Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 191.6 | ||
Character | \(\chi\) | \(=\) | 1110.191 |
Dual form | 1110.2.u.e.401.6 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.912132 | + | 1.47242i | −0.526620 | + | 0.850101i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 1.68613 | − | 0.396182i | 0.688360 | − | 0.161741i | ||||
\(7\) | 0.363832 | 0.137516 | 0.0687578 | − | 0.997633i | \(-0.478096\pi\) | ||||
0.0687578 | + | 0.997633i | \(0.478096\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −1.33603 | − | 2.68608i | −0.445344 | − | 0.895360i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.23669 | 0.372877 | 0.186438 | − | 0.982467i | \(-0.440306\pi\) | ||||
0.186438 | + | 0.982467i | \(0.440306\pi\) | |||||||
\(12\) | −1.47242 | − | 0.912132i | −0.425051 | − | 0.263310i | ||||
\(13\) | 2.54719 | + | 2.54719i | 0.706464 | + | 0.706464i | 0.965790 | − | 0.259326i | \(-0.0835002\pi\) |
−0.259326 | + | 0.965790i | \(0.583500\pi\) | |||||||
\(14\) | −0.257268 | − | 0.257268i | −0.0687578 | − | 0.0687578i | ||||
\(15\) | −0.396182 | − | 1.68613i | −0.102294 | − | 0.435357i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.79453 | − | 2.79453i | 0.677773 | − | 0.677773i | −0.281723 | − | 0.959496i | \(-0.590906\pi\) |
0.959496 | + | 0.281723i | \(0.0909058\pi\) | |||||||
\(18\) | −0.954629 | + | 2.84406i | −0.225008 | + | 0.670352i | ||||
\(19\) | 1.40229 | + | 1.40229i | 0.321706 | + | 0.321706i | 0.849421 | − | 0.527715i | \(-0.176951\pi\) |
−0.527715 | + | 0.849421i | \(0.676951\pi\) | |||||||
\(20\) | −0.707107 | − | 0.707107i | −0.158114 | − | 0.158114i | ||||
\(21\) | −0.331863 | + | 0.535713i | −0.0724184 | + | 0.116902i | ||||
\(22\) | −0.874474 | − | 0.874474i | −0.186438 | − | 0.186438i | ||||
\(23\) | 0.456993 | − | 0.456993i | 0.0952897 | − | 0.0952897i | −0.657855 | − | 0.753145i | \(-0.728536\pi\) |
0.753145 | + | 0.657855i | \(0.228536\pi\) | |||||||
\(24\) | 0.396182 | + | 1.68613i | 0.0808704 | + | 0.344180i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | − | 3.60228i | − | 0.706464i | ||||||
\(27\) | 5.17367 | + | 0.482863i | 0.995673 | + | 0.0929270i | ||||
\(28\) | 0.363832i | 0.0687578i | ||||||||
\(29\) | −1.61230 | − | 1.61230i | −0.299397 | − | 0.299397i | 0.541381 | − | 0.840778i | \(-0.317902\pi\) |
−0.840778 | + | 0.541381i | \(0.817902\pi\) | |||||||
\(30\) | −0.912132 | + | 1.47242i | −0.166532 | + | 0.268826i | ||||
\(31\) | 0.163461 | − | 0.163461i | 0.0293585 | − | 0.0293585i | −0.692275 | − | 0.721634i | \(-0.743392\pi\) |
0.721634 | + | 0.692275i | \(0.243392\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −1.12803 | + | 1.82093i | −0.196364 | + | 0.316983i | ||||
\(34\) | −3.95206 | −0.677773 | ||||||||
\(35\) | −0.257268 | + | 0.257268i | −0.0434863 | + | 0.0434863i | ||||
\(36\) | 2.68608 | − | 1.33603i | 0.447680 | − | 0.222672i | ||||
\(37\) | 5.07126 | + | 3.35892i | 0.833709 | + | 0.552204i | ||||
\(38\) | − | 1.98313i | − | 0.321706i | ||||||
\(39\) | −6.07391 | + | 1.42716i | −0.972604 | + | 0.228528i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −0.545166 | −0.0851406 | −0.0425703 | − | 0.999093i | \(-0.513555\pi\) | ||||
−0.0425703 | + | 0.999093i | \(0.513555\pi\) | |||||||
\(42\) | 0.613469 | − | 0.144144i | 0.0946603 | − | 0.0222419i | ||||
\(43\) | 4.75447 | + | 4.75447i | 0.725050 | + | 0.725050i | 0.969629 | − | 0.244579i | \(-0.0786498\pi\) |
−0.244579 | + | 0.969629i | \(0.578650\pi\) | |||||||
\(44\) | 1.23669i | 0.186438i | ||||||||
\(45\) | 2.84406 | + | 0.954629i | 0.423968 | + | 0.142308i | ||||
\(46\) | −0.646286 | −0.0952897 | ||||||||
\(47\) | − | 1.60456i | − | 0.234049i | −0.993129 | − | 0.117025i | \(-0.962664\pi\) | ||
0.993129 | − | 0.117025i | \(-0.0373357\pi\) | |||||||
\(48\) | 0.912132 | − | 1.47242i | 0.131655 | − | 0.212525i | ||||
\(49\) | −6.86763 | −0.981089 | ||||||||
\(50\) | −0.707107 | + | 0.707107i | −0.100000 | + | 0.100000i | ||||
\(51\) | 1.56574 | + | 6.66370i | 0.219247 | + | 0.933105i | ||||
\(52\) | −2.54719 | + | 2.54719i | −0.353232 | + | 0.353232i | ||||
\(53\) | 8.02046i | 1.10169i | 0.834606 | + | 0.550847i | \(0.185695\pi\) | ||||
−0.834606 | + | 0.550847i | \(0.814305\pi\) | |||||||
\(54\) | −3.31690 | − | 3.99977i | −0.451373 | − | 0.544300i | ||||
\(55\) | −0.874474 | + | 0.874474i | −0.117914 | + | 0.117914i | ||||
\(56\) | 0.257268 | − | 0.257268i | 0.0343789 | − | 0.0343789i | ||||
\(57\) | −3.34382 | + | 0.785681i | −0.442900 | + | 0.104066i | ||||
\(58\) | 2.28014i | 0.299397i | ||||||||
\(59\) | −6.45749 | + | 6.45749i | −0.840694 | + | 0.840694i | −0.988949 | − | 0.148255i | \(-0.952634\pi\) |
0.148255 | + | 0.988949i | \(0.452634\pi\) | |||||||
\(60\) | 1.68613 | − | 0.396182i | 0.217679 | − | 0.0511469i | ||||
\(61\) | 2.60993 | − | 2.60993i | 0.334167 | − | 0.334167i | −0.520000 | − | 0.854167i | \(-0.674068\pi\) |
0.854167 | + | 0.520000i | \(0.174068\pi\) | |||||||
\(62\) | −0.231169 | −0.0293585 | ||||||||
\(63\) | −0.486091 | − | 0.977282i | −0.0612417 | − | 0.123126i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −3.60228 | −0.446807 | ||||||||
\(66\) | 2.08523 | − | 0.489956i | 0.256674 | − | 0.0603094i | ||||
\(67\) | 4.94984i | 0.604719i | 0.953194 | + | 0.302359i | \(0.0977743\pi\) | ||||
−0.953194 | + | 0.302359i | \(0.902226\pi\) | |||||||
\(68\) | 2.79453 | + | 2.79453i | 0.338887 | + | 0.338887i | ||||
\(69\) | 0.256047 | + | 1.08972i | 0.0308244 | + | 0.131187i | ||||
\(70\) | 0.363832 | 0.0434863 | ||||||||
\(71\) | 14.8100i | 1.75762i | 0.477174 | + | 0.878809i | \(0.341661\pi\) | ||||
−0.477174 | + | 0.878809i | \(0.658339\pi\) | |||||||
\(72\) | −2.84406 | − | 0.954629i | −0.335176 | − | 0.112504i | ||||
\(73\) | 1.60743i | 0.188135i | 0.995566 | + | 0.0940675i | \(0.0299869\pi\) | ||||
−0.995566 | + | 0.0940675i | \(0.970013\pi\) | |||||||
\(74\) | −1.21080 | − | 5.96104i | −0.140753 | − | 0.692956i | ||||
\(75\) | 1.47242 | + | 0.912132i | 0.170020 | + | 0.105324i | ||||
\(76\) | −1.40229 | + | 1.40229i | −0.160853 | + | 0.160853i | ||||
\(77\) | 0.449949 | 0.0512764 | ||||||||
\(78\) | 5.30406 | + | 3.28575i | 0.600566 | + | 0.372038i | ||||
\(79\) | 2.32156 | + | 2.32156i | 0.261196 | + | 0.261196i | 0.825540 | − | 0.564344i | \(-0.190871\pi\) |
−0.564344 | + | 0.825540i | \(0.690871\pi\) | |||||||
\(80\) | 0.707107 | − | 0.707107i | 0.0790569 | − | 0.0790569i | ||||
\(81\) | −5.43004 | + | 7.17737i | −0.603338 | + | 0.797485i | ||||
\(82\) | 0.385490 | + | 0.385490i | 0.0425703 | + | 0.0425703i | ||||
\(83\) | 8.43976i | 0.926384i | 0.886258 | + | 0.463192i | \(0.153296\pi\) | ||||
−0.886258 | + | 0.463192i | \(0.846704\pi\) | |||||||
\(84\) | −0.535713 | − | 0.331863i | −0.0584511 | − | 0.0362092i | ||||
\(85\) | 3.95206i | 0.428662i | ||||||||
\(86\) | − | 6.72384i | − | 0.725050i | ||||||
\(87\) | 3.84461 | − | 0.903350i | 0.412186 | − | 0.0968493i | ||||
\(88\) | 0.874474 | − | 0.874474i | 0.0932192 | − | 0.0932192i | ||||
\(89\) | −0.550261 | − | 0.550261i | −0.0583276 | − | 0.0583276i | 0.677341 | − | 0.735669i | \(-0.263132\pi\) |
−0.735669 | + | 0.677341i | \(0.763132\pi\) | |||||||
\(90\) | −1.33603 | − | 2.68608i | −0.140830 | − | 0.283138i | ||||
\(91\) | 0.926751 | + | 0.926751i | 0.0971499 | + | 0.0971499i | ||||
\(92\) | 0.456993 | + | 0.456993i | 0.0476448 | + | 0.0476448i | ||||
\(93\) | 0.0915850 | + | 0.389781i | 0.00949692 | + | 0.0404184i | ||||
\(94\) | −1.13460 | + | 1.13460i | −0.117025 | + | 0.117025i | ||||
\(95\) | −1.98313 | −0.203465 | ||||||||
\(96\) | −1.68613 | + | 0.396182i | −0.172090 | + | 0.0404352i | ||||
\(97\) | −0.870659 | − | 0.870659i | −0.0884021 | − | 0.0884021i | 0.661523 | − | 0.749925i | \(-0.269910\pi\) |
−0.749925 | + | 0.661523i | \(0.769910\pi\) | |||||||
\(98\) | 4.85614 | + | 4.85614i | 0.490545 | + | 0.490545i | ||||
\(99\) | −1.65226 | − | 3.32185i | −0.166058 | − | 0.333859i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.868845 | 0.0864533 | 0.0432267 | − | 0.999065i | \(-0.486236\pi\) | ||||
0.0432267 | + | 0.999065i | \(0.486236\pi\) | |||||||
\(102\) | 3.60480 | − | 5.81909i | 0.356929 | − | 0.576176i | ||||
\(103\) | 7.68967 | − | 7.68967i | 0.757686 | − | 0.757686i | −0.218215 | − | 0.975901i | \(-0.570023\pi\) |
0.975901 | + | 0.218215i | \(0.0700234\pi\) | |||||||
\(104\) | 3.60228 | 0.353232 | ||||||||
\(105\) | −0.144144 | − | 0.613469i | −0.0140670 | − | 0.0598684i | ||||
\(106\) | 5.67132 | − | 5.67132i | 0.550847 | − | 0.550847i | ||||
\(107\) | 8.05854i | 0.779048i | 0.921016 | + | 0.389524i | \(0.127361\pi\) | ||||
−0.921016 | + | 0.389524i | \(0.872639\pi\) | |||||||
\(108\) | −0.482863 | + | 5.17367i | −0.0464635 | + | 0.497836i | ||||
\(109\) | 0.884855 | + | 0.884855i | 0.0847537 | + | 0.0847537i | 0.748213 | − | 0.663459i | \(-0.230912\pi\) |
−0.663459 | + | 0.748213i | \(0.730912\pi\) | |||||||
\(110\) | 1.23669 | 0.117914 | ||||||||
\(111\) | −9.57139 | + | 4.40323i | −0.908477 | + | 0.417936i | ||||
\(112\) | −0.363832 | −0.0343789 | ||||||||
\(113\) | 7.40005 | + | 7.40005i | 0.696138 | + | 0.696138i | 0.963575 | − | 0.267437i | \(-0.0861769\pi\) |
−0.267437 | + | 0.963575i | \(0.586177\pi\) | |||||||
\(114\) | 2.92000 | + | 1.80888i | 0.273483 | + | 0.169417i | ||||
\(115\) | 0.646286i | 0.0602665i | ||||||||
\(116\) | 1.61230 | − | 1.61230i | 0.149698 | − | 0.149698i | ||||
\(117\) | 3.43884 | − | 10.2451i | 0.317920 | − | 0.947159i | ||||
\(118\) | 9.13227 | 0.840694 | ||||||||
\(119\) | 1.01674 | − | 1.01674i | 0.0932044 | − | 0.0932044i | ||||
\(120\) | −1.47242 | − | 0.912132i | −0.134413 | − | 0.0832659i | ||||
\(121\) | −9.47059 | −0.860963 | ||||||||
