Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.701538 + 0.227943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.49 |
Dual form | 825.2.bx.h.724.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33569 | + | 0.758911i | −1.65158 | + | 0.536631i | −0.979082 | − | 0.203468i | \(-0.934779\pi\) |
−0.672499 | + | 0.740098i | \(0.734779\pi\) | |||||||
\(3\) | −0.587785 | + | 0.809017i | −0.339358 | + | 0.467086i | ||||
\(4\) | 3.26145 | − | 2.36959i | 1.63073 | − | 1.18479i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.758911 | − | 2.33569i | 0.309824 | − | 0.953540i | ||||
\(7\) | −1.93196 | − | 2.65911i | −0.730211 | − | 1.00505i | −0.999122 | − | 0.0418845i | \(-0.986664\pi\) |
0.268911 | − | 0.963165i | \(-0.413336\pi\) | |||||||
\(8\) | −2.93237 | + | 4.03606i | −1.03675 | + | 1.42696i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.96813 | + | 1.47994i | 0.894924 | + | 0.446218i | ||||
\(12\) | 4.03138i | 1.16376i | ||||||||
\(13\) | −0.297808 | + | 0.0967635i | −0.0825970 | + | 0.0268374i | −0.350024 | − | 0.936741i | \(-0.613827\pi\) |
0.267427 | + | 0.963578i | \(0.413827\pi\) | |||||||
\(14\) | 6.53048 | + | 4.74467i | 1.74534 | + | 1.26807i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.29455 | − | 3.98423i | 0.323638 | − | 0.996057i | ||||
\(17\) | 4.75528 | + | 1.54508i | 1.15333 | + | 0.374738i | 0.822395 | − | 0.568917i | \(-0.192637\pi\) |
0.330930 | + | 0.943655i | \(0.392637\pi\) | |||||||
\(18\) | 1.44353 | + | 1.98685i | 0.340244 | + | 0.468306i | ||||
\(19\) | −6.03048 | − | 4.38140i | −1.38349 | − | 1.00516i | −0.996545 | − | 0.0830568i | \(-0.973532\pi\) |
−0.386941 | − | 0.922104i | \(-0.626468\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.28684 | 0.717248 | ||||||||
\(22\) | −8.05576 | − | 1.20413i | −1.71749 | − | 0.256721i | ||||
\(23\) | − | 1.07392i | − | 0.223928i | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||
0.993712 | − | 0.111964i | \(-0.0357141\pi\) | |||||||
\(24\) | −1.54164 | − | 4.74467i | −0.314685 | − | 0.968501i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.622150 | − | 0.452019i | 0.122014 | − | 0.0886482i | ||||
\(27\) | 0.951057 | + | 0.309017i | 0.183031 | + | 0.0594703i | ||||
\(28\) | −12.6020 | − | 4.09463i | −2.38155 | − | 0.773813i | ||||
\(29\) | −4.07459 | + | 2.96036i | −0.756632 | + | 0.549725i | −0.897875 | − | 0.440250i | \(-0.854890\pi\) |
0.141243 | + | 0.989975i | \(0.454890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.06580 | + | 3.28018i | 0.191423 | + | 0.589138i | 1.00000 | 0.000748050i | \(0.000238112\pi\) | |
−0.808577 | + | 0.588390i | \(0.799762\pi\) | |||||||
\(32\) | 0.310680i | 0.0549210i | ||||||||
\(33\) | −2.94192 | + | 1.53138i | −0.512122 | + | 0.266579i | ||||
\(34\) | −12.2794 | −2.10591 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.26145 | − | 2.36959i | −0.543576 | − | 0.394931i | ||||
\(37\) | −1.54839 | − | 2.13118i | −0.254554 | − | 0.350364i | 0.662546 | − | 0.749022i | \(-0.269476\pi\) |
−0.917100 | + | 0.398658i | \(0.869476\pi\) | |||||||
\(38\) | 17.4104 | + | 5.65698i | 2.82434 | + | 0.917683i | ||||
\(39\) | 0.0967635 | − | 0.297808i | 0.0154946 | − | 0.0476874i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.77557 | − | 6.37583i | −1.37051 | − | 0.995737i | −0.997697 | − | 0.0678321i | \(-0.978392\pi\) |
−0.372817 | − | 0.927905i | \(-0.621608\pi\) | |||||||
\(42\) | −7.67703 | + | 2.49442i | −1.18459 | + | 0.384897i | ||||
\(43\) | 5.51468i | 0.840980i | 0.907297 | + | 0.420490i | \(0.138142\pi\) | ||||
−0.907297 | + | 0.420490i | \(0.861858\pi\) | |||||||
\(44\) | 13.1873 | − | 2.20648i | 1.98805 | − | 0.332640i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.815010 | + | 2.50834i | 0.120167 | + | 0.369835i | ||||
\(47\) | −7.05236 | + | 9.70674i | −1.02869 | + | 1.41587i | −0.122767 | + | 0.992435i | \(0.539177\pi\) |
−0.905925 | + | 0.423438i | \(0.860823\pi\) | |||||||
\(48\) | 2.46239 | + | 3.38919i | 0.355415 | + | 0.489187i | ||||
\(49\) | −1.17529 | + | 3.61718i | −0.167899 | + | 0.516740i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.04508 | + | 2.93893i | −0.566425 | + | 0.411532i | ||||
\(52\) | −0.741996 | + | 1.02127i | −0.102896 | + | 0.141625i | ||||
\(53\) | 4.69387 | − | 1.52513i | 0.644753 | − | 0.209493i | 0.0316539 | − | 0.999499i | \(-0.489923\pi\) |
0.613099 | + | 0.790006i | \(0.289923\pi\) | |||||||
\(54\) | −2.45589 | −0.334204 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 16.3975 | 2.19121 | ||||||||
\(57\) | 7.08925 | − | 2.30344i | 0.938994 | − | 0.305098i | ||||
\(58\) | 7.27031 | − | 10.0067i | 0.954639 | − | 1.31395i | ||||
\(59\) | −7.41391 | + | 5.38652i | −0.965208 | + | 0.701265i | −0.954354 | − | 0.298676i | \(-0.903455\pi\) |
−0.0108537 | + | 0.999941i | \(0.503455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.83811 | − | 8.73480i | 0.363382 | − | 1.11838i | −0.587605 | − | 0.809148i | \(-0.699929\pi\) |
0.950988 | − | 0.309229i | \(-0.100071\pi\) | |||||||
\(62\) | −4.97873 | − | 6.85264i | −0.632300 | − | 0.870286i | ||||
\(63\) | −1.93196 | + | 2.65911i | −0.243404 | + | 0.335016i | ||||
\(64\) | 2.35333 | + | 7.24280i | 0.294166 | + | 0.905350i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.70922 | − | 5.80948i | 0.702756 | − | 0.715097i | ||||
\(67\) | − | 15.2739i | − | 1.86600i | −0.359876 | − | 0.933000i | \(-0.617181\pi\) | ||
0.359876 | − | 0.933000i | \(-0.382819\pi\) | |||||||
\(68\) | 19.1704 | − | 6.22882i | 2.32475 | − | 0.755356i | ||||
\(69\) | 0.868820 | + | 0.631235i | 0.104594 | + | 0.0759917i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.949335 | − | 2.92175i | 0.112665 | − | 0.346748i | −0.878788 | − | 0.477213i | \(-0.841647\pi\) |
0.991453 | + | 0.130465i | \(0.0416470\pi\) | |||||||
\(72\) | 4.74467 | + | 1.54164i | 0.559164 | + | 0.181684i | ||||
\(73\) | −5.08592 | − | 7.00018i | −0.595262 | − | 0.819309i | 0.400002 | − | 0.916514i | \(-0.369009\pi\) |
−0.995264 | + | 0.0972058i | \(0.969009\pi\) | |||||||
\(74\) | 5.23394 | + | 3.80268i | 0.608433 | + | 0.442052i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −30.0502 | −3.44700 | ||||||||
\(77\) | −1.79898 | − | 10.7518i | −0.205012 | − | 1.22528i | ||||
\(78\) | 0.769020i | 0.0870744i | ||||||||
\(79\) | −1.67316 | − | 5.14946i | −0.188245 | − | 0.579360i | 0.811744 | − | 0.584014i | \(-0.198519\pi\) |
−0.999989 | + | 0.00465401i | \(0.998519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 25.3357 | + | 8.23206i | 2.79786 | + | 0.909079i | ||||
\(83\) | −15.4503 | − | 5.02011i | −1.69589 | − | 0.551029i | −0.708006 | − | 0.706207i | \(-0.750405\pi\) |
−0.987887 | + | 0.155178i | \(0.950405\pi\) | |||||||
\(84\) | 10.7199 | − | 7.78845i | 1.16964 | − | 0.849790i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.18515 | − | 12.8806i | −0.451296 | − | 1.38895i | ||||
\(87\) | − | 5.03647i | − | 0.539966i | ||||||
\(88\) | −14.6768 | + | 7.63981i | −1.56455 | + | 0.814406i | ||||
\(89\) | −1.62118 | −0.171845 | −0.0859223 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859223 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.832656 | + | 0.604960i | 0.0872861 | + | 0.0634171i | ||||
\(92\) | −2.54475 | − | 3.50254i | −0.265308 | − | 0.365165i | ||||
\(93\) | −3.28018 | − | 1.06580i | −0.340139 | − | 0.110518i | ||||
\(94\) | 9.10556 | − | 28.0240i | 0.939166 | − | 2.89046i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.251345 | − | 0.182613i | −0.0256528 | − | 0.0186379i | ||||
\(97\) | −0.213115 | + | 0.0692451i | −0.0216385 | + | 0.00703078i | −0.319816 | − | 0.947480i | \(-0.603621\pi\) |
0.298178 | + | 0.954510i | \(0.403621\pi\) | |||||||
\(98\) | − | 9.34054i | − | 0.943537i | ||||||
\(99\) | 0.490303 | − | 3.28018i | 0.0492773 | − | 0.329671i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.156154 | − | 0.480593i | −0.0155379 | − | 0.0478208i | 0.942987 | − | 0.332830i | \(-0.108003\pi\) |
−0.958525 | + | 0.285009i | \(0.908003\pi\) | |||||||
\(102\) | 7.21767 | − | 9.93427i | 0.714656 | − | 0.983639i | ||||
\(103\) | −3.76298 | − | 5.17930i | −0.370778 | − | 0.510332i | 0.582334 | − | 0.812949i | \(-0.302139\pi\) |
−0.953112 | + | 0.302618i | \(0.902139\pi\) | |||||||
\(104\) | 0.482738 | − | 1.48571i | 0.0473363 | − | 0.145686i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.80598 | + | 7.12446i | −0.952441 | + | 0.691989i | ||||
\(107\) | 1.22993 | − | 1.69286i | 0.118902 | − | 0.163655i | −0.745417 | − | 0.666598i | \(-0.767750\pi\) |
0.864319 | + | 0.502943i | \(0.167750\pi\) | |||||||
\(108\) | 3.83407 | − | 1.24576i | 0.368934 | − | 0.119874i | ||||
\(109\) | 6.69278 | 0.641052 | 0.320526 | − | 0.947240i | \(-0.396140\pi\) | ||||
0.320526 | + | 0.947240i | \(0.396140\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.63428 | 0.250035 | ||||||||
