Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,8,Mod(1,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(79.9705665239\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 163x^{4} + 4820x^{2} - 15296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{27} \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(11.2068\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −21.9408 | −0.469168 | −0.234584 | − | 0.972096i | \(-0.575373\pi\) | ||||
−0.234584 | + | 0.972096i | \(0.575373\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 184.916 | 0.661574 | 0.330787 | − | 0.943705i | \(-0.392686\pi\) | ||||
0.330787 | + | 0.943705i | \(0.392686\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1051.96 | −1.15919 | −0.579595 | − | 0.814905i | \(-0.696789\pi\) | ||||
−0.579595 | + | 0.814905i | \(0.696789\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1705.60 | −0.779882 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4324.35 | −0.979596 | −0.489798 | − | 0.871836i | \(-0.662929\pi\) | ||||
−0.489798 | + | 0.871836i | \(0.662929\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11253.2 | −1.42061 | −0.710307 | − | 0.703892i | \(-0.751444\pi\) | ||||
−0.710307 | + | 0.703892i | \(0.751444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4057.20 | −0.310389 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21746.4 | −1.07354 | −0.536768 | − | 0.843730i | \(-0.680355\pi\) | ||||
−0.536768 | + | 0.843730i | \(0.680355\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 45466.5 | 1.52074 | 0.760368 | − | 0.649492i | \(-0.225019\pi\) | ||||
0.760368 | + | 0.649492i | \(0.225019\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 23080.8 | 0.543855 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4414.37 | −0.0756522 | −0.0378261 | − | 0.999284i | \(-0.512043\pi\) | ||||
−0.0378261 | + | 0.999284i | \(0.512043\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −43931.2 | −0.562320 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 85406.8 | 0.835063 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 23687.1 | 0.180351 | 0.0901756 | − | 0.995926i | \(-0.471257\pi\) | ||||
0.0901756 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72941.9 | 0.439755 | 0.219878 | − | 0.975527i | \(-0.429434\pi\) | ||||
0.219878 | + | 0.975527i | \(0.429434\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 94879.8 | 0.459595 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −194523. | −0.766890 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −483338. | −1.56872 | −0.784359 | − | 0.620307i | \(-0.787008\pi\) | ||||
−0.784359 | + | 0.620307i | \(0.787008\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 246905. | 0.666506 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 411040. | 0.931410 | 0.465705 | − | 0.884940i | \(-0.345801\pi\) | ||||
0.465705 | + | 0.884940i | \(0.345801\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 96165.3 | 0.184450 | 0.0922250 | − | 0.995738i | \(-0.470602\pi\) | ||||
0.0922250 | + | 0.995738i | \(0.470602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −315392. | −0.515949 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −156171. | −0.219411 | −0.109705 | − | 0.993964i | \(-0.534991\pi\) | ||||
−0.109705 | + | 0.993964i | \(0.534991\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 283070. | 0.343722 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 477134. | 0.503668 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 686962. | 0.633822 | 0.316911 | − | 0.948455i | \(-0.397354\pi\) | ||||
0.316911 | + | 0.948455i | \(0.397354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −799641. | −0.648075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −997572. | −0.713480 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.79961e6 | −1.14077 | −0.570384 | − | 0.821378i | \(-0.693206\pi\) | ||||
−0.570384 | + | 0.821378i | \(0.693206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.36394e6 | −0.769379 | −0.384690 | − | 0.923046i | \(-0.625692\pi\) | ||||
−0.384690 | + | 0.923046i | \(0.625692\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.79422e6 | 0.904031 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.08090e6 | −0.939841 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.08853e6 | −0.442160 | −0.221080 | − | 0.975256i | \(-0.570958\pi\) | ||||
−0.221080 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 96854.8 | 0.0354936 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.60830e6 | 1.85963 | 0.929816 | − | 0.368025i | \(-0.119966\pi\) | ||||
0.929816 | + | 0.368025i | \(0.119966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21698.7 | −0.00652837 | −0.00326418 | − | 0.999995i | \(-0.501039\pi\) | ||||
−0.00326418 | + | 0.999995i | \(0.501039\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 963886. | 0.263822 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.54903e6 | 1.13554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.34010e6 | 0.533998 | 0.266999 | − | 0.963697i | \(-0.413968\pi\) | ||||
0.266999 | + | 0.963697i | \(0.413968\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.85626e6 | 0.388097 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −882169. | −0.169347 | −0.0846736 | − | 0.996409i | \(-0.526985\pi\) | ||||
−0.0846736 | + | 0.996409i | \(0.526985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.02125e6 | −0.710223 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −519714. | −0.0846150 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.34738e6 | 0.202594 | 0.101297 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101297 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18379e7 | 1.64676 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.60040e6 | −0.206319 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.40746e6 | 1.00608 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.32798e6 | 0.815236 | 0.407618 | − | 0.913153i | \(-0.366360\pi\) | ||||
0.407618 | + | 0.913153i | \(0.366360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.37562e6 | 0.763969 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.66027e6 | 0.932963 | 0.466482 | − | 0.884531i | \(-0.345521\pi\) | ||||
0.466482 | + | 0.884531i | \(0.345521\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.38659e7 | 1.25031 | 0.625154 | − | 0.780501i | \(-0.285036\pi\) | ||||
0.625154 | + | 0.780501i | \(0.285036\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.26800e6 | 0.359800 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.88354e7 | −1.48638 | −0.743192 | − | 0.669078i | \(-0.766689\pi\) | ||||
