Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(373,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.447703281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 445.3 | ||
Root | \(-1.38232 - 0.298668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.445 |
Dual form | 546.2.k.b.373.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.14553 | + | 1.98411i | 0.512295 | + | 0.887321i | 0.999898 | + | 0.0142554i | \(0.00453779\pi\) |
−0.487604 | + | 0.873065i | \(0.662129\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −1.12588 | − | 2.39424i | −0.425543 | − | 0.904938i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.29105 | −0.724494 | ||||||||
\(11\) | 0.878558 | 0.264895 | 0.132448 | − | 0.991190i | \(-0.457716\pi\) | ||||
0.132448 | + | 0.991190i | \(0.457716\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −0.786978 | + | 3.51862i | −0.218268 | + | 0.975889i | ||||
\(14\) | 2.63641 | + | 0.222079i | 0.704611 | + | 0.0593532i | ||||
\(15\) | −1.14553 | − | 1.98411i | −0.295774 | − | 0.512295i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.20391 | + | 5.54934i | 0.777062 | + | 1.34591i | 0.933628 | + | 0.358244i | \(0.116624\pi\) |
−0.156565 | + | 0.987668i | \(0.550042\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.50820 | 0.346004 | 0.173002 | − | 0.984921i | \(-0.444653\pi\) | ||||
0.173002 | + | 0.984921i | \(0.444653\pi\) | |||||||
\(20\) | 1.14553 | − | 1.98411i | 0.256147 | − | 0.443660i | ||||
\(21\) | 1.12588 | + | 2.39424i | 0.245687 | + | 0.522466i | ||||
\(22\) | −0.439279 | + | 0.760853i | −0.0936545 | + | 0.162214i | ||||
\(23\) | −0.658760 | + | 1.14101i | −0.137361 | + | 0.237916i | −0.926497 | − | 0.376302i | \(-0.877195\pi\) |
0.789136 | + | 0.614219i | \(0.210529\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −0.124459 | + | 0.215569i | −0.0248918 | + | 0.0431139i | ||||
\(26\) | −2.65372 | − | 2.44085i | −0.520438 | − | 0.478690i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.51053 | + | 2.17216i | −0.285464 | + | 0.410500i | ||||
\(29\) | −0.669294 | − | 1.15925i | −0.124285 | − | 0.215267i | 0.797168 | − | 0.603757i | \(-0.206330\pi\) |
−0.921453 | + | 0.388490i | \(0.872997\pi\) | |||||||
\(30\) | 2.29105 | 0.418287 | ||||||||
\(31\) | −1.94748 | + | 3.37313i | −0.349777 | + | 0.605831i | −0.986210 | − | 0.165501i | \(-0.947076\pi\) |
0.636433 | + | 0.771332i | \(0.280409\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.878558 | −0.152937 | ||||||||
\(34\) | −6.40782 | −1.09893 | ||||||||
\(35\) | 3.46071 | − | 4.97654i | 0.584967 | − | 0.841188i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −4.69338 | + | 8.12917i | −0.771586 | + | 1.33643i | 0.165107 | + | 0.986276i | \(0.447203\pi\) |
−0.936693 | + | 0.350151i | \(0.886130\pi\) | |||||||
\(38\) | −0.754098 | + | 1.30614i | −0.122331 | + | 0.211883i | ||||
\(39\) | 0.786978 | − | 3.51862i | 0.126017 | − | 0.563430i | ||||
\(40\) | 1.14553 | + | 1.98411i | 0.181124 | + | 0.313715i | ||||
\(41\) | 1.80195 | + | 3.12107i | 0.281417 | + | 0.487429i | 0.971734 | − | 0.236078i | \(-0.0758622\pi\) |
−0.690317 | + | 0.723507i | \(0.742529\pi\) | |||||||
\(42\) | −2.63641 | − | 0.222079i | −0.406808 | − | 0.0342676i | ||||
\(43\) | −4.95801 | + | 8.58752i | −0.756089 | + | 1.30959i | 0.188742 | + | 0.982027i | \(0.439559\pi\) |
−0.944831 | + | 0.327558i | \(0.893774\pi\) | |||||||
\(44\) | −0.439279 | − | 0.760853i | −0.0662238 | − | 0.114703i | ||||
\(45\) | 1.14553 | + | 1.98411i | 0.170765 | + | 0.295774i | ||||
\(46\) | −0.658760 | − | 1.14101i | −0.0971289 | − | 0.168232i | ||||
\(47\) | −0.188939 | − | 0.327251i | −0.0275595 | − | 0.0477345i | 0.851917 | − | 0.523677i | \(-0.175440\pi\) |
−0.879476 | + | 0.475943i | \(0.842107\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −4.46478 | + | 5.39126i | −0.637826 | + | 0.770180i | ||||
\(50\) | −0.124459 | − | 0.215569i | −0.0176012 | − | 0.0304861i | ||||
\(51\) | −3.20391 | − | 5.54934i | −0.448637 | − | 0.777062i | ||||
\(52\) | 3.44070 | − | 1.07777i | 0.477139 | − | 0.149459i | ||||
\(53\) | −1.22356 | + | 2.11926i | −0.168068 | + | 0.291103i | −0.937741 | − | 0.347336i | \(-0.887086\pi\) |
0.769672 | + | 0.638439i | \(0.220420\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 1.00641 | + | 1.74315i | 0.135704 | + | 0.235047i | ||||
\(56\) | −1.12588 | − | 2.39424i | −0.150452 | − | 0.319944i | ||||
\(57\) | −1.50820 | −0.199766 | ||||||||
\(58\) | 1.33859 | 0.175765 | ||||||||
\(59\) | 2.98411 | + | 5.16864i | 0.388498 | + | 0.672899i | 0.992248 | − | 0.124275i | \(-0.0396605\pi\) |
−0.603749 | + | 0.797174i | \(0.706327\pi\) | |||||||
\(60\) | −1.14553 | + | 1.98411i | −0.147887 | + | 0.256147i | ||||
\(61\) | 4.81564 | 0.616580 | 0.308290 | − | 0.951292i | \(-0.400243\pi\) | ||||
0.308290 | + | 0.951292i | \(0.400243\pi\) | |||||||
\(62\) | −1.94748 | − | 3.37313i | −0.247330 | − | 0.428388i | ||||
\(63\) | −1.12588 | − | 2.39424i | −0.141848 | − | 0.301646i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.88282 | + | 2.46922i | −0.977744 | + | 0.306269i | ||||
\(66\) | 0.439279 | − | 0.760853i | 0.0540715 | − | 0.0936545i | ||||
\(67\) | 9.75996 | 1.19237 | 0.596184 | − | 0.802848i | \(-0.296683\pi\) | ||||
0.596184 | + | 0.802848i | \(0.296683\pi\) | |||||||
\(68\) | 3.20391 | − | 5.54934i | 0.388531 | − | 0.672956i | ||||
\(69\) | 0.658760 | − | 1.14101i | 0.0793054 | − | 0.137361i | ||||
\(70\) | 2.57945 | + | 5.48533i | 0.308303 | + | 0.655622i | ||||
\(71\) | 1.02408 | − | 1.77376i | 0.121536 | − | 0.210507i | −0.798837 | − | 0.601547i | \(-0.794551\pi\) |
0.920374 | + | 0.391040i | \(0.127885\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.432504 | − | 0.749119i | 0.0506207 | − | 0.0876777i | −0.839605 | − | 0.543198i | \(-0.817213\pi\) |
0.890225 | + | 0.455520i | \(0.150547\pi\) | |||||||
\(74\) | −4.69338 | − | 8.12917i | −0.545594 | − | 0.944997i | ||||
\(75\) | 0.124459 | − | 0.215569i | 0.0143713 | − | 0.0248918i | ||||
\(76\) | −0.754098 | − | 1.30614i | −0.0865010 | − | 0.149824i | ||||
\(77\) | −0.989151 | − | 2.10348i | −0.112724 | − | 0.239714i | ||||
\(78\) | 2.65372 | + | 2.44085i | 0.300475 | + | 0.276372i | ||||
\(79\) | −4.18014 | − | 7.24022i | −0.470303 | − | 0.814588i | 0.529120 | − | 0.848547i | \(-0.322522\pi\) |
−0.999423 | + | 0.0339584i | \(0.989189\pi\) | |||||||
\(80\) | −2.29105 | −0.256147 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.60390 | −0.397984 | ||||||||
\(83\) | 8.66710 | 0.951338 | 0.475669 | − | 0.879624i | \(-0.342206\pi\) | ||||
0.475669 | + | 0.879624i | \(0.342206\pi\) | |||||||
\(84\) | 1.51053 | − | 2.17216i | 0.164813 | − | 0.237002i | ||||
\(85\) | −7.34033 | + | 12.7138i | −0.796170 | + | 1.37901i | ||||
\(86\) | −4.95801 | − | 8.58752i | −0.534636 | − | 0.926016i | ||||
\(87\) | 0.669294 | + | 1.15925i | 0.0717558 | + | 0.124285i | ||||
\(88\) | 0.878558 | 0.0936545 | ||||||||
\(89\) | 6.41693 | − | 11.1145i | 0.680194 | − | 1.17813i | −0.294728 | − | 0.955581i | \(-0.595229\pi\) |
0.974922 | − | 0.222549i | \(-0.0714376\pi\) | |||||||
\(90\) | −2.29105 | −0.241498 | ||||||||
\(91\) | 9.31046 | − | 2.07733i | 0.976002 | − | 0.217763i | ||||
\(92\) | 1.31752 | 0.137361 | ||||||||
\(93\) | 1.94748 | − | 3.37313i | 0.201944 | − | 0.349777i | ||||
\(94\) | 0.377877 | 0.0389751 | ||||||||
\(95\) | 1.72768 | + | 2.99243i | 0.177256 | + | 0.307017i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 4.40338 | − | 7.62688i | 0.447096 | − | 0.774393i | −0.551100 | − | 0.834439i | \(-0.685792\pi\) |
0.998196 | + | 0.0600467i | \(0.0191250\pi\) | |||||||
\(98\) | −2.43658 | − | 6.56225i | −0.246132 | − | 0.662887i | ||||
\(99\) | 0.878558 | 0.0882984 | ||||||||
\(100\) | 0.248918 | 0.0248918 | ||||||||
\(101\) | −10.0539 | −1.00040 | −0.500198 | − | 0.865911i | \(-0.666739\pi\) | ||||
−0.500198 | + | 0.865911i | \(0.666739\pi\) | |||||||
\(102\) | 6.40782 | 0.634469 | ||||||||
\(103\) | −6.17983 | − | 10.7038i | −0.608916 | − | 1.05467i | −0.991419 | − | 0.130720i | \(-0.958271\pi\) |
0.382503 | − | 0.923954i | \(-0.375062\pi\) | |||||||
\(104\) | −0.786978 | + | 3.51862i | −0.0771695 | + | 0.345029i | ||||
\(105\) | −3.46071 | + | 4.97654i | −0.337731 | + | 0.485660i | ||||
\(106\) | −1.22356 | − | 2.11926i | −0.118842 | − | 0.205841i | ||||
\(107\) | 3.40406 | − | 5.89601i | 0.329083 | − | 0.569989i | −0.653247 | − | 0.757145i | \(-0.726594\pi\) |
0.982330 | + | 0.187156i | \(0.0599270\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −0.460710 | + | 0.797973i | −0.0441280 | + | 0.0764320i | −0.887246 | − | 0.461297i | \(-0.847384\pi\) |
0.843118 | + | 0.537729i | \(0.180718\pi\) | |||||||
\(110\) | −2.01282 | −0.191915 | ||||||||
\(111\) | 4.69338 | − | 8.12917i | 0.445476 | − | 0.771586i | ||||
\(112\) | 2.63641 | + | 0.222079i | 0.249118 | + | 0.0209845i | ||||
\(113\) | 5.68802 | − | 9.85195i | 0.535084 | − | 0.926793i | −0.464075 | − | 0.885796i | \(-0.653613\pi\) |
0.999159 | − | 0.0409973i | \(-0.0130535\pi\) | |||||||
\(114\) | 0.754098 | − | 1.30614i | 0.0706278 | − | 0.122331i | ||||
\(115\) | −3.01851 | −0.281477 | ||||||||
\(116\) | −0.669294 | + | 1.15925i | −0.0621424 | + | 0.107634i | ||||
\(117\) | −0.786978 | + | 3.51862i | −0.0727561 | + | 0.325296i | ||||
\(118\) | −5.96823 | −0.549420 | ||||||||
\(119\) | 9.67923 | − | 13.9188i | 0.887293 | − | 1.27594i | ||||
\(120\) | −1.14553 | − | 1.98411i | −0.104572 | − | 0.181124i | ||||
\(121\) | −10.2281 | −0.929831 | ||||||||
\(122\) | −2.40782 | + | 4.17047i | −0.217994 | + | 0.377576i | ||||
\(123\) | −1.80195 | − | 3.12107i | −0.162476 | − | 0.281417i | ||||
\(124\) | 3.89495 | 0.349777 | ||||||||
\(125\) | 10.8850 | 0.973582 | ||||||||
