Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(67,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.i (of order \(3\), degree \(2\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.331 |
Dual form | 462.2.i.a.67.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.50000 | + | 4.33013i | 0.606339 | + | 1.05021i | 0.991838 | + | 0.127502i | \(0.0406959\pi\) |
−0.385499 | + | 0.922708i | \(0.625971\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 3.00000 | 0.670820 | ||||||||
\(21\) | 2.00000 | + | 1.73205i | 0.436436 | + | 0.377964i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.50000 | + | 4.33013i | −0.521286 | + | 0.902894i | 0.478407 | + | 0.878138i | \(0.341214\pi\) |
−0.999694 | + | 0.0247559i | \(0.992119\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 3.00000 | − | 5.19615i | 0.588348 | − | 1.01905i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 1.50000 | − | 2.59808i | 0.273861 | − | 0.474342i | ||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0.500000 | − | 0.866025i | 0.0870388 | − | 0.150756i | ||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | 1.50000 | − | 7.79423i | 0.253546 | − | 1.31747i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.00000 | − | 1.73205i | 0.164399 | − | 0.284747i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | 3.00000 | + | 5.19615i | 0.486664 | + | 0.842927i | ||||
\(39\) | −3.00000 | − | 5.19615i | −0.480384 | − | 0.832050i | ||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | 2.50000 | − | 0.866025i | 0.385758 | − | 0.133631i | ||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | −1.50000 | − | 2.59808i | −0.223607 | − | 0.387298i | ||||
\(46\) | 2.50000 | + | 4.33013i | 0.368605 | + | 0.638442i | ||||
\(47\) | −4.50000 | + | 7.79423i | −0.656392 | + | 1.13691i | 0.325150 | + | 0.945662i | \(0.394585\pi\) |
−0.981543 | + | 0.191243i | \(0.938748\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | 2.50000 | − | 4.33013i | 0.350070 | − | 0.606339i | ||||
\(52\) | −3.00000 | − | 5.19615i | −0.416025 | − | 0.720577i | ||||
\(53\) | −1.00000 | − | 1.73205i | −0.137361 | − | 0.237915i | 0.789136 | − | 0.614218i | \(-0.210529\pi\) |
−0.926497 | + | 0.376303i | \(0.877195\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | −3.00000 | + | 5.19615i | −0.393919 | + | 0.682288i | ||||
\(59\) | 6.00000 | + | 10.3923i | 0.781133 | + | 1.35296i | 0.931282 | + | 0.364299i | \(0.118692\pi\) |
−0.150148 | + | 0.988663i | \(0.547975\pi\) | |||||||
\(60\) | −1.50000 | − | 2.59808i | −0.193649 | − | 0.335410i | ||||
\(61\) | 2.50000 | − | 4.33013i | 0.320092 | − | 0.554416i | −0.660415 | − | 0.750901i | \(-0.729619\pi\) |
0.980507 | + | 0.196485i | \(0.0629528\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0.500000 | − | 2.59808i | 0.0629941 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.00000 | + | 15.5885i | −1.11631 | + | 1.93351i | ||||
\(66\) | −0.500000 | − | 0.866025i | −0.0615457 | − | 0.106600i | ||||
\(67\) | −2.50000 | − | 4.33013i | −0.305424 | − | 0.529009i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 2.50000 | − | 4.33013i | 0.303170 | − | 0.525105i | ||||
\(69\) | 5.00000 | 0.601929 | ||||||||
\(70\) | −6.00000 | − | 5.19615i | −0.717137 | − | 0.621059i | ||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −6.00000 | − | 10.3923i | −0.702247 | − | 1.21633i | −0.967676 | − | 0.252197i | \(-0.918847\pi\) |
0.265429 | − | 0.964130i | \(-0.414486\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | −2.00000 | + | 3.46410i | −0.230940 | + | 0.400000i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | −2.00000 | − | 1.73205i | −0.227921 | − | 0.197386i | ||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.50000 | − | 4.33013i | 0.276079 | − | 0.478183i | ||||
\(83\) | 1.00000 | 0.109764 | 0.0548821 | − | 0.998493i | \(-0.482522\pi\) | ||||
0.0548821 | + | 0.998493i | \(0.482522\pi\) | |||||||
\(84\) | 0.500000 | − | 2.59808i | 0.0545545 | − | 0.283473i | ||||
\(85\) | −15.0000 | −1.62698 | ||||||||
\(86\) | −5.00000 | + | 8.66025i | −0.539164 | + | 0.933859i | ||||
\(87\) | 3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | −3.00000 | −0.316228 | ||||||||
\(91\) | −15.0000 | + | 5.19615i | −1.57243 | + | 0.544705i | ||||
\(92\) | 5.00000 | 0.521286 | ||||||||
\(93\) | −2.00000 | + | 3.46410i | −0.207390 | + | 0.359211i | ||||
\(94\) | 4.50000 | + | 7.79423i | 0.464140 | + | 0.803913i | ||||
\(95\) | −9.00000 | − | 15.5885i | −0.923381 | − | 1.59934i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 9.00000 | 0.913812 | 0.456906 | − | 0.889515i | \(-0.348958\pi\) | ||||
0.456906 | + | 0.889515i | \(0.348958\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | 4.00000 | + | 6.92820i | 0.398015 | + | 0.689382i | 0.993481 | − | 0.113998i | \(-0.0363659\pi\) |
−0.595466 | + | 0.803380i | \(0.703033\pi\) | |||||||
\(102\) | −2.50000 | − | 4.33013i | −0.247537 | − | 0.428746i | ||||
\(103\) | 1.00000 | − | 1.73205i | 0.0985329 | − | 0.170664i | −0.812545 | − | 0.582899i | \(-0.801918\pi\) |
0.911078 | + | 0.412235i | \(0.135252\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | −7.50000 | + | 2.59808i | −0.731925 | + | 0.253546i | ||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | 6.50000 | − | 11.2583i | 0.628379 | − | 1.08838i | −0.359498 | − | 0.933146i | \(-0.617052\pi\) |
0.987877 | − | 0.155238i | \(-0.0496145\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 5.50000 | + | 9.52628i | 0.526804 | + | 0.912452i | 0.999512 | + | 0.0312328i | \(0.00994332\pi\) |
−0.472708 | + | 0.881219i | \(0.656723\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 3.00000 | − | 5.19615i | 0.280976 | − | 0.486664i | ||||
\(115\) | −7.50000 | − | 12.9904i | −0.699379 | − | 1.21136i | ||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | −3.00000 | + | 5.19615i | −0.277350 | + | 0.480384i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | −10.0000 | − | 8.66025i | −0.916698 | − | 0.793884i | ||||
\(120\) | −3.00000 | −0.273861 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −2.50000 | − | 4.33013i | −0.226339 | − | 0.392031i | ||||
\(123\) | −2.50000 | − | 4.33013i | −0.225417 | − | 0.390434i | ||||
\(124\) | −2.00000 | + | 3.46410i | −0.179605 | + | 0.311086i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | −2.00000 | − | 1.73205i | −0.178174 | − | 0.154303i | ||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 5.00000 | + | 8.66025i | 0.440225 | + | 0.762493i | ||||
\(130\) | 9.00000 | + | 15.5885i | 0.789352 | + | 1.36720i | ||||
\(131\) | 2.00000 | − | 3.46410i | 0.174741 | − | 0.302660i | −0.765331 | − | 0.643637i | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 3.00000 | − | 15.5885i | 0.260133 | − | 1.35169i | ||||
\(134\) | −5.00000 | −0.431934 | ||||||||
\(135\) | −1.50000 | + | 2.59808i | −0.129099 | + | 0.223607i | ||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | 1.00000 | + | 1.73205i | 0.0854358 | + | 0.147979i | 0.905577 | − | 0.424182i | \(-0.139438\pi\) |
−0.820141 | + | 0.572161i | \(0.806105\pi\) | |||||||
\(138\) | 2.50000 | − | 4.33013i | 0.212814 | − | 0.368605i | ||||
\(139\) | 22.0000 | 1.86602 | 0.933008 | − | 0.359856i | \(-0.117174\pi\) | ||||
0.933008 | + | 0.359856i | \(0.117174\pi\) | |||||||
\(140\) | −7.50000 | + | 2.59808i | −0.633866 | + | 0.219578i | ||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | 2.00000 | − | 3.46410i | 0.167836 | − | 0.290701i | ||||
\(143\) | 3.00000 | + | 5.19615i | 0.250873 | + | 0.434524i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 9.00000 | − | 15.5885i | 0.747409 | − | 1.29455i | ||||
\(146\) | −12.0000 | −0.993127 | ||||||||
\(147\) | −6.50000 | − | 2.59808i | −0.536111 | − | 0.214286i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | 2.00000 | + | 3.46410i | 0.163299 | + | 0.282843i | ||||
\(151\) | −4.50000 | − | 7.79423i | −0.366205 | − | 0.634285i | 0.622764 | − | 0.782410i | \(-0.286010\pi\) |
−0.988969 | + | 0.148124i | \(0.952676\pi\) | |||||||
\(152\) | 3.00000 | − | 5.19615i | 0.243332 | − | 0.421464i | ||||
\(153\) | −5.00000 | −0.404226 | ||||||||
\(154\) | −2.50000 | + | 0.866025i | −0.201456 | + | 0.0697863i | ||||
\(155\) | 12.0000 | 0.963863 | ||||||||
\(156\) | −3.00000 | + | 5.19615i | −0.240192 | + | 0.416025i | ||||
\(157\) | 12.0000 | + | 20.7846i | 0.957704 | + | 1.65879i | 0.728055 | + | 0.685519i | \(0.240425\pi\) |
0.229650 | + | 0.973273i | \(0.426242\pi\) | |||||||
\(158\) | −0.500000 | − | 0.866025i | −0.0397779 | − | 0.0688973i | ||||
\(159\) | −1.00000 | + | 1.73205i | −0.0793052 | + | 0.137361i | ||||
