Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,22,Mod(1,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.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: | \(201.223687887\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 4963x + 96223 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{5}\cdot 5\cdot 7 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-78.2002\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.39292e7 | 1.55378 | 0.776889 | − | 0.629638i | \(-0.216797\pi\) | ||||
0.776889 | + | 0.629638i | \(0.216797\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.28731e8 | −0.707466 | −0.353733 | − | 0.935346i | \(-0.615088\pi\) | ||||
−0.353733 | + | 0.935346i | \(0.615088\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.21955e11 | 1.41767 | 0.708835 | − | 0.705375i | \(-0.249221\pi\) | ||||
0.708835 | + | 0.705375i | \(0.249221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.33605e11 | 0.872346 | 0.436173 | − | 0.899863i | \(-0.356334\pi\) | ||||
0.436173 | + | 0.899863i | \(0.356334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.31741e13 | 1.58492 | 0.792461 | − | 0.609922i | \(-0.208799\pi\) | ||||
0.792461 | + | 0.609922i | \(0.208799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.18808e13 | 0.818747 | 0.409373 | − | 0.912367i | \(-0.365747\pi\) | ||||
0.409373 | + | 0.912367i | \(0.365747\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.40779e14 | −0.708589 | −0.354294 | − | 0.935134i | \(-0.615279\pi\) | ||||
−0.354294 | + | 0.935134i | \(0.615279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.74355e14 | 1.41423 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17115e15 | −0.516934 | −0.258467 | − | 0.966020i | \(-0.583217\pi\) | ||||
−0.258467 | + | 0.966020i | \(0.583217\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.57156e14 | 0.209742 | 0.104871 | − | 0.994486i | \(-0.466557\pi\) | ||||
0.104871 | + | 0.994486i | \(0.466557\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.79394e16 | −1.09925 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.53720e16 | −1.20932 | −0.604661 | − | 0.796483i | \(-0.706691\pi\) | ||||
−0.604661 | + | 0.796483i | \(0.706691\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.71456e17 | 1.99490 | 0.997451 | − | 0.0713504i | \(-0.0227309\pi\) | ||||
0.997451 | + | 0.0713504i | \(0.0227309\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.35679e17 | 0.957398 | 0.478699 | − | 0.877979i | \(-0.341108\pi\) | ||||
0.478699 | + | 0.877979i | \(0.341108\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.75514e17 | 1.59598 | 0.797991 | − | 0.602669i | \(-0.205896\pi\) | ||||
0.797991 | + | 0.602669i | \(0.205896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.78989e17 | −0.499492 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.62123e17 | 0.755673 | 0.377837 | − | 0.925872i | \(-0.376668\pi\) | ||||
0.377837 | + | 0.925872i | \(0.376668\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.13782e18 | 2.20274 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.87671e18 | −1.24217 | −0.621085 | − | 0.783743i | \(-0.713308\pi\) | ||||
−0.621085 | + | 0.783743i | \(0.713308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.59195e18 | 0.824202 | 0.412101 | − | 0.911138i | \(-0.364795\pi\) | ||||
0.412101 | + | 0.911138i | \(0.364795\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.47119e19 | 1.35543 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.78611e19 | −1.19708 | −0.598539 | − | 0.801094i | \(-0.704252\pi\) | ||||
−0.598539 | + | 0.801094i | \(0.704252\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.93629e19 | −1.07050 | −0.535250 | − | 0.844694i | \(-0.679783\pi\) | ||||
−0.535250 | + | 0.844694i | \(0.679783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.32585e18 | −0.226745 | −0.113373 | − | 0.993553i | \(-0.536165\pi\) | ||||
−0.113373 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.44812e19 | −1.00295 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.05718e19 | −0.838584 | −0.419292 | − | 0.907851i | \(-0.637722\pi\) | ||||
−0.419292 | + | 0.907851i | \(0.637722\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.11929e20 | −1.49924 | −0.749620 | − | 0.661869i | \(-0.769764\pi\) | ||||
−0.749620 | + | 0.661869i | \(0.769764\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.46988e20 | 2.46262 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.62972e20 | −0.893952 | −0.446976 | − | 0.894546i | \(-0.647499\pi\) | ||||
−0.446976 | + | 0.894546i | \(0.647499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.29260e20 | −0.617155 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.42397e20 | 1.27215 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.84293e20 | 0.529126 | 0.264563 | − | 0.964368i | \(-0.414772\pi\) | ||||
0.264563 | + | 0.964368i | \(0.414772\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.92132e21 | 1.73071 | 0.865356 | − | 0.501158i | \(-0.167092\pi\) | ||||
0.865356 | + | 0.501158i | \(0.167092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.06205e20 | 0.444456 | 0.222228 | − | 0.974995i | \(-0.428667\pi\) | ||||
