Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(101,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.l (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 651.1 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.651 |
Dual form | 950.2.l.b.251.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.939693 | − | 0.342020i | 0.664463 | − | 0.241845i | ||||
\(3\) | 0.439693 | − | 2.49362i | 0.253857 | − | 1.43969i | −0.545134 | − | 0.838349i | \(-0.683521\pi\) |
0.798991 | − | 0.601344i | \(-0.205368\pi\) | |||||||
\(4\) | 0.766044 | − | 0.642788i | 0.383022 | − | 0.321394i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.439693 | − | 2.49362i | −0.179504 | − | 1.01802i | ||||
\(7\) | −0.326352 | − | 0.565258i | −0.123349 | − | 0.213647i | 0.797737 | − | 0.603005i | \(-0.206030\pi\) |
−0.921087 | + | 0.389358i | \(0.872697\pi\) | |||||||
\(8\) | 0.500000 | − | 0.866025i | 0.176777 | − | 0.306186i | ||||
\(9\) | −3.20574 | − | 1.16679i | −1.06858 | − | 0.388931i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | −1.26604 | − | 2.19285i | −0.365476 | − | 0.633022i | ||||
\(13\) | −0.500000 | − | 2.83564i | −0.138675 | − | 0.786465i | −0.972230 | − | 0.234028i | \(-0.924809\pi\) |
0.833555 | − | 0.552437i | \(-0.186302\pi\) | |||||||
\(14\) | −0.500000 | − | 0.419550i | −0.133631 | − | 0.112129i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.173648 | − | 0.984808i | 0.0434120 | − | 0.246202i | ||||
\(17\) | 0.439693 | − | 0.160035i | 0.106641 | − | 0.0388142i | −0.288149 | − | 0.957586i | \(-0.593040\pi\) |
0.394790 | + | 0.918772i | \(0.370817\pi\) | |||||||
\(18\) | −3.41147 | −0.804092 | ||||||||
\(19\) | −4.07398 | + | 1.55007i | −0.934635 | + | 0.355609i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.55303 | + | 0.565258i | −0.338900 | + | 0.123349i | ||||
\(22\) | 0.173648 | − | 0.984808i | 0.0370219 | − | 0.209962i | ||||
\(23\) | 2.56418 | − | 2.15160i | 0.534668 | − | 0.448640i | −0.335042 | − | 0.942203i | \(-0.608750\pi\) |
0.869710 | + | 0.493564i | \(0.164306\pi\) | |||||||
\(24\) | −1.93969 | − | 1.62760i | −0.395938 | − | 0.332232i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.43969 | − | 2.49362i | −0.282347 | − | 0.489039i | ||||
\(27\) | −0.520945 | + | 0.902302i | −0.100256 | + | 0.173648i | ||||
\(28\) | −0.613341 | − | 0.223238i | −0.115911 | − | 0.0421880i | ||||
\(29\) | −6.41147 | − | 2.33359i | −1.19058 | − | 0.433336i | −0.330653 | − | 0.943752i | \(-0.607269\pi\) |
−0.859927 | + | 0.510416i | \(0.829491\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.03209 | + | 3.51968i | 0.364974 | + | 0.632153i | 0.988772 | − | 0.149432i | \(-0.0477446\pi\) |
−0.623798 | + | 0.781586i | \(0.714411\pi\) | |||||||
\(32\) | −0.173648 | − | 0.984808i | −0.0306970 | − | 0.174091i | ||||
\(33\) | −1.93969 | − | 1.62760i | −0.337657 | − | 0.283328i | ||||
\(34\) | 0.358441 | − | 0.300767i | 0.0614721 | − | 0.0515812i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.20574 | + | 1.16679i | −0.534290 | + | 0.194465i | ||||
\(37\) | 7.63816 | 1.25571 | 0.627853 | − | 0.778332i | \(-0.283934\pi\) | ||||
0.627853 | + | 0.778332i | \(0.283934\pi\) | |||||||
\(38\) | −3.29813 | + | 2.84997i | −0.535028 | + | 0.462326i | ||||
\(39\) | −7.29086 | −1.16747 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.854570 | + | 4.84651i | −0.133461 | + | 0.756898i | 0.842457 | + | 0.538763i | \(0.181108\pi\) |
−0.975919 | + | 0.218134i | \(0.930003\pi\) | |||||||
\(42\) | −1.26604 | + | 1.06234i | −0.195355 | + | 0.163922i | ||||
\(43\) | −2.40760 | − | 2.02022i | −0.367156 | − | 0.308081i | 0.440479 | − | 0.897763i | \(-0.354809\pi\) |
−0.807635 | + | 0.589682i | \(0.799253\pi\) | |||||||
\(44\) | −0.173648 | − | 0.984808i | −0.0261784 | − | 0.148465i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.67365 | − | 2.89884i | 0.246766 | − | 0.427411i | ||||
\(47\) | 6.02481 | + | 2.19285i | 0.878810 | + | 0.319861i | 0.741729 | − | 0.670699i | \(-0.234006\pi\) |
0.137080 | + | 0.990560i | \(0.456228\pi\) | |||||||
\(48\) | −2.37939 | − | 0.866025i | −0.343435 | − | 0.125000i | ||||
\(49\) | 3.28699 | − | 5.69323i | 0.469570 | − | 0.813319i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.205737 | − | 1.16679i | −0.0288090 | − | 0.163384i | ||||
\(52\) | −2.20574 | − | 1.85083i | −0.305881 | − | 0.256664i | ||||
\(53\) | −2.96064 | + | 2.48427i | −0.406675 | + | 0.341241i | −0.823067 | − | 0.567944i | \(-0.807739\pi\) |
0.416392 | + | 0.909185i | \(0.363294\pi\) | |||||||
\(54\) | −0.180922 | + | 1.02606i | −0.0246204 | + | 0.139629i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.652704 | −0.0872212 | ||||||||
\(57\) | 2.07398 | + | 10.8405i | 0.274705 | + | 1.43586i | ||||
\(58\) | −6.82295 | −0.895897 | ||||||||
\(59\) | 5.68479 | − | 2.06910i | 0.740097 | − | 0.269373i | 0.0556645 | − | 0.998450i | \(-0.482272\pi\) |
0.684432 | + | 0.729076i | \(0.260050\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.96064 | + | 3.32337i | −0.507108 | + | 0.425514i | −0.860110 | − | 0.510109i | \(-0.829605\pi\) |
0.353002 | + | 0.935622i | \(0.385161\pi\) | |||||||
\(62\) | 3.11334 | + | 2.61240i | 0.395395 | + | 0.331776i | ||||
\(63\) | 0.386659 | + | 2.19285i | 0.0487145 | + | 0.276274i | ||||
\(64\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.37939 | − | 0.866025i | −0.292882 | − | 0.106600i | ||||
\(67\) | −0.826352 | − | 0.300767i | −0.100955 | − | 0.0367446i | 0.291049 | − | 0.956708i | \(-0.405996\pi\) |
−0.392004 | + | 0.919964i | \(0.628218\pi\) | |||||||
\(68\) | 0.233956 | − | 0.405223i | 0.0283713 | − | 0.0491405i | ||||
\(69\) | −4.23783 | − | 7.34013i | −0.510174 | − | 0.883648i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.35504 | + | 7.84981i | 1.11024 | + | 0.931601i | 0.998071 | − | 0.0620884i | \(-0.0197761\pi\) |
0.112168 | + | 0.993689i | \(0.464221\pi\) | |||||||
\(72\) | −2.61334 | + | 2.19285i | −0.307985 | + | 0.258430i | ||||
\(73\) | −0.0885259 | + | 0.502055i | −0.0103612 | + | 0.0587611i | −0.989550 | − | 0.144190i | \(-0.953942\pi\) |
0.979189 | + | 0.202951i | \(0.0650534\pi\) | |||||||
\(74\) | 7.17752 | − | 2.61240i | 0.834370 | − | 0.303686i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.12449 | + | 3.80612i | −0.243695 | + | 0.436592i | ||||
\(77\) | −0.652704 | −0.0743825 | ||||||||
\(78\) | −6.85117 | + | 2.49362i | −0.775742 | + | 0.282347i | ||||
\(79\) | −1.51367 | + | 8.58445i | −0.170301 | + | 0.965826i | 0.773127 | + | 0.634251i | \(0.218691\pi\) |
−0.943429 | + | 0.331576i | \(0.892420\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.81908 | − | 4.88279i | −0.646564 | − | 0.542532i | ||||
\(82\) | 0.854570 | + | 4.84651i | 0.0943715 | + | 0.535207i | ||||
\(83\) | 8.95471 | + | 15.5100i | 0.982907 | + | 1.70244i | 0.650892 | + | 0.759170i | \(0.274395\pi\) |
0.332015 | + | 0.943274i | \(0.392272\pi\) | |||||||
\(84\) | −0.826352 | + | 1.43128i | −0.0901624 | + | 0.156166i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.95336 | − | 1.07494i | −0.318469 | − | 0.115913i | ||||
\(87\) | −8.63816 | + | 14.9617i | −0.926108 | + | 1.60407i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | −3.06418 | − | 17.3778i | −0.324802 | − | 1.84204i | −0.511061 | − | 0.859544i | \(-0.670748\pi\) |
0.186259 | − | 0.982501i | \(-0.440364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.43969 | + | 1.20805i | −0.150921 | + | 0.126638i | ||||
\(92\) | 0.581252 | − | 3.29644i | 0.0605997 | − | 0.343678i | ||||
\(93\) | 9.67024 | − | 3.51968i | 1.00276 | − | 0.364974i | ||||
\(94\) | 6.41147 | 0.661293 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.53209 | −0.258430 | ||||||||
\(97\) | 13.6284 | − | 4.96032i | 1.38375 | − | 0.503644i | 0.460437 | − | 0.887692i | \(-0.347693\pi\) |
0.923313 | + | 0.384049i | \(0.125471\pi\) | |||||||
\(98\) | 1.14156 | − | 6.47410i | 0.115315 | − | 0.653983i | ||||
\(99\) | −2.61334 | + | 2.19285i | −0.262651 | + | 0.220390i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.59580 | − | 14.7215i | −0.258292 | − | 1.46485i | −0.787480 | − | 0.616341i | \(-0.788614\pi\) |
0.529188 | − | 0.848505i | \(-0.322497\pi\) | |||||||
\(102\) | −0.592396 | − | 1.02606i | −0.0586560 | − | 0.101595i | ||||
\(103\) | −3.61334 | + | 6.25849i | −0.356033 | + | 0.616667i | −0.987294 | − | 0.158903i | \(-0.949204\pi\) |
0.631261 | + | 0.775570i | \(0.282538\pi\) | |||||||
\(104\) | −2.70574 | − | 0.984808i | −0.265319 | − | 0.0965683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.93242 | + | 3.34705i | −0.187693 | + | 0.325094i | ||||
\(107\) | −3.63429 | − | 6.29477i | −0.351340 | − | 0.608538i | 0.635145 | − | 0.772393i | \(-0.280940\pi\) |
−0.986484 | + | 0.163855i | \(0.947607\pi\) | |||||||
\(108\) | 0.180922 | + | 1.02606i | 0.0174092 | + | 0.0987327i | ||||
\(109\) | 6.77584 | + | 5.68561i | 0.649008 | + | 0.544583i | 0.906770 | − | 0.421626i | \(-0.138540\pi\) |
−0.257762 | + | 0.966209i | \(0.582985\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.35844 | − | 19.0467i | 0.318769 | − | 1.80783i | ||||
\(112\) | −0.613341 | + | 0.223238i | −0.0579553 | + | 0.0210940i | ||||
\(113\) | −1.49020 | −0.140186 | −0.0700931 | − | 0.997540i | \(-0.522330\pi\) | ||||
−0.0700931 | + | 0.997540i | \(0.522330\pi\) | |||||||
\(114\) | 5.65657 | + | 9.47740i | 0.529787 | + | 0.887640i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.41147 | + | 2.33359i | −0.595290 | + | 0.216668i | ||||
