Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,9,Mod(65,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.65");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.e (of order \(2\), degree \(1\), 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: | \(78.2166931317\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 78x^{6} + 144x^{5} + 2079x^{4} + 936x^{3} - 658x^{2} + 2884x + 30633 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(-1.50551 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.65 |
Dual form | 192.9.e.i.65.2 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −80.7366 | − | 6.52720i | −0.996748 | − | 0.0805827i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 920.542i | − | 1.47287i | −0.676510 | − | 0.736434i | \(-0.736508\pi\) | ||
0.676510 | − | 0.736434i | \(-0.263492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2012.50 | −0.838191 | −0.419096 | − | 0.907942i | \(-0.637653\pi\) | ||||
−0.419096 | + | 0.907942i | \(0.637653\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6475.79 | + | 1053.97i | 0.987013 | + | 0.160641i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 9968.11i | − | 0.680835i | −0.940274 | − | 0.340418i | \(-0.889432\pi\) | ||
0.940274 | − | 0.340418i | \(-0.110568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11295.6 | 0.395489 | 0.197745 | − | 0.980254i | \(-0.436638\pi\) | ||||
0.197745 | + | 0.980254i | \(0.436638\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6008.56 | + | 74321.4i | −0.118688 | + | 1.46808i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 151773.i | 1.81719i | 0.417680 | + | 0.908594i | \(0.362843\pi\) | ||||
−0.417680 | + | 0.908594i | \(0.637157\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −186183. | −1.42865 | −0.714325 | − | 0.699814i | \(-0.753266\pi\) | ||||
−0.714325 | + | 0.699814i | \(0.753266\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 162482. | + | 13136.0i | 0.835465 | + | 0.0675437i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 224838.i | − | 0.803450i | −0.915760 | − | 0.401725i | \(-0.868411\pi\) | ||
0.915760 | − | 0.401725i | \(-0.131589\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −456773. | −1.16934 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −515954. | − | 127363.i | −0.970858 | − | 0.239655i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.17495e6i | 1.66122i | 0.556854 | + | 0.830611i | \(0.312008\pi\) | ||||
−0.556854 | + | 0.830611i | \(0.687992\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 300789. | 0.325698 | 0.162849 | − | 0.986651i | \(-0.447932\pi\) | ||||
0.162849 | + | 0.986651i | \(0.447932\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −65063.8 | + | 804791.i | −0.0548635 | + | 0.678621i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.85259e6i | 1.23454i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.47981e6 | 0.789585 | 0.394792 | − | 0.918770i | \(-0.370817\pi\) | ||||
0.394792 | + | 0.918770i | \(0.370817\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −911966. | − | 73728.5i | −0.394203 | − | 0.0318696i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.69503e6i | − | 0.953735i | −0.878975 | − | 0.476868i | \(-0.841772\pi\) | ||
0.878975 | − | 0.476868i | \(-0.158228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.09749e6 | −1.49102 | −0.745508 | − | 0.666496i | \(-0.767793\pi\) | ||||
−0.745508 | + | 0.666496i | \(0.767793\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 970221. | − | 5.96124e6i | 0.236603 | − | 1.45374i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.64836e6i | 0.542732i | 0.962476 | + | 0.271366i | \(0.0874753\pi\) | ||||
−0.962476 | + | 0.271366i | \(0.912525\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.71466e6 | −0.297436 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 990655. | − | 1.22537e7i | 0.146434 | − | 1.81128i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.07581e6i | − | 0.389812i | −0.980822 | − | 0.194906i | \(-0.937560\pi\) | ||
0.980822 | − | 0.194906i | \(-0.0624402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.17606e6 | −1.00278 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.50318e7 | + | 1.21525e6i | 1.42400 | + | 0.115125i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.78203e7i | 1.47064i | 0.677720 | + | 0.735320i | \(0.262968\pi\) | ||||
−0.677720 | + | 0.735320i | \(0.737032\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.90915e6 | −0.643453 | −0.321727 | − | 0.946833i | \(-0.604263\pi\) | ||||
−0.321727 | + | 0.946833i | \(0.604263\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.30325e7 | − | 2.12111e6i | −0.827305 | − | 0.134648i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.03981e7i | − | 0.582504i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.07217e7 | 0.532063 | 0.266032 | − | 0.963964i | \(-0.414287\pi\) | ||||
0.266032 | + | 0.963964i | \(0.414287\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.46756e6 | + | 1.81527e7i | −0.0647442 | + | 0.800837i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.05459e6i | 0.0415001i | 0.999785 | + | 0.0207501i | \(0.00660542\pi\) | ||||
−0.999785 | + | 0.0207501i | \(0.993395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.03895e7 | 0.365850 | 0.182925 | − | 0.983127i | \(-0.441443\pi\) | ||||
0.182925 | + | 0.983127i | \(0.441443\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.68783e7 | + | 2.98145e6i | 1.16554 | + | 0.0942285i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00608e7i | 0.570670i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.99649e7 | 1.79627 | 0.898135 | − | 0.439720i | \(-0.144922\pi\) | ||||
0.898135 | + | 0.439720i | \(0.144922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.08250e7 | + | 1.36505e7i | 0.948389 | + | 0.317110i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.34028e7i | − | 0.493124i | −0.969127 | − | 0.246562i | \(-0.920699\pi\) | ||
0.969127 | − | 0.246562i | \(-0.0793009\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.39714e8 | 2.67648 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.66913e6 | − | 9.48615e7i | 0.133866 | − | 1.65582i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.62936e7i | 1.21598i | 0.793943 | + | 0.607992i | \(0.208025\pi\) | ||||
−0.793943 | + | 0.607992i | \(0.791975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.27323e7 | −0.331496 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.42847e7 | − | 1.96331e6i | −0.324639 | − | 0.0262456i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.71389e8i | 2.10421i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.70613e7 | 0.531590 | 0.265795 | − | 0.964030i | \(-0.414366\pi\) | ||||
0.265795 | + | 0.964030i | \(0.414366\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.05061e7 | − | 6.45514e7i | 0.109370 | − | 0.671993i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.33013e8i | − | 1.27823i | −0.769110 | − | 0.639116i | \(-0.779300\pi\) | ||
0.769110 | − | 0.639116i | \(-0.220700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.03845e8 | 0.922649 | 0.461324 | − | 0.887231i | \(-0.347374\pi\) | ||||
0.461324 | + | 0.887231i | \(0.347374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.20922e7 | − | 1.49572e8i | 0.0994829 | − | 1.23053i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.24148e7i | 0.628739i | 0.949301 | + | 0.314369i | \(0.101793\pi\) | ||||
