Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,25,Mod(17,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 25, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.17");
S:= CuspForms(chi, 25);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 25 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(175.184233084\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + \cdots + 21\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{60}\cdot 3^{34}\cdot 17^{2} \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.7 | ||
Root | \(-1.03344e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.17 |
Dual form | 48.25.e.d.17.8 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 490828. | − | 203759.i | 0.923579 | − | 0.383409i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.24013e8i | − | 0.507958i | −0.967210 | − | 0.253979i | \(-0.918261\pi\) | ||
0.967210 | − | 0.253979i | \(-0.0817394\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50611e10 | −1.08813 | −0.544066 | − | 0.839043i | \(-0.683116\pi\) | ||||
−0.544066 | + | 0.839043i | \(0.683116\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.99394e11 | − | 2.00021e11i | 0.705995 | − | 0.708216i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.25660e12i | − | 0.719023i | −0.933141 | − | 0.359512i | \(-0.882943\pi\) | ||
0.933141 | − | 0.359512i | \(-0.117057\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.78761e12 | 0.205494 | 0.102747 | − | 0.994708i | \(-0.467237\pi\) | ||||
0.102747 | + | 0.994708i | \(0.467237\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.52688e13 | − | 6.08691e13i | −0.194756 | − | 0.469139i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.31661e14i | − | 0.912531i | −0.889844 | − | 0.456265i | \(-0.849187\pi\) | ||
0.889844 | − | 0.456265i | \(-0.150813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.04629e15 | 0.924537 | 0.462269 | − | 0.886740i | \(-0.347036\pi\) | ||||
0.462269 | + | 0.886740i | \(0.347036\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.39242e15 | + | 3.06885e15i | −1.00498 | + | 0.417199i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.16079e16i | − | 1.44232i | −0.692768 | − | 0.721161i | \(-0.743609\pi\) | ||
0.692768 | − | 0.721161i | \(-0.256391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.42254e16 | 0.741979 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.71119e16 | − | 1.38804e17i | 0.380506 | − | 0.924779i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.82228e17i | 1.92821i | 0.265527 | + | 0.964103i | \(0.414454\pi\) | ||||
−0.265527 | + | 0.964103i | \(0.585546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.83154e17 | 0.867318 | 0.433659 | − | 0.901077i | \(-0.357222\pi\) | ||||
0.433659 | + | 0.901077i | \(0.357222\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.59804e17 | − | 1.10760e18i | −0.275680 | − | 0.664075i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.86778e18i | 0.552725i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.74472e18 | 1.48030 | 0.740148 | − | 0.672444i | \(-0.234755\pi\) | ||||
0.740148 | + | 0.672444i | \(0.234755\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.34989e18 | − | 9.75520e17i | 0.189790 | − | 0.0787882i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.91167e19i | − | 0.847242i | −0.905840 | − | 0.423621i | \(-0.860759\pi\) | ||
0.905840 | − | 0.423621i | \(-0.139241\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.07042e19 | −1.51914 | −0.759569 | − | 0.650426i | \(-0.774590\pi\) | ||||
−0.759569 | + | 0.650426i | \(0.774590\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.48053e19 | − | 2.47275e19i | −0.359744 | − | 0.358616i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.14305e20i | − | 0.983766i | −0.870661 | − | 0.491883i | \(-0.836309\pi\) | ||
0.870661 | − | 0.491883i | \(-0.163691\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.52568e19 | 0.184030 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.08331e20 | − | 2.60954e20i | −0.349872 | − | 0.842794i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.21591e20i | 1.06174i | 0.847452 | + | 0.530872i | \(0.178136\pi\) | ||||
−0.847452 | + | 0.530872i | \(0.821864\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.79848e20 | −0.365233 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00438e21 | − | 4.16951e20i | 0.853883 | − | 0.354476i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.99992e20i | − | 0.337226i | −0.985682 | − | 0.168613i | \(-0.946071\pi\) | ||
0.985682 | − | 0.168613i | \(-0.0539289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.42263e19 | 0.0279640 | 0.0139820 | − | 0.999902i | \(-0.495549\pi\) | ||||
0.0139820 | + | 0.999902i | \(0.495549\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.00310e21 | + | 3.01255e21i | −0.768216 | + | 0.770633i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.93727e20i | − | 0.104382i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.52972e21 | −1.04241 | −0.521203 | − | 0.853433i | \(-0.674517\pi\) | ||||
−0.521203 | + | 0.853433i | \(0.674517\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.44041e21 | − | 1.55140e22i | −0.552999 | − | 1.33210i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.05121e22i | − | 1.25000i | −0.780625 | − | 0.624999i | \(-0.785099\pi\) | ||
0.780625 | − | 0.624999i | \(-0.214901\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.58499e22 | −1.56536 | −0.782679 | − | 0.622425i | \(-0.786148\pi\) | ||||
−0.782679 | + | 0.622425i | \(0.786148\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.17070e22 | − | 9.01133e21i | 0.685276 | − | 0.284481i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.39870e22i | 0.782392i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.61248e22 | −0.442108 | −0.221054 | − | 0.975262i | \(-0.570950\pi\) | ||||
−0.221054 | + | 0.975262i | \(0.570950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.50559e20 | − | 7.97660e22i | −0.00314115 | − | 0.999995i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.17460e23i | − | 1.09889i | −0.835530 | − | 0.549445i | \(-0.814839\pi\) | ||
0.835530 | − | 0.549445i | \(-0.185161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.59329e22 | −0.463527 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.39010e23 | + | 3.34856e23i | 0.739291 | + | 1.78085i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.60364e23i | − | 0.649273i | −0.945839 | − | 0.324637i | \(-0.894758\pi\) | ||
0.945839 | − | 0.324637i | \(-0.105242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.21069e22 | −0.223604 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.35311e23 | − | 1.39199e23i | 0.801036 | − | 0.332537i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2.53767e23i | − | 0.469626i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.32244e22 | −0.119947 | −0.0599736 | − | 0.998200i | \(-0.519102\pi\) | ||||
−0.0599736 | + | 0.998200i | \(0.519102\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.51369e23 | − | 4.49953e23i | −0.509224 | − | 0.507627i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.20951e24i | 1.96083i | 0.196945 | + | 0.980415i | \(0.436898\pi\) | ||||
−0.196945 | + | 0.980415i | \(0.563102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.85825e23 | −0.270610 | −0.135305 | − | 0.990804i | \(-0.543201\pi\) | ||||
