Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(149,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.q (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 149.3 | ||
Root | \(-1.41313 + 0.0554252i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.149 |
Dual form | 400.2.q.f.349.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0554252 | − | 1.41313i | 0.0391915 | − | 0.999232i | ||||
\(3\) | −0.488516 | − | 0.488516i | −0.282045 | − | 0.282045i | 0.551879 | − | 0.833924i | \(-0.313911\pi\) |
−0.833924 | + | 0.551879i | \(0.813911\pi\) | |||||||
\(4\) | −1.99386 | − | 0.156646i | −0.996928 | − | 0.0783229i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.717411 | + | 0.663259i | −0.292882 | + | 0.270774i | ||||
\(7\) | 4.71540 | 1.78226 | 0.891128 | − | 0.453753i | \(-0.149915\pi\) | ||||
0.891128 | + | 0.453753i | \(0.149915\pi\) | |||||||
\(8\) | −0.331870 | + | 2.80889i | −0.117334 | + | 0.993093i | ||||
\(9\) | − | 2.52270i | − | 0.840901i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.91360 | − | 3.91360i | −1.17999 | − | 1.17999i | −0.979745 | − | 0.200249i | \(-0.935825\pi\) |
−0.200249 | − | 0.979745i | \(-0.564175\pi\) | |||||||
\(12\) | 0.897506 | + | 1.05055i | 0.259088 | + | 0.303269i | ||||
\(13\) | −0.0878822 | − | 0.0878822i | −0.0243741 | − | 0.0243741i | 0.694815 | − | 0.719189i | \(-0.255486\pi\) |
−0.719189 | + | 0.694815i | \(0.755486\pi\) | |||||||
\(14\) | 0.261352 | − | 6.66346i | 0.0698493 | − | 1.78089i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95092 | + | 0.624658i | 0.987731 | + | 0.156165i | ||||
\(17\) | − | 4.67442i | − | 1.13371i | −0.823816 | − | 0.566857i | \(-0.808159\pi\) | ||
0.823816 | − | 0.566857i | \(-0.191841\pi\) | |||||||
\(18\) | −3.56490 | − | 0.139821i | −0.840255 | − | 0.0329562i | ||||
\(19\) | −1.81249 | + | 1.81249i | −0.415813 | + | 0.415813i | −0.883758 | − | 0.467945i | \(-0.844995\pi\) |
0.467945 | + | 0.883758i | \(0.344995\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.30355 | − | 2.30355i | −0.502676 | − | 0.502676i | ||||
\(22\) | −5.74732 | + | 5.31350i | −1.22533 | + | 1.13284i | ||||
\(23\) | 1.63007 | 0.339893 | 0.169946 | − | 0.985453i | \(-0.445641\pi\) | ||||
0.169946 | + | 0.985453i | \(0.445641\pi\) | |||||||
\(24\) | 1.53431 | − | 1.21006i | 0.313190 | − | 0.247003i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.129060 | + | 0.119318i | −0.0253107 | + | 0.0234002i | ||||
\(27\) | −2.69793 | + | 2.69793i | −0.519217 | + | 0.519217i | ||||
\(28\) | −9.40184 | − | 0.738648i | −1.77678 | − | 0.139591i | ||||
\(29\) | −3.26362 | + | 3.26362i | −0.606039 | + | 0.606039i | −0.941909 | − | 0.335869i | \(-0.890970\pi\) |
0.335869 | + | 0.941909i | \(0.390970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.12875 | −0.382334 | −0.191167 | − | 0.981557i | \(-0.561227\pi\) | ||||
−0.191167 | + | 0.981557i | \(0.561227\pi\) | |||||||
\(32\) | 1.10170 | − | 5.54854i | 0.194755 | − | 0.980852i | ||||
\(33\) | 3.82371i | 0.665622i | ||||||||
\(34\) | −6.60555 | − | 0.259081i | −1.13284 | − | 0.0444320i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.395171 | + | 5.02991i | −0.0658618 | + | 0.838318i | ||||
\(37\) | 3.97797 | − | 3.97797i | 0.653974 | − | 0.653974i | −0.299973 | − | 0.953948i | \(-0.596978\pi\) |
0.953948 | + | 0.299973i | \(0.0969778\pi\) | |||||||
\(38\) | 2.46082 | + | 2.66173i | 0.399197 | + | 0.431790i | ||||
\(39\) | 0.0858637i | 0.0137492i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.25504i | − | 1.28922i | −0.764511 | − | 0.644611i | \(-0.777020\pi\) | ||
0.764511 | − | 0.644611i | \(-0.222980\pi\) | |||||||
\(42\) | −3.38288 | + | 3.12753i | −0.521990 | + | 0.482589i | ||||
\(43\) | −2.27336 | + | 2.27336i | −0.346685 | + | 0.346685i | −0.858873 | − | 0.512188i | \(-0.828835\pi\) |
0.512188 | + | 0.858873i | \(0.328835\pi\) | |||||||
\(44\) | 7.19010 | + | 8.41620i | 1.08395 | + | 1.26879i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0903468 | − | 2.30349i | 0.0133209 | − | 0.339631i | ||||
\(47\) | 4.06129i | 0.592400i | 0.955126 | + | 0.296200i | \(0.0957195\pi\) | ||||
−0.955126 | + | 0.296200i | \(0.904281\pi\) | |||||||
\(48\) | −1.62493 | − | 2.23524i | −0.234539 | − | 0.322630i | ||||
\(49\) | 15.2350 | 2.17643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.28353 | + | 2.28353i | −0.319758 | + | 0.319758i | ||||
\(52\) | 0.161458 | + | 0.188991i | 0.0223902 | + | 0.0262083i | ||||
\(53\) | 5.03938 | − | 5.03938i | 0.692211 | − | 0.692211i | −0.270507 | − | 0.962718i | \(-0.587191\pi\) |
0.962718 | + | 0.270507i | \(0.0871912\pi\) | |||||||
\(54\) | 3.66298 | + | 3.96205i | 0.498469 | + | 0.539167i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.56490 | + | 13.2450i | −0.209119 | + | 1.76994i | ||||
\(57\) | 1.77086 | 0.234556 | ||||||||
\(58\) | 4.43103 | + | 4.79280i | 0.581822 | + | 0.629325i | ||||
\(59\) | 5.16453 | + | 5.16453i | 0.672365 | + | 0.672365i | 0.958261 | − | 0.285896i | \(-0.0922911\pi\) |
−0.285896 | + | 0.958261i | \(0.592291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.12726 | − | 7.12726i | 0.912552 | − | 0.912552i | −0.0839206 | − | 0.996472i | \(-0.526744\pi\) |
0.996472 | + | 0.0839206i | \(0.0267442\pi\) | |||||||
\(62\) | −0.117986 | + | 3.00819i | −0.0149843 | + | 0.382041i | ||||
\(63\) | − | 11.8956i | − | 1.49870i | ||||||
\(64\) | −7.77972 | − | 1.86437i | −0.972466 | − | 0.233047i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.40339 | + | 0.211930i | 0.665111 | + | 0.0260868i | ||||
\(67\) | 7.49920 | + | 7.49920i | 0.916173 | + | 0.916173i | 0.996748 | − | 0.0805758i | \(-0.0256759\pi\) |
−0.0805758 | + | 0.996748i | \(0.525676\pi\) | |||||||
\(68\) | −0.732228 | + | 9.32012i | −0.0887957 | + | 1.13023i | ||||
\(69\) | −0.796314 | − | 0.796314i | −0.0958649 | − | 0.0958649i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.54072i | 0.538884i | 0.963017 | + | 0.269442i | \(0.0868393\pi\) | ||||
−0.963017 | + | 0.269442i | \(0.913161\pi\) | |||||||
\(72\) | 7.08600 | + | 0.837210i | 0.835093 | + | 0.0986662i | ||||
\(73\) | 8.30557 | 0.972093 | 0.486047 | − | 0.873933i | \(-0.338439\pi\) | ||||
0.486047 | + | 0.873933i | \(0.338439\pi\) | |||||||
\(74\) | −5.40090 | − | 5.84186i | −0.627842 | − | 0.679102i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.89776 | − | 3.32992i | 0.447104 | − | 0.381968i | ||||
\(77\) | −18.4542 | − | 18.4542i | −2.10305 | − | 2.10305i | ||||
\(78\) | 0.121336 | + | 0.00475901i | 0.0137386 | + | 0.000538852i | ||||
\(79\) | −11.5317 | −1.29742 | −0.648709 | − | 0.761037i | \(-0.724691\pi\) | ||||
−0.648709 | + | 0.761037i | \(0.724691\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.93215 | −0.548017 | ||||||||
\(82\) | −11.6654 | − | 0.457537i | −1.28823 | − | 0.0505266i | ||||
\(83\) | −1.16919 | − | 1.16919i | −0.128335 | − | 0.128335i | 0.640022 | − | 0.768357i | \(-0.278925\pi\) |
−0.768357 | + | 0.640022i | \(0.778925\pi\) | |||||||
\(84\) | 4.23211 | + | 4.95379i | 0.461761 | + | 0.540503i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.08655 | + | 3.33855i | 0.332831 | + | 0.360006i | ||||
\(87\) | 3.18866 | 0.341861 | ||||||||
\(88\) | 12.2917 | − | 9.69406i | 1.31030 | − | 1.03339i | ||||
\(89\) | − | 3.24572i | − | 0.344046i | −0.985093 | − | 0.172023i | \(-0.944970\pi\) | ||
0.985093 | − | 0.172023i | \(-0.0550304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.414400 | − | 0.414400i | −0.0434409 | − | 0.0434409i | ||||
\(92\) | −3.25012 | − | 0.255343i | −0.338848 | − | 0.0266214i | ||||
\(93\) | 1.03993 | + | 1.03993i | 0.107835 | + | 0.107835i | ||||
\(94\) | 5.73912 | + | 0.225098i | 0.591945 | + | 0.0232171i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.24875 | + | 2.17235i | −0.331574 | + | 0.221714i | ||||
\(97\) | 13.9581i | 1.41723i | 0.705598 | + | 0.708613i | \(0.250679\pi\) | ||||
−0.705598 | + | 0.708613i | \(0.749321\pi\) | |||||||
\(98\) | 0.844405 | − | 21.5290i | 0.0852978 | − | 2.17476i | ||||
\(99\) | −9.87285 | + | 9.87285i | −0.992258 | + | 0.992258i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4088 | + | 13.4088i | 1.33422 | + | 1.33422i | 0.901552 | + | 0.432672i | \(0.142429\pi\) |
0.432672 | + | 0.901552i | \(0.357571\pi\) | |||||||
\(102\) | 3.10035 | + | 3.35348i | 0.306981 | + | 0.332044i | ||||
\(103\) | 13.7638 | 1.35618 | 0.678092 | − | 0.734977i | \(-0.262807\pi\) | ||||
0.678092 | + | 0.734977i | \(0.262807\pi\) | |||||||
\(104\) | 0.276017 | − | 0.217686i | 0.0270657 | − | 0.0213459i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.84197 | − | 7.40059i | −0.664551 | − | 0.718808i | ||||
\(107\) | −0.327996 | + | 0.327996i | −0.0317086 | + | 0.0317086i | −0.722783 | − | 0.691075i | \(-0.757138\pi\) |
0.691075 | + | 0.722783i | \(0.257138\pi\) | |||||||
\(108\) | 5.80190 | − | 4.95666i | 0.558288 | − | 0.476955i | ||||
\(109\) | 0.149698 | − | 0.149698i | 0.0143385 | − | 0.0143385i | −0.699901 | − | 0.714240i | \(-0.746773\pi\) |
0.714240 | + | 0.699901i | \(0.246773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.88660 | −0.368900 | ||||||||
\(112\) | 18.6302 | + | 2.94551i | 1.76039 | + | 0.278325i | ||||
\(113\) | 5.97999i | 0.562550i | 0.959627 | + | 0.281275i | \(0.0907573\pi\) | ||||