−0.949301 | + | 0.314369i | \(0.898207\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.22099e8 | 1.57340 | 0.786701 | − | 0.617334i | \(-0.211787\pi\) | ||||
0.786701 | + | 0.617334i | \(0.211787\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.19475e8 | − | 9.65901e6i | −0.787017 | − | 0.0636269i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.17665e7i | − | 0.562821i | −0.959587 | − | 0.281411i | \(-0.909198\pi\) | ||
0.959587 | − | 0.281411i | \(-0.0908023\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.06973e8 | −1.18337 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.31478e7 | + | 1.19052e7i | 0.390353 | + | 0.0635319i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.05443e8i | − | 1.52315i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.14996e8 | 0.536463 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.75910e7 | + | 2.17587e8i | −0.0768545 | + | 0.950633i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.08919e7i | 0.249413i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.87904e8 | −0.722305 | −0.361153 | − | 0.932507i | \(-0.617617\pi\) | ||||
−0.361153 | + | 0.932507i | \(0.617617\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.11554e8 | + | 3.32723e7i | 1.48617 | + | 0.120150i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.06519e8i | − | 0.701253i | −0.936515 | − | 0.350626i | \(-0.885969\pi\) | ||
0.936515 | − | 0.350626i | \(-0.114031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.74693e8 | 1.19748 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.17243e8 | + | 4.74957e8i | −0.352980 | + | 1.42995i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.15371e8i | − | 0.611371i | −0.952133 | − | 0.305686i | \(-0.901114\pi\) | ||
0.952133 | − | 0.305686i | \(-0.0988856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.49471e8 | 0.668285 | 0.334142 | − | 0.942523i | \(-0.391553\pi\) | ||||
0.334142 | + | 0.942523i | \(0.391553\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.72864e7 | − | 2.13819e8i | 0.0437348 | − | 0.540967i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.12596e8i | − | 0.269263i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.08159e9 | 2.44676 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.38436e8 | + | 1.11919e7i | 0.296469 | + | 0.0239682i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.89834e8i | 0.790923i | 0.918483 | + | 0.395461i | \(0.129415\pi\) | ||||
−0.918483 | + | 0.395461i | \(0.870585\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.94946e8 | −0.759679 | −0.379840 | − | 0.925052i | \(-0.624021\pi\) | ||||
−0.379840 | + | 0.925052i | \(0.624021\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.59964e8 | + | 9.82853e8i | −0.291915 | + | 1.79359i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.76889e8i | − | 0.479710i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.13244e8 | −0.680155 | −0.340077 | − | 0.940397i | \(-0.610453\pi\) | ||||
−0.340077 | + | 0.940397i | \(0.610453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00764e7 | + | 2.48330e8i | −0.0314121 | + | 0.388544i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.52486e8i | 0.673444i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.52612e8 | 0.216191 | 0.108095 | − | 0.994141i | \(-0.465525\pi\) | ||||
0.108095 | + | 0.994141i | \(0.465525\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.40844e8 | + | 5.98940e7i | 0.999519 | + | 0.0808067i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.84359e8i | − | 0.365596i | −0.983151 | − | 0.182798i | \(-0.941485\pi\) | ||
0.983151 | − | 0.182798i | \(-0.0585154\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.88141e8 | −0.843588 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.20568e9 | − | 1.96231e8i | −1.41010 | − | 0.229500i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.67130e7i | 0.0633138i | 0.999499 | + | 0.0316569i | \(0.0100784\pi\) | ||||
−0.999499 | + | 0.0316569i | \(0.989922\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.19254e8 | 0.980129 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.16317e8 | − | 1.43875e9i | 0.118508 | − | 1.46586i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.02066e9i | 0.994185i | 0.867697 | + | 0.497093i | \(0.165599\pi\) | ||||
−0.867697 | + | 0.497093i | \(0.834401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.37279e8 | 0.593766 | 0.296883 | − | 0.954914i | \(-0.404053\pi\) | ||||
0.296883 | + | 0.954914i | \(0.404053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.19294e8 | + | 5.81518e7i | 0.641361 | + | 0.0518512i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.36223e9i | − | 1.16295i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.51289e9 | 1.23721 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.03836e9 | + | 2.56317e8i | 0.813765 | + | 0.200877i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.25733e9i | − | 0.944750i | −0.881398 | − | 0.472375i | \(-0.843397\pi\) | ||
0.881398 | − | 0.472375i | \(-0.156603\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.98104e7 | 0.0214851 | 0.0107426 | − | 0.999942i | \(-0.496580\pi\) | ||||
0.0107426 | + | 0.999942i | \(0.496580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.78702e7 | + | 8.39503e8i | −0.0469397 | + | 0.580609i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.19401e9i | − | 1.45671i | −0.685199 | − | 0.728356i | \(-0.740285\pi\) | ||
0.685199 | − | 0.728356i | \(-0.259715\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.23376e9 | 0.786714 | 0.393357 | − | 0.919386i | \(-0.371314\pi\) | ||||
0.393357 | + | 0.919386i | \(0.371314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.65631e8 | − | 6.99825e7i | −0.530333 | − | 0.0428751i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.36458e9i | − | 1.39242i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.48089e9 | −1.40473 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.36972e8 | − | 1.45601e9i | 0.129067 | − | 0.793015i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.85589e9i | 0.972675i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.81426e8 | 0.293335 | 0.146668 | − | 0.989186i | \(-0.453145\pi\) | ||||
0.146668 | + | 0.989186i | \(0.453145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.88350e6 | − | 8.51438e7i | 0.00334419 | − | 0.0413652i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.69245e9i | 2.19607i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.05337e8 | −0.272997 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.38813e8 | − | 6.78143e7i | −0.364660 | − | 0.0294812i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.71437e9i | 0.718679i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.29312e9 | −0.522901 | −0.261450 | − | 0.965217i | \(-0.584201\pi\) | ||||
−0.261450 | + | 0.965217i | \(0.584201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.95797e9 | − | 4.81424e8i | −1.15415 | − | 0.187844i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.25456e8i | 0.160233i | 0.996786 | + | 0.0801163i | \(0.0255292\pi\) | ||||
−0.996786 | + | 0.0801163i | \(0.974471\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.34280e9 | −0.488280 | −0.244140 | − | 0.969740i | \(-0.578506\pi\) | ||||
−0.244140 | + | 0.969740i | \(0.578506\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.30941e8 | − | 1.61964e9i | 0.0459861 | − | 0.568814i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.62002e9i | 0.888956i | 0.895790 | + | 0.444478i | \(0.146611\pi\) | ||||
