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 | 251.1 | ||
Root | \(-0.173648 - 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.251 |
Dual form | 950.2.l.e.651.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{9}\right)\) |
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 | −0.798991 | − | 0.601344i | \(-0.794632\pi\) |
0.545134 | − | 0.838349i | \(-0.316479\pi\) | |||||||
\(4\) | 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 | \(-0.793970\pi\) |
0.921087 | + | 0.389358i | \(0.127303\pi\) | |||||||
\(8\) | −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 | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | 1.26604 | − | 2.19285i | 0.365476 | − | 0.633022i | ||||
\(13\) | 0.500000 | − | 2.83564i | 0.138675 | − | 0.786465i | −0.833555 | − | 0.552437i | \(-0.813698\pi\) |
0.972230 | − | 0.234028i | \(-0.0751909\pi\) | |||||||
\(14\) | −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 | \(-0.406960\pi\) |
−0.394790 | + | 0.918772i | \(0.629183\pi\) | |||||||
\(18\) | 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 | \(-0.391250\pi\) |
−0.869710 | + | 0.493564i | \(0.835694\pi\) | |||||||
\(24\) | −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 | −0.859927 | − | 0.510416i | \(-0.829491\pi\) |
−0.330653 | + | 0.943752i | \(0.607269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.03209 | − | 3.51968i | 0.364974 | − | 0.632153i | −0.623798 | − | 0.781586i | \(-0.714411\pi\) |
0.988772 | + | 0.149432i | \(0.0477446\pi\) | |||||||
\(32\) | 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 | \(-0.716066\pi\) | ||||
−0.627853 | + | 0.778332i | \(0.716066\pi\) | |||||||
\(38\) | 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 | −0.975919 | − | 0.218134i | \(-0.930003\pi\) |
0.842457 | − | 0.538763i | \(-0.181108\pi\) | |||||||
\(42\) | 1.26604 | + | 1.06234i | 0.195355 | + | 0.163922i | ||||
\(43\) | 2.40760 | − | 2.02022i | 0.367156 | − | 0.308081i | −0.440479 | − | 0.897763i | \(-0.645191\pi\) |
0.807635 | + | 0.589682i | \(0.200747\pi\) | |||||||
\(44\) | −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 | \(-0.765994\pi\) |
−0.137080 | + | 0.990560i | \(0.543772\pi\) | |||||||
\(48\) | 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 | \(-0.192261\pi\) |
−0.416392 | + | 0.909185i | \(0.636706\pi\) | |||||||
\(54\) | −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 | 0.684432 | − | 0.729076i | \(-0.260050\pi\) |
0.0556645 | + | 0.998450i | \(0.482272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.96064 | − | 3.32337i | −0.507108 | − | 0.425514i | 0.353002 | − | 0.935622i | \(-0.385161\pi\) |
−0.860110 | + | 0.510109i | \(0.829605\pi\) | |||||||
\(62\) | −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 | \(-0.594004\pi\) |
0.392004 | + | 0.919964i | \(0.371782\pi\) | |||||||
\(68\) | −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 | 0.112168 | − | 0.993689i | \(-0.464221\pi\) |
0.998071 | + | 0.0620884i | \(0.0197761\pi\) | |||||||
\(72\) | 2.61334 | + | 2.19285i | 0.307985 | + | 0.258430i | ||||
\(73\) | 0.0885259 | + | 0.502055i | 0.0103612 | + | 0.0587611i | 0.989550 | − | 0.144190i | \(-0.0460578\pi\) |
−0.979189 | + | 0.202951i | \(0.934947\pi\) | |||||||
\(74\) | 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 | −0.943429 | − | 0.331576i | \(-0.892420\pi\) |
0.773127 | − | 0.634251i | \(-0.218691\pi\) | |||||||
