Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,22,Mod(49,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.b (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: | \(139.738672144\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 237265x^{2} + 14073551424 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(344.930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.22.b.d.49.4 |
$q$-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 \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1024.00i | − 0.707107i | ||||||||
\(3\) | − 194815.i | − 1.90480i | −0.304856 | − | 0.952398i | \(-0.598608\pi\) | ||||
0.304856 | − | 0.952398i | \(-0.401392\pi\) | |||||||
\(4\) | −1.04858e6 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.99490e8 | −1.34689 | ||||||||
\(7\) | 9.63461e8i | 1.28915i | 0.764539 | + | 0.644577i | \(0.222967\pi\) | ||||
−0.764539 | + | 0.644577i | \(0.777033\pi\) | |||||||
\(8\) | 1.07374e9i | 0.353553i | ||||||||
\(9\) | −2.74924e10 | −2.62825 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.10882e10 | 0.710124 | 0.355062 | − | 0.934843i | \(-0.384460\pi\) | ||||
0.355062 | + | 0.934843i | \(0.384460\pi\) | |||||||
\(12\) | 2.04278e11i | 0.952398i | ||||||||
\(13\) | − 5.25383e10i | − 0.105699i | −0.998602 | − | 0.0528495i | \(-0.983170\pi\) | ||||
0.998602 | − | 0.0528495i | \(-0.0168303\pi\) | |||||||
\(14\) | 9.86584e11 | 0.911570 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.09951e12 | 0.250000 | ||||||||
\(17\) | − 1.13179e13i | − 1.36161i | −0.732466 | − | 0.680803i | \(-0.761631\pi\) | ||||
0.732466 | − | 0.680803i | \(-0.238369\pi\) | |||||||
\(18\) | 2.81522e13i | 1.85845i | ||||||||
\(19\) | 4.53240e13 | 1.69596 | 0.847979 | − | 0.530030i | \(-0.177819\pi\) | ||||
0.847979 | + | 0.530030i | \(0.177819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.87696e14 | 2.45558 | ||||||||
\(22\) | − 6.25543e13i | − 0.502133i | ||||||||
\(23\) | − 2.47091e14i | − 1.24370i | −0.783137 | − | 0.621849i | \(-0.786382\pi\) | ||||
0.783137 | − | 0.621849i | \(-0.213618\pi\) | |||||||
\(24\) | 2.09181e14 | 0.673447 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.37992e13 | −0.0747404 | ||||||||
\(27\) | 3.31810e15i | 3.10149i | ||||||||
\(28\) | − 1.01026e15i | − 0.644577i | ||||||||
\(29\) | 2.58718e15 | 1.14195 | 0.570977 | − | 0.820966i | \(-0.306565\pi\) | ||||
0.570977 | + | 0.820966i | \(0.306565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.35601e15 | −0.297142 | −0.148571 | − | 0.988902i | \(-0.547467\pi\) | ||||
−0.148571 | + | 0.988902i | \(0.547467\pi\) | |||||||
\(32\) | − 1.12590e15i | − 0.176777i | ||||||||
\(33\) | − 1.19009e16i | − 1.35264i | ||||||||
\(34\) | −1.15895e16 | −0.962801 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.88279e16 | 1.31413 | ||||||||
\(37\) | − 1.35920e16i | − 0.464692i | −0.972633 | − | 0.232346i | \(-0.925360\pi\) | ||||
0.972633 | − | 0.232346i | \(-0.0746401\pi\) | |||||||
\(38\) | − 4.64117e16i | − 1.19922i | ||||||||
\(39\) | −1.02352e16 | −0.201335 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.72480e16 | 0.782436 | 0.391218 | − | 0.920298i | \(-0.372054\pi\) | ||||
0.391218 | + | 0.920298i | \(0.372054\pi\) | |||||||
\(42\) | − 1.92201e17i | − 1.73636i | ||||||||
\(43\) | 3.70641e16i | 0.261538i | 0.991413 | + | 0.130769i | \(0.0417446\pi\) | ||||
−0.991413 | + | 0.130769i | \(0.958255\pi\) | |||||||
\(44\) | −6.40556e16 | −0.355062 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.53021e17 | −0.879427 | ||||||||
\(47\) | 3.17182e17i | 0.879592i | 0.898098 | + | 0.439796i | \(0.144949\pi\) | ||||
−0.898098 | + | 0.439796i | \(0.855051\pi\) | |||||||
\(48\) | − 2.14201e17i | − 0.476199i | ||||||||
\(49\) | −3.69712e17 | −0.661919 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.20489e18 | −2.59358 | ||||||||
\(52\) | 5.50904e16i | 0.0528495i | ||||||||
\(53\) | − 1.44909e18i | − 1.13815i | −0.822286 | − | 0.569074i | \(-0.807302\pi\) | ||||
0.822286 | − | 0.569074i | \(-0.192698\pi\) | |||||||
\(54\) | 3.39773e18 | 2.19308 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.03451e18 | −0.455785 | ||||||||
\(57\) | − 8.82978e18i | − 3.23046i | ||||||||
\(58\) | − 2.64928e18i | − 0.807483i | ||||||||
\(59\) | 1.08957e18 | 0.277529 | 0.138764 | − | 0.990325i | \(-0.455687\pi\) | ||||
0.138764 | + | 0.990325i | \(0.455687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.59498e17 | −0.0286281 | −0.0143140 | − | 0.999898i | \(-0.504556\pi\) | ||||
−0.0143140 | + | 0.999898i | \(0.504556\pi\) | |||||||
\(62\) | 1.38855e18i | 0.210111i | ||||||||
\(63\) | − 2.64879e19i | − 3.38822i | ||||||||
\(64\) | −1.15292e18 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.21865e19 | −0.956462 | ||||||||
\(67\) | 8.71262e18i | 0.583934i | 0.956428 | + | 0.291967i | \(0.0943097\pi\) | ||||
−0.956428 | + | 0.291967i | \(0.905690\pi\) | |||||||
\(68\) | 1.18677e19i | 0.680803i | ||||||||
\(69\) | −4.81370e19 | −2.36899 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.06845e19 | −1.11868 | −0.559340 | − | 0.828938i | \(-0.688946\pi\) | ||||
−0.559340 | + | 0.828938i | \(0.688946\pi\) | |||||||
\(72\) | − 2.95198e19i | − 0.929227i | ||||||||
\(73\) | − 2.36491e19i | − 0.644059i | −0.946730 | − | 0.322029i | \(-0.895635\pi\) | ||||
0.946730 | − | 0.322029i | \(-0.104365\pi\) | |||||||
\(74\) | −1.39182e19 | −0.328587 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.75256e19 | −0.847979 | ||||||||
\(77\) | 5.88561e19i | 0.915459i | ||||||||
\(78\) | 1.04809e19i | 0.142365i | ||||||||
\(79\) | 9.35354e19 | 1.11145 | 0.555727 | − | 0.831365i | \(-0.312440\pi\) | ||||
0.555727 | + | 0.831365i | \(0.312440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.58834e20 | 3.27945 | ||||||||
\(82\) | − 6.88619e19i | − 0.553266i | ||||||||
\(83\) | 2.00855e20i | 1.42090i | 0.703750 | + | 0.710448i | \(0.251508\pi\) | ||||
−0.703750 | + | 0.710448i | \(0.748492\pi\) | |||||||
\(84\) | −1.96814e20 | −1.22779 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.79536e19 | 0.184935 | ||||||||
\(87\) | − 5.04022e20i | − 2.17519i | ||||||||
\(88\) | 6.55929e19i | 0.251067i | ||||||||
\(89\) | −3.85510e19 | −0.131051 | −0.0655255 | − | 0.997851i | \(-0.520872\pi\) | ||||
−0.0655255 | + | 0.997851i | \(0.520872\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.06186e19 | 0.136262 | ||||||||
\(92\) | 2.59094e20i | 0.621849i | ||||||||
\(93\) | 2.64170e20i | 0.565996i | ||||||||
\(94\) | 3.24795e20 | 0.621965 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.19342e20 | −0.336724 | ||||||||
\(97\) | − 5.46564e20i | − 0.752554i | −0.926507 | − | 0.376277i | \(-0.877204\pi\) | ||||
0.926507 | − | 0.376277i | \(-0.122796\pi\) | |||||||
\(98\) | 3.78585e20i | 0.468047i | ||||||||
\(99\) | −1.67946e21 | −1.86638 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.87063e21 | 1.68505 | 0.842524 | − | 0.538658i | \(-0.181069\pi\) | ||||
0.842524 | + | 0.538658i | \(0.181069\pi\) | |||||||
\(102\) | 2.25781e21i | 1.83394i | ||||||||
\(103\) | 8.63482e20i | 0.633086i | 0.948578 | + | 0.316543i | \(0.102522\pi\) | ||||
−0.948578 | + | 0.316543i | \(0.897478\pi\) | |||||||
\(104\) | 5.64125e19 | 0.0373702 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.48387e21 | −0.804792 | ||||||||
\(107\) | − 3.65685e21i | − 1.79712i | −0.438848 | − | 0.898561i | \(-0.644613\pi\) | ||||
0.438848 | − | 0.898561i | \(-0.355387\pi\) | |||||||
