.173243i | \(0.0554245\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.47013e8 | + | 4.23652e9i | 0.271635 | + | 1.54052i | 0.749451 | + | 0.662060i | \(0.230318\pi\) |
−0.477816 | + | 0.878460i | \(0.658571\pi\) | |||||||
\(230\) | 3.32993e7 | − | 5.87157e6i | 0.0118994 | − | 0.00209818i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.66563e9 | − | 1.39763e9i | −0.574947 | − | 0.482438i | ||||
\(233\) | 2.49677e9 | − | 1.44151e9i | 0.847138 | − | 0.489095i | −0.0125463 | − | 0.999921i | \(-0.503994\pi\) |
0.859684 | + | 0.510826i | \(0.170660\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.96932e7 | + | 1.72674e8i | −0.0326884 | + | 0.0566180i | ||||
\(236\) | −1.20717e9 | − | 3.31667e9i | −0.389153 | − | 1.06919i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.37546e9 | + | 1.99324e9i | −0.740353 | + | 0.621230i | ||||
\(239\) | 6.28233e8 | − | 1.72606e9i | 0.192544 | − | 0.529010i | −0.805426 | − | 0.592696i | \(-0.798064\pi\) |
0.997970 | + | 0.0636865i | \(0.0202858\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.37356e8 | + | 4.18175e9i | −0.218579 | + | 1.23962i | 0.656007 | + | 0.754755i | \(0.272244\pi\) |
−0.874586 | + | 0.484870i | \(0.838867\pi\) | |||||||
\(242\) | 1.23705e9i | 0.360682i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.42698e9 | −0.684711 | ||||||||
\(245\) | 6.94374e7 | + | 1.22437e7i | 0.0192721 | + | 0.00339819i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.94549e9 | − | 1.07207e9i | −0.791353 | − | 0.288029i | ||||
\(248\) | −2.44264e9 | − | 2.91102e9i | −0.645733 | − | 0.769554i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.13483e8 | − | 7.77013e7i | 0.0546516 | − | 0.0198915i | ||||
\(251\) | −6.55995e9 | − | 3.78739e9i | −1.65274 | − | 0.954212i | −0.975937 | − | 0.218052i | \(-0.930030\pi\) |
−0.676807 | − | 0.736160i | \(-0.736637\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.32181e8 | − | 7.48559e8i | −0.105483 | − | 0.182702i | ||||
\(254\) | −1.66493e8 | + | 1.98419e8i | −0.0400001 | + | 0.0476703i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.59760e8 | − | 2.60743e9i | −0.107046 | − | 0.607089i | ||||
\(257\) | 1.33863e8 | − | 2.36037e7i | 0.0306852 | − | 0.00541062i | −0.158285 | − | 0.987394i | \(-0.550596\pi\) |
0.188970 | + | 0.981983i | \(0.439485\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.14673e9 | + | 3.47952e9i | 0.921525 | + | 0.773251i | ||||
\(260\) | 9.78782e7 | − | 5.65100e7i | 0.0214187 | − | 0.0123661i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.84297e9 | + | 3.19212e9i | −0.391123 | + | 0.677445i | ||||
\(263\) | 3.23234e9 | + | 8.88079e9i | 0.675608 | + | 1.85622i | 0.484899 | + | 0.874570i | \(0.338856\pi\) |
0.190709 | + | 0.981647i | \(0.438921\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.90265e7 | − | 8.30931e7i | 0.0200802 | − | 0.0168493i | ||||
\(266\) | 1.49331e9 | − | 4.10283e9i | 0.298279 | − | 0.819515i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.76989e8 | + | 2.13801e9i | −0.0730784 | + | 0.414448i | ||||
\(269\) | − | 1.18549e8i | − | 0.0226407i | −0.999936 | − | 0.0113204i | \(-0.996397\pi\) | ||
0.999936 | − | 0.0113204i | \(-0.00360346\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.58270e9 | 0.664252 | 0.332126 | − | 0.943235i | \(-0.392234\pi\) | ||||
0.332126 | + | 0.943235i | \(0.392234\pi\) | |||||||
\(272\) | 3.21453e9 | + | 5.66809e8i | 0.587276 | + | 0.103553i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.05589e9 | − | 7.48281e8i | −0.364751 | − | 0.132759i | ||||
\(275\) | −1.86314e9 | − | 2.22040e9i | −0.325773 | − | 0.388241i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.39013e9 | − | 5.05965e8i | 0.236122 | − | 0.0859412i | −0.221249 | − | 0.975217i | \(-0.571013\pi\) |
0.457371 | + | 0.889276i | \(0.348791\pi\) | |||||||
\(278\) | 4.85301e9 | + | 2.80189e9i | 0.812517 | + | 0.469107i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.81842e8 | + | 3.14960e8i | 0.0295844 | + | 0.0512417i | ||||
\(281\) | 3.91017e9 | − | 4.65996e9i | 0.627149 | − | 0.747407i | −0.355133 | − | 0.934816i | \(-0.615565\pi\) |
0.982282 | + | 0.187409i | \(0.0600090\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.05969e8 | − | 4.57088e9i | −0.125653 | − | 0.712613i | −0.980918 | − | 0.194422i | \(-0.937717\pi\) |
0.855265 | − | 0.518191i | \(-0.173394\pi\) | |||||||
\(284\) | −5.21016e9 | + | 9.18691e8i | −0.800898 | + | 0.141220i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.86472e8 | + | 5.76018e8i | 0.102603 | + | 0.0860938i | ||||
\(287\) | −3.39189e9 | + | 1.95831e9i | −0.499935 | + | 0.288638i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.88348e9 | − | 1.19225e10i | 0.986772 | − | 1.70914i | ||||
\(290\) | 6.16496e7 | + | 1.69381e8i | 0.00871643 | + | 0.0239482i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.84847e9 | − | 3.22925e9i | 0.529366 | − | 0.444191i | ||||
\(293\) | −3.86218e9 | + | 1.06113e10i | −0.524037 | + | 1.43978i | 0.341952 | + | 0.939717i | \(0.388912\pi\) |
−0.865989 | + | 0.500063i | \(0.833310\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17377e8 | + | 6.65679e8i | −0.0154987 | + | 0.0878976i | ||||
\(296\) | 6.87800e9i | 0.895974i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.04357e9 | 0.893158 | ||||||||
\(299\) | 1.76687e9 | + | 3.11546e8i | 0.221065 | + | 0.0389797i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.95353e9 | − | 2.53088e9i | −0.847109 | − | 0.308323i | ||||
\(302\) | −1.61906e9 | − | 1.92952e9i | −0.194642 | − | 0.231965i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.31874e9 | + | 1.57189e9i | −0.505665 | + | 0.184047i | ||||
\(305\) | 4.02526e8 | + | 2.32399e8i | 0.0465152 | + | 0.0268556i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.60427e9 | + | 2.77868e9i | 0.180603 | + | 0.312813i | 0.942086 | − | 0.335372i | \(-0.108862\pi\) |
−0.761483 | + | 0.648185i | \(0.775529\pi\) | |||||||
\(308\) | 2.58678e9 | − | 3.08281e9i | 0.287446 | − | 0.342565i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.47035e7 | + | 3.10239e8i | 0.00592336 | + | 0.0335931i | ||||
\(311\) | 5.93601e9 | − | 1.04668e9i | 0.634531 | − | 0.111885i | 0.152875 | − | 0.988245i | \(-0.451147\pi\) |
0.481656 | + | 0.876361i | \(0.340036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.47074e9 | + | 2.07320e9i | 0.257425 | + | 0.216005i | 0.762362 | − | 0.647151i | \(-0.224040\pi\) |
−0.504937 | + | 0.863156i | \(0.668484\pi\) | |||||||
\(314\) | 5.24441e9 | − | 3.02786e9i | 0.539484 | − | 0.311471i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.52254e8 | − | 9.56532e8i | 0.0553848 | − | 0.0959292i | ||||
\(317\) | −1.44241e9 | − | 3.96300e9i | −0.142841 | − | 0.392452i | 0.847556 | − | 0.530706i | \(-0.178073\pi\) |
−0.990397 | + | 0.138254i | \(0.955851\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.52975e9 | − | 2.96181e9i | 0.340864 | − | 0.286019i | ||||
\(320\) | −3.29566e7 | + | 9.05476e7i | −0.00314299 | + | 0.00863529i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.33959e8 | + | 2.46110e9i | −0.0403669 | + | 0.228932i | ||||