\(126\) | 2.63641 | + | 0.222079i | 0.234870 | + | 0.0197844i | ||||
\(127\) | 4.26019 | + | 7.37887i | 0.378031 | + | 0.654769i | 0.990776 | − | 0.135512i | \(-0.0432679\pi\) |
−0.612745 | + | 0.790281i | \(0.709935\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.95801 | − | 8.58752i | 0.436528 | − | 0.756089i | ||||
\(130\) | 1.80301 | − | 8.06133i | 0.158134 | − | 0.707026i | ||||
\(131\) | 2.51964 | + | 4.36415i | 0.220142 | + | 0.381298i | 0.954851 | − | 0.297085i | \(-0.0960145\pi\) |
−0.734709 | + | 0.678383i | \(0.762681\pi\) | |||||||
\(132\) | 0.439279 | + | 0.760853i | 0.0382343 | + | 0.0662238i | ||||
\(133\) | −1.69805 | − | 3.61099i | −0.147240 | − | 0.313112i | ||||
\(134\) | −4.87998 | + | 8.45237i | −0.421566 | + | 0.730174i | ||||
\(135\) | −1.14553 | − | 1.98411i | −0.0985912 | − | 0.170765i | ||||
\(136\) | 3.20391 | + | 5.54934i | 0.274733 | + | 0.475852i | ||||
\(137\) | 9.47262 | + | 16.4071i | 0.809300 | + | 1.40175i | 0.913349 | + | 0.407177i | \(0.133487\pi\) |
−0.104049 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(138\) | 0.658760 | + | 1.14101i | 0.0560774 | + | 0.0971289i | ||||
\(139\) | 0.565160 | − | 0.978885i | 0.0479362 | − | 0.0830280i | −0.841062 | − | 0.540939i | \(-0.818069\pi\) |
0.888998 | + | 0.457911i | \(0.151402\pi\) | |||||||
\(140\) | −6.04016 | − | 0.508795i | −0.510487 | − | 0.0430010i | ||||
\(141\) | 0.188939 | + | 0.327251i | 0.0159115 | + | 0.0275595i | ||||
\(142\) | 1.02408 | + | 1.77376i | 0.0859392 | + | 0.148851i | ||||
\(143\) | −0.691405 | + | 3.09131i | −0.0578182 | + | 0.258508i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 1.53339 | − | 2.65590i | 0.127341 | − | 0.220561i | ||||
\(146\) | 0.432504 | + | 0.749119i | 0.0357943 | + | 0.0619975i | ||||
\(147\) | 4.46478 | − | 5.39126i | 0.368249 | − | 0.444664i | ||||
\(148\) | 9.38675 | 0.771586 | ||||||||
\(149\) | 1.60500 | 0.131487 | 0.0657433 | − | 0.997837i | \(-0.479058\pi\) | ||||
0.0657433 | + | 0.997837i | \(0.479058\pi\) | |||||||
\(150\) | 0.124459 | + | 0.215569i | 0.0101620 | + | 0.0176012i | ||||
\(151\) | 10.2417 | − | 17.7391i | 0.833457 | − | 1.44359i | −0.0618242 | − | 0.998087i | \(-0.519692\pi\) |
0.895281 | − | 0.445502i | \(-0.146975\pi\) | |||||||
\(152\) | 1.50820 | 0.122331 | ||||||||
\(153\) | 3.20391 | + | 5.54934i | 0.259021 | + | 0.448637i | ||||
\(154\) | 2.31624 | + | 0.195109i | 0.186648 | + | 0.0157224i | ||||
\(155\) | −8.92354 | −0.716756 | ||||||||
\(156\) | −3.44070 | + | 1.07777i | −0.275477 | + | 0.0862903i | ||||
\(157\) | −5.16462 | + | 8.94539i | −0.412182 | + | 0.713919i | −0.995128 | − | 0.0985911i | \(-0.968566\pi\) |
0.582946 | + | 0.812511i | \(0.301900\pi\) | |||||||
\(158\) | 8.36029 | 0.665109 | ||||||||
\(159\) | 1.22356 | − | 2.11926i | 0.0970343 | − | 0.168068i | ||||
\(160\) | 1.14553 | − | 1.98411i | 0.0905618 | − | 0.156858i | ||||
\(161\) | 3.47353 | + | 0.292594i | 0.273753 | + | 0.0230596i | ||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −6.89780 | −0.540277 | −0.270139 | − | 0.962821i | \(-0.587069\pi\) | ||||
−0.270139 | + | 0.962821i | \(0.587069\pi\) | |||||||
\(164\) | 1.80195 | − | 3.12107i | 0.140709 | − | 0.243715i | ||||
\(165\) | −1.00641 | − | 1.74315i | −0.0783489 | − | 0.135704i | ||||
\(166\) | −4.33355 | + | 7.50593i | −0.336349 | + | 0.582573i | ||||
\(167\) | 9.73115 | + | 16.8549i | 0.753019 | + | 1.30427i | 0.946353 | + | 0.323135i | \(0.104737\pi\) |
−0.193334 | + | 0.981133i | \(0.561930\pi\) | |||||||
\(168\) | 1.12588 | + | 2.39424i | 0.0868636 | + | 0.184720i | ||||
\(169\) | −11.7613 | − | 5.53815i | −0.904718 | − | 0.426011i | ||||
\(170\) | −7.34033 | − | 12.7138i | −0.562977 | − | 0.975105i | ||||
\(171\) | 1.50820 | 0.115335 | ||||||||
\(172\) | 9.91602 | 0.756089 | ||||||||
\(173\) | 22.0138 | 1.67368 | 0.836840 | − | 0.547447i | \(-0.184400\pi\) | ||||
0.836840 | + | 0.547447i | \(0.184400\pi\) | |||||||
\(174\) | −1.33859 | −0.101478 | ||||||||
\(175\) | 0.656251 | + | 0.0552795i | 0.0496079 | + | 0.00417874i | ||||
\(176\) | −0.439279 | + | 0.760853i | −0.0331119 | + | 0.0573515i | ||||
\(177\) | −2.98411 | − | 5.16864i | −0.224300 | − | 0.388498i | ||||
\(178\) | 6.41693 | + | 11.1145i | 0.480969 | + | 0.833064i | ||||
\(179\) | −9.81637 | −0.733710 | −0.366855 | − | 0.930278i | \(-0.619565\pi\) | ||||
−0.366855 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(180\) | 1.14553 | − | 1.98411i | 0.0853825 | − | 0.147887i | ||||
\(181\) | 22.9753 | 1.70774 | 0.853869 | − | 0.520487i | \(-0.174250\pi\) | ||||
0.853869 | + | 0.520487i | \(0.174250\pi\) | |||||||
\(182\) | −2.85621 | + | 9.10176i | −0.211716 | + | 0.674667i | ||||
\(183\) | −4.81564 | −0.355983 | ||||||||
\(184\) | −0.658760 | + | 1.14101i | −0.0485645 | + | 0.0841161i | ||||
\(185\) | −21.5055 | −1.58112 | ||||||||
\(186\) | 1.94748 | + | 3.37313i | 0.142796 | + | 0.247330i | ||||
\(187\) | 2.81482 | + | 4.87541i | 0.205840 | + | 0.356525i | ||||
\(188\) | −0.188939 | + | 0.327251i | −0.0137798 | + | 0.0238673i | ||||
\(189\) | 1.12588 | + | 2.39424i | 0.0818958 | + | 0.174155i | ||||
\(190\) | −3.45536 | −0.250678 | ||||||||
\(191\) | −9.69073 | −0.701196 | −0.350598 | − | 0.936526i | \(-0.614022\pi\) | ||||
−0.350598 | + | 0.936526i | \(0.614022\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −21.1067 | −1.51929 | −0.759647 | − | 0.650336i | \(-0.774628\pi\) | ||||
−0.759647 | + | 0.650336i | \(0.774628\pi\) | |||||||
\(194\) | 4.40338 | + | 7.62688i | 0.316144 | + | 0.547578i | ||||
\(195\) | 7.88282 | − | 2.46922i | 0.564501 | − | 0.176824i | ||||
\(196\) | 6.90136 | + | 1.17099i | 0.492954 | + | 0.0836418i | ||||
\(197\) | −6.76019 | − | 11.7090i | −0.481644 | − | 0.834232i | 0.518134 | − | 0.855299i | \(-0.326627\pi\) |
−0.999778 | + | 0.0210677i | \(0.993293\pi\) | |||||||
\(198\) | −0.439279 | + | 0.760853i | −0.0312182 | + | 0.0540715i | ||||
\(199\) | 3.79449 | + | 6.57226i | 0.268985 | + | 0.465895i | 0.968600 | − | 0.248625i | \(-0.0799786\pi\) |
−0.699615 | + | 0.714520i | \(0.746645\pi\) | |||||||
\(200\) | −0.124459 | + | 0.215569i | −0.00880058 | + | 0.0152431i | ||||
\(201\) | −9.75996 | −0.688414 | ||||||||
\(202\) | 5.02693 | − | 8.70689i | 0.353693 | − | 0.612615i | ||||
\(203\) | −2.02198 | + | 2.90763i | −0.141915 | + | 0.204076i | ||||
\(204\) | −3.20391 | + | 5.54934i | −0.224319 | + | 0.388531i | ||||
\(205\) | −4.12836 | + | 7.15053i | −0.288337 | + | 0.499415i | ||||
\(206\) | 12.3597 | 0.861138 | ||||||||
\(207\) | −0.658760 | + | 1.14101i | −0.0457870 | + | 0.0793054i | ||||
\(208\) | −2.65372 | − | 2.44085i | −0.184003 | − | 0.169243i | ||||
\(209\) | 1.32504 | 0.0916548 | ||||||||
\(210\) | −2.57945 | − | 5.48533i | −0.177999 | − | 0.378524i | ||||
\(211\) | −6.06832 | − | 10.5106i | −0.417760 | − | 0.723582i | 0.577954 | − | 0.816070i | \(-0.303851\pi\) |
−0.995714 | + | 0.0924876i | \(0.970518\pi\) | |||||||
\(212\) | 2.44711 | 0.168068 | ||||||||
\(213\) | −1.02408 | + | 1.77376i | −0.0701690 | + | 0.121536i | ||||
\(214\) | 3.40406 | + | 5.89601i | 0.232697 | + | 0.403043i | ||||
\(215\) | −22.7181 | −1.54936 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 10.2687 | + | 0.864988i | 0.697085 | + | 0.0587192i | ||||
\(218\) | −0.460710 | − | 0.797973i | −0.0312032 | − | 0.0540456i | ||||
\(219\) | −0.432504 | + | 0.749119i | −0.0292259 | + | 0.0506207i | ||||
\(220\) | 1.00641 | − | 1.74315i | 0.0678522 | − | 0.117523i | ||||
\(221\) | −22.0474 | + | 6.90613i | −1.48307 | + | 0.464557i | ||||
\(222\) | 4.69338 | + | 8.12917i | 0.314999 | + | 0.545594i | ||||
\(223\) | −11.0968 | − | 19.2202i | −0.743094 | − | 1.28708i | −0.951080 | − | 0.308945i | \(-0.900024\pi\) |
0.207986 | − | 0.978132i | \(-0.433309\pi\) | |||||||
\(224\) | −1.51053 | + | 2.17216i | −0.100927 | + | 0.145134i | ||||
\(225\) | −0.124459 | + | 0.215569i | −0.00829727 | + | 0.0143713i | ||||
\(226\) | 5.68802 | + | 9.85195i | 0.378362 | + | 0.655342i | ||||
\(227\) | 12.2142 | + | 21.1556i | 0.810686 | + | 1.40415i | 0.912385 | + | 0.409333i | \(0.134239\pi\) |
−0.101699 | + | 0.994815i | \(0.532428\pi\) | |||||||
\(228\) | 0.754098 | + | 1.30614i | 0.0499414 | + | 0.0865010i | ||||
\(229\) | −14.9717 | − | 25.9317i | −0.989358 | − | 1.71362i | −0.620688 | − | 0.784058i | \(-0.713147\pi\) |
−0.368670 | − | 0.929560i | \(-0.620187\pi\) | |||||||
\(230\) | 1.50925 | − | 2.61410i | 0.0995173 | − | 0.172369i | ||||
\(231\) | 0.989151 | + | 2.10348i | 0.0650814 | + | 0.138399i | ||||
\(232\) | −0.669294 | − | 1.15925i | −0.0439413 | − | 0.0761086i | ||||
\(233\) | −11.4574 | − | 19.8448i | −0.750600 | − | 1.30008i | −0.947532 | − | 0.319660i | \(-0.896431\pi\) |
0.196932 | − | 0.980417i | \(-0.436902\pi\) | |||||||
\(234\) | −2.65372 | − | 2.44085i | −0.173479 | − | 0.159563i | ||||
\(235\) | 0.432868 | − | 0.749750i | 0.0282372 | − | 0.0489083i | ||||
\(236\) | 2.98411 | − | 5.16864i | 0.194249 | − | 0.336450i | ||||
\(237\) | 4.18014 | + | 7.24022i | 0.271529 | + | 0.470303i | ||||
\(238\) | 7.21444 | + | 15.3419i | 0.467643 | + | 0.994466i | ||||
\(239\) | −1.03992 | −0.0672669 | −0.0336334 | − | 0.999434i | \(-0.510708\pi\) | ||||
−0.0336334 | + | 0.999434i | \(0.510708\pi\) | |||||||
\(240\) | 2.29105 | 0.147887 | ||||||||
\(241\) | −3.23944 | − | 5.61088i | −0.208671 | − | 0.361428i | 0.742625 | − | 0.669707i | \(-0.233580\pi\) |
−0.951296 | + | 0.308279i | \(0.900247\pi\) | |||||||
\(242\) | 5.11407 | − | 8.85783i | 0.328745 | − | 0.569403i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.40782 | − | 4.17047i | −0.154145 | − | 0.266987i | ||||
\(245\) | −15.8114 | − | 2.68279i | −1.01015 | − | 0.171397i | ||||