\(160\) | −3.00000 | −0.237171 | ||||||||
\(161\) | 2.50000 | − | 12.9904i | 0.197028 | − | 1.02379i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 0.500000 | − | 0.866025i | 0.0391630 | − | 0.0678323i | −0.845780 | − | 0.533533i | \(-0.820864\pi\) |
0.884943 | + | 0.465700i | \(0.154198\pi\) | |||||||
\(164\) | −2.50000 | − | 4.33013i | −0.195217 | − | 0.338126i | ||||
\(165\) | 1.50000 | + | 2.59808i | 0.116775 | + | 0.202260i | ||||
\(166\) | 0.500000 | − | 0.866025i | 0.0388075 | − | 0.0672166i | ||||
\(167\) | −24.0000 | −1.85718 | −0.928588 | − | 0.371113i | \(-0.878976\pi\) | ||||
−0.928588 | + | 0.371113i | \(0.878976\pi\) | |||||||
\(168\) | −2.00000 | − | 1.73205i | −0.154303 | − | 0.133631i | ||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | −7.50000 | + | 12.9904i | −0.575224 | + | 0.996317i | ||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | 5.00000 | + | 8.66025i | 0.381246 | + | 0.660338i | ||||
\(173\) | 6.00000 | − | 10.3923i | 0.456172 | − | 0.790112i | −0.542583 | − | 0.840002i | \(-0.682554\pi\) |
0.998755 | + | 0.0498898i | \(0.0158870\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | 8.00000 | + | 6.92820i | 0.604743 | + | 0.523723i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 6.00000 | − | 10.3923i | 0.450988 | − | 0.781133i | ||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | 4.00000 | + | 6.92820i | 0.298974 | + | 0.517838i | 0.975901 | − | 0.218212i | \(-0.0700223\pi\) |
−0.676927 | + | 0.736050i | \(0.736689\pi\) | |||||||
\(180\) | −1.50000 | + | 2.59808i | −0.111803 | + | 0.193649i | ||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | −3.00000 | + | 15.5885i | −0.222375 | + | 1.15549i | ||||
\(183\) | −5.00000 | −0.369611 | ||||||||
\(184\) | 2.50000 | − | 4.33013i | 0.184302 | − | 0.319221i | ||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | 2.00000 | + | 3.46410i | 0.146647 | + | 0.254000i | ||||
\(187\) | −2.50000 | + | 4.33013i | −0.182818 | + | 0.316650i | ||||
\(188\) | 9.00000 | 0.656392 | ||||||||
\(189\) | −2.50000 | + | 0.866025i | −0.181848 | + | 0.0629941i | ||||
\(190\) | −18.0000 | −1.30586 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −3.00000 | − | 5.19615i | −0.215945 | − | 0.374027i | 0.737620 | − | 0.675216i | \(-0.235950\pi\) |
−0.953564 | + | 0.301189i | \(0.902616\pi\) | |||||||
\(194\) | 4.50000 | − | 7.79423i | 0.323081 | − | 0.559593i | ||||
\(195\) | 18.0000 | 1.28901 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | −24.0000 | −1.70993 | −0.854965 | − | 0.518686i | \(-0.826421\pi\) | ||||
−0.854965 | + | 0.518686i | \(0.826421\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | −5.00000 | − | 8.66025i | −0.354441 | − | 0.613909i | 0.632581 | − | 0.774494i | \(-0.281995\pi\) |
−0.987022 | + | 0.160585i | \(0.948662\pi\) | |||||||
\(200\) | 2.00000 | + | 3.46410i | 0.141421 | + | 0.244949i | ||||
\(201\) | −2.50000 | + | 4.33013i | −0.176336 | + | 0.305424i | ||||
\(202\) | 8.00000 | 0.562878 | ||||||||
\(203\) | 15.0000 | − | 5.19615i | 1.05279 | − | 0.364698i | ||||
\(204\) | −5.00000 | −0.350070 | ||||||||
\(205\) | −7.50000 | + | 12.9904i | −0.523823 | + | 0.907288i | ||||
\(206\) | −1.00000 | − | 1.73205i | −0.0696733 | − | 0.120678i | ||||
\(207\) | −2.50000 | − | 4.33013i | −0.173762 | − | 0.300965i | ||||
\(208\) | −3.00000 | + | 5.19615i | −0.208013 | + | 0.360288i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | −1.50000 | + | 7.79423i | −0.103510 | + | 0.537853i | ||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | −1.00000 | + | 1.73205i | −0.0686803 | + | 0.118958i | ||||
\(213\) | −2.00000 | − | 3.46410i | −0.137038 | − | 0.237356i | ||||
\(214\) | −6.50000 | − | 11.2583i | −0.444331 | − | 0.769604i | ||||
\(215\) | 15.0000 | − | 25.9808i | 1.02299 | − | 1.77187i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 8.00000 | + | 6.92820i | 0.543075 | + | 0.470317i | ||||
\(218\) | 11.0000 | 0.745014 | ||||||||
\(219\) | −6.00000 | + | 10.3923i | −0.405442 | + | 0.702247i | ||||
\(220\) | 1.50000 | + | 2.59808i | 0.101130 | + | 0.175162i | ||||
\(221\) | 15.0000 | + | 25.9808i | 1.00901 | + | 1.74766i | ||||
\(222\) | −1.00000 | + | 1.73205i | −0.0671156 | + | 0.116248i | ||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 5.00000 | − | 8.66025i | 0.332595 | − | 0.576072i | ||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | −3.00000 | − | 5.19615i | −0.198680 | − | 0.344124i | ||||
\(229\) | −13.0000 | + | 22.5167i | −0.859064 | + | 1.48794i | 0.0137585 | + | 0.999905i | \(0.495620\pi\) |
−0.872823 | + | 0.488037i | \(0.837713\pi\) | |||||||
\(230\) | −15.0000 | −0.989071 | ||||||||
\(231\) | −0.500000 | + | 2.59808i | −0.0328976 | + | 0.170941i | ||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | 14.5000 | − | 25.1147i | 0.949927 | − | 1.64532i | 0.204354 | − | 0.978897i | \(-0.434491\pi\) |
0.745573 | − | 0.666424i | \(-0.232176\pi\) | |||||||
\(234\) | 3.00000 | + | 5.19615i | 0.196116 | + | 0.339683i | ||||
\(235\) | −13.5000 | − | 23.3827i | −0.880643 | − | 1.52532i | ||||
\(236\) | 6.00000 | − | 10.3923i | 0.390567 | − | 0.676481i | ||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −12.5000 | + | 4.33013i | −0.810255 | + | 0.280680i | ||||
\(239\) | 26.0000 | 1.68180 | 0.840900 | − | 0.541190i | \(-0.182026\pi\) | ||||
0.840900 | + | 0.541190i | \(0.182026\pi\) | |||||||
\(240\) | −1.50000 | + | 2.59808i | −0.0968246 | + | 0.167705i | ||||
\(241\) | 13.0000 | + | 22.5167i | 0.837404 | + | 1.45043i | 0.892058 | + | 0.451920i | \(0.149261\pi\) |
−0.0546547 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.00000 | −0.320092 | ||||||||
\(245\) | 3.00000 | + | 20.7846i | 0.191663 | + | 1.32788i | ||||
\(246\) | −5.00000 | −0.318788 | ||||||||
\(247\) | −18.0000 | + | 31.1769i | −1.14531 | + | 1.98374i | ||||
\(248\) | 2.00000 | + | 3.46410i | 0.127000 | + | 0.219971i | ||||
\(249\) | −0.500000 | − | 0.866025i | −0.0316862 | − | 0.0548821i | ||||
\(250\) | −1.50000 | + | 2.59808i | −0.0948683 | + | 0.164317i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −2.50000 | + | 0.866025i | −0.157485 | + | 0.0545545i | ||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | 2.50000 | − | 4.33013i | 0.156864 | − | 0.271696i | ||||
\(255\) | 7.50000 | + | 12.9904i | 0.469668 | + | 0.813489i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.00000 | − | 12.1244i | 0.436648 | − | 0.756297i | −0.560781 | − | 0.827964i | \(-0.689499\pi\) |
0.997429 | + | 0.0716680i | \(0.0228322\pi\) | |||||||
\(258\) | 10.0000 | 0.622573 | ||||||||
\(259\) | −1.00000 | + | 5.19615i | −0.0621370 | + | 0.322873i | ||||
\(260\) | 18.0000 | 1.11631 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | −2.00000 | − | 3.46410i | −0.123560 | − | 0.214013i | ||||
\(263\) | −12.0000 | − | 20.7846i | −0.739952 | − | 1.28163i | −0.952517 | − | 0.304487i | \(-0.901515\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −12.0000 | − | 10.3923i | −0.735767 | − | 0.637193i | ||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | −2.50000 | + | 4.33013i | −0.152712 | + | 0.264505i | ||||
\(269\) | 4.50000 | + | 7.79423i | 0.274370 | + | 0.475223i | 0.969976 | − | 0.243201i | \(-0.0781974\pi\) |
−0.695606 | + | 0.718423i | \(0.744864\pi\) | |||||||
\(270\) | 1.50000 | + | 2.59808i | 0.0912871 | + | 0.158114i | ||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | −5.00000 | −0.303170 | ||||||||
\(273\) | 12.0000 | + | 10.3923i | 0.726273 | + | 0.628971i | ||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | −2.50000 | − | 4.33013i | −0.150482 | − | 0.260643i | ||||
\(277\) | −9.00000 | − | 15.5885i | −0.540758 | − | 0.936620i | −0.998861 | − | 0.0477206i | \(-0.984804\pi\) |
0.458103 | − | 0.888899i | \(-0.348529\pi\) | |||||||
\(278\) | 11.0000 | − | 19.0526i | 0.659736 | − | 1.14270i | ||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | −1.50000 | + | 7.79423i | −0.0896421 | + | 0.465794i | ||||
\(281\) | 11.0000 | 0.656205 | 0.328102 | − | 0.944642i | \(-0.393591\pi\) | ||||
0.328102 | + | 0.944642i | \(0.393591\pi\) | |||||||
\(282\) | 4.50000 | − | 7.79423i | 0.267971 | − | 0.464140i | ||||
\(283\) | 3.00000 | + | 5.19615i | 0.178331 | + | 0.308879i | 0.941309 | − | 0.337546i | \(-0.109597\pi\) |
−0.762978 | + | 0.646425i | \(0.776263\pi\) | |||||||
\(284\) | −2.00000 | − | 3.46410i | −0.118678 | − | 0.205557i | ||||
\(285\) | −9.00000 | + | 15.5885i | −0.533114 | + | 0.923381i | ||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | −12.5000 | + | 4.33013i | −0.737852 | + | 0.255599i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | −9.00000 | − | 15.5885i | −0.528498 | − | 0.915386i | ||||