\(323\) | 2.92059e10i | 2.68325i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.01637e9 | 0.539264 | ||||||||
\(326\) | 8.36487e9 | + | 1.47495e9i | 0.740609 | + | 0.130589i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.67634e9 | − | 1.70205e9i | −0.404028 | − | 0.147054i | ||||
\(329\) | −9.47233e9 | − | 1.12887e10i | −0.808488 | − | 0.963518i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.24937e9 | + | 1.91061e9i | −0.437316 | + | 0.159170i | −0.551290 | − | 0.834314i | \(-0.685864\pi\) |
0.113974 | + | 0.993484i | \(0.463642\pi\) | |||||||
\(332\) | 1.01513e9 | + | 5.86083e8i | 0.0835541 | + | 0.0482400i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.38244e9 | + | 9.32265e9i | 0.432507 | + | 0.749124i | ||||
\(335\) | 2.67253e8 | − | 3.18500e8i | 0.0212199 | − | 0.0252889i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.28023e8 | − | 1.86031e9i | −0.0254322 | − | 0.144233i | 0.969448 | − | 0.245299i | \(-0.0788860\pi\) |
−0.994880 | + | 0.101065i | \(0.967775\pi\) | |||||||
\(338\) | 4.42217e9 | − | 7.79747e8i | 0.338819 | − | 0.0597430i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.06692e8 | − | 6.76895e8i | −0.0603659 | − | 0.0506530i | ||||
\(341\) | 6.97408e9 | − | 4.02649e9i | 0.515786 | − | 0.297789i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.36623e9 | − | 9.29458e9i | 0.387697 | − | 0.671511i | ||||
\(344\) | −3.21574e9 | − | 8.83518e9i | −0.229640 | − | 0.630931i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.35643e8 | + | 1.97728e8i | −0.0164418 | + | 0.0137963i | ||||
\(347\) | 4.26463e9 | − | 1.17170e10i | 0.294146 | − | 0.808160i | −0.701303 | − | 0.712864i | \(-0.747398\pi\) |
0.995449 | − | 0.0952965i | \(-0.0303799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.62191e9 | + | 1.48696e10i | −0.176733 | + | 1.00230i | 0.759392 | + | 0.650633i | \(0.225496\pi\) |
−0.936125 | + | 0.351667i | \(0.885615\pi\) | |||||||
\(350\) | 8.38032e9i | 0.558455i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.01323e9 | 0.521960 | ||||||||
\(353\) | 1.77537e10 | + | 3.13045e9i | 1.14338 | + | 0.201608i | 0.713083 | − | 0.701080i | \(-0.247298\pi\) |
0.430295 | + | 0.902688i | \(0.358409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.52100e8 | + | 3.46536e8i | 0.0599472 | + | 0.0218190i | ||||
\(356\) | 4.77513e9 | + | 5.69077e9i | 0.297293 | + | 0.354300i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.63772e9 | − | 1.68799e9i | 0.282340 | − | 0.102763i | ||||
\(359\) | −2.52845e10 | − | 1.45980e10i | −1.52222 | − | 0.878852i | −0.999655 | − | 0.0262509i | \(-0.991643\pi\) |
−0.522562 | − | 0.852602i | \(-0.675024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.20693e10 | − | 2.09046e10i | −0.710644 | − | 1.23087i | ||||
\(362\) | −4.29513e9 | + | 5.11874e9i | −0.250117 | + | 0.298077i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.45051e9 | + | 8.22623e9i | 0.0826255 | + | 0.468592i | ||||
\(365\) | −9.47507e8 | + | 1.67071e8i | −0.0533840 | + | 0.00941304i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.35266e9 | + | 5.33051e9i | 0.350180 | + | 0.293836i | 0.800862 | − | 0.598849i | \(-0.204375\pi\) |
−0.450682 | + | 0.892684i | \(0.648819\pi\) | |||||||
\(368\) | 2.27815e9 | − | 1.31529e9i | 0.124220 | − | 0.0717184i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.85092e8 | − | 4.93794e8i | 0.0152117 | − | 0.0263475i | ||||
\(371\) | 3.26771e9 | + | 8.97795e9i | 0.172483 | + | 0.473894i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.11366e10 | + | 1.77357e10i | −1.09194 | + | 0.916248i | −0.996857 | − | 0.0792207i | \(-0.974757\pi\) |
−0.0950853 | + | 0.995469i | \(0.530312\pi\) | |||||||
\(374\) | 2.85574e9 | − | 7.84608e9i | 0.145960 | − | 0.401020i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.25139e9 | − | 1.84396e10i | 0.162674 | − | 0.922570i | ||||
\(377\) | 9.56417e9i | 0.473458i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.32513e10 | 1.12691 | 0.563457 | − | 0.826145i | \(-0.309471\pi\) | ||||
0.563457 | + | 0.826145i | \(0.309471\pi\) | |||||||
\(380\) | 1.46019e9 | + | 2.57471e8i | 0.0700286 | + | 0.0123479i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.91126e9 | − | 1.78755e9i | −0.230642 | − | 0.0839470i | ||||
\(383\) | −3.20145e9 | − | 3.81534e9i | −0.148782 | − | 0.177312i | 0.686506 | − | 0.727124i | \(-0.259144\pi\) |
−0.835288 | + | 0.549812i | \(0.814699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.24228e8 | + | 2.63597e8i | −0.0329634 | + | 0.0119977i | ||||
\(386\) | −2.13746e8 | − | 1.23406e8i | −0.00962829 | − | 0.00555890i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.26537e9 | − | 2.19169e9i | −0.0558331 | − | 0.0967057i | ||||
\(389\) | −6.62163e9 | + | 7.89136e9i | −0.289179 | + | 0.344630i | −0.891002 | − | 0.453999i | \(-0.849997\pi\) |
0.601823 | + | 0.798630i | \(0.294441\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.90283e9 | − | 1.64628e10i | −0.124198 | − | 0.704361i | ||||
\(392\) | −6.52075e9 | + | 1.14978e9i | −0.276155 | + | 0.0486936i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.97047e9 | + | 5.00982e9i | 0.247756 | + | 0.207892i | ||||
\(395\) | −1.83188e8 | + | 1.05764e8i | −0.00752503 | + | 0.00434458i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.12454e10 | + | 1.94777e10i | −0.452704 | + | 0.784107i | −0.998553 | − | 0.0537771i | \(-0.982874\pi\) |
0.545849 | + | 0.837884i | \(0.316207\pi\) | |||||||
\(398\) | 7.74882e8 | + | 2.12897e9i | 0.0308818 | + | 0.0848472i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.75753e9 | − | 5.67024e9i | 0.263966 | − | 0.221494i | ||||
\(401\) | 1.26623e10 | − | 3.47894e10i | 0.489705 | − | 1.34545i | −0.411242 | − | 0.911526i | \(-0.634905\pi\) |
0.900947 | − | 0.433928i | \(-0.142873\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.90258e9 | + | 1.64613e10i | −0.110043 | + | 0.624086i | ||||
\(404\) | 1.45386e10i | 0.545756i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.33221e10 | −0.490308 | ||||||||
\(407\) | −1.43542e10 | − | 2.53103e9i | −0.523119 | − | 0.0922400i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.04727e10 | − | 3.81173e9i | −0.374251 | − | 0.136216i | 0.148044 | − | 0.988981i | \(-0.452702\pi\) |
−0.522296 | + | 0.852764i | \(0.674924\pi\) | |||||||
\(410\) | 2.65180e8 | + | 3.16029e8i | 0.00938438 | + | 0.0111839i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.55817e9 | − | 3.47889e9i | 0.331731 | − | 0.120740i | ||||
\(413\) | −4.32652e10 | − | 2.49792e10i | −1.48709 | − | 0.858574i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.12242e8 | − | 1.94409e8i | −0.00378411 | − | 0.00655428i | ||||
\(416\) | −1.06913e10 | + | 1.27414e10i | −0.356992 | + | 0.425447i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.04147e9 | + | 1.15777e10i | 0.0668709 | + | 0.379244i | ||||
\(419\) | −2.88812e10 | + | 5.09254e9i | −0.937044 | + | 0.165226i | −0.621259 | − | 0.783605i | \(-0.713379\pi\) |
−0.315784 | + | 0.948831i | \(0.602268\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.97225e10 | − | 3.33311e10i | −1.26447 | − | 1.06102i | −0.995191 | − | 0.0979530i | \(-0.968771\pi\) |
