Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(79,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.e (of order \(3\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.79 |
Dual form | 637.2.e.g.508.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(3\) | 0.707107 | + | 1.22474i | 0.408248 | + | 0.707107i | 0.994694 | − | 0.102882i | \(-0.0328064\pi\) |
−0.586445 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.792893 | − | 1.37333i | 0.354593 | − | 0.614172i | −0.632456 | − | 0.774597i | \(-0.717953\pi\) |
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.12132 | − | 1.94218i | −0.354593 | − | 0.614172i | ||||
\(11\) | −2.12132 | − | 3.67423i | −0.639602 | − | 1.10782i | −0.985520 | − | 0.169559i | \(-0.945766\pi\) |
0.345918 | − | 0.938265i | \(-0.387568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.24264 | 0.579047 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 0.707107 | + | 1.22474i | 0.171499 | + | 0.297044i | 0.938944 | − | 0.344070i | \(-0.111806\pi\) |
−0.767445 | + | 0.641114i | \(0.778472\pi\) | |||||||
\(18\) | −0.707107 | − | 1.22474i | −0.166667 | − | 0.288675i | ||||
\(19\) | −3.62132 | + | 6.27231i | −0.830788 | + | 1.43897i | 0.0666264 | + | 0.997778i | \(0.478776\pi\) |
−0.897414 | + | 0.441189i | \(0.854557\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | 2.91421 | − | 5.04757i | 0.607656 | − | 1.05249i | −0.383970 | − | 0.923345i | \(-0.625443\pi\) |
0.991626 | − | 0.129145i | \(-0.0412232\pi\) | |||||||
\(24\) | 2.00000 | + | 3.46410i | 0.408248 | + | 0.707107i | ||||
\(25\) | 1.24264 | + | 2.15232i | 0.248528 | + | 0.430463i | ||||
\(26\) | 0.707107 | − | 1.22474i | 0.138675 | − | 0.240192i | ||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.171573 | 0.0318603 | 0.0159301 | − | 0.999873i | \(-0.494929\pi\) | ||||
0.0159301 | + | 0.999873i | \(0.494929\pi\) | |||||||
\(30\) | 1.58579 | − | 2.74666i | 0.289524 | − | 0.501470i | ||||
\(31\) | 1.62132 | + | 2.80821i | 0.291198 | + | 0.504369i | 0.974093 | − | 0.226147i | \(-0.0726129\pi\) |
−0.682895 | + | 0.730516i | \(0.739280\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | − | 5.19615i | 0.522233 | − | 0.904534i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.12132 | + | 1.94218i | −0.184344 | + | 0.319293i | −0.943355 | − | 0.331784i | \(-0.892349\pi\) |
0.759011 | + | 0.651077i | \(0.225683\pi\) | |||||||
\(38\) | 5.12132 | + | 8.87039i | 0.830788 | + | 1.43897i | ||||
\(39\) | 0.707107 | + | 1.22474i | 0.113228 | + | 0.196116i | ||||
\(40\) | 2.24264 | − | 3.88437i | 0.354593 | − | 0.614172i | ||||
\(41\) | −8.82843 | −1.37877 | −0.689384 | − | 0.724396i | \(-0.742119\pi\) | ||||
−0.689384 | + | 0.724396i | \(0.742119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.792893 | − | 1.37333i | −0.118198 | − | 0.204724i | ||||
\(46\) | −4.12132 | − | 7.13834i | −0.607656 | − | 1.05249i | ||||
\(47\) | 0.792893 | − | 1.37333i | 0.115655 | − | 0.200321i | −0.802386 | − | 0.596805i | \(-0.796437\pi\) |
0.918042 | + | 0.396484i | \(0.129770\pi\) | |||||||
\(48\) | 5.65685 | 0.816497 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.51472 | 0.497056 | ||||||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0857864 | + | 0.148586i | 0.0117837 | + | 0.0204099i | 0.871857 | − | 0.489760i | \(-0.162916\pi\) |
−0.860073 | + | 0.510170i | \(0.829582\pi\) | |||||||
\(54\) | 4.00000 | − | 6.92820i | 0.544331 | − | 0.942809i | ||||
\(55\) | −6.72792 | −0.907193 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.2426 | −1.35667 | ||||||||
\(58\) | 0.121320 | − | 0.210133i | 0.0159301 | − | 0.0275918i | ||||
\(59\) | 0.171573 | + | 0.297173i | 0.0223369 | + | 0.0386886i | 0.876978 | − | 0.480531i | \(-0.159556\pi\) |
−0.854641 | + | 0.519220i | \(0.826223\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | 4.58579 | 0.582395 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0.792893 | − | 1.37333i | 0.0983463 | − | 0.170341i | ||||
\(66\) | −4.24264 | − | 7.34847i | −0.522233 | − | 0.904534i | ||||
\(67\) | 7.24264 | + | 12.5446i | 0.884829 | + | 1.53257i | 0.845909 | + | 0.533327i | \(0.179059\pi\) |
0.0389203 | + | 0.999242i | \(0.487608\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.24264 | 0.992297 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.0711 | −1.55125 | −0.775625 | − | 0.631194i | \(-0.782565\pi\) | ||||
−0.775625 | + | 0.631194i | \(0.782565\pi\) | |||||||
\(72\) | 1.41421 | − | 2.44949i | 0.166667 | − | 0.288675i | ||||
\(73\) | −4.62132 | − | 8.00436i | −0.540885 | − | 0.936840i | −0.998854 | − | 0.0478714i | \(-0.984756\pi\) |
0.457969 | − | 0.888968i | \(-0.348577\pi\) | |||||||
\(74\) | 1.58579 | + | 2.74666i | 0.184344 | + | 0.319293i | ||||
\(75\) | −1.75736 | + | 3.04384i | −0.202922 | + | 0.351472i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | −7.74264 | + | 13.4106i | −0.871115 | + | 1.50882i | −0.0102708 | + | 0.999947i | \(0.503269\pi\) |
−0.860844 | + | 0.508868i | \(0.830064\pi\) | |||||||
\(80\) | −3.17157 | − | 5.49333i | −0.354593 | − | 0.614172i | ||||
\(81\) | 2.50000 | + | 4.33013i | 0.277778 | + | 0.481125i | ||||
\(82\) | −6.24264 | + | 10.8126i | −0.689384 | + | 1.19405i | ||||
\(83\) | −13.2426 | −1.45357 | −0.726784 | − | 0.686866i | \(-0.758986\pi\) | ||||
−0.726784 | + | 0.686866i | \(0.758986\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.24264 | 0.243249 | ||||||||
\(86\) | −3.53553 | + | 6.12372i | −0.381246 | + | 0.660338i | ||||
\(87\) | 0.121320 | + | 0.210133i | 0.0130069 | + | 0.0225286i | ||||
\(88\) | −6.00000 | − | 10.3923i | −0.639602 | − | 1.10782i | ||||
\(89\) | 0.792893 | − | 1.37333i | 0.0840465 | − | 0.145573i | −0.820938 | − | 0.571017i | \(-0.806549\pi\) |
0.904985 | + | 0.425445i | \(0.139882\pi\) | |||||||
\(90\) | −2.24264 | −0.236395 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.29289 | + | 3.97141i | −0.237762 | + | 0.411816i | ||||
\(94\) | −1.12132 | − | 1.94218i | −0.115655 | − | 0.200321i | ||||
\(95\) | 5.74264 | + | 9.94655i | 0.589183 | + | 1.02049i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.7279 | −1.19079 | −0.595395 | − | 0.803433i | \(-0.703004\pi\) | ||||
−0.595395 | + | 0.803433i | \(0.703004\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.24264 | −0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.12132 | + | 8.87039i | 0.509590 | + | 0.882636i | 0.999938 | + | 0.0111097i | \(0.00353640\pi\) |
−0.490348 | + | 0.871527i | \(0.663130\pi\) | |||||||
\(102\) | 1.41421 | + | 2.44949i | 0.140028 | + | 0.242536i | ||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.242641 | 0.0235673 | ||||||||
\(107\) | 10.0711 | − | 17.4436i | 0.973607 | − | 1.68634i | 0.289149 | − | 0.957284i | \(-0.406628\pi\) |
0.684458 | − | 0.729052i | \(-0.260039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.36396 | − | 14.4868i | −0.801122 | − | 1.38758i | −0.918878 | − | 0.394542i | \(-0.870903\pi\) |
0.117756 | − | 0.993043i | \(-0.462430\pi\) | |||||||
\(110\) | −4.75736 | + | 8.23999i | −0.453596 | + | 0.785652i | ||||
\(111\) | −3.17157 | −0.301032 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.31371 | 0.217655 | 0.108828 | − | 0.994061i | \(-0.465290\pi\) | ||||
0.108828 | + | 0.994061i | \(0.465290\pi\) | |||||||
\(114\) | −7.24264 | + | 12.5446i | −0.678335 | + | 1.17491i | ||||
\(115\) | −4.62132 | − | 8.00436i | −0.430940 | − | 0.746411i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | − | 0.866025i | 0.0462250 | − | 0.0800641i | ||||
\(118\) | 0.485281 | 0.0446738 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.34315 | 0.579047 | ||||||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | −4.24264 | − | 7.34847i | −0.384111 | − | 0.665299i | ||||
\(123\) | −6.24264 | − | 10.8126i | −0.562880 | − | 0.974937i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8701 | 1.06169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.500000 | − | 0.866025i | ||||
\(129\) | −3.53553 | − | 6.12372i | −0.311286 | − | 0.539164i | ||||
\(130\) | −1.12132 | − | 1.94218i | −0.0983463 | − | 0.170341i | ||||
\(131\) | −1.41421 | + | 2.44949i | −0.123560 | + | 0.214013i | −0.921169 | − | 0.389162i | \(-0.872765\pi\) |
