Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,10,Mod(49,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.c (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: | \(51.5035836164\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{79})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 39x^{2} + 400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(4.44410 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 100.49 |
Dual form | 100.10.c.c.49.3 |
$q$-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 \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 12.2111i | − 0.0870381i | −0.999053 | − | 0.0435191i | \(-0.986143\pi\) | ||||
0.999053 | − | 0.0435191i | \(-0.0138569\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9622.57i | 1.51478i | 0.652962 | + | 0.757390i | \(0.273526\pi\) | ||||
−0.652962 | + | 0.757390i | \(0.726474\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 19533.9 | 0.992424 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 55626.3 | 1.14555 | 0.572774 | − | 0.819713i | \(-0.305867\pi\) | ||||
0.572774 | + | 0.819713i | \(0.305867\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 169777.i | − 1.64867i | −0.566102 | − | 0.824335i | \(-0.691549\pi\) | ||||
0.566102 | − | 0.824335i | \(-0.308451\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 207499.i | 0.602555i | 0.953536 | + | 0.301278i | \(0.0974131\pi\) | ||||
−0.953536 | + | 0.301278i | \(0.902587\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −802445. | −1.41262 | −0.706308 | − | 0.707904i | \(-0.749641\pi\) | ||||
−0.706308 | + | 0.707904i | \(0.749641\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 117502. | 0.131844 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.24189e6i | 0.925351i | 0.886528 | + | 0.462675i | \(0.153110\pi\) | ||||
−0.886528 | + | 0.462675i | \(0.846890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 478882.i | − 0.173417i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.28308e6 | 1.12451 | 0.562257 | − | 0.826963i | \(-0.309933\pi\) | ||||
0.562257 | + | 0.826963i | \(0.309933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.58713e6 | −0.697620 | −0.348810 | − | 0.937193i | \(-0.613414\pi\) | ||||
−0.348810 | + | 0.937193i | \(0.613414\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 679259.i | − 0.0997064i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.89856e6i | − 0.254258i | −0.991886 | − | 0.127129i | \(-0.959424\pi\) | ||||
0.991886 | − | 0.127129i | \(-0.0405763\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.07317e6 | −0.143497 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.51515e7 | 1.39007 | 0.695035 | − | 0.718975i | \(-0.255389\pi\) | ||||
0.695035 | + | 0.718975i | \(0.255389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00204e7i | 0.893029i | 0.894776 | + | 0.446515i | \(0.147335\pi\) | ||||
−0.894776 | + | 0.446515i | \(0.852665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.73010e7i | 1.11501i | 0.830172 | + | 0.557507i | \(0.188242\pi\) | ||||
−0.830172 | + | 0.557507i | \(0.811758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.22402e7 | −1.29456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53380e6 | 0.0524453 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.55155e7i | 0.444184i | 0.975026 | + | 0.222092i | \(0.0712886\pi\) | ||||
−0.975026 | + | 0.222092i | \(0.928711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.79875e6i | 0.122951i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.96495e7 | 1.07063 | 0.535317 | − | 0.844651i | \(-0.320192\pi\) | ||||
0.535317 | + | 0.844651i | \(0.320192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00434e8 | 1.85347 | 0.926737 | − | 0.375710i | \(-0.122601\pi\) | ||||
0.926737 | + | 0.375710i | \(0.122601\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.87966e8i | 1.50331i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.09951e7i | − 0.491046i | −0.969391 | − | 0.245523i | \(-0.921040\pi\) | ||||
0.969391 | − | 0.245523i | \(-0.0789597\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.51648e7 | 0.0805408 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.31522e7 | −0.201530 | −0.100765 | − | 0.994910i | \(-0.532129\pi\) | ||||
−0.100765 | + | 0.994910i | \(0.532129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.40820e8i | 1.40466i | 0.711850 | + | 0.702332i | \(0.247858\pi\) | ||||
−0.711850 | + | 0.702332i | \(0.752142\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.35268e8i | 1.73525i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.81089e8 | −0.811935 | −0.405967 | − | 0.913888i | \(-0.633065\pi\) | ||||
−0.405967 | + | 0.913888i | \(0.633065\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.78638e8 | 0.977330 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.01017e8i | 1.39007i | 0.718978 | + | 0.695033i | \(0.244610\pi\) | ||||
−0.718978 | + | 0.695033i | \(0.755390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 5.23011e7i | − 0.0978756i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.39917e8 | −0.912162 | −0.456081 | − | 0.889938i | \(-0.650747\pi\) | ||||
−0.456081 | + | 0.889938i | \(0.650747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.63369e9 | 2.49737 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.38028e7i | 0.0607195i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.23026e8i | 0.485170i | 0.970130 | + | 0.242585i | \(0.0779953\pi\) | ||||
−0.970130 | + | 0.242585i | \(0.922005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.08660e9 | 1.13687 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.09286e9 | −1.04501 | −0.522503 | − | 0.852637i | \(-0.675002\pi\) | ||||
−0.522503 | + | 0.852637i | \(0.675002\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.50494e7i | 0.0744567i | 0.999307 | + | 0.0372284i | \(0.0118529\pi\) | ||||