−0.959627 | + | 0.281275i | \(0.909243\pi\) | |||||||
\(114\) | 0.0981502 | − | 2.50245i | 0.00919261 | − | 0.234376i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.01843 | − | 5.99596i | 0.651644 | − | 0.556711i | ||||
\(117\) | −0.221701 | + | 0.221701i | −0.0204962 | + | 0.0204962i | ||||
\(118\) | 7.58439 | − | 7.01189i | 0.698199 | − | 0.645497i | ||||
\(119\) | − | 22.0418i | − | 2.02057i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.6325i | 1.78477i | ||||||||
\(122\) | −9.67669 | − | 10.4668i | −0.876086 | − | 0.947615i | ||||
\(123\) | −4.03272 | + | 4.03272i | −0.363618 | + | 0.363618i | ||||
\(124\) | 4.24442 | + | 0.333459i | 0.381160 | + | 0.0299455i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −16.8100 | − | 0.659314i | −1.49755 | − | 0.0587364i | ||||
\(127\) | 2.73076i | 0.242315i | 0.992633 | + | 0.121158i | \(0.0386607\pi\) | ||||
−0.992633 | + | 0.121158i | \(0.961339\pi\) | |||||||
\(128\) | −3.06579 | + | 10.8904i | −0.270980 | + | 0.962585i | ||||
\(129\) | 2.22115 | 0.195561 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.813555 | + | 0.813555i | −0.0710806 | + | 0.0710806i | −0.741753 | − | 0.670673i | \(-0.766006\pi\) |
0.670673 | + | 0.741753i | \(0.266006\pi\) | |||||||
\(132\) | 0.598967 | − | 7.62392i | 0.0521334 | − | 0.663577i | ||||
\(133\) | −8.54661 | + | 8.54661i | −0.741085 | + | 0.741085i | ||||
\(134\) | 11.0130 | − | 10.1817i | 0.951375 | − | 0.879563i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.1299 | + | 1.55130i | 1.12588 | + | 0.133023i | ||||
\(137\) | 0.199812 | 0.0170711 | 0.00853557 | − | 0.999964i | \(-0.497283\pi\) | ||||
0.00853557 | + | 0.999964i | \(0.497283\pi\) | |||||||
\(138\) | −1.16943 | + | 1.08116i | −0.0995484 | + | 0.0920342i | ||||
\(139\) | 11.6301 | + | 11.6301i | 0.986448 | + | 0.986448i | 0.999909 | − | 0.0134610i | \(-0.00428488\pi\) |
−0.0134610 | + | 0.999909i | \(0.504285\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.98400 | − | 1.98400i | 0.167083 | − | 0.167083i | ||||
\(142\) | 6.41661 | + | 0.251670i | 0.538470 | + | 0.0211197i | ||||
\(143\) | 0.687871i | 0.0575227i | ||||||||
\(144\) | 1.57583 | − | 9.96701i | 0.131319 | − | 0.830585i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.460338 | − | 11.7368i | 0.0380978 | − | 0.971346i | ||||
\(147\) | −7.44256 | − | 7.44256i | −0.613852 | − | 0.613852i | ||||
\(148\) | −8.55463 | + | 7.30837i | −0.703186 | + | 0.600744i | ||||
\(149\) | 1.13384 | + | 1.13384i | 0.0928880 | + | 0.0928880i | 0.752024 | − | 0.659136i | \(-0.229078\pi\) |
−0.659136 | + | 0.752024i | \(0.729078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.12216i | 0.579593i | 0.957088 | + | 0.289797i | \(0.0935877\pi\) | ||||
−0.957088 | + | 0.289797i | \(0.906412\pi\) | |||||||
\(152\) | −4.48957 | − | 5.69259i | −0.364152 | − | 0.461730i | ||||
\(153\) | −11.7922 | −0.953341 | ||||||||
\(154\) | −27.1009 | + | 25.0553i | −2.18386 | + | 2.01901i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0134502 | − | 0.171200i | 0.00107688 | − | 0.0137070i | ||||
\(157\) | 5.32145 | + | 5.32145i | 0.424698 | + | 0.424698i | 0.886818 | − | 0.462120i | \(-0.152911\pi\) |
−0.462120 | + | 0.886818i | \(0.652911\pi\) | |||||||
\(158\) | −0.639147 | + | 16.2957i | −0.0508478 | + | 1.29642i | ||||
\(159\) | −4.92363 | −0.390469 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.68643 | 0.605775 | ||||||||
\(162\) | −0.273365 | + | 6.96976i | −0.0214776 | + | 0.547596i | ||||
\(163\) | −12.3010 | − | 12.3010i | −0.963488 | − | 0.963488i | 0.0358685 | − | 0.999357i | \(-0.488580\pi\) |
−0.999357 | + | 0.0358685i | \(0.988580\pi\) | |||||||
\(164\) | −1.29312 | + | 16.4594i | −0.100975 | + | 1.28526i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.71702 | + | 1.58741i | −0.133266 | + | 0.123207i | ||||
\(167\) | 9.86820 | 0.763624 | 0.381812 | − | 0.924240i | \(-0.375300\pi\) | ||||
0.381812 | + | 0.924240i | \(0.375300\pi\) | |||||||
\(168\) | 7.23490 | − | 5.70594i | 0.558184 | − | 0.440223i | ||||
\(169\) | − | 12.9846i | − | 0.998812i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.57237 | + | 4.57237i | 0.349658 | + | 0.349658i | ||||
\(172\) | 4.88887 | − | 4.17665i | 0.372773 | − | 0.318466i | ||||
\(173\) | −13.4089 | − | 13.4089i | −1.01946 | − | 1.01946i | −0.999807 | − | 0.0196525i | \(-0.993744\pi\) |
−0.0196525 | − | 0.999807i | \(-0.506256\pi\) | |||||||
\(174\) | 0.176732 | − | 4.50599i | 0.0133980 | − | 0.341598i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.0177 | − | 17.9070i | −0.981243 | − | 1.34979i | ||||
\(177\) | − | 5.04591i | − | 0.379274i | ||||||
\(178\) | −4.58662 | − | 0.179895i | −0.343782 | − | 0.0134837i | ||||
\(179\) | −0.419587 | + | 0.419587i | −0.0313614 | + | 0.0313614i | −0.722614 | − | 0.691252i | \(-0.757059\pi\) |
0.691252 | + | 0.722614i | \(0.257059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2605 | − | 14.2605i | −1.05998 | − | 1.05998i | −0.998083 | − | 0.0618956i | \(-0.980285\pi\) |
−0.0618956 | − | 0.998083i | \(-0.519715\pi\) | |||||||
\(182\) | −0.608568 | + | 0.562632i | −0.0451101 | + | 0.0417050i | ||||
\(183\) | −6.96356 | −0.514761 | ||||||||
\(184\) | −0.540971 | + | 4.57868i | −0.0398809 | + | 0.337545i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.52719 | − | 1.41191i | 0.111979 | − | 0.103526i | ||||
\(187\) | −18.2938 | + | 18.2938i | −1.33777 | + | 1.33777i | ||||
\(188\) | 0.636183 | − | 8.09762i | 0.0463984 | − | 0.590580i | ||||
\(189\) | −12.7218 | + | 12.7218i | −0.925377 | + | 0.925377i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3304 | 1.25399 | 0.626993 | − | 0.779025i | \(-0.284285\pi\) | ||||
0.626993 | + | 0.779025i | \(0.284285\pi\) | |||||||
\(192\) | 2.88974 | + | 4.71130i | 0.208549 | + | 0.340008i | ||||
\(193\) | 16.8667i | 1.21409i | 0.794667 | + | 0.607045i | \(0.207645\pi\) | ||||
−0.794667 | + | 0.607045i | \(0.792355\pi\) | |||||||
\(194\) | 19.7245 | + | 0.773628i | 1.41614 | + | 0.0555432i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.3765 | − | 2.38650i | −2.16975 | − | 0.170464i | ||||
\(197\) | −3.58908 | + | 3.58908i | −0.255712 | + | 0.255712i | −0.823307 | − | 0.567596i | \(-0.807874\pi\) |
0.567596 | + | 0.823307i | \(0.307874\pi\) | |||||||
\(198\) | 13.4044 | + | 14.4988i | 0.952608 | + | 1.03038i | ||||
\(199\) | − | 6.64501i | − | 0.471052i | −0.971868 | − | 0.235526i | \(-0.924319\pi\) | ||
0.971868 | − | 0.235526i | \(-0.0756813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.32695i | − | 0.516803i | ||||||
\(202\) | 19.6915 | − | 18.2051i | 1.38549 | − | 1.28091i | ||||
\(203\) | −15.3893 | + | 15.3893i | −1.08012 | + | 1.08012i | ||||
\(204\) | 4.91073 | − | 4.19532i | 0.343820 | − | 0.293731i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.762860 | − | 19.4500i | 0.0531510 | − | 1.35514i | ||||
\(207\) | − | 4.11218i | − | 0.285816i | ||||||
\(208\) | −0.292320 | − | 0.402112i | −0.0202687 | − | 0.0278815i | ||||
\(209\) | 14.1867 | 0.981314 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.90906 | − | 1.90906i | 0.131425 | − | 0.131425i | −0.638334 | − | 0.769759i | \(-0.720376\pi\) |
0.769759 | + | 0.638334i | \(0.220376\pi\) | |||||||
\(212\) | −10.8372 | + | 9.25839i | −0.744301 | + | 0.635869i | ||||
\(213\) | 2.21821 | − | 2.21821i | 0.151989 | − | 0.151989i | ||||
\(214\) | 0.445321 | + | 0.481680i | 0.0304415 | + | 0.0329270i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.68282 | − | 8.47355i | −0.454709 | − | 0.576552i | ||||
\(217\) | −10.0379 | −0.681418 | ||||||||
\(218\) | −0.203245 | − | 0.219839i | −0.0137655 | − | 0.0148894i | ||||
\(219\) | −4.05740 | − | 4.05740i | −0.274174 | − | 0.274174i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.410798 | + | 0.410798i | −0.0276333 | + | 0.0276333i | ||||
\(222\) | −0.215416 | + | 5.49226i | −0.0144578 | + | 0.368617i | ||||
\(223\) | 24.1071i | 1.61433i | 0.590326 | + | 0.807165i | \(0.298999\pi\) | ||||
−0.590326 | + | 0.807165i | \(0.701001\pi\) | |||||||
\(224\) | 5.19497 | − | 26.1636i | 0.347103 | − | 1.74813i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.45048 | + | 0.331442i | 0.562118 | + | 0.0220472i | ||||
\(227\) | −6.67411 | − | 6.67411i | −0.442977 | − | 0.442977i | 0.450035 | − | 0.893011i | \(-0.351412\pi\) |
−0.893011 | + | 0.450035i | \(0.851412\pi\) | |||||||
\(228\) | −3.53084 | − | 0.277397i | −0.233835 | − | 0.0183711i | ||||
\(229\) | −16.0807 | − | 16.0807i | −1.06264 | − | 1.06264i | −0.997902 | − | 0.0647388i | \(-0.979379\pi\) |
−0.0647388 | − | 0.997902i | \(-0.520621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0303i | 1.18631i | ||||||||
\(232\) | −8.08406 | − | 10.2503i | −0.530744 | − | 0.672962i | ||||
\(233\) | 16.4976 | 1.08079 | 0.540396 | − | 0.841411i | \(-0.318274\pi\) | ||||
0.540396 | + | 0.841411i | \(0.318274\pi\) | |||||||
\(234\) | 0.301004 | + | 0.325579i | 0.0196772 | + | 0.0212838i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.48833 | − | 11.1063i | −0.617638 | − | 0.722961i | ||||
\(237\) | 5.63342 | + | 5.63342i | 0.365930 | + | 0.365930i | ||||
\(238\) | −31.1478 | − | 1.22167i | −2.01901 | − | 0.0791891i | ||||
\(239\) | −5.25917 | −0.340188 | −0.170094 | − | 0.985428i | \(-0.554407\pi\) | ||||
