Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(89,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.k (of order \(6\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6 x^{19} + 19 x^{18} - 42 x^{17} + 62 x^{16} - 42 x^{15} - 25 x^{14} + 6 x^{13} + 445 x^{12} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.2 | ||
Root | \(1.68119 + 0.416664i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.89 |
Dual form | 462.2.k.g.353.2 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −1.20144 | + | 1.24762i | −0.693649 | + | 0.720313i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.798258 | + | 1.38262i | −0.356992 | + | 0.618328i | −0.987457 | − | 0.157890i | \(-0.949531\pi\) |
0.630465 | + | 0.776218i | \(0.282864\pi\) | |||||||
\(6\) | 1.66428 | − | 0.479752i | 0.679441 | − | 0.195858i | ||||
\(7\) | 0.157053 | − | 2.64109i | 0.0593605 | − | 0.998237i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.113106 | − | 2.99787i | −0.0377021 | − | 0.999289i | ||||
\(10\) | 1.38262 | − | 0.798258i | 0.437224 | − | 0.252431i | ||||
\(11\) | 0.866025 | − | 0.500000i | 0.261116 | − | 0.150756i | ||||
\(12\) | −1.68119 | − | 0.416664i | −0.485317 | − | 0.120281i | ||||
\(13\) | − | 4.50963i | − | 1.25074i | −0.780326 | − | 0.625372i | \(-0.784947\pi\) | ||
0.780326 | − | 0.625372i | \(-0.215053\pi\) | |||||||
\(14\) | −1.45655 | + | 2.20872i | −0.389281 | + | 0.590305i | ||||
\(15\) | −0.765932 | − | 2.65705i | −0.197763 | − | 0.686048i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.12084 | + | 5.40545i | 0.756914 | + | 1.31101i | 0.944417 | + | 0.328750i | \(0.106627\pi\) |
−0.187503 | + | 0.982264i | \(0.560039\pi\) | |||||||
\(18\) | −1.40098 | + | 2.65278i | −0.330214 | + | 0.625267i | ||||
\(19\) | 6.07449 | + | 3.50711i | 1.39358 | + | 0.804586i | 0.993710 | − | 0.111983i | \(-0.0357203\pi\) |
0.399875 | + | 0.916570i | \(0.369054\pi\) | |||||||
\(20\) | −1.59652 | −0.356992 | ||||||||
\(21\) | 3.10638 | + | 3.36904i | 0.677868 | + | 0.735184i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −4.03733 | − | 2.33096i | −0.841842 | − | 0.486038i | 0.0160479 | − | 0.999871i | \(-0.494892\pi\) |
−0.857890 | + | 0.513834i | \(0.828225\pi\) | |||||||
\(24\) | 1.24762 | + | 1.20144i | 0.254669 | + | 0.245242i | ||||
\(25\) | 1.22557 | + | 2.12275i | 0.245114 | + | 0.424550i | ||||
\(26\) | −2.25481 | + | 3.90545i | −0.442205 | + | 0.765922i | ||||
\(27\) | 3.87609 | + | 3.46063i | 0.745953 | + | 0.665998i | ||||
\(28\) | 2.36577 | − | 1.18453i | 0.447089 | − | 0.223855i | ||||
\(29\) | 5.53777i | 1.02834i | 0.857689 | + | 0.514169i | \(0.171900\pi\) | ||||
−0.857689 | + | 0.514169i | \(0.828100\pi\) | |||||||
\(30\) | −0.665210 | + | 2.68404i | −0.121450 | + | 0.490037i | ||||
\(31\) | 7.88004 | − | 4.54954i | 1.41530 | − | 0.817122i | 0.419415 | − | 0.907794i | \(-0.362235\pi\) |
0.995881 | + | 0.0906728i | \(0.0289017\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −0.416664 | + | 1.68119i | −0.0725319 | + | 0.292657i | ||||
\(34\) | − | 6.24168i | − | 1.07044i | ||||||
\(35\) | 3.52626 | + | 2.32541i | 0.596046 | + | 0.393066i | ||||
\(36\) | 2.53968 | − | 1.59689i | 0.423279 | − | 0.266148i | ||||
\(37\) | −0.285736 | + | 0.494910i | −0.0469747 | + | 0.0813626i | −0.888557 | − | 0.458767i | \(-0.848291\pi\) |
0.841582 | + | 0.540129i | \(0.181625\pi\) | |||||||
\(38\) | −3.50711 | − | 6.07449i | −0.568929 | − | 0.985413i | ||||
\(39\) | 5.62629 | + | 5.41802i | 0.900928 | + | 0.867578i | ||||
\(40\) | 1.38262 | + | 0.798258i | 0.218612 | + | 0.126216i | ||||
\(41\) | 1.59652 | 0.249334 | 0.124667 | − | 0.992199i | \(-0.460214\pi\) | ||||
0.124667 | + | 0.992199i | \(0.460214\pi\) | |||||||
\(42\) | −1.00569 | − | 4.47086i | −0.155181 | − | 0.689869i | ||||
\(43\) | −1.54158 | −0.235088 | −0.117544 | − | 0.993068i | \(-0.537502\pi\) | ||||
−0.117544 | + | 0.993068i | \(0.537502\pi\) | |||||||
\(44\) | 0.866025 | + | 0.500000i | 0.130558 | + | 0.0753778i | ||||
\(45\) | 4.23521 | + | 2.23669i | 0.631347 | + | 0.333426i | ||||
\(46\) | 2.33096 | + | 4.03733i | 0.343681 | + | 0.595272i | ||||
\(47\) | 3.56927 | − | 6.18215i | 0.520631 | − | 0.901759i | −0.479081 | − | 0.877771i | \(-0.659030\pi\) |
0.999712 | − | 0.0239887i | \(-0.00763658\pi\) | |||||||
\(48\) | −0.479752 | − | 1.66428i | −0.0692463 | − | 0.240219i | ||||
\(49\) | −6.95067 | − | 0.829582i | −0.992953 | − | 0.118512i | ||||
\(50\) | − | 2.45114i | − | 0.346643i | ||||||
\(51\) | −10.4934 | − | 2.60068i | −1.46937 | − | 0.364168i | ||||
\(52\) | 3.90545 | − | 2.25481i | 0.541588 | − | 0.312686i | ||||
\(53\) | 8.14614 | − | 4.70318i | 1.11896 | − | 0.646031i | 0.177824 | − | 0.984062i | \(-0.443094\pi\) |
0.941135 | + | 0.338031i | \(0.109761\pi\) | |||||||
\(54\) | −1.62647 | − | 4.93504i | −0.221335 | − | 0.671573i | ||||
\(55\) | 1.59652i | 0.215274i | ||||||||
\(56\) | −2.64109 | − | 0.157053i | −0.352930 | − | 0.0209871i | ||||
\(57\) | −11.6737 | + | 3.36509i | −1.54621 | + | 0.445717i | ||||
\(58\) | 2.76889 | − | 4.79585i | 0.363573 | − | 0.629726i | ||||
\(59\) | 2.62379 | + | 4.54453i | 0.341588 | + | 0.591648i | 0.984728 | − | 0.174101i | \(-0.0557019\pi\) |
−0.643140 | + | 0.765749i | \(0.722369\pi\) | |||||||
\(60\) | 1.91811 | − | 1.99184i | 0.247627 | − | 0.257146i | ||||
\(61\) | 1.88976 | + | 1.09105i | 0.241959 | + | 0.139695i | 0.616077 | − | 0.787686i | \(-0.288721\pi\) |
−0.374118 | + | 0.927381i | \(0.622054\pi\) | |||||||
\(62\) | −9.09908 | −1.15558 | ||||||||
\(63\) | −7.93539 | − | 0.172101i | −0.999765 | − | 0.0216827i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.23511 | + | 3.59984i | 0.773370 | + | 0.446506i | ||||
\(66\) | 1.20144 | − | 1.24762i | 0.147886 | − | 0.153571i | ||||
\(67\) | 0.613735 | + | 1.06302i | 0.0749797 | + | 0.129869i | 0.901077 | − | 0.433658i | \(-0.142777\pi\) |
−0.826098 | + | 0.563527i | \(0.809444\pi\) | |||||||
\(68\) | −3.12084 | + | 5.40545i | −0.378457 | + | 0.655507i | ||||
\(69\) | 7.75874 | − | 2.23656i | 0.934042 | − | 0.269250i | ||||
\(70\) | −1.89112 | − | 3.77699i | −0.226032 | − | 0.451437i | ||||
\(71\) | − | 9.47281i | − | 1.12422i | −0.827064 | − | 0.562108i | \(-0.809991\pi\) | ||
0.827064 | − | 0.562108i | \(-0.190009\pi\) | |||||||
\(72\) | −2.99787 | + | 0.113106i | −0.353302 | + | 0.0133297i | ||||
\(73\) | 3.56995 | − | 2.06111i | 0.417831 | − | 0.241235i | −0.276318 | − | 0.961066i | \(-0.589114\pi\) |
0.694149 | + | 0.719832i | \(0.255781\pi\) | |||||||
\(74\) | 0.494910 | − | 0.285736i | 0.0575321 | − | 0.0332162i | ||||
\(75\) | −4.12082 | − | 1.02130i | −0.475832 | − | 0.117930i | ||||
\(76\) | 7.01422i | 0.804586i | ||||||||
\(77\) | −1.18453 | − | 2.36577i | −0.134990 | − | 0.269605i | ||||
\(78\) | −2.16350 | − | 7.50529i | −0.244968 | − | 0.849807i | ||||
\(79\) | 3.87063 | − | 6.70413i | 0.435480 | − | 0.754273i | −0.561855 | − | 0.827236i | \(-0.689912\pi\) |
0.997335 | + | 0.0729625i | \(0.0232453\pi\) | |||||||
\(80\) | −0.798258 | − | 1.38262i | −0.0892479 | − | 0.154582i | ||||
\(81\) | −8.97441 | + | 0.678156i | −0.997157 | + | 0.0753506i | ||||
\(82\) | −1.38262 | − | 0.798258i | −0.152685 | − | 0.0881528i | ||||
\(83\) | 17.4510 | 1.91550 | 0.957748 | − | 0.287608i | \(-0.0928599\pi\) | ||||
0.957748 | + | 0.287608i | \(0.0928599\pi\) | |||||||
\(84\) | −1.36448 | + | 4.37472i | −0.148877 | + | 0.477321i | ||||
\(85\) | −9.96493 | −1.08085 | ||||||||
\(86\) | 1.33504 | + | 0.770788i | 0.143962 | + | 0.0831163i | ||||
\(87\) | −6.90903 | − | 6.65328i | −0.740726 | − | 0.713306i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | −6.69358 | + | 11.5936i | −0.709518 | + | 1.22892i | 0.255519 | + | 0.966804i | \(0.417754\pi\) |
−0.965036 | + | 0.262116i | \(0.915580\pi\) | |||||||
\(90\) | −2.54945 | − | 4.05463i | −0.268736 | − | 0.427396i | ||||
\(91\) | −11.9103 | − | 0.708251i | −1.24854 | − | 0.0742448i | ||||
\(92\) | − | 4.66191i | − | 0.486038i | ||||||
\(93\) | −3.79126 | + | 15.2973i | −0.393135 | + | 1.58625i | ||||
\(94\) | −6.18215 | + | 3.56927i | −0.637640 | + | 0.368142i | ||||
\(95\) | −9.69802 | + | 5.59916i | −0.994996 | + | 0.574461i | ||||
\(96\) | −0.416664 | + | 1.68119i | −0.0425256 | + | 0.171585i | ||||
\(97\) | 7.11516i | 0.722435i | 0.932482 | + | 0.361218i | \(0.117639\pi\) | ||||
−0.932482 | + | 0.361218i | \(0.882361\pi\) | |||||||
\(98\) | 5.60466 | + | 4.19377i | 0.566157 | + | 0.423635i | ||||
\(99\) | −1.59689 | − | 2.53968i | −0.160493 | − | 0.255247i | ||||
\(100\) | −1.22557 | + | 2.12275i | −0.122557 | + | 0.212275i | ||||
\(101\) | −0.150693 | − | 0.261008i | −0.0149945 | − | 0.0259713i | 0.858431 | − | 0.512929i | \(-0.171440\pi\) |
−0.873425 | + | 0.486958i | \(0.838106\pi\) | |||||||
\(102\) | 7.78723 | + | 7.49897i | 0.771051 | + | 0.742509i | ||||
\(103\) | −7.95453 | − | 4.59255i | −0.783783 | − | 0.452517i | 0.0539862 | − | 0.998542i | \(-0.482807\pi\) |
−0.837769 | + | 0.546024i | \(0.816141\pi\) | |||||||
\(104\) | −4.50963 | −0.442205 | ||||||||
\(105\) | −7.13780 | + | 1.60559i | −0.696578 | + | 0.156690i | ||||
\(106\) | −9.40636 | −0.913626 | ||||||||
\(107\) | −7.30325 | − | 4.21653i | −0.706032 | − | 0.407628i | 0.103558 | − | 0.994623i | \(-0.466977\pi\) |
−0.809590 | + | 0.586996i | \(0.800311\pi\) | |||||||
\(108\) | −1.05895 | + | 5.08710i | −0.101898 | + | 0.489507i | ||||
\(109\) | 7.34270 | + | 12.7179i | 0.703303 | + | 1.21816i | 0.967301 | + | 0.253633i | \(0.0816255\pi\) |
−0.263998 | + | 0.964523i | \(0.585041\pi\) | |||||||
\(110\) | 0.798258 | − | 1.38262i | 0.0761109 | − | 0.131828i | ||||
\(111\) | −0.274165 | − | 0.951092i | −0.0260226 | − | 0.0902736i | ||||
\(112\) | 2.20872 | + | 1.45655i | 0.208705 | + | 0.137632i | ||||
\(113\) | − | 10.5424i | − | 0.991750i | −0.868394 | − | 0.495875i | \(-0.834847\pi\) | ||
0.868394 | − | 0.495875i | \(-0.165153\pi\) | |||||||
\(114\) | 11.7922 | + | 2.92257i | 1.10444 | + | 0.273724i | ||||
\(115\) | 6.44566 | − | 3.72141i | 0.601061 | − | 0.347023i | ||||
