Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(429,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.429");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.c (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: | \(5.76519902594\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 653.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.653 |
Dual form | 722.2.c.g.429.1 |
$q$-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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).
\(n\) | \(363\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | + | 2.59808i | 0.866025 | + | 1.50000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | −1.50000 | + | 2.59808i | −0.612372 | + | 1.06066i | ||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | + | 5.19615i | −1.00000 | + | 1.73205i | ||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | −3.00000 | −0.866025 | ||||||||
\(13\) | −1.50000 | + | 2.59808i | −0.416025 | + | 0.720577i | −0.995535 | − | 0.0943882i | \(-0.969911\pi\) |
0.579510 | + | 0.814965i | \(0.303244\pi\) | |||||||
\(14\) | −1.50000 | − | 2.59808i | −0.400892 | − | 0.694365i | ||||
\(15\) | 3.00000 | − | 5.19615i | 0.774597 | − | 1.34164i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.500000 | + | 0.866025i | 0.121268 | + | 0.210042i | 0.920268 | − | 0.391289i | \(-0.127971\pi\) |
−0.799000 | + | 0.601331i | \(0.794637\pi\) | |||||||
\(18\) | −6.00000 | −1.41421 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | −4.50000 | − | 7.79423i | −0.981981 | − | 1.70084i | ||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | −2.50000 | + | 4.33013i | −0.521286 | + | 0.902894i | 0.478407 | + | 0.878138i | \(0.341214\pi\) |
−0.999694 | + | 0.0247559i | \(0.992119\pi\) | |||||||
\(24\) | −1.50000 | − | 2.59808i | −0.306186 | − | 0.530330i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | −9.00000 | −1.73205 | ||||||||
\(28\) | 1.50000 | − | 2.59808i | 0.283473 | − | 0.490990i | ||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 6.00000 | 1.09545 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −3.00000 | − | 5.19615i | −0.522233 | − | 0.904534i | ||||
\(34\) | −0.500000 | + | 0.866025i | −0.0857493 | + | 0.148522i | ||||
\(35\) | 3.00000 | + | 5.19615i | 0.507093 | + | 0.878310i | ||||
\(36\) | −3.00000 | − | 5.19615i | −0.500000 | − | 0.866025i | ||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.00000 | −1.44115 | ||||||||
\(40\) | 1.00000 | + | 1.73205i | 0.158114 | + | 0.273861i | ||||
\(41\) | 6.00000 | + | 10.3923i | 0.937043 | + | 1.62301i | 0.770950 | + | 0.636895i | \(0.219782\pi\) |
0.166092 | + | 0.986110i | \(0.446885\pi\) | |||||||
\(42\) | 4.50000 | − | 7.79423i | 0.694365 | − | 1.20268i | ||||
\(43\) | 5.00000 | + | 8.66025i | 0.762493 | + | 1.32068i | 0.941562 | + | 0.336840i | \(0.109358\pi\) |
−0.179069 | + | 0.983836i | \(0.557309\pi\) | |||||||
\(44\) | 1.00000 | − | 1.73205i | 0.150756 | − | 0.261116i | ||||
\(45\) | 12.0000 | 1.78885 | ||||||||
\(46\) | −5.00000 | −0.737210 | ||||||||
\(47\) | 4.00000 | − | 6.92820i | 0.583460 | − | 1.01058i | −0.411606 | − | 0.911362i | \(-0.635032\pi\) |
0.995066 | − | 0.0992202i | \(-0.0316348\pi\) | |||||||
\(48\) | 1.50000 | − | 2.59808i | 0.216506 | − | 0.375000i | ||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | −1.50000 | − | 2.59808i | −0.208013 | − | 0.360288i | ||||
\(53\) | −1.50000 | + | 2.59808i | −0.206041 | + | 0.356873i | −0.950464 | − | 0.310835i | \(-0.899391\pi\) |
0.744423 | + | 0.667708i | \(0.232725\pi\) | |||||||
\(54\) | −4.50000 | − | 7.79423i | −0.612372 | − | 1.06066i | ||||
\(55\) | 2.00000 | + | 3.46410i | 0.269680 | + | 0.467099i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | −0.393919 | ||||||||
\(59\) | 1.50000 | + | 2.59808i | 0.195283 | + | 0.338241i | 0.946993 | − | 0.321253i | \(-0.104104\pi\) |
−0.751710 | + | 0.659494i | \(0.770771\pi\) | |||||||
\(60\) | 3.00000 | + | 5.19615i | 0.387298 | + | 0.670820i | ||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 3.00000 | + | 5.19615i | 0.381000 | + | 0.659912i | ||||
\(63\) | 9.00000 | − | 15.5885i | 1.13389 | − | 1.96396i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 3.00000 | − | 5.19615i | 0.369274 | − | 0.639602i | ||||
\(67\) | 7.50000 | − | 12.9904i | 0.916271 | − | 1.58703i | 0.111241 | − | 0.993793i | \(-0.464517\pi\) |
0.805030 | − | 0.593234i | \(-0.202149\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −15.0000 | −1.80579 | ||||||||
\(70\) | −3.00000 | + | 5.19615i | −0.358569 | + | 0.621059i | ||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | 3.00000 | − | 5.19615i | 0.353553 | − | 0.612372i | ||||
\(73\) | 5.50000 | + | 9.52628i | 0.643726 | + | 1.11497i | 0.984594 | + | 0.174855i | \(0.0559458\pi\) |
−0.340868 | + | 0.940111i | \(0.610721\pi\) | |||||||
\(74\) | −3.00000 | − | 5.19615i | −0.348743 | − | 0.604040i | ||||
\(75\) | 3.00000 | 0.346410 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | −4.50000 | − | 7.79423i | −0.509525 | − | 0.882523i | ||||
\(79\) | −6.00000 | − | 10.3923i | −0.675053 | − | 1.16923i | −0.976453 | − | 0.215728i | \(-0.930788\pi\) |
0.301401 | − | 0.953498i | \(-0.402546\pi\) | |||||||
\(80\) | −1.00000 | + | 1.73205i | −0.111803 | + | 0.193649i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −6.00000 | + | 10.3923i | −0.662589 | + | 1.14764i | ||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | 9.00000 | 0.981981 | ||||||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | −5.00000 | + | 8.66025i | −0.539164 | + | 0.933859i | ||||
\(87\) | −9.00000 | −0.964901 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 6.00000 | + | 10.3923i | 0.632456 | + | 1.09545i | ||||
\(91\) | 4.50000 | − | 7.79423i | 0.471728 | − | 0.817057i | ||||
\(92\) | −2.50000 | − | 4.33013i | −0.260643 | − | 0.451447i | ||||
\(93\) | 9.00000 | + | 15.5885i | 0.933257 | + | 1.61645i | ||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.00000 | 0.306186 | ||||||||
\(97\) | 6.00000 | + | 10.3923i | 0.609208 | + | 1.05518i | 0.991371 | + | 0.131084i | \(0.0418458\pi\) |
−0.382164 | + | 0.924095i | \(0.624821\pi\) | |||||||
\(98\) | 1.00000 | + | 1.73205i | 0.101015 | + | 0.174964i | ||||
\(99\) | 6.00000 | − | 10.3923i | 0.603023 | − | 1.04447i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −5.00000 | + | 8.66025i | −0.497519 | + | 0.861727i | −0.999996 | − | 0.00286291i | \(-0.999089\pi\) |
0.502477 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(102\) | −3.00000 | −0.297044 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | 1.50000 | − | 2.59808i | 0.147087 | − | 0.254762i | ||||
\(105\) | −9.00000 | + | 15.5885i | −0.878310 | + | 1.52128i | ||||
\(106\) | −3.00000 | −0.291386 | ||||||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | 4.50000 | − | 7.79423i | 0.433013 | − | 0.750000i | ||||
\(109\) | 1.50000 | + | 2.59808i | 0.143674 | + | 0.248851i | 0.928877 | − | 0.370387i | \(-0.120775\pi\) |
−0.785203 | + | 0.619238i | \(0.787442\pi\) | |||||||
\(110\) | −2.00000 | + | 3.46410i | −0.190693 | + | 0.330289i | ||||
\(111\) | −9.00000 | − | 15.5885i | −0.854242 | − | 1.47959i | ||||
\(112\) | 1.50000 | + | 2.59808i | 0.141737 | + | 0.245495i | ||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0000 | 0.932505 | ||||||||
\(116\) | −1.50000 | − | 2.59808i | −0.139272 | − | 0.241225i | ||||
\(117\) | −9.00000 | − | 15.5885i | −0.832050 | − | 1.44115i | ||||
\(118\) | −1.50000 | + | 2.59808i | −0.138086 | + | 0.239172i | ||||
\(119\) | −1.50000 | − | 2.59808i | −0.137505 | − | 0.238165i | ||||
\(120\) | −3.00000 | + | 5.19615i | −0.273861 | + | 0.474342i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.0000 | + | 31.1769i | −1.62301 | + | 2.81113i | ||||
\(124\) | −3.00000 | + | 5.19615i | −0.269408 | + | 0.466628i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 18.0000 | 1.60357 | ||||||||
\(127\) | 6.00000 | − | 10.3923i | 0.532414 | − | 0.922168i | −0.466870 | − | 0.884326i | \(-0.654618\pi\) |
0.999284 | − | 0.0378419i | \(-0.0120483\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −15.0000 | + | 25.9808i | −1.32068 | + | 2.28748i | ||||
\(130\) | 3.00000 | + | 5.19615i | 0.263117 | + | 0.455733i | ||||
\(131\) | −7.00000 | − | 12.1244i | −0.611593 | − | 1.05931i | −0.990972 | − | 0.134069i | \(-0.957196\pi\) |
0.379379 | − | 0.925241i | \(-0.376138\pi\) | |||||||
\(132\) | 6.00000 | 0.522233 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.0000 | 1.29580 | ||||||||
\(135\) | 9.00000 | + | 15.5885i | 0.774597 | + | 1.34164i | ||||
