Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [696,2,Mod(347,696)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(696, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("696.347");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 696 = 2^{3} \cdot 3 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 696.l (of order \(2\), degree \(1\), 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: | \(5.55758798068\) |
Analytic rank: | \(0\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 347.14 | ||
Character | \(\chi\) | \(=\) | 696.347 |
Dual form | 696.2.l.b.347.15 |
$q$-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 \(\left(\mathbb{Z}/696\mathbb{Z}\right)^\times\).
\(n\) | \(175\) | \(233\) | \(349\) | \(553\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30342 | − | 0.548731i | −0.921655 | − | 0.388011i | ||||
\(3\) | 1.37036 | + | 1.05930i | 0.791177 | + | 0.611587i | ||||
\(4\) | 1.39779 | + | 1.43045i | 0.698895 | + | 0.715225i | ||||
\(5\) | −1.96366 | −0.878177 | −0.439088 | − | 0.898444i | \(-0.644698\pi\) | ||||
−0.439088 | + | 0.898444i | \(0.644698\pi\) | |||||||
\(6\) | −1.20488 | − | 2.13267i | −0.491889 | − | 0.870658i | ||||
\(7\) | − | 2.07610i | − | 0.784691i | −0.919818 | − | 0.392346i | \(-0.871664\pi\) | ||
0.919818 | − | 0.392346i | \(-0.128336\pi\) | |||||||
\(8\) | −1.03697 | − | 2.63148i | −0.366624 | − | 0.930369i | ||||
\(9\) | 0.755764 | + | 2.90324i | 0.251921 | + | 0.967748i | ||||
\(10\) | 2.55947 | + | 1.07752i | 0.809375 | + | 0.340742i | ||||
\(11\) | −4.32719 | −1.30470 | −0.652349 | − | 0.757919i | \(-0.726216\pi\) | ||||
−0.652349 | + | 0.757919i | \(0.726216\pi\) | |||||||
\(12\) | 0.400196 | + | 3.44091i | 0.115527 | + | 0.993304i | ||||
\(13\) | − | 2.09729i | − | 0.581682i | −0.956771 | − | 0.290841i | \(-0.906065\pi\) | ||
0.956771 | − | 0.290841i | \(-0.0939351\pi\) | |||||||
\(14\) | −1.13922 | + | 2.70602i | −0.304469 | + | 0.723214i | ||||
\(15\) | −2.69092 | − | 2.08011i | −0.694793 | − | 0.537082i | ||||
\(16\) | −0.0923716 | + | 3.99893i | −0.0230929 | + | 0.999733i | ||||
\(17\) | −4.93860 | −1.19779 | −0.598893 | − | 0.800829i | \(-0.704392\pi\) | ||||
−0.598893 | + | 0.800829i | \(0.704392\pi\) | |||||||
\(18\) | 0.608023 | − | 4.19885i | 0.143312 | − | 0.989678i | ||||
\(19\) | 6.72758i | 1.54341i | 0.635979 | + | 0.771706i | \(0.280596\pi\) | ||||
−0.635979 | + | 0.771706i | \(0.719404\pi\) | |||||||
\(20\) | −2.74479 | − | 2.80892i | −0.613753 | − | 0.628094i | ||||
\(21\) | 2.19921 | − | 2.84500i | 0.479907 | − | 0.620829i | ||||
\(22\) | 5.64014 | + | 2.37446i | 1.20248 | + | 0.506238i | ||||
\(23\) | 1.88085 | 0.392185 | 0.196093 | − | 0.980585i | \(-0.437175\pi\) | ||||
0.196093 | + | 0.980585i | \(0.437175\pi\) | |||||||
\(24\) | 1.36651 | − | 4.70454i | 0.278938 | − | 0.960309i | ||||
\(25\) | −1.14403 | −0.228806 | ||||||||
\(26\) | −1.15084 | + | 2.73364i | −0.225699 | + | 0.536110i | ||||
\(27\) | −2.03974 | + | 4.77907i | −0.392548 | + | 0.919732i | ||||
\(28\) | 2.96975 | − | 2.90195i | 0.561230 | − | 0.548416i | ||||
\(29\) | 0.219453 | + | 5.38069i | 0.0407514 | + | 0.999169i | ||||
\(30\) | 2.36597 | + | 4.18784i | 0.431965 | + | 0.764591i | ||||
\(31\) | −8.14094 | −1.46216 | −0.731078 | − | 0.682294i | \(-0.760982\pi\) | ||||
−0.731078 | + | 0.682294i | \(0.760982\pi\) | |||||||
\(32\) | 2.31474 | − | 5.16159i | 0.409191 | − | 0.912449i | ||||
\(33\) | −5.92981 | − | 4.58380i | −1.03225 | − | 0.797937i | ||||
\(34\) | 6.43705 | + | 2.70996i | 1.10394 | + | 0.464754i | ||||
\(35\) | 4.07675i | 0.689097i | ||||||||
\(36\) | −3.09654 | + | 5.13920i | −0.516091 | + | 0.856534i | ||||
\(37\) | −9.56194 | −1.57197 | −0.785987 | − | 0.618243i | \(-0.787845\pi\) | ||||
−0.785987 | + | 0.618243i | \(0.787845\pi\) | |||||||
\(38\) | 3.69163 | − | 8.76884i | 0.598861 | − | 1.42249i | ||||
\(39\) | 2.22166 | − | 2.87403i | 0.355750 | − | 0.460213i | ||||
\(40\) | 2.03626 | + | 5.16734i | 0.321961 | + | 0.817028i | ||||
\(41\) | 5.31532 | 0.830114 | 0.415057 | − | 0.909795i | \(-0.363762\pi\) | ||||
0.415057 | + | 0.909795i | \(0.363762\pi\) | |||||||
\(42\) | −4.42763 | + | 2.50144i | −0.683197 | + | 0.385981i | ||||
\(43\) | − | 5.06216i | − | 0.771971i | −0.922505 | − | 0.385986i | \(-0.873861\pi\) | ||
0.922505 | − | 0.385986i | \(-0.126139\pi\) | |||||||
\(44\) | −6.04850 | − | 6.18983i | −0.911846 | − | 0.933152i | ||||
\(45\) | −1.48407 | − | 5.70099i | −0.221232 | − | 0.849853i | ||||
\(46\) | −2.45154 | − | 1.03208i | −0.361459 | − | 0.152172i | ||||
\(47\) | − | 6.70159i | − | 0.977528i | −0.872416 | − | 0.488764i | \(-0.837448\pi\) | ||
0.872416 | − | 0.488764i | \(-0.162552\pi\) | |||||||
\(48\) | −4.36265 | + | 5.38212i | −0.629695 | + | 0.776842i | ||||
\(49\) | 2.68982 | 0.384260 | ||||||||
\(50\) | 1.49115 | + | 0.627765i | 0.210880 | + | 0.0887793i | ||||
\(51\) | −6.76765 | − | 5.23146i | −0.947660 | − | 0.732550i | ||||
\(52\) | 3.00006 | − | 2.93156i | 0.416034 | − | 0.406535i | ||||
\(53\) | −13.7107 | −1.88331 | −0.941654 | − | 0.336582i | \(-0.890729\pi\) | ||||
−0.941654 | + | 0.336582i | \(0.890729\pi\) | |||||||
\(54\) | 5.28105 | − | 5.10984i | 0.718660 | − | 0.695362i | ||||
\(55\) | 8.49715 | 1.14576 | ||||||||
\(56\) | −5.46321 | + | 2.15285i | −0.730052 | + | 0.287687i | ||||
\(57\) | −7.12653 | + | 9.21919i | −0.943932 | + | 1.22111i | ||||
\(58\) | 2.66651 | − | 7.13370i | 0.350130 | − | 0.936701i | ||||
\(59\) | − | 7.04044i | − | 0.916587i | −0.888801 | − | 0.458293i | \(-0.848461\pi\) | ||
0.888801 | − | 0.458293i | \(-0.151539\pi\) | |||||||
\(60\) | −0.785850 | − | 6.75678i | −0.101453 | − | 0.872297i | ||||
\(61\) | 11.7831 | 1.50867 | 0.754336 | − | 0.656489i | \(-0.227959\pi\) | ||||
0.754336 | + | 0.656489i | \(0.227959\pi\) | |||||||
\(62\) | 10.6110 | + | 4.46718i | 1.34760 | + | 0.567333i | ||||
\(63\) | 6.02742 | − | 1.56904i | 0.759383 | − | 0.197681i | ||||
\(64\) | −5.84939 | + | 5.45753i | −0.731174 | + | 0.682192i | ||||
\(65\) | 4.11836i | 0.510820i | ||||||||
\(66\) | 5.21374 | + | 9.22847i | 0.641767 | + | 1.13595i | ||||
\(67\) | −1.72208 | −0.210385 | −0.105193 | − | 0.994452i | \(-0.533546\pi\) | ||||
−0.105193 | + | 0.994452i | \(0.533546\pi\) | |||||||
\(68\) | −6.90311 | − | 7.06441i | −0.837126 | − | 0.856686i | ||||
\(69\) | 2.57744 | + | 1.99239i | 0.310288 | + | 0.239856i | ||||
\(70\) | 2.23704 | − | 5.31371i | 0.267377 | − | 0.635110i | ||||
\(71\) | 2.62273 | 0.311260 | 0.155630 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155630 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(72\) | 6.85613 | − | 4.99935i | 0.808002 | − | 0.589180i | ||||
\(73\) | − | 9.08611i | − | 1.06345i | −0.846917 | − | 0.531724i | \(-0.821544\pi\) | ||
0.846917 | − | 0.531724i | \(-0.178456\pi\) | |||||||
\(74\) | 12.4632 | + | 5.24693i | 1.44882 | + | 0.609944i | ||||
\(75\) | −1.56773 | − | 1.21187i | −0.181026 | − | 0.139935i | ||||
\(76\) | −9.62346 | + | 9.40374i | −1.10389 | + | 1.07868i | ||||
\(77\) | 8.98368i | 1.02378i | ||||||||
\(78\) | −4.47281 | + | 2.52697i | −0.506446 | + | 0.286123i | ||||
\(79\) | −9.00744 | −1.01342 | −0.506708 | − | 0.862118i | \(-0.669138\pi\) | ||||
−0.506708 | + | 0.862118i | \(0.669138\pi\) | |||||||
\(80\) | 0.181387 | − | 7.85255i | 0.0202796 | − | 0.877942i | ||||
\(81\) | −7.85764 | + | 4.38834i | −0.873071 | + | 0.487593i | ||||
\(82\) | −6.92808 | − | 2.91668i | −0.765078 | − | 0.322094i | ||||
\(83\) | 13.3661i | 1.46712i | 0.679626 | + | 0.733559i | \(0.262142\pi\) | ||||
−0.679626 | + | 0.733559i | \(0.737858\pi\) | |||||||
\(84\) | 7.14366 | − | 0.830846i | 0.779437 | − | 0.0906527i | ||||
\(85\) | 9.69773 | 1.05187 | ||||||||
\(86\) | −2.77776 | + | 6.59810i | −0.299534 | + | 0.711491i | ||||
\(87\) | −5.39904 | + | 7.60594i | −0.578838 | + | 0.815443i | ||||
\(88\) | 4.48717 | + | 11.3869i | 0.478334 | + | 1.21385i | ||||
\(89\) | −5.04147 | −0.534395 | −0.267198 | − | 0.963642i | \(-0.586098\pi\) | ||||
−0.267198 | + | 0.963642i | \(0.586098\pi\) | |||||||
\(90\) | −1.19395 | + | 8.24512i | −0.125854 | + | 0.869112i | ||||
\(91\) | −4.35417 | −0.456441 | ||||||||
\(92\) | 2.62904 | + | 2.69047i | 0.274096 | + | 0.280501i | ||||
\(93\) | −11.1560 | − | 8.62370i | −1.15682 | − | 0.894236i | ||||
\(94\) | −3.67737 | + | 8.73496i | −0.379292 | + | 0.900943i | ||||
\(95\) | − | 13.2107i | − | 1.35539i | ||||||
\(96\) | 8.63969 | − | 4.62122i | 0.881785 | − | 0.471652i | ||||
\(97\) | 9.01124i | 0.914952i | 0.889222 | + | 0.457476i | \(0.151247\pi\) | ||||
−0.889222 | + | 0.457476i | \(0.848753\pi\) | |||||||
\(98\) | −3.50596 | − | 1.47599i | −0.354155 | − | 0.149097i | ||||
\(99\) | −3.27034 | − | 12.5629i | −0.328681 | − | 1.26262i | ||||
\(100\) | −1.59911 | − | 1.63648i | −0.159911 | − | 0.163648i | ||||
\(101\) | 13.3504i | 1.32841i | 0.747549 | + | 0.664207i | \(0.231231\pi\) | ||||
−0.747549 | + | 0.664207i | \(0.768769\pi\) | |||||||
\(102\) | 5.95040 | + | 10.5324i | 0.589177 | + | 1.04286i | ||||
\(103\) | − | 3.69126i | − | 0.363710i | −0.983325 | − | 0.181855i | \(-0.941790\pi\) | ||
0.983325 | − | 0.181855i | \(-0.0582102\pi\) | |||||||
\(104\) | −5.51897 | + | 2.17482i | −0.541179 | + | 0.213259i | ||||
\(105\) | −4.31851 | + | 5.58661i | −0.421443 | + | 0.545198i | ||||
\(106\) | 17.8707 | + | 7.52348i | 1.73576 | + | 0.730745i | ||||
\(107\) | 3.25638i | 0.314806i | 0.987534 | + | 0.157403i | \(0.0503122\pi\) | ||||
−0.987534 | + | 0.157403i | \(0.949688\pi\) | |||||||
\(108\) | −9.68734 | + | 3.76238i | −0.932164 | + | 0.362035i | ||||
\(109\) | 9.06882i | 0.868635i | 0.900760 | + | 0.434318i | \(0.143010\pi\) | ||||
−0.900760 | + | 0.434318i | \(0.856990\pi\) | |||||||