−0.895790 | + | 0.444478i | \(0.853389\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.43792e9 | 0.799372 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.64872e9 | − | 4.56675e8i | −1.79043 | − | 0.144748i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00705e8i | 0.184107i | 0.995754 | + | 0.0920534i | \(0.0293430\pi\) | ||||
−0.995754 | + | 0.0920534i | \(0.970657\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.91474e7 | 0.0145691 | 0.00728454 | − | 0.999973i | \(-0.497681\pi\) | ||||
0.00728454 | + | 0.999973i | \(0.497681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.20697e9 | − | 1.36857e9i | −0.919751 | − | 0.392502i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.57842e9i | 0.438084i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.10305e9 | −0.565016 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.52755e8 | + | 1.88946e9i | −0.0397372 | + | 0.491520i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.49890e9i | 1.38542i | 0.721217 | + | 0.692709i | \(0.243583\pi\) | ||||
−0.721217 | + | 0.692709i | \(0.756417\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.24121e9 | −0.547017 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.12800e10 | − | 9.11940e8i | −2.66777 | − | 0.215678i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.62748e9i | − | 0.373065i | −0.982449 | − | 0.186532i | \(-0.940275\pi\) | ||
0.982449 | − | 0.186532i | \(-0.0597249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.97811e9 | −0.661823 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.23836e9 | + | 7.60873e9i | −0.266861 | + | 1.63965i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 3.55235e9i | − | 0.742494i | −0.928534 | − | 0.371247i | \(-0.878930\pi\) | ||
0.928534 | − | 0.371247i | \(-0.121070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.83141e9 | −0.574142 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.97984e8 | − | 6.15968e9i | 0.0979873 | − | 1.21203i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.16296e9i | 0.413086i | 0.978438 | + | 0.206543i | \(0.0662213\pi\) | ||||
−0.978438 | + | 0.206543i | \(0.933779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.12387e9 | 0.764589 | 0.382294 | − | 0.924041i | \(-0.375134\pi\) | ||||
0.382294 | + | 0.924041i | \(0.375134\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.83533e9 | + | 1.48378e8i | 0.330418 | + | 0.0267128i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.55316e9i | 0.796127i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.01959e9 | −0.852608 | −0.426304 | − | 0.904580i | \(-0.640185\pi\) | ||||
−0.426304 | + | 0.904580i | \(0.640185\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.94785e9 | + | 3.17022e8i | 0.321468 | + | 0.0523205i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.64527e9i | − | 1.54700i | −0.633799 | − | 0.773498i | \(-0.718505\pi\) | ||
0.633799 | − | 0.773498i | \(-0.281495\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.72563e9 | 0.580836 | 0.290418 | − | 0.956900i | \(-0.406206\pi\) | ||||
0.290418 | + | 0.956900i | \(0.406206\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.11869e9 | − | 1.38374e10i | 0.169563 | − | 2.09737i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.42373e9i | 0.799412i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.60594e10 | −2.30217 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.79957e9 | − | 3.07178e8i | −0.529861 | − | 0.0428370i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.12558e10i | − | 1.52724i | −0.645667 | − | 0.763619i | \(-0.723421\pi\) | ||
0.645667 | − | 0.763619i | \(-0.276579\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.64043e10 | 2.16606 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.26956e9 | + | 5.14308e9i | −0.163166 | + | 0.660994i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 2.53968e9i | − | 0.317756i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.02587e10 | 1.24976 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.68205e8 | + | 1.07390e10i | −0.103003 | + | 1.27408i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.20125e9i | 0.947721i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.70242e8 | −0.109226 | −0.0546131 | − | 0.998508i | \(-0.517393\pi\) | ||||
−0.0546131 | + | 0.998508i | \(0.517393\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.38409e9 | − | 6.77817e8i | −0.919648 | − | 0.0743495i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.23353e10i | − | 1.31859i | −0.751886 | − | 0.659294i | \(-0.770855\pi\) | ||
0.751886 | − | 0.659294i | \(-0.229145\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47417e9 | −0.257781 | −0.128891 | − | 0.991659i | \(-0.541142\pi\) | ||||
−0.128891 | + | 0.991659i | \(0.541142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.95257e9 | + | 1.19970e10i | −0.198319 | + | 1.21851i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.69441e10i | 1.67796i | 0.544162 | + | 0.838980i | \(0.316848\pi\) | ||||
−0.544162 | + | 0.838980i | \(0.683152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.17120e10 | 1.13102 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.37938e8 | − | 6.65389e9i | 0.0506655 | − | 0.626694i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.82576e10i | − | 2.59613i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.15951e9 | −0.462461 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.79315e10 | − | 1.44968e9i | −1.56829 | − | 0.126789i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.32981e9i | − | 0.454913i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.73248e10 | 1.44330 | 0.721651 | − | 0.692257i | \(-0.243383\pi\) | ||||
0.721651 | + | 0.692257i | \(0.243383\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.58293e9 | + | 1.55967e9i | 0.779330 | + | 0.126840i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 9.86975e9i | − | 0.783659i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.54415e9 | 0.584912 | 0.292456 | − | 0.956279i | \(-0.405528\pi\) | ||||
0.292456 | + | 0.956279i | \(0.405528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.98978e8 | + | 7.40891e9i | −0.0453536 | + | 0.560991i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.99830e9i | − | 0.221747i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.50524e10 | 1.08750 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.67103e10 | + | 1.35095e9i | 1.17953 | + | 0.0953596i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.20011e10i | 1.51749i | 0.651387 | + | 0.758746i | \(0.274188\pi\) | ||||
−0.651387 | + | 0.758746i | \(0.725812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.10710e10 | 0.746251 | 0.373126 | − | 0.927781i | \(-0.378286\pi\) | ||||
0.373126 | + | 0.927781i | \(0.378286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.82799e9 | − | 1.43863e9i | −0.383964 | − | 0.0947810i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.54479e10i | 0.994880i | 0.867498 | + | 0.497440i | \(0.165727\pi\) | ||||
−0.867498 | + | 0.497440i | \(0.834273\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.70792e8 | 0.0611242 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.99369e9 | + | 2.46605e10i | −0.122740 | + | 1.51820i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.17345e10i | 0.706458i | 0.935537 | + | 0.353229i | \(0.114916\pi\) | ||||