\(108\) | − 3.47928e21i | − 1.55074i | ||||||||
\(109\) | 6.39944e20 | 0.258919 | 0.129459 | − | 0.991585i | \(-0.458676\pi\) | ||||
0.129459 | + | 0.991585i | \(0.458676\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.64792e21 | −0.885143 | ||||||||
\(112\) | 1.05934e21i | 0.322289i | ||||||||
\(113\) | − 6.17070e20i | − 0.171006i | −0.996338 | − | 0.0855029i | \(-0.972750\pi\) | ||||
0.996338 | − | 0.0855029i | \(-0.0272497\pi\) | |||||||
\(114\) | −9.04169e21 | −2.28428 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.71286e21 | −0.570977 | ||||||||
\(117\) | 1.44440e21i | 0.277803i | ||||||||
\(118\) | − 1.11572e21i | − 0.196242i | ||||||||
\(119\) | 1.09043e22 | 1.75532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.66848e21 | −0.495724 | ||||||||
\(122\) | 1.63326e20i | 0.0202431i | ||||||||
\(123\) | − 1.31009e22i | − 1.49038i | ||||||||
\(124\) | 1.42188e21 | 0.148571 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.71236e22 | −2.39583 | ||||||||
\(127\) | − 1.40405e22i | − 1.14142i | −0.821152 | − | 0.570709i | \(-0.806668\pi\) | ||||
0.821152 | − | 0.570709i | \(-0.193332\pi\) | |||||||
\(128\) | 1.18059e21i | 0.0883883i | ||||||||
\(129\) | 7.22063e21 | 0.498176 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.03410e22 | 1.19405 | 0.597025 | − | 0.802222i | \(-0.296349\pi\) | ||||
0.597025 | + | 0.802222i | \(0.296349\pi\) | |||||||
\(132\) | 1.24790e22i | 0.676321i | ||||||||
\(133\) | 4.36679e22i | 2.18635i | ||||||||
\(134\) | 8.92173e21 | 0.412903 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.21525e22 | 0.481401 | ||||||||
\(137\) | − 1.10091e21i | − 0.0403819i | −0.999796 | − | 0.0201909i | \(-0.993573\pi\) | ||||
0.999796 | − | 0.0201909i | \(-0.00642741\pi\) | |||||||
\(138\) | 4.92923e22i | 1.67513i | ||||||||
\(139\) | −4.14583e22 | −1.30604 | −0.653019 | − | 0.757342i | \(-0.726498\pi\) | ||||
−0.653019 | + | 0.757342i | \(0.726498\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.17918e22 | 1.67544 | ||||||||
\(142\) | 3.14209e22i | 0.791027i | ||||||||
\(143\) | − 3.20947e21i | − 0.0750593i | ||||||||
\(144\) | −3.02282e22 | −0.657063 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.42167e22 | −0.455418 | ||||||||
\(147\) | 7.20253e22i | 1.26082i | ||||||||
\(148\) | 1.42522e22i | 0.232346i | ||||||||
\(149\) | −9.61610e22 | −1.46064 | −0.730320 | − | 0.683106i | \(-0.760629\pi\) | ||||
−0.730320 | + | 0.683106i | \(0.760629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.13093e23 | −1.49340 | −0.746700 | − | 0.665161i | \(-0.768363\pi\) | ||||
−0.746700 | + | 0.665161i | \(0.768363\pi\) | |||||||
\(152\) | 4.86662e22i | 0.599612i | ||||||||
\(153\) | 3.11156e23i | 3.57864i | ||||||||
\(154\) | 6.02687e22 | 0.647327 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.07324e22 | 0.100667 | ||||||||
\(157\) | 3.75753e22i | 0.329576i | 0.986329 | + | 0.164788i | \(0.0526940\pi\) | ||||
−0.986329 | + | 0.164788i | \(0.947306\pi\) | |||||||
\(158\) | − 9.57802e22i | − 0.785917i | ||||||||
\(159\) | −2.82304e23 | −2.16794 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.38063e23 | 1.60332 | ||||||||
\(162\) | − 3.67446e23i | − 2.31892i | ||||||||
\(163\) | − 2.53934e23i | − 1.50228i | −0.660143 | − | 0.751140i | \(-0.729504\pi\) | ||||
0.660143 | − | 0.751140i | \(-0.270496\pi\) | |||||||
\(164\) | −7.05146e22 | −0.391218 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.05675e23 | 1.00472 | ||||||||
\(167\) | − 7.88087e22i | − 0.361452i | −0.983533 | − | 0.180726i | \(-0.942155\pi\) | ||||
0.983533 | − | 0.180726i | \(-0.0578448\pi\) | |||||||
\(168\) | 2.01538e23i | 0.868178i | ||||||||
\(169\) | 2.44304e23 | 0.988828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.24607e24 | −4.45740 | ||||||||
\(172\) | − 3.88645e22i | − 0.130769i | ||||||||
\(173\) | 3.30387e23i | 1.04602i | 0.852327 | + | 0.523009i | \(0.175191\pi\) | ||||
−0.852327 | + | 0.523009i | \(0.824809\pi\) | |||||||
\(174\) | −5.16118e23 | −1.53809 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.71672e22 | 0.177531 | ||||||||
\(177\) | − 2.12264e23i | − 0.528636i | ||||||||
\(178\) | 3.94762e22i | 0.0926671i | ||||||||
\(179\) | −4.40276e23 | −0.974470 | −0.487235 | − | 0.873271i | \(-0.661995\pi\) | ||||
−0.487235 | + | 0.873271i | \(0.661995\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.24093e23 | −1.62312 | −0.811561 | − | 0.584268i | \(-0.801382\pi\) | ||||
−0.811561 | + | 0.584268i | \(0.801382\pi\) | |||||||
\(182\) | − 5.18334e22i | − 0.0963519i | ||||||||
\(183\) | 3.10726e22i | 0.0545306i | ||||||||
\(184\) | 2.65312e23 | 0.439714 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.70510e23 | 0.400219 | ||||||||
\(187\) | − 6.91389e23i | − 0.966909i | ||||||||
\(188\) | − 3.32590e23i | − 0.439796i | ||||||||
\(189\) | −3.19686e24 | −3.99829 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.97957e23 | 0.333659 | 0.166830 | − | 0.985986i | \(-0.446647\pi\) | ||||
0.166830 | + | 0.985986i | \(0.446647\pi\) | |||||||
\(192\) | 2.24606e23i | 0.238100i | ||||||||
\(193\) | − 9.58444e23i | − 0.962088i | −0.876696 | − | 0.481044i | \(-0.840258\pi\) | ||||
0.876696 | − | 0.481044i | \(-0.159742\pi\) | |||||||
\(194\) | −5.59682e23 | −0.532136 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.87671e23 | 0.330959 | ||||||||
\(197\) | − 7.67214e23i | − 0.620899i | −0.950590 | − | 0.310450i | \(-0.899520\pi\) | ||||
0.950590 | − | 0.310450i | \(-0.100480\pi\) | |||||||
\(198\) | 1.71977e24i | 1.31973i | ||||||||
\(199\) | 2.93227e23 | 0.213426 | 0.106713 | − | 0.994290i | \(-0.465967\pi\) | ||||
0.106713 | + | 0.994290i | \(0.465967\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.69735e24 | 1.11227 | ||||||||
\(202\) | − 1.91552e24i | − 1.19151i | ||||||||
\(203\) | 2.49265e24i | 1.47215i | ||||||||
\(204\) | 2.31200e24 | 1.29679 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.84206e23 | 0.447659 | ||||||||
\(207\) | 6.79314e24i | 3.26875i | ||||||||
\(208\) | − 5.77664e22i | − 0.0264247i | ||||||||
\(209\) | 2.76876e24 | 1.20434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.05920e24 | −0.810464 | −0.405232 | − | 0.914214i | \(-0.632809\pi\) | ||||
−0.405232 | + | 0.914214i | \(0.632809\pi\) | |||||||
\(212\) | 1.51948e24i | 0.569074i | ||||||||
\(213\) | 5.97779e24i | 2.13086i | ||||||||
\(214\) | −3.74462e24 | −1.27076 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.56278e24 | −1.09654 | ||||||||
\(217\) | − 1.30646e24i | − 0.383062i | ||||||||
\(218\) | − 6.55303e23i | − 0.183083i | ||||||||
\(219\) | −4.60720e24 | −1.22680 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.94622e23 | −0.143920 | ||||||||
\(222\) | 2.71147e24i | 0.625891i | ||||||||
\(223\) | 3.95841e24i | 0.871605i | 0.900042 | + | 0.435803i | \(0.143535\pi\) | ||||
−0.900042 | + | 0.435803i | \(0.856465\pi\) | |||||||
\(224\) | 1.08476e24 | 0.227892 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.31880e23 | −0.120919 | ||||||||
\(227\) | − 6.66876e23i | − 0.121835i | −0.998143 | − | 0.0609177i | \(-0.980597\pi\) | ||||
0.998143 | − | 0.0609177i | \(-0.0194027\pi\) | |||||||
\(228\) | 9.25869e24i | 1.61523i | ||||||||
\(229\) | 7.22731e24 | 1.20421 | 0.602107 | − | 0.798415i | \(-0.294328\pi\) | ||||
0.602107 | + | 0.798415i | \(0.294328\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.14660e25 | 1.74376 | ||||||||
\(232\) | 2.77797e24i | 0.403742i | ||||||||