\(246\) | 3.60390 | 0.229776 | ||||||||
\(247\) | −1.18692 | + | 5.30677i | −0.0755218 | + | 0.337662i | ||||
\(248\) | −1.94748 | + | 3.37313i | −0.123665 | + | 0.214194i | ||||
\(249\) | −8.66710 | −0.549255 | ||||||||
\(250\) | −5.44249 | + | 9.42666i | −0.344213 | + | 0.596195i | ||||
\(251\) | 5.33039 | − | 9.23251i | 0.336451 | − | 0.582751i | −0.647311 | − | 0.762226i | \(-0.724107\pi\) |
0.983763 | + | 0.179475i | \(0.0574399\pi\) | |||||||
\(252\) | −1.51053 | + | 2.17216i | −0.0951547 | + | 0.136833i | ||||
\(253\) | −0.578759 | + | 1.00244i | −0.0363863 | + | 0.0630229i | ||||
\(254\) | −8.52039 | −0.534617 | ||||||||
\(255\) | 7.34033 | − | 12.7138i | 0.459669 | − | 0.796170i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −14.0419 | + | 24.3213i | −0.875910 | + | 1.51712i | −0.0201190 | + | 0.999798i | \(0.506405\pi\) |
−0.855791 | + | 0.517322i | \(0.826929\pi\) | |||||||
\(258\) | 4.95801 | + | 8.58752i | 0.308672 | + | 0.534636i | ||||
\(259\) | 24.7474 | + | 2.08460i | 1.53773 | + | 0.129531i | ||||
\(260\) | 6.07982 | + | 5.59212i | 0.377054 | + | 0.346808i | ||||
\(261\) | −0.669294 | − | 1.15925i | −0.0414282 | − | 0.0717558i | ||||
\(262\) | −5.03929 | −0.311328 | ||||||||
\(263\) | −24.1769 | −1.49081 | −0.745407 | − | 0.666610i | \(-0.767745\pi\) | ||||
−0.745407 | + | 0.666610i | \(0.767745\pi\) | |||||||
\(264\) | −0.878558 | −0.0540715 | ||||||||
\(265\) | −5.60646 | −0.344402 | ||||||||
\(266\) | 3.97623 | + | 0.334939i | 0.243798 | + | 0.0205364i | ||||
\(267\) | −6.41693 | + | 11.1145i | −0.392710 | + | 0.680194i | ||||
\(268\) | −4.87998 | − | 8.45237i | −0.298092 | − | 0.516311i | ||||
\(269\) | 3.96946 | + | 6.87530i | 0.242022 | + | 0.419195i | 0.961290 | − | 0.275538i | \(-0.0888560\pi\) |
−0.719268 | + | 0.694733i | \(0.755523\pi\) | |||||||
\(270\) | 2.29105 | 0.139429 | ||||||||
\(271\) | 14.3347 | − | 24.8284i | 0.870770 | − | 1.50822i | 0.00956909 | − | 0.999954i | \(-0.496954\pi\) |
0.861201 | − | 0.508264i | \(-0.169713\pi\) | |||||||
\(272\) | −6.40782 | −0.388531 | ||||||||
\(273\) | −9.31046 | + | 2.07733i | −0.563495 | + | 0.125726i | ||||
\(274\) | −18.9452 | −1.14452 | ||||||||
\(275\) | −0.109344 | + | 0.189390i | −0.00659372 | + | 0.0114207i | ||||
\(276\) | −1.31752 | −0.0793054 | ||||||||
\(277\) | −6.24357 | − | 10.8142i | −0.375139 | − | 0.649761i | 0.615208 | − | 0.788364i | \(-0.289072\pi\) |
−0.990348 | + | 0.138604i | \(0.955739\pi\) | |||||||
\(278\) | 0.565160 | + | 0.978885i | 0.0338960 | + | 0.0587096i | ||||
\(279\) | −1.94748 | + | 3.37313i | −0.116592 | + | 0.201944i | ||||
\(280\) | 3.46071 | − | 4.97654i | 0.206817 | − | 0.297405i | ||||
\(281\) | 23.4616 | 1.39960 | 0.699800 | − | 0.714339i | \(-0.253272\pi\) | ||||
0.699800 | + | 0.714339i | \(0.253272\pi\) | |||||||
\(282\) | −0.377877 | −0.0225023 | ||||||||
\(283\) | −15.7899 | −0.938612 | −0.469306 | − | 0.883036i | \(-0.655496\pi\) | ||||
−0.469306 | + | 0.883036i | \(0.655496\pi\) | |||||||
\(284\) | −2.04817 | −0.121536 | ||||||||
\(285\) | −1.72768 | − | 2.99243i | −0.102339 | − | 0.177256i | ||||
\(286\) | −2.33145 | − | 2.14443i | −0.137861 | − | 0.126803i | ||||
\(287\) | 5.44381 | − | 7.82825i | 0.321338 | − | 0.462087i | ||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −12.0301 | + | 20.8367i | −0.707652 | + | 1.22569i | ||||
\(290\) | 1.53339 | + | 2.65590i | 0.0900436 | + | 0.155960i | ||||
\(291\) | −4.40338 | + | 7.62688i | −0.258131 | + | 0.447096i | ||||
\(292\) | −0.865008 | −0.0506207 | ||||||||
\(293\) | 3.38969 | − | 5.87112i | 0.198028 | − | 0.342994i | −0.749861 | − | 0.661595i | \(-0.769880\pi\) |
0.947889 | + | 0.318601i | \(0.103213\pi\) | |||||||
\(294\) | 2.43658 | + | 6.56225i | 0.142104 | + | 0.382718i | ||||
\(295\) | −6.83676 | + | 11.8416i | −0.398051 | + | 0.689445i | ||||
\(296\) | −4.69338 | + | 8.12917i | −0.272797 | + | 0.472498i | ||||
\(297\) | −0.878558 | −0.0509791 | ||||||||
\(298\) | −0.802500 | + | 1.38997i | −0.0464876 | + | 0.0805188i | ||||
\(299\) | −3.49634 | − | 3.21587i | −0.202198 | − | 0.185979i | ||||
\(300\) | −0.248918 | −0.0143713 | ||||||||
\(301\) | 26.1427 | + | 2.20214i | 1.50684 | + | 0.126929i | ||||
\(302\) | 10.2417 | + | 17.7391i | 0.589343 | + | 1.02077i | ||||
\(303\) | 10.0539 | 0.577579 | ||||||||
\(304\) | −0.754098 | + | 1.30614i | −0.0432505 | + | 0.0749121i | ||||
\(305\) | 5.51644 | + | 9.55476i | 0.315871 | + | 0.547104i | ||||
\(306\) | −6.40782 | −0.366311 | ||||||||
\(307\) | −1.27687 | −0.0728749 | −0.0364374 | − | 0.999336i | \(-0.511601\pi\) | ||||
−0.0364374 | + | 0.999336i | \(0.511601\pi\) | |||||||
\(308\) | −1.32709 | + | 1.90837i | −0.0756180 | + | 0.108739i | ||||
\(309\) | 6.17983 | + | 10.7038i | 0.351558 | + | 0.608916i | ||||
\(310\) | 4.46177 | − | 7.72801i | 0.253411 | − | 0.438921i | ||||
\(311\) | −12.4336 | + | 21.5357i | −0.705047 | + | 1.22118i | 0.261627 | + | 0.965169i | \(0.415741\pi\) |
−0.966675 | + | 0.256009i | \(0.917592\pi\) | |||||||
\(312\) | 0.786978 | − | 3.51862i | 0.0445539 | − | 0.199202i | ||||
\(313\) | 13.1601 | + | 22.7940i | 0.743855 | + | 1.28839i | 0.950728 | + | 0.310026i | \(0.100338\pi\) |
−0.206873 | + | 0.978368i | \(0.566329\pi\) | |||||||
\(314\) | −5.16462 | − | 8.94539i | −0.291456 | − | 0.504817i | ||||
\(315\) | 3.46071 | − | 4.97654i | 0.194989 | − | 0.280396i | ||||
\(316\) | −4.18014 | + | 7.24022i | −0.235151 | + | 0.407294i | ||||
\(317\) | 9.33620 | + | 16.1708i | 0.524373 | + | 0.908241i | 0.999597 | + | 0.0283764i | \(0.00903370\pi\) |
−0.475224 | + | 0.879865i | \(0.657633\pi\) | |||||||
\(318\) | 1.22356 | + | 2.11926i | 0.0686136 | + | 0.118842i | ||||
\(319\) | −0.588013 | − | 1.01847i | −0.0329224 | − | 0.0570233i | ||||
\(320\) | 1.14553 | + | 1.98411i | 0.0640368 | + | 0.110915i | ||||
\(321\) | −3.40406 | + | 5.89601i | −0.189996 | + | 0.329083i | ||||
\(322\) | −1.99016 | + | 2.86187i | −0.110907 | + | 0.159486i | ||||
\(323\) | 4.83213 | + | 8.36949i | 0.268867 | + | 0.465691i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −0.660560 | − | 0.607572i | −0.0366413 | − | 0.0337020i | ||||
\(326\) | 3.44890 | − | 5.97367i | 0.191017 | − | 0.330851i | ||||
\(327\) | 0.460710 | − | 0.797973i | 0.0254773 | − | 0.0441280i | ||||
\(328\) | 1.80195 | + | 3.12107i | 0.0994960 | + | 0.172332i | ||||
\(329\) | −0.570797 | + | 0.820811i | −0.0314690 | + | 0.0452528i | ||||
\(330\) | 2.01282 | 0.110802 | ||||||||
\(331\) | 36.0485 | 1.98140 | 0.990701 | − | 0.136057i | \(-0.0434429\pi\) | ||||
0.990701 | + | 0.136057i | \(0.0434429\pi\) | |||||||
\(332\) | −4.33355 | − | 7.50593i | −0.237834 | − | 0.411941i | ||||
\(333\) | −4.69338 | + | 8.12917i | −0.257195 | + | 0.445476i | ||||
\(334\) | −19.4623 | −1.06493 | ||||||||
\(335\) | 11.1803 | + | 19.3648i | 0.610844 | + | 1.05801i | ||||
\(336\) | −2.63641 | − | 0.222079i | −0.143828 | − | 0.0121154i | ||||
\(337\) | 16.9888 | 0.925440 | 0.462720 | − | 0.886504i | \(-0.346873\pi\) | ||||
0.462720 | + | 0.886504i | \(0.346873\pi\) | |||||||
\(338\) | 10.6768 | − | 7.41654i | 0.580744 | − | 0.403406i | ||||
\(339\) | −5.68802 | + | 9.85195i | −0.308931 | + | 0.535084i | ||||
\(340\) | 14.6807 | 0.796170 | ||||||||
\(341\) | −1.71097 | + | 2.96349i | −0.0926542 | + | 0.160482i | ||||
\(342\) | −0.754098 | + | 1.30614i | −0.0407770 | + | 0.0706278i | ||||
\(343\) | 17.9348 | + | 4.61985i | 0.968388 | + | 0.249449i | ||||
\(344\) | −4.95801 | + | 8.58752i | −0.267318 | + | 0.463008i | ||||
\(345\) | 3.01851 | 0.162511 | ||||||||
\(346\) | −11.0069 | + | 19.0645i | −0.591736 | + | 1.02492i | ||||
\(347\) | −6.01805 | − | 10.4236i | −0.323066 | − | 0.559566i | 0.658053 | − | 0.752971i | \(-0.271380\pi\) |
−0.981119 | + | 0.193405i | \(0.938047\pi\) | |||||||
\(348\) | 0.669294 | − | 1.15925i | 0.0358779 | − | 0.0621424i | ||||
\(349\) | −11.4544 | − | 19.8396i | −0.613140 | − | 1.06199i | −0.990708 | − | 0.136007i | \(-0.956573\pi\) |
0.377568 | − | 0.925982i | \(-0.376760\pi\) | |||||||
\(350\) | −0.375999 | + | 0.540690i | −0.0200980 | + | 0.0289011i | ||||
\(351\) | 0.786978 | − | 3.51862i | 0.0420058 | − | 0.187810i | ||||
\(352\) | −0.439279 | − | 0.760853i | −0.0234136 | − | 0.0405536i | ||||
\(353\) | 24.3166 | 1.29424 | 0.647121 | − | 0.762387i | \(-0.275973\pi\) | ||||
0.647121 | + | 0.762387i | \(0.275973\pi\) | |||||||
\(354\) | 5.96823 | 0.317208 | ||||||||
\(355\) | 4.69246 | 0.249050 | ||||||||
\(356\) | −12.8339 | −0.680194 | ||||||||
\(357\) | −9.67923 | + | 13.9188i | −0.512279 | + | 0.736662i | ||||
\(358\) | 4.90819 | − | 8.50123i | 0.259406 | − | 0.449304i | ||||
\(359\) | −14.4734 | − | 25.0686i | −0.763875 | − | 1.32307i | −0.940840 | − | 0.338853i | \(-0.889961\pi\) |
0.176965 | − | 0.984217i | \(-0.443372\pi\) | |||||||
\(360\) | 1.14553 | + | 1.98411i | 0.0603745 | + | 0.104572i | ||||
\(361\) | −16.7253 | −0.880281 | ||||||||
\(362\) | −11.4876 | + | 19.8972i | −0.603777 | + | 1.04577i | ||||
\(363\) | 10.2281 | 0.536838 | ||||||||
\(364\) | −6.45425 | − | 7.02443i | −0.338295 | − | 0.368180i | ||||
\(365\) | 1.98178 | 0.103731 | ||||||||
\(366\) | 2.40782 | − | 4.17047i | 0.125859 | − | 0.217994i | ||||
\(367\) | −27.0045 | −1.40962 | −0.704811 | − | 0.709395i | \(-0.748968\pi\) | ||||
−0.704811 | + | 0.709395i | \(0.748968\pi\) | |||||||
\(368\) | −0.658760 | − | 1.14101i | −0.0343403 | − | 0.0594791i | ||||
\(369\) | 1.80195 | + | 3.12107i | 0.0938058 | + | 0.162476i | ||||
\(370\) | 10.7528 | − | 18.6243i | 0.559010 | − | 0.968234i | ||||
\(371\) | 6.45160 | + | 0.543452i | 0.334950 | + | 0.0282146i | ||||
\(372\) | −3.89495 | −0.201944 | ||||||||
\(373\) | 19.2350 | 0.995952 | 0.497976 | − | 0.867191i | \(-0.334077\pi\) | ||||
