Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,22,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
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: | yes |
Analytic conductor: | \(27.9477344287\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{474529}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 118632 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-343.930\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1024.00 | −0.707107 | ||||||||
\(3\) | 194815. | 1.90480 | 0.952398 | − | 0.304856i | \(-0.0986084\pi\) | ||||
0.952398 | + | 0.304856i | \(0.0986084\pi\) | |||||||
\(4\) | 1.04858e6 | 0.500000 | ||||||||
\(5\) | 9.76562e6 | 0.447214 | ||||||||
\(6\) | −1.99490e8 | −1.34689 | ||||||||
\(7\) | 9.63461e8 | 1.28915 | 0.644577 | − | 0.764539i | \(-0.277033\pi\) | ||||
0.644577 | + | 0.764539i | \(0.277033\pi\) | |||||||
\(8\) | −1.07374e9 | −0.353553 | ||||||||
\(9\) | 2.74924e10 | 2.62825 | ||||||||
\(10\) | −1.00000e10 | −0.316228 | ||||||||
\(11\) | 6.10882e10 | 0.710124 | 0.355062 | − | 0.934843i | \(-0.384460\pi\) | ||||
0.355062 | + | 0.934843i | \(0.384460\pi\) | |||||||
\(12\) | 2.04278e11 | 0.952398 | ||||||||
\(13\) | 5.25383e10 | 0.105699 | 0.0528495 | − | 0.998602i | \(-0.483170\pi\) | ||||
0.0528495 | + | 0.998602i | \(0.483170\pi\) | |||||||
\(14\) | −9.86584e11 | −0.911570 | ||||||||
\(15\) | 1.90249e12 | 0.851851 | ||||||||
\(16\) | 1.09951e12 | 0.250000 | ||||||||
\(17\) | −1.13179e13 | −1.36161 | −0.680803 | − | 0.732466i | \(-0.738369\pi\) | ||||
−0.680803 | + | 0.732466i | \(0.738369\pi\) | |||||||
\(18\) | −2.81522e13 | −1.85845 | ||||||||
\(19\) | −4.53240e13 | −1.69596 | −0.847979 | − | 0.530030i | \(-0.822181\pi\) | ||||
−0.847979 | + | 0.530030i | \(0.822181\pi\) | |||||||
\(20\) | 1.02400e13 | 0.223607 | ||||||||
\(21\) | 1.87696e14 | 2.45558 | ||||||||
\(22\) | −6.25543e13 | −0.502133 | ||||||||
\(23\) | 2.47091e14 | 1.24370 | 0.621849 | − | 0.783137i | \(-0.286382\pi\) | ||||
0.621849 | + | 0.783137i | \(0.286382\pi\) | |||||||
\(24\) | −2.09181e14 | −0.673447 | ||||||||
\(25\) | 9.53674e13 | 0.200000 | ||||||||
\(26\) | −5.37992e13 | −0.0747404 | ||||||||
\(27\) | 3.31810e15 | 3.10149 | ||||||||
\(28\) | 1.01026e15 | 0.644577 | ||||||||
\(29\) | −2.58718e15 | −1.14195 | −0.570977 | − | 0.820966i | \(-0.693435\pi\) | ||||
−0.570977 | + | 0.820966i | \(0.693435\pi\) | |||||||
\(30\) | −1.94815e15 | −0.602350 | ||||||||
\(31\) | −1.35601e15 | −0.297142 | −0.148571 | − | 0.988902i | \(-0.547467\pi\) | ||||
−0.148571 | + | 0.988902i | \(0.547467\pi\) | |||||||
\(32\) | −1.12590e15 | −0.176777 | ||||||||
\(33\) | 1.19009e16 | 1.35264 | ||||||||
\(34\) | 1.15895e16 | 0.962801 | ||||||||
\(35\) | 9.40880e15 | 0.576527 | ||||||||
\(36\) | 2.88279e16 | 1.31413 | ||||||||
\(37\) | −1.35920e16 | −0.464692 | −0.232346 | − | 0.972633i | \(-0.574640\pi\) | ||||
−0.232346 | + | 0.972633i | \(0.574640\pi\) | |||||||
\(38\) | 4.64117e16 | 1.19922 | ||||||||
\(39\) | 1.02352e16 | 0.201335 | ||||||||
\(40\) | −1.04858e16 | −0.158114 | ||||||||
\(41\) | 6.72480e16 | 0.782436 | 0.391218 | − | 0.920298i | \(-0.372054\pi\) | ||||
0.391218 | + | 0.920298i | \(0.372054\pi\) | |||||||
\(42\) | −1.92201e17 | −1.73636 | ||||||||
\(43\) | −3.70641e16 | −0.261538 | −0.130769 | − | 0.991413i | \(-0.541745\pi\) | ||||
−0.130769 | + | 0.991413i | \(0.541745\pi\) | |||||||
\(44\) | 6.40556e16 | 0.355062 | ||||||||
\(45\) | 2.68481e17 | 1.17539 | ||||||||
\(46\) | −2.53021e17 | −0.879427 | ||||||||
\(47\) | 3.17182e17 | 0.879592 | 0.439796 | − | 0.898098i | \(-0.355051\pi\) | ||||
0.439796 | + | 0.898098i | \(0.355051\pi\) | |||||||
\(48\) | 2.14201e17 | 0.476199 | ||||||||
\(49\) | 3.69712e17 | 0.661919 | ||||||||
\(50\) | −9.76562e16 | −0.141421 | ||||||||
\(51\) | −2.20489e18 | −2.59358 | ||||||||
\(52\) | 5.50904e16 | 0.0528495 | ||||||||
\(53\) | 1.44909e18 | 1.13815 | 0.569074 | − | 0.822286i | \(-0.307302\pi\) | ||||
0.569074 | + | 0.822286i | \(0.307302\pi\) | |||||||
\(54\) | −3.39773e18 | −2.19308 | ||||||||
\(55\) | 5.96564e17 | 0.317577 | ||||||||
\(56\) | −1.03451e18 | −0.455785 | ||||||||
\(57\) | −8.82978e18 | −3.23046 | ||||||||
\(58\) | 2.64928e18 | 0.807483 | ||||||||
\(59\) | −1.08957e18 | −0.277529 | −0.138764 | − | 0.990325i | \(-0.544313\pi\) | ||||
−0.138764 | + | 0.990325i | \(0.544313\pi\) | |||||||
\(60\) | 1.99490e18 | 0.425925 | ||||||||
\(61\) | −1.59498e17 | −0.0286281 | −0.0143140 | − | 0.999898i | \(-0.504556\pi\) | ||||
−0.0143140 | + | 0.999898i | \(0.504556\pi\) | |||||||
\(62\) | 1.38855e18 | 0.210111 | ||||||||
\(63\) | 2.64879e19 | 3.38822 | ||||||||
\(64\) | 1.15292e18 | 0.125000 | ||||||||
\(65\) | 5.13069e17 | 0.0472700 | ||||||||
\(66\) | −1.21865e19 | −0.956462 | ||||||||
\(67\) | 8.71262e18 | 0.583934 | 0.291967 | − | 0.956428i | \(-0.405690\pi\) | ||||
0.291967 | + | 0.956428i | \(0.405690\pi\) | |||||||
\(68\) | −1.18677e19 | −0.680803 | ||||||||
\(69\) | 4.81370e19 | 2.36899 | ||||||||
\(70\) | −9.63461e18 | −0.407666 | ||||||||
\(71\) | −3.06845e19 | −1.11868 | −0.559340 | − | 0.828938i | \(-0.688946\pi\) | ||||
−0.559340 | + | 0.828938i | \(0.688946\pi\) | |||||||
\(72\) | −2.95198e19 | −0.929227 | ||||||||
\(73\) | 2.36491e19 | 0.644059 | 0.322029 | − | 0.946730i | \(-0.395635\pi\) | ||||
0.322029 | + | 0.946730i | \(0.395635\pi\) | |||||||
\(74\) | 1.39182e19 | 0.328587 | ||||||||
\(75\) | 1.85790e19 | 0.380959 | ||||||||
\(76\) | −4.75256e19 | −0.847979 | ||||||||
\(77\) | 5.88561e19 | 0.915459 | ||||||||
\(78\) | −1.04809e19 | −0.142365 | ||||||||
\(79\) | −9.35354e19 | −1.11145 | −0.555727 | − | 0.831365i | \(-0.687560\pi\) | ||||
−0.555727 | + | 0.831365i | \(0.687560\pi\) | |||||||
\(80\) | 1.07374e19 | 0.111803 | ||||||||
\(81\) | 3.58834e20 | 3.27945 | ||||||||
\(82\) | −6.88619e19 | −0.553266 | ||||||||
\(83\) | −2.00855e20 | −1.42090 | −0.710448 | − | 0.703750i | \(-0.751508\pi\) | ||||
−0.710448 | + | 0.703750i | \(0.751508\pi\) | |||||||
\(84\) | 1.96814e20 | 1.22779 | ||||||||
\(85\) | −1.10526e20 | −0.608929 | ||||||||
\(86\) | 3.79536e19 | 0.184935 | ||||||||
\(87\) | −5.04022e20 | −2.17519 | ||||||||
\(88\) | −6.55929e19 | −0.251067 | ||||||||
\(89\) | 3.85510e19 | 0.131051 | 0.0655255 | − | 0.997851i | \(-0.479128\pi\) | ||||
0.0655255 | + | 0.997851i | \(0.479128\pi\) | |||||||
\(90\) | −2.74924e20 | −0.831126 | ||||||||
\(91\) | 5.06186e19 | 0.136262 | ||||||||
\(92\) | 2.59094e20 | 0.621849 | ||||||||
\(93\) | −2.64170e20 | −0.565996 | ||||||||
\(94\) | −3.24795e20 | −0.621965 | ||||||||
\(95\) | −4.42617e20 | −0.758456 | ||||||||
\(96\) | −2.19342e20 | −0.336724 | ||||||||
\(97\) | −5.46564e20 | −0.752554 | −0.376277 | − | 0.926507i | \(-0.622796\pi\) | ||||
−0.376277 | + | 0.926507i | \(0.622796\pi\) | |||||||
\(98\) | −3.78585e20 | −0.468047 | ||||||||
\(99\) | 1.67946e21 | 1.86638 | ||||||||
\(100\) | 1.00000e20 | 0.100000 | ||||||||
\(101\) | 1.87063e21 | 1.68505 | 0.842524 | − | 0.538658i | \(-0.181069\pi\) | ||||
0.842524 | + | 0.538658i | \(0.181069\pi\) | |||||||
\(102\) | 2.25781e21 | 1.83394 | ||||||||
\(103\) | −8.63482e20 | −0.633086 | −0.316543 | − | 0.948578i | \(-0.602522\pi\) | ||||
−0.316543 | + | 0.948578i | \(0.602522\pi\) | |||||||
\(104\) | −5.64125e19 | −0.0373702 | ||||||||
\(105\) | 1.83297e21 | 1.09817 | ||||||||
\(106\) | −1.48387e21 | −0.804792 | ||||||||
\(107\) | −3.65685e21 | −1.79712 | −0.898561 | − | 0.438848i | \(-0.855387\pi\) | ||||
−0.898561 | + | 0.438848i | \(0.855387\pi\) | |||||||
\(108\) | 3.47928e21 | 1.55074 | ||||||||
\(109\) | −6.39944e20 | −0.258919 | −0.129459 | − | 0.991585i | \(-0.541324\pi\) | ||||