\(110\) | −11.0753 | − | 4.66265i | −1.05599 | − | 0.444566i | ||||
\(111\) | −13.1033 | − | 10.1290i | −1.24371 | − | 0.961399i | ||||
\(112\) | 8.30217 | + | 0.191772i | 0.784482 | + | 0.0181208i | ||||
\(113\) | 20.8820 | 1.96441 | 0.982207 | − | 0.187801i | \(-0.0601362\pi\) | ||||
0.982207 | + | 0.187801i | \(0.0601362\pi\) | |||||||
\(114\) | 14.3477 | − | 8.10590i | 1.34378 | − | 0.759188i | ||||
\(115\) | −3.69336 | −0.344408 | ||||||||
\(116\) | −7.39006 | + | 7.83499i | −0.686150 | + | 0.727460i | ||||
\(117\) | 6.08893 | − | 1.58505i | 0.562922 | − | 0.146538i | ||||
\(118\) | −3.86331 | + | 9.17662i | −0.355646 | + | 0.844777i | ||||
\(119\) | 10.2530i | 0.939891i | ||||||||
\(120\) | −2.68336 | + | 9.23812i | −0.244956 | + | 0.843321i | ||||
\(121\) | 7.72461 | 0.702237 | ||||||||
\(122\) | −15.3583 | − | 6.46575i | −1.39047 | − | 0.585382i | ||||
\(123\) | 7.28390 | + | 5.63053i | 0.656767 | + | 0.507687i | ||||
\(124\) | −11.3793 | − | 11.6452i | −1.02189 | − | 1.04577i | ||||
\(125\) | 12.0648 | 1.07911 | ||||||||
\(126\) | −8.71721 | − | 1.26231i | −0.776591 | − | 0.112456i | ||||
\(127\) | −7.89886 | −0.700911 | −0.350455 | − | 0.936579i | \(-0.613973\pi\) | ||||
−0.350455 | + | 0.936579i | \(0.613973\pi\) | |||||||
\(128\) | 10.6189 | − | 3.90370i | 0.938587 | − | 0.345041i | ||||
\(129\) | 5.36234 | − | 6.93697i | 0.472128 | − | 0.610766i | ||||
\(130\) | 2.25987 | − | 5.36794i | 0.198204 | − | 0.470799i | ||||
\(131\) | −0.760056 | −0.0664064 | −0.0332032 | − | 0.999449i | \(-0.510571\pi\) | ||||
−0.0332032 | + | 0.999449i | \(0.510571\pi\) | |||||||
\(132\) | −1.73173 | − | 14.8895i | −0.150727 | − | 1.29596i | ||||
\(133\) | 13.9671 | 1.21110 | ||||||||
\(134\) | 2.24458 | + | 0.944956i | 0.193902 | + | 0.0816318i | ||||
\(135\) | 4.00536 | − | 9.38447i | 0.344726 | − | 0.807687i | ||||
\(136\) | 5.12117 | + | 12.9958i | 0.439137 | + | 1.11438i | ||||
\(137\) | 9.11021 | 0.778338 | 0.389169 | − | 0.921166i | \(-0.372762\pi\) | ||||
0.389169 | + | 0.921166i | \(0.372762\pi\) | |||||||
\(138\) | −2.26620 | − | 4.01124i | −0.192912 | − | 0.341459i | ||||
\(139\) | −5.62933 | −0.477473 | −0.238737 | − | 0.971084i | \(-0.576733\pi\) | ||||
−0.238737 | + | 0.971084i | \(0.576733\pi\) | |||||||
\(140\) | −5.83159 | + | 5.69844i | −0.492859 | + | 0.481606i | ||||
\(141\) | 7.09900 | − | 9.18358i | 0.597844 | − | 0.773397i | ||||
\(142\) | −3.41850 | − | 1.43917i | −0.286875 | − | 0.120773i | ||||
\(143\) | 9.07536i | 0.758920i | ||||||||
\(144\) | −11.6797 | + | 2.75407i | −0.973307 | + | 0.229506i | ||||
\(145\) | −0.430932 | − | 10.5659i | −0.0357869 | − | 0.877447i | ||||
\(146\) | −4.98583 | + | 11.8430i | −0.412630 | + | 0.980132i | ||||
\(147\) | 3.68602 | + | 2.84933i | 0.304018 | + | 0.235009i | ||||
\(148\) | −13.3656 | − | 13.6779i | −1.09864 | − | 1.12431i | ||||
\(149\) | 4.52749 | 0.370906 | 0.185453 | − | 0.982653i | \(-0.440625\pi\) | ||||
0.185453 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(150\) | 1.37842 | + | 2.43984i | 0.112547 | + | 0.199212i | ||||
\(151\) | − | 18.7745i | − | 1.52785i | −0.645308 | − | 0.763923i | \(-0.723271\pi\) | ||
0.645308 | − | 0.763923i | \(-0.276729\pi\) | |||||||
\(152\) | 17.7035 | − | 6.97629i | 1.43594 | − | 0.565852i | ||||
\(153\) | −3.73241 | − | 14.3379i | −0.301748 | − | 1.15915i | ||||
\(154\) | 4.92962 | − | 11.7095i | 0.397240 | − | 0.943576i | ||||
\(155\) | 15.9861 | 1.28403 | ||||||||
\(156\) | 7.21656 | − | 0.839325i | 0.577788 | − | 0.0671998i | ||||
\(157\) | 6.23944 | 0.497961 | 0.248981 | − | 0.968508i | \(-0.419904\pi\) | ||||
0.248981 | + | 0.968508i | \(0.419904\pi\) | |||||||
\(158\) | 11.7405 | + | 4.94266i | 0.934020 | + | 0.393217i | ||||
\(159\) | −18.7886 | − | 14.5237i | −1.49003 | − | 1.15181i | ||||
\(160\) | −4.54536 | + | 10.1356i | −0.359342 | + | 0.801291i | ||||
\(161\) | − | 3.90484i | − | 0.307744i | ||||||
\(162\) | 12.6498 | − | 1.40810i | 0.993862 | − | 0.110631i | ||||
\(163\) | − | 17.4983i | − | 1.37057i | −0.728275 | − | 0.685285i | \(-0.759678\pi\) | ||
0.728275 | − | 0.685285i | \(-0.240322\pi\) | |||||||
\(164\) | 7.42970 | + | 7.60330i | 0.580162 | + | 0.593718i | ||||
\(165\) | 11.6441 | + | 9.00103i | 0.906495 | + | 0.700730i | ||||
\(166\) | 7.33438 | − | 17.4216i | 0.569258 | − | 1.35218i | ||||
\(167\) | −16.5928 | −1.28399 | −0.641993 | − | 0.766711i | \(-0.721892\pi\) | ||||
−0.641993 | + | 0.766711i | \(0.721892\pi\) | |||||||
\(168\) | −9.76707 | − | 2.83701i | −0.753546 | − | 0.218880i | ||||
\(169\) | 8.60140 | 0.661646 | ||||||||
\(170\) | −12.6402 | − | 5.32144i | −0.969458 | − | 0.408136i | ||||
\(171\) | −19.5318 | + | 5.08446i | −1.49363 | + | 0.388819i | ||||
\(172\) | 7.24116 | − | 7.07583i | 0.552133 | − | 0.539527i | ||||
\(173\) | −1.89421 | −0.144014 | −0.0720069 | − | 0.997404i | \(-0.522940\pi\) | ||||
−0.0720069 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(174\) | 11.2108 | − | 6.95109i | 0.849890 | − | 0.526961i | ||||
\(175\) | 2.37512i | 0.179542i | ||||||||
\(176\) | 0.399710 | − | 17.3042i | 0.0301293 | − | 1.30435i | ||||
\(177\) | 7.45794 | − | 9.64792i | 0.560573 | − | 0.725182i | ||||
\(178\) | 6.57114 | + | 2.76641i | 0.492528 | + | 0.207351i | ||||
\(179\) | − | 2.40985i | − | 0.180121i | −0.995936 | − | 0.0900603i | \(-0.971294\pi\) | ||
0.995936 | − | 0.0900603i | \(-0.0287060\pi\) | |||||||
\(180\) | 6.08057 | − | 10.0917i | 0.453219 | − | 0.752188i | ||||
\(181\) | 23.2465i | 1.72790i | 0.503577 | + | 0.863950i | \(0.332017\pi\) | ||||
−0.503577 | + | 0.863950i | \(0.667983\pi\) | |||||||
\(182\) | 5.67529 | + | 2.38927i | 0.420681 | + | 0.177104i | ||||
\(183\) | 16.1471 | + | 12.4818i | 1.19363 | + | 0.922685i | ||||
\(184\) | −1.95039 | − | 4.94943i | −0.143785 | − | 0.364877i | ||||
\(185\) | 18.7764 | 1.38047 | ||||||||
\(186\) | 9.80883 | + | 17.3619i | 0.719218 | + | 1.27304i | ||||
\(187\) | 21.3703 | 1.56275 | ||||||||
\(188\) | 9.58629 | − | 9.36741i | 0.699152 | − | 0.683189i | ||||
\(189\) | 9.92180 | + | 4.23470i | 0.721705 | + | 0.308029i | ||||
\(190\) | −7.24911 | + | 17.2190i | −0.525906 | + | 1.24920i | ||||
\(191\) | − | 1.00718i | − | 0.0728769i | −0.999336 | − | 0.0364384i | \(-0.988399\pi\) | ||
0.999336 | − | 0.0364384i | \(-0.0116013\pi\) | |||||||
\(192\) | −13.7969 | + | 1.28251i | −0.995707 | + | 0.0925575i | ||||
\(193\) | − | 7.26070i | − | 0.522637i | −0.965253 | − | 0.261318i | \(-0.915843\pi\) | ||
0.965253 | − | 0.261318i | \(-0.0841572\pi\) | |||||||
\(194\) | 4.94474 | − | 11.7454i | 0.355012 | − | 0.843270i | ||||
\(195\) | −4.36258 | + | 5.64363i | −0.312411 | + | 0.404149i | ||||
\(196\) | 3.75980 | + | 3.84765i | 0.268557 | + | 0.274832i | ||||
\(197\) | 8.52791 | 0.607589 | 0.303794 | − | 0.952738i | \(-0.401746\pi\) | ||||
0.303794 | + | 0.952738i | \(0.401746\pi\) | |||||||
\(198\) | −2.63103 | + | 18.1692i | −0.186979 | + | 1.29123i | ||||
\(199\) | − | 2.01449i | − | 0.142803i | −0.997448 | − | 0.0714017i | \(-0.977253\pi\) | ||
0.997448 | − | 0.0714017i | \(-0.0227472\pi\) | |||||||
\(200\) | 1.18632 | + | 3.01049i | 0.0838858 | + | 0.212874i | ||||
\(201\) | −2.35986 | − | 1.82420i | −0.166452 | − | 0.128669i | ||||
\(202\) | 7.32577 | − | 17.4011i | 0.515440 | − | 1.22434i | ||||
\(203\) | 11.1708 | − | 0.455606i | 0.784039 | − | 0.0319773i | ||||
\(204\) | −1.97641 | − | 16.9932i | −0.138376 | − | 1.18977i | ||||
\(205\) | −10.4375 | −0.728987 | ||||||||
\(206\) | −2.02551 | + | 4.81124i | −0.141124 | + | 0.335215i | ||||
\(207\) | 1.42148 | + | 5.46058i | 0.0987999 | + | 0.379536i | ||||
\(208\) | 8.38690 | + | 0.193730i | 0.581527 | + | 0.0134327i | ||||
\(209\) | − | 29.1115i | − | 2.01369i | ||||||
\(210\) | 8.69436 | − | 4.91199i | 0.599968 | − | 0.338959i | ||||
\(211\) | 20.6650i | 1.42263i | 0.702871 | + | 0.711317i | \(0.251901\pi\) | ||||
−0.702871 | + | 0.711317i | \(0.748099\pi\) | |||||||
\(212\) | −19.1647 | − | 19.6124i | −1.31623 | − | 1.34699i | ||||
\(213\) | 3.59408 | + | 2.77826i | 0.246262 | + | 0.190363i | ||||
\(214\) | 1.78688 | − | 4.24442i | 0.122148 | − | 0.290143i | ||||
\(215\) | 9.94036i | 0.677927i | ||||||||
\(216\) | 14.6912 | + | 0.411790i | 0.999607 | + | 0.0280187i | ||||
\(217\) | 16.9014i | 1.14734i | ||||||||
\(218\) | 4.97634 | − | 11.8204i | 0.337040 | − | 0.800582i | ||||
\(219\) | 9.62492 | − | 12.4512i | 0.650392 | − | 0.841376i | ||||
\(220\) | 11.8772 | + | 12.1547i | 0.800762 | + | 0.819472i | ||||
\(221\) | 10.3576i | 0.696730i | ||||||||
\(222\) | 11.5210 | + | 20.3924i | 0.773236 | + | 1.36865i | ||||
\(223\) | 1.54064i | 0.103169i | 0.998669 | + | 0.0515844i | \(0.0164271\pi\) | ||||
−0.998669 | + | 0.0515844i | \(0.983573\pi\) | |||||||
\(224\) | −10.7160 | − | 4.80562i | −0.715990 | − | 0.321089i | ||||
\(225\) | −0.864617 | − | 3.32140i | −0.0576411 | − | 0.221426i | ||||
\(226\) | −27.2180 | − | 11.4586i | −1.81051 | − | 0.762215i | ||||
\(227\) | − | 8.60601i | − | 0.571201i | −0.958349 | − | 0.285600i | \(-0.907807\pi\) | ||
0.958349 | − | 0.285600i | \(-0.0921930\pi\) | |||||||
\(228\) | −23.1490 | + | 2.69235i | −1.53308 | + | 0.178305i | ||||
\(229\) | −6.21209 | −0.410507 | −0.205253 | − | 0.978709i | \(-0.565802\pi\) | ||||
−0.205253 | + | 0.978709i | \(0.565802\pi\) | |||||||
\(230\) | 4.81399 | + | 2.02666i | 0.317425 | + | 0.133634i | ||||
\(231\) | −9.51641 | + | 12.3109i | −0.626134 | + | 0.809995i | ||||
\(232\) | 13.9316 | − | 6.15710i | 0.914656 | − | 0.404233i | ||||
\(233\) | 20.5496i | 1.34625i | 0.739529 | + | 0.673125i | \(0.235048\pi\) | ||||
−0.739529 | + | 0.673125i | \(0.764952\pi\) | |||||||
\(234\) | −8.80618 | − | 1.27520i | −0.575678 | − | 0.0833623i | ||||
\(235\) | 13.1597i | 0.858442i | ||||||||