\(291\) | −4.50000 | − | 7.79423i | −0.263795 | − | 0.456906i | ||||
\(292\) | −6.00000 | + | 10.3923i | −0.351123 | + | 0.608164i | ||||
\(293\) | 8.00000 | 0.467365 | 0.233682 | − | 0.972313i | \(-0.424922\pi\) | ||||
0.233682 | + | 0.972313i | \(0.424922\pi\) | |||||||
\(294\) | −5.50000 | + | 4.33013i | −0.320767 | + | 0.252538i | ||||
\(295\) | −36.0000 | −2.09600 | ||||||||
\(296\) | −1.00000 | + | 1.73205i | −0.0581238 | + | 0.100673i | ||||
\(297\) | 0.500000 | + | 0.866025i | 0.0290129 | + | 0.0502519i | ||||
\(298\) | 9.00000 | + | 15.5885i | 0.521356 | + | 0.903015i | ||||
\(299\) | −15.0000 | + | 25.9808i | −0.867472 | + | 1.50251i | ||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 25.0000 | − | 8.66025i | 1.44098 | − | 0.499169i | ||||
\(302\) | −9.00000 | −0.517892 | ||||||||
\(303\) | 4.00000 | − | 6.92820i | 0.229794 | − | 0.398015i | ||||
\(304\) | −3.00000 | − | 5.19615i | −0.172062 | − | 0.298020i | ||||
\(305\) | 7.50000 | + | 12.9904i | 0.429449 | + | 0.743827i | ||||
\(306\) | −2.50000 | + | 4.33013i | −0.142915 | + | 0.247537i | ||||
\(307\) | 18.0000 | 1.02731 | 0.513657 | − | 0.857996i | \(-0.328290\pi\) | ||||
0.513657 | + | 0.857996i | \(0.328290\pi\) | |||||||
\(308\) | −0.500000 | + | 2.59808i | −0.0284901 | + | 0.148039i | ||||
\(309\) | −2.00000 | −0.113776 | ||||||||
\(310\) | 6.00000 | − | 10.3923i | 0.340777 | − | 0.590243i | ||||
\(311\) | 10.5000 | + | 18.1865i | 0.595400 | + | 1.03126i | 0.993490 | + | 0.113917i | \(0.0363399\pi\) |
−0.398090 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(312\) | 3.00000 | + | 5.19615i | 0.169842 | + | 0.294174i | ||||
\(313\) | 3.00000 | − | 5.19615i | 0.169570 | − | 0.293704i | −0.768699 | − | 0.639611i | \(-0.779095\pi\) |
0.938269 | + | 0.345907i | \(0.112429\pi\) | |||||||
\(314\) | 24.0000 | 1.35440 | ||||||||
\(315\) | 6.00000 | + | 5.19615i | 0.338062 | + | 0.292770i | ||||
\(316\) | −1.00000 | −0.0562544 | ||||||||
\(317\) | −4.50000 | + | 7.79423i | −0.252745 | + | 0.437767i | −0.964281 | − | 0.264883i | \(-0.914667\pi\) |
0.711535 | + | 0.702650i | \(0.248000\pi\) | |||||||
\(318\) | 1.00000 | + | 1.73205i | 0.0560772 | + | 0.0971286i | ||||
\(319\) | −3.00000 | − | 5.19615i | −0.167968 | − | 0.290929i | ||||
\(320\) | −1.50000 | + | 2.59808i | −0.0838525 | + | 0.145237i | ||||
\(321\) | −13.0000 | −0.725589 | ||||||||
\(322\) | −10.0000 | − | 8.66025i | −0.557278 | − | 0.482617i | ||||
\(323\) | −30.0000 | −1.66924 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −12.0000 | − | 20.7846i | −0.665640 | − | 1.15292i | ||||
\(326\) | −0.500000 | − | 0.866025i | −0.0276924 | − | 0.0479647i | ||||
\(327\) | 5.50000 | − | 9.52628i | 0.304151 | − | 0.526804i | ||||
\(328\) | −5.00000 | −0.276079 | ||||||||
\(329\) | 4.50000 | − | 23.3827i | 0.248093 | − | 1.28913i | ||||
\(330\) | 3.00000 | 0.165145 | ||||||||
\(331\) | −17.5000 | + | 30.3109i | −0.961887 | + | 1.66604i | −0.244131 | + | 0.969742i | \(0.578503\pi\) |
−0.717756 | + | 0.696295i | \(0.754831\pi\) | |||||||
\(332\) | −0.500000 | − | 0.866025i | −0.0274411 | − | 0.0475293i | ||||
\(333\) | 1.00000 | + | 1.73205i | 0.0547997 | + | 0.0949158i | ||||
\(334\) | −12.0000 | + | 20.7846i | −0.656611 | + | 1.13728i | ||||
\(335\) | 15.0000 | 0.819538 | ||||||||
\(336\) | −2.50000 | + | 0.866025i | −0.136386 | + | 0.0472456i | ||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 11.5000 | − | 19.9186i | 0.625518 | − | 1.08343i | ||||
\(339\) | −5.00000 | − | 8.66025i | −0.271563 | − | 0.470360i | ||||
\(340\) | 7.50000 | + | 12.9904i | 0.406745 | + | 0.704502i | ||||
\(341\) | 2.00000 | − | 3.46410i | 0.108306 | − | 0.187592i | ||||
\(342\) | −6.00000 | −0.324443 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 10.0000 | 0.539164 | ||||||||
\(345\) | −7.50000 | + | 12.9904i | −0.403786 | + | 0.699379i | ||||
\(346\) | −6.00000 | − | 10.3923i | −0.322562 | − | 0.558694i | ||||
\(347\) | −3.50000 | − | 6.06218i | −0.187890 | − | 0.325435i | 0.756657 | − | 0.653812i | \(-0.226831\pi\) |
−0.944547 | + | 0.328378i | \(0.893498\pi\) | |||||||
\(348\) | 3.00000 | − | 5.19615i | 0.160817 | − | 0.278543i | ||||
\(349\) | −19.0000 | −1.01705 | −0.508523 | − | 0.861048i | \(-0.669808\pi\) | ||||
−0.508523 | + | 0.861048i | \(0.669808\pi\) | |||||||
\(350\) | 10.0000 | − | 3.46410i | 0.534522 | − | 0.185164i | ||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | −12.0000 | − | 20.7846i | −0.638696 | − | 1.10625i | −0.985719 | − | 0.168397i | \(-0.946141\pi\) |
0.347024 | − | 0.937856i | \(-0.387192\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −2.50000 | + | 12.9904i | −0.132314 | + | 0.687524i | ||||
\(358\) | 8.00000 | 0.422813 | ||||||||
\(359\) | 5.00000 | − | 8.66025i | 0.263890 | − | 0.457071i | −0.703382 | − | 0.710812i | \(-0.748328\pi\) |
0.967272 | + | 0.253741i | \(0.0816611\pi\) | |||||||
\(360\) | 1.50000 | + | 2.59808i | 0.0790569 | + | 0.136931i | ||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | −11.0000 | + | 19.0526i | −0.578147 | + | 1.00138i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 12.0000 | + | 10.3923i | 0.628971 | + | 0.544705i | ||||
\(365\) | 36.0000 | 1.88433 | ||||||||
\(366\) | −2.50000 | + | 4.33013i | −0.130677 | + | 0.226339i | ||||
\(367\) | 7.00000 | + | 12.1244i | 0.365397 | + | 0.632886i | 0.988840 | − | 0.148983i | \(-0.0475999\pi\) |
−0.623443 | + | 0.781869i | \(0.714267\pi\) | |||||||
\(368\) | −2.50000 | − | 4.33013i | −0.130322 | − | 0.225723i | ||||
\(369\) | −2.50000 | + | 4.33013i | −0.130145 | + | 0.225417i | ||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | 4.00000 | + | 3.46410i | 0.207670 | + | 0.179847i | ||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | 3.50000 | − | 6.06218i | 0.181223 | − | 0.313888i | −0.761074 | − | 0.648665i | \(-0.775328\pi\) |
0.942297 | + | 0.334777i | \(0.108661\pi\) | |||||||
\(374\) | 2.50000 | + | 4.33013i | 0.129272 | + | 0.223906i | ||||
\(375\) | 1.50000 | + | 2.59808i | 0.0774597 | + | 0.134164i | ||||
\(376\) | 4.50000 | − | 7.79423i | 0.232070 | − | 0.401957i | ||||
\(377\) | −36.0000 | −1.85409 | ||||||||
\(378\) | −0.500000 | + | 2.59808i | −0.0257172 | + | 0.133631i | ||||
\(379\) | 13.0000 | 0.667765 | 0.333883 | − | 0.942615i | \(-0.391641\pi\) | ||||
0.333883 | + | 0.942615i | \(0.391641\pi\) | |||||||
\(380\) | −9.00000 | + | 15.5885i | −0.461690 | + | 0.799671i | ||||
\(381\) | −2.50000 | − | 4.33013i | −0.128079 | − | 0.221839i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.00000 | + | 6.92820i | −0.204390 | + | 0.354015i | −0.949938 | − | 0.312437i | \(-0.898855\pi\) |
0.745548 | + | 0.666452i | \(0.232188\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 7.50000 | − | 2.59808i | 0.382235 | − | 0.132410i | ||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | 5.00000 | − | 8.66025i | 0.254164 | − | 0.440225i | ||||
\(388\) | −4.50000 | − | 7.79423i | −0.228453 | − | 0.395692i | ||||
\(389\) | 10.5000 | + | 18.1865i | 0.532371 | + | 0.922094i | 0.999286 | + | 0.0377914i | \(0.0120322\pi\) |
−0.466915 | + | 0.884302i | \(0.654634\pi\) | |||||||
\(390\) | 9.00000 | − | 15.5885i | 0.455733 | − | 0.789352i | ||||
\(391\) | −25.0000 | −1.26430 | ||||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | −12.0000 | + | 20.7846i | −0.604551 | + | 1.04711i | ||||
\(395\) | 1.50000 | + | 2.59808i | 0.0754732 | + | 0.130723i | ||||
\(396\) | 0.500000 | + | 0.866025i | 0.0251259 | + | 0.0435194i | ||||
\(397\) | −13.0000 | + | 22.5167i | −0.652451 | + | 1.13008i | 0.330075 | + | 0.943955i | \(0.392926\pi\) |
−0.982526 | + | 0.186124i | \(0.940407\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | −15.0000 | + | 5.19615i | −0.750939 | + | 0.260133i | ||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 2.50000 | + | 4.33013i | 0.124689 | + | 0.215967i | ||||
\(403\) | −12.0000 | − | 20.7846i | −0.597763 | − | 1.03536i | ||||
\(404\) | 4.00000 | − | 6.92820i | 0.199007 | − | 0.344691i | ||||
\(405\) | 3.00000 | 0.149071 | ||||||||
\(406\) | 3.00000 | − | 15.5885i | 0.148888 | − | 0.773642i | ||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | −2.50000 | + | 4.33013i | −0.123768 | + | 0.214373i | ||||
\(409\) | −5.00000 | − | 8.66025i | −0.247234 | − | 0.428222i | 0.715523 | − | 0.698589i | \(-0.246188\pi\) |
−0.962757 | + | 0.270367i | \(0.912855\pi\) | |||||||
\(410\) | 7.50000 | + | 12.9904i | 0.370399 | + | 0.641549i | ||||
\(411\) | 1.00000 | − | 1.73205i | 0.0493264 | − | 0.0854358i | ||||