−0.170094 | + | 0.985428i | \(0.554407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1126 | −0.909075 | −0.454538 | − | 0.890728i | \(-0.650196\pi\) | ||||
−0.454538 | + | 0.890728i | \(0.650196\pi\) | |||||||
\(242\) | 27.7432 | + | 1.08813i | 1.78340 | + | 0.0699479i | ||||
\(243\) | 10.5032 | + | 10.5032i | 0.673782 | + | 0.673782i | ||||
\(244\) | −15.3272 | + | 13.0943i | −0.981222 | + | 0.838275i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.47523 | + | 5.92226i | 0.349088 | + | 0.377589i | ||||
\(247\) | 0.318571 | 0.0202702 | ||||||||
\(248\) | 0.706468 | − | 5.97942i | 0.0448608 | − | 0.379693i | ||||
\(249\) | 1.14234i | 0.0723927i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.98825 | − | 9.98825i | −0.630453 | − | 0.630453i | 0.317729 | − | 0.948182i | \(-0.397080\pi\) |
−0.948182 | + | 0.317729i | \(0.897080\pi\) | |||||||
\(252\) | −1.86339 | + | 23.7181i | −0.117383 | + | 1.49410i | ||||
\(253\) | −6.37943 | − | 6.37943i | −0.401071 | − | 0.401071i | ||||
\(254\) | 3.85890 | + | 0.151353i | 0.242129 | + | 0.00949671i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.2196 | + | 4.93595i | 0.951225 | + | 0.308497i | ||||
\(257\) | 8.44760i | 0.526947i | 0.964667 | + | 0.263474i | \(0.0848682\pi\) | ||||
−0.964667 | + | 0.263474i | \(0.915132\pi\) | |||||||
\(258\) | 0.123108 | − | 3.13877i | 0.00766435 | − | 0.195411i | ||||
\(259\) | 18.7577 | − | 18.7577i | 1.16555 | − | 1.16555i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.23315 | + | 8.23315i | 0.509619 | + | 0.509619i | ||||
\(262\) | 1.10457 | + | 1.19475i | 0.0682403 | + | 0.0738118i | ||||
\(263\) | −18.3064 | −1.12882 | −0.564410 | − | 0.825494i | \(-0.690896\pi\) | ||||
−0.564410 | + | 0.825494i | \(0.690896\pi\) | |||||||
\(264\) | −10.7404 | − | 1.26897i | −0.661024 | − | 0.0781000i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.6037 | + | 12.5511i | 0.711472 | + | 0.769560i | ||||
\(267\) | −1.58559 | + | 1.58559i | −0.0970364 | + | 0.0970364i | ||||
\(268\) | −13.7776 | − | 16.1270i | −0.841601 | − | 0.985115i | ||||
\(269\) | −13.5631 | + | 13.5631i | −0.826955 | + | 0.826955i | −0.987094 | − | 0.160140i | \(-0.948806\pi\) |
0.160140 | + | 0.987094i | \(0.448806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.24520 | −0.136386 | −0.0681930 | − | 0.997672i | \(-0.521723\pi\) | ||||
−0.0681930 | + | 0.997672i | \(0.521723\pi\) | |||||||
\(272\) | 2.91991 | − | 18.4683i | 0.177046 | − | 1.11980i | ||||
\(273\) | 0.404882i | 0.0245046i | ||||||||
\(274\) | 0.0110746 | − | 0.282360i | 0.000669044 | − | 0.0170580i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.46300 | + | 1.71247i | 0.0880620 | + | 0.103079i | ||||
\(277\) | 7.28255 | − | 7.28255i | 0.437566 | − | 0.437566i | −0.453626 | − | 0.891192i | \(-0.649870\pi\) |
0.891192 | + | 0.453626i | \(0.149870\pi\) | |||||||
\(278\) | 17.0793 | − | 15.7901i | 1.02435 | − | 0.947030i | ||||
\(279\) | 5.37020i | 0.321506i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.04084i | 0.360367i | 0.983633 | + | 0.180183i | \(0.0576691\pi\) | ||||
−0.983633 | + | 0.180183i | \(0.942331\pi\) | |||||||
\(282\) | −2.69369 | − | 2.91361i | −0.160407 | − | 0.173503i | ||||
\(283\) | 15.1350 | − | 15.1350i | 0.899682 | − | 0.899682i | −0.0957259 | − | 0.995408i | \(-0.530517\pi\) |
0.995408 | + | 0.0957259i | \(0.0305172\pi\) | |||||||
\(284\) | 0.711284 | − | 9.05354i | 0.0422070 | − | 0.537229i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.972049 | + | 0.0381254i | 0.0574785 | + | 0.00225440i | ||||
\(287\) | − | 38.9259i | − | 2.29772i | ||||||
\(288\) | −13.9973 | − | 2.77927i | −0.824800 | − | 0.163770i | ||||
\(289\) | −4.85021 | −0.285306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.81873 | − | 6.81873i | 0.399721 | − | 0.399721i | ||||
\(292\) | −16.5601 | − | 1.30103i | −0.969107 | − | 0.0761371i | ||||
\(293\) | 10.7777 | − | 10.7777i | 0.629637 | − | 0.629637i | −0.318339 | − | 0.947977i | \(-0.603125\pi\) |
0.947977 | + | 0.318339i | \(0.103125\pi\) | |||||||
\(294\) | −10.9298 | + | 10.1048i | −0.637438 | + | 0.589322i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.85351 | + | 12.4939i | 0.572724 | + | 0.726190i | ||||
\(297\) | 21.1172 | 1.22534 | ||||||||
\(298\) | 1.66511 | − | 1.53942i | 0.0964571 | − | 0.0891762i | ||||
\(299\) | −0.143254 | − | 0.143254i | −0.00828459 | − | 0.00828459i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7198 | + | 10.7198i | −0.617881 | + | 0.617881i | ||||
\(302\) | 10.0645 | + | 0.394747i | 0.579148 | + | 0.0227152i | ||||
\(303\) | − | 13.1008i | − | 0.752621i | ||||||
\(304\) | −8.29319 | + | 6.02882i | −0.475647 | + | 0.345776i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.653584 | + | 16.6639i | −0.0373629 | + | 0.952609i | ||||
\(307\) | −7.94378 | − | 7.94378i | −0.453376 | − | 0.453376i | 0.443098 | − | 0.896473i | \(-0.353880\pi\) |
−0.896473 | + | 0.443098i | \(0.853880\pi\) | |||||||
\(308\) | 33.9042 | + | 39.6858i | 1.93187 | + | 2.26131i | ||||
\(309\) | −6.72382 | − | 6.72382i | −0.382505 | − | 0.382505i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.1649i | − | 1.76720i | −0.468244 | − | 0.883599i | \(-0.655113\pi\) | ||
0.468244 | − | 0.883599i | \(-0.344887\pi\) | |||||||
\(312\) | −0.241182 | − | 0.0284956i | −0.0136542 | − | 0.00161325i | ||||
\(313\) | −5.35842 | −0.302876 | −0.151438 | − | 0.988467i | \(-0.548390\pi\) | ||||
−0.151438 | + | 0.988467i | \(0.548390\pi\) | |||||||
\(314\) | 7.81482 | − | 7.22494i | 0.441016 | − | 0.407727i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.9925 | + | 1.80639i | 1.29343 | + | 0.101617i | ||||
\(317\) | 8.88165 | + | 8.88165i | 0.498843 | + | 0.498843i | 0.911078 | − | 0.412235i | \(-0.135252\pi\) |
−0.412235 | + | 0.911078i | \(0.635252\pi\) | |||||||
\(318\) | −0.272893 | + | 6.95771i | −0.0153031 | + | 0.390169i | ||||
\(319\) | 25.5450 | 1.43025 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.320463 | 0.0178865 | ||||||||
\(322\) | 0.426022 | − | 10.8619i | 0.0237413 | − | 0.605310i | ||||
\(323\) | 8.47233 | + | 8.47233i | 0.471413 | + | 0.471413i | ||||
\(324\) | 9.83400 | + | 0.772600i | 0.546333 | + | 0.0429222i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.0646 | + | 16.7011i | −1.00051 | + | 0.924987i | ||||
\(327\) | −0.146260 | −0.00808817 | ||||||||
\(328\) | 23.1875 | + | 2.73960i | 1.28032 | + | 0.151269i | ||||
\(329\) | 19.1506i | 1.05581i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.07281 | + | 6.07281i | 0.333792 | + | 0.333792i | 0.854025 | − | 0.520233i | \(-0.174155\pi\) |
−0.520233 | + | 0.854025i | \(0.674155\pi\) | |||||||
\(332\) | 2.14805 | + | 2.51435i | 0.117890 | + | 0.137993i | ||||
\(333\) | −10.0352 | − | 10.0352i | −0.549928 | − | 0.549928i | ||||
\(334\) | 0.546947 | − | 13.9450i | 0.0299276 | − | 0.763038i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.66222 | − | 10.5401i | −0.418008 | − | 0.575009i | ||||
\(337\) | 22.0227i | 1.19965i | 0.800130 | + | 0.599827i | \(0.204764\pi\) | ||||
−0.800130 | + | 0.599827i | \(0.795236\pi\) | |||||||
\(338\) | −18.3488 | − | 0.719672i | −0.998044 | − | 0.0391450i | ||||
\(339\) | 2.92132 | − | 2.92132i | 0.158664 | − | 0.158664i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.33106 | + | 8.33106i | 0.451152 | + | 0.451152i | ||||
\(342\) | 6.71477 | − | 6.20792i | 0.363093 | − | 0.335686i | ||||
\(343\) | 38.8315 | 2.09670 | ||||||||
\(344\) | −5.63117 | − | 7.14009i | −0.303612 | − | 0.384968i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.6917 | + | 18.2053i | −1.05863 | + | 0.978722i | ||||
\(347\) | 11.8920 | − | 11.8920i | 0.638395 | − | 0.638395i | −0.311765 | − | 0.950159i | \(-0.600920\pi\) |
0.950159 | + | 0.311765i | \(0.100920\pi\) | |||||||
\(348\) | −6.35773 | − | 0.499490i | −0.340810 | − | 0.0267755i | ||||
\(349\) | 8.65696 | − | 8.65696i | 0.463396 | − | 0.463396i | −0.436371 | − | 0.899767i | \(-0.643736\pi\) |
0.899767 | + | 0.436371i | \(0.143736\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.474200 | 0.0253109 | ||||||||
\(352\) | −26.0263 | + | 17.4031i | −1.38721 | + | 0.927589i | ||||
\(353\) | − | 26.6153i | − | 1.41659i | −0.705916 | − | 0.708296i | \(-0.749464\pi\) | ||
0.705916 | − | 0.708296i | \(-0.250536\pi\) | |||||||
\(354\) | −7.13051 | − | 0.279671i | −0.378983 | − | 0.0148643i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.508429 | + | 6.47151i | −0.0269467 | + | 0.342989i | ||||
\(357\) | −10.7678 | + | 10.7678i | −0.569890 | + | 0.569890i | ||||
\(358\) | 0.569674 | + | 0.616185i | 0.0301082 | + | 0.0325664i | ||||
\(359\) | 4.85032i | 0.255990i | 0.991775 | + | 0.127995i | \(0.0408542\pi\) | ||||
−0.991775 | + | 0.127995i | \(0.959146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4298i | 0.654199i | ||||||||
\(362\) | −20.9424 | + | 19.3616i | −1.10071 | + | 1.01762i | ||||
\(363\) | 9.59078 | − | 9.59078i | 0.503385 | − | 0.503385i | ||||
\(364\) | 0.761340 | + | 0.891168i | 0.0399051 | + | 0.0467099i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.385957 | + | 9.84039i | −0.0201743 | + | 0.514365i | ||||
\(367\) | 15.6741i | 0.818182i | 0.912494 | + | 0.409091i | \(0.134154\pi\) | ||||
−0.912494 | + | 0.409091i | \(0.865846\pi\) | |||||||