\(116\) | −4.79585 | + | 2.76889i | −0.445284 | + | 0.257085i | ||||
\(117\) | −13.5193 | + | 0.510067i | −1.24986 | + | 0.0471557i | ||||
\(118\) | − | 5.24757i | − | 0.483078i | ||||||
\(119\) | 14.7664 | − | 7.39346i | 1.35363 | − | 0.677757i | ||||
\(120\) | −2.65705 | + | 0.765932i | −0.242555 | + | 0.0699197i | ||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | −1.09105 | − | 1.88976i | −0.0987792 | − | 0.171091i | ||||
\(123\) | −1.91811 | + | 1.99184i | −0.172950 | + | 0.179598i | ||||
\(124\) | 7.88004 | + | 4.54954i | 0.707648 | + | 0.408561i | ||||
\(125\) | −11.8959 | −1.06400 | ||||||||
\(126\) | 6.78620 | + | 4.11674i | 0.604562 | + | 0.366748i | ||||
\(127\) | −3.58256 | −0.317901 | −0.158950 | − | 0.987287i | \(-0.550811\pi\) | ||||
−0.158950 | + | 0.987287i | \(0.550811\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 1.85210 | − | 1.92330i | 0.163069 | − | 0.169337i | ||||
\(130\) | −3.59984 | − | 6.23511i | −0.315727 | − | 0.546855i | ||||
\(131\) | 10.9882 | − | 19.0321i | 0.960045 | − | 1.66285i | 0.237667 | − | 0.971347i | \(-0.423617\pi\) |
0.722377 | − | 0.691499i | \(-0.243049\pi\) | |||||||
\(132\) | −1.66428 | + | 0.479752i | −0.144857 | + | 0.0417571i | ||||
\(133\) | 10.2166 | − | 15.4925i | 0.885892 | − | 1.34337i | ||||
\(134\) | − | 1.22747i | − | 0.106037i | ||||||
\(135\) | −7.87886 | + | 2.59669i | −0.678104 | + | 0.223488i | ||||
\(136\) | 5.40545 | − | 3.12084i | 0.463513 | − | 0.267610i | ||||
\(137\) | −10.0400 | + | 5.79657i | −0.857771 | + | 0.495235i | −0.863265 | − | 0.504750i | \(-0.831585\pi\) |
0.00549399 | + | 0.999985i | \(0.498251\pi\) | |||||||
\(138\) | −7.83754 | − | 1.94245i | −0.667176 | − | 0.165352i | ||||
\(139\) | 12.3113i | 1.04423i | 0.852874 | + | 0.522116i | \(0.174857\pi\) | ||||
−0.852874 | + | 0.522116i | \(0.825143\pi\) | |||||||
\(140\) | −0.250738 | + | 4.21653i | −0.0211912 | + | 0.356362i | ||||
\(141\) | 3.42473 | + | 11.8805i | 0.288414 | + | 1.00052i | ||||
\(142\) | −4.73640 | + | 8.20369i | −0.397470 | + | 0.688439i | ||||
\(143\) | −2.25481 | − | 3.90545i | −0.188557 | − | 0.326590i | ||||
\(144\) | 2.65278 | + | 1.40098i | 0.221065 | + | 0.116748i | ||||
\(145\) | −7.65665 | − | 4.42057i | −0.635850 | − | 0.367108i | ||||
\(146\) | −4.12222 | −0.341157 | ||||||||
\(147\) | 9.38578 | − | 7.67510i | 0.774126 | − | 0.633031i | ||||
\(148\) | −0.571472 | −0.0469747 | ||||||||
\(149\) | −11.1729 | − | 6.45067i | −0.915318 | − | 0.528459i | −0.0331799 | − | 0.999449i | \(-0.510563\pi\) |
−0.882139 | + | 0.470990i | \(0.843897\pi\) | |||||||
\(150\) | 3.05809 | + | 2.94489i | 0.249692 | + | 0.240449i | ||||
\(151\) | 4.50486 | + | 7.80264i | 0.366600 | + | 0.634970i | 0.989032 | − | 0.147704i | \(-0.0471884\pi\) |
−0.622432 | + | 0.782674i | \(0.713855\pi\) | |||||||
\(152\) | 3.50711 | − | 6.07449i | 0.284464 | − | 0.492707i | ||||
\(153\) | 15.8518 | − | 9.96725i | 1.28154 | − | 0.805804i | ||||
\(154\) | −0.157053 | + | 2.64109i | −0.0126557 | + | 0.212825i | ||||
\(155\) | 14.5268i | 1.16682i | ||||||||
\(156\) | −1.87900 | + | 7.58152i | −0.150440 | + | 0.607008i | ||||
\(157\) | 2.83438 | − | 1.63643i | 0.226208 | − | 0.130601i | −0.382613 | − | 0.923909i | \(-0.624976\pi\) |
0.608822 | + | 0.793307i | \(0.291643\pi\) | |||||||
\(158\) | −6.70413 | + | 3.87063i | −0.533352 | + | 0.307931i | ||||
\(159\) | −3.91929 | + | 15.8138i | −0.310820 | + | 1.25412i | ||||
\(160\) | 1.59652i | 0.126216i | ||||||||
\(161\) | −6.79033 | + | 10.2969i | −0.535153 | + | 0.811506i | ||||
\(162\) | 8.11115 | + | 3.89991i | 0.637272 | + | 0.306406i | ||||
\(163\) | 7.81342 | − | 13.5332i | 0.611994 | − | 1.06001i | −0.378910 | − | 0.925434i | \(-0.623701\pi\) |
0.990904 | − | 0.134572i | \(-0.0429658\pi\) | |||||||
\(164\) | 0.798258 | + | 1.38262i | 0.0623334 | + | 0.107965i | ||||
\(165\) | −1.99184 | − | 1.91811i | −0.155065 | − | 0.149325i | ||||
\(166\) | −15.1130 | − | 8.72550i | −1.17300 | − | 0.677230i | ||||
\(167\) | −19.7228 | −1.52620 | −0.763099 | − | 0.646282i | \(-0.776323\pi\) | ||||
−0.763099 | + | 0.646282i | \(0.776323\pi\) | |||||||
\(168\) | 3.36904 | − | 3.10638i | 0.259927 | − | 0.239662i | ||||
\(169\) | −7.33672 | −0.564363 | ||||||||
\(170\) | 8.62988 | + | 4.98247i | 0.661882 | + | 0.382138i | ||||
\(171\) | 9.82679 | − | 18.6072i | 0.751473 | − | 1.42293i | ||||
\(172\) | −0.770788 | − | 1.33504i | −0.0587721 | − | 0.101796i | ||||
\(173\) | −0.301207 | + | 0.521706i | −0.0229003 | + | 0.0396645i | −0.877248 | − | 0.480037i | \(-0.840623\pi\) |
0.854348 | + | 0.519701i | \(0.173957\pi\) | |||||||
\(174\) | 2.65676 | + | 9.21642i | 0.201408 | + | 0.698695i | ||||
\(175\) | 5.79884 | − | 2.90345i | 0.438351 | − | 0.219480i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | −8.82216 | − | 2.18648i | −0.663114 | − | 0.164346i | ||||
\(178\) | 11.5936 | − | 6.69358i | 0.868978 | − | 0.501705i | ||||
\(179\) | 20.9583 | − | 12.1003i | 1.56650 | − | 0.904417i | 0.569924 | − | 0.821698i | \(-0.306973\pi\) |
0.996573 | − | 0.0827196i | \(-0.0263606\pi\) | |||||||
\(180\) | 0.180576 | + | 4.78614i | 0.0134593 | + | 0.356738i | ||||
\(181\) | 25.2747i | 1.87865i | 0.343026 | + | 0.939326i | \(0.388548\pi\) | ||||
−0.343026 | + | 0.939326i | \(0.611452\pi\) | |||||||
\(182\) | 9.96050 | + | 6.56852i | 0.738322 | + | 0.486891i | ||||
\(183\) | −3.63164 | + | 1.04687i | −0.268458 | + | 0.0773868i | ||||
\(184\) | −2.33096 | + | 4.03733i | −0.171840 | + | 0.297636i | ||||
\(185\) | −0.456182 | − | 0.790131i | −0.0335392 | − | 0.0580916i | ||||
\(186\) | 10.9320 | − | 11.3522i | 0.801570 | − | 0.832383i | ||||
\(187\) | 5.40545 | + | 3.12084i | 0.395286 | + | 0.228218i | ||||
\(188\) | 7.13853 | 0.520631 | ||||||||
\(189\) | 9.74857 | − | 9.69357i | 0.709104 | − | 0.705104i | ||||
\(190\) | 11.1983 | 0.812411 | ||||||||
\(191\) | −9.98570 | − | 5.76525i | −0.722540 | − | 0.417159i | 0.0931470 | − | 0.995652i | \(-0.470307\pi\) |
−0.815687 | + | 0.578494i | \(0.803641\pi\) | |||||||
\(192\) | 1.20144 | − | 1.24762i | 0.0867061 | − | 0.0900391i | ||||
\(193\) | −6.21106 | − | 10.7579i | −0.447082 | − | 0.774368i | 0.551113 | − | 0.834431i | \(-0.314203\pi\) |
−0.998195 | + | 0.0600625i | \(0.980870\pi\) | |||||||
\(194\) | 3.55758 | − | 6.16191i | 0.255419 | − | 0.442399i | ||||
\(195\) | −11.9823 | + | 3.45406i | −0.858071 | + | 0.247351i | ||||
\(196\) | −2.75690 | − | 6.43425i | −0.196921 | − | 0.459589i | ||||
\(197\) | 6.78332i | 0.483291i | 0.970365 | + | 0.241646i | \(0.0776872\pi\) | ||||
−0.970365 | + | 0.241646i | \(0.922313\pi\) | |||||||
\(198\) | 0.113106 | + | 2.99787i | 0.00803812 | + | 0.213049i | ||||
\(199\) | −7.19446 | + | 4.15372i | −0.510002 | + | 0.294450i | −0.732834 | − | 0.680407i | \(-0.761803\pi\) |
0.222833 | + | 0.974857i | \(0.428470\pi\) | |||||||
\(200\) | 2.12275 | − | 1.22557i | 0.150101 | − | 0.0866609i | ||||
\(201\) | −2.06361 | − | 0.511443i | −0.145556 | − | 0.0360744i | ||||
\(202\) | 0.301386i | 0.0212055i | ||||||||
\(203\) | 14.6257 | + | 0.869725i | 1.02653 | + | 0.0610427i | ||||
\(204\) | −2.99446 | − | 10.3879i | −0.209654 | − | 0.727300i | ||||
\(205\) | −1.27443 | + | 2.20738i | −0.0890101 | + | 0.154170i | ||||
\(206\) | 4.59255 | + | 7.95453i | 0.319978 | + | 0.554218i | ||||
\(207\) | −6.53125 | + | 12.3670i | −0.453953 | + | 0.859568i | ||||
\(208\) | 3.90545 | + | 2.25481i | 0.270794 | + | 0.156343i | ||||
\(209\) | 7.01422 | 0.485184 | ||||||||
\(210\) | 6.98431 | + | 2.17841i | 0.481963 | + | 0.150325i | ||||
\(211\) | −2.69698 | −0.185668 | −0.0928339 | − | 0.995682i | \(-0.529593\pi\) | ||||
−0.0928339 | + | 0.995682i | \(0.529593\pi\) | |||||||
\(212\) | 8.14614 | + | 4.70318i | 0.559479 | + | 0.323016i | ||||
\(213\) | 11.8185 | + | 11.3810i | 0.809787 | + | 0.779811i | ||||
\(214\) | 4.21653 | + | 7.30325i | 0.288236 | + | 0.499240i | ||||
\(215\) | 1.23058 | − | 2.13142i | 0.0839245 | − | 0.145362i | ||||
\(216\) | 3.46063 | − | 3.87609i | 0.235466 | − | 0.263734i | ||||
\(217\) | −10.7781 | − | 21.5264i | −0.731668 | − | 1.46131i | ||||
\(218\) | − | 14.6854i | − | 0.994620i | ||||||
\(219\) | −1.71758 | + | 6.93022i | −0.116063 | + | 0.468301i | ||||
\(220\) | −1.38262 | + | 0.798258i | −0.0932164 | + | 0.0538185i | ||||
\(221\) | 24.3766 | − | 14.0738i | 1.63974 | − | 0.946707i | ||||
\(222\) | −0.238112 | + | 0.960752i | −0.0159810 | + | 0.0644815i | ||||
\(223\) | − | 14.2135i | − | 0.951806i | −0.879498 | − | 0.475903i | \(-0.842121\pi\) | ||
0.879498 | − | 0.475903i | \(-0.157879\pi\) | |||||||
\(224\) | −1.18453 | − | 2.36577i | −0.0791448 | − | 0.158070i | ||||
\(225\) | 6.22510 | − | 3.91419i | 0.415007 | − | 0.260946i | ||||
\(226\) | −5.27122 | + | 9.13003i | −0.350637 | + | 0.607320i | ||||
\(227\) | −2.67241 | − | 4.62875i | −0.177374 | − | 0.307221i | 0.763606 | − | 0.645682i | \(-0.223427\pi\) |
−0.940980 | + | 0.338461i | \(0.890094\pi\) | |||||||
\(228\) | −8.75108 | − | 8.42713i | −0.579554 | − | 0.558101i | ||||
\(229\) | 11.6567 | + | 6.73002i | 0.770299 | + | 0.444732i | 0.832981 | − | 0.553301i | \(-0.186632\pi\) |
−0.0626824 | + | 0.998034i | \(0.519966\pi\) | |||||||
\(230\) | −7.44281 | −0.490764 | ||||||||
\(231\) | 4.37472 | + | 1.36448i | 0.287836 | + | 0.0897763i | ||||
\(232\) | 5.53777 | 0.363573 | ||||||||
\(233\) | 0.0187672 | + | 0.0108352i | 0.00122948 | + | 0.000709840i | 0.500615 | − | 0.865670i | \(-0.333107\pi\) |
−0.499385 | + | 0.866380i | \(0.666441\pi\) | |||||||
\(234\) | 11.9631 | + | 6.31790i | 0.782049 | + | 0.413014i | ||||
\(235\) | 5.69839 | + | 9.86990i | 0.371722 | + | 0.643841i | ||||
\(236\) | −2.62379 | + | 4.54453i | −0.170794 | + | 0.295824i | ||||
\(237\) | 3.71389 | + | 12.8837i | 0.241243 | + | 0.836883i | ||||
\(238\) | −16.4848 | − | 0.980275i | −1.06855 | − | 0.0635418i | ||||
\(239\) | 10.4498i | 0.675939i | 0.941157 | + | 0.337970i | \(0.109740\pi\) | ||||
−0.941157 | + | 0.337970i | \(0.890260\pi\) | |||||||
\(240\) | 2.68404 | + | 0.665210i | 0.173254 | + | 0.0429391i | ||||
