Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 484.1 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.484 |
Dual form | 507.2.e.g.22.1 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.780776 | − | 1.35234i | −0.552092 | − | 0.956252i | −0.998123 | − | 0.0612344i | \(-0.980496\pi\) |
0.446031 | − | 0.895017i | \(-0.352837\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.219224 | + | 0.379706i | −0.109612 | + | 0.189853i | ||||
\(5\) | 3.56155 | 1.59277 | 0.796387 | − | 0.604787i | \(-0.206742\pi\) | ||||
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | −0.780776 | + | 1.35234i | −0.318751 | + | 0.552092i | ||||
\(7\) | 0.280776 | − | 0.486319i | 0.106124 | − | 0.183811i | −0.808073 | − | 0.589082i | \(-0.799489\pi\) |
0.914197 | + | 0.405271i | \(0.132823\pi\) | |||||||
\(8\) | −2.43845 | −0.862121 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −2.78078 | − | 4.81645i | −0.879359 | − | 1.52309i | ||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0.438447 | 0.126569 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.876894 | −0.234360 | ||||||||
\(15\) | −1.78078 | − | 3.08440i | −0.459794 | − | 0.796387i | ||||
\(16\) | 2.34233 | + | 4.05703i | 0.585582 | + | 1.01426i | ||||
\(17\) | 0.780776 | − | 1.35234i | 0.189366 | − | 0.327992i | −0.755673 | − | 0.654949i | \(-0.772690\pi\) |
0.945039 | + | 0.326957i | \(0.106023\pi\) | |||||||
\(18\) | 1.56155 | 0.368062 | ||||||||
\(19\) | 3.56155 | − | 6.16879i | 0.817076 | − | 1.41522i | −0.0907512 | − | 0.995874i | \(-0.528927\pi\) |
0.907827 | − | 0.419344i | \(-0.137740\pi\) | |||||||
\(20\) | −0.780776 | + | 1.35234i | −0.174587 | + | 0.302393i | ||||
\(21\) | −0.561553 | −0.122541 | ||||||||
\(22\) | −1.56155 | + | 2.70469i | −0.332924 | + | 0.576642i | ||||
\(23\) | −1.00000 | − | 1.73205i | −0.208514 | − | 0.361158i | 0.742732 | − | 0.669588i | \(-0.233529\pi\) |
−0.951247 | + | 0.308431i | \(0.900196\pi\) | |||||||
\(24\) | 1.21922 | + | 2.11176i | 0.248873 | + | 0.431061i | ||||
\(25\) | 7.68466 | 1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.123106 | + | 0.213225i | 0.0232648 | + | 0.0402958i | ||||
\(29\) | −3.34233 | − | 5.78908i | −0.620655 | − | 1.07501i | −0.989364 | − | 0.145461i | \(-0.953533\pi\) |
0.368709 | − | 0.929545i | \(-0.379800\pi\) | |||||||
\(30\) | −2.78078 | + | 4.81645i | −0.507698 | + | 0.879359i | ||||
\(31\) | −2.56155 | −0.460068 | −0.230034 | − | 0.973183i | \(-0.573884\pi\) | ||||
−0.230034 | + | 0.973183i | \(0.573884\pi\) | |||||||
\(32\) | 1.21922 | − | 2.11176i | 0.215530 | − | 0.373309i | ||||
\(33\) | −1.00000 | + | 1.73205i | −0.174078 | + | 0.301511i | ||||
\(34\) | −2.43845 | −0.418190 | ||||||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | −0.219224 | − | 0.379706i | −0.0365373 | − | 0.0632844i | ||||
\(37\) | 3.78078 | + | 6.54850i | 0.621556 | + | 1.07657i | 0.989196 | + | 0.146598i | \(0.0468324\pi\) |
−0.367640 | + | 0.929968i | \(0.619834\pi\) | |||||||
\(38\) | −11.1231 | −1.80441 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.68466 | −1.37317 | ||||||||
\(41\) | −0.780776 | − | 1.35234i | −0.121937 | − | 0.211201i | 0.798595 | − | 0.601869i | \(-0.205577\pi\) |
−0.920531 | + | 0.390669i | \(0.872244\pi\) | |||||||
\(42\) | 0.438447 | + | 0.759413i | 0.0676539 | + | 0.117180i | ||||
\(43\) | −2.28078 | + | 3.95042i | −0.347815 | + | 0.602433i | −0.985861 | − | 0.167565i | \(-0.946410\pi\) |
0.638046 | + | 0.769998i | \(0.279743\pi\) | |||||||
\(44\) | 0.876894 | 0.132197 | ||||||||
\(45\) | −1.78078 | + | 3.08440i | −0.265462 | + | 0.459794i | ||||
\(46\) | −1.56155 | + | 2.70469i | −0.230238 | + | 0.398785i | ||||
\(47\) | −8.24621 | −1.20283 | −0.601417 | − | 0.798935i | \(-0.705397\pi\) | ||||
−0.601417 | + | 0.798935i | \(0.705397\pi\) | |||||||
\(48\) | 2.34233 | − | 4.05703i | 0.338086 | − | 0.585582i | ||||
\(49\) | 3.34233 | + | 5.78908i | 0.477476 | + | 0.827012i | ||||
\(50\) | −6.00000 | − | 10.3923i | −0.848528 | − | 1.46969i | ||||
\(51\) | −1.56155 | −0.218661 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.684658 | −0.0940451 | −0.0470225 | − | 0.998894i | \(-0.514973\pi\) | ||||
−0.0470225 | + | 0.998894i | \(0.514973\pi\) | |||||||
\(54\) | −0.780776 | − | 1.35234i | −0.106250 | − | 0.184031i | ||||
\(55\) | −3.56155 | − | 6.16879i | −0.480240 | − | 0.831800i | ||||
\(56\) | −0.684658 | + | 1.18586i | −0.0914913 | + | 0.158468i | ||||
\(57\) | −7.12311 | −0.943478 | ||||||||
\(58\) | −5.21922 | + | 9.03996i | −0.685318 | + | 1.18700i | ||||
\(59\) | −1.43845 | + | 2.49146i | −0.187270 | + | 0.324361i | −0.944339 | − | 0.328974i | \(-0.893297\pi\) |
0.757069 | + | 0.653335i | \(0.226631\pi\) | |||||||
\(60\) | 1.56155 | 0.201596 | ||||||||
\(61\) | −1.93845 | + | 3.35749i | −0.248193 | + | 0.429882i | −0.963024 | − | 0.269414i | \(-0.913170\pi\) |
0.714832 | + | 0.699297i | \(0.246503\pi\) | |||||||
\(62\) | 2.00000 | + | 3.46410i | 0.254000 | + | 0.439941i | ||||
\(63\) | 0.280776 | + | 0.486319i | 0.0353745 | + | 0.0612704i | ||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.12311 | 0.384428 | ||||||||
\(67\) | 2.28078 | + | 3.95042i | 0.278641 | + | 0.482621i | 0.971047 | − | 0.238887i | \(-0.0767826\pi\) |
−0.692406 | + | 0.721508i | \(0.743449\pi\) | |||||||
\(68\) | 0.342329 | + | 0.592932i | 0.0415135 | + | 0.0719035i | ||||
\(69\) | −1.00000 | + | 1.73205i | −0.120386 | + | 0.208514i | ||||
\(70\) | −3.12311 | −0.373283 | ||||||||
\(71\) | 7.00000 | − | 12.1244i | 0.830747 | − | 1.43890i | −0.0666994 | − | 0.997773i | \(-0.521247\pi\) |
0.897447 | − | 0.441123i | \(-0.145420\pi\) | |||||||
\(72\) | 1.21922 | − | 2.11176i | 0.143687 | − | 0.248873i | ||||
\(73\) | 10.1231 | 1.18482 | 0.592410 | − | 0.805637i | \(-0.298177\pi\) | ||||
0.592410 | + | 0.805637i | \(0.298177\pi\) | |||||||
\(74\) | 5.90388 | − | 10.2258i | 0.686312 | − | 1.18873i | ||||
\(75\) | −3.84233 | − | 6.65511i | −0.443674 | − | 0.768466i | ||||
\(76\) | 1.56155 | + | 2.70469i | 0.179122 | + | 0.310249i | ||||
\(77\) | −1.12311 | −0.127990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.43845 | 0.611873 | 0.305937 | − | 0.952052i | \(-0.401030\pi\) | ||||
0.305937 | + | 0.952052i | \(0.401030\pi\) | |||||||
\(80\) | 8.34233 | + | 14.4493i | 0.932701 | + | 1.61549i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.21922 | + | 2.11176i | −0.134641 | + | 0.233205i | ||||
\(83\) | 0.876894 | 0.0962517 | 0.0481258 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481258 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(84\) | 0.123106 | − | 0.213225i | 0.0134319 | − | 0.0232648i | ||||
\(85\) | 2.78078 | − | 4.81645i | 0.301618 | − | 0.522417i | ||||
\(86\) | 7.12311 | 0.768104 | ||||||||
\(87\) | −3.34233 | + | 5.78908i | −0.358335 | + | 0.620655i | ||||
\(88\) | 2.43845 | + | 4.22351i | 0.259939 | + | 0.450228i | ||||
\(89\) | 2.43845 | + | 4.22351i | 0.258475 | + | 0.447692i | 0.965834 | − | 0.259163i | \(-0.0834467\pi\) |
−0.707359 | + | 0.706855i | \(0.750113\pi\) | |||||||
\(90\) | 5.56155 | 0.586239 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.876894 | 0.0914226 | ||||||||
\(93\) | 1.28078 | + | 2.21837i | 0.132810 | + | 0.230034i | ||||
\(94\) | 6.43845 | + | 11.1517i | 0.664075 | + | 1.15021i | ||||
\(95\) | 12.6847 | − | 21.9705i | 1.30142 | − | 2.25412i | ||||
\(96\) | −2.43845 | −0.248873 | ||||||||
\(97\) | −4.28078 | + | 7.41452i | −0.434647 | + | 0.752831i | −0.997267 | − | 0.0738851i | \(-0.976460\pi\) |
0.562620 | + | 0.826716i | \(0.309794\pi\) | |||||||
\(98\) | 5.21922 | − | 9.03996i | 0.527221 | − | 0.913174i | ||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −1.68466 | + | 2.91791i | −0.168466 | + | 0.291791i | ||||
\(101\) | 3.78078 | + | 6.54850i | 0.376201 | + | 0.651600i | 0.990506 | − | 0.137469i | \(-0.0438968\pi\) |
−0.614305 | + | 0.789069i | \(0.710563\pi\) | |||||||
\(102\) | 1.21922 | + | 2.11176i | 0.120721 | + | 0.209095i | ||||
\(103\) | −3.43845 | −0.338800 | −0.169400 | − | 0.985547i | \(-0.554183\pi\) | ||||
−0.169400 | + | 0.985547i | \(0.554183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 0.534565 | + | 0.925894i | 0.0519216 | + | 0.0899308i | ||||
\(107\) | 4.12311 | + | 7.14143i | 0.398596 | + | 0.690388i | 0.993553 | − | 0.113369i | \(-0.0361644\pi\) |
−0.594957 | + | 0.803757i | \(0.702831\pi\) | |||||||
\(108\) | −0.219224 | + | 0.379706i | −0.0210948 | + | 0.0365373i | ||||
\(109\) | 2.80776 | 0.268935 | 0.134468 | − | 0.990918i | \(-0.457068\pi\) | ||||
0.134468 | + | 0.990918i | \(0.457068\pi\) | |||||||
\(110\) | −5.56155 | + | 9.63289i | −0.530273 | + | 0.918460i | ||||
\(111\) | 3.78078 | − | 6.54850i | 0.358855 | − | 0.621556i | ||||
\(112\) | 2.63068 | 0.248576 | ||||||||
\(113\) | −2.90388 | + | 5.02967i | −0.273174 | + | 0.473152i | −0.969673 | − | 0.244406i | \(-0.921407\pi\) |
0.696499 | + | 0.717558i | \(0.254740\pi\) | |||||||
\(114\) | 5.56155 | + | 9.63289i | 0.520887 | + | 0.902203i | ||||
\(115\) | −3.56155 | − | 6.16879i | −0.332117 | − | 0.575243i | ||||
\(116\) | 2.93087 | 0.272124 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.49242 | 0.413561 | ||||||||
\(119\) | −0.438447 | − | 0.759413i | −0.0401924 | − | 0.0696153i | ||||
\(120\) | 4.34233 | + | 7.52113i | 0.396399 | + | 0.686583i | ||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 6.05398 | 0.548101 | ||||||||
\(123\) | −0.780776 | + | 1.35234i | −0.0704002 | + | 0.121937i | ||||
