Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), not 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 107.3 | ||
Character | \(\chi\) | \(=\) | 750.107 |
Dual form | 750.2.l.c.743.3 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.891007 | − | 0.453990i | −0.630037 | − | 0.321020i | ||||
\(3\) | 0.631448 | − | 1.61285i | 0.364566 | − | 0.931177i | ||||
\(4\) | 0.587785 | + | 0.809017i | 0.293893 | + | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.29484 | + | 1.15039i | −0.528617 | + | 0.469643i | ||||
\(7\) | −2.97677 | − | 2.97677i | −1.12511 | − | 1.12511i | −0.990960 | − | 0.134155i | \(-0.957168\pi\) |
−0.134155 | − | 0.990960i | \(-0.542832\pi\) | |||||||
\(8\) | −0.156434 | − | 0.987688i | −0.0553079 | − | 0.349201i | ||||
\(9\) | −2.20255 | − | 2.03686i | −0.734183 | − | 0.678952i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.73921 | − | 1.53986i | 1.42893 | − | 0.464286i | 0.510499 | − | 0.859878i | \(-0.329461\pi\) |
0.918426 | + | 0.395592i | \(0.129461\pi\) | |||||||
\(12\) | 1.67598 | − | 0.437156i | 0.483813 | − | 0.126196i | ||||
\(13\) | −0.801995 | − | 1.57400i | −0.222433 | − | 0.436550i | 0.752640 | − | 0.658432i | \(-0.228780\pi\) |
−0.975074 | + | 0.221882i | \(0.928780\pi\) | |||||||
\(14\) | 1.30090 | + | 4.00375i | 0.347680 | + | 1.07005i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 1.40961 | − | 0.223260i | 0.341881 | − | 0.0541486i | 0.0168665 | − | 0.999858i | \(-0.494631\pi\) |
0.325014 | + | 0.945709i | \(0.394631\pi\) | |||||||
\(18\) | 1.03777 | + | 2.81479i | 0.244605 | + | 0.663452i | ||||
\(19\) | −1.09331 | + | 1.50481i | −0.250823 | + | 0.345228i | −0.915799 | − | 0.401636i | \(-0.868442\pi\) |
0.664977 | + | 0.746864i | \(0.268442\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.68076 | + | 2.92140i | −1.45786 | + | 0.637502i | ||||
\(22\) | −4.92175 | − | 0.779529i | −1.04932 | − | 0.166196i | ||||
\(23\) | −0.951606 | + | 1.86763i | −0.198424 | + | 0.389428i | −0.968682 | − | 0.248303i | \(-0.920127\pi\) |
0.770259 | + | 0.637731i | \(0.220127\pi\) | |||||||
\(24\) | −1.69177 | − | 0.371369i | −0.345331 | − | 0.0758053i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.76655i | 0.346448i | ||||||||
\(27\) | −4.67593 | + | 2.26620i | −0.899883 | + | 0.436131i | ||||
\(28\) | 0.658557 | − | 4.15797i | 0.124456 | − | 0.785782i | ||||
\(29\) | −4.57938 | + | 3.32712i | −0.850370 | + | 0.617830i | −0.925248 | − | 0.379363i | \(-0.876143\pi\) |
0.0748779 | + | 0.997193i | \(0.476143\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.23835 | − | 3.80588i | −0.940835 | − | 0.683557i | 0.00778619 | − | 0.999970i | \(-0.497522\pi\) |
−0.948622 | + | 0.316413i | \(0.897522\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0.509001 | − | 8.61596i | 0.0886057 | − | 1.49985i | ||||
\(34\) | −1.35733 | − | 0.441023i | −0.232780 | − | 0.0756348i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.353226 | − | 2.97913i | 0.0588710 | − | 0.496522i | ||||
\(37\) | −2.29429 | + | 1.16900i | −0.377178 | + | 0.192182i | −0.632294 | − | 0.774729i | \(-0.717886\pi\) |
0.255116 | + | 0.966911i | \(0.417886\pi\) | |||||||
\(38\) | 1.65732 | − | 0.844446i | 0.268852 | − | 0.136987i | ||||
\(39\) | −3.04504 | + | 0.299594i | −0.487597 | + | 0.0479734i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.58757 | − | 1.16567i | −0.560285 | − | 0.182048i | 0.0151644 | − | 0.999885i | \(-0.495173\pi\) |
−0.575449 | + | 0.817837i | \(0.695173\pi\) | |||||||
\(42\) | 7.27889 | + | 0.430011i | 1.12316 | + | 0.0663522i | ||||
\(43\) | 6.26505 | − | 6.26505i | 0.955411 | − | 0.955411i | −0.0436361 | − | 0.999047i | \(-0.513894\pi\) |
0.999047 | + | 0.0436361i | \(0.0138942\pi\) | |||||||
\(44\) | 4.03141 | + | 2.92899i | 0.607758 | + | 0.441562i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.69577 | − | 1.23205i | 0.250028 | − | 0.181656i | ||||
\(47\) | −0.732319 | + | 4.62368i | −0.106820 | + | 0.674433i | 0.874929 | + | 0.484251i | \(0.160908\pi\) |
−0.981749 | + | 0.190182i | \(0.939092\pi\) | |||||||
\(48\) | 1.33878 | + | 1.09894i | 0.193236 | + | 0.158618i | ||||
\(49\) | 10.7224i | 1.53177i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.530010 | − | 2.41446i | 0.0742163 | − | 0.338092i | ||||
\(52\) | 0.801995 | − | 1.57400i | 0.111217 | − | 0.218275i | ||||
\(53\) | −5.05783 | − | 0.801081i | −0.694746 | − | 0.110037i | −0.200933 | − | 0.979605i | \(-0.564397\pi\) |
−0.493813 | + | 0.869568i | \(0.664397\pi\) | |||||||
\(54\) | 5.19512 | + | 0.103626i | 0.706966 | + | 0.0141017i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.47446 | + | 3.40580i | −0.330663 | + | 0.455119i | ||||
\(57\) | 1.73666 | + | 2.71355i | 0.230027 | + | 0.359419i | ||||
\(58\) | 5.59074 | − | 0.885486i | 0.734100 | − | 0.116270i | ||||
\(59\) | 3.44032 | − | 10.5882i | 0.447892 | − | 1.37847i | −0.431389 | − | 0.902166i | \(-0.641976\pi\) |
0.879281 | − | 0.476303i | \(-0.158024\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.99979 | − | 9.23241i | −0.384084 | − | 1.18209i | −0.937142 | − | 0.348947i | \(-0.886539\pi\) |
0.553058 | − | 0.833143i | \(-0.313461\pi\) | |||||||
\(62\) | 2.93957 | + | 5.76923i | 0.373326 | + | 0.732693i | ||||
\(63\) | 0.493226 | + | 12.6197i | 0.0621407 | + | 1.58994i | ||||
\(64\) | −0.951057 | + | 0.309017i | −0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.36509 | + | 7.44580i | −0.537305 | + | 0.916514i | ||||
\(67\) | −1.01259 | − | 6.39326i | −0.123708 | − | 0.781061i | −0.969055 | − | 0.246844i | \(-0.920607\pi\) |
0.845347 | − | 0.534217i | \(-0.179393\pi\) | |||||||
\(68\) | 1.00917 | + | 1.00917i | 0.122380 | + | 0.122380i | ||||
\(69\) | 2.41131 | + | 2.71411i | 0.290288 | + | 0.326740i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.85681 | + | 12.1904i | 1.05111 | + | 1.44673i | 0.887842 | + | 0.460147i | \(0.152203\pi\) |
0.163268 | + | 0.986582i | \(0.447797\pi\) | |||||||
\(72\) | −1.66722 | + | 2.49407i | −0.196484 | + | 0.293928i | ||||
\(73\) | −8.23800 | − | 4.19747i | −0.964185 | − | 0.491277i | −0.100295 | − | 0.994958i | \(-0.531979\pi\) |
−0.863890 | + | 0.503681i | \(0.831979\pi\) | |||||||
\(74\) | 2.57494 | 0.299330 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.86005 | −0.213363 | ||||||||
\(77\) | −18.6914 | − | 9.52374i | −2.13008 | − | 1.08533i | ||||
\(78\) | 2.84917 | + | 1.11548i | 0.322605 | + | 0.126303i | ||||
\(79\) | −2.20434 | − | 3.03401i | −0.248007 | − | 0.341353i | 0.666805 | − | 0.745232i | \(-0.267661\pi\) |
−0.914812 | + | 0.403880i | \(0.867661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.702433 | + | 8.97255i | 0.0780482 | + | 0.996950i | ||||
\(82\) | 2.66735 | + | 2.66735i | 0.294559 | + | 0.294559i | ||||
\(83\) | 2.63941 | + | 16.6646i | 0.289713 | + | 1.82918i | 0.517761 | + | 0.855525i | \(0.326766\pi\) |
−0.228048 | + | 0.973650i | \(0.573234\pi\) | |||||||
\(84\) | −6.29032 | − | 3.68769i | −0.686330 | − | 0.402360i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.42648 | + | 2.73793i | −0.908650 | + | 0.295238i | ||||
\(87\) | 2.47449 | + | 9.48674i | 0.265293 | + | 1.01709i | ||||
\(88\) | −2.26228 | − | 4.43998i | −0.241160 | − | 0.473303i | ||||
\(89\) | −0.351151 | − | 1.08073i | −0.0372219 | − | 0.114557i | 0.930719 | − | 0.365735i | \(-0.119182\pi\) |
−0.967941 | + | 0.251177i | \(0.919182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.29810 | + | 7.07281i | −0.240906 | + | 0.741432i | ||||
\(92\) | −2.07029 | + | 0.327901i | −0.215842 | + | 0.0341860i | ||||
\(93\) | −9.44605 | + | 6.04544i | −0.979510 | + | 0.626883i | ||||
\(94\) | 2.75161 | − | 3.78726i | 0.283807 | − | 0.390626i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.693954 | − | 1.58696i | −0.0708264 | − | 0.161968i | ||||
\(97\) | 3.47236 | + | 0.549968i | 0.352565 | + | 0.0558408i | 0.330205 | − | 0.943909i | \(-0.392882\pi\) |
0.0223598 | + | 0.999750i | \(0.492882\pi\) | |||||||
\(98\) | 4.86785 | − | 9.55370i | 0.491728 | − | 0.965070i | ||||
\(99\) | −13.5748 | − | 6.26147i | −1.36432 | − | 0.629301i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 16.6740i | − | 1.65912i | −0.558415 | − | 0.829562i | \(-0.688590\pi\) | ||
0.558415 | − | 0.829562i | \(-0.311410\pi\) | |||||||
\(102\) | −1.56838 | + | 1.91068i | −0.155293 | + | 0.189186i | ||||
\(103\) | −0.415010 | + | 2.62027i | −0.0408921 | + | 0.258183i | −0.999662 | − | 0.0260012i | \(-0.991723\pi\) |
0.958770 | + | 0.284184i | \(0.0917226\pi\) | |||||||
\(104\) | −1.42917 | + | 1.03835i | −0.140141 | + | 0.101819i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.14287 | + | 3.00997i | 0.402391 | + | 0.292355i | ||||
\(107\) | 8.35067 | − | 8.35067i | 0.807290 | − | 0.807290i | −0.176933 | − | 0.984223i | \(-0.556618\pi\) |
0.984223 | + | 0.176933i | \(0.0566176\pi\) | |||||||
\(108\) | −4.58184 | − | 2.45087i | −0.440888 | − | 0.235835i | ||||
\(109\) | 12.6666 | + | 4.11563i | 1.21324 | + | 0.394206i | 0.844617 | − | 0.535372i | \(-0.179828\pi\) |
0.368625 | + | 0.929578i | \(0.379828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.436691 | + | 4.43849i | 0.0414489 | + | 0.421283i | ||||
\(112\) | 3.75095 | − | 1.91121i | 0.354432 | − | 0.180592i | ||||
\(113\) | −1.33349 | + | 0.679445i | −0.125444 | + | 0.0639168i | −0.515586 | − | 0.856838i | \(-0.672426\pi\) |
0.390142 | + | 0.920755i | \(0.372426\pi\) | |||||||
\(114\) | −0.315452 | − | 3.20622i | −0.0295448 | − | 0.300290i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.38339 | − | 1.74917i | −0.499835 | − | 0.162406i | ||||
\(117\) | −1.43959 | + | 5.10037i | −0.133090 | + | 0.471529i | ||||
\(118\) | −7.87230 | + | 7.87230i | −0.724704 | + | 0.724704i | ||||