0.797609 | + | 0.603175i | \(0.206098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 20.4853 | 1.76966 | ||||||||
\(135\) | 4.48528 | − | 7.76874i | 0.386032 | − | 0.668626i | ||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | 2.29289 | + | 3.97141i | 0.195895 | + | 0.339300i | 0.947194 | − | 0.320662i | \(-0.103905\pi\) |
−0.751298 | + | 0.659963i | \(0.770572\pi\) | |||||||
\(138\) | 5.82843 | − | 10.0951i | 0.496149 | − | 0.859355i | ||||
\(139\) | −6.24264 | −0.529494 | −0.264747 | − | 0.964318i | \(-0.585288\pi\) | ||||
−0.264747 | + | 0.964318i | \(0.585288\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.24264 | 0.188864 | ||||||||
\(142\) | −9.24264 | + | 16.0087i | −0.775625 | + | 1.34342i | ||||
\(143\) | −2.12132 | − | 3.67423i | −0.177394 | − | 0.307255i | ||||
\(144\) | −2.00000 | − | 3.46410i | −0.166667 | − | 0.288675i | ||||
\(145\) | 0.136039 | − | 0.235626i | 0.0112974 | − | 0.0195677i | ||||
\(146\) | −13.0711 | −1.08177 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.12132 | + | 14.0665i | −0.665324 | + | 1.15238i | 0.313873 | + | 0.949465i | \(0.398373\pi\) |
−0.979197 | + | 0.202911i | \(0.934960\pi\) | |||||||
\(150\) | 2.48528 | + | 4.30463i | 0.202922 | + | 0.351472i | ||||
\(151\) | 4.87868 | + | 8.45012i | 0.397021 | + | 0.687661i | 0.993357 | − | 0.115074i | \(-0.0367106\pi\) |
−0.596336 | + | 0.802735i | \(0.703377\pi\) | |||||||
\(152\) | −10.2426 | + | 17.7408i | −0.830788 | + | 1.43897i | ||||
\(153\) | 1.41421 | 0.114332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.14214 | 0.413026 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.87868 | − | 3.25397i | −0.149935 | − | 0.259695i | 0.781268 | − | 0.624195i | \(-0.214573\pi\) |
−0.931203 | + | 0.364500i | \(0.881240\pi\) | |||||||
\(158\) | 10.9497 | + | 18.9655i | 0.871115 | + | 1.50882i | ||||
\(159\) | −0.121320 | + | 0.210133i | −0.00962133 | + | 0.0166646i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.07107 | 0.555556 | ||||||||
\(163\) | −4.24264 | + | 7.34847i | −0.332309 | + | 0.575577i | −0.982964 | − | 0.183797i | \(-0.941161\pi\) |
0.650655 | + | 0.759374i | \(0.274494\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.75736 | − | 8.23999i | −0.370360 | − | 0.641482i | ||||
\(166\) | −9.36396 | + | 16.2189i | −0.726784 | + | 1.25883i | ||||
\(167\) | −15.3848 | −1.19051 | −0.595255 | − | 0.803537i | \(-0.702949\pi\) | ||||
−0.595255 | + | 0.803537i | \(0.702949\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.58579 | − | 2.74666i | 0.121624 | − | 0.210659i | ||||
\(171\) | 3.62132 | + | 6.27231i | 0.276929 | + | 0.479656i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3640 | − | 21.4150i | 0.940015 | − | 1.62815i | 0.174576 | − | 0.984644i | \(-0.444144\pi\) |
0.765438 | − | 0.643509i | \(-0.222522\pi\) | |||||||
\(174\) | 0.343146 | 0.0260138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.9706 | −1.27920 | ||||||||
\(177\) | −0.242641 | + | 0.420266i | −0.0182380 | + | 0.0315891i | ||||
\(178\) | −1.12132 | − | 1.94218i | −0.0840465 | − | 0.145573i | ||||
\(179\) | 4.50000 | + | 7.79423i | 0.336346 | + | 0.582568i | 0.983742 | − | 0.179585i | \(-0.0574756\pi\) |
−0.647397 | + | 0.762153i | \(0.724142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7279 | 1.39204 | 0.696018 | − | 0.718025i | \(-0.254953\pi\) | ||||
0.696018 | + | 0.718025i | \(0.254953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.48528 | 0.627250 | ||||||||
\(184\) | 8.24264 | − | 14.2767i | 0.607656 | − | 1.05249i | ||||
\(185\) | 1.77817 | + | 3.07989i | 0.130734 | + | 0.226438i | ||||
\(186\) | 3.24264 | + | 5.61642i | 0.237762 | + | 0.411816i | ||||
\(187\) | 3.00000 | − | 5.19615i | 0.219382 | − | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.2426 | 1.17837 | ||||||||
\(191\) | −7.58579 | + | 13.1390i | −0.548888 | + | 0.950702i | 0.449463 | + | 0.893299i | \(0.351615\pi\) |
−0.998351 | + | 0.0574033i | \(0.981718\pi\) | |||||||
\(192\) | 5.65685 | + | 9.79796i | 0.408248 | + | 0.707107i | ||||
\(193\) | 7.24264 | + | 12.5446i | 0.521337 | + | 0.902982i | 0.999692 | + | 0.0248153i | \(0.00789976\pi\) |
−0.478355 | + | 0.878166i | \(0.658767\pi\) | |||||||
\(194\) | −8.29289 | + | 14.3637i | −0.595395 | + | 1.03125i | ||||
\(195\) | 2.24264 | 0.160599 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3431 | 0.879413 | 0.439706 | − | 0.898142i | \(-0.355083\pi\) | ||||
0.439706 | + | 0.898142i | \(0.355083\pi\) | |||||||
\(198\) | −3.00000 | + | 5.19615i | −0.213201 | + | 0.369274i | ||||
\(199\) | −1.87868 | − | 3.25397i | −0.133176 | − | 0.230668i | 0.791723 | − | 0.610880i | \(-0.209184\pi\) |
−0.924899 | + | 0.380212i | \(0.875851\pi\) | |||||||
\(200\) | 3.51472 | + | 6.08767i | 0.248528 | + | 0.430463i | ||||
\(201\) | −10.2426 | + | 17.7408i | −0.722460 | + | 1.25134i | ||||
\(202\) | 14.4853 | 1.01918 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.00000 | + | 12.1244i | −0.488901 | + | 0.846802i | ||||
\(206\) | 5.65685 | + | 9.79796i | 0.394132 | + | 0.682656i | ||||
\(207\) | −2.91421 | − | 5.04757i | −0.202552 | − | 0.350830i | ||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 30.7279 | 2.12549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9706 | −1.09946 | −0.549729 | − | 0.835343i | \(-0.685269\pi\) | ||||
−0.549729 | + | 0.835343i | \(0.685269\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.24264 | − | 16.0087i | −0.633295 | − | 1.09690i | ||||
\(214\) | −14.2426 | − | 24.6690i | −0.973607 | − | 1.68634i | ||||
\(215\) | −3.96447 | + | 6.86666i | −0.270374 | + | 0.468302i | ||||
\(216\) | 16.0000 | 1.08866 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −23.6569 | −1.60224 | ||||||||
\(219\) | 6.53553 | − | 11.3199i | 0.441630 | − | 0.764926i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.707107 | + | 1.22474i | 0.0475651 | + | 0.0823853i | ||||
\(222\) | −2.24264 | + | 3.88437i | −0.150516 | + | 0.260702i | ||||
\(223\) | −0.757359 | −0.0507165 | −0.0253583 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253583 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.48528 | 0.165685 | ||||||||
\(226\) | 1.63604 | − | 2.83370i | 0.108828 | − | 0.188495i | ||||
\(227\) | 13.4142 | + | 23.2341i | 0.890333 | + | 1.54210i | 0.839477 | + | 0.543395i | \(0.182862\pi\) |
0.0508557 | + | 0.998706i | \(0.483805\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.7279 | − | 25.5095i | 0.973248 | − | 1.68572i | 0.287651 | − | 0.957735i | \(-0.407126\pi\) |
0.685598 | − | 0.727980i | \(-0.259541\pi\) | |||||||
\(230\) | −13.0711 | −0.861881 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.485281 | 0.0318603 | ||||||||
\(233\) | 7.32843 | − | 12.6932i | 0.480101 | − | 0.831560i | −0.519638 | − | 0.854386i | \(-0.673933\pi\) |
0.999739 | + | 0.0228267i | \(0.00726659\pi\) | |||||||
\(234\) | −0.707107 | − | 1.22474i | −0.0462250 | − | 0.0800641i | ||||
\(235\) | −1.25736 | − | 2.17781i | −0.0820211 | − | 0.142065i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.8995 | −1.42253 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.51472 | 0.227348 | 0.113674 | − | 0.993518i | \(-0.463738\pi\) | ||||
0.113674 | + | 0.993518i | \(0.463738\pi\) | |||||||
\(240\) | 4.48528 | − | 7.76874i | 0.289524 | − | 0.501470i | ||||
\(241\) | −10.1066 | − | 17.5051i | −0.651023 | − | 1.12761i | −0.982875 | − | 0.184274i | \(-0.941007\pi\) |
0.331851 | − | 0.943332i | \(-0.392327\pi\) | |||||||
\(242\) | 4.94975 | + | 8.57321i | 0.318182 | + | 0.551107i | ||||
\(243\) | 4.94975 | − | 8.57321i | 0.317526 | − | 0.549972i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −17.6569 | −1.12576 | ||||||||
\(247\) | −3.62132 | + | 6.27231i | −0.230419 | + | 0.399098i | ||||
\(248\) | 4.58579 | + | 7.94282i | 0.291198 | + | 0.504369i | ||||
\(249\) | −9.36396 | − | 16.2189i | −0.593417 | − | 1.02783i | ||||
\(250\) | 8.39340 | − | 14.5378i | 0.530845 | − | 0.919451i | ||||
\(251\) | −16.5858 | −1.04689 | −0.523443 | − | 0.852061i | \(-0.675353\pi\) | ||||
−0.523443 | + | 0.852061i | \(0.675353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.7279 | −1.55463 | ||||||||
\(254\) | 1.41421 | − | 2.44949i | 0.0887357 | − | 0.153695i | ||||