−0.743192 | + | 0.669078i | \(0.766689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.60619e6 | 0.636529 | 0.318265 | − | 0.948002i | \(-0.396900\pi\) | ||||
0.318265 | + | 0.948002i | \(0.396900\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.06048e7 | 0.735992 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.31340e7 | −0.856292 | −0.428146 | − | 0.903709i | \(-0.640833\pi\) | ||||
−0.428146 | + | 0.903709i | \(0.640833\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −816286. | −0.0500495 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.91935e7 | 1.10791 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.28763e7 | 1.24443 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −787128. | −0.0403921 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.01856e6 | −0.436988 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.25701e7 | −1.03359 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.18768e7 | 1.38090 | 0.690449 | − | 0.723381i | \(-0.257413\pi\) | ||||
0.690449 | + | 0.723381i | \(0.257413\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.10994e6 | −0.0865380 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.17050e7 | −0.454905 | −0.227453 | − | 0.973789i | \(-0.573040\pi\) | ||||
−0.227453 | + | 0.973789i | \(0.573040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.78288e7 | −1.76282 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.57931e7 | 0.552456 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.79174e7 | −1.25984 | −0.629921 | − | 0.776659i | \(-0.716913\pi\) | ||||
−0.629921 | + | 0.776659i | \(0.716913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.80300e7 | 0.885260 | 0.442630 | − | 0.896704i | \(-0.354045\pi\) | ||||
0.442630 | + | 0.896704i | \(0.354045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.42652e6 | 0.102941 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.86630e7 | 1.39163 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.38012e6 | 0.119316 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.21078e6 | −0.161263 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.82083e6 | −0.168922 | −0.0844608 | − | 0.996427i | \(-0.526917\pi\) | ||||
−0.0844608 | + | 0.996427i | \(0.526917\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.62068e7 | 1.80125 | 0.900626 | − | 0.434595i | \(-0.143109\pi\) | ||||
0.900626 | + | 0.434595i | \(0.143109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.70907e7 | 0.837230 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.34881e7 | 0.290931 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.28737e7 | 0.884183 | 0.442092 | − | 0.896970i | \(-0.354237\pi\) | ||||
0.442092 | + | 0.896970i | \(0.354237\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.50725e7 | −0.297369 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.64373e6 | 0.0876952 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.12127e7 | −0.745374 | −0.372687 | − | 0.927957i | \(-0.621563\pi\) | ||||
−0.372687 | + | 0.927957i | \(0.621563\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.75448e7 | 0.304056 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.41703e7 | −0.401582 | −0.200791 | − | 0.979634i | \(-0.564351\pi\) | ||||
−0.200791 | + | 0.979634i | \(0.564351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38869e7 | 1.01814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.75477e7 | −1.18599 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.90454e7 | −0.867011 | −0.433505 | − | 0.901151i | \(-0.642723\pi\) | ||||
−0.433505 | + | 0.901151i | \(0.642723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.62137e7 | 0.651835 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.94850e7 | 0.535212 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.20311e8 | 1.56791 | 0.783954 | − | 0.620819i | \(-0.213200\pi\) | ||||
0.783954 | + | 0.620819i | \(0.213200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.21539e6 | −0.0403049 | −0.0201525 | − | 0.999797i | \(-0.506415\pi\) | ||||
−0.0201525 | + | 0.999797i | \(0.506415\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.99259e7 | 0.360968 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.93768e7 | −1.03782 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.40392e7 | 1.05163 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.98443e7 | −0.967997 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.04122e7 | 0.731191 | 0.365596 | − | 0.930774i | \(-0.380865\pi\) | ||||
0.365596 | + | 0.930774i | \(0.380865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.17861e7 | 0.118010 | 0.0590050 | − | 0.998258i | \(-0.481207\pi\) | ||||
0.0590050 | + | 0.998258i | \(0.481207\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.56566e7 | 0.440943 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.97008e7 | 0.835920 | 0.417960 | − | 0.908465i | \(-0.362745\pi\) | ||||
0.417960 | + | 0.908465i | \(0.362745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.98955e7 | 0.358871 | 0.179436 | − | 0.983770i | \(-0.442573\pi\) | ||||
0.179436 | + | 0.983770i | \(0.442573\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.38833e7 | 0.207447 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.49178e7 | −0.209061 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.60078e7 | 0.616197 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.52915e6 | 0.0589997 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.96613e8 | −1.48971 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.63604e7 | −0.486318 | −0.243159 | − | 0.969986i | \(-0.578184\pi\) | ||||
−0.243159 | + | 0.969986i | \(0.578184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.23051e8 | −0.872479 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.77825e7 | 0.122027 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.67317e7 | −0.509760 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 476088. | 0.00306290 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.44718e8 | 1.52508 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.57269e8 | −0.949675 | −0.474837 | − | 0.880074i | \(-0.657493\pi\) | ||||
−0.474837 | + | 0.880074i | \(0.657493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.49291e7 | 0.438543 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.95129e8 | −1.10721 | −0.553607 | − | 0.832778i | \(-0.686749\pi\) | ||||
−0.553607 | + | 0.832778i | \(0.686749\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.95136e7 | 0.382512 | 0.191256 | − | 0.981540i | \(-0.438744\pi\) | ||||
0.191256 | + | 0.981540i | \(0.438744\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.98095e7 | −0.532758 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.81872e7 | 0.197776 | 0.0988878 | − | 0.995099i | \(-0.468472\pi\) | ||||