\(136\) | −0.500000 | − | 0.866025i | −0.0428746 | − | 0.0742611i | ||||
\(137\) | −9.50000 | + | 16.4545i | −0.811640 | + | 1.40580i | 0.100076 | + | 0.994980i | \(0.468091\pi\) |
−0.911716 | + | 0.410822i | \(0.865242\pi\) | |||||||
\(138\) | −7.50000 | − | 12.9904i | −0.638442 | − | 1.10581i | ||||
\(139\) | −3.00000 | + | 5.19615i | −0.254457 | + | 0.440732i | −0.964748 | − | 0.263176i | \(-0.915230\pi\) |
0.710291 | + | 0.703908i | \(0.248563\pi\) | |||||||
\(140\) | −6.00000 | −0.507093 | ||||||||
\(141\) | 24.0000 | 2.02116 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | − | 5.19615i | 0.250873 | − | 0.434524i | ||||
\(144\) | 6.00000 | 0.500000 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | −5.50000 | + | 9.52628i | −0.455183 | + | 0.788400i | ||||
\(147\) | 3.00000 | + | 5.19615i | 0.247436 | + | 0.428571i | ||||
\(148\) | 3.00000 | − | 5.19615i | 0.246598 | − | 0.427121i | ||||
\(149\) | 4.00000 | + | 6.92820i | 0.327693 | + | 0.567581i | 0.982054 | − | 0.188602i | \(-0.0603956\pi\) |
−0.654361 | + | 0.756182i | \(0.727062\pi\) | |||||||
\(150\) | 1.50000 | + | 2.59808i | 0.122474 | + | 0.212132i | ||||
\(151\) | 18.0000 | 1.46482 | 0.732410 | − | 0.680864i | \(-0.238396\pi\) | ||||
0.732410 | + | 0.680864i | \(0.238396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 3.00000 | + | 5.19615i | 0.241747 | + | 0.418718i | ||||
\(155\) | −6.00000 | − | 10.3923i | −0.481932 | − | 0.834730i | ||||
\(156\) | 4.50000 | − | 7.79423i | 0.360288 | − | 0.624038i | ||||
\(157\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(158\) | 6.00000 | − | 10.3923i | 0.477334 | − | 0.826767i | ||||
\(159\) | −9.00000 | −0.713746 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 7.50000 | − | 12.9904i | 0.591083 | − | 1.02379i | ||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | −6.00000 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | −6.00000 | + | 10.3923i | −0.467099 | + | 0.809040i | ||||
\(166\) | 1.00000 | + | 1.73205i | 0.0776151 | + | 0.134433i | ||||
\(167\) | −6.00000 | + | 10.3923i | −0.464294 | + | 0.804181i | −0.999169 | − | 0.0407502i | \(-0.987025\pi\) |
0.534875 | + | 0.844931i | \(0.320359\pi\) | |||||||
\(168\) | 4.50000 | + | 7.79423i | 0.347183 | + | 0.601338i | ||||
\(169\) | 2.00000 | + | 3.46410i | 0.153846 | + | 0.266469i | ||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | −9.00000 | − | 15.5885i | −0.684257 | − | 1.18517i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.289412 | − | 0.957205i | \(-0.406540\pi\) | |||||||
\(174\) | −4.50000 | − | 7.79423i | −0.341144 | − | 0.590879i | ||||
\(175\) | −1.50000 | + | 2.59808i | −0.113389 | + | 0.196396i | ||||
\(176\) | 1.00000 | + | 1.73205i | 0.0753778 | + | 0.130558i | ||||
\(177\) | −4.50000 | + | 7.79423i | −0.338241 | + | 0.585850i | ||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | −6.00000 | + | 10.3923i | −0.447214 | + | 0.774597i | ||||
\(181\) | 9.00000 | − | 15.5885i | 0.668965 | − | 1.15868i | −0.309229 | − | 0.950988i | \(-0.600071\pi\) |
0.978194 | − | 0.207693i | \(-0.0665956\pi\) | |||||||
\(182\) | 9.00000 | 0.667124 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.50000 | − | 4.33013i | 0.184302 | − | 0.319221i | ||||
\(185\) | 6.00000 | + | 10.3923i | 0.441129 | + | 0.764057i | ||||
\(186\) | −9.00000 | + | 15.5885i | −0.659912 | + | 1.14300i | ||||
\(187\) | −1.00000 | − | 1.73205i | −0.0731272 | − | 0.126660i | ||||
\(188\) | 4.00000 | + | 6.92820i | 0.291730 | + | 0.505291i | ||||
\(189\) | 27.0000 | 1.96396 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0000 | −0.795932 | −0.397966 | − | 0.917400i | \(-0.630284\pi\) | ||||
−0.397966 | + | 0.917400i | \(0.630284\pi\) | |||||||
\(192\) | 1.50000 | + | 2.59808i | 0.108253 | + | 0.187500i | ||||
\(193\) | 3.00000 | + | 5.19615i | 0.215945 | + | 0.374027i | 0.953564 | − | 0.301189i | \(-0.0973836\pi\) |
−0.737620 | + | 0.675216i | \(0.764050\pi\) | |||||||
\(194\) | −6.00000 | + | 10.3923i | −0.430775 | + | 0.746124i | ||||
\(195\) | 9.00000 | + | 15.5885i | 0.644503 | + | 1.11631i | ||||
\(196\) | −1.00000 | + | 1.73205i | −0.0714286 | + | 0.123718i | ||||
\(197\) | 4.00000 | 0.284988 | 0.142494 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142494 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(198\) | 12.0000 | 0.852803 | ||||||||
\(199\) | 3.50000 | − | 6.06218i | 0.248108 | − | 0.429736i | −0.714893 | − | 0.699234i | \(-0.753524\pi\) |
0.963001 | + | 0.269498i | \(0.0868577\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 45.0000 | 3.17406 | ||||||||
\(202\) | −10.0000 | −0.703598 | ||||||||
\(203\) | 4.50000 | − | 7.79423i | 0.315838 | − | 0.547048i | ||||
\(204\) | −1.50000 | − | 2.59808i | −0.105021 | − | 0.181902i | ||||
\(205\) | 12.0000 | − | 20.7846i | 0.838116 | − | 1.45166i | ||||
\(206\) | −3.00000 | − | 5.19615i | −0.209020 | − | 0.362033i | ||||
\(207\) | −15.0000 | − | 25.9808i | −1.04257 | − | 1.80579i | ||||
\(208\) | 3.00000 | 0.208013 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −18.0000 | −1.24212 | ||||||||
\(211\) | 1.50000 | + | 2.59808i | 0.103264 | + | 0.178859i | 0.913028 | − | 0.407898i | \(-0.133738\pi\) |
−0.809763 | + | 0.586756i | \(0.800405\pi\) | |||||||
\(212\) | −1.50000 | − | 2.59808i | −0.103020 | − | 0.178437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.50000 | + | 2.59808i | 0.102538 | + | 0.177601i | ||||
\(215\) | 10.0000 | − | 17.3205i | 0.681994 | − | 1.18125i | ||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | −18.0000 | −1.22192 | ||||||||
\(218\) | −1.50000 | + | 2.59808i | −0.101593 | + | 0.175964i | ||||
\(219\) | −16.5000 | + | 28.5788i | −1.11497 | + | 1.93118i | ||||
\(220\) | −4.00000 | −0.269680 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 9.00000 | − | 15.5885i | 0.604040 | − | 1.04623i | ||||
\(223\) | 9.00000 | + | 15.5885i | 0.602685 | + | 1.04388i | 0.992413 | + | 0.122950i | \(0.0392356\pi\) |
−0.389728 | + | 0.920930i | \(0.627431\pi\) | |||||||
\(224\) | −1.50000 | + | 2.59808i | −0.100223 | + | 0.173591i | ||||
\(225\) | 3.00000 | + | 5.19615i | 0.200000 | + | 0.346410i | ||||
\(226\) | −6.00000 | − | 10.3923i | −0.399114 | − | 0.691286i | ||||
\(227\) | −3.00000 | −0.199117 | −0.0995585 | − | 0.995032i | \(-0.531743\pi\) | ||||
−0.0995585 | + | 0.995032i | \(0.531743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | 5.00000 | + | 8.66025i | 0.329690 | + | 0.571040i | ||||
\(231\) | 9.00000 | + | 15.5885i | 0.592157 | + | 1.02565i | ||||
\(232\) | 1.50000 | − | 2.59808i | 0.0984798 | − | 0.170572i | ||||
\(233\) | −7.00000 | − | 12.1244i | −0.458585 | − | 0.794293i | 0.540301 | − | 0.841472i | \(-0.318310\pi\) |
−0.998886 | + | 0.0471787i | \(0.984977\pi\) | |||||||
\(234\) | 9.00000 | − | 15.5885i | 0.588348 | − | 1.01905i | ||||
\(235\) | −16.0000 | −1.04372 | ||||||||
\(236\) | −3.00000 | −0.195283 | ||||||||
\(237\) | 18.0000 | − | 31.1769i | 1.16923 | − | 2.02516i | ||||
\(238\) | 1.50000 | − | 2.59808i | 0.0972306 | − | 0.168408i | ||||
\(239\) | 1.00000 | 0.0646846 | 0.0323423 | − | 0.999477i | \(-0.489703\pi\) | ||||
0.0323423 | + | 0.999477i | \(0.489703\pi\) | |||||||
\(240\) | −6.00000 | −0.387298 | ||||||||
\(241\) | 12.0000 | − | 20.7846i | 0.772988 | − | 1.33885i | −0.162930 | − | 0.986638i | \(-0.552095\pi\) |
0.935918 | − | 0.352217i | \(-0.114572\pi\) | |||||||
\(242\) | −3.50000 | − | 6.06218i | −0.224989 | − | 0.389692i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.00000 | − | 3.46410i | −0.127775 | − | 0.221313i | ||||
\(246\) | −36.0000 | −2.29528 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 3.00000 | + | 5.19615i | 0.190117 | + | 0.329293i | ||||
\(250\) | −6.00000 | − | 10.3923i | −0.379473 | − | 0.657267i | ||||
\(251\) | 10.0000 | − | 17.3205i | 0.631194 | − | 1.09326i | −0.356113 | − | 0.934443i | \(-0.615898\pi\) |
0.987308 | − | 0.158818i | \(-0.0507683\pi\) | |||||||
\(252\) | 9.00000 | + | 15.5885i | 0.566947 | + | 0.981981i | ||||
\(253\) | 5.00000 | − | 8.66025i | 0.314347 | − | 0.544466i | ||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 6.00000 | 0.375735 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | −30.0000 | −1.86772 | ||||||||
\(259\) | 18.0000 | 1.11847 | ||||||||
\(260\) | −3.00000 | + | 5.19615i | −0.186052 | + | 0.322252i | ||||
\(261\) | −9.00000 | − | 15.5885i | −0.557086 | − | 0.964901i | ||||
\(262\) | 7.00000 | − | 12.1244i | 0.432461 | − | 0.749045i | ||||
\(263\) | 4.00000 | + | 6.92820i | 0.246651 | + | 0.427211i | 0.962594 | − | 0.270947i | \(-0.0873367\pi\) |
−0.715944 | + | 0.698158i | \(0.754003\pi\) | |||||||
