Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(571,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("572.571");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.b (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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 571.14 | ||
Character | \(\chi\) | \(=\) | 572.571 |
Dual form | 572.2.b.c.571.15 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.913620 | − | 1.07949i | −0.646027 | − | 0.763315i | ||||
\(3\) | 1.67751i | 0.968510i | 0.874927 | + | 0.484255i | \(0.160909\pi\) | ||||
−0.874927 | + | 0.484255i | \(0.839091\pi\) | |||||||
\(4\) | −0.330598 | + | 1.97249i | −0.165299 | + | 0.986244i | ||||
\(5\) | 1.10479i | 0.494075i | 0.969006 | + | 0.247038i | \(0.0794571\pi\) | ||||
−0.969006 | + | 0.247038i | \(0.920543\pi\) | |||||||
\(6\) | 1.81085 | − | 1.53260i | 0.739278 | − | 0.625683i | ||||
\(7\) | − | 1.27047i | − | 0.480193i | −0.970749 | − | 0.240097i | \(-0.922821\pi\) | ||
0.970749 | − | 0.240097i | \(-0.0771791\pi\) | |||||||
\(8\) | 2.43132 | − | 1.44523i | 0.859602 | − | 0.510965i | ||||
\(9\) | 0.185967 | 0.0619890 | ||||||||
\(10\) | 1.19260 | − | 1.00935i | 0.377135 | − | 0.319186i | ||||
\(11\) | 2.94635 | − | 1.52284i | 0.888358 | − | 0.459152i | ||||
\(12\) | −3.30886 | − | 0.554581i | −0.955186 | − | 0.160094i | ||||
\(13\) | 1.61864 | + | 3.22180i | 0.448931 | + | 0.893567i | ||||
\(14\) | −1.37146 | + | 1.16073i | −0.366538 | + | 0.310218i | ||||
\(15\) | −1.85329 | −0.478516 | ||||||||
\(16\) | −3.78141 | − | 1.30420i | −0.945353 | − | 0.326050i | ||||
\(17\) | − | 1.40862i | − | 0.341640i | −0.985302 | − | 0.170820i | \(-0.945358\pi\) | ||
0.985302 | − | 0.170820i | \(-0.0546416\pi\) | |||||||
\(18\) | −0.169903 | − | 0.200750i | −0.0400466 | − | 0.0473171i | ||||
\(19\) | 0.947603i | 0.217395i | 0.994075 | + | 0.108698i | \(0.0346680\pi\) | ||||
−0.994075 | + | 0.108698i | \(0.965332\pi\) | |||||||
\(20\) | −2.17917 | − | 0.365240i | −0.487278 | − | 0.0816701i | ||||
\(21\) | 2.13123 | 0.465072 | ||||||||
\(22\) | −4.33573 | − | 1.78926i | −0.924381 | − | 0.381472i | ||||
\(23\) | − | 2.58512i | − | 0.539036i | −0.962995 | − | 0.269518i | \(-0.913136\pi\) | ||
0.962995 | − | 0.269518i | \(-0.0868643\pi\) | |||||||
\(24\) | 2.42438 | + | 4.07856i | 0.494874 | + | 0.832533i | ||||
\(25\) | 3.77945 | 0.755890 | ||||||||
\(26\) | 1.99908 | − | 4.69081i | 0.392051 | − | 0.919943i | ||||
\(27\) | 5.34449i | 1.02855i | ||||||||
\(28\) | 2.50599 | + | 0.420015i | 0.473587 | + | 0.0793754i | ||||
\(29\) | 9.78308i | 1.81667i | 0.418241 | + | 0.908336i | \(0.362647\pi\) | ||||
−0.418241 | + | 0.908336i | \(0.637353\pi\) | |||||||
\(30\) | 1.69320 | + | 2.00060i | 0.309134 | + | 0.365259i | ||||
\(31\) | −5.63936 | −1.01286 | −0.506430 | − | 0.862281i | \(-0.669035\pi\) | ||||
−0.506430 | + | 0.862281i | \(0.669035\pi\) | |||||||
\(32\) | 2.04690 | + | 5.27354i | 0.361844 | + | 0.932239i | ||||
\(33\) | 2.55457 | + | 4.94252i | 0.444694 | + | 0.860383i | ||||
\(34\) | −1.52059 | + | 1.28694i | −0.260779 | + | 0.220708i | ||||
\(35\) | 1.40360 | 0.237251 | ||||||||
\(36\) | −0.0614803 | + | 0.366818i | −0.0102467 | + | 0.0611363i | ||||
\(37\) | 7.85601i | 1.29152i | 0.763541 | + | 0.645760i | \(0.223459\pi\) | ||||
−0.763541 | + | 0.645760i | \(0.776541\pi\) | |||||||
\(38\) | 1.02293 | − | 0.865749i | 0.165941 | − | 0.140443i | ||||
\(39\) | −5.40460 | + | 2.71529i | −0.865428 | + | 0.434794i | ||||
\(40\) | 1.59666 | + | 2.68609i | 0.252455 | + | 0.424708i | ||||
\(41\) | 1.57573 | 0.246087 | 0.123044 | − | 0.992401i | \(-0.460735\pi\) | ||||
0.123044 | + | 0.992401i | \(0.460735\pi\) | |||||||
\(42\) | −1.94713 | − | 2.30064i | −0.300449 | − | 0.354996i | ||||
\(43\) | −4.24023 | −0.646629 | −0.323314 | − | 0.946292i | \(-0.604797\pi\) | ||||
−0.323314 | + | 0.946292i | \(0.604797\pi\) | |||||||
\(44\) | 2.02972 | + | 6.31508i | 0.305992 | + | 0.952034i | ||||
\(45\) | 0.205454i | 0.0306272i | ||||||||
\(46\) | −2.79062 | + | 2.36182i | −0.411454 | + | 0.348232i | ||||
\(47\) | −0.265145 | −0.0386753 | −0.0193377 | − | 0.999813i | \(-0.506156\pi\) | ||||
−0.0193377 | + | 0.999813i | \(0.506156\pi\) | |||||||
\(48\) | 2.18781 | − | 6.34335i | 0.315783 | − | 0.915583i | ||||
\(49\) | 5.38590 | 0.769415 | ||||||||
\(50\) | −3.45298 | − | 4.07988i | −0.488325 | − | 0.576982i | ||||
\(51\) | 2.36297 | 0.330881 | ||||||||
\(52\) | −6.89008 | + | 2.12763i | −0.955482 | + | 0.295049i | ||||
\(53\) | 5.33730 | 0.733135 | 0.366568 | − | 0.930391i | \(-0.380533\pi\) | ||||
0.366568 | + | 0.930391i | \(0.380533\pi\) | |||||||
\(54\) | 5.76932 | − | 4.88283i | 0.785105 | − | 0.664469i | ||||
\(55\) | 1.68241 | + | 3.25508i | 0.226856 | + | 0.438915i | ||||
\(56\) | −1.83612 | − | 3.08892i | −0.245362 | − | 0.412775i | ||||
\(57\) | −1.58961 | −0.210549 | ||||||||
\(58\) | 10.5607 | − | 8.93802i | 1.38669 | − | 1.17362i | ||||
\(59\) | −0.801256 | −0.104315 | −0.0521573 | − | 0.998639i | \(-0.516610\pi\) | ||||
−0.0521573 | + | 0.998639i | \(0.516610\pi\) | |||||||
\(60\) | 0.612692 | − | 3.65558i | 0.0790983 | − | 0.471934i | ||||
\(61\) | − | 4.22552i | − | 0.541022i | −0.962717 | − | 0.270511i | \(-0.912807\pi\) | ||
0.962717 | − | 0.270511i | \(-0.0871926\pi\) | |||||||
\(62\) | 5.15224 | + | 6.08764i | 0.654335 | + | 0.773131i | ||||
\(63\) | − | 0.236266i | − | 0.0297667i | ||||||
\(64\) | 3.82264 | − | 7.02762i | 0.477830 | − | 0.878452i | ||||
\(65\) | −3.55940 | + | 1.78825i | −0.441489 | + | 0.221805i | ||||
\(66\) | 3.00150 | − | 7.27322i | 0.369459 | − | 0.895271i | ||||
\(67\) | −10.3107 | −1.25965 | −0.629826 | − | 0.776736i | \(-0.716874\pi\) | ||||
−0.629826 | + | 0.776736i | \(0.716874\pi\) | |||||||
\(68\) | 2.77848 | + | 0.465686i | 0.336940 | + | 0.0564727i | ||||
\(69\) | 4.33657 | 0.522061 | ||||||||
\(70\) | −1.28236 | − | 1.51517i | −0.153271 | − | 0.181098i | ||||
\(71\) | 11.1238 | 1.32015 | 0.660074 | − | 0.751201i | \(-0.270525\pi\) | ||||
0.660074 | + | 0.751201i | \(0.270525\pi\) | |||||||
\(72\) | 0.452146 | − | 0.268764i | 0.0532859 | − | 0.0316742i | ||||
\(73\) | −10.0124 | −1.17186 | −0.585932 | − | 0.810360i | \(-0.699271\pi\) | ||||
−0.585932 | + | 0.810360i | \(0.699271\pi\) | |||||||
\(74\) | 8.48048 | − | 7.17740i | 0.985836 | − | 0.834356i | ||||
\(75\) | 6.34006i | 0.732087i | ||||||||
\(76\) | −1.86913 | − | 0.313276i | −0.214404 | − | 0.0359352i | ||||
\(77\) | −1.93472 | − | 3.74325i | −0.220482 | − | 0.426583i | ||||
\(78\) | 7.86887 | + | 3.35347i | 0.890974 | + | 0.379705i | ||||
\(79\) | 7.91992 | 0.891061 | 0.445530 | − | 0.895267i | \(-0.353015\pi\) | ||||
0.445530 | + | 0.895267i | \(0.353015\pi\) | |||||||
\(80\) | 1.44086 | − | 4.17765i | 0.161093 | − | 0.467075i | ||||
\(81\) | −8.40751 | −0.934168 | ||||||||
\(82\) | −1.43961 | − | 1.70098i | −0.158979 | − | 0.187842i | ||||
\(83\) | − | 12.5969i | − | 1.38269i | −0.722525 | − | 0.691345i | \(-0.757019\pi\) | ||
0.722525 | − | 0.691345i | \(-0.242981\pi\) | |||||||
\(84\) | −0.704579 | + | 4.20382i | −0.0768758 | + | 0.458674i | ||||
\(85\) | 1.55622 | 0.168796 | ||||||||
\(86\) | 3.87396 | + | 4.57728i | 0.417739 | + | 0.493581i | ||||
\(87\) | −16.4112 | −1.75946 | ||||||||
\(88\) | 4.96268 | − | 7.96064i | 0.529023 | − | 0.848607i | ||||
\(89\) | 5.03112i | 0.533298i | 0.963794 | + | 0.266649i | \(0.0859164\pi\) | ||||
−0.963794 | + | 0.266649i | \(0.914084\pi\) | |||||||
\(90\) | 0.221785 | − | 0.187707i | 0.0233782 | − | 0.0197860i | ||||
\(91\) | 4.09321 | − | 2.05644i | 0.429084 | − | 0.215573i | ||||
\(92\) | 5.09913 | + | 0.854637i | 0.531621 | + | 0.0891020i | ||||
\(93\) | − | 9.46008i | − | 0.980964i | ||||||
\(94\) | 0.242241 | + | 0.286221i | 0.0249853 | + | 0.0295214i | ||||
\(95\) | −1.04690 | −0.107409 | ||||||||
\(96\) | −8.84640 | + | 3.43369i | −0.902882 | + | 0.350450i | ||||
\(97\) | − | 15.8353i | − | 1.60783i | −0.594743 | − | 0.803916i | \(-0.702746\pi\) | ||
0.594743 | − | 0.803916i | \(-0.297254\pi\) | |||||||
\(98\) | −4.92067 | − | 5.81403i | −0.497062 | − | 0.587306i | ||||
\(99\) | 0.547924 | − | 0.283197i | 0.0550684 | − | 0.0284624i | ||||
\(100\) | −1.24948 | + | 7.45491i | −0.124948 | + | 0.745491i | ||||
\(101\) | 2.96407i | 0.294936i | 0.989067 | + | 0.147468i | \(0.0471123\pi\) | ||||
−0.989067 | + | 0.147468i | \(0.952888\pi\) | |||||||
\(102\) | −2.15885 | − | 2.55080i | −0.213758 | − | 0.252567i | ||||
\(103\) | 8.90842i | 0.877772i | 0.898543 | + | 0.438886i | \(0.144627\pi\) | ||||
−0.898543 | + | 0.438886i | \(0.855373\pi\) | |||||||
\(104\) | 8.59167 | + | 5.49393i | 0.842483 | + | 0.538724i | ||||
\(105\) | 2.35455i | 0.229780i | ||||||||
\(106\) | −4.87627 | − | 5.76157i | −0.473625 | − | 0.559613i | ||||
\(107\) | 13.6915 | 1.32361 | 0.661805 | − | 0.749676i | \(-0.269791\pi\) | ||||
0.661805 | + | 0.749676i | \(0.269791\pi\) | |||||||
\(108\) | −10.5419 | − | 1.76688i | −1.01440 | − | 0.170018i | ||||
\(109\) | −7.99559 | −0.765839 | −0.382919 | − | 0.923782i | \(-0.625081\pi\) | ||||
−0.382919 | + | 0.923782i | \(0.625081\pi\) | |||||||
\(110\) | 1.97675 | − | 4.79005i | 0.188476 | − | 0.456713i | ||||
\(111\) | −13.1785 | −1.25085 | ||||||||
\(112\) | −1.65695 | + | 4.80417i | −0.156567 | + | 0.453952i | ||||
\(113\) | 4.48064 | 0.421503 | 0.210751 | − | 0.977540i | \(-0.432409\pi\) | ||||
0.210751 | + | 0.977540i | \(0.432409\pi\) | |||||||
