Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (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: | \(11.7380090971\) |
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 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.79 |
Dual form | 1470.2.n.a.949.2 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.86603 | + | 1.23205i | −0.834512 | + | 0.550990i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −2.23205 | + | 0.133975i | −0.705836 | + | 0.0423665i | ||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 6.00000i | 1.66410i | 0.554700 | + | 0.832050i | \(0.312833\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | − | 2.00000i | 0.258199 | − | 0.516398i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.73205 | + | 1.00000i | −0.420084 | + | 0.242536i | −0.695113 | − | 0.718900i | \(-0.744646\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | −3.46410 | − | 2.00000i | −0.722315 | − | 0.417029i | 0.0932891 | − | 0.995639i | \(-0.470262\pi\) |
−0.815604 | + | 0.578610i | \(0.803595\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 1.96410 | − | 4.59808i | 0.392820 | − | 0.919615i | ||||
\(26\) | −3.00000 | + | 5.19615i | −0.588348 | + | 1.01905i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 1.86603 | − | 1.23205i | 0.340688 | − | 0.224941i | ||||
\(31\) | −4.00000 | − | 6.92820i | −0.718421 | − | 1.24434i | −0.961625 | − | 0.274367i | \(-0.911532\pi\) |
0.243204 | − | 0.969975i | \(-0.421802\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 1.73205 | + | 1.00000i | 0.301511 | + | 0.174078i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.73205 | − | 1.00000i | −0.284747 | − | 0.164399i | 0.350823 | − | 0.936442i | \(-0.385902\pi\) |
−0.635571 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | − | 5.19615i | −0.480384 | − | 0.832050i | ||||
\(40\) | −1.23205 | − | 1.86603i | −0.194804 | − | 0.295045i | ||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 1.00000 | − | 1.73205i | 0.150756 | − | 0.261116i | ||||
\(45\) | 0.133975 | + | 2.23205i | 0.0199718 | + | 0.332734i | ||||
\(46\) | −2.00000 | − | 3.46410i | −0.294884 | − | 0.510754i | ||||
\(47\) | −6.92820 | − | 4.00000i | −1.01058 | − | 0.583460i | −0.0992202 | − | 0.995066i | \(-0.531635\pi\) |
−0.911362 | + | 0.411606i | \(0.864968\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 1.00000 | − | 1.73205i | 0.140028 | − | 0.242536i | ||||
\(52\) | −5.19615 | + | 3.00000i | −0.720577 | + | 0.416025i | ||||
\(53\) | −5.19615 | + | 3.00000i | −0.713746 | + | 0.412082i | −0.812447 | − | 0.583036i | \(-0.801865\pi\) |
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 4.00000 | + | 2.00000i | 0.539360 | + | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.00000 | − | 8.66025i | −0.650945 | − | 1.12747i | −0.982894 | − | 0.184172i | \(-0.941040\pi\) |
0.331949 | − | 0.943297i | \(-0.392294\pi\) | |||||||
\(60\) | 2.23205 | − | 0.133975i | 0.288157 | − | 0.0172960i | ||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | − | 8.00000i | − | 1.01600i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −7.39230 | − | 11.1962i | −0.916903 | − | 1.38871i | ||||
\(66\) | 1.00000 | + | 1.73205i | 0.123091 | + | 0.213201i | ||||
\(67\) | −6.92820 | + | 4.00000i | −0.846415 | + | 0.488678i | −0.859440 | − | 0.511237i | \(-0.829187\pi\) |
0.0130248 | + | 0.999915i | \(0.495854\pi\) | |||||||
\(68\) | −1.73205 | − | 1.00000i | −0.210042 | − | 0.121268i | ||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −3.46410 | + | 2.00000i | −0.405442 | + | 0.234082i | −0.688830 | − | 0.724923i | \(-0.741875\pi\) |
0.283387 | + | 0.959006i | \(0.408542\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | 0.598076 | + | 4.96410i | 0.0690599 | + | 0.573205i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 6.00000i | − | 0.679366i | ||||||
\(79\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(80\) | −0.133975 | − | 2.23205i | −0.0149788 | − | 0.249551i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.73205 | − | 1.00000i | −0.191273 | − | 0.110432i | ||||
\(83\) | − | 4.00000i | − | 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | − | 4.00000i | 0.216930 | − | 0.433861i | ||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.73205 | − | 1.00000i | 0.184637 | − | 0.106600i | ||||
\(89\) | 5.00000 | − | 8.66025i | 0.529999 | − | 0.917985i | −0.469389 | − | 0.882992i | \(-0.655526\pi\) |
0.999388 | − | 0.0349934i | \(-0.0111410\pi\) | |||||||
\(90\) | −1.00000 | + | 2.00000i | −0.105409 | + | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 4.00000i | − | 0.417029i | ||||||
\(93\) | 6.92820 | + | 4.00000i | 0.718421 | + | 0.414781i | ||||
\(94\) | −4.00000 | − | 6.92820i | −0.412568 | − | 0.714590i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 8.00000i | 0.812277i | 0.913812 | + | 0.406138i | \(0.133125\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 4.96410 | − | 0.598076i | 0.496410 | − | 0.0598076i | ||||
\(101\) | −4.00000 | − | 6.92820i | −0.398015 | − | 0.689382i | 0.595466 | − | 0.803380i | \(-0.296967\pi\) |
−0.993481 | + | 0.113998i | \(0.963634\pi\) | |||||||
\(102\) | 1.73205 | − | 1.00000i | 0.171499 | − | 0.0990148i | ||||
\(103\) | 12.1244 | + | 7.00000i | 1.19465 | + | 0.689730i | 0.959357 | − | 0.282194i | \(-0.0910623\pi\) |
0.235291 | + | 0.971925i | \(0.424396\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −10.3923 | − | 6.00000i | −1.00466 | − | 0.580042i | −0.0950377 | − | 0.995474i | \(-0.530297\pi\) |
−0.909624 | + | 0.415432i | \(0.863630\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | 5.00000 | + | 8.66025i | 0.478913 | + | 0.829502i | 0.999708 | − | 0.0241802i | \(-0.00769755\pi\) |
−0.520794 | + | 0.853682i | \(0.674364\pi\) | |||||||
\(110\) | 2.46410 | + | 3.73205i | 0.234943 | + | 0.355837i | ||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.92820 | − | 0.535898i | 0.832559 | − | 0.0499728i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.19615 | + | 3.00000i | 0.480384 | + | 0.277350i | ||||
\(118\) | − | 10.0000i | − | 0.920575i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.00000 | + | 1.00000i | 0.182574 | + | 0.0912871i | ||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 1.73205 | − | 1.00000i | 0.156813 | − | 0.0905357i | ||||
\(123\) | 1.73205 | − | 1.00000i | 0.156174 | − | 0.0901670i | ||||
\(124\) | 4.00000 | − | 6.92820i | 0.359211 | − | 0.622171i | ||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −2.00000 | − | 3.46410i | −0.176090 | − | 0.304997i | ||||
\(130\) | −0.803848 | − | 13.3923i | −0.0705021 | − | 1.17458i | ||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 2.00000i | 0.174078i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | −1.23205 | − | 1.86603i | −0.106038 | − | 0.160602i | ||||
\(136\) | −1.00000 | − | 1.73205i | −0.0857493 | − | 0.148522i | ||||
\(137\) | −15.5885 | + | 9.00000i | −1.33181 | + | 0.768922i | −0.985577 | − | 0.169226i | \(-0.945873\pi\) |
−0.346235 | + | 0.938148i | \(0.612540\pi\) | |||||||
