Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [133,2,Mod(12,133)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(133, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("133.12");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 133 = 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 133.i (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: | \(1.06201034688\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 122.2 | ||
Root | \(1.39564 + 0.228425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 133.122 |
Dual form | 133.2.i.c.12.1 |
$q$-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 \(\left(\mathbb{Z}/133\mathbb{Z}\right)^\times\).
\(n\) | \(78\) | \(115\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.456850i | 0.323042i | 0.986869 | + | 0.161521i | \(0.0516399\pi\) | ||||
−0.986869 | + | 0.161521i | \(0.948360\pi\) | |||||||
\(3\) | −0.895644 | − | 1.55130i | −0.517100 | − | 0.895644i | −0.999803 | − | 0.0198595i | \(-0.993678\pi\) |
0.482703 | − | 0.875784i | \(-0.339655\pi\) | |||||||
\(4\) | 1.79129 | 0.895644 | ||||||||
\(5\) | 1.27520i | 0.570287i | 0.958485 | + | 0.285144i | \(0.0920413\pi\) | ||||
−0.958485 | + | 0.285144i | \(0.907959\pi\) | |||||||
\(6\) | 0.708712 | − | 0.409175i | 0.289331 | − | 0.167045i | ||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −0.104356 | + | 0.180750i | −0.0347854 | + | 0.0602500i | ||||
\(10\) | −0.582576 | −0.184227 | ||||||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | −1.60436 | − | 2.77883i | −0.463138 | − | 0.802178i | ||||
\(13\) | 1.89564 | + | 3.28335i | 0.525757 | + | 0.910638i | 0.999550 | + | 0.0300015i | \(0.00955122\pi\) |
−0.473793 | + | 0.880636i | \(0.657115\pi\) | |||||||
\(14\) | 1.18693 | + | 0.228425i | 0.317221 | + | 0.0610492i | ||||
\(15\) | 1.97822 | − | 1.14213i | 0.510774 | − | 0.294896i | ||||
\(16\) | 2.79129 | 0.697822 | ||||||||
\(17\) | −3.79129 | + | 2.18890i | −0.919522 | + | 0.530886i | −0.883483 | − | 0.468464i | \(-0.844808\pi\) |
−0.0360397 | + | 0.999350i | \(0.511474\pi\) | |||||||
\(18\) | −0.0825757 | − | 0.0476751i | −0.0194633 | − | 0.0112371i | ||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | 2.28425i | 0.510774i | ||||||||
\(21\) | −4.47822 | + | 1.55130i | −0.977228 | + | 0.338522i | ||||
\(22\) | 1.18693 | + | 0.685275i | 0.253055 | + | 0.146101i | ||||
\(23\) | −3.79129 | + | 6.56670i | −0.790538 | + | 1.36925i | 0.135096 | + | 0.990833i | \(0.456866\pi\) |
−0.925634 | + | 0.378420i | \(0.876468\pi\) | |||||||
\(24\) | 2.68693 | − | 1.55130i | 0.548468 | − | 0.316658i | ||||
\(25\) | 3.37386 | 0.674773 | ||||||||
\(26\) | −1.50000 | + | 0.866025i | −0.294174 | + | 0.169842i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0.895644 | − | 4.65390i | 0.169261 | − | 0.879505i | ||||
\(29\) | −3.08258 | + | 1.77973i | −0.572420 | + | 0.330487i | −0.758115 | − | 0.652121i | \(-0.773880\pi\) |
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0.521780 | + | 0.903750i | 0.0952636 | + | 0.165001i | ||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 4.73930i | 0.837798i | ||||||||
\(33\) | −5.37386 | −0.935470 | ||||||||
\(34\) | −1.00000 | − | 1.73205i | −0.171499 | − | 0.297044i | ||||
\(35\) | 3.31307 | + | 0.637600i | 0.560011 | + | 0.107774i | ||||
\(36\) | −0.186932 | + | 0.323775i | −0.0311553 | + | 0.0539626i | ||||
\(37\) | −8.68693 | + | 5.01540i | −1.42812 | + | 0.824527i | −0.996973 | − | 0.0777531i | \(-0.975225\pi\) |
−0.431150 | + | 0.902280i | \(0.641892\pi\) | |||||||
\(38\) | 0.791288 | − | 1.82740i | 0.128364 | − | 0.296444i | ||||
\(39\) | 3.39564 | − | 5.88143i | 0.543738 | − | 0.941782i | ||||
\(40\) | −2.20871 | −0.349228 | ||||||||
\(41\) | 2.68693 | − | 4.65390i | 0.419628 | − | 0.726817i | −0.576274 | − | 0.817257i | \(-0.695494\pi\) |
0.995902 | + | 0.0904393i | \(0.0288271\pi\) | |||||||
\(42\) | −0.708712 | − | 2.04588i | −0.109357 | − | 0.315685i | ||||
\(43\) | 3.39564 | − | 5.88143i | 0.517831 | − | 0.896909i | −0.481955 | − | 0.876196i | \(-0.660073\pi\) |
0.999785 | − | 0.0207131i | \(-0.00659367\pi\) | |||||||
\(44\) | 2.68693 | − | 4.65390i | 0.405070 | − | 0.701602i | ||||
\(45\) | −0.230493 | − | 0.133075i | −0.0343598 | − | 0.0198376i | ||||
\(46\) | −3.00000 | − | 1.73205i | −0.442326 | − | 0.255377i | ||||
\(47\) | 5.29129 | + | 3.05493i | 0.771814 | + | 0.445607i | 0.833521 | − | 0.552487i | \(-0.186321\pi\) |
−0.0617076 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(48\) | −2.50000 | − | 4.33013i | −0.360844 | − | 0.625000i | ||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 1.54135i | 0.217980i | ||||||||
\(51\) | 6.79129 | + | 3.92095i | 0.950971 | + | 0.549043i | ||||
\(52\) | 3.39564 | + | 5.88143i | 0.470891 | + | 0.815607i | ||||
\(53\) | − | 1.27520i | − | 0.175162i | −0.996157 | − | 0.0875811i | \(-0.972086\pi\) | ||
0.996157 | − | 0.0875811i | \(-0.0279137\pi\) | |||||||
\(54\) | − | 2.28425i | − | 0.310847i | ||||||
\(55\) | 3.31307 | + | 1.91280i | 0.446734 | + | 0.257922i | ||||
\(56\) | 4.50000 | + | 0.866025i | 0.601338 | + | 0.115728i | ||||
\(57\) | 0.895644 | + | 7.75650i | 0.118631 | + | 1.02737i | ||||
\(58\) | −0.813068 | − | 1.40828i | −0.106761 | − | 0.184916i | ||||
\(59\) | 4.89564 | + | 8.47950i | 0.637359 | + | 1.10394i | 0.986010 | + | 0.166685i | \(0.0533063\pi\) |
−0.348652 | + | 0.937252i | \(0.613360\pi\) | |||||||
\(60\) | 3.54356 | − | 2.04588i | 0.457472 | − | 0.264121i | ||||
\(61\) | 1.18693 | + | 0.685275i | 0.151971 | + | 0.0877405i | 0.574057 | − | 0.818815i | \(-0.305369\pi\) |
−0.422086 | + | 0.906556i | \(0.638702\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.417424 | + | 0.361500i | 0.0525905 | + | 0.0455447i | ||||
\(64\) | 3.41742 | 0.427178 | ||||||||
\(65\) | −4.18693 | + | 2.41733i | −0.519325 | + | 0.299832i | ||||
\(66\) | − | 2.45505i | − | 0.302196i | ||||||
\(67\) | 3.46410i | 0.423207i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | −6.79129 | + | 3.92095i | −0.823565 | + | 0.475485i | ||||
\(69\) | 13.5826 | 1.63515 | ||||||||
\(70\) | −0.291288 | + | 1.51358i | −0.0348156 | + | 0.180907i | ||||
\(71\) | −3.08258 | − | 1.77973i | −0.365834 | − | 0.211215i | 0.305803 | − | 0.952095i | \(-0.401075\pi\) |
−0.671637 | + | 0.740880i | \(0.734409\pi\) | |||||||
\(72\) | −0.313068 | − | 0.180750i | −0.0368954 | − | 0.0213016i | ||||
\(73\) | 5.37386 | − | 3.10260i | 0.628963 | − | 0.363132i | −0.151387 | − | 0.988475i | \(-0.548374\pi\) |
0.780350 | + | 0.625342i | \(0.215041\pi\) | |||||||
\(74\) | −2.29129 | − | 3.96863i | −0.266357 | − | 0.461344i | ||||
\(75\) | −3.02178 | − | 5.23388i | −0.348925 | − | 0.604356i | ||||
\(76\) | −7.16515 | − | 3.10260i | −0.821899 | − | 0.355893i | ||||
\(77\) | −6.00000 | − | 5.19615i | −0.683763 | − | 0.592157i | ||||
\(78\) | 2.68693 | + | 1.55130i | 0.304235 | + | 0.175650i | ||||
\(79\) | − | 6.92820i | − | 0.779484i | −0.920924 | − | 0.389742i | \(-0.872564\pi\) | ||
0.920924 | − | 0.389742i | \(-0.127436\pi\) | |||||||
\(80\) | 3.55945i | 0.397959i | ||||||||
\(81\) | 4.79129 | + | 8.29875i | 0.532365 | + | 0.922084i | ||||
\(82\) | 2.12614 | + | 1.22753i | 0.234792 | + | 0.135558i | ||||
\(83\) | − | 13.5903i | − | 1.49172i | −0.666100 | − | 0.745862i | \(-0.732038\pi\) | ||
0.666100 | − | 0.745862i | \(-0.267962\pi\) | |||||||
\(84\) | −8.02178 | + | 2.77883i | −0.875248 | + | 0.303195i | ||||
\(85\) | −2.79129 | − | 4.83465i | −0.302758 | − | 0.524392i | ||||
\(86\) | 2.68693 | + | 1.55130i | 0.289739 | + | 0.167281i | ||||
\(87\) | 5.52178 | + | 3.18800i | 0.591997 | + | 0.341790i | ||||
\(88\) | 4.50000 | + | 2.59808i | 0.479702 | + | 0.276956i | ||||
\(89\) | 1.18693 | − | 2.05583i | 0.125815 | − | 0.217917i | −0.796237 | − | 0.604985i | \(-0.793179\pi\) |
0.922051 | + | 0.387068i | \(0.126512\pi\) | |||||||
\(90\) | 0.0607953 | − | 0.105301i | 0.00640839 | − | 0.0110997i | ||||
\(91\) | 9.47822 | − | 3.28335i | 0.993587 | − | 0.344189i | ||||
\(92\) | −6.79129 | + | 11.7629i | −0.708041 | + | 1.22636i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.39564 | + | 2.41733i | −0.143950 | + | 0.249328i | ||||
\(95\) | 2.20871 | − | 5.10080i | 0.226609 | − | 0.523331i | ||||
\(96\) | 7.35208 | − | 4.24473i | 0.750369 | − | 0.433226i | ||||
\(97\) | 1.00000 | − | 1.73205i | 0.101535 | − | 0.175863i | −0.810782 | − | 0.585348i | \(-0.800958\pi\) |
0.912317 | + | 0.409484i | \(0.134291\pi\) | |||||||
\(98\) | 1.18693 | − | 2.96953i | 0.119898 | − | 0.299967i | ||||
\(99\) | 0.313068 | + | 0.542250i | 0.0314645 | + | 0.0544982i | ||||
\(100\) | 6.04356 | 0.604356 | ||||||||
\(101\) | − | 8.56490i | − | 0.852240i | −0.904667 | − | 0.426120i | \(-0.859880\pi\) | ||
0.904667 | − | 0.426120i | \(-0.140120\pi\) | |||||||
\(102\) | −1.79129 | + | 3.10260i | −0.177364 | + | 0.307203i | ||||
\(103\) | −1.68693 | − | 2.92185i | −0.166218 | − | 0.287899i | 0.770869 | − | 0.636994i | \(-0.219822\pi\) |
−0.937087 | + | 0.349095i | \(0.886489\pi\) | |||||||
\(104\) | −5.68693 | + | 3.28335i | −0.557650 | + | 0.321959i | ||||
\(105\) | −1.97822 | − | 5.71063i | −0.193054 | − | 0.557300i | ||||
\(106\) | 0.582576 | 0.0565848 | ||||||||
\(107\) | −8.20871 | + | 4.73930i | −0.793566 | + | 0.458166i | −0.841216 | − | 0.540698i | \(-0.818160\pi\) |
0.0476503 | + | 0.998864i | \(0.484827\pi\) | |||||||
\(108\) | −8.95644 | −0.861834 | ||||||||
\(109\) | −11.6869 | + | 6.74745i | −1.11941 | + | 0.646289i | −0.941249 | − | 0.337713i | \(-0.890347\pi\) |
−0.178156 | + | 0.984002i | \(0.557013\pi\) | |||||||
\(110\) | −0.873864 | + | 1.51358i | −0.0833196 | + | 0.144314i | ||||
\(111\) | 15.5608 | + | 8.98403i | 1.47697 | + | 0.852726i | ||||
\(112\) | 1.39564 | − | 7.25198i | 0.131876 | − | 0.685248i | ||||