−0.935537 | + | 0.353229i | \(0.885084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.76806e10 | 1.04104 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.28436e9 | − | 7.50600e8i | −0.534719 | − | 0.0432297i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.56397e9i | − | 0.538849i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.18806e10 | −1.75737 | −0.878684 | − | 0.477404i | \(-0.841578\pi\) | ||||
−0.878684 | + | 0.477404i | \(0.841578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.84047e9 | − | 1.74524e10i | 0.153209 | − | 0.941349i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.19005e9i | 0.326737i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.99978e9 | 0.258295 | 0.129147 | − | 0.991625i | \(-0.458776\pi\) | ||||
0.129147 | + | 0.991625i | \(0.458776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.97453e8 | − | 4.91620e9i | 0.0200984 | − | 0.248602i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.32717e10i | 0.656996i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.07635e10 | 1.49101 | 0.745503 | − | 0.666502i | \(-0.232209\pi\) | ||||
0.745503 | + | 0.666502i | \(0.232209\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.51707e10 | + | 1.22649e9i | 0.719956 | + | 0.0582053i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.94789e10i | 0.905251i | 0.891701 | + | 0.452625i | \(0.149512\pi\) | ||||
−0.891701 | + | 0.452625i | \(0.850488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.84668e10 | 0.840521 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.30103e10 | − | 5.37259e9i | −1.47165 | − | 0.239519i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 4.42619e9i | − | 0.193300i | −0.995318 | − | 0.0966499i | \(-0.969187\pi\) | ||
0.995318 | − | 0.0966499i | \(-0.0308127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.41244e10 | 1.46002 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.34799e9 | + | 1.66736e10i | −0.0565089 | + | 0.698972i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 6.44056e10i | − | 2.64567i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.25488e10 | −0.505172 | −0.252586 | − | 0.967574i | \(-0.581281\pi\) | ||||
−0.252586 | + | 0.967574i | \(0.581281\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.02514e10 | − | 2.44570e9i | −1.19359 | − | 0.0964963i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.35459e10i | − | 0.523879i | −0.965084 | − | 0.261939i | \(-0.915638\pi\) | ||
0.965084 | − | 0.261939i | \(-0.0843621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.39758e9 | 0.128810 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.25659e10 | − | 3.75812e10i | 0.467061 | − | 1.39685i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.47509e10i | − | 0.537577i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.31951e10 | 1.54362 | 0.771812 | − | 0.635850i | \(-0.219350\pi\) | ||||
0.771812 | + | 0.635850i | \(0.219350\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.40577e9 | + | 1.73883e10i | −0.0492659 | + | 0.609383i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.58633e10i | − | 1.23268i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.15433e10 | −0.726306 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.01415e10 | − | 1.62835e9i | −0.666111 | − | 0.0538522i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.59494e10i | 1.81526i | 0.419770 | + | 0.907631i | \(0.362111\pi\) | ||||
−0.419770 | + | 0.907631i | \(0.637889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.82532e10 | 1.21770 | 0.608848 | − | 0.793287i | \(-0.291632\pi\) | ||||
0.608848 | + | 0.793287i | \(0.291632\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.79128e9 | + | 1.71502e10i | −0.0871851 | + | 0.535683i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 6.93260e10i | − | 2.12491i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.79296e10 | 0.539337 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.34933e8 | + | 9.09058e9i | −0.0216980 | + | 0.268387i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.42900e9i | − | 0.128350i | −0.997939 | − | 0.0641751i | \(-0.979558\pi\) | ||
0.997939 | − | 0.0641751i | \(-0.0204416\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.29438e8 | −0.00368222 | −0.00184111 | − | 0.999998i | \(-0.500586\pi\) | ||||
−0.00184111 | + | 0.999998i | \(0.500586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.73240e10 | − | 7.05976e9i | −2.43880 | − | 0.197166i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.18611e10i | 1.14785i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.59331e10 | 1.23671 | 0.618355 | − | 0.785899i | \(-0.287800\pi\) | ||||
0.618355 | + | 0.785899i | \(0.287800\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.11038e10 | − | 1.80719e9i | −0.293573 | − | 0.0477805i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.70397e10i | 0.961728i | 0.876795 | + | 0.480864i | \(0.159677\pi\) | ||||
−0.876795 | + | 0.480864i | \(0.840323\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.02315e10 | 1.79098 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.54452e9 | − | 3.14738e10i | 0.0637347 | − | 0.788351i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.63633e10i | 0.648657i | 0.945945 | + | 0.324328i | \(0.105138\pi\) | ||||
−0.945945 | + | 0.324328i | \(0.894862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.68643e10 | −0.649336 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.18866e10 | + | 2.57789e9i | 0.757209 | + | 0.0612170i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.09260e10i | 0.488249i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.51289e10 | 0.346850 | 0.173425 | − | 0.984847i | \(-0.444517\pi\) | ||||
0.173425 | + | 0.984847i | \(0.444517\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.93302e10 | − | 7.83081e10i | 0.435498 | − | 1.76423i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.13740e10i | 1.13747i | 0.822521 | + | 0.568735i | \(0.192567\pi\) | ||||
−0.822521 | + | 0.568735i | \(0.807433\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.82665e10 | −0.397495 | −0.198747 | − | 0.980051i | \(-0.563687\pi\) | ||||
−0.198747 | + | 0.980051i | \(0.563687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.80731e9 | + | 2.23551e10i | −0.0386563 | + | 0.478150i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.75031e10i | 1.20899i | 0.796608 | + | 0.604496i | \(0.206626\pi\) | ||||
−0.796608 | + | 0.604496i | \(0.793374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.15773e10 | −0.445971 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.33639e10 | + | 2.69733e9i | 0.677943 | + | 0.0548087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.08123e10i | 1.01514i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.50434e10 | 1.67058 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.24180e9 | − | 1.99183e10i | 0.0626199 | − | 0.384750i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 4.64781e10i | − | 0.882889i | −0.897288 | − | 0.441445i | \(-0.854466\pi\) | ||
0.897288 | − | 0.441445i | \(-0.145534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.67153e10 | 0.312272 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.95347e9 | − | 3.65322e10i | 0.0542680 | − | 0.671254i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4.33219e10i | − | 0.782961i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.02986e10 | 1.24977 | 0.624886 | − | 0.780716i | \(-0.285145\pi\) | ||||