\(138\) | 3.46410 | + | 2.00000i | 0.294884 | + | 0.170251i | ||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 10.3923 | + | 6.00000i | 0.872103 | + | 0.503509i | ||||
\(143\) | 10.3923 | − | 6.00000i | 0.869048 | − | 0.501745i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 2.00000i | − | 0.164399i | ||||||
\(149\) | −10.0000 | + | 17.3205i | −0.819232 | + | 1.41895i | 0.0870170 | + | 0.996207i | \(0.472267\pi\) |
−0.906249 | + | 0.422744i | \(0.861067\pi\) | |||||||
\(150\) | −1.96410 | + | 4.59808i | −0.160368 | + | 0.375431i | ||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | + | 8.00000i | 1.28515 | + | 0.642575i | ||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | −19.0526 | + | 11.0000i | −1.52056 | + | 0.877896i | −0.520854 | + | 0.853646i | \(0.674386\pi\) |
−0.999706 | + | 0.0242497i | \(0.992280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 1.00000 | − | 2.00000i | 0.0790569 | − | 0.158114i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 13.8564 | + | 8.00000i | 1.08532 | + | 0.626608i | 0.932326 | − | 0.361619i | \(-0.117776\pi\) |
0.152992 | + | 0.988227i | \(0.451109\pi\) | |||||||
\(164\) | −1.00000 | − | 1.73205i | −0.0780869 | − | 0.135250i | ||||
\(165\) | −4.46410 | + | 0.267949i | −0.347530 | + | 0.0208598i | ||||
\(166\) | 2.00000 | − | 3.46410i | 0.155230 | − | 0.268866i | ||||
\(167\) | − | 12.0000i | − | 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | 3.73205 | − | 2.46410i | 0.286235 | − | 0.188988i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.46410 | + | 2.00000i | −0.264135 | + | 0.152499i | ||||
\(173\) | 12.1244 | + | 7.00000i | 0.921798 | + | 0.532200i | 0.884208 | − | 0.467093i | \(-0.154699\pi\) |
0.0375896 | + | 0.999293i | \(0.488032\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 8.66025 | + | 5.00000i | 0.650945 | + | 0.375823i | ||||
\(178\) | 8.66025 | − | 5.00000i | 0.649113 | − | 0.374766i | ||||
\(179\) | 5.00000 | + | 8.66025i | 0.373718 | + | 0.647298i | 0.990134 | − | 0.140122i | \(-0.0447496\pi\) |
−0.616417 | + | 0.787420i | \(0.711416\pi\) | |||||||
\(180\) | −1.86603 | + | 1.23205i | −0.139085 | + | 0.0918316i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | 4.46410 | − | 0.267949i | 0.328207 | − | 0.0197000i | ||||
\(186\) | 4.00000 | + | 6.92820i | 0.293294 | + | 0.508001i | ||||
\(187\) | 3.46410 | + | 2.00000i | 0.253320 | + | 0.146254i | ||||
\(188\) | − | 8.00000i | − | 0.583460i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 3.46410 | − | 2.00000i | 0.249351 | − | 0.143963i | −0.370116 | − | 0.928986i | \(-0.620682\pi\) |
0.619467 | + | 0.785022i | \(0.287349\pi\) | |||||||
\(194\) | −4.00000 | + | 6.92820i | −0.287183 | + | 0.497416i | ||||
\(195\) | 12.0000 | + | 6.00000i | 0.859338 | + | 0.429669i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.0000i | 1.56744i | 0.621117 | + | 0.783718i | \(0.286679\pi\) | ||||
−0.621117 | + | 0.783718i | \(0.713321\pi\) | |||||||
\(198\) | −1.73205 | − | 1.00000i | −0.123091 | − | 0.0710669i | ||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 4.59808 | + | 1.96410i | 0.325133 | + | 0.138883i | ||||
\(201\) | 4.00000 | − | 6.92820i | 0.282138 | − | 0.488678i | ||||
\(202\) | − | 8.00000i | − | 0.562878i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | 3.73205 | − | 2.46410i | 0.260658 | − | 0.172100i | ||||
\(206\) | 7.00000 | + | 12.1244i | 0.487713 | + | 0.844744i | ||||
\(207\) | −3.46410 | + | 2.00000i | −0.240772 | + | 0.139010i | ||||
\(208\) | −5.19615 | − | 3.00000i | −0.360288 | − | 0.208013i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | −5.19615 | − | 3.00000i | −0.356873 | − | 0.206041i | ||||
\(213\) | −10.3923 | + | 6.00000i | −0.712069 | + | 0.411113i | ||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | −4.92820 | − | 7.46410i | −0.336101 | − | 0.509048i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0000i | 0.677285i | ||||||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | 0.267949 | + | 4.46410i | 0.0180651 | + | 0.300970i | ||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | 1.73205 | + | 1.00000i | 0.116248 | + | 0.0671156i | ||||
\(223\) | 26.0000i | 1.74109i | 0.492090 | + | 0.870544i | \(0.336233\pi\) | ||||
−0.492090 | + | 0.870544i | \(0.663767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | 24.2487 | − | 14.0000i | 1.60944 | − | 0.929213i | 0.619949 | − | 0.784642i | \(-0.287153\pi\) |
0.989494 | − | 0.144571i | \(-0.0461801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 8.00000 | + | 4.00000i | 0.527504 | + | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1244 | − | 7.00000i | −0.794293 | − | 0.458585i | 0.0471787 | − | 0.998886i | \(-0.484977\pi\) |
−0.841472 | + | 0.540301i | \(0.818310\pi\) | |||||||
\(234\) | 3.00000 | + | 5.19615i | 0.196116 | + | 0.339683i | ||||
\(235\) | 17.8564 | − | 1.07180i | 1.16482 | − | 0.0699163i | ||||
\(236\) | 5.00000 | − | 8.66025i | 0.325472 | − | 0.563735i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 1.23205 | + | 1.86603i | 0.0795285 | + | 0.120451i | ||||
\(241\) | 11.0000 | + | 19.0526i | 0.708572 | + | 1.22728i | 0.965387 | + | 0.260822i | \(0.0839937\pi\) |
−0.256814 | + | 0.966461i | \(0.582673\pi\) | |||||||
\(242\) | 6.06218 | − | 3.50000i | 0.389692 | − | 0.224989i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.92820 | − | 4.00000i | 0.439941 | − | 0.254000i | ||||
\(249\) | 2.00000 | + | 3.46410i | 0.126745 | + | 0.219529i | ||||
\(250\) | −3.76795 | + | 10.5263i | −0.238306 | + | 0.665740i | ||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000i | 0.502956i | ||||||||
\(254\) | −1.00000 | + | 1.73205i | −0.0627456 | + | 0.108679i | ||||
\(255\) | 0.267949 | + | 4.46410i | 0.0167796 | + | 0.279553i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −15.5885 | − | 9.00000i | −0.972381 | − | 0.561405i | −0.0724199 | − | 0.997374i | \(-0.523072\pi\) |
−0.899961 | + | 0.435970i | \(0.856405\pi\) | |||||||
\(258\) | − | 4.00000i | − | 0.249029i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | − | 12.0000i | 0.372104 | − | 0.744208i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.5885 | + | 9.00000i | −0.963058 | + | 0.556022i | ||||
\(263\) | 3.46410 | − | 2.00000i | 0.213606 | − | 0.123325i | −0.389380 | − | 0.921077i | \(-0.627311\pi\) |
0.602986 | + | 0.797752i | \(0.293977\pi\) | |||||||
\(264\) | −1.00000 | + | 1.73205i | −0.0615457 | + | 0.106600i | ||||
\(265\) | 6.00000 | − | 12.0000i | 0.368577 | − | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | −6.92820 | − | 4.00000i | −0.423207 | − | 0.244339i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | −0.133975 | − | 2.23205i | −0.00815343 | − | 0.135838i | ||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | −9.92820 | + | 1.19615i | −0.598693 | + | 0.0721307i | ||||
\(276\) | 2.00000 | + | 3.46410i | 0.120386 | + | 0.208514i | ||||
\(277\) | 1.73205 | − | 1.00000i | 0.104069 | − | 0.0600842i | −0.447062 | − | 0.894503i | \(-0.647530\pi\) |
0.551131 | + | 0.834419i | \(0.314196\pi\) | |||||||