\(119\) | −4.86069 | − | 3.53149i | −0.445578 | − | 0.323732i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.1898 | − | 8.12983i | 1.01725 | − | 0.739076i | ||||
\(122\) | −1.51859 | + | 9.58802i | −0.137487 | + | 0.868058i | ||||
\(123\) | −4.14542 | + | 5.05015i | −0.373780 | + | 0.455356i | ||||
\(124\) | − | 6.47496i | − | 0.581468i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.28978 | − | 11.4682i | 0.471251 | − | 1.02167i | ||||
\(127\) | −0.704349 | + | 1.38236i | −0.0625009 | + | 0.122665i | −0.920144 | − | 0.391581i | \(-0.871928\pi\) |
0.857643 | + | 0.514246i | \(0.171928\pi\) | |||||||
\(128\) | 0.987688 | + | 0.156434i | 0.0873001 | + | 0.0138270i | ||||
\(129\) | −6.14851 | − | 14.0606i | −0.541347 | − | 1.23797i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.74251 | − | 5.15112i | 0.326984 | − | 0.450055i | −0.613599 | − | 0.789618i | \(-0.710279\pi\) |
0.940584 | + | 0.339562i | \(0.110279\pi\) | |||||||
\(132\) | 7.26964 | − | 4.65255i | 0.632741 | − | 0.404952i | ||||
\(133\) | 7.73403 | − | 1.22495i | 0.670625 | − | 0.106217i | ||||
\(134\) | −2.00025 | + | 6.15614i | −0.172795 | + | 0.531810i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.441023 | − | 1.35733i | −0.0378174 | − | 0.116390i | ||||
\(137\) | −1.86549 | − | 3.66124i | −0.159380 | − | 0.312800i | 0.797483 | − | 0.603342i | \(-0.206165\pi\) |
−0.956862 | + | 0.290542i | \(0.906165\pi\) | |||||||
\(138\) | −0.916318 | − | 3.51300i | −0.0780022 | − | 0.299046i | ||||
\(139\) | 10.1584 | − | 3.30065i | 0.861621 | − | 0.279958i | 0.155316 | − | 0.987865i | \(-0.450361\pi\) |
0.706305 | + | 0.707907i | \(0.250361\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.99487 | + | 4.10073i | 0.589074 | + | 0.345344i | ||||
\(142\) | −2.35717 | − | 14.8826i | −0.197809 | − | 1.24892i | ||||
\(143\) | −6.22457 | − | 6.22457i | −0.520525 | − | 0.520525i | ||||
\(144\) | 2.61779 | − | 1.46532i | 0.218149 | − | 0.122110i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.43450 | + | 7.47994i | 0.449762 | + | 0.619045i | ||||
\(147\) | 17.2935 | + | 6.77062i | 1.42635 | + | 0.558431i | ||||
\(148\) | −2.29429 | − | 1.16900i | −0.188589 | − | 0.0960909i | ||||
\(149\) | 5.13270 | 0.420487 | 0.210244 | − | 0.977649i | \(-0.432574\pi\) | ||||
0.210244 | + | 0.977649i | \(0.432574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1314 | 1.63827 | 0.819136 | − | 0.573600i | \(-0.194454\pi\) | ||||
0.819136 | + | 0.573600i | \(0.194454\pi\) | |||||||
\(152\) | 1.65732 | + | 0.844446i | 0.134426 | + | 0.0684936i | ||||
\(153\) | −3.55948 | − | 2.37943i | −0.287767 | − | 0.192366i | ||||
\(154\) | 12.3305 | + | 16.9714i | 0.993617 | + | 1.36760i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.03221 | − | 2.28740i | −0.162707 | − | 0.183138i | ||||
\(157\) | −7.13510 | − | 7.13510i | −0.569443 | − | 0.569443i | 0.362529 | − | 0.931972i | \(-0.381913\pi\) |
−0.931972 | + | 0.362529i | \(0.881913\pi\) | |||||||
\(158\) | 0.586667 | + | 3.70407i | 0.0466727 | + | 0.294680i | ||||
\(159\) | −4.48577 | + | 7.65166i | −0.355745 | + | 0.606816i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.39223 | − | 2.72680i | 0.661401 | − | 0.214902i | ||||
\(162\) | 3.44758 | − | 8.31350i | 0.270867 | − | 0.653170i | ||||
\(163\) | 2.55156 | + | 5.00771i | 0.199853 | + | 0.392234i | 0.969082 | − | 0.246739i | \(-0.0793592\pi\) |
−0.769228 | + | 0.638974i | \(0.779359\pi\) | |||||||
\(164\) | −1.16567 | − | 3.58757i | −0.0910238 | − | 0.280143i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.21383 | − | 16.0465i | 0.404672 | − | 1.24545i | ||||
\(167\) | 16.5614 | − | 2.62306i | 1.28156 | − | 0.202979i | 0.521734 | − | 0.853109i | \(-0.325286\pi\) |
0.759823 | + | 0.650130i | \(0.225286\pi\) | |||||||
\(168\) | 3.93054 | + | 6.14150i | 0.303247 | + | 0.473827i | ||||
\(169\) | 5.80692 | − | 7.99254i | 0.446686 | − | 0.614810i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.47316 | − | 1.08751i | 0.418543 | − | 0.0831637i | ||||
\(172\) | 8.75104 | + | 1.38603i | 0.667260 | + | 0.105684i | ||||
\(173\) | 2.03214 | − | 3.98829i | 0.154500 | − | 0.303224i | −0.800763 | − | 0.598982i | \(-0.795572\pi\) |
0.955263 | + | 0.295758i | \(0.0955721\pi\) | |||||||
\(174\) | 2.10211 | − | 9.57614i | 0.159360 | − | 0.725966i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.98310i | 0.375615i | ||||||||
\(177\) | −14.9048 | − | 12.2346i | −1.12031 | − | 0.919610i | ||||
\(178\) | −0.177764 | + | 1.12236i | −0.0133240 | + | 0.0841243i | ||||
\(179\) | −0.141142 | + | 0.102546i | −0.0105495 | + | 0.00766463i | −0.593047 | − | 0.805167i | \(-0.702075\pi\) |
0.582498 | + | 0.812832i | \(0.302075\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.20445 | + | 6.68743i | 0.684162 | + | 0.497072i | 0.874736 | − | 0.484600i | \(-0.161035\pi\) |
−0.190574 | + | 0.981673i | \(0.561035\pi\) | |||||||
\(182\) | 5.25861 | − | 5.25861i | 0.389794 | − | 0.389794i | ||||
\(183\) | −16.7847 | − | 0.991580i | −1.24076 | − | 0.0732997i | ||||
\(184\) | 1.99350 | + | 0.647728i | 0.146963 | + | 0.0477511i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.1611 | − | 1.09811i | 0.818369 | − | 0.0805172i | ||||
\(187\) | 6.33665 | − | 3.22868i | 0.463382 | − | 0.236105i | ||||
\(188\) | −4.17108 | + | 2.12527i | −0.304207 | + | 0.155001i | ||||
\(189\) | 20.6652 | + | 7.17321i | 1.50317 | + | 0.521774i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.5527 | − | 5.70322i | −1.27007 | − | 0.412671i | −0.404998 | − | 0.914318i | \(-0.632728\pi\) |
−0.865072 | + | 0.501647i | \(0.832728\pi\) | |||||||
\(192\) | −0.102145 | + | 1.72904i | −0.00737171 | + | 0.124782i | ||||
\(193\) | −3.31568 | + | 3.31568i | −0.238668 | + | 0.238668i | −0.816298 | − | 0.577630i | \(-0.803977\pi\) |
0.577630 | + | 0.816298i | \(0.303977\pi\) | |||||||
\(194\) | −2.84422 | − | 2.06644i | −0.204203 | − | 0.148362i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.67458 | + | 6.30245i | −0.619613 | + | 0.450175i | ||||
\(197\) | −1.98370 | + | 12.5246i | −0.141333 | + | 0.892341i | 0.810503 | + | 0.585734i | \(0.199194\pi\) |
−0.951836 | + | 0.306607i | \(0.900806\pi\) | |||||||
\(198\) | 9.25260 | + | 11.7418i | 0.657554 | + | 0.834457i | ||||
\(199\) | 1.62602i | 0.115266i | 0.998338 | + | 0.0576328i | \(0.0183553\pi\) | ||||
−0.998338 | + | 0.0576328i | \(0.981645\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.9507 | − | 2.40385i | −0.772406 | − | 0.169555i | ||||
\(202\) | −7.56983 | + | 14.8566i | −0.532612 | + | 1.04531i | ||||
\(203\) | 23.5359 | + | 3.72772i | 1.65189 | + | 0.261634i | ||||
\(204\) | 2.26487 | − | 0.990397i | 0.158573 | − | 0.0693417i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.55935 | − | 2.14627i | 0.108645 | − | 0.149537i | ||||
\(207\) | 5.90005 | − | 2.17526i | 0.410082 | − | 0.151191i | ||||
\(208\) | 1.74480 | − | 0.276349i | 0.120980 | − | 0.0191613i | ||||
\(209\) | −2.86422 | + | 8.81517i | −0.198123 | + | 0.609758i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.73259 | − | 11.4877i | −0.256962 | − | 0.790848i | −0.993437 | − | 0.114383i | \(-0.963511\pi\) |
0.736475 | − | 0.676465i | \(-0.236489\pi\) | |||||||
\(212\) | −2.32483 | − | 4.56273i | −0.159670 | − | 0.313370i | ||||
\(213\) | 25.2538 | − | 6.58711i | 1.73036 | − | 0.451341i | ||||
\(214\) | −11.2316 | + | 3.64938i | −0.767778 | + | 0.249466i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.96978 | + | 4.26385i | 0.202068 | + | 0.290118i | ||||
\(217\) | 4.26413 | + | 26.9226i | 0.289468 | + | 1.82763i | ||||
\(218\) | −9.41758 | − | 9.41758i | −0.637839 | − | 0.637839i | ||||
\(219\) | −11.9717 | + | 10.6361i | −0.808975 | + | 0.718724i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.48191 | − | 2.03968i | −0.0996842 | − | 0.137204i | ||||
\(222\) | 1.62594 | − | 4.15298i | 0.109126 | − | 0.278730i | ||||
\(223\) | −5.54645 | − | 2.82606i | −0.371418 | − | 0.189247i | 0.258311 | − | 0.966062i | \(-0.416834\pi\) |
−0.629729 | + | 0.776815i | \(0.716834\pi\) | |||||||
\(224\) | −4.20979 | −0.281279 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.49661 | 0.0995528 | ||||||||
\(227\) | 8.15754 | + | 4.15647i | 0.541435 | + | 0.275875i | 0.703246 | − | 0.710947i | \(-0.251733\pi\) |
−0.161811 | + | 0.986822i | \(0.551733\pi\) | |||||||
\(228\) | −1.17452 | + | 2.99998i | −0.0777848 | + | 0.198678i | ||||
\(229\) | −10.8714 | − | 14.9632i | −0.718400 | − | 0.988793i | −0.999575 | − | 0.0291365i | \(-0.990724\pi\) |
0.281175 | − | 0.959656i | \(-0.409276\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −27.1630 | + | 24.1326i | −1.78719 | + | 1.58781i | ||||
\(232\) | 4.00253 | + | 4.00253i | 0.262779 | + | 0.262779i | ||||
\(233\) | −2.15478 | − | 13.6047i | −0.141164 | − | 0.891276i | −0.952021 | − | 0.306032i | \(-0.900999\pi\) |
0.810857 | − | 0.585244i | \(-0.199001\pi\) | |||||||
\(234\) | 3.59820 | − | 3.89090i | 0.235222 | − | 0.254356i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.5882 | − | 3.44032i | 0.689234 | − | 0.223946i | ||||
\(237\) | −6.28531 | + | 1.63944i | −0.408275 | + | 0.106493i | ||||
\(238\) | 2.72764 | + | 5.35329i | 0.176806 | + | 0.347002i | ||||
\(239\) | −6.40747 | − | 19.7202i | −0.414465 | − | 1.27559i | −0.912729 | − | 0.408566i | \(-0.866029\pi\) |
0.498264 | − | 0.867025i | \(-0.333971\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.92274 | + | 5.91757i | −0.123854 | + | 0.381184i | −0.993691 | − | 0.112156i | \(-0.964224\pi\) |
0.869836 | + | 0.493340i | \(0.164224\pi\) | |||||||
\(242\) | −13.6610 | + | 2.16369i | −0.878163 | + | 0.139087i | ||||