\(124\) | 0.561553 | − | 0.972638i | 0.0504289 | − | 0.0873455i | ||||
\(125\) | 9.56155 | 0.855211 | ||||||||
\(126\) | 0.438447 | − | 0.759413i | 0.0390600 | − | 0.0676539i | ||||
\(127\) | −2.71922 | − | 4.70983i | −0.241292 | − | 0.417930i | 0.719791 | − | 0.694191i | \(-0.244238\pi\) |
−0.961083 | + | 0.276261i | \(0.910905\pi\) | |||||||
\(128\) | −6.78078 | − | 11.7446i | −0.599342 | − | 1.03809i | ||||
\(129\) | 4.56155 | 0.401622 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.36932 | 0.643860 | 0.321930 | − | 0.946763i | \(-0.395668\pi\) | ||||
0.321930 | + | 0.946763i | \(0.395668\pi\) | |||||||
\(132\) | −0.438447 | − | 0.759413i | −0.0381619 | − | 0.0660984i | ||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | 3.56155 | − | 6.16879i | 0.307671 | − | 0.532902i | ||||
\(135\) | 3.56155 | 0.306530 | ||||||||
\(136\) | −1.90388 | + | 3.29762i | −0.163257 | + | 0.282769i | ||||
\(137\) | −2.78078 | + | 4.81645i | −0.237578 | + | 0.411497i | −0.960019 | − | 0.279936i | \(-0.909687\pi\) |
0.722441 | + | 0.691433i | \(0.243020\pi\) | |||||||
\(138\) | 3.12311 | 0.265856 | ||||||||
\(139\) | 8.96543 | − | 15.5286i | 0.760438 | − | 1.31712i | −0.182187 | − | 0.983264i | \(-0.558318\pi\) |
0.942625 | − | 0.333854i | \(-0.108349\pi\) | |||||||
\(140\) | 0.438447 | + | 0.759413i | 0.0370556 | + | 0.0641821i | ||||
\(141\) | 4.12311 | + | 7.14143i | 0.347228 | + | 0.601417i | ||||
\(142\) | −21.8617 | −1.83460 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.68466 | −0.390388 | ||||||||
\(145\) | −11.9039 | − | 20.6181i | −0.988564 | − | 1.71224i | ||||
\(146\) | −7.90388 | − | 13.6899i | −0.654130 | − | 1.13299i | ||||
\(147\) | 3.34233 | − | 5.78908i | 0.275671 | − | 0.477476i | ||||
\(148\) | −3.31534 | −0.272519 | ||||||||
\(149\) | −1.21922 | + | 2.11176i | −0.0998827 | + | 0.173002i | −0.911636 | − | 0.410999i | \(-0.865180\pi\) |
0.811753 | + | 0.584001i | \(0.198513\pi\) | |||||||
\(150\) | −6.00000 | + | 10.3923i | −0.489898 | + | 0.848528i | ||||
\(151\) | 9.36932 | 0.762464 | 0.381232 | − | 0.924479i | \(-0.375500\pi\) | ||||
0.381232 | + | 0.924479i | \(0.375500\pi\) | |||||||
\(152\) | −8.68466 | + | 15.0423i | −0.704419 | + | 1.22009i | ||||
\(153\) | 0.780776 | + | 1.35234i | 0.0631220 | + | 0.109331i | ||||
\(154\) | 0.876894 | + | 1.51883i | 0.0706622 | + | 0.122390i | ||||
\(155\) | −9.12311 | −0.732785 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3693 | 1.62565 | 0.812824 | − | 0.582509i | \(-0.197929\pi\) | ||||
0.812824 | + | 0.582509i | \(0.197929\pi\) | |||||||
\(158\) | −4.24621 | − | 7.35465i | −0.337810 | − | 0.585105i | ||||
\(159\) | 0.342329 | + | 0.592932i | 0.0271485 | + | 0.0470225i | ||||
\(160\) | 4.34233 | − | 7.52113i | 0.343291 | − | 0.594598i | ||||
\(161\) | −1.12311 | −0.0885131 | ||||||||
\(162\) | −0.780776 | + | 1.35234i | −0.0613436 | + | 0.106250i | ||||
\(163\) | −2.40388 | + | 4.16365i | −0.188287 | + | 0.326122i | −0.944679 | − | 0.327996i | \(-0.893627\pi\) |
0.756393 | + | 0.654118i | \(0.226960\pi\) | |||||||
\(164\) | 0.684658 | 0.0534628 | ||||||||
\(165\) | −3.56155 | + | 6.16879i | −0.277267 | + | 0.480240i | ||||
\(166\) | −0.684658 | − | 1.18586i | −0.0531398 | − | 0.0920408i | ||||
\(167\) | 5.12311 | + | 8.87348i | 0.396438 | + | 0.686650i | 0.993284 | − | 0.115706i | \(-0.0369129\pi\) |
−0.596846 | + | 0.802356i | \(0.703580\pi\) | |||||||
\(168\) | 1.36932 | 0.105645 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.68466 | −0.666083 | ||||||||
\(171\) | 3.56155 | + | 6.16879i | 0.272359 | + | 0.471739i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | −10.1231 | + | 17.5337i | −0.769645 | + | 1.33307i | 0.168110 | + | 0.985768i | \(0.446234\pi\) |
−0.937755 | + | 0.347297i | \(0.887100\pi\) | |||||||
\(174\) | 10.4384 | 0.791337 | ||||||||
\(175\) | 2.15767 | − | 3.73720i | 0.163105 | − | 0.282505i | ||||
\(176\) | 4.68466 | − | 8.11407i | 0.353119 | − | 0.611621i | ||||
\(177\) | 2.87689 | 0.216241 | ||||||||
\(178\) | 3.80776 | − | 6.59524i | 0.285404 | − | 0.494334i | ||||
\(179\) | 2.43845 | + | 4.22351i | 0.182258 | + | 0.315680i | 0.942649 | − | 0.333785i | \(-0.108326\pi\) |
−0.760391 | + | 0.649466i | \(0.774993\pi\) | |||||||
\(180\) | −0.780776 | − | 1.35234i | −0.0581956 | − | 0.100798i | ||||
\(181\) | −2.68466 | −0.199549 | −0.0997745 | − | 0.995010i | \(-0.531812\pi\) | ||||
−0.0997745 | + | 0.995010i | \(0.531812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.87689 | 0.286588 | ||||||||
\(184\) | 2.43845 | + | 4.22351i | 0.179765 | + | 0.311362i | ||||
\(185\) | 13.4654 | + | 23.3228i | 0.989998 | + | 1.71473i | ||||
\(186\) | 2.00000 | − | 3.46410i | 0.146647 | − | 0.254000i | ||||
\(187\) | −3.12311 | −0.228384 | ||||||||
\(188\) | 1.80776 | − | 3.13114i | 0.131845 | − | 0.228362i | ||||
\(189\) | 0.280776 | − | 0.486319i | 0.0204235 | − | 0.0353745i | ||||
\(190\) | −39.6155 | −2.87401 | ||||||||
\(191\) | 4.56155 | − | 7.90084i | 0.330062 | − | 0.571685i | −0.652461 | − | 0.757822i | \(-0.726264\pi\) |
0.982524 | + | 0.186137i | \(0.0595969\pi\) | |||||||
\(192\) | −2.78078 | − | 4.81645i | −0.200685 | − | 0.347597i | ||||
\(193\) | −6.74621 | − | 11.6848i | −0.485603 | − | 0.841089i | 0.514260 | − | 0.857634i | \(-0.328067\pi\) |
−0.999863 | + | 0.0165453i | \(0.994733\pi\) | |||||||
\(194\) | 13.3693 | 0.959861 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.93087 | −0.209348 | ||||||||
\(197\) | 6.68466 | + | 11.5782i | 0.476262 | + | 0.824910i | 0.999630 | − | 0.0271965i | \(-0.00865798\pi\) |
−0.523368 | + | 0.852107i | \(0.675325\pi\) | |||||||
\(198\) | −1.56155 | − | 2.70469i | −0.110975 | − | 0.192214i | ||||
\(199\) | −11.0885 | + | 19.2059i | −0.786046 | + | 1.36147i | 0.142327 | + | 0.989820i | \(0.454542\pi\) |
−0.928372 | + | 0.371651i | \(0.878792\pi\) | |||||||
\(200\) | −18.7386 | −1.32502 | ||||||||
\(201\) | 2.28078 | − | 3.95042i | 0.160874 | − | 0.278641i | ||||
\(202\) | 5.90388 | − | 10.2258i | 0.415396 | − | 0.719486i | ||||
\(203\) | −3.75379 | −0.263464 | ||||||||
\(204\) | 0.342329 | − | 0.592932i | 0.0239678 | − | 0.0415135i | ||||
\(205\) | −2.78078 | − | 4.81645i | −0.194218 | − | 0.336395i | ||||
\(206\) | 2.68466 | + | 4.64996i | 0.187049 | + | 0.323978i | ||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.2462 | −0.985431 | ||||||||
\(210\) | 1.56155 | + | 2.70469i | 0.107757 | + | 0.186641i | ||||
\(211\) | −9.84233 | − | 17.0474i | −0.677574 | − | 1.17359i | −0.975709 | − | 0.219069i | \(-0.929698\pi\) |
0.298136 | − | 0.954524i | \(-0.403635\pi\) | |||||||
\(212\) | 0.150093 | − | 0.259969i | 0.0103084 | − | 0.0178548i | ||||
\(213\) | −14.0000 | −0.959264 | ||||||||
\(214\) | 6.43845 | − | 11.1517i | 0.440123 | − | 0.762316i | ||||
\(215\) | −8.12311 | + | 14.0696i | −0.553991 | + | 0.959541i | ||||
\(216\) | −2.43845 | −0.165915 | ||||||||
\(217\) | −0.719224 | + | 1.24573i | −0.0488241 | + | 0.0845658i | ||||
\(218\) | −2.19224 | − | 3.79706i | −0.148477 | − | 0.257170i | ||||
\(219\) | −5.06155 | − | 8.76687i | −0.342028 | − | 0.592410i | ||||
\(220\) | 3.12311 | 0.210560 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −11.8078 | −0.792485 | ||||||||
\(223\) | 4.00000 | + | 6.92820i | 0.267860 | + | 0.463947i | 0.968309 | − | 0.249756i | \(-0.0803503\pi\) |
−0.700449 | + | 0.713702i | \(0.747017\pi\) | |||||||
\(224\) | −0.684658 | − | 1.18586i | −0.0457457 | − | 0.0792338i | ||||
\(225\) | −3.84233 | + | 6.65511i | −0.256155 | + | 0.443674i | ||||
\(226\) | 9.06913 | 0.603270 | ||||||||
\(227\) | 3.56155 | − | 6.16879i | 0.236389 | − | 0.409437i | −0.723287 | − | 0.690548i | \(-0.757370\pi\) |
0.959675 | + | 0.281111i | \(0.0907028\pi\) | |||||||
\(228\) | 1.56155 | − | 2.70469i | 0.103416 | − | 0.179122i | ||||
\(229\) | 16.2462 | 1.07358 | 0.536790 | − | 0.843716i | \(-0.319637\pi\) | ||||
0.536790 | + | 0.843716i | \(0.319637\pi\) | |||||||
\(230\) | −5.56155 | + | 9.63289i | −0.366718 | + | 0.635174i | ||||
\(231\) | 0.561553 | + | 0.972638i | 0.0369475 | + | 0.0639949i | ||||
\(232\) | 8.15009 | + | 14.1164i | 0.535080 | + | 0.926785i | ||||
\(233\) | 26.0000 | 1.70332 | 0.851658 | − | 0.524097i | \(-0.175597\pi\) | ||||
0.851658 | + | 0.524097i | \(0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.3693 | −1.91584 | ||||||||
\(236\) | −0.630683 | − | 1.09238i | −0.0410540 | − | 0.0711076i | ||||
\(237\) | −2.71922 | − | 4.70983i | −0.176633 | − | 0.305937i | ||||
\(238\) | −0.684658 | + | 1.18586i | −0.0443798 | + | 0.0768681i | ||||
\(239\) | 25.3693 | 1.64100 | 0.820502 | − | 0.571643i | \(-0.193694\pi\) | ||||
0.820502 | + | 0.571643i | \(0.193694\pi\) | |||||||
\(240\) | 8.34233 | − | 14.4493i | 0.538495 | − | 0.932701i | ||||
\(241\) | −8.90388 | + | 15.4220i | −0.573549 | + | 0.993417i | 0.422648 | + | 0.906294i | \(0.361101\pi\) |
−0.996198 | + | 0.0871229i | \(0.972233\pi\) | |||||||
\(242\) | −10.9309 | −0.702663 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −0.849907 | − | 1.47208i | −0.0544097 | − | 0.0942404i | ||||
\(245\) | 11.9039 | + | 20.6181i | 0.760511 | + | 1.31724i | ||||
\(246\) | 2.43845 | 0.155470 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.24621 | 0.396635 | ||||||||
\(249\) | −0.438447 | − | 0.759413i | −0.0277855 | − | 0.0481258i | ||||
\(250\) | −7.46543 | − | 12.9305i | −0.472156 | − | 0.817797i | ||||