\(233\) | − 1.07597e25i | − 1.49474i | −0.664410 | − | 0.747368i | \(-0.731317\pi\) | ||||
0.664410 | − | 0.747368i | \(-0.268683\pi\) | |||||||
\(234\) | 1.47907e24 | 0.196437 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.14249e24 | −0.138764 | ||||||||
\(237\) | − 1.82221e25i | − 2.11709i | ||||||||
\(238\) | − 1.11661e25i | − 1.24120i | ||||||||
\(239\) | −3.16911e24 | −0.337101 | −0.168550 | − | 0.985693i | \(-0.553909\pi\) | ||||
−0.168550 | + | 0.985693i | \(0.553909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.75468e24 | −0.171009 | −0.0855043 | − | 0.996338i | \(-0.527250\pi\) | ||||
−0.0855043 | + | 0.996338i | \(0.527250\pi\) | |||||||
\(242\) | 3.75653e24i | 0.350530i | ||||||||
\(243\) | − 3.51977e25i | − 3.14520i | ||||||||
\(244\) | 1.67246e23 | 0.0143140 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.34153e25 | −1.05386 | ||||||||
\(247\) | − 2.38124e24i | − 0.179261i | ||||||||
\(248\) | − 1.45600e24i | − 0.105056i | ||||||||
\(249\) | 3.91295e25 | 2.70652 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.75868e25 | 1.11844 | 0.559221 | − | 0.829019i | \(-0.311100\pi\) | ||||
0.559221 | + | 0.829019i | \(0.311100\pi\) | |||||||
\(252\) | 2.77746e25i | 1.69411i | ||||||||
\(253\) | − 1.50944e25i | − 0.883179i | ||||||||
\(254\) | −1.43775e25 | −0.807104 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.20893e24 | 0.0625000 | ||||||||
\(257\) | − 9.88264e24i | − 0.490428i | −0.969469 | − | 0.245214i | \(-0.921142\pi\) | ||||
0.969469 | − | 0.245214i | \(-0.0788582\pi\) | |||||||
\(258\) | − 7.39392e24i | − 0.352264i | ||||||||
\(259\) | 1.30954e25 | 0.599059 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.11280e25 | −3.00134 | ||||||||
\(262\) | − 2.08291e25i | − 0.844321i | ||||||||
\(263\) | 1.60390e25i | 0.624656i | 0.949974 | + | 0.312328i | \(0.101109\pi\) | ||||
−0.949974 | + | 0.312328i | \(0.898891\pi\) | |||||||
\(264\) | 1.27785e25 | 0.478231 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.47159e25 | 1.54598 | ||||||||
\(267\) | 7.51030e24i | 0.249626i | ||||||||
\(268\) | − 9.13585e24i | − 0.291967i | ||||||||
\(269\) | −1.76073e25 | −0.541122 | −0.270561 | − | 0.962703i | \(-0.587209\pi\) | ||||
−0.270561 | + | 0.962703i | \(0.587209\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.45015e25 | 0.980981 | 0.490490 | − | 0.871447i | \(-0.336818\pi\) | ||||
0.490490 | + | 0.871447i | \(0.336818\pi\) | |||||||
\(272\) | − 1.24441e25i | − 0.340402i | ||||||||
\(273\) | − 9.86125e24i | − 0.259552i | ||||||||
\(274\) | −1.12733e24 | −0.0285543 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.04753e25 | 1.18450 | ||||||||
\(277\) | − 2.59482e25i | − 0.586231i | −0.956077 | − | 0.293116i | \(-0.905308\pi\) | ||||
0.956077 | − | 0.293116i | \(-0.0946921\pi\) | |||||||
\(278\) | 4.24533e25i | 0.923508i | ||||||||
\(279\) | 3.72799e25 | 0.780964 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.82254e25 | 1.52031 | 0.760154 | − | 0.649743i | \(-0.225124\pi\) | ||||
0.760154 | + | 0.649743i | \(0.225124\pi\) | |||||||
\(282\) | − 6.32748e25i | − 1.18472i | ||||||||
\(283\) | − 8.38167e24i | − 0.151207i | −0.997138 | − | 0.0756037i | \(-0.975912\pi\) | ||||
0.997138 | − | 0.0756037i | \(-0.0240884\pi\) | |||||||
\(284\) | 3.21750e25 | 0.559340 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.28649e24 | −0.0530749 | ||||||||
\(287\) | 6.47908e25i | 1.00868i | ||||||||
\(288\) | 3.09537e25i | 0.464613i | ||||||||
\(289\) | −5.90026e25 | −0.853973 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.06479e26 | −1.43346 | ||||||||
\(292\) | 2.47979e25i | 0.322029i | ||||||||
\(293\) | − 4.97478e25i | − 0.623252i | −0.950205 | − | 0.311626i | \(-0.899126\pi\) | ||||
0.950205 | − | 0.311626i | \(-0.100874\pi\) | |||||||
\(294\) | 7.37540e25 | 0.891535 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.45943e25 | 0.164293 | ||||||||
\(297\) | 2.02697e26i | 2.20244i | ||||||||
\(298\) | 9.84688e25i | 1.03283i | ||||||||
\(299\) | −1.29817e25 | −0.131458 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.57098e25 | −0.337163 | ||||||||
\(302\) | 1.15807e26i | 1.05599i | ||||||||
\(303\) | − 3.64425e26i | − 3.20967i | ||||||||
\(304\) | 4.98342e25 | 0.423990 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.18624e26 | 2.53048 | ||||||||
\(307\) | − 1.41280e26i | − 1.08425i | −0.840299 | − | 0.542123i | \(-0.817621\pi\) | ||||
0.840299 | − | 0.542123i | \(-0.182379\pi\) | |||||||
\(308\) | − 6.17151e25i | − 0.457730i | ||||||||
\(309\) | 1.68219e26 | 1.20590 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.39904e26 | 0.937232 | 0.468616 | − | 0.883402i | \(-0.344753\pi\) | ||||
0.468616 | + | 0.883402i | \(0.344753\pi\) | |||||||
\(312\) | − 1.09900e25i | − 0.0711827i | ||||||||
\(313\) | 2.79550e26i | 1.75083i | 0.483373 | + | 0.875414i | \(0.339411\pi\) | ||||
−0.483373 | + | 0.875414i | \(0.660589\pi\) | |||||||
\(314\) | 3.84771e25 | 0.233045 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.80789e25 | −0.555727 | ||||||||
\(317\) | − 1.16992e26i | − 0.641259i | −0.947205 | − | 0.320629i | \(-0.896106\pi\) | ||||
0.947205 | − | 0.320629i | \(-0.103894\pi\) | |||||||
\(318\) | 2.89079e26i | 1.53297i | ||||||||
\(319\) | 1.58046e26 | 0.810928 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.12409e26 | −3.42315 | ||||||||
\(322\) | − 2.43776e26i | − 1.13372i | ||||||||
\(323\) | − 5.12972e26i | − 2.30923i | ||||||||
\(324\) | −3.76265e26 | −1.63973 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.60028e26 | −1.06227 | ||||||||
\(327\) | − 1.24671e26i | − 0.493188i | ||||||||
\(328\) | 7.22070e25i | 0.276633i | ||||||||
\(329\) | −3.05593e26 | −1.13393 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.83627e26 | −1.33572 | −0.667859 | − | 0.744288i | \(-0.732789\pi\) | ||||
−0.667859 | + | 0.744288i | \(0.732789\pi\) | |||||||
\(332\) | − 2.10612e26i | − 0.710448i | ||||||||
\(333\) | 3.73677e26i | 1.22133i | ||||||||
\(334\) | −8.07001e25 | −0.255585 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.06374e26 | 0.613894 | ||||||||
\(337\) | 1.36118e26i | 0.392465i | 0.980557 | + | 0.196233i | \(0.0628708\pi\) | ||||
−0.980557 | + | 0.196233i | \(0.937129\pi\) | |||||||
\(338\) | − 2.50168e26i | − 0.699207i | ||||||||
\(339\) | −1.20214e26 | −0.325731 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.28360e25 | −0.211008 | ||||||||
\(342\) | 1.27597e27i | 3.15186i | ||||||||
\(343\) | 1.81934e26i | 0.435839i | ||||||||
\(344\) | −3.97973e25 | −0.0924676 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.38316e26 | 0.739646 | ||||||||
\(347\) | 2.49928e26i | 0.530097i | 0.964235 | + | 0.265048i | \(0.0853879\pi\) | ||||
−0.964235 | + | 0.265048i | \(0.914612\pi\) | |||||||
\(348\) | 5.28505e26i | 1.08759i | ||||||||
\(349\) | −1.05322e26 | −0.210307 | −0.105153 | − | 0.994456i | \(-0.533533\pi\) | ||||
−0.105153 | + | 0.994456i | \(0.533533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.74327e26 | 0.327824 | ||||||||
\(352\) | − 6.87792e25i | − 0.125533i | ||||||||
\(353\) | 1.44843e26i | 0.256604i | 0.991735 | + | 0.128302i | \(0.0409527\pi\) | ||||
−0.991735 | + | 0.128302i | \(0.959047\pi\) | |||||||
\(354\) | −2.17358e26 | −0.373802 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.04236e25 | 0.0655255 | ||||||||
\(357\) | − 2.12433e27i | − 3.34353i | ||||||||
\(358\) | 4.50843e26i | 0.689055i | ||||||||