\(122\) | −3.69100 | −0.334167 | ||||||||
\(123\) | 0.497263 | − | 0.802712i | 0.0448367 | − | 0.0723781i | ||||
\(124\) | 0.163461 | + | 0.163461i | 0.0146792 | + | 0.0146792i | ||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | −0.347325 | + | 1.03476i | −0.0309421 | + | 0.0921839i | ||||
\(127\) | 18.9130 | 1.67825 | 0.839127 | − | 0.543936i | \(-0.183067\pi\) | ||||
0.839127 | + | 0.543936i | \(0.183067\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −11.3373 | + | 2.66386i | −0.998191 | + | 0.234540i | ||||
\(130\) | 2.54719 | + | 2.54719i | 0.223404 | + | 0.223404i | ||||
\(131\) | 1.74566 | + | 1.74566i | 0.152519 | + | 0.152519i | 0.779242 | − | 0.626723i | \(-0.215604\pi\) |
−0.626723 | + | 0.779242i | \(0.715604\pi\) | |||||||
\(132\) | −1.82093 | − | 1.12803i | −0.158491 | − | 0.0981821i | ||||
\(133\) | 0.510197 | + | 0.510197i | 0.0442397 | + | 0.0442397i | ||||
\(134\) | 3.50006 | − | 3.50006i | 0.302359 | − | 0.302359i | ||||
\(135\) | −3.99977 | + | 3.31690i | −0.344246 | + | 0.285473i | ||||
\(136\) | − | 3.95206i | − | 0.338887i | ||||||
\(137\) | − | 8.31134i | − | 0.710085i | −0.934850 | − | 0.355043i | \(-0.884466\pi\) | ||
0.934850 | − | 0.355043i | \(-0.115534\pi\) | |||||||
\(138\) | 0.589498 | − | 0.951603i | 0.0501814 | − | 0.0810058i | ||||
\(139\) | 2.62959i | 0.223039i | 0.993762 | + | 0.111520i | \(0.0355718\pi\) | ||||
−0.993762 | + | 0.111520i | \(0.964428\pi\) | |||||||
\(140\) | −0.257268 | − | 0.257268i | −0.0217431 | − | 0.0217431i | ||||
\(141\) | 2.36259 | + | 1.46357i | 0.198966 | + | 0.123255i | ||||
\(142\) | 10.4722 | − | 10.4722i | 0.878809 | − | 0.878809i | ||||
\(143\) | 3.15010 | + | 3.15010i | 0.263424 | + | 0.263424i | ||||
\(144\) | 1.33603 | + | 2.68608i | 0.111336 | + | 0.223840i | ||||
\(145\) | 2.28014 | 0.189355 | ||||||||
\(146\) | 1.13662 | − | 1.13662i | 0.0940675 | − | 0.0940675i | ||||
\(147\) | 6.26418 | − | 10.1120i | 0.516661 | − | 0.834025i | ||||
\(148\) | −3.35892 | + | 5.07126i | −0.276102 | + | 0.416855i | ||||
\(149\) | − | 10.2673i | − | 0.841131i | −0.907262 | − | 0.420566i | \(-0.861832\pi\) | ||
0.907262 | − | 0.420566i | \(-0.138168\pi\) | |||||||
\(150\) | −0.396182 | − | 1.68613i | −0.0323481 | − | 0.137672i | ||||
\(151\) | − | 5.53248i | − | 0.450226i | −0.974333 | − | 0.225113i | \(-0.927725\pi\) | ||
0.974333 | − | 0.225113i | \(-0.0722752\pi\) | |||||||
\(152\) | 1.98313 | 0.160853 | ||||||||
\(153\) | −11.2399 | − | 3.77275i | −0.908693 | − | 0.305009i | ||||
\(154\) | −0.318162 | − | 0.318162i | −0.0256382 | − | 0.0256382i | ||||
\(155\) | 0.231169i | 0.0185679i | ||||||||
\(156\) | −1.42716 | − | 6.07391i | −0.114264 | − | 0.486302i | ||||
\(157\) | 7.35707 | 0.587158 | 0.293579 | − | 0.955935i | \(-0.405154\pi\) | ||||
0.293579 | + | 0.955935i | \(0.405154\pi\) | |||||||
\(158\) | − | 3.28319i | − | 0.261196i | ||||||
\(159\) | −11.8095 | − | 7.31572i | −0.936552 | − | 0.580174i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.166269 | − | 0.166269i | 0.0131038 | − | 0.0131038i | ||||
\(162\) | 8.91479 | − | 1.23555i | 0.700412 | − | 0.0970736i | ||||
\(163\) | 8.15725 | − | 8.15725i | 0.638925 | − | 0.638925i | −0.311365 | − | 0.950290i | \(-0.600786\pi\) |
0.950290 | + | 0.311365i | \(0.100786\pi\) | |||||||
\(164\) | − | 0.545166i | − | 0.0425703i | ||||||
\(165\) | −0.489956 | − | 2.08523i | −0.0381430 | − | 0.162335i | ||||
\(166\) | 5.96781 | − | 5.96781i | 0.463192 | − | 0.463192i | ||||
\(167\) | −7.06777 | + | 7.06777i | −0.546921 | + | 0.546921i | −0.925549 | − | 0.378628i | \(-0.876396\pi\) |
0.378628 | + | 0.925549i | \(0.376396\pi\) | |||||||
\(168\) | 0.144144 | + | 0.613469i | 0.0111209 | + | 0.0473302i | ||||
\(169\) | − | 0.0236067i | − | 0.00181590i | ||||||
\(170\) | 2.79453 | − | 2.79453i | 0.214331 | − | 0.214331i | ||||
\(171\) | 1.89315 | − | 5.64015i | 0.144773 | − | 0.431313i | ||||
\(172\) | −4.75447 | + | 4.75447i | −0.362525 | + | 0.362525i | ||||
\(173\) | −6.52900 | −0.496391 | −0.248195 | − | 0.968710i | \(-0.579837\pi\) | ||||
−0.248195 | + | 0.968710i | \(0.579837\pi\) | |||||||
\(174\) | −3.35732 | − | 2.07979i | −0.254517 | − | 0.157668i | ||||
\(175\) | − | 0.363832i | − | 0.0275031i | ||||||
\(176\) | −1.23669 | −0.0932192 | ||||||||
\(177\) | −3.61804 | − | 15.3982i | −0.271949 | − | 1.15740i | ||||
\(178\) | 0.778187i | 0.0583276i | ||||||||
\(179\) | −5.04499 | − | 5.04499i | −0.377080 | − | 0.377080i | 0.492968 | − | 0.870048i | \(-0.335912\pi\) |
−0.870048 | + | 0.492968i | \(0.835912\pi\) | |||||||
\(180\) | −0.954629 | + | 2.84406i | −0.0711538 | + | 0.211984i | ||||
\(181\) | 1.67529 | 0.124523 | 0.0622617 | − | 0.998060i | \(-0.480169\pi\) | ||||
0.0622617 | + | 0.998060i | \(0.480169\pi\) | |||||||
\(182\) | − | 1.31062i | − | 0.0971499i | ||||||
\(183\) | 1.46231 | + | 6.22350i | 0.108097 | + | 0.460055i | ||||
\(184\) | − | 0.646286i | − | 0.0476448i | ||||||
\(185\) | −5.96104 | + | 1.21080i | −0.438264 | + | 0.0890199i | ||||
\(186\) | 0.210857 | − | 0.340377i | 0.0154608 | − | 0.0249577i | ||||
\(187\) | 3.45598 | − | 3.45598i | 0.252726 | − | 0.252726i | ||||
\(188\) | 1.60456 | 0.117025 | ||||||||
\(189\) | 1.88235 | + | 0.175681i | 0.136921 | + | 0.0127789i | ||||
\(190\) | 1.40229 | + | 1.40229i | 0.101732 | + | 0.101732i | ||||
\(191\) | −6.28026 | + | 6.28026i | −0.454424 | + | 0.454424i | −0.896820 | − | 0.442396i | \(-0.854129\pi\) |
0.442396 | + | 0.896820i | \(0.354129\pi\) | |||||||
\(192\) | 1.47242 | + | 0.912132i | 0.106263 | + | 0.0658275i | ||||
\(193\) | 4.14557 | + | 4.14557i | 0.298405 | + | 0.298405i | 0.840389 | − | 0.541984i | \(-0.182327\pi\) |
−0.541984 | + | 0.840389i | \(0.682327\pi\) | |||||||
\(194\) | 1.23130i | 0.0884021i | ||||||||
\(195\) | 3.28575 | − | 5.30406i | 0.235298 | − | 0.379831i | ||||
\(196\) | − | 6.86763i | − | 0.490545i | ||||||
\(197\) | − | 17.9073i | − | 1.27584i | −0.770102 | − | 0.637921i | \(-0.779795\pi\) | ||
0.770102 | − | 0.637921i | \(-0.220205\pi\) | |||||||
\(198\) | −1.18058 | + | 3.51723i | −0.0839003 | + | 0.249959i | ||||
\(199\) | −16.9444 | + | 16.9444i | −1.20116 | + | 1.20116i | −0.227343 | + | 0.973815i | \(0.573004\pi\) |
−0.973815 | + | 0.227343i | \(0.926996\pi\) | |||||||
\(200\) | −0.707107 | − | 0.707107i | −0.0500000 | − | 0.0500000i | ||||
\(201\) | −7.28823 | − | 4.51490i | −0.514072 | − | 0.318457i | ||||
\(202\) | −0.614366 | − | 0.614366i | −0.0432267 | − | 0.0432267i | ||||
\(203\) | −0.586607 | − | 0.586607i | −0.0411717 | − | 0.0411717i | ||||
\(204\) | −6.66370 | + | 1.56574i | −0.466552 | + | 0.109624i | ||||
\(205\) | 0.385490 | − | 0.385490i | 0.0269238 | − | 0.0269238i | ||||
\(206\) | −10.8748 | −0.757686 | ||||||||
\(207\) | −1.83808 | − | 0.616963i | −0.127755 | − | 0.0428819i | ||||
\(208\) | −2.54719 | − | 2.54719i | −0.176616 | − | 0.176616i | ||||
\(209\) | 1.73420 | + | 1.73420i | 0.119957 | + | 0.119957i | ||||
\(210\) | −0.331863 | + | 0.535713i | −0.0229007 | + | 0.0369677i | ||||
\(211\) | 21.7223 | 1.49543 | 0.747714 | − | 0.664021i | \(-0.231152\pi\) | ||||
0.747714 | + | 0.664021i | \(0.231152\pi\) | |||||||
\(212\) | −8.02046 | −0.550847 | ||||||||
\(213\) | −21.8064 | − | 13.5086i | −1.49415 | − | 0.925596i | ||||
\(214\) | 5.69825 | − | 5.69825i | 0.389524 | − | 0.389524i | ||||
\(215\) | −6.72384 | −0.458562 | ||||||||
\(216\) | 3.99977 | − | 3.31690i | 0.272150 | − | 0.225686i | ||||
\(217\) | 0.0594724 | − | 0.0594724i | 0.00403725 | − | 0.00403725i | ||||
\(218\) | − | 1.25137i | − | 0.0847537i | ||||||
\(219\) | −2.36680 | − | 1.46618i | −0.159934 | − | 0.0990755i | ||||
\(220\) | −0.874474 | − | 0.874474i | −0.0589570 | − | 0.0589570i | ||||
\(221\) | 14.2364 | 0.957646 | ||||||||
\(222\) | 9.88155 | + | 3.65445i | 0.663206 | + | 0.245270i | ||||
\(223\) | 7.24611 | 0.485235 | 0.242618 | − | 0.970122i | \(-0.421994\pi\) | ||||
0.242618 | + | 0.970122i | \(0.421994\pi\) | |||||||
\(224\) | 0.257268 | + | 0.257268i | 0.0171895 | + | 0.0171895i | ||||
\(225\) | −2.68608 | + | 1.33603i | −0.179072 | + | 0.0890687i | ||||
\(226\) | − | 10.4652i | − | 0.696138i | ||||||
\(227\) | −7.21839 | + | 7.21839i | −0.479102 | + | 0.479102i | −0.904844 | − | 0.425743i | \(-0.860013\pi\) |
0.425743 | + | 0.904844i | \(0.360013\pi\) | |||||||
\(228\) | −0.785681 | − | 3.34382i | −0.0520330 | − | 0.221450i | ||||
\(229\) | −15.0972 | −0.997648 | −0.498824 | − | 0.866703i | \(-0.666235\pi\) | ||||
−0.498824 | + | 0.866703i | \(0.666235\pi\) | |||||||
\(230\) | 0.456993 | − | 0.456993i | 0.0301332 | − | 0.0301332i | ||||
\(231\) | −0.410412 | + | 0.662512i | −0.0270032 | + | 0.0435901i | ||||
\(232\) | −2.28014 | −0.149698 | ||||||||
\(233\) | −1.67396 | −0.109665 | −0.0548324 | − | 0.998496i | \(-0.517462\pi\) | ||||
−0.0548324 | + | 0.998496i | \(0.517462\pi\) | |||||||
\(234\) | −9.67600 | + | 4.81275i | −0.632540 | + | 0.314619i | ||||
\(235\) | 1.13460 | + | 1.13460i | 0.0740129 | + | 0.0740129i | ||||
\(236\) | −6.45749 | − | 6.45749i | −0.420347 | − | 0.420347i | ||||
\(237\) | −5.53589 | + | 1.30074i | −0.359595 | + | 0.0844922i | ||||
\(238\) | −1.43789 | −0.0932044 | ||||||||
\(239\) | 8.93980 | − | 8.93980i | 0.578268 | − | 0.578268i | −0.356158 | − | 0.934426i | \(-0.615914\pi\) |
0.934426 | + | 0.356158i | \(0.115914\pi\) | |||||||
\(240\) | 0.396182 | + | 1.68613i | 0.0255735 | + | 0.108839i | ||||
\(241\) | −1.90045 | − | 1.90045i | −0.122419 | − | 0.122419i | 0.643243 | − | 0.765662i | \(-0.277588\pi\) |
−0.765662 | + | 0.643243i | \(0.777588\pi\) | |||||||
\(242\) | 6.69672 | + | 6.69672i | 0.430481 | + | 0.430481i | ||||