\(255\) | 1.58579 | + | 2.74666i | 0.0993058 | + | 0.172003i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.70711 | + | 16.8132i | −0.605513 | + | 1.04878i | 0.386458 | + | 0.922307i | \(0.373699\pi\) |
−0.991970 | + | 0.126472i | \(0.959635\pi\) | |||||||
\(258\) | −10.0000 | −0.622573 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0857864 | − | 0.148586i | 0.00531005 | − | 0.00919727i | ||||
\(262\) | 2.00000 | + | 3.46410i | 0.123560 | + | 0.214013i | ||||
\(263\) | −0.985281 | − | 1.70656i | −0.0607551 | − | 0.105231i | 0.834048 | − | 0.551692i | \(-0.186018\pi\) |
−0.894803 | + | 0.446461i | \(0.852684\pi\) | |||||||
\(264\) | 8.48528 | − | 14.6969i | 0.522233 | − | 0.904534i | ||||
\(265\) | 0.272078 | 0.0167136 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.24264 | 0.137247 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.58579 | + | 7.94282i | 0.279600 | + | 0.484282i | 0.971285 | − | 0.237917i | \(-0.0764647\pi\) |
−0.691685 | + | 0.722199i | \(0.743131\pi\) | |||||||
\(270\) | −6.34315 | − | 10.9867i | −0.386032 | − | 0.668626i | ||||
\(271\) | 10.0000 | − | 17.3205i | 0.607457 | − | 1.05215i | −0.384201 | − | 0.923249i | \(-0.625523\pi\) |
0.991658 | − | 0.128897i | \(-0.0411435\pi\) | |||||||
\(272\) | 5.65685 | 0.342997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.48528 | 0.391790 | ||||||||
\(275\) | 5.27208 | − | 9.13151i | 0.317918 | − | 0.550651i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.74264 | + | 6.48244i | 0.224873 | + | 0.389492i | 0.956281 | − | 0.292448i | \(-0.0944698\pi\) |
−0.731408 | + | 0.681940i | \(0.761136\pi\) | |||||||
\(278\) | −4.41421 | + | 7.64564i | −0.264747 | + | 0.458555i | ||||
\(279\) | 3.24264 | 0.194132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.5563 | 0.928014 | 0.464007 | − | 0.885832i | \(-0.346411\pi\) | ||||
0.464007 | + | 0.885832i | \(0.346411\pi\) | |||||||
\(282\) | 1.58579 | − | 2.74666i | 0.0944322 | − | 0.163561i | ||||
\(283\) | −4.24264 | − | 7.34847i | −0.252199 | − | 0.436821i | 0.711932 | − | 0.702248i | \(-0.247820\pi\) |
−0.964131 | + | 0.265427i | \(0.914487\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.12132 | + | 14.0665i | −0.481065 | + | 0.833230i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.50000 | − | 12.9904i | 0.441176 | − | 0.764140i | ||||
\(290\) | −0.192388 | − | 0.333226i | −0.0112974 | − | 0.0195677i | ||||
\(291\) | −8.29289 | − | 14.3637i | −0.486138 | − | 0.842016i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3848 | −0.898788 | −0.449394 | − | 0.893334i | \(-0.648360\pi\) | ||||
−0.449394 | + | 0.893334i | \(0.648360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.544156 | 0.0316820 | ||||||||
\(296\) | −3.17157 | + | 5.49333i | −0.184344 | + | 0.319293i | ||||
\(297\) | −12.0000 | − | 20.7846i | −0.696311 | − | 1.20605i | ||||
\(298\) | 11.4853 | + | 19.8931i | 0.665324 | + | 1.15238i | ||||
\(299\) | 2.91421 | − | 5.04757i | 0.168533 | − | 0.291908i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.7990 | 0.794043 | ||||||||
\(303\) | −7.24264 | + | 12.5446i | −0.416079 | + | 0.720670i | ||||
\(304\) | 14.4853 | + | 25.0892i | 0.830788 | + | 1.43897i | ||||
\(305\) | −4.75736 | − | 8.23999i | −0.272406 | − | 0.471820i | ||||
\(306\) | 1.00000 | − | 1.73205i | 0.0571662 | − | 0.0990148i | ||||
\(307\) | −13.2426 | −0.755797 | −0.377899 | − | 0.925847i | \(-0.623353\pi\) | ||||
−0.377899 | + | 0.925847i | \(0.623353\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.3137 | −0.643614 | ||||||||
\(310\) | 3.63604 | − | 6.29780i | 0.206513 | − | 0.357691i | ||||
\(311\) | −3.70711 | − | 6.42090i | −0.210211 | − | 0.364096i | 0.741570 | − | 0.670876i | \(-0.234082\pi\) |
−0.951780 | + | 0.306780i | \(0.900748\pi\) | |||||||
\(312\) | 2.00000 | + | 3.46410i | 0.113228 | + | 0.196116i | ||||
\(313\) | 11.6066 | − | 20.1032i | 0.656044 | − | 1.13630i | −0.325587 | − | 0.945512i | \(-0.605562\pi\) |
0.981631 | − | 0.190789i | \(-0.0611047\pi\) | |||||||
\(314\) | −5.31371 | −0.299870 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.65685 | − | 9.79796i | 0.317721 | − | 0.550308i | −0.662291 | − | 0.749246i | \(-0.730416\pi\) |
0.980012 | + | 0.198938i | \(0.0637493\pi\) | |||||||
\(318\) | 0.171573 | + | 0.297173i | 0.00962133 | + | 0.0166646i | ||||
\(319\) | −0.363961 | − | 0.630399i | −0.0203779 | − | 0.0352956i | ||||
\(320\) | 6.34315 | − | 10.9867i | 0.354593 | − | 0.614172i | ||||
\(321\) | 28.4853 | 1.58989 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.2426 | −0.569916 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.24264 | + | 2.15232i | 0.0689293 | + | 0.119389i | ||||
\(326\) | 6.00000 | + | 10.3923i | 0.332309 | + | 0.575577i | ||||
\(327\) | 11.8284 | − | 20.4874i | 0.654114 | − | 1.13296i | ||||
\(328\) | −24.9706 | −1.37877 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −13.4558 | −0.740720 | ||||||||
\(331\) | 9.00000 | − | 15.5885i | 0.494685 | − | 0.856819i | −0.505296 | − | 0.862946i | \(-0.668617\pi\) |
0.999981 | + | 0.00612670i | \(0.00195020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.12132 | + | 1.94218i | 0.0614480 | + | 0.106431i | ||||
\(334\) | −10.8787 | + | 18.8424i | −0.595255 | + | 1.03101i | ||||
\(335\) | 22.9706 | 1.25502 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0000 | −1.79762 | −0.898812 | − | 0.438334i | \(-0.855569\pi\) | ||||
−0.898812 | + | 0.438334i | \(0.855569\pi\) | |||||||
\(338\) | 0.707107 | − | 1.22474i | 0.0384615 | − | 0.0666173i | ||||
\(339\) | 1.63604 | + | 2.83370i | 0.0888574 | + | 0.153906i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.87868 | − | 11.9142i | 0.372501 | − | 0.645191i | ||||
\(342\) | 10.2426 | 0.553859 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −14.1421 | −0.762493 | ||||||||
\(345\) | 6.53553 | − | 11.3199i | 0.351861 | − | 0.609442i | ||||
\(346\) | −17.4853 | − | 30.2854i | −0.940015 | − | 1.62815i | ||||
\(347\) | 2.82843 | + | 4.89898i | 0.151838 | + | 0.262991i | 0.931903 | − | 0.362707i | \(-0.118147\pi\) |
−0.780065 | + | 0.625698i | \(0.784814\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7279 | 1.37718 | 0.688592 | − | 0.725149i | \(-0.258229\pi\) | ||||
0.688592 | + | 0.725149i | \(0.258229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.65685 | 0.301941 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.24264 | − | 7.34847i | −0.225813 | − | 0.391120i | 0.730750 | − | 0.682645i | \(-0.239170\pi\) |
−0.956563 | + | 0.291526i | \(0.905837\pi\) | |||||||
\(354\) | 0.343146 | + | 0.594346i | 0.0182380 | + | 0.0315891i | ||||
\(355\) | −10.3640 | + | 17.9509i | −0.550062 | + | 0.952735i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.7279 | 0.672692 | ||||||||
\(359\) | 13.9497 | − | 24.1617i | 0.736240 | − | 1.27520i | −0.217938 | − | 0.975963i | \(-0.569933\pi\) |
0.954177 | − | 0.299242i | \(-0.0967337\pi\) | |||||||
\(360\) | −2.24264 | − | 3.88437i | −0.118198 | − | 0.204724i | ||||
\(361\) | −16.7279 | − | 28.9736i | −0.880417 | − | 1.52493i | ||||
\(362\) | 13.2426 | − | 22.9369i | 0.696018 | − | 1.20554i | ||||
\(363\) | −9.89949 | −0.519589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.6569 | −0.767175 | ||||||||
\(366\) | 6.00000 | − | 10.3923i | 0.313625 | − | 0.543214i | ||||
\(367\) | 5.12132 | + | 8.87039i | 0.267331 | + | 0.463030i | 0.968172 | − | 0.250287i | \(-0.0805250\pi\) |
−0.700841 | + | 0.713318i | \(0.747192\pi\) | |||||||
\(368\) | −11.6569 | − | 20.1903i | −0.607656 | − | 1.05249i | ||||
\(369\) | −4.41421 | + | 7.64564i | −0.229795 | + | 0.398016i | ||||
\(370\) | 5.02944 | 0.261468 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.24264 | + | 7.34847i | −0.219676 | + | 0.380489i | −0.954709 | − | 0.297542i | \(-0.903833\pi\) |
0.735033 | + | 0.678031i | \(0.237167\pi\) | |||||||
\(374\) | −4.24264 | − | 7.34847i | −0.219382 | − | 0.379980i | ||||
\(375\) | 8.39340 | + | 14.5378i | 0.433433 | + | 0.750728i | ||||
\(376\) | 2.24264 | − | 3.88437i | 0.115655 | − | 0.200321i | ||||
\(377\) | 0.171573 | 0.00883645 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.7574 | 1.22033 | 0.610167 | − | 0.792273i | \(-0.291102\pi\) | ||||
0.610167 | + | 0.792273i | \(0.291102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.41421 | + | 2.44949i | 0.0724524 | + | 0.125491i | ||||