\(359\) | −5.68219e25 | −0.0843382 | −0.0421691 | − | 0.999110i | \(-0.513427\pi\) | ||||
−0.0421691 | + | 0.999110i | \(0.513427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.34005e27 | 1.87627 | ||||||||
\(362\) | 8.43871e26i | 1.14772i | ||||||||
\(363\) | 7.14675e26i | 0.944254i | ||||||||
\(364\) | −5.30774e25 | −0.0681311 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.18183e25 | 0.0385590 | ||||||||
\(367\) | 3.29729e25i | 0.0388296i | 0.999812 | + | 0.0194148i | \(0.00618032\pi\) | ||||
−0.999812 | + | 0.0194148i | \(0.993820\pi\) | |||||||
\(368\) | − 2.71680e26i | − 0.310924i | ||||||||
\(369\) | −1.84881e27 | −2.05644 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.39614e27 | 1.46725 | ||||||||
\(372\) | − 2.77003e26i | − 0.282998i | ||||||||
\(373\) | 6.24564e25i | 0.0620346i | 0.999519 | + | 0.0310173i | \(0.00987470\pi\) | ||||
−0.999519 | + | 0.0310173i | \(0.990125\pi\) | |||||||
\(374\) | −7.07983e26 | −0.683708 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.40572e26 | −0.310983 | ||||||||
\(377\) | − 1.35926e26i | − 0.120703i | ||||||||
\(378\) | 3.27359e27i | 2.82722i | ||||||||
\(379\) | −1.65025e27 | −1.38624 | −0.693119 | − | 0.720823i | \(-0.743764\pi\) | ||||
−0.693119 | + | 0.720823i | \(0.743764\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.73530e27 | −2.17417 | ||||||||
\(382\) | − 3.05108e26i | − 0.235933i | ||||||||
\(383\) | − 1.20420e27i | − 0.905967i | −0.891519 | − | 0.452983i | \(-0.850360\pi\) | ||||
0.891519 | − | 0.452983i | \(-0.149640\pi\) | |||||||
\(384\) | 2.29997e26 | 0.168362 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.81446e26 | −0.680299 | ||||||||
\(387\) | − 1.01898e27i | − 0.687387i | ||||||||
\(388\) | 5.73114e26i | 0.376277i | ||||||||
\(389\) | −1.68483e26 | −0.107667 | −0.0538337 | − | 0.998550i | \(-0.517144\pi\) | ||||
−0.0538337 | + | 0.998550i | \(0.517144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.79655e27 | −1.69343 | ||||||||
\(392\) | − 3.96975e26i | − 0.234024i | ||||||||
\(393\) | − 3.96272e27i | − 2.27442i | ||||||||
\(394\) | −7.85627e26 | −0.439042 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.76104e27 | 0.933192 | ||||||||
\(397\) | 1.48612e27i | 0.766925i | 0.923557 | + | 0.383462i | \(0.125268\pi\) | ||||
−0.923557 | + | 0.383462i | \(0.874732\pi\) | |||||||
\(398\) | − 3.00264e26i | − 0.150915i | ||||||||
\(399\) | 8.50715e27 | 4.16456 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.25371e26 | −0.290484 | −0.145242 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145242 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(402\) | − 1.73808e27i | − 0.786497i | ||||||||
\(403\) | 7.12423e25i | 0.0314076i | ||||||||
\(404\) | −1.96149e27 | −0.842524 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.55248e27 | 1.04097 | ||||||||
\(407\) | − 8.30310e26i | − 0.329989i | ||||||||
\(408\) | − 2.36748e27i | − 0.916970i | ||||||||
\(409\) | −3.35895e27 | −1.26797 | −0.633985 | − | 0.773345i | \(-0.718582\pi\) | ||||
−0.633985 | + | 0.773345i | \(0.718582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.14474e26 | −0.0769192 | ||||||||
\(412\) | − 9.05427e26i | − 0.316543i | ||||||||
\(413\) | 1.04976e27i | 0.357777i | ||||||||
\(414\) | 6.95617e27 | 2.31136 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.91528e25 | −0.0186851 | ||||||||
\(417\) | 8.07668e27i | 2.48774i | ||||||||
\(418\) | − 2.83521e27i | − 0.851597i | ||||||||
\(419\) | 1.39454e27 | 0.408492 | 0.204246 | − | 0.978920i | \(-0.434526\pi\) | ||||
0.204246 | + | 0.978920i | \(0.434526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.26111e27 | −1.46594 | −0.732968 | − | 0.680263i | \(-0.761866\pi\) | ||||
−0.732968 | + | 0.680263i | \(0.761866\pi\) | |||||||
\(422\) | 2.10862e27i | 0.573084i | ||||||||
\(423\) | − 8.72011e27i | − 2.31179i | ||||||||
\(424\) | 1.55595e27 | 0.402396 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.12126e27 | 1.50675 | ||||||||
\(427\) | − 1.53670e26i | − 0.0369060i | ||||||||
\(428\) | 3.83449e27i | 0.898561i | ||||||||
\(429\) | −6.25252e26 | −0.142973 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.99327e27 | −0.869595 | −0.434797 | − | 0.900528i | \(-0.643180\pi\) | ||||
−0.434797 | + | 0.900528i | \(0.643180\pi\) | |||||||
\(432\) | 3.64829e27i | 0.775372i | ||||||||
\(433\) | − 1.71947e27i | − 0.356674i | −0.983969 | − | 0.178337i | \(-0.942928\pi\) | ||||
0.983969 | − | 0.178337i | \(-0.0570717\pi\) | |||||||
\(434\) | −1.33782e27 | −0.270866 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.71030e26 | −0.129459 | ||||||||
\(437\) | − 1.11992e28i | − 2.10926i | ||||||||
\(438\) | 4.71777e27i | 0.867479i | ||||||||
\(439\) | −2.57641e27 | −0.462528 | −0.231264 | − | 0.972891i | \(-0.574286\pi\) | ||||
−0.231264 | + | 0.972891i | \(0.574286\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.01643e28 | 1.73969 | ||||||||
\(442\) | 6.08893e26i | 0.101767i | ||||||||
\(443\) | 1.26523e27i | 0.206504i | 0.994655 | + | 0.103252i | \(0.0329249\pi\) | ||||
−0.994655 | + | 0.103252i | \(0.967075\pi\) | |||||||
\(444\) | 2.77655e27 | 0.442572 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.05341e27 | 0.616318 | ||||||||
\(447\) | 1.87336e28i | 2.78222i | ||||||||
\(448\) | − 1.11080e27i | − 0.161144i | ||||||||
\(449\) | −3.20858e26 | −0.0454702 | −0.0227351 | − | 0.999742i | \(-0.507237\pi\) | ||||
−0.0227351 | + | 0.999742i | \(0.507237\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.10806e27 | 0.555626 | ||||||||
\(452\) | 6.47045e26i | 0.0855029i | ||||||||
\(453\) | 2.20321e28i | 2.84462i | ||||||||
\(454\) | −6.82881e26 | −0.0861506 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.48090e27 | 1.14214 | ||||||||
\(457\) | − 1.41432e28i | − 1.66506i | −0.553983 | − | 0.832528i | \(-0.686893\pi\) | ||||
0.553983 | − | 0.832528i | \(-0.313107\pi\) | |||||||
\(458\) | − 7.40076e27i | − 0.851508i | ||||||||
\(459\) | 3.75539e28 | 4.22300 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.08545e27 | 0.653782 | 0.326891 | − | 0.945062i | \(-0.393999\pi\) | ||||
0.326891 | + | 0.945062i | \(0.393999\pi\) | |||||||
\(462\) | − 1.17412e28i | − 1.23303i | ||||||||
\(463\) | − 6.53768e27i | − 0.671155i | −0.942013 | − | 0.335578i | \(-0.891069\pi\) | ||||
0.942013 | − | 0.335578i | \(-0.108931\pi\) | |||||||
\(464\) | 2.84464e27 | 0.285488 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.10180e28 | −1.05694 | ||||||||
\(467\) | − 9.77307e27i | − 0.916651i | −0.888784 | − | 0.458325i | \(-0.848449\pi\) | ||||
0.888784 | − | 0.458325i | \(-0.151551\pi\) | |||||||
\(468\) | − 1.51457e27i | − 0.138902i | ||||||||
\(469\) | −8.39428e27 | −0.752781 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.32022e27 | 0.627775 | ||||||||
\(472\) | 1.16991e27i | 0.0981212i | ||||||||
\(473\) | 2.26418e27i | 0.185724i | ||||||||
\(474\) | −1.86594e28 | −1.49701 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.14340e28 | −0.877661 | ||||||||
\(477\) | 3.98390e28i | 2.99134i | ||||||||
\(478\) | 3.24517e27i | 0.238366i | ||||||||
\(479\) | 1.53019e28 | 1.09957 | 0.549784 | − | 0.835307i | \(-0.314710\pi\) | ||||
0.549784 | + | 0.835307i | \(0.314710\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.14100e26 | −0.0491174 | ||||||||
\(482\) | 1.79679e27i | 0.120921i | ||||||||
\(483\) | − 4.63781e28i | − 3.05400i | ||||||||
\(484\) | 3.84668e27 | 0.247862 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.60424e28 | −2.22399 | ||||||||