0.0988878 | + | 0.995099i | \(0.468472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.88785e7 | −0.145157 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.13437e7 | −0.250535 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.63549e8 | −1.24873 | −0.624366 | − | 0.781132i | \(-0.714643\pi\) | ||||
−0.624366 | + | 0.781132i | \(0.714643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.21337e8 | 0.558386 | 0.279193 | − | 0.960235i | \(-0.409933\pi\) | ||||
0.279193 | + | 0.960235i | \(0.409933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.27512e8 | −1.01715 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.23441e7 | 0.227398 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.11645e8 | −2.16038 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.93555e7 | 0.0794523 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.62042e7 | −0.144511 | −0.0722555 | − | 0.997386i | \(-0.523020\pi\) | ||||
−0.0722555 | + | 0.997386i | \(0.523020\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.90893e7 | 0.0741085 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.82295e7 | 0.333214 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.75550e8 | 0.645111 | 0.322555 | − | 0.946551i | \(-0.395458\pi\) | ||||
0.322555 | + | 0.946551i | \(0.395458\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.08451e8 | 1.81844 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.04008e7 | −0.140653 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.10733e8 | 0.375348 | 0.187674 | − | 0.982231i | \(-0.439905\pi\) | ||||
0.187674 | + | 0.982231i | \(0.439905\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.27030e8 | 0.419320 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.95627e7 | −0.0950505 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.07561e8 | −0.963382 | −0.481691 | − | 0.876341i | \(-0.659977\pi\) | ||||
−0.481691 | + | 0.876341i | \(0.659977\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.86036e8 | −0.873027 | −0.436513 | − | 0.899698i | \(-0.643787\pi\) | ||||
−0.436513 | + | 0.899698i | \(0.643787\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.59734e8 | −0.772607 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.89974e8 | 0.550846 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.15642e8 | 0.892309 | 0.446155 | − | 0.894956i | \(-0.352793\pi\) | ||||
0.446155 | + | 0.894956i | \(0.352793\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.24410e8 | −0.342957 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.50451e8 | 0.673366 | 0.336683 | − | 0.941618i | \(-0.390695\pi\) | ||||
0.336683 | + | 0.941618i | \(0.390695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.47387e7 | −0.0911088 | −0.0455544 | − | 0.998962i | \(-0.514505\pi\) | ||||
−0.0455544 | + | 0.998962i | \(0.514505\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.84467e8 | −0.472020 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.32397e8 | −1.07968 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.25676e7 | 0.152478 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.60782e8 | −0.382482 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.34336e8 | −1.24102 | −0.620508 | − | 0.784200i | \(-0.713074\pi\) | ||||
−0.620508 | + | 0.784200i | \(0.713074\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.32777e8 | −0.754703 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.69329e8 | −0.818024 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.96760e7 | 0.107472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.01162e8 | −0.213813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.11954e8 | −0.437716 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.52214e8 | −0.509002 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.68851e8 | 0.333057 | 0.166529 | − | 0.986037i | \(-0.446744\pi\) | ||||
0.166529 | + | 0.986037i | \(0.446744\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.04229e8 | −0.586605 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.99677e8 | −1.31897 | −0.659487 | − | 0.751716i | \(-0.729226\pi\) | ||||
−0.659487 | + | 0.751716i | \(0.729226\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.06345e8 | −0.933343 | −0.466671 | − | 0.884431i | \(-0.654547\pi\) | ||||
−0.466671 | + | 0.884431i | \(0.654547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.31779e8 | 0.598084 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.78996e8 | 0.844548 | 0.422274 | − | 0.906468i | \(-0.361232\pi\) | ||||
0.422274 | + | 0.906468i | \(0.361232\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.02431e8 | −0.176671 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.13263e8 | 0.697364 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.88733e8 | −1.63256 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.94369e8 | 0.798839 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.88827e8 | −0.298639 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.64285e8 | 0.254339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.20825e8 | 0.637828 | 0.318914 | − | 0.947784i | \(-0.396682\pi\) | ||||
0.318914 | + | 0.947784i | \(0.396682\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.24382e8 | 1.22341 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.01287e8 | −0.292522 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.02987e9 | −1.46580 | −0.732902 | − | 0.680334i | \(-0.761835\pi\) | ||||
−0.732902 | + | 0.680334i | \(0.761835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.88170e8 | 0.401745 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.15427e8 | −0.430782 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.68554e8 | 0.760751 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.79100e7 | 0.0234816 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.31496e8 | −0.682883 | −0.341442 | − | 0.939903i | \(-0.610915\pi\) | ||||
−0.341442 | + | 0.939903i | \(0.610915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.31436e9 | −1.65511 | −0.827555 | − | 0.561385i | \(-0.810269\pi\) | ||||
−0.827555 | + | 0.561385i | \(0.810269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.61103e8 | −1.18630 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.42031e9 | 1.71858 | 0.859291 | − | 0.511486i | \(-0.170905\pi\) | ||||
0.859291 | + | 0.511486i | \(0.170905\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.03706e9 | 1.23028 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.01924e8 | −0.583847 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.59524e8 | −0.866385 | −0.433193 | − | 0.901301i | \(-0.642613\pi\) | ||||
