Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [338,2,Mod(23,338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(338, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("338.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 338 = 2 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 338.e (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: | \(2.69894358832\) |
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 26) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 147.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 338.147 |
Dual form | 338.2.e.d.23.1 |
$q$-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 \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).
\(n\) | \(171\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 1.50000 | − | 2.59808i | 0.866025 | − | 1.50000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | −0.974679 | − | 0.223607i | \(-0.928217\pi\) | ||
0.974679 | − | 0.223607i | \(-0.0717831\pi\) | |||||||
\(6\) | −2.59808 | + | 1.50000i | −1.06066 | + | 0.612372i | ||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) |
0.327327 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −1.73205 | − | 1.00000i | −0.522233 | − | 0.301511i | 0.215615 | − | 0.976478i | \(-0.430824\pi\) |
−0.737848 | + | 0.674967i | \(0.764158\pi\) | |||||||
\(12\) | 3.00000 | 0.866025 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.59808 | − | 1.50000i | −0.670820 | − | 0.387298i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 6.00000i | 1.41421i | ||||||||
\(19\) | 5.19615 | − | 3.00000i | 1.19208 | − | 0.688247i | 0.233301 | − | 0.972404i | \(-0.425047\pi\) |
0.958778 | + | 0.284157i | \(0.0917138\pi\) | |||||||
\(20\) | 0.866025 | − | 0.500000i | 0.193649 | − | 0.111803i | ||||
\(21\) | 3.00000i | 0.654654i | ||||||||
\(22\) | 1.00000 | + | 1.73205i | 0.213201 | + | 0.369274i | ||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | −2.59808 | − | 1.50000i | −0.530330 | − | 0.306186i | ||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.00000 | −1.73205 | ||||||||
\(28\) | −0.866025 | − | 0.500000i | −0.163663 | − | 0.0944911i | ||||
\(29\) | −1.00000 | + | 1.73205i | −0.185695 | + | 0.321634i | −0.943811 | − | 0.330487i | \(-0.892787\pi\) |
0.758115 | + | 0.652121i | \(0.226120\pi\) | |||||||
\(30\) | 1.50000 | + | 2.59808i | 0.273861 | + | 0.474342i | ||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −5.19615 | + | 3.00000i | −0.904534 | + | 0.522233i | ||||
\(34\) | 3.00000i | 0.514496i | ||||||||
\(35\) | 0.500000 | + | 0.866025i | 0.0845154 | + | 0.146385i | ||||
\(36\) | 3.00000 | − | 5.19615i | 0.500000 | − | 0.866025i | ||||
\(37\) | 2.59808 | + | 1.50000i | 0.427121 | + | 0.246598i | 0.698119 | − | 0.715981i | \(-0.254020\pi\) |
−0.270998 | + | 0.962580i | \(0.587354\pi\) | |||||||
\(38\) | −6.00000 | −0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | 1.50000 | − | 2.59808i | 0.231455 | − | 0.400892i | ||||
\(43\) | −2.50000 | − | 4.33013i | −0.381246 | − | 0.660338i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | − | 2.00000i | − | 0.301511i | ||||||
\(45\) | −5.19615 | + | 3.00000i | −0.774597 | + | 0.447214i | ||||
\(46\) | 3.46410 | − | 2.00000i | 0.510754 | − | 0.294884i | ||||
\(47\) | − | 13.0000i | − | 1.89624i | −0.317905 | − | 0.948122i | \(-0.602979\pi\) | ||
0.317905 | − | 0.948122i | \(-0.397021\pi\) | |||||||
\(48\) | 1.50000 | + | 2.59808i | 0.216506 | + | 0.375000i | ||||
\(49\) | −3.00000 | + | 5.19615i | −0.428571 | + | 0.742307i | ||||
\(50\) | −3.46410 | − | 2.00000i | −0.489898 | − | 0.282843i | ||||
\(51\) | −9.00000 | −1.26025 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0000 | 1.64833 | 0.824163 | − | 0.566352i | \(-0.191646\pi\) | ||||
0.824163 | + | 0.566352i | \(0.191646\pi\) | |||||||
\(54\) | 7.79423 | + | 4.50000i | 1.06066 | + | 0.612372i | ||||
\(55\) | −1.00000 | + | 1.73205i | −0.134840 | + | 0.233550i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | − | 18.0000i | − | 2.38416i | ||||||
\(58\) | 1.73205 | − | 1.00000i | 0.227429 | − | 0.131306i | ||||
\(59\) | 8.66025 | − | 5.00000i | 1.12747 | − | 0.650945i | 0.184172 | − | 0.982894i | \(-0.441040\pi\) |
0.943297 | + | 0.331949i | \(0.107706\pi\) | |||||||
\(60\) | − | 3.00000i | − | 0.387298i | ||||||
\(61\) | 4.00000 | + | 6.92820i | 0.512148 | + | 0.887066i | 0.999901 | + | 0.0140840i | \(0.00448323\pi\) |
−0.487753 | + | 0.872982i | \(0.662183\pi\) | |||||||
\(62\) | 2.00000 | − | 3.46410i | 0.254000 | − | 0.439941i | ||||
\(63\) | 5.19615 | + | 3.00000i | 0.654654 | + | 0.377964i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.00000 | 0.738549 | ||||||||
\(67\) | 1.73205 | + | 1.00000i | 0.211604 | + | 0.122169i | 0.602056 | − | 0.798454i | \(-0.294348\pi\) |
−0.390453 | + | 0.920623i | \(0.627682\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 6.00000 | + | 10.3923i | 0.722315 | + | 1.25109i | ||||
\(70\) | − | 1.00000i | − | 0.119523i | ||||||
\(71\) | −4.33013 | + | 2.50000i | −0.513892 | + | 0.296695i | −0.734432 | − | 0.678682i | \(-0.762551\pi\) |
0.220540 | + | 0.975378i | \(0.429218\pi\) | |||||||
\(72\) | −5.19615 | + | 3.00000i | −0.612372 | + | 0.353553i | ||||
\(73\) | 10.0000i | 1.17041i | 0.810885 | + | 0.585206i | \(0.198986\pi\) | ||||
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | −1.50000 | − | 2.59808i | −0.174371 | − | 0.302020i | ||||
\(75\) | 6.00000 | − | 10.3923i | 0.692820 | − | 1.20000i | ||||
\(76\) | 5.19615 | + | 3.00000i | 0.596040 | + | 0.344124i | ||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −2.59808 | + | 1.50000i | −0.283473 | + | 0.163663i | ||||
\(85\) | −2.59808 | + | 1.50000i | −0.281801 | + | 0.162698i | ||||
\(86\) | 5.00000i | 0.539164i | ||||||||
\(87\) | 3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | ||||
\(88\) | −1.00000 | + | 1.73205i | −0.106600 | + | 0.184637i | ||||
\(89\) | 5.19615 | + | 3.00000i | 0.550791 | + | 0.317999i | 0.749441 | − | 0.662071i | \(-0.230322\pi\) |
−0.198650 | + | 0.980071i | \(0.563656\pi\) | |||||||
\(90\) | 6.00000 | 0.632456 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 10.3923 | + | 6.00000i | 1.07763 | + | 0.622171i | ||||
\(94\) | −6.50000 | + | 11.2583i | −0.670424 | + | 1.16121i | ||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | − | 3.00000i | − | 0.306186i | ||||||
\(97\) | 12.1244 | − | 7.00000i | 1.23104 | − | 0.710742i | 0.263795 | − | 0.964579i | \(-0.415026\pi\) |
0.967247 | + | 0.253837i | \(0.0816925\pi\) | |||||||
\(98\) | 5.19615 | − | 3.00000i | 0.524891 | − | 0.303046i | ||||
\(99\) | 12.0000i | 1.20605i | ||||||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | 2.00000 | − | 3.46410i | 0.199007 | − | 0.344691i | −0.749199 | − | 0.662344i | \(-0.769562\pi\) |
0.948207 | + | 0.317653i | \(0.102895\pi\) | |||||||
\(102\) | 7.79423 | + | 4.50000i | 0.771744 | + | 0.445566i | ||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.00000 | 0.292770 | ||||||||
\(106\) | −10.3923 | − | 6.00000i | −1.00939 | − | 0.582772i | ||||
\(107\) | 2.00000 | − | 3.46410i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(108\) | −4.50000 | − | 7.79423i | −0.433013 | − | 0.750000i | ||||
\(109\) | 19.0000i | 1.81987i | 0.414751 | + | 0.909935i | \(0.363869\pi\) | ||||
−0.414751 | + | 0.909935i | \(0.636131\pi\) | |||||||
\(110\) | 1.73205 | − | 1.00000i | 0.165145 | − | 0.0953463i | ||||
\(111\) | 7.79423 | − | 4.50000i | 0.739795 | − | 0.427121i | ||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | −1.00000 | − | 1.73205i | −0.0940721 | − | 0.162938i | 0.815149 | − | 0.579252i | \(-0.196655\pi\) |
−0.909221 | + | 0.416314i | \(0.863322\pi\) | |||||||
\(114\) | −9.00000 | + | 15.5885i | −0.842927 | + | 1.45999i | ||||
\(115\) | 3.46410 | + | 2.00000i | 0.323029 | + | 0.186501i | ||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.0000 | −0.920575 | ||||||||
\(119\) | 2.59808 | + | 1.50000i | 0.238165 | + | 0.137505i | ||||
\(120\) | −1.50000 | + | 2.59808i | −0.136931 | + | 0.237171i | ||||
\(121\) | −3.50000 | − | 6.06218i | −0.318182 | − | 0.551107i | ||||
\(122\) | − | 8.00000i | − | 0.724286i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.46410 | + | 2.00000i | −0.311086 | + | 0.179605i | ||||
\(125\) | − | 9.00000i | − | 0.804984i | ||||||
\(126\) | −3.00000 | − | 5.19615i | −0.267261 | − | 0.462910i | ||||