\(487\) | − 2.24122e28i | − 1.35341i | −0.736254 | − | 0.676705i | \(-0.763407\pi\) | ||||
0.736254 | − | 0.676705i | \(-0.236593\pi\) | |||||||
\(488\) | − 1.71260e26i | − 0.0101215i | ||||||||
\(489\) | −4.94701e28 | −2.86154 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.97103e28 | 1.09229 | 0.546145 | − | 0.837691i | \(-0.316095\pi\) | ||||
0.546145 | + | 0.837691i | \(0.316095\pi\) | |||||||
\(492\) | 1.37373e28i | 0.745191i | ||||||||
\(493\) | − 2.92815e28i | − 1.55489i | ||||||||
\(494\) | −2.43839e27 | −0.126757 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.49095e27 | −0.0742856 | ||||||||
\(497\) | − 2.95633e28i | − 1.44215i | ||||||||
\(498\) | − 4.00686e28i | − 1.91380i | ||||||||
\(499\) | −3.08705e28 | −1.44374 | −0.721869 | − | 0.692030i | \(-0.756717\pi\) | ||||
−0.721869 | + | 0.692030i | \(0.756717\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.53531e28 | −0.688493 | ||||||||
\(502\) | − 1.80089e28i | − 0.790858i | ||||||||
\(503\) | 2.52448e28i | 1.08570i | 0.839831 | + | 0.542848i | \(0.182654\pi\) | ||||
−0.839831 | + | 0.542848i | \(0.817346\pi\) | |||||||
\(504\) | 2.84412e28 | 1.19792 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.54566e28 | −0.624502 | ||||||||
\(507\) | − 4.75941e28i | − 1.88352i | ||||||||
\(508\) | 1.47226e28i | 0.570709i | ||||||||
\(509\) | −2.42632e28 | −0.921323 | −0.460661 | − | 0.887576i | \(-0.652388\pi\) | ||||
−0.460661 | + | 0.887576i | \(0.652388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.27850e28 | 0.830291 | ||||||||
\(512\) | − 1.23794e27i | − 0.0441942i | ||||||||
\(513\) | 1.50389e29i | 5.25999i | ||||||||
\(514\) | −1.01198e28 | −0.346785 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.57138e27 | −0.249088 | ||||||||
\(517\) | 1.93761e28i | 0.624619i | ||||||||
\(518\) | − 1.34096e28i | − 0.423599i | ||||||||
\(519\) | 6.43643e28 | 1.99245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.28803e28 | −0.382939 | −0.191470 | − | 0.981499i | \(-0.561325\pi\) | ||||
−0.191470 | + | 0.981499i | \(0.561325\pi\) | |||||||
\(522\) | 7.28351e28i | 2.12227i | ||||||||
\(523\) | − 4.72268e28i | − 1.34872i | −0.738404 | − | 0.674359i | \(-0.764420\pi\) | ||||
0.738404 | − | 0.674359i | \(-0.235580\pi\) | |||||||
\(524\) | −2.13290e28 | −0.597025 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.64239e28 | 0.441699 | ||||||||
\(527\) | 1.53471e28i | 0.404591i | ||||||||
\(528\) | − 1.30852e28i | − 0.338160i | ||||||||
\(529\) | −2.15825e28 | −0.546785 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.99548e28 | −0.729415 | ||||||||
\(532\) | − 4.57891e28i | − 1.09318i | ||||||||
\(533\) | − 3.53309e27i | − 0.0827026i | ||||||||
\(534\) | 7.69055e27 | 0.176512 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.35511e27 | −0.206452 | ||||||||
\(537\) | 8.57723e28i | 1.85617i | ||||||||
\(538\) | 1.80299e28i | 0.382631i | ||||||||
\(539\) | −2.25850e28 | −0.470044 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.70978e28 | 0.342270 | 0.171135 | − | 0.985248i | \(-0.445257\pi\) | ||||
0.171135 | + | 0.985248i | \(0.445257\pi\) | |||||||
\(542\) | − 3.53295e28i | − 0.693658i | ||||||||
\(543\) | 1.60545e29i | 3.09172i | ||||||||
\(544\) | −1.27428e28 | −0.240700 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.00979e28 | −0.183531 | ||||||||
\(547\) | 6.17365e28i | 1.10072i | 0.834929 | + | 0.550358i | \(0.185509\pi\) | ||||
−0.834929 | + | 0.550358i | \(0.814491\pi\) | |||||||
\(548\) | 1.15439e27i | 0.0201909i | ||||||||
\(549\) | 4.38499e27 | 0.0752417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.17262e29 | 1.93671 | ||||||||
\(552\) | − 5.16867e28i | − 0.837565i | ||||||||
\(553\) | 9.01177e28i | 1.43284i | ||||||||
\(554\) | −2.65709e28 | −0.414528 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.34721e28 | 0.653019 | ||||||||
\(557\) | − 1.03162e29i | − 1.52069i | −0.649518 | − | 0.760346i | \(-0.725029\pi\) | ||||
0.649518 | − | 0.760346i | \(-0.274971\pi\) | |||||||
\(558\) | − 3.81747e28i | − 0.552225i | ||||||||
\(559\) | 1.94728e27 | 0.0276443 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.34693e29 | −1.84177 | ||||||||
\(562\) | − 8.01028e28i | − 1.07502i | ||||||||
\(563\) | 3.65428e28i | 0.481353i | 0.970605 | + | 0.240677i | \(0.0773693\pi\) | ||||
−0.970605 | + | 0.240677i | \(0.922631\pi\) | |||||||
\(564\) | −6.47934e28 | −0.837722 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.58283e27 | −0.106920 | ||||||||
\(567\) | 3.45723e29i | 4.22772i | ||||||||
\(568\) | − 3.29472e28i | − 0.395513i | ||||||||
\(569\) | −4.54287e28 | −0.535367 | −0.267683 | − | 0.963507i | \(-0.586258\pi\) | ||||
−0.267683 | + | 0.963507i | \(0.586258\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.49843e29 | 1.70200 | 0.850998 | − | 0.525168i | \(-0.175998\pi\) | ||||
0.850998 | + | 0.525168i | \(0.175998\pi\) | |||||||
\(572\) | 3.36537e27i | 0.0375297i | ||||||||
\(573\) | − 5.80464e28i | − 0.635553i | ||||||||
\(574\) | 6.63458e28 | 0.713245 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.16966e28 | 0.328531 | ||||||||
\(577\) | − 1.44438e29i | − 1.47006i | −0.678035 | − | 0.735029i | \(-0.737168\pi\) | ||||
0.678035 | − | 0.735029i | \(-0.262832\pi\) | |||||||
\(578\) | 6.04187e28i | 0.603850i | ||||||||
\(579\) | −1.86719e29 | −1.83258 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.93516e29 | −1.83175 | ||||||||
\(582\) | 1.09034e29i | 1.01361i | ||||||||
\(583\) | − 8.85223e28i | − 0.808226i | ||||||||
\(584\) | 2.53931e28 | 0.227709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.09417e28 | −0.440706 | ||||||||
\(587\) | − 1.82681e29i | − 1.55237i | −0.630508 | − | 0.776183i | \(-0.717154\pi\) | ||||
0.630508 | − | 0.776183i | \(-0.282846\pi\) | |||||||
\(588\) | − 7.55241e28i | − 0.630410i | ||||||||
\(589\) | −6.14597e28 | −0.503941 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.49465e29 | −1.18269 | ||||||||
\(592\) | − 1.49446e28i | − 0.116173i | ||||||||
\(593\) | − 1.28812e29i | − 0.983742i | −0.870668 | − | 0.491871i | \(-0.836313\pi\) | ||||
0.870668 | − | 0.491871i | \(-0.163687\pi\) | |||||||
\(594\) | 2.07561e29 | 1.55736 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.00832e29 | 0.730320 | ||||||||
\(597\) | − 5.71249e28i | − 0.406532i | ||||||||
\(598\) | 1.32933e28i | 0.0929545i | ||||||||
\(599\) | 1.90622e28 | 0.130976 | 0.0654879 | − | 0.997853i | \(-0.479140\pi\) | ||||
0.0654879 | + | 0.997853i | \(0.479140\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.02359e28 | −0.266951 | −0.133476 | − | 0.991052i | \(-0.542614\pi\) | ||||
−0.133476 | + | 0.991052i | \(0.542614\pi\) | |||||||
\(602\) | 3.65668e28i | 0.238410i | ||||||||
\(603\) | − 2.39531e29i | − 1.53472i | ||||||||
\(604\) | 1.18586e29 | 0.746700 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.73172e29 | −2.26958 | ||||||||
\(607\) | 1.34619e29i | 0.804681i | 0.915490 | + | 0.402340i | \(0.131803\pi\) | ||||
−0.915490 | + | 0.402340i | \(0.868197\pi\) | |||||||
\(608\) | − 5.10303e28i | − 0.299806i | ||||||||
\(609\) | 4.85606e29 | 2.80416 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.66642e28 | 0.0929719 | ||||||||
\(612\) | − 3.26271e29i | − 1.78932i | ||||||||
\(613\) | − 6.61541e28i | − 0.356633i | −0.983973 | − | 0.178316i | \(-0.942935\pi\) | ||||
0.983973 | − | 0.178316i | \(-0.0570651\pi\) | |||||||