0.497976 | + | 0.867191i | \(0.334077\pi\) | |||||||
\(374\) | −5.62964 | −0.291102 | ||||||||
\(375\) | −10.8850 | −0.562098 | ||||||||
\(376\) | −0.188939 | − | 0.327251i | −0.00974377 | − | 0.0168767i | ||||
\(377\) | 4.60568 | − | 1.44268i | 0.237205 | − | 0.0743020i | ||||
\(378\) | −2.63641 | − | 0.222079i | −0.135603 | − | 0.0114225i | ||||
\(379\) | −16.1551 | − | 27.9815i | −0.829834 | − | 1.43731i | −0.898168 | − | 0.439652i | \(-0.855102\pi\) |
0.0683340 | − | 0.997662i | \(-0.478232\pi\) | |||||||
\(380\) | 1.72768 | − | 2.99243i | 0.0886280 | − | 0.153508i | ||||
\(381\) | −4.26019 | − | 7.37887i | −0.218256 | − | 0.378031i | ||||
\(382\) | 4.84536 | − | 8.39241i | 0.247910 | − | 0.429393i | ||||
\(383\) | −31.4223 | −1.60560 | −0.802802 | − | 0.596246i | \(-0.796658\pi\) | ||||
−0.802802 | + | 0.596246i | \(0.796658\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 3.04043 | − | 4.37217i | 0.154955 | − | 0.222827i | ||||
\(386\) | 10.5533 | − | 18.2789i | 0.537151 | − | 0.930373i | ||||
\(387\) | −4.95801 | + | 8.58752i | −0.252030 | + | 0.436528i | ||||
\(388\) | −8.80677 | −0.447096 | ||||||||
\(389\) | 2.89119 | − | 5.00769i | 0.146589 | − | 0.253900i | −0.783375 | − | 0.621549i | \(-0.786504\pi\) |
0.929965 | + | 0.367649i | \(0.119837\pi\) | |||||||
\(390\) | −1.80301 | + | 8.06133i | −0.0912988 | + | 0.408201i | ||||
\(391\) | −8.44244 | −0.426952 | ||||||||
\(392\) | −4.46478 | + | 5.39126i | −0.225506 | + | 0.272300i | ||||
\(393\) | −2.51964 | − | 4.36415i | −0.127099 | − | 0.220142i | ||||
\(394\) | 13.5204 | 0.681147 | ||||||||
\(395\) | 9.57692 | − | 16.5877i | 0.481867 | − | 0.834619i | ||||
\(396\) | −0.439279 | − | 0.760853i | −0.0220746 | − | 0.0382343i | ||||
\(397\) | 6.98708 | 0.350672 | 0.175336 | − | 0.984509i | \(-0.443899\pi\) | ||||
0.175336 | + | 0.984509i | \(0.443899\pi\) | |||||||
\(398\) | −7.58899 | −0.380402 | ||||||||
\(399\) | 1.69805 | + | 3.61099i | 0.0850088 | + | 0.180775i | ||||
\(400\) | −0.124459 | − | 0.215569i | −0.00622295 | − | 0.0107785i | ||||
\(401\) | 2.96749 | − | 5.13984i | 0.148189 | − | 0.256671i | −0.782369 | − | 0.622815i | \(-0.785989\pi\) |
0.930558 | + | 0.366144i | \(0.119322\pi\) | |||||||
\(402\) | 4.87998 | − | 8.45237i | 0.243391 | − | 0.421566i | ||||
\(403\) | −10.3361 | − | 9.50700i | −0.514879 | − | 0.473577i | ||||
\(404\) | 5.02693 | + | 8.70689i | 0.250099 | + | 0.433184i | ||||
\(405\) | 1.14553 | + | 1.98411i | 0.0569216 | + | 0.0985912i | ||||
\(406\) | −1.50709 | − | 3.20490i | −0.0747956 | − | 0.159057i | ||||
\(407\) | −4.12340 | + | 7.14194i | −0.204389 | + | 0.354013i | ||||
\(408\) | −3.20391 | − | 5.54934i | −0.158617 | − | 0.274733i | ||||
\(409\) | 7.38923 | + | 12.7985i | 0.365374 | + | 0.632846i | 0.988836 | − | 0.149007i | \(-0.0476077\pi\) |
−0.623462 | + | 0.781854i | \(0.714274\pi\) | |||||||
\(410\) | −4.12836 | − | 7.15053i | −0.203885 | − | 0.353139i | ||||
\(411\) | −9.47262 | − | 16.4071i | −0.467250 | − | 0.809300i | ||||
\(412\) | −6.17983 | + | 10.7038i | −0.304458 | + | 0.527337i | ||||
\(413\) | 9.01521 | − | 12.9640i | 0.443609 | − | 0.637915i | ||||
\(414\) | −0.658760 | − | 1.14101i | −0.0323763 | − | 0.0560774i | ||||
\(415\) | 9.92839 | + | 17.1965i | 0.487365 | + | 0.844142i | ||||
\(416\) | 3.44070 | − | 1.07777i | 0.168694 | − | 0.0528418i | ||||
\(417\) | −0.565160 | + | 0.978885i | −0.0276760 | + | 0.0479362i | ||||
\(418\) | −0.662519 | + | 1.14752i | −0.0324049 | + | 0.0561269i | ||||
\(419\) | −5.07336 | − | 8.78731i | −0.247850 | − | 0.429288i | 0.715079 | − | 0.699043i | \(-0.246391\pi\) |
−0.962929 | + | 0.269755i | \(0.913057\pi\) | |||||||
\(420\) | 6.04016 | + | 0.508795i | 0.294730 | + | 0.0248266i | ||||
\(421\) | 7.70885 | 0.375706 | 0.187853 | − | 0.982197i | \(-0.439847\pi\) | ||||
0.187853 | + | 0.982197i | \(0.439847\pi\) | |||||||
\(422\) | 12.1366 | 0.590802 | ||||||||
\(423\) | −0.188939 | − | 0.327251i | −0.00918652 | − | 0.0159115i | ||||
\(424\) | −1.22356 | + | 2.11926i | −0.0594211 | + | 0.102920i | ||||
\(425\) | −1.59502 | −0.0773700 | ||||||||
\(426\) | −1.02408 | − | 1.77376i | −0.0496170 | − | 0.0859392i | ||||
\(427\) | −5.42184 | − | 11.5298i | −0.262381 | − | 0.557967i | ||||
\(428\) | −6.80813 | −0.329083 | ||||||||
\(429\) | 0.691405 | − | 3.09131i | 0.0333814 | − | 0.149250i | ||||
\(430\) | 11.3591 | − | 19.6745i | 0.547782 | − | 0.948787i | ||||
\(431\) | 35.7786 | 1.72339 | 0.861696 | − | 0.507424i | \(-0.169402\pi\) | ||||
0.861696 | + | 0.507424i | \(0.169402\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −6.32535 | + | 10.9558i | −0.303977 | + | 0.526504i | −0.977033 | − | 0.213088i | \(-0.931648\pi\) |
0.673056 | + | 0.739592i | \(0.264981\pi\) | |||||||
\(434\) | −5.88345 | + | 8.46047i | −0.282415 | + | 0.406115i | ||||
\(435\) | −1.53339 | + | 2.65590i | −0.0735203 | + | 0.127341i | ||||
\(436\) | 0.921420 | 0.0441280 | ||||||||
\(437\) | −0.993540 | + | 1.72086i | −0.0475275 | + | 0.0823200i | ||||
\(438\) | −0.432504 | − | 0.749119i | −0.0206658 | − | 0.0357943i | ||||
\(439\) | 13.6023 | − | 23.5598i | 0.649200 | − | 1.12445i | −0.334114 | − | 0.942533i | \(-0.608437\pi\) |
0.983314 | − | 0.181915i | \(-0.0582296\pi\) | |||||||
\(440\) | 1.00641 | + | 1.74315i | 0.0479787 | + | 0.0831016i | ||||
\(441\) | −4.46478 | + | 5.39126i | −0.212609 | + | 0.256727i | ||||
\(442\) | 5.04281 | − | 22.5467i | 0.239862 | − | 1.07244i | ||||
\(443\) | −1.74860 | − | 3.02867i | −0.0830786 | − | 0.143896i | 0.821492 | − | 0.570220i | \(-0.193142\pi\) |
−0.904571 | + | 0.426323i | \(0.859809\pi\) | |||||||
\(444\) | −9.38675 | −0.445476 | ||||||||
\(445\) | 29.4030 | 1.39384 | ||||||||
\(446\) | 22.1935 | 1.05089 | ||||||||
\(447\) | −1.60500 | −0.0759139 | ||||||||
\(448\) | −1.12588 | − | 2.39424i | −0.0531929 | − | 0.113117i | ||||
\(449\) | 8.08366 | − | 14.0013i | 0.381491 | − | 0.660762i | −0.609784 | − | 0.792567i | \(-0.708744\pi\) |
0.991276 | + | 0.131805i | \(0.0420773\pi\) | |||||||
\(450\) | −0.124459 | − | 0.215569i | −0.00586706 | − | 0.0101620i | ||||
\(451\) | 1.58312 | + | 2.74204i | 0.0745460 | + | 0.129118i | ||||
\(452\) | −11.3760 | −0.535084 | ||||||||
\(453\) | −10.2417 | + | 17.7391i | −0.481196 | + | 0.833457i | ||||
\(454\) | −24.4284 | −1.14648 | ||||||||
\(455\) | 14.7870 | + | 16.0933i | 0.693226 | + | 0.754467i | ||||
\(456\) | −1.50820 | −0.0706278 | ||||||||
\(457\) | −13.1305 | + | 22.7426i | −0.614217 | + | 1.06386i | 0.376304 | + | 0.926496i | \(0.377195\pi\) |
−0.990521 | + | 0.137359i | \(0.956139\pi\) | |||||||
\(458\) | 29.9434 | 1.39916 | ||||||||
\(459\) | −3.20391 | − | 5.54934i | −0.149546 | − | 0.259021i | ||||
\(460\) | 1.50925 | + | 2.61410i | 0.0703693 | + | 0.121883i | ||||
\(461\) | −4.94386 | + | 8.56302i | −0.230259 | + | 0.398819i | −0.957884 | − | 0.287155i | \(-0.907291\pi\) |
0.727626 | + | 0.685974i | \(0.240624\pi\) | |||||||
\(462\) | −2.31624 | − | 0.195109i | −0.107761 | − | 0.00907731i | ||||
\(463\) | −14.2082 | −0.660310 | −0.330155 | − | 0.943927i | \(-0.607101\pi\) | ||||
−0.330155 | + | 0.943927i | \(0.607101\pi\) | |||||||
\(464\) | 1.33859 | 0.0621424 | ||||||||
\(465\) | 8.92354 | 0.413819 | ||||||||
\(466\) | 22.9148 | 1.06151 | ||||||||
\(467\) | −1.47500 | − | 2.55478i | −0.0682550 | − | 0.118221i | 0.829878 | − | 0.557944i | \(-0.188410\pi\) |
−0.898133 | + | 0.439723i | \(0.855076\pi\) | |||||||
\(468\) | 3.44070 | − | 1.07777i | 0.159046 | − | 0.0498197i | ||||
\(469\) | −10.9886 | − | 23.3677i | −0.507404 | − | 1.07902i | ||||
\(470\) | 0.432868 | + | 0.749750i | 0.0199667 | + | 0.0345834i | ||||
\(471\) | 5.16462 | − | 8.94539i | 0.237973 | − | 0.412182i | ||||
\(472\) | 2.98411 | + | 5.16864i | 0.137355 | + | 0.237906i | ||||
\(473\) | −4.35590 | + | 7.54463i | −0.200284 | + | 0.346903i | ||||
\(474\) | −8.36029 | −0.384001 | ||||||||
\(475\) | −0.187709 | + | 0.325121i | −0.00861267 | + | 0.0149176i | ||||
\(476\) | −16.8937 | − | 1.42304i | −0.774320 | − | 0.0652251i | ||||
\(477\) | −1.22356 | + | 2.11926i | −0.0560228 | + | 0.0970343i | ||||
\(478\) | 0.519960 | − | 0.900598i | 0.0237824 | − | 0.0411924i | ||||
\(479\) | 19.8096 | 0.905124 | 0.452562 | − | 0.891733i | \(-0.350510\pi\) | ||||
0.452562 | + | 0.891733i | \(0.350510\pi\) | |||||||
\(480\) | −1.14553 | + | 1.98411i | −0.0522859 | + | 0.0905618i | ||||
\(481\) | −24.9098 | − | 22.9117i | −1.13579 | − | 1.04468i | ||||
\(482\) | 6.47888 | 0.295105 | ||||||||
\(483\) | −3.47353 | − | 0.292594i | −0.158051 | − | 0.0133135i | ||||
\(484\) | 5.11407 | + | 8.85783i | 0.232458 | + | 0.402628i | ||||
\(485\) | 20.1768 | 0.916179 | ||||||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 6.29728 | + | 10.9072i | 0.285357 | + | 0.494253i | 0.972696 | − | 0.232084i | \(-0.0745546\pi\) |
−0.687339 | + | 0.726337i | \(0.741221\pi\) | |||||||
\(488\) | 4.81564 | 0.217994 | ||||||||
\(489\) | 6.89780 | 0.311929 | ||||||||
\(490\) | 10.2291 | − | 12.3517i | 0.462101 | − | 0.557991i | ||||
\(491\) | 5.81280 | + | 10.0681i | 0.262328 | + | 0.454365i | 0.966860 | − | 0.255307i | \(-0.0821765\pi\) |
−0.704532 | + | 0.709672i | \(0.748843\pi\) | |||||||
\(492\) | −1.80195 | + | 3.12107i | −0.0812382 | + | 0.140709i | ||||
\(493\) | 4.28872 | − | 7.42827i | 0.193154 | − | 0.334553i | ||||
\(494\) | −4.00234 | − | 3.68128i | −0.180074 | − | 0.165629i | ||||
\(495\) | 1.00641 | + | 1.74315i | 0.0452348 | + | 0.0783489i | ||||
\(496\) | −1.94748 | − | 3.37313i | −0.0874442 | − | 0.151458i | ||||
\(497\) | −5.39982 | − | 0.454855i | −0.242215 | − | 0.0204030i | ||||
\(498\) | 4.33355 | − | 7.50593i | 0.194191 | − | 0.336349i | ||||