\(251\) | −9.36932 | + | 16.2281i | −0.591386 | + | 1.02431i | 0.402660 | + | 0.915350i | \(0.368086\pi\) |
−0.994046 | + | 0.108961i | \(0.965248\pi\) | |||||||
\(252\) | −0.246211 | −0.0155099 | ||||||||
\(253\) | −2.00000 | + | 3.46410i | −0.125739 | + | 0.217786i | ||||
\(254\) | −4.24621 | + | 7.35465i | −0.266431 | + | 0.461472i | ||||
\(255\) | −5.56155 | −0.348278 | ||||||||
\(256\) | −5.02699 | + | 8.70700i | −0.314187 | + | 0.544187i | ||||
\(257\) | −14.5885 | − | 25.2681i | −0.910008 | − | 1.57618i | −0.814050 | − | 0.580795i | \(-0.802742\pi\) |
−0.0959583 | − | 0.995385i | \(-0.530592\pi\) | |||||||
\(258\) | −3.56155 | − | 6.16879i | −0.221733 | − | 0.384052i | ||||
\(259\) | 4.24621 | 0.263847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.68466 | 0.413770 | ||||||||
\(262\) | −5.75379 | − | 9.96585i | −0.355470 | − | 0.615693i | ||||
\(263\) | −4.68466 | − | 8.11407i | −0.288868 | − | 0.500335i | 0.684672 | − | 0.728852i | \(-0.259946\pi\) |
−0.973540 | + | 0.228517i | \(0.926612\pi\) | |||||||
\(264\) | 2.43845 | − | 4.22351i | 0.150076 | − | 0.259939i | ||||
\(265\) | −2.43845 | −0.149793 | ||||||||
\(266\) | −3.12311 | + | 5.40938i | −0.191490 | + | 0.331670i | ||||
\(267\) | 2.43845 | − | 4.22351i | 0.149231 | − | 0.258475i | ||||
\(268\) | −2.00000 | −0.122169 | ||||||||
\(269\) | 10.6847 | − | 18.5064i | 0.651455 | − | 1.12835i | −0.331315 | − | 0.943520i | \(-0.607492\pi\) |
0.982770 | − | 0.184833i | \(-0.0591745\pi\) | |||||||
\(270\) | −2.78078 | − | 4.81645i | −0.169233 | − | 0.293120i | ||||
\(271\) | −14.9654 | − | 25.9209i | −0.909085 | − | 1.57458i | −0.815337 | − | 0.578986i | \(-0.803449\pi\) |
−0.0937481 | − | 0.995596i | \(-0.529885\pi\) | |||||||
\(272\) | 7.31534 | 0.443558 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.68466 | 0.524659 | ||||||||
\(275\) | −7.68466 | − | 13.3102i | −0.463402 | − | 0.802636i | ||||
\(276\) | −0.438447 | − | 0.759413i | −0.0263914 | − | 0.0457113i | ||||
\(277\) | −2.65767 | + | 4.60322i | −0.159684 | + | 0.276581i | −0.934755 | − | 0.355294i | \(-0.884381\pi\) |
0.775071 | + | 0.631874i | \(0.217714\pi\) | |||||||
\(278\) | −28.0000 | −1.67933 | ||||||||
\(279\) | 1.28078 | − | 2.21837i | 0.0766781 | − | 0.132810i | ||||
\(280\) | −2.43845 | + | 4.22351i | −0.145725 | + | 0.252403i | ||||
\(281\) | −17.8078 | −1.06232 | −0.531161 | − | 0.847271i | \(-0.678244\pi\) | ||||
−0.531161 | + | 0.847271i | \(0.678244\pi\) | |||||||
\(282\) | 6.43845 | − | 11.1517i | 0.383404 | − | 0.664075i | ||||
\(283\) | 6.84233 | + | 11.8513i | 0.406734 | + | 0.704484i | 0.994522 | − | 0.104531i | \(-0.0333342\pi\) |
−0.587787 | + | 0.809015i | \(0.700001\pi\) | |||||||
\(284\) | 3.06913 | + | 5.31589i | 0.182119 | + | 0.315440i | ||||
\(285\) | −25.3693 | −1.50275 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.876894 | −0.0517614 | ||||||||
\(288\) | 1.21922 | + | 2.11176i | 0.0718434 | + | 0.124436i | ||||
\(289\) | 7.28078 | + | 12.6107i | 0.428281 | + | 0.741804i | ||||
\(290\) | −18.5885 | + | 32.1963i | −1.09156 | + | 1.89063i | ||||
\(291\) | 8.56155 | 0.501887 | ||||||||
\(292\) | −2.21922 | + | 3.84381i | −0.129870 | + | 0.224942i | ||||
\(293\) | 10.2192 | − | 17.7002i | 0.597013 | − | 1.03406i | −0.396246 | − | 0.918144i | \(-0.629687\pi\) |
0.993259 | − | 0.115913i | \(-0.0369794\pi\) | |||||||
\(294\) | −10.4384 | −0.608783 | ||||||||
\(295\) | −5.12311 | + | 8.87348i | −0.298279 | + | 0.516634i | ||||
\(296\) | −9.21922 | − | 15.9682i | −0.535856 | − | 0.928131i | ||||
\(297\) | −1.00000 | − | 1.73205i | −0.0580259 | − | 0.100504i | ||||
\(298\) | 3.80776 | 0.220578 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.36932 | 0.194528 | ||||||||
\(301\) | 1.28078 | + | 2.21837i | 0.0738227 | + | 0.127865i | ||||
\(302\) | −7.31534 | − | 12.6705i | −0.420951 | − | 0.729108i | ||||
\(303\) | 3.78078 | − | 6.54850i | 0.217200 | − | 0.376201i | ||||
\(304\) | 33.3693 | 1.91386 | ||||||||
\(305\) | −6.90388 | + | 11.9579i | −0.395315 | + | 0.684706i | ||||
\(306\) | 1.21922 | − | 2.11176i | 0.0696984 | − | 0.120721i | ||||
\(307\) | −30.8078 | −1.75829 | −0.879146 | − | 0.476553i | \(-0.841886\pi\) | ||||
−0.879146 | + | 0.476553i | \(0.841886\pi\) | |||||||
\(308\) | 0.246211 | − | 0.426450i | 0.0140292 | − | 0.0242993i | ||||
\(309\) | 1.71922 | + | 2.97778i | 0.0978032 | + | 0.169400i | ||||
\(310\) | 7.12311 | + | 12.3376i | 0.404565 | + | 0.700728i | ||||
\(311\) | −19.1231 | −1.08437 | −0.542186 | − | 0.840259i | \(-0.682403\pi\) | ||||
−0.542186 | + | 0.840259i | \(0.682403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.6847 | −0.773503 | −0.386751 | − | 0.922184i | \(-0.626403\pi\) | ||||
−0.386751 | + | 0.922184i | \(0.626403\pi\) | |||||||
\(314\) | −15.9039 | − | 27.5463i | −0.897508 | − | 1.55453i | ||||
\(315\) | 1.00000 | + | 1.73205i | 0.0563436 | + | 0.0975900i | ||||
\(316\) | −1.19224 | + | 2.06501i | −0.0670685 | + | 0.116166i | ||||
\(317\) | −14.0540 | −0.789350 | −0.394675 | − | 0.918821i | \(-0.629143\pi\) | ||||
−0.394675 | + | 0.918821i | \(0.629143\pi\) | |||||||
\(318\) | 0.534565 | − | 0.925894i | 0.0299769 | − | 0.0519216i | ||||
\(319\) | −6.68466 | + | 11.5782i | −0.374269 | + | 0.648253i | ||||
\(320\) | 19.8078 | 1.10729 | ||||||||
\(321\) | 4.12311 | − | 7.14143i | 0.230129 | − | 0.398596i | ||||
\(322\) | 0.876894 | + | 1.51883i | 0.0488674 | + | 0.0846408i | ||||
\(323\) | −5.56155 | − | 9.63289i | −0.309453 | − | 0.535988i | ||||
\(324\) | 0.438447 | 0.0243582 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.50758 | 0.415806 | ||||||||
\(327\) | −1.40388 | − | 2.43160i | −0.0776349 | − | 0.134468i | ||||
\(328\) | 1.90388 | + | 3.29762i | 0.105124 | + | 0.182081i | ||||
\(329\) | −2.31534 | + | 4.01029i | −0.127649 | + | 0.221094i | ||||
\(330\) | 11.1231 | 0.612307 | ||||||||
\(331\) | −1.59612 | + | 2.76456i | −0.0877306 | + | 0.151954i | −0.906552 | − | 0.422095i | \(-0.861295\pi\) |
0.818821 | + | 0.574049i | \(0.194628\pi\) | |||||||
\(332\) | −0.192236 | + | 0.332962i | −0.0105503 | + | 0.0182737i | ||||
\(333\) | −7.56155 | −0.414371 | ||||||||
\(334\) | 8.00000 | − | 13.8564i | 0.437741 | − | 0.758189i | ||||
\(335\) | 8.12311 | + | 14.0696i | 0.443813 | + | 0.768706i | ||||
\(336\) | −1.31534 | − | 2.27824i | −0.0717578 | − | 0.124288i | ||||
\(337\) | −6.12311 | −0.333547 | −0.166773 | − | 0.985995i | \(-0.553335\pi\) | ||||
−0.166773 | + | 0.985995i | \(0.553335\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.80776 | 0.315434 | ||||||||
\(340\) | 1.21922 | + | 2.11176i | 0.0661217 | + | 0.114526i | ||||
\(341\) | 2.56155 | + | 4.43674i | 0.138716 | + | 0.240263i | ||||
\(342\) | 5.56155 | − | 9.63289i | 0.300734 | − | 0.520887i | ||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | 5.56155 | − | 9.63289i | 0.299859 | − | 0.519371i | ||||
\(345\) | −3.56155 | + | 6.16879i | −0.191748 | + | 0.332117i | ||||
\(346\) | 31.6155 | 1.69966 | ||||||||
\(347\) | −13.8078 | + | 23.9157i | −0.741240 | + | 1.28386i | 0.210692 | + | 0.977553i | \(0.432428\pi\) |
−0.951931 | + | 0.306312i | \(0.900905\pi\) | |||||||
\(348\) | −1.46543 | − | 2.53821i | −0.0785556 | − | 0.136062i | ||||
\(349\) | 3.40388 | + | 5.89570i | 0.182206 | + | 0.315589i | 0.942631 | − | 0.333836i | \(-0.108343\pi\) |
−0.760426 | + | 0.649425i | \(0.775010\pi\) | |||||||
\(350\) | −6.73863 | −0.360195 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.87689 | −0.259939 | ||||||||
\(353\) | 2.65767 | + | 4.60322i | 0.141454 | + | 0.245005i | 0.928044 | − | 0.372470i | \(-0.121489\pi\) |
−0.786591 | + | 0.617475i | \(0.788156\pi\) | |||||||
\(354\) | −2.24621 | − | 3.89055i | −0.119385 | − | 0.206781i | ||||
\(355\) | 24.9309 | − | 43.1815i | 1.32319 | − | 2.29184i | ||||
\(356\) | −2.13826 | −0.113328 | ||||||||
\(357\) | −0.438447 | + | 0.759413i | −0.0232051 | + | 0.0401924i | ||||
\(358\) | 3.80776 | − | 6.59524i | 0.201247 | − | 0.348569i | ||||
\(359\) | 9.36932 | 0.494494 | 0.247247 | − | 0.968953i | \(-0.420474\pi\) | ||||
0.247247 | + | 0.968953i | \(0.420474\pi\) | |||||||
\(360\) | 4.34233 | − | 7.52113i | 0.228861 | − | 0.396399i | ||||
\(361\) | −15.8693 | − | 27.4865i | −0.835227 | − | 1.44666i | ||||
\(362\) | 2.09612 | + | 3.63058i | 0.110170 | + | 0.190819i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.0540 | 1.88715 | ||||||||
\(366\) | −3.02699 | − | 5.24290i | −0.158223 | − | 0.274051i | ||||
\(367\) | 8.52699 | + | 14.7692i | 0.445105 | + | 0.770945i | 0.998060 | − | 0.0622668i | \(-0.0198330\pi\) |
−0.552954 | + | 0.833212i | \(0.686500\pi\) | |||||||
\(368\) | 4.68466 | − | 8.11407i | 0.244205 | − | 0.422975i | ||||
\(369\) | 1.56155 | 0.0812912 | ||||||||
\(370\) | 21.0270 | − | 36.4198i | 1.09314 | − | 1.89338i | ||||
\(371\) | −0.192236 | + | 0.332962i | −0.00998039 | + | 0.0172865i | ||||
\(372\) | −1.12311 | −0.0582303 | ||||||||
\(373\) | −14.1847 | + | 24.5685i | −0.734454 | + | 1.27211i | 0.220509 | + | 0.975385i | \(0.429228\pi\) |
−0.954963 | + | 0.296726i | \(0.904105\pi\) | |||||||
\(374\) | 2.43845 | + | 4.22351i | 0.126089 | + | 0.218393i | ||||
\(375\) | −4.78078 | − | 8.28055i | −0.246878 | − | 0.427606i | ||||
\(376\) | 20.1080 | 1.03699 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.876894 | −0.0451026 | ||||||||
\(379\) | 11.8423 | + | 20.5115i | 0.608300 | + | 1.05361i | 0.991521 | + | 0.129949i | \(0.0414814\pi\) |
−0.383221 | + | 0.923657i | \(0.625185\pi\) | |||||||