\(243\) | −5.61517 | − | 14.5420i | −0.360213 | − | 0.932870i | ||||
\(244\) | 2.60993 | + | 2.60993i | 0.167084 | + | 0.167084i | ||||
\(245\) | 4.85614 | − | 4.85614i | 0.310248 | − | 0.310248i | ||||
\(246\) | −0.919221 | + | 0.215985i | −0.0586074 | + | 0.0137707i | ||||
\(247\) | 7.14379i | 0.454548i | ||||||||
\(248\) | − | 0.231169i | − | 0.0146792i | ||||||
\(249\) | −12.4269 | − | 7.69817i | −0.787520 | − | 0.487852i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 7.01214 | + | 7.01214i | 0.442602 | + | 0.442602i | 0.892886 | − | 0.450283i | \(-0.148677\pi\) |
−0.450283 | + | 0.892886i | \(0.648677\pi\) | |||||||
\(252\) | 0.977282 | − | 0.486091i | 0.0615630 | − | 0.0306209i | ||||
\(253\) | 0.565160 | − | 0.565160i | 0.0355313 | − | 0.0355313i | ||||
\(254\) | −13.3735 | − | 13.3735i | −0.839127 | − | 0.839127i | ||||
\(255\) | −5.81909 | − | 3.60480i | −0.364406 | − | 0.225742i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.2100 | + | 14.2100i | −0.886395 | + | 0.886395i | −0.994175 | − | 0.107779i | \(-0.965626\pi\) |
0.107779 | + | 0.994175i | \(0.465626\pi\) | |||||||
\(258\) | 9.90030 | + | 6.13303i | 0.616366 | + | 0.381826i | ||||
\(259\) | 1.84509 | + | 1.22208i | 0.114648 | + | 0.0759367i | ||||
\(260\) | − | 3.60228i | − | 0.223404i | ||||||
\(261\) | −2.17668 | + | 6.48485i | −0.134733 | + | 0.401402i | ||||
\(262\) | − | 2.46874i | − | 0.152519i | ||||||
\(263\) | 19.1855 | 1.18303 | 0.591514 | − | 0.806295i | \(-0.298530\pi\) | ||||
0.591514 | + | 0.806295i | \(0.298530\pi\) | |||||||
\(264\) | 0.489956 | + | 2.08523i | 0.0301547 | + | 0.128337i | ||||
\(265\) | −5.67132 | − | 5.67132i | −0.348386 | − | 0.348386i | ||||
\(266\) | − | 0.721527i | − | 0.0442397i | ||||||
\(267\) | 1.31213 | − | 0.308304i | 0.0803008 | − | 0.0188679i | ||||
\(268\) | −4.94984 | −0.302359 | ||||||||
\(269\) | − | 28.0625i | − | 1.71100i | −0.517804 | − | 0.855499i | \(-0.673250\pi\) | ||
0.517804 | − | 0.855499i | \(-0.326750\pi\) | |||||||
\(270\) | 5.17367 | + | 0.482863i | 0.314859 | + | 0.0293861i | ||||
\(271\) | 16.3324 | 0.992121 | 0.496060 | − | 0.868288i | \(-0.334779\pi\) | ||||
0.496060 | + | 0.868288i | \(0.334779\pi\) | |||||||
\(272\) | −2.79453 | + | 2.79453i | −0.169443 | + | 0.169443i | ||||
\(273\) | −2.20988 | + | 0.519246i | −0.133748 | + | 0.0314262i | ||||
\(274\) | −5.87700 | + | 5.87700i | −0.355043 | + | 0.355043i | ||||
\(275\) | − | 1.23669i | − | 0.0745754i | ||||||
\(276\) | −1.08972 | + | 0.256047i | −0.0655936 | + | 0.0154122i | ||||
\(277\) | −3.32318 | + | 3.32318i | −0.199670 | + | 0.199670i | −0.799859 | − | 0.600188i | \(-0.795092\pi\) |
0.600188 | + | 0.799859i | \(0.295092\pi\) | |||||||
\(278\) | 1.85940 | − | 1.85940i | 0.111520 | − | 0.111520i | ||||
\(279\) | −0.657458 | − | 0.220680i | −0.0393610 | − | 0.0132118i | ||||
\(280\) | 0.363832i | 0.0217431i | ||||||||
\(281\) | 2.25670 | − | 2.25670i | 0.134624 | − | 0.134624i | −0.636584 | − | 0.771207i | \(-0.719653\pi\) |
0.771207 | + | 0.636584i | \(0.219653\pi\) | |||||||
\(282\) | −0.635699 | − | 2.70550i | −0.0378553 | − | 0.161110i | ||||
\(283\) | 13.9425 | − | 13.9425i | 0.828796 | − | 0.828796i | −0.158554 | − | 0.987350i | \(-0.550683\pi\) |
0.987350 | + | 0.158554i | \(0.0506833\pi\) | |||||||
\(284\) | −14.8100 | −0.878809 | ||||||||
\(285\) | 1.80888 | − | 2.92000i | 0.107149 | − | 0.172966i | ||||
\(286\) | − | 4.45491i | − | 0.263424i | ||||||
\(287\) | −0.198349 | −0.0117082 | ||||||||
\(288\) | 0.954629 | − | 2.84406i | 0.0562520 | − | 0.167588i | ||||
\(289\) | 1.38119i | 0.0812466i | ||||||||
\(290\) | −1.61230 | − | 1.61230i | −0.0946776 | − | 0.0946776i | ||||
\(291\) | 2.07613 | − | 0.487818i | 0.121705 | − | 0.0285964i | ||||
\(292\) | −1.60743 | −0.0940675 | ||||||||
\(293\) | 17.4323i | 1.01841i | 0.860646 | + | 0.509203i | \(0.170060\pi\) | ||||
−0.860646 | + | 0.509203i | \(0.829940\pi\) | |||||||
\(294\) | −11.5797 | + | 2.72083i | −0.675343 | + | 0.158682i | ||||
\(295\) | − | 9.13227i | − | 0.531702i | ||||||
\(296\) | 5.96104 | − | 1.21080i | 0.346478 | − | 0.0703764i | ||||
\(297\) | 6.39824 | + | 0.597153i | 0.371263 | + | 0.0346503i | ||||
\(298\) | −7.26009 | + | 7.26009i | −0.420566 | + | 0.420566i | ||||
\(299\) | 2.32810 | 0.134638 | ||||||||
\(300\) | −0.912132 | + | 1.47242i | −0.0526620 | + | 0.0850101i | ||||
\(301\) | 1.72983 | + | 1.72983i | 0.0997057 | + | 0.0997057i | ||||
\(302\) | −3.91205 | + | 3.91205i | −0.225113 | + | 0.225113i | ||||
\(303\) | −0.792501 | + | 1.27930i | −0.0455280 | + | 0.0734941i | ||||
\(304\) | −1.40229 | − | 1.40229i | −0.0804266 | − | 0.0804266i | ||||
\(305\) | 3.69100i | 0.211346i | ||||||||
\(306\) | 5.28008 | + | 10.6156i | 0.301842 | + | 0.606851i | ||||
\(307\) | 5.19902i | 0.296724i | 0.988933 | + | 0.148362i | \(0.0474001\pi\) | ||||
−0.988933 | + | 0.148362i | \(0.952600\pi\) | |||||||
\(308\) | 0.449949i | 0.0256382i | ||||||||
\(309\) | 4.30842 | + | 18.3364i | 0.245097 | + | 1.04312i | ||||
\(310\) | 0.163461 | − | 0.163461i | 0.00928397 | − | 0.00928397i | ||||
\(311\) | 3.82476 | + | 3.82476i | 0.216882 | + | 0.216882i | 0.807183 | − | 0.590301i | \(-0.200991\pi\) |
−0.590301 | + | 0.807183i | \(0.700991\pi\) | |||||||
\(312\) | −3.28575 | + | 5.30406i | −0.186019 | + | 0.300283i | ||||
\(313\) | −23.6109 | − | 23.6109i | −1.33457 | − | 1.33457i | −0.901235 | − | 0.433331i | \(-0.857338\pi\) |
−0.433331 | − | 0.901235i | \(-0.642662\pi\) | |||||||
\(314\) | −5.20223 | − | 5.20223i | −0.293579 | − | 0.293579i | ||||
\(315\) | 1.03476 | + | 0.347325i | 0.0583022 | + | 0.0195695i | ||||
\(316\) | −2.32156 | + | 2.32156i | −0.130598 | + | 0.130598i | ||||
\(317\) | −14.6490 | −0.822767 | −0.411384 | − | 0.911462i | \(-0.634954\pi\) | ||||
−0.411384 | + | 0.911462i | \(0.634954\pi\) | |||||||
\(318\) | 3.17756 | + | 13.5235i | 0.178189 | + | 0.758363i | ||||
\(319\) | −1.99392 | − | 1.99392i | −0.111638 | − | 0.111638i | ||||
\(320\) | 0.707107 | + | 0.707107i | 0.0395285 | + | 0.0395285i | ||||
\(321\) | −11.8655 | − | 7.35045i | −0.662270 | − | 0.410262i | ||||
\(322\) | −0.235140 | −0.0131038 | ||||||||
\(323\) | 7.83746 | 0.436088 | ||||||||
\(324\) | −7.17737 | − | 5.43004i | −0.398743 | − | 0.301669i | ||||
\(325\) | 2.54719 | − | 2.54719i | 0.141293 | − | 0.141293i | ||||
\(326\) | −11.5361 | −0.638925 | ||||||||
\(327\) | −2.10998 | + | 0.495772i | −0.116682 | + | 0.0274163i | ||||
\(328\) | −0.385490 | + | 0.385490i | −0.0212851 | + | 0.0212851i | ||||
\(329\) | − | 0.583791i | − | 0.0321855i | ||||||
\(330\) | −1.12803 | + | 1.82093i | −0.0620958 | + | 0.100239i | ||||
\(331\) | −2.77763 | − | 2.77763i | −0.152672 | − | 0.152672i | 0.626638 | − | 0.779310i | \(-0.284430\pi\) |
−0.779310 | + | 0.626638i | \(0.784430\pi\) | |||||||
\(332\) | −8.43976 | −0.463192 | ||||||||
\(333\) | 2.24698 | − | 18.1094i | 0.123134 | − | 0.992390i | ||||
\(334\) | 9.99534 | 0.546921 | ||||||||
\(335\) | −3.50006 | − | 3.50006i | −0.191229 | − | 0.191229i | ||||
\(336\) | 0.331863 | − | 0.535713i | 0.0181046 | − | 0.0292256i | ||||
\(337\) | 11.7097i | 0.637870i | 0.947777 | + | 0.318935i | \(0.103325\pi\) | ||||
−0.947777 | + | 0.318935i | \(0.896675\pi\) | |||||||
\(338\) | −0.0166925 | + | 0.0166925i | −0.000907951 | + | 0.000907951i | ||||
\(339\) | −17.6458 | + | 4.14614i | −0.958387 | + | 0.225188i | ||||
\(340\) | −3.95206 | −0.214331 | ||||||||
\(341\) | 0.202151 | − | 0.202151i | 0.0109471 | − | 0.0109471i | ||||
\(342\) | −5.32685 | + | 2.64952i | −0.288043 | + | 0.143270i | ||||
\(343\) | −5.04549 | −0.272431 | ||||||||
\(344\) | 6.72384 | 0.362525 | ||||||||
\(345\) | −0.951603 | − | 0.589498i | −0.0512326 | − | 0.0317375i | ||||
\(346\) | 4.61670 | + | 4.61670i | 0.248195 | + | 0.248195i | ||||
\(347\) | 19.9380 | + | 19.9380i | 1.07033 | + | 1.07033i | 0.997332 | + | 0.0729969i | \(0.0232563\pi\) |
0.0729969 | + | 0.997332i | \(0.476744\pi\) | |||||||
\(348\) | 0.903350 | + | 3.84461i | 0.0484246 | + | 0.206093i | ||||
\(349\) | −20.6832 | −1.10715 | −0.553574 | − | 0.832800i | \(-0.686736\pi\) | ||||
−0.553574 | + | 0.832800i | \(0.686736\pi\) | |||||||
\(350\) | −0.257268 | + | 0.257268i | −0.0137516 | + | 0.0137516i | ||||
\(351\) | 11.9484 | + | 14.4083i | 0.637758 | + | 0.769057i | ||||
\(352\) | 0.874474 | + | 0.874474i | 0.0466096 | + | 0.0466096i | ||||
\(353\) | −5.36743 | − | 5.36743i | −0.285680 | − | 0.285680i | 0.549690 | − | 0.835369i | \(-0.314746\pi\) |
−0.835369 | + | 0.549690i | \(0.814746\pi\) | |||||||
\(354\) | −8.32984 | + | 13.4465i | −0.442726 | + | 0.714675i | ||||
\(355\) | −10.4722 | − | 10.4722i | −0.555808 | − | 0.555808i | ||||
\(356\) | 0.550261 | − | 0.550261i | 0.0291638 | − | 0.0291638i | ||||
\(357\) | 0.569666 | + | 2.42447i | 0.0301499 | + | 0.128316i | ||||
\(358\) | 7.13469i | 0.377080i | ||||||||
\(359\) | − | 15.5141i | − | 0.818802i | −0.912355 | − | 0.409401i | \(-0.865738\pi\) | ||
0.912355 | − | 0.409401i | \(-0.134262\pi\) | |||||||
\(360\) | 2.68608 | − | 1.33603i | 0.141569 | − | 0.0704150i | ||||
\(361\) | − | 15.0672i | − | 0.793010i | ||||||
\(362\) | −1.18461 | − | 1.18461i | −0.0622617 | − | 0.0622617i | ||||
\(363\) | 8.63843 | − | 13.9447i | 0.453400 | − | 0.731905i | ||||
\(364\) | −0.926751 | + | 0.926751i | −0.0485750 | + | 0.0485750i | ||||
\(365\) | −1.13662 | − | 1.13662i | −0.0594935 | − | 0.0594935i | ||||
\(366\) | 3.36667 | − | 5.43469i | 0.175979 | − | 0.284076i | ||||
\(367\) | −23.5145 | −1.22745 | −0.613724 | − | 0.789521i | \(-0.710329\pi\) | ||||
−0.613724 | + | 0.789521i | \(0.710329\pi\) | |||||||
\(368\) | −0.456993 | + | 0.456993i | −0.0238224 | + | 0.0238224i | ||||