0.222228 | + | 0.974995i | \(0.428667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.79821e20 | −0.383235 | −0.191618 | − | 0.981470i | \(-0.561373\pi\) | ||||
−0.191618 | + | 0.981470i | \(0.561373\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.58673e20 | −0.104658 | −0.0523291 | − | 0.998630i | \(-0.516664\pi\) | ||||
−0.0523291 | + | 0.998630i | \(0.516664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.56041e21 | −0.432428 | −0.216214 | − | 0.976346i | \(-0.569371\pi\) | ||||
−0.216214 | + | 0.976346i | \(0.569371\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.77651e21 | −1.10099 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.96557e21 | −1.12128 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.47267e21 | 1.00979 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.70164e21 | 0.643615 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.53317e21 | −0.612405 | −0.306202 | − | 0.951966i | \(-0.599058\pi\) | ||||
−0.306202 | + | 0.951966i | \(0.599058\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.41613e22 | 0.831291 | 0.415645 | − | 0.909527i | \(-0.363556\pi\) | ||||
0.415645 | + | 0.909527i | \(0.363556\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.15690e22 | −0.579236 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.76400e22 | −1.01385 | −0.506924 | − | 0.861991i | \(-0.669218\pi\) | ||||
−0.506924 | + | 0.861991i | \(0.669218\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.98007e21 | 0.0623770 | 0.0311885 | − | 0.999514i | \(-0.490071\pi\) | ||||
0.0311885 | + | 0.999514i | \(0.490071\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.28801e22 | 1.23670 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.97363e22 | −0.803200 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.76024e22 | −0.419268 | −0.209634 | − | 0.977780i | \(-0.567227\pi\) | ||||
−0.209634 | + | 0.977780i | \(0.567227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.72139e22 | 0.623465 | 0.311732 | − | 0.950170i | \(-0.399091\pi\) | ||||
0.311732 | + | 0.950170i | \(0.399091\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.24756e22 | 0.325892 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.89837e23 | 1.66508 | 0.832540 | − | 0.553965i | \(-0.186886\pi\) | ||||
0.832540 | + | 0.553965i | \(0.186886\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.44340e22 | 0.501302 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.59931e23 | 0.946158 | 0.473079 | − | 0.881020i | \(-0.343143\pi\) | ||||
0.473079 | + | 0.881020i | \(0.343143\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.26974e22 | −0.149965 | −0.0749825 | − | 0.997185i | \(-0.523890\pi\) | ||||
−0.0749825 | + | 0.997185i | \(0.523890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.90514e22 | −0.239012 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.17436e22 | 0.163822 | 0.0819111 | − | 0.996640i | \(-0.473898\pi\) | ||||
0.0819111 | + | 0.996640i | \(0.473898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.56553e23 | −1.00052 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.75079e22 | −0.0830167 | −0.0415084 | − | 0.999138i | \(-0.513216\pi\) | ||||
−0.0415084 | + | 0.999138i | \(0.513216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.65662e22 | −0.0720203 | −0.0360102 | − | 0.999351i | \(-0.511465\pi\) | ||||
−0.0360102 | + | 0.999351i | \(0.511465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.20015e24 | −1.87902 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.60664e24 | 2.24690 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.61401e23 | 0.516688 | 0.258344 | − | 0.966053i | \(-0.416823\pi\) | ||||
0.258344 | + | 0.966053i | \(0.416823\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.52365e23 | 0.253324 | 0.126662 | − | 0.991946i | \(-0.459574\pi\) | ||||
0.126662 | + | 0.991946i | \(0.459574\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.91314e23 | 0.640403 | 0.320202 | − | 0.947349i | \(-0.396249\pi\) | ||||
0.320202 | + | 0.947349i | \(0.396249\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.46245e24 | −1.79230 | −0.896150 | − | 0.443752i | \(-0.853647\pi\) | ||||
−0.896150 | + | 0.443752i | \(0.853647\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.19226e23 | 0.365713 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.81736e24 | 3.09964 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.66846e24 | 1.16071 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.79516e24 | −0.706542 | −0.353271 | − | 0.935521i | \(-0.614931\pi\) | ||||
−0.353271 | + | 0.935521i | \(0.614931\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.60347e24 | 1.48758 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.06079e23 | −0.148385 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.71236e24 | 1.38260 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.76539e24 | 0.829103 | 0.414551 | − | 0.910026i | \(-0.363939\pi\) | ||||
0.414551 | + | 0.910026i | \(0.363939\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.37475e24 | −1.53003 | −0.765016 | − | 0.644011i | \(-0.777269\pi\) | ||||