\(614\) | −1.44671e29 | −0.766677 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.31963e28 | −0.323664 | ||||||||
\(617\) | − 5.23241e28i | − 0.263456i | −0.991286 | − | 0.131728i | \(-0.957948\pi\) | ||||
0.991286 | − | 0.131728i | \(-0.0420525\pi\) | |||||||
\(618\) | − 1.72256e29i | − 0.852700i | ||||||||
\(619\) | −1.15227e29 | −0.560793 | −0.280397 | − | 0.959884i | \(-0.590466\pi\) | ||||
−0.280397 | + | 0.959884i | \(0.590466\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.19873e29 | 3.85731 | ||||||||
\(622\) | − 1.43262e29i | − 0.662723i | ||||||||
\(623\) | − 3.71424e28i | − 0.168945i | ||||||||
\(624\) | −1.12538e28 | −0.0503337 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.86259e29 | 1.23802 | ||||||||
\(627\) | − 5.39395e29i | − 2.29402i | ||||||||
\(628\) | − 3.94005e28i | − 0.164788i | ||||||||
\(629\) | −1.53833e29 | −0.632727 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.82557e29 | −0.726257 | −0.363128 | − | 0.931739i | \(-0.618291\pi\) | ||||
−0.363128 | + | 0.931739i | \(0.618291\pi\) | |||||||
\(632\) | 1.00433e29i | 0.392958i | ||||||||
\(633\) | 4.01163e29i | 1.54377i | ||||||||
\(634\) | −1.19800e29 | −0.453438 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.96017e29 | 1.08397 | ||||||||
\(637\) | 1.94240e28i | 0.0699641i | ||||||||
\(638\) | − 1.61840e29i | − 0.573413i | ||||||||
\(639\) | 8.43591e29 | 2.94017 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.06750e29 | 1.37189 | 0.685943 | − | 0.727655i | \(-0.259390\pi\) | ||||
0.685943 | + | 0.727655i | \(0.259390\pi\) | |||||||
\(642\) | 7.29506e29i | 2.42053i | ||||||||
\(643\) | − 1.10344e29i | − 0.360192i | −0.983649 | − | 0.180096i | \(-0.942359\pi\) | ||||
0.983649 | − | 0.180096i | \(-0.0576409\pi\) | |||||||
\(644\) | −2.49627e29 | −0.801659 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.25283e29 | −1.63287 | ||||||||
\(647\) | 5.65654e29i | 1.73004i | 0.501737 | + | 0.865020i | \(0.332694\pi\) | ||||
−0.501737 | + | 0.865020i | \(0.667306\pi\) | |||||||
\(648\) | 3.85295e29i | 1.15946i | ||||||||
\(649\) | 6.65597e28 | 0.197080 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.54518e29 | −0.729656 | ||||||||
\(652\) | 2.66269e29i | 0.751140i | ||||||||
\(653\) | − 9.98139e28i | − 0.277078i | −0.990357 | − | 0.138539i | \(-0.955759\pi\) | ||||
0.990357 | − | 0.138539i | \(-0.0442407\pi\) | |||||||
\(654\) | −1.27663e29 | −0.348736 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.39399e28 | 0.195609 | ||||||||
\(657\) | 6.50172e29i | 1.69275i | ||||||||
\(658\) | 3.12927e29i | 0.801809i | ||||||||
\(659\) | −4.27384e29 | −1.07776 | −0.538880 | − | 0.842383i | \(-0.681152\pi\) | ||||
−0.538880 | + | 0.842383i | \(0.681152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.06580e29 | 0.260352 | 0.130176 | − | 0.991491i | \(-0.458446\pi\) | ||||
0.130176 | + | 0.991491i | \(0.458446\pi\) | |||||||
\(662\) | 3.92834e29i | 0.944495i | ||||||||
\(663\) | 1.15841e29i | 0.274139i | ||||||||
\(664\) | −2.15666e29 | −0.502362 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.82645e29 | 0.863608 | ||||||||
\(667\) | − 6.39271e29i | − 1.42025i | ||||||||
\(668\) | 8.26369e28i | 0.180726i | ||||||||
\(669\) | 7.71157e29 | 1.66023 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.74344e27 | −0.0203295 | ||||||||
\(672\) | − 2.11327e29i | − 0.434089i | ||||||||
\(673\) | − 9.20636e29i | − 1.86179i | −0.365292 | − | 0.930893i | \(-0.619031\pi\) | ||||
0.365292 | − | 0.930893i | \(-0.380969\pi\) | |||||||
\(674\) | 1.39385e29 | 0.277515 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.56172e29 | −0.494414 | ||||||||
\(677\) | 1.03701e29i | 0.197062i | 0.995134 | + | 0.0985309i | \(0.0314143\pi\) | ||||
−0.995134 | + | 0.0985309i | \(0.968586\pi\) | |||||||
\(678\) | 1.23100e29i | 0.230327i | ||||||||
\(679\) | 5.26593e29 | 0.970159 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.29917e29 | −0.232072 | ||||||||
\(682\) | 8.48241e28i | 0.149205i | ||||||||
\(683\) | 1.05066e30i | 1.81988i | 0.414735 | + | 0.909942i | \(0.363874\pi\) | ||||
−0.414735 | + | 0.909942i | \(0.636126\pi\) | |||||||
\(684\) | 1.30660e30 | 2.22870 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.86301e29 | 0.308185 | ||||||||
\(687\) | − 1.40799e30i | − 2.29378i | ||||||||
\(688\) | 4.07524e28i | 0.0653844i | ||||||||
\(689\) | −7.61327e28 | −0.120301 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.09599e29 | −0.321270 | −0.160635 | − | 0.987014i | \(-0.551354\pi\) | ||||
−0.160635 | + | 0.987014i | \(0.551354\pi\) | |||||||
\(692\) | − 3.46436e29i | − 0.523009i | ||||||||
\(693\) | − 1.61810e30i | − 2.40606i | ||||||||
\(694\) | 2.55926e29 | 0.374835 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.41189e29 | 0.769046 | ||||||||
\(697\) | − 7.61105e29i | − 1.06537i | ||||||||
\(698\) | 1.07850e29i | 0.148709i | ||||||||
\(699\) | −2.09616e30 | −2.84717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.09765e29 | −1.19920 | −0.599598 | − | 0.800301i | \(-0.704673\pi\) | ||||
−0.599598 | + | 0.800301i | \(0.704673\pi\) | |||||||
\(702\) | − 1.78511e29i | − 0.231806i | ||||||||
\(703\) | − 6.16043e29i | − 0.788098i | ||||||||
\(704\) | −7.04299e28 | −0.0887655 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.48319e29 | 0.181446 | ||||||||
\(707\) | 1.80228e30i | 2.17229i | ||||||||
\(708\) | 2.22575e29i | 0.264318i | ||||||||
\(709\) | 1.17415e30 | 1.37385 | 0.686925 | − | 0.726728i | \(-0.258960\pi\) | ||||
0.686925 | + | 0.726728i | \(0.258960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.57151e30 | −2.92118 | ||||||||
\(712\) | − 4.13938e28i | − 0.0463335i | ||||||||
\(713\) | 3.35057e29i | 0.369555i | ||||||||
\(714\) | −2.17531e30 | −2.36423 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.61663e29 | 0.487235 | ||||||||
\(717\) | 6.17390e29i | 0.642108i | ||||||||
\(718\) | 5.81857e28i | 0.0596361i | ||||||||
\(719\) | −2.38367e29 | −0.240765 | −0.120382 | − | 0.992728i | \(-0.538412\pi\) | ||||
−0.120382 | + | 0.992728i | \(0.538412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.31932e29 | −0.816145 | ||||||||
\(722\) | − 1.37221e30i | − 1.32673i | ||||||||
\(723\) | 3.41837e29i | 0.325737i | ||||||||
\(724\) | 8.64124e29 | 0.811561 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.31827e29 | 0.667688 | ||||||||
\(727\) | 1.60120e30i | 1.43991i | 0.694022 | + | 0.719954i | \(0.255837\pi\) | ||||
−0.694022 | + | 0.719954i | \(0.744163\pi\) | |||||||
\(728\) | 5.43513e28i | 0.0481760i | ||||||||
\(729\) | −3.10350e30 | −2.71152 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.19487e29 | 0.356112 | ||||||||
\(732\) | − 3.25819e28i | − 0.0272653i | ||||||||
\(733\) | 8.02614e28i | 0.0662087i | 0.999452 | + | 0.0331043i | \(0.0105394\pi\) | ||||
−0.999452 | + | 0.0331043i | \(0.989461\pi\) | |||||||
\(734\) | 3.37642e28 | 0.0274567 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.78200e29 | −0.219857 | ||||||||
\(737\) | 5.32238e29i | 0.414665i | ||||||||
\(738\) | 1.89318e30i | 1.45412i | ||||||||
\(739\) | −2.07121e30 | −1.56840 | −0.784200 | − | 0.620508i | \(-0.786927\pi\) | ||||
−0.784200 | + | 0.620508i | \(0.786927\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.63901e29 | −0.341456 | ||||||||
\(742\) | − 1.42965e30i | − 1.03750i | ||||||||
\(743\) | 2.00787e30i | 1.43666i | 0.695704 | + | 0.718329i | \(0.255093\pi\) | ||||
−0.695704 | + | 0.718329i | \(0.744907\pi\) | |||||||