\(369\) | 0.728358 | + | 1.46436i | 0.0379168 | + | 0.0762315i | ||||
\(370\) | 5.07126 | + | 3.35892i | 0.263642 | + | 0.174622i | ||||
\(371\) | 2.91810i | 0.151500i | ||||||||
\(372\) | −0.389781 | + | 0.0915850i | −0.0202092 | + | 0.00474846i | ||||
\(373\) | − | 37.4002i | − | 1.93651i | −0.249963 | − | 0.968255i | \(-0.580419\pi\) | ||
0.249963 | − | 0.968255i | \(-0.419581\pi\) | |||||||
\(374\) | −4.88749 | −0.252726 | ||||||||
\(375\) | −1.68613 | + | 0.396182i | −0.0870715 | + | 0.0204588i | ||||
\(376\) | −1.13460 | − | 1.13460i | −0.0585124 | − | 0.0585124i | ||||
\(377\) | − | 8.21369i | − | 0.423026i | ||||||
\(378\) | −1.20680 | − | 1.45525i | −0.0620709 | − | 0.0748498i | ||||
\(379\) | 30.3654 | 1.55977 | 0.779883 | − | 0.625925i | \(-0.215279\pi\) | ||||
0.779883 | + | 0.625925i | \(0.215279\pi\) | |||||||
\(380\) | − | 1.98313i | − | 0.101732i | ||||||
\(381\) | −17.2511 | + | 27.8478i | −0.883801 | + | 1.42668i | ||||
\(382\) | 8.88163 | 0.454424 | ||||||||
\(383\) | −3.46804 | + | 3.46804i | −0.177209 | + | 0.177209i | −0.790138 | − | 0.612929i | \(-0.789991\pi\) |
0.612929 | + | 0.790138i | \(0.289991\pi\) | |||||||
\(384\) | −0.396182 | − | 1.68613i | −0.0202176 | − | 0.0860450i | ||||
\(385\) | −0.318162 | + | 0.318162i | −0.0162150 | + | 0.0162150i | ||||
\(386\) | − | 5.86272i | − | 0.298405i | ||||||
\(387\) | 6.41877 | − | 19.1230i | 0.326284 | − | 0.972077i | ||||
\(388\) | 0.870659 | − | 0.870659i | 0.0442010 | − | 0.0442010i | ||||
\(389\) | 7.62835 | − | 7.62835i | 0.386772 | − | 0.386772i | −0.486762 | − | 0.873535i | \(-0.661822\pi\) |
0.873535 | + | 0.486762i | \(0.161822\pi\) | |||||||
\(390\) | −6.07391 | + | 1.42716i | −0.307564 | + | 0.0722669i | ||||
\(391\) | − | 2.55416i | − | 0.129170i | ||||||
\(392\) | −4.85614 | + | 4.85614i | −0.245272 | + | 0.245272i | ||||
\(393\) | −4.16262 | + | 0.978070i | −0.209976 | + | 0.0493371i | ||||
\(394\) | −12.6624 | + | 12.6624i | −0.637921 | + | 0.637921i | ||||
\(395\) | −3.28319 | −0.165195 | ||||||||
\(396\) | 3.32185 | − | 1.65226i | 0.166929 | − | 0.0830291i | ||||
\(397\) | 15.6581i | 0.785860i | 0.919568 | + | 0.392930i | \(0.128539\pi\) | ||||
−0.919568 | + | 0.392930i | \(0.871461\pi\) | |||||||
\(398\) | 23.9630 | 1.20116 | ||||||||
\(399\) | −1.21659 | + | 0.285856i | −0.0609057 | + | 0.0143107i | ||||
\(400\) | 1.00000i | 0.0500000i | ||||||||
\(401\) | −12.5130 | − | 12.5130i | −0.624871 | − | 0.624871i | 0.321902 | − | 0.946773i | \(-0.395678\pi\) |
−0.946773 | + | 0.321902i | \(0.895678\pi\) | |||||||
\(402\) | 1.96104 | + | 8.34608i | 0.0978077 | + | 0.416264i | ||||
\(403\) | 0.832734 | 0.0414814 | ||||||||
\(404\) | 0.868845i | 0.0432267i | ||||||||
\(405\) | −1.23555 | − | 8.91479i | −0.0613947 | − | 0.442979i | ||||
\(406\) | 0.829588i | 0.0411717i | ||||||||
\(407\) | 6.27158 | + | 4.15396i | 0.310871 | + | 0.205904i | ||||
\(408\) | 5.81909 | + | 3.60480i | 0.288088 | + | 0.178464i | ||||
\(409\) | −10.4273 | + | 10.4273i | −0.515599 | + | 0.515599i | −0.916236 | − | 0.400638i | \(-0.868789\pi\) |
0.400638 | + | 0.916236i | \(0.368789\pi\) | |||||||
\(410\) | −0.545166 | −0.0269238 | ||||||||
\(411\) | 12.2378 | + | 7.58103i | 0.603644 | + | 0.373945i | ||||
\(412\) | 7.68967 | + | 7.68967i | 0.378843 | + | 0.378843i | ||||
\(413\) | −2.34944 | + | 2.34944i | −0.115609 | + | 0.115609i | ||||
\(414\) | 0.863458 | + | 1.73598i | 0.0424366 | + | 0.0853185i | ||||
\(415\) | −5.96781 | − | 5.96781i | −0.292948 | − | 0.292948i | ||||
\(416\) | 3.60228i | 0.176616i | ||||||||
\(417\) | −3.87186 | − | 2.39854i | −0.189606 | − | 0.117457i | ||||
\(418\) | − | 2.45252i | − | 0.119957i | ||||||
\(419\) | − | 7.73667i | − | 0.377961i | −0.981981 | − | 0.188980i | \(-0.939482\pi\) | ||
0.981981 | − | 0.188980i | \(-0.0605183\pi\) | |||||||
\(420\) | 0.613469 | − | 0.144144i | 0.0299342 | − | 0.00703350i | ||||
\(421\) | −7.36859 | + | 7.36859i | −0.359123 | + | 0.359123i | −0.863490 | − | 0.504366i | \(-0.831726\pi\) |
0.504366 | + | 0.863490i | \(0.331726\pi\) | |||||||
\(422\) | −15.3600 | − | 15.3600i | −0.747714 | − | 0.747714i | ||||
\(423\) | −4.30998 | + | 2.14374i | −0.209558 | + | 0.104232i | ||||
\(424\) | 5.67132 | + | 5.67132i | 0.275424 | + | 0.275424i | ||||
\(425\) | −2.79453 | − | 2.79453i | −0.135555 | − | 0.135555i | ||||
\(426\) | 5.86744 | + | 24.9715i | 0.284278 | + | 1.20987i | ||||
\(427\) | 0.949576 | − | 0.949576i | 0.0459532 | − | 0.0459532i | ||||
\(428\) | −8.05854 | −0.389524 | ||||||||
\(429\) | −7.51156 | + | 1.76496i | −0.362662 | + | 0.0852128i | ||||
\(430\) | 4.75447 | + | 4.75447i | 0.229281 | + | 0.229281i | ||||
\(431\) | 21.5577 | + | 21.5577i | 1.03840 | + | 1.03840i | 0.999233 | + | 0.0391638i | \(0.0124694\pi\) |
0.0391638 | + | 0.999233i | \(0.487531\pi\) | |||||||
\(432\) | −5.17367 | − | 0.482863i | −0.248918 | − | 0.0232317i | ||||
\(433\) | 35.8755 | 1.72407 | 0.862034 | − | 0.506851i | \(-0.169190\pi\) | ||||
0.862034 | + | 0.506851i | \(0.169190\pi\) | |||||||
\(434\) | −0.0841067 | −0.00403725 | ||||||||
\(435\) | −2.07979 | + | 3.35732i | −0.0997181 | + | 0.160971i | ||||
\(436\) | −0.884855 | + | 0.884855i | −0.0423769 | + | 0.0423769i | ||||
\(437\) | 1.28167 | 0.0613106 | ||||||||
\(438\) | 0.636833 | + | 2.71033i | 0.0304291 | + | 0.129505i | ||||
\(439\) | 13.1830 | − | 13.1830i | 0.629190 | − | 0.629190i | −0.318674 | − | 0.947864i | \(-0.603238\pi\) |
0.947864 | + | 0.318674i | \(0.103238\pi\) | |||||||
\(440\) | 1.23669i | 0.0589570i | ||||||||
\(441\) | 9.17536 | + | 18.4470i | 0.436922 | + | 0.878428i | ||||
\(442\) | −10.0667 | − | 10.0667i | −0.478823 | − | 0.478823i | ||||
\(443\) | 39.5691 | 1.87999 | 0.939993 | − | 0.341193i | \(-0.110831\pi\) | ||||
0.939993 | + | 0.341193i | \(0.110831\pi\) | |||||||
\(444\) | −4.40323 | − | 9.57139i | −0.208968 | − | 0.454238i | ||||
\(445\) | 0.778187 | 0.0368896 | ||||||||
\(446\) | −5.12377 | − | 5.12377i | −0.242618 | − | 0.242618i | ||||
\(447\) | 15.1178 | + | 9.36514i | 0.715046 | + | 0.442956i | ||||
\(448\) | − | 0.363832i | − | 0.0171895i | ||||||
\(449\) | 12.2930 | − | 12.2930i | 0.580144 | − | 0.580144i | −0.354799 | − | 0.934943i | \(-0.615451\pi\) |
0.934943 | + | 0.354799i | \(0.115451\pi\) | |||||||
\(450\) | 2.84406 | + | 0.954629i | 0.134070 | + | 0.0450016i | ||||
\(451\) | −0.674202 | −0.0317470 | ||||||||
\(452\) | −7.40005 | + | 7.40005i | −0.348069 | + | 0.348069i | ||||
\(453\) | 8.14612 | + | 5.04635i | 0.382738 | + | 0.237098i | ||||
\(454\) | 10.2083 | 0.479102 | ||||||||
\(455\) | −1.31062 | −0.0614430 | ||||||||
\(456\) | −1.80888 | + | 2.92000i | −0.0847084 | + | 0.136741i | ||||
\(457\) | 16.2368 | + | 16.2368i | 0.759525 | + | 0.759525i | 0.976236 | − | 0.216711i | \(-0.0695328\pi\) |
−0.216711 | + | 0.976236i | \(0.569533\pi\) | |||||||
\(458\) | 10.6753 | + | 10.6753i | 0.498824 | + | 0.498824i | ||||
\(459\) | 15.8074 | − | 13.1086i | 0.737824 | − | 0.611857i | ||||
\(460\) | −0.646286 | −0.0301332 | ||||||||
\(461\) | 24.0001 | − | 24.0001i | 1.11780 | − | 1.11780i | 0.125733 | − | 0.992064i | \(-0.459872\pi\) |
0.992064 | − | 0.125733i | \(-0.0401282\pi\) | |||||||
\(462\) | 0.758672 | − | 0.178262i | 0.0352966 | − | 0.00829348i | ||||
\(463\) | −9.18675 | − | 9.18675i | −0.426945 | − | 0.426945i | 0.460642 | − | 0.887586i | \(-0.347619\pi\) |
−0.887586 | + | 0.460642i | \(0.847619\pi\) | |||||||
\(464\) | 1.61230 | + | 1.61230i | 0.0748492 | + | 0.0748492i | ||||
\(465\) | −0.340377 | − | 0.210857i | −0.0157846 | − | 0.00977824i | ||||
\(466\) | 1.18367 | + | 1.18367i | 0.0548324 | + | 0.0548324i | ||||
\(467\) | −19.8576 | + | 19.8576i | −0.918901 | + | 0.918901i | −0.996950 | − | 0.0780485i | \(-0.975131\pi\) |
0.0780485 | + | 0.996950i | \(0.475131\pi\) | |||||||
\(468\) | 10.2451 | + | 3.43884i | 0.473580 | + | 0.158960i | ||||
\(469\) | 1.80091i | 0.0831583i | ||||||||
\(470\) | − | 1.60456i | − | 0.0740129i | ||||||
\(471\) | −6.71061 | + | 10.8327i | −0.309209 | + | 0.499143i | ||||
\(472\) | 9.13227i | 0.420347i | ||||||||
\(473\) | 5.87982 | + | 5.87982i | 0.270354 | + | 0.270354i | ||||
\(474\) | 4.83423 | + | 2.99470i | 0.222043 | + | 0.137551i | ||||
\(475\) | 1.40229 | − | 1.40229i | 0.0643413 | − | 0.0643413i | ||||
\(476\) | 1.01674 | + | 1.01674i | 0.0466022 | + | 0.0466022i | ||||
\(477\) | 21.5436 | − | 10.7156i | 0.986413 | − | 0.490633i | ||||
\(478\) | −12.6428 | −0.578268 | ||||||||
\(479\) | −11.7978 | + | 11.7978i | −0.539054 | + | 0.539054i | −0.923251 | − | 0.384197i | \(-0.874478\pi\) |
0.384197 | + | 0.923251i | \(0.374478\pi\) | |||||||
\(480\) | 0.912132 | − | 1.47242i | 0.0416329 | − | 0.0672064i | ||||
\(481\) | 4.36164 | + | 21.4733i | 0.198874 | + | 0.979098i | ||||
\(482\) | 2.68764i | 0.122419i | ||||||||
\(483\) | 0.0931582 | + | 0.396476i | 0.00423884 | + | 0.0180403i | ||||
\(484\) | − | 9.47059i | − | 0.430481i | ||||||
\(485\) | 1.23130 | 0.0559104 | ||||||||
\(486\) | −6.31222 | + | 14.2533i | −0.286328 | + | 0.646542i | ||||
\(487\) | −25.1254 | − | 25.1254i | −1.13854 | − | 1.13854i | −0.988712 | − | 0.149830i | \(-0.952127\pi\) |
−0.149830 | − | 0.988712i | \(-0.547873\pi\) | |||||||
\(488\) | − | 3.69100i | − | 0.167084i | ||||||
\(489\) | 4.57039 | + | 19.4514i | 0.206680 | + | 0.879621i | ||||
\(490\) | −6.86763 | −0.310248 | ||||||||
\(491\) | − | 4.62838i | − | 0.208876i | −0.994531 | − | 0.104438i | \(-0.966696\pi\) | ||
0.994531 | − | 0.104438i | \(-0.0333044\pi\) | |||||||
\(492\) | 0.802712 | + | 0.497263i | 0.0361891 | + | 0.0224184i | ||||
\(493\) | −9.01125 | −0.405846 | ||||||||
\(494\) | 5.05142 | − | 5.05142i | 0.227274 | − | 0.227274i | ||||