\(412\) | −2.00000 | −0.0985329 | ||||||||
\(413\) | −24.0000 | − | 20.7846i | −1.18096 | − | 1.02274i | ||||
\(414\) | −5.00000 | −0.245737 | ||||||||
\(415\) | −1.50000 | + | 2.59808i | −0.0736321 | + | 0.127535i | ||||
\(416\) | 3.00000 | + | 5.19615i | 0.147087 | + | 0.254762i | ||||
\(417\) | −11.0000 | − | 19.0526i | −0.538672 | − | 0.933008i | ||||
\(418\) | −3.00000 | + | 5.19615i | −0.146735 | + | 0.254152i | ||||
\(419\) | −20.0000 | −0.977064 | −0.488532 | − | 0.872546i | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 6.00000 | + | 5.19615i | 0.292770 | + | 0.253546i | ||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 7.00000 | − | 12.1244i | 0.340755 | − | 0.590204i | ||||
\(423\) | −4.50000 | − | 7.79423i | −0.218797 | − | 0.378968i | ||||
\(424\) | 1.00000 | + | 1.73205i | 0.0485643 | + | 0.0841158i | ||||
\(425\) | 10.0000 | − | 17.3205i | 0.485071 | − | 0.840168i | ||||
\(426\) | −4.00000 | −0.193801 | ||||||||
\(427\) | −2.50000 | + | 12.9904i | −0.120983 | + | 0.628649i | ||||
\(428\) | −13.0000 | −0.628379 | ||||||||
\(429\) | 3.00000 | − | 5.19615i | 0.144841 | − | 0.250873i | ||||
\(430\) | −15.0000 | − | 25.9808i | −0.723364 | − | 1.25290i | ||||
\(431\) | −11.0000 | − | 19.0526i | −0.529851 | − | 0.917729i | −0.999394 | − | 0.0348195i | \(-0.988914\pi\) |
0.469542 | − | 0.882910i | \(-0.344419\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 11.0000 | 0.528626 | 0.264313 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264313 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(434\) | 10.0000 | − | 3.46410i | 0.480015 | − | 0.166282i | ||||
\(435\) | −18.0000 | −0.863034 | ||||||||
\(436\) | 5.50000 | − | 9.52628i | 0.263402 | − | 0.456226i | ||||
\(437\) | −15.0000 | − | 25.9808i | −0.717547 | − | 1.24283i | ||||
\(438\) | 6.00000 | + | 10.3923i | 0.286691 | + | 0.496564i | ||||
\(439\) | 2.50000 | − | 4.33013i | 0.119318 | − | 0.206666i | −0.800179 | − | 0.599761i | \(-0.795262\pi\) |
0.919498 | + | 0.393095i | \(0.128596\pi\) | |||||||
\(440\) | 3.00000 | 0.143019 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | −1.00000 | + | 1.73205i | −0.0475114 | + | 0.0822922i | −0.888803 | − | 0.458289i | \(-0.848462\pi\) |
0.841292 | + | 0.540581i | \(0.181796\pi\) | |||||||
\(444\) | 1.00000 | + | 1.73205i | 0.0474579 | + | 0.0821995i | ||||
\(445\) | −9.00000 | − | 15.5885i | −0.426641 | − | 0.738964i | ||||
\(446\) | 8.00000 | − | 13.8564i | 0.378811 | − | 0.656120i | ||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 2.00000 | − | 3.46410i | 0.0942809 | − | 0.163299i | ||||
\(451\) | 2.50000 | + | 4.33013i | 0.117720 | + | 0.203898i | ||||
\(452\) | −5.00000 | − | 8.66025i | −0.235180 | − | 0.407344i | ||||
\(453\) | −4.50000 | + | 7.79423i | −0.211428 | + | 0.366205i | ||||
\(454\) | −3.00000 | −0.140797 | ||||||||
\(455\) | 9.00000 | − | 46.7654i | 0.421927 | − | 2.19239i | ||||
\(456\) | −6.00000 | −0.280976 | ||||||||
\(457\) | 13.0000 | − | 22.5167i | 0.608114 | − | 1.05328i | −0.383437 | − | 0.923567i | \(-0.625260\pi\) |
0.991551 | − | 0.129718i | \(-0.0414071\pi\) | |||||||
\(458\) | 13.0000 | + | 22.5167i | 0.607450 | + | 1.05213i | ||||
\(459\) | 2.50000 | + | 4.33013i | 0.116690 | + | 0.202113i | ||||
\(460\) | −7.50000 | + | 12.9904i | −0.349689 | + | 0.605680i | ||||
\(461\) | −10.0000 | −0.465746 | −0.232873 | − | 0.972507i | \(-0.574813\pi\) | ||||
−0.232873 | + | 0.972507i | \(0.574813\pi\) | |||||||
\(462\) | 2.00000 | + | 1.73205i | 0.0930484 | + | 0.0805823i | ||||
\(463\) | 28.0000 | 1.30127 | 0.650635 | − | 0.759390i | \(-0.274503\pi\) | ||||
0.650635 | + | 0.759390i | \(0.274503\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | −6.00000 | − | 10.3923i | −0.278243 | − | 0.481932i | ||||
\(466\) | −14.5000 | − | 25.1147i | −0.671700 | − | 1.16342i | ||||
\(467\) | −8.00000 | + | 13.8564i | −0.370196 | + | 0.641198i | −0.989595 | − | 0.143878i | \(-0.954043\pi\) |
0.619400 | + | 0.785076i | \(0.287376\pi\) | |||||||
\(468\) | 6.00000 | 0.277350 | ||||||||
\(469\) | 10.0000 | + | 8.66025i | 0.461757 | + | 0.399893i | ||||
\(470\) | −27.0000 | −1.24542 | ||||||||
\(471\) | 12.0000 | − | 20.7846i | 0.552931 | − | 0.957704i | ||||
\(472\) | −6.00000 | − | 10.3923i | −0.276172 | − | 0.478345i | ||||
\(473\) | −5.00000 | − | 8.66025i | −0.229900 | − | 0.398199i | ||||
\(474\) | −0.500000 | + | 0.866025i | −0.0229658 | + | 0.0397779i | ||||
\(475\) | 24.0000 | 1.10120 | ||||||||
\(476\) | −2.50000 | + | 12.9904i | −0.114587 | + | 0.595413i | ||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 13.0000 | − | 22.5167i | 0.594606 | − | 1.02989i | ||||
\(479\) | −6.00000 | − | 10.3923i | −0.274147 | − | 0.474837i | 0.695773 | − | 0.718262i | \(-0.255062\pi\) |
−0.969920 | + | 0.243426i | \(0.921729\pi\) | |||||||
\(480\) | 1.50000 | + | 2.59808i | 0.0684653 | + | 0.118585i | ||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | 26.0000 | 1.18427 | ||||||||
\(483\) | −12.5000 | + | 4.33013i | −0.568770 | + | 0.197028i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −13.5000 | + | 23.3827i | −0.613003 | + | 1.06175i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 2.00000 | + | 3.46410i | 0.0906287 | + | 0.156973i | 0.907776 | − | 0.419456i | \(-0.137779\pi\) |
−0.817147 | + | 0.576429i | \(0.804446\pi\) | |||||||
\(488\) | −2.50000 | + | 4.33013i | −0.113170 | + | 0.196016i | ||||
\(489\) | −1.00000 | −0.0452216 | ||||||||
\(490\) | 19.5000 | + | 7.79423i | 0.880920 | + | 0.352107i | ||||
\(491\) | −3.00000 | −0.135388 | −0.0676941 | − | 0.997706i | \(-0.521564\pi\) | ||||
−0.0676941 | + | 0.997706i | \(0.521564\pi\) | |||||||
\(492\) | −2.50000 | + | 4.33013i | −0.112709 | + | 0.195217i | ||||
\(493\) | −15.0000 | − | 25.9808i | −0.675566 | − | 1.17011i | ||||
\(494\) | 18.0000 | + | 31.1769i | 0.809858 | + | 1.40272i | ||||
\(495\) | 1.50000 | − | 2.59808i | 0.0674200 | − | 0.116775i | ||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | −10.0000 | + | 3.46410i | −0.448561 | + | 0.155386i | ||||
\(498\) | −1.00000 | −0.0448111 | ||||||||
\(499\) | −6.00000 | + | 10.3923i | −0.268597 | + | 0.465223i | −0.968500 | − | 0.249015i | \(-0.919893\pi\) |
0.699903 | + | 0.714238i | \(0.253227\pi\) | |||||||
\(500\) | 1.50000 | + | 2.59808i | 0.0670820 | + | 0.116190i | ||||
\(501\) | 12.0000 | + | 20.7846i | 0.536120 | + | 0.928588i | ||||
\(502\) | 6.00000 | − | 10.3923i | 0.267793 | − | 0.463831i | ||||
\(503\) | −42.0000 | −1.87269 | −0.936344 | − | 0.351085i | \(-0.885813\pi\) | ||||
−0.936344 | + | 0.351085i | \(0.885813\pi\) | |||||||
\(504\) | −0.500000 | + | 2.59808i | −0.0222718 | + | 0.115728i | ||||
\(505\) | −24.0000 | −1.06799 | ||||||||
\(506\) | −2.50000 | + | 4.33013i | −0.111139 | + | 0.192498i | ||||
\(507\) | −11.5000 | − | 19.9186i | −0.510733 | − | 0.884615i | ||||
\(508\) | −2.50000 | − | 4.33013i | −0.110920 | − | 0.192118i | ||||
\(509\) | −1.00000 | + | 1.73205i | −0.0443242 | + | 0.0767718i | −0.887336 | − | 0.461123i | \(-0.847447\pi\) |
0.843012 | + | 0.537895i | \(0.180780\pi\) | |||||||
\(510\) | 15.0000 | 0.664211 | ||||||||
\(511\) | 24.0000 | + | 20.7846i | 1.06170 | + | 0.919457i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.00000 | + | 5.19615i | −0.132453 | + | 0.229416i | ||||
\(514\) | −7.00000 | − | 12.1244i | −0.308757 | − | 0.534782i | ||||
\(515\) | 3.00000 | + | 5.19615i | 0.132196 | + | 0.228970i | ||||
\(516\) | 5.00000 | − | 8.66025i | 0.220113 | − | 0.381246i | ||||
\(517\) | −9.00000 | −0.395820 | ||||||||
\(518\) | 4.00000 | + | 3.46410i | 0.175750 | + | 0.152204i | ||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 9.00000 | − | 15.5885i | 0.394676 | − | 0.683599i | ||||
\(521\) | −1.00000 | − | 1.73205i | −0.0438108 | − | 0.0758825i | 0.843288 | − | 0.537461i | \(-0.180617\pi\) |
−0.887099 | + | 0.461579i | \(0.847283\pi\) | |||||||
\(522\) | −3.00000 | − | 5.19615i | −0.131306 | − | 0.227429i | ||||
\(523\) | −3.00000 | + | 5.19615i | −0.131181 | + | 0.227212i | −0.924132 | − | 0.382073i | \(-0.875210\pi\) |
0.792951 | + | 0.609285i | \(0.208544\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 2.00000 | − | 10.3923i | 0.0872872 | − | 0.453557i | ||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 10.0000 | − | 17.3205i | 0.435607 | − | 0.754493i | ||||
\(528\) | 0.500000 | + | 0.866025i | 0.0217597 | + | 0.0376889i | ||||
\(529\) | −1.00000 | − | 1.73205i | −0.0434783 | − | 0.0753066i | ||||
