Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1151,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.t (of order \(6\), 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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.1601 |
Dual form | 1890.2.t.a.1151.2 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.866025 | − | 0.500000i | 0.273861 | − | 0.158114i | ||||
\(11\) | 4.73205i | 1.42677i | 0.700774 | + | 0.713384i | \(0.252838\pi\) | ||||
−0.700774 | + | 0.713384i | \(0.747162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 1.73205i | 0.832050 | − | 0.480384i | −0.0225039 | − | 0.999747i | \(-0.507164\pi\) |
0.854554 | + | 0.519362i | \(0.173830\pi\) | |||||||
\(14\) | 1.73205 | + | 2.00000i | 0.462910 | + | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.09808 | − | 0.633975i | −0.251916 | − | 0.145444i | 0.368725 | − | 0.929538i | \(-0.379794\pi\) |
−0.620641 | + | 0.784095i | \(0.713128\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.36603 | + | 4.09808i | 0.504438 | + | 0.873713i | ||||
\(23\) | 2.53590i | 0.528771i | 0.964417 | + | 0.264386i | \(0.0851692\pi\) | ||||
−0.964417 | + | 0.264386i | \(0.914831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.73205 | − | 3.00000i | 0.339683 | − | 0.588348i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.50000 | + | 0.866025i | 0.472456 | + | 0.163663i | ||||
\(29\) | 5.59808 | + | 3.23205i | 1.03954 | + | 0.600177i | 0.919702 | − | 0.392617i | \(-0.128430\pi\) |
0.119835 | + | 0.992794i | \(0.461764\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.09808 | − | 4.09808i | −1.27485 | − | 0.736036i | −0.298955 | − | 0.954267i | \(-0.596638\pi\) |
−0.975897 | + | 0.218231i | \(0.929971\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | + | 2.59808i | 0.0845154 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.09808 | + | 5.36603i | −0.509321 | + | 0.882169i | 0.490621 | + | 0.871373i | \(0.336770\pi\) |
−0.999942 | + | 0.0107961i | \(0.996563\pi\) | |||||||
\(38\) | −1.26795 | −0.205689 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 4.50000 | + | 7.79423i | 0.702782 | + | 1.21725i | 0.967486 | + | 0.252924i | \(0.0813924\pi\) |
−0.264704 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.59808 | + | 2.76795i | −0.243704 | + | 0.422108i | −0.961767 | − | 0.273871i | \(-0.911696\pi\) |
0.718062 | + | 0.695979i | \(0.245029\pi\) | |||||||
\(44\) | 4.09808 | + | 2.36603i | 0.617808 | + | 0.356692i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.26795 | + | 2.19615i | 0.186949 | + | 0.323805i | ||||
\(47\) | 4.50000 | + | 7.79423i | 0.656392 | + | 1.13691i | 0.981543 | + | 0.191243i | \(0.0612518\pi\) |
−0.325150 | + | 0.945662i | \(0.605415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 3.46410i | − | 0.480384i | ||||||
\(53\) | 6.29423 | − | 3.63397i | 0.864579 | − | 0.499165i | −0.000964138 | − | 1.00000i | \(-0.500307\pi\) |
0.865543 | + | 0.500835i | \(0.166974\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.73205i | 0.638070i | ||||||||
\(56\) | 2.59808 | − | 0.500000i | 0.347183 | − | 0.0668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.46410 | 0.848778 | ||||||||
\(59\) | −1.09808 | + | 1.90192i | −0.142957 | + | 0.247609i | −0.928609 | − | 0.371060i | \(-0.878995\pi\) |
0.785652 | + | 0.618669i | \(0.212328\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1962 | − | 6.46410i | 1.43352 | − | 0.827643i | 0.436133 | − | 0.899882i | \(-0.356348\pi\) |
0.997387 | + | 0.0722388i | \(0.0230144\pi\) | |||||||
\(62\) | −8.19615 | −1.04091 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.00000 | − | 1.73205i | 0.372104 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.73205 | + | 2.00000i | 0.207020 | + | 0.239046i | ||||
\(71\) | − | 4.73205i | − | 0.561591i | −0.959768 | − | 0.280796i | \(-0.909402\pi\) | ||
0.959768 | − | 0.280796i | \(-0.0905983\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | − | 3.46410i | 0.702247 | − | 0.405442i | −0.105937 | − | 0.994373i | \(-0.533784\pi\) |
0.808184 | + | 0.588930i | \(0.200451\pi\) | |||||||
\(74\) | 6.19615i | 0.720288i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.09808 | + | 0.633975i | −0.125958 | + | 0.0727219i | ||||
\(77\) | −12.2942 | + | 2.36603i | −1.40106 | + | 0.269634i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.29423 | − | 12.6340i | −0.820665 | − | 1.42143i | −0.905188 | − | 0.425012i | \(-0.860270\pi\) |
0.0845230 | − | 0.996422i | \(-0.473063\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.79423 | + | 4.50000i | 0.860729 | + | 0.496942i | ||||
\(83\) | −5.59808 | + | 9.69615i | −0.614469 | + | 1.06429i | 0.376009 | + | 0.926616i | \(0.377296\pi\) |
−0.990477 | + | 0.137675i | \(0.956037\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.19615i | 0.344650i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.73205 | 0.504438 | ||||||||
\(89\) | 2.19615 | − | 3.80385i | 0.232792 | − | 0.403207i | −0.725837 | − | 0.687867i | \(-0.758547\pi\) |
0.958629 | + | 0.284660i | \(0.0918806\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 6.92820i | 0.628971 | + | 0.726273i | ||||
\(92\) | 2.19615 | + | 1.26795i | 0.228965 | + | 0.132193i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.79423 | + | 4.50000i | 0.803913 | + | 0.464140i | ||||
\(95\) | −1.09808 | − | 0.633975i | −0.112660 | − | 0.0650444i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.39230 | + | 4.26795i | 0.750575 | + | 0.433345i | 0.825902 | − | 0.563814i | \(-0.190667\pi\) |
−0.0753267 | + | 0.997159i | \(0.524000\pi\) | |||||||
\(98\) | −4.33013 | + | 5.50000i | −0.437409 | + | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 11.1962 | 1.11406 | 0.557029 | − | 0.830493i | \(-0.311941\pi\) | ||||
0.557029 | + | 0.830493i | \(0.311941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.1244i | − | 1.19465i | −0.802000 | − | 0.597324i | \(-0.796231\pi\) | ||
0.802000 | − | 0.597324i | \(-0.203769\pi\) | |||||||
\(104\) | −1.73205 | − | 3.00000i | −0.169842 | − | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.63397 | − | 6.29423i | 0.352963 | − | 0.611350i | ||||
\(107\) | −13.7942 | − | 7.96410i | −1.33354 | − | 0.769919i | −0.347698 | − | 0.937606i | \(-0.613037\pi\) |
−0.985840 | + | 0.167688i | \(0.946370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.59808 | + | 6.23205i | 0.344633 | + | 0.596922i | 0.985287 | − | 0.170908i | \(-0.0546700\pi\) |
−0.640654 | + | 0.767830i | \(0.721337\pi\) | |||||||
\(110\) | 2.36603 | + | 4.09808i | 0.225592 | + | 0.390736i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | − | 1.73205i | 0.188982 | − | 0.163663i | ||||
\(113\) | 10.9019 | − | 6.29423i | 1.02557 | − | 0.592111i | 0.109855 | − | 0.993948i | \(-0.464961\pi\) |
0.915711 | + | 0.401836i | \(0.131628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.53590i | 0.236474i | ||||||||
\(116\) | 5.59808 | − | 3.23205i | 0.519768 | − | 0.300088i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.19615i | 0.202172i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.3923 | −1.03566 | ||||||||
\(122\) | 6.46410 | − | 11.1962i | 0.585232 | − | 1.01365i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.09808 | + | 4.09808i | −0.637426 | + | 0.368018i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3923 | −1.01090 | −0.505452 | − | 0.862855i | \(-0.668674\pi\) | ||||
−0.505452 | + | 0.862855i | \(0.668674\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.73205 | − | 3.00000i | 0.151911 | − | 0.263117i | ||||
\(131\) | −4.39230 | −0.383757 | −0.191879 | − | 0.981419i | \(-0.561458\pi\) | ||||
−0.191879 | + | 0.981419i | \(0.561458\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.09808 | − | 3.16987i | 0.0952153 | − | 0.274863i | ||||