−0.765016 | + | 0.644011i | \(0.777269\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.14314e24 | 0.523710 | 0.261855 | − | 0.965107i | \(-0.415666\pi\) | ||||
0.261855 | + | 0.965107i | \(0.415666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.21087e24 | 0.584971 | 0.292486 | − | 0.956270i | \(-0.405518\pi\) | ||||
0.292486 | + | 0.956270i | \(0.405518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.95267e25 | 2.47980 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.27921e24 | 0.987036 | 0.493518 | − | 0.869736i | \(-0.335711\pi\) | ||||
0.493518 | + | 0.869736i | \(0.335711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.45105e24 | 0.141418 | 0.0707090 | − | 0.997497i | \(-0.477474\pi\) | ||||
0.0707090 | + | 0.997497i | \(0.477474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.46588e24 | −0.776099 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.48760e24 | 0.714231 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.04939e25 | −1.30332 | −0.651658 | − | 0.758513i | \(-0.725926\pi\) | ||||
−0.651658 | + | 0.758513i | \(0.725926\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.71686e25 | −1.00454 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.77825e25 | −0.882462 | −0.441231 | − | 0.897394i | \(-0.645458\pi\) | ||||
−0.441231 | + | 0.897394i | \(0.645458\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.87023e25 | 0.855554 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.76203e25 | 1.46517 | 0.732583 | − | 0.680678i | \(-0.238315\pi\) | ||||
0.732583 | + | 0.680678i | \(0.238315\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.26441e25 | 1.17415 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.82547e25 | 1.79033 | 0.895163 | − | 0.445739i | \(-0.147059\pi\) | ||||
0.895163 | + | 0.445739i | \(0.147059\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00531e25 | 1.13883 | 0.569414 | − | 0.822051i | \(-0.307170\pi\) | ||||
0.569414 | + | 0.822051i | \(0.307170\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.22407e25 | 2.00490 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.12820e25 | 1.15858 | 0.579292 | − | 0.815120i | \(-0.303329\pi\) | ||||
0.579292 | + | 0.815120i | \(0.303329\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.22313e25 | 0.237714 | 0.118857 | − | 0.992911i | \(-0.462077\pi\) | ||||
0.118857 | + | 0.992911i | \(0.462077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.45355e25 | 1.52504 | 0.762520 | − | 0.646964i | \(-0.223962\pi\) | ||||
0.762520 | + | 0.646964i | \(0.223962\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.06541e25 | −1.41133 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.04466e26 | 1.51198 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.19428e25 | 0.274905 | 0.137453 | − | 0.990508i | \(-0.456109\pi\) | ||||
0.137453 | + | 0.990508i | \(0.456109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.65463e26 | −1.93006 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.10422e25 | −0.618135 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.17375e25 | −0.677327 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.55801e26 | 1.28063 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.79642e25 | 0.291354 | 0.145677 | − | 0.989332i | \(-0.453464\pi\) | ||||
0.145677 | + | 0.989332i | \(0.453464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.02783e25 | −0.470801 | −0.235401 | − | 0.971898i | \(-0.575640\pi\) | ||||
−0.235401 | + | 0.971898i | \(0.575640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.09673e25 | −0.569731 | −0.284865 | − | 0.958568i | \(-0.591949\pi\) | ||||
−0.284865 | + | 0.958568i | \(0.591949\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.99033e25 | 0.163907 | 0.0819533 | − | 0.996636i | \(-0.473884\pi\) | ||||
0.0819533 | + | 0.996636i | \(0.473884\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.42828e26 | −0.732841 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.88260e26 | 1.29765 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.92404e26 | 1.23369 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.04292e26 | −1.12910 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.61150e25 | −0.230200 | −0.115100 | − | 0.993354i | \(-0.536719\pi\) | ||||
−0.115100 | + | 0.993354i | \(0.536719\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.06013e26 | −1.85999 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.11607e26 | −0.321793 | −0.160896 | − | 0.986971i | \(-0.551438\pi\) | ||||
−0.160896 | + | 0.986971i | \(0.551438\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.16730e26 | 0.297345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.42831e26 | 1.06084 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.94900e26 | 1.26178 | 0.630891 | − | 0.775872i | \(-0.282690\pi\) | ||||
0.630891 | + | 0.775872i | \(0.282690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.45113e26 | 0.888799 | 0.444400 | − | 0.895829i | \(-0.353417\pi\) | ||||
0.444400 | + | 0.895829i | \(0.353417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.37403e26 | −0.420584 | −0.210292 | − | 0.977639i | \(-0.567441\pi\) | ||||
