Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,10,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.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: | \(41.2028668931\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.7117.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 19x - 22 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{3}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.33466\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.1 |
$q$-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 | ||||||||
\(3\) | −262.608 | −1.87181 | −0.935907 | − | 0.352248i | \(-0.885417\pi\) | ||||
−0.935907 | + | 0.352248i | \(0.885417\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 625.000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1790.86 | 0.281917 | 0.140959 | − | 0.990016i | \(-0.454982\pi\) | ||||
0.140959 | + | 0.990016i | \(0.454982\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 49280.0 | 2.50368 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −74296.8 | −1.53004 | −0.765020 | − | 0.644006i | \(-0.777271\pi\) | ||||
−0.765020 | + | 0.644006i | \(0.777271\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −97294.3 | −0.944805 | −0.472402 | − | 0.881383i | \(-0.656613\pi\) | ||||
−0.472402 | + | 0.881383i | \(0.656613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −164130. | −0.837100 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −252081. | −0.732014 | −0.366007 | − | 0.930612i | \(-0.619275\pi\) | ||||
−0.366007 | + | 0.930612i | \(0.619275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −726765. | −1.27939 | −0.639695 | − | 0.768629i | \(-0.720939\pi\) | ||||
−0.639695 | + | 0.768629i | \(0.720939\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −470295. | −0.527696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.75568e6 | 1.30819 | 0.654096 | − | 0.756412i | \(-0.273049\pi\) | ||||
0.654096 | + | 0.756412i | \(0.273049\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.77242e6 | −2.81462 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.18968e6 | −0.312349 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.58664e6 | −1.28096 | −0.640481 | − | 0.767974i | \(-0.721265\pi\) | ||||
−0.640481 | + | 0.767974i | \(0.721265\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.95109e7 | 2.86395 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.11929e6 | 0.126077 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.30493e7 | 1.14467 | 0.572333 | − | 0.820021i | \(-0.306038\pi\) | ||||
0.572333 | + | 0.820021i | \(0.306038\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.55503e7 | 1.76850 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.70456e6 | 0.425815 | 0.212907 | − | 0.977072i | \(-0.431707\pi\) | ||||
0.212907 | + | 0.977072i | \(0.431707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.14232e7 | 1.84772 | 0.923858 | − | 0.382735i | \(-0.125018\pi\) | ||||
0.923858 | + | 0.382735i | \(0.125018\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.08000e7 | 1.11968 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.58216e7 | −0.771868 | −0.385934 | − | 0.922526i | \(-0.626121\pi\) | ||||
−0.385934 | + | 0.922526i | \(0.626121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.71464e7 | −0.920523 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.61984e7 | 1.37019 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.64763e7 | −1.33133 | −0.665664 | − | 0.746251i | \(-0.731852\pi\) | ||||
−0.665664 | + | 0.746251i | \(0.731852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.64355e7 | −0.684255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.90855e8 | 2.39478 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.38341e7 | 0.256073 | 0.128037 | − | 0.991769i | \(-0.459133\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459133\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.74311e7 | 0.161191 | 0.0805956 | − | 0.996747i | \(-0.474318\pi\) | ||||
0.0805956 | + | 0.996747i | \(0.474318\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.82538e7 | 0.705831 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.08089e7 | −0.422530 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.27463e8 | 0.772763 | 0.386382 | − | 0.922339i | \(-0.373725\pi\) | ||||
0.386382 | + | 0.922339i | \(0.373725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.61057e8 | −2.44869 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.12637e8 | 0.993063 | 0.496531 | − | 0.868019i | \(-0.334607\pi\) | ||||
0.496531 | + | 0.868019i | \(0.334607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.55049e8 | 0.639021 | 0.319510 | − | 0.947583i | \(-0.396482\pi\) | ||||
0.319510 | + | 0.947583i | \(0.396482\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.02581e8 | −0.374363 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.33055e8 | −0.431344 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.83656e8 | 0.530497 | 0.265248 | − | 0.964180i | \(-0.414546\pi\) | ||||
0.265248 | + | 0.964180i | \(0.414546\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.07112e9 | 2.76475 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.98914e8 | 0.691344 | 0.345672 | − | 0.938355i | \(-0.387651\pi\) | ||||
0.345672 | + | 0.938355i | \(0.387651\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.57550e8 | −0.327366 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.12420e8 | 0.584658 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.86300e8 | 1.49736 | 0.748679 | − | 0.662933i | \(-0.230689\pi\) | ||||
0.748679 | + | 0.662933i | \(0.230689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.74241e8 | −0.266357 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.72971e9 | 2.39772 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.54228e8 | −0.572161 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.88680e8 | −0.789850 | −0.394925 | − | 0.918713i | \(-0.629230\pi\) | ||||
−0.394925 | + | 0.918713i | \(0.629230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.66135e9 | −3.83074 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.08541e9 | −1.03788 | −0.518939 | − | 0.854811i | \(-0.673673\pi\) | ||||
−0.518939 | + | 0.854811i | \(0.673673\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.61017e9 | 1.40963 | 0.704814 | − | 0.709392i | \(-0.251030\pi\) | ||||
0.704814 | + | 0.709392i | \(0.251030\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.93935e8 | −0.235993 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.51299e9 | 1.85338 | 0.926690 | − | 0.375826i | \(-0.122641\pi\) | ||||
0.926690 | + | 0.375826i | \(0.122641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.30997e9 | −1.56743 | −0.783713 | − | 0.621123i | \(-0.786677\pi\) | ||||