\(117\) | −1.70574 | + | 9.67372i | −0.157695 | + | 0.894335i | ||||
\(118\) | 4.63429 | − | 3.88863i | 0.426621 | − | 0.357977i | ||||
\(119\) | −0.233956 | − | 0.196312i | −0.0214467 | − | 0.0179959i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | −2.58512 | + | 4.47756i | −0.234046 | + | 0.405380i | ||||
\(123\) | 11.7096 | + | 4.26195i | 1.05582 | + | 0.384287i | ||||
\(124\) | 3.81908 | + | 1.39003i | 0.342963 | + | 0.124828i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.11334 | + | 1.92836i | 0.0991843 | + | 0.171792i | ||||
\(127\) | −3.18392 | − | 18.0569i | −0.282527 | − | 1.60229i | −0.713988 | − | 0.700158i | \(-0.753113\pi\) |
0.431461 | − | 0.902131i | \(-0.357998\pi\) | |||||||
\(128\) | −0.766044 | − | 0.642788i | −0.0677094 | − | 0.0568149i | ||||
\(129\) | −6.09627 | + | 5.11538i | −0.536746 | + | 0.450384i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.72416 | + | 2.44739i | −0.587492 | + | 0.213830i | −0.618626 | − | 0.785686i | \(-0.712310\pi\) |
0.0311339 | + | 0.999515i | \(0.490088\pi\) | |||||||
\(132\) | −2.53209 | −0.220390 | ||||||||
\(133\) | 2.20574 | + | 1.79698i | 0.191262 | + | 0.155818i | ||||
\(134\) | −0.879385 | −0.0759673 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.0812519 | − | 0.460802i | 0.00696729 | − | 0.0395135i | ||||
\(137\) | 12.9855 | − | 10.8961i | 1.10942 | − | 0.930916i | 0.111400 | − | 0.993776i | \(-0.464467\pi\) |
0.998022 | + | 0.0628601i | \(0.0200222\pi\) | |||||||
\(138\) | −6.49273 | − | 5.44804i | −0.552698 | − | 0.463768i | ||||
\(139\) | 2.20321 | + | 12.4950i | 0.186874 | + | 1.05981i | 0.923524 | + | 0.383541i | \(0.125295\pi\) |
−0.736650 | + | 0.676274i | \(0.763594\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.11721 | − | 14.0594i | 0.683592 | − | 1.18402i | ||||
\(142\) | 11.4757 | + | 4.17680i | 0.963015 | + | 0.350509i | ||||
\(143\) | −2.70574 | − | 0.984808i | −0.226265 | − | 0.0823538i | ||||
\(144\) | −1.70574 | + | 2.95442i | −0.142145 | + | 0.246202i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0885259 | + | 0.502055i | 0.00732645 | + | 0.0415504i | ||||
\(147\) | −12.7515 | − | 10.6998i | −1.05173 | − | 0.882503i | ||||
\(148\) | 5.85117 | − | 4.90971i | 0.480963 | − | 0.403576i | ||||
\(149\) | −0.593740 | + | 3.36727i | −0.0486411 | + | 0.275857i | −0.999422 | − | 0.0340079i | \(-0.989173\pi\) |
0.950780 | + | 0.309865i | \(0.100284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.5594 | 1.26621 | 0.633104 | − | 0.774067i | \(-0.281780\pi\) | ||||
0.633104 | + | 0.774067i | \(0.281780\pi\) | |||||||
\(152\) | −0.694593 | + | 4.30320i | −0.0563389 | + | 0.349036i | ||||
\(153\) | −1.59627 | −0.129051 | ||||||||
\(154\) | −0.613341 | + | 0.223238i | −0.0494244 | + | 0.0179890i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.58512 | + | 4.68647i | −0.447168 | + | 0.375218i | ||||
\(157\) | 10.1762 | + | 8.53882i | 0.812147 | + | 0.681472i | 0.951119 | − | 0.308824i | \(-0.0999354\pi\) |
−0.138972 | + | 0.990296i | \(0.544380\pi\) | |||||||
\(158\) | 1.51367 | + | 8.58445i | 0.120421 | + | 0.682942i | ||||
\(159\) | 4.89306 | + | 8.47502i | 0.388045 | + | 0.672113i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.05303 | − | 0.747243i | −0.161802 | − | 0.0588910i | ||||
\(162\) | −7.13816 | − | 2.59808i | −0.560826 | − | 0.204124i | ||||
\(163\) | 2.63563 | − | 4.56504i | 0.206438 | − | 0.357562i | −0.744152 | − | 0.668011i | \(-0.767146\pi\) |
0.950590 | + | 0.310449i | \(0.100479\pi\) | |||||||
\(164\) | 2.46064 | + | 4.26195i | 0.192143 | + | 0.332802i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.7194 | + | 11.5119i | 1.06483 | + | 0.893501i | ||||
\(167\) | −1.66843 | + | 1.39998i | −0.129107 | + | 0.108334i | −0.705055 | − | 0.709153i | \(-0.749078\pi\) |
0.575948 | + | 0.817487i | \(0.304633\pi\) | |||||||
\(168\) | −0.286989 | + | 1.62760i | −0.0221417 | + | 0.125572i | ||||
\(169\) | 4.42514 | − | 1.61062i | 0.340396 | − | 0.123894i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.8687 | − | 0.215615i | 1.13704 | − | 0.0164885i | ||||
\(172\) | −3.14290 | −0.239644 | ||||||||
\(173\) | 6.99912 | − | 2.54747i | 0.532133 | − | 0.193681i | −0.0619572 | − | 0.998079i | \(-0.519734\pi\) |
0.594091 | + | 0.804398i | \(0.297512\pi\) | |||||||
\(174\) | −3.00000 | + | 17.0138i | −0.227429 | + | 1.28982i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.766044 | − | 0.642788i | −0.0577428 | − | 0.0484519i | ||||
\(177\) | −2.65998 | − | 15.0855i | −0.199936 | − | 1.13389i | ||||
\(178\) | −8.82295 | − | 15.2818i | −0.661308 | − | 1.14542i | ||||
\(179\) | −3.17617 | + | 5.50130i | −0.237398 | + | 0.411186i | −0.959967 | − | 0.280113i | \(-0.909628\pi\) |
0.722569 | + | 0.691299i | \(0.242961\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5449 | − | 4.56596i | −0.932454 | − | 0.339385i | −0.169272 | − | 0.985569i | \(-0.554142\pi\) |
−0.763182 | + | 0.646184i | \(0.776364\pi\) | |||||||
\(182\) | −0.939693 | + | 1.62760i | −0.0696547 | + | 0.120645i | ||||
\(183\) | 6.54576 | + | 11.3376i | 0.483876 | + | 0.838099i | ||||
\(184\) | −0.581252 | − | 3.29644i | −0.0428505 | − | 0.243017i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.88326 | − | 6.61484i | 0.578028 | − | 0.485023i | ||||
\(187\) | 0.0812519 | − | 0.460802i | 0.00594173 | − | 0.0336972i | ||||
\(188\) | 6.02481 | − | 2.19285i | 0.439405 | − | 0.159930i | ||||
\(189\) | 0.680045 | 0.0494660 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.17530 | 0.663901 | 0.331951 | − | 0.943297i | \(-0.392293\pi\) | ||||
0.331951 | + | 0.943297i | \(0.392293\pi\) | |||||||
\(192\) | −2.37939 | + | 0.866025i | −0.171717 | + | 0.0625000i | ||||
\(193\) | 2.64022 | − | 14.9734i | 0.190047 | − | 1.07781i | −0.729251 | − | 0.684246i | \(-0.760131\pi\) |
0.919298 | − | 0.393563i | \(-0.128758\pi\) | |||||||
\(194\) | 11.1099 | − | 9.32234i | 0.797647 | − | 0.669305i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.14156 | − | 6.47410i | −0.0815399 | − | 0.462436i | ||||
\(197\) | −8.97906 | − | 15.5522i | −0.639731 | − | 1.10805i | −0.985492 | − | 0.169724i | \(-0.945712\pi\) |
0.345760 | − | 0.938323i | \(-0.387621\pi\) | |||||||
\(198\) | −1.70574 | + | 2.95442i | −0.121221 | + | 0.209962i | ||||
\(199\) | 23.2729 | + | 8.47065i | 1.64977 | + | 0.600468i | 0.988707 | − | 0.149860i | \(-0.0478823\pi\) |
0.661065 | + | 0.750328i | \(0.270105\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.11334 | + | 1.92836i | −0.0785290 | + | 0.136016i | ||||
\(202\) | −7.47431 | − | 12.9459i | −0.525890 | − | 0.910869i | ||||
\(203\) | 0.773318 | + | 4.38571i | 0.0542763 | + | 0.307816i | ||||
\(204\) | −0.907604 | − | 0.761570i | −0.0635450 | − | 0.0533206i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.25490 | + | 7.11689i | −0.0874330 | + | 0.495857i | ||||
\(207\) | −10.7306 | + | 3.90560i | −0.745825 | + | 0.271458i | ||||
\(208\) | −2.87939 | −0.199649 | ||||||||
\(209\) | −0.694593 | + | 4.30320i | −0.0480460 | + | 0.297659i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0522 | + | 3.65869i | −0.692019 | + | 0.251874i | −0.663999 | − | 0.747733i | \(-0.731142\pi\) |
−0.0280195 | + | 0.999607i | \(0.508920\pi\) | |||||||
\(212\) | −0.671122 | + | 3.80612i | −0.0460928 | + | 0.261406i | ||||
\(213\) | 23.6878 | − | 19.8764i | 1.62306 | − | 1.36191i | ||||
\(214\) | −5.56805 | − | 4.67215i | −0.380624 | − | 0.319381i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.520945 | + | 0.902302i | 0.0354458 | + | 0.0613939i | ||||
\(217\) | 1.32635 | − | 2.29731i | 0.0900386 | − | 0.155951i | ||||
\(218\) | 8.31180 | + | 3.02525i | 0.562946 | + | 0.204896i | ||||
\(219\) | 1.21301 | + | 0.441500i | 0.0819677 | + | 0.0298338i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.673648 | − | 1.16679i | −0.0453145 | − | 0.0784870i | ||||
\(222\) | −3.35844 | − | 19.0467i | −0.225404 | − | 1.27833i | ||||
\(223\) | −8.76857 | − | 7.35770i | −0.587187 | − | 0.492708i | 0.300111 | − | 0.953904i | \(-0.402976\pi\) |
−0.887298 | + | 0.461196i | \(0.847421\pi\) | |||||||
\(224\) | −0.500000 | + | 0.419550i | −0.0334077 | + | 0.0280324i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.40033 | + | 0.509678i | −0.0931486 | + | 0.0339033i | ||||
\(227\) | −14.3250 | −0.950784 | −0.475392 | − | 0.879774i | \(-0.657694\pi\) | ||||
−0.475392 | + | 0.879774i | \(0.657694\pi\) | |||||||
\(228\) | 8.55690 | + | 6.97118i | 0.566695 | + | 0.461678i | ||||
\(229\) | −6.08647 | −0.402205 | −0.201103 | − | 0.979570i | \(-0.564452\pi\) | ||||
−0.201103 | + | 0.979570i | \(0.564452\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.286989 | + | 1.62760i | −0.0188825 | + | 0.107088i | ||||
\(232\) | −5.22668 | + | 4.38571i | −0.343148 | + | 0.287936i | ||||
\(233\) | 8.46451 | + | 7.10257i | 0.554528 | + | 0.465305i | 0.876471 | − | 0.481455i | \(-0.159891\pi\) |
−0.321943 | + | 0.946759i | \(0.604336\pi\) | |||||||
\(234\) | 1.70574 | + | 9.67372i | 0.111508 | + | 0.632391i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.02481 | − | 5.23913i | 0.196899 | − | 0.341039i | ||||
\(237\) | 20.7408 | + | 7.54904i | 1.34726 | + | 0.490363i | ||||
\(238\) | −0.286989 | − | 0.104455i | −0.0186027 | − | 0.00677084i | ||||
\(239\) | 4.02481 | − | 6.97118i | 0.260344 | − | 0.450928i | −0.705990 | − | 0.708222i | \(-0.749497\pi\) |
0.966333 | + | 0.257294i | \(0.0828308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.80019 | + | 27.2232i | 0.309208 | + | 1.75360i | 0.603007 | + | 0.797736i | \(0.293969\pi\) |