\(112\) | −13.0955 | + | 4.25499i | −1.23741 | + | 0.402059i | ||||
\(113\) | 6.34462 | − | 8.73262i | 0.596852 | − | 0.821496i | −0.398564 | − | 0.917141i | \(-0.630491\pi\) |
0.995416 | + | 0.0956448i | \(0.0304913\pi\) | |||||||
\(114\) | −14.8102 | + | 10.7602i | −1.38710 | + | 1.00779i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.27426 | + | 19.3102i | −0.582550 | + | 1.79290i | ||||
\(117\) | 0.184055 | + | 0.253330i | 0.0170159 | + | 0.0234204i | ||||
\(118\) | 13.2287 | − | 18.2077i | 1.21780 | − | 1.67616i | ||||
\(119\) | −5.07845 | − | 15.6299i | −0.465541 | − | 1.43279i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.61956 | + | 8.78529i | 0.601779 | + | 0.798663i | ||||
\(122\) | 22.5556i | 2.04209i | ||||||||
\(123\) | 10.3163 | − | 3.35197i | 0.930190 | − | 0.302237i | ||||
\(124\) | 11.2487 | + | 8.17267i | 1.01017 | + | 0.733928i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.49442 | − | 7.67703i | 0.222221 | − | 0.683925i | ||||
\(127\) | −16.1711 | − | 5.25430i | −1.43495 | − | 0.466244i | −0.514632 | − | 0.857411i | \(-0.672071\pi\) |
−0.920320 | + | 0.391167i | \(0.872071\pi\) | |||||||
\(128\) | −11.3585 | − | 15.6336i | −1.00396 | − | 1.38183i | ||||
\(129\) | −4.46147 | − | 3.24145i | −0.392810 | − | 0.285393i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0430508 | −0.00376136 | −0.00188068 | − | 0.999998i | \(-0.500599\pi\) | ||||
−0.00188068 | + | 0.999998i | \(0.500599\pi\) | |||||||
\(132\) | −5.96619 | + | 11.9657i | −0.519291 | + | 1.04148i | ||||
\(133\) | 24.5004i | 2.12445i | ||||||||
\(134\) | 11.5915 | + | 35.6750i | 1.00135 | + | 3.08185i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.1803 | + | 14.6618i | −1.73044 | + | 1.25724i | ||||
\(137\) | 7.00222 | + | 2.27516i | 0.598240 | + | 0.194380i | 0.592455 | − | 0.805603i | \(-0.298159\pi\) |
0.00578480 | + | 0.999983i | \(0.498159\pi\) | |||||||
\(138\) | −2.50834 | − | 0.815010i | −0.213524 | − | 0.0693783i | ||||
\(139\) | 10.7109 | − | 7.78189i | 0.908483 | − | 0.660052i | −0.0321478 | − | 0.999483i | \(-0.510235\pi\) |
0.940631 | + | 0.339432i | \(0.110235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.70764 | − | 11.4110i | −0.312240 | − | 0.960976i | ||||
\(142\) | 7.54476i | 0.633142i | ||||||||
\(143\) | −1.02713 | − | 0.153530i | −0.0858933 | − | 0.0128388i | ||||
\(144\) | −4.18926 | −0.349105 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.1916 | + | 12.4905i | 1.42279 | + | 1.03372i | ||||
\(147\) | −2.23554 | − | 3.07696i | −0.184384 | − | 0.253783i | ||||
\(148\) | −10.1000 | − | 3.28170i | −0.830217 | − | 0.269754i | ||||
\(149\) | 1.81658 | − | 5.59087i | 0.148820 | − | 0.458022i | −0.848662 | − | 0.528935i | \(-0.822591\pi\) |
0.997482 | + | 0.0709136i | \(0.0225915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.17135 | − | 4.48375i | −0.502217 | − | 0.364882i | 0.307646 | − | 0.951501i | \(-0.400459\pi\) |
−0.809863 | + | 0.586619i | \(0.800459\pi\) | |||||||
\(152\) | 35.3671 | − | 11.4915i | 2.86865 | − | 0.932082i | ||||
\(153\) | − | 5.00000i | − | 0.404226i | ||||||
\(154\) | 12.3615 | + | 23.7475i | 0.996116 | + | 1.91363i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.390091 | − | 1.20058i | −0.0312322 | − | 0.0961230i | ||||
\(157\) | −5.95616 | + | 8.19795i | −0.475353 | + | 0.654267i | −0.977604 | − | 0.210455i | \(-0.932506\pi\) |
0.502250 | + | 0.864722i | \(0.332506\pi\) | |||||||
\(158\) | 7.81596 | + | 10.7578i | 0.621805 | + | 0.855841i | ||||
\(159\) | −1.52513 | + | 4.69387i | −0.120951 | + | 0.372248i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.85567 | + | 2.07477i | −0.225059 | + | 0.163515i | ||||
\(162\) | 1.44353 | − | 1.98685i | 0.113415 | − | 0.156102i | ||||
\(163\) | −4.78292 | + | 1.55407i | −0.374627 | + | 0.121724i | −0.490278 | − | 0.871566i | \(-0.663105\pi\) |
0.115651 | + | 0.993290i | \(0.463105\pi\) | |||||||
\(164\) | −43.7292 | −3.41468 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 39.8969 | 3.09660 | ||||||||
\(167\) | −5.50761 | + | 1.78953i | −0.426192 | + | 0.138478i | −0.514256 | − | 0.857637i | \(-0.671932\pi\) |
0.0880642 | + | 0.996115i | \(0.471932\pi\) | |||||||
\(168\) | −9.63822 | + | 13.2659i | −0.743605 | + | 1.02348i | ||||
\(169\) | −10.4379 | + | 7.58357i | −0.802915 | + | 0.583352i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.30344 | + | 7.08925i | −0.176148 | + | 0.542128i | ||||
\(172\) | 13.0675 | + | 17.9859i | 0.996387 | + | 1.37141i | ||||
\(173\) | −9.44290 | + | 12.9970i | −0.717930 | + | 0.988146i | 0.281660 | + | 0.959514i | \(0.409115\pi\) |
−0.999590 | + | 0.0286316i | \(0.990885\pi\) | |||||||
\(174\) | 3.82223 | + | 11.7636i | 0.289762 | + | 0.891797i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.73881 | − | 9.90983i | 0.734090 | − | 0.746982i | ||||
\(177\) | − | 9.16409i | − | 0.688815i | ||||||
\(178\) | 3.78657 | − | 1.23033i | 0.283815 | − | 0.0922171i | ||||
\(179\) | −6.71734 | − | 4.88043i | −0.502078 | − | 0.364781i | 0.307732 | − | 0.951473i | \(-0.400430\pi\) |
−0.809810 | + | 0.586692i | \(0.800430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.99756 | + | 6.14787i | −0.148478 | + | 0.456968i | −0.997442 | − | 0.0714830i | \(-0.977227\pi\) |
0.848964 | + | 0.528451i | \(0.177227\pi\) | |||||||
\(182\) | −2.40394 | − | 0.781086i | −0.178192 | − | 0.0578980i | ||||
\(183\) | 5.39840 | + | 7.43026i | 0.399061 | + | 0.549261i | ||||
\(184\) | 4.33440 | + | 3.14913i | 0.319536 | + | 0.232157i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.47033 | 0.621074 | ||||||||
\(187\) | 11.8277 | + | 11.6235i | 0.864924 | + | 0.849997i | ||||
\(188\) | 48.3693i | 3.52769i | ||||||||
\(189\) | −1.01569 | − | 3.12597i | −0.0738806 | − | 0.227381i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4340 | + | 9.03384i | −0.899694 | + | 0.653666i | −0.938387 | − | 0.345585i | \(-0.887680\pi\) |
0.0386935 | + | 0.999251i | \(0.487680\pi\) | |||||||
\(192\) | −7.24280 | − | 2.35333i | −0.522704 | − | 0.169837i | ||||
\(193\) | −14.9808 | − | 4.86757i | −1.07834 | − | 0.350375i | −0.284612 | − | 0.958643i | \(-0.591865\pi\) |
−0.793732 | + | 0.608267i | \(0.791865\pi\) | |||||||
\(194\) | 0.445218 | − | 0.323470i | 0.0319648 | − | 0.0232238i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.73805 | + | 14.5822i | 0.338432 | + | 1.04159i | ||||
\(197\) | 16.3940i | 1.16802i | 0.811746 | + | 0.584010i | \(0.198517\pi\) | ||||
−0.811746 | + | 0.584010i | \(0.801483\pi\) | |||||||
\(198\) | 1.34417 | + | 8.03358i | 0.0955261 | + | 0.570922i | ||||
\(199\) | −6.96500 | −0.493736 | −0.246868 | − | 0.969049i | \(-0.579401\pi\) | ||||
−0.246868 | + | 0.969049i | \(0.579401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.3568 | + | 8.97776i | 0.871583 | + | 0.633242i | ||||
\(202\) | 0.729455 | + | 1.00401i | 0.0513242 | + | 0.0706418i | ||||
\(203\) | 15.7439 | + | 5.11549i | 1.10500 | + | 0.359037i | ||||
\(204\) | −6.22882 | + | 19.1704i | −0.436105 | + | 1.34219i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.7198 | + | 9.24146i | 0.886229 | + | 0.643883i | ||||
\(207\) | −1.02136 | + | 0.331860i | −0.0709894 | + | 0.0230658i | ||||
\(208\) | 1.31180i | 0.0909569i | ||||||||
\(209\) | −11.4150 | − | 21.9293i | −0.789594 | − | 1.51688i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.16585 | − | 18.9765i | −0.424475 | − | 1.30640i | −0.903496 | − | 0.428596i | \(-0.859008\pi\) |
0.479022 | − | 0.877803i | \(-0.340992\pi\) | |||||||
\(212\) | 11.6949 | − | 16.0967i | 0.803211 | − | 1.10552i | ||||
\(213\) | 1.80574 | + | 2.48539i | 0.123727 | + | 0.170296i | ||||
\(214\) | −1.58801 | + | 4.88740i | −0.108554 | + | 0.334096i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.03606 | + | 2.93237i | −0.274619 | + | 0.199522i | ||||
\(217\) | 6.66330 | − | 9.17124i | 0.452334 | − | 0.622585i | ||||
\(218\) | −15.6322 | + | 5.07922i | −1.05875 | + | 0.344008i | ||||
\(219\) | 8.65269 | 0.584695 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56567 | −0.105318 | ||||||||
\(222\) | −6.15286 | + | 1.99919i | −0.412953 | + | 0.134177i | ||||
\(223\) | 11.8419 | − | 16.2990i | 0.792992 | − | 1.09146i | −0.200737 | − | 0.979645i | \(-0.564334\pi\) |
0.993729 | − | 0.111815i | \(-0.0356664\pi\) | |||||||
\(224\) | 0.826133 | − | 0.600220i | 0.0551983 | − | 0.0401039i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.19177 | + | 25.2117i | −0.544908 | + | 1.67706i | ||||
\(227\) | −0.313840 | − | 0.431964i | −0.0208303 | − | 0.0286705i | 0.798475 | − | 0.602028i | \(-0.205641\pi\) |
−0.819305 | + | 0.573358i | \(0.805641\pi\) | |||||||
\(228\) | 17.6631 | − | 24.3111i | 1.16977 | − | 1.61004i | ||||
\(229\) | 6.85803 | + | 21.1068i | 0.453191 | + | 1.39478i | 0.873245 | + | 0.487281i | \(0.162011\pi\) |