−0.433193 | + | 0.901301i | \(0.642613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.17333e9 | 1.31264 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.72702e7 | 0.0189507 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.01244e6 | −0.00431900 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.76159e8 | 0.397228 | 0.198614 | − | 0.980078i | \(-0.436356\pi\) | ||||
0.198614 | + | 0.980078i | \(0.436356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.01071e8 | −0.726390 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.22655e8 | −0.734720 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.57130e8 | 0.456099 | 0.228049 | − | 0.973650i | \(-0.426765\pi\) | ||||
0.228049 | + | 0.973650i | \(0.426765\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.95206e8 | 0.484927 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.66557e8 | −0.256209 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.91565e9 | −1.80750 | −0.903752 | − | 0.428056i | \(-0.859199\pi\) | ||||
−0.903752 | + | 0.428056i | \(0.859199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.99402e8 | −0.647873 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.57853e9 | 1.43568 | 0.717839 | − | 0.696209i | \(-0.245131\pi\) | ||||
0.717839 | + | 0.696209i | \(0.245131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.41187e8 | 0.751243 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.64020e8 | −0.143849 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.21214e9 | 1.90541 | 0.952707 | − | 0.303890i | \(-0.0982854\pi\) | ||||
0.952707 | + | 0.303890i | \(0.0982854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.59967e7 | 0.0812153 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.56817e8 | 0.213427 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.32721e8 | 0.353279 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.30879e9 | 1.04979 | 0.524896 | − | 0.851167i | \(-0.324104\pi\) | ||||
0.524896 | + | 0.851167i | \(0.324104\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.04940e9 | 0.827060 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.04514e8 | 0.0809413 | 0.0404706 | − | 0.999181i | \(-0.487114\pi\) | ||||
0.0404706 | + | 0.999181i | \(0.487114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.20832e8 | −0.624722 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.43251e8 | 0.256755 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.09013e9 | 1.53671 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.94107e9 | −1.40284 | −0.701421 | − | 0.712747i | \(-0.747451\pi\) | ||||
−0.701421 | + | 0.712747i | \(0.747451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.31937e8 | 0.591077 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.89312e9 | 1.32237 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.63127e8 | −0.112036 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.15000e8 | −0.415336 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.96429e9 | 1.30454 | 0.652268 | − | 0.757989i | \(-0.273818\pi\) | ||||
0.652268 | + | 0.757989i | \(0.273818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.33176e9 | −1.52299 | −0.761493 | − | 0.648174i | \(-0.775533\pi\) | ||||
−0.761493 | + | 0.648174i | \(0.775533\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.66366e8 | 0.171115 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.55346e8 | 0.603670 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.43480e9 | 0.891857 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.06771e9 | −0.652907 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.72745e8 | 0.103929 | 0.0519643 | − | 0.998649i | \(-0.483452\pi\) | ||||
0.0519643 | + | 0.998649i | \(0.483452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.71381e9 | −1.60647 | −0.803233 | − | 0.595665i | \(-0.796889\pi\) | ||||
−0.803233 | + | 0.595665i | \(0.796889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.61033e7 | −0.0559791 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00706e8 | −0.115047 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.73808e8 | 0.154461 | 0.0772307 | − | 0.997013i | \(-0.475392\pi\) | ||||
0.0772307 | + | 0.997013i | \(0.475392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.82804e8 | −0.268063 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.72048e9 | 1.48673 | 0.743365 | − | 0.668886i | \(-0.233229\pi\) | ||||
0.743365 | + | 0.668886i | \(0.233229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.49152e8 | 0.134031 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.49654e8 | 0.0792526 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.69111e9 | 0.881675 | 0.440837 | − | 0.897587i | \(-0.354682\pi\) | ||||
0.440837 | + | 0.897587i | \(0.354682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.77748e9 | −0.912406 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.67204e9 | −0.845089 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.18902e9 | 1.08945 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.15773e8 | 0.0567413 | 0.0283706 | − | 0.999597i | \(-0.490968\pi\) | ||||
0.0283706 | + | 0.999597i | \(0.490968\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.85729e9 | −0.896470 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.34713e8 | −0.444350 | −0.222175 | − | 0.975007i | \(-0.571316\pi\) | ||||
−0.222175 | + | 0.975007i | \(0.571316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.91738e9 | 0.897790 | 0.448895 | − | 0.893584i | \(-0.351818\pi\) | ||||
0.448895 | + | 0.893584i | \(0.351818\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.95940e8 | −0.136495 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.65838e9 | 0.753485 | 0.376742 | − | 0.926318i | \(-0.377044\pi\) | ||||
0.376742 | + | 0.926318i | \(0.377044\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.14509e9 | 0.512548 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.40684e8 | −0.414830 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.15853e8 | −0.180686 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.99740e9 | −0.855140 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.17168e9 | −0.494306 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.09755e9 | 1.70353 | 0.851766 | − | 0.523923i | \(-0.175532\pi\) | ||||
0.851766 | + | 0.523923i | \(0.175532\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.43912e9 | 2.22854 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.01887e8 | −0.0411438 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.35506e9 | 0.539339 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.24167e9 | 1.27180 | 0.635898 | − | 0.771773i | \(-0.280630\pi\) | ||||
0.635898 | + | 0.771773i | \(0.280630\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.04239e8 | 0.349705 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.16351e9 | −0.824847 | −0.412423 | − | 0.910992i | \(-0.635318\pi\) | ||||