\(530\) | 3.00000 | − | 5.19615i | 0.130312 | − | 0.225706i | ||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | −15.0000 | + | 5.19615i | −0.650332 | + | 0.225282i | ||||
\(533\) | 30.0000 | 1.29944 | ||||||||
\(534\) | 3.00000 | − | 5.19615i | 0.129823 | − | 0.224860i | ||||
\(535\) | 19.5000 | + | 33.7750i | 0.843059 | + | 1.46022i | ||||
\(536\) | 2.50000 | + | 4.33013i | 0.107984 | + | 0.187033i | ||||
\(537\) | 4.00000 | − | 6.92820i | 0.172613 | − | 0.298974i | ||||
\(538\) | 9.00000 | 0.388018 | ||||||||
\(539\) | 6.50000 | + | 2.59808i | 0.279975 | + | 0.111907i | ||||
\(540\) | 3.00000 | 0.129099 | ||||||||
\(541\) | 19.5000 | − | 33.7750i | 0.838370 | − | 1.45210i | −0.0528859 | − | 0.998601i | \(-0.516842\pi\) |
0.891256 | − | 0.453500i | \(-0.149825\pi\) | |||||||
\(542\) | −12.0000 | − | 20.7846i | −0.515444 | − | 0.892775i | ||||
\(543\) | 11.0000 | + | 19.0526i | 0.472055 | + | 0.817624i | ||||
\(544\) | −2.50000 | + | 4.33013i | −0.107187 | + | 0.185653i | ||||
\(545\) | −33.0000 | −1.41356 | ||||||||
\(546\) | 15.0000 | − | 5.19615i | 0.641941 | − | 0.222375i | ||||
\(547\) | −42.0000 | −1.79579 | −0.897895 | − | 0.440209i | \(-0.854904\pi\) | ||||
−0.897895 | + | 0.440209i | \(0.854904\pi\) | |||||||
\(548\) | 1.00000 | − | 1.73205i | 0.0427179 | − | 0.0739895i | ||||
\(549\) | 2.50000 | + | 4.33013i | 0.106697 | + | 0.184805i | ||||
\(550\) | −2.00000 | − | 3.46410i | −0.0852803 | − | 0.147710i | ||||
\(551\) | 18.0000 | − | 31.1769i | 0.766826 | − | 1.32818i | ||||
\(552\) | −5.00000 | −0.212814 | ||||||||
\(553\) | −0.500000 | + | 2.59808i | −0.0212622 | + | 0.110481i | ||||
\(554\) | −18.0000 | −0.764747 | ||||||||
\(555\) | 3.00000 | − | 5.19615i | 0.127343 | − | 0.220564i | ||||
\(556\) | −11.0000 | − | 19.0526i | −0.466504 | − | 0.808008i | ||||
\(557\) | 16.0000 | + | 27.7128i | 0.677942 | + | 1.17423i | 0.975600 | + | 0.219557i | \(0.0704612\pi\) |
−0.297658 | + | 0.954673i | \(0.596205\pi\) | |||||||
\(558\) | 2.00000 | − | 3.46410i | 0.0846668 | − | 0.146647i | ||||
\(559\) | −60.0000 | −2.53773 | ||||||||
\(560\) | 6.00000 | + | 5.19615i | 0.253546 | + | 0.219578i | ||||
\(561\) | 5.00000 | 0.211100 | ||||||||
\(562\) | 5.50000 | − | 9.52628i | 0.232003 | − | 0.401842i | ||||
\(563\) | 8.00000 | + | 13.8564i | 0.337160 | + | 0.583978i | 0.983897 | − | 0.178735i | \(-0.0572004\pi\) |
−0.646737 | + | 0.762713i | \(0.723867\pi\) | |||||||
\(564\) | −4.50000 | − | 7.79423i | −0.189484 | − | 0.328196i | ||||
\(565\) | −15.0000 | + | 25.9808i | −0.631055 | + | 1.09302i | ||||
\(566\) | 6.00000 | 0.252199 | ||||||||
\(567\) | 2.00000 | + | 1.73205i | 0.0839921 | + | 0.0727393i | ||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | 9.00000 | + | 15.5885i | 0.376969 | + | 0.652929i | ||||
\(571\) | 17.0000 | + | 29.4449i | 0.711428 | + | 1.23223i | 0.964321 | + | 0.264735i | \(0.0852845\pi\) |
−0.252893 | + | 0.967494i | \(0.581382\pi\) | |||||||
\(572\) | 3.00000 | − | 5.19615i | 0.125436 | − | 0.217262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.50000 | + | 12.9904i | −0.104348 | + | 0.542208i | ||||
\(575\) | 20.0000 | 0.834058 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 3.50000 | + | 6.06218i | 0.145707 | + | 0.252372i | 0.929636 | − | 0.368478i | \(-0.120121\pi\) |
−0.783930 | + | 0.620850i | \(0.786788\pi\) | |||||||
\(578\) | 4.00000 | + | 6.92820i | 0.166378 | + | 0.288175i | ||||
\(579\) | −3.00000 | + | 5.19615i | −0.124676 | + | 0.215945i | ||||
\(580\) | −18.0000 | −0.747409 | ||||||||
\(581\) | −2.50000 | + | 0.866025i | −0.103717 | + | 0.0359288i | ||||
\(582\) | −9.00000 | −0.373062 | ||||||||
\(583\) | 1.00000 | − | 1.73205i | 0.0414158 | − | 0.0717342i | ||||
\(584\) | 6.00000 | + | 10.3923i | 0.248282 | + | 0.430037i | ||||
\(585\) | −9.00000 | − | 15.5885i | −0.372104 | − | 0.644503i | ||||
\(586\) | 4.00000 | − | 6.92820i | 0.165238 | − | 0.286201i | ||||
\(587\) | −24.0000 | −0.990586 | −0.495293 | − | 0.868726i | \(-0.664939\pi\) | ||||
−0.495293 | + | 0.868726i | \(0.664939\pi\) | |||||||
\(588\) | 1.00000 | + | 6.92820i | 0.0412393 | + | 0.285714i | ||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | −18.0000 | + | 31.1769i | −0.741048 | + | 1.28353i | ||||
\(591\) | 12.0000 | + | 20.7846i | 0.493614 | + | 0.854965i | ||||
\(592\) | 1.00000 | + | 1.73205i | 0.0410997 | + | 0.0711868i | ||||
\(593\) | −7.00000 | + | 12.1244i | −0.287456 | + | 0.497888i | −0.973202 | − | 0.229953i | \(-0.926143\pi\) |
0.685746 | + | 0.727841i | \(0.259476\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 37.5000 | − | 12.9904i | 1.53735 | − | 0.532554i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | −5.00000 | + | 8.66025i | −0.204636 | + | 0.354441i | ||||
\(598\) | 15.0000 | + | 25.9808i | 0.613396 | + | 1.06243i | ||||
\(599\) | 1.50000 | + | 2.59808i | 0.0612883 | + | 0.106155i | 0.895042 | − | 0.445983i | \(-0.147146\pi\) |
−0.833753 | + | 0.552137i | \(0.813812\pi\) | |||||||
\(600\) | 2.00000 | − | 3.46410i | 0.0816497 | − | 0.141421i | ||||
\(601\) | −44.0000 | −1.79480 | −0.897399 | − | 0.441221i | \(-0.854546\pi\) | ||||
−0.897399 | + | 0.441221i | \(0.854546\pi\) | |||||||
\(602\) | 5.00000 | − | 25.9808i | 0.203785 | − | 1.05890i | ||||
\(603\) | 5.00000 | 0.203616 | ||||||||
\(604\) | −4.50000 | + | 7.79423i | −0.183102 | + | 0.317143i | ||||
\(605\) | −1.50000 | − | 2.59808i | −0.0609837 | − | 0.105627i | ||||
\(606\) | −4.00000 | − | 6.92820i | −0.162489 | − | 0.281439i | ||||
\(607\) | −16.5000 | + | 28.5788i | −0.669714 | + | 1.15998i | 0.308270 | + | 0.951299i | \(0.400250\pi\) |
−0.977984 | + | 0.208680i | \(0.933083\pi\) | |||||||
\(608\) | −6.00000 | −0.243332 | ||||||||
\(609\) | −12.0000 | − | 10.3923i | −0.486265 | − | 0.421117i | ||||
\(610\) | 15.0000 | 0.607332 | ||||||||
\(611\) | −27.0000 | + | 46.7654i | −1.09230 | + | 1.89192i | ||||
\(612\) | 2.50000 | + | 4.33013i | 0.101057 | + | 0.175035i | ||||
\(613\) | 20.5000 | + | 35.5070i | 0.827987 | + | 1.43412i | 0.899615 | + | 0.436684i | \(0.143847\pi\) |
−0.0716275 | + | 0.997431i | \(0.522819\pi\) | |||||||
\(614\) | 9.00000 | − | 15.5885i | 0.363210 | − | 0.629099i | ||||
\(615\) | 15.0000 | 0.604858 | ||||||||
\(616\) | 2.00000 | + | 1.73205i | 0.0805823 | + | 0.0697863i | ||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | −1.00000 | + | 1.73205i | −0.0402259 | + | 0.0696733i | ||||
\(619\) | 14.5000 | + | 25.1147i | 0.582804 | + | 1.00945i | 0.995145 | + | 0.0984169i | \(0.0313779\pi\) |
−0.412341 | + | 0.911030i | \(0.635289\pi\) | |||||||
\(620\) | −6.00000 | − | 10.3923i | −0.240966 | − | 0.417365i | ||||
\(621\) | −2.50000 | + | 4.33013i | −0.100322 | + | 0.173762i | ||||
\(622\) | 21.0000 | 0.842023 | ||||||||
\(623\) | 3.00000 | − | 15.5885i | 0.120192 | − | 0.624538i | ||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −3.00000 | − | 5.19615i | −0.119904 | − | 0.207680i | ||||
\(627\) | 3.00000 | + | 5.19615i | 0.119808 | + | 0.207514i | ||||
\(628\) | 12.0000 | − | 20.7846i | 0.478852 | − | 0.829396i | ||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | 7.50000 | − | 2.59808i | 0.298807 | − | 0.103510i | ||||
\(631\) | 28.0000 | 1.11466 | 0.557331 | − | 0.830290i | \(-0.311825\pi\) | ||||
0.557331 | + | 0.830290i | \(0.311825\pi\) | |||||||
\(632\) | −0.500000 | + | 0.866025i | −0.0198889 | + | 0.0344486i | ||||
\(633\) | −7.00000 | − | 12.1244i | −0.278225 | − | 0.481900i | ||||
\(634\) | 4.50000 | + | 7.79423i | 0.178718 | + | 0.309548i | ||||
\(635\) | −7.50000 | + | 12.9904i | −0.297628 | + | 0.515508i | ||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | 33.0000 | − | 25.9808i | 1.30751 | − | 1.02940i | ||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | −2.00000 | + | 3.46410i | −0.0791188 | + | 0.137038i | ||||
\(640\) | 1.50000 | + | 2.59808i | 0.0592927 | + | 0.102698i | ||||
\(641\) | 20.0000 | + | 34.6410i | 0.789953 | + | 1.36824i | 0.925995 | + | 0.377535i | \(0.123228\pi\) |
−0.136043 | + | 0.990703i | \(0.543438\pi\) | |||||||
\(642\) | −6.50000 | + | 11.2583i | −0.256535 | + | 0.444331i | ||||
\(643\) | 36.0000 | 1.41970 | 0.709851 | − | 0.704352i | \(-0.248762\pi\) | ||||
0.709851 | + | 0.704352i | \(0.248762\pi\) | |||||||
\(644\) | −12.5000 | + | 4.33013i | −0.492569 | + | 0.170631i | ||||
\(645\) | −30.0000 | −1.18125 | ||||||||
\(646\) | −15.0000 | + | 25.9808i | −0.590167 | + | 1.02220i | ||||
\(647\) | −8.50000 | − | 14.7224i | −0.334169 | − | 0.578799i | 0.649155 | − | 0.760656i | \(-0.275122\pi\) |
−0.983325 | + | 0.181857i | \(0.941789\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | −24.0000 | −0.941357 | ||||||||
