Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(31,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("980.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.o (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: | \(7.82533939809\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.31 |
Dual form | 980.2.o.b.411.1 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | + | 0.366025i | −0.965926 | + | 0.258819i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | 0.633975 | − | 2.36603i | 0.258819 | − | 0.965926i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | + | 1.00000i | −0.316228 | + | 0.316228i | ||||
\(11\) | 0.232051 | + | 0.133975i | 0.0699660 | + | 0.0403949i | 0.534575 | − | 0.845121i | \(-0.320472\pi\) |
−0.464609 | + | 0.885516i | \(0.653805\pi\) | |||||||
\(12\) | 3.46410i | 1.00000i | ||||||||
\(13\) | 0.464102i | 0.128719i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) | ||||
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205i | 0.447214i | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −5.59808 | − | 3.23205i | −1.35773 | − | 0.783887i | −0.368415 | − | 0.929661i | \(-0.620099\pi\) |
−0.989318 | + | 0.145774i | \(0.953433\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 5.19615i | 0.688247 | + | 1.19208i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(20\) | 1.00000 | − | 1.73205i | 0.223607 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.366025 | − | 0.0980762i | −0.0780369 | − | 0.0209099i | ||||
\(23\) | −1.26795 | + | 0.732051i | −0.264386 | + | 0.152643i | −0.626334 | − | 0.779555i | \(-0.715445\pi\) |
0.361948 | + | 0.932198i | \(0.382112\pi\) | |||||||
\(24\) | −1.26795 | − | 4.73205i | −0.258819 | − | 0.965926i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −0.169873 | − | 0.633975i | −0.0333148 | − | 0.124333i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.92820 | 1.47223 | 0.736115 | − | 0.676856i | \(-0.236658\pi\) | ||||
0.736115 | + | 0.676856i | \(0.236658\pi\) | |||||||
\(30\) | −0.633975 | − | 2.36603i | −0.115747 | − | 0.431975i | ||||
\(31\) | −3.00000 | + | 5.19615i | −0.538816 | + | 0.933257i | 0.460152 | + | 0.887840i | \(0.347795\pi\) |
−0.998968 | + | 0.0454165i | \(0.985539\pi\) | |||||||
\(32\) | −1.46410 | + | 5.46410i | −0.258819 | + | 0.965926i | ||||
\(33\) | −0.401924 | + | 0.232051i | −0.0699660 | + | 0.0403949i | ||||
\(34\) | 8.83013 | + | 2.36603i | 1.51435 | + | 0.405770i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.73205 | + | 8.19615i | 0.777944 | + | 1.34744i | 0.933125 | + | 0.359553i | \(0.117071\pi\) |
−0.155180 | + | 0.987886i | \(0.549596\pi\) | |||||||
\(38\) | −6.00000 | − | 6.00000i | −0.973329 | − | 0.973329i | ||||
\(39\) | −0.696152 | − | 0.401924i | −0.111474 | − | 0.0643593i | ||||
\(40\) | −0.732051 | + | 2.73205i | −0.115747 | + | 0.431975i | ||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 0.535898 | 0.0807897 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.46410 | − | 1.46410i | 0.215870 | − | 0.215870i | ||||
\(47\) | 0.866025 | + | 1.50000i | 0.126323 | + | 0.218797i | 0.922249 | − | 0.386596i | \(-0.126349\pi\) |
−0.795926 | + | 0.605393i | \(0.793016\pi\) | |||||||
\(48\) | 3.46410 | + | 6.00000i | 0.500000 | + | 0.866025i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.366025 | + | 1.36603i | −0.0517638 | + | 0.193185i | ||||
\(51\) | 9.69615 | − | 5.59808i | 1.35773 | − | 0.783887i | ||||
\(52\) | 0.464102 | + | 0.803848i | 0.0643593 | + | 0.111474i | ||||
\(53\) | −1.00000 | + | 1.73205i | −0.137361 | + | 0.237915i | −0.926497 | − | 0.376303i | \(-0.877195\pi\) |
0.789136 | + | 0.614218i | \(0.210529\pi\) | |||||||
\(54\) | 7.09808 | − | 1.90192i | 0.965926 | − | 0.258819i | ||||
\(55\) | 0.267949 | 0.0361303 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.3923 | −1.37649 | ||||||||
\(58\) | −10.8301 | + | 2.90192i | −1.42207 | + | 0.381041i | ||||
\(59\) | −1.73205 | + | 3.00000i | −0.225494 | + | 0.390567i | −0.956467 | − | 0.291839i | \(-0.905733\pi\) |
0.730974 | + | 0.682406i | \(0.239066\pi\) | |||||||
\(60\) | 1.73205 | + | 3.00000i | 0.223607 | + | 0.387298i | ||||
\(61\) | −8.19615 | + | 4.73205i | −1.04941 | + | 0.605877i | −0.922484 | − | 0.386035i | \(-0.873844\pi\) |
−0.126926 | + | 0.991912i | \(0.540511\pi\) | |||||||
\(62\) | 2.19615 | − | 8.19615i | 0.278912 | − | 1.04091i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0.232051 | + | 0.401924i | 0.0287824 | + | 0.0498525i | ||||
\(66\) | 0.464102 | − | 0.464102i | 0.0571270 | − | 0.0571270i | ||||
\(67\) | −3.00000 | − | 1.73205i | −0.366508 | − | 0.211604i | 0.305424 | − | 0.952217i | \(-0.401202\pi\) |
−0.671932 | + | 0.740613i | \(0.734535\pi\) | |||||||
\(68\) | −12.9282 | −1.56777 | ||||||||
\(69\) | − | 2.53590i | − | 0.305286i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.46410i | − | 0.885826i | −0.896565 | − | 0.442913i | \(-0.853945\pi\) | ||
0.896565 | − | 0.442913i | \(-0.146055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1962 | + | 6.46410i | 1.31041 | + | 0.756566i | 0.982164 | − | 0.188026i | \(-0.0602090\pi\) |
0.328247 | + | 0.944592i | \(0.393542\pi\) | |||||||
\(74\) | −9.46410 | − | 9.46410i | −1.10018 | − | 1.10018i | ||||
\(75\) | 0.866025 | + | 1.50000i | 0.100000 | + | 0.173205i | ||||
\(76\) | 10.3923 | + | 6.00000i | 1.19208 | + | 0.688247i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.09808 | + | 0.294229i | 0.124333 | + | 0.0333148i | ||||
\(79\) | −12.6962 | + | 7.33013i | −1.42843 | + | 0.824704i | −0.996997 | − | 0.0774418i | \(-0.975325\pi\) |
−0.431432 | + | 0.902146i | \(0.641991\pi\) | |||||||
\(80\) | − | 4.00000i | − | 0.447214i | ||||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | −1.26795 | − | 4.73205i | −0.140022 | − | 0.522568i | ||||
\(83\) | −15.4641 | −1.69741 | −0.848703 | − | 0.528870i | \(-0.822616\pi\) | ||||
−0.848703 | + | 0.528870i | \(0.822616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.46410 | −0.701130 | ||||||||
\(86\) | 0.732051 | + | 2.73205i | 0.0789391 | + | 0.294605i | ||||
\(87\) | −6.86603 | + | 11.8923i | −0.736115 | + | 1.27499i | ||||
\(88\) | −0.732051 | + | 0.196152i | −0.0780369 | + | 0.0209099i | ||||
\(89\) | −2.19615 | + | 1.26795i | −0.232792 | + | 0.134402i | −0.611859 | − | 0.790967i | \(-0.709578\pi\) |
0.379068 | + | 0.925369i | \(0.376245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.46410 | + | 2.53590i | −0.152643 | + | 0.264386i | ||||
\(93\) | −5.19615 | − | 9.00000i | −0.538816 | − | 0.933257i | ||||
\(94\) | −1.73205 | − | 1.73205i | −0.178647 | − | 0.178647i | ||||
\(95\) | 5.19615 | + | 3.00000i | 0.533114 | + | 0.307794i | ||||
\(96\) | −6.92820 | − | 6.92820i | −0.707107 | − | 0.707107i | ||||
\(97\) | 13.3923i | 1.35978i | 0.733313 | + | 0.679891i | \(0.237973\pi\) | ||||
−0.733313 | + | 0.679891i | \(0.762027\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | − | 2.00000i | − | 0.200000i | ||||||
\(101\) | −13.3923 | − | 7.73205i | −1.33258 | − | 0.769368i | −0.346889 | − | 0.937906i | \(-0.612762\pi\) |
−0.985695 | + | 0.168538i | \(0.946095\pi\) | |||||||
\(102\) | −11.1962 | + | 11.1962i | −1.10858 | + | 1.10858i | ||||
\(103\) | −3.40192 | − | 5.89230i | −0.335202 | − | 0.580586i | 0.648322 | − | 0.761366i | \(-0.275471\pi\) |
−0.983524 | + | 0.180780i | \(0.942138\pi\) | |||||||
\(104\) | −0.928203 | − | 0.928203i | −0.0910178 | − | 0.0910178i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.732051 | − | 2.73205i | 0.0711031 | − | 0.265360i | ||||
\(107\) | 2.07180 | − | 1.19615i | 0.200288 | − | 0.115636i | −0.396502 | − | 0.918034i | \(-0.629776\pi\) |
0.596790 | + | 0.802398i | \(0.296443\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.866025 | + | 0.500000i | ||||
\(109\) | −1.03590 | + | 1.79423i | −0.0992211 | + | 0.171856i | −0.911362 | − | 0.411605i | \(-0.864968\pi\) |
0.812141 | + | 0.583461i | \(0.198302\pi\) | |||||||
\(110\) | −0.366025 | + | 0.0980762i | −0.0348992 | + | 0.00935120i | ||||
\(111\) | −16.3923 | −1.55589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.46410 | 0.514019 | 0.257010 | − | 0.966409i | \(-0.417263\pi\) | ||||
0.257010 | + | 0.966409i | \(0.417263\pi\) | |||||||
\(114\) | 14.1962 | − | 3.80385i | 1.32959 | − | 0.356263i | ||||
\(115\) | −0.732051 | + | 1.26795i | −0.0682641 | + | 0.118237i | ||||
\(116\) | 13.7321 | − | 7.92820i | 1.27499 | − | 0.736115i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.26795 | − | 4.73205i | 0.116724 | − | 0.435621i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.46410 | − | 3.46410i | −0.316228 | − | 0.316228i | ||||
\(121\) | −5.46410 | − | 9.46410i | −0.496737 | − | 0.860373i | ||||