−0.135305 | + | 0.990804i | \(0.543201\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.80577e23 | + | 9.16758e23i | 0.211920 | + | 0.510485i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.07071e24i | 1.36343i | 0.731617 | + | 0.681716i | \(0.238766\pi\) | ||||
−0.731617 | + | 0.681716i | \(0.761234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.69282e24 | 0.601857 | 0.300929 | − | 0.953647i | \(-0.402703\pi\) | ||||
0.300929 | + | 0.953647i | \(0.402703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.78298e24 | − | 1.98558e24i | 1.36717 | − | 0.567558i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.70784e24i | − | 0.624715i | −0.949965 | − | 0.312358i | \(-0.898881\pi\) | ||
0.949965 | − | 0.312358i | \(-0.101119\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.91980e24 | −0.732638 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.54621e23 | − | 9.57624e23i | 0.145078 | − | 0.145534i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.00742e24i | 0.992954i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.75748e24 | 0.483006 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.89521e24 | − | 9.38302e24i | −0.324840 | − | 0.782495i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.28763e25i | − | 0.884852i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.15801e25 | 1.22577 | 0.612886 | − | 0.790172i | \(-0.290009\pi\) | ||||
0.612886 | + | 0.790172i | \(0.290009\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.97953e25 | + | 1.23690e25i | −1.40304 | + | 0.582451i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.13650e25i | − | 0.444954i | −0.974938 | − | 0.222477i | \(-0.928586\pi\) | ||
0.974938 | − | 0.222477i | \(-0.0714143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.08195e25 | −1.00602 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.72136e25 | − | 7.08262e24i | −0.469748 | − | 0.193281i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.38297e25i | 0.316349i | 0.987411 | + | 0.158175i | \(0.0505609\pi\) | ||||
−0.987411 | + | 0.158175i | \(0.949439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.91088e25 | −1.32848 | −0.664241 | − | 0.747518i | \(-0.731245\pi\) | ||||
−0.664241 | + | 0.747518i | \(0.731245\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.32907e25 | − | 5.61042e25i | −0.377185 | − | 0.908586i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.08037e25i | − | 0.147755i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.46052e25 | 0.979448 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73050e25 | − | 7.18389e24i | 0.169967 | − | 0.0705589i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.45823e25i | − | 0.121785i | −0.998144 | − | 0.0608923i | \(-0.980605\pi\) | ||
0.998144 | − | 0.0608923i | \(-0.0193946\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.28532e26 | −0.914720 | −0.457360 | − | 0.889282i | \(-0.651205\pi\) | ||||
−0.457360 | + | 0.889282i | \(0.651205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.06343e26 | − | 1.06010e26i | −0.646269 | − | 0.644242i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.47200e25i | − | 0.440561i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.95529e26 | 0.871796 | 0.435898 | − | 0.899996i | \(-0.356431\pi\) | ||||
0.435898 | + | 0.899996i | \(0.356431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.06279e26 | + | 2.56011e26i | 0.407082 | + | 0.980604i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.76052e26i | 1.56944i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.44368e26 | −0.410413 | −0.205206 | − | 0.978719i | \(-0.565787\pi\) | ||||
−0.205206 | + | 0.978719i | \(0.565787\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.37357e26 | + | 5.70217e25i | −0.337322 | + | 0.140034i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.74707e26i | − | 1.00885i | −0.863455 | − | 0.504426i | \(-0.831704\pi\) | ||
0.863455 | − | 0.504426i | \(-0.168296\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.19880e26 | −0.957772 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.08018e26 | − | 4.09302e26i | 0.652719 | − | 0.654772i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.88219e26i | − | 1.09671i | −0.836244 | − | 0.548357i | \(-0.815253\pi\) | ||
0.836244 | − | 0.548357i | \(-0.184747\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.66085e26 | −0.807371 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.22254e26 | − | 2.94493e26i | −0.129296 | − | 0.311455i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.71671e27i | 1.58657i | 0.608847 | + | 0.793287i | \(0.291632\pi\) | ||||
−0.608847 | + | 0.793287i | \(0.708368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.59970e26 | −0.533804 | −0.266902 | − | 0.963724i | \(-0.586000\pi\) | ||||
−0.266902 | + | 0.963724i | \(0.586000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.64323e25 | − | 1.51243e25i | 0.0258270 | − | 0.0107217i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.20847e27i | − | 0.751928i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.19975e27 | −0.656131 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.60170e26 | + | 2.09055e27i | −0.414040 | + | 1.00628i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.80733e26i | − | 0.373632i | −0.982395 | − | 0.186816i | \(-0.940183\pi\) | ||
0.982395 | − | 0.186816i | \(-0.0598168\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.65998e27 | −0.621461 | −0.310730 | − | 0.950498i | \(-0.600574\pi\) | ||||
−0.310730 | + | 0.950498i | \(0.600574\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.20977e26 | − | 2.91418e26i | −0.0400211 | − | 0.0964052i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.80575e27i | − | 0.821209i | −0.911814 | − | 0.410604i | \(-0.865318\pi\) | ||
0.911814 | − | 0.410604i | \(-0.134682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.04163e27 | −1.56645 | −0.783226 | − | 0.621737i | \(-0.786427\pi\) | ||||
−0.783226 | + | 0.621737i | \(0.786427\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.18662e27 | + | 1.73801e27i | −0.962745 | + | 0.399668i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.02751e28i | − | 2.09814i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.37073e27 | −0.430363 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.32226e27 | − | 6.30243e27i | −1.02148 | − | 1.01827i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.61767e27i | − | 0.664764i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.62629e27 | −1.23615 | −0.618073 | − | 0.786121i | \(-0.712086\pi\) | ||||
−0.618073 | + | 0.786121i | \(0.712086\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.17952e27 | − | 1.00679e28i | −0.479260 | − | 1.15447i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.52812e27i | 0.771658i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.02891e28 | −0.943756 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.75961e28 | + | 7.30475e27i | −1.44573 | + | 0.600172i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.54539e27i | − | 0.187519i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.86863e28 | 1.23556 | 0.617782 | − | 0.786349i | \(-0.288031\pi\) | ||||
0.617782 | + | 0.786349i | \(0.288031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.81827e27 | − | 8.84602e27i | 0.523834 | − | 0.525482i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.80444e28i | − | 0.963901i | −0.876198 | − | 0.481951i | \(-0.839928\pi\) | ||
0.876198 | − | 0.481951i | \(-0.160072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.96660e28 | −0.945562 | −0.472781 | − | 0.881180i | \(-0.656750\pi\) | ||||