\(80\) | 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 | −0.332015 | + | 0.943274i | \(0.607728\pi\) |
−0.650892 | + | 0.759170i | \(0.725605\pi\) | |||||||
\(84\) | −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 | 0.186259 | + | 0.982501i | \(0.440364\pi\) |
−0.511061 | + | 0.859544i | \(0.670748\pi\) | |||||||
\(90\) | 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 | \(-0.652307\pi\) |
−0.923313 | + | 0.384049i | \(0.874529\pi\) | |||||||
\(98\) | −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 | 0.529188 | + | 0.848505i | \(0.322497\pi\) |
−0.787480 | + | 0.616341i | \(0.788614\pi\) | |||||||
\(102\) | 0.592396 | − | 1.02606i | 0.0586560 | − | 0.101595i | ||||
\(103\) | 3.61334 | + | 6.25849i | 0.356033 | + | 0.616667i | 0.987294 | − | 0.158903i | \(-0.0507957\pi\) |
−0.631261 | + | 0.775570i | \(0.717462\pi\) | |||||||
\(104\) | −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 | \(-0.719060\pi\) |
0.986484 | + | 0.163855i | \(0.0523929\pi\) | |||||||
\(108\) | −0.180922 | + | 1.02606i | −0.0174092 | + | 0.0987327i | ||||
\(109\) | 6.77584 | − | 5.68561i | 0.649008 | − | 0.544583i | −0.257762 | − | 0.966209i | \(-0.582985\pi\) |
0.906770 | + | 0.421626i | \(0.138540\pi\) | |||||||
\(110\) | 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 | \(-0.477670\pi\) | ||||
0.0700931 | + | 0.997540i | \(0.477670\pi\) | |||||||
\(114\) | 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 | −0.431461 | − | 0.902131i | \(-0.642002\pi\) |
0.713988 | − | 0.700158i | \(-0.246887\pi\) | |||||||
\(128\) | 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 | 0.0311339 | − | 0.999515i | \(-0.490088\pi\) |
−0.618626 | + | 0.785686i | \(0.712310\pi\) | |||||||
\(132\) | 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 | \(-0.535533\pi\) |
−0.998022 | + | 0.0628601i | \(0.979978\pi\) | |||||||
\(138\) | 6.49273 | − | 5.44804i | 0.552698 | − | 0.463768i | ||||
\(139\) | 2.20321 | − | 12.4950i | 0.186874 | − | 1.05981i | −0.736650 | − | 0.676274i | \(-0.763594\pi\) |
0.923524 | − | 0.383541i | \(-0.125295\pi\) | |||||||
\(140\) | 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 | 0.950780 | − | 0.309865i | \(-0.100284\pi\) |
−0.999422 | + | 0.0340079i | \(0.989173\pi\) | |||||||
\(150\) | 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 | \(-0.900065\pi\) |
0.138972 | + | 0.990296i | \(0.455620\pi\) | |||||||
\(158\) | −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 | \(-0.232854\pi\) |
−0.950590 | + | 0.310449i | \(0.899521\pi\) | |||||||
\(164\) | 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 | \(-0.250922\pi\) |
−0.575948 | + | 0.817487i | \(0.695367\pi\) | |||||||
\(168\) | 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 | \(-0.480266\pi\) |
−0.594091 | + | 0.804398i | \(0.702488\pi\) | |||||||
\(174\) | −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 | 0.722569 | − | 0.691299i | \(-0.242961\pi\) |
−0.959967 | + | 0.280113i | \(0.909628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5449 | + | 4.56596i | −0.932454 | + | 0.339385i | −0.763182 | − | 0.646184i | \(-0.776364\pi\) |
−0.169272 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(182\) | 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 | −0.919298 | − | 0.393563i | \(-0.871242\pi\) |
0.729251 | − | 0.684246i | \(-0.239869\pi\) | |||||||