\(122\) | 9.46410 | − | 9.46410i | 0.856840 | − | 0.856840i | ||||
\(123\) | −5.19615 | − | 3.00000i | −0.468521 | − | 0.270501i | ||||
\(124\) | 12.0000i | 1.07763i | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4641i | 1.37222i | 0.727499 | + | 0.686109i | \(0.240683\pi\) | ||||
−0.727499 | + | 0.686109i | \(0.759317\pi\) | |||||||
\(128\) | 2.92820 | + | 10.9282i | 0.258819 | + | 0.965926i | ||||
\(129\) | 3.00000 | + | 1.73205i | 0.264135 | + | 0.152499i | ||||
\(130\) | −0.464102 | − | 0.464102i | −0.0407044 | − | 0.0407044i | ||||
\(131\) | 1.26795 | + | 2.19615i | 0.110781 | + | 0.191879i | 0.916085 | − | 0.400983i | \(-0.131331\pi\) |
−0.805304 | + | 0.592862i | \(0.797998\pi\) | |||||||
\(132\) | −0.464102 | + | 0.803848i | −0.0403949 | + | 0.0699660i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.73205 | + | 1.26795i | 0.408787 | + | 0.109534i | ||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | 17.6603 | − | 4.73205i | 1.51435 | − | 0.405770i | ||||
\(137\) | −10.1962 | + | 17.6603i | −0.871116 | + | 1.50882i | −0.0102728 | + | 0.999947i | \(0.503270\pi\) |
−0.860843 | + | 0.508870i | \(0.830063\pi\) | |||||||
\(138\) | 0.928203 | + | 3.46410i | 0.0790139 | + | 0.294884i | ||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | 2.73205 | + | 10.1962i | 0.229269 | + | 0.855642i | ||||
\(143\) | −0.0621778 | + | 0.107695i | −0.00519957 | + | 0.00900592i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.86603 | − | 3.96410i | 0.570192 | − | 0.329201i | ||||
\(146\) | −17.6603 | − | 4.73205i | −1.46157 | − | 0.391627i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.3923 | + | 9.46410i | 1.34744 | + | 0.777944i | ||||
\(149\) | −1.53590 | − | 2.66025i | −0.125826 | − | 0.217937i | 0.796230 | − | 0.604994i | \(-0.206825\pi\) |
−0.922055 | + | 0.387058i | \(0.873491\pi\) | |||||||
\(150\) | −1.73205 | − | 1.73205i | −0.141421 | − | 0.141421i | ||||
\(151\) | 13.1603 | + | 7.59808i | 1.07097 | + | 0.618323i | 0.928445 | − | 0.371469i | \(-0.121146\pi\) |
0.142521 | + | 0.989792i | \(0.454479\pi\) | |||||||
\(152\) | −16.3923 | − | 4.39230i | −1.32959 | − | 0.356263i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | −1.60770 | −0.128719 | ||||||||
\(157\) | 6.80385 | + | 3.92820i | 0.543006 | + | 0.313505i | 0.746296 | − | 0.665614i | \(-0.231830\pi\) |
−0.203290 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(158\) | 14.6603 | − | 14.6603i | 1.16631 | − | 1.16631i | ||||
\(159\) | −1.73205 | − | 3.00000i | −0.137361 | − | 0.237915i | ||||
\(160\) | 1.46410 | + | 5.46410i | 0.115747 | + | 0.431975i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.29423 | + | 12.2942i | −0.258819 | + | 0.965926i | ||||
\(163\) | 18.0000 | − | 10.3923i | 1.40987 | − | 0.813988i | 0.414494 | − | 0.910052i | \(-0.363959\pi\) |
0.995375 | + | 0.0960641i | \(0.0306254\pi\) | |||||||
\(164\) | 3.46410 | + | 6.00000i | 0.270501 | + | 0.468521i | ||||
\(165\) | −0.232051 | + | 0.401924i | −0.0180651 | + | 0.0312897i | ||||
\(166\) | 21.1244 | − | 5.66025i | 1.63957 | − | 0.439321i | ||||
\(167\) | 5.19615 | 0.402090 | 0.201045 | − | 0.979582i | \(-0.435566\pi\) | ||||
0.201045 | + | 0.979582i | \(0.435566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7846 | 0.983432 | ||||||||
\(170\) | 8.83013 | − | 2.36603i | 0.677240 | − | 0.181466i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | − | 3.46410i | −0.152499 | − | 0.264135i | ||||
\(173\) | 12.4019 | − | 7.16025i | 0.942901 | − | 0.544384i | 0.0520323 | − | 0.998645i | \(-0.483430\pi\) |
0.890868 | + | 0.454261i | \(0.150097\pi\) | |||||||
\(174\) | 5.02628 | − | 18.7583i | 0.381041 | − | 1.42207i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.928203 | − | 0.535898i | 0.0699660 | − | 0.0403949i | ||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | 2.53590 | − | 2.53590i | 0.190074 | − | 0.190074i | ||||
\(179\) | −5.53590 | − | 3.19615i | −0.413772 | − | 0.238892i | 0.278637 | − | 0.960397i | \(-0.410117\pi\) |
−0.692409 | + | 0.721505i | \(0.743451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.928203i | 0.0689928i | 0.999405 | + | 0.0344964i | \(0.0109827\pi\) | ||||
−0.999405 | + | 0.0344964i | \(0.989017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 16.3923i | − | 1.21175i | ||||||
\(184\) | 1.07180 | − | 4.00000i | 0.0790139 | − | 0.294884i | ||||
\(185\) | 8.19615 | + | 4.73205i | 0.602593 | + | 0.347907i | ||||
\(186\) | 10.3923 | + | 10.3923i | 0.762001 | + | 0.762001i | ||||
\(187\) | −0.866025 | − | 1.50000i | −0.0633300 | − | 0.109691i | ||||
\(188\) | 3.00000 | + | 1.73205i | 0.218797 | + | 0.126323i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.19615 | − | 2.19615i | −0.594611 | − | 0.159326i | ||||
\(191\) | −6.23205 | + | 3.59808i | −0.450935 | + | 0.260348i | −0.708225 | − | 0.705987i | \(-0.750504\pi\) |
0.257290 | + | 0.966334i | \(0.417171\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | 4.73205 | − | 8.19615i | 0.340620 | − | 0.589972i | −0.643928 | − | 0.765086i | \(-0.722696\pi\) |
0.984548 | + | 0.175114i | \(0.0560296\pi\) | |||||||
\(194\) | −4.90192 | − | 18.2942i | −0.351938 | − | 1.31345i | ||||
\(195\) | −0.803848 | −0.0575647 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.3205 | −0.949047 | −0.474523 | − | 0.880243i | \(-0.657380\pi\) | ||||
−0.474523 | + | 0.880243i | \(0.657380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.73205 | − | 3.00000i | 0.122782 | − | 0.212664i | −0.798082 | − | 0.602549i | \(-0.794152\pi\) |
0.920864 | + | 0.389885i | \(0.127485\pi\) | |||||||
\(200\) | 0.732051 | + | 2.73205i | 0.0517638 | + | 0.193185i | ||||
\(201\) | 5.19615 | − | 3.00000i | 0.366508 | − | 0.211604i | ||||
\(202\) | 21.1244 | + | 5.66025i | 1.48630 | + | 0.398254i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 11.1962 | − | 19.3923i | 0.783887 | − | 1.35773i | ||||
\(205\) | 1.73205 | + | 3.00000i | 0.120972 | + | 0.209529i | ||||
\(206\) | 6.80385 | + | 6.80385i | 0.474047 | + | 0.474047i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.60770 | + | 0.928203i | 0.111474 | + | 0.0643593i | ||||
\(209\) | 1.60770i | 0.111207i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.19615i | − | 0.220032i | −0.993930 | − | 0.110016i | \(-0.964910\pi\) | ||
0.993930 | − | 0.110016i | \(-0.0350902\pi\) | |||||||
\(212\) | 4.00000i | 0.274721i | ||||||||
\(213\) | 11.1962 | + | 6.46410i | 0.767148 | + | 0.442913i | ||||
\(214\) | −2.39230 | + | 2.39230i | −0.163535 | + | 0.163535i | ||||
\(215\) | −1.00000 | − | 1.73205i | −0.0681994 | − | 0.118125i | ||||
\(216\) | 10.3923 | − | 10.3923i | 0.707107 | − | 0.707107i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.758330 | − | 2.83013i | 0.0513606 | − | 0.191680i | ||||
\(219\) | −19.3923 | + | 11.1962i | −1.31041 | + | 0.756566i | ||||
\(220\) | 0.464102 | − | 0.267949i | 0.0312897 | − | 0.0180651i | ||||
\(221\) | 1.50000 | − | 2.59808i | 0.100901 | − | 0.174766i | ||||
\(222\) | 22.3923 | − | 6.00000i | 1.50287 | − | 0.402694i | ||||
\(223\) | 13.7321 | 0.919566 | 0.459783 | − | 0.888031i | \(-0.347927\pi\) | ||||
0.459783 | + | 0.888031i | \(0.347927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.46410 | + | 2.00000i | −0.496505 | + | 0.133038i | ||||
\(227\) | 10.3301 | − | 17.8923i | 0.685635 | − | 1.18755i | −0.287602 | − | 0.957750i | \(-0.592858\pi\) |
0.973237 | − | 0.229804i | \(-0.0738085\pi\) | |||||||
\(228\) | −18.0000 | + | 10.3923i | −1.19208 | + | 0.688247i | ||||
\(229\) | 7.39230 | − | 4.26795i | 0.488497 | − | 0.282034i | −0.235454 | − | 0.971886i | \(-0.575658\pi\) |
0.723951 | + | 0.689852i | \(0.242324\pi\) | |||||||
\(230\) | 0.535898 | − | 2.00000i | 0.0353361 | − | 0.131876i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.8564 | + | 15.8564i | −1.04102 | + | 1.04102i | ||||
\(233\) | 4.53590 | + | 7.85641i | 0.297157 | + | 0.514690i | 0.975484 | − | 0.220069i | \(-0.0706283\pi\) |
−0.678328 | + | 0.734760i | \(0.737295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.50000 | + | 0.866025i | 0.0978492 | + | 0.0564933i | ||||
\(236\) | 6.92820i | 0.450988i | ||||||||
\(237\) | − | 25.3923i | − | 1.64941i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.9808i | 1.55119i | 0.631233 | + | 0.775593i | \(0.282549\pi\) | ||||
−0.631233 | + | 0.775593i | \(0.717451\pi\) | |||||||
\(240\) | 6.00000 | + | 3.46410i | 0.387298 | + | 0.223607i | ||||
\(241\) | 14.1962 | + | 8.19615i | 0.914455 | + | 0.527961i | 0.881862 | − | 0.471508i | \(-0.156290\pi\) |
0.0325928 | + | 0.999469i | \(0.489624\pi\) | |||||||
\(242\) | 10.9282 | + | 10.9282i | 0.702492 | + | 0.702492i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.46410 | + | 16.3923i | −0.605877 | + | 1.04941i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.19615 | + | 2.19615i | 0.522568 | + | 0.140022i | ||||