\(278\) | −17.3205 | − | 10.0000i | −1.03882 | − | 0.599760i | ||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 6.92820 | + | 4.00000i | 0.412568 | + | 0.238197i | ||||
\(283\) | 13.8564 | − | 8.00000i | 0.823678 | − | 0.475551i | −0.0280052 | − | 0.999608i | \(-0.508916\pi\) |
0.851683 | + | 0.524057i | \(0.175582\pi\) | |||||||
\(284\) | 6.00000 | + | 10.3923i | 0.356034 | + | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | − | 6.92820i | −0.234484 | − | 0.406138i | ||||
\(292\) | −3.46410 | − | 2.00000i | −0.202721 | − | 0.117041i | ||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.0000 | + | 10.0000i | 1.16445 | + | 0.582223i | ||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | 1.73205 | − | 1.00000i | 0.100504 | − | 0.0580259i | ||||
\(298\) | −17.3205 | + | 10.0000i | −1.00335 | + | 0.579284i | ||||
\(299\) | 12.0000 | − | 20.7846i | 0.693978 | − | 1.20201i | ||||
\(300\) | −4.00000 | + | 3.00000i | −0.230940 | + | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.00000i | 0.460348i | ||||||||
\(303\) | 6.92820 | + | 4.00000i | 0.398015 | + | 0.229794i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.267949 | + | 4.46410i | 0.0153427 | + | 0.255614i | ||||
\(306\) | −1.00000 | + | 1.73205i | −0.0571662 | + | 0.0990148i | ||||
\(307\) | − | 12.0000i | − | 0.684876i | −0.939540 | − | 0.342438i | \(-0.888747\pi\) | ||
0.939540 | − | 0.342438i | \(-0.111253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.0000 | −0.796432 | ||||||||
\(310\) | 9.85641 | + | 14.9282i | 0.559806 | + | 0.847865i | ||||
\(311\) | 6.00000 | + | 10.3923i | 0.340229 | + | 0.589294i | 0.984475 | − | 0.175525i | \(-0.0561621\pi\) |
−0.644246 | + | 0.764818i | \(0.722829\pi\) | |||||||
\(312\) | 5.19615 | − | 3.00000i | 0.294174 | − | 0.169842i | ||||
\(313\) | 3.46410 | + | 2.00000i | 0.195803 | + | 0.113047i | 0.594696 | − | 0.803951i | \(-0.297272\pi\) |
−0.398894 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(314\) | −22.0000 | −1.24153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.73205 | − | 1.00000i | −0.0972817 | − | 0.0561656i | 0.450570 | − | 0.892741i | \(-0.351221\pi\) |
−0.547852 | + | 0.836576i | \(0.684554\pi\) | |||||||
\(318\) | 5.19615 | − | 3.00000i | 0.291386 | − | 0.168232i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.86603 | − | 1.23205i | 0.104314 | − | 0.0688737i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 27.5885 | + | 11.7846i | 1.53033 | + | 0.653693i | ||||
\(326\) | 8.00000 | + | 13.8564i | 0.443079 | + | 0.767435i | ||||
\(327\) | −8.66025 | − | 5.00000i | −0.478913 | − | 0.276501i | ||||
\(328\) | − | 2.00000i | − | 0.110432i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.00000 | − | 2.00000i | −0.220193 | − | 0.110096i | ||||
\(331\) | 4.00000 | − | 6.92820i | 0.219860 | − | 0.380808i | −0.734905 | − | 0.678170i | \(-0.762773\pi\) |
0.954765 | + | 0.297361i | \(0.0961066\pi\) | |||||||
\(332\) | 3.46410 | − | 2.00000i | 0.190117 | − | 0.109764i | ||||
\(333\) | −1.73205 | + | 1.00000i | −0.0949158 | + | 0.0547997i | ||||
\(334\) | 6.00000 | − | 10.3923i | 0.328305 | − | 0.568642i | ||||
\(335\) | 8.00000 | − | 16.0000i | 0.437087 | − | 0.874173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 28.0000i | − | 1.52526i | −0.646837 | − | 0.762629i | \(-0.723908\pi\) | ||
0.646837 | − | 0.762629i | \(-0.276092\pi\) | |||||||
\(338\) | −19.9186 | − | 11.5000i | −1.08343 | − | 0.625518i | ||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | 4.46410 | − | 0.267949i | 0.242100 | − | 0.0145316i | ||||
\(341\) | −8.00000 | + | 13.8564i | −0.433224 | + | 0.750366i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | −7.46410 | + | 4.92820i | −0.401854 | + | 0.265326i | ||||
\(346\) | 7.00000 | + | 12.1244i | 0.376322 | + | 0.651809i | ||||
\(347\) | 10.3923 | − | 6.00000i | 0.557888 | − | 0.322097i | −0.194409 | − | 0.980921i | \(-0.562279\pi\) |
0.752297 | + | 0.658824i | \(0.228946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.00000 | −0.320256 | ||||||||
\(352\) | 1.73205 | + | 1.00000i | 0.0923186 | + | 0.0533002i | ||||
\(353\) | −12.1244 | + | 7.00000i | −0.645314 | + | 0.372572i | −0.786659 | − | 0.617388i | \(-0.788191\pi\) |
0.141344 | + | 0.989960i | \(0.454858\pi\) | |||||||
\(354\) | 5.00000 | + | 8.66025i | 0.265747 | + | 0.460287i | ||||
\(355\) | −22.3923 | + | 14.7846i | −1.18846 | + | 0.784686i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000i | 0.528516i | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | −2.23205 | + | 0.133975i | −0.117639 | + | 0.00706108i | ||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | −1.73205 | − | 1.00000i | −0.0910346 | − | 0.0525588i | ||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | − | 8.00000i | 0.209370 | − | 0.418739i | ||||
\(366\) | −1.00000 | + | 1.73205i | −0.0522708 | + | 0.0905357i | ||||
\(367\) | −1.73205 | + | 1.00000i | −0.0904123 | + | 0.0521996i | −0.544524 | − | 0.838745i | \(-0.683290\pi\) |
0.454112 | + | 0.890945i | \(0.349957\pi\) | |||||||
\(368\) | 3.46410 | − | 2.00000i | 0.180579 | − | 0.104257i | ||||
\(369\) | −1.00000 | + | 1.73205i | −0.0520579 | + | 0.0901670i | ||||
\(370\) | 4.00000 | + | 2.00000i | 0.207950 | + | 0.103975i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.00000i | 0.414781i | ||||||||
\(373\) | 5.19615 | + | 3.00000i | 0.269047 | + | 0.155334i | 0.628454 | − | 0.777847i | \(-0.283688\pi\) |
−0.359408 | + | 0.933181i | \(0.617021\pi\) | |||||||
\(374\) | 2.00000 | + | 3.46410i | 0.103418 | + | 0.179124i | ||||
\(375\) | −7.23205 | − | 8.52628i | −0.373461 | − | 0.440295i | ||||
\(376\) | 4.00000 | − | 6.92820i | 0.206284 | − | 0.357295i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.00000 | − | 1.73205i | −0.0512316 | − | 0.0887357i | ||||
\(382\) | −10.3923 | + | 6.00000i | −0.531717 | + | 0.306987i | ||||
\(383\) | −13.8564 | − | 8.00000i | −0.708029 | − | 0.408781i | 0.102302 | − | 0.994753i | \(-0.467379\pi\) |
−0.810331 | + | 0.585973i | \(0.800713\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.00000 | 0.203595 | ||||||||
\(387\) | 3.46410 | + | 2.00000i | 0.176090 | + | 0.101666i | ||||
\(388\) | −6.92820 | + | 4.00000i | −0.351726 | + | 0.203069i | ||||
\(389\) | 10.0000 | + | 17.3205i | 0.507020 | + | 0.878185i | 0.999967 | + | 0.00812520i | \(0.00258636\pi\) |
−0.492947 | + | 0.870059i | \(0.664080\pi\) | |||||||
\(390\) | 7.39230 | + | 11.1962i | 0.374324 | + | 0.566939i | ||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 18.0000i | − | 0.907980i | ||||||
\(394\) | −11.0000 | + | 19.0526i | −0.554172 | + | 0.959854i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | − | 1.73205i | −0.0502519 | − | 0.0870388i | ||||
\(397\) | 1.73205 | + | 1.00000i | 0.0869291 | + | 0.0501886i | 0.542834 | − | 0.839840i | \(-0.317351\pi\) |
−0.455905 | + | 0.890028i | \(0.650684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | −11.0000 | + | 19.0526i | −0.549314 | + | 0.951439i | 0.449008 | + | 0.893528i | \(0.351777\pi\) |
−0.998322 | + | 0.0579116i | \(0.981556\pi\) | |||||||
\(402\) | 6.92820 | − | 4.00000i | 0.345547 | − | 0.199502i | ||||