\(380\) | 5.56155 | + | 9.63289i | 0.285302 | + | 0.494157i | ||||
\(381\) | −2.71922 | + | 4.70983i | −0.139310 | + | 0.241292i | ||||
\(382\) | −14.2462 | −0.728900 | ||||||||
\(383\) | −11.3693 | + | 19.6922i | −0.580945 | + | 1.00623i | 0.414423 | + | 0.910085i | \(0.363984\pi\) |
−0.995368 | + | 0.0961417i | \(0.969350\pi\) | |||||||
\(384\) | −6.78078 | + | 11.7446i | −0.346030 | + | 0.599342i | ||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | −10.5346 | + | 18.2464i | −0.536195 | + | 0.928717i | ||||
\(387\) | −2.28078 | − | 3.95042i | −0.115938 | − | 0.200811i | ||||
\(388\) | −1.87689 | − | 3.25088i | −0.0952849 | − | 0.165038i | ||||
\(389\) | 34.0540 | 1.72661 | 0.863303 | − | 0.504687i | \(-0.168392\pi\) | ||||
0.863303 | + | 0.504687i | \(0.168392\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.12311 | −0.157942 | ||||||||
\(392\) | −8.15009 | − | 14.1164i | −0.411642 | − | 0.712985i | ||||
\(393\) | −3.68466 | − | 6.38202i | −0.185866 | − | 0.321930i | ||||
\(394\) | 10.4384 | − | 18.0799i | 0.525881 | − | 0.910853i | ||||
\(395\) | 19.3693 | 0.974576 | ||||||||
\(396\) | −0.438447 | + | 0.759413i | −0.0220328 | + | 0.0381619i | ||||
\(397\) | 12.5270 | − | 21.6974i | 0.628711 | − | 1.08896i | −0.359099 | − | 0.933299i | \(-0.616916\pi\) |
0.987811 | − | 0.155661i | \(-0.0497507\pi\) | |||||||
\(398\) | 34.6307 | 1.73588 | ||||||||
\(399\) | −2.00000 | + | 3.46410i | −0.100125 | + | 0.173422i | ||||
\(400\) | 18.0000 | + | 31.1769i | 0.900000 | + | 1.55885i | ||||
\(401\) | 7.21922 | + | 12.5041i | 0.360511 | + | 0.624423i | 0.988045 | − | 0.154166i | \(-0.0492691\pi\) |
−0.627534 | + | 0.778589i | \(0.715936\pi\) | |||||||
\(402\) | −7.12311 | −0.355268 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.31534 | −0.164944 | ||||||||
\(405\) | −1.78078 | − | 3.08440i | −0.0884875 | − | 0.153265i | ||||
\(406\) | 2.93087 | + | 5.07642i | 0.145457 | + | 0.251938i | ||||
\(407\) | 7.56155 | − | 13.0970i | 0.374812 | − | 0.649194i | ||||
\(408\) | 3.80776 | 0.188512 | ||||||||
\(409\) | 3.18466 | − | 5.51599i | 0.157471 | − | 0.272748i | −0.776485 | − | 0.630136i | \(-0.782999\pi\) |
0.933956 | + | 0.357388i | \(0.116333\pi\) | |||||||
\(410\) | −4.34233 | + | 7.52113i | −0.214452 | + | 0.371442i | ||||
\(411\) | 5.56155 | 0.274331 | ||||||||
\(412\) | 0.753789 | − | 1.30560i | 0.0371365 | − | 0.0643223i | ||||
\(413\) | 0.807764 | + | 1.39909i | 0.0397475 | + | 0.0688446i | ||||
\(414\) | −1.56155 | − | 2.70469i | −0.0767461 | − | 0.132928i | ||||
\(415\) | 3.12311 | 0.153307 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.9309 | −0.878078 | ||||||||
\(418\) | 11.1231 | + | 19.2658i | 0.544049 | + | 0.942320i | ||||
\(419\) | 17.1231 | + | 29.6581i | 0.836518 | + | 1.44889i | 0.892788 | + | 0.450477i | \(0.148746\pi\) |
−0.0562697 | + | 0.998416i | \(0.517921\pi\) | |||||||
\(420\) | 0.438447 | − | 0.759413i | 0.0213940 | − | 0.0370556i | ||||
\(421\) | −31.2462 | −1.52285 | −0.761424 | − | 0.648255i | \(-0.775499\pi\) | ||||
−0.761424 | + | 0.648255i | \(0.775499\pi\) | |||||||
\(422\) | −15.3693 | + | 26.6204i | −0.748167 | + | 1.29586i | ||||
\(423\) | 4.12311 | − | 7.14143i | 0.200472 | − | 0.347228i | ||||
\(424\) | 1.66950 | 0.0810783 | ||||||||
\(425\) | 6.00000 | − | 10.3923i | 0.291043 | − | 0.504101i | ||||
\(426\) | 10.9309 | + | 18.9328i | 0.529602 | + | 0.917298i | ||||
\(427\) | 1.08854 | + | 1.88541i | 0.0526782 | + | 0.0912413i | ||||
\(428\) | −3.61553 | −0.174763 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25.3693 | 1.22342 | ||||||||
\(431\) | −5.56155 | − | 9.63289i | −0.267891 | − | 0.464000i | 0.700426 | − | 0.713725i | \(-0.252993\pi\) |
−0.968317 | + | 0.249725i | \(0.919660\pi\) | |||||||
\(432\) | 2.34233 | + | 4.05703i | 0.112695 | + | 0.195194i | ||||
\(433\) | −4.37689 | + | 7.58100i | −0.210340 | + | 0.364320i | −0.951821 | − | 0.306654i | \(-0.900790\pi\) |
0.741481 | + | 0.670974i | \(0.234124\pi\) | |||||||
\(434\) | 2.24621 | 0.107822 | ||||||||
\(435\) | −11.9039 | + | 20.6181i | −0.570747 | + | 0.988564i | ||||
\(436\) | −0.615528 | + | 1.06613i | −0.0294785 | + | 0.0510582i | ||||
\(437\) | −14.2462 | −0.681489 | ||||||||
\(438\) | −7.90388 | + | 13.6899i | −0.377662 | + | 0.654130i | ||||
\(439\) | 6.84233 | + | 11.8513i | 0.326567 | + | 0.565630i | 0.981828 | − | 0.189772i | \(-0.0607749\pi\) |
−0.655262 | + | 0.755402i | \(0.727442\pi\) | |||||||
\(440\) | 8.68466 | + | 15.0423i | 0.414025 | + | 0.717112i | ||||
\(441\) | −6.68466 | −0.318317 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.7386 | −1.65048 | −0.825241 | − | 0.564781i | \(-0.808961\pi\) | ||||
−0.825241 | + | 0.564781i | \(0.808961\pi\) | |||||||
\(444\) | 1.65767 | + | 2.87117i | 0.0786696 | + | 0.136260i | ||||
\(445\) | 8.68466 | + | 15.0423i | 0.411692 | + | 0.713072i | ||||
\(446\) | 6.24621 | − | 10.8188i | 0.295767 | − | 0.512283i | ||||
\(447\) | 2.43845 | 0.115335 | ||||||||
\(448\) | 1.56155 | − | 2.70469i | 0.0737764 | − | 0.127785i | ||||
\(449\) | −4.12311 | + | 7.14143i | −0.194581 | + | 0.337025i | −0.946763 | − | 0.321931i | \(-0.895668\pi\) |
0.752182 | + | 0.658956i | \(0.229002\pi\) | |||||||
\(450\) | 12.0000 | 0.565685 | ||||||||
\(451\) | −1.56155 | + | 2.70469i | −0.0735307 | + | 0.127359i | ||||
\(452\) | −1.27320 | − | 2.20525i | −0.0598862 | − | 0.103726i | ||||
\(453\) | −4.68466 | − | 8.11407i | −0.220104 | − | 0.381232i | ||||
\(454\) | −11.1231 | −0.522033 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 17.3693 | 0.813393 | ||||||||
\(457\) | 6.30776 | + | 10.9254i | 0.295065 | + | 0.511067i | 0.975000 | − | 0.222205i | \(-0.0713254\pi\) |
−0.679935 | + | 0.733272i | \(0.737992\pi\) | |||||||
\(458\) | −12.6847 | − | 21.9705i | −0.592715 | − | 1.02661i | ||||
\(459\) | 0.780776 | − | 1.35234i | 0.0364435 | − | 0.0631220i | ||||
\(460\) | 3.12311 | 0.145616 | ||||||||
\(461\) | −8.09612 | + | 14.0229i | −0.377074 | + | 0.653111i | −0.990635 | − | 0.136536i | \(-0.956403\pi\) |
0.613561 | + | 0.789647i | \(0.289736\pi\) | |||||||
\(462\) | 0.876894 | − | 1.51883i | 0.0407968 | − | 0.0706622i | ||||
\(463\) | 14.3153 | 0.665290 | 0.332645 | − | 0.943052i | \(-0.392059\pi\) | ||||
0.332645 | + | 0.943052i | \(0.392059\pi\) | |||||||
\(464\) | 15.6577 | − | 27.1199i | 0.726889 | − | 1.25901i | ||||
\(465\) | 4.56155 | + | 7.90084i | 0.211537 | + | 0.366393i | ||||
\(466\) | −20.3002 | − | 35.1610i | −0.940388 | − | 1.62880i | ||||
\(467\) | −26.0000 | −1.20314 | −0.601568 | − | 0.798821i | \(-0.705457\pi\) | ||||
−0.601568 | + | 0.798821i | \(0.705457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.56155 | 0.118282 | ||||||||
\(470\) | 22.9309 | + | 39.7174i | 1.05772 | + | 1.83203i | ||||
\(471\) | −10.1847 | − | 17.6403i | −0.469284 | − | 0.812824i | ||||
\(472\) | 3.50758 | − | 6.07530i | 0.161449 | − | 0.279638i | ||||
\(473\) | 9.12311 | 0.419481 | ||||||||
\(474\) | −4.24621 | + | 7.35465i | −0.195035 | + | 0.337810i | ||||
\(475\) | 27.3693 | − | 47.4050i | 1.25579 | − | 2.17509i | ||||
\(476\) | 0.384472 | 0.0176222 | ||||||||
\(477\) | 0.342329 | − | 0.592932i | 0.0156742 | − | 0.0271485i | ||||
\(478\) | −19.8078 | − | 34.3081i | −0.905986 | − | 1.56921i | ||||
\(479\) | 5.12311 | + | 8.87348i | 0.234081 | + | 0.405440i | 0.959005 | − | 0.283389i | \(-0.0914587\pi\) |
−0.724924 | + | 0.688828i | \(0.758125\pi\) | |||||||
\(480\) | −8.68466 | −0.396399 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 27.8078 | 1.26661 | ||||||||
\(483\) | 0.561553 | + | 0.972638i | 0.0255515 | + | 0.0442566i | ||||
\(484\) | 1.53457 | + | 2.65794i | 0.0697530 | + | 0.120816i | ||||
\(485\) | −15.2462 | + | 26.4072i | −0.692295 | + | 1.19909i | ||||
\(486\) | 1.56155 | 0.0708335 | ||||||||
\(487\) | 3.56155 | − | 6.16879i | 0.161389 | − | 0.279535i | −0.773978 | − | 0.633213i | \(-0.781736\pi\) |
0.935367 | + | 0.353678i | \(0.115069\pi\) | |||||||
\(488\) | 4.72680 | − | 8.18706i | 0.213972 | − | 0.370611i | ||||
\(489\) | 4.80776 | 0.217415 | ||||||||
\(490\) | 18.5885 | − | 32.1963i | 0.839745 | − | 1.45448i | ||||
\(491\) | 18.1231 | + | 31.3901i | 0.817884 | + | 1.41662i | 0.907238 | + | 0.420617i | \(0.138186\pi\) |
−0.0893539 | + | 0.996000i | \(0.528480\pi\) | |||||||
\(492\) | −0.342329 | − | 0.592932i | −0.0154334 | − | 0.0267314i | ||||
\(493\) | −10.4384 | −0.470124 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.12311 | 0.320160 | ||||||||
\(496\) | −6.00000 | − | 10.3923i | −0.269408 | − | 0.466628i | ||||
\(497\) | −3.93087 | − | 6.80847i | −0.176324 | − | 0.305401i | ||||
\(498\) | −0.684658 | + | 1.18586i | −0.0306803 | + | 0.0531398i | ||||
\(499\) | −4.49242 | −0.201108 | −0.100554 | − | 0.994932i | \(-0.532062\pi\) | ||||
−0.100554 | + | 0.994932i | \(0.532062\pi\) | |||||||
\(500\) | −2.09612 | + | 3.63058i | −0.0937412 | + | 0.162365i | ||||
\(501\) | 5.12311 | − | 8.87348i | 0.228883 | − | 0.396438i | ||||
\(502\) | 29.2614 | 1.30600 | ||||||||
\(503\) | 14.1231 | − | 24.4619i | 0.629718 | − | 1.09070i | −0.357890 | − | 0.933764i | \(-0.616504\pi\) |
0.987608 | − | 0.156940i | \(-0.0501630\pi\) | |||||||
\(504\) | −0.684658 | − | 1.18586i | −0.0304971 | − | 0.0528225i | ||||
\(505\) | 13.4654 | + | 23.3228i | 0.599204 | + | 1.03785i | ||||
\(506\) | 6.24621 | 0.277678 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.38447 | 0.105794 | ||||||||