\(194\) | 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 | −0.345760 | − | 0.938323i | \(-0.612379\pi\) |
0.985492 | − | 0.169724i | \(-0.0542877\pi\) | |||||||
\(198\) | 1.70574 | + | 2.95442i | 0.121221 | + | 0.209962i | ||||
\(199\) | 23.2729 | − | 8.47065i | 1.64977 | − | 0.600468i | 0.661065 | − | 0.750328i | \(-0.270105\pi\) |
0.988707 | + | 0.149860i | \(0.0478823\pi\) | |||||||
\(200\) | 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 | −0.0280195 | − | 0.999607i | \(-0.508920\pi\) |
−0.663999 | + | 0.747733i | \(0.731142\pi\) | |||||||
\(212\) | 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 | \(-0.597024\pi\) |
0.887298 | + | 0.461196i | \(0.152579\pi\) | |||||||
\(224\) | −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 | \(-0.342306\pi\) | ||||
0.475392 | + | 0.879774i | \(0.342306\pi\) | |||||||
\(228\) | −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 | \(-0.840109\pi\) |
0.321943 | + | 0.946759i | \(0.395664\pi\) | |||||||
\(234\) | 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 | 0.966333 | − | 0.257294i | \(-0.0828308\pi\) |
−0.705990 | + | 0.708222i | \(0.749497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.80019 | − | 27.2232i | 0.309208 | − | 1.75360i | −0.293799 | − | 0.955867i | \(-0.594920\pi\) |
0.603007 | − | 0.797736i | \(-0.293969\pi\) | |||||||
\(242\) | −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 | −0.0699563 | − | 0.997550i | \(-0.522286\pi\) |
−0.994543 | + | 0.104329i | \(0.966730\pi\) | |||||||
\(252\) | −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 | \(-0.463756\pi\) |
0.725662 | + | 0.688051i | \(0.241533\pi\) | |||||||
\(258\) | 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 | \(-0.00856652\pi\) |
−0.948556 | + | 0.316610i | \(0.897455\pi\) | |||||||
\(264\) | −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 | 0.994276 | − | 0.106839i | \(-0.0340730\pi\) |
−0.970855 | + | 0.239666i | \(0.922962\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3917 | − | 13.7543i | 0.995726 | − | 0.835513i | 0.00933905 | − | 0.999956i | \(-0.497027\pi\) |
0.986387 | + | 0.164443i | \(0.0525828\pi\) | |||||||
\(272\) | 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 | \(-0.0919262\pi\) |
−0.725935 | + | 0.687763i | \(0.758593\pi\) | |||||||
\(278\) | −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 | 0.261186 | − | 0.965288i | \(-0.415886\pi\) |
−0.905269 | + | 0.424839i | \(0.860331\pi\) | |||||||
\(282\) | −2.81908 | − | 15.9878i | −0.167874 | − | 0.952059i | ||||
\(283\) | −4.89053 | − | 1.78001i | −0.290712 | − | 0.105810i | 0.192548 | − | 0.981288i | \(-0.438325\pi\) |
−0.483259 | + | 0.875477i | \(0.660547\pi\) | |||||||
\(284\) | 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 | 0.932527 | + | 0.361101i | \(0.117599\pi\) |
−0.153541 | + | 0.988142i | \(0.549068\pi\) | |||||||
\(294\) | −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 | 0.403684 | + | 0.914899i | \(0.367730\pi\) |
−0.0664248 | + | 0.997791i | \(0.521159\pi\) | |||||||
\(308\) | 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 | −0.458875 | − | 0.888501i | \(-0.651748\pi\) |
0.998902 | − | 0.0468526i | \(-0.0149191\pi\) | |||||||
\(312\) | 3.64543 | + | 6.31407i | 0.206382 | + | 0.357464i | ||||
\(313\) | 3.37211 | − | 1.22735i | 0.190603 | − | 0.0693738i | −0.244955 | − | 0.969534i | \(-0.578773\pi\) |
0.435558 | + | 0.900161i | \(0.356551\pi\) | |||||||
