Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(136,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 136.4 | ||
Character | \(\chi\) | \(=\) | 819.136 |
Dual form | 819.2.et.c.271.4 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.556084 | + | 0.556084i | −0.393211 | + | 0.393211i | −0.875830 | − | 0.482619i | \(-0.839685\pi\) |
0.482619 | + | 0.875830i | \(0.339685\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.38154i | 0.690770i | ||||||||
\(5\) | −0.542987 | + | 2.02645i | −0.242831 | + | 0.906258i | 0.731630 | + | 0.681702i | \(0.238760\pi\) |
−0.974461 | + | 0.224556i | \(0.927907\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.405927 | − | 2.61443i | −0.153426 | − | 0.988160i | ||||
\(8\) | −1.88042 | − | 1.88042i | −0.664829 | − | 0.664829i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.824932 | − | 1.42882i | −0.260867 | − | 0.451834i | ||||
\(11\) | 0.632763 | − | 2.36150i | 0.190785 | − | 0.712020i | −0.802532 | − | 0.596608i | \(-0.796515\pi\) |
0.993318 | − | 0.115412i | \(-0.0368188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.96880 | − | 3.02057i | 0.546048 | − | 0.837754i | ||||
\(14\) | 1.67957 | + | 1.22811i | 0.448884 | + | 0.328227i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.671737 | −0.167934 | ||||||||
\(17\) | −6.55339 | −1.58943 | −0.794715 | − | 0.606983i | \(-0.792380\pi\) | ||||
−0.794715 | + | 0.606983i | \(0.792380\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.74006 | + | 2.07394i | −1.77569 | + | 0.475795i | −0.989787 | − | 0.142552i | \(-0.954469\pi\) |
−0.785905 | + | 0.618347i | \(0.787803\pi\) | |||||||
\(20\) | −2.79963 | − | 0.750158i | −0.626016 | − | 0.167740i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.961326 | + | 1.66506i | 0.204955 | + | 0.354993i | ||||
\(23\) | − | 3.84618i | − | 0.801984i | −0.916082 | − | 0.400992i | \(-0.868665\pi\) | ||
0.916082 | − | 0.400992i | \(-0.131335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.518448 | + | 0.299326i | 0.103690 | + | 0.0598652i | ||||
\(26\) | 0.584868 | + | 2.77451i | 0.114702 | + | 0.544126i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.61194 | − | 0.560804i | 0.682592 | − | 0.105982i | ||||
\(29\) | 1.25425 | − | 2.17242i | 0.232908 | − | 0.403408i | −0.725755 | − | 0.687954i | \(-0.758509\pi\) |
0.958663 | + | 0.284545i | \(0.0918426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.457027 | + | 0.122460i | −0.0820844 | + | 0.0219945i | −0.299628 | − | 0.954056i | \(-0.596862\pi\) |
0.217543 | + | 0.976051i | \(0.430196\pi\) | |||||||
\(32\) | 4.13438 | − | 4.13438i | 0.730863 | − | 0.730863i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.64424 | − | 3.64424i | 0.624981 | − | 0.624981i | ||||
\(35\) | 5.51843 | + | 0.597007i | 0.932784 | + | 0.100913i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00037 | − | 5.00037i | −0.822055 | − | 0.822055i | 0.164347 | − | 0.986403i | \(-0.447448\pi\) |
−0.986403 | + | 0.164347i | \(0.947448\pi\) | |||||||
\(38\) | 3.15084 | − | 5.45741i | 0.511134 | − | 0.885309i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.83163 | − | 2.78954i | 0.763948 | − | 0.441065i | ||||
\(41\) | 11.0034 | − | 2.94834i | 1.71844 | − | 0.460454i | 0.740970 | − | 0.671538i | \(-0.234366\pi\) |
0.977468 | + | 0.211084i | \(0.0676993\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.810492 | − | 0.467938i | 0.123599 | − | 0.0713598i | −0.436926 | − | 0.899497i | \(-0.643933\pi\) |
0.560525 | + | 0.828138i | \(0.310599\pi\) | |||||||
\(44\) | 3.26252 | + | 0.874188i | 0.491843 | + | 0.131789i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.13880 | + | 2.13880i | 0.315349 | + | 0.315349i | ||||
\(47\) | −7.03848 | − | 1.88596i | −1.02667 | − | 0.275095i | −0.294090 | − | 0.955778i | \(-0.595017\pi\) |
−0.732578 | + | 0.680683i | \(0.761683\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.67045 | + | 2.12253i | −0.952921 | + | 0.303219i | ||||
\(50\) | −0.454751 | + | 0.121850i | −0.0643115 | + | 0.0172322i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.17303 | + | 2.71998i | 0.578696 | + | 0.377194i | ||||
\(53\) | 1.08341 | − | 1.87652i | 0.148818 | − | 0.257760i | −0.781973 | − | 0.623312i | \(-0.785787\pi\) |
0.930791 | + | 0.365552i | \(0.119120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.44190 | + | 2.56453i | 0.598945 | + | 0.345801i | ||||
\(56\) | −4.15291 | + | 5.67954i | −0.554956 | + | 0.758960i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.510581 | + | 1.90552i | 0.0670426 | + | 0.250206i | ||||
\(59\) | 3.92820 | − | 3.92820i | 0.511408 | − | 0.511408i | −0.403550 | − | 0.914958i | \(-0.632224\pi\) |
0.914958 | + | 0.403550i | \(0.132224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.13407 | + | 4.69621i | 1.04146 | + | 0.601288i | 0.920247 | − | 0.391339i | \(-0.127988\pi\) |
0.121214 | + | 0.992626i | \(0.461321\pi\) | |||||||
\(62\) | 0.186047 | − | 0.322243i | 0.0236280 | − | 0.0409249i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.25466i | 0.406832i | ||||||||
\(65\) | 5.05200 | + | 5.62981i | 0.626624 | + | 0.698293i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1395 | − | 2.98482i | −1.36091 | − | 0.364653i | −0.496756 | − | 0.867890i | \(-0.665476\pi\) |
−0.864149 | + | 0.503237i | \(0.832142\pi\) | |||||||
\(68\) | − | 9.05378i | − | 1.09793i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.40069 | + | 2.73672i | −0.406461 | + | 0.327101i | ||||
\(71\) | −9.44098 | − | 2.52970i | −1.12044 | − | 0.300221i | −0.349377 | − | 0.936982i | \(-0.613607\pi\) |
−0.771061 | + | 0.636762i | \(0.780274\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.62580 | + | 9.79963i | 0.307327 | + | 1.14696i | 0.930924 | + | 0.365214i | \(0.119004\pi\) |
−0.623597 | + | 0.781746i | \(0.714329\pi\) | |||||||
\(74\) | 5.56125 | 0.646482 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.86524 | − | 10.6932i | −0.328665 | − | 1.22660i | ||||
\(77\) | −6.43083 | − | 0.695715i | −0.732862 | − | 0.0792841i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.07540 | + | 1.86264i | 0.120992 | + | 0.209564i | 0.920159 | − | 0.391545i | \(-0.128059\pi\) |
−0.799167 | + | 0.601109i | \(0.794726\pi\) | |||||||
\(80\) | 0.364744 | − | 1.36124i | 0.0407796 | − | 0.152192i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.47927 | + | 7.75833i | −0.494653 | + | 0.856764i | ||||
\(83\) | −1.52436 | − | 1.52436i | −0.167320 | − | 0.167320i | 0.618480 | − | 0.785801i | \(-0.287749\pi\) |
−0.785801 | + | 0.618480i | \(0.787749\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.55840 | − | 13.2801i | 0.385963 | − | 1.44043i | ||||
\(86\) | −0.190489 | + | 0.710914i | −0.0205409 | + | 0.0766598i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.63048 | + | 3.25076i | −0.600212 | + | 0.346532i | ||||
\(89\) | −4.45304 | + | 4.45304i | −0.472021 | + | 0.472021i | −0.902568 | − | 0.430547i | \(-0.858321\pi\) |
0.430547 | + | 0.902568i | \(0.358321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.69623 | − | 3.92116i | −0.911613 | − | 0.411050i | ||||
\(92\) | 5.31366 | 0.553987 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.96274 | − | 2.86524i | 0.511867 | − | 0.295527i | ||||
\(95\) | − | 16.8110i | − | 1.72477i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.17950 | − | 15.5981i | 0.424363 | − | 1.58375i | −0.340946 | − | 0.940083i | \(-0.610747\pi\) |
0.765309 | − | 0.643663i | \(-0.222586\pi\) | |||||||
\(98\) | 2.52902 | − | 4.88964i | 0.255470 | − | 0.493928i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.413531 | + | 0.716257i | −0.0413531 | + | 0.0716257i | ||||
\(101\) | 1.76991 | + | 3.06558i | 0.176113 | + | 0.305037i | 0.940546 | − | 0.339667i | \(-0.110314\pi\) |
−0.764433 | + | 0.644703i | \(0.776981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.58234 | − | 7.93684i | −0.451511 | − | 0.782041i | 0.546969 | − | 0.837153i | \(-0.315782\pi\) |
−0.998480 | + | 0.0551124i | \(0.982448\pi\) | |||||||
\(104\) | −9.38211 | + | 1.97776i | −0.919992 | + | 0.193935i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.441036 | + | 1.64597i | 0.0428372 | + | 0.159871i | ||||
\(107\) | 2.01759 | 0.195048 | 0.0975240 | − | 0.995233i | \(-0.468908\pi\) | ||||
0.0975240 | + | 0.995233i | \(0.468908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.45769 | − | 5.44016i | −0.139621 | − | 0.521073i | −0.999936 | − | 0.0113102i | \(-0.996400\pi\) |
0.860315 | − | 0.509763i | \(-0.170267\pi\) | |||||||
\(110\) | −3.89616 | + | 1.04397i | −0.371485 | + | 0.0995390i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.272676 | + | 1.75621i | 0.0257655 | + | 0.165946i | ||||
\(113\) | 6.20648 | + | 10.7499i | 0.583857 | + | 1.01127i | 0.995017 | + | 0.0997064i | \(0.0317904\pi\) |
−0.411160 | + | 0.911563i | \(0.634876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.79411 | + | 2.08842i | 0.726804 | + | 0.194747i | ||||