\(495\) | 3.51723 | + | 1.18058i | 0.158088 | + | 0.0530632i | ||||
\(496\) | −0.163461 | + | 0.163461i | −0.00733962 | + | 0.00733962i | ||||
\(497\) | 5.38834i | 0.241700i | ||||||||
\(498\) | 3.34368 | + | 14.2305i | 0.149834 | + | 0.637686i | ||||
\(499\) | −5.53591 | + | 5.53591i | −0.247822 | + | 0.247822i | −0.820076 | − | 0.572255i | \(-0.806069\pi\) |
0.572255 | + | 0.820076i | \(0.306069\pi\) | |||||||
\(500\) | −0.707107 | + | 0.707107i | −0.0316228 | + | 0.0316228i | ||||
\(501\) | −3.95998 | − | 16.8535i | −0.176919 | − | 0.752957i | ||||
\(502\) | − | 9.91666i | − | 0.442602i | ||||||
\(503\) | 17.6402 | − | 17.6402i | 0.786536 | − | 0.786536i | −0.194388 | − | 0.980925i | \(-0.562272\pi\) |
0.980925 | + | 0.194388i | \(0.0622721\pi\) | |||||||
\(504\) | −1.03476 | − | 0.347325i | −0.0460919 | − | 0.0154711i | ||||
\(505\) | −0.614366 | + | 0.614366i | −0.0273389 | + | 0.0273389i | ||||
\(506\) | −0.799257 | −0.0355313 | ||||||||
\(507\) | 0.0347590 | + | 0.0215324i | 0.00154370 | + | 0.000956289i | ||||
\(508\) | 18.9130i | 0.839127i | ||||||||
\(509\) | 24.0229 | 1.06480 | 0.532398 | − | 0.846494i | \(-0.321291\pi\) | ||||
0.532398 | + | 0.846494i | \(0.321291\pi\) | |||||||
\(510\) | 1.56574 | + | 6.66370i | 0.0693320 | + | 0.295074i | ||||
\(511\) | 0.584833i | 0.0258715i | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 6.57785 | + | 7.93207i | 0.290419 | + | 0.350210i | ||||
\(514\) | 20.0960 | 0.886395 | ||||||||
\(515\) | 10.8748i | 0.479203i | ||||||||
\(516\) | −2.66386 | − | 11.3373i | −0.117270 | − | 0.499096i | ||||
\(517\) | − | 1.98435i | − | 0.0872716i | ||||||
\(518\) | −0.440529 | − | 2.16882i | −0.0193557 | − | 0.0952924i | ||||
\(519\) | 5.95531 | − | 9.61342i | 0.261409 | − | 0.421982i | ||||
\(520\) | −2.54719 | + | 2.54719i | −0.111702 | + | 0.111702i | ||||
\(521\) | 15.1389 | 0.663247 | 0.331623 | − | 0.943412i | \(-0.392404\pi\) | ||||
0.331623 | + | 0.943412i | \(0.392404\pi\) | |||||||
\(522\) | 6.12463 | − | 3.04633i | 0.268068 | − | 0.133334i | ||||
\(523\) | −1.01795 | − | 1.01795i | −0.0445119 | − | 0.0445119i | 0.684500 | − | 0.729012i | \(-0.260020\pi\) |
−0.729012 | + | 0.684500i | \(0.760020\pi\) | |||||||
\(524\) | −1.74566 | + | 1.74566i | −0.0762596 | + | 0.0762596i | ||||
\(525\) | 0.535713 | + | 0.331863i | 0.0233804 | + | 0.0144837i | ||||
\(526\) | −13.5662 | − | 13.5662i | −0.591514 | − | 0.591514i | ||||
\(527\) | − | 0.913594i | − | 0.0397968i | ||||||
\(528\) | 1.12803 | − | 1.82093i | 0.0490911 | − | 0.0792457i | ||||
\(529\) | 22.5823i | 0.981840i | ||||||||
\(530\) | 8.02046i | 0.348386i | ||||||||
\(531\) | 25.9727 | + | 8.71793i | 1.12712 | + | 0.378326i | ||||
\(532\) | −0.510197 | + | 0.510197i | −0.0221198 | + | 0.0221198i | ||||
\(533\) | −1.38864 | − | 1.38864i | −0.0601488 | − | 0.0601488i | ||||
\(534\) | −1.14582 | − | 0.709809i | −0.0495843 | − | 0.0307165i | ||||
\(535\) | −5.69825 | − | 5.69825i | −0.246357 | − | 0.246357i | ||||
\(536\) | 3.50006 | + | 3.50006i | 0.151180 | + | 0.151180i | ||||
\(537\) | 12.0300 | − | 2.82664i | 0.519134 | − | 0.121978i | ||||
\(538\) | −19.8432 | + | 19.8432i | −0.855499 | + | 0.855499i | ||||
\(539\) | −8.49314 | −0.365825 | ||||||||
\(540\) | −3.31690 | − | 3.99977i | −0.142737 | − | 0.172123i | ||||
\(541\) | 8.31756 | + | 8.31756i | 0.357600 | + | 0.357600i | 0.862928 | − | 0.505328i | \(-0.168628\pi\) |
−0.505328 | + | 0.862928i | \(0.668628\pi\) | |||||||
\(542\) | −11.5487 | − | 11.5487i | −0.496060 | − | 0.496060i | ||||
\(543\) | −1.52809 | + | 2.46673i | −0.0655765 | + | 0.105857i | ||||
\(544\) | 3.95206 | 0.169443 | ||||||||
\(545\) | −1.25137 | −0.0536030 | ||||||||
\(546\) | 1.92979 | + | 1.19546i | 0.0825873 | + | 0.0511611i | ||||
\(547\) | −11.6801 | + | 11.6801i | −0.499403 | + | 0.499403i | −0.911252 | − | 0.411849i | \(-0.864883\pi\) |
0.411849 | + | 0.911252i | \(0.364883\pi\) | |||||||
\(548\) | 8.31134 | 0.355043 | ||||||||
\(549\) | −10.4974 | − | 3.52353i | −0.448019 | − | 0.150381i | ||||
\(550\) | −0.874474 | + | 0.874474i | −0.0372877 | + | 0.0372877i | ||||
\(551\) | − | 4.52181i | − | 0.192636i | ||||||
\(552\) | 0.951603 | + | 0.589498i | 0.0405029 | + | 0.0250907i | ||||
\(553\) | 0.844660 | + | 0.844660i | 0.0359186 | + | 0.0359186i | ||||
\(554\) | 4.69968 | 0.199670 | ||||||||
\(555\) | 3.65445 | − | 9.88155i | 0.155123 | − | 0.419448i | ||||
\(556\) | −2.62959 | −0.111520 | ||||||||
\(557\) | 31.2058 | + | 31.2058i | 1.32223 | + | 1.32223i | 0.911964 | + | 0.410270i | \(0.134566\pi\) |
0.410270 | + | 0.911964i | \(0.365434\pi\) | |||||||
\(558\) | 0.308849 | + | 0.620938i | 0.0130746 | + | 0.0262864i | ||||
\(559\) | 24.2211i | 1.02444i | ||||||||
\(560\) | 0.257268 | − | 0.257268i | 0.0108716 | − | 0.0108716i | ||||
\(561\) | 1.93634 | + | 8.24095i | 0.0817522 | + | 0.347933i | ||||
\(562\) | −3.19146 | −0.134624 | ||||||||
\(563\) | −2.07352 | + | 2.07352i | −0.0873885 | + | 0.0873885i | −0.749450 | − | 0.662061i | \(-0.769682\pi\) |
0.662061 | + | 0.749450i | \(0.269682\pi\) | |||||||
\(564\) | −1.46357 | + | 2.36259i | −0.0616275 | + | 0.0994828i | ||||
\(565\) | −10.4652 | −0.440276 | ||||||||
\(566\) | −19.7177 | −0.828796 | ||||||||
\(567\) | −1.97563 | + | 2.61136i | −0.0829685 | + | 0.109667i | ||||
\(568\) | 10.4722 | + | 10.4722i | 0.439404 | + | 0.439404i | ||||
\(569\) | 14.1395 | + | 14.1395i | 0.592758 | + | 0.592758i | 0.938376 | − | 0.345617i | \(-0.112330\pi\) |
−0.345617 | + | 0.938376i | \(0.612330\pi\) | |||||||
\(570\) | −3.34382 | + | 0.785681i | −0.140057 | + | 0.0329086i | ||||
\(571\) | −17.4906 | −0.731960 | −0.365980 | − | 0.930623i | \(-0.619266\pi\) | ||||
−0.365980 | + | 0.930623i | \(0.619266\pi\) | |||||||
\(572\) | −3.15010 | + | 3.15010i | −0.131712 | + | 0.131712i | ||||
\(573\) | −3.51874 | − | 14.9756i | −0.146998 | − | 0.625615i | ||||
\(574\) | 0.140254 | + | 0.140254i | 0.00585408 | + | 0.00585408i | ||||
\(575\) | −0.456993 | − | 0.456993i | −0.0190579 | − | 0.0190579i | ||||
\(576\) | −2.68608 | + | 1.33603i | −0.111920 | + | 0.0556679i | ||||
\(577\) | 23.1142 | + | 23.1142i | 0.962256 | + | 0.962256i | 0.999313 | − | 0.0370574i | \(-0.0117984\pi\) |
−0.0370574 | + | 0.999313i | \(0.511798\pi\) | |||||||
\(578\) | 0.976650 | − | 0.976650i | 0.0406233 | − | 0.0406233i | ||||
\(579\) | −9.88532 | + | 2.32271i | −0.410820 | + | 0.0965284i | ||||
\(580\) | 2.28014i | 0.0946776i | ||||||||
\(581\) | 3.07066i | 0.127392i | ||||||||
\(582\) | −1.81299 | − | 1.12311i | −0.0751507 | − | 0.0465543i | ||||
\(583\) | 9.91884i | 0.410796i | ||||||||
\(584\) | 1.13662 | + | 1.13662i | 0.0470337 | + | 0.0470337i | ||||
\(585\) | 4.81275 | + | 9.67600i | 0.198983 | + | 0.400053i | ||||
\(586\) | 12.3265 | − | 12.3265i | 0.509203 | − | 0.509203i | ||||
\(587\) | 16.8989 | + | 16.8989i | 0.697491 | + | 0.697491i | 0.963869 | − | 0.266378i | \(-0.0858268\pi\) |
−0.266378 | + | 0.963869i | \(0.585827\pi\) | |||||||
\(588\) | 10.1120 | + | 6.26418i | 0.417013 | + | 0.258330i | ||||
\(589\) | 0.458438 | 0.0188896 | ||||||||
\(590\) | −6.45749 | + | 6.45749i | −0.265851 | + | 0.265851i | ||||
\(591\) | 26.3670 | + | 16.3338i | 1.08459 | + | 0.671883i | ||||
\(592\) | −5.07126 | − | 3.35892i | −0.208427 | − | 0.138051i | ||||
\(593\) | − | 35.3242i | − | 1.45059i | −0.688438 | − | 0.725295i | \(-0.741703\pi\) | ||
0.688438 | − | 0.725295i | \(-0.258297\pi\) | |||||||
\(594\) | −4.10199 | − | 4.94649i | −0.168307 | − | 0.202957i | ||||
\(595\) | 1.43789i | 0.0589477i | ||||||||
\(596\) | 10.2673 | 0.420566 | ||||||||
\(597\) | −9.49372 | − | 40.4048i | −0.388552 | − | 1.65366i | ||||
\(598\) | −1.64622 | − | 1.64622i | −0.0673188 | − | 0.0673188i | ||||
\(599\) | − | 14.7052i | − | 0.600838i | −0.953807 | − | 0.300419i | \(-0.902874\pi\) | ||
0.953807 | − | 0.300419i | \(-0.0971264\pi\) | |||||||
\(600\) | 1.68613 | − | 0.396182i | 0.0688360 | − | 0.0161741i | ||||
\(601\) | −5.81380 | −0.237150 | −0.118575 | − | 0.992945i | \(-0.537833\pi\) | ||||
−0.118575 | + | 0.992945i | \(0.537833\pi\) | |||||||
\(602\) | − | 2.44635i | − | 0.0997057i | ||||||
\(603\) | 13.2957 | − | 6.61313i | 0.541441 | − | 0.269308i | ||||
\(604\) | 5.53248 | 0.225113 | ||||||||
\(605\) | 6.69672 | − | 6.69672i | 0.272260 | − | 0.272260i | ||||
\(606\) | 1.46499 | − | 0.344221i | 0.0595110 | − | 0.0139830i | ||||
\(607\) | −4.11260 | + | 4.11260i | −0.166925 | + | 0.166925i | −0.785626 | − | 0.618701i | \(-0.787659\pi\) |
0.618701 | + | 0.785626i | \(0.287659\pi\) | |||||||
\(608\) | 1.98313i | 0.0804266i | ||||||||
\(609\) | 1.39879 | − | 0.328668i | 0.0566820 | − | 0.0133183i | ||||
\(610\) | 2.60993 | − | 2.60993i | 0.105673 | − | 0.105673i | ||||
\(611\) | 4.08713 | − | 4.08713i | 0.165348 | − | 0.165348i | ||||
\(612\) | 3.77275 | − | 11.2399i | 0.152504 | − | 0.454346i | ||||
\(613\) | − | 9.41341i | − | 0.380204i | −0.981764 | − | 0.190102i | \(-0.939118\pi\) | ||
0.981764 | − | 0.190102i | \(-0.0608819\pi\) | |||||||
\(614\) | 3.67626 | − | 3.67626i | 0.148362 | − | 0.148362i | ||||
\(615\) | 0.215985 | + | 0.919221i | 0.00870936 | + | 0.0370666i | ||||
\(616\) | 0.318162 | − | 0.318162i | 0.0128191 | − | 0.0128191i | ||||
\(617\) | −24.1161 | −0.970877 | −0.485438 | − | 0.874271i | \(-0.661340\pi\) | ||||
−0.485438 | + | 0.874271i | \(0.661340\pi\) | |||||||
\(618\) | 9.91928 | − | 16.0123i | 0.399012 | − | 0.644109i | ||||
\(619\) | − | 36.1762i | − | 1.45404i | −0.686614 | − | 0.727022i | \(-0.740904\pi\) | ||
0.686614 | − | 0.727022i | \(-0.259096\pi\) | |||||||
\(620\) | −0.231169 | −0.00928397 | ||||||||