\(314\) | 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 | −0.463484 | − | 0.886105i | \(-0.653401\pi\) |
0.738599 | − | 0.674145i | \(-0.235488\pi\) | |||||||
\(318\) | −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 | 0.730258 | − | 0.683172i | \(-0.239400\pi\) |
−0.956773 | + | 0.290836i | \(0.906067\pi\) | |||||||
\(332\) | −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 | \(-0.686446\pi\) |
0.724650 | + | 0.689117i | \(0.242001\pi\) | |||||||
\(338\) | −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 | \(-0.714226\pi\) |
0.661827 | + | 0.749657i | \(0.269781\pi\) | |||||||
\(348\) | −3.00000 | + | 17.0138i | −0.160817 | + | 0.912038i | ||||
\(349\) | 7.03936 | − | 12.1925i | 0.376808 | − | 0.652651i | −0.613787 | − | 0.789471i | \(-0.710355\pi\) |
0.990596 | + | 0.136820i | \(0.0436882\pi\) | |||||||
\(350\) | 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 | 1.00000 | 0.000224734i | \(7.15350e-5\pi\) | |
−0.499805 | + | 0.866138i | \(0.666595\pi\) | |||||||
\(354\) | −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 | −0.501984 | − | 0.864877i | \(-0.667396\pi\) |
−0.940474 | + | 0.339865i | \(0.889619\pi\) | |||||||
\(360\) | 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 | 0.805883 | + | 0.592074i | \(0.201691\pi\) |
−0.959784 | + | 0.280739i | \(0.909420\pi\) | |||||||
\(368\) | 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 | \(-0.799255\pi\) |
0.914495 | + | 0.404598i | \(0.132589\pi\) | |||||||
\(374\) | −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 | −0.710876 | − | 0.703318i | \(-0.751701\pi\) |
0.427456 | − | 0.904036i | \(-0.359410\pi\) | |||||||
\(384\) | −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 | 0.410943 | − | 0.911661i | \(-0.365200\pi\) |
0.900805 | + | 0.434224i | \(0.142977\pi\) | |||||||
\(390\) | 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 | \(-0.630805\pi\) |
−0.895284 | + | 0.445497i | \(0.853027\pi\) | |||||||
\(398\) | −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 | −0.337831 | − | 0.941207i | \(-0.609693\pi\) |
−0.863789 | + | 0.503853i | \(0.831915\pi\) | |||||||
\(402\) | 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 | 0.0988809 | − | 0.995099i | \(-0.468474\pi\) |
0.715385 | + | 0.698731i | \(0.246252\pi\) | |||||||
\(410\) | 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 | 0.953676 | − | 0.300835i | \(-0.0972652\pi\) |
−0.999054 | + | 0.0434844i | \(0.986154\pi\) | |||||||
\(422\) | 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 | 0.744802 | + | 0.667285i | \(0.232544\pi\) |
−0.928110 | + | 0.372305i | \(0.878567\pi\) | |||||||
\(432\) | −0.798133 | + | 0.669713i | −0.0384002 | + | 0.0322216i | ||||
\(433\) | 6.11515 | + | 5.13122i | 0.293875 | + | 0.246591i | 0.777790 | − | 0.628525i | \(-0.216341\pi\) |
−0.483914 | + | 0.875115i | \(0.660785\pi\) | |||||||
\(434\) | 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 | 0.881290 | − | 0.472575i | \(-0.156675\pi\) |
0.371342 | + | 0.928496i | \(0.378898\pi\) | |||||||
\(440\) | 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 | −0.936741 | − | 0.350024i | \(-0.886173\pi\) |
0.999964 | − | 0.00853096i | \(-0.00271552\pi\) | |||||||
\(444\) | −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 | −0.999981 | − | 0.00620692i | \(-0.998024\pi\) |
0.505366 | + | 0.862905i | \(0.331358\pi\) | |||||||