\(127\) | 8.00000 | − | 13.8564i | 0.709885 | − | 1.22956i | −0.255014 | − | 0.966937i | \(-0.582080\pi\) |
0.964899 | − | 0.262620i | \(-0.0845865\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −15.0000 | −1.32068 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | −0.0873704 | −0.0436852 | − | 0.999045i | \(-0.513910\pi\) | ||||
−0.0436852 | + | 0.999045i | \(0.513910\pi\) | |||||||
\(132\) | −5.19615 | − | 3.00000i | −0.452267 | − | 0.261116i | ||||
\(133\) | −3.00000 | + | 5.19615i | −0.260133 | + | 0.450564i | ||||
\(134\) | −1.00000 | − | 1.73205i | −0.0863868 | − | 0.149626i | ||||
\(135\) | 9.00000i | 0.774597i | ||||||||
\(136\) | −2.59808 | + | 1.50000i | −0.222783 | + | 0.128624i | ||||
\(137\) | −10.3923 | + | 6.00000i | −0.887875 | + | 0.512615i | −0.873247 | − | 0.487278i | \(-0.837990\pi\) |
−0.0146279 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(138\) | − | 12.0000i | − | 1.02151i | ||||||
\(139\) | −3.50000 | − | 6.06218i | −0.296866 | − | 0.514187i | 0.678551 | − | 0.734553i | \(-0.262608\pi\) |
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | −0.500000 | + | 0.866025i | −0.0422577 | + | 0.0731925i | ||||
\(141\) | −33.7750 | − | 19.5000i | −2.84437 | − | 1.64220i | ||||
\(142\) | 5.00000 | 0.419591 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | 0.500000 | ||||||||
\(145\) | 1.73205 | + | 1.00000i | 0.143839 | + | 0.0830455i | ||||
\(146\) | 5.00000 | − | 8.66025i | 0.413803 | − | 0.716728i | ||||
\(147\) | 9.00000 | + | 15.5885i | 0.742307 | + | 1.28571i | ||||
\(148\) | 3.00000i | 0.246598i | ||||||||
\(149\) | −15.5885 | + | 9.00000i | −1.27706 | + | 0.737309i | −0.976306 | − | 0.216394i | \(-0.930570\pi\) |
−0.300750 | + | 0.953703i | \(0.597237\pi\) | |||||||
\(150\) | −10.3923 | + | 6.00000i | −0.848528 | + | 0.489898i | ||||
\(151\) | 9.00000i | 0.732410i | 0.930534 | + | 0.366205i | \(0.119343\pi\) | ||||
−0.930534 | + | 0.366205i | \(0.880657\pi\) | |||||||
\(152\) | −3.00000 | − | 5.19615i | −0.243332 | − | 0.421464i | ||||
\(153\) | −9.00000 | + | 15.5885i | −0.727607 | + | 1.26025i | ||||
\(154\) | −1.73205 | − | 1.00000i | −0.139573 | − | 0.0805823i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 3.46410 | + | 2.00000i | 0.275589 | + | 0.159111i | ||||
\(159\) | 18.0000 | − | 31.1769i | 1.42749 | − | 2.47249i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | − | 4.00000i | − | 0.315244i | ||||||
\(162\) | 7.79423 | − | 4.50000i | 0.612372 | − | 0.353553i | ||||
\(163\) | 3.46410 | − | 2.00000i | 0.271329 | − | 0.156652i | −0.358162 | − | 0.933659i | \(-0.616597\pi\) |
0.629492 | + | 0.777007i | \(0.283263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.00000 | + | 5.19615i | 0.233550 | + | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.00000 | 0.230089 | ||||||||
\(171\) | −31.1769 | − | 18.0000i | −2.38416 | − | 1.37649i | ||||
\(172\) | 2.50000 | − | 4.33013i | 0.190623 | − | 0.330169i | ||||
\(173\) | 10.0000 | + | 17.3205i | 0.760286 | + | 1.31685i | 0.942703 | + | 0.333633i | \(0.108275\pi\) |
−0.182417 | + | 0.983221i | \(0.558392\pi\) | |||||||
\(174\) | − | 6.00000i | − | 0.454859i | ||||||
\(175\) | −3.46410 | + | 2.00000i | −0.261861 | + | 0.151186i | ||||
\(176\) | 1.73205 | − | 1.00000i | 0.130558 | − | 0.0753778i | ||||
\(177\) | − | 30.0000i | − | 2.25494i | ||||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | −4.50000 | + | 7.79423i | −0.336346 | + | 0.582568i | −0.983742 | − | 0.179585i | \(-0.942524\pi\) |
0.647397 | + | 0.762153i | \(0.275858\pi\) | |||||||
\(180\) | −5.19615 | − | 3.00000i | −0.387298 | − | 0.223607i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.0000 | 1.77413 | ||||||||
\(184\) | 3.46410 | + | 2.00000i | 0.255377 | + | 0.147442i | ||||
\(185\) | 1.50000 | − | 2.59808i | 0.110282 | − | 0.191014i | ||||
\(186\) | −6.00000 | − | 10.3923i | −0.439941 | − | 0.762001i | ||||
\(187\) | 6.00000i | 0.438763i | ||||||||
\(188\) | 11.2583 | − | 6.50000i | 0.821098 | − | 0.474061i | ||||
\(189\) | 7.79423 | − | 4.50000i | 0.566947 | − | 0.327327i | ||||
\(190\) | 6.00000i | 0.435286i | ||||||||
\(191\) | −5.00000 | − | 8.66025i | −0.361787 | − | 0.626634i | 0.626468 | − | 0.779447i | \(-0.284500\pi\) |
−0.988255 | + | 0.152813i | \(0.951167\pi\) | |||||||
\(192\) | −1.50000 | + | 2.59808i | −0.108253 | + | 0.187500i | ||||
\(193\) | −13.8564 | − | 8.00000i | −0.997406 | − | 0.575853i | −0.0899262 | − | 0.995948i | \(-0.528663\pi\) |
−0.907480 | + | 0.420096i | \(0.861996\pi\) | |||||||
\(194\) | −14.0000 | −1.00514 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | −7.79423 | − | 4.50000i | −0.555316 | − | 0.320612i | 0.195947 | − | 0.980614i | \(-0.437222\pi\) |
−0.751263 | + | 0.660003i | \(0.770555\pi\) | |||||||
\(198\) | 6.00000 | − | 10.3923i | 0.426401 | − | 0.738549i | ||||
\(199\) | −5.00000 | − | 8.66025i | −0.354441 | − | 0.613909i | 0.632581 | − | 0.774494i | \(-0.281995\pi\) |
−0.987022 | + | 0.160585i | \(0.948662\pi\) | |||||||
\(200\) | − | 4.00000i | − | 0.282843i | ||||||
\(201\) | 5.19615 | − | 3.00000i | 0.366508 | − | 0.211604i | ||||
\(202\) | −3.46410 | + | 2.00000i | −0.243733 | + | 0.140720i | ||||
\(203\) | − | 2.00000i | − | 0.140372i | ||||||
\(204\) | −4.50000 | − | 7.79423i | −0.315063 | − | 0.545705i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.92820 | − | 4.00000i | −0.482711 | − | 0.278693i | ||||
\(207\) | 24.0000 | 1.66812 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | −2.59808 | − | 1.50000i | −0.179284 | − | 0.103510i | ||||
\(211\) | −11.5000 | + | 19.9186i | −0.791693 | + | 1.37125i | 0.133226 | + | 0.991086i | \(0.457467\pi\) |
−0.924918 | + | 0.380166i | \(0.875867\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | 15.0000i | 1.02778i | ||||||||
\(214\) | −3.46410 | + | 2.00000i | −0.236801 | + | 0.136717i | ||||
\(215\) | −4.33013 | + | 2.50000i | −0.295312 | + | 0.170499i | ||||
\(216\) | 9.00000i | 0.612372i | ||||||||
\(217\) | −2.00000 | − | 3.46410i | −0.135769 | − | 0.235159i | ||||
\(218\) | 9.50000 | − | 16.4545i | 0.643421 | − | 1.11444i | ||||
\(219\) | 25.9808 | + | 15.0000i | 1.75562 | + | 1.01361i | ||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −9.00000 | −0.604040 | ||||||||
\(223\) | 18.1865 | + | 10.5000i | 1.21786 | + | 0.703132i | 0.964460 | − | 0.264229i | \(-0.0851176\pi\) |
0.253401 | + | 0.967361i | \(0.418451\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | −12.0000 | − | 20.7846i | −0.800000 | − | 1.38564i | ||||
\(226\) | 2.00000i | 0.133038i | ||||||||
\(227\) | −20.7846 | + | 12.0000i | −1.37952 | + | 0.796468i | −0.992102 | − | 0.125435i | \(-0.959967\pi\) |
−0.387421 | + | 0.921903i | \(0.626634\pi\) | |||||||
\(228\) | 15.5885 | − | 9.00000i | 1.03237 | − | 0.596040i | ||||
\(229\) | 15.0000i | 0.991228i | 0.868543 | + | 0.495614i | \(0.165057\pi\) | ||||
−0.868543 | + | 0.495614i | \(0.834943\pi\) | |||||||
\(230\) | −2.00000 | − | 3.46410i | −0.131876 | − | 0.228416i | ||||
\(231\) | 3.00000 | − | 5.19615i | 0.197386 | − | 0.341882i | ||||
\(232\) | 1.73205 | + | 1.00000i | 0.113715 | + | 0.0656532i | ||||
\(233\) | 11.0000 | 0.720634 | 0.360317 | − | 0.932830i | \(-0.382669\pi\) | ||||
0.360317 | + | 0.932830i | \(0.382669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.0000 | −0.848026 | ||||||||
\(236\) | 8.66025 | + | 5.00000i | 0.563735 | + | 0.325472i | ||||
\(237\) | −6.00000 | + | 10.3923i | −0.389742 | + | 0.675053i | ||||
\(238\) | −1.50000 | − | 2.59808i | −0.0972306 | − | 0.168408i | ||||
\(239\) | 9.00000i | 0.582162i | 0.956698 | + | 0.291081i | \(0.0940149\pi\) | ||||
−0.956698 | + | 0.291081i | \(0.905985\pi\) | |||||||
\(240\) | 2.59808 | − | 1.50000i | 0.167705 | − | 0.0968246i | ||||
\(241\) | −15.5885 | + | 9.00000i | −1.00414 | + | 0.579741i | −0.909471 | − | 0.415768i | \(-0.863513\pi\) |
−0.0946700 | + | 0.995509i | \(0.530180\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.00000 | + | 6.92820i | −0.256074 | + | 0.443533i | ||||
\(245\) | 5.19615 | + | 3.00000i | 0.331970 | + | 0.191663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.50000 | + | 7.79423i | −0.284605 | + | 0.492950i | ||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | 6.00000i | 0.377964i | ||||||||
\(253\) | 6.92820 | − | 4.00000i | 0.435572 | − | 0.251478i | ||||
\(254\) | −13.8564 | + | 8.00000i | −0.869428 | + | 0.501965i | ||||