\(236\) | 10.0710 | − | 9.84105i | 0.655566 | − | 0.640598i | ||||
\(237\) | −12.3434 | − | 9.54159i | −0.801792 | − | 0.619793i | ||||
\(238\) | 5.62614 | − | 13.3639i | 0.364688 | − | 0.866255i | ||||
\(239\) | 3.72056 | 0.240663 | 0.120331 | − | 0.992734i | \(-0.461604\pi\) | ||||
0.120331 | + | 0.992734i | \(0.461604\pi\) | |||||||
\(240\) | 8.56678 | − | 10.5687i | 0.552983 | − | 0.682205i | ||||
\(241\) | −12.8782 | −0.829556 | −0.414778 | − | 0.909923i | \(-0.636141\pi\) | ||||
−0.414778 | + | 0.909923i | \(0.636141\pi\) | |||||||
\(242\) | −10.0684 | − | 4.23873i | −0.647220 | − | 0.272476i | ||||
\(243\) | −15.4164 | − | 2.31001i | −0.988959 | − | 0.148187i | ||||
\(244\) | 16.4703 | + | 16.8551i | 1.05440 | + | 1.07904i | ||||
\(245\) | −5.28190 | −0.337448 | ||||||||
\(246\) | −6.40431 | − | 11.3358i | −0.408324 | − | 0.722745i | ||||
\(247\) | 14.1097 | 0.897776 | ||||||||
\(248\) | 8.44190 | + | 21.4227i | 0.536061 | + | 1.36034i | ||||
\(249\) | −14.1587 | + | 18.3163i | −0.897270 | + | 1.16075i | ||||
\(250\) | −15.7255 | − | 6.62033i | −0.994565 | − | 0.418706i | ||||
\(251\) | −6.14205 | −0.387683 | −0.193842 | − | 0.981033i | \(-0.562095\pi\) | ||||
−0.193842 | + | 0.981033i | \(0.562095\pi\) | |||||||
\(252\) | 10.6695 | + | 6.42873i | 0.672115 | + | 0.404972i | ||||
\(253\) | −8.13882 | −0.511683 | ||||||||
\(254\) | 10.2955 | + | 4.33435i | 0.645998 | + | 0.271961i | ||||
\(255\) | 13.2894 | + | 10.2728i | 0.832213 | + | 0.643309i | ||||
\(256\) | −15.9829 | − | 0.738776i | −0.998933 | − | 0.0461735i | ||||
\(257\) | 0.622954i | 0.0388588i | 0.999811 | + | 0.0194294i | \(0.00618496\pi\) | ||||
−0.999811 | + | 0.0194294i | \(0.993815\pi\) | |||||||
\(258\) | −10.7959 | + | 6.09927i | −0.672123 | + | 0.379724i | ||||
\(259\) | 19.8515i | 1.23351i | ||||||||
\(260\) | −5.89111 | + | 5.75660i | −0.365351 | + | 0.357009i | ||||
\(261\) | −15.4556 | + | 4.70366i | −0.956678 | + | 0.291149i | ||||
\(262\) | 0.990669 | + | 0.417066i | 0.0612037 | + | 0.0257664i | ||||
\(263\) | − | 1.27900i | − | 0.0788667i | −0.999222 | − | 0.0394333i | \(-0.987445\pi\) | ||
0.999222 | − | 0.0394333i | \(-0.0125553\pi\) | |||||||
\(264\) | −5.91315 | + | 20.3574i | −0.363929 | + | 1.25291i | ||||
\(265\) | 26.9232 | 1.65388 | ||||||||
\(266\) | −18.2050 | − | 7.66418i | −1.11622 | − | 0.469921i | ||||
\(267\) | −6.90863 | − | 5.34044i | −0.422801 | − | 0.326829i | ||||
\(268\) | −2.40710 | − | 2.46334i | −0.147037 | − | 0.150473i | ||||
\(269\) | − | 27.0208i | − | 1.64749i | −0.566960 | − | 0.823745i | \(-0.691881\pi\) | ||
0.566960 | − | 0.823745i | \(-0.308119\pi\) | |||||||
\(270\) | −10.3702 | + | 10.0340i | −0.631110 | + | 0.610650i | ||||
\(271\) | −5.00662 | −0.304131 | −0.152065 | − | 0.988370i | \(-0.548592\pi\) | ||||
−0.152065 | + | 0.988370i | \(0.548592\pi\) | |||||||
\(272\) | 0.456186 | − | 19.7491i | 0.0276603 | − | 1.19747i | ||||
\(273\) | −5.96677 | − | 4.61237i | −0.361125 | − | 0.279154i | ||||
\(274\) | −11.8744 | − | 4.99905i | −0.717359 | − | 0.302004i | ||||
\(275\) | 4.95044 | 0.298523 | ||||||||
\(276\) | 0.752710 | + | 6.47185i | 0.0453078 | + | 0.389559i | ||||
\(277\) | 12.9186i | 0.776200i | 0.921617 | + | 0.388100i | \(0.126869\pi\) | ||||
−0.921617 | + | 0.388100i | \(0.873131\pi\) | |||||||
\(278\) | 7.33736 | + | 3.08899i | 0.440066 | + | 0.185265i | ||||
\(279\) | −6.15263 | − | 23.6351i | −0.368348 | − | 1.41500i | ||||
\(280\) | 10.7279 | − | 4.22747i | 0.641115 | − | 0.252640i | ||||
\(281\) | − | 4.75037i | − | 0.283383i | −0.989911 | − | 0.141692i | \(-0.954746\pi\) | ||
0.989911 | − | 0.141692i | \(-0.0452542\pi\) | |||||||
\(282\) | −14.2923 | + | 8.07459i | −0.851092 | + | 0.480835i | ||||
\(283\) | −1.05572 | −0.0627559 | −0.0313779 | − | 0.999508i | \(-0.509990\pi\) | ||||
−0.0313779 | + | 0.999508i | \(0.509990\pi\) | |||||||
\(284\) | 3.66602 | + | 3.75168i | 0.217538 | + | 0.222621i | ||||
\(285\) | 13.9941 | − | 18.1034i | 0.828939 | − | 1.07235i | ||||
\(286\) | 4.97993 | − | 11.8290i | 0.294469 | − | 0.699462i | ||||
\(287\) | − | 11.0351i | − | 0.651383i | ||||||
\(288\) | 16.7347 | + | 2.81930i | 0.986104 | + | 0.166129i | ||||
\(289\) | 7.38972 | 0.434690 | ||||||||
\(290\) | −5.23613 | + | 14.0082i | −0.307476 | + | 0.822589i | ||||
\(291\) | −9.54561 | + | 12.3486i | −0.559573 | + | 0.723889i | ||||
\(292\) | 12.9972 | − | 12.7005i | 0.760605 | − | 0.743238i | ||||
\(293\) | 19.2849i | 1.12664i | 0.826240 | + | 0.563319i | \(0.190476\pi\) | ||||
−0.826240 | + | 0.563319i | \(0.809524\pi\) | |||||||
\(294\) | −3.24090 | − | 5.73649i | −0.189013 | − | 0.334559i | ||||
\(295\) | 13.8250i | 0.804925i | ||||||||
\(296\) | 9.91544 | + | 25.1621i | 0.576323 | + | 1.46252i | ||||
\(297\) | 8.82635 | − | 20.6799i | 0.512157 | − | 1.19997i | ||||
\(298\) | −5.90120 | − | 2.48437i | −0.341847 | − | 0.143916i | ||||
\(299\) | − | 3.94469i | − | 0.228127i | ||||||
\(300\) | −0.457836 | − | 3.93650i | −0.0264332 | − | 0.227274i | ||||
\(301\) | −10.5095 | −0.605759 | ||||||||
\(302\) | −10.3021 | + | 24.4710i | −0.592821 | + | 1.40815i | ||||
\(303\) | −14.1421 | + | 18.2948i | −0.812442 | + | 1.05101i | ||||
\(304\) | −26.9031 | − | 0.621437i | −1.54300 | − | 0.0356419i | ||||
\(305\) | −23.1380 | −1.32488 | ||||||||
\(306\) | −3.00278 | + | 20.7364i | −0.171657 | + | 1.18542i | ||||
\(307\) | − | 21.8596i | − | 1.24759i | −0.781588 | − | 0.623795i | \(-0.785590\pi\) | ||
0.781588 | − | 0.623795i | \(-0.214410\pi\) | |||||||
\(308\) | −12.8507 | + | 12.5573i | −0.732236 | + | 0.715518i | ||||
\(309\) | 3.91015 | − | 5.05834i | 0.222441 | − | 0.287759i | ||||
\(310\) | −20.8365 | − | 8.77204i | −1.18343 | − | 0.498218i | ||||
\(311\) | − | 6.18026i | − | 0.350450i | −0.984528 | − | 0.175225i | \(-0.943935\pi\) | ||
0.984528 | − | 0.175225i | \(-0.0560653\pi\) | |||||||
\(312\) | −9.86675 | − | 2.86596i | −0.558595 | − | 0.162253i | ||||
\(313\) | −6.80564 | −0.384677 | −0.192339 | − | 0.981329i | \(-0.561607\pi\) | ||||
−0.192339 | + | 0.981329i | \(0.561607\pi\) | |||||||
\(314\) | −8.13259 | − | 3.42377i | −0.458948 | − | 0.193215i | ||||
\(315\) | −11.8358 | + | 3.08107i | −0.666872 | + | 0.173598i | ||||
\(316\) | −12.5905 | − | 12.8847i | −0.708271 | − | 0.724821i | ||||
\(317\) | 15.0701i | 0.846421i | 0.906031 | + | 0.423211i | \(0.139097\pi\) | ||||
−0.906031 | + | 0.423211i | \(0.860903\pi\) | |||||||
\(318\) | 16.5197 | + | 29.2403i | 0.926378 | + | 1.63972i | ||||
\(319\) | −0.949616 | − | 23.2833i | −0.0531683 | − | 1.30361i | ||||
\(320\) | 11.4862 | − | 10.7168i | 0.642099 | − | 0.599085i | ||||
\(321\) | −3.44949 | + | 4.46241i | −0.192532 | + | 0.249067i | ||||
\(322\) | −2.14270 | + | 5.08963i | −0.119408 | + | 0.283634i | ||||
\(323\) | − | 33.2248i | − | 1.84868i | ||||||
\(324\) | −17.2606 | − | 5.10599i | −0.958923 | − | 0.283666i | ||||
\(325\) | 2.39936i | 0.133092i | ||||||||
\(326\) | −9.60183 | + | 22.8075i | −0.531796 | + | 1.26319i | ||||
\(327\) | −9.60661 | + | 12.4275i | −0.531247 | + | 0.687244i | ||||
\(328\) | −5.51183 | − | 13.9872i | −0.304340 | − | 0.772313i | ||||
\(329\) | −13.9132 | −0.767057 | ||||||||
\(330\) | −10.2380 | − | 18.1216i | −0.563584 | − | 0.997561i | ||||
\(331\) | 3.20058i | 0.175920i | 0.996124 | + | 0.0879598i | \(0.0280347\pi\) | ||||
−0.996124 | + | 0.0879598i | \(0.971965\pi\) | |||||||
\(332\) | −19.1195 | + | 18.6829i | −1.04932 | + | 1.02536i | ||||
\(333\) | −7.22658 | − | 27.7606i | −0.396014 | − | 1.52127i | ||||
\(334\) | 21.6273 | + | 9.10495i | 1.18339 | + | 0.498201i | ||||
\(335\) | 3.38157 | 0.184755 | ||||||||
\(336\) | 11.1738 | + | 9.05730i | 0.609581 | + | 0.494116i | ||||
\(337\) | 2.17304i | 0.118373i | 0.998247 | + | 0.0591864i | \(0.0188506\pi\) | ||||
−0.998247 | + | 0.0591864i | \(0.981149\pi\) | |||||||
\(338\) | −11.2112 | − | 4.71985i | −0.609809 | − | 0.256726i | ||||
\(339\) | 28.6158 | + | 22.1203i | 1.55420 | + | 1.20141i | ||||
\(340\) | 13.5554 | + | 13.8721i | 0.735144 | + | 0.752321i | ||||
\(341\) | 35.2274 | 1.90767 | ||||||||
\(342\) | 28.2481 | + | 4.09052i | 1.52748 | + | 0.221190i | ||||
\(343\) | − | 20.1170i | − | 1.08622i | ||||||
\(344\) | −13.3210 | + | 5.24930i | −0.718218 | + | 0.283023i | ||||
\(345\) | −5.06123 | − | 3.91238i | −0.272487 | − | 0.210636i | ||||
\(346\) | 2.46894 | + | 1.03941i | 0.132731 | + | 0.0558790i | ||||
\(347\) | 10.4049i | 0.558567i | 0.960209 | + | 0.279283i | \(0.0900969\pi\) | ||||
−0.960209 | + | 0.279283i | \(0.909903\pi\) | |||||||
\(348\) | −18.4266 | + | 2.90845i | −0.987771 | + | 0.155909i | ||||
\(349\) | 28.9456i | 1.54942i | 0.632316 | + | 0.774711i | \(0.282105\pi\) | ||||
−0.632316 | + | 0.774711i | \(0.717895\pi\) | |||||||
\(350\) | 1.30330 | − | 3.09577i | 0.0696643 | − | 0.165476i | ||||
\(351\) | 10.0231 | + | 4.27791i | 0.534992 | + | 0.228338i | ||||
\(352\) | −10.0163 | + | 22.3352i | −0.533871 | + | 1.19047i | ||||
\(353\) | 9.11546i | 0.485167i | 0.970131 | + | 0.242584i | \(0.0779949\pi\) | ||||
−0.970131 | + | 0.242584i | \(0.922005\pi\) | |||||||
\(354\) | −15.0149 | + | 8.48286i | −0.798034 | + | 0.450859i | ||||
\(355\) | −5.15015 | −0.273342 | ||||||||
\(356\) | −7.04692 | − | 7.21157i | −0.373486 | − | 0.382213i | ||||
\(357\) | −10.8610 | + | 14.0503i | −0.574826 | + | 0.743620i | ||||
\(358\) | −1.32236 | + | 3.14104i | −0.0698888 | + | 0.166009i | ||||
\(359\) | 12.2766i | 0.647932i | 0.946069 | + | 0.323966i | \(0.105016\pi\) | ||||
−0.946069 | + | 0.323966i | \(0.894984\pi\) | |||||||
\(360\) | −13.4631 | + | 9.81704i | −0.709568 | + | 0.517404i | ||||
\(361\) | −26.2603 | −1.38212 | ||||||||
\(362\) | 12.7561 | − | 30.2999i | 0.670445 | − | 1.59253i | ||||
