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 | 17.6 | ||
Root | \(5.64115e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.17 |
Dual form | 48.25.e.d.17.5 |
$q$-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 | ||||||||
\(3\) | 317945. | + | 425841.i | 0.598270 | + | 0.801295i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.76938e7i | 0.277274i | 0.990343 | + | 0.138637i | \(0.0442721\pi\) | ||||
−0.990343 | + | 0.138637i | \(0.955728\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41596e10 | 1.74547 | 0.872736 | − | 0.488192i | \(-0.162343\pi\) | ||||
0.872736 | + | 0.488192i | \(0.162343\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.02515e10 | + | 2.70788e11i | −0.284147 | + | 0.958781i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00004e12i | 1.27454i | 0.770642 | + | 0.637268i | \(0.219936\pi\) | ||||
−0.770642 | + | 0.637268i | \(0.780064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.67023e13 | 1.14612 | 0.573058 | − | 0.819515i | \(-0.305757\pi\) | ||||
0.573058 | + | 0.819515i | \(0.305757\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.88268e13 | + | 2.15229e13i | −0.222178 | + | 0.165885i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.60084e14i | 1.13295i | 0.824078 | + | 0.566477i | \(0.191694\pi\) | ||||
−0.824078 | + | 0.566477i | \(0.808306\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.05285e14 | 0.137931 | 0.0689656 | − | 0.997619i | \(-0.478030\pi\) | ||||
0.0689656 | + | 0.997619i | \(0.478030\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.68142e15 | + | 1.02881e16i | 1.04426 | + | 1.39864i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.66067e14i | − | 0.0349569i | −0.999847 | − | 0.0174784i | \(-0.994436\pi\) | ||
0.999847 | − | 0.0174784i | \(-0.00556384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.50222e16 | 0.923119 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.40828e17 | + | 5.19213e16i | −0.938263 | + | 0.345924i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00191e17i | 1.13107i | 0.824723 | + | 0.565537i | \(0.191331\pi\) | ||||
−0.824723 | + | 0.565537i | \(0.808669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.08492e18 | −1.37739 | −0.688696 | − | 0.725051i | \(-0.741816\pi\) | ||||
−0.688696 | + | 0.725051i | \(0.741816\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.70338e18 | + | 1.27179e18i | −1.02128 | + | 0.762517i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.63546e18i | 0.483974i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.67466e18 | 0.406302 | 0.203151 | − | 0.979147i | \(-0.434882\pi\) | ||||
0.203151 | + | 0.979147i | \(0.434882\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.48986e18 | + | 1.13709e19i | 0.685686 | + | 0.918377i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.10777e19i | − | 1.37734i | −0.725074 | − | 0.688671i | \(-0.758194\pi\) | ||
0.725074 | − | 0.688671i | \(-0.241806\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.43678e19 | 0.609810 | 0.304905 | − | 0.952383i | \(-0.401375\pi\) | ||||
0.304905 | + | 0.952383i | \(0.401375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.83307e19 | − | 5.43253e18i | −0.265845 | − | 0.0787866i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.79896e19i | − | 0.326957i | −0.986547 | − | 0.163478i | \(-0.947729\pi\) | ||
0.986547 | − | 0.163478i | \(-0.0522714\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.92105e20 | 2.04668 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.81091e20 | + | 2.09870e20i | −0.907830 | + | 0.677811i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.82597e19i | 0.179660i | 0.995957 | + | 0.0898301i | \(0.0286324\pi\) | ||||
−0.995957 | + | 0.0898301i | \(0.971368\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.70778e20 | −0.353396 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.70638e19 | + | 1.30003e20i | 0.0825200 | + | 0.110524i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.88092e21i | 1.05718i | 0.848879 | + | 0.528588i | \(0.177278\pi\) | ||||
−0.848879 | + | 0.528588i | \(0.822722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.92240e21 | −0.724244 | −0.362122 | − | 0.932131i | \(-0.617948\pi\) | ||||
−0.362122 | + | 0.932131i | \(0.617948\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.93884e21 | + | 6.54213e21i | −0.495971 | + | 1.67353i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.80758e21i | 0.317788i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.96234e21 | 0.973068 | 0.486534 | − | 0.873662i | \(-0.338261\pi\) | ||||
0.486534 | + | 0.873662i | \(0.338261\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.26223e20 | − | 2.43567e20i | 0.0280108 | − | 0.0209136i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.04327e22i | − | 1.24516i | −0.782557 | − | 0.622579i | \(-0.786085\pi\) | ||
0.782557 | − | 0.622579i | \(-0.213915\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.28296e22 | 1.43348 | 0.716740 | − | 0.697340i | \(-0.245633\pi\) | ||||
0.716740 | + | 0.697340i | \(0.245633\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.74940e22 | + | 2.34307e22i | 0.552274 | + | 0.739691i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.66394e22i | 2.22467i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.13170e21 | −0.0868433 | −0.0434216 | − | 0.999057i | \(-0.513826\pi\) | ||||
−0.0434216 | + | 0.999057i | \(0.513826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.68858e22 | − | 4.34623e22i | −0.838521 | − | 0.544870i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.14963e21i | 0.0107552i | 0.999986 | + | 0.00537761i | \(0.00171175\pi\) | ||||
−0.999986 | + | 0.00537761i | \(0.998288\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.46836e22 | −0.314138 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.70418e23 | + | 1.27239e23i | −0.906324 | + | 0.676688i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.69857e23i | 1.49745i | 0.662879 | + | 0.748727i | \(0.269335\pi\) | ||||
−0.662879 | + | 0.748727i | \(0.730665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.45117e23 | 2.00051 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.44945e23 | − | 4.62003e23i | −0.824051 | − | 1.10370i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.06659e22i | 0.0382447i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.10819e24 | 1.59718 | 0.798592 | − | 0.601873i | \(-0.205579\pi\) | ||||
0.798592 | + | 0.601873i | \(0.205579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.08316e24 | − | 3.21010e23i | −1.22200 | − | 0.362156i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.86377e24i | − | 1.65400i | −0.562202 | − | 0.827000i | \(-0.690046\pi\) | ||
0.562202 | − | 0.827000i | \(-0.309954\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.22843e24 | −0.861594 | −0.430797 | − | 0.902449i | \(-0.641768\pi\) | ||||
−0.430797 | + | 0.902449i | \(0.641768\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.96444e23 | + | 5.19985e23i | −0.387806 | + | 0.289547i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.55456e24i | − | 1.57827i | −0.614220 | − | 0.789134i | \(-0.710529\pi\) | ||
0.614220 | − | 0.789134i | \(-0.289471\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.18543e23 | 0.0776995 | 0.0388497 | − | 0.999245i | \(-0.487631\pi\) | ||||