\(403\) | 41.5692 | − | 24.0000i | 2.07071 | − | 1.19553i | ||||
\(404\) | 4.00000 | − | 6.92820i | 0.199007 | − | 0.344691i | ||||
\(405\) | 2.00000 | + | 1.00000i | 0.0993808 | + | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000i | 0.198273i | ||||||||
\(408\) | 1.73205 | + | 1.00000i | 0.0857493 | + | 0.0495074i | ||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 4.46410 | − | 0.267949i | 0.220466 | − | 0.0132331i | ||||
\(411\) | 9.00000 | − | 15.5885i | 0.443937 | − | 0.768922i | ||||
\(412\) | 14.0000i | 0.689730i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.00000 | −0.196589 | ||||||||
\(415\) | 4.92820 | + | 7.46410i | 0.241916 | + | 0.366398i | ||||
\(416\) | −3.00000 | − | 5.19615i | −0.147087 | − | 0.254762i | ||||
\(417\) | 17.3205 | − | 10.0000i | 0.848189 | − | 0.489702i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0000 | −0.488532 | −0.244266 | − | 0.969708i | \(-0.578547\pi\) | ||||
−0.244266 | + | 0.969708i | \(0.578547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 10.3923 | + | 6.00000i | 0.505889 | + | 0.292075i | ||||
\(423\) | −6.92820 | + | 4.00000i | −0.336861 | + | 0.194487i | ||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 1.19615 | + | 9.92820i | 0.0580219 | + | 0.481589i | ||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | −6.00000 | + | 10.3923i | −0.289683 | + | 0.501745i | ||||
\(430\) | −0.535898 | − | 8.92820i | −0.0258433 | − | 0.430556i | ||||
\(431\) | −16.0000 | − | 27.7128i | −0.770693 | − | 1.33488i | −0.937184 | − | 0.348836i | \(-0.886577\pi\) |
0.166491 | − | 0.986043i | \(-0.446756\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 4.00000i | − | 0.192228i | −0.995370 | − | 0.0961139i | \(-0.969359\pi\) | ||
0.995370 | − | 0.0961139i | \(-0.0306413\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.00000 | + | 8.66025i | −0.239457 | + | 0.414751i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3.46410 | − | 2.00000i | 0.165521 | − | 0.0955637i | ||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | −2.00000 | + | 4.00000i | −0.0953463 | + | 0.190693i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 12.0000i | − | 0.570782i | ||||||
\(443\) | 31.1769 | + | 18.0000i | 1.48126 | + | 0.855206i | 0.999774 | − | 0.0212481i | \(-0.00676401\pi\) |
0.481486 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(444\) | 1.00000 | + | 1.73205i | 0.0474579 | + | 0.0821995i | ||||
\(445\) | 1.33975 | + | 22.3205i | 0.0635100 | + | 1.05809i | ||||
\(446\) | −13.0000 | + | 22.5167i | −0.615568 | + | 1.06619i | ||||
\(447\) | − | 20.0000i | − | 0.945968i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | −0.598076 | − | 4.96410i | −0.0281936 | − | 0.234010i | ||||
\(451\) | 2.00000 | + | 3.46410i | 0.0941763 | + | 0.163118i | ||||
\(452\) | 5.19615 | − | 3.00000i | 0.244406 | − | 0.141108i | ||||
\(453\) | −6.92820 | − | 4.00000i | −0.325515 | − | 0.187936i | ||||
\(454\) | 28.0000 | 1.31411 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.7128 | − | 16.0000i | −1.29635 | − | 0.748448i | −0.316579 | − | 0.948566i | \(-0.602534\pi\) |
−0.979772 | + | 0.200118i | \(0.935868\pi\) | |||||||
\(458\) | 8.66025 | − | 5.00000i | 0.404667 | − | 0.233635i | ||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 4.92820 | + | 7.46410i | 0.229779 | + | 0.348016i | ||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.00000i | − | 0.278844i | −0.990233 | − | 0.139422i | \(-0.955476\pi\) | ||
0.990233 | − | 0.139422i | \(-0.0445244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.8564 | + | 1.07180i | −0.828071 | + | 0.0497034i | ||||
\(466\) | −7.00000 | − | 12.1244i | −0.324269 | − | 0.561650i | ||||
\(467\) | 10.3923 | + | 6.00000i | 0.480899 | + | 0.277647i | 0.720791 | − | 0.693153i | \(-0.243779\pi\) |
−0.239892 | + | 0.970799i | \(0.577112\pi\) | |||||||
\(468\) | 6.00000i | 0.277350i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 16.0000 | + | 8.00000i | 0.738025 | + | 0.369012i | ||||
\(471\) | 11.0000 | − | 19.0526i | 0.506853 | − | 0.877896i | ||||
\(472\) | 8.66025 | − | 5.00000i | 0.398621 | − | 0.230144i | ||||
\(473\) | 6.92820 | − | 4.00000i | 0.318559 | − | 0.183920i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | −17.3205 | − | 10.0000i | −0.792222 | − | 0.457389i | ||||
\(479\) | −10.0000 | − | 17.3205i | −0.456912 | − | 0.791394i | 0.541884 | − | 0.840453i | \(-0.317711\pi\) |
−0.998796 | + | 0.0490589i | \(0.984378\pi\) | |||||||
\(480\) | 0.133975 | + | 2.23205i | 0.00611508 | + | 0.101879i | ||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | 22.0000i | 1.00207i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | −9.85641 | − | 14.9282i | −0.447556 | − | 0.677855i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −15.5885 | + | 9.00000i | −0.706380 | + | 0.407829i | −0.809719 | − | 0.586817i | \(-0.800381\pi\) |
0.103339 | + | 0.994646i | \(0.467047\pi\) | |||||||
\(488\) | 1.73205 | + | 1.00000i | 0.0784063 | + | 0.0452679i | ||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | −0.812329 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(492\) | 1.73205 | + | 1.00000i | 0.0780869 | + | 0.0450835i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.73205 | − | 2.46410i | 0.167743 | − | 0.110753i | ||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.00000i | 0.179244i | ||||||||
\(499\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(500\) | −8.52628 | + | 7.23205i | −0.381307 | + | 0.323427i | ||||
\(501\) | 6.00000 | + | 10.3923i | 0.268060 | + | 0.464294i | ||||
\(502\) | 15.5885 | + | 9.00000i | 0.695747 | + | 0.401690i | ||||
\(503\) | − | 24.0000i | − | 1.07011i | −0.844818 | − | 0.535054i | \(-0.820291\pi\) | ||
0.844818 | − | 0.535054i | \(-0.179709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | + | 8.00000i | 0.711991 | + | 0.355995i | ||||
\(506\) | −4.00000 | + | 6.92820i | −0.177822 | + | 0.307996i | ||||
\(507\) | 19.9186 | − | 11.5000i | 0.884615 | − | 0.510733i | ||||
\(508\) | −1.73205 | + | 1.00000i | −0.0768473 | + | 0.0443678i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | −2.00000 | + | 4.00000i | −0.0885615 | + | 0.177123i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.00000 | − | 15.5885i | −0.396973 | − | 0.687577i | ||||
\(515\) | −31.2487 | + | 1.87564i | −1.37698 | + | 0.0826508i | ||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | 16.0000i | 0.703679i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | 11.1962 | − | 7.39230i | 0.490984 | − | 0.324174i | ||||
\(521\) | 11.0000 | + | 19.0526i | 0.481919 | + | 0.834708i | 0.999785 | − | 0.0207541i | \(-0.00660670\pi\) |
−0.517866 | + | 0.855462i | \(0.673273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.8564 | − | 8.00000i | −0.605898 | − | 0.349816i | 0.165460 | − | 0.986216i | \(-0.447089\pi\) |
−0.771358 | + | 0.636401i | \(0.780422\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.00000 | 0.174408 | ||||||||
\(527\) | 13.8564 | + | 8.00000i | 0.603595 | + | 0.348485i | ||||
\(528\) | −1.73205 | + | 1.00000i | −0.0753778 | + | 0.0435194i | ||||
