Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,8,Mod(55,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.55");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.c (of order \(3\), degree \(2\), 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: | \(50.6063741284\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.109 |
Dual form | 162.8.c.j.55.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | + | 6.92820i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −32.0000 | + | 55.4256i | −0.250000 | + | 0.433013i | ||||
\(5\) | −52.5000 | + | 90.9327i | −0.187830 | + | 0.325331i | −0.944526 | − | 0.328436i | \(-0.893479\pi\) |
0.756697 | + | 0.653766i | \(0.226812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 468.500 | + | 811.466i | 0.516258 | + | 0.894184i | 0.999822 | + | 0.0188755i | \(0.00600862\pi\) |
−0.483564 | + | 0.875309i | \(0.660658\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −840.000 | −0.265631 | ||||||||
\(11\) | −2971.50 | − | 5146.79i | −0.673134 | − | 1.16590i | −0.977011 | − | 0.213190i | \(-0.931615\pi\) |
0.303877 | − | 0.952711i | \(-0.401719\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −34.0000 | + | 58.8897i | −0.00429217 | + | 0.00743426i | −0.868164 | − | 0.496278i | \(-0.834700\pi\) |
0.863871 | + | 0.503713i | \(0.168033\pi\) | |||||||
\(14\) | −3748.00 | + | 6491.73i | −0.365049 | + | 0.632284i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2048.00 | − | 3547.24i | −0.125000 | − | 0.216506i | ||||
\(17\) | −5400.00 | −0.266577 | −0.133288 | − | 0.991077i | \(-0.542554\pi\) | ||||
−0.133288 | + | 0.991077i | \(0.542554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −48382.0 | −1.61825 | −0.809126 | − | 0.587635i | \(-0.800059\pi\) | ||||
−0.809126 | + | 0.587635i | \(0.800059\pi\) | |||||||
\(20\) | −3360.00 | − | 5819.69i | −0.0939149 | − | 0.162665i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 23772.0 | − | 41174.3i | 0.475977 | − | 0.824417i | ||||
\(23\) | 321.000 | − | 555.988i | 0.00550120 | − | 0.00952836i | −0.863262 | − | 0.504757i | \(-0.831582\pi\) |
0.868763 | + | 0.495228i | \(0.164916\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 33550.0 | + | 58110.3i | 0.429440 | + | 0.743812i | ||||
\(26\) | −544.000 | −0.00607005 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −59968.0 | −0.516258 | ||||||||
\(29\) | 62967.0 | + | 109062.i | 0.479424 | + | 0.830387i | 0.999722 | − | 0.0235980i | \(-0.00751219\pi\) |
−0.520297 | + | 0.853985i | \(0.674179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 80637.5 | − | 139668.i | 0.486151 | − | 0.842038i | −0.513722 | − | 0.857956i | \(-0.671734\pi\) |
0.999873 | + | 0.0159184i | \(0.00506719\pi\) | |||||||
\(32\) | 16384.0 | − | 28377.9i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −21600.0 | − | 37412.3i | −0.0942492 | − | 0.163244i | ||||
\(35\) | −98385.0 | −0.387874 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −414286. | −1.34460 | −0.672302 | − | 0.740277i | \(-0.734694\pi\) | ||||
−0.672302 | + | 0.740277i | \(0.734694\pi\) | |||||||
\(38\) | −193528. | − | 335200.i | −0.572139 | − | 0.990973i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 26880.0 | − | 46557.5i | 0.0664078 | − | 0.115022i | ||||
\(41\) | 313737. | − | 543408.i | 0.710922 | − | 1.23135i | −0.253589 | − | 0.967312i | \(-0.581611\pi\) |
0.964511 | − | 0.264042i | \(-0.0850557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −285295. | − | 494145.i | −0.547211 | − | 0.947797i | −0.998464 | − | 0.0554009i | \(-0.982356\pi\) |
0.451254 | − | 0.892396i | \(-0.350977\pi\) | |||||||
\(44\) | 380352. | 0.673134 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5136.00 | 0.00777987 | ||||||||
\(47\) | −269349. | − | 466526.i | −0.378419 | − | 0.655441i | 0.612413 | − | 0.790538i | \(-0.290199\pi\) |
−0.990832 | + | 0.135097i | \(0.956865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −27213.0 | + | 47134.3i | −0.0330438 | + | 0.0572336i | ||||
\(50\) | −268400. | + | 464882.i | −0.303660 | + | 0.525954i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2176.00 | − | 3768.94i | −0.00214609 | − | 0.00371713i | ||||
\(53\) | 356283. | 0.328723 | 0.164361 | − | 0.986400i | \(-0.447444\pi\) | ||||
0.164361 | + | 0.986400i | \(0.447444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 624015. | 0.505738 | ||||||||
\(56\) | −239872. | − | 415470.i | −0.182525 | − | 0.316142i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −503736. | + | 872496.i | −0.339004 | + | 0.587172i | ||||
\(59\) | 1.45541e6 | − | 2.52085e6i | 0.922581 | − | 1.59796i | 0.127175 | − | 0.991880i | \(-0.459409\pi\) |
0.795406 | − | 0.606077i | \(-0.207258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.34208e6 | − | 2.32456e6i | −0.757051 | − | 1.31125i | −0.944348 | − | 0.328948i | \(-0.893306\pi\) |
0.187297 | − | 0.982303i | \(-0.440027\pi\) | |||||||
\(62\) | 1.29020e6 | 0.687521 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −3570.00 | − | 6183.42i | −0.00161240 | − | 0.00279275i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.34054e6 | + | 2.32188e6i | −0.544525 | + | 0.943145i | 0.454112 | + | 0.890945i | \(0.349957\pi\) |
−0.998637 | + | 0.0521999i | \(0.983377\pi\) | |||||||
\(68\) | 172800. | − | 299298.i | 0.0666442 | − | 0.115431i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −393540. | − | 681631.i | −0.137134 | − | 0.237523i | ||||
\(71\) | −3.70548e6 | −1.22868 | −0.614342 | − | 0.789040i | \(-0.710578\pi\) | ||||
−0.614342 | + | 0.789040i | \(0.710578\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −153151. | −0.0460776 | −0.0230388 | − | 0.999735i | \(-0.507334\pi\) | ||||
−0.0230388 | + | 0.999735i | \(0.507334\pi\) | |||||||
\(74\) | −1.65714e6 | − | 2.87026e6i | −0.475389 | − | 0.823398i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.54822e6 | − | 2.68160e6i | 0.404563 | − | 0.700724i | ||||
\(77\) | 2.78430e6 | − | 4.82254e6i | 0.695021 | − | 1.20381i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.78964e6 | + | 6.56386e6i | 0.864776 | + | 1.49784i | 0.867269 | + | 0.497839i | \(0.165873\pi\) |
−0.00249356 | + | 0.999997i | \(0.500794\pi\) | |||||||
\(80\) | 430080. | 0.0939149 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.01979e6 | 1.00540 | ||||||||
\(83\) | −4.67300e6 | − | 8.09387e6i | −0.897062 | − | 1.55376i | −0.831232 | − | 0.555926i | \(-0.812364\pi\) |
−0.0658301 | − | 0.997831i | \(-0.520970\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 283500. | − | 491036.i | 0.0500711 | − | 0.0867256i | ||||
\(86\) | 2.28236e6 | − | 3.95316e6i | 0.386936 | − | 0.670193i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.52141e6 | + | 2.63516e6i | 0.237989 | + | 0.412209i | ||||
\(89\) | 4.03360e6 | 0.606496 | 0.303248 | − | 0.952912i | \(-0.401929\pi\) | ||||
0.303248 | + | 0.952912i | \(0.401929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −63716.0 | −0.00886347 | ||||||||
\(92\) | 20544.0 | + | 35583.3i | 0.00275060 | + | 0.00476418i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.15479e6 | − | 3.73221e6i | 0.267583 | − | 0.463467i | ||||
\(95\) | 2.54006e6 | − | 4.39950e6i | 0.303956 | − | 0.526467i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.87705e6 | + | 4.98319e6i | 0.320071 | + | 0.554379i | 0.980502 | − | 0.196507i | \(-0.0629599\pi\) |
−0.660432 | + | 0.750886i | \(0.729627\pi\) | |||||||
\(98\) | −435408. | −0.0467310 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.29440e6 | −0.429440 | ||||||||
\(101\) | −4.43961e6 | − | 7.68963e6i | −0.428766 | − | 0.742644i | 0.567998 | − | 0.823030i | \(-0.307718\pi\) |
−0.996764 | + | 0.0803857i | \(0.974385\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.32783e6 | − | 2.29986e6i | 0.119732 | − | 0.207382i | −0.799929 | − | 0.600094i | \(-0.795130\pi\) |
0.919662 | + | 0.392712i | \(0.128463\pi\) | |||||||
\(104\) | 17408.0 | − | 30151.5i | 0.00151751 | − | 0.00262841i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.42513e6 | + | 2.46840e6i | 0.116221 | + | 0.201301i | ||||
\(107\) | 2.11234e7 | 1.66694 | 0.833471 | − | 0.552564i | \(-0.186350\pi\) | ||||
0.833471 | + | 0.552564i | \(0.186350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.84213e7 | −1.36247 | −0.681237 | − | 0.732063i | \(-0.738558\pi\) | ||||
−0.681237 | + | 0.732063i | \(0.738558\pi\) | |||||||
\(110\) | 2.49606e6 | + | 4.32330e6i | 0.178805 | + | 0.309700i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.91898e6 | − | 3.32376e6i | 0.129064 | − | 0.223546i | ||||
\(113\) | 9.31424e6 | − | 1.61327e7i | 0.607258 | − | 1.05180i | −0.384433 | − | 0.923153i | \(-0.625603\pi\) |