\(264\) | 3.00000 | + | 5.19615i | 0.184637 | + | 0.319801i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | 7.50000 | + | 12.9904i | 0.458135 | + | 0.793514i | ||||
\(269\) | −3.00000 | − | 5.19615i | −0.182913 | − | 0.316815i | 0.759958 | − | 0.649972i | \(-0.225219\pi\) |
−0.942871 | + | 0.333157i | \(0.891886\pi\) | |||||||
\(270\) | −9.00000 | + | 15.5885i | −0.547723 | + | 0.948683i | ||||
\(271\) | 5.50000 | + | 9.52628i | 0.334101 | + | 0.578680i | 0.983312 | − | 0.181928i | \(-0.0582339\pi\) |
−0.649211 | + | 0.760609i | \(0.724901\pi\) | |||||||
\(272\) | 0.500000 | − | 0.866025i | 0.0303170 | − | 0.0525105i | ||||
\(273\) | 27.0000 | 1.63411 | ||||||||
\(274\) | −19.0000 | −1.14783 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 7.50000 | − | 12.9904i | 0.451447 | − | 0.781929i | ||||
\(277\) | 30.0000 | 1.80253 | 0.901263 | − | 0.433273i | \(-0.142641\pi\) | ||||
0.901263 | + | 0.433273i | \(0.142641\pi\) | |||||||
\(278\) | −6.00000 | −0.359856 | ||||||||
\(279\) | −18.0000 | + | 31.1769i | −1.07763 | + | 1.86651i | ||||
\(280\) | −3.00000 | − | 5.19615i | −0.179284 | − | 0.310530i | ||||
\(281\) | 6.00000 | − | 10.3923i | 0.357930 | − | 0.619953i | −0.629685 | − | 0.776851i | \(-0.716816\pi\) |
0.987615 | + | 0.156898i | \(0.0501493\pi\) | |||||||
\(282\) | 12.0000 | + | 20.7846i | 0.714590 | + | 1.23771i | ||||
\(283\) | 7.00000 | + | 12.1244i | 0.416107 | + | 0.720718i | 0.995544 | − | 0.0942988i | \(-0.0300609\pi\) |
−0.579437 | + | 0.815017i | \(0.696728\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | −18.0000 | − | 31.1769i | −1.06251 | − | 1.84032i | ||||
\(288\) | 3.00000 | + | 5.19615i | 0.176777 | + | 0.306186i | ||||
\(289\) | 8.00000 | − | 13.8564i | 0.470588 | − | 0.815083i | ||||
\(290\) | 3.00000 | + | 5.19615i | 0.176166 | + | 0.305129i | ||||
\(291\) | −18.0000 | + | 31.1769i | −1.05518 | + | 1.82762i | ||||
\(292\) | −11.0000 | −0.643726 | ||||||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | −3.00000 | + | 5.19615i | −0.174964 | + | 0.303046i | ||||
\(295\) | 3.00000 | − | 5.19615i | 0.174667 | − | 0.302532i | ||||
\(296\) | 6.00000 | 0.348743 | ||||||||
\(297\) | 18.0000 | 1.04447 | ||||||||
\(298\) | −4.00000 | + | 6.92820i | −0.231714 | + | 0.401340i | ||||
\(299\) | −7.50000 | − | 12.9904i | −0.433736 | − | 0.751253i | ||||
\(300\) | −1.50000 | + | 2.59808i | −0.0866025 | + | 0.150000i | ||||
\(301\) | −15.0000 | − | 25.9808i | −0.864586 | − | 1.49751i | ||||
\(302\) | 9.00000 | + | 15.5885i | 0.517892 | + | 0.897015i | ||||
\(303\) | −30.0000 | −1.72345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.00000 | − | 5.19615i | −0.171499 | − | 0.297044i | ||||
\(307\) | 6.00000 | + | 10.3923i | 0.342438 | + | 0.593120i | 0.984885 | − | 0.173210i | \(-0.0554140\pi\) |
−0.642447 | + | 0.766330i | \(0.722081\pi\) | |||||||
\(308\) | −3.00000 | + | 5.19615i | −0.170941 | + | 0.296078i | ||||
\(309\) | −9.00000 | − | 15.5885i | −0.511992 | − | 0.886796i | ||||
\(310\) | 6.00000 | − | 10.3923i | 0.340777 | − | 0.590243i | ||||
\(311\) | −11.0000 | −0.623753 | −0.311876 | − | 0.950123i | \(-0.600957\pi\) | ||||
−0.311876 | + | 0.950123i | \(0.600957\pi\) | |||||||
\(312\) | 9.00000 | 0.509525 | ||||||||
\(313\) | −10.5000 | + | 18.1865i | −0.593495 | + | 1.02796i | 0.400262 | + | 0.916401i | \(0.368919\pi\) |
−0.993757 | + | 0.111563i | \(0.964414\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −36.0000 | −2.02837 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | −16.5000 | + | 28.5788i | −0.926732 | + | 1.60515i | −0.137981 | + | 0.990435i | \(0.544061\pi\) |
−0.788751 | + | 0.614713i | \(0.789272\pi\) | |||||||
\(318\) | −4.50000 | − | 7.79423i | −0.252347 | − | 0.437079i | ||||
\(319\) | 3.00000 | − | 5.19615i | 0.167968 | − | 0.290929i | ||||
\(320\) | −1.00000 | − | 1.73205i | −0.0559017 | − | 0.0968246i | ||||
\(321\) | 4.50000 | + | 7.79423i | 0.251166 | + | 0.435031i | ||||
\(322\) | 15.0000 | 0.835917 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 1.50000 | + | 2.59808i | 0.0832050 | + | 0.144115i | ||||
\(326\) | −3.00000 | − | 5.19615i | −0.166155 | − | 0.287788i | ||||
\(327\) | −4.50000 | + | 7.79423i | −0.248851 | + | 0.431022i | ||||
\(328\) | −6.00000 | − | 10.3923i | −0.331295 | − | 0.573819i | ||||
\(329\) | −12.0000 | + | 20.7846i | −0.661581 | + | 1.14589i | ||||
\(330\) | −12.0000 | −0.660578 | ||||||||
\(331\) | −9.00000 | −0.494685 | −0.247342 | − | 0.968928i | \(-0.579557\pi\) | ||||
−0.247342 | + | 0.968928i | \(0.579557\pi\) | |||||||
\(332\) | −1.00000 | + | 1.73205i | −0.0548821 | + | 0.0950586i | ||||
\(333\) | 18.0000 | − | 31.1769i | 0.986394 | − | 1.70848i | ||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | −30.0000 | −1.63908 | ||||||||
\(336\) | −4.50000 | + | 7.79423i | −0.245495 | + | 0.425210i | ||||
\(337\) | 9.00000 | + | 15.5885i | 0.490261 | + | 0.849157i | 0.999937 | − | 0.0112091i | \(-0.00356804\pi\) |
−0.509676 | + | 0.860366i | \(0.670235\pi\) | |||||||
\(338\) | −2.00000 | + | 3.46410i | −0.108786 | + | 0.188422i | ||||
\(339\) | −18.0000 | − | 31.1769i | −0.977626 | − | 1.69330i | ||||
\(340\) | 1.00000 | + | 1.73205i | 0.0542326 | + | 0.0939336i | ||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −5.00000 | − | 8.66025i | −0.269582 | − | 0.466930i | ||||
\(345\) | 15.0000 | + | 25.9808i | 0.807573 | + | 1.39876i | ||||
\(346\) | 9.00000 | − | 15.5885i | 0.483843 | − | 0.838041i | ||||
\(347\) | −8.00000 | − | 13.8564i | −0.429463 | − | 0.743851i | 0.567363 | − | 0.823468i | \(-0.307964\pi\) |
−0.996826 | + | 0.0796169i | \(0.974630\pi\) | |||||||
\(348\) | 4.50000 | − | 7.79423i | 0.241225 | − | 0.417815i | ||||
\(349\) | 28.0000 | 1.49881 | 0.749403 | − | 0.662114i | \(-0.230341\pi\) | ||||
0.749403 | + | 0.662114i | \(0.230341\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | 13.5000 | − | 23.3827i | 0.720577 | − | 1.24808i | ||||
\(352\) | −1.00000 | + | 1.73205i | −0.0533002 | + | 0.0923186i | ||||
\(353\) | −31.0000 | −1.64996 | −0.824982 | − | 0.565159i | \(-0.808815\pi\) | ||||
−0.824982 | + | 0.565159i | \(0.808815\pi\) | |||||||
\(354\) | −9.00000 | −0.478345 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | + | 5.19615i | 0.159000 | + | 0.275396i | ||||
\(357\) | 4.50000 | − | 7.79423i | 0.238165 | − | 0.412514i | ||||
\(358\) | 6.00000 | + | 10.3923i | 0.317110 | + | 0.549250i | ||||
\(359\) | −9.50000 | − | 16.4545i | −0.501391 | − | 0.868434i | −0.999999 | − | 0.00160673i | \(-0.999489\pi\) |
0.498608 | − | 0.866828i | \(-0.333845\pi\) | |||||||
\(360\) | −12.0000 | −0.632456 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 18.0000 | 0.946059 | ||||||||
\(363\) | −10.5000 | − | 18.1865i | −0.551107 | − | 0.954545i | ||||
\(364\) | 4.50000 | + | 7.79423i | 0.235864 | + | 0.408529i | ||||
\(365\) | 11.0000 | − | 19.0526i | 0.575766 | − | 0.997257i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | + | 6.92820i | −0.208798 | + | 0.361649i | −0.951336 | − | 0.308155i | \(-0.900289\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(368\) | 5.00000 | 0.260643 | ||||||||
\(369\) | −72.0000 | −3.74817 | ||||||||
\(370\) | −6.00000 | + | 10.3923i | −0.311925 | + | 0.540270i | ||||
\(371\) | 4.50000 | − | 7.79423i | 0.233628 | − | 0.404656i | ||||
\(372\) | −18.0000 | −0.933257 | ||||||||
\(373\) | 21.0000 | 1.08734 | 0.543669 | − | 0.839299i | \(-0.317035\pi\) | ||||
0.543669 | + | 0.839299i | \(0.317035\pi\) | |||||||
\(374\) | 1.00000 | − | 1.73205i | 0.0517088 | − | 0.0895622i | ||||
\(375\) | −18.0000 | − | 31.1769i | −0.929516 | − | 1.60997i | ||||
\(376\) | −4.00000 | + | 6.92820i | −0.206284 | + | 0.357295i | ||||
\(377\) | −4.50000 | − | 7.79423i | −0.231762 | − | 0.401423i | ||||
\(378\) | 13.5000 | + | 23.3827i | 0.694365 | + | 1.20268i | ||||
\(379\) | −3.00000 | −0.154100 | −0.0770498 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770498 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.0000 | 1.84434 | ||||||||
\(382\) | −5.50000 | − | 9.52628i | −0.281404 | − | 0.487407i | ||||
\(383\) | 9.00000 | + | 15.5885i | 0.459879 | + | 0.796533i | 0.998954 | − | 0.0457244i | \(-0.0145596\pi\) |
−0.539076 | + | 0.842257i | \(0.681226\pi\) | |||||||
\(384\) | −1.50000 | + | 2.59808i | −0.0765466 | + | 0.132583i | ||||
\(385\) | −6.00000 | − | 10.3923i | −0.305788 | − | 0.529641i | ||||
\(386\) | −3.00000 | + | 5.19615i | −0.152696 | + | 0.264477i | ||||
\(387\) | −60.0000 | −3.04997 | ||||||||
\(388\) | −12.0000 | −0.609208 | ||||||||
\(389\) | −13.0000 | + | 22.5167i | −0.659126 | + | 1.14164i | 0.321716 | + | 0.946836i | \(0.395740\pi\) |