\(363\) | 10.5855 | + | 8.18268i | 0.555594 | + | 0.429479i | ||||
\(364\) | −6.08621 | − | 6.22842i | −0.319004 | − | 0.326458i | ||||
\(365\) | 17.8421i | 0.933896i | ||||||||
\(366\) | −14.1972 | − | 25.1294i | −0.742099 | − | 1.31354i | ||||
\(367\) | 8.04220 | 0.419799 | 0.209900 | − | 0.977723i | \(-0.432686\pi\) | ||||
0.209900 | + | 0.977723i | \(0.432686\pi\) | |||||||
\(368\) | −0.173738 | + | 7.52141i | −0.00905670 | + | 0.392081i | ||||
\(369\) | 4.01713 | + | 15.4317i | 0.209124 | + | 0.803341i | ||||
\(370\) | −24.4735 | − | 10.3032i | −1.27232 | − | 0.535638i | ||||
\(371\) | 28.4647i | 1.47781i | ||||||||
\(372\) | −3.25797 | − | 28.0122i | −0.168918 | − | 1.45237i | ||||
\(373\) | − | 4.77531i | − | 0.247256i | −0.992329 | − | 0.123628i | \(-0.960547\pi\) | ||
0.992329 | − | 0.123628i | \(-0.0394530\pi\) | |||||||
\(374\) | −27.8543 | − | 11.7265i | −1.44031 | − | 0.606364i | ||||
\(375\) | 16.5331 | + | 12.7803i | 0.853766 | + | 0.659969i | ||||
\(376\) | −17.6351 | + | 6.94935i | −0.909462 | + | 0.358385i | ||||
\(377\) | 11.2848 | − | 0.460255i | 0.581199 | − | 0.0237044i | ||||
\(378\) | −10.6085 | − | 10.9640i | −0.545644 | − | 0.563926i | ||||
\(379\) | − | 17.8655i | − | 0.917688i | −0.888517 | − | 0.458844i | \(-0.848264\pi\) | ||
0.888517 | − | 0.458844i | \(-0.151736\pi\) | |||||||
\(380\) | 18.8972 | − | 18.4658i | 0.969407 | − | 0.947274i | ||||
\(381\) | −10.8243 | − | 8.36727i | −0.554544 | − | 0.428668i | ||||
\(382\) | −0.552670 | + | 1.31277i | −0.0282771 | + | 0.0671673i | ||||
\(383\) | −16.1041 | −0.822880 | −0.411440 | − | 0.911437i | \(-0.634974\pi\) | ||||
−0.411440 | + | 0.911437i | \(0.634974\pi\) | |||||||
\(384\) | 18.6869 | + | 5.89915i | 0.953612 | + | 0.301040i | ||||
\(385\) | − | 17.6409i | − | 0.899064i | ||||||
\(386\) | −3.98417 | + | 9.46372i | −0.202789 | + | 0.481691i | ||||
\(387\) | 14.6967 | − | 3.82580i | 0.747074 | − | 0.194476i | ||||
\(388\) | −12.8901 | + | 12.5958i | −0.654397 | + | 0.639455i | ||||
\(389\) | − | 13.5780i | − | 0.688432i | −0.938891 | − | 0.344216i | \(-0.888145\pi\) | ||
0.938891 | − | 0.344216i | \(-0.111855\pi\) | |||||||
\(390\) | 8.78309 | − | 4.96212i | 0.444749 | − | 0.251267i | ||||
\(391\) | −9.28878 | −0.469754 | ||||||||
\(392\) | −2.78926 | − | 7.07821i | −0.140879 | − | 0.357504i | ||||
\(393\) | −1.04155 | − | 0.805127i | −0.0525392 | − | 0.0406133i | ||||
\(394\) | −11.1154 | − | 4.67953i | −0.559987 | − | 0.235751i | ||||
\(395\) | 17.6876 | 0.889959 | ||||||||
\(396\) | 13.3993 | − | 22.2383i | 0.673342 | − | 1.11752i | ||||
\(397\) | 12.2193i | 0.613271i | 0.951827 | + | 0.306635i | \(0.0992032\pi\) | ||||
−0.951827 | + | 0.306635i | \(0.900797\pi\) | |||||||
\(398\) | −1.10541 | + | 2.62572i | −0.0554093 | + | 0.131615i | ||||
\(399\) | 19.1399 | + | 14.7954i | 0.958196 | + | 0.740695i | ||||
\(400\) | 0.105676 | − | 4.57490i | 0.00528380 | − | 0.228745i | ||||
\(401\) | 18.9027i | 0.943958i | 0.881610 | + | 0.471979i | \(0.156460\pi\) | ||||
−0.881610 | + | 0.471979i | \(0.843540\pi\) | |||||||
\(402\) | 2.07489 | + | 3.67261i | 0.103486 | + | 0.183173i | ||||
\(403\) | 17.0739i | 0.850510i | ||||||||
\(404\) | −19.0971 | + | 18.6610i | −0.950115 | + | 0.928421i | ||||
\(405\) | 15.4298 | − | 8.61721i | 0.766711 | − | 0.428193i | ||||
\(406\) | −14.8103 | − | 5.53594i | −0.735021 | − | 0.274744i | ||||
\(407\) | 41.3764 | 2.05095 | ||||||||
\(408\) | −6.74864 | + | 23.2338i | −0.334107 | + | 1.15024i | ||||
\(409\) | − | 10.2779i | − | 0.508210i | −0.967177 | − | 0.254105i | \(-0.918219\pi\) | ||
0.967177 | − | 0.254105i | \(-0.0817809\pi\) | |||||||
\(410\) | 13.6044 | + | 5.72738i | 0.671874 | + | 0.282855i | ||||
\(411\) | 12.4843 | + | 9.65045i | 0.615803 | + | 0.476022i | ||||
\(412\) | 5.28016 | − | 5.15960i | 0.260135 | − | 0.254195i | ||||
\(413\) | −14.6166 | −0.719238 | ||||||||
\(414\) | 1.14360 | − | 7.89742i | 0.0562050 | − | 0.388137i | ||||
\(415\) | − | 26.2465i | − | 1.28839i | ||||||
\(416\) | −10.8253 | − | 4.85466i | −0.530755 | − | 0.238019i | ||||
\(417\) | −7.71420 | − | 5.96315i | −0.377766 | − | 0.292017i | ||||
\(418\) | −15.9744 | + | 37.9445i | −0.781333 | + | 1.85592i | ||||
\(419\) | − | 31.6772i | − | 1.54753i | −0.633472 | − | 0.773765i | \(-0.718371\pi\) | ||
0.633472 | − | 0.773765i | \(-0.281629\pi\) | |||||||
\(420\) | −14.0277 | + | 1.63150i | −0.684483 | + | 0.0796091i | ||||
\(421\) | 7.12287 | 0.347147 | 0.173574 | − | 0.984821i | \(-0.444469\pi\) | ||||
0.173574 | + | 0.984821i | \(0.444469\pi\) | |||||||
\(422\) | 11.3395 | − | 26.9351i | 0.551998 | − | 1.31118i | ||||
\(423\) | 19.4563 | − | 5.06482i | 0.946000 | − | 0.246260i | ||||
\(424\) | 14.2176 | + | 36.0794i | 0.690466 | + | 1.75217i | ||||
\(425\) | 5.64990 | 0.274060 | ||||||||
\(426\) | −3.16006 | − | 5.59340i | −0.153106 | − | 0.271001i | ||||
\(427\) | − | 24.4629i | − | 1.18384i | ||||||
\(428\) | −4.65809 | + | 4.55174i | −0.225157 | + | 0.220016i | ||||
\(429\) | −9.61353 | + | 12.4365i | −0.464146 | + | 0.600440i | ||||
\(430\) | 5.45458 | − | 12.9564i | 0.263043 | − | 0.624815i | ||||
\(431\) | −5.38353 | −0.259315 | −0.129658 | − | 0.991559i | \(-0.541388\pi\) | ||||
−0.129658 | + | 0.991559i | \(0.541388\pi\) | |||||||
\(432\) | −18.9227 | − | 8.59823i | −0.910421 | − | 0.413683i | ||||
\(433\) | 34.8684i | 1.67567i | 0.545926 | + | 0.837834i | \(0.316178\pi\) | ||||
−0.545926 | + | 0.837834i | \(0.683822\pi\) | |||||||
\(434\) | 9.27431 | − | 22.0295i | 0.445181 | − | 1.05745i | ||||
\(435\) | 10.6019 | − | 14.9355i | 0.508322 | − | 0.716103i | ||||
\(436\) | −12.9725 | + | 12.6763i | −0.621270 | + | 0.607084i | ||||
\(437\) | 12.6536i | 0.605304i | ||||||||
\(438\) | −19.3777 | + | 10.9476i | −0.925900 | + | 0.523099i | ||||
\(439\) | 10.9877i | 0.524413i | 0.965012 | + | 0.262207i | \(0.0844502\pi\) | ||||
−0.965012 | + | 0.262207i | \(0.915550\pi\) | |||||||
\(440\) | −8.81128 | − | 22.3601i | −0.420061 | − | 1.06598i | ||||
\(441\) | 2.03287 | + | 7.80920i | 0.0968033 | + | 0.371867i | ||||
\(442\) | 5.68356 | − | 13.5003i | 0.270339 | − | 0.642145i | ||||
\(443\) | −24.7425 | −1.17555 | −0.587776 | − | 0.809024i | \(-0.699996\pi\) | ||||
−0.587776 | + | 0.809024i | \(0.699996\pi\) | |||||||
\(444\) | −3.82665 | − | 32.9018i | −0.181605 | − | 1.56145i | ||||
\(445\) | 9.89975 | 0.469293 | ||||||||
\(446\) | 0.845395 | − | 2.00809i | 0.0400306 | − | 0.0950860i | ||||
\(447\) | 6.20428 | + | 4.79597i | 0.293452 | + | 0.226842i | ||||
\(448\) | 11.3304 | + | 12.1439i | 0.535310 | + | 0.573745i | ||||
\(449\) | −16.6966 | −0.787962 | −0.393981 | − | 0.919118i | \(-0.628902\pi\) | ||||
−0.393981 | + | 0.919118i | \(0.628902\pi\) | |||||||
\(450\) | −0.695597 | + | 4.80361i | −0.0327907 | + | 0.226444i | ||||
\(451\) | −23.0004 | −1.08305 | ||||||||
\(452\) | 29.1886 | + | 29.8707i | 1.37292 | + | 1.40500i | ||||
\(453\) | 19.8878 | − | 25.7278i | 0.934411 | − | 1.20880i | ||||
\(454\) | −4.72238 | + | 11.2172i | −0.221632 | + | 0.526450i | ||||
\(455\) | 8.55012 | 0.400836 | ||||||||
\(456\) | 31.6501 | + | 9.19330i | 1.48215 | + | 0.430516i | ||||
\(457\) | 24.6038 | 1.15092 | 0.575459 | − | 0.817831i | \(-0.304823\pi\) | ||||
0.575459 | + | 0.817831i | \(0.304823\pi\) | |||||||
\(458\) | 8.09694 | + | 3.40877i | 0.378345 | + | 0.159281i | ||||
\(459\) | 10.0734 | − | 23.6019i | 0.470188 | − | 1.10164i | ||||
\(460\) | −5.16254 | − | 5.28317i | −0.240705 | − | 0.246329i | ||||
\(461\) | − | 37.8537i | − | 1.76302i | −0.472161 | − | 0.881512i | \(-0.656526\pi\) | ||
0.472161 | − | 0.881512i | \(-0.343474\pi\) | |||||||
\(462\) | 19.1592 | − | 10.8242i | 0.891366 | − | 0.503588i | ||||
\(463\) | 24.3762i | 1.13286i | 0.824110 | + | 0.566429i | \(0.191676\pi\) | ||||
−0.824110 | + | 0.566429i | \(0.808324\pi\) | |||||||
\(464\) | −21.5373 | + | 0.380555i | −0.999844 | + | 0.0176668i | ||||
\(465\) | 21.9066 | + | 16.9340i | 1.01590 | + | 0.785297i | ||||
\(466\) | 11.2762 | − | 26.7847i | 0.522360 | − | 1.24078i | ||||
\(467\) | −30.1355 | −1.39450 | −0.697252 | − | 0.716826i | \(-0.745594\pi\) | ||||
−0.697252 | + | 0.716826i | \(0.745594\pi\) | |||||||
\(468\) | 10.7784 | + | 6.49433i | 0.498231 | + | 0.300201i | ||||
\(469\) | 3.57520i | 0.165087i | ||||||||
\(470\) | 7.22111 | − | 17.1525i | 0.333085 | − | 0.791187i | ||||
\(471\) | 8.55027 | + | 6.60944i | 0.393976 | + | 0.304547i | ||||
\(472\) | −18.5268 | + | 7.30072i | −0.852764 | + | 0.336043i | ||||
\(473\) | 21.9049i | 1.00719i | ||||||||
\(474\) | 10.8529 | + | 19.2099i | 0.498488 | + | 0.882339i | ||||
\(475\) | − | 7.69655i | − | 0.353142i | ||||||
\(476\) | −14.6664 | + | 14.3315i | −0.672234 | + | 0.656885i | ||||
\(477\) | −10.3621 | − | 39.8055i | −0.474446 | − | 1.82257i | ||||
\(478\) | −4.84944 | − | 2.04158i | −0.221808 | − | 0.0933799i | ||||
\(479\) | 11.4675i | 0.523962i | 0.965073 | + | 0.261981i | \(0.0843757\pi\) | ||||
−0.965073 | + | 0.261981i | \(0.915624\pi\) | |||||||
\(480\) | −16.9654 | + | 9.07452i | −0.774363 | + | 0.414193i | ||||
\(481\) | 20.0541i | 0.914389i | ||||||||
\(482\) | 16.7856 | + | 7.06665i | 0.764564 | + | 0.321877i | ||||
\(483\) | 4.13640 | − | 5.35103i | 0.188213 | − | 0.243480i | ||||
\(484\) | 10.7974 | + | 11.0497i | 0.490790 | + | 0.502257i | ||||
\(485\) | − | 17.6950i | − | 0.803490i | ||||||
\(486\) | 18.8264 | + | 11.4703i | 0.853981 | + | 0.520305i | ||||
\(487\) | 2.01108i | 0.0911307i | 0.998961 | + | 0.0455653i | \(0.0145089\pi\) | ||||
−0.998961 | + | 0.0455653i | \(0.985491\pi\) | |||||||
\(488\) | −12.2187 | − | 31.0070i | −0.553115 | − | 1.40362i | ||||
\(489\) | 18.5359 | − | 23.9789i | 0.838223 | − | 1.08436i | ||||
\(490\) | 6.88451 | + | 2.89834i | 0.311011 | + | 0.130934i | ||||