\(450\) | 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 | \(-0.285724\pi\) | ||||
0.623465 | + | 0.781851i | \(0.285724\pi\) | |||||||
\(458\) | 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 | −0.740957 | − | 0.671553i | \(-0.765628\pi\) |
0.532685 | + | 0.846314i | \(0.321183\pi\) | |||||||
\(462\) | −0.286989 | + | 1.62760i | −0.0133519 | + | 0.0757226i | ||||
\(463\) | 13.8610 | − | 24.0079i | 0.644174 | − | 1.11574i | −0.340318 | − | 0.940310i | \(-0.610535\pi\) |
0.984492 | − | 0.175431i | \(-0.0561320\pi\) | |||||||
\(464\) | −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 | \(-0.0130125\pi\) |
−0.534975 | + | 0.844868i | \(0.679679\pi\) | |||||||
\(468\) | −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 | 0.234796 | − | 0.972045i | \(-0.424558\pi\) |
−0.916505 | + | 0.400023i | \(0.869002\pi\) | |||||||
\(480\) | 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 | 0.271353 | + | 0.962480i | \(0.412529\pi\) |
−0.969209 | + | 0.246241i | \(0.920804\pi\) | |||||||
\(488\) | −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 | 0.997905 | + | 0.0646952i | \(0.0206075\pi\) |
−0.915597 | + | 0.402097i | \(0.868281\pi\) | |||||||
\(492\) | −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 | −0.495936 | − | 0.868359i | \(-0.665175\pi\) |
0.769048 | + | 0.639191i | \(0.220731\pi\) | |||||||
\(500\) | 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 | \(-0.696581\pi\) |
0.0804683 | + | 0.996757i | \(0.474358\pi\) | |||||||
\(504\) | 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 | 0.401036 | − | 0.916062i | \(-0.368650\pi\) |
−0.832506 | + | 0.554016i | \(0.813095\pi\) | |||||||
\(510\) | 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 | 0.998084 | + | 0.0618674i | \(0.0197056\pi\) |
−0.445463 | + | 0.895300i | \(0.646961\pi\) | |||||||
\(522\) | −21.8726 | + | 7.96097i | −0.957337 | + | 0.348442i | ||||
\(523\) | 41.4406 | − | 15.0832i | 1.81207 | − | 0.659540i | 0.815320 | − | 0.579011i | \(-0.196561\pi\) |
0.996752 | − | 0.0805294i | \(-0.0256611\pi\) | |||||||
\(524\) | −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 | 0.448202 | − | 0.893933i | \(-0.352065\pi\) |
0.917951 | + | 0.396694i | \(0.129842\pi\) | |||||||
\(542\) | −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 | \(-0.465527\pi\) |
−0.960269 | + | 0.279077i | \(0.909972\pi\) | |||||||
\(548\) | −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 | −0.829529 | − | 0.558464i | \(-0.811391\pi\) |
0.970508 | − | 0.241069i | \(-0.0774980\pi\) | |||||||
\(558\) | 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 | \(-0.779852\pi\) |
0.937444 | + | 0.348136i | \(0.113185\pi\) | |||||||
\(564\) | −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 | 0.248278 | + | 0.968689i | \(0.420135\pi\) |
−0.963048 | + | 0.269329i | \(0.913198\pi\) | |||||||
\(578\) | 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 | \(-0.234390\pi\) |
0.135886 | + | 0.990724i | \(0.456612\pi\) | |||||||
\(588\) | 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 | \(-0.0472208\pi\) |
0.0261814 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(594\) | 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 | −0.237029 | − | 0.971503i | \(-0.576173\pi\) |
0.442895 | + | 0.896573i | \(0.353951\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.8319 | + | 30.8857i | −0.727377 | + | 1.25985i | 0.230611 | + | 0.973046i | \(0.425928\pi\) |
