Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(209,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.10070523904.11 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.8 | ||
Root | \(-1.68014 + 0.420861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.209 |
Dual form | 1680.2.k.e.209.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.68014 | + | 0.420861i | 0.970030 | + | 0.242984i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.08495 | + | 1.95522i | −0.485206 | + | 0.874400i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.595188 | + | 2.57794i | −0.224960 | + | 0.974368i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.64575 | + | 1.41421i | 0.881917 | + | 0.471405i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.36028 | 0.931975 | 0.465987 | − | 0.884791i | \(-0.345699\pi\) | ||||
0.465987 | + | 0.884791i | \(0.345699\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.64575 | + | 2.82843i | −0.683130 | + | 0.730297i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.75216i | − | 1.15257i | −0.817250 | − | 0.576284i | \(-0.804502\pi\) | ||
0.817250 | − | 0.576284i | \(-0.195498\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.59388i | 1.28332i | 0.766987 | + | 0.641662i | \(0.221755\pi\) | ||||
−0.766987 | + | 0.641662i | \(0.778245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08495 | + | 4.08080i | −0.454974 | + | 0.890505i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.29150 | −1.52038 | −0.760192 | − | 0.649699i | \(-0.774895\pi\) | ||||
−0.760192 | + | 0.649699i | \(0.774895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.64575 | − | 4.24264i | −0.529150 | − | 0.848528i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.85005 | + | 3.48957i | 0.740942 | + | 0.671569i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.500983i | 0.0930303i | 0.998918 | + | 0.0465151i | \(0.0148116\pi\) | ||||
−0.998918 | + | 0.0465151i | \(0.985188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.06871i | − | 0.551157i | −0.961279 | − | 0.275578i | \(-0.911131\pi\) | ||
0.961279 | − | 0.275578i | \(-0.0888694\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.19038 | + | 4.75216i | −0.207218 | + | 0.827245i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.39467 | − | 3.96066i | −0.742835 | − | 0.669474i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.32941i | 0.547352i | 0.961822 | + | 0.273676i | \(0.0882396\pi\) | ||||
−0.961822 | + | 0.273676i | \(0.911760\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.64575 | + | 1.41421i | 0.904044 | + | 0.226455i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.33981 | 0.677765 | 0.338883 | − | 0.940829i | \(-0.389951\pi\) | ||||
0.338883 | + | 0.940829i | \(0.389951\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.3117i | − | 1.57253i | −0.617892 | − | 0.786263i | \(-0.712013\pi\) | ||
0.617892 | − | 0.786263i | \(-0.287987\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.63561 | + | 3.63866i | −0.840108 | + | 0.542420i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.82087i | 1.14079i | 0.821370 | + | 0.570396i | \(0.193210\pi\) | ||||
−0.821370 | + | 0.570396i | \(0.806790\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.29150 | − | 3.06871i | −0.898786 | − | 0.438387i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | − | 7.98430i | 0.280056 | − | 1.11803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.58301 | −1.17897 | −0.589483 | − | 0.807781i | \(-0.700669\pi\) | ||||
−0.589483 | + | 0.807781i | \(0.700669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.53019 | − | 3.06871i | −0.745691 | − | 0.413785i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.35425 | + | 9.39851i | −0.311828 | + | 1.24486i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.16991 | 0.282498 | 0.141249 | − | 0.989974i | \(-0.454888\pi\) | ||||
0.141249 | + | 0.989974i | \(0.454888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.52517i | 0.323315i | 0.986847 | + | 0.161657i | \(0.0516839\pi\) | ||||
−0.986847 | + | 0.161657i | \(0.948316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.22047 | + | 5.97885i | −0.657717 | + | 0.753265i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.64575 | + | 6.57008i | −0.452200 | + | 0.814919i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3117i | 1.25978i | 0.776684 | + | 0.629890i | \(0.216900\pi\) | ||||
−0.776684 | + | 0.629890i | \(0.783100\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.2508 | − | 3.06871i | −1.47482 | − | 0.369430i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.81076i | 1.16432i | 0.813073 | + | 0.582161i | \(0.197793\pi\) | ||||
−0.813073 | + | 0.582161i | \(0.802207\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.53019 | 0.647260 | 0.323630 | − | 0.946184i | \(-0.395097\pi\) | ||||
0.323630 | + | 0.946184i | \(0.395097\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.65967 | − | 8.24173i | −0.307113 | − | 0.951673i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.29150 | − | 1.68345i | −0.830944 | − | 0.191846i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.29150 | −0.370323 | −0.185161 | − | 0.982708i | \(-0.559281\pi\) | ||||
−0.185161 | + | 0.982708i | \(0.559281\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | + | 7.48331i | 0.555556 | + | 0.831479i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.97915i | − | 0.766061i | −0.923736 | − | 0.383030i | \(-0.874880\pi\) | ||
0.923736 | − | 0.383030i | \(-0.125120\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.29150 | + | 5.15587i | 1.00780 | + | 0.559233i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.210845 | + | 0.841723i | −0.0226049 | + | 0.0902422i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8219 | 1.67712 | 0.838558 | − | 0.544812i | \(-0.183399\pi\) | ||||
0.838558 | + | 0.544812i | \(0.183399\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | + | 8.66259i | −0.209657 | + | 0.908086i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.29150 | − | 5.15587i | 0.133923 | − | 0.534639i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.9373 | − | 6.06910i | −1.12214 | − | 0.622677i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.6315 | −1.48560 | −0.742802 | − | 0.669511i | \(-0.766504\pi\) | ||||
−0.742802 | + | 0.669511i | \(0.766504\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | + | 7.48331i | −0.402015 | + | 0.752101i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.16991 | 0.215914 | 0.107957 | − | 0.994156i | \(-0.465569\pi\) | ||||
0.107957 | + | 0.994156i | \(0.465569\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.14944 | 0.310323 | 0.155162 | − | 0.987889i | \(-0.450410\pi\) | ||||
0.155162 | + | 0.987889i | \(0.450410\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.71678 | − | 8.50402i | −0.557901 | − | 0.829908i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.40122 | + | 5.59388i | −0.132998 | + | 0.530948i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.91094 | − | 14.2565i | 0.737699 | − | 1.32942i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.89047 | + | 4.75216i | 0.821925 | + | 0.439337i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.2508 | + | 2.82843i | 1.12303 | + | 0.259281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.29150 | + | 1.82646i | 0.657453 | + | 0.164686i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1658 | − | 0.569951i | 0.998700 | − | 0.0509780i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.32941i | 0.295437i | 0.989029 | + | 0.147719i | \(0.0471930\pi\) | ||||