\(491\) | 9.94480 | 0.448802 | 0.224401 | − | 0.974497i | \(-0.427957\pi\) | ||||
0.224401 | + | 0.974497i | \(0.427957\pi\) | |||||||
\(492\) | 2.12717 | + | 18.2895i | 0.0959003 | + | 0.824556i | ||||
\(493\) | −1.08379 | − | 26.5731i | −0.0488114 | − | 1.19679i | ||||
\(494\) | −18.3908 | − | 7.74240i | −0.827439 | − | 0.348347i | ||||
\(495\) | 6.42184 | + | 24.6693i | 0.288640 | + | 1.10880i | ||||
\(496\) | 0.751992 | − | 32.5551i | 0.0337654 | − | 1.46177i | ||||
\(497\) | − | 5.44504i | − | 0.244243i | ||||||
\(498\) | 28.5054 | − | 16.1045i | 1.27736 | − | 0.721659i | ||||
\(499\) | 4.16291 | 0.186358 | 0.0931788 | − | 0.995649i | \(-0.470297\pi\) | ||||
0.0931788 | + | 0.995649i | \(0.470297\pi\) | |||||||
\(500\) | 16.8640 | + | 17.2581i | 0.754183 | + | 0.771805i | ||||
\(501\) | −22.7380 | − | 17.5767i | −1.01586 | − | 0.785270i | ||||
\(502\) | 8.00565 | + | 3.37033i | 0.357310 | + | 0.150425i | ||||
\(503\) | 9.71293i | 0.433078i | 0.976274 | + | 0.216539i | \(0.0694769\pi\) | ||||
−0.976274 | + | 0.216539i | \(0.930523\pi\) | |||||||
\(504\) | −10.3791 | − | 14.2340i | −0.462324 | − | 0.634032i | ||||
\(505\) | − | 26.2157i | − | 1.16658i | ||||||
\(506\) | 10.6083 | + | 4.46602i | 0.471595 | + | 0.198539i | ||||
\(507\) | 11.7870 | + | 9.11146i | 0.523479 | + | 0.404654i | ||||
\(508\) | −11.0409 | − | 11.2989i | −0.489863 | − | 0.501309i | ||||
\(509\) | −39.9855 | −1.77233 | −0.886163 | − | 0.463374i | \(-0.846639\pi\) | ||||
−0.886163 | + | 0.463374i | \(0.846639\pi\) | |||||||
\(510\) | −11.6846 | − | 20.6820i | −0.517402 | − | 0.915816i | ||||
\(511\) | −18.8636 | −0.834479 | ||||||||
\(512\) | 20.4270 | + | 9.73326i | 0.902756 | + | 0.430153i | ||||
\(513\) | −32.1515 | − | 13.7225i | −1.41953 | − | 0.605863i | ||||
\(514\) | 0.341834 | − | 0.811968i | 0.0150776 | − | 0.0358144i | ||||
\(515\) | 7.24838i | 0.319402i | ||||||||
\(516\) | 17.4184 | − | 2.02585i | 0.766803 | − | 0.0891833i | ||||
\(517\) | 28.9991i | 1.27538i | ||||||||
\(518\) | 10.8931 | − | 25.8748i | 0.478617 | − | 1.13687i | ||||
\(519\) | −2.59574 | − | 2.00653i | −0.113940 | − | 0.0880771i | ||||
\(520\) | 10.8374 | − | 4.27061i | 0.475251 | − | 0.187279i | ||||
\(521\) | − | 16.7131i | − | 0.732212i | −0.930573 | − | 0.366106i | \(-0.880691\pi\) | ||
0.930573 | − | 0.366106i | \(-0.119309\pi\) | |||||||
\(522\) | 22.7261 | + | 2.35014i | 0.994696 | + | 0.102863i | ||||
\(523\) | −21.9455 | −0.959612 | −0.479806 | − | 0.877375i | \(-0.659293\pi\) | ||||
−0.479806 | + | 0.877375i | \(0.659293\pi\) | |||||||
\(524\) | −1.06240 | − | 1.08722i | −0.0464111 | − | 0.0474955i | ||||
\(525\) | −2.51596 | + | 3.25476i | −0.109806 | + | 0.142049i | ||||
\(526\) | −0.701828 | + | 1.66707i | −0.0306012 | + | 0.0726878i | ||||
\(527\) | 40.2048 | 1.75135 | ||||||||
\(528\) | 18.8781 | − | 23.2895i | 0.821562 | − | 1.01354i | ||||
\(529\) | −19.4624 | −0.846191 | ||||||||
\(530\) | −35.0921 | − | 14.7736i | −1.52430 | − | 0.641723i | ||||
\(531\) | 20.4401 | − | 5.32091i | 0.887025 | − | 0.230908i | ||||
\(532\) | 19.5231 | + | 19.9792i | 0.846433 | + | 0.866210i | ||||
\(533\) | − | 11.1477i | − | 0.482863i | ||||||
\(534\) | 6.07435 | + | 10.7518i | 0.262863 | + | 0.465275i | ||||
\(535\) | − | 6.39443i | − | 0.276456i | ||||||
\(536\) | 1.78574 | + | 4.53161i | 0.0771322 | + | 0.195736i | ||||
\(537\) | 2.55275 | − | 3.30236i | 0.110160 | − | 0.142507i | ||||
\(538\) | −14.8272 | + | 35.2194i | −0.639245 | + | 1.51842i | ||||
\(539\) | −11.6394 | −0.501343 | ||||||||
\(540\) | 19.0227 | − | 7.38805i | 0.818605 | − | 0.317931i | ||||
\(541\) | −3.70442 | −0.159265 | −0.0796327 | − | 0.996824i | \(-0.525375\pi\) | ||||
−0.0796327 | + | 0.996824i | \(0.525375\pi\) | |||||||
\(542\) | 6.52572 | + | 2.74729i | 0.280304 | + | 0.118006i | ||||
\(543\) | −24.6251 | + | 31.8561i | −1.05676 | + | 1.36707i | ||||
\(544\) | −11.4315 | + | 25.4910i | −0.490124 | + | 1.09292i | ||||
\(545\) | − | 17.8081i | − | 0.762815i | ||||||
\(546\) | 5.24624 | + | 9.28599i | 0.224518 | + | 0.397404i | ||||
\(547\) | 26.5790 | 1.13644 | 0.568219 | − | 0.822878i | \(-0.307633\pi\) | ||||
0.568219 | + | 0.822878i | \(0.307633\pi\) | |||||||
\(548\) | 12.7342 | + | 13.0317i | 0.543976 | + | 0.556686i | ||||
\(549\) | 8.90525 | + | 34.2092i | 0.380067 | + | 1.46001i | ||||
\(550\) | −6.45249 | − | 2.71646i | −0.275135 | − | 0.115830i | ||||
\(551\) | −36.1990 | + | 1.47639i | −1.54213 | + | 0.0628962i | ||||
\(552\) | 2.57021 | − | 8.84854i | 0.109395 | − | 0.376619i | ||||
\(553\) | 18.7003i | 0.795219i | ||||||||
\(554\) | 7.08881 | − | 16.8383i | 0.301175 | − | 0.715389i | ||||
\(555\) | 25.7304 | + | 19.8899i | 1.09220 | + | 0.844278i | ||||
\(556\) | −7.86861 | − | 8.05247i | −0.333703 | − | 0.341501i | ||||
\(557\) | −39.1813 | −1.66016 | −0.830082 | − | 0.557641i | \(-0.811707\pi\) | ||||
−0.830082 | + | 0.557641i | \(0.811707\pi\) | |||||||
\(558\) | −4.94988 | + | 34.1825i | −0.209545 | + | 1.44706i | ||||
\(559\) | −10.6168 | −0.449042 | ||||||||
\(560\) | −16.3027 | − | 0.376576i | −0.688913 | − | 0.0159133i | ||||
\(561\) | 29.2849 | + | 22.6375i | 1.23641 | + | 0.955757i | ||||
\(562\) | −2.60667 | + | 6.19171i | −0.109956 | + | 0.261182i | ||||
\(563\) | 9.03341 | 0.380713 | 0.190356 | − | 0.981715i | \(-0.439036\pi\) | ||||
0.190356 | + | 0.981715i | \(0.439036\pi\) | |||||||
\(564\) | 23.0596 | − | 2.68195i | 0.970982 | − | 0.112930i | ||||
\(565\) | −41.0052 | −1.72510 | ||||||||
\(566\) | 1.37604 | + | 0.579305i | 0.0578392 | + | 0.0243500i | ||||
\(567\) | 9.11061 | + | 16.3132i | 0.382610 | + | 0.685091i | ||||
\(568\) | −2.71969 | − | 6.90166i | −0.114116 | − | 0.289587i | ||||
\(569\) | −5.48409 | −0.229905 | −0.114952 | − | 0.993371i | \(-0.536672\pi\) | ||||
−0.114952 | + | 0.993371i | \(0.536672\pi\) | |||||||
\(570\) | −28.1740 | + | 15.9173i | −1.18008 | + | 0.666701i | ||||
\(571\) | −43.5754 | −1.82357 | −0.911787 | − | 0.410664i | \(-0.865297\pi\) | ||||
−0.911787 | + | 0.410664i | \(0.865297\pi\) | |||||||
\(572\) | −12.9818 | + | 12.6854i | −0.542798 | + | 0.530405i | ||||
\(573\) | 1.06690 | − | 1.38020i | 0.0445706 | − | 0.0576585i | ||||
\(574\) | −6.05532 | + | 14.3834i | −0.252744 | + | 0.600350i | ||||
\(575\) | −2.15175 | −0.0897343 | ||||||||
\(576\) | −20.2653 | − | 12.8576i | −0.844388 | − | 0.535733i | ||||
\(577\) | − | 36.7415i | − | 1.52957i | −0.644287 | − | 0.764784i | \(-0.722846\pi\) | ||
0.644287 | − | 0.764784i | \(-0.277154\pi\) | |||||||
\(578\) | −9.63189 | − | 4.05497i | −0.400634 | − | 0.168664i | ||||
\(579\) | 7.69127 | − | 9.94976i | 0.319638 | − | 0.413498i | ||||
\(580\) | 14.5116 | − | 15.3853i | 0.602561 | − | 0.638839i | ||||
\(581\) | 27.7493 | 1.15123 | ||||||||
\(582\) | 19.2180 | − | 10.8574i | 0.796611 | − | 0.450055i | ||||
\(583\) | 59.3288 | 2.45715 | ||||||||
\(584\) | −23.9099 | + | 9.42202i | −0.989400 | + | 0.389886i | ||||
\(585\) | −11.9566 | + | 3.11251i | −0.494345 | + | 0.128686i | ||||
\(586\) | 10.5822 | − | 25.1363i | 0.437148 | − | 1.03837i | ||||
\(587\) | − | 31.1727i | − | 1.28664i | −0.765599 | − | 0.643318i | \(-0.777557\pi\) | ||
0.765599 | − | 0.643318i | \(-0.222443\pi\) | |||||||
\(588\) | 1.07645 | + | 9.25542i | 0.0443923 | + | 0.381687i | ||||
\(589\) | − | 54.7688i | − | 2.25671i | ||||||
\(590\) | 7.58623 | − | 18.0198i | 0.312320 | − | 0.741863i | ||||
\(591\) | 11.6863 | + | 9.03362i | 0.480710 | + | 0.371594i | ||||
\(592\) | 0.883252 | − | 38.2376i | 0.0363014 | − | 1.57155i | ||||
\(593\) | 1.04978i | 0.0431095i | 0.999768 | + | 0.0215548i | \(0.00686162\pi\) | ||||
−0.999768 | + | 0.0215548i | \(0.993138\pi\) | |||||||
\(594\) | −22.8521 | + | 22.1113i | −0.937634 | + | 0.907237i | ||||
\(595\) | − | 20.1334i | − | 0.825391i | ||||||
\(596\) | 6.32847 | + | 6.47634i | 0.259224 | + | 0.265281i | ||||
\(597\) | 2.13395 | − | 2.76057i | 0.0873367 | − | 0.112983i | ||||
\(598\) | −2.16457 | + | 5.14157i | −0.0885159 | + | 0.210254i | ||||
\(599\) | 13.3246i | 0.544429i | 0.962237 | + | 0.272215i | \(0.0877561\pi\) | ||||
−0.962237 | + | 0.272215i | \(0.912244\pi\) | |||||||
\(600\) | −1.56333 | + | 5.38213i | −0.0638226 | + | 0.219725i | ||||
\(601\) | − | 0.0187465i | − | 0.000764687i | −1.00000 | 0.000382344i | \(-0.999878\pi\) | |||
1.00000 | 0.000382344i | \(-0.000121704\pi\) | ||||||||
\(602\) | 13.6983 | + | 5.76690i | 0.558301 | + | 0.235041i | ||||
\(603\) | −1.30148 | − | 4.99960i | −0.0530005 | − | 0.203600i | ||||
\(604\) | 26.8559 | − | 26.2428i | 1.09275 | − | 1.06780i | ||||
\(605\) | −15.1685 | −0.616688 | ||||||||
\(606\) | 28.4720 | − | 16.0856i | 1.15659 | − | 0.653432i | ||||
\(607\) | 36.3818 | 1.47669 | 0.738345 | − | 0.674423i | \(-0.235608\pi\) | ||||
0.738345 | + | 0.674423i | \(0.235608\pi\) | |||||||
\(608\) | 34.7250 | + | 15.5726i | 1.40828 | + | 0.631551i | ||||
\(609\) | 15.7907 | + | 11.2089i | 0.639871 | + | 0.454209i | ||||
\(610\) | 30.1585 | + | 12.6966i | 1.22108 | + | 0.514068i | ||||
\(611\) | −14.0551 | −0.568610 | ||||||||
\(612\) | 15.2926 | − | 25.3804i | 0.618166 | − | 1.02594i | ||||
\(613\) | − | 22.5092i | − | 0.909136i | −0.890712 | − | 0.454568i | \(-0.849794\pi\) | ||
0.890712 | − | 0.454568i | \(-0.150206\pi\) | |||||||
\(614\) | −11.9950 | + | 28.4921i | −0.484079 | + | 1.14985i | ||||
\(615\) | −14.3031 | − | 11.0565i | −0.576757 | − | 0.445839i | ||||
\(616\) | 23.6404 | − | 9.31580i | 0.952498 | − | 0.375344i | ||||
\(617\) | 18.8536 | 0.759016 | 0.379508 | − | 0.925188i | \(-0.376093\pi\) | ||||
0.379508 | + | 0.925188i | \(0.376093\pi\) | |||||||
\(618\) | −7.87222 | + | 4.44751i | −0.316667 | + | 0.178905i | ||||
\(619\) | − | 10.7359i | − | 0.431513i | −0.976447 | − | 0.215757i | \(-0.930778\pi\) | ||