\(114\) | 1.45230 | + | 1.71597i | 0.136020 | + | 0.160715i | ||||
\(115\) | 2.85601 | 0.266324 | ||||||||
\(116\) | −19.2970 | − | 3.23427i | −1.79168 | − | 0.300294i | ||||
\(117\) | 0.301014 | + | 0.599149i | 0.0278288 | + | 0.0553913i | ||||
\(118\) | 0.732044 | + | 0.864948i | 0.0673901 | + | 0.0796249i | ||||
\(119\) | −1.78961 | −0.164053 | ||||||||
\(120\) | −4.50593 | + | 2.67842i | −0.411334 | + | 0.244505i | ||||
\(121\) | 6.36194 | − | 8.97361i | 0.578358 | − | 0.815783i | ||||
\(122\) | −4.56140 | + | 3.86051i | −0.412970 | + | 0.349515i | ||||
\(123\) | 2.64329i | 0.238338i | ||||||||
\(124\) | 1.86436 | − | 11.1236i | 0.167425 | − | 0.998926i | ||||
\(125\) | 9.69941i | 0.867541i | ||||||||
\(126\) | −0.255047 | + | 0.215857i | −0.0227214 | + | 0.0192301i | ||||
\(127\) | −17.4581 | −1.54916 | −0.774578 | − | 0.632479i | \(-0.782038\pi\) | ||||
−0.774578 | + | 0.632479i | \(0.782038\pi\) | |||||||
\(128\) | −11.0787 | + | 2.29406i | −0.979227 | + | 0.202768i | ||||
\(129\) | − | 7.11301i | − | 0.626266i | ||||||
\(130\) | 5.18234 | + | 2.20855i | 0.454521 | + | 0.193703i | ||||
\(131\) | 7.08768 | 0.619253 | 0.309627 | − | 0.950858i | \(-0.399796\pi\) | ||||
0.309627 | + | 0.950858i | \(0.399796\pi\) | |||||||
\(132\) | −10.5936 | + | 3.40487i | −0.922054 | + | 0.296356i | ||||
\(133\) | 1.20390 | 0.104392 | ||||||||
\(134\) | 9.42005 | + | 11.1303i | 0.813769 | + | 0.961511i | ||||
\(135\) | −5.90451 | −0.508179 | ||||||||
\(136\) | −2.03577 | − | 3.42480i | −0.174566 | − | 0.293674i | ||||
\(137\) | − | 14.1974i | − | 1.21296i | −0.795098 | − | 0.606481i | \(-0.792580\pi\) | ||
0.795098 | − | 0.606481i | \(-0.207420\pi\) | |||||||
\(138\) | −3.96197 | − | 4.68128i | −0.337266 | − | 0.398497i | ||||
\(139\) | −9.45130 | −0.801649 | −0.400824 | − | 0.916155i | \(-0.631276\pi\) | ||||
−0.400824 | + | 0.916155i | \(0.631276\pi\) | |||||||
\(140\) | −0.464027 | + | 2.76858i | −0.0392174 | + | 0.233988i | ||||
\(141\) | − | 0.444782i | − | 0.0374574i | ||||||
\(142\) | −10.1629 | − | 12.0080i | −0.852851 | − | 1.00769i | ||||
\(143\) | 9.67536 | + | 7.02762i | 0.809094 | + | 0.587679i | ||||
\(144\) | −0.703218 | − | 0.242538i | −0.0586015 | − | 0.0202115i | ||||
\(145\) | −10.8082 | −0.897573 | ||||||||
\(146\) | 9.14754 | + | 10.8083i | 0.757056 | + | 0.894501i | ||||
\(147\) | 9.03489i | 0.745185i | ||||||||
\(148\) | −15.4959 | − | 2.59718i | −1.27375 | − | 0.213487i | ||||
\(149\) | 11.5223 | 0.943943 | 0.471972 | − | 0.881614i | \(-0.343543\pi\) | ||||
0.471972 | + | 0.881614i | \(0.343543\pi\) | |||||||
\(150\) | 6.84403 | − | 5.79240i | 0.558813 | − | 0.472948i | ||||
\(151\) | 4.94593i | 0.402494i | 0.979541 | + | 0.201247i | \(0.0644994\pi\) | ||||
−0.979541 | + | 0.201247i | \(0.935501\pi\) | |||||||
\(152\) | 1.36950 | + | 2.30393i | 0.111081 | + | 0.186873i | ||||
\(153\) | − | 0.261956i | − | 0.0211779i | ||||||
\(154\) | −2.27321 | + | 5.50842i | −0.183180 | + | 0.443881i | ||||
\(155\) | − | 6.23029i | − | 0.500429i | ||||||
\(156\) | −3.56912 | − | 11.5582i | −0.285758 | − | 0.925394i | ||||
\(157\) | −14.3545 | −1.14562 | −0.572808 | − | 0.819690i | \(-0.694146\pi\) | ||||
−0.572808 | + | 0.819690i | \(0.694146\pi\) | |||||||
\(158\) | −7.23580 | − | 8.54948i | −0.575649 | − | 0.680160i | ||||
\(159\) | 8.95337i | 0.710049i | ||||||||
\(160\) | −5.82613 | + | 2.26139i | −0.460596 | + | 0.178778i | ||||
\(161\) | −3.28433 | −0.258841 | ||||||||
\(162\) | 7.68127 | + | 9.07583i | 0.603498 | + | 0.713064i | ||||
\(163\) | 9.26462 | 0.725661 | 0.362831 | − | 0.931855i | \(-0.381810\pi\) | ||||
0.362831 | + | 0.931855i | \(0.381810\pi\) | |||||||
\(164\) | −0.520932 | + | 3.10810i | −0.0406779 | + | 0.242702i | ||||
\(165\) | −5.46043 | + | 2.82225i | −0.425094 | + | 0.219712i | ||||
\(166\) | −13.5982 | + | 11.5088i | −1.05543 | + | 0.893254i | ||||
\(167\) | 18.2430i | 1.41168i | 0.708370 | + | 0.705841i | \(0.249431\pi\) | ||||
−0.708370 | + | 0.705841i | \(0.750569\pi\) | |||||||
\(168\) | 5.18169 | − | 3.08010i | 0.399776 | − | 0.237635i | ||||
\(169\) | −7.75999 | + | 10.4299i | −0.596922 | + | 0.802299i | ||||
\(170\) | −1.42179 | − | 1.67992i | −0.109047 | − | 0.128844i | ||||
\(171\) | 0.176223i | 0.0134761i | ||||||||
\(172\) | 1.40181 | − | 8.36379i | 0.106887 | − | 0.637733i | ||||
\(173\) | − | 13.9837i | − | 1.06316i | −0.847009 | − | 0.531579i | \(-0.821599\pi\) | ||
0.847009 | − | 0.531579i | \(-0.178401\pi\) | |||||||
\(174\) | 14.9936 | + | 17.7157i | 1.13666 | + | 1.34303i | ||||
\(175\) | − | 4.80168i | − | 0.362973i | ||||||
\(176\) | −13.1274 | + | 1.91584i | −0.989518 | + | 0.144412i | ||||
\(177\) | − | 1.34411i | − | 0.101030i | ||||||
\(178\) | 5.43104 | − | 4.59653i | 0.407074 | − | 0.344525i | ||||
\(179\) | − | 13.8697i | − | 1.03667i | −0.855178 | − | 0.518334i | \(-0.826552\pi\) | ||
0.855178 | − | 0.518334i | \(-0.173448\pi\) | |||||||
\(180\) | −0.405255 | − | 0.0679226i | −0.0302059 | − | 0.00506265i | ||||
\(181\) | 10.5358 | 0.783123 | 0.391561 | − | 0.920152i | \(-0.371935\pi\) | ||||
0.391561 | + | 0.920152i | \(0.371935\pi\) | |||||||
\(182\) | −5.95954 | − | 2.53977i | −0.441750 | − | 0.188260i | ||||
\(183\) | 7.08834 | 0.523985 | ||||||||
\(184\) | −3.73609 | − | 6.28527i | −0.275428 | − | 0.463356i | ||||
\(185\) | −8.67920 | −0.638108 | ||||||||
\(186\) | −10.2121 | + | 8.64292i | −0.748785 | + | 0.633729i | ||||
\(187\) | −2.14509 | − | 4.15028i | −0.156865 | − | 0.303498i | ||||
\(188\) | 0.0876562 | − | 0.522994i | 0.00639299 | − | 0.0381433i | ||||
\(189\) | 6.79002 | 0.493901 | ||||||||
\(190\) | 0.956467 | + | 1.13012i | 0.0693894 | + | 0.0819872i | ||||
\(191\) | − | 26.4504i | − | 1.91388i | −0.290283 | − | 0.956941i | \(-0.593750\pi\) | ||
0.290283 | − | 0.956941i | \(-0.406250\pi\) | |||||||
\(192\) | 11.7889 | + | 6.41251i | 0.850789 | + | 0.462783i | ||||
\(193\) | −23.3881 | −1.68351 | −0.841755 | − | 0.539860i | \(-0.818477\pi\) | ||||
−0.841755 | + | 0.539860i | \(0.818477\pi\) | |||||||
\(194\) | −17.0941 | + | 14.4675i | −1.22728 | + | 1.03870i | ||||
\(195\) | −2.99981 | − | 5.97092i | −0.214821 | − | 0.427586i | ||||
\(196\) | −1.78057 | + | 10.6236i | −0.127183 | + | 0.758830i | ||||
\(197\) | 18.4367 | 1.31356 | 0.656782 | − | 0.754081i | \(-0.271917\pi\) | ||||
0.656782 | + | 0.754081i | \(0.271917\pi\) | |||||||
\(198\) | −0.806303 | − | 0.332744i | −0.0573015 | − | 0.0236471i | ||||
\(199\) | − | 16.5580i | − | 1.17377i | −0.809671 | − | 0.586884i | \(-0.800354\pi\) | ||
0.809671 | − | 0.586884i | \(-0.199646\pi\) | |||||||
\(200\) | 9.18905 | − | 5.46216i | 0.649764 | − | 0.386233i | ||||
\(201\) | − | 17.2963i | − | 1.21998i | ||||||
\(202\) | 3.19968 | − | 2.70803i | 0.225129 | − | 0.190536i | ||||
\(203\) | 12.4291 | 0.872354 | ||||||||
\(204\) | −0.781191 | + | 4.66092i | −0.0546943 | + | 0.326330i | ||||
\(205\) | 1.74084i | 0.121585i | ||||||||
\(206\) | 9.61655 | − | 8.13890i | 0.670017 | − | 0.567064i | ||||
\(207\) | − | 0.480748i | − | 0.0334143i | ||||||
\(208\) | −1.91888 | − | 14.2940i | −0.133050 | − | 0.991109i | ||||
\(209\) | 1.44304 | + | 2.79197i | 0.0998175 | + | 0.193125i | ||||
\(210\) | 2.54171 | − | 2.15116i | 0.175395 | − | 0.148444i | ||||
\(211\) | 21.6526 | 1.49063 | 0.745314 | − | 0.666714i | \(-0.232300\pi\) | ||||
0.745314 | + | 0.666714i | \(0.232300\pi\) | |||||||
\(212\) | −1.76450 | + | 10.5278i | −0.121186 | + | 0.723050i | ||||
\(213\) | 18.6602i | 1.27858i | ||||||||
\(214\) | −12.5089 | − | 14.7799i | −0.855087 | − | 1.01033i | ||||
\(215\) | − | 4.68454i | − | 0.319483i | ||||||
\(216\) | 7.72399 | + | 12.9942i | 0.525551 | + | 0.884141i | ||||
\(217\) | 7.16465i | 0.486368i | ||||||||
\(218\) | 7.30493 | + | 8.63116i | 0.494752 | + | 0.584576i | ||||
\(219\) | − | 16.7959i | − | 1.13496i | ||||||
\(220\) | −6.97681 | + | 2.24240i | −0.470376 | + | 0.151183i | ||||
\(221\) | 4.53828 | − | 2.28005i | 0.305278 | − | 0.153373i | ||||
\(222\) | 12.0402 | + | 14.2261i | 0.808082 | + | 0.954792i | ||||
\(223\) | 4.27837 | 0.286501 | 0.143251 | − | 0.989686i | \(-0.454245\pi\) | ||||
0.143251 | + | 0.989686i | \(0.454245\pi\) | |||||||
\(224\) | 6.69988 | − | 2.60053i | 0.447655 | − | 0.173755i | ||||
\(225\) | 0.702853 | 0.0468569 | ||||||||
\(226\) | −4.09360 | − | 4.83680i | −0.272302 | − | 0.321739i | ||||
\(227\) | − | 1.22344i | − | 0.0812028i | −0.999175 | − | 0.0406014i | \(-0.987073\pi\) | ||
0.999175 | − | 0.0406014i | \(-0.0129274\pi\) | |||||||
\(228\) | 0.525522 | − | 3.13549i | 0.0348036 | − | 0.207653i | ||||
\(229\) | − | 11.1604i | − | 0.737498i | −0.929529 | − | 0.368749i | \(-0.879786\pi\) | ||
0.929529 | − | 0.368749i | \(-0.120214\pi\) | |||||||
\(230\) | −2.60931 | − | 3.08303i | −0.172053 | − | 0.203289i | ||||
\(231\) | 6.27933 | − | 3.24551i | 0.413150 | − | 0.213539i | ||||
\(232\) | 14.1388 | + | 23.7858i | 0.928255 | + | 1.56161i | ||||
\(233\) | − | 9.25724i | − | 0.606462i | −0.952917 | − | 0.303231i | \(-0.901935\pi\) | ||
0.952917 | − | 0.303231i | \(-0.0980654\pi\) | |||||||
\(234\) | 0.371763 | − | 0.872336i | 0.0243029 | − | 0.0570264i | ||||
\(235\) | − | 0.292928i | − | 0.0191085i | ||||||
\(236\) | 0.264894 | − | 1.58047i | 0.0172431 | − | 0.102880i | ||||
\(237\) | 13.2857i | 0.863001i | ||||||||
\(238\) | 1.63502 | + | 1.93186i | 0.105983 | + | 0.125224i | ||||
\(239\) | 20.7938i | 1.34504i | 0.740079 | + | 0.672520i | \(0.234788\pi\) | ||||