\(255\) | 9.00000i | 0.563602i | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −7.50000 | + | 12.9904i | −0.467837 | + | 0.810318i | −0.999325 | − | 0.0367485i | \(-0.988300\pi\) |
0.531487 | + | 0.847066i | \(0.321633\pi\) | |||||||
\(258\) | 12.9904 | + | 7.50000i | 0.808746 | + | 0.466930i | ||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0000 | 0.742781 | ||||||||
\(262\) | 0.866025 | + | 0.500000i | 0.0535032 | + | 0.0308901i | ||||
\(263\) | −6.00000 | + | 10.3923i | −0.369976 | + | 0.640817i | −0.989561 | − | 0.144112i | \(-0.953967\pi\) |
0.619586 | + | 0.784929i | \(0.287301\pi\) | |||||||
\(264\) | 3.00000 | + | 5.19615i | 0.184637 | + | 0.319801i | ||||
\(265\) | − | 12.0000i | − | 0.737154i | ||||||
\(266\) | 5.19615 | − | 3.00000i | 0.318597 | − | 0.183942i | ||||
\(267\) | 15.5885 | − | 9.00000i | 0.953998 | − | 0.550791i | ||||
\(268\) | 2.00000i | 0.122169i | ||||||||
\(269\) | 12.0000 | + | 20.7846i | 0.731653 | + | 1.26726i | 0.956176 | + | 0.292791i | \(0.0945841\pi\) |
−0.224523 | + | 0.974469i | \(0.572083\pi\) | |||||||
\(270\) | 4.50000 | − | 7.79423i | 0.273861 | − | 0.474342i | ||||
\(271\) | 11.2583 | + | 6.50000i | 0.683895 | + | 0.394847i | 0.801321 | − | 0.598235i | \(-0.204131\pi\) |
−0.117426 | + | 0.993082i | \(0.537464\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | −6.92820 | − | 4.00000i | −0.417786 | − | 0.241209i | ||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | 6.00000 | + | 10.3923i | 0.360505 | + | 0.624413i | 0.988044 | − | 0.154172i | \(-0.0492710\pi\) |
−0.627539 | + | 0.778585i | \(0.715938\pi\) | |||||||
\(278\) | 7.00000i | 0.419832i | ||||||||
\(279\) | 20.7846 | − | 12.0000i | 1.24434 | − | 0.718421i | ||||
\(280\) | 0.866025 | − | 0.500000i | 0.0517549 | − | 0.0298807i | ||||
\(281\) | 26.0000i | 1.55103i | 0.631329 | + | 0.775515i | \(0.282510\pi\) | ||||
−0.631329 | + | 0.775515i | \(0.717490\pi\) | |||||||
\(282\) | 19.5000 | + | 33.7750i | 1.16121 | + | 2.01127i | ||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | −4.33013 | − | 2.50000i | −0.256946 | − | 0.148348i | ||||
\(285\) | −18.0000 | −1.06623 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.19615 | − | 3.00000i | −0.306186 | − | 0.176777i | ||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | −1.00000 | − | 1.73205i | −0.0587220 | − | 0.101710i | ||||
\(291\) | − | 42.0000i | − | 2.46208i | ||||||
\(292\) | −8.66025 | + | 5.00000i | −0.506803 | + | 0.292603i | ||||
\(293\) | −6.06218 | + | 3.50000i | −0.354156 | + | 0.204472i | −0.666514 | − | 0.745492i | \(-0.732214\pi\) |
0.312358 | + | 0.949964i | \(0.398881\pi\) | |||||||
\(294\) | − | 18.0000i | − | 1.04978i | ||||||
\(295\) | −5.00000 | − | 8.66025i | −0.291111 | − | 0.504219i | ||||
\(296\) | 1.50000 | − | 2.59808i | 0.0871857 | − | 0.151010i | ||||
\(297\) | 15.5885 | + | 9.00000i | 0.904534 | + | 0.522233i | ||||
\(298\) | 18.0000 | 1.04271 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 12.0000 | 0.692820 | ||||||||
\(301\) | 4.33013 | + | 2.50000i | 0.249584 | + | 0.144098i | ||||
\(302\) | 4.50000 | − | 7.79423i | 0.258946 | − | 0.448507i | ||||
\(303\) | −6.00000 | − | 10.3923i | −0.344691 | − | 0.597022i | ||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | 6.92820 | − | 4.00000i | 0.396708 | − | 0.229039i | ||||
\(306\) | 15.5885 | − | 9.00000i | 0.891133 | − | 0.514496i | ||||
\(307\) | − | 14.0000i | − | 0.799022i | −0.916728 | − | 0.399511i | \(-0.869180\pi\) | ||
0.916728 | − | 0.399511i | \(-0.130820\pi\) | |||||||
\(308\) | 1.00000 | + | 1.73205i | 0.0569803 | + | 0.0986928i | ||||
\(309\) | 12.0000 | − | 20.7846i | 0.682656 | − | 1.18240i | ||||
\(310\) | −3.46410 | − | 2.00000i | −0.196748 | − | 0.113592i | ||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | −0.0565233 | −0.0282617 | − | 0.999601i | \(-0.508997\pi\) | ||||
−0.0282617 | + | 0.999601i | \(0.508997\pi\) | |||||||
\(314\) | 8.66025 | + | 5.00000i | 0.488726 | + | 0.282166i | ||||
\(315\) | 3.00000 | − | 5.19615i | 0.169031 | − | 0.292770i | ||||
\(316\) | −2.00000 | − | 3.46410i | −0.112509 | − | 0.194871i | ||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | −31.1769 | + | 18.0000i | −1.74831 | + | 1.00939i | ||||
\(319\) | 3.46410 | − | 2.00000i | 0.193952 | − | 0.111979i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −6.00000 | − | 10.3923i | −0.334887 | − | 0.580042i | ||||
\(322\) | −2.00000 | + | 3.46410i | −0.111456 | + | 0.193047i | ||||
\(323\) | −15.5885 | − | 9.00000i | −0.867365 | − | 0.500773i | ||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 49.3634 | + | 28.5000i | 2.72980 | + | 1.57605i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.50000 | + | 11.2583i | 0.358357 | + | 0.620692i | ||||
\(330\) | − | 6.00000i | − | 0.330289i | ||||||
\(331\) | −3.46410 | + | 2.00000i | −0.190404 | + | 0.109930i | −0.592172 | − | 0.805812i | \(-0.701729\pi\) |
0.401768 | + | 0.915742i | \(0.368396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 18.0000i | − | 0.986394i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.00000 | − | 1.73205i | 0.0546358 | − | 0.0946320i | ||||
\(336\) | −2.59808 | − | 1.50000i | −0.141737 | − | 0.0818317i | ||||
\(337\) | −23.0000 | −1.25289 | −0.626445 | − | 0.779466i | \(-0.715491\pi\) | ||||
−0.626445 | + | 0.779466i | \(0.715491\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | −2.59808 | − | 1.50000i | −0.140900 | − | 0.0813489i | ||||
\(341\) | 4.00000 | − | 6.92820i | 0.216612 | − | 0.375183i | ||||
\(342\) | 18.0000 | + | 31.1769i | 0.973329 | + | 1.68585i | ||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | −4.33013 | + | 2.50000i | −0.233465 | + | 0.134791i | ||||
\(345\) | 10.3923 | − | 6.00000i | 0.559503 | − | 0.323029i | ||||
\(346\) | − | 20.0000i | − | 1.07521i | ||||||
\(347\) | 4.50000 | + | 7.79423i | 0.241573 | + | 0.418416i | 0.961162 | − | 0.275983i | \(-0.0890035\pi\) |
−0.719590 | + | 0.694399i | \(0.755670\pi\) | |||||||
\(348\) | −3.00000 | + | 5.19615i | −0.160817 | + | 0.278543i | ||||
\(349\) | 6.06218 | + | 3.50000i | 0.324501 | + | 0.187351i | 0.653397 | − | 0.757015i | \(-0.273343\pi\) |
−0.328896 | + | 0.944366i | \(0.606677\pi\) | |||||||
\(350\) | 4.00000 | 0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | −3.46410 | − | 2.00000i | −0.184376 | − | 0.106449i | 0.404971 | − | 0.914329i | \(-0.367282\pi\) |
−0.589347 | + | 0.807880i | \(0.700615\pi\) | |||||||
\(354\) | −15.0000 | + | 25.9808i | −0.797241 | + | 1.38086i | ||||
\(355\) | 2.50000 | + | 4.33013i | 0.132686 | + | 0.229819i | ||||
\(356\) | 6.00000i | 0.317999i | ||||||||
\(357\) | 7.79423 | − | 4.50000i | 0.412514 | − | 0.238165i | ||||
\(358\) | 7.79423 | − | 4.50000i | 0.411938 | − | 0.237832i | ||||
\(359\) | − | 24.0000i | − | 1.26667i | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||
0.773877 | − | 0.633336i | \(-0.218315\pi\) | |||||||
\(360\) | 3.00000 | + | 5.19615i | 0.158114 | + | 0.273861i | ||||
\(361\) | 8.50000 | − | 14.7224i | 0.447368 | − | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.0000 | −1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | −20.7846 | − | 12.0000i | −1.08643 | − | 0.627250i | ||||
\(367\) | 5.00000 | − | 8.66025i | 0.260998 | − | 0.452062i | −0.705509 | − | 0.708700i | \(-0.749282\pi\) |
0.966507 | + | 0.256639i | \(0.0826151\pi\) | |||||||
\(368\) | −2.00000 | − | 3.46410i | −0.104257 | − | 0.180579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.59808 | + | 1.50000i | −0.135068 | + | 0.0779813i | ||||
\(371\) | −10.3923 | + | 6.00000i | −0.539542 | + | 0.311504i | ||||
\(372\) | 12.0000i | 0.622171i | ||||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | 3.00000 | − | 5.19615i | 0.155126 | − | 0.268687i | ||||
\(375\) | −23.3827 | − | 13.5000i | −1.20748 | − | 0.697137i | ||||
\(376\) | −13.0000 | −0.670424 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −9.00000 | −0.462910 | ||||||||
\(379\) | −13.8564 | − | 8.00000i | −0.711756 | − | 0.410932i | 0.0999550 | − | 0.994992i | \(-0.468130\pi\) |
−0.811711 | + | 0.584060i | \(0.801463\pi\) | |||||||
\(380\) | 3.00000 | − | 5.19615i | 0.153897 | − | 0.266557i | ||||
\(381\) | −24.0000 | − | 41.5692i | −1.22956 | − | 2.12966i | ||||
\(382\) | 10.0000i | 0.511645i | ||||||||