0.0388497 | + | 0.999245i | \(0.487631\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.50396e23 | + | 1.13898e24i | 0.243078 | + | 0.325567i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.66320e24i | − | 1.30653i | −0.757128 | − | 0.653267i | \(-0.773398\pi\) | ||
0.757128 | − | 0.653267i | \(-0.226602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.18580e22 | 0.00969263 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.14290e24 | + | 7.23066e24i | −0.325666 | + | 1.09887i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.59474e25i | 1.97754i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.15061e24 | −0.624444 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.32341e25 | − | 9.88098e24i | 1.10366 | − | 0.824022i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.75953e24i | 0.533231i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.31873e25 | −0.749051 | −0.374526 | − | 0.927217i | \(-0.622194\pi\) | ||||
−0.374526 | + | 0.927217i | \(0.622194\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.74761e24 | + | 1.03768e25i | 0.364831 | + | 0.488638i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.72828e25i | − | 1.06815i | −0.845436 | − | 0.534077i | \(-0.820659\pi\) | ||
0.845436 | − | 0.534077i | \(-0.179341\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.37556e24 | 0.240755 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.51475e24 | − | 9.53320e24i | −0.0959156 | − | 0.260156i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.88032e25i | 0.430115i | 0.976601 | + | 0.215058i | \(0.0689939\pi\) | ||||
−0.976601 | + | 0.215058i | \(0.931006\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.16312e24 | −0.0800279 | −0.0400140 | − | 0.999199i | \(-0.512740\pi\) | ||||
−0.0400140 | + | 0.999199i | \(0.512740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.61775e25 | − | 1.20786e25i | 0.261989 | − | 0.195608i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.06810e26i | 1.46077i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.70905e25 | −0.313618 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.24668e26 | + | 1.66974e26i | 1.22446 | + | 1.63999i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.17379e25i | 0.766149i | 0.923717 | + | 0.383075i | \(0.125135\pi\) | ||||
−0.923717 | + | 0.383075i | \(0.874865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.86184e26 | −1.32501 | −0.662505 | − | 0.749058i | \(-0.730507\pi\) | ||||
−0.662505 | + | 0.749058i | \(0.730507\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.78743e26 | − | 5.29727e25i | −1.08625 | − | 0.321925i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 7.34424e25i | − | 0.381915i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.58923e26 | 0.708584 | 0.354292 | − | 0.935135i | \(-0.384722\pi\) | ||||
0.354292 | + | 0.935135i | \(0.384722\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.75846e25 | + | 2.80617e25i | −0.143961 | + | 0.107485i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.85079e25i | − | 0.0610163i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.86804e26 | −1.38390 | −0.691948 | − | 0.721948i | \(-0.743247\pi\) | ||||
−0.691948 | + | 0.721948i | \(0.743247\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.60926e25 | − | 1.15308e26i | −0.211426 | − | 0.283174i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.29000e26i | − | 1.33676i | −0.743821 | − | 0.668379i | \(-0.766989\pi\) | ||
0.743821 | − | 0.668379i | \(-0.233011\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.70212e26 | 0.313582 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.44996e25 | + | 8.26675e25i | −0.0391927 | + | 0.132246i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.85146e26i | 0.257609i | 0.991670 | + | 0.128805i | \(0.0411140\pi\) | ||||
−0.991670 | + | 0.128805i | \(0.958886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.32931e27 | 1.61128 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.00974e26 | + | 5.98030e26i | −0.847109 | + | 0.632476i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.47704e27i | 1.36507i | 0.730853 | + | 0.682535i | \(0.239123\pi\) | ||||
−0.730853 | + | 0.682535i | \(0.760877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.65463e26 | −0.538246 | −0.269123 | − | 0.963106i | \(-0.586734\pi\) | ||||
−0.269123 | + | 0.963106i | \(0.586734\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.11216e26 | − | 8.18635e26i | −0.433293 | − | 0.580333i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.81058e26i | 0.112657i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.64036e27 | −1.44399 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.40235e27 | + | 1.25440e27i | −1.63771 | + | 0.603800i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.76451e27i | 1.17279i | 0.810027 | + | 0.586393i | \(0.199452\pi\) | ||||
−0.810027 | + | 0.586393i | \(0.800548\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.06698e26 | 0.264573 | 0.132287 | − | 0.991212i | \(-0.457768\pi\) | ||||
0.132287 | + | 0.991212i | \(0.457768\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.69742e26 | + | 5.74711e26i | −0.254642 | + | 0.190123i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.71662e27i | 1.38050i | 0.723571 | + | 0.690250i | \(0.242499\pi\) | ||||
−0.723571 | + | 0.690250i | \(0.757501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.25704e27 | −0.585197 | −0.292598 | − | 0.956235i | \(-0.594520\pi\) | ||||
−0.292598 | + | 0.956235i | \(0.594520\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.53159e27 | + | 3.39069e27i | 0.582157 | + | 0.779714i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.66845e27i | 1.97426i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.10377e27 | 0.381901 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.07442e26 | + | 6.14780e25i | 0.0335160 | + | 0.00993289i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.22115e27i | 0.175798i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.37907e27 | −0.433918 | −0.216959 | − | 0.976181i | \(-0.569614\pi\) | ||||
−0.216959 | + | 0.976181i | \(0.569614\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.70106e27 | − | 6.49646e27i | 0.997739 | − | 0.744940i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.64955e27i | 0.169084i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.62112e28 | −2.40420 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.04380e28 | + | 1.39802e28i | 0.857608 | + | 1.14864i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.76258e28i | 1.29850i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.36332e28 | −0.901443 | −0.450722 | − | 0.892665i | \(-0.648833\pi\) | ||||
−0.450722 | + | 0.892665i | \(0.648833\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41562e27 | + | 1.48993e28i | −0.262302 | + | 0.885069i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.82027e27i | − | 0.364327i | −0.983268 | − | 0.182164i | \(-0.941690\pi\) | ||
0.983268 | − | 0.182164i | \(-0.0583100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.90439e28 | −1.39646 | −0.698231 | − | 0.715872i | \(-0.746029\pi\) | ||||
−0.698231 | + | 0.715872i | \(0.746029\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.11530e28 | + | 3.07260e28i | −1.78262 | + | 1.33095i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.69231e27i | 0.339519i | 0.985486 | + | 0.169760i | \(0.0542991\pi\) | ||||