\(241\) | 3.78807 | − | 2.18704i | 0.244011 | − | 0.140880i | −0.373008 | − | 0.927828i | \(-0.621674\pi\) |
0.617019 | + | 0.786948i | \(0.288340\pi\) | |||||||
\(242\) | −0.866025 | + | 0.500000i | −0.0556702 | + | 0.0321412i | ||||
\(243\) | 9.93610 | − | 12.0114i | 0.637401 | − | 0.770532i | ||||
\(244\) | 2.18210i | 0.139695i | ||||||||
\(245\) | 6.69542 | − | 8.94793i | 0.427755 | − | 0.571662i | ||||
\(246\) | 2.65705 | − | 0.765932i | 0.169408 | − | 0.0488340i | ||||
\(247\) | 15.8158 | − | 27.3937i | 1.00633 | − | 1.74302i | ||||
\(248\) | −4.54954 | − | 7.88004i | −0.288896 | − | 0.500383i | ||||
\(249\) | −20.9663 | + | 21.7722i | −1.32868 | + | 1.37976i | ||||
\(250\) | 10.3021 | + | 5.94793i | 0.651563 | + | 0.376180i | ||||
\(251\) | −6.32543 | −0.399258 | −0.199629 | − | 0.979872i | \(-0.563974\pi\) | ||||
−0.199629 | + | 0.979872i | \(0.563974\pi\) | |||||||
\(252\) | −3.81865 | − | 6.95830i | −0.240552 | − | 0.438332i | ||||
\(253\) | −4.66191 | −0.293092 | ||||||||
\(254\) | 3.10259 | + | 1.79128i | 0.194674 | + | 0.112395i | ||||
\(255\) | 11.9722 | − | 12.4324i | 0.749729 | − | 0.778549i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.91340 | − | 8.51025i | 0.306489 | − | 0.530855i | −0.671103 | − | 0.741364i | \(-0.734179\pi\) |
0.977592 | + | 0.210510i | \(0.0675123\pi\) | |||||||
\(258\) | −2.56562 | + | 0.739575i | −0.159729 | + | 0.0460439i | ||||
\(259\) | 1.26222 | + | 0.832381i | 0.0784307 | + | 0.0517216i | ||||
\(260\) | 7.19968i | 0.446506i | ||||||||
\(261\) | 16.6015 | − | 0.626358i | 1.02761 | − | 0.0387706i | ||||
\(262\) | −19.0321 | + | 10.9882i | −1.17581 | + | 0.678854i | ||||
\(263\) | −16.8992 | + | 9.75675i | −1.04205 | + | 0.601627i | −0.920413 | − | 0.390948i | \(-0.872147\pi\) |
−0.121635 | + | 0.992575i | \(0.538814\pi\) | |||||||
\(264\) | 1.68119 | + | 0.416664i | 0.103470 | + | 0.0256439i | ||||
\(265\) | 15.0174i | 0.922511i | ||||||||
\(266\) | −16.5941 | + | 8.30856i | −1.01745 | + | 0.509431i | ||||
\(267\) | −6.42251 | − | 22.2800i | −0.393051 | − | 1.36351i | ||||
\(268\) | −0.613735 | + | 1.06302i | −0.0374898 | + | 0.0649343i | ||||
\(269\) | −3.36084 | − | 5.82115i | −0.204914 | − | 0.354922i | 0.745191 | − | 0.666851i | \(-0.232358\pi\) |
−0.950105 | + | 0.311929i | \(0.899025\pi\) | |||||||
\(270\) | 8.12164 | + | 1.69063i | 0.494267 | + | 0.102888i | ||||
\(271\) | 8.89324 | + | 5.13451i | 0.540226 | + | 0.311899i | 0.745170 | − | 0.666874i | \(-0.232368\pi\) |
−0.204945 | + | 0.978774i | \(0.565701\pi\) | |||||||
\(272\) | −6.24168 | −0.378457 | ||||||||
\(273\) | 15.1931 | − | 14.0086i | 0.919528 | − | 0.847840i | ||||
\(274\) | 11.5931 | 0.700367 | ||||||||
\(275\) | 2.12275 | + | 1.22557i | 0.128007 | + | 0.0739046i | ||||
\(276\) | 5.81629 | + | 5.60098i | 0.350099 | + | 0.337140i | ||||
\(277\) | −0.340360 | − | 0.589521i | −0.0204502 | − | 0.0354209i | 0.855619 | − | 0.517606i | \(-0.173177\pi\) |
−0.876069 | + | 0.482185i | \(0.839843\pi\) | |||||||
\(278\) | 6.15566 | − | 10.6619i | 0.369192 | − | 0.639459i | ||||
\(279\) | −14.5302 | − | 23.1087i | −0.869900 | − | 1.38348i | ||||
\(280\) | 2.32541 | − | 3.52626i | 0.138970 | − | 0.210734i | ||||
\(281\) | 22.1693i | 1.32251i | 0.750162 | + | 0.661254i | \(0.229976\pi\) | ||||
−0.750162 | + | 0.661254i | \(0.770024\pi\) | |||||||
\(282\) | 2.97437 | − | 12.0012i | 0.177121 | − | 0.714662i | ||||
\(283\) | −22.0002 | + | 12.7018i | −1.30778 | + | 0.755044i | −0.981724 | − | 0.190308i | \(-0.939051\pi\) |
−0.326051 | + | 0.945352i | \(0.605718\pi\) | |||||||
\(284\) | 8.20369 | − | 4.73640i | 0.486800 | − | 0.281054i | ||||
\(285\) | 4.66593 | − | 18.8265i | 0.276386 | − | 1.11518i | ||||
\(286\) | 4.50963i | 0.266660i | ||||||||
\(287\) | 0.250738 | − | 4.21653i | 0.0148006 | − | 0.248894i | ||||
\(288\) | −1.59689 | − | 2.53968i | −0.0940974 | − | 0.149652i | ||||
\(289\) | −10.9793 | + | 19.0166i | −0.645839 | + | 1.11863i | ||||
\(290\) | 4.42057 | + | 7.65665i | 0.259585 | + | 0.449614i | ||||
\(291\) | −8.87701 | − | 8.54841i | −0.520380 | − | 0.501116i | ||||
\(292\) | 3.56995 | + | 2.06111i | 0.208915 | + | 0.120617i | ||||
\(293\) | 4.91386 | 0.287070 | 0.143535 | − | 0.989645i | \(-0.454153\pi\) | ||||
0.143535 | + | 0.989645i | \(0.454153\pi\) | |||||||
\(294\) | −11.9659 | + | 1.95394i | −0.697864 | + | 0.113956i | ||||
\(295\) | −8.37783 | −0.487776 | ||||||||
\(296\) | 0.494910 | + | 0.285736i | 0.0287660 | + | 0.0166081i | ||||
\(297\) | 5.08710 | + | 1.05895i | 0.295184 | + | 0.0614465i | ||||
\(298\) | 6.45067 | + | 11.1729i | 0.373677 | + | 0.647228i | ||||
\(299\) | −10.5117 | + | 18.2069i | −0.607909 | + | 1.05293i | ||||
\(300\) | −1.17594 | − | 4.07939i | −0.0678929 | − | 0.235524i | ||||
\(301\) | −0.242109 | + | 4.07144i | −0.0139550 | + | 0.234674i | ||||
\(302\) | − | 9.00971i | − | 0.518451i | ||||||
\(303\) | 0.506687 | + | 0.125577i | 0.0291084 | + | 0.00721420i | ||||
\(304\) | −6.07449 | + | 3.50711i | −0.348396 | + | 0.201147i | ||||
\(305\) | −3.01703 | + | 1.74188i | −0.172754 | + | 0.0997398i | ||||
\(306\) | −18.7117 | + | 0.705973i | −1.06968 | + | 0.0403578i | ||||
\(307\) | 17.5786i | 1.00326i | 0.865082 | + | 0.501631i | \(0.167266\pi\) | ||||
−0.865082 | + | 0.501631i | \(0.832734\pi\) | |||||||
\(308\) | 1.45655 | − | 2.20872i | 0.0829949 | − | 0.125854i | ||||
\(309\) | 15.2866 | − | 4.40657i | 0.869625 | − | 0.250681i | ||||
\(310\) | 7.26341 | − | 12.5806i | 0.412534 | − | 0.714530i | ||||
\(311\) | 7.05301 | + | 12.2162i | 0.399939 | + | 0.692715i | 0.993718 | − | 0.111913i | \(-0.0356979\pi\) |
−0.593779 | + | 0.804628i | \(0.702365\pi\) | |||||||
\(312\) | 5.41802 | − | 5.62629i | 0.306735 | − | 0.318526i | ||||
\(313\) | −22.2006 | − | 12.8175i | −1.25485 | − | 0.724490i | −0.282784 | − | 0.959184i | \(-0.591258\pi\) |
−0.972069 | + | 0.234694i | \(0.924591\pi\) | |||||||
\(314\) | −3.27286 | −0.184698 | ||||||||
\(315\) | 6.57243 | − | 10.8343i | 0.370315 | − | 0.610442i | ||||
\(316\) | 7.74126 | 0.435480 | ||||||||
\(317\) | 2.94082 | + | 1.69789i | 0.165173 | + | 0.0953628i | 0.580308 | − | 0.814397i | \(-0.302932\pi\) |
−0.415135 | + | 0.909760i | \(0.636266\pi\) | |||||||
\(318\) | 11.3011 | − | 11.7355i | 0.633736 | − | 0.658097i | ||||
\(319\) | 2.76889 | + | 4.79585i | 0.155028 | + | 0.268516i | ||||
\(320\) | 0.798258 | − | 1.38262i | 0.0446240 | − | 0.0772910i | ||||
\(321\) | 14.0350 | − | 4.04578i | 0.783358 | − | 0.225814i | ||||
\(322\) | 11.0290 | − | 5.52218i | 0.614624 | − | 0.307739i | ||||
\(323\) | 43.7805i | 2.43601i | ||||||||
\(324\) | −5.07451 | − | 7.43299i | −0.281917 | − | 0.412944i | ||||
\(325\) | 9.57280 | − | 5.52686i | 0.531003 | − | 0.306575i | ||||
\(326\) | −13.5332 | + | 7.81342i | −0.749537 | + | 0.432745i | ||||
\(327\) | −24.6889 | − | 6.11887i | −1.36530 | − | 0.338375i | ||||
\(328\) | − | 1.59652i | − | 0.0881528i | ||||||
\(329\) | −15.7670 | − | 10.3977i | −0.869264 | − | 0.573242i | ||||
\(330\) | 0.765932 | + | 2.65705i | 0.0421631 | + | 0.146266i | ||||
\(331\) | −1.09383 | + | 1.89457i | −0.0601223 | + | 0.104135i | −0.894520 | − | 0.447028i | \(-0.852482\pi\) |
0.834398 | + | 0.551163i | \(0.185816\pi\) | |||||||
\(332\) | 8.72550 | + | 15.1130i | 0.478874 | + | 0.829434i | ||||
\(333\) | 1.51599 | + | 0.800622i | 0.0830758 | + | 0.0438738i | ||||
\(334\) | 17.0805 | + | 9.86141i | 0.934601 | + | 0.539592i | ||||
\(335\) | −1.95968 | −0.107069 | ||||||||
\(336\) | −4.47086 | + | 1.00569i | −0.243905 | + | 0.0548646i | ||||
\(337\) | 29.9526 | 1.63162 | 0.815811 | − | 0.578318i | \(-0.196291\pi\) | ||||
0.815811 | + | 0.578318i | \(0.196291\pi\) | |||||||
\(338\) | 6.35378 | + | 3.66836i | 0.345600 | + | 0.199532i | ||||
\(339\) | 13.1530 | + | 12.6661i | 0.714371 | + | 0.687926i | ||||
\(340\) | −4.98247 | − | 8.62988i | −0.270212 | − | 0.468021i | ||||
\(341\) | 4.54954 | − | 7.88004i | 0.246371 | − | 0.426728i | ||||
\(342\) | −17.8139 | + | 11.2009i | −0.963263 | + | 0.605676i | ||||
\(343\) | −3.28262 | + | 18.2270i | −0.177245 | + | 0.984167i | ||||
\(344\) | 1.54158i | 0.0831163i | ||||||||
\(345\) | −3.10115 | + | 12.5128i | −0.166960 | + | 0.673664i | ||||
\(346\) | 0.521706 | − | 0.301207i | 0.0280471 | − | 0.0161930i | ||||
\(347\) | −29.0172 | + | 16.7531i | −1.55772 | + | 0.899352i | −0.560249 | + | 0.828324i | \(0.689294\pi\) |
−0.997474 | + | 0.0710275i | \(0.977372\pi\) | |||||||
\(348\) | 2.30739 | − | 9.31004i | 0.123689 | − | 0.499070i | ||||
\(349\) | − | 20.9221i | − | 1.11993i | −0.828516 | − | 0.559966i | \(-0.810814\pi\) | ||
0.828516 | − | 0.559966i | \(-0.189186\pi\) | |||||||
\(350\) | −6.47367 | − | 0.384959i | −0.346032 | − | 0.0205769i | ||||
\(351\) | 15.6061 | − | 17.4797i | 0.832994 | − | 0.932997i | ||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | −2.78452 | − | 4.82293i | −0.148205 | − | 0.256698i | 0.782359 | − | 0.622828i | \(-0.214016\pi\) |
−0.930564 | + | 0.366129i | \(0.880683\pi\) | |||||||
\(354\) | 6.54697 | + | 6.30462i | 0.347968 | + | 0.335087i | ||||
\(355\) | 13.0973 | + | 7.56174i | 0.695134 | + | 0.401336i | ||||
\(356\) | −13.3872 | −0.709518 | ||||||||
\(357\) | −8.51665 | + | 27.3056i | −0.450749 | + | 1.44517i | ||||
\(358\) | −24.2006 | −1.27904 | ||||||||
\(359\) | 7.29047 | + | 4.20916i | 0.384776 | + | 0.222151i | 0.679894 | − | 0.733310i | \(-0.262026\pi\) |
−0.295118 | + | 0.955461i | \(0.595359\pi\) | |||||||
\(360\) | 2.23669 | − | 4.23521i | 0.117884 | − | 0.223215i | ||||
\(361\) | 15.0997 | + | 26.1534i | 0.794719 | + | 1.37649i | ||||
\(362\) | 12.6373 | − | 21.8885i | 0.664204 | − | 1.15043i | ||||
\(363\) | 0.479752 | + | 1.66428i | 0.0251805 | + | 0.0873522i | ||||
\(364\) | −5.34179 | − | 10.6688i | −0.279986 | − | 0.559195i | ||||
\(365\) | 6.58119i | 0.344475i | ||||||||
\(366\) | 3.66853 | + | 0.909204i | 0.191757 | + | 0.0475249i | ||||
\(367\) | −31.8854 | + | 18.4090i | −1.66440 | + | 0.960944i | −0.693831 | + | 0.720138i | \(0.744078\pi\) |
−0.970573 | + | 0.240806i | \(0.922588\pi\) | |||||||