\(621\) | 2.58500 | − | 2.14367i | 0.103732 | − | 0.0860224i | ||||
\(622\) | − | 5.40903i | − | 0.216882i | ||||||
\(623\) | −0.200203 | − | 0.200203i | −0.00802096 | − | 0.00802096i | ||||
\(624\) | 6.07391 | − | 1.42716i | 0.243151 | − | 0.0571320i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 33.3908i | 1.33457i | ||||||||
\(627\) | −4.13528 | + | 0.971646i | −0.165147 | + | 0.0388038i | ||||
\(628\) | 7.35707i | 0.293579i | ||||||||
\(629\) | 23.5584 | − | 4.78516i | 0.939335 | − | 0.190797i | ||||
\(630\) | −0.486091 | − | 0.977282i | −0.0193663 | − | 0.0389359i | ||||
\(631\) | −21.7680 | + | 21.7680i | −0.866571 | + | 0.866571i | −0.992091 | − | 0.125520i | \(-0.959940\pi\) |
0.125520 | + | 0.992091i | \(0.459940\pi\) | |||||||
\(632\) | 3.28319 | 0.130598 | ||||||||
\(633\) | −19.8136 | + | 31.9844i | −0.787521 | + | 1.27126i | ||||
\(634\) | 10.3584 | + | 10.3584i | 0.411384 | + | 0.411384i | ||||
\(635\) | −13.3735 | + | 13.3735i | −0.530710 | + | 0.530710i | ||||
\(636\) | 7.31572 | − | 11.8095i | 0.290087 | − | 0.468276i | ||||
\(637\) | −17.4932 | − | 17.4932i | −0.693105 | − | 0.693105i | ||||
\(638\) | 2.81983i | 0.111638i | ||||||||
\(639\) | 39.7807 | − | 19.7865i | 1.57370 | − | 0.782744i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 4.70643i | 0.185893i | 0.995671 | + | 0.0929463i | \(0.0296285\pi\) | ||||
−0.995671 | + | 0.0929463i | \(0.970371\pi\) | |||||||
\(642\) | 3.19265 | + | 13.5878i | 0.126004 | + | 0.536266i | ||||
\(643\) | −17.4164 | + | 17.4164i | −0.686836 | + | 0.686836i | −0.961531 | − | 0.274695i | \(-0.911423\pi\) |
0.274695 | + | 0.961531i | \(0.411423\pi\) | |||||||
\(644\) | 0.166269 | + | 0.166269i | 0.00655191 | + | 0.00655191i | ||||
\(645\) | 6.13303 | − | 9.90030i | 0.241488 | − | 0.389824i | ||||
\(646\) | −5.54192 | − | 5.54192i | −0.218044 | − | 0.218044i | ||||
\(647\) | 4.39908 | + | 4.39908i | 0.172946 | + | 0.172946i | 0.788272 | − | 0.615327i | \(-0.210976\pi\) |
−0.615327 | + | 0.788272i | \(0.710976\pi\) | |||||||
\(648\) | 1.23555 | + | 8.91479i | 0.0485368 | + | 0.350206i | ||||
\(649\) | −7.98593 | + | 7.98593i | −0.313475 | + | 0.313475i | ||||
\(650\) | −3.60228 | −0.141293 | ||||||||
\(651\) | 0.0333216 | + | 0.141815i | 0.00130598 | + | 0.00555817i | ||||
\(652\) | 8.15725 | + | 8.15725i | 0.319463 | + | 0.319463i | ||||
\(653\) | −29.2611 | − | 29.2611i | −1.14507 | − | 1.14507i | −0.987508 | − | 0.157567i | \(-0.949635\pi\) |
−0.157567 | − | 0.987508i | \(-0.550365\pi\) | |||||||
\(654\) | 1.84255 | + | 1.14142i | 0.0720492 | + | 0.0446330i | ||||
\(655\) | −2.46874 | −0.0964616 | ||||||||
\(656\) | 0.545166 | 0.0212851 | ||||||||
\(657\) | 4.31767 | − | 2.14757i | 0.168448 | − | 0.0837847i | ||||
\(658\) | −0.412803 | + | 0.412803i | −0.0160927 | + | 0.0160927i | ||||
\(659\) | −1.26482 | −0.0492703 | −0.0246351 | − | 0.999697i | \(-0.507842\pi\) | ||||
−0.0246351 | + | 0.999697i | \(0.507842\pi\) | |||||||
\(660\) | 2.08523 | − | 0.489956i | 0.0811673 | − | 0.0190715i | ||||
\(661\) | −14.4067 | + | 14.4067i | −0.560357 | + | 0.560357i | −0.929409 | − | 0.369052i | \(-0.879682\pi\) |
0.369052 | + | 0.929409i | \(0.379682\pi\) | |||||||
\(662\) | 3.92816i | 0.152672i | ||||||||
\(663\) | −12.9855 | + | 20.9620i | −0.504315 | + | 0.814096i | ||||
\(664\) | 5.96781 | + | 5.96781i | 0.231596 | + | 0.231596i | ||||
\(665\) | −0.721527 | −0.0279796 | ||||||||
\(666\) | −14.3941 | + | 11.2164i | −0.557762 | + | 0.434628i | ||||
\(667\) | −1.47362 | −0.0570588 | ||||||||
\(668\) | −7.06777 | − | 7.06777i | −0.273460 | − | 0.273460i | ||||
\(669\) | −6.60940 | + | 10.6693i | −0.255534 | + | 0.412499i | ||||
\(670\) | 4.94984i | 0.191229i | ||||||||
\(671\) | 3.22768 | − | 3.22768i | 0.124603 | − | 0.124603i | ||||
\(672\) | −0.613469 | + | 0.144144i | −0.0236651 | + | 0.00556047i | ||||
\(673\) | −4.92341 | −0.189784 | −0.0948918 | − | 0.995488i | \(-0.530251\pi\) | ||||
−0.0948918 | + | 0.995488i | \(0.530251\pi\) | |||||||
\(674\) | 8.28004 | − | 8.28004i | 0.318935 | − | 0.318935i | ||||
\(675\) | 0.482863 | − | 5.17367i | 0.0185854 | − | 0.199135i | ||||
\(676\) | 0.0236067 | 0.000907951 | ||||||||
\(677\) | 27.8288 | 1.06955 | 0.534775 | − | 0.844995i | \(-0.320396\pi\) | ||||
0.534775 | + | 0.844995i | \(0.320396\pi\) | |||||||
\(678\) | 15.4092 | + | 9.54569i | 0.591788 | + | 0.366600i | ||||
\(679\) | −0.316774 | − | 0.316774i | −0.0121567 | − | 0.0121567i | ||||
\(680\) | 2.79453 | + | 2.79453i | 0.107165 | + | 0.107165i | ||||
\(681\) | −4.04437 | − | 17.2126i | −0.154980 | − | 0.659589i | ||||
\(682\) | −0.285885 | −0.0109471 | ||||||||
\(683\) | 0.306666 | − | 0.306666i | 0.0117343 | − | 0.0117343i | −0.701215 | − | 0.712950i | \(-0.747359\pi\) |
0.712950 | + | 0.701215i | \(0.247359\pi\) | |||||||
\(684\) | 5.64015 | + | 1.89315i | 0.215656 | + | 0.0723865i | ||||
\(685\) | 5.87700 | + | 5.87700i | 0.224549 | + | 0.224549i | ||||
\(686\) | 3.56770 | + | 3.56770i | 0.136215 | + | 0.136215i | ||||
\(687\) | 13.7706 | − | 22.2293i | 0.525381 | − | 0.848102i | ||||
\(688\) | −4.75447 | − | 4.75447i | −0.181263 | − | 0.181263i | ||||
\(689\) | −20.4297 | + | 20.4297i | −0.778308 | + | 0.778308i | ||||
\(690\) | 0.256047 | + | 1.08972i | 0.00974754 | + | 0.0414851i | ||||
\(691\) | − | 6.54668i | − | 0.249048i | −0.992217 | − | 0.124524i | \(-0.960260\pi\) | ||
0.992217 | − | 0.124524i | \(-0.0397403\pi\) | |||||||
\(692\) | − | 6.52900i | − | 0.248195i | ||||||
\(693\) | −0.601145 | − | 1.20860i | −0.0228356 | − | 0.0459108i | ||||
\(694\) | − | 28.1966i | − | 1.07033i | ||||||
\(695\) | −1.85940 | − | 1.85940i | −0.0705312 | − | 0.0705312i | ||||
\(696\) | 2.07979 | − | 3.35732i | 0.0788341 | − | 0.127259i | ||||
\(697\) | −1.52348 | + | 1.52348i | −0.0577060 | + | 0.0577060i | ||||
\(698\) | 14.6252 | + | 14.6252i | 0.553574 | + | 0.553574i | ||||
\(699\) | 1.52687 | − | 2.46477i | 0.0577517 | − | 0.0932262i | ||||
\(700\) | 0.363832 | 0.0137516 | ||||||||
\(701\) | −15.0325 | + | 15.0325i | −0.567769 | + | 0.567769i | −0.931503 | − | 0.363734i | \(-0.881502\pi\) |
0.363734 | + | 0.931503i | \(0.381502\pi\) | |||||||
\(702\) | 1.73940 | − | 18.6370i | 0.0656496 | − | 0.703408i | ||||
\(703\) | 2.40118 | + | 11.8215i | 0.0905621 | + | 0.445857i | ||||
\(704\) | − | 1.23669i | − | 0.0466096i | ||||||
\(705\) | −2.70550 | + | 0.635699i | −0.101895 | + | 0.0239418i | ||||
\(706\) | 7.59069i | 0.285680i | ||||||||
\(707\) | 0.316114 | 0.0118887 | ||||||||
\(708\) | 15.3982 | − | 3.61804i | 0.578700 | − | 0.135974i | ||||
\(709\) | −36.1363 | − | 36.1363i | −1.35713 | − | 1.35713i | −0.877438 | − | 0.479690i | \(-0.840749\pi\) |
−0.479690 | − | 0.877438i | \(-0.659251\pi\) | |||||||
\(710\) | 14.8100i | 0.555808i | ||||||||
\(711\) | 3.13422 | − | 9.33759i | 0.117543 | − | 0.350187i | ||||
\(712\) | −0.778187 | −0.0291638 | ||||||||
\(713\) | − | 0.149401i | − | 0.00559512i | ||||||
\(714\) | 1.31154 | − | 2.11717i | 0.0490833 | − | 0.0792332i | ||||
\(715\) | −4.45491 | −0.166604 | ||||||||
\(716\) | 5.04499 | − | 5.04499i | 0.188540 | − | 0.188540i | ||||
\(717\) | 5.00885 | + | 21.3174i | 0.187059 | + | 0.796113i | ||||
\(718\) | −10.9701 | + | 10.9701i | −0.409401 | + | 0.409401i | ||||
\(719\) | − | 17.6902i | − | 0.659734i | −0.944027 | − | 0.329867i | \(-0.892996\pi\) | ||
0.944027 | − | 0.329867i | \(-0.107004\pi\) | |||||||
\(720\) | −2.84406 | − | 0.954629i | −0.105992 | − | 0.0355769i | ||||
\(721\) | 2.79775 | − | 2.79775i | 0.104194 | − | 0.104194i | ||||
\(722\) | −10.6541 | + | 10.6541i | −0.396505 | + | 0.396505i | ||||
\(723\) | 4.53172 | − | 1.06480i | 0.168536 | − | 0.0396002i | ||||
\(724\) | 1.67529i | 0.0622617i | ||||||||
\(725\) | −1.61230 | + | 1.61230i | −0.0598793 | + | 0.0598793i | ||||
\(726\) | −15.9687 | + | 3.75208i | −0.592653 | + | 0.139253i | ||||
\(727\) | −28.1049 | + | 28.1049i | −1.04235 | + | 1.04235i | −0.0432905 | + | 0.999063i | \(0.513784\pi\) |
−0.999063 | + | 0.0432905i | \(0.986216\pi\) | |||||||
\(728\) | 1.31062 | 0.0485750 | ||||||||
\(729\) | 26.5337 | + | 4.99634i | 0.982729 | + | 0.185050i | ||||
\(730\) | 1.60743i | 0.0594935i | ||||||||
\(731\) | 26.5730 | 0.982839 | ||||||||
\(732\) | −6.22350 | + | 1.46231i | −0.230027 | + | 0.0540484i | ||||
\(733\) | − | 13.3828i | − | 0.494305i | −0.968977 | − | 0.247152i | \(-0.920505\pi\) | ||
0.968977 | − | 0.247152i | \(-0.0794948\pi\) | |||||||
\(734\) | 16.6273 | + | 16.6273i | 0.613724 | + | 0.613724i | ||||
\(735\) | 2.72083 | + | 11.5797i | 0.100359 | + | 0.427124i | ||||
\(736\) | 0.646286 | 0.0238224 | ||||||||
\(737\) | 6.12143i | 0.225486i | ||||||||
\(738\) | 0.520431 | − | 1.55048i | 0.0191573 | − | 0.0570741i | ||||
\(739\) | − | 16.3486i | − | 0.601394i | −0.953720 | − | 0.300697i | \(-0.902781\pi\) | ||
0.953720 | − | 0.300697i | \(-0.0972192\pi\) | |||||||
\(740\) | −1.21080 | − | 5.96104i | −0.0445099 | − | 0.219132i | ||||
\(741\) | −10.5186 | − | 6.51608i | −0.386412 | − | 0.239374i | ||||
\(742\) | 2.06341 | − | 2.06341i | 0.0757501 | − | 0.0757501i | ||||
\(743\) | −30.1894 | −1.10754 | −0.553770 | − | 0.832670i | \(-0.686811\pi\) | ||||
−0.553770 | + | 0.832670i | \(0.686811\pi\) | |||||||
\(744\) | 0.340377 | + | 0.210857i | 0.0124788 | + | 0.00773038i | ||||
\(745\) | 7.26009 | + | 7.26009i | 0.265989 | + | 0.265989i | ||||
\(746\) | −26.4460 | + | 26.4460i | −0.968255 | + | 0.968255i | ||||
\(747\) | 22.6699 | − | 11.2758i | 0.829447 | − | 0.412559i | ||||
\(748\) | 3.45598 | + | 3.45598i | 0.126363 | + | 0.126363i | ||||
\(749\) | 2.93196i | 0.107131i | ||||||||
\(750\) | 1.47242 | + | 0.912132i | 0.0537651 | + | 0.0333063i | ||||