−0.293799 | + | 0.955867i | \(0.594920\pi\) | |||||||
\(242\) | 7.66044 | + | 6.42788i | 0.492432 | + | 0.413200i | ||||
\(243\) | −17.1288 | + | 14.3728i | −1.09881 | + | 0.922015i | ||||
\(244\) | −0.897804 | + | 5.09170i | −0.0574760 | + | 0.325962i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.4611 | 0.794491 | ||||||||
\(247\) | 6.43242 | + | 10.7773i | 0.409285 | + | 0.685744i | ||||
\(248\) | 4.06418 | 0.258076 | ||||||||
\(249\) | 42.6134 | − | 15.5100i | 2.70051 | − | 0.982907i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.8648 | + | 14.1513i | −1.06450 | + | 0.893221i | −0.994543 | − | 0.104329i | \(-0.966730\pi\) |
−0.0699563 | + | 0.997550i | \(0.522286\pi\) | |||||||
\(252\) | 1.70574 | + | 1.43128i | 0.107451 | + | 0.0901624i | ||||
\(253\) | −0.581252 | − | 3.29644i | −0.0365430 | − | 0.207246i | ||||
\(254\) | −9.16772 | − | 15.8790i | −0.575234 | − | 0.996334i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.939693 | − | 0.342020i | −0.0587308 | − | 0.0213763i | ||||
\(257\) | −13.4547 | − | 4.89711i | −0.839282 | − | 0.305474i | −0.113619 | − | 0.993524i | \(-0.536244\pi\) |
−0.725662 | + | 0.688051i | \(0.758467\pi\) | |||||||
\(258\) | −3.97906 | + | 6.89193i | −0.247725 | + | 0.429073i | ||||
\(259\) | −2.49273 | − | 4.31753i | −0.154890 | − | 0.268278i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.8307 | + | 14.9617i | 1.10369 | + | 0.926108i | ||||
\(262\) | −5.48158 | + | 4.59959i | −0.338653 | + | 0.284164i | ||||
\(263\) | −0.828411 | + | 4.69815i | −0.0510820 | + | 0.289701i | −0.999638 | − | 0.0269093i | \(-0.991433\pi\) |
0.948556 | + | 0.316610i | \(0.102545\pi\) | |||||||
\(264\) | −2.37939 | + | 0.866025i | −0.146441 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.68732 | + | 0.934204i | 0.164770 | + | 0.0572797i | ||||
\(267\) | −44.6810 | −2.73443 | ||||||||
\(268\) | −0.826352 | + | 0.300767i | −0.0504775 | + | 0.0183723i | ||||
\(269\) | 0.384133 | − | 2.17853i | 0.0234210 | − | 0.132827i | −0.970855 | − | 0.239666i | \(-0.922962\pi\) |
0.994276 | + | 0.106839i | \(0.0340730\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3917 | + | 13.7543i | 0.995726 | + | 0.835513i | 0.986387 | − | 0.164443i | \(-0.0525828\pi\) |
0.00933905 | + | 0.999956i | \(0.497027\pi\) | |||||||
\(272\) | −0.0812519 | − | 0.460802i | −0.00492662 | − | 0.0279403i | ||||
\(273\) | 2.37939 | + | 4.12122i | 0.144007 | + | 0.249427i | ||||
\(274\) | 8.47565 | − | 14.6803i | 0.512033 | − | 0.886867i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.96451 | − | 2.89884i | −0.479407 | − | 0.174490i | ||||
\(277\) | −3.87211 | + | 6.70669i | −0.232653 | + | 0.402966i | −0.958588 | − | 0.284797i | \(-0.908074\pi\) |
0.725935 | + | 0.687763i | \(0.241407\pi\) | |||||||
\(278\) | 6.34389 | + | 10.9879i | 0.380481 | + | 0.659013i | ||||
\(279\) | −2.40760 | − | 13.6542i | −0.144139 | − | 0.817456i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.7968 | + | 9.05958i | −0.644082 | + | 0.540449i | −0.905269 | − | 0.424839i | \(-0.860331\pi\) |
0.261186 | + | 0.965288i | \(0.415886\pi\) | |||||||
\(282\) | 2.81908 | − | 15.9878i | 0.167874 | − | 0.952059i | ||||
\(283\) | 4.89053 | − | 1.78001i | 0.290712 | − | 0.105810i | −0.192548 | − | 0.981288i | \(-0.561675\pi\) |
0.483259 | + | 0.875477i | \(0.339453\pi\) | |||||||
\(284\) | 12.2121 | 0.724657 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.87939 | −0.170262 | ||||||||
\(287\) | 3.01842 | − | 1.09861i | 0.178172 | − | 0.0648492i | ||||
\(288\) | −0.592396 | + | 3.35965i | −0.0349073 | + | 0.197969i | ||||
\(289\) | −12.8550 | + | 10.7867i | −0.756179 | + | 0.634509i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.37686 | − | 36.1650i | −0.373818 | − | 2.12003i | ||||
\(292\) | 0.254900 | + | 0.441500i | 0.0149169 | + | 0.0258368i | ||||
\(293\) | −13.3341 | + | 23.0953i | −0.778986 | + | 1.34924i | 0.153541 | + | 0.988142i | \(0.450932\pi\) |
−0.932527 | + | 0.361101i | \(0.882401\pi\) | |||||||
\(294\) | −15.6420 | − | 5.69323i | −0.912261 | − | 0.332036i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.81908 | − | 6.61484i | 0.221979 | − | 0.384480i | ||||
\(297\) | 0.520945 | + | 0.902302i | 0.0302283 | + | 0.0523569i | ||||
\(298\) | 0.593740 | + | 3.36727i | 0.0343945 | + | 0.195061i | ||||
\(299\) | −7.38326 | − | 6.19529i | −0.426985 | − | 0.358283i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.356219 | + | 2.02022i | −0.0205321 | + | 0.116444i | ||||
\(302\) | 14.6211 | − | 5.32164i | 0.841349 | − | 0.306226i | ||||
\(303\) | −37.8512 | −2.17450 | ||||||||
\(304\) | 0.819078 | + | 4.28125i | 0.0469773 | + | 0.245547i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.50000 | + | 0.545955i | −0.0857493 | + | 0.0312102i | ||||
\(307\) | −5.90925 | + | 33.5130i | −0.337259 | + | 1.91269i | 0.0664248 | + | 0.997791i | \(0.478841\pi\) |
−0.403684 | + | 0.914899i | \(0.632270\pi\) | |||||||
\(308\) | −0.500000 | + | 0.419550i | −0.0284901 | + | 0.0239061i | ||||
\(309\) | 14.0175 | + | 11.7621i | 0.797430 | + | 0.669123i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.52347 | + | 16.4951i | 0.540026 | + | 0.935353i | 0.998902 | + | 0.0468526i | \(0.0149191\pi\) |
−0.458875 | + | 0.888501i | \(0.651748\pi\) | |||||||
\(312\) | −3.64543 | + | 6.31407i | −0.206382 | + | 0.357464i | ||||
\(313\) | −3.37211 | − | 1.22735i | −0.190603 | − | 0.0693738i | 0.244955 | − | 0.969534i | \(-0.421227\pi\) |
−0.435558 | + | 0.900161i | \(0.643449\pi\) | |||||||
\(314\) | 12.4829 | + | 4.54341i | 0.704452 | + | 0.256400i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.35844 | + | 7.54904i | 0.245181 | + | 0.424667i | ||||
\(317\) | −4.89827 | − | 27.7795i | −0.275114 | − | 1.56025i | −0.738599 | − | 0.674145i | \(-0.764512\pi\) |
0.463484 | − | 0.886105i | \(-0.346599\pi\) | |||||||
\(318\) | 7.49660 | + | 6.29039i | 0.420388 | + | 0.352748i | ||||
\(319\) | −5.22668 | + | 4.38571i | −0.292638 | + | 0.245552i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.2947 | + | 6.29477i | −0.965298 | + | 0.351340i | ||||
\(322\) | −2.18479 | −0.121754 | ||||||||
\(323\) | −1.54323 | + | 1.33353i | −0.0858678 | + | 0.0741997i | ||||
\(324\) | −7.59627 | −0.422015 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.915345 | − | 5.19118i | 0.0506962 | − | 0.287513i | ||||
\(327\) | 17.1570 | − | 14.3965i | 0.948787 | − | 0.796126i | ||||
\(328\) | 3.76991 | + | 3.16333i | 0.208159 | + | 0.174666i | ||||
\(329\) | −0.726682 | − | 4.12122i | −0.0400633 | − | 0.227210i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.12108 | + | 7.13792i | −0.226515 | + | 0.392336i | −0.956773 | − | 0.290836i | \(-0.906067\pi\) |
0.730258 | + | 0.683172i | \(0.239400\pi\) | |||||||
\(332\) | 16.8293 | + | 6.12538i | 0.923630 | + | 0.336174i | ||||
\(333\) | −24.4859 | − | 8.91215i | −1.34182 | − | 0.488383i | ||||
\(334\) | −1.08899 | + | 1.88619i | −0.0595870 | + | 0.103208i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.286989 | + | 1.62760i | 0.0156565 | + | 0.0887926i | ||||
\(337\) | −3.15451 | − | 2.64695i | −0.171837 | − | 0.144189i | 0.552813 | − | 0.833305i | \(-0.313554\pi\) |
−0.724650 | + | 0.689117i | \(0.757999\pi\) | |||||||
\(338\) | 3.60741 | − | 3.02698i | 0.196217 | − | 0.164646i | ||||
\(339\) | −0.655230 | + | 3.71599i | −0.0355872 | + | 0.201825i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.06418 | 0.220088 | ||||||||
\(342\) | 13.8983 | − | 5.28801i | 0.751532 | − | 0.285943i | ||||
\(343\) | −8.85978 | −0.478383 | ||||||||
\(344\) | −2.95336 | + | 1.07494i | −0.159235 | + | 0.0579567i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.70574 | − | 4.78768i | 0.306742 | − | 0.257387i | ||||
\(347\) | −0.716881 | − | 0.601535i | −0.0384842 | − | 0.0322921i | 0.623343 | − | 0.781949i | \(-0.285774\pi\) |
−0.661827 | + | 0.749657i | \(0.730219\pi\) | |||||||
\(348\) | 3.00000 | + | 17.0138i | 0.160817 | + | 0.912038i | ||||
\(349\) | 7.03936 | + | 12.1925i | 0.376808 | + | 0.652651i | 0.990596 | − | 0.136820i | \(-0.0436882\pi\) |
−0.613787 | + | 0.789471i | \(0.710355\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.81908 | + | 1.02606i | 0.150471 | + | 0.0547671i | ||||
\(352\) | −0.939693 | − | 0.342020i | −0.0500858 | − | 0.0182297i | ||||
\(353\) | −9.39780 | + | 16.2775i | −0.500195 | + | 0.866362i | 0.499805 | + | 0.866138i | \(0.333405\pi\) |
−1.00000 | 0.000224734i | \(0.999928\pi\) | ||||||||
\(354\) | −7.65910 | − | 13.2660i | −0.407077 | − | 0.705077i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.5175 | − | 11.3426i | −0.716428 | − | 0.601155i | ||||
\(357\) | −0.592396 | + | 0.497079i | −0.0313529 | + | 0.0263082i | ||||
\(358\) | −1.10307 | + | 6.25584i | −0.0582993 | + | 0.330632i | ||||
\(359\) | −27.3307 | + | 9.94756i | −1.44246 | + | 0.525012i | −0.940474 | − | 0.339865i | \(-0.889619\pi\) |
−0.501984 | + | 0.864877i | \(0.667396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1946 | − | 12.6299i | 0.747084 | − | 0.664730i | ||||
\(362\) | −13.3500 | −0.701660 | ||||||||
\(363\) | 23.7939 | − | 8.66025i | 1.24885 | − | 0.454545i | ||||
\(364\) | −0.326352 | + | 1.85083i | −0.0171055 | + | 0.0970100i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.0287 | + | 8.41507i | 0.524208 | + | 0.439863i | ||||
\(367\) | 2.94831 | + | 16.7207i | 0.153901 | + | 0.872813i | 0.959784 | + | 0.280739i | \(0.0905796\pi\) |
−0.805883 | + | 0.592074i | \(0.798309\pi\) | |||||||