−0.999307 | + | 0.0372284i | \(0.988147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.23881e8i | 0.386372i | 0.981162 | + | 0.193186i | \(0.0618821\pi\) | ||||
−0.981162 | + | 0.193186i | \(0.938118\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.59417e8 | 0.379591 | 0.189796 | − | 0.981824i | \(-0.439217\pi\) | ||||
0.189796 | + | 0.981824i | \(0.439217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.53947e7 | −0.0221302 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.63801e9i | 1.52203i | 0.648733 | + | 0.761016i | \(0.275299\pi\) | ||||
−0.648733 | + | 0.761016i | \(0.724701\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 3.31641e9i | − 1.63618i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.99668e9 | −0.912739 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.36341e8 | 0.312281 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 3.07128e8i | − 0.120989i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.33268e9i | 1.13678i | 0.822758 | + | 0.568391i | \(0.192434\pi\) | ||||
−0.822758 | + | 0.568391i | \(0.807566\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.44472e8 | 0.0777276 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.78884e9 | −1.12405 | −0.562024 | − | 0.827121i | \(-0.689977\pi\) | ||||
−0.562024 | + | 0.827121i | \(0.689977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 7.72158e9i | − 2.13980i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2.15185e9i | − 0.521879i | −0.965355 | − | 0.260940i | \(-0.915968\pi\) | ||||
0.965355 | − | 0.260940i | \(-0.0840323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.75086e8 | −0.0625032 | −0.0312516 | − | 0.999512i | \(-0.509949\pi\) | ||||
−0.0312516 | + | 0.999512i | \(0.509949\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.55487e8 | 0.0970487 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 9.44408e9i | − 1.88863i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.37911e8i | 0.112676i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.16582e9 | 1.02483 | 0.512416 | − | 0.858737i | \(-0.328751\pi\) | ||||
0.512416 | + | 0.858737i | \(0.328751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.28376e9 | −0.514014 | −0.257007 | − | 0.966410i | \(-0.582736\pi\) | ||||
−0.257007 | + | 0.966410i | \(0.582736\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.05327e9i | 0.597990i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.89255e9i | − 0.248599i | −0.992245 | − | 0.124299i | \(-0.960332\pi\) | ||||
0.992245 | − | 0.124299i | \(-0.0396683\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.11573e8 | 0.0386610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.19501e10 | −1.40170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.14293e8i | − 0.0459688i | −0.999736 | − | 0.0229844i | \(-0.992683\pi\) | ||||
0.999736 | − | 0.0229844i | \(-0.00731681\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.56225e10i | − 1.55427i | −0.629332 | − | 0.777136i | \(-0.716672\pi\) | ||||
0.629332 | − | 0.777136i | \(-0.283328\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.82198e10 | −1.71812 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.56749e10 | −1.40191 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.16058e10i | − 0.985069i | −0.870293 | − | 0.492535i | \(-0.836070\pi\) | ||||
0.870293 | − | 0.492535i | \(-0.163930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1.21683e9i | − 0.0931860i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.45556e10 | 1.78777 | 0.893886 | − | 0.448294i | \(-0.147968\pi\) | ||||
0.893886 | + | 0.448294i | \(0.147968\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.21032e9 | 0.222328 | 0.111164 | − | 0.993802i | \(-0.464542\pi\) | ||||
0.111164 | + | 0.993802i | \(0.464542\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2.44752e9i | − 0.161323i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.15424e10i | 0.690256i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.60807e9 | 0.262689 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.41548e10 | 1.85695 | 0.928477 | − | 0.371390i | \(-0.121119\pi\) | ||||
0.928477 | + | 0.371390i | \(0.121119\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 2.50875e10i | − 1.30152i | −0.759284 | − | 0.650759i | \(-0.774451\pi\) | ||||
0.759284 | − | 0.650759i | \(-0.225549\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.64109e9i | 0.456067i | 0.973653 | + | 0.228033i | \(0.0732295\pi\) | ||||
−0.973653 | + | 0.228033i | \(0.926771\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.34318e9 | −0.151120 | −0.0755598 | − | 0.997141i | \(-0.524074\pi\) | ||||
−0.0755598 | + | 0.997141i | \(0.524074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.89040e8 | −0.0427397 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.12142e10i | 1.70339i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.42589e10i | 0.918341i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.46371e10 | −1.61822 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.76087e10 | −0.611585 | −0.305792 | − | 0.952098i | \(-0.598921\pi\) | ||||
−0.305792 | + | 0.952098i | \(0.598921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.26936e8i | 0.0175408i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 3.45174e10i | − 1.05674i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.16179e9 | 0.122259 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.52287e10 | 0.993415 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.00503e10i | 1.35530i | 0.735386 | + | 0.677649i | \(0.237001\pi\) | ||||
−0.735386 | + | 0.677649i | \(0.762999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.68117e9i | − 0.217001i | −0.994096 | − | 0.108501i | \(-0.965395\pi\) | ||||
0.994096 | − | 0.108501i | \(-0.0346049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.96014e10 | 0.711299 | 0.355649 | − | 0.934619i | \(-0.384260\pi\) | ||||