\(247\) | −2.41154 | + | 1.39230i | −0.153443 | + | 0.0885902i | ||||
\(248\) | −4.39230 | − | 16.3923i | −0.278912 | − | 1.04091i | ||||
\(249\) | 13.3923 | − | 23.1962i | 0.848703 | − | 1.47000i | ||||
\(250\) | 0.366025 | + | 1.36603i | 0.0231495 | + | 0.0863950i | ||||
\(251\) | 25.8564 | 1.63204 | 0.816021 | − | 0.578022i | \(-0.196175\pi\) | ||||
0.816021 | + | 0.578022i | \(0.196175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.392305 | −0.0246640 | ||||||||
\(254\) | −5.66025 | − | 21.1244i | −0.355156 | − | 1.32546i | ||||
\(255\) | 5.59808 | − | 9.69615i | 0.350565 | − | 0.607197i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −5.19615 | + | 3.00000i | −0.324127 | + | 0.187135i | −0.653231 | − | 0.757159i | \(-0.726587\pi\) |
0.329104 | + | 0.944294i | \(0.393253\pi\) | |||||||
\(258\) | −4.73205 | − | 1.26795i | −0.294605 | − | 0.0789391i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.803848 | + | 0.464102i | 0.0498525 | + | 0.0287824i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.53590 | − | 2.53590i | −0.156668 | − | 0.156668i | ||||
\(263\) | −9.92820 | − | 5.73205i | −0.612199 | − | 0.353453i | 0.161626 | − | 0.986852i | \(-0.448326\pi\) |
−0.773826 | + | 0.633399i | \(0.781659\pi\) | |||||||
\(264\) | 0.339746 | − | 1.26795i | 0.0209099 | − | 0.0780369i | ||||
\(265\) | 2.00000i | 0.122859i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.39230i | − | 0.268805i | ||||||
\(268\) | −6.92820 | −0.423207 | ||||||||
\(269\) | −10.3923 | − | 6.00000i | −0.633630 | − | 0.365826i | 0.148527 | − | 0.988908i | \(-0.452547\pi\) |
−0.782157 | + | 0.623082i | \(0.785880\pi\) | |||||||
\(270\) | 5.19615 | − | 5.19615i | 0.316228 | − | 0.316228i | ||||
\(271\) | 4.73205 | + | 8.19615i | 0.287452 | + | 0.497881i | 0.973201 | − | 0.229957i | \(-0.0738586\pi\) |
−0.685749 | + | 0.727838i | \(0.740525\pi\) | |||||||
\(272\) | −22.3923 | + | 12.9282i | −1.35773 | + | 0.783887i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.46410 | − | 27.8564i | 0.450923 | − | 1.68287i | ||||
\(275\) | 0.232051 | − | 0.133975i | 0.0139932 | − | 0.00807897i | ||||
\(276\) | −2.53590 | − | 4.39230i | −0.152643 | − | 0.264386i | ||||
\(277\) | −8.39230 | + | 14.5359i | −0.504245 | + | 0.873377i | 0.495743 | + | 0.868469i | \(0.334896\pi\) |
−0.999988 | + | 0.00490834i | \(0.998438\pi\) | |||||||
\(278\) | 9.46410 | − | 2.53590i | 0.567619 | − | 0.152093i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.92820 | −0.472957 | −0.236478 | − | 0.971637i | \(-0.575993\pi\) | ||||
−0.236478 | + | 0.971637i | \(0.575993\pi\) | |||||||
\(282\) | 4.09808 | − | 1.09808i | 0.244037 | − | 0.0653895i | ||||
\(283\) | 6.06218 | − | 10.5000i | 0.360359 | − | 0.624160i | −0.627661 | − | 0.778487i | \(-0.715988\pi\) |
0.988020 | + | 0.154327i | \(0.0493208\pi\) | |||||||
\(284\) | −7.46410 | − | 12.9282i | −0.442913 | − | 0.767148i | ||||
\(285\) | −9.00000 | + | 5.19615i | −0.533114 | + | 0.307794i | ||||
\(286\) | 0.0455173 | − | 0.169873i | 0.00269150 | − | 0.0100448i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.3923 | + | 21.4641i | 0.728959 | + | 1.26259i | ||||
\(290\) | −7.92820 | + | 7.92820i | −0.465560 | + | 0.465560i | ||||
\(291\) | −20.0885 | − | 11.5981i | −1.17761 | − | 0.679891i | ||||
\(292\) | 25.8564 | 1.51313 | ||||||||
\(293\) | − | 20.3205i | − | 1.18714i | −0.804784 | − | 0.593568i | \(-0.797719\pi\) | ||
0.804784 | − | 0.593568i | \(-0.202281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410i | 0.201688i | ||||||||
\(296\) | −25.8564 | − | 6.92820i | −1.50287 | − | 0.402694i | ||||
\(297\) | −1.20577 | − | 0.696152i | −0.0699660 | − | 0.0403949i | ||||
\(298\) | 3.07180 | + | 3.07180i | 0.177944 | + | 0.177944i | ||||
\(299\) | −0.339746 | − | 0.588457i | −0.0196480 | − | 0.0340314i | ||||
\(300\) | 3.00000 | + | 1.73205i | 0.173205 | + | 0.100000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −20.7583 | − | 5.56218i | −1.19451 | − | 0.320067i | ||||
\(303\) | 23.1962 | − | 13.3923i | 1.33258 | − | 0.769368i | ||||
\(304\) | 24.0000 | 1.37649 | ||||||||
\(305\) | −4.73205 | + | 8.19615i | −0.270956 | + | 0.469310i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.73205 | −0.0988534 | −0.0494267 | − | 0.998778i | \(-0.515739\pi\) | ||||
−0.0494267 | + | 0.998778i | \(0.515739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.7846 | 0.670403 | ||||||||
\(310\) | −2.19615 | − | 8.19615i | −0.124733 | − | 0.465510i | ||||
\(311\) | 3.92820 | − | 6.80385i | 0.222748 | − | 0.385811i | −0.732893 | − | 0.680343i | \(-0.761831\pi\) |
0.955641 | + | 0.294533i | \(0.0951640\pi\) | |||||||
\(312\) | 2.19615 | − | 0.588457i | 0.124333 | − | 0.0333148i | ||||
\(313\) | 15.1865 | − | 8.76795i | 0.858394 | − | 0.495594i | −0.00508040 | − | 0.999987i | \(-0.501617\pi\) |
0.863474 | + | 0.504393i | \(0.168284\pi\) | |||||||
\(314\) | −10.7321 | − | 2.87564i | −0.605645 | − | 0.162282i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.6603 | + | 25.3923i | −0.824704 | + | 1.42843i | ||||
\(317\) | 1.53590 | + | 2.66025i | 0.0862646 | + | 0.149415i | 0.905929 | − | 0.423429i | \(-0.139174\pi\) |
−0.819665 | + | 0.572844i | \(0.805840\pi\) | |||||||
\(318\) | 3.46410 | + | 3.46410i | 0.194257 | + | 0.194257i | ||||
\(319\) | 1.83975 | + | 1.06218i | 0.103006 | + | 0.0594705i | ||||
\(320\) | −4.00000 | − | 6.92820i | −0.223607 | − | 0.387298i | ||||
\(321\) | 4.14359i | 0.231273i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 38.7846i | − | 2.15803i | ||||||
\(324\) | − | 18.0000i | − | 1.00000i | ||||||
\(325\) | 0.401924 | + | 0.232051i | 0.0222947 | + | 0.0128719i | ||||
\(326\) | −20.7846 | + | 20.7846i | −1.15115 | + | 1.15115i | ||||
\(327\) | −1.79423 | − | 3.10770i | −0.0992211 | − | 0.171856i | ||||
\(328\) | −6.92820 | − | 6.92820i | −0.382546 | − | 0.382546i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.169873 | − | 0.633975i | 0.00935120 | − | 0.0348992i | ||||
\(331\) | 22.8564 | − | 13.1962i | 1.25630 | − | 0.725326i | 0.283948 | − | 0.958840i | \(-0.408356\pi\) |
0.972354 | + | 0.233513i | \(0.0750223\pi\) | |||||||
\(332\) | −26.7846 | + | 15.4641i | −1.47000 | + | 0.848703i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.09808 | + | 1.90192i | −0.388389 | + | 0.104069i | ||||
\(335\) | −3.46410 | −0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | −17.4641 | + | 4.67949i | −0.949922 | + | 0.254531i | ||||
\(339\) | −4.73205 | + | 8.19615i | −0.257010 | + | 0.445154i | ||||
\(340\) | −11.1962 | + | 6.46410i | −0.607197 | + | 0.350565i | ||||
\(341\) | −1.39230 | + | 0.803848i | −0.0753975 | + | 0.0435308i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | + | 4.00000i | 0.215666 | + | 0.215666i | ||||
\(345\) | −1.26795 | − | 2.19615i | −0.0682641 | − | 0.118237i | ||||
\(346\) | −14.3205 | + | 14.3205i | −0.769875 | + | 0.769875i | ||||
\(347\) | 29.6603 | + | 17.1244i | 1.59225 | + | 0.919284i | 0.992921 | + | 0.118778i | \(0.0378976\pi\) |
0.599325 | + | 0.800506i | \(0.295436\pi\) | |||||||
\(348\) | 27.4641i | 1.47223i | ||||||||
\(349\) | 5.32051i | 0.284800i | 0.989809 | + | 0.142400i | \(0.0454820\pi\) | ||||
−0.989809 | + | 0.142400i | \(0.954518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.41154i | − | 0.128719i | ||||||
\(352\) | −1.07180 | + | 1.07180i | −0.0571270 | + | 0.0571270i | ||||
\(353\) | −6.40192 | − | 3.69615i | −0.340740 | − | 0.196726i | 0.319859 | − | 0.947465i | \(-0.396364\pi\) |
−0.660599 | + | 0.750739i | \(0.729698\pi\) | |||||||
\(354\) | 6.00000 | + | 6.00000i | 0.318896 | + | 0.318896i | ||||
\(355\) | −3.73205 | − | 6.46410i | −0.198077 | − | 0.343079i | ||||
\(356\) | −2.53590 | + | 4.39230i | −0.134402 | + | 0.232792i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.73205 | + | 2.33975i | 0.461503 | + | 0.123659i | ||||
\(359\) | −21.9282 | + | 12.6603i | −1.15733 | + | 0.668183i | −0.950662 | − | 0.310229i | \(-0.899594\pi\) |
−0.206665 | + | 0.978412i | \(0.566261\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | −0.339746 | − | 1.26795i | −0.0178567 | − | 0.0666419i | ||||
\(363\) | 18.9282 | 0.993473 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.9282 | 0.676693 | ||||||||
\(366\) | 6.00000 | + | 22.3923i | 0.313625 | + | 1.17046i | ||||
\(367\) | 5.93782 | − | 10.2846i | 0.309952 | − | 0.536852i | −0.668400 | − | 0.743802i | \(-0.733020\pi\) |
0.978352 | + | 0.206950i | \(0.0663537\pi\) | |||||||
\(368\) | 5.85641i | 0.305286i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.9282 | − | 3.46410i | −0.672105 | − | 0.180090i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −18.0000 | − | 10.3923i | −0.933257 | − | 0.538816i | ||||