\(382\) | 10.7279 | + | 18.5813i | 0.548888 | + | 0.950702i | ||||
\(383\) | −10.2426 | + | 17.7408i | −0.523374 | + | 0.906511i | 0.476255 | + | 0.879307i | \(0.341994\pi\) |
−0.999630 | + | 0.0272042i | \(0.991340\pi\) | |||||||
\(384\) | 16.0000 | 0.816497 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.4853 | 1.04267 | ||||||||
\(387\) | −2.50000 | + | 4.33013i | −0.127082 | + | 0.220113i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.8284 | − | 25.6836i | −0.751831 | − | 1.30221i | −0.946934 | − | 0.321427i | \(-0.895838\pi\) |
0.195103 | − | 0.980783i | \(-0.437496\pi\) | |||||||
\(390\) | 1.58579 | − | 2.74666i | 0.0802994 | − | 0.139083i | ||||
\(391\) | 8.24264 | 0.416848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 8.72792 | − | 15.1172i | 0.439706 | − | 0.761594i | ||||
\(395\) | 12.2782 | + | 21.2664i | 0.617782 | + | 1.07003i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.10660 | + | 15.7731i | −0.457047 | + | 0.791629i | −0.998803 | − | 0.0489067i | \(-0.984426\pi\) |
0.541756 | + | 0.840536i | \(0.317760\pi\) | |||||||
\(398\) | −5.31371 | −0.266352 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.94113 | 0.497056 | ||||||||
\(401\) | −3.17157 | + | 5.49333i | −0.158381 | + | 0.274324i | −0.934285 | − | 0.356527i | \(-0.883961\pi\) |
0.775904 | + | 0.630851i | \(0.217294\pi\) | |||||||
\(402\) | 14.4853 | + | 25.0892i | 0.722460 | + | 1.25134i | ||||
\(403\) | 1.62132 | + | 2.80821i | 0.0807637 | + | 0.139887i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.92893 | 0.393992 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.51472 | 0.471627 | ||||||||
\(408\) | −2.82843 | + | 4.89898i | −0.140028 | + | 0.242536i | ||||
\(409\) | 1.62132 | + | 2.80821i | 0.0801691 | + | 0.138857i | 0.903322 | − | 0.428962i | \(-0.141121\pi\) |
−0.823153 | + | 0.567819i | \(0.807787\pi\) | |||||||
\(410\) | 9.89949 | + | 17.1464i | 0.488901 | + | 0.846802i | ||||
\(411\) | −3.24264 | + | 5.61642i | −0.159948 | + | 0.277037i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.24264 | −0.405104 | ||||||||
\(415\) | −10.5000 | + | 18.1865i | −0.515425 | + | 0.892742i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.41421 | − | 7.64564i | −0.216165 | − | 0.374409i | ||||
\(418\) | 21.7279 | − | 37.6339i | 1.06275 | − | 1.84073i | ||||
\(419\) | 20.8701 | 1.01957 | 0.509785 | − | 0.860302i | \(-0.329725\pi\) | ||||
0.509785 | + | 0.860302i | \(0.329725\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.72792 | 0.327899 | 0.163949 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163949 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(422\) | −11.2929 | + | 19.5599i | −0.549729 | + | 0.952159i | ||||
\(423\) | −0.792893 | − | 1.37333i | −0.0385518 | − | 0.0667737i | ||||
\(424\) | 0.242641 | + | 0.420266i | 0.0117837 | + | 0.0204099i | ||||
\(425\) | −1.75736 | + | 3.04384i | −0.0852444 | + | 0.147648i | ||||
\(426\) | −26.1421 | −1.26659 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.00000 | − | 5.19615i | 0.144841 | − | 0.250873i | ||||
\(430\) | 5.60660 | + | 9.71092i | 0.270374 | + | 0.468302i | ||||
\(431\) | 6.17157 | + | 10.6895i | 0.297274 | + | 0.514894i | 0.975511 | − | 0.219949i | \(-0.0705891\pi\) |
−0.678237 | + | 0.734843i | \(0.737256\pi\) | |||||||
\(432\) | 11.3137 | − | 19.5959i | 0.544331 | − | 0.942809i | ||||
\(433\) | 24.9706 | 1.20001 | 0.600004 | − | 0.799997i | \(-0.295166\pi\) | ||||
0.600004 | + | 0.799997i | \(0.295166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.384776 | 0.0184486 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.1066 | + | 36.5577i | 1.00967 | + | 1.74879i | ||||
\(438\) | −9.24264 | − | 16.0087i | −0.441630 | − | 0.764926i | ||||
\(439\) | −17.2426 | + | 29.8651i | −0.822946 | + | 1.42538i | 0.0805324 | + | 0.996752i | \(0.474338\pi\) |
−0.903479 | + | 0.428633i | \(0.858995\pi\) | |||||||
\(440\) | −19.0294 | −0.907193 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | 1.84315 | − | 3.19242i | 0.0875705 | − | 0.151677i | −0.818913 | − | 0.573917i | \(-0.805423\pi\) |
0.906484 | + | 0.422241i | \(0.138756\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.25736 | − | 2.17781i | −0.0596045 | − | 0.103238i | ||||
\(446\) | −0.535534 | + | 0.927572i | −0.0253583 | + | 0.0439218i | ||||
\(447\) | −22.9706 | −1.08647 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.1716 | 0.999148 | 0.499574 | − | 0.866271i | \(-0.333490\pi\) | ||||
0.499574 | + | 0.866271i | \(0.333490\pi\) | |||||||
\(450\) | 1.75736 | − | 3.04384i | 0.0828427 | − | 0.143488i | ||||
\(451\) | 18.7279 | + | 32.4377i | 0.881863 | + | 1.52743i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.89949 | + | 11.9503i | −0.324167 | + | 0.561473i | ||||
\(454\) | 37.9411 | 1.78067 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −28.9706 | −1.35667 | ||||||||
\(457\) | 3.60660 | − | 6.24682i | 0.168710 | − | 0.292214i | −0.769257 | − | 0.638940i | \(-0.779373\pi\) |
0.937966 | + | 0.346726i | \(0.112707\pi\) | |||||||
\(458\) | −20.8284 | − | 36.0759i | −0.973248 | − | 1.68572i | ||||
\(459\) | 4.00000 | + | 6.92820i | 0.186704 | + | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.82843 | −0.411181 | −0.205590 | − | 0.978638i | \(-0.565911\pi\) | ||||
−0.205590 | + | 0.978638i | \(0.565911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.24264 | −0.197172 | −0.0985861 | − | 0.995129i | \(-0.531432\pi\) | ||||
−0.0985861 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(464\) | 0.343146 | − | 0.594346i | 0.0159301 | − | 0.0275918i | ||||
\(465\) | 3.63604 | + | 6.29780i | 0.168617 | + | 0.292054i | ||||
\(466\) | −10.3640 | − | 17.9509i | −0.480101 | − | 0.831560i | ||||
\(467\) | −1.94975 | + | 3.37706i | −0.0902236 | + | 0.156272i | −0.907605 | − | 0.419825i | \(-0.862091\pi\) |
0.817382 | + | 0.576097i | \(0.195425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.55635 | −0.164042 | ||||||||
\(471\) | 2.65685 | − | 4.60181i | 0.122421 | − | 0.212040i | ||||
\(472\) | 0.485281 | + | 0.840532i | 0.0223369 | + | 0.0386886i | ||||
\(473\) | 10.6066 | + | 18.3712i | 0.487692 | + | 0.844707i | ||||
\(474\) | −15.4853 | + | 26.8213i | −0.711263 | + | 1.23194i | ||||
\(475\) | −18.0000 | −0.825897 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.171573 | 0.00785578 | ||||||||
\(478\) | 2.48528 | − | 4.30463i | 0.113674 | − | 0.196889i | ||||
\(479\) | −3.10660 | − | 5.38079i | −0.141944 | − | 0.245855i | 0.786284 | − | 0.617865i | \(-0.212002\pi\) |
−0.928229 | + | 0.372010i | \(0.878669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.12132 | + | 1.94218i | −0.0511278 | + | 0.0885560i | ||||
\(482\) | −28.5858 | −1.30205 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.29899 | + | 16.1063i | −0.422245 | + | 0.731350i | ||||
\(486\) | −7.00000 | − | 12.1244i | −0.317526 | − | 0.549972i | ||||
\(487\) | 5.72792 | + | 9.92105i | 0.259557 | + | 0.449566i | 0.966123 | − | 0.258081i | \(-0.0830901\pi\) |
−0.706566 | + | 0.707647i | \(0.749757\pi\) | |||||||
\(488\) | 8.48528 | − | 14.6969i | 0.384111 | − | 0.665299i | ||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.6274 | 0.750385 | 0.375192 | − | 0.926947i | \(-0.377577\pi\) | ||||
0.375192 | + | 0.926947i | \(0.377577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.121320 | + | 0.210133i | 0.00546399 | + | 0.00946391i | ||||
\(494\) | 5.12132 | + | 8.87039i | 0.230419 | + | 0.399098i | ||||
\(495\) | −3.36396 | + | 5.82655i | −0.151199 | + | 0.261884i | ||||
\(496\) | 12.9706 | 0.582395 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −26.4853 | −1.18683 | ||||||||
\(499\) | 6.63604 | − | 11.4940i | 0.297070 | − | 0.514540i | −0.678394 | − | 0.734698i | \(-0.737324\pi\) |
0.975464 | + | 0.220158i | \(0.0706572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.8787 | − | 18.8424i | −0.486024 | − | 0.841818i | ||||
\(502\) | −11.7279 | + | 20.3134i | −0.523443 | + | 0.906629i | ||||
\(503\) | 28.6274 | 1.27643 | 0.638217 | − | 0.769857i | \(-0.279672\pi\) | ||||
0.638217 | + | 0.769857i | \(0.279672\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.2426 | 0.722788 | ||||||||