0.355649 | + | 0.934619i | \(0.384260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.53622e9 | 0.151033 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.42617e10i | 1.65068i | 0.564634 | + | 0.825341i | \(0.309017\pi\) | ||||
−0.564634 | + | 0.825341i | \(0.690983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.43240e9i | 0.0706693i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.65577e10 | 0.328253 | 0.164126 | − | 0.986439i | \(-0.447519\pi\) | ||||
0.164126 | + | 0.986439i | \(0.447519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.61072e10 | 0.689473 | 0.344737 | − | 0.938699i | \(-0.387968\pi\) | ||||
0.344737 | + | 0.938699i | \(0.387968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.40494e10i | − 0.258482i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.36237e11i | 2.32894i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.33909e9 | 0.120989 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.32959e10 | 0.370465 | 0.185232 | − | 0.982695i | \(-0.440696\pi\) | ||||
0.185232 | + | 0.982695i | \(0.440696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.90815e10i | 1.06003i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 4.57624e10i | − 0.654350i | −0.944964 | − | 0.327175i | \(-0.893903\pi\) | ||||
0.944964 | − | 0.327175i | \(-0.106097\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.78916e10 | 0.385145 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.36651e10 | 1.11599 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 9.93911e10i | − 1.28099i | −0.767961 | − | 0.640496i | \(-0.778729\pi\) | ||||
0.767961 | − | 0.640496i | \(-0.221271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.59299e9i | 0.0793929i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.57475e11 | −1.83369 | −0.916845 | − | 0.399242i | \(-0.869273\pi\) | ||||
−0.916845 | + | 0.399242i | \(0.869273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.79292e10 | 0.314555 | 0.157278 | − | 0.987554i | \(-0.449728\pi\) | ||||
0.157278 | + | 0.987554i | \(0.449728\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 1.99492e10i | − 0.217367i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.68307e11i | − 1.71768i | −0.512240 | − | 0.858842i | \(-0.671184\pi\) | ||||
0.512240 | − | 0.858842i | \(-0.328816\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.00705e10 | −0.692335 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.51877e10 | −0.815076 | −0.407538 | − | 0.913188i | \(-0.633613\pi\) | ||||
−0.407538 | + | 0.913188i | \(0.633613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.02954e11i | 1.88087i | 0.339970 | + | 0.940436i | \(0.389583\pi\) | ||||
−0.339970 | + | 0.940436i | \(0.610417\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.42022e11i | 2.10565i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.55318e10 | 0.636927 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.16561e9 | 0.0422283 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.31572e11i | − 1.04294i | −0.853270 | − | 0.521470i | \(-0.825384\pi\) | ||||
0.853270 | − | 0.521470i | \(-0.174616\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.66384e10i | − 0.198657i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.10844e11 | 1.52560 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.92648e11 | −1.35274 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.33450e10i | 0.0909554i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.88785e11i | − 1.21296i | −0.795099 | − | 0.606479i | \(-0.792581\pi\) | ||||
0.795099 | − | 0.606479i | \(-0.207419\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.03855e9 | 0.00648057 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.10454e10 | −0.430640 | −0.215320 | − | 0.976544i | \(-0.569079\pi\) | ||||
−0.215320 | + | 0.976544i | \(0.569079\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 3.35032e11i | − 1.97305i | −0.163623 | − | 0.986523i | \(-0.552318\pi\) | ||||
0.163623 | − | 0.986523i | \(-0.447682\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.98163e11i | − 1.10219i | −0.834443 | − | 0.551094i | \(-0.814211\pi\) | ||||
0.834443 | − | 0.551094i | \(-0.185789\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.38252e11 | 1.28818 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.39717e9 | 0.0336291 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.66507e11i | − 0.851179i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 6.83110e9i | − 0.0330389i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.58931e11 | −1.68900 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.60576e11 | −0.735284 | −0.367642 | − | 0.929967i | \(-0.619835\pi\) | ||||
−0.367642 | + | 0.929967i | \(0.619835\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 5.66202e10i | − 0.252332i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.77234e10i | 0.370494i | 0.982692 | + | 0.185247i | \(0.0593085\pi\) | ||||
−0.982692 | + | 0.185247i | \(0.940692\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.22130e10 | 0.132475 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.99539e11 | −0.799157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.14379e11i | − 0.446194i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.89987e11i | 0.703464i | 0.936101 | + | 0.351732i | \(0.114407\pi\) | ||||
−0.936101 | + | 0.351732i | \(0.885593\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.85678e11 | −1.75240 | −0.876201 | − | 0.481946i | \(-0.839930\pi\) | ||||
−0.876201 | + | 0.481946i | \(0.839930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.13031e10 | −0.285907 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 5.15816e10i | − 0.176811i | −0.996085 | − | 0.0884054i | \(-0.971823\pi\) | ||||
0.996085 | − | 0.0884054i | \(-0.0281771\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.43816e10i | 0.0794431i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.79131e11 | 0.569176 | 0.284588 | − | 0.958650i | \(-0.408143\pi\) | ||||