−0.420054 | + | 0.907499i | \(0.637989\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.75577 | + | 4.86432i | 0.641882 | + | 0.320049i | ||||
\(232\) | − | 25.1261i | − | 1.64961i | ||||||
\(233\) | −4.34221 | + | 1.41087i | −0.284467 | + | 0.0924291i | −0.447775 | − | 0.894146i | \(-0.647784\pi\) |
0.163308 | + | 0.986575i | \(0.447784\pi\) | |||||||
\(234\) | −0.622150 | − | 0.452019i | −0.0406712 | − | 0.0295494i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.4163 | + | 35.1358i | −0.743138 | + | 2.28714i | ||||
\(237\) | 5.14946 | + | 1.67316i | 0.334493 | + | 0.108684i | ||||
\(238\) | 23.7233 | + | 32.6524i | 1.53776 | + | 2.11654i | ||||
\(239\) | −4.74126 | − | 3.44473i | −0.306687 | − | 0.222821i | 0.423787 | − | 0.905762i | \(-0.360701\pi\) |
−0.730474 | + | 0.682941i | \(0.760701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.96074 | 0.641628 | 0.320814 | − | 0.947142i | \(-0.396044\pi\) | ||||
0.320814 | + | 0.947142i | \(0.396044\pi\) | |||||||
\(242\) | −22.1285 | − | 15.4960i | −1.42247 | − | 0.996123i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −11.4415 | − | 35.2133i | −0.732466 | − | 2.25430i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −21.5518 | + | 15.6583i | −1.37409 | + | 0.998337i | ||||
\(247\) | 2.21988 | + | 0.721283i | 0.141248 | + | 0.0458941i | ||||
\(248\) | −16.3643 | − | 5.31709i | −1.03913 | − | 0.337635i | ||||
\(249\) | 13.1428 | − | 9.54882i | 0.832892 | − | 0.605132i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.21584 | − | 16.0527i | −0.329221 | − | 1.01324i | −0.969499 | − | 0.245094i | \(-0.921181\pi\) |
0.640279 | − | 0.768143i | \(-0.278819\pi\) | |||||||
\(252\) | 13.2505i | 0.834704i | ||||||||
\(253\) | 1.58934 | − | 3.18753i | 0.0999207 | − | 0.200399i | ||||
\(254\) | 41.7581 | 2.62014 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 26.0723 | + | 18.9426i | 1.62952 | + | 1.18391i | ||||
\(257\) | −6.55003 | − | 9.01534i | −0.408580 | − | 0.562362i | 0.554292 | − | 0.832323i | \(-0.312989\pi\) |
−0.962871 | + | 0.269961i | \(0.912989\pi\) | |||||||
\(258\) | 12.8806 | + | 4.18515i | 0.801909 | + | 0.260556i | ||||
\(259\) | −2.67561 | + | 8.23470i | −0.166255 | + | 0.511679i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.07459 | + | 2.96036i | 0.252211 | + | 0.183242i | ||||
\(262\) | 0.100553 | − | 0.0326717i | 0.00621220 | − | 0.00201846i | ||||
\(263\) | 26.8726i | 1.65704i | 0.559961 | + | 0.828519i | \(0.310816\pi\) | ||||
−0.559961 | + | 0.828519i | \(0.689184\pi\) | |||||||
\(264\) | 2.44604 | − | 16.3643i | 0.150544 | − | 1.00715i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −18.5936 | − | 57.2252i | −1.14005 | − | 3.50870i | ||||
\(267\) | 0.952905 | − | 1.31156i | 0.0583168 | − | 0.0802662i | ||||
\(268\) | −36.1927 | − | 49.8150i | −2.21082 | − | 3.04294i | ||||
\(269\) | 3.10961 | − | 9.57038i | 0.189596 | − | 0.583516i | −0.810401 | − | 0.585875i | \(-0.800751\pi\) |
0.999997 | + | 0.00235886i | \(0.000750850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.53037 | + | 6.19767i | −0.518183 | + | 0.376482i | −0.815919 | − | 0.578166i | \(-0.803768\pi\) |
0.297736 | + | 0.954648i | \(0.403768\pi\) | |||||||
\(272\) | 12.3119 | − | 16.9459i | 0.746521 | − | 1.02750i | ||||
\(273\) | −0.978846 | + | 0.318046i | −0.0592425 | + | 0.0192490i | ||||
\(274\) | −18.0816 | −1.09235 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.32938 | 0.260598 | ||||||||
\(277\) | 17.0597 | − | 5.54302i | 1.02502 | − | 0.333048i | 0.252198 | − | 0.967676i | \(-0.418847\pi\) |
0.772818 | + | 0.634628i | \(0.218847\pi\) | |||||||
\(278\) | −19.1114 | + | 26.3047i | −1.14623 | + | 1.57765i | ||||
\(279\) | 2.79029 | − | 2.02726i | 0.167050 | − | 0.121369i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.29013 | − | 7.04830i | 0.136618 | − | 0.420467i | −0.859220 | − | 0.511606i | \(-0.829051\pi\) |
0.995838 | + | 0.0911392i | \(0.0290508\pi\) | |||||||
\(282\) | 17.3198 | + | 23.8387i | 1.03138 | + | 1.41957i | ||||
\(283\) | −3.16630 | + | 4.35804i | −0.188217 | + | 0.259059i | −0.892689 | − | 0.450673i | \(-0.851184\pi\) |
0.704472 | + | 0.709732i | \(0.251184\pi\) | |||||||
\(284\) | −3.82713 | − | 11.7787i | −0.227098 | − | 0.698937i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.51558 | − | 0.420905i | 0.148749 | − | 0.0248886i | ||||
\(287\) | 35.6530i | 2.10453i | ||||||||
\(288\) | 0.295474 | − | 0.0960054i | 0.0174110 | − | 0.00565717i | ||||
\(289\) | 6.47214 | + | 4.70228i | 0.380714 | + | 0.276605i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0692451 | − | 0.213115i | 0.00405922 | − | 0.0124930i | ||||
\(292\) | −33.1750 | − | 10.7792i | −1.94142 | − | 0.630806i | ||||
\(293\) | −1.02278 | − | 1.40774i | −0.0597515 | − | 0.0822409i | 0.778096 | − | 0.628146i | \(-0.216186\pi\) |
−0.837847 | + | 0.545905i | \(0.816186\pi\) | |||||||
\(294\) | 7.55666 | + | 5.49023i | 0.440713 | + | 0.320197i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.1420 | 0.763864 | ||||||||
\(297\) | 2.36553 | + | 2.32471i | 0.137262 | + | 0.134893i | ||||
\(298\) | 14.4371i | 0.836321i | ||||||||
\(299\) | 0.103916 | + | 0.319822i | 0.00600964 | + | 0.0184958i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.6641 | − | 10.6541i | 0.845227 | − | 0.614093i | ||||
\(302\) | 17.8171 | + | 5.78913i | 1.02526 | + | 0.333127i | ||||
\(303\) | 0.480593 | + | 0.156154i | 0.0276094 | + | 0.00897082i | ||||
\(304\) | −25.2633 | + | 18.3548i | −1.44895 | + | 1.05272i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.79455 | + | 11.6784i | 0.216920 | + | 0.667612i | ||||
\(307\) | 21.3566i | 1.21889i | 0.792829 | + | 0.609444i | \(0.208607\pi\) | ||||
−0.792829 | + | 0.609444i | \(0.791393\pi\) | |||||||
\(308\) | −31.3445 | − | 30.8035i | −1.78602 | − | 1.75519i | ||||
\(309\) | 6.40197 | 0.364195 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.5435 | − | 19.2850i | −1.50514 | − | 1.09355i | −0.968275 | − | 0.249886i | \(-0.919607\pi\) |
−0.536870 | − | 0.843665i | \(-0.680393\pi\) | |||||||
\(312\) | 0.918222 | + | 1.26382i | 0.0519841 | + | 0.0715499i | ||||
\(313\) | 3.28925 | + | 1.06874i | 0.185919 | + | 0.0604089i | 0.400497 | − | 0.916298i | \(-0.368837\pi\) |
−0.214578 | + | 0.976707i | \(0.568837\pi\) | |||||||
\(314\) | 7.69021 | − | 23.6680i | 0.433984 | − | 1.33566i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.6590 | − | 12.8300i | −0.993398 | − | 0.721746i | ||||
\(317\) | 2.73491 | − | 0.888626i | 0.153608 | − | 0.0499102i | −0.231204 | − | 0.972905i | \(-0.574266\pi\) |
0.384812 | + | 0.922995i | \(0.374266\pi\) | |||||||
\(318\) | − | 12.1209i | − | 0.679704i | ||||||
\(319\) | −16.4751 | + | 2.75659i | −0.922426 | + | 0.154340i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.646615 | + | 1.99008i | 0.0360905 | + | 0.111075i | ||||
\(322\) | 5.09540 | − | 7.01321i | 0.283955 | − | 0.390831i | ||||
\(323\) | −21.9070 | − | 30.1524i | −1.21894 | − | 1.67772i | ||||
\(324\) | −1.24576 | + | 3.83407i | −0.0692092 | + | 0.213004i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.99201 | − | 7.25962i | 0.553406 | − | 0.402073i | ||||
\(327\) | −3.93392 | + | 5.41457i | −0.217546 | + | 0.299427i | ||||
\(328\) | 51.4664 | − | 16.7224i | 2.84176 | − | 0.923342i | ||||
\(329\) | 39.4362 | 2.17419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1221 | −0.776219 | −0.388109 | − | 0.921613i | \(-0.626872\pi\) | ||||
−0.388109 | + | 0.921613i | \(0.626872\pi\) | |||||||
\(332\) | −62.2861 | + | 20.2380i | −3.41839 | + | 1.11070i | ||||
\(333\) | −1.54839 | + | 2.13118i | −0.0848514 | + | 0.116788i | ||||
\(334\) | 11.5060 | − | 8.35958i | 0.629579 | − | 0.457416i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.25499 | − | 13.0955i | 0.232129 | − | 0.714419i | ||||
\(337\) | −9.37457 | − | 12.9030i | −0.510665 | − | 0.702870i | 0.473366 | − | 0.880866i | \(-0.343039\pi\) |
−0.984031 | + | 0.177995i | \(0.943039\pi\) | |||||||
\(338\) | 18.6244 | − | 25.6343i | 1.01303 | − | 1.39432i | ||||
\(339\) | 3.33556 | + | 10.2658i | 0.181163 | + | 0.557562i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.69105 | + | 11.3133i | −0.0915755 | + | 0.612650i | ||||
\(342\) | − | 18.3064i | − | 0.989895i | ||||||
\(343\) | −9.99271 | + | 3.24683i | −0.539555 | + | 0.175312i | ||||
\(344\) | −22.2575 | − | 16.1711i | −1.20005 | − | 0.871885i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.1921 | − | 37.5233i | 0.655449 | − | 2.01727i | ||||
\(347\) | 28.2275 | + | 9.17166i | 1.51533 | + | 0.492360i | 0.944445 | − | 0.328670i | \(-0.106600\pi\) |
0.570884 | + | 0.821030i | \(0.306600\pi\) | |||||||
\(348\) | −11.9343 | − | 16.4262i | −0.639748 | − | 0.880537i | ||||