−0.957988 | + | 0.286808i | \(0.907406\pi\) | |||||||
\(602\) | −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 | \(-0.455079\pi\) | ||||
0.140656 | + | 0.990059i | \(0.455079\pi\) | |||||||
\(608\) | −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 | \(-0.858659\pi\) |
0.266251 | + | 0.963904i | \(0.414215\pi\) | |||||||
\(614\) | 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 | \(-0.430435\pi\) |
0.793583 | + | 0.608462i | \(0.208213\pi\) | |||||||
\(618\) | −17.1951 | + | 6.25849i | −0.691687 | + | 0.251753i | ||||
\(619\) | 2.15405 | + | 3.73092i | 0.0865785 | + | 0.149958i | 0.906063 | − | 0.423143i | \(-0.139073\pi\) |
−0.819484 | + | 0.573102i | \(0.805740\pi\) | |||||||
\(620\) | 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 | 0.406966 | − | 0.913443i | \(-0.366587\pi\) |
−0.828897 | + | 0.559401i | \(0.811031\pi\) | |||||||
\(632\) | −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 | −0.593334 | − | 0.804956i | \(-0.702189\pi\) |
0.689696 | + | 0.724099i | \(0.257744\pi\) | |||||||
\(642\) | 14.0988 | + | 11.8303i | 0.556435 | + | 0.466904i | ||||
\(643\) | 2.09327 | + | 11.8715i | 0.0825507 | + | 0.468168i | 0.997858 | + | 0.0654126i | \(0.0208364\pi\) |
−0.915308 | + | 0.402755i | \(0.868053\pi\) | |||||||
\(644\) | −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 | \(-0.334241\pi\) | ||||
0.497528 | + | 0.867448i | \(0.334241\pi\) | |||||||
\(648\) | 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 | \(-0.842281\pi\) |
0.851630 | + | 0.524143i | \(0.175614\pi\) | |||||||
\(654\) | 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 | −0.986209 | − | 0.165504i | \(-0.947075\pi\) |
0.983339 | + | 0.181780i | \(0.0581860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.34074 | − | 6.99871i | −0.324417 | − | 0.272218i | 0.466003 | − | 0.884783i | \(-0.345693\pi\) |
−0.790420 | + | 0.612565i | \(0.790138\pi\) | |||||||
\(662\) | 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 | 0.974487 | + | 0.224446i | \(0.0720573\pi\) |
−0.292867 | + | 0.956153i | \(0.594609\pi\) | |||||||
\(674\) | −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 | −0.376566 | − | 0.926390i | \(-0.622895\pi\) |
0.990560 | − | 0.137079i | \(-0.0437715\pi\) | |||||||
\(678\) | −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 | \(-0.303673\pi\) | ||||
0.578410 | + | 0.815746i | \(0.303673\pi\) | |||||||
\(684\) | 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 | −0.147170 | − | 0.989111i | \(-0.547016\pi\) |
0.930180 | − | 0.367103i | \(-0.119650\pi\) | |||||||
\(692\) | −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 | 0.651261 | − | 0.758854i | \(-0.274240\pi\) |
0.0111135 | + | 0.999938i | \(0.496462\pi\) | |||||||
\(702\) | −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 | 0.562629 | + | 0.826710i | \(0.309790\pi\) |
−0.811449 | + | 0.584423i | \(0.801321\pi\) | |||||||
\(710\) | 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 | 0.989178 | + | 0.146720i | \(0.0468715\pi\) |
−0.879342 | + | 0.476190i | \(0.842017\pi\) | |||||||
\(720\) | 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 | \(-0.918651\pi\) |
0.0809452 | + | 0.996719i | \(0.474206\pi\) | |||||||
\(728\) | −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 | \(-0.232308\pi\) |
−0.950057 | + | 0.312078i | \(0.898975\pi\) | |||||||