0.284588 | + | 0.958650i | \(0.408143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.21231e11 | 0.995485 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 8.99154e9i | − 0.0271803i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.76314e10i | − 0.0795071i | −0.999210 | − | 0.0397536i | \(-0.987343\pi\) | ||||
0.999210 | − | 0.0397536i | \(-0.0126573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.91307e11 | 1.37954 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.45525e11 | −0.672842 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.35196e11i | − 0.629129i | −0.949236 | − | 0.314565i | \(-0.898142\pi\) | ||||
0.949236 | − | 0.314565i | \(-0.101858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7.27168e11i | − 1.85395i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.11965e11 | 0.776658 | 0.388329 | − | 0.921521i | \(-0.373052\pi\) | ||||
0.388329 | + | 0.921521i | \(0.373052\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.06958e10 | 0.0989434 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.78535e10i | 0.113637i | 0.998385 | + | 0.0568185i | \(0.0180956\pi\) | ||||
−0.998385 | + | 0.0568185i | \(0.981904\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.91077e11i | 0.886264i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.19528e11 | −0.264665 | −0.132332 | − | 0.991205i | \(-0.542247\pi\) | ||||
−0.132332 | + | 0.991205i | \(0.542247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.57691e11 | −0.557575 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.62659e10i | 0.0978351i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.08892e10i | 0.143226i | 0.997432 | + | 0.0716132i | \(0.0228147\pi\) | ||||
−0.997432 | + | 0.0716132i | \(0.977185\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.42891e10 | −0.186245 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.62486e11 | 1.08633 | 0.543165 | − | 0.839626i | \(-0.317226\pi\) | ||||
0.543165 | + | 0.839626i | \(0.317226\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.09012e11i | 1.15015i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.61236e11i | − 0.291265i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.23341e11 | −0.394651 | −0.197325 | − | 0.980338i | \(-0.563226\pi\) | ||||
−0.197325 | + | 0.980338i | \(0.563226\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.62765e10 | −0.0454234 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.58884e11i | 1.62178i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.35911e9i | 0.00544016i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.54170e11 | −0.561370 | −0.280685 | − | 0.959800i | \(-0.590562\pi\) | ||||
−0.280685 | + | 0.959800i | \(0.590562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.29294e11 | 0.821159 | 0.410580 | − | 0.911825i | \(-0.365326\pi\) | ||||
0.410580 | + | 0.911825i | \(0.365326\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.28634e11i | 1.10657i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.92869e12i | 2.80761i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.15323e11 | −0.164383 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.26760e12 | 1.76944 | 0.884718 | − | 0.466127i | \(-0.154351\pi\) | ||||
0.884718 | + | 0.466127i | \(0.154351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 3.28861e11i | − 0.449591i | −0.974406 | − | 0.224795i | \(-0.927829\pi\) | ||||
0.974406 | − | 0.224795i | \(-0.0721713\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 9.96545e11i | − 1.30717i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.69396e11 | −0.346178 | −0.173089 | − | 0.984906i | \(-0.555375\pi\) | ||||
−0.173089 | + | 0.984906i | \(0.555375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.02045e12 | −1.28475 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4.20444e11i | − 0.518671i | −0.965787 | − | 0.259335i | \(-0.916497\pi\) | ||||
0.965787 | − | 0.259335i | \(-0.0835035\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 7.52915e10i | − 0.0891995i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.19773e11 | −0.139075 | −0.0695376 | − | 0.997579i | \(-0.522152\pi\) | ||||
−0.0695376 | + | 0.997579i | \(0.522152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.39909e12 | 1.59239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00984e10i | 0.0447388i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.34943e12i | 1.44719i | 0.690223 | + | 0.723597i | \(0.257512\pi\) | ||||
−0.690223 | + | 0.723597i | \(0.742488\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.93677e10 | 0.104493 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.09834e11 | 0.216383 | 0.108191 | − | 0.994130i | \(-0.465494\pi\) | ||||
0.108191 | + | 0.994130i | \(0.465494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.60348e11i | 0.667819i | 0.942605 | + | 0.333909i | \(0.108368\pi\) | ||||
−0.942605 | + | 0.333909i | \(0.891632\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.28966e11i | − 0.806512i | −0.915087 | − | 0.403256i | \(-0.867878\pi\) | ||||
0.915087 | − | 0.403256i | \(-0.132122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.79381e11 | 0.743827 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.31102e10 | −0.0216376 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.11366e12i | 1.02301i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.98417e11i | 0.440819i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.48710e11 | 0.563042 | 0.281521 | − | 0.959555i | \(-0.409161\pi\) | ||||
0.281521 | + | 0.959555i | \(0.409161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.92110e11 | −0.419188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.45924e11i | 0.122002i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.75979e12i | − 1.41768i | −0.705367 | − | 0.708842i | \(-0.749218\pi\) | ||||