\(113\) | − | 13.2288i | − | 1.24446i | −0.782836 | − | 0.622228i | \(-0.786228\pi\) | ||
0.782836 | − | 0.622228i | \(-0.213772\pi\) | |||||||
\(114\) | −3.54356 | + | 0.409175i | −0.331885 | + | 0.0383228i | ||||
\(115\) | −8.37386 | − | 4.83465i | −0.780867 | − | 0.450834i | ||||
\(116\) | −5.52178 | + | 3.18800i | −0.512684 | + | 0.295998i | ||||
\(117\) | −0.791288 | −0.0731546 | ||||||||
\(118\) | −3.87386 | + | 2.23658i | −0.356618 | + | 0.205894i | ||||
\(119\) | 3.79129 | + | 10.9445i | 0.347547 | + | 1.00328i | ||||
\(120\) | 1.97822 | + | 3.42638i | 0.180586 | + | 0.312784i | ||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | −0.313068 | + | 0.542250i | −0.0283439 | + | 0.0490930i | ||||
\(123\) | −9.62614 | −0.867959 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6784i | 0.955101i | ||||||||
\(126\) | −0.165151 | + | 0.190700i | −0.0147129 | + | 0.0169889i | ||||
\(127\) | 10.1869 | − | 5.88143i | 0.903944 | − | 0.521892i | 0.0254663 | − | 0.999676i | \(-0.491893\pi\) |
0.878478 | + | 0.477783i | \(0.158560\pi\) | |||||||
\(128\) | 11.0399i | 0.975795i | ||||||||
\(129\) | −12.1652 | −1.07108 | ||||||||
\(130\) | −1.10436 | − | 1.91280i | −0.0968584 | − | 0.167764i | ||||
\(131\) | 7.11890i | 0.621981i | 0.950413 | + | 0.310991i | \(0.100661\pi\) | ||||
−0.950413 | + | 0.310991i | \(0.899339\pi\) | |||||||
\(132\) | −9.62614 | −0.837848 | ||||||||
\(133\) | −6.50000 | + | 9.52628i | −0.563621 | + | 0.826033i | ||||
\(134\) | −1.58258 | −0.136714 | ||||||||
\(135\) | − | 6.37600i | − | 0.548759i | ||||||
\(136\) | −3.79129 | − | 6.56670i | −0.325100 | − | 0.563090i | ||||
\(137\) | −9.95644 | −0.850636 | −0.425318 | − | 0.905044i | \(-0.639838\pi\) | ||||
−0.425318 | + | 0.905044i | \(0.639838\pi\) | |||||||
\(138\) | 6.20520i | 0.528222i | ||||||||
\(139\) | −9.24773 | + | 5.33918i | −0.784382 | + | 0.452863i | −0.837981 | − | 0.545699i | \(-0.816264\pi\) |
0.0535990 | + | 0.998563i | \(0.482931\pi\) | |||||||
\(140\) | 5.93466 | + | 1.14213i | 0.501570 | + | 0.0965272i | ||||
\(141\) | − | 10.9445i | − | 0.921694i | ||||||
\(142\) | 0.813068 | − | 1.40828i | 0.0682312 | − | 0.118180i | ||||
\(143\) | 11.3739 | 0.951130 | ||||||||
\(144\) | −0.291288 | + | 0.504525i | −0.0242740 | + | 0.0420438i | ||||
\(145\) | −2.26951 | − | 3.93090i | −0.188472 | − | 0.326444i | ||||
\(146\) | 1.41742 | + | 2.45505i | 0.117307 | + | 0.203181i | ||||
\(147\) | 1.79129 | + | 12.4104i | 0.147743 | + | 1.02359i | ||||
\(148\) | −15.5608 | + | 8.98403i | −1.27909 | + | 0.738483i | ||||
\(149\) | 11.2087 | 0.918253 | 0.459127 | − | 0.888371i | \(-0.348162\pi\) | ||||
0.459127 | + | 0.888371i | \(0.348162\pi\) | |||||||
\(150\) | 2.39110 | − | 1.38050i | 0.195232 | − | 0.112717i | ||||
\(151\) | 15.5608 | + | 8.98403i | 1.26632 | + | 0.731110i | 0.974290 | − | 0.225299i | \(-0.0723360\pi\) |
0.292030 | + | 0.956409i | \(0.405669\pi\) | |||||||
\(152\) | 3.00000 | − | 6.92820i | 0.243332 | − | 0.561951i | ||||
\(153\) | − | 0.913701i | − | 0.0738683i | ||||||
\(154\) | 2.37386 | − | 2.74110i | 0.191291 | − | 0.220884i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.08258 | − | 10.5353i | 0.486996 | − | 0.843501i | ||||
\(157\) | −10.1869 | + | 5.88143i | −0.813006 | + | 0.469389i | −0.847999 | − | 0.529999i | \(-0.822192\pi\) |
0.0349929 | + | 0.999388i | \(0.488859\pi\) | |||||||
\(158\) | 3.16515 | 0.251806 | ||||||||
\(159\) | −1.97822 | + | 1.14213i | −0.156883 | + | 0.0905765i | ||||
\(160\) | −6.04356 | −0.477785 | ||||||||
\(161\) | 15.1652 | + | 13.1334i | 1.19518 | + | 1.03506i | ||||
\(162\) | −3.79129 | + | 2.18890i | −0.297872 | + | 0.171976i | ||||
\(163\) | 3.00000 | + | 5.19615i | 0.234978 | + | 0.406994i | 0.959266 | − | 0.282503i | \(-0.0911648\pi\) |
−0.724288 | + | 0.689497i | \(0.757831\pi\) | |||||||
\(164\) | 4.81307 | − | 8.33648i | 0.375837 | − | 0.650970i | ||||
\(165\) | − | 6.85275i | − | 0.533486i | ||||||
\(166\) | 6.20871 | 0.481890 | ||||||||
\(167\) | −9.56080 | − | 16.5598i | −0.739837 | − | 1.28143i | −0.952569 | − | 0.304324i | \(-0.901569\pi\) |
0.212732 | − | 0.977111i | \(-0.431764\pi\) | |||||||
\(168\) | −2.68693 | − | 7.75650i | −0.207301 | − | 0.598427i | ||||
\(169\) | −0.686932 | + | 1.18980i | −0.0528409 | + | 0.0915231i | ||||
\(170\) | 2.20871 | − | 1.27520i | 0.169400 | − | 0.0978034i | ||||
\(171\) | 0.730493 | − | 0.542250i | 0.0558622 | − | 0.0414669i | ||||
\(172\) | 6.08258 | − | 10.5353i | 0.463792 | − | 0.803311i | ||||
\(173\) | 19.7477 | 1.50139 | 0.750696 | − | 0.660648i | \(-0.229718\pi\) | ||||
0.750696 | + | 0.660648i | \(0.229718\pi\) | |||||||
\(174\) | −1.45644 | + | 2.52263i | −0.110412 | + | 0.191240i | ||||
\(175\) | 1.68693 | − | 8.76555i | 0.127520 | − | 0.662614i | ||||
\(176\) | 4.18693 | − | 7.25198i | 0.315602 | − | 0.546638i | ||||
\(177\) | 8.76951 | − | 15.1892i | 0.659157 | − | 1.14169i | ||||
\(178\) | 0.939205 | + | 0.542250i | 0.0703964 | + | 0.0406434i | ||||
\(179\) | −12.7913 | − | 7.38505i | −0.956066 | − | 0.551985i | −0.0611058 | − | 0.998131i | \(-0.519463\pi\) |
−0.894960 | + | 0.446146i | \(0.852796\pi\) | |||||||
\(180\) | −0.412878 | − | 0.238375i | −0.0307741 | − | 0.0177675i | ||||
\(181\) | 5.87386 | + | 10.1738i | 0.436601 | + | 0.756215i | 0.997425 | − | 0.0717202i | \(-0.0228489\pi\) |
−0.560824 | + | 0.827935i | \(0.689516\pi\) | |||||||
\(182\) | 1.50000 | + | 4.33013i | 0.111187 | + | 0.320970i | ||||
\(183\) | − | 2.45505i | − | 0.181483i | ||||||
\(184\) | −11.3739 | − | 6.56670i | −0.838492 | − | 0.484104i | ||||
\(185\) | −6.39564 | − | 11.0776i | −0.470217 | − | 0.814440i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.1334i | 0.960410i | ||||||||
\(188\) | 9.47822 | + | 5.47225i | 0.691270 | + | 0.399105i | ||||
\(189\) | −2.50000 | + | 12.9904i | −0.181848 | + | 0.944911i | ||||
\(190\) | 2.33030 | + | 1.00905i | 0.169058 | + | 0.0732042i | ||||
\(191\) | −10.2695 | − | 17.7873i | −0.743075 | − | 1.28704i | −0.951089 | − | 0.308918i | \(-0.900033\pi\) |
0.208013 | − | 0.978126i | \(-0.433300\pi\) | |||||||
\(192\) | −3.06080 | − | 5.30145i | −0.220894 | − | 0.382599i | ||||
\(193\) | 21.2477 | − | 12.2674i | 1.52944 | − | 0.883025i | 0.530060 | − | 0.847960i | \(-0.322169\pi\) |
0.999385 | − | 0.0350652i | \(-0.0111639\pi\) | |||||||
\(194\) | 0.791288 | + | 0.456850i | 0.0568112 | + | 0.0327999i | ||||
\(195\) | 7.50000 | + | 4.33013i | 0.537086 | + | 0.310087i | ||||
\(196\) | −11.6434 | − | 4.65390i | −0.831669 | − | 0.332422i | ||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | −0.247727 | + | 0.143025i | −0.0176052 | + | 0.0101644i | ||||
\(199\) | 22.0797i | 1.56519i | 0.622532 | + | 0.782595i | \(0.286104\pi\) | ||||
−0.622532 | + | 0.782595i | \(0.713896\pi\) | |||||||
\(200\) | 5.84370i | 0.413212i | ||||||||
\(201\) | 5.37386 | − | 3.10260i | 0.379043 | − | 0.218841i | ||||
\(202\) | 3.91288 | 0.275309 | ||||||||
\(203\) | 3.08258 | + | 8.89863i | 0.216354 | + | 0.624561i | ||||
\(204\) | 12.1652 | + | 7.02355i | 0.851731 | + | 0.491747i | ||||
\(205\) | 5.93466 | + | 3.42638i | 0.414495 | + | 0.239309i | ||||
\(206\) | 1.33485 | − | 0.770675i | 0.0930033 | − | 0.0536955i | ||||
\(207\) | −0.791288 | − | 1.37055i | −0.0549983 | − | 0.0952599i | ||||
\(208\) | 5.29129 | + | 9.16478i | 0.366885 | + | 0.635463i | ||||
\(209\) | −10.5000 | + | 7.79423i | −0.726300 | + | 0.539138i | ||||
\(210\) | 2.60890 | − | 0.903750i | 0.180031 | − | 0.0623647i | ||||
\(211\) | −12.2477 | − | 7.07123i | −0.843168 | − | 0.486803i | 0.0151716 | − | 0.999885i | \(-0.495171\pi\) |
−0.858340 | + | 0.513081i | \(0.828504\pi\) | |||||||
\(212\) | − | 2.28425i | − | 0.156883i | ||||||
\(213\) | 6.37600i | 0.436877i | ||||||||
\(214\) | −2.16515 | − | 3.75015i | −0.148007 | − | 0.256355i | ||||
\(215\) | 7.50000 | + | 4.33013i | 0.511496 | + | 0.295312i | ||||
\(216\) | − | 8.66025i | − | 0.589256i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.08258 | − | 5.33918i | −0.208778 | − | 0.361615i | ||||
\(219\) | −9.62614 | − | 5.55765i | −0.650474 | − | 0.375551i | ||||
\(220\) | 5.93466 | + | 3.42638i | 0.400115 | + | 0.231006i | ||||
\(221\) | −14.3739 | − | 8.29875i | −0.966891 | − | 0.558235i | ||||
\(222\) | −4.10436 | + | 7.10895i | −0.275466 | + | 0.477122i | ||||
\(223\) | 6.79129 | − | 11.7629i | 0.454778 | − | 0.787699i | −0.543897 | − | 0.839152i | \(-0.683052\pi\) |
0.998675 | + | 0.0514528i | \(0.0163852\pi\) | |||||||
\(224\) | 12.3131 | + | 2.36965i | 0.822701 | + | 0.158329i | ||||
\(225\) | −0.352083 | + | 0.609826i | −0.0234722 | + | 0.0406551i | ||||
\(226\) | 6.04356 | 0.402012 | ||||||||
\(227\) | 13.2695 | − | 22.9835i | 0.880728 | − | 1.52547i | 0.0301953 | − | 0.999544i | \(-0.490387\pi\) |
0.850533 | − | 0.525922i | \(-0.176280\pi\) | |||||||
\(228\) | 1.60436 | + | 13.8941i | 0.106251 | + | 0.920161i | ||||
\(229\) | 6.00000 | − | 3.46410i | 0.396491 | − | 0.228914i | −0.288478 | − | 0.957487i | \(-0.593149\pi\) |
0.684969 | + | 0.728572i | \(0.259816\pi\) | |||||||
\(230\) | 2.20871 | − | 3.82560i | 0.145638 | − | 0.252253i | ||||
\(231\) | −2.68693 | + | 13.9617i | −0.176787 | + | 0.918613i | ||||
\(232\) | −3.08258 | − | 5.33918i | −0.202381 | − | 0.350534i | ||||
\(233\) | −13.4174 | −0.879005 | −0.439502 | − | 0.898241i | \(-0.644845\pi\) | ||||
−0.439502 | + | 0.898241i | \(0.644845\pi\) | |||||||
\(234\) | − | 0.361500i | − | 0.0236320i | ||||||
\(235\) | −3.89564 | + | 6.74745i | −0.254124 | + | 0.440155i | ||||
\(236\) | 8.76951 | + | 15.1892i | 0.570846 | + | 0.988735i | ||||
\(237\) | −10.7477 | + | 6.20520i | −0.698140 | + | 0.403071i | ||||
\(238\) | −5.00000 | + | 1.73205i | −0.324102 | + | 0.112272i | ||||
\(239\) | 14.5390 | 0.940451 | 0.470225 | − | 0.882546i | \(-0.344173\pi\) | ||||