0.624886 | + | 0.780716i | \(0.285145\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.23213e10 | − | 9.96126e8i | −0.215488 | − | 0.0174212i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.95781e10i | − | 0.336857i | −0.985714 | − | 0.168428i | \(-0.946131\pi\) | ||
0.985714 | − | 0.168428i | \(-0.0538692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.78326e11 | −3.01875 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.94223e10 | − | 9.67127e9i | −0.989757 | − | 0.161088i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.12235e9i | − | 0.0347850i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.94522e10 | 0.636311 | 0.318155 | − | 0.948039i | \(-0.396937\pi\) | ||||
0.318155 | + | 0.948039i | \(0.396937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.85607e9 | + | 2.29582e10i | −0.0294607 | + | 0.364407i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.64015e10i | 1.50595i | 0.658047 | + | 0.752977i | \(0.271383\pi\) | ||||
−0.658047 | + | 0.752977i | \(0.728617\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.22444e11 | −1.88267 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.55581e10 | + | 4.49163e9i | 0.840845 | + | 0.0679786i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.54849e10i | 0.677635i | 0.940852 | + | 0.338818i | \(0.110027\pi\) | ||||
−0.940852 | + | 0.338818i | \(0.889973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.09088e10 | −0.306652 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.60619e10 | + | 2.37128e10i | 1.38702 | + | 0.342383i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 9.55937e10i | − | 1.35894i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.63991e10 | 0.369511 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.70177e8 | − | 4.57882e9i | 0.00510200 | − | 0.0631079i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.36756e10i | 1.13566i | 0.823146 | + | 0.567829i | \(0.192217\pi\) | ||||
−0.823146 | + | 0.567829i | \(0.807783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.10989e10 | 0.682975 | 0.341487 | − | 0.939886i | \(-0.389069\pi\) | ||||
0.341487 | + | 0.939886i | \(0.389069\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.42174e10 | − | 6.00015e9i | −0.976942 | − | 0.0789814i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.56517e10i | 0.591854i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.77588e10 | 0.354469 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.87820e10 | + | 1.15400e11i | −0.236246 | + | 1.45154i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.04419e10i | − | 0.377192i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.58663e10 | 0.926049 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.66203e9 | − | 8.24043e10i | 0.0801141 | − | 0.990952i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.70919e10i | 0.202505i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.61169e10 | 0.538358 | 0.269179 | − | 0.963090i | \(-0.413248\pi\) | ||||
0.269179 | + | 0.963090i | \(0.413248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.14517e10 | − | 4.15965e9i | −0.591835 | − | 0.0478473i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.04451e11i | − | 2.31741i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.61213e10 | −0.738571 | −0.369285 | − | 0.929316i | \(-0.620397\pi\) | ||||
−0.369285 | + | 0.929316i | \(0.620397\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.76938e10 | − | 9.38996e9i | −0.635097 | − | 0.103365i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.18756e11i | − | 2.37330i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.40804e11 | −1.50562 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.89152e9 | + | 1.09982e11i | −0.0937140 | + | 1.15917i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.26433e11i | − | 1.31353i | −0.754095 | − | 0.656766i | \(-0.771924\pi\) | ||
0.754095 | − | 0.656766i | \(-0.228076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.75791e10 | −0.589681 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.22146e11 | − | 9.87496e9i | −1.23318 | − | 0.0996974i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 6.46239e10i | − | 0.643220i | −0.946872 | − | 0.321610i | \(-0.895776\pi\) | ||
0.946872 | − | 0.321610i | \(-0.104224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.44749e10 | −0.828961 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.21602e10 | − | 2.74717e10i | −0.794931 | − | 0.265799i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.65015e10i | 0.348226i | 0.984726 | + | 0.174113i | \(0.0557059\pi\) | ||||
−0.984726 | + | 0.174113i | \(0.944294\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.26958e11 | −1.19431 | −0.597153 | − | 0.802127i | \(-0.703702\pi\) | ||||
−0.597153 | + | 0.802127i | \(0.703702\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.20686e9 | + | 1.01513e11i | −0.0761305 | + | 0.941678i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.02700e11i | 0.939505i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.91393e10 | −0.172673 | −0.0863363 | − | 0.996266i | \(-0.527516\pi\) | ||||
−0.0863363 | + | 0.996266i | \(0.527516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.40679e9 | − | 1.94578e8i | −0.0214153 | − | 0.00173133i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.70981e10i | 0.413332i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.06600e10 | −0.265398 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.09592e10 | − | 6.73356e10i | 0.0935741 | − | 0.574938i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.68383e10i | − | 0.731406i | −0.930732 | − | 0.365703i | \(-0.880829\pi\) | ||
0.930732 | − | 0.365703i | \(-0.119171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.60018e10 | −0.465308 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.43207e10 | + | 1.77137e11i | −0.117386 | + | 1.45198i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.91939e10i | 0.721301i | 0.932701 | + | 0.360650i | \(0.117445\pi\) | ||||
−0.932701 | + | 0.360650i | \(0.882555\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.81174e11 | −2.24340 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.96093e10 | − | 8.05297e9i | −0.784156 | − | 0.0633956i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.31780e9i | 0.0723779i | 0.999345 | + | 0.0361889i | \(0.0115218\pi\) | ||||
−0.999345 | + | 0.0361889i | \(0.988478\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.87743e11 | −1.43901 | −0.719507 | − | 0.694485i | \(-0.755632\pi\) | ||||
−0.719507 | + | 0.694485i | \(0.755632\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.94313e10 | + | 1.13003e10i | 0.525153 | + | 0.0854713i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1.05858e11i | − | 0.790140i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.11762e10 | −0.450638 | −0.225319 | − | 0.974285i | \(-0.572342\pi\) | ||||
−0.225319 | + | 0.974285i | \(0.572342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.54341e10 | + | 1.90908e11i | −0.112205 | + | 1.38789i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.99147e10i | 0.214645i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.31009e11 | 0.927814 | 0.463907 | − | 0.885884i | \(-0.346447\pi\) | ||||
0.463907 | + | 0.885884i | \(0.346447\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.00298e11 | + | 1.61932e10i | 1.40016 | + | 0.113197i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.05077e11i | 1.41506i | 0.706682 | + | 0.707531i | \(0.250191\pi\) | ||||