−0.989029 | + | 0.147719i | \(0.952807\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.33981 | − | 17.3252i | 0.382099 | − | 1.52540i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.9918 | 1.57195 | 0.785975 | − | 0.618258i | \(-0.212161\pi\) | ||||
0.785975 | + | 0.618258i | \(0.212161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.4207 | − | 3.32941i | −1.25043 | − | 0.288696i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.0000 | + | 3.74166i | −0.946729 | + | 0.322031i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.29150 | 0.110341 | 0.0551703 | − | 0.998477i | \(-0.482430\pi\) | ||||
0.0551703 | + | 0.998477i | \(0.482430\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.543544i | 0.0461028i | 0.999734 | + | 0.0230514i | \(0.00733813\pi\) | ||||
−0.999734 | + | 0.0230514i | \(0.992662\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.29150 | + | 13.1402i | −0.277195 | + | 1.10660i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.50432i | 0.794791i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.979531 | − | 0.543544i | −0.0813457 | − | 0.0451388i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.27911 | − | 7.80372i | −0.765328 | − | 0.643640i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.8127i | 0.885813i | 0.896568 | + | 0.442906i | \(0.146053\pi\) | ||||
−0.896568 | + | 0.442906i | \(0.853947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.41699 | 0.115313 | 0.0576567 | − | 0.998336i | \(-0.481637\pi\) | ||||
0.0576567 | + | 0.998336i | \(0.481637\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.72057 | − | 12.5730i | 0.543326 | − | 1.01647i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | + | 3.32941i | 0.481932 | + | 0.267425i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3797 | 1.30724 | 0.653622 | − | 0.756821i | \(-0.273249\pi\) | ||||
0.653622 | + | 0.756821i | \(0.273249\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.4207 | − | 3.61226i | −1.14363 | − | 0.286471i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.33981 | − | 18.7970i | 0.342025 | − | 1.48141i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | − | 7.48331i | −0.622799 | − | 0.582575i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.6921i | − | 1.60120i | −0.599198 | − | 0.800601i | \(-0.704514\pi\) | ||
0.599198 | − | 0.800601i | \(-0.295486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.70850 | −0.131423 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.91094 | + | 14.8000i | −0.604965 | + | 1.13179i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.22699i | − | 0.169315i | −0.996410 | − | 0.0846574i | \(-0.973020\pi\) | ||
0.996410 | − | 0.0846574i | \(-0.0269796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5120 | − | 4.29541i | 0.945816 | − | 0.324702i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.64575 | + | 0.913230i | 0.274031 | + | 0.0686426i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 24.4539i | − | 1.82777i | −0.405975 | − | 0.913884i | \(-0.633068\pi\) | ||
0.405975 | − | 0.913884i | \(-0.366932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8000i | 1.10008i | 0.835139 | + | 0.550038i | \(0.185387\pi\) | ||||
−0.835139 | + | 0.550038i | \(0.814613\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.06275 | + | 4.24264i | −0.0785604 | + | 0.313625i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.50972 | − | 3.61226i | −0.478604 | − | 0.265578i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.4411 | 0.982913 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.2874 | + | 7.84823i | −0.821037 | + | 0.570874i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.500983i | − | 0.0362499i | −0.999836 | − | 0.0181249i | \(-0.994230\pi\) | ||
0.999836 | − | 0.0181249i | \(-0.00576966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48528i | 0.610784i | 0.952227 | + | 0.305392i | \(0.0987875\pi\) | ||||
−0.952227 | + | 0.305392i | \(0.901213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.89047 | + | 9.50432i | −0.636660 | + | 0.680618i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.20614i | − | 0.652606i | −0.945265 | − | 0.326303i | \(-0.894197\pi\) | ||
0.945265 | − | 0.326303i | \(-0.105803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.33981 | + | 17.3252i | −0.306107 | + | 1.22202i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.29150 | − | 0.298179i | −0.0906457 | − | 0.0209281i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.70850 | + | 8.48528i | −0.328856 | + | 0.592638i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.2915 | − | 10.3117i | −1.34085 | − | 0.716716i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.8219 | −1.09442 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.1660 | 1.45713 | 0.728564 | − | 0.684978i | \(-0.240188\pi\) | ||||
0.728564 | + | 0.684978i | \(0.240188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.12897 | + | 16.4835i | −0.282912 | + | 1.12943i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.1617 | + | 11.1878i | 1.37502 | + | 0.762999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.91094 | + | 1.82646i | 0.537030 | + | 0.123988i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.29150 | + | 2.32744i | 0.627862 | + | 0.157274i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 15.9686i | − | 1.07416i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.19038 | −0.0797135 | −0.0398567 | − | 0.999205i | \(-0.512690\pi\) | ||||
−0.0398567 | + | 0.999205i | \(0.512690\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | − | 14.9666i | −0.0666667 | − | 0.997775i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 18.1669i | − | 1.20578i | −0.797824 | − | 0.602890i | \(-0.794016\pi\) | ||
0.797824 | − | 0.602890i | \(-0.205984\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.9007i | − | 1.64548i | −0.568415 | − | 0.822742i | \(-0.692443\pi\) | ||
0.568415 | − | 0.822742i | \(-0.307557\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.5423 | − | 5.89714i | −0.759425 | − | 0.388003i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2915 | 0.870755 | 0.435378 | − | 0.900248i | \(-0.356615\pi\) | ||||
0.435378 | + | 0.900248i | \(0.356615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.2915 | − | 8.48528i | −0.997508 | − | 0.553519i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.53019 | − | 1.38527i | −0.359224 | − | 0.0899827i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6431i | 0.947185i | 0.880744 | + | 0.473592i | \(0.157043\pi\) | ||||
−0.880744 | + | 0.473592i | \(0.842957\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.3252i | 1.11601i | 0.829836 | + | 0.558007i | \(0.188434\pi\) | ||||
−0.829836 | + | 0.558007i | \(0.811566\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.25127 | + | 14.6773i | 0.336869 | + | 0.941551i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.8260 | − | 8.97185i | 0.819422 | − | 0.573190i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.7970i | 1.19603i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.93725 | − | 11.7260i | 0.186141 | − | 0.743102i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.50972 | −0.410890 | −0.205445 | − | 0.978669i | \(-0.565864\pi\) | ||||