0.470225 | + | 0.882546i | \(0.344173\pi\) | |||||||
\(240\) | 5.52178 | − | 3.18800i | 0.356429 | − | 0.205785i | ||||
\(241\) | 7.37386 | 0.474992 | 0.237496 | − | 0.971388i | \(-0.423673\pi\) | ||||
0.237496 | + | 0.971388i | \(0.423673\pi\) | |||||||
\(242\) | −0.791288 | + | 0.456850i | −0.0508659 | + | 0.0293674i | ||||
\(243\) | 1.08258 | − | 1.87508i | 0.0694473 | − | 0.120286i | ||||
\(244\) | 2.12614 | + | 1.22753i | 0.136112 | + | 0.0785843i | ||||
\(245\) | 3.31307 | − | 8.28880i | 0.211664 | − | 0.529552i | ||||
\(246\) | − | 4.39770i | − | 0.280387i | ||||||
\(247\) | −1.89564 | − | 16.4168i | −0.120617 | − | 1.04457i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.0826 | + | 12.1720i | −1.33605 | + | 0.771371i | ||||
\(250\) | −4.87841 | −0.308538 | ||||||||
\(251\) | −8.29129 | + | 4.78698i | −0.523341 | + | 0.302151i | −0.738301 | − | 0.674472i | \(-0.764371\pi\) |
0.214959 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(252\) | 0.747727 | + | 0.647551i | 0.0471024 | + | 0.0407919i | ||||
\(253\) | 11.3739 | + | 19.7001i | 0.715069 | + | 1.23854i | ||||
\(254\) | 2.68693 | + | 4.65390i | 0.168593 | + | 0.292012i | ||||
\(255\) | −5.00000 | + | 8.66025i | −0.313112 | + | 0.542326i | ||||
\(256\) | 1.79129 | 0.111955 | ||||||||
\(257\) | 9.87386 | − | 17.1020i | 0.615915 | − | 1.06680i | −0.374309 | − | 0.927304i | \(-0.622120\pi\) |
0.990223 | − | 0.139491i | \(-0.0445467\pi\) | |||||||
\(258\) | − | 5.55765i | − | 0.346004i | ||||||
\(259\) | 8.68693 | + | 25.0770i | 0.539780 | + | 1.55821i | ||||
\(260\) | −7.50000 | + | 4.33013i | −0.465130 | + | 0.268543i | ||||
\(261\) | − | 0.742901i | − | 0.0459844i | ||||||
\(262\) | −3.25227 | −0.200926 | ||||||||
\(263\) | −6.00000 | − | 10.3923i | −0.369976 | − | 0.640817i | 0.619586 | − | 0.784929i | \(-0.287301\pi\) |
−0.989561 | + | 0.144112i | \(0.953967\pi\) | |||||||
\(264\) | − | 9.30780i | − | 0.572856i | ||||||
\(265\) | 1.62614 | 0.0998928 | ||||||||
\(266\) | −4.35208 | − | 2.96953i | −0.266843 | − | 0.182073i | ||||
\(267\) | −4.25227 | −0.260235 | ||||||||
\(268\) | 6.20520i | 0.379043i | ||||||||
\(269\) | −3.79129 | − | 6.56670i | −0.231159 | − | 0.400379i | 0.726991 | − | 0.686647i | \(-0.240918\pi\) |
−0.958149 | + | 0.286269i | \(0.907585\pi\) | |||||||
\(270\) | 2.91288 | 0.177272 | ||||||||
\(271\) | − | 13.4949i | − | 0.819757i | −0.912140 | − | 0.409879i | \(-0.865571\pi\) | ||
0.912140 | − | 0.409879i | \(-0.134429\pi\) | |||||||
\(272\) | −10.5826 | + | 6.10985i | −0.641663 | + | 0.370464i | ||||
\(273\) | −13.5826 | − | 11.7629i | −0.822055 | − | 0.711920i | ||||
\(274\) | − | 4.54860i | − | 0.274791i | ||||||
\(275\) | 5.06080 | − | 8.76555i | 0.305177 | − | 0.528583i | ||||
\(276\) | 24.3303 | 1.46451 | ||||||||
\(277\) | −11.7695 | + | 20.3854i | −0.707161 | + | 1.22484i | 0.258745 | + | 0.965946i | \(0.416691\pi\) |
−0.965906 | + | 0.258893i | \(0.916642\pi\) | |||||||
\(278\) | −2.43920 | − | 4.22483i | −0.146294 | − | 0.253388i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.10436 | + | 5.73840i | −0.0659979 | + | 0.342935i | ||||
\(281\) | 1.02178 | − | 0.589925i | 0.0609543 | − | 0.0351920i | −0.469213 | − | 0.883085i | \(-0.655462\pi\) |
0.530167 | + | 0.847893i | \(0.322129\pi\) | |||||||
\(282\) | 5.00000 | 0.297746 | ||||||||
\(283\) | −8.37386 | + | 4.83465i | −0.497775 | + | 0.287390i | −0.727794 | − | 0.685796i | \(-0.759454\pi\) |
0.230020 | + | 0.973186i | \(0.426121\pi\) | |||||||
\(284\) | −5.52178 | − | 3.18800i | −0.327657 | − | 0.189173i | ||||
\(285\) | −9.89110 | + | 1.14213i | −0.585898 | + | 0.0676537i | ||||
\(286\) | 5.19615i | 0.307255i | ||||||||
\(287\) | −10.7477 | − | 9.30780i | −0.634418 | − | 0.549422i | ||||
\(288\) | −0.856629 | − | 0.494575i | −0.0504773 | − | 0.0291431i | ||||
\(289\) | 1.08258 | − | 1.87508i | 0.0636809 | − | 0.110299i | ||||
\(290\) | 1.79583 | − | 1.03683i | 0.105455 | − | 0.0608845i | ||||
\(291\) | −3.58258 | −0.210014 | ||||||||
\(292\) | 9.62614 | − | 5.55765i | 0.563327 | − | 0.325237i | ||||
\(293\) | 21.0000 | 1.22683 | 0.613417 | − | 0.789760i | \(-0.289795\pi\) | ||||
0.613417 | + | 0.789760i | \(0.289795\pi\) | |||||||
\(294\) | −5.66970 | + | 0.818350i | −0.330663 | + | 0.0477272i | ||||
\(295\) | −10.8131 | + | 6.24293i | −0.629561 | + | 0.363477i | ||||
\(296\) | −8.68693 | − | 15.0462i | −0.504918 | − | 0.874543i | ||||
\(297\) | −7.50000 | + | 12.9904i | −0.435194 | + | 0.753778i | ||||
\(298\) | 5.12070i | 0.296634i | ||||||||
\(299\) | −28.7477 | −1.66252 | ||||||||
\(300\) | −5.41288 | − | 9.37538i | −0.312513 | − | 0.541288i | ||||
\(301\) | −13.5826 | − | 11.7629i | −0.782887 | − | 0.678000i | ||||
\(302\) | −4.10436 | + | 7.10895i | −0.236179 | + | 0.409074i | ||||
\(303\) | −13.2867 | + | 7.67110i | −0.763303 | + | 0.440693i | ||||
\(304\) | −11.1652 | − | 4.83465i | −0.640365 | − | 0.277286i | ||||
\(305\) | −0.873864 | + | 1.51358i | −0.0500373 | + | 0.0866671i | ||||
\(306\) | 0.417424 | 0.0238626 | ||||||||
\(307\) | −10.1044 | + | 17.5013i | −0.576686 | + | 0.998850i | 0.419170 | + | 0.907908i | \(0.362321\pi\) |
−0.995856 | + | 0.0909419i | \(0.971012\pi\) | |||||||
\(308\) | −10.7477 | − | 9.30780i | −0.612409 | − | 0.530361i | ||||
\(309\) | −3.02178 | + | 5.23388i | −0.171903 | + | 0.297745i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.7695 | + | 11.9913i | 1.17773 | + | 0.679963i | 0.955489 | − | 0.295028i | \(-0.0953291\pi\) |
0.222242 | + | 0.974991i | \(0.428662\pi\) | |||||||
\(312\) | 10.1869 | + | 5.88143i | 0.576721 | + | 0.332970i | ||||
\(313\) | −7.50000 | − | 4.33013i | −0.423925 | − | 0.244753i | 0.272830 | − | 0.962062i | \(-0.412040\pi\) |
−0.696755 | + | 0.717309i | \(0.745374\pi\) | |||||||
\(314\) | −2.68693 | − | 4.65390i | −0.151632 | − | 0.262635i | ||||
\(315\) | −0.460985 | + | 0.532300i | −0.0259736 | + | 0.0299917i | ||||
\(316\) | − | 12.4104i | − | 0.698140i | ||||||
\(317\) | 12.7087 | + | 7.33738i | 0.713792 | + | 0.412108i | 0.812464 | − | 0.583012i | \(-0.198126\pi\) |
−0.0986713 | + | 0.995120i | \(0.531459\pi\) | |||||||
\(318\) | −0.521780 | − | 0.903750i | −0.0292600 | − | 0.0506798i | ||||
\(319\) | 10.6784i | 0.597873i | ||||||||
\(320\) | 4.35790i | 0.243614i | ||||||||
\(321\) | 14.7042 | + | 8.48945i | 0.820707 | + | 0.473835i | ||||
\(322\) | −6.00000 | + | 6.92820i | −0.334367 | + | 0.386094i | ||||
\(323\) | 18.9564 | − | 2.18890i | 1.05476 | − | 0.121794i | ||||
\(324\) | 8.58258 | + | 14.8655i | 0.476810 | + | 0.825859i | ||||
\(325\) | 6.39564 | + | 11.0776i | 0.354766 | + | 0.614474i | ||||
\(326\) | −2.37386 | + | 1.37055i | −0.131476 | + | 0.0759078i | ||||
\(327\) | 20.9347 | + | 12.0866i | 1.15769 | + | 0.668392i | ||||
\(328\) | 8.06080 | + | 4.65390i | 0.445083 | + | 0.256969i | ||||
\(329\) | 10.5826 | − | 12.2197i | 0.583436 | − | 0.673694i | ||||
\(330\) | 3.13068 | 0.172338 | ||||||||
\(331\) | 1.81307 | − | 1.04678i | 0.0996552 | − | 0.0575360i | −0.449344 | − | 0.893359i | \(-0.648342\pi\) |
0.548999 | + | 0.835823i | \(0.315009\pi\) | |||||||
\(332\) | − | 24.3441i | − | 1.33605i | ||||||
\(333\) | − | 2.09355i | − | 0.114726i | ||||||
\(334\) | 7.56534 | − | 4.36785i | 0.413957 | − | 0.238998i | ||||
\(335\) | −4.41742 | −0.241350 | ||||||||
\(336\) | −12.5000 | + | 4.33013i | −0.681931 | + | 0.236228i | ||||
\(337\) | −2.12614 | − | 1.22753i | −0.115818 | − | 0.0668676i | 0.440972 | − | 0.897521i | \(-0.354634\pi\) |
−0.556790 | + | 0.830653i | \(0.687967\pi\) | |||||||
\(338\) | −0.543561 | − | 0.313825i | −0.0295658 | − | 0.0170698i | ||||
\(339\) | −20.5218 | + | 11.8483i | −1.11459 | + | 0.643509i | ||||
\(340\) | −5.00000 | − | 8.66025i | −0.271163 | − | 0.469668i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.247727 | + | 0.333726i | 0.0133955 | + | 0.0180458i | ||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 10.1869 | + | 5.88143i | 0.549243 | + | 0.317105i | ||||
\(345\) | 17.3205i | 0.932505i | ||||||||
\(346\) | 9.02175i | 0.485013i | ||||||||
\(347\) | −15.6434 | − | 27.0951i | −0.839780 | − | 1.45454i | −0.890078 | − | 0.455808i | \(-0.849350\pi\) |
0.0502981 | − | 0.998734i | \(-0.483983\pi\) | |||||||
\(348\) | 9.89110 | + | 5.71063i | 0.530219 | + | 0.306122i | ||||
\(349\) | − | 32.1105i | − | 1.71884i | −0.511273 | − | 0.859418i | \(-0.670826\pi\) | ||
0.511273 | − | 0.859418i | \(-0.329174\pi\) | |||||||
\(350\) | 4.00455 | + | 0.770675i | 0.214052 | + | 0.0411943i | ||||
\(351\) | −9.47822 | − | 16.4168i | −0.505910 | − | 0.876262i | ||||
\(352\) | 12.3131 | + | 7.10895i | 0.656289 | + | 0.378908i | ||||
\(353\) | −0.230493 | − | 0.133075i | −0.0122679 | − | 0.00708286i | 0.493854 | − | 0.869545i | \(-0.335588\pi\) |
−0.506121 | + | 0.862462i | \(0.668921\pi\) | |||||||
\(354\) | 6.93920 | + | 4.00635i | 0.368815 | + | 0.212935i | ||||
\(355\) | 2.26951 | − | 3.93090i | 0.120453 | − | 0.208631i | ||||
\(356\) | 2.12614 | − | 3.68258i | 0.112685 | − | 0.195176i | ||||
\(357\) | 13.5826 | − | 15.6838i | 0.718866 | − | 0.830075i | ||||
\(358\) | 3.37386 | − | 5.84370i | 0.178314 | − | 0.308849i | ||||
\(359\) | −0.626136 | −0.0330462 | −0.0165231 | − | 0.999863i | \(-0.505260\pi\) | ||||
−0.0165231 | + | 0.999863i | \(0.505260\pi\) | |||||||
\(360\) | 0.230493 | − | 0.399225i | 0.0121480 | − | 0.0210410i | ||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | −4.64792 | + | 2.68348i | −0.244289 | + | 0.141040i | ||||
\(363\) | 1.79129 | − | 3.10260i | 0.0940182 | − | 0.162844i | ||||
\(364\) | 16.9782 | − | 5.88143i | 0.889901 | − | 0.308271i | ||||
\(365\) | 3.95644 | + | 6.85275i | 0.207089 | + | 0.358690i | ||||
\(366\) | 1.12159 | 0.0586265 | ||||||||