\(506\) | −17.4853 | + | 30.2854i | −0.777316 | + | 1.34635i | ||||
\(507\) | 0.707107 | + | 1.22474i | 0.0314037 | + | 0.0543928i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.55025 | + | 4.41717i | −0.113038 | + | 0.195787i | −0.916994 | − | 0.398902i | \(-0.869392\pi\) |
0.803956 | + | 0.594689i | \(0.202725\pi\) | |||||||
\(510\) | 4.48528 | 0.198612 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −20.4853 | + | 35.4815i | −0.904447 | + | 1.56655i | ||||
\(514\) | 13.7279 | + | 23.7775i | 0.605513 | + | 1.04878i | ||||
\(515\) | 6.34315 | + | 10.9867i | 0.279512 | + | 0.484130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.72792 | −0.295894 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.9706 | 1.53504 | ||||||||
\(520\) | 2.24264 | − | 3.88437i | 0.0983463 | − | 0.170341i | ||||
\(521\) | −3.17157 | − | 5.49333i | −0.138949 | − | 0.240667i | 0.788150 | − | 0.615483i | \(-0.211039\pi\) |
−0.927099 | + | 0.374816i | \(0.877706\pi\) | |||||||
\(522\) | −0.121320 | − | 0.210133i | −0.00531005 | − | 0.00919727i | ||||
\(523\) | 15.4853 | − | 26.8213i | 0.677124 | − | 1.17281i | −0.298719 | − | 0.954341i | \(-0.596559\pi\) |
0.975843 | − | 0.218472i | \(-0.0701073\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.78680 | −0.121510 | ||||||||
\(527\) | −2.29289 | + | 3.97141i | −0.0998800 | + | 0.172997i | ||||
\(528\) | −12.0000 | − | 20.7846i | −0.522233 | − | 0.904534i | ||||
\(529\) | −5.48528 | − | 9.50079i | −0.238490 | − | 0.413078i | ||||
\(530\) | 0.192388 | − | 0.333226i | 0.00835681 | − | 0.0144744i | ||||
\(531\) | 0.343146 | 0.0148913 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.82843 | −0.382402 | ||||||||
\(534\) | 1.58579 | − | 2.74666i | 0.0686237 | − | 0.118860i | ||||
\(535\) | −15.9706 | − | 27.6618i | −0.690468 | − | 1.19593i | ||||
\(536\) | 20.4853 | + | 35.4815i | 0.884829 | + | 1.53257i | ||||
\(537\) | −6.36396 | + | 11.0227i | −0.274625 | + | 0.475665i | ||||
\(538\) | 12.9706 | 0.559201 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.60660 | − | 6.24682i | 0.155060 | − | 0.268572i | −0.778021 | − | 0.628238i | \(-0.783776\pi\) |
0.933081 | + | 0.359667i | \(0.117110\pi\) | |||||||
\(542\) | −14.1421 | − | 24.4949i | −0.607457 | − | 1.05215i | ||||
\(543\) | 13.2426 | + | 22.9369i | 0.568296 | + | 0.984318i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.5269 | −1.13629 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.4853 | 1.51724 | 0.758621 | − | 0.651533i | \(-0.225874\pi\) | ||||
0.758621 | + | 0.651533i | \(0.225874\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.00000 | − | 5.19615i | −0.128037 | − | 0.221766i | ||||
\(550\) | −7.45584 | − | 12.9139i | −0.317918 | − | 0.550651i | ||||
\(551\) | −0.621320 | + | 1.07616i | −0.0264691 | + | 0.0458459i | ||||
\(552\) | 23.3137 | 0.992297 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.5858 | 0.449747 | ||||||||
\(555\) | −2.51472 | + | 4.35562i | −0.106744 | + | 0.184886i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | − | 10.3923i | −0.254228 | − | 0.440336i | 0.710457 | − | 0.703740i | \(-0.248488\pi\) |
−0.964686 | + | 0.263404i | \(0.915155\pi\) | |||||||
\(558\) | 2.29289 | − | 3.97141i | 0.0970659 | − | 0.168123i | ||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.48528 | 0.358249 | ||||||||
\(562\) | 11.0000 | − | 19.0526i | 0.464007 | − | 0.803684i | ||||
\(563\) | −3.17157 | − | 5.49333i | −0.133666 | − | 0.231516i | 0.791421 | − | 0.611271i | \(-0.209342\pi\) |
−0.925087 | + | 0.379755i | \(0.876008\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.83452 | − | 3.17749i | 0.0771790 | − | 0.133678i | ||||
\(566\) | −12.0000 | −0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −36.9706 | −1.55125 | ||||||||
\(569\) | −2.57107 | + | 4.45322i | −0.107785 | + | 0.186689i | −0.914873 | − | 0.403743i | \(-0.867709\pi\) |
0.807088 | + | 0.590431i | \(0.201042\pi\) | |||||||
\(570\) | 11.4853 | + | 19.8931i | 0.481065 | + | 0.833230i | ||||
\(571\) | −21.2279 | − | 36.7678i | −0.888361 | − | 1.53869i | −0.841812 | − | 0.539770i | \(-0.818511\pi\) |
−0.0465485 | − | 0.998916i | \(-0.514822\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.4558 | −0.896331 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.4853 | 0.604078 | ||||||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | −3.48528 | − | 6.03668i | −0.145094 | − | 0.251310i | 0.784314 | − | 0.620364i | \(-0.213015\pi\) |
−0.929408 | + | 0.369054i | \(0.879682\pi\) | |||||||
\(578\) | −10.6066 | − | 18.3712i | −0.441176 | − | 0.764140i | ||||
\(579\) | −10.2426 | + | 17.7408i | −0.425670 | + | 0.737281i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −23.4558 | −0.972276 | ||||||||
\(583\) | 0.363961 | − | 0.630399i | 0.0150737 | − | 0.0261085i | ||||
\(584\) | −13.0711 | − | 22.6398i | −0.540885 | − | 0.936840i | ||||
\(585\) | −0.792893 | − | 1.37333i | −0.0327821 | − | 0.0567803i | ||||
\(586\) | −10.8787 | + | 18.8424i | −0.449394 | + | 0.778373i | ||||
\(587\) | 6.55635 | 0.270609 | 0.135305 | − | 0.990804i | \(-0.456799\pi\) | ||||
0.135305 | + | 0.990804i | \(0.456799\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.4853 | −0.967694 | ||||||||
\(590\) | 0.384776 | − | 0.666452i | 0.0158410 | − | 0.0274374i | ||||
\(591\) | 8.72792 | + | 15.1172i | 0.359019 | + | 0.621839i | ||||
\(592\) | 4.48528 | + | 7.76874i | 0.184344 | + | 0.319293i | ||||
\(593\) | −0.278175 | + | 0.481813i | −0.0114233 | + | 0.0197857i | −0.871681 | − | 0.490075i | \(-0.836970\pi\) |
0.860257 | + | 0.509860i | \(0.170303\pi\) | |||||||
\(594\) | −33.9411 | −1.39262 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.65685 | − | 4.60181i | 0.108738 | − | 0.188339i | ||||
\(598\) | −4.12132 | − | 7.13834i | −0.168533 | − | 0.291908i | ||||
\(599\) | 14.3995 | + | 24.9407i | 0.588347 | + | 1.01905i | 0.994449 | + | 0.105220i | \(0.0335546\pi\) |
−0.406102 | + | 0.913828i | \(0.633112\pi\) | |||||||
\(600\) | −4.97056 | + | 8.60927i | −0.202922 | + | 0.351472i | ||||
\(601\) | 38.9706 | 1.58964 | 0.794821 | − | 0.606844i | \(-0.207565\pi\) | ||||
0.794821 | + | 0.606844i | \(0.207565\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.4853 | 0.589886 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.55025 | + | 9.61332i | 0.225650 | + | 0.390837i | ||||
\(606\) | 10.2426 | + | 17.7408i | 0.416079 | + | 0.720670i | ||||
\(607\) | −13.3640 | + | 23.1471i | −0.542426 | + | 0.939510i | 0.456338 | + | 0.889807i | \(0.349161\pi\) |
−0.998764 | + | 0.0497034i | \(0.984172\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.4558 | −0.544811 | ||||||||
\(611\) | 0.792893 | − | 1.37333i | 0.0320770 | − | 0.0555590i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | + | 13.8564i | 0.323117 | + | 0.559655i | 0.981129 | − | 0.193352i | \(-0.0619359\pi\) |
−0.658012 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(614\) | −9.36396 | + | 16.2189i | −0.377899 | + | 0.654540i | ||||
\(615\) | −19.7990 | −0.798372 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.3431 | 0.496916 | 0.248458 | − | 0.968643i | \(-0.420076\pi\) | ||||
0.248458 | + | 0.968643i | \(0.420076\pi\) | |||||||
\(618\) | −8.00000 | + | 13.8564i | −0.321807 | + | 0.557386i | ||||
\(619\) | 0.485281 | + | 0.840532i | 0.0195051 | + | 0.0337838i | 0.875613 | − | 0.483013i | \(-0.160458\pi\) |
−0.856108 | + | 0.516797i | \(0.827124\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.4853 | − | 28.5533i | 0.661532 | − | 1.14581i | ||||
\(622\) | −10.4853 | −0.420421 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.65685 | 0.226455 | ||||||||
\(625\) | 3.19848 | − | 5.53994i | 0.127939 | − | 0.221598i | ||||
\(626\) | −16.4142 | − | 28.4303i | −0.656044 | − | 1.13630i | ||||
\(627\) | 21.7279 | + | 37.6339i | 0.867730 | + | 1.50295i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.17157 | −0.126459 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | −21.8995 | + | 37.9310i | −0.871115 | + | 1.50882i | ||||
\(633\) | −11.2929 | − | 19.5599i | −0.448852 | − | 0.777435i | ||||
\(634\) | −8.00000 | − | 13.8564i | −0.317721 | − | 0.550308i | ||||
\(635\) | 1.58579 | − | 2.74666i | 0.0629300 | − | 0.108998i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.02944 | −0.0407558 | ||||||||