\(134\) | − | 4.00000i | − | 0.345547i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.26795i | − | 0.620943i | −0.950583 | − | 0.310471i | \(-0.899513\pi\) | ||
0.950583 | − | 0.310471i | \(-0.100487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0981 | − | 11.0263i | 1.61988 | − | 0.935237i | 0.632927 | − | 0.774211i | \(-0.281853\pi\) |
0.986950 | − | 0.161026i | \(-0.0514802\pi\) | |||||||
\(140\) | 2.50000 | + | 0.866025i | 0.211289 | + | 0.0731925i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.36603 | − | 4.09808i | −0.198552 | − | 0.343903i | ||||
\(143\) | 8.19615 | + | 14.1962i | 0.685397 | + | 1.18714i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.59808 | + | 3.23205i | 0.464895 | + | 0.268407i | ||||
\(146\) | 3.46410 | − | 6.00000i | 0.286691 | − | 0.496564i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.09808 | + | 5.36603i | 0.254660 | + | 0.441085i | ||||
\(149\) | 12.0000i | 0.983078i | 0.870855 | + | 0.491539i | \(0.163566\pi\) | ||||
−0.870855 | + | 0.491539i | \(0.836434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.19615 | −0.341478 | −0.170739 | − | 0.985316i | \(-0.554616\pi\) | ||||
−0.170739 | + | 0.985316i | \(0.554616\pi\) | |||||||
\(152\) | −0.633975 | + | 1.09808i | −0.0514221 | + | 0.0890657i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.46410 | + | 8.19615i | −0.762639 | + | 0.660465i | ||||
\(155\) | −7.09808 | − | 4.09808i | −0.570131 | − | 0.329165i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.2942 | − | 8.83013i | −1.22061 | − | 0.704721i | −0.255564 | − | 0.966792i | \(-0.582261\pi\) |
−0.965049 | + | 0.262071i | \(0.915594\pi\) | |||||||
\(158\) | −12.6340 | − | 7.29423i | −1.00511 | − | 0.580298i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.866025 | − | 0.500000i | −0.0684653 | − | 0.0395285i | ||||
\(161\) | −6.58846 | + | 1.26795i | −0.519243 | + | 0.0999284i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.19615 | − | 7.26795i | 0.328668 | − | 0.569270i | −0.653580 | − | 0.756858i | \(-0.726734\pi\) |
0.982248 | + | 0.187588i | \(0.0600669\pi\) | |||||||
\(164\) | 9.00000 | 0.702782 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.1962i | 0.868990i | ||||||||
\(167\) | −5.19615 | − | 9.00000i | −0.402090 | − | 0.696441i | 0.591888 | − | 0.806020i | \(-0.298383\pi\) |
−0.993978 | + | 0.109580i | \(0.965050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.59808 | + | 2.76795i | 0.121852 | + | 0.211054i | ||||
\(173\) | −4.09808 | − | 7.09808i | −0.311571 | − | 0.539657i | 0.667132 | − | 0.744940i | \(-0.267522\pi\) |
−0.978703 | + | 0.205283i | \(0.934188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | + | 2.59808i | 0.0377964 | + | 0.196396i | ||||
\(176\) | 4.09808 | − | 2.36603i | 0.308904 | − | 0.178346i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 4.39230i | − | 0.329217i | ||||||
\(179\) | −21.2942 | + | 12.2942i | −1.59161 | + | 0.918914i | −0.598573 | + | 0.801068i | \(0.704266\pi\) |
−0.993032 | + | 0.117846i | \(0.962401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3923i | 0.995442i | 0.867337 | + | 0.497721i | \(0.165830\pi\) | ||||
−0.867337 | + | 0.497721i | \(0.834170\pi\) | |||||||
\(182\) | 8.66025 | + | 3.00000i | 0.641941 | + | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.53590 | 0.186949 | ||||||||
\(185\) | −3.09808 | + | 5.36603i | −0.227775 | + | 0.394518i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.00000 | 0.656392 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.26795 | −0.0919867 | ||||||||
\(191\) | −3.00000 | + | 1.73205i | −0.217072 | + | 0.125327i | −0.604594 | − | 0.796534i | \(-0.706665\pi\) |
0.387522 | + | 0.921861i | \(0.373331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.90192 | + | 11.9545i | −0.496811 | + | 0.860502i | −0.999993 | − | 0.00367804i | \(-0.998829\pi\) |
0.503182 | + | 0.864181i | \(0.332163\pi\) | |||||||
\(194\) | 8.53590 | 0.612842 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | + | 6.92820i | −0.0714286 | + | 0.494872i | ||||
\(197\) | − | 23.6603i | − | 1.68572i | −0.538130 | − | 0.842862i | \(-0.680869\pi\) | ||
0.538130 | − | 0.842862i | \(-0.319131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.00000 | − | 3.46410i | 0.425329 | − | 0.245564i | −0.272026 | − | 0.962290i | \(-0.587694\pi\) |
0.697355 | + | 0.716726i | \(0.254360\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.69615 | − | 5.59808i | 0.682219 | − | 0.393879i | ||||
\(203\) | −5.59808 | + | 16.1603i | −0.392908 | + | 1.13423i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | + | 7.79423i | 0.314294 | + | 0.544373i | ||||
\(206\) | −6.06218 | − | 10.5000i | −0.422372 | − | 0.731570i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | − | 1.73205i | −0.208013 | − | 0.120096i | ||||
\(209\) | 3.00000 | − | 5.19615i | 0.207514 | − | 0.359425i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2942 | + | 17.8301i | 0.708684 | + | 1.22748i | 0.965345 | + | 0.260975i | \(0.0840441\pi\) |
−0.256662 | + | 0.966501i | \(0.582623\pi\) | |||||||
\(212\) | − | 7.26795i | − | 0.499165i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.9282 | −1.08883 | ||||||||
\(215\) | −1.59808 | + | 2.76795i | −0.108988 | + | 0.188773i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.09808 | − | 20.4904i | 0.481849 | − | 1.39098i | ||||
\(218\) | 6.23205 | + | 3.59808i | 0.422088 | + | 0.243692i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.09808 | + | 2.36603i | 0.276292 | + | 0.159517i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8923 | + | 6.86603i | 0.796368 | + | 0.459783i | 0.842199 | − | 0.539166i | \(-0.181260\pi\) |
−0.0458318 | + | 0.998949i | \(0.514594\pi\) | |||||||
\(224\) | 0.866025 | − | 2.50000i | 0.0578638 | − | 0.167038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.29423 | − | 10.9019i | 0.418686 | − | 0.725185i | ||||
\(227\) | 16.3923 | 1.08800 | 0.543998 | − | 0.839087i | \(-0.316910\pi\) | ||||
0.543998 | + | 0.839087i | \(0.316910\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.0718i | − | 0.929891i | −0.885339 | − | 0.464945i | \(-0.846074\pi\) | ||
0.885339 | − | 0.464945i | \(-0.153926\pi\) | |||||||
\(230\) | 1.26795 | + | 2.19615i | 0.0836061 | + | 0.144810i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.23205 | − | 5.59808i | 0.212195 | − | 0.367532i | ||||
\(233\) | −1.09808 | − | 0.633975i | −0.0719374 | − | 0.0415331i | 0.463600 | − | 0.886045i | \(-0.346558\pi\) |
−0.535537 | + | 0.844512i | \(0.679891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.50000 | + | 7.79423i | 0.293548 | + | 0.508439i | ||||
\(236\) | 1.09808 | + | 1.90192i | 0.0714787 | + | 0.123805i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.70577 | + | 1.56218i | −0.175022 | + | 0.101049i | −0.584952 | − | 0.811068i | \(-0.698887\pi\) |
0.409930 | + | 0.912117i | \(0.365553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.33975i | − | 0.215132i | −0.994198 | − | 0.107566i | \(-0.965694\pi\) | ||
0.994198 | − | 0.107566i | \(-0.0343057\pi\) | |||||||
\(242\) | −9.86603 | + | 5.69615i | −0.634212 | + | 0.366163i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 12.9282i | − | 0.827643i | ||||||
\(245\) | −6.50000 | + | 2.59808i | −0.415270 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.39230 | −0.279476 | ||||||||
\(248\) | −4.09808 | + | 7.09808i | −0.260228 | + | 0.450728i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.866025 | − | 0.500000i | 0.0547723 | − | 0.0316228i | ||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | −9.86603 | + | 5.69615i | −0.619049 | + | 0.357408i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −28.3923 | −1.77106 | −0.885532 | − | 0.464579i | \(-0.846206\pi\) | ||||
−0.885532 | + | 0.464579i | \(0.846206\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.4904 | − | 5.36603i | −0.962525 | − | 0.333429i | ||||