\(367\) | − | 9.66930i | − | 0.504734i | −0.967632 | − | 0.252367i | \(-0.918791\pi\) | ||
0.967632 | − | 0.252367i | \(-0.0812090\pi\) | |||||||
\(368\) | −10.5826 | + | 18.3296i | −0.551655 | + | 0.955494i | ||||
\(369\) | 0.560795 | + | 0.971326i | 0.0291938 | + | 0.0505652i | ||||
\(370\) | 5.06080 | − | 2.92185i | 0.263098 | − | 0.151900i | ||||
\(371\) | −3.31307 | − | 0.637600i | −0.172006 | − | 0.0331026i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.8085 | + | 10.8591i | −0.973868 | + | 0.562263i | −0.900413 | − | 0.435035i | \(-0.856736\pi\) |
−0.0734550 | + | 0.997299i | \(0.523403\pi\) | |||||||
\(374\) | −6.00000 | −0.310253 | ||||||||
\(375\) | 16.5653 | − | 9.56400i | 0.855431 | − | 0.493883i | ||||
\(376\) | −5.29129 | + | 9.16478i | −0.272877 | + | 0.472637i | ||||
\(377\) | −11.6869 | − | 6.74745i | −0.601908 | − | 0.347512i | ||||
\(378\) | −5.93466 | − | 1.14213i | −0.305246 | − | 0.0587446i | ||||
\(379\) | − | 26.3423i | − | 1.35311i | −0.736392 | − | 0.676556i | \(-0.763472\pi\) | ||
0.736392 | − | 0.676556i | \(-0.236528\pi\) | |||||||
\(380\) | 3.95644 | − | 9.13701i | 0.202961 | − | 0.468718i | ||||
\(381\) | −18.2477 | − | 10.5353i | −0.934859 | − | 0.539741i | ||||
\(382\) | 8.12614 | − | 4.69163i | 0.415769 | − | 0.240045i | ||||
\(383\) | −16.9129 | −0.864208 | −0.432104 | − | 0.901824i | \(-0.642229\pi\) | ||||
−0.432104 | + | 0.901824i | \(0.642229\pi\) | |||||||
\(384\) | 17.1261 | − | 9.88778i | 0.873964 | − | 0.504584i | ||||
\(385\) | 6.62614 | − | 7.65120i | 0.337699 | − | 0.389941i | ||||
\(386\) | 5.60436 | + | 9.70703i | 0.285254 | + | 0.494075i | ||||
\(387\) | 0.708712 | + | 1.22753i | 0.0360259 | + | 0.0623986i | ||||
\(388\) | 1.79129 | − | 3.10260i | 0.0909389 | − | 0.157511i | ||||
\(389\) | 33.9564 | 1.72166 | 0.860830 | − | 0.508893i | \(-0.169945\pi\) | ||||
0.860830 | + | 0.508893i | \(0.169945\pi\) | |||||||
\(390\) | −1.97822 | + | 3.42638i | −0.100171 | + | 0.173501i | ||||
\(391\) | − | 33.1950i | − | 1.67874i | ||||||
\(392\) | 4.50000 | − | 11.2583i | 0.227284 | − | 0.568632i | ||||
\(393\) | 11.0436 | − | 6.37600i | 0.557074 | − | 0.321627i | ||||
\(394\) | − | 5.48220i | − | 0.276189i | ||||||
\(395\) | 8.83485 | 0.444529 | ||||||||
\(396\) | 0.560795 | + | 0.971326i | 0.0281810 | + | 0.0488110i | ||||
\(397\) | 4.47315i | 0.224501i | 0.993680 | + | 0.112251i | \(0.0358059\pi\) | ||||
−0.993680 | + | 0.112251i | \(0.964194\pi\) | |||||||
\(398\) | −10.0871 | −0.505622 | ||||||||
\(399\) | 20.5998 | + | 1.55130i | 1.03128 | + | 0.0776622i | ||||
\(400\) | 9.41742 | 0.470871 | ||||||||
\(401\) | 4.20700i | 0.210088i | 0.994468 | + | 0.105044i | \(0.0334983\pi\) | ||||
−0.994468 | + | 0.105044i | \(0.966502\pi\) | |||||||
\(402\) | 1.41742 | + | 2.45505i | 0.0706947 | + | 0.122447i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 15.3422i | − | 0.763303i | ||||||
\(405\) | −10.5826 | + | 6.10985i | −0.525852 | + | 0.303601i | ||||
\(406\) | −4.06534 | + | 1.40828i | −0.201759 | + | 0.0698915i | ||||
\(407\) | 30.0924i | 1.49163i | ||||||||
\(408\) | −6.79129 | + | 11.7629i | −0.336219 | + | 0.582348i | ||||
\(409\) | −14.8348 | −0.733536 | −0.366768 | − | 0.930312i | \(-0.619536\pi\) | ||||
−0.366768 | + | 0.930312i | \(0.619536\pi\) | |||||||
\(410\) | −1.56534 | + | 2.71125i | −0.0773067 | + | 0.133899i | ||||
\(411\) | 8.91742 | + | 15.4454i | 0.439864 | + | 0.761867i | ||||
\(412\) | −3.02178 | − | 5.23388i | −0.148872 | − | 0.257855i | ||||
\(413\) | 24.4782 | − | 8.47950i | 1.20449 | − | 0.417249i | ||||
\(414\) | 0.626136 | − | 0.361500i | 0.0307729 | − | 0.0177668i | ||||
\(415\) | 17.3303 | 0.850711 | ||||||||
\(416\) | −15.5608 | + | 8.98403i | −0.762931 | + | 0.440478i | ||||
\(417\) | 16.5653 | + | 9.56400i | 0.811208 | + | 0.468351i | ||||
\(418\) | −3.56080 | − | 4.79693i | −0.174164 | − | 0.234625i | ||||
\(419\) | 38.7726i | 1.89416i | 0.320992 | + | 0.947082i | \(0.395984\pi\) | ||||
−0.320992 | + | 0.947082i | \(0.604016\pi\) | |||||||
\(420\) | −3.54356 | − | 10.2294i | −0.172908 | − | 0.499143i | ||||
\(421\) | 13.8131 | + | 7.97498i | 0.673208 | + | 0.388677i | 0.797291 | − | 0.603595i | \(-0.206266\pi\) |
−0.124083 | + | 0.992272i | \(0.539599\pi\) | |||||||
\(422\) | 3.23049 | − | 5.59538i | 0.157258 | − | 0.272379i | ||||
\(423\) | −1.10436 | + | 0.637600i | −0.0536956 | + | 0.0310012i | ||||
\(424\) | 2.20871 | 0.107265 | ||||||||
\(425\) | −12.7913 | + | 7.38505i | −0.620469 | + | 0.358228i | ||||
\(426\) | −2.91288 | −0.141129 | ||||||||
\(427\) | 2.37386 | − | 2.74110i | 0.114879 | − | 0.132651i | ||||
\(428\) | −14.7042 | + | 8.48945i | −0.710753 | + | 0.410353i | ||||
\(429\) | −10.1869 | − | 17.6443i | −0.491830 | − | 0.851874i | ||||
\(430\) | −1.97822 | + | 3.42638i | −0.0953982 | + | 0.165235i | ||||
\(431\) | − | 18.1389i | − | 0.873718i | −0.899530 | − | 0.436859i | \(-0.856091\pi\) | ||
0.899530 | − | 0.436859i | \(-0.143909\pi\) | |||||||
\(432\) | −13.9564 | −0.671479 | ||||||||
\(433\) | 18.1869 | + | 31.5007i | 0.874008 | + | 1.51383i | 0.857816 | + | 0.513958i | \(0.171821\pi\) |
0.0161926 | + | 0.999869i | \(0.494846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.06534 | + | 7.04138i | −0.194918 | + | 0.337608i | ||||
\(436\) | −20.9347 | + | 12.0866i | −1.00259 | + | 0.578845i | ||||
\(437\) | 26.5390 | − | 19.7001i | 1.26953 | − | 0.942384i | ||||
\(438\) | 2.53901 | − | 4.39770i | 0.121319 | − | 0.210130i | ||||
\(439\) | −3.16515 | −0.151064 | −0.0755322 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755322 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(440\) | −3.31307 | + | 5.73840i | −0.157944 | + | 0.273568i | ||||
\(441\) | 1.14792 | − | 0.903750i | 0.0546627 | − | 0.0430357i | ||||
\(442\) | 3.79129 | − | 6.56670i | 0.180333 | − | 0.312346i | ||||
\(443\) | −10.6652 | + | 18.4726i | −0.506717 | + | 0.877659i | 0.493253 | + | 0.869886i | \(0.335808\pi\) |
−0.999970 | + | 0.00777314i | \(0.997526\pi\) | |||||||
\(444\) | 27.8739 | + | 16.0930i | 1.32284 | + | 0.763739i | ||||
\(445\) | 2.62159 | + | 1.51358i | 0.124275 | + | 0.0717504i | ||||
\(446\) | 5.37386 | + | 3.10260i | 0.254460 | + | 0.146912i | ||||
\(447\) | −10.0390 | − | 17.3881i | −0.474829 | − | 0.822428i | ||||
\(448\) | 1.70871 | − | 8.87873i | 0.0807291 | − | 0.419481i | ||||
\(449\) | − | 12.6766i | − | 0.598244i | −0.954215 | − | 0.299122i | \(-0.903306\pi\) | ||
0.954215 | − | 0.299122i | \(-0.0966937\pi\) | |||||||
\(450\) | −0.278599 | − | 0.160849i | −0.0131333 | − | 0.00758251i | ||||
\(451\) | −8.06080 | − | 13.9617i | −0.379568 | − | 0.657431i | ||||
\(452\) | − | 23.6965i | − | 1.11459i | ||||||
\(453\) | − | 32.1860i | − | 1.51223i | ||||||
\(454\) | 10.5000 | + | 6.06218i | 0.492789 | + | 0.284512i | ||||
\(455\) | 4.18693 | + | 12.0866i | 0.196286 | + | 0.566630i | ||||
\(456\) | −13.4347 | + | 1.55130i | −0.629136 | + | 0.0726463i | ||||
\(457\) | 19.0390 | + | 32.9765i | 0.890608 | + | 1.54258i | 0.839148 | + | 0.543902i | \(0.183054\pi\) |
0.0514591 | + | 0.998675i | \(0.483613\pi\) | |||||||
\(458\) | 1.58258 | + | 2.74110i | 0.0739489 | + | 0.128083i | ||||
\(459\) | 18.9564 | − | 10.9445i | 0.884811 | − | 0.510846i | ||||
\(460\) | −15.0000 | − | 8.66025i | −0.699379 | − | 0.403786i | ||||
\(461\) | 4.66515 | + | 2.69343i | 0.217278 | + | 0.125445i | 0.604689 | − | 0.796462i | \(-0.293297\pi\) |
−0.387411 | + | 0.921907i | \(0.626631\pi\) | |||||||
\(462\) | −6.37841 | − | 1.22753i | −0.296750 | − | 0.0571097i | ||||
\(463\) | −19.0000 | −0.883005 | −0.441502 | − | 0.897260i | \(-0.645554\pi\) | ||||
−0.441502 | + | 0.897260i | \(0.645554\pi\) | |||||||
\(464\) | −8.60436 | + | 4.96773i | −0.399447 | + | 0.230621i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 6.12975i | − | 0.283955i | ||||||
\(467\) | −17.7695 | + | 10.2592i | −0.822275 | + | 0.474741i | −0.851200 | − | 0.524841i | \(-0.824125\pi\) |
0.0289255 | + | 0.999582i | \(0.490791\pi\) | |||||||
\(468\) | −1.41742 | −0.0655205 | ||||||||
\(469\) | 9.00000 | + | 1.73205i | 0.415581 | + | 0.0799787i | ||||
\(470\) | −3.08258 | − | 1.77973i | −0.142189 | − | 0.0820926i | ||||
\(471\) | 18.2477 | + | 10.5353i | 0.840811 | + | 0.485442i | ||||
\(472\) | −14.6869 | + | 8.47950i | −0.676021 | + | 0.390301i | ||||
\(473\) | −10.1869 | − | 17.6443i | −0.468396 | − | 0.811285i | ||||
\(474\) | −2.83485 | − | 4.91010i | −0.130209 | − | 0.225528i | ||||
\(475\) | −13.4955 | − | 5.84370i | −0.619214 | − | 0.268127i | ||||
\(476\) | 6.79129 | + | 19.6048i | 0.311278 | + | 0.898583i | ||||
\(477\) | 0.230493 | + | 0.133075i | 0.0105535 | + | 0.00609308i | ||||
\(478\) | 6.64215i | 0.303805i | ||||||||
\(479\) | − | 0.190700i | − | 0.00871332i | −0.999991 | − | 0.00435666i | \(-0.998613\pi\) | ||
0.999991 | − | 0.00435666i | \(-0.00138677\pi\) | |||||||
\(480\) | 5.41288 | + | 9.37538i | 0.247063 | + | 0.427926i | ||||
\(481\) | −32.9347 | − | 19.0148i | −1.50169 | − | 0.867002i | ||||
\(482\) | 3.36875i | 0.153442i | ||||||||
\(483\) | 6.79129 | − | 35.2886i | 0.309014 | − | 1.60569i | ||||
\(484\) | 1.79129 | + | 3.10260i | 0.0814222 | + | 0.141027i | ||||
\(485\) | 2.20871 | + | 1.27520i | 0.100292 | + | 0.0579039i | ||||
\(486\) | 0.856629 | + | 0.494575i | 0.0388575 | + | 0.0224344i | ||||
\(487\) | 8.68693 | + | 5.01540i | 0.393642 | + | 0.227270i | 0.683737 | − | 0.729728i | \(-0.260353\pi\) |
−0.290095 | + | 0.956998i | \(0.593687\pi\) | |||||||
\(488\) | −1.18693 | + | 2.05583i | −0.0537299 | + | 0.0930629i | ||||
\(489\) | 5.37386 | − | 9.30780i | 0.243015 | − | 0.420913i | ||||
\(490\) | 3.78674 | + | 1.51358i | 0.171068 | + | 0.0683764i | ||||
\(491\) | −19.0390 | + | 32.9765i | −0.859219 | + | 1.48821i | 0.0134566 | + | 0.999909i | \(0.495717\pi\) |