−0.205445 | + | 0.978669i | \(0.565864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 20.6235i | − | 1.29659i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.4411 | + | 12.5730i | 0.841716 | + | 0.787354i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7105i | 1.16713i | 0.812068 | + | 0.583563i | \(0.198342\pi\) | ||||
−0.812068 | + | 0.583563i | \(0.801658\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.58301 | − | 1.98162i | −0.533322 | − | 0.123132i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.708497 | + | 1.32548i | −0.0438549 | + | 0.0820450i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.5830 | −0.899227 | −0.449613 | − | 0.893223i | \(-0.648438\pi\) | ||||
−0.449613 | + | 0.893223i | \(0.648438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.31216 | − | 16.7816i | 0.572042 | − | 1.03089i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.5830 | + | 6.65882i | 1.62685 | + | 0.407513i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.31216 | 0.567773 | 0.283886 | − | 0.958858i | \(-0.408376\pi\) | ||||
0.283886 | + | 0.958858i | \(0.408376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3939i | 1.23884i | 0.785059 | + | 0.619421i | \(0.212632\pi\) | ||||
−0.785059 | + | 0.619421i | \(0.787368\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.00603 | + | 13.7127i | −0.424024 | + | 0.829928i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0000 | − | 7.48331i | 0.723627 | − | 0.451261i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.98233i | 0.419528i | 0.977752 | + | 0.209764i | \(0.0672695\pi\) | ||||
−0.977752 | + | 0.209764i | \(0.932730\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.33981 | − | 8.11905i | 0.259818 | − | 0.486075i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.30978i | 0.555375i | 0.960672 | + | 0.277687i | \(0.0895679\pi\) | ||||
−0.960672 | + | 0.277687i | \(0.910432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32.2016 | −1.91419 | −0.957094 | − | 0.289779i | \(-0.906418\pi\) | ||||
−0.957094 | + | 0.289779i | \(0.906418\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.8219 | − | 14.8000i | −0.937208 | − | 0.876677i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.58301 | + | 11.1878i | −0.152470 | + | 0.660393i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.58301 | −0.328412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.5830 | − | 6.15784i | −1.44108 | − | 0.360979i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.27733i | − | 0.425146i | −0.977145 | − | 0.212573i | \(-0.931816\pi\) | ||
0.977145 | − | 0.212573i | \(-0.0681843\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.35425 | + | 4.24264i | −0.137070 | + | 0.247016i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.87000 | + | 10.8896i | −0.572716 | + | 0.631878i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.5015 | −1.41696 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.5830 | + | 6.13742i | 1.53222 | + | 0.353755i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.64575 | + | 0.913230i | 0.209443 | + | 0.0524637i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.93725 | − | 2.73969i | −0.282706 | − | 0.156874i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0399 | −0.687154 | −0.343577 | − | 0.939124i | \(-0.611639\pi\) | ||||
−0.343577 | + | 0.939124i | \(0.611639\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.29150 | + | 1.32548i | 0.301023 | + | 0.0754038i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.5015 | 1.38935 | 0.694677 | − | 0.719322i | \(-0.255547\pi\) | ||||
0.694677 | + | 0.719322i | \(0.255547\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6315 | −0.827022 | −0.413511 | − | 0.910499i | \(-0.635698\pi\) | ||||
−0.413511 | + | 0.910499i | \(0.635698\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.02599 | − | 16.6939i | −0.339526 | − | 0.940597i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.41699 | −0.0793365 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.5830 | 1.47912 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.89047 | − | 14.2565i | −0.493155 | − | 0.790807i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.36028 | + | 0.841723i | 0.185824 | + | 0.0465474i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.1617 | − | 4.65489i | −1.11155 | − | 0.256632i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.70850 | + | 8.80879i | −0.258024 | + | 0.482719i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.1617 | − | 11.1878i | −1.10155 | − | 0.611253i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.4499i | − | 1.22293i | −0.791273 | − | 0.611463i | \(-0.790581\pi\) | ||
0.791273 | − | 0.611463i | \(-0.209419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.0808 | − | 2.52517i | −0.547517 | − | 0.137148i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.67963 | 0.470028 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.6556 | − | 14.3926i | 0.629342 | − | 0.777129i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.2915 | − | 20.6235i | 1.03862 | − | 1.11033i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0000 | 1.28839 | 0.644194 | − | 0.764862i | \(-0.277193\pi\) | ||||
0.644194 | + | 0.764862i | \(0.277193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.7129i | 0.734036i | 0.930214 | + | 0.367018i | \(0.119621\pi\) | ||||
−0.930214 | + | 0.367018i | \(0.880379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.9373 | + | 11.7260i | 0.690540 | + | 0.625885i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.80250i | − | 0.521734i | −0.965375 | − | 0.260867i | \(-0.915992\pi\) | ||
0.965375 | − | 0.260867i | \(-0.0840084\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.1822 | − | 10.6442i | −1.01808 | − | 0.564936i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.3926 | + | 9.90803i | 1.02637 | + | 0.524388i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.33138i | 0.228601i | 0.993446 | + | 0.114301i | \(0.0364627\pi\) | ||||
−0.993446 | + | 0.114301i | \(0.963537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2915 | −0.646921 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.04042 | + | 1.26258i | 0.264554 | + | 0.0662685i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | + | 10.8127i | −0.314054 | + | 0.565964i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6315 | 0.763759 | 0.381879 | − | 0.924212i | \(-0.375277\pi\) | ||||
0.381879 | + | 0.924212i | \(0.375277\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.4821 | + | 6.13742i | 0.597733 | + | 0.319502i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.10850 | − | 22.1264i | 0.265220 | − | 1.14875i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.98233i | − | 0.361531i | −0.983526 | − | 0.180766i | \(-0.942142\pi\) | ||
0.983526 | − | 0.180766i | \(-0.0578576\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.0000 | + | 3.74166i | 0.981156 | + | 0.193218i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.68345i | 0.0867019i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.58301 | 0.338146 | 0.169073 | − | 0.985604i | \(-0.445923\pi\) | ||||
0.169073 | + | 0.985604i | \(0.445923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.40122 | + | 5.59388i | −0.0717867 | + | 0.286583i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 20.6921i | − | 1.05732i | −0.848835 | − | 0.528658i | \(-0.822695\pi\) | ||
