Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,10,Mod(1,100)]
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, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.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: | \(51.5035836164\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{79}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 79 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 20) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.88819\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 100.1 |
$q$-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 | ||||||||
\(3\) | −12.2111 | −0.0870381 | −0.0435191 | − | 0.999053i | \(-0.513857\pi\) | ||||
−0.0435191 | + | 0.999053i | \(0.513857\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9622.57 | −1.51478 | −0.757390 | − | 0.652962i | \(-0.773526\pi\) | ||||
−0.757390 | + | 0.652962i | \(0.773526\pi\) | |||||||
\(8\) | 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. | −1.64867 | −0.824335 | − | 0.566102i | \(-0.808451\pi\) | ||||
−0.824335 | + | 0.566102i | \(0.808451\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −207499. | −0.602555 | −0.301278 | − | 0.953536i | \(-0.597413\pi\) | ||||
−0.301278 | + | 0.953536i | \(0.597413\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 802445. | 1.41262 | 0.706308 | − | 0.707904i | \(-0.250359\pi\) | ||||
0.706308 | + | 0.707904i | \(0.250359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 117502. | 0.131844 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.24189e6 | 0.925351 | 0.462675 | − | 0.886528i | \(-0.346890\pi\) | ||||
0.462675 | + | 0.886528i | \(0.346890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 478882. | 0.173417 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.28308e6 | −1.12451 | −0.562257 | − | 0.826963i | \(-0.690067\pi\) | ||||
−0.562257 | + | 0.826963i | \(0.690067\pi\) | |||||||
\(30\) | 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. | −0.0997064 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.89856e6 | 0.254258 | 0.127129 | − | 0.991886i | \(-0.459424\pi\) | ||||
0.127129 | + | 0.991886i | \(0.459424\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 2.00204e7 | 0.893029 | 0.446515 | − | 0.894776i | \(-0.352665\pi\) | ||||
0.446515 | + | 0.894776i | \(0.352665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.73010e7 | −1.11501 | −0.557507 | − | 0.830172i | \(-0.688242\pi\) | ||||
−0.557507 | + | 0.830172i | \(0.688242\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.22402e7 | 1.29456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53380e6 | 0.0524453 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.55155e7 | 0.444184 | 0.222092 | − | 0.975026i | \(-0.428711\pi\) | ||||
0.222092 | + | 0.975026i | \(0.428711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.79875e6 | −0.122951 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.96495e7 | −1.07063 | −0.535317 | − | 0.844651i | \(-0.679808\pi\) | ||||
−0.535317 | + | 0.844651i | \(0.679808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00434e8 | 1.85347 | 0.926737 | − | 0.375710i | \(-0.122601\pi\) | ||||
0.926737 | + | 0.375710i | \(0.122601\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.87966e8 | 1.50331 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.09951e7 | 0.491046 | 0.245523 | − | 0.969391i | \(-0.421040\pi\) | ||||
0.245523 | + | 0.969391i | \(0.421040\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 3.40820e8 | 1.40466 | 0.702332 | − | 0.711850i | \(-0.252142\pi\) | ||||
0.702332 | + | 0.711850i | \(0.252142\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.35268e8 | −1.73525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.81089e8 | 0.811935 | 0.405967 | − | 0.913888i | \(-0.366935\pi\) | ||||
0.405967 | + | 0.913888i | \(0.366935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.78638e8 | 0.977330 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.01017e8 | 1.39007 | 0.695033 | − | 0.718978i | \(-0.255390\pi\) | ||||
0.695033 | + | 0.718978i | \(0.255390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.23011e7 | 0.0978756 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.39917e8 | 0.912162 | 0.456081 | − | 0.889938i | \(-0.349253\pi\) | ||||
0.456081 | + | 0.889938i | \(0.349253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.63369e9 | 2.49737 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.38028e7 | 0.0607195 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.23026e8 | −0.485170 | −0.242585 | − | 0.970130i | \(-0.577995\pi\) | ||||
−0.242585 | + | 0.970130i | \(0.577995\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 8.50494e7 | 0.0744567 | 0.0372284 | − | 0.999307i | \(-0.488147\pi\) | ||||
0.0372284 | + | 0.999307i | \(0.488147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.23881e8 | −0.386372 | −0.193186 | − | 0.981162i | \(-0.561882\pi\) | ||||