−0.740079 | + | 0.672520i | \(0.765212\pi\) | |||||||
\(240\) | 7.00804 | + | 2.41706i | 0.452367 | + | 0.156020i | ||||
\(241\) | −0.892259 | −0.0574755 | −0.0287377 | − | 0.999587i | \(-0.509149\pi\) | ||||
−0.0287377 | + | 0.999587i | \(0.509149\pi\) | |||||||
\(242\) | −15.4993 | + | 1.33082i | −0.996334 | + | 0.0855483i | ||||
\(243\) | 1.92978i | 0.123796i | ||||||||
\(244\) | 8.33478 | + | 1.39695i | 0.533579 | + | 0.0894303i | ||||
\(245\) | 5.95027i | 0.380149i | ||||||||
\(246\) | 2.85341 | − | 2.41496i | 0.181927 | − | 0.153973i | ||||
\(247\) | −3.05299 | + | 1.53383i | −0.194257 | + | 0.0975953i | ||||
\(248\) | −13.7111 | + | 8.15016i | −0.870656 | + | 0.517535i | ||||
\(249\) | 21.1314 | 1.33915 | ||||||||
\(250\) | 10.4704 | − | 8.86157i | 0.662207 | − | 0.560455i | ||||
\(251\) | − | 16.1974i | − | 1.02237i | −0.859471 | − | 0.511185i | \(-0.829207\pi\) | ||
0.859471 | − | 0.511185i | \(-0.170793\pi\) | |||||||
\(252\) | 0.466031 | + | 0.0781090i | 0.0293572 | + | 0.00492040i | ||||
\(253\) | −3.93672 | − | 7.61668i | −0.247500 | − | 0.478856i | ||||
\(254\) | 15.9501 | + | 18.8458i | 1.00080 | + | 1.18249i | ||||
\(255\) | 2.61057i | 0.163480i | ||||||||
\(256\) | 12.5981 | + | 9.86343i | 0.787383 | + | 0.616464i | ||||
\(257\) | −24.6407 | −1.53705 | −0.768523 | − | 0.639822i | \(-0.779008\pi\) | ||||
−0.768523 | + | 0.639822i | \(0.779008\pi\) | |||||||
\(258\) | −7.67843 | + | 6.49859i | −0.478038 | + | 0.404585i | ||||
\(259\) | 9.98083 | 0.620179 | ||||||||
\(260\) | −2.35058 | − | 7.61206i | −0.145777 | − | 0.472080i | ||||
\(261\) | 1.81933i | 0.112614i | ||||||||
\(262\) | −6.47544 | − | 7.65108i | −0.400054 | − | 0.472685i | ||||
\(263\) | 7.39174 | 0.455794 | 0.227897 | − | 0.973685i | \(-0.426815\pi\) | ||||
0.227897 | + | 0.973685i | \(0.426815\pi\) | |||||||
\(264\) | 13.3540 | + | 8.32493i | 0.821884 | + | 0.512364i | ||||
\(265\) | 5.89658i | 0.362224i | ||||||||
\(266\) | −1.09991 | − | 1.29960i | −0.0674398 | − | 0.0796836i | ||||
\(267\) | −8.43974 | −0.516504 | ||||||||
\(268\) | 3.40869 | − | 20.3377i | 0.208219 | − | 1.24232i | ||||
\(269\) | −17.0000 | −1.03651 | −0.518254 | − | 0.855227i | \(-0.673418\pi\) | ||||
−0.518254 | + | 0.855227i | \(0.673418\pi\) | |||||||
\(270\) | 5.39448 | + | 6.37386i | 0.328297 | + | 0.387901i | ||||
\(271\) | 7.36919i | 0.447647i | 0.974630 | + | 0.223823i | \(0.0718539\pi\) | ||||
−0.974630 | + | 0.223823i | \(0.928146\pi\) | |||||||
\(272\) | −1.83712 | + | 5.32656i | −0.111392 | + | 0.322970i | ||||
\(273\) | 3.44969 | + | 6.86638i | 0.208785 | + | 0.415572i | ||||
\(274\) | −15.3259 | + | 12.9710i | −0.925872 | + | 0.783606i | ||||
\(275\) | 11.1356 | − | 5.75548i | 0.671500 | − | 0.347069i | ||||
\(276\) | −1.43366 | + | 8.55382i | −0.0862962 | + | 0.514880i | ||||
\(277\) | − | 17.7070i | − | 1.06391i | −0.846772 | − | 0.531955i | \(-0.821457\pi\) | ||
0.846772 | − | 0.531955i | \(-0.178543\pi\) | |||||||
\(278\) | 8.63490 | + | 10.2026i | 0.517887 | + | 0.611910i | ||||
\(279\) | −1.04874 | −0.0627862 | ||||||||
\(280\) | 3.41260 | − | 2.02852i | 0.203942 | − | 0.121227i | ||||
\(281\) | 13.3348 | 0.795485 | 0.397743 | − | 0.917497i | \(-0.369794\pi\) | ||||
0.397743 | + | 0.917497i | \(0.369794\pi\) | |||||||
\(282\) | −0.480138 | + | 0.406362i | −0.0285918 | + | 0.0241985i | ||||
\(283\) | −0.959367 | −0.0570284 | −0.0285142 | − | 0.999593i | \(-0.509078\pi\) | ||||
−0.0285142 | + | 0.999593i | \(0.509078\pi\) | |||||||
\(284\) | −3.67749 | + | 21.9415i | −0.218219 | + | 1.30199i | ||||
\(285\) | − | 1.75618i | − | 0.104027i | ||||||
\(286\) | −1.25336 | − | 16.8650i | −0.0741125 | − | 0.997250i | ||||
\(287\) | − | 2.00191i | − | 0.118169i | ||||||
\(288\) | 0.380656 | + | 0.980704i | 0.0224304 | + | 0.0577886i | ||||
\(289\) | 15.0158 | 0.883282 | ||||||||
\(290\) | 9.87459 | + | 11.6674i | 0.579856 | + | 0.685130i | ||||
\(291\) | 26.5639 | 1.55720 | ||||||||
\(292\) | 3.31008 | − | 19.7494i | 0.193708 | − | 1.15574i | ||||
\(293\) | 6.63138 | 0.387409 | 0.193705 | − | 0.981060i | \(-0.437950\pi\) | ||||
0.193705 | + | 0.981060i | \(0.437950\pi\) | |||||||
\(294\) | 9.75308 | − | 8.25446i | 0.568811 | − | 0.481410i | ||||
\(295\) | − | 0.885216i | − | 0.0515393i | ||||||
\(296\) | 11.3537 | + | 19.1005i | 0.659921 | + | 1.11019i | ||||
\(297\) | 8.13878 | + | 15.7467i | 0.472260 | + | 0.913717i | ||||
\(298\) | −10.5270 | − | 12.4382i | −0.609812 | − | 0.720526i | ||||
\(299\) | 8.32876 | − | 4.18439i | 0.481664 | − | 0.241990i | ||||
\(300\) | −12.5057 | − | 2.09601i | −0.722016 | − | 0.121013i | ||||
\(301\) | 5.38709i | 0.310507i | ||||||||
\(302\) | 5.33908 | − | 4.51870i | 0.307230 | − | 0.260022i | ||||
\(303\) | −4.97225 | −0.285648 | ||||||||
\(304\) | 1.23586 | − | 3.58328i | 0.0708816 | − | 0.205515i | ||||
\(305\) | 4.66829 | 0.267305 | ||||||||
\(306\) | −0.282779 | + | 0.239328i | −0.0161654 | + | 0.0136815i | ||||
\(307\) | − | 7.55650i | − | 0.431272i | −0.976474 | − | 0.215636i | \(-0.930818\pi\) | ||
0.976474 | − | 0.215636i | \(-0.0691825\pi\) | |||||||
\(308\) | 8.02313 | − | 2.57870i | 0.457160 | − | 0.146935i | ||||
\(309\) | −14.9439 | −0.850131 | ||||||||
\(310\) | −6.72553 | + | 5.69211i | −0.381985 | + | 0.323290i | ||||
\(311\) | − | 5.99168i | − | 0.339757i | −0.985465 | − | 0.169879i | \(-0.945662\pi\) | ||
0.985465 | − | 0.169879i | \(-0.0543376\pi\) | |||||||
\(312\) | −9.21610 | + | 14.4126i | −0.521759 | + | 0.815952i | ||||
\(313\) | −3.35058 | −0.189386 | −0.0946931 | − | 0.995507i | \(-0.530187\pi\) | ||||
−0.0946931 | + | 0.995507i | \(0.530187\pi\) | |||||||
\(314\) | 13.1146 | + | 15.4956i | 0.740098 | + | 0.874466i | ||||
\(315\) | 0.261023 | 0.0147070 | ||||||||
\(316\) | −2.61831 | + | 15.6219i | −0.147291 | + | 0.878803i | ||||
\(317\) | − | 13.8147i | − | 0.775912i | −0.921678 | − | 0.387956i | \(-0.873181\pi\) | ||
0.921678 | − | 0.387956i | \(-0.126819\pi\) | |||||||
\(318\) | 9.66508 | − | 8.17998i | 0.541991 | − | 0.458710i | ||||
\(319\) | 14.8980 | + | 28.8244i | 0.834129 | + | 1.61385i | ||||
\(320\) | 7.76401 | + | 4.22320i | 0.434021 | + | 0.236084i | ||||
\(321\) | 22.9676i | 1.28193i | ||||||||
\(322\) | 3.00063 | + | 3.54540i | 0.167218 | + | 0.197577i | ||||
\(323\) | 1.33481 | 0.0742708 | ||||||||
\(324\) | 2.77951 | − | 16.5837i | 0.154417 | − | 0.921317i | ||||
\(325\) | 6.11758 | + | 12.1766i | 0.339342 | + | 0.675438i | ||||
\(326\) | −8.46434 | − | 10.0011i | −0.468797 | − | 0.553908i | ||||
\(327\) | − | 13.4127i | − | 0.741722i | ||||||
\(328\) | 3.83110 | − | 2.27728i | 0.211537 | − | 0.125742i | ||||
\(329\) | 0.336859i | 0.0185716i | ||||||||
\(330\) | 8.03535 | + | 3.31601i | 0.442331 | + | 0.182540i | ||||
\(331\) | −5.70350 | −0.313493 | −0.156746 | − | 0.987639i | \(-0.550100\pi\) | ||||
−0.156746 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(332\) | 24.8472 | + | 4.16451i | 1.36367 | + | 0.228557i | ||||
\(333\) | 1.46096i | 0.0800600i | ||||||||
\(334\) | 19.6931 | − | 16.6671i | 1.07756 | − | 0.911984i | ||||
\(335\) | − | 11.3911i | − | 0.622363i | ||||||
\(336\) | −8.05904 | − | 2.77954i | −0.439657 | − | 0.151637i | ||||
\(337\) | − | 21.1705i | − | 1.15323i | −0.817015 | − | 0.576616i | \(-0.804373\pi\) | ||
0.817015 | − | 0.576616i | \(-0.195627\pi\) | |||||||
\(338\) | 18.3486 | − | 1.15212i | 0.998034 | − | 0.0626669i | ||||
\(339\) | 7.51630i | 0.408230i | ||||||||
\(340\) | −0.514483 | + | 3.06962i | −0.0279017 | + | 0.166474i | ||||
\(341\) | −16.6155 | + | 8.58783i | −0.899782 | + | 0.465057i | ||||
\(342\) | 0.190231 | − | 0.161001i | 0.0102865 | − | 0.00870593i | ||||
\(343\) | − | 15.7359i | − | 0.849661i | ||||||
\(344\) | −10.3094 | + | 6.12809i | −0.555843 | + | 0.330404i | ||||
\(345\) | 4.79098i | 0.257937i | ||||||||
\(346\) | −15.0952 | + | 12.7758i | −0.811525 | + | 0.686829i | ||||
\(347\) | −26.1754 | −1.40517 | −0.702584 | − | 0.711601i | \(-0.747970\pi\) | ||||
−0.702584 | + | 0.711601i | \(0.747970\pi\) | |||||||
\(348\) | 5.42551 | − | 32.3709i | 0.290838 | − | 1.73526i | ||||
\(349\) | 0.953092 | 0.0510179 | 0.0255089 | − | 0.999675i | \(-0.491879\pi\) | ||||
0.0255089 | + | 0.999675i | \(0.491879\pi\) | |||||||
\(350\) | −5.18337 | + | 4.38691i | −0.277063 | + | 0.234490i | ||||
\(351\) | −17.2189 | + | 8.65081i | −0.919075 | + | 0.461746i | ||||
\(352\) | 14.0616 | + | 12.4206i | 0.749487 | + | 0.662020i | ||||
\(353\) | − | 34.4757i | − | 1.83496i | −0.397786 | − | 0.917478i | \(-0.630221\pi\) | ||
0.397786 | − | 0.917478i | \(-0.369779\pi\) | |||||||
\(354\) | −1.45096 | + | 1.22801i | −0.0771175 | + | 0.0652679i | ||||
\(355\) | 12.2894i | 0.652252i | ||||||||
\(356\) | −9.92382 | − | 1.66328i | −0.525961 | − | 0.0881535i | ||||
\(357\) | − | 3.00208i | − | 0.158887i | ||||||
\(358\) | −14.9722 | + | 12.6716i | −0.791304 | + | 0.669716i | ||||
\(359\) | − | 3.10906i | − | 0.164090i | −0.996629 | − | 0.0820450i | \(-0.973855\pi\) | ||
0.996629 | − | 0.0820450i | \(-0.0261451\pi\) | |||||||
\(360\) | 0.296927 | + | 0.499524i | 0.0156494 | + | 0.0263272i | ||||
\(361\) | 18.1020 | 0.952739 | ||||||||
\(362\) | −9.62575 | − | 11.3733i | −0.505918 | − | 0.597769i | ||||
\(363\) | 15.0533 | + | 10.6722i | 0.790094 | + | 0.560145i | ||||
\(364\) | 2.70310 | + | 8.75365i | 0.141681 | + | 0.458816i | ||||
\(365\) | − | 11.0616i | − | 0.578989i | ||||||
\(366\) | −6.47604 | − | 7.65179i | −0.338508 | − | 0.399965i | ||||