0.848835 | − | 0.528658i | \(-0.177305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.2024 | − | 12.4300i | 0.570929 | − | 0.633492i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.5830 | − | 27.2823i | 0.741296 | − | 1.38684i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 37.0931i | − | 1.88069i | −0.340218 | − | 0.940346i | \(-0.610501\pi\) | ||
0.340218 | − | 0.940346i | \(-0.389499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.6504i | 1.75234i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.2288 | + | 7.57205i | 1.52484 | + | 0.381959i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.57113 | − | 6.43560i | 0.179683 | − | 0.323810i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8424 | 0.744916 | 0.372458 | − | 0.928049i | \(-0.378515\pi\) | ||||
0.372458 | + | 0.928049i | \(0.378515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.8275 | − | 11.6630i | −1.14281 | − | 0.583879i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.48331i | 0.373699i | 0.982389 | + | 0.186849i | \(0.0598277\pi\) | ||||
−0.982389 | + | 0.186849i | \(0.940172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10.3117i | − | 0.513664i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.0563 | + | 1.65704i | −0.996604 | + | 0.0823389i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.41699 | −0.466783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.4626i | 1.16015i | 0.814563 | + | 0.580076i | \(0.196977\pi\) | ||||
−0.814563 | + | 0.580076i | \(0.803023\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.16991 | + | 0.543544i | 0.107034 | + | 0.0268110i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.29150 | + | 5.59388i | −0.0635507 | + | 0.275257i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.6458 | + | 7.57205i | 0.669844 | + | 0.371697i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.228757 | + | 0.913230i | −0.0112023 | + | 0.0447211i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.8137 | 1.65191 | 0.825953 | − | 0.563739i | \(-0.190638\pi\) | ||||
0.825953 | + | 0.563739i | \(0.190638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.0604 | + | 20.6921i | −0.537774 | + | 1.00608i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.1617 | + | 12.5730i | −0.977986 | + | 0.609881i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.50972 | − | 1.50295i | −0.315028 | − | 0.0727328i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | + | 15.9686i | −0.193122 | + | 0.770971i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.98626i | − | 0.432853i | −0.976299 | − | 0.216427i | \(-0.930560\pi\) | ||
0.976299 | − | 0.216427i | \(-0.0694402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5496 | 0.891439 | 0.445719 | − | 0.895173i | \(-0.352948\pi\) | ||||
0.445719 | + | 0.895173i | \(0.352948\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41699 | − | 1.32548i | −0.0679397 | − | 0.0635518i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 40.7878i | − | 1.95114i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 26.5313i | − | 1.26627i | −0.774041 | − | 0.633135i | \(-0.781768\pi\) | ||
0.774041 | − | 0.633135i | \(-0.218232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.3059 | − | 17.0166i | −0.585997 | − | 0.810313i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.1660 | 1.38572 | 0.692859 | − | 0.721073i | \(-0.256351\pi\) | ||||
0.692859 | + | 0.721073i | \(0.256351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.1660 | + | 30.9352i | −0.813747 | + | 1.46647i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.55066 | + | 18.1669i | −0.215239 | + | 0.859265i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.5921i | 1.72689i | 0.504446 | + | 0.863444i | \(0.331697\pi\) | ||||
−0.504446 | + | 0.863444i | \(0.668303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.2748i | 0.578000i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.38075 | + | 0.596358i | 0.111857 | + | 0.0280194i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.7673 | − | 13.3089i | −0.692304 | − | 0.623933i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.48528i | − | 0.396925i | −0.980109 | − | 0.198462i | \(-0.936405\pi\) | ||
0.980109 | − | 0.198462i | \(-0.0635948\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.5830 | − | 18.2960i | 0.774028 | − | 0.853986i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.9918 | 0.837961 | 0.418981 | − | 0.907995i | \(-0.362388\pi\) | ||||
0.418981 | + | 0.907995i | \(0.362388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.50295i | 0.0698480i | 0.999390 | + | 0.0349240i | \(0.0111189\pi\) | ||||
−0.999390 | + | 0.0349240i | \(0.988881\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.67963 | + | 8.11905i | 0.402508 | + | 0.376512i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 0.841723i | − | 0.0389503i | −0.999810 | − | 0.0194751i | \(-0.993800\pi\) | ||
0.999810 | − | 0.0194751i | \(-0.00619952\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.5830 | − | 6.13742i | −1.22749 | − | 0.283400i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.5203 | + | 6.89360i | 1.26807 | + | 0.317640i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.1660 | 1.34105 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.7328 | − | 14.8000i | 1.08894 | − | 0.679071i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.7085 | − | 12.1382i | −1.03975 | − | 0.555770i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.6991 | −0.991456 | −0.495728 | − | 0.868478i | \(-0.665099\pi\) | ||||
−0.495728 | + | 0.868478i | \(0.665099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1878i | 0.510118i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.2024 | − | 29.7552i | 0.691735 | − | 1.35391i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.8745 | − | 28.6078i | 0.720824 | − | 1.29901i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.98823i | − | 0.452610i | −0.974056 | − | 0.226305i | \(-0.927335\pi\) | ||
0.974056 | − | 0.226305i | \(-0.0726646\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.1421i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.38075 | 0.107224 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.2917 | − | 15.9399i | −0.462577 | − | 0.716446i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.2915 | − | 5.83925i | −1.13448 | − | 0.261926i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.5830 | −1.01095 | −0.505477 | − | 0.862840i | \(-0.668683\pi\) | ||||
−0.505477 | + | 0.862840i | \(0.668683\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.70850 | − | 34.7656i | 0.389067 | − | 1.55321i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 15.6417i | − | 0.697431i | −0.937229 | − | 0.348715i | \(-0.886618\pi\) | ||
0.937229 | − | 0.348715i | \(-0.113382\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.35425 | + | 4.24264i | −0.104763 | + | 0.188795i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.87052 | − | 0.719041i | −0.127484 | − | 0.0319337i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.6909 | 1.75927 | 0.879633 | − | 0.475652i | \(-0.157788\pi\) | ||||