−0.872675 | + | 0.488301i | \(0.837617\pi\) | |||||||
\(492\) | −17.2432 | −0.777383 | ||||||||
\(493\) | 7.79129 | − | 13.4949i | 0.350902 | − | 0.607780i | ||||
\(494\) | 7.50000 | − | 0.866025i | 0.337441 | − | 0.0389643i | ||||
\(495\) | −0.691478 | + | 0.399225i | −0.0310796 | + | 0.0179438i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.16515 | + | 7.11890i | −0.276545 | + | 0.319326i | ||||
\(498\) | −5.56080 | − | 9.63158i | −0.249185 | − | 0.431601i | ||||
\(499\) | −17.7477 | −0.794497 | −0.397249 | − | 0.917711i | \(-0.630035\pi\) | ||||
−0.397249 | + | 0.917711i | \(0.630035\pi\) | |||||||
\(500\) | 19.1280i | 0.855431i | ||||||||
\(501\) | −17.1261 | + | 29.6633i | −0.765139 | + | 1.32526i | ||||
\(502\) | −2.18693 | − | 3.78788i | −0.0976075 | − | 0.169061i | ||||
\(503\) | 10.4174 | − | 6.01450i | 0.464490 | − | 0.268173i | −0.249440 | − | 0.968390i | \(-0.580247\pi\) |
0.713930 | + | 0.700217i | \(0.246913\pi\) | |||||||
\(504\) | −0.626136 | + | 0.723000i | −0.0278903 | + | 0.0322050i | ||||
\(505\) | 10.9220 | 0.486021 | ||||||||
\(506\) | −9.00000 | + | 5.19615i | −0.400099 | + | 0.230997i | ||||
\(507\) | 2.46099 | 0.109296 | ||||||||
\(508\) | 18.2477 | − | 10.5353i | 0.809612 | − | 0.467430i | ||||
\(509\) | −7.50000 | + | 12.9904i | −0.332432 | + | 0.575789i | −0.982988 | − | 0.183669i | \(-0.941202\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(510\) | −3.95644 | − | 2.28425i | −0.175194 | − | 0.101148i | ||||
\(511\) | −5.37386 | − | 15.5130i | −0.237726 | − | 0.686255i | ||||
\(512\) | 22.8981i | 1.01196i | ||||||||
\(513\) | 20.0000 | + | 8.66025i | 0.883022 | + | 0.382360i | ||||
\(514\) | 7.81307 | + | 4.51088i | 0.344620 | + | 0.198966i | ||||
\(515\) | 3.72595 | − | 2.15118i | 0.164185 | − | 0.0947922i | ||||
\(516\) | −21.7913 | −0.959308 | ||||||||
\(517\) | 15.8739 | − | 9.16478i | 0.698132 | − | 0.403067i | ||||
\(518\) | −11.4564 | + | 3.96863i | −0.503367 | + | 0.174371i | ||||
\(519\) | −17.6869 | − | 30.6347i | −0.776370 | − | 1.34471i | ||||
\(520\) | −4.18693 | − | 7.25198i | −0.183609 | − | 0.318020i | ||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0.339394 | 0.0148549 | ||||||||
\(523\) | −10.7477 | + | 18.6156i | −0.469965 | + | 0.814004i | −0.999410 | − | 0.0343406i | \(-0.989067\pi\) |
0.529445 | + | 0.848344i | \(0.322400\pi\) | |||||||
\(524\) | 12.7520i | 0.557074i | ||||||||
\(525\) | −15.1089 | + | 5.23388i | −0.659407 | + | 0.228425i | ||||
\(526\) | 4.74773 | − | 2.74110i | 0.207011 | − | 0.119518i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −15.0000 | −0.652791 | ||||||||
\(529\) | −17.2477 | − | 29.8739i | −0.749901 | − | 1.29887i | ||||
\(530\) | 0.742901i | 0.0322696i | ||||||||
\(531\) | −2.04356 | −0.0886830 | ||||||||
\(532\) | −11.6434 | + | 17.0643i | −0.504804 | + | 0.739832i | ||||
\(533\) | 20.3739 | 0.882490 | ||||||||
\(534\) | − | 1.94265i | − | 0.0840668i | ||||||
\(535\) | −6.04356 | − | 10.4678i | −0.261286 | − | 0.452560i | ||||
\(536\) | −6.00000 | −0.259161 | ||||||||
\(537\) | 26.4575i | 1.14173i | ||||||||
\(538\) | 3.00000 | − | 1.73205i | 0.129339 | − | 0.0746740i | ||||
\(539\) | −16.5000 | + | 12.9904i | −0.710705 | + | 0.559535i | ||||
\(540\) | − | 11.4213i | − | 0.491493i | ||||||
\(541\) | 1.87386 | − | 3.24563i | 0.0805637 | − | 0.139540i | −0.822929 | − | 0.568145i | \(-0.807661\pi\) |
0.903492 | + | 0.428605i | \(0.140995\pi\) | |||||||
\(542\) | 6.16515 | 0.264816 | ||||||||
\(543\) | 10.5218 | − | 18.2243i | 0.451533 | − | 0.782078i | ||||
\(544\) | −10.3739 | − | 17.9681i | −0.444776 | − | 0.770374i | ||||
\(545\) | −8.60436 | − | 14.9032i | −0.368570 | − | 0.638382i | ||||
\(546\) | 5.37386 | − | 6.20520i | 0.229980 | − | 0.265558i | ||||
\(547\) | −10.4347 | + | 6.02445i | −0.446154 | + | 0.257587i | −0.706204 | − | 0.708008i | \(-0.749594\pi\) |
0.260051 | + | 0.965595i | \(0.416261\pi\) | |||||||
\(548\) | −17.8348 | −0.761867 | ||||||||
\(549\) | −0.247727 | + | 0.143025i | −0.0105727 | + | 0.00610417i | ||||
\(550\) | 4.00455 | + | 2.31203i | 0.170754 | + | 0.0985851i | ||||
\(551\) | 15.4129 | − | 1.77973i | 0.656611 | − | 0.0758189i | ||||
\(552\) | 23.5257i | 1.00132i | ||||||||
\(553\) | −18.0000 | − | 3.46410i | −0.765438 | − | 0.147309i | ||||
\(554\) | −9.31307 | − | 5.37690i | −0.395674 | − | 0.228443i | ||||
\(555\) | −11.4564 | + | 19.8431i | −0.486299 | + | 0.842294i | ||||
\(556\) | −16.5653 | + | 9.56400i | −0.702527 | + | 0.405604i | ||||
\(557\) | 12.0000 | 0.508456 | 0.254228 | − | 0.967144i | \(-0.418179\pi\) | ||||
0.254228 | + | 0.967144i | \(0.418179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.7477 | 1.08901 | ||||||||
\(560\) | 9.24773 | + | 1.77973i | 0.390788 | + | 0.0752071i | ||||
\(561\) | 20.3739 | − | 11.7629i | 0.860185 | − | 0.496628i | ||||
\(562\) | 0.269507 | + | 0.466801i | 0.0113685 | + | 0.0196908i | ||||
\(563\) | 17.8521 | − | 30.9207i | 0.752376 | − | 1.30315i | −0.194293 | − | 0.980944i | \(-0.562241\pi\) |
0.946668 | − | 0.322209i | \(-0.104425\pi\) | |||||||
\(564\) | − | 19.6048i | − | 0.825509i | ||||||
\(565\) | 16.8693 | 0.709698 | ||||||||
\(566\) | −2.20871 | − | 3.82560i | −0.0928391 | − | 0.160802i | ||||
\(567\) | 23.9564 | − | 8.29875i | 1.00608 | − | 0.348515i | ||||
\(568\) | 3.08258 | − | 5.33918i | 0.129342 | − | 0.224027i | ||||
\(569\) | 2.76951 | − | 1.59898i | 0.116104 | − | 0.0670326i | −0.440823 | − | 0.897594i | \(-0.645314\pi\) |
0.556927 | + | 0.830561i | \(0.311980\pi\) | |||||||
\(570\) | −0.521780 | − | 4.51875i | −0.0218550 | − | 0.189270i | ||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | 20.3739 | 0.851874 | ||||||||
\(573\) | −18.3956 | + | 31.8622i | −0.768489 | + | 1.33106i | ||||
\(574\) | 4.25227 | − | 4.91010i | 0.177486 | − | 0.204944i | ||||
\(575\) | −12.7913 | + | 22.1552i | −0.533434 | + | 0.923934i | ||||
\(576\) | −0.356629 | + | 0.617700i | −0.0148595 | + | 0.0257375i | ||||
\(577\) | 26.3085 | + | 15.1892i | 1.09524 | + | 0.632336i | 0.934966 | − | 0.354737i | \(-0.115430\pi\) |
0.160272 | + | 0.987073i | \(0.448763\pi\) | |||||||
\(578\) | 0.856629 | + | 0.494575i | 0.0356311 | + | 0.0205716i | ||||
\(579\) | −38.0608 | − | 21.9744i | −1.58175 | − | 0.913225i | ||||
\(580\) | −4.06534 | − | 7.04138i | −0.168804 | − | 0.292377i | ||||
\(581\) | −35.3085 | − | 6.79513i | −1.46484 | − | 0.281909i | ||||
\(582\) | − | 1.63670i | − | 0.0678434i | ||||||
\(583\) | −3.31307 | − | 1.91280i | −0.137213 | − | 0.0792201i | ||||
\(584\) | 5.37386 | + | 9.30780i | 0.222372 | + | 0.385160i | ||||
\(585\) | − | 1.00905i | − | 0.0417191i | ||||||
\(586\) | 9.59386i | 0.396319i | ||||||||
\(587\) | −7.26951 | − | 4.19705i | −0.300045 | − | 0.173231i | 0.342418 | − | 0.939548i | \(-0.388754\pi\) |
−0.642463 | + | 0.766317i | \(0.722087\pi\) | |||||||
\(588\) | 3.20871 | + | 22.2306i | 0.132325 | + | 0.916775i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.85208 | − | 4.93995i | −0.117418 | − | 0.203375i | ||||
\(591\) | 10.7477 | + | 18.6156i | 0.442102 | + | 0.765744i | ||||
\(592\) | −24.2477 | + | 13.9994i | −0.996575 | + | 0.575373i | ||||
\(593\) | 14.8348 | + | 8.56490i | 0.609194 | + | 0.351718i | 0.772650 | − | 0.634832i | \(-0.218931\pi\) |
−0.163456 | + | 0.986551i | \(0.552264\pi\) | |||||||
\(594\) | −5.93466 | − | 3.42638i | −0.243502 | − | 0.140586i | ||||
\(595\) | −13.9564 | + | 4.83465i | −0.572158 | + | 0.198201i | ||||
\(596\) | 20.0780 | 0.822428 | ||||||||
\(597\) | 34.2523 | − | 19.7756i | 1.40185 | − | 0.809360i | ||||
\(598\) | − | 13.1334i | − | 0.537065i | ||||||
\(599\) | 36.2023i | 1.47918i | 0.673055 | + | 0.739592i | \(0.264982\pi\) | ||||
−0.673055 | + | 0.739592i | \(0.735018\pi\) | |||||||
\(600\) | 9.06534 | − | 5.23388i | 0.370091 | − | 0.213672i | ||||
\(601\) | −20.4955 | −0.836027 | −0.418014 | − | 0.908441i | \(-0.637274\pi\) | ||||
−0.418014 | + | 0.908441i | \(0.637274\pi\) | |||||||
\(602\) | 5.37386 | − | 6.20520i | 0.219022 | − | 0.252905i | ||||
\(603\) | −0.626136 | − | 0.361500i | −0.0254982 | − | 0.0147214i | ||||
\(604\) | 27.8739 | + | 16.0930i | 1.13417 | + | 0.654814i | ||||
\(605\) | −2.20871 | + | 1.27520i | −0.0897969 | + | 0.0518443i | ||||
\(606\) | −3.50455 | − | 6.07005i | −0.142362 | − | 0.246579i | ||||
\(607\) | −7.00000 | − | 12.1244i | −0.284121 | − | 0.492112i | 0.688274 | − | 0.725450i | \(-0.258368\pi\) |
−0.972396 | + | 0.233338i | \(0.925035\pi\) | |||||||
\(608\) | 8.20871 | − | 18.9572i | 0.332907 | − | 0.768816i | ||||
\(609\) | 11.0436 | − | 12.7520i | 0.447508 | − | 0.516737i | ||||
\(610\) | −0.691478 | − | 0.399225i | −0.0279971 | − | 0.0161641i | ||||
\(611\) | 23.1642i | 0.937124i | ||||||||
\(612\) | − | 1.63670i | − | 0.0661597i | ||||||
\(613\) | 2.68693 | + | 4.65390i | 0.108524 | + | 0.187969i | 0.915173 | − | 0.403062i | \(-0.132054\pi\) |
−0.806648 | + | 0.591032i | \(0.798721\pi\) | |||||||
\(614\) | −7.99545 | − | 4.61618i | −0.322670 | − | 0.186294i | ||||
\(615\) | − | 12.2753i | − | 0.494986i | ||||||
\(616\) | 9.00000 | − | 10.3923i | 0.362620 | − | 0.418718i | ||||
\(617\) | 22.5826 | + | 39.1142i | 0.909140 | + | 1.57468i | 0.815261 | + | 0.579094i | \(0.196593\pi\) |
0.0938792 | + | 0.995584i | \(0.470073\pi\) | |||||||
\(618\) | −2.39110 | − | 1.38050i | −0.0961841 | − | 0.0555319i | ||||
\(619\) | 7.50000 | + | 4.33013i | 0.301450 | + | 0.174042i | 0.643094 | − | 0.765787i | \(-0.277650\pi\) |
−0.341644 | + | 0.939829i | \(0.610984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9564 | − | 32.8335i | 0.760696 | − | 1.31756i | ||||
\(622\) | −5.47822 | + | 9.48855i | −0.219657 | + | 0.380456i | ||||
\(623\) | −4.74773 | − | 4.11165i | −0.190214 | − | 0.164730i | ||||
\(624\) | 9.47822 | − | 16.4168i | 0.379432 | − | 0.657196i | ||||