\(260\) | − | 3.46410i | − | 0.214834i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.80385 | + | 2.19615i | −0.235002 | + | 0.135679i | ||||
\(263\) | 13.7321i | 0.846755i | 0.905953 | + | 0.423377i | \(0.139156\pi\) | ||||
−0.905953 | + | 0.423377i | \(0.860844\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.29423 | − | 3.63397i | 0.386651 | − | 0.223233i | ||||
\(266\) | −0.633975 | − | 3.29423i | −0.0388715 | − | 0.201982i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.00000 | − | 3.46410i | −0.122169 | − | 0.211604i | ||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.70577 | + | 3.29423i | 0.346601 | + | 0.200110i | 0.663187 | − | 0.748454i | \(-0.269203\pi\) |
−0.316586 | + | 0.948564i | \(0.602537\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.63397 | − | 6.29423i | −0.219536 | − | 0.380248i | ||||
\(275\) | 4.73205i | 0.285353i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.1962 | −1.45381 | −0.726903 | − | 0.686740i | \(-0.759041\pi\) | ||||
−0.726903 | + | 0.686740i | \(0.759041\pi\) | |||||||
\(278\) | 11.0263 | − | 19.0981i | 0.661312 | − | 1.14543i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.59808 | − | 0.500000i | 0.155265 | − | 0.0298807i | ||||
\(281\) | −12.6962 | − | 7.33013i | −0.757389 | − | 0.437279i | 0.0709685 | − | 0.997479i | \(-0.477391\pi\) |
−0.828357 | + | 0.560200i | \(0.810724\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5981 | − | 8.42820i | −0.867766 | − | 0.501005i | −0.00116049 | − | 0.999999i | \(-0.500369\pi\) |
−0.866605 | + | 0.498995i | \(0.833703\pi\) | |||||||
\(284\) | −4.09808 | − | 2.36603i | −0.243176 | − | 0.140398i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.1962 | + | 8.19615i | 0.839436 | + | 0.484649i | ||||
\(287\) | −18.0000 | + | 15.5885i | −1.06251 | + | 0.920158i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 6.46410 | 0.379585 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 6.92820i | − | 0.405442i | ||||||
\(293\) | 8.19615 | + | 14.1962i | 0.478824 | + | 0.829348i | 0.999705 | − | 0.0242813i | \(-0.00772975\pi\) |
−0.520881 | + | 0.853629i | \(0.674396\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.09808 | + | 1.90192i | −0.0639325 | + | 0.110734i | ||||
\(296\) | 5.36603 | + | 3.09808i | 0.311894 | + | 0.180072i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | + | 10.3923i | 0.347571 | + | 0.602010i | ||||
\(299\) | 4.39230 | + | 7.60770i | 0.254014 | + | 0.439964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.99038 | − | 2.76795i | −0.460558 | − | 0.159542i | ||||
\(302\) | −3.63397 | + | 2.09808i | −0.209112 | + | 0.120731i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.26795i | 0.0727219i | ||||||||
\(305\) | 11.1962 | − | 6.46410i | 0.641090 | − | 0.370133i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.7846i | − | 1.35746i | −0.734388 | − | 0.678730i | \(-0.762531\pi\) | ||
0.734388 | − | 0.678730i | \(-0.237469\pi\) | |||||||
\(308\) | −4.09808 | + | 11.8301i | −0.233510 | + | 0.674084i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.19615 | −0.465510 | ||||||||
\(311\) | 7.90192 | − | 13.6865i | 0.448077 | − | 0.776092i | −0.550184 | − | 0.835044i | \(-0.685442\pi\) |
0.998261 | + | 0.0589514i | \(0.0187757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4904 | + | 10.0981i | −0.988615 | + | 0.570777i | −0.904860 | − | 0.425709i | \(-0.860025\pi\) |
−0.0837548 | + | 0.996486i | \(0.526691\pi\) | |||||||
\(314\) | −17.6603 | −0.996626 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.5885 | −0.820665 | ||||||||
\(317\) | −17.7846 | + | 10.2679i | −0.998883 | + | 0.576705i | −0.907918 | − | 0.419149i | \(-0.862329\pi\) |
−0.0909655 | + | 0.995854i | \(0.528995\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.2942 | + | 26.4904i | −0.856312 | + | 1.48318i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.07180 | + | 4.39230i | −0.282640 | + | 0.244774i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | − | 1.73205i | 0.166410 | − | 0.0960769i | ||||
\(326\) | − | 8.39230i | − | 0.464807i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.79423 | − | 4.50000i | 0.430364 | − | 0.248471i | ||||
\(329\) | −18.0000 | + | 15.5885i | −0.992372 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | 5.59808 | + | 9.69615i | 0.307234 | + | 0.532145i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.00000 | − | 5.19615i | −0.492458 | − | 0.284321i | ||||
\(335\) | 2.00000 | − | 3.46410i | 0.109272 | − | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | − | 8.66025i | −0.272367 | − | 0.471754i | 0.697100 | − | 0.716974i | \(-0.254473\pi\) |
−0.969468 | + | 0.245220i | \(0.921140\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.3923 | − | 33.5885i | 1.05015 | − | 1.81892i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 2.76795 | + | 1.59808i | 0.149238 | + | 0.0861625i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.09808 | − | 4.09808i | −0.381595 | − | 0.220314i | ||||
\(347\) | −18.4019 | − | 10.6244i | −0.987867 | − | 0.570345i | −0.0832310 | − | 0.996530i | \(-0.526524\pi\) |
−0.904636 | + | 0.426185i | \(0.859857\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.1962 | + | 8.19615i | 0.759903 | + | 0.438730i | 0.829261 | − | 0.558862i | \(-0.188762\pi\) |
−0.0693582 | + | 0.997592i | \(0.522095\pi\) | |||||||
\(350\) | 1.73205 | + | 2.00000i | 0.0925820 | + | 0.106904i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.36603 | − | 4.09808i | 0.126110 | − | 0.218428i | ||||
\(353\) | 0.588457 | 0.0313204 | 0.0156602 | − | 0.999877i | \(-0.495015\pi\) | ||||
0.0156602 | + | 0.999877i | \(0.495015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.73205i | − | 0.251151i | ||||||
\(356\) | −2.19615 | − | 3.80385i | −0.116396 | − | 0.201604i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.2942 | + | 21.2942i | −0.649770 | + | 1.12543i | ||||
\(359\) | 13.6865 | + | 7.90192i | 0.722348 | + | 0.417048i | 0.815616 | − | 0.578593i | \(-0.196398\pi\) |
−0.0932685 | + | 0.995641i | \(0.529732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.69615 | − | 15.0622i | −0.457692 | − | 0.792746i | ||||
\(362\) | 6.69615 | + | 11.5981i | 0.351942 | + | 0.609581i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.00000 | − | 1.73205i | 0.471728 | − | 0.0907841i | ||||
\(365\) | 6.00000 | − | 3.46410i | 0.314054 | − | 0.181319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.1962i | 1.52403i | 0.647561 | + | 0.762013i | \(0.275789\pi\) | ||||
−0.647561 | + | 0.762013i | \(0.724211\pi\) | |||||||
\(368\) | 2.19615 | − | 1.26795i | 0.114482 | − | 0.0660964i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.19615i | 0.322123i | ||||||||
\(371\) | 12.5885 | + | 14.5359i | 0.653560 | + | 0.754666i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1962 | 0.527937 | 0.263968 | − | 0.964531i | \(-0.414969\pi\) | ||||
0.263968 | + | 0.964531i | \(0.414969\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.79423 | − | 4.50000i | 0.401957 | − | 0.232070i | ||||
\(377\) | 22.3923 | 1.15326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.60770 | −0.493514 | −0.246757 | − | 0.969077i | \(-0.579365\pi\) | ||||
−0.246757 | + | 0.969077i | \(0.579365\pi\) | |||||||
\(380\) | −1.09808 | + | 0.633975i | −0.0563301 | + | 0.0325222i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.73205 | + | 3.00000i | −0.0886194 | + | 0.153493i | ||||
\(383\) | −19.3923 | −0.990900 | −0.495450 | − | 0.868636i | \(-0.664997\pi\) | ||||
−0.495450 | + | 0.868636i | \(0.664997\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.2942 | + | 2.36603i | −0.626572 | + | 0.120584i | ||||
\(386\) | 13.8038i | 0.702597i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.39230 | − | 4.26795i | 0.375287 | − | 0.216672i | ||||