0.976447 | − | 0.215757i | \(-0.0692217\pi\) | |||||||
\(620\) | 22.3451 | + | 22.8672i | 0.897402 | + | 0.918371i | ||||
\(621\) | −3.83645 | + | 8.98873i | −0.153951 | + | 0.360705i | ||||
\(622\) | −3.39130 | + | 8.05545i | −0.135979 | + | 0.322994i | ||||
\(623\) | 10.4666i | 0.419335i | ||||||||
\(624\) | 11.2878 | + | 9.14973i | 0.451875 | + | 0.366282i | ||||
\(625\) | −17.9710 | −0.718842 | ||||||||
\(626\) | 8.87058 | + | 3.73446i | 0.354540 | + | 0.149259i | ||||
\(627\) | 30.8379 | − | 39.8932i | 1.23155 | − | 1.59318i | ||||
\(628\) | 8.72142 | + | 8.92520i | 0.348022 | + | 0.356154i | ||||
\(629\) | 47.2226 | 1.88289 | ||||||||
\(630\) | 17.1177 | + | 2.47876i | 0.681984 | + | 0.0987562i | ||||
\(631\) | − | 26.0984i | − | 1.03896i | −0.854483 | − | 0.519480i | \(-0.826126\pi\) | ||
0.854483 | − | 0.519480i | \(-0.173874\pi\) | |||||||
\(632\) | 9.34044 | + | 23.7029i | 0.371543 | + | 0.942851i | ||||
\(633\) | −21.8904 | + | 28.3184i | −0.870066 | + | 1.12556i | ||||
\(634\) | 8.26943 | − | 19.6426i | 0.328421 | − | 0.780108i | ||||
\(635\) | 15.5107 | 0.615523 | ||||||||
\(636\) | −5.48696 | − | 47.1772i | −0.217572 | − | 1.87070i | ||||
\(637\) | − | 5.64132i | − | 0.223517i | ||||||
\(638\) | −11.5385 | + | 30.8689i | −0.456814 | + | 1.22211i | ||||
\(639\) | 1.98216 | + | 7.61441i | 0.0784132 | + | 0.301221i | ||||
\(640\) | −20.8519 | + | 7.66554i | −0.824245 | + | 0.303007i | ||||
\(641\) | −5.91097 | −0.233469 | −0.116735 | − | 0.993163i | \(-0.537243\pi\) | ||||
−0.116735 | + | 0.993163i | \(0.537243\pi\) | |||||||
\(642\) | 6.94478 | − | 3.92354i | 0.274089 | − | 0.154850i | ||||
\(643\) | −41.3587 | −1.63103 | −0.815514 | − | 0.578737i | \(-0.803546\pi\) | ||||
−0.815514 | + | 0.578737i | \(0.803546\pi\) | |||||||
\(644\) | 5.58567 | − | 5.45814i | 0.220106 | − | 0.215081i | ||||
\(645\) | −10.5298 | + | 13.6219i | −0.414612 | + | 0.536360i | ||||
\(646\) | −18.2315 | + | 43.3057i | −0.717307 | + | 1.70384i | ||||
\(647\) | −26.9548 | −1.05970 | −0.529850 | − | 0.848091i | \(-0.677752\pi\) | ||||
−0.529850 | + | 0.848091i | \(0.677752\pi\) | |||||||
\(648\) | 19.6960 | + | 16.1267i | 0.773730 | + | 0.633515i | ||||
\(649\) | 30.4653i | 1.19587i | ||||||||
\(650\) | 1.31660 | − | 3.12736i | 0.0516413 | − | 0.122665i | ||||
\(651\) | −17.9036 | + | 23.1609i | −0.701699 | + | 0.907749i | ||||
\(652\) | 25.0304 | − | 24.4589i | 0.980265 | − | 0.957883i | ||||
\(653\) | − | 37.4648i | − | 1.46611i | −0.680170 | − | 0.733055i | \(-0.738094\pi\) | ||
0.680170 | − | 0.733055i | \(-0.261906\pi\) | |||||||
\(654\) | 19.3408 | − | 10.9268i | 0.756284 | − | 0.427272i | ||||
\(655\) | 1.49249 | 0.0583165 | ||||||||
\(656\) | −0.490985 | + | 21.2556i | −0.0191697 | + | 0.829893i | ||||
\(657\) | 26.3792 | − | 6.86696i | 1.02915 | − | 0.267906i | ||||
\(658\) | 18.1346 | + | 7.63458i | 0.706962 | + | 0.297627i | ||||
\(659\) | 32.6896 | 1.27341 | 0.636703 | − | 0.771109i | \(-0.280298\pi\) | ||||
0.636703 | + | 0.771109i | \(0.280298\pi\) | |||||||
\(660\) | 3.40052 | + | 29.2379i | 0.132365 | + | 1.13808i | ||||
\(661\) | 21.4743i | 0.835255i | 0.908618 | + | 0.417628i | \(0.137138\pi\) | ||||
−0.908618 | + | 0.417628i | \(0.862862\pi\) | |||||||
\(662\) | 1.75626 | − | 4.17169i | 0.0682588 | − | 0.162137i | ||||
\(663\) | −10.9719 | + | 14.1937i | −0.426112 | + | 0.551237i | ||||
\(664\) | 35.1726 | − | 13.8602i | 1.36496 | − | 0.537880i | ||||
\(665\) | −27.4267 | −1.06356 | ||||||||
\(666\) | −5.81388 | + | 40.1491i | −0.225283 | + | 1.55575i | ||||
\(667\) | 0.412759 | + | 10.1203i | 0.0159821 | + | 0.391859i | ||||
\(668\) | −23.1932 | − | 23.7351i | −0.897370 | − | 0.918338i | ||||
\(669\) | −1.63200 | + | 2.11123i | −0.0630967 | + | 0.0816247i | ||||
\(670\) | −4.40760 | − | 1.85557i | −0.170280 | − | 0.0716871i | ||||
\(671\) | −50.9878 | −1.96836 | ||||||||
\(672\) | −9.59411 | − | 17.9368i | −0.370101 | − | 0.691929i | ||||
\(673\) | 46.7441 | 1.80185 | 0.900926 | − | 0.433973i | \(-0.142889\pi\) | ||||
0.900926 | + | 0.433973i | \(0.142889\pi\) | |||||||
\(674\) | 1.19241 | − | 2.83237i | 0.0459300 | − | 0.109099i | ||||
\(675\) | 2.33352 | − | 5.46739i | 0.0898173 | − | 0.210440i | ||||
\(676\) | 12.0229 | + | 12.3039i | 0.462421 | + | 0.473225i | ||||
\(677\) | − | 35.4077i | − | 1.36083i | −0.732828 | − | 0.680414i | \(-0.761800\pi\) | ||
0.732828 | − | 0.680414i | \(-0.238200\pi\) | |||||||
\(678\) | −25.1602 | − | 44.5344i | −0.966274 | − | 1.71033i | ||||
\(679\) | 18.7082 | 0.717955 | ||||||||
\(680\) | −10.0563 | − | 25.5194i | −0.385640 | − | 0.978625i | ||||
\(681\) | 9.11635 | − | 11.7933i | 0.349339 | − | 0.451921i | ||||
\(682\) | −45.9160 | − | 19.3304i | −1.75821 | − | 0.740198i | ||||
\(683\) | 20.1991i | 0.772898i | 0.922311 | + | 0.386449i | \(0.126299\pi\) | ||||
−0.922311 | + | 0.386449i | \(0.873701\pi\) | |||||||
\(684\) | −34.5744 | − | 20.8322i | −1.32199 | − | 0.796541i | ||||
\(685\) | −17.8894 | −0.683518 | ||||||||
\(686\) | −11.0388 | + | 26.2208i | −0.421464 | + | 1.00112i | ||||
\(687\) | −8.51279 | − | 6.58047i | −0.324783 | − | 0.251061i | ||||
\(688\) | 20.2432 | + | 0.467599i | 0.771766 | + | 0.0178271i | ||||
\(689\) | 28.7552i | 1.09549i | ||||||||
\(690\) | 4.45005 | + | 7.87672i | 0.169410 | + | 0.299861i | ||||
\(691\) | −0.237432 | −0.00903233 | −0.00451616 | − | 0.999990i | \(-0.501438\pi\) | ||||
−0.00451616 | + | 0.999990i | \(0.501438\pi\) | |||||||
\(692\) | −2.64770 | − | 2.70957i | −0.100651 | − | 0.103002i | ||||
\(693\) | −26.0818 | + | 6.78954i | −0.990765 | + | 0.257913i | ||||
\(694\) | 5.70951 | − | 13.5620i | 0.216730 | − | 0.514806i | ||||
\(695\) | 11.0541 | 0.419306 | ||||||||
\(696\) | 25.6135 | + | 6.32034i | 0.970879 | + | 0.239572i | ||||
\(697\) | −26.2502 | −0.994298 | ||||||||
\(698\) | 15.8833 | − | 37.7281i | 0.601193 | − | 1.42803i | ||||
\(699\) | −21.7682 | + | 28.1603i | −0.823349 | + | 1.06512i | ||||
\(700\) | −3.39749 | + | 3.31991i | −0.128413 | + | 0.125481i | ||||
\(701\) | −41.5222 | −1.56827 | −0.784136 | − | 0.620589i | \(-0.786893\pi\) | ||||
−0.784136 | + | 0.620589i | \(0.786893\pi\) | |||||||
\(702\) | −10.7168 | − | 11.0759i | −0.404480 | − | 0.418032i | ||||
\(703\) | − | 64.3287i | − | 2.42620i | ||||||
\(704\) | 25.3114 | − | 23.6158i | 0.953961 | − | 0.890054i | ||||
\(705\) | −13.9400 | + | 18.0335i | −0.525012 | + | 0.679179i | ||||
\(706\) | 5.00193 | − | 11.8812i | 0.188250 | − | 0.447156i | ||||
\(707\) | 27.7167 | 1.04239 | ||||||||
\(708\) | 24.2255 | − | 2.81755i | 0.910450 | − | 0.105890i | ||||
\(709\) | 29.4416i | 1.10570i | 0.833280 | + | 0.552852i | \(0.186460\pi\) | ||||
−0.833280 | + | 0.552852i | \(0.813540\pi\) | |||||||
\(710\) | 6.71279 | + | 2.82605i | 0.251926 | + | 0.106060i | ||||
\(711\) | −6.80751 | − | 26.1508i | −0.255301 | − | 0.980732i | ||||
\(712\) | 5.22785 | + | 13.2665i | 0.195922 | + | 0.497185i | ||||
\(713\) | −15.3119 | −0.573436 | ||||||||
\(714\) | 21.8663 | − | 12.3536i | 0.818324 | − | 0.462322i | ||||
\(715\) | − | 17.8209i | − | 0.666465i | ||||||
\(716\) | 3.44717 | − | 3.36846i | 0.128827 | − | 0.125885i | ||||
\(717\) | 5.09850 | + | 3.94119i | 0.190407 | + | 0.147186i | ||||
\(718\) | 6.73652 | − | 16.0015i | 0.251405 | − | 0.597169i | ||||
\(719\) | 42.1831 | 1.57316 | 0.786582 | − | 0.617486i | \(-0.211849\pi\) | ||||
0.786582 | + | 0.617486i | \(0.211849\pi\) | |||||||
\(720\) | 22.9350 | − | 5.40807i | 0.854736 | − | 0.201547i | ||||
\(721\) | −7.66341 | −0.285400 | ||||||||
\(722\) | 34.2281 | + | 14.4098i | 1.27384 | + | 0.536279i | ||||
\(723\) | −17.6477 | − | 13.6419i | −0.656326 | − | 0.507346i | ||||
\(724\) | −33.2530 | + | 32.4937i | −1.23584 | + | 1.20762i | ||||
\(725\) | −0.251061 | − | 6.15567i | −0.00932416 | − | 0.228616i | ||||
\(726\) | −9.30720 | − | 16.4740i | −0.345423 | − | 0.611408i | ||||
\(727\) | −6.89099 | −0.255573 | −0.127786 | − | 0.991802i | \(-0.540787\pi\) | ||||
−0.127786 | + | 0.991802i | \(0.540787\pi\) | |||||||
\(728\) | 4.51514 | + | 11.4579i | 0.167342 | + | 0.424658i | ||||
\(729\) | −18.6789 | − | 19.4961i | −0.691812 | − | 0.722077i | ||||
\(730\) | 9.79048 | − | 23.2556i | 0.362362 | − | 0.860729i | ||||
\(731\) | 24.9999i | 0.924656i | ||||||||
\(732\) | 4.71555 | + | 40.5446i | 0.174292 | + | 1.49857i | ||||
\(733\) | −7.86962 | −0.290671 | −0.145335 | − | 0.989382i | \(-0.546426\pi\) | ||||
−0.145335 | + | 0.989382i | \(0.546426\pi\) | |||||||
\(734\) | −10.4823 | − | 4.41300i | −0.386910 | − | 0.162887i | ||||
\(735\) | −7.23809 | − | 5.59512i | −0.266981 | − | 0.206379i | ||||
\(736\) | 4.35368 | − | 9.70820i | 0.160479 | − | 0.357849i | ||||
\(737\) | 7.45175 | 0.274489 | ||||||||
\(738\) | 3.23184 | − | 22.3182i | 0.118966 | − | 0.821545i | ||||
\(739\) | 47.3048i | 1.74013i | 0.492934 | + | 0.870067i | \(0.335924\pi\) | ||||
−0.492934 | + | 0.870067i | \(0.664076\pi\) | |||||||
\(740\) | 26.2455 | + | 26.8587i | 0.964803 | + | 0.987347i | ||||
\(741\) | 19.3353 | + | 14.9464i | 0.710299 | + | 0.549068i | ||||
\(742\) | 15.6195 | − | 37.1014i | 0.573409 | − | 1.36203i | ||||
\(743\) | 18.1882i | 0.667260i | 0.942704 | + | 0.333630i | \(0.108274\pi\) | ||||
−0.942704 | + | 0.333630i | \(0.891726\pi\) | |||||||
\(744\) | −11.1247 | + | 38.2993i | −0.407850 | + | 1.40412i | ||||
\(745\) | −8.89045 | −0.325721 | ||||||||
\(746\) | −2.62036 | + | 6.22422i | −0.0959382 | + | 0.227885i | ||||
\(747\) | −38.8050 | + | 10.1016i | −1.41980 | + | 0.369598i | ||||
\(748\) | 29.8711 | + | 30.5691i | 1.09220 | + | 1.11772i | ||||
\(749\) | 6.76057 | 0.247026 | ||||||||
\(750\) | −14.5366 | − | 25.7302i | −0.530802 | − | 0.939534i | ||||