−0.412423 | + | 0.910992i | \(0.635318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.15110e8 | −0.193613 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.36387e9 | 0.505422 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.89969e9 | −2.15567 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.16713e9 | −0.780787 | −0.390394 | − | 0.920648i | \(-0.627661\pi\) | ||||
−0.390394 | + | 0.920648i | \(0.627661\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.30316e8 | 0.188409 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.58480e9 | 0.905606 | 0.452803 | − | 0.891611i | \(-0.350424\pi\) | ||||
0.452803 | + | 0.891611i | \(0.350424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.78633e9 | 0.617224 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.40173e9 | −0.477680 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.11747e9 | −0.711712 | −0.355856 | − | 0.934541i | \(-0.615811\pi\) | ||||
−0.355856 | + | 0.934541i | \(0.615811\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.28261e7 | 0.00756762 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.88315e9 | 1.26991 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.56402e9 | 0.827172 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.75339e8 | 0.214934 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.29550e9 | 0.406773 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.34354e9 | 0.726006 | 0.363003 | − | 0.931788i | \(-0.381751\pi\) | ||||
0.363003 | + | 0.931788i | \(0.381751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.26155e9 | 0.996939 | 0.498470 | − | 0.866907i | \(-0.333896\pi\) | ||||
0.498470 | + | 0.866907i | \(0.333896\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.01397e9 | −0.305820 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.58622e9 | −0.472093 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.38534e9 | −0.994277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.06942e9 | 0.889664 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.62554e9 | −1.32317 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.48296e9 | −0.983354 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.63973e9 | −0.735612 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.22409e9 | −0.336709 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.24638e9 | 1.96757 | 0.983787 | − | 0.179344i | \(-0.0573974\pi\) | ||||
0.983787 | + | 0.179344i | \(0.0573974\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.05482e7 | 0.0189098 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.59142e9 | 0.421111 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.41460e9 | −1.67577 | −0.837884 | − | 0.545848i | \(-0.816207\pi\) | ||||
−0.837884 | + | 0.545848i | \(0.816207\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.32634e9 | 0.600025 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.07697e9 | 0.274267 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.46168e9 | −0.619005 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.96100e9 | 0.486914 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.76223e9 | −0.432085 | −0.216042 | − | 0.976384i | \(-0.569315\pi\) | ||||
−0.216042 | + | 0.976384i | \(0.569315\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.08217e9 | −0.262032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.06330e9 | −0.493391 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.33270e9 | −0.550909 | −0.275454 | − | 0.961314i | \(-0.588828\pi\) | ||||
−0.275454 | + | 0.961314i | \(0.588828\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.42868e9 | −0.566501 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.95270e9 | −0.449878 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.53591e9 | −1.25978 | −0.629892 | − | 0.776683i | \(-0.716901\pi\) | ||||
−0.629892 | + | 0.776683i | \(0.716901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.70890e9 | 0.833717 | 0.416858 | − | 0.908971i | \(-0.363131\pi\) | ||||
0.416858 | + | 0.908971i | \(0.363131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.54490e9 | −0.343051 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.93929e8 | 0.0425407 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.63713e9 | 0.788212 | 0.394106 | − | 0.919065i | \(-0.371054\pi\) | ||||
0.394106 | + | 0.919065i | \(0.371054\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.58596e8 | −0.0553665 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.28003e8 | 0.196306 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.97067e9 | −0.620889 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.54919e9 | 0.732965 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.04311e9 | −0.416926 | −0.208463 | − | 0.978030i | \(-0.566846\pi\) | ||||
−0.208463 | + | 0.978030i | \(0.566846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.31641e9 | 0.668752 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.96811e9 | −0.392187 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.74764e9 | −1.13187 | −0.565937 | − | 0.824448i | \(-0.691486\pi\) | ||||
−0.565937 | + | 0.824448i | \(0.691486\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.23018e9 | 0.823284 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.75341e8 | −0.168371 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.14564e8 | −0.0598020 | −0.0299010 | − | 0.999553i | \(-0.509519\pi\) | ||||
−0.0299010 | + | 0.999553i | \(0.509519\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.49586e9 | 0.468985 | 0.234493 | − | 0.972118i | \(-0.424657\pi\) | ||||
0.234493 | + | 0.972118i | \(0.424657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.85660e9 | 0.344833 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.45552e8 | −0.0267224 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.81126e9 | −0.510200 | −0.255100 | − | 0.966915i | \(-0.582108\pi\) | ||||
−0.255100 | + | 0.966915i | \(0.582108\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.46717e8 | 0.0980849 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.75743e9 | 0.311698 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.34343e9 | 0.410904 | 0.205452 | − | 0.978667i | \(-0.434134\pi\) | ||||
0.205452 | + | 0.978667i | \(0.434134\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.66767e9 | −0.289100 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.26737e8 | 0.107420 | 0.0537102 | − | 0.998557i | \(-0.482895\pi\) | ||||
0.0537102 | + | 0.998557i | \(0.482895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.90879e9 | −1.50974 | −0.754869 | − | 0.655876i | \(-0.772300\pi\) | ||||