−0.129459 | + | 0.991585i | \(0.541324\pi\) | |||||||
\(110\) | −6.10882e20 | −0.224561 | ||||||||
\(111\) | −2.64792e21 | −0.885143 | ||||||||
\(112\) | 1.05934e21 | 0.322289 | ||||||||
\(113\) | 6.17070e20 | 0.171006 | 0.0855029 | − | 0.996338i | \(-0.472750\pi\) | ||||
0.0855029 | + | 0.996338i | \(0.472750\pi\) | |||||||
\(114\) | 9.04169e21 | 2.28428 | ||||||||
\(115\) | 2.41300e21 | 0.556199 | ||||||||
\(116\) | −2.71286e21 | −0.570977 | ||||||||
\(117\) | 1.44440e21 | 0.277803 | ||||||||
\(118\) | 1.11572e21 | 0.196242 | ||||||||
\(119\) | −1.09043e22 | −1.75532 | ||||||||
\(120\) | −2.04278e21 | −0.301175 | ||||||||
\(121\) | −3.66848e21 | −0.495724 | ||||||||
\(122\) | 1.63326e20 | 0.0202431 | ||||||||
\(123\) | 1.31009e22 | 1.49038 | ||||||||
\(124\) | −1.42188e21 | −0.148571 | ||||||||
\(125\) | 9.31323e20 | 0.0894427 | ||||||||
\(126\) | −2.71236e22 | −2.39583 | ||||||||
\(127\) | −1.40405e22 | −1.14142 | −0.570709 | − | 0.821152i | \(-0.693332\pi\) | ||||
−0.570709 | + | 0.821152i | \(0.693332\pi\) | |||||||
\(128\) | −1.18059e21 | −0.0883883 | ||||||||
\(129\) | −7.22063e21 | −0.498176 | ||||||||
\(130\) | −5.25383e20 | −0.0334249 | ||||||||
\(131\) | 2.03410e22 | 1.19405 | 0.597025 | − | 0.802222i | \(-0.296349\pi\) | ||||
0.597025 | + | 0.802222i | \(0.296349\pi\) | |||||||
\(132\) | 1.24790e22 | 0.676321 | ||||||||
\(133\) | −4.36679e22 | −2.18635 | ||||||||
\(134\) | −8.92173e21 | −0.412903 | ||||||||
\(135\) | 3.24033e22 | 1.38703 | ||||||||
\(136\) | 1.21525e22 | 0.481401 | ||||||||
\(137\) | −1.10091e21 | −0.0403819 | −0.0201909 | − | 0.999796i | \(-0.506427\pi\) | ||||
−0.0201909 | + | 0.999796i | \(0.506427\pi\) | |||||||
\(138\) | −4.92923e22 | −1.67513 | ||||||||
\(139\) | 4.14583e22 | 1.30604 | 0.653019 | − | 0.757342i | \(-0.273502\pi\) | ||||
0.653019 | + | 0.757342i | \(0.273502\pi\) | |||||||
\(140\) | 9.86584e21 | 0.288264 | ||||||||
\(141\) | 6.17918e22 | 1.67544 | ||||||||
\(142\) | 3.14209e22 | 0.791027 | ||||||||
\(143\) | 3.20947e21 | 0.0750593 | ||||||||
\(144\) | 3.02282e22 | 0.657063 | ||||||||
\(145\) | −2.52655e22 | −0.510697 | ||||||||
\(146\) | −2.42167e22 | −0.455418 | ||||||||
\(147\) | 7.20253e22 | 1.26082 | ||||||||
\(148\) | −1.42522e22 | −0.232346 | ||||||||
\(149\) | 9.61610e22 | 1.46064 | 0.730320 | − | 0.683106i | \(-0.239371\pi\) | ||||
0.730320 | + | 0.683106i | \(0.239371\pi\) | |||||||
\(150\) | −1.90249e22 | −0.269379 | ||||||||
\(151\) | −1.13093e23 | −1.49340 | −0.746700 | − | 0.665161i | \(-0.768363\pi\) | ||||
−0.746700 | + | 0.665161i | \(0.768363\pi\) | |||||||
\(152\) | 4.86662e22 | 0.599612 | ||||||||
\(153\) | −3.11156e23 | −3.57864 | ||||||||
\(154\) | −6.02687e22 | −0.647327 | ||||||||
\(155\) | −1.32423e22 | −0.132886 | ||||||||
\(156\) | 1.07324e22 | 0.100667 | ||||||||
\(157\) | 3.75753e22 | 0.329576 | 0.164788 | − | 0.986329i | \(-0.447306\pi\) | ||||
0.164788 | + | 0.986329i | \(0.447306\pi\) | |||||||
\(158\) | 9.57802e22 | 0.785917 | ||||||||
\(159\) | 2.82304e23 | 2.16794 | ||||||||
\(160\) | −1.09951e22 | −0.0790569 | ||||||||
\(161\) | 2.38063e23 | 1.60332 | ||||||||
\(162\) | −3.67446e23 | −2.31892 | ||||||||
\(163\) | 2.53934e23 | 1.50228 | 0.751140 | − | 0.660143i | \(-0.229504\pi\) | ||||
0.751140 | + | 0.660143i | \(0.229504\pi\) | |||||||
\(164\) | 7.05146e22 | 0.391218 | ||||||||
\(165\) | 1.16220e23 | 0.604920 | ||||||||
\(166\) | 2.05675e23 | 1.00472 | ||||||||
\(167\) | −7.88087e22 | −0.361452 | −0.180726 | − | 0.983533i | \(-0.557845\pi\) | ||||
−0.180726 | + | 0.983533i | \(0.557845\pi\) | |||||||
\(168\) | −2.01538e23 | −0.868178 | ||||||||
\(169\) | −2.44304e23 | −0.988828 | ||||||||
\(170\) | 1.13179e23 | 0.430578 | ||||||||
\(171\) | −1.24607e24 | −4.45740 | ||||||||
\(172\) | −3.88645e22 | −0.130769 | ||||||||
\(173\) | −3.30387e23 | −1.04602 | −0.523009 | − | 0.852327i | \(-0.675191\pi\) | ||||
−0.523009 | + | 0.852327i | \(0.675191\pi\) | |||||||
\(174\) | 5.16118e23 | 1.53809 | ||||||||
\(175\) | 9.18828e22 | 0.257831 | ||||||||
\(176\) | 6.71672e22 | 0.177531 | ||||||||
\(177\) | −2.12264e23 | −0.528636 | ||||||||
\(178\) | −3.94762e22 | −0.0926671 | ||||||||
\(179\) | 4.40276e23 | 0.974470 | 0.487235 | − | 0.873271i | \(-0.338005\pi\) | ||||
0.487235 | + | 0.873271i | \(0.338005\pi\) | |||||||
\(180\) | 2.81522e23 | 0.587695 | ||||||||
\(181\) | −8.24093e23 | −1.62312 | −0.811561 | − | 0.584268i | \(-0.801382\pi\) | ||||
−0.811561 | + | 0.584268i | \(0.801382\pi\) | |||||||
\(182\) | −5.18334e22 | −0.0963519 | ||||||||
\(183\) | −3.10726e22 | −0.0545306 | ||||||||
\(184\) | −2.65312e23 | −0.439714 | ||||||||
\(185\) | −1.32734e23 | −0.207816 | ||||||||
\(186\) | 2.70510e23 | 0.400219 | ||||||||
\(187\) | −6.91389e23 | −0.966909 | ||||||||
\(188\) | 3.32590e23 | 0.439796 | ||||||||
\(189\) | 3.19686e24 | 3.99829 | ||||||||
\(190\) | 4.53240e23 | 0.536309 | ||||||||
\(191\) | 2.97957e23 | 0.333659 | 0.166830 | − | 0.985986i | \(-0.446647\pi\) | ||||
0.166830 | + | 0.985986i | \(0.446647\pi\) | |||||||
\(192\) | 2.24606e23 | 0.238100 | ||||||||
\(193\) | 9.58444e23 | 0.962088 | 0.481044 | − | 0.876696i | \(-0.340258\pi\) | ||||
0.481044 | + | 0.876696i | \(0.340258\pi\) | |||||||
\(194\) | 5.59682e23 | 0.532136 | ||||||||
\(195\) | 9.99534e22 | 0.0900397 | ||||||||
\(196\) | 3.87671e23 | 0.330959 | ||||||||
\(197\) | −7.67214e23 | −0.620899 | −0.310450 | − | 0.950590i | \(-0.600480\pi\) | ||||
−0.310450 | + | 0.950590i | \(0.600480\pi\) | |||||||
\(198\) | −1.71977e24 | −1.31973 | ||||||||
\(199\) | −2.93227e23 | −0.213426 | −0.106713 | − | 0.994290i | \(-0.534033\pi\) | ||||
−0.106713 | + | 0.994290i | \(0.534033\pi\) | |||||||
\(200\) | −1.02400e23 | −0.0707107 | ||||||||
\(201\) | 1.69735e24 | 1.11227 | ||||||||
\(202\) | −1.91552e24 | −1.19151 | ||||||||
\(203\) | −2.49265e24 | −1.47215 | ||||||||
\(204\) | −2.31200e24 | −1.29679 | ||||||||
\(205\) | 6.56719e23 | 0.349916 | ||||||||
\(206\) | 8.84206e23 | 0.447659 | ||||||||
\(207\) | 6.79314e24 | 3.26875 | ||||||||
\(208\) | 5.77664e22 | 0.0264247 | ||||||||
\(209\) | −2.76876e24 | −1.20434 | ||||||||
\(210\) | −1.87696e24 | −0.776522 | ||||||||
\(211\) | −2.05920e24 | −0.810464 | −0.405232 | − | 0.914214i | \(-0.632809\pi\) | ||||
−0.405232 | + | 0.914214i | \(0.632809\pi\) | |||||||
\(212\) | 1.51948e24 | 0.569074 | ||||||||
\(213\) | −5.97779e24 | −2.13086 | ||||||||
\(214\) | 3.74462e24 | 1.27076 | ||||||||
\(215\) | −3.61954e23 | −0.116963 | ||||||||
\(216\) | −3.56278e24 | −1.09654 | ||||||||
\(217\) | −1.30646e24 | −0.383062 | ||||||||
\(218\) | 6.55303e23 | 0.183083 | ||||||||
\(219\) | 4.60720e24 | 1.22680 | ||||||||
\(220\) | 6.25543e23 | 0.158788 | ||||||||
\(221\) | −5.94622e23 | −0.143920 | ||||||||
\(222\) | 2.71147e24 | 0.625891 | ||||||||
\(223\) | −3.95841e24 | −0.871605 | −0.435803 | − | 0.900042i | \(-0.643535\pi\) | ||||
−0.435803 | + | 0.900042i | \(0.643535\pi\) | |||||||
\(224\) | −1.08476e24 | −0.227892 | ||||||||
\(225\) | 2.62188e24 | 0.525650 | ||||||||
\(226\) | −6.31880e23 | −0.120919 | ||||||||
\(227\) | −6.66876e23 | −0.121835 | −0.0609177 | − | 0.998143i | \(-0.519403\pi\) | ||||
−0.0609177 | + | 0.998143i | \(0.519403\pi\) | |||||||
\(228\) | −9.25869e24 | −1.61523 | ||||||||
\(229\) | −7.22731e24 | −1.20421 | −0.602107 | − | 0.798415i | \(-0.705672\pi\) | ||||
−0.602107 | + | 0.798415i | \(0.705672\pi\) | |||||||
\(230\) | −2.47091e24 | −0.393292 | ||||||||
\(231\) | 1.14660e25 | 1.74376 | ||||||||
\(232\) | 2.77797e24 | 0.403742 | ||||||||
\(233\) | 1.07597e25 | 1.49474 | 0.747368 | − | 0.664410i | \(-0.231317\pi\) | ||||