\(751\) | −25.1488 | −0.917691 | −0.458846 | − | 0.888516i | \(-0.651737\pi\) | ||||
−0.458846 | + | 0.888516i | \(0.651737\pi\) | |||||||
\(752\) | 26.7992 | + | 0.619037i | 0.977267 | + | 0.0225740i | ||||
\(753\) | −8.41682 | − | 6.50628i | −0.306726 | − | 0.237102i | ||||
\(754\) | −14.9614 | − | 5.59244i | −0.544862 | − | 0.203665i | ||||
\(755\) | 36.8667i | 1.34172i | ||||||||
\(756\) | 7.81107 | + | 20.1119i | 0.284086 | + | 0.731461i | ||||
\(757\) | −35.9086 | −1.30512 | −0.652561 | − | 0.757736i | \(-0.726305\pi\) | ||||
−0.652561 | + | 0.757736i | \(0.726305\pi\) | |||||||
\(758\) | −9.80334 | + | 23.2862i | −0.356073 | + | 0.845792i | ||||
\(759\) | −11.1531 | − | 8.62146i | −0.404832 | − | 0.312939i | ||||
\(760\) | −34.7637 | + | 13.6991i | −1.26101 | + | 0.496918i | ||||
\(761\) | 1.16063i | 0.0420728i | 0.999779 | + | 0.0210364i | \(0.00669659\pi\) | ||||
−0.999779 | + | 0.0210364i | \(0.993303\pi\) | |||||||
\(762\) | 9.51716 | + | 16.8456i | 0.344770 | + | 0.610253i | ||||
\(763\) | 18.8278 | 0.681610 | ||||||||
\(764\) | 1.44072 | − | 1.40782i | 0.0521233 | − | 0.0509333i | ||||
\(765\) | 7.32920 | + | 28.1549i | 0.264988 | + | 1.01794i | ||||
\(766\) | 20.9903 | + | 8.83680i | 0.758411 | + | 0.319287i | ||||
\(767\) | −14.7658 | −0.533162 | ||||||||
\(768\) | −21.1198 | − | 17.9431i | −0.762094 | − | 0.647467i | ||||
\(769\) | 44.0832i | 1.58968i | 0.606817 | + | 0.794841i | \(0.292446\pi\) | ||||
−0.606817 | + | 0.794841i | \(0.707554\pi\) | |||||||
\(770\) | −9.68011 | + | 22.9934i | −0.348847 | + | 0.828626i | ||||
\(771\) | −0.659895 | + | 0.853670i | −0.0237655 | + | 0.0307442i | ||||
\(772\) | 10.3861 | − | 10.1489i | 0.373803 | − | 0.365268i | ||||
\(773\) | − | 37.6792i | − | 1.35523i | −0.735418 | − | 0.677614i | \(-0.763014\pi\) | ||
0.735418 | − | 0.677614i | \(-0.236986\pi\) | |||||||
\(774\) | −21.2552 | − | 3.07791i | −0.764003 | − | 0.110633i | ||||
\(775\) | 9.31348 | 0.334550 | ||||||||
\(776\) | 23.7129 | − | 9.34438i | 0.851244 | − | 0.335444i | ||||
\(777\) | −21.0287 | + | 27.2037i | −0.754402 | + | 0.975927i | ||||
\(778\) | −7.45067 | + | 17.6978i | −0.267119 | + | 0.634496i | ||||
\(779\) | 35.7593i | 1.28121i | ||||||||
\(780\) | −14.1709 | + | 1.64815i | −0.507399 | + | 0.0590133i | ||||
\(781\) | −11.3490 | −0.406101 | ||||||||
\(782\) | 12.1071 | + | 5.09704i | 0.432951 | + | 0.182270i | ||||
\(783\) | −26.1623 | − | 9.92643i | −0.934964 | − | 0.354742i | ||||
\(784\) | −0.248463 | + | 10.7564i | −0.00887368 | + | 0.384158i | ||||
\(785\) | −12.2522 | −0.437298 | ||||||||
\(786\) | 0.915774 | + | 1.62095i | 0.0326646 | + | 0.0578172i | ||||
\(787\) | −40.0972 | −1.42931 | −0.714655 | − | 0.699478i | \(-0.753416\pi\) | ||||
−0.714655 | + | 0.699478i | \(0.753416\pi\) | |||||||
\(788\) | 11.9202 | + | 12.1987i | 0.424640 | + | 0.434562i | ||||
\(789\) | 1.35485 | − | 1.75269i | 0.0482339 | − | 0.0623975i | ||||
\(790\) | −23.0543 | − | 9.70572i | −0.820234 | − | 0.345314i | ||||
\(791\) | − | 43.3531i | − | 1.54146i | ||||||
\(792\) | −29.6678 | + | 21.6332i | −1.05420 | + | 0.768701i | ||||
\(793\) | − | 24.7125i | − | 0.877568i | ||||||
\(794\) | 6.70512 | − | 15.9269i | 0.237956 | − | 0.565224i | ||||
\(795\) | 36.8944 | + | 28.5197i | 1.30851 | + | 1.01149i | ||||
\(796\) | 2.88163 | − | 2.81583i | 0.102136 | − | 0.0998045i | ||||
\(797\) | 20.8449i | 0.738364i | 0.929357 | + | 0.369182i | \(0.120362\pi\) | ||||
−0.929357 | + | 0.369182i | \(0.879638\pi\) | |||||||
\(798\) | −16.8286 | − | 29.7872i | −0.595728 | − | 1.05446i | ||||
\(799\) | 33.0964i | 1.17087i | ||||||||
\(800\) | −2.64813 | + | 5.90501i | −0.0936255 | + | 0.208774i | ||||
\(801\) | −3.81017 | − | 14.6366i | −0.134626 | − | 0.517160i | ||||
\(802\) | 10.3725 | − | 24.6382i | 0.366266 | − | 0.870003i | ||||
\(803\) | 39.3174i | 1.38748i | ||||||||
\(804\) | −0.689168 | − | 5.92550i | −0.0243051 | − | 0.208976i | ||||
\(805\) | 7.66778i | 0.270254i | ||||||||
\(806\) | 9.36896 | − | 22.2544i | 0.330007 | − | 0.783876i | ||||
\(807\) | 28.6232 | − | 37.0282i | 1.00758 | − | 1.30346i | ||||
\(808\) | 35.1313 | − | 13.8440i | 1.23592 | − | 0.487029i | ||||
\(809\) | −16.1878 | −0.569133 | −0.284567 | − | 0.958656i | \(-0.591850\pi\) | ||||
−0.284567 | + | 0.958656i | \(0.591850\pi\) | |||||||
\(810\) | −24.8399 | + | 2.76503i | −0.872786 | + | 0.0971533i | ||||
\(811\) | −8.92823 | −0.313513 | −0.156756 | − | 0.987637i | \(-0.550104\pi\) | ||||
−0.156756 | + | 0.987637i | \(0.550104\pi\) | |||||||
\(812\) | 16.2662 | + | 15.3425i | 0.570832 | + | 0.538416i | ||||
\(813\) | −6.86087 | − | 5.30352i | −0.240621 | − | 0.186003i | ||||
\(814\) | −53.9307 | − | 22.7045i | −1.89027 | − | 0.795792i | ||||
\(815\) | 34.3607i | 1.20360i | ||||||||
\(816\) | 21.5454 | − | 26.5801i | 0.754239 | − | 0.930490i | ||||
\(817\) | 34.0560 | 1.19147 | ||||||||
\(818\) | −5.63981 | + | 13.3964i | −0.197191 | + | 0.468394i | ||||
\(819\) | −3.29073 | − | 12.6412i | −0.114987 | − | 0.441720i | ||||
\(820\) | −14.5894 | − | 14.9303i | −0.509485 | − | 0.521389i | ||||
\(821\) | −5.47330 | −0.191019 | −0.0955097 | − | 0.995428i | \(-0.530448\pi\) | ||||
−0.0955097 | + | 0.995428i | \(0.530448\pi\) | |||||||
\(822\) | −10.9767 | − | 19.4291i | −0.382856 | − | 0.677666i | ||||
\(823\) | 16.0731 | 0.560274 | 0.280137 | − | 0.959960i | \(-0.409620\pi\) | ||||
0.280137 | + | 0.959960i | \(0.409620\pi\) | |||||||
\(824\) | −9.71347 | + | 3.82772i | −0.338385 | + | 0.133345i | ||||
\(825\) | 6.78388 | + | 5.24400i | 0.236184 | + | 0.182573i | ||||
\(826\) | 19.0516 | + | 8.02060i | 0.662889 | + | 0.279072i | ||||
\(827\) | −36.6105 | −1.27307 | −0.636536 | − | 0.771247i | \(-0.719634\pi\) | ||||
−0.636536 | + | 0.771247i | \(0.719634\pi\) | |||||||
\(828\) | −5.82415 | + | 9.66609i | −0.202403 | + | 0.335920i | ||||
\(829\) | 44.2971 | 1.53850 | 0.769251 | − | 0.638947i | \(-0.220630\pi\) | ||||
0.769251 | + | 0.638947i | \(0.220630\pi\) | |||||||
\(830\) | −14.4022 | + | 34.2101i | −0.499909 | + | 1.18745i | ||||
\(831\) | −13.6846 | + | 17.7030i | −0.474715 | + | 0.614112i | ||||
\(832\) | 11.4460 | + | 12.2678i | 0.396819 | + | 0.425311i | ||||
\(833\) | −13.2839 | −0.460261 | ||||||||
\(834\) | 6.78265 | + | 12.0055i | 0.234864 | + | 0.415716i | ||||
\(835\) | 32.5826 | 1.12757 | ||||||||
\(836\) | 41.6426 | − | 40.6918i | 1.44024 | − | 1.40735i | ||||
\(837\) | 16.6054 | − | 38.9061i | 0.573966 | − | 1.34479i | ||||
\(838\) | −17.3822 | + | 41.2885i | −0.600459 | + | 1.42629i | ||||
\(839\) | 24.2758i | 0.838094i | 0.907964 | + | 0.419047i | \(0.137636\pi\) | ||||
−0.907964 | + | 0.419047i | \(0.862364\pi\) | |||||||
\(840\) | 19.1792 | + | 5.57092i | 0.661746 | + | 0.192215i | ||||
\(841\) | −28.9037 | + | 2.36162i | −0.996679 | + | 0.0814351i | ||||
\(842\) | −9.28406 | − | 3.90854i | −0.319950 | − | 0.134697i | ||||
\(843\) | 5.03207 | − | 6.50971i | 0.173314 | − | 0.224206i | ||||
\(844\) | −29.5602 | + | 28.8853i | −1.01750 | + | 0.994272i | ||||
\(845\) | −16.8902 | −0.581042 | ||||||||
\(846\) | −28.1390 | − | 4.07472i | −0.967437 | − | 0.140092i | ||||
\(847\) | − | 16.0370i | − | 0.551039i | ||||||
\(848\) | 1.26648 | − | 54.8281i | 0.0434911 | − | 1.88281i | ||||
\(849\) | −1.44671 | − | 1.11832i | −0.0496510 | − | 0.0383807i | ||||
\(850\) | −7.36417 | − | 3.10027i | −0.252589 | − | 0.106339i | ||||
\(851\) | −17.9846 | −0.616505 | ||||||||
\(852\) | 1.04960 | + | 9.02456i | 0.0359589 | + | 0.309176i | ||||
\(853\) | −17.7494 | −0.607727 | −0.303863 | − | 0.952716i | \(-0.598277\pi\) | ||||
−0.303863 | + | 0.952716i | \(0.598277\pi\) | |||||||
\(854\) | −13.4235 | + | 31.8853i | −0.459344 | + | 1.09109i | ||||
\(855\) | 38.3539 | − | 9.98417i | 1.31167 | − | 0.341451i | ||||
\(856\) | 8.56911 | − | 3.37677i | 0.292886 | − | 0.115416i | ||||
\(857\) | − | 0.647482i | − | 0.0221176i | −0.999939 | − | 0.0110588i | \(-0.996480\pi\) | ||
0.999939 | − | 0.0110588i | \(-0.00352019\pi\) | |||||||
\(858\) | 19.3547 | − | 10.9347i | 0.660759 | − | 0.373304i | ||||
\(859\) | − | 36.6021i | − | 1.24885i | −0.781085 | − | 0.624424i | \(-0.785334\pi\) | ||
0.781085 | − | 0.624424i | \(-0.214666\pi\) | |||||||
\(860\) | −14.2192 | + | 13.8945i | −0.484870 | + | 0.473800i | ||||
\(861\) | 11.6895 | − | 15.1221i | 0.398378 | − | 0.515359i | ||||
\(862\) | 7.01698 | + | 2.95411i | 0.238999 | + | 0.100617i | ||||
\(863\) | −13.0617 | −0.444627 | −0.222313 | − | 0.974975i | \(-0.571361\pi\) | ||||
−0.222313 | + | 0.974975i | \(0.571361\pi\) | |||||||
\(864\) | 19.9461 | + | 21.5906i | 0.678580 | + | 0.734526i | ||||
\(865\) | 3.71958 | 0.126470 | ||||||||
\(866\) | 19.1334 | − | 45.4480i | 0.650178 | − | 1.54439i | ||||
\(867\) | 10.1266 | + | 7.82794i | 0.343916 | + | 0.265851i | ||||
\(868\) | −24.1766 | + | 23.6246i | −0.820606 | + | 0.801870i | ||||
\(869\) | 38.9770 | 1.32220 | ||||||||
\(870\) | −22.0143 | + | 13.6496i | −0.746353 | + | 0.462765i | ||||
\(871\) | 3.61168i | 0.122377i | ||||||||
\(872\) | 23.8644 | − | 9.40409i | 0.808152 | − | 0.318463i | ||||
\(873\) | −26.1618 | + | 6.81037i | −0.885443 | + | 0.230496i | ||||
\(874\) | 6.94342 | − | 16.4929i | 0.234865 | − | 0.557881i | ||||
\(875\) | − | 25.0477i | − | 0.846767i | ||||||
\(876\) | 31.2645 | − | 3.63622i | 1.05633 | − | 0.122857i | ||||
\(877\) | − | 18.2462i | − | 0.616132i | −0.951365 | − | 0.308066i | \(-0.900318\pi\) | ||
0.951365 | − | 0.308066i | \(-0.0996817\pi\) | |||||||
\(878\) | 6.02928 | − | 14.3215i | 0.203478 | − | 0.483328i | ||||
\(879\) | −20.4285 | + | 26.4273i | −0.689037 | + | 0.891369i | ||||
\(880\) | −0.784895 | + | 33.9795i | −0.0264588 | + | 1.14545i | ||||
\(881\) | −30.7299 | −1.03532 | −0.517658 | − | 0.855588i | \(-0.673196\pi\) | ||||