0.705367 | − | 0.708842i | \(-0.250782\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.05898e9 | −0.00400104 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.02135e11 | 0.234603 | 0.117302 | − | 0.993096i | \(-0.462576\pi\) | ||||
0.117302 | + | 0.993096i | \(0.462576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.88736e11i | 0.677582i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 4.15235e11i | − 0.305274i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.11758e11 | −0.369498 | −0.184749 | − | 0.982786i | \(-0.559147\pi\) | ||||
−0.184749 | + | 0.982786i | \(0.559147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.90768e11 | −0.135281 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.69213e12i | − 1.17863i | −0.807904 | − | 0.589314i | \(-0.799398\pi\) | ||||
0.807904 | − | 0.589314i | \(-0.200602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.22483e11i | 0.149542i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.10216e11 | −0.468986 | −0.234493 | − | 0.972118i | \(-0.575343\pi\) | ||||
−0.234493 | + | 0.972118i | \(0.575343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.27956e12 | −2.12776 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.84276e11i | 0.244972i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.07492e12i | 1.27730i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.41719e11 | −0.0857386 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.88794e11 | −0.528483 | −0.264242 | − | 0.964456i | \(-0.585122\pi\) | ||||
−0.264242 | + | 0.964456i | \(0.585122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.01046e12i | − 0.590555i | −0.955412 | − | 0.295277i | \(-0.904588\pi\) | ||||
0.955412 | − | 0.295277i | \(-0.0954121\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 7.44327e11i | − 0.420355i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.58873e11 | 0.143726 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.94654e12 | 1.06252 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.27015e12i | − 2.29177i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2.99851e11i | − 0.155604i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.90593e12 | −1.48298 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.39951e12 | 1.70619 | 0.853097 | − | 0.521753i | \(-0.174722\pi\) | ||||
0.853097 | + | 0.521753i | \(0.174722\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 3.92015e10i | − 0.0193510i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.10308e12i | − 1.48201i | −0.671501 | − | 0.741004i | \(-0.734350\pi\) | ||||
0.671501 | − | 0.741004i | \(-0.265650\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.91525e12 | 1.83943 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.43693e12 | −1.58851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 2.70479e12i | − 1.22990i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4.92558e11i | − 0.216825i | −0.994106 | − | 0.108412i | \(-0.965423\pi\) | ||||
0.994106 | − | 0.108412i | \(-0.0345767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.39901e12 | 1.47231 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.40946e11 | 0.0600786 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.67786e12i | − 0.703832i | −0.936032 | − | 0.351916i | \(-0.885530\pi\) | ||||
0.936032 | − | 0.351916i | \(-0.114470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.64347e12i | 1.48044i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.40646e12 | −1.36238 | −0.681190 | − | 0.732107i | \(-0.738537\pi\) | ||||
−0.681190 | + | 0.732107i | \(0.738537\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.05234e12 | −1.59530 | −0.797651 | − | 0.603119i | \(-0.793924\pi\) | ||||
−0.797651 | + | 0.603119i | \(0.793924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4.17068e11i | − 0.161626i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 4.55977e11i | − 0.171258i | −0.996327 | − | 0.0856291i | \(-0.972710\pi\) | ||||
0.996327 | − | 0.0856291i | \(-0.0272900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.06347e11 | −0.113282 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.78333e12 | −2.10565 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.41933e12i | 0.508834i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.83858e12i | − 0.986801i | −0.869802 | − | 0.493401i | \(-0.835754\pi\) | ||||
0.869802 | − | 0.493401i | \(-0.164246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.87847e12 | 0.985470 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.17728e11 | 0.0396952 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.08687e12i | 1.35720i | 0.734507 | + | 0.678601i | \(0.237414\pi\) | ||||
−0.734507 | + | 0.678601i | \(0.762586\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.08240e10i | 0.0131532i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.47524e12 | −1.42035 | −0.710175 | − | 0.704025i | \(-0.751384\pi\) | ||||
−0.710175 | + | 0.704025i | \(0.751384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.83907e11 | −0.151296 | −0.0756478 | − | 0.997135i | \(-0.524102\pi\) | ||||
−0.0756478 | + | 0.997135i | \(0.524102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.58215e12i | − 0.487326i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4.96609e12i | − 1.48479i | −0.669962 | − | 0.742395i | \(-0.733690\pi\) | ||||
0.669962 | − | 0.742395i | \(-0.266310\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.03271e11 | 0.148260 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.33285e12 | 1.83829 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.43460e12i | 0.696396i | 0.937421 | + | 0.348198i | \(0.113206\pi\) | ||||
−0.937421 | + | 0.348198i | \(0.886794\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.82614e12i | 0.507284i | 0.967298 | + | 0.253642i | \(0.0816285\pi\) | ||||
−0.967298 | + | 0.253642i | \(0.918372\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.13058e12 | 0.309523 | 0.154761 | − | 0.987952i | \(-0.450539\pi\) | ||||