−0.980842 | + | 0.194804i | \(0.937593\pi\) | |||||||
\(390\) | −9.00000 | + | 15.5885i | −0.455733 | + | 0.789352i | ||||
\(391\) | −5.00000 | −0.252861 | ||||||||
\(392\) | −2.00000 | −0.101015 | ||||||||
\(393\) | 21.0000 | − | 36.3731i | 1.05931 | − | 1.83478i | ||||
\(394\) | 2.00000 | + | 3.46410i | 0.100759 | + | 0.174519i | ||||
\(395\) | −12.0000 | + | 20.7846i | −0.603786 | + | 1.04579i | ||||
\(396\) | 6.00000 | + | 10.3923i | 0.301511 | + | 0.522233i | ||||
\(397\) | −1.00000 | − | 1.73205i | −0.0501886 | − | 0.0869291i | 0.839840 | − | 0.542834i | \(-0.182649\pi\) |
−0.890028 | + | 0.455905i | \(0.849316\pi\) | |||||||
\(398\) | 7.00000 | 0.350878 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 18.0000 | + | 31.1769i | 0.898877 | + | 1.55690i | 0.828932 | + | 0.559350i | \(0.188949\pi\) |
0.0699455 | + | 0.997551i | \(0.477717\pi\) | |||||||
\(402\) | 22.5000 | + | 38.9711i | 1.12220 | + | 1.94370i | ||||
\(403\) | −9.00000 | + | 15.5885i | −0.448322 | + | 0.776516i | ||||
\(404\) | −5.00000 | − | 8.66025i | −0.248759 | − | 0.430864i | ||||
\(405\) | −9.00000 | + | 15.5885i | −0.447214 | + | 0.774597i | ||||
\(406\) | 9.00000 | 0.446663 | ||||||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 1.50000 | − | 2.59808i | 0.0742611 | − | 0.128624i | ||||
\(409\) | 3.00000 | − | 5.19615i | 0.148340 | − | 0.256933i | −0.782274 | − | 0.622935i | \(-0.785940\pi\) |
0.930614 | + | 0.366002i | \(0.119274\pi\) | |||||||
\(410\) | 24.0000 | 1.18528 | ||||||||
\(411\) | −57.0000 | −2.81160 | ||||||||
\(412\) | 3.00000 | − | 5.19615i | 0.147799 | − | 0.255996i | ||||
\(413\) | −4.50000 | − | 7.79423i | −0.221431 | − | 0.383529i | ||||
\(414\) | 15.0000 | − | 25.9808i | 0.737210 | − | 1.27688i | ||||
\(415\) | −2.00000 | − | 3.46410i | −0.0981761 | − | 0.170046i | ||||
\(416\) | 1.50000 | + | 2.59808i | 0.0735436 | + | 0.127381i | ||||
\(417\) | −18.0000 | −0.881464 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.0000 | −0.683945 | −0.341972 | − | 0.939710i | \(-0.611095\pi\) | ||||
−0.341972 | + | 0.939710i | \(0.611095\pi\) | |||||||
\(420\) | −9.00000 | − | 15.5885i | −0.439155 | − | 0.760639i | ||||
\(421\) | −13.5000 | − | 23.3827i | −0.657950 | − | 1.13960i | −0.981146 | − | 0.193270i | \(-0.938091\pi\) |
0.323196 | − | 0.946332i | \(-0.395243\pi\) | |||||||
\(422\) | −1.50000 | + | 2.59808i | −0.0730189 | + | 0.126472i | ||||
\(423\) | 24.0000 | + | 41.5692i | 1.16692 | + | 2.02116i | ||||
\(424\) | 1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | ||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.50000 | + | 2.59808i | −0.0725052 | + | 0.125583i | ||||
\(429\) | 18.0000 | 0.869048 | ||||||||
\(430\) | 20.0000 | 0.964486 | ||||||||
\(431\) | 12.0000 | − | 20.7846i | 0.578020 | − | 1.00116i | −0.417687 | − | 0.908591i | \(-0.637159\pi\) |
0.995706 | − | 0.0925683i | \(-0.0295076\pi\) | |||||||
\(432\) | 4.50000 | + | 7.79423i | 0.216506 | + | 0.375000i | ||||
\(433\) | 15.0000 | − | 25.9808i | 0.720854 | − | 1.24856i | −0.239804 | − | 0.970821i | \(-0.577083\pi\) |
0.960658 | − | 0.277734i | \(-0.0895835\pi\) | |||||||
\(434\) | −9.00000 | − | 15.5885i | −0.432014 | − | 0.748270i | ||||
\(435\) | 9.00000 | + | 15.5885i | 0.431517 | + | 0.747409i | ||||
\(436\) | −3.00000 | −0.143674 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −33.0000 | −1.57680 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | −2.00000 | − | 3.46410i | −0.0953463 | − | 0.165145i | ||||
\(441\) | −6.00000 | + | 10.3923i | −0.285714 | + | 0.494872i | ||||
\(442\) | −1.50000 | − | 2.59808i | −0.0713477 | − | 0.123578i | ||||
\(443\) | 11.0000 | − | 19.0526i | 0.522626 | − | 0.905214i | −0.477028 | − | 0.878888i | \(-0.658286\pi\) |
0.999653 | − | 0.0263261i | \(-0.00838082\pi\) | |||||||
\(444\) | 18.0000 | 0.854242 | ||||||||
\(445\) | −12.0000 | −0.568855 | ||||||||
\(446\) | −9.00000 | + | 15.5885i | −0.426162 | + | 0.738135i | ||||
\(447\) | −12.0000 | + | 20.7846i | −0.567581 | + | 0.983078i | ||||
\(448\) | −3.00000 | −0.141737 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | −3.00000 | + | 5.19615i | −0.141421 | + | 0.244949i | ||||
\(451\) | −12.0000 | − | 20.7846i | −0.565058 | − | 0.978709i | ||||
\(452\) | 6.00000 | − | 10.3923i | 0.282216 | − | 0.488813i | ||||
\(453\) | 27.0000 | + | 46.7654i | 1.26857 | + | 2.19723i | ||||
\(454\) | −1.50000 | − | 2.59808i | −0.0703985 | − | 0.121934i | ||||
\(455\) | −18.0000 | −0.843853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00000 | 0.0467780 | 0.0233890 | − | 0.999726i | \(-0.492554\pi\) | ||||
0.0233890 | + | 0.999726i | \(0.492554\pi\) | |||||||
\(458\) | −6.00000 | − | 10.3923i | −0.280362 | − | 0.485601i | ||||
\(459\) | −4.50000 | − | 7.79423i | −0.210042 | − | 0.363803i | ||||
\(460\) | −5.00000 | + | 8.66025i | −0.233126 | + | 0.403786i | ||||
\(461\) | −2.00000 | − | 3.46410i | −0.0931493 | − | 0.161339i | 0.815685 | − | 0.578496i | \(-0.196360\pi\) |
−0.908835 | + | 0.417156i | \(0.863027\pi\) | |||||||
\(462\) | −9.00000 | + | 15.5885i | −0.418718 | + | 0.725241i | ||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 18.0000 | − | 31.1769i | 0.834730 | − | 1.44579i | ||||
\(466\) | 7.00000 | − | 12.1244i | 0.324269 | − | 0.561650i | ||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 18.0000 | 0.832050 | ||||||||
\(469\) | −22.5000 | + | 38.9711i | −1.03895 | + | 1.79952i | ||||
\(470\) | −8.00000 | − | 13.8564i | −0.369012 | − | 0.639148i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.50000 | − | 2.59808i | −0.0690431 | − | 0.119586i | ||||
\(473\) | −10.0000 | − | 17.3205i | −0.459800 | − | 0.796398i | ||||
\(474\) | 36.0000 | 1.65353 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.00000 | 0.137505 | ||||||||
\(477\) | −9.00000 | − | 15.5885i | −0.412082 | − | 0.713746i | ||||
\(478\) | 0.500000 | + | 0.866025i | 0.0228695 | + | 0.0396111i | ||||
\(479\) | 20.0000 | − | 34.6410i | 0.913823 | − | 1.58279i | 0.105208 | − | 0.994450i | \(-0.466449\pi\) |
0.808615 | − | 0.588338i | \(-0.200218\pi\) | |||||||
\(480\) | −3.00000 | − | 5.19615i | −0.136931 | − | 0.237171i | ||||
\(481\) | 9.00000 | − | 15.5885i | 0.410365 | − | 0.710772i | ||||
\(482\) | 24.0000 | 1.09317 | ||||||||
\(483\) | 45.0000 | 2.04757 | ||||||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | 12.0000 | − | 20.7846i | 0.544892 | − | 0.943781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0000 | 0.815658 | 0.407829 | − | 0.913058i | \(-0.366286\pi\) | ||||
0.407829 | + | 0.913058i | \(0.366286\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.00000 | − | 15.5885i | −0.406994 | − | 0.704934i | ||||
\(490\) | 2.00000 | − | 3.46410i | 0.0903508 | − | 0.156492i | ||||
\(491\) | −4.00000 | − | 6.92820i | −0.180517 | − | 0.312665i | 0.761539 | − | 0.648119i | \(-0.224444\pi\) |
−0.942057 | + | 0.335453i | \(0.891111\pi\) | |||||||
\(492\) | −18.0000 | − | 31.1769i | −0.811503 | − | 1.40556i | ||||
\(493\) | −3.00000 | −0.135113 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −24.0000 | −1.07872 | ||||||||
\(496\) | −3.00000 | − | 5.19615i | −0.134704 | − | 0.233314i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00000 | + | 5.19615i | −0.134433 | + | 0.232845i | ||||
\(499\) | −9.00000 | − | 15.5885i | −0.402895 | − | 0.697835i | 0.591179 | − | 0.806541i | \(-0.298663\pi\) |
−0.994074 | + | 0.108705i | \(0.965329\pi\) | |||||||
\(500\) | 6.00000 | − | 10.3923i | 0.268328 | − | 0.464758i | ||||
\(501\) | −36.0000 | −1.60836 | ||||||||
\(502\) | 20.0000 | 0.892644 | ||||||||
\(503\) | −0.500000 | + | 0.866025i | −0.0222939 | + | 0.0386142i | −0.876957 | − | 0.480569i | \(-0.840430\pi\) |
0.854663 | + | 0.519183i | \(0.173764\pi\) | |||||||
\(504\) | −9.00000 | + | 15.5885i | −0.400892 | + | 0.694365i | ||||
\(505\) | 20.0000 | 0.889988 | ||||||||
\(506\) | 10.0000 | 0.444554 | ||||||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 6.00000 | + | 10.3923i | 0.266207 | + | 0.461084i | ||||
\(509\) | 9.00000 | − | 15.5885i | 0.398918 | − | 0.690946i | −0.594675 | − | 0.803966i | \(-0.702719\pi\) |
0.993593 | + | 0.113020i | \(0.0360525\pi\) | |||||||
\(510\) | 3.00000 | + | 5.19615i | 0.132842 | + | 0.230089i | ||||
\(511\) | −16.5000 | − | 28.5788i | −0.729917 | − | 1.26425i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 6.00000 | + | 10.3923i | 0.264392 | + | 0.457940i | ||||
\(516\) | −15.0000 | − | 25.9808i | −0.660338 | − | 1.14374i | ||||
\(517\) | −8.00000 | + | 13.8564i | −0.351840 | + | 0.609404i | ||||
\(518\) | 9.00000 | + | 15.5885i | 0.395437 | + | 0.684917i | ||||