\(389\) | − | 24.7128i | − | 1.25299i | −0.779426 | − | 0.626495i | \(-0.784489\pi\) | ||
0.779426 | − | 0.626495i | \(-0.215511\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.59808 | + | 6.50000i | 0.131223 | + | 0.328300i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.8301 | − | 20.4904i | −0.595993 | − | 1.03229i | ||||
\(395\) | −7.29423 | − | 12.6340i | −0.367012 | − | 0.635684i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.4904 | − | 15.2942i | −1.32951 | − | 0.767595i | −0.344290 | − | 0.938863i | \(-0.611880\pi\) |
−0.985224 | + | 0.171268i | \(0.945214\pi\) | |||||||
\(398\) | 3.46410 | − | 6.00000i | 0.173640 | − | 0.300753i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 3.58846i | 0.179199i | 0.995978 | + | 0.0895995i | \(0.0285587\pi\) | ||||
−0.995978 | + | 0.0895995i | \(0.971441\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.3923 | −1.41432 | ||||||||
\(404\) | 5.59808 | − | 9.69615i | 0.278515 | − | 0.482402i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.23205 | + | 16.7942i | 0.160404 | + | 0.833484i | ||||
\(407\) | −25.3923 | − | 14.6603i | −1.25865 | − | 0.726682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.10770 | − | 5.25833i | −0.450347 | − | 0.260008i | 0.257630 | − | 0.966244i | \(-0.417058\pi\) |
−0.707977 | + | 0.706236i | \(0.750392\pi\) | |||||||
\(410\) | 7.79423 | + | 4.50000i | 0.384930 | + | 0.222239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.5000 | − | 6.06218i | −0.517298 | − | 0.298662i | ||||
\(413\) | −5.49038 | − | 1.90192i | −0.270164 | − | 0.0935876i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.59808 | + | 9.69615i | −0.274799 | + | 0.475965i | ||||
\(416\) | −3.46410 | −0.169842 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 6.00000i | − | 0.293470i | ||||||
\(419\) | −5.19615 | − | 9.00000i | −0.253849 | − | 0.439679i | 0.710734 | − | 0.703461i | \(-0.248363\pi\) |
−0.964582 | + | 0.263783i | \(0.915030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.9904 | − | 25.9641i | 0.730586 | − | 1.26541i | −0.226046 | − | 0.974117i | \(-0.572580\pi\) |
0.956633 | − | 0.291296i | \(-0.0940866\pi\) | |||||||
\(422\) | 17.8301 | + | 10.2942i | 0.867957 | + | 0.501115i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.63397 | − | 6.29423i | −0.176481 | − | 0.305675i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.3923 | + | 25.8564i | 1.08364 | + | 1.25128i | ||||
\(428\) | −13.7942 | + | 7.96410i | −0.666769 | + | 0.384959i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.19615i | 0.154132i | ||||||||
\(431\) | 33.5885 | − | 19.3923i | 1.61790 | − | 0.934094i | 0.630437 | − | 0.776241i | \(-0.282876\pi\) |
0.987463 | − | 0.157854i | \(-0.0504574\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0000i | 0.865025i | 0.901628 | + | 0.432512i | \(0.142373\pi\) | ||||
−0.901628 | + | 0.432512i | \(0.857627\pi\) | |||||||
\(434\) | −4.09808 | − | 21.2942i | −0.196714 | − | 1.02216i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.19615 | 0.344633 | ||||||||
\(437\) | 1.60770 | − | 2.78461i | 0.0769065 | − | 0.133206i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.6865 | − | 14.8301i | 1.22595 | − | 0.707803i | 0.259771 | − | 0.965670i | \(-0.416353\pi\) |
0.966180 | + | 0.257867i | \(0.0830196\pi\) | |||||||
\(440\) | 4.73205 | 0.225592 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.79423 | + | 4.50000i | −0.370315 | + | 0.213801i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.19615 | − | 3.80385i | 0.104108 | − | 0.180320i | ||||
\(446\) | 13.7321 | 0.650231 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | − | 2.59808i | −0.0236228 | − | 0.122748i | ||||
\(449\) | 9.58846i | 0.452507i | 0.974068 | + | 0.226254i | \(0.0726478\pi\) | ||||
−0.974068 | + | 0.226254i | \(0.927352\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.8827 | + | 21.2942i | −1.73674 | + | 1.00271i | ||||
\(452\) | − | 12.5885i | − | 0.592111i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.1962 | − | 8.19615i | 0.666258 | − | 0.384664i | ||||
\(455\) | 6.00000 | + | 6.92820i | 0.281284 | + | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.19615 | − | 2.07180i | −0.0559537 | − | 0.0969146i | 0.836692 | − | 0.547674i | \(-0.184487\pi\) |
−0.892645 | + | 0.450759i | \(0.851153\pi\) | |||||||
\(458\) | −7.03590 | − | 12.1865i | −0.328766 | − | 0.569439i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.19615 | + | 1.26795i | 0.102396 | + | 0.0591184i | ||||
\(461\) | 2.59808 | − | 4.50000i | 0.121004 | − | 0.209586i | −0.799160 | − | 0.601119i | \(-0.794722\pi\) |
0.920164 | + | 0.391533i | \(0.128055\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.30385 | + | 2.25833i | 0.0605949 | + | 0.104954i | 0.894731 | − | 0.446604i | \(-0.147367\pi\) |
−0.834137 | + | 0.551558i | \(0.814034\pi\) | |||||||
\(464\) | − | 6.46410i | − | 0.300088i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.26795 | −0.0587366 | ||||||||
\(467\) | −3.40192 | + | 5.89230i | −0.157422 | + | 0.272663i | −0.933938 | − | 0.357434i | \(-0.883652\pi\) |
0.776516 | + | 0.630097i | \(0.216985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | + | 3.46410i | 0.461757 | + | 0.159957i | ||||
\(470\) | 7.79423 | + | 4.50000i | 0.359521 | + | 0.207570i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.90192 | + | 1.09808i | 0.0875431 | + | 0.0505431i | ||||
\(473\) | −13.0981 | − | 7.56218i | −0.602250 | − | 0.347709i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.09808 | − | 0.633975i | −0.0503832 | − | 0.0290887i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.56218 | + | 2.70577i | −0.0714524 | + | 0.123759i | ||||
\(479\) | 10.3923 | 0.474837 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.4641i | 0.978679i | ||||||||
\(482\) | −1.66987 | − | 2.89230i | −0.0760606 | − | 0.131741i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.69615 | + | 9.86603i | −0.258916 | + | 0.448456i | ||||
\(485\) | 7.39230 | + | 4.26795i | 0.335667 | + | 0.193798i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.0000 | − | 29.4449i | −0.770344 | − | 1.33427i | −0.937375 | − | 0.348323i | \(-0.886751\pi\) |
0.167031 | − | 0.985952i | \(-0.446582\pi\) | |||||||
\(488\) | −6.46410 | − | 11.1962i | −0.292616 | − | 0.506826i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.33013 | + | 5.50000i | −0.195615 | + | 0.248465i | ||||
\(491\) | 23.4904 | − | 13.5622i | 1.06011 | − | 0.612053i | 0.134644 | − | 0.990894i | \(-0.457011\pi\) |
0.925462 | + | 0.378841i | \(0.123677\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3.80385 | + | 2.19615i | −0.171143 | + | 0.0988096i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.19615i | 0.368018i | ||||||||
\(497\) | 12.2942 | − | 2.36603i | 0.551472 | − | 0.106131i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.1962 | −0.725039 | −0.362520 | − | 0.931976i | \(-0.618083\pi\) | ||||
−0.362520 | + | 0.931976i | \(0.618083\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.5885 | − | 9.00000i | 0.695747 | − | 0.401690i | ||||
\(503\) | 7.39230 | 0.329607 | 0.164803 | − | 0.986326i | \(-0.447301\pi\) | ||||
0.164803 | + | 0.986326i | \(0.447301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.1962 | 0.498222 | ||||||||
\(506\) | −10.3923 | + | 6.00000i | −0.461994 | + | 0.266733i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.69615 | + | 9.86603i | −0.252726 | + | 0.437734i | ||||
\(509\) | −9.58846 | −0.425001 | −0.212500 | − | 0.977161i | \(-0.568161\pi\) | ||||
−0.212500 | + | 0.977161i | \(0.568161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 13.8564i | 0.530849 | + | 0.612971i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.5885 | + | 14.1962i | −1.08455 | + | 0.626165i | ||||