−0.706682 | + | 0.707531i | \(0.749809\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.25693e11 | 1.53729 | 0.768643 | − | 0.639678i | \(-0.220932\pi\) | ||||
0.768643 | + | 0.639678i | \(0.220932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.86360e10 | + | 1.16006e11i | −0.192551 | + | 0.780036i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.53541e11i | − | 1.01923i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.22373e11 | −0.801986 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.21138e10 | − | 1.49839e11i | 0.0783808 | − | 0.969512i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.24596e11i | 1.43482i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.05261e11 | 1.29476 | 0.647380 | − | 0.762167i | \(-0.275865\pi\) | ||||
0.647380 | + | 0.762167i | \(0.275865\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.69423e10 | − | 3.79508e9i | −0.292381 | − | 0.0236377i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.72973e11i | 1.06386i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.93681e10 | −0.117633 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.11150e9 | + | 6.82929e9i | −0.00666663 | + | 0.0409611i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 2.63885e10i | − | 0.156308i | −0.996941 | − | 0.0781541i | \(-0.975097\pi\) | ||
0.996941 | − | 0.0781541i | \(-0.0249026\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.90994e11 | −1.70232 | −0.851158 | − | 0.524910i | \(-0.824099\pi\) | ||||
−0.851158 | + | 0.524910i | \(0.824099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.06286e10 | − | 3.78853e11i | 0.176965 | − | 2.18893i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.95056e10i | 0.453712i | 0.973928 | + | 0.226856i | \(0.0728447\pi\) | ||||
−0.973928 | + | 0.226856i | \(0.927155\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.77635e11 | 1.00126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.88728e10 | + | 3.95115e9i | 0.272109 | + | 0.0219988i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.44238e11i | 0.793282i | 0.917974 | + | 0.396641i | \(0.129824\pi\) | ||||
−0.917974 | + | 0.396641i | \(0.870176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.90109e11 | −1.03285 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.72802e10 | + | 1.09502e10i | 0.361099 | + | 0.0587706i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.94035e11i | − | 1.02882i | −0.857545 | − | 0.514410i | \(-0.828011\pi\) | ||
0.857545 | − | 0.514410i | \(-0.171989\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.71719e10 | 0.404253 | 0.202127 | − | 0.979359i | \(-0.435215\pi\) | ||||
0.202127 | + | 0.979359i | \(0.435215\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.11900e10 | − | 1.38412e11i | 0.0579131 | − | 0.716342i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.44921e11i | − | 1.76373i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.64174e11 | 1.33471 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.04402e11 | + | 8.44045e9i | 0.521200 | + | 0.0421367i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.88074e10i | 0.438086i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.72425e11 | 1.32796 | 0.663982 | − | 0.747749i | \(-0.268865\pi\) | ||||
0.663982 | + | 0.747749i | \(0.268865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.35674e11 | + | 5.81757e10i | 1.13526 | + | 0.280238i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.44635e11i | 1.16457i | 0.812986 | + | 0.582283i | \(0.197841\pi\) | ||||
−0.812986 | + | 0.582283i | \(0.802159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.47107e10 | −0.445574 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.77703e9 | − | 3.43499e10i | 0.0129120 | − | 0.159712i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.20799e11i | 1.47418i | 0.675794 | + | 0.737090i | \(0.263801\pi\) | ||||
−0.675794 | + | 0.737090i | \(0.736199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.98258e11 | −0.900468 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.08413e11 | + | 8.76472e9i | 0.486692 | + | 0.0393469i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 3.47430e10i | − | 0.154167i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.33613e11 | 1.02467 | 0.512335 | − | 0.858785i | \(-0.328780\pi\) | ||||
0.512335 | + | 0.858785i | \(0.328780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.11434e10 | + | 1.29909e11i | −0.0916732 | + | 0.563259i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2.29649e11i | − | 0.984295i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.09033e11 | 1.73312 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.71014e10 | − | 2.11531e11i | 0.0716345 | − | 0.886065i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.88649e11i | − | 1.19536i | −0.801736 | − | 0.597679i | \(-0.796090\pi\) | ||
0.801736 | − | 0.597679i | \(-0.203910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.75515e11 | −1.12804 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.96830e11 | − | 1.59128e10i | −0.796772 | − | 0.0644155i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.67689e11i | 1.07140i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.36081e11 | −0.538533 | −0.269266 | − | 0.963066i | \(-0.586781\pi\) | ||||
−0.269266 | + | 0.963066i | \(0.586781\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.53078e11 | + | 7.37407e10i | 1.77294 | + | 0.288555i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.76288e10i | − | 0.261682i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.03649e11 | −0.396589 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.92092e9 | − | 4.84989e10i | 0.0148358 | − | 0.183508i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 5.50687e10i | − | 0.206058i | −0.994678 | − | 0.103029i | \(-0.967147\pi\) | ||
0.994678 | − | 0.103029i | \(-0.0328534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.08988e11 | −0.773356 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.96799e9 | − | 3.20795e8i | −0.0145217 | − | 0.00117402i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.36685e11i | − | 1.94253i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.15315e11 | −1.84474 | −0.922371 | − | 0.386306i | \(-0.873751\pi\) | ||||
−0.922371 | + | 0.386306i | \(0.873751\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.49987e11 | + | 1.31426e11i | 0.885131 | + | 0.465342i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.73663e11i | − | 2.70946i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.66106e11 | 1.61462 | 0.807308 | − | 0.590131i | \(-0.200924\pi\) | ||||
0.807308 | + | 0.590131i | \(0.200924\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.03026e10 | − | 1.27436e11i | 0.0353020 | − | 0.436659i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.06875e11i | − | 0.362247i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.67363e11 | −0.561154 | −0.280577 | − | 0.959831i | \(-0.590526\pi\) | ||||
−0.280577 | + | 0.959831i | \(0.590526\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.69793e11 | + | 1.37270e10i | 0.563179 | + | 0.0455305i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.57723e11i | 1.83005i | 0.403395 | + | 0.915026i | \(0.367830\pi\) | ||||
−0.403395 | + | 0.915026i | \(0.632170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.58858e11 | 1.16492 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.46658e10 | − | 1.51552e11i | 0.0792160 | − | 0.486720i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.65860e11i | − | 0.527003i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.22604e11 | 1.64291 | 0.821454 | − | 0.570275i | \(-0.193164\pi\) | ||||