\(368\) | 6.44027 | + | 1.01823i | 0.335722 | + | 0.0530792i | ||||
\(369\) | −20.8250 | −1.08411 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.7627 | − | 23.7627i | 1.23370 | − | 1.23370i | ||||
\(372\) | −1.91057 | − | 2.23637i | −0.0990582 | − | 0.115950i | ||||
\(373\) | −5.44481 | + | 5.44481i | −0.281922 | + | 0.281922i | −0.833875 | − | 0.551953i | \(-0.813883\pi\) |
0.551953 | + | 0.833875i | \(0.313883\pi\) | |||||||
\(374\) | 24.8375 | + | 26.8654i | 1.28432 | + | 1.38918i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.4077 | − | 1.34782i | −0.588308 | − | 0.0695085i | ||||
\(377\) | 0.573629 | 0.0295434 | ||||||||
\(378\) | 17.2724 | + | 18.6827i | 0.888399 | + | 0.960933i | ||||
\(379\) | 17.4103 | + | 17.4103i | 0.894309 | + | 0.894309i | 0.994925 | − | 0.100616i | \(-0.0320814\pi\) |
−0.100616 | + | 0.994925i | \(0.532081\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.33402 | − | 1.33402i | 0.0683438 | − | 0.0683438i | ||||
\(382\) | 0.960543 | − | 24.4901i | 0.0491457 | − | 1.25302i | ||||
\(383\) | − | 9.04928i | − | 0.462396i | −0.972907 | − | 0.231198i | \(-0.925735\pi\) | ||
0.972907 | − | 0.231198i | \(-0.0742646\pi\) | |||||||
\(384\) | 6.81782 | − | 3.82245i | 0.347921 | − | 0.195064i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.8348 | + | 0.934839i | 1.21316 | + | 0.0475821i | ||||
\(387\) | 5.73503 | + | 5.73503i | 0.291528 | + | 0.291528i | ||||
\(388\) | 2.18647 | − | 27.8303i | 0.111001 | − | 1.41287i | ||||
\(389\) | 15.3617 | + | 15.3617i | 0.778871 | + | 0.778871i | 0.979639 | − | 0.200768i | \(-0.0643437\pi\) |
−0.200768 | + | 0.979639i | \(0.564344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.61962i | − | 0.385341i | ||||||
\(392\) | −5.05605 | + | 42.7935i | −0.255369 | + | 2.16140i | ||||
\(393\) | 0.794869 | 0.0400959 | ||||||||
\(394\) | 4.87291 | + | 5.27076i | 0.245493 | + | 0.265537i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 21.2316 | − | 18.1385i | 1.06693 | − | 0.911494i | ||||
\(397\) | 9.44519 | + | 9.44519i | 0.474041 | + | 0.474041i | 0.903220 | − | 0.429179i | \(-0.141197\pi\) |
−0.429179 | + | 0.903220i | \(0.641197\pi\) | |||||||
\(398\) | −9.39024 | − | 0.368301i | −0.470690 | − | 0.0184613i | ||||
\(399\) | 8.35031 | 0.418038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.5765 | −1.07748 | −0.538739 | − | 0.842473i | \(-0.681099\pi\) | ||||
−0.538739 | + | 0.842473i | \(0.681099\pi\) | |||||||
\(402\) | −10.3539 | − | 0.406098i | −0.516406 | − | 0.0202543i | ||||
\(403\) | 0.187079 | + | 0.187079i | 0.00931907 | + | 0.00931907i | ||||
\(404\) | −24.6347 | − | 28.8356i | −1.22562 | − | 1.43462i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.8941 | + | 22.6000i | 1.03696 | + | 1.12162i | ||||
\(407\) | −31.1363 | −1.54337 | ||||||||
\(408\) | −5.65635 | − | 7.17202i | −0.280031 | − | 0.355068i | ||||
\(409\) | 4.17336i | 0.206359i | 0.994663 | + | 0.103180i | \(0.0329017\pi\) | ||||
−0.994663 | + | 0.103180i | \(0.967098\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0976116 | − | 0.0976116i | −0.00481482 | − | 0.00481482i | ||||
\(412\) | −27.4430 | − | 2.15604i | −1.35202 | − | 0.106220i | ||||
\(413\) | 24.3529 | + | 24.3529i | 1.19833 | + | 1.19833i | ||||
\(414\) | −5.81103 | − | 0.227918i | −0.285597 | − | 0.0112016i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.584438 | + | 0.390798i | −0.0286544 | + | 0.0191604i | ||||
\(417\) | − | 11.3629i | − | 0.556445i | ||||||
\(418\) | 0.786300 | − | 20.0476i | 0.0384592 | − | 0.980560i | ||||
\(419\) | −27.1191 | + | 27.1191i | −1.32485 | + | 1.32485i | −0.415060 | + | 0.909794i | \(0.636239\pi\) |
−0.909794 | + | 0.415060i | \(0.863761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.9594 | − | 26.9594i | −1.31392 | − | 1.31392i | −0.918500 | − | 0.395421i | \(-0.870599\pi\) |
−0.395421 | − | 0.918500i | \(-0.629401\pi\) | |||||||
\(422\) | −2.59193 | − | 2.80355i | −0.126173 | − | 0.136475i | ||||
\(423\) | 10.2454 | 0.498150 | ||||||||
\(424\) | 12.4826 | + | 15.8275i | 0.606210 | + | 0.768650i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.01167 | − | 3.25756i | −0.145916 | − | 0.157829i | ||||
\(427\) | 33.6079 | − | 33.6079i | 1.62640 | − | 1.62640i | ||||
\(428\) | 0.705357 | − | 0.602598i | 0.0340947 | − | 0.0291277i | ||||
\(429\) | 0.336036 | − | 0.336036i | 0.0162240 | − | 0.0162240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.4059 | −1.07925 | −0.539626 | − | 0.841905i | \(-0.681434\pi\) | ||||
−0.539626 | + | 0.841905i | \(0.681434\pi\) | |||||||
\(432\) | −12.3446 | + | 8.97403i | −0.593930 | + | 0.431763i | ||||
\(433\) | − | 16.8061i | − | 0.807649i | −0.914837 | − | 0.403824i | \(-0.867681\pi\) | ||
0.914837 | − | 0.403824i | \(-0.132319\pi\) | |||||||
\(434\) | −0.556353 | + | 14.1848i | −0.0267058 | + | 0.680894i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.321925 | + | 0.275026i | −0.0154174 | + | 0.0131714i | ||||
\(437\) | −2.95448 | + | 2.95448i | −0.141332 | + | 0.141332i | ||||
\(438\) | −5.95851 | + | 5.50874i | −0.284708 | + | 0.263218i | ||||
\(439\) | − | 9.08322i | − | 0.433519i | −0.976225 | − | 0.216759i | \(-0.930451\pi\) | ||
0.976225 | − | 0.216759i | \(-0.0695487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 38.4335i | − | 1.83017i | ||||||
\(442\) | 0.557742 | + | 0.603279i | 0.0265291 | + | 0.0286951i | ||||
\(443\) | −12.5397 | + | 12.5397i | −0.595781 | + | 0.595781i | −0.939187 | − | 0.343406i | \(-0.888419\pi\) |
0.343406 | + | 0.939187i | \(0.388419\pi\) | |||||||
\(444\) | 7.74933 | + | 0.608820i | 0.367767 | + | 0.0288933i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 34.0664 | + | 1.33614i | 1.61309 | + | 0.0632681i | ||||
\(447\) | − | 1.10780i | − | 0.0523972i | ||||||
\(448\) | −36.6845 | − | 8.79127i | −1.73318 | − | 0.415349i | ||||
\(449\) | −18.0707 | −0.852811 | −0.426406 | − | 0.904532i | \(-0.640220\pi\) | ||||
−0.426406 | + | 0.904532i | \(0.640220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.3069 | + | 32.3069i | −1.52127 | + | 1.52127i | ||||
\(452\) | 0.936740 | − | 11.9232i | 0.0440605 | − | 0.560822i | ||||
\(453\) | 3.47929 | − | 3.47929i | 0.163471 | − | 0.163471i | ||||
\(454\) | −9.80129 | + | 9.06146i | −0.459997 | + | 0.425275i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.587695 | + | 4.97415i | −0.0275213 | + | 0.232936i | ||||
\(457\) | 18.6637 | 0.873052 | 0.436526 | − | 0.899692i | \(-0.356209\pi\) | ||||
0.436526 | + | 0.899692i | \(0.356209\pi\) | |||||||
\(458\) | −23.6153 | + | 21.8328i | −1.10347 | + | 1.02018i | ||||
\(459\) | 12.6113 | + | 12.6113i | 0.588643 | + | 0.588643i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.831229 | + | 0.831229i | −0.0387142 | + | 0.0387142i | −0.726199 | − | 0.687485i | \(-0.758715\pi\) |
0.687485 | + | 0.726199i | \(0.258715\pi\) | |||||||
\(462\) | 25.4791 | + | 0.999335i | 1.18540 | + | 0.0464933i | ||||
\(463\) | 7.82533i | 0.363674i | 0.983329 | + | 0.181837i | \(0.0582043\pi\) | ||||
−0.983329 | + | 0.181837i | \(0.941796\pi\) | |||||||
\(464\) | −14.9330 | + | 10.8557i | −0.693246 | + | 0.503962i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.914382 | − | 23.3132i | 0.0423579 | − | 1.07996i | ||||
\(467\) | −8.75068 | − | 8.75068i | −0.404933 | − | 0.404933i | 0.475034 | − | 0.879967i | \(-0.342436\pi\) |
−0.879967 | + | 0.475034i | \(0.842436\pi\) | |||||||
\(468\) | 0.476768 | − | 0.407311i | 0.0220386 | − | 0.0188280i | ||||
\(469\) | 35.3617 | + | 35.3617i | 1.63285 | + | 1.63285i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.19922i | − | 0.239568i | ||||||
\(472\) | −16.2206 | + | 12.7926i | −0.746612 | + | 0.588829i | ||||
\(473\) | 17.7941 | 0.818172 | ||||||||
\(474\) | 8.27297 | − | 7.64850i | 0.379990 | − | 0.351307i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.45275 | + | 43.9481i | −0.158257 | + | 2.01436i | ||||
\(477\) | −12.7129 | − | 12.7129i | −0.582082 | − | 0.582082i | ||||
\(478\) | −0.291491 | + | 7.43188i | −0.0133325 | + | 0.339926i | ||||
\(479\) | −2.10417 | −0.0961421 | −0.0480710 | − | 0.998844i | \(-0.515307\pi\) | ||||
−0.0480710 | + | 0.998844i | \(0.515307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.699186 | −0.0318801 | ||||||||
\(482\) | −0.782196 | + | 19.9430i | −0.0356281 | + | 0.908377i | ||||
\(483\) | −3.75494 | − | 3.75494i | −0.170856 | − | 0.170856i | ||||
\(484\) | 3.07534 | − | 39.1443i | 0.139788 | − | 1.77929i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.4245 | − | 14.2602i | 0.699671 | − | 0.646858i | ||||
\(487\) | 4.87183 | 0.220764 | 0.110382 | − | 0.993889i | \(-0.464793\pi\) | ||||
0.110382 | + | 0.993889i | \(0.464793\pi\) | |||||||
\(488\) | 17.6544 | + | 22.3850i | 0.799175 | + | 1.01332i | ||||
\(489\) | 12.0185i | 0.543494i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.3582 | + | 14.3582i | 0.647975 | + | 0.647975i | 0.952503 | − | 0.304528i | \(-0.0984987\pi\) |
−0.304528 | + | 0.952503i | \(0.598499\pi\) | |||||||
\(492\) | 8.67237 | − | 7.40895i | 0.390981 | − | 0.334021i | ||||
\(493\) | 15.2555 | + | 15.2555i | 0.687075 | + | 0.687075i | ||||
\(494\) | 0.0176569 | − | 0.450181i | 0.000794419 | − | 0.0202546i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.41052 | − | 1.32974i | −0.377644 | − | 0.0597071i | ||||