−0.783713 | + | 0.621123i | \(0.786677\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.42685e9 | −2.14260 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.20437e8 | 0.531057 | 0.265528 | − | 0.964103i | \(-0.414454\pi\) | ||||
0.265528 | + | 0.964103i | \(0.414454\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.09730e9 | 0.585041 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.79466e9 | −2.36549 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.51442e8 | −0.206367 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.16206e9 | 1.34102 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.02328e9 | −0.797045 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.44141e8 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.36637e8 | −0.114827 | −0.0574137 | − | 0.998350i | \(-0.518285\pi\) | ||||
−0.0574137 | + | 0.998350i | \(0.518285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.08781e10 | −3.45858 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.15471e8 | −0.182594 | −0.0912971 | − | 0.995824i | \(-0.529101\pi\) | ||||
−0.0912971 | + | 0.995824i | \(0.529101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.30154e9 | −0.360682 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.85776e9 | −1.25873 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.19267e9 | 0.531777 | 0.265889 | − | 0.964004i | \(-0.414335\pi\) | ||||
0.265889 | + | 0.964004i | \(0.414335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.29088e9 | −0.747730 | −0.373865 | − | 0.927483i | \(-0.621968\pi\) | ||||
−0.373865 | + | 0.927483i | \(0.621968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.78097e9 | 1.44479 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.22865e9 | 1.44559 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.43551e8 | −0.139687 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.75495e9 | 1.72305 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.23469e9 | 0.703856 | 0.351928 | − | 0.936027i | \(-0.385526\pi\) | ||||
0.351928 | + | 0.936027i | \(0.385526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.47035e9 | 1.48241 | 0.741207 | − | 0.671276i | \(-0.234254\pi\) | ||||
0.741207 | + | 0.671276i | \(0.234254\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.24225e10 | −1.83273 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.11665e9 | −0.572864 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.23215e9 | 0.818633 | 0.409317 | − | 0.912392i | \(-0.365767\pi\) | ||||
0.409317 | + | 0.912392i | \(0.365767\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.00833e10 | 2.49200 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.14419e9 | 0.368801 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.38381e9 | −0.930244 | −0.465122 | − | 0.885247i | \(-0.653990\pi\) | ||||
−0.465122 | + | 0.885247i | \(0.653990\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.21943e10 | 1.28080 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.59311e10 | −1.58497 | −0.792486 | − | 0.609890i | \(-0.791214\pi\) | ||||
−0.792486 | + | 0.609890i | \(0.791214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.13833e9 | −0.107344 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.58150e10 | −3.20319 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.13803e9 | 0.605858 | 0.302929 | − | 0.953013i | \(-0.402035\pi\) | ||||
0.302929 | + | 0.953013i | \(0.402035\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.99556e8 | 0.0563834 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.25902e9 | −0.479321 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.60283e9 | 0.407915 | 0.203957 | − | 0.978980i | \(-0.434620\pi\) | ||||
0.203957 | + | 0.978980i | \(0.434620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.93283e10 | 1.33857 | 0.669284 | − | 0.743006i | \(-0.266601\pi\) | ||||
0.669284 | + | 0.743006i | \(0.266601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.57756e9 | −0.301720 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.15581e9 | 0.511911 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.87288e10 | 1.12001 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.39193e10 | −0.793488 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.27550e10 | −1.23716 | −0.618581 | − | 0.785721i | \(-0.712292\pi\) | ||||
−0.618581 | + | 0.785721i | \(0.712292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00595e10 | 0.521877 | 0.260939 | − | 0.965355i | \(-0.415968\pi\) | ||||
0.260939 | + | 0.965355i | \(0.415968\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.59689e10 | 0.790896 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.37043e9 | 0.206741 | 0.103370 | − | 0.994643i | \(-0.467037\pi\) | ||||
0.103370 | + | 0.994643i | \(0.467037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.08708e10 | 0.491387 | 0.245694 | − | 0.969348i | \(-0.420984\pi\) | ||||
0.245694 | + | 0.969348i | \(0.420984\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.34727e10 | −1.44647 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.13056e9 | −0.0880564 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.81535e9 | 0.190430 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.65202e10 | 3.27530 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.39963e10 | 1.95752 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.28210e10 | 0.445298 | 0.222649 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222649 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.58402e10 | −1.85883 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.58895e10 | 0.826324 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17958e10 | −0.361125 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.07170e10 | −1.19613 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.45260e10 | 0.691610 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.10020e8 | 0.0192264 | 0.00961322 | − | 0.999954i | \(-0.496940\pi\) | ||||
0.00961322 | + | 0.999954i | \(0.496940\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.92500e10 | 0.500737 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.75775e9 | 0.143925 | 0.0719626 | − | 0.997407i | \(-0.477074\pi\) | ||||
0.0719626 | + | 0.997407i | \(0.477074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.10494e10 | 0.986386 | 0.493193 | − | 0.869920i | \(-0.335830\pi\) | ||||
0.493193 | + | 0.869920i | \(0.335830\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.49414e10 | 0.807396 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.94945e10 | 0.433322 | 0.216661 | − | 0.976247i | \(-0.430483\pi\) | ||||