0.821454 | + | 0.570275i | \(0.193164\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.58924e10 | − | 4.43962e11i | 0.111641 | − | 1.38091i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.63565e11i | 1.11891i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.71867e10 | −0.204597 | −0.102299 | − | 0.994754i | \(-0.532620\pi\) | ||||
−0.102299 | + | 0.994754i | \(0.532620\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.80948e11 | + | 1.46288e10i | 0.545238 | + | 0.0440801i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.17807e11i | 1.84211i | 0.389438 | + | 0.921053i | \(0.372669\pi\) | ||||
−0.389438 | + | 0.921053i | \(0.627331\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.46973e11 | −1.31881 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.04757e11 | + | 1.47254e11i | 2.64172 | + | 0.429953i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.01290e11i | 0.581623i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.52656e11 | −0.436524 | −0.218262 | − | 0.975890i | \(-0.570039\pi\) | ||||
−0.218262 | + | 0.975890i | \(0.570039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.06229e10 | + | 1.31397e11i | −0.0300626 | + | 0.371851i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.38021e11i | 1.22681i | 0.789769 | + | 0.613404i | \(0.210200\pi\) | ||||
−0.789769 | + | 0.613404i | \(0.789800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.37392e11 | −0.380851 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.40442e11 | + | 1.94387e10i | 0.659671 | + | 0.0533315i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.01769e11i | 1.36255i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.05122e10 | 0.0282547 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.49645e11 | − | 6.06220e11i | 0.398120 | − | 1.61281i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.80408e11i | 1.00178i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.77780e11 | 0.463429 | 0.231714 | − | 0.972784i | \(-0.425567\pi\) | ||||
0.231714 | + | 0.972784i | \(0.425567\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.31869e10 | + | 2.86805e11i | −0.0598322 | + | 0.740079i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.84680e11i | 0.471752i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.00634e11 | −0.254479 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.28598e11 | + | 1.84812e10i | 0.572275 | + | 0.0462659i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.28725e11i | 0.566867i | 0.958992 | + | 0.283433i | \(0.0914734\pi\) | ||||
−0.958992 | + | 0.283433i | \(0.908527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.01950e11 | −0.986245 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.04110e10 | + | 4.94061e11i | −0.195337 | + | 1.20019i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.03564e11i | − | 0.249084i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.16532e11 | 0.991894 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.41181e10 | − | 1.74630e11i | 0.0332876 | − | 0.411742i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.42295e11i | − | 1.49948i | −0.661733 | − | 0.749739i | \(-0.730179\pi\) | ||
0.661733 | − | 0.749739i | \(-0.269821\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.90320e11 | −1.59576 | −0.797879 | − | 0.602817i | \(-0.794045\pi\) | ||||
−0.797879 | + | 0.602817i | \(0.794045\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.32947e11 | − | 2.69173e10i | −0.762102 | − | 0.0616126i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.40485e11i | − | 0.318420i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.49067e11 | 2.13014 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.47210e11 | − | 2.39591e10i | −0.327191 | − | 0.0532519i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.41129e11i | − | 0.530735i | −0.964147 | − | 0.265367i | \(-0.914507\pi\) | ||
0.964147 | − | 0.265367i | \(-0.0854932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.33487e11 | −1.38082 | −0.690412 | − | 0.723416i | \(-0.742571\pi\) | ||||
−0.690412 | + | 0.723416i | \(0.742571\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.97194e10 | − | 3.67607e11i | 0.0641540 | − | 0.793538i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.42766e11i | − | 1.16035i | −0.814491 | − | 0.580177i | \(-0.802983\pi\) | ||
0.814491 | − | 0.580177i | \(-0.197017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.78621e11 | 1.01338 | 0.506691 | − | 0.862128i | \(-0.330868\pi\) | ||||
0.506691 | + | 0.862128i | \(0.330868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.05265e11 | + | 3.27639e10i | 0.849836 | + | 0.0687055i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.60239e11i | − | 0.540497i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.61765e11 | −0.538474 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.55193e11 | − | 3.83092e10i | −0.316206 | − | 0.0780552i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.51190e11i | − | 0.708753i | −0.935103 | − | 0.354376i | \(-0.884693\pi\) | ||
0.935103 | − | 0.354376i | \(-0.115307\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.80262e11 | −1.75966 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.29566e10 | + | 7.78726e11i | −0.124661 | + | 1.54196i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.33463e11i | 1.24249i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.31428e11 | −0.449659 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.00794e11 | − | 2.43179e10i | −0.578947 | − | 0.0468054i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.32718e11i | − | 0.634392i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.13313e11 | −0.402922 | −0.201461 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201461 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.80639e11 | + | 1.10988e12i | −0.338023 | + | 2.07688i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.64415e11i | 0.675575i | 0.941222 | + | 0.337787i | \(0.109678\pi\) | ||||
−0.941222 | + | 0.337787i | \(0.890322\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.33725e11 | −0.980269 | −0.490135 | − | 0.871647i | \(-0.663052\pi\) | ||||
−0.490135 | + | 0.871647i | \(0.663052\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.54018e10 | − | 4.37894e11i | 0.0644188 | − | 0.796812i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.88098e11i | − | 1.42081i | −0.703792 | − | 0.710406i | \(-0.748511\pi\) | ||
0.703792 | − | 0.710406i | \(-0.251489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.22067e10 | 0.0932528 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.29658e12 | + | 1.04823e11i | 2.29469 | + | 0.185515i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6.97417e11i | − | 1.22296i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.21107e11 | 0.210425 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.04759e11 | + | 4.96011e10i | 0.524686 | + | 0.0853953i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.22545e11i | − | 0.209056i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.10907e11 | −1.03271 | −0.516353 | − | 0.856376i | \(-0.672711\pi\) | ||||
−0.516353 | + | 0.856376i | \(0.672711\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.34690e10 | + | 9.08757e11i | −0.123069 | + | 1.52227i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.52172e11i | 0.418595i | 0.977852 | + | 0.209297i | \(0.0671177\pi\) | ||||