\(751\) | − | 18.3159i | − | 0.668356i | −0.942510 | − | 0.334178i | \(-0.891541\pi\) | ||
0.942510 | − | 0.334178i | \(-0.108459\pi\) | |||||||
\(752\) | 1.60456i | 0.0585124i | ||||||||
\(753\) | −16.7208 | + | 3.92880i | −0.609340 | + | 0.143174i | ||||
\(754\) | −5.80795 | + | 5.80795i | −0.211513 | + | 0.211513i | ||||
\(755\) | 3.91205 | + | 3.91205i | 0.142374 | + | 0.142374i | ||||
\(756\) | −0.175681 | + | 1.88235i | −0.00638946 | + | 0.0684603i | ||||
\(757\) | −24.8581 | − | 24.8581i | −0.903485 | − | 0.903485i | 0.0922511 | − | 0.995736i | \(-0.470594\pi\) |
−0.995736 | + | 0.0922511i | \(0.970594\pi\) | |||||||
\(758\) | −21.4716 | − | 21.4716i | −0.779883 | − | 0.779883i | ||||
\(759\) | 0.316651 | + | 1.34765i | 0.0114937 | + | 0.0489167i | ||||
\(760\) | −1.40229 | + | 1.40229i | −0.0508662 | + | 0.0508662i | ||||
\(761\) | −5.56719 | −0.201811 | −0.100905 | − | 0.994896i | \(-0.532174\pi\) | ||||
−0.100905 | + | 0.994896i | \(0.532174\pi\) | |||||||
\(762\) | 31.8897 | − | 7.49298i | 1.15524 | − | 0.271442i | ||||
\(763\) | 0.321939 | + | 0.321939i | 0.0116550 | + | 0.0116550i | ||||
\(764\) | −6.28026 | − | 6.28026i | −0.227212 | − | 0.227212i | ||||
\(765\) | 10.6156 | − | 5.28008i | 0.383806 | − | 0.190902i | ||||
\(766\) | 4.90455 | 0.177209 | ||||||||
\(767\) | −32.8970 | −1.18784 | ||||||||
\(768\) | −0.912132 | + | 1.47242i | −0.0329137 | + | 0.0531313i | ||||
\(769\) | −27.1725 | + | 27.1725i | −0.979867 | + | 0.979867i | −0.999801 | − | 0.0199341i | \(-0.993654\pi\) |
0.0199341 | + | 0.999801i | \(0.493654\pi\) | |||||||
\(770\) | 0.449949 | 0.0162150 | ||||||||
\(771\) | −7.96167 | − | 33.8845i | −0.286732 | − | 1.22032i | ||||
\(772\) | −4.14557 | + | 4.14557i | −0.149202 | + | 0.149202i | ||||
\(773\) | − | 33.3633i | − | 1.19999i | −0.800002 | − | 0.599997i | \(-0.795168\pi\) | ||
0.800002 | − | 0.599997i | \(-0.204832\pi\) | |||||||
\(774\) | −18.0608 | + | 8.98325i | −0.649181 | + | 0.322896i | ||||
\(775\) | −0.163461 | − | 0.163461i | −0.00587170 | − | 0.00587170i | ||||
\(776\) | −1.23130 | −0.0442010 | ||||||||
\(777\) | −3.48238 | + | 1.60204i | −0.124930 | + | 0.0574727i | ||||
\(778\) | −10.7881 | −0.386772 | ||||||||
\(779\) | −0.764478 | − | 0.764478i | −0.0273903 | − | 0.0273903i | ||||
\(780\) | 5.30406 | + | 3.28575i | 0.189916 | + | 0.117649i | ||||
\(781\) | 18.3154i | 0.655375i | ||||||||
\(782\) | −1.80607 | + | 1.80607i | −0.0645848 | + | 0.0645848i | ||||
\(783\) | −7.56299 | − | 9.12003i | −0.270279 | − | 0.325923i | ||||
\(784\) | 6.86763 | 0.245272 | ||||||||
\(785\) | −5.20223 | + | 5.20223i | −0.185676 | + | 0.185676i | ||||
\(786\) | 3.63502 | + | 2.25182i | 0.129657 | + | 0.0803196i | ||||
\(787\) | −33.9347 | −1.20964 | −0.604820 | − | 0.796362i | \(-0.706755\pi\) | ||||
−0.604820 | + | 0.796362i | \(0.706755\pi\) | |||||||
\(788\) | 17.9073 | 0.637921 | ||||||||
\(789\) | −17.4997 | + | 28.2491i | −0.623006 | + | 1.00569i | ||||
\(790\) | 2.32156 | + | 2.32156i | 0.0825976 | + | 0.0825976i | ||||
\(791\) | 2.69238 | + | 2.69238i | 0.0957299 | + | 0.0957299i | ||||
\(792\) | −3.51723 | − | 1.18058i | −0.124979 | − | 0.0419501i | ||||
\(793\) | 13.2960 | 0.472154 | ||||||||
\(794\) | 11.0720 | − | 11.0720i | 0.392930 | − | 0.392930i | ||||
\(795\) | 13.5235 | − | 3.17756i | 0.479631 | − | 0.112697i | ||||
\(796\) | −16.9444 | − | 16.9444i | −0.600579 | − | 0.600579i | ||||
\(797\) | −13.6606 | − | 13.6606i | −0.483882 | − | 0.483882i | 0.422487 | − | 0.906369i | \(-0.361157\pi\) |
−0.906369 | + | 0.422487i | \(0.861157\pi\) | |||||||
\(798\) | 1.06239 | + | 0.658128i | 0.0376082 | + | 0.0232975i | ||||
\(799\) | −4.48400 | − | 4.48400i | −0.158632 | − | 0.158632i | ||||
\(800\) | 0.707107 | − | 0.707107i | 0.0250000 | − | 0.0250000i | ||||
\(801\) | −0.742880 | + | 2.21321i | −0.0262484 | + | 0.0782000i | ||||
\(802\) | 17.6961i | 0.624871i | ||||||||
\(803\) | 1.98789i | 0.0701511i | ||||||||
\(804\) | 4.51490 | − | 7.28823i | 0.159228 | − | 0.257036i | ||||
\(805\) | 0.235140i | 0.00828758i | ||||||||
\(806\) | −0.588832 | − | 0.588832i | −0.0207407 | − | 0.0207407i | ||||
\(807\) | 41.3197 | + | 25.5967i | 1.45452 | + | 0.901045i | ||||
\(808\) | 0.614366 | − | 0.614366i | 0.0216133 | − | 0.0216133i | ||||
\(809\) | 34.7920 | + | 34.7920i | 1.22322 | + | 1.22322i | 0.966481 | + | 0.256739i | \(0.0826481\pi\) |
0.256739 | + | 0.966481i | \(0.417352\pi\) | |||||||
\(810\) | −5.43004 | + | 7.17737i | −0.190792 | + | 0.252187i | ||||
\(811\) | 26.1483 | 0.918190 | 0.459095 | − | 0.888387i | \(-0.348174\pi\) | ||||
0.459095 | + | 0.888387i | \(0.348174\pi\) | |||||||
\(812\) | 0.586607 | − | 0.586607i | 0.0205859 | − | 0.0205859i | ||||
\(813\) | −14.8973 | + | 24.0481i | −0.522470 | + | 0.843403i | ||||
\(814\) | −1.49739 | − | 7.37197i | −0.0524834 | − | 0.258387i | ||||
\(815\) | 11.5361i | 0.404092i | ||||||||
\(816\) | −1.56574 | − | 6.66370i | −0.0548118 | − | 0.233276i | ||||
\(817\) | 13.3343i | 0.466506i | ||||||||
\(818\) | 14.7465 | 0.515599 | ||||||||
\(819\) | 1.25116 | − | 3.72750i | 0.0437190 | − | 0.130249i | ||||
\(820\) | 0.385490 | + | 0.385490i | 0.0134619 | + | 0.0134619i | ||||
\(821\) | − | 47.8121i | − | 1.66865i | −0.551271 | − | 0.834326i | \(-0.685857\pi\) | ||
0.551271 | − | 0.834326i | \(-0.314143\pi\) | |||||||
\(822\) | −3.29280 | − | 14.0140i | −0.114850 | − | 0.488795i | ||||
\(823\) | 40.9071 | 1.42593 | 0.712967 | − | 0.701198i | \(-0.247351\pi\) | ||||
0.712967 | + | 0.701198i | \(0.247351\pi\) | |||||||
\(824\) | − | 10.8748i | − | 0.378843i | ||||||
\(825\) | 1.82093 | + | 1.12803i | 0.0633966 | + | 0.0392728i | ||||
\(826\) | 3.32262 | 0.115609 | ||||||||
\(827\) | −5.09416 | + | 5.09416i | −0.177141 | + | 0.177141i | −0.790108 | − | 0.612967i | \(-0.789976\pi\) |
0.612967 | + | 0.790108i | \(0.289976\pi\) | |||||||
\(828\) | 0.616963 | − | 1.83808i | 0.0214409 | − | 0.0638776i | ||||
\(829\) | 0.526668 | − | 0.526668i | 0.0182919 | − | 0.0182919i | −0.697902 | − | 0.716194i | \(-0.745883\pi\) |
0.716194 | + | 0.697902i | \(0.245883\pi\) | |||||||
\(830\) | 8.43976i | 0.292948i | ||||||||
\(831\) | −1.86193 | − | 7.92428i | −0.0645897 | − | 0.274890i | ||||
\(832\) | 2.54719 | − | 2.54719i | 0.0883081 | − | 0.0883081i | ||||
\(833\) | −19.1918 | + | 19.1918i | −0.664956 | + | 0.664956i | ||||
\(834\) | 1.04180 | + | 4.43384i | 0.0360745 | + | 0.153531i | ||||
\(835\) | − | 9.99534i | − | 0.345903i | ||||||
\(836\) | −1.73420 | + | 1.73420i | −0.0599784 | + | 0.0599784i | ||||
\(837\) | 0.924623 | − | 0.766764i | 0.0319596 | − | 0.0265032i | ||||
\(838\) | −5.47065 | + | 5.47065i | −0.188980 | + | 0.188980i | ||||
\(839\) | 5.09230 | 0.175806 | 0.0879029 | − | 0.996129i | \(-0.471983\pi\) | ||||
0.0879029 | + | 0.996129i | \(0.471983\pi\) | |||||||
\(840\) | −0.535713 | − | 0.331863i | −0.0184839 | − | 0.0114504i | ||||
\(841\) | − | 23.8010i | − | 0.820723i | ||||||
\(842\) | 10.4208 | 0.359123 | ||||||||
\(843\) | 1.26440 | + | 5.38122i | 0.0435483 | + | 0.185339i | ||||
\(844\) | 21.7223i | 0.747714i | ||||||||
\(845\) | 0.0166925 | + | 0.0166925i | 0.000574239 | + | 0.000574239i | ||||
\(846\) | 4.56347 | + | 1.53176i | 0.156895 | + | 0.0526630i | ||||
\(847\) | −3.44571 | −0.118396 | ||||||||
\(848\) | − | 8.02046i | − | 0.275424i | ||||||
\(849\) | 7.81179 | + | 33.2466i | 0.268100 | + | 1.14102i | ||||
\(850\) | 3.95206i | 0.135555i | ||||||||
\(851\) | 3.85253 | − | 0.782524i | 0.132063 | − | 0.0268246i | ||||
\(852\) | 13.5086 | − | 21.8064i | 0.462798 | − | 0.747076i | ||||
\(853\) | −4.43543 | + | 4.43543i | −0.151866 | + | 0.151866i | −0.778951 | − | 0.627085i | \(-0.784248\pi\) |
0.627085 | + | 0.778951i | \(0.284248\pi\) | |||||||
\(854\) | −1.34290 | −0.0459532 | ||||||||
\(855\) | 2.64952 | + | 5.32685i | 0.0906118 | + | 0.182174i | ||||
\(856\) | 5.69825 | + | 5.69825i | 0.194762 | + | 0.194762i | ||||
\(857\) | −26.3940 | + | 26.3940i | −0.901603 | + | 0.901603i | −0.995575 | − | 0.0939721i | \(-0.970044\pi\) |
0.0939721 | + | 0.995575i | \(0.470044\pi\) | |||||||
\(858\) | 6.55949 | + | 4.06346i | 0.223937 | + | 0.138724i | ||||
\(859\) | 10.3149 | + | 10.3149i | 0.351939 | + | 0.351939i | 0.860831 | − | 0.508891i | \(-0.169945\pi\) |
−0.508891 | + | 0.860831i | \(0.669945\pi\) | |||||||
\(860\) | − | 6.72384i | − | 0.229281i | ||||||
\(861\) | 0.180920 | − | 0.292053i | 0.00616575 | − | 0.00995312i | ||||
\(862\) | − | 30.4872i | − | 1.03840i | ||||||
\(863\) | − | 23.7580i | − | 0.808733i | −0.914597 | − | 0.404366i | \(-0.867492\pi\) | ||
0.914597 | − | 0.404366i | \(-0.132508\pi\) | |||||||
\(864\) | 3.31690 | + | 3.99977i | 0.112843 | + | 0.136075i | ||||
\(865\) | 4.61670 | − | 4.61670i | 0.156973 | − | 0.156973i | ||||
\(866\) | −25.3678 | − | 25.3678i | −0.862034 | − | 0.862034i | ||||
\(867\) | −2.03369 | − | 1.25983i | −0.0690678 | − | 0.0427860i | ||||
\(868\) | 0.0594724 | + | 0.0594724i | 0.00201863 | + | 0.00201863i | ||||
\(869\) | 2.87106 | + | 2.87106i | 0.0973941 | + | 0.0973941i | ||||
\(870\) | 3.84461 | − | 0.903350i | 0.130345 | − | 0.0306264i | ||||
\(871\) | −12.6082 | + | 12.6082i | −0.427212 | + | 0.427212i | ||||
\(872\) | 1.25137 | 0.0423769 | ||||||||
\(873\) | −1.17543 | + | 3.50189i | −0.0397824 | + | 0.118521i | ||||
\(874\) | −0.906278 | − | 0.906278i | −0.0306553 | − | 0.0306553i | ||||
\(875\) | 0.257268 | + | 0.257268i | 0.00869725 | + | 0.00869725i | ||||
\(876\) | 1.46618 | − | 2.36680i | 0.0495378 | − | 0.0799668i | ||||
\(877\) | 26.5447 | 0.896350 | 0.448175 | − | 0.893946i | \(-0.352074\pi\) | ||||
0.448175 | + | 0.893946i | \(0.352074\pi\) | |||||||