−0.210292 | + | 0.977639i | \(0.567441\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.96262e26 | −1.66332 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.45652e26 | 0.513036 | 0.256518 | − | 0.966539i | \(-0.417425\pi\) | ||||
0.256518 | + | 0.966539i | \(0.417425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.35442e26 | −0.329654 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.82490e26 | −0.352312 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.76689e26 | −1.03241 | −0.516205 | − | 0.856465i | \(-0.672656\pi\) | ||||
−0.516205 | + | 0.856465i | \(0.672656\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.08705e26 | −0.534613 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.54618e27 | −1.53573 | −0.767867 | − | 0.640609i | \(-0.778682\pi\) | ||||
−0.767867 | + | 0.640609i | \(0.778682\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.07818e26 | −0.450945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.48367e27 | 1.24631 | 0.623156 | − | 0.782097i | \(-0.285850\pi\) | ||||
0.623156 | + | 0.782097i | \(0.285850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.86137e27 | −1.40038 | −0.700190 | − | 0.713956i | \(-0.746901\pi\) | ||||
−0.700190 | + | 0.713956i | \(0.746901\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.18780e27 | −1.55837 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.43791e26 | 0.283601 | 0.141801 | − | 0.989895i | \(-0.454711\pi\) | ||||
0.141801 | + | 0.989895i | \(0.454711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.85463e27 | −1.12306 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.39445e27 | −1.30297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.85978e26 | −0.199188 | −0.0995939 | − | 0.995028i | \(-0.531754\pi\) | ||||
−0.0995939 | + | 0.995028i | \(0.531754\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.65938e26 | 0.402227 | 0.201113 | − | 0.979568i | \(-0.435544\pi\) | ||||
0.201113 | + | 0.979568i | \(0.435544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.15028e26 | 0.182967 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.31378e27 | −1.71442 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.19682e26 | 0.233924 | 0.116962 | − | 0.993136i | \(-0.462684\pi\) | ||||
0.116962 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.57847e27 | 0.878793 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.19060e27 | −2.32948 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.87299e27 | 0.841562 | 0.420781 | − | 0.907162i | \(-0.361756\pi\) | ||||
0.420781 | + | 0.907162i | \(0.361756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.25957e27 | 0.629598 | 0.314799 | − | 0.949158i | \(-0.398063\pi\) | ||||
0.314799 | + | 0.949158i | \(0.398063\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.88404e27 | 2.24144 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.42791e27 | −0.583095 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.01840e27 | 0.657303 | 0.328652 | − | 0.944451i | \(-0.393406\pi\) | ||||
0.328652 | + | 0.944451i | \(0.393406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.44418e27 | 1.33673 | 0.668367 | − | 0.743832i | \(-0.266994\pi\) | ||||
0.668367 | + | 0.743832i | \(0.266994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.08034e27 | −0.580155 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.50049e27 | −1.52604 | −0.763021 | − | 0.646374i | \(-0.776285\pi\) | ||||
−0.763021 | + | 0.646374i | \(0.776285\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00246e27 | −0.979694 | −0.489847 | − | 0.871809i | \(-0.662947\pi\) | ||||
−0.489847 | + | 0.871809i | \(0.662947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.92243e27 | −1.38900 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.58205e27 | −1.21620 | −0.608100 | − | 0.793861i | \(-0.708068\pi\) | ||||
−0.608100 | + | 0.793861i | \(0.708068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.09098e28 | 2.82811 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.77863e27 | −0.958922 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.09251e28 | 1.28619 | 0.643093 | − | 0.765788i | \(-0.277651\pi\) | ||||
0.643093 | + | 0.765788i | \(0.277651\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.29500e27 | 0.783728 | 0.391864 | − | 0.920023i | \(-0.371830\pi\) | ||||
0.391864 | + | 0.920023i | \(0.371830\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.13930e28 | −1.16960 | −0.584800 | − | 0.811178i | \(-0.698827\pi\) | ||||
−0.584800 | + | 0.811178i | \(0.698827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.51114e28 | −1.41735 | −0.708677 | − | 0.705533i | \(-0.750708\pi\) | ||||
−0.708677 | + | 0.705533i | \(0.750708\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.44371e27 | 0.846892 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.65466e28 | 1.35727 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.47554e28 | 1.15789 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.89042e27 | −0.279559 | −0.139779 | − | 0.990183i | \(-0.544639\pi\) | ||||