\(515\) | − | 12.1244i | − | 0.534263i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.8827 | + | 21.2942i | −1.62210 | + | 0.936519i | ||||
\(518\) | −16.0981 | + | 3.09808i | −0.707309 | + | 0.136122i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.73205 | − | 3.00000i | −0.0759555 | − | 0.131559i | ||||
\(521\) | −10.5000 | − | 18.1865i | −0.460013 | − | 0.796766i | 0.538948 | − | 0.842339i | \(-0.318822\pi\) |
−0.998961 | + | 0.0455727i | \(0.985489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.5788 | + | 16.5000i | 1.24967 | + | 0.721495i | 0.971043 | − | 0.238906i | \(-0.0767888\pi\) |
0.278623 | + | 0.960401i | \(0.410122\pi\) | |||||||
\(524\) | −2.19615 | + | 3.80385i | −0.0959394 | + | 0.166172i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.86603 | + | 11.8923i | 0.299373 | + | 0.518529i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.5692 | 0.720401 | ||||||||
\(530\) | 3.63397 | − | 6.29423i | 0.157850 | − | 0.273404i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.19615 | − | 2.53590i | −0.0952153 | − | 0.109945i | ||||
\(533\) | 27.0000 | + | 15.5885i | 1.16950 | + | 0.675211i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.7942 | − | 7.96410i | −0.596377 | − | 0.344318i | ||||
\(536\) | −3.46410 | − | 2.00000i | −0.149626 | − | 0.0863868i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.5885 | − | 9.00000i | −0.672066 | − | 0.388018i | ||||
\(539\) | −12.2942 | − | 30.7583i | −0.529550 | − | 1.32486i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | + | 6.92820i | −0.171973 | + | 0.297867i | −0.939110 | − | 0.343617i | \(-0.888348\pi\) |
0.767136 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(542\) | 6.58846 | 0.282998 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.59808 | + | 6.23205i | 0.154125 | + | 0.266952i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.79423 | + | 4.83975i | −0.119473 | + | 0.206933i | −0.919559 | − | 0.392952i | \(-0.871454\pi\) |
0.800086 | + | 0.599885i | \(0.204787\pi\) | |||||||
\(548\) | −6.29423 | − | 3.63397i | −0.268876 | − | 0.155236i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.36603 | + | 4.09808i | 0.100888 | + | 0.174743i | ||||
\(551\) | −4.09808 | − | 7.09808i | −0.174584 | − | 0.302388i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.1769 | − | 25.2679i | 1.24073 | − | 1.07450i | ||||
\(554\) | −20.9545 | + | 12.0981i | −0.890271 | + | 0.513998i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 22.0526i | − | 0.935237i | ||||||
\(557\) | −28.3923 | + | 16.3923i | −1.20302 | + | 0.694564i | −0.961226 | − | 0.275763i | \(-0.911069\pi\) |
−0.241795 | + | 0.970327i | \(0.577736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0718i | 0.468287i | ||||||||
\(560\) | 2.00000 | − | 1.73205i | 0.0845154 | − | 0.0731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.6603 | −0.618405 | ||||||||
\(563\) | 6.80385 | − | 11.7846i | 0.286748 | − | 0.496662i | −0.686284 | − | 0.727334i | \(-0.740759\pi\) |
0.973032 | + | 0.230672i | \(0.0740924\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.9019 | − | 6.29423i | 0.458647 | − | 0.264800i | ||||
\(566\) | −16.8564 | −0.708528 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.73205 | −0.198552 | ||||||||
\(569\) | 5.19615 | − | 3.00000i | 0.217834 | − | 0.125767i | −0.387113 | − | 0.922032i | \(-0.626528\pi\) |
0.604947 | + | 0.796266i | \(0.293194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8038 | + | 18.7128i | −0.452127 | + | 0.783107i | −0.998518 | − | 0.0544234i | \(-0.982668\pi\) |
0.546391 | + | 0.837530i | \(0.316001\pi\) | |||||||
\(572\) | 16.3923 | 0.685397 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.79423 | + | 22.5000i | −0.325325 | + | 0.939132i | ||||
\(575\) | 2.53590i | 0.105754i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.7846 | − | 12.0000i | 0.865275 | − | 0.499567i | −0.000500448 | − | 1.00000i | \(-0.500159\pi\) |
0.865775 | + | 0.500433i | \(0.166826\pi\) | |||||||
\(578\) | − | 17.0000i | − | 0.707107i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.59808 | − | 3.23205i | 0.232447 | − | 0.134204i | ||||
\(581\) | −27.9904 | − | 9.69615i | −1.16124 | − | 0.402264i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.1962 | + | 29.7846i | 0.712192 | + | 1.23355i | ||||
\(584\) | −3.46410 | − | 6.00000i | −0.143346 | − | 0.248282i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.1962 | + | 8.19615i | 0.586438 | + | 0.338580i | ||||
\(587\) | −15.4019 | + | 26.6769i | −0.635705 | + | 1.10107i | 0.350660 | + | 0.936503i | \(0.385957\pi\) |
−0.986365 | + | 0.164571i | \(0.947376\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.19615 | + | 9.00000i | 0.214104 | + | 0.370839i | ||||
\(590\) | 2.19615i | 0.0904142i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.19615 | 0.254660 | ||||||||
\(593\) | 13.3923 | − | 23.1962i | 0.549956 | − | 0.952552i | −0.448321 | − | 0.893873i | \(-0.647978\pi\) |
0.998277 | − | 0.0586791i | \(-0.0186889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.3923 | + | 6.00000i | 0.425685 | + | 0.245770i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.60770 | + | 4.39230i | 0.311102 | + | 0.179615i | ||||
\(599\) | −3.80385 | − | 2.19615i | −0.155421 | − | 0.0897324i | 0.420272 | − | 0.907398i | \(-0.361934\pi\) |
−0.575693 | + | 0.817666i | \(0.695268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.5885 | + | 15.9282i | 1.12536 | + | 0.649725i | 0.942763 | − | 0.333464i | \(-0.108217\pi\) |
0.182594 | + | 0.983188i | \(0.441551\pi\) | |||||||
\(602\) | −8.30385 | + | 1.59808i | −0.338440 | + | 0.0651327i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.09808 | + | 3.63397i | −0.0853695 | + | 0.147864i | ||||
\(605\) | −11.3923 | −0.463163 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.12436i | − | 0.248580i | −0.992246 | − | 0.124290i | \(-0.960335\pi\) | ||
0.992246 | − | 0.124290i | \(-0.0396653\pi\) | |||||||
\(608\) | 0.633975 | + | 1.09808i | 0.0257111 | + | 0.0445329i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.46410 | − | 11.1962i | 0.261724 | − | 0.453319i | ||||
\(611\) | 27.0000 | + | 15.5885i | 1.09230 | + | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.39230 | + | 5.87564i | 0.137014 | + | 0.237315i | 0.926365 | − | 0.376627i | \(-0.122916\pi\) |
−0.789351 | + | 0.613942i | \(0.789583\pi\) | |||||||
\(614\) | −11.8923 | − | 20.5981i | −0.479934 | − | 0.831271i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.36603 | + | 12.2942i | 0.0953299 | + | 0.495349i | ||||
\(617\) | −15.8038 | + | 9.12436i | −0.636239 | + | 0.367333i | −0.783164 | − | 0.621815i | \(-0.786396\pi\) |
0.146925 | + | 0.989148i | \(0.453062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16.3923i | − | 0.658862i | −0.944180 | − | 0.329431i | \(-0.893143\pi\) | ||
0.944180 | − | 0.329431i | \(-0.106857\pi\) | |||||||
\(620\) | −7.09808 | + | 4.09808i | −0.285066 | + | 0.164583i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 15.8038i | − | 0.633677i | ||||||
\(623\) | 10.9808 | + | 3.80385i | 0.439935 | + | 0.152398i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.0981 | + | 17.4904i | −0.403600 | + | 0.699056i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.2942 | + | 8.83013i | −0.610306 | + | 0.352360i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.3923 | 0.493330 | 0.246665 | − | 0.969101i | \(-0.420665\pi\) | ||||
0.246665 | + | 0.969101i | \(0.420665\pi\) | |||||||
\(632\) | −12.6340 | + | 7.29423i | −0.502553 | + | 0.290149i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.2679 | + | 17.7846i | −0.407792 | + | 0.706317i | ||||
\(635\) | −11.3923 | −0.452090 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0000 | + | 19.0526i | −0.594322 | + | 0.754890i | ||||