−0.472781 | + | 0.881180i | \(0.656750\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.92517e27 | + | 1.66818e28i | 0.299976 | + | 0.722601i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.90415e28i | 1.52495i | 0.647018 | + | 0.762474i | \(0.276016\pi\) | ||||
−0.647018 | + | 0.762474i | \(0.723984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.41754e28 | −0.499712 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.28228e28 | + | 5.32317e27i | −0.408321 | + | 0.169508i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.14900e28i | 0.330785i | 0.986228 | + | 0.165392i | \(0.0528891\pi\) | ||||
−0.986228 | + | 0.165392i | \(0.947111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.26729e28 | −0.590612 | −0.295306 | − | 0.955403i | \(-0.595422\pi\) | ||||
−0.295306 | + | 0.955403i | \(0.595422\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.63760e28 | − | 3.91003e28i | −0.386308 | − | 0.922370i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 4.37231e27i | − | 0.0934797i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.79685e27 | 0.189987 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.39336e28 | − | 5.76528e28i | −0.421324 | − | 1.01491i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.74981e27i | 0.0439762i | 0.999758 | + | 0.0219881i | \(0.00699960\pi\) | ||||
−0.999758 | + | 0.0219881i | \(0.993000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.13265e28 | −1.03706 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.23617e28 | + | 1.34344e28i | −0.428104 | + | 0.177720i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.14943e29i | − | 1.38447i | −0.721671 | − | 0.692236i | \(-0.756626\pi\) | ||
0.721671 | − | 0.692236i | \(-0.243374\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.46767e29 | −1.61076 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.36460e29 | + | 1.36032e29i | 1.36559 | + | 1.36130i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.67988e28i | 0.153394i | 0.997054 | + | 0.0766970i | \(0.0244374\pi\) | ||||
−0.997054 | + | 0.0766970i | \(0.975563\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.46842e28 | 0.539321 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.26757e28 | − | 7.87112e28i | −0.248937 | − | 0.599655i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 7.11629e28i | − | 0.495708i | −0.968797 | − | 0.247854i | \(-0.920275\pi\) | ||
0.968797 | − | 0.247854i | \(-0.0797254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.35305e28 | 0.532370 | 0.266185 | − | 0.963922i | \(-0.414237\pi\) | ||||
0.266185 | + | 0.963922i | \(0.414237\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.53921e28 | + | 1.46924e28i | −0.206516 | + | 0.0857319i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 9.97991e28i | − | 0.533500i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.50267e29 | −0.736389 | −0.368194 | − | 0.929749i | \(-0.620024\pi\) | ||||
−0.368194 | + | 0.929749i | \(0.620024\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.36217e29 | − | 1.36645e29i | 0.612322 | − | 0.614249i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.37645e29i | 0.567918i | 0.958836 | + | 0.283959i | \(0.0916479\pi\) | ||||
−0.958836 | + | 0.283959i | \(0.908352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.27935e28 | 0.162159 | 0.0810794 | − | 0.996708i | \(-0.474163\pi\) | ||||
0.0810794 | + | 0.996708i | \(0.474163\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.17074e28 | − | 1.24556e29i | −0.180059 | − | 0.433737i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.87920e29i | 0.921911i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.67855e28 | 0.167288 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.08489e28 | + | 1.69577e28i | −0.110781 | + | 0.0459888i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.71498e29i | 0.428397i | 0.976790 | + | 0.214199i | \(0.0687140\pi\) | ||||
−0.976790 | + | 0.214199i | \(0.931286\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.44069e28 | −0.171297 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.13226e29 | − | 1.28879e29i | −0.664937 | − | 0.273593i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.51327e29i | − | 0.296388i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.14275e29 | 1.65302 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.50208e29 | + | 1.08449e30i | 0.751799 | + | 1.81098i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 9.20503e27i | − | 0.0142045i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.60156e29 | 1.36988 | 0.684938 | − | 0.728601i | \(-0.259829\pi\) | ||||
0.684938 | + | 0.728601i | \(0.259829\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.89374e29 | + | 7.86154e28i | −0.249930 | + | 0.103754i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.83314e29i | 0.223909i | 0.993713 | + | 0.111955i | \(0.0357111\pi\) | ||||
−0.993713 | + | 0.111955i | \(0.964289\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.66337e30 | 1.88130 | 0.940648 | − | 0.339385i | \(-0.110219\pi\) | ||||
0.940648 | + | 0.339385i | \(0.110219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.73596e29 | + | 3.72424e29i | 0.391449 | + | 0.390221i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.50864e29i | 0.534975i | 0.963561 | + | 0.267487i | \(0.0861934\pi\) | ||||
−0.963561 | + | 0.267487i | \(0.913807\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.53952e30 | 1.38643 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.25685e29 | + | 1.50719e30i | 0.522752 | + | 1.25924i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.08793e30i | − | 0.843669i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.11734e29 | 0.152472 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.30884e29 | − | 3.44928e29i | 0.555862 | − | 0.230757i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.72157e30i | 1.07047i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.52531e30 | −1.46009 | −0.730045 | − | 0.683399i | \(-0.760501\pi\) | ||||
−0.730045 | + | 0.683399i | \(0.760501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.94304e30 | − | 1.94915e30i | 1.04508 | − | 1.04837i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.05780e30i | 0.529499i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.18579e29 | 0.288295 | 0.144147 | − | 0.989556i | \(-0.453956\pi\) | ||||
0.144147 | + | 0.989556i | \(0.453956\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.51748e29 | − | 1.32908e30i | −0.239521 | − | 0.576974i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.54161e30i | − | 0.623621i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.35442e30 | 0.887882 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.92395e30 | + | 7.98695e29i | −0.676649 | + | 0.280900i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.27882e30i | 1.07588i | 0.842983 | + | 0.537940i | \(0.180797\pi\) | ||||
−0.842983 | + | 0.537940i | \(0.819203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.23269e30 | −0.377527 | −0.188764 | − | 0.982023i | \(-0.560448\pi\) | ||||
−0.188764 | + | 0.982023i | \(0.560448\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.73430e29 | − | 6.64541e29i | 0.0781916 | − | 0.190036i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5.25121e30i | − | 1.40269i | −0.712820 | − | 0.701347i | \(-0.752582\pi\) | ||