\(497\) | 21.4113i | 0.960429i | ||||||||
\(498\) | 1.61427 | + | 0.0633143i | 0.0723370 | + | 0.00283718i | ||||
\(499\) | 25.1060 | − | 25.1060i | 1.12390 | − | 1.12390i | 0.132748 | − | 0.991150i | \(-0.457620\pi\) |
0.991150 | − | 0.132748i | \(-0.0423801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.82077 | − | 4.82077i | −0.215376 | − | 0.215376i | ||||
\(502\) | −14.6683 | + | 13.5611i | −0.654677 | + | 0.605260i | ||||
\(503\) | −18.8868 | −0.842120 | −0.421060 | − | 0.907033i | \(-0.638342\pi\) | ||||
−0.421060 | + | 0.907033i | \(0.638342\pi\) | |||||||
\(504\) | 33.4133 | + | 3.94778i | 1.48835 | + | 0.175848i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.36852 | + | 8.66136i | −0.416482 | + | 0.385044i | ||||
\(507\) | −6.34316 | + | 6.34316i | −0.281710 | + | 0.281710i | ||||
\(508\) | 0.427761 | − | 5.44473i | 0.0189788 | − | 0.241571i | ||||
\(509\) | 22.9756 | − | 22.9756i | 1.01837 | − | 1.01837i | 0.0185459 | − | 0.999828i | \(-0.494096\pi\) |
0.999828 | − | 0.0185459i | \(-0.00590369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.1641 | 1.73252 | ||||||||
\(512\) | 7.81868 | − | 21.2337i | 0.345540 | − | 0.938404i | ||||
\(513\) | − | 9.77993i | − | 0.431794i | ||||||
\(514\) | 11.9375 | + | 0.468210i | 0.526542 | + | 0.0206519i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.42865 | − | 0.347933i | −0.194961 | − | 0.0153169i | ||||
\(517\) | 15.8942 | − | 15.8942i | 0.699028 | − | 0.699028i | ||||
\(518\) | −25.4674 | − | 27.5467i | −1.11897 | − | 1.21033i | ||||
\(519\) | 13.1009i | 0.575066i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2089i | 0.885367i | 0.896678 | + | 0.442683i | \(0.145973\pi\) | ||||
−0.896678 | + | 0.442683i | \(0.854027\pi\) | |||||||
\(522\) | 12.0908 | − | 11.1782i | 0.529201 | − | 0.489255i | ||||
\(523\) | 3.93445 | − | 3.93445i | 0.172042 | − | 0.172042i | −0.615834 | − | 0.787876i | \(-0.711181\pi\) |
0.787876 | + | 0.615834i | \(0.211181\pi\) | |||||||
\(524\) | 1.74955 | − | 1.49467i | 0.0764295 | − | 0.0652951i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.01464 | + | 25.8693i | −0.0442402 | + | 1.12795i | ||||
\(527\) | 9.95066i | 0.433458i | ||||||||
\(528\) | −2.38851 | + | 15.1072i | −0.103947 | + | 0.657456i | ||||
\(529\) | −20.3429 | −0.884473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.0286 | − | 13.0286i | 0.565393 | − | 0.565393i | ||||
\(532\) | 18.3795 | − | 15.7019i | 0.796853 | − | 0.680765i | ||||
\(533\) | −0.725471 | + | 0.725471i | −0.0314237 | + | 0.0314237i | ||||
\(534\) | 2.15276 | + | 2.32852i | 0.0931589 | + | 0.100765i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −23.5532 | + | 18.5757i | −1.01734 | + | 0.802346i | ||||
\(537\) | 0.409950 | 0.0176906 | ||||||||
\(538\) | 18.4146 | + | 19.9181i | 0.793910 | + | 0.858729i | ||||
\(539\) | −59.6238 | − | 59.6238i | −2.56818 | − | 2.56818i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.17895 | + | 3.17895i | −0.136674 | + | 0.136674i | −0.772134 | − | 0.635460i | \(-0.780811\pi\) |
0.635460 | + | 0.772134i | \(0.280811\pi\) | |||||||
\(542\) | −0.124440 | + | 3.17275i | −0.00534518 | + | 0.136281i | ||||
\(543\) | 13.9330i | 0.597923i | ||||||||
\(544\) | −25.9362 | − | 5.14982i | −1.11201 | − | 0.220797i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.572150 | + | 0.0224407i | 0.0244857 | + | 0.000960372i | ||||
\(547\) | 1.32918 | + | 1.32918i | 0.0568317 | + | 0.0568317i | 0.734951 | − | 0.678120i | \(-0.237205\pi\) |
−0.678120 | + | 0.734951i | \(0.737205\pi\) | |||||||
\(548\) | −0.398397 | − | 0.0312998i | −0.0170187 | − | 0.00133706i | ||||
\(549\) | −17.9800 | − | 17.9800i | −0.767366 | − | 0.767366i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.8306i | − | 0.503998i | ||||||
\(552\) | 2.50103 | − | 1.97249i | 0.106451 | − | 0.0839545i | ||||
\(553\) | −54.3766 | −2.31233 | ||||||||
\(554\) | −9.88754 | − | 10.6948i | −0.420081 | − | 0.454379i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.3669 | − | 25.0105i | −0.906157 | − | 1.06068i | ||||
\(557\) | 24.9082 | + | 24.9082i | 1.05539 | + | 1.05539i | 0.998373 | + | 0.0570196i | \(0.0181598\pi\) |
0.0570196 | + | 0.998373i | \(0.481840\pi\) | |||||||
\(558\) | 7.58878 | + | 0.297645i | 0.321259 | + | 0.0126003i | ||||
\(559\) | 0.399576 | 0.0169003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.8736 | 0.754625 | ||||||||
\(562\) | 8.53648 | + | 0.334815i | 0.360090 | + | 0.0141233i | ||||
\(563\) | −3.80804 | − | 3.80804i | −0.160490 | − | 0.160490i | 0.622294 | − | 0.782784i | \(-0.286201\pi\) |
−0.782784 | + | 0.622294i | \(0.786201\pi\) | |||||||
\(564\) | −4.26660 | + | 3.64503i | −0.179656 | + | 0.153484i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.5488 | − | 22.2265i | −0.863731 | − | 0.934251i | ||||
\(567\) | −23.2571 | −0.976706 | ||||||||
\(568\) | −12.7544 | − | 1.50693i | −0.535162 | − | 0.0632293i | ||||
\(569\) | 8.43971i | 0.353811i | 0.984228 | + | 0.176905i | \(0.0566087\pi\) | ||||
−0.984228 | + | 0.176905i | \(0.943391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2821 | − | 21.2821i | −0.890629 | − | 0.890629i | 0.103953 | − | 0.994582i | \(-0.466851\pi\) |
−0.994582 | + | 0.103953i | \(0.966851\pi\) | |||||||
\(572\) | 0.107752 | − | 1.37152i | 0.00450534 | − | 0.0573460i | ||||
\(573\) | −8.46619 | − | 8.46619i | −0.353680 | − | 0.353680i | ||||
\(574\) | −55.0072 | − | 2.15747i | −2.29596 | − | 0.0900512i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.70326 | + | 19.6259i | −0.195969 | + | 0.817748i | ||||
\(577\) | − | 36.3491i | − | 1.51323i | −0.653860 | − | 0.756615i | \(-0.726852\pi\) | ||
0.653860 | − | 0.756615i | \(-0.273148\pi\) | |||||||
\(578\) | −0.268824 | + | 6.85396i | −0.0111816 | + | 0.285087i | ||||
\(579\) | 8.23964 | − | 8.23964i | 0.342428 | − | 0.342428i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.51321 | − | 5.51321i | −0.228726 | − | 0.228726i | ||||
\(582\) | −9.25780 | − | 10.0137i | −0.383748 | − | 0.415080i | ||||
\(583\) | −39.4442 | −1.63361 | ||||||||
\(584\) | −2.75637 | + | 23.3294i | −0.114059 | + | 0.965379i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6328 | − | 15.8275i | −0.604477 | − | 0.653830i | ||||
\(587\) | 6.55994 | − | 6.55994i | 0.270758 | − | 0.270758i | −0.558647 | − | 0.829405i | \(-0.688679\pi\) |
0.829405 | + | 0.558647i | \(0.188679\pi\) | |||||||
\(588\) | 13.6735 | + | 16.0052i | 0.563887 | + | 0.660044i | ||||
\(589\) | 3.85833 | − | 3.85833i | 0.158980 | − | 0.158980i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.50665 | 0.144244 | ||||||||
\(592\) | 18.2015 | − | 13.2318i | 0.748078 | − | 0.543823i | ||||
\(593\) | 1.40974i | 0.0578911i | 0.999581 | + | 0.0289455i | \(0.00921494\pi\) | ||||
−0.999581 | + | 0.0289455i | \(0.990785\pi\) | |||||||
\(594\) | 1.17043 | − | 29.8413i | 0.0480231 | − | 1.22440i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.08311 | − | 2.43833i | −0.0853274 | − | 0.0998779i | ||||
\(597\) | −3.24619 | + | 3.24619i | −0.132858 | + | 0.132858i | ||||
\(598\) | −0.210376 | + | 0.194496i | −0.00860291 | + | 0.00795354i | ||||
\(599\) | 23.3593i | 0.954435i | 0.878785 | + | 0.477218i | \(0.158355\pi\) | ||||
−0.878785 | + | 0.477218i | \(0.841645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.4138i | − | 0.832695i | −0.909206 | − | 0.416347i | \(-0.863310\pi\) | ||
0.909206 | − | 0.416347i | \(-0.136690\pi\) | |||||||
\(602\) | 14.5543 | + | 15.7426i | 0.593190 | + | 0.641622i | ||||
\(603\) | 18.9183 | − | 18.9183i | 0.770411 | − | 0.770411i | ||||
\(604\) | 1.11566 | − | 14.2006i | 0.0453954 | − | 0.577813i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.5131 | − | 0.726115i | −0.752043 | − | 0.0294964i | ||||
\(607\) | 0.758240i | 0.0307760i | 0.999882 | + | 0.0153880i | \(0.00489835\pi\) | ||||
−0.999882 | + | 0.0153880i | \(0.995102\pi\) | |||||||
\(608\) | 8.05983 | + | 12.0535i | 0.326869 | + | 0.488833i | ||||
\(609\) | 15.0358 | 0.609283 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.356915 | − | 0.356915i | 0.0144392 | − | 0.0144392i | ||||
\(612\) | 23.5119 | + | 1.84719i | 0.950413 | + | 0.0746684i | ||||
\(613\) | 12.0341 | − | 12.0341i | 0.486052 | − | 0.486052i | −0.421006 | − | 0.907058i | \(-0.638323\pi\) |
0.907058 | + | 0.421006i | \(0.138323\pi\) | |||||||
\(614\) | −11.6659 | + | 10.7853i | −0.470796 | + | 0.435259i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 57.9602 | − | 45.7114i | 2.33528 | − | 1.84176i | ||||
\(617\) | −32.6899 | −1.31605 | −0.658023 | − | 0.752998i | \(-0.728607\pi\) | ||||
−0.658023 | + | 0.752998i | \(0.728607\pi\) | |||||||
\(618\) | −9.87428 | + | 9.12894i | −0.397202 | + | 0.367220i | ||||
\(619\) | −26.3836 | − | 26.3836i | −1.06045 | − | 1.06045i | −0.998052 | − | 0.0623934i | \(-0.980127\pi\) |
−0.0623934 | − | 0.998052i | \(-0.519873\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.39781 | + | 4.39781i | −0.176478 | + | 0.176478i | ||||
\(622\) | −44.0399 | − | 1.72732i | −1.76584 | − | 0.0692592i | ||||
\(623\) | − | 15.3049i | − | 0.613178i | ||||||
\(624\) | −0.0536355 | + | 0.339241i | −0.00214714 | + | 0.0135805i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.296991 | + | 7.57213i | −0.0118702 | + | 0.302643i | ||||