−0.139779 | + | 0.990183i | \(0.544639\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.53375e28 | −1.05495 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.30388e28 | 0.822145 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.89704e28 | 1.14557 | 0.572787 | − | 0.819704i | \(-0.305862\pi\) | ||||
0.572787 | + | 0.819704i | \(0.305862\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.33589e28 | 0.740313 | 0.370157 | − | 0.928969i | \(-0.379304\pi\) | ||||
0.370157 | + | 0.928969i | \(0.379304\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.54289e28 | −0.819300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.55251e28 | 0.757343 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.86135e28 | −1.33818 | −0.669090 | − | 0.743181i | \(-0.733316\pi\) | ||||
−0.669090 | + | 0.743181i | \(0.733316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.44655e27 | −0.406265 | −0.203133 | − | 0.979151i | \(-0.565112\pi\) | ||||
−0.203133 | + | 0.979151i | \(0.565112\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.51888e28 | 2.68914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.06060e28 | −0.782452 | −0.391226 | − | 0.920295i | \(-0.627949\pi\) | ||||
−0.391226 | + | 0.920295i | \(0.627949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.40214e27 | 0.160415 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.05681e28 | 0.690586 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.01865e28 | 2.26258 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.30969e28 | 1.28130 | 0.640649 | − | 0.767834i | \(-0.278665\pi\) | ||||
0.640649 | + | 0.767834i | \(0.278665\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.08864e28 | 0.310897 | 0.155448 | − | 0.987844i | \(-0.450318\pi\) | ||||
0.155448 | + | 0.987844i | \(0.450318\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.26097e28 | 0.332425 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.96530e28 | −0.497902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.43441e28 | 1.74025 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.64587e28 | −0.595462 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.40240e28 | −0.708114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.99516e28 | 0.799765 | 0.399883 | − | 0.916566i | \(-0.369051\pi\) | ||||
0.399883 | + | 0.916566i | \(0.369051\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.77658e27 | −0.162616 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.58498e28 | −0.995760 | −0.497880 | − | 0.867246i | \(-0.665888\pi\) | ||||
−0.497880 | + | 0.867246i | \(0.665888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.56257e28 | −0.423238 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.73135e28 | 0.593270 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.87710e28 | 1.30855 | 0.654277 | − | 0.756255i | \(-0.272973\pi\) | ||||
0.654277 | + | 0.756255i | \(0.272973\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.88309e28 | 0.835183 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.63115e28 | −1.00520 | −0.502599 | − | 0.864520i | \(-0.667623\pi\) | ||||
−0.502599 | + | 0.864520i | \(0.667623\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.29434e28 | −0.671898 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.48073e29 | −1.74500 | −0.872502 | − | 0.488610i | \(-0.837504\pi\) | ||||
−0.872502 | + | 0.488610i | \(0.837504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.51419e28 | −0.853499 | −0.426749 | − | 0.904370i | \(-0.640341\pi\) | ||||
−0.426749 | + | 0.904370i | \(0.640341\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.49348e28 | −1.00210 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.56608e28 | 0.159392 | 0.0796961 | − | 0.996819i | \(-0.474605\pi\) | ||||
0.0796961 | + | 0.996819i | \(0.474605\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.12054e29 | 1.06066 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17335e29 | 1.07129 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.19163e29 | −1.01260 | −0.506302 | − | 0.862356i | \(-0.668988\pi\) | ||||
−0.506302 | + | 0.862356i | \(0.668988\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.09433e28 | 0.171725 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.34770e28 | −0.255666 | −0.127833 | − | 0.991796i | \(-0.540802\pi\) | ||||
−0.127833 | + | 0.991796i | \(0.540802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.36337e29 | −1.74222 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.39785e29 | −0.960461 | −0.480231 | − | 0.877142i | \(-0.659447\pi\) | ||||
−0.480231 | + | 0.877142i | \(0.659447\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.02954e27 | −0.00683061 | −0.00341531 | − | 0.999994i | \(-0.501087\pi\) | ||||
−0.00341531 | + | 0.999994i | \(0.501087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.53542e29 | 1.56898 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.61045e29 | 0.962647 | 0.481323 | − | 0.876543i | \(-0.340156\pi\) | ||||
0.481323 | + | 0.876543i | \(0.340156\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.49546e29 | 1.39225 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.08394e29 | −0.584345 | −0.292173 | − | 0.956366i | \(-0.594378\pi\) | ||||