0.991690 | − | 0.128648i | \(-0.0410637\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33705.0 | + | 58378.8i | 0.00206658 | + | 0.00357942i | ||||
\(116\) | −8.05978e6 | −0.479424 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.32866e7 | 1.30473 | ||||||||
\(119\) | −2.52990e6 | − | 4.38192e6i | −0.137622 | − | 0.238369i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.91604e6 | + | 1.37110e7i | −0.406218 | + | 0.703590i | ||||
\(122\) | 1.07367e7 | − | 1.85965e7i | 0.535316 | − | 0.927195i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.16080e6 | + | 8.93877e6i | 0.243075 | + | 0.421019i | ||||
\(125\) | −1.52486e7 | −0.698306 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.58380e6 | −0.111930 | −0.0559649 | − | 0.998433i | \(-0.517823\pi\) | ||||
−0.0559649 | + | 0.998433i | \(0.517823\pi\) | |||||||
\(128\) | 1.04858e6 | + | 1.81619e6i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 28560.0 | − | 49467.4i | 0.00114014 | − | 0.00197477i | ||||
\(131\) | −2.09642e7 | + | 3.63110e7i | −0.814757 | + | 1.41120i | 0.0947460 | + | 0.995501i | \(0.469796\pi\) |
−0.909503 | + | 0.415698i | \(0.863537\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.26670e7 | − | 3.92603e7i | −0.835435 | − | 1.44702i | ||||
\(134\) | −2.14486e7 | −0.770074 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.76480e6 | 0.0942492 | ||||||||
\(137\) | −633309. | − | 1.09692e6i | −0.0210423 | − | 0.0364464i | 0.855312 | − | 0.518112i | \(-0.173365\pi\) |
−0.876355 | + | 0.481666i | \(0.840032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.15281e7 | + | 1.99672e7i | −0.364086 | + | 0.630616i | −0.988629 | − | 0.150374i | \(-0.951952\pi\) |
0.624543 | + | 0.780991i | \(0.285285\pi\) | |||||||
\(140\) | 3.14832e6 | − | 5.45305e6i | 0.0969685 | − | 0.167954i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.48219e7 | − | 2.56723e7i | −0.434405 | − | 0.752412i | ||||
\(143\) | 404124. | 0.0115568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.32231e7 | −0.360200 | ||||||||
\(146\) | −612604. | − | 1.06106e6i | −0.0162909 | − | 0.0282167i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.32572e7 | − | 2.29621e7i | 0.336151 | − | 0.582230i | ||||
\(149\) | −1.19133e7 | + | 2.06345e7i | −0.295040 | + | 0.511024i | −0.974994 | − | 0.222230i | \(-0.928666\pi\) |
0.679954 | + | 0.733255i | \(0.262000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.25247e7 | − | 3.90139e7i | −0.532401 | − | 0.922146i | −0.999284 | − | 0.0378270i | \(-0.987956\pi\) |
0.466883 | − | 0.884319i | \(-0.345377\pi\) | |||||||
\(152\) | 2.47716e7 | 0.572139 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.45487e7 | 0.982908 | ||||||||
\(155\) | 8.46694e6 | + | 1.46652e7i | 0.182627 | + | 0.316320i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.76288e7 | + | 3.05339e7i | −0.363558 | + | 0.629700i | −0.988544 | − | 0.150936i | \(-0.951771\pi\) |
0.624986 | + | 0.780636i | \(0.285105\pi\) | |||||||
\(158\) | −3.03172e7 | + | 5.25108e7i | −0.611489 | + | 1.05913i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.72032e6 | + | 2.97968e6i | 0.0332039 | + | 0.0575109i | ||||
\(161\) | 601554. | 0.0113601 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.55009e7 | −1.18465 | −0.592326 | − | 0.805699i | \(-0.701790\pi\) | ||||
−0.592326 | + | 0.805699i | \(0.701790\pi\) | |||||||
\(164\) | 2.00792e7 | + | 3.47781e7i | 0.355461 | + | 0.615677i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.73840e7 | − | 6.47510e7i | 0.634319 | − | 1.09867i | ||||
\(167\) | −2.64045e7 | + | 4.57339e7i | −0.438703 | + | 0.759855i | −0.997590 | − | 0.0693886i | \(-0.977895\pi\) |
0.558887 | + | 0.829244i | \(0.311228\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.13719e7 | + | 5.43378e7i | 0.499963 | + | 0.865962i | ||||
\(170\) | 4.53600e6 | 0.0708112 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.65178e7 | 0.547211 | ||||||||
\(173\) | 5.53665e7 | + | 9.58976e7i | 0.812991 | + | 1.40814i | 0.910762 | + | 0.412932i | \(0.135495\pi\) |
−0.0977712 | + | 0.995209i | \(0.531171\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.14364e7 | + | 5.44494e7i | −0.443403 | + | 0.767997i | ||||
\(176\) | −1.21713e7 | + | 2.10812e7i | −0.168283 | + | 0.291475i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.61344e7 | + | 2.79456e7i | 0.214429 | + | 0.371402i | ||||
\(179\) | −1.19427e7 | −0.155639 | −0.0778195 | − | 0.996967i | \(-0.524796\pi\) | ||||
−0.0778195 | + | 0.996967i | \(0.524796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.95226e7 | −0.996817 | −0.498408 | − | 0.866942i | \(-0.666082\pi\) | ||||
−0.498408 | + | 0.866942i | \(0.666082\pi\) | |||||||
\(182\) | −254864. | − | 441437.i | −0.00313371 | − | 0.00542774i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −164352. | + | 284666.i | −0.00194497 | + | 0.00336878i | ||||
\(185\) | 2.17500e7 | − | 3.76721e7i | 0.252556 | − | 0.437441i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.60461e7 | + | 2.77927e7i | 0.179442 | + | 0.310802i | ||||
\(188\) | 3.44767e7 | 0.378419 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.06409e7 | 0.429858 | ||||||||
\(191\) | 3.01157e6 | + | 5.21620e6i | 0.0312735 | + | 0.0541673i | 0.881239 | − | 0.472672i | \(-0.156710\pi\) |
−0.849965 | + | 0.526839i | \(0.823377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.92925e7 | − | 5.07361e7i | 0.293296 | − | 0.508003i | −0.681291 | − | 0.732012i | \(-0.738581\pi\) |
0.974587 | + | 0.224009i | \(0.0719147\pi\) | |||||||
\(194\) | −2.30164e7 | + | 3.98656e7i | −0.226324 | + | 0.392005i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.74163e6 | − | 3.01660e6i | −0.0165219 | − | 0.0286168i | ||||
\(197\) | −1.68414e8 | −1.56945 | −0.784725 | − | 0.619844i | \(-0.787196\pi\) | ||||
−0.784725 | + | 0.619844i | \(0.787196\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.01669e8 | −0.914543 | −0.457271 | − | 0.889327i | \(-0.651173\pi\) | ||||
−0.457271 | + | 0.889327i | \(0.651173\pi\) | |||||||
\(200\) | −1.71776e7 | − | 2.97525e7i | −0.151830 | − | 0.262977i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.55169e7 | − | 6.15171e7i | 0.303183 | − | 0.525129i | ||||
\(203\) | −5.90001e7 | + | 1.02191e8i | −0.495013 | + | 0.857387i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.29424e7 | + | 5.70579e7i | 0.267065 | + | 0.462570i | ||||
\(206\) | 2.12452e7 | 0.169327 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 278528. | 0.00214609 | ||||||||
\(209\) | 1.43767e8 | + | 2.49012e8i | 1.08930 | + | 1.88672i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.31910e7 | − | 7.48090e7i | 0.316523 | − | 0.548233i | −0.663237 | − | 0.748409i | \(-0.730818\pi\) |
0.979760 | + | 0.200176i | \(0.0641513\pi\) | |||||||
\(212\) | −1.14011e7 | + | 1.97472e7i | −0.0821806 | + | 0.142341i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.44935e7 | + | 1.46347e8i | 0.589353 | + | 1.02079i | ||||
\(215\) | 5.99120e7 | 0.411130 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.51115e8 | 1.00392 | ||||||||
\(218\) | −7.36854e7 | − | 1.27627e8i | −0.481708 | − | 0.834342i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.99685e7 | + | 3.45864e7i | −0.126435 | + | 0.218991i | ||||
\(221\) | 183600. | − | 318005.i | 0.00114419 | − | 0.00198180i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.08087e7 | − | 3.60416e7i | −0.125654 | − | 0.217639i | 0.796334 | − | 0.604857i | \(-0.206770\pi\) |
−0.921988 | + | 0.387217i | \(0.873436\pi\) | |||||||
\(224\) | 3.07036e7 | 0.182525 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.49028e8 | 0.858792 | ||||||||
\(227\) | −1.04658e8 | − | 1.81272e8i | −0.593855 | − | 1.02859i | −0.993707 | − | 0.112007i | \(-0.964272\pi\) |
0.399852 | − | 0.916580i | \(-0.369061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.66459e8 | + | 2.88316e8i | −0.915976 | + | 1.58652i | −0.110510 | + | 0.993875i | \(0.535248\pi\) |
−0.805466 | + | 0.592642i | \(0.798085\pi\) | |||||||
\(230\) | −269640. | + | 467030.i | −0.00146129 | + | 0.00253103i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.22391e7 | − | 5.58398e7i | −0.169502 | − | 0.293586i | ||||
\(233\) | 7.95428e7 | 0.411960 | 0.205980 | − | 0.978556i | \(-0.433962\pi\) | ||||
0.205980 | + | 0.978556i | \(0.433962\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.65633e7 | 0.284313 | ||||||||
\(236\) | 9.31465e7 | + | 1.61334e8i | 0.461291 | + | 0.798979i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.02392e7 | − | 3.50553e7i | 0.0973137 | − | 0.168552i | ||||
\(239\) | −7.34502e7 | + | 1.27220e8i | −0.348017 | + | 0.602783i | −0.985897 | − | 0.167352i | \(-0.946478\pi\) |