0.879633 | + | 0.475652i | \(0.157788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.29150 | + | 14.2565i | −0.145608 | + | 0.630669i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.5203 | + | 21.5367i | −0.861840 | + | 0.950869i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.41699 | + | 6.15784i | −0.150571 | + | 0.271347i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.1208 | −0.972870 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.937254 | − | 3.74166i | 0.0411409 | − | 0.164241i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0194 | −0.570392 | −0.285196 | − | 0.958469i | \(-0.592059\pi\) | ||||
−0.285196 | + | 0.958469i | \(0.592059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.8014 | 0.734675 | 0.367337 | − | 0.930088i | \(-0.380269\pi\) | ||||
0.367337 | + | 0.930088i | \(0.380269\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.8297 | − | 1.95109i | 0.996368 | − | 0.0851524i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.5830 | −0.635246 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.1660 | 1.31157 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.74103 | + | 3.06871i | 0.249140 | + | 0.133171i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.5830 | 0.631660 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.2917 | − | 41.0860i | 0.444119 | − | 1.77299i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.67963 | − | 17.7951i | 0.373858 | − | 0.766487i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.22876 | + | 24.8661i | −0.267302 | + | 1.06711i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.16991 | + | 3.91044i | −0.0929486 | + | 0.167505i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.9706i | − | 0.725609i | −0.931865 | − | 0.362804i | \(-0.881819\pi\) | ||
0.931865 | − | 0.362804i | \(-0.118181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.57113 | + | 6.68097i | −0.152412 | + | 0.285137i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.80244 | −0.119388 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.95906 | − | 8.48528i | 0.0833078 | − | 0.360831i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.41699 | − | 8.80879i | −0.399729 | − | 0.373912i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.1660 | −1.49003 | −0.745016 | − | 0.667047i | \(-0.767558\pi\) | ||||
−0.745016 | + | 0.667047i | \(0.767558\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.6504i | − | 1.46555i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.5830 | + | 5.65685i | 0.953455 | + | 0.238833i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 13.1166i | − | 0.552798i | −0.961043 | − | 0.276399i | \(-0.910859\pi\) | ||
0.961043 | − | 0.276399i | \(-0.0891411\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.50972 | − | 11.7313i | 0.273866 | − | 0.493540i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.2674 | + | 8.43570i | −0.935145 | + | 0.354266i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 33.7637i | − | 1.41545i | −0.706490 | − | 0.707723i | \(-0.749722\pi\) | ||
0.706490 | − | 0.707723i | \(-0.250278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.4170 | 0.561484 | 0.280742 | − | 0.959783i | \(-0.409420\pi\) | ||||
0.280742 | + | 0.959783i | \(0.409420\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.210845 | − | 0.841723i | 0.00880816 | − | 0.0351635i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.2915 | + | 30.9352i | 0.804511 | + | 1.29009i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.3306 | −1.51246 | −0.756231 | − | 0.654305i | \(-0.772961\pi\) | ||||
−0.756231 | + | 0.654305i | \(0.772961\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.57113 | + | 14.2565i | −0.148411 | + | 0.592479i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.9918 | + | 4.15390i | 0.746425 | + | 0.172333i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.2764i | − | 1.00543i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.9373 | + | 12.2269i | −0.782959 | + | 0.505522i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.7719i | 1.55901i | 0.626394 | + | 0.779507i | \(0.284530\pi\) | ||||
−0.626394 | + | 0.779507i | \(0.715470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1660 | 0.707313 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.2425 | + | 7.57551i | 1.24401 | + | 0.311615i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.43560i | 0.264279i | 0.991231 | + | 0.132139i | \(0.0421846\pi\) | ||||
−0.991231 | + | 0.132139i | \(0.957815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.8217 | + | 20.8842i | −0.771614 | + | 0.856168i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.87451 | − | 15.4676i | 0.158573 | − | 0.633047i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.15390i | − | 0.169724i | −0.996393 | − | 0.0848620i | \(-0.972955\pi\) | ||
0.996393 | − | 0.0848620i | \(-0.0270449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.13742i | 0.250351i | 0.992135 | + | 0.125175i | \(0.0399494\pi\) | ||||
−0.992135 | + | 0.125175i | \(0.960051\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.5830 | + | 27.2823i | −0.593866 | + | 1.11102i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.25486 | + | 5.86565i | −0.132329 | + | 0.238473i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.95188 | 0.241579 | 0.120790 | − | 0.992678i | \(-0.461457\pi\) | ||||
0.120790 | + | 0.992678i | \(0.461457\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.04442 | − | 1.04453i | −0.0828439 | − | 0.0423264i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.2803i | 1.06319i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 47.5823i | − | 1.92183i | −0.276843 | − | 0.960915i | \(-0.589288\pi\) | ||
0.276843 | − | 0.960915i | \(-0.410712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.4821 | + | 12.2748i | −0.463002 | + | 0.494970i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.1660 | 1.89883 | 0.949416 | − | 0.314021i | \(-0.101676\pi\) | ||||
0.949416 | + | 0.314021i | \(0.101676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.2443i | 1.61755i | 0.588116 | + | 0.808777i | \(0.299870\pi\) | ||||
−0.588116 | + | 0.808777i | \(0.700130\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.0726 | − | 25.4442i | −1.12652 | − | 1.02104i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.41699 | + | 40.7878i | −0.377284 | + | 1.63413i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | + | 22.4499i | −0.440000 | + | 0.897998i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −26.5830 | − | 6.65882i | −1.06162 | − | 0.265928i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8219 | 0.630860 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.4575 | −1.29211 | −0.646057 | − | 0.763290i | \(-0.723583\pi\) | ||||
−0.646057 | + | 0.763290i | \(0.723583\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 35.5619 | + | 8.90796i | 1.41346 | + | 0.354060i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.50972 | − | 3.61226i | −0.258330 | − | 0.143348i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.1412 | − | 10.3117i | −0.837646 | − | 0.408566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.8745 | + | 25.9568i | −0.548867 | + | 1.02684i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.1068i | 1.11015i | 0.831800 | + | 0.555076i | \(0.187311\pi\) | ||||
−0.831800 | + | 0.555076i | \(0.812689\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.6786 | 0.894357 | 0.447178 | − | 0.894445i | \(-0.352429\pi\) | ||||