0.216661 | + | 0.976247i | \(0.430483\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.61385e10 | −0.345190 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.82295e10 | −0.992991 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.20617e10 | 0.437370 | 0.218685 | − | 0.975795i | \(-0.429823\pi\) | ||||
0.218685 | + | 0.975795i | \(0.429823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.40915e9 | −0.0460031 | −0.0230016 | − | 0.999735i | \(-0.507322\pi\) | ||||
−0.0230016 | + | 0.999735i | \(0.507322\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.28301e11 | −2.36048 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.32165e10 | −0.411670 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.07101e10 | 1.20877 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.84971e10 | −1.29407 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.76707e10 | −1.39419 | −0.697096 | − | 0.716978i | \(-0.745525\pi\) | ||||
−0.697096 | + | 0.716978i | \(0.745525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.30442e11 | −2.00159 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.13740e10 | 0.612769 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.22904e11 | 1.75738 | 0.878692 | − | 0.477390i | \(-0.158417\pi\) | ||||
0.878692 | + | 0.477390i | \(0.158417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.33695e10 | 0.322701 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.86275e10 | −0.782022 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.90580e10 | −1.27670 | −0.638350 | − | 0.769747i | \(-0.720383\pi\) | ||||
−0.638350 | + | 0.769747i | \(0.720383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.77977e10 | −0.595388 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.32749e11 | −2.80277 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.22117e11 | −1.42197 | −0.710984 | − | 0.703208i | \(-0.751750\pi\) | ||||
−0.710984 | + | 0.703208i | \(0.751750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.12907e10 | 0.915544 | 0.457772 | − | 0.889070i | \(-0.348648\pi\) | ||||
0.457772 | + | 0.889070i | \(0.348648\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.57570e10 | 0.498570 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.90222e10 | −0.306008 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.99587e10 | 0.713974 | 0.356987 | − | 0.934109i | \(-0.383804\pi\) | ||||
0.356987 | + | 0.934109i | \(0.383804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.24590e11 | −3.20713 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.35412e10 | −0.895003 | −0.447501 | − | 0.894283i | \(-0.647686\pi\) | ||||
−0.447501 | + | 0.894283i | \(0.647686\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.21829e11 | 1.12904 | 0.564522 | − | 0.825418i | \(-0.309061\pi\) | ||||
0.564522 | + | 0.825418i | \(0.309061\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.19284e11 | 1.07098 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.37978e10 | 0.120044 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.50433e10 | −0.464156 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.80853e11 | 1.47845 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.82742e10 | 0.699728 | 0.349864 | − | 0.936800i | \(-0.386228\pi\) | ||||
0.349864 | + | 0.936800i | \(0.386228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.48963e10 | 0.114519 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.77466e11 | 4.30648 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.70818e11 | −1.23599 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.41832e10 | 0.520903 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.85037e11 | 1.94271 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.08945e10 | 0.0720869 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.96176e10 | −0.318796 | −0.159398 | − | 0.987214i | \(-0.550955\pi\) | ||||
−0.159398 | + | 0.987214i | \(0.550955\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.22844e11 | −2.63856 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.79571e10 | −0.593765 | −0.296882 | − | 0.954914i | \(-0.595947\pi\) | ||||
−0.296882 | + | 0.954914i | \(0.595947\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.67697e10 | −0.393215 | −0.196608 | − | 0.980482i | \(-0.562992\pi\) | ||||
−0.196608 | + | 0.980482i | \(0.562992\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.51586e10 | 0.315657 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.70962e10 | 0.0950898 | 0.0475449 | − | 0.998869i | \(-0.484860\pi\) | ||||
0.0475449 | + | 0.998869i | \(0.484860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.83895e10 | 0.477906 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.59933e11 | −3.46918 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.83203e11 | 0.936531 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.80056e10 | −0.188961 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.06617e11 | 2.93393 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.62430e10 | −0.217603 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.24431e11 | 0.569774 | 0.284887 | − | 0.958561i | \(-0.408044\pi\) | ||||
0.284887 | + | 0.958561i | \(0.408044\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.43069e11 | 2.86588 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.96642e10 | 0.345590 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.99860e10 | 0.0844097 | 0.0422048 | − | 0.999109i | \(-0.486562\pi\) | ||||
0.0422048 | + | 0.999109i | \(0.486562\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.41714e11 | −0.994039 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.89366e11 | 1.95992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.38792e11 | −0.541428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.88161e11 | −1.09509 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.26402e11 | −0.838298 | −0.419149 | − | 0.907918i | \(-0.637671\pi\) | ||||
−0.419149 | + | 0.907918i | \(0.637671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.42665e10 | −0.231884 | −0.115942 | − | 0.993256i | \(-0.536989\pi\) | ||||
−0.115942 | + | 0.993256i | \(0.536989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.56212e11 | 2.65926 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.97107e11 | −1.36120 | −0.680599 | − | 0.732656i | \(-0.738280\pi\) | ||||
−0.680599 | + | 0.732656i | \(0.738280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.32898e11 | 0.444111 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.18552e11 | 0.386281 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.16303e11 | −1.32277 | −0.661385 | − | 0.750046i | \(-0.730031\pi\) | ||||