\(383\) | 23.3827 | − | 13.5000i | 1.19480 | − | 0.689818i | 0.235408 | − | 0.971897i | \(-0.424357\pi\) |
0.959391 | + | 0.282079i | \(0.0910240\pi\) | |||||||
\(384\) | 2.59808 | − | 1.50000i | 0.132583 | − | 0.0765466i | ||||
\(385\) | − | 2.00000i | − | 0.101929i | ||||||
\(386\) | 8.00000 | + | 13.8564i | 0.407189 | + | 0.705273i | ||||
\(387\) | −15.0000 | + | 25.9808i | −0.762493 | + | 1.32068i | ||||
\(388\) | 12.1244 | + | 7.00000i | 0.615521 | + | 0.355371i | ||||
\(389\) | 30.0000 | 1.52106 | 0.760530 | − | 0.649303i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649303i | \(0.224939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 5.19615 | + | 3.00000i | 0.262445 | + | 0.151523i | ||||
\(393\) | −1.50000 | + | 2.59808i | −0.0756650 | + | 0.131056i | ||||
\(394\) | 4.50000 | + | 7.79423i | 0.226707 | + | 0.392668i | ||||
\(395\) | 4.00000i | 0.201262i | ||||||||
\(396\) | −10.3923 | + | 6.00000i | −0.522233 | + | 0.301511i | ||||
\(397\) | 19.0526 | − | 11.0000i | 0.956221 | − | 0.552074i | 0.0612128 | − | 0.998125i | \(-0.480503\pi\) |
0.895008 | + | 0.446051i | \(0.147170\pi\) | |||||||
\(398\) | 10.0000i | 0.501255i | ||||||||
\(399\) | 9.00000 | + | 15.5885i | 0.450564 | + | 0.780399i | ||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 20.7846 | + | 12.0000i | 1.03793 | + | 0.599251i | 0.919247 | − | 0.393680i | \(-0.128798\pi\) |
0.118686 | + | 0.992932i | \(0.462132\pi\) | |||||||
\(402\) | −6.00000 | −0.299253 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.00000 | 0.199007 | ||||||||
\(405\) | 7.79423 | + | 4.50000i | 0.387298 | + | 0.223607i | ||||
\(406\) | −1.00000 | + | 1.73205i | −0.0496292 | + | 0.0859602i | ||||
\(407\) | −3.00000 | − | 5.19615i | −0.148704 | − | 0.257564i | ||||
\(408\) | 9.00000i | 0.445566i | ||||||||
\(409\) | 3.46410 | − | 2.00000i | 0.171289 | − | 0.0988936i | −0.411905 | − | 0.911227i | \(-0.635136\pi\) |
0.583193 | + | 0.812333i | \(0.301803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.0000i | 1.77575i | ||||||||
\(412\) | 4.00000 | + | 6.92820i | 0.197066 | + | 0.341328i | ||||
\(413\) | −5.00000 | + | 8.66025i | −0.246034 | + | 0.426143i | ||||
\(414\) | −20.7846 | − | 12.0000i | −1.02151 | − | 0.589768i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.0000 | −1.02837 | ||||||||
\(418\) | 10.3923 | + | 6.00000i | 0.508304 | + | 0.293470i | ||||
\(419\) | −10.5000 | + | 18.1865i | −0.512959 | + | 0.888470i | 0.486928 | + | 0.873442i | \(0.338117\pi\) |
−0.999887 | + | 0.0150285i | \(0.995216\pi\) | |||||||
\(420\) | 1.50000 | + | 2.59808i | 0.0731925 | + | 0.126773i | ||||
\(421\) | − | 5.00000i | − | 0.243685i | −0.992549 | − | 0.121843i | \(-0.961120\pi\) | ||
0.992549 | − | 0.121843i | \(-0.0388803\pi\) | |||||||
\(422\) | 19.9186 | − | 11.5000i | 0.969622 | − | 0.559811i | ||||
\(423\) | −67.5500 | + | 39.0000i | −3.28439 | + | 1.89624i | ||||
\(424\) | − | 12.0000i | − | 0.582772i | ||||||
\(425\) | −6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | ||||
\(426\) | 7.50000 | − | 12.9904i | 0.363376 | − | 0.629386i | ||||
\(427\) | −6.92820 | − | 4.00000i | −0.335279 | − | 0.193574i | ||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.00000 | 0.241121 | ||||||||
\(431\) | −28.5788 | − | 16.5000i | −1.37659 | − | 0.794777i | −0.384846 | − | 0.922981i | \(-0.625746\pi\) |
−0.991748 | + | 0.128204i | \(0.959079\pi\) | |||||||
\(432\) | 4.50000 | − | 7.79423i | 0.216506 | − | 0.375000i | ||||
\(433\) | 3.50000 | + | 6.06218i | 0.168199 | + | 0.291330i | 0.937787 | − | 0.347212i | \(-0.112871\pi\) |
−0.769588 | + | 0.638541i | \(0.779538\pi\) | |||||||
\(434\) | 4.00000i | 0.192006i | ||||||||
\(435\) | 5.19615 | − | 3.00000i | 0.249136 | − | 0.143839i | ||||
\(436\) | −16.4545 | + | 9.50000i | −0.788027 | + | 0.454967i | ||||
\(437\) | 24.0000i | 1.14808i | ||||||||
\(438\) | −15.0000 | − | 25.9808i | −0.716728 | − | 1.24141i | ||||
\(439\) | −11.0000 | + | 19.0526i | −0.525001 | + | 0.909329i | 0.474575 | + | 0.880215i | \(0.342602\pi\) |
−0.999576 | + | 0.0291138i | \(0.990731\pi\) | |||||||
\(440\) | 1.73205 | + | 1.00000i | 0.0825723 | + | 0.0476731i | ||||
\(441\) | 36.0000 | 1.71429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39.0000 | −1.85295 | −0.926473 | − | 0.376361i | \(-0.877175\pi\) | ||||
−0.926473 | + | 0.376361i | \(0.877175\pi\) | |||||||
\(444\) | 7.79423 | + | 4.50000i | 0.369898 | + | 0.213561i | ||||
\(445\) | 3.00000 | − | 5.19615i | 0.142214 | − | 0.246321i | ||||
\(446\) | −10.5000 | − | 18.1865i | −0.497189 | − | 0.861157i | ||||
\(447\) | 54.0000i | 2.55411i | ||||||||
\(448\) | 0.866025 | − | 0.500000i | 0.0409159 | − | 0.0236228i | ||||
\(449\) | 22.5167 | − | 13.0000i | 1.06263 | − | 0.613508i | 0.136469 | − | 0.990644i | \(-0.456425\pi\) |
0.926158 | + | 0.377136i | \(0.123091\pi\) | |||||||
\(450\) | 24.0000i | 1.13137i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.00000 | − | 1.73205i | 0.0470360 | − | 0.0814688i | ||||
\(453\) | 23.3827 | + | 13.5000i | 1.09861 | + | 0.634285i | ||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0000 | −0.842927 | ||||||||
\(457\) | −8.66025 | − | 5.00000i | −0.405110 | − | 0.233890i | 0.283577 | − | 0.958950i | \(-0.408479\pi\) |
−0.688686 | + | 0.725059i | \(0.741812\pi\) | |||||||
\(458\) | 7.50000 | − | 12.9904i | 0.350452 | − | 0.607001i | ||||
\(459\) | 13.5000 | + | 23.3827i | 0.630126 | + | 1.09141i | ||||
\(460\) | 4.00000i | 0.186501i | ||||||||
\(461\) | −18.1865 | + | 10.5000i | −0.847031 | + | 0.489034i | −0.859648 | − | 0.510887i | \(-0.829317\pi\) |
0.0126168 | + | 0.999920i | \(0.495984\pi\) | |||||||
\(462\) | −5.19615 | + | 3.00000i | −0.241747 | + | 0.139573i | ||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | −1.00000 | − | 1.73205i | −0.0464238 | − | 0.0804084i | ||||
\(465\) | 6.00000 | − | 10.3923i | 0.278243 | − | 0.481932i | ||||
\(466\) | −9.52628 | − | 5.50000i | −0.441296 | − | 0.254783i | ||||
\(467\) | −20.0000 | −0.925490 | −0.462745 | − | 0.886492i | \(-0.653135\pi\) | ||||
−0.462745 | + | 0.886492i | \(0.653135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | 11.2583 | + | 6.50000i | 0.519308 | + | 0.299823i | ||||
\(471\) | −15.0000 | + | 25.9808i | −0.691164 | + | 1.19713i | ||||
\(472\) | −5.00000 | − | 8.66025i | −0.230144 | − | 0.398621i | ||||
\(473\) | 10.0000i | 0.459800i | ||||||||
\(474\) | 10.3923 | − | 6.00000i | 0.477334 | − | 0.275589i | ||||
\(475\) | 20.7846 | − | 12.0000i | 0.953663 | − | 0.550598i | ||||
\(476\) | 3.00000i | 0.137505i | ||||||||
\(477\) | −36.0000 | − | 62.3538i | −1.64833 | − | 2.85499i | ||||
\(478\) | 4.50000 | − | 7.79423i | 0.205825 | − | 0.356500i | ||||
\(479\) | −2.59808 | − | 1.50000i | −0.118709 | − | 0.0685367i | 0.439470 | − | 0.898257i | \(-0.355166\pi\) |
−0.558179 | + | 0.829721i | \(0.688500\pi\) | |||||||
\(480\) | −3.00000 | −0.136931 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.0000 | 0.819878 | ||||||||
\(483\) | −10.3923 | − | 6.00000i | −0.472866 | − | 0.273009i | ||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | −7.00000 | − | 12.1244i | −0.317854 | − | 0.550539i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.8564 | + | 8.00000i | −0.627894 | + | 0.362515i | −0.779936 | − | 0.625859i | \(-0.784748\pi\) |
0.152042 | + | 0.988374i | \(0.451415\pi\) | |||||||
\(488\) | 6.92820 | − | 4.00000i | 0.313625 | − | 0.181071i | ||||
\(489\) | − | 12.0000i | − | 0.542659i | ||||||
\(490\) | −3.00000 | − | 5.19615i | −0.135526 | − | 0.234738i | ||||
\(491\) | −2.50000 | + | 4.33013i | −0.112823 | + | 0.195416i | −0.916908 | − | 0.399100i | \(-0.869323\pi\) |
0.804084 | + | 0.594515i | \(0.202656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | 0.270226 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | 0.539360 | ||||||||
\(496\) | −3.46410 | − | 2.00000i | −0.155543 | − | 0.0898027i | ||||
\(497\) | 2.50000 | − | 4.33013i | 0.112140 | − | 0.194233i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 32.0000i | − | 1.43252i | −0.697835 | − | 0.716258i | \(-0.745853\pi\) | ||
0.697835 | − | 0.716258i | \(-0.254147\pi\) | |||||||
\(500\) | 7.79423 | − | 4.50000i | 0.348569 | − | 0.201246i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.00000 | + | 12.1244i | 0.312115 | + | 0.540598i | 0.978820 | − | 0.204723i | \(-0.0656294\pi\) |
−0.666705 | + | 0.745321i | \(0.732296\pi\) | |||||||