\(499\) | 6.22713 | + | 10.7857i | 0.278765 | + | 0.482834i | 0.971078 | − | 0.238763i | \(-0.0767418\pi\) |
−0.692313 | + | 0.721597i | \(0.743408\pi\) | |||||||
\(500\) | −5.44249 | − | 9.42666i | −0.243395 | − | 0.421573i | ||||
\(501\) | −9.73115 | − | 16.8549i | −0.434756 | − | 0.753019i | ||||
\(502\) | 5.33039 | + | 9.23251i | 0.237907 | + | 0.412067i | ||||
\(503\) | −15.7073 | + | 27.2058i | −0.700354 | + | 1.21305i | 0.267988 | + | 0.963422i | \(0.413641\pi\) |
−0.968342 | + | 0.249627i | \(0.919692\pi\) | |||||||
\(504\) | −1.12588 | − | 2.39424i | −0.0501507 | − | 0.106648i | ||||
\(505\) | −11.5170 | − | 19.9479i | −0.512498 | − | 0.887672i | ||||
\(506\) | −0.578759 | − | 1.00244i | −0.0257290 | − | 0.0445639i | ||||
\(507\) | 11.7613 | + | 5.53815i | 0.522339 | + | 0.245958i | ||||
\(508\) | 4.26019 | − | 7.37887i | 0.189016 | − | 0.327384i | ||||
\(509\) | −3.59886 | + | 6.23341i | −0.159517 | + | 0.276291i | −0.934695 | − | 0.355452i | \(-0.884327\pi\) |
0.775178 | + | 0.631743i | \(0.217660\pi\) | |||||||
\(510\) | 7.34033 | + | 12.7138i | 0.325035 | + | 0.562977i | ||||
\(511\) | −2.28052 | − | 0.192100i | −0.100884 | − | 0.00849801i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.50820 | −0.0665885 | ||||||||
\(514\) | −14.0419 | − | 24.3213i | −0.619362 | − | 1.07277i | ||||
\(515\) | 14.1583 | − | 24.5229i | 0.623889 | − | 1.08061i | ||||
\(516\) | −9.91602 | −0.436528 | ||||||||
\(517\) | −0.165994 | − | 0.287509i | −0.00730039 | − | 0.0126446i | ||||
\(518\) | −14.1790 | + | 20.3896i | −0.622990 | + | 0.895866i | ||||
\(519\) | −22.0138 | −0.966300 | ||||||||
\(520\) | −7.88282 | + | 2.46922i | −0.345685 | + | 0.108282i | ||||
\(521\) | 11.2983 | − | 19.5692i | 0.494987 | − | 0.857342i | −0.504996 | − | 0.863121i | \(-0.668506\pi\) |
0.999983 | + | 0.00577905i | \(0.00183954\pi\) | |||||||
\(522\) | 1.33859 | 0.0585884 | ||||||||
\(523\) | 3.03635 | − | 5.25912i | 0.132770 | − | 0.229965i | −0.791973 | − | 0.610556i | \(-0.790946\pi\) |
0.924744 | + | 0.380591i | \(0.124279\pi\) | |||||||
\(524\) | 2.51964 | − | 4.36415i | 0.110071 | − | 0.190649i | ||||
\(525\) | −0.656251 | − | 0.0552795i | −0.0286412 | − | 0.00241260i | ||||
\(526\) | 12.0885 | − | 20.9378i | 0.527082 | − | 0.912933i | ||||
\(527\) | −24.9582 | −1.08719 | ||||||||
\(528\) | 0.439279 | − | 0.760853i | 0.0191172 | − | 0.0331119i | ||||
\(529\) | 10.6321 | + | 18.4153i | 0.462264 | + | 0.800665i | ||||
\(530\) | 2.80323 | − | 4.85534i | 0.121764 | − | 0.210902i | ||||
\(531\) | 2.98411 | + | 5.16864i | 0.129499 | + | 0.224300i | ||||
\(532\) | −2.27818 | + | 3.27605i | −0.0987717 | + | 0.142035i | ||||
\(533\) | −12.3999 | + | 3.88416i | −0.537101 | + | 0.168242i | ||||
\(534\) | −6.41693 | − | 11.1145i | −0.277688 | − | 0.480969i | ||||
\(535\) | 15.5978 | 0.674350 | ||||||||
\(536\) | 9.75996 | 0.421566 | ||||||||
\(537\) | 9.81637 | 0.423608 | ||||||||
\(538\) | −7.93891 | −0.342271 | ||||||||
\(539\) | −3.92257 | + | 4.73653i | −0.168957 | + | 0.204017i | ||||
\(540\) | −1.14553 | + | 1.98411i | −0.0492956 | + | 0.0853825i | ||||
\(541\) | 3.16494 | + | 5.48183i | 0.136071 | + | 0.235682i | 0.926006 | − | 0.377508i | \(-0.123219\pi\) |
−0.789935 | + | 0.613191i | \(0.789886\pi\) | |||||||
\(542\) | 14.3347 | + | 24.8284i | 0.615728 | + | 1.06647i | ||||
\(543\) | −22.9753 | −0.985963 | ||||||||
\(544\) | 3.20391 | − | 5.54934i | 0.137367 | − | 0.237926i | ||||
\(545\) | −2.11102 | −0.0904262 | ||||||||
\(546\) | 2.85621 | − | 9.10176i | 0.122235 | − | 0.389519i | ||||
\(547\) | 17.3685 | 0.742625 | 0.371312 | − | 0.928508i | \(-0.378908\pi\) | ||||
0.371312 | + | 0.928508i | \(0.378908\pi\) | |||||||
\(548\) | 9.47262 | − | 16.4071i | 0.404650 | − | 0.700875i | ||||
\(549\) | 4.81564 | 0.205527 | ||||||||
\(550\) | −0.109344 | − | 0.189390i | −0.00466246 | − | 0.00807562i | ||||
\(551\) | −1.00943 | − | 1.74838i | −0.0430030 | − | 0.0744834i | ||||
\(552\) | 0.658760 | − | 1.14101i | 0.0280387 | − | 0.0485645i | ||||
\(553\) | −12.6285 | + | 18.1599i | −0.537018 | + | 0.772237i | ||||
\(554\) | 12.4871 | 0.530527 | ||||||||
\(555\) | 21.5055 | 0.912859 | ||||||||
\(556\) | −1.13032 | −0.0479362 | ||||||||
\(557\) | 39.8232 | 1.68736 | 0.843681 | − | 0.536845i | \(-0.180384\pi\) | ||||
0.843681 | + | 0.536845i | \(0.180384\pi\) | |||||||
\(558\) | −1.94748 | − | 3.37313i | −0.0824432 | − | 0.142796i | ||||
\(559\) | −26.3144 | − | 24.2035i | −1.11298 | − | 1.02370i | ||||
\(560\) | 2.57945 | + | 5.48533i | 0.109002 | + | 0.231798i | ||||
\(561\) | −2.81482 | − | 4.87541i | −0.118842 | − | 0.205840i | ||||
\(562\) | −11.7308 | + | 20.3183i | −0.494833 | + | 0.857077i | ||||
\(563\) | 2.29585 | + | 3.97654i | 0.0967587 | + | 0.167591i | 0.910341 | − | 0.413858i | \(-0.135819\pi\) |
−0.813583 | + | 0.581449i | \(0.802486\pi\) | |||||||
\(564\) | 0.188939 | − | 0.327251i | 0.00795576 | − | 0.0137798i | ||||
\(565\) | 26.0631 | 1.09648 | ||||||||
\(566\) | 7.89495 | − | 13.6745i | 0.331850 | − | 0.574780i | ||||
\(567\) | −1.12588 | − | 2.39424i | −0.0472826 | − | 0.100549i | ||||
\(568\) | 1.02408 | − | 1.77376i | 0.0429696 | − | 0.0744255i | ||||
\(569\) | 8.74146 | − | 15.1407i | 0.366461 | − | 0.634729i | −0.622548 | − | 0.782581i | \(-0.713903\pi\) |
0.989010 | + | 0.147852i | \(0.0472359\pi\) | |||||||
\(570\) | 3.45536 | 0.144729 | ||||||||
\(571\) | 8.05500 | − | 13.9517i | 0.337091 | − | 0.583859i | −0.646793 | − | 0.762666i | \(-0.723890\pi\) |
0.983884 | + | 0.178806i | \(0.0572235\pi\) | |||||||
\(572\) | 3.02285 | − | 0.946879i | 0.126392 | − | 0.0395910i | ||||
\(573\) | 9.69073 | 0.404836 | ||||||||
\(574\) | 4.05756 | + | 8.62861i | 0.169359 | + | 0.360151i | ||||
\(575\) | −0.163977 | − | 0.284017i | −0.00683833 | − | 0.0118443i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 3.99841 | − | 6.92544i | 0.166456 | − | 0.288310i | −0.770716 | − | 0.637179i | \(-0.780101\pi\) |
0.937171 | + | 0.348870i | \(0.113434\pi\) | |||||||
\(578\) | −12.0301 | − | 20.8367i | −0.500386 | − | 0.866693i | ||||
\(579\) | 21.1067 | 0.877164 | ||||||||
\(580\) | −3.06677 | −0.127341 | ||||||||
\(581\) | −9.75812 | − | 20.7511i | −0.404835 | − | 0.860902i | ||||
\(582\) | −4.40338 | − | 7.62688i | −0.182526 | − | 0.316144i | ||||
\(583\) | −1.07496 | + | 1.86189i | −0.0445205 | + | 0.0771117i | ||||
\(584\) | 0.432504 | − | 0.749119i | 0.0178971 | − | 0.0309987i | ||||
\(585\) | −7.88282 | + | 2.46922i | −0.325915 | + | 0.102090i | ||||
\(586\) | 3.38969 | + | 5.87112i | 0.140027 | + | 0.242534i | ||||
\(587\) | 10.4049 | + | 18.0219i | 0.429458 | + | 0.743842i | 0.996825 | − | 0.0796223i | \(-0.0253714\pi\) |
−0.567367 | + | 0.823465i | \(0.692038\pi\) | |||||||
\(588\) | −6.90136 | − | 1.17099i | −0.284607 | − | 0.0482906i | ||||
\(589\) | −2.93718 | + | 5.08734i | −0.121024 | + | 0.209620i | ||||
\(590\) | −6.83676 | − | 11.8416i | −0.281465 | − | 0.487511i | ||||
\(591\) | 6.76019 | + | 11.7090i | 0.278077 | + | 0.481644i | ||||
\(592\) | −4.69338 | − | 8.12917i | −0.192897 | − | 0.334107i | ||||
\(593\) | −12.2317 | − | 21.1859i | −0.502296 | − | 0.870002i | −0.999996 | − | 0.00265305i | \(-0.999156\pi\) |
0.497701 | − | 0.867349i | \(-0.334178\pi\) | |||||||
\(594\) | 0.439279 | − | 0.760853i | 0.0180238 | − | 0.0312182i | ||||
\(595\) | 38.7043 | + | 3.26027i | 1.58672 | + | 0.133658i | ||||
\(596\) | −0.802500 | − | 1.38997i | −0.0328717 | − | 0.0569354i | ||||
\(597\) | −3.79449 | − | 6.57226i | −0.155298 | − | 0.268985i | ||||
\(598\) | 4.53319 | − | 1.41998i | 0.185376 | − | 0.0580672i | ||||
\(599\) | −22.4292 | + | 38.8484i | −0.916431 | + | 1.58730i | −0.111638 | + | 0.993749i | \(0.535610\pi\) |
−0.804793 | + | 0.593555i | \(0.797724\pi\) | |||||||
\(600\) | 0.124459 | − | 0.215569i | 0.00508102 | − | 0.00880058i | ||||
\(601\) | 12.2159 | + | 21.1585i | 0.498296 | + | 0.863073i | 0.999998 | − | 0.00196699i | \(-0.000626114\pi\) |
−0.501702 | + | 0.865040i | \(0.667293\pi\) | |||||||
\(602\) | −14.9785 | + | 21.5392i | −0.610477 | + | 0.877872i | ||||
\(603\) | 9.75996 | 0.397456 | ||||||||
\(604\) | −20.4834 | −0.833457 | ||||||||
\(605\) | −11.7166 | − | 20.2937i | −0.476347 | − | 0.825058i | ||||
\(606\) | −5.02693 | + | 8.70689i | −0.204205 | + | 0.353693i | ||||
\(607\) | −36.1822 | −1.46859 | −0.734296 | − | 0.678829i | \(-0.762488\pi\) | ||||
−0.734296 | + | 0.678829i | \(0.762488\pi\) | |||||||
\(608\) | −0.754098 | − | 1.30614i | −0.0305827 | − | 0.0529708i | ||||
\(609\) | 2.02198 | − | 2.90763i | 0.0819348 | − | 0.117823i | ||||
\(610\) | −11.0329 | −0.446709 | ||||||||
\(611\) | 1.30016 | − | 0.407263i | 0.0525990 | − | 0.0164761i | ||||
\(612\) | 3.20391 | − | 5.54934i | 0.129510 | − | 0.224319i | ||||
\(613\) | 6.21294 | 0.250938 | 0.125469 | − | 0.992098i | \(-0.459956\pi\) | ||||
0.125469 | + | 0.992098i | \(0.459956\pi\) | |||||||
\(614\) | 0.638435 | − | 1.10580i | 0.0257652 | − | 0.0446266i | ||||
\(615\) | 4.12836 | − | 7.15053i | 0.166472 | − | 0.288337i | ||||
\(616\) | −0.989151 | − | 2.10348i | −0.0398540 | − | 0.0847516i | ||||
\(617\) | 21.8788 | − | 37.8953i | 0.880809 | − | 1.52561i | 0.0303660 | − | 0.999539i | \(-0.490333\pi\) |
0.850443 | − | 0.526067i | \(-0.176334\pi\) | |||||||
\(618\) | −12.3597 | −0.497178 | ||||||||
\(619\) | 9.54369 | − | 16.5301i | 0.383593 | − | 0.664403i | −0.607980 | − | 0.793952i | \(-0.708020\pi\) |
0.991573 | + | 0.129550i | \(0.0413532\pi\) | |||||||
\(620\) | 4.46177 | + | 7.72801i | 0.179189 | + | 0.310364i | ||||
\(621\) | 0.658760 | − | 1.14101i | 0.0264351 | − | 0.0457870i | ||||
\(622\) | −12.4336 | − | 21.5357i | −0.498544 | − | 0.863503i | ||||
\(623\) | −33.8354 | − | 2.85013i | −1.35559 | − | 0.114188i | ||||