−0.661385 | + | 0.750046i | \(0.730031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.05500e11 | 0.636840 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.30383e11 | −2.51014 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.69053e10 | 0.285779 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.95175e11 | −0.561599 | −0.280800 | − | 0.959766i | \(-0.590600\pi\) | ||||
−0.280800 | + | 0.959766i | \(0.590600\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.79681e11 | 1.06611 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.36959e11 | −0.375324 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.55125e11 | −1.48491 | −0.742457 | − | 0.669894i | \(-0.766339\pi\) | ||||
−0.742457 | + | 0.669894i | \(0.766339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.41133e10 | −0.167420 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.15749e11 | 0.295108 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.59738e11 | −1.14455 | −0.572274 | − | 0.820062i | \(-0.693939\pi\) | ||||
−0.572274 | + | 0.820062i | \(0.693939\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.84037e10 | 0.214935 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.96945e10 | 0.141755 | 0.0708777 | − | 0.997485i | \(-0.477420\pi\) | ||||
0.0708777 | + | 0.997485i | \(0.477420\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.31596e10 | −0.192903 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.04133e12 | 4.62610 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.73040e11 | 1.49028 | 0.745139 | − | 0.666909i | \(-0.232383\pi\) | ||||
0.745139 | + | 0.666909i | \(0.232383\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.42574e11 | −0.957614 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.61628e11 | 0.341782 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.14785e11 | 0.237245 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.35202e11 | −0.475207 | −0.237604 | − | 0.971362i | \(-0.576362\pi\) | ||||
−0.237604 | + | 0.971362i | \(0.576362\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.41794e11 | 0.675129 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.72146e11 | −0.718726 | −0.359363 | − | 0.933198i | \(-0.617006\pi\) | ||||
−0.359363 | + | 0.933198i | \(0.617006\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.40843e11 | 1.21026 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.69451e11 | 1.23643 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.69520e11 | −1.75139 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.33730e10 | 0.0589712 | 0.0294856 | − | 0.999565i | \(-0.490613\pi\) | ||||
0.0294856 | + | 0.999565i | \(0.490613\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.75812e11 | −0.995388 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.26836e10 | 0.0721914 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.86821e11 | 0.309178 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.64211e11 | 1.39961 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.92302e11 | −0.304804 | −0.152402 | − | 0.988319i | \(-0.548701\pi\) | ||||
−0.152402 | + | 0.988319i | \(0.548701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.70273e11 | 1.50530 | 0.752652 | − | 0.658418i | \(-0.228774\pi\) | ||||
0.752652 | + | 0.658418i | \(0.228774\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.27249e12 | −1.93251 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.84690e10 | −0.146403 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.12168e10 | 0.0454426 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.89830e12 | −2.70587 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.36679e11 | −1.02832 | −0.514162 | − | 0.857693i | \(-0.671897\pi\) | ||||
−0.514162 | + | 0.857693i | \(0.671897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.80729e11 | 1.20406 | 0.602028 | − | 0.798475i | \(-0.294359\pi\) | ||||
0.602028 | + | 0.798475i | \(0.294359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.95262e11 | 0.261467 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.27597e12 | −1.67369 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.17797e12 | 1.51371 | 0.756855 | − | 0.653583i | \(-0.226735\pi\) | ||||
0.756855 | + | 0.653583i | \(0.226735\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.83058e12 | −2.30470 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.87856e11 | −0.231744 | −0.115872 | − | 0.993264i | \(-0.536966\pi\) | ||||
−0.115872 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.53937e11 | 0.669639 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.11206e12 | −1.31749 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.90451e11 | −0.337260 | −0.168630 | − | 0.985679i | \(-0.553934\pi\) | ||||
−0.168630 | + | 0.985679i | \(0.553934\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.72424e11 | −0.651513 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.48699e12 | −2.77480 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.08900e11 | −0.119118 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.43829e12 | 1.54249 | 0.771247 | − | 0.636536i | \(-0.219633\pi\) | ||||
0.771247 | + | 0.636536i | \(0.219633\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.95928e12 | 2.06034 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.38486e11 | 0.245928 | 0.122964 | − | 0.992411i | \(-0.460760\pi\) | ||||
0.122964 | + | 0.992411i | \(0.460760\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.90337e11 | 0.900409 | 0.450205 | − | 0.892925i | \(-0.351351\pi\) | ||||
0.450205 | + | 0.892925i | \(0.351351\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.08107e12 | 1.07229 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.21545e10 | −0.0312836 | −0.0156418 | − | 0.999878i | \(-0.504979\pi\) | ||||
−0.0156418 | + | 0.999878i | \(0.504979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.28268e11 | 0.217855 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.63661e12 | −1.53233 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.07761e12 | −2.82708 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.83893e11 | −0.255878 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.76875e12 | −3.33323 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.03356e12 | 0.897072 | 0.448536 | − | 0.893765i | \(-0.351946\pi\) | ||||
0.448536 | + | 0.893765i | \(0.351946\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.26962e12 | −1.08149 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.25690e11 | −0.690327 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.30425e11 | −0.353232 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.00503e11 | 0.564325 | 0.282163 | − | 0.959367i | \(-0.408948\pi\) | ||||
0.282163 | + | 0.959367i | \(0.408948\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.20166e12 | 1.74124 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.92501e11 | 0.382420 | 0.191210 | − | 0.981549i | \(-0.438759\pi\) | ||||