−0.985486 | + | 0.169760i | \(0.945701\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.57166e27 | 0.0906566 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.63160e27 | − | 2.18529e27i | −0.0519557 | − | 0.0695871i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.86579e28i | − | 1.11292i | −0.830875 | − | 0.556459i | \(-0.812160\pi\) | ||
0.830875 | − | 0.556459i | \(-0.187840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.20605e28 | 0.314168 | 0.157084 | − | 0.987585i | \(-0.449791\pi\) | ||||
0.157084 | + | 0.987585i | \(0.449791\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.75798e27 | − | 4.23013e28i | −0.0650603 | − | 0.997881i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.65431e28i | 0.567490i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.15181e27 | 0.158085 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.89557e26 | + | 3.65518e26i | −0.00861810 | + | 0.00643452i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.43194e28i | 1.34848i | 0.738515 | + | 0.674238i | \(0.235528\pi\) | ||||
−0.738515 | + | 0.674238i | \(0.764472\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.06430e27 | 0.0445538 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.42069e28 | − | 1.90281e28i | −0.187939 | − | 0.251717i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5.82077e28i | − | 0.701105i | −0.936543 | − | 0.350553i | \(-0.885994\pi\) | ||
0.936543 | − | 0.350553i | \(-0.114006\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.46188e28 | 0.709189 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.08367e29 | − | 3.21159e28i | −1.08445 | − | 0.321392i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.33775e29i | 1.22153i | 0.791810 | + | 0.610767i | \(0.209139\pi\) | ||||
−0.791810 | + | 0.610767i | \(0.790861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.97464e27 | −0.0498151 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.57500e29 | + | 1.17594e29i | −1.19990 | + | 0.895881i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.31823e28i | 0.300800i | 0.988625 | + | 0.150400i | \(0.0480562\pi\) | ||||
−0.988625 | + | 0.150400i | \(0.951944\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.25855e28 | −0.0802119 | −0.0401059 | − | 0.999195i | \(-0.512770\pi\) | ||||
−0.0401059 | + | 0.999195i | \(0.512770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.05112e29 | + | 2.74717e29i | 1.19685 | + | 1.60300i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.20091e29i | 1.17655i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.17464e28 | 0.449606 | 0.224803 | − | 0.974404i | \(-0.427826\pi\) | ||||
0.224803 | + | 0.974404i | \(0.427826\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.70665e28 | − | 2.93783e29i | 0.391382 | − | 1.32062i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.21314e28i | 0.0913131i | 0.998957 | + | 0.0456566i | \(0.0145380\pi\) | ||||
−0.998957 | + | 0.0456566i | \(0.985462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.26573e28 | −0.123749 | −0.0618747 | − | 0.998084i | \(-0.519708\pi\) | ||||
−0.0618747 | + | 0.998084i | \(0.519708\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.80039e27 | + | 6.57062e27i | −0.0306453 | + | 0.0228806i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7.50824e29i | − | 2.40411i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.62619e28 | −0.283583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.52344e29 | + | 4.71914e29i | 0.955546 | + | 1.27981i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3.37056e29i | − | 0.841958i | −0.907070 | − | 0.420979i | \(-0.861687\pi\) | ||
0.907070 | − | 0.420979i | \(-0.138313\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.27327e29 | −0.293127 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.07687e29 | − | 5.63319e29i | −0.440892 | − | 1.19585i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 2.04557e28i | − | 0.0400646i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.88716e29 | 1.06441 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.93669e29 | − | 5.92576e29i | 1.32534 | − | 0.989538i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.30134e29i | − | 0.200814i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.58441e29 | 0.939412 | 0.469706 | − | 0.882823i | \(-0.344360\pi\) | ||||
0.469706 | + | 0.882823i | \(0.344360\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.90572e29 | − | 5.23115e29i | −0.515466 | − | 0.690391i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.25703e30i | − | 1.53540i | −0.640810 | − | 0.767700i | \(-0.721401\pi\) | ||
0.640810 | − | 0.767700i | \(-0.278599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.01699e29 | −0.454328 | −0.227164 | − | 0.973857i | \(-0.572945\pi\) | ||||
−0.227164 | + | 0.973857i | \(0.572945\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.42862e29 | − | 1.31248e29i | −0.464025 | − | 0.137520i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.83365e29i | 0.469422i | 0.972065 | + | 0.234711i | \(0.0754144\pi\) | ||||
−0.972065 | + | 0.234711i | \(0.924586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.60078e30 | −1.44160 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.51368e30 | − | 1.13016e30i | 1.26466 | − | 0.944230i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.01514e29i | 0.156270i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.46922e30 | 1.05800 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.94845e28 | + | 9.30644e28i | 0.0464852 | + | 0.0622602i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.17814e29i | − | 0.570694i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.33834e29 | 0.0773802 | 0.0386901 | − | 0.999251i | \(-0.487681\pi\) | ||||
0.0386901 | + | 0.999251i | \(0.487681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.14646e29 | + | 7.24267e29i | −0.115449 | + | 0.389554i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.39001e29i | 0.269806i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.49698e26 | 0.000116374 | 5.81870e−5 | − | 1.00000i | \(-0.499981\pi\) | ||||
5.81870e−5 | 1.00000i | \(0.499981\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.41162e30 | − | 1.80059e30i | 1.04692 | − | 0.781660i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.33973e30i | − | 1.75554i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.84457e30 | 1.82694 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.64880e28 | + | 2.20833e28i | 0.00579880 | + | 0.00776665i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1.01133e30i | − | 0.331847i | −0.986139 | − | 0.165923i | \(-0.946940\pi\) | ||
0.986139 | − | 0.165923i | \(-0.0530605\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.79831e30 | 1.46955 | 0.734773 | − | 0.678314i | \(-0.237289\pi\) | ||||
0.734773 | + | 0.678314i | \(0.237289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.76044e30 | + | 1.38642e30i | −1.07536 | + | 0.396469i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.36735e29i | 0.116660i | 0.998297 | + | 0.0583300i | \(0.0185776\pi\) | ||||
−0.998297 | + | 0.0583300i | \(0.981422\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.38316e30 | 0.345250 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.79104e30 | + | 5.07038e30i | −1.58459 | + | 1.18310i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.36292e30i | 0.297397i | 0.988883 | + | 0.148699i | \(0.0475084\pi\) | ||||