−0.193186 | + | 0.981162i | \(0.561882\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.59417e8 | −0.379591 | −0.189796 | − | 0.981824i | \(-0.560783\pi\) | ||||
−0.189796 | + | 0.981824i | \(0.560783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.53947e7 | −0.0221302 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.63801e9 | 1.52203 | 0.761016 | − | 0.648733i | \(-0.224701\pi\) | ||||
0.761016 | + | 0.648733i | \(0.224701\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.31641e9 | 1.63618 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.99668e9 | 0.912739 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.36341e8 | 0.312281 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.07128e8 | −0.120989 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.33268e9 | −1.13678 | −0.568391 | − | 0.822758i | \(-0.692434\pi\) | ||||
−0.568391 | + | 0.822758i | \(0.692434\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | −7.72158e9 | −2.13980 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.15185e9 | 0.521879 | 0.260940 | − | 0.965355i | \(-0.415968\pi\) | ||||
0.260940 | + | 0.965355i | \(0.415968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.75086e8 | 0.0625032 | 0.0312516 | − | 0.999512i | \(-0.490051\pi\) | ||||
0.0312516 | + | 0.999512i | \(0.490051\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.55487e8 | 0.0970487 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.44408e9 | −1.88863 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.37911e8 | −0.112676 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.16582e9 | −1.02483 | −0.512416 | − | 0.858737i | \(-0.671249\pi\) | ||||
−0.512416 | + | 0.858737i | \(0.671249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.28376e9 | −0.514014 | −0.257007 | − | 0.966410i | \(-0.582736\pi\) | ||||
−0.257007 | + | 0.966410i | \(0.582736\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.05327e9 | 0.597990 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.89255e9 | 0.248599 | 0.124299 | − | 0.992245i | \(-0.460332\pi\) | ||||
0.124299 | + | 0.992245i | \(0.460332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.11573e8 | −0.0386610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.19501e10 | −1.40170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.14293e8 | −0.0459688 | −0.0229844 | − | 0.999736i | \(-0.507317\pi\) | ||||
−0.0229844 | + | 0.999736i | \(0.507317\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.56225e10 | 1.55427 | 0.777136 | − | 0.629332i | \(-0.216672\pi\) | ||||
0.777136 | + | 0.629332i | \(0.216672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.82198e10 | 1.71812 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.56749e10 | −1.40191 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.16058e10 | −0.985069 | −0.492535 | − | 0.870293i | \(-0.663930\pi\) | ||||
−0.492535 | + | 0.870293i | \(0.663930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.21683e9 | 0.0931860 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.45556e10 | −1.78777 | −0.893886 | − | 0.448294i | \(-0.852032\pi\) | ||||
−0.893886 | + | 0.448294i | \(0.852032\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.21032e9 | 0.222328 | 0.111164 | − | 0.993802i | \(-0.464542\pi\) | ||||
0.111164 | + | 0.993802i | \(0.464542\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.44752e9 | −0.161323 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.15424e10 | −0.690256 | ||||||||
\(188\) | 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 | ||||||||
\(193\) | −2.50875e10 | −1.30152 | −0.650759 | − | 0.759284i | \(-0.725549\pi\) | ||||
−0.650759 | + | 0.759284i | \(0.725549\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.64109e9 | −0.456067 | −0.228033 | − | 0.973653i | \(-0.573229\pi\) | ||||
−0.228033 | + | 0.973653i | \(0.573229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.34318e9 | 0.151120 | 0.0755598 | − | 0.997141i | \(-0.475926\pi\) | ||||
0.0755598 | + | 0.997141i | \(0.475926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.89040e8 | −0.0427397 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.12142e10 | 1.70339 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.42589e10 | −0.918341 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 5.26936e8 | 0.0175408 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.45174e10 | 1.05674 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.16179e9 | −0.122259 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.52287e10 | 0.993415 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.00503e10 | 1.35530 | 0.677649 | − | 0.735386i | \(-0.262999\pi\) | ||||
0.677649 | + | 0.735386i | \(0.262999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.68117e9 | 0.217001 | 0.108501 | − | 0.994096i | \(-0.465395\pi\) | ||||
0.108501 | + | 0.994096i | \(0.465395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.96014e10 | −0.711299 | −0.355649 | − | 0.934619i | \(-0.615740\pi\) | ||||