\(638\) | 30.5885i | 1.21101i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.866025 | + | 0.500000i | −0.0342327 | + | 0.0197642i | ||||
\(641\) | − | 3.21539i | − | 0.127000i | −0.997982 | − | 0.0635001i | \(-0.979774\pi\) | ||
0.997982 | − | 0.0635001i | \(-0.0202263\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.2058 | − | 9.35641i | 0.639093 | − | 0.368981i | −0.145172 | − | 0.989406i | \(-0.546374\pi\) |
0.784265 | + | 0.620426i | \(0.213040\pi\) | |||||||
\(644\) | −2.19615 | + | 6.33975i | −0.0865405 | + | 0.249821i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.30385 | − | 3.99038i | −0.0905736 | − | 0.156878i | 0.817179 | − | 0.576384i | \(-0.195537\pi\) |
−0.907753 | + | 0.419506i | \(0.862203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | − | 5.19615i | −0.353281 | − | 0.203967i | ||||
\(650\) | 1.73205 | − | 3.00000i | 0.0679366 | − | 0.117670i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.19615 | − | 7.26795i | −0.164334 | − | 0.284635i | ||||
\(653\) | − | 49.8564i | − | 1.95103i | −0.219929 | − | 0.975516i | \(-0.570582\pi\) | ||
0.219929 | − | 0.975516i | \(-0.429418\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.39230 | −0.171622 | ||||||||
\(656\) | 4.50000 | − | 7.79423i | 0.175695 | − | 0.304314i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.79423 | + | 22.5000i | −0.303851 | + | 0.877141i | ||||
\(659\) | 33.2942 | + | 19.2224i | 1.29696 | + | 0.748800i | 0.979878 | − | 0.199599i | \(-0.0639639\pi\) |
0.317081 | + | 0.948398i | \(0.397297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3827 | + | 6.57180i | 0.442735 | + | 0.255613i | 0.704757 | − | 0.709449i | \(-0.251056\pi\) |
−0.262022 | + | 0.965062i | \(0.584389\pi\) | |||||||
\(662\) | 6.92820 | + | 4.00000i | 0.269272 | + | 0.155464i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.69615 | + | 5.59808i | 0.376284 | + | 0.217247i | ||||
\(665\) | 1.09808 | − | 3.16987i | 0.0425816 | − | 0.122922i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.19615 | + | 14.1962i | −0.317356 | + | 0.549677i | ||||
\(668\) | −10.3923 | −0.402090 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 4.00000i | − | 0.154533i | ||||||
\(671\) | 30.5885 | + | 52.9808i | 1.18085 | + | 2.04530i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4904 | − | 21.6340i | 0.481469 | − | 0.833928i | −0.518305 | − | 0.855196i | \(-0.673437\pi\) |
0.999774 | + | 0.0212674i | \(0.00677013\pi\) | |||||||
\(674\) | −8.66025 | − | 5.00000i | −0.333581 | − | 0.192593i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | + | 0.866025i | 0.0192308 | + | 0.0333087i | ||||
\(677\) | −11.4904 | − | 19.9019i | −0.441611 | − | 0.764893i | 0.556198 | − | 0.831050i | \(-0.312260\pi\) |
−0.997809 | + | 0.0661567i | \(0.978926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.39230 | + | 21.3397i | −0.283691 | + | 0.818944i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 38.7846i | − | 1.48514i | ||||||
\(683\) | −30.7750 | + | 17.7679i | −1.17757 | + | 0.679872i | −0.955452 | − | 0.295148i | \(-0.904631\pi\) |
−0.222121 | + | 0.975019i | \(0.571298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.26795i | − | 0.277694i | ||||||
\(686\) | −16.4545 | − | 8.50000i | −0.628235 | − | 0.324532i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.19615 | 0.121852 | ||||||||
\(689\) | 12.5885 | − | 21.8038i | 0.479582 | − | 0.830660i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.39230 | + | 2.53590i | −0.167091 | + | 0.0964701i | −0.581214 | − | 0.813751i | \(-0.697422\pi\) |
0.414122 | + | 0.910221i | \(0.364089\pi\) | |||||||
\(692\) | −8.19615 | −0.311571 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.2487 | −0.806590 | ||||||||
\(695\) | 19.0981 | − | 11.0263i | 0.724431 | − | 0.418251i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 16.3923 | 0.620458 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.50000 | + | 0.866025i | 0.0944911 | + | 0.0327327i | ||||
\(701\) | 44.3205i | 1.67396i | 0.547232 | + | 0.836981i | \(0.315682\pi\) | ||||
−0.547232 | + | 0.836981i | \(0.684318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.80385 | − | 3.92820i | 0.256612 | − | 0.148155i | ||||
\(704\) | − | 4.73205i | − | 0.178346i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.509619 | − | 0.294229i | 0.0191798 | − | 0.0110734i | ||||
\(707\) | 5.59808 | + | 29.0885i | 0.210537 | + | 1.09398i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.3923 | + | 40.5167i | 0.878516 | + | 1.52164i | 0.852969 | + | 0.521962i | \(0.174800\pi\) |
0.0255474 | + | 0.999674i | \(0.491867\pi\) | |||||||
\(710\) | −2.36603 | − | 4.09808i | −0.0887954 | − | 0.153798i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.80385 | − | 2.19615i | −0.142555 | − | 0.0823043i | ||||
\(713\) | 10.3923 | − | 18.0000i | 0.389195 | − | 0.674105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.19615 | + | 14.1962i | 0.306519 | + | 0.530906i | ||||
\(716\) | 24.5885i | 0.918914i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.8038 | 0.589794 | ||||||||
\(719\) | −20.7846 | + | 36.0000i | −0.775135 | + | 1.34257i | 0.159583 | + | 0.987184i | \(0.448985\pi\) |
−0.934718 | + | 0.355389i | \(0.884348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.5000 | − | 6.06218i | 1.17312 | − | 0.225767i | ||||
\(722\) | −15.0622 | − | 8.69615i | −0.560556 | − | 0.323637i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.5981 | + | 6.69615i | 0.431039 | + | 0.248861i | ||||
\(725\) | 5.59808 | + | 3.23205i | 0.207907 | + | 0.120035i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.7846 | − | 24.1244i | −1.54971 | − | 0.894723i | −0.998164 | − | 0.0605756i | \(-0.980706\pi\) |
−0.551542 | − | 0.834147i | \(-0.685960\pi\) | |||||||
\(728\) | 6.92820 | − | 6.00000i | 0.256776 | − | 0.222375i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.46410 | − | 6.00000i | 0.128212 | − | 0.222070i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.0526i | − | 1.25776i | −0.777502 | − | 0.628880i | \(-0.783514\pi\) | ||
0.777502 | − | 0.628880i | \(-0.216486\pi\) | |||||||
\(734\) | 14.5981 | + | 25.2846i | 0.538825 | + | 0.933272i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.26795 | − | 2.19615i | 0.0467372 | − | 0.0809513i | ||||
\(737\) | 16.3923 | + | 9.46410i | 0.603818 | + | 0.348615i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5885 | − | 28.7321i | −0.610216 | − | 1.05693i | −0.991204 | − | 0.132345i | \(-0.957749\pi\) |
0.380987 | − | 0.924580i | \(-0.375584\pi\) | |||||||
\(740\) | 3.09808 | + | 5.36603i | 0.113888 | + | 0.197259i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.1699 | + | 6.29423i | 0.667037 | + | 0.231068i | ||||
\(743\) | 23.6769 | − | 13.6699i | 0.868622 | − | 0.501499i | 0.00173176 | − | 0.999999i | \(-0.499449\pi\) |
0.866890 | + | 0.498499i | \(0.166115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0000i | 0.439646i | ||||||||
\(746\) | 8.83013 | − | 5.09808i | 0.323294 | − | 0.186654i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.7942 | − | 39.8205i | 0.504030 | − | 1.45501i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6077 | −0.788476 | −0.394238 | − | 0.919008i | \(-0.628991\pi\) | ||||
−0.394238 | + | 0.919008i | \(0.628991\pi\) | |||||||
\(752\) | 4.50000 | − | 7.79423i | 0.164098 | − | 0.284226i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.3923 | − | 11.1962i | 0.706226 | − | 0.407740i | ||||
\(755\) | −4.19615 | −0.152714 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.58846 | −0.312153 | −0.156076 | − | 0.987745i | \(-0.549885\pi\) | ||||
−0.156076 | + | 0.987745i | \(0.549885\pi\) | |||||||
\(758\) | −8.32051 | + | 4.80385i | −0.302214 | + | 0.174484i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.633975 | + | 1.09808i | −0.0229967 | + | 0.0398314i | ||||