−0.988883 | + | 0.148699i | \(0.952492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.80556e30 | −0.980975 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.95556e30 | − | 2.61918e30i | −0.373586 | − | 0.500364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.22236e30i | 0.397467i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.44710e30 | −0.242384 | −0.121192 | − | 0.992629i | \(-0.538672\pi\) | ||||
−0.121192 | + | 0.992629i | \(0.538672\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.41546e30 | + | 2.49403e30i | 1.32057 | + | 0.391368i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.13232e30i | 0.313592i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.12953e30 | 0.293614 | 0.146807 | − | 0.989165i | \(-0.453100\pi\) | ||||
0.146807 | + | 0.989165i | \(0.453100\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.30433e30 | + | 2.46710e30i | −0.427275 | + | 0.319016i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.06860e31i | 1.29634i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.51756e30 | 0.514320 | 0.257160 | − | 0.966369i | \(-0.417213\pi\) | ||||
0.257160 | + | 0.966369i | \(0.417213\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.19284e30 | − | 5.61570e30i | −0.448135 | − | 0.600211i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.00583e30i | − | 0.502448i | −0.967929 | − | 0.251224i | \(-0.919167\pi\) | ||
0.967929 | − | 0.251224i | \(-0.0808330\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.54189e30 | −0.616843 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.95555e30 | + | 6.59850e30i | −0.173276 | + | 0.584674i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7.79334e30i | − | 0.649125i | −0.945864 | − | 0.324563i | \(-0.894783\pi\) | ||
0.945864 | − | 0.324563i | \(-0.105217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.05668e29 | 0.0396045 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.16181e31 | − | 8.67443e30i | 0.855906 | − | 0.639044i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.47384e29i | − | 0.0240794i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.68507e31 | −1.09934 | −0.549669 | − | 0.835383i | \(-0.685246\pi\) | ||||
−0.549669 | + | 0.835383i | \(0.685246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.34502e30 | + | 3.14082e30i | 0.144036 | + | 0.192916i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.09723e31i | − | 0.634693i | −0.948310 | − | 0.317346i | \(-0.897208\pi\) | ||
0.948310 | − | 0.317346i | \(-0.102792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.89699e31 | −1.57865 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.94213e30 | − | 4.52776e30i | 0.151078 | − | 0.232500i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.06988e31i | 0.517846i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.46568e31 | −1.58164 | −0.790822 | − | 0.612046i | \(-0.790347\pi\) | ||||
−0.790822 | + | 0.612046i | \(0.790347\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.00717e30 | + | 5.97838e30i | −0.344649 | + | 0.257325i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.54423e31i | 1.84527i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.78225e28 | −0.00298214 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.32364e30 | − | 1.77283e30i | −0.0478783 | − | 0.0641260i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.32637e30i | 0.147759i | 0.997267 | + | 0.0738797i | \(0.0235381\pi\) | ||||
−0.997267 | + | 0.0738797i | \(0.976462\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.35766e31 | 1.72818 | 0.864092 | − | 0.503334i | \(-0.167893\pi\) | ||||
0.864092 | + | 0.503334i | \(0.167893\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.02871e31 | + | 3.04872e30i | 0.313480 | + | 0.0929039i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.63193e31i | 1.04585i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.64443e31 | −1.26415 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.54842e31 | + | 3.39598e31i | −1.17051 | + | 0.873932i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.38282e31i | 1.79678i | 0.439197 | + | 0.898391i | \(0.355263\pi\) | ||||
−0.439197 | + | 0.898391i | \(0.644737\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.54475e30 | 0.0585856 | 0.0292928 | − | 0.999571i | \(-0.490674\pi\) | ||||
0.0292928 | + | 0.999571i | \(0.490674\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.61327e30 | − | 1.15362e31i | −0.187628 | − | 0.251300i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.33869e29i | − | 0.00482164i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.51383e31 | 1.27134 | 0.635671 | − | 0.771960i | \(-0.280724\pi\) | ||||
0.635671 | + | 0.771960i | \(0.280724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.14670e31 | + | 1.06177e32i | −0.581557 | + | 1.96231i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 3.26967e31i | − | 0.572347i | −0.958178 | − | 0.286173i | \(-0.907617\pi\) | ||
0.958178 | − | 0.286173i | \(-0.0923833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.50370e31 | −0.415205 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.90657e31 | + | 2.91676e31i | −0.613912 | + | 0.458364i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.64915e31i | − | 1.13935i | −0.821870 | − | 0.569675i | \(-0.807069\pi\) | ||
0.821870 | − | 0.569675i | \(-0.192931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.24312e32 | 1.75547 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.91963e31 | − | 7.92848e31i | −0.792713 | − | 1.06172i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.36704e31i | 0.554690i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.89189e31 | 0.710003 | 0.355001 | − | 0.934866i | \(-0.384480\pi\) | ||||
0.355001 | + | 0.934866i | \(0.384480\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.42724e31 | − | 9.29584e31i | −0.391915 | − | 1.06301i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.35731e31i | − | 0.472941i | −0.971639 | − | 0.236470i | \(-0.924009\pi\) | ||
0.971639 | − | 0.236470i | \(-0.0759907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.14041e32 | −1.17514 | −0.587569 | − | 0.809174i | \(-0.699915\pi\) | ||||
−0.587569 | + | 0.809174i | \(0.699915\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.12748e31 | − | 2.33506e31i | 0.306026 | − | 0.228488i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.25380e31i | − | 0.209466i | −0.994500 | − | 0.104733i | \(-0.966601\pi\) | ||
0.994500 | − | 0.104733i | \(-0.0333988\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.92367e32 | 1.69846 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.05288e31 | + | 6.76760e31i | 0.423924 | + | 0.567785i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.74722e31i | 0.777225i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.67975e31 | 0.127327 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.38997e31 | − | 7.08298e30i | −0.172255 | − | 0.0510499i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 8.30835e31i | − | 0.569493i | −0.958603 | − | 0.284747i | \(-0.908090\pi\) | ||
0.958603 | − | 0.284747i | \(-0.0919095\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.14197e31 | 0.465669 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.88140e30 | − | 5.88448e30i | 0.0488920 | − | 0.0365042i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.50178e31i | 0.442857i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.38724e32 | −1.34137 | −0.670686 | − | 0.741741i | \(-0.734000\pi\) | ||||