0.447178 | + | 0.894445i | \(0.352429\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.1660 | + | 27.2823i | 1.14841 | + | 1.07424i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.9583i | 0.548757i | 0.961622 | + | 0.274379i | \(0.0884721\pi\) | ||||
−0.961622 | + | 0.274379i | \(0.911528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.13742i | 0.240915i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.5228 | + | 6.39812i | 0.490808 | + | 0.250762i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.1660 | −0.906556 | −0.453278 | − | 0.891369i | \(-0.649746\pi\) | ||||
−0.453278 | + | 0.891369i | \(0.649746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.5203 | + | 35.1779i | −0.762720 | + | 1.37451i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6315 | + | 7.82087i | 0.570830 | + | 0.305121i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.1048i | 1.05585i | 0.849290 | + | 0.527927i | \(0.177031\pi\) | ||||
−0.849290 | + | 0.527927i | \(0.822969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.66259i | 0.336936i | 0.985707 | + | 0.168468i | \(0.0538820\pi\) | ||||
−0.985707 | + | 0.168468i | \(0.946118\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.72057 | − | 26.8295i | 0.261005 | − | 1.04197i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.1555 | − | 24.5833i | 0.859152 | − | 0.953299i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.65292i | − | 0.141442i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.00000 | − | 0.500983i | −0.0773245 | − | 0.0193691i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.14226 | −0.275724 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.6294i | 0.910846i | 0.890275 | + | 0.455423i | \(0.150512\pi\) | ||||
−0.890275 | + | 0.455423i | \(0.849488\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.61874 | − | 25.5669i | 0.177775 | − | 0.984071i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 6.19024i | − | 0.237910i | −0.992900 | − | 0.118955i | \(-0.962046\pi\) | ||
0.992900 | − | 0.118955i | \(-0.0379545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.70850 | − | 37.7191i | 0.334201 | − | 1.44753i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.64575 | − | 30.5230i | 0.292986 | − | 1.16964i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.5830 | −1.01717 | −0.508585 | − | 0.861012i | \(-0.669831\pi\) | ||||
−0.508585 | + | 0.861012i | \(0.669831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.40122 | + | 2.52517i | −0.0535379 | + | 0.0964817i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.4797 | − | 41.8367i | 0.399827 | − | 1.59617i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.8413 | −1.09877 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 11.7313i | − | 0.446280i | −0.974786 | − | 0.223140i | \(-0.928369\pi\) | ||
0.974786 | − | 0.223140i | \(-0.0716307\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.9108 | − | 14.7657i | −0.642386 | − | 0.560903i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.06275 | − | 0.589720i | −0.0403123 | − | 0.0223693i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 20.6235i | − | 0.781170i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.3316 | + | 5.59388i | 0.844659 | + | 0.211580i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.1245i | 0.797860i | 0.916981 | + | 0.398930i | \(0.130618\pi\) | ||||
−0.916981 | + | 0.398930i | \(0.869382\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.6243 | −0.702430 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.1208 | − | 20.6921i | −0.833116 | − | 0.779309i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.29150 | + | 5.59388i | −0.0485720 | + | 0.210380i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.583005 | −0.0218952 | −0.0109476 | − | 0.999940i | \(-0.503485\pi\) | ||||
−0.0109476 | + | 0.999940i | \(0.503485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.70850 | − | 4.65489i | −0.326594 | − | 0.174572i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.3755i | 0.837970i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.5830 | − | 10.3117i | −0.694965 | − | 0.385637i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.16272 | + | 24.6025i | −0.230151 | + | 0.918798i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.80244 | −0.104513 | −0.0522567 | − | 0.998634i | \(-0.516641\pi\) | ||||
−0.0522567 | + | 0.998634i | \(0.516641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.87451 | + | 8.11905i | −0.0698103 | + | 0.302369i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.29150 | + | 29.1088i | −0.271174 | + | 1.08257i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.12549 | − | 1.32548i | 0.0789388 | − | 0.0492270i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.8536 | −1.70062 | −0.850308 | − | 0.526286i | \(-0.823584\pi\) | ||||
−0.850308 | + | 0.526286i | \(0.823584\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.64575 | + | 26.8701i | 0.0979908 | + | 0.995187i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49.0030 | −1.81244 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.2835 | −1.04467 | −0.522337 | − | 0.852739i | \(-0.674940\pi\) | ||||
−0.522337 | + | 0.852739i | \(0.674940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.3254 | − | 9.67601i | 0.934141 | − | 0.356905i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.1660 | −1.07434 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.1660 | 1.22003 | 0.610016 | − | 0.792389i | \(-0.291163\pi\) | ||||
0.610016 | + | 0.792389i | \(0.291163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.91094 | + | 31.5817i | −0.290616 | + | 1.16018i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.12549 | 0.0779767 | 0.0389884 | − | 0.999240i | \(-0.487586\pi\) | ||||
0.0389884 | + | 0.999240i | \(0.487586\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.1412 | − | 11.7313i | −0.774555 | − | 0.429802i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.87000 | − | 18.4651i | 0.361125 | − | 0.675602i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.1660 | 0.772359 | 0.386179 | − | 0.922424i | \(-0.373795\pi\) | ||||
0.386179 | + | 0.922424i | \(0.373795\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.9373 | − | 2.73969i | −0.398576 | − | 0.0998399i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.53737 | + | 2.77053i | −0.0559508 | + | 0.100830i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.2646i | 1.24537i | 0.782473 | + | 0.622685i | \(0.213958\pi\) | ||||
−0.782473 | + | 0.622685i | \(0.786042\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.67963 | − | 34.6504i | 0.315051 | − | 1.25773i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.4821 | −0.416225 | −0.208112 | − | 0.978105i | \(-0.566732\pi\) | ||||
−0.208112 | + | 0.978105i | \(0.566732\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.19038 | + | 5.15587i | −0.0430945 | + | 0.186655i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.2915 | + | 26.7813i | 0.625176 | + | 0.968281i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.29150 | 0.263281 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35.7375i | − | 1.28873i | −0.764720 | − | 0.644363i | \(-0.777123\pi\) | ||
0.764720 | − | 0.644363i | \(-0.222877\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.87451 | + | 31.4362i | −0.283593 | + | 1.13215i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 41.9277i | − | 1.50803i | −0.656855 | − | 0.754017i | \(-0.728113\pi\) | ||