−0.754869 | + | 0.655876i | \(0.772300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.77017e8 | −0.0631743 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.41739e9 | −0.234845 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.41437e8 | −0.121477 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.31385e9 | 0.698922 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.05109e10 | 1.68407 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.21942e9 | 0.351671 | 0.175835 | − | 0.984420i | \(-0.443737\pi\) | ||||
0.175835 | + | 0.984420i | \(0.443737\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.45600e9 | 0.228165 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.89451e9 | 0.913566 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.18545e9 | −0.488296 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.56552e9 | −1.45029 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.58104e9 | 1.28688 | 0.643438 | − | 0.765498i | \(-0.277507\pi\) | ||||
0.643438 | + | 0.765498i | \(0.277507\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.71279e9 | 1.14412 | 0.572062 | − | 0.820210i | \(-0.306144\pi\) | ||||
0.572062 | + | 0.820210i | \(0.306144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.90161e8 | −0.0572513 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.18898e10 | −1.72587 | −0.862935 | − | 0.505316i | \(-0.831376\pi\) | ||||
−0.862935 | + | 0.505316i | \(0.831376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.78217e9 | 1.11749 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.68356e9 | 0.239163 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.00345e9 | 0.281567 | 0.140784 | − | 0.990040i | \(-0.455038\pi\) | ||||
0.140784 | + | 0.990040i | \(0.455038\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.16443e9 | −0.300954 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.70094e7 | 0.00509135 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.66944e9 | −1.04391 | −0.521957 | − | 0.852972i | \(-0.674798\pi\) | ||||
−0.521957 | + | 0.852972i | \(0.674798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.04041e9 | 0.544152 | 0.272076 | − | 0.962276i | \(-0.412290\pi\) | ||||
0.272076 | + | 0.962276i | \(0.412290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.36930e9 | −0.715518 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.84429e9 | −1.16624 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.04564e8 | −0.0136440 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.45060e9 | 0.445557 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.89816e9 | 0.753681 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.11138e9 | 0.519918 | 0.259959 | − | 0.965620i | \(-0.416291\pi\) | ||||
0.259959 | + | 0.965620i | \(0.416291\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.75203e9 | −0.469572 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.12671e10 | −1.39557 | −0.697787 | − | 0.716305i | \(-0.745832\pi\) | ||||
−0.697787 | + | 0.716305i | \(0.745832\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.70872e9 | −0.945014 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.28129e9 | 0.519469 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.00228e9 | −0.961039 | −0.480520 | − | 0.876984i | \(-0.659552\pi\) | ||||
−0.480520 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.01151e9 | −0.833479 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.52518e9 | −0.179462 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.73055e9 | −0.900416 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.24716e9 | −0.835593 | −0.417797 | − | 0.908541i | \(-0.637197\pi\) | ||||
−0.417797 | + | 0.908541i | \(0.637197\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.75884e9 | −0.885585 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.18318e9 | 0.585665 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.93865e9 | −0.999902 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.37859e8 | −0.0927899 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.68293e8 | 0.0513458 | 0.0256729 | − | 0.999670i | \(-0.491827\pi\) | ||||
0.0256729 | + | 0.999670i | \(0.491827\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.19757e10 | −2.38561 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.33617e8 | 0.0681028 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.01622e10 | −1.08148 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.08926e10 | −1.14781 | −0.573903 | − | 0.818923i | \(-0.694571\pi\) | ||||
−0.573903 | + | 0.818923i | \(0.694571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.99128e9 | −0.416455 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.21992e8 | −0.0332684 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.99855e9 | 0.920664 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.78249e9 | 0.585865 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.40284e9 | −0.742758 | −0.371379 | − | 0.928481i | \(-0.621115\pi\) | ||||
−0.371379 | + | 0.928481i | \(0.621115\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.45863e10 | −1.44935 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.66224e9 | −0.261977 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.04060e9 | −0.101415 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04295e10 | −1.00668 | −0.503342 | − | 0.864087i | \(-0.667897\pi\) | ||||
−0.503342 | + | 0.864087i | \(0.667897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.32176e8 | 0.0891152 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.09125e9 | −0.198014 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.55538e10 | −1.45873 | −0.729363 | − | 0.684127i | \(-0.760184\pi\) | ||||
−0.729363 | + | 0.684127i | \(0.760184\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.14847e9 | −0.106688 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.70720e9 | 0.433138 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.07140e10 | 0.976554 | 0.488277 | − | 0.872689i | \(-0.337626\pi\) | ||||
0.488277 | + | 0.872689i | \(0.337626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.12259e10 | 1.01358 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.46982e9 | 0.489229 | 0.244615 | − | 0.969620i | \(-0.421339\pi\) | ||||
0.244615 | + | 0.969620i | \(0.421339\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.26128e9 | −0.111754 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.50463e9 | 0.132071 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.98140e10 | 1.72300 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.68185e9 | 0.489497 | 0.244749 | − | 0.969587i | \(-0.421295\pi\) | ||||