0.637880 | + | 0.770136i | \(0.279812\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.51528e7 | + | 2.62454e7i | 0.0697320 | + | 0.120779i | 0.898783 | − | 0.438393i | \(-0.144452\pi\) |
−0.829051 | + | 0.559173i | \(0.811119\pi\) | |||||||
\(242\) | −1.26657e8 | −0.574479 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.71787e8 | 0.757051 | ||||||||
\(245\) | −2.85736e6 | − | 4.94910e6i | −0.0124132 | − | 0.0215003i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.64499e6 | − | 2.84920e6i | 0.00694582 | − | 0.0120305i | ||||
\(248\) | −4.12864e7 | + | 7.15101e7i | −0.171880 | + | 0.297705i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.09945e7 | − | 1.05646e8i | −0.246888 | − | 0.427623i | ||||
\(251\) | 1.47027e8 | 0.586866 | 0.293433 | − | 0.955980i | \(-0.405202\pi\) | ||||
0.293433 | + | 0.955980i | \(0.405202\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.81541e6 | −0.0148122 | ||||||||
\(254\) | −1.03352e7 | − | 1.79011e7i | −0.0395732 | − | 0.0685427i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.38861e6 | + | 1.45295e7i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.83888e8 | − | 3.18503e8i | 0.675752 | − | 1.17044i | −0.300496 | − | 0.953783i | \(-0.597152\pi\) |
0.976248 | − | 0.216654i | \(-0.0695144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.94093e8 | − | 3.36179e8i | −0.694162 | − | 1.20232i | ||||
\(260\) | 456960. | 0.00161240 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.35427e8 | −1.15224 | ||||||||
\(263\) | −1.62928e8 | − | 2.82200e8i | −0.552270 | − | 0.956559i | −0.998110 | − | 0.0614470i | \(-0.980428\pi\) |
0.445840 | − | 0.895112i | \(-0.352905\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.87049e7 | + | 3.23978e7i | −0.0617439 | + | 0.106944i | ||||
\(266\) | 1.81336e8 | − | 3.14083e8i | 0.590742 | − | 1.02319i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.57945e7 | − | 1.48600e8i | −0.272262 | − | 0.471572i | ||||
\(269\) | −3.39029e8 | −1.06195 | −0.530976 | − | 0.847387i | \(-0.678174\pi\) | ||||
−0.530976 | + | 0.847387i | \(0.678174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.50778e6 | −0.00765416 | −0.00382708 | − | 0.999993i | \(-0.501218\pi\) | ||||
−0.00382708 | + | 0.999993i | \(0.501218\pi\) | |||||||
\(272\) | 1.10592e7 | + | 1.91551e7i | 0.0333221 | + | 0.0577156i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.06647e6 | − | 8.77539e6i | 0.0148792 | − | 0.0257715i | ||||
\(275\) | 1.99388e8 | − | 3.45350e8i | 0.578141 | − | 1.00137i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.64293e7 | + | 4.57768e7i | 0.0747146 | + | 0.129410i | 0.900962 | − | 0.433898i | \(-0.142862\pi\) |
−0.826248 | + | 0.563307i | \(0.809529\pi\) | |||||||
\(278\) | −1.84449e8 | −0.514896 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.03731e7 | 0.137134 | ||||||||
\(281\) | −2.69776e8 | − | 4.67266e8i | −0.725322 | − | 1.25630i | −0.958841 | − | 0.283943i | \(-0.908357\pi\) |
0.233519 | − | 0.972352i | \(-0.424976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.29283e7 | + | 5.70334e7i | −0.0863607 | + | 0.149581i | −0.905970 | − | 0.423341i | \(-0.860857\pi\) |
0.819609 | + | 0.572923i | \(0.194190\pi\) | |||||||
\(284\) | 1.18575e8 | − | 2.05379e8i | 0.307171 | − | 0.532036i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.61650e6 | + | 2.79985e6i | 0.00408595 | + | 0.00707708i | ||||
\(287\) | 5.87943e8 | 1.46808 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.81179e8 | −0.928937 | ||||||||
\(290\) | −5.28923e7 | − | 9.16121e7i | −0.127350 | − | 0.220577i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.90083e6 | − | 8.48849e6i | 0.0115194 | − | 0.0199522i | ||||
\(293\) | 1.76292e7 | − | 3.05346e7i | 0.0409444 | − | 0.0709179i | −0.844827 | − | 0.535040i | \(-0.820297\pi\) |
0.885771 | + | 0.464122i | \(0.153630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.52818e8 | + | 2.64689e8i | 0.346576 | + | 0.600288i | ||||
\(296\) | 2.12114e8 | 0.475389 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.90613e8 | −0.417249 | ||||||||
\(299\) | 21828.0 | + | 37807.2i | 4.72242e−5 | + | 8.17947e-5i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.67321e8 | − | 4.63014e8i | 0.565003 | − | 0.978614i | ||||
\(302\) | 1.80197e8 | − | 3.12111e8i | 0.376465 | − | 0.652056i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.90863e7 | + | 1.71623e8i | 0.202282 | + | 0.350362i | ||||
\(305\) | 2.81838e8 | 0.568787 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.14259e8 | 0.225376 | 0.112688 | − | 0.993630i | \(-0.464054\pi\) | ||||
0.112688 | + | 0.993630i | \(0.464054\pi\) | |||||||
\(308\) | 1.78195e8 | + | 3.08643e8i | 0.347510 | + | 0.601906i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.77355e7 | + | 1.17321e8i | −0.129137 | + | 0.223672i | ||||
\(311\) | −7.77314e7 | + | 1.34635e8i | −0.146533 | + | 0.253802i | −0.929944 | − | 0.367702i | \(-0.880145\pi\) |
0.783411 | + | 0.621504i | \(0.213478\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.91150e8 | − | 3.31081e8i | −0.352345 | − | 0.610280i | 0.634315 | − | 0.773075i | \(-0.281282\pi\) |
−0.986660 | + | 0.162795i | \(0.947949\pi\) | |||||||
\(314\) | −2.82060e8 | −0.514148 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.85074e8 | −0.864776 | ||||||||
\(317\) | −2.22443e8 | − | 3.85283e8i | −0.392204 | − | 0.679317i | 0.600536 | − | 0.799598i | \(-0.294954\pi\) |
−0.992740 | + | 0.120281i | \(0.961621\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.74213e8 | − | 6.48156e8i | 0.645433 | − | 1.11792i | ||||
\(320\) | −1.37626e7 | + | 2.38375e7i | −0.0234787 | + | 0.0406663i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.40622e6 | + | 4.16769e6i | 0.00401642 | + | 0.00695664i | ||||
\(323\) | 2.61263e8 | 0.431389 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.56280e6 | −0.00737292 | ||||||||
\(326\) | −2.62004e8 | − | 4.53804e8i | −0.418838 | − | 0.725448i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.60633e8 | + | 2.78225e8i | −0.251349 | + | 0.435349i | ||||
\(329\) | 2.52380e8 | − | 4.37135e8i | 0.390723 | − | 0.676753i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.75444e8 | + | 4.77083e8i | 0.417480 | + | 0.723096i | 0.995685 | − | 0.0927950i | \(-0.0295801\pi\) |
−0.578205 | + | 0.815891i | \(0.696247\pi\) | |||||||
\(332\) | 5.98144e8 | 0.897062 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.22472e8 | −0.620419 | ||||||||
\(335\) | −1.40757e8 | − | 2.43798e8i | −0.204556 | − | 0.354301i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.48397e8 | − | 4.30236e8i | 0.353542 | − | 0.612353i | −0.633325 | − | 0.773886i | \(-0.718310\pi\) |
0.986867 | + | 0.161533i | \(0.0516438\pi\) | |||||||
\(338\) | −2.50976e8 | + | 4.34702e8i | −0.353527 | + | 0.612327i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.81440e7 | + | 3.14263e7i | 0.0250355 | + | 0.0433628i | ||||
\(341\) | −9.58457e8 | −1.30898 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.20663e8 | 0.964279 | ||||||||
\(344\) | 1.46071e8 | + | 2.53002e8i | 0.193468 | + | 0.335097i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.42932e8 | + | 7.67180e8i | −0.574871 | + | 0.995706i | ||||
\(347\) | 1.25581e8 | − | 2.17512e8i | 0.161350 | − | 0.279467i | −0.774003 | − | 0.633182i | \(-0.781748\pi\) |
0.935353 | + | 0.353715i | \(0.115082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.41457e8 | + | 4.18216e8i | 0.304054 | + | 0.526637i | 0.977050 | − | 0.213009i | \(-0.0683263\pi\) |
−0.672996 | + | 0.739646i | \(0.734993\pi\) | |||||||
\(350\) | −5.02982e8 | −0.627067 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.94740e8 | −0.237989 | ||||||||
\(353\) | 2.43467e8 | + | 4.21698e8i | 0.294598 | + | 0.510258i | 0.974891 | − | 0.222682i | \(-0.0714811\pi\) |
−0.680294 | + | 0.732940i | \(0.738148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.94538e8 | − | 3.36949e8i | 0.230783 | − | 0.399729i | ||||
\(356\) | −1.29075e8 | + | 2.23565e8i | −0.151624 | + | 0.262621i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.77710e7 | − | 8.27417e7i | −0.0550267 | − | 0.0953090i | ||||
\(359\) | −4.59969e8 | −0.524684 | −0.262342 | − | 0.964975i | \(-0.584495\pi\) | ||||
−0.262342 | + | 0.964975i | \(0.584495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44695e9 | 1.61874 | ||||||||
\(362\) | −3.18090e8 | − | 5.50949e8i | −0.352428 | − | 0.610423i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.03891e6 | − | 3.53150e6i | 0.00221587 | − | 0.00383799i | ||||
\(365\) | 8.04043e6 | − | 1.39264e7i | 0.00865474 | − | 0.0149905i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.26252e8 | − | 5.65084e8i | −0.344526 | − | 0.596736i | 0.640742 | − | 0.767756i | \(-0.278627\pi\) |