\(368\) | 4.03733 | − | 2.33096i | 0.210461 | − | 0.121509i | ||||
\(369\) | −0.180576 | − | 4.78614i | −0.00940041 | − | 0.249157i | ||||
\(370\) | 0.912364i | 0.0474316i | ||||||||
\(371\) | −11.1421 | − | 22.2533i | −0.578470 | − | 1.15533i | ||||
\(372\) | −15.1434 | + | 4.36530i | −0.785151 | + | 0.226330i | ||||
\(373\) | −4.54391 | + | 7.87029i | −0.235275 | + | 0.407508i | −0.959353 | − | 0.282210i | \(-0.908932\pi\) |
0.724078 | + | 0.689718i | \(0.242266\pi\) | |||||||
\(374\) | −3.12084 | − | 5.40545i | −0.161375 | − | 0.279509i | ||||
\(375\) | 14.2921 | − | 14.8415i | 0.738041 | − | 0.766412i | ||||
\(376\) | −6.18215 | − | 3.56927i | −0.318820 | − | 0.184071i | ||||
\(377\) | 24.9733 | 1.28619 | ||||||||
\(378\) | −13.2893 | + | 3.52059i | −0.683528 | + | 0.181080i | ||||
\(379\) | −25.4673 | −1.30817 | −0.654085 | − | 0.756421i | \(-0.726946\pi\) | ||||
−0.654085 | + | 0.756421i | \(0.726946\pi\) | |||||||
\(380\) | −9.69802 | − | 5.59916i | −0.497498 | − | 0.287231i | ||||
\(381\) | 4.30421 | − | 4.46967i | 0.220511 | − | 0.228988i | ||||
\(382\) | 5.76525 | + | 9.98570i | 0.294976 | + | 0.510913i | ||||
\(383\) | 4.27006 | − | 7.39596i | 0.218190 | − | 0.377916i | −0.736065 | − | 0.676911i | \(-0.763318\pi\) |
0.954255 | + | 0.298995i | \(0.0966515\pi\) | |||||||
\(384\) | −1.66428 | + | 0.479752i | −0.0849301 | + | 0.0244822i | ||||
\(385\) | 4.21653 | + | 0.250738i | 0.214894 | + | 0.0127788i | ||||
\(386\) | 12.4221i | 0.632269i | ||||||||
\(387\) | 0.174362 | + | 4.62144i | 0.00886333 | + | 0.234921i | ||||
\(388\) | −6.16191 | + | 3.55758i | −0.312824 | + | 0.180609i | ||||
\(389\) | −1.09167 | + | 0.630275i | −0.0553498 | + | 0.0319562i | −0.527420 | − | 0.849605i | \(-0.676840\pi\) |
0.472070 | + | 0.881561i | \(0.343507\pi\) | |||||||
\(390\) | 12.1040 | + | 2.99985i | 0.612911 | + | 0.151903i | ||||
\(391\) | − | 29.0981i | − | 1.47156i | ||||||
\(392\) | −0.829582 | + | 6.95067i | −0.0419002 | + | 0.351062i | ||||
\(393\) | 10.5432 | + | 36.5750i | 0.531836 | + | 1.84496i | ||||
\(394\) | 3.39166 | − | 5.87453i | 0.170869 | − | 0.295954i | ||||
\(395\) | 6.17952 | + | 10.7032i | 0.310925 | + | 0.538539i | ||||
\(396\) | 1.40098 | − | 2.65278i | 0.0704019 | − | 0.133307i | ||||
\(397\) | 1.93996 | + | 1.12004i | 0.0973638 | + | 0.0562130i | 0.547891 | − | 0.836550i | \(-0.315431\pi\) |
−0.450528 | + | 0.892763i | \(0.648764\pi\) | |||||||
\(398\) | 8.30745 | 0.416415 | ||||||||
\(399\) | 7.05410 | + | 31.3596i | 0.353147 | + | 1.56994i | ||||
\(400\) | −2.45114 | −0.122557 | ||||||||
\(401\) | −21.8208 | − | 12.5982i | −1.08968 | − | 0.629125i | −0.156187 | − | 0.987728i | \(-0.549920\pi\) |
−0.933491 | + | 0.358602i | \(0.883254\pi\) | |||||||
\(402\) | 1.53142 | + | 1.47473i | 0.0763801 | + | 0.0735527i | ||||
\(403\) | −20.5167 | − | 35.5360i | −1.02201 | − | 1.77017i | ||||
\(404\) | 0.150693 | − | 0.261008i | 0.00749726 | − | 0.0129856i | ||||
\(405\) | 6.22626 | − | 12.9496i | 0.309385 | − | 0.643469i | ||||
\(406\) | −12.2314 | − | 8.06607i | −0.607034 | − | 0.400312i | ||||
\(407\) | 0.571472i | 0.0283268i | ||||||||
\(408\) | −2.60068 | + | 10.4934i | −0.128753 | + | 0.519502i | ||||
\(409\) | −15.7714 | + | 9.10565i | −0.779848 | + | 0.450245i | −0.836376 | − | 0.548156i | \(-0.815330\pi\) |
0.0565286 | + | 0.998401i | \(0.481997\pi\) | |||||||
\(410\) | 2.20738 | − | 1.27443i | 0.109015 | − | 0.0629396i | ||||
\(411\) | 4.83045 | − | 19.4902i | 0.238268 | − | 0.961383i | ||||
\(412\) | − | 9.18510i | − | 0.452517i | ||||||
\(413\) | 12.4146 | − | 6.21591i | 0.610881 | − | 0.305865i | ||||
\(414\) | 11.8397 | − | 7.44454i | 0.581891 | − | 0.365879i | ||||
\(415\) | −13.9304 | + | 24.1282i | −0.683816 | + | 1.18440i | ||||
\(416\) | −2.25481 | − | 3.90545i | −0.110551 | − | 0.191480i | ||||
\(417\) | −15.3598 | − | 14.7912i | −0.752174 | − | 0.724330i | ||||
\(418\) | −6.07449 | − | 3.50711i | −0.297113 | − | 0.171538i | ||||
\(419\) | −4.09314 | −0.199963 | −0.0999814 | − | 0.994989i | \(-0.531878\pi\) | ||||
−0.0999814 | + | 0.994989i | \(0.531878\pi\) | |||||||
\(420\) | −4.95938 | − | 5.37872i | −0.241993 | − | 0.262455i | ||||
\(421\) | −31.3561 | −1.52820 | −0.764101 | − | 0.645097i | \(-0.776817\pi\) | ||||
−0.764101 | + | 0.645097i | \(0.776817\pi\) | |||||||
\(422\) | 2.33565 | + | 1.34849i | 0.113698 | + | 0.0656435i | ||||
\(423\) | −18.9370 | − | 10.0009i | −0.920747 | − | 0.486263i | ||||
\(424\) | −4.70318 | − | 8.14614i | −0.228407 | − | 0.395612i | ||||
\(425\) | −7.64961 | + | 13.2495i | −0.371060 | + | 0.642696i | ||||
\(426\) | −4.54460 | − | 15.7654i | −0.220187 | − | 0.763838i | ||||
\(427\) | 3.17835 | − | 4.81966i | 0.153811 | − | 0.233240i | ||||
\(428\) | − | 8.43307i | − | 0.407628i | ||||||
\(429\) | 7.58152 | + | 1.87900i | 0.366039 | + | 0.0907189i | ||||
\(430\) | −2.13142 | + | 1.23058i | −0.102786 | + | 0.0593436i | ||||
\(431\) | 5.56332 | − | 3.21199i | 0.267976 | − | 0.154716i | −0.359992 | − | 0.932956i | \(-0.617220\pi\) |
0.627967 | + | 0.778240i | \(0.283887\pi\) | |||||||
\(432\) | −4.93504 | + | 1.62647i | −0.237437 | + | 0.0782538i | ||||
\(433\) | 9.32492i | 0.448127i | 0.974575 | + | 0.224063i | \(0.0719323\pi\) | ||||
−0.974575 | + | 0.224063i | \(0.928068\pi\) | |||||||
\(434\) | −1.42904 | + | 24.0315i | −0.0685961 | + | 1.15355i | ||||
\(435\) | 14.7142 | − | 4.24156i | 0.705490 | − | 0.203367i | ||||
\(436\) | −7.34270 | + | 12.7179i | −0.351651 | + | 0.609078i | ||||
\(437\) | −16.3498 | − | 28.3187i | −0.782119 | − | 1.35467i | ||||
\(438\) | 4.95258 | − | 5.14296i | 0.236643 | − | 0.245740i | ||||
\(439\) | 6.17648 | + | 3.56599i | 0.294787 | + | 0.170196i | 0.640099 | − | 0.768293i | \(-0.278893\pi\) |
−0.345311 | + | 0.938488i | \(0.612227\pi\) | |||||||
\(440\) | 1.59652 | 0.0761109 | ||||||||
\(441\) | −1.70081 | + | 20.9310i | −0.0809910 | + | 0.996715i | ||||
\(442\) | −28.1476 | −1.33885 | ||||||||
\(443\) | −7.28448 | − | 4.20570i | −0.346096 | − | 0.199819i | 0.316868 | − | 0.948470i | \(-0.397369\pi\) |
−0.662965 | + | 0.748651i | \(0.730702\pi\) | |||||||
\(444\) | 0.686587 | − | 0.712980i | 0.0325840 | − | 0.0338365i | ||||
\(445\) | −10.6864 | − | 18.5094i | −0.506584 | − | 0.877429i | ||||
\(446\) | −7.10675 | + | 12.3092i | −0.336514 | + | 0.582860i | ||||
\(447\) | 21.4715 | − | 6.18944i | 1.01557 | − | 0.292751i | ||||
\(448\) | −0.157053 | + | 2.64109i | −0.00742006 | + | 0.124780i | ||||
\(449\) | − | 16.9926i | − | 0.801933i | −0.916093 | − | 0.400966i | \(-0.868674\pi\) | ||
0.916093 | − | 0.400966i | \(-0.131326\pi\) | |||||||
\(450\) | −7.34819 | + | 0.277239i | −0.346397 | + | 0.0130692i | ||||
\(451\) | 1.38262 | − | 0.798258i | 0.0651052 | − | 0.0375885i | ||||
\(452\) | 9.13003 | − | 5.27122i | 0.429440 | − | 0.247938i | ||||
\(453\) | −15.1470 | − | 3.75402i | −0.711669 | − | 0.176379i | ||||
\(454\) | 5.34482i | 0.250845i | ||||||||
\(455\) | 10.4867 | − | 15.9021i | 0.491626 | − | 0.745502i | ||||
\(456\) | 3.36509 | + | 11.6737i | 0.157585 | + | 0.546669i | ||||
\(457\) | 16.0161 | − | 27.7407i | 0.749203 | − | 1.29766i | −0.199002 | − | 0.979999i | \(-0.563770\pi\) |
0.948205 | − | 0.317658i | \(-0.102897\pi\) | |||||||
\(458\) | −6.73002 | − | 11.6567i | −0.314473 | − | 0.544684i | ||||
\(459\) | −6.60962 | + | 31.7521i | −0.308511 | + | 1.48206i | ||||
\(460\) | 6.44566 | + | 3.72141i | 0.300531 | + | 0.173511i | ||||
\(461\) | 6.80255 | 0.316826 | 0.158413 | − | 0.987373i | \(-0.449362\pi\) | ||||
0.158413 | + | 0.987373i | \(0.449362\pi\) | |||||||
\(462\) | −3.10638 | − | 3.36904i | −0.144522 | − | 0.156742i | ||||
\(463\) | −7.62180 | −0.354215 | −0.177108 | − | 0.984192i | \(-0.556674\pi\) | ||||
−0.177108 | + | 0.984192i | \(0.556674\pi\) | |||||||
\(464\) | −4.79585 | − | 2.76889i | −0.222642 | − | 0.128542i | ||||
\(465\) | −18.1239 | − | 17.4530i | −0.840478 | − | 0.809365i | ||||
\(466\) | −0.0108352 | − | 0.0187672i | −0.000501933 | − | 0.000869373i | ||||
\(467\) | 9.28685 | − | 16.0853i | 0.429744 | − | 0.744339i | −0.567106 | − | 0.823645i | \(-0.691937\pi\) |
0.996850 | + | 0.0793060i | \(0.0252704\pi\) | |||||||
\(468\) | −7.20136 | − | 11.4530i | −0.332883 | − | 0.529414i | ||||
\(469\) | 2.90392 | − | 1.45398i | 0.134090 | − | 0.0671384i | ||||
\(470\) | − | 11.3968i | − | 0.525694i | ||||||
\(471\) | −1.36368 | + | 5.50229i | −0.0628352 | + | 0.253532i | ||||
\(472\) | 4.54453 | − | 2.62379i | 0.209179 | − | 0.120770i | ||||
\(473\) | −1.33504 | + | 0.770788i | −0.0613854 | + | 0.0354409i | ||||
\(474\) | 3.22551 | − | 13.0145i | 0.148152 | − | 0.597776i | ||||
\(475\) | 17.1928i | 0.788861i | ||||||||
\(476\) | 13.7861 | + | 9.09134i | 0.631886 | + | 0.416701i | ||||
\(477\) | −15.0209 | − | 23.8891i | −0.687759 | − | 1.09381i | ||||
\(478\) | 5.22488 | − | 9.04976i | 0.238981 | − | 0.413927i | ||||
\(479\) | 6.60898 | + | 11.4471i | 0.301972 | + | 0.523031i | 0.976583 | − | 0.215143i | \(-0.0690217\pi\) |
−0.674610 | + | 0.738174i | \(0.735688\pi\) | |||||||
\(480\) | −1.99184 | − | 1.91811i | −0.0909148 | − | 0.0875493i | ||||
\(481\) | 2.23186 | + | 1.28856i | 0.101764 | + | 0.0587534i | ||||
\(482\) | −4.37409 | −0.199234 | ||||||||
\(483\) | −4.68842 | − | 20.8428i | −0.213330 | − | 0.948378i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −9.83758 | − | 5.67973i | −0.446702 | − | 0.257903i | ||||
\(486\) | −14.6106 | + | 5.43414i | −0.662751 | + | 0.246497i | ||||
\(487\) | 10.7246 | + | 18.5756i | 0.485980 | + | 0.841741i | 0.999870 | − | 0.0161145i | \(-0.00512963\pi\) |
−0.513891 | + | 0.857856i | \(0.671796\pi\) | |||||||
\(488\) | 1.09105 | − | 1.88976i | 0.0493896 | − | 0.0855453i | ||||
\(489\) | 7.49701 | + | 26.0075i | 0.339026 | + | 1.17610i | ||||
\(490\) | −10.2724 | + | 4.40143i | −0.464058 | + | 0.198836i | ||||
\(491\) | − | 4.02472i | − | 0.181633i | −0.995868 | − | 0.0908166i | \(-0.971052\pi\) | ||
0.995868 | − | 0.0908166i | \(-0.0289477\pi\) | |||||||
\(492\) | −2.68404 | − | 0.665210i | −0.121006 | − | 0.0299900i | ||||