−0.269278 | − | 0.963062i | \(-0.586785\pi\) | |||||||
\(422\) | 2.26883e10 | − | 1.30991e10i | 0.715406 | − | 0.413040i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.06976e9 | + | 1.05131e10i | −0.187805 | + | 0.325288i | ||||
\(425\) | −1.91728e10 | − | 5.26768e10i | −0.587664 | − | 1.61459i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.63155e10 | + | 2.20813e10i | −0.791590 | + | 0.664223i | ||||
\(428\) | −1.46780e10 | + | 4.03274e10i | −0.437412 | + | 1.20178i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.35348e8 | + | 7.67598e8i | −0.00395894 | + | 0.0224523i | ||||
\(431\) | − | 2.99834e9i | − | 0.0868905i | −0.999056 | − | 0.0434452i | \(-0.986167\pi\) | ||
0.999056 | − | 0.0434452i | \(-0.0138334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.72699e10 | −1.91368 | −0.956839 | − | 0.290617i | \(-0.906139\pi\) | ||||
−0.956839 | + | 0.290617i | \(0.906139\pi\) | |||||||
\(434\) | −2.29293e10 | − | 4.04305e9i | −0.646296 | − | 0.113959i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.88398e10 | + | 1.77762e10i | 1.35154 | + | 0.491919i | ||||
\(437\) | 1.51295e10 | + | 1.80306e10i | 0.414856 | + | 0.494406i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.83773e10 | + | 1.76079e10i | −1.30252 | + | 0.474078i | −0.897816 | − | 0.440371i | \(-0.854847\pi\) |
−0.404702 | + | 0.914449i | \(0.632625\pi\) | |||||||
\(440\) | −8.48067e8 | − | 4.89631e8i | −0.0226266 | − | 0.0130635i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.66551e9 | + | 1.50091e10i | 0.227041 | + | 0.393247i | ||||
\(443\) | 1.96213e10 | − | 2.33837e10i | 0.509463 | − | 0.607154i | −0.448593 | − | 0.893736i | \(-0.648075\pi\) |
0.958056 | + | 0.286582i | \(0.0925191\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.47050e8 | − | 1.40109e9i | −0.00630006 | − | 0.0357294i | ||||
\(446\) | −3.13417e9 | + | 5.52639e8i | −0.0792107 | + | 0.0139670i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.45556e9 | − | 4.57776e9i | −0.135434 | − | 0.113642i | ||||
\(449\) | 4.45495e10 | − | 2.57207e10i | 1.09612 | − | 0.632845i | 0.160920 | − | 0.986967i | \(-0.448554\pi\) |
0.935199 | + | 0.354123i | \(0.115220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.27297e9 | − | 9.13304e9i | 0.127453 | − | 0.220754i | ||||
\(452\) | −7.93894e8 | − | 2.18121e9i | −0.0190199 | − | 0.0522568i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.58462e10 | − | 1.32965e10i | 0.372993 | − | 0.312978i | ||||
\(455\) | 5.47140e8 | − | 1.50325e9i | 0.0127659 | − | 0.0350741i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.83947e9 | − | 1.04321e10i | 0.0421723 | − | 0.239171i | −0.956434 | − | 0.291949i | \(-0.905696\pi\) |
0.998606 | + | 0.0527778i | \(0.0168075\pi\) | |||||||
\(458\) | 3.34900e10i | 0.761120i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.48670e8 | −0.0189543 | ||||||||
\(461\) | 1.61670e10 | + | 2.85068e9i | 0.357953 | + | 0.0631168i | 0.349733 | − | 0.936849i | \(-0.386272\pi\) |
0.00822026 | + | 0.999966i | \(0.497383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.17181e10 | + | 7.90475e9i | 0.472605 | + | 0.172014i | 0.567332 | − | 0.823489i | \(-0.307976\pi\) |
−0.0947270 | + | 0.995503i | \(0.530198\pi\) | |||||||
\(464\) | 9.01393e9 | + | 1.07424e10i | 0.194465 | + | 0.231755i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.10906e10 | − | 7.67637e9i | 0.447246 | − | 0.162784i | ||||
\(467\) | −3.17397e10 | − | 1.83249e10i | −0.667322 | − | 0.385278i | 0.127739 | − | 0.991808i | \(-0.459228\pi\) |
−0.795061 | + | 0.606529i | \(0.792561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.53645e10 | + | 2.66121e10i | 0.317562 | + | 0.550033i | ||||
\(470\) | −9.97745e8 | + | 1.18907e9i | −0.0204469 | + | 0.0243677i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.10227e10 | − | 6.25128e10i | −0.222085 | − | 1.25951i | ||||
\(473\) | 1.96221e10 | − | 3.45990e9i | 0.392013 | − | 0.0691225i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.04633e10 | + | 5.07348e10i | 1.18773 | + | 0.996624i | ||||
\(476\) | 6.74029e10 | − | 3.89151e10i | 1.31296 | − | 0.758036i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.14984e9 | − | 1.23839e10i | 0.136957 | − | 0.237217i | ||||
\(479\) | 3.04605e10 | + | 8.36895e10i | 0.578622 | + | 1.58975i | 0.790505 | + | 0.612456i | \(0.209818\pi\) |
−0.211883 | + | 0.977295i | \(0.567960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.31759e10 | − | 1.94469e10i | 0.432969 | − | 0.363304i | ||||
\(482\) | −1.13062e10 | + | 3.10634e10i | −0.209473 | + | 0.575521i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.39153e9 | − | 3.05769e10i | 0.0982495 | − | 0.557200i | ||||
\(485\) | 4.84670e8i | 0.00875949i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.06487e10 | −0.367093 | −0.183547 | − | 0.983011i | \(-0.558758\pi\) | ||||
−0.183547 | + | 0.983011i | \(0.558758\pi\) | |||||||
\(488\) | −4.29852e10 | − | 7.57945e9i | −0.757948 | − | 0.133647i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.15804e8 | + | 1.87737e8i | 0.00894748 | + | 0.00325662i | ||||
\(491\) | 1.51222e10 | + | 1.80220e10i | 0.260190 | + | 0.310082i | 0.880286 | − | 0.474444i | \(-0.157351\pi\) |
−0.620096 | + | 0.784526i | \(0.712906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.37397e10 | − | 3.04788e10i | 1.41757 | − | 0.515953i | ||||
\(494\) | −2.11329e10 | − | 1.22011e10i | −0.354856 | − | 0.204876i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.22541e10 | + | 2.12248e10i | 0.202468 | + | 0.350684i | ||||
\(497\) | −4.81347e10 | + | 5.73647e10i | −0.788919 | + | 0.940198i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.39743e9 | + | 2.49391e10i | 0.0709246 | + | 0.402233i | 0.999515 | + | 0.0311280i | \(0.00990996\pi\) |
−0.928591 | + | 0.371105i | \(0.878979\pi\) | |||||||
\(500\) | −5.61543e9 | + | 9.90152e8i | −0.0898469 | + | 0.0158424i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.51732e10 | − | 3.79048e10i | −0.711322 | − | 0.596870i | ||||
\(503\) | 8.07649e10 | − | 4.66296e10i | 1.26168 | − | 0.728434i | 0.288284 | − | 0.957545i | \(-0.406915\pi\) |
0.973400 | + | 0.229111i | \(0.0735819\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.39217e9 | − | 2.41130e9i | 0.0214055 | − | 0.0370754i | ||||
\(506\) | −2.30146e9 | − | 6.32322e9i | −0.0351077 | − | 0.0964575i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.98009e9 | − | 4.17879e9i | 0.0747795 | − | 0.0627474i | ||||
\(509\) | −2.18961e10 | + | 6.01590e10i | −0.326208 | + | 0.896250i | 0.662854 | + | 0.748749i | \(0.269345\pi\) |
−0.989062 | + | 0.147501i | \(0.952877\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.23480e10 | − | 7.00288e10i | 0.181097 | − | 1.02705i | ||||
\(512\) | 4.47759e10i | 0.651575i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.05820e9 | 0.0151605 | ||||||||
\(515\) | −1.91839e9 | − | 3.38265e8i | −0.0272715 | − | 0.00480870i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.72863e10 | + | 1.35711e10i | 0.521900 | + | 0.189956i | ||||