0.712820 | − | 0.701347i | \(-0.247418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.54377e30 | −0.634946 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.63158e30 | + | 3.93026e30i | 0.380707 | + | 0.917071i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.10562e30i | 0.677664i | 0.940847 | + | 0.338832i | \(0.110032\pi\) | ||||
−0.940847 | + | 0.338832i | \(0.889968\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.11452e29 | −0.145231 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.33510e30 | − | 9.69379e29i | 0.446094 | − | 0.185189i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.44586e30i | 0.795136i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.54480e30 | 0.258749 | 0.129374 | − | 0.991596i | \(-0.458703\pi\) | ||||
0.129374 | + | 0.991596i | \(0.458703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.82375e30 | − | 3.81176e30i | −0.600031 | − | 0.598149i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.85576e30i | − | 1.15532i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.17121e30 | −1.12663 | −0.563314 | − | 0.826243i | \(-0.690474\pi\) | ||||
−0.563314 | + | 0.826243i | \(0.690474\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.62366e30 | − | 6.32004e30i | −0.339260 | − | 0.817230i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.26624e30i | 0.396235i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.36135e31 | 1.54989 | 0.774944 | − | 0.632029i | \(-0.217778\pi\) | ||||
0.774944 | + | 0.632029i | \(0.217778\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.05921e31 | − | 4.39715e30i | 1.13210 | − | 0.469971i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.14155e29i | 0.0214953i | 0.999942 | + | 0.0107477i | \(0.00342115\pi\) | ||||
−0.999942 | + | 0.0107477i | \(0.996579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.21484e30 | 0.397422 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.21041e31 | + | 1.21421e31i | −1.07250 | + | 1.07588i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.46642e30i | − | 0.205433i | −0.994711 | − | 0.102717i | \(-0.967246\pi\) | ||
0.994711 | − | 0.102717i | \(-0.0327535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.68047e31 | −1.31616 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.31573e30 | − | 5.57828e30i | −0.170599 | − | 0.410950i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.23982e30i | 0.224572i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.20449e31 | −0.785809 | −0.392904 | − | 0.919579i | \(-0.628530\pi\) | ||||
−0.392904 | + | 0.919579i | \(0.628530\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.51271e31 | + | 6.27976e30i | −0.929137 | + | 0.385716i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.88143e30i | 0.282367i | 0.989983 | + | 0.141184i | \(0.0450908\pi\) | ||||
−0.989983 | + | 0.141184i | \(0.954909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.27068e30 | 0.178228 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.89204e30 | + | 3.10726e28i | −0.507955 | + | 0.00159557i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.19900e31i | − | 1.06437i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.14098e31 | 0.977085 | 0.488543 | − | 0.872540i | \(-0.337529\pi\) | ||||
0.488543 | + | 0.872540i | \(0.337529\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.81793e30 | + | 6.78801e30i | 0.121291 | + | 0.292173i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.03657e30i | 0.366947i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.45666e31 | −0.558190 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.39205e31 | + | 1.40816e31i | −1.22696 | + | 0.509352i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 9.90044e28i | − | 0.00338132i | −0.999999 | − | 0.00169066i | \(-0.999462\pi\) | ||
0.999999 | − | 0.00169066i | \(-0.000538154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.38801e31 | −0.447720 | −0.223860 | − | 0.974621i | \(-0.571866\pi\) | ||||
−0.223860 | + | 0.974621i | \(0.571866\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.28635e31 | − | 2.27918e31i | −0.696720 | − | 0.694535i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2.35129e31i | − | 0.677079i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.11793e30 | −0.0304285 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.20136e30 | − | 5.30277e30i | −0.0566505 | − | 0.136463i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.58411e31i | − | 1.11565i | −0.829959 | − | 0.557824i | \(-0.811636\pi\) | ||
0.829959 | − | 0.557824i | \(-0.188364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.04562e31 | −1.39183 | −0.695915 | − | 0.718124i | \(-0.745001\pi\) | ||||
−0.695915 | + | 0.718124i | \(0.745001\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.15266e31 | − | 1.72391e31i | 0.904597 | − | 0.375529i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.46790e31i | − | 1.33348i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.04585e31 | −0.789652 | −0.394826 | − | 0.918756i | \(-0.629195\pi\) | ||||
−0.394826 | + | 0.918756i | \(0.629195\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.02999e30 | − | 7.05211e30i | 0.129925 | − | 0.130333i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.03672e32i | 1.81474i | 0.420329 | + | 0.907372i | \(0.361915\pi\) | ||||
−0.420329 | + | 0.907372i | \(0.638085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.98873e31 | −0.329803 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.97129e30 | − | 7.15742e30i | −0.0466933 | − | 0.112478i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.40229e31i | − | 0.804677i | −0.915491 | − | 0.402338i | \(-0.868197\pi\) | ||
0.915491 | − | 0.402338i | \(-0.131803\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.31389e31 | −0.609187 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.30871e31 | + | 2.61896e31i | −0.844816 | + | 0.350712i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.94221e30i | 0.113582i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.79920e31 | 0.698834 | 0.349417 | − | 0.936967i | \(-0.386380\pi\) | ||||
0.349417 | + | 0.936967i | \(0.386380\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.37968e31 | − | 3.03641e31i | −0.843889 | − | 0.347223i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.22421e31i | 0.567034i | 0.958967 | + | 0.283517i | \(0.0915013\pi\) | ||||
−0.958967 | + | 0.283517i | \(0.908499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.10907e31 | 0.217330 | 0.108665 | − | 0.994078i | \(-0.465342\pi\) | ||||
0.108665 | + | 0.994078i | \(0.465342\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.72625e31 | − | 4.15829e31i | −0.168915 | − | 0.406893i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.62891e32i | − | 1.51389i | −0.653479 | − | 0.756945i | \(-0.726691\pi\) | ||
0.653479 | − | 0.756945i | \(-0.273309\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28467e32 | 1.13428 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.59709e31 | − | 3.98408e31i | 0.805172 | − | 0.334254i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.36985e32i | 1.09230i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.04981e31 | 0.685987 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.04329e32 | + | 1.04002e32i | 0.751945 | + | 0.749587i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.75158e32i | 1.20062i | 0.799769 | + | 0.600308i | \(0.204955\pi\) | ||||