−0.355649 | + | 0.934619i | \(0.615740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.53622e9 | 0.151033 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.42617e10 | 1.65068 | 0.825341 | − | 0.564634i | \(-0.190983\pi\) | ||||
0.825341 | + | 0.564634i | \(0.190983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.43240e9 | −0.0706693 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.65577e10 | −0.328253 | −0.164126 | − | 0.986439i | \(-0.552481\pi\) | ||||
−0.164126 | + | 0.986439i | \(0.552481\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.61072e10 | 0.689473 | 0.344737 | − | 0.938699i | \(-0.387968\pi\) | ||||
0.344737 | + | 0.938699i | \(0.387968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.40494e10 | −0.258482 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.36237e11 | −2.32894 | ||||||||
\(248\) | 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 | ||||||||
\(253\) | 6.90815e10 | 1.06003 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.57624e10 | 0.654350 | 0.327175 | − | 0.944964i | \(-0.393903\pi\) | ||||
0.327175 | + | 0.944964i | \(0.393903\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.78916e10 | −0.385145 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.36651e10 | 1.11599 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.93911e10 | −1.28099 | −0.640496 | − | 0.767961i | \(-0.721271\pi\) | ||||
−0.640496 | + | 0.767961i | \(0.721271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.59299e9 | −0.0793929 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.57475e11 | 1.83369 | 0.916845 | − | 0.399242i | \(-0.130727\pi\) | ||||
0.916845 | + | 0.399242i | \(0.130727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.79292e10 | 0.314555 | 0.157278 | − | 0.987554i | \(-0.449728\pi\) | ||||
0.157278 | + | 0.987554i | \(0.449728\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.99492e10 | −0.217367 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.68307e11 | 1.71768 | 0.858842 | − | 0.512240i | \(-0.171184\pi\) | ||||
0.858842 | + | 0.512240i | \(0.171184\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 2.02954e11 | 1.88087 | 0.940436 | − | 0.339970i | \(-0.110417\pi\) | ||||
0.940436 | + | 0.339970i | \(0.110417\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.42022e11 | −2.10565 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.55318e10 | −0.636927 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.16561e9 | 0.0422283 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.31572e11 | −1.04294 | −0.521470 | − | 0.853270i | \(-0.674616\pi\) | ||||
−0.521470 | + | 0.853270i | \(0.674616\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.66384e10 | 0.198657 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.10844e11 | −1.52560 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.92648e11 | −1.35274 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.33450e10 | 0.0909554 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.88785e11 | 1.21296 | 0.606479 | − | 0.795099i | \(-0.292581\pi\) | ||||
0.606479 | + | 0.795099i | \(0.292581\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −3.35032e11 | −1.97305 | −0.986523 | − | 0.163623i | \(-0.947682\pi\) | ||||
−0.986523 | + | 0.163623i | \(0.947682\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.98163e11 | 1.10219 | 0.551094 | − | 0.834443i | \(-0.314211\pi\) | ||||
0.551094 | + | 0.834443i | \(0.314211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.38252e11 | −1.28818 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.39717e9 | 0.0336291 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.66507e11 | −0.851179 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.83110e9 | 0.0330389 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | −5.66202e10 | −0.252332 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.77234e10 | −0.370494 | −0.185247 | − | 0.982692i | \(-0.559308\pi\) | ||||
−0.185247 | + | 0.982692i | \(0.559308\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.22130e10 | −0.132475 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.99539e11 | −0.799157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.14379e11 | −0.446194 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.89987e11 | −0.703464 | −0.351732 | − | 0.936101i | \(-0.614407\pi\) | ||||
−0.351732 | + | 0.936101i | \(0.614407\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.85678e11 | 1.75240 | 0.876201 | − | 0.481946i | \(-0.160070\pi\) | ||||
0.876201 | + | 0.481946i | \(0.160070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.13031e10 | −0.285907 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.15816e10 | −0.176811 | −0.0884054 | − | 0.996085i | \(-0.528177\pi\) | ||||
−0.0884054 | + | 0.996085i | \(0.528177\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.43816e10 | −0.0794431 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.79131e11 | −0.569176 | −0.284588 | − | 0.958650i | \(-0.591857\pi\) | ||||