−0.977852 | + | 0.209297i | \(0.932882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.10902e11 | 0.182431 | 0.0912154 | − | 0.995831i | \(-0.470925\pi\) | ||||
0.0912154 | + | 0.995831i | \(0.470925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.32443e12 | − | 1.07074e11i | −2.15901 | − | 0.174547i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.58698e11i | − | 0.256377i | −0.991750 | − | 0.128188i | \(-0.959084\pi\) | ||
0.991750 | − | 0.128188i | \(-0.0409162\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.78156e11 | 0.605430 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.36070e11 | − | 4.06948e11i | 0.215900 | − | 0.645696i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 4.93079e11i | − | 0.775374i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.39557e11 | 1.46430 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.65770e10 | + | 2.05045e11i | −0.0256056 | + | 0.316723i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.53412e11i | 0.541056i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.66825e11 | 0.708362 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.28251e11 | − | 6.69605e10i | −1.24569 | − | 0.100709i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 5.86642e11i | − | 0.874538i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.28126e12 | 1.89326 | 0.946629 | − | 0.322325i | \(-0.104464\pi\) | ||||
0.946629 | + | 0.322325i | \(0.104464\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.40192e11 | − | 8.61367e11i | 0.205337 | − | 1.26163i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.55958e11i | 0.807176i | 0.914941 | + | 0.403588i | \(0.132237\pi\) | ||||
−0.914941 | + | 0.403588i | \(0.867763\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.33282e11 | −0.335736 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.35312e10 | − | 6.62141e11i | 0.0763699 | − | 0.944639i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.15619e11i | 0.587784i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.94315e11 | 0.412619 | 0.206310 | − | 0.978487i | \(-0.433855\pi\) | ||||
0.206310 | + | 0.978487i | \(0.433855\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.83340e10 | + | 6.33296e9i | 0.108871 | + | 0.00880174i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.19122e10i | 0.0164129i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.75937e11 | −0.923292 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.72478e11 | + | 1.09449e11i | 0.910666 | + | 0.148216i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 6.48271e11i | − | 0.870350i | −0.900346 | − | 0.435175i | \(-0.856687\pi\) | ||
0.900346 | − | 0.435175i | \(-0.143313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.19240e11 | 0.424932 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.05151e10 | + | 9.95912e11i | −0.106255 | + | 1.31430i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.39268e12i | − | 1.82224i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.26935e11 | −1.20252 | −0.601258 | − | 0.799055i | \(-0.705334\pi\) | ||||
−0.601258 | + | 0.799055i | \(0.705334\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.99756e11 | + | 1.61494e10i | 0.256943 | + | 0.0207727i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.98701e11i | 1.01865i | 0.860574 | + | 0.509326i | \(0.170105\pi\) | ||||
−0.860574 | + | 0.509326i | \(0.829895\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.05945e11 | −0.766278 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.35950e11 | − | 9.55850e11i | 0.295865 | − | 1.19857i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.06154e11i | − | 0.380663i | −0.981720 | − | 0.190331i | \(-0.939044\pi\) | ||
0.981720 | − | 0.190331i | \(-0.0609562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.17355e11 | 0.144690 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.10598e11 | − | 1.36801e12i | 0.135215 | − | 1.67250i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.70654e11i | − | 0.206892i | −0.994635 | − | 0.103446i | \(-0.967013\pi\) | ||
0.994635 | − | 0.103446i | \(-0.0329869\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.15743e12 | −1.39149 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.45589e11 | − | 7.64468e10i | −1.12734 | − | 0.0911405i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.33433e11i | 0.512446i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.62417e11 | −0.893921 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.68626e10 | + | 5.33701e11i | −0.101001 | + | 0.620573i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2.74417e10i | − | 0.0316448i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.15354e11 | 0.932482 | 0.466241 | − | 0.884658i | \(-0.345608\pi\) | ||||
0.466241 | + | 0.884658i | \(0.345608\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.84443e11 | + | 2.28143e12i | −0.209203 | + | 2.58768i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.27970e12i | 1.43956i | 0.694200 | + | 0.719782i | \(0.255758\pi\) | ||||
−0.694200 | + | 0.719782i | \(0.744242\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.02060e11 | −0.560150 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.16561e11 | + | 3.36772e10i | 0.460957 | + | 0.0372664i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.07767e12i | 1.18279i | 0.806382 | + | 0.591395i | \(0.201423\pi\) | ||||
−0.806382 | + | 0.591395i | \(0.798577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.60503e11 | 0.827885 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.43826e12 | + | 2.34085e11i | 1.55297 | + | 0.252753i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.12637e11i | 0.870328i | 0.900351 | + | 0.435164i | \(0.143310\pi\) | ||||
−0.900351 | + | 0.435164i | \(0.856690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.01968e12 | −2.14554 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.47887e10 | + | 4.30311e11i | −0.0366581 | + | 0.453433i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.14611e12i | 1.19796i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.61365e12 | 1.67307 | 0.836537 | − | 0.547911i | \(-0.184577\pi\) | ||||
0.836537 | + | 0.547911i | \(0.184577\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.39875e12 | − | 1.13083e11i | −1.43861 | − | 0.116305i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.13572e12i | − | 1.15873i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.63148e11 | −0.165121 | −0.0825604 | − | 0.996586i | \(-0.526310\pi\) | ||||
−0.0825604 | + | 0.996586i | \(0.526310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.63513e11 | − | 1.88472e11i | −0.766575 | − | 0.189228i |
(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 | 192.9.e.i.65.1 | 8 | ||
3.2 | odd | 2 | inner | 192.9.e.i.65.2 | 8 | ||
4.3 | odd | 2 | 192.9.e.j.65.8 | 8 | |||
8.3 | odd | 2 | 48.9.e.e.17.1 | 8 | |||
8.5 | even | 2 | 24.9.e.a.17.8 | yes | 8 | ||
12.11 | even | 2 | 192.9.e.j.65.7 | 8 | |||
24.5 | odd | 2 | 24.9.e.a.17.7 | ✓ | 8 | ||
24.11 | even | 2 | 48.9.e.e.17.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.9.e.a.17.7 | ✓ | 8 | 24.5 | odd | 2 | ||
24.9.e.a.17.8 | yes | 8 | 8.5 | even | 2 | ||
48.9.e.e.17.1 | 8 | 8.3 | odd | 2 | |||
48.9.e.e.17.2 | 8 | 24.11 | even | 2 | |||
192.9.e.i.65.1 | 8 | 1.1 | even | 1 | trivial | ||
192.9.e.i.65.2 | 8 | 3.2 | odd | 2 | inner | ||
192.9.e.j.65.7 | 8 | 12.11 | even | 2 | |||
192.9.e.j.65.8 | 8 | 4.3 | odd | 2 |