0.747368 | + | 0.664410i | \(0.231317\pi\) | |||||||
\(234\) | −1.47907e24 | −0.196437 | ||||||||
\(235\) | 3.09748e24 | 0.393365 | ||||||||
\(236\) | −1.14249e24 | −0.138764 | ||||||||
\(237\) | −1.82221e25 | −2.11709 | ||||||||
\(238\) | 1.11661e25 | 1.24120 | ||||||||
\(239\) | 3.16911e24 | 0.337101 | 0.168550 | − | 0.985693i | \(-0.446091\pi\) | ||||
0.168550 | + | 0.985693i | \(0.446091\pi\) | |||||||
\(240\) | 2.09181e24 | 0.212963 | ||||||||
\(241\) | −1.75468e24 | −0.171009 | −0.0855043 | − | 0.996338i | \(-0.527250\pi\) | ||||
−0.0855043 | + | 0.996338i | \(0.527250\pi\) | |||||||
\(242\) | 3.75653e24 | 0.350530 | ||||||||
\(243\) | 3.51977e25 | 3.14520 | ||||||||
\(244\) | −1.67246e23 | −0.0143140 | ||||||||
\(245\) | 3.61047e24 | 0.296019 | ||||||||
\(246\) | −1.34153e25 | −1.05386 | ||||||||
\(247\) | −2.38124e24 | −0.179261 | ||||||||
\(248\) | 1.45600e24 | 0.105056 | ||||||||
\(249\) | −3.91295e25 | −2.70652 | ||||||||
\(250\) | −9.53674e23 | −0.0632456 | ||||||||
\(251\) | 1.75868e25 | 1.11844 | 0.559221 | − | 0.829019i | \(-0.311100\pi\) | ||||
0.559221 | + | 0.829019i | \(0.311100\pi\) | |||||||
\(252\) | 2.77746e25 | 1.69411 | ||||||||
\(253\) | 1.50944e25 | 0.883179 | ||||||||
\(254\) | 1.43775e25 | 0.807104 | ||||||||
\(255\) | −2.15321e25 | −1.15989 | ||||||||
\(256\) | 1.20893e24 | 0.0625000 | ||||||||
\(257\) | −9.88264e24 | −0.490428 | −0.245214 | − | 0.969469i | \(-0.578858\pi\) | ||||
−0.245214 | + | 0.969469i | \(0.578858\pi\) | |||||||
\(258\) | 7.39392e24 | 0.352264 | ||||||||
\(259\) | −1.30954e25 | −0.599059 | ||||||||
\(260\) | 5.37992e23 | 0.0236350 | ||||||||
\(261\) | −7.11280e25 | −3.00134 | ||||||||
\(262\) | −2.08291e25 | −0.844321 | ||||||||
\(263\) | −1.60390e25 | −0.624656 | −0.312328 | − | 0.949974i | \(-0.601109\pi\) | ||||
−0.312328 | + | 0.949974i | \(0.601109\pi\) | |||||||
\(264\) | −1.27785e25 | −0.478231 | ||||||||
\(265\) | 1.41513e25 | 0.508995 | ||||||||
\(266\) | 4.47159e25 | 1.54598 | ||||||||
\(267\) | 7.51030e24 | 0.249626 | ||||||||
\(268\) | 9.13585e24 | 0.291967 | ||||||||
\(269\) | 1.76073e25 | 0.541122 | 0.270561 | − | 0.962703i | \(-0.412791\pi\) | ||||
0.270561 | + | 0.962703i | \(0.412791\pi\) | |||||||
\(270\) | −3.31810e25 | −0.980776 | ||||||||
\(271\) | 3.45015e25 | 0.980981 | 0.490490 | − | 0.871447i | \(-0.336818\pi\) | ||||
0.490490 | + | 0.871447i | \(0.336818\pi\) | |||||||
\(272\) | −1.24441e25 | −0.340402 | ||||||||
\(273\) | 9.86125e24 | 0.259552 | ||||||||
\(274\) | 1.12733e24 | 0.0285543 | ||||||||
\(275\) | 5.82582e24 | 0.142025 | ||||||||
\(276\) | 5.04753e25 | 1.18450 | ||||||||
\(277\) | −2.59482e25 | −0.586231 | −0.293116 | − | 0.956077i | \(-0.594692\pi\) | ||||
−0.293116 | + | 0.956077i | \(0.594692\pi\) | |||||||
\(278\) | −4.24533e25 | −0.923508 | ||||||||
\(279\) | −3.72799e25 | −0.780964 | ||||||||
\(280\) | −1.01026e25 | −0.203833 | ||||||||
\(281\) | 7.82254e25 | 1.52031 | 0.760154 | − | 0.649743i | \(-0.225124\pi\) | ||||
0.760154 | + | 0.649743i | \(0.225124\pi\) | |||||||
\(282\) | −6.32748e25 | −1.18472 | ||||||||
\(283\) | 8.38167e24 | 0.151207 | 0.0756037 | − | 0.997138i | \(-0.475912\pi\) | ||||
0.0756037 | + | 0.997138i | \(0.475912\pi\) | |||||||
\(284\) | −3.21750e25 | −0.559340 | ||||||||
\(285\) | −8.62283e25 | −1.44470 | ||||||||
\(286\) | −3.28649e24 | −0.0530749 | ||||||||
\(287\) | 6.47908e25 | 1.00868 | ||||||||
\(288\) | −3.09537e25 | −0.464613 | ||||||||
\(289\) | 5.90026e25 | 0.853973 | ||||||||
\(290\) | 2.58718e25 | 0.361117 | ||||||||
\(291\) | −1.06479e26 | −1.43346 | ||||||||
\(292\) | 2.47979e25 | 0.322029 | ||||||||
\(293\) | 4.97478e25 | 0.623252 | 0.311626 | − | 0.950205i | \(-0.399126\pi\) | ||||
0.311626 | + | 0.950205i | \(0.399126\pi\) | |||||||
\(294\) | −7.37540e25 | −0.891535 | ||||||||
\(295\) | −1.06403e25 | −0.124115 | ||||||||
\(296\) | 1.45943e25 | 0.164293 | ||||||||
\(297\) | 2.02697e26 | 2.20244 | ||||||||
\(298\) | −9.84688e25 | −1.03283 | ||||||||
\(299\) | 1.29817e25 | 0.131458 | ||||||||
\(300\) | 1.94815e25 | 0.190480 | ||||||||
\(301\) | −3.57098e25 | −0.337163 | ||||||||
\(302\) | 1.15807e26 | 1.05599 | ||||||||
\(303\) | 3.64425e26 | 3.20967 | ||||||||
\(304\) | −4.98342e25 | −0.423990 | ||||||||
\(305\) | −1.55760e24 | −0.0128029 | ||||||||
\(306\) | 3.18624e26 | 2.53048 | ||||||||
\(307\) | −1.41280e26 | −1.08425 | −0.542123 | − | 0.840299i | \(-0.682379\pi\) | ||||
−0.542123 | + | 0.840299i | \(0.682379\pi\) | |||||||
\(308\) | 6.17151e25 | 0.457730 | ||||||||
\(309\) | −1.68219e26 | −1.20590 | ||||||||
\(310\) | 1.35601e25 | 0.0939646 | ||||||||
\(311\) | 1.39904e26 | 0.937232 | 0.468616 | − | 0.883402i | \(-0.344753\pi\) | ||||
0.468616 | + | 0.883402i | \(0.344753\pi\) | |||||||
\(312\) | −1.09900e25 | −0.0711827 | ||||||||
\(313\) | −2.79550e26 | −1.75083 | −0.875414 | − | 0.483373i | \(-0.839411\pi\) | ||||
−0.875414 | + | 0.483373i | \(0.839411\pi\) | |||||||
\(314\) | −3.84771e25 | −0.233045 | ||||||||
\(315\) | 2.58671e26 | 1.51526 | ||||||||
\(316\) | −9.80789e25 | −0.555727 | ||||||||
\(317\) | −1.16992e26 | −0.641259 | −0.320629 | − | 0.947205i | \(-0.603894\pi\) | ||||
−0.320629 | + | 0.947205i | \(0.603894\pi\) | |||||||
\(318\) | −2.89079e26 | −1.53297 | ||||||||
\(319\) | −1.58046e26 | −0.810928 | ||||||||
\(320\) | 1.12590e25 | 0.0559017 | ||||||||
\(321\) | −7.12409e26 | −3.42315 | ||||||||
\(322\) | −2.43776e26 | −1.13372 | ||||||||
\(323\) | 5.12972e26 | 2.30923 | ||||||||
\(324\) | 3.76265e26 | 1.63973 | ||||||||
\(325\) | 5.01044e24 | 0.0211398 | ||||||||
\(326\) | −2.60028e26 | −1.06227 | ||||||||
\(327\) | −1.24671e26 | −0.493188 | ||||||||
\(328\) | −7.22070e25 | −0.276633 | ||||||||
\(329\) | 3.05593e26 | 1.13393 | ||||||||
\(330\) | −1.19009e26 | −0.427743 | ||||||||
\(331\) | −3.83627e26 | −1.33572 | −0.667859 | − | 0.744288i | \(-0.732789\pi\) | ||||
−0.667859 | + | 0.744288i | \(0.732789\pi\) | |||||||
\(332\) | −2.10612e26 | −0.710448 | ||||||||
\(333\) | −3.73677e26 | −1.22133 | ||||||||
\(334\) | 8.07001e25 | 0.255585 | ||||||||
\(335\) | 8.50842e25 | 0.261143 | ||||||||
\(336\) | 2.06374e26 | 0.613894 | ||||||||
\(337\) | 1.36118e26 | 0.392465 | 0.196233 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196233 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(338\) | 2.50168e26 | 0.699207 | ||||||||
\(339\) | 1.20214e26 | 0.325731 | ||||||||
\(340\) | −1.15895e26 | −0.304465 | ||||||||
\(341\) | −8.28360e25 | −0.211008 | ||||||||
\(342\) | 1.27597e27 | 3.15186 | ||||||||
\(343\) | −1.81934e26 | −0.435839 | ||||||||
\(344\) | 3.97973e25 | 0.0924676 | ||||||||
\(345\) | 4.70088e26 | 1.05945 | ||||||||
\(346\) | 3.38316e26 | 0.739646 | ||||||||
\(347\) | 2.49928e26 | 0.530097 | 0.265048 | − | 0.964235i | \(-0.414612\pi\) | ||||
0.265048 | + | 0.964235i | \(0.414612\pi\) | |||||||
\(348\) | −5.28505e26 | −1.08759 | ||||||||
\(349\) | 1.05322e26 | 0.210307 | 0.105153 | − | 0.994456i | \(-0.466467\pi\) | ||||
0.105153 | + | 0.994456i | \(0.466467\pi\) | |||||||
\(350\) | −9.40880e25 | −0.182314 | ||||||||
\(351\) | 1.74327e26 | 0.327824 | ||||||||
\(352\) | −6.87792e25 | −0.125533 | ||||||||
\(353\) | −1.44843e26 | −0.256604 | −0.128302 | − | 0.991735i | \(-0.540953\pi\) | ||||
−0.128302 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(354\) | 2.17358e26 | 0.373802 | ||||||||
\(355\) | −2.99653e26 | −0.500289 | ||||||||
\(356\) | 4.04236e25 | 0.0655255 | ||||||||
\(357\) | −2.12433e27 | −3.34353 | ||||||||
\(358\) | −4.50843e26 | −0.689055 | ||||||||
\(359\) | 5.68219e25 | 0.0843382 | 0.0421691 | − | 0.999110i | \(-0.486573\pi\) | ||||