\(878\) | −18.6436 | −0.629190 | ||||||||
\(879\) | −25.6676 | − | 15.9006i | −0.865748 | − | 0.536313i | ||||
\(880\) | 0.874474 | − | 0.874474i | 0.0294785 | − | 0.0294785i | ||||
\(881\) | −42.4433 | −1.42995 | −0.714975 | − | 0.699150i | \(-0.753562\pi\) | ||||
−0.714975 | + | 0.699150i | \(0.753562\pi\) | |||||||
\(882\) | 6.55603 | − | 19.5319i | 0.220753 | − | 0.657675i | ||||
\(883\) | 5.29583 | − | 5.29583i | 0.178219 | − | 0.178219i | −0.612360 | − | 0.790579i | \(-0.709780\pi\) |
0.790579 | + | 0.612360i | \(0.209780\pi\) | |||||||
\(884\) | 14.2364i | 0.478823i | ||||||||
\(885\) | 13.4465 | + | 8.32984i | 0.452000 | + | 0.280004i | ||||
\(886\) | −27.9796 | − | 27.9796i | −0.939993 | − | 0.939993i | ||||
\(887\) | −24.9714 | −0.838457 | −0.419228 | − | 0.907881i | \(-0.637699\pi\) | ||||
−0.419228 | + | 0.907881i | \(0.637699\pi\) | |||||||
\(888\) | −3.65445 | + | 9.88155i | −0.122635 | + | 0.331603i | ||||
\(889\) | 6.88114 | 0.230786 | ||||||||
\(890\) | −0.550261 | − | 0.550261i | −0.0184448 | − | 0.0184448i | ||||
\(891\) | −6.71529 | + | 8.87620i | −0.224971 | + | 0.297364i | ||||
\(892\) | 7.24611i | 0.242618i | ||||||||
\(893\) | 2.25005 | − | 2.25005i | 0.0752952 | − | 0.0752952i | ||||
\(894\) | −4.06773 | − | 17.3120i | −0.136045 | − | 0.579001i | ||||
\(895\) | 7.13469 | 0.238486 | ||||||||
\(896\) | −0.257268 | + | 0.257268i | −0.00859473 | + | 0.00859473i | ||||
\(897\) | −2.12353 | + | 3.42794i | −0.0709028 | + | 0.114456i | ||||
\(898\) | −17.3850 | −0.580144 | ||||||||
\(899\) | −0.527097 | −0.0175797 | ||||||||
\(900\) | −1.33603 | − | 2.68608i | −0.0445344 | − | 0.0895360i | ||||
\(901\) | 22.4134 | + | 22.4134i | 0.746699 | + | 0.746699i | ||||
\(902\) | 0.476733 | + | 0.476733i | 0.0158735 | + | 0.0158735i | ||||
\(903\) | −4.12487 | + | 0.969200i | −0.137267 | + | 0.0322530i | ||||
\(904\) | 10.4652 | 0.348069 | ||||||||
\(905\) | −1.18461 | + | 1.18461i | −0.0393778 | + | 0.0393778i | ||||
\(906\) | −2.19187 | − | 9.32848i | −0.0728199 | − | 0.309918i | ||||
\(907\) | −18.6705 | − | 18.6705i | −0.619943 | − | 0.619943i | 0.325573 | − | 0.945517i | \(-0.394443\pi\) |
−0.945517 | + | 0.325573i | \(0.894443\pi\) | |||||||
\(908\) | −7.21839 | − | 7.21839i | −0.239551 | − | 0.239551i | ||||
\(909\) | −1.16080 | − | 2.33379i | −0.0385014 | − | 0.0774068i | ||||
\(910\) | 0.926751 | + | 0.926751i | 0.0307215 | + | 0.0307215i | ||||
\(911\) | −27.8252 | + | 27.8252i | −0.921888 | + | 0.921888i | −0.997163 | − | 0.0752744i | \(-0.976017\pi\) |
0.0752744 | + | 0.997163i | \(0.476017\pi\) | |||||||
\(912\) | 3.34382 | − | 0.785681i | 0.110725 | − | 0.0260165i | ||||
\(913\) | 10.4374i | 0.345427i | ||||||||
\(914\) | − | 22.9623i | − | 0.759525i | ||||||
\(915\) | −5.43469 | − | 3.36667i | −0.179665 | − | 0.111299i | ||||
\(916\) | − | 15.0972i | − | 0.498824i | ||||||
\(917\) | 0.635128 | + | 0.635128i | 0.0209738 | + | 0.0209738i | ||||
\(918\) | −20.4467 | − | 1.90830i | −0.674841 | − | 0.0629834i | ||||
\(919\) | −3.11659 | + | 3.11659i | −0.102807 | + | 0.102807i | −0.756639 | − | 0.653833i | \(-0.773160\pi\) |
0.653833 | + | 0.756639i | \(0.273160\pi\) | |||||||
\(920\) | 0.456993 | + | 0.456993i | 0.0150666 | + | 0.0150666i | ||||
\(921\) | −7.65513 | − | 4.74219i | −0.252245 | − | 0.156261i | ||||
\(922\) | −33.9413 | −1.11780 | ||||||||
\(923\) | −37.7238 | + | 37.7238i | −1.24169 | + | 1.24169i | ||||
\(924\) | −0.662512 | − | 0.410412i | −0.0217951 | − | 0.0135016i | ||||
\(925\) | 3.35892 | − | 5.07126i | 0.110441 | − | 0.166742i | ||||
\(926\) | 12.9920i | 0.426945i | ||||||||
\(927\) | −30.9287 | − | 10.3814i | −1.01583 | − | 0.340971i | ||||
\(928\) | − | 2.28014i | − | 0.0748492i | ||||||
\(929\) | 27.4680 | 0.901196 | 0.450598 | − | 0.892727i | \(-0.351211\pi\) | ||||
0.450598 | + | 0.892727i | \(0.351211\pi\) | |||||||
\(930\) | 0.0915850 | + | 0.389781i | 0.00300319 | + | 0.0127814i | ||||
\(931\) | −9.63037 | − | 9.63037i | −0.315623 | − | 0.315623i | ||||
\(932\) | − | 1.67396i | − | 0.0548324i | ||||||
\(933\) | −9.12033 | + | 2.14296i | −0.298586 | + | 0.0701574i | ||||
\(934\) | 28.0829 | 0.918901 | ||||||||
\(935\) | 4.88749i | 0.159838i | ||||||||
\(936\) | −4.81275 | − | 9.67600i | −0.157310 | − | 0.316270i | ||||
\(937\) | 3.88068 | 0.126776 | 0.0633881 | − | 0.997989i | \(-0.479809\pi\) | ||||
0.0633881 | + | 0.997989i | \(0.479809\pi\) | |||||||
\(938\) | 1.27344 | − | 1.27344i | 0.0415792 | − | 0.0415792i | ||||
\(939\) | 56.3013 | − | 13.2289i | 1.83732 | − | 0.431707i | ||||
\(940\) | −1.13460 | + | 1.13460i | −0.0370065 | + | 0.0370065i | ||||
\(941\) | − | 6.69963i | − | 0.218402i | −0.994020 | − | 0.109201i | \(-0.965171\pi\) | ||
0.994020 | − | 0.109201i | \(-0.0348292\pi\) | |||||||
\(942\) | 12.4050 | − | 2.91474i | 0.404176 | − | 0.0949673i | ||||
\(943\) | −0.249137 | + | 0.249137i | −0.00811302 | + | 0.00811302i | ||||
\(944\) | 6.45749 | − | 6.45749i | 0.210174 | − | 0.210174i | ||||
\(945\) | −1.45525 | + | 1.20680i | −0.0473391 | + | 0.0392571i | ||||
\(946\) | − | 8.31532i | − | 0.270354i | ||||||
\(947\) | −36.9175 | + | 36.9175i | −1.19966 | + | 1.19966i | −0.225387 | + | 0.974269i | \(0.572365\pi\) |
−0.974269 | + | 0.225387i | \(0.927635\pi\) | |||||||
\(948\) | −1.30074 | − | 5.53589i | −0.0422461 | − | 0.179797i | ||||
\(949\) | −4.09442 | + | 4.09442i | −0.132911 | + | 0.132911i | ||||
\(950\) | −1.98313 | −0.0643413 | ||||||||
\(951\) | 13.3618 | − | 21.5694i | 0.433285 | − | 0.699435i | ||||
\(952\) | − | 1.43789i | − | 0.0466022i | ||||||
\(953\) | −39.3439 | −1.27447 | −0.637237 | − | 0.770668i | \(-0.719923\pi\) | ||||
−0.637237 | + | 0.770668i | \(0.719923\pi\) | |||||||
\(954\) | −22.8107 | − | 7.65656i | −0.738523 | − | 0.247890i | ||||
\(955\) | − | 8.88163i | − | 0.287403i | ||||||
\(956\) | 8.93980 | + | 8.93980i | 0.289134 | + | 0.289134i | ||||
\(957\) | 4.75460 | − | 1.11717i | 0.153694 | − | 0.0361129i | ||||
\(958\) | 16.6846 | 0.539054 | ||||||||
\(959\) | − | 3.02393i | − | 0.0976478i | ||||||
\(960\) | −1.68613 | + | 0.396182i | −0.0544197 | + | 0.0127867i | ||||
\(961\) | 30.9466i | 0.998276i | ||||||||
\(962\) | 12.0998 | − | 18.2681i | 0.390112 | − | 0.588986i | ||||
\(963\) | 21.6459 | − | 10.7665i | 0.697528 | − | 0.346944i | ||||
\(964\) | 1.90045 | − | 1.90045i | 0.0612094 | − | 0.0612094i | ||||
\(965\) | −5.86272 | −0.188728 | ||||||||
\(966\) | 0.214478 | − | 0.346224i | 0.00690073 | − | 0.0111396i | ||||
\(967\) | −37.0888 | − | 37.0888i | −1.19269 | − | 1.19269i | −0.976308 | − | 0.216386i | \(-0.930573\pi\) |
−0.216386 | − | 0.976308i | \(-0.569427\pi\) | |||||||
\(968\) | −6.69672 | + | 6.69672i | −0.215241 | + | 0.215241i | ||||
\(969\) | −7.14880 | + | 11.5400i | −0.229653 | + | 0.370719i | ||||
\(970\) | −0.870659 | − | 0.870659i | −0.0279552 | − | 0.0279552i | ||||
\(971\) | − | 56.6923i | − | 1.81934i | −0.415328 | − | 0.909672i | \(-0.636333\pi\) | ||
0.415328 | − | 0.909672i | \(-0.363667\pi\) | |||||||
\(972\) | 14.5420 | − | 5.61517i | 0.466435 | − | 0.180107i | ||||
\(973\) | 0.956730i | 0.0306714i | ||||||||
\(974\) | 35.5327i | 1.13854i | ||||||||
\(975\) | 1.42716 | + | 6.07391i | 0.0457056 | + | 0.194521i | ||||
\(976\) | −2.60993 | + | 2.60993i | −0.0835418 | + | 0.0835418i | ||||
\(977\) | −3.60270 | − | 3.60270i | −0.115261 | − | 0.115261i | 0.647124 | − | 0.762385i | \(-0.275972\pi\) |
−0.762385 | + | 0.647124i | \(0.775972\pi\) | |||||||
\(978\) | 10.5224 | − | 16.9860i | 0.336470 | − | 0.543151i | ||||
\(979\) | −0.680504 | − | 0.680504i | −0.0217490 | − | 0.0217490i | ||||
\(980\) | 4.85614 | + | 4.85614i | 0.155124 | + | 0.155124i | ||||
\(981\) | 1.19460 | − | 3.55898i | 0.0381405 | − | 0.113630i | ||||
\(982\) | −3.27276 | + | 3.27276i | −0.104438 | + | 0.104438i | ||||
\(983\) | −1.73393 | −0.0553037 | −0.0276518 | − | 0.999618i | \(-0.508803\pi\) | ||||
−0.0276518 | + | 0.999618i | \(0.508803\pi\) | |||||||
\(984\) | −0.215985 | − | 0.919221i | −0.00688535 | − | 0.0293037i | ||||
\(985\) | 12.6624 | + | 12.6624i | 0.403457 | + | 0.403457i | ||||
\(986\) | 6.37192 | + | 6.37192i | 0.202923 | + | 0.202923i | ||||
\(987\) | 0.859585 | + | 0.532495i | 0.0273609 | + | 0.0169495i | ||||
\(988\) | −7.14379 | −0.227274 | ||||||||
\(989\) | 4.34552 | 0.138180 | ||||||||
\(990\) | −1.65226 | − | 3.32185i | −0.0525122 | − | 0.105575i | ||||
\(991\) | 2.15717 | − | 2.15717i | 0.0685249 | − | 0.0685249i | −0.672014 | − | 0.740539i | \(-0.734570\pi\) |
0.740539 | + | 0.672014i | \(0.234570\pi\) | |||||||
\(992\) | 0.231169 | 0.00733962 | ||||||||
\(993\) | 6.62340 | − | 1.55627i | 0.210187 | − | 0.0493867i | ||||
\(994\) | 3.81013 | − | 3.81013i | 0.120850 | − | 0.120850i | ||||
\(995\) | − | 23.9630i | − | 0.759679i | ||||||
\(996\) | 7.69817 | − | 12.4269i | 0.243926 | − | 0.393760i | ||||
\(997\) | −22.8790 | − | 22.8790i | −0.724584 | − | 0.724584i | 0.244951 | − | 0.969535i | \(-0.421228\pi\) |
−0.969535 | + | 0.244951i | \(0.921228\pi\) | |||||||
\(998\) | 7.82896 | 0.247822 | ||||||||
\(999\) | 24.6151 | + | 19.8267i | 0.778787 | + | 0.627288i |
(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 | 1110.2.u.e.191.6 | ✓ | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.e.191.17 | yes | 40 | |
37.31 | odd | 4 | inner | 1110.2.u.e.401.17 | yes | 40 | |
111.68 | even | 4 | inner | 1110.2.u.e.401.6 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.e.191.6 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1110.2.u.e.191.17 | yes | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.e.401.6 | yes | 40 | 111.68 | even | 4 | inner | |
1110.2.u.e.401.17 | yes | 40 | 37.31 | odd | 4 | inner |