\(368\) | −1.67365 | − | 2.89884i | −0.0872449 | − | 0.151113i | ||||
\(369\) | 8.39440 | − | 14.5395i | 0.436995 | − | 0.756898i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.37046 | + | 0.862778i | 0.123068 | + | 0.0447932i | ||||
\(372\) | 5.14543 | − | 8.91215i | 0.266778 | − | 0.462073i | ||||
\(373\) | −2.06371 | − | 3.57445i | −0.106855 | − | 0.185078i | 0.807640 | − | 0.589676i | \(-0.200745\pi\) |
−0.914495 | + | 0.404598i | \(0.867411\pi\) | |||||||
\(374\) | −0.0812519 | − | 0.460802i | −0.00420144 | − | 0.0238275i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.91147 | − | 4.12122i | 0.253290 | − | 0.212535i | ||||
\(377\) | −3.41147 | + | 19.3474i | −0.175700 | + | 0.996443i | ||||
\(378\) | 0.639033 | − | 0.232589i | 0.0328683 | − | 0.0119631i | ||||
\(379\) | −23.1702 | −1.19018 | −0.595088 | − | 0.803661i | \(-0.702883\pi\) | ||||
−0.595088 | + | 0.803661i | \(0.702883\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −46.4270 | −2.37852 | ||||||||
\(382\) | 8.62196 | − | 3.13814i | 0.441138 | − | 0.160561i | ||||
\(383\) | 5.54664 | − | 31.4565i | 0.283420 | − | 1.60735i | −0.427456 | − | 0.904036i | \(-0.640590\pi\) |
0.710876 | − | 0.703318i | \(-0.248299\pi\) | |||||||
\(384\) | −1.93969 | + | 1.62760i | −0.0989845 | + | 0.0830579i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.64022 | − | 14.9734i | −0.134383 | − | 0.762126i | ||||
\(387\) | 5.36097 | + | 9.28547i | 0.272513 | + | 0.472007i | ||||
\(388\) | 7.25150 | − | 12.5600i | 0.368139 | − | 0.637635i | ||||
\(389\) | 25.8717 | + | 9.41653i | 1.31175 | + | 0.477437i | 0.900805 | − | 0.434224i | \(-0.142977\pi\) |
0.410943 | + | 0.911661i | \(0.365200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.783119 | − | 1.35640i | 0.0396040 | − | 0.0685962i | ||||
\(392\) | −3.28699 | − | 5.69323i | −0.166018 | − | 0.287552i | ||||
\(393\) | 3.14631 | + | 17.8436i | 0.158710 | + | 0.900090i | ||||
\(394\) | −13.7567 | − | 11.5433i | −0.693053 | − | 0.581541i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.592396 | + | 3.35965i | −0.0297690 | + | 0.168829i | ||||
\(397\) | 25.7977 | − | 9.38960i | 1.29475 | − | 0.471251i | 0.399467 | − | 0.916748i | \(-0.369195\pi\) |
0.895284 | + | 0.445497i | \(0.146973\pi\) | |||||||
\(398\) | 24.7665 | 1.24143 | ||||||||
\(399\) | 5.45084 | − | 4.71015i | 0.272883 | − | 0.235803i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0624 | + | 8.75801i | −1.20162 | + | 0.437354i | −0.863789 | − | 0.503853i | \(-0.831915\pi\) |
−0.337831 | + | 0.941207i | \(0.609693\pi\) | |||||||
\(402\) | −0.386659 | + | 2.19285i | −0.0192848 | + | 0.109370i | ||||
\(403\) | 8.96451 | − | 7.52211i | 0.446554 | − | 0.374703i | ||||
\(404\) | −11.4513 | − | 9.60878i | −0.569724 | − | 0.478055i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.22668 | + | 3.85673i | 0.110508 | + | 0.191406i | ||||
\(407\) | 3.81908 | − | 6.61484i | 0.189305 | − | 0.327885i | ||||
\(408\) | −1.11334 | − | 0.405223i | −0.0551186 | − | 0.0200615i | ||||
\(409\) | 16.4675 | + | 5.99368i | 0.814265 | + | 0.296368i | 0.715385 | − | 0.698731i | \(-0.246252\pi\) |
0.0988809 | + | 0.995099i | \(0.468474\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.4611 | − | 37.1717i | −1.05860 | − | 1.83355i | ||||
\(412\) | 1.25490 | + | 7.11689i | 0.0618245 | + | 0.350624i | ||||
\(413\) | −3.02481 | − | 2.53812i | −0.148841 | − | 0.124893i | ||||
\(414\) | −8.74763 | + | 7.34013i | −0.429922 | + | 0.360748i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.70574 | + | 0.984808i | −0.132660 | + | 0.0482842i | ||||
\(417\) | 32.1266 | 1.57325 | ||||||||
\(418\) | 0.819078 | + | 4.28125i | 0.0400624 | + | 0.209403i | ||||
\(419\) | −32.8776 | −1.60618 | −0.803089 | − | 0.595860i | \(-0.796812\pi\) | ||||
−0.803089 | + | 0.595860i | \(0.796812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.931074 | + | 5.28039i | −0.0453778 | + | 0.257350i | −0.999054 | − | 0.0434844i | \(-0.986154\pi\) |
0.953676 | + | 0.300835i | \(0.0972652\pi\) | |||||||
\(422\) | −8.19459 | + | 6.87608i | −0.398907 | + | 0.334722i | ||||
\(423\) | −16.7554 | − | 14.0594i | −0.814674 | − | 0.683592i | ||||
\(424\) | 0.671122 | + | 3.80612i | 0.0325926 | + | 0.184842i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 15.4611 | − | 26.7794i | 0.749093 | − | 1.29747i | ||||
\(427\) | 3.17112 | + | 1.15419i | 0.153461 | + | 0.0558554i | ||||
\(428\) | −6.83022 | − | 2.48600i | −0.330151 | − | 0.120165i | ||||
\(429\) | −3.64543 | + | 6.31407i | −0.176003 | + | 0.304846i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.80557 | − | 21.5825i | −0.183308 | − | 1.03959i | −0.928110 | − | 0.372305i | \(-0.878567\pi\) |
0.744802 | − | 0.667285i | \(-0.232544\pi\) | |||||||
\(432\) | 0.798133 | + | 0.669713i | 0.0384002 | + | 0.0322216i | ||||
\(433\) | −6.11515 | + | 5.13122i | −0.293875 | + | 0.246591i | −0.777790 | − | 0.628525i | \(-0.783659\pi\) |
0.483914 | + | 0.875115i | \(0.339215\pi\) | |||||||
\(434\) | 0.460637 | − | 2.61240i | 0.0221113 | − | 0.125399i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.84524 | 0.423610 | ||||||||
\(437\) | −7.11128 | + | 12.7402i | −0.340179 | + | 0.609447i | ||||
\(438\) | 1.29086 | 0.0616796 | ||||||||
\(439\) | 26.2456 | − | 9.55261i | 1.25263 | − | 0.455921i | 0.371342 | − | 0.928496i | \(-0.378898\pi\) |
0.881290 | + | 0.472575i | \(0.156675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.1800 | + | 14.4158i | −0.818097 | + | 0.686465i | ||||
\(442\) | −1.03209 | − | 0.866025i | −0.0490915 | − | 0.0411926i | ||||
\(443\) | −1.33069 | − | 7.54671i | −0.0632229 | − | 0.358555i | −0.999964 | − | 0.00853096i | \(-0.997284\pi\) |
0.936741 | − | 0.350024i | \(-0.113827\pi\) | |||||||
\(444\) | −9.67024 | − | 16.7494i | −0.458929 | − | 0.794889i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.7562 | − | 3.91495i | −0.509323 | − | 0.185378i | ||||
\(447\) | 8.13563 | + | 2.96113i | 0.384802 | + | 0.140057i | ||||
\(448\) | −0.326352 | + | 0.565258i | −0.0154187 | + | 0.0267059i | ||||
\(449\) | −10.4807 | − | 18.1531i | −0.494615 | − | 0.856698i | 0.505366 | − | 0.862905i | \(-0.331358\pi\) |
−0.999981 | + | 0.00620692i | \(0.998024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.76991 | + | 3.16333i | 0.177518 | + | 0.148956i | ||||
\(452\) | −1.14156 | + | 0.957882i | −0.0536944 | + | 0.0450550i | ||||
\(453\) | 6.84137 | − | 38.7993i | 0.321435 | − | 1.82295i | ||||
\(454\) | −13.4611 | + | 4.89944i | −0.631761 | + | 0.229942i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.4251 | + | 3.62414i | 0.488202 | + | 0.169716i | ||||
\(457\) | −26.6563 | −1.24693 | −0.623465 | − | 0.781851i | \(-0.714276\pi\) | ||||
−0.623465 | + | 0.781851i | \(0.714276\pi\) | |||||||
\(458\) | −5.71941 | + | 2.08169i | −0.267250 | + | 0.0972712i | ||||
\(459\) | −0.0846555 | + | 0.480105i | −0.00395138 | + | 0.0224094i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.47178 | − | 3.75227i | −0.208272 | − | 0.174761i | 0.532685 | − | 0.846314i | \(-0.321183\pi\) |
−0.740957 | + | 0.671553i | \(0.765628\pi\) | |||||||
\(462\) | 0.286989 | + | 1.62760i | 0.0133519 | + | 0.0757226i | ||||
\(463\) | −13.8610 | − | 24.0079i | −0.644174 | − | 1.11574i | −0.984492 | − | 0.175431i | \(-0.943868\pi\) |
0.340318 | − | 0.940310i | \(-0.389465\pi\) | |||||||
\(464\) | −3.41147 | + | 5.90885i | −0.158374 | + | 0.274311i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.3833 | + | 3.77920i | 0.480995 | + | 0.175068i | ||||
\(467\) | −10.0312 | + | 17.3746i | −0.464189 | + | 0.803999i | −0.999165 | − | 0.0408685i | \(-0.986988\pi\) |
0.534975 | + | 0.844868i | \(0.320321\pi\) | |||||||
\(468\) | 4.91147 | + | 8.50692i | 0.227033 | + | 0.393233i | ||||
\(469\) | 0.0996702 | + | 0.565258i | 0.00460234 | + | 0.0261012i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.7670 | − | 21.6211i | 1.18728 | − | 0.996246i | ||||
\(472\) | 1.05051 | − | 5.95772i | 0.0483535 | − | 0.274226i | ||||
\(473\) | −2.95336 | + | 1.07494i | −0.135796 | + | 0.0494256i | ||||
\(474\) | 22.0719 | 1.01380 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.305407 | −0.0139983 | ||||||||
\(477\) | 12.3897 | − | 4.50946i | 0.567283 | − | 0.206474i | ||||
\(478\) | 1.39780 | − | 7.92734i | 0.0639340 | − | 0.362588i | ||||
\(479\) | −14.9199 | + | 12.5193i | −0.681709 | + | 0.572022i | −0.916505 | − | 0.400023i | \(-0.869002\pi\) |
0.234796 | + | 0.972045i | \(0.424558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.81908 | − | 21.6591i | −0.174135 | − | 0.987568i | ||||
\(482\) | 13.8216 | + | 23.9397i | 0.629557 | + | 1.09042i | ||||
\(483\) | −2.76604 | + | 4.79093i | −0.125859 | + | 0.217995i | ||||
\(484\) | 9.39693 | + | 3.42020i | 0.427133 | + | 0.155464i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11.1800 | + | 19.3644i | −0.507137 | + | 0.878387i | ||||
\(487\) | 15.4003 | + | 26.6742i | 0.697856 | + | 1.20872i | 0.969209 | + | 0.246241i | \(0.0791956\pi\) |
−0.271353 | + | 0.962480i | \(0.587471\pi\) | |||||||
\(488\) | 0.897804 | + | 5.09170i | 0.0406417 | + | 0.230490i | ||||
\(489\) | −10.2246 | − | 8.57948i | −0.462373 | − | 0.387977i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.82383 | − | 10.3434i | 0.0823081 | − | 0.466792i | −0.915597 | − | 0.402097i | \(-0.868281\pi\) |
0.997905 | − | 0.0646952i | \(-0.0206075\pi\) | |||||||
\(492\) | 11.7096 | − | 4.26195i | 0.527910 | − | 0.192143i | ||||
\(493\) | −3.19253 | −0.143784 | ||||||||