\(518\) | 2.70880e10 | + | 3.22822e10i | 0.376234 | + | 0.448378i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.91004e9 | − | 6.95197e8i | 0.0261233 | − | 0.00950812i | ||||
\(521\) | −9.62836e10 | − | 5.55894e10i | −1.30678 | − | 0.754468i | −0.325220 | − | 0.945638i | \(-0.605438\pi\) |
−0.981557 | + | 0.191170i | \(0.938772\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.92357e10 | − | 6.79583e10i | −0.524415 | − | 0.908313i | −0.999596 | − | 0.0284250i | \(-0.990951\pi\) |
0.475181 | − | 0.879888i | \(-0.342383\pi\) | |||||||
\(524\) | 5.94663e10 | − | 7.08692e10i | 0.788761 | − | 0.940009i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.27759e10 | + | 7.24560e10i | 0.166898 | + | 0.946523i | ||||
\(527\) | 1.53378e11 | − | 2.70447e10i | 1.98848 | − | 0.350622i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.96694e10 | + | 4.16776e10i | 0.634259 | + | 0.532206i | ||||
\(530\) | 8.71535e8 | − | 5.03181e8i | 0.0110454 | − | 0.00637706i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.47927e10 | + | 9.49037e10i | −0.684031 | + | 1.18478i | ||||
\(533\) | 7.48676e9 | + | 2.05697e10i | 0.0927651 | + | 0.254870i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.29601e9 | − | 5.28298e9i | 0.0768512 | − | 0.0644858i | ||||
\(536\) | −1.33540e10 | + | 3.66898e10i | −0.161790 | + | 0.444514i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.60261e8 | − | 9.08883e8i | 0.00191292 | − | 0.0108487i | ||||
\(539\) | − | 1.40317e10i | − | 0.166248i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.30837e10 | 0.619687 | 0.309844 | − | 0.950788i | \(-0.399723\pi\) | ||||
0.309844 | + | 0.950788i | \(0.399723\pi\) | |||||||
\(542\) | 2.74675e10 | + | 4.84326e9i | 0.318289 | + | 0.0561229i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.45629e11 | + | 5.30047e10i | 1.66285 | + | 0.605228i | ||||
\(545\) | −6.39813e9 | − | 7.62499e9i | −0.0725215 | − | 0.0864278i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.28786e10 | − | 8.32712e9i | 0.255552 | − | 0.0930134i | −0.211067 | − | 0.977472i | \(-0.567694\pi\) |
0.466620 | + | 0.884458i | \(0.345472\pi\) | |||||||
\(548\) | 4.75553e10 | + | 2.74560e10i | 0.527323 | + | 0.304450i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.12825e10 | − | 1.95418e10i | −0.123297 | − | 0.213557i | ||||
\(551\) | −8.06525e10 | + | 9.61180e10i | −0.875007 | + | 1.04279i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.71475e9 | − | 1.53961e10i | −0.0290288 | − | 0.164631i | ||||
\(554\) | 1.13417e10 | − | 1.99984e9i | 0.120403 | − | 0.0212303i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.07743e11 | − | 9.04073e10i | −1.12743 | − | 0.946028i | ||||
\(557\) | 5.15104e10 | − | 2.97396e10i | 0.535149 | − | 0.308968i | −0.207962 | − | 0.978137i | \(-0.566683\pi\) |
0.743111 | + | 0.669169i | \(0.233350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.06786e10 | + | 3.58164e10i | −0.211775 | + | 0.366804i | ||||
\(560\) | −8.02227e8 | − | 2.20410e9i | −0.00815728 | − | 0.0224119i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.62776e10 | − | 3.04406e10i | 0.363659 | − | 0.305146i | ||||
\(563\) | 8.78895e9 | − | 2.41474e10i | 0.0874789 | − | 0.240346i | −0.888237 | − | 0.459385i | \(-0.848070\pi\) |
0.975716 | + | 0.219039i | \(0.0702921\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.71931e7 | + | 4.37784e8i | −0.000757503 | + | 0.00429601i | ||||
\(566\) | − | 3.61331e10i | − | 0.352078i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.51482e10 | −0.914128 | ||||||||
\(569\) | −1.36983e11 | − | 2.41538e10i | −1.30683 | − | 0.230429i | −0.523493 | − | 0.852030i | \(-0.675371\pi\) |
−0.783334 | + | 0.621601i | \(0.786483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.21798e10 | − | 1.17125e10i | −0.302719 | − | 0.110181i | 0.186195 | − | 0.982513i | \(-0.440384\pi\) |
−0.488913 | + | 0.872332i | \(0.662607\pi\) | |||||||
\(572\) | −1.44574e10 | − | 1.72297e10i | −0.135054 | − | 0.160951i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.86519e10 | + | 1.04284e10i | −0.263940 | + | 0.0960664i | ||||
\(575\) | −3.91245e10 | − | 2.25886e10i | −0.357913 | − | 0.206641i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.06482e10 | − | 7.04048e10i | −0.366723 | − | 0.635183i | 0.622328 | − | 0.782756i | \(-0.286187\pi\) |
−0.989051 | + | 0.147574i | \(0.952854\pi\) | |||||||
\(578\) | 6.88910e10 | − | 8.21011e10i | 0.617236 | − | 0.735593i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.85604e8 | − | 4.45538e9i | −0.00694212 | − | 0.0393707i | ||||
\(581\) | 1.63392e10 | − | 2.88105e9i | 0.143393 | − | 0.0252840i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.97070e10 | − | 1.65361e10i | −0.170587 | − | 0.143139i | ||||
\(584\) | 7.82466e10 | − | 4.51757e10i | 0.672689 | − | 0.388377i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.39549e10 | + | 7.61322e10i | −0.372750 | + | 0.645621i | ||||
\(587\) | −1.12180e10 | − | 3.08212e10i | −0.0944850 | − | 0.259595i | 0.883443 | − | 0.468539i | \(-0.155220\pi\) |
−0.977928 | + | 0.208944i | \(0.932997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.67985e11 | + | 1.40956e11i | −1.39576 | + | 1.17118i | ||||
\(590\) | −1.79979e9 | + | 4.94489e9i | −0.0148530 | + | 0.0408083i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.70288e9 | − | 4.36852e10i | 0.0627142 | − | 0.355670i | ||||
\(593\) | 1.79096e11i | 1.44833i | 0.689628 | + | 0.724164i | \(0.257774\pi\) | ||||
−0.689628 | + | 0.724164i | \(0.742226\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.49054e10 | −0.118926 | ||||||||
\(596\) | −1.74100e11 | − | 3.06986e10i | −1.37979 | − | 0.243295i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.31249e10 | + | 4.77706e9i | 0.102634 | + | 0.0373557i | ||||
\(599\) | 3.31382e10 | + | 3.94926e10i | 0.257408 | + | 0.306767i | 0.879235 | − | 0.476387i | \(-0.158054\pi\) |
−0.621828 | + | 0.783154i | \(0.713610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.52122e10 | + | 5.53680e9i | −0.116599 | + | 0.0424386i | −0.399661 | − | 0.916663i | \(-0.630872\pi\) |
0.283062 | + | 0.959102i | \(0.408650\pi\) | |||||||
\(602\) | −4.98893e10 | − | 2.88036e10i | −0.379858 | − | 0.219311i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.16097e10 | + | 5.47497e10i | 0.237505 | + | 0.411371i | ||||
\(605\) | −3.82214e9 | + | 4.55504e9i | −0.0285289 | + | 0.0339994i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.49937e9 | + | 3.68597e10i | 0.0478758 | + | 0.271517i | 0.999343 | − | 0.0362316i | \(-0.0115354\pi\) |
−0.951468 | + | 0.307749i | \(0.900424\pi\) | |||||||
\(608\) | −2.14892e11 | + | 3.78912e10i | −1.57255 | + | 0.277283i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.77188e9 | + | 2.32588e9i | 0.0200196 | + | 0.0167984i | ||||
\(611\) | −7.13266e10 | + | 4.11804e10i | −0.511784 | + | 0.295479i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.05930e11 | − | 1.83475e11i | 0.750197 | − | 1.29938i | −0.197530 | − | 0.980297i | \(-0.563292\pi\) |
0.947727 | − | 0.319083i | \(-0.103375\pi\) | |||||||