\(493\) | −29.9342 | + | 17.2825i | −1.34817 | + | 0.778365i | ||||
\(494\) | −27.3937 | + | 15.8158i | −1.23250 | + | 0.711585i | ||||
\(495\) | 4.78614 | − | 0.180576i | 0.215121 | − | 0.00811629i | ||||
\(496\) | 9.09908i | 0.408561i | ||||||||
\(497\) | −25.0185 | − | 1.48773i | −1.12223 | − | 0.0667340i | ||||
\(498\) | 29.0434 | − | 8.37216i | 1.30147 | − | 0.375165i | ||||
\(499\) | 0.903651 | − | 1.56517i | 0.0404530 | − | 0.0700666i | −0.845090 | − | 0.534624i | \(-0.820453\pi\) |
0.885543 | + | 0.464557i | \(0.153787\pi\) | |||||||
\(500\) | −5.94793 | − | 10.3021i | −0.265999 | − | 0.460725i | ||||
\(501\) | 23.6957 | − | 24.6066i | 1.05865 | − | 1.09934i | ||||
\(502\) | 5.47798 | + | 3.16272i | 0.244494 | + | 0.141159i | ||||
\(503\) | 5.18163 | 0.231037 | 0.115519 | − | 0.993305i | \(-0.463147\pi\) | ||||
0.115519 | + | 0.993305i | \(0.463147\pi\) | |||||||
\(504\) | −0.172101 | + | 7.93539i | −0.00766598 | + | 0.353470i | ||||
\(505\) | 0.481168 | 0.0214117 | ||||||||
\(506\) | 4.03733 | + | 2.33096i | 0.179481 | + | 0.103624i | ||||
\(507\) | 8.81459 | − | 9.15343i | 0.391470 | − | 0.406518i | ||||
\(508\) | −1.79128 | − | 3.10259i | −0.0794752 | − | 0.137655i | ||||
\(509\) | −2.70116 | + | 4.67854i | −0.119727 | + | 0.207373i | −0.919659 | − | 0.392717i | \(-0.871535\pi\) |
0.799933 | + | 0.600090i | \(0.204868\pi\) | |||||||
\(510\) | −16.5845 | + | 4.78070i | −0.734372 | + | 0.211693i | ||||
\(511\) | −4.88290 | − | 9.75224i | −0.216007 | − | 0.431414i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 11.4085 | + | 34.6154i | 0.503695 | + | 1.52831i | ||||
\(514\) | −8.51025 | + | 4.91340i | −0.375371 | + | 0.216721i | ||||
\(515\) | 12.6995 | − | 7.33208i | 0.559608 | − | 0.323090i | ||||
\(516\) | 2.59168 | + | 0.642320i | 0.114092 | + | 0.0282765i | ||||
\(517\) | − | 7.13853i | − | 0.313952i | ||||||
\(518\) | −0.676927 | − | 1.35197i | −0.0297425 | − | 0.0594024i | ||||
\(519\) | −0.289009 | − | 1.00259i | −0.0126861 | − | 0.0440087i | ||||
\(520\) | 3.59984 | − | 6.23511i | 0.157864 | − | 0.273428i | ||||
\(521\) | −0.537919 | − | 0.931703i | −0.0235667 | − | 0.0408187i | 0.854002 | − | 0.520270i | \(-0.174169\pi\) |
−0.877568 | + | 0.479452i | \(0.840836\pi\) | |||||||
\(522\) | −14.6905 | − | 7.75831i | −0.642986 | − | 0.339572i | ||||
\(523\) | 22.3360 | + | 12.8957i | 0.976686 | + | 0.563890i | 0.901268 | − | 0.433262i | \(-0.142637\pi\) |
0.0754184 | + | 0.997152i | \(0.475971\pi\) | |||||||
\(524\) | 21.9764 | 0.960045 | ||||||||
\(525\) | −3.34453 | + | 10.7231i | −0.145967 | + | 0.467992i | ||||
\(526\) | 19.5135 | 0.850829 | ||||||||
\(527\) | 49.1846 | + | 28.3968i | 2.14252 | + | 1.23698i | ||||
\(528\) | −1.24762 | − | 1.20144i | −0.0542956 | − | 0.0522858i | ||||
\(529\) | −0.633298 | − | 1.09690i | −0.0275347 | − | 0.0476915i | ||||
\(530\) | 7.50870 | − | 13.0054i | 0.326157 | − | 0.564920i | ||||
\(531\) | 13.3271 | − | 8.37978i | 0.578349 | − | 0.363652i | ||||
\(532\) | 18.5252 | + | 1.10161i | 0.803168 | + | 0.0477607i | ||||
\(533\) | − | 7.19968i | − | 0.311853i | ||||||
\(534\) | −5.57794 | + | 22.5063i | −0.241381 | + | 0.973943i | ||||
\(535\) | 11.6598 | − | 6.73176i | 0.504095 | − | 0.291039i | ||||
\(536\) | 1.06302 | − | 0.613735i | 0.0459155 | − | 0.0265093i | ||||
\(537\) | −10.0835 | + | 40.6857i | −0.435135 | + | 1.75572i | ||||
\(538\) | 6.72169i | 0.289792i | ||||||||
\(539\) | −6.43425 | + | 2.75690i | −0.277143 | + | 0.118748i | ||||
\(540\) | −6.18823 | − | 5.52495i | −0.266299 | − | 0.237756i | ||||
\(541\) | 7.73940 | − | 13.4050i | 0.332743 | − | 0.576327i | −0.650306 | − | 0.759672i | \(-0.725359\pi\) |
0.983049 | + | 0.183345i | \(0.0586926\pi\) | |||||||
\(542\) | −5.13451 | − | 8.89324i | −0.220546 | − | 0.381997i | ||||
\(543\) | −31.5332 | − | 30.3659i | −1.35322 | − | 1.30312i | ||||
\(544\) | 5.40545 | + | 3.12084i | 0.231757 | + | 0.133805i | ||||
\(545\) | −23.4455 | −1.00429 | ||||||||
\(546\) | −20.1619 | + | 4.53526i | −0.862850 | + | 0.194091i | ||||
\(547\) | 6.19696 | 0.264963 | 0.132481 | − | 0.991185i | \(-0.457706\pi\) | ||||
0.132481 | + | 0.991185i | \(0.457706\pi\) | |||||||
\(548\) | −10.0400 | − | 5.79657i | −0.428886 | − | 0.247617i | ||||
\(549\) | 3.05709 | − | 5.78865i | 0.130473 | − | 0.247053i | ||||
\(550\) | −1.22557 | − | 2.12275i | −0.0522585 | − | 0.0905143i | ||||
\(551\) | −19.4216 | + | 33.6392i | −0.827388 | + | 1.43308i | ||||
\(552\) | −2.23656 | − | 7.75874i | −0.0951944 | − | 0.330234i | ||||
\(553\) | −17.0983 | − | 11.2756i | −0.727093 | − | 0.479486i | ||||
\(554\) | 0.680720i | 0.0289210i | ||||||||
\(555\) | 1.53386 | + | 0.380149i | 0.0651085 | + | 0.0161364i | ||||
\(556\) | −10.6619 | + | 6.15566i | −0.452166 | + | 0.261058i | ||||
\(557\) | 6.93926 | − | 4.00638i | 0.294026 | − | 0.169756i | −0.345730 | − | 0.938334i | \(-0.612369\pi\) |
0.639756 | + | 0.768578i | \(0.279035\pi\) | |||||||
\(558\) | 1.02916 | + | 27.2778i | 0.0435680 | + | 1.15476i | ||||
\(559\) | 6.95193i | 0.294035i | ||||||||
\(560\) | −3.77699 | + | 1.89112i | −0.159607 | + | 0.0799145i | ||||
\(561\) | −10.3879 | + | 2.99446i | −0.438578 | + | 0.126426i | ||||
\(562\) | 11.0846 | − | 19.1992i | 0.467577 | − | 0.809868i | ||||
\(563\) | 18.8825 | + | 32.7054i | 0.795801 | + | 1.37837i | 0.922329 | + | 0.386405i | \(0.126283\pi\) |
−0.126528 | + | 0.991963i | \(0.540383\pi\) | |||||||
\(564\) | −8.57648 | + | 8.90617i | −0.361135 | + | 0.375017i | ||||
\(565\) | 14.5762 | + | 8.41559i | 0.613227 | + | 0.354046i | ||||
\(566\) | 25.4036 | 1.06779 | ||||||||
\(567\) | 0.381608 | + | 23.8087i | 0.0160260 | + | 0.999872i | ||||
\(568\) | −9.47281 | −0.397470 | ||||||||
\(569\) | 30.7607 | + | 17.7597i | 1.28956 | + | 0.744525i | 0.978575 | − | 0.205891i | \(-0.0660091\pi\) |
0.310981 | + | 0.950416i | \(0.399342\pi\) | |||||||
\(570\) | −13.4540 | + | 13.9712i | −0.563528 | + | 0.585190i | ||||
\(571\) | −21.7959 | − | 37.7517i | −0.912132 | − | 1.57986i | −0.811047 | − | 0.584981i | \(-0.801102\pi\) |
−0.101085 | − | 0.994878i | \(-0.532231\pi\) | |||||||
\(572\) | 2.25481 | − | 3.90545i | 0.0942784 | − | 0.163295i | ||||
\(573\) | 19.1900 | − | 5.53178i | 0.801674 | − | 0.231093i | ||||
\(574\) | −2.32541 | + | 3.52626i | −0.0970608 | + | 0.147183i | ||||
\(575\) | − | 11.4270i | − | 0.476538i | ||||||
\(576\) | 0.113106 | + | 2.99787i | 0.00471277 | + | 0.124911i | ||||
\(577\) | 24.5749 | − | 14.1883i | 1.02307 | − | 0.590668i | 0.108076 | − | 0.994143i | \(-0.465531\pi\) |
0.914991 | + | 0.403475i | \(0.132198\pi\) | |||||||
\(578\) | 19.0166 | − | 10.9793i | 0.790988 | − | 0.456677i | ||||
\(579\) | 20.8839 | + | 5.17585i | 0.867905 | + | 0.215101i | ||||
\(580\) | − | 8.84114i | − | 0.367108i | ||||||
\(581\) | 2.74073 | − | 46.0896i | 0.113705 | − | 1.91212i | ||||
\(582\) | 3.41351 | + | 11.8416i | 0.141495 | + | 0.490852i | ||||
\(583\) | 4.70318 | − | 8.14614i | 0.194786 | − | 0.337379i | ||||
\(584\) | −2.06111 | − | 3.56995i | −0.0852893 | − | 0.147725i | ||||
\(585\) | 10.0866 | − | 19.0992i | 0.417030 | − | 0.789655i | ||||
\(586\) | −4.25552 | − | 2.45693i | −0.175794 | − | 0.101495i | ||||
\(587\) | 4.02886 | 0.166289 | 0.0831444 | − | 0.996538i | \(-0.473504\pi\) | ||||
0.0831444 | + | 0.996538i | \(0.473504\pi\) | |||||||
\(588\) | 11.3397 | + | 4.29078i | 0.467642 | + | 0.176949i | ||||
\(589\) | 63.8230 | 2.62978 | ||||||||
\(590\) | 7.25542 | + | 4.18892i | 0.298701 | + | 0.172455i | ||||
\(591\) | −8.46300 | − | 8.14972i | −0.348121 | − | 0.335235i | ||||
\(592\) | −0.285736 | − | 0.494910i | −0.0117437 | − | 0.0203407i | ||||
\(593\) | −16.6336 | + | 28.8102i | −0.683060 | + | 1.18309i | 0.290982 | + | 0.956729i | \(0.406018\pi\) |
−0.974042 | + | 0.226366i | \(0.927315\pi\) | |||||||
\(594\) | −3.87609 | − | 3.46063i | −0.159038 | − | 0.141991i | ||||
\(595\) | −1.56502 | + | 26.3182i | −0.0641597 | + | 1.07894i | ||||
\(596\) | − | 12.9013i | − | 0.528459i | ||||||
\(597\) | 3.46141 | − | 13.9664i | 0.141666 | − | 0.571606i | ||||
\(598\) | 18.2069 | − | 10.5117i | 0.744534 | − | 0.429857i | ||||
\(599\) | 18.2896 | − | 10.5595i | 0.747291 | − | 0.431449i | −0.0774232 | − | 0.996998i | \(-0.524669\pi\) |
0.824714 | + | 0.565550i | \(0.191336\pi\) | |||||||
\(600\) | −1.02130 | + | 4.12082i | −0.0416945 | + | 0.168232i | ||||
\(601\) | − | 13.1521i | − | 0.536484i | −0.963352 | − | 0.268242i | \(-0.913557\pi\) | ||
0.963352 | − | 0.268242i | \(-0.0864427\pi\) | |||||||
\(602\) | 2.24539 | − | 3.40491i | 0.0915153 | − | 0.138774i | ||||
\(603\) | 3.11738 | − | 1.96013i | 0.126949 | − | 0.0798227i | ||||
\(604\) | −4.50486 | + | 7.80264i | −0.183300 | + | 0.317485i | ||||
\(605\) | 0.798258 | + | 1.38262i | 0.0324538 | + | 0.0562116i | ||||
\(606\) | −0.376015 | − | 0.362096i | −0.0152746 | − | 0.0147091i | ||||
\(607\) | 29.6701 | + | 17.1300i | 1.20427 | + | 0.695286i | 0.961502 | − | 0.274798i | \(-0.0886110\pi\) |
0.242769 | + | 0.970084i | \(0.421944\pi\) | |||||||
\(608\) | 7.01422 | 0.284464 | ||||||||
\(609\) | −18.6570 | + | 17.2024i | −0.756018 | + | 0.697078i | ||||
\(610\) | 3.48376 | 0.141053 | ||||||||
\(611\) | −27.8792 | − | 16.0961i | −1.12787 | − | 0.651177i | ||||
\(612\) | 16.5578 | + | 8.74447i | 0.669310 | + | 0.353474i | ||||
\(613\) | 0.628750 | + | 1.08903i | 0.0253950 | + | 0.0439854i | 0.878444 | − | 0.477846i | \(-0.158582\pi\) |
−0.853049 | + | 0.521831i | \(0.825249\pi\) | |||||||
\(614\) | 8.78928 | − | 15.2235i | 0.354707 | − | 0.614370i | ||||
\(615\) | −1.22282 | − | 4.24203i | −0.0493089 | − | 0.171055i | ||||
\(616\) | −2.36577 | + | 1.18453i | −0.0953197 | + | 0.0477261i | ||||
\(617\) | − | 8.09880i | − | 0.326045i | −0.986622 | − | 0.163023i | \(-0.947876\pi\) | ||
0.986622 | − | 0.163023i | \(-0.0521244\pi\) | |||||||
\(618\) | −15.4419 | − | 3.82710i | −0.621163 | − | 0.153949i | ||||
\(619\) | 11.2505 | − | 6.49551i | 0.452198 | − | 0.261076i | −0.256560 | − | 0.966528i | \(-0.582589\pi\) |