0.0421691 | + | 0.999110i | \(0.486573\pi\) | |||||||
\(360\) | −2.88279e26 | −0.415563 | ||||||||
\(361\) | 1.34005e27 | 1.87627 | ||||||||
\(362\) | 8.43871e26 | 1.14772 | ||||||||
\(363\) | −7.14675e26 | −0.944254 | ||||||||
\(364\) | 5.30774e25 | 0.0681311 | ||||||||
\(365\) | 2.30949e26 | 0.288032 | ||||||||
\(366\) | 3.18183e25 | 0.0385590 | ||||||||
\(367\) | 3.29729e25 | 0.0388296 | 0.0194148 | − | 0.999812i | \(-0.493820\pi\) | ||||
0.0194148 | + | 0.999812i | \(0.493820\pi\) | |||||||
\(368\) | 2.71680e26 | 0.310924 | ||||||||
\(369\) | 1.84881e27 | 2.05644 | ||||||||
\(370\) | 1.35920e26 | 0.146948 | ||||||||
\(371\) | 1.39614e27 | 1.46725 | ||||||||
\(372\) | −2.77003e26 | −0.282998 | ||||||||
\(373\) | −6.24564e25 | −0.0620346 | −0.0310173 | − | 0.999519i | \(-0.509875\pi\) | ||||
−0.0310173 | + | 0.999519i | \(0.509875\pi\) | |||||||
\(374\) | 7.07983e26 | 0.683708 | ||||||||
\(375\) | 1.81435e26 | 0.170370 | ||||||||
\(376\) | −3.40572e26 | −0.310983 | ||||||||
\(377\) | −1.35926e26 | −0.120703 | ||||||||
\(378\) | −3.27359e27 | −2.82722 | ||||||||
\(379\) | 1.65025e27 | 1.38624 | 0.693119 | − | 0.720823i | \(-0.256236\pi\) | ||||
0.693119 | + | 0.720823i | \(0.256236\pi\) | |||||||
\(380\) | −4.64117e26 | −0.379228 | ||||||||
\(381\) | −2.73530e27 | −2.17417 | ||||||||
\(382\) | −3.05108e26 | −0.235933 | ||||||||
\(383\) | 1.20420e27 | 0.905967 | 0.452983 | − | 0.891519i | \(-0.350360\pi\) | ||||
0.452983 | + | 0.891519i | \(0.350360\pi\) | |||||||
\(384\) | −2.29997e26 | −0.168362 | ||||||||
\(385\) | 5.74767e26 | 0.409406 | ||||||||
\(386\) | −9.81446e26 | −0.680299 | ||||||||
\(387\) | −1.01898e27 | −0.687387 | ||||||||
\(388\) | −5.73114e26 | −0.376277 | ||||||||
\(389\) | 1.68483e26 | 0.107667 | 0.0538337 | − | 0.998550i | \(-0.482856\pi\) | ||||
0.0538337 | + | 0.998550i | \(0.482856\pi\) | |||||||
\(390\) | −1.02352e26 | −0.0636677 | ||||||||
\(391\) | −2.79655e27 | −1.69343 | ||||||||
\(392\) | −3.96975e26 | −0.234024 | ||||||||
\(393\) | 3.96272e27 | 2.27442 | ||||||||
\(394\) | 7.85627e26 | 0.439042 | ||||||||
\(395\) | −9.13431e26 | −0.497057 | ||||||||
\(396\) | 1.76104e27 | 0.933192 | ||||||||
\(397\) | 1.48612e27 | 0.766925 | 0.383462 | − | 0.923557i | \(-0.374732\pi\) | ||||
0.383462 | + | 0.923557i | \(0.374732\pi\) | |||||||
\(398\) | 3.00264e26 | 0.150915 | ||||||||
\(399\) | −8.50715e27 | −4.16456 | ||||||||
\(400\) | 1.04858e26 | 0.0500000 | ||||||||
\(401\) | −6.25371e26 | −0.290484 | −0.145242 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145242 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(402\) | −1.73808e27 | −0.786497 | ||||||||
\(403\) | −7.12423e25 | −0.0314076 | ||||||||
\(404\) | 1.96149e27 | 0.842524 | ||||||||
\(405\) | 3.50424e27 | 1.46661 | ||||||||
\(406\) | 2.55248e27 | 1.04097 | ||||||||
\(407\) | −8.30310e26 | −0.329989 | ||||||||
\(408\) | 2.36748e27 | 0.916970 | ||||||||
\(409\) | 3.35895e27 | 1.26797 | 0.633985 | − | 0.773345i | \(-0.281418\pi\) | ||||
0.633985 | + | 0.773345i | \(0.281418\pi\) | |||||||
\(410\) | −6.72480e26 | −0.247428 | ||||||||
\(411\) | −2.14474e26 | −0.0769192 | ||||||||
\(412\) | −9.05427e26 | −0.316543 | ||||||||
\(413\) | −1.04976e27 | −0.357777 | ||||||||
\(414\) | −6.95617e27 | −2.31136 | ||||||||
\(415\) | −1.96147e27 | −0.635444 | ||||||||
\(416\) | −5.91528e25 | −0.0186851 | ||||||||
\(417\) | 8.07668e27 | 2.48774 | ||||||||
\(418\) | 2.83521e27 | 0.851597 | ||||||||
\(419\) | −1.39454e27 | −0.408492 | −0.204246 | − | 0.978920i | \(-0.565474\pi\) | ||||
−0.204246 | + | 0.978920i | \(0.565474\pi\) | |||||||
\(420\) | 1.92201e27 | 0.549084 | ||||||||
\(421\) | −5.26111e27 | −1.46594 | −0.732968 | − | 0.680263i | \(-0.761866\pi\) | ||||
−0.732968 | + | 0.680263i | \(0.761866\pi\) | |||||||
\(422\) | 2.10862e27 | 0.573084 | ||||||||
\(423\) | 8.72011e27 | 2.31179 | ||||||||
\(424\) | −1.55595e27 | −0.402396 | ||||||||
\(425\) | −1.07936e27 | −0.272321 | ||||||||
\(426\) | 6.12126e27 | 1.50675 | ||||||||
\(427\) | −1.53670e26 | −0.0369060 | ||||||||
\(428\) | −3.83449e27 | −0.898561 | ||||||||
\(429\) | 6.25252e26 | 0.142973 | ||||||||
\(430\) | 3.70641e26 | 0.0827055 | ||||||||
\(431\) | −3.99327e27 | −0.869595 | −0.434797 | − | 0.900528i | \(-0.643180\pi\) | ||||
−0.434797 | + | 0.900528i | \(0.643180\pi\) | |||||||
\(432\) | 3.64829e27 | 0.775372 | ||||||||
\(433\) | 1.71947e27 | 0.356674 | 0.178337 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178337 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(434\) | 1.33782e27 | 0.270866 | ||||||||
\(435\) | −4.92209e27 | −0.972774 | ||||||||
\(436\) | −6.71030e26 | −0.129459 | ||||||||
\(437\) | −1.11992e28 | −2.10926 | ||||||||
\(438\) | −4.71777e27 | −0.867479 | ||||||||
\(439\) | 2.57641e27 | 0.462528 | 0.231264 | − | 0.972891i | \(-0.425714\pi\) | ||||
0.231264 | + | 0.972891i | \(0.425714\pi\) | |||||||
\(440\) | −6.40556e26 | −0.112280 | ||||||||
\(441\) | 1.01643e28 | 1.73969 | ||||||||
\(442\) | 6.08893e26 | 0.101767 | ||||||||
\(443\) | −1.26523e27 | −0.206504 | −0.103252 | − | 0.994655i | \(-0.532925\pi\) | ||||
−0.103252 | + | 0.994655i | \(0.532925\pi\) | |||||||
\(444\) | −2.77655e27 | −0.442572 | ||||||||
\(445\) | 3.76475e26 | 0.0586078 | ||||||||
\(446\) | 4.05341e27 | 0.616318 | ||||||||
\(447\) | 1.87336e28 | 2.78222 | ||||||||
\(448\) | 1.11080e27 | 0.161144 | ||||||||
\(449\) | 3.20858e26 | 0.0454702 | 0.0227351 | − | 0.999742i | \(-0.492763\pi\) | ||||
0.0227351 | + | 0.999742i | \(0.492763\pi\) | |||||||
\(450\) | −2.68481e27 | −0.371691 | ||||||||
\(451\) | 4.10806e27 | 0.555626 | ||||||||
\(452\) | 6.47045e26 | 0.0855029 | ||||||||
\(453\) | −2.20321e28 | −2.84462 | ||||||||
\(454\) | 6.82881e26 | 0.0861506 | ||||||||
\(455\) | 4.94322e26 | 0.0609383 | ||||||||
\(456\) | 9.48090e27 | 1.14214 | ||||||||
\(457\) | −1.41432e28 | −1.66506 | −0.832528 | − | 0.553983i | \(-0.813107\pi\) | ||||
−0.832528 | + | 0.553983i | \(0.813107\pi\) | |||||||
\(458\) | 7.40076e27 | 0.851508 | ||||||||
\(459\) | −3.75539e28 | −4.22300 | ||||||||
\(460\) | 2.53021e27 | 0.278099 | ||||||||
\(461\) | 6.08545e27 | 0.653782 | 0.326891 | − | 0.945062i | \(-0.393999\pi\) | ||||
0.326891 | + | 0.945062i | \(0.393999\pi\) | |||||||
\(462\) | −1.17412e28 | −1.23303 | ||||||||
\(463\) | 6.53768e27 | 0.671155 | 0.335578 | − | 0.942013i | \(-0.391069\pi\) | ||||
0.335578 | + | 0.942013i | \(0.391069\pi\) | |||||||
\(464\) | −2.84464e27 | −0.285488 | ||||||||
\(465\) | −2.57979e27 | −0.253121 | ||||||||
\(466\) | −1.10180e28 | −1.05694 | ||||||||
\(467\) | −9.77307e27 | −0.916651 | −0.458325 | − | 0.888784i | \(-0.651551\pi\) | ||||
−0.458325 | + | 0.888784i | \(0.651551\pi\) | |||||||
\(468\) | 1.51457e27 | 0.138902 | ||||||||
\(469\) | 8.39428e27 | 0.752781 | ||||||||
\(470\) | −3.17182e27 | −0.278151 | ||||||||
\(471\) | 7.32022e27 | 0.627775 | ||||||||
\(472\) | 1.16991e27 | 0.0981212 | ||||||||
\(473\) | −2.26418e27 | −0.185724 | ||||||||
\(474\) | 1.86594e28 | 1.49701 | ||||||||
\(475\) | −4.32243e27 | −0.339192 | ||||||||
\(476\) | −1.14340e28 | −0.877661 | ||||||||
\(477\) | 3.98390e28 | 2.99134 | ||||||||
\(478\) | −3.24517e27 | −0.238366 | ||||||||
\(479\) | −1.53019e28 | −1.09957 | −0.549784 | − | 0.835307i | \(-0.685290\pi\) | ||||
−0.549784 | + | 0.835307i | \(0.685290\pi\) | |||||||
\(480\) | −2.14201e27 | −0.150587 | ||||||||
\(481\) | −7.14100e26 | −0.0491174 | ||||||||
\(482\) | 1.79679e27 | 0.120921 | ||||||||
\(483\) | 4.63781e28 | 3.05400 | ||||||||
\(484\) | −3.84668e27 | −0.247862 | ||||||||
\(485\) | −5.33754e27 | −0.336553 | ||||||||