−0.517658 | + | 0.855588i | \(0.673196\pi\) | |||||||
\(882\) | 1.63547 | − | 11.2941i | 0.0550692 | − | 0.380293i | ||||
\(883\) | 46.7068 | 1.57181 | 0.785905 | − | 0.618347i | \(-0.212197\pi\) | ||||
0.785905 | + | 0.618347i | \(0.212197\pi\) | |||||||
\(884\) | −14.8161 | + | 14.4778i | −0.498319 | + | 0.486941i | ||||
\(885\) | −14.6449 | + | 18.9453i | −0.492282 | + | 0.636838i | ||||
\(886\) | 32.2498 | + | 13.5770i | 1.08345 | + | 0.456127i | ||||
\(887\) | 54.4701i | 1.82893i | 0.404668 | + | 0.914464i | \(0.367387\pi\) | ||||
−0.404668 | + | 0.914464i | \(0.632613\pi\) | |||||||
\(888\) | −13.0665 | + | 44.9845i | −0.438483 | + | 1.50958i | ||||
\(889\) | 16.3988i | 0.549998i | ||||||||
\(890\) | −12.9035 | − | 5.43230i | −0.432526 | − | 0.182091i | ||||
\(891\) | 34.0015 | − | 18.9892i | 1.13909 | − | 0.636161i | ||||
\(892\) | −2.20380 | + | 2.15349i | −0.0737888 | + | 0.0721041i | ||||
\(893\) | 45.0855 | 1.50873 | ||||||||
\(894\) | −5.45506 | − | 9.65562i | −0.182445 | − | 0.322932i | ||||
\(895\) | 4.73213i | 0.158178i | ||||||||
\(896\) | −8.10446 | − | 22.0459i | −0.270751 | − | 0.736501i | ||||
\(897\) | 4.17861 | − | 5.40564i | 0.139520 | − | 0.180489i | ||||
\(898\) | 21.7627 | + | 9.16195i | 0.726229 | + | 0.305738i | ||||
\(899\) | −1.78655 | − | 43.8039i | −0.0595849 | − | 1.46094i | ||||
\(900\) | 3.54254 | − | 5.87940i | 0.118085 | − | 0.195980i | ||||
\(901\) | 67.7115 | 2.25580 | ||||||||
\(902\) | 29.9791 | + | 12.6210i | 0.998196 | + | 0.420235i | ||||
\(903\) | −14.4018 | − | 11.1327i | −0.479263 | − | 0.370475i | ||||
\(904\) | −21.6540 | − | 54.9506i | −0.720202 | − | 1.82763i | ||||
\(905\) | − | 45.6483i | − | 1.51740i | ||||||
\(906\) | −40.0397 | + | 22.6209i | −1.33023 | + | 0.751530i | ||||
\(907\) | 9.46685i | 0.314341i | 0.987571 | + | 0.157171i | \(0.0502373\pi\) | ||||
−0.987571 | + | 0.157171i | \(0.949763\pi\) | |||||||
\(908\) | 12.3105 | − | 12.0294i | 0.408537 | − | 0.399209i | ||||
\(909\) | −38.7594 | + | 10.0898i | −1.28557 | + | 0.334656i | ||||
\(910\) | −11.1444 | − | 4.69171i | −0.369432 | − | 0.155529i | ||||
\(911\) | − | 46.0659i | − | 1.52623i | −0.646262 | − | 0.763116i | \(-0.723669\pi\) | ||
0.646262 | − | 0.763116i | \(-0.276331\pi\) | |||||||
\(912\) | −36.2087 | − | 29.3501i | −1.19899 | − | 0.971879i | ||||
\(913\) | − | 57.8376i | − | 1.91414i | ||||||
\(914\) | −32.0690 | − | 13.5009i | −1.06075 | − | 0.446569i | ||||
\(915\) | −31.7074 | − | 24.5101i | −1.04821 | − | 0.810280i | ||||
\(916\) | −8.68319 | − | 8.88608i | −0.286901 | − | 0.293604i | ||||
\(917\) | 1.57795i | 0.0521085i | ||||||||
\(918\) | −26.0810 | + | 25.2355i | −0.860800 | + | 0.832894i | ||||
\(919\) | 43.2586i | 1.42697i | 0.700670 | + | 0.713485i | \(0.252884\pi\) | ||||
−0.700670 | + | 0.713485i | \(0.747116\pi\) | |||||||
\(920\) | 3.82990 | + | 9.71901i | 0.126268 | + | 0.320426i | ||||
\(921\) | 23.1558 | − | 29.9554i | 0.763011 | − | 0.987065i | ||||
\(922\) | −20.7715 | + | 49.3392i | −0.684073 | + | 1.62490i | ||||
\(923\) | − | 5.50060i | − | 0.181055i | ||||||
\(924\) | −30.9120 | + | 3.59523i | −1.01693 | + | 0.118274i | ||||
\(925\) | 10.9392 | 0.359677 | ||||||||
\(926\) | 13.3760 | − | 31.7724i | 0.439562 | − | 1.04410i | ||||
\(927\) | 10.7166 | − | 2.78972i | 0.351980 | − | 0.0916264i | ||||
\(928\) | 28.2809 | + | 11.3222i | 0.928366 | + | 0.371668i | ||||
\(929\) | − | 13.2344i | − | 0.434208i | −0.976149 | − | 0.217104i | \(-0.930339\pi\) | ||
0.976149 | − | 0.217104i | \(-0.0696610\pi\) | |||||||
\(930\) | −19.2612 | − | 34.0929i | −0.631600 | − | 1.11795i | ||||
\(931\) | 18.0960i | 0.593072i | ||||||||
\(932\) | −29.3952 | + | 28.7240i | −0.962871 | + | 0.940886i | ||||
\(933\) | 6.54675 | − | 8.46917i | 0.214331 | − | 0.277268i | ||||
\(934\) | 39.2791 | + | 16.5363i | 1.28525 | + | 0.541083i | ||||
\(935\) | −41.9640 | −1.37237 | ||||||||
\(936\) | −10.4851 | − | 14.3792i | −0.342715 | − | 0.470000i | ||||
\(937\) | 10.8006 | 0.352841 | 0.176420 | − | 0.984315i | \(-0.443548\pi\) | ||||
0.176420 | + | 0.984315i | \(0.443548\pi\) | |||||||
\(938\) | 1.96182 | − | 4.65997i | 0.0640557 | − | 0.152153i | ||||
\(939\) | −9.32616 | − | 7.20921i | −0.304348 | − | 0.235264i | ||||
\(940\) | −18.8242 | + | 18.3944i | −0.613979 | + | 0.599960i | ||||
\(941\) | 34.1094 | 1.11193 | 0.555967 | − | 0.831204i | \(-0.312348\pi\) | ||||
0.555967 | + | 0.831204i | \(0.312348\pi\) | |||||||
\(942\) | −7.51776 | − | 13.3066i | −0.244942 | − | 0.433554i | ||||
\(943\) | 9.99735 | 0.325558 | ||||||||
\(944\) | 28.1542 | + | 0.650337i | 0.916343 | + | 0.0211667i | ||||
\(945\) | −19.4831 | − | 8.31551i | −0.633784 | − | 0.270504i | ||||
\(946\) | 12.0199 | − | 28.5512i | 0.390801 | − | 0.928281i | ||||
\(947\) | 24.3264 | 0.790503 | 0.395251 | − | 0.918573i | \(-0.370657\pi\) | ||||
0.395251 | + | 0.918573i | \(0.370657\pi\) | |||||||
\(948\) | −3.60474 | − | 30.9938i | −0.117077 | − | 1.00663i | ||||
\(949\) | −19.0562 | −0.618589 | ||||||||
\(950\) | −4.22334 | + | 10.0318i | −0.137023 | + | 0.325475i | ||||
\(951\) | −15.9638 | + | 20.6514i | −0.517661 | + | 0.669669i | ||||
\(952\) | 26.9806 | − | 10.6321i | 0.874446 | − | 0.344587i | ||||
\(953\) | − | 15.4131i | − | 0.499280i | −0.968339 | − | 0.249640i | \(-0.919688\pi\) | ||
0.968339 | − | 0.249640i | \(-0.0803123\pi\) | |||||||
\(954\) | −8.33641 | + | 57.5691i | −0.269901 | + | 1.86387i | ||||
\(955\) | 1.97776i | 0.0639988i | ||||||||
\(956\) | 5.20055 | + | 5.32207i | 0.168198 | + | 0.172128i | ||||
\(957\) | 23.3627 | − | 32.9124i | 0.755209 | − | 1.06391i | ||||
\(958\) | 6.29255 | − | 14.9469i | 0.203303 | − | 0.482912i | ||||
\(959\) | − | 18.9137i | − | 0.610755i | ||||||
\(960\) | 27.0925 | − | 2.51843i | 0.874407 | − | 0.0812818i | ||||
\(961\) | 35.2749 | 1.13790 | ||||||||
\(962\) | 11.0043 | − | 26.1389i | 0.354793 | − | 0.842751i | ||||
\(963\) | −9.45407 | + | 2.46106i | −0.304653 | + | 0.0793065i | ||||
\(964\) | −18.0010 | − | 18.4216i | −0.579772 | − | 0.593319i | ||||
\(965\) | 14.2576i | 0.458967i | ||||||||
\(966\) | −8.32772 | + | 4.70485i | −0.267940 | + | 0.151376i | ||||
\(967\) | −58.7655 | −1.88977 | −0.944885 | − | 0.327401i | \(-0.893827\pi\) | ||||
−0.944885 | + | 0.327401i | \(0.893827\pi\) | |||||||
\(968\) | −8.01018 | − | 20.3272i | −0.257457 | − | 0.653340i | ||||
\(969\) | 35.1950 | − | 45.5299i | 1.13063 | − | 1.46263i | ||||
\(970\) | −9.70981 | + | 23.0640i | −0.311763 | + | 0.740540i | ||||
\(971\) | −22.1575 | −0.711069 | −0.355535 | − | 0.934663i | \(-0.615701\pi\) | ||||
−0.355535 | + | 0.934663i | \(0.615701\pi\) | |||||||
\(972\) | −18.2445 | − | 25.2812i | −0.585191 | − | 0.810895i | ||||
\(973\) | 11.6870i | 0.374669i | ||||||||
\(974\) | 1.10354 | − | 2.62127i | 0.0353597 | − | 0.0839910i | ||||
\(975\) | −2.54164 | + | 3.28798i | −0.0813976 | + | 0.105300i | ||||
\(976\) | −1.08842 | + | 47.1198i | −0.0348396 | + | 1.50827i | ||||
\(977\) | 46.5956i | 1.49072i | 0.666660 | + | 0.745362i | \(0.267723\pi\) | ||||
−0.666660 | + | 0.745362i | \(0.732277\pi\) | |||||||
\(978\) | −37.3180 | + | 21.0832i | −1.19330 | + | 0.674168i | ||||
\(979\) | 21.8154 | 0.697224 | ||||||||
\(980\) | −7.38298 | − | 7.55549i | −0.235841 | − | 0.241351i | ||||
\(981\) | −26.3290 | + | 6.85389i | −0.840620 | + | 0.218828i | ||||
\(982\) | −12.9622 | − | 5.45702i | −0.413641 | − | 0.174140i | ||||
\(983\) | − | 3.49122i | − | 0.111352i | −0.998449 | − | 0.0556762i | \(-0.982269\pi\) | ||
0.998449 | − | 0.0556762i | \(-0.0177315\pi\) | |||||||
\(984\) | 7.26344 | − | 25.0061i | 0.231550 | − | 0.797166i | ||||
\(985\) | −16.7459 | −0.533570 | ||||||||
\(986\) | −13.1688 | + | 35.2305i | −0.419381 | + | 1.12197i | ||||
\(987\) | −19.0660 | − | 14.7382i | −0.606878 | − | 0.469123i | ||||
\(988\) | 19.7223 | + | 20.1831i | 0.627450 | + | 0.642111i | ||||
\(989\) | − | 9.52118i | − | 0.302756i | ||||||
\(990\) | 5.16646 | − | 35.6782i | 0.164201 | − | 1.13393i | ||||
\(991\) | − | 29.3482i | − | 0.932276i | −0.884712 | − | 0.466138i | \(-0.845645\pi\) | ||
0.884712 | − | 0.466138i | \(-0.154355\pi\) | |||||||
\(992\) | −18.8441 | + | 42.0202i | −0.598302 | + | 1.33414i | ||||
\(993\) | −3.39037 | + | 4.38594i | −0.107590 | + | 0.139184i | ||||
\(994\) | −2.98786 | + | 7.09715i | −0.0947691 | + | 0.225108i | ||||
\(995\) | 3.95578i | 0.125407i | ||||||||
\(996\) | −45.9914 | + | 5.34905i | −1.45729 | + | 0.169491i | ||||
\(997\) | 52.5786 | 1.66518 | 0.832591 | − | 0.553888i | \(-0.186856\pi\) | ||||
0.832591 | + | 0.553888i | \(0.186856\pi\) | |||||||
\(998\) | −5.42601 | − | 2.28432i | −0.171757 | − | 0.0723088i | ||||
\(999\) | 19.5039 | − | 45.6971i | 0.617075 | − | 1.44579i |
(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 | 696.2.l.b.347.14 | yes | 104 | |
3.2 | odd | 2 | inner | 696.2.l.b.347.92 | yes | 104 | |
8.3 | odd | 2 | inner | 696.2.l.b.347.16 | yes | 104 | |
24.11 | even | 2 | inner | 696.2.l.b.347.90 | yes | 104 | |
29.28 | even | 2 | inner | 696.2.l.b.347.91 | yes | 104 | |
87.86 | odd | 2 | inner | 696.2.l.b.347.13 | ✓ | 104 | |
232.115 | odd | 2 | inner | 696.2.l.b.347.89 | yes | 104 | |
696.347 | even | 2 | inner | 696.2.l.b.347.15 | yes | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
696.2.l.b.347.13 | ✓ | 104 | 87.86 | odd | 2 | inner | |
696.2.l.b.347.14 | yes | 104 | 1.1 | even | 1 | trivial | |
696.2.l.b.347.15 | yes | 104 | 696.347 | even | 2 | inner | |
696.2.l.b.347.16 | yes | 104 | 8.3 | odd | 2 | inner | |
696.2.l.b.347.89 | yes | 104 | 232.115 | odd | 2 | inner | |
696.2.l.b.347.90 | yes | 104 | 24.11 | even | 2 | inner | |
696.2.l.b.347.91 | yes | 104 | 29.28 | even | 2 | inner | |
696.2.l.b.347.92 | yes | 104 | 3.2 | odd | 2 | inner |