0.154761 | + | 0.987952i | \(0.450539\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.94716e11 | 0.160471 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5.19539e12i | − 1.38173i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.45068e11i | 0.140847i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.01450e11 | 0.153205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.96900e12 | 0.494440 | 0.247220 | − | 0.968959i | \(-0.420483\pi\) | ||||
0.247220 | + | 0.968959i | \(0.420483\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.15022e11i | 0.0532312i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.86918e12i | 2.13430i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.42930e11 | −0.200003 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.69141e12 | 0.629679 | 0.314840 | − | 0.949145i | \(-0.398049\pi\) | ||||
0.314840 | + | 0.949145i | \(0.398049\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.27990e12i | 0.525977i | 0.964799 | + | 0.262989i | \(0.0847081\pi\) | ||||
−0.964799 | + | 0.262989i | \(0.915292\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 4.86871e12i | − 1.09231i | −0.837685 | − | 0.546153i | \(-0.816092\pi\) | ||||
0.837685 | − | 0.546153i | \(-0.183908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.54314e12 | 1.22646 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.21495e11 | −0.0919768 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.30610e12i | − 0.496329i | −0.968718 | − | 0.248164i | \(-0.920173\pi\) | ||||
0.968718 | − | 0.248164i | \(-0.0798273\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.65754e12i | 1.39402i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.40069e12 | −1.52858 | −0.764289 | − | 0.644873i | \(-0.776910\pi\) | ||||
−0.764289 | + | 0.644873i | \(0.776910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.00760e12 | −0.409045 | −0.204522 | − | 0.978862i | \(-0.565564\pi\) | ||||
−0.204522 | + | 0.978862i | \(0.565564\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 4.30181e11i | − 0.0864650i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.31909e12i | 1.04057i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.11170e11 | 0.117963 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.11494e13 | 2.12324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.01154e13i | 1.90071i | 0.311167 | + | 0.950355i | \(0.399280\pi\) | ||||
−0.311167 | + | 0.950355i | \(0.600720\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 8.91166e12i | − 1.63046i | −0.579139 | − | 0.815229i | \(-0.696611\pi\) | ||||
0.579139 | − | 0.815229i | \(-0.303389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.07059e12 | −0.734926 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.06007e11 | −0.0188874 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.26863e12i | 1.62976i | 0.579633 | + | 0.814878i | \(0.303196\pi\) | ||||
−0.579633 | + | 0.814878i | \(0.696804\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 3.61466e11i | − 0.0619101i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.33195e12 | 0.732313 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.03490e11 | 0.0172682 | 0.00863409 | − | 0.999963i | \(-0.497252\pi\) | ||||
0.00863409 | + | 0.999963i | \(0.497252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.04559e13i | 1.72211i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.21893e12i | 0.837594i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.06818e11 | 0.143672 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.77133e12 | 0.746291 | 0.373145 | − | 0.927773i | \(-0.378279\pi\) | ||||
0.373145 | + | 0.927773i | \(0.378279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.32594e12i | 0.359169i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.05161e13i | − 1.58295i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.58922e12 | −1.12795 | −0.563974 | − | 0.825793i | \(-0.690728\pi\) | ||||
−0.563974 | + | 0.825793i | \(0.690728\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.49075e12 | −0.805784 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.45480e12i | − 0.645543i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.02188e11i | − 0.0285705i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.50766e12 | −0.210389 | −0.105194 | − | 0.994452i | \(-0.533546\pi\) | ||||
−0.105194 | + | 0.994452i | \(0.533546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.18394e11 | −0.112786 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 4.40909e11i | − 0.0600105i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.12985e13i | 1.50009i | 0.661387 | + | 0.750045i | \(0.269968\pi\) | ||||
−0.661387 | + | 0.750045i | \(0.730032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.28117e12 | 0.954833 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.15423e12 | −0.538100 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.07062e12i | − 0.136984i | −0.997652 | − | 0.0684919i | \(-0.978181\pi\) | ||||
0.997652 | − | 0.0684919i | \(-0.0218187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 4.50546e12i | − 0.562517i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.44855e13 | 1.78662 | 0.893311 | − | 0.449439i | \(-0.148376\pi\) | ||||
0.893311 | + | 0.449439i | \(0.148376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.66360e12 | 0.202707 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.24339e13i | − 1.49678i | −0.663261 | − | 0.748388i | \(-0.730828\pi\) | ||||
0.663261 | − | 0.748388i | \(-0.269172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.17402e13i | 1.37954i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.04108e12 | −0.585269 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.79097e12 | 1.00846 | 0.504228 | − | 0.863570i | \(-0.331777\pi\) | ||||