\(509\) | −6.90388 | − | 11.9579i | −0.306009 | − | 0.530023i | 0.671476 | − | 0.741026i | \(-0.265660\pi\) |
−0.977486 | + | 0.211003i | \(0.932327\pi\) | |||||||
\(510\) | 4.34233 | + | 7.52113i | 0.192282 | + | 0.333041i | ||||
\(511\) | 2.84233 | − | 4.92306i | 0.125737 | − | 0.217783i | ||||
\(512\) | −11.4233 | −0.504843 | ||||||||
\(513\) | 3.56155 | − | 6.16879i | 0.157246 | − | 0.272359i | ||||
\(514\) | −22.7808 | + | 39.4575i | −1.00482 | + | 1.74039i | ||||
\(515\) | −12.2462 | −0.539633 | ||||||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | 8.24621 | + | 14.2829i | 0.362668 | + | 0.628159i | ||||
\(518\) | −3.31534 | − | 5.74234i | −0.145668 | − | 0.252304i | ||||
\(519\) | 20.2462 | 0.888710 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.06913 | −0.397326 | −0.198663 | − | 0.980068i | \(-0.563660\pi\) | ||||
−0.198663 | + | 0.980068i | \(0.563660\pi\) | |||||||
\(522\) | −5.21922 | − | 9.03996i | −0.228439 | − | 0.395668i | ||||
\(523\) | −16.9309 | − | 29.3251i | −0.740335 | − | 1.28230i | −0.952343 | − | 0.305030i | \(-0.901333\pi\) |
0.212007 | − | 0.977268i | \(-0.432000\pi\) | |||||||
\(524\) | −1.61553 | + | 2.79818i | −0.0705747 | + | 0.122239i | ||||
\(525\) | −4.31534 | −0.188337 | ||||||||
\(526\) | −7.31534 | + | 12.6705i | −0.318964 | + | 0.552462i | ||||
\(527\) | −2.00000 | + | 3.46410i | −0.0871214 | + | 0.150899i | ||||
\(528\) | −9.36932 | −0.407747 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 1.90388 | + | 3.29762i | 0.0826994 | + | 0.143239i | ||||
\(531\) | −1.43845 | − | 2.49146i | −0.0624233 | − | 0.108120i | ||||
\(532\) | 1.75379 | 0.0760364 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7.61553 | −0.329556 | ||||||||
\(535\) | 14.6847 | + | 25.4346i | 0.634873 | + | 1.09963i | ||||
\(536\) | −5.56155 | − | 9.63289i | −0.240222 | − | 0.416078i | ||||
\(537\) | 2.43845 | − | 4.22351i | 0.105227 | − | 0.182258i | ||||
\(538\) | −33.3693 | −1.43865 | ||||||||
\(539\) | 6.68466 | − | 11.5782i | 0.287929 | − | 0.498707i | ||||
\(540\) | −0.780776 | + | 1.35234i | −0.0335993 | + | 0.0581956i | ||||
\(541\) | −19.7386 | −0.848630 | −0.424315 | − | 0.905515i | \(-0.639485\pi\) | ||||
−0.424315 | + | 0.905515i | \(0.639485\pi\) | |||||||
\(542\) | −23.3693 | + | 40.4768i | −1.00380 | + | 1.73863i | ||||
\(543\) | 1.34233 | + | 2.32498i | 0.0576049 | + | 0.0997745i | ||||
\(544\) | −1.90388 | − | 3.29762i | −0.0816283 | − | 0.141384i | ||||
\(545\) | 10.0000 | 0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.93087 | 0.168072 | 0.0840359 | − | 0.996463i | \(-0.473219\pi\) | ||||
0.0840359 | + | 0.996463i | \(0.473219\pi\) | |||||||
\(548\) | −1.21922 | − | 2.11176i | −0.0520827 | − | 0.0902098i | ||||
\(549\) | −1.93845 | − | 3.35749i | −0.0827309 | − | 0.143294i | ||||
\(550\) | −12.0000 | + | 20.7846i | −0.511682 | + | 0.886259i | ||||
\(551\) | −47.6155 | −2.02849 | ||||||||
\(552\) | 2.43845 | − | 4.22351i | 0.103787 | − | 0.179765i | ||||
\(553\) | 1.52699 | − | 2.64482i | 0.0649341 | − | 0.112469i | ||||
\(554\) | 8.30019 | 0.352641 | ||||||||
\(555\) | 13.4654 | − | 23.3228i | 0.571576 | − | 0.989998i | ||||
\(556\) | 3.93087 | + | 6.80847i | 0.166706 | + | 0.288743i | ||||
\(557\) | −21.4654 | − | 37.1792i | −0.909520 | − | 1.57533i | −0.814733 | − | 0.579837i | \(-0.803116\pi\) |
−0.0947869 | − | 0.995498i | \(-0.530217\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 9.36932 | 0.395926 | ||||||||
\(561\) | 1.56155 | + | 2.70469i | 0.0659288 | + | 0.114192i | ||||
\(562\) | 13.9039 | + | 24.0822i | 0.586500 | + | 1.01585i | ||||
\(563\) | 11.6847 | − | 20.2384i | 0.492450 | − | 0.852948i | −0.507513 | − | 0.861644i | \(-0.669435\pi\) |
0.999962 | + | 0.00869657i | \(0.00276824\pi\) | |||||||
\(564\) | −3.61553 | −0.152241 | ||||||||
\(565\) | −10.3423 | + | 17.9134i | −0.435105 | + | 0.753624i | ||||
\(566\) | 10.6847 | − | 18.5064i | 0.449110 | − | 0.777881i | ||||
\(567\) | −0.561553 | −0.0235830 | ||||||||
\(568\) | −17.0691 | + | 29.5646i | −0.716205 | + | 1.24050i | ||||
\(569\) | 4.36932 | + | 7.56788i | 0.183171 | + | 0.317262i | 0.942959 | − | 0.332910i | \(-0.108030\pi\) |
−0.759787 | + | 0.650171i | \(0.774697\pi\) | |||||||
\(570\) | 19.8078 | + | 34.3081i | 0.829656 | + | 1.43701i | ||||
\(571\) | −5.36932 | −0.224699 | −0.112349 | − | 0.993669i | \(-0.535838\pi\) | ||||
−0.112349 | + | 0.993669i | \(0.535838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.12311 | −0.381123 | ||||||||
\(574\) | 0.684658 | + | 1.18586i | 0.0285771 | + | 0.0494970i | ||||
\(575\) | −7.68466 | − | 13.3102i | −0.320472 | − | 0.555074i | ||||
\(576\) | −2.78078 | + | 4.81645i | −0.115866 | + | 0.200685i | ||||
\(577\) | 17.3153 | 0.720847 | 0.360424 | − | 0.932789i | \(-0.382632\pi\) | ||||
0.360424 | + | 0.932789i | \(0.382632\pi\) | |||||||
\(578\) | 11.3693 | − | 19.6922i | 0.472901 | − | 0.819089i | ||||
\(579\) | −6.74621 | + | 11.6848i | −0.280363 | + | 0.485603i | ||||
\(580\) | 10.4384 | 0.433433 | ||||||||
\(581\) | 0.246211 | − | 0.426450i | 0.0102146 | − | 0.0176921i | ||||
\(582\) | −6.68466 | − | 11.5782i | −0.277088 | − | 0.479931i | ||||
\(583\) | 0.684658 | + | 1.18586i | 0.0283557 | + | 0.0491134i | ||||
\(584\) | −24.6847 | −1.02146 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.9157 | −1.31843 | ||||||||
\(587\) | 19.6847 | + | 34.0948i | 0.812473 | + | 1.40724i | 0.911128 | + | 0.412123i | \(0.135212\pi\) |
−0.0986556 | + | 0.995122i | \(0.531454\pi\) | |||||||
\(588\) | 1.46543 | + | 2.53821i | 0.0604335 | + | 0.104674i | ||||
\(589\) | −9.12311 | + | 15.8017i | −0.375911 | + | 0.651097i | ||||
\(590\) | 16.0000 | 0.658710 | ||||||||
\(591\) | 6.68466 | − | 11.5782i | 0.274970 | − | 0.476262i | ||||
\(592\) | −17.7116 | + | 30.6775i | −0.727944 | + | 1.26084i | ||||
\(593\) | 17.4233 | 0.715489 | 0.357744 | − | 0.933820i | \(-0.383546\pi\) | ||||
0.357744 | + | 0.933820i | \(0.383546\pi\) | |||||||
\(594\) | −1.56155 | + | 2.70469i | −0.0640713 | + | 0.110975i | ||||
\(595\) | −1.56155 | − | 2.70469i | −0.0640174 | − | 0.110881i | ||||
\(596\) | −0.534565 | − | 0.925894i | −0.0218966 | − | 0.0379261i | ||||
\(597\) | 22.1771 | 0.907648 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.6155 | −1.70036 | −0.850182 | − | 0.526489i | \(-0.823508\pi\) | ||||
−0.850182 | + | 0.526489i | \(0.823508\pi\) | |||||||
\(600\) | 9.36932 | + | 16.2281i | 0.382501 | + | 0.662511i | ||||
\(601\) | 3.53457 | + | 6.12205i | 0.144178 | + | 0.249723i | 0.929066 | − | 0.369914i | \(-0.120613\pi\) |
−0.784888 | + | 0.619638i | \(0.787280\pi\) | |||||||
\(602\) | 2.00000 | − | 3.46410i | 0.0815139 | − | 0.141186i | ||||
\(603\) | −4.56155 | −0.185761 | ||||||||
\(604\) | −2.05398 | + | 3.55759i | −0.0835751 | + | 0.144756i | ||||
\(605\) | 12.4654 | − | 21.5908i | 0.506792 | − | 0.877789i | ||||
\(606\) | −11.8078 | −0.479658 | ||||||||
\(607\) | 8.00000 | − | 13.8564i | 0.324710 | − | 0.562414i | −0.656744 | − | 0.754114i | \(-0.728067\pi\) |
0.981454 | + | 0.191700i | \(0.0614000\pi\) | |||||||
\(608\) | −8.68466 | − | 15.0423i | −0.352209 | − | 0.610045i | ||||
\(609\) | 1.87689 | + | 3.25088i | 0.0760556 | + | 0.131732i | ||||
\(610\) | 21.5616 | 0.873002 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.684658 | −0.0276757 | ||||||||
\(613\) | −17.4309 | − | 30.1912i | −0.704026 | − | 1.21941i | −0.967042 | − | 0.254618i | \(-0.918050\pi\) |
0.263016 | − | 0.964792i | \(-0.415283\pi\) | |||||||
\(614\) | 24.0540 | + | 41.6627i | 0.970739 | + | 1.68137i | ||||
\(615\) | −2.78078 | + | 4.81645i | −0.112132 | + | 0.194218i | ||||
\(616\) | 2.73863 | 0.110343 | ||||||||
\(617\) | 4.90388 | − | 8.49377i | 0.197423 | − | 0.341946i | −0.750269 | − | 0.661132i | \(-0.770076\pi\) |
0.947692 | + | 0.319186i | \(0.103409\pi\) | |||||||
\(618\) | 2.68466 | − | 4.64996i | 0.107993 | − | 0.187049i | ||||
\(619\) | −29.3002 | −1.17767 | −0.588837 | − | 0.808252i | \(-0.700414\pi\) | ||||
−0.588837 | + | 0.808252i | \(0.700414\pi\) | |||||||
\(620\) | 2.00000 | − | 3.46410i | 0.0803219 | − | 0.139122i | ||||
\(621\) | −1.00000 | − | 1.73205i | −0.0401286 | − | 0.0695048i | ||||
\(622\) | 14.9309 | + | 25.8610i | 0.598673 | + | 1.03693i | ||||
\(623\) | 2.73863 | 0.109721 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | 10.6847 | + | 18.5064i | 0.427045 | + | 0.739663i | ||||
\(627\) | 7.12311 | + | 12.3376i | 0.284469 | + | 0.492716i | ||||
\(628\) | −4.46543 | + | 7.73436i | −0.178190 | + | 0.308635i | ||||
\(629\) | 11.8078 | 0.470806 | ||||||||
\(630\) | 1.56155 | − | 2.70469i | 0.0622138 | − | 0.107757i | ||||
\(631\) | −9.28078 | + | 16.0748i | −0.369462 | + | 0.639927i | −0.989481 | − | 0.144660i | \(-0.953791\pi\) |
0.620020 | + | 0.784586i | \(0.287125\pi\) | |||||||
\(632\) | −13.2614 | −0.527509 | ||||||||
\(633\) | −9.84233 | + | 17.0474i | −0.391197 | + | 0.677574i | ||||
\(634\) | 10.9730 | + | 19.0058i | 0.435794 | + | 0.754817i | ||||
\(635\) | −9.68466 | − | 16.7743i | −0.384324 | − | 0.665669i | ||||
\(636\) | −0.300187 | −0.0119032 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.8769 | 0.826524 | ||||||||
\(639\) | 7.00000 | + | 12.1244i | 0.276916 | + | 0.479632i | ||||
\(640\) | −24.1501 | − | 41.8292i | −0.954616 | − | 1.65344i | ||||
\(641\) | 9.58854 | − | 16.6078i | 0.378725 | − | 0.655970i | −0.612152 | − | 0.790740i | \(-0.709696\pi\) |
0.990877 | + | 0.134770i | \(0.0430294\pi\) | |||||||