\(639\) | −6.53553 | + | 11.3199i | −0.258542 | + | 0.447807i | ||||
\(640\) | −8.97056 | − | 15.5375i | −0.354593 | − | 0.614172i | ||||
\(641\) | −7.67157 | − | 13.2876i | −0.303009 | − | 0.524827i | 0.673807 | − | 0.738907i | \(-0.264658\pi\) |
−0.976816 | + | 0.214080i | \(0.931325\pi\) | |||||||
\(642\) | 20.1421 | − | 34.8872i | 0.794947 | − | 1.37689i | ||||
\(643\) | 12.4853 | 0.492371 | 0.246186 | − | 0.969223i | \(-0.420823\pi\) | ||||
0.246186 | + | 0.969223i | \(0.420823\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.2132 | −0.441519 | ||||||||
\(646\) | −7.24264 | + | 12.5446i | −0.284958 | + | 0.493562i | ||||
\(647\) | 7.26346 | + | 12.5807i | 0.285556 | + | 0.494597i | 0.972744 | − | 0.231882i | \(-0.0744884\pi\) |
−0.687188 | + | 0.726480i | \(0.741155\pi\) | |||||||
\(648\) | 7.07107 | + | 12.2474i | 0.277778 | + | 0.481125i | ||||
\(649\) | 0.727922 | − | 1.26080i | 0.0285734 | − | 0.0494907i | ||||
\(650\) | 3.51472 | 0.137859 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.65685 | + | 14.9941i | −0.338769 | + | 0.586765i | −0.984201 | − | 0.177052i | \(-0.943344\pi\) |
0.645433 | + | 0.763817i | \(0.276677\pi\) | |||||||
\(654\) | −16.7279 | − | 28.9736i | −0.654114 | − | 1.13296i | ||||
\(655\) | 2.24264 | + | 3.88437i | 0.0876272 | + | 0.151775i | ||||
\(656\) | −17.6569 | + | 30.5826i | −0.689384 | + | 1.19405i | ||||
\(657\) | −9.24264 | −0.360590 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.3431 | −0.597684 | −0.298842 | − | 0.954303i | \(-0.596600\pi\) | ||||
−0.298842 | + | 0.954303i | \(0.596600\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.37868 | − | 9.31615i | −0.209206 | − | 0.362356i | 0.742258 | − | 0.670114i | \(-0.233755\pi\) |
−0.951465 | + | 0.307758i | \(0.900421\pi\) | |||||||
\(662\) | −12.7279 | − | 22.0454i | −0.494685 | − | 0.856819i | ||||
\(663\) | −1.00000 | + | 1.73205i | −0.0388368 | + | 0.0672673i | ||||
\(664\) | −37.4558 | −1.45357 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.17157 | 0.122896 | ||||||||
\(667\) | 0.500000 | − | 0.866025i | 0.0193601 | − | 0.0335326i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.535534 | − | 0.927572i | −0.0207049 | − | 0.0358620i | ||||
\(670\) | 16.2426 | − | 28.1331i | 0.627508 | − | 1.08688i | ||||
\(671\) | −25.4558 | −0.982712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.9411 | −1.03850 | −0.519252 | − | 0.854621i | \(-0.673789\pi\) | ||||
−0.519252 | + | 0.854621i | \(0.673789\pi\) | |||||||
\(674\) | −23.3345 | + | 40.4166i | −0.898812 | + | 1.55679i | ||||
\(675\) | 7.02944 | + | 12.1753i | 0.270563 | + | 0.468629i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.6777 | + | 35.8148i | −0.794707 | + | 1.37647i | 0.128317 | + | 0.991733i | \(0.459042\pi\) |
−0.923025 | + | 0.384740i | \(0.874291\pi\) | |||||||
\(678\) | 4.62742 | 0.177715 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.34315 | 0.243249 | ||||||||
\(681\) | −18.9706 | + | 32.8580i | −0.726954 | + | 1.25912i | ||||
\(682\) | −9.72792 | − | 16.8493i | −0.372501 | − | 0.645191i | ||||
\(683\) | 10.5858 | + | 18.3351i | 0.405054 | + | 0.701574i | 0.994328 | − | 0.106359i | \(-0.0339194\pi\) |
−0.589274 | + | 0.807933i | \(0.700586\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.27208 | 0.277852 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.6569 | 1.58931 | ||||||||
\(688\) | −10.0000 | + | 17.3205i | −0.381246 | + | 0.660338i | ||||
\(689\) | 0.0857864 | + | 0.148586i | 0.00326820 | + | 0.00566069i | ||||
\(690\) | −9.24264 | − | 16.0087i | −0.351861 | − | 0.609442i | ||||
\(691\) | 14.3492 | − | 24.8536i | 0.545871 | − | 0.945476i | −0.452681 | − | 0.891673i | \(-0.649532\pi\) |
0.998552 | − | 0.0538034i | \(-0.0171344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.00000 | 0.303676 | ||||||||
\(695\) | −4.94975 | + | 8.57321i | −0.187755 | + | 0.325201i | ||||
\(696\) | 0.343146 | + | 0.594346i | 0.0130069 | + | 0.0225286i | ||||
\(697\) | −6.24264 | − | 10.8126i | −0.236457 | − | 0.409555i | ||||
\(698\) | 18.1924 | − | 31.5101i | 0.688592 | − | 1.19268i | ||||
\(699\) | 20.7279 | 0.784002 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.7990 | −0.407872 | −0.203936 | − | 0.978984i | \(-0.565373\pi\) | ||||
−0.203936 | + | 0.978984i | \(0.565373\pi\) | |||||||
\(702\) | 4.00000 | − | 6.92820i | 0.150970 | − | 0.261488i | ||||
\(703\) | −8.12132 | − | 14.0665i | −0.306301 | − | 0.530530i | ||||
\(704\) | −16.9706 | − | 29.3939i | −0.639602 | − | 1.10782i | ||||
\(705\) | 1.77817 | − | 3.07989i | 0.0669699 | − | 0.115995i | ||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.363961 | + | 0.630399i | −0.0136688 | + | 0.0236751i | −0.872779 | − | 0.488116i | \(-0.837684\pi\) |
0.859110 | + | 0.511791i | \(0.171018\pi\) | |||||||
\(710\) | 14.6569 | + | 25.3864i | 0.550062 | + | 0.952735i | ||||
\(711\) | 7.74264 | + | 13.4106i | 0.290372 | + | 0.502939i | ||||
\(712\) | 2.24264 | − | 3.88437i | 0.0840465 | − | 0.145573i | ||||
\(713\) | 18.8995 | 0.707792 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.72792 | −0.251610 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.48528 | + | 4.30463i | 0.0928145 | + | 0.160759i | ||||
\(718\) | −19.7279 | − | 34.1698i | −0.736240 | − | 1.27520i | ||||
\(719\) | −0.878680 | + | 1.52192i | −0.0327692 | + | 0.0567580i | −0.881945 | − | 0.471352i | \(-0.843766\pi\) |
0.849176 | + | 0.528110i | \(0.177099\pi\) | |||||||
\(720\) | −6.34315 | −0.236395 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −47.3137 | −1.76083 | ||||||||
\(723\) | 14.2929 | − | 24.7560i | 0.531558 | − | 0.920686i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.213203 | + | 0.369279i | 0.00791818 | + | 0.0137147i | ||||
\(726\) | −7.00000 | + | 12.1244i | −0.259794 | + | 0.449977i | ||||
\(727\) | −42.0000 | −1.55769 | −0.778847 | − | 0.627214i | \(-0.784195\pi\) | ||||
−0.778847 | + | 0.627214i | \(0.784195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −10.3640 | + | 17.9509i | −0.383587 | + | 0.664393i | ||||
\(731\) | −3.53553 | − | 6.12372i | −0.130766 | − | 0.226494i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.34924 | + | 14.4613i | −0.308386 | + | 0.534141i | −0.978010 | − | 0.208560i | \(-0.933122\pi\) |
0.669623 | + | 0.742701i | \(0.266456\pi\) | |||||||
\(734\) | 14.4853 | 0.534661 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.7279 | − | 53.2223i | 1.13188 | − | 1.96047i | ||||
\(738\) | 6.24264 | + | 10.8126i | 0.229795 | + | 0.398016i | ||||
\(739\) | 8.84924 | + | 15.3273i | 0.325525 | + | 0.563825i | 0.981618 | − | 0.190854i | \(-0.0611258\pi\) |
−0.656094 | + | 0.754679i | \(0.727792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.2426 | −0.376273 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.6569 | −1.08800 | −0.544002 | − | 0.839084i | \(-0.683092\pi\) | ||||
−0.544002 | + | 0.839084i | \(0.683092\pi\) | |||||||
\(744\) | −6.48528 | + | 11.2328i | −0.237762 | + | 0.411816i | ||||
\(745\) | 12.8787 | + | 22.3065i | 0.471838 | + | 0.817248i | ||||
\(746\) | 6.00000 | + | 10.3923i | 0.219676 | + | 0.380489i | ||||
\(747\) | −6.62132 | + | 11.4685i | −0.242261 | + | 0.419609i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 23.7401 | 0.866866 | ||||||||
\(751\) | −7.74264 | + | 13.4106i | −0.282533 | + | 0.489361i | −0.972008 | − | 0.234948i | \(-0.924508\pi\) |
0.689475 | + | 0.724310i | \(0.257841\pi\) | |||||||
\(752\) | −3.17157 | − | 5.49333i | −0.115655 | − | 0.200321i | ||||
\(753\) | −11.7279 | − | 20.3134i | −0.427389 | − | 0.740260i | ||||
\(754\) | 0.121320 | − | 0.210133i | 0.00441823 | − | 0.00765259i | ||||
\(755\) | 15.4731 | 0.563123 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.4853 | 0.780896 | 0.390448 | − | 0.920625i | \(-0.372320\pi\) | ||||
0.390448 | + | 0.920625i | \(0.372320\pi\) | |||||||
\(758\) | 16.7990 | − | 29.0967i | 0.610167 | − | 1.05684i | ||||
\(759\) | −17.4853 | − | 30.2854i | −0.634676 | − | 1.09929i | ||||
\(760\) | 16.2426 | + | 28.1331i | 0.589183 | + | 1.02049i | ||||
\(761\) | 17.3787 | − | 30.1008i | 0.629977 | − | 1.09115i | −0.357579 | − | 0.933883i | \(-0.616398\pi\) |
0.987556 | − | 0.157269i | \(-0.0502689\pi\) | |||||||