−0.985267 | + | 0.171021i | \(0.945294\pi\) | |||||||
\(368\) | −2.62963e6 | −0.00275060 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.48000e8 | 0.357169 | ||||||||
\(371\) | 1.66919e8 | + | 2.89111e8i | 0.169706 | + | 0.293939i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.58955e8 | + | 1.66096e9i | −0.956791 | + | 1.65721i | −0.226577 | + | 0.973993i | \(0.572754\pi\) |
−0.730214 | + | 0.683218i | \(0.760580\pi\) | |||||||
\(374\) | −1.28369e8 | + | 2.22341e8i | −0.126885 | + | 0.219771i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.37907e8 | + | 2.38861e8i | 0.133791 | + | 0.231733i | ||||
\(377\) | −8.56351e6 | −0.00823109 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.43151e9 | 1.35070 | 0.675348 | − | 0.737499i | \(-0.263993\pi\) | ||||
0.675348 | + | 0.737499i | \(0.263993\pi\) | |||||||
\(380\) | 1.62564e8 | + | 2.81568e8i | 0.151978 | + | 0.263233i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.40926e7 | + | 4.17296e7i | −0.0221137 | + | 0.0383021i | ||||
\(383\) | 6.99297e7 | − | 1.21122e8i | 0.0636013 | − | 0.110161i | −0.832471 | − | 0.554068i | \(-0.813075\pi\) |
0.896073 | + | 0.443907i | \(0.146408\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.92351e8 | + | 5.06367e8i | 0.261091 | + | 0.452223i | ||||
\(386\) | 4.68680e8 | 0.414783 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.68262e8 | −0.320071 | ||||||||
\(389\) | 8.87960e8 | + | 1.53799e9i | 0.764838 | + | 1.32474i | 0.940332 | + | 0.340258i | \(0.110515\pi\) |
−0.175494 | + | 0.984481i | \(0.556152\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.73340e6 | + | 3.00234e6i | −0.00146649 | + | 0.00254004i | ||||
\(392\) | 1.39331e7 | − | 2.41328e7i | 0.0116828 | − | 0.0202351i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.73658e8 | − | 1.16681e9i | −0.554884 | − | 0.961088i | ||||
\(395\) | −7.95825e8 | −0.649722 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.05301e9 | −0.844630 | −0.422315 | − | 0.906449i | \(-0.638782\pi\) | ||||
−0.422315 | + | 0.906449i | \(0.638782\pi\) | |||||||
\(398\) | −4.06677e8 | − | 7.04385e8i | −0.323340 | − | 0.560041i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.37421e8 | − | 2.38020e8i | 0.107360 | − | 0.185953i | ||||
\(401\) | −1.16506e9 | + | 2.01794e9i | −0.902284 | + | 1.56280i | −0.0777620 | + | 0.996972i | \(0.524777\pi\) |
−0.824522 | + | 0.565830i | \(0.808556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.48335e6 | + | 9.49744e6i | 0.00417329 | + | 0.00722835i | ||||
\(404\) | 5.68270e8 | 0.428766 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.44001e8 | −0.700054 | ||||||||
\(407\) | 1.23105e9 | + | 2.13224e9i | 0.905098 | + | 1.56768i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.52109e7 | − | 1.30269e8i | 0.0543562 | − | 0.0941478i | −0.837567 | − | 0.546335i | \(-0.816023\pi\) |
0.891923 | + | 0.452187i | \(0.149356\pi\) | |||||||
\(410\) | −2.63539e8 | + | 4.56463e8i | −0.188843 | + | 0.327086i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.49809e7 | + | 1.47191e8i | 0.0598661 | + | 0.103691i | ||||
\(413\) | 2.72745e9 | 1.90516 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.81330e8 | 0.673980 | ||||||||
\(416\) | 1.11411e6 | + | 1.92970e6i | 0.000758756 | + | 0.00131420i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.15014e9 | + | 1.99210e9i | −0.770251 | + | 1.33411i | ||||
\(419\) | −4.55716e8 | + | 7.89324e8i | −0.302653 | + | 0.524211i | −0.976736 | − | 0.214445i | \(-0.931206\pi\) |
0.674083 | + | 0.738656i | \(0.264539\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.76741e8 | + | 6.52535e8i | 0.246068 | + | 0.426203i | 0.962431 | − | 0.271525i | \(-0.0875279\pi\) |
−0.716363 | + | 0.697728i | \(0.754195\pi\) | |||||||
\(422\) | 6.91056e8 | 0.447631 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.82417e8 | −0.116221 | ||||||||
\(425\) | −1.81170e8 | − | 3.13796e8i | −0.114479 | − | 0.198283i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.25753e9 | − | 2.17811e9i | 0.781667 | − | 1.35389i | ||||
\(428\) | −6.75948e8 | + | 1.17078e9i | −0.416735 | + | 0.721807i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.39648e8 | + | 4.15082e8i | 0.145356 | + | 0.251764i | ||||
\(431\) | −2.72892e9 | −1.64180 | −0.820900 | − | 0.571072i | \(-0.806528\pi\) | ||||
−0.820900 | + | 0.571072i | \(0.806528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.84699e9 | 1.09335 | 0.546673 | − | 0.837346i | \(-0.315894\pi\) | ||||
0.546673 | + | 0.837346i | \(0.315894\pi\) | |||||||
\(434\) | 6.04459e8 | + | 1.04695e9i | 0.354938 | + | 0.614771i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.89483e8 | − | 1.02101e9i | 0.340619 | − | 0.589969i | ||||
\(437\) | −1.55306e7 | + | 2.68998e7i | −0.00890233 | + | 0.0154193i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.50330e8 | − | 1.29961e9i | −0.423279 | − | 0.733140i | 0.572979 | − | 0.819570i | \(-0.305788\pi\) |
−0.996258 | + | 0.0864296i | \(0.972454\pi\) | |||||||
\(440\) | −3.19496e8 | −0.178805 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.93760e6 | 0.00161813 | ||||||||
\(443\) | −6.58449e8 | − | 1.14047e9i | −0.359840 | − | 0.623261i | 0.628094 | − | 0.778138i | \(-0.283835\pi\) |
−0.987934 | + | 0.154876i | \(0.950502\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.11764e8 | + | 3.66786e8i | −0.113918 | + | 0.197312i | ||||
\(446\) | 1.66469e8 | − | 2.88333e8i | 0.0888509 | − | 0.153894i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.22814e8 | + | 2.12721e8i | 0.0645322 | + | 0.111773i | ||||
\(449\) | 2.71216e8 | 0.141401 | 0.0707006 | − | 0.997498i | \(-0.477477\pi\) | ||||
0.0707006 | + | 0.997498i | \(0.477477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.72908e9 | −1.91418 | ||||||||
\(452\) | 5.96111e8 | + | 1.03250e9i | 0.303629 | + | 0.525900i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.37261e8 | − | 1.45018e9i | 0.419919 | − | 0.727321i | ||||
\(455\) | 3.34509e6 | − | 5.79387e6i | 0.00166482 | − | 0.00288356i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.07531e9 | + | 1.86249e9i | 0.527018 | + | 0.912822i | 0.999504 | + | 0.0314843i | \(0.0100234\pi\) |
−0.472486 | + | 0.881338i | \(0.656643\pi\) | |||||||
\(458\) | −2.66335e9 | −1.29539 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.31424e6 | −0.00206658 | ||||||||
\(461\) | −4.92094e8 | − | 8.52332e8i | −0.233935 | − | 0.405187i | 0.725028 | − | 0.688720i | \(-0.241827\pi\) |
−0.958963 | + | 0.283533i | \(0.908494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.28374e9 | − | 2.22351e9i | 0.601096 | − | 1.04113i | −0.391559 | − | 0.920153i | \(-0.628064\pi\) |
0.992655 | − | 0.120976i | \(-0.0386025\pi\) | |||||||
\(464\) | 2.57913e8 | − | 4.46718e8i | 0.119856 | − | 0.207597i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.18171e8 | + | 5.51089e8i | 0.145650 | + | 0.252273i | ||||
\(467\) | −6.97867e8 | −0.317076 | −0.158538 | − | 0.987353i | \(-0.550678\pi\) | ||||
−0.158538 | + | 0.987353i | \(0.550678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.51217e9 | −1.12446 | ||||||||
\(470\) | 2.26253e8 | + | 3.91882e8i | 0.100520 | + | 0.174106i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.45172e8 | + | 1.29068e9i | −0.326182 | + | 0.564963i | ||||
\(473\) | −1.69551e9 | + | 2.93671e9i | −0.736692 | + | 1.27599i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.62322e9 | − | 2.81149e9i | −0.694942 | − | 1.20368i | ||||
\(476\) | 3.23827e8 | 0.137622 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.17520e9 | −0.492171 | ||||||||
\(479\) | 1.53533e9 | + | 2.65927e9i | 0.638304 | + | 1.10557i | 0.985805 | + | 0.167895i | \(0.0536970\pi\) |
−0.347501 | + | 0.937680i | \(0.612970\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.40857e7 | − | 2.43972e7i | 0.00577127 | − | 0.00999613i | ||||
\(482\) | −1.21222e8 | + | 2.09963e8i | −0.0493080 | + | 0.0854039i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.06626e8 | − | 8.77503e8i | −0.203109 | − | 0.351795i | ||||
\(485\) | −6.04180e8 | −0.240475 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.74254e9 | −0.683646 | −0.341823 | − | 0.939764i | \(-0.611044\pi\) | ||||
−0.341823 | + | 0.939764i | \(0.611044\pi\) | |||||||
\(488\) | 6.87147e8 | + | 1.19017e9i | 0.267658 | + | 0.463597i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.28589e7 | − | 3.95928e7i | 0.00877747 | − | 0.0152030i | ||||
\(491\) | 5.05269e8 | − | 8.75152e8i | 0.192636 | − | 0.333655i | −0.753487 | − | 0.657463i | \(-0.771630\pi\) |