\(494\) | 9.73055 | + | 7.92734i | 0.437798 | + | 0.356668i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.81908 | − | 1.39003i | 0.171482 | − | 0.0624142i | ||||
\(497\) | 1.38413 | − | 7.84981i | 0.0620868 | − | 0.352112i | ||||
\(498\) | 34.7388 | − | 29.1493i | 1.55668 | − | 1.30621i | ||||
\(499\) | 6.10085 | + | 5.11922i | 0.273112 | + | 0.229168i | 0.769048 | − | 0.639191i | \(-0.220731\pi\) |
−0.495936 | + | 0.868359i | \(0.665175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.75743 | + | 4.77600i | 0.123193 | + | 0.213376i | ||||
\(502\) | −11.0077 | + | 19.0660i | −0.491300 | + | 0.850956i | ||||
\(503\) | 11.1823 | + | 4.07001i | 0.498593 | + | 0.181473i | 0.579061 | − | 0.815284i | \(-0.303419\pi\) |
−0.0804683 | + | 0.996757i | \(0.525642\pi\) | |||||||
\(504\) | 2.09240 | + | 0.761570i | 0.0932027 | + | 0.0339230i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.67365 | − | 2.89884i | −0.0744027 | − | 0.128869i | ||||
\(507\) | −2.07057 | − | 11.7428i | −0.0919574 | − | 0.521517i | ||||
\(508\) | −14.0458 | − | 11.7858i | −0.623180 | − | 0.522910i | ||||
\(509\) | −9.73442 | + | 8.16815i | −0.431471 | + | 0.362047i | −0.832506 | − | 0.554016i | \(-0.813095\pi\) |
0.401036 | + | 0.916062i | \(0.368650\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.312681 | − | 0.113807i | 0.0138322 | − | 0.00503451i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.723689 | − | 4.48346i | 0.0319516 | − | 0.197950i | ||||
\(514\) | −14.3182 | −0.631549 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.38191 | + | 7.83721i | −0.0608353 | + | 0.345014i | ||||
\(517\) | 4.91147 | − | 4.12122i | 0.216006 | − | 0.181251i | ||||
\(518\) | −3.81908 | − | 3.20459i | −0.167801 | − | 0.140801i | ||||
\(519\) | −3.27497 | − | 18.5733i | −0.143755 | − | 0.815276i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6138 | − | 21.8478i | 0.552621 | − | 0.957168i | −0.445463 | − | 0.895300i | \(-0.646961\pi\) |
0.998084 | − | 0.0618674i | \(-0.0197056\pi\) | |||||||
\(522\) | 21.8726 | + | 7.96097i | 0.957337 | + | 0.348442i | ||||
\(523\) | −41.4406 | − | 15.0832i | −1.81207 | − | 0.659540i | −0.996752 | − | 0.0805294i | \(-0.974339\pi\) |
−0.815320 | − | 0.579011i | \(-0.803439\pi\) | |||||||
\(524\) | −3.57785 | + | 6.19702i | −0.156299 | + | 0.270718i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.828411 | + | 4.69815i | 0.0361204 | + | 0.204849i | ||||
\(527\) | 1.45677 | + | 1.22237i | 0.0634578 | + | 0.0532474i | ||||
\(528\) | −1.93969 | + | 1.62760i | −0.0844143 | + | 0.0708320i | ||||
\(529\) | −2.04829 | + | 11.6164i | −0.0890559 | + | 0.505061i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.6382 | −0.895620 | ||||||||
\(532\) | 2.84477 | − | 0.0412527i | 0.123336 | − | 0.00178853i | ||||
\(533\) | 14.1702 | 0.613781 | ||||||||
\(534\) | −41.9864 | + | 15.2818i | −1.81693 | + | 0.661308i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.673648 | + | 0.565258i | −0.0290972 | + | 0.0244154i | ||||
\(537\) | 12.3216 | + | 10.3391i | 0.531716 | + | 0.446163i | ||||
\(538\) | −0.384133 | − | 2.17853i | −0.0165611 | − | 0.0939229i | ||||
\(539\) | −3.28699 | − | 5.69323i | −0.141581 | − | 0.245225i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7759 | + | 11.5655i | 1.36615 | + | 0.497239i | 0.917951 | − | 0.396694i | \(-0.129842\pi\) |
0.448202 | + | 0.893933i | \(0.352065\pi\) | |||||||
\(542\) | 20.1074 | + | 7.31850i | 0.863687 | + | 0.314356i | ||||
\(543\) | −16.9017 | + | 29.2746i | −0.725320 | + | 1.25629i | ||||
\(544\) | −0.233956 | − | 0.405223i | −0.0100308 | − | 0.0173738i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.64543 | + | 3.05888i | 0.156010 | + | 0.130908i | ||||
\(547\) | 19.9308 | − | 16.7239i | 0.852181 | − | 0.715064i | −0.108088 | − | 0.994141i | \(-0.534473\pi\) |
0.960269 | + | 0.279077i | \(0.0900284\pi\) | |||||||
\(548\) | 2.94356 | − | 16.6938i | 0.125743 | − | 0.713123i | ||||
\(549\) | 16.5744 | − | 6.03260i | 0.707380 | − | 0.257465i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.7374 | − | 0.431229i | 1.26686 | − | 0.0183710i | ||||
\(552\) | −8.47565 | −0.360748 | ||||||||
\(553\) | 5.34642 | − | 1.94594i | 0.227353 | − | 0.0827497i | ||||
\(554\) | −1.34477 | + | 7.62657i | −0.0571338 | + | 0.324022i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.71941 | + | 8.15555i | 0.412195 | + | 0.345872i | ||||
\(557\) | −3.32723 | − | 18.8697i | −0.140979 | − | 0.799533i | −0.970508 | − | 0.241069i | \(-0.922502\pi\) |
0.829529 | − | 0.558464i | \(-0.188609\pi\) | |||||||
\(558\) | −6.93242 | − | 12.0073i | −0.293473 | − | 0.508310i | ||||
\(559\) | −4.52481 | + | 7.83721i | −0.191379 | + | 0.331479i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.11334 | − | 0.405223i | −0.0470053 | − | 0.0171085i | ||||
\(562\) | −7.04710 | + | 12.2059i | −0.297264 | + | 0.514877i | ||||
\(563\) | −3.96791 | − | 6.87262i | −0.167228 | − | 0.289647i | 0.770217 | − | 0.637782i | \(-0.220148\pi\) |
−0.937444 | + | 0.348136i | \(0.886815\pi\) | |||||||
\(564\) | −2.81908 | − | 15.9878i | −0.118705 | − | 0.673207i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.98680 | − | 3.34532i | 0.167578 | − | 0.140614i | ||||
\(567\) | −0.860967 | + | 4.88279i | −0.0361572 | + | 0.205058i | ||||
\(568\) | 11.4757 | − | 4.17680i | 0.481508 | − | 0.175254i | ||||
\(569\) | 9.12929 | 0.382720 | 0.191360 | − | 0.981520i | \(-0.438710\pi\) | ||||
0.191360 | + | 0.981520i | \(0.438710\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.4587 | −0.898020 | −0.449010 | − | 0.893527i | \(-0.648223\pi\) | ||||
−0.449010 | + | 0.893527i | \(0.648223\pi\) | |||||||
\(572\) | −2.70574 | + | 0.984808i | −0.113133 | + | 0.0411769i | ||||
\(573\) | 4.03431 | − | 22.8797i | 0.168536 | − | 0.955814i | ||||
\(574\) | 2.46064 | − | 2.06472i | 0.102705 | − | 0.0861797i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.592396 | + | 3.35965i | 0.0246832 | + | 0.139985i | ||||
\(577\) | 17.1694 | + | 29.7382i | 0.714770 | + | 1.23802i | 0.963048 | + | 0.269329i | \(0.0868020\pi\) |
−0.248278 | + | 0.968689i | \(0.579865\pi\) | |||||||
\(578\) | −8.39053 | + | 14.5328i | −0.349000 | + | 0.604486i | ||||
\(579\) | −36.1771 | − | 13.1674i | −1.50347 | − | 0.547218i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.84477 | − | 10.1234i | 0.242482 | − | 0.419991i | ||||
\(582\) | −18.3614 | − | 31.8029i | −0.761106 | − | 1.31827i | ||||
\(583\) | 0.671122 | + | 3.80612i | 0.0277950 | + | 0.157633i | ||||
\(584\) | 0.390530 | + | 0.327693i | 0.0161602 | + | 0.0135600i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.63088 | + | 26.2630i | −0.191300 | + | 1.08492i | ||||
\(587\) | −21.2433 | + | 7.73195i | −0.876807 | + | 0.319132i | −0.740920 | − | 0.671593i | \(-0.765610\pi\) |
−0.135886 | + | 0.990724i | \(0.543388\pi\) | |||||||
\(588\) | −16.6459 | −0.686465 | ||||||||
\(589\) | −13.7344 | − | 11.1892i | −0.565917 | − | 0.461044i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −42.7293 | + | 15.5522i | −1.75765 | + | 0.639731i | ||||
\(592\) | 1.32635 | − | 7.52211i | 0.0545127 | − | 0.309157i | ||||
\(593\) | −24.7217 | + | 20.7440i | −1.01520 | + | 0.851852i | −0.989017 | − | 0.147805i | \(-0.952779\pi\) |
−0.0261814 | + | 0.999657i | \(0.508335\pi\) | |||||||
\(594\) | 0.798133 | + | 0.669713i | 0.0327478 | + | 0.0274787i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.70961 | + | 2.96113i | 0.0700283 | + | 0.121292i | ||||
\(597\) | 31.3555 | − | 54.3093i | 1.28330 | − | 2.22273i | ||||
\(598\) | −9.05690 | − | 3.29644i | −0.370364 | − | 0.134802i | ||||
\(599\) | 5.03849 | + | 1.83386i | 0.205867 | + | 0.0749294i | 0.442895 | − | 0.896573i | \(-0.353951\pi\) |
−0.237029 | + | 0.971503i | \(0.576173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.8319 | − | 30.8857i | −0.727377 | − | 1.25985i | −0.957988 | − | 0.286808i | \(-0.907406\pi\) |
0.230611 | − | 0.973046i | \(-0.425928\pi\) | |||||||
\(602\) | 0.356219 | + | 2.02022i | 0.0145184 | + | 0.0823380i | ||||
\(603\) | 2.29813 | + | 1.92836i | 0.0935872 | + | 0.0785290i | ||||
\(604\) | 11.9192 | − | 10.0014i | 0.484986 | − | 0.406952i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −35.5685 | + | 12.9459i | −1.44487 | + | 0.525890i | ||||
\(607\) | −6.93077 | −0.281311 | −0.140656 | − | 0.990059i | \(-0.544921\pi\) | ||||
−0.140656 | + | 0.990059i | \(0.544921\pi\) | |||||||
\(608\) | 2.23396 | + | 3.74292i | 0.0905989 | + | 0.151795i | ||||
\(609\) | 11.2763 | 0.456939 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.20574 | − | 18.1806i | 0.129690 | − | 0.735510i | ||||
\(612\) | −1.22281 | + | 1.02606i | −0.0494292 | + | 0.0414760i | ||||
\(613\) | 15.7658 | + | 13.2291i | 0.636775 | + | 0.534317i | 0.903026 | − | 0.429586i | \(-0.141341\pi\) |
−0.266251 | + | 0.963904i | \(0.585785\pi\) | |||||||
\(614\) | 5.90925 | + | 33.5130i | 0.238478 | + | 1.35248i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.326352 | + | 0.565258i | −0.0131491 | + | 0.0227749i | ||||
\(617\) | −25.0976 | − | 9.13478i | −1.01039 | − | 0.367753i | −0.216808 | − | 0.976214i | \(-0.569565\pi\) |
−0.793583 | + | 0.608462i | \(0.791787\pi\) | |||||||
\(618\) | 17.1951 | + | 6.25849i | 0.691687 | + | 0.251753i | ||||
\(619\) | 2.15405 | − | 3.73092i | 0.0865785 | − | 0.149958i | −0.819484 | − | 0.573102i | \(-0.805740\pi\) |
0.906063 | + | 0.423143i | \(0.139073\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.605600 | + | 3.43453i | 0.0243019 | + | 0.137823i | ||||