\(529\) | −3.50000 | − | 6.06218i | −0.152174 | − | 0.263573i | ||||
\(530\) | 11.1962 | − | 7.39230i | 0.486330 | − | 0.321101i | ||||
\(531\) | −10.0000 | −0.433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.0000i | − | 0.519778i | ||||||
\(534\) | −5.00000 | + | 8.66025i | −0.216371 | + | 0.374766i | ||||
\(535\) | 26.7846 | − | 1.60770i | 1.15800 | − | 0.0695067i | ||||
\(536\) | −4.00000 | − | 6.92820i | −0.172774 | − | 0.299253i | ||||
\(537\) | −8.66025 | − | 5.00000i | −0.373718 | − | 0.215766i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | − | 2.00000i | 0.0430331 | − | 0.0860663i | ||||
\(541\) | 19.0000 | − | 32.9090i | 0.816874 | − | 1.41487i | −0.0911008 | − | 0.995842i | \(-0.529039\pi\) |
0.907975 | − | 0.419025i | \(-0.137628\pi\) | |||||||
\(542\) | −6.92820 | + | 4.00000i | −0.297592 | + | 0.171815i | ||||
\(543\) | 1.73205 | − | 1.00000i | 0.0743294 | − | 0.0429141i | ||||
\(544\) | 1.00000 | − | 1.73205i | 0.0428746 | − | 0.0742611i | ||||
\(545\) | −20.0000 | − | 10.0000i | −0.856706 | − | 0.428353i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 28.0000i | − | 1.19719i | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||
0.801050 | − | 0.598597i | \(-0.204275\pi\) | |||||||
\(548\) | −15.5885 | − | 9.00000i | −0.665906 | − | 0.384461i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | −9.19615 | − | 3.92820i | −0.392125 | − | 0.167499i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 4.00000i | 0.170251i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | −3.73205 | + | 2.46410i | −0.158417 | + | 0.104595i | ||||
\(556\) | −10.0000 | − | 17.3205i | −0.424094 | − | 0.734553i | ||||
\(557\) | −15.5885 | + | 9.00000i | −0.660504 | + | 0.381342i | −0.792469 | − | 0.609912i | \(-0.791205\pi\) |
0.131965 | + | 0.991254i | \(0.457871\pi\) | |||||||
\(558\) | −6.92820 | − | 4.00000i | −0.293294 | − | 0.169334i | ||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | −15.5885 | − | 9.00000i | −0.657559 | − | 0.379642i | ||||
\(563\) | −38.1051 | + | 22.0000i | −1.60594 | + | 0.927189i | −0.615673 | + | 0.788002i | \(0.711116\pi\) |
−0.990266 | + | 0.139188i | \(0.955551\pi\) | |||||||
\(564\) | 4.00000 | + | 6.92820i | 0.168430 | + | 0.291730i | ||||
\(565\) | 7.39230 | + | 11.1962i | 0.310997 | + | 0.471026i | ||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000i | 0.503509i | ||||||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | + | 6.92820i | 0.167395 | + | 0.289936i | 0.937503 | − | 0.347977i | \(-0.113131\pi\) |
−0.770108 | + | 0.637913i | \(0.779798\pi\) | |||||||
\(572\) | 10.3923 | + | 6.00000i | 0.434524 | + | 0.250873i | ||||
\(573\) | − | 12.0000i | − | 0.501307i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0000 | + | 12.0000i | −0.667246 | + | 0.500435i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −27.7128 | + | 16.0000i | −1.15370 | + | 0.666089i | −0.949786 | − | 0.312900i | \(-0.898699\pi\) |
−0.203913 | + | 0.978989i | \(0.565366\pi\) | |||||||
\(578\) | −11.2583 | + | 6.50000i | −0.468285 | + | 0.270364i | ||||
\(579\) | −2.00000 | + | 3.46410i | −0.0831172 | + | 0.143963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 8.00000i | − | 0.331611i | ||||||
\(583\) | 10.3923 | + | 6.00000i | 0.430405 | + | 0.248495i | ||||
\(584\) | −2.00000 | − | 3.46410i | −0.0827606 | − | 0.143346i | ||||
\(585\) | −13.3923 | + | 0.803848i | −0.553704 | + | 0.0332350i | ||||
\(586\) | −3.00000 | + | 5.19615i | −0.123929 | + | 0.214651i | ||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 12.3205 | + | 18.6603i | 0.507227 | + | 0.768231i | ||||
\(591\) | −11.0000 | − | 19.0526i | −0.452480 | − | 0.783718i | ||||
\(592\) | 1.73205 | − | 1.00000i | 0.0711868 | − | 0.0410997i | ||||
\(593\) | −5.19615 | − | 3.00000i | −0.213380 | − | 0.123195i | 0.389501 | − | 0.921026i | \(-0.372647\pi\) |
−0.602881 | + | 0.797831i | \(0.705981\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.0000 | −0.819232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.7846 | − | 12.0000i | 0.849946 | − | 0.490716i | ||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | −4.96410 | + | 0.598076i | −0.202659 | + | 0.0244164i | ||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −4.00000 | + | 6.92820i | −0.162758 | + | 0.281905i | ||||
\(605\) | 0.937822 | + | 15.6244i | 0.0381279 | + | 0.635220i | ||||
\(606\) | 4.00000 | + | 6.92820i | 0.162489 | + | 0.281439i | ||||
\(607\) | 19.0526 | + | 11.0000i | 0.773320 | + | 0.446476i | 0.834058 | − | 0.551678i | \(-0.186012\pi\) |
−0.0607380 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.00000 | + | 4.00000i | −0.0809776 | + | 0.161955i | ||||
\(611\) | 24.0000 | − | 41.5692i | 0.970936 | − | 1.68171i | ||||
\(612\) | −1.73205 | + | 1.00000i | −0.0700140 | + | 0.0404226i | ||||
\(613\) | −22.5167 | + | 13.0000i | −0.909439 | + | 0.525065i | −0.880251 | − | 0.474509i | \(-0.842626\pi\) |
−0.0291886 | + | 0.999574i | \(0.509292\pi\) | |||||||
\(614\) | 6.00000 | − | 10.3923i | 0.242140 | − | 0.419399i | ||||
\(615\) | −2.00000 | + | 4.00000i | −0.0806478 | + | 0.161296i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000i | 0.0805170i | 0.999189 | + | 0.0402585i | \(0.0128181\pi\) | ||||
−0.999189 | + | 0.0402585i | \(0.987182\pi\) | |||||||
\(618\) | −12.1244 | − | 7.00000i | −0.487713 | − | 0.281581i | ||||
\(619\) | −10.0000 | − | 17.3205i | −0.401934 | − | 0.696170i | 0.592025 | − | 0.805919i | \(-0.298329\pi\) |
−0.993959 | + | 0.109749i | \(0.964995\pi\) | |||||||
\(620\) | 1.07180 | + | 17.8564i | 0.0430444 | + | 0.717131i | ||||
\(621\) | 2.00000 | − | 3.46410i | 0.0802572 | − | 0.139010i | ||||
\(622\) | 12.0000i | 0.481156i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | 2.00000 | + | 3.46410i | 0.0799361 | + | 0.138453i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.0526 | − | 11.0000i | −0.760280 | − | 0.438948i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.3923 | + | 6.00000i | −0.413057 | + | 0.238479i | ||||
\(634\) | −1.00000 | − | 1.73205i | −0.0397151 | − | 0.0687885i | ||||
\(635\) | −2.46410 | − | 3.73205i | −0.0977849 | − | 0.148102i | ||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | − | 10.3923i | 0.237356 | − | 0.411113i | ||||
\(640\) | 2.23205 | − | 0.133975i | 0.0882296 | − | 0.00529581i | ||||
\(641\) | −1.00000 | − | 1.73205i | −0.0394976 | − | 0.0684119i | 0.845601 | − | 0.533816i | \(-0.179242\pi\) |
−0.885098 | + | 0.465404i | \(0.845909\pi\) | |||||||
\(642\) | 10.3923 | + | 6.00000i | 0.410152 | + | 0.236801i | ||||
\(643\) | − | 24.0000i | − | 0.946468i | −0.880937 | − | 0.473234i | \(-0.843087\pi\) | ||
0.880937 | − | 0.473234i | \(-0.156913\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | + | 4.00000i | 0.315000 | + | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.5692 | − | 24.0000i | 1.63425 | − | 0.943537i | 0.651494 | − | 0.758654i | \(-0.274142\pi\) |
0.982760 | − | 0.184884i | \(-0.0591909\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −10.0000 | + | 17.3205i | −0.392534 | + | 0.679889i | ||||