\(642\) | −12.8769 | −0.508210 | ||||||||
\(643\) | −15.7732 | + | 27.3200i | −0.622034 | + | 1.07739i | 0.367072 | + | 0.930192i | \(0.380360\pi\) |
−0.989106 | + | 0.147202i | \(0.952973\pi\) | |||||||
\(644\) | 0.246211 | − | 0.426450i | 0.00970208 | − | 0.0168045i | ||||
\(645\) | 16.2462 | 0.639694 | ||||||||
\(646\) | −8.68466 | + | 15.0423i | −0.341693 | + | 0.591830i | ||||
\(647\) | 3.19224 | + | 5.52911i | 0.125500 | + | 0.217372i | 0.921928 | − | 0.387361i | \(-0.126613\pi\) |
−0.796428 | + | 0.604733i | \(0.793280\pi\) | |||||||
\(648\) | 1.21922 | + | 2.11176i | 0.0478956 | + | 0.0829577i | ||||
\(649\) | 5.75379 | 0.225856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.43845 | 0.0563772 | ||||||||
\(652\) | −1.05398 | − | 1.82554i | −0.0412769 | − | 0.0714936i | ||||
\(653\) | −11.5616 | − | 20.0252i | −0.452439 | − | 0.783647i | 0.546098 | − | 0.837721i | \(-0.316112\pi\) |
−0.998537 | + | 0.0540745i | \(0.982779\pi\) | |||||||
\(654\) | −2.19224 | + | 3.79706i | −0.0857232 | + | 0.148477i | ||||
\(655\) | 26.2462 | 1.02552 | ||||||||
\(656\) | 3.65767 | − | 6.33527i | 0.142808 | − | 0.247351i | ||||
\(657\) | −5.06155 | + | 8.76687i | −0.197470 | + | 0.342028i | ||||
\(658\) | 7.23106 | 0.281896 | ||||||||
\(659\) | 1.12311 | − | 1.94528i | 0.0437500 | − | 0.0757772i | −0.843321 | − | 0.537410i | \(-0.819403\pi\) |
0.887071 | + | 0.461633i | \(0.152736\pi\) | |||||||
\(660\) | −1.56155 | − | 2.70469i | −0.0607834 | − | 0.105280i | ||||
\(661\) | 2.81534 | + | 4.87631i | 0.109504 | + | 0.189667i | 0.915569 | − | 0.402160i | \(-0.131740\pi\) |
−0.806065 | + | 0.591827i | \(0.798407\pi\) | |||||||
\(662\) | 4.98485 | 0.193742 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.13826 | −0.0829806 | ||||||||
\(665\) | −7.12311 | − | 12.3376i | −0.276222 | − | 0.478431i | ||||
\(666\) | 5.90388 | + | 10.2258i | 0.228771 | + | 0.396243i | ||||
\(667\) | −6.68466 | + | 11.5782i | −0.258831 | + | 0.448308i | ||||
\(668\) | −4.49242 | −0.173817 | ||||||||
\(669\) | 4.00000 | − | 6.92820i | 0.154649 | − | 0.267860i | ||||
\(670\) | 12.6847 | − | 21.9705i | 0.490051 | − | 0.848793i | ||||
\(671\) | 7.75379 | 0.299332 | ||||||||
\(672\) | −0.684658 | + | 1.18586i | −0.0264113 | + | 0.0457457i | ||||
\(673\) | 11.6231 | + | 20.1318i | 0.448038 | + | 0.776024i | 0.998258 | − | 0.0589952i | \(-0.0187897\pi\) |
−0.550220 | + | 0.835019i | \(0.685456\pi\) | |||||||
\(674\) | 4.78078 | + | 8.28055i | 0.184149 | + | 0.318955i | ||||
\(675\) | 7.68466 | 0.295783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.6155 | −0.600153 | −0.300077 | − | 0.953915i | \(-0.597012\pi\) | ||||
−0.300077 | + | 0.953915i | \(0.597012\pi\) | |||||||
\(678\) | −4.53457 | − | 7.85410i | −0.174149 | − | 0.301635i | ||||
\(679\) | 2.40388 | + | 4.16365i | 0.0922525 | + | 0.159786i | ||||
\(680\) | −6.78078 | + | 11.7446i | −0.260031 | + | 0.450387i | ||||
\(681\) | −7.12311 | −0.272958 | ||||||||
\(682\) | 4.00000 | − | 6.92820i | 0.153168 | − | 0.265295i | ||||
\(683\) | −19.0540 | + | 33.0025i | −0.729080 | + | 1.26280i | 0.228192 | + | 0.973616i | \(0.426719\pi\) |
−0.957272 | + | 0.289188i | \(0.906615\pi\) | |||||||
\(684\) | −3.12311 | −0.119415 | ||||||||
\(685\) | −9.90388 | + | 17.1540i | −0.378408 | + | 0.655422i | ||||
\(686\) | −6.00000 | − | 10.3923i | −0.229081 | − | 0.396780i | ||||
\(687\) | −8.12311 | − | 14.0696i | −0.309916 | − | 0.536790i | ||||
\(688\) | −21.3693 | −0.814698 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 11.1231 | 0.423449 | ||||||||
\(691\) | −25.6501 | − | 44.4273i | −0.975776 | − | 1.69009i | −0.677352 | − | 0.735659i | \(-0.736872\pi\) |
−0.298424 | − | 0.954433i | \(-0.596461\pi\) | |||||||
\(692\) | −4.43845 | − | 7.68762i | −0.168724 | − | 0.292239i | ||||
\(693\) | 0.561553 | − | 0.972638i | 0.0213316 | − | 0.0369475i | ||||
\(694\) | 43.1231 | 1.63693 | ||||||||
\(695\) | 31.9309 | − | 55.3059i | 1.21121 | − | 2.09787i | ||||
\(696\) | 8.15009 | − | 14.1164i | 0.308928 | − | 0.535080i | ||||
\(697\) | −2.43845 | −0.0923628 | ||||||||
\(698\) | 5.31534 | − | 9.20644i | 0.201189 | − | 0.348469i | ||||
\(699\) | −13.0000 | − | 22.5167i | −0.491705 | − | 0.851658i | ||||
\(700\) | 0.946025 | + | 1.63856i | 0.0357564 | + | 0.0619319i | ||||
\(701\) | −5.36932 | −0.202796 | −0.101398 | − | 0.994846i | \(-0.532332\pi\) | ||||
−0.101398 | + | 0.994846i | \(0.532332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 53.8617 | 2.03143 | ||||||||
\(704\) | −5.56155 | − | 9.63289i | −0.209609 | − | 0.363053i | ||||
\(705\) | 14.6847 | + | 25.4346i | 0.553056 | + | 0.957921i | ||||
\(706\) | 4.15009 | − | 7.18817i | 0.156191 | − | 0.270530i | ||||
\(707\) | 4.24621 | 0.159695 | ||||||||
\(708\) | −0.630683 | + | 1.09238i | −0.0237025 | + | 0.0410540i | ||||
\(709\) | −3.74621 | + | 6.48863i | −0.140692 | + | 0.243686i | −0.927757 | − | 0.373184i | \(-0.878266\pi\) |
0.787065 | + | 0.616869i | \(0.211599\pi\) | |||||||
\(710\) | −77.8617 | −2.92210 | ||||||||
\(711\) | −2.71922 | + | 4.70983i | −0.101979 | + | 0.176633i | ||||
\(712\) | −5.94602 | − | 10.2988i | −0.222837 | − | 0.385964i | ||||
\(713\) | 2.56155 | + | 4.43674i | 0.0959309 | + | 0.166157i | ||||
\(714\) | 1.36932 | 0.0512454 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.13826 | −0.0799106 | ||||||||
\(717\) | −12.6847 | − | 21.9705i | −0.473717 | − | 0.820502i | ||||
\(718\) | −7.31534 | − | 12.6705i | −0.273006 | − | 0.472860i | ||||
\(719\) | 11.6847 | − | 20.2384i | 0.435764 | − | 0.754766i | −0.561593 | − | 0.827413i | \(-0.689811\pi\) |
0.997358 | + | 0.0726475i | \(0.0231448\pi\) | |||||||
\(720\) | −16.6847 | −0.621801 | ||||||||
\(721\) | −0.965435 | + | 1.67218i | −0.0359547 | + | 0.0622753i | ||||
\(722\) | −24.7808 | + | 42.9216i | −0.922245 | + | 1.59738i | ||||
\(723\) | 17.8078 | 0.662278 | ||||||||
\(724\) | 0.588540 | − | 1.01938i | 0.0218729 | − | 0.0378850i | ||||
\(725\) | −25.6847 | − | 44.4871i | −0.953904 | − | 1.65221i | ||||
\(726\) | 5.46543 | + | 9.46641i | 0.202841 | + | 0.351331i | ||||
\(727\) | −38.6695 | −1.43417 | −0.717086 | − | 0.696984i | \(-0.754525\pi\) | ||||
−0.717086 | + | 0.696984i | \(0.754525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −28.1501 | − | 48.7574i | −1.04188 | − | 1.80459i | ||||
\(731\) | 3.56155 | + | 6.16879i | 0.131729 | + | 0.228161i | ||||
\(732\) | −0.849907 | + | 1.47208i | −0.0314135 | + | 0.0544097i | ||||
\(733\) | −20.5076 | −0.757465 | −0.378732 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378732 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(734\) | 13.3153 | − | 23.0628i | 0.491478 | − | 0.851265i | ||||
\(735\) | 11.9039 | − | 20.6181i | 0.439081 | − | 0.760511i | ||||
\(736\) | −4.87689 | −0.179765 | ||||||||
\(737\) | 4.56155 | − | 7.90084i | 0.168027 | − | 0.291031i | ||||
\(738\) | −1.21922 | − | 2.11176i | −0.0448802 | − | 0.0777349i | ||||
\(739\) | 5.12311 | + | 8.87348i | 0.188456 | + | 0.326416i | 0.944736 | − | 0.327833i | \(-0.106318\pi\) |
−0.756279 | + | 0.654249i | \(0.772985\pi\) | |||||||
\(740\) | −11.8078 | −0.434062 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.600373 | 0.0220404 | ||||||||
\(743\) | −6.31534 | − | 10.9385i | −0.231687 | − | 0.401294i | 0.726617 | − | 0.687042i | \(-0.241091\pi\) |
−0.958305 | + | 0.285748i | \(0.907758\pi\) | |||||||
\(744\) | −3.12311 | − | 5.40938i | −0.114499 | − | 0.198317i | ||||
\(745\) | −4.34233 | + | 7.52113i | −0.159091 | + | 0.275553i | ||||
\(746\) | 44.3002 | 1.62195 | ||||||||
\(747\) | −0.438447 | + | 0.759413i | −0.0160419 | + | 0.0277855i | ||||
\(748\) | 0.684658 | − | 1.18586i | 0.0250336 | − | 0.0433595i | ||||
\(749\) | 4.63068 | 0.169201 | ||||||||
\(750\) | −7.46543 | + | 12.9305i | −0.272599 | + | 0.472156i | ||||
\(751\) | −22.0540 | − | 38.1986i | −0.804761 | − | 1.39389i | −0.916452 | − | 0.400144i | \(-0.868960\pi\) |
0.111691 | − | 0.993743i | \(-0.464373\pi\) | |||||||
\(752\) | −19.3153 | − | 33.4552i | −0.704358 | − | 1.21998i | ||||
\(753\) | 18.7386 | 0.682874 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.3693 | 1.21443 | ||||||||
\(756\) | 0.123106 | + | 0.213225i | 0.00447731 | + | 0.00775493i | ||||
\(757\) | −15.0000 | − | 25.9808i | −0.545184 | − | 0.944287i | −0.998595 | − | 0.0529853i | \(-0.983126\pi\) |
0.453411 | − | 0.891302i | \(-0.350207\pi\) | |||||||
\(758\) | 18.4924 | − | 32.0298i | 0.671675 | − | 1.16338i | ||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | −30.9309 | + | 53.5738i | −1.12198 | + | 1.94333i | ||||
\(761\) | 4.68466 | − | 8.11407i | 0.169819 | − | 0.294135i | −0.768537 | − | 0.639805i | \(-0.779015\pi\) |
0.938356 | + | 0.345670i | \(0.112348\pi\) | |||||||
\(762\) | 8.49242 | 0.307648 | ||||||||
\(763\) | 0.788354 | − | 1.36547i | 0.0285403 | − | 0.0494333i | ||||
\(764\) | 2.00000 | + | 3.46410i | 0.0723575 | + | 0.125327i | ||||
\(765\) | 2.78078 | + | 4.81645i | 0.100539 | + | 0.174139i | ||||
\(766\) | 35.5076 | 1.28294 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 10.0540 | 0.362792 | ||||||||
\(769\) | −9.00000 | − | 15.5885i | −0.324548 | − | 0.562134i | 0.656873 | − | 0.754002i | \(-0.271879\pi\) |
−0.981421 | + | 0.191867i | \(0.938546\pi\) | |||||||
\(770\) | 3.12311 | + | 5.40938i | 0.112549 | + | 0.194940i | ||||
\(771\) | −14.5885 | + | 25.2681i | −0.525393 | + | 0.910008i | ||||
\(772\) | 5.91571 | 0.212911 | ||||||||