−0.799769 | + | 0.600308i | \(0.795045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.66539e31 | 0.304192 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.69999e31 | + | 2.33659e32i | 0.601735 | + | 1.44950i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.03209e31i | 0.0609281i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.23439e31 | 0.406494 | 0.203247 | − | 0.979127i | \(-0.434851\pi\) | ||||
0.203247 | + | 0.979127i | \(0.434851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.08600e31 | + | 2.94164e31i | −0.379049 | + | 0.157356i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.04300e32i | − | 0.531260i | −0.964075 | − | 0.265630i | \(-0.914420\pi\) | ||
0.964075 | − | 0.265630i | \(-0.0855799\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.62714e32 | 1.75955 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.58001e31 | + | 5.59756e31i | −0.257853 | + | 0.258664i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.08935e32i | 1.36016i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.57053e32 | 0.658931 | 0.329466 | − | 0.944168i | \(-0.393131\pi\) | ||||
0.329466 | + | 0.944168i | \(0.393131\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.67258e31 | − | 2.32999e32i | −0.386803 | − | 0.931755i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.71086e32i | 1.03345i | 0.856151 | + | 0.516726i | \(0.172850\pi\) | ||||
−0.856151 | + | 0.516726i | \(0.827150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.74008e32 | 0.996019 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.55171e32 | + | 1.05930e32i | −0.884578 | + | 0.367218i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.32358e31i | 0.0768324i | 0.999262 | + | 0.0384162i | \(0.0122313\pi\) | ||||
−0.999262 | + | 0.0384162i | \(0.987769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.39941e32 | 1.70332 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.16868e32 | − | 2.84034e32i | 0.351792 | − | 0.854992i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.78474e31i | 0.137458i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.57942e32 | −0.707351 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.60607e32 | − | 3.86879e32i | −0.420490 | − | 1.01290i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.99413e32i | − | 0.748546i | −0.927319 | − | 0.374273i | \(-0.877892\pi\) | ||
0.927319 | − | 0.374273i | \(-0.122108\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.02363e32 | 1.19949 | 0.599746 | − | 0.800190i | \(-0.295268\pi\) | ||||
0.599746 | + | 0.800190i | \(0.295268\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.26933e32 | + | 1.35721e32i | −0.745670 | + | 0.309553i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.63206e32i | − | 0.791454i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.18810e32 | −1.08029 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.20011e32 | − | 1.19635e32i | −0.238829 | − | 0.238080i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.15235e31i | − | 0.174103i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.80808e32 | 0.692566 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.49795e32 | + | 8.42609e32i | 0.608307 | + | 1.46533i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 7.95606e31i | − | 0.132322i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.14877e33 | 1.82754 | 0.913768 | − | 0.406236i | \(-0.133159\pi\) | ||||
0.913768 | + | 0.406236i | \(0.133159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.23932e32 | + | 1.34475e32i | −0.493010 | + | 0.204665i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.09932e32i | − | 0.305718i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.72421e32 | −0.379658 | −0.189829 | − | 0.981817i | \(-0.560793\pi\) | ||||
−0.189829 | + | 0.981817i | \(0.560793\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.48003e31 | − | 1.48468e31i | 0.0197425 | − | 0.0198046i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.39604e33i | 1.78270i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.93470e32 | 0.481072 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.46237e32 | − | 5.93152e32i | −0.288296 | − | 0.694465i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.73854e32i | 0.419218i | 0.977785 | + | 0.209609i | \(0.0672191\pi\) | ||||
−0.977785 | + | 0.209609i | \(0.932781\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.90628e32 | −0.312174 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.88869e32 | + | 2.44459e32i | −0.605988 | + | 0.251566i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 3.96278e32i | − | 0.390751i | −0.980729 | − | 0.195375i | \(-0.937408\pi\) | ||
0.980729 | − | 0.195375i | \(-0.0625925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.35808e32 | −0.317329 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.77370e30 | + | 1.20137e33i | 0.00341799 | + | 1.08813i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.91705e33i | − | 1.66451i | −0.554395 | − | 0.832254i | \(-0.687050\pi\) | ||
0.554395 | − | 0.832254i | \(-0.312950\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.07277e32 | −0.588784 | −0.294392 | − | 0.955685i | \(-0.595117\pi\) | ||||
−0.294392 | + | 0.955685i | \(0.595117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.79457e32 | − | 4.32288e32i | −0.143254 | − | 0.345078i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.39787e33i | − | 1.07017i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.60843e32 | −0.411843 | −0.205921 | − | 0.978569i | \(-0.566019\pi\) | ||||
−0.205921 | + | 0.978569i | \(0.566019\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.14762e32 | + | 3.38235e32i | −0.573968 | + | 0.238274i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.76909e33i | 1.19574i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17702e33 | 0.763419 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.18758e32 | − | 1.18386e32i | −0.0739252 | − | 0.0736934i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.55484e33i | − | 0.929027i | −0.885566 | − | 0.464514i | \(-0.846229\pi\) | ||
0.885566 | − | 0.464514i | \(-0.153771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.39793e33 | 0.801867 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.71696e32 | − | 1.37714e33i | −0.314859 | − | 0.758451i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.57869e32i | 0.453696i | 0.973930 | + | 0.226848i | \(0.0728420\pi\) | ||||
−0.973930 | + | 0.226848i | \(0.927158\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.93025e32 | 0.504379 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.96540e33 | + | 1.23104e33i | −1.44674 | + | 0.600592i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.41388e33i | 0.662658i | 0.943515 | + | 0.331329i | \(0.107497\pi\) | ||||
−0.943515 | + | 0.331329i | \(0.892503\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.65022e33 | −0.743103 | −0.371552 | − | 0.928412i | \(-0.621174\pi\) | ||||
−0.371552 | + | 0.928412i | \(0.621174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.70077e33 | + | 1.70613e33i | −0.735934 | + | 0.738250i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 5.89990e32i | − | 0.245346i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.77181e33 | 1.10790 | 0.553948 | − | 0.832552i | \(-0.313121\pi\) | ||||
0.553948 | + | 0.832552i | \(0.313121\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.09365e33 | − | 5.04332e33i | −0.804446 | − | 1.93780i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.47249e32i | − | 0.202158i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.92257e33 | 1.39330 | 0.696651 | − | 0.717410i | \(-0.254673\pi\) | ||||