0.191210 | + | 0.981549i | \(0.438759\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.99895e11 | 0.228643 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.28834e12 | −1.71316 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.80804e11 | 0.279961 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.05504e11 | −0.148377 | −0.0741886 | − | 0.997244i | \(-0.523637\pi\) | ||||
−0.0741886 | + | 0.997244i | \(0.523637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.18364e12 | 2.96677 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.53216e11 | 0.106720 | 0.0533602 | − | 0.998575i | \(-0.483007\pi\) | ||||
0.0533602 | + | 0.998575i | \(0.483007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.78380e11 | −0.464153 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.98934e11 | 0.200928 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.94403e11 | −0.524579 | −0.262289 | − | 0.964989i | \(-0.584477\pi\) | ||||
−0.262289 | + | 0.964989i | \(0.584477\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.77671e11 | 0.180151 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.64873e12 | 3.60099 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.00636e12 | 0.630405 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.91846e12 | 1.18099 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.87451e12 | −1.13405 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.88431e12 | 1.71503 | 0.857515 | − | 0.514460i | \(-0.172007\pi\) | ||||
0.857515 | + | 0.514460i | \(0.172007\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.79973e12 | 1.63628 | 0.818140 | − | 0.575019i | \(-0.195005\pi\) | ||||
0.818140 | + | 0.575019i | \(0.195005\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.83709e11 | −0.105539 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.66036e12 | 0.937682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.28128e12 | 0.711365 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.17454e12 | 0.641127 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.49609e11 | −0.402312 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.57062e12 | 0.828857 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.47135e12 | −0.763540 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.75986e12 | 1.40844 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.30075e12 | 1.15473 | 0.577367 | − | 0.816485i | \(-0.304080\pi\) | ||||
0.577367 | + | 0.816485i | \(0.304080\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.07577e12 | −2.50555 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.44373e12 | −0.700974 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.21728e11 | 0.153655 | 0.0768274 | − | 0.997044i | \(-0.475521\pi\) | ||||
0.0768274 | + | 0.997044i | \(0.475521\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.59007e11 | 0.403572 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.64619e11 | 0.399616 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.28902e11 | 0.149556 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.14178e12 | −0.958201 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.29743e12 | −0.571131 | −0.285566 | − | 0.958359i | \(-0.592181\pi\) | ||||
−0.285566 | + | 0.958359i | \(0.592181\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.03024e12 | −1.74573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.91833e12 | −2.09645 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.19196e12 | 0.919484 | 0.459742 | − | 0.888053i | \(-0.347942\pi\) | ||||
0.459742 | + | 0.888053i | \(0.347942\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.75273e11 | 0.237496 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.91823e12 | 0.779431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.65886e12 | −1.46332 | −0.731662 | − | 0.681667i | \(-0.761255\pi\) | ||||
−0.731662 | + | 0.681667i | \(0.761255\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.14528e11 | −0.123822 | −0.0619108 | − | 0.998082i | \(-0.519719\pi\) | ||||
−0.0619108 | + | 0.998082i | \(0.519719\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.97564e12 | 2.31573 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.85814e11 | 0.261638 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.08041e12 | −1.53254 | −0.766271 | − | 0.642517i | \(-0.777890\pi\) | ||||
−0.766271 | + | 0.642517i | \(0.777890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.64171e12 | −0.976857 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.35313e11 | 0.194902 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.68194e12 | 2.03699 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.99666e12 | −1.05788 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.54171e12 | −0.883597 | −0.441799 | − | 0.897114i | \(-0.645659\pi\) | ||||
−0.441799 | + | 0.897114i | \(0.645659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.78695e12 | 1.63885 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.14771e12 | −0.386980 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.98120e10 | −0.0231838 | −0.0115919 | − | 0.999933i | \(-0.503690\pi\) | ||||
−0.0115919 | + | 0.999933i | \(0.503690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.82151e11 | −0.0922902 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.85477e12 | −0.919785 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.85948e12 | −1.22492 | −0.612461 | − | 0.790501i | \(-0.709820\pi\) | ||||
−0.612461 | + | 0.790501i | \(0.709820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.90355e12 | 1.53312 | 0.766559 | − | 0.642174i | \(-0.221967\pi\) | ||||
0.766559 | + | 0.642174i | \(0.221967\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.28137e12 | 1.93476 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.97629e12 | 0.599724 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.93319e12 | −0.876984 | −0.438492 | − | 0.898735i | \(-0.644487\pi\) | ||||
−0.438492 | + | 0.898735i | \(0.644487\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.59501e11 | 0.164825 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.51229e12 | 0.729265 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.93933e12 | 0.554727 | 0.277363 | − | 0.960765i | \(-0.410539\pi\) | ||||
0.277363 | + | 0.960765i | \(0.410539\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.26455e12 | −0.356450 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.12737e10 | −0.00868752 | −0.00434376 | − | 0.999991i | \(-0.501383\pi\) | ||||
−0.00434376 | + | 0.999991i | \(0.501383\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.31775e12 | 1.45586 | 0.727931 | − | 0.685651i | \(-0.240482\pi\) | ||||