\(243\) | 14.9149 | + | 4.53278i | 0.956791 | + | 0.290778i | ||||
\(244\) | 5.70595 | − | 7.85356i | 0.365286 | − | 0.502773i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.98631 | − | 2.61773i | 0.381673 | − | 0.166900i | ||||
\(247\) | 3.24541 | + | 0.514023i | 0.206501 | + | 0.0327065i | ||||
\(248\) | −2.93957 | + | 5.76923i | −0.186663 | + | 0.366346i | ||||
\(249\) | 28.5441 | + | 6.26585i | 1.80891 | + | 0.397082i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.76896i | 0.237895i | 0.992901 | + | 0.118947i | \(0.0379520\pi\) | ||||
−0.992901 | + | 0.118947i | \(0.962048\pi\) | |||||||
\(252\) | −9.91968 | + | 7.81673i | −0.624881 | + | 0.492408i | ||||
\(253\) | −1.63396 | + | 10.3164i | −0.102726 | + | 0.648589i | ||||
\(254\) | 1.25516 | − | 0.911927i | 0.0787557 | − | 0.0572194i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 21.7693 | − | 21.7693i | 1.35793 | − | 1.35793i | 0.481471 | − | 0.876462i | \(-0.340103\pi\) |
0.876462 | − | 0.481471i | \(-0.159897\pi\) | |||||||
\(258\) | −0.905021 | + | 15.3195i | −0.0563441 | + | 0.953749i | ||||
\(259\) | 10.3094 | + | 3.34973i | 0.640596 | + | 0.208142i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.8632 | + | 1.99941i | 1.04380 | + | 0.123760i | ||||
\(262\) | −5.67316 | + | 2.89062i | −0.350489 | + | 0.178583i | ||||
\(263\) | 4.93937 | − | 2.51673i | 0.304574 | − | 0.155188i | −0.295023 | − | 0.955490i | \(-0.595327\pi\) |
0.599598 | + | 0.800302i | \(0.295327\pi\) | |||||||
\(264\) | −8.58951 | + | 0.845099i | −0.528648 | + | 0.0520123i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.44718 | − | 2.41974i | −0.456616 | − | 0.148364i | ||||
\(267\) | −1.96479 | − | 0.116073i | −0.120243 | − | 0.00710354i | ||||
\(268\) | 4.57707 | − | 4.57707i | 0.279589 | − | 0.279589i | ||||
\(269\) | 2.80188 | + | 2.03568i | 0.170834 | + | 0.124118i | 0.669917 | − | 0.742436i | \(-0.266330\pi\) |
−0.499083 | + | 0.866554i | \(0.666330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.81142 | + | 2.76916i | −0.231528 | + | 0.168215i | −0.697500 | − | 0.716584i | \(-0.745704\pi\) |
0.465973 | + | 0.884799i | \(0.345704\pi\) | |||||||
\(272\) | −0.223260 | + | 1.40961i | −0.0135371 | + | 0.0854701i | ||||
\(273\) | 9.95623 | + | 8.17259i | 0.602579 | + | 0.494627i | ||||
\(274\) | 4.10910i | 0.248240i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.778423 | + | 3.54611i | −0.0468556 | + | 0.213450i | ||||
\(277\) | 11.2980 | − | 22.1735i | 0.678829 | − | 1.33228i | −0.252321 | − | 0.967644i | \(-0.581194\pi\) |
0.931151 | − | 0.364634i | \(-0.118806\pi\) | |||||||
\(278\) | −10.5496 | − | 1.67090i | −0.632725 | − | 0.100214i | ||||
\(279\) | 3.78568 | + | 19.0524i | 0.226643 | + | 1.14064i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.67900 | − | 7.81648i | 0.338781 | − | 0.466292i | −0.605304 | − | 0.795994i | \(-0.706948\pi\) |
0.944085 | + | 0.329702i | \(0.106948\pi\) | |||||||
\(282\) | −4.37078 | − | 6.82938i | −0.260276 | − | 0.406684i | ||||
\(283\) | −1.00775 | + | 0.159612i | −0.0599044 | + | 0.00948793i | −0.186315 | − | 0.982490i | \(-0.559654\pi\) |
0.126410 | + | 0.991978i | \(0.459654\pi\) | |||||||
\(284\) | −4.65630 | + | 14.3306i | −0.276301 | + | 0.850366i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.72024 | + | 8.37203i | 0.160851 | + | 0.495049i | ||||
\(287\) | 7.20945 | + | 14.1493i | 0.425561 | + | 0.835210i | ||||
\(288\) | −2.99771 | + | 0.117162i | −0.176642 | + | 0.00690381i | ||||
\(289\) | −14.2308 | + | 4.62387i | −0.837106 | + | 0.271992i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.07963 | − | 5.25311i | 0.180531 | − | 0.307943i | ||||
\(292\) | −1.44635 | − | 9.13189i | −0.0846412 | − | 0.534403i | ||||
\(293\) | 1.45604 | + | 1.45604i | 0.0850625 | + | 0.0850625i | 0.748358 | − | 0.663295i | \(-0.230843\pi\) |
−0.663295 | + | 0.748358i | \(0.730843\pi\) | |||||||
\(294\) | −12.3349 | − | 13.8838i | −0.719384 | − | 0.809718i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.51351 | + | 2.08317i | 0.0879710 | + | 0.121082i | ||||
\(297\) | −18.6706 | + | 17.9403i | −1.08338 | + | 1.04100i | ||||
\(298\) | −4.57327 | − | 2.33020i | −0.264922 | − | 0.134985i | ||||
\(299\) | 3.70284 | 0.214141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −37.2993 | −2.14990 | ||||||||
\(302\) | −17.9372 | − | 9.13947i | −1.03217 | − | 0.525917i | ||||
\(303\) | −26.8926 | − | 10.5288i | −1.54494 | − | 0.604861i | ||||
\(304\) | −1.09331 | − | 1.50481i | −0.0627057 | − | 0.0863069i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.09128 | + | 3.73606i | 0.119551 | + | 0.213576i | ||||
\(307\) | −11.9806 | − | 11.9806i | −0.683767 | − | 0.683767i | 0.277080 | − | 0.960847i | \(-0.410633\pi\) |
−0.960847 | + | 0.277080i | \(0.910633\pi\) | |||||||
\(308\) | −3.28166 | − | 20.7196i | −0.186990 | − | 1.18061i | ||||
\(309\) | 3.96403 | + | 2.32391i | 0.225506 | + | 0.132203i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.64396 | + | 1.18399i | −0.206630 | + | 0.0671381i | −0.410503 | − | 0.911859i | \(-0.634647\pi\) |
0.203873 | + | 0.978997i | \(0.434647\pi\) | |||||||
\(312\) | 0.772255 | + | 2.96069i | 0.0437203 | + | 0.167616i | ||||
\(313\) | −10.3817 | − | 20.3753i | −0.586809 | − | 1.15168i | −0.973333 | − | 0.229398i | \(-0.926324\pi\) |
0.386523 | − | 0.922280i | \(-0.373676\pi\) | |||||||
\(314\) | 3.11815 | + | 9.59669i | 0.175968 | + | 0.541573i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.15889 | − | 3.56669i | 0.0651926 | − | 0.200642i | ||||
\(317\) | 8.64943 | − | 1.36994i | 0.485800 | − | 0.0769432i | 0.0912701 | − | 0.995826i | \(-0.470907\pi\) |
0.394530 | + | 0.918883i | \(0.370907\pi\) | |||||||
\(318\) | 7.47063 | − | 4.78118i | 0.418932 | − | 0.268115i | ||||
\(319\) | −16.5794 | + | 22.8195i | −0.928266 | + | 1.27765i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.19534 | − | 18.7414i | −0.457419 | − | 1.04604i | ||||
\(322\) | −8.71548 | − | 1.38040i | −0.485695 | − | 0.0769265i | ||||
\(323\) | −1.20518 | + | 2.36529i | −0.0670578 | + | 0.131608i | ||||
\(324\) | −6.84606 | + | 5.84221i | −0.380337 | + | 0.324567i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 5.62029i | − | 0.311279i | ||||||
\(327\) | 14.6362 | − | 17.8305i | 0.809383 | − | 0.986029i | ||||
\(328\) | −0.590102 | + | 3.72576i | −0.0325829 | + | 0.205721i | ||||
\(329\) | 15.9436 | − | 11.5837i | 0.878999 | − | 0.638630i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.85309 | + | 3.52598i | 0.266750 | + | 0.193805i | 0.713118 | − | 0.701044i | \(-0.247283\pi\) |
−0.446367 | + | 0.894850i | \(0.647283\pi\) | |||||||
\(332\) | −11.9305 | + | 11.9305i | −0.654773 | + | 0.654773i | ||||
\(333\) | 7.43435 | + | 2.09836i | 0.407400 | + | 0.114989i | ||||
\(334\) | −15.9471 | − | 5.18154i | −0.872588 | − | 0.283521i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.713952 | − | 7.25654i | −0.0389493 | − | 0.395877i | ||||
\(337\) | −2.16556 | + | 1.10341i | −0.117965 | + | 0.0601063i | −0.511977 | − | 0.858999i | \(-0.671087\pi\) |
0.394012 | + | 0.919105i | \(0.371087\pi\) | |||||||
\(338\) | −8.80254 | + | 4.48512i | −0.478795 | + | 0.243958i | ||||
\(339\) | 0.253814 | + | 2.57974i | 0.0137853 | + | 0.140112i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.6862 | − | 9.97055i | −1.66175 | − | 0.539935i | ||||
\(342\) | −5.37034 | − | 1.51579i | −0.290394 | − | 0.0819643i | ||||
\(343\) | 11.0807 | − | 11.0807i | 0.598299 | − | 0.598299i | ||||
\(344\) | −7.16799 | − | 5.20785i | −0.386472 | − | 0.280788i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.62129 | + | 2.63102i | −0.194682 | + | 0.141445i | ||||
\(347\) | −3.55504 | + | 22.4456i | −0.190844 | + | 1.20494i | 0.687237 | + | 0.726433i | \(0.258823\pi\) |
−0.878082 | + | 0.478511i | \(0.841177\pi\) | |||||||
\(348\) | −6.22047 | + | 7.57807i | −0.333452 | + | 0.406227i | ||||
\(349\) | − | 12.5328i | − | 0.670865i | −0.942064 | − | 0.335432i | \(-0.891118\pi\) | ||
0.942064 | − | 0.335432i | \(-0.108882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.31708 | + | 5.54245i | 0.390557 | + | 0.295834i | ||||
\(352\) | 2.26228 | − | 4.43998i | 0.120580 | − | 0.236651i | ||||
\(353\) | 7.05688 | + | 1.11770i | 0.375600 | + | 0.0594892i | 0.341381 | − | 0.939925i | \(-0.389106\pi\) |
0.0342193 | + | 0.999414i | \(0.489106\pi\) | |||||||
\(354\) | 7.72587 | + | 17.6678i | 0.410625 | + | 0.939031i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.667929 | − | 0.919325i | 0.0354002 | − | 0.0487241i | ||||
\(357\) | −8.76503 | + | 5.60959i | −0.463894 | + | 0.296891i | ||||
\(358\) | 0.172313 | − | 0.0272918i | 0.00910704 | − | 0.00144241i | ||||
\(359\) | −3.28973 | + | 10.1247i | −0.173625 | + | 0.534363i | −0.999568 | − | 0.0293907i | \(-0.990643\pi\) |
0.825943 | + | 0.563754i | \(0.190643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.80219 | + | 14.7796i | 0.252747 | + | 0.777875i | ||||
\(362\) | −5.16520 | − | 10.1373i | −0.271477 | − | 0.532803i | ||||
\(363\) | −6.04643 | − | 23.1809i | −0.317355 | − | 1.21668i | ||||
\(364\) | −7.07281 | + | 2.29810i | −0.370716 | + | 0.120453i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.5051 | + | 8.50359i | 0.758193 | + | 0.444490i | ||||
\(367\) | 0.656708 | + | 4.14629i | 0.0342799 | + | 0.216435i | 0.998882 | − | 0.0472753i | \(-0.0150538\pi\) |
−0.964602 | + | 0.263710i | \(0.915054\pi\) | |||||||
\(368\) | −1.48216 | − | 1.48216i | −0.0772630 | − | 0.0772630i | ||||
\(369\) | 5.52749 | + | 9.87483i | 0.287750 | + | 0.514063i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.6714 | + | 17.4406i | 0.657865 | + | 0.905473i | ||||
\(372\) | −10.4431 | − | 4.08860i | −0.541450 | − | 0.211984i | ||||