\(744\) | −2.83651e29 | −0.200110 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.39554e28 | 0.0438651 | ||||||||
\(747\) | − 5.52199e30i | − 3.73447i | ||||||||
\(748\) | 7.24974e29i | 0.483455i | ||||||||
\(749\) | 3.52324e30 | 2.31677 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.68196e30 | 1.71488 | 0.857440 | − | 0.514584i | \(-0.172054\pi\) | ||||
0.857440 | + | 0.514584i | \(0.172054\pi\) | |||||||
\(752\) | 3.48745e29i | 0.219898i | ||||||||
\(753\) | − 3.42617e30i | − 2.13040i | ||||||||
\(754\) | −1.39188e29 | −0.0853501 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.35215e30 | 1.99915 | ||||||||
\(757\) | 2.29494e30i | 1.34979i | 0.737915 | + | 0.674894i | \(0.235811\pi\) | ||||
−0.737915 | + | 0.674894i | \(0.764189\pi\) | |||||||
\(758\) | 1.68986e30i | 0.980219i | ||||||||
\(759\) | −2.94060e30 | −1.68228 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.17369e29 | 0.176614 | 0.0883072 | − | 0.996093i | \(-0.471854\pi\) | ||||
0.0883072 | + | 0.996093i | \(0.471854\pi\) | |||||||
\(762\) | 2.80095e30i | 1.53737i | ||||||||
\(763\) | 6.16561e29i | 0.333786i | ||||||||
\(764\) | −3.12430e29 | −0.166830 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.23310e30 | −0.640615 | ||||||||
\(767\) | − 5.72440e28i | − 0.0293345i | ||||||||
\(768\) | − 2.35517e29i | − 0.119050i | ||||||||
\(769\) | −3.31592e30 | −1.65340 | −0.826699 | − | 0.562644i | \(-0.809784\pi\) | ||||
−0.826699 | + | 0.562644i | \(0.809784\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.92528e30 | −0.934166 | ||||||||
\(772\) | 1.00500e30i | 0.481044i | ||||||||
\(773\) | 2.86833e29i | 0.135439i | 0.997704 | + | 0.0677196i | \(0.0215723\pi\) | ||||
−0.997704 | + | 0.0677196i | \(0.978428\pi\) | |||||||
\(774\) | −1.04344e30 | −0.486056 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.86869e29 | 0.266068 | ||||||||
\(777\) | − 2.55117e30i | − 1.14109i | ||||||||
\(778\) | 1.72526e29i | 0.0761323i | ||||||||
\(779\) | 3.04795e30 | 1.32698 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.87446e30 | −0.794402 | ||||||||
\(782\) | 2.86367e30i | 1.19743i | ||||||||
\(783\) | 8.58454e30i | 3.54175i | ||||||||
\(784\) | −4.06503e29 | −0.165480 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.05782e30 | −1.60826 | ||||||||
\(787\) | 1.37451e30i | 0.537544i | 0.963204 | + | 0.268772i | \(0.0866179\pi\) | ||||
−0.963204 | + | 0.268772i | \(0.913382\pi\) | |||||||
\(788\) | 8.04482e29i | 0.310450i | ||||||||
\(789\) | 3.12463e30 | 1.18984 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.94523e29 | 0.220453 | ||||||||
\(792\) | − 1.80331e30i | − 0.659866i | ||||||||
\(793\) | 8.37975e27i | 0.00302596i | ||||||||
\(794\) | 1.52178e30 | 0.542298 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.07471e29 | −0.106713 | ||||||||
\(797\) | − 4.30808e30i | − 1.47561i | −0.675014 | − | 0.737805i | \(-0.735862\pi\) | ||||
0.675014 | − | 0.737805i | \(-0.264138\pi\) | |||||||
\(798\) | − 8.71132e30i | − 2.94479i | ||||||||
\(799\) | 3.58983e30 | 1.19766 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.05986e30 | 0.344435 | ||||||||
\(802\) | 6.40380e29i | 0.205403i | ||||||||
\(803\) | − 1.44468e30i | − 0.457361i | ||||||||
\(804\) | −1.77980e30 | −0.556137 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.29521e28 | 0.0222085 | ||||||||
\(807\) | 3.43017e30i | 1.03073i | ||||||||
\(808\) | 2.00857e30i | 0.595755i | ||||||||
\(809\) | 8.36783e29 | 0.244993 | 0.122496 | − | 0.992469i | \(-0.460910\pi\) | ||||
0.122496 | + | 0.992469i | \(0.460910\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.30696e30 | 0.943432 | 0.471716 | − | 0.881751i | \(-0.343635\pi\) | ||||
0.471716 | + | 0.881751i | \(0.343635\pi\) | |||||||
\(812\) | − 2.61374e30i | − 0.736077i | ||||||||
\(813\) | − 6.72140e30i | − 1.86857i | ||||||||
\(814\) | −8.50237e29 | −0.233337 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.42430e30 | −0.648396 | ||||||||
\(817\) | 1.67989e30i | 0.443557i | ||||||||
\(818\) | 3.43957e30i | 0.896591i | ||||||||
\(819\) | −1.39163e30 | −0.358131 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.58969e30 | 1.90380 | 0.951899 | − | 0.306413i | \(-0.0991290\pi\) | ||||
0.951899 | + | 0.306413i | \(0.0991290\pi\) | |||||||
\(822\) | 2.19621e29i | 0.0543901i | ||||||||
\(823\) | − 5.61508e30i | − 1.37296i | −0.727149 | − | 0.686479i | \(-0.759155\pi\) | ||||
0.727149 | − | 0.686479i | \(-0.240845\pi\) | |||||||
\(824\) | −9.27157e29 | −0.223830 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.07495e30 | 0.252987 | ||||||||
\(827\) | 5.39629e30i | 1.25397i | 0.779031 | + | 0.626985i | \(0.215711\pi\) | ||||
−0.779031 | + | 0.626985i | \(0.784289\pi\) | |||||||
\(828\) | − 7.12312e30i | − 1.63437i | ||||||||
\(829\) | 4.47440e30 | 1.01371 | 0.506853 | − | 0.862032i | \(-0.330809\pi\) | ||||
0.506853 | + | 0.862032i | \(0.330809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.05508e30 | −1.11665 | ||||||||
\(832\) | 6.05725e28i | 0.0132124i | ||||||||
\(833\) | 4.18436e30i | 0.901273i | ||||||||
\(834\) | 8.27052e30 | 1.75910 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.90325e30 | −0.602170 | ||||||||
\(837\) | − 4.49937e30i | − 0.921582i | ||||||||
\(838\) | − 1.42801e30i | − 0.288847i | ||||||||
\(839\) | 1.16605e30 | 0.232925 | 0.116462 | − | 0.993195i | \(-0.462845\pi\) | ||||
0.116462 | + | 0.993195i | \(0.462845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.56068e30 | 0.304058 | ||||||||
\(842\) | 5.38738e30i | 1.03657i | ||||||||
\(843\) | − 1.52395e31i | − 2.89588i | ||||||||
\(844\) | 2.15923e30 | 0.405232 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.92939e30 | −1.63468 | ||||||||
\(847\) | − 3.53444e30i | − 0.639065i | ||||||||
\(848\) | − 1.59329e30i | − 0.284537i | ||||||||
\(849\) | −1.63287e30 | −0.288019 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.35846e30 | −0.577936 | ||||||||
\(852\) | − 6.26817e30i | − 1.06543i | ||||||||
\(853\) | 1.08909e31i | 1.82852i | 0.405123 | + | 0.914262i | \(0.367229\pi\) | ||||
−0.405123 | + | 0.914262i | \(0.632771\pi\) | |||||||
\(854\) | −1.57358e29 | −0.0260965 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.92651e30 | 0.635379 | ||||||||
\(857\) | 1.32603e30i | 0.211960i | 0.994368 | + | 0.105980i | \(0.0337979\pi\) | ||||
−0.994368 | + | 0.105980i | \(0.966202\pi\) | |||||||
\(858\) | 6.40258e29i | 0.101097i | ||||||||
\(859\) | 6.84458e30 | 1.06762 | 0.533812 | − | 0.845603i | \(-0.320759\pi\) | ||||
0.533812 | + | 0.845603i | \(0.320759\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.26222e31 | 1.92133 | ||||||||
\(862\) | 4.08910e30i | 0.614896i | ||||||||
\(863\) | − 3.45729e30i | − 0.513597i | −0.966465 | − | 0.256799i | \(-0.917332\pi\) | ||||
0.966465 | − | 0.256799i | \(-0.0826677\pi\) | |||||||
\(864\) | 3.73585e30 | 0.548270 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.76074e30 | −0.252206 | ||||||||
\(867\) | 1.14946e31i | 1.62664i | ||||||||
\(868\) | 1.36992e30i | 0.191531i | ||||||||
\(869\) | 5.71391e30 | 0.789270 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.57746e29 | 0.0617212 | ||||||||
\(872\) | 6.87135e29i | 0.0915416i | ||||||||
\(873\) | 1.50264e31i | 1.97790i | ||||||||
\(874\) | −1.14679e31 | −1.49147 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.83100e30 | 0.613400 | ||||||||
\(877\) | − 1.37025e30i | − 0.171912i | −0.996299 | − | 0.0859558i | \(-0.972606\pi\) | ||||