−0.284588 | + | 0.958650i | \(0.591857\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.21231e11 | 0.995485 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.99154e9 | −0.0271803 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.76314e10 | 0.0795071 | 0.0397536 | − | 0.999210i | \(-0.487343\pi\) | ||||
0.0397536 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.91307e11 | −1.37954 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.45525e11 | −0.672842 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.35196e11 | −0.629129 | −0.314565 | − | 0.949236i | \(-0.601858\pi\) | ||||
−0.314565 | + | 0.949236i | \(0.601858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.27168e11 | 1.85395 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.11965e11 | −0.776658 | −0.388329 | − | 0.921521i | \(-0.626948\pi\) | ||||
−0.388329 | + | 0.921521i | \(0.626948\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.06958e10 | 0.0989434 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.78535e10 | 0.113637 | 0.0568185 | − | 0.998385i | \(-0.481904\pi\) | ||||
0.0568185 | + | 0.998385i | \(0.481904\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.91077e11 | −0.886264 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.19528e11 | 0.264665 | 0.132332 | − | 0.991205i | \(-0.457753\pi\) | ||||
0.132332 | + | 0.991205i | \(0.457753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.57691e11 | −0.557575 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.62659e10 | 0.0978351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.08892e10 | −0.143226 | −0.0716132 | − | 0.997432i | \(-0.522815\pi\) | ||||
−0.0716132 | + | 0.997432i | \(0.522815\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 6.09012e11 | 1.15015 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.61236e11 | 0.291265 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.23341e11 | 0.394651 | 0.197325 | − | 0.980338i | \(-0.436774\pi\) | ||||
0.197325 | + | 0.980338i | \(0.436774\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.62765e10 | −0.0454234 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.58884e11 | 1.62178 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.35911e9 | −0.00544016 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.54170e11 | 0.561370 | 0.280685 | − | 0.959800i | \(-0.409438\pi\) | ||||
0.280685 | + | 0.959800i | \(0.409438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.29294e11 | 0.821159 | 0.410580 | − | 0.911825i | \(-0.365326\pi\) | ||||
0.410580 | + | 0.911825i | \(0.365326\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.28634e11 | 1.10657 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.92869e12 | −2.80761 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | −3.28861e11 | −0.449591 | −0.224795 | − | 0.974406i | \(-0.572171\pi\) | ||||
−0.224795 | + | 0.974406i | \(0.572171\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.96545e11 | 1.30717 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.69396e11 | 0.346178 | 0.173089 | − | 0.984906i | \(-0.444625\pi\) | ||||
0.173089 | + | 0.984906i | \(0.444625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.02045e12 | −1.28475 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.20444e11 | −0.518671 | −0.259335 | − | 0.965787i | \(-0.583503\pi\) | ||||
−0.259335 | + | 0.965787i | \(0.583503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.52915e10 | 0.0891995 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.19773e11 | 0.139075 | 0.0695376 | − | 0.997579i | \(-0.477848\pi\) | ||||
0.0695376 | + | 0.997579i | \(0.477848\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.39909e12 | 1.59239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00984e10 | 0.0447388 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.34943e12 | −1.44719 | −0.723597 | − | 0.690223i | \(-0.757512\pi\) | ||||
−0.723597 | + | 0.690223i | \(0.757512\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 6.60348e11 | 0.667819 | 0.333909 | − | 0.942605i | \(-0.391632\pi\) | ||||
0.333909 | + | 0.942605i | \(0.391632\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.28966e11 | 0.806512 | 0.403256 | − | 0.915087i | \(-0.367878\pi\) | ||||
0.403256 | + | 0.915087i | \(0.367878\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.79381e11 | −0.743827 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.31102e10 | −0.0216376 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.11366e12 | 1.02301 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.98417e11 | −0.440819 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.48710e11 | −0.563042 | −0.281521 | − | 0.959555i | \(-0.590839\pi\) | ||||
−0.281521 | + | 0.959555i | \(0.590839\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.92110e11 | −0.419188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.45924e11 | 0.122002 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.75979e12 | 1.41768 | 0.708842 | − | 0.705367i | \(-0.249218\pi\) | ||||