\(373\) | 4.05536 | + | 2.06631i | 0.209979 | + | 0.106990i | 0.555817 | − | 0.831305i | \(-0.312405\pi\) |
−0.345838 | + | 0.938294i | \(0.612405\pi\) | |||||||
\(374\) | −7.11179 | −0.367742 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.68132 | 0.241420 | ||||||||
\(377\) | 8.90954 | + | 4.53964i | 0.458864 | + | 0.233803i | ||||
\(378\) | −15.1562 | − | 15.7732i | −0.779552 | − | 0.811284i | ||||
\(379\) | −19.3891 | − | 26.6869i | −0.995954 | − | 1.37081i | −0.927775 | − | 0.373139i | \(-0.878281\pi\) |
−0.0681783 | − | 0.997673i | \(-0.521719\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.78478 | + | 2.00890i | 0.0914371 | + | 0.102919i | ||||
\(382\) | 13.0504 | + | 13.0504i | 0.667715 | + | 0.667715i | ||||
\(383\) | 2.67339 | + | 16.8791i | 0.136604 | + | 0.862482i | 0.956873 | + | 0.290505i | \(0.0938233\pi\) |
−0.820270 | + | 0.571977i | \(0.806177\pi\) | |||||||
\(384\) | 0.875978 | − | 1.49421i | 0.0447021 | − | 0.0762511i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.45958 | − | 1.44901i | 0.226987 | − | 0.0737525i | ||||
\(387\) | −26.5601 | + | 1.03807i | −1.35012 | + | 0.0527679i | ||||
\(388\) | 1.59607 | + | 3.13246i | 0.0810281 | + | 0.159027i | ||||
\(389\) | −4.34112 | − | 13.3606i | −0.220104 | − | 0.677409i | −0.998752 | − | 0.0499484i | \(-0.984094\pi\) |
0.778648 | − | 0.627461i | \(-0.215906\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.924425 | + | 2.84509i | −0.0467502 | + | 0.143882i | ||||
\(392\) | 10.5904 | − | 1.67735i | 0.534894 | − | 0.0847189i | ||||
\(393\) | −5.94477 | − | 9.28875i | −0.299874 | − | 0.468556i | ||||
\(394\) | 7.45354 | − | 10.2589i | 0.375504 | − | 0.516837i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.91344 | − | 14.6627i | −0.146406 | − | 0.736826i | ||||
\(397\) | −3.64376 | − | 0.577115i | −0.182875 | − | 0.0289646i | 0.0643251 | − | 0.997929i | \(-0.479511\pi\) |
−0.247200 | + | 0.968964i | \(0.579511\pi\) | |||||||
\(398\) | 0.738199 | − | 1.44880i | 0.0370026 | − | 0.0726216i | ||||
\(399\) | 2.90798 | − | 13.2473i | 0.145581 | − | 0.663194i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.3144i | 1.46389i | 0.681364 | + | 0.731945i | \(0.261387\pi\) | ||||
−0.681364 | + | 0.731945i | \(0.738613\pi\) | |||||||
\(402\) | 8.66586 | + | 7.11338i | 0.432214 | + | 0.354783i | ||||
\(403\) | −1.78935 | + | 11.2975i | −0.0891336 | + | 0.562768i | ||||
\(404\) | 13.4895 | − | 9.80073i | 0.671130 | − | 0.487604i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.2783 | − | 14.0065i | −0.956764 | − | 0.695130i | ||||
\(407\) | −9.07301 | + | 9.07301i | −0.449732 | + | 0.449732i | ||||
\(408\) | −2.46765 | − | 0.145780i | −0.122167 | − | 0.00721718i | ||||
\(409\) | −7.27469 | − | 2.36369i | −0.359710 | − | 0.116877i | 0.123586 | − | 0.992334i | \(-0.460561\pi\) |
−0.483296 | + | 0.875457i | \(0.660561\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.08297 | + | 0.696875i | −0.349377 | + | 0.0343743i | ||||
\(412\) | −2.36378 | + | 1.20440i | −0.116455 | + | 0.0593368i | ||||
\(413\) | −41.7598 | + | 21.2777i | −2.05487 | + | 1.04701i | ||||
\(414\) | −6.24454 | − | 0.740395i | −0.306902 | − | 0.0363884i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.68008 | − | 0.545893i | −0.0823729 | − | 0.0267646i | ||||
\(417\) | 1.09103 | − | 18.4681i | 0.0534279 | − | 0.904385i | ||||
\(418\) | 6.55405 | − | 6.55405i | 0.320569 | − | 0.320569i | ||||
\(419\) | 8.86483 | + | 6.44067i | 0.433075 | + | 0.314648i | 0.782877 | − | 0.622176i | \(-0.213751\pi\) |
−0.349802 | + | 0.936824i | \(0.613751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3681 | + | 8.25943i | −0.554048 | + | 0.402540i | −0.829276 | − | 0.558839i | \(-0.811247\pi\) |
0.275227 | + | 0.961379i | \(0.411247\pi\) | |||||||
\(422\) | −1.88956 | + | 11.9302i | −0.0919823 | + | 0.580753i | ||||
\(423\) | 11.0307 | − | 8.69225i | 0.536333 | − | 0.422632i | ||||
\(424\) | 5.12087i | 0.248692i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −25.4918 | − | 5.59582i | −1.23508 | − | 0.271119i | ||||
\(427\) | −18.5531 | + | 36.4125i | −0.897848 | + | 1.76213i | ||||
\(428\) | 11.6642 | + | 1.84743i | 0.563812 | + | 0.0892991i | ||||
\(429\) | −13.9698 | + | 6.10879i | −0.674467 | + | 0.294935i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.55158 | − | 3.51195i | 0.122905 | − | 0.169164i | −0.743131 | − | 0.669146i | \(-0.766660\pi\) |
0.866036 | + | 0.499982i | \(0.166660\pi\) | |||||||
\(432\) | −0.710346 | − | 5.14737i | −0.0341765 | − | 0.247653i | ||||
\(433\) | 7.75206 | − | 1.22781i | 0.372540 | − | 0.0590046i | 0.0326428 | − | 0.999467i | \(-0.489608\pi\) |
0.339897 | + | 0.940463i | \(0.389608\pi\) | |||||||
\(434\) | 8.42326 | − | 25.9241i | 0.404329 | − | 1.24440i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.11563 | + | 12.6666i | 0.197103 | + | 0.606621i | ||||
\(437\) | −1.77004 | − | 3.47389i | −0.0846723 | − | 0.166179i | ||||
\(438\) | 15.4956 | − | 4.04182i | 0.740409 | − | 0.193126i | ||||
\(439\) | 19.1294 | − | 6.21551i | 0.912994 | − | 0.296650i | 0.185405 | − | 0.982662i | \(-0.440640\pi\) |
0.727590 | + | 0.686012i | \(0.240640\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.8399 | − | 23.6165i | 1.04000 | − | 1.12460i | ||||
\(442\) | 0.394399 | + | 2.49014i | 0.0187597 | + | 0.118444i | ||||
\(443\) | 11.8995 | + | 11.8995i | 0.565363 | + | 0.565363i | 0.930826 | − | 0.365463i | \(-0.119089\pi\) |
−0.365463 | + | 0.930826i | \(0.619089\pi\) | |||||||
\(444\) | −3.33413 | + | 2.96217i | −0.158231 | + | 0.140578i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.65892 | + | 5.03607i | 0.173255 | + | 0.238465i | ||||
\(447\) | 3.24103 | − | 8.27826i | 0.153296 | − | 0.391548i | ||||
\(448\) | 3.75095 | + | 1.91121i | 0.177216 | + | 0.0902960i | ||||
\(449\) | −3.55771 | −0.167899 | −0.0839495 | − | 0.996470i | \(-0.526753\pi\) | ||||
−0.0839495 | + | 0.996470i | \(0.526753\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.7973 | −0.885128 | ||||||||
\(452\) | −1.33349 | − | 0.679445i | −0.0627219 | − | 0.0319584i | ||||
\(453\) | 12.7119 | − | 32.4689i | 0.597259 | − | 1.52552i | ||||
\(454\) | −5.38142 | − | 7.40689i | −0.252563 | − | 0.347623i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.40847 | − | 2.13978i | 0.112787 | − | 0.100204i | ||||
\(457\) | −13.4412 | − | 13.4412i | −0.628754 | − | 0.628754i | 0.319001 | − | 0.947754i | \(-0.396653\pi\) |
−0.947754 | + | 0.319001i | \(0.896653\pi\) | |||||||
\(458\) | 2.89333 | + | 18.2678i | 0.135196 | + | 0.853597i | ||||
\(459\) | −6.08528 | + | 4.23841i | −0.284037 | + | 0.197832i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.4642 | + | 9.89843i | −1.41886 | + | 0.461016i | −0.915240 | − | 0.402908i | \(-0.867999\pi\) |
−0.503621 | + | 0.863925i | \(0.667999\pi\) | |||||||
\(462\) | 35.1583 | − | 9.17058i | 1.63571 | − | 0.426654i | ||||
\(463\) | −1.40792 | − | 2.76320i | −0.0654317 | − | 0.128417i | 0.855974 | − | 0.517019i | \(-0.172958\pi\) |
−0.921406 | + | 0.388602i | \(0.872958\pi\) | |||||||
\(464\) | −1.74917 | − | 5.38339i | −0.0812031 | − | 0.249918i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.25650 | + | 13.1002i | −0.197179 | + | 0.606853i | ||||
\(467\) | −39.1577 | + | 6.20197i | −1.81200 | + | 0.286993i | −0.968295 | − | 0.249811i | \(-0.919632\pi\) |
−0.843707 | + | 0.536804i | \(0.819632\pi\) | |||||||
\(468\) | −4.97245 | + | 1.83327i | −0.229852 | + | 0.0847429i | ||||
\(469\) | −16.0170 | + | 22.0455i | −0.739598 | + | 1.01797i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.0133 | + | 7.00238i | −0.737852 | + | 0.322653i | ||||
\(472\) | −10.9960 | − | 1.74160i | −0.506134 | − | 0.0801638i | ||||
\(473\) | 20.0441 | − | 39.3387i | 0.921628 | − | 1.80880i | ||||
\(474\) | 6.34454 | + | 1.39272i | 0.291415 | + | 0.0639698i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 6.00814i | − | 0.275383i | ||||||
\(477\) | 9.50842 | + | 12.0665i | 0.435361 | + | 0.552486i | ||||
\(478\) | −3.24367 | + | 20.4797i | −0.148362 | + | 0.936721i | ||||
\(479\) | −10.9031 | + | 7.92157i | −0.498176 | + | 0.361946i | −0.808320 | − | 0.588744i | \(-0.799623\pi\) |
0.310144 | + | 0.950690i | \(0.399623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.68001 | + | 2.67368i | 0.167794 | + | 0.121910i | ||||
\(482\) | 4.39969 | − | 4.39969i | 0.200400 | − | 0.200400i | ||||
\(483\) | 0.901343 | − | 15.2572i | 0.0410125 | − | 0.694227i | ||||
\(484\) | 13.1543 | + | 4.27411i | 0.597925 | + | 0.194278i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11.2314 | − | 10.8100i | −0.509468 | − | 0.490349i | ||||
\(487\) | −1.85919 | + | 0.947305i | −0.0842480 | + | 0.0429265i | −0.495607 | − | 0.868547i | \(-0.665054\pi\) |
0.411359 | + | 0.911473i | \(0.365054\pi\) | |||||||
\(488\) | −8.64948 | + | 4.40713i | −0.391543 | + | 0.199501i | ||||
\(489\) | 9.68785 | − | 0.953162i | 0.438100 | − | 0.0431035i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8067 | + | 5.13592i | 0.713348 | + | 0.231781i | 0.643137 | − | 0.765751i | \(-0.277633\pi\) |
0.0702111 | + | 0.997532i | \(0.477633\pi\) | |||||||
\(492\) | −6.52227 | − | 0.385313i | −0.294047 | − | 0.0173712i | ||||
\(493\) | −5.71233 | + | 5.71233i | −0.257270 | + | 0.257270i | ||||
\(494\) | −2.65832 | − | 1.93138i | −0.119604 | − | 0.0868970i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.23835 | − | 3.80588i | 0.235209 | − | 0.170889i | ||||
\(497\) | 9.92321 | − | 62.6527i | 0.445117 | − | 2.81036i | ||||
\(498\) | −22.5883 | − | 18.5416i | −1.01221 | − | 0.830871i | ||||
\(499\) | 36.0457i | 1.61363i | 0.590806 | + | 0.806813i | \(0.298810\pi\) | ||||