\(367\) | 15.9489i | 0.832526i | 0.909244 | + | 0.416263i | \(0.136660\pi\) | ||||
−0.909244 | + | 0.416263i | \(0.863340\pi\) | |||||||
\(368\) | −3.37152 | + | 9.77542i | −0.175753 | + | 0.509579i | ||||
\(369\) | 0.293033 | 0.0152547 | ||||||||
\(370\) | 7.92949 | + | 9.36911i | 0.412235 | + | 0.487077i | ||||
\(371\) | − | 6.78089i | − | 0.352046i | ||||||
\(372\) | 18.6599 | + | 3.12748i | 0.967470 | + | 0.162152i | ||||
\(373\) | 12.2599i | 0.634792i | 0.948293 | + | 0.317396i | \(0.102808\pi\) | ||||
−0.948293 | + | 0.317396i | \(0.897192\pi\) | |||||||
\(374\) | −2.52038 | + | 6.10738i | −0.130326 | + | 0.315805i | ||||
\(375\) | −16.2708 | −0.840222 | ||||||||
\(376\) | −0.644652 | + | 0.383194i | −0.0332454 | + | 0.0197617i | ||||
\(377\) | −31.5191 | + | 15.8353i | −1.62332 | + | 0.815560i | ||||
\(378\) | −6.20349 | − | 7.32976i | −0.319073 | − | 0.377002i | ||||
\(379\) | −8.20078 | −0.421246 | −0.210623 | − | 0.977567i | \(-0.567549\pi\) | ||||
−0.210623 | + | 0.977567i | \(0.567549\pi\) | |||||||
\(380\) | 0.346102 | − | 2.06499i | 0.0177547 | − | 0.105932i | ||||
\(381\) | − | 29.2861i | − | 1.50037i | ||||||
\(382\) | −28.5529 | + | 24.1656i | −1.46089 | + | 1.23642i | ||||
\(383\) | −37.2973 | −1.90581 | −0.952903 | − | 0.303276i | \(-0.901920\pi\) | ||||
−0.952903 | + | 0.303276i | \(0.901920\pi\) | |||||||
\(384\) | −3.84831 | − | 18.5846i | −0.196383 | − | 0.948391i | ||||
\(385\) | 4.13549 | − | 2.13745i | 0.210764 | − | 0.108935i | ||||
\(386\) | 21.3678 | + | 25.2472i | 1.08759 | + | 1.28505i | ||||
\(387\) | −0.788543 | −0.0400839 | ||||||||
\(388\) | 31.2349 | + | 5.23512i | 1.58571 | + | 0.265773i | ||||
\(389\) | −8.68887 | −0.440543 | −0.220272 | − | 0.975439i | \(-0.570694\pi\) | ||||
−0.220272 | + | 0.975439i | \(0.570694\pi\) | |||||||
\(390\) | −3.70486 | + | 8.69341i | −0.187603 | + | 0.440208i | ||||
\(391\) | −3.64145 | −0.184156 | ||||||||
\(392\) | 13.0949 | − | 7.78385i | 0.661390 | − | 0.393144i | ||||
\(393\) | 11.8896i | 0.599753i | ||||||||
\(394\) | −16.8442 | − | 19.9023i | −0.848597 | − | 1.00266i | ||||
\(395\) | 8.74981i | 0.440251i | ||||||||
\(396\) | 0.377461 | + | 1.17440i | 0.0189681 | + | 0.0590157i | ||||
\(397\) | − | 21.4029i | − | 1.07418i | −0.843524 | − | 0.537091i | \(-0.819523\pi\) | ||
0.843524 | − | 0.537091i | \(-0.180477\pi\) | |||||||
\(398\) | −17.8742 | + | 15.1278i | −0.895955 | + | 0.758286i | ||||
\(399\) | 2.01956i | 0.101104i | ||||||||
\(400\) | −14.2916 | − | 4.92916i | −0.714582 | − | 0.246458i | ||||
\(401\) | 13.9031i | 0.694288i | 0.937812 | + | 0.347144i | \(0.112848\pi\) | ||||
−0.937812 | + | 0.347144i | \(0.887152\pi\) | |||||||
\(402\) | −18.6712 | + | 15.8022i | −0.931233 | + | 0.788143i | ||||
\(403\) | −9.12812 | − | 18.1689i | −0.454704 | − | 0.905058i | ||||
\(404\) | −5.84658 | − | 0.979914i | −0.290878 | − | 0.0487526i | ||||
\(405\) | − | 9.28850i | − | 0.461549i | ||||||
\(406\) | −11.3555 | − | 13.4171i | −0.563564 | − | 0.665880i | ||||
\(407\) | 11.9634 | + | 23.1465i | 0.593004 | + | 1.14733i | ||||
\(408\) | 5.74513 | − | 3.41502i | 0.284426 | − | 0.169069i | ||||
\(409\) | 35.8638 | 1.77335 | 0.886676 | − | 0.462391i | \(-0.153008\pi\) | ||||
0.886676 | + | 0.462391i | \(0.153008\pi\) | |||||||
\(410\) | 1.87922 | − | 1.59046i | 0.0928080 | − | 0.0785475i | ||||
\(411\) | 23.8162 | 1.17477 | ||||||||
\(412\) | −17.5717 | − | 2.94510i | −0.865697 | − | 0.145095i | ||||
\(413\) | 1.01797i | 0.0500912i | ||||||||
\(414\) | −0.518963 | + | 0.439221i | −0.0255056 | + | 0.0215865i | ||||
\(415\) | 13.9169 | 0.683152 | ||||||||
\(416\) | −13.6771 | + | 15.1307i | −0.670574 | + | 0.741842i | ||||
\(417\) | − | 15.8546i | − | 0.776405i | ||||||
\(418\) | 1.69551 | − | 4.10855i | 0.0829301 | − | 0.200956i | ||||
\(419\) | − | 1.60374i | − | 0.0783479i | −0.999232 | − | 0.0391740i | \(-0.987527\pi\) | ||
0.999232 | − | 0.0391740i | \(-0.0124726\pi\) | |||||||
\(420\) | −4.64431 | − | 0.778408i | −0.226619 | − | 0.0379824i | ||||
\(421\) | 6.30644i | 0.307357i | 0.988121 | + | 0.153679i | \(0.0491120\pi\) | ||||
−0.988121 | + | 0.153679i | \(0.950888\pi\) | |||||||
\(422\) | −19.7823 | − | 23.3738i | −0.962985 | − | 1.13782i | ||||
\(423\) | −0.0493082 | −0.00239745 | ||||||||
\(424\) | 12.9767 | − | 7.71361i | 0.630204 | − | 0.374606i | ||||
\(425\) | − | 5.32379i | − | 0.258242i | ||||||
\(426\) | 20.1435 | − | 17.0483i | 0.975956 | − | 0.825994i | ||||
\(427\) | −5.36840 | −0.259795 | ||||||||
\(428\) | −4.52639 | + | 27.0064i | −0.218791 | + | 1.30540i | ||||
\(429\) | −11.7889 | + | 16.2305i | −0.569173 | + | 0.783616i | ||||
\(430\) | −5.05692 | + | 4.27989i | −0.243866 | + | 0.206395i | ||||
\(431\) | 16.3244i | 0.786317i | 0.919471 | + | 0.393158i | \(0.128618\pi\) | ||||
−0.919471 | + | 0.393158i | \(0.871382\pi\) | |||||||
\(432\) | 6.97028 | − | 20.2097i | 0.335358 | − | 0.972339i | ||||
\(433\) | 19.7915 | 0.951118 | 0.475559 | − | 0.879684i | \(-0.342246\pi\) | ||||
0.475559 | + | 0.879684i | \(0.342246\pi\) | |||||||
\(434\) | 7.73417 | − | 6.54577i | 0.371252 | − | 0.314207i | ||||
\(435\) | − | 18.1308i | − | 0.869308i | ||||||
\(436\) | 2.64332 | − | 15.7712i | 0.126592 | − | 0.755303i | ||||
\(437\) | 2.44967 | 0.117184 | ||||||||
\(438\) | −18.1310 | + | 15.3451i | −0.866333 | + | 0.733216i | ||||
\(439\) | −30.0570 | −1.43454 | −0.717272 | − | 0.696794i | \(-0.754609\pi\) | ||||
−0.717272 | + | 0.696794i | \(0.754609\pi\) | |||||||
\(440\) | 8.79480 | + | 5.48269i | 0.419276 | + | 0.261377i | ||||
\(441\) | 1.00160 | 0.0476953 | ||||||||
\(442\) | −6.60755 | − | 2.81593i | −0.314289 | − | 0.133940i | ||||
\(443\) | 10.8198i | 0.514065i | 0.966403 | + | 0.257032i | \(0.0827447\pi\) | ||||
−0.966403 | + | 0.257032i | \(0.917255\pi\) | |||||||
\(444\) | 4.35679 | − | 25.9944i | 0.206764 | − | 1.23364i | ||||
\(445\) | −5.55831 | −0.263489 | ||||||||
\(446\) | −3.90881 | − | 4.61846i | −0.185087 | − | 0.218690i | ||||
\(447\) | 19.3287i | 0.914218i | ||||||||
\(448\) | −8.92839 | − | 4.85656i | −0.421827 | − | 0.229451i | ||||
\(449\) | − | 9.35084i | − | 0.441293i | −0.975354 | − | 0.220647i | \(-0.929183\pi\) | ||
0.975354 | − | 0.220647i | \(-0.0708168\pi\) | |||||||
\(450\) | −0.642141 | − | 0.758723i | −0.0302708 | − | 0.0357665i | ||||
\(451\) | 4.64264 | − | 2.39957i | 0.218613 | − | 0.112991i | ||||
\(452\) | −1.48129 | + | 8.83800i | −0.0696740 | + | 0.415704i | ||||
\(453\) | −8.29683 | −0.389819 | ||||||||
\(454\) | −1.32070 | + | 1.11776i | −0.0619833 | + | 0.0524592i | ||||
\(455\) | 2.27192 | + | 4.52211i | 0.106509 | + | 0.212000i | ||||
\(456\) | −3.86486 | + | 2.29735i | −0.180988 | + | 0.107583i | ||||
\(457\) | −8.51503 | −0.398316 | −0.199158 | − | 0.979967i | \(-0.563821\pi\) | ||||
−0.199158 | + | 0.979967i | \(0.563821\pi\) | |||||||
\(458\) | −12.0475 | + | 10.1963i | −0.562943 | + | 0.476443i | ||||
\(459\) | 7.52833 | 0.351392 | ||||||||
\(460\) | −0.944190 | + | 5.63344i | −0.0440231 | + | 0.262660i | ||||
\(461\) | −23.3707 | −1.08848 | −0.544241 | − | 0.838929i | \(-0.683182\pi\) | ||||
−0.544241 | + | 0.838929i | \(0.683182\pi\) | |||||||
\(462\) | −9.24042 | − | 3.81332i | −0.429903 | − | 0.177412i | ||||
\(463\) | −23.0963 | −1.07337 | −0.536687 | − | 0.843781i | \(-0.680324\pi\) | ||||
−0.536687 | + | 0.843781i | \(0.680324\pi\) | |||||||
\(464\) | 12.7591 | − | 36.9938i | 0.592326 | − | 1.71740i | ||||
\(465\) | 10.4514 | 0.484670 | ||||||||
\(466\) | −9.99310 | + | 8.45760i | −0.462922 | + | 0.391791i | ||||
\(467\) | 25.7065i | 1.18956i | 0.803890 | + | 0.594778i | \(0.202760\pi\) | ||||
−0.803890 | + | 0.594778i | \(0.797240\pi\) | |||||||
\(468\) | −1.28133 | + | 0.395669i | −0.0592294 | + | 0.0182898i | ||||
\(469\) | 13.0994i | 0.604876i | ||||||||
\(470\) | −0.316213 | + | 0.267625i | −0.0145858 | + | 0.0123446i | ||||
\(471\) | − | 24.0798i | − | 1.10954i | ||||||
\(472\) | −1.94811 | + | 1.15800i | −0.0896691 | + | 0.0533011i | ||||
\(473\) | −12.4932 | + | 6.45717i | −0.574437 | + | 0.296901i | ||||
\(474\) | 14.3418 | − | 12.1381i | 0.658741 | − | 0.557522i | ||||
\(475\) | 3.58142i | 0.164327i | ||||||||
\(476\) | 0.591640 | − | 3.52998i | 0.0271178 | − | 0.161796i | ||||
\(477\) | 0.992563 | 0.0454463 | ||||||||
\(478\) | 22.4467 | − | 18.9976i | 1.02669 | − | 0.868932i | ||||
\(479\) | − | 6.79360i | − | 0.310408i | −0.987882 | − | 0.155204i | \(-0.950397\pi\) | ||
0.987882 | − | 0.155204i | \(-0.0496034\pi\) | |||||||
\(480\) | −3.79349 | − | 9.77338i | −0.173148 | − | 0.446092i | ||||
\(481\) | −25.3105 | + | 12.7161i | −1.15406 | + | 0.579803i | ||||
\(482\) | 0.815186 | + | 0.963185i | 0.0371307 | + | 0.0438719i | ||||
\(483\) | − | 5.50949i | − | 0.250690i | ||||||
\(484\) | 15.5971 | + | 15.5155i | 0.708959 | + | 0.705250i | ||||
\(485\) | 17.4946 | 0.794390 | ||||||||
\(486\) | 2.08318 | − | 1.76309i | 0.0944950 | − | 0.0799753i | ||||
\(487\) | −11.9308 | −0.540638 | −0.270319 | − | 0.962771i | \(-0.587129\pi\) | ||||
−0.270319 | + | 0.962771i | \(0.587129\pi\) | |||||||
\(488\) | −6.10683 | − | 10.2736i | −0.276443 | − | 0.465063i | ||||
\(489\) | 15.5415i | 0.702810i | ||||||||
\(490\) | 6.42325 | − | 5.43628i | 0.290173 | − | 0.245586i | ||||
\(491\) | −20.2617 | −0.914398 | −0.457199 | − | 0.889364i | \(-0.651147\pi\) | ||||
−0.457199 | + | 0.889364i | \(0.651147\pi\) | |||||||