\(761\) | 33.0000 | 1.19625 | 0.598125 | − | 0.801403i | \(-0.295913\pi\) | ||||
0.598125 | + | 0.801403i | \(0.295913\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.3923 | + | 12.4641i | −0.521036 | + | 0.451231i | ||||
\(764\) | 3.46410i | 0.125327i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.7942 | + | 9.69615i | −0.606800 | + | 0.350336i | ||||
\(767\) | 7.60770i | 0.274698i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5000 | − | 7.79423i | 0.486822 | − | 0.281067i | −0.236433 | − | 0.971648i | \(-0.575978\pi\) |
0.723255 | + | 0.690581i | \(0.242645\pi\) | |||||||
\(770\) | −9.46410 | + | 8.19615i | −0.341063 | + | 0.295369i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.90192 | + | 11.9545i | 0.248406 | + | 0.430251i | ||||
\(773\) | 9.00000 | + | 15.5885i | 0.323708 | + | 0.560678i | 0.981250 | − | 0.192740i | \(-0.0617373\pi\) |
−0.657542 | + | 0.753418i | \(0.728404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.09808 | − | 4.09808i | −0.254970 | − | 0.147207i | ||||
\(776\) | 4.26795 | − | 7.39230i | 0.153210 | − | 0.265368i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.3564 | − | 21.4019i | −0.442999 | − | 0.767296i | ||||
\(779\) | − | 11.4115i | − | 0.408861i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.3923 | 0.801260 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.50000 | + | 4.33013i | 0.196429 | + | 0.154647i | ||||
\(785\) | −15.2942 | − | 8.83013i | −0.545874 | − | 0.315161i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.00962 | − | 4.62436i | −0.285512 | − | 0.164840i | 0.350404 | − | 0.936599i | \(-0.386044\pi\) |
−0.635916 | + | 0.771758i | \(0.719378\pi\) | |||||||
\(788\) | −20.4904 | − | 11.8301i | −0.729940 | − | 0.421431i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.6340 | − | 7.29423i | −0.449497 | − | 0.259517i | ||||
\(791\) | 21.8038 | + | 25.1769i | 0.775256 | + | 0.895188i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.3923 | − | 38.7846i | 0.795174 | − | 1.37728i | ||||
\(794\) | −30.5885 | −1.08554 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 6.92820i | − | 0.245564i | ||||||
\(797\) | 9.58846 | + | 16.6077i | 0.339641 | + | 0.588275i | 0.984365 | − | 0.176140i | \(-0.0563612\pi\) |
−0.644724 | + | 0.764415i | \(0.723028\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.866025 | − | 0.500000i | −0.0306186 | − | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.79423 | + | 3.10770i | 0.0633564 | + | 0.109737i | ||||
\(803\) | 16.3923 | + | 28.3923i | 0.578472 | + | 1.00194i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.58846 | + | 1.26795i | −0.232213 | + | 0.0446893i | ||||
\(806\) | −24.5885 | + | 14.1962i | −0.866091 | + | 0.500038i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 11.1962i | − | 0.393879i | ||||||
\(809\) | −45.4808 | + | 26.2583i | −1.59902 | + | 0.923194i | −0.607342 | + | 0.794441i | \(0.707764\pi\) |
−0.991677 | + | 0.128753i | \(0.958903\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 44.5359i | − | 1.56387i | −0.623362 | − | 0.781933i | \(-0.714234\pi\) | ||
0.623362 | − | 0.781933i | \(-0.285766\pi\) | |||||||
\(812\) | 11.1962 | + | 12.9282i | 0.392908 | + | 0.453691i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.3205 | −1.02768 | ||||||||
\(815\) | 4.19615 | − | 7.26795i | 0.146985 | − | 0.254585i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.50962 | − | 2.02628i | 0.122786 | − | 0.0708905i | ||||
\(818\) | −10.5167 | −0.367706 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | −31.7942 | + | 18.3564i | −1.10963 | + | 0.640643i | −0.938733 | − | 0.344646i | \(-0.887999\pi\) |
−0.170894 | + | 0.985289i | \(0.554665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.3038 | + | 26.5070i | −0.533459 | + | 0.923977i | 0.465778 | + | 0.884902i | \(0.345775\pi\) |
−0.999236 | + | 0.0390756i | \(0.987559\pi\) | |||||||
\(824\) | −12.1244 | −0.422372 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.70577 | + | 1.09808i | −0.198529 | + | 0.0382070i | ||||
\(827\) | − | 31.6410i | − | 1.10027i | −0.835077 | − | 0.550133i | \(-0.814577\pi\) | ||
0.835077 | − | 0.550133i | \(-0.185423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.1865 | − | 17.4282i | 1.04842 | − | 0.605307i | 0.126215 | − | 0.992003i | \(-0.459717\pi\) |
0.922207 | + | 0.386696i | \(0.126384\pi\) | |||||||
\(830\) | 11.1962i | 0.388624i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.00000 | + | 1.73205i | −0.104006 | + | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.19615 | − | 9.00000i | −0.179820 | − | 0.311458i | ||||
\(836\) | −3.00000 | − | 5.19615i | −0.103757 | − | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.00000 | − | 5.19615i | −0.310900 | − | 0.179498i | ||||
\(839\) | −1.90192 | + | 3.29423i | −0.0656617 | + | 0.113729i | −0.896987 | − | 0.442056i | \(-0.854249\pi\) |
0.831326 | + | 0.555786i | \(0.187582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.39230 | + | 11.0718i | 0.220424 | + | 0.381786i | ||||
\(842\) | − | 29.9808i | − | 1.03321i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.5885 | 0.708684 | ||||||||
\(845\) | −0.500000 | + | 0.866025i | −0.0172005 | + | 0.0297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.69615 | − | 29.5981i | −0.195722 | − | 1.01700i | ||||
\(848\) | −6.29423 | − | 3.63397i | −0.216145 | − | 0.124791i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.6077 | − | 7.85641i | −0.466466 | − | 0.269314i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.78461 | − | 1.60770i | −0.0953432 | − | 0.0550464i | 0.451570 | − | 0.892236i | \(-0.350864\pi\) |
−0.546914 | + | 0.837189i | \(0.684197\pi\) | |||||||
\(854\) | 32.3205 | + | 11.1962i | 1.10599 | + | 0.383124i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.96410 | + | 13.7942i | −0.272207 | + | 0.471477i | ||||
\(857\) | 17.4115 | 0.594767 | 0.297383 | − | 0.954758i | \(-0.403886\pi\) | ||||
0.297383 | + | 0.954758i | \(0.403886\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.8038i | − | 0.539220i | −0.962970 | − | 0.269610i | \(-0.913105\pi\) | ||
0.962970 | − | 0.269610i | \(-0.0868948\pi\) | |||||||
\(860\) | 1.59808 | + | 2.76795i | 0.0544939 | + | 0.0943863i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.3923 | − | 33.5885i | 0.660505 | − | 1.14403i | ||||
\(863\) | −25.3923 | − | 14.6603i | −0.864364 | − | 0.499041i | 0.00110718 | − | 0.999999i | \(-0.499648\pi\) |
−0.865471 | + | 0.500959i | \(0.832981\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.09808 | − | 7.09808i | −0.139339 | − | 0.241342i | ||||
\(866\) | 9.00000 | + | 15.5885i | 0.305832 | + | 0.529717i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.1962 | − | 16.3923i | −0.481849 | − | 0.556391i | ||||
\(869\) | 59.7846 | − | 34.5167i | 2.02805 | − | 1.17090i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 13.8564i | − | 0.469506i | ||||||
\(872\) | 6.23205 | − | 3.59808i | 0.211044 | − | 0.121846i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3.21539i | − | 0.108762i | ||||||
\(875\) | 0.500000 | + | 2.59808i | 0.0169031 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.7654 | 1.74799 | 0.873996 | − | 0.485933i | \(-0.161520\pi\) | ||||
0.873996 | + | 0.485933i | \(0.161520\pi\) | |||||||
\(878\) | 14.8301 | − | 25.6865i | 0.500493 | − | 0.866879i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.09808 | − | 2.36603i | 0.138146 | − | 0.0797587i | ||||
\(881\) | 16.3923 | 0.552271 | 0.276135 | − | 0.961119i | \(-0.410946\pi\) | ||||
0.276135 | + | 0.961119i | \(0.410946\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.3731 | 0.954830 | 0.477415 | − | 0.878678i | \(-0.341574\pi\) | ||||
0.477415 | + | 0.878678i | \(0.341574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.50000 | + | 7.79423i | −0.151180 | + | 0.261852i | ||||