\(349\) | 25.6408 | + | 18.6291i | 1.37252 | + | 0.997194i | 0.997536 | + | 0.0701620i | \(0.0223516\pi\) |
0.374984 | + | 0.927031i | \(0.377648\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.313133 | −0.0167138 | ||||||||
\(352\) | −0.459787 | + | 0.922138i | −0.0245067 | + | 0.0491501i | ||||
\(353\) | − | 1.20189i | − | 0.0639703i | −0.999488 | − | 0.0319852i | \(-0.989817\pi\) | ||
0.999488 | − | 0.0319852i | \(-0.0101829\pi\) | |||||||
\(354\) | 6.95473 | + | 21.4044i | 0.369640 | + | 1.13763i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.28740 | + | 3.84152i | −0.280232 | + | 0.203600i | ||||
\(357\) | 15.6299 | + | 5.07845i | 0.827220 | + | 0.268780i | ||||
\(358\) | 19.3934 | + | 6.30130i | 1.02497 | + | 0.333034i | ||||
\(359\) | −9.43239 | + | 6.85304i | −0.497823 | + | 0.361689i | −0.808185 | − | 0.588929i | \(-0.799550\pi\) |
0.310362 | + | 0.950618i | \(0.399550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2987 | + | 34.7737i | 0.594667 | + | 1.83020i | ||||
\(362\) | − | 15.8755i | − | 0.834396i | ||||||
\(363\) | −10.9983 | + | 0.191475i | −0.577263 | + | 0.0100498i | ||||
\(364\) | 4.14918 | 0.217476 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −18.2479 | − | 13.2579i | −0.953832 | − | 0.693000i | ||||
\(367\) | −9.39636 | − | 12.9330i | −0.490486 | − | 0.675096i | 0.489991 | − | 0.871727i | \(-0.337000\pi\) |
−0.980478 | + | 0.196631i | \(0.937000\pi\) | |||||||
\(368\) | −4.27874 | − | 1.39025i | −0.223045 | − | 0.0724717i | ||||
\(369\) | −3.35197 | + | 10.3163i | −0.174497 | + | 0.537045i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1239 | − | 9.53504i | −0.681357 | − | 0.495035i | ||||
\(372\) | −13.2237 | + | 4.29663i | −0.685615 | + | 0.222770i | ||||
\(373\) | − | 0.321975i | − | 0.0166712i | −0.999965 | − | 0.00833561i | \(-0.997347\pi\) | ||
0.999965 | − | 0.00833561i | \(-0.00265334\pi\) | |||||||
\(374\) | −36.4469 | − | 18.1728i | −1.88463 | − | 0.939693i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.4968 | − | 56.9274i | −0.953902 | − | 2.93581i | ||||
\(377\) | 0.926988 | − | 1.27589i | 0.0477423 | − | 0.0657117i | ||||
\(378\) | 4.74467 | + | 6.53048i | 0.244039 | + | 0.335891i | ||||
\(379\) | −3.52819 | + | 10.8586i | −0.181231 | + | 0.557771i | −0.999863 | − | 0.0165471i | \(-0.994733\pi\) |
0.818632 | + | 0.574318i | \(0.194733\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.7559 | − | 9.99428i | 0.704738 | − | 0.512022i | ||||
\(382\) | 22.1861 | − | 30.5365i | 1.13514 | − | 1.56239i | ||||
\(383\) | 26.9789 | − | 8.76597i | 1.37856 | − | 0.447920i | 0.476362 | − | 0.879249i | \(-0.341955\pi\) |
0.902195 | + | 0.431329i | \(0.141955\pi\) | |||||||
\(384\) | 19.3242 | 0.986136 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 38.6846 | 1.96899 | ||||||||
\(387\) | 5.24477 | − | 1.70413i | 0.266607 | − | 0.0866257i | ||||
\(388\) | −0.530981 | + | 0.730833i | −0.0269565 | + | 0.0371024i | ||||
\(389\) | 12.2810 | − | 8.92269i | 0.622673 | − | 0.452398i | −0.231181 | − | 0.972911i | \(-0.574259\pi\) |
0.853854 | + | 0.520513i | \(0.174259\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.65930 | − | 5.10680i | 0.0839143 | − | 0.258262i | ||||
\(392\) | −11.1528 | − | 15.3504i | −0.563299 | − | 0.775315i | ||||
\(393\) | 0.0253046 | − | 0.0348288i | 0.00127645 | − | 0.00175688i | ||||
\(394\) | −12.4415 | − | 38.2911i | −0.626796 | − | 1.92908i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.17357 | − | 11.8600i | −0.310234 | − | 0.595987i | ||||
\(397\) | 5.22461i | 0.262216i | 0.991368 | + | 0.131108i | \(0.0418534\pi\) | ||||
−0.991368 | + | 0.131108i | \(0.958147\pi\) | |||||||
\(398\) | 16.2681 | − | 5.28581i | 0.815444 | − | 0.264954i | ||||
\(399\) | −19.8212 | − | 14.4010i | −0.992302 | − | 0.720950i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.32644 | − | 13.3154i | 0.216052 | − | 0.664941i | −0.783025 | − | 0.621990i | \(-0.786324\pi\) |
0.999077 | − | 0.0429502i | \(-0.0136757\pi\) | |||||||
\(402\) | −35.6750 | − | 11.5915i | −1.77931 | − | 0.578132i | ||||
\(403\) | −0.634804 | − | 0.873733i | −0.0316219 | − | 0.0435238i | ||||
\(404\) | −1.64810 | − | 1.19741i | −0.0819959 | − | 0.0595735i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −40.6549 | −2.01767 | ||||||||
\(407\) | −1.44181 | − | 8.61714i | −0.0714680 | − | 0.427136i | ||||
\(408\) | − | 24.9442i | − | 1.23492i | ||||||
\(409\) | −10.2937 | − | 31.6809i | −0.508993 | − | 1.56652i | −0.793953 | − | 0.607979i | \(-0.791980\pi\) |
0.284960 | − | 0.958539i | \(-0.408020\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.95645 | + | 4.32761i | −0.293810 | + | 0.213465i | ||||
\(412\) | −24.5456 | − | 7.97535i | −1.20927 | − | 0.392917i | ||||
\(413\) | 28.6467 | + | 9.30787i | 1.40961 | + | 0.458011i | ||||
\(414\) | 2.13372 | − | 1.55024i | 0.104867 | − | 0.0761902i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0300625 | − | 0.0925229i | −0.00147394 | − | 0.00453631i | ||||
\(417\) | 13.2393i | 0.648334i | ||||||||
\(418\) | 43.3043 | + | 42.5569i | 2.11808 | + | 2.08153i | ||||
\(419\) | 5.28460 | 0.258170 | 0.129085 | − | 0.991634i | \(-0.458796\pi\) | ||||
0.129085 | + | 0.991634i | \(0.458796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9023 | + | 18.0926i | 1.21367 | + | 0.881780i | 0.995558 | − | 0.0941452i | \(-0.0300118\pi\) |
0.218107 | + | 0.975925i | \(0.430012\pi\) | |||||||
\(422\) | 28.8030 | + | 39.6439i | 1.40211 | + | 1.92984i | ||||
\(423\) | 11.4110 | + | 3.70764i | 0.554820 | + | 0.180272i | ||||
\(424\) | −7.60864 | + | 23.4170i | −0.369508 | + | 1.13723i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.10384 | − | 4.43470i | −0.295732 | − | 0.214862i | ||||
\(427\) | −28.7099 | + | 9.32841i | −1.38937 | + | 0.451433i | ||||
\(428\) | − | 8.43562i | − | 0.407751i | ||||||
\(429\) | 0.727943 | − | 0.740727i | 0.0351454 | − | 0.0357626i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.81656 | + | 11.7462i | 0.183837 | + | 0.565793i | 0.999926 | − | 0.0121333i | \(-0.00386225\pi\) |
−0.816089 | + | 0.577926i | \(0.803862\pi\) | |||||||
\(432\) | 2.46239 | − | 3.38919i | 0.118472 | − | 0.163062i | ||||
\(433\) | 0.830465 | + | 1.14304i | 0.0399096 | + | 0.0549308i | 0.828505 | − | 0.559981i | \(-0.189192\pi\) |
−0.788596 | + | 0.614912i | \(0.789192\pi\) | |||||||
\(434\) | −8.60323 | + | 26.4780i | −0.412968 | + | 1.27098i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.8282 | − | 15.8591i | 1.04538 | − | 0.759514i | ||||
\(437\) | −4.70527 | + | 6.47625i | −0.225084 | + | 0.309801i | ||||
\(438\) | −20.2100 | + | 6.56662i | −0.965670 | + | 0.313765i | ||||
\(439\) | 7.58532 | 0.362028 | 0.181014 | − | 0.983481i | \(-0.442062\pi\) | ||||
0.181014 | + | 0.983481i | \(0.442062\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.80333 | 0.181111 | ||||||||
\(442\) | 3.65691 | − | 1.18820i | 0.173941 | − | 0.0565170i | ||||
\(443\) | −6.50455 | + | 8.95274i | −0.309040 | + | 0.425358i | −0.935082 | − | 0.354432i | \(-0.884674\pi\) |
0.626041 | + | 0.779790i | \(0.284674\pi\) | |||||||
\(444\) | 8.59160 | − | 6.24216i | 0.407739 | − | 0.296240i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.2895 | + | 47.0562i | −0.723979 | + | 2.22818i | ||||
\(447\) | 3.45534 | + | 4.75587i | 0.163432 | + | 0.224945i | ||||
\(448\) | 14.7129 | − | 20.2505i | 0.695118 | − | 0.956748i | ||||
\(449\) | −1.95563 | − | 6.01882i | −0.0922920 | − | 0.284045i | 0.894247 | − | 0.447575i | \(-0.147712\pi\) |
−0.986538 | + | 0.163529i | \(0.947712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.6112 | − | 31.9116i | −0.782190 | − | 1.50266i | ||||
\(452\) | − | 43.5152i | − | 2.04678i | ||||||
\(453\) | 7.25486 | − | 2.35725i | 0.340863 | − | 0.110753i | ||||
\(454\) | 1.06085 | + | 0.770756i | 0.0497884 | + | 0.0361734i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.4915 | + | 35.3671i | −0.538138 | + | 1.65622i | ||||
\(457\) | −0.180300 | − | 0.0585832i | −0.00843410 | − | 0.00274040i | 0.304797 | − | 0.952417i | \(-0.401411\pi\) |
−0.313231 | + | 0.949677i | \(0.601411\pi\) | |||||||
\(458\) | −32.0364 | − | 44.0944i | −1.49696 | − | 2.06039i | ||||
\(459\) | 4.04508 | + | 2.93893i | 0.188808 | + | 0.137177i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.6198 | −1.23981 | −0.619904 | − | 0.784678i | \(-0.712828\pi\) | ||||
−0.619904 | + | 0.784678i | \(0.712828\pi\) | |||||||
\(462\) | −26.4780 | − | 3.95778i | −1.23187 | − | 0.184133i | ||||
\(463\) | − | 20.9935i | − | 0.975652i | −0.872941 | − | 0.487826i | \(-0.837790\pi\) | ||
0.872941 | − | 0.487826i | \(-0.162210\pi\) | |||||||
\(464\) | 6.51998 | + | 20.0664i | 0.302682 | + | 0.931561i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.07131 | − | 6.59070i | 0.420221 | − | 0.305308i | ||||