\(773\) | −12.1231 | + | 20.9978i | −0.436038 | + | 0.755240i | −0.997380 | − | 0.0723444i | \(-0.976952\pi\) |
0.561342 | + | 0.827584i | \(0.310285\pi\) | |||||||
\(774\) | −3.56155 | + | 6.16879i | −0.128017 | + | 0.221733i | ||||
\(775\) | −19.6847 | −0.707094 | ||||||||
\(776\) | 10.4384 | − | 18.0799i | 0.374718 | − | 0.649031i | ||||
\(777\) | −2.12311 | − | 3.67733i | −0.0761660 | − | 0.131923i | ||||
\(778\) | −26.5885 | − | 46.0527i | −0.953245 | − | 1.65107i | ||||
\(779\) | −11.1231 | −0.398527 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0000 | −1.00192 | ||||||||
\(782\) | 2.43845 | + | 4.22351i | 0.0871987 | + | 0.151033i | ||||
\(783\) | −3.34233 | − | 5.78908i | −0.119445 | − | 0.206885i | ||||
\(784\) | −15.6577 | + | 27.1199i | −0.559203 | + | 0.968567i | ||||
\(785\) | 72.5464 | 2.58929 | ||||||||
\(786\) | −5.75379 | + | 9.96585i | −0.205231 | + | 0.355470i | ||||
\(787\) | 22.0885 | − | 38.2585i | 0.787371 | − | 1.36377i | −0.140201 | − | 0.990123i | \(-0.544775\pi\) |
0.927572 | − | 0.373644i | \(-0.121892\pi\) | |||||||
\(788\) | −5.86174 | −0.208816 | ||||||||
\(789\) | −4.68466 | + | 8.11407i | −0.166778 | + | 0.288868i | ||||
\(790\) | −15.1231 | − | 26.1940i | −0.538056 | − | 0.931940i | ||||
\(791\) | 1.63068 | + | 2.82443i | 0.0579804 | + | 0.100425i | ||||
\(792\) | −4.87689 | −0.173293 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −39.1231 | −1.38843 | ||||||||
\(795\) | 1.21922 | + | 2.11176i | 0.0432414 | + | 0.0748963i | ||||
\(796\) | −4.86174 | − | 8.42078i | −0.172320 | − | 0.298467i | ||||
\(797\) | 0.192236 | − | 0.332962i | 0.00680935 | − | 0.0117941i | −0.862601 | − | 0.505885i | \(-0.831166\pi\) |
0.869410 | + | 0.494091i | \(0.164499\pi\) | |||||||
\(798\) | 6.24621 | 0.221113 | ||||||||
\(799\) | −6.43845 | + | 11.1517i | −0.227776 | + | 0.394519i | ||||
\(800\) | 9.36932 | − | 16.2281i | 0.331255 | − | 0.573751i | ||||
\(801\) | −4.87689 | −0.172317 | ||||||||
\(802\) | 11.2732 | − | 19.5258i | 0.398070 | − | 0.689478i | ||||
\(803\) | −10.1231 | − | 17.5337i | −0.357237 | − | 0.618752i | ||||
\(804\) | 1.00000 | + | 1.73205i | 0.0352673 | + | 0.0610847i | ||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.3693 | −0.752236 | ||||||||
\(808\) | −9.21922 | − | 15.9682i | −0.324331 | − | 0.561758i | ||||
\(809\) | 8.15009 | + | 14.1164i | 0.286542 | + | 0.496305i | 0.972982 | − | 0.230881i | \(-0.0741609\pi\) |
−0.686440 | + | 0.727187i | \(0.740828\pi\) | |||||||
\(810\) | −2.78078 | + | 4.81645i | −0.0977065 | + | 0.169233i | ||||
\(811\) | −2.56155 | −0.0899483 | −0.0449741 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449741 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(812\) | 0.822919 | − | 1.42534i | 0.0288788 | − | 0.0500195i | ||||
\(813\) | −14.9654 | + | 25.9209i | −0.524861 | + | 0.909085i | ||||
\(814\) | −23.6155 | −0.827724 | ||||||||
\(815\) | −8.56155 | + | 14.8290i | −0.299898 | + | 0.519439i | ||||
\(816\) | −3.65767 | − | 6.33527i | −0.128044 | − | 0.221779i | ||||
\(817\) | 16.2462 | + | 28.1393i | 0.568383 | + | 0.984468i | ||||
\(818\) | −9.94602 | −0.347755 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.43845 | 0.0851543 | ||||||||
\(821\) | 3.24621 | + | 5.62260i | 0.113294 | + | 0.196230i | 0.917096 | − | 0.398666i | \(-0.130527\pi\) |
−0.803803 | + | 0.594896i | \(0.797193\pi\) | |||||||
\(822\) | −4.34233 | − | 7.52113i | −0.151456 | − | 0.262330i | ||||
\(823\) | −4.00000 | + | 6.92820i | −0.139431 | + | 0.241502i | −0.927281 | − | 0.374365i | \(-0.877861\pi\) |
0.787850 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(824\) | 8.38447 | 0.292087 | ||||||||
\(825\) | −7.68466 | + | 13.3102i | −0.267545 | + | 0.463402i | ||||
\(826\) | 1.26137 | − | 2.18475i | 0.0438885 | − | 0.0760172i | ||||
\(827\) | 14.7386 | 0.512513 | 0.256256 | − | 0.966609i | \(-0.417511\pi\) | ||||
0.256256 | + | 0.966609i | \(0.417511\pi\) | |||||||
\(828\) | −0.438447 | + | 0.759413i | −0.0152371 | + | 0.0263914i | ||||
\(829\) | −6.74621 | − | 11.6848i | −0.234306 | − | 0.405829i | 0.724765 | − | 0.688996i | \(-0.241948\pi\) |
−0.959071 | + | 0.283167i | \(0.908615\pi\) | |||||||
\(830\) | −2.43845 | − | 4.22351i | −0.0846397 | − | 0.146600i | ||||
\(831\) | 5.31534 | 0.184387 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.4384 | 0.361671 | ||||||||
\(834\) | 14.0000 | + | 24.2487i | 0.484780 | + | 0.839664i | ||||
\(835\) | 18.2462 | + | 31.6034i | 0.631436 | + | 1.09368i | ||||
\(836\) | 3.12311 | − | 5.40938i | 0.108015 | − | 0.187087i | ||||
\(837\) | −2.56155 | −0.0885402 | ||||||||
\(838\) | 26.7386 | − | 46.3127i | 0.923671 | − | 1.59984i | ||||
\(839\) | 10.8078 | − | 18.7196i | 0.373125 | − | 0.646272i | −0.616919 | − | 0.787027i | \(-0.711619\pi\) |
0.990045 | + | 0.140754i | \(0.0449528\pi\) | |||||||
\(840\) | 4.87689 | 0.168269 | ||||||||
\(841\) | −7.84233 | + | 13.5833i | −0.270425 | + | 0.468390i | ||||
\(842\) | 24.3963 | + | 42.2556i | 0.840752 | + | 1.45623i | ||||
\(843\) | 8.90388 | + | 15.4220i | 0.306666 | + | 0.531161i | ||||
\(844\) | 8.63068 | 0.297080 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.8769 | −0.442717 | ||||||||
\(847\) | −1.96543 | − | 3.40423i | −0.0675331 | − | 0.116971i | ||||
\(848\) | −1.60370 | − | 2.77768i | −0.0550711 | − | 0.0953860i | ||||
\(849\) | 6.84233 | − | 11.8513i | 0.234828 | − | 0.406734i | ||||
\(850\) | −18.7386 | −0.642730 | ||||||||
\(851\) | 7.56155 | − | 13.0970i | 0.259207 | − | 0.448959i | ||||
\(852\) | 3.06913 | − | 5.31589i | 0.105147 | − | 0.182119i | ||||
\(853\) | −2.12311 | −0.0726938 | −0.0363469 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363469 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(854\) | 1.69981 | − | 2.94416i | 0.0581664 | − | 0.100747i | ||||
\(855\) | 12.6847 | + | 21.9705i | 0.433806 | + | 0.751374i | ||||
\(856\) | −10.0540 | − | 17.4140i | −0.343638 | − | 0.595198i | ||||
\(857\) | 35.5616 | 1.21476 | 0.607380 | − | 0.794412i | \(-0.292221\pi\) | ||||
0.607380 | + | 0.794412i | \(0.292221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5616 | 0.838029 | 0.419015 | − | 0.907979i | \(-0.362376\pi\) | ||||
0.419015 | + | 0.907979i | \(0.362376\pi\) | |||||||
\(860\) | −3.56155 | − | 6.16879i | −0.121448 | − | 0.210354i | ||||
\(861\) | 0.438447 | + | 0.759413i | 0.0149422 | + | 0.0258807i | ||||
\(862\) | −8.68466 | + | 15.0423i | −0.295801 | + | 0.512342i | ||||
\(863\) | −30.4924 | −1.03797 | −0.518987 | − | 0.854782i | \(-0.673691\pi\) | ||||
−0.518987 | + | 0.854782i | \(0.673691\pi\) | |||||||
\(864\) | 1.21922 | − | 2.11176i | 0.0414788 | − | 0.0718434i | ||||
\(865\) | −36.0540 | + | 62.4473i | −1.22587 | + | 2.12327i | ||||
\(866\) | 13.6695 | 0.464509 | ||||||||
\(867\) | 7.28078 | − | 12.6107i | 0.247268 | − | 0.428281i | ||||
\(868\) | −0.315342 | − | 0.546188i | −0.0107034 | − | 0.0185388i | ||||
\(869\) | −5.43845 | − | 9.41967i | −0.184487 | − | 0.319540i | ||||
\(870\) | 37.1771 | 1.26042 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.84658 | −0.231855 | ||||||||
\(873\) | −4.28078 | − | 7.41452i | −0.144882 | − | 0.250944i | ||||
\(874\) | 11.1231 | + | 19.2658i | 0.376245 | + | 0.651675i | ||||
\(875\) | 2.68466 | − | 4.64996i | 0.0907580 | − | 0.157198i | ||||
\(876\) | 4.43845 | 0.149961 | ||||||||
\(877\) | 11.7808 | − | 20.4049i | 0.397809 | − | 0.689025i | −0.595647 | − | 0.803247i | \(-0.703104\pi\) |
0.993455 | + | 0.114222i | \(0.0364375\pi\) | |||||||
\(878\) | 10.6847 | − | 18.5064i | 0.360590 | − | 0.624560i | ||||
\(879\) | −20.4384 | −0.689372 | ||||||||
\(880\) | 16.6847 | − | 28.8987i | 0.562440 | − | 0.974174i | ||||
\(881\) | 4.53457 | + | 7.85410i | 0.152773 | + | 0.264611i | 0.932246 | − | 0.361825i | \(-0.117846\pi\) |
−0.779473 | + | 0.626436i | \(0.784513\pi\) | |||||||
\(882\) | 5.21922 | + | 9.03996i | 0.175740 | + | 0.304391i | ||||
\(883\) | 8.80776 | 0.296405 | 0.148202 | − | 0.988957i | \(-0.452651\pi\) | ||||
0.148202 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.2462 | 0.344423 | ||||||||
\(886\) | 27.1231 | + | 46.9786i | 0.911219 | + | 1.57828i | ||||
\(887\) | −12.3153 | − | 21.3308i | −0.413509 | − | 0.716218i | 0.581762 | − | 0.813359i | \(-0.302364\pi\) |
−0.995271 | + | 0.0971410i | \(0.969030\pi\) | |||||||
\(888\) | −9.21922 | + | 15.9682i | −0.309377 | + | 0.535856i | ||||
\(889\) | −3.05398 | −0.102427 | ||||||||
\(890\) | 13.5616 | − | 23.4893i | 0.454584 | − | 0.787363i | ||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | −3.50758 | −0.117442 | ||||||||
\(893\) | −29.3693 | + | 50.8691i | −0.982807 | + | 1.70227i | ||||
\(894\) | −1.90388 | − | 3.29762i | −0.0636753 | − | 0.110289i | ||||
\(895\) | 8.68466 | + | 15.0423i | 0.290296 | + | 0.502808i | ||||
\(896\) | −7.61553 | −0.254417 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.8769 | 0.429708 | ||||||||
\(899\) | 8.56155 | + | 14.8290i | 0.285544 | + | 0.494576i | ||||
\(900\) | −1.68466 | − | 2.91791i | −0.0561553 | − | 0.0972638i | ||||
\(901\) | −0.534565 | + | 0.925894i | −0.0178089 | + | 0.0308460i | ||||
\(902\) | 4.87689 | 0.162383 | ||||||||
\(903\) | 1.28078 | − | 2.21837i | 0.0426216 | − | 0.0738227i | ||||
\(904\) | 7.08096 | − | 12.2646i | 0.235509 | − | 0.407914i | ||||
\(905\) | −9.56155 | −0.317837 | ||||||||
\(906\) | −7.31534 | + | 12.6705i | −0.243036 | + | 0.420951i | ||||
\(907\) | −14.0000 | − | 24.2487i | −0.464862 | − | 0.805165i | 0.534333 | − | 0.845274i | \(-0.320563\pi\) |