0.656855 | − | 0.754017i | \(-0.271887\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.0194 | + | 8.11905i | −0.467672 | + | 0.291645i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.5867 | − | 6.94167i | −0.487419 | − | 0.249031i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.2764i | 0.869792i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.7490 | −0.992938 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.74822 | + | 1.92881i | −0.0624762 | + | 0.0689301i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.7712 | + | 32.0259i | −0.634283 | + | 1.14305i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.2835 | 1.00820 | 0.504099 | − | 0.863646i | \(-0.331825\pi\) | ||||
0.504099 | + | 0.863646i | \(0.331825\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.5015 | − | 6.13742i | −0.872277 | − | 0.218498i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.57113 | − | 15.4676i | 0.126975 | − | 0.549965i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.48528i | 0.301321i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.7085 | − | 24.2764i | 0.805387 | − | 0.860995i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.0982i | 0.534806i | 0.963585 | + | 0.267403i | \(0.0861654\pi\) | ||||
−0.963585 | + | 0.267403i | \(0.913835\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.1660 | 1.31484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.8608 | + | 22.3755i | 1.47908 | + | 0.790600i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.6417i | 0.551985i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.0438 | + | 28.8792i | 1.12939 | + | 1.01786i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.6458 | + | 3.91913i | 0.550757 | + | 0.137960i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.1362i | 0.391529i | 0.980651 | + | 0.195765i | \(0.0627188\pi\) | ||||
−0.980651 | + | 0.195765i | \(0.937281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.0062i | − | 0.842970i | −0.906835 | − | 0.421485i | \(-0.861509\pi\) | ||
0.906835 | − | 0.421485i | \(-0.138491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.58301 | + | 34.2646i | −0.301019 | + | 1.20171i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 57.6827 | 2.01806 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.5423 | + | 20.0906i | −0.612976 | + | 0.702024i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.4362i | 1.09713i | 0.836107 | + | 0.548566i | \(0.184826\pi\) | ||||
−0.836107 | + | 0.548566i | \(0.815174\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 11.8147i | − | 0.411834i | −0.978569 | − | 0.205917i | \(-0.933982\pi\) | ||
0.978569 | − | 0.205917i | \(-0.0660177\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.3111 | − | 7.52269i | 0.811590 | − | 0.261906i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 33.2123i | − | 1.15351i | −0.816917 | − | 0.576755i | \(-0.804319\pi\) | ||
0.816917 | − | 0.576755i | \(-0.195681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.93859 | + | 11.7313i | −0.101939 | + | 0.406954i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.5830 | + | 29.8982i | −0.505271 | + | 1.03591i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.4575 | + | 22.4499i | 1.40009 | + | 0.776912i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.7085 | − | 11.8147i | 0.370140 | − | 0.408375i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.5210 | −1.29537 | −0.647684 | − | 0.761909i | \(-0.724262\pi\) | ||||
−0.647684 | + | 0.761909i | \(0.724262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7490 | 0.991345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.91813 | + | 15.6417i | −0.134947 | + | 0.538730i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.85364 | − | 3.34048i | 0.0637672 | − | 0.114916i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.78556 | + | 7.73381i | −0.0613527 | + | 0.265737i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.1033 | − | 13.5524i | −1.85682 | − | 0.465118i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 24.2764i | − | 0.832184i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.5220 | 0.805377 | 0.402689 | − | 0.915337i | \(-0.368076\pi\) | ||||
0.402689 | + | 0.915337i | \(0.368076\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.3542 | − | 31.5249i | −0.696101 | − | 1.07813i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.1363i | 1.57599i | 0.615684 | + | 0.787993i | \(0.288880\pi\) | ||||
−0.615684 | + | 0.787993i | \(0.711120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.9191i | 0.781988i | 0.920393 | + | 0.390994i | \(0.127869\pi\) | ||||
−0.920393 | + | 0.390994i | \(0.872131\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.04831 | + | 17.7099i | −0.308366 | + | 0.603553i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.35425 | + | 2.41618i | 0.148049 | + | 0.0821526i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.38024 | − | 2.34967i | −0.318570 | − | 0.0797990i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.30978i | − | 0.315812i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.6504i | 1.17408i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38.7113 | − | 20.6921i | −1.31018 | − | 0.700321i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.17645 | + | 29.1239i | −0.174996 | + | 0.984569i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.9529i | 0.808832i | 0.914575 | + | 0.404416i | \(0.132525\pi\) | ||||
−0.914575 | + | 0.404416i | \(0.867475\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.06275 | − | 12.2269i | 0.103304 | − | 0.412404i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.8219 | −0.533053 | −0.266526 | − | 0.963828i | \(-0.585876\pi\) | ||||
−0.266526 | + | 0.963828i | \(0.585876\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 30.9352i | − | 1.04105i | −0.853845 | − | 0.520527i | \(-0.825736\pi\) | ||
0.853845 | − | 0.520527i | \(-0.174264\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.74103 | + | 6.13742i | −0.192983 | + | 0.206307i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.27980i | − | 0.0765483i | −0.999267 | − | 0.0382742i | \(-0.987814\pi\) | ||
0.999267 | − | 0.0382742i | \(-0.0121860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.58301 | − | 1.98162i | −0.287865 | − | 0.0664616i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.1660 | + | 14.1421i | −0.709088 | + | 0.473779i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.7490 | −1.46400 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.8127 | + | 26.5313i | 1.59820 | + | 0.886844i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41.1660 | − | 10.3117i | −1.37449 | − | 0.344299i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.53737 | 0.0512743 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.7878i | 1.35884i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42.0802 | + | 21.4995i | 1.40034 | + | 0.715459i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.9373 | − | 16.0573i | −0.961907 | − | 0.533764i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.9411i | 1.12700i | 0.826117 | + | 0.563498i | \(0.190545\pi\) | ||||
−0.826117 | + | 0.563498i | \(0.809455\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.74103 | + | 3.06871i | 0.190418 | + | 0.101783i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.2960i | 0.606175i | 0.952963 | + | 0.303087i | \(0.0980174\pi\) | ||||