−0.590806 | + | 0.806813i | \(0.701190\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.22704 | − | 28.3673i | 0.278203 | − | 1.26736i | ||||
\(502\) | 1.71107 | − | 3.35817i | 0.0763689 | − | 0.149882i | ||||
\(503\) | 31.1126 | + | 4.92776i | 1.38724 | + | 0.219718i | 0.804990 | − | 0.593289i | \(-0.202171\pi\) |
0.582255 | + | 0.813007i | \(0.302171\pi\) | |||||||
\(504\) | 12.3872 | − | 2.46132i | 0.551771 | − | 0.109636i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.13944 | − | 8.45021i | 0.272931 | − | 0.375658i | ||||
\(507\) | −9.22397 | − | 14.4125i | −0.409651 | − | 0.640083i | ||||
\(508\) | −1.53236 | + | 0.242702i | −0.0679876 | + | 0.0107682i | ||||
\(509\) | 0.189892 | − | 0.584428i | 0.00841683 | − | 0.0259043i | −0.946760 | − | 0.321941i | \(-0.895665\pi\) |
0.955177 | + | 0.296036i | \(0.0956649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0277 | + | 37.0176i | 0.532076 | + | 1.63756i | ||||
\(512\) | 0.453990 | + | 0.891007i | 0.0200637 | + | 0.0393773i | ||||
\(513\) | 1.70203 | − | 9.51406i | 0.0751465 | − | 0.420056i | ||||
\(514\) | −29.2797 | + | 9.51354i | −1.29147 | + | 0.419624i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.76127 | − | 13.2389i | 0.341671 | − | 0.582809i | ||||
\(517\) | 3.64922 | + | 23.0403i | 0.160493 | + | 1.01331i | ||||
\(518\) | −7.66501 | − | 7.66501i | −0.336781 | − | 0.336781i | ||||
\(519\) | −5.14932 | − | 5.79592i | −0.226030 | − | 0.254413i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.3712 | + | 26.6622i | 0.848668 | + | 1.16809i | 0.984155 | + | 0.177312i | \(0.0567401\pi\) |
−0.135487 | + | 0.990779i | \(0.543260\pi\) | |||||||
\(522\) | −14.1175 | − | 9.43721i | −0.617905 | − | 0.413055i | ||||
\(523\) | 35.5580 | + | 18.1177i | 1.55484 | + | 0.792232i | 0.999231 | − | 0.0392100i | \(-0.0124841\pi\) |
0.555612 | + | 0.831442i | \(0.312484\pi\) | |||||||
\(524\) | 6.36713 | 0.278150 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.54358 | −0.241712 | ||||||||
\(527\) | −8.23373 | − | 4.19530i | −0.358667 | − | 0.182750i | ||||
\(528\) | 8.03698 | + | 3.14657i | 0.349765 | + | 0.136937i | ||||
\(529\) | 10.9366 | + | 15.0529i | 0.475503 | + | 0.654474i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.1442 | + | 16.3136i | −1.26475 | + | 0.707951i | ||||
\(532\) | 5.53695 | + | 5.53695i | 0.240057 | + | 0.240057i | ||||
\(533\) | 1.04244 | + | 6.58172i | 0.0451532 | + | 0.285086i | ||||
\(534\) | 1.69794 | + | 0.995416i | 0.0734771 | + | 0.0430759i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.15614 | + | 2.00025i | −0.265905 | + | 0.0863977i | ||||
\(537\) | 0.0762667 | + | 0.292393i | 0.00329115 | + | 0.0126177i | ||||
\(538\) | −1.57231 | − | 3.08583i | −0.0677872 | − | 0.133040i | ||||
\(539\) | 16.5110 | + | 50.8156i | 0.711178 | + | 2.18878i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.82078 | − | 24.0699i | 0.336242 | − | 1.03485i | −0.629865 | − | 0.776704i | \(-0.716890\pi\) |
0.966107 | − | 0.258141i | \(-0.0831100\pi\) | |||||||
\(542\) | 4.65318 | − | 0.736991i | 0.199871 | − | 0.0316565i | ||||
\(543\) | 16.5979 | − | 10.6226i | 0.712285 | − | 0.455860i | ||||
\(544\) | 0.838876 | − | 1.15461i | 0.0359665 | − | 0.0495036i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.16079 | − | 11.8019i | −0.220861 | − | 0.505073i | ||||
\(547\) | 40.6790 | + | 6.44292i | 1.73931 | + | 0.275479i | 0.943812 | − | 0.330482i | \(-0.107211\pi\) |
0.795495 | + | 0.605961i | \(0.207211\pi\) | |||||||
\(548\) | 1.86549 | − | 3.66124i | 0.0796899 | − | 0.156400i | ||||
\(549\) | −12.1979 | + | 26.4450i | −0.520594 | + | 1.12864i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.5287i | − | 0.448537i | ||||||
\(552\) | 2.30348 | − | 2.80621i | 0.0980425 | − | 0.119440i | ||||
\(553\) | −2.46975 | + | 15.5934i | −0.105024 | + | 0.663098i | ||||
\(554\) | −20.1331 | + | 14.6276i | −0.855375 | + | 0.621466i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.64122 | + | 6.27821i | 0.366469 | + | 0.266256i | ||||
\(557\) | −17.7694 | + | 17.7694i | −0.752915 | + | 0.752915i | −0.975022 | − | 0.222107i | \(-0.928707\pi\) |
0.222107 | + | 0.975022i | \(0.428707\pi\) | |||||||
\(558\) | 5.27655 | − | 18.6945i | 0.223374 | − | 0.791400i | ||||
\(559\) | −14.8858 | − | 4.83667i | −0.629600 | − | 0.204570i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.20611 | − | 12.2588i | −0.0509220 | − | 0.517566i | ||||
\(562\) | −8.60864 | + | 4.38632i | −0.363133 | + | 0.185026i | ||||
\(563\) | −9.23868 | + | 4.70734i | −0.389364 | + | 0.198391i | −0.637703 | − | 0.770282i | \(-0.720115\pi\) |
0.248339 | + | 0.968673i | \(0.420115\pi\) | |||||||
\(564\) | 0.793919 | + | 8.06931i | 0.0334300 | + | 0.339779i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.970373 | + | 0.315293i | 0.0407878 | + | 0.0132528i | ||||
\(567\) | 24.6183 | − | 28.8002i | 1.03387 | − | 1.20950i | ||||
\(568\) | 10.6548 | − | 10.6548i | 0.447064 | − | 0.447064i | ||||
\(569\) | 15.6879 | + | 11.3979i | 0.657671 | + | 0.477826i | 0.865876 | − | 0.500259i | \(-0.166762\pi\) |
−0.208205 | + | 0.978085i | \(0.566762\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.7088 | − | 10.6866i | 0.615544 | − | 0.447219i | −0.235818 | − | 0.971797i | \(-0.575777\pi\) |
0.851362 | + | 0.524579i | \(0.175777\pi\) | |||||||
\(572\) | 1.37707 | − | 8.69450i | 0.0575783 | − | 0.363535i | ||||
\(573\) | −20.2820 | + | 24.7086i | −0.847295 | + | 1.03221i | ||||
\(574\) | − | 15.8802i | − | 0.662826i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.72417 | + | 1.25654i | 0.113507 | + | 0.0523559i | ||||
\(577\) | 2.69918 | − | 5.29743i | 0.112368 | − | 0.220535i | −0.827973 | − | 0.560768i | \(-0.810506\pi\) |
0.940341 | + | 0.340233i | \(0.110506\pi\) | |||||||
\(578\) | 14.7789 | + | 2.34075i | 0.614723 | + | 0.0973625i | ||||
\(579\) | 3.25401 | + | 7.44137i | 0.135232 | + | 0.309253i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.7498 | − | 57.4636i | 1.73207 | − | 2.38399i | ||||
\(582\) | −5.12883 | + | 3.28243i | −0.212597 | + | 0.136061i | ||||
\(583\) | −25.2037 | + | 3.99187i | −1.04383 | + | 0.165326i | ||||
\(584\) | −2.85708 | + | 8.79320i | −0.118227 | + | 0.363865i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.636311 | − | 1.95836i | −0.0262858 | − | 0.0808992i | ||||
\(587\) | 11.8794 | + | 23.3146i | 0.490314 | + | 0.962295i | 0.995083 | + | 0.0990406i | \(0.0315774\pi\) |
−0.504770 | + | 0.863254i | \(0.668423\pi\) | |||||||
\(588\) | 4.68734 | + | 17.9704i | 0.193303 | + | 0.741088i | ||||
\(589\) | 11.4543 | − | 3.72172i | 0.471966 | − | 0.153351i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.9476 | + | 11.1080i | 0.779402 | + | 0.456923i | ||||
\(592\) | −0.402809 | − | 2.54323i | −0.0165553 | − | 0.104526i | ||||
\(593\) | −23.6228 | − | 23.6228i | −0.970072 | − | 0.970072i | 0.0294930 | − | 0.999565i | \(-0.490611\pi\) |
−0.999565 | + | 0.0294930i | \(0.990611\pi\) | |||||||
\(594\) | 24.7803 | − | 7.50867i | 1.01675 | − | 0.308084i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.01693 | + | 4.15244i | 0.123578 | + | 0.170091i | ||||
\(597\) | 2.62253 | + | 1.02675i | 0.107333 | + | 0.0420220i | ||||
\(598\) | −3.29926 | − | 1.68106i | −0.134917 | − | 0.0687435i | ||||
\(599\) | −7.73976 | −0.316238 | −0.158119 | − | 0.987420i | \(-0.550543\pi\) | ||||
−0.158119 | + | 0.987420i | \(0.550543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.7407 | −0.682866 | −0.341433 | − | 0.939906i | \(-0.610912\pi\) | ||||
−0.341433 | + | 0.939906i | \(0.610912\pi\) | |||||||
\(602\) | 33.2339 | + | 16.9335i | 1.35451 | + | 0.690159i | ||||
\(603\) | −10.7919 | + | 16.1440i | −0.439479 | + | 0.657433i | ||||
\(604\) | 11.8329 | + | 16.2867i | 0.481476 | + | 0.662695i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 19.1815 | + | 21.5902i | 0.779196 | + | 0.877041i | ||||
\(607\) | 22.6982 | + | 22.6982i | 0.921293 | + | 0.921293i | 0.997121 | − | 0.0758281i | \(-0.0241600\pi\) |
−0.0758281 | + | 0.997121i | \(0.524160\pi\) | |||||||
\(608\) | 0.290976 | + | 1.83715i | 0.0118006 | + | 0.0745063i | ||||
\(609\) | 20.8739 | − | 35.6059i | 0.845853 | − | 1.44282i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.86501 | − | 2.55550i | 0.318184 | − | 0.103384i | ||||
\(612\) | −0.167211 | − | 4.27828i | −0.00675909 | − | 0.172939i | ||||
\(613\) | 19.6701 | + | 38.6048i | 0.794470 | + | 1.55923i | 0.828616 | + | 0.559818i | \(0.189129\pi\) |
−0.0341460 | + | 0.999417i | \(0.510871\pi\) | |||||||
\(614\) | 5.23570 | + | 16.1138i | 0.211296 | + | 0.650301i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.48251 | + | 19.9511i | −0.261188 | + | 0.803853i | ||||
\(617\) | 24.0808 | − | 3.81403i | 0.969458 | − | 0.153547i | 0.348429 | − | 0.937335i | \(-0.386715\pi\) |
0.621028 | + | 0.783788i | \(0.286715\pi\) | |||||||
\(618\) | −2.47695 | − | 3.87025i | −0.0996374 | − | 0.155684i | ||||
\(619\) | 23.7633 | − | 32.7074i | 0.955130 | − | 1.31462i | 0.00591868 | − | 0.999982i | \(-0.498116\pi\) |
0.949211 | − | 0.314641i | \(-0.101884\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.217209 | − | 10.8894i | 0.00871630 | − | 0.436978i | ||||
\(622\) | 3.78431 | + | 0.599376i | 0.151737 | + | 0.0240328i | ||||
\(623\) | −2.17180 | + | 4.26239i | −0.0870112 | + | 0.170769i | ||||
\(624\) | 0.656040 | − | 2.98859i | 0.0262626 | − | 0.119639i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.8677i | 0.913977i | ||||||||
\(627\) | 12.4089 | + | 10.1859i | 0.495564 | + | 0.406785i | ||||
\(628\) | 1.57851 | − | 9.96632i | 0.0629894 | − | 0.397700i | ||||