\(373\) | 1.80385 | + | 3.12436i | 0.0933997 | + | 0.161773i | 0.908940 | − | 0.416928i | \(-0.136893\pi\) |
−0.815540 | + | 0.578701i | \(0.803560\pi\) | |||||||
\(374\) | 1.73205 | + | 1.73205i | 0.0895622 | + | 0.0895622i | ||||
\(375\) | 1.50000 | + | 0.866025i | 0.0774597 | + | 0.0447214i | ||||
\(376\) | −4.73205 | − | 1.26795i | −0.244037 | − | 0.0653895i | ||||
\(377\) | 3.67949i | 0.189503i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.60770i | − | 0.288048i | −0.989574 | − | 0.144024i | \(-0.953996\pi\) | ||
0.989574 | − | 0.144024i | \(-0.0460042\pi\) | |||||||
\(380\) | 12.0000 | 0.615587 | ||||||||
\(381\) | −23.1962 | − | 13.3923i | −1.18837 | − | 0.686109i | ||||
\(382\) | 7.19615 | − | 7.19615i | 0.368187 | − | 0.368187i | ||||
\(383\) | 13.7321 | + | 23.7846i | 0.701675 | + | 1.21534i | 0.967878 | + | 0.251420i | \(0.0808975\pi\) |
−0.266203 | + | 0.963917i | \(0.585769\pi\) | |||||||
\(384\) | −18.9282 | − | 5.07180i | −0.965926 | − | 0.258819i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.46410 | + | 12.9282i | −0.176318 | + | 0.658028i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.3923 | + | 23.1962i | 0.679891 | + | 1.17761i | ||||
\(389\) | 10.4282 | − | 18.0622i | 0.528731 | − | 0.915789i | −0.470708 | − | 0.882289i | \(-0.656001\pi\) |
0.999439 | − | 0.0334996i | \(-0.0106653\pi\) | |||||||
\(390\) | 1.09808 | − | 0.294229i | 0.0556033 | − | 0.0148988i | ||||
\(391\) | 9.46410 | 0.478620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.39230 | −0.221562 | ||||||||
\(394\) | 18.1962 | − | 4.87564i | 0.916709 | − | 0.245631i | ||||
\(395\) | −7.33013 | + | 12.6962i | −0.368819 | + | 0.638813i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.7942 | + | 6.23205i | −0.541747 | + | 0.312778i | −0.745787 | − | 0.666185i | \(-0.767926\pi\) |
0.204040 | + | 0.978963i | \(0.434593\pi\) | |||||||
\(398\) | −1.26795 | + | 4.73205i | −0.0635566 | + | 0.237196i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | 5.03590 | + | 8.72243i | 0.251481 | + | 0.435577i | 0.963934 | − | 0.266142i | \(-0.0857491\pi\) |
−0.712453 | + | 0.701720i | \(0.752416\pi\) | |||||||
\(402\) | −6.00000 | + | 6.00000i | −0.299253 | + | 0.299253i | ||||
\(403\) | −2.41154 | − | 1.39230i | −0.120127 | − | 0.0693556i | ||||
\(404\) | −30.9282 | −1.53874 | ||||||||
\(405\) | − | 9.00000i | − | 0.447214i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.53590i | 0.125700i | ||||||||
\(408\) | −8.19615 | + | 30.5885i | −0.405770 | + | 1.51435i | ||||
\(409\) | 3.58846 | + | 2.07180i | 0.177438 | + | 0.102444i | 0.586088 | − | 0.810247i | \(-0.300667\pi\) |
−0.408651 | + | 0.912691i | \(0.634000\pi\) | |||||||
\(410\) | −3.46410 | − | 3.46410i | −0.171080 | − | 0.171080i | ||||
\(411\) | −17.6603 | − | 30.5885i | −0.871116 | − | 1.50882i | ||||
\(412\) | −11.7846 | − | 6.80385i | −0.580586 | − | 0.335202i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.3923 | + | 7.73205i | −0.657402 | + | 0.379551i | ||||
\(416\) | −2.53590 | − | 0.679492i | −0.124333 | − | 0.0333148i | ||||
\(417\) | 6.00000 | − | 10.3923i | 0.293821 | − | 0.508913i | ||||
\(418\) | −0.588457 | − | 2.19615i | −0.0287824 | − | 0.107417i | ||||
\(419\) | 24.2487 | 1.18463 | 0.592314 | − | 0.805708i | \(-0.298215\pi\) | ||||
0.592314 | + | 0.805708i | \(0.298215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 1.16987 | + | 4.36603i | 0.0569485 | + | 0.212535i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.46410 | − | 5.46410i | −0.0711031 | − | 0.265360i | ||||
\(425\) | −5.59808 | + | 3.23205i | −0.271547 | + | 0.156777i | ||||
\(426\) | −17.6603 | − | 4.73205i | −0.855642 | − | 0.229269i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.39230 | − | 4.14359i | 0.115636 | − | 0.200288i | ||||
\(429\) | −0.107695 | − | 0.186533i | −0.00519957 | − | 0.00900592i | ||||
\(430\) | 2.00000 | + | 2.00000i | 0.0964486 | + | 0.0964486i | ||||
\(431\) | −11.7679 | − | 6.79423i | −0.566842 | − | 0.327266i | 0.189045 | − | 0.981968i | \(-0.439461\pi\) |
−0.755887 | + | 0.654702i | \(0.772794\pi\) | |||||||
\(432\) | −10.3923 | + | 18.0000i | −0.500000 | + | 0.866025i | ||||
\(433\) | 31.8564i | 1.53092i | 0.643483 | + | 0.765461i | \(0.277489\pi\) | ||||
−0.643483 | + | 0.765461i | \(0.722511\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.7321i | 0.658401i | ||||||||
\(436\) | 4.14359i | 0.198442i | ||||||||
\(437\) | −7.60770 | − | 4.39230i | −0.363925 | − | 0.210112i | ||||
\(438\) | 22.3923 | − | 22.3923i | 1.06995 | − | 1.06995i | ||||
\(439\) | −19.8564 | − | 34.3923i | −0.947695 | − | 1.64146i | −0.750264 | − | 0.661138i | \(-0.770074\pi\) |
−0.197430 | − | 0.980317i | \(-0.563260\pi\) | |||||||
\(440\) | −0.535898 | + | 0.535898i | −0.0255480 | + | 0.0255480i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.09808 | + | 4.09808i | −0.0522302 | + | 0.194926i | ||||
\(443\) | 22.5167 | − | 13.0000i | 1.06980 | − | 0.617649i | 0.141672 | − | 0.989914i | \(-0.454752\pi\) |
0.928126 | + | 0.372265i | \(0.121419\pi\) | |||||||
\(444\) | −28.3923 | + | 16.3923i | −1.34744 | + | 0.777944i | ||||
\(445\) | −1.26795 | + | 2.19615i | −0.0601066 | + | 0.104108i | ||||
\(446\) | −18.7583 | + | 5.02628i | −0.888233 | + | 0.238001i | ||||
\(447\) | 5.32051 | 0.251651 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.9282 | 0.562927 | 0.281463 | − | 0.959572i | \(-0.409180\pi\) | ||||
0.281463 | + | 0.959572i | \(0.409180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.464102 | + | 0.803848i | −0.0218537 | + | 0.0378517i | ||||
\(452\) | 9.46410 | − | 5.46410i | 0.445154 | − | 0.257010i | ||||
\(453\) | −22.7942 | + | 13.1603i | −1.07097 | + | 0.618323i | ||||
\(454\) | −7.56218 | + | 28.2224i | −0.354911 | + | 1.32454i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.7846 | − | 20.7846i | 0.973329 | − | 0.973329i | ||||
\(457\) | −10.2679 | − | 17.7846i | −0.480314 | − | 0.831929i | 0.519431 | − | 0.854513i | \(-0.326144\pi\) |
−0.999745 | + | 0.0225837i | \(0.992811\pi\) | |||||||
\(458\) | −8.53590 | + | 8.53590i | −0.398856 | + | 0.398856i | ||||
\(459\) | 29.0885 | + | 16.7942i | 1.35773 | + | 0.783887i | ||||
\(460\) | 2.92820i | 0.136528i | ||||||||
\(461\) | − | 27.7128i | − | 1.29071i | −0.763881 | − | 0.645357i | \(-0.776709\pi\) | ||
0.763881 | − | 0.645357i | \(-0.223291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.3923i | 0.761815i | 0.924613 | + | 0.380908i | \(0.124388\pi\) | ||||
−0.924613 | + | 0.380908i | \(0.875612\pi\) | |||||||
\(464\) | 15.8564 | − | 27.4641i | 0.736115 | − | 1.27499i | ||||
\(465\) | −9.00000 | − | 5.19615i | −0.417365 | − | 0.240966i | ||||
\(466\) | −9.07180 | − | 9.07180i | −0.420243 | − | 0.420243i | ||||
\(467\) | 11.2583 | + | 19.5000i | 0.520973 | + | 0.902352i | 0.999703 | + | 0.0243897i | \(0.00776426\pi\) |
−0.478729 | + | 0.877963i | \(0.658902\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.36603 | − | 0.633975i | −0.109137 | − | 0.0292431i | ||||
\(471\) | −11.7846 | + | 6.80385i | −0.543006 | + | 0.313505i | ||||
\(472\) | −2.53590 | − | 9.46410i | −0.116724 | − | 0.435621i | ||||
\(473\) | 0.267949 | − | 0.464102i | 0.0123203 | − | 0.0213394i | ||||
\(474\) | 9.29423 | + | 34.6865i | 0.426898 | + | 1.59321i | ||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.77757 | − | 32.7583i | −0.401477 | − | 1.49833i | ||||
\(479\) | 12.5885 | − | 21.8038i | 0.575181 | − | 0.996243i | −0.420841 | − | 0.907135i | \(-0.638265\pi\) |
0.996022 | − | 0.0891086i | \(-0.0284018\pi\) | |||||||
\(480\) | −9.46410 | − | 2.53590i | −0.431975 | − | 0.115747i | ||||
\(481\) | −3.80385 | + | 2.19615i | −0.173441 | + | 0.100136i | ||||
\(482\) | −22.3923 | − | 6.00000i | −1.01994 | − | 0.273293i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.9282 | − | 10.9282i | −0.860373 | − | 0.496737i | ||||
\(485\) | 6.69615 | + | 11.5981i | 0.304057 | + | 0.526642i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0718 | − | 6.39230i | −0.501711 | − | 0.289663i | 0.227709 | − | 0.973729i | \(-0.426877\pi\) |
−0.729420 | + | 0.684066i | \(0.760210\pi\) | |||||||
\(488\) | 6.92820 | − | 25.8564i | 0.313625 | − | 1.17046i | ||||
\(489\) | 36.0000i | 1.62798i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.87564i | 0.445682i | 0.974855 | + | 0.222841i | \(0.0715330\pi\) | ||||
−0.974855 | + | 0.222841i | \(0.928467\pi\) | |||||||
\(492\) | −12.0000 | −0.541002 | ||||||||
\(493\) | −44.3827 | − | 25.6244i | −1.99890 | − | 1.15406i | ||||