\(734\) | 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 | 0.537744 | − | 0.843108i | \(-0.319277\pi\) |
−0.130004 | + | 0.991514i | \(0.541499\pi\) | |||||||
\(740\) | 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 | \(-0.321303\pi\) |
−0.136313 | + | 0.990666i | \(0.543525\pi\) | |||||||
\(744\) | 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 | 0.495243 | − | 0.868755i | \(-0.335079\pi\) |
0.937803 | + | 0.347169i | \(0.112857\pi\) | |||||||
\(752\) | −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 | 0.708280 | + | 0.705932i | \(0.249471\pi\) |
−0.424123 | + | 0.905605i | \(0.639417\pi\) | |||||||
\(758\) | 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 | 0.290204 | − | 0.956965i | \(-0.406277\pi\) |
0.837434 | + | 0.546538i | \(0.184055\pi\) | |||||||
\(770\) | 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 | −0.758263 | − | 0.651949i | \(-0.773952\pi\) |
0.935514 | − | 0.353290i | \(-0.114937\pi\) | |||||||
\(774\) | 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 | \(-0.298416\pi\) |
−0.993989 | + | 0.109477i | \(0.965083\pi\) | |||||||
\(788\) | 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 | \(-0.679186\pi\) | ||||
−0.533665 | + | 0.845696i | \(0.679186\pi\) | |||||||
\(798\) | −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 | 0.958380 | − | 0.285496i | \(-0.0921583\pi\) |
−0.726437 | + | 0.687233i | \(0.758825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.92144 | + | 33.5821i | −0.207930 | + | 1.17923i | 0.684833 | + | 0.728700i | \(0.259875\pi\) |
−0.892762 | + | 0.450528i | \(0.851236\pi\) | |||||||
\(812\) | −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 | 0.714279 | − | 0.699861i | \(-0.246755\pi\) |
−0.565195 | + | 0.824957i | \(0.691199\pi\) | |||||||
\(822\) | 32.8803 | − | 27.5899i | 1.14683 | − | 0.962307i | ||||
\(823\) | 1.23648 | − | 7.01244i | 0.0431010 | − | 0.244438i | −0.955644 | − | 0.294525i | \(-0.904839\pi\) |
0.998745 | + | 0.0500866i | \(0.0159497\pi\) | |||||||
\(824\) | 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 | \(-0.625251\pi\) |
0.299954 | + | 0.953954i | \(0.403029\pi\) | |||||||
\(828\) | 5.70961 | + | 9.88933i | 0.198423 | + | 0.343678i | ||||
\(829\) | 16.1022 | − | 27.8898i | 0.559252 | − | 0.968654i | −0.438307 | − | 0.898826i | \(-0.644422\pi\) |
0.997559 | − | 0.0698281i | \(-0.0222451\pi\) | |||||||
\(830\) | 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 | −0.804422 | − | 0.594058i | \(-0.797525\pi\) |
0.552730 | − | 0.833360i | \(-0.313586\pi\) | |||||||
\(840\) | 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 | \(-0.604673\pi\) |
−0.855736 | + | 0.517413i | \(0.826895\pi\) | |||||||
\(854\) | 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 | \(-0.144302\pi\) |
0.407145 | + | 0.913363i | \(0.366524\pi\) | |||||||
\(858\) | 1.26604 | + | 7.18009i | 0.0432220 | + | 0.245124i | ||||
\(859\) | −10.0018 | − | 8.39252i | −0.341257 | − | 0.286349i | 0.456011 | − | 0.889974i | \(-0.349278\pi\) |
−0.797268 | + | 0.603625i | \(0.793722\pi\) | |||||||
\(860\) | 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 | −0.935465 | − | 0.353420i | \(-0.885019\pi\) |
0.161662 | − | 0.986846i | \(-0.448315\pi\) | |||||||
\(864\) | 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 | −0.578670 | − | 0.815562i | \(-0.696428\pi\) |
0.264834 | − | 0.964294i | \(-0.414683\pi\) | |||||||