0.696651 | + | 0.717410i | \(0.254673\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.16362e33 | + | 4.83057e32i | −0.397474 | + | 0.165005i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.49852e33i | 0.820844i | 0.911896 | + | 0.410422i | \(0.134619\pi\) | ||||
−0.911896 | + | 0.410422i | \(0.865381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.36013e33 | −1.06186 | −0.530931 | − | 0.847415i | \(-0.678158\pi\) | ||||
−0.530931 | + | 0.847415i | \(0.678158\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.38732e33 | − | 1.80519e33i | −1.33383 | − | 0.548812i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.41527e33i | 0.706495i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.03921e33 | 0.292511 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.40892e32 | − | 2.26648e33i | −0.254876 | − | 0.613962i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.18088e33i | − | 1.35082i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.71285e33 | −1.18285 | −0.591427 | − | 0.806359i | \(-0.701435\pi\) | ||||
−0.591427 | + | 0.806359i | \(0.701435\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.72485e33 | + | 1.96145e33i | −1.14168 | + | 0.473949i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 2.67622e33i | − | 0.622640i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.68796e32 | 0.0378171 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.10285e33 | − | 4.08998e33i | −0.885269 | − | 0.882493i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.12036e33i | − | 0.856326i | −0.903702 | − | 0.428163i | \(-0.859161\pi\) | ||
0.903702 | − | 0.428163i | \(-0.140839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.45104e33 | 0.290501 | 0.145250 | − | 0.989395i | \(-0.453601\pi\) | ||||
0.145250 | + | 0.989395i | \(0.453601\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.53392e33 | + | 3.69501e33i | 0.295861 | + | 0.712687i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 9.20942e33i | − | 1.71152i | −0.517377 | − | 0.855758i | \(-0.673091\pi\) | ||
0.517377 | − | 0.855758i | \(-0.326909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.35394e33 | −0.242474 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.05016e33 | + | 2.09649e33i | −0.871633 | + | 0.361844i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.83686e33i | 0.638289i | 0.947706 | + | 0.319144i | \(0.103396\pi\) | ||||
−0.947706 | + | 0.319144i | \(0.896604\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.40941e33 | −0.226018 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.14826e33 | + | 7.17075e33i | −1.10514 | + | 1.10861i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.22388e34i | 1.82437i | 0.409774 | + | 0.912187i | \(0.365608\pi\) | ||||
−0.409774 | + | 0.912187i | \(0.634392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.50499e33 | 0.647555 | 0.323777 | − | 0.946133i | \(-0.395047\pi\) | ||||
0.323777 | + | 0.946133i | \(0.395047\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.18646e32 | − | 1.24935e33i | −0.0718966 | − | 0.173189i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.82202e33i | 0.511015i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.15638e34 | 2.78109 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.17176e33 | − | 3.80751e33i | 1.14114 | − | 0.473726i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.67499e32i | − | 0.0201068i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.47939e34 | 1.71356 | 0.856782 | − | 0.515678i | \(-0.172460\pi\) | ||||
0.856782 | + | 0.515678i | \(0.172460\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.52580e33 | − | 6.13867e33i | 0.282327 | − | 0.686166i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.47154e33i | − | 1.02178i | −0.859647 | − | 0.510889i | \(-0.829316\pi\) | ||
0.859647 | − | 0.510889i | \(-0.170684\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.25346e33 | 0.130518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.67672e33 | − | 8.85670e33i | −0.369568 | − | 0.890239i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.32859e34i | 1.28927i | 0.764492 | + | 0.644633i | \(0.222990\pi\) | ||||
−0.764492 | + | 0.644633i | \(0.777010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.71507e33 | 0.160692 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.65261e33 | + | 4.00713e33i | −0.873301 | + | 0.362537i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.49718e33i | 0.218182i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.22829e34 | 1.03649 | 0.518246 | − | 0.855232i | \(-0.326585\pi\) | ||||
0.518246 | + | 0.855232i | \(0.326585\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.79813e33 | + | 6.77681e33i | 0.554103 | + | 0.552365i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.57040e33i | 0.674813i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.01636e34 | −0.773134 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.95506e33 | + | 1.91626e34i | 0.584679 | + | 1.40841i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.57975e34i | 1.83215i | 0.401007 | + | 0.916075i | \(0.368660\pi\) | ||||
−0.401007 | + | 0.916075i | \(0.631340\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.99405e34 | 1.36859 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.95766e33 | + | 2.88836e33i | −0.461523 | + | 0.191594i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 3.32778e34i | − | 2.13364i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.67711e34 | 1.03946 | 0.519728 | − | 0.854332i | \(-0.326033\pi\) | ||||
0.519728 | + | 0.854332i | \(0.326033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.20913e33 | + | 5.22552e33i | −0.312126 | + | 0.313108i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.15931e34i | − | 1.25095i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.33981e33 | −0.0750532 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.34120e33 | + | 5.63961e33i | 0.126826 | + | 0.305506i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.42987e34i | − | 0.749115i | −0.927204 | − | 0.374558i | \(-0.877795\pi\) | ||
0.927204 | − | 0.374558i | \(-0.122205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.81097e33 | 0.294459 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.11285e34 | + | 4.61981e33i | −0.545477 | + | 0.226446i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.01718e34i | 1.43069i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.19847e34 | 0.549813 | 0.274907 | − | 0.961471i | \(-0.411353\pi\) | ||||
0.274907 | + | 0.961471i | \(0.411353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.60049e34 | − | 1.58547e34i | −0.710431 | − | 0.703767i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.22740e34i | 1.38626i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.29541e34 | 1.36981 | 0.684906 | − | 0.728631i | \(-0.259843\pi\) | ||||
0.684906 | + | 0.728631i | \(0.259843\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.90897e32 | − | 2.14605e33i | −0.0358410 | − | 0.0863359i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.92482e34i | 0.749515i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.97092e34 | 0.742909 | 0.371455 | − | 0.928451i | \(-0.378859\pi\) | ||||
0.371455 | + | 0.928451i | \(0.378859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.80857e33 | − | 1.99620e33i | 0.175468 | − | 0.0728426i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.02403e34i | − | 0.361780i | −0.983503 | − | 0.180890i | \(-0.942102\pi\) | ||