−0.952963 | + | 0.303087i | \(0.901983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.7400 | 0.653299 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.14226 | − | 6.68097i | −0.236116 | − | 0.220866i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.7085 | + | 46.3817i | −0.353626 | + | 1.53166i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.8745 | −1.38131 | −0.690656 | − | 0.723183i | \(-0.742678\pi\) | ||||
−0.690656 | + | 0.723183i | \(0.742678\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.2288 | − | 5.06713i | −0.666560 | − | 0.166968i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.9669i | 1.08512i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1255 | − | 8.80879i | 0.464443 | − | 0.289631i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.33263 | + | 4.45398i | 0.273680 | + | 0.146288i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.8055 | −1.69968 | −0.849841 | − | 0.527039i | \(-0.823302\pi\) | ||||
−0.849841 | + | 0.527039i | \(0.823302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.1660 | − | 35.1939i | 0.562593 | − | 1.15343i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41.1660 | + | 10.3117i | 1.34771 | + | 0.337591i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.5830 | + | 26.2803i | −0.476915 | + | 0.859459i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.53019 | 0.180663 | 0.0903317 | − | 0.995912i | \(-0.471207\pi\) | ||||
0.0903317 | + | 0.995912i | \(0.471207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.5830 | − | 6.15784i | −0.802236 | − | 0.200953i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.632534 | 0.0206200 | 0.0103100 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103100 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.6438 | −1.03046 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.09868 | − | 30.5843i | −0.100800 | − | 0.994907i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.0000 | −0.779895 | −0.389948 | − | 0.920837i | \(-0.627507\pi\) | ||||
−0.389948 | + | 0.920837i | \(0.627507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.5830 | 0.603230 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.0808 | + | 2.52517i | 0.326894 | + | 0.0818842i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.87451 | 0.125508 | 0.0627538 | − | 0.998029i | \(-0.480012\pi\) | ||||
0.0627538 | + | 0.998029i | \(0.480012\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.979531 | + | 0.543544i | 0.0316969 | + | 0.0175887i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.38075 | − | 0.596358i | −0.0769588 | − | 0.0192775i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.768687 | + | 3.32941i | −0.0248222 | + | 0.107512i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.5830 | 0.696226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.5906 | − | 9.20614i | −0.534069 | − | 0.296356i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.9588i | 0.866936i | 0.901169 | + | 0.433468i | \(0.142710\pi\) | ||||
−0.901169 | + | 0.433468i | \(0.857290\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44.6632 | + | 11.1878i | 1.43479 | + | 0.359403i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.31216 | −0.298842 | −0.149421 | − | 0.988774i | \(-0.547741\pi\) | ||||
−0.149421 | + | 0.988774i | \(0.547741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.40122 | − | 0.323511i | −0.0449211 | − | 0.0103713i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.93725 | − | 27.6946i | −0.286221 | − | 0.886935i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.1255 | −0.643872 | −0.321936 | − | 0.946762i | \(-0.604334\pi\) | ||||
−0.321936 | + | 0.946762i | \(0.604334\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.7510i | 1.43025i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.29150 | + | 2.82843i | 0.168945 | + | 0.0903047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 29.0037i | − | 0.925074i | −0.886600 | − | 0.462537i | \(-0.846939\pi\) | ||
0.886600 | − | 0.462537i | \(-0.153061\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.5292 | + | 35.1939i | −0.622251 | + | 1.12137i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.9154 | − | 16.3062i | −1.01588 | − | 0.519031i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 75.1881i | 2.39084i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.2915 | 0.358686 | 0.179343 | − | 0.983787i | \(-0.442603\pi\) | ||||
0.179343 | + | 0.983787i | \(0.442603\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.4411 | − | 3.36689i | −0.426541 | − | 0.106845i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0000 | + | 9.98823i | 0.570638 | + | 0.316648i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.3244 | 0.833703 | 0.416851 | − | 0.908975i | \(-0.363134\pi\) | ||||
0.416851 | + | 0.908975i | \(0.363134\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.6182 | + | 12.8184i | −0.367584 | + | 0.405556i |
(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 | 1680.2.k.e.209.8 | 8 | ||
3.2 | odd | 2 | 1680.2.k.f.209.7 | 8 | |||
4.3 | odd | 2 | 210.2.d.a.209.1 | ✓ | 8 | ||
5.4 | even | 2 | 1680.2.k.f.209.1 | 8 | |||
7.6 | odd | 2 | inner | 1680.2.k.e.209.1 | 8 | ||
12.11 | even | 2 | 210.2.d.b.209.2 | yes | 8 | ||
15.14 | odd | 2 | inner | 1680.2.k.e.209.2 | 8 | ||
20.3 | even | 4 | 1050.2.b.f.251.13 | 16 | |||
20.7 | even | 4 | 1050.2.b.f.251.4 | 16 | |||
20.19 | odd | 2 | 210.2.d.b.209.8 | yes | 8 | ||
21.20 | even | 2 | 1680.2.k.f.209.2 | 8 | |||
28.27 | even | 2 | 210.2.d.a.209.8 | yes | 8 | ||
35.34 | odd | 2 | 1680.2.k.f.209.8 | 8 | |||
60.23 | odd | 4 | 1050.2.b.f.251.3 | 16 | |||
60.47 | odd | 4 | 1050.2.b.f.251.14 | 16 | |||
60.59 | even | 2 | 210.2.d.a.209.7 | yes | 8 | ||
84.83 | odd | 2 | 210.2.d.b.209.7 | yes | 8 | ||
105.104 | even | 2 | inner | 1680.2.k.e.209.7 | 8 | ||
140.27 | odd | 4 | 1050.2.b.f.251.5 | 16 | |||
140.83 | odd | 4 | 1050.2.b.f.251.12 | 16 | |||
140.139 | even | 2 | 210.2.d.b.209.1 | yes | 8 | ||
420.83 | even | 4 | 1050.2.b.f.251.6 | 16 | |||
420.167 | even | 4 | 1050.2.b.f.251.11 | 16 | |||
420.419 | odd | 2 | 210.2.d.a.209.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.d.a.209.1 | ✓ | 8 | 4.3 | odd | 2 | ||
210.2.d.a.209.2 | yes | 8 | 420.419 | odd | 2 | ||
210.2.d.a.209.7 | yes | 8 | 60.59 | even | 2 | ||
210.2.d.a.209.8 | yes | 8 | 28.27 | even | 2 | ||
210.2.d.b.209.1 | yes | 8 | 140.139 | even | 2 | ||
210.2.d.b.209.2 | yes | 8 | 12.11 | even | 2 | ||
210.2.d.b.209.7 | yes | 8 | 84.83 | odd | 2 | ||
210.2.d.b.209.8 | yes | 8 | 20.19 | odd | 2 | ||
1050.2.b.f.251.3 | 16 | 60.23 | odd | 4 | |||
1050.2.b.f.251.4 | 16 | 20.7 | even | 4 | |||
1050.2.b.f.251.5 | 16 | 140.27 | odd | 4 | |||
1050.2.b.f.251.6 | 16 | 420.83 | even | 4 | |||
1050.2.b.f.251.11 | 16 | 420.167 | even | 4 | |||
1050.2.b.f.251.12 | 16 | 140.83 | odd | 4 | |||
1050.2.b.f.251.13 | 16 | 20.3 | even | 4 | |||
1050.2.b.f.251.14 | 16 | 60.47 | odd | 4 | |||
1680.2.k.e.209.1 | 8 | 7.6 | odd | 2 | inner | ||
1680.2.k.e.209.2 | 8 | 15.14 | odd | 2 | inner | ||
1680.2.k.e.209.7 | 8 | 105.104 | even | 2 | inner | ||
1680.2.k.e.209.8 | 8 | 1.1 | even | 1 | trivial | ||
1680.2.k.f.209.1 | 8 | 5.4 | even | 2 | |||
1680.2.k.f.209.2 | 8 | 21.20 | even | 2 | |||
1680.2.k.f.209.7 | 8 | 3.2 | odd | 2 | |||
1680.2.k.f.209.8 | 8 | 35.34 | odd | 2 |