\(878\) | −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 | −0.926634 | − | 0.375965i | \(-0.877311\pi\) |
0.788912 | + | 0.614506i | \(0.210645\pi\) | |||||||
\(882\) | 11.2135 | + | 19.4223i | 0.377577 | + | 0.653983i | ||||
\(883\) | −29.0672 | + | 10.5796i | −0.978188 | + | 0.356031i | −0.781136 | − | 0.624362i | \(-0.785359\pi\) |
−0.197053 | + | 0.980393i | \(0.563137\pi\) | |||||||
\(884\) | −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 | 0.939025 | + | 0.343848i | \(0.111730\pi\) |
−0.999998 | + | 0.00194565i | \(0.999381\pi\) | |||||||
\(888\) | 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 | \(-0.855669\pi\) |
0.275296 | + | 0.961360i | \(0.411224\pi\) | |||||||
\(908\) | 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 | −0.107965 | − | 0.994155i | \(-0.534433\pi\) |
0.914946 | − | 0.403577i | \(-0.132233\pi\) | |||||||
\(920\) | 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 | −0.192123 | − | 0.981371i | \(-0.561537\pi\) |
−0.777988 | + | 0.628279i | \(0.783760\pi\) | |||||||
\(930\) | 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 | \(-0.909715\pi\) |
0.997860 | + | 0.0653804i | \(0.0208261\pi\) | |||||||
\(938\) | −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 | −0.633194 | − | 0.773994i | \(-0.718256\pi\) |
0.0124591 | + | 0.999922i | \(0.496034\pi\) | |||||||
\(942\) | −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 | \(-0.0268705\pi\) |
−0.965184 | + | 0.261571i | \(0.915759\pi\) | |||||||
\(948\) | −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 | −0.894833 | − | 0.446401i | \(-0.852705\pi\) |
0.688190 | − | 0.725531i | \(-0.258406\pi\) | |||||||
\(954\) | 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 | \(-0.0163570\pi\) |
0.732017 | + | 0.681286i | \(0.238579\pi\) | |||||||
\(968\) | −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 | 0.311647 | − | 0.950198i | \(-0.399119\pi\) |
−0.372040 | + | 0.928217i | \(0.621342\pi\) | |||||||
\(972\) | 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 | \(-0.310348\pi\) |
−0.997394 | + | 0.0721487i | \(0.977014\pi\) | |||||||
\(978\) | 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 | \(-0.923527\pi\) |
0.0656666 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(984\) | 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 | 0.997781 | + | 0.0665790i | \(0.0212085\pi\) |
−0.914836 | + | 0.403825i | \(0.867680\pi\) | |||||||
\(992\) | −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 | \(-0.532569\pi\) |
0.561182 | + | 0.827693i | \(0.310347\pi\) | |||||||
\(998\) | −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.e.251.1 | yes | 6 | |
5.2 | odd | 4 | 950.2.u.d.99.2 | 12 | |||
5.3 | odd | 4 | 950.2.u.d.99.1 | 12 | |||
5.4 | even | 2 | 950.2.l.b.251.1 | ✓ | 6 | ||
19.5 | even | 9 | inner | 950.2.l.e.651.1 | yes | 6 | |
95.24 | even | 18 | 950.2.l.b.651.1 | yes | 6 | ||
95.43 | odd | 36 | 950.2.u.d.499.2 | 12 | |||
95.62 | odd | 36 | 950.2.u.d.499.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.l.b.251.1 | ✓ | 6 | 5.4 | even | 2 | ||
950.2.l.b.651.1 | yes | 6 | 95.24 | even | 18 | ||
950.2.l.e.251.1 | yes | 6 | 1.1 | even | 1 | trivial | |
950.2.l.e.651.1 | yes | 6 | 19.5 | even | 9 | inner | |
950.2.u.d.99.1 | 12 | 5.3 | odd | 4 | |||
950.2.u.d.99.2 | 12 | 5.2 | odd | 4 | |||
950.2.u.d.499.1 | 12 | 95.62 | odd | 36 | |||
950.2.u.d.499.2 | 12 | 95.43 | odd | 36 |