0.983503 | − | 0.180890i | \(-0.0578979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.80840e33 | −0.0618614 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.34946e34 | − | 2.34209e34i | −0.778252 | − | 0.775811i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4.62484e34i | − | 1.48359i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.34386e34 | 0.417519 | 0.208759 | − | 0.977967i | \(-0.433057\pi\) | ||||
0.208759 | + | 0.977967i | \(0.433057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.60299e32 | + | 1.34968e33i | 0.0168609 | + | 0.0406155i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.59397e34i | 0.464639i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.51041e34 | 1.55608 | 0.778042 | − | 0.628212i | \(-0.216213\pi\) | ||||
0.778042 | + | 0.628212i | \(0.216213\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.50090e34 | + | 1.45334e34i | −0.957809 | + | 0.397619i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.30641e34i | − | 1.14156i | −0.821102 | − | 0.570781i | \(-0.806640\pi\) | ||
0.821102 | − | 0.570781i | \(-0.193360\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.54958e34 | −0.654900 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.31466e34 | + | 1.31880e34i | −0.327248 | + | 0.328278i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.87253e33i | − | 0.0692980i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.03466e34 | −0.709567 | −0.354784 | − | 0.934948i | \(-0.615445\pi\) | ||||
−0.354784 | + | 0.934948i | \(0.615445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.34207e34 | − | 5.64171e34i | −0.530819 | − | 1.27867i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.67755e34i | 0.368571i | 0.982873 | + | 0.184286i | \(0.0589972\pi\) | ||||
−0.982873 | + | 0.184286i | \(0.941003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.02127e34 | 0.643531 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.20371e34 | + | 2.99050e34i | −1.48766 | + | 0.617578i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 3.91184e34i | − | 0.783307i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.62876e34 | −0.898778 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.46962e34 | + | 3.89633e34i | 1.78316 | + | 0.733694i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.42481e34i | − | 0.442835i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.01739e34 | −0.534484 | −0.267242 | − | 0.963629i | \(-0.586112\pi\) | ||||
−0.267242 | + | 0.963629i | \(0.586112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.42290e33 | + | 8.24530e33i | 0.0588126 | + | 0.141671i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.07832e34i | 0.679773i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.55367e32 | 0.00574644 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.17488e34 | − | 1.31800e34i | 0.498106 | − | 0.206781i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.59723e34i | 1.15653i | 0.815850 | + | 0.578263i | \(0.196269\pi\) | ||||
−0.815850 | + | 0.578263i | \(0.803731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.07716e34 | −0.897717 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.20763e34 | − | 3.19757e34i | −0.459826 | − | 0.458384i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.08990e34i | 1.12553i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.90366e34 | 0.797207 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.45001e34 | − | 3.49287e34i | −0.190059 | − | 0.457826i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.59731e33i | − | 0.0712192i | −0.999366 | − | 0.0356096i | \(-0.988663\pi\) | ||
0.999366 | − | 0.0356096i | \(-0.0113373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.95151e34 | −0.488104 | −0.244052 | − | 0.969762i | \(-0.578477\pi\) | ||||
−0.244052 | + | 0.969762i | \(0.578477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.09991e34 | − | 1.70201e34i | 0.491686 | − | 0.204115i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.79036e34i | 0.208472i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.24219e35 | −1.40450 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.43777e34 | + | 1.44229e34i | −0.157864 | + | 0.158360i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 9.13276e33i | − | 0.0973832i | −0.998814 | − | 0.0486916i | \(-0.984495\pi\) | ||
0.998814 | − | 0.0486916i | \(-0.0155051\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.85735e34 | −0.192352 | −0.0961760 | − | 0.995364i | \(-0.530661\pi\) | ||||
−0.0961760 | + | 0.995364i | \(0.530661\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.03350e34 | − | 4.89842e34i | −0.204549 | − | 0.492729i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.06740e35i | − | 1.04295i | −0.853267 | − | 0.521474i | \(-0.825382\pi\) | ||
0.853267 | − | 0.521474i | \(-0.174618\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.82567e35 | 1.73288 | 0.866440 | − | 0.499281i | \(-0.166403\pi\) | ||||
0.866440 | + | 0.499281i | \(0.166403\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.37553e34 | + | 3.06183e34i | −0.680113 | + | 0.282338i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.87447e34i | − | 0.167933i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.88699e34 | −0.512454 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.90162e34 | − | 9.48247e34i | 0.330019 | − | 0.802077i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.68970e34i | 0.138888i | 0.997586 | + | 0.0694442i | \(0.0221226\pi\) | ||||
−0.997586 | + | 0.0694442i | \(0.977877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.40250e35 | −2.71798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.80465e34 | + | 6.75601e34i | 0.217745 | + | 0.524517i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.44719e34i | 0.486508i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.16530e34 | −0.525574 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.10042e34 | − | 8.71957e33i | 0.149766 | − | 0.0621731i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.08010e35i | − | 2.13506i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.01848e34 | −0.338208 | −0.169104 | − | 0.985598i | \(-0.554087\pi\) | ||||
−0.169104 | + | 0.985598i | \(0.554087\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.07588e34 | − | 5.05996e34i | −0.332597 | − | 0.331554i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.02720e35i | − | 0.654465i | −0.944944 | − | 0.327233i | \(-0.893884\pi\) | ||
0.944944 | − | 0.327233i | \(-0.106116\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.27721e35 | −0.791304 | −0.395652 | − | 0.918400i | \(-0.629481\pi\) | ||||
−0.395652 | + | 0.918400i | \(0.629481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.86663e34 | + | 1.41319e35i | 0.353469 | + | 0.851457i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.40446e35i | − | 1.40893i | −0.709740 | − | 0.704463i | \(-0.751188\pi\) | ||
0.709740 | − | 0.704463i | \(-0.248812\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.77495e34 | −0.557085 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.78719e34 | − | 1.15706e34i | 0.154503 | − | 0.0641395i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.89533e34i | 0.317886i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.08370e34 | −0.214208 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.65944e34 | + | 1.66467e34i | −0.0846822 | + | 0.0849486i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.93932e35i | 0.962835i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.99000e35 | 0.961300 | 0.480650 | − | 0.876912i | \(-0.340401\pi\) | ||||