\(629\) | −2.97306 | + | 2.16005i | −0.118544 | + | 0.0861269i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6592 | − | 14.2832i | −0.782619 | − | 0.568606i | 0.123145 | − | 0.992389i | \(-0.460702\pi\) |
−0.905764 | + | 0.423783i | \(0.860702\pi\) | |||||||
\(632\) | −2.65182 | + | 2.65182i | −0.105484 | + | 0.105484i | ||||
\(633\) | −20.8849 | − | 1.23381i | −0.830100 | − | 0.0490394i | ||||
\(634\) | −8.32864 | − | 2.70614i | −0.330772 | − | 0.107474i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.82699 | + | 0.868465i | −0.350013 | + | 0.0344369i | ||||
\(637\) | 16.8771 | − | 8.59929i | 0.668693 | − | 0.340716i | ||||
\(638\) | 25.1322 | − | 12.8055i | 0.994992 | − | 0.506974i | ||||
\(639\) | 5.32245 | − | 44.8899i | 0.210553 | − | 1.77582i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.76326 | + | 2.84736i | 0.346128 | + | 0.112464i | 0.476922 | − | 0.878946i | \(-0.341753\pi\) |
−0.130794 | + | 0.991410i | \(0.541753\pi\) | |||||||
\(642\) | −1.20630 | + | 20.4193i | −0.0476089 | + | 0.805885i | ||||
\(643\) | −32.6751 | + | 32.6751i | −1.28858 | + | 1.28858i | −0.352932 | + | 0.935649i | \(0.614815\pi\) |
−0.935649 | + | 0.352932i | \(0.885185\pi\) | |||||||
\(644\) | 7.13886 | + | 5.18669i | 0.281311 | + | 0.204384i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.14764 | − | 1.56035i | 0.0844978 | − | 0.0613912i | ||||
\(647\) | 7.60579 | − | 48.0211i | 0.299015 | − | 1.88790i | −0.141152 | − | 0.989988i | \(-0.545081\pi\) |
0.440167 | − | 0.897916i | \(-0.354919\pi\) | |||||||
\(648\) | 8.75219 | − | 2.09740i | 0.343819 | − | 0.0823937i | ||||
\(649\) | − | 55.4774i | − | 2.17768i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.1147 | + | 10.1229i | 1.80738 | + | 0.396746i | ||||
\(652\) | −2.55156 | + | 5.00771i | −0.0999267 | + | 0.196117i | ||||
\(653\) | −19.6349 | − | 3.10987i | −0.768375 | − | 0.121699i | −0.240073 | − | 0.970755i | \(-0.577171\pi\) |
−0.528302 | + | 0.849056i | \(0.677171\pi\) | |||||||
\(654\) | −21.1358 | + | 9.24240i | −0.826476 | + | 0.361407i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.21724 | − | 3.05177i | 0.0865688 | − | 0.119152i | ||||
\(657\) | 9.59494 | + | 26.0247i | 0.374334 | + | 1.01532i | ||||
\(658\) | −19.4647 | + | 3.08291i | −0.758815 | + | 0.120184i | ||||
\(659\) | 9.29483 | − | 28.6066i | 0.362075 | − | 1.11435i | −0.589717 | − | 0.807610i | \(-0.700761\pi\) |
0.951792 | − | 0.306743i | \(-0.0992393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.51392 | − | 13.8924i | −0.175571 | − | 0.540352i | 0.824088 | − | 0.566462i | \(-0.191688\pi\) |
−0.999659 | + | 0.0261096i | \(0.991688\pi\) | |||||||
\(662\) | −2.72338 | − | 5.34493i | −0.105847 | − | 0.207736i | ||||
\(663\) | −4.22544 | + | 1.10215i | −0.164102 | + | 0.0428039i | ||||
\(664\) | 16.0465 | − | 5.21383i | 0.622726 | − | 0.202336i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.67142 | − | 5.24478i | −0.219763 | − | 0.203231i | ||||
\(667\) | −1.85606 | − | 11.7187i | −0.0718670 | − | 0.453750i | ||||
\(668\) | 11.8566 | + | 11.8566i | 0.458747 | + | 0.458747i | ||||
\(669\) | −8.06029 | + | 7.16107i | −0.311629 | + | 0.276863i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.4333 | − | 39.1351i | −1.09766 | − | 1.51079i | ||||
\(672\) | −2.65826 | + | 6.78975i | −0.102545 | + | 0.261920i | ||||
\(673\) | −30.1630 | − | 15.3688i | −1.16270 | − | 0.592425i | −0.237306 | − | 0.971435i | \(-0.576264\pi\) |
−0.925392 | + | 0.379010i | \(0.876264\pi\) | |||||||
\(674\) | 2.43046 | 0.0936178 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.87932 | 0.379974 | ||||||||
\(677\) | −6.85459 | − | 3.49259i | −0.263443 | − | 0.134231i | 0.317280 | − | 0.948332i | \(-0.397230\pi\) |
−0.580724 | + | 0.814101i | \(0.697230\pi\) | |||||||
\(678\) | 0.945029 | − | 2.41380i | 0.0362936 | − | 0.0927013i | ||||
\(679\) | −8.69931 | − | 11.9736i | −0.333849 | − | 0.459503i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8548 | − | 10.5323i | 0.454278 | − | 0.403597i | ||||
\(682\) | 22.8151 | + | 22.8151i | 0.873634 | + | 0.873634i | ||||
\(683\) | −0.454547 | − | 2.86990i | −0.0173928 | − | 0.109814i | 0.977465 | − | 0.211099i | \(-0.0677043\pi\) |
−0.994857 | + | 0.101286i | \(0.967704\pi\) | |||||||
\(684\) | 4.09685 | + | 3.78866i | 0.156647 | + | 0.144863i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −14.9035 | + | 4.84242i | −0.569016 | + | 0.184885i | ||||
\(687\) | −30.9980 | + | 8.08540i | −1.18265 | + | 0.308477i | ||||
\(688\) | 4.02241 | + | 7.89443i | 0.153353 | + | 0.300972i | ||||
\(689\) | 2.79545 | + | 8.60350i | 0.106498 | + | 0.327767i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.12811 | + | 28.0934i | −0.347249 | + | 1.06872i | 0.613119 | + | 0.789991i | \(0.289915\pi\) |
−0.960368 | + | 0.278733i | \(0.910085\pi\) | |||||||
\(692\) | 4.42106 | − | 0.700227i | 0.168063 | − | 0.0266186i | ||||
\(693\) | 21.7702 | + | 59.0481i | 0.826981 | + | 2.24305i | ||||
\(694\) | 13.3577 | − | 18.3852i | 0.507050 | − | 0.697894i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.98285 | − | 3.92808i | 0.340494 | − | 0.148893i | ||||
\(697\) | −5.31733 | − | 0.842182i | −0.201408 | − | 0.0318999i | ||||
\(698\) | −5.68977 | + | 11.1668i | −0.215361 | + | 0.422670i | ||||
\(699\) | −23.3030 | − | 5.11535i | −0.881400 | − | 0.193480i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.1646i | 1.55476i | 0.629028 | + | 0.777382i | \(0.283453\pi\) | ||||
−0.629028 | + | 0.777382i | \(0.716547\pi\) | |||||||
\(702\) | −4.00335 | − | 8.26024i | −0.151097 | − | 0.311763i | ||||
\(703\) | 0.749245 | − | 4.73055i | 0.0282583 | − | 0.178416i | ||||
\(704\) | −4.03141 | + | 2.92899i | −0.151940 | + | 0.110391i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.78030 | − | 4.19963i | −0.217544 | − | 0.158055i | ||||
\(707\) | −49.6347 | + | 49.6347i | −1.86671 | + | 1.86671i | ||||
\(708\) | 1.13720 | − | 19.2496i | 0.0427385 | − | 0.723443i | ||||
\(709\) | −16.1533 | − | 5.24852i | −0.606650 | − | 0.197112i | −0.0104457 | − | 0.999945i | \(-0.503325\pi\) |
−0.596204 | + | 0.802833i | \(0.703325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.32468 | + | 11.1725i | −0.0496795 | + | 0.419000i | ||||
\(712\) | −1.01249 | + | 0.515891i | −0.0379448 | + | 0.0193338i | ||||
\(713\) | 12.0928 | − | 6.16161i | 0.452880 | − | 0.230754i | ||||
\(714\) | 10.3564 | − | 1.01894i | 0.387578 | − | 0.0381328i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.165923 | − | 0.0539115i | −0.00620082 | − | 0.00201477i | ||||
\(717\) | −35.8516 | − | 2.11799i | −1.33890 | − | 0.0790976i | ||||
\(718\) | 7.52770 | − | 7.52770i | 0.280931 | − | 0.280931i | ||||
\(719\) | −17.4118 | − | 12.6504i | −0.649349 | − | 0.471780i | 0.213700 | − | 0.976899i | \(-0.431448\pi\) |
−0.863049 | + | 0.505120i | \(0.831448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.03534 | − | 6.56456i | 0.336493 | − | 0.244477i | ||||
\(722\) | 2.43102 | − | 15.3489i | 0.0904734 | − | 0.571226i | ||||
\(723\) | 8.33003 | + | 6.83771i | 0.309797 | + | 0.254297i | ||||
\(724\) | 11.3773i | 0.422835i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.13651 | + | 23.3994i | −0.190634 | + | 0.868432i | ||||
\(727\) | 15.5168 | − | 30.4534i | 0.575485 | − | 1.12945i | −0.401443 | − | 0.915884i | \(-0.631491\pi\) |
0.976928 | − | 0.213569i | \(-0.0685088\pi\) | |||||||
\(728\) | 7.34523 | + | 1.16337i | 0.272233 | + | 0.0431174i | ||||
\(729\) | 16.7286 | − | 21.1932i | 0.619579 | − | 0.784934i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.43254 | − | 10.2300i | 0.274902 | − | 0.378371i | ||||
\(732\) | −9.06358 | − | 14.1619i | −0.335000 | − | 0.523440i | ||||
\(733\) | 18.4191 | − | 2.91730i | 0.680326 | − | 0.107753i | 0.193299 | − | 0.981140i | \(-0.438081\pi\) |
0.487027 | + | 0.873387i | \(0.338081\pi\) | |||||||
\(734\) | 1.29725 | − | 3.99251i | 0.0478822 | − | 0.147366i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.647728 | + | 1.99350i | 0.0238756 | + | 0.0734815i | ||||
\(737\) | −14.6436 | − | 28.7397i | −0.539405 | − | 1.05864i | ||||
\(738\) | −0.441957 | − | 11.3080i | −0.0162687 | − | 0.416252i | ||||
\(739\) | 1.28835 | − | 0.418609i | 0.0473926 | − | 0.0153988i | −0.285225 | − | 0.958461i | \(-0.592068\pi\) |
0.332617 | + | 0.943062i | \(0.392068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.87835 | − | 4.90977i | 0.105739 | − | 0.180365i | ||||
\(742\) | −3.37239 | − | 21.2924i | −0.123804 | − | 0.781669i | ||||
\(743\) | −8.68111 | − | 8.68111i | −0.318479 | − | 0.318479i | 0.529704 | − | 0.848183i | \(-0.322303\pi\) |
−0.848183 | + | 0.529704i | \(0.822303\pi\) | |||||||
\(744\) | 7.44870 | + | 8.38404i | 0.273082 | + | 0.307374i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.67527 | − | 3.68219i | −0.0979486 | − | 0.134815i | ||||
\(747\) | 28.1299 | − | 42.0806i | 1.02922 | − | 1.53965i | ||||
\(748\) | 6.33665 | + | 3.22868i | 0.231691 | + | 0.118052i | ||||
\(749\) | −49.7161 | −1.81659 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.0140 | 1.46013 | 0.730066 | − | 0.683377i | \(-0.239489\pi\) | ||||
0.730066 | + | 0.683377i | \(0.239489\pi\) | |||||||
\(752\) | −4.17108 | − | 2.12527i | −0.152104 | − | 0.0775007i | ||||
\(753\) | 6.07875 | + | 2.37990i | 0.221522 | + | 0.0867284i | ||||
\(754\) | −5.87750 | − | 8.08969i | −0.214046 | − | 0.294609i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.34343 | + | 20.9348i | 0.230708 | + | 0.761391i | ||||
\(757\) | 23.3400 | + | 23.3400i | 0.848305 | + | 0.848305i | 0.989922 | − | 0.141616i | \(-0.0452299\pi\) |
−0.141616 | + | 0.989922i | \(0.545230\pi\) | |||||||
\(758\) | 5.16027 | + | 32.5807i | 0.187429 | + | 1.18338i | ||||