\(625\) | 3.25227 | 0.130091 | ||||||||
\(626\) | 1.97822 | − | 3.42638i | 0.0790656 | − | 0.136946i | ||||
\(627\) | 21.4955 | + | 9.30780i | 0.858446 | + | 0.371718i | ||||
\(628\) | −18.2477 | + | 10.5353i | −0.728164 | + | 0.420405i | ||||
\(629\) | 21.9564 | − | 38.0297i | 0.875461 | − | 1.51634i | ||||
\(630\) | −0.243181 | − | 0.210601i | −0.00968857 | − | 0.00839055i | ||||
\(631\) | 17.1434 | + | 29.6932i | 0.682467 | + | 1.18207i | 0.974226 | + | 0.225575i | \(0.0724262\pi\) |
−0.291759 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(632\) | 12.0000 | 0.477334 | ||||||||
\(633\) | 25.3332i | 1.00690i | ||||||||
\(634\) | −3.35208 | + | 5.80598i | −0.133128 | + | 0.230585i | ||||
\(635\) | 7.50000 | + | 12.9904i | 0.297628 | + | 0.515508i | ||||
\(636\) | −3.54356 | + | 2.04588i | −0.140511 | + | 0.0811243i | ||||
\(637\) | −3.79129 | − | 26.2668i | −0.150216 | − | 1.04073i | ||||
\(638\) | −4.87841 | −0.193138 | ||||||||
\(639\) | 0.643371 | − | 0.371450i | 0.0254514 | − | 0.0146944i | ||||
\(640\) | −14.0780 | −0.556483 | ||||||||
\(641\) | 6.16515 | − | 3.55945i | 0.243509 | − | 0.140590i | −0.373280 | − | 0.927719i | \(-0.621767\pi\) |
0.616788 | + | 0.787129i | \(0.288433\pi\) | |||||||
\(642\) | −3.87841 | + | 6.71760i | −0.153069 | + | 0.265123i | ||||
\(643\) | 9.24773 | + | 5.33918i | 0.364695 | + | 0.210557i | 0.671138 | − | 0.741332i | \(-0.265806\pi\) |
−0.306443 | + | 0.951889i | \(0.599139\pi\) | |||||||
\(644\) | 27.1652 | + | 23.5257i | 1.07046 | + | 0.927043i | ||||
\(645\) | − | 15.5130i | − | 0.610824i | ||||||
\(646\) | 1.00000 | + | 8.66025i | 0.0393445 | + | 0.340733i | ||||
\(647\) | −5.76951 | − | 3.33103i | −0.226823 | − | 0.130956i | 0.382283 | − | 0.924045i | \(-0.375138\pi\) |
−0.609105 | + | 0.793089i | \(0.708471\pi\) | |||||||
\(648\) | −14.3739 | + | 8.29875i | −0.564659 | + | 0.326006i | ||||
\(649\) | 29.3739 | 1.15303 | ||||||||
\(650\) | −5.06080 | + | 2.92185i | −0.198501 | + | 0.114604i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.37386 | + | 9.30780i | 0.210457 | + | 0.364522i | ||||
\(653\) | −7.50000 | − | 12.9904i | −0.293498 | − | 0.508353i | 0.681137 | − | 0.732156i | \(-0.261486\pi\) |
−0.974634 | + | 0.223803i | \(0.928153\pi\) | |||||||
\(654\) | −5.52178 | + | 9.56400i | −0.215919 | + | 0.373982i | ||||
\(655\) | −9.07803 | −0.354708 | ||||||||
\(656\) | 7.50000 | − | 12.9904i | 0.292826 | − | 0.507189i | ||||
\(657\) | 1.29510i | 0.0505267i | ||||||||
\(658\) | 5.58258 | + | 4.83465i | 0.217631 | + | 0.188474i | ||||
\(659\) | −25.4174 | + | 14.6748i | −0.990122 | + | 0.571647i | −0.905311 | − | 0.424750i | \(-0.860362\pi\) |
−0.0848114 | + | 0.996397i | \(0.527029\pi\) | |||||||
\(660\) | − | 12.2753i | − | 0.477814i | ||||||
\(661\) | −30.4955 | −1.18614 | −0.593068 | − | 0.805152i | \(-0.702083\pi\) | ||||
−0.593068 | + | 0.805152i | \(0.702083\pi\) | |||||||
\(662\) | 0.478220 | + | 0.828301i | 0.0185865 | + | 0.0321928i | ||||
\(663\) | 29.7309i | 1.15465i | ||||||||
\(664\) | 23.5390 | 0.913491 | ||||||||
\(665\) | −12.1479 | − | 8.28880i | −0.471076 | − | 0.321426i | ||||
\(666\) | 0.956439 | 0.0370613 | ||||||||
\(667\) | − | 26.9898i | − | 1.04505i | ||||||
\(668\) | −17.1261 | − | 29.6633i | −0.662630 | − | 1.14771i | ||||
\(669\) | −24.3303 | −0.940664 | ||||||||
\(670\) | − | 2.01810i | − | 0.0779661i | ||||||
\(671\) | 3.56080 | − | 2.05583i | 0.137463 | − | 0.0793643i | ||||
\(672\) | −7.35208 | − | 21.2236i | −0.283613 | − | 0.818720i | ||||
\(673\) | − | 11.6874i | − | 0.450516i | −0.974299 | − | 0.225258i | \(-0.927677\pi\) | ||
0.974299 | − | 0.225258i | \(-0.0723226\pi\) | |||||||
\(674\) | 0.560795 | − | 0.971326i | 0.0216010 | − | 0.0374141i | ||||
\(675\) | −16.8693 | −0.649300 | ||||||||
\(676\) | −1.23049 | + | 2.13128i | −0.0473266 | + | 0.0819721i | ||||
\(677\) | −1.33485 | − | 2.31203i | −0.0513024 | − | 0.0888584i | 0.839234 | − | 0.543771i | \(-0.183004\pi\) |
−0.890536 | + | 0.454912i | \(0.849671\pi\) | |||||||
\(678\) | −5.41288 | − | 9.37538i | −0.207880 | − | 0.360059i | ||||
\(679\) | −4.00000 | − | 3.46410i | −0.153506 | − | 0.132940i | ||||
\(680\) | 8.37386 | − | 4.83465i | 0.321123 | − | 0.185400i | ||||
\(681\) | −47.5390 | −1.82170 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.2650 | + | 17.4735i | 1.15806 | + | 0.668604i | 0.950837 | − | 0.309690i | \(-0.100225\pi\) |
0.207219 | + | 0.978295i | \(0.433559\pi\) | |||||||
\(684\) | 1.30852 | − | 0.971326i | 0.0500326 | − | 0.0371396i | ||||
\(685\) | − | 12.6965i | − | 0.485107i | ||||||
\(686\) | −7.12159 | − | 4.56850i | −0.271904 | − | 0.174426i | ||||
\(687\) | −10.7477 | − | 6.20520i | −0.410051 | − | 0.236743i | ||||
\(688\) | 9.47822 | − | 16.4168i | 0.361354 | − | 0.625883i | ||||
\(689\) | 4.18693 | − | 2.41733i | 0.159509 | − | 0.0920928i | ||||
\(690\) | −7.91288 | −0.301238 | ||||||||
\(691\) | 37.5000 | − | 21.6506i | 1.42657 | − | 0.823629i | 0.429719 | − | 0.902963i | \(-0.358613\pi\) |
0.996848 | + | 0.0793336i | \(0.0252792\pi\) | |||||||
\(692\) | 35.3739 | 1.34471 | ||||||||
\(693\) | 1.56534 | − | 0.542250i | 0.0594624 | − | 0.0205984i | ||||
\(694\) | 12.3784 | − | 7.14668i | 0.469878 | − | 0.271284i | ||||
\(695\) | −6.80852 | − | 11.7927i | −0.258262 | − | 0.447323i | ||||
\(696\) | −5.52178 | + | 9.56400i | −0.209303 | + | 0.362523i | ||||
\(697\) | 23.5257i | 0.891100i | ||||||||
\(698\) | 14.6697 | 0.555256 | ||||||||
\(699\) | 12.0172 | + | 20.8145i | 0.454534 | + | 0.787275i | ||||
\(700\) | 3.02178 | − | 15.7016i | 0.114213 | − | 0.593466i | ||||
\(701\) | 10.7477 | − | 18.6156i | 0.405936 | − | 0.703102i | −0.588494 | − | 0.808502i | \(-0.700279\pi\) |
0.994430 | + | 0.105400i | \(0.0336122\pi\) | |||||||
\(702\) | 7.50000 | − | 4.33013i | 0.283069 | − | 0.163430i | ||||
\(703\) | 43.4347 | − | 5.01540i | 1.63817 | − | 0.189159i | ||||
\(704\) | 5.12614 | − | 8.87873i | 0.193199 | − | 0.334630i | ||||
\(705\) | 13.9564 | 0.525630 | ||||||||
\(706\) | 0.0607953 | − | 0.105301i | 0.00228806 | − | 0.00396304i | ||||
\(707\) | −22.2523 | − | 4.28245i | −0.836883 | − | 0.161058i | ||||
\(708\) | 15.7087 | − | 27.2083i | 0.590370 | − | 1.02255i | ||||
\(709\) | 6.70871 | − | 11.6198i | 0.251951 | − | 0.436392i | −0.712112 | − | 0.702066i | \(-0.752261\pi\) |
0.964063 | + | 0.265674i | \(0.0855945\pi\) | |||||||
\(710\) | 1.79583 | + | 1.03683i | 0.0673964 | + | 0.0389114i | ||||
\(711\) | 1.25227 | + | 0.723000i | 0.0469639 | + | 0.0271146i | ||||
\(712\) | 3.56080 | + | 2.05583i | 0.133446 | + | 0.0770453i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 7.16515 | + | 6.20520i | 0.268149 | + | 0.232224i | ||||
\(715\) | 14.5040i | 0.542417i | ||||||||
\(716\) | −22.9129 | − | 13.2288i | −0.856294 | − | 0.494382i | ||||
\(717\) | −13.0218 | − | 22.5544i | −0.486307 | − | 0.842309i | ||||
\(718\) | − | 0.286051i | − | 0.0106753i | ||||||
\(719\) | 31.3676i | 1.16981i | 0.811100 | + | 0.584907i | \(0.198869\pi\) | ||||
−0.811100 | + | 0.584907i | \(0.801131\pi\) | |||||||
\(720\) | −0.643371 | − | 0.371450i | −0.0239770 | − | 0.0138431i | ||||
\(721\) | −8.43466 | + | 2.92185i | −0.314123 | + | 0.108815i | ||||
\(722\) | −6.33030 | + | 5.93905i | −0.235589 | + | 0.221029i | ||||
\(723\) | −6.60436 | − | 11.4391i | −0.245619 | − | 0.425424i | ||||
\(724\) | 10.5218 | + | 18.2243i | 0.391039 | + | 0.677299i | ||||
\(725\) | −10.4002 | + | 6.00455i | −0.386253 | + | 0.223003i | ||||
\(726\) | 1.41742 | + | 0.818350i | 0.0526055 | + | 0.0303718i | ||||
\(727\) | −39.2477 | − | 22.6597i | −1.45562 | − | 0.840401i | −0.456826 | − | 0.889556i | \(-0.651014\pi\) |
−0.998791 | + | 0.0491546i | \(0.984347\pi\) | |||||||
\(728\) | 5.68693 | + | 16.4168i | 0.210772 | + | 0.608446i | ||||
\(729\) | 24.8693 | 0.921086 | ||||||||
\(730\) | −3.13068 | + | 1.80750i | −0.115872 | + | 0.0668986i | ||||
\(731\) | 29.7309i | 1.09964i | ||||||||
\(732\) | − | 4.39770i | − | 0.162544i | ||||||
\(733\) | 24.8085 | − | 14.3232i | 0.916324 | − | 0.529040i | 0.0338633 | − | 0.999426i | \(-0.489219\pi\) |
0.882460 | + | 0.470387i | \(0.155886\pi\) | |||||||
\(734\) | 4.41742 | 0.163050 | ||||||||
\(735\) | −15.8258 | + | 2.28425i | −0.583742 | + | 0.0842559i | ||||
\(736\) | −31.1216 | − | 17.9681i | −1.14716 | − | 0.662311i | ||||
\(737\) | 9.00000 | + | 5.19615i | 0.331519 | + | 0.191403i | ||||
\(738\) | −0.443751 | + | 0.256199i | −0.0163347 | + | 0.00943083i | ||||
\(739\) | −12.8739 | − | 22.2982i | −0.473573 | − | 0.820252i | 0.525970 | − | 0.850503i | \(-0.323703\pi\) |
−0.999542 | + | 0.0302513i | \(0.990369\pi\) | |||||||
\(740\) | −11.4564 | − | 19.8431i | −0.421147 | − | 0.729448i | ||||
\(741\) | −23.7695 | + | 17.6443i | −0.873195 | + | 0.648179i | ||||
\(742\) | 0.291288 | − | 1.51358i | 0.0106935 | − | 0.0555651i | ||||
\(743\) | 28.8956 | + | 16.6829i | 1.06008 | + | 0.612037i | 0.925454 | − | 0.378860i | \(-0.123684\pi\) |
0.134624 | + | 0.990897i | \(0.457017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.2934i | 0.523668i | ||||||||
\(746\) | −4.96099 | − | 8.59268i | −0.181635 | − | 0.314600i | ||||
\(747\) | 2.45644 | + | 1.41823i | 0.0898764 | + | 0.0518902i | ||||
\(748\) | 23.5257i | 0.860185i | ||||||||
\(749\) | 8.20871 | + | 23.6965i | 0.299940 | + | 0.865852i | ||||
\(750\) | 4.36932 | + | 7.56788i | 0.159545 | + | 0.276340i | ||||
\(751\) | −7.81307 | − | 4.51088i | −0.285103 | − | 0.164604i | 0.350628 | − | 0.936515i | \(-0.385968\pi\) |
−0.635731 | + | 0.771910i | \(0.719301\pi\) | |||||||
\(752\) | 14.7695 | + | 8.52718i | 0.538589 | + | 0.310954i | ||||
\(753\) | 14.8521 | + | 8.57485i | 0.541240 | + | 0.312485i | ||||
\(754\) | 3.08258 | − | 5.33918i | 0.112261 | − | 0.194441i | ||||