\(467\) | 7.51324 | + | 2.44120i | 0.347671 | + | 0.112965i | 0.477647 | − | 0.878552i | \(-0.341490\pi\) |
−0.129976 | + | 0.991517i | \(0.541490\pi\) | |||||||
\(468\) | 1.20058 | + | 0.390091i | 0.0554966 | + | 0.0180319i | ||||
\(469\) | −40.6149 | + | 29.5085i | −1.87542 | + | 1.36257i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.13134 | − | 9.63727i | −0.144284 | − | 0.444062i | ||||
\(472\) | − | 45.7182i | − | 2.10435i | ||||||
\(473\) | −8.16138 | + | 16.3683i | −0.375261 | + | 0.752614i | ||||
\(474\) | −13.2973 | −0.610766 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −53.5994 | − | 38.9423i | −2.45673 | − | 1.78492i | ||||
\(477\) | −2.90097 | − | 3.99285i | −0.132826 | − | 0.182820i | ||||
\(478\) | 13.6884 | + | 4.44762i | 0.626091 | + | 0.203429i | ||||
\(479\) | −12.3523 | + | 38.0164i | −0.564389 | + | 1.73701i | 0.105369 | + | 0.994433i | \(0.466398\pi\) |
−0.669758 | + | 0.742579i | \(0.733602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.667344 | + | 0.484854i | 0.0304282 | + | 0.0221074i | ||||
\(482\) | −23.2652 | + | 7.55931i | −1.05970 | + | 0.344317i | ||||
\(483\) | − | 3.52981i | − | 0.160612i | ||||||
\(484\) | 42.4069 | + | 12.9672i | 1.92759 | + | 0.589419i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.758911 | + | 2.33569i | 0.0344249 | + | 0.105949i | ||||
\(487\) | −5.83998 | + | 8.03804i | −0.264635 | + | 0.364238i | −0.920569 | − | 0.390579i | \(-0.872275\pi\) |
0.655935 | + | 0.754818i | \(0.272275\pi\) | |||||||
\(488\) | 26.9318 | + | 37.0684i | 1.21914 | + | 1.67801i | ||||
\(489\) | 1.55407 | − | 4.78292i | 0.0702773 | − | 0.216291i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.02364 | + | 2.92335i | −0.181584 | + | 0.131929i | −0.674864 | − | 0.737942i | \(-0.735798\pi\) |
0.493280 | + | 0.869871i | \(0.335798\pi\) | |||||||
\(492\) | 25.7034 | − | 35.3777i | 1.15880 | − | 1.59495i | ||||
\(493\) | −23.9498 | + | 7.78177i | −1.07865 | + | 0.350473i | ||||
\(494\) | −5.73234 | −0.257910 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.4487 | 0.648767 | ||||||||
\(497\) | −9.60333 | + | 3.12031i | −0.430768 | + | 0.139965i | ||||
\(498\) | −23.4508 | + | 32.2773i | −1.05086 | + | 1.44638i | ||||
\(499\) | 35.4153 | − | 25.7307i | 1.58541 | − | 1.15186i | 0.675256 | − | 0.737584i | \(-0.264033\pi\) |
0.910149 | − | 0.414281i | \(-0.135967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.78953 | − | 5.50761i | 0.0799504 | − | 0.246062i | ||||
\(502\) | 24.3651 | + | 33.5357i | 1.08747 | + | 1.49677i | ||||
\(503\) | −3.69268 | + | 5.08254i | −0.164648 | + | 0.226619i | −0.883367 | − | 0.468682i | \(-0.844729\pi\) |
0.718718 | + | 0.695301i | \(0.244729\pi\) | |||||||
\(504\) | −5.06711 | − | 15.5950i | −0.225707 | − | 0.694655i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.29314 | + | 8.65125i | −0.0574870 | + | 0.384595i | ||||
\(507\) | − | 12.9019i | − | 0.572996i | ||||||
\(508\) | −65.1918 | + | 21.1821i | −2.89242 | + | 0.939803i | ||||
\(509\) | 20.0945 | + | 14.5995i | 0.890671 | + | 0.647111i | 0.936053 | − | 0.351859i | \(-0.114450\pi\) |
−0.0453816 | + | 0.998970i | \(0.514450\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.78845 | + | 27.0481i | −0.388778 | + | 1.19654i | ||||
\(512\) | −38.5155 | − | 12.5144i | −1.70216 | − | 0.553066i | ||||
\(513\) | −4.38140 | − | 6.03048i | −0.193443 | − | 0.266252i | ||||
\(514\) | 22.1407 | + | 16.0861i | 0.976583 | + | 0.709529i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −22.2318 | −0.978699 | ||||||||
\(517\) | −35.2977 | + | 18.3738i | −1.55239 | + | 0.808078i | ||||
\(518\) | − | 21.2642i | − | 0.934296i | ||||||
\(519\) | −4.96442 | − | 15.2789i | −0.217914 | − | 0.670670i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.62161 | − | 4.08434i | 0.246287 | − | 0.178938i | −0.457792 | − | 0.889059i | \(-0.651360\pi\) |
0.704080 | + | 0.710121i | \(0.251360\pi\) | |||||||
\(522\) | −11.7636 | − | 3.82223i | −0.514879 | − | 0.167294i | ||||
\(523\) | 25.4417 | + | 8.26650i | 1.11249 | + | 0.361469i | 0.806896 | − | 0.590694i | \(-0.201146\pi\) |
0.305591 | + | 0.952163i | \(0.401146\pi\) | |||||||
\(524\) | −0.140408 | + | 0.102013i | −0.00613376 | + | 0.00445644i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.3939 | − | 62.7661i | −0.889218 | − | 2.73673i | ||||
\(527\) | 17.2449i | 0.751202i | ||||||||
\(528\) | 2.29290 | + | 13.7037i | 0.0997854 | + | 0.596378i | ||||
\(529\) | 21.8467 | 0.949856 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.41391 | + | 5.38652i | 0.321736 | + | 0.233755i | ||||
\(532\) | 58.0557 | + | 79.9069i | 2.51704 | + | 3.46440i | ||||
\(533\) | 3.23038 | + | 1.04961i | 0.139923 | + | 0.0454638i | ||||
\(534\) | −1.23033 | + | 3.78657i | −0.0532416 | + | 0.163861i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 61.6462 | + | 44.7886i | 2.66271 | + | 1.93457i | ||||
\(537\) | 7.89671 | − | 2.56580i | 0.340768 | − | 0.110722i | ||||
\(538\) | 24.7133i | 1.06547i | ||||||||
\(539\) | −8.84162 | + | 8.99689i | −0.380836 | + | 0.387524i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.48336 | + | 13.7984i | 0.192755 | + | 0.593237i | 0.999995 | + | 0.00301536i | \(0.000959822\pi\) |
−0.807241 | + | 0.590222i | \(0.799040\pi\) | |||||||
\(542\) | 15.2208 | − | 20.9496i | 0.653789 | − | 0.899863i | ||||
\(543\) | −3.79959 | − | 5.22969i | −0.163056 | − | 0.224428i | ||||
\(544\) | −0.480027 | + | 1.47737i | −0.0205810 | + | 0.0633418i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.04491 | − | 1.48571i | 0.0875141 | − | 0.0635827i | ||||
\(547\) | −15.7142 | + | 21.6287i | −0.671890 | + | 0.924777i | −0.999801 | − | 0.0199316i | \(-0.993655\pi\) |
0.327912 | + | 0.944708i | \(0.393655\pi\) | |||||||
\(548\) | 28.2286 | − | 9.17203i | 1.20587 | − | 0.391810i | ||||
\(549\) | −9.18431 | −0.391977 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.5422 | 1.59935 | ||||||||
\(552\) | −5.09540 | + | 1.65559i | −0.216875 | + | 0.0704668i | ||||
\(553\) | −10.4605 | + | 14.3977i | −0.444826 | + | 0.612251i | ||||
\(554\) | −35.6394 | + | 25.8935i | −1.51417 | + | 1.10011i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4931 | − | 50.7606i | 0.699464 | − | 2.15273i | ||||
\(557\) | −10.1360 | − | 13.9510i | −0.429477 | − | 0.591125i | 0.538356 | − | 0.842718i | \(-0.319046\pi\) |
−0.967833 | + | 0.251593i | \(0.919046\pi\) | |||||||
\(558\) | −4.97873 | + | 6.85264i | −0.210767 | + | 0.290095i | ||||
\(559\) | −0.533620 | − | 1.64231i | −0.0225697 | − | 0.0694624i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.3558 | + | 2.73663i | −0.690541 | + | 0.115541i | ||||
\(562\) | 18.2006i | 0.767748i | ||||||||
\(563\) | −0.791197 | + | 0.257075i | −0.0333450 | + | 0.0108344i | −0.325642 | − | 0.945493i | \(-0.605580\pi\) |
0.292297 | + | 0.956328i | \(0.405580\pi\) | |||||||
\(564\) | −39.1316 | − | 28.4307i | −1.64774 | − | 1.19715i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.08813 | − | 12.5820i | 0.171837 | − | 0.528860i | ||||
\(567\) | 3.12597 | + | 1.01569i | 0.131278 | + | 0.0426550i | ||||
\(568\) | 9.00855 | + | 12.3992i | 0.377991 | + | 0.520259i | ||||
\(569\) | 9.38141 | + | 6.81599i | 0.393289 | + | 0.285741i | 0.766802 | − | 0.641884i | \(-0.221847\pi\) |
−0.373513 | + | 0.927625i | \(0.621847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.8414 | 0.914034 | 0.457017 | − | 0.889458i | \(-0.348918\pi\) | ||||
0.457017 | + | 0.889458i | \(0.348918\pi\) | |||||||
\(572\) | −3.71376 | + | 1.93315i | −0.155280 | + | 0.0808292i | ||||
\(573\) | − | 15.3693i | − | 0.642061i | ||||||
\(574\) | −27.0575 | − | 83.2744i | −1.12936 | − | 3.47580i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.16110 | − | 4.47630i | 0.256712 | − | 0.186512i | ||||
\(577\) | 9.26888 | + | 3.01164i | 0.385868 | + | 0.125376i | 0.495526 | − | 0.868593i | \(-0.334975\pi\) |
−0.109657 | + | 0.993969i | \(0.534975\pi\) | |||||||
\(578\) | −18.6855 | − | 6.07129i | −0.777214 | − | 0.252532i | ||||
\(579\) | 12.7435 | − | 9.25867i | 0.529600 | − | 0.384777i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5003 | + | 50.7827i | 0.684548 | + | 2.10682i | ||||
\(582\) | 0.550320i | 0.0228115i | ||||||||
\(583\) | 16.1891 | + | 2.41986i | 0.670485 | + | 0.100220i | ||||
\(584\) | 43.1669 | 1.78626 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.45724 | + | 2.51183i | 0.142817 | + | 0.103763i | ||||
\(587\) | −13.4862 | − | 18.5622i | −0.556635 | − | 0.766143i | 0.434258 | − | 0.900788i | \(-0.357010\pi\) |
−0.990894 | + | 0.134645i | \(0.957010\pi\) | |||||||
\(588\) | −14.5822 | − | 4.73805i | −0.601361 | − | 0.195394i | ||||
\(589\) | 7.94453 | − | 24.4507i | 0.327349 | − | 1.00748i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2630 | − | 9.63612i | −0.545566 | − | 0.396377i | ||||