\(504\) | 3.00000 | − | 5.19615i | 0.133631 | − | 0.231455i | ||||
\(505\) | −3.46410 | − | 2.00000i | −0.154150 | − | 0.0889988i | ||||
\(506\) | −8.00000 | −0.355643 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.0000 | 0.709885 | ||||||||
\(509\) | −29.4449 | − | 17.0000i | −1.30512 | − | 0.753512i | −0.323843 | − | 0.946111i | \(-0.604975\pi\) |
−0.981278 | + | 0.192599i | \(0.938308\pi\) | |||||||
\(510\) | 4.50000 | − | 7.79423i | 0.199263 | − | 0.345134i | ||||
\(511\) | −5.00000 | − | 8.66025i | −0.221187 | − | 0.383107i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −46.7654 | + | 27.0000i | −2.06474 | + | 1.19208i | ||||
\(514\) | 12.9904 | − | 7.50000i | 0.572981 | − | 0.330811i | ||||
\(515\) | − | 8.00000i | − | 0.352522i | ||||||
\(516\) | −7.50000 | − | 12.9904i | −0.330169 | − | 0.571870i | ||||
\(517\) | −13.0000 | + | 22.5167i | −0.571739 | + | 0.990282i | ||||
\(518\) | 2.59808 | + | 1.50000i | 0.114153 | + | 0.0659062i | ||||
\(519\) | 60.0000 | 2.63371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.0000 | 1.70862 | 0.854311 | − | 0.519763i | \(-0.173980\pi\) | ||||
0.854311 | + | 0.519763i | \(0.173980\pi\) | |||||||
\(522\) | −10.3923 | − | 6.00000i | −0.454859 | − | 0.262613i | ||||
\(523\) | 18.0000 | − | 31.1769i | 0.787085 | − | 1.36327i | −0.140660 | − | 0.990058i | \(-0.544923\pi\) |
0.927746 | − | 0.373213i | \(-0.121744\pi\) | |||||||
\(524\) | −0.500000 | − | 0.866025i | −0.0218426 | − | 0.0378325i | ||||
\(525\) | 12.0000i | 0.523723i | ||||||||
\(526\) | 10.3923 | − | 6.00000i | 0.453126 | − | 0.261612i | ||||
\(527\) | 10.3923 | − | 6.00000i | 0.452696 | − | 0.261364i | ||||
\(528\) | − | 6.00000i | − | 0.261116i | ||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | −6.00000 | + | 10.3923i | −0.260623 | + | 0.451413i | ||||
\(531\) | −51.9615 | − | 30.0000i | −2.25494 | − | 1.30189i | ||||
\(532\) | −6.00000 | −0.260133 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18.0000 | −0.778936 | ||||||||
\(535\) | −3.46410 | − | 2.00000i | −0.149766 | − | 0.0864675i | ||||
\(536\) | 1.00000 | − | 1.73205i | 0.0431934 | − | 0.0748132i | ||||
\(537\) | 13.5000 | + | 23.3827i | 0.582568 | + | 1.00904i | ||||
\(538\) | − | 24.0000i | − | 1.03471i | ||||||
\(539\) | 10.3923 | − | 6.00000i | 0.447628 | − | 0.258438i | ||||
\(540\) | −7.79423 | + | 4.50000i | −0.335410 | + | 0.193649i | ||||
\(541\) | − | 17.0000i | − | 0.730887i | −0.930834 | − | 0.365444i | \(-0.880917\pi\) | ||
0.930834 | − | 0.365444i | \(-0.119083\pi\) | |||||||
\(542\) | −6.50000 | − | 11.2583i | −0.279199 | − | 0.483587i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.59808 | − | 1.50000i | −0.111392 | − | 0.0643120i | ||||
\(545\) | 19.0000 | 0.813871 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.0000 | 1.58201 | 0.791003 | − | 0.611812i | \(-0.209559\pi\) | ||||
0.791003 | + | 0.611812i | \(0.209559\pi\) | |||||||
\(548\) | −10.3923 | − | 6.00000i | −0.443937 | − | 0.256307i | ||||
\(549\) | 24.0000 | − | 41.5692i | 1.02430 | − | 1.77413i | ||||
\(550\) | 4.00000 | + | 6.92820i | 0.170561 | + | 0.295420i | ||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | 10.3923 | − | 6.00000i | 0.442326 | − | 0.255377i | ||||
\(553\) | 3.46410 | − | 2.00000i | 0.147309 | − | 0.0850487i | ||||
\(554\) | − | 12.0000i | − | 0.509831i | ||||||
\(555\) | −4.50000 | − | 7.79423i | −0.191014 | − | 0.330847i | ||||
\(556\) | 3.50000 | − | 6.06218i | 0.148433 | − | 0.257094i | ||||
\(557\) | 28.5788 | + | 16.5000i | 1.21092 | + | 0.699127i | 0.962961 | − | 0.269642i | \(-0.0869053\pi\) |
0.247964 | + | 0.968769i | \(0.420239\pi\) | |||||||
\(558\) | −24.0000 | −1.01600 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 15.5885 | + | 9.00000i | 0.658145 | + | 0.379980i | ||||
\(562\) | 13.0000 | − | 22.5167i | 0.548372 | − | 0.949808i | ||||
\(563\) | 5.50000 | + | 9.52628i | 0.231797 | + | 0.401485i | 0.958337 | − | 0.285640i | \(-0.0922060\pi\) |
−0.726540 | + | 0.687124i | \(0.758873\pi\) | |||||||
\(564\) | − | 39.0000i | − | 1.64220i | ||||||
\(565\) | −1.73205 | + | 1.00000i | −0.0728679 | + | 0.0420703i | ||||
\(566\) | −3.46410 | + | 2.00000i | −0.145607 | + | 0.0840663i | ||||
\(567\) | − | 9.00000i | − | 0.377964i | ||||||
\(568\) | 2.50000 | + | 4.33013i | 0.104898 | + | 0.181688i | ||||
\(569\) | 15.5000 | − | 26.8468i | 0.649794 | − | 1.12548i | −0.333378 | − | 0.942793i | \(-0.608189\pi\) |
0.983172 | − | 0.182683i | \(-0.0584781\pi\) | |||||||
\(570\) | 15.5885 | + | 9.00000i | 0.652929 | + | 0.376969i | ||||
\(571\) | −33.0000 | −1.38101 | −0.690504 | − | 0.723329i | \(-0.742611\pi\) | ||||
−0.690504 | + | 0.723329i | \(0.742611\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.0000 | −1.25327 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.00000 | + | 13.8564i | −0.333623 | + | 0.577852i | ||||
\(576\) | 3.00000 | + | 5.19615i | 0.125000 | + | 0.216506i | ||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | −6.92820 | + | 4.00000i | −0.288175 | + | 0.166378i | ||||
\(579\) | −41.5692 | + | 24.0000i | −1.72756 | + | 0.997406i | ||||
\(580\) | 2.00000i | 0.0830455i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.0000 | + | 36.3731i | −0.870478 | + | 1.50771i | ||||
\(583\) | −20.7846 | − | 12.0000i | −0.860811 | − | 0.496989i | ||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.00000 | 0.289167 | ||||||||
\(587\) | 24.2487 | + | 14.0000i | 1.00085 | + | 0.577842i | 0.908500 | − | 0.417885i | \(-0.137228\pi\) |
0.0923513 | + | 0.995726i | \(0.470562\pi\) | |||||||
\(588\) | −9.00000 | + | 15.5885i | −0.371154 | + | 0.642857i | ||||
\(589\) | 12.0000 | + | 20.7846i | 0.494451 | + | 0.856415i | ||||
\(590\) | 10.0000i | 0.411693i | ||||||||
\(591\) | −23.3827 | + | 13.5000i | −0.961835 | + | 0.555316i | ||||
\(592\) | −2.59808 | + | 1.50000i | −0.106780 | + | 0.0616496i | ||||
\(593\) | 22.0000i | 0.903432i | 0.892162 | + | 0.451716i | \(0.149188\pi\) | ||||
−0.892162 | + | 0.451716i | \(0.850812\pi\) | |||||||
\(594\) | −9.00000 | − | 15.5885i | −0.369274 | − | 0.639602i | ||||
\(595\) | 1.50000 | − | 2.59808i | 0.0614940 | − | 0.106511i | ||||
\(596\) | −15.5885 | − | 9.00000i | −0.638528 | − | 0.368654i | ||||
\(597\) | −30.0000 | −1.22782 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.00000 | −0.0817178 | −0.0408589 | − | 0.999165i | \(-0.513009\pi\) | ||||
−0.0408589 | + | 0.999165i | \(0.513009\pi\) | |||||||
\(600\) | −10.3923 | − | 6.00000i | −0.424264 | − | 0.244949i | ||||
\(601\) | 17.5000 | − | 30.3109i | 0.713840 | − | 1.23641i | −0.249565 | − | 0.968358i | \(-0.580288\pi\) |
0.963405 | − | 0.268049i | \(-0.0863789\pi\) | |||||||
\(602\) | −2.50000 | − | 4.33013i | −0.101892 | − | 0.176483i | ||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | −7.79423 | + | 4.50000i | −0.317143 | + | 0.183102i | ||||
\(605\) | −6.06218 | + | 3.50000i | −0.246463 | + | 0.142295i | ||||
\(606\) | 12.0000i | 0.487467i | ||||||||
\(607\) | −3.00000 | − | 5.19615i | −0.121766 | − | 0.210905i | 0.798698 | − | 0.601732i | \(-0.205522\pi\) |
−0.920464 | + | 0.390827i | \(0.872189\pi\) | |||||||
\(608\) | 3.00000 | − | 5.19615i | 0.121666 | − | 0.210732i | ||||
\(609\) | −5.19615 | − | 3.00000i | −0.210559 | − | 0.121566i | ||||
\(610\) | −8.00000 | −0.323911 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −18.0000 | −0.727607 | ||||||||
\(613\) | −22.5167 | − | 13.0000i | −0.909439 | − | 0.525065i | −0.0291886 | − | 0.999574i | \(-0.509292\pi\) |
−0.880251 | + | 0.474509i | \(0.842626\pi\) | |||||||
\(614\) | −7.00000 | + | 12.1244i | −0.282497 | + | 0.489299i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 2.00000i | − | 0.0805823i | ||||||
\(617\) | 13.8564 | − | 8.00000i | 0.557838 | − | 0.322068i | −0.194439 | − | 0.980915i | \(-0.562289\pi\) |
0.752277 | + | 0.658847i | \(0.228955\pi\) | |||||||
\(618\) | −20.7846 | + | 12.0000i | −0.836080 | + | 0.482711i | ||||
\(619\) | − | 4.00000i | − | 0.160774i | −0.996764 | − | 0.0803868i | \(-0.974384\pi\) | ||
0.996764 | − | 0.0803868i | \(-0.0256155\pi\) | |||||||
\(620\) | 2.00000 | + | 3.46410i | 0.0803219 | + | 0.139122i | ||||
\(621\) | 18.0000 | − | 31.1769i | 0.722315 | − | 1.25109i | ||||
\(622\) | 15.5885 | + | 9.00000i | 0.625040 | + | 0.360867i | ||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0.866025 | + | 0.500000i | 0.0346133 | + | 0.0199840i | ||||