\(116\) | 3.00129 | + | 1.73279i | 0.278663 | + | 0.160886i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.36881i | 0.402182i | ||||||||
\(119\) | 2.66020 | + | 17.1334i | 0.243860 | + | 1.57061i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.34997 | + | 2.51145i | 0.395451 | + | 0.228314i | ||||
\(122\) | −7.13471 | + | 1.91174i | −0.645947 | + | 0.173081i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.169183 | − | 0.631401i | −0.0151931 | − | 0.0567015i | ||||
\(125\) | −8.30541 | + | 8.30541i | −0.742859 | + | 0.742859i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.05461 | − | 5.22768i | −0.803467 | − | 0.463882i | 0.0412153 | − | 0.999150i | \(-0.486877\pi\) |
−0.844682 | + | 0.535269i | \(0.820210\pi\) | |||||||
\(128\) | 6.45891 | + | 6.45891i | 0.570892 | + | 0.570892i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.93999 | − | 0.321313i | −0.520971 | − | 0.0281810i | ||||
\(131\) | −18.0680 | + | 10.4315i | −1.57860 | + | 0.911408i | −0.583550 | + | 0.812077i | \(0.698337\pi\) |
−0.995055 | + | 0.0993303i | \(0.968330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.56407 | + | 19.3940i | 0.742599 | + | 1.68167i | ||||
\(134\) | 7.85430 | − | 4.53468i | 0.678508 | − | 0.391737i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.3231 | + | 12.3231i | 1.05670 | + | 1.05670i | ||||
\(137\) | −7.97181 | − | 7.97181i | −0.681078 | − | 0.681078i | 0.279165 | − | 0.960243i | \(-0.409942\pi\) |
−0.960243 | + | 0.279165i | \(0.909942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.83314 | + | 5.09981i | −0.749217 | + | 0.432561i | −0.825411 | − | 0.564532i | \(-0.809057\pi\) |
0.0761940 | + | 0.997093i | \(0.475723\pi\) | |||||||
\(140\) | −0.824789 | + | 7.62393i | −0.0697074 | + | 0.644340i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.65671 | − | 3.84325i | 0.558618 | − | 0.322518i | ||||
\(143\) | −5.88729 | − | 6.56064i | −0.492320 | − | 0.548628i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.72127 | + | 3.72127i | 0.309035 | + | 0.309035i | ||||
\(146\) | −6.90958 | − | 3.98925i | −0.571841 | − | 0.330153i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.90821 | − | 6.90821i | 0.567852 | − | 0.567852i | ||||
\(149\) | 1.21789 | + | 4.54523i | 0.0997734 | + | 0.372359i | 0.997700 | − | 0.0677861i | \(-0.0215935\pi\) |
−0.897926 | + | 0.440145i | \(0.854927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.563961 | − | 0.151113i | 0.0458945 | − | 0.0122974i | −0.235799 | − | 0.971802i | \(-0.575771\pi\) |
0.281693 | + | 0.959505i | \(0.409104\pi\) | |||||||
\(152\) | 18.4545 | + | 10.6547i | 1.49685 | + | 0.864210i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.96296 | − | 3.18921i | 0.319344 | − | 0.256994i | ||||
\(155\) | − | 0.992638i | − | 0.0797306i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.61395 | − | 5.55061i | −0.767276 | − | 0.442987i | 0.0646257 | − | 0.997910i | \(-0.479415\pi\) |
−0.831902 | + | 0.554922i | \(0.812748\pi\) | |||||||
\(158\) | −1.63380 | − | 0.437774i | −0.129978 | − | 0.0348275i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.13322 | + | 10.6231i | 0.484874 | + | 0.839826i | ||||
\(161\) | −10.0556 | + | 1.56127i | −0.792489 | + | 0.123045i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9158 | − | 4.26463i | 1.24662 | − | 0.334031i | 0.425592 | − | 0.904915i | \(-0.360066\pi\) |
0.821031 | + | 0.570884i | \(0.193399\pi\) | |||||||
\(164\) | 4.07326 | + | 15.2016i | 0.318068 | + | 1.18705i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.69535 | 0.131584 | ||||||||
\(167\) | −0.00245012 | − | 0.00914399i | −0.000189596 | − | 0.000707583i | 0.965831 | − | 0.259173i | \(-0.0834499\pi\) |
−0.966021 | + | 0.258465i | \(0.916783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.24763 | − | 11.8938i | −0.403664 | − | 0.914907i | ||||
\(170\) | 5.40610 | + | 9.36364i | 0.414629 | + | 0.718159i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.646475 | + | 1.11973i | 0.0492933 | + | 0.0853784i | ||||
\(173\) | −10.4806 | + | 18.1529i | −0.796823 | + | 1.38014i | 0.124852 | + | 0.992175i | \(0.460154\pi\) |
−0.921675 | + | 0.387963i | \(0.873179\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.572114 | − | 1.47695i | 0.0432478 | − | 0.111647i | ||||
\(176\) | −0.425051 | + | 1.58631i | −0.0320394 | + | 0.119573i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 4.95253i | − | 0.371208i | ||||||
\(179\) | 8.35625 | − | 4.82448i | 0.624576 | − | 0.360599i | −0.154073 | − | 0.988060i | \(-0.549239\pi\) |
0.778648 | + | 0.627461i | \(0.215906\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.25766 | 0.0934813 | 0.0467407 | − | 0.998907i | \(-0.485117\pi\) | ||||
0.0467407 | + | 0.998907i | \(0.485117\pi\) | |||||||
\(182\) | 7.01633 | − | 2.65534i | 0.520085 | − | 0.196827i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.23244 | + | 7.23244i | −0.533183 | + | 0.533183i | ||||
\(185\) | 12.8481 | − | 7.41788i | 0.944614 | − | 0.545373i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.14674 | + | 15.4759i | −0.303240 | + | 1.13171i | ||||
\(188\) | 2.60552 | − | 9.72395i | 0.190027 | − | 0.709192i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.34833 | + | 9.34833i | 0.678199 | + | 0.678199i | ||||
\(191\) | 1.22251 | − | 2.11745i | 0.0884578 | − | 0.153213i | −0.818402 | − | 0.574647i | \(-0.805139\pi\) |
0.906859 | + | 0.421433i | \(0.138473\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.45444 | − | 16.6242i | 0.320638 | − | 1.19664i | −0.597987 | − | 0.801506i | \(-0.704033\pi\) |
0.918625 | − | 0.395131i | \(-0.129301\pi\) | |||||||
\(194\) | 6.34970 | + | 10.9980i | 0.455882 | + | 0.789610i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.93236 | − | 9.21550i | −0.209454 | − | 0.658250i | ||||
\(197\) | −6.05858 | − | 22.6109i | −0.431656 | − | 1.61096i | −0.748944 | − | 0.662634i | \(-0.769439\pi\) |
0.317287 | − | 0.948329i | \(-0.397228\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.6415 | −1.32146 | −0.660732 | − | 0.750622i | \(-0.729754\pi\) | ||||
−0.660732 | + | 0.750622i | \(0.729754\pi\) | |||||||
\(200\) | −0.412042 | − | 1.53776i | −0.0291357 | − | 0.108736i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.68894 | − | 0.720500i | −0.189193 | − | 0.0506942i | ||||
\(203\) | −6.18877 | − | 2.39729i | −0.434366 | − | 0.168257i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.8987i | 1.66916i | ||||||||
\(206\) | 6.96172 | + | 1.86539i | 0.485046 | + | 0.129968i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.32252 | + | 2.02903i | −0.0917002 | + | 0.140688i | ||||
\(209\) | 19.5905i | 1.35510i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.61294 | + | 9.72190i | −0.386411 | + | 0.669283i | −0.991964 | − | 0.126522i | \(-0.959619\pi\) |
0.605553 | + | 0.795805i | \(0.292952\pi\) | |||||||
\(212\) | 2.59249 | + | 1.49677i | 0.178053 | + | 0.102799i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.12195 | + | 1.12195i | −0.0766950 | + | 0.0766950i | ||||
\(215\) | 0.508168 | + | 1.89651i | 0.0346567 | + | 0.129341i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.505682 | + | 1.14515i | 0.0343279 | + | 0.0777381i | ||||
\(218\) | 3.83579 | + | 2.21459i | 0.259792 | + | 0.149991i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.54300 | + | 6.13666i | −0.238869 | + | 0.413734i | ||||
\(221\) | −12.9023 | + | 19.7949i | −0.867905 | + | 1.33155i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.81982 | − | 2.63121i | 0.657584 | − | 0.176199i | 0.0854284 | − | 0.996344i | \(-0.472774\pi\) |
0.572155 | + | 0.820145i | \(0.306107\pi\) | |||||||
\(224\) | −12.4873 | − | 9.13079i | −0.834343 | − | 0.610076i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.42920 | − | 2.52655i | −0.627221 | − | 0.168063i | ||||
\(227\) | 4.65548 | + | 4.65548i | 0.308995 | + | 0.308995i | 0.844520 | − | 0.535524i | \(-0.179886\pi\) |
−0.535524 | + | 0.844520i | \(0.679886\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.20056 | + | 0.321690i | 0.0793354 | + | 0.0212578i | 0.298268 | − | 0.954482i | \(-0.403591\pi\) |
−0.218933 | + | 0.975740i | \(0.570258\pi\) | |||||||
\(230\) | −5.49552 | + | 3.17284i | −0.362364 | + | 0.209211i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.44358 | + | 1.72655i | −0.423042 | + | 0.113354i | ||||
\(233\) | −12.6928 | + | 7.32822i | −0.831536 | + | 0.480088i | −0.854378 | − | 0.519652i | \(-0.826062\pi\) |
0.0228423 | + | 0.999739i | \(0.492728\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.64360 | − | 13.2391i | 0.498614 | − | 0.863624i | ||||
\(236\) | 5.42696 | + | 5.42696i | 0.353265 | + | 0.353265i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.0069 | − | 8.04829i | −0.713470 | − | 0.521693i | ||||