\(650\) | 18.0000 | + | 24.0000i | 0.706018 | + | 0.941357i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.0000i | 0.626608i | ||||||||
\(653\) | 22.5167 | + | 13.0000i | 0.881145 | + | 0.508729i | 0.871036 | − | 0.491220i | \(-0.163449\pi\) |
0.0101092 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(654\) | −5.00000 | − | 8.66025i | −0.195515 | − | 0.338643i | ||||
\(655\) | −2.41154 | − | 40.1769i | −0.0942268 | − | 1.56984i | ||||
\(656\) | 1.00000 | − | 1.73205i | 0.0390434 | − | 0.0676252i | ||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 50.0000 | 1.94772 | 0.973862 | − | 0.227142i | \(-0.0729380\pi\) | ||||
0.973862 | + | 0.227142i | \(0.0729380\pi\) | |||||||
\(660\) | −2.46410 | − | 3.73205i | −0.0959150 | − | 0.145270i | ||||
\(661\) | 1.00000 | + | 1.73205i | 0.0388955 | + | 0.0673690i | 0.884818 | − | 0.465937i | \(-0.154283\pi\) |
−0.845922 | + | 0.533306i | \(0.820949\pi\) | |||||||
\(662\) | 6.92820 | − | 4.00000i | 0.269272 | − | 0.155464i | ||||
\(663\) | 10.3923 | + | 6.00000i | 0.403604 | + | 0.233021i | ||||
\(664\) | 4.00000 | 0.155230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 10.3923 | − | 6.00000i | 0.402090 | − | 0.232147i | ||||
\(669\) | −13.0000 | − | 22.5167i | −0.502609 | − | 0.870544i | ||||
\(670\) | 14.9282 | − | 9.85641i | 0.576727 | − | 0.380786i | ||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.0000i | − | 1.38770i | −0.720121 | − | 0.693849i | \(-0.755914\pi\) | ||
0.720121 | − | 0.693849i | \(-0.244086\pi\) | |||||||
\(674\) | 14.0000 | − | 24.2487i | 0.539260 | − | 0.934025i | ||||
\(675\) | 4.59808 | + | 1.96410i | 0.176980 | + | 0.0755983i | ||||
\(676\) | −11.5000 | − | 19.9186i | −0.442308 | − | 0.766099i | ||||
\(677\) | 1.73205 | + | 1.00000i | 0.0665681 | + | 0.0384331i | 0.532915 | − | 0.846169i | \(-0.321097\pi\) |
−0.466347 | + | 0.884602i | \(0.654430\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.00000 | + | 2.00000i | 0.153393 | + | 0.0766965i | ||||
\(681\) | −14.0000 | + | 24.2487i | −0.536481 | + | 0.929213i | ||||
\(682\) | −13.8564 | + | 8.00000i | −0.530589 | + | 0.306336i | ||||
\(683\) | 3.46410 | − | 2.00000i | 0.132550 | − | 0.0765279i | −0.432259 | − | 0.901750i | \(-0.642283\pi\) |
0.564809 | + | 0.825222i | \(0.308950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | − | 36.0000i | 0.687745 | − | 1.37549i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0000i | 0.381524i | ||||||||
\(688\) | −3.46410 | − | 2.00000i | −0.132068 | − | 0.0762493i | ||||
\(689\) | −18.0000 | − | 31.1769i | −0.685745 | − | 1.18775i | ||||
\(690\) | −8.92820 | + | 0.535898i | −0.339891 | + | 0.0204013i | ||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 14.0000i | 0.532200i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 37.3205 | − | 24.6410i | 1.41565 | − | 0.934687i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.46410 | − | 2.00000i | 0.131212 | − | 0.0757554i | ||||
\(698\) | 8.66025 | + | 5.00000i | 0.327795 | + | 0.189253i | ||||
\(699\) | 14.0000 | 0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.0000 | 1.20862 | 0.604312 | − | 0.796748i | \(-0.293448\pi\) | ||||
0.604312 | + | 0.796748i | \(0.293448\pi\) | |||||||
\(702\) | −5.19615 | − | 3.00000i | −0.196116 | − | 0.113228i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.00000 | + | 1.73205i | 0.0376889 | + | 0.0652791i | ||||
\(705\) | −14.9282 | + | 9.85641i | −0.562229 | + | 0.371214i | ||||
\(706\) | −14.0000 | −0.526897 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.0000i | 0.375823i | ||||||||
\(709\) | 15.0000 | − | 25.9808i | 0.563337 | − | 0.975728i | −0.433865 | − | 0.900978i | \(-0.642851\pi\) |
0.997202 | − | 0.0747503i | \(-0.0238160\pi\) | |||||||
\(710\) | −26.7846 | + | 1.60770i | −1.00521 | + | 0.0603357i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.66025 | + | 5.00000i | 0.324557 | + | 0.187383i | ||||
\(713\) | 32.0000i | 1.19841i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | + | 24.0000i | −0.448775 | + | 0.897549i | ||||
\(716\) | −5.00000 | + | 8.66025i | −0.186859 | + | 0.323649i | ||||
\(717\) | 17.3205 | − | 10.0000i | 0.646846 | − | 0.373457i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.0000 | − | 34.6410i | 0.745874 | − | 1.29189i | −0.203911 | − | 0.978989i | \(-0.565365\pi\) |
0.949785 | − | 0.312903i | \(-0.101301\pi\) | |||||||
\(720\) | −2.00000 | − | 1.00000i | −0.0745356 | − | 0.0372678i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.0000i | 0.707107i | ||||||||
\(723\) | −19.0526 | − | 11.0000i | −0.708572 | − | 0.409094i | ||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.50000 | + | 6.06218i | −0.129897 | + | 0.224989i | ||||
\(727\) | 18.0000i | 0.667583i | 0.942647 | + | 0.333792i | \(0.108328\pi\) | ||||
−0.942647 | + | 0.333792i | \(0.891672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 7.46410 | − | 4.92820i | 0.276259 | − | 0.182401i | ||||
\(731\) | −4.00000 | − | 6.92820i | −0.147945 | − | 0.256249i | ||||
\(732\) | −1.73205 | + | 1.00000i | −0.0640184 | + | 0.0369611i | ||||
\(733\) | 12.1244 | + | 7.00000i | 0.447823 | + | 0.258551i | 0.706910 | − | 0.707303i | \(-0.250088\pi\) |
−0.259087 | + | 0.965854i | \(0.583422\pi\) | |||||||
\(734\) | −2.00000 | −0.0738213 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 13.8564 | + | 8.00000i | 0.510407 | + | 0.294684i | ||||
\(738\) | −1.73205 | + | 1.00000i | −0.0637577 | + | 0.0368105i | ||||
\(739\) | 20.0000 | + | 34.6410i | 0.735712 | + | 1.27429i | 0.954410 | + | 0.298498i | \(0.0964856\pi\) |
−0.218698 | + | 0.975793i | \(0.570181\pi\) | |||||||
\(740\) | 2.46410 | + | 3.73205i | 0.0905822 | + | 0.137193i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | −4.00000 | + | 6.92820i | −0.146647 | + | 0.254000i | ||||
\(745\) | −2.67949 | − | 44.6410i | −0.0981690 | − | 1.63552i | ||||
\(746\) | 3.00000 | + | 5.19615i | 0.109838 | + | 0.190245i | ||||
\(747\) | −3.46410 | − | 2.00000i | −0.126745 | − | 0.0731762i | ||||
\(748\) | 4.00000i | 0.146254i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.00000 | − | 11.0000i | −0.0730297 | − | 0.401663i | ||||
\(751\) | −16.0000 | + | 27.7128i | −0.583848 | + | 1.01125i | 0.411170 | + | 0.911559i | \(0.365120\pi\) |
−0.995018 | + | 0.0996961i | \(0.968213\pi\) | |||||||
\(752\) | 6.92820 | − | 4.00000i | 0.252646 | − | 0.145865i | ||||
\(753\) | −15.5885 | + | 9.00000i | −0.568075 | + | 0.327978i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | − | 8.00000i | −0.582300 | − | 0.291150i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | −17.3205 | − | 10.0000i | −0.629109 | − | 0.363216i | ||||
\(759\) | −4.00000 | − | 6.92820i | −0.145191 | − | 0.251478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | + | 15.5885i | −0.326250 | + | 0.565081i | −0.981764 | − | 0.190101i | \(-0.939118\pi\) |
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(762\) | − | 2.00000i | − | 0.0724524i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | −2.46410 | − | 3.73205i | −0.0890898 | − | 0.134933i | ||||
\(766\) | −8.00000 | − | 13.8564i | −0.289052 | − | 0.500652i | ||||