−0.670686 | + | 0.741741i | \(0.734000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.54777e32 | − | 2.07301e32i | −0.827942 | − | 1.10891i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.30787e32i | − | 0.666173i | −0.942896 | − | 0.333087i | \(-0.891910\pi\) | ||
0.942896 | − | 0.333087i | \(-0.108090\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.64160e32 | −1.28145 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.17304e31 | − | 7.33235e31i | 0.100416 | − | 0.338829i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4.93645e32i | − | 2.17339i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.33308e32 | 0.978868 | 0.489434 | − | 0.872040i | \(-0.337203\pi\) | ||||
0.489434 | + | 0.872040i | \(0.337203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.67854e32 | − | 1.99987e32i | 1.07114 | − | 0.799741i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.12030e32i | − | 1.18954i | −0.803895 | − | 0.594772i | \(-0.797242\pi\) | ||
0.803895 | − | 0.594772i | \(-0.202758\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.26166e32 | 0.458611 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.41182e31 | + | 7.24834e31i | 0.187606 | + | 0.251271i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 7.26199e31i | − | 0.240128i | −0.992766 | − | 0.120064i | \(-0.961690\pi\) | ||
0.992766 | − | 0.120064i | \(-0.0383099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.93151e32 | 2.50210 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.29927e31 | + | 1.58508e31i | −0.129416 | + | 0.0477136i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 8.31569e31i | − | 0.238898i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.51960e32 | 0.416719 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.88429e31 | + | 5.88663e31i | −0.206421 | + | 0.154120i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.64395e32i | 1.66102i | 0.557007 | + | 0.830508i | \(0.311950\pi\) | ||||
−0.557007 | + | 0.830508i | \(0.688050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.25543e31 | 0.125484 | 0.0627420 | − | 0.998030i | \(-0.480015\pi\) | ||||
0.0627420 | + | 0.998030i | \(0.480015\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.22649e32 | + | 5.66076e32i | 0.963980 | + | 1.29111i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 7.16138e32i | − | 1.56052i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.79664e32 | 0.998778 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.09332e32 | − | 1.50947e32i | −1.01360 | − | 0.300393i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.29845e32i | − | 1.57859i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.40622e32 | 0.437613 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.28983e32 | + | 4.69616e32i | −1.09382 | + | 0.816680i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.56844e33i | 2.60856i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00798e32 | −0.160356 | −0.0801778 | − | 0.996781i | \(-0.525549\pi\) | ||||
−0.0801778 | + | 0.996781i | \(0.525549\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.11581e32 | − | 2.83381e32i | −0.322016 | − | 0.431294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.47940e31i | 0.0215440i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.11119e32 | −0.294225 | −0.147113 | − | 0.989120i | \(-0.546998\pi\) | ||||
−0.147113 | + | 0.989120i | \(0.546998\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.54275e32 | − | 5.20562e32i | 0.205792 | − | 0.694391i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.22172e32i | 0.156010i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.23980e32 | −0.151583 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.71020e31 | + | 5.75666e31i | −0.0902714 | + | 0.0673992i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.33948e32i | 0.150201i | 0.997176 | + | 0.0751005i | \(0.0239278\pi\) | ||||
−0.997176 | + | 0.0751005i | \(0.976072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.50676e32 | 0.698913 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.39490e32 | − | 1.12437e33i | −0.863896 | − | 1.15706i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.33412e32i | 0.624576i | 0.949987 | + | 0.312288i | \(0.101095\pi\) | ||||
−0.949987 | + | 0.312288i | \(0.898905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.83364e32 | 0.362268 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.61593e33 | − | 1.05003e33i | −1.46362 | − | 0.951055i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.30678e32i | − | 0.287116i | −0.989642 | − | 0.143558i | \(-0.954146\pi\) | ||
0.989642 | − | 0.143558i | \(-0.0458544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.57897e33 | 1.31444 | 0.657218 | − | 0.753700i | \(-0.271733\pi\) | ||||
0.657218 | + | 0.753700i | \(0.271733\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.17724e33 | + | 8.78964e32i | −0.939747 | + | 0.701642i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.21507e31i | − | 0.0322694i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.68744e33 | 1.97346 | 0.986730 | − | 0.162371i | \(-0.0519140\pi\) | ||||
0.986730 | + | 0.162371i | \(0.0519140\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.24691e32 | + | 3.00941e32i | 0.158286 | + | 0.212001i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.77745e31i | 0.0187729i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.53043e32 | −0.228984 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.89471e32 | − | 1.45061e32i | −0.304689 | − | 0.0902986i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.59247e33i | − | 0.951510i | −0.879578 | − | 0.475755i | \(-0.842175\pi\) | ||
0.879578 | − | 0.475755i | \(-0.157825\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.31210e32 | −0.189985 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.00853e33 | + | 1.49963e33i | −1.10619 | + | 0.825911i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.89338e33i | 1.53020i | 0.643910 | + | 0.765102i | \(0.277311\pi\) | ||||
−0.643910 | + | 0.765102i | \(0.722689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.07954e33 | −0.548320 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.17614e32 | − | 9.61139e32i | −0.350105 | − | 0.468915i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.27146e33i | − | 0.595911i | −0.954580 | − | 0.297955i | \(-0.903695\pi\) | ||
0.954580 | − | 0.297955i | \(-0.0963047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.15108e33 | −0.518337 | −0.259169 | − | 0.965832i | \(-0.583449\pi\) | ||||
−0.259169 | + | 0.965832i | \(0.583449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.38990e32 | + | 2.15611e33i | −0.276494 | + | 0.932959i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 4.16358e32i | − | 0.173142i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.18715e32 | −0.167361 | −0.0836805 | − | 0.996493i | \(-0.526668\pi\) | ||||
−0.0836805 | + | 0.996493i | \(0.526668\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.11722e33 | + | 3.07404e33i | −1.58196 | + | 1.18114i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.01441e33i | − | 0.374731i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.03008e33 | −1.07629 | −0.538144 | − | 0.842853i | \(-0.680874\pi\) | ||||
−0.538144 | + | 0.842853i | \(0.680874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.68882e32 | + | 8.95870e32i | 0.228480 | + | 0.306015i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.78856e33i | 1.24466i | 0.782753 | + | 0.622332i | \(0.213815\pi\) | ||||