\(627\) | −18.0000 | + | 31.1769i | −0.718851 | + | 1.24509i | ||||
\(628\) | −5.00000 | − | 8.66025i | −0.199522 | − | 0.345582i | ||||
\(629\) | − | 9.00000i | − | 0.358854i | ||||||
\(630\) | −5.19615 | + | 3.00000i | −0.207020 | + | 0.119523i | ||||
\(631\) | 4.33013 | − | 2.50000i | 0.172380 | − | 0.0995234i | −0.411328 | − | 0.911487i | \(-0.634935\pi\) |
0.583707 | + | 0.811964i | \(0.301602\pi\) | |||||||
\(632\) | 4.00000i | 0.159111i | ||||||||
\(633\) | 34.5000 | + | 59.7558i | 1.37125 | + | 2.37508i | ||||
\(634\) | −9.00000 | + | 15.5885i | −0.357436 | + | 0.619097i | ||||
\(635\) | −13.8564 | − | 8.00000i | −0.549875 | − | 0.317470i | ||||
\(636\) | 36.0000 | 1.42749 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 25.9808 | + | 15.0000i | 1.02778 | + | 0.593391i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −1.00000 | − | 1.73205i | −0.0394976 | − | 0.0684119i | 0.845601 | − | 0.533816i | \(-0.179242\pi\) |
−0.885098 | + | 0.465404i | \(0.845909\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | 12.1244 | − | 7.00000i | 0.478138 | − | 0.276053i | −0.241502 | − | 0.970400i | \(-0.577640\pi\) |
0.719640 | + | 0.694347i | \(0.244307\pi\) | |||||||
\(644\) | 3.46410 | − | 2.00000i | 0.136505 | − | 0.0788110i | ||||
\(645\) | 15.0000i | 0.590624i | ||||||||
\(646\) | 9.00000 | + | 15.5885i | 0.354100 | + | 0.613320i | ||||
\(647\) | −19.0000 | + | 32.9090i | −0.746967 | + | 1.29378i | 0.202303 | + | 0.979323i | \(0.435157\pi\) |
−0.949270 | + | 0.314462i | \(0.898176\pi\) | |||||||
\(648\) | 7.79423 | + | 4.50000i | 0.306186 | + | 0.176777i | ||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | 3.46410 | + | 2.00000i | 0.135665 | + | 0.0783260i | ||||
\(653\) | −12.0000 | + | 20.7846i | −0.469596 | + | 0.813365i | −0.999396 | − | 0.0347583i | \(-0.988934\pi\) |
0.529799 | + | 0.848123i | \(0.322267\pi\) | |||||||
\(654\) | −28.5000 | − | 49.3634i | −1.11444 | − | 1.93026i | ||||
\(655\) | 1.00000i | 0.0390732i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 51.9615 | − | 30.0000i | 2.02721 | − | 1.17041i | ||||
\(658\) | − | 13.0000i | − | 0.506793i | ||||||
\(659\) | 6.00000 | + | 10.3923i | 0.233727 | + | 0.404827i | 0.958902 | − | 0.283738i | \(-0.0915745\pi\) |
−0.725175 | + | 0.688565i | \(0.758241\pi\) | |||||||
\(660\) | −3.00000 | + | 5.19615i | −0.116775 | + | 0.202260i | ||||
\(661\) | −8.66025 | − | 5.00000i | −0.336845 | − | 0.194477i | 0.322031 | − | 0.946729i | \(-0.395634\pi\) |
−0.658876 | + | 0.752252i | \(0.728968\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.19615 | + | 3.00000i | 0.201498 | + | 0.116335i | ||||
\(666\) | −9.00000 | + | 15.5885i | −0.348743 | + | 0.604040i | ||||
\(667\) | −4.00000 | − | 6.92820i | −0.154881 | − | 0.268261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 54.5596 | − | 31.5000i | 2.10940 | − | 1.21786i | ||||
\(670\) | −1.73205 | + | 1.00000i | −0.0669150 | + | 0.0386334i | ||||
\(671\) | − | 16.0000i | − | 0.617673i | ||||||
\(672\) | 1.50000 | + | 2.59808i | 0.0578638 | + | 0.100223i | ||||
\(673\) | 18.5000 | − | 32.0429i | 0.713123 | − | 1.23516i | −0.250557 | − | 0.968102i | \(-0.580614\pi\) |
0.963679 | − | 0.267063i | \(-0.0860531\pi\) | |||||||
\(674\) | 19.9186 | + | 11.5000i | 0.767235 | + | 0.442963i | ||||
\(675\) | −36.0000 | −1.38564 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.0000 | −1.38359 | −0.691796 | − | 0.722093i | \(-0.743180\pi\) | ||||
−0.691796 | + | 0.722093i | \(0.743180\pi\) | |||||||
\(678\) | 5.19615 | + | 3.00000i | 0.199557 | + | 0.115214i | ||||
\(679\) | −7.00000 | + | 12.1244i | −0.268635 | + | 0.465290i | ||||
\(680\) | 1.50000 | + | 2.59808i | 0.0575224 | + | 0.0996317i | ||||
\(681\) | 72.0000i | 2.75905i | ||||||||
\(682\) | −6.92820 | + | 4.00000i | −0.265295 | + | 0.153168i | ||||
\(683\) | 38.1051 | − | 22.0000i | 1.45805 | − | 0.841807i | 0.459136 | − | 0.888366i | \(-0.348159\pi\) |
0.998916 | + | 0.0465592i | \(0.0148256\pi\) | |||||||
\(684\) | − | 36.0000i | − | 1.37649i | ||||||
\(685\) | 6.00000 | + | 10.3923i | 0.229248 | + | 0.397070i | ||||
\(686\) | −6.50000 | + | 11.2583i | −0.248171 | + | 0.429845i | ||||
\(687\) | 38.9711 | + | 22.5000i | 1.48684 | + | 0.858429i | ||||
\(688\) | 5.00000 | 0.190623 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −12.0000 | −0.456832 | ||||||||
\(691\) | 6.92820 | + | 4.00000i | 0.263561 | + | 0.152167i | 0.625958 | − | 0.779857i | \(-0.284708\pi\) |
−0.362397 | + | 0.932024i | \(0.618041\pi\) | |||||||
\(692\) | −10.0000 | + | 17.3205i | −0.380143 | + | 0.658427i | ||||
\(693\) | −6.00000 | − | 10.3923i | −0.227921 | − | 0.394771i | ||||
\(694\) | − | 9.00000i | − | 0.341635i | ||||||
\(695\) | −6.06218 | + | 3.50000i | −0.229952 | + | 0.132763i | ||||
\(696\) | 5.19615 | − | 3.00000i | 0.196960 | − | 0.113715i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −3.50000 | − | 6.06218i | −0.132477 | − | 0.229457i | ||||
\(699\) | 16.5000 | − | 28.5788i | 0.624087 | − | 1.08095i | ||||
\(700\) | −3.46410 | − | 2.00000i | −0.130931 | − | 0.0755929i | ||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | 0.678883 | ||||||||
\(704\) | 1.73205 | + | 1.00000i | 0.0652791 | + | 0.0376889i | ||||
\(705\) | −19.5000 | + | 33.7750i | −0.734412 | + | 1.27204i | ||||
\(706\) | 2.00000 | + | 3.46410i | 0.0752710 | + | 0.130373i | ||||
\(707\) | 4.00000i | 0.150435i | ||||||||
\(708\) | 25.9808 | − | 15.0000i | 0.976417 | − | 0.563735i | ||||
\(709\) | −32.9090 | + | 19.0000i | −1.23592 | + | 0.713560i | −0.968258 | − | 0.249952i | \(-0.919585\pi\) |
−0.267664 | + | 0.963512i | \(0.586252\pi\) | |||||||
\(710\) | − | 5.00000i | − | 0.187647i | ||||||
\(711\) | 12.0000 | + | 20.7846i | 0.450035 | + | 0.779484i | ||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | −13.8564 | − | 8.00000i | −0.518927 | − | 0.299602i | ||||
\(714\) | −9.00000 | −0.336817 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.00000 | −0.336346 | ||||||||
\(717\) | 23.3827 | + | 13.5000i | 0.873242 | + | 0.504167i | ||||
\(718\) | −12.0000 | + | 20.7846i | −0.447836 | + | 0.775675i | ||||
\(719\) | −11.0000 | − | 19.0526i | −0.410231 | − | 0.710541i | 0.584684 | − | 0.811261i | \(-0.301219\pi\) |
−0.994915 | + | 0.100721i | \(0.967885\pi\) | |||||||
\(720\) | − | 6.00000i | − | 0.223607i | ||||||
\(721\) | −6.92820 | + | 4.00000i | −0.258020 | + | 0.148968i | ||||
\(722\) | −14.7224 | + | 8.50000i | −0.547912 | + | 0.316337i | ||||
\(723\) | 54.0000i | 2.00828i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.00000 | + | 6.92820i | −0.148556 | + | 0.257307i | ||||
\(726\) | 18.1865 | + | 10.5000i | 0.674966 | + | 0.389692i | ||||
\(727\) | 14.0000 | 0.519231 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −8.66025 | − | 5.00000i | −0.320530 | − | 0.185058i | ||||
\(731\) | −7.50000 | + | 12.9904i | −0.277398 | + | 0.480467i | ||||
\(732\) | 12.0000 | + | 20.7846i | 0.443533 | + | 0.768221i | ||||
\(733\) | − | 43.0000i | − | 1.58824i | −0.607760 | − | 0.794121i | \(-0.707932\pi\) | ||
0.607760 | − | 0.794121i | \(-0.292068\pi\) | |||||||
\(734\) | −8.66025 | + | 5.00000i | −0.319656 | + | 0.184553i | ||||
\(735\) | 15.5885 | − | 9.00000i | 0.574989 | − | 0.331970i | ||||
\(736\) | 4.00000i | 0.147442i | ||||||||
\(737\) | −2.00000 | − | 3.46410i | −0.0736709 | − | 0.127602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3923 | + | 6.00000i | 0.382287 | + | 0.220714i | 0.678813 | − | 0.734311i | \(-0.262495\pi\) |
−0.296526 | + | 0.955025i | \(0.595828\pi\) | |||||||
\(740\) | 3.00000 | 0.110282 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | 40.7032 | + | 23.5000i | 1.49326 | + | 0.862131i | 0.999970 | − | 0.00773621i | \(-0.00246254\pi\) |
0.493285 | + | 0.869868i | \(0.335796\pi\) | |||||||
\(744\) | 6.00000 | − | 10.3923i | 0.219971 | − | 0.381000i | ||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | − | 4.00000i | − | 0.146450i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.19615 | + | 3.00000i | −0.189990 | + | 0.109691i | ||||
\(749\) | 4.00000i | 0.146157i | ||||||||
\(750\) | 13.5000 | + | 23.3827i | 0.492950 | + | 0.853815i | ||||
\(751\) | 12.0000 | − | 20.7846i | 0.437886 | − | 0.758441i | −0.559640 | − | 0.828736i | \(-0.689061\pi\) |
0.997526 | + | 0.0702946i | \(0.0223939\pi\) | |||||||