\(592\) | −10.4956 | + | 3.41022i | −0.431366 | + | 0.140159i | ||||
\(593\) | − | 28.7819i | − | 1.18193i | −0.806697 | − | 0.590965i | \(-0.798747\pi\) | ||
0.806697 | − | 0.590965i | \(-0.201253\pi\) | |||||||
\(594\) | −7.28939 | − | 3.63456i | −0.299087 | − | 0.149128i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.32333 | − | 22.5389i | −0.299975 | − | 0.923229i | ||||
\(597\) | 4.09392 | − | 5.63480i | 0.167553 | − | 0.230617i | ||||
\(598\) | −0.485432 | − | 0.668140i | −0.0198508 | − | 0.0273223i | ||||
\(599\) | 9.02179 | − | 27.7662i | 0.368620 | − | 1.13450i | −0.579062 | − | 0.815283i | \(-0.696581\pi\) |
0.947683 | − | 0.319214i | \(-0.103419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.40494 | − | 3.92692i | 0.220472 | − | 0.160182i | −0.472067 | − | 0.881563i | \(-0.656492\pi\) |
0.692539 | + | 0.721380i | \(0.256492\pi\) | |||||||
\(602\) | −26.1653 | + | 36.0135i | −1.06642 | + | 1.46780i | ||||
\(603\) | −14.5263 | + | 4.71989i | −0.591557 | + | 0.192209i | ||||
\(604\) | −30.7522 | −1.25129 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.24102 | −0.0504131 | ||||||||
\(607\) | 40.5252 | − | 13.1674i | 1.64487 | − | 0.534450i | 0.667250 | − | 0.744834i | \(-0.267471\pi\) |
0.977619 | + | 0.210384i | \(0.0674713\pi\) | |||||||
\(608\) | 1.36121 | − | 1.87355i | 0.0552044 | − | 0.0759824i | ||||
\(609\) | −13.3925 | + | 9.73024i | −0.542693 | + | 0.394289i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.16099 | − | 3.57315i | 0.0469685 | − | 0.144554i | ||||
\(612\) | −11.8479 | − | 16.3073i | −0.478924 | − | 0.659182i | ||||
\(613\) | 3.42771 | − | 4.71783i | 0.138444 | − | 0.190552i | −0.734165 | − | 0.678971i | \(-0.762426\pi\) |
0.872609 | + | 0.488419i | \(0.162426\pi\) | |||||||
\(614\) | −16.2078 | − | 49.8824i | −0.654093 | − | 2.01309i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.6699 | + | 24.2673i | 1.96097 | + | 0.977758i | ||||
\(617\) | − | 33.6386i | − | 1.35424i | −0.735874 | − | 0.677119i | \(-0.763228\pi\) | ||
0.735874 | − | 0.677119i | \(-0.236772\pi\) | |||||||
\(618\) | −14.9530 | + | 4.85852i | −0.601498 | + | 0.195438i | ||||
\(619\) | 34.4331 | + | 25.0171i | 1.38398 | + | 1.00552i | 0.996495 | + | 0.0836477i | \(0.0266570\pi\) |
0.387488 | + | 0.921875i | \(0.373343\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.331860 | − | 1.02136i | 0.0133171 | − | 0.0409857i | ||||
\(622\) | 76.6329 | + | 24.8996i | 3.07270 | + | 0.998381i | ||||
\(623\) | 3.13205 | + | 4.31089i | 0.125483 | + | 0.172712i | ||||
\(624\) | −1.06127 | − | 0.771056i | −0.0424847 | − | 0.0308669i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.49374 | −0.339478 | ||||||||
\(627\) | 24.4507 | + | 3.65476i | 0.976468 | + | 0.145957i | ||||
\(628\) | 40.8509i | 1.63013i | ||||||||
\(629\) | −4.07019 | − | 12.5268i | −0.162289 | − | 0.499475i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.20016 | − | 5.23122i | 0.286634 | − | 0.208252i | −0.435172 | − | 0.900347i | \(-0.643312\pi\) |
0.721806 | + | 0.692096i | \(0.243312\pi\) | |||||||
\(632\) | 25.6898 | + | 8.34713i | 1.02189 | + | 0.332031i | ||||
\(633\) | 18.9765 | + | 6.16585i | 0.754250 | + | 0.245071i | ||||
\(634\) | −5.71351 | + | 4.15111i | −0.226912 | + | 0.164862i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.14839 | + | 18.9228i | 0.243799 | + | 0.750337i | ||||
\(637\) | − | 1.19095i | − | 0.0471871i | ||||||
\(638\) | 36.3886 | − | 18.9416i | 1.44064 | − | 0.749906i | ||||
\(639\) | −3.07211 | −0.121531 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.99007 | + | 3.62549i | 0.197096 | + | 0.143198i | 0.681956 | − | 0.731393i | \(-0.261130\pi\) |
−0.484860 | + | 0.874592i | \(0.661130\pi\) | |||||||
\(642\) | −3.02058 | − | 4.15747i | −0.119213 | − | 0.164082i | ||||
\(643\) | −4.14029 | − | 1.34526i | −0.163277 | − | 0.0530519i | 0.226238 | − | 0.974072i | \(-0.427357\pi\) |
−0.389515 | + | 0.921020i | \(0.627357\pi\) | |||||||
\(644\) | −4.39731 | + | 13.5335i | −0.173278 | + | 0.533296i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 74.0508 | + | 53.8011i | 2.91349 | + | 2.11677i | ||||
\(647\) | −12.8329 | + | 4.16967i | −0.504514 | + | 0.163927i | −0.550206 | − | 0.835029i | \(-0.685451\pi\) |
0.0456916 | + | 0.998956i | \(0.485451\pi\) | |||||||
\(648\) | − | 4.98884i | − | 0.195980i | ||||||
\(649\) | −29.9771 | + | 5.01575i | −1.17671 | + | 0.196885i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.50310 | + | 10.7814i | 0.137297 | + | 0.422558i | ||||
\(652\) | −11.9168 | + | 16.4021i | −0.466697 | + | 0.642354i | ||||
\(653\) | 16.1336 | + | 22.2060i | 0.631357 | + | 0.868988i | 0.998118 | − | 0.0613270i | \(-0.0195332\pi\) |
−0.366761 | + | 0.930315i | \(0.619533\pi\) | |||||||
\(654\) | 5.07922 | − | 15.6322i | 0.198613 | − | 0.611269i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.7632 | + | 26.7100i | −1.43536 | + | 1.04285i | ||||
\(657\) | −5.08592 | + | 7.00018i | −0.198421 | + | 0.273103i | ||||
\(658\) | −92.1105 | + | 29.9285i | −3.59084 | + | 1.16674i | ||||
\(659\) | 18.7768 | 0.731441 | 0.365721 | − | 0.930725i | \(-0.380823\pi\) | ||||
0.365721 | + | 0.930725i | \(0.380823\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6525 | −0.842184 | −0.421092 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421092 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(662\) | 32.9847 | − | 10.7174i | 1.28199 | − | 0.416543i | ||||
\(663\) | 0.920276 | − | 1.26665i | 0.0357406 | − | 0.0491927i | ||||
\(664\) | 65.5674 | − | 47.6375i | 2.54451 | − | 1.84869i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.99919 | − | 6.15286i | 0.0774669 | − | 0.238419i | ||||
\(667\) | 3.17919 | + | 4.37578i | 0.123099 | + | 0.169431i | ||||
\(668\) | −13.7224 | + | 18.8872i | −0.530935 | + | 0.730769i | ||||
\(669\) | 6.22565 | + | 19.1606i | 0.240698 | + | 0.740791i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.3508 | − | 21.7258i | 0.824240 | − | 0.838714i | ||||
\(672\) | 1.02116i | 0.0393919i | ||||||||
\(673\) | 22.1617 | − | 7.20076i | 0.854269 | − | 0.277569i | 0.151036 | − | 0.988528i | \(-0.451739\pi\) |
0.703233 | + | 0.710959i | \(0.251739\pi\) | |||||||
\(674\) | 31.6883 | + | 23.0229i | 1.22059 | + | 0.886808i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.0728 | + | 49.4670i | −0.618184 | + | 1.90258i | ||||
\(677\) | 31.6519 | + | 10.2843i | 1.21648 | + | 0.395259i | 0.845800 | − | 0.533501i | \(-0.179124\pi\) |
0.370683 | + | 0.928760i | \(0.379124\pi\) | |||||||
\(678\) | −15.5817 | − | 21.4463i | −0.598410 | − | 0.823641i | ||||
\(679\) | 0.595859 | + | 0.432917i | 0.0228670 | + | 0.0166138i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.533937 | 0.0204605 | ||||||||
\(682\) | −4.63603 | − | 27.7077i | −0.177523 | − | 1.06098i | ||||
\(683\) | − | 16.9244i | − | 0.647593i | −0.946127 | − | 0.323796i | \(-0.895041\pi\) | ||
0.946127 | − | 0.323796i | \(-0.104959\pi\) | |||||||
\(684\) | 9.28603 | + | 28.5795i | 0.355060 | + | 1.09276i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.8758 | − | 15.1671i | 0.797041 | − | 0.579084i | ||||
\(687\) | −21.1068 | − | 6.85803i | −0.805276 | − | 0.261650i | ||||
\(688\) | 21.9717 | + | 7.13905i | 0.837664 | + | 0.272174i | ||||
\(689\) | −1.25029 | + | 0.908392i | −0.0476324 | + | 0.0346070i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9668 | − | 46.0630i | −0.569363 | − | 1.75232i | −0.654617 | − | 0.755961i | \(-0.727170\pi\) |
0.0852532 | − | 0.996359i | \(-0.472830\pi\) | |||||||
\(692\) | 64.7650i | 2.46200i | ||||||||
\(693\) | −9.66962 | + | 5.03340i | −0.367318 | + | 0.191203i | ||||
\(694\) | −72.8910 | −2.76690 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20.3275 | + | 14.7688i | 0.770511 | + | 0.559809i | ||||
\(697\) | −31.8791 | − | 43.8779i | −1.20751 | − | 1.66199i | ||||
\(698\) | −74.0267 | − | 24.0527i | −2.80195 | − | 0.910409i | ||||
\(699\) | 1.41087 | − | 4.34221i | 0.0533640 | − | 0.164237i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.7424 | + | 26.6949i | 1.38774 | + | 1.00825i | 0.996109 | + | 0.0881330i | \(0.0280900\pi\) |
0.391634 | + | 0.920121i | \(0.371910\pi\) | |||||||
\(702\) | 0.731382 | − | 0.237640i | 0.0276042 | − | 0.00896916i | ||||
\(703\) | 19.6361i | 0.740591i | ||||||||
\(704\) | −3.73392 | + | 24.9803i | −0.140727 | + | 0.941482i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.912130 | + | 2.80725i | 0.0343285 | + | 0.105652i | ||||
\(707\) | −0.976267 | + | 1.34372i | −0.0367163 | + | 0.0505357i | ||||
\(708\) | −21.7151 | − | 29.8883i | −0.816103 | − | 1.12327i | ||||
\(709\) | 0.545405 | − | 1.67858i | 0.0204831 | − | 0.0630406i | −0.940292 | − | 0.340368i | \(-0.889449\pi\) |
0.960776 | + | 0.277327i | \(0.0894485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.38039 | + | 3.18254i | −0.164278 | + | 0.119355i | ||||