0.946123 | + | 0.323807i | \(0.104963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.40022e8 | − | 5.88935e8i | −0.127803 | − | 0.221362i | ||||
\(494\) | 2.63198e7 | 0.00982287 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.60582e8 | −0.243075 | ||||||||
\(497\) | −1.73602e9 | − | 3.00687e9i | −0.634318 | − | 1.09867i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.80436e8 | + | 1.35176e9i | −0.281181 | + | 0.487019i | −0.971676 | − | 0.236318i | \(-0.924059\pi\) |
0.690495 | + | 0.723337i | \(0.257393\pi\) | |||||||
\(500\) | 4.87956e8 | − | 8.45165e8i | 0.174576 | − | 0.302375i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.88108e8 | + | 1.01863e9i | 0.207488 | + | 0.359380i | ||||
\(503\) | 1.63663e9 | 0.573407 | 0.286704 | − | 0.958019i | \(-0.407441\pi\) | ||||
0.286704 | + | 0.958019i | \(0.407441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.32318e8 | 0.322140 | ||||||||
\(506\) | −1.52616e7 | − | 2.64339e7i | −0.00523690 | − | 0.00907057i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.26816e7 | − | 1.43209e8i | 0.0279824 | − | 0.0484670i | ||||
\(509\) | 2.64263e8 | − | 4.57717e8i | 0.0888227 | − | 0.153845i | −0.818191 | − | 0.574946i | \(-0.805023\pi\) |
0.907014 | + | 0.421101i | \(0.138356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.17512e7 | − | 1.24277e8i | −0.0237879 | − | 0.0412019i | ||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.94221e9 | 0.955658 | ||||||||
\(515\) | 1.39422e8 | + | 2.41486e8i | 0.0449785 | + | 0.0779051i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.60074e9 | + | 2.77256e9i | −0.509453 | + | 0.882399i | ||||
\(518\) | 1.55274e9 | − | 2.68943e9i | 0.490846 | − | 0.850171i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.82784e6 | + | 3.16591e6i | 0.000570068 | + | 0.000987386i | ||||
\(521\) | 4.50707e9 | 1.39625 | 0.698124 | − | 0.715977i | \(-0.254018\pi\) | ||||
0.698124 | + | 0.715977i | \(0.254018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.60454e9 | 1.10178 | 0.550888 | − | 0.834579i | \(-0.314289\pi\) | ||||
0.550888 | + | 0.834579i | \(0.314289\pi\) | |||||||
\(524\) | −1.34171e9 | − | 2.32390e9i | −0.407378 | − | 0.705600i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.30343e9 | − | 2.25760e9i | 0.390514 | − | 0.676390i | ||||
\(527\) | −4.35443e8 | + | 7.54209e8i | −0.129597 | + | 0.224468i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.70221e9 | + | 2.94831e9i | 0.499939 | + | 0.865921i | ||||
\(530\) | −2.99278e8 | −0.0873190 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.90137e9 | 0.835435 | ||||||||
\(533\) | 2.13341e7 | + | 3.69518e7i | 0.00610280 | + | 0.0105704i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.10898e9 | + | 1.92081e9i | −0.313101 | + | 0.542307i | ||||
\(536\) | 6.86356e8 | − | 1.18880e9i | 0.192519 | − | 0.333452i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.35612e9 | − | 2.34887e9i | −0.375456 | − | 0.650310i | ||||
\(539\) | 3.23454e8 | 0.0889716 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.24714e9 | −0.610154 | −0.305077 | − | 0.952328i | \(-0.598682\pi\) | ||||
−0.305077 | + | 0.952328i | \(0.598682\pi\) | |||||||
\(542\) | −1.00311e7 | − | 1.73744e7i | −0.00270616 | − | 0.00468720i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.84736e7 | + | 1.53241e8i | −0.0235623 | + | 0.0408111i | ||||
\(545\) | 9.67120e8 | − | 1.67510e9i | 0.255913 | − | 0.443255i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.13370e9 | − | 3.69568e9i | −0.557415 | − | 0.965470i | −0.997711 | − | 0.0676181i | \(-0.978460\pi\) |
0.440297 | − | 0.897852i | \(-0.354873\pi\) | |||||||
\(548\) | 8.10636e7 | 0.0210423 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.19020e9 | 0.817615 | ||||||||
\(551\) | −3.04647e9 | − | 5.27664e9i | −0.775829 | − | 1.34378i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.55090e9 | + | 6.15033e9i | −0.892894 | + | 1.54654i | ||||
\(554\) | −2.11434e8 | + | 3.66214e8i | −0.0528312 | + | 0.0915064i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.37796e8 | − | 1.27790e9i | −0.182043 | − | 0.315308i | ||||
\(557\) | 7.18311e8 | 0.176124 | 0.0880622 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880622 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.88001e7 | 0.00939489 | ||||||||
\(560\) | 2.01492e8 | + | 3.48995e8i | 0.0484843 | + | 0.0839772i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.15821e9 | − | 3.73812e9i | 0.512880 | − | 0.888335i | ||||
\(563\) | 2.85577e9 | − | 4.94635e9i | 0.674442 | − | 1.16817i | −0.302190 | − | 0.953248i | \(-0.597718\pi\) |
0.976632 | − | 0.214920i | \(-0.0689489\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.77995e8 | + | 1.69394e9i | 0.228122 | + | 0.395119i | ||||
\(566\) | −5.26852e8 | −0.122133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.89721e9 | 0.434405 | ||||||||
\(569\) | −3.18000e9 | − | 5.50793e9i | −0.723660 | − | 1.25342i | −0.959523 | − | 0.281629i | \(-0.909125\pi\) |
0.235863 | − | 0.971786i | \(-0.424208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.37475e9 | − | 4.11319e9i | 0.533816 | − | 0.924597i | −0.465403 | − | 0.885099i | \(-0.654091\pi\) |
0.999220 | − | 0.0394982i | \(-0.0125760\pi\) | |||||||
\(572\) | −1.29320e7 | + | 2.23988e7i | −0.00288921 | + | 0.00500425i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.35177e9 | + | 4.07339e9i | 0.519043 | + | 0.899010i | ||||
\(575\) | 4.30782e7 | 0.00944975 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.95938e8 | −0.194161 | −0.0970807 | − | 0.995277i | \(-0.530950\pi\) | ||||
−0.0970807 | + | 0.995277i | \(0.530950\pi\) | |||||||
\(578\) | −1.52471e9 | − | 2.64088e9i | −0.328429 | − | 0.568855i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.23138e8 | − | 7.32897e8i | 0.0900501 | − | 0.155971i | ||||
\(581\) | 4.37860e9 | − | 7.58396e9i | 0.926230 | − | 1.60428i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.05869e9 | − | 1.83371e9i | −0.221274 | − | 0.383258i | ||||
\(584\) | 7.84133e7 | 0.0162909 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.82067e8 | 0.0579042 | ||||||||
\(587\) | 3.21382e9 | + | 5.56650e9i | 0.655826 | + | 1.13592i | 0.981686 | + | 0.190505i | \(0.0610127\pi\) |
−0.325861 | + | 0.945418i | \(0.605654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.90140e9 | + | 6.75743e9i | −0.786715 | + | 1.36263i | ||||
\(590\) | −1.22255e9 | + | 2.11751e9i | −0.245066 | + | 0.424467i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.48458e8 | + | 1.46957e9i | 0.168075 | + | 0.291115i | ||||
\(593\) | −6.89741e9 | −1.35830 | −0.679148 | − | 0.734001i | \(-0.737651\pi\) | ||||
−0.679148 | + | 0.734001i | \(0.737651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.31279e8 | 0.103398 | ||||||||
\(596\) | −7.62452e8 | − | 1.32061e9i | −0.147520 | − | 0.255512i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −174624. | + | 302458.i | −3.33926e−5 | + | 5.78376e-5i | ||||
\(599\) | 4.25282e9 | − | 7.36610e9i | 0.808506 | − | 1.40037i | −0.105393 | − | 0.994431i | \(-0.533610\pi\) |
0.913899 | − | 0.405942i | \(-0.133057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.51840e9 | + | 6.09404e9i | 0.661126 | + | 1.14510i | 0.980320 | + | 0.197415i | \(0.0632545\pi\) |
−0.319194 | + | 0.947689i | \(0.603412\pi\) | |||||||
\(602\) | 4.27714e9 | 0.799035 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.88316e9 | 0.532401 | ||||||||
\(605\) | −8.31184e8 | − | 1.43965e9i | −0.152600 | − | 0.264310i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.58441e9 | − | 7.94042e9i | 0.831999 | − | 1.44106i | −0.0644524 | − | 0.997921i | \(-0.520530\pi\) |
0.896451 | − | 0.443143i | \(-0.146137\pi\) | |||||||
\(608\) | −7.92691e8 | + | 1.37298e9i | −0.143035 | + | 0.247743i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.12735e9 | + | 1.95263e9i | 0.201097 | + | 0.348309i | ||||
\(611\) | 3.66315e7 | 0.00649696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.89814e9 | 0.332826 | 0.166413 | − | 0.986056i | \(-0.446781\pi\) | ||||
0.166413 | + | 0.986056i | \(0.446781\pi\) | |||||||
\(614\) | 4.57038e8 | + | 7.91613e8i | 0.0796825 | + | 0.138014i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.42556e9 | + | 2.46914e9i | −0.245727 | + | 0.425612i | ||||
\(617\) | −5.04005e9 | + | 8.72962e9i | −0.863847 | + | 1.49623i | 0.00434118 | + | 0.999991i | \(0.498618\pi\) |
−0.868188 | + | 0.496236i | \(0.834715\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.03899e9 | + | 1.79957e9i | 0.176073 | + | 0.304967i | 0.940532 | − | 0.339705i | \(-0.110327\pi\) |
−0.764459 | + | 0.644672i | \(0.776994\pi\) | |||||||