\(494\) | 2.78461 | − | 2.78461i | 0.125286 | − | 0.125286i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0000 | + | 20.7846i | 0.538816 | + | 0.933257i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.80385 | + | 36.5885i | −0.439321 | + | 1.63957i | ||||
\(499\) | −22.1603 | + | 12.7942i | −0.992029 | + | 0.572748i | −0.905880 | − | 0.423534i | \(-0.860789\pi\) |
−0.0861490 | + | 0.996282i | \(0.527456\pi\) | |||||||
\(500\) | −1.00000 | − | 1.73205i | −0.0447214 | − | 0.0774597i | ||||
\(501\) | −4.50000 | + | 7.79423i | −0.201045 | + | 0.348220i | ||||
\(502\) | −35.3205 | + | 9.46410i | −1.57643 | + | 0.422404i | ||||
\(503\) | 15.5885 | 0.695055 | 0.347527 | − | 0.937670i | \(-0.387021\pi\) | ||||
0.347527 | + | 0.937670i | \(0.387021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.4641 | −0.688143 | ||||||||
\(506\) | 0.535898 | − | 0.143594i | 0.0238236 | − | 0.00638351i | ||||
\(507\) | −11.0718 | + | 19.1769i | −0.491716 | + | 0.851677i | ||||
\(508\) | 15.4641 | + | 26.7846i | 0.686109 | + | 1.18837i | ||||
\(509\) | −22.3923 | + | 12.9282i | −0.992521 | + | 0.573033i | −0.906027 | − | 0.423220i | \(-0.860900\pi\) |
−0.0864944 | + | 0.996252i | \(0.527566\pi\) | |||||||
\(510\) | −4.09808 | + | 15.2942i | −0.181466 | + | 0.677240i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | −15.5885 | − | 27.0000i | −0.688247 | − | 1.19208i | ||||
\(514\) | 6.00000 | − | 6.00000i | 0.264649 | − | 0.264649i | ||||
\(515\) | −5.89230 | − | 3.40192i | −0.259646 | − | 0.149907i | ||||
\(516\) | 6.92820 | 0.304997 | ||||||||
\(517\) | 0.464102i | 0.0204112i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.8038i | 1.08877i | ||||||||
\(520\) | −1.26795 | − | 0.339746i | −0.0556033 | − | 0.0148988i | ||||
\(521\) | 11.7846 | + | 6.80385i | 0.516293 | + | 0.298082i | 0.735417 | − | 0.677615i | \(-0.236986\pi\) |
−0.219124 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.1244 | − | 21.0000i | −0.530161 | − | 0.918266i | −0.999381 | − | 0.0351845i | \(-0.988798\pi\) |
0.469220 | − | 0.883081i | \(-0.344535\pi\) | |||||||
\(524\) | 4.39230 | + | 2.53590i | 0.191879 | + | 0.110781i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.6603 | + | 4.19615i | 0.682820 | + | 0.182961i | ||||
\(527\) | 33.5885 | − | 19.3923i | 1.46314 | − | 0.844742i | ||||
\(528\) | 1.85641i | 0.0807897i | ||||||||
\(529\) | −10.4282 | + | 18.0622i | −0.453400 | + | 0.785312i | ||||
\(530\) | −0.732051 | − | 2.73205i | −0.0317983 | − | 0.118673i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.60770 | −0.0696370 | ||||||||
\(534\) | 1.60770 | + | 6.00000i | 0.0695718 | + | 0.259645i | ||||
\(535\) | 1.19615 | − | 2.07180i | 0.0517142 | − | 0.0895716i | ||||
\(536\) | 9.46410 | − | 2.53590i | 0.408787 | − | 0.109534i | ||||
\(537\) | 9.58846 | − | 5.53590i | 0.413772 | − | 0.238892i | ||||
\(538\) | 16.3923 | + | 4.39230i | 0.706722 | + | 0.189366i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.19615 | + | 9.00000i | −0.223607 | + | 0.387298i | ||||
\(541\) | −3.89230 | − | 6.74167i | −0.167343 | − | 0.289847i | 0.770142 | − | 0.637873i | \(-0.220185\pi\) |
−0.937485 | + | 0.348026i | \(0.886852\pi\) | |||||||
\(542\) | −9.46410 | − | 9.46410i | −0.406518 | − | 0.406518i | ||||
\(543\) | −1.39230 | − | 0.803848i | −0.0597495 | − | 0.0344964i | ||||
\(544\) | 25.8564 | − | 25.8564i | 1.10858 | − | 1.10858i | ||||
\(545\) | 2.07180i | 0.0887460i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.4641i | − | 0.917739i | −0.888504 | − | 0.458869i | \(-0.848255\pi\) | ||
0.888504 | − | 0.458869i | \(-0.151745\pi\) | |||||||
\(548\) | 40.7846i | 1.74223i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.267949 | + | 0.267949i | −0.0114254 | + | 0.0114254i | ||||
\(551\) | 23.7846 | + | 41.1962i | 1.01326 | + | 1.75502i | ||||
\(552\) | 5.07180 | + | 5.07180i | 0.215870 | + | 0.215870i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.14359 | − | 22.9282i | 0.261016 | − | 0.974126i | ||||
\(555\) | −14.1962 | + | 8.19615i | −0.602593 | + | 0.347907i | ||||
\(556\) | −12.0000 | + | 6.92820i | −0.508913 | + | 0.293821i | ||||
\(557\) | 10.9282 | − | 18.9282i | 0.463043 | − | 0.802014i | −0.536068 | − | 0.844175i | \(-0.680091\pi\) |
0.999111 | + | 0.0421611i | \(0.0134243\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.928203 | 0.0392588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 10.8301 | − | 2.90192i | 0.456841 | − | 0.122410i | ||||
\(563\) | 9.58846 | − | 16.6077i | 0.404105 | − | 0.699931i | −0.590112 | − | 0.807322i | \(-0.700916\pi\) |
0.994217 | + | 0.107391i | \(0.0342496\pi\) | |||||||
\(564\) | −5.19615 | + | 3.00000i | −0.218797 | + | 0.126323i | ||||
\(565\) | 4.73205 | − | 2.73205i | 0.199079 | − | 0.114938i | ||||
\(566\) | −4.43782 | + | 16.5622i | −0.186536 | + | 0.696160i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.9282 | + | 14.9282i | 0.626373 | + | 0.626373i | ||||
\(569\) | −3.53590 | − | 6.12436i | −0.148233 | − | 0.256746i | 0.782342 | − | 0.622849i | \(-0.214025\pi\) |
−0.930574 | + | 0.366103i | \(0.880692\pi\) | |||||||
\(570\) | 10.3923 | − | 10.3923i | 0.435286 | − | 0.435286i | ||||
\(571\) | −5.78461 | − | 3.33975i | −0.242078 | − | 0.139764i | 0.374053 | − | 0.927407i | \(-0.377968\pi\) |
−0.616132 | + | 0.787643i | \(0.711301\pi\) | |||||||
\(572\) | 0.248711i | 0.0103991i | ||||||||
\(573\) | − | 12.4641i | − | 0.520695i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.46410i | 0.0610573i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.7942 | + | 9.69615i | 0.699153 | + | 0.403656i | 0.807032 | − | 0.590508i | \(-0.201073\pi\) |
−0.107879 | + | 0.994164i | \(0.534406\pi\) | |||||||
\(578\) | −24.7846 | − | 24.7846i | −1.03090 | − | 1.03090i | ||||
\(579\) | 8.19615 | + | 14.1962i | 0.340620 | + | 0.589972i | ||||
\(580\) | 7.92820 | − | 13.7321i | 0.329201 | − | 0.570192i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 31.6865 | + | 8.49038i | 1.31345 | + | 0.351938i | ||||
\(583\) | −0.464102 | + | 0.267949i | −0.0192211 | + | 0.0110973i | ||||
\(584\) | −35.3205 | + | 9.46410i | −1.46157 | + | 0.391627i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.43782 | + | 27.7583i | 0.307254 | + | 1.14669i | ||||
\(587\) | 20.5359 | 0.847607 | 0.423804 | − | 0.905754i | \(-0.360695\pi\) | ||||
0.423804 | + | 0.905754i | \(0.360695\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | −1.26795 | − | 4.73205i | −0.0522006 | − | 0.194815i | ||||
\(591\) | 11.5359 | − | 19.9808i | 0.474523 | − | 0.821899i | ||||
\(592\) | 37.8564 | 1.55589 | ||||||||
\(593\) | −26.3827 | + | 15.2321i | −1.08341 | + | 0.625505i | −0.931813 | − | 0.362938i | \(-0.881774\pi\) |
−0.151594 | + | 0.988443i | \(0.548440\pi\) | |||||||
\(594\) | 1.90192 | + | 0.509619i | 0.0780369 | + | 0.0209099i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.32051 | − | 3.07180i | −0.217937 | − | 0.125826i | ||||
\(597\) | 3.00000 | + | 5.19615i | 0.122782 | + | 0.212664i | ||||
\(598\) | 0.679492 | + | 0.679492i | 0.0277865 | + | 0.0277865i | ||||
\(599\) | −8.76795 | − | 5.06218i | −0.358249 | − | 0.206835i | 0.310064 | − | 0.950716i | \(-0.399650\pi\) |
−0.668312 | + | 0.743881i | \(0.732983\pi\) | |||||||
\(600\) | −4.73205 | − | 1.26795i | −0.193185 | − | 0.0517638i | ||||
\(601\) | 14.7846i | 0.603077i | 0.953454 | + | 0.301538i | \(0.0975001\pi\) | ||||
−0.953454 | + | 0.301538i | \(0.902500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30.3923 | 1.23665 | ||||||||
\(605\) | −9.46410 | − | 5.46410i | −0.384770 | − | 0.222147i | ||||
\(606\) | −26.7846 | + | 26.7846i | −1.08805 | + | 1.08805i | ||||
\(607\) | −14.5981 | − | 25.2846i | −0.592518 | − | 1.02627i | −0.993892 | − | 0.110357i | \(-0.964801\pi\) |
0.401374 | − | 0.915914i | \(-0.368533\pi\) | |||||||
\(608\) | −32.7846 | + | 8.78461i | −1.32959 | + | 0.356263i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.46410 | − | 12.9282i | 0.140257 | − | 0.523448i | ||||
\(611\) | −0.696152 | + | 0.401924i | −0.0281633 | + | 0.0162601i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.00000 | − | 8.66025i | 0.201948 | − | 0.349784i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
0.949156 | + | 0.314806i | \(0.101939\pi\) | |||||||
\(614\) | 2.36603 | − | 0.633975i | 0.0954850 | − | 0.0255851i | ||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.9282 | −0.923055 | −0.461527 | − | 0.887126i | \(-0.652698\pi\) | ||||
−0.461527 | + | 0.887126i | \(0.652698\pi\) | |||||||
\(618\) | −16.0981 | + | 4.31347i | −0.647560 | + | 0.173513i | ||||
\(619\) | 0.339746 | − | 0.588457i | 0.0136555 | − | 0.0236521i | −0.859117 | − | 0.511779i | \(-0.828987\pi\) |
0.872772 | + | 0.488127i | \(0.162320\pi\) | |||||||
\(620\) | 6.00000 | + | 10.3923i | 0.240966 | + | 0.417365i | ||||