\(239\) | 4.85743 | − | 4.85743i | 0.314201 | − | 0.314201i | −0.532334 | − | 0.846535i | \(-0.678685\pi\) |
0.846535 | + | 0.532334i | \(0.178685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5158 | + | 13.5158i | −0.870627 | + | 0.870627i | −0.992541 | − | 0.121914i | \(-0.961097\pi\) |
0.121914 | + | 0.992541i | \(0.461097\pi\) | |||||||
\(242\) | −3.81553 | + | 1.02237i | −0.245271 | + | 0.0657202i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.48800 | + | 11.2375i | −0.415352 | + | 0.719410i | ||||
\(245\) | −0.679246 | − | 14.6699i | −0.0433955 | − | 0.937223i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.97418 | + | 27.4626i | −0.571013 | + | 1.74740i | ||||
\(248\) | 1.08968 | + | 0.629127i | 0.0691947 | + | 0.0399496i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 9.23702i | − | 0.584200i | ||||||
\(251\) | 1.37023 | + | 2.37330i | 0.0864880 | + | 0.149802i | 0.906024 | − | 0.423226i | \(-0.139102\pi\) |
−0.819536 | + | 0.573027i | \(0.805769\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.08277 | − | 2.43372i | −0.571029 | − | 0.153007i | ||||
\(254\) | 7.94215 | − | 2.12809i | 0.498335 | − | 0.133528i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.6927 | −0.855794 | ||||||||
\(257\) | 10.9615 | 0.683758 | 0.341879 | − | 0.939744i | \(-0.388937\pi\) | ||||
0.341879 | + | 0.939744i | \(0.388937\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.0433 | + | 15.1029i | −0.686198 | + | 0.938447i | ||||
\(260\) | −7.77782 | + | 6.97955i | −0.482360 | + | 0.432853i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.24649 | − | 15.8481i | 0.262349 | − | 0.979100i | ||||
\(263\) | −11.0595 | − | 19.1556i | −0.681958 | − | 1.18119i | −0.974383 | − | 0.224897i | \(-0.927795\pi\) |
0.292425 | − | 0.956289i | \(-0.405538\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.21440 | + | 3.21440i | 0.197459 | + | 0.197459i | ||||
\(266\) | −15.5470 | − | 6.02233i | −0.953249 | − | 0.369252i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.12365 | − | 15.3897i | 0.251892 | − | 0.940073i | ||||
\(269\) | − | 9.12867i | − | 0.556585i | −0.960496 | − | 0.278292i | \(-0.910232\pi\) | ||
0.960496 | − | 0.278292i | \(-0.0897684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7284 | − | 13.7284i | 0.833942 | − | 0.833942i | −0.154112 | − | 0.988053i | \(-0.549252\pi\) |
0.988053 | + | 0.154112i | \(0.0492516\pi\) | |||||||
\(272\) | 4.40216 | 0.266920 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.86600 | 0.535614 | ||||||||
\(275\) | 1.03491 | − | 1.03491i | 0.0624077 | − | 0.0624077i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.0822i | 1.68730i | 0.536896 | + | 0.843649i | \(0.319597\pi\) | ||||
−0.536896 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(278\) | 2.07604 | − | 7.74789i | 0.124513 | − | 0.464688i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.25434 | − | 11.4996i | −0.553053 | − | 0.687232i | ||||
\(281\) | −3.79779 | − | 3.79779i | −0.226557 | − | 0.226557i | 0.584695 | − | 0.811253i | \(-0.301214\pi\) |
−0.811253 | + | 0.584695i | \(0.801214\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.692540 | + | 1.19951i | 0.0411672 | + | 0.0713037i | 0.885875 | − | 0.463924i | \(-0.153559\pi\) |
−0.844708 | + | 0.535228i | \(0.820226\pi\) | |||||||
\(284\) | 3.49489 | − | 13.0431i | 0.207383 | − | 0.773966i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.92210 | + | 0.374439i | 0.409312 | + | 0.0221410i | ||||
\(287\) | −12.1748 | − | 27.5707i | −0.718655 | − | 1.62745i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.9469 | 1.52629 | ||||||||
\(290\) | −4.13868 | −0.243032 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.5386 | + | 3.62765i | −0.792286 | + | 0.212292i | ||||
\(293\) | 17.3288 | + | 4.64324i | 1.01236 | + | 0.271261i | 0.726615 | − | 0.687045i | \(-0.241092\pi\) |
0.285745 | + | 0.958306i | \(0.407759\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.82735 | + | 10.0933i | 0.339281 | + | 0.587653i | ||||
\(296\) | 18.8056i | 1.09305i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.20478 | − | 1.85028i | −0.185648 | − | 0.107184i | ||||
\(299\) | −11.6176 | − | 7.57237i | −0.671866 | − | 0.437922i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.55239 | − | 1.92902i | −0.0894782 | − | 0.111187i | ||||
\(302\) | −0.229578 | + | 0.397641i | −0.0132107 | + | 0.0228817i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.19929 | − | 1.39315i | 0.298200 | − | 0.0799024i | ||||
\(305\) | −13.9333 | + | 13.9333i | −0.797820 | + | 0.797820i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.47242 | + | 5.47242i | −0.312327 | + | 0.312327i | −0.845811 | − | 0.533483i | \(-0.820883\pi\) |
0.533483 | + | 0.845811i | \(0.320883\pi\) | |||||||
\(308\) | 0.961159 | − | 8.88446i | 0.0547671 | − | 0.506239i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.551990 | + | 0.551990i | 0.0313509 | + | 0.0313509i | ||||
\(311\) | −3.27357 | + | 5.66998i | −0.185627 | + | 0.321515i | −0.943788 | − | 0.330553i | \(-0.892765\pi\) |
0.758161 | + | 0.652068i | \(0.226098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.8538 | + | 8.57583i | −0.839585 | + | 0.484735i | −0.857123 | − | 0.515111i | \(-0.827751\pi\) |
0.0175379 | + | 0.999846i | \(0.494417\pi\) | |||||||
\(314\) | 8.43277 | − | 2.25955i | 0.475889 | − | 0.127514i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.57332 | + | 1.48570i | −0.144760 | + | 0.0835774i | ||||
\(317\) | 15.5081 | + | 4.15537i | 0.871019 | + | 0.233389i | 0.666528 | − | 0.745480i | \(-0.267780\pi\) |
0.204491 | + | 0.978869i | \(0.434446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.33654 | − | 4.33654i | −0.242800 | − | 0.242800i | ||||
\(320\) | −6.59541 | − | 1.76723i | −0.368695 | − | 0.0987914i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.72354 | − | 6.45993i | 0.263233 | − | 0.359998i | ||||
\(323\) | 50.7236 | − | 13.5914i | 2.82234 | − | 0.756243i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.92486 | − | 0.976692i | 0.106772 | − | 0.0541771i | ||||
\(326\) | −6.47904 | + | 11.2220i | −0.358841 | + | 0.621530i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26.2351 | − | 15.1468i | −1.44859 | − | 0.836345i | ||||
\(329\) | −2.07358 | + | 19.1672i | −0.114320 | + | 1.05672i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.47690 | − | 5.51186i | −0.0811776 | − | 0.302959i | 0.913385 | − | 0.407096i | \(-0.133459\pi\) |
−0.994563 | + | 0.104137i | \(0.966792\pi\) | |||||||
\(332\) | 2.10597 | − | 2.10597i | 0.115580 | − | 0.115580i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.00644730 | + | 0.00372235i | 0.000352781 | + | 0.000203678i | ||||
\(335\) | 12.0972 | − | 20.9529i | 0.660940 | − | 1.14478i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.54996i | − | 0.356799i | −0.983958 | − | 0.178399i | \(-0.942908\pi\) | ||
0.983958 | − | 0.178399i | \(-0.0570919\pi\) | |||||||
\(338\) | 9.53207 | + | 3.69583i | 0.518476 | + | 0.201027i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.3471 | + | 4.91608i | 0.995009 | + | 0.266612i | ||||
\(341\) | 1.15676i | 0.0626420i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.25691 | + | 16.5778i | 0.445831 | + | 0.895117i | ||||
\(344\) | −2.40399 | − | 0.644146i | −0.129614 | − | 0.0347300i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.26645 | − | 15.9226i | −0.229366 | − | 0.856005i | ||||
\(347\) | 22.8051 | 1.22424 | 0.612120 | − | 0.790765i | \(-0.290317\pi\) | ||||
0.612120 | + | 0.790765i | \(0.290317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.529316 | − | 1.97543i | −0.0283336 | − | 0.105743i | 0.950311 | − | 0.311302i | \(-0.100765\pi\) |
−0.978645 | + | 0.205560i | \(0.934099\pi\) | |||||||
\(350\) | 0.503164 | + | 1.13945i | 0.0268953 | + | 0.0609062i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.14728 | − | 12.3795i | −0.380951 | − | 0.659827i | ||||
\(353\) | −6.69454 | + | 24.9843i | −0.356314 | + | 1.32978i | 0.522508 | + | 0.852634i | \(0.324996\pi\) |
−0.878823 | + | 0.477149i | \(0.841670\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.2527 | − | 17.7581i | 0.544154 | − | 0.942503i | ||||
\(356\) | −6.15206 | − | 6.15206i | −0.326058 | − | 0.326058i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.96396 | + | 7.32960i | −0.103798 | + | 0.387381i | ||||
\(359\) | 3.89528 | − | 14.5374i | 0.205585 | − | 0.767255i | −0.783685 | − | 0.621158i | \(-0.786662\pi\) |
0.989270 | − | 0.146096i | \(-0.0466709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.1529 | − | 22.6049i | 2.06068 | − | 1.18973i | ||||
\(362\) | −0.699366 | + | 0.699366i | −0.0367579 | + | 0.0367579i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.41725 | − | 12.0142i | 0.283941 | − | 0.629715i | ||||
\(365\) | −21.2843 | −1.11407 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.2477 | − | 7.64858i | 0.691526 | − | 0.399253i | −0.112657 | − | 0.993634i | \(-0.535936\pi\) |