\(651\) | 2.00000 | − | 10.3923i | 0.0783862 | − | 0.407307i | ||||
\(652\) | −1.00000 | −0.0391630 | ||||||||
\(653\) | 13.5000 | − | 23.3827i | 0.528296 | − | 0.915035i | −0.471160 | − | 0.882048i | \(-0.656165\pi\) |
0.999456 | − | 0.0329874i | \(-0.0105021\pi\) | |||||||
\(654\) | −5.50000 | − | 9.52628i | −0.215067 | − | 0.372507i | ||||
\(655\) | 6.00000 | + | 10.3923i | 0.234439 | + | 0.406061i | ||||
\(656\) | −2.50000 | + | 4.33013i | −0.0976086 | + | 0.169063i | ||||
\(657\) | 12.0000 | 0.468165 | ||||||||
\(658\) | −18.0000 | − | 15.5885i | −0.701713 | − | 0.607701i | ||||
\(659\) | 31.0000 | 1.20759 | 0.603794 | − | 0.797140i | \(-0.293655\pi\) | ||||
0.603794 | + | 0.797140i | \(0.293655\pi\) | |||||||
\(660\) | 1.50000 | − | 2.59808i | 0.0583874 | − | 0.101130i | ||||
\(661\) | −2.00000 | − | 3.46410i | −0.0777910 | − | 0.134738i | 0.824506 | − | 0.565854i | \(-0.191453\pi\) |
−0.902297 | + | 0.431116i | \(0.858120\pi\) | |||||||
\(662\) | 17.5000 | + | 30.3109i | 0.680157 | + | 1.17807i | ||||
\(663\) | 15.0000 | − | 25.9808i | 0.582552 | − | 1.00901i | ||||
\(664\) | −1.00000 | −0.0388075 | ||||||||
\(665\) | 36.0000 | + | 31.1769i | 1.39602 | + | 1.20899i | ||||
\(666\) | 2.00000 | 0.0774984 | ||||||||
\(667\) | 15.0000 | − | 25.9808i | 0.580802 | − | 1.00598i | ||||
\(668\) | 12.0000 | + | 20.7846i | 0.464294 | + | 0.804181i | ||||
\(669\) | −8.00000 | − | 13.8564i | −0.309298 | − | 0.535720i | ||||
\(670\) | 7.50000 | − | 12.9904i | 0.289750 | − | 0.501862i | ||||
\(671\) | 5.00000 | 0.193023 | ||||||||
\(672\) | −0.500000 | + | 2.59808i | −0.0192879 | + | 0.100223i | ||||
\(673\) | −26.0000 | −1.00223 | −0.501113 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | −1.00000 | + | 1.73205i | −0.0385186 | + | 0.0667161i | ||||
\(675\) | −2.00000 | − | 3.46410i | −0.0769800 | − | 0.133333i | ||||
\(676\) | −11.5000 | − | 19.9186i | −0.442308 | − | 0.766099i | ||||
\(677\) | 9.00000 | − | 15.5885i | 0.345898 | − | 0.599113i | −0.639618 | − | 0.768693i | \(-0.720908\pi\) |
0.985517 | + | 0.169580i | \(0.0542410\pi\) | |||||||
\(678\) | −10.0000 | −0.384048 | ||||||||
\(679\) | −22.5000 | + | 7.79423i | −0.863471 | + | 0.299115i | ||||
\(680\) | 15.0000 | 0.575224 | ||||||||
\(681\) | −1.50000 | + | 2.59808i | −0.0574801 | + | 0.0995585i | ||||
\(682\) | −2.00000 | − | 3.46410i | −0.0765840 | − | 0.132647i | ||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | −3.00000 | + | 5.19615i | −0.114708 | + | 0.198680i | ||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | 26.0000 | 0.991962 | ||||||||
\(688\) | 5.00000 | − | 8.66025i | 0.190623 | − | 0.330169i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 7.50000 | + | 12.9904i | 0.285520 | + | 0.494535i | ||||
\(691\) | 13.5000 | − | 23.3827i | 0.513564 | − | 0.889519i | −0.486312 | − | 0.873785i | \(-0.661658\pi\) |
0.999876 | − | 0.0157341i | \(-0.00500851\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 2.50000 | − | 0.866025i | 0.0949671 | − | 0.0328976i | ||||
\(694\) | −7.00000 | −0.265716 | ||||||||
\(695\) | −33.0000 | + | 57.1577i | −1.25176 | + | 2.16811i | ||||
\(696\) | −3.00000 | − | 5.19615i | −0.113715 | − | 0.196960i | ||||
\(697\) | 12.5000 | + | 21.6506i | 0.473471 | + | 0.820076i | ||||
\(698\) | −9.50000 | + | 16.4545i | −0.359580 | + | 0.622811i | ||||
\(699\) | −29.0000 | −1.09688 | ||||||||
\(700\) | 2.00000 | − | 10.3923i | 0.0755929 | − | 0.392792i | ||||
\(701\) | −10.0000 | −0.377695 | −0.188847 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188847 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(702\) | 3.00000 | − | 5.19615i | 0.113228 | − | 0.196116i | ||||
\(703\) | 6.00000 | + | 10.3923i | 0.226294 | + | 0.391953i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | −13.5000 | + | 23.3827i | −0.508439 | + | 0.880643i | ||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | −16.0000 | − | 13.8564i | −0.601742 | − | 0.521124i | ||||
\(708\) | −12.0000 | −0.450988 | ||||||||
\(709\) | −10.0000 | + | 17.3205i | −0.375558 | + | 0.650485i | −0.990410 | − | 0.138157i | \(-0.955882\pi\) |
0.614852 | + | 0.788642i | \(0.289216\pi\) | |||||||
\(710\) | 6.00000 | + | 10.3923i | 0.225176 | + | 0.390016i | ||||
\(711\) | 0.500000 | + | 0.866025i | 0.0187515 | + | 0.0324785i | ||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | 20.0000 | 0.749006 | ||||||||
\(714\) | 10.0000 | + | 8.66025i | 0.374241 | + | 0.324102i | ||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 4.00000 | − | 6.92820i | 0.149487 | − | 0.258919i | ||||
\(717\) | −13.0000 | − | 22.5167i | −0.485494 | − | 0.840900i | ||||
\(718\) | −5.00000 | − | 8.66025i | −0.186598 | − | 0.323198i | ||||
\(719\) | −18.5000 | + | 32.0429i | −0.689934 | + | 1.19500i | 0.281925 | + | 0.959436i | \(0.409027\pi\) |
−0.971859 | + | 0.235564i | \(0.924306\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | −1.00000 | + | 5.19615i | −0.0372419 | + | 0.193515i | ||||
\(722\) | −17.0000 | −0.632674 | ||||||||
\(723\) | 13.0000 | − | 22.5167i | 0.483475 | − | 0.837404i | ||||
\(724\) | 11.0000 | + | 19.0526i | 0.408812 | + | 0.708083i | ||||
\(725\) | 12.0000 | + | 20.7846i | 0.445669 | + | 0.771921i | ||||
\(726\) | 0.500000 | − | 0.866025i | 0.0185567 | − | 0.0321412i | ||||
\(727\) | 22.0000 | 0.815935 | 0.407967 | − | 0.912996i | \(-0.366238\pi\) | ||||
0.407967 | + | 0.912996i | \(0.366238\pi\) | |||||||
\(728\) | 15.0000 | − | 5.19615i | 0.555937 | − | 0.192582i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.0000 | − | 31.1769i | 0.666210 | − | 1.15391i | ||||
\(731\) | −25.0000 | − | 43.3013i | −0.924658 | − | 1.60156i | ||||
\(732\) | 2.50000 | + | 4.33013i | 0.0924027 | + | 0.160046i | ||||
\(733\) | 7.50000 | − | 12.9904i | 0.277019 | − | 0.479811i | −0.693624 | − | 0.720338i | \(-0.743987\pi\) |
0.970642 | + | 0.240527i | \(0.0773202\pi\) | |||||||
\(734\) | 14.0000 | 0.516749 | ||||||||
\(735\) | 16.5000 | − | 12.9904i | 0.608612 | − | 0.479157i | ||||
\(736\) | −5.00000 | −0.184302 | ||||||||
\(737\) | 2.50000 | − | 4.33013i | 0.0920887 | − | 0.159502i | ||||
\(738\) | 2.50000 | + | 4.33013i | 0.0920263 | + | 0.159394i | ||||
\(739\) | 5.00000 | + | 8.66025i | 0.183928 | + | 0.318573i | 0.943215 | − | 0.332184i | \(-0.107785\pi\) |
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(740\) | 3.00000 | − | 5.19615i | 0.110282 | − | 0.191014i | ||||
\(741\) | 36.0000 | 1.32249 | ||||||||
\(742\) | 5.00000 | − | 1.73205i | 0.183556 | − | 0.0635856i | ||||
\(743\) | 22.0000 | 0.807102 | 0.403551 | − | 0.914957i | \(-0.367776\pi\) | ||||
0.403551 | + | 0.914957i | \(0.367776\pi\) | |||||||
\(744\) | 2.00000 | − | 3.46410i | 0.0733236 | − | 0.127000i | ||||
\(745\) | −27.0000 | − | 46.7654i | −0.989203 | − | 1.71335i | ||||
\(746\) | −3.50000 | − | 6.06218i | −0.128144 | − | 0.221952i | ||||
\(747\) | −0.500000 | + | 0.866025i | −0.0182940 | + | 0.0316862i | ||||
\(748\) | 5.00000 | 0.182818 | ||||||||
\(749\) | −6.50000 | + | 33.7750i | −0.237505 | + | 1.23411i | ||||
\(750\) | 3.00000 | 0.109545 | ||||||||
\(751\) | 1.00000 | − | 1.73205i | 0.0364905 | − | 0.0632034i | −0.847203 | − | 0.531269i | \(-0.821715\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(752\) | −4.50000 | − | 7.79423i | −0.164098 | − | 0.284226i | ||||
\(753\) | −6.00000 | − | 10.3923i | −0.218652 | − | 0.378717i | ||||
\(754\) | −18.0000 | + | 31.1769i | −0.655521 | + | 1.13540i | ||||
\(755\) | 27.0000 | 0.982631 | ||||||||
\(756\) | 2.00000 | + | 1.73205i | 0.0727393 | + | 0.0629941i | ||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 6.50000 | − | 11.2583i | 0.236091 | − | 0.408921i | ||||
\(759\) | 2.50000 | + | 4.33013i | 0.0907443 | + | 0.157174i | ||||
\(760\) | 9.00000 | + | 15.5885i | 0.326464 | + | 0.565453i | ||||
\(761\) | −23.5000 | + | 40.7032i | −0.851874 | + | 1.47549i | 0.0276404 | + | 0.999618i | \(0.491201\pi\) |
−0.879515 | + | 0.475872i | \(0.842133\pi\) | |||||||
\(762\) | −5.00000 | −0.181131 | ||||||||
\(763\) | −22.0000 | − | 19.0526i | −0.796453 | − | 0.689749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.50000 | − | 12.9904i | 0.271163 | − | 0.469668i | ||||
\(766\) | 4.00000 | + | 6.92820i | 0.144526 | + | 0.250326i | ||||
\(767\) | 36.0000 | + | 62.3538i | 1.29988 | + | 2.25147i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 46.0000 | 1.65880 | 0.829401 | − | 0.558653i | \(-0.188682\pi\) | ||||
0.829401 | + | 0.558653i | \(0.188682\pi\) | |||||||
\(770\) | 1.50000 | − | 7.79423i | 0.0540562 | − | 0.280885i | ||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | −3.00000 | + | 5.19615i | −0.107972 | + | 0.187014i | ||||