\(624\) | 2.65372 | + | 2.44085i | 0.106234 | + | 0.0977123i | ||||
\(625\) | 13.0913 | + | 22.6748i | 0.523653 | + | 0.906993i | ||||
\(626\) | −26.3203 | −1.05197 | ||||||||
\(627\) | −1.32504 | −0.0529169 | ||||||||
\(628\) | 10.3292 | 0.412182 | ||||||||
\(629\) | −60.1486 | −2.39828 | ||||||||
\(630\) | 2.57945 | + | 5.48533i | 0.102768 | + | 0.218541i | ||||
\(631\) | −11.2873 | + | 19.5502i | −0.449340 | + | 0.778280i | −0.998343 | − | 0.0575405i | \(-0.981674\pi\) |
0.549003 | + | 0.835820i | \(0.315008\pi\) | |||||||
\(632\) | −4.18014 | − | 7.24022i | −0.166277 | − | 0.288000i | ||||
\(633\) | 6.06832 | + | 10.5106i | 0.241194 | + | 0.417760i | ||||
\(634\) | −18.6724 | −0.741576 | ||||||||
\(635\) | −9.76032 | + | 16.9054i | −0.387327 | + | 0.670869i | ||||
\(636\) | −2.44711 | −0.0970343 | ||||||||
\(637\) | −15.4561 | − | 19.9527i | −0.612393 | − | 0.790554i | ||||
\(638\) | 1.17603 | 0.0465593 | ||||||||
\(639\) | 1.02408 | − | 1.77376i | 0.0405121 | − | 0.0701690i | ||||
\(640\) | −2.29105 | −0.0905618 | ||||||||
\(641\) | −10.9122 | − | 18.9004i | −0.431005 | − | 0.746523i | 0.565955 | − | 0.824436i | \(-0.308508\pi\) |
−0.996960 | + | 0.0779133i | \(0.975174\pi\) | |||||||
\(642\) | −3.40406 | − | 5.89601i | −0.134348 | − | 0.232697i | ||||
\(643\) | 7.72503 | − | 13.3801i | 0.304645 | − | 0.527661i | −0.672537 | − | 0.740064i | \(-0.734795\pi\) |
0.977182 | + | 0.212402i | \(0.0681287\pi\) | |||||||
\(644\) | −1.48337 | − | 3.15446i | −0.0584530 | − | 0.124303i | ||||
\(645\) | 22.7181 | 0.894525 | ||||||||
\(646\) | −9.66426 | −0.380235 | ||||||||
\(647\) | 10.7846 | 0.423986 | 0.211993 | − | 0.977271i | \(-0.432005\pi\) | ||||
0.211993 | + | 0.977271i | \(0.432005\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 2.62172 | + | 4.54094i | 0.102911 | + | 0.178248i | ||||
\(650\) | 0.856453 | − | 0.268275i | 0.0335928 | − | 0.0105226i | ||||
\(651\) | −10.2687 | − | 0.864988i | −0.402462 | − | 0.0339015i | ||||
\(652\) | 3.44890 | + | 5.97367i | 0.135069 | + | 0.233947i | ||||
\(653\) | 10.1666 | − | 17.6091i | 0.397850 | − | 0.689096i | −0.595611 | − | 0.803273i | \(-0.703090\pi\) |
0.993460 | + | 0.114178i | \(0.0364233\pi\) | |||||||
\(654\) | 0.460710 | + | 0.797973i | 0.0180152 | + | 0.0312032i | ||||
\(655\) | −5.77264 | + | 9.99850i | −0.225556 | + | 0.390674i | ||||
\(656\) | −3.60390 | −0.140709 | ||||||||
\(657\) | 0.432504 | − | 0.749119i | 0.0168736 | − | 0.0292259i | ||||
\(658\) | −0.425445 | − | 0.904730i | −0.0165856 | − | 0.0352700i | ||||
\(659\) | 15.1395 | − | 26.2224i | 0.589752 | − | 1.02148i | −0.404512 | − | 0.914532i | \(-0.632559\pi\) |
0.994265 | − | 0.106948i | \(-0.0341079\pi\) | |||||||
\(660\) | −1.00641 | + | 1.74315i | −0.0391745 | + | 0.0678522i | ||||
\(661\) | 9.88743 | 0.384577 | 0.192288 | − | 0.981338i | \(-0.438409\pi\) | ||||
0.192288 | + | 0.981338i | \(0.438409\pi\) | |||||||
\(662\) | −18.0242 | + | 31.2189i | −0.700531 | + | 1.21336i | ||||
\(663\) | 22.0474 | − | 6.90613i | 0.856250 | − | 0.268212i | ||||
\(664\) | 8.66710 | 0.336349 | ||||||||
\(665\) | 5.21943 | − | 7.50560i | 0.202401 | − | 0.291055i | ||||
\(666\) | −4.69338 | − | 8.12917i | −0.181865 | − | 0.314999i | ||||
\(667\) | 1.76362 | 0.0682875 | ||||||||
\(668\) | 9.73115 | − | 16.8549i | 0.376510 | − | 0.652134i | ||||
\(669\) | 11.0968 | + | 19.2202i | 0.429026 | + | 0.743094i | ||||
\(670\) | −22.3606 | −0.863864 | ||||||||
\(671\) | 4.23082 | 0.163329 | ||||||||
\(672\) | 1.51053 | − | 2.17216i | 0.0582701 | − | 0.0837930i | ||||
\(673\) | −7.13518 | − | 12.3585i | −0.275041 | − | 0.476385i | 0.695104 | − | 0.718909i | \(-0.255358\pi\) |
−0.970146 | + | 0.242524i | \(0.922025\pi\) | |||||||
\(674\) | −8.49441 | + | 14.7128i | −0.327193 | + | 0.566714i | ||||
\(675\) | 0.124459 | − | 0.215569i | 0.00479043 | − | 0.00829727i | ||||
\(676\) | 1.08449 | + | 12.9547i | 0.0417111 | + | 0.498257i | ||||
\(677\) | 16.7860 | + | 29.0742i | 0.645139 | + | 1.11741i | 0.984269 | + | 0.176674i | \(0.0565338\pi\) |
−0.339130 | + | 0.940739i | \(0.610133\pi\) | |||||||
\(678\) | −5.68802 | − | 9.85195i | −0.218447 | − | 0.378362i | ||||
\(679\) | −23.2183 | − | 1.95580i | −0.891036 | − | 0.0750567i | ||||
\(680\) | −7.34033 | + | 12.7138i | −0.281489 | + | 0.487553i | ||||
\(681\) | −12.2142 | − | 21.1556i | −0.468050 | − | 0.810686i | ||||
\(682\) | −1.71097 | − | 2.96349i | −0.0655164 | − | 0.113478i | ||||
\(683\) | 8.84505 | + | 15.3201i | 0.338446 | + | 0.586206i | 0.984141 | − | 0.177390i | \(-0.0567653\pi\) |
−0.645694 | + | 0.763596i | \(0.723432\pi\) | |||||||
\(684\) | −0.754098 | − | 1.30614i | −0.0288337 | − | 0.0499414i | ||||
\(685\) | −21.7023 | + | 37.5894i | −0.829201 | + | 1.43622i | ||||
\(686\) | −12.9683 | + | 13.2221i | −0.495132 | + | 0.504821i | ||||
\(687\) | 14.9717 | + | 25.9317i | 0.571206 | + | 0.989358i | ||||
\(688\) | −4.95801 | − | 8.58752i | −0.189022 | − | 0.327396i | ||||
\(689\) | −6.49395 | − | 5.97303i | −0.247400 | − | 0.227554i | ||||
\(690\) | −1.50925 | + | 2.61410i | −0.0574563 | + | 0.0995173i | ||||
\(691\) | −19.1359 | + | 33.1443i | −0.727963 | + | 1.26087i | 0.229780 | + | 0.973243i | \(0.426199\pi\) |
−0.957743 | + | 0.287626i | \(0.907134\pi\) | |||||||
\(692\) | −11.0069 | − | 19.0645i | −0.418420 | − | 0.724725i | ||||
\(693\) | −0.989151 | − | 2.10348i | −0.0375747 | − | 0.0799046i | ||||
\(694\) | 12.0361 | 0.456884 | ||||||||
\(695\) | 2.58962 | 0.0982299 | ||||||||
\(696\) | 0.669294 | + | 1.15925i | 0.0253695 | + | 0.0439413i | ||||
\(697\) | −11.5466 | + | 19.9992i | −0.437358 | + | 0.757526i | ||||
\(698\) | 22.9088 | 0.867110 | ||||||||
\(699\) | 11.4574 | + | 19.8448i | 0.433359 | + | 0.750600i | ||||
\(700\) | −0.280252 | − | 0.595970i | −0.0105925 | − | 0.0225255i | ||||
\(701\) | −29.3574 | −1.10882 | −0.554408 | − | 0.832245i | \(-0.687055\pi\) | ||||
−0.554408 | + | 0.832245i | \(0.687055\pi\) | |||||||
\(702\) | 2.65372 | + | 2.44085i | 0.100158 | + | 0.0921240i | ||||
\(703\) | −7.07854 | + | 12.2604i | −0.266972 | + | 0.462409i | ||||
\(704\) | 0.878558 | 0.0331119 | ||||||||
\(705\) | −0.432868 | + | 0.749750i | −0.0163028 | + | 0.0282372i | ||||
\(706\) | −12.1583 | + | 21.0588i | −0.457584 | + | 0.792558i | ||||
\(707\) | 11.3194 | + | 24.0714i | 0.425711 | + | 0.905296i | ||||
\(708\) | −2.98411 | + | 5.16864i | −0.112150 | + | 0.194249i | ||||
\(709\) | −1.32163 | −0.0496347 | −0.0248174 | − | 0.999692i | \(-0.507900\pi\) | ||||
−0.0248174 | + | 0.999692i | \(0.507900\pi\) | |||||||
\(710\) | −2.34623 | + | 4.06379i | −0.0880524 | + | 0.152511i | ||||
\(711\) | −4.18014 | − | 7.24022i | −0.156768 | − | 0.271529i | ||||
\(712\) | 6.41693 | − | 11.1145i | 0.240485 | − | 0.416532i | ||||
\(713\) | −2.56584 | − | 4.44416i | −0.0960915 | − | 0.166435i | ||||
\(714\) | −7.21444 | − | 15.3419i | −0.269994 | − | 0.574155i | ||||
\(715\) | −6.92551 | + | 2.16935i | −0.259000 | + | 0.0811291i | ||||
\(716\) | 4.90819 | + | 8.50123i | 0.183428 | + | 0.317706i | ||||
\(717\) | 1.03992 | 0.0388365 | ||||||||
\(718\) | 28.9467 | 1.08028 | ||||||||
\(719\) | 24.7181 | 0.921830 | 0.460915 | − | 0.887444i | \(-0.347521\pi\) | ||||
0.460915 | + | 0.887444i | \(0.347521\pi\) | |||||||
\(720\) | −2.29105 | −0.0853825 | ||||||||
\(721\) | −18.6697 | + | 26.8472i | −0.695295 | + | 0.999841i | ||||
\(722\) | 8.36267 | − | 14.4846i | 0.311226 | − | 0.539060i | ||||
\(723\) | 3.23944 | + | 5.61088i | 0.120476 | + | 0.208671i | ||||
\(724\) | −11.4876 | − | 19.8972i | −0.426935 | − | 0.739473i | ||||
\(725\) | 0.333199 | 0.0123747 | ||||||||
\(726\) | −5.11407 | + | 8.85783i | −0.189801 | + | 0.328745i | ||||
\(727\) | 8.76033 | 0.324903 | 0.162451 | − | 0.986717i | \(-0.448060\pi\) | ||||
0.162451 | + | 0.986717i | \(0.448060\pi\) | |||||||
\(728\) | 9.31046 | − | 2.07733i | 0.345069 | − | 0.0769909i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.990889 | + | 1.71627i | −0.0366744 | + | 0.0635220i | ||||
\(731\) | −63.5401 | −2.35011 | ||||||||
\(732\) | 2.40782 | + | 4.17047i | 0.0889956 | + | 0.154145i | ||||
\(733\) | −6.38026 | − | 11.0509i | −0.235660 | − | 0.408176i | 0.723804 | − | 0.690006i | \(-0.242392\pi\) |
−0.959464 | + | 0.281830i | \(0.909059\pi\) | |||||||
\(734\) | 13.5022 | − | 23.3866i | 0.498377 | − | 0.863214i | ||||
\(735\) | 15.8114 | + | 2.68279i | 0.583211 | + | 0.0989561i | ||||
\(736\) | 1.31752 | 0.0485645 | ||||||||
\(737\) | 8.57469 | 0.315853 | ||||||||
\(738\) | −3.60390 | −0.132661 | ||||||||
\(739\) | 21.6648 | 0.796953 | 0.398476 | − | 0.917179i | \(-0.369539\pi\) | ||||
0.398476 | + | 0.917179i | \(0.369539\pi\) | |||||||
\(740\) | 10.7528 | + | 18.6243i | 0.395280 | + | 0.684645i | ||||
\(741\) | 1.18692 | − | 5.30677i | 0.0436025 | − | 0.194949i | ||||
\(742\) | −3.69644 | + | 5.31552i | −0.135701 | + | 0.195139i | ||||
\(743\) | 6.46703 | + | 11.2012i | 0.237252 | + | 0.410933i | 0.959925 | − | 0.280258i | \(-0.0904199\pi\) |
−0.722673 | + | 0.691191i | \(0.757087\pi\) | |||||||
\(744\) | 1.94748 | − | 3.37313i | 0.0713979 | − | 0.123665i | ||||
\(745\) | 1.83857 | + | 3.18449i | 0.0673599 | + | 0.116671i | ||||
\(746\) | −9.61751 | + | 16.6580i | −0.352122 | + | 0.609893i | ||||
\(747\) | 8.66710 | 0.317113 | ||||||||
\(748\) | 2.81482 | − | 4.87541i | 0.102920 | − | 0.178263i | ||||
\(749\) | −17.9490 | − | 1.51194i | −0.655844 | − | 0.0552452i | ||||
\(750\) | 5.44249 | − | 9.42666i | 0.198732 | − | 0.344213i | ||||
\(751\) | −4.30364 | + | 7.45412i | −0.157042 | + | 0.272005i | −0.933801 | − | 0.357794i | \(-0.883529\pi\) |
0.776759 | + | 0.629798i | \(0.216862\pi\) | |||||||
\(752\) | 0.377877 | 0.0137798 | ||||||||