\(767\) | 51.9615 | − | 30.0000i | 1.87622 | − | 1.08324i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −30.0000 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681921\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 3.46410 | + | 2.00000i | 0.124676 | + | 0.0719816i | ||||
\(773\) | −46.7654 | + | 27.0000i | −1.68203 | + | 0.971123i | −0.721726 | + | 0.692179i | \(0.756651\pi\) |
−0.960307 | + | 0.278944i | \(0.910016\pi\) | |||||||
\(774\) | 2.00000 | + | 3.46410i | 0.0718885 | + | 0.124515i | ||||
\(775\) | −39.7128 | + | 4.78461i | −1.42653 | + | 0.171868i | ||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.0000i | 0.717035i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.803848 | + | 13.3923i | 0.0287824 | + | 0.479521i | ||||
\(781\) | −12.0000 | − | 20.7846i | −0.429394 | − | 0.743732i | ||||
\(782\) | 6.92820 | + | 4.00000i | 0.247752 | + | 0.143040i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.0000 | − | 44.0000i | 0.785214 | − | 1.57043i | ||||
\(786\) | 9.00000 | − | 15.5885i | 0.321019 | − | 0.556022i | ||||
\(787\) | −27.7128 | + | 16.0000i | −0.987855 | + | 0.570338i | −0.904632 | − | 0.426193i | \(-0.859855\pi\) |
−0.0832226 | + | 0.996531i | \(0.526521\pi\) | |||||||
\(788\) | −19.0526 | + | 11.0000i | −0.678719 | + | 0.391859i | ||||
\(789\) | −2.00000 | + | 3.46410i | −0.0712019 | + | 0.123325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 2.00000i | − | 0.0710669i | ||||||
\(793\) | 10.3923 | + | 6.00000i | 0.369042 | + | 0.213066i | ||||
\(794\) | 1.00000 | + | 1.73205i | 0.0354887 | + | 0.0614682i | ||||
\(795\) | 0.803848 | + | 13.3923i | 0.0285095 | + | 0.474976i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.00000i | − | 0.0708436i | −0.999372 | − | 0.0354218i | \(-0.988723\pi\) | ||
0.999372 | − | 0.0354218i | \(-0.0112775\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0.598076 | + | 4.96410i | 0.0211452 | + | 0.175507i | ||||
\(801\) | −5.00000 | − | 8.66025i | −0.176666 | − | 0.305995i | ||||
\(802\) | −19.0526 | + | 11.0000i | −0.672769 | + | 0.388424i | ||||
\(803\) | 6.92820 | + | 4.00000i | 0.244491 | + | 0.141157i | ||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 48.0000 | 1.69073 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.92820 | − | 4.00000i | 0.243733 | − | 0.140720i | ||||
\(809\) | −15.0000 | − | 25.9808i | −0.527372 | − | 0.913435i | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
0.472119 | − | 0.881535i | \(-0.343489\pi\) | |||||||
\(810\) | 1.23205 | + | 1.86603i | 0.0432899 | + | 0.0655654i | ||||
\(811\) | −52.0000 | −1.82597 | −0.912983 | − | 0.407997i | \(-0.866228\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.00000i | − | 0.280572i | ||||||
\(814\) | −2.00000 | + | 3.46410i | −0.0701000 | + | 0.121417i | ||||
\(815\) | −35.7128 | + | 2.14359i | −1.25097 | + | 0.0750868i | ||||
\(816\) | 1.00000 | + | 1.73205i | 0.0350070 | + | 0.0606339i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | + | 2.00000i | 0.139686 | + | 0.0698430i | ||||
\(821\) | 4.00000 | − | 6.92820i | 0.139601 | − | 0.241796i | −0.787745 | − | 0.616002i | \(-0.788751\pi\) |
0.927346 | + | 0.374206i | \(0.122085\pi\) | |||||||
\(822\) | 15.5885 | − | 9.00000i | 0.543710 | − | 0.313911i | ||||
\(823\) | −5.19615 | + | 3.00000i | −0.181126 | + | 0.104573i | −0.587822 | − | 0.808990i | \(-0.700014\pi\) |
0.406695 | + | 0.913564i | \(0.366681\pi\) | |||||||
\(824\) | −7.00000 | + | 12.1244i | −0.243857 | + | 0.422372i | ||||
\(825\) | 8.00000 | − | 6.00000i | 0.278524 | − | 0.208893i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 28.0000i | − | 0.973655i | −0.873498 | − | 0.486828i | \(-0.838154\pi\) | ||
0.873498 | − | 0.486828i | \(-0.161846\pi\) | |||||||
\(828\) | −3.46410 | − | 2.00000i | −0.120386 | − | 0.0695048i | ||||
\(829\) | 15.0000 | + | 25.9808i | 0.520972 | + | 0.902349i | 0.999703 | + | 0.0243876i | \(0.00776357\pi\) |
−0.478731 | + | 0.877962i | \(0.658903\pi\) | |||||||
\(830\) | 0.535898 | + | 8.92820i | 0.0186013 | + | 0.309902i | ||||
\(831\) | −1.00000 | + | 1.73205i | −0.0346896 | + | 0.0600842i | ||||
\(832\) | − | 6.00000i | − | 0.208013i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.0000 | 0.692543 | ||||||||
\(835\) | 14.7846 | + | 22.3923i | 0.511643 | + | 0.774918i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.92820 | − | 4.00000i | 0.239474 | − | 0.138260i | ||||
\(838\) | −8.66025 | − | 5.00000i | −0.299164 | − | 0.172722i | ||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 19.0526 | + | 11.0000i | 0.656595 | + | 0.379085i | ||||
\(843\) | 15.5885 | − | 9.00000i | 0.536895 | − | 0.309976i | ||||
\(844\) | 6.00000 | + | 10.3923i | 0.206529 | + | 0.357718i | ||||
\(845\) | 42.9186 | − | 28.3372i | 1.47644 | − | 0.974828i | ||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −8.00000 | + | 13.8564i | −0.274559 | + | 0.475551i | ||||
\(850\) | −3.92820 | + | 9.19615i | −0.134736 | + | 0.315425i | ||||
\(851\) | 4.00000 | + | 6.92820i | 0.137118 | + | 0.237496i | ||||
\(852\) | −10.3923 | − | 6.00000i | −0.356034 | − | 0.205557i | ||||
\(853\) | − | 14.0000i | − | 0.479351i | −0.970853 | − | 0.239675i | \(-0.922959\pi\) | ||
0.970853 | − | 0.239675i | \(-0.0770410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | − | 10.3923i | 0.205076 | − | 0.355202i | ||||
\(857\) | −36.3731 | + | 21.0000i | −1.24248 | + | 0.717346i | −0.969599 | − | 0.244701i | \(-0.921310\pi\) |
−0.272882 | + | 0.962048i | \(0.587977\pi\) | |||||||
\(858\) | −10.3923 | + | 6.00000i | −0.354787 | + | 0.204837i | ||||
\(859\) | −10.0000 | + | 17.3205i | −0.341196 | + | 0.590968i | −0.984655 | − | 0.174512i | \(-0.944165\pi\) |
0.643459 | + | 0.765480i | \(0.277499\pi\) | |||||||
\(860\) | 4.00000 | − | 8.00000i | 0.136399 | − | 0.272798i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 32.0000i | − | 1.08992i | ||||||
\(863\) | 31.1769 | + | 18.0000i | 1.06127 | + | 0.612727i | 0.925785 | − | 0.378052i | \(-0.123406\pi\) |
0.135490 | + | 0.990779i | \(0.456739\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −31.2487 | + | 1.87564i | −1.06249 | + | 0.0637738i | ||||
\(866\) | 2.00000 | − | 3.46410i | 0.0679628 | − | 0.117715i | ||||
\(867\) | − | 13.0000i | − | 0.441503i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | − | 41.5692i | −0.813209 | − | 1.40852i | ||||
\(872\) | −8.66025 | + | 5.00000i | −0.293273 | + | 0.169321i | ||||
\(873\) | 6.92820 | + | 4.00000i | 0.234484 | + | 0.135379i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | −19.0526 | − | 11.0000i | −0.643359 | − | 0.371444i | 0.142548 | − | 0.989788i | \(-0.454470\pi\) |
−0.785907 | + | 0.618344i | \(0.787804\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.00000 | − | 5.19615i | −0.101187 | − | 0.175262i | ||||
\(880\) | −3.73205 | + | 2.46410i | −0.125807 | + | 0.0830648i | ||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0000i | 0.807664i | 0.914833 | + | 0.403832i | \(0.132322\pi\) | ||||
−0.914833 | + | 0.403832i | \(0.867678\pi\) | |||||||