\(627\) | −6.93042 | − | 6.93042i | −0.276774 | − | 0.276774i | ||||
\(628\) | −9.77662 | − | 11.4438i | −0.390130 | − | 0.456657i | ||||
\(629\) | −18.5947 | − | 18.5947i | −0.741420 | − | 0.741420i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.08765i | − | 0.242345i | −0.992631 | − | 0.121173i | \(-0.961335\pi\) | ||
0.992631 | − | 0.121173i | \(-0.0386655\pi\) | |||||||
\(632\) | 3.82703 | − | 32.3913i | 0.152231 | − | 1.28846i | ||||
\(633\) | −1.86521 | −0.0741354 | ||||||||
\(634\) | 13.0432 | − | 12.0586i | 0.518010 | − | 0.478909i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.81701 | + | 0.771266i | 0.389270 | + | 0.0305827i | ||||
\(637\) | −1.33889 | − | 1.33889i | −0.0530487 | − | 0.0530487i | ||||
\(638\) | 1.41584 | − | 36.0983i | 0.0560535 | − | 1.42915i | ||||
\(639\) | 11.4549 | 0.453149 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1680 | 0.441111 | 0.220555 | − | 0.975374i | \(-0.429213\pi\) | ||||
0.220555 | + | 0.975374i | \(0.429213\pi\) | |||||||
\(642\) | 0.0177617 | − | 0.452855i | 0.000700999 | − | 0.0178728i | ||||
\(643\) | 21.9585 | + | 21.9585i | 0.865957 | + | 0.865957i | 0.992022 | − | 0.126065i | \(-0.0402348\pi\) |
−0.126065 | + | 0.992022i | \(0.540235\pi\) | |||||||
\(644\) | −15.3256 | − | 1.20405i | −0.603914 | − | 0.0474460i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.4421 | − | 11.5029i | 0.489526 | − | 0.452575i | ||||
\(647\) | 36.9848 | 1.45402 | 0.727011 | − | 0.686625i | \(-0.240909\pi\) | ||||
0.727011 | + | 0.686625i | \(0.240909\pi\) | |||||||
\(648\) | 1.63683 | − | 13.8539i | 0.0643009 | − | 0.544231i | ||||
\(649\) | − | 40.4238i | − | 1.58677i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.90368 | + | 4.90368i | 0.192190 | + | 0.192190i | ||||
\(652\) | 22.5995 | + | 26.4533i | 0.885065 | + | 1.03599i | ||||
\(653\) | 18.4157 | + | 18.4157i | 0.720663 | + | 0.720663i | 0.968740 | − | 0.248077i | \(-0.0797986\pi\) |
−0.248077 | + | 0.968740i | \(0.579799\pi\) | |||||||
\(654\) | −0.00810646 | + | 0.206683i | −0.000316988 | + | 0.00808196i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.15658 | − | 32.6150i | 0.201331 | − | 1.27340i | ||||
\(657\) | − | 20.9525i | − | 0.817435i | ||||||
\(658\) | 27.0622 | + | 1.06143i | 1.05500 | + | 0.0413787i | ||||
\(659\) | 15.5421 | − | 15.5421i | 0.605434 | − | 0.605434i | −0.336316 | − | 0.941749i | \(-0.609181\pi\) |
0.941749 | + | 0.336316i | \(0.109181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.6677 | + | 29.6677i | 1.15394 | + | 1.15394i | 0.985755 | + | 0.168185i | \(0.0537906\pi\) |
0.168185 | + | 0.985755i | \(0.446209\pi\) | |||||||
\(662\) | 8.91825 | − | 8.24507i | 0.346617 | − | 0.320454i | ||||
\(663\) | 0.401363 | 0.0155877 | ||||||||
\(664\) | 3.67215 | − | 2.89611i | 0.142507 | − | 0.112391i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.7373 | + | 13.6249i | −0.571058 | + | 0.527953i | ||||
\(667\) | −5.31992 | + | 5.31992i | −0.205988 | + | 0.205988i | ||||
\(668\) | −19.6758 | − | 1.54581i | −0.761278 | − | 0.0598092i | ||||
\(669\) | 11.7767 | − | 11.7767i | 0.455313 | − | 0.455313i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −55.7864 | −2.15361 | ||||||||
\(672\) | −15.3192 | + | 10.2435i | −0.590949 | + | 0.395152i | ||||
\(673\) | 29.2198i | 1.12634i | 0.826340 | + | 0.563171i | \(0.190419\pi\) | ||||
−0.826340 | + | 0.563171i | \(0.809581\pi\) | |||||||
\(674\) | 31.1209 | + | 1.22061i | 1.19873 | + | 0.0470163i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.03397 | + | 25.8893i | −0.0782298 | + | 0.995743i | ||||
\(677\) | −17.2591 | + | 17.2591i | −0.663320 | + | 0.663320i | −0.956161 | − | 0.292841i | \(-0.905399\pi\) |
0.292841 | + | 0.956161i | \(0.405399\pi\) | |||||||
\(678\) | −3.96628 | − | 4.29011i | −0.152324 | − | 0.164761i | ||||
\(679\) | 65.8179i | 2.52586i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.52082i | 0.249878i | ||||||||
\(682\) | 12.2346 | − | 11.3111i | 0.468487 | − | 0.433124i | ||||
\(683\) | 1.10407 | − | 1.10407i | 0.0422459 | − | 0.0422459i | −0.685668 | − | 0.727914i | \(-0.740490\pi\) |
0.727914 | + | 0.685668i | \(0.240490\pi\) | |||||||
\(684\) | −8.40041 | − | 9.83289i | −0.321198 | − | 0.375970i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.15224 | − | 54.8738i | 0.0821731 | − | 2.09509i | ||||
\(687\) | 15.7113i | 0.599425i | ||||||||
\(688\) | −10.4020 | + | 7.56181i | −0.396571 | + | 0.288291i | ||||
\(689\) | −0.885743 | −0.0337441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.4233 | + | 28.4233i | −1.08127 | + | 1.08127i | −0.0848830 | + | 0.996391i | \(0.527052\pi\) |
−0.996391 | + | 0.0848830i | \(0.972948\pi\) | |||||||
\(692\) | 24.6350 | + | 28.8359i | 0.936481 | + | 1.09617i | ||||
\(693\) | −46.5545 | + | 46.5545i | −1.76846 | + | 1.76846i | ||||
\(694\) | −16.1458 | − | 17.4640i | −0.612885 | − | 0.662924i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.05822 | + | 8.95660i | −0.0401118 | + | 0.339499i | ||||
\(697\) | −38.5875 | −1.46161 | ||||||||
\(698\) | −11.7536 | − | 12.7132i | −0.444879 | − | 0.481201i | ||||
\(699\) | −8.05933 | − | 8.05933i | −0.304832 | − | 0.304832i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.7991 | + | 23.7991i | −0.898880 | + | 0.898880i | −0.995337 | − | 0.0964573i | \(-0.969249\pi\) |
0.0964573 | + | 0.995337i | \(0.469249\pi\) | |||||||
\(702\) | 0.0262826 | − | 0.670105i | 0.000991974 | − | 0.0252915i | ||||
\(703\) | 14.4200i | 0.543862i | ||||||||
\(704\) | 23.1503 | + | 37.7431i | 0.872510 | + | 1.42250i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −37.6109 | − | 1.47516i | −1.41550 | − | 0.0555184i | ||||
\(707\) | 63.2278 | + | 63.2278i | 2.37793 | + | 2.37793i | ||||
\(708\) | −0.790421 | + | 10.0608i | −0.0297058 | + | 0.378109i | ||||
\(709\) | −1.49921 | − | 1.49921i | −0.0563039 | − | 0.0563039i | 0.678394 | − | 0.734698i | \(-0.262676\pi\) |
−0.734698 | + | 0.678394i | \(0.762676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.0911i | 1.09100i | ||||||||
\(712\) | 9.11688 | + | 1.07716i | 0.341670 | + | 0.0403682i | ||||
\(713\) | −3.47000 | −0.129953 | ||||||||
\(714\) | 14.6194 | + | 15.8130i | 0.547118 | + | 0.591787i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.902323 | − | 0.770870i | 0.0337214 | − | 0.0288088i | ||||
\(717\) | 2.56919 | + | 2.56919i | 0.0959482 | + | 0.0959482i | ||||
\(718\) | 6.85412 | + | 0.268830i | 0.255794 | + | 0.0100327i | ||||
\(719\) | −7.37612 | −0.275083 | −0.137541 | − | 0.990496i | \(-0.543920\pi\) | ||||
−0.137541 | + | 0.990496i | \(0.543920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 64.9017 | 2.41707 | ||||||||
\(722\) | 17.5649 | + | 0.688923i | 0.653696 | + | 0.0256391i | ||||
\(723\) | 6.89425 | + | 6.89425i | 0.256400 | + | 0.256400i | ||||
\(724\) | 26.1996 | + | 30.6673i | 0.973702 | + | 1.13974i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13.0214 | − | 14.0846i | −0.483270 | − | 0.522727i | ||||
\(727\) | −30.1470 | −1.11809 | −0.559045 | − | 0.829137i | \(-0.688832\pi\) | ||||
−0.559045 | + | 0.829137i | \(0.688832\pi\) | |||||||
\(728\) | 1.30153 | − | 1.02648i | 0.0482380 | − | 0.0380438i | ||||
\(729\) | 4.53447i | 0.167943i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.6267 | + | 10.6267i | 0.393041 | + | 0.393041i | ||||
\(732\) | 13.8843 | + | 1.09081i | 0.513180 | + | 0.0403176i | ||||
\(733\) | 1.43297 | + | 1.43297i | 0.0529279 | + | 0.0529279i | 0.733075 | − | 0.680147i | \(-0.238084\pi\) |
−0.680147 | + | 0.733075i | \(0.738084\pi\) | |||||||
\(734\) | 22.1495 | + | 0.868740i | 0.817553 | + | 0.0320658i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.79585 | − | 9.04449i | 0.0661959 | − | 0.333384i | ||||
\(737\) | − | 58.6977i | − | 2.16216i | ||||||
\(738\) | −1.15423 | + | 29.4284i | −0.0424879 | + | 1.08328i | ||||
\(739\) | −31.0001 | + | 31.0001i | −1.14036 | + | 1.14036i | −0.151973 | + | 0.988385i | \(0.548563\pi\) |
−0.988385 | + | 0.151973i | \(0.951437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.155627 | − | 0.155627i | −0.00571710 | − | 0.00571710i | ||||
\(742\) | −32.2626 | − | 34.8968i | −1.18440 | − | 1.28110i | ||||
\(743\) | −38.5395 | −1.41388 | −0.706938 | − | 0.707276i | \(-0.749924\pi\) | ||||
−0.706938 | + | 0.707276i | \(0.749924\pi\) | |||||||
\(744\) | −3.26616 | + | 2.57592i | −0.119743 | + | 0.0944378i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.39243 | + | 7.99599i | 0.270656 | + | 0.292754i | ||||
\(747\) | −2.94952 | + | 2.94952i | −0.107917 | + | 0.107917i | ||||
\(748\) | 39.3408 | − | 33.6096i | 1.43844 | − | 1.22889i | ||||
\(749\) | −1.54664 | + | 1.54664i | −0.0565128 | + | 0.0565128i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.9523 | 0.983503 | 0.491751 | − | 0.870736i | \(-0.336357\pi\) | ||||
0.491751 | + | 0.870736i | \(0.336357\pi\) | |||||||
\(752\) | −2.53692 | + | 16.0458i | −0.0925118 | + | 0.585132i | ||||
\(753\) | 9.75884i | 0.355632i | ||||||||
\(754\) | 0.0317935 | − | 0.810610i | 0.00115785 | − | 0.0295207i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 27.3583 | − | 23.3727i | 0.995012 | − | 0.850056i | ||||
\(757\) | −17.0688 | + | 17.0688i | −0.620377 | + | 0.620377i | −0.945628 | − | 0.325251i | \(-0.894551\pi\) |