\(752\) | 11.2583 | + | 6.50000i | 0.410549 | + | 0.237031i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.00000 | 0.327544 | ||||||||
\(756\) | 7.79423 | + | 4.50000i | 0.283473 | + | 0.163663i | ||||
\(757\) | 6.00000 | − | 10.3923i | 0.218074 | − | 0.377715i | −0.736145 | − | 0.676824i | \(-0.763356\pi\) |
0.954219 | + | 0.299109i | \(0.0966893\pi\) | |||||||
\(758\) | 8.00000 | + | 13.8564i | 0.290573 | + | 0.503287i | ||||
\(759\) | − | 24.0000i | − | 0.871145i | ||||||
\(760\) | −5.19615 | + | 3.00000i | −0.188484 | + | 0.108821i | ||||
\(761\) | −5.19615 | + | 3.00000i | −0.188360 | + | 0.108750i | −0.591215 | − | 0.806514i | \(-0.701351\pi\) |
0.402854 | + | 0.915264i | \(0.368018\pi\) | |||||||
\(762\) | 48.0000i | 1.73886i | ||||||||
\(763\) | −9.50000 | − | 16.4545i | −0.343923 | − | 0.595692i | ||||
\(764\) | 5.00000 | − | 8.66025i | 0.180894 | − | 0.313317i | ||||
\(765\) | 15.5885 | + | 9.00000i | 0.563602 | + | 0.325396i | ||||
\(766\) | −27.0000 | −0.975550 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.00000 | −0.108253 | ||||||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | −1.00000 | + | 1.73205i | −0.0360375 | + | 0.0624188i | ||||
\(771\) | 22.5000 | + | 38.9711i | 0.810318 | + | 1.40351i | ||||
\(772\) | − | 16.0000i | − | 0.575853i | ||||||
\(773\) | 9.52628 | − | 5.50000i | 0.342636 | − | 0.197821i | −0.318801 | − | 0.947822i | \(-0.603280\pi\) |
0.661437 | + | 0.750000i | \(0.269947\pi\) | |||||||
\(774\) | 25.9808 | − | 15.0000i | 0.933859 | − | 0.539164i | ||||
\(775\) | 16.0000i | 0.574737i | ||||||||
\(776\) | −7.00000 | − | 12.1244i | −0.251285 | − | 0.435239i | ||||
\(777\) | −4.50000 | + | 7.79423i | −0.161437 | + | 0.279616i | ||||
\(778\) | −25.9808 | − | 15.0000i | −0.931455 | − | 0.537776i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | 0.357828 | ||||||||
\(782\) | −10.3923 | − | 6.00000i | −0.371628 | − | 0.214560i | ||||
\(783\) | 9.00000 | − | 15.5885i | 0.321634 | − | 0.557086i | ||||
\(784\) | −3.00000 | − | 5.19615i | −0.107143 | − | 0.185577i | ||||
\(785\) | 10.0000i | 0.356915i | ||||||||
\(786\) | 2.59808 | − | 1.50000i | 0.0926703 | − | 0.0535032i | ||||
\(787\) | −27.7128 | + | 16.0000i | −0.987855 | + | 0.570338i | −0.904632 | − | 0.426193i | \(-0.859855\pi\) |
−0.0832226 | + | 0.996531i | \(0.526521\pi\) | |||||||
\(788\) | − | 9.00000i | − | 0.320612i | ||||||
\(789\) | 18.0000 | + | 31.1769i | 0.640817 | + | 1.10993i | ||||
\(790\) | 2.00000 | − | 3.46410i | 0.0711568 | − | 0.123247i | ||||
\(791\) | 1.73205 | + | 1.00000i | 0.0615846 | + | 0.0355559i | ||||
\(792\) | 12.0000 | 0.426401 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −22.0000 | −0.780751 | ||||||||
\(795\) | −31.1769 | − | 18.0000i | −1.10573 | − | 0.638394i | ||||
\(796\) | 5.00000 | − | 8.66025i | 0.177220 | − | 0.306955i | ||||
\(797\) | −21.0000 | − | 36.3731i | −0.743858 | − | 1.28840i | −0.950726 | − | 0.310031i | \(-0.899660\pi\) |
0.206868 | − | 0.978369i | \(-0.433673\pi\) | |||||||
\(798\) | − | 18.0000i | − | 0.637193i | ||||||
\(799\) | −33.7750 | + | 19.5000i | −1.19487 | + | 0.689860i | ||||
\(800\) | 3.46410 | − | 2.00000i | 0.122474 | − | 0.0707107i | ||||
\(801\) | − | 36.0000i | − | 1.27200i | ||||||
\(802\) | −12.0000 | − | 20.7846i | −0.423735 | − | 0.733930i | ||||
\(803\) | 10.0000 | − | 17.3205i | 0.352892 | − | 0.611227i | ||||
\(804\) | 5.19615 | + | 3.00000i | 0.183254 | + | 0.105802i | ||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 72.0000 | 2.53452 | ||||||||
\(808\) | −3.46410 | − | 2.00000i | −0.121867 | − | 0.0703598i | ||||
\(809\) | 4.50000 | − | 7.79423i | 0.158212 | − | 0.274030i | −0.776012 | − | 0.630718i | \(-0.782761\pi\) |
0.934224 | + | 0.356687i | \(0.116094\pi\) | |||||||
\(810\) | −4.50000 | − | 7.79423i | −0.158114 | − | 0.273861i | ||||
\(811\) | − | 28.0000i | − | 0.983213i | −0.870817 | − | 0.491606i | \(-0.836410\pi\) | ||
0.870817 | − | 0.491606i | \(-0.163590\pi\) | |||||||
\(812\) | 1.73205 | − | 1.00000i | 0.0607831 | − | 0.0350931i | ||||
\(813\) | 33.7750 | − | 19.5000i | 1.18454 | − | 0.683895i | ||||
\(814\) | 6.00000i | 0.210300i | ||||||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 4.50000 | − | 7.79423i | 0.157532 | − | 0.272853i | ||||
\(817\) | −25.9808 | − | 15.0000i | −0.908952 | − | 0.524784i | ||||
\(818\) | −4.00000 | −0.139857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.6506 | + | 12.5000i | 0.755612 | + | 0.436253i | 0.827718 | − | 0.561144i | \(-0.189639\pi\) |
−0.0721058 | + | 0.997397i | \(0.522972\pi\) | |||||||
\(822\) | 18.0000 | − | 31.1769i | 0.627822 | − | 1.08742i | ||||
\(823\) | 27.0000 | + | 46.7654i | 0.941161 | + | 1.63014i | 0.763261 | + | 0.646090i | \(0.223597\pi\) |
0.177899 | + | 0.984049i | \(0.443070\pi\) | |||||||
\(824\) | − | 8.00000i | − | 0.278693i | ||||||
\(825\) | −20.7846 | + | 12.0000i | −0.723627 | + | 0.417786i | ||||
\(826\) | 8.66025 | − | 5.00000i | 0.301329 | − | 0.173972i | ||||
\(827\) | − | 30.0000i | − | 1.04320i | −0.853189 | − | 0.521601i | \(-0.825335\pi\) | ||
0.853189 | − | 0.521601i | \(-0.174665\pi\) | |||||||
\(828\) | 12.0000 | + | 20.7846i | 0.417029 | + | 0.722315i | ||||
\(829\) | −19.0000 | + | 32.9090i | −0.659897 | + | 1.14298i | 0.320745 | + | 0.947166i | \(0.396067\pi\) |
−0.980642 | + | 0.195810i | \(0.937266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.0000 | 1.24883 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | 18.1865 | + | 10.5000i | 0.629748 | + | 0.363585i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.00000 | − | 10.3923i | −0.207514 | − | 0.359425i | ||||
\(837\) | − | 36.0000i | − | 1.24434i | ||||||
\(838\) | 18.1865 | − | 10.5000i | 0.628243 | − | 0.362716i | ||||
\(839\) | −48.4974 | + | 28.0000i | −1.67432 | + | 0.966667i | −0.709141 | + | 0.705067i | \(0.750917\pi\) |
−0.965176 | + | 0.261600i | \(0.915750\pi\) | |||||||
\(840\) | − | 3.00000i | − | 0.103510i | ||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | −2.50000 | + | 4.33013i | −0.0861557 | + | 0.149226i | ||||
\(843\) | 67.5500 | + | 39.0000i | 2.32654 | + | 1.34323i | ||||
\(844\) | −23.0000 | −0.791693 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 78.0000 | 2.68170 | ||||||||
\(847\) | 6.06218 | + | 3.50000i | 0.208299 | + | 0.120261i | ||||
\(848\) | −6.00000 | + | 10.3923i | −0.206041 | + | 0.356873i | ||||
\(849\) | −6.00000 | − | 10.3923i | −0.205919 | − | 0.356663i | ||||
\(850\) | 12.0000i | 0.411597i | ||||||||
\(851\) | −10.3923 | + | 6.00000i | −0.356244 | + | 0.205677i | ||||
\(852\) | −12.9904 | + | 7.50000i | −0.445043 | + | 0.256946i | ||||
\(853\) | − | 49.0000i | − | 1.67773i | −0.544341 | − | 0.838864i | \(-0.683220\pi\) | ||
0.544341 | − | 0.838864i | \(-0.316780\pi\) | |||||||
\(854\) | 4.00000 | + | 6.92820i | 0.136877 | + | 0.237078i | ||||
\(855\) | −18.0000 | + | 31.1769i | −0.615587 | + | 1.06623i | ||||
\(856\) | −3.46410 | − | 2.00000i | −0.118401 | − | 0.0683586i | ||||
\(857\) | −46.0000 | −1.57133 | −0.785665 | − | 0.618652i | \(-0.787679\pi\) | ||||
−0.785665 | + | 0.618652i | \(0.787679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | −4.33013 | − | 2.50000i | −0.147656 | − | 0.0852493i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.5000 | + | 28.5788i | 0.561992 | + | 0.973399i | ||||
\(863\) | − | 11.0000i | − | 0.374444i | −0.982318 | − | 0.187222i | \(-0.940052\pi\) | ||
0.982318 | − | 0.187222i | \(-0.0599484\pi\) | |||||||
\(864\) | −7.79423 | + | 4.50000i | −0.265165 | + | 0.153093i | ||||
\(865\) | 17.3205 | − | 10.0000i | 0.588915 | − | 0.340010i | ||||
\(866\) | − | 7.00000i | − | 0.237870i | ||||||
\(867\) | −12.0000 | − | 20.7846i | −0.407541 | − | 0.705882i | ||||
\(868\) | 2.00000 | − | 3.46410i | 0.0678844 | − | 0.117579i | ||||
\(869\) | 6.92820 | + | 4.00000i | 0.235023 | + | 0.135691i | ||||
\(870\) | −6.00000 | −0.203419 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19.0000 | 0.643421 | ||||||||
\(873\) | −72.7461 | − | 42.0000i | −2.46208 | − | 1.42148i | ||||
\(874\) | 12.0000 | − | 20.7846i | 0.405906 | − | 0.703050i | ||||
\(875\) | 4.50000 | + | 7.79423i | 0.152128 | + | 0.263493i | ||||
\(876\) | 30.0000i | 1.01361i | ||||||||
\(877\) | −33.7750 | + | 19.5000i | −1.14050 | + | 0.658468i | −0.946554 | − | 0.322544i | \(-0.895462\pi\) |