\(622\) | 14.5908 | + | 12.2431i | 0.585038 | + | 0.490905i | ||||
\(623\) | −8.82295 | + | 7.40333i | −0.353484 | + | 0.296608i | ||||
\(624\) | −1.26604 | + | 7.18009i | −0.0506823 | + | 0.287434i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.58853 | −0.143426 | ||||||||
\(627\) | 10.4251 | + | 3.62414i | 0.416340 | + | 0.144734i | ||||
\(628\) | 13.2841 | 0.530091 | ||||||||
\(629\) | 3.35844 | − | 1.22237i | 0.133910 | − | 0.0487392i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.5988 | + | 8.89344i | −0.421931 | + | 0.354042i | −0.828897 | − | 0.559401i | \(-0.811031\pi\) |
0.406966 | + | 0.913443i | \(0.366587\pi\) | |||||||
\(632\) | 6.67752 | + | 5.60310i | 0.265617 | + | 0.222879i | ||||
\(633\) | 4.70352 | + | 26.6750i | 0.186948 | + | 1.06023i | ||||
\(634\) | −14.1040 | − | 24.4289i | −0.560142 | − | 0.970194i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.19594 | + | 3.34705i | 0.364643 | + | 0.132719i | ||||
\(637\) | −17.7875 | − | 6.47410i | −0.704765 | − | 0.256513i | ||||
\(638\) | −3.41147 | + | 5.90885i | −0.135062 | + | 0.233933i | ||||
\(639\) | −20.8307 | − | 36.0798i | −0.824049 | − | 1.42730i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.43969 | + | 2.04715i | 0.0963621 | + | 0.0808574i | 0.689696 | − | 0.724099i | \(-0.257744\pi\) |
−0.593334 | + | 0.804956i | \(0.702189\pi\) | |||||||
\(642\) | −14.0988 | + | 11.8303i | −0.556435 | + | 0.466904i | ||||
\(643\) | −2.09327 | + | 11.8715i | −0.0825507 | + | 0.468168i | 0.915308 | + | 0.402755i | \(0.131947\pi\) |
−0.997858 | + | 0.0654126i | \(0.979164\pi\) | |||||||
\(644\) | −2.05303 | + | 0.747243i | −0.0809009 | + | 0.0294455i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.994070 | + | 1.78093i | −0.0391112 | + | 0.0700696i | ||||
\(647\) | −25.3105 | −0.995057 | −0.497528 | − | 0.867448i | \(-0.665759\pi\) | ||||
−0.497528 | + | 0.867448i | \(0.665759\pi\) | |||||||
\(648\) | −7.13816 | + | 2.59808i | −0.280413 | + | 0.102062i | ||||
\(649\) | 1.05051 | − | 5.95772i | 0.0412360 | − | 0.233861i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.14543 | − | 4.31753i | −0.201665 | − | 0.169217i | ||||
\(652\) | −0.915345 | − | 5.19118i | −0.0358477 | − | 0.203302i | ||||
\(653\) | 0.718226 | + | 1.24400i | 0.0281063 | + | 0.0486816i | 0.879736 | − | 0.475462i | \(-0.157719\pi\) |
−0.851630 | + | 0.524143i | \(0.824386\pi\) | |||||||
\(654\) | 11.1985 | − | 19.3963i | 0.437895 | − | 0.758456i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.62449 | + | 1.68317i | 0.180556 | + | 0.0657169i | ||||
\(657\) | 0.869585 | − | 1.50617i | 0.0339257 | − | 0.0587611i | ||||
\(658\) | −2.09240 | − | 3.62414i | −0.0815701 | − | 0.141284i | ||||
\(659\) | −0.0736733 | − | 0.417822i | −0.00286990 | − | 0.0162760i | 0.983339 | − | 0.181780i | \(-0.0581860\pi\) |
−0.986209 | + | 0.165504i | \(0.947075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.34074 | + | 6.99871i | −0.324417 | + | 0.272218i | −0.790420 | − | 0.612565i | \(-0.790138\pi\) |
0.466003 | + | 0.884783i | \(0.345693\pi\) | |||||||
\(662\) | −1.43124 | + | 8.11695i | −0.0556266 | + | 0.315474i | ||||
\(663\) | −3.20574 | + | 1.16679i | −0.124501 | + | 0.0453145i | ||||
\(664\) | 17.9094 | 0.695020 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.0574 | −1.00970 | ||||||||
\(667\) | −21.4611 | + | 7.81120i | −0.830977 | + | 0.302451i | ||||
\(668\) | −0.378203 | + | 2.14490i | −0.0146331 | + | 0.0829886i | ||||
\(669\) | −22.2028 | + | 18.6304i | −0.858410 | + | 0.720291i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.897804 | + | 5.09170i | 0.0346593 | + | 0.196563i | ||||
\(672\) | 0.826352 | + | 1.43128i | 0.0318772 | + | 0.0552130i | ||||
\(673\) | −17.6827 | + | 30.6274i | −0.681619 | + | 1.18060i | 0.292867 | + | 0.956153i | \(0.405391\pi\) |
−0.974487 | + | 0.224446i | \(0.927943\pi\) | |||||||
\(674\) | −3.86959 | − | 1.40841i | −0.149051 | − | 0.0542501i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.35457 | − | 4.07824i | 0.0905604 | − | 0.156855i | ||||
\(677\) | −15.9757 | − | 27.6706i | −0.613994 | − | 1.06347i | −0.990560 | − | 0.137079i | \(-0.956228\pi\) |
0.376566 | − | 0.926390i | \(-0.377105\pi\) | |||||||
\(678\) | 0.655230 | + | 3.71599i | 0.0251640 | + | 0.142712i | ||||
\(679\) | −7.25150 | − | 6.08473i | −0.278287 | − | 0.233510i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.29860 | + | 35.7211i | −0.241363 | + | 1.36884i | ||||
\(682\) | 3.81908 | − | 1.39003i | 0.146240 | − | 0.0532270i | ||||
\(683\) | −30.2327 | −1.15682 | −0.578410 | − | 0.815746i | \(-0.696327\pi\) | ||||
−0.578410 | + | 0.815746i | \(0.696327\pi\) | |||||||
\(684\) | 11.2515 | − | 9.72259i | 0.430212 | − | 0.371753i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.32547 | + | 3.03022i | −0.317868 | + | 0.115695i | ||||
\(687\) | −2.67617 | + | 15.1773i | −0.102102 | + | 0.579052i | ||||
\(688\) | −2.40760 | + | 2.02022i | −0.0917890 | + | 0.0770201i | ||||
\(689\) | 8.52481 | + | 7.15317i | 0.324770 | + | 0.272514i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.5829 | + | 35.6506i | 0.783010 | + | 1.35621i | 0.930180 | + | 0.367103i | \(0.119650\pi\) |
−0.147170 | + | 0.989111i | \(0.547016\pi\) | |||||||
\(692\) | 3.72416 | − | 6.45043i | 0.141571 | − | 0.245208i | ||||
\(693\) | 2.09240 | + | 0.761570i | 0.0794836 | + | 0.0289297i | ||||
\(694\) | −0.879385 | − | 0.320070i | −0.0333810 | − | 0.0121497i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.63816 | + | 14.9617i | 0.327428 | + | 0.567123i | ||||
\(697\) | 0.399863 | + | 2.26774i | 0.0151459 | + | 0.0858966i | ||||
\(698\) | 10.7849 | + | 9.04963i | 0.408216 | + | 0.342534i | ||||
\(699\) | 21.4329 | − | 17.9843i | 0.810666 | − | 0.680230i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.5373 | − | 6.38306i | 0.662375 | − | 0.241085i | 0.0111135 | − | 0.999938i | \(-0.496462\pi\) |
0.651261 | + | 0.758854i | \(0.274240\pi\) | |||||||
\(702\) | 3.00000 | 0.113228 | ||||||||
\(703\) | −31.1177 | + | 11.8396i | −1.17363 | + | 0.446541i | ||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.26382 | + | 18.5101i | −0.122836 | + | 0.696635i | ||||
\(707\) | −7.47431 | + | 6.27169i | −0.281100 | + | 0.235871i | ||||
\(708\) | −11.7344 | − | 9.84635i | −0.441007 | − | 0.370048i | ||||
\(709\) | −6.62536 | − | 37.5743i | −0.248821 | − | 1.41113i | −0.811449 | − | 0.584423i | \(-0.801321\pi\) |
0.562629 | − | 0.826710i | \(-0.309790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.8687 | − | 25.7534i | 0.557620 | − | 0.965826i | ||||
\(712\) | −16.5817 | − | 6.03525i | −0.621426 | − | 0.226181i | ||||
\(713\) | 12.7836 | + | 4.65284i | 0.478749 | + | 0.174250i | ||||
\(714\) | −0.386659 | + | 0.669713i | −0.0144704 | + | 0.0250634i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.10307 | + | 6.25584i | 0.0412238 | + | 0.233792i | ||||
\(717\) | −15.6138 | − | 13.1015i | −0.583108 | − | 0.489286i | ||||
\(718\) | −22.2802 | + | 18.6953i | −0.831489 | + | 0.697702i | ||||
\(719\) | 2.94516 | − | 16.7028i | 0.109836 | − | 0.622910i | −0.879342 | − | 0.476190i | \(-0.842017\pi\) |
0.989178 | − | 0.146720i | \(-0.0468715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.71688 | 0.175666 | ||||||||
\(722\) | 9.01889 | − | 16.7230i | 0.335648 | − | 0.622367i | ||||
\(723\) | 69.9951 | 2.60314 | ||||||||
\(724\) | −12.5449 | + | 4.56596i | −0.466227 | + | 0.169693i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 19.3969 | − | 16.2760i | 0.719887 | − | 0.604057i | ||||
\(727\) | 23.9047 | + | 20.0584i | 0.886575 | + | 0.743925i | 0.967520 | − | 0.252794i | \(-0.0813494\pi\) |
−0.0809452 | + | 0.996719i | \(0.525794\pi\) | |||||||
\(728\) | 0.326352 | + | 1.85083i | 0.0120954 | + | 0.0685964i | ||||
\(729\) | 16.9145 | + | 29.2967i | 0.626462 | + | 1.08506i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.38191 | − | 0.502975i | −0.0511118 | − | 0.0186032i | ||||
\(732\) | 12.3020 | + | 4.47756i | 0.454695 | + | 0.165495i | ||||
\(733\) | 5.54370 | − | 9.60197i | 0.204761 | − | 0.354657i | −0.745295 | − | 0.666734i | \(-0.767692\pi\) |
0.950057 | + | 0.312078i | \(0.101025\pi\) | |||||||
\(734\) | 8.48932 | + | 14.7039i | 0.313347 | + | 0.542732i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.56418 | − | 2.15160i | −0.0945168 | − | 0.0793091i | ||||
\(737\) | −0.673648 | + | 0.565258i | −0.0248141 | + | 0.0208215i | ||||
\(738\) | 2.91534 | − | 16.5337i | 0.107315 | − | 0.608615i | ||||
\(739\) | 11.0842 | − | 4.03434i | 0.407741 | − | 0.148405i | −0.130004 | − | 0.991514i | \(-0.541499\pi\) |
0.537744 | + | 0.843108i | \(0.319277\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.7028 | − | 11.3013i | 1.09116 | − | 0.415164i | ||||
\(742\) | 2.52259 | 0.0926073 | ||||||||
\(743\) | −10.7956 | + | 3.92928i | −0.396052 | + | 0.144151i | −0.532366 | − | 0.846514i | \(-0.678697\pi\) |
0.136313 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(744\) | 1.78699 | − | 10.1345i | 0.0655142 | − | 0.371549i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.16179 | − | 2.65306i | −0.115761 | − | 0.0971353i | ||||
\(747\) | −10.6095 | − | 60.1693i | −0.388180 | − | 2.20148i | ||||
\(748\) | −0.233956 | − | 0.405223i | −0.00855426 | − | 0.0148164i | ||||
\(749\) | −2.37211 | + | 4.10862i | −0.0866751 | + | 0.150126i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.2717 | + | 14.2937i | 1.43305 | + | 0.521586i | 0.937803 | − | 0.347169i | \(-0.112857\pi\) |