\(614\) | 8.54311e9 | + | 2.34720e10i | 0.0601094 | + | 0.165149i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.54431e10 | − | 4.65223e10i | 0.385057 | − | 0.323101i | ||||
\(617\) | 5.33383e10 | − | 1.46546e11i | 0.368043 | − | 1.01119i | −0.608062 | − | 0.793889i | \(-0.708053\pi\) |
0.976105 | − | 0.217300i | \(-0.0697249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.73618e9 | − | 4.38741e10i | 0.0526944 | − | 0.298845i | −0.947059 | − | 0.321060i | \(-0.895961\pi\) |
0.999753 | + | 0.0222154i | \(0.00707198\pi\) | |||||||
\(620\) | − | 7.90678e9i | − | 0.0535098i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.69245e10 | 0.313501 | ||||||||
\(623\) | 1.03552e11 | + | 1.82591e10i | 0.687397 | + | 0.121207i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.41846e11 | − | 5.16276e10i | −0.929599 | − | 0.338346i | ||||
\(626\) | 1.61398e10 | + | 1.92347e10i | 0.105100 | + | 0.125253i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.42826e11 | + | 5.19844e10i | −0.918266 | + | 0.334221i | ||||
\(629\) | −2.44125e11 | − | 1.40946e11i | −1.55959 | − | 0.900429i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.52325e10 | + | 1.64948e11i | 0.600714 | + | 1.04047i | 0.992713 | + | 0.120502i | \(0.0384503\pi\) |
−0.391999 | + | 0.919966i | \(0.628216\pi\) | |||||||
\(632\) | 1.27684e10 | − | 1.52168e10i | 0.0800330 | − | 0.0953796i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.70119e9 | − | 3.23330e10i | −0.0352865 | − | 0.200120i | ||||
\(635\) | −1.22612e9 | + | 2.16198e8i | −0.00754114 | + | 0.00132971i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.23111e10 | + | 1.87213e10i | 0.135508 | + | 0.113704i | ||||
\(638\) | 3.10655e10 | − | 1.79357e10i | 0.187497 | − | 0.108252i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.77898e9 | − | 8.27744e9i | 0.0284850 | − | 0.0493374i | ||||
\(641\) | 1.00079e10 | + | 2.74965e10i | 0.0592804 | + | 0.162871i | 0.965797 | − | 0.259298i | \(-0.0834911\pi\) |
−0.906517 | + | 0.422169i | \(0.861269\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.94608e10 | + | 7.50665e10i | −0.523346 | + | 0.439139i | −0.865796 | − | 0.500397i | \(-0.833188\pi\) |
0.342450 | + | 0.939536i | \(0.388743\pi\) | |||||||
\(644\) | 2.14528e10 | − | 5.89412e10i | 0.124721 | − | 0.342670i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.94819e10 | + | 2.23913e11i | −0.226708 | + | 1.28573i | ||||
\(647\) | 2.25850e11i | 1.28885i | 0.764667 | + | 0.644425i | \(0.222903\pi\) | ||||
−0.764667 | + | 0.644425i | \(0.777097\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.34518e11 | 0.758234 | ||||||||
\(650\) | 4.61257e10 | + | 8.13321e9i | 0.258398 | + | 0.0455626i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00331e11 | − | 7.29146e10i | −1.10856 | − | 0.403482i | ||||
\(653\) | −1.81964e11 | − | 2.16856e11i | −1.00077 | − | 1.19267i | −0.981227 | − | 0.192858i | \(-0.938224\pi\) |
−0.0195398 | − | 0.999809i | \(-0.506220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.66489e10 | + | 6.05972e9i | −0.0904526 | + | 0.0329221i | ||||
\(656\) | 2.77953e10 | + | 1.60476e10i | 0.150092 | + | 0.0866554i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.73610e10 | − | 9.93521e10i | −0.305994 | − | 0.529997i | ||||
\(659\) | −3.52316e10 | + | 4.19873e10i | −0.186806 | + | 0.222626i | −0.851317 | − | 0.524652i | \(-0.824195\pi\) |
0.664511 | + | 0.747278i | \(0.268640\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.81789e10 | − | 1.03098e11i | −0.0952276 | − | 0.540063i | −0.994677 | − | 0.103038i | \(-0.967144\pi\) |
0.899450 | − | 0.437024i | \(-0.143968\pi\) | |||||||
\(662\) | −4.28282e10 | + | 7.55176e9i | −0.222996 | + | 0.0393202i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.61490e10 | + | 1.35506e10i | 0.0830753 | + | 0.0697085i | ||||
\(665\) | 1.81753e10 | − | 1.04935e10i | 0.0929381 | − | 0.0536578i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.59088e10 | − | 6.21959e10i | 0.181425 | − | 0.314238i | ||||
\(668\) | −9.24093e10 | − | 2.53892e11i | −0.464098 | − | 1.27510i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.47951e9 | − | 2.08056e9i | 0.0123046 | − | 0.0103248i | ||||
\(671\) | 3.16361e10 | − | 8.69196e10i | 0.156061 | − | 0.428773i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.36410e10 | + | 1.90788e11i | −0.163987 | + | 0.930015i | 0.786116 | + | 0.618079i | \(0.212089\pi\) |
−0.950103 | + | 0.311936i | \(0.899022\pi\) | |||||||
\(674\) | − | 1.47059e10i | − | 0.0712609i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.12704e11 | −0.539699 | ||||||||
\(677\) | 3.16004e11 | + | 5.57200e10i | 1.50431 | + | 0.265250i | 0.864245 | − | 0.503071i | \(-0.167796\pi\) |
0.640065 | + | 0.768321i | \(0.278908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.36609e10 | − | 1.22516e10i | −0.158360 | − | 0.0576385i | ||||
\(680\) | −1.21737e10 | − | 1.45080e10i | −0.0569360 | − | 0.0678536i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.89114e10 | − | 2.14420e10i | 0.272309 | − | 0.0991123i | ||||
\(683\) | 3.37083e11 | + | 1.94615e11i | 1.54901 | + | 0.894321i | 0.998218 | + | 0.0596780i | \(0.0190074\pi\) |
0.550792 | + | 0.834643i | \(0.314326\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.25818e9 | − | 9.10743e9i | −0.0238821 | − | 0.0413650i | ||||
\(686\) | 5.37061e10 | − | 6.40044e10i | 0.242509 | − | 0.289010i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.05298e10 | + | 5.97175e10i | 0.0469966 | + | 0.266531i | ||||
\(689\) | 5.25865e10 | − | 9.27242e9i | 0.233344 | − | 0.0411449i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.64622e11 | + | 2.22045e11i | 1.16069 | + | 0.973930i | 0.999915 | − | 0.0130614i | \(-0.00415771\pi\) |
0.160770 | + | 0.986992i | \(0.448602\pi\) | |||||||
\(692\) | 6.68630e9 | − | 3.86034e9i | 0.0291583 | − | 0.0168345i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.85352e10 | − | 8.40654e10i | 0.209227 | − | 0.362392i | ||||
\(695\) | 9.21265e9 | + | 2.53116e10i | 0.0394862 | + | 0.108487i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.56241e11 | − | 1.31102e11i | 0.662008 | − | 0.555491i | ||||
\(698\) | −4.02028e10 | + | 1.10456e11i | −0.169369 | + | 0.465339i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.65246e10 | − | 2.07141e11i | 0.152122 | − | 0.862729i | ||||
\(701\) | 7.99935e9i | 0.0331271i | 0.999863 | + | 0.0165635i | \(0.00527258\pi\) | ||||
−0.999863 | + | 0.0165635i | \(0.994727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.96905e11 | 1.62505 | ||||||||
\(704\) | 1.88847e10 | + | 3.32989e9i | 0.0768812 | + | 0.0135562i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.31880e11 | + | 4.80005e10i | 0.530837 | + | 0.193209i | ||||
\(707\) | 1.32277e11 | + | 1.57641e11i | 0.529426 | + | 0.630945i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.58748e11 | + | 9.41764e10i | −1.02398 | + | 0.372698i | −0.798786 | − | 0.601616i | \(-0.794524\pi\) |
−0.225194 | + | 0.974314i | \(0.572302\pi\) | |||||||