\(712\) | 4.75389 | − | 6.54317i | 0.178160 | − | 0.245216i | ||||
\(713\) | 3.52266 | − | 1.14458i | 0.131925 | − | 0.0428649i | ||||
\(714\) | −40.3606 | −1.51046 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −33.4729 | −1.25094 | ||||||||
\(717\) | 5.57369 | − | 1.81100i | 0.208153 | − | 0.0676331i | ||||
\(718\) | 16.8303 | − | 23.1649i | 0.628100 | − | 0.864506i | ||||
\(719\) | −2.66974 | + | 1.93968i | −0.0995645 | + | 0.0723379i | −0.636454 | − | 0.771315i | \(-0.719599\pi\) |
0.536889 | + | 0.843653i | \(0.319599\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.50241 | + | 20.0124i | −0.242163 | + | 0.745300i | ||||
\(722\) | −52.7803 | − | 72.6459i | −1.96428 | − | 2.70360i | ||||
\(723\) | −5.85477 | + | 8.05841i | −0.217741 | + | 0.299695i | ||||
\(724\) | 8.05294 | + | 24.7844i | 0.299285 | + | 0.921105i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.5434 | − | 8.79398i | 0.948003 | − | 0.326375i | ||||
\(727\) | 11.7838i | 0.437037i | 0.975833 | + | 0.218519i | \(0.0701225\pi\) | ||||
−0.975833 | + | 0.218519i | \(0.929878\pi\) | |||||||
\(728\) | −4.88331 | + | 1.58668i | −0.180987 | + | 0.0588064i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.52064 | + | 26.2238i | −0.315147 | + | 0.969924i | ||||
\(732\) | 35.2133 | + | 11.4415i | 1.30152 | + | 0.422890i | ||||
\(733\) | 3.36865 | + | 4.63654i | 0.124424 | + | 0.171255i | 0.866685 | − | 0.498856i | \(-0.166246\pi\) |
−0.742261 | + | 0.670111i | \(0.766246\pi\) | |||||||
\(734\) | 31.7619 | + | 23.0764i | 1.17235 | + | 0.851765i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.333646 | 0.0122983 | ||||||||
\(737\) | 22.6044 | − | 45.3348i | 0.832643 | − | 1.66993i | ||||
\(738\) | − | 26.6395i | − | 0.980614i | ||||||
\(739\) | 6.50638 | + | 20.0246i | 0.239341 | + | 0.736616i | 0.996516 | + | 0.0834038i | \(0.0265791\pi\) |
−0.757175 | + | 0.653212i | \(0.773421\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.88834 | + | 1.37196i | −0.0693700 | + | 0.0504003i | ||||
\(742\) | 37.8895 | + | 12.3110i | 1.39097 | + | 0.451952i | ||||
\(743\) | −12.4857 | − | 4.05686i | −0.458058 | − | 0.148832i | 0.0708942 | − | 0.997484i | \(-0.477415\pi\) |
−0.528952 | + | 0.848652i | \(0.677415\pi\) | |||||||
\(744\) | 13.9203 | − | 10.1137i | 0.510343 | − | 0.370786i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.244350 | + | 0.752032i | 0.00894629 | + | 0.0275339i | ||||
\(747\) | 16.2454i | 0.594389i | ||||||||
\(748\) | 66.1183 | + | 9.88299i | 2.41753 | + | 0.361358i | ||||
\(749\) | −6.87768 | −0.251305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.7311 | − | 15.0621i | −0.756490 | − | 0.549622i | 0.141342 | − | 0.989961i | \(-0.454858\pi\) |
−0.897832 | + | 0.440339i | \(0.854858\pi\) | |||||||
\(752\) | 29.5442 | + | 40.6641i | 1.07737 | + | 1.48287i | ||||
\(753\) | 16.0527 | + | 5.21584i | 0.584993 | + | 0.190076i | ||||
\(754\) | −1.19687 | + | 3.68358i | −0.0435874 | + | 0.134148i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.7199 | − | 7.78845i | −0.389878 | − | 0.283263i | ||||
\(757\) | −29.6701 | + | 9.64039i | −1.07838 | + | 0.350386i | −0.793745 | − | 0.608251i | \(-0.791871\pi\) |
−0.284632 | + | 0.958637i | \(0.591871\pi\) | |||||||
\(758\) | − | 28.0400i | − | 1.01846i | ||||||
\(759\) | 1.64458 | + | 3.15939i | 0.0596945 | + | 0.114678i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.51539 | + | 10.8193i | 0.127433 | + | 0.392198i | 0.994336 | − | 0.106278i | \(-0.0338932\pi\) |
−0.866904 | + | 0.498476i | \(0.833893\pi\) | |||||||
\(762\) | −24.5448 | + | 33.7830i | −0.889165 | + | 1.22383i | ||||
\(763\) | −12.9302 | − | 17.7968i | −0.468103 | − | 0.644289i | ||||
\(764\) | −19.1465 | + | 58.9269i | −0.692697 | + | 2.13190i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −56.3617 | + | 40.9491i | −2.03643 | + | 1.47955i | ||||
\(767\) | 1.68670 | − | 2.32154i | 0.0609032 | − | 0.0838260i | ||||
\(768\) | −30.6498 | + | 9.95872i | −1.10598 | + | 0.359354i | ||||
\(769\) | −10.3938 | −0.374811 | −0.187405 | − | 0.982283i | \(-0.560008\pi\) | ||||
−0.187405 | + | 0.982283i | \(0.560008\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1436 | 0.401326 | ||||||||
\(772\) | −60.3935 | + | 19.6230i | −2.17361 | + | 0.706248i | ||||
\(773\) | −8.24944 | + | 11.3544i | −0.296712 | + | 0.408389i | −0.931180 | − | 0.364560i | \(-0.881219\pi\) |
0.634468 | + | 0.772949i | \(0.281219\pi\) | |||||||
\(774\) | −10.9569 | + | 7.96062i | −0.393836 | + | 0.286139i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.345453 | − | 1.06319i | 0.0124010 | − | 0.0381665i | ||||
\(777\) | −5.08932 | − | 7.00485i | −0.182578 | − | 0.251298i | ||||
\(778\) | −21.9131 | + | 30.1608i | −0.785623 | + | 1.08132i | ||||
\(779\) | 24.9858 | + | 76.8985i | 0.895211 | + | 2.75518i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.14176 | − | 7.26717i | 0.255552 | − | 0.260040i | ||||
\(782\) | 13.1871i | 0.471571i | ||||||||
\(783\) | −4.78997 | + | 1.55635i | −0.171179 | + | 0.0556196i | ||||
\(784\) | 12.8902 | + | 9.36527i | 0.460364 | + | 0.334474i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.0326717 | + | 0.100553i | −0.00116536 | + | 0.00358661i | ||||
\(787\) | −13.1414 | − | 4.26988i | −0.468439 | − | 0.152205i | 0.0652802 | − | 0.997867i | \(-0.479206\pi\) |
−0.533719 | + | 0.845662i | \(0.679206\pi\) | |||||||
\(788\) | 38.8469 | + | 53.4681i | 1.38386 | + | 1.90472i | ||||
\(789\) | −21.7404 | − | 15.7953i | −0.773980 | − | 0.562329i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.4785 | −1.26147 | ||||||||
\(792\) | 11.8013 | + | 11.5976i | 0.419339 | + | 0.412102i | ||||
\(793\) | 2.87591i | 0.102127i | ||||||||
\(794\) | −3.96502 | − | 12.2031i | −0.140713 | − | 0.433070i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.7160 | + | 16.5042i | −0.805149 | + | 0.584975i | ||||
\(797\) | −5.12233 | − | 1.66435i | −0.181442 | − | 0.0589541i | 0.216887 | − | 0.976197i | \(-0.430410\pi\) |
−0.398329 | + | 0.917243i | \(0.630410\pi\) | |||||||
\(798\) | 57.2252 | + | 18.5936i | 2.02575 | + | 0.658206i | ||||
\(799\) | −48.5337 | + | 35.2618i | −1.71700 | + | 1.24747i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.500972 | + | 1.54183i | 0.0177010 | + | 0.0544780i | ||||
\(802\) | 34.3840i | 1.21414i | ||||||||
\(803\) | −4.73585 | − | 28.3043i | −0.167124 | − | 0.998836i | ||||
\(804\) | 61.5748 | 2.17157 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.14579 | + | 1.55901i | 0.0755822 | + | 0.0549137i | ||||
\(807\) | 5.91482 | + | 8.14105i | 0.208212 | + | 0.286579i | ||||
\(808\) | 2.39760 | + | 0.779028i | 0.0843473 | + | 0.0274061i | ||||
\(809\) | −7.34680 | + | 22.6111i | −0.258300 | + | 0.794965i | 0.734862 | + | 0.678217i | \(0.237247\pi\) |
−0.993162 | + | 0.116748i | \(0.962753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.65601 | − | 5.56242i | −0.268839 | − | 0.195323i | 0.445196 | − | 0.895433i | \(-0.353134\pi\) |
−0.714035 | + | 0.700110i | \(0.753134\pi\) | |||||||
\(812\) | 63.4695 | − | 20.6225i | 2.22734 | − | 0.723707i | ||||
\(813\) | − | 10.5441i | − | 0.369798i | ||||||
\(814\) | 9.90726 | + | 19.0327i | 0.347249 | + | 0.667097i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.47277 | + | 19.9211i | 0.226592 | + | 0.697379i | ||||
\(817\) | 24.1620 | − | 33.2561i | 0.845321 | − | 1.16348i | ||||
\(818\) | 48.0859 | + | 66.1846i | 1.68128 | + | 2.31409i | ||||
\(819\) | 0.318046 | − | 0.978846i | 0.0111134 | − | 0.0342037i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.42906 | − | 6.12407i | 0.294176 | − | 0.213731i | −0.430901 | − | 0.902399i | \(-0.641804\pi\) |
0.725077 | + | 0.688668i | \(0.241804\pi\) | |||||||
\(822\) | 10.6281 | − | 14.6284i | 0.370698 | − | 0.510223i | ||||
\(823\) | 23.1620 | − | 7.52581i | 0.807378 | − | 0.262333i | 0.123891 | − | 0.992296i | \(-0.460463\pi\) |
0.683487 | + | 0.729963i | \(0.260463\pi\) | |||||||
\(824\) | 31.9384 | 1.11263 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −73.9736 | −2.57387 | ||||||||
\(827\) | 20.9239 | − | 6.79857i | 0.727594 | − | 0.236410i | 0.0782813 | − | 0.996931i | \(-0.475057\pi\) |
0.649312 | + | 0.760522i | \(0.275057\pi\) | |||||||
\(828\) | −2.54475 | + | 3.50254i | −0.0884361 | + | 0.121722i | ||||
\(829\) | 2.45366 | − | 1.78269i | 0.0852191 | − | 0.0619153i | −0.544360 | − | 0.838852i | \(-0.683227\pi\) |
0.629579 | + | 0.776936i | \(0.283227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.54302 | + | 17.0597i | −0.192285 | + | 0.591793i | ||||
\(832\) | −1.40168 | − | 1.92924i | −0.0485945 | − | 0.0668845i | ||||
\(833\) | −11.1777 | + | 15.3848i | −0.387284 | + | 0.533051i | ||||