\(519\) | 27.0000 | − | 46.7654i | 1.18517 | − | 2.05277i | ||||
\(520\) | −6.00000 | −0.263117 | ||||||||
\(521\) | 12.0000 | 0.525730 | 0.262865 | − | 0.964833i | \(-0.415333\pi\) | ||||
0.262865 | + | 0.964833i | \(0.415333\pi\) | |||||||
\(522\) | 9.00000 | − | 15.5885i | 0.393919 | − | 0.682288i | ||||
\(523\) | 4.50000 | − | 7.79423i | 0.196771 | − | 0.340818i | −0.750708 | − | 0.660634i | \(-0.770288\pi\) |
0.947480 | + | 0.319816i | \(0.103621\pi\) | |||||||
\(524\) | 14.0000 | 0.611593 | ||||||||
\(525\) | −9.00000 | −0.392792 | ||||||||
\(526\) | −4.00000 | + | 6.92820i | −0.174408 | + | 0.302084i | ||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | −3.00000 | + | 5.19615i | −0.130558 | + | 0.226134i | ||||
\(529\) | −1.00000 | − | 1.73205i | −0.0434783 | − | 0.0753066i | ||||
\(530\) | 3.00000 | + | 5.19615i | 0.130312 | + | 0.225706i | ||||
\(531\) | −18.0000 | −0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.0000 | −1.55933 | ||||||||
\(534\) | 9.00000 | + | 15.5885i | 0.389468 | + | 0.674579i | ||||
\(535\) | −3.00000 | − | 5.19615i | −0.129701 | − | 0.224649i | ||||
\(536\) | −7.50000 | + | 12.9904i | −0.323951 | + | 0.561099i | ||||
\(537\) | 18.0000 | + | 31.1769i | 0.776757 | + | 1.34538i | ||||
\(538\) | 3.00000 | − | 5.19615i | 0.129339 | − | 0.224022i | ||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | −18.0000 | −0.774597 | ||||||||
\(541\) | −1.00000 | + | 1.73205i | −0.0429934 | + | 0.0744667i | −0.886721 | − | 0.462304i | \(-0.847023\pi\) |
0.843728 | + | 0.536771i | \(0.180356\pi\) | |||||||
\(542\) | −5.50000 | + | 9.52628i | −0.236245 | + | 0.409189i | ||||
\(543\) | 54.0000 | 2.31736 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 3.00000 | − | 5.19615i | 0.128506 | − | 0.222579i | ||||
\(546\) | 13.5000 | + | 23.3827i | 0.577747 | + | 1.00069i | ||||
\(547\) | −18.0000 | + | 31.1769i | −0.769624 | + | 1.33303i | 0.168142 | + | 0.985763i | \(0.446223\pi\) |
−0.937767 | + | 0.347266i | \(0.887110\pi\) | |||||||
\(548\) | −9.50000 | − | 16.4545i | −0.405820 | − | 0.702901i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 15.0000 | 0.638442 | ||||||||
\(553\) | 18.0000 | + | 31.1769i | 0.765438 | + | 1.32578i | ||||
\(554\) | 15.0000 | + | 25.9808i | 0.637289 | + | 1.10382i | ||||
\(555\) | −18.0000 | + | 31.1769i | −0.764057 | + | 1.32339i | ||||
\(556\) | −3.00000 | − | 5.19615i | −0.127228 | − | 0.220366i | ||||
\(557\) | −11.0000 | + | 19.0526i | −0.466085 | + | 0.807283i | −0.999250 | − | 0.0387286i | \(-0.987669\pi\) |
0.533165 | + | 0.846011i | \(0.321003\pi\) | |||||||
\(558\) | −36.0000 | −1.52400 | ||||||||
\(559\) | −30.0000 | −1.26886 | ||||||||
\(560\) | 3.00000 | − | 5.19615i | 0.126773 | − | 0.219578i | ||||
\(561\) | 3.00000 | − | 5.19615i | 0.126660 | − | 0.219382i | ||||
\(562\) | 12.0000 | 0.506189 | ||||||||
\(563\) | 24.0000 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | −12.0000 | + | 20.7846i | −0.505291 | + | 0.875190i | ||||
\(565\) | 12.0000 | + | 20.7846i | 0.504844 | + | 0.874415i | ||||
\(566\) | −7.00000 | + | 12.1244i | −0.294232 | + | 0.509625i | ||||
\(567\) | 13.5000 | + | 23.3827i | 0.566947 | + | 0.981981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.0000 | −1.33916 | −0.669579 | − | 0.742741i | \(-0.733526\pi\) | ||||
−0.669579 | + | 0.742741i | \(0.733526\pi\) | |||||||
\(572\) | 3.00000 | + | 5.19615i | 0.125436 | + | 0.217262i | ||||
\(573\) | −16.5000 | − | 28.5788i | −0.689297 | − | 1.19390i | ||||
\(574\) | 18.0000 | − | 31.1769i | 0.751305 | − | 1.30130i | ||||
\(575\) | 2.50000 | + | 4.33013i | 0.104257 | + | 0.180579i | ||||
\(576\) | −3.00000 | + | 5.19615i | −0.125000 | + | 0.216506i | ||||
\(577\) | 15.0000 | 0.624458 | 0.312229 | − | 0.950007i | \(-0.398924\pi\) | ||||
0.312229 | + | 0.950007i | \(0.398924\pi\) | |||||||
\(578\) | 16.0000 | 0.665512 | ||||||||
\(579\) | −9.00000 | + | 15.5885i | −0.374027 | + | 0.647834i | ||||
\(580\) | −3.00000 | + | 5.19615i | −0.124568 | + | 0.215758i | ||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | −36.0000 | −1.49225 | ||||||||
\(583\) | 3.00000 | − | 5.19615i | 0.124247 | − | 0.215203i | ||||
\(584\) | −5.50000 | − | 9.52628i | −0.227592 | − | 0.394200i | ||||
\(585\) | −18.0000 | + | 31.1769i | −0.744208 | + | 1.28901i | ||||
\(586\) | 4.50000 | + | 7.79423i | 0.185893 | + | 0.321977i | ||||
\(587\) | 14.0000 | + | 24.2487i | 0.577842 | + | 1.00085i | 0.995726 | + | 0.0923513i | \(0.0294383\pi\) |
−0.417885 | + | 0.908500i | \(0.637228\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 6.00000 | 0.247016 | ||||||||
\(591\) | 6.00000 | + | 10.3923i | 0.246807 | + | 0.427482i | ||||
\(592\) | 3.00000 | + | 5.19615i | 0.123299 | + | 0.213561i | ||||
\(593\) | 1.00000 | − | 1.73205i | 0.0410651 | − | 0.0711268i | −0.844762 | − | 0.535142i | \(-0.820258\pi\) |
0.885827 | + | 0.464015i | \(0.153592\pi\) | |||||||
\(594\) | 9.00000 | + | 15.5885i | 0.369274 | + | 0.639602i | ||||
\(595\) | −3.00000 | + | 5.19615i | −0.122988 | + | 0.213021i | ||||
\(596\) | −8.00000 | −0.327693 | ||||||||
\(597\) | 21.0000 | 0.859473 | ||||||||
\(598\) | 7.50000 | − | 12.9904i | 0.306698 | − | 0.531216i | ||||
\(599\) | −18.0000 | + | 31.1769i | −0.735460 | + | 1.27385i | 0.219061 | + | 0.975711i | \(0.429701\pi\) |
−0.954521 | + | 0.298143i | \(0.903633\pi\) | |||||||
\(600\) | −3.00000 | −0.122474 | ||||||||
\(601\) | 6.00000 | 0.244745 | 0.122373 | − | 0.992484i | \(-0.460950\pi\) | ||||
0.122373 | + | 0.992484i | \(0.460950\pi\) | |||||||
\(602\) | 15.0000 | − | 25.9808i | 0.611354 | − | 1.05890i | ||||
\(603\) | 45.0000 | + | 77.9423i | 1.83254 | + | 3.17406i | ||||
\(604\) | −9.00000 | + | 15.5885i | −0.366205 | + | 0.634285i | ||||
\(605\) | 7.00000 | + | 12.1244i | 0.284590 | + | 0.492925i | ||||
\(606\) | −15.0000 | − | 25.9808i | −0.609333 | − | 1.05540i | ||||
\(607\) | 12.0000 | 0.487065 | 0.243532 | − | 0.969893i | \(-0.421694\pi\) | ||||
0.243532 | + | 0.969893i | \(0.421694\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.0000 | 1.09410 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000 | + | 20.7846i | 0.485468 | + | 0.840855i | ||||
\(612\) | 3.00000 | − | 5.19615i | 0.121268 | − | 0.210042i | ||||
\(613\) | −9.00000 | − | 15.5885i | −0.363507 | − | 0.629612i | 0.625029 | − | 0.780602i | \(-0.285087\pi\) |
−0.988535 | + | 0.150990i | \(0.951754\pi\) | |||||||
\(614\) | −6.00000 | + | 10.3923i | −0.242140 | + | 0.419399i | ||||
\(615\) | 72.0000 | 2.90332 | ||||||||
\(616\) | −6.00000 | −0.241747 | ||||||||
\(617\) | −5.00000 | + | 8.66025i | −0.201292 | + | 0.348649i | −0.948945 | − | 0.315441i | \(-0.897847\pi\) |
0.747653 | + | 0.664090i | \(0.231181\pi\) | |||||||
\(618\) | 9.00000 | − | 15.5885i | 0.362033 | − | 0.627060i | ||||
\(619\) | −24.0000 | −0.964641 | −0.482321 | − | 0.875995i | \(-0.660206\pi\) | ||||
−0.482321 | + | 0.875995i | \(0.660206\pi\) | |||||||
\(620\) | 12.0000 | 0.481932 | ||||||||
\(621\) | 22.5000 | − | 38.9711i | 0.902894 | − | 1.56386i | ||||
\(622\) | −5.50000 | − | 9.52628i | −0.220530 | − | 0.381969i | ||||
\(623\) | −9.00000 | + | 15.5885i | −0.360577 | + | 0.624538i | ||||
\(624\) | 4.50000 | + | 7.79423i | 0.180144 | + | 0.312019i | ||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | −21.0000 | −0.839329 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.00000 | − | 5.19615i | −0.119618 | − | 0.207184i | ||||
\(630\) | −18.0000 | − | 31.1769i | −0.717137 | − | 1.24212i | ||||
\(631\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(632\) | 6.00000 | + | 10.3923i | 0.238667 | + | 0.413384i | ||||
\(633\) | −4.50000 | + | 7.79423i | −0.178859 | + | 0.309793i | ||||
\(634\) | −33.0000 | −1.31060 | ||||||||
\(635\) | −24.0000 | −0.952411 | ||||||||
\(636\) | 4.50000 | − | 7.79423i | 0.178437 | − | 0.309061i | ||||
\(637\) | −3.00000 | + | 5.19615i | −0.118864 | + | 0.205879i | ||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | 9.00000 | + | 15.5885i | 0.355479 | + | 0.615707i | 0.987200 | − | 0.159489i | \(-0.0509845\pi\) |
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(642\) | −4.50000 | + | 7.79423i | −0.177601 | + | 0.307614i | ||||
\(643\) | −16.0000 | − | 27.7128i | −0.630978 | − | 1.09289i | −0.987352 | − | 0.158543i | \(-0.949320\pi\) |
0.356374 | − | 0.934344i | \(-0.384013\pi\) | |||||||
\(644\) | 7.50000 | + | 12.9904i | 0.295541 | + | 0.511893i | ||||
\(645\) | 60.0000 | 2.36250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.0000 | −0.904223 | −0.452112 | − | 0.891961i | \(-0.649329\pi\) | ||||