0.325251 | + | 0.945628i | \(0.394551\pi\) | |||||||
\(758\) | 25.5680 | − | 23.6380i | 0.928671 | − | 0.858573i | ||||
\(759\) | 6.23290i | 0.226240i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.89608i | − | 0.249983i | −0.992158 | − | 0.124991i | \(-0.960110\pi\) | ||
0.992158 | − | 0.124991i | \(-0.0398903\pi\) | |||||||
\(762\) | −1.81120 | − | 1.95907i | −0.0656128 | − | 0.0709698i | ||||
\(763\) | 0.705886 | − | 0.705886i | 0.0255548 | − | 0.0255548i | ||||
\(764\) | −34.5544 | − | 2.71474i | −1.25013 | − | 0.0982158i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.7878 | − | 0.501558i | −0.462041 | − | 0.0181220i | ||||
\(767\) | − | 0.907741i | − | 0.0327766i | ||||||
\(768\) | −5.02373 | − | 9.84631i | −0.181278 | − | 0.355298i | ||||
\(769\) | −11.8443 | −0.427117 | −0.213558 | − | 0.976930i | \(-0.568505\pi\) | ||||
−0.213558 | + | 0.976930i | \(0.568505\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.12679 | − | 4.12679i | 0.148623 | − | 0.148623i | ||||
\(772\) | 2.64209 | − | 33.6297i | 0.0950910 | − | 1.21036i | ||||
\(773\) | −3.58865 | + | 3.58865i | −0.129075 | + | 0.129075i | −0.768693 | − | 0.639618i | \(-0.779093\pi\) |
0.639618 | + | 0.768693i | \(0.279093\pi\) | |||||||
\(774\) | 8.42219 | − | 7.78646i | 0.302729 | − | 0.279878i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −39.2066 | − | 4.63226i | −1.40744 | − | 0.166288i | ||||
\(777\) | −18.3269 | −0.657474 | ||||||||
\(778\) | 22.5595 | − | 20.8567i | 0.808798 | − | 0.747748i | ||||
\(779\) | 14.9622 | + | 14.9622i | 0.536075 | + | 0.536075i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.7705 | − | 17.7705i | 0.635880 | − | 0.635880i | ||||
\(782\) | −10.7675 | − | 0.422319i | −0.385045 | − | 0.0151021i | ||||
\(783\) | − | 17.6100i | − | 0.629332i | ||||||
\(784\) | 60.1925 | + | 9.51668i | 2.14973 | + | 0.339882i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0440558 | − | 1.12325i | 0.00157142 | − | 0.0400650i | ||||
\(787\) | −22.4800 | − | 22.4800i | −0.801326 | − | 0.801326i | 0.181977 | − | 0.983303i | \(-0.441750\pi\) |
−0.983303 | + | 0.181977i | \(0.941750\pi\) | |||||||
\(788\) | 7.71833 | − | 6.59390i | 0.274954 | − | 0.234898i | ||||
\(789\) | 8.94296 | + | 8.94296i | 0.318378 | + | 0.318378i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.1981i | 1.00261i | ||||||||
\(792\) | −24.4552 | − | 31.0082i | −0.868979 | − | 1.10183i | ||||
\(793\) | −1.25272 | −0.0444853 | ||||||||
\(794\) | 13.8708 | − | 12.8238i | 0.492255 | − | 0.455098i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.04091 | + | 13.2492i | −0.0368941 | + | 0.469605i | ||||
\(797\) | −8.67589 | − | 8.67589i | −0.307316 | − | 0.307316i | 0.536552 | − | 0.843867i | \(-0.319727\pi\) |
−0.843867 | + | 0.536552i | \(0.819727\pi\) | |||||||
\(798\) | 0.462818 | − | 11.8001i | 0.0163836 | − | 0.417717i | ||||
\(799\) | 18.9842 | 0.671612 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.18800 | −0.289309 | ||||||||
\(802\) | −1.19588 | + | 30.4903i | −0.0422280 | + | 1.07665i | ||||
\(803\) | −32.5046 | − | 32.5046i | −1.14706 | − | 1.14706i | ||||
\(804\) | −1.14774 | + | 14.6089i | −0.0404775 | + | 0.515216i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.274735 | − | 0.253998i | 0.00967714 | − | 0.00894668i | ||||
\(807\) | 13.2515 | 0.466476 | ||||||||
\(808\) | −42.1138 | + | 33.2138i | −1.48156 | + | 1.16846i | ||||
\(809\) | 27.9066i | 0.981143i | 0.871401 | + | 0.490571i | \(0.163212\pi\) | ||||
−0.871401 | + | 0.490571i | \(0.836788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.2635 | + | 15.2635i | 0.535974 | + | 0.535974i | 0.922344 | − | 0.386370i | \(-0.126271\pi\) |
−0.386370 | + | 0.922344i | \(0.626271\pi\) | |||||||
\(812\) | 33.0947 | − | 28.2734i | 1.16140 | − | 0.992201i | ||||
\(813\) | 1.09681 | + | 1.09681i | 0.0384670 | + | 0.0384670i | ||||
\(814\) | −1.72574 | + | 43.9996i | −0.0604871 | + | 1.54219i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.4485 | + | 7.59562i | −0.365770 | + | 0.265900i | ||||
\(817\) | − | 8.24089i | − | 0.288312i | ||||||
\(818\) | 5.89749 | + | 0.231309i | 0.206201 | + | 0.00808754i | ||||
\(819\) | −1.04541 | + | 1.04541i | −0.0365295 | + | 0.0365295i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2883 | + | 25.2883i | 0.882567 | + | 0.882567i | 0.993795 | − | 0.111228i | \(-0.0354782\pi\) |
−0.111228 | + | 0.993795i | \(0.535478\pi\) | |||||||
\(822\) | −0.143348 | + | 0.132527i | −0.00499983 | + | 0.00462242i | ||||
\(823\) | −7.12228 | −0.248267 | −0.124133 | − | 0.992266i | \(-0.539615\pi\) | ||||
−0.124133 | + | 0.992266i | \(0.539615\pi\) | |||||||
\(824\) | −4.56778 | + | 38.6609i | −0.159126 | + | 1.34682i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 35.7634 | − | 33.0639i | 1.24437 | − | 1.15044i | ||||
\(827\) | −32.1618 | + | 32.1618i | −1.11837 | + | 1.11837i | −0.126394 | + | 0.991980i | \(0.540340\pi\) |
−0.991980 | + | 0.126394i | \(0.959660\pi\) | |||||||
\(828\) | −0.644155 | + | 8.19909i | −0.0223859 | + | 0.284938i | ||||
\(829\) | 34.9802 | − | 34.9802i | 1.21491 | − | 1.21491i | 0.245522 | − | 0.969391i | \(-0.421041\pi\) |
0.969391 | − | 0.245522i | \(-0.0789594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.11529 | −0.246827 | ||||||||
\(832\) | 0.519854 | + | 0.847545i | 0.0180227 | + | 0.0293833i | ||||
\(833\) | − | 71.2149i | − | 2.46745i | ||||||
\(834\) | −16.0573 | − | 0.629793i | −0.556018 | − | 0.0218079i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28.2862 | − | 2.22228i | −0.978299 | − | 0.0768593i | ||||
\(837\) | 5.74321 | − | 5.74321i | 0.198514 | − | 0.198514i | ||||
\(838\) | 36.8196 | + | 39.8258i | 1.27191 | + | 1.37576i | ||||
\(839\) | − | 11.1147i | − | 0.383721i | −0.981422 | − | 0.191861i | \(-0.938548\pi\) | ||
0.981422 | − | 0.191861i | \(-0.0614521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.69754i | 0.265432i | ||||||||
\(842\) | −39.5913 | + | 36.6028i | −1.36441 | + | 1.26142i | ||||
\(843\) | 2.95105 | − | 2.95105i | 0.101640 | − | 0.101640i | ||||
\(844\) | −4.10543 | + | 3.50734i | −0.141315 | + | 0.120728i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.567855 | − | 14.4781i | 0.0195233 | − | 0.497767i | ||||
\(847\) | 92.5750i | 3.18092i | ||||||||
\(848\) | 23.0581 | − | 16.7623i | 0.791818 | − | 0.575620i | ||||
\(849\) | −14.7874 | −0.507501 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.48436 | − | 6.48436i | 0.222281 | − | 0.222281i | ||||
\(852\) | −4.77027 | + | 4.07532i | −0.163427 | + | 0.139618i | ||||
\(853\) | 28.9107 | − | 28.9107i | 0.989884 | − | 0.989884i | −0.0100656 | − | 0.999949i | \(-0.503204\pi\) |
0.999949 | + | 0.0100656i | \(0.00320402\pi\) | |||||||
\(854\) | −45.6295 | − | 49.3550i | −1.56141 | − | 1.68889i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.812454 | − | 1.03016i | −0.0277691 | − | 0.0352101i | ||||
\(857\) | 34.1485 | 1.16649 | 0.583245 | − | 0.812296i | \(-0.301783\pi\) | ||||
0.583245 | + | 0.812296i | \(0.301783\pi\) | |||||||
\(858\) | −0.456237 | − | 0.493486i | −0.0155757 | − | 0.0168473i | ||||
\(859\) | −20.4589 | − | 20.4589i | −0.698047 | − | 0.698047i | 0.265942 | − | 0.963989i | \(-0.414317\pi\) |
−0.963989 | + | 0.265942i | \(0.914317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.0159 | + | 19.0159i | −0.648060 | + | 0.648060i | ||||
\(862\) | −1.24185 | + | 31.6623i | −0.0422976 | + | 1.07842i | ||||
\(863\) | 35.3591i | 1.20364i | 0.798633 | + | 0.601818i | \(0.205557\pi\) | ||||
−0.798633 | + | 0.601818i | \(0.794443\pi\) | |||||||
\(864\) | 11.9972 | + | 17.9419i | 0.408154 | + | 0.610395i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.7491 | − | 0.931480i | −0.807028 | − | 0.0316530i | ||||
\(867\) | 2.36940 | + | 2.36940i | 0.0804692 | + | 0.0804692i | ||||
\(868\) | 20.0141 | + | 1.57240i | 0.679324 | + | 0.0533706i | ||||
\(869\) | 45.1304 | + | 45.1304i | 1.53094 | + | 1.53094i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.31809i | − | 0.0446618i | ||||||
\(872\) | 0.370804 | + | 0.470165i | 0.0125570 | + | 0.0159218i | ||||
\(873\) | 35.2120 | 1.19175 | ||||||||
\(874\) | 4.01130 | + | 4.33880i | 0.135684 | + | 0.146762i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.45430 | + | 8.72545i | 0.251857 | + | 0.294806i | ||||
\(877\) | −3.15415 | − | 3.15415i | −0.106508 | − | 0.106508i | 0.651845 | − | 0.758353i | \(-0.273995\pi\) |
−0.758353 | + | 0.651845i | \(0.773995\pi\) | |||||||
\(878\) | −12.8358 | − | 0.503440i | −0.433186 | − | 0.0169903i | ||||
\(879\) | −10.5301 | −0.355172 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.3066 | 0.684146 | 0.342073 | − | 0.939673i | \(-0.388871\pi\) | ||||
0.342073 | + | 0.939673i | \(0.388871\pi\) | |||||||
\(882\) | −54.3114 | − | 2.13018i | −1.82876 | − | 0.0717270i | ||||
\(883\) | −0.523303 | − | 0.523303i | −0.0176105 | − | 0.0176105i | 0.698247 | − | 0.715857i | \(-0.253964\pi\) |
−0.715857 | + | 0.698247i | \(0.753964\pi\) | |||||||
\(884\) | 0.883423 | − | 0.754723i | 0.0297127 | − | 0.0253841i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.0252 | + | 18.4153i | 0.571973 | + | 0.618673i | ||||
\(887\) | −34.8129 | −1.16890 | −0.584452 | − | 0.811429i | \(-0.698690\pi\) | ||||
−0.584452 | + | 0.811429i | \(0.698690\pi\) | |||||||