\(884\) | 6.00000 | − | 10.3923i | 0.201802 | − | 0.349531i | ||||
\(885\) | −22.3205 | + | 1.33975i | −0.750296 | + | 0.0450351i | ||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | 10.3923 | + | 6.00000i | 0.348939 | + | 0.201460i | 0.664218 | − | 0.747539i | \(-0.268765\pi\) |
−0.315279 | + | 0.948999i | \(0.602098\pi\) | |||||||
\(888\) | 2.00000i | 0.0671156i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −10.0000 | + | 20.0000i | −0.335201 | + | 0.670402i | ||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | −22.5167 | + | 13.0000i | −0.753914 | + | 0.435272i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 10.0000 | − | 17.3205i | 0.334450 | − | 0.579284i | ||||
\(895\) | −20.0000 | − | 10.0000i | −0.668526 | − | 0.334263i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000i | 0.801337i | ||||||||
\(898\) | −25.9808 | − | 15.0000i | −0.866989 | − | 0.500556i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.96410 | − | 4.59808i | 0.0654701 | − | 0.153269i | ||||
\(901\) | 6.00000 | − | 10.3923i | 0.199889 | − | 0.346218i | ||||
\(902\) | 4.00000i | 0.133185i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 3.73205 | − | 2.46410i | 0.124058 | − | 0.0819095i | ||||
\(906\) | −4.00000 | − | 6.92820i | −0.132891 | − | 0.230174i | ||||
\(907\) | 10.3923 | − | 6.00000i | 0.345071 | − | 0.199227i | −0.317441 | − | 0.948278i | \(-0.602824\pi\) |
0.662512 | + | 0.749051i | \(0.269490\pi\) | |||||||
\(908\) | 24.2487 | + | 14.0000i | 0.804722 | + | 0.464606i | ||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.92820 | + | 4.00000i | −0.229290 | + | 0.132381i | ||||
\(914\) | −16.0000 | − | 27.7128i | −0.529233 | − | 0.916658i | ||||
\(915\) | −2.46410 | − | 3.73205i | −0.0814607 | − | 0.123378i | ||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 2.00000i | − | 0.0660098i | ||||||
\(919\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(920\) | 0.535898 | + | 8.92820i | 0.0176680 | + | 0.294354i | ||||
\(921\) | 6.00000 | + | 10.3923i | 0.197707 | + | 0.342438i | ||||
\(922\) | −10.3923 | − | 6.00000i | −0.342252 | − | 0.197599i | ||||
\(923\) | 72.0000i | 2.36991i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.00000 | + | 6.00000i | −0.263038 | + | 0.197279i | ||||
\(926\) | 3.00000 | − | 5.19615i | 0.0985861 | − | 0.170756i | ||||
\(927\) | 12.1244 | − | 7.00000i | 0.398216 | − | 0.229910i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.0000 | + | 25.9808i | −0.492134 | + | 0.852401i | −0.999959 | − | 0.00905914i | \(-0.997116\pi\) |
0.507825 | + | 0.861460i | \(0.330450\pi\) | |||||||
\(930\) | −16.0000 | − | 8.00000i | −0.524661 | − | 0.262330i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 14.0000i | − | 0.458585i | ||||||
\(933\) | −10.3923 | − | 6.00000i | −0.340229 | − | 0.196431i | ||||
\(934\) | 6.00000 | + | 10.3923i | 0.196326 | + | 0.340047i | ||||
\(935\) | −8.92820 | + | 0.535898i | −0.291983 | + | 0.0175258i | ||||
\(936\) | −3.00000 | + | 5.19615i | −0.0980581 | + | 0.169842i | ||||
\(937\) | 8.00000i | 0.261349i | 0.991425 | + | 0.130674i | \(0.0417142\pi\) | ||||
−0.991425 | + | 0.130674i | \(0.958286\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.00000 | −0.130535 | ||||||||
\(940\) | 9.85641 | + | 14.9282i | 0.321481 | + | 0.486904i | ||||
\(941\) | −14.0000 | − | 24.2487i | −0.456387 | − | 0.790485i | 0.542380 | − | 0.840133i | \(-0.317523\pi\) |
−0.998767 | + | 0.0496480i | \(0.984190\pi\) | |||||||
\(942\) | 19.0526 | − | 11.0000i | 0.620766 | − | 0.358399i | ||||
\(943\) | 6.92820 | + | 4.00000i | 0.225613 | + | 0.130258i | ||||
\(944\) | 10.0000 | 0.325472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | −10.3923 | − | 6.00000i | −0.337705 | − | 0.194974i | 0.321552 | − | 0.946892i | \(-0.395796\pi\) |
−0.659256 | + | 0.751918i | \(0.729129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | − | 20.7846i | −0.389536 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.00000 | 0.0648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 46.0000i | − | 1.49009i | −0.667016 | − | 0.745043i | \(-0.732429\pi\) | ||
0.667016 | − | 0.745043i | \(-0.267571\pi\) | |||||||
\(954\) | −3.00000 | + | 5.19615i | −0.0971286 | + | 0.168232i | ||||
\(955\) | −1.60770 | − | 26.7846i | −0.0520238 | − | 0.866730i | ||||
\(956\) | −10.0000 | − | 17.3205i | −0.323423 | − | 0.560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 20.0000i | − | 0.646171i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | + | 2.00000i | −0.0322749 | + | 0.0645497i | ||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 10.3923 | − | 6.00000i | 0.335061 | − | 0.193448i | ||||
\(963\) | −10.3923 | + | 6.00000i | −0.334887 | + | 0.193347i | ||||
\(964\) | −11.0000 | + | 19.0526i | −0.354286 | + | 0.613642i | ||||
\(965\) | −4.00000 | + | 8.00000i | −0.128765 | + | 0.257529i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.0000i | − | 1.22200i | −0.791632 | − | 0.610999i | \(-0.790768\pi\) | ||
0.791632 | − | 0.610999i | \(-0.209232\pi\) | |||||||
\(968\) | 6.06218 | + | 3.50000i | 0.194846 | + | 0.112494i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.07180 | − | 17.8564i | −0.0344133 | − | 0.573335i | ||||
\(971\) | −9.00000 | + | 15.5885i | −0.288824 | + | 0.500257i | −0.973529 | − | 0.228562i | \(-0.926597\pi\) |
0.684706 | + | 0.728820i | \(0.259931\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.0000 | −0.576757 | ||||||||
\(975\) | −29.7846 | + | 3.58846i | −0.953871 | + | 0.114923i | ||||
\(976\) | 1.00000 | + | 1.73205i | 0.0320092 | + | 0.0554416i | ||||
\(977\) | 36.3731 | − | 21.0000i | 1.16368 | − | 0.671850i | 0.211495 | − | 0.977379i | \(-0.432167\pi\) |
0.952183 | + | 0.305530i | \(0.0988335\pi\) | |||||||
\(978\) | −13.8564 | − | 8.00000i | −0.443079 | − | 0.255812i | ||||
\(979\) | −20.0000 | −0.639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | −15.5885 | − | 9.00000i | −0.497448 | − | 0.287202i | ||||
\(983\) | 13.8564 | − | 8.00000i | 0.441951 | − | 0.255160i | −0.262474 | − | 0.964939i | \(-0.584538\pi\) |
0.704425 | + | 0.709779i | \(0.251205\pi\) | |||||||
\(984\) | 1.00000 | + | 1.73205i | 0.0318788 | + | 0.0552158i | ||||
\(985\) | −27.1051 | − | 41.0526i | −0.863641 | − | 1.30804i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | − | 13.8564i | 0.254385 | − | 0.440608i | ||||
\(990\) | 4.46410 | − | 0.267949i | 0.141878 | − | 0.00851598i | ||||
\(991\) | 4.00000 | + | 6.92820i | 0.127064 | + | 0.220082i | 0.922538 | − | 0.385906i | \(-0.126111\pi\) |
−0.795474 | + | 0.605988i | \(0.792778\pi\) | |||||||
\(992\) | 6.92820 | + | 4.00000i | 0.219971 | + | 0.127000i | ||||
\(993\) | 8.00000i | 0.253872i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.00000 | + | 3.46410i | −0.0633724 | + | 0.109764i | ||||
\(997\) | 15.5885 | − | 9.00000i | 0.493691 | − | 0.285033i | −0.232413 | − | 0.972617i | \(-0.574662\pi\) |
0.726105 | + | 0.687584i | \(0.241329\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.00000 | − | 1.73205i | 0.0316386 | − | 0.0547997i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))