0.495243 | + | 0.868755i | \(0.335079\pi\) | |||||||
\(752\) | 3.20574 | − | 5.55250i | 0.116901 | − | 0.202479i | ||||
\(753\) | 27.8726 | + | 48.2767i | 1.01573 | + | 1.75930i | ||||
\(754\) | 3.41147 | + | 19.3474i | 0.124239 | + | 0.704592i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.520945 | − | 0.437124i | 0.0189466 | − | 0.0158981i | ||||
\(757\) | −7.81820 | + | 44.3392i | −0.284157 | + | 1.61154i | 0.424123 | + | 0.905605i | \(0.360583\pi\) |
−0.708280 | + | 0.705932i | \(0.750529\pi\) | |||||||
\(758\) | −21.7729 | + | 7.92469i | −0.790828 | + | 0.287838i | ||||
\(759\) | −8.47565 | −0.307647 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.3604 | −0.991814 | −0.495907 | − | 0.868376i | \(-0.665164\pi\) | ||||
−0.495907 | + | 0.868376i | \(0.665164\pi\) | |||||||
\(762\) | −43.6271 | + | 15.8790i | −1.58044 | + | 0.575234i | ||||
\(763\) | 1.00253 | − | 5.68561i | 0.0362939 | − | 0.205833i | ||||
\(764\) | 7.02869 | − | 5.89777i | 0.254289 | − | 0.213374i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.54664 | − | 31.4565i | −0.200408 | − | 1.13657i | ||||
\(767\) | −8.70961 | − | 15.0855i | −0.314486 | − | 0.544705i | ||||
\(768\) | −1.26604 | + | 2.19285i | −0.0456844 | + | 0.0791278i | ||||
\(769\) | 31.2704 | + | 11.3815i | 1.12764 | + | 0.410427i | 0.837434 | − | 0.546538i | \(-0.184055\pi\) |
0.290204 | + | 0.956965i | \(0.406277\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.1275 | + | 31.3977i | −0.652845 | + | 1.13076i | ||||
\(772\) | −7.60220 | − | 13.1674i | −0.273609 | − | 0.473905i | ||||
\(773\) | −4.92808 | − | 27.9485i | −0.177251 | − | 1.00524i | −0.935514 | − | 0.353290i | \(-0.885063\pi\) |
0.758263 | − | 0.651949i | \(-0.226048\pi\) | |||||||
\(774\) | 8.21348 | + | 6.89193i | 0.295227 | + | 0.247725i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.51842 | − | 14.2827i | 0.0904059 | − | 0.512718i | ||||
\(777\) | −11.8623 | + | 4.31753i | −0.425558 | + | 0.154890i | ||||
\(778\) | 27.5321 | 0.987073 | ||||||||
\(779\) | −4.03091 | − | 21.0692i | −0.144422 | − | 0.754883i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4757 | − | 4.17680i | 0.410631 | − | 0.149458i | ||||
\(782\) | 0.271974 | − | 1.54244i | 0.00972578 | − | 0.0551576i | ||||
\(783\) | 5.44562 | − | 4.56942i | 0.194611 | − | 0.163298i | ||||
\(784\) | −5.03596 | − | 4.22567i | −0.179856 | − | 0.150917i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.05943 | + | 15.6914i | 0.323139 | + | 0.559693i | ||||
\(787\) | 11.2827 | − | 19.5422i | 0.402185 | − | 0.696605i | −0.591804 | − | 0.806082i | \(-0.701584\pi\) |
0.993989 | + | 0.109477i | \(0.0349175\pi\) | |||||||
\(788\) | −16.8751 | − | 6.14204i | −0.601151 | − | 0.218801i | ||||
\(789\) | 11.3512 | + | 4.13149i | 0.404112 | + | 0.147085i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.486329 | + | 0.842347i | 0.0172919 | + | 0.0299504i | ||||
\(792\) | 0.592396 | + | 3.35965i | 0.0210499 | + | 0.119380i | ||||
\(793\) | 11.4042 | + | 9.56926i | 0.404975 | + | 0.339814i | ||||
\(794\) | 21.0305 | − | 17.6467i | 0.746344 | − | 0.626257i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.2729 | − | 8.47065i | 0.824886 | − | 0.300234i | ||||
\(797\) | 30.1320 | 1.06733 | 0.533665 | − | 0.845696i | \(-0.320814\pi\) | ||||
0.533665 | + | 0.845696i | \(0.320814\pi\) | |||||||
\(798\) | 3.51114 | − | 6.29039i | 0.124293 | − | 0.222677i | ||||
\(799\) | 3.00000 | 0.106132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.4534 | + | 59.2840i | −0.369351 | + | 2.09470i | ||||
\(802\) | −19.6159 | + | 16.4597i | −0.692660 | + | 0.581211i | ||||
\(803\) | 0.390530 | + | 0.327693i | 0.0137815 | + | 0.0115640i | ||||
\(804\) | 0.386659 | + | 2.19285i | 0.0136364 | + | 0.0773360i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.85117 | − | 10.1345i | 0.206099 | − | 0.356973i | ||||
\(807\) | −5.26352 | − | 1.91576i | −0.185285 | − | 0.0674381i | ||||
\(808\) | −14.0471 | − | 5.11273i | −0.494175 | − | 0.179865i | ||||
\(809\) | 6.59714 | − | 11.4266i | 0.231943 | − | 0.401737i | −0.726437 | − | 0.687233i | \(-0.758825\pi\) |
0.958380 | + | 0.285496i | \(0.0921583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.92144 | − | 33.5821i | −0.207930 | − | 1.17923i | −0.892762 | − | 0.450528i | \(-0.851236\pi\) |
0.684833 | − | 0.728700i | \(-0.259875\pi\) | |||||||
\(812\) | 3.41147 | + | 2.86257i | 0.119719 | + | 0.100456i | ||||
\(813\) | 41.5053 | − | 34.8271i | 1.45565 | − | 1.22144i | ||||
\(814\) | 1.32635 | − | 7.52211i | 0.0464886 | − | 0.263650i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.18479 | −0.0414760 | ||||||||
\(817\) | 12.9400 | + | 4.49839i | 0.452713 | + | 0.157379i | ||||
\(818\) | 17.5243 | 0.612724 | ||||||||
\(819\) | 6.02481 | − | 2.19285i | 0.210524 | − | 0.0766245i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.27173 | − | 3.58440i | 0.149084 | − | 0.125097i | −0.565195 | − | 0.824957i | \(-0.691199\pi\) |
0.714279 | + | 0.699861i | \(0.246755\pi\) | |||||||
\(822\) | −32.8803 | − | 27.5899i | −1.14683 | − | 0.962307i | ||||
\(823\) | −1.23648 | − | 7.01244i | −0.0431010 | − | 0.244438i | 0.955644 | − | 0.294525i | \(-0.0951614\pi\) |
−0.998745 | + | 0.0500866i | \(0.984050\pi\) | |||||||
\(824\) | 3.61334 | + | 6.25849i | 0.125877 | + | 0.218025i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.71048 | − | 1.35051i | −0.129104 | − | 0.0469901i | ||||
\(827\) | 2.40003 | + | 0.873538i | 0.0834570 | + | 0.0303759i | 0.383411 | − | 0.923578i | \(-0.374749\pi\) |
−0.299954 | + | 0.953954i | \(0.596971\pi\) | |||||||
\(828\) | −5.70961 | + | 9.88933i | −0.198423 | + | 0.343678i | ||||
\(829\) | 16.1022 | + | 27.8898i | 0.559252 | + | 0.968654i | 0.997559 | + | 0.0698281i | \(0.0222451\pi\) |
−0.438307 | + | 0.898826i | \(0.644422\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.0214 | + | 12.6045i | 0.521087 | + | 0.437244i | ||||
\(832\) | −2.20574 | + | 1.85083i | −0.0764702 | + | 0.0641661i | ||||
\(833\) | 0.534148 | − | 3.02931i | 0.0185071 | − | 0.104959i | ||||
\(834\) | 30.1891 | − | 10.9879i | 1.04536 | − | 0.380481i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.23396 | + | 3.74292i | 0.0772630 | + | 0.129452i | ||||
\(837\) | −4.23442 | −0.146363 | ||||||||
\(838\) | −30.8949 | + | 11.2448i | −1.06725 | + | 0.388446i | ||||
\(839\) | −7.29039 | + | 41.3459i | −0.251692 | + | 1.42742i | 0.552730 | + | 0.833360i | \(0.313586\pi\) |
−0.804422 | + | 0.594058i | \(0.797525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.4461 | + | 11.2826i | 0.463658 | + | 0.389055i | ||||
\(842\) | 0.931074 | + | 5.28039i | 0.0320869 | + | 0.181974i | ||||
\(843\) | 17.8439 | + | 30.9065i | 0.614576 | + | 1.06448i | ||||
\(844\) | −5.34864 | + | 9.26412i | −0.184108 | + | 0.318884i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −20.5535 | − | 7.48086i | −0.706644 | − | 0.257197i | ||||
\(847\) | 3.26352 | − | 5.65258i | 0.112136 | − | 0.194225i | ||||
\(848\) | 1.93242 | + | 3.34705i | 0.0663595 | + | 0.114938i | ||||
\(849\) | −2.28833 | − | 12.9778i | −0.0785354 | − | 0.445396i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.5856 | − | 16.4343i | 0.671385 | − | 0.563359i | ||||
\(852\) | 5.36959 | − | 30.4524i | 0.183959 | − | 1.04328i | ||||
\(853\) | 34.4247 | − | 12.5296i | 1.17868 | − | 0.429005i | 0.322945 | − | 0.946418i | \(-0.395327\pi\) |
0.855736 | + | 0.517413i | \(0.173105\pi\) | |||||||
\(854\) | 3.37464 | 0.115478 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.26857 | −0.248435 | ||||||||
\(857\) | −38.2365 | + | 13.9170i | −1.30614 | + | 0.475394i | −0.898990 | − | 0.437969i | \(-0.855698\pi\) |
−0.407145 | + | 0.913363i | \(0.633476\pi\) | |||||||
\(858\) | −1.26604 | + | 7.18009i | −0.0432220 | + | 0.245124i | ||||
\(859\) | −10.0018 | + | 8.39252i | −0.341257 | + | 0.286349i | −0.797268 | − | 0.603625i | \(-0.793722\pi\) |
0.456011 | + | 0.889974i | \(0.349278\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.41235 | − | 8.00984i | −0.0481328 | − | 0.272975i | ||||
\(862\) | −10.9577 | − | 18.9793i | −0.373221 | − | 0.646437i | ||||
\(863\) | 22.7319 | − | 39.3728i | 0.773803 | − | 1.34027i | −0.161662 | − | 0.986846i | \(-0.551685\pi\) |
0.935465 | − | 0.353420i | \(-0.114981\pi\) | |||||||
\(864\) | 0.979055 | + | 0.356347i | 0.0333081 | + | 0.0121232i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.99138 | + | 6.91328i | −0.135633 | + | 0.234923i | ||||
\(867\) | 21.2456 | + | 36.7984i | 0.721537 | + | 1.24974i | ||||
\(868\) | −0.460637 | − | 2.61240i | −0.0156350 | − | 0.0886707i | ||||
\(869\) | 6.67752 | + | 5.60310i | 0.226519 | + | 0.190072i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.439693 | + | 2.49362i | −0.0148984 | + | 0.0844931i | ||||
\(872\) | 8.31180 | − | 3.02525i | 0.281473 | − | 0.102448i | ||||
\(873\) | −49.4766 | −1.67453 | ||||||||
\(874\) | −2.32501 | + | 14.4041i | −0.0786446 | + | 0.487226i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.21301 | − | 0.441500i | 0.0409838 | − | 0.0149169i | ||||
\(877\) | 9.29401 | − | 52.7090i | 0.313837 | − | 1.77986i | −0.264834 | − | 0.964294i | \(-0.585317\pi\) |
0.578670 | − | 0.815562i | \(-0.303572\pi\) | |||||||
\(878\) | 21.3956 | − | 17.9530i | 0.722066 | − | 0.605885i | ||||
\(879\) | 51.7281 | + | 43.4050i | 1.74474 | + | 1.46401i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.08781 | − | 7.08030i | −0.137722 | − | 0.238541i | 0.788912 | − | 0.614506i | \(-0.210645\pi\) |