−0.292173 | + | 0.956366i | \(0.594378\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.69220e29 | 0.852033 | 0.426017 | − | 0.904715i | \(-0.359916\pi\) | ||||
0.426017 | + | 0.904715i | \(0.359916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.72000e28 | 0.229715 | 0.114858 | − | 0.993382i | \(-0.463359\pi\) | ||||
0.114858 | + | 0.993382i | \(0.463359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.39041e29 | 0.632441 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.41762e28 | −0.414191 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.65995e29 | −1.91668 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.15217e29 | −1.65184 | −0.825918 | − | 0.563790i | \(-0.809343\pi\) | ||||
−0.825918 | + | 0.563790i | \(0.809343\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.55595e29 | −0.951541 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.20971e29 | −0.435730 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.51731e28 | −0.321000 | −0.160500 | − | 0.987036i | \(-0.551311\pi\) | ||||
−0.160500 | + | 0.987036i | \(0.551311\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.25707e29 | −1.06319 | −0.531596 | − | 0.846998i | \(-0.678408\pi\) | ||||
−0.531596 | + | 0.846998i | \(0.678408\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.06325e28 | 0.0936888 | 0.0468444 | − | 0.998902i | \(-0.485084\pi\) | ||||
0.0468444 | + | 0.998902i | \(0.485084\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.94737e29 | −1.76099 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.66491e28 | 0.240534 | 0.120267 | − | 0.992742i | \(-0.461625\pi\) | ||||
0.120267 | + | 0.992742i | \(0.461625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.80480e29 | 1.29164 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.32944e29 | −1.84831 | −0.924154 | − | 0.382021i | \(-0.875228\pi\) | ||||
−0.924154 | + | 0.382021i | \(0.875228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.06204e29 | −1.23655 | −0.618273 | − | 0.785964i | \(-0.712167\pi\) | ||||
−0.618273 | + | 0.785964i | \(0.712167\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.92529e29 | −0.900004 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.64873e29 | 0.366293 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.60009e29 | 1.16845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.74688e29 | 0.959953 | 0.479977 | − | 0.877281i | \(-0.340645\pi\) | ||||
0.479977 | + | 0.877281i | \(0.340645\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.45182e29 | −1.22603 | −0.613015 | − | 0.790071i | \(-0.710044\pi\) | ||||
−0.613015 | + | 0.790071i | \(0.710044\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.03188e29 | −0.374339 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.14621e29 | 0.891394 | 0.445697 | − | 0.895184i | \(-0.352956\pi\) | ||||
0.445697 | + | 0.895184i | \(0.352956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.37805e29 | −1.57529 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.17181e29 | 0.659209 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.06801e30 | −1.63702 | −0.818512 | − | 0.574489i | \(-0.805201\pi\) | ||||
−0.818512 | + | 0.574489i | \(0.805201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.71821e28 | 0.0969199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.25878e30 | 3.16177 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.04529e30 | 1.37784 | 0.688919 | − | 0.724839i | \(-0.258086\pi\) | ||||
0.688919 | + | 0.724839i | \(0.258086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.73967e29 | −0.990128 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.01586e30 | −1.22442 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.68030e28 | 0.101566 | 0.0507831 | − | 0.998710i | \(-0.483828\pi\) | ||||
0.0507831 | + | 0.998710i | \(0.483828\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.34747e29 | −0.148621 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.79418e30 | 1.92155 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.16156e30 | 1.17325 | 0.586624 | − | 0.809859i | \(-0.300457\pi\) | ||||
0.586624 | + | 0.809859i | \(0.300457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.20520e29 | −0.314438 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.89774e29 | −0.731061 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.77822e29 | 0.249836 | 0.124918 | − | 0.992167i | \(-0.460133\pi\) | ||||
0.124918 | + | 0.992167i | \(0.460133\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.78745e30 | 1.51740 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.16010e30 | 1.78189 | 0.890947 | − | 0.454107i | \(-0.150042\pi\) | ||||
0.890947 | + | 0.454107i | \(0.150042\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.17824e30 | −1.69706 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.74302e30 | 1.31988 | 0.659942 | − | 0.751317i | \(-0.270581\pi\) | ||||