\(755\) | −11.4564 | + | 19.8431i | −0.416943 | + | 0.722166i | ||||
\(756\) | −4.47822 | + | 23.2695i | −0.162871 | + | 0.846304i | ||||
\(757\) | 14.1216 | − | 24.4593i | 0.513258 | − | 0.888989i | −0.486624 | − | 0.873612i | \(-0.661772\pi\) |
0.999882 | − | 0.0153772i | \(-0.00489491\pi\) | |||||||
\(758\) | 12.0345 | 0.437112 | ||||||||
\(759\) | 20.3739 | − | 35.2886i | 0.739524 | − | 1.28089i | ||||
\(760\) | 8.83485 | + | 3.82560i | 0.320474 | + | 0.138769i | ||||
\(761\) | −17.7695 | + | 10.2592i | −0.644144 | + | 0.371897i | −0.786209 | − | 0.617961i | \(-0.787959\pi\) |
0.142065 | + | 0.989857i | \(0.454626\pi\) | |||||||
\(762\) | 4.81307 | − | 8.33648i | 0.174359 | − | 0.301999i | ||||
\(763\) | 11.6869 | + | 33.7373i | 0.423095 | + | 1.22137i | ||||
\(764\) | −18.3956 | − | 31.8622i | −0.665531 | − | 1.15273i | ||||
\(765\) | 1.16515 | 0.0421261 | ||||||||
\(766\) | − | 7.72665i | − | 0.279175i | ||||||
\(767\) | −18.5608 | + | 32.1482i | −0.670191 | + | 1.16081i | ||||
\(768\) | −1.60436 | − | 2.77883i | −0.0578922 | − | 0.100272i | ||||
\(769\) | −25.1869 | + | 14.5417i | −0.908264 | + | 0.524386i | −0.879872 | − | 0.475210i | \(-0.842372\pi\) |
−0.0283918 | + | 0.999597i | \(0.509039\pi\) | |||||||
\(770\) | 3.49545 | + | 3.02715i | 0.125967 | + | 0.109091i | ||||
\(771\) | −35.3739 | −1.27396 | ||||||||
\(772\) | 38.0608 | − | 21.9744i | 1.36984 | − | 0.790876i | ||||
\(773\) | −39.6606 | −1.42649 | −0.713246 | − | 0.700913i | \(-0.752776\pi\) | ||||
−0.713246 | + | 0.700913i | \(0.752776\pi\) | |||||||
\(774\) | −0.560795 | + | 0.323775i | −0.0201574 | + | 0.0116379i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.00000 | + | 1.73205i | 0.107694 | + | 0.0621770i | ||||
\(777\) | 31.1216 | − | 35.9361i | 1.11648 | − | 1.28920i | ||||
\(778\) | 15.5130i | 0.556168i | ||||||||
\(779\) | −18.8085 | + | 13.9617i | −0.673885 | + | 0.500230i | ||||
\(780\) | 13.4347 | + | 7.75650i | 0.481038 | + | 0.277727i | ||||
\(781\) | −9.24773 | + | 5.33918i | −0.330910 | + | 0.191051i | ||||
\(782\) | 15.1652 | 0.542305 | ||||||||
\(783\) | 15.4129 | − | 8.89863i | 0.550811 | − | 0.318011i | ||||
\(784\) | −18.1434 | − | 7.25198i | −0.647978 | − | 0.258999i | ||||
\(785\) | −7.50000 | − | 12.9904i | −0.267686 | − | 0.463647i | ||||
\(786\) | 2.91288 | + | 5.04525i | 0.103899 | + | 0.179958i | ||||
\(787\) | 12.7913 | − | 22.1552i | 0.455960 | − | 0.789746i | −0.542783 | − | 0.839873i | \(-0.682629\pi\) |
0.998743 | + | 0.0501270i | \(0.0159626\pi\) | |||||||
\(788\) | −21.4955 | −0.765744 | ||||||||
\(789\) | −10.7477 | + | 18.6156i | −0.382629 | + | 0.662733i | ||||
\(790\) | 4.03620i | 0.143602i | ||||||||
\(791\) | −34.3693 | − | 6.61438i | −1.22203 | − | 0.235180i | ||||
\(792\) | −0.939205 | + | 0.542250i | −0.0333732 | + | 0.0192680i | ||||
\(793\) | 5.19615i | 0.184521i | ||||||||
\(794\) | −2.04356 | −0.0725233 | ||||||||
\(795\) | −1.45644 | − | 2.52263i | −0.0516546 | − | 0.0894684i | ||||
\(796\) | 39.5511i | 1.40185i | ||||||||
\(797\) | −48.4955 | −1.71780 | −0.858899 | − | 0.512146i | \(-0.828851\pi\) | ||||
−0.858899 | + | 0.512146i | \(0.828851\pi\) | |||||||
\(798\) | −0.708712 | + | 9.41103i | −0.0250881 | + | 0.333147i | ||||
\(799\) | −26.7477 | −0.946267 | ||||||||
\(800\) | 15.9898i | 0.565323i | ||||||||
\(801\) | 0.247727 | + | 0.429076i | 0.00875301 | + | 0.0151607i | ||||
\(802\) | −1.92197 | −0.0678671 | ||||||||
\(803\) | − | 18.6156i | − | 0.656931i | ||||||
\(804\) | 9.62614 | − | 5.55765i | 0.339488 | − | 0.196003i | ||||
\(805\) | −16.7477 | + | 19.3386i | −0.590280 | + | 0.681596i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.79129 | + | 11.7629i | −0.239065 | + | 0.414072i | ||||
\(808\) | 14.8348 | 0.521888 | ||||||||
\(809\) | −25.0390 | + | 43.3688i | −0.880325 | + | 1.52477i | −0.0293449 | + | 0.999569i | \(0.509342\pi\) |
−0.850980 | + | 0.525198i | \(0.823991\pi\) | |||||||
\(810\) | −2.79129 | − | 4.83465i | −0.0980759 | − | 0.169872i | ||||
\(811\) | 7.56080 | + | 13.0957i | 0.265495 | + | 0.459852i | 0.967693 | − | 0.252130i | \(-0.0811311\pi\) |
−0.702198 | + | 0.711982i | \(0.747798\pi\) | |||||||
\(812\) | 5.52178 | + | 15.9400i | 0.193777 | + | 0.559385i | ||||
\(813\) | −20.9347 | + | 12.0866i | −0.734211 | + | 0.423897i | ||||
\(814\) | −13.7477 | −0.481858 | ||||||||
\(815\) | −6.62614 | + | 3.82560i | −0.232103 | + | 0.134005i | ||||
\(816\) | 18.9564 | + | 10.9445i | 0.663608 | + | 0.383134i | ||||
\(817\) | −23.7695 | + | 17.6443i | −0.831590 | + | 0.617295i | ||||
\(818\) | − | 6.77730i | − | 0.236963i | ||||||
\(819\) | −0.395644 | + | 2.05583i | −0.0138249 | + | 0.0718364i | ||||
\(820\) | 10.6307 | + | 6.13763i | 0.371240 | + | 0.214335i | ||||
\(821\) | 8.52178 | − | 14.7602i | 0.297412 | − | 0.515133i | −0.678131 | − | 0.734941i | \(-0.737210\pi\) |
0.975543 | + | 0.219808i | \(0.0705431\pi\) | |||||||
\(822\) | −7.05625 | + | 4.07393i | −0.246115 | + | 0.142095i | ||||
\(823\) | −25.4174 | −0.885996 | −0.442998 | − | 0.896523i | \(-0.646085\pi\) | ||||
−0.442998 | + | 0.896523i | \(0.646085\pi\) | |||||||
\(824\) | 5.06080 | − | 2.92185i | 0.176301 | − | 0.101788i | ||||
\(825\) | −18.1307 | −0.631229 | ||||||||
\(826\) | 3.87386 | + | 11.1829i | 0.134789 | + | 0.389102i | ||||
\(827\) | 26.7042 | − | 15.4177i | 0.928595 | − | 0.536124i | 0.0422280 | − | 0.999108i | \(-0.486554\pi\) |
0.886367 | + | 0.462984i | \(0.153221\pi\) | |||||||
\(828\) | −1.41742 | − | 2.45505i | −0.0492589 | − | 0.0853189i | ||||
\(829\) | −7.12614 | + | 12.3428i | −0.247501 | + | 0.428684i | −0.962832 | − | 0.270102i | \(-0.912943\pi\) |
0.715331 | + | 0.698786i | \(0.246276\pi\) | |||||||
\(830\) | 7.91735i | 0.274815i | ||||||||
\(831\) | 42.1652 | 1.46269 | ||||||||
\(832\) | 6.47822 | + | 11.2206i | 0.224592 | + | 0.389005i | ||||
\(833\) | 30.3303 | − | 4.37780i | 1.05088 | − | 0.151682i | ||||
\(834\) | −4.36932 | + | 7.56788i | −0.151297 | + | 0.262054i | ||||
\(835\) | 21.1170 | − | 12.1919i | 0.730785 | − | 0.421919i | ||||
\(836\) | −18.8085 | + | 13.9617i | −0.650506 | + | 0.482876i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.7133 | −0.611894 | ||||||||
\(839\) | −11.9174 | + | 20.6416i | −0.411435 | + | 0.712627i | −0.995047 | − | 0.0994062i | \(-0.968306\pi\) |
0.583612 | + | 0.812033i | \(0.301639\pi\) | |||||||
\(840\) | 9.89110 | − | 3.42638i | 0.341275 | − | 0.118221i | ||||
\(841\) | −8.16515 | + | 14.1425i | −0.281557 | + | 0.487671i | ||||
\(842\) | −3.64337 | + | 6.31050i | −0.125559 | + | 0.217474i | ||||
\(843\) | −1.83030 | − | 1.05673i | −0.0630390 | − | 0.0363956i | ||||
\(844\) | −21.9392 | − | 12.6666i | −0.755179 | − | 0.436003i | ||||
\(845\) | −1.51723 | − | 0.875976i | −0.0521945 | − | 0.0301345i | ||||
\(846\) | −0.291288 | − | 0.504525i | −0.0100147 | − | 0.0173459i | ||||
\(847\) | 5.00000 | − | 1.73205i | 0.171802 | − | 0.0595140i | ||||
\(848\) | − | 3.55945i | − | 0.122232i | ||||||
\(849\) | 15.0000 | + | 8.66025i | 0.514799 | + | 0.297219i | ||||
\(850\) | −3.37386 | − | 5.84370i | −0.115723 | − | 0.200437i | ||||
\(851\) | − | 76.0593i | − | 2.60728i | ||||||
\(852\) | 11.4213i | 0.391286i | ||||||||
\(853\) | −0.873864 | − | 0.504525i | −0.0299205 | − | 0.0172746i | 0.484965 | − | 0.874533i | \(-0.338832\pi\) |
−0.514886 | + | 0.857259i | \(0.672166\pi\) | |||||||
\(854\) | 1.25227 | + | 1.08450i | 0.0428519 | + | 0.0371108i | ||||
\(855\) | 0.691478 | + | 0.931524i | 0.0236480 | + | 0.0318575i | ||||
\(856\) | −8.20871 | − | 14.2179i | −0.280568 | − | 0.485958i | ||||
\(857\) | −6.56080 | − | 11.3636i | −0.224112 | − | 0.388174i | 0.731940 | − | 0.681369i | \(-0.238615\pi\) |
−0.956053 | + | 0.293195i | \(0.905282\pi\) | |||||||
\(858\) | 8.06080 | − | 4.65390i | 0.275191 | − | 0.158882i | ||||
\(859\) | −5.68693 | − | 3.28335i | −0.194036 | − | 0.112027i | 0.399835 | − | 0.916587i | \(-0.369067\pi\) |
−0.593870 | + | 0.804561i | \(0.702401\pi\) | |||||||
\(860\) | 13.4347 | + | 7.75650i | 0.458118 | + | 0.264495i | ||||
\(861\) | −4.81307 | + | 25.0094i | −0.164029 | + | 0.852319i | ||||
\(862\) | 8.28674 | 0.282248 | ||||||||
\(863\) | 16.0390 | − | 9.26013i | 0.545974 | − | 0.315218i | −0.201522 | − | 0.979484i | \(-0.564589\pi\) |
0.747497 | + | 0.664265i | \(0.231256\pi\) | |||||||
\(864\) | − | 23.6965i | − | 0.806172i | ||||||
\(865\) | 25.1823i | 0.856224i | ||||||||
\(866\) | −14.3911 | + | 8.30870i | −0.489029 | + | 0.282341i | ||||
\(867\) | −3.87841 | −0.131718 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.0000 | − | 10.3923i | −0.610608 | − | 0.352535i | ||||
\(870\) | −3.21686 | − | 1.85725i | −0.109062 | − | 0.0629667i | ||||
\(871\) | −11.3739 | + | 6.56670i | −0.385389 | + | 0.222504i | ||||
\(872\) | −11.6869 | − | 20.2424i | −0.395769 | − | 0.685493i | ||||
\(873\) | 0.208712 | + | 0.361500i | 0.00706384 | + | 0.0122349i | ||||
\(874\) | 9.00000 | + | 12.1244i | 0.304430 | + | 0.410112i | ||||
\(875\) | 27.7432 | + | 5.33918i | 0.937891 | + | 0.180497i | ||||
\(876\) | −17.2432 | − | 9.95536i | −0.582593 | − | 0.336360i | ||||
\(877\) | − | 42.8643i | − | 1.44743i | −0.690101 | − | 0.723713i | \(-0.742434\pi\) | ||
0.690101 | − | 0.723713i | \(-0.257566\pi\) | |||||||
\(878\) | − | 1.44600i | − | 0.0488001i | ||||||
\(879\) | −18.8085 | − | 32.5773i | −0.634396 | − | 1.09881i | ||||
\(880\) | 9.24773 | + | 5.33918i | 0.311741 | + | 0.179984i | ||||
\(881\) | − | 13.5903i | − | 0.457867i | −0.973442 | − | 0.228934i | \(-0.926476\pi\) | ||
0.973442 | − | 0.228934i | \(-0.0735239\pi\) | |||||||
\(882\) | 0.412878 | + | 0.524426i | 0.0139023 | + | 0.0176583i | ||||
\(883\) | −20.5000 | − | 35.5070i | −0.689880 | − | 1.19491i | −0.971876 | − | 0.235492i | \(-0.924330\pi\) |