\(486\) | −3.60424e28 | −2.22399 | ||||||||
\(487\) | −2.24122e28 | −1.35341 | −0.676705 | − | 0.736254i | \(-0.736593\pi\) | ||||
−0.676705 | + | 0.736254i | \(0.736593\pi\) | |||||||
\(488\) | 1.71260e26 | 0.0101215 | ||||||||
\(489\) | 4.94701e28 | 2.86154 | ||||||||
\(490\) | −3.69712e27 | −0.209317 | ||||||||
\(491\) | 1.97103e28 | 1.09229 | 0.546145 | − | 0.837691i | \(-0.316095\pi\) | ||||
0.546145 | + | 0.837691i | \(0.316095\pi\) | |||||||
\(492\) | 1.37373e28 | 0.745191 | ||||||||
\(493\) | 2.92815e28 | 1.55489 | ||||||||
\(494\) | 2.43839e27 | 0.126757 | ||||||||
\(495\) | 1.64010e28 | 0.834672 | ||||||||
\(496\) | −1.49095e27 | −0.0742856 | ||||||||
\(497\) | −2.95633e28 | −1.44215 | ||||||||
\(498\) | 4.00686e28 | 1.91380 | ||||||||
\(499\) | 3.08705e28 | 1.44374 | 0.721869 | − | 0.692030i | \(-0.243283\pi\) | ||||
0.721869 | + | 0.692030i | \(0.243283\pi\) | |||||||
\(500\) | 9.76563e26 | 0.0447214 | ||||||||
\(501\) | −1.53531e28 | −0.688493 | ||||||||
\(502\) | −1.80089e28 | −0.790858 | ||||||||
\(503\) | −2.52448e28 | −1.08570 | −0.542848 | − | 0.839831i | \(-0.682654\pi\) | ||||
−0.542848 | + | 0.839831i | \(0.682654\pi\) | |||||||
\(504\) | −2.84412e28 | −1.19792 | ||||||||
\(505\) | 1.82678e28 | 0.753577 | ||||||||
\(506\) | −1.54566e28 | −0.624502 | ||||||||
\(507\) | −4.75941e28 | −1.88352 | ||||||||
\(508\) | −1.47226e28 | −0.570709 | ||||||||
\(509\) | 2.42632e28 | 0.921323 | 0.460661 | − | 0.887576i | \(-0.347612\pi\) | ||||
0.460661 | + | 0.887576i | \(0.347612\pi\) | |||||||
\(510\) | 2.20489e28 | 0.820163 | ||||||||
\(511\) | 2.27850e28 | 0.830291 | ||||||||
\(512\) | −1.23794e27 | −0.0441942 | ||||||||
\(513\) | −1.50389e29 | −5.25999 | ||||||||
\(514\) | 1.01198e28 | 0.346785 | ||||||||
\(515\) | −8.43244e27 | −0.283125 | ||||||||
\(516\) | −7.57138e27 | −0.249088 | ||||||||
\(517\) | 1.93761e28 | 0.624619 | ||||||||
\(518\) | 1.34096e28 | 0.423599 | ||||||||
\(519\) | −6.43643e28 | −1.99245 | ||||||||
\(520\) | −5.50904e26 | −0.0167125 | ||||||||
\(521\) | −1.28803e28 | −0.382939 | −0.191470 | − | 0.981499i | \(-0.561325\pi\) | ||||
−0.191470 | + | 0.981499i | \(0.561325\pi\) | |||||||
\(522\) | 7.28351e28 | 2.12227 | ||||||||
\(523\) | 4.72268e28 | 1.34872 | 0.674359 | − | 0.738404i | \(-0.264420\pi\) | ||||
0.674359 | + | 0.738404i | \(0.264420\pi\) | |||||||
\(524\) | 2.13290e28 | 0.597025 | ||||||||
\(525\) | 1.79001e28 | 0.491115 | ||||||||
\(526\) | 1.64239e28 | 0.441699 | ||||||||
\(527\) | 1.53471e28 | 0.404591 | ||||||||
\(528\) | 1.30852e28 | 0.338160 | ||||||||
\(529\) | 2.15825e28 | 0.546785 | ||||||||
\(530\) | −1.44909e28 | −0.359914 | ||||||||
\(531\) | −2.99548e28 | −0.729415 | ||||||||
\(532\) | −4.57891e28 | −1.09318 | ||||||||
\(533\) | 3.53309e27 | 0.0827026 | ||||||||
\(534\) | −7.69055e27 | −0.176512 | ||||||||
\(535\) | −3.57114e28 | −0.803698 | ||||||||
\(536\) | −9.35511e27 | −0.206452 | ||||||||
\(537\) | 8.57723e28 | 1.85617 | ||||||||
\(538\) | −1.80299e28 | −0.382631 | ||||||||
\(539\) | 2.25850e28 | 0.470044 | ||||||||
\(540\) | 3.39773e28 | 0.693513 | ||||||||
\(541\) | 1.70978e28 | 0.342270 | 0.171135 | − | 0.985248i | \(-0.445257\pi\) | ||||
0.171135 | + | 0.985248i | \(0.445257\pi\) | |||||||
\(542\) | −3.53295e28 | −0.693658 | ||||||||
\(543\) | −1.60545e29 | −3.09172 | ||||||||
\(544\) | 1.27428e28 | 0.240700 | ||||||||
\(545\) | −6.24945e27 | −0.115792 | ||||||||
\(546\) | −1.00979e28 | −0.183531 | ||||||||
\(547\) | 6.17365e28 | 1.10072 | 0.550358 | − | 0.834929i | \(-0.314491\pi\) | ||||
0.550358 | + | 0.834929i | \(0.314491\pi\) | |||||||
\(548\) | −1.15439e27 | −0.0201909 | ||||||||
\(549\) | −4.38499e27 | −0.0752417 | ||||||||
\(550\) | −5.96564e27 | −0.100427 | ||||||||
\(551\) | 1.17262e29 | 1.93671 | ||||||||
\(552\) | −5.16867e28 | −0.837565 | ||||||||
\(553\) | −9.01177e28 | −1.43284 | ||||||||
\(554\) | 2.65709e28 | 0.414528 | ||||||||
\(555\) | −2.58586e28 | −0.395848 | ||||||||
\(556\) | 4.34721e28 | 0.653019 | ||||||||
\(557\) | −1.03162e29 | −1.52069 | −0.760346 | − | 0.649518i | \(-0.774971\pi\) | ||||
−0.760346 | + | 0.649518i | \(0.774971\pi\) | |||||||
\(558\) | 3.81747e28 | 0.552225 | ||||||||
\(559\) | −1.94728e27 | −0.0276443 | ||||||||
\(560\) | 1.03451e28 | 0.144132 | ||||||||
\(561\) | −1.34693e29 | −1.84177 | ||||||||
\(562\) | −8.01028e28 | −1.07502 | ||||||||
\(563\) | −3.65428e28 | −0.481353 | −0.240677 | − | 0.970605i | \(-0.577369\pi\) | ||||
−0.240677 | + | 0.970605i | \(0.577369\pi\) | |||||||
\(564\) | 6.47934e28 | 0.837722 | ||||||||
\(565\) | 6.02608e27 | 0.0764761 | ||||||||
\(566\) | −8.58283e27 | −0.106920 | ||||||||
\(567\) | 3.45723e29 | 4.22772 | ||||||||
\(568\) | 3.29472e28 | 0.395513 | ||||||||
\(569\) | 4.54287e28 | 0.535367 | 0.267683 | − | 0.963507i | \(-0.413742\pi\) | ||||
0.267683 | + | 0.963507i | \(0.413742\pi\) | |||||||
\(570\) | 8.82978e28 | 1.02156 | ||||||||
\(571\) | 1.49843e29 | 1.70200 | 0.850998 | − | 0.525168i | \(-0.175998\pi\) | ||||
0.850998 | + | 0.525168i | \(0.175998\pi\) | |||||||
\(572\) | 3.36537e27 | 0.0375297 | ||||||||
\(573\) | 5.80464e28 | 0.635553 | ||||||||
\(574\) | −6.63458e28 | −0.713245 | ||||||||
\(575\) | 2.35644e28 | 0.248740 | ||||||||
\(576\) | 3.16966e28 | 0.328531 | ||||||||
\(577\) | −1.44438e29 | −1.47006 | −0.735029 | − | 0.678035i | \(-0.762832\pi\) | ||||
−0.735029 | + | 0.678035i | \(0.762832\pi\) | |||||||
\(578\) | −6.04187e28 | −0.603850 | ||||||||
\(579\) | 1.86719e29 | 1.83258 | ||||||||
\(580\) | −2.64928e28 | −0.255349 | ||||||||
\(581\) | −1.93516e29 | −1.83175 | ||||||||
\(582\) | 1.09034e29 | 1.01361 | ||||||||
\(583\) | 8.85223e28 | 0.808226 | ||||||||
\(584\) | −2.53931e28 | −0.227709 | ||||||||
\(585\) | 1.41055e28 | 0.124237 | ||||||||
\(586\) | −5.09417e28 | −0.440706 | ||||||||
\(587\) | −1.82681e29 | −1.55237 | −0.776183 | − | 0.630508i | \(-0.782846\pi\) | ||||
−0.776183 | + | 0.630508i | \(0.782846\pi\) | |||||||
\(588\) | 7.55241e28 | 0.630410 | ||||||||
\(589\) | 6.14597e28 | 0.503941 | ||||||||
\(590\) | 1.08957e28 | 0.0877623 | ||||||||
\(591\) | −1.49465e29 | −1.18269 | ||||||||
\(592\) | −1.49446e28 | −0.116173 | ||||||||
\(593\) | 1.28812e29 | 0.983742 | 0.491871 | − | 0.870668i | \(-0.336313\pi\) | ||||
0.491871 | + | 0.870668i | \(0.336313\pi\) | |||||||
\(594\) | −2.07561e29 | −1.55736 | ||||||||
\(595\) | −1.06488e29 | −0.785004 | ||||||||
\(596\) | 1.00832e29 | 0.730320 | ||||||||
\(597\) | −5.71249e28 | −0.406532 | ||||||||
\(598\) | −1.32933e28 | −0.0929545 | ||||||||
\(599\) | −1.90622e28 | −0.130976 | −0.0654879 | − | 0.997853i | \(-0.520860\pi\) | ||||
−0.0654879 | + | 0.997853i | \(0.520860\pi\) | |||||||
\(600\) | −1.99490e28 | −0.134689 | ||||||||
\(601\) | −4.02359e28 | −0.266951 | −0.133476 | − | 0.991052i | \(-0.542614\pi\) | ||||
−0.133476 | + | 0.991052i | \(0.542614\pi\) | |||||||
\(602\) | 3.65668e28 | 0.238410 | ||||||||
\(603\) | 2.39531e29 | 1.53472 | ||||||||
\(604\) | −1.18586e29 | −0.746700 | ||||||||
\(605\) | −3.58250e28 | −0.221695 | ||||||||
\(606\) | −3.73172e29 | −2.26958 | ||||||||
\(607\) | 1.34619e29 | 0.804681 | 0.402340 | − | 0.915490i | \(-0.368197\pi\) | ||||
0.402340 | + | 0.915490i | \(0.368197\pi\) | |||||||
\(608\) | 5.10303e28 | 0.299806 | ||||||||
\(609\) | −4.85606e29 | −2.80416 | ||||||||
\(610\) | 1.59498e27 | 0.00905299 | ||||||||
\(611\) | 1.66642e28 | 0.0929719 | ||||||||
\(612\) | −3.26271e29 | −1.78932 | ||||||||
\(613\) | 6.61541e28 | 0.356633 | 0.178316 | − | 0.983973i | \(-0.442935\pi\) | ||||
0.178316 | + | 0.983973i | \(0.442935\pi\) | |||||||
\(614\) | 1.44671e29 | 0.766677 | ||||||||