0.804184 | + | 0.594381i | \(0.202603\pi\) | |||||||
\(368\) | 2.58362i | 0.134681i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.01968 | + | 11.2696i | −0.156986 | + | 0.585879i | ||||
\(371\) | −5.34581 | − | 2.07076i | −0.277540 | − | 0.107509i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2210 | − | 17.7032i | 0.529221 | − | 0.916638i | −0.470198 | − | 0.882561i | \(-0.655817\pi\) |
0.999419 | − | 0.0340771i | \(-0.0108492\pi\) | |||||||
\(374\) | −6.29994 | − | 10.9118i | −0.325762 | − | 0.564237i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.68892 | + | 16.7817i | 0.499668 | + | 0.865450i | ||||
\(377\) | −4.09257 | − | 8.06561i | −0.210778 | − | 0.415400i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.64237 | − | 6.12940i | −0.0843628 | − | 0.314846i | 0.910830 | − | 0.412782i | \(-0.135443\pi\) |
−0.995193 | + | 0.0979355i | \(0.968776\pi\) | |||||||
\(380\) | 23.2251 | 1.19142 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.497662 | + | 1.85730i | 0.0254626 | + | 0.0950277i | ||||
\(383\) | 6.04679 | − | 1.62023i | 0.308976 | − | 0.0827899i | −0.100999 | − | 0.994887i | \(-0.532204\pi\) |
0.409975 | + | 0.912097i | \(0.365537\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.90169 | − | 12.6540i | 0.249813 | − | 0.644909i | ||||
\(386\) | 6.76741 | + | 11.7215i | 0.344452 | + | 0.596609i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.5494 | + | 5.77414i | 1.09400 | + | 0.293138i | ||||
\(389\) | −4.72095 | − | 2.72564i | −0.239362 | − | 0.138196i | 0.375522 | − | 0.926814i | \(-0.377464\pi\) |
−0.614883 | + | 0.788618i | \(0.710797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.2055i | 1.27470i | ||||||||
\(392\) | 16.5345 | + | 8.55200i | 0.835118 | + | 0.431941i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.9427 | + | 9.20450i | 0.803180 | + | 0.463716i | ||||
\(395\) | −4.35848 | + | 1.16785i | −0.219299 | + | 0.0587610i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.48129 | + | 9.26032i | 0.124533 | + | 0.464762i | 0.999823 | − | 0.0188365i | \(-0.00599620\pi\) |
−0.875290 | + | 0.483598i | \(0.839330\pi\) | |||||||
\(398\) | 10.3663 | − | 10.3663i | 0.519614 | − | 0.519614i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.348261 | − | 0.201069i | −0.0174130 | − | 0.0100534i | ||||
\(401\) | −26.5226 | − | 26.5226i | −1.32447 | − | 1.32447i | −0.910112 | − | 0.414362i | \(-0.864005\pi\) |
−0.414362 | − | 0.910112i | \(-0.635995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.529898 | + | 1.62158i | −0.0263961 | + | 0.0807766i | ||||
\(404\) | −4.23523 | + | 2.44521i | −0.210710 | + | 0.121654i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.77457 | − | 2.10838i | 0.236958 | − | 0.104637i | ||||
\(407\) | −14.9724 | + | 8.64434i | −0.742156 | + | 0.428484i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.7339 | − | 21.7339i | −1.07467 | − | 1.07467i | −0.996977 | − | 0.0776962i | \(-0.975244\pi\) |
−0.0776962 | − | 0.996977i | \(-0.524756\pi\) | |||||||
\(410\) | −13.2897 | − | 13.2897i | −0.656332 | − | 0.656332i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.9651 | − | 6.33069i | 0.540210 | − | 0.311891i | ||||
\(413\) | −11.8645 | − | 8.67542i | −0.583816 | − | 0.426889i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.91676 | − | 2.26134i | 0.192266 | − | 0.111005i | ||||
\(416\) | −4.34839 | − | 20.6280i | −0.213197 | − | 1.01137i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.8940 | − | 10.8940i | −0.532842 | − | 0.532842i | ||||
\(419\) | −20.2493 | − | 11.6909i | −0.989241 | − | 0.571138i | −0.0841936 | − | 0.996449i | \(-0.526831\pi\) |
−0.905047 | + | 0.425311i | \(0.860165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.1492 | − | 14.1492i | 0.689589 | − | 0.689589i | −0.272552 | − | 0.962141i | \(-0.587868\pi\) |
0.962141 | + | 0.272552i | \(0.0878676\pi\) | |||||||
\(422\) | −2.28493 | − | 8.52747i | −0.111229 | − | 0.415111i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.56591 | + | 1.49138i | −0.270305 | + | 0.0724279i | ||||
\(425\) | −3.39759 | − | 1.96160i | −0.164807 | − | 0.0951516i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.97605 | − | 23.1722i | 0.434382 | − | 1.12138i | ||||
\(428\) | 2.78739i | 0.134733i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.33720 | − | 0.772034i | −0.0644856 | − | 0.0372308i | ||||
\(431\) | 12.7388 | + | 3.41335i | 0.613606 | + | 0.164415i | 0.552220 | − | 0.833699i | \(-0.313781\pi\) |
0.0613869 | + | 0.998114i | \(0.480448\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.53868 | − | 9.59327i | −0.266172 | − | 0.461023i | 0.701698 | − | 0.712474i | \(-0.252426\pi\) |
−0.967870 | + | 0.251451i | \(0.919092\pi\) | |||||||
\(434\) | −0.918003 | − | 0.355600i | −0.0440656 | − | 0.0170693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.51581 | − | 2.01385i | 0.359942 | − | 0.0964462i | ||||
\(437\) | 7.97676 | + | 29.7697i | 0.381580 | + | 1.42408i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2330 | 0.631578 | 0.315789 | − | 0.948829i | \(-0.397731\pi\) | ||||
0.315789 | + | 0.948829i | \(0.397731\pi\) | |||||||
\(440\) | −3.53024 | − | 13.1750i | −0.168298 | − | 0.628095i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.83287 | − | 18.1824i | −0.182311 | − | 0.864850i | ||||
\(443\) | −2.45582 | − | 4.25360i | −0.116679 | − | 0.202095i | 0.801770 | − | 0.597632i | \(-0.203892\pi\) |
−0.918450 | + | 0.395537i | \(0.870558\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.60594 | − | 11.4418i | −0.313151 | − | 0.542394i | ||||
\(446\) | −3.99747 | + | 6.92382i | −0.189286 | + | 0.327852i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.50906 | − | 1.32115i | 0.402015 | − | 0.0624186i | ||||
\(449\) | −0.246197 | + | 0.918821i | −0.0116188 | + | 0.0433618i | −0.971492 | − | 0.237073i | \(-0.923812\pi\) |
0.959873 | + | 0.280435i | \(0.0904786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 27.8501i | − | 1.31141i | ||||||
\(452\) | −14.8515 | + | 8.57451i | −0.698555 | + | 0.403311i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.17768 | −0.243001 | ||||||||
\(455\) | 12.6680 | − | 15.4934i | 0.593885 | − | 0.726341i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.6046 | + | 13.6046i | −0.636394 | + | 0.636394i | −0.949664 | − | 0.313270i | \(-0.898576\pi\) |
0.313270 | + | 0.949664i | \(0.398576\pi\) | |||||||
\(458\) | −0.846500 | + | 0.488727i | −0.0395543 | + | 0.0228367i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.88524 | + | 10.7679i | −0.134525 | + | 0.502055i | ||||
\(461\) | −1.66867 | + | 6.22758i | −0.0777179 | + | 0.290047i | −0.993836 | − | 0.110862i | \(-0.964639\pi\) |
0.916118 | + | 0.400909i | \(0.131306\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.67988 | + | 7.67988i | 0.356914 | + | 0.356914i | 0.862674 | − | 0.505760i | \(-0.168788\pi\) |
−0.505760 | + | 0.862674i | \(0.668788\pi\) | |||||||
\(464\) | −0.842525 | + | 1.45930i | −0.0391132 | + | 0.0677461i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.98318 | − | 11.1334i | 0.138193 | − | 0.515745i | ||||
\(467\) | 10.7238 | + | 18.5741i | 0.496236 | + | 0.859507i | 0.999991 | − | 0.00434034i | \(-0.00138158\pi\) |
−0.503754 | + | 0.863847i | \(0.668048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.28177 | + | 30.3350i | −0.151538 | + | 1.40074i | ||||
\(470\) | 3.11157 | + | 11.6125i | 0.143526 | + | 0.535647i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.7733 | −0.679997 | ||||||||
\(473\) | −0.592187 | − | 2.21007i | −0.0272288 | − | 0.101619i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.63361 | − | 1.24157i | −0.212604 | − | 0.0569672i | ||||
\(476\) | −23.6704 | + | 3.67517i | −1.08493 | + | 0.168451i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.40228i | 0.247095i | ||||||||
\(479\) | 17.4860 | + | 4.68536i | 0.798956 | + | 0.214080i | 0.635126 | − | 0.772409i | \(-0.280948\pi\) |
0.163831 | + | 0.986489i | \(0.447615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.9487 | + | 5.25920i | −1.13756 | + | 0.239799i | ||||
\(482\) | − | 15.0318i | − | 0.684680i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.46968 | + | 6.00966i | −0.157713 | + | 0.273166i | ||||
\(485\) | 29.3394 | + | 16.9391i | 1.33223 | + | 0.769165i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.09200 | − | 5.09200i | 0.230740 | − | 0.230740i | −0.582261 | − | 0.813002i | \(-0.697832\pi\) |
0.813002 | + | 0.582261i | \(0.197832\pi\) | |||||||
\(488\) | −6.46463 | − | 24.1263i | −0.292640 | − | 1.09215i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.53539 | + | 7.77996i | 0.385590 | + | 0.351463i | ||||
\(491\) | 24.3966 | + | 14.0854i | 1.10101 | + | 0.635666i | 0.936485 | − | 0.350708i | \(-0.114059\pi\) |