0.659942 | + | 0.751317i | \(0.270581\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.89639e29 | 0.421895 | 0.210947 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210947 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.36530e29 | −0.651449 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.12316e29 | 0.271126 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.31754e28 | −0.0531833 | −0.0265917 | − | 0.999646i | \(-0.508465\pi\) | ||||
−0.0265917 | + | 0.999646i | \(0.508465\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.60193e30 | 0.968726 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.67582e29 | −0.157380 | −0.0786902 | − | 0.996899i | \(-0.525074\pi\) | ||||
−0.0786902 | + | 0.996899i | \(0.525074\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.95107e30 | −1.64225 | −0.821127 | − | 0.570745i | \(-0.806654\pi\) | ||||
−0.821127 | + | 0.570745i | \(0.806654\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.36769e29 | 0.0740421 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.11457e30 | −1.08360 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.62362e30 | −1.30820 | −0.654100 | − | 0.756408i | \(-0.726953\pi\) | ||||
−0.654100 | + | 0.756408i | \(0.726953\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.36482e29 | −0.442196 | −0.221098 | − | 0.975252i | \(-0.570964\pi\) | ||||
−0.221098 | + | 0.975252i | \(0.570964\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.45464e29 | 0.296622 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.75158e30 | 1.63332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.58094e30 | −1.51762 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.44103e30 | 2.58716 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.42850e30 | 0.949736 | 0.474868 | − | 0.880057i | \(-0.342496\pi\) | ||||
0.474868 | + | 0.880057i | \(0.342496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.25036e29 | 0.305929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.99109e30 | 0.718990 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.99411e29 | 0.0683025 | 0.0341513 | − | 0.999417i | \(-0.489127\pi\) | ||||
0.0341513 | + | 0.999417i | \(0.489127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.58189e30 | 2.52951 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.01537e30 | −0.321450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.52549e30 | 0.778913 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.77765e30 | −1.10602 | −0.553010 | − | 0.833175i | \(-0.686521\pi\) | ||||
−0.553010 | + | 0.833175i | \(0.686521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.72778e30 | 0.778199 | 0.389099 | − | 0.921196i | \(-0.372786\pi\) | ||||
0.389099 | + | 0.921196i | \(0.372786\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.42635e30 | 1.47012 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.96875e30 | 0.783867 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.90653e30 | 0.478234 | 0.239117 | − | 0.970991i | \(-0.423142\pi\) | ||||
0.239117 | + | 0.970991i | \(0.423142\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.39146e30 | −0.829255 | −0.414628 | − | 0.909991i | \(-0.636088\pi\) | ||||
−0.414628 | + | 0.909991i | \(0.636088\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.99616e30 | 0.928613 | 0.464307 | − | 0.885675i | \(-0.346304\pi\) | ||||
0.464307 | + | 0.885675i | \(0.346304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.80835e30 | −0.636251 | −0.318126 | − | 0.948049i | \(-0.603053\pi\) | ||||
−0.318126 | + | 0.948049i | \(0.603053\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.67544e30 | −0.791656 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.10940e30 | −0.233012 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.63065e30 | −1.12475 | −0.562377 | − | 0.826881i | \(-0.690113\pi\) | ||||
−0.562377 | + | 0.826881i | \(0.690113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.76124e30 | −0.732779 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.00357e30 | −0.371372 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.95103e30 | −0.714389 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.97962e30 | 0.856911 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.25429e30 | 0.714269 | 0.357135 | − | 0.934053i | \(-0.383754\pi\) | ||||
0.357135 | + | 0.934053i | \(0.383754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.42388e29 | 0.0866984 | 0.0433492 | − | 0.999060i | \(-0.486197\pi\) | ||||
0.0433492 | + | 0.999060i | \(0.486197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.77718e30 | −0.589169 | −0.294585 | − | 0.955625i | \(-0.595181\pi\) | ||||
−0.294585 | + | 0.955625i | \(0.595181\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.65328e30 | −1.43404 | −0.717021 | − | 0.697052i | \(-0.754495\pi\) | ||||
−0.717021 | + | 0.697052i | \(0.754495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.75562e30 | 0.254543 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.60655e30 | −1.18883 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.74465e30 | −1.04427 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.54337e30 | −0.455336 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.26757e30 | −1.03725 | −0.518623 | − | 0.855003i | \(-0.673555\pi\) | ||||