0.708758 | + | 0.705452i | \(0.249256\pi\) | |||||||
\(620\) | −12.5806 | + | 7.26341i | −0.505249 | + | 0.291706i | ||||
\(621\) | −7.58248 | − | 23.0067i | −0.304274 | − | 0.923227i | ||||
\(622\) | − | 14.1060i | − | 0.565600i | ||||||
\(623\) | 29.5685 | + | 19.4991i | 1.18464 | + | 0.781216i | ||||
\(624\) | −7.50529 | + | 2.16350i | −0.300452 | + | 0.0866094i | ||||
\(625\) | 3.36811 | − | 5.83374i | 0.134724 | − | 0.233350i | ||||
\(626\) | 12.8175 | + | 22.2006i | 0.512292 | + | 0.887315i | ||||
\(627\) | −8.42713 | + | 8.75108i | −0.336547 | + | 0.349484i | ||||
\(628\) | 2.83438 | + | 1.63643i | 0.113104 | + | 0.0653007i | ||||
\(629\) | −3.56695 | −0.142223 | ||||||||
\(630\) | −11.1090 | + | 6.09653i | −0.442594 | + | 0.242892i | ||||
\(631\) | −4.49319 | −0.178871 | −0.0894356 | − | 0.995993i | \(-0.528506\pi\) | ||||
−0.0894356 | + | 0.995993i | \(0.528506\pi\) | |||||||
\(632\) | −6.70413 | − | 3.87063i | −0.266676 | − | 0.153965i | ||||
\(633\) | 3.24025 | − | 3.36480i | 0.128788 | − | 0.133739i | ||||
\(634\) | −1.69789 | − | 2.94082i | −0.0674317 | − | 0.116795i | ||||
\(635\) | 2.85980 | − | 4.95333i | 0.113488 | − | 0.196567i | ||||
\(636\) | −15.6548 | + | 4.51272i | −0.620755 | + | 0.178941i | ||||
\(637\) | −3.74110 | + | 31.3449i | −0.148228 | + | 1.24193i | ||||
\(638\) | − | 5.53777i | − | 0.219243i | ||||||
\(639\) | −28.3982 | + | 1.07144i | −1.12342 | + | 0.0423853i | ||||
\(640\) | −1.38262 | + | 0.798258i | −0.0546530 | + | 0.0315539i | ||||
\(641\) | −23.9171 | + | 13.8085i | −0.944668 | + | 0.545404i | −0.891420 | − | 0.453177i | \(-0.850290\pi\) |
−0.0532472 | + | 0.998581i | \(0.516957\pi\) | |||||||
\(642\) | −14.1776 | − | 3.51376i | −0.559544 | − | 0.138677i | ||||
\(643\) | 2.44235i | 0.0963168i | 0.998840 | + | 0.0481584i | \(0.0153352\pi\) | ||||
−0.998840 | + | 0.0481584i | \(0.984665\pi\) | |||||||
\(644\) | −12.3125 | − | 0.732168i | −0.485181 | − | 0.0288514i | ||||
\(645\) | 1.18074 | + | 4.09605i | 0.0464917 | + | 0.161282i | ||||
\(646\) | 21.8903 | − | 37.9150i | 0.861260 | − | 1.49175i | ||||
\(647\) | 6.42484 | + | 11.1282i | 0.252587 | + | 0.437493i | 0.964237 | − | 0.265041i | \(-0.0853854\pi\) |
−0.711651 | + | 0.702534i | \(0.752052\pi\) | |||||||
\(648\) | 0.678156 | + | 8.97441i | 0.0266405 | + | 0.352548i | ||||
\(649\) | 4.54453 | + | 2.62379i | 0.178389 | + | 0.102993i | ||||
\(650\) | −11.0537 | −0.433563 | ||||||||
\(651\) | 39.8060 | + | 12.4155i | 1.56012 | + | 0.486603i | ||||
\(652\) | 15.6268 | 0.611994 | ||||||||
\(653\) | 7.70766 | + | 4.45002i | 0.301624 | + | 0.174143i | 0.643172 | − | 0.765722i | \(-0.277618\pi\) |
−0.341548 | + | 0.939864i | \(0.610951\pi\) | |||||||
\(654\) | 18.3218 | + | 17.6435i | 0.716438 | + | 0.689917i | ||||
\(655\) | 17.5428 | + | 30.3851i | 0.685456 | + | 1.18724i | ||||
\(656\) | −0.798258 | + | 1.38262i | −0.0311667 | + | 0.0539823i | ||||
\(657\) | −6.58272 | − | 10.4691i | −0.256816 | − | 0.408439i | ||||
\(658\) | 8.45581 | + | 16.8882i | 0.329642 | + | 0.658369i | ||||
\(659\) | 31.7573i | 1.23709i | 0.785751 | + | 0.618544i | \(0.212277\pi\) | ||||
−0.785751 | + | 0.618544i | \(0.787723\pi\) | |||||||
\(660\) | 0.665210 | − | 2.68404i | 0.0258933 | − | 0.104476i | ||||
\(661\) | −15.9605 | + | 9.21478i | −0.620790 | + | 0.358413i | −0.777177 | − | 0.629283i | \(-0.783349\pi\) |
0.156387 | + | 0.987696i | \(0.450015\pi\) | |||||||
\(662\) | 1.89457 | − | 1.09383i | 0.0736345 | − | 0.0425129i | ||||
\(663\) | −11.7281 | + | 47.3214i | −0.455482 | + | 1.83781i | ||||
\(664\) | − | 17.4510i | − | 0.677230i | ||||||
\(665\) | 13.2647 | + | 26.4927i | 0.514385 | + | 1.02734i | ||||
\(666\) | −0.912577 | − | 1.45135i | −0.0353616 | − | 0.0562389i | ||||
\(667\) | 12.9083 | − | 22.3578i | 0.499812 | − | 0.865699i | ||||
\(668\) | −9.86141 | − | 17.0805i | −0.381549 | − | 0.660863i | ||||
\(669\) | 17.7330 | + | 17.0766i | 0.685599 | + | 0.660219i | ||||
\(670\) | 1.69713 | + | 0.979838i | 0.0655658 | + | 0.0378544i | ||||
\(671\) | 2.18210 | 0.0842392 | ||||||||
\(672\) | 4.37472 | + | 1.36448i | 0.168759 | + | 0.0526360i | ||||
\(673\) | −5.66645 | −0.218426 | −0.109213 | − | 0.994018i | \(-0.534833\pi\) | ||||
−0.109213 | + | 0.994018i | \(0.534833\pi\) | |||||||
\(674\) | −25.9397 | − | 14.9763i | −0.999161 | − | 0.576866i | ||||
\(675\) | −2.59563 | + | 12.4692i | −0.0999060 | + | 0.479940i | ||||
\(676\) | −3.66836 | − | 6.35378i | −0.141091 | − | 0.244376i | ||||
\(677\) | −21.6601 | + | 37.5163i | −0.832464 | + | 1.44187i | 0.0636151 | + | 0.997975i | \(0.479737\pi\) |
−0.896079 | + | 0.443895i | \(0.853596\pi\) | |||||||
\(678\) | −5.05776 | − | 17.5456i | −0.194242 | − | 0.673835i | ||||
\(679\) | 18.7918 | + | 1.11746i | 0.721161 | + | 0.0428841i | ||||
\(680\) | 9.96493i | 0.382138i | ||||||||
\(681\) | 8.98564 | + | 2.22699i | 0.344331 | + | 0.0853386i | ||||
\(682\) | −7.88004 | + | 4.54954i | −0.301742 | + | 0.174211i | ||||
\(683\) | −10.9764 | + | 6.33724i | −0.420001 | + | 0.242488i | −0.695078 | − | 0.718934i | \(-0.744630\pi\) |
0.275077 | + | 0.961422i | \(0.411297\pi\) | |||||||
\(684\) | 21.0277 | − | 0.793353i | 0.804014 | − | 0.0303346i | ||||
\(685\) | − | 18.5086i | − | 0.707178i | ||||||
\(686\) | 11.9563 | − | 14.1438i | 0.456495 | − | 0.540011i | ||||
\(687\) | −22.4013 | + | 6.45748i | −0.854663 | + | 0.246368i | ||||
\(688\) | 0.770788 | − | 1.33504i | 0.0293860 | − | 0.0508981i | ||||
\(689\) | −21.2096 | − | 36.7361i | −0.808020 | − | 1.39953i | ||||
\(690\) | 8.94206 | − | 9.28579i | 0.340418 | − | 0.353504i | ||||
\(691\) | −30.5975 | − | 17.6655i | −1.16398 | − | 0.672026i | −0.211728 | − | 0.977329i | \(-0.567909\pi\) |
−0.952256 | + | 0.305302i | \(0.901243\pi\) | |||||||
\(692\) | −0.602414 | −0.0229003 | ||||||||
\(693\) | −6.95830 | + | 3.81865i | −0.264324 | + | 0.145059i | ||||
\(694\) | 33.5061 | 1.27188 | ||||||||
\(695\) | −17.0219 | − | 9.82760i | −0.645678 | − | 0.372782i | ||||
\(696\) | −6.65328 | + | 6.90903i | −0.252192 | + | 0.261886i | ||||
\(697\) | 4.98247 | + | 8.62988i | 0.188724 | + | 0.326880i | ||||
\(698\) | −10.4610 | + | 18.1190i | −0.395956 | + | 0.685815i | ||||
\(699\) | −0.0360658 | + | 0.0103965i | −0.00136413 | + | 0.000393230i | ||||
\(700\) | 5.41388 | + | 3.57022i | 0.204626 | + | 0.134942i | ||||
\(701\) | − | 33.9878i | − | 1.28370i | −0.766830 | − | 0.641851i | \(-0.778167\pi\) | ||
0.766830 | − | 0.641851i | \(-0.221833\pi\) | |||||||
\(702\) | −22.2552 | + | 7.33479i | −0.839967 | + | 0.276834i | ||||
\(703\) | −3.47141 | + | 2.00422i | −0.130927 | + | 0.0755905i | ||||
\(704\) | −0.866025 | + | 0.500000i | −0.0326396 | + | 0.0188445i | ||||
\(705\) | −19.1601 | − | 4.74863i | −0.721612 | − | 0.178844i | ||||
\(706\) | 5.56904i | 0.209593i | ||||||||
\(707\) | −0.713012 | + | 0.357001i | −0.0268156 | + | 0.0134264i | ||||
\(708\) | −2.51753 | − | 8.73345i | −0.0946148 | − | 0.328223i | ||||
\(709\) | 16.3651 | − | 28.3452i | 0.614604 | − | 1.06452i | −0.375850 | − | 0.926680i | \(-0.622649\pi\) |
0.990454 | − | 0.137844i | \(-0.0440174\pi\) | |||||||
\(710\) | −7.56174 | − | 13.0973i | −0.283787 | − | 0.491534i | ||||
\(711\) | −20.5359 | − | 10.8454i | −0.770156 | − | 0.406733i | ||||
\(712\) | 11.5936 | + | 6.69358i | 0.434489 | + | 0.250852i | ||||
\(713\) | −42.4191 | −1.58861 | ||||||||
\(714\) | 21.0284 | − | 19.3890i | 0.786969 | − | 0.725616i | ||||
\(715\) | 7.19968 | 0.269253 | ||||||||
\(716\) | 20.9583 | + | 12.1003i | 0.783248 | + | 0.452209i | ||||
\(717\) | −13.0373 | − | 12.5547i | −0.486888 | − | 0.468865i | ||||
\(718\) | −4.20916 | − | 7.29047i | −0.157084 | − | 0.272078i | ||||
\(719\) | 12.5536 | − | 21.7435i | 0.468172 | − | 0.810897i | −0.531167 | − | 0.847267i | \(-0.678246\pi\) |
0.999338 | + | 0.0363702i | \(0.0115795\pi\) | |||||||
\(720\) | −4.05463 | + | 2.54945i | −0.151107 | + | 0.0950125i | ||||
\(721\) | −13.3786 | + | 20.2873i | −0.498245 | + | 0.755539i | ||||
\(722\) | − | 30.1993i | − | 1.12390i | ||||||
\(723\) | −1.82253 | + | 7.35366i | −0.0677805 | + | 0.273486i | ||||
\(724\) | −21.8885 | + | 12.6373i | −0.813480 | + | 0.469663i | ||||
\(725\) | −11.7553 | + | 6.78693i | −0.436581 | + | 0.252060i | ||||
\(726\) | 0.416664 | − | 1.68119i | 0.0154639 | − | 0.0623947i | ||||
\(727\) | − | 32.7918i | − | 1.21618i | −0.793868 | − | 0.608090i | \(-0.791936\pi\) | ||
0.793868 | − | 0.608090i | \(-0.208064\pi\) | |||||||
\(728\) | −0.708251 | + | 11.9103i | −0.0262495 | + | 0.441425i | ||||
\(729\) | 3.04808 | + | 26.8274i | 0.112892 | + | 0.993607i | ||||
\(730\) | 3.29059 | − | 5.69947i | 0.121790 | − | 0.210947i | ||||
\(731\) | −4.81101 | − | 8.33292i | −0.177942 | − | 0.308204i | ||||
\(732\) | −2.72243 | − | 2.62166i | −0.100624 | − | 0.0968992i | ||||
\(733\) | 8.36398 | + | 4.82895i | 0.308931 | + | 0.178361i | 0.646448 | − | 0.762958i | \(-0.276254\pi\) |
−0.337517 | + | 0.941319i | \(0.609587\pi\) | |||||||
\(734\) | 36.8181 | 1.35898 | ||||||||
\(735\) | 3.11949 | + | 19.1037i | 0.115064 | + | 0.704651i | ||||
\(736\) | −4.66191 | −0.171840 | ||||||||
\(737\) | 1.06302 | + | 0.613735i | 0.0391569 | + | 0.0226072i | ||||
\(738\) | −2.23669 | + | 4.23521i | −0.0823336 | + | 0.155900i | ||||
\(739\) | −5.82847 | − | 10.0952i | −0.214404 | − | 0.371358i | 0.738684 | − | 0.674052i | \(-0.235447\pi\) |
−0.953088 | + | 0.302693i | \(0.902114\pi\) | |||||||
\(740\) | 0.456182 | − | 0.790131i | 0.0167696 | − | 0.0290458i | ||||
\(741\) | 15.1753 | + | 52.6438i | 0.557478 | + | 1.93392i | ||||
\(742\) | −1.47730 | + | 24.8430i | −0.0542333 | + | 0.912015i | ||||
\(743\) | − | 5.87724i | − | 0.215615i | −0.994172 | − | 0.107807i | \(-0.965617\pi\) | ||
0.994172 | − | 0.107807i | \(-0.0343830\pi\) | |||||||
\(744\) | 15.2973 | + | 3.79126i | 0.560825 | + | 0.138994i | ||||
\(745\) | 17.8377 | − | 10.2986i | 0.653522 | − | 0.377311i | ||||
\(746\) | 7.87029 | − | 4.54391i | 0.288152 | − | 0.166364i | ||||
\(747\) | −1.97382 | − | 52.3158i | −0.0722183 | − | 1.91413i | ||||
\(748\) | 6.24168i | 0.228218i | ||||||||