\(620\) | −1.08377e9 | −0.182627 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.24370e9 | −0.207229 | ||||||||
\(623\) | 1.88974e9 | + | 3.27313e9i | 0.313108 | + | 0.542319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.82054e9 | + | 3.15327e9i | −0.298277 | + | 0.516632i | ||||
\(626\) | 1.52920e9 | − | 2.64865e9i | 0.249146 | − | 0.431533i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.12824e9 | − | 1.95417e9i | −0.181779 | − | 0.314850i | ||||
\(629\) | 2.23714e9 | 0.358440 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.91619e9 | −1.41279 | −0.706393 | − | 0.707820i | \(-0.749679\pi\) | ||||
−0.706393 | + | 0.707820i | \(0.749679\pi\) | |||||||
\(632\) | −1.94030e9 | − | 3.36069e9i | −0.305744 | − | 0.529565i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.77955e9 | − | 3.08227e9i | 0.277330 | − | 0.480350i | ||||
\(635\) | 1.35649e8 | − | 2.34952e8i | 0.0210237 | − | 0.0364142i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.85048e6 | − | 3.20513e6i | −0.000283659 | − | 0.000491313i | ||||
\(638\) | 5.98741e9 | 0.912780 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.20201e8 | −0.0332039 | ||||||||
\(641\) | 9.39525e8 | + | 1.62730e9i | 0.140898 | + | 0.244043i | 0.927835 | − | 0.372991i | \(-0.121668\pi\) |
−0.786937 | + | 0.617033i | \(0.788334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.15260e9 | − | 1.99636e9i | 0.170978 | − | 0.296143i | −0.767784 | − | 0.640709i | \(-0.778641\pi\) |
0.938762 | + | 0.344566i | \(0.111974\pi\) | |||||||
\(644\) | −1.92497e7 | + | 3.33415e7i | −0.00284004 | + | 0.00491909i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.04505e9 | + | 1.81008e9i | 0.152519 | + | 0.264171i | ||||
\(647\) | −5.73867e9 | −0.833002 | −0.416501 | − | 0.909135i | \(-0.636744\pi\) | ||||
−0.416501 | + | 0.909135i | \(0.636744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.72991e10 | −2.48408 | ||||||||
\(650\) | −1.82512e7 | − | 3.16120e7i | −0.00260672 | − | 0.00451497i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.09603e9 | − | 3.63043e9i | 0.296163 | − | 0.512969i | ||||
\(653\) | 3.68438e9 | − | 6.38153e9i | 0.517807 | − | 0.896868i | −0.481979 | − | 0.876183i | \(-0.660082\pi\) |
0.999786 | − | 0.0206853i | \(-0.00658480\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.20124e9 | − | 3.81265e9i | −0.306071 | − | 0.530130i | ||||
\(656\) | −2.57013e9 | −0.355461 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.03808e9 | 0.552566 | ||||||||
\(659\) | −6.22699e9 | − | 1.07855e10i | −0.847577 | − | 1.46805i | −0.883364 | − | 0.468687i | \(-0.844727\pi\) |
0.0357868 | − | 0.999359i | \(-0.488606\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.76604e9 | − | 4.79091e9i | 0.372523 | − | 0.645228i | −0.617430 | − | 0.786626i | \(-0.711826\pi\) |
0.989953 | + | 0.141398i | \(0.0451596\pi\) | |||||||
\(662\) | −2.20355e9 | + | 3.81667e9i | −0.295203 | + | 0.511306i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.39258e9 | + | 4.14406e9i | 0.317159 | + | 0.549336i | ||||
\(665\) | 4.76006e9 | 0.627678 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.08496e7 | 0.0105496 | ||||||||
\(668\) | −1.68989e9 | − | 2.92697e9i | −0.219351 | − | 0.379928i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.12605e9 | − | 1.95038e9i | 0.144643 | − | 0.250529i | ||||
\(671\) | −7.97601e9 | + | 1.38148e10i | −1.01919 | + | 1.76529i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.58942e9 | − | 9.68116e9i | −0.706829 | − | 1.22426i | −0.966028 | − | 0.258439i | \(-0.916792\pi\) |
0.259199 | − | 0.965824i | \(-0.416541\pi\) | |||||||
\(674\) | 3.97435e9 | 0.499984 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.01561e9 | −0.499963 | ||||||||
\(677\) | 8.00186e9 | + | 1.38596e10i | 0.991130 | + | 1.71669i | 0.610654 | + | 0.791898i | \(0.290907\pi\) |
0.380476 | + | 0.924791i | \(0.375760\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.69579e9 | + | 4.66925e9i | −0.330478 | + | 0.572405i | ||||
\(680\) | −1.45152e8 | + | 2.51411e8i | −0.0177028 | + | 0.0306621i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.83383e9 | − | 6.64039e9i | −0.462794 | − | 0.801582i | ||||
\(683\) | 9.70052e8 | 0.116499 | 0.0582496 | − | 0.998302i | \(-0.481448\pi\) | ||||
0.0582496 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.32995e8 | 0.0158095 | ||||||||
\(686\) | 2.88265e9 | + | 4.99290e9i | 0.340924 | + | 0.590498i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.16857e9 | + | 2.02402e9i | −0.136803 | + | 0.236949i | ||||
\(689\) | −1.21136e7 | + | 2.09814e7i | −0.00141093 | + | 0.00244381i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.04881e8 | − | 1.81659e8i | −0.0120927 | − | 0.0209451i | 0.859916 | − | 0.510436i | \(-0.170516\pi\) |
−0.872008 | + | 0.489491i | \(0.837183\pi\) | |||||||
\(692\) | −7.08691e9 | −0.812991 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.00929e9 | 0.228184 | ||||||||
\(695\) | −1.21045e9 | − | 2.09655e9i | −0.136773 | − | 0.236897i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.69418e9 | + | 2.93441e9i | −0.189516 | + | 0.328251i | ||||
\(698\) | −1.93166e9 | + | 3.34573e9i | −0.214999 | + | 0.372389i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.01193e9 | − | 3.48476e9i | −0.221702 | − | 0.383999i | ||||
\(701\) | −1.65792e10 | −1.81782 | −0.908910 | − | 0.416993i | \(-0.863084\pi\) | ||||
−0.908910 | + | 0.416993i | \(0.863084\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00440e10 | 2.17591 | ||||||||
\(704\) | −7.78961e8 | − | 1.34920e9i | −0.0841417 | − | 0.145738i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.94774e9 | + | 3.37358e9i | −0.208312 | + | 0.360807i | ||||
\(707\) | 4.15992e9 | − | 7.20519e9i | 0.442707 | − | 0.766791i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.89451e9 | + | 8.47753e9i | 0.515759 | + | 0.893321i | 0.999833 | + | 0.0182937i | \(0.00582340\pi\) |
−0.484073 | + | 0.875027i | \(0.660843\pi\) | |||||||
\(710\) | 3.11260e9 | 0.326377 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.06520e9 | −0.214429 | ||||||||
\(713\) | −5.17693e7 | − | 8.96670e7i | −0.00534883 | − | 0.00926444i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.12165e7 | + | 3.67481e7i | −0.00217071 | + | 0.00375979i | ||||
\(716\) | 3.82168e8 | − | 6.61934e8i | 0.0389097 | − | 0.0673936i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.83987e9 | − | 3.18676e9i | −0.185504 | − | 0.321302i | ||||
\(719\) | 1.08605e10 | 1.08968 | 0.544838 | − | 0.838541i | \(-0.316591\pi\) | ||||
0.544838 | + | 0.838541i | \(0.316591\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48835e9 | 0.247251 | ||||||||
\(722\) | 5.78778e9 | + | 1.00247e10i | 0.572311 | + | 0.991272i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.54472e9 | − | 4.40759e9i | 0.249204 | − | 0.431634i | ||||
\(725\) | −4.22509e9 | + | 7.31806e9i | −0.411768 | + | 0.713203i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.00529e9 | − | 6.93737e9i | −0.386602 | − | 0.669614i | 0.605388 | − | 0.795930i | \(-0.293018\pi\) |
−0.991990 | + | 0.126317i | \(0.959685\pi\) | |||||||
\(728\) | 3.26226e7 | 0.00313371 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.28647e8 | 0.0122397 | ||||||||
\(731\) | 1.54059e9 | + | 2.66839e9i | 0.145874 | + | 0.252661i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.35865e9 | + | 1.44776e10i | −0.783921 | + | 1.35779i | 0.145720 | + | 0.989326i | \(0.453450\pi\) |
−0.929641 | + | 0.368466i | \(0.879883\pi\) | |||||||
\(734\) | 2.61001e9 | − | 4.52068e9i | 0.243616 | − | 0.421956i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.05185e7 | − | 1.82186e7i | −0.000972484 | − | 0.00168439i | ||||
\(737\) | 1.59336e10 | 1.46615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.35702e9 | −0.852869 | −0.426434 | − | 0.904519i | \(-0.640230\pi\) | ||||
−0.426434 | + | 0.904519i | \(0.640230\pi\) | |||||||
\(740\) | 1.39200e9 | + | 2.41102e9i | 0.126278 | + | 0.218720i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.33535e9 | + | 2.31289e9i | −0.120000 | + | 0.207846i | ||||
\(743\) | −7.91592e9 | + | 1.37108e10i | −0.708012 | + | 1.22631i | 0.257582 | + | 0.966256i | \(0.417074\pi\) |
−0.965594 | + | 0.260056i | \(0.916259\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.25090e9 | − | 2.16662e9i | −0.110835 | − | 0.191971i | ||||
\(746\) | −1.53433e10 | −1.35311 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.05390e9 | −0.179442 | ||||||||
\(749\) | 9.89631e9 | + | 1.71409e10i | 0.860571 | + | 1.49055i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.52700e9 | − | 1.30371e10i | 0.648458 | − | 1.12316i | −0.335033 | − | 0.942206i | \(-0.608748\pi\) |