\(492\) | −5.21386 | − | 0.873867i | −0.235059 | − | 0.0393970i | ||||
\(493\) | 13.7806 | 0.620647 | ||||||||
\(494\) | 4.44502 | + | 1.89433i | 0.199991 | + | 0.0852300i | ||||
\(495\) | 0.312872 | + | 0.605338i | 0.0140626 | + | 0.0272079i | ||||
\(496\) | 21.3248 | + | 7.35486i | 0.957510 | + | 0.330243i | ||||
\(497\) | − | 14.1324i | − | 0.633926i | ||||||
\(498\) | −19.3061 | − | 22.8111i | −0.865125 | − | 1.02219i | ||||
\(499\) | 25.9523 | 1.16178 | 0.580891 | − | 0.813981i | \(-0.302704\pi\) | ||||
0.580891 | + | 0.813981i | \(0.302704\pi\) | |||||||
\(500\) | −19.1320 | − | 3.20660i | −0.855607 | − | 0.143404i | ||||
\(501\) | −30.6027 | −1.36723 | ||||||||
\(502\) | −17.4849 | + | 14.7983i | −0.780391 | + | 0.660479i | ||||
\(503\) | −21.2219 | −0.946236 | −0.473118 | − | 0.880999i | \(-0.656872\pi\) | ||||
−0.473118 | + | 0.880999i | \(0.656872\pi\) | |||||||
\(504\) | −0.341458 | − | 0.574438i | −0.0152097 | − | 0.0255875i | ||||
\(505\) | −3.27466 | −0.145720 | ||||||||
\(506\) | −4.62546 | + | 11.2084i | −0.205627 | + | 0.498274i | ||||
\(507\) | −17.4962 | − | 13.0174i | −0.777034 | − | 0.578125i | ||||
\(508\) | 5.77161 | − | 34.4359i | 0.256074 | − | 1.52784i | ||||
\(509\) | − | 3.90141i | − | 0.172927i | −0.996255 | − | 0.0864635i | \(-0.972443\pi\) | ||
0.996255 | − | 0.0864635i | \(-0.0275566\pi\) | |||||||
\(510\) | 2.81808 | − | 2.38507i | 0.124787 | − | 0.105613i | ||||
\(511\) | 12.7205i | 0.562721i | ||||||||
\(512\) | −0.862421 | − | 22.6110i | −0.0381140 | − | 0.999273i | ||||
\(513\) | −5.06445 | −0.223601 | ||||||||
\(514\) | 22.5123 | + | 26.5994i | 0.992973 | + | 1.17325i | ||||
\(515\) | −9.84189 | −0.433685 | ||||||||
\(516\) | 14.0303 | + | 2.35155i | 0.617651 | + | 0.103521i | ||||
\(517\) | −0.781208 | + | 0.403772i | −0.0343575 | + | 0.0177579i | ||||
\(518\) | −9.11869 | − | 10.7742i | −0.400652 | − | 0.473392i | ||||
\(519\) | 23.4577 | 1.02968 | ||||||||
\(520\) | −6.06961 | + | 9.49195i | −0.266170 | + | 0.416250i | ||||
\(521\) | 1.17608 | 0.0515252 | 0.0257626 | − | 0.999668i | \(-0.491799\pi\) | ||||
0.0257626 | + | 0.999668i | \(0.491799\pi\) | |||||||
\(522\) | 1.96395 | − | 1.66218i | 0.0859597 | − | 0.0727515i | ||||
\(523\) | −37.3218 | −1.63197 | −0.815983 | − | 0.578076i | \(-0.803804\pi\) | ||||
−0.815983 | + | 0.578076i | \(0.803804\pi\) | |||||||
\(524\) | −2.34317 | + | 13.9803i | −0.102362 | + | 0.610734i | ||||
\(525\) | 8.05486 | 0.351543 | ||||||||
\(526\) | −6.75324 | − | 7.97931i | −0.294455 | − | 0.347914i | ||||
\(527\) | 7.94370i | 0.346033i | ||||||||
\(528\) | −3.21384 | − | 22.0214i | −0.139864 | − | 0.958357i | ||||
\(529\) | 16.3171 | 0.709440 | ||||||||
\(530\) | 6.36530 | − | 5.38723i | 0.276491 | − | 0.234006i | ||||
\(531\) | −0.149007 | −0.00646637 | ||||||||
\(532\) | −0.398008 | + | 2.37468i | −0.0172558 | + | 0.102956i | ||||
\(533\) | 2.55054 | + | 5.07667i | 0.110476 | + | 0.219895i | ||||
\(534\) | 7.71072 | + | 9.11062i | 0.333675 | + | 0.394255i | ||||
\(535\) | 15.1262i | 0.653963i | ||||||||
\(536\) | −25.0686 | + | 14.9013i | −1.08280 | + | 0.643637i | ||||
\(537\) | 23.2665 | 1.00402 | ||||||||
\(538\) | 15.5315 | + | 18.3513i | 0.669612 | + | 0.791181i | ||||
\(539\) | 15.8687 | − | 8.20185i | 0.683515 | − | 0.353279i | ||||
\(540\) | 1.95202 | − | 11.6466i | 0.0840015 | − | 0.501188i | ||||
\(541\) | −18.2148 | −0.783113 | −0.391557 | − | 0.920154i | \(-0.628063\pi\) | ||||
−0.391557 | + | 0.920154i | \(0.628063\pi\) | |||||||
\(542\) | 7.95497 | − | 6.73264i | 0.341695 | − | 0.289192i | ||||
\(543\) | 17.6739i | 0.758462i | ||||||||
\(544\) | 7.42839 | − | 2.88330i | 0.318490 | − | 0.123620i | ||||
\(545\) | − | 8.83341i | − | 0.378382i | ||||||
\(546\) | 4.26049 | − | 9.99717i | 0.182332 | − | 0.427840i | ||||
\(547\) | 22.5434 | 0.963886 | 0.481943 | − | 0.876203i | \(-0.339931\pi\) | ||||
0.481943 | + | 0.876203i | \(0.339931\pi\) | |||||||
\(548\) | 28.0041 | + | 4.69362i | 1.19628 | + | 0.200501i | ||||
\(549\) | − | 0.785807i | − | 0.0335374i | ||||||
\(550\) | −16.3867 | − | 6.76242i | −0.698730 | − | 0.288351i | ||||
\(551\) | −9.27048 | −0.394936 | ||||||||
\(552\) | 10.5436 | − | 6.26732i | 0.448765 | − | 0.266755i | ||||
\(553\) | − | 10.0620i | − | 0.427881i | ||||||
\(554\) | −19.1145 | + | 16.1775i | −0.812099 | + | 0.687315i | ||||
\(555\) | − | 14.5594i | − | 0.618013i | ||||||
\(556\) | 3.12458 | − | 18.6426i | 0.132512 | − | 0.790621i | ||||
\(557\) | −8.53866 | −0.361795 | −0.180897 | − | 0.983502i | \(-0.557900\pi\) | ||||
−0.180897 | + | 0.983502i | \(0.557900\pi\) | |||||||
\(558\) | 0.958146 | + | 1.13210i | 0.0405616 | + | 0.0479256i | ||||
\(559\) | −6.86341 | − | 13.6612i | −0.290291 | − | 0.577806i | ||||
\(560\) | −5.30758 | − | 1.83057i | −0.224286 | − | 0.0773558i | ||||
\(561\) | 6.96212 | − | 3.59841i | 0.293941 | − | 0.151925i | ||||
\(562\) | −12.1829 | − | 14.3947i | −0.513905 | − | 0.607206i | ||||
\(563\) | 27.5197 | 1.15982 | 0.579908 | − | 0.814682i | \(-0.303089\pi\) | ||||
0.579908 | + | 0.814682i | \(0.303089\pi\) | |||||||
\(564\) | 0.877327 | + | 0.147044i | 0.0369421 | + | 0.00619167i | ||||
\(565\) | 4.95014i | 0.208254i | ||||||||
\(566\) | 0.876497 | + | 1.03563i | 0.0368419 | + | 0.0435307i | ||||
\(567\) | 10.6815i | 0.448581i | ||||||||
\(568\) | 27.0454 | − | 16.0764i | 1.13480 | − | 0.674549i | ||||
\(569\) | 18.7923i | 0.787815i | 0.919150 | + | 0.393908i | \(0.128877\pi\) | ||||
−0.919150 | + | 0.393908i | \(0.871123\pi\) | |||||||
\(570\) | −1.89578 | + | 1.60448i | −0.0794054 | + | 0.0672043i | ||||
\(571\) | 19.1261 | 0.800401 | 0.400200 | − | 0.916428i | \(-0.368941\pi\) | ||||
0.400200 | + | 0.916428i | \(0.368941\pi\) | |||||||
\(572\) | −17.0605 | + | 16.7612i | −0.713337 | + | 0.700821i | ||||
\(573\) | 44.3707 | 1.85361 | ||||||||
\(574\) | −2.16105 | + | 1.82899i | −0.0902004 | + | 0.0763405i | ||||
\(575\) | − | 9.77035i | − | 0.407452i | ||||||
\(576\) | 0.710886 | − | 1.30691i | 0.0296202 | − | 0.0544544i | ||||
\(577\) | 39.2228i | 1.63287i | 0.577440 | + | 0.816433i | \(0.304052\pi\) | ||||
−0.577440 | + | 0.816433i | \(0.695948\pi\) | |||||||
\(578\) | −13.7187 | − | 16.2094i | −0.570624 | − | 0.674222i | ||||
\(579\) | − | 39.2337i | − | 1.63049i | ||||||
\(580\) | 3.57317 | − | 21.3190i | 0.148368 | − | 0.885225i | ||||
\(581\) | −16.0040 | −0.663958 | ||||||||
\(582\) | −24.2693 | − | 28.6754i | −1.00599 | − | 1.18863i | ||||
\(583\) | 15.7256 | − | 8.12784i | 0.651286 | − | 0.336621i | ||||
\(584\) | −24.3434 | + | 14.4702i | −1.00734 | + | 0.598781i | ||||
\(585\) | −0.661931 | + | 0.332556i | −0.0273675 | + | 0.0137495i | ||||
\(586\) | −6.05856 | − | 7.15851i | −0.250277 | − | 0.295715i | ||||
\(587\) | 30.2126 | 1.24701 | 0.623504 | − | 0.781820i | \(-0.285709\pi\) | ||||
0.623504 | + | 0.781820i | \(0.285709\pi\) | |||||||
\(588\) | −17.8212 | − | 2.98692i | −0.734934 | − | 0.123178i | ||||
\(589\) | − | 5.34388i | − | 0.220191i | ||||||
\(590\) | −0.955582 | + | 0.808751i | −0.0393407 | + | 0.0332958i | ||||
\(591\) | 30.9278i | 1.27220i | ||||||||
\(592\) | 10.2458 | − | 29.7068i | 0.421100 | − | 1.22094i | ||||
\(593\) | −13.8113 | −0.567164 | −0.283582 | − | 0.958948i | \(-0.591523\pi\) | ||||
−0.283582 | + | 0.958948i | \(0.591523\pi\) | |||||||
\(594\) | 9.56268 | − | 23.1722i | 0.392361 | − | 0.950768i | ||||
\(595\) | − | 1.97713i | − | 0.0810545i | ||||||
\(596\) | −3.80925 | + | 22.7276i | −0.156033 | + | 0.930958i | ||||
\(597\) | 27.7762 | 1.13681 | ||||||||
\(598\) | −12.1263 | − | 5.16786i | −0.495882 | − | 0.211330i | ||||
\(599\) | − | 5.16630i | − | 0.211089i | −0.994415 | − | 0.105545i | \(-0.966341\pi\) | ||
0.994415 | − | 0.105545i | \(-0.0336586\pi\) | |||||||
\(600\) | 9.16281 | + | 15.4147i | 0.374070 | + | 0.629303i | ||||
\(601\) | 5.45833i | 0.222650i | 0.993784 | + | 0.111325i | \(0.0355094\pi\) | ||||
−0.993784 | + | 0.111325i | \(0.964491\pi\) | |||||||
\(602\) | 5.81531 | − | 4.92175i | 0.237014 | − | 0.200596i | ||||
\(603\) | −1.91745 | −0.0780846 | ||||||||
\(604\) | −9.75578 | − | 1.63511i | −0.396957 | − | 0.0665318i | ||||
\(605\) | 9.91392 | + | 7.02858i | 0.403058 | + | 0.285752i | ||||
\(606\) | 4.54274 | + | 5.36749i | 0.184536 | + | 0.218039i | ||||
\(607\) | −22.9795 | −0.932709 | −0.466355 | − | 0.884598i | \(-0.654433\pi\) | ||||
−0.466355 | + | 0.884598i | \(0.654433\pi\) | |||||||
\(608\) | −4.99722 | + | 1.93965i | −0.202664 | + | 0.0786631i | ||||
\(609\) | 20.8500i | 0.844883i | ||||||||
\(610\) | −4.26504 | − | 5.03937i | −0.172686 | − | 0.204038i | ||||
\(611\) | −0.429174 | − | 0.854243i | −0.0173625 | − | 0.0345590i | ||||
\(612\) | 0.516705 | + | 0.0866022i | 0.0208866 | + | 0.00350069i | ||||
\(613\) | −15.8032 | −0.638287 | −0.319143 | − | 0.947706i | \(-0.603395\pi\) | ||||
−0.319143 | + | 0.947706i | \(0.603395\pi\) | |||||||
\(614\) | −8.15717 | + | 6.90377i | −0.329196 | + | 0.278613i | ||||
\(615\) | −2.92027 | −0.117757 | ||||||||
\(616\) | −10.1138 | − | 6.30494i | −0.407495 | − | 0.254033i | ||||
\(617\) | − | 39.9111i | − | 1.60676i | −0.595467 | − | 0.803380i | \(-0.703033\pi\) | ||
0.595467 | − | 0.803380i | \(-0.296967\pi\) | |||||||
\(618\) | 13.6531 | + | 16.1318i | 0.549207 | + | 0.648917i | ||||
\(619\) | −30.1748 | −1.21283 | −0.606413 | − | 0.795150i | \(-0.707392\pi\) | ||||
−0.606413 | + | 0.795150i | \(0.707392\pi\) | |||||||