\(749\) | −12.2832 | + | 18.6263i | −0.448819 | + | 0.680590i | ||||
\(750\) | −19.7981 | + | 5.70706i | −0.722923 | + | 0.208392i | ||||
\(751\) | 9.95620 | − | 17.2447i | 0.363307 | − | 0.629266i | −0.625196 | − | 0.780468i | \(-0.714981\pi\) |
0.988503 | + | 0.151202i | \(0.0483143\pi\) | |||||||
\(752\) | 3.56927 | + | 6.18215i | 0.130158 | + | 0.225440i | ||||
\(753\) | 7.59960 | − | 7.89173i | 0.276945 | − | 0.287591i | ||||
\(754\) | −21.6275 | − | 12.4866i | −0.787627 | − | 0.454737i | ||||
\(755\) | −14.3841 | −0.523493 | ||||||||
\(756\) | 13.2692 | + | 3.59572i | 0.482595 | + | 0.130775i | ||||
\(757\) | 9.77216 | 0.355175 | 0.177588 | − | 0.984105i | \(-0.443171\pi\) | ||||
0.177588 | + | 0.984105i | \(0.443171\pi\) | |||||||
\(758\) | 22.0554 | + | 12.7337i | 0.801087 | + | 0.462508i | ||||
\(759\) | 5.60098 | − | 5.81629i | 0.203303 | − | 0.211118i | ||||
\(760\) | 5.59916 | + | 9.69802i | 0.203103 | + | 0.351784i | ||||
\(761\) | −5.18661 | + | 8.98347i | −0.188014 | + | 0.325650i | −0.944588 | − | 0.328258i | \(-0.893538\pi\) |
0.756574 | + | 0.653908i | \(0.226872\pi\) | |||||||
\(762\) | −5.96239 | + | 1.71874i | −0.215995 | + | 0.0622634i | ||||
\(763\) | 34.7423 | − | 17.3953i | 1.25776 | − | 0.629752i | ||||
\(764\) | − | 11.5305i | − | 0.417159i | ||||||
\(765\) | 1.12710 | + | 29.8735i | 0.0407503 | + | 1.08008i | ||||
\(766\) | −7.39596 | + | 4.27006i | −0.267227 | + | 0.154283i | ||||
\(767\) | 20.4941 | − | 11.8323i | 0.740000 | − | 0.427239i | ||||
\(768\) | 1.68119 | + | 0.416664i | 0.0606646 | + | 0.0150351i | ||||
\(769\) | − | 20.5641i | − | 0.741560i | −0.928721 | − | 0.370780i | \(-0.879090\pi\) | ||
0.928721 | − | 0.370780i | \(-0.120910\pi\) | |||||||
\(770\) | −3.52626 | − | 2.32541i | −0.127077 | − | 0.0838020i | ||||
\(771\) | 4.71442 | + | 16.3546i | 0.169786 | + | 0.588995i | ||||
\(772\) | 6.21106 | − | 10.7579i | 0.223541 | − | 0.387184i | ||||
\(773\) | −13.0535 | − | 22.6093i | −0.469501 | − | 0.813200i | 0.529891 | − | 0.848066i | \(-0.322233\pi\) |
−0.999392 | + | 0.0348658i | \(0.988900\pi\) | |||||||
\(774\) | 2.15972 | − | 4.08947i | 0.0776295 | − | 0.146993i | ||||
\(775\) | 19.3151 | + | 11.1516i | 0.693818 | + | 0.400576i | ||||
\(776\) | 7.11516 | 0.255419 | ||||||||
\(777\) | −2.55497 | + | 0.574722i | −0.0916592 | + | 0.0206180i | ||||
\(778\) | 1.26055 | 0.0451929 | ||||||||
\(779\) | 9.69802 | + | 5.59916i | 0.347468 | + | 0.200611i | ||||
\(780\) | −8.98246 | − | 8.64996i | −0.321624 | − | 0.309718i | ||||
\(781\) | −4.73640 | − | 8.20369i | −0.169482 | − | 0.293551i | ||||
\(782\) | −14.5491 | + | 25.1997i | −0.520274 | + | 0.901140i | ||||
\(783\) | −19.1642 | + | 21.4649i | −0.684872 | + | 0.767093i | ||||
\(784\) | 4.19377 | − | 5.60466i | 0.149778 | − | 0.200167i | ||||
\(785\) | 5.22517i | 0.186494i | ||||||||
\(786\) | 9.15678 | − | 36.9465i | 0.326612 | − | 1.31784i | ||||
\(787\) | −41.8059 | + | 24.1366i | −1.49022 | + | 0.860378i | −0.999937 | − | 0.0111869i | \(-0.996439\pi\) |
−0.490281 | + | 0.871565i | \(0.663106\pi\) | |||||||
\(788\) | −5.87453 | + | 3.39166i | −0.209271 | + | 0.120823i | ||||
\(789\) | 8.13057 | − | 32.8058i | 0.289456 | − | 1.16792i | ||||
\(790\) | − | 12.3590i | − | 0.439715i | ||||||
\(791\) | −27.8435 | − | 1.65572i | −0.990001 | − | 0.0588708i | ||||
\(792\) | −2.53968 | + | 1.59689i | −0.0902435 | + | 0.0567429i | ||||
\(793\) | 4.92024 | − | 8.52210i | 0.174723 | − | 0.302629i | ||||
\(794\) | −1.12004 | − | 1.93996i | −0.0397486 | − | 0.0688466i | ||||
\(795\) | −18.7360 | − | 18.0424i | −0.664497 | − | 0.639899i | ||||
\(796\) | −7.19446 | − | 4.15372i | −0.255001 | − | 0.147225i | ||||
\(797\) | 36.1754 | 1.28140 | 0.640699 | − | 0.767793i | \(-0.278645\pi\) | ||||
0.640699 | + | 0.767793i | \(0.278645\pi\) | |||||||
\(798\) | 9.57077 | − | 30.6853i | 0.338802 | − | 1.08625i | ||||
\(799\) | 44.5564 | 1.57629 | ||||||||
\(800\) | 2.12275 | + | 1.22557i | 0.0750505 | + | 0.0433304i | ||||
\(801\) | 35.5132 | + | 18.7551i | 1.25480 | + | 0.662680i | ||||
\(802\) | 12.5982 | + | 21.8208i | 0.444859 | + | 0.770518i | ||||
\(803\) | 2.06111 | − | 3.56995i | 0.0727350 | − | 0.125981i | ||||
\(804\) | −0.588882 | − | 2.04286i | −0.0207683 | − | 0.0720461i | ||||
\(805\) | −8.81624 | − | 17.6080i | −0.310732 | − | 0.620601i | ||||
\(806\) | 41.0334i | 1.44534i | ||||||||
\(807\) | 11.3004 | + | 2.80068i | 0.397793 | + | 0.0985888i | ||||
\(808\) | −0.261008 | + | 0.150693i | −0.00918224 | + | 0.00530137i | ||||
\(809\) | 46.6225 | − | 26.9175i | 1.63916 | − | 0.946369i | 0.658035 | − | 0.752987i | \(-0.271388\pi\) |
0.981124 | − | 0.193382i | \(-0.0619457\pi\) | |||||||
\(810\) | −11.8669 | + | 8.10153i | −0.416960 | + | 0.284659i | ||||
\(811\) | 23.9638i | 0.841481i | 0.907181 | + | 0.420741i | \(0.138230\pi\) | ||||
−0.907181 | + | 0.420741i | \(0.861770\pi\) | |||||||
\(812\) | 6.55967 | + | 13.1011i | 0.230199 | + | 0.459759i | ||||
\(813\) | −17.0906 | + | 4.92659i | −0.599392 | + | 0.172783i | ||||
\(814\) | 0.285736 | − | 0.494910i | 0.0100150 | − | 0.0173466i | ||||
\(815\) | 12.4742 | + | 21.6060i | 0.436954 | + | 0.756826i | ||||
\(816\) | 7.49897 | − | 7.78723i | 0.262516 | − | 0.272608i | ||||
\(817\) | −9.36430 | − | 5.40648i | −0.327615 | − | 0.189149i | ||||
\(818\) | 18.2113 | 0.636743 | ||||||||
\(819\) | −0.776110 | + | 35.7856i | −0.0271195 | + | 1.25045i | ||||
\(820\) | −2.54886 | −0.0890101 | ||||||||
\(821\) | −22.9984 | − | 13.2781i | −0.802648 | − | 0.463409i | 0.0417481 | − | 0.999128i | \(-0.486707\pi\) |
−0.844396 | + | 0.535719i | \(0.820041\pi\) | |||||||
\(822\) | −13.9284 | + | 14.4638i | −0.485809 | + | 0.504484i | ||||
\(823\) | −20.3657 | − | 35.2745i | −0.709905 | − | 1.22959i | −0.964892 | − | 0.262647i | \(-0.915404\pi\) |
0.254987 | − | 0.966945i | \(-0.417929\pi\) | |||||||
\(824\) | −4.59255 | + | 7.95453i | −0.159989 | + | 0.277109i | ||||
\(825\) | −4.07939 | + | 1.17594i | −0.142026 | + | 0.0409409i | ||||
\(826\) | −13.8593 | − | 0.824148i | −0.482227 | − | 0.0286758i | ||||
\(827\) | 16.2449i | 0.564889i | 0.959284 | + | 0.282444i | \(0.0911453\pi\) | ||||
−0.959284 | + | 0.282444i | \(0.908855\pi\) | |||||||
\(828\) | −13.9758 | + | 0.527292i | −0.485692 | + | 0.0183247i | ||||
\(829\) | −38.4036 | + | 22.1723i | −1.33381 | + | 0.770077i | −0.985882 | − | 0.167444i | \(-0.946449\pi\) |
−0.347930 | + | 0.937520i | \(0.613115\pi\) | |||||||
\(830\) | 24.1282 | − | 13.9304i | 0.837501 | − | 0.483531i | ||||
\(831\) | 1.14442 | + | 0.283631i | 0.0396994 | + | 0.00983906i | ||||
\(832\) | 4.50963i | 0.156343i | ||||||||
\(833\) | −17.2076 | − | 40.1605i | −0.596210 | − | 1.39148i | ||||
\(834\) | 5.90638 | + | 20.4895i | 0.204521 | + | 0.709494i | ||||
\(835\) | 15.7439 | − | 27.2692i | 0.544840 | − | 0.943690i | ||||
\(836\) | 3.50711 | + | 6.07449i | 0.121296 | + | 0.210091i | ||||
\(837\) | 46.2880 | + | 9.63548i | 1.59995 | + | 0.333051i | ||||
\(838\) | 3.54476 | + | 2.04657i | 0.122452 | + | 0.0706975i | ||||
\(839\) | −29.9098 | −1.03260 | −0.516301 | − | 0.856407i | \(-0.672691\pi\) | ||||
−0.516301 | + | 0.856407i | \(0.672691\pi\) | |||||||
\(840\) | 1.60559 | + | 7.13780i | 0.0553982 | + | 0.246277i | ||||
\(841\) | −1.66695 | −0.0574811 | ||||||||
\(842\) | 27.1552 | + | 15.6780i | 0.935829 | + | 0.540301i | ||||
\(843\) | −27.6588 | − | 26.6350i | −0.952621 | − | 0.917357i | ||||
\(844\) | −1.34849 | − | 2.33565i | −0.0464169 | − | 0.0803965i | ||||
\(845\) | 5.85659 | − | 10.1439i | 0.201473 | − | 0.348961i | ||||
\(846\) | 11.3994 | + | 18.1296i | 0.391920 | + | 0.623307i | ||||
\(847\) | −2.20872 | − | 1.45655i | −0.0758925 | − | 0.0500478i | ||||
\(848\) | 9.40636i | 0.323016i | ||||||||
\(849\) | 10.5848 | − | 42.7083i | 0.363269 | − | 1.46574i | ||||
\(850\) | 13.2495 | − | 7.64961i | 0.454454 | − | 0.262379i | ||||
\(851\) | 2.30722 | − | 1.33208i | 0.0790906 | − | 0.0456630i | ||||
\(852\) | −3.94698 | + | 15.9256i | −0.135221 | + | 0.545601i | ||||
\(853\) | − | 23.4111i | − | 0.801581i | −0.916170 | − | 0.400790i | \(-0.868736\pi\) | ||
0.916170 | − | 0.400790i | \(-0.131264\pi\) | |||||||
\(854\) | −5.16237 | + | 2.58477i | −0.176653 | + | 0.0884490i | ||||
\(855\) | 17.8824 | + | 28.4401i | 0.611566 | + | 0.972630i | ||||
\(856\) | −4.21653 | + | 7.30325i | −0.144118 | + | 0.249620i | ||||
\(857\) | −17.0375 | − | 29.5098i | −0.581990 | − | 1.00804i | −0.995243 | − | 0.0974207i | \(-0.968941\pi\) |
0.413253 | − | 0.910616i | \(-0.364393\pi\) | |||||||
\(858\) | −5.62629 | − | 5.41802i | −0.192079 | − | 0.184968i | ||||
\(859\) | −18.3460 | − | 10.5921i | −0.625958 | − | 0.361397i | 0.153227 | − | 0.988191i | \(-0.451033\pi\) |
−0.779185 | + | 0.626794i | \(0.784367\pi\) | |||||||
\(860\) | 2.46115 | 0.0839245 | ||||||||
\(861\) | 4.95938 | + | 5.37872i | 0.169015 | + | 0.183306i | ||||
\(862\) | −6.42397 | −0.218801 | ||||||||
\(863\) | −29.6507 | − | 17.1188i | −1.00932 | − | 0.582731i | −0.0983275 | − | 0.995154i | \(-0.531349\pi\) |
−0.910992 | + | 0.412423i | \(0.864683\pi\) | |||||||
\(864\) | 5.08710 | + | 1.05895i | 0.173067 | + | 0.0360262i | ||||
\(865\) | −0.480881 | − | 0.832911i | −0.0163505 | − | 0.0283198i | ||||
\(866\) | 4.66246 | − | 8.07562i | 0.158437 | − | 0.274421i | ||||
\(867\) | −10.5346 | − | 36.5452i | −0.357775 | − | 1.24114i | ||||
\(868\) | 13.2533 | − | 20.0973i | 0.449847 | − | 0.682148i | ||||
\(869\) | − | 7.74126i | − | 0.262604i | ||||||
\(870\) | −14.8636 | − | 3.68379i | −0.503924 | − | 0.124892i | ||||
\(871\) | 4.79382 | − | 2.76772i | 0.162433 | − | 0.0937805i | ||||
\(872\) | 12.7179 | − | 7.34270i | 0.430683 | − | 0.248655i | ||||
\(873\) | 21.3303 | − | 0.804770i | 0.721921 | − | 0.0272373i | ||||
\(874\) | 32.6997i | 1.10608i | ||||||||
\(875\) | −1.86828 | + | 31.4180i | −0.0631594 | + | 1.06212i | ||||
\(876\) | −6.86054 | + | 1.97764i | −0.231796 | + | 0.0668184i | ||||
\(877\) | −23.3704 | + | 40.4788i | −0.789164 | + | 1.36687i | 0.137316 | + | 0.990527i | \(0.456152\pi\) |