\(621\) | 6.58846 | − | 3.80385i | 0.264386 | − | 0.152643i | ||||
\(622\) | −2.87564 | + | 10.7321i | −0.115303 | + | 0.430316i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.78461 | + | 1.60770i | −0.111474 | + | 0.0643593i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −17.5359 | + | 17.5359i | −0.700875 | + | 0.700875i | ||||
\(627\) | −2.41154 | − | 1.39230i | −0.0963077 | − | 0.0556033i | ||||
\(628\) | 15.7128 | 0.627009 | ||||||||
\(629\) | − | 61.1769i | − | 2.43928i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.9090i | − | 1.54894i | −0.632610 | − | 0.774471i | \(-0.718016\pi\) | ||
0.632610 | − | 0.774471i | \(-0.281984\pi\) | |||||||
\(632\) | 10.7321 | − | 40.0526i | 0.426898 | − | 1.59321i | ||||
\(633\) | 4.79423 | + | 2.76795i | 0.190553 | + | 0.110016i | ||||
\(634\) | −3.07180 | − | 3.07180i | −0.121997 | − | 0.121997i | ||||
\(635\) | 7.73205 | + | 13.3923i | 0.306837 | + | 0.531457i | ||||
\(636\) | −6.00000 | − | 3.46410i | −0.237915 | − | 0.137361i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.90192 | − | 0.777568i | −0.114888 | − | 0.0307842i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.00000 | + | 8.00000i | 0.316228 | + | 0.316228i | ||||
\(641\) | −4.46410 | + | 7.73205i | −0.176321 | + | 0.305398i | −0.940618 | − | 0.339468i | \(-0.889753\pi\) |
0.764296 | + | 0.644865i | \(0.223086\pi\) | |||||||
\(642\) | −1.51666 | − | 5.66025i | −0.0598578 | − | 0.223392i | ||||
\(643\) | −7.05256 | −0.278126 | −0.139063 | − | 0.990284i | \(-0.544409\pi\) | ||||
−0.139063 | + | 0.990284i | \(0.544409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.46410 | 0.136399 | ||||||||
\(646\) | 14.1962 | + | 52.9808i | 0.558540 | + | 2.08450i | ||||
\(647\) | −5.19615 | + | 9.00000i | −0.204282 | + | 0.353827i | −0.949904 | − | 0.312543i | \(-0.898819\pi\) |
0.745622 | + | 0.666369i | \(0.232153\pi\) | |||||||
\(648\) | 6.58846 | + | 24.5885i | 0.258819 | + | 0.965926i | ||||
\(649\) | −0.803848 | + | 0.464102i | −0.0315538 | + | 0.0182176i | ||||
\(650\) | −0.633975 | − | 0.169873i | −0.0248665 | − | 0.00666297i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.7846 | − | 36.0000i | 0.813988 | − | 1.40987i | ||||
\(653\) | −8.80385 | − | 15.2487i | −0.344521 | − | 0.596728i | 0.640745 | − | 0.767753i | \(-0.278625\pi\) |
−0.985267 | + | 0.171025i | \(0.945292\pi\) | |||||||
\(654\) | 3.58846 | + | 3.58846i | 0.140320 | + | 0.140320i | ||||
\(655\) | 2.19615 | + | 1.26795i | 0.0858108 | + | 0.0495429i | ||||
\(656\) | 12.0000 | + | 6.92820i | 0.468521 | + | 0.270501i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.1962i | 1.21523i | 0.794232 | + | 0.607615i | \(0.207874\pi\) | ||||
−0.794232 | + | 0.607615i | \(0.792126\pi\) | |||||||
\(660\) | 0.928203i | 0.0361303i | ||||||||
\(661\) | 34.3923 | + | 19.8564i | 1.33771 | + | 0.772325i | 0.986467 | − | 0.163961i | \(-0.0524272\pi\) |
0.351239 | + | 0.936286i | \(0.385761\pi\) | |||||||
\(662\) | −26.3923 | + | 26.3923i | −1.02577 | + | 1.02577i | ||||
\(663\) | 2.59808 | + | 4.50000i | 0.100901 | + | 0.174766i | ||||
\(664\) | 30.9282 | − | 30.9282i | 1.20025 | − | 1.20025i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0526 | + | 5.80385i | −0.389237 | + | 0.224726i | ||||
\(668\) | 9.00000 | − | 5.19615i | 0.348220 | − | 0.201045i | ||||
\(669\) | −11.8923 | + | 20.5981i | −0.459783 | + | 0.796368i | ||||
\(670\) | 4.73205 | − | 1.26795i | 0.182815 | − | 0.0489852i | ||||
\(671\) | −2.53590 | −0.0978973 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.1769 | −0.507933 | −0.253966 | − | 0.967213i | \(-0.581735\pi\) | ||||
−0.253966 | + | 0.967213i | \(0.581735\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.59808 | + | 4.50000i | −0.100000 | + | 0.173205i | ||||
\(676\) | 22.1436 | − | 12.7846i | 0.851677 | − | 0.491716i | ||||
\(677\) | 21.9904 | − | 12.6962i | 0.845159 | − | 0.487953i | −0.0138555 | − | 0.999904i | \(-0.504410\pi\) |
0.859015 | + | 0.511951i | \(0.171077\pi\) | |||||||
\(678\) | 3.46410 | − | 12.9282i | 0.133038 | − | 0.496505i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.9282 | − | 12.9282i | 0.495774 | − | 0.495774i | ||||
\(681\) | 17.8923 | + | 30.9904i | 0.685635 | + | 1.18755i | ||||
\(682\) | 1.60770 | − | 1.60770i | 0.0615618 | − | 0.0615618i | ||||
\(683\) | 6.33975 | + | 3.66025i | 0.242584 | + | 0.140056i | 0.616364 | − | 0.787462i | \(-0.288605\pi\) |
−0.373780 | + | 0.927517i | \(0.621938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3923i | 0.779150i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.7846i | 0.564068i | ||||||||
\(688\) | −6.92820 | − | 4.00000i | −0.264135 | − | 0.152499i | ||||
\(689\) | −0.803848 | − | 0.464102i | −0.0306242 | − | 0.0176809i | ||||
\(690\) | 2.53590 | + | 2.53590i | 0.0965400 | + | 0.0965400i | ||||
\(691\) | −11.3205 | − | 19.6077i | −0.430652 | − | 0.745912i | 0.566277 | − | 0.824215i | \(-0.308383\pi\) |
−0.996930 | + | 0.0783030i | \(0.975050\pi\) | |||||||
\(692\) | 14.3205 | − | 24.8038i | 0.544384 | − | 0.942901i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −46.7846 | − | 12.5359i | −1.77592 | − | 0.475856i | ||||
\(695\) | −6.00000 | + | 3.46410i | −0.227593 | + | 0.131401i | ||||
\(696\) | −10.0526 | − | 37.5167i | −0.381041 | − | 1.42207i | ||||
\(697\) | 11.1962 | − | 19.3923i | 0.424085 | − | 0.734536i | ||||
\(698\) | −1.94744 | − | 7.26795i | −0.0737117 | − | 0.275096i | ||||
\(699\) | −15.7128 | −0.594313 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.7846 | −1.42711 | −0.713553 | − | 0.700602i | \(-0.752915\pi\) | ||||
−0.713553 | + | 0.700602i | \(0.752915\pi\) | |||||||
\(702\) | 0.882686 | + | 3.29423i | 0.0333148 | + | 0.124333i | ||||
\(703\) | −28.3923 | + | 49.1769i | −1.07084 | + | 1.85474i | ||||
\(704\) | 1.07180 | − | 1.85641i | 0.0403949 | − | 0.0699660i | ||||
\(705\) | −2.59808 | + | 1.50000i | −0.0978492 | + | 0.0564933i | ||||
\(706\) | 10.0981 | + | 2.70577i | 0.380046 | + | 0.101833i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −10.3923 | − | 6.00000i | −0.390567 | − | 0.225494i | ||||
\(709\) | −10.5000 | − | 18.1865i | −0.394336 | − | 0.683010i | 0.598680 | − | 0.800988i | \(-0.295692\pi\) |
−0.993016 | + | 0.117978i | \(0.962359\pi\) | |||||||
\(710\) | 7.46410 | + | 7.46410i | 0.280123 | + | 0.280123i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.85641 | − | 6.92820i | 0.0695718 | − | 0.259645i | ||||
\(713\) | − | 8.78461i | − | 0.328986i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.124356i | 0.00465064i | ||||||||
\(716\) | −12.7846 | −0.477783 | ||||||||
\(717\) | −35.9711 | − | 20.7679i | −1.34337 | − | 0.775593i | ||||
\(718\) | 25.3205 | − | 25.3205i | 0.944953 | − | 0.944953i | ||||
\(719\) | 19.2679 | + | 33.3731i | 0.718573 | + | 1.24461i | 0.961565 | + | 0.274577i | \(0.0885378\pi\) |
−0.242992 | + | 0.970028i | \(0.578129\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.22243 | − | 23.2224i | 0.231575 | − | 0.864249i | ||||
\(723\) | −24.5885 | + | 14.1962i | −0.914455 | + | 0.527961i | ||||
\(724\) | 0.928203 | + | 1.60770i | 0.0344964 | + | 0.0597495i | ||||
\(725\) | 3.96410 | − | 6.86603i | 0.147223 | − | 0.254998i | ||||
\(726\) | −25.8564 | + | 6.92820i | −0.959621 | + | 0.257130i | ||||
\(727\) | 13.6077 | 0.504681 | 0.252341 | − | 0.967638i | \(-0.418800\pi\) | ||||
0.252341 | + | 0.967638i | \(0.418800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −17.6603 | + | 4.73205i | −0.653635 | + | 0.175141i | ||||
\(731\) | −6.46410 | + | 11.1962i | −0.239083 | + | 0.414105i | ||||
\(732\) | −16.3923 | − | 28.3923i | −0.605877 | − | 1.04941i | ||||
\(733\) | −9.99038 | + | 5.76795i | −0.369003 | + | 0.213044i | −0.673023 | − | 0.739622i | \(-0.735004\pi\) |
0.304020 | + | 0.952666i | \(0.401671\pi\) | |||||||
\(734\) | −4.34679 | + | 16.2224i | −0.160443 | + | 0.598781i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.14359 | − | 8.00000i | −0.0790139 | − | 0.294884i | ||||
\(737\) | −0.464102 | − | 0.803848i | −0.0170954 | − | 0.0296101i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.69615 | − | 2.13397i | −0.135965 | − | 0.0784995i | 0.430474 | − | 0.902603i | \(-0.358346\pi\) |
−0.566440 | + | 0.824103i | \(0.691680\pi\) | |||||||
\(740\) | 18.9282 | 0.695815 | ||||||||
\(741\) | − | 4.82309i | − | 0.177180i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.3923i | − | 1.11499i | −0.830182 | − | 0.557493i | \(-0.811763\pi\) | ||
0.830182 | − | 0.557493i | \(-0.188237\pi\) | |||||||
\(744\) | 28.3923 | + | 7.60770i | 1.04091 | + | 0.278912i | ||||
\(745\) | −2.66025 | − | 1.53590i | −0.0974642 | − | 0.0562710i | ||||