0.708842 | + | 0.705367i | \(0.249218\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 8.88736e11 | 0.677582 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.15235e11 | 0.305274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.11758e11 | 0.369498 | 0.184749 | − | 0.982786i | \(-0.440853\pi\) | ||||
0.184749 | + | 0.982786i | \(0.440853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.90768e11 | −0.135281 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.69213e12 | −1.17863 | −0.589314 | − | 0.807904i | \(-0.700602\pi\) | ||||
−0.589314 | + | 0.807904i | \(0.700602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.22483e11 | −0.149542 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.10216e11 | 0.468986 | 0.234493 | − | 0.972118i | \(-0.424657\pi\) | ||||
0.234493 | + | 0.972118i | \(0.424657\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.27956e12 | −2.12776 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.84276e11 | 0.244972 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.07492e12 | −1.27730 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | −1.01046e12 | −0.590555 | −0.295277 | − | 0.955412i | \(-0.595412\pi\) | ||||
−0.295277 | + | 0.955412i | \(0.595412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.44327e11 | 0.420355 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.58873e11 | −0.143726 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.94654e12 | 1.06252 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.27015e12 | −2.29177 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.99851e11 | 0.155604 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | −3.92015e10 | −0.0193510 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.10308e12 | 1.48201 | 0.741004 | − | 0.671501i | \(-0.234350\pi\) | ||||
0.741004 | + | 0.671501i | \(0.234350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.91525e12 | −1.83943 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.43693e12 | −1.58851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.70479e12 | −1.22990 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.92558e11 | 0.216825 | 0.108412 | − | 0.994106i | \(-0.465423\pi\) | ||||
0.108412 | + | 0.994106i | \(0.465423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.39901e12 | −1.47231 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.40946e11 | 0.0600786 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.67786e12 | −0.703832 | −0.351916 | − | 0.936032i | \(-0.614470\pi\) | ||||
−0.351916 | + | 0.936032i | \(0.614470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.64347e12 | −1.48044 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.40646e12 | 1.36238 | 0.681190 | − | 0.732107i | \(-0.261463\pi\) | ||||
0.681190 | + | 0.732107i | \(0.261463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.05234e12 | −1.59530 | −0.797651 | − | 0.603119i | \(-0.793924\pi\) | ||||
−0.797651 | + | 0.603119i | \(0.793924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.17068e11 | −0.161626 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.55977e11 | 0.171258 | 0.0856291 | − | 0.996327i | \(-0.472710\pi\) | ||||
0.0856291 | + | 0.996327i | \(0.472710\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.06347e11 | 0.113282 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.78333e12 | −2.10565 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.41933e12 | 0.508834 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.83858e12 | 0.986801 | 0.493401 | − | 0.869802i | \(-0.335754\pi\) | ||||
0.493401 | + | 0.869802i | \(0.335754\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.87847e12 | −0.985470 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.17728e11 | 0.0396952 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.08687e12 | 1.35720 | 0.678601 | − | 0.734507i | \(-0.262586\pi\) | ||||
0.678601 | + | 0.734507i | \(0.262586\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.08240e10 | −0.0131532 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.47524e12 | 1.42035 | 0.710175 | − | 0.704025i | \(-0.248616\pi\) | ||||
0.710175 | + | 0.704025i | \(0.248616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.83907e11 | −0.151296 | −0.0756478 | − | 0.997135i | \(-0.524102\pi\) | ||||
−0.0756478 | + | 0.997135i | \(0.524102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.58215e12 | −0.487326 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.96609e12 | 1.48479 | 0.742395 | − | 0.669962i | \(-0.233690\pi\) | ||||
0.742395 | + | 0.669962i | \(0.233690\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.03271e11 | −0.148260 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.33285e12 | 1.83829 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.43460e12 | 0.696396 | 0.348198 | − | 0.937421i | \(-0.386794\pi\) | ||||