0.281996 | − | 0.959415i | \(-0.409003\pi\) | |||||||
\(884\) | −25.7477 | − | 14.8655i | −0.865990 | − | 0.499979i | ||||
\(885\) | 19.3693 | + | 11.1829i | 0.651092 | + | 0.375908i | ||||
\(886\) | −8.43920 | − | 4.87238i | −0.283521 | − | 0.163691i | ||||
\(887\) | 0.708712 | − | 1.22753i | 0.0237962 | − | 0.0412163i | −0.853882 | − | 0.520467i | \(-0.825758\pi\) |
0.877678 | + | 0.479250i | \(0.159091\pi\) | |||||||
\(888\) | −15.5608 | + | 26.9521i | −0.522186 | + | 0.904453i | ||||
\(889\) | −10.1869 | − | 29.4071i | −0.341659 | − | 0.986284i | ||||
\(890\) | −0.691478 | + | 1.19767i | −0.0231784 | + | 0.0401461i | ||||
\(891\) | 28.7477 | 0.963085 | ||||||||
\(892\) | 12.1652 | − | 21.0707i | 0.407319 | − | 0.705498i | ||||
\(893\) | −15.8739 | − | 21.3845i | −0.531199 | − | 0.715605i | ||||
\(894\) | 7.94375 | − | 4.58633i | 0.265679 | − | 0.153390i | ||||
\(895\) | 9.41742 | − | 16.3115i | 0.314790 | − | 0.545232i | ||||
\(896\) | 28.6824 | + | 5.51993i | 0.958211 | + | 0.184408i | ||||
\(897\) | 25.7477 | + | 44.5964i | 0.859692 | + | 1.48903i | ||||
\(898\) | 5.79129 | 0.193258 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.630682 | + | 1.09237i | −0.0210227 | + | 0.0364125i | ||||
\(901\) | 2.79129 | + | 4.83465i | 0.0929913 | + | 0.161066i | ||||
\(902\) | 6.37841 | − | 3.68258i | 0.212378 | − | 0.122616i | ||||
\(903\) | −6.08258 | + | 31.6060i | −0.202415 | + | 1.05178i | ||||
\(904\) | 22.9129 | 0.762071 | ||||||||
\(905\) | −12.9737 | + | 7.49035i | −0.431260 | + | 0.248988i | ||||
\(906\) | 14.7042 | 0.488513 | ||||||||
\(907\) | 34.9955 | − | 20.2046i | 1.16200 | − | 0.670884i | 0.210221 | − | 0.977654i | \(-0.432582\pi\) |
0.951784 | + | 0.306770i | \(0.0992482\pi\) | |||||||
\(908\) | 23.7695 | − | 41.1700i | 0.788819 | − | 1.36627i | ||||
\(909\) | 1.54811 | + | 0.893800i | 0.0513475 | + | 0.0296455i | ||||
\(910\) | −5.52178 | + | 1.91280i | −0.183045 | + | 0.0634087i | ||||
\(911\) | 7.38505i | 0.244678i | 0.992488 | + | 0.122339i | \(0.0390395\pi\) | ||||
−0.992488 | + | 0.122339i | \(0.960961\pi\) | |||||||
\(912\) | 2.50000 | + | 21.6506i | 0.0827833 | + | 0.716924i | ||||
\(913\) | −35.3085 | − | 20.3854i | −1.16854 | − | 0.674658i | ||||
\(914\) | −15.0653 | + | 8.69798i | −0.498317 | + | 0.287704i | ||||
\(915\) | 3.13068 | 0.103497 | ||||||||
\(916\) | 10.7477 | − | 6.20520i | 0.355115 | − | 0.205026i | ||||
\(917\) | 18.4955 | + | 3.55945i | 0.610774 | + | 0.117543i | ||||
\(918\) | 5.00000 | + | 8.66025i | 0.165025 | + | 0.285831i | ||||
\(919\) | −11.0000 | − | 19.0526i | −0.362857 | − | 0.628486i | 0.625573 | − | 0.780165i | \(-0.284865\pi\) |
−0.988430 | + | 0.151680i | \(0.951532\pi\) | |||||||
\(920\) | 8.37386 | − | 14.5040i | 0.276078 | − | 0.478181i | ||||
\(921\) | 36.1996 | 1.19282 | ||||||||
\(922\) | −1.23049 | + | 2.13128i | −0.0405241 | + | 0.0701898i | ||||
\(923\) | − | 13.4949i | − | 0.444190i | ||||||
\(924\) | −4.81307 | + | 25.0094i | −0.158338 | + | 0.822750i | ||||
\(925\) | −29.3085 | + | 16.9213i | −0.963658 | + | 0.556368i | ||||
\(926\) | − | 8.68015i | − | 0.285248i | ||||||
\(927\) | 0.704166 | 0.0231279 | ||||||||
\(928\) | −8.43466 | − | 14.6093i | −0.276881 | − | 0.479572i | ||||
\(929\) | − | 4.01630i | − | 0.131771i | −0.997827 | − | 0.0658853i | \(-0.979013\pi\) | ||
0.997827 | − | 0.0658853i | \(-0.0209871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.5000 | + | 21.6506i | 0.704634 | + | 0.709571i | ||||
\(932\) | −24.0345 | −0.787275 | ||||||||
\(933\) | − | 42.9597i | − | 1.40644i | ||||||
\(934\) | −4.68693 | − | 8.11800i | −0.153361 | − | 0.265629i | ||||
\(935\) | −16.7477 | −0.547709 | ||||||||
\(936\) | − | 1.37055i | − | 0.0447979i | ||||||
\(937\) | 9.93920 | − | 5.73840i | 0.324700 | − | 0.187465i | −0.328786 | − | 0.944405i | \(-0.606639\pi\) |
0.653485 | + | 0.756939i | \(0.273306\pi\) | |||||||
\(938\) | −0.791288 | + | 4.11165i | −0.0258365 | + | 0.134250i | ||||
\(939\) | 15.5130i | 0.506248i | ||||||||
\(940\) | −6.97822 | + | 12.0866i | −0.227604 | + | 0.394222i | ||||
\(941\) | 5.20871 | 0.169799 | 0.0848996 | − | 0.996390i | \(-0.472943\pi\) | ||||
0.0848996 | + | 0.996390i | \(0.472943\pi\) | |||||||
\(942\) | −4.81307 | + | 8.33648i | −0.156818 | + | 0.271617i | ||||
\(943\) | 20.3739 | + | 35.2886i | 0.663464 | + | 1.14915i | ||||
\(944\) | 13.6652 | + | 23.6687i | 0.444763 | + | 0.770352i | ||||
\(945\) | −16.5653 | − | 3.18800i | −0.538871 | − | 0.103706i | ||||
\(946\) | 8.06080 | − | 4.65390i | 0.262079 | − | 0.151311i | ||||
\(947\) | 35.8348 | 1.16448 | 0.582238 | − | 0.813018i | \(-0.302177\pi\) | ||||
0.582238 | + | 0.813018i | \(0.302177\pi\) | |||||||
\(948\) | −19.2523 | + | 11.1153i | −0.625285 | + | 0.361008i | ||||
\(949\) | 20.3739 | + | 11.7629i | 0.661364 | + | 0.381838i | ||||
\(950\) | 2.66970 | − | 6.16540i | 0.0866164 | − | 0.200032i | ||||
\(951\) | − | 26.2867i | − | 0.852405i | ||||||
\(952\) | −18.9564 | + | 6.56670i | −0.614382 | + | 0.212828i | ||||
\(953\) | −42.8911 | − | 24.7632i | −1.38938 | − | 0.802158i | −0.396134 | − | 0.918193i | \(-0.629648\pi\) |
−0.993245 | + | 0.116035i | \(0.962982\pi\) | |||||||
\(954\) | −0.0607953 | + | 0.105301i | −0.00196832 | + | 0.00340923i | ||||
\(955\) | 22.6824 | − | 13.0957i | 0.733985 | − | 0.423766i | ||||
\(956\) | 26.0436 | 0.842309 | ||||||||
\(957\) | 16.5653 | − | 9.56400i | 0.535481 | − | 0.309160i | ||||
\(958\) | 0.0871215 | 0.00281477 | ||||||||
\(959\) | −4.97822 | + | 25.8676i | −0.160755 | + | 0.835308i | ||||
\(960\) | 6.76042 | − | 3.90313i | 0.218191 | − | 0.125973i | ||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 8.68693 | − | 15.0462i | 0.280078 | − | 0.485109i | ||||
\(963\) | − | 1.97830i | − | 0.0637498i | ||||||
\(964\) | 13.2087 | 0.425424 | ||||||||
\(965\) | 15.6434 | + | 27.0951i | 0.503578 | + | 0.872223i | ||||
\(966\) | 16.1216 | + | 3.10260i | 0.518704 | + | 0.0998246i | ||||
\(967\) | −11.2087 | + | 19.4141i | −0.360448 | + | 0.624314i | −0.988035 | − | 0.154233i | \(-0.950709\pi\) |
0.627587 | + | 0.778547i | \(0.284043\pi\) | |||||||
\(968\) | −3.00000 | + | 1.73205i | −0.0964237 | + | 0.0556702i | ||||
\(969\) | −20.3739 | − | 27.4467i | −0.654503 | − | 0.881714i | ||||
\(970\) | −0.582576 | + | 1.00905i | −0.0187054 | + | 0.0323987i | ||||
\(971\) | −43.4519 | −1.39444 | −0.697219 | − | 0.716858i | \(-0.745579\pi\) | ||||
−0.697219 | + | 0.716858i | \(0.745579\pi\) | |||||||
\(972\) | 1.93920 | − | 3.35880i | 0.0622000 | − | 0.107734i | ||||
\(973\) | 9.24773 | + | 26.6959i | 0.296469 | + | 0.855831i | ||||
\(974\) | −2.29129 | + | 3.96863i | −0.0734176 | + | 0.127163i | ||||
\(975\) | 11.4564 | − | 19.8431i | 0.366900 | − | 0.635489i | ||||
\(976\) | 3.31307 | + | 1.91280i | 0.106049 | + | 0.0612273i | ||||
\(977\) | 16.4174 | + | 9.47860i | 0.525240 | + | 0.303247i | 0.739076 | − | 0.673622i | \(-0.235262\pi\) |
−0.213836 | + | 0.976870i | \(0.568596\pi\) | |||||||
\(978\) | 4.25227 | + | 2.45505i | 0.135973 | + | 0.0785039i | ||||
\(979\) | −3.56080 | − | 6.16748i | −0.113804 | − | 0.197113i | ||||
\(980\) | 5.93466 | − | 14.8476i | 0.189576 | − | 0.474290i | ||||
\(981\) | − | 2.81655i | − | 0.0899256i | ||||||
\(982\) | −15.0653 | − | 8.69798i | −0.480754 | − | 0.277564i | ||||
\(983\) | 29.1434 | + | 50.4778i | 0.929529 | + | 1.60999i | 0.784110 | + | 0.620622i | \(0.213120\pi\) |
0.145419 | + | 0.989370i | \(0.453547\pi\) | |||||||
\(984\) | − | 16.6730i | − | 0.531514i | ||||||
\(985\) | − | 15.3024i | − | 0.487575i | ||||||
\(986\) | 6.16515 | + | 3.55945i | 0.196338 | + | 0.113356i | ||||
\(987\) | −28.4347 | − | 5.47225i | −0.905085 | − | 0.174184i | ||||
\(988\) | −3.39564 | − | 29.4071i | −0.108030 | − | 0.935566i | ||||
\(989\) | 25.7477 | + | 44.5964i | 0.818730 | + | 1.41808i | ||||
\(990\) | −0.182386 | − | 0.315902i | −0.00579661 | − | 0.0100400i | ||||
\(991\) | 30.3131 | − | 17.5013i | 0.962926 | − | 0.555946i | 0.0658539 | − | 0.997829i | \(-0.479023\pi\) |
0.897072 | + | 0.441883i | \(0.145690\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.24773 | − | 1.87508i | −0.103064 | − | 0.0595037i | ||||
\(994\) | −3.25227 | − | 2.81655i | −0.103156 | − | 0.0893356i | ||||
\(995\) | −28.1561 | −0.892607 | ||||||||
\(996\) | −37.7650 | + | 21.8036i | −1.19663 | + | 0.690874i | ||||
\(997\) | − | 5.48220i | − | 0.173623i | −0.996225 | − | 0.0868116i | \(-0.972332\pi\) | ||
0.996225 | − | 0.0868116i | \(-0.0276678\pi\) | |||||||
\(998\) | − | 8.10805i | − | 0.256656i | ||||||
\(999\) | 43.4347 | − | 25.0770i | 1.37421 | − | 0.793402i |
(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 | 133.2.i.c.122.2 | yes | 4 | |
7.2 | even | 3 | 931.2.s.c.901.2 | 4 | |||
7.3 | odd | 6 | 931.2.p.e.293.1 | 4 | |||
7.4 | even | 3 | 931.2.p.f.293.1 | 4 | |||
7.5 | odd | 6 | 133.2.s.c.103.2 | yes | 4 | ||
7.6 | odd | 2 | 931.2.i.d.521.2 | 4 | |||
19.12 | odd | 6 | 133.2.s.c.31.2 | yes | 4 | ||
133.12 | even | 6 | inner | 133.2.i.c.12.1 | ✓ | 4 | |
133.31 | even | 6 | 931.2.p.f.734.1 | 4 | |||
133.69 | even | 6 | 931.2.s.c.31.2 | 4 | |||
133.88 | odd | 6 | 931.2.p.e.734.1 | 4 | |||
133.107 | odd | 6 | 931.2.i.d.411.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.i.c.12.1 | ✓ | 4 | 133.12 | even | 6 | inner | |
133.2.i.c.122.2 | yes | 4 | 1.1 | even | 1 | trivial | |
133.2.s.c.31.2 | yes | 4 | 19.12 | odd | 6 | ||
133.2.s.c.103.2 | yes | 4 | 7.5 | odd | 6 | ||
931.2.i.d.411.1 | 4 | 133.107 | odd | 6 | |||
931.2.i.d.521.2 | 4 | 7.6 | odd | 2 | |||
931.2.p.e.293.1 | 4 | 7.3 | odd | 6 | |||
931.2.p.e.734.1 | 4 | 133.88 | odd | 6 | |||
931.2.p.f.293.1 | 4 | 7.4 | even | 3 | |||
931.2.p.f.734.1 | 4 | 133.31 | even | 6 | |||
931.2.s.c.31.2 | 4 | 133.69 | even | 6 | |||
931.2.s.c.901.2 | 4 | 7.2 | even | 3 |