\(887\) | 49.3923 | 1.65843 | 0.829216 | − | 0.558929i | \(-0.188788\pi\) | ||||
0.829216 | + | 0.558929i | \(0.188788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.69615 | − | 29.5981i | −0.191043 | − | 0.992688i | ||||
\(890\) | − | 4.39230i | − | 0.147230i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.8923 | − | 6.86603i | 0.398184 | − | 0.229892i | ||||
\(893\) | − | 11.4115i | − | 0.381873i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.2942 | + | 12.2942i | −0.711788 | + | 0.410951i | ||||
\(896\) | −1.73205 | − | 2.00000i | −0.0578638 | − | 0.0668153i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.79423 | + | 8.30385i | 0.159985 | + | 0.277103i | ||||
\(899\) | −26.4904 | − | 45.8827i | −0.883504 | − | 1.53027i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −21.2942 | + | 36.8827i | −0.709020 | + | 1.22806i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.29423 | − | 10.9019i | −0.209343 | − | 0.362593i | ||||
\(905\) | 13.3923i | 0.445175i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.8038 | 0.757189 | 0.378595 | − | 0.925563i | \(-0.376407\pi\) | ||||
0.378595 | + | 0.925563i | \(0.376407\pi\) | |||||||
\(908\) | 8.19615 | − | 14.1962i | 0.271999 | − | 0.471116i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.66025 | + | 3.00000i | 0.287085 | + | 0.0994490i | ||||
\(911\) | −10.0981 | − | 5.83013i | −0.334564 | − | 0.193161i | 0.323301 | − | 0.946296i | \(-0.395207\pi\) |
−0.657866 | + | 0.753135i | \(0.728541\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.8827 | − | 26.4904i | −1.51850 | − | 0.876704i | ||||
\(914\) | −2.07180 | − | 1.19615i | −0.0685289 | − | 0.0395652i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.1865 | − | 7.03590i | −0.402654 | − | 0.232473i | ||||
\(917\) | −2.19615 | − | 11.4115i | −0.0725233 | − | 0.376842i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.29423 | + | 3.97372i | −0.0756796 | + | 0.131081i | −0.901382 | − | 0.433026i | \(-0.857446\pi\) |
0.825702 | + | 0.564107i | \(0.190779\pi\) | |||||||
\(920\) | 2.53590 | 0.0836061 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 5.19615i | − | 0.171126i | ||||||
\(923\) | −8.19615 | − | 14.1962i | −0.269780 | − | 0.467272i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.09808 | + | 5.36603i | −0.101864 | + | 0.176434i | ||||
\(926\) | 2.25833 | + | 1.30385i | 0.0742133 | + | 0.0428471i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.23205 | − | 5.59808i | −0.106097 | − | 0.183766i | ||||
\(929\) | 25.2846 | + | 43.7942i | 0.829561 | + | 1.43684i | 0.898383 | + | 0.439213i | \(0.144743\pi\) |
−0.0688218 | + | 0.997629i | \(0.521924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.78461 | + | 1.26795i | 0.287904 | + | 0.0415554i | ||||
\(932\) | −1.09808 | + | 0.633975i | −0.0359687 | + | 0.0207665i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.80385i | 0.222629i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.5885i | 1.39130i | 0.718379 | + | 0.695652i | \(0.244884\pi\) | ||||
−0.718379 | + | 0.695652i | \(0.755116\pi\) | |||||||
\(938\) | 10.3923 | − | 2.00000i | 0.339321 | − | 0.0653023i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.00000 | 0.293548 | ||||||||
\(941\) | 12.9904 | − | 22.5000i | 0.423474 | − | 0.733479i | −0.572802 | − | 0.819694i | \(-0.694144\pi\) |
0.996277 | + | 0.0862145i | \(0.0274771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.7654 | + | 11.4115i | −0.643649 | + | 0.371611i | ||||
\(944\) | 2.19615 | 0.0714787 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.1244 | −0.491735 | ||||||||
\(947\) | 20.4115 | − | 11.7846i | 0.663286 | − | 0.382948i | −0.130242 | − | 0.991482i | \(-0.541575\pi\) |
0.793528 | + | 0.608534i | \(0.208242\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | − | 20.7846i | 0.389536 | − | 0.674697i | ||||
\(950\) | −1.26795 | −0.0411377 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.26795i | − | 0.0410729i | −0.999789 | − | 0.0205365i | \(-0.993463\pi\) | ||
0.999789 | − | 0.0205365i | \(-0.00653742\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.00000 | + | 1.73205i | −0.0970777 | + | 0.0560478i | ||||
\(956\) | 3.12436i | 0.101049i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.00000 | − | 5.19615i | 0.290777 | − | 0.167880i | ||||
\(959\) | 18.8827 | − | 3.63397i | 0.609754 | − | 0.117347i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0885 | + | 31.3301i | 0.583499 | + | 1.01065i | ||||
\(962\) | 10.7321 | + | 18.5885i | 0.346015 | + | 0.599316i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.89230 | − | 1.66987i | −0.0931549 | − | 0.0537830i | ||||
\(965\) | −6.90192 | + | 11.9545i | −0.222181 | + | 0.384828i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | + | 13.8564i | 0.257263 | + | 0.445592i | 0.965508 | − | 0.260375i | \(-0.0838461\pi\) |
−0.708245 | + | 0.705967i | \(0.750513\pi\) | |||||||
\(968\) | 11.3923i | 0.366163i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.53590 | 0.274071 | ||||||||
\(971\) | −7.39230 | + | 12.8038i | −0.237230 | + | 0.410895i | −0.959919 | − | 0.280279i | \(-0.909573\pi\) |
0.722688 | + | 0.691174i | \(0.242906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.1962 | + | 44.1051i | 1.22451 | + | 1.41395i | ||||
\(974\) | −29.4449 | − | 17.0000i | −0.943474 | − | 0.544715i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.1962 | − | 6.46410i | −0.358380 | − | 0.206911i | ||||
\(977\) | −4.39230 | − | 2.53590i | −0.140522 | − | 0.0811306i | 0.428091 | − | 0.903736i | \(-0.359186\pi\) |
−0.568613 | + | 0.822605i | \(0.692520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | + | 10.3923i | 0.575282 | + | 0.332140i | ||||
\(980\) | −1.00000 | + | 6.92820i | −0.0319438 | + | 0.221313i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.5622 | − | 23.4904i | 0.432786 | − | 0.749608i | ||||
\(983\) | 31.3923 | 1.00126 | 0.500630 | − | 0.865662i | \(-0.333102\pi\) | ||||
0.500630 | + | 0.865662i | \(0.333102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 23.6603i | − | 0.753878i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.19615 | + | 3.80385i | −0.0698689 | + | 0.121017i | ||||
\(989\) | −7.01924 | − | 4.05256i | −0.223199 | − | 0.128864i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.70577 | + | 11.6147i | 0.213016 | + | 0.368954i | 0.952657 | − | 0.304047i | \(-0.0983381\pi\) |
−0.739641 | + | 0.673002i | \(0.765005\pi\) | |||||||
\(992\) | 4.09808 | + | 7.09808i | 0.130114 | + | 0.225364i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.46410 | − | 8.19615i | 0.300183 | − | 0.259966i | ||||
\(995\) | 6.00000 | − | 3.46410i | 0.190213 | − | 0.109819i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.5167i | 0.998143i | 0.866561 | + | 0.499071i | \(0.166325\pi\) | ||||
−0.866561 | + | 0.499071i | \(0.833675\pi\) | |||||||
\(998\) | −14.0263 | + | 8.09808i | −0.443994 | + | 0.256340i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1890.2.t.a.1601.2 | 4 | ||
3.2 | odd | 2 | 630.2.t.a.551.1 | yes | 4 | ||
7.3 | odd | 6 | 1890.2.bk.a.521.2 | 4 | |||
9.4 | even | 3 | 630.2.bk.a.131.2 | yes | 4 | ||
9.5 | odd | 6 | 1890.2.bk.a.341.1 | 4 | |||
21.17 | even | 6 | 630.2.bk.a.101.1 | yes | 4 | ||
63.31 | odd | 6 | 630.2.t.a.311.1 | ✓ | 4 | ||
63.59 | even | 6 | inner | 1890.2.t.a.1151.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.a.311.1 | ✓ | 4 | 63.31 | odd | 6 | ||
630.2.t.a.551.1 | yes | 4 | 3.2 | odd | 2 | ||
630.2.bk.a.101.1 | yes | 4 | 21.17 | even | 6 | ||
630.2.bk.a.131.2 | yes | 4 | 9.4 | even | 3 | ||
1890.2.t.a.1151.2 | 4 | 63.59 | even | 6 | inner | ||
1890.2.t.a.1601.2 | 4 | 1.1 | even | 1 | trivial | ||
1890.2.bk.a.341.1 | 4 | 9.5 | odd | 6 | |||
1890.2.bk.a.521.2 | 4 | 7.3 | odd | 6 |