\(746\) | −3.60770 | − | 3.60770i | −0.132087 | − | 0.132087i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.00000 | − | 1.73205i | −0.109691 | − | 0.0633300i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.36603 | − | 0.633975i | −0.0863950 | − | 0.0231495i | ||||
\(751\) | 22.1603 | − | 12.7942i | 0.808639 | − | 0.466868i | −0.0378439 | − | 0.999284i | \(-0.512049\pi\) |
0.846483 | + | 0.532416i | \(0.178716\pi\) | |||||||
\(752\) | 6.92820 | 0.252646 | ||||||||
\(753\) | −22.3923 | + | 38.7846i | −0.816021 | + | 1.41339i | ||||
\(754\) | −1.34679 | − | 5.02628i | −0.0490471 | − | 0.183046i | ||||
\(755\) | 15.1962 | 0.553045 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.8564 | 1.37591 | 0.687957 | − | 0.725751i | \(-0.258508\pi\) | ||||
0.687957 | + | 0.725751i | \(0.258508\pi\) | |||||||
\(758\) | 2.05256 | + | 7.66025i | 0.0745523 | + | 0.278233i | ||||
\(759\) | 0.339746 | − | 0.588457i | 0.0123320 | − | 0.0213596i | ||||
\(760\) | −16.3923 | + | 4.39230i | −0.594611 | + | 0.159326i | ||||
\(761\) | 36.5885 | − | 21.1244i | 1.32633 | − | 0.765757i | 0.341600 | − | 0.939845i | \(-0.389031\pi\) |
0.984730 | + | 0.174088i | \(0.0556977\pi\) | |||||||
\(762\) | 36.5885 | + | 9.80385i | 1.32546 | + | 0.355156i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.19615 | + | 12.4641i | −0.260348 | + | 0.450935i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.4641 | − | 27.4641i | −0.992318 | − | 0.992318i | ||||
\(767\) | −1.39230 | − | 0.803848i | −0.0502732 | − | 0.0290253i | ||||
\(768\) | 27.7128 | 1.00000 | ||||||||
\(769\) | − | 18.0000i | − | 0.649097i | −0.945869 | − | 0.324548i | \(-0.894788\pi\) | ||
0.945869 | − | 0.324548i | \(-0.105212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 10.3923i | − | 0.374270i | ||||||
\(772\) | − | 18.9282i | − | 0.681241i | ||||||
\(773\) | −4.79423 | − | 2.76795i | −0.172436 | − | 0.0995562i | 0.411298 | − | 0.911501i | \(-0.365076\pi\) |
−0.583734 | + | 0.811945i | \(0.698409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.00000 | + | 5.19615i | 0.107763 | + | 0.186651i | ||||
\(776\) | −26.7846 | − | 26.7846i | −0.961511 | − | 0.961511i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.63397 | + | 28.4904i | −0.273691 | + | 1.02143i | ||||
\(779\) | −18.0000 | + | 10.3923i | −0.644917 | + | 0.372343i | ||||
\(780\) | −1.39230 | + | 0.803848i | −0.0498525 | + | 0.0287824i | ||||
\(781\) | 1.00000 | − | 1.73205i | 0.0357828 | − | 0.0619777i | ||||
\(782\) | −12.9282 | + | 3.46410i | −0.462312 | + | 0.123876i | ||||
\(783\) | −41.1962 | −1.47223 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.85641 | 0.280407 | ||||||||
\(786\) | 6.00000 | − | 1.60770i | 0.214013 | − | 0.0573446i | ||||
\(787\) | 16.3301 | − | 28.2846i | 0.582106 | − | 1.00824i | −0.413123 | − | 0.910675i | \(-0.635562\pi\) |
0.995229 | − | 0.0975623i | \(-0.0311045\pi\) | |||||||
\(788\) | −23.0718 | + | 13.3205i | −0.821899 | + | 0.474523i | ||||
\(789\) | 17.1962 | − | 9.92820i | 0.612199 | − | 0.353453i | ||||
\(790\) | 5.36603 | − | 20.0263i | 0.190915 | − | 0.712503i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.19615 | − | 3.80385i | −0.0779877 | − | 0.135079i | ||||
\(794\) | 12.4641 | − | 12.4641i | 0.442334 | − | 0.442334i | ||||
\(795\) | −3.00000 | − | 1.73205i | −0.106399 | − | 0.0614295i | ||||
\(796\) | − | 6.92820i | − | 0.245564i | ||||||
\(797\) | 22.1769i | 0.785547i | 0.919635 | + | 0.392773i | \(0.128484\pi\) | ||||
−0.919635 | + | 0.392773i | \(0.871516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.1962i | − | 0.396091i | ||||||
\(800\) | 4.00000 | + | 4.00000i | 0.141421 | + | 0.141421i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.0718 | − | 10.0718i | −0.355648 | − | 0.355648i | ||||
\(803\) | 1.73205 | + | 3.00000i | 0.0611227 | + | 0.105868i | ||||
\(804\) | 6.00000 | − | 10.3923i | 0.211604 | − | 0.366508i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.80385 | + | 1.01924i | 0.133985 | + | 0.0359011i | ||||
\(807\) | 18.0000 | − | 10.3923i | 0.633630 | − | 0.365826i | ||||
\(808\) | 42.2487 | − | 11.3205i | 1.48630 | − | 0.398254i | ||||
\(809\) | −3.96410 | + | 6.86603i | −0.139370 | + | 0.241397i | −0.927258 | − | 0.374422i | \(-0.877841\pi\) |
0.787888 | + | 0.615818i | \(0.211175\pi\) | |||||||
\(810\) | 3.29423 | + | 12.2942i | 0.115747 | + | 0.431975i | ||||
\(811\) | −29.0718 | −1.02085 | −0.510424 | − | 0.859923i | \(-0.670512\pi\) | ||||
−0.510424 | + | 0.859923i | \(0.670512\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.3923 | −0.574903 | ||||||||
\(814\) | −0.928203 | − | 3.46410i | −0.0325335 | − | 0.121417i | ||||
\(815\) | 10.3923 | − | 18.0000i | 0.364027 | − | 0.630512i | ||||
\(816\) | − | 44.7846i | − | 1.56777i | ||||||
\(817\) | 10.3923 | − | 6.00000i | 0.363581 | − | 0.209913i | ||||
\(818\) | −5.66025 | − | 1.51666i | −0.197906 | − | 0.0530288i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | + | 3.46410i | 0.209529 | + | 0.120972i | ||||
\(821\) | −13.8923 | − | 24.0622i | −0.484845 | − | 0.839776i | 0.515004 | − | 0.857188i | \(-0.327791\pi\) |
−0.999848 | + | 0.0174122i | \(0.994457\pi\) | |||||||
\(822\) | 35.3205 | + | 35.3205i | 1.23194 | + | 1.23194i | ||||
\(823\) | 9.58846 | + | 5.53590i | 0.334233 | + | 0.192969i | 0.657719 | − | 0.753264i | \(-0.271522\pi\) |
−0.323486 | + | 0.946233i | \(0.604855\pi\) | |||||||
\(824\) | 18.5885 | + | 4.98076i | 0.647560 | + | 0.173513i | ||||
\(825\) | 0.464102i | 0.0161579i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14.1436i | − | 0.491821i | −0.969293 | − | 0.245910i | \(-0.920913\pi\) | ||
0.969293 | − | 0.245910i | \(-0.0790869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.215390 | + | 0.124356i | 0.00748081 | + | 0.00431905i | 0.503736 | − | 0.863858i | \(-0.331959\pi\) |
−0.496255 | + | 0.868177i | \(0.665292\pi\) | |||||||
\(830\) | 15.4641 | − | 15.4641i | 0.536767 | − | 0.536767i | ||||
\(831\) | −14.5359 | − | 25.1769i | −0.504245 | − | 0.873377i | ||||
\(832\) | 3.71281 | 0.128719 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.39230 | + | 16.3923i | −0.152093 | + | 0.567619i | ||||
\(835\) | 4.50000 | − | 2.59808i | 0.155729 | − | 0.0899101i | ||||
\(836\) | 1.60770 | + | 2.78461i | 0.0556033 | + | 0.0963077i | ||||
\(837\) | 15.5885 | − | 27.0000i | 0.538816 | − | 0.933257i | ||||
\(838\) | −33.1244 | + | 8.87564i | −1.14426 | + | 0.306604i | ||||
\(839\) | −4.39230 | −0.151639 | −0.0758196 | − | 0.997122i | \(-0.524157\pi\) | ||||
−0.0758196 | + | 0.997122i | \(0.524157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8564 | 1.16746 | ||||||||
\(842\) | −25.9545 | + | 6.95448i | −0.894451 | + | 0.239667i | ||||
\(843\) | 6.86603 | − | 11.8923i | 0.236478 | − | 0.409593i | ||||
\(844\) | −3.19615 | − | 5.53590i | −0.110016 | − | 0.190553i | ||||
\(845\) | 11.0718 | − | 6.39230i | 0.380881 | − | 0.219902i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | + | 6.92820i | 0.137361 | + | 0.237915i | ||||
\(849\) | 10.5000 | + | 18.1865i | 0.360359 | + | 0.624160i | ||||
\(850\) | 6.46410 | − | 6.46410i | 0.221717 | − | 0.221717i | ||||
\(851\) | −12.0000 | − | 6.92820i | −0.411355 | − | 0.237496i | ||||
\(852\) | 25.8564 | 0.885826 | ||||||||
\(853\) | 2.78461i | 0.0953432i | 0.998863 | + | 0.0476716i | \(0.0151801\pi\) | ||||
−0.998863 | + | 0.0476716i | \(0.984820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.75129 | + | 6.53590i | −0.0598578 | + | 0.223392i | ||||
\(857\) | 49.9808 | + | 28.8564i | 1.70731 | + | 0.985716i | 0.937863 | + | 0.347006i | \(0.112802\pi\) |
0.769447 | + | 0.638710i | \(0.220532\pi\) | |||||||
\(858\) | 0.215390 | + | 0.215390i | 0.00735330 | + | 0.00735330i | ||||
\(859\) | 19.8564 | + | 34.3923i | 0.677492 | + | 1.17345i | 0.975734 | + | 0.218960i | \(0.0702664\pi\) |
−0.298242 | + | 0.954490i | \(0.596400\pi\) | |||||||
\(860\) | −3.46410 | − | 2.00000i | −0.118125 | − | 0.0681994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.5622 | + | 4.97372i | 0.632230 | + | 0.169406i | ||||
\(863\) | 34.5167 | − | 19.9282i | 1.17496 | − | 0.678364i | 0.220117 | − | 0.975473i | \(-0.429356\pi\) |
0.954843 | + | 0.297109i | \(0.0960226\pi\) | |||||||
\(864\) | 7.60770 | − | 28.3923i | 0.258819 | − | 0.965926i | ||||
\(865\) | 7.16025 | − | 12.4019i | 0.243456 | − | 0.421678i | ||||
\(866\) | −11.6603 | − | 43.5167i | −0.396232 | − | 1.47876i | ||||
\(867\) | −42.9282 | −1.45792 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.92820 | −0.133255 | ||||||||
\(870\) | −5.02628 | − | 18.7583i | −0.170407 | − | 0.635967i | ||||
\(871\) | 0.803848 | − | 1.39230i | 0.0272373 | − | 0.0471764i | ||||