\(753\) | −5.33039 | + | 9.23251i | −0.194250 | + | 0.336451i | ||||
\(754\) | −1.05344 | + | 4.70998i | −0.0383640 | + | 0.171527i | ||||
\(755\) | 46.9285 | 1.70790 | ||||||||
\(756\) | 1.51053 | − | 2.17216i | 0.0549376 | − | 0.0790008i | ||||
\(757\) | 7.93369 | + | 13.7416i | 0.288355 | + | 0.499445i | 0.973417 | − | 0.229039i | \(-0.0735584\pi\) |
−0.685062 | + | 0.728484i | \(0.740225\pi\) | |||||||
\(758\) | 32.3103 | 1.17356 | ||||||||
\(759\) | 0.578759 | − | 1.00244i | 0.0210076 | − | 0.0363863i | ||||
\(760\) | 1.72768 | + | 2.99243i | 0.0626695 | + | 0.108547i | ||||
\(761\) | 26.0348 | 0.943761 | 0.471880 | − | 0.881663i | \(-0.343575\pi\) | ||||
0.471880 | + | 0.881663i | \(0.343575\pi\) | |||||||
\(762\) | 8.52039 | 0.308661 | ||||||||
\(763\) | 2.42925 | + | 0.204628i | 0.0879446 | + | 0.00740804i | ||||
\(764\) | 4.84536 | + | 8.39241i | 0.175299 | + | 0.303627i | ||||
\(765\) | −7.34033 | + | 12.7138i | −0.265390 | + | 0.459669i | ||||
\(766\) | 15.7111 | − | 27.2125i | 0.567667 | − | 0.983228i | ||||
\(767\) | −20.5349 | + | 6.43235i | −0.741472 | + | 0.232259i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 18.9239 | + | 32.7772i | 0.682415 | + | 1.18198i | 0.974242 | + | 0.225506i | \(0.0724036\pi\) |
−0.291827 | + | 0.956471i | \(0.594263\pi\) | |||||||
\(770\) | 2.26620 | + | 4.81918i | 0.0816681 | + | 0.173671i | ||||
\(771\) | 14.0419 | − | 24.3213i | 0.505707 | − | 0.875910i | ||||
\(772\) | 10.5533 | + | 18.2789i | 0.379823 | + | 0.657873i | ||||
\(773\) | −21.3629 | − | 37.0016i | −0.768370 | − | 1.33086i | −0.938446 | − | 0.345425i | \(-0.887735\pi\) |
0.170076 | − | 0.985431i | \(-0.445599\pi\) | |||||||
\(774\) | −4.95801 | − | 8.58752i | −0.178212 | − | 0.308672i | ||||
\(775\) | −0.484762 | − | 0.839632i | −0.0174132 | − | 0.0301605i | ||||
\(776\) | 4.40338 | − | 7.62688i | 0.158072 | − | 0.273789i | ||||
\(777\) | −24.7474 | − | 2.08460i | −0.887807 | − | 0.0747847i | ||||
\(778\) | 2.89119 | + | 5.00769i | 0.103654 | + | 0.179534i | ||||
\(779\) | 2.71770 | + | 4.70719i | 0.0973715 | + | 0.168652i | ||||
\(780\) | −6.07982 | − | 5.59212i | −0.217692 | − | 0.200230i | ||||
\(781\) | 0.899716 | − | 1.55835i | 0.0321944 | − | 0.0557623i | ||||
\(782\) | 4.22122 | − | 7.31137i | 0.150950 | − | 0.261454i | ||||
\(783\) | 0.669294 | + | 1.15925i | 0.0239186 | + | 0.0414282i | ||||
\(784\) | −2.43658 | − | 6.56225i | −0.0870206 | − | 0.234366i | ||||
\(785\) | −23.6648 | −0.844634 | ||||||||
\(786\) | 5.03929 | 0.179746 | ||||||||
\(787\) | −3.51846 | − | 6.09415i | −0.125419 | − | 0.217233i | 0.796477 | − | 0.604668i | \(-0.206694\pi\) |
−0.921897 | + | 0.387435i | \(0.873361\pi\) | |||||||
\(788\) | −6.76019 | + | 11.7090i | −0.240822 | + | 0.417116i | ||||
\(789\) | 24.1769 | 0.860722 | ||||||||
\(790\) | 9.57692 | + | 16.5877i | 0.340732 | + | 0.590165i | ||||
\(791\) | −29.9920 | − | 2.52638i | −1.06639 | − | 0.0898279i | ||||
\(792\) | 0.878558 | 0.0312182 | ||||||||
\(793\) | −3.78980 | + | 16.9444i | −0.134580 | + | 0.601713i | ||||
\(794\) | −3.49354 | + | 6.05099i | −0.123981 | + | 0.214742i | ||||
\(795\) | 5.60646 | 0.198841 | ||||||||
\(796\) | 3.79449 | − | 6.57226i | 0.134492 | − | 0.232947i | ||||
\(797\) | 6.48013 | − | 11.2239i | 0.229538 | − | 0.397572i | −0.728133 | − | 0.685436i | \(-0.759612\pi\) |
0.957671 | + | 0.287864i | \(0.0929451\pi\) | |||||||
\(798\) | −3.97623 | − | 0.334939i | −0.140757 | − | 0.0118567i | ||||
\(799\) | 1.21069 | − | 2.09697i | 0.0428310 | − | 0.0741854i | ||||
\(800\) | 0.248918 | 0.00880058 | ||||||||
\(801\) | 6.41693 | − | 11.1145i | 0.226731 | − | 0.392710i | ||||
\(802\) | 2.96749 | + | 5.13984i | 0.104786 | + | 0.181494i | ||||
\(803\) | 0.379979 | − | 0.658144i | 0.0134092 | − | 0.0232254i | ||||
\(804\) | 4.87998 | + | 8.45237i | 0.172104 | + | 0.298092i | ||||
\(805\) | 3.39848 | + | 7.22704i | 0.119781 | + | 0.254720i | ||||
\(806\) | 13.4014 | − | 4.19784i | 0.472043 | − | 0.147863i | ||||
\(807\) | −3.96946 | − | 6.87530i | −0.139732 | − | 0.242022i | ||||
\(808\) | −10.0539 | −0.353693 | ||||||||
\(809\) | 24.0929 | 0.847060 | 0.423530 | − | 0.905882i | \(-0.360791\pi\) | ||||
0.423530 | + | 0.905882i | \(0.360791\pi\) | |||||||
\(810\) | −2.29105 | −0.0804994 | ||||||||
\(811\) | −0.569121 | −0.0199845 | −0.00999227 | − | 0.999950i | \(-0.503181\pi\) | ||||
−0.00999227 | + | 0.999950i | \(0.503181\pi\) | |||||||
\(812\) | 3.52907 | + | 0.297272i | 0.123846 | + | 0.0104322i | ||||
\(813\) | −14.3347 | + | 24.8284i | −0.502739 | + | 0.870770i | ||||
\(814\) | −4.12340 | − | 7.14194i | −0.144525 | − | 0.250325i | ||||
\(815\) | −7.90160 | − | 13.6860i | −0.276781 | − | 0.479399i | ||||
\(816\) | 6.40782 | 0.224319 | ||||||||
\(817\) | −7.47765 | + | 12.9517i | −0.261610 | + | 0.453122i | ||||
\(818\) | −14.7785 | −0.516717 | ||||||||
\(819\) | 9.31046 | − | 2.07733i | 0.325334 | − | 0.0725877i | ||||
\(820\) | 8.25672 | 0.288337 | ||||||||
\(821\) | −25.7343 | + | 44.5731i | −0.898134 | + | 1.55561i | −0.0682560 | + | 0.997668i | \(0.521743\pi\) |
−0.829878 | + | 0.557945i | \(0.811590\pi\) | |||||||
\(822\) | 18.9452 | 0.660791 | ||||||||
\(823\) | −19.4326 | − | 33.6583i | −0.677379 | − | 1.17326i | −0.975767 | − | 0.218811i | \(-0.929782\pi\) |
0.298388 | − | 0.954445i | \(-0.403551\pi\) | |||||||
\(824\) | −6.17983 | − | 10.7038i | −0.215284 | − | 0.372884i | ||||
\(825\) | 0.109344 | − | 0.189390i | 0.00380688 | − | 0.00659372i | ||||
\(826\) | 6.71951 | + | 14.2894i | 0.233802 | + | 0.497191i | ||||
\(827\) | 28.2170 | 0.981203 | 0.490601 | − | 0.871384i | \(-0.336777\pi\) | ||||
0.490601 | + | 0.871384i | \(0.336777\pi\) | |||||||
\(828\) | 1.31752 | 0.0457870 | ||||||||
\(829\) | −11.5781 | −0.402124 | −0.201062 | − | 0.979579i | \(-0.564439\pi\) | ||||
−0.201062 | + | 0.979579i | \(0.564439\pi\) | |||||||
\(830\) | −19.8568 | −0.689239 | ||||||||
\(831\) | 6.24357 | + | 10.8142i | 0.216587 | + | 0.375139i | ||||
\(832\) | −0.786978 | + | 3.51862i | −0.0272835 | + | 0.121986i | ||||
\(833\) | −44.2227 | − | 7.50347i | −1.53223 | − | 0.259980i | ||||
\(834\) | −0.565160 | − | 0.978885i | −0.0195699 | − | 0.0338960i | ||||
\(835\) | −22.2946 | + | 38.6153i | −0.771536 | + | 1.33634i | ||||
\(836\) | −0.662519 | − | 1.14752i | −0.0229137 | − | 0.0396877i | ||||
\(837\) | 1.94748 | − | 3.37313i | 0.0673146 | − | 0.116592i | ||||
\(838\) | 10.1467 | 0.350512 | ||||||||
\(839\) | −15.9568 | + | 27.6379i | −0.550889 | + | 0.954167i | 0.447322 | + | 0.894373i | \(0.352378\pi\) |
−0.998211 | + | 0.0597941i | \(0.980956\pi\) | |||||||
\(840\) | −3.46071 | + | 4.97654i | −0.119406 | + | 0.171707i | ||||
\(841\) | 13.6041 | − | 23.5630i | 0.469107 | − | 0.812516i | ||||
\(842\) | −3.85442 | + | 6.67606i | −0.132832 | + | 0.230072i | ||||
\(843\) | −23.4616 | −0.808060 | ||||||||
\(844\) | −6.06832 | + | 10.5106i | −0.208880 | + | 0.361791i | ||||
\(845\) | −2.48462 | − | 29.6799i | −0.0854736 | − | 1.02102i | ||||
\(846\) | 0.377877 | 0.0129917 | ||||||||
\(847\) | 11.5157 | + | 24.4886i | 0.395683 | + | 0.841439i | ||||
\(848\) | −1.22356 | − | 2.11926i | −0.0420171 | − | 0.0727757i | ||||
\(849\) | 15.7899 | 0.541908 | ||||||||
\(850\) | 0.797511 | − | 1.38133i | 0.0273544 | − | 0.0473792i | ||||
\(851\) | −6.18362 | − | 10.7103i | −0.211972 | − | 0.367146i | ||||
\(852\) | 2.04817 | 0.0701690 | ||||||||
\(853\) | 6.06219 | 0.207565 | 0.103783 | − | 0.994600i | \(-0.466905\pi\) | ||||
0.103783 | + | 0.994600i | \(0.466905\pi\) | |||||||
\(854\) | 12.6960 | + | 1.06945i | 0.434449 | + | 0.0365960i | ||||
\(855\) | 1.72768 | + | 2.99243i | 0.0590854 | + | 0.102339i | ||||
\(856\) | 3.40406 | − | 5.89601i | 0.116348 | − | 0.201521i | ||||
\(857\) | 27.2702 | − | 47.2333i | 0.931531 | − | 1.61346i | 0.150825 | − | 0.988560i | \(-0.451807\pi\) |
0.780706 | − | 0.624899i | \(-0.214860\pi\) | |||||||
\(858\) | 2.33145 | + | 2.14443i | 0.0795943 | + | 0.0732096i | ||||
\(859\) | 27.3472 | + | 47.3667i | 0.933074 | + | 1.61613i | 0.778033 | + | 0.628224i | \(0.216218\pi\) |
0.155042 | + | 0.987908i | \(0.450449\pi\) | |||||||
\(860\) | 11.3591 | + | 19.6745i | 0.387341 | + | 0.670894i | ||||
\(861\) | −5.44381 | + | 7.82825i | −0.185525 | + | 0.266786i | ||||
\(862\) | −17.8893 | + | 30.9851i | −0.609311 | + | 1.05536i | ||||
\(863\) | −2.28666 | − | 3.96062i | −0.0778389 | − | 0.134821i | 0.824478 | − | 0.565893i | \(-0.191469\pi\) |
−0.902317 | + | 0.431073i | \(0.858135\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 25.2174 | + | 43.6778i | 0.857418 | + | 1.48509i | ||||
\(866\) | −6.32535 | − | 10.9558i | −0.214944 | − | 0.372294i | ||||
\(867\) | 12.0301 | − | 20.8367i | 0.408563 | − | 0.707652i | ||||
\(868\) | −4.38525 | − | 9.32545i | −0.148845 | − | 0.316527i | ||||
\(869\) | −3.67250 | − | 6.36095i | −0.124581 | − | 0.215780i | ||||
\(870\) | −1.53339 | − | 2.65590i | −0.0519867 | − | 0.0900436i | ||||
\(871\) | −7.68087 | + | 34.3416i | −0.260256 | + | 1.16362i | ||||
\(872\) | −0.460710 | + | 0.797973i | −0.0156016 | + | 0.0270228i | ||||
\(873\) | 4.40338 | − | 7.62688i | 0.149032 | − | 0.258131i | ||||
\(874\) | −0.993540 | − | 1.72086i | −0.0336070 | − | 0.0582090i | ||||
\(875\) | −12.2552 | − | 26.0613i | −0.414301 | − | 0.881031i | ||||
\(876\) | 0.865008 | 0.0292259 | ||||||||
\(877\) | 58.7214 | 1.98288 | 0.991440 | − | 0.130560i | \(-0.0416775\pi\) | ||||
0.991440 | + | 0.130560i | \(0.0416775\pi\) | |||||||
\(878\) | 13.6023 | + | 23.5598i | 0.459054 | + | 0.795105i | ||||
\(879\) | −3.38969 | + | 5.87112i | −0.114331 | + | 0.198028i | ||||
\(880\) | −2.01282 | −0.0678522 | ||||||||
\(881\) | 6.95948 | + | 12.0542i | 0.234471 | + | 0.406115i | 0.959119 | − | 0.283004i | \(-0.0913309\pi\) |