\(620\) | 12.2892 | + | 2.05972i | 0.493545 | + | 0.0827203i | ||||
\(621\) | 13.8162 | 0.554423 | ||||||||
\(622\) | −6.46796 | + | 5.47412i | −0.259342 | + | 0.219492i | ||||
\(623\) | 6.39189 | 0.256086 | ||||||||
\(624\) | 23.9783 | − | 3.21894i | 0.959899 | − | 0.128861i | ||||
\(625\) | 8.18148 | 0.327259 | ||||||||
\(626\) | 3.06116 | + | 3.61692i | 0.122349 | + | 0.144561i | ||||
\(627\) | −4.68355 | + | 2.42072i | −0.187043 | + | 0.0966742i | ||||
\(628\) | 4.74558 | − | 28.3141i | 0.189369 | − | 1.12986i | ||||
\(629\) | 11.0661 | 0.441234 | ||||||||
\(630\) | −0.238476 | − | 0.281772i | −0.00950111 | − | 0.0112261i | ||||
\(631\) | 31.8586 | 1.26827 | 0.634136 | − | 0.773222i | \(-0.281356\pi\) | ||||
0.634136 | + | 0.773222i | \(0.281356\pi\) | |||||||
\(632\) | 19.2559 | − | 11.4461i | 0.765957 | − | 0.455300i | ||||
\(633\) | 36.3224i | 1.44369i | ||||||||
\(634\) | −14.9129 | + | 12.6214i | −0.592265 | + | 0.501260i | ||||
\(635\) | − | 19.2874i | − | 0.765399i | ||||||
\(636\) | −17.6604 | − | 2.95997i | −0.700281 | − | 0.117370i | ||||
\(637\) | 8.71785 | + | 17.3523i | 0.345414 | + | 0.687523i | ||||
\(638\) | 17.5045 | − | 42.4168i | 0.693009 | − | 1.67930i | ||||
\(639\) | 2.06865 | 0.0818347 | ||||||||
\(640\) | −2.53445 | − | 12.2396i | −0.100183 | − | 0.483811i | ||||
\(641\) | −16.9700 | −0.670275 | −0.335137 | − | 0.942169i | \(-0.608783\pi\) | ||||
−0.335137 | + | 0.942169i | \(0.608783\pi\) | |||||||
\(642\) | 24.7933 | − | 20.9837i | 0.978515 | − | 0.828160i | ||||
\(643\) | −16.2635 | −0.641370 | −0.320685 | − | 0.947186i | \(-0.603913\pi\) | ||||
−0.320685 | + | 0.947186i | \(0.603913\pi\) | |||||||
\(644\) | 1.08579 | − | 6.47829i | 0.0427862 | − | 0.255281i | ||||
\(645\) | 7.85836 | 0.309422 | ||||||||
\(646\) | −1.21951 | − | 1.44091i | −0.0479809 | − | 0.0566920i | ||||
\(647\) | − | 17.5307i | − | 0.689205i | −0.938749 | − | 0.344602i | \(-0.888014\pi\) | ||
0.938749 | − | 0.344602i | \(-0.111986\pi\) | |||||||
\(648\) | −20.4414 | + | 12.1508i | −0.803013 | + | 0.477327i | ||||
\(649\) | −2.36078 | + | 1.22018i | −0.0926687 | + | 0.0478963i | ||||
\(650\) | 7.55541 | − | 17.7287i | 0.296348 | − | 0.695376i | ||||
\(651\) | −12.0188 | −0.471052 | ||||||||
\(652\) | −3.06286 | + | 18.2743i | −0.119951 | + | 0.715679i | ||||
\(653\) | 39.6406 | 1.55126 | 0.775628 | − | 0.631190i | \(-0.217433\pi\) | ||||
0.775628 | + | 0.631190i | \(0.217433\pi\) | |||||||
\(654\) | −14.4788 | + | 12.2541i | −0.566167 | + | 0.479172i | ||||
\(655\) | 7.83036i | 0.305958i | ||||||||
\(656\) | −5.95847 | − | 2.05506i | −0.232639 | − | 0.0802367i | ||||
\(657\) | −1.86198 | −0.0726427 | ||||||||
\(658\) | 0.363636 | − | 0.307761i | 0.0141760 | − | 0.0119978i | ||||
\(659\) | 15.2238 | 0.593036 | 0.296518 | − | 0.955027i | \(-0.404175\pi\) | ||||
0.296518 | + | 0.955027i | \(0.404175\pi\) | |||||||
\(660\) | −3.76165 | − | 11.7037i | −0.146422 | − | 0.455564i | ||||
\(661\) | − | 25.4504i | − | 0.989906i | −0.868920 | − | 0.494953i | \(-0.835185\pi\) | ||
0.868920 | − | 0.494953i | \(-0.164815\pi\) | |||||||
\(662\) | 5.21083 | + | 6.15687i | 0.202525 | + | 0.239294i | ||||
\(663\) | 3.82480 | + | 7.61300i | 0.148543 | + | 0.295665i | ||||
\(664\) | −18.2054 | − | 30.6271i | −0.706505 | − | 1.18856i | ||||
\(665\) | 1.33005i | 0.0515773i | ||||||||
\(666\) | 1.57709 | − | 1.33476i | 0.0611110 | − | 0.0517209i | ||||
\(667\) | 25.2905 | 0.979251 | ||||||||
\(668\) | −35.9840 | − | 6.03108i | −1.39226 | − | 0.233350i | ||||
\(669\) | 7.17700i | 0.277479i | ||||||||
\(670\) | −12.2966 | + | 10.4071i | −0.475059 | + | 0.402063i | ||||
\(671\) | −6.43477 | − | 12.4498i | −0.248411 | − | 0.480621i | ||||
\(672\) | 4.36241 | + | 11.2391i | 0.168283 | + | 0.433558i | ||||
\(673\) | 2.38318i | 0.0918648i | 0.998945 | + | 0.0459324i | \(0.0146259\pi\) | ||||
−0.998945 | + | 0.0459324i | \(0.985374\pi\) | |||||||
\(674\) | −22.8534 | + | 19.3418i | −0.880279 | + | 0.745019i | ||||
\(675\) | 20.1992i | 0.777468i | ||||||||
\(676\) | −18.0074 | − | 18.7546i | −0.692592 | − | 0.721330i | ||||
\(677\) | − | 45.9970i | − | 1.76781i | −0.467668 | − | 0.883904i | \(-0.654906\pi\) | ||
0.467668 | − | 0.883904i | \(-0.345094\pi\) | |||||||
\(678\) | 8.11378 | − | 6.86704i | 0.311608 | − | 0.263727i | ||||
\(679\) | −20.1183 | −0.772070 | ||||||||
\(680\) | 3.78367 | − | 2.24909i | 0.145097 | − | 0.0862486i | ||||
\(681\) | 2.05234 | 0.0786457 | ||||||||
\(682\) | 24.4508 | + | 10.0903i | 0.936268 | + | 0.386377i | ||||
\(683\) | −11.4042 | −0.436371 | −0.218186 | − | 0.975907i | \(-0.570014\pi\) | ||||
−0.218186 | + | 0.975907i | \(0.570014\pi\) | |||||||
\(684\) | −0.347598 | − | 0.0582589i | −0.0132907 | − | 0.00222759i | ||||
\(685\) | 15.6850 | 0.599295 | ||||||||
\(686\) | −16.9868 | + | 14.3767i | −0.648559 | + | 0.548904i | ||||
\(687\) | 18.7216 | 0.714274 | ||||||||
\(688\) | 16.0340 | + | 5.53010i | 0.611292 | + | 0.210833i | ||||
\(689\) | 8.63919 | + | 17.1957i | 0.329127 | + | 0.655105i | ||||
\(690\) | 5.17181 | − | 4.37713i | 0.196888 | − | 0.166635i | ||||
\(691\) | −13.8920 | −0.528478 | −0.264239 | − | 0.964457i | \(-0.585121\pi\) | ||||
−0.264239 | + | 0.964457i | \(0.585121\pi\) | |||||||
\(692\) | 27.5826 | + | 4.62297i | 1.04853 | + | 0.175739i | ||||
\(693\) | −0.359794 | − | 0.696122i | −0.0136675 | − | 0.0264435i | ||||
\(694\) | 23.9143 | + | 28.2561i | 0.907776 | + | 1.07259i | ||||
\(695\) | − | 10.4417i | − | 0.396075i | ||||||
\(696\) | −39.9009 | + | 23.7179i | −1.51244 | + | 0.899024i | ||||
\(697\) | − | 2.21959i | − | 0.0840731i | ||||||
\(698\) | −0.870764 | − | 1.02885i | −0.0329589 | − | 0.0389427i | ||||
\(699\) | 15.5291 | 0.587364 | ||||||||
\(700\) | 9.47126 | + | 1.58743i | 0.357980 | + | 0.0599991i | ||||
\(701\) | − | 21.5113i | − | 0.812471i | −0.913768 | − | 0.406236i | \(-0.866841\pi\) | ||
0.913768 | − | 0.406236i | \(-0.133159\pi\) | |||||||
\(702\) | 25.0700 | + | 10.6840i | 0.946205 | + | 0.403243i | ||||
\(703\) | −7.44438 | −0.280770 | ||||||||
\(704\) | 0.560931 | − | 26.5271i | 0.0211409 | − | 0.999777i | ||||
\(705\) | 0.491389 | 0.0185068 | ||||||||
\(706\) | −37.2162 | + | 31.4977i | −1.40065 | + | 1.18543i | ||||
\(707\) | 3.76576 | 0.141626 | ||||||||
\(708\) | 2.65125 | + | 0.444361i | 0.0996400 | + | 0.0167001i | ||||
\(709\) | 43.6867i | 1.64069i | 0.571871 | + | 0.820344i | \(0.306218\pi\) | ||||
−0.571871 | + | 0.820344i | \(0.693782\pi\) | |||||||
\(710\) | 13.2663 | − | 11.2278i | 0.497874 | − | 0.421372i | ||||
\(711\) | 1.47284 | 0.0552360 | ||||||||
\(712\) | 7.27110 | + | 12.2323i | 0.272496 | + | 0.458424i | ||||
\(713\) | 14.5785i | 0.545968i | ||||||||
\(714\) | −3.24072 | + | 2.74276i | −0.121281 | + | 0.102645i | ||||
\(715\) | −7.76401 | + | 10.6892i | −0.290358 | + | 0.399753i | ||||
\(716\) | 27.3578 | + | 4.58529i | 1.02241 | + | 0.171360i | ||||
\(717\) | −34.8818 | −1.30268 | ||||||||
\(718\) | −3.35620 | + | 2.84050i | −0.125252 | + | 0.106007i | ||||
\(719\) | 30.3223i | 1.13083i | 0.824806 | + | 0.565416i | \(0.191284\pi\) | ||||
−0.824806 | + | 0.565416i | \(0.808716\pi\) | |||||||
\(720\) | 0.267953 | − | 0.776905i | 0.00998601 | − | 0.0289535i | ||||
\(721\) | 11.3179 | 0.421500 | ||||||||
\(722\) | −16.5384 | − | 19.5410i | −0.615495 | − | 0.727240i | ||||
\(723\) | − | 1.49677i | − | 0.0556656i | ||||||
\(724\) | −3.48312 | + | 20.7818i | −0.129449 | + | 0.772349i | ||||
\(725\) | 36.9747i | 1.37320i | ||||||||
\(726\) | −2.23246 | − | 26.0002i | −0.0828543 | − | 0.964959i | ||||
\(727\) | 31.9183i | 1.18379i | 0.806017 | + | 0.591893i | \(0.201619\pi\) | ||||
−0.806017 | + | 0.591893i | \(0.798381\pi\) | |||||||
\(728\) | 6.97988 | − | 10.9155i | 0.258691 | − | 0.404554i | ||||
\(729\) | −28.4598 | −1.05407 | ||||||||
\(730\) | −11.9409 | + | 10.1061i | −0.441951 | + | 0.374042i | ||||
\(731\) | 5.97285i | 0.220914i | ||||||||
\(732\) | −2.34339 | + | 13.9817i | −0.0866141 | + | 0.516777i | ||||
\(733\) | −17.4514 | −0.644582 | −0.322291 | − | 0.946641i | \(-0.604453\pi\) | ||||
−0.322291 | + | 0.946641i | \(0.604453\pi\) | |||||||
\(734\) | 17.2167 | − | 14.5712i | 0.635480 | − | 0.537834i | ||||
\(735\) | −9.98162 | −0.368178 | ||||||||
\(736\) | 13.6328 | − | 5.29149i | 0.502510 | − | 0.195047i | ||||
\(737\) | −30.3789 | + | 15.7015i | −1.11902 | + | 0.578372i | ||||
\(738\) | −0.267721 | − | 0.316326i | −0.00985494 | − | 0.0116441i | ||||
\(739\) | 28.6608i | 1.05431i | 0.849770 | + | 0.527153i | \(0.176740\pi\) | ||||
−0.849770 | + | 0.527153i | \(0.823260\pi\) | |||||||
\(740\) | 2.86933 | − | 17.1196i | 0.105479 | − | 0.629330i | ||||
\(741\) | −2.57301 | − | 5.12141i | −0.0945220 | − | 0.188140i | ||||
\(742\) | −7.31991 | + | 6.19516i | −0.268722 | + | 0.227431i | ||||
\(743\) | 26.5050i | 0.972373i | 0.873855 | + | 0.486186i | \(0.161612\pi\) | ||||
−0.873855 | + | 0.486186i | \(0.838388\pi\) | |||||||
\(744\) | −13.6720 | − | 23.0005i | −0.501238 | − | 0.843239i | ||||
\(745\) | 12.7297i | 0.466379i | ||||||||
\(746\) | 13.2344 | − | 11.2009i | 0.484546 | − | 0.410092i | ||||
\(747\) | − | 2.34261i | − | 0.0857116i | ||||||
\(748\) | 8.89553 | − | 2.85909i | 0.325253 | − | 0.104539i | ||||
\(749\) | − | 17.3947i | − | 0.635588i | ||||||
\(750\) | 14.8654 | + | 17.5642i | 0.542806 | + | 0.641354i | ||||
\(751\) | − | 0.329262i | − | 0.0120149i | −0.999982 | − | 0.00600746i | \(-0.998088\pi\) | ||