0.983491 | − | 0.180956i | \(-0.0579192\pi\) | |||||||
\(752\) | −1.10325e9 | + | 1.91089e9i | −0.0946047 | + | 0.163860i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.42540e7 | − | 5.93298e7i | −0.00291013 | − | 0.00504049i | ||||
\(755\) | 4.73018e9 | 0.400003 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.81448e9 | 0.570949 | 0.285474 | − | 0.958386i | \(-0.407849\pi\) | ||||
0.285474 | + | 0.958386i | \(0.407849\pi\) | |||||||
\(758\) | 5.72605e9 | + | 9.91781e9i | 0.477543 | + | 0.827129i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.30051e9 | + | 2.25255e9i | −0.107465 | + | 0.186134i | ||||
\(761\) | −1.71134e9 | + | 2.96413e9i | −0.140764 | + | 0.243810i | −0.927784 | − | 0.373117i | \(-0.878289\pi\) |
0.787021 | + | 0.616927i | \(0.211622\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.63040e9 | − | 1.49483e10i | −0.703388 | − | 1.21830i | ||||
\(764\) | −3.85481e8 | −0.0312735 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.11887e9 | 0.0899458 | ||||||||
\(767\) | 9.89682e7 | + | 1.71418e8i | 0.00791975 | + | 0.0137174i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.81185e9 | + | 8.33437e9i | −0.381566 | + | 0.660892i | −0.991286 | − | 0.131725i | \(-0.957949\pi\) |
0.609720 | + | 0.792617i | \(0.291282\pi\) | |||||||
\(770\) | −2.33881e9 | + | 4.05093e9i | −0.184619 | + | 0.319770i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.87472e9 | + | 3.24711e9i | 0.146648 | + | 0.254001i | ||||
\(773\) | −2.46796e10 | −1.92181 | −0.960905 | − | 0.276880i | \(-0.910700\pi\) | ||||
−0.960905 | + | 0.276880i | \(0.910700\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.08216e10 | 0.835091 | ||||||||
\(776\) | −1.47305e9 | − | 2.55140e9i | −0.113162 | − | 0.196003i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.10368e9 | + | 1.23039e10i | −0.540822 | + | 0.936732i | ||||
\(779\) | −1.51792e10 | + | 2.62912e10i | −1.15045 | + | 1.99264i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.10108e10 | + | 1.90713e10i | 0.827069 | + | 1.43253i | ||||
\(782\) | −2.77344e7 | −0.00207393 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.22929e8 | 0.0165219 | ||||||||
\(785\) | −1.85102e9 | − | 3.20606e9i | −0.136574 | − | 0.236553i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.23130e10 | − | 2.13268e10i | 0.900436 | − | 1.55960i | 0.0735075 | − | 0.997295i | \(-0.476581\pi\) |
0.826929 | − | 0.562307i | \(-0.190086\pi\) | |||||||
\(788\) | 5.38926e9 | − | 9.33448e9i | 0.392363 | − | 0.679592i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.18330e9 | − | 5.51364e9i | −0.229712 | − | 0.397872i | ||||
\(791\) | 1.74549e10 | 1.25401 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.82523e8 | 0.0129976 | ||||||||
\(794\) | −4.21205e9 | − | 7.29548e9i | −0.298622 | − | 0.517228i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.25342e9 | − | 5.63508e9i | 0.228636 | − | 0.396009i | ||||
\(797\) | −2.23164e9 | + | 3.86532e9i | −0.156142 | + | 0.270446i | −0.933474 | − | 0.358644i | \(-0.883239\pi\) |
0.777332 | + | 0.629091i | \(0.216573\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.45448e9 | + | 2.51924e9i | 0.100878 | + | 0.174725i | ||||
\(800\) | 2.19873e9 | 0.151830 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.86410e10 | −1.27602 | ||||||||
\(803\) | 4.55088e8 | + | 7.88236e8i | 0.0310164 | + | 0.0537220i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.15816e7 | + | 5.47009e7i | −0.00213377 | + | 0.00369580i | ||||
\(806\) | −4.38668e7 | + | 7.59795e7i | −0.00295096 | + | 0.00511121i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.27308e9 | + | 3.93709e9i | 0.151592 | + | 0.262564i | ||||
\(809\) | −2.56496e9 | −0.170318 | −0.0851590 | − | 0.996367i | \(-0.527140\pi\) | ||||
−0.0851590 | + | 0.996367i | \(0.527140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.95820e9 | 0.260570 | 0.130285 | − | 0.991477i | \(-0.458411\pi\) | ||||
0.130285 | + | 0.991477i | \(0.458411\pi\) | |||||||
\(812\) | −3.77601e9 | − | 6.54023e9i | −0.247506 | − | 0.428694i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.84841e9 | + | 1.70579e10i | −0.640001 | + | 1.10851i | ||||
\(815\) | 3.43880e9 | − | 5.95617e9i | 0.222513 | − | 0.385403i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.38031e10 | + | 2.39077e10i | 0.885525 | + | 1.53377i | ||||
\(818\) | 1.20337e9 | 0.0768713 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.21663e9 | −0.267065 | ||||||||
\(821\) | −7.92551e9 | − | 1.37274e10i | −0.499835 | − | 0.865739i | 0.500165 | − | 0.865930i | \(-0.333273\pi\) |
−1.00000 | 0.000191070i | \(0.999939\pi\) | ||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.87267e9 | − | 1.36359e10i | 0.492292 | − | 0.852674i | −0.507669 | − | 0.861552i | \(-0.669493\pi\) |
0.999961 | + | 0.00887803i | \(0.00282600\pi\) | |||||||
\(824\) | −6.79847e8 | + | 1.17753e9i | −0.0423317 | + | 0.0733207i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.09098e10 | + | 1.88963e10i | 0.673575 | + | 1.16667i | ||||
\(827\) | −2.15640e9 | −0.132574 | −0.0662872 | − | 0.997801i | \(-0.521115\pi\) | ||||
−0.0662872 | + | 0.997801i | \(0.521115\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.95703e10 | 1.80267 | 0.901333 | − | 0.433126i | \(-0.142589\pi\) | ||||
0.901333 | + | 0.433126i | \(0.142589\pi\) | |||||||
\(830\) | 3.92532e9 | + | 6.79885e9i | 0.238288 | + | 0.412726i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.91290e6 | + | 1.54376e7i | −0.000536522 | + | 0.000929283i | ||||
\(833\) | 1.46950e8 | − | 2.54525e8i | 0.00880872 | − | 0.0152571i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.77247e9 | − | 4.80206e9i | −0.164803 | − | 0.285447i | ||||
\(836\) | −1.84022e10 | −1.08930 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.29146e9 | −0.428016 | ||||||||
\(839\) | 1.55991e9 | + | 2.70184e9i | 0.0911869 | + | 0.157940i | 0.908011 | − | 0.418947i | \(-0.137601\pi\) |
−0.816824 | + | 0.576887i | \(0.804267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.95252e8 | − | 1.20421e9i | 0.0403048 | − | 0.0698099i | ||||
\(842\) | −3.01393e9 | + | 5.22028e9i | −0.173997 | + | 0.301371i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.76422e9 | + | 4.78778e9i | 0.158261 | + | 0.274117i | ||||
\(845\) | −6.58811e9 | −0.375632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.48347e10 | −0.838852 | ||||||||
\(848\) | −7.29668e8 | − | 1.26382e9i | −0.0410903 | − | 0.0711705i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.44936e9 | − | 2.51037e9i | 0.0809487 | − | 0.140207i | ||||
\(851\) | −1.32986e8 | + | 2.30338e8i | −0.00739694 | + | 0.0128119i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.19709e9 | + | 1.24657e10i | 0.397041 | + | 0.687695i | 0.993359 | − | 0.115053i | \(-0.0367038\pi\) |
−0.596319 | + | 0.802748i | \(0.703370\pi\) | |||||||
\(854\) | 2.01205e10 | 1.10544 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.08152e10 | −0.589353 | ||||||||
\(857\) | −2.36600e9 | − | 4.09804e9i | −0.128405 | − | 0.222404i | 0.794654 | − | 0.607063i | \(-0.207652\pi\) |
−0.923059 | + | 0.384659i | \(0.874319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.41867e9 | − | 4.18926e9i | 0.130197 | − | 0.225508i | −0.793555 | − | 0.608498i | \(-0.791772\pi\) |
0.923752 | + | 0.382990i | \(0.125106\pi\) | |||||||
\(860\) | −1.91718e9 | + | 3.32066e9i | −0.102782 | + | 0.178024i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.09157e10 | − | 1.89065e10i | −0.580464 | − | 1.00539i | ||||
\(863\) | −1.90890e10 | −1.01099 | −0.505493 | − | 0.862831i | \(-0.668689\pi\) | ||||
−0.505493 | + | 0.862831i | \(0.668689\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.16270e10 | −0.610815 | ||||||||
\(866\) | 7.38797e9 | + | 1.27963e10i | 0.386556 | + | 0.669535i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.83567e9 | + | 8.37563e9i | −0.250979 | + | 0.434709i | ||||
\(869\) | 2.25219e10 | − | 3.90090e10i | 1.16422 | − | 2.01649i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.11567e7 | − | 1.57888e8i | −0.00467439 | − | 0.00809628i | ||||
\(872\) | 9.43173e9 | 0.481708 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.48490e8 | −0.0125898 | ||||||||
\(875\) | −7.14398e9 | − | 1.23737e10i | −0.360506 | − | 0.624414i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.68182e10 | − | 2.91299e10i | 0.841938 | − | 1.45828i | −0.0463168 | − | 0.998927i | \(-0.514748\pi\) |
0.888254 | − | 0.459352i | \(-0.151918\pi\) | |||||||
\(878\) | 6.00264e9 | − | 1.03969e10i | 0.299303 | − | 0.518408i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.27798e9 | − | 2.21353e9i | −0.0632173 | − | 0.109495i | ||||