0.164520 | + | 0.986374i | \(0.447392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.21957 | + | 14.2367i | −0.370191 | + | 0.641190i | ||||
\(494\) | −10.2811 | − | 20.2619i | −0.462568 | − | 0.911625i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.307002 | − | 0.0822609i | 0.0137848 | − | 0.00369362i | ||||
\(497\) | −2.78138 | + | 25.7096i | −0.124762 | + | 1.15323i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3207 | − | 5.44491i | −0.909678 | − | 0.243748i | −0.226510 | − | 0.974009i | \(-0.572732\pi\) |
−0.683168 | + | 0.730261i | \(0.739398\pi\) | |||||||
\(500\) | −11.4743 | − | 11.4743i | −0.513145 | − | 0.513145i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.08172 | − | 0.557794i | −0.0929116 | − | 0.0248956i | ||||
\(503\) | 18.9822 | − | 10.9594i | 0.846374 | − | 0.488655i | −0.0130514 | − | 0.999915i | \(-0.504155\pi\) |
0.859426 | + | 0.511260i | \(0.170821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.17330 | + | 1.92208i | −0.319208 | + | 0.0855314i | ||||
\(506\) | 6.40414 | − | 3.69743i | 0.284699 | − | 0.164371i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.22226 | − | 12.5093i | 0.320436 | − | 0.555011i | ||||
\(509\) | 2.12967 | + | 2.12967i | 0.0943961 | + | 0.0943961i | 0.752728 | − | 0.658332i | \(-0.228738\pi\) |
−0.658332 | + | 0.752728i | \(0.728738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.5545 | − | 10.8429i | 1.08623 | − | 0.479661i | ||||
\(512\) | −5.30352 | + | 5.30352i | −0.234385 | + | 0.234385i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.09550 | + | 6.09550i | −0.268861 | + | 0.268861i | ||||
\(515\) | 18.5718 | − | 4.97630i | 0.818371 | − | 0.219282i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.90738 | + | 15.4280i | −0.391746 | + | 0.678525i | ||||
\(518\) | −2.25746 | − | 14.5395i | −0.0991871 | − | 0.638828i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.08653 | − | 20.0863i | 0.0476476 | − | 0.880843i | ||||
\(521\) | −20.7786 | − | 11.9965i | −0.910328 | − | 0.525578i | −0.0297912 | − | 0.999556i | \(-0.509484\pi\) |
−0.880537 | + | 0.473978i | \(0.842818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.58298i | − | 0.419034i | −0.977805 | − | 0.209517i | \(-0.932811\pi\) | ||
0.977805 | − | 0.209517i | \(-0.0671892\pi\) | |||||||
\(524\) | −14.4116 | − | 24.9616i | −0.629573 | − | 1.09045i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.8021 | + | 4.50212i | 0.732608 | + | 0.196302i | ||||
\(527\) | 2.99507 | − | 0.802528i | 0.130467 | − | 0.0349587i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.20689 | 0.356821 | ||||||||
\(530\) | −3.57496 | −0.155286 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.7935 | + | 11.8316i | −1.16165 | + | 0.512966i | ||||
\(533\) | 12.7578 | − | 39.0411i | 0.552602 | − | 1.69106i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.09553 | + | 4.08856i | −0.0473637 | + | 0.176764i | ||||
\(536\) | 15.3342 | + | 26.5596i | 0.662337 | + | 1.14720i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.07631 | + | 5.07631i | 0.218855 | + | 0.218855i | ||||
\(539\) | 0.791552 | + | 17.0953i | 0.0340946 | + | 0.736349i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.61424 | + | 20.9526i | −0.241375 | + | 0.900823i | 0.733796 | + | 0.679370i | \(0.237747\pi\) |
−0.975171 | + | 0.221454i | \(0.928920\pi\) | |||||||
\(542\) | 15.2683i | 0.655830i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −27.0942 | + | 27.0942i | −1.16166 | + | 1.16166i | ||||
\(545\) | 11.8157 | 0.506131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.6132 | −1.05238 | −0.526191 | − | 0.850366i | \(-0.676380\pi\) | ||||
−0.526191 | + | 0.850366i | \(0.676380\pi\) | |||||||
\(548\) | 11.0134 | − | 11.0134i | 0.470468 | − | 0.470468i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.15100i | 0.0490788i | ||||||||
\(551\) | −5.20248 | + | 19.4159i | −0.221633 | + | 0.827146i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.43321 | − | 3.56764i | 0.188519 | − | 0.151712i | ||||
\(554\) | −15.6161 | − | 15.6161i | −0.663464 | − | 0.663464i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.04560 | − | 12.2033i | −0.298800 | − | 0.517537i | ||||
\(557\) | −0.132844 | + | 0.495782i | −0.00562880 | + | 0.0210070i | −0.968683 | − | 0.248300i | \(-0.920128\pi\) |
0.963054 | + | 0.269307i | \(0.0867947\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.182263 | − | 3.36942i | 0.00770889 | − | 0.142511i | ||||
\(560\) | −3.70693 | − | 0.401032i | −0.156646 | − | 0.0169467i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.22379 | 0.178170 | ||||||||
\(563\) | 43.2008 | 1.82070 | 0.910349 | − | 0.413842i | \(-0.135813\pi\) | ||||
0.910349 | + | 0.413842i | \(0.135813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.1543 | + | 6.74007i | −1.05825 | + | 0.283557i | ||||
\(566\) | −1.05214 | − | 0.281920i | −0.0442248 | − | 0.0118500i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.9961 | + | 22.5099i | 0.545305 | + | 0.944496i | ||||
\(569\) | − | 30.7249i | − | 1.28805i | −0.765003 | − | 0.644027i | \(-0.777263\pi\) | ||
0.765003 | − | 0.644027i | \(-0.222737\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1885 | + | 10.5012i | 0.761167 | + | 0.439460i | 0.829715 | − | 0.558188i | \(-0.188503\pi\) |
−0.0685475 | + | 0.997648i | \(0.521836\pi\) | |||||||
\(572\) | 9.06379 | − | 8.13353i | 0.378976 | − | 0.340080i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 22.1018 | + | 8.56142i | 0.922513 | + | 0.357347i | ||||
\(575\) | 1.15126 | − | 1.99405i | 0.0480110 | − | 0.0831574i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.56673 | + | 2.29545i | −0.356638 | + | 0.0955608i | −0.432689 | − | 0.901543i | \(-0.642435\pi\) |
0.0760516 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(578\) | −14.4287 | + | 14.4287i | −0.600153 | + | 0.600153i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.14109 | + | 5.14109i | −0.213472 | + | 0.213472i | ||||
\(581\) | −3.36655 | + | 4.60411i | −0.139668 | + | 0.191011i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.74587 | − | 3.74587i | −0.155138 | − | 0.155138i | ||||
\(584\) | 13.4898 | − | 23.3650i | 0.558212 | − | 0.966852i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.2183 | + | 7.05424i | −0.504734 | + | 0.291408i | ||||
\(587\) | −30.5954 | + | 8.19801i | −1.26281 | + | 0.338368i | −0.827271 | − | 0.561803i | \(-0.810108\pi\) |
−0.435536 | + | 0.900171i | \(0.643441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.28344 | − | 1.89570i | 0.135292 | − | 0.0781108i | ||||
\(590\) | −8.85320 | − | 2.37221i | −0.364480 | − | 0.0976622i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.35893 | + | 3.35893i | 0.138051 | + | 0.138051i | ||||
\(593\) | 5.48978 | + | 1.47098i | 0.225438 | + | 0.0604060i | 0.369770 | − | 0.929123i | \(-0.379437\pi\) |
−0.144332 | + | 0.989529i | \(0.546103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.1644 | − | 3.91242i | −1.48260 | − | 0.160393i | ||||
\(596\) | −6.27941 | + | 1.68256i | −0.257215 | + | 0.0689205i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.6713 | − | 2.24951i | 0.436380 | − | 0.0919892i | ||||
\(599\) | −5.44521 | + | 9.43138i | −0.222485 | + | 0.385356i | −0.955562 | − | 0.294790i | \(-0.904750\pi\) |
0.733077 | + | 0.680146i | \(0.238084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.42936 | − | 0.825243i | −0.0583049 | − | 0.0336624i | 0.470564 | − | 0.882366i | \(-0.344050\pi\) |
−0.528869 | + | 0.848703i | \(0.677384\pi\) | |||||||
\(602\) | 1.93596 | + | 0.209440i | 0.0789037 | + | 0.00853614i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.208769 | + | 0.779135i | 0.00849468 | + | 0.0317026i | ||||
\(605\) | −7.45132 | + | 7.45132i | −0.302939 | + | 0.302939i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.6877 | + | 13.0987i | 0.920865 | + | 0.531662i | 0.883911 | − | 0.467655i | \(-0.154901\pi\) |
0.0369540 | + | 0.999317i | \(0.488234\pi\) | |||||||
\(608\) | −23.4259 | + | 40.5749i | −0.950046 | + | 1.64553i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 15.4962i | − | 0.627423i | ||||||
\(611\) | −19.5540 | + | 17.5471i | −0.791072 | + | 0.709880i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.6882 | + | 6.07928i | 0.916367 | + | 0.245540i | 0.686032 | − | 0.727571i | \(-0.259351\pi\) |
0.230335 | + | 0.973111i | \(0.426018\pi\) | |||||||
\(614\) | − | 6.08625i | − | 0.245621i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.7844 | + | 13.4009i | 0.434517 | + | 0.539938i | ||||
\(617\) | 7.41451 | + | 1.98671i | 0.298497 | + | 0.0799820i | 0.404959 | − | 0.914335i | \(-0.367286\pi\) |
−0.106462 | + | 0.994317i | \(0.533952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.36942 | − | 27.5031i | −0.296202 | − | 1.10544i | −0.940258 | − | 0.340463i | \(-0.889416\pi\) |
0.644056 | − | 0.764978i | \(-0.277250\pi\) | |||||||