\(762\) | 4.00000 | 0.144905 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.12132 | − | 1.94218i | 0.0405414 | − | 0.0702198i | ||||
\(766\) | 14.4853 | + | 25.0892i | 0.523374 | + | 0.906511i | ||||
\(767\) | 0.171573 | + | 0.297173i | 0.00619514 | + | 0.0107303i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.2132 | −1.88286 | −0.941428 | − | 0.337214i | \(-0.890516\pi\) | ||||
−0.941428 | + | 0.337214i | \(0.890516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.4558 | −0.988798 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.4142 | − | 28.4303i | −0.590378 | − | 1.02257i | −0.994181 | − | 0.107719i | \(-0.965645\pi\) |
0.403803 | − | 0.914846i | \(-0.367688\pi\) | |||||||
\(774\) | 3.53553 | + | 6.12372i | 0.127082 | + | 0.220113i | ||||
\(775\) | −4.02944 | + | 6.97919i | −0.144742 | + | 0.250700i | ||||
\(776\) | −33.1716 | −1.19079 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.9411 | −1.50366 | ||||||||
\(779\) | 31.9706 | − | 55.3746i | 1.14546 | − | 1.98400i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.7279 | + | 48.0262i | 0.992183 | + | 1.71851i | ||||
\(782\) | 5.82843 | − | 10.0951i | 0.208424 | − | 0.361001i | ||||
\(783\) | 0.970563 | 0.0346851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.95837 | −0.212663 | ||||||||
\(786\) | −2.82843 | + | 4.89898i | −0.100887 | + | 0.174741i | ||||
\(787\) | −12.3787 | − | 21.4405i | −0.441252 | − | 0.764271i | 0.556530 | − | 0.830827i | \(-0.312132\pi\) |
−0.997783 | + | 0.0665559i | \(0.978799\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.39340 | − | 2.41344i | 0.0496063 | − | 0.0859206i | ||||
\(790\) | 34.7279 | 1.23556 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.0000 | −0.426401 | ||||||||
\(793\) | 3.00000 | − | 5.19615i | 0.106533 | − | 0.184521i | ||||
\(794\) | 12.8787 | + | 22.3065i | 0.457047 | + | 0.791629i | ||||
\(795\) | 0.192388 | + | 0.333226i | 0.00682330 | + | 0.0118183i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.3431 | 0.862278 | 0.431139 | − | 0.902285i | \(-0.358112\pi\) | ||||
0.431139 | + | 0.902285i | \(0.358112\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.24264 | 0.0793389 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.792893 | − | 1.37333i | −0.0280155 | − | 0.0485243i | ||||
\(802\) | 4.48528 | + | 7.76874i | 0.158381 | + | 0.274324i | ||||
\(803\) | −19.6066 | + | 33.9596i | −0.691902 | + | 1.19841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.58579 | 0.161527 | ||||||||
\(807\) | −6.48528 | + | 11.2328i | −0.228293 | + | 0.395415i | ||||
\(808\) | 14.4853 | + | 25.0892i | 0.509590 | + | 0.882636i | ||||
\(809\) | −8.74264 | − | 15.1427i | −0.307375 | − | 0.532389i | 0.670412 | − | 0.741989i | \(-0.266117\pi\) |
−0.977787 | + | 0.209600i | \(0.932784\pi\) | |||||||
\(810\) | 5.60660 | − | 9.71092i | 0.196996 | − | 0.341207i | ||||
\(811\) | 21.9411 | 0.770457 | 0.385229 | − | 0.922821i | \(-0.374123\pi\) | ||||
0.385229 | + | 0.922821i | \(0.374123\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.2843 | 0.991973 | ||||||||
\(814\) | 6.72792 | − | 11.6531i | 0.235814 | − | 0.408441i | ||||
\(815\) | 6.72792 | + | 11.6531i | 0.235669 | + | 0.408190i | ||||
\(816\) | 4.00000 | + | 6.92820i | 0.140028 | + | 0.242536i | ||||
\(817\) | 18.1066 | − | 31.3616i | 0.633470 | − | 1.09720i | ||||
\(818\) | 4.58579 | 0.160338 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0711 | − | 17.4436i | 0.351483 | − | 0.608786i | −0.635027 | − | 0.772490i | \(-0.719011\pi\) |
0.986509 | + | 0.163704i | \(0.0523443\pi\) | |||||||
\(822\) | 4.58579 | + | 7.94282i | 0.159948 | + | 0.277037i | ||||
\(823\) | −5.24264 | − | 9.08052i | −0.182747 | − | 0.316527i | 0.760068 | − | 0.649844i | \(-0.225166\pi\) |
−0.942815 | + | 0.333316i | \(0.891832\pi\) | |||||||
\(824\) | −11.3137 | + | 19.5959i | −0.394132 | + | 0.682656i | ||||
\(825\) | 14.9117 | 0.519158 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −49.4558 | −1.71975 | −0.859874 | − | 0.510506i | \(-0.829458\pi\) | ||||
−0.859874 | + | 0.510506i | \(0.829458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.3640 | + | 43.9317i | 0.880927 | + | 1.52581i | 0.850312 | + | 0.526279i | \(0.176413\pi\) |
0.0306146 | + | 0.999531i | \(0.490254\pi\) | |||||||
\(830\) | 14.8492 | + | 25.7196i | 0.515425 | + | 0.892742i | ||||
\(831\) | −5.29289 | + | 9.16756i | −0.183608 | + | 0.318019i | ||||
\(832\) | 8.00000 | 0.277350 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.4853 | −0.432330 | ||||||||
\(835\) | −12.1985 | + | 21.1284i | −0.422146 | + | 0.731178i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.17157 | + | 15.8856i | 0.317016 | + | 0.549088i | ||||
\(838\) | 14.7574 | − | 25.5605i | 0.509785 | − | 0.882973i | ||||
\(839\) | 33.1716 | 1.14521 | 0.572605 | − | 0.819831i | \(-0.305933\pi\) | ||||
0.572605 | + | 0.819831i | \(0.305933\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9706 | −0.998985 | ||||||||
\(842\) | 4.75736 | − | 8.23999i | 0.163949 | − | 0.283969i | ||||
\(843\) | 11.0000 | + | 19.0526i | 0.378860 | + | 0.656205i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.792893 | − | 1.37333i | 0.0272764 | − | 0.0472440i | ||||
\(846\) | −2.24264 | −0.0771036 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.686292 | 0.0235673 | ||||||||
\(849\) | 6.00000 | − | 10.3923i | 0.205919 | − | 0.356663i | ||||
\(850\) | 2.48528 | + | 4.30463i | 0.0852444 | + | 0.147648i | ||||
\(851\) | 6.53553 | + | 11.3199i | 0.224035 | + | 0.388040i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.7279 | −1.36026 | −0.680129 | − | 0.733092i | \(-0.738076\pi\) | ||||
−0.680129 | + | 0.733092i | \(0.738076\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.4853 | 0.392788 | ||||||||
\(856\) | 28.4853 | − | 49.3380i | 0.973607 | − | 1.68634i | ||||
\(857\) | −27.3848 | − | 47.4318i | −0.935446 | − | 1.62024i | −0.773836 | − | 0.633385i | \(-0.781665\pi\) |
−0.161610 | − | 0.986855i | \(-0.551669\pi\) | |||||||
\(858\) | −4.24264 | − | 7.34847i | −0.144841 | − | 0.250873i | ||||
\(859\) | 15.4853 | − | 26.8213i | 0.528351 | − | 0.915131i | −0.471103 | − | 0.882078i | \(-0.656144\pi\) |
0.999454 | − | 0.0330523i | \(-0.0105228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.4558 | 0.594548 | ||||||||
\(863\) | −14.1421 | + | 24.4949i | −0.481404 | + | 0.833816i | −0.999772 | − | 0.0213414i | \(-0.993206\pi\) |
0.518368 | + | 0.855157i | \(0.326540\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.6066 | − | 33.9596i | −0.666644 | − | 1.15466i | ||||
\(866\) | 17.6569 | − | 30.5826i | 0.600004 | − | 1.03924i | ||||
\(867\) | 21.2132 | 0.720438 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 65.6985 | 2.22867 | ||||||||
\(870\) | 0.272078 | − | 0.471253i | 0.00922431 | − | 0.0159770i | ||||
\(871\) | 7.24264 | + | 12.5446i | 0.245408 | + | 0.425058i | ||||
\(872\) | −23.6569 | − | 40.9749i | −0.801122 | − | 1.38758i | ||||
\(873\) | −5.86396 | + | 10.1567i | −0.198465 | + | 0.343751i | ||||
\(874\) | 59.6985 | 2.01933 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.12132 | − | 8.87039i | 0.172935 | − | 0.299532i | −0.766510 | − | 0.642232i | \(-0.778008\pi\) |
0.939445 | + | 0.342701i | \(0.111342\pi\) | |||||||
\(878\) | 24.3848 | + | 42.2357i | 0.822946 | + | 1.42538i | ||||
\(879\) | −10.8787 | − | 18.8424i | −0.366929 | − | 0.635539i | ||||
\(880\) | −13.4558 | + | 23.3062i | −0.453596 | + | 0.785652i | ||||
\(881\) | −13.1127 | −0.441778 | −0.220889 | − | 0.975299i | \(-0.570896\pi\) | ||||
−0.220889 | + | 0.975299i | \(0.570896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.384776 | + | 0.666452i | 0.0129341 | + | 0.0224025i | ||||
\(886\) | −2.60660 | − | 4.51477i | −0.0875705 | − | 0.151677i | ||||
\(887\) | 9.55635 | − | 16.5521i | 0.320871 | − | 0.555765i | −0.659797 | − | 0.751444i | \(-0.729358\pi\) |
0.980668 | + | 0.195679i | \(0.0626911\pi\) | |||||||
\(888\) | −8.97056 | −0.301032 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.55635 | −0.119209 | ||||||||
\(891\) | 10.6066 | − | 18.3712i | 0.355335 | − | 0.615457i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.74264 | + | 9.94655i | 0.192170 | + | 0.332848i | ||||