\(710\) | 6.83100e9 | + | 3.94388e9i | 0.0268813 | + | 0.0155199i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.68018e10 | + | 1.15704e11i | 0.259937 | + | 0.450224i | ||||
\(713\) | 8.06798e10 | − | 9.61504e10i | 0.312181 | − | 0.372043i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.47982e8 | + | 4.24201e9i | 0.00286198 | + | 0.0162311i | ||||
\(716\) | −1.21990e11 | + | 2.15102e10i | −0.464166 | + | 0.0818450i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.74114e11 | − | 1.46099e11i | −0.655144 | − | 0.549731i | ||||
\(719\) | −2.56982e11 | + | 1.48369e11i | −0.961585 | + | 0.555172i | −0.896661 | − | 0.442719i | \(-0.854014\pi\) |
−0.0649248 | + | 0.997890i | \(0.520681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.19864e10 | − | 1.24684e11i | 0.266385 | − | 0.461392i | ||||
\(722\) | −6.42717e10 | − | 1.76585e11i | −0.236522 | − | 0.649838i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.28475e11 | − | 1.07803e11i | 0.467588 | − | 0.392353i | ||||
\(725\) | 8.23692e10 | − | 2.26308e11i | 0.298135 | − | 0.819119i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.88255e10 | + | 2.76903e11i | −0.174787 | + | 0.991267i | 0.763602 | + | 0.645687i | \(0.223429\pi\) |
−0.938389 | + | 0.345580i | \(0.887682\pi\) | |||||||
\(728\) | 1.50228e11i | 0.534841i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.49011e9 | −0.0263752 | ||||||||
\(731\) | 3.79490e11 | + | 6.69144e10i | 1.32902 | + | 0.234342i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.89034e11 | − | 1.41597e11i | −1.34763 | − | 0.490498i | −0.435424 | − | 0.900225i | \(-0.643402\pi\) |
−0.912208 | + | 0.409728i | \(0.865624\pi\) | |||||||
\(734\) | 4.14979e10 | + | 4.94552e10i | 0.142969 | + | 0.170384i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.17364e11 | − | 4.27169e10i | 0.399966 | − | 0.145576i | ||||
\(737\) | −7.16562e10 | − | 4.13708e10i | −0.242876 | − | 0.140224i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.10244e10 | − | 1.23018e11i | −0.238139 | − | 0.412468i | 0.722042 | − | 0.691850i | \(-0.243204\pi\) |
−0.960180 | + | 0.279382i | \(0.909871\pi\) | |||||||
\(740\) | −9.19893e9 | + | 1.09629e10i | −0.0306768 | + | 0.0365592i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.29157e10 | + | 7.32487e10i | 0.0426092 | + | 0.241649i | ||||
\(743\) | −1.74447e11 | + | 3.07596e10i | −0.572410 | + | 0.100931i | −0.452358 | − | 0.891836i | \(-0.649417\pi\) |
−0.120052 | + | 0.992768i | \(0.538306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.59358e10 | + | 2.17627e10i | 0.0841926 | + | 0.0706460i | ||||
\(746\) | −1.86024e11 | + | 1.07401e11i | −0.600639 | + | 0.346779i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.04783e11 | + | 1.81490e11i | −0.334723 | + | 0.579757i | ||||
\(749\) | 2.07758e11 | + | 5.70810e11i | 0.660131 | + | 1.81370i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.35565e11 | − | 1.13753e11i | 0.426175 | − | 0.357603i | −0.404331 | − | 0.914613i | \(-0.632496\pi\) |
0.830506 | + | 0.557009i | \(0.188051\pi\) | |||||||
\(752\) | −4.13021e10 | + | 1.13476e11i | −0.129152 | + | 0.354841i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.29293e10 | + | 7.33256e10i | −0.0400027 | + | 0.226866i | ||||
\(755\) | − | 1.21073e10i | − | 0.0372615i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.71823e11 | −0.827755 | −0.413878 | − | 0.910333i | \(-0.635826\pi\) | ||||
−0.413878 | + | 0.910333i | \(0.635826\pi\) | |||||||
\(758\) | 1.78261e11 | + | 3.14322e10i | 0.539982 | + | 0.0952134i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.50579e10 | + | 9.12035e9i | 0.0751088 | + | 0.0273374i | ||||
\(761\) | −2.67176e11 | − | 3.18408e11i | −0.796634 | − | 0.949391i | 0.202922 | − | 0.979195i | \(-0.434956\pi\) |
−0.999556 | + | 0.0298038i | \(0.990512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.91298e11 | − | 2.51612e11i | 2.03970 | − | 0.742392i | ||||
\(764\) | 1.13604e11 | + | 6.55891e10i | 0.333441 | + | 0.192512i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.93868e10 | − | 3.35789e10i | −0.0563107 | − | 0.0975330i | ||||
\(767\) | −1.79476e11 | + | 2.13891e11i | −0.518591 | + | 0.618033i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.30732e10 | − | 3.00993e11i | −0.151765 | − | 0.860699i | −0.961684 | − | 0.274159i | \(-0.911601\pi\) |
0.809920 | − | 0.586540i | \(-0.199511\pi\) | |||||||
\(770\) | −5.90878e9 | + | 1.04188e9i | −0.0168087 | + | 0.00296383i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.74544e9 | + | 3.98190e9i | 0.0133600 | + | 0.0112104i | ||||
\(773\) | −1.31306e11 | + | 7.58097e10i | −0.367763 | + | 0.212328i | −0.672481 | − | 0.740115i | \(-0.734771\pi\) |
0.304718 | + | 0.952443i | \(0.401438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.10450e11 | − | 3.64510e11i | 0.583368 | − | 1.01042i | ||||
\(776\) | −1.55669e10 | − | 4.27696e10i | −0.0429294 | − | 0.117947i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.14340e10 | + | 5.15492e10i | −0.167683 | + | 0.140703i | ||||
\(779\) | −9.82193e10 | + | 2.69855e11i | −0.266715 | + | 0.732793i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.50135e10 | − | 1.98571e11i | 0.0941090 | − | 0.533718i | ||||
\(782\) | − | 1.30139e11i | − | 0.348001i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.27038e10 | 0.113032 | ||||||||
\(785\) | 2.86662e10 | + | 5.05462e9i | 0.0754903 | + | 0.0133110i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.69477e11 | − | 6.16845e10i | −0.441786 | − | 0.160797i | 0.111543 | − | 0.993760i | \(-0.464421\pi\) |
−0.553329 | + | 0.832963i | \(0.686643\pi\) | |||||||
\(788\) | −1.25741e11 | − | 1.49852e11i | −0.326116 | − | 0.388650i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.54742e9 | + | 5.63215e8i | −0.00397283 | + | 0.00144599i | ||||
\(791\) | −2.84533e10 | − | 1.64275e10i | −0.0726820 | − | 0.0419630i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.59973e10 | + | 1.66272e11i | 0.242754 | + | 0.420462i | ||||
\(794\) | −1.12546e11 | + | 1.34127e11i | −0.283171 | + | 0.337470i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.87436e9 | − | 5.60003e10i | −0.0245956 | − | 0.139488i | ||||
\(797\) | 5.56877e11 | − | 9.81924e10i | 1.38015 | − | 0.243357i | 0.566187 | − | 0.824277i | \(-0.308418\pi\) |
0.813961 | + | 0.580919i | \(0.197307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.87859e11 | + | 4.93272e11i | 1.44240 | + | 1.21032i | ||||
\(800\) | 3.62711e11 | − | 2.09412e11i | 0.885526 | − | 0.511259i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.44108e11 | − | 2.49602e11i | 0.348329 | − | 0.603324i | ||||
\(803\) | 6.54864e10 | + | 1.79922e11i | 0.157503 | + | 0.432736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.20204e9 | + | 7.72143e9i | −0.0219129 | + | 0.0183871i | ||||
\(806\) | −4.45063e10 | + | 1.22280e11i | −0.105459 | + | 0.289745i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.54041e10 | + | 2.57500e11i | −0.106525 | + | 0.604131i | ||||
\(809\) | − | 5.05250e10i | − | 0.117954i | −0.998259 | − | 0.0589769i | \(-0.981216\pi\) | ||
0.998259 | − | 0.0589769i | \(-0.0187838\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.28251e11 | 0.758791 | 0.379396 | − | 0.925235i | \(-0.376132\pi\) | ||||