\(620\) | 1.37137 | 0.0550755 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.33261 | − | 4.97337i | −0.0534328 | − | 0.199414i | ||||
\(623\) | 13.4498 | + | 9.83454i | 0.538853 | + | 0.394012i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.8242 | − | 18.7480i | −0.432967 | − | 0.749921i | ||||
\(626\) | 3.49107 | − | 13.0288i | 0.139531 | − | 0.520737i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.66840 | − | 13.2821i | 0.306003 | − | 0.530012i | ||||
\(629\) | 32.7694 | + | 32.7694i | 1.30660 | + | 1.30660i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.62809 | + | 9.80818i | −0.104623 | + | 0.390458i | −0.998302 | − | 0.0582487i | \(-0.981448\pi\) |
0.893679 | + | 0.448706i | \(0.148115\pi\) | |||||||
\(632\) | 1.48035 | − | 5.52475i | 0.0588852 | − | 0.219763i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.9345 | + | 6.31305i | −0.434265 | + | 0.250723i | ||||
\(635\) | 15.5102 | − | 15.5102i | 0.615503 | − | 0.615503i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.72156 | + | 24.3274i | −0.266318 | + | 0.963885i | ||||
\(638\) | 4.82296 | 0.190943 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.5958 | + | 9.58157i | −0.656005 | + | 0.378745i | ||||
\(641\) | − | 23.1705i | − | 0.915180i | −0.889163 | − | 0.457590i | \(-0.848713\pi\) | ||
0.889163 | − | 0.457590i | \(-0.151287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.46488 | − | 24.1273i | 0.254950 | − | 0.951486i | −0.713168 | − | 0.700993i | \(-0.752741\pi\) |
0.968118 | − | 0.250493i | \(-0.0805928\pi\) | |||||||
\(644\) | −2.15696 | − | 13.8922i | −0.0849959 | − | 0.547428i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.6487 | + | 35.7646i | −0.812411 | + | 1.40714i | ||||
\(647\) | −2.29221 | − | 3.97022i | −0.0901160 | − | 0.156085i | 0.817444 | − | 0.576008i | \(-0.195390\pi\) |
−0.907560 | + | 0.419923i | \(0.862057\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.79083 | − | 11.7621i | −0.266564 | − | 0.461702i | ||||
\(650\) | −0.527259 | + | 1.61350i | −0.0206808 | + | 0.0632869i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.89176 | + | 21.9883i | 0.230739 | + | 0.861130i | ||||
\(653\) | 25.4566 | 0.996192 | 0.498096 | − | 0.867122i | \(-0.334033\pi\) | ||||
0.498096 | + | 0.867122i | \(0.334033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.3284 | − | 42.2780i | −0.442636 | − | 1.65194i | ||||
\(656\) | −7.39138 | + | 1.98051i | −0.288585 | + | 0.0773260i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.50546 | − | 11.8116i | −0.370561 | − | 0.460465i | ||||
\(659\) | 6.21741 | + | 10.7689i | 0.242196 | + | 0.419496i | 0.961339 | − | 0.275366i | \(-0.0887990\pi\) |
−0.719144 | + | 0.694861i | \(0.755466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.4077 | + | 9.75540i | 1.41609 | + | 0.379441i | 0.884096 | − | 0.467305i | \(-0.154775\pi\) |
0.531998 | + | 0.846746i | \(0.321442\pi\) | |||||||
\(662\) | 3.88634 | + | 2.24378i | 0.151047 | + | 0.0872069i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.73288i | 0.222479i | ||||||||
\(665\) | −43.9511 | + | 6.82403i | −1.70435 | + | 0.264625i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.35552 | − | 4.82406i | −0.323527 | − | 0.186788i | ||||
\(668\) | 0.0126328 | − | 0.00338495i | 0.000488778 | − | 0.000130968i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.92454 | + | 18.3786i | 0.190252 | + | 0.710029i | ||||
\(671\) | 16.2371 | − | 16.2371i | 0.626825 | − | 0.626825i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.1591 | + | 12.2162i | 0.815624 | + | 0.470901i | 0.848905 | − | 0.528545i | \(-0.177262\pi\) |
−0.0332811 | + | 0.999446i | \(0.510596\pi\) | |||||||
\(674\) | 3.64233 | + | 3.64233i | 0.140297 | + | 0.140297i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.4318 | − | 7.24981i | 0.631991 | − | 0.278839i | ||||
\(677\) | 3.00229 | − | 1.73338i | 0.115388 | − | 0.0666190i | −0.441195 | − | 0.897411i | \(-0.645445\pi\) |
0.556583 | + | 0.830792i | \(0.312112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.4766 | − | 4.59530i | −1.63010 | − | 0.176351i | ||||
\(680\) | −31.6635 | + | 18.2810i | −1.21424 | + | 0.701043i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.643255 | − | 0.643255i | −0.0246315 | − | 0.0246315i | ||||
\(683\) | −26.9394 | − | 26.9394i | −1.03081 | − | 1.03081i | −0.999510 | − | 0.0312978i | \(-0.990036\pi\) |
−0.0312978 | − | 0.999510i | \(-0.509964\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.4831 | − | 11.8259i | 0.782619 | − | 0.451845i | ||||
\(686\) | −13.8102 | − | 4.62711i | −0.527275 | − | 0.176664i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.544437 | + | 0.314331i | −0.0207565 | + | 0.0119838i | ||||
\(689\) | −3.53513 | − | 6.96700i | −0.134678 | − | 0.265422i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.8802 | + | 15.8802i | 0.604110 | + | 0.604110i | 0.941401 | − | 0.337290i | \(-0.109510\pi\) |
−0.337290 | + | 0.941401i | \(0.609510\pi\) | |||||||
\(692\) | −25.0789 | − | 14.4793i | −0.953359 | − | 0.550422i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.6815 | + | 12.6815i | −0.481384 | + | 0.481384i | ||||
\(695\) | −5.53826 | − | 20.6691i | −0.210078 | − | 0.784023i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −72.1094 | + | 19.3217i | −2.73134 | + | 0.731860i | ||||
\(698\) | 1.39285 | + | 0.804163i | 0.0527202 | + | 0.0304380i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.04047 | + | 0.790399i | 0.0771223 | + | 0.0298743i | ||||
\(701\) | 43.0296i | 1.62520i | 0.582819 | + | 0.812602i | \(0.301950\pi\) | ||||
−0.582819 | + | 0.812602i | \(0.698050\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.0736 | + | 28.3327i | 1.85085 | + | 1.06859i | ||||
\(704\) | 7.68589 | + | 2.05943i | 0.289673 | + | 0.0776176i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.1707 | − | 17.6161i | −0.382778 | − | 0.662992i | ||||
\(707\) | 7.29628 | − | 5.87171i | 0.274405 | − | 0.220829i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.1430 | − | 5.12936i | 0.718932 | − | 0.192637i | 0.119237 | − | 0.992866i | \(-0.461955\pi\) |
0.599695 | + | 0.800228i | \(0.295288\pi\) | |||||||
\(710\) | 4.17367 | + | 15.5763i | 0.156635 | + | 0.584570i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.7472 | 0.627627 | ||||||||
\(713\) | 0.471003 | + | 1.75781i | 0.0176392 | + | 0.0658304i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.4916 | − | 8.36798i | 0.616749 | − | 0.312945i | ||||
\(716\) | 6.66522 | + | 11.5445i | 0.249091 | + | 0.431438i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.91791 | + | 10.2501i | 0.220854 | + | 0.382531i | ||||
\(719\) | −23.2898 | + | 40.3391i | −0.868563 | + | 1.50440i | −0.00509796 | + | 0.999987i | \(0.501623\pi\) |
−0.863465 | + | 0.504408i | \(0.831711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.8902 | + | 15.2020i | −0.703508 | + | 0.566151i | ||||
\(722\) | −9.20205 | + | 34.3425i | −0.342465 | + | 1.27810i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.73751i | 0.0645742i | ||||||||
\(725\) | 1.30052 | − | 0.750858i | 0.0483003 | − | 0.0278862i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.0896 | 1.41266 | 0.706332 | − | 0.707880i | \(-0.250348\pi\) | ||||
0.706332 | + | 0.707880i | \(0.250348\pi\) | |||||||
\(728\) | 8.97914 | + | 23.7260i | 0.332789 | + | 0.879345i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.8358 | − | 11.8358i | 0.438064 | − | 0.438064i | ||||
\(731\) | −5.31147 | + | 3.06658i | −0.196452 | + | 0.113421i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.16549 | − | 30.4740i | 0.301599 | − | 1.12558i | −0.634234 | − | 0.773141i | \(-0.718684\pi\) |
0.935833 | − | 0.352443i | \(-0.114649\pi\) | |||||||
\(734\) | −3.11360 | + | 11.6201i | −0.114925 | + | 0.428906i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.9016 | − | 15.9016i | −0.586140 | − | 0.586140i | ||||
\(737\) | −14.0973 | + | 24.4173i | −0.519281 | + | 0.899422i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.67265 | + | 28.6347i | −0.282243 | + | 1.05335i | 0.668587 | + | 0.743634i | \(0.266899\pi\) |
−0.950830 | + | 0.309712i | \(0.899767\pi\) | |||||||
\(740\) | 10.2481 | + | 17.7502i | 0.376728 | + | 0.652512i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.12424 | − | 1.82120i | 0.151405 | − | 0.0668583i | ||||
\(743\) | −6.49849 | − | 24.2527i | −0.238406 | − | 0.889745i | −0.976584 | − | 0.215138i | \(-0.930980\pi\) |
0.738177 | − | 0.674607i | \(-0.235687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.87198 | −0.361682 | ||||||||
\(746\) | 4.16077 | + | 15.5282i | 0.152337 | + | 0.568528i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.3805 | − | 5.72890i | −0.781750 | − | 0.209469i | ||||
\(749\) | −0.818995 | − | 5.27485i | −0.0299254 | − | 0.192739i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 31.1328i | − | 1.13605i | −0.823011 | − | 0.568025i | \(-0.807707\pi\) | ||