−0.926480 | + | 0.376344i | \(0.877181\pi\) | |||||||
\(878\) | −3.56599 | − | 6.17648i | −0.120346 | − | 0.208446i | ||||
\(879\) | −5.90368 | + | 6.13062i | −0.199126 | + | 0.206781i | ||||
\(880\) | −1.38262 | − | 0.798258i | −0.0466082 | − | 0.0269093i | ||||
\(881\) | 0.862730 | 0.0290661 | 0.0145331 | − | 0.999894i | \(-0.495374\pi\) | ||||
0.0145331 | + | 0.999894i | \(0.495374\pi\) | |||||||
\(882\) | 11.9385 | − | 17.2764i | 0.401989 | − | 0.581726i | ||||
\(883\) | 11.0309 | 0.371221 | 0.185610 | − | 0.982623i | \(-0.440574\pi\) | ||||
0.185610 | + | 0.982623i | \(0.440574\pi\) | |||||||
\(884\) | 24.3766 | + | 14.0738i | 0.819872 | + | 0.473353i | ||||
\(885\) | 10.0654 | − | 10.4523i | 0.338346 | − | 0.351352i | ||||
\(886\) | 4.20570 | + | 7.28448i | 0.141293 | + | 0.244727i | ||||
\(887\) | 21.4444 | − | 37.1429i | 0.720034 | − | 1.24713i | −0.240952 | − | 0.970537i | \(-0.577460\pi\) |
0.960986 | − | 0.276598i | \(-0.0892070\pi\) | |||||||
\(888\) | −0.951092 | + | 0.274165i | −0.0319166 | + | 0.00920038i | ||||
\(889\) | −0.562652 | + | 9.46184i | −0.0188707 | + | 0.317340i | ||||
\(890\) | 21.3728i | 0.716418i | ||||||||
\(891\) | −7.43299 | + | 5.07451i | −0.249015 | + | 0.170002i | ||||
\(892\) | 12.3092 | − | 7.10675i | 0.412144 | − | 0.237952i | ||||
\(893\) | 43.3630 | − | 25.0356i | 1.45109 | − | 0.837785i | ||||
\(894\) | −21.6896 | − | 5.37552i | −0.725408 | − | 0.179784i | ||||
\(895\) | 38.6366i | 1.29148i | ||||||||
\(896\) | 1.45655 | − | 2.20872i | 0.0486601 | − | 0.0737882i | ||||
\(897\) | −10.0861 | − | 34.9890i | −0.336763 | − | 1.16825i | ||||
\(898\) | −8.49632 | + | 14.7161i | −0.283526 | + | 0.491081i | ||||
\(899\) | 25.1943 | + | 43.6379i | 0.840278 | + | 1.45540i | ||||
\(900\) | 6.50234 | + | 3.43400i | 0.216745 | + | 0.114467i | ||||
\(901\) | 50.8456 | + | 29.3557i | 1.69391 | + | 0.977981i | ||||
\(902\) | −1.59652 | −0.0531581 | ||||||||
\(903\) | −4.78872 | − | 5.19363i | −0.159359 | − | 0.172833i | ||||
\(904\) | −10.5424 | −0.350637 | ||||||||
\(905\) | −34.9453 | − | 20.1757i | −1.16162 | − | 0.670663i | ||||
\(906\) | 11.2407 | + | 10.8246i | 0.373447 | + | 0.359623i | ||||
\(907\) | 7.81046 | + | 13.5281i | 0.259342 | + | 0.449194i | 0.966066 | − | 0.258296i | \(-0.0831609\pi\) |
−0.706724 | + | 0.707490i | \(0.749828\pi\) | |||||||
\(908\) | 2.67241 | − | 4.62875i | 0.0886870 | − | 0.153610i | ||||
\(909\) | −0.765423 | + | 0.481280i | −0.0253875 | + | 0.0159630i | ||||
\(910\) | −17.0328 | + | 8.52825i | −0.564633 | + | 0.282709i | ||||
\(911\) | − | 39.7371i | − | 1.31655i | −0.752778 | − | 0.658274i | \(-0.771287\pi\) | ||
0.752778 | − | 0.658274i | \(-0.228713\pi\) | |||||||
\(912\) | 2.92257 | − | 11.7922i | 0.0967761 | − | 0.390480i | ||||
\(913\) | 15.1130 | − | 8.72550i | 0.500168 | − | 0.288772i | ||||
\(914\) | −27.7407 | + | 16.0161i | −0.917582 | + | 0.529766i | ||||
\(915\) | 1.45156 | − | 5.85686i | 0.0479870 | − | 0.193622i | ||||
\(916\) | 13.4600i | 0.444732i | ||||||||
\(917\) | −48.5398 | − | 32.0099i | −1.60292 | − | 1.05706i | ||||
\(918\) | 21.6001 | − | 24.1933i | 0.712910 | − | 0.798497i | ||||
\(919\) | −1.87670 | + | 3.25054i | −0.0619066 | + | 0.107225i | −0.895318 | − | 0.445428i | \(-0.853051\pi\) |
0.833411 | + | 0.552654i | \(0.186385\pi\) | |||||||
\(920\) | −3.72141 | − | 6.44566i | −0.122691 | − | 0.212507i | ||||
\(921\) | −21.9314 | − | 21.1195i | −0.722663 | − | 0.695912i | ||||
\(922\) | −5.89118 | − | 3.40127i | −0.194016 | − | 0.112015i | ||||
\(923\) | −42.7188 | −1.40611 | ||||||||
\(924\) | 1.00569 | + | 4.47086i | 0.0330846 | + | 0.147081i | ||||
\(925\) | −1.40076 | −0.0460567 | ||||||||
\(926\) | 6.60067 | + | 3.81090i | 0.216912 | + | 0.125234i | ||||
\(927\) | −12.8681 | + | 24.3661i | −0.422645 | + | 0.800287i | ||||
\(928\) | 2.76889 | + | 4.79585i | 0.0908932 | + | 0.157432i | ||||
\(929\) | −23.1654 | + | 40.1236i | −0.760031 | + | 1.31641i | 0.182803 | + | 0.983149i | \(0.441483\pi\) |
−0.942834 | + | 0.333262i | \(0.891851\pi\) | |||||||
\(930\) | 6.96927 | + | 24.1767i | 0.228531 | + | 0.792787i | ||||
\(931\) | −39.3124 | − | 29.4161i | −1.28841 | − | 0.964072i | ||||
\(932\) | 0.0216705i | 0.000709840i | ||||||||
\(933\) | −23.7148 | − | 5.87747i | −0.776389 | − | 0.192420i | ||||
\(934\) | −16.0853 | + | 9.28685i | −0.526327 | + | 0.303875i | ||||
\(935\) | −8.62988 | + | 4.98247i | −0.282227 | + | 0.162944i | ||||
\(936\) | 0.510067 | + | 13.5193i | 0.0166721 | + | 0.441891i | ||||
\(937\) | 8.98564i | 0.293548i | 0.989170 | + | 0.146774i | \(0.0468890\pi\) | ||||
−0.989170 | + | 0.146774i | \(0.953111\pi\) | |||||||
\(938\) | −3.24186 | − | 0.192778i | −0.105850 | − | 0.00629443i | ||||
\(939\) | 42.6640 | − | 12.2985i | 1.39229 | − | 0.401346i | ||||
\(940\) | −5.69839 | + | 9.86990i | −0.185861 | + | 0.321921i | ||||
\(941\) | 2.58343 | + | 4.47464i | 0.0842176 | + | 0.145869i | 0.905058 | − | 0.425289i | \(-0.139828\pi\) |
−0.820840 | + | 0.571158i | \(0.806494\pi\) | |||||||
\(942\) | 3.93213 | − | 4.08328i | 0.128116 | − | 0.133041i | ||||
\(943\) | −6.44566 | − | 3.72141i | −0.209900 | − | 0.121186i | ||||
\(944\) | −5.24757 | −0.170794 | ||||||||
\(945\) | 5.62068 | + | 21.2166i | 0.182841 | + | 0.690175i | ||||
\(946\) | 1.54158 | 0.0501210 | ||||||||
\(947\) | −10.8381 | − | 6.25737i | −0.352190 | − | 0.203337i | 0.313459 | − | 0.949602i | \(-0.398512\pi\) |
−0.665649 | + | 0.746265i | \(0.731845\pi\) | |||||||
\(948\) | −9.30063 | + | 9.65815i | −0.302070 | + | 0.313682i | ||||
\(949\) | −9.29483 | − | 16.0991i | −0.301723 | − | 0.522600i | ||||
\(950\) | 8.59642 | − | 14.8894i | 0.278905 | − | 0.483077i | ||||
\(951\) | −5.65152 | + | 1.62913i | −0.183263 | + | 0.0528281i | ||||
\(952\) | −7.39346 | − | 14.7664i | −0.239623 | − | 0.478582i | ||||
\(953\) | 11.7126i | 0.379409i | 0.981841 | + | 0.189704i | \(0.0607529\pi\) | ||||
−0.981841 | + | 0.189704i | \(0.939247\pi\) | |||||||
\(954\) | 1.06392 | + | 28.1990i | 0.0344456 | + | 0.912976i | ||||
\(955\) | 15.9423 | − | 9.20430i | 0.515881 | − | 0.297844i | ||||
\(956\) | −9.04976 | + | 5.22488i | −0.292690 | + | 0.168985i | ||||
\(957\) | −9.31004 | − | 2.30739i | −0.300951 | − | 0.0745874i | ||||
\(958\) | − | 13.2180i | − | 0.427053i | ||||||
\(959\) | 13.7324 | + | 27.4268i | 0.443443 | + | 0.885656i | ||||
\(960\) | 0.765932 | + | 2.65705i | 0.0247203 | + | 0.0857560i | ||||
\(961\) | 25.8966 | − | 44.8543i | 0.835376 | − | 1.44691i | ||||
\(962\) | −1.28856 | − | 2.23186i | −0.0415449 | − | 0.0719580i | ||||
\(963\) | −11.8146 | + | 22.3711i | −0.380719 | + | 0.720898i | ||||
\(964\) | 3.78807 | + | 2.18704i | 0.122006 | + | 0.0704400i | ||||
\(965\) | 19.8321 | 0.638418 | ||||||||
\(966\) | −6.36109 | + | 20.3946i | −0.204665 | + | 0.656184i | ||||
\(967\) | −31.1290 | −1.00104 | −0.500521 | − | 0.865724i | \(-0.666858\pi\) | ||||
−0.500521 | + | 0.865724i | \(0.666858\pi\) | |||||||
\(968\) | −0.866025 | − | 0.500000i | −0.0278351 | − | 0.0160706i | ||||
\(969\) | −54.6214 | − | 52.5994i | −1.75469 | − | 1.68974i | ||||
\(970\) | 5.67973 | + | 9.83758i | 0.182365 | + | 0.315866i | ||||
\(971\) | −22.8332 | + | 39.5482i | −0.732751 | + | 1.26916i | 0.222952 | + | 0.974829i | \(0.428431\pi\) |
−0.955703 | + | 0.294333i | \(0.904903\pi\) | |||||||
\(972\) | 15.3702 | + | 2.59921i | 0.493001 | + | 0.0833696i | ||||
\(973\) | 32.5152 | + | 1.93353i | 1.04239 | + | 0.0619861i | ||||
\(974\) | − | 21.4493i | − | 0.687279i | ||||||
\(975\) | −4.60569 | + | 18.5834i | −0.147500 | + | 0.595144i | ||||
\(976\) | −1.88976 | + | 1.09105i | −0.0604897 | + | 0.0349237i | ||||
\(977\) | 2.20831 | − | 1.27497i | 0.0706500 | − | 0.0407898i | −0.464259 | − | 0.885700i | \(-0.653679\pi\) |
0.534909 | + | 0.844910i | \(0.320346\pi\) | |||||||
\(978\) | 6.51114 | − | 26.2716i | 0.208203 | − | 0.840075i | ||||
\(979\) | 13.3872i | 0.427855i | ||||||||
\(980\) | 11.0968 | + | 1.32444i | 0.354476 | + | 0.0423077i | ||||
\(981\) | 37.2961 | − | 23.4509i | 1.19077 | − | 0.748730i | ||||
\(982\) | −2.01236 | + | 3.48551i | −0.0642170 | + | 0.111227i | ||||
\(983\) | 23.9192 | + | 41.4293i | 0.762905 | + | 1.32139i | 0.941347 | + | 0.337439i | \(0.109561\pi\) |
−0.178443 | + | 0.983950i | \(0.557106\pi\) | |||||||
\(984\) | 1.99184 | + | 1.91811i | 0.0634976 | + | 0.0611471i | ||||
\(985\) | −9.37877 | − | 5.41483i | −0.298832 | − | 0.172531i | ||||
\(986\) | 34.5650 | 1.10077 | ||||||||
\(987\) | 31.9154 | − | 7.17912i | 1.01588 | − | 0.228514i | ||||
\(988\) | 31.6315 | 1.00633 | ||||||||
\(989\) | 6.22386 | + | 3.59335i | 0.197907 | + | 0.114262i | ||||
\(990\) | −4.23521 | − | 2.23669i | −0.134604 | − | 0.0710866i | ||||
\(991\) | −22.8840 | − | 39.6363i | −0.726935 | − | 1.25909i | −0.958173 | − | 0.286191i | \(-0.907611\pi\) |
0.231238 | − | 0.972897i | \(-0.425722\pi\) | |||||||
\(992\) | 4.54954 | − | 7.88004i | 0.144448 | − | 0.250191i | ||||
\(993\) | −1.04953 | − | 3.64088i | −0.0333059 | − | 0.115540i | ||||
\(994\) | 20.9228 | + | 13.7977i | 0.663631 | + | 0.437635i | ||||
\(995\) | − | 13.2630i | − | 0.420464i | ||||||
\(996\) | −29.3384 | − | 7.27121i | −0.929623 | − | 0.230397i | ||||
\(997\) | −13.7032 | + | 7.91153i | −0.433984 | + | 0.250561i | −0.701042 | − | 0.713120i | \(-0.747282\pi\) |
0.267058 | + | 0.963680i | \(0.413948\pi\) | |||||||
\(998\) | −1.56517 | + | 0.903651i | −0.0495445 | + | 0.0286046i | ||||
\(999\) | −2.82024 | + | 0.929485i | −0.0892284 | + | 0.0294076i |
(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 | 462.2.k.g.89.2 | ✓ | 20 | |
3.2 | odd | 2 | inner | 462.2.k.g.89.7 | yes | 20 | |
7.3 | odd | 6 | inner | 462.2.k.g.353.7 | yes | 20 | |
21.17 | even | 6 | inner | 462.2.k.g.353.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.k.g.89.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
462.2.k.g.89.7 | yes | 20 | 3.2 | odd | 2 | inner | |
462.2.k.g.353.2 | yes | 20 | 21.17 | even | 6 | inner | |
462.2.k.g.353.7 | yes | 20 | 7.3 | odd | 6 | inner |