0.379396 | + | 0.925235i | \(0.376132\pi\) | |||||||
\(812\) | 3.29291e11 | + | 5.80628e10i | 0.757452 | + | 0.133559i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.06628e11 | − | 3.88092e10i | −0.242869 | − | 0.0883970i | ||||
\(815\) | 2.62439e10 | + | 3.12762e10i | 0.0594836 | + | 0.0708898i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.09847e11 | + | 1.85569e11i | −1.14433 | + | 0.416503i | ||||
\(818\) | −7.51378e10 | − | 4.33808e10i | −0.167821 | − | 0.0968913i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.17724e9 | − | 8.96724e9i | −0.0114510 | − | 0.0198337i | ||||
\(821\) | 4.35639e11 | − | 5.19174e11i | 0.958857 | − | 1.14272i | −0.0308373 | − | 0.999524i | \(-0.509817\pi\) |
0.989694 | − | 0.143197i | \(-0.0457382\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.04516e11 | + | 5.92737e11i | 0.227815 | + | 1.29200i | 0.857231 | + | 0.514933i | \(0.172183\pi\) |
−0.629416 | + | 0.777069i | \(0.716706\pi\) | |||||||
\(824\) | 1.80153e11 | − | 3.17658e10i | 0.390780 | − | 0.0689051i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.97933e11 | − | 2.49995e11i | −0.640027 | − | 0.537047i | ||||
\(827\) | −3.13017e11 | + | 1.80720e11i | −0.669184 | + | 0.386353i | −0.795767 | − | 0.605603i | \(-0.792932\pi\) |
0.126584 | + | 0.991956i | \(0.459599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.85216e11 | + | 3.20803e11i | −0.392157 | + | 0.679235i | −0.992734 | − | 0.120332i | \(-0.961604\pi\) |
0.600577 | + | 0.799567i | \(0.294938\pi\) | |||||||
\(830\) | −5.97716e8 | − | 1.64221e9i | −0.00125946 | − | 0.00346032i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.04909e10 | + | 2.55849e10i | −0.0636322 | + | 0.0533938i | ||||
\(833\) | 9.28149e10 | − | 2.55007e11i | 0.192769 | − | 0.529629i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.98527e9 | + | 5.09580e10i | −0.0184835 | + | 0.104825i | ||||
\(836\) | − | 2.95071e11i | − | 0.604090i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.28308e11 | −0.462962 | ||||||||
\(839\) | −4.93790e11 | − | 8.70685e10i | −0.996539 | − | 0.175717i | −0.348488 | − | 0.937313i | \(-0.613305\pi\) |
−0.648051 | + | 0.761597i | \(0.724416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.10319e11 | − | 4.01528e10i | −0.220529 | − | 0.0802660i | ||||
\(842\) | −2.59482e11 | − | 3.09238e11i | −0.516248 | − | 0.615241i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.17892e11 | + | 2.24894e11i | −1.21771 | + | 0.443209i | ||||
\(845\) | 1.86925e10 | + | 1.07921e10i | 0.0366640 | + | 0.0211679i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.19737e11 | − | 3.80595e11i | −0.426942 | − | 0.739486i | ||||
\(848\) | 5.03256e10 | − | 5.99758e10i | 0.0973209 | − | 0.115982i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.57810e10 | − | 4.29775e11i | −0.145173 | − | 0.823315i | ||||
\(851\) | −2.23727e11 | + | 3.94491e10i | −0.426580 | + | 0.0752176i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.25556e11 | − | 1.05354e11i | −0.237160 | − | 0.199001i | 0.516460 | − | 0.856312i | \(-0.327250\pi\) |
−0.753620 | + | 0.657310i | \(0.771694\pi\) | |||||||
\(854\) | −2.31604e11 | + | 1.33716e11i | −0.435425 | + | 0.251393i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.85910e11 | + | 6.68415e11i | −0.718771 | + | 1.24495i | ||||
\(857\) | −2.24707e11 | − | 6.17377e11i | −0.416575 | − | 1.14453i | −0.953630 | − | 0.300982i | \(-0.902685\pi\) |
0.537055 | − | 0.843547i | \(-0.319537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.05655e11 | + | 1.72565e11i | −0.377717 | + | 0.316943i | −0.811806 | − | 0.583928i | \(-0.801515\pi\) |
0.434088 | + | 0.900870i | \(0.357071\pi\) | |||||||
\(860\) | 6.69097e9 | − | 1.83833e10i | 0.0122319 | − | 0.0336070i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.05330e9 | − | 2.29874e10i | 0.00734141 | − | 0.0416352i | ||||
\(863\) | − | 7.75412e11i | − | 1.39794i | −0.715150 | − | 0.698971i | \(-0.753642\pi\) | ||
0.715150 | − | 0.698971i | \(-0.246358\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.47861e9 | −0.00264112 | ||||||||
\(866\) | −5.15738e11 | − | 9.09385e10i | −0.916975 | − | 0.161687i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.49136e11 | + | 1.99869e11i | 0.967388 | + | 0.352101i | ||||
\(869\) | 2.70584e10 | + | 3.22469e10i | 0.0474485 | + | 0.0565469i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.61386e11 | − | 5.87398e10i | 0.280410 | − | 0.102061i | ||||
\(872\) | 8.09506e11 | + | 4.67368e11i | 1.40008 | + | 0.808339i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.16184e10 | + | 1.58688e11i | 0.157014 | + | 0.271955i | ||||
\(875\) | −5.18789e10 | + | 6.18268e10i | −0.0885031 | + | 0.105474i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.75848e10 | + | 3.26579e11i | 0.0973440 | + | 0.552065i | 0.994004 | + | 0.109345i | \(0.0348754\pi\) |
−0.896660 | + | 0.442720i | \(0.854014\pi\) | |||||||
\(878\) | −3.94698e11 | + | 6.95958e10i | −0.664181 | + | 0.117113i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.83809e9 | + | 4.05964e9i | 0.00806758 | + | 0.00676950i | ||||
\(881\) | −3.43576e11 | + | 1.98364e11i | −0.570320 | + | 0.329275i | −0.757277 | − | 0.653094i | \(-0.773471\pi\) |
0.186957 | + | 0.982368i | \(0.440138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.25631e11 | + | 3.90804e11i | −0.371155 | + | 0.642860i | −0.989744 | − | 0.142856i | \(-0.954372\pi\) |
0.618588 | + | 0.785715i | \(0.287705\pi\) | |||||||
\(884\) | −1.48775e11 | − | 4.08757e11i | −0.243625 | − | 0.669354i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.82042e11 | − | 1.52751e11i | 0.295417 | − | 0.247885i | ||||
\(887\) | −1.74390e11 | + | 4.79133e11i | −0.281726 | + | 0.774037i | 0.715431 | + | 0.698684i | \(0.246231\pi\) |
−0.997157 | + | 0.0753529i | \(0.975992\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.59788e10 | − | 9.06204e10i | 0.0255822 | − | 0.145084i | ||||
\(890\) | − | 1.10757e10i | − | 0.0176527i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.98779e10 | 0.126173 | ||||||||
\(893\) | −1.06408e12 | − | 1.87627e11i | −1.67328 | − | 0.295045i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.22924e10 | + | 8.11377e9i | 0.0347428 | + | 0.0126453i | ||||
\(896\) | 4.54074e11 | + | 5.41145e11i | 0.704523 | + | 0.839617i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.76318e11 | − | 1.36969e11i | 0.578695 | − | 0.210628i | ||||
\(899\) | 5.79459e11 | + | 3.34551e11i | 0.887123 | + | 0.512181i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.48766e11 | − | 4.30875e11i | −0.377478 | − | 0.653812i | ||||
\(902\) | 5.27727e10 | − | 6.28921e10i | 0.0797229 | − | 0.0950101i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.24907e9 | − | 4.11115e10i | −0.0108545 | − | 0.0615587i | ||||
\(905\) | −3.16310e10 | + | 5.57740e9i | −0.0471540 | + | 0.00831452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.86132e11 | − | 7.43553e11i | −1.30939 | − | 1.09871i | −0.988440 | − | 0.151614i | \(-0.951553\pi\) |