0.504228 | + | 0.863570i | \(0.331777\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 2.84468e11i | − 0.0322446i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.93877e12i | 0.878662i | 0.898325 | + | 0.439331i | \(0.144784\pi\) | ||||
−0.898325 | + | 0.439331i | \(0.855216\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.43562e11 | 0.0922633 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.12763e13 | 1.21881 | 0.609405 | − | 0.792859i | \(-0.291408\pi\) | ||||
0.609405 | + | 0.792859i | \(0.291408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.38303e12i | 0.574998i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.69182e13i | − 1.76512i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.80743e12 | −0.392612 | −0.196306 | − | 0.980543i | \(-0.562895\pi\) | ||||
−0.196306 | + | 0.980543i | \(0.562895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.58810e11 | −0.0569534 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.89254e12i | 0.392126i | 0.980591 | + | 0.196063i | \(0.0628156\pi\) | ||||
−0.980591 | + | 0.196063i | \(0.937184\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3.40588e11i | − 0.0335223i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.01827e13 | −1.96364 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.40040e12 | −0.230862 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.05109e12i | − 0.195010i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.70256e12i | − 0.251124i | −0.992086 | − | 0.125562i | \(-0.959927\pi\) | ||||
0.992086 | − | 0.125562i | \(-0.0400734\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.21368e12 | −0.111495 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.53844e13 | −2.30554 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 3.40291e13i | − 3.05577i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.58748e12i | − 0.139363i | −0.997569 | − | 0.0696813i | \(-0.977802\pi\) | ||||
0.997569 | − | 0.0696813i | \(-0.0221982\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.73994e12 | −0.671857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.05467e13 | −0.905252 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.89586e13i | 1.60911i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.92294e12i | 0.159601i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.55705e12 | 0.374038 | 0.187019 | − | 0.982356i | \(-0.440117\pi\) | ||||
0.187019 | + | 0.982356i | \(0.440117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.77014e12 | −0.224858 | −0.112429 | − | 0.993660i | \(-0.535863\pi\) | ||||
−0.112429 | + | 0.993660i | \(0.535863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 3.41047e11i | − 0.0273783i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.60653e13i | − 1.26151i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.19123e13 | 2.47846 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.21734e13 | −0.935124 | −0.467562 | − | 0.883960i | \(-0.654868\pi\) | ||||
−0.467562 | + | 0.883960i | \(0.654868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.75355e13i | − 1.33235i | −0.745796 | − | 0.666175i | \(-0.767931\pi\) | ||||
0.745796 | − | 0.666175i | \(-0.232069\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 9.15138e12i | − 0.680318i | −0.940368 | − | 0.340159i | \(-0.889519\pi\) | ||||
0.940368 | − | 0.340159i | \(-0.110481\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.76678e12 | 0.424071 | 0.212035 | − | 0.977262i | \(-0.431991\pi\) | ||||
0.212035 | + | 0.977262i | \(0.431991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.05522e12 | −0.149504 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.08398e13i | − 0.780044i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.71781e12i | 0.120979i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.69274e11 | −0.0605658 | −0.0302829 | − | 0.999541i | \(-0.509641\pi\) | ||||
−0.0302829 | + | 0.999541i | \(0.509641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.83759e12 | 0.264531 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.04024e12i | 0.0709427i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.08549e12i | 0.473037i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.47830e12 | 0.163708 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.59968e12 | 0.235278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.19943e12i | 0.594963i | 0.954728 | + | 0.297482i | \(0.0961467\pi\) | ||||
−0.954728 | + | 0.297482i | \(0.903853\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 6.57679e12i | − 0.416486i | −0.978077 | − | 0.208243i | \(-0.933225\pi\) | ||||
0.978077 | − | 0.208243i | \(-0.0667745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.80030e13 | 1.12817 | 0.564085 | − | 0.825717i | \(-0.309229\pi\) | ||||
0.564085 | + | 0.825717i | \(0.309229\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.95536e12 | 0.183272 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 3.08737e13i | − 1.89470i | −0.320200 | − | 0.947350i | \(-0.603750\pi\) | ||||
0.320200 | − | 0.947350i | \(-0.396250\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 9.22328e11i | − 0.0554370i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.56359e13 | −0.930110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.37511e13 | −0.809573 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.26334e12i | 0.481495i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.77535e12i | 0.158424i | 0.996858 | + | 0.0792118i | \(0.0252403\pi\) | ||||
−0.996858 | + | 0.0792118i | \(0.974760\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.60664e12 | −0.0907755 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.64369e13 | −0.919241 | −0.459620 | − | 0.888116i | \(-0.652014\pi\) | ||||
−0.459620 | + | 0.888116i | \(0.652014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.38106e12i | 0.297882i | 0.988846 | + | 0.148941i | \(0.0475865\pi\) | ||||