0.999982 | − | 0.00600746i | \(-0.00191225\pi\) | |||||||
\(752\) | 1.00262 | + | 0.345802i | 0.0365618 | + | 0.0126101i | ||||
\(753\) | 27.1713 | 0.990176 | ||||||||
\(754\) | 45.8906 | + | 19.5571i | 1.67124 | + | 0.712229i | ||||
\(755\) | −5.46419 | −0.198862 | ||||||||
\(756\) | −2.24476 | + | 13.3932i | −0.0816413 | + | 0.487107i | ||||
\(757\) | −6.45006 | −0.234431 | −0.117216 | − | 0.993106i | \(-0.537397\pi\) | ||||
−0.117216 | + | 0.993106i | \(0.537397\pi\) | |||||||
\(758\) | 7.49240 | + | 8.85266i | 0.272136 | + | 0.321543i | ||||
\(759\) | 12.7770 | − | 6.60388i | 0.463777 | − | 0.239706i | ||||
\(760\) | −2.54535 | + | 1.51300i | −0.0923294 | + | 0.0548824i | ||||
\(761\) | 29.8226 | 1.08107 | 0.540535 | − | 0.841322i | \(-0.318222\pi\) | ||||
0.540535 | + | 0.841322i | \(0.318222\pi\) | |||||||
\(762\) | −31.6140 | + | 26.7564i | −1.14526 | + | 0.969280i | ||||
\(763\) | 10.1582i | 0.367750i | ||||||||
\(764\) | 52.1730 | + | 8.74443i | 1.88755 | + | 0.316363i | ||||
\(765\) | 0.289406 | 0.0104635 | ||||||||
\(766\) | 34.0756 | + | 40.2621i | 1.23120 | + | 1.45473i | ||||
\(767\) | −1.29695 | − | 2.58149i | −0.0468301 | − | 0.0932121i | ||||
\(768\) | −16.5460 | + | 21.1335i | −0.597052 | + | 0.762588i | ||||
\(769\) | 49.1057 | 1.77080 | 0.885399 | − | 0.464832i | \(-0.153885\pi\) | ||||
0.885399 | + | 0.464832i | \(0.153885\pi\) | |||||||
\(770\) | −6.08562 | − | 2.51140i | −0.219311 | − | 0.0905047i | ||||
\(771\) | − | 41.3350i | − | 1.48864i | ||||||
\(772\) | 7.73204 | − | 46.1326i | 0.278282 | − | 1.66035i | ||||
\(773\) | 21.3112i | 0.766511i | 0.923642 | + | 0.383256i | \(0.125197\pi\) | ||||
−0.923642 | + | 0.383256i | \(0.874803\pi\) | |||||||
\(774\) | 0.720428 | + | 0.851224i | 0.0258953 | + | 0.0305966i | ||||
\(775\) | −21.3137 | −0.765610 | ||||||||
\(776\) | −22.8856 | − | 38.5007i | −0.821545 | − | 1.38210i | ||||
\(777\) | 16.7429i | 0.600649i | ||||||||
\(778\) | 7.93832 | + | 9.37955i | 0.284603 | + | 0.336273i | ||||
\(779\) | 1.49316i | 0.0534981i | ||||||||
\(780\) | 12.7693 | − | 3.94311i | 0.457214 | − | 0.141186i | ||||
\(781\) | 32.7745 | − | 16.9397i | 1.17276 | − | 0.606149i | ||||
\(782\) | 3.32690 | + | 3.93091i | 0.118970 | + | 0.140569i | ||||
\(783\) | −52.2855 | −1.86853 | ||||||||
\(784\) | −20.3663 | − | 7.02429i | −0.727368 | − | 0.250868i | ||||
\(785\) | − | 15.8587i | − | 0.566020i | ||||||
\(786\) | 12.8347 | − | 10.8626i | 0.457800 | − | 0.387456i | ||||
\(787\) | − | 32.9070i | − | 1.17301i | −0.809946 | − | 0.586504i | \(-0.800504\pi\) | ||
0.809946 | − | 0.586504i | \(-0.199496\pi\) | |||||||
\(788\) | −6.09515 | + | 36.3662i | −0.217131 | + | 1.29549i | ||||
\(789\) | 12.3997i | 0.441441i | ||||||||
\(790\) | 9.44534 | − | 7.99400i | 0.336050 | − | 0.284414i | ||||
\(791\) | − | 5.69252i | − | 0.202403i | ||||||
\(792\) | 0.922895 | − | 1.48042i | 0.0327936 | − | 0.0526043i | ||||
\(793\) | 13.6138 | − | 6.83960i | 0.483439 | − | 0.242881i | ||||
\(794\) | −23.1043 | + | 19.5541i | −0.819939 | + | 0.693951i | ||||
\(795\) | −9.89155 | −0.350817 | ||||||||
\(796\) | 32.6605 | + | 5.47405i | 1.15762 | + | 0.194023i | ||||
\(797\) | −51.0946 | −1.80986 | −0.904931 | − | 0.425558i | \(-0.860078\pi\) | ||||
−0.904931 | + | 0.425558i | \(0.860078\pi\) | |||||||
\(798\) | 2.18009 | − | 1.84511i | 0.0771744 | − | 0.0653161i | ||||
\(799\) | 0.373487i | 0.0132130i | ||||||||
\(800\) | 7.73615 | + | 19.9311i | 0.273514 | + | 0.704670i | ||||
\(801\) | 0.935623i | 0.0330586i | ||||||||
\(802\) | 15.0083 | − | 12.7021i | 0.529960 | − | 0.448528i | ||||
\(803\) | −29.5001 | + | 15.2473i | −1.04103 | + | 0.538064i | ||||
\(804\) | 34.1167 | + | 5.71811i | 1.20320 | + | 0.201662i | ||||
\(805\) | − | 3.62848i | − | 0.127887i | ||||||
\(806\) | −11.2735 | + | 26.4532i | −0.397093 | + | 0.931774i | ||||
\(807\) | − | 28.5176i | − | 1.00387i | ||||||
\(808\) | 4.28375 | + | 7.20660i | 0.150702 | + | 0.253527i | ||||
\(809\) | − | 29.9457i | − | 1.05283i | −0.850227 | − | 0.526417i | \(-0.823535\pi\) | ||
0.850227 | − | 0.526417i | \(-0.176465\pi\) | |||||||
\(810\) | −10.0268 | + | 8.48616i | −0.352307 | + | 0.298173i | ||||
\(811\) | 33.3267i | 1.17026i | 0.810940 | + | 0.585130i | \(0.198957\pi\) | ||||
−0.810940 | + | 0.585130i | \(0.801043\pi\) | |||||||
\(812\) | −4.10904 | + | 24.5163i | −0.144199 | + | 0.860353i | ||||
\(813\) | −12.3619 | −0.433550 | ||||||||
\(814\) | 14.0564 | − | 34.0615i | 0.492678 | − | 1.19386i | ||||
\(815\) | 10.2354i | 0.358531i | ||||||||
\(816\) | −8.93534 | − | 3.08178i | −0.312800 | − | 0.107884i | ||||
\(817\) | − | 4.01805i | − | 0.140574i | ||||||
\(818\) | −32.7659 | − | 38.7146i | −1.14563 | − | 1.35363i | ||||
\(819\) | 0.761201 | − | 0.382430i | 0.0265985 | − | 0.0133632i | ||||
\(820\) | −3.43378 | − | 0.575518i | −0.119913 | − | 0.0200979i | ||||
\(821\) | −24.6890 | −0.861652 | −0.430826 | − | 0.902435i | \(-0.641778\pi\) | ||||
−0.430826 | + | 0.902435i | \(0.641778\pi\) | |||||||
\(822\) | −21.7589 | − | 25.7093i | −0.758930 | − | 0.896716i | ||||
\(823\) | 16.3287i | 0.569183i | 0.958649 | + | 0.284592i | \(0.0918580\pi\) | ||||
−0.958649 | + | 0.284592i | \(0.908142\pi\) | |||||||
\(824\) | 12.8747 | + | 21.6592i | 0.448511 | + | 0.754535i | ||||
\(825\) | 9.65487 | + | 18.6800i | 0.336139 | + | 0.650355i | ||||
\(826\) | 1.09889 | − | 0.930041i | 0.0382354 | − | 0.0323603i | ||||
\(827\) | − | 15.4227i | − | 0.536299i | −0.963377 | − | 0.268150i | \(-0.913588\pi\) | ||
0.963377 | − | 0.268150i | \(-0.0864122\pi\) | |||||||
\(828\) | 0.948269 | + | 0.158934i | 0.0329546 | + | 0.00552335i | ||||
\(829\) | −48.9319 | −1.69947 | −0.849737 | − | 0.527207i | \(-0.823239\pi\) | ||||
−0.849737 | + | 0.527207i | \(0.823239\pi\) | |||||||
\(830\) | −12.7147 | − | 15.0231i | −0.441335 | − | 0.521460i | ||||
\(831\) | 29.7036 | 1.03041 | ||||||||
\(832\) | 28.8291 | + | 0.940592i | 0.999468 | + | 0.0326092i | ||||
\(833\) | − | 7.58667i | − | 0.262863i | ||||||
\(834\) | −17.1149 | + | 14.4851i | −0.592641 | + | 0.501578i | ||||
\(835\) | −20.1546 | −0.697477 | ||||||||
\(836\) | −5.98419 | + | 1.92337i | −0.206968 | + | 0.0665210i | ||||
\(837\) | − | 30.1395i | − | 1.04177i | ||||||
\(838\) | −1.73122 | + | 1.46521i | −0.0598041 | + | 0.0506148i | ||||
\(839\) | −4.51783 | −0.155973 | −0.0779865 | − | 0.996954i | \(-0.524849\pi\) | ||||
−0.0779865 | + | 0.996954i | \(0.524849\pi\) | |||||||
\(840\) | 3.40285 | + | 5.72466i | 0.117410 | + | 0.197520i | ||||
\(841\) | −66.7087 | −2.30030 | ||||||||
\(842\) | 6.80774 | − | 5.76169i | 0.234610 | − | 0.198561i | ||||
\(843\) | 22.3692i | 0.770435i | ||||||||
\(844\) | −7.15831 | + | 42.7095i | −0.246399 | + | 1.47012i | ||||
\(845\) | −11.5228 | − | 8.57312i | −0.396396 | − | 0.294924i | ||||
\(846\) | 0.0450489 | + | 0.0532277i | 0.00154881 | + | 0.00183001i | ||||
\(847\) | −11.4007 | − | 8.08266i | −0.391733 | − | 0.277724i | ||||
\(848\) | −20.1825 | − | 6.96091i | −0.693071 | − | 0.239039i | ||||
\(849\) | − | 1.60935i | − | 0.0552326i | ||||||
\(850\) | −5.74698 | + | 4.86392i | −0.197120 | + | 0.166831i | ||||
\(851\) | 20.3088 | 0.696175 | ||||||||
\(852\) | −36.8070 | − | 6.16902i | −1.26099 | − | 0.211347i | ||||
\(853\) | 37.0817 | 1.26965 | 0.634826 | − | 0.772655i | \(-0.281072\pi\) | ||||
0.634826 | + | 0.772655i | \(0.281072\pi\) | |||||||
\(854\) | 4.90467 | + | 5.79513i | 0.167834 | + | 0.198305i | ||||
\(855\) | −0.194689 | −0.00665821 | ||||||||
\(856\) | 33.2885 | − | 19.7874i | 1.13778 | − | 0.676318i | ||||
\(857\) | − | 51.0814i | − | 1.74491i | −0.488698 | − | 0.872453i | \(-0.662528\pi\) | ||
0.488698 | − | 0.872453i | \(-0.337472\pi\) | |||||||
\(858\) | 28.2912 | − | 2.10251i | 0.965846 | − | 0.0717786i | ||||
\(859\) | 36.8343i | 1.25677i | 0.777903 | + | 0.628385i | \(0.216284\pi\) | ||||
−0.777903 | + | 0.628385i | \(0.783716\pi\) | |||||||
\(860\) | 9.24020 | + | 1.54870i | 0.315088 | + | 0.0528102i | ||||
\(861\) | 3.35823 | 0.114448 | ||||||||
\(862\) | 17.6220 | − | 14.9143i | 0.600207 | − | 0.507981i | ||||
\(863\) | −47.1911 | −1.60640 | −0.803202 | − | 0.595707i | \(-0.796872\pi\) | ||||
−0.803202 | + | 0.595707i | \(0.796872\pi\) | |||||||
\(864\) | −28.1843 | + | 10.9396i | −0.958851 | + | 0.372174i | ||||
\(865\) | 15.4489 | 0.525280 | ||||||||
\(866\) | −18.0819 | − | 21.3647i | −0.614448 | − | 0.726002i | ||||
\(867\) | 25.1891i | 0.855467i | ||||||||
\(868\) | −14.1322 | − | 2.36862i | −0.479678 | − | 0.0803962i | ||||
\(869\) | 23.3348 | − | 12.0607i | 0.791581 | − | 0.409133i | ||||
\(870\) | −19.5721 | + | 16.5647i | −0.663555 | + | 0.561596i | ||||
\(871\) | −16.6893 | − | 33.2190i | −0.565496 | − | 1.12558i | ||||
\(872\) | −19.4398 | + | 11.5554i | −0.658316 | + | 0.391316i | ||||
\(873\) | − | 2.94485i | − | 0.0996680i | ||||||
\(874\) | −2.23807 | − | 2.64440i | −0.0757038 | − | 0.0894481i | ||||
\(875\) | 12.3228 | 0.416587 | ||||||||
\(876\) | 33.1297 | + | 5.55269i | 1.11935 | + | 0.187608i | ||||
\(877\) | 30.8744 | 1.04255 | 0.521277 | − | 0.853388i | \(-0.325456\pi\) | ||||
0.521277 | + | 0.853388i | \(0.325456\pi\) | |||||||
\(878\) | 27.4607 | + | 32.4462i | 0.926753 | + | 1.09501i | ||||
\(879\) | 11.1242i | 0.375210i | ||||||||
\(880\) | −2.11659 | − | 14.5030i | −0.0713503 | − | 0.488896i | ||||
\(881\) | −23.1218 | −0.778994 | −0.389497 | − | 0.921028i | \(-0.627351\pi\) | ||||
−0.389497 | + | 0.921028i | \(0.627351\pi\) | |||||||