\(881\) | 2.81256e10 | 1.38575 | 0.692876 | − | 0.721057i | \(-0.256343\pi\) | ||||
0.692876 | + | 0.721057i | \(0.256343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.99944e10 | 0.977341 | 0.488671 | − | 0.872468i | \(-0.337482\pi\) | ||||
0.488671 | + | 0.872468i | \(0.337482\pi\) | |||||||
\(884\) | 1.17504e7 | + | 2.03523e7i | 0.000572097 | + | 0.000990901i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.26760e9 | − | 9.12374e9i | 0.254445 | − | 0.440712i | ||||
\(887\) | 1.61338e10 | − | 2.79446e10i | 0.776255 | − | 1.34451i | −0.157832 | − | 0.987466i | \(-0.550450\pi\) |
0.934087 | − | 0.357047i | \(-0.116216\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.21051e9 | − | 2.09666e9i | −0.0577846 | − | 0.100086i | ||||
\(890\) | −3.38823e9 | −0.161104 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.66351e9 | 0.125654 | ||||||||
\(893\) | 1.30316e10 | + | 2.25715e10i | 0.612377 | + | 1.06067i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.26994e8 | − | 1.08599e9i | 0.0292336 | − | 0.0506341i | ||||
\(896\) | −9.82516e8 | + | 1.70177e9i | −0.0456312 | + | 0.0790355i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.08486e9 | + | 1.87904e9i | 0.0499929 | + | 0.0865902i | ||||
\(899\) | 2.03100e10 | 0.932290 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.92393e9 | −0.0876299 | ||||||||
\(902\) | −1.49163e10 | − | 2.58358e10i | −0.676766 | − | 1.17219i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.76889e9 | + | 8.25996e9i | −0.214698 | + | 0.371868i | ||||
\(905\) | 4.17494e9 | − | 7.23120e9i | 0.187232 | − | 0.324295i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.76161e9 | − | 9.97941e9i | −0.256400 | − | 0.444098i | 0.708875 | − | 0.705335i | \(-0.249203\pi\) |
−0.965275 | + | 0.261236i | \(0.915870\pi\) | |||||||
\(908\) | 1.33962e10 | 0.593855 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.35214e7 | 0.00235441 | ||||||||
\(911\) | 2.94854e9 | + | 5.10703e9i | 0.129209 | + | 0.223797i | 0.923370 | − | 0.383910i | \(-0.125423\pi\) |
−0.794161 | + | 0.607707i | \(0.792089\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.77716e10 | + | 4.81019e10i | −1.20769 | + | 2.09177i | ||||
\(914\) | −8.60245e9 | + | 1.48999e10i | −0.372658 | + | 0.645463i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.06534e10 | − | 1.84522e10i | −0.457988 | − | 0.793258i | ||||
\(917\) | −3.92868e10 | −1.68250 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.37679e9 | 0.186017 | 0.0930083 | − | 0.995665i | \(-0.470352\pi\) | ||||
0.0930083 | + | 0.995665i | \(0.470352\pi\) | |||||||
\(920\) | −1.72570e7 | − | 2.98899e7i | −0.000730646 | − | 0.00126552i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.93675e9 | − | 6.81866e9i | 0.165417 | − | 0.286511i | ||||
\(923\) | 1.25986e8 | − | 2.18215e8i | 0.00527372 | − | 0.00913436i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.38993e10 | − | 2.40743e10i | −0.577427 | − | 1.00013i | ||||
\(926\) | 2.05399e10 | 0.850078 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.12661e9 | 0.169502 | ||||||||
\(929\) | −1.51512e10 | − | 2.62426e10i | −0.620000 | − | 1.07387i | −0.989485 | − | 0.144635i | \(-0.953799\pi\) |
0.369485 | − | 0.929237i | \(-0.379534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.31662e9 | − | 2.28045e9i | 0.0534732 | − | 0.0926183i | ||||
\(932\) | −2.54537e9 | + | 4.40871e9i | −0.102990 | + | 0.178384i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.79147e9 | − | 4.83496e9i | −0.112103 | − | 0.194169i | ||||
\(935\) | −3.36968e9 | −0.134818 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.61397e10 | 1.03804 | 0.519018 | − | 0.854763i | \(-0.326298\pi\) | ||||
0.519018 | + | 0.854763i | \(0.326298\pi\) | |||||||
\(938\) | −1.00487e10 | − | 1.74048e10i | −0.397557 | − | 0.688588i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.81003e9 | + | 3.13506e9i | −0.0710783 | + | 0.123111i | ||||
\(941\) | 1.21220e10 | − | 2.09959e10i | 0.474253 | − | 0.821429i | −0.525313 | − | 0.850909i | \(-0.676052\pi\) |
0.999565 | + | 0.0294797i | \(0.00938504\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.01419e8 | − | 3.48868e8i | −0.00782186 | − | 0.0135479i | ||||
\(944\) | −1.19228e10 | −0.461291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.71281e10 | −1.04184 | ||||||||
\(947\) | −1.28877e10 | − | 2.23222e10i | −0.493119 | − | 0.854106i | 0.506850 | − | 0.862034i | \(-0.330810\pi\) |
−0.999969 | + | 0.00792781i | \(0.997476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.20713e6 | − | 9.01902e6i | 0.000197773 | − | 0.000342553i | ||||
\(950\) | 1.29857e10 | − | 2.24919e10i | 0.491398 | − | 0.851127i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.29531e9 | + | 2.24354e9i | 0.0486569 | + | 0.0842761i | ||||
\(953\) | 2.22288e10 | 0.831937 | 0.415968 | − | 0.909379i | \(-0.363443\pi\) | ||||
0.415968 | + | 0.909379i | \(0.363443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.32431e8 | −0.0234964 | ||||||||
\(956\) | −4.70082e9 | − | 8.14205e9i | −0.174009 | − | 0.301392i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.22826e10 | + | 2.12742e10i | −0.451349 | + | 0.781759i | ||||
\(959\) | 5.93411e8 | − | 1.02782e9i | 0.0217265 | − | 0.0376314i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.51494e8 | + | 1.30163e9i | 0.0273145 | + | 0.0473102i | ||||
\(962\) | 2.25372e8 | 0.00816181 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.93955e9 | −0.0697320 | ||||||||
\(965\) | 3.07571e9 | + | 5.32729e9i | 0.110179 | + | 0.190836i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.54705e9 | − | 2.67957e9i | 0.0550189 | − | 0.0952956i | −0.837204 | − | 0.546890i | \(-0.815811\pi\) |
0.892223 | + | 0.451595i | \(0.149145\pi\) | |||||||
\(968\) | 4.05301e9 | − | 7.02002e9i | 0.143620 | − | 0.248757i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.41672e9 | − | 4.18588e9i | −0.0850208 | − | 0.147260i | ||||
\(971\) | −1.62621e10 | −0.570044 | −0.285022 | − | 0.958521i | \(-0.592001\pi\) | ||||
−0.285022 | + | 0.958521i | \(0.592001\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.16036e10 | −0.751850 | ||||||||
\(974\) | −6.97016e9 | − | 1.20727e10i | −0.241705 | − | 0.418646i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.49718e9 | + | 9.52139e9i | −0.189263 | + | 0.327813i | ||||
\(977\) | −2.21128e9 | + | 3.83005e9i | −0.0758601 | + | 0.131393i | −0.901460 | − | 0.432863i | \(-0.857504\pi\) |
0.825600 | + | 0.564256i | \(0.190837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.19858e10 | − | 2.07601e10i | −0.408253 | − | 0.707115i | ||||
\(980\) | 3.65743e8 | 0.0124132 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.08431e9 | 0.272428 | ||||||||
\(983\) | −1.86923e10 | − | 3.23761e10i | −0.627663 | − | 1.08714i | −0.988019 | − | 0.154329i | \(-0.950678\pi\) |
0.360357 | − | 0.932815i | \(-0.382655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.84176e9 | − | 1.53144e10i | 0.294789 | − | 0.510590i | ||||
\(986\) | 2.72017e9 | − | 4.71148e9i | 0.0903707 | − | 0.156527i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.05279e8 | + | 1.82349e8i | 0.00347291 | + | 0.00601525i | ||||
\(989\) | −3.66319e8 | −0.0120413 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.24473e10 | −0.406273 | −0.203136 | − | 0.979150i | \(-0.565113\pi\) | ||||
−0.203136 | + | 0.979150i | \(0.565113\pi\) | |||||||
\(992\) | −2.64233e9 | − | 4.57665e9i | −0.0859402 | − | 0.148853i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.38881e10 | − | 2.40550e10i | 0.448530 | − | 0.776877i | ||||
\(995\) | 5.33764e9 | − | 9.24506e9i | 0.171778 | − | 0.297529i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.42168e10 | − | 2.46241e10i | −0.454326 | − | 0.786915i | 0.544323 | − | 0.838876i | \(-0.316786\pi\) |
−0.998649 | + | 0.0519600i | \(0.983453\pi\) | |||||||
\(998\) | −1.24870e10 | −0.397650 | ||||||||
\(999\) | 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 | 162.8.c.j.109.1 | 2 | ||
3.2 | odd | 2 | 162.8.c.c.109.1 | 2 | |||
9.2 | odd | 6 | 162.8.c.c.55.1 | 2 | |||
9.4 | even | 3 | 54.8.a.b.1.1 | ✓ | 1 | ||
9.5 | odd | 6 | 54.8.a.e.1.1 | yes | 1 | ||
9.7 | even | 3 | inner | 162.8.c.j.55.1 | 2 | ||
36.23 | even | 6 | 432.8.a.c.1.1 | 1 | |||
36.31 | odd | 6 | 432.8.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.8.a.b.1.1 | ✓ | 1 | 9.4 | even | 3 | ||
54.8.a.e.1.1 | yes | 1 | 9.5 | odd | 6 | ||
162.8.c.c.55.1 | 2 | 9.2 | odd | 6 | |||
162.8.c.c.109.1 | 2 | 3.2 | odd | 2 | |||
162.8.c.j.55.1 | 2 | 9.7 | even | 3 | inner | ||
162.8.c.j.109.1 | 2 | 1.1 | even | 1 | trivial | ||
432.8.a.c.1.1 | 1 | 36.23 | even | 6 | |||
432.8.a.f.1.1 | 1 | 36.31 | odd | 6 |