−0.452112 | + | 0.891961i | \(0.649329\pi\) | |||||||
\(648\) | 4.50000 | + | 7.79423i | 0.176777 | + | 0.306186i | ||||
\(649\) | −3.00000 | − | 5.19615i | −0.117760 | − | 0.203967i | ||||
\(650\) | −1.50000 | + | 2.59808i | −0.0588348 | + | 0.101905i | ||||
\(651\) | −27.0000 | − | 46.7654i | −1.05821 | − | 1.83288i | ||||
\(652\) | 3.00000 | − | 5.19615i | 0.117489 | − | 0.203497i | ||||
\(653\) | −10.0000 | −0.391330 | −0.195665 | − | 0.980671i | \(-0.562687\pi\) | ||||
−0.195665 | + | 0.980671i | \(0.562687\pi\) | |||||||
\(654\) | −9.00000 | −0.351928 | ||||||||
\(655\) | −14.0000 | + | 24.2487i | −0.547025 | + | 0.947476i | ||||
\(656\) | 6.00000 | − | 10.3923i | 0.234261 | − | 0.405751i | ||||
\(657\) | −66.0000 | −2.57491 | ||||||||
\(658\) | −24.0000 | −0.935617 | ||||||||
\(659\) | −7.50000 | + | 12.9904i | −0.292159 | + | 0.506033i | −0.974320 | − | 0.225168i | \(-0.927707\pi\) |
0.682161 | + | 0.731202i | \(0.261040\pi\) | |||||||
\(660\) | −6.00000 | − | 10.3923i | −0.233550 | − | 0.404520i | ||||
\(661\) | 7.50000 | − | 12.9904i | 0.291716 | − | 0.505267i | −0.682499 | − | 0.730886i | \(-0.739107\pi\) |
0.974216 | + | 0.225619i | \(0.0724404\pi\) | |||||||
\(662\) | −4.50000 | − | 7.79423i | −0.174897 | − | 0.302931i | ||||
\(663\) | −4.50000 | − | 7.79423i | −0.174766 | − | 0.302703i | ||||
\(664\) | −2.00000 | −0.0776151 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 36.0000 | 1.39497 | ||||||||
\(667\) | −7.50000 | − | 12.9904i | −0.290401 | − | 0.502990i | ||||
\(668\) | −6.00000 | − | 10.3923i | −0.232147 | − | 0.402090i | ||||
\(669\) | −27.0000 | + | 46.7654i | −1.04388 | + | 1.80805i | ||||
\(670\) | −15.0000 | − | 25.9808i | −0.579501 | − | 1.00372i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −9.00000 | −0.347183 | ||||||||
\(673\) | 48.0000 | 1.85026 | 0.925132 | − | 0.379646i | \(-0.123954\pi\) | ||||
0.925132 | + | 0.379646i | \(0.123954\pi\) | |||||||
\(674\) | −9.00000 | + | 15.5885i | −0.346667 | + | 0.600445i | ||||
\(675\) | −4.50000 | + | 7.79423i | −0.173205 | + | 0.300000i | ||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | −3.00000 | −0.115299 | −0.0576497 | − | 0.998337i | \(-0.518361\pi\) | ||||
−0.0576497 | + | 0.998337i | \(0.518361\pi\) | |||||||
\(678\) | 18.0000 | − | 31.1769i | 0.691286 | − | 1.19734i | ||||
\(679\) | −18.0000 | − | 31.1769i | −0.690777 | − | 1.19646i | ||||
\(680\) | −1.00000 | + | 1.73205i | −0.0383482 | + | 0.0664211i | ||||
\(681\) | −4.50000 | − | 7.79423i | −0.172440 | − | 0.298675i | ||||
\(682\) | −6.00000 | − | 10.3923i | −0.229752 | − | 0.397942i | ||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.0000 | 1.45191 | ||||||||
\(686\) | 7.50000 | + | 12.9904i | 0.286351 | + | 0.495975i | ||||
\(687\) | −18.0000 | − | 31.1769i | −0.686743 | − | 1.18947i | ||||
\(688\) | 5.00000 | − | 8.66025i | 0.190623 | − | 0.330169i | ||||
\(689\) | −4.50000 | − | 7.79423i | −0.171436 | − | 0.296936i | ||||
\(690\) | −15.0000 | + | 25.9808i | −0.571040 | + | 0.989071i | ||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | −18.0000 | + | 31.1769i | −0.683763 | + | 1.18431i | ||||
\(694\) | 8.00000 | − | 13.8564i | 0.303676 | − | 0.525982i | ||||
\(695\) | 12.0000 | 0.455186 | ||||||||
\(696\) | 9.00000 | 0.341144 | ||||||||
\(697\) | −6.00000 | + | 10.3923i | −0.227266 | + | 0.393637i | ||||
\(698\) | 14.0000 | + | 24.2487i | 0.529908 | + | 0.917827i | ||||
\(699\) | 21.0000 | − | 36.3731i | 0.794293 | − | 1.37576i | ||||
\(700\) | −1.50000 | − | 2.59808i | −0.0566947 | − | 0.0981981i | ||||
\(701\) | 20.0000 | + | 34.6410i | 0.755390 | + | 1.30837i | 0.945180 | + | 0.326549i | \(0.105886\pi\) |
−0.189791 | + | 0.981825i | \(0.560781\pi\) | |||||||
\(702\) | 27.0000 | 1.01905 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | −24.0000 | − | 41.5692i | −0.903892 | − | 1.56559i | ||||
\(706\) | −15.5000 | − | 26.8468i | −0.583350 | − | 1.01039i | ||||
\(707\) | 15.0000 | − | 25.9808i | 0.564133 | − | 0.977107i | ||||
\(708\) | −4.50000 | − | 7.79423i | −0.169120 | − | 0.292925i | ||||
\(709\) | 4.00000 | − | 6.92820i | 0.150223 | − | 0.260194i | −0.781086 | − | 0.624423i | \(-0.785334\pi\) |
0.931309 | + | 0.364229i | \(0.118667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 72.0000 | 2.70021 | ||||||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | −15.0000 | + | 25.9808i | −0.561754 | + | 0.972987i | ||||
\(714\) | 9.00000 | 0.336817 | ||||||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | −6.00000 | + | 10.3923i | −0.224231 | + | 0.388379i | ||||
\(717\) | 1.50000 | + | 2.59808i | 0.0560185 | + | 0.0970269i | ||||
\(718\) | 9.50000 | − | 16.4545i | 0.354537 | − | 0.614076i | ||||
\(719\) | 21.5000 | + | 37.2391i | 0.801815 | + | 1.38878i | 0.918421 | + | 0.395606i | \(0.129465\pi\) |
−0.116606 | + | 0.993178i | \(0.537201\pi\) | |||||||
\(720\) | −6.00000 | − | 10.3923i | −0.223607 | − | 0.387298i | ||||
\(721\) | 18.0000 | 0.670355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 72.0000 | 2.67771 | ||||||||
\(724\) | 9.00000 | + | 15.5885i | 0.334482 | + | 0.579340i | ||||
\(725\) | 1.50000 | + | 2.59808i | 0.0557086 | + | 0.0964901i | ||||
\(726\) | 10.5000 | − | 18.1865i | 0.389692 | − | 0.674966i | ||||
\(727\) | 17.5000 | + | 30.3109i | 0.649039 | + | 1.12417i | 0.983353 | + | 0.181707i | \(0.0581622\pi\) |
−0.334314 | + | 0.942462i | \(0.608504\pi\) | |||||||
\(728\) | −4.50000 | + | 7.79423i | −0.166781 | + | 0.288873i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 22.0000 | 0.814257 | ||||||||
\(731\) | −5.00000 | + | 8.66025i | −0.184932 | + | 0.320311i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 6.00000 | − | 10.3923i | 0.221313 | − | 0.383326i | ||||
\(736\) | 2.50000 | + | 4.33013i | 0.0921512 | + | 0.159611i | ||||
\(737\) | −15.0000 | + | 25.9808i | −0.552532 | + | 0.957014i | ||||
\(738\) | −36.0000 | − | 62.3538i | −1.32518 | − | 2.29528i | ||||
\(739\) | 6.00000 | + | 10.3923i | 0.220714 | + | 0.382287i | 0.955025 | − | 0.296526i | \(-0.0958281\pi\) |
−0.734311 | + | 0.678813i | \(0.762495\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.00000 | 0.330400 | ||||||||
\(743\) | 3.00000 | + | 5.19615i | 0.110059 | + | 0.190628i | 0.915794 | − | 0.401648i | \(-0.131563\pi\) |
−0.805735 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(744\) | −9.00000 | − | 15.5885i | −0.329956 | − | 0.571501i | ||||
\(745\) | 8.00000 | − | 13.8564i | 0.293097 | − | 0.507659i | ||||
\(746\) | 10.5000 | + | 18.1865i | 0.384432 | + | 0.665856i | ||||
\(747\) | −6.00000 | + | 10.3923i | −0.219529 | + | 0.380235i | ||||
\(748\) | 2.00000 | 0.0731272 | ||||||||
\(749\) | −9.00000 | −0.328853 | ||||||||
\(750\) | 18.0000 | − | 31.1769i | 0.657267 | − | 1.13842i | ||||
\(751\) | 6.00000 | − | 10.3923i | 0.218943 | − | 0.379221i | −0.735542 | − | 0.677479i | \(-0.763072\pi\) |
0.954485 | + | 0.298259i | \(0.0964058\pi\) | |||||||
\(752\) | −8.00000 | −0.291730 | ||||||||
\(753\) | 60.0000 | 2.18652 | ||||||||
\(754\) | 4.50000 | − | 7.79423i | 0.163880 | − | 0.283849i | ||||
\(755\) | −18.0000 | − | 31.1769i | −0.655087 | − | 1.13464i | ||||
\(756\) | −13.5000 | + | 23.3827i | −0.490990 | + | 0.850420i | ||||
\(757\) | −6.00000 | − | 10.3923i | −0.218074 | − | 0.377715i | 0.736145 | − | 0.676824i | \(-0.236644\pi\) |
−0.954219 | + | 0.299109i | \(0.903311\pi\) | |||||||
\(758\) | −1.50000 | − | 2.59808i | −0.0544825 | − | 0.0943664i | ||||
\(759\) | 30.0000 | 1.08893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.0000 | −0.471250 | −0.235625 | − | 0.971844i | \(-0.575714\pi\) | ||||
−0.235625 | + | 0.971844i | \(0.575714\pi\) | |||||||
\(762\) | 18.0000 | + | 31.1769i | 0.652071 | + | 1.12942i | ||||
\(763\) | −4.50000 | − | 7.79423i | −0.162911 | − | 0.282170i | ||||
\(764\) | 5.50000 | − | 9.52628i | 0.198983 | − | 0.344649i | ||||
\(765\) | 6.00000 | + | 10.3923i | 0.216930 | + | 0.375735i | ||||
\(766\) | −9.00000 | + | 15.5885i | −0.325183 | + | 0.563234i | ||||
\(767\) | −9.00000 | −0.324971 | ||||||||
\(768\) | −3.00000 | −0.108253 | ||||||||
\(769\) | 7.50000 | − | 12.9904i | 0.270457 | − | 0.468445i | −0.698522 | − | 0.715589i | \(-0.746159\pi\) |
0.968979 | + | 0.247143i | \(0.0794919\pi\) | |||||||
\(770\) | 6.00000 | − | 10.3923i | 0.216225 | − | 0.374513i | ||||
\(771\) | −54.0000 | −1.94476 | ||||||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | 7.50000 | − | 12.9904i | 0.269756 | − | 0.467232i | −0.699043 | − | 0.715080i | \(-0.746390\pi\) |
0.968799 | + | 0.247849i | \(0.0797235\pi\) | |||||||
\(774\) | −30.0000 | − | 51.9615i | −1.07833 | − | 1.86772i | ||||