−0.988846 | + | 0.148941i | \(0.952414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.61191e13i | 0.874347i | 0.899377 | + | 0.437174i | \(0.144020\pi\) | ||||
−0.899377 | + | 0.437174i | \(0.855980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.20690e13 | −1.72198 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.10622e13 | 1.11958 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.99320e13i | − 1.57509i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 2.57464e12i | − 0.132785i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.53639e13 | −0.784483 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.29446e12 | −0.267645 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.35245e12i | 0.117740i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.50156e13i | 0.736734i | 0.929681 | + | 0.368367i | \(0.120083\pi\) | ||||
−0.929681 | + | 0.368367i | \(0.879917\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.13478e13 | −1.03709 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.12904e12 | −0.102412 | −0.0512061 | − | 0.998688i | \(-0.516307\pi\) | ||||
−0.0512061 | + | 0.998688i | \(0.516307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.34324e13i | 1.59239i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 3.64583e13i | − 1.70269i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.82600e13 | 1.30693 | 0.653464 | − | 0.756957i | \(-0.273315\pi\) | ||||
0.653464 | + | 0.756957i | \(0.273315\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.30528e12 | −0.105574 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.32625e12i | 0.332257i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.66135e12i | 0.0738927i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.74749e11 | 0.00769739 | 0.00384869 | − | 0.999993i | \(-0.498775\pi\) | ||||
0.00384869 | + | 0.999993i | \(0.498775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.19199e13 | 1.82872 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.67543e11i | 0.0374821i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.04012e12i | 0.255987i | 0.991775 | + | 0.127993i | \(0.0408536\pi\) | ||||
−0.991775 | + | 0.127993i | \(0.959146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.09112e12 | −0.171730 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.13848e13 | 0.889104 | 0.444552 | − | 0.895753i | \(-0.353363\pi\) | ||||
0.444552 | + | 0.895753i | \(0.353363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.12353e13i | 1.28630i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.58008e13i | 1.85054i | 0.379312 | + | 0.925269i | \(0.376161\pi\) | ||||
−0.379312 | + | 0.925269i | \(0.623839\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.78634e13 | 2.31583 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.41979e12 | −0.0959323 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.57835e13i | 0.619847i | 0.950761 | + | 0.309924i | \(0.100304\pi\) | ||||
−0.950761 | + | 0.309924i | \(0.899696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.90932e12i | − 0.112121i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.07063e13 | 0.790533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.35722e13 | −0.513326 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.02334e13i | 0.383445i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.61550e13i | 0.594140i | 0.954856 | + | 0.297070i | \(0.0960095\pi\) | ||||
−0.954856 | + | 0.297070i | \(0.903991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.03324e12 | −0.0740851 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.05363e12 | −0.182439 | −0.0912194 | − | 0.995831i | \(-0.529076\pi\) | ||||
−0.0912194 | + | 0.995831i | \(0.529076\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.64703e12i | − 0.0946786i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 3.22726e13i | − 1.13321i | −0.823991 | − | 0.566603i | \(-0.808257\pi\) | ||||
0.823991 | − | 0.566603i | \(-0.191743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00336e13 | −1.04493 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.09276e13 | 0.376716 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.11820e13i | 0.723561i | 0.932263 | + | 0.361781i | \(0.117831\pi\) | ||||
−0.932263 | + | 0.361781i | \(0.882169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.38295e12i | 0.147007i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.48631e13 | −0.826365 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.18946e13 | −0.721116 | −0.360558 | − | 0.932737i | \(-0.617414\pi\) | ||||
−0.360558 | + | 0.932737i | \(0.617414\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.96081e12i | 0.0639977i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.15332e13i | − 1.33127i | −0.746277 | − | 0.665636i | \(-0.768160\pi\) | ||||
0.746277 | − | 0.665636i | \(-0.231840\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.38807e12 | −0.0440927 |
(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 | 100.10.c.c.49.2 | 4 | ||
4.3 | odd | 2 | 400.10.c.l.49.3 | 4 | |||
5.2 | odd | 4 | 100.10.a.c.1.1 | 2 | |||
5.3 | odd | 4 | 20.10.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 100.10.c.c.49.3 | 4 | ||
15.8 | even | 4 | 180.10.a.e.1.2 | 2 | |||
20.3 | even | 4 | 80.10.a.j.1.1 | 2 | |||
20.7 | even | 4 | 400.10.a.l.1.2 | 2 | |||
20.19 | odd | 2 | 400.10.c.l.49.2 | 4 | |||
40.3 | even | 4 | 320.10.a.l.1.2 | 2 | |||
40.13 | odd | 4 | 320.10.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.10.a.b.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
80.10.a.j.1.1 | 2 | 20.3 | even | 4 | |||
100.10.a.c.1.1 | 2 | 5.2 | odd | 4 | |||
100.10.c.c.49.2 | 4 | 1.1 | even | 1 | trivial | ||
100.10.c.c.49.3 | 4 | 5.4 | even | 2 | inner | ||
180.10.a.e.1.2 | 2 | 15.8 | even | 4 | |||
320.10.a.l.1.2 | 2 | 40.3 | even | 4 | |||
320.10.a.t.1.1 | 2 | 40.13 | odd | 4 | |||
400.10.a.l.1.2 | 2 | 20.7 | even | 4 | |||
400.10.c.l.49.2 | 4 | 20.19 | odd | 2 | |||
400.10.c.l.49.3 | 4 | 4.3 | odd | 2 |