−0.926634 | + | 0.375965i | \(0.877311\pi\) | |||||||
\(882\) | −11.2135 | + | 19.4223i | −0.377577 | + | 0.653983i | ||||
\(883\) | 29.0672 | + | 10.5796i | 0.978188 | + | 0.356031i | 0.781136 | − | 0.624362i | \(-0.214641\pi\) |
0.197053 | + | 0.980393i | \(0.436863\pi\) | |||||||
\(884\) | −1.26604 | − | 0.460802i | −0.0425817 | − | 0.0154985i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.83157 | − | 6.63647i | −0.128724 | − | 0.222956i | ||||
\(887\) | 1.81592 | + | 10.2986i | 0.0609727 | + | 0.345793i | 0.999998 | + | 0.00194565i | \(0.000619320\pi\) |
−0.939025 | + | 0.343848i | \(0.888270\pi\) | |||||||
\(888\) | −14.8157 | − | 12.4318i | −0.497181 | − | 0.417185i | ||||
\(889\) | −9.16772 | + | 7.69263i | −0.307475 | + | 0.258002i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.13816 | + | 2.59808i | −0.239137 | + | 0.0870388i | ||||
\(892\) | −11.4466 | −0.383259 | ||||||||
\(893\) | −27.9440 | + | 0.405223i | −0.935111 | + | 0.0135603i | ||||
\(894\) | 8.65776 | 0.289559 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.113341 | + | 0.642788i | −0.00378645 | + | 0.0214740i | ||||
\(897\) | −18.6951 | + | 15.6870i | −0.624210 | + | 0.523774i | ||||
\(898\) | −16.0574 | − | 13.4737i | −0.535841 | − | 0.449624i | ||||
\(899\) | −4.81521 | − | 27.3084i | −0.160596 | − | 0.910786i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.904200 | + | 1.56612i | −0.0301233 | + | 0.0521750i | ||||
\(902\) | 4.62449 | + | 1.68317i | 0.153979 | + | 0.0560436i | ||||
\(903\) | 4.88103 | + | 1.77655i | 0.162431 | + | 0.0591199i | ||||
\(904\) | −0.745100 | + | 1.29055i | −0.0247817 | + | 0.0429231i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.84137 | − | 38.7993i | −0.227289 | − | 1.28902i | ||||
\(907\) | 18.7822 | + | 15.7602i | 0.623654 | + | 0.523308i | 0.898950 | − | 0.438052i | \(-0.144331\pi\) |
−0.275296 | + | 0.961360i | \(0.588776\pi\) | |||||||
\(908\) | −10.9736 | + | 9.20794i | −0.364171 | + | 0.305576i | ||||
\(909\) | −8.85550 | + | 50.2221i | −0.293719 | + | 1.66576i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.2927 | 1.46748 | 0.733742 | − | 0.679428i | \(-0.237772\pi\) | ||||
0.733742 | + | 0.679428i | \(0.237772\pi\) | |||||||
\(912\) | 11.0360 | − | 0.160035i | 0.365437 | − | 0.00529929i | ||||
\(913\) | 17.9094 | 0.592715 | ||||||||
\(914\) | −25.0488 | + | 9.11700i | −0.828539 | + | 0.301564i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.66250 | + | 3.91231i | −0.154053 | + | 0.129266i | ||||
\(917\) | 3.57785 | + | 3.00217i | 0.118151 | + | 0.0991404i | ||||
\(918\) | 0.0846555 | + | 0.480105i | 0.00279405 | + | 0.0158458i | ||||
\(919\) | 24.4636 | + | 42.3723i | 0.806981 | + | 1.39773i | 0.914946 | + | 0.403577i | \(0.132233\pi\) |
−0.107965 | + | 0.994155i | \(0.534433\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 80.9705 | + | 29.4709i | 2.66807 | + | 0.971098i | ||||
\(922\) | −5.48545 | − | 1.99654i | −0.180654 | − | 0.0657526i | ||||
\(923\) | 17.5817 | − | 30.4524i | 0.578709 | − | 1.00235i | ||||
\(924\) | 0.826352 | + | 1.43128i | 0.0271850 | + | 0.0470858i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.2362 | − | 17.8193i | −0.697866 | − | 0.585579i | ||||
\(927\) | 18.8858 | − | 15.8471i | 0.620290 | − | 0.520485i | ||||
\(928\) | −1.18479 | + | 6.71929i | −0.0388927 | + | 0.220572i | ||||
\(929\) | −29.5685 | + | 10.7621i | −0.970112 | + | 0.353092i | −0.777988 | − | 0.628279i | \(-0.783760\pi\) |
−0.192123 | + | 0.981371i | \(0.561537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.56624 | + | 28.2892i | −0.149652 | + | 0.927139i | ||||
\(932\) | 11.0496 | 0.361943 | ||||||||
\(933\) | 45.3200 | − | 16.4951i | 1.48371 | − | 0.540026i | ||||
\(934\) | −3.48380 | + | 19.7576i | −0.113994 | + | 0.646489i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.52481 | + | 6.31407i | 0.245956 | + | 0.206382i | ||||
\(937\) | −1.15759 | − | 6.56504i | −0.0378169 | − | 0.214471i | 0.960043 | − | 0.279851i | \(-0.0902850\pi\) |
−0.997860 | + | 0.0653804i | \(0.979174\pi\) | |||||||
\(938\) | 0.286989 | + | 0.497079i | 0.00937052 | + | 0.0162302i | ||||
\(939\) | −4.54323 | + | 7.86911i | −0.148263 | + | 0.256799i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.0415 | − | 6.93053i | −0.620734 | − | 0.225929i | 0.0124591 | − | 0.999922i | \(-0.496034\pi\) |
−0.633194 | + | 0.773994i | \(0.718256\pi\) | |||||||
\(942\) | 16.8182 | − | 29.1300i | 0.547967 | − | 0.949106i | ||||
\(943\) | 8.23648 | + | 14.2660i | 0.268217 | + | 0.464565i | ||||
\(944\) | −1.05051 | − | 5.95772i | −0.0341911 | − | 0.193907i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.40760 | + | 2.02022i | −0.0782779 | + | 0.0656830i | ||||
\(947\) | −0.961819 | + | 5.45475i | −0.0312549 | + | 0.177255i | −0.996439 | − | 0.0843158i | \(-0.973130\pi\) |
0.965184 | + | 0.261571i | \(0.0842407\pi\) | |||||||
\(948\) | 20.7408 | − | 7.54904i | 0.673630 | − | 0.245181i | ||||
\(949\) | 1.46791 | 0.0476504 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −71.4252 | −2.31612 | ||||||||
\(952\) | −0.286989 | + | 0.104455i | −0.00930137 | + | 0.00338542i | ||||
\(953\) | 6.37922 | − | 36.1784i | 0.206643 | − | 1.17193i | −0.688190 | − | 0.725531i | \(-0.741594\pi\) |
0.894833 | − | 0.446401i | \(-0.147295\pi\) | |||||||
\(954\) | 10.1001 | − | 8.47502i | 0.327004 | − | 0.274389i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.39780 | − | 7.92734i | −0.0452082 | − | 0.256388i | ||||
\(957\) | 8.63816 | + | 14.9617i | 0.279232 | + | 0.483644i | ||||
\(958\) | −9.73829 | + | 16.8672i | −0.314630 | + | 0.544955i | ||||
\(959\) | −10.3969 | − | 3.78417i | −0.335734 | − | 0.122197i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.24123 | − | 12.5422i | 0.233588 | − | 0.404586i | ||||
\(962\) | −10.9966 | − | 19.0467i | −0.354544 | − | 0.614089i | ||||
\(963\) | 4.30587 | + | 24.4198i | 0.138755 | + | 0.786918i | ||||
\(964\) | 21.1759 | + | 17.7687i | 0.682031 | + | 0.572292i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.960637 | + | 5.44804i | −0.0309080 | + | 0.175288i | ||||
\(967\) | −53.8188 | + | 19.5885i | −1.73070 | + | 0.629922i | −0.998680 | − | 0.0513643i | \(-0.983643\pi\) |
−0.732017 | + | 0.681286i | \(0.761421\pi\) | |||||||
\(968\) | 10.0000 | 0.321412 | ||||||||
\(969\) | 2.64677 | + | 4.43458i | 0.0850266 | + | 0.142459i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.88191 | + | 0.684960i | −0.0603934 | + | 0.0219814i | −0.372040 | − | 0.928217i | \(-0.621342\pi\) |
0.311647 | + | 0.950198i | \(0.399119\pi\) | |||||||
\(972\) | −3.88279 | + | 22.0204i | −0.124541 | + | 0.706304i | ||||
\(973\) | 6.34389 | − | 5.32316i | 0.203376 | − | 0.170653i | ||||
\(974\) | 23.5947 | + | 19.7983i | 0.756022 | + | 0.634378i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.58512 | + | 4.47756i | 0.0827477 | + | 0.143323i | ||||
\(977\) | 13.6348 | − | 23.6161i | 0.436214 | − | 0.755545i | −0.561180 | − | 0.827694i | \(-0.689652\pi\) |
0.997394 | + | 0.0721487i | \(0.0229856\pi\) | |||||||
\(978\) | −12.5424 | − | 4.56504i | −0.401060 | − | 0.145974i | ||||
\(979\) | −16.5817 | − | 6.03525i | −0.529954 | − | 0.192887i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.0876 | − | 26.1326i | −0.481712 | − | 0.834349i | ||||
\(982\) | −1.82383 | − | 10.3434i | −0.0582006 | − | 0.330072i | ||||
\(983\) | 28.3935 | + | 23.8250i | 0.905613 | + | 0.759899i | 0.971279 | − | 0.237942i | \(-0.0764729\pi\) |
−0.0656666 | + | 0.997842i | \(0.520917\pi\) | |||||||
\(984\) | 9.54576 | − | 8.00984i | 0.304308 | − | 0.255344i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.00000 | + | 1.09191i | −0.0955395 | + | 0.0347735i | ||||
\(987\) | −10.5963 | −0.337283 | ||||||||
\(988\) | 11.8550 | + | 4.12122i | 0.377159 | + | 0.131113i | ||||
\(989\) | −10.5202 | −0.334524 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.61112 | − | 14.8084i | 0.0829449 | − | 0.470404i | −0.914836 | − | 0.403825i | \(-0.867680\pi\) |
0.997781 | − | 0.0665790i | \(-0.0212085\pi\) | |||||||
\(992\) | 3.11334 | − | 2.61240i | 0.0988487 | − | 0.0829439i | ||||
\(993\) | 15.9873 | + | 13.4149i | 0.507340 | + | 0.425709i | ||||
\(994\) | −1.38413 | − | 7.84981i | −0.0439020 | − | 0.248981i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 22.6741 | − | 39.2727i | 0.718457 | − | 1.24440i | ||||
\(997\) | −14.4944 | − | 5.27552i | −0.459041 | − | 0.167077i | 0.102140 | − | 0.994770i | \(-0.467431\pi\) |
−0.561182 | + | 0.827693i | \(0.689653\pi\) | |||||||
\(998\) | 7.48380 | + | 2.72388i | 0.236896 | + | 0.0862230i | ||||
\(999\) | −3.97906 | + | 6.89193i | −0.125892 | + | 0.218051i |
(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 | 950.2.l.b.651.1 | yes | 6 | |
5.2 | odd | 4 | 950.2.u.d.499.2 | 12 | |||
5.3 | odd | 4 | 950.2.u.d.499.1 | 12 | |||
5.4 | even | 2 | 950.2.l.e.651.1 | yes | 6 | ||
19.4 | even | 9 | inner | 950.2.l.b.251.1 | ✓ | 6 | |
95.4 | even | 18 | 950.2.l.e.251.1 | yes | 6 | ||
95.23 | odd | 36 | 950.2.u.d.99.2 | 12 | |||
95.42 | odd | 36 | 950.2.u.d.99.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.l.b.251.1 | ✓ | 6 | 19.4 | even | 9 | inner | |
950.2.l.b.651.1 | yes | 6 | 1.1 | even | 1 | trivial | |
950.2.l.e.251.1 | yes | 6 | 95.4 | even | 18 | ||
950.2.l.e.651.1 | yes | 6 | 5.4 | even | 2 | ||
950.2.u.d.99.1 | 12 | 95.42 | odd | 36 | |||
950.2.u.d.99.2 | 12 | 95.23 | odd | 36 | |||
950.2.u.d.499.1 | 12 | 5.3 | odd | 4 | |||
950.2.u.d.499.2 | 12 | 5.2 | odd | 4 |