−0.999195 | + | 0.0401089i | \(0.987230\pi\) | |||||||
\(908\) | 1.56155 | + | 2.70469i | 0.0518220 | + | 0.0897583i | ||||
\(909\) | −7.56155 | −0.250801 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.7386 | 1.28347 | 0.641734 | − | 0.766927i | \(-0.278215\pi\) | ||||
0.641734 | + | 0.766927i | \(0.278215\pi\) | |||||||
\(912\) | −16.6847 | − | 28.8987i | −0.552484 | − | 0.956931i | ||||
\(913\) | −0.876894 | − | 1.51883i | −0.0290210 | − | 0.0502658i | ||||
\(914\) | 9.84991 | − | 17.0605i | 0.325806 | − | 0.564312i | ||||
\(915\) | 13.8078 | 0.456471 | ||||||||
\(916\) | −3.56155 | + | 6.16879i | −0.117677 | + | 0.203823i | ||||
\(917\) | 2.06913 | − | 3.58384i | 0.0683287 | − | 0.118349i | ||||
\(918\) | −2.43845 | −0.0804807 | ||||||||
\(919\) | −5.75379 | + | 9.96585i | −0.189800 | + | 0.328743i | −0.945183 | − | 0.326540i | \(-0.894117\pi\) |
0.755383 | + | 0.655283i | \(0.227451\pi\) | |||||||
\(920\) | 8.68466 | + | 15.0423i | 0.286325 | + | 0.495929i | ||||
\(921\) | 15.4039 | + | 26.6803i | 0.507575 | + | 0.879146i | ||||
\(922\) | 25.2850 | 0.832718 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.492423 | −0.0161995 | ||||||||
\(925\) | 29.0540 | + | 50.3230i | 0.955289 | + | 1.65461i | ||||
\(926\) | −11.1771 | − | 19.3593i | −0.367302 | − | 0.636185i | ||||
\(927\) | 1.71922 | − | 2.97778i | 0.0564667 | − | 0.0978032i | ||||
\(928\) | −16.3002 | −0.535080 | ||||||||
\(929\) | −3.90388 | + | 6.76172i | −0.128082 | + | 0.221845i | −0.922934 | − | 0.384959i | \(-0.874215\pi\) |
0.794851 | + | 0.606804i | \(0.207549\pi\) | |||||||
\(930\) | 7.12311 | − | 12.3376i | 0.233576 | − | 0.404565i | ||||
\(931\) | 47.6155 | 1.56054 | ||||||||
\(932\) | −5.69981 | + | 9.87237i | −0.186704 | + | 0.323380i | ||||
\(933\) | 9.56155 | + | 16.5611i | 0.313031 | + | 0.542186i | ||||
\(934\) | 20.3002 | + | 35.1610i | 0.664242 | + | 1.15050i | ||||
\(935\) | −11.1231 | −0.363764 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.56155 | −0.247025 | −0.123513 | − | 0.992343i | \(-0.539416\pi\) | ||||
−0.123513 | + | 0.992343i | \(0.539416\pi\) | |||||||
\(938\) | −2.00000 | − | 3.46410i | −0.0653023 | − | 0.113107i | ||||
\(939\) | 6.84233 | + | 11.8513i | 0.223291 | + | 0.386751i | ||||
\(940\) | 6.43845 | − | 11.1517i | 0.209999 | − | 0.363729i | ||||
\(941\) | −30.4924 | −0.994025 | −0.497012 | − | 0.867744i | \(-0.665570\pi\) | ||||
−0.497012 | + | 0.867744i | \(0.665570\pi\) | |||||||
\(942\) | −15.9039 | + | 27.5463i | −0.518176 | + | 0.897508i | ||||
\(943\) | −1.56155 | + | 2.70469i | −0.0508512 | + | 0.0880768i | ||||
\(944\) | −13.4773 | −0.438648 | ||||||||
\(945\) | 1.00000 | − | 1.73205i | 0.0325300 | − | 0.0563436i | ||||
\(946\) | −7.12311 | − | 12.3376i | −0.231592 | − | 0.401129i | ||||
\(947\) | −19.3693 | − | 33.5486i | −0.629418 | − | 1.09018i | −0.987669 | − | 0.156559i | \(-0.949960\pi\) |
0.358250 | − | 0.933626i | \(-0.383373\pi\) | |||||||
\(948\) | 2.38447 | 0.0774440 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −85.4773 | −2.77325 | ||||||||
\(951\) | 7.02699 | + | 12.1711i | 0.227866 | + | 0.394675i | ||||
\(952\) | 1.06913 | + | 1.85179i | 0.0346507 | + | 0.0600168i | ||||
\(953\) | −15.4924 | + | 26.8337i | −0.501849 | + | 0.869228i | 0.498149 | + | 0.867091i | \(0.334013\pi\) |
−0.999998 | + | 0.00213612i | \(0.999320\pi\) | |||||||
\(954\) | −1.06913 | −0.0346144 | ||||||||
\(955\) | 16.2462 | − | 28.1393i | 0.525715 | − | 0.910565i | ||||
\(956\) | −5.56155 | + | 9.63289i | −0.179873 | + | 0.311550i | ||||
\(957\) | 13.3693 | 0.432169 | ||||||||
\(958\) | 8.00000 | − | 13.8564i | 0.258468 | − | 0.447680i | ||||
\(959\) | 1.56155 | + | 2.70469i | 0.0504252 | + | 0.0873390i | ||||
\(960\) | −9.90388 | − | 17.1540i | −0.319646 | − | 0.553644i | ||||
\(961\) | −24.4384 | −0.788337 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.24621 | −0.265730 | ||||||||
\(964\) | −3.90388 | − | 6.76172i | −0.125736 | − | 0.217780i | ||||
\(965\) | −24.0270 | − | 41.6160i | −0.773456 | − | 1.33967i | ||||
\(966\) | 0.876894 | − | 1.51883i | 0.0282136 | − | 0.0488674i | ||||
\(967\) | 0.876894 | 0.0281990 | 0.0140995 | − | 0.999901i | \(-0.495512\pi\) | ||||
0.0140995 | + | 0.999901i | \(0.495512\pi\) | |||||||
\(968\) | −8.53457 | + | 14.7823i | −0.274311 | + | 0.475121i | ||||
\(969\) | −5.56155 | + | 9.63289i | −0.178663 | + | 0.309453i | ||||
\(970\) | 47.6155 | 1.52884 | ||||||||
\(971\) | 6.49242 | − | 11.2452i | 0.208352 | − | 0.360876i | −0.742844 | − | 0.669465i | \(-0.766523\pi\) |
0.951195 | + | 0.308589i | \(0.0998568\pi\) | |||||||
\(972\) | −0.219224 | − | 0.379706i | −0.00703160 | − | 0.0121791i | ||||
\(973\) | −5.03457 | − | 8.72012i | −0.161401 | − | 0.279554i | ||||
\(974\) | −11.1231 | −0.356407 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.1619 | −0.581349 | ||||||||
\(977\) | 30.5885 | + | 52.9809i | 0.978614 | + | 1.69501i | 0.667453 | + | 0.744652i | \(0.267385\pi\) |
0.311162 | + | 0.950357i | \(0.399282\pi\) | |||||||
\(978\) | −3.75379 | − | 6.50175i | −0.120033 | − | 0.207903i | ||||
\(979\) | 4.87689 | − | 8.44703i | 0.155866 | − | 0.269968i | ||||
\(980\) | −10.4384 | −0.333444 | ||||||||
\(981\) | −1.40388 | + | 2.43160i | −0.0448225 | + | 0.0776349i | ||||
\(982\) | 28.3002 | − | 49.0174i | 0.903095 | − | 1.56421i | ||||
\(983\) | −13.6155 | −0.434268 | −0.217134 | − | 0.976142i | \(-0.569671\pi\) | ||||
−0.217134 | + | 0.976142i | \(0.569671\pi\) | |||||||
\(984\) | 1.90388 | − | 3.29762i | 0.0606935 | − | 0.105124i | ||||
\(985\) | 23.8078 | + | 41.2363i | 0.758578 | + | 1.31390i | ||||
\(986\) | 8.15009 | + | 14.1164i | 0.259552 | + | 0.449557i | ||||
\(987\) | 4.63068 | 0.147396 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.12311 | 0.290098 | ||||||||
\(990\) | −5.56155 | − | 9.63289i | −0.176758 | − | 0.306153i | ||||
\(991\) | 25.1771 | + | 43.6080i | 0.799776 | + | 1.38525i | 0.919762 | + | 0.392478i | \(0.128382\pi\) |
−0.119985 | + | 0.992776i | \(0.538285\pi\) | |||||||
\(992\) | −3.12311 | + | 5.40938i | −0.0991587 | + | 0.171748i | ||||
\(993\) | 3.19224 | 0.101303 | ||||||||
\(994\) | −6.13826 | + | 10.6318i | −0.194694 | + | 0.337220i | ||||
\(995\) | −39.4924 | + | 68.4029i | −1.25199 | + | 2.16852i | ||||
\(996\) | 0.384472 | 0.0121825 | ||||||||
\(997\) | 10.3078 | − | 17.8536i | 0.326450 | − | 0.565428i | −0.655355 | − | 0.755321i | \(-0.727481\pi\) |
0.981805 | + | 0.189893i | \(0.0608141\pi\) | |||||||
\(998\) | 3.50758 | + | 6.07530i | 0.111030 | + | 0.192310i | ||||
\(999\) | 3.78078 | + | 6.54850i | 0.119618 | + | 0.207185i |
(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 | 507.2.e.g.484.1 | 4 | ||
13.2 | odd | 12 | 507.2.b.d.337.2 | 4 | |||
13.3 | even | 3 | 507.2.a.d.1.2 | 2 | |||
13.4 | even | 6 | 39.2.e.b.22.2 | yes | 4 | ||
13.5 | odd | 4 | 507.2.j.g.361.2 | 8 | |||
13.6 | odd | 12 | 507.2.j.g.316.3 | 8 | |||
13.7 | odd | 12 | 507.2.j.g.316.2 | 8 | |||
13.8 | odd | 4 | 507.2.j.g.361.3 | 8 | |||
13.9 | even | 3 | inner | 507.2.e.g.22.1 | 4 | ||
13.10 | even | 6 | 507.2.a.g.1.1 | 2 | |||
13.11 | odd | 12 | 507.2.b.d.337.3 | 4 | |||
13.12 | even | 2 | 39.2.e.b.16.2 | ✓ | 4 | ||
39.2 | even | 12 | 1521.2.b.h.1351.3 | 4 | |||
39.11 | even | 12 | 1521.2.b.h.1351.2 | 4 | |||
39.17 | odd | 6 | 117.2.g.c.100.1 | 4 | |||
39.23 | odd | 6 | 1521.2.a.g.1.2 | 2 | |||
39.29 | odd | 6 | 1521.2.a.m.1.1 | 2 | |||
39.38 | odd | 2 | 117.2.g.c.55.1 | 4 | |||
52.3 | odd | 6 | 8112.2.a.bo.1.2 | 2 | |||
52.23 | odd | 6 | 8112.2.a.bk.1.1 | 2 | |||
52.43 | odd | 6 | 624.2.q.h.529.1 | 4 | |||
52.51 | odd | 2 | 624.2.q.h.289.1 | 4 | |||
65.4 | even | 6 | 975.2.i.k.451.1 | 4 | |||
65.12 | odd | 4 | 975.2.bb.i.874.2 | 8 | |||
65.17 | odd | 12 | 975.2.bb.i.724.3 | 8 | |||
65.38 | odd | 4 | 975.2.bb.i.874.3 | 8 | |||
65.43 | odd | 12 | 975.2.bb.i.724.2 | 8 | |||
65.64 | even | 2 | 975.2.i.k.601.1 | 4 | |||
156.95 | even | 6 | 1872.2.t.r.1153.2 | 4 | |||
156.155 | even | 2 | 1872.2.t.r.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.2.e.b.16.2 | ✓ | 4 | 13.12 | even | 2 | ||
39.2.e.b.22.2 | yes | 4 | 13.4 | even | 6 | ||
117.2.g.c.55.1 | 4 | 39.38 | odd | 2 | |||
117.2.g.c.100.1 | 4 | 39.17 | odd | 6 | |||
507.2.a.d.1.2 | 2 | 13.3 | even | 3 | |||
507.2.a.g.1.1 | 2 | 13.10 | even | 6 | |||
507.2.b.d.337.2 | 4 | 13.2 | odd | 12 | |||
507.2.b.d.337.3 | 4 | 13.11 | odd | 12 | |||
507.2.e.g.22.1 | 4 | 13.9 | even | 3 | inner | ||
507.2.e.g.484.1 | 4 | 1.1 | even | 1 | trivial | ||
507.2.j.g.316.2 | 8 | 13.7 | odd | 12 | |||
507.2.j.g.316.3 | 8 | 13.6 | odd | 12 | |||
507.2.j.g.361.2 | 8 | 13.5 | odd | 4 | |||
507.2.j.g.361.3 | 8 | 13.8 | odd | 4 | |||
624.2.q.h.289.1 | 4 | 52.51 | odd | 2 | |||
624.2.q.h.529.1 | 4 | 52.43 | odd | 6 | |||
975.2.i.k.451.1 | 4 | 65.4 | even | 6 | |||
975.2.i.k.601.1 | 4 | 65.64 | even | 2 | |||
975.2.bb.i.724.2 | 8 | 65.43 | odd | 12 | |||
975.2.bb.i.724.3 | 8 | 65.17 | odd | 12 | |||
975.2.bb.i.874.2 | 8 | 65.12 | odd | 4 | |||
975.2.bb.i.874.3 | 8 | 65.38 | odd | 4 | |||
1521.2.a.g.1.2 | 2 | 39.23 | odd | 6 | |||
1521.2.a.m.1.1 | 2 | 39.29 | odd | 6 | |||
1521.2.b.h.1351.2 | 4 | 39.11 | even | 12 | |||
1521.2.b.h.1351.3 | 4 | 39.2 | even | 12 | |||
1872.2.t.r.289.2 | 4 | 156.155 | even | 2 | |||
1872.2.t.r.1153.2 | 4 | 156.95 | even | 6 | |||
8112.2.a.bk.1.1 | 2 | 52.23 | odd | 6 | |||
8112.2.a.bo.1.2 | 2 | 52.3 | odd | 6 |