\(615\) | 1.27938e29 | 0.666519 | ||||||||
\(616\) | −6.31963e28 | −0.323664 | ||||||||
\(617\) | −5.23241e28 | −0.263456 | −0.131728 | − | 0.991286i | \(-0.542052\pi\) | ||||
−0.131728 | + | 0.991286i | \(0.542052\pi\) | |||||||
\(618\) | 1.72256e29 | 0.852700 | ||||||||
\(619\) | 1.15227e29 | 0.560793 | 0.280397 | − | 0.959884i | \(-0.409534\pi\) | ||||
0.280397 | + | 0.959884i | \(0.409534\pi\) | |||||||
\(620\) | −1.38855e28 | −0.0664430 | ||||||||
\(621\) | 8.19873e29 | 3.85731 | ||||||||
\(622\) | −1.43262e29 | −0.662723 | ||||||||
\(623\) | 3.71424e28 | 0.168945 | ||||||||
\(624\) | 1.12538e28 | 0.0503337 | ||||||||
\(625\) | 9.09495e27 | 0.0400000 | ||||||||
\(626\) | 2.86259e29 | 1.23802 | ||||||||
\(627\) | −5.39395e29 | −2.29402 | ||||||||
\(628\) | 3.94005e28 | 0.164788 | ||||||||
\(629\) | 1.53833e29 | 0.632727 | ||||||||
\(630\) | −2.64879e29 | −1.07145 | ||||||||
\(631\) | −1.82557e29 | −0.726257 | −0.363128 | − | 0.931739i | \(-0.618291\pi\) | ||||
−0.363128 | + | 0.931739i | \(0.618291\pi\) | |||||||
\(632\) | 1.00433e29 | 0.392958 | ||||||||
\(633\) | −4.01163e29 | −1.54377 | ||||||||
\(634\) | 1.19800e29 | 0.453438 | ||||||||
\(635\) | −1.37115e29 | −0.510458 | ||||||||
\(636\) | 2.96017e29 | 1.08397 | ||||||||
\(637\) | 1.94240e28 | 0.0699641 | ||||||||
\(638\) | 1.61840e29 | 0.573413 | ||||||||
\(639\) | −8.43591e29 | −2.94017 | ||||||||
\(640\) | −1.15292e28 | −0.0395285 | ||||||||
\(641\) | 4.06750e29 | 1.37189 | 0.685943 | − | 0.727655i | \(-0.259390\pi\) | ||||
0.685943 | + | 0.727655i | \(0.259390\pi\) | |||||||
\(642\) | 7.29506e29 | 2.42053 | ||||||||
\(643\) | 1.10344e29 | 0.360192 | 0.180096 | − | 0.983649i | \(-0.442359\pi\) | ||||
0.180096 | + | 0.983649i | \(0.442359\pi\) | |||||||
\(644\) | 2.49627e29 | 0.801659 | ||||||||
\(645\) | −7.05140e28 | −0.222791 | ||||||||
\(646\) | −5.25283e29 | −1.63287 | ||||||||
\(647\) | 5.65654e29 | 1.73004 | 0.865020 | − | 0.501737i | \(-0.167306\pi\) | ||||
0.865020 | + | 0.501737i | \(0.167306\pi\) | |||||||
\(648\) | −3.85295e29 | −1.15946 | ||||||||
\(649\) | −6.65597e28 | −0.197080 | ||||||||
\(650\) | −5.13069e27 | −0.0149481 | ||||||||
\(651\) | −2.54518e29 | −0.729656 | ||||||||
\(652\) | 2.66269e29 | 0.751140 | ||||||||
\(653\) | 9.98139e28 | 0.277078 | 0.138539 | − | 0.990357i | \(-0.455759\pi\) | ||||
0.138539 | + | 0.990357i | \(0.455759\pi\) | |||||||
\(654\) | 1.27663e29 | 0.348736 | ||||||||
\(655\) | 1.98642e29 | 0.533996 | ||||||||
\(656\) | 7.39399e28 | 0.195609 | ||||||||
\(657\) | 6.50172e29 | 1.69275 | ||||||||
\(658\) | −3.12927e29 | −0.801809 | ||||||||
\(659\) | 4.27384e29 | 1.07776 | 0.538880 | − | 0.842383i | \(-0.318848\pi\) | ||||
0.538880 | + | 0.842383i | \(0.318848\pi\) | |||||||
\(660\) | 1.21865e29 | 0.302460 | ||||||||
\(661\) | 1.06580e29 | 0.260352 | 0.130176 | − | 0.991491i | \(-0.458446\pi\) | ||||
0.130176 | + | 0.991491i | \(0.458446\pi\) | |||||||
\(662\) | 3.92834e29 | 0.944495 | ||||||||
\(663\) | −1.15841e29 | −0.274139 | ||||||||
\(664\) | 2.15666e29 | 0.502362 | ||||||||
\(665\) | −4.26444e29 | −0.977766 | ||||||||
\(666\) | 3.82645e29 | 0.863608 | ||||||||
\(667\) | −6.39271e29 | −1.42025 | ||||||||
\(668\) | −8.26369e28 | −0.180726 | ||||||||
\(669\) | −7.71157e29 | −1.66023 | ||||||||
\(670\) | −8.71262e28 | −0.184656 | ||||||||
\(671\) | −9.74344e27 | −0.0203295 | ||||||||
\(672\) | −2.11327e29 | −0.434089 | ||||||||
\(673\) | 9.20636e29 | 1.86179 | 0.930893 | − | 0.365292i | \(-0.119031\pi\) | ||||
0.930893 | + | 0.365292i | \(0.119031\pi\) | |||||||
\(674\) | −1.39385e29 | −0.277515 | ||||||||
\(675\) | 3.16439e29 | 0.620297 | ||||||||
\(676\) | −2.56172e29 | −0.494414 | ||||||||
\(677\) | 1.03701e29 | 0.197062 | 0.0985309 | − | 0.995134i | \(-0.468586\pi\) | ||||
0.0985309 | + | 0.995134i | \(0.468586\pi\) | |||||||
\(678\) | −1.23100e29 | −0.230327 | ||||||||
\(679\) | −5.26593e29 | −0.970159 | ||||||||
\(680\) | 1.18677e29 | 0.215289 | ||||||||
\(681\) | −1.29917e29 | −0.232072 | ||||||||
\(682\) | 8.48241e28 | 0.149205 | ||||||||
\(683\) | −1.05066e30 | −1.81988 | −0.909942 | − | 0.414735i | \(-0.863874\pi\) | ||||
−0.909942 | + | 0.414735i | \(0.863874\pi\) | |||||||
\(684\) | −1.30660e30 | −2.22870 | ||||||||
\(685\) | −1.07511e28 | −0.0180593 | ||||||||
\(686\) | 1.86301e29 | 0.308185 | ||||||||
\(687\) | −1.40799e30 | −2.29378 | ||||||||
\(688\) | −4.07524e28 | −0.0653844 | ||||||||
\(689\) | 7.61327e28 | 0.120301 | ||||||||
\(690\) | −4.81370e29 | −0.749141 | ||||||||
\(691\) | −2.09599e29 | −0.321270 | −0.160635 | − | 0.987014i | \(-0.551354\pi\) | ||||
−0.160635 | + | 0.987014i | \(0.551354\pi\) | |||||||
\(692\) | −3.46436e29 | −0.523009 | ||||||||
\(693\) | 1.61810e30 | 2.40606 | ||||||||
\(694\) | −2.55926e29 | −0.374835 | ||||||||
\(695\) | 4.04866e29 | 0.584078 | ||||||||
\(696\) | 5.41189e29 | 0.769046 | ||||||||
\(697\) | −7.61105e29 | −1.06537 | ||||||||
\(698\) | −1.07850e29 | −0.148709 | ||||||||
\(699\) | 2.09616e30 | 2.84717 | ||||||||
\(700\) | 9.63461e28 | 0.128915 | ||||||||
\(701\) | −9.09765e29 | −1.19920 | −0.599598 | − | 0.800301i | \(-0.704673\pi\) | ||||
−0.599598 | + | 0.800301i | \(0.704673\pi\) | |||||||
\(702\) | −1.78511e29 | −0.231806 | ||||||||
\(703\) | 6.16043e29 | 0.788098 | ||||||||
\(704\) | 7.04299e28 | 0.0887655 | ||||||||
\(705\) | 6.03435e29 | 0.749281 | ||||||||
\(706\) | 1.48319e29 | 0.181446 | ||||||||
\(707\) | 1.80228e30 | 2.17229 | ||||||||
\(708\) | −2.22575e29 | −0.264318 | ||||||||
\(709\) | −1.17415e30 | −1.37385 | −0.686925 | − | 0.726728i | \(-0.741040\pi\) | ||||
−0.686925 | + | 0.726728i | \(0.741040\pi\) | |||||||
\(710\) | 3.06845e29 | 0.353758 | ||||||||
\(711\) | −2.57151e30 | −2.92118 | ||||||||
\(712\) | −4.13938e28 | −0.0463335 | ||||||||
\(713\) | −3.35057e29 | −0.369555 | ||||||||
\(714\) | 2.17531e30 | 2.36423 | ||||||||
\(715\) | 3.13425e28 | 0.0335675 | ||||||||
\(716\) | 4.61663e29 | 0.487235 | ||||||||
\(717\) | 6.17390e29 | 0.642108 | ||||||||
\(718\) | −5.81857e28 | −0.0596361 | ||||||||
\(719\) | 2.38367e29 | 0.240765 | 0.120382 | − | 0.992728i | \(-0.461588\pi\) | ||||
0.120382 | + | 0.992728i | \(0.461588\pi\) | |||||||
\(720\) | 2.95198e29 | 0.293847 | ||||||||
\(721\) | −8.31932e29 | −0.816145 | ||||||||
\(722\) | −1.37221e30 | −1.32673 | ||||||||
\(723\) | −3.41837e29 | −0.325737 | ||||||||
\(724\) | −8.64124e29 | −0.811561 | ||||||||
\(725\) | −2.46733e29 | −0.228391 | ||||||||
\(726\) | 7.31827e29 | 0.667688 | ||||||||
\(727\) | 1.60120e30 | 1.43991 | 0.719954 | − | 0.694022i | \(-0.244163\pi\) | ||||
0.719954 | + | 0.694022i | \(0.244163\pi\) | |||||||
\(728\) | −5.43513e28 | −0.0481760 | ||||||||
\(729\) | 3.10350e30 | 2.71152 | ||||||||
\(730\) | −2.36491e29 | −0.203669 | ||||||||
\(731\) | 4.19487e29 | 0.356112 | ||||||||
\(732\) | −3.25819e28 | −0.0272653 | ||||||||
\(733\) | −8.02614e28 | −0.0662087 | −0.0331043 | − | 0.999452i | \(-0.510539\pi\) | ||||
−0.0331043 | + | 0.999452i | \(0.510539\pi\) | |||||||
\(734\) | −3.37642e28 | −0.0274567 | ||||||||
\(735\) | 7.03373e29 | 0.563856 | ||||||||
\(736\) | −2.78200e29 | −0.219857 | ||||||||
\(737\) | 5.32238e29 | 0.414665 | ||||||||
\(738\) | −1.89318e30 | −1.45412 | ||||||||
\(739\) | 2.07121e30 | 1.56840 | 0.784200 | − | 0.620508i | \(-0.213073\pi\) | ||||
0.784200 | + | 0.620508i | \(0.213073\pi\) | |||||||
\(740\) | −1.39182e29 | −0.103908 | ||||||||
\(741\) | −4.63901e29 | −0.341456 | ||||||||
\(742\) | −1.42965e30 | −1.03750 | ||||||||
\(743\) | −2.00787e30 | −1.43666 | −0.718329 | − | 0.695704i | \(-0.755093\pi\) | ||||
−0.718329 | + | 0.695704i | \(0.755093\pi\) | |||||||