−0.782753 | + | 0.622332i | \(0.786185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.01070e33 | 0.635418 | 0.317709 | − | 0.948188i | \(-0.397087\pi\) | ||||
0.317709 | + | 0.948188i | \(0.397087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.97752e31 | + | 1.07884e32i | 0.0120924 | + | 0.0327987i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.93559e33i | 2.61377i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.75431e33 | 0.775268 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.20017e32 | + | 3.88260e32i | −0.140866 | + | 0.105175i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.76550e33i | 0.460321i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.99733e33 | −0.752284 | −0.376142 | − | 0.926562i | \(-0.622750\pi\) | ||||
−0.376142 | + | 0.926562i | \(0.622750\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.07436e33 | − | 1.43895e33i | −0.259600 | − | 0.347696i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 8.92699e32i | − | 0.207692i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.04701e34 | 2.34573 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.53292e33 | + | 1.63975e33i | 1.19383 | + | 0.353808i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 6.59215e33i | − | 1.37003i | −0.728528 | − | 0.685016i | \(-0.759795\pi\) | ||
0.728528 | − | 0.685016i | \(-0.240205\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.70251e32 | −0.0340845 | −0.0170423 | − | 0.999855i | \(-0.505425\pi\) | ||||
−0.0170423 | + | 0.999855i | \(0.505425\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.02445e32 | + | 5.24466e32i | −0.135486 | + | 0.101158i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.44965e33i | − | 0.455253i | −0.973749 | − | 0.227626i | \(-0.926904\pi\) | ||
0.973749 | − | 0.227626i | \(-0.0730965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.52378e33 | −1.34741 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.33373e33 | − | 1.11618e34i | −1.43836 | − | 1.92647i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.61675e32i | 0.0268958i | 0.999910 | + | 0.0134479i | \(0.00428073\pi\) | ||||
−0.999910 | + | 0.0134479i | \(0.995719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.84688e33 | 0.296171 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.63463e33 | + | 8.88987e33i | −0.407319 | + | 1.37439i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.23809e34i | 1.84556i | 0.385333 | + | 0.922778i | \(0.374087\pi\) | ||||
−0.385333 | + | 0.922778i | \(0.625913\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.28758e34 | 1.85079 | 0.925395 | − | 0.379003i | \(-0.123733\pi\) | ||||
0.925395 | + | 0.379003i | \(0.123733\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.50577e33 | + | 5.60402e33i | −1.04048 | + | 0.776850i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.99280e32i | 0.0667551i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.06573e32 | 0.0395388 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.33460e33 | − | 5.80556e33i | −0.539306 | − | 0.722322i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.68967e33i | − | 0.923076i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.97150e33 | −0.575847 | −0.287923 | − | 0.957653i | \(-0.592965\pi\) | ||||
−0.287923 | + | 0.957653i | \(0.592965\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.74868e33 | + | 2.85682e33i | −0.866128 | + | 0.319329i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3.16889e33i | − | 0.341856i | −0.985283 | − | 0.170928i | \(-0.945323\pi\) | ||
0.985283 | − | 0.170928i | \(-0.0546766\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.67735e34 | 2.78784 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.90435e33 | − | 2.16847e33i | 0.291933 | − | 0.217966i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 6.57986e33i | − | 0.638510i | −0.947669 | − | 0.319255i | \(-0.896567\pi\) | ||
0.947669 | − | 0.319255i | \(-0.103433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.27286e33 | −0.119260 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.23436e33 | − | 1.23681e34i | −0.835461 | − | 1.11898i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.35674e33i | 0.205911i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.28870e34 | 1.93131 | 0.965657 | − | 0.259819i | \(-0.0836629\pi\) | ||||
0.965657 | + | 0.259819i | \(0.0836629\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.61688e34 | − | 7.75546e33i | −2.13297 | − | 0.632133i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2.81818e32i | − | 0.0221897i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.05139e34 | 1.56046 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.70154e33 | + | 2.76368e33i | −0.272055 | + | 0.203124i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.42814e34i | − | 1.72448i | −0.506504 | − | 0.862238i | \(-0.669062\pi\) | ||
0.506504 | − | 0.862238i | \(-0.330938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.16535e32 | 0.0560417 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.17647e32 | + | 1.09512e33i | 0.0542371 | + | 0.0726427i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.50279e34i | − | 2.88701i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.13216e34 | 1.94129 | 0.970643 | − | 0.240526i | \(-0.0773201\pi\) | ||||
0.970643 | + | 0.240526i | \(0.0773201\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.11827e32 | − | 1.38960e33i | 0.0246763 | − | 0.0832636i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.31121e32i | 0.0481493i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.23040e33 | −0.405033 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.64621e34 | − | 1.22911e34i | 0.891775 | − | 0.665825i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 6.69265e33i | − | 0.350632i | −0.984512 | − | 0.175316i | \(-0.943905\pi\) | ||
0.984512 | − | 0.175316i | \(-0.0560947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.96783e34 | −1.50389 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.83458e33 | + | 5.13586e33i | 0.187957 | + | 0.251741i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.20194e34i | 1.04412i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.17481e32 | 0.0145648 | 0.00728241 | − | 0.999973i | \(-0.497682\pi\) | ||||
0.00728241 | + | 0.999973i | \(0.497682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.71368e34 | − | 1.46240e34i | 0.760674 | − | 0.649135i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.60848e34i | 0.690886i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.81929e33 | 0.408162 | 0.204081 | − | 0.978954i | \(-0.434579\pi\) | ||||
0.204081 | + | 0.978954i | \(0.434579\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.13031e34 | + | 8.43923e33i | −0.454727 | + | 0.339512i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.18497e34i | 1.24021i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.87359e33 | 0.372171 | 0.186085 | − | 0.982534i | \(-0.440420\pi\) | ||||
0.186085 | + | 0.982534i | \(0.440420\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.59183e33 | + | 3.47138e33i | 0.0945775 | + | 0.126673i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.57424e34i | 1.61604i | 0.589153 | + | 0.808022i | \(0.299462\pi\) | ||||