0.727931 | + | 0.685651i | \(0.240482\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.36459e13 | −3.68206 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.58724e12 | 0.422131 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.41799e13 | −3.66411 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.28947e12 | −0.837912 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.71843e12 | 1.68708 | 0.843540 | − | 0.537067i | \(-0.180468\pi\) | ||||
0.843540 | + | 0.537067i | \(0.180468\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.36690e12 | −0.833515 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.10398e11 | −0.0513524 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.61413e12 | 0.869714 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.04788e13 | 2.48632 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.75365e12 | −0.644241 | −0.322120 | − | 0.946699i | \(-0.604396\pi\) | ||||
−0.322120 | + | 0.946699i | \(0.604396\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.65440e11 | −0.130448 | −0.0652240 | − | 0.997871i | \(-0.520776\pi\) | ||||
−0.0652240 | + | 0.997871i | \(0.520776\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.79879e12 | −1.54672 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.20397e10 | −0.0206493 | −0.0103247 | − | 0.999947i | \(-0.503287\pi\) | ||||
−0.0103247 | + | 0.999947i | \(0.503287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.77079e12 | −0.391802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.09767e12 | 0.675959 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.59205e12 | 0.773095 | 0.386548 | − | 0.922269i | \(-0.373668\pi\) | ||||
0.386548 | + | 0.922269i | \(0.373668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.84670e11 | −0.0816586 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.64080e12 | 1.59991 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.31342e12 | 0.271281 | 0.135641 | − | 0.990758i | \(-0.456691\pi\) | ||||
0.135641 | + | 0.990758i | \(0.456691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.85738e12 | 1.80467 | 0.902336 | − | 0.431032i | \(-0.141851\pi\) | ||||
0.902336 | + | 0.431032i | \(0.141851\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.44072e12 | −1.29456 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.13461e11 | −0.161302 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.08871e12 | −0.408612 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.86457e11 | −0.0359883 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.29508e12 | −0.246629 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.70061e12 | −0.319549 | −0.159774 | − | 0.987154i | \(-0.551077\pi\) | ||||
−0.159774 | + | 0.987154i | \(0.551077\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.03610e12 | −0.562923 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.11829e12 | 0.753473 | 0.376737 | − | 0.926320i | \(-0.377046\pi\) | ||||
0.376737 | + | 0.926320i | \(0.377046\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.23333e12 | −0.222672 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.51203e12 | −0.269401 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.26877e12 | −1.10227 | −0.551136 | − | 0.834415i | \(-0.685806\pi\) | ||||
−0.551136 | + | 0.834415i | \(0.685806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.37042e12 | 0.237818 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.07799e13 | −1.84633 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.44070e12 | 1.25785 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.47796e12 | −0.580328 | −0.290164 | − | 0.956977i | \(-0.593710\pi\) | ||||
−0.290164 | + | 0.956977i | \(0.593710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.55697e12 | −1.07995 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.05680e12 | −0.334395 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.94217e12 | −0.311702 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.11941e12 | −0.811097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.04006e12 | −0.944736 | −0.472368 | − | 0.881401i | \(-0.656601\pi\) | ||||
−0.472368 | + | 0.881401i | \(0.656601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.48377e12 | −1.46448 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.23810e12 | 0.646131 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.94382e12 | −0.292596 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.62958e12 | 0.688072 | 0.344036 | − | 0.938956i | \(-0.388206\pi\) | ||||
0.344036 | + | 0.938956i | \(0.388206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.05056e12 | 1.32820 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.15641e13 | −1.67574 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.51791e12 | 0.646487 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.79359e12 | −0.818675 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.29476e12 | −0.599320 | −0.299660 | − | 0.954046i | \(-0.596873\pi\) | ||||
−0.299660 | + | 0.954046i | \(0.596873\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.88360e12 | 0.397398 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.32662e11 | 0.0861092 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.64719e11 | −0.0624697 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.28809e12 | −0.171017 | −0.0855087 | − | 0.996337i | \(-0.527252\pi\) | ||||
−0.0855087 | + | 0.996337i | \(0.527252\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.26099e13 | 1.65363 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.04420e13 | −1.35255 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.68182e12 | −0.982870 | −0.491435 | − | 0.870914i | \(-0.663528\pi\) | ||||
−0.491435 | + | 0.870914i | \(0.663528\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.09684e12 | 0.770570 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.47007e12 | −1.18236 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.62651e12 | −0.323951 | −0.161976 | − | 0.986795i | \(-0.551787\pi\) | ||||
−0.161976 | + | 0.986795i | \(0.551787\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.85690e13 | −2.26260 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.00060e13 | 1.20451 | 0.602253 | − | 0.798305i | \(-0.294270\pi\) | ||||
0.602253 | + | 0.798305i | \(0.294270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.64668e12 | 0.314774 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.47305e13 | 1.73091 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.50043e12 | 0.522499 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.57014e13 | 1.80118 | 0.900591 | − | 0.434668i | \(-0.143134\pi\) | ||||