0.348198 | + | 0.937421i | \(0.386794\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.82614e12 | −0.507284 | −0.253642 | − | 0.967298i | \(-0.581628\pi\) | ||||
−0.253642 | + | 0.967298i | \(0.581628\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.13058e12 | −0.309523 | −0.154761 | − | 0.987952i | \(-0.549461\pi\) | ||||
−0.154761 | + | 0.987952i | \(0.549461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.94716e11 | 0.160471 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.19539e12 | −1.38173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.45068e11 | −0.140847 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 2.15022e11 | 0.0532312 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.86918e12 | −2.13430 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 2.27990e12 | 0.525977 | 0.262989 | − | 0.964799i | \(-0.415292\pi\) | ||||
0.262989 | + | 0.964799i | \(0.415292\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.86871e12 | 1.09231 | 0.546153 | − | 0.837685i | \(-0.316092\pi\) | ||||
0.546153 | + | 0.837685i | \(0.316092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.54314e12 | −1.22646 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.21495e11 | −0.0919768 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.30610e12 | −0.496329 | −0.248164 | − | 0.968718i | \(-0.579827\pi\) | ||||
−0.248164 | + | 0.968718i | \(0.579827\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.65754e12 | −1.39402 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.40069e12 | 1.52858 | 0.764289 | − | 0.644873i | \(-0.223090\pi\) | ||||
0.764289 | + | 0.644873i | \(0.223090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.00760e12 | −0.409045 | −0.204522 | − | 0.978862i | \(-0.565564\pi\) | ||||
−0.204522 | + | 0.978862i | \(0.565564\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.30181e11 | −0.0864650 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.31909e12 | −1.04057 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.11170e11 | −0.117963 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.11494e13 | 2.12324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.01154e13 | 1.90071 | 0.950355 | − | 0.311167i | \(-0.100720\pi\) | ||||
0.950355 | + | 0.311167i | \(0.100720\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.91166e12 | 1.63046 | 0.815229 | − | 0.579139i | \(-0.196611\pi\) | ||||
0.815229 | + | 0.579139i | \(0.196611\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.07059e12 | 0.734926 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.06007e11 | −0.0188874 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.26863e12 | 1.62976 | 0.814878 | − | 0.579633i | \(-0.196804\pi\) | ||||
0.814878 | + | 0.579633i | \(0.196804\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.61466e11 | 0.0619101 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 1.04559e13 | 1.72211 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.21893e12 | −0.837594 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | 2.32594e12 | 0.359169 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.05161e13 | 1.58295 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.58922e12 | 1.12795 | 0.563974 | − | 0.825793i | \(-0.309272\pi\) | ||||
0.563974 | + | 0.825793i | \(0.309272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.49075e12 | −0.805784 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.45480e12 | −0.645543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.02188e11 | 0.0285705 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.50766e12 | 0.210389 | 0.105194 | − | 0.994452i | \(-0.466454\pi\) | ||||
0.105194 | + | 0.994452i | \(0.466454\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.18394e11 | −0.112786 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.40909e11 | −0.0600105 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.12985e13 | −1.50009 | −0.750045 | − | 0.661387i | \(-0.769968\pi\) | ||||
−0.750045 | + | 0.661387i | \(0.769968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.28117e12 | −0.954833 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.15423e12 | −0.538100 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.07062e12 | −0.136984 | −0.0684919 | − | 0.997652i | \(-0.521819\pi\) | ||||
−0.0684919 | + | 0.997652i | \(0.521819\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.50546e12 | 0.562517 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.44855e13 | −1.78662 | −0.893311 | − | 0.449439i | \(-0.851624\pi\) | ||||
−0.893311 | + | 0.449439i | \(0.851624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.66360e12 | 0.202707 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.24339e13 | −1.49678 | −0.748388 | − | 0.663261i | \(-0.769172\pi\) | ||||
−0.748388 | + | 0.663261i | \(0.769172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.17402e13 | −1.37954 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | −2.84468e11 | −0.0322446 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.93877e12 | −0.878662 | −0.439331 | − | 0.898325i | \(-0.644784\pi\) | ||||