0.244749 | + | 0.969587i | \(0.421295\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.94349e8 | 0.0677999 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.40918e10 | 1.19166 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.38304e9 | 0.451016 | 0.225508 | − | 0.974241i | \(-0.427596\pi\) | ||||
0.225508 | + | 0.974241i | \(0.427596\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.18835e8 | −0.0347693 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.28593e9 | 0.270279 | 0.135139 | − | 0.990827i | \(-0.456852\pi\) | ||||
0.135139 | + | 0.990827i | \(0.456852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.05334e9 | −0.737858 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.85865e9 | 0.553890 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.02515e10 | 1.62059 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.10914e9 | 0.563735 | 0.281868 | − | 0.959453i | \(-0.409046\pi\) | ||||
0.281868 | + | 0.959453i | \(0.409046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.85170e9 | −0.302665 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.08690e10 | 0.846370 | 0.423185 | − | 0.906043i | \(-0.360912\pi\) | ||||
0.423185 | + | 0.906043i | \(0.360912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.20443e9 | −0.247283 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.11558e10 | −0.853155 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.86886e10 | 1.41643 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.42523e10 | −1.82169 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.02304e9 | 0.150605 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.92802e9 | 0.584953 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.94246e10 | 1.42050 | 0.710248 | − | 0.703951i | \(-0.248583\pi\) | ||||
0.710248 | + | 0.703951i | \(0.248583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.42958e9 | −0.176101 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.38164e10 | 0.992606 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.53487e10 | 1.09299 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.78714e9 | −0.196732 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.30309e10 | −1.61141 | −0.805707 | − | 0.592314i | \(-0.798214\pi\) | ||||
−0.805707 | + | 0.592314i | \(0.798214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.39616e9 | 0.235545 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.29810e9 | −0.157999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.38331e7 | 0.00639516 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.58697e8 | 0.0580169 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.74814e9 | 0.451988 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.50546e10 | 0.999656 | 0.499828 | − | 0.866125i | \(-0.333397\pi\) | ||||
0.499828 | + | 0.866125i | \(0.333397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.98821e10 | −1.30885 | −0.654424 | − | 0.756128i | \(-0.727089\pi\) | ||||
−0.654424 | + | 0.756128i | \(0.727089\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.27585e9 | 0.409596 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.62086e9 | −0.493120 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.37230e9 | 0.280500 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.01908e10 | −1.28428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.29870e10 | −1.44971 | −0.724855 | − | 0.688901i | \(-0.758093\pi\) | ||||
−0.724855 | + | 0.688901i | \(0.758093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.46696e10 | −0.917316 | −0.458658 | − | 0.888613i | \(-0.651670\pi\) | ||||
−0.458658 | + | 0.888613i | \(0.651670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.16819e9 | −0.258439 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.26591e9 | 0.0778277 | 0.0389138 | − | 0.999243i | \(-0.487610\pi\) | ||||
0.0389138 | + | 0.999243i | \(0.487610\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.49778e10 | 1.52270 | 0.761349 | − | 0.648342i | \(-0.224537\pi\) | ||||
0.761349 | + | 0.648342i | \(0.224537\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.92544e9 | −0.418643 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.15576e9 | −0.368998 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.46947e9 | −0.265676 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.22973e9 | 0.367223 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.09477e10 | 1.80909 | 0.904547 | − | 0.426373i | \(-0.140209\pi\) | ||||
0.904547 | + | 0.426373i | \(0.140209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.66888e10 | −0.967473 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.49510e9 | −0.315921 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.18137e10 | 0.673577 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.28024e8 | 0.0468221 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.62194e8 | 0.0427453 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.13363e9 | 0.118677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.86385e10 | 1.02823 | 0.514113 | − | 0.857723i | \(-0.328121\pi\) | ||||
0.514113 | + | 0.857723i | \(0.328121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.43398e10 | −0.784623 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.37366e10 | 1.28821 | 0.644103 | − | 0.764939i | \(-0.277231\pi\) | ||||
0.644103 | + | 0.764939i | \(0.277231\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.46268e10 | 1.32566 | 0.662830 | − | 0.748770i | \(-0.269355\pi\) | ||||
0.662830 | + | 0.748770i | \(0.269355\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.48713e9 | 0.506552 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.50051e10 | 1.32431 | 0.662157 | − | 0.749365i | \(-0.269641\pi\) | ||||
0.662157 | + | 0.749365i | \(0.269641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.09184e10 | −0.573592 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.37278e9 | −0.0715378 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.01194e10 | −0.523102 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22495e10 | 0.628139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.24986e10 | −0.635788 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.37428e10 | 1.19813 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.07280e10 | 0.537057 | 0.268528 | − | 0.963272i | \(-0.413463\pi\) | ||||
0.268528 | + | 0.963272i | \(0.413463\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.17238e10 | 0.582245 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.94499e9 | 0.292911 | 0.146455 | − | 0.989217i | \(-0.453214\pi\) | ||||
0.146455 | + | 0.989217i | \(0.453214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.60870e10 | −0.786342 | −0.393171 | − | 0.919465i | \(-0.628622\pi\) | ||||