\(773\) | −5.50000 | − | 9.52628i | −0.197821 | − | 0.342636i | 0.750000 | − | 0.661437i | \(-0.230053\pi\) |
−0.947822 | + | 0.318801i | \(0.896720\pi\) | |||||||
\(774\) | −5.00000 | − | 8.66025i | −0.179721 | − | 0.311286i | ||||
\(775\) | −8.00000 | + | 13.8564i | −0.287368 | + | 0.497737i | ||||
\(776\) | −9.00000 | −0.323081 | ||||||||
\(777\) | 5.00000 | − | 1.73205i | 0.179374 | − | 0.0621370i | ||||
\(778\) | 21.0000 | 0.752886 | ||||||||
\(779\) | −15.0000 | + | 25.9808i | −0.537431 | + | 0.930857i | ||||
\(780\) | −9.00000 | − | 15.5885i | −0.322252 | − | 0.558156i | ||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | −12.5000 | + | 21.6506i | −0.446999 | + | 0.774225i | ||||
\(783\) | −6.00000 | −0.214423 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | −72.0000 | −2.56979 | ||||||||
\(786\) | −2.00000 | + | 3.46410i | −0.0713376 | + | 0.123560i | ||||
\(787\) | 25.0000 | + | 43.3013i | 0.891154 | + | 1.54352i | 0.838494 | + | 0.544911i | \(0.183437\pi\) |
0.0526599 | + | 0.998613i | \(0.483230\pi\) | |||||||
\(788\) | 12.0000 | + | 20.7846i | 0.427482 | + | 0.740421i | ||||
\(789\) | −12.0000 | + | 20.7846i | −0.427211 | + | 0.739952i | ||||
\(790\) | 3.00000 | 0.106735 | ||||||||
\(791\) | −25.0000 | + | 8.66025i | −0.888898 | + | 0.307923i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 15.0000 | − | 25.9808i | 0.532666 | − | 0.922604i | ||||
\(794\) | 13.0000 | + | 22.5167i | 0.461353 | + | 0.799086i | ||||
\(795\) | −3.00000 | − | 5.19615i | −0.106399 | − | 0.184289i | ||||
\(796\) | −5.00000 | + | 8.66025i | −0.177220 | + | 0.306955i | ||||
\(797\) | −53.0000 | −1.87736 | −0.938678 | − | 0.344795i | \(-0.887949\pi\) | ||||
−0.938678 | + | 0.344795i | \(0.887949\pi\) | |||||||
\(798\) | −3.00000 | + | 15.5885i | −0.106199 | + | 0.551825i | ||||
\(799\) | −45.0000 | −1.59199 | ||||||||
\(800\) | 2.00000 | − | 3.46410i | 0.0707107 | − | 0.122474i | ||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | −3.00000 | − | 5.19615i | −0.105934 | − | 0.183483i | ||||
\(803\) | 6.00000 | − | 10.3923i | 0.211735 | − | 0.366736i | ||||
\(804\) | 5.00000 | 0.176336 | ||||||||
\(805\) | 30.0000 | + | 25.9808i | 1.05736 | + | 0.915702i | ||||
\(806\) | −24.0000 | −0.845364 | ||||||||
\(807\) | 4.50000 | − | 7.79423i | 0.158408 | − | 0.274370i | ||||
\(808\) | −4.00000 | − | 6.92820i | −0.140720 | − | 0.243733i | ||||
\(809\) | −7.50000 | − | 12.9904i | −0.263686 | − | 0.456717i | 0.703533 | − | 0.710663i | \(-0.251605\pi\) |
−0.967219 | + | 0.253946i | \(0.918272\pi\) | |||||||
\(810\) | 1.50000 | − | 2.59808i | 0.0527046 | − | 0.0912871i | ||||
\(811\) | 42.0000 | 1.47482 | 0.737410 | − | 0.675446i | \(-0.236049\pi\) | ||||
0.737410 | + | 0.675446i | \(0.236049\pi\) | |||||||
\(812\) | −12.0000 | − | 10.3923i | −0.421117 | − | 0.364698i | ||||
\(813\) | −24.0000 | −0.841717 | ||||||||
\(814\) | 1.00000 | − | 1.73205i | 0.0350500 | − | 0.0607083i | ||||
\(815\) | 1.50000 | + | 2.59808i | 0.0525427 | + | 0.0910066i | ||||
\(816\) | 2.50000 | + | 4.33013i | 0.0875175 | + | 0.151585i | ||||
\(817\) | 30.0000 | − | 51.9615i | 1.04957 | − | 1.81790i | ||||
\(818\) | −10.0000 | −0.349642 | ||||||||
\(819\) | 3.00000 | − | 15.5885i | 0.104828 | − | 0.544705i | ||||
\(820\) | 15.0000 | 0.523823 | ||||||||
\(821\) | 4.00000 | − | 6.92820i | 0.139601 | − | 0.241796i | −0.787745 | − | 0.616002i | \(-0.788751\pi\) |
0.927346 | + | 0.374206i | \(0.122085\pi\) | |||||||
\(822\) | −1.00000 | − | 1.73205i | −0.0348790 | − | 0.0604122i | ||||
\(823\) | −5.00000 | − | 8.66025i | −0.174289 | − | 0.301877i | 0.765626 | − | 0.643286i | \(-0.222429\pi\) |
−0.939915 | + | 0.341409i | \(0.889096\pi\) | |||||||
\(824\) | −1.00000 | + | 1.73205i | −0.0348367 | + | 0.0603388i | ||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | −30.0000 | + | 10.3923i | −1.04383 | + | 0.361595i | ||||
\(827\) | −15.0000 | −0.521601 | −0.260801 | − | 0.965393i | \(-0.583986\pi\) | ||||
−0.260801 | + | 0.965393i | \(0.583986\pi\) | |||||||
\(828\) | −2.50000 | + | 4.33013i | −0.0868810 | + | 0.150482i | ||||
\(829\) | 27.0000 | + | 46.7654i | 0.937749 | + | 1.62423i | 0.769657 | + | 0.638457i | \(0.220427\pi\) |
0.168091 | + | 0.985771i | \(0.446240\pi\) | |||||||
\(830\) | 1.50000 | + | 2.59808i | 0.0520658 | + | 0.0901805i | ||||
\(831\) | −9.00000 | + | 15.5885i | −0.312207 | + | 0.540758i | ||||
\(832\) | 6.00000 | 0.208013 | ||||||||
\(833\) | 32.5000 | + | 12.9904i | 1.12606 | + | 0.450090i | ||||
\(834\) | −22.0000 | −0.761798 | ||||||||
\(835\) | 36.0000 | − | 62.3538i | 1.24583 | − | 2.15784i | ||||
\(836\) | 3.00000 | + | 5.19615i | 0.103757 | + | 0.179713i | ||||
\(837\) | −2.00000 | − | 3.46410i | −0.0691301 | − | 0.119737i | ||||
\(838\) | −10.0000 | + | 17.3205i | −0.345444 | + | 0.598327i | ||||
\(839\) | −9.00000 | −0.310715 | −0.155357 | − | 0.987858i | \(-0.549653\pi\) | ||||
−0.155357 | + | 0.987858i | \(0.549653\pi\) | |||||||
\(840\) | 7.50000 | − | 2.59808i | 0.258775 | − | 0.0896421i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 4.00000 | − | 6.92820i | 0.137849 | − | 0.238762i | ||||
\(843\) | −5.50000 | − | 9.52628i | −0.189430 | − | 0.328102i | ||||
\(844\) | −7.00000 | − | 12.1244i | −0.240950 | − | 0.417338i | ||||
\(845\) | −34.5000 | + | 59.7558i | −1.18684 | + | 2.05566i | ||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 0.500000 | − | 2.59808i | 0.0171802 | − | 0.0892710i | ||||
\(848\) | 2.00000 | 0.0686803 | ||||||||
\(849\) | 3.00000 | − | 5.19615i | 0.102960 | − | 0.178331i | ||||
\(850\) | −10.0000 | − | 17.3205i | −0.342997 | − | 0.594089i | ||||
\(851\) | 5.00000 | + | 8.66025i | 0.171398 | + | 0.296870i | ||||
\(852\) | −2.00000 | + | 3.46410i | −0.0685189 | + | 0.118678i | ||||
\(853\) | 15.0000 | 0.513590 | 0.256795 | − | 0.966466i | \(-0.417333\pi\) | ||||
0.256795 | + | 0.966466i | \(0.417333\pi\) | |||||||
\(854\) | 10.0000 | + | 8.66025i | 0.342193 | + | 0.296348i | ||||
\(855\) | 18.0000 | 0.615587 | ||||||||
\(856\) | −6.50000 | + | 11.2583i | −0.222165 | + | 0.384802i | ||||
\(857\) | −1.50000 | − | 2.59808i | −0.0512390 | − | 0.0887486i | 0.839268 | − | 0.543718i | \(-0.182984\pi\) |
−0.890507 | + | 0.454969i | \(0.849650\pi\) | |||||||
\(858\) | −3.00000 | − | 5.19615i | −0.102418 | − | 0.177394i | ||||
\(859\) | 22.5000 | − | 38.9711i | 0.767690 | − | 1.32968i | −0.171122 | − | 0.985250i | \(-0.554739\pi\) |
0.938813 | − | 0.344428i | \(-0.111927\pi\) | |||||||
\(860\) | −30.0000 | −1.02299 | ||||||||
\(861\) | 10.0000 | + | 8.66025i | 0.340799 | + | 0.295141i | ||||
\(862\) | −22.0000 | −0.749323 | ||||||||
\(863\) | 19.5000 | − | 33.7750i | 0.663788 | − | 1.14971i | −0.315825 | − | 0.948818i | \(-0.602281\pi\) |
0.979612 | − | 0.200897i | \(-0.0643855\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 18.0000 | + | 31.1769i | 0.612018 | + | 1.06005i | ||||
\(866\) | 5.50000 | − | 9.52628i | 0.186898 | − | 0.323716i | ||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 2.00000 | − | 10.3923i | 0.0678844 | − | 0.352738i | ||||
\(869\) | 1.00000 | 0.0339227 | ||||||||
\(870\) | −9.00000 | + | 15.5885i | −0.305129 | + | 0.528498i | ||||
\(871\) | −15.0000 | − | 25.9808i | −0.508256 | − | 0.880325i | ||||
\(872\) | −5.50000 | − | 9.52628i | −0.186254 | − | 0.322601i | ||||
\(873\) | −4.50000 | + | 7.79423i | −0.152302 | + | 0.263795i | ||||
\(874\) | −30.0000 | −1.01477 | ||||||||
\(875\) | 7.50000 | − | 2.59808i | 0.253546 | − | 0.0878310i | ||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | 1.50000 | − | 2.59808i | 0.0506514 | − | 0.0877308i | −0.839588 | − | 0.543224i | \(-0.817204\pi\) |
0.890239 | + | 0.455493i | \(0.150537\pi\) | |||||||
\(878\) | −2.50000 | − | 4.33013i | −0.0843709 | − | 0.146135i | ||||
\(879\) | −4.00000 | − | 6.92820i | −0.134917 | − | 0.233682i | ||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | −26.0000 | −0.875962 | −0.437981 | − | 0.898984i | \(-0.644306\pi\) | ||||
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(882\) | 6.50000 | + | 2.59808i | 0.218866 | + | 0.0874818i | ||||
\(883\) | −13.0000 | −0.437485 | −0.218742 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218742 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(884\) | 15.0000 | − | 25.9808i | 0.504505 | − | 0.873828i | ||||
\(885\) | 18.0000 | + | 31.1769i | 0.605063 | + | 1.04800i | ||||
\(886\) | 1.00000 | + | 1.73205i | 0.0335957 | + | 0.0581894i | ||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | −12.5000 | + | 4.33013i | −0.419237 | + | 0.145228i | ||||