0.480650 | + | 0.876912i | \(0.340401\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.49442e34 | + | 8.41758e34i | 0.164251 | + | 0.395659i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.97792e35i | − | 0.904684i | −0.891845 | − | 0.452342i | \(-0.850589\pi\) | ||
0.891845 | − | 0.452342i | \(-0.149411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.50399e35 | 0.669446 | 0.334723 | − | 0.942317i | \(-0.391357\pi\) | ||||
0.334723 | + | 0.942317i | \(0.391357\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.65210e34 | + | 1.51611e34i | −0.158206 | + | 0.0656767i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.11037e35i | 1.31138i | 0.755031 | + | 0.655689i | \(0.227622\pi\) | ||||
−0.755031 | + | 0.655689i | \(0.772378\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.25021e35 | −1.33380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.80000e35 | + | 5.65411e32i | −0.719020 | + | 0.00225856i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.33902e35i | − | 0.909529i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.12895e35 | 0.805913 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.08342e34 | − | 7.42752e34i | −0.113638 | − | 0.273738i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.66067e35i | 1.67237i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.77310e35 | 0.968874 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.48751e35 | − | 1.86292e35i | 1.52670 | − | 0.633783i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.18450e34i | 0.271150i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.62862e35 | 0.525450 | 0.262725 | − | 0.964871i | \(-0.415379\pi\) | ||||
0.262725 | + | 0.964871i | \(0.415379\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.41949e35 | + | 4.40563e35i | 1.38869 | + | 1.38434i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.31582e35i | − | 0.402695i | −0.979520 | − | 0.201347i | \(-0.935468\pi\) | ||
0.979520 | − | 0.201347i | \(-0.0645320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.65061e35 | −0.790128 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.87561e33 | − | 4.51809e33i | −0.00544615 | − | 0.0131190i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.71171e35i | 0.484169i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.38423e35 | 0.381435 | 0.190718 | − | 0.981645i | \(-0.438919\pi\) | ||||
0.190718 | + | 0.981645i | \(0.438919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.71271e35 | − | 1.95641e35i | 1.26519 | − | 0.525223i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 9.82039e34i | − | 0.256867i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.30964e35 | 1.09835 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.69312e34 | + | 7.71732e34i | −0.191049 | + | 0.191650i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.79667e35i | 1.40278i | 0.712776 | + | 0.701391i | \(0.247437\pi\) | ||||
−0.712776 | + | 0.701391i | \(0.752563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.21457e34 | 0.170143 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.73520e34 | + | 8.99758e34i | 0.0858488 | + | 0.206798i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.48784e35i | 0.333287i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.61380e35 | −0.570685 | −0.285343 | − | 0.958426i | \(-0.592107\pi\) | ||||
−0.285343 | + | 0.958426i | \(0.592107\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.16428e35 | − | 3.38927e35i | 1.73752 | − | 0.721305i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.84502e35i | 0.590215i | 0.955464 | + | 0.295107i | \(0.0953554\pi\) | ||||
−0.955464 | + | 0.295107i | \(0.904645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.04240e35 | −1.22200 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.59256e35 | + | 1.06672e35i | 0.511148 | + | 0.210315i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.03824e35i | 0.391792i | 0.980625 | + | 0.195896i | \(0.0627615\pi\) | ||||
−0.980625 | + | 0.195896i | \(0.937239\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.71636e35 | −0.321672 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.12244e35 | + | 2.70379e35i | 0.205114 | + | 0.494091i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.97399e35i | − | 0.351746i | −0.984413 | − | 0.175873i | \(-0.943725\pi\) | ||
0.984413 | − | 0.175873i | \(-0.0562748\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.09222e35 | −0.189789 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.55638e35 | − | 3.13691e35i | 1.28047 | − | 0.531568i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2.08291e35i | − | 0.344230i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.53714e35 | −0.247760 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.14207e35 | + | 6.12281e35i | 0.965605 | + | 0.962576i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.05859e35i | 0.315676i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.81298e35 | −1.01911 | −0.509553 | − | 0.860439i | \(-0.670189\pi\) | ||||
−0.509553 | + | 0.860439i | \(0.670189\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.21676e35 | − | 5.33988e35i | −0.323470 | − | 0.779194i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.00910e35i | − | 0.570711i | −0.958422 | − | 0.285355i | \(-0.907888\pi\) | ||
0.958422 | − | 0.285355i | \(-0.0921117\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.04086e36 | 1.44556 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.03925e35 | − | 4.31428e34i | 0.140820 | − | 0.0584591i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.43289e36i | − | 1.89443i | −0.320600 | − | 0.947215i | \(-0.603884\pi\) | ||
0.320600 | − | 0.947215i | \(-0.396116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.61878e35 | −0.466843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.37539e35 | − | 3.38600e35i | 0.424908 | − | 0.426245i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 8.32748e35i | − | 1.02299i | −0.859286 | − | 0.511495i | \(-0.829092\pi\) | ||
0.859286 | − | 0.511495i | \(-0.170908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.47949e35 | −0.417139 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.50785e35 | + | 8.44993e35i | 0.410427 | + | 0.988661i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.91873e36i | 2.19109i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.31096e35 | 0.257578 | 0.128789 | − | 0.991672i | \(-0.458891\pi\) | ||||
0.128789 | + | 0.991672i | \(0.458891\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.23949e36 | + | 5.14556e35i | −1.34851 | + | 0.559811i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.49241e35i | 0.795692i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.99382e35 | −0.932400 | −0.466200 | − | 0.884679i | \(-0.654377\pi\) | ||||
−0.466200 | + | 0.884679i | \(0.654377\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.56539e35 | − | 1.35261e36i | 0.563261 | − | 1.36895i |
(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 | 48.25.e.d.17.7 | 8 | ||
3.2 | odd | 2 | inner | 48.25.e.d.17.8 | 8 | ||
4.3 | odd | 2 | 6.25.b.a.5.5 | yes | 8 | ||
12.11 | even | 2 | 6.25.b.a.5.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.25.b.a.5.1 | ✓ | 8 | 12.11 | even | 2 | ||
6.25.b.a.5.5 | yes | 8 | 4.3 | odd | 2 | ||
48.25.e.d.17.7 | 8 | 1.1 | even | 1 | trivial | ||
48.25.e.d.17.8 | 8 | 3.2 | odd | 2 | inner |