0.996299 | − | 0.0859558i | \(-0.0273944\pi\) | |||||||
\(878\) | 2.63825e30i | 0.327057i | ||||||||
\(879\) | −9.69160e30 | −1.18717 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.75611e30 | −0.449253 | −0.224627 | − | 0.974445i | \(-0.572116\pi\) | ||||
−0.224627 | + | 0.974445i | \(0.572116\pi\) | |||||||
\(882\) | − 1.04082e31i | − 1.23015i | ||||||||
\(883\) | − 6.64376e30i | − 0.775937i | −0.921673 | − | 0.387968i | \(-0.873177\pi\) | ||||
0.921673 | − | 0.387968i | \(-0.126823\pi\) | |||||||
\(884\) | 6.23507e29 | 0.0719602 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.29559e30 | 0.146021 | ||||||||
\(887\) | − 6.01786e30i | − 0.670261i | −0.942172 | − | 0.335131i | \(-0.891220\pi\) | ||||
0.942172 | − | 0.335131i | \(-0.108780\pi\) | |||||||
\(888\) | − 2.84318e30i | − 0.312945i | ||||||||
\(889\) | 1.35275e31 | 1.47146 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.19205e31 | 2.32882 | ||||||||
\(892\) | − 4.15070e30i | − 0.435803i | ||||||||
\(893\) | 1.43760e31i | 1.49175i | ||||||||
\(894\) | 1.91832e31 | 1.96733 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.13745e30 | −0.113946 | ||||||||
\(897\) | 2.52903e30i | 0.250400i | ||||||||
\(898\) | 3.28559e29i | 0.0321523i | ||||||||
\(899\) | −3.50824e30 | −0.339323 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.64006e31 | −1.54971 | ||||||||
\(902\) | − 4.20665e30i | − 0.392887i | ||||||||
\(903\) | 6.95680e30i | 0.642226i | ||||||||
\(904\) | 6.62574e29 | 0.0604597 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.25609e31 | 2.01145 | ||||||||
\(907\) | 1.42699e31i | 1.25761i | 0.777564 | + | 0.628804i | \(0.216455\pi\) | ||||
−0.777564 | + | 0.628804i | \(0.783545\pi\) | |||||||
\(908\) | 6.99270e29i | 0.0609177i | ||||||||
\(909\) | −5.14280e31 | −4.42873 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.18912e31 | 1.00065 | 0.500326 | − | 0.865837i | \(-0.333214\pi\) | ||||
0.500326 | + | 0.865837i | \(0.333214\pi\) | |||||||
\(912\) | − 9.70844e30i | − 0.807614i | ||||||||
\(913\) | 1.22699e31i | 1.00901i | ||||||||
\(914\) | −1.44827e31 | −1.17737 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.57838e30 | −0.602107 | ||||||||
\(917\) | 1.95977e31i | 1.53932i | ||||||||
\(918\) | − 3.84552e31i | − 2.98612i | ||||||||
\(919\) | 3.13990e30 | 0.241047 | 0.120524 | − | 0.992710i | \(-0.461543\pi\) | ||||
0.120524 | + | 0.992710i | \(0.461543\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.75234e31 | −2.06527 | ||||||||
\(922\) | − 6.23150e30i | − 0.462294i | ||||||||
\(923\) | 1.61211e30i | 0.118243i | ||||||||
\(924\) | −1.20230e31 | −0.871882 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.69458e30 | −0.474578 | ||||||||
\(927\) | − 2.37392e31i | − 1.66391i | ||||||||
\(928\) | − 2.91291e30i | − 0.201871i | ||||||||
\(929\) | −1.39588e30 | −0.0956498 | −0.0478249 | − | 0.998856i | \(-0.515229\pi\) | ||||
−0.0478249 | + | 0.998856i | \(0.515229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.67568e31 | −1.12259 | ||||||||
\(932\) | 1.12824e31i | 0.747368i | ||||||||
\(933\) | − 2.72554e31i | − 1.78524i | ||||||||
\(934\) | −1.00076e31 | −0.648170 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.55092e30 | −0.0982183 | ||||||||
\(937\) | − 2.22831e31i | − 1.39543i | −0.716374 | − | 0.697717i | \(-0.754199\pi\) | ||||
0.716374 | − | 0.697717i | \(-0.245801\pi\) | |||||||
\(938\) | 8.59574e30i | 0.532296i | ||||||||
\(939\) | 5.44604e31 | 3.33497 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.09348e31 | 1.25366 | 0.626828 | − | 0.779157i | \(-0.284353\pi\) | ||||
0.626828 | + | 0.779157i | \(0.284353\pi\) | |||||||
\(942\) | − 7.49590e30i | − 0.443904i | ||||||||
\(943\) | − 1.66164e31i | − 0.973114i | ||||||||
\(944\) | 1.19799e30 | 0.0693822 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.31852e30 | 0.131327 | ||||||||
\(947\) | 2.96424e31i | 1.66050i | 0.557393 | + | 0.830249i | \(0.311802\pi\) | ||||
−0.557393 | + | 0.830249i | \(0.688198\pi\) | |||||||
\(948\) | 1.91072e31i | 1.05855i | ||||||||
\(949\) | −1.24248e30 | −0.0680763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.27917e31 | −1.22147 | ||||||||
\(952\) | 1.17085e31i | 0.620600i | ||||||||
\(953\) | − 3.78184e30i | − 0.198257i | −0.995075 | − | 0.0991283i | \(-0.968395\pi\) | ||||
0.995075 | − | 0.0991283i | \(-0.0316054\pi\) | |||||||
\(954\) | 4.07952e31 | 2.11520 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.32305e30 | 0.168550 | ||||||||
\(957\) | − 3.07898e31i | − 1.54465i | ||||||||
\(958\) | − 1.56691e31i | − 0.777512i | ||||||||
\(959\) | 1.06069e30 | 0.0520584 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.89867e31 | −0.911707 | ||||||||
\(962\) | 7.31238e29i | 0.0347313i | ||||||||
\(963\) | 1.00536e32i | 4.72329i | ||||||||
\(964\) | 1.83991e30 | 0.0855043 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.74912e31 | −2.15950 | ||||||||
\(967\) | − 2.27343e31i | − 1.02259i | −0.859404 | − | 0.511297i | \(-0.829165\pi\) | ||||
0.859404 | − | 0.511297i | \(-0.170835\pi\) | |||||||
\(968\) | − 3.93900e30i | − 0.175265i | ||||||||
\(969\) | −9.99344e31 | −4.39861 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.59388e31 | 1.54797 | 0.773983 | − | 0.633206i | \(-0.218261\pi\) | ||||
0.773983 | + | 0.633206i | \(0.218261\pi\) | |||||||
\(972\) | 3.69074e31i | 1.57260i | ||||||||
\(973\) | − 3.99434e31i | − 1.68368i | ||||||||
\(974\) | −2.29500e31 | −0.957006 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.75370e29 | −0.00715702 | ||||||||
\(977\) | 8.76227e30i | 0.353772i | 0.984231 | + | 0.176886i | \(0.0566024\pi\) | ||||
−0.984231 | + | 0.176886i | \(0.943398\pi\) | |||||||
\(978\) | 5.06574e31i | 2.02341i | ||||||||
\(979\) | −2.35501e30 | −0.0930625 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75936e31 | −0.680504 | ||||||||
\(982\) | − 2.01834e31i | − 0.772365i | ||||||||
\(983\) | − 3.99246e31i | − 1.51157i | −0.654819 | − | 0.755786i | \(-0.727255\pi\) | ||||
0.654819 | − | 0.755786i | \(-0.272745\pi\) | |||||||
\(984\) | 1.40670e31 | 0.526929 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.99842e31 | −1.09947 | ||||||||
\(987\) | 5.95340e31i | 2.15991i | ||||||||
\(988\) | 2.49691e30i | 0.0896305i | ||||||||
\(989\) | 9.15821e30 | 0.325274 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.03797e31 | 1.40407 | 0.702037 | − | 0.712141i | \(-0.252274\pi\) | ||||
0.702037 | + | 0.712141i | \(0.252274\pi\) | |||||||
\(992\) | 1.52673e30i | 0.0525278i | ||||||||
\(993\) | 7.47361e31i | 2.54427i | ||||||||
\(994\) | −3.02728e31 | −1.01976 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.10302e31 | −1.35326 | ||||||||
\(997\) | 1.29884e31i | 0.423894i | 0.977281 | + | 0.211947i | \(0.0679803\pi\) | ||||
−0.977281 | + | 0.211947i | \(0.932020\pi\) | |||||||
\(998\) | 3.16114e31i | 1.02088i | ||||||||
\(999\) | 4.50996e31 | 1.44124 |
(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 | 50.22.b.d.49.1 | 4 | ||
5.2 | odd | 4 | 50.22.a.e.1.1 | 2 | |||
5.3 | odd | 4 | 10.22.a.c.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 50.22.b.d.49.4 | 4 | ||
20.3 | even | 4 | 80.22.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.22.a.c.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
50.22.a.e.1.1 | 2 | 5.2 | odd | 4 | |||
50.22.b.d.49.1 | 4 | 1.1 | even | 1 | trivial | ||
50.22.b.d.49.4 | 4 | 5.4 | even | 2 | inner | ||
80.22.a.b.1.1 | 2 | 20.3 | even | 4 |