\(888\) | 1.28985 | − | 10.9170i | 0.0432845 | − | 0.366352i | ||||
\(889\) | 12.8766i | 0.431868i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.3024 | + | 19.3024i | 0.646656 | + | 0.646656i | ||||
\(892\) | 3.77627 | − | 48.0661i | 0.126439 | − | 1.60937i | ||||
\(893\) | −7.36103 | − | 7.36103i | −0.246328 | − | 0.246328i | ||||
\(894\) | −1.56546 | − | 0.0614001i | −0.0523569 | − | 0.00205353i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −14.4564 | + | 51.3527i | −0.482956 | + | 1.71557i | ||||
\(897\) | 0.139964i | 0.00467325i | ||||||||
\(898\) | −1.00157 | + | 25.5363i | −0.0334230 | + | 0.852156i | ||||
\(899\) | 6.94743 | − | 6.94743i | 0.231710 | − | 0.231710i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.5562 | − | 23.5562i | −0.784770 | − | 0.784770i | ||||
\(902\) | 43.8631 | + | 47.4444i | 1.46048 | + | 1.57973i | ||||
\(903\) | 10.4736 | 0.348540 | ||||||||
\(904\) | −16.7971 | − | 1.98458i | −0.558664 | − | 0.0660061i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.72384 | − | 5.10952i | −0.156939 | − | 0.169752i | ||||
\(907\) | 13.3188 | − | 13.3188i | 0.442244 | − | 0.442244i | −0.450521 | − | 0.892766i | \(-0.648762\pi\) |
0.892766 | + | 0.450521i | \(0.148762\pi\) | |||||||
\(908\) | 12.2618 | + | 14.3527i | 0.406921 | + | 0.476311i | ||||
\(909\) | 33.8264 | − | 33.8264i | 1.12195 | − | 1.12195i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.0117 | −1.55757 | −0.778783 | − | 0.627294i | \(-0.784163\pi\) | ||||
−0.778783 | + | 0.627294i | \(0.784163\pi\) | |||||||
\(912\) | 6.99653 | + | 1.10618i | 0.231678 | + | 0.0366293i | ||||
\(913\) | 9.15148i | 0.302870i | ||||||||
\(914\) | 1.03444 | − | 26.3742i | 0.0342163 | − | 0.872382i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.5436 | + | 34.5815i | 0.976148 | + | 1.14261i | ||||
\(917\) | −3.83624 | + | 3.83624i | −0.126684 | + | 0.126684i | ||||
\(918\) | 18.5203 | − | 17.1223i | 0.611261 | − | 0.565121i | ||||
\(919\) | − | 31.3426i | − | 1.03390i | −0.856016 | − | 0.516949i | \(-0.827068\pi\) | ||
0.856016 | − | 0.516949i | \(-0.172932\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.76133i | 0.255745i | ||||||||
\(922\) | 1.12856 | + | 1.22070i | 0.0371672 | + | 0.0402017i | ||||
\(923\) | 0.399048 | − | 0.399048i | 0.0131348 | − | 0.0131348i | ||||
\(924\) | 2.82437 | − | 35.9499i | 0.0929151 | − | 1.18266i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.0582 | + | 0.433721i | 0.363395 | + | 0.0142529i | ||||
\(927\) | − | 34.7219i | − | 1.14042i | ||||||
\(928\) | 14.5128 | + | 21.7039i | 0.476406 | + | 0.712464i | ||||
\(929\) | −30.3384 | −0.995369 | −0.497685 | − | 0.867358i | \(-0.665816\pi\) | ||||
−0.497685 | + | 0.867358i | \(0.665816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.6133 | + | 27.6133i | −0.904990 | + | 0.904990i | ||||
\(932\) | −32.8938 | − | 2.58427i | −1.07747 | − | 0.0846507i | ||||
\(933\) | −15.2245 | + | 15.2245i | −0.498429 | + | 0.498429i | ||||
\(934\) | −12.8508 | + | 11.8808i | −0.420492 | + | 0.388752i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.549157 | − | 0.696309i | −0.0179498 | − | 0.0227596i | ||||
\(937\) | −14.5267 | −0.474565 | −0.237283 | − | 0.971441i | \(-0.576257\pi\) | ||||
−0.237283 | + | 0.971441i | \(0.576257\pi\) | |||||||
\(938\) | 51.9306 | − | 48.0107i | 1.69559 | − | 1.56760i | ||||
\(939\) | 2.61767 | + | 2.61767i | 0.0854245 | + | 0.0854245i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.2863 | − | 37.2863i | 1.21550 | − | 1.21550i | 0.246307 | − | 0.969192i | \(-0.420783\pi\) |
0.969192 | − | 0.246307i | \(-0.0792172\pi\) | |||||||
\(942\) | −7.34716 | − | 0.288168i | −0.239384 | − | 0.00938902i | ||||
\(943\) | − | 13.4563i | − | 0.438197i | ||||||
\(944\) | 17.1786 | + | 23.6307i | 0.559116 | + | 0.769115i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.986239 | − | 25.1453i | 0.0320654 | − | 0.817543i | ||||
\(947\) | 15.8961 | + | 15.8961i | 0.516553 | + | 0.516553i | 0.916527 | − | 0.399973i | \(-0.130981\pi\) |
−0.399973 | + | 0.916527i | \(0.630981\pi\) | |||||||
\(948\) | −10.3498 | − | 12.1147i | −0.336145 | − | 0.393466i | ||||
\(949\) | −0.729912 | − | 0.729912i | −0.0236939 | − | 0.0236939i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 8.67765i | − | 0.281392i | ||||||
\(952\) | 61.9129 | + | 7.31501i | 2.00661 | + | 0.237081i | ||||
\(953\) | 33.2248 | 1.07626 | 0.538129 | − | 0.842862i | \(-0.319131\pi\) | ||||
0.538129 | + | 0.842862i | \(0.319131\pi\) | |||||||
\(954\) | −18.6695 | + | 17.2603i | −0.604447 | + | 0.558822i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.4860 | + | 0.823827i | 0.339143 | + | 0.0266445i | ||||
\(957\) | −12.4791 | − | 12.4791i | −0.403393 | − | 0.403393i | ||||
\(958\) | −0.116624 | + | 2.97346i | −0.00376796 | + | 0.0960682i | ||||
\(959\) | 0.942197 | 0.0304251 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4684 | −0.853820 | ||||||||
\(962\) | −0.0387525 | + | 0.988038i | −0.00124943 | + | 0.0318556i | ||||
\(963\) | 0.827438 | + | 0.827438i | 0.0266638 | + | 0.0266638i | ||||
\(964\) | 28.1386 | + | 2.21069i | 0.906283 | + | 0.0712014i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.51433 | + | 5.09809i | −0.177421 | + | 0.164028i | ||||
\(967\) | 1.79116 | 0.0576000 | 0.0288000 | − | 0.999585i | \(-0.490831\pi\) | ||||
0.0288000 | + | 0.999585i | \(0.490831\pi\) | |||||||
\(968\) | −55.1455 | − | 6.51543i | −1.77244 | − | 0.209414i | ||||
\(969\) | − | 8.27774i | − | 0.265919i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.31278 | + | 5.31278i | 0.170495 | + | 0.170495i | 0.787197 | − | 0.616702i | \(-0.211531\pi\) |
−0.616702 | + | 0.787197i | \(0.711531\pi\) | |||||||
\(972\) | −19.2966 | − | 22.5872i | −0.618940 | − | 0.724485i | ||||
\(973\) | 54.8404 | + | 54.8404i | 1.75810 | + | 1.75810i | ||||
\(974\) | 0.270022 | − | 6.88451i | 0.00865207 | − | 0.220594i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.6114 | − | 23.7072i | 1.04386 | − | 0.758848i | ||||
\(977\) | 6.81676i | 0.218088i | 0.994037 | + | 0.109044i | \(0.0347789\pi\) | ||||
−0.994037 | + | 0.109044i | \(0.965221\pi\) | |||||||
\(978\) | 16.9836 | + | 0.666126i | 0.543076 | + | 0.0213003i | ||||
\(979\) | −12.7025 | + | 12.7025i | −0.405972 | + | 0.405972i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.377643 | − | 0.377643i | −0.0120572 | − | 0.0120572i | ||||
\(982\) | 21.0857 | − | 19.4941i | 0.672873 | − | 0.622082i | ||||
\(983\) | 5.49468 | 0.175253 | 0.0876265 | − | 0.996153i | \(-0.472072\pi\) | ||||
0.0876265 | + | 0.996153i | \(0.472072\pi\) | |||||||
\(984\) | −9.98913 | − | 12.6658i | −0.318442 | − | 0.403771i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22.4036 | − | 20.7125i | 0.713475 | − | 0.659620i | ||||
\(987\) | 9.35538 | − | 9.35538i | 0.297785 | − | 0.297785i | ||||
\(988\) | −0.635184 | − | 0.0499028i | −0.0202079 | − | 0.00158762i | ||||
\(989\) | −3.70574 | + | 3.70574i | −0.117836 | + | 0.117836i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.7524 | 1.54867 | 0.774335 | − | 0.632775i | \(-0.218084\pi\) | ||||
0.774335 | + | 0.632775i | \(0.218084\pi\) | |||||||
\(992\) | −2.34525 | + | 11.8114i | −0.0744616 | + | 0.375013i | ||||
\(993\) | − | 5.93333i | − | 0.188289i | ||||||
\(994\) | 30.2569 | + | 1.18673i | 0.959691 | + | 0.0376407i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.178942 | − | 2.27766i | 0.00567000 | − | 0.0721703i | ||||
\(997\) | 42.5246 | − | 42.5246i | 1.34677 | − | 1.34677i | 0.457618 | − | 0.889149i | \(-0.348703\pi\) |
0.889149 | − | 0.457618i | \(-0.151297\pi\) | |||||||
\(998\) | −34.0864 | − | 36.8694i | −1.07899 | − | 1.16708i | ||||
\(999\) | 21.4646i | 0.679109i |
(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 | 400.2.q.f.149.3 | 12 | ||
4.3 | odd | 2 | 1600.2.q.f.49.4 | 12 | |||
5.2 | odd | 4 | 400.2.l.f.101.6 | ✓ | 12 | ||
5.3 | odd | 4 | 400.2.l.g.101.1 | yes | 12 | ||
5.4 | even | 2 | 400.2.q.e.149.4 | 12 | |||
16.3 | odd | 4 | 1600.2.q.e.849.3 | 12 | |||
16.13 | even | 4 | 400.2.q.e.349.4 | 12 | |||
20.3 | even | 4 | 1600.2.l.f.1201.3 | 12 | |||
20.7 | even | 4 | 1600.2.l.g.1201.4 | 12 | |||
20.19 | odd | 2 | 1600.2.q.e.49.3 | 12 | |||
80.3 | even | 4 | 1600.2.l.f.401.3 | 12 | |||
80.13 | odd | 4 | 400.2.l.g.301.1 | yes | 12 | ||
80.19 | odd | 4 | 1600.2.q.f.849.4 | 12 | |||
80.29 | even | 4 | inner | 400.2.q.f.349.3 | 12 | ||
80.67 | even | 4 | 1600.2.l.g.401.4 | 12 | |||
80.77 | odd | 4 | 400.2.l.f.301.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.6 | ✓ | 12 | 5.2 | odd | 4 | ||
400.2.l.f.301.6 | yes | 12 | 80.77 | odd | 4 | ||
400.2.l.g.101.1 | yes | 12 | 5.3 | odd | 4 | ||
400.2.l.g.301.1 | yes | 12 | 80.13 | odd | 4 | ||
400.2.q.e.149.4 | 12 | 5.4 | even | 2 | |||
400.2.q.e.349.4 | 12 | 16.13 | even | 4 | |||
400.2.q.f.149.3 | 12 | 1.1 | even | 1 | trivial | ||
400.2.q.f.349.3 | 12 | 80.29 | even | 4 | inner | ||
1600.2.l.f.401.3 | 12 | 80.3 | even | 4 | |||
1600.2.l.f.1201.3 | 12 | 20.3 | even | 4 | |||
1600.2.l.g.401.4 | 12 | 80.67 | even | 4 | |||
1600.2.l.g.1201.4 | 12 | 20.7 | even | 4 | |||
1600.2.q.e.49.3 | 12 | 20.19 | odd | 2 | |||
1600.2.q.e.849.3 | 12 | 16.3 | odd | 4 | |||
1600.2.q.f.49.4 | 12 | 4.3 | odd | 2 | |||
1600.2.q.f.849.4 | 12 | 80.19 | odd | 4 |