\(775\) | 3.00000 | − | 5.19615i | 0.107763 | − | 0.186651i | ||||
\(776\) | −6.00000 | − | 10.3923i | −0.215387 | − | 0.373062i | ||||
\(777\) | 27.0000 | + | 46.7654i | 0.968620 | + | 1.67770i | ||||
\(778\) | −26.0000 | −0.932145 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −18.0000 | −0.644503 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.50000 | − | 4.33013i | −0.0893998 | − | 0.154845i | ||||
\(783\) | 13.5000 | − | 23.3827i | 0.482451 | − | 0.835629i | ||||
\(784\) | −1.00000 | − | 1.73205i | −0.0357143 | − | 0.0618590i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 42.0000 | 1.49809 | ||||||||
\(787\) | 9.00000 | 0.320815 | 0.160408 | − | 0.987051i | \(-0.448719\pi\) | ||||
0.160408 | + | 0.987051i | \(0.448719\pi\) | |||||||
\(788\) | −2.00000 | + | 3.46410i | −0.0712470 | + | 0.123404i | ||||
\(789\) | −12.0000 | + | 20.7846i | −0.427211 | + | 0.739952i | ||||
\(790\) | −24.0000 | −0.853882 | ||||||||
\(791\) | 36.0000 | 1.28001 | ||||||||
\(792\) | −6.00000 | + | 10.3923i | −0.213201 | + | 0.369274i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.00000 | − | 1.73205i | 0.0354887 | − | 0.0614682i | ||||
\(795\) | 9.00000 | + | 15.5885i | 0.319197 | + | 0.552866i | ||||
\(796\) | 3.50000 | + | 6.06218i | 0.124054 | + | 0.214868i | ||||
\(797\) | −33.0000 | −1.16892 | −0.584460 | − | 0.811423i | \(-0.698694\pi\) | ||||
−0.584460 | + | 0.811423i | \(0.698694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 18.0000 | + | 31.1769i | 0.635999 | + | 1.10158i | ||||
\(802\) | −18.0000 | + | 31.1769i | −0.635602 | + | 1.10090i | ||||
\(803\) | −11.0000 | − | 19.0526i | −0.388182 | − | 0.672350i | ||||
\(804\) | −22.5000 | + | 38.9711i | −0.793514 | + | 1.37441i | ||||
\(805\) | −30.0000 | −1.05736 | ||||||||
\(806\) | −18.0000 | −0.634023 | ||||||||
\(807\) | 9.00000 | − | 15.5885i | 0.316815 | − | 0.548740i | ||||
\(808\) | 5.00000 | − | 8.66025i | 0.175899 | − | 0.304667i | ||||
\(809\) | −11.0000 | −0.386739 | −0.193370 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193370 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(810\) | −18.0000 | −0.632456 | ||||||||
\(811\) | 16.5000 | − | 28.5788i | 0.579393 | − | 1.00354i | −0.416156 | − | 0.909293i | \(-0.636623\pi\) |
0.995549 | − | 0.0942453i | \(-0.0300438\pi\) | |||||||
\(812\) | 4.50000 | + | 7.79423i | 0.157919 | + | 0.273524i | ||||
\(813\) | −16.5000 | + | 28.5788i | −0.578680 | + | 1.00230i | ||||
\(814\) | 6.00000 | + | 10.3923i | 0.210300 | + | 0.364250i | ||||
\(815\) | 6.00000 | + | 10.3923i | 0.210171 | + | 0.364027i | ||||
\(816\) | 3.00000 | 0.105021 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 6.00000 | 0.209785 | ||||||||
\(819\) | 27.0000 | + | 46.7654i | 0.943456 | + | 1.63411i | ||||
\(820\) | 12.0000 | + | 20.7846i | 0.419058 | + | 0.725830i | ||||
\(821\) | −1.00000 | + | 1.73205i | −0.0349002 | + | 0.0604490i | −0.882948 | − | 0.469471i | \(-0.844445\pi\) |
0.848048 | + | 0.529920i | \(0.177778\pi\) | |||||||
\(822\) | −28.5000 | − | 49.3634i | −0.994052 | − | 1.72175i | ||||
\(823\) | −1.50000 | + | 2.59808i | −0.0522867 | + | 0.0905632i | −0.890984 | − | 0.454034i | \(-0.849984\pi\) |
0.838697 | + | 0.544598i | \(0.183318\pi\) | |||||||
\(824\) | 6.00000 | 0.209020 | ||||||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | 4.50000 | − | 7.79423i | 0.156575 | − | 0.271196i | ||||
\(827\) | 7.50000 | − | 12.9904i | 0.260801 | − | 0.451720i | −0.705654 | − | 0.708556i | \(-0.749347\pi\) |
0.966455 | + | 0.256836i | \(0.0826802\pi\) | |||||||
\(828\) | 30.0000 | 1.04257 | ||||||||
\(829\) | −51.0000 | −1.77130 | −0.885652 | − | 0.464350i | \(-0.846288\pi\) | ||||
−0.885652 | + | 0.464350i | \(0.846288\pi\) | |||||||
\(830\) | 2.00000 | − | 3.46410i | 0.0694210 | − | 0.120241i | ||||
\(831\) | 45.0000 | + | 77.9423i | 1.56103 | + | 2.70379i | ||||
\(832\) | −1.50000 | + | 2.59808i | −0.0520031 | + | 0.0900721i | ||||
\(833\) | 1.00000 | + | 1.73205i | 0.0346479 | + | 0.0600120i | ||||
\(834\) | −9.00000 | − | 15.5885i | −0.311645 | − | 0.539784i | ||||
\(835\) | 24.0000 | 0.830554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −54.0000 | −1.86651 | ||||||||
\(838\) | −7.00000 | − | 12.1244i | −0.241811 | − | 0.418829i | ||||
\(839\) | −9.00000 | − | 15.5885i | −0.310715 | − | 0.538173i | 0.667803 | − | 0.744338i | \(-0.267235\pi\) |
−0.978517 | + | 0.206165i | \(0.933902\pi\) | |||||||
\(840\) | 9.00000 | − | 15.5885i | 0.310530 | − | 0.537853i | ||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 13.5000 | − | 23.3827i | 0.465241 | − | 0.805821i | ||||
\(843\) | 36.0000 | 1.23991 | ||||||||
\(844\) | −3.00000 | −0.103264 | ||||||||
\(845\) | 4.00000 | − | 6.92820i | 0.137604 | − | 0.238337i | ||||
\(846\) | −24.0000 | + | 41.5692i | −0.825137 | + | 1.42918i | ||||
\(847\) | 21.0000 | 0.721569 | ||||||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | −21.0000 | + | 36.3731i | −0.720718 | + | 1.24832i | ||||
\(850\) | 0.500000 | + | 0.866025i | 0.0171499 | + | 0.0297044i | ||||
\(851\) | 15.0000 | − | 25.9808i | 0.514193 | − | 0.890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.0000 | − | 39.8372i | −0.787505 | − | 1.36400i | −0.927491 | − | 0.373845i | \(-0.878039\pi\) |
0.139986 | − | 0.990153i | \(-0.455294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | 12.0000 | + | 20.7846i | 0.409912 | + | 0.709989i | 0.994880 | − | 0.101068i | \(-0.0322260\pi\) |
−0.584967 | + | 0.811057i | \(0.698893\pi\) | |||||||
\(858\) | 9.00000 | + | 15.5885i | 0.307255 | + | 0.532181i | ||||
\(859\) | −27.0000 | + | 46.7654i | −0.921228 | + | 1.59561i | −0.123710 | + | 0.992318i | \(0.539479\pi\) |
−0.797518 | + | 0.603296i | \(0.793854\pi\) | |||||||
\(860\) | 10.0000 | + | 17.3205i | 0.340997 | + | 0.590624i | ||||
\(861\) | 54.0000 | − | 93.5307i | 1.84032 | − | 3.18752i | ||||
\(862\) | 24.0000 | 0.817443 | ||||||||
\(863\) | −48.0000 | −1.63394 | −0.816970 | − | 0.576681i | \(-0.804348\pi\) | ||||
−0.816970 | + | 0.576681i | \(0.804348\pi\) | |||||||
\(864\) | −4.50000 | + | 7.79423i | −0.153093 | + | 0.265165i | ||||
\(865\) | −18.0000 | + | 31.1769i | −0.612018 | + | 1.06005i | ||||
\(866\) | 30.0000 | 1.01944 | ||||||||
\(867\) | 48.0000 | 1.63017 | ||||||||
\(868\) | 9.00000 | − | 15.5885i | 0.305480 | − | 0.529107i | ||||
\(869\) | 12.0000 | + | 20.7846i | 0.407072 | + | 0.705070i | ||||
\(870\) | −9.00000 | + | 15.5885i | −0.305129 | + | 0.528498i | ||||
\(871\) | 22.5000 | + | 38.9711i | 0.762383 | + | 1.32049i | ||||
\(872\) | −1.50000 | − | 2.59808i | −0.0507964 | − | 0.0879820i | ||||
\(873\) | −72.0000 | −2.43683 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.0000 | 1.21702 | ||||||||
\(876\) | −16.5000 | − | 28.5788i | −0.557483 | − | 0.965589i | ||||
\(877\) | 13.5000 | + | 23.3827i | 0.455863 | + | 0.789577i | 0.998737 | − | 0.0502365i | \(-0.0159975\pi\) |
−0.542875 | + | 0.839814i | \(0.682664\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.5000 | + | 23.3827i | 0.455344 | + | 0.788678i | ||||
\(880\) | 2.00000 | − | 3.46410i | 0.0674200 | − | 0.116775i | ||||
\(881\) | 34.0000 | 1.14549 | 0.572745 | − | 0.819734i | \(-0.305879\pi\) | ||||
0.572745 | + | 0.819734i | \(0.305879\pi\) | |||||||
\(882\) | −12.0000 | −0.404061 | ||||||||
\(883\) | 12.0000 | − | 20.7846i | 0.403832 | − | 0.699458i | −0.590353 | − | 0.807145i | \(-0.701011\pi\) |
0.994185 | + | 0.107688i | \(0.0343446\pi\) | |||||||
\(884\) | 1.50000 | − | 2.59808i | 0.0504505 | − | 0.0873828i | ||||
\(885\) | 18.0000 | 0.605063 | ||||||||
\(886\) | 22.0000 | 0.739104 | ||||||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | 9.00000 | + | 15.5885i | 0.302020 | + | 0.523114i | ||||
\(889\) | −18.0000 | + | 31.1769i | −0.603701 | + | 1.04564i | ||||
\(890\) | −6.00000 | − | 10.3923i | −0.201120 | − | 0.348351i | ||||
\(891\) | 9.00000 | + | 15.5885i | 0.301511 | + | 0.522233i | ||||
\(892\) | −18.0000 | −0.602685 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −24.0000 | −0.802680 | ||||||||
\(895\) | −12.0000 | − | 20.7846i | −0.401116 | − | 0.694753i | ||||
\(896\) | −1.50000 | − | 2.59808i | −0.0501115 | − | 0.0867956i | ||||
\(897\) | 22.5000 | − | 38.9711i | 0.751253 | − | 1.30121i | ||||
\(898\) | −3.00000 | − | 5.19615i | −0.100111 | − | 0.173398i | ||||
\(899\) | −9.00000 | + | 15.5885i | −0.300167 | + | 0.519904i | ||||
\(900\) | −6.00000 | −0.200000 | ||||||||
\(901\) | −3.00000 | −0.0999445 | ||||||||
\(902\) | 12.0000 | − | 20.7846i | 0.399556 | − | 0.692052i | ||||
\(903\) | 45.0000 | − | 77.9423i | 1.49751 | − | 2.59376i | ||||