−0.193946 | + | 0.981012i | \(0.562129\pi\) | |||||||
\(878\) | 19.0526 | − | 11.0000i | 0.642993 | − | 0.371232i | ||||
\(879\) | 21.0000i | 0.708312i | ||||||||
\(880\) | −1.00000 | − | 1.73205i | −0.0337100 | − | 0.0583874i | ||||
\(881\) | 10.5000 | − | 18.1865i | 0.353754 | − | 0.612720i | −0.633150 | − | 0.774029i | \(-0.718238\pi\) |
0.986904 | + | 0.161309i | \(0.0515717\pi\) | |||||||
\(882\) | −31.1769 | − | 18.0000i | −1.04978 | − | 0.606092i | ||||
\(883\) | 47.0000 | 1.58168 | 0.790838 | − | 0.612026i | \(-0.209645\pi\) | ||||
0.790838 | + | 0.612026i | \(0.209645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.0000 | −1.00844 | ||||||||
\(886\) | 33.7750 | + | 19.5000i | 1.13469 | + | 0.655115i | ||||
\(887\) | 4.00000 | − | 6.92820i | 0.134307 | − | 0.232626i | −0.791026 | − | 0.611783i | \(-0.790453\pi\) |
0.925332 | + | 0.379157i | \(0.123786\pi\) | |||||||
\(888\) | −4.50000 | − | 7.79423i | −0.151010 | − | 0.261557i | ||||
\(889\) | 16.0000i | 0.536623i | ||||||||
\(890\) | −5.19615 | + | 3.00000i | −0.174175 | + | 0.100560i | ||||
\(891\) | 15.5885 | − | 9.00000i | 0.522233 | − | 0.301511i | ||||
\(892\) | 21.0000i | 0.703132i | ||||||||
\(893\) | −39.0000 | − | 67.5500i | −1.30509 | − | 2.26047i | ||||
\(894\) | 27.0000 | − | 46.7654i | 0.903015 | − | 1.56407i | ||||
\(895\) | 7.79423 | + | 4.50000i | 0.260532 | + | 0.150418i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.0000 | −0.867631 | ||||||||
\(899\) | −6.92820 | − | 4.00000i | −0.231069 | − | 0.133407i | ||||
\(900\) | 12.0000 | − | 20.7846i | 0.400000 | − | 0.692820i | ||||
\(901\) | −18.0000 | − | 31.1769i | −0.599667 | − | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.9904 | − | 7.50000i | 0.432293 | − | 0.249584i | ||||
\(904\) | −1.73205 | + | 1.00000i | −0.0576072 | + | 0.0332595i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.5000 | − | 23.3827i | −0.448507 | − | 0.776838i | ||||
\(907\) | −4.50000 | + | 7.79423i | −0.149420 | + | 0.258803i | −0.931013 | − | 0.364985i | \(-0.881074\pi\) |
0.781593 | + | 0.623788i | \(0.214407\pi\) | |||||||
\(908\) | −20.7846 | − | 12.0000i | −0.689761 | − | 0.398234i | ||||
\(909\) | −24.0000 | −0.796030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.0000 | −1.78910 | −0.894550 | − | 0.446968i | \(-0.852504\pi\) | ||||
−0.894550 | + | 0.446968i | \(0.852504\pi\) | |||||||
\(912\) | 15.5885 | + | 9.00000i | 0.516185 | + | 0.298020i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.00000 | + | 8.66025i | 0.165385 | + | 0.286456i | ||||
\(915\) | − | 24.0000i | − | 0.793416i | ||||||
\(916\) | −12.9904 | + | 7.50000i | −0.429214 | + | 0.247807i | ||||
\(917\) | 0.866025 | − | 0.500000i | 0.0285987 | − | 0.0165115i | ||||
\(918\) | − | 27.0000i | − | 0.891133i | ||||||
\(919\) | −12.0000 | − | 20.7846i | −0.395843 | − | 0.685621i | 0.597365 | − | 0.801970i | \(-0.296214\pi\) |
−0.993208 | + | 0.116348i | \(0.962881\pi\) | |||||||
\(920\) | 2.00000 | − | 3.46410i | 0.0659380 | − | 0.114208i | ||||
\(921\) | −36.3731 | − | 21.0000i | −1.19853 | − | 0.691974i | ||||
\(922\) | 21.0000 | 0.691598 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6.00000 | 0.197386 | ||||||||
\(925\) | 10.3923 | + | 6.00000i | 0.341697 | + | 0.197279i | ||||
\(926\) | −8.00000 | + | 13.8564i | −0.262896 | + | 0.455350i | ||||
\(927\) | −24.0000 | − | 41.5692i | −0.788263 | − | 1.36531i | ||||
\(928\) | 2.00000i | 0.0656532i | ||||||||
\(929\) | −31.1769 | + | 18.0000i | −1.02288 | + | 0.590561i | −0.914937 | − | 0.403596i | \(-0.867760\pi\) |
−0.107944 | + | 0.994157i | \(0.534427\pi\) | |||||||
\(930\) | −10.3923 | + | 6.00000i | −0.340777 | + | 0.196748i | ||||
\(931\) | 36.0000i | 1.17985i | ||||||||
\(932\) | 5.50000 | + | 9.52628i | 0.180158 | + | 0.312044i | ||||
\(933\) | −27.0000 | + | 46.7654i | −0.883940 | + | 1.53103i | ||||
\(934\) | 17.3205 | + | 10.0000i | 0.566744 | + | 0.327210i | ||||
\(935\) | 6.00000 | 0.196221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0000 | −1.37208 | −0.686040 | − | 0.727564i | \(-0.740653\pi\) | ||||
−0.686040 | + | 0.727564i | \(0.740653\pi\) | |||||||
\(938\) | 1.73205 | + | 1.00000i | 0.0565535 | + | 0.0326512i | ||||
\(939\) | −1.50000 | + | 2.59808i | −0.0489506 | + | 0.0847850i | ||||
\(940\) | −6.50000 | − | 11.2583i | −0.212007 | − | 0.367206i | ||||
\(941\) | 25.0000i | 0.814977i | 0.913210 | + | 0.407488i | \(0.133595\pi\) | ||||
−0.913210 | + | 0.407488i | \(0.866405\pi\) | |||||||
\(942\) | 25.9808 | − | 15.0000i | 0.846499 | − | 0.488726i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 10.0000i | 0.325472i | ||||||||
\(945\) | −4.50000 | − | 7.79423i | −0.146385 | − | 0.253546i | ||||
\(946\) | 5.00000 | − | 8.66025i | 0.162564 | − | 0.281569i | ||||
\(947\) | −15.5885 | − | 9.00000i | −0.506557 | − | 0.292461i | 0.224860 | − | 0.974391i | \(-0.427807\pi\) |
−0.731417 | + | 0.681930i | \(0.761141\pi\) | |||||||
\(948\) | −12.0000 | −0.389742 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −24.0000 | −0.778663 | ||||||||
\(951\) | −46.7654 | − | 27.0000i | −1.51647 | − | 0.875535i | ||||
\(952\) | 1.50000 | − | 2.59808i | 0.0486153 | − | 0.0842041i | ||||
\(953\) | 11.5000 | + | 19.9186i | 0.372522 | + | 0.645226i | 0.989953 | − | 0.141399i | \(-0.0451599\pi\) |
−0.617431 | + | 0.786625i | \(0.711827\pi\) | |||||||
\(954\) | 72.0000i | 2.33109i | ||||||||
\(955\) | −8.66025 | + | 5.00000i | −0.280239 | + | 0.161796i | ||||
\(956\) | −7.79423 | + | 4.50000i | −0.252083 | + | 0.145540i | ||||
\(957\) | − | 12.0000i | − | 0.387905i | ||||||
\(958\) | 1.50000 | + | 2.59808i | 0.0484628 | + | 0.0839400i | ||||
\(959\) | 6.00000 | − | 10.3923i | 0.193750 | − | 0.335585i | ||||
\(960\) | 2.59808 | + | 1.50000i | 0.0838525 | + | 0.0484123i | ||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.0000 | −0.773389 | ||||||||
\(964\) | −15.5885 | − | 9.00000i | −0.502070 | − | 0.289870i | ||||
\(965\) | −8.00000 | + | 13.8564i | −0.257529 | + | 0.446054i | ||||
\(966\) | 6.00000 | + | 10.3923i | 0.193047 | + | 0.334367i | ||||
\(967\) | 23.0000i | 0.739630i | 0.929105 | + | 0.369815i | \(0.120579\pi\) | ||||
−0.929105 | + | 0.369815i | \(0.879421\pi\) | |||||||
\(968\) | −6.06218 | + | 3.50000i | −0.194846 | + | 0.112494i | ||||
\(969\) | −46.7654 | + | 27.0000i | −1.50232 | + | 0.867365i | ||||
\(970\) | 14.0000i | 0.449513i | ||||||||
\(971\) | 7.50000 | + | 12.9904i | 0.240686 | + | 0.416881i | 0.960910 | − | 0.276861i | \(-0.0892941\pi\) |
−0.720224 | + | 0.693742i | \(0.755961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.06218 | + | 3.50000i | 0.194344 | + | 0.112205i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 25.9808 | + | 15.0000i | 0.831198 | + | 0.479893i | 0.854263 | − | 0.519841i | \(-0.174009\pi\) |
−0.0230645 | + | 0.999734i | \(0.507342\pi\) | |||||||
\(978\) | −6.00000 | + | 10.3923i | −0.191859 | + | 0.332309i | ||||
\(979\) | −6.00000 | − | 10.3923i | −0.191761 | − | 0.332140i | ||||
\(980\) | 6.00000i | 0.191663i | ||||||||
\(981\) | 98.7269 | − | 57.0000i | 3.15211 | − | 1.81987i | ||||
\(982\) | 4.33013 | − | 2.50000i | 0.138180 | − | 0.0797782i | ||||
\(983\) | 31.0000i | 0.988746i | 0.869250 | + | 0.494373i | \(0.164602\pi\) | ||||
−0.869250 | + | 0.494373i | \(0.835398\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.50000 | + | 7.79423i | −0.143382 | + | 0.248345i | ||||
\(986\) | −5.19615 | − | 3.00000i | −0.165479 | − | 0.0955395i | ||||
\(987\) | 39.0000 | 1.24138 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.0000 | 0.635963 | ||||||||
\(990\) | −10.3923 | − | 6.00000i | −0.330289 | − | 0.190693i | ||||
\(991\) | 15.0000 | − | 25.9808i | 0.476491 | − | 0.825306i | −0.523146 | − | 0.852243i | \(-0.675242\pi\) |
0.999637 | + | 0.0269367i | \(0.00857526\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | 12.0000i | 0.380808i | ||||||||
\(994\) | −4.33013 | + | 2.50000i | −0.137343 | + | 0.0792952i | ||||
\(995\) | −8.66025 | + | 5.00000i | −0.274549 | + | 0.158511i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | + | 8.66025i | 0.158352 | + | 0.274273i | 0.934274 | − | 0.356555i | \(-0.116049\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | −16.0000 | + | 27.7128i | −0.506471 | + | 0.877234i | ||||
\(999\) | −23.3827 | − | 13.5000i | −0.739795 | − | 0.427121i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))