0.823011 | − | 0.568025i | \(-0.192293\pi\) | |||||||
\(752\) | 4.72801 | + | 1.26687i | 0.172413 | + | 0.0461979i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.76097 | + | 2.20934i | 0.246220 | + | 0.0804595i | ||||
\(755\) | 1.22489i | 0.0445784i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.51455 | − | 2.62328i | 0.0550472 | − | 0.0953446i | −0.837189 | − | 0.546914i | \(-0.815802\pi\) |
0.892236 | + | 0.451570i | \(0.149136\pi\) | |||||||
\(758\) | 4.32176 | + | 2.49517i | 0.156973 | + | 0.0906286i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −31.6118 | + | 31.6118i | −1.14668 | + | 1.14668i | ||||
\(761\) | −7.59236 | − | 28.3351i | −0.275223 | − | 1.02715i | −0.955692 | − | 0.294369i | \(-0.904890\pi\) |
0.680469 | − | 0.732777i | \(-0.261776\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.6312 | + | 6.01932i | −0.493482 | + | 0.217914i | ||||
\(764\) | 2.92535 | + | 1.68895i | 0.105835 | + | 0.0611040i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.46154 | + | 4.26351i | −0.0889389 | + | 0.154047i | ||||
\(767\) | −4.13153 | − | 19.5992i | −0.149181 | − | 0.707687i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.9694 | + | 8.29823i | −1.11679 | + | 0.299242i | −0.769582 | − | 0.638548i | \(-0.779535\pi\) |
−0.347203 | + | 0.937790i | \(0.612869\pi\) | |||||||
\(770\) | 4.31095 | + | 9.76245i | 0.155356 | + | 0.351814i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.9670 | + | 6.15399i | 0.826601 | + | 0.221487i | ||||
\(773\) | 31.5168 | + | 31.5168i | 1.13358 | + | 1.13358i | 0.989577 | + | 0.144005i | \(0.0459983\pi\) |
0.144005 | + | 0.989577i | \(0.454002\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.273600 | − | 0.0733109i | −0.00982801 | − | 0.00263341i | ||||
\(776\) | −37.1902 | + | 21.4718i | −1.33505 | + | 0.770791i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.14094 | − | 1.10956i | 0.148460 | − | 0.0397797i | ||||
\(779\) | −79.0521 | + | 45.6408i | −2.83234 | + | 1.63525i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.9478 | + | 20.6942i | −0.427526 | + | 0.740497i | ||||
\(782\) | −14.0164 | − | 14.0164i | −0.501225 | − | 0.501225i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.48079 | − | 1.42578i | 0.160028 | − | 0.0509208i | ||||
\(785\) | 16.4683 | − | 16.4683i | 0.587779 | − | 0.587779i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0345 | − | 13.0345i | 0.464631 | − | 0.464631i | −0.435539 | − | 0.900170i | \(-0.643442\pi\) |
0.900170 | + | 0.435539i | \(0.143442\pi\) | |||||||
\(788\) | 31.2379 | − | 8.37018i | 1.11281 | − | 0.298175i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.77426 | − | 3.07311i | 0.0631253 | − | 0.109336i | ||||
\(791\) | 25.5856 | − | 20.5901i | 0.909718 | − | 0.732099i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.1996 | − | 15.3236i | 1.07242 | − | 0.544156i | ||||
\(794\) | −6.52932 | − | 3.76971i | −0.231717 | − | 0.133782i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 25.7540i | − | 0.912828i | ||||||
\(797\) | 6.45241 | + | 11.1759i | 0.228556 | + | 0.395871i | 0.957380 | − | 0.288830i | \(-0.0932662\pi\) |
−0.728824 | + | 0.684701i | \(0.759933\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.1259 | + | 12.3594i | 1.63182 | + | 0.437244i | ||||
\(800\) | 3.38099 | − | 0.905934i | 0.119536 | − | 0.0320296i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.4976 | 1.04160 | ||||||||
\(803\) | 24.8034 | 0.875292 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.29620 | − | 21.2249i | 0.0809303 | − | 0.748078i | ||||
\(806\) | −0.607067 | − | 1.19640i | −0.0213830 | − | 0.0421415i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.43640 | − | 9.09277i | 0.0857123 | − | 0.319883i | ||||
\(809\) | 19.0726 | + | 33.0347i | 0.670558 | + | 1.16144i | 0.977746 | + | 0.209791i | \(0.0672784\pi\) |
−0.307189 | + | 0.951649i | \(0.599388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.6932 | − | 10.6932i | −0.375490 | − | 0.375490i | 0.493982 | − | 0.869472i | \(-0.335541\pi\) |
−0.869472 | + | 0.493982i | \(0.835541\pi\) | |||||||
\(812\) | 3.31196 | − | 8.55003i | 0.116227 | − | 0.300047i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.51895 | − | 13.1329i | 0.123339 | − | 0.460308i | ||||
\(815\) | 34.5683i | 1.21087i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.30278 | + | 5.30278i | −0.185521 | + | 0.185521i | ||||
\(818\) | 24.1718 | 0.845146 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −33.0171 | −1.15301 | ||||||||
\(821\) | 17.3195 | − | 17.3195i | 0.604455 | − | 0.604455i | −0.337036 | − | 0.941492i | \(-0.609425\pi\) |
0.941492 | + | 0.337036i | \(0.109425\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.5237i | 0.471408i | 0.971825 | + | 0.235704i | \(0.0757396\pi\) | ||||
−0.971825 | + | 0.235704i | \(0.924260\pi\) | |||||||
\(824\) | −6.30788 | + | 23.5413i | −0.219746 | + | 0.820101i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.4219 | − | 1.77342i | 0.397420 | − | 0.0617051i | ||||
\(827\) | −24.6131 | − | 24.6131i | −0.855881 | − | 0.855881i | 0.134969 | − | 0.990850i | \(-0.456906\pi\) |
−0.990850 | + | 0.134969i | \(0.956906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.85463 | + | 17.0687i | 0.342266 | + | 0.592821i | 0.984853 | − | 0.173391i | \(-0.0554724\pi\) |
−0.642588 | + | 0.766212i | \(0.722139\pi\) | |||||||
\(830\) | −0.920551 | + | 3.43554i | −0.0319528 | + | 0.119249i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.83090 | + | 6.40778i | 0.340825 | + | 0.222150i | ||||
\(833\) | 43.7140 | − | 13.9098i | 1.51460 | − | 0.481945i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0198603 | 0.000687292 | ||||||||
\(836\) | −27.0651 | −0.936066 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.7614 | − | 4.75916i | 0.613558 | − | 0.164402i | ||||
\(839\) | −22.4087 | − | 6.00440i | −0.773635 | − | 0.207295i | −0.149658 | − | 0.988738i | \(-0.547817\pi\) |
−0.623977 | + | 0.781443i | \(0.714484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.3537 | + | 19.6652i | 0.391508 | + | 0.678111i | ||||
\(842\) | 15.7363i | 0.542308i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.4312 | − | 7.75451i | −0.462321 | − | 0.266921i | ||||
\(845\) | 26.9516 | − | 4.17590i | 0.927164 | − | 0.143655i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.80024 | − | 12.3921i | 0.164938 | − | 0.425799i | ||||
\(848\) | −0.727766 | + | 1.26053i | −0.0249916 | + | 0.0432867i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.98016 | − | 0.798532i | 0.102219 | − | 0.0273894i | ||||
\(851\) | −19.2323 | + | 19.2323i | −0.659275 | + | 0.659275i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.2631 | + | 25.2631i | −0.864993 | + | 0.864993i | −0.991913 | − | 0.126920i | \(-0.959491\pi\) |
0.126920 | + | 0.991913i | \(0.459491\pi\) | |||||||
\(854\) | 7.89427 | + | 17.8772i | 0.270137 | + | 0.611744i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.79392 | − | 3.79392i | −0.129674 | − | 0.129674i | ||||
\(857\) | 3.17108 | − | 5.49248i | 0.108322 | − | 0.187619i | −0.806769 | − | 0.590868i | \(-0.798786\pi\) |
0.915091 | + | 0.403248i | \(0.132119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1601 | − | 7.02065i | 0.414898 | − | 0.239541i | −0.277994 | − | 0.960583i | \(-0.589670\pi\) |
0.692892 | + | 0.721041i | \(0.256336\pi\) | |||||||
\(860\) | −2.62010 | + | 0.702054i | −0.0893448 | + | 0.0239399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.98196 | + | 5.18573i | −0.305927 | + | 0.176627i | ||||
\(863\) | −33.5781 | − | 8.99722i | −1.14301 | − | 0.306269i | −0.362850 | − | 0.931848i | \(-0.618196\pi\) |
−0.780161 | + | 0.625579i | \(0.784863\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.0952 | − | 31.0952i | −1.05727 | − | 1.05727i | ||||
\(866\) | 8.41464 | + | 2.25470i | 0.285941 | + | 0.0766177i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.58208 | + | 0.698620i | −0.0536991 | + | 0.0237127i | ||||
\(869\) | 5.07911 | − | 1.36094i | 0.172297 | − | 0.0461668i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.9473 | + | 27.7710i | −1.04861 | + | 0.940986i | ||||
\(872\) | −7.48873 | + | 12.9709i | −0.253600 | + | 0.439249i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.9902 | − | 12.1187i | −0.710004 | − | 0.409921i | ||||
\(875\) | 25.0853 | + | 18.3425i | 0.848037 | + | 0.620090i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.21350 | + | 26.9211i | 0.243583 | + | 0.909062i | 0.974091 | + | 0.226158i | \(0.0726167\pi\) |
−0.730508 | + | 0.682904i | \(0.760717\pi\) | |||||||
\(878\) | −7.35868 | + | 7.35868i | −0.248343 | + | 0.248343i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.98379 | − | 1.72269i | −0.100583 | − | 0.0580719i | ||||