\(890\) | −18.0000 | −0.603361 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | −8.00000 | − | 13.8564i | −0.267860 | − | 0.463947i | ||||
\(893\) | −27.0000 | − | 46.7654i | −0.903521 | − | 1.56494i | ||||
\(894\) | 9.00000 | − | 15.5885i | 0.301005 | − | 0.521356i | ||||
\(895\) | −24.0000 | −0.802232 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 30.0000 | 1.00167 | ||||||||
\(898\) | 1.00000 | − | 1.73205i | 0.0333704 | − | 0.0577993i | ||||
\(899\) | 12.0000 | + | 20.7846i | 0.400222 | + | 0.693206i | ||||
\(900\) | −2.00000 | − | 3.46410i | −0.0666667 | − | 0.115470i | ||||
\(901\) | 5.00000 | − | 8.66025i | 0.166574 | − | 0.288515i | ||||
\(902\) | 5.00000 | 0.166482 | ||||||||
\(903\) | −20.0000 | − | 17.3205i | −0.665558 | − | 0.576390i | ||||
\(904\) | −10.0000 | −0.332595 | ||||||||
\(905\) | 33.0000 | − | 57.1577i | 1.09696 | − | 1.89999i | ||||
\(906\) | 4.50000 | + | 7.79423i | 0.149502 | + | 0.258946i | ||||
\(907\) | −11.5000 | − | 19.9186i | −0.381851 | − | 0.661386i | 0.609476 | − | 0.792805i | \(-0.291380\pi\) |
−0.991327 | + | 0.131419i | \(0.958047\pi\) | |||||||
\(908\) | −1.50000 | + | 2.59808i | −0.0497792 | + | 0.0862202i | ||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | −36.0000 | − | 31.1769i | −1.19339 | − | 1.03350i | ||||
\(911\) | 51.0000 | 1.68971 | 0.844853 | − | 0.534999i | \(-0.179688\pi\) | ||||
0.844853 | + | 0.534999i | \(0.179688\pi\) | |||||||
\(912\) | −3.00000 | + | 5.19615i | −0.0993399 | + | 0.172062i | ||||
\(913\) | 0.500000 | + | 0.866025i | 0.0165476 | + | 0.0286613i | ||||
\(914\) | −13.0000 | − | 22.5167i | −0.430002 | − | 0.744785i | ||||
\(915\) | 7.50000 | − | 12.9904i | 0.247942 | − | 0.429449i | ||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | −2.00000 | + | 10.3923i | −0.0660458 | + | 0.343184i | ||||
\(918\) | 5.00000 | 0.165025 | ||||||||
\(919\) | 8.50000 | − | 14.7224i | 0.280389 | − | 0.485648i | −0.691091 | − | 0.722767i | \(-0.742870\pi\) |
0.971481 | + | 0.237119i | \(0.0762032\pi\) | |||||||
\(920\) | 7.50000 | + | 12.9904i | 0.247268 | + | 0.428280i | ||||
\(921\) | −9.00000 | − | 15.5885i | −0.296560 | − | 0.513657i | ||||
\(922\) | −5.00000 | + | 8.66025i | −0.164666 | + | 0.285210i | ||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 2.50000 | − | 0.866025i | 0.0822440 | − | 0.0284901i | ||||
\(925\) | −8.00000 | −0.263038 | ||||||||
\(926\) | 14.0000 | − | 24.2487i | 0.460069 | − | 0.796862i | ||||
\(927\) | 1.00000 | + | 1.73205i | 0.0328443 | + | 0.0568880i | ||||
\(928\) | −3.00000 | − | 5.19615i | −0.0984798 | − | 0.170572i | ||||
\(929\) | 13.0000 | − | 22.5167i | 0.426516 | − | 0.738748i | −0.570045 | − | 0.821614i | \(-0.693074\pi\) |
0.996561 | + | 0.0828661i | \(0.0264074\pi\) | |||||||
\(930\) | −12.0000 | −0.393496 | ||||||||
\(931\) | 6.00000 | + | 41.5692i | 0.196642 | + | 1.36238i | ||||
\(932\) | −29.0000 | −0.949927 | ||||||||
\(933\) | 10.5000 | − | 18.1865i | 0.343755 | − | 0.595400i | ||||
\(934\) | 8.00000 | + | 13.8564i | 0.261768 | + | 0.453395i | ||||
\(935\) | −7.50000 | − | 12.9904i | −0.245276 | − | 0.424831i | ||||
\(936\) | 3.00000 | − | 5.19615i | 0.0980581 | − | 0.169842i | ||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 12.5000 | − | 4.33013i | 0.408139 | − | 0.141384i | ||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | −13.5000 | + | 23.3827i | −0.440321 | + | 0.762659i | ||||
\(941\) | −3.00000 | − | 5.19615i | −0.0977972 | − | 0.169390i | 0.812975 | − | 0.582298i | \(-0.197846\pi\) |
−0.910773 | + | 0.412908i | \(0.864513\pi\) | |||||||
\(942\) | −12.0000 | − | 20.7846i | −0.390981 | − | 0.677199i | ||||
\(943\) | −12.5000 | + | 21.6506i | −0.407056 | + | 0.705042i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 1.50000 | − | 7.79423i | 0.0487950 | − | 0.253546i | ||||
\(946\) | −10.0000 | −0.325128 | ||||||||
\(947\) | 15.0000 | − | 25.9808i | 0.487435 | − | 0.844261i | −0.512461 | − | 0.858710i | \(-0.671266\pi\) |
0.999896 | + | 0.0144491i | \(0.00459946\pi\) | |||||||
\(948\) | 0.500000 | + | 0.866025i | 0.0162392 | + | 0.0281272i | ||||
\(949\) | −36.0000 | − | 62.3538i | −1.16861 | − | 2.02409i | ||||
\(950\) | 12.0000 | − | 20.7846i | 0.389331 | − | 0.674342i | ||||
\(951\) | 9.00000 | 0.291845 | ||||||||
\(952\) | 10.0000 | + | 8.66025i | 0.324102 | + | 0.280680i | ||||
\(953\) | −21.0000 | −0.680257 | −0.340128 | − | 0.940379i | \(-0.610471\pi\) | ||||
−0.340128 | + | 0.940379i | \(0.610471\pi\) | |||||||
\(954\) | 1.00000 | − | 1.73205i | 0.0323762 | − | 0.0560772i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.0000 | − | 22.5167i | −0.420450 | − | 0.728241i | ||||
\(957\) | −3.00000 | + | 5.19615i | −0.0969762 | + | 0.167968i | ||||
\(958\) | −12.0000 | −0.387702 | ||||||||
\(959\) | −4.00000 | − | 3.46410i | −0.129167 | − | 0.111862i | ||||
\(960\) | 3.00000 | 0.0968246 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | −6.00000 | − | 10.3923i | −0.193448 | − | 0.335061i | ||||
\(963\) | 6.50000 | + | 11.2583i | 0.209460 | + | 0.362795i | ||||
\(964\) | 13.0000 | − | 22.5167i | 0.418702 | − | 0.725213i | ||||
\(965\) | 18.0000 | 0.579441 | ||||||||
\(966\) | −2.50000 | + | 12.9904i | −0.0804362 | + | 0.417959i | ||||
\(967\) | −21.0000 | −0.675314 | −0.337657 | − | 0.941269i | \(-0.609634\pi\) | ||||
−0.337657 | + | 0.941269i | \(0.609634\pi\) | |||||||
\(968\) | 0.500000 | − | 0.866025i | 0.0160706 | − | 0.0278351i | ||||
\(969\) | 15.0000 | + | 25.9808i | 0.481869 | + | 0.834622i | ||||
\(970\) | 13.5000 | + | 23.3827i | 0.433459 | + | 0.750773i | ||||
\(971\) | 17.0000 | − | 29.4449i | 0.545556 | − | 0.944931i | −0.453016 | − | 0.891503i | \(-0.649652\pi\) |
0.998572 | − | 0.0534281i | \(-0.0170148\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −55.0000 | + | 19.0526i | −1.76322 | + | 0.610797i | ||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | −12.0000 | + | 20.7846i | −0.384308 | + | 0.665640i | ||||
\(976\) | 2.50000 | + | 4.33013i | 0.0800230 | + | 0.138604i | ||||
\(977\) | 14.0000 | + | 24.2487i | 0.447900 | + | 0.775785i | 0.998249 | − | 0.0591494i | \(-0.0188388\pi\) |
−0.550349 | + | 0.834934i | \(0.685506\pi\) | |||||||
\(978\) | −0.500000 | + | 0.866025i | −0.0159882 | + | 0.0276924i | ||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 16.5000 | − | 12.9904i | 0.527073 | − | 0.414963i | ||||
\(981\) | −11.0000 | −0.351203 | ||||||||
\(982\) | −1.50000 | + | 2.59808i | −0.0478669 | + | 0.0829079i | ||||
\(983\) | 29.5000 | + | 51.0955i | 0.940904 | + | 1.62969i | 0.763752 | + | 0.645510i | \(0.223355\pi\) |
0.177152 | + | 0.984184i | \(0.443312\pi\) | |||||||
\(984\) | 2.50000 | + | 4.33013i | 0.0796971 | + | 0.138039i | ||||
\(985\) | 36.0000 | − | 62.3538i | 1.14706 | − | 1.98676i | ||||
\(986\) | −30.0000 | −0.955395 | ||||||||
\(987\) | −22.5000 | + | 7.79423i | −0.716183 | + | 0.248093i | ||||
\(988\) | 36.0000 | 1.14531 | ||||||||
\(989\) | 25.0000 | − | 43.3013i | 0.794954 | − | 1.37690i | ||||
\(990\) | −1.50000 | − | 2.59808i | −0.0476731 | − | 0.0825723i | ||||
\(991\) | −11.0000 | − | 19.0526i | −0.349427 | − | 0.605224i | 0.636721 | − | 0.771094i | \(-0.280290\pi\) |
−0.986148 | + | 0.165870i | \(0.946957\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | 35.0000 | 1.11069 | ||||||||
\(994\) | −2.00000 | + | 10.3923i | −0.0634361 | + | 0.329624i | ||||
\(995\) | 30.0000 | 0.951064 | ||||||||
\(996\) | −0.500000 | + | 0.866025i | −0.0158431 | + | 0.0274411i | ||||
\(997\) | −7.00000 | − | 12.1244i | −0.221692 | − | 0.383982i | 0.733630 | − | 0.679549i | \(-0.237825\pi\) |
−0.955322 | + | 0.295567i | \(0.904491\pi\) | |||||||
\(998\) | 6.00000 | + | 10.3923i | 0.189927 | + | 0.328963i | ||||
\(999\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 462.2.i.a.331.1 | yes | 2 | |
3.2 | odd | 2 | 1386.2.k.j.793.1 | 2 | |||
7.2 | even | 3 | 3234.2.a.o.1.1 | 1 | |||
7.4 | even | 3 | inner | 462.2.i.a.67.1 | ✓ | 2 | |
7.5 | odd | 6 | 3234.2.a.a.1.1 | 1 | |||
21.2 | odd | 6 | 9702.2.a.be.1.1 | 1 | |||
21.5 | even | 6 | 9702.2.a.ce.1.1 | 1 | |||
21.11 | odd | 6 | 1386.2.k.j.991.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.a.67.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
462.2.i.a.331.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1386.2.k.j.793.1 | 2 | 3.2 | odd | 2 | |||
1386.2.k.j.991.1 | 2 | 21.11 | odd | 6 | |||
3234.2.a.a.1.1 | 1 | 7.5 | odd | 6 | |||
3234.2.a.o.1.1 | 1 | 7.2 | even | 3 | |||
9702.2.a.be.1.1 | 1 | 21.2 | odd | 6 | |||
9702.2.a.ce.1.1 | 1 | 21.5 | even | 6 |