\(872\) | −1.51666 | − | 5.66025i | −0.0513606 | − | 0.191680i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.0000 | + | 3.21539i | 0.405906 | + | 0.108762i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.3923 | + | 38.7846i | −0.756566 | + | 1.31041i | ||||
\(877\) | 9.19615 | + | 15.9282i | 0.310532 | + | 0.537857i | 0.978478 | − | 0.206353i | \(-0.0661595\pi\) |
−0.667946 | + | 0.744210i | \(0.732826\pi\) | |||||||
\(878\) | 39.7128 | + | 39.7128i | 1.34024 | + | 1.34024i | ||||
\(879\) | 30.4808 | + | 17.5981i | 1.02809 | + | 0.593568i | ||||
\(880\) | 0.535898 | − | 0.928203i | 0.0180651 | − | 0.0312897i | ||||
\(881\) | 29.0718i | 0.979454i | 0.871876 | + | 0.489727i | \(0.162904\pi\) | ||||
−0.871876 | + | 0.489727i | \(0.837096\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.6077i | 0.794462i | 0.917719 | + | 0.397231i | \(0.130029\pi\) | ||||
−0.917719 | + | 0.397231i | \(0.869971\pi\) | |||||||
\(884\) | − | 6.00000i | − | 0.201802i | ||||||
\(885\) | −5.19615 | − | 3.00000i | −0.174667 | − | 0.100844i | ||||
\(886\) | −26.0000 | + | 26.0000i | −0.873487 | + | 0.873487i | ||||
\(887\) | −4.26795 | − | 7.39230i | −0.143304 | − | 0.248209i | 0.785435 | − | 0.618944i | \(-0.212439\pi\) |
−0.928739 | + | 0.370735i | \(0.879106\pi\) | |||||||
\(888\) | 32.7846 | − | 32.7846i | 1.10018 | − | 1.10018i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.928203 | − | 3.46410i | 0.0311134 | − | 0.116117i | ||||
\(891\) | 2.08846 | − | 1.20577i | 0.0699660 | − | 0.0403949i | ||||
\(892\) | 23.7846 | − | 13.7321i | 0.796368 | − | 0.459783i | ||||
\(893\) | −5.19615 | + | 9.00000i | −0.173883 | + | 0.301174i | ||||
\(894\) | −7.26795 | + | 1.94744i | −0.243077 | + | 0.0651322i | ||||
\(895\) | −6.39230 | −0.213671 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.17691 | 0.0392960 | ||||||||
\(898\) | −16.2942 | + | 4.36603i | −0.543745 | + | 0.145696i | ||||
\(899\) | −23.7846 | + | 41.1962i | −0.793261 | + | 1.37397i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.1962 | − | 6.46410i | 0.372998 | − | 0.215350i | ||||
\(902\) | 0.339746 | − | 1.26795i | 0.0113123 | − | 0.0422181i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.9282 | + | 10.9282i | −0.363467 | + | 0.363467i | ||||
\(905\) | 0.464102 | + | 0.803848i | 0.0154273 | + | 0.0267208i | ||||
\(906\) | 26.3205 | − | 26.3205i | 0.874440 | − | 0.874440i | ||||
\(907\) | −28.0526 | − | 16.1962i | −0.931470 | − | 0.537784i | −0.0441938 | − | 0.999023i | \(-0.514072\pi\) |
−0.887276 | + | 0.461239i | \(0.847405\pi\) | |||||||
\(908\) | − | 41.3205i | − | 1.37127i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.2487i | 0.670870i | 0.942063 | + | 0.335435i | \(0.108883\pi\) | ||||
−0.942063 | + | 0.335435i | \(0.891117\pi\) | |||||||
\(912\) | −20.7846 | + | 36.0000i | −0.688247 | + | 1.19208i | ||||
\(913\) | −3.58846 | − | 2.07180i | −0.118761 | − | 0.0685665i | ||||
\(914\) | 20.5359 | + | 20.5359i | 0.679267 | + | 0.679267i | ||||
\(915\) | −8.19615 | − | 14.1962i | −0.270956 | − | 0.469310i | ||||
\(916\) | 8.53590 | − | 14.7846i | 0.282034 | − | 0.488497i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −45.8827 | − | 12.2942i | −1.51435 | − | 0.405770i | ||||
\(919\) | 5.55256 | − | 3.20577i | 0.183162 | − | 0.105749i | −0.405615 | − | 0.914044i | \(-0.632943\pi\) |
0.588777 | + | 0.808295i | \(0.299609\pi\) | |||||||
\(920\) | −1.07180 | − | 4.00000i | −0.0353361 | − | 0.131876i | ||||
\(921\) | 1.50000 | − | 2.59808i | 0.0494267 | − | 0.0856095i | ||||
\(922\) | 10.1436 | + | 37.8564i | 0.334061 | + | 1.24673i | ||||
\(923\) | 3.46410 | 0.114022 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.46410 | 0.311178 | ||||||||
\(926\) | −6.00000 | − | 22.3923i | −0.197172 | − | 0.735857i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.6077 | + | 43.3205i | −0.381041 | + | 1.42207i | ||||
\(929\) | 47.1962 | − | 27.2487i | 1.54846 | − | 0.894001i | 0.550196 | − | 0.835036i | \(-0.314553\pi\) |
0.998260 | − | 0.0589653i | \(-0.0187801\pi\) | |||||||
\(930\) | 14.1962 | + | 3.80385i | 0.465510 | + | 0.124733i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.7128 | + | 9.07180i | 0.514690 | + | 0.297157i | ||||
\(933\) | 6.80385 | + | 11.7846i | 0.222748 | + | 0.385811i | ||||
\(934\) | −22.5167 | − | 22.5167i | −0.736768 | − | 0.736768i | ||||
\(935\) | −1.50000 | − | 0.866025i | −0.0490552 | − | 0.0283221i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.3923i | 0.829530i | 0.909928 | + | 0.414765i | \(0.136136\pi\) | ||||
−0.909928 | + | 0.414765i | \(0.863864\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.3731i | 0.991188i | ||||||||
\(940\) | 3.46410 | 0.112987 | ||||||||
\(941\) | 33.8038 | + | 19.5167i | 1.10197 | + | 0.636225i | 0.936739 | − | 0.350029i | \(-0.113828\pi\) |
0.165235 | + | 0.986254i | \(0.447162\pi\) | |||||||
\(942\) | 13.6077 | − | 13.6077i | 0.443363 | − | 0.443363i | ||||
\(943\) | −2.53590 | − | 4.39230i | −0.0825802 | − | 0.143033i | ||||
\(944\) | 6.92820 | + | 12.0000i | 0.225494 | + | 0.390567i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.196152 | + | 0.732051i | −0.00637747 | + | 0.0238010i | ||||
\(947\) | −19.7321 | + | 11.3923i | −0.641205 | + | 0.370200i | −0.785079 | − | 0.619396i | \(-0.787378\pi\) |
0.143873 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(948\) | −25.3923 | − | 43.9808i | −0.824704 | − | 1.42843i | ||||
\(949\) | −3.00000 | + | 5.19615i | −0.0973841 | + | 0.168674i | ||||
\(950\) | −8.19615 | + | 2.19615i | −0.265918 | + | 0.0712526i | ||||
\(951\) | −5.32051 | −0.172529 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.3205 | 0.690639 | 0.345320 | − | 0.938485i | \(-0.387771\pi\) | ||||
0.345320 | + | 0.938485i | \(0.387771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.59808 | + | 6.23205i | −0.116431 | + | 0.201664i | ||||
\(956\) | 23.9808 | + | 41.5359i | 0.775593 | + | 1.34337i | ||||
\(957\) | −3.18653 | + | 1.83975i | −0.103006 | + | 0.0594705i | ||||
\(958\) | −9.21539 | + | 34.3923i | −0.297736 | + | 1.11116i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.8564 | 0.447214 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 4.39230 | − | 4.39230i | 0.141614 | − | 0.141614i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32.7846 | 1.05592 | ||||||||
\(965\) | − | 9.46410i | − | 0.304660i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.1769i | − | 1.00258i | −0.865279 | − | 0.501291i | \(-0.832859\pi\) | ||
0.865279 | − | 0.501291i | \(-0.167141\pi\) | |||||||
\(968\) | 29.8564 | + | 8.00000i | 0.959621 | + | 0.257130i | ||||
\(969\) | 58.1769 | + | 33.5885i | 1.86891 | + | 1.07902i | ||||
\(970\) | −13.3923 | − | 13.3923i | −0.430001 | − | 0.430001i | ||||
\(971\) | 7.39230 | + | 12.8038i | 0.237230 | + | 0.410895i | 0.959919 | − | 0.280279i | \(-0.0904271\pi\) |
−0.722688 | + | 0.691174i | \(0.757094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17.4641 | + | 4.67949i | 0.559586 | + | 0.149941i | ||||
\(975\) | −0.696152 | + | 0.401924i | −0.0222947 | + | 0.0128719i | ||||
\(976\) | 37.8564i | 1.21175i | ||||||||
\(977\) | 2.12436 | − | 3.67949i | 0.0679642 | − | 0.117717i | −0.830041 | − | 0.557703i | \(-0.811683\pi\) |
0.898005 | + | 0.439985i | \(0.145016\pi\) | |||||||
\(978\) | −13.1769 | − | 49.1769i | −0.421351 | − | 1.57250i | ||||
\(979\) | −0.679492 | −0.0217167 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.61474 | − | 13.4904i | −0.115351 | − | 0.430495i | ||||
\(983\) | −13.7942 | + | 23.8923i | −0.439968 | + | 0.762046i | −0.997686 | − | 0.0679837i | \(-0.978343\pi\) |
0.557719 | + | 0.830030i | \(0.311677\pi\) | |||||||
\(984\) | 16.3923 | − | 4.39230i | 0.522568 | − | 0.140022i | ||||
\(985\) | −11.5359 | + | 6.66025i | −0.367564 | + | 0.212213i | ||||
\(986\) | 70.0070 | + | 18.7583i | 2.22948 | + | 0.597387i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.78461 | + | 4.82309i | −0.0885902 | + | 0.153443i | ||||
\(989\) | 1.46410 | + | 2.53590i | 0.0465557 | + | 0.0806369i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.8564 | + | 23.5885i | 1.29785 | + | 0.749312i | 0.980032 | − | 0.198841i | \(-0.0637177\pi\) |
0.317815 | + | 0.948153i | \(0.397051\pi\) | |||||||
\(992\) | −24.0000 | − | 24.0000i | −0.762001 | − | 0.762001i | ||||
\(993\) | 45.7128i | 1.45065i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3.46410i | − | 0.109819i | ||||||
\(996\) | − | 53.5692i | − | 1.69741i | ||||||
\(997\) | 4.79423 | + | 2.76795i | 0.151835 | + | 0.0876618i | 0.573993 | − | 0.818861i | \(-0.305394\pi\) |
−0.422158 | + | 0.906522i | \(0.638727\pi\) | |||||||
\(998\) | 25.5885 | − | 25.5885i | 0.809988 | − | 0.809988i | ||||
\(999\) | −24.5885 | − | 42.5885i | −0.777944 | − | 1.34744i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))