−0.320952 | − | 0.947096i | \(-0.604003\pi\) | |||||||
\(908\) | −4.49630e11 | + | 2.59594e11i | −0.661473 | + | 0.381901i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.22692e9 | − | 1.07853e10i | 0.00908046 | − | 0.0157278i | ||||
\(911\) | 1.13732e11 | + | 3.12476e11i | 0.165124 | + | 0.453673i | 0.994465 | − | 0.105069i | \(-0.0335063\pi\) |
−0.829341 | + | 0.558742i | \(0.811284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.42223e10 | + | 2.87159e10i | −0.0492522 | + | 0.0413275i | ||||
\(914\) | 2.82053e10 | − | 7.74933e10i | 0.0404153 | − | 0.111040i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.45962e11 | − | 8.27792e11i | 0.207328 | − | 1.17582i | ||||
\(917\) | − | 1.30947e12i | − | 1.85190i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.61529e11 | −0.226459 | −0.113229 | − | 0.993569i | \(-0.536120\pi\) | ||||
−0.113229 | + | 0.993569i | \(0.536120\pi\) | |||||||
\(920\) | −1.50311e10 | − | 2.65039e9i | −0.0209817 | − | 0.00369964i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.20094e11 | + | 4.37107e10i | 0.166187 | + | 0.0604872i | ||||
\(923\) | 2.69023e11 | + | 3.20609e11i | 0.370666 | + | 0.441742i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.15872e11 | + | 2.60556e11i | −0.977842 | + | 0.355905i | ||||
\(926\) | 1.55820e11 | + | 8.99629e10i | 0.211924 | + | 0.122354i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.32899e11 | + | 5.76599e11i | 0.448871 | + | 0.777467i | ||||
\(929\) | −4.01736e11 | + | 4.78770e11i | −0.539359 | + | 0.642783i | −0.965044 | − | 0.262088i | \(-0.915589\pi\) |
0.425685 | + | 0.904872i | \(0.360033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.63500e10 | + | 3.76290e11i | 0.0883166 | + | 0.500868i | ||||
\(932\) | −5.54767e11 | + | 9.78203e10i | −0.735270 | + | 0.129648i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.18566e11 | − | 1.83399e11i | −0.287207 | − | 0.240996i | ||||
\(935\) | 3.47576e10 | − | 2.00673e10i | 0.0454782 | − | 0.0262569i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.07728e10 | + | 3.59796e10i | −0.0269487 | + | 0.0466765i | −0.879185 | − | 0.476480i | \(-0.841912\pi\) |
0.852237 | + | 0.523157i | \(0.175246\pi\) | |||||||
\(938\) | 8.18197e10 | + | 2.24798e11i | 0.105693 | + | 0.290389i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.98443e10 | − | 2.50423e10i | 0.0382252 | − | 0.0320747i | ||||
\(941\) | 1.12104e11 | − | 3.08003e11i | 0.142976 | − | 0.392822i | −0.847449 | − | 0.530877i | \(-0.821863\pi\) |
0.990425 | + | 0.138055i | \(0.0440850\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.85428e10 | − | 1.61874e11i | 0.0360952 | − | 0.204706i | ||||
\(944\) | 4.09391e11i | 0.515526i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.55114e11 | 0.193681 | ||||||||
\(947\) | −1.83765e11 | − | 3.24028e10i | −0.228488 | − | 0.0402886i | 0.0582317 | − | 0.998303i | \(-0.481454\pi\) |
−0.286720 | + | 0.958014i | \(0.592565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.73458e11 | − | 1.35928e11i | −0.460445 | − | 0.167588i | ||||
\(950\) | 3.94969e11 | + | 4.70705e11i | 0.484918 | + | 0.577902i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.31533e12 | − | 4.78741e11i | 1.60135 | − | 0.582845i | ||||
\(953\) | −2.43325e11 | − | 1.40483e11i | −0.294995 | − | 0.170315i | 0.345197 | − | 0.938530i | \(-0.387812\pi\) |
−0.640192 | + | 0.768215i | \(0.721145\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.25611e10 | − | 2.17565e10i | −0.0151013 | − | 0.0261563i | ||||
\(956\) | −2.30701e11 | + | 2.74938e11i | −0.276196 | + | 0.329157i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.20396e11 | + | 6.82800e11i | 0.142939 | + | 0.810647i | ||||
\(959\) | 7.65439e11 | − | 1.34968e11i | 0.904974 | − | 0.159571i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.42449e11 | + | 2.03439e11i | 0.284268 | + | 0.238529i | ||||
\(962\) | 2.03972e11 | − | 1.17763e11i | 0.238161 | − | 0.137502i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.14848e11 | − | 7.18537e11i | 0.480375 | − | 0.832034i | ||||
\(965\) | −4.05762e8 | − | 1.11482e9i | −0.000467910 | − | 0.00128557i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.59916e11 | − | 3.02005e11i | 0.411619 | − | 0.345389i | −0.413345 | − | 0.910574i | \(-0.635640\pi\) |
0.824964 | + | 0.565185i | \(0.191195\pi\) | |||||||
\(968\) | 1.90983e11 | − | 5.24721e11i | 0.217517 | − | 0.597622i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.55198e8 | + | 3.71582e9i | −0.000740092 | + | 0.00419727i | ||||
\(971\) | − | 1.13211e12i | − | 1.27354i | −0.771056 | − | 0.636768i | \(-0.780271\pi\) | ||
0.771056 | − | 0.636768i | \(-0.219729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.99080e12 | −2.22114 | ||||||||
\(974\) | −1.58307e11 | − | 2.79138e10i | −0.175899 | − | 0.0310158i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.64529e11 | + | 9.62808e10i | 0.291524 | + | 0.106106i | ||||
\(977\) | 1.01318e11 | + | 1.20746e11i | 0.111201 | + | 0.132524i | 0.818774 | − | 0.574117i | \(-0.194654\pi\) |
−0.707573 | + | 0.706640i | \(0.750210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.66053e11 | + | 9.68355e10i | −0.289626 | + | 0.105415i | ||||
\(980\) | −1.19312e10 | − | 6.88849e9i | −0.0129354 | − | 0.00746827i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.15746e10 | + | 1.58612e11i | 0.0984757 | + | 0.170565i | ||||
\(983\) | −2.32916e11 | + | 2.77578e11i | −0.249451 | + | 0.297284i | −0.876210 | − | 0.481929i | \(-0.839936\pi\) |
0.626760 | + | 0.779213i | \(0.284381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.50544e9 | + | 3.68942e10i | 0.00691085 | + | 0.0391934i | ||||
\(986\) | 6.83210e11 | − | 1.20468e11i | 0.722847 | − | 0.127457i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.69178e11 | + | 3.93687e11i | 0.492391 | + | 0.413165i | ||||
\(989\) | 2.68946e11 | − | 1.55276e11i | 0.281113 | − | 0.162300i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.02286e11 | − | 3.50370e11i | 0.209735 | − | 0.363272i | −0.741896 | − | 0.670515i | \(-0.766073\pi\) |
0.951631 | + | 0.307243i | \(0.0994064\pi\) | |||||||
\(992\) | 3.97980e11 | + | 1.09344e12i | 0.410974 | + | 1.12914i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.46582e11 | + | 3.74727e11i | −0.457463 | + | 0.383857i | ||||
\(995\) | −3.72467e9 | + | 1.02334e10i | −0.00380010 | + | 0.0104407i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.68798e11 | − | 1.52443e12i | 0.272048 | − | 1.54286i | −0.476137 | − | 0.879371i | \(-0.657963\pi\) |
0.748185 | − | 0.663490i | \(-0.230926\pi\) | |||||||
\(998\) | 1.97145e11i | 0.198730i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 81.9.f.a.8.14 | 138 | ||
3.2 | odd | 2 | 27.9.f.a.2.10 | ✓ | 138 | ||
27.13 | even | 9 | 27.9.f.a.14.10 | yes | 138 | ||
27.14 | odd | 18 | inner | 81.9.f.a.71.14 | 138 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.9.f.a.2.10 | ✓ | 138 | 3.2 | odd | 2 | ||
27.9.f.a.14.10 | yes | 138 | 27.13 | even | 9 | ||
81.9.f.a.8.14 | 138 | 1.1 | even | 1 | trivial | ||
81.9.f.a.71.14 | 138 | 27.14 | odd | 18 | inner |