\(759\) | 15.6071 | + | 9.14963i | 0.566501 | + | 0.332110i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.88486 | + | 2.23703i | −0.249576 | + | 0.0810921i | −0.431133 | − | 0.902288i | \(-0.641886\pi\) |
0.181558 | + | 0.983380i | \(0.441886\pi\) | |||||||
\(762\) | −0.678231 | − | 2.60021i | −0.0245697 | − | 0.0941958i | ||||
\(763\) | −25.4544 | − | 49.9570i | −0.921509 | − | 1.80856i | ||||
\(764\) | −5.70322 | − | 17.5527i | −0.206335 | − | 0.635035i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.28095 | − | 16.2531i | 0.190808 | − | 0.587248i | ||||
\(767\) | −19.4250 | + | 3.07662i | −0.701397 | + | 0.111090i | ||||
\(768\) | −1.45886 | + | 0.933665i | −0.0526420 | + | 0.0336907i | ||||
\(769\) | 2.15066 | − | 2.96013i | 0.0775549 | − | 0.106745i | −0.768477 | − | 0.639877i | \(-0.778985\pi\) |
0.846032 | + | 0.533132i | \(0.178985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.3644 | − | 48.8568i | −0.769420 | − | 1.75953i | ||||
\(772\) | −4.63135 | − | 0.733534i | −0.166686 | − | 0.0264005i | ||||
\(773\) | −15.0283 | + | 29.4947i | −0.540531 | + | 1.06085i | 0.445655 | + | 0.895205i | \(0.352971\pi\) |
−0.986185 | + | 0.165646i | \(0.947029\pi\) | |||||||
\(774\) | 24.1365 | + | 11.1331i | 0.867568 | + | 0.400171i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 3.51564i | − | 0.126204i | ||||||
\(777\) | 11.9125 | − | 14.5123i | 0.427357 | − | 0.520626i | ||||
\(778\) | −2.19762 | + | 13.8752i | −0.0787884 | + | 0.497450i | ||||
\(779\) | 5.67645 | − | 4.12419i | 0.203380 | − | 0.147764i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60.7458 | + | 44.1344i | 2.17366 | + | 1.57925i | ||||
\(782\) | 2.11531 | − | 2.11531i | 0.0756434 | − | 0.0756434i | ||||
\(783\) | 13.8730 | − | 25.9352i | 0.495779 | − | 0.926848i | ||||
\(784\) | −10.1976 | − | 3.31339i | −0.364199 | − | 0.118336i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.07982 | + | 10.9752i | 0.0385160 | + | 0.391473i | ||||
\(787\) | 14.7464 | − | 7.51367i | 0.525653 | − | 0.267833i | −0.170964 | − | 0.985277i | \(-0.554688\pi\) |
0.696616 | + | 0.717444i | \(0.254688\pi\) | |||||||
\(788\) | −11.2986 | + | 5.75693i | −0.402496 | + | 0.205082i | ||||
\(789\) | −0.940153 | − | 9.55563i | −0.0334703 | − | 0.340189i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.99204 | + | 1.94693i | 0.213053 | + | 0.0692250i | ||||
\(792\) | −4.06081 | + | 14.3872i | −0.144295 | + | 0.511227i | ||||
\(793\) | −12.1260 | + | 12.1260i | −0.430608 | + | 0.430608i | ||||
\(794\) | 2.98461 | + | 2.16845i | 0.105920 | + | 0.0769552i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.31548 | + | 0.955752i | −0.0466260 | + | 0.0338757i | ||||
\(797\) | −6.28166 | + | 39.6609i | −0.222508 | + | 1.40486i | 0.583095 | + | 0.812404i | \(0.301842\pi\) |
−0.805603 | + | 0.592456i | \(0.798158\pi\) | |||||||
\(798\) | −8.60517 | + | 10.4832i | −0.304620 | + | 0.371102i | ||||
\(799\) | 6.68108i | 0.236360i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.42787 | + | 3.09561i | −0.0504512 | + | 0.109378i | ||||
\(802\) | 13.3084 | − | 26.1193i | 0.469937 | − | 0.922304i | ||||
\(803\) | −45.5051 | − | 7.20730i | −1.60584 | − | 0.254340i | ||||
\(804\) | −4.49193 | − | 10.2723i | −0.158418 | − | 0.362276i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.72327 | − | 9.25378i | 0.236817 | − | 0.325951i | ||||
\(807\) | 5.05249 | − | 3.23357i | 0.177856 | − | 0.113827i | ||||
\(808\) | −16.4687 | + | 2.60839i | −0.579367 | + | 0.0917627i | ||||
\(809\) | 5.01595 | − | 15.4375i | 0.176351 | − | 0.542753i | −0.823341 | − | 0.567546i | \(-0.807893\pi\) |
0.999693 | + | 0.0247932i | \(0.00789272\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.6792 | − | 39.0226i | −0.445227 | − | 1.37027i | −0.882234 | − | 0.470811i | \(-0.843961\pi\) |
0.437007 | − | 0.899458i | \(-0.356039\pi\) | |||||||
\(812\) | 10.8183 | + | 21.2320i | 0.379646 | + | 0.745098i | ||||
\(813\) | 2.05952 | + | 7.89582i | 0.0722305 | + | 0.276919i | ||||
\(814\) | 12.2032 | − | 3.96505i | 0.427721 | − | 0.138975i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.13251 | + | 1.25018i | 0.0746527 | + | 0.0437650i | ||||
\(817\) | 2.57808 | + | 16.2774i | 0.0901957 | + | 0.569473i | ||||
\(818\) | 5.40870 | + | 5.40870i | 0.189111 | + | 0.189111i | ||||
\(819\) | 19.4680 | − | 10.8973i | 0.680266 | − | 0.380783i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.20025 | − | 11.2867i | −0.286191 | − | 0.393907i | 0.641582 | − | 0.767055i | \(-0.278279\pi\) |
−0.927772 | + | 0.373147i | \(0.878279\pi\) | |||||||
\(822\) | 6.62735 | + | 2.59468i | 0.231155 | + | 0.0904999i | ||||
\(823\) | 15.2645 | + | 7.77764i | 0.532086 | + | 0.271112i | 0.699324 | − | 0.714805i | \(-0.253485\pi\) |
−0.167237 | + | 0.985917i | \(0.553485\pi\) | |||||||
\(824\) | 2.65293 | 0.0924192 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 46.8681 | 1.63075 | ||||||||
\(827\) | 35.0129 | + | 17.8399i | 1.21752 | + | 0.620356i | 0.940266 | − | 0.340442i | \(-0.110577\pi\) |
0.277251 | + | 0.960798i | \(0.410577\pi\) | |||||||
\(828\) | 5.22779 | + | 3.49466i | 0.181678 | + | 0.121448i | ||||
\(829\) | 16.9229 | + | 23.2923i | 0.587756 | + | 0.808977i | 0.994519 | − | 0.104557i | \(-0.0333425\pi\) |
−0.406763 | + | 0.913534i | \(0.633343\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.6284 | − | 32.2233i | −0.993109 | − | 1.11781i | ||||
\(832\) | 1.24914 | + | 1.24914i | 0.0433060 | + | 0.0433060i | ||||
\(833\) | 2.39388 | + | 15.1144i | 0.0829430 | + | 0.523681i | ||||
\(834\) | −9.35644 | + | 15.9599i | −0.323987 | + | 0.552644i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.81517 | + | 2.86422i | −0.304879 | + | 0.0990613i | ||||
\(837\) | 33.1191 | + | 5.92488i | 1.14476 | + | 0.204794i | ||||
\(838\) | −4.97461 | − | 9.76323i | −0.171845 | − | 0.337265i | ||||
\(839\) | −10.2985 | − | 31.6954i | −0.355542 | − | 1.09425i | −0.955695 | − | 0.294360i | \(-0.904893\pi\) |
0.600152 | − | 0.799886i | \(-0.295107\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.939554 | − | 2.89165i | 0.0323984 | − | 0.0997121i | ||||
\(842\) | 13.8788 | − | 2.19818i | 0.478294 | − | 0.0757544i | ||||
\(843\) | −9.02079 | − | 14.0951i | −0.310692 | − | 0.485460i | ||||
\(844\) | 7.09981 | − | 9.77205i | 0.244385 | − | 0.336368i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.7747 | + | 2.73700i | −0.473583 | + | 0.0941000i | ||||
\(847\) | −57.5100 | − | 9.10870i | −1.97607 | − | 0.312979i | ||||
\(848\) | 2.32483 | − | 4.56273i | 0.0798349 | − | 0.156685i | ||||
\(849\) | −0.378911 | + | 1.72613i | −0.0130042 | + | 0.0592406i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 5.39730i | − | 0.185017i | ||||||
\(852\) | 20.1729 | + | 16.5589i | 0.691112 | + | 0.567300i | ||||
\(853\) | 7.73248 | − | 48.8210i | 0.264755 | − | 1.67160i | −0.393900 | − | 0.919153i | \(-0.628874\pi\) |
0.658655 | − | 0.752445i | \(-0.271126\pi\) | |||||||
\(854\) | 33.0619 | − | 24.0209i | 1.13135 | − | 0.821977i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.55419 | − | 6.94153i | −0.326556 | − | 0.237257i | ||||
\(857\) | −5.79343 | + | 5.79343i | −0.197900 | + | 0.197900i | −0.799099 | − | 0.601199i | \(-0.794690\pi\) |
0.601199 | + | 0.799099i | \(0.294690\pi\) | |||||||
\(858\) | 15.2205 | + | 0.899173i | 0.519619 | + | 0.0306973i | ||||
\(859\) | −3.26295 | − | 1.06020i | −0.111330 | − | 0.0361734i | 0.252822 | − | 0.967513i | \(-0.418641\pi\) |
−0.364152 | + | 0.931339i | \(0.618641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.3731 | − | 2.69317i | 0.932873 | − | 0.0917829i | ||||
\(862\) | −3.86786 | + | 1.97077i | −0.131740 | + | 0.0671249i | ||||
\(863\) | 22.7707 | − | 11.6022i | 0.775122 | − | 0.394944i | −0.0212325 | − | 0.999775i | \(-0.506759\pi\) |
0.796354 | + | 0.604830i | \(0.206759\pi\) | |||||||
\(864\) | −1.70393 | + | 4.90883i | −0.0579690 | + | 0.167002i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.46455 | − | 2.42538i | −0.253656 | − | 0.0824177i | ||||
\(867\) | −1.52842 | + | 25.8718i | −0.0519078 | + | 0.878654i | ||||
\(868\) | −19.2745 | + | 19.2745i | −0.654219 | + | 0.654219i | ||||
\(869\) | −15.1188 | − | 10.9844i | −0.512869 | − | 0.372621i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.25092 | + | 6.72119i | −0.313455 | + | 0.227739i | ||||
\(872\) | 2.08347 | − | 13.1545i | 0.0705551 | − | 0.445468i | ||||
\(873\) | −6.52784 | − | 8.28403i | −0.220934 | − | 0.280372i | ||||
\(874\) | 3.89884i | 0.131880i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.6416 | − | 3.43357i | −0.528482 | − | 0.116010i | ||||
\(877\) | −13.6895 | + | 26.8672i | −0.462262 | + | 0.907241i | 0.535759 | + | 0.844371i | \(0.320025\pi\) |
−0.998022 | + | 0.0628704i | \(0.979975\pi\) | |||||||
\(878\) | −19.8662 | − | 3.14649i | −0.670451 | − | 0.106189i | ||||
\(879\) | 3.26777 | − | 1.42895i | 0.110219 | − | 0.0481973i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.7770 | + | 40.9845i | −1.00321 | + | 1.38080i | −0.0798773 | + | 0.996805i | \(0.525453\pi\) |
−0.923334 | + | 0.383997i | \(0.874547\pi\) | |||||||
\(882\) | −30.1812 | + | 11.1274i | −1.01625 | + | 0.374678i | ||||
\(883\) | 11.1388 | − | 1.76422i | 0.374852 | − | 0.0593707i | 0.0338339 | − | 0.999427i | \(-0.489228\pi\) |
0.341018 | + | 0.940057i | \(0.389228\pi\) | |||||||
\(884\) | 0.779087 | − | 2.39778i | 0.0262035 | − | 0.0806462i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.20028 | − | 16.0048i | −0.174707 | − | 0.537692i | ||||
\(887\) | −8.52333 | − | 16.7280i | −0.286186 | − | 0.561671i | 0.702498 | − | 0.711686i | \(-0.252068\pi\) |
−0.988684 | + | 0.150015i | \(0.952068\pi\) | |||||||