−0.393171 | + | 0.919465i | \(0.628622\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.30139e9 | 0.354082 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.61884e10 | 1.26001 | 0.630007 | − | 0.776589i | \(-0.283052\pi\) | ||||
0.630007 | + | 0.776589i | \(0.283052\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.35330e10 | −1.60072 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.02711e9 | −0.380178 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.10056e9 | −0.333666 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.22474e10 | 1.03729 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.08993e9 | −0.0504226 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.72778e9 | 0.0793104 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.49390e10 | −0.680430 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.21957e9 | 0.100314 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.94575e8 | −0.0266647 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.79753e9 | −0.0799929 | −0.0399964 | − | 0.999200i | \(-0.512735\pi\) | ||||
−0.0399964 | + | 0.999200i | \(0.512735\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.64766e10 | −0.727601 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.70021e10 | 1.62148 | 0.810740 | − | 0.585406i | \(-0.199065\pi\) | ||||
0.810740 | + | 0.585406i | \(0.199065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.81481e9 | 0.165892 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.53377e9 | 0.238807 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.23131e10 | 0.527322 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.44812e10 | 1.04047 | 0.520234 | − | 0.854024i | \(-0.325845\pi\) | ||||
0.520234 | + | 0.854024i | \(0.325845\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.70472e9 | −0.156260 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.31115e10 | −2.64182 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.12336e10 | 0.882121 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.36497e10 | −0.975093 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.19981e9 | −0.253702 | −0.126851 | − | 0.991922i | \(-0.540487\pi\) | ||||
−0.126851 | + | 0.991922i | \(0.540487\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.28702e10 | 0.522711 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.53515e10 | 0.618820 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.73893e10 | 0.695732 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.78747e10 | 1.10693 | 0.553466 | − | 0.832871i | \(-0.313305\pi\) | ||||
0.553466 | + | 0.832871i | \(0.313305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.11096e10 | 0.437894 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.45921e10 | −1.35336 | −0.676680 | − | 0.736277i | \(-0.736582\pi\) | ||||
−0.676680 | + | 0.736277i | \(0.736582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.81448e9 | −0.0704632 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.66136e10 | −0.640402 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.20475e10 | −0.843598 | −0.421799 | − | 0.906689i | \(-0.638601\pi\) | ||||
−0.421799 | + | 0.906689i | \(0.638601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.44181e8 | 0.00927429 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.05096e10 | −0.396235 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.95876e9 | 0.148161 | 0.0740805 | − | 0.997252i | \(-0.476398\pi\) | ||||
0.0740805 | + | 0.997252i | \(0.476398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.30203e10 | 0.483737 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.24743e9 | 0.0828885 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.98874e10 | 1.46040 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.21921e10 | −0.806615 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.21256e10 | 1.15920 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.17943e9 | 0.0780724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.76598e9 | 0.347315 | 0.173657 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.16936e10 | 0.765946 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.15553e10 | −0.755589 | −0.377795 | − | 0.925889i | \(-0.623317\pi\) | ||||
−0.377795 | + | 0.925889i | \(0.623317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.94863e10 | −1.02619 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.08468e10 | −0.374789 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.24340e10 | 1.79880 | 0.899398 | − | 0.437131i | \(-0.144005\pi\) | ||||
0.899398 | + | 0.437131i | \(0.144005\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.82657e9 | −0.198460 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.46787e10 | −0.496417 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.85116e10 | 0.957380 | 0.478690 | − | 0.877984i | \(-0.341112\pi\) | ||||
0.478690 | + | 0.877984i | \(0.341112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.65871e10 | 0.553023 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.60455e9 | −0.119328 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.24509e8 | −0.0139540 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.72290e10 | −0.888738 | −0.444369 | − | 0.895844i | \(-0.646572\pi\) | ||||
−0.444369 | + | 0.895844i | \(0.646572\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.23324e9 | −0.299248 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.37731e9 | 0.237420 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.30057e10 | −0.415624 | −0.207812 | − | 0.978169i | \(-0.566634\pi\) | ||||
−0.207812 | + | 0.978169i | \(0.566634\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.12804e10 | −1.30998 |
(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 | 256.8.a.r.1.3 | 6 | ||
4.3 | odd | 2 | 256.8.a.q.1.4 | 6 | |||
8.3 | odd | 2 | 256.8.a.q.1.3 | 6 | |||
8.5 | even | 2 | inner | 256.8.a.r.1.4 | 6 | ||
16.3 | odd | 4 | 32.8.b.a.17.4 | 6 | |||
16.5 | even | 4 | 8.8.b.a.5.4 | yes | 6 | ||
16.11 | odd | 4 | 32.8.b.a.17.3 | 6 | |||
16.13 | even | 4 | 8.8.b.a.5.3 | ✓ | 6 | ||
48.5 | odd | 4 | 72.8.d.b.37.3 | 6 | |||
48.11 | even | 4 | 288.8.d.b.145.3 | 6 | |||
48.29 | odd | 4 | 72.8.d.b.37.4 | 6 | |||
48.35 | even | 4 | 288.8.d.b.145.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.b.a.5.3 | ✓ | 6 | 16.13 | even | 4 | ||
8.8.b.a.5.4 | yes | 6 | 16.5 | even | 4 | ||
32.8.b.a.17.3 | 6 | 16.11 | odd | 4 | |||
32.8.b.a.17.4 | 6 | 16.3 | odd | 4 | |||
72.8.d.b.37.3 | 6 | 48.5 | odd | 4 | |||
72.8.d.b.37.4 | 6 | 48.29 | odd | 4 | |||
256.8.a.q.1.3 | 6 | 8.3 | odd | 2 | |||
256.8.a.q.1.4 | 6 | 4.3 | odd | 2 | |||
256.8.a.r.1.3 | 6 | 1.1 | even | 1 | trivial | ||
256.8.a.r.1.4 | 6 | 8.5 | even | 2 | inner | ||
288.8.d.b.145.3 | 6 | 48.11 | even | 4 | |||
288.8.d.b.145.4 | 6 | 48.35 | even | 4 |