\(882\) | −0.915082 | − | 1.08122i | −0.0308124 | − | 0.0364065i | ||||
\(883\) | − | 2.56715i | − | 0.0863915i | −0.999067 | − | 0.0431958i | \(-0.986246\pi\) | ||
0.999067 | − | 0.0431958i | \(-0.0137539\pi\) | |||||||
\(884\) | 2.99702 | + | 9.70548i | 0.100801 | + | 0.326431i | ||||
\(885\) | 1.48496 | 0.0499163 | ||||||||
\(886\) | 11.6799 | − | 9.88520i | 0.392393 | − | 0.332100i | ||||
\(887\) | 15.8965 | 0.533752 | 0.266876 | − | 0.963731i | \(-0.414009\pi\) | ||||
0.266876 | + | 0.963731i | \(0.414009\pi\) | |||||||
\(888\) | −32.0412 | + | 19.0459i | −1.07523 | + | 0.639140i | ||||
\(889\) | 22.1800i | 0.743894i | ||||||||
\(890\) | 5.07818 | + | 6.00014i | 0.170221 | + | 0.201125i | ||||
\(891\) | −24.7715 | + | 12.8033i | −0.829875 | + | 0.428926i | ||||
\(892\) | −1.41442 | + | 8.43903i | −0.0473583 | + | 0.282560i | ||||
\(893\) | − | 0.251252i | − | 0.00840782i | ||||||
\(894\) | 20.8652 | − | 17.6591i | 0.697836 | − | 0.590609i | ||||
\(895\) | 15.3230 | 0.512192 | ||||||||
\(896\) | 2.91454 | + | 14.0752i | 0.0973680 | + | 0.470218i | ||||
\(897\) | 7.01935 | + | 13.9716i | 0.234369 | + | 0.466497i | ||||
\(898\) | −10.0941 | + | 8.54311i | −0.336846 | + | 0.285087i | ||||
\(899\) | − | 55.1704i | − | 1.84003i | ||||||
\(900\) | −0.232362 | + | 1.38637i | −0.00774539 | + | 0.0462123i | ||||
\(901\) | − | 7.51822i | − | 0.250468i | ||||||
\(902\) | −6.83192 | − | 2.81938i | −0.227478 | − | 0.0938752i | ||||
\(903\) | −9.03688 | −0.300729 | ||||||||
\(904\) | 10.8939 | − | 6.47553i | 0.362325 | − | 0.215373i | ||||
\(905\) | 11.6398i | 0.386921i | ||||||||
\(906\) | 7.58015 | + | 8.95635i | 0.251834 | + | 0.297555i | ||||
\(907\) | − | 29.8657i | − | 0.991674i | −0.868416 | − | 0.495837i | \(-0.834861\pi\) | ||
0.868416 | − | 0.495837i | \(-0.165139\pi\) | |||||||
\(908\) | 2.41323 | + | 0.404468i | 0.0800858 | + | 0.0134227i | ||||
\(909\) | 0.551219i | 0.0182828i | ||||||||
\(910\) | 2.80590 | − | 6.58401i | 0.0930147 | − | 0.218258i | ||||
\(911\) | − | 8.02735i | − | 0.265958i | −0.991119 | − | 0.132979i | \(-0.957546\pi\) | ||
0.991119 | − | 0.132979i | \(-0.0424543\pi\) | |||||||
\(912\) | 6.01097 | + | 2.07317i | 0.199043 | + | 0.0686496i | ||||
\(913\) | −19.1830 | − | 37.1149i | −0.634865 | − | 1.22832i | ||||
\(914\) | 7.77950 | + | 9.19189i | 0.257323 | + | 0.304041i | ||||
\(915\) | 7.83109i | 0.258888i | ||||||||
\(916\) | 22.0137 | + | 3.68959i | 0.727352 | + | 0.121908i | ||||
\(917\) | − | 9.00469i | − | 0.297361i | ||||||
\(918\) | −6.87803 | − | 8.12676i | −0.227009 | − | 0.268223i | ||||
\(919\) | 51.9419 | 1.71340 | 0.856702 | − | 0.515811i | \(-0.172509\pi\) | ||||
0.856702 | + | 0.515811i | \(0.172509\pi\) | |||||||
\(920\) | 6.94387 | − | 4.12758i | 0.228933 | − | 0.136082i | ||||
\(921\) | 12.6761 | 0.417691 | ||||||||
\(922\) | 21.3519 | + | 25.2284i | 0.703189 | + | 0.830855i | ||||
\(923\) | 18.0054 | + | 35.8385i | 0.592655 | + | 1.17964i | ||||
\(924\) | 4.32579 | + | 13.4589i | 0.142308 | + | 0.442764i | ||||
\(925\) | 29.6914i | 0.976247i | ||||||||
\(926\) | 21.1012 | + | 24.9322i | 0.693428 | + | 0.819322i | ||||
\(927\) | 1.65667i | 0.0544122i | ||||||||
\(928\) | −51.5914 | + | 20.0250i | −1.69357 | + | 0.657352i | ||||
\(929\) | 12.3727i | 0.405936i | 0.979185 | + | 0.202968i | \(0.0650588\pi\) | ||||
−0.979185 | + | 0.202968i | \(0.934941\pi\) | |||||||
\(930\) | −9.54857 | − | 11.2821i | −0.313110 | − | 0.369956i | ||||
\(931\) | 5.10370i | 0.167267i | ||||||||
\(932\) | 18.2598 | + | 3.06042i | 0.598119 | + | 0.100248i | ||||
\(933\) | 10.0511 | 0.329058 | ||||||||
\(934\) | 27.7499 | − | 23.4860i | 0.908006 | − | 0.768485i | ||||
\(935\) | 4.58516 | − | 2.36987i | 0.149951 | − | 0.0775029i | ||||
\(936\) | 1.59777 | + | 1.02169i | 0.0522247 | + | 0.0333950i | ||||
\(937\) | 23.1504i | 0.756292i | 0.925746 | + | 0.378146i | \(0.123438\pi\) | ||||
−0.925746 | + | 0.378146i | \(0.876562\pi\) | |||||||
\(938\) | 14.1407 | − | 11.9679i | 0.461711 | − | 0.390766i | ||||
\(939\) | − | 5.62063i | − | 0.183422i | ||||||
\(940\) | 0.577796 | + | 0.0968413i | 0.0188456 | + | 0.00315862i | ||||
\(941\) | 45.1728 | 1.47259 | 0.736296 | − | 0.676660i | \(-0.236573\pi\) | ||||
0.736296 | + | 0.676660i | \(0.236573\pi\) | |||||||
\(942\) | −25.9939 | + | 21.9998i | −0.846928 | + | 0.716793i | ||||
\(943\) | − | 4.07345i | − | 0.132650i | ||||||
\(944\) | 3.02988 | + | 1.04500i | 0.0986142 | + | 0.0340118i | ||||
\(945\) | 7.50151i | 0.244024i | ||||||||
\(946\) | 18.3845 | + | 7.58687i | 0.597731 | + | 0.246671i | ||||
\(947\) | 22.7811 | 0.740286 | 0.370143 | − | 0.928975i | \(-0.379309\pi\) | ||||
0.370143 | + | 0.928975i | \(0.379309\pi\) | |||||||
\(948\) | −26.2059 | − | 4.39223i | −0.851129 | − | 0.142653i | ||||
\(949\) | −16.2065 | − | 32.2580i | −0.526086 | − | 1.04714i | ||||
\(950\) | 3.86610 | − | 3.27205i | 0.125433 | − | 0.106159i | ||||
\(951\) | 23.1743 | 0.751478 | ||||||||
\(952\) | −4.35111 | + | 2.58639i | −0.141020 | + | 0.0838253i | ||||
\(953\) | 32.8772i | 1.06500i | 0.846431 | + | 0.532498i | \(0.178747\pi\) | ||||
−0.846431 | + | 0.532498i | \(0.821253\pi\) | |||||||
\(954\) | −0.906825 | − | 1.07146i | −0.0293595 | − | 0.0346899i | ||||
\(955\) | 29.2220 | 0.945601 | ||||||||
\(956\) | −41.0155 | − | 6.87439i | −1.32654 | − | 0.222334i | ||||
\(957\) | −48.3531 | + | 24.9916i | −1.56303 | + | 0.807862i | ||||
\(958\) | −7.33362 | + | 6.20677i | −0.236939 | + | 0.200532i | ||||
\(959\) | −18.0373 | −0.582456 | ||||||||
\(960\) | −7.08445 | + | 13.0242i | −0.228650 | + | 0.420354i | ||||
\(961\) | 0.802434 | 0.0258850 | ||||||||
\(962\) | 36.8510 | + | 15.7048i | 1.18812 | + | 0.506342i | ||||
\(963\) | 2.54617 | 0.0820493 | ||||||||
\(964\) | 0.294979 | − | 1.75997i | 0.00950063 | − | 0.0566848i | ||||
\(965\) | − | 25.8388i | − | 0.831780i | ||||||
\(966\) | −5.94743 | + | 5.03357i | −0.191356 | + | 0.161953i | ||||
\(967\) | − | 58.8056i | − | 1.89106i | −0.325535 | − | 0.945530i | \(-0.605544\pi\) | ||
0.325535 | − | 0.945530i | \(-0.394456\pi\) | |||||||
\(968\) | 2.49902 | − | 31.0122i | 0.0803215 | − | 0.996769i | ||||
\(969\) | 2.23915i | 0.0719320i | ||||||||
\(970\) | −15.9834 | − | 18.8853i | −0.513197 | − | 0.606370i | ||||
\(971\) | − | 12.7843i | − | 0.410268i | −0.978734 | − | 0.205134i | \(-0.934237\pi\) | ||
0.978734 | − | 0.205134i | \(-0.0657630\pi\) | |||||||
\(972\) | −3.80647 | − | 0.637982i | −0.122093 | − | 0.0204633i | ||||
\(973\) | 12.0076i | 0.384946i | ||||||||
\(974\) | 10.9003 | + | 12.8792i | 0.349267 | + | 0.412677i | ||||
\(975\) | −20.4264 | + | 10.2623i | −0.654168 | + | 0.328656i | ||||
\(976\) | −5.51092 | + | 15.9784i | −0.176400 | + | 0.511456i | ||||
\(977\) | − | 35.1203i | − | 1.12360i | −0.827274 | − | 0.561799i | \(-0.810109\pi\) | ||
0.827274 | − | 0.561799i | \(-0.189891\pi\) | |||||||
\(978\) | 16.7769 | − | 14.1990i | 0.536465 | − | 0.454034i | ||||
\(979\) | 7.66157 | + | 14.8234i | 0.244865 | + | 0.473759i | ||||
\(980\) | −11.7368 | − | 1.96715i | −0.374919 | − | 0.0628381i | ||||
\(981\) | −1.48692 | −0.0474736 | ||||||||
\(982\) | 18.5115 | + | 21.8723i | 0.590726 | + | 0.697974i | ||||
\(983\) | 11.3212 | 0.361090 | 0.180545 | − | 0.983567i | \(-0.442214\pi\) | ||||
0.180545 | + | 0.983567i | \(0.442214\pi\) | |||||||
\(984\) | 3.82016 | + | 6.42669i | 0.121782 | + | 0.204875i | ||||
\(985\) | 20.3686i | 0.648999i | ||||||||
\(986\) | −12.5902 | − | 14.8760i | −0.400955 | − | 0.473749i | ||||
\(987\) | −0.565083 | −0.0179868 | ||||||||
\(988\) | −2.01615 | − | 6.52906i | −0.0641423 | − | 0.207717i | ||||
\(989\) | 10.9615i | 0.348556i | ||||||||
\(990\) | 0.367610 | − | 0.890792i | 0.0116834 | − | 0.0283112i | ||||
\(991\) | − | 48.1334i | − | 1.52901i | −0.644618 | − | 0.764505i | \(-0.722984\pi\) | ||
0.644618 | − | 0.764505i | \(-0.277016\pi\) | |||||||
\(992\) | −11.5432 | − | 29.7394i | −0.366497 | − | 0.944227i | ||||
\(993\) | − | 9.56766i | − | 0.303621i | ||||||
\(994\) | −15.2558 | + | 12.9117i | −0.483885 | + | 0.409533i | ||||
\(995\) | 18.2931 | 0.579930 | ||||||||
\(996\) | −6.98599 | + | 41.6814i | −0.221360 | + | 1.32073i | ||||
\(997\) | 54.8576i | 1.73736i | 0.495375 | + | 0.868679i | \(0.335031\pi\) | ||||
−0.495375 | + | 0.868679i | \(0.664969\pi\) | |||||||
\(998\) | −23.7105 | − | 28.0152i | −0.750543 | − | 0.886806i | ||||
\(999\) | −41.9863 | −1.32839 |
(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 | 572.2.b.c.571.14 | yes | 56 | |
4.3 | odd | 2 | inner | 572.2.b.c.571.16 | yes | 56 | |
11.10 | odd | 2 | inner | 572.2.b.c.571.44 | yes | 56 | |
13.12 | even | 2 | inner | 572.2.b.c.571.43 | yes | 56 | |
44.43 | even | 2 | inner | 572.2.b.c.571.42 | yes | 56 | |
52.51 | odd | 2 | inner | 572.2.b.c.571.41 | yes | 56 | |
143.142 | odd | 2 | inner | 572.2.b.c.571.13 | ✓ | 56 | |
572.571 | even | 2 | inner | 572.2.b.c.571.15 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.b.c.571.13 | ✓ | 56 | 143.142 | odd | 2 | inner | |
572.2.b.c.571.14 | yes | 56 | 1.1 | even | 1 | trivial | |
572.2.b.c.571.15 | yes | 56 | 572.571 | even | 2 | inner | |
572.2.b.c.571.16 | yes | 56 | 4.3 | odd | 2 | inner | |
572.2.b.c.571.41 | yes | 56 | 52.51 | odd | 2 | inner | |
572.2.b.c.571.42 | yes | 56 | 44.43 | even | 2 | inner | |
572.2.b.c.571.43 | yes | 56 | 13.12 | even | 2 | inner | |
572.2.b.c.571.44 | yes | 56 | 11.10 | odd | 2 | inner |