0.900591 | + | 0.434668i | \(0.143134\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.30230e13 | 2.60967 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.91897e12 | 0.662956 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.27309e12 | 0.251585 | 0.125793 | − | 0.992057i | \(-0.459853\pi\) | ||||
0.125793 | + | 0.992057i | \(0.459853\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.42551e13 | 3.74659 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.89429e12 | 0.420918 | 0.210459 | − | 0.977603i | \(-0.432504\pi\) | ||||
0.210459 | + | 0.977603i | \(0.432504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.13684e12 | −0.441884 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.76408e12 | −0.819622 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.31892e12 | −0.241939 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.12387e12 | 0.219008 | 0.109504 | − | 0.993986i | \(-0.465074\pi\) | ||||
0.109504 | + | 0.993986i | \(0.465074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.22756e13 | −3.28949 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.42990e13 | 1.44045 | 0.720225 | − | 0.693741i | \(-0.244039\pi\) | ||||
0.720225 | + | 0.693741i | \(0.244039\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.57291e12 | −0.256193 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.13702e12 | −0.604036 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.59941e12 | −0.544783 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.57983e13 | −1.51943 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.24670e12 | 0.879142 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.89509e12 | 0.366104 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.64830e12 | 0.710688 | 0.355344 | − | 0.934736i | \(-0.384364\pi\) | ||||
0.355344 | + | 0.934736i | \(0.384364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.60134e13 | 2.38974 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.64838e12 | 0.149714 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.69595e12 | −0.152294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.25521e13 | 1.11446 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.39736e12 | −0.561615 | −0.280807 | − | 0.959764i | \(-0.590602\pi\) | ||||
−0.280807 | + | 0.959764i | \(0.590602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.50913e12 | 0.565018 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.36769e13 | 3.74891 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.15196e13 | −0.977727 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.96512e12 | 0.164933 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.20688e13 | 2.66166 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.78388e13 | −1.46419 | −0.732096 | − | 0.681202i | \(-0.761458\pi\) | ||||
−0.732096 | + | 0.681202i | \(0.761458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.30537e13 | 1.87132 | 0.935658 | − | 0.352908i | \(-0.114807\pi\) | ||||
0.935658 | + | 0.352908i | \(0.114807\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.13476e13 | −1.71373 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.23988e12 | −0.416018 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.01049e13 | −2.36395 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.58659e12 | −0.666873 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.76669e13 | 1.35712 | 0.678558 | − | 0.734547i | \(-0.262605\pi\) | ||||
0.678558 | + | 0.734547i | \(0.262605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.29445e12 | −0.0983524 | −0.0491762 | − | 0.998790i | \(-0.515660\pi\) | ||||
−0.0491762 | + | 0.998790i | \(0.515660\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.62146e12 | 0.572790 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.47158e13 | −1.09398 | −0.546988 | − | 0.837140i | \(-0.684226\pi\) | ||||
−0.546988 | + | 0.837140i | \(0.684226\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.78954e12 | −0.719891 | −0.359945 | − | 0.932973i | \(-0.617205\pi\) | ||||
−0.359945 | + | 0.932973i | \(0.617205\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.83717e13 | −1.33643 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.36389e12 | 0.673835 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.95694e12 | −0.708821 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.11942e13 | 3.60542 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.41875e12 | −0.516894 | −0.258447 | − | 0.966025i | \(-0.583211\pi\) | ||||
−0.258447 | + | 0.966025i | \(0.583211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.30918e13 | −0.902438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.45647e13 | 1.67528 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.11455e11 | −0.0480056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.66282e12 | 0.378057 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.19932e13 | −2.11336 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.29104e13 | 1.49744 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.96552e12 | −0.191792 | −0.0958960 | − | 0.995391i | \(-0.530572\pi\) | ||||
−0.0958960 | + | 0.995391i | \(0.530572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.23844e13 | −1.43251 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.92054e13 | −1.21621 | −0.608105 | − | 0.793856i | \(-0.708070\pi\) | ||||
−0.608105 | + | 0.793856i | \(0.708070\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.71424e13 | −1.07424 | −0.537122 | − | 0.843505i | \(-0.680488\pi\) | ||||
−0.537122 | + | 0.843505i | \(0.680488\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.62342e12 | −0.224701 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.24289e13 | −1.37645 | −0.688225 | − | 0.725497i | \(-0.741610\pi\) | ||||
−0.688225 | + | 0.725497i | \(0.741610\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.46127e12 | 0.270948 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.44548e13 | 0.868813 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.36450e13 | −0.811681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.24014e13 | −0.730111 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.39382e13 | −1.97754 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.37223e11 | 0.0252154 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.36456e13 | 1.92057 | 0.960286 | − | 0.279018i | \(-0.0900090\pi\) | ||||
0.960286 | + | 0.279018i | \(0.0900090\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.31815e13 | −1.30976 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.90224e12 | 0.162309 | 0.0811544 | − | 0.996702i | \(-0.474139\pi\) | ||||
0.0811544 | + | 0.996702i | \(0.474139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.82428e12 | 0.488490 | 0.244245 | − | 0.969714i | \(-0.421460\pi\) | ||||