−0.589153 | + | 0.808022i | \(0.700538\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.21009e33 | −0.212433 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.11305e32 | − | 9.22592e31i | −0.0103119 | − | 0.00305606i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 8.58768e34i | − | 2.75483i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.95235e34 | 0.917253 | 0.458626 | − | 0.888629i | \(-0.348342\pi\) | ||||
0.458626 | + | 0.888629i | \(0.348342\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.59067e34 | + | 2.68089e34i | −1.08053 | + | 0.806752i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.26035e34i | − | 0.367391i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.19612e34 | 0.620163 | 0.310082 | − | 0.950710i | \(-0.399644\pi\) | ||||
0.310082 | + | 0.950710i | \(0.399644\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.74278e32 | + | 1.30490e33i | 0.0266552 | + | 0.0357007i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.02417e34i | 1.06675i | 0.845880 | + | 0.533373i | \(0.179076\pi\) | ||||
−0.845880 | + | 0.533373i | \(0.820924\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.27990e33 | 0.135622 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.58593e33 | − | 1.20998e34i | 0.0892615 | − | 0.301190i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.02250e34i | 1.21165i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.32227e34 | −0.309175 | −0.154587 | − | 0.987979i | \(-0.549405\pi\) | ||||
−0.154587 | + | 0.987979i | \(0.549405\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.47872e34 | − | 1.85069e34i | 0.561792 | − | 0.419450i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.79581e33i | − | 0.0614261i | −0.999528 | − | 0.0307131i | \(-0.990222\pi\) | ||
0.999528 | − | 0.0307131i | \(-0.00977781\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.96947e34 | −1.27150 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.05452e34 | + | 2.75173e34i | 0.424286 | + | 0.568269i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 9.48754e33i | − | 0.189978i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.17315e34 | 1.58700 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.07784e34 | − | 5.63582e34i | −0.391266 | − | 1.06125i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.07581e34i | 0.196472i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.02458e33 | 0.0181489 | 0.00907443 | − | 0.999959i | \(-0.497111\pi\) | ||||
0.00907443 | + | 0.999959i | \(0.497111\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.69668e34 | + | 4.25331e34i | −0.978809 | + | 0.730807i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.36821e35i | − | 2.28052i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.13324e34 | −0.830068 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.89961e33 | − | 2.54425e33i | −0.0298029 | − | 0.0399166i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.28416e34i | − | 0.195487i | −0.995212 | − | 0.0977437i | \(-0.968837\pi\) | ||
0.995212 | − | 0.0977437i | \(-0.0311625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.50763e34 | 0.370427 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.00153e35 | − | 2.96816e34i | −1.43573 | − | 0.425497i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.31320e35i | 1.82702i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.25287e33 | 0.0169182 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.83888e34 | + | 1.37296e34i | −0.241030 | + | 0.179960i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.52757e34i | 0.321604i | 0.986987 | + | 0.160802i | \(0.0514081\pi\) | ||||
−0.986987 | + | 0.160802i | \(0.948592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.11893e34 | −0.755832 | −0.377916 | − | 0.925840i | \(-0.623359\pi\) | ||||
−0.377916 | + | 0.925840i | \(0.623359\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.00149e33 | − | 5.35942e33i | −0.0479883 | − | 0.0642734i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 3.29536e34i | − | 0.383718i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.43912e33 | 0.0841118 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.17716e34 | + | 1.74690e35i | −0.568440 | + | 1.91805i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.06023e35i | − | 1.13053i | −0.824910 | − | 0.565264i | \(-0.808774\pi\) | ||
0.824910 | − | 0.565264i | \(-0.191226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.36678e34 | −0.245110 | −0.122555 | − | 0.992462i | \(-0.539109\pi\) | ||||
−0.122555 | + | 0.992462i | \(0.539109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.37238e34 | + | 6.99769e34i | −0.942763 | + | 0.703894i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.95156e34i | 0.874647i | 0.899304 | + | 0.437324i | \(0.144074\pi\) | ||||
−0.899304 | + | 0.437324i | \(0.855926\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.98135e34 | −0.947404 | −0.473702 | − | 0.880685i | \(-0.657083\pi\) | ||||
−0.473702 | + | 0.880685i | \(0.657083\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.91703e34 | + | 3.90694e34i | 0.268985 | + | 0.360267i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.58822e35i | 2.31879i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.25794e34 | 0.370648 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.52787e35 | − | 5.63304e34i | 1.29235 | − | 0.476472i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 6.41910e34i | − | 0.527631i | −0.964573 | − | 0.263816i | \(-0.915019\pi\) | ||
0.964573 | − | 0.263816i | \(-0.0849811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.49679e34 | −0.279330 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.42446e33 | + | 7.03657e33i | −0.0731687 | + | 0.0546299i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.15223e34i | 0.0869480i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.48596e35 | −1.08995 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.03832e34 | − | 1.39068e34i | −0.0740355 | − | 0.0991598i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.04897e33i | − | 0.0142030i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.28735e35 | 0.867577 | 0.433788 | − | 0.901015i | \(-0.357177\pi\) | ||||
0.433788 | + | 0.901015i | \(0.357177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.59608e33 | − | 1.65847e33i | −0.0366683 | − | 0.0108671i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.19549e35i | 0.761686i | 0.924640 | + | 0.380843i | \(0.124366\pi\) | ||||
−0.924640 | + | 0.380843i | \(0.875634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.64373e33 | −0.0225750 | −0.0112875 | − | 0.999936i | \(-0.503593\pi\) | ||||
−0.0112875 | + | 0.999936i | \(0.503593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.19731e35 | − | 2.38721e35i | 1.92640 | − | 1.43831i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.13114e35i | 0.662808i | 0.943489 | + | 0.331404i | \(0.107522\pi\) | ||||
−0.943489 | + | 0.331404i | \(0.892478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.25333e34 | −0.0714284 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.06060e34 | − | 4.09923e34i | −0.169659 | − | 0.227234i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.05270e34i | − | 0.110685i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.12613e35 | 1.11525 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.89342e34 | + | 3.00085e35i | −0.453835 | + | 1.53135i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.87467e35i | 0.930740i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.74651e35 | −1.32674 | −0.663371 | − | 0.748291i | \(-0.730875\pi\) | ||||