\(744\) | 2.83651e29 | 0.200110 | ||||||||
\(745\) | 9.39072e29 | 0.653218 | ||||||||
\(746\) | 6.39554e28 | 0.0438651 | ||||||||
\(747\) | −5.52199e30 | −3.73447 | ||||||||
\(748\) | −7.24974e29 | −0.483455 | ||||||||
\(749\) | −3.52324e30 | −2.31677 | ||||||||
\(750\) | −1.85790e29 | −0.120470 | ||||||||
\(751\) | 2.68196e30 | 1.71488 | 0.857440 | − | 0.514584i | \(-0.172054\pi\) | ||||
0.857440 | + | 0.514584i | \(0.172054\pi\) | |||||||
\(752\) | 3.48745e29 | 0.219898 | ||||||||
\(753\) | 3.42617e30 | 2.13040 | ||||||||
\(754\) | 1.39188e29 | 0.0853501 | ||||||||
\(755\) | −1.10442e30 | −0.667869 | ||||||||
\(756\) | 3.35215e30 | 1.99915 | ||||||||
\(757\) | 2.29494e30 | 1.34979 | 0.674894 | − | 0.737915i | \(-0.264189\pi\) | ||||
0.674894 | + | 0.737915i | \(0.264189\pi\) | |||||||
\(758\) | −1.68986e30 | −0.980219 | ||||||||
\(759\) | 2.94060e30 | 1.68228 | ||||||||
\(760\) | 4.75256e29 | 0.268155 | ||||||||
\(761\) | 3.17369e29 | 0.176614 | 0.0883072 | − | 0.996093i | \(-0.471854\pi\) | ||||
0.0883072 | + | 0.996093i | \(0.471854\pi\) | |||||||
\(762\) | 2.80095e30 | 1.53737 | ||||||||
\(763\) | −6.16561e29 | −0.333786 | ||||||||
\(764\) | 3.12430e29 | 0.166830 | ||||||||
\(765\) | −3.03863e30 | −1.60042 | ||||||||
\(766\) | −1.23310e30 | −0.640615 | ||||||||
\(767\) | −5.72440e28 | −0.0293345 | ||||||||
\(768\) | 2.35517e29 | 0.119050 | ||||||||
\(769\) | 3.31592e30 | 1.65340 | 0.826699 | − | 0.562644i | \(-0.190216\pi\) | ||||
0.826699 | + | 0.562644i | \(0.190216\pi\) | |||||||
\(770\) | −5.88561e29 | −0.289494 | ||||||||
\(771\) | −1.92528e30 | −0.934166 | ||||||||
\(772\) | 1.00500e30 | 0.481044 | ||||||||
\(773\) | −2.86833e29 | −0.135439 | −0.0677196 | − | 0.997704i | \(-0.521572\pi\) | ||||
−0.0677196 | + | 0.997704i | \(0.521572\pi\) | |||||||
\(774\) | 1.04344e30 | 0.486056 | ||||||||
\(775\) | −1.29319e29 | −0.0594284 | ||||||||
\(776\) | 5.86869e29 | 0.266068 | ||||||||
\(777\) | −2.55117e30 | −1.14109 | ||||||||
\(778\) | −1.72526e29 | −0.0761323 | ||||||||
\(779\) | −3.04795e30 | −1.32698 | ||||||||
\(780\) | 1.04809e29 | 0.0450199 | ||||||||
\(781\) | −1.87446e30 | −0.794402 | ||||||||
\(782\) | 2.86367e30 | 1.19743 | ||||||||
\(783\) | −8.58454e30 | −3.54175 | ||||||||
\(784\) | 4.06503e29 | 0.165480 | ||||||||
\(785\) | 3.66946e29 | 0.147391 | ||||||||
\(786\) | −4.05782e30 | −1.60826 | ||||||||
\(787\) | 1.37451e30 | 0.537544 | 0.268772 | − | 0.963204i | \(-0.413382\pi\) | ||||
0.268772 | + | 0.963204i | \(0.413382\pi\) | |||||||
\(788\) | −8.04482e29 | −0.310450 | ||||||||
\(789\) | −3.12463e30 | −1.18984 | ||||||||
\(790\) | 9.35354e29 | 0.351473 | ||||||||
\(791\) | 5.94523e29 | 0.220453 | ||||||||
\(792\) | −1.80331e30 | −0.659866 | ||||||||
\(793\) | −8.37975e27 | −0.00302596 | ||||||||
\(794\) | −1.52178e30 | −0.542298 | ||||||||
\(795\) | 2.75688e30 | 0.969533 | ||||||||
\(796\) | −3.07471e29 | −0.106713 | ||||||||
\(797\) | −4.30808e30 | −1.47561 | −0.737805 | − | 0.675014i | \(-0.764138\pi\) | ||||
−0.737805 | + | 0.675014i | \(0.764138\pi\) | |||||||
\(798\) | 8.71132e30 | 2.94479 | ||||||||
\(799\) | −3.58983e30 | −1.19766 | ||||||||
\(800\) | −1.07374e29 | −0.0353553 | ||||||||
\(801\) | 1.05986e30 | 0.344435 | ||||||||
\(802\) | 6.40380e29 | 0.205403 | ||||||||
\(803\) | 1.44468e30 | 0.457361 | ||||||||
\(804\) | 1.77980e30 | 0.556137 | ||||||||
\(805\) | 2.32483e30 | 0.717026 | ||||||||
\(806\) | 7.29521e28 | 0.0222085 | ||||||||
\(807\) | 3.43017e30 | 1.03073 | ||||||||
\(808\) | −2.00857e30 | −0.595755 | ||||||||
\(809\) | −8.36783e29 | −0.244993 | −0.122496 | − | 0.992469i | \(-0.539090\pi\) | ||||
−0.122496 | + | 0.992469i | \(0.539090\pi\) | |||||||
\(810\) | −3.58834e30 | −1.03705 | ||||||||
\(811\) | 3.30696e30 | 0.943432 | 0.471716 | − | 0.881751i | \(-0.343635\pi\) | ||||
0.471716 | + | 0.881751i | \(0.343635\pi\) | |||||||
\(812\) | −2.61374e30 | −0.736077 | ||||||||
\(813\) | 6.72140e30 | 1.86857 | ||||||||
\(814\) | 8.50237e29 | 0.233337 | ||||||||
\(815\) | 2.47982e30 | 0.671840 | ||||||||
\(816\) | −2.42430e30 | −0.648396 | ||||||||
\(817\) | 1.67989e30 | 0.443557 | ||||||||
\(818\) | −3.43957e30 | −0.896591 | ||||||||
\(819\) | 1.39163e30 | 0.358131 | ||||||||
\(820\) | 6.88619e29 | 0.174958 | ||||||||
\(821\) | 7.58969e30 | 1.90380 | 0.951899 | − | 0.306413i | \(-0.0991290\pi\) | ||||
0.951899 | + | 0.306413i | \(0.0991290\pi\) | |||||||
\(822\) | 2.19621e29 | 0.0543901 | ||||||||
\(823\) | 5.61508e30 | 1.37296 | 0.686479 | − | 0.727149i | \(-0.259155\pi\) | ||||
0.686479 | + | 0.727149i | \(0.259155\pi\) | |||||||
\(824\) | 9.27157e29 | 0.223830 | ||||||||
\(825\) | 1.13496e30 | 0.270528 | ||||||||
\(826\) | 1.07495e30 | 0.252987 | ||||||||
\(827\) | 5.39629e30 | 1.25397 | 0.626985 | − | 0.779031i | \(-0.284289\pi\) | ||||
0.626985 | + | 0.779031i | \(0.284289\pi\) | |||||||
\(828\) | 7.12312e30 | 1.63437 | ||||||||
\(829\) | −4.47440e30 | −1.01371 | −0.506853 | − | 0.862032i | \(-0.669191\pi\) | ||||
−0.506853 | + | 0.862032i | \(0.669191\pi\) | |||||||
\(830\) | 2.00855e30 | 0.449327 | ||||||||
\(831\) | −5.05508e30 | −1.11665 | ||||||||
\(832\) | 6.05725e28 | 0.0132124 | ||||||||
\(833\) | −4.18436e30 | −0.901273 | ||||||||
\(834\) | −8.27052e30 | −1.75910 | ||||||||
\(835\) | −7.69616e29 | −0.161646 | ||||||||
\(836\) | −2.90325e30 | −0.602170 | ||||||||
\(837\) | −4.49937e30 | −0.921582 | ||||||||
\(838\) | 1.42801e30 | 0.288847 | ||||||||
\(839\) | −1.16605e30 | −0.232925 | −0.116462 | − | 0.993195i | \(-0.537155\pi\) | ||||
−0.116462 | + | 0.993195i | \(0.537155\pi\) | |||||||
\(840\) | −1.96814e30 | −0.388261 | ||||||||
\(841\) | 1.56068e30 | 0.304058 | ||||||||
\(842\) | 5.38738e30 | 1.03657 | ||||||||
\(843\) | 1.52395e31 | 2.89588 | ||||||||
\(844\) | −2.15923e30 | −0.405232 | ||||||||
\(845\) | −2.38578e30 | −0.442217 | ||||||||
\(846\) | −8.92939e30 | −1.63468 | ||||||||
\(847\) | −3.53444e30 | −0.639065 | ||||||||
\(848\) | 1.59329e30 | 0.284537 | ||||||||
\(849\) | 1.63287e30 | 0.288019 | ||||||||
\(850\) | 1.10526e30 | 0.192560 | ||||||||
\(851\) | −3.35846e30 | −0.577936 | ||||||||
\(852\) | −6.26817e30 | −1.06543 | ||||||||
\(853\) | −1.08909e31 | −1.82852 | −0.914262 | − | 0.405123i | \(-0.867229\pi\) | ||||
−0.914262 | + | 0.405123i | \(0.867229\pi\) | |||||||
\(854\) | 1.57358e29 | 0.0260965 | ||||||||
\(855\) | −1.21686e31 | −1.99341 | ||||||||
\(856\) | 3.92651e30 | 0.635379 | ||||||||
\(857\) | 1.32603e30 | 0.211960 | 0.105980 | − | 0.994368i | \(-0.466202\pi\) | ||||
0.105980 | + | 0.994368i | \(0.466202\pi\) | |||||||
\(858\) | −6.40258e29 | −0.101097 | ||||||||
\(859\) | −6.84458e30 | −1.06762 | −0.533812 | − | 0.845603i | \(-0.679241\pi\) | ||||
−0.533812 | + | 0.845603i | \(0.679241\pi\) | |||||||
\(860\) | −3.79536e29 | −0.0584816 | ||||||||
\(861\) | 1.26222e31 | 1.92133 | ||||||||
\(862\) | 4.08910e30 | 0.614896 | ||||||||
\(863\) | 3.45729e30 | 0.513597 | 0.256799 | − | 0.966465i | \(-0.417332\pi\) | ||||
0.256799 | + | 0.966465i | \(0.417332\pi\) | |||||||
\(864\) | −3.73585e30 | −0.548270 | ||||||||
\(865\) | −3.22644e30 | −0.467793 | ||||||||
\(866\) | −1.76074e30 | −0.252206 | ||||||||
\(867\) | 1.14946e31 | 1.62664 | ||||||||
\(868\) | −1.36992e30 | −0.191531 | ||||||||
\(869\) | −5.71391e30 | −0.789270 | ||||||||
\(870\) | 5.04022e30 | 0.687855 | ||||||||
\(871\) | 4.57746e29 | 0.0617212 | ||||||||
\(872\) | 6.87135e29 | 0.0915416 | ||||||||
\(873\) | −1.50264e31 | −1.97790 | ||||||||
\(874\) | 1.14679e31 | 1.49147 | ||||||||
\(875\) | 8.97293e29 | 0.115305 | ||||||||
\(876\) | 4.83100e30 | 0.613400 | ||||||||