0.244245 | + | 0.969714i | \(0.421460\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.91189e12 | −0.214359 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.64834e13 | −1.43654 | −0.718271 | − | 0.695764i | \(-0.755066\pi\) | ||||
−0.718271 | + | 0.695764i | \(0.755066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.02871e11 | −0.0323718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.95809e13 | −4.23018 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.87663e13 | 0.987521 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.50177e12 | 0.182425 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.48582e13 | 2.31353 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.83601e12 | 0.400107 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.92782e13 | 0.974551 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.94811e13 | −0.975032 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.20802e13 | 0.598626 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.42297e12 | −0.0698172 | −0.0349086 | − | 0.999391i | \(-0.511114\pi\) | ||||
−0.0349086 | + | 0.999391i | \(0.511114\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.34889e13 | −2.59852 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.15891e13 | 1.51951 | 0.759756 | − | 0.650209i | \(-0.225319\pi\) | ||||
0.759756 | + | 0.650209i | \(0.225319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.22083e13 | −1.05778 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.86097e12 | −0.134933 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.10223e12 | −0.0514764 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.00471e12 | −0.231451 | −0.115726 | − | 0.993281i | \(-0.536919\pi\) | ||||
−0.115726 | + | 0.993281i | \(0.536919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.30300e13 | 0.596726 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.06884e13 | −0.938250 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.09738e12 | 0.228933 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.93493e13 | 3.52927 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.47313e13 | −1.52985 | −0.764927 | − | 0.644117i | \(-0.777225\pi\) | ||||
−0.764927 | + | 0.644117i | \(0.777225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.69967e13 | 1.17771 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.57243e13 | 1.11142 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.17055e13 | 0.500884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.08909e13 | −1.73300 | −0.866500 | − | 0.499177i | \(-0.833636\pi\) | ||||
−0.866500 | + | 0.499177i | \(0.833636\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.75343e13 | 0.736025 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.21978e13 | 0.922904 | 0.461452 | − | 0.887165i | \(-0.347329\pi\) | ||||
0.461452 | + | 0.887165i | \(0.347329\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.35268e13 | 0.557047 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.69959e12 | −0.354859 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.61559e13 | −0.652766 | −0.326383 | − | 0.945238i | \(-0.605830\pi\) | ||||
−0.326383 | + | 0.945238i | \(0.605830\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.50853e13 | −0.603750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.48961e12 | −0.177990 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.71696e13 | 1.45972 | 0.729860 | − | 0.683596i | \(-0.239585\pi\) | ||||
0.729860 | + | 0.683596i | \(0.239585\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.42219e13 | −0.553275 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.32118e13 | −0.894551 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.92677e12 | 0.149917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.69443e13 | 0.640866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.23840e14 | 4.64028 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.28719e12 | 0.233391 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.99486e13 | −0.733659 | −0.366829 | − | 0.930288i | \(-0.619557\pi\) | ||||
−0.366829 | + | 0.930288i | \(0.619557\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.81107e13 | −1.75301 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.69341e13 | −0.972335 | −0.486167 | − | 0.873866i | \(-0.661605\pi\) | ||||
−0.486167 | + | 0.873866i | \(0.661605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.89351e12 | −0.210798 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.98057e12 | 0.353700 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.45379e13 | 0.510477 | 0.255239 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255239 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.58492e13 | −2.29102 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.13835e14 | −3.92434 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.53908e13 | −0.525741 | −0.262870 | − | 0.964831i | \(-0.584669\pi\) | ||||
−0.262870 | + | 0.964831i | \(0.584669\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.73152e12 | 0.0924573 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.21438e13 | 0.407312 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.27260e13 | 2.41717 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.55743e13 | 0.512951 | 0.256476 | − | 0.966551i | \(-0.417439\pi\) | ||||
0.256476 | + | 0.966551i | \(0.417439\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.26766e13 | −1.06651 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.79427e12 | 0.219755 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.59021e13 | −1.47131 | −0.735656 | − | 0.677356i | \(-0.763126\pi\) | ||||
−0.735656 | + | 0.677356i | \(0.763126\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.01425e14 | −3.22180 |
(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 | 80.10.a.k.1.1 | 3 | ||
4.3 | odd | 2 | 40.10.a.d.1.3 | ✓ | 3 | ||
5.2 | odd | 4 | 400.10.c.r.49.6 | 6 | |||
5.3 | odd | 4 | 400.10.c.r.49.1 | 6 | |||
5.4 | even | 2 | 400.10.a.x.1.3 | 3 | |||
8.3 | odd | 2 | 320.10.a.u.1.1 | 3 | |||
8.5 | even | 2 | 320.10.a.v.1.3 | 3 | |||
12.11 | even | 2 | 360.10.a.j.1.2 | 3 | |||
20.3 | even | 4 | 200.10.c.f.49.6 | 6 | |||
20.7 | even | 4 | 200.10.c.f.49.1 | 6 | |||
20.19 | odd | 2 | 200.10.a.f.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.10.a.d.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
80.10.a.k.1.1 | 3 | 1.1 | even | 1 | trivial | ||
200.10.a.f.1.1 | 3 | 20.19 | odd | 2 | |||
200.10.c.f.49.1 | 6 | 20.7 | even | 4 | |||
200.10.c.f.49.6 | 6 | 20.3 | even | 4 | |||
320.10.a.u.1.1 | 3 | 8.3 | odd | 2 | |||
320.10.a.v.1.3 | 3 | 8.5 | even | 2 | |||
360.10.a.j.1.2 | 3 | 12.11 | even | 2 | |||
400.10.a.x.1.3 | 3 | 5.4 | even | 2 | |||
400.10.c.r.49.1 | 6 | 5.3 | odd | 4 | |||
400.10.c.r.49.6 | 6 | 5.2 | odd | 4 |