\(888\) | 4.31553 | − | 1.12565i | 0.144820 | − | 0.0377743i | ||||
\(889\) | 6.21167 | − | 2.01830i | 0.208333 | − | 0.0676914i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.1455 | + | 41.4411i | 0.574395 | + | 1.38833i | ||||
\(892\) | −0.973793 | − | 6.14829i | −0.0326050 | − | 0.205860i | ||||
\(893\) | −6.15712 | − | 6.15712i | −0.206040 | − | 0.206040i | ||||
\(894\) | −6.64603 | + | 5.90458i | −0.222277 | + | 0.197479i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.47446 | − | 3.40580i | −0.0826657 | − | 0.113780i | ||||
\(897\) | 2.33815 | − | 5.97212i | 0.0780686 | − | 0.199403i | ||||
\(898\) | 3.16995 | + | 1.61517i | 0.105783 | + | 0.0538989i | ||||
\(899\) | 36.6510 | 1.22238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.30841 | −0.243478 | ||||||||
\(902\) | 16.7485 | + | 8.53377i | 0.557663 | + | 0.284144i | ||||
\(903\) | −23.5525 | + | 60.1580i | −0.783780 | + | 2.00193i | ||||
\(904\) | 0.879683 | + | 1.21078i | 0.0292578 | + | 0.0402699i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −26.0670 | + | 23.1589i | −0.866017 | + | 0.769402i | ||||
\(907\) | −29.1272 | − | 29.1272i | −0.967153 | − | 0.967153i | 0.0323248 | − | 0.999477i | \(-0.489709\pi\) |
−0.999477 | + | 0.0323248i | \(0.989709\pi\) | |||||||
\(908\) | 1.43222 | + | 9.04270i | 0.0475300 | + | 0.300093i | ||||
\(909\) | −33.9625 | + | 36.7253i | −1.12647 | + | 1.21810i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.21439 | − | 0.394580i | 0.0402346 | − | 0.0130730i | −0.288831 | − | 0.957380i | \(-0.593266\pi\) |
0.329065 | + | 0.944307i | \(0.393266\pi\) | |||||||
\(912\) | −3.11740 | + | 0.813132i | −0.103227 | + | 0.0269255i | ||||
\(913\) | 38.1699 | + | 74.9126i | 1.26324 | + | 2.47925i | ||||
\(914\) | 5.87403 | + | 18.0784i | 0.194296 | + | 0.597980i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.71542 | − | 17.5902i | 0.188843 | − | 0.581198i | ||||
\(917\) | −26.4743 | + | 4.19312i | −0.874259 | + | 0.138469i | ||||
\(918\) | 7.34623 | − | 1.01379i | 0.242462 | − | 0.0334601i | ||||
\(919\) | −14.7998 | + | 20.3701i | −0.488199 | + | 0.671949i | −0.980055 | − | 0.198728i | \(-0.936319\pi\) |
0.491855 | + | 0.870677i | \(0.336319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.8879 | + | 11.7577i | −0.885987 | + | 0.387430i | ||||
\(922\) | 31.6376 | + | 5.01091i | 1.04193 | + | 0.165026i | ||||
\(923\) | 12.0845 | − | 23.7173i | 0.397768 | − | 0.780663i | ||||
\(924\) | −35.4897 | − | 7.79051i | −1.16752 | − | 0.256289i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.10121i | 0.101912i | ||||||||
\(927\) | 6.25119 | − | 4.92595i | 0.205316 | − | 0.161789i | ||||
\(928\) | −0.885486 | + | 5.59074i | −0.0290675 | + | 0.183525i | ||||
\(929\) | −24.8975 | + | 18.0891i | −0.816859 | + | 0.593483i | −0.915811 | − | 0.401609i | \(-0.868451\pi\) |
0.0989519 | + | 0.995092i | \(0.468451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.1352 | − | 11.7229i | −0.528809 | − | 0.384202i | ||||
\(932\) | 9.73992 | − | 9.73992i | 0.319042 | − | 0.319042i | ||||
\(933\) | −0.391369 | + | 6.62478i | −0.0128128 | + | 0.216885i | ||||
\(934\) | 37.7054 | + | 12.2512i | 1.23376 | + | 0.400872i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.26277 | + | 0.623990i | 0.172019 | + | 0.0203958i | ||||
\(937\) | −1.21310 | + | 0.618103i | −0.0396301 | + | 0.0201925i | −0.473693 | − | 0.880690i | \(-0.657079\pi\) |
0.434063 | + | 0.900882i | \(0.357079\pi\) | |||||||
\(938\) | 24.2797 | − | 12.3711i | 0.792762 | − | 0.403932i | ||||
\(939\) | −39.4177 | + | 3.87820i | −1.28635 | + | 0.126560i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.0374 | − | 4.56102i | −0.457606 | − | 0.148685i | 0.0711384 | − | 0.997466i | \(-0.477337\pi\) |
−0.528744 | + | 0.848781i | \(0.677337\pi\) | |||||||
\(942\) | 17.4469 | + | 1.03070i | 0.568452 | + | 0.0335821i | ||||
\(943\) | 5.59101 | − | 5.59101i | 0.182068 | − | 0.182068i | ||||
\(944\) | 9.00688 | + | 6.54388i | 0.293149 | + | 0.212985i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35.7188 | + | 25.9512i | −1.16132 | + | 0.843747i | ||||
\(947\) | 1.05799 | − | 6.67988i | 0.0343800 | − | 0.217067i | −0.964517 | − | 0.264021i | \(-0.914951\pi\) |
0.998897 | + | 0.0469536i | \(0.0149513\pi\) | |||||||
\(948\) | −5.02075 | − | 4.12129i | −0.163066 | − | 0.133853i | ||||
\(949\) | 16.3330i | 0.530191i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.25217 | − | 14.8152i | 0.105459 | − | 0.480417i | ||||
\(952\) | −2.72764 | + | 5.35329i | −0.0884032 | + | 0.173501i | ||||
\(953\) | −16.8097 | − | 2.66239i | −0.544519 | − | 0.0862434i | −0.121886 | − | 0.992544i | \(-0.538894\pi\) |
−0.422633 | + | 0.906301i | \(0.638894\pi\) | |||||||
\(954\) | −2.99399 | − | 15.0681i | −0.0969341 | − | 0.487846i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.1877 | − | 16.7750i | 0.394180 | − | 0.542542i | ||||
\(957\) | 26.3354 | + | 41.1493i | 0.851303 | + | 1.33017i | ||||
\(958\) | 13.3111 | − | 2.10827i | 0.430061 | − | 0.0681150i | ||||
\(959\) | −5.34552 | + | 16.4518i | −0.172616 | + | 0.531257i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.37603 | + | 10.3904i | 0.108904 | + | 0.335173i | ||||
\(962\) | −2.06509 | − | 4.05296i | −0.0665811 | − | 0.130673i | ||||
\(963\) | −35.4019 | + | 1.38364i | −1.14081 | + | 0.0445870i | ||||
\(964\) | −5.91757 | + | 1.92274i | −0.190592 | + | 0.0619271i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.72973 | + | 13.1851i | −0.248700 | + | 0.424223i | ||||
\(967\) | 6.13865 | + | 38.7579i | 0.197406 | + | 1.24637i | 0.864972 | + | 0.501820i | \(0.167336\pi\) |
−0.667566 | + | 0.744550i | \(0.732664\pi\) | |||||||
\(968\) | −9.78020 | − | 9.78020i | −0.314348 | − | 0.314348i | ||||
\(969\) | 3.05385 | + | 3.43732i | 0.0981037 | + | 0.110423i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.7969 | + | 24.4953i | 0.571129 | + | 0.786091i | 0.992688 | − | 0.120710i | \(-0.0385171\pi\) |
−0.421559 | + | 0.906801i | \(0.638517\pi\) | |||||||
\(972\) | 5.09966 | + | 14.7307i | 0.163572 | + | 0.472487i | ||||
\(973\) | −40.0644 | − | 20.4139i | −1.28441 | − | 0.654438i | ||||
\(974\) | 2.08662 | 0.0668596 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.70753 | 0.310731 | ||||||||
\(977\) | 37.5797 | + | 19.1478i | 1.20228 | + | 0.612593i | 0.936238 | − | 0.351368i | \(-0.114283\pi\) |
0.266044 | + | 0.963961i | \(0.414283\pi\) | |||||||
\(978\) | −9.06466 | − | 3.54892i | −0.289856 | − | 0.113482i | ||||
\(979\) | −3.32836 | − | 4.58109i | −0.106375 | − | 0.146412i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.5159 | − | 34.8650i | −0.623094 | − | 1.11315i | ||||
\(982\) | −11.7522 | − | 11.7522i | −0.375029 | − | 0.375029i | ||||
\(983\) | 2.25288 | + | 14.2241i | 0.0718557 | + | 0.453679i | 0.997215 | + | 0.0745867i | \(0.0237638\pi\) |
−0.925359 | + | 0.379092i | \(0.876236\pi\) | |||||||
\(984\) | 5.63646 | + | 3.30436i | 0.179684 | + | 0.105339i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.68307 | − | 2.49638i | 0.244679 | − | 0.0795009i | ||||
\(987\) | −8.61519 | − | 33.0291i | −0.274224 | − | 1.05133i | ||||
\(988\) | 1.49175 | + | 2.92773i | 0.0474589 | + | 0.0931434i | ||||
\(989\) | 5.73895 | + | 17.6627i | 0.182488 | + | 0.561640i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.477429 | − | 1.46938i | 0.0151660 | − | 0.0466762i | −0.943187 | − | 0.332262i | \(-0.892188\pi\) |
0.958353 | + | 0.285586i | \(0.0921882\pi\) | |||||||
\(992\) | −6.39524 | + | 1.01291i | −0.203049 | + | 0.0321598i | ||||
\(993\) | 8.75133 | − | 5.60082i | 0.277715 | − | 0.177737i | ||||
\(994\) | −37.2854 | + | 51.3189i | −1.18262 | + | 1.62774i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 11.7086 | + | 26.7756i | 0.371001 | + | 0.848417i | ||||
\(997\) | −49.1277 | − | 7.78106i | −1.55589 | − | 0.246429i | −0.681560 | − | 0.731762i | \(-0.738698\pi\) |
−0.874329 | + | 0.485333i | \(0.838698\pi\) | |||||||
\(998\) | 16.3644 | − | 32.1169i | 0.518006 | − | 1.01664i | ||||
\(999\) | 8.07873 | − | 10.6655i | 0.255600 | − | 0.337440i |
(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 | 750.2.l.c.107.3 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.c.107.8 | 80 | ||
5.2 | odd | 4 | 750.2.l.b.143.6 | 80 | |||
5.3 | odd | 4 | 150.2.l.a.83.5 | yes | 80 | ||
5.4 | even | 2 | 750.2.l.a.107.8 | 80 | |||
15.2 | even | 4 | 750.2.l.b.143.1 | 80 | |||
15.8 | even | 4 | 150.2.l.a.83.10 | yes | 80 | ||
15.14 | odd | 2 | 750.2.l.a.107.3 | 80 | |||
25.3 | odd | 20 | inner | 750.2.l.c.743.8 | 80 | ||
25.4 | even | 10 | 750.2.l.b.257.1 | 80 | |||
25.21 | even | 5 | 150.2.l.a.47.10 | yes | 80 | ||
25.22 | odd | 20 | 750.2.l.a.743.3 | 80 | |||
75.29 | odd | 10 | 750.2.l.b.257.6 | 80 | |||
75.47 | even | 20 | 750.2.l.a.743.8 | 80 | |||
75.53 | even | 20 | inner | 750.2.l.c.743.3 | 80 | ||
75.71 | odd | 10 | 150.2.l.a.47.5 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.47.5 | ✓ | 80 | 75.71 | odd | 10 | ||
150.2.l.a.47.10 | yes | 80 | 25.21 | even | 5 | ||
150.2.l.a.83.5 | yes | 80 | 5.3 | odd | 4 | ||
150.2.l.a.83.10 | yes | 80 | 15.8 | even | 4 | ||
750.2.l.a.107.3 | 80 | 15.14 | odd | 2 | |||
750.2.l.a.107.8 | 80 | 5.4 | even | 2 | |||
750.2.l.a.743.3 | 80 | 25.22 | odd | 20 | |||
750.2.l.a.743.8 | 80 | 75.47 | even | 20 | |||
750.2.l.b.143.1 | 80 | 15.2 | even | 4 | |||
750.2.l.b.143.6 | 80 | 5.2 | odd | 4 | |||
750.2.l.b.257.1 | 80 | 25.4 | even | 10 | |||
750.2.l.b.257.6 | 80 | 75.29 | odd | 10 | |||
750.2.l.c.107.3 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.c.107.8 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.c.743.3 | 80 | 75.53 | even | 20 | inner | ||
750.2.l.c.743.8 | 80 | 25.3 | odd | 20 | inner |