\(904\) | 12.0000 | 0.399114 | ||||||||
\(905\) | −36.0000 | −1.19668 | ||||||||
\(906\) | −27.0000 | + | 46.7654i | −0.897015 | + | 1.55368i | ||||
\(907\) | −7.50000 | − | 12.9904i | −0.249033 | − | 0.431339i | 0.714224 | − | 0.699917i | \(-0.246780\pi\) |
−0.963258 | + | 0.268578i | \(0.913446\pi\) | |||||||
\(908\) | 1.50000 | − | 2.59808i | 0.0497792 | − | 0.0862202i | ||||
\(909\) | −30.0000 | − | 51.9615i | −0.995037 | − | 1.72345i | ||||
\(910\) | −9.00000 | − | 15.5885i | −0.298347 | − | 0.516752i | ||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.00000 | −0.132381 | ||||||||
\(914\) | 0.500000 | + | 0.866025i | 0.0165385 | + | 0.0286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.00000 | − | 10.3923i | 0.198246 | − | 0.343371i | ||||
\(917\) | 21.0000 | + | 36.3731i | 0.693481 | + | 1.20114i | ||||
\(918\) | 4.50000 | − | 7.79423i | 0.148522 | − | 0.257248i | ||||
\(919\) | 15.0000 | 0.494804 | 0.247402 | − | 0.968913i | \(-0.420423\pi\) | ||||
0.247402 | + | 0.968913i | \(0.420423\pi\) | |||||||
\(920\) | −10.0000 | −0.329690 | ||||||||
\(921\) | −18.0000 | + | 31.1769i | −0.593120 | + | 1.02731i | ||||
\(922\) | 2.00000 | − | 3.46410i | 0.0658665 | − | 0.114084i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −18.0000 | −0.592157 | ||||||||
\(925\) | −3.00000 | + | 5.19615i | −0.0986394 | + | 0.170848i | ||||
\(926\) | 16.0000 | + | 27.7128i | 0.525793 | + | 0.910700i | ||||
\(927\) | 18.0000 | − | 31.1769i | 0.591198 | − | 1.02398i | ||||
\(928\) | 1.50000 | + | 2.59808i | 0.0492399 | + | 0.0852860i | ||||
\(929\) | −20.5000 | − | 35.5070i | −0.672583 | − | 1.16495i | −0.977169 | − | 0.212463i | \(-0.931851\pi\) |
0.304586 | − | 0.952485i | \(-0.401482\pi\) | |||||||
\(930\) | 36.0000 | 1.18049 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.0000 | 0.458585 | ||||||||
\(933\) | −16.5000 | − | 28.5788i | −0.540186 | − | 0.935629i | ||||
\(934\) | 4.00000 | + | 6.92820i | 0.130884 | + | 0.226698i | ||||
\(935\) | −2.00000 | + | 3.46410i | −0.0654070 | + | 0.113288i | ||||
\(936\) | 9.00000 | + | 15.5885i | 0.294174 | + | 0.509525i | ||||
\(937\) | 23.5000 | − | 40.7032i | 0.767712 | − | 1.32972i | −0.171089 | − | 0.985255i | \(-0.554729\pi\) |
0.938801 | − | 0.344460i | \(-0.111938\pi\) | |||||||
\(938\) | −45.0000 | −1.46930 | ||||||||
\(939\) | −63.0000 | −2.05593 | ||||||||
\(940\) | 8.00000 | − | 13.8564i | 0.260931 | − | 0.451946i | ||||
\(941\) | −13.5000 | + | 23.3827i | −0.440087 | + | 0.762254i | −0.997695 | − | 0.0678506i | \(-0.978386\pi\) |
0.557608 | + | 0.830104i | \(0.311719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −60.0000 | −1.95387 | ||||||||
\(944\) | 1.50000 | − | 2.59808i | 0.0488208 | − | 0.0845602i | ||||
\(945\) | −27.0000 | − | 46.7654i | −0.878310 | − | 1.52128i | ||||
\(946\) | 10.0000 | − | 17.3205i | 0.325128 | − | 0.563138i | ||||
\(947\) | 23.0000 | + | 39.8372i | 0.747400 | + | 1.29453i | 0.949065 | + | 0.315080i | \(0.102031\pi\) |
−0.201666 | + | 0.979454i | \(0.564635\pi\) | |||||||
\(948\) | 18.0000 | + | 31.1769i | 0.584613 | + | 1.01258i | ||||
\(949\) | −33.0000 | −1.07123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −99.0000 | −3.21029 | ||||||||
\(952\) | 1.50000 | + | 2.59808i | 0.0486153 | + | 0.0842041i | ||||
\(953\) | −15.0000 | − | 25.9808i | −0.485898 | − | 0.841599i | 0.513971 | − | 0.857808i | \(-0.328174\pi\) |
−0.999869 | + | 0.0162081i | \(0.994841\pi\) | |||||||
\(954\) | 9.00000 | − | 15.5885i | 0.291386 | − | 0.504695i | ||||
\(955\) | 11.0000 | + | 19.0526i | 0.355952 | + | 0.616526i | ||||
\(956\) | −0.500000 | + | 0.866025i | −0.0161712 | + | 0.0280093i | ||||
\(957\) | 18.0000 | 0.581857 | ||||||||
\(958\) | 40.0000 | 1.29234 | ||||||||
\(959\) | 28.5000 | − | 49.3634i | 0.920313 | − | 1.59403i | ||||
\(960\) | 3.00000 | − | 5.19615i | 0.0968246 | − | 0.167705i | ||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 18.0000 | 0.580343 | ||||||||
\(963\) | −9.00000 | + | 15.5885i | −0.290021 | + | 0.502331i | ||||
\(964\) | 12.0000 | + | 20.7846i | 0.386494 | + | 0.669427i | ||||
\(965\) | 6.00000 | − | 10.3923i | 0.193147 | − | 0.334540i | ||||
\(966\) | 22.5000 | + | 38.9711i | 0.723926 | + | 1.25388i | ||||
\(967\) | 12.0000 | + | 20.7846i | 0.385894 | + | 0.668388i | 0.991893 | − | 0.127078i | \(-0.0405597\pi\) |
−0.605999 | + | 0.795466i | \(0.707226\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.0000 | 0.770594 | ||||||||
\(971\) | −24.0000 | − | 41.5692i | −0.770197 | − | 1.33402i | −0.937455 | − | 0.348107i | \(-0.886825\pi\) |
0.167258 | − | 0.985913i | \(-0.446509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.00000 | − | 15.5885i | 0.288527 | − | 0.499743i | ||||
\(974\) | 9.00000 | + | 15.5885i | 0.288379 | + | 0.499486i | ||||
\(975\) | −4.50000 | + | 7.79423i | −0.144115 | + | 0.249615i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.0000 | 0.959785 | 0.479893 | − | 0.877327i | \(-0.340676\pi\) | ||||
0.479893 | + | 0.877327i | \(0.340676\pi\) | |||||||
\(978\) | 9.00000 | − | 15.5885i | 0.287788 | − | 0.498464i | ||||
\(979\) | −6.00000 | + | 10.3923i | −0.191761 | + | 0.332140i | ||||
\(980\) | 4.00000 | 0.127775 | ||||||||
\(981\) | −18.0000 | −0.574696 | ||||||||
\(982\) | 4.00000 | − | 6.92820i | 0.127645 | − | 0.221088i | ||||
\(983\) | −12.0000 | − | 20.7846i | −0.382741 | − | 0.662926i | 0.608712 | − | 0.793391i | \(-0.291686\pi\) |
−0.991453 | + | 0.130465i | \(0.958353\pi\) | |||||||
\(984\) | 18.0000 | − | 31.1769i | 0.573819 | − | 0.993884i | ||||
\(985\) | −4.00000 | − | 6.92820i | −0.127451 | − | 0.220751i | ||||
\(986\) | −1.50000 | − | 2.59808i | −0.0477697 | − | 0.0827396i | ||||
\(987\) | −72.0000 | −2.29179 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.0000 | −1.58991 | ||||||||
\(990\) | −12.0000 | − | 20.7846i | −0.381385 | − | 0.660578i | ||||
\(991\) | 3.00000 | + | 5.19615i | 0.0952981 | + | 0.165061i | 0.909733 | − | 0.415194i | \(-0.136286\pi\) |
−0.814435 | + | 0.580255i | \(0.802953\pi\) | |||||||
\(992\) | 3.00000 | − | 5.19615i | 0.0952501 | − | 0.164978i | ||||
\(993\) | −13.5000 | − | 23.3827i | −0.428410 | − | 0.742027i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0000 | −0.443830 | ||||||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | −3.00000 | + | 5.19615i | −0.0950110 | + | 0.164564i | −0.909613 | − | 0.415456i | \(-0.863622\pi\) |
0.814602 | + | 0.580020i | \(0.196955\pi\) | |||||||
\(998\) | 9.00000 | − | 15.5885i | 0.284890 | − | 0.493444i | ||||
\(999\) | 54.0000 | 1.70848 |
(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 | 722.2.c.g.653.1 | 2 | ||
19.2 | odd | 18 | 722.2.e.g.389.1 | 6 | |||
19.3 | odd | 18 | 722.2.e.g.595.1 | 6 | |||
19.4 | even | 9 | 722.2.e.h.245.1 | 6 | |||
19.5 | even | 9 | 722.2.e.h.99.1 | 6 | |||
19.6 | even | 9 | 722.2.e.h.423.1 | 6 | |||
19.7 | even | 3 | 722.2.a.a.1.1 | ✓ | 1 | ||
19.8 | odd | 6 | 722.2.c.a.429.1 | 2 | |||
19.9 | even | 9 | 722.2.e.h.415.1 | 6 | |||
19.10 | odd | 18 | 722.2.e.g.415.1 | 6 | |||
19.11 | even | 3 | inner | 722.2.c.g.429.1 | 2 | ||
19.12 | odd | 6 | 722.2.a.f.1.1 | yes | 1 | ||
19.13 | odd | 18 | 722.2.e.g.423.1 | 6 | |||
19.14 | odd | 18 | 722.2.e.g.99.1 | 6 | |||
19.15 | odd | 18 | 722.2.e.g.245.1 | 6 | |||
19.16 | even | 9 | 722.2.e.h.595.1 | 6 | |||
19.17 | even | 9 | 722.2.e.h.389.1 | 6 | |||
19.18 | odd | 2 | 722.2.c.a.653.1 | 2 | |||
57.26 | odd | 6 | 6498.2.a.m.1.1 | 1 | |||
57.50 | even | 6 | 6498.2.a.a.1.1 | 1 | |||
76.7 | odd | 6 | 5776.2.a.q.1.1 | 1 | |||
76.31 | even | 6 | 5776.2.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.a.1.1 | ✓ | 1 | 19.7 | even | 3 | ||
722.2.a.f.1.1 | yes | 1 | 19.12 | odd | 6 | ||
722.2.c.a.429.1 | 2 | 19.8 | odd | 6 | |||
722.2.c.a.653.1 | 2 | 19.18 | odd | 2 | |||
722.2.c.g.429.1 | 2 | 19.11 | even | 3 | inner | ||
722.2.c.g.653.1 | 2 | 1.1 | even | 1 | trivial | ||
722.2.e.g.99.1 | 6 | 19.14 | odd | 18 | |||
722.2.e.g.245.1 | 6 | 19.15 | odd | 18 | |||
722.2.e.g.389.1 | 6 | 19.2 | odd | 18 | |||
722.2.e.g.415.1 | 6 | 19.10 | odd | 18 | |||
722.2.e.g.423.1 | 6 | 19.13 | odd | 18 | |||
722.2.e.g.595.1 | 6 | 19.3 | odd | 18 | |||
722.2.e.h.99.1 | 6 | 19.5 | even | 9 | |||
722.2.e.h.245.1 | 6 | 19.4 | even | 9 | |||
722.2.e.h.389.1 | 6 | 19.17 | even | 9 | |||
722.2.e.h.415.1 | 6 | 19.9 | even | 9 | |||
722.2.e.h.423.1 | 6 | 19.6 | even | 9 | |||
722.2.e.h.595.1 | 6 | 19.16 | even | 9 | |||
5776.2.a.a.1.1 | 1 | 76.31 | even | 6 | |||
5776.2.a.q.1.1 | 1 | 76.7 | odd | 6 | |||
6498.2.a.a.1.1 | 1 | 57.50 | even | 6 | |||
6498.2.a.m.1.1 | 1 | 57.26 | odd | 6 |