\(894\) | −16.2426 | + | 28.1331i | −0.543235 | + | 0.940911i | ||||
\(895\) | 14.2721 | 0.477063 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.24264 | 0.275214 | ||||||||
\(898\) | 14.9706 | − | 25.9298i | 0.499574 | − | 0.865288i | ||||
\(899\) | 0.278175 | + | 0.481813i | 0.00927764 | + | 0.0160693i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.121320 | + | 0.210133i | −0.00404177 | + | 0.00700055i | ||||
\(902\) | 52.9706 | 1.76373 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.54416 | 0.217655 | ||||||||
\(905\) | 14.8492 | − | 25.7196i | 0.493606 | − | 0.854950i | ||||
\(906\) | 9.75736 | + | 16.9002i | 0.324167 | + | 0.561473i | ||||
\(907\) | −0.985281 | − | 1.70656i | −0.0327157 | − | 0.0566653i | 0.849204 | − | 0.528065i | \(-0.177082\pi\) |
−0.881920 | + | 0.471400i | \(0.843749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.2426 | 0.339727 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.9706 | −1.45681 | −0.728405 | − | 0.685147i | \(-0.759738\pi\) | ||||
−0.728405 | + | 0.685147i | \(0.759738\pi\) | |||||||
\(912\) | −20.4853 | + | 35.4815i | −0.678335 | + | 1.17491i | ||||
\(913\) | 28.0919 | + | 48.6566i | 0.929706 | + | 1.61030i | ||||
\(914\) | −5.10051 | − | 8.83433i | −0.168710 | − | 0.292214i | ||||
\(915\) | 6.72792 | − | 11.6531i | 0.222418 | − | 0.385240i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 11.3137 | 0.373408 | ||||||||
\(919\) | −12.0000 | + | 20.7846i | −0.395843 | + | 0.685621i | −0.993208 | − | 0.116348i | \(-0.962881\pi\) |
0.597365 | + | 0.801970i | \(0.296214\pi\) | |||||||
\(920\) | −13.0711 | − | 22.6398i | −0.430940 | − | 0.746411i | ||||
\(921\) | −9.36396 | − | 16.2189i | −0.308553 | − | 0.534429i | ||||
\(922\) | −6.24264 | + | 10.8126i | −0.205590 | + | 0.356093i | ||||
\(923\) | −13.0711 | −0.430239 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.57359 | −0.183259 | ||||||||
\(926\) | −3.00000 | + | 5.19615i | −0.0985861 | + | 0.170756i | ||||
\(927\) | 4.00000 | + | 6.92820i | 0.131377 | + | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.4497 | − | 31.9559i | 0.605317 | − | 1.04844i | −0.386685 | − | 0.922212i | \(-0.626380\pi\) |
0.992001 | − | 0.126227i | \(-0.0402868\pi\) | |||||||
\(930\) | 10.2843 | 0.337235 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.24264 | − | 9.08052i | 0.171636 | − | 0.297283i | ||||
\(934\) | 2.75736 | + | 4.77589i | 0.0902236 | + | 0.156272i | ||||
\(935\) | −4.75736 | − | 8.23999i | −0.155582 | − | 0.269476i | ||||
\(936\) | 1.41421 | − | 2.44949i | 0.0462250 | − | 0.0800641i | ||||
\(937\) | −45.2132 | −1.47705 | −0.738525 | − | 0.674226i | \(-0.764478\pi\) | ||||
−0.738525 | + | 0.674226i | \(0.764478\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.8284 | 1.07132 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.0355 | + | 34.7026i | 0.653140 | + | 1.13127i | 0.982357 | + | 0.187017i | \(0.0598819\pi\) |
−0.329217 | + | 0.944254i | \(0.606785\pi\) | |||||||
\(942\) | −3.75736 | − | 6.50794i | −0.122421 | − | 0.212040i | ||||
\(943\) | −25.7279 | + | 44.5621i | −0.837816 | + | 1.45114i | ||||
\(944\) | 1.37258 | 0.0446738 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.0000 | 0.975384 | ||||||||
\(947\) | −7.58579 | + | 13.1390i | −0.246505 | + | 0.426959i | −0.962554 | − | 0.271091i | \(-0.912615\pi\) |
0.716049 | + | 0.698050i | \(0.245949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.62132 | − | 8.00436i | −0.150014 | − | 0.259833i | ||||
\(950\) | −12.7279 | + | 22.0454i | −0.412948 | + | 0.715247i | ||||
\(951\) | 16.0000 | 0.518836 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.1421 | 0.360929 | 0.180465 | − | 0.983581i | \(-0.442240\pi\) | ||||
0.180465 | + | 0.983581i | \(0.442240\pi\) | |||||||
\(954\) | 0.121320 | − | 0.210133i | 0.00392789 | − | 0.00680331i | ||||
\(955\) | 12.0294 | + | 20.8356i | 0.389263 | + | 0.674224i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.514719 | − | 0.891519i | 0.0166385 | − | 0.0288187i | ||||
\(958\) | −8.78680 | −0.283889 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 17.9411 | 0.579047 | ||||||||
\(961\) | 10.2426 | − | 17.7408i | 0.330408 | − | 0.572283i | ||||
\(962\) | 1.58579 | + | 2.74666i | 0.0511278 | + | 0.0885560i | ||||
\(963\) | −10.0711 | − | 17.4436i | −0.324536 | − | 0.562112i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.9706 | 0.739449 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.6985 | 0.569145 | 0.284572 | − | 0.958655i | \(-0.408148\pi\) | ||||
0.284572 | + | 0.958655i | \(0.408148\pi\) | |||||||
\(968\) | −9.89949 | + | 17.1464i | −0.318182 | + | 0.551107i | ||||
\(969\) | −7.24264 | − | 12.5446i | −0.232667 | − | 0.402991i | ||||
\(970\) | 13.1508 | + | 22.7778i | 0.422245 | + | 0.731350i | ||||
\(971\) | 21.7279 | − | 37.6339i | 0.697282 | − | 1.20773i | −0.272123 | − | 0.962262i | \(-0.587726\pi\) |
0.969405 | − | 0.245466i | \(-0.0789409\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.2010 | 0.519114 | ||||||||
\(975\) | −1.75736 | + | 3.04384i | −0.0562805 | + | 0.0974808i | ||||
\(976\) | −12.0000 | − | 20.7846i | −0.384111 | − | 0.665299i | ||||
\(977\) | −12.0208 | − | 20.8207i | −0.384580 | − | 0.666112i | 0.607131 | − | 0.794602i | \(-0.292320\pi\) |
−0.991711 | + | 0.128490i | \(0.958987\pi\) | |||||||
\(978\) | −8.48528 | + | 14.6969i | −0.271329 | + | 0.469956i | ||||
\(979\) | −6.72792 | −0.215025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.7279 | −0.534081 | ||||||||
\(982\) | 11.7574 | − | 20.3643i | 0.375192 | − | 0.649852i | ||||
\(983\) | −7.52082 | − | 13.0264i | −0.239877 | − | 0.415479i | 0.720802 | − | 0.693141i | \(-0.243774\pi\) |
−0.960679 | + | 0.277662i | \(0.910440\pi\) | |||||||
\(984\) | −17.6569 | − | 30.5826i | −0.562880 | − | 0.974937i | ||||
\(985\) | 9.78680 | − | 16.9512i | 0.311833 | − | 0.540111i | ||||
\(986\) | 0.343146 | 0.0109280 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5711 | + | 25.2378i | −0.463333 | + | 0.802516i | ||||
\(990\) | 4.75736 | + | 8.23999i | 0.151199 | + | 0.261884i | ||||
\(991\) | −0.514719 | − | 0.891519i | −0.0163506 | − | 0.0283200i | 0.857734 | − | 0.514093i | \(-0.171871\pi\) |
−0.874085 | + | 0.485773i | \(0.838538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.4558 | 0.807817 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.95837 | −0.188893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.75736 | − | 9.97204i | −0.182337 | − | 0.315818i | 0.760339 | − | 0.649527i | \(-0.225033\pi\) |
−0.942676 | + | 0.333709i | \(0.891700\pi\) | |||||||
\(998\) | −9.38478 | − | 16.2549i | −0.297070 | − | 0.514540i | ||||
\(999\) | −6.34315 | + | 10.9867i | −0.200688 | + | 0.347602i |
(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 | 637.2.e.g.79.2 | 4 | ||
7.2 | even | 3 | 637.2.a.g.1.1 | 2 | |||
7.3 | odd | 6 | 637.2.e.f.508.2 | 4 | |||
7.4 | even | 3 | inner | 637.2.e.g.508.2 | 4 | ||
7.5 | odd | 6 | 91.2.a.c.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 637.2.e.f.79.2 | 4 | |||
21.2 | odd | 6 | 5733.2.a.s.1.2 | 2 | |||
21.5 | even | 6 | 819.2.a.h.1.2 | 2 | |||
28.19 | even | 6 | 1456.2.a.q.1.1 | 2 | |||
35.19 | odd | 6 | 2275.2.a.j.1.2 | 2 | |||
56.5 | odd | 6 | 5824.2.a.bl.1.1 | 2 | |||
56.19 | even | 6 | 5824.2.a.bk.1.2 | 2 | |||
91.5 | even | 12 | 1183.2.c.d.337.4 | 4 | |||
91.12 | odd | 6 | 1183.2.a.d.1.2 | 2 | |||
91.47 | even | 12 | 1183.2.c.d.337.2 | 4 | |||
91.51 | even | 6 | 8281.2.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.c.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
637.2.a.g.1.1 | 2 | 7.2 | even | 3 | |||
637.2.e.f.79.2 | 4 | 7.6 | odd | 2 | |||
637.2.e.f.508.2 | 4 | 7.3 | odd | 6 | |||
637.2.e.g.79.2 | 4 | 1.1 | even | 1 | trivial | ||
637.2.e.g.508.2 | 4 | 7.4 | even | 3 | inner | ||
819.2.a.h.1.2 | 2 | 21.5 | even | 6 | |||
1183.2.a.d.1.2 | 2 | 91.12 | odd | 6 | |||
1183.2.c.d.337.2 | 4 | 91.47 | even | 12 | |||
1183.2.c.d.337.4 | 4 | 91.5 | even | 12 | |||
1456.2.a.q.1.1 | 2 | 28.19 | even | 6 | |||
2275.2.a.j.1.2 | 2 | 35.19 | odd | 6 | |||
5733.2.a.s.1.2 | 2 | 21.2 | odd | 6 | |||
5824.2.a.bk.1.2 | 2 | 56.19 | even | 6 | |||
5824.2.a.bl.1.1 | 2 | 56.5 | odd | 6 | |||
8281.2.a.v.1.2 | 2 | 91.51 | even | 6 |