−0.724648 | + | 0.689119i | \(0.757998\pi\) | |||||||
\(882\) | −2.43658 | − | 6.56225i | −0.0820438 | − | 0.220962i | ||||
\(883\) | 40.5135 | 1.36339 | 0.681695 | − | 0.731637i | \(-0.261243\pi\) | ||||
0.681695 | + | 0.731637i | \(0.261243\pi\) | |||||||
\(884\) | 17.0046 | + | 15.6405i | 0.571926 | + | 0.526048i | ||||
\(885\) | 6.83676 | − | 11.8416i | 0.229815 | − | 0.398051i | ||||
\(886\) | 3.49721 | 0.117491 | ||||||||
\(887\) | −23.9892 | + | 41.5506i | −0.805480 | + | 1.39513i | 0.110487 | + | 0.993878i | \(0.464759\pi\) |
−0.915967 | + | 0.401255i | \(0.868574\pi\) | |||||||
\(888\) | 4.69338 | − | 8.12917i | 0.157499 | − | 0.272797i | ||||
\(889\) | 12.8703 | − | 18.5077i | 0.431657 | − | 0.620727i | ||||
\(890\) | −14.7015 | + | 25.4638i | −0.492796 | + | 0.853548i | ||||
\(891\) | 0.878558 | 0.0294328 | ||||||||
\(892\) | −11.0968 | + | 19.2202i | −0.371547 | + | 0.643538i | ||||
\(893\) | −0.284957 | − | 0.493560i | −0.00953572 | − | 0.0165163i | ||||
\(894\) | 0.802500 | − | 1.38997i | 0.0268396 | − | 0.0464876i | ||||
\(895\) | −11.2449 | − | 19.4768i | −0.375876 | − | 0.651036i | ||||
\(896\) | 2.63641 | + | 0.222079i | 0.0880764 | + | 0.00741914i | ||||
\(897\) | 3.49634 | + | 3.21587i | 0.116739 | + | 0.107375i | ||||
\(898\) | 8.08366 | + | 14.0013i | 0.269755 | + | 0.467230i | ||||
\(899\) | 5.21373 | 0.173888 | ||||||||
\(900\) | 0.248918 | 0.00829727 | ||||||||
\(901\) | −15.6807 | −0.522398 | ||||||||
\(902\) | −3.16623 | −0.105424 | ||||||||
\(903\) | −26.1427 | − | 2.20214i | −0.869976 | − | 0.0732827i | ||||
\(904\) | 5.68802 | − | 9.85195i | 0.189181 | − | 0.327671i | ||||
\(905\) | 26.3188 | + | 45.5854i | 0.874866 | + | 1.51531i | ||||
\(906\) | −10.2417 | − | 17.7391i | −0.340257 | − | 0.589343i | ||||
\(907\) | −25.3615 | −0.842114 | −0.421057 | − | 0.907034i | \(-0.638341\pi\) | ||||
−0.421057 | + | 0.907034i | \(0.638341\pi\) | |||||||
\(908\) | 12.2142 | − | 21.1556i | 0.405343 | − | 0.702074i | ||||
\(909\) | −10.0539 | −0.333465 | ||||||||
\(910\) | −21.3308 | + | 4.75927i | −0.707107 | + | 0.157768i | ||||
\(911\) | −50.6581 | −1.67838 | −0.839189 | − | 0.543840i | \(-0.816970\pi\) | ||||
−0.839189 | + | 0.543840i | \(0.816970\pi\) | |||||||
\(912\) | 0.754098 | − | 1.30614i | 0.0249707 | − | 0.0432505i | ||||
\(913\) | 7.61455 | 0.252005 | ||||||||
\(914\) | −13.1305 | − | 22.7426i | −0.434317 | − | 0.752259i | ||||
\(915\) | −5.51644 | − | 9.55476i | −0.182368 | − | 0.315871i | ||||
\(916\) | −14.9717 | + | 25.9317i | −0.494679 | + | 0.856809i | ||||
\(917\) | 7.61202 | − | 10.9462i | 0.251371 | − | 0.361474i | ||||
\(918\) | 6.40782 | 0.211490 | ||||||||
\(919\) | −25.1562 | −0.829825 | −0.414913 | − | 0.909861i | \(-0.636188\pi\) | ||||
−0.414913 | + | 0.909861i | \(0.636188\pi\) | |||||||
\(920\) | −3.01851 | −0.0995173 | ||||||||
\(921\) | 1.27687 | 0.0420743 | ||||||||
\(922\) | −4.94386 | − | 8.56302i | −0.162817 | − | 0.282008i | ||||
\(923\) | 5.43527 | + | 4.99927i | 0.178904 | + | 0.164553i | ||||
\(924\) | 1.32709 | − | 1.90837i | 0.0436581 | − | 0.0627807i | ||||
\(925\) | −1.16827 | − | 2.02350i | −0.0384124 | − | 0.0665322i | ||||
\(926\) | 7.10408 | − | 12.3046i | 0.233455 | − | 0.404355i | ||||
\(927\) | −6.17983 | − | 10.7038i | −0.202972 | − | 0.351558i | ||||
\(928\) | −0.669294 | + | 1.15925i | −0.0219706 | + | 0.0380543i | ||||
\(929\) | 30.2210 | 0.991519 | 0.495759 | − | 0.868460i | \(-0.334890\pi\) | ||||
0.495759 | + | 0.868460i | \(0.334890\pi\) | |||||||
\(930\) | −4.46177 | + | 7.72801i | −0.146307 | + | 0.253411i | ||||
\(931\) | −6.73377 | + | 8.13108i | −0.220691 | + | 0.266486i | ||||
\(932\) | −11.4574 | + | 19.8448i | −0.375300 | + | 0.650039i | ||||
\(933\) | 12.4336 | − | 21.5357i | 0.407059 | − | 0.705047i | ||||
\(934\) | 2.95000 | 0.0965271 | ||||||||
\(935\) | −6.44890 | + | 11.1698i | −0.210902 | + | 0.365292i | ||||
\(936\) | −0.786978 | + | 3.51862i | −0.0257232 | + | 0.115010i | ||||
\(937\) | −33.2013 | −1.08464 | −0.542320 | − | 0.840172i | \(-0.682454\pi\) | ||||
−0.542320 | + | 0.840172i | \(0.682454\pi\) | |||||||
\(938\) | 25.7313 | + | 2.16748i | 0.840157 | + | 0.0707709i | ||||
\(939\) | −13.1601 | − | 22.7940i | −0.429465 | − | 0.743855i | ||||
\(940\) | −0.865737 | −0.0282372 | ||||||||
\(941\) | 10.3309 | − | 17.8937i | 0.336779 | − | 0.583318i | −0.647046 | − | 0.762451i | \(-0.723996\pi\) |
0.983825 | + | 0.179133i | \(0.0573292\pi\) | |||||||
\(942\) | 5.16462 | + | 8.94539i | 0.168272 | + | 0.291456i | ||||
\(943\) | −4.74821 | −0.154623 | ||||||||
\(944\) | −5.96823 | −0.194249 | ||||||||
\(945\) | −3.46071 | + | 4.97654i | −0.112577 | + | 0.161887i | ||||
\(946\) | −4.35590 | − | 7.54463i | −0.141622 | − | 0.245297i | ||||
\(947\) | −2.50723 | + | 4.34266i | −0.0814741 | + | 0.141117i | −0.903883 | − | 0.427779i | \(-0.859296\pi\) |
0.822409 | + | 0.568896i | \(0.192629\pi\) | |||||||
\(948\) | 4.18014 | − | 7.24022i | 0.135765 | − | 0.235151i | ||||
\(949\) | 2.29549 | + | 2.11135i | 0.0745148 | + | 0.0685375i | ||||
\(950\) | −0.187709 | − | 0.325121i | −0.00609008 | − | 0.0105483i | ||||
\(951\) | −9.33620 | − | 16.1708i | −0.302747 | − | 0.524373i | ||||
\(952\) | 9.67923 | − | 13.9188i | 0.313706 | − | 0.451112i | ||||
\(953\) | 20.4600 | − | 35.4378i | 0.662765 | − | 1.14794i | −0.317121 | − | 0.948385i | \(-0.602716\pi\) |
0.979886 | − | 0.199558i | \(-0.0639505\pi\) | |||||||
\(954\) | −1.22356 | − | 2.11926i | −0.0396141 | − | 0.0686136i | ||||
\(955\) | −11.1010 | − | 19.2275i | −0.359219 | − | 0.622186i | ||||
\(956\) | 0.519960 | + | 0.900598i | 0.0168167 | + | 0.0291274i | ||||
\(957\) | 0.588013 | + | 1.01847i | 0.0190078 | + | 0.0329224i | ||||
\(958\) | −9.90480 | + | 17.1556i | −0.320010 | + | 0.554273i | ||||
\(959\) | 28.6174 | − | 41.1521i | 0.924104 | − | 1.32887i | ||||
\(960\) | −1.14553 | − | 1.98411i | −0.0369717 | − | 0.0640368i | ||||
\(961\) | 7.91468 | + | 13.7086i | 0.255312 | + | 0.442214i | ||||
\(962\) | 32.2970 | − | 10.1167i | 1.04130 | − | 0.326176i | ||||
\(963\) | 3.40406 | − | 5.89601i | 0.109694 | − | 0.189996i | ||||
\(964\) | −3.23944 | + | 5.61088i | −0.104335 | + | 0.180714i | ||||
\(965\) | −24.1783 | − | 41.8780i | −0.778326 | − | 1.34810i | ||||
\(966\) | 1.99016 | − | 2.86187i | 0.0640323 | − | 0.0920791i | ||||
\(967\) | 48.1932 | 1.54979 | 0.774894 | − | 0.632091i | \(-0.217803\pi\) | ||||
0.774894 | + | 0.632091i | \(0.217803\pi\) | |||||||
\(968\) | −10.2281 | −0.328745 | ||||||||
\(969\) | −4.83213 | − | 8.36949i | −0.155230 | − | 0.268867i | ||||
\(970\) | −10.0884 | + | 17.4736i | −0.323918 | + | 0.561043i | ||||
\(971\) | −32.1224 | −1.03086 | −0.515428 | − | 0.856933i | \(-0.672367\pi\) | ||||
−0.515428 | + | 0.856933i | \(0.672367\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −2.97999 | − | 0.251020i | −0.0955341 | − | 0.00804735i | ||||
\(974\) | −12.5946 | −0.403556 | ||||||||
\(975\) | 0.660560 | + | 0.607572i | 0.0211548 | + | 0.0194579i | ||||
\(976\) | −2.40782 | + | 4.17047i | −0.0770725 | + | 0.133493i | ||||
\(977\) | 19.9484 | 0.638205 | 0.319102 | − | 0.947720i | \(-0.396619\pi\) | ||||
0.319102 | + | 0.947720i | \(0.396619\pi\) | |||||||
\(978\) | −3.44890 | + | 5.97367i | −0.110284 | + | 0.191017i | ||||
\(979\) | 5.63764 | − | 9.76469i | 0.180180 | − | 0.312081i | ||||
\(980\) | 5.58233 | + | 15.0344i | 0.178321 | + | 0.480258i | ||||
\(981\) | −0.460710 | + | 0.797973i | −0.0147093 | + | 0.0254773i | ||||
\(982\) | −11.6256 | −0.370988 | ||||||||
\(983\) | 4.74110 | − | 8.21182i | 0.151218 | − | 0.261916i | −0.780458 | − | 0.625208i | \(-0.785014\pi\) |
0.931675 | + | 0.363292i | \(0.118347\pi\) | |||||||
\(984\) | −1.80195 | − | 3.12107i | −0.0574441 | − | 0.0994960i | ||||
\(985\) | 15.4880 | − | 26.8259i | 0.493487 | − | 0.854745i | ||||
\(986\) | 4.28872 | + | 7.42827i | 0.136581 | + | 0.236564i | ||||
\(987\) | 0.570797 | − | 0.820811i | 0.0181687 | − | 0.0261267i | ||||
\(988\) | 5.18925 | − | 1.62548i | 0.165092 | − | 0.0517135i | ||||
\(989\) | −6.53228 | − | 11.3142i | −0.207714 | − | 0.359772i | ||||
\(990\) | −2.01282 | −0.0639716 | ||||||||
\(991\) | 25.5305 | 0.811002 | 0.405501 | − | 0.914095i | \(-0.367097\pi\) | ||||
0.405501 | + | 0.914095i | \(0.367097\pi\) | |||||||
\(992\) | 3.89495 | 0.123665 | ||||||||
\(993\) | −36.0485 | −1.14396 | ||||||||
\(994\) | 3.09382 | − | 4.44895i | 0.0981301 | − | 0.141112i | ||||
\(995\) | −8.69338 | + | 15.0574i | −0.275599 | + | 0.477351i | ||||
\(996\) | 4.33355 | + | 7.50593i | 0.137314 | + | 0.237834i | ||||
\(997\) | −26.0704 | − | 45.1552i | −0.825657 | − | 1.43008i | −0.901416 | − | 0.432954i | \(-0.857471\pi\) |
0.0757592 | − | 0.997126i | \(-0.475862\pi\) | |||||||
\(998\) | −12.4543 | −0.394233 | ||||||||
\(999\) | 4.69338 | − | 8.12917i | 0.148492 | − | 0.257195i |
(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 | 546.2.k.b.445.3 | yes | 8 | |
3.2 | odd | 2 | 1638.2.p.i.991.2 | 8 | |||
7.2 | even | 3 | 546.2.j.d.289.3 | ✓ | 8 | ||
13.9 | even | 3 | 546.2.j.d.529.3 | yes | 8 | ||
21.2 | odd | 6 | 1638.2.m.g.289.2 | 8 | |||
39.35 | odd | 6 | 1638.2.m.g.1621.2 | 8 | |||
91.9 | even | 3 | inner | 546.2.k.b.373.3 | yes | 8 | |
273.191 | odd | 6 | 1638.2.p.i.919.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.d.289.3 | ✓ | 8 | 7.2 | even | 3 | ||
546.2.j.d.529.3 | yes | 8 | 13.9 | even | 3 | ||
546.2.k.b.373.3 | yes | 8 | 91.9 | even | 3 | inner | |
546.2.k.b.445.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1638.2.m.g.289.2 | 8 | 21.2 | odd | 6 | |||
1638.2.m.g.1621.2 | 8 | 39.35 | odd | 6 | |||
1638.2.p.i.919.2 | 8 | 273.191 | odd | 6 | |||
1638.2.p.i.991.2 | 8 | 3.2 | odd | 2 |