−0.663371 | + | 0.748291i | \(0.730875\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.43532e35 | − | 1.07165e35i | 0.674657 | − | 0.503718i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.92641e33i | − | 0.0179591i | −0.999960 | − | 0.00897954i | \(-0.997142\pi\) | ||
0.999960 | − | 0.00897954i | \(-0.00285832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.14107e35 | −1.39814 | −0.699068 | − | 0.715055i | \(-0.746402\pi\) | ||||
−0.699068 | + | 0.715055i | \(0.746402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.04830e34 | − | 5.42210e34i | −0.175369 | − | 0.234881i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.36842e35i | 0.576949i | 0.957488 | + | 0.288474i | \(0.0931480\pi\) | ||||
−0.957488 | + | 0.288474i | \(0.906852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.18600e35 | −1.30745 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.73851e35 | − | 2.67546e35i | 0.694456 | − | 1.06873i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.15977e34i | − | 0.0450975i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.99863e34 | −0.378498 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.71089e33 | − | 6.50380e33i | 0.0321036 | − | 0.0239694i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4.34175e35i | − | 1.55793i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.82588e34 | −0.203547 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.87179e35 | + | 2.50699e35i | 0.636802 | + | 0.852904i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.50477e34i | − | 0.149242i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.89113e35 | 1.57805 | 0.789027 | − | 0.614359i | \(-0.210585\pi\) | ||||
0.789027 | + | 0.614359i | \(0.210585\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.04686e35 | + | 1.49570e35i | 1.58582 | + | 0.469979i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.37776e35i | 0.421652i | 0.977524 | + | 0.210826i | \(0.0676153\pi\) | ||||
−0.977524 | + | 0.210826i | \(0.932385\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.59855e33 | −0.0137079 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.54166e34 | − | 4.13756e34i | 0.160911 | − | 0.120141i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 6.59142e35i | − | 1.86443i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.77554e35 | −1.59150 | −0.795749 | − | 0.605626i | \(-0.792923\pi\) | ||||
−0.795749 | + | 0.605626i | \(0.792923\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.09348e35 | + | 2.80391e35i | 0.562022 | + | 0.752746i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 5.45599e35i | − | 1.42710i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.47166e35 | 0.375065 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.85832e34 | − | 3.32643e35i | 0.244820 | − | 0.826080i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 4.96289e35i | − | 1.20101i | −0.799621 | − | 0.600504i | \(-0.794967\pi\) | ||
0.799621 | − | 0.600504i | \(-0.205033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.19704e35 | 0.282300 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.35295e35 | − | 3.99667e35i | 1.23031 | − | 0.918583i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.78736e35i | − | 0.400381i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.65386e35 | −1.45278 | −0.726388 | − | 0.687284i | \(-0.758803\pi\) | ||||
−0.726388 | + | 0.687284i | \(0.758803\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.27718e35 | − | 1.71060e35i | −0.271810 | − | 0.364050i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 5.63970e35i | − | 1.16999i | −0.811038 | − | 0.584993i | \(-0.801097\pi\) | ||
0.811038 | − | 0.584993i | \(-0.198903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.38076e34 | −0.0481476 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.49149e34 | − | 2.30318e35i | −0.167418 | − | 0.454095i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 7.06990e35i | − | 1.35898i | −0.733684 | − | 0.679491i | \(-0.762201\pi\) | ||
0.733684 | − | 0.679491i | \(-0.237799\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.76627e35 | 1.64294 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.05836e35 | + | 1.53683e35i | −0.376146 | + | 0.280841i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.01676e36i | 1.81177i | 0.423527 | + | 0.905883i | \(0.360792\pi\) | ||||
−0.423527 | + | 0.905883i | \(0.639208\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.87141e35 | −0.325183 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.08960e35 | − | 6.81678e35i | −0.862463 | − | 1.15514i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.54278e35i | 0.750755i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.56638e35 | 0.897207 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.62533e35 | + | 2.85259e35i | 1.51321 | + | 0.448461i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.78391e34i | 0.0733593i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.91788e35 | 1.48355 | 0.741773 | − | 0.670651i | \(-0.233985\pi\) | ||||
0.741773 | + | 0.670651i | \(0.233985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.58128e34 | + | 6.40703e34i | −0.125218 | + | 0.0934913i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.14482e36i | 1.62970i | 0.579675 | + | 0.814848i | \(0.303180\pi\) | ||||
−0.579675 | + | 0.814848i | \(0.696820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.00579e35 | −0.139687 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.67131e35 | + | 6.25654e35i | 0.632970 | + | 0.847771i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.52947e35i | 0.202212i | 0.994876 | + | 0.101106i | \(0.0322380\pi\) | ||||
−0.994876 | + | 0.101106i | \(0.967762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.47944e36 | −1.90856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75384e34 | + | 5.91787e34i | −0.0220781 | + | 0.0744967i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 8.83352e35i | − | 1.08515i | −0.840006 | − | 0.542577i | \(-0.817448\pi\) | ||
0.840006 | − | 0.542577i | \(-0.182552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.19286e35 | −0.382777 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.90843e35 | − | 2.91814e35i | 0.457295 | − | 0.341429i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.86673e34i | − | 0.0213171i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.62104e35 | 0.403598 | 0.201799 | − | 0.979427i | \(-0.435321\pi\) | ||||
0.201799 | + | 0.979427i | \(0.435321\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.25518e34 | + | 5.69919e34i | 0.0462942 | + | 0.0620043i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.52788e35i | − | 0.162260i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.31697e35 | 0.136532 | 0.0682662 | − | 0.997667i | \(-0.478253\pi\) | ||||
0.0682662 | + | 0.997667i | \(0.478253\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.76668e35 | + | 1.38872e35i | −0.381218 | + | 0.140549i |
(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.17.6 | 8 | ||
3.2 | odd | 2 | inner | 48.25.e.d.17.5 | 8 | ||
4.3 | odd | 2 | 6.25.b.a.5.6 | yes | 8 | ||
12.11 | even | 2 | 6.25.b.a.5.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.25.b.a.5.2 | ✓ | 8 | 12.11 | even | 2 | ||
6.25.b.a.5.6 | yes | 8 | 4.3 | odd | 2 | ||
48.25.e.d.17.5 | 8 | 3.2 | odd | 2 | inner | ||
48.25.e.d.17.6 | 8 | 1.1 | even | 1 | trivial |