−0.439331 | + | 0.898325i | \(0.644784\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 5.38303e12 | 0.574998 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.69182e13 | 1.76512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.80743e12 | 0.392612 | 0.196306 | − | 0.980543i | \(-0.437105\pi\) | ||||
0.196306 | + | 0.980543i | \(0.437105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.58810e11 | −0.0569534 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.89254e12 | 0.392126 | 0.196063 | − | 0.980591i | \(-0.437184\pi\) | ||||
0.196063 | + | 0.980591i | \(0.437184\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.40588e11 | 0.0335223 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.01827e13 | 1.96364 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.40040e12 | −0.230862 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.05109e12 | −0.195010 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.70256e12 | 0.251124 | 0.125562 | − | 0.992086i | \(-0.459927\pi\) | ||||
0.125562 | + | 0.992086i | \(0.459927\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.21368e12 | 0.111495 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.53844e13 | −2.30554 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.40291e13 | −3.05577 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.58748e12 | 0.139363 | 0.0696813 | − | 0.997569i | \(-0.477802\pi\) | ||||
0.0696813 | + | 0.997569i | \(0.477802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.73994e12 | 0.671857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.05467e13 | −0.905252 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.89586e13 | 1.60911 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.92294e12 | −0.159601 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.55705e12 | −0.374038 | −0.187019 | − | 0.982356i | \(-0.559883\pi\) | ||||
−0.187019 | + | 0.982356i | \(0.559883\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.77014e12 | −0.224858 | −0.112429 | − | 0.993660i | \(-0.535863\pi\) | ||||
−0.112429 | + | 0.993660i | \(0.535863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.41047e11 | −0.0273783 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.60653e13 | 1.26151 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | −1.75355e13 | −1.33235 | −0.666175 | − | 0.745796i | \(-0.732069\pi\) | ||||
−0.666175 | + | 0.745796i | \(0.732069\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.15138e12 | 0.680318 | 0.340159 | − | 0.940368i | \(-0.389519\pi\) | ||||
0.340159 | + | 0.940368i | \(0.389519\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.76678e12 | −0.424071 | −0.212035 | − | 0.977262i | \(-0.568009\pi\) | ||||
−0.212035 | + | 0.977262i | \(0.568009\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.05522e12 | −0.149504 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.08398e13 | −0.780044 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.71781e12 | −0.120979 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.69274e11 | 0.0605658 | 0.0302829 | − | 0.999541i | \(-0.490359\pi\) | ||||
0.0302829 | + | 0.999541i | \(0.490359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.83759e12 | 0.264531 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.04024e12 | 0.0709427 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.08549e12 | −0.473037 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.47830e12 | −0.163708 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.59968e12 | 0.235278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.19943e12 | 0.594963 | 0.297482 | − | 0.954728i | \(-0.403853\pi\) | ||||
0.297482 | + | 0.954728i | \(0.403853\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.57679e12 | 0.416486 | 0.208243 | − | 0.978077i | \(-0.433225\pi\) | ||||
0.208243 | + | 0.978077i | \(0.433225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.80030e13 | −1.12817 | −0.564085 | − | 0.825717i | \(-0.690771\pi\) | ||||
−0.564085 | + | 0.825717i | \(0.690771\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.95536e12 | 0.183272 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.08737e13 | −1.89470 | −0.947350 | − | 0.320200i | \(-0.896250\pi\) | ||||
−0.947350 | + | 0.320200i | \(0.896250\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.22328e11 | 0.0554370 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.56359e13 | 0.930110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.37511e13 | −0.809573 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.26334e12 | 0.481495 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.77535e12 | −0.158424 | −0.0792118 | − | 0.996858i | \(-0.525240\pi\) | ||||
−0.0792118 | + | 0.996858i | \(0.525240\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 5.38106e12 | 0.297882 | 0.148941 | − | 0.988846i | \(-0.452414\pi\) | ||||