−0.518623 | + | 0.855003i | \(0.673555\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.71573e30 | −0.444423 | −0.222212 | − | 0.974998i | \(-0.571328\pi\) | ||||
−0.222212 | + | 0.974998i | \(0.571328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.53555e29 | 0.0412923 | 0.0206462 | − | 0.999787i | \(-0.493428\pi\) | ||||
0.0206462 | + | 0.999787i | \(0.493428\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.78376e28 | −0.00866944 | −0.00433472 | − | 0.999991i | \(-0.501380\pi\) | ||||
−0.00433472 | + | 0.999991i | \(0.501380\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.98302e30 | 0.433256 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.25927e31 | 1.30671 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.27261e30 | −0.128990 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.12098e30 | −0.108423 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26751e31 | 1.19768 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.24066e30 | −0.111904 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.49286e30 | 0.660345 | 0.330173 | − | 0.943921i | \(-0.392893\pi\) | ||||
0.330173 | + | 0.943921i | \(0.392893\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.85880e31 | −1.56419 | −0.782096 | − | 0.623159i | \(-0.785849\pi\) | ||||
−0.782096 | + | 0.623159i | \(0.785849\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.58457e31 | −2.12543 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.48750e30 | −0.588110 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.21998e31 | −0.936573 | −0.468286 | − | 0.883577i | \(-0.655128\pi\) | ||||
−0.468286 | + | 0.883577i | \(0.655128\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.27319e31 | −0.933847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.38533e31 | −1.71025 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.53725e31 | 1.05337 | 0.526684 | − | 0.850061i | \(-0.323435\pi\) | ||||
0.526684 | + | 0.850061i | \(0.323435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.10449e30 | −0.408957 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.45122e31 | 3.49118 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.67237e31 | 1.04729 | 0.523645 | − | 0.851937i | \(-0.324572\pi\) | ||||
0.523645 | + | 0.851937i | \(0.324572\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.77704e30 | −0.166299 | −0.0831497 | − | 0.996537i | \(-0.526498\pi\) | ||||
−0.0831497 | + | 0.996537i | \(0.526498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.41373e31 | −1.41357 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.06419e30 | −0.0596132 | −0.0298066 | − | 0.999556i | \(-0.509489\pi\) | ||||
−0.0298066 | + | 0.999556i | \(0.509489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.61013e30 | −0.197800 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.76399e31 | −1.44897 | −0.724487 | − | 0.689289i | \(-0.757923\pi\) | ||||
−0.724487 | + | 0.689289i | \(0.757923\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.56550e31 | 0.802818 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.46142e31 | 0.717263 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.99094e31 | −0.956008 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.56254e30 | 0.393610 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.28234e31 | 0.576800 | 0.288400 | − | 0.957510i | \(-0.406877\pi\) | ||||
0.288400 | + | 0.957510i | \(0.406877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.42766e30 | −0.319926 | −0.159963 | − | 0.987123i | \(-0.551138\pi\) | ||||
−0.159963 | + | 0.987123i | \(0.551138\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.04692e30 | −0.0441296 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.93176e31 | 1.18368 | 0.591842 | − | 0.806054i | \(-0.298401\pi\) | ||||
0.591842 | + | 0.806054i | \(0.298401\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.20706e31 | −1.26733 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.75461e31 | −1.80013 | −0.900064 | − | 0.435758i | \(-0.856480\pi\) | ||||
−0.900064 | + | 0.435758i | \(0.856480\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.68487e31 | 0.995044 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.91006e31 | −0.678401 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.88614e31 | 1.69900 | 0.849498 | − | 0.527592i | \(-0.176905\pi\) | ||||
0.849498 | + | 0.527592i | \(0.176905\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.35491e31 | −2.78484 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.22919e31 | 1.70661 | 0.853306 | − | 0.521410i | \(-0.174594\pi\) | ||||
0.853306 | + | 0.521410i | \(0.174594\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 72.22.a.f.1.3 | 3 | ||
3.2 | odd | 2 | 8.22.a.b.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 16.22.a.f.1.3 | 3 | |||
24.5 | odd | 2 | 64.22.a.l.1.3 | 3 | |||
24.11 | even | 2 | 64.22.a.m.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.22.a.b.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
16.22.a.f.1.3 | 3 | 12.11 | even | 2 | |||
64.22.a.l.1.3 | 3 | 24.5 | odd | 2 | |||
64.22.a.m.1.1 | 3 | 24.11 | even | 2 | |||
72.22.a.f.1.3 | 3 | 1.1 | even | 1 | trivial |