\(877\) | −1.37025e30 | −0.171912 | −0.0859558 | − | 0.996299i | \(-0.527394\pi\) | ||||
−0.0859558 | + | 0.996299i | \(0.527394\pi\) | |||||||
\(878\) | −2.63825e30 | −0.327057 | ||||||||
\(879\) | 9.69160e30 | 1.18717 | ||||||||
\(880\) | 6.55929e29 | 0.0793942 | ||||||||
\(881\) | −3.75611e30 | −0.449253 | −0.224627 | − | 0.974445i | \(-0.572116\pi\) | ||||
−0.224627 | + | 0.974445i | \(0.572116\pi\) | |||||||
\(882\) | −1.04082e31 | −1.23015 | ||||||||
\(883\) | 6.64376e30 | 0.775937 | 0.387968 | − | 0.921673i | \(-0.373177\pi\) | ||||
0.387968 | + | 0.921673i | \(0.373177\pi\) | |||||||
\(884\) | −6.23507e29 | −0.0719602 | ||||||||
\(885\) | −2.07289e30 | −0.236413 | ||||||||
\(886\) | 1.29559e30 | 0.146021 | ||||||||
\(887\) | −6.01786e30 | −0.670261 | −0.335131 | − | 0.942172i | \(-0.608780\pi\) | ||||
−0.335131 | + | 0.942172i | \(0.608780\pi\) | |||||||
\(888\) | 2.84318e30 | 0.312945 | ||||||||
\(889\) | −1.35275e31 | −1.47146 | ||||||||
\(890\) | −3.85510e29 | −0.0414420 | ||||||||
\(891\) | 2.19205e31 | 2.32882 | ||||||||
\(892\) | −4.15070e30 | −0.435803 | ||||||||
\(893\) | −1.43760e31 | −1.49175 | ||||||||
\(894\) | −1.91832e31 | −1.96733 | ||||||||
\(895\) | 4.29957e30 | 0.435796 | ||||||||
\(896\) | −1.13745e30 | −0.113946 | ||||||||
\(897\) | 2.52903e30 | 0.250400 | ||||||||
\(898\) | −3.28559e29 | −0.0321523 | ||||||||
\(899\) | 3.50824e30 | 0.339323 | ||||||||
\(900\) | 2.74924e30 | 0.262825 | ||||||||
\(901\) | −1.64006e31 | −1.54971 | ||||||||
\(902\) | −4.20665e30 | −0.392887 | ||||||||
\(903\) | −6.95680e30 | −0.642226 | ||||||||
\(904\) | −6.62574e29 | −0.0604597 | ||||||||
\(905\) | −8.04778e30 | −0.725882 | ||||||||
\(906\) | 2.25609e31 | 2.01145 | ||||||||
\(907\) | 1.42699e31 | 1.25761 | 0.628804 | − | 0.777564i | \(-0.283545\pi\) | ||||
0.628804 | + | 0.777564i | \(0.283545\pi\) | |||||||
\(908\) | −6.99270e29 | −0.0609177 | ||||||||
\(909\) | 5.14280e31 | 4.42873 | ||||||||
\(910\) | −5.06186e29 | −0.0430899 | ||||||||
\(911\) | 1.18912e31 | 1.00065 | 0.500326 | − | 0.865837i | \(-0.333214\pi\) | ||||
0.500326 | + | 0.865837i | \(0.333214\pi\) | |||||||
\(912\) | −9.70844e30 | −0.807614 | ||||||||
\(913\) | −1.22699e31 | −1.00901 | ||||||||
\(914\) | 1.44827e31 | 1.17737 | ||||||||
\(915\) | −3.03443e29 | −0.0243868 | ||||||||
\(916\) | −7.57838e30 | −0.602107 | ||||||||
\(917\) | 1.95977e31 | 1.53932 | ||||||||
\(918\) | 3.84552e31 | 2.98612 | ||||||||
\(919\) | −3.13990e30 | −0.241047 | −0.120524 | − | 0.992710i | \(-0.538457\pi\) | ||||
−0.120524 | + | 0.992710i | \(0.538457\pi\) | |||||||
\(920\) | −2.59094e30 | −0.196646 | ||||||||
\(921\) | −2.75234e31 | −2.06527 | ||||||||
\(922\) | −6.23150e30 | −0.462294 | ||||||||
\(923\) | −1.61211e30 | −0.118243 | ||||||||
\(924\) | 1.20230e31 | 0.871882 | ||||||||
\(925\) | −1.29623e30 | −0.0929383 | ||||||||
\(926\) | −6.69458e30 | −0.474578 | ||||||||
\(927\) | −2.37392e31 | −1.66391 | ||||||||
\(928\) | 2.91291e30 | 0.201871 | ||||||||
\(929\) | 1.39588e30 | 0.0956498 | 0.0478249 | − | 0.998856i | \(-0.484771\pi\) | ||||
0.0478249 | + | 0.998856i | \(0.484771\pi\) | |||||||
\(930\) | 2.64170e30 | 0.178983 | ||||||||
\(931\) | −1.67568e31 | −1.12259 | ||||||||
\(932\) | 1.12824e31 | 0.747368 | ||||||||
\(933\) | 2.72554e31 | 1.78524 | ||||||||
\(934\) | 1.00076e31 | 0.648170 | ||||||||
\(935\) | −6.75185e30 | −0.432415 | ||||||||
\(936\) | −1.55092e30 | −0.0982183 | ||||||||
\(937\) | −2.22831e31 | −1.39543 | −0.697717 | − | 0.716374i | \(-0.745801\pi\) | ||||
−0.697717 | + | 0.716374i | \(0.745801\pi\) | |||||||
\(938\) | −8.59574e30 | −0.532296 | ||||||||
\(939\) | −5.44604e31 | −3.33497 | ||||||||
\(940\) | 3.24795e30 | 0.196683 | ||||||||
\(941\) | 2.09348e31 | 1.25366 | 0.626828 | − | 0.779157i | \(-0.284353\pi\) | ||||
0.626828 | + | 0.779157i | \(0.284353\pi\) | |||||||
\(942\) | −7.49590e30 | −0.443904 | ||||||||
\(943\) | 1.66164e31 | 0.973114 | ||||||||
\(944\) | −1.19799e30 | −0.0693822 | ||||||||
\(945\) | 3.12193e31 | 1.78809 | ||||||||
\(946\) | 2.31852e30 | 0.131327 | ||||||||
\(947\) | 2.96424e31 | 1.66050 | 0.830249 | − | 0.557393i | \(-0.188198\pi\) | ||||
0.830249 | + | 0.557393i | \(0.188198\pi\) | |||||||
\(948\) | −1.91072e31 | −1.05855 | ||||||||
\(949\) | 1.24248e30 | 0.0680763 | ||||||||
\(950\) | 4.42617e30 | 0.239845 | ||||||||
\(951\) | −2.27917e31 | −1.22147 | ||||||||
\(952\) | 1.17085e31 | 0.620600 | ||||||||
\(953\) | 3.78184e30 | 0.198257 | 0.0991283 | − | 0.995075i | \(-0.468395\pi\) | ||||
0.0991283 | + | 0.995075i | \(0.468395\pi\) | |||||||
\(954\) | −4.07952e31 | −2.11520 | ||||||||
\(955\) | 2.90973e30 | 0.149217 | ||||||||
\(956\) | 3.32305e30 | 0.168550 | ||||||||
\(957\) | −3.07898e31 | −1.54465 | ||||||||
\(958\) | 1.56691e31 | 0.777512 | ||||||||
\(959\) | −1.06069e30 | −0.0520584 | ||||||||
\(960\) | 2.19342e30 | 0.106481 | ||||||||
\(961\) | −1.89867e31 | −0.911707 | ||||||||
\(962\) | 7.31238e29 | 0.0347313 | ||||||||
\(963\) | −1.00536e32 | −4.72329 | ||||||||
\(964\) | −1.83991e30 | −0.0855043 | ||||||||
\(965\) | 9.35980e30 | 0.430259 | ||||||||
\(966\) | −4.74912e31 | −2.15950 | ||||||||
\(967\) | −2.27343e31 | −1.02259 | −0.511297 | − | 0.859404i | \(-0.670835\pi\) | ||||
−0.511297 | + | 0.859404i | \(0.670835\pi\) | |||||||
\(968\) | 3.93900e30 | 0.175265 | ||||||||
\(969\) | 9.99344e31 | 4.39861 | ||||||||
\(970\) | 5.46564e30 | 0.237979 | ||||||||
\(971\) | 3.59388e31 | 1.54797 | 0.773983 | − | 0.633206i | \(-0.218261\pi\) | ||||
0.773983 | + | 0.633206i | \(0.218261\pi\) | |||||||
\(972\) | 3.69074e31 | 1.57260 | ||||||||
\(973\) | 3.99434e31 | 1.68368 | ||||||||
\(974\) | 2.29500e31 | 0.957006 | ||||||||
\(975\) | 9.76107e29 | 0.0402670 | ||||||||
\(976\) | −1.75370e29 | −0.00715702 | ||||||||
\(977\) | 8.76227e30 | 0.353772 | 0.176886 | − | 0.984231i | \(-0.443398\pi\) | ||||
0.176886 | + | 0.984231i | \(0.443398\pi\) | |||||||
\(978\) | −5.06574e31 | −2.02341 | ||||||||
\(979\) | 2.35501e30 | 0.0930625 | ||||||||
\(980\) | 3.78585e30 | 0.148010 | ||||||||
\(981\) | −1.75936e31 | −0.680504 | ||||||||
\(982\) | −2.01834e31 | −0.772365 | ||||||||
\(983\) | 3.99246e31 | 1.51157 | 0.755786 | − | 0.654819i | \(-0.227255\pi\) | ||||
0.755786 | + | 0.654819i | \(0.227255\pi\) | |||||||
\(984\) | −1.40670e31 | −0.526929 | ||||||||
\(985\) | −7.49232e30 | −0.277675 | ||||||||
\(986\) | −2.99842e31 | −1.09947 | ||||||||
\(987\) | 5.95340e31 | 2.15991 | ||||||||
\(988\) | −2.49691e30 | −0.0896305 | ||||||||
\(989\) | −9.15821e30 | −0.325274 | ||||||||
\(990\) | −1.67946e31 | −0.590202 | ||||||||
\(991\) | 4.03797e31 | 1.40407 | 0.702037 | − | 0.712141i | \(-0.252274\pi\) | ||||
0.702037 | + | 0.712141i | \(0.252274\pi\) | |||||||
\(992\) | 1.52673e30 | 0.0525278 | ||||||||
\(993\) | −7.47361e31 | −2.54427 | ||||||||
\(994\) | 3.02728e31 | 1.01976 | ||||||||
\(995\) | −2.86354e30 | −0.0954468 | ||||||||
\(996\) | −4.10302e31 | −1.35326 | ||||||||
\(997\) | 1.29884e31 | 0.423894 | 0.211947 | − | 0.977281i | \(-0.432020\pi\) | ||||
0.211947 | + | 0.977281i | \(0.432020\pi\) | |||||||
\(998\) | −3.16114e31 | −1.02088 | ||||||||
\(999\) | −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 | 10.22.a.c.1.2 | ✓ | 2 | |
4.3 | odd | 2 | 80.22.a.b.1.1 | 2 | |||
5.2 | odd | 4 | 50.22.b.d.49.1 | 4 | |||
5.3 | odd | 4 | 50.22.b.d.49.4 | 4 | |||
5.4 | even | 2 | 50.22.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.22.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.22.a.e.1.1 | 2 | 5.4 | even | 2 | |||
50.22.b.d.49.1 | 4 | 5.2 | odd | 4 | |||
50.22.b.d.49.4 | 4 | 5.3 | odd | 4 | |||
80.22.a.b.1.1 | 2 | 4.3 | odd | 2 |