\(881\) | −4.46832 | + | 7.73936i | −0.150542 | + | 0.260746i | −0.931427 | − | 0.363929i | \(-0.881435\pi\) |
0.780885 | + | 0.624675i | \(0.214768\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 17.8140i | − | 0.599488i | −0.954020 | − | 0.299744i | \(-0.903099\pi\) | ||
0.954020 | − | 0.299744i | \(-0.0969012\pi\) | |||||||
\(884\) | −27.3475 | − | 17.8251i | −0.919797 | − | 0.599523i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.73100 | + | 0.999719i | 0.125345 | + | 0.0335862i | ||||
\(887\) | − | 43.3313i | − | 1.45492i | −0.686149 | − | 0.727461i | \(-0.740700\pi\) | ||
0.686149 | − | 0.727461i | \(-0.259300\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.99188 | + | 25.7947i | −0.335117 | + | 0.865125i | ||||
\(890\) | 10.0361 | + | 2.68916i | 0.336410 | + | 0.0901407i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.63513 | + | 13.5665i | 0.121713 | + | 0.454239i | ||||
\(893\) | 58.3897 | 1.95394 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.23926 | + | 19.5532i | 0.175129 | + | 0.653591i | ||||
\(896\) | 14.2645 | − | 19.5082i | 0.476543 | − | 0.651722i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.374035 | − | 0.647848i | −0.0124817 | − | 0.0216190i | ||||
\(899\) | −0.307190 | + | 1.14645i | −0.0102454 | + | 0.0382362i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.10000 | + | 12.2976i | −0.236535 | + | 0.409691i | ||||
\(902\) | 15.4870 | + | 15.4870i | 0.515661 | + | 0.515661i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.54362 | − | 31.8852i | 0.284157 | − | 1.06049i | ||||
\(905\) | −0.682894 | + | 2.54860i | −0.0227002 | + | 0.0847182i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.7649 | − | 17.7621i | 1.02153 | − | 0.589781i | 0.106984 | − | 0.994261i | \(-0.465881\pi\) |
0.914547 | + | 0.404480i | \(0.132547\pi\) | |||||||
\(908\) | −6.43174 | + | 6.43174i | −0.213445 | + | 0.213445i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.57115 | + | 15.6601i | 0.0520831 | + | 0.519127i | ||||
\(911\) | 56.1740 | 1.86113 | 0.930564 | − | 0.366130i | \(-0.119318\pi\) | ||||
0.930564 | + | 0.366130i | \(0.119318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.56435 | + | 2.63523i | −0.151058 | + | 0.0872133i | ||||
\(914\) | − | 15.1306i | − | 0.500474i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.444427 | + | 1.65863i | −0.0146843 | + | 0.0548025i | ||||
\(917\) | 34.6067 | + | 43.0029i | 1.14282 | + | 1.42008i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.2328 | − | 36.7763i | 0.700405 | − | 1.21314i | −0.267919 | − | 0.963441i | \(-0.586336\pi\) |
0.968324 | − | 0.249696i | \(-0.0803306\pi\) | |||||||
\(920\) | −10.7291 | − | 18.5833i | −0.353727 | − | 0.612674i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.53513 | − | 4.39098i | −0.0834902 | − | 0.144609i | ||||
\(923\) | −26.2286 | + | 23.5366i | −0.863324 | + | 0.774717i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.09569 | − | 4.08917i | −0.0360261 | − | 0.134451i | ||||
\(926\) | −8.54132 | −0.280685 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.79608 | − | 14.1672i | −0.124612 | − | 0.465060i | ||||
\(929\) | −27.8702 | + | 7.46779i | −0.914391 | + | 0.245010i | −0.685186 | − | 0.728368i | \(-0.740279\pi\) |
−0.229205 | + | 0.973378i | \(0.573612\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.2277 | − | 30.2627i | 1.54782 | − | 0.991818i | ||||
\(932\) | −10.1242 | − | 17.5357i | −0.331630 | − | 0.574400i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.2921 | − | 4.36545i | −0.533093 | − | 0.142842i | ||||
\(935\) | −29.1095 | − | 16.8064i | −0.951982 | − | 0.549627i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.4230i | − | 0.503847i | −0.967747 | − | 0.251923i | \(-0.918937\pi\) | ||
0.967747 | − | 0.251923i | \(-0.0810631\pi\) | |||||||
\(938\) | −15.0439 | − | 18.6937i | −0.491200 | − | 0.610372i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.2904 | + | 10.5599i | 0.596566 | + | 0.344428i | ||||
\(941\) | −31.8491 | + | 8.53393i | −1.03825 | + | 0.278198i | −0.737388 | − | 0.675470i | \(-0.763941\pi\) |
−0.300862 | + | 0.953668i | \(0.597274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.3399 | − | 42.3210i | −0.369277 | − | 1.37816i | ||||
\(944\) | −2.63872 | + | 2.63872i | −0.0858829 | + | 0.0858829i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.55829 | + | 0.899681i | 0.0506645 | + | 0.0292511i | ||||
\(947\) | 17.4962 | + | 17.4962i | 0.568550 | + | 0.568550i | 0.931722 | − | 0.363172i | \(-0.118306\pi\) |
−0.363172 | + | 0.931722i | \(0.618306\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.7701 | + | 11.3621i | 1.12869 | + | 0.368830i | ||||
\(950\) | 3.26709 | − | 1.88626i | 0.105998 | − | 0.0611983i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 27.2156 | − | 37.2202i | 0.882064 | − | 1.20631i | ||||
\(953\) | −38.7397 | + | 22.3663i | −1.25490 | + | 0.724517i | −0.972079 | − | 0.234655i | \(-0.924604\pi\) |
−0.282822 | + | 0.959172i | \(0.591271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.62711 | + | 3.62711i | 0.117371 | + | 0.117371i | ||||
\(956\) | 6.71074 | + | 6.71074i | 0.217041 | + | 0.217041i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.3291 | + | 7.11824i | −0.398337 | + | 0.229980i | ||||
\(959\) | −17.6057 | + | 24.0777i | −0.568519 | + | 0.777509i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.6529 | + | 15.3881i | −0.859771 | + | 0.496389i | ||||
\(962\) | 10.9490 | − | 16.7981i | 0.353010 | − | 0.541593i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.6726 | − | 18.6726i | −0.601403 | − | 0.601403i | ||||
\(965\) | 31.2695 | + | 18.0534i | 1.00660 | + | 0.581161i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.27104 | + | 7.27104i | −0.233821 | + | 0.233821i | −0.814285 | − | 0.580465i | \(-0.802871\pi\) |
0.580465 | + | 0.814285i | \(0.302871\pi\) | |||||||
\(968\) | −3.45718 | − | 12.9024i | −0.111118 | − | 0.414697i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.7347 | + | 6.89560i | −0.826293 | + | 0.221404i | ||||
\(971\) | −18.9111 | − | 10.9184i | −0.606887 | − | 0.350387i | 0.164859 | − | 0.986317i | \(-0.447283\pi\) |
−0.771746 | + | 0.635931i | \(0.780616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9187 | + | 21.0234i | 0.542388 | + | 0.673980i | ||||
\(974\) | 5.66316i | 0.181459i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.46396 | − | 3.15462i | −0.174897 | − | 0.100977i | ||||
\(977\) | 3.64839 | + | 0.977584i | 0.116722 | + | 0.0312757i | 0.316707 | − | 0.948523i | \(-0.397423\pi\) |
−0.199985 | + | 0.979799i | \(0.564089\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.69815 | + | 13.3336i | 0.246034 | + | 0.426143i | ||||
\(980\) | 20.2670 | − | 0.938407i | 0.647406 | − | 0.0299763i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.3993 | + | 5.73392i | −0.682878 | + | 0.182977i | ||||
\(983\) | −12.2540 | − | 45.7327i | −0.390843 | − | 1.45865i | −0.828746 | − | 0.559625i | \(-0.810945\pi\) |
0.437903 | − | 0.899022i | \(-0.355721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.1098 | 1.56477 | ||||||||
\(986\) | −3.34604 | − | 12.4876i | −0.106560 | − | 0.397686i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.9406 | − | 12.3982i | −1.20705 | − | 0.394439i | ||||
\(989\) | −1.79977 | − | 3.11730i | −0.0572294 | − | 0.0991243i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.24867 | + | 9.09095i | 0.166729 | + | 0.288784i | 0.937268 | − | 0.348610i | \(-0.113346\pi\) |
−0.770539 | + | 0.637393i | \(0.780013\pi\) | |||||||
\(992\) | −1.38323 | + | 2.39582i | −0.0439175 | + | 0.0760674i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.7500 | − | 15.8434i | −0.404406 | − | 0.502522i | ||||
\(995\) | 10.1221 | − | 37.7762i | 0.320892 | − | 1.19759i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.0853i | 1.17450i | 0.809405 | + | 0.587251i | \(0.199790\pi\) | ||||
−0.809405 | + | 0.587251i | \(0.800210\pi\) | |||||||
\(998\) | 14.3278 | − | 8.27218i | 0.453540 | − | 0.261851i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.et.c.136.4 | 36 | ||
3.2 | odd | 2 | 273.2.bt.a.136.6 | ✓ | 36 | ||
7.5 | odd | 6 | 819.2.gh.c.19.6 | 36 | |||
13.11 | odd | 12 | 819.2.gh.c.388.6 | 36 | |||
21.5 | even | 6 | 273.2.cg.a.19.4 | yes | 36 | ||
39.11 | even | 12 | 273.2.cg.a.115.4 | yes | 36 | ||
91.89 | even | 12 | inner | 819.2.et.c.271.4 | 36 | ||
273.89 | odd | 12 | 273.2.bt.a.271.6 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bt.a.136.6 | ✓ | 36 | 3.2 | odd | 2 | ||
273.2.bt.a.271.6 | yes | 36 | 273.89 | odd | 12 | ||
273.2.cg.a.19.4 | yes | 36 | 21.5 | even | 6 | ||
273.2.cg.a.115.4 | yes | 36 | 39.11 | even | 12 | ||
819.2.et.c.136.4 | 36 | 1.1 | even | 1 | trivial | ||
819.2.et.c.271.4 | 36 | 91.89 | even | 12 | inner | ||
819.2.gh.c.19.6 | 36 | 7.5 | odd | 6 | |||
819.2.gh.c.388.6 | 36 | 13.11 | odd | 12 |