0.148941 | + | 0.988846i | \(0.452414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.61191e13 | −0.874347 | −0.437174 | − | 0.899377i | \(-0.644020\pi\) | ||||
−0.437174 | + | 0.899377i | \(0.644020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.20690e13 | 1.72198 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.10622e13 | 1.11958 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.99320e13 | −1.57509 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.57464e12 | 0.132785 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.53639e13 | 0.784483 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.29446e12 | −0.267645 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.35245e12 | 0.117740 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.50156e13 | −0.736734 | −0.368367 | − | 0.929681i | \(-0.620083\pi\) | ||||
−0.368367 | + | 0.929681i | \(0.620083\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 3.34324e13 | 1.59239 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.64583e13 | 1.70269 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.82600e13 | −1.30693 | −0.653464 | − | 0.756957i | \(-0.726685\pi\) | ||||
−0.653464 | + | 0.756957i | \(0.726685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.30528e12 | −0.105574 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.32625e12 | 0.332257 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.66135e12 | −0.0738927 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.74749e11 | −0.00769739 | −0.00384869 | − | 0.999993i | \(-0.501225\pi\) | ||||
−0.00384869 | + | 0.999993i | \(0.501225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.19199e13 | 1.82872 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.67543e11 | 0.0374821 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.04012e12 | −0.255987 | −0.127993 | − | 0.991775i | \(-0.540854\pi\) | ||||
−0.127993 | + | 0.991775i | \(0.540854\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 3.12353e13 | 1.28630 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.58008e13 | −1.85054 | −0.925269 | − | 0.379312i | \(-0.876161\pi\) | ||||
−0.925269 | + | 0.379312i | \(0.876161\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.78634e13 | −2.31583 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.41979e12 | −0.0959323 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.57835e13 | 0.619847 | 0.309924 | − | 0.950761i | \(-0.399696\pi\) | ||||
0.309924 | + | 0.950761i | \(0.399696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.90932e12 | 0.112121 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.07063e13 | −0.790533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.35722e13 | −0.513326 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.02334e13 | 0.383445 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.61550e13 | −0.594140 | −0.297070 | − | 0.954856i | \(-0.596009\pi\) | ||||
−0.297070 | + | 0.954856i | \(0.596009\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −2.64703e12 | −0.0946786 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.22726e13 | 1.13321 | 0.566603 | − | 0.823991i | \(-0.308257\pi\) | ||||
0.566603 | + | 0.823991i | \(0.308257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.00336e13 | 1.04493 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.09276e13 | 0.376716 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.11820e13 | 0.723561 | 0.361781 | − | 0.932263i | \(-0.382169\pi\) | ||||
0.361781 | + | 0.932263i | \(0.382169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.38295e12 | −0.147007 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 1.96081e12 | 0.0639977 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.15332e13 | 1.33127 | 0.665636 | − | 0.746277i | \(-0.268160\pi\) | ||||
0.665636 | + | 0.746277i | \(0.268160\pi\) | |||||||
\(998\) | 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.a.c.1.1 | 2 | ||
4.3 | odd | 2 | 400.10.a.l.1.2 | 2 | |||
5.2 | odd | 4 | 100.10.c.c.49.3 | 4 | |||
5.3 | odd | 4 | 100.10.c.c.49.2 | 4 | |||
5.4 | even | 2 | 20.10.a.b.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 180.10.a.e.1.2 | 2 | |||
20.3 | even | 4 | 400.10.c.l.49.3 | 4 | |||
20.7 | even | 4 | 400.10.c.l.49.2 | 4 | |||
20.19 | odd | 2 | 80.10.a.j.1.1 | 2 | |||
40.19 | odd | 2 | 320.10.a.l.1.2 | 2 | |||
40.29 | even | 2 | 320.10.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.10.a.b.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
80.10.a.j.1.1 | 2 | 20.19 | odd | 2 | |||
100.10.a.c.1.1 | 2 | 1.1 | even | 1 | trivial | ||
100.10.c.c.49.2 | 4 | 5.3 | odd | 4 | |||
100.10.c.c.49.3 | 4 | 5.2 | odd | 4 | |||
180.10.a.e.1.2 | 2 | 15.14 | odd | 2 | |||
320.10.a.l.1.2 | 2 | 40.19 | odd | 2 | |||
320.10.a.t.1.1 | 2 | 40.29 | even | 2 | |||
400.10.a.l.1.2 | 2 | 4.3 | odd | 2 | |||
400.10.c.l.49.2 | 4 | 20.7 | even | 4 | |||
400.10.c.l.49.3 | 4 | 20.3 | even | 4 |