\(834\) | −10.0475 | − | 30.9230i | −0.347916 | − | 1.07077i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −89.1929 | − | 44.4725i | −3.08480 | − | 1.53811i | ||||
\(837\) | 3.44899i | 0.119214i | ||||||||
\(838\) | −12.3432 | + | 4.01054i | −0.426388 | + | 0.138542i | ||||
\(839\) | −39.2683 | − | 28.5301i | −1.35569 | − | 0.984968i | −0.998706 | − | 0.0508591i | \(-0.983804\pi\) |
−0.356987 | − | 0.934109i | \(-0.616196\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.12296 | + | 3.45613i | −0.0387229 | + | 0.119177i | ||||
\(842\) | −71.8947 | − | 23.3600i | −2.47766 | − | 0.805039i | ||||
\(843\) | 4.35609 | + | 5.99565i | 0.150032 | + | 0.206501i | ||||
\(844\) | −65.0762 | − | 47.2806i | −2.24001 | − | 1.62747i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −29.4662 | −1.01307 | ||||||||
\(847\) | 10.5723 | − | 34.5750i | 0.363270 | − | 1.18801i | ||||
\(848\) | − | 20.6758i | − | 0.710011i | ||||||
\(849\) | −1.66462 | − | 5.12319i | −0.0571298 | − | 0.175827i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.28872 | + | 1.66285i | −0.0784563 | + | 0.0570018i | ||||
\(852\) | 11.7787 | + | 3.82713i | 0.403531 | + | 0.131115i | ||||
\(853\) | 11.1875 | + | 3.63504i | 0.383053 | + | 0.124461i | 0.494213 | − | 0.869341i | \(-0.335456\pi\) |
−0.111160 | + | 0.993803i | \(0.535456\pi\) | |||||||
\(854\) | 59.9779 | − | 43.5765i | 2.05240 | − | 1.49116i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.22586 | + | 9.92817i | 0.110258 | + | 0.339338i | ||||
\(857\) | 1.61311i | 0.0551026i | 0.999620 | + | 0.0275513i | \(0.00877097\pi\) | ||||
−0.999620 | + | 0.0275513i | \(0.991229\pi\) | |||||||
\(858\) | −1.13810 | + | 2.28255i | −0.0388542 | + | 0.0779250i | ||||
\(859\) | −47.3263 | −1.61475 | −0.807376 | − | 0.590038i | \(-0.799113\pi\) | ||||
−0.807376 | + | 0.590038i | \(0.799113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.8439 | − | 20.9563i | −0.982998 | − | 0.714190i | ||||
\(862\) | −17.8286 | − | 24.5389i | −0.607244 | − | 0.835799i | ||||
\(863\) | 9.48425 | + | 3.08162i | 0.322848 | + | 0.104900i | 0.465957 | − | 0.884807i | \(-0.345710\pi\) |
−0.143109 | + | 0.989707i | \(0.545710\pi\) | |||||||
\(864\) | −0.0960054 | + | 0.295474i | −0.00326617 | + | 0.0100522i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.80717 | − | 2.03953i | −0.0953915 | − | 0.0693060i | ||||
\(867\) | −7.60845 | + | 2.47214i | −0.258397 | + | 0.0839581i | ||||
\(868\) | − | 45.7009i | − | 1.55119i | ||||||
\(869\) | 2.65473 | − | 17.7604i | 0.0900555 | − | 0.602482i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.47795 | + | 4.54867i | 0.0500786 | + | 0.154126i | ||||
\(872\) | −19.6257 | + | 27.0124i | −0.664609 | + | 0.914756i | ||||
\(873\) | 0.131712 | + | 0.181286i | 0.00445778 | + | 0.00613560i | ||||
\(874\) | 6.07515 | − | 18.6974i | 0.205495 | − | 0.632448i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 28.2204 | − | 20.5033i | 0.953478 | − | 0.692742i | ||||
\(877\) | 15.2858 | − | 21.0391i | 0.516164 | − | 0.710439i | −0.468779 | − | 0.883315i | \(-0.655306\pi\) |
0.984944 | + | 0.172876i | \(0.0553060\pi\) | |||||||
\(878\) | −17.7169 | + | 5.75658i | −0.597918 | + | 0.194275i | ||||
\(879\) | 1.74006 | 0.0586907 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.4081 | 0.350657 | 0.175329 | − | 0.984510i | \(-0.443901\pi\) | ||||
0.175329 | + | 0.984510i | \(0.443901\pi\) | |||||||
\(882\) | −8.88338 | + | 2.88639i | −0.299119 | + | 0.0971897i | ||||
\(883\) | 31.5807 | − | 43.4671i | 1.06278 | − | 1.46279i | 0.185595 | − | 0.982626i | \(-0.440579\pi\) |
0.877181 | − | 0.480159i | \(-0.159421\pi\) | |||||||
\(884\) | −5.10635 | + | 3.70998i | −0.171745 | + | 0.124780i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.39826 | − | 25.8472i | 0.282145 | − | 0.868353i | ||||
\(887\) | 23.8786 | + | 32.8660i | 0.801763 | + | 1.10353i | 0.992542 | + | 0.121900i | \(0.0388986\pi\) |
−0.190779 | + | 0.981633i | \(0.561101\pi\) | |||||||
\(888\) | −7.72468 | + | 10.6321i | −0.259223 | + | 0.356790i | ||||
\(889\) | 17.2701 | + | 53.1518i | 0.579219 | + | 1.78265i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.27115 | + | 0.547326i | −0.109588 | + | 0.0183361i | ||||
\(892\) | − | 81.2188i | − | 2.71941i | ||||||
\(893\) | 85.0582 | − | 27.6371i | 2.84636 | − | 0.924839i | ||||
\(894\) | −11.6799 | − | 8.48594i | −0.390634 | − | 0.283812i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.6274 | + | 60.4071i | −0.655707 | + | 2.01806i | ||||
\(897\) | −0.319822 | − | 0.103916i | −0.0106785 | − | 0.00346967i | ||||
\(898\) | 9.13549 | + | 12.5739i | 0.304855 | + | 0.419597i | ||||
\(899\) | −14.0532 | − | 10.2103i | −0.468701 | − | 0.340531i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.6772 | 0.822115 | ||||||||
\(902\) | 63.0166 | + | 61.9290i | 2.09822 | + | 2.06201i | ||||
\(903\) | 18.1259i | 0.603191i | ||||||||
\(904\) | 16.6406 | + | 51.2145i | 0.553458 | + | 1.70337i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.1561 | + | 11.0116i | −0.503529 | + | 0.365835i | ||||
\(907\) | −18.4571 | − | 5.99708i | −0.612859 | − | 0.199130i | −0.0138917 | − | 0.999904i | \(-0.504422\pi\) |
−0.598967 | + | 0.800774i | \(0.704422\pi\) | |||||||
\(908\) | −2.04715 | − | 0.665160i | −0.0679371 | − | 0.0220741i | ||||
\(909\) | −0.408817 | + | 0.297023i | −0.0135596 | + | 0.00985163i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.31290 | + | 10.1960i | 0.109761 | + | 0.337810i | 0.990818 | − | 0.135200i | \(-0.0431676\pi\) |
−0.881057 | + | 0.473010i | \(0.843168\pi\) | |||||||
\(912\) | − | 31.2271i | − | 1.03403i | ||||||
\(913\) | −38.4290 | − | 37.7658i | −1.27182 | − | 1.24987i | ||||
\(914\) | 0.465585 | 0.0154002 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 72.3816 | + | 52.5883i | 2.39156 | + | 1.73757i | ||||
\(917\) | 0.0831723 | + | 0.114477i | 0.00274659 | + | 0.00378036i | ||||
\(918\) | −11.6784 | − | 3.79455i | −0.385446 | − | 0.125239i | ||||
\(919\) | 7.14787 | − | 21.9989i | 0.235787 | − | 0.725676i | −0.761230 | − | 0.648483i | \(-0.775404\pi\) |
0.997016 | − | 0.0771939i | \(-0.0245960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.2779 | − | 12.5531i | −0.569325 | − | 0.413639i | ||||
\(922\) | 62.1755 | − | 20.2020i | 2.04764 | − | 0.665319i | ||||
\(923\) | 0.961981i | 0.0316640i | ||||||||
\(924\) | 43.3444 | − | 7.25235i | 1.42593 | − | 0.238585i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.9322 | + | 49.0343i | 0.523565 | + | 1.61137i | ||||
\(927\) | −3.76298 | + | 5.17930i | −0.123593 | + | 0.170111i | ||||
\(928\) | −0.919725 | − | 1.26589i | −0.0301915 | − | 0.0415550i | ||||
\(929\) | −8.10467 | + | 24.9436i | −0.265906 | + | 0.818374i | 0.725578 | + | 0.688140i | \(0.241573\pi\) |
−0.991483 | + | 0.130233i | \(0.958427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.9359 | − | 16.6639i | 0.751693 | − | 0.546137i | ||||
\(932\) | −10.8187 | + | 14.8907i | −0.354380 | + | 0.487762i | ||||
\(933\) | 31.2038 | − | 10.1387i | 1.02157 | − | 0.331927i | ||||
\(934\) | −19.4012 | −0.634828 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.56217 | −0.0510612 | ||||||||
\(937\) | −22.2557 | + | 7.23133i | −0.727063 | + | 0.236237i | −0.649083 | − | 0.760718i | \(-0.724847\pi\) |
−0.0779804 | + | 0.996955i | \(0.524847\pi\) | |||||||
\(938\) | 72.4694 | − | 99.7456i | 2.36621 | − | 3.25681i | ||||
\(939\) | −2.79800 | + | 2.03287i | −0.0913094 | + | 0.0663401i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.38952 | + | 10.4319i | −0.110495 | + | 0.340069i | −0.990981 | − | 0.134004i | \(-0.957217\pi\) |
0.880486 | + | 0.474073i | \(0.157217\pi\) | |||||||
\(942\) | 14.6276 | + | 20.1332i | 0.476595 | + | 0.655976i | ||||
\(943\) | −6.84713 | + | 9.42427i | −0.222973 | + | 0.306896i | ||||
\(944\) | 11.8634 | + | 36.5118i | 0.386121 | + | 1.18836i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.64038 | − | 44.4249i | 0.215897 | − | 1.44438i | ||||
\(947\) | − | 13.3652i | − | 0.434310i | −0.976137 | − | 0.217155i | \(-0.930322\pi\) | ||
0.976137 | − | 0.217155i | \(-0.0696777\pi\) | |||||||
\(948\) | 20.7594 | − | 6.74515i | 0.674235 | − | 0.219072i | ||||
\(949\) | 2.19199 | + | 1.59257i | 0.0711550 | + | 0.0516971i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.888626 | + | 2.73491i | −0.0288157 | + | 0.0886856i | ||||
\(952\) | 77.9749 | + | 25.3356i | 2.52718 | + | 0.821130i | ||||
\(953\) | −12.8280 | − | 17.6562i | −0.415538 | − | 0.571939i | 0.549020 | − | 0.835809i | \(-0.315001\pi\) |
−0.964558 | + | 0.263870i | \(0.915001\pi\) | |||||||
\(954\) | 9.80598 | + | 7.12446i | 0.317480 | + | 0.230663i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −23.6260 | −0.764120 | ||||||||
\(957\) | 7.45366 | − | 14.9489i | 0.240943 | − | 0.483229i | ||||
\(958\) | − | 98.1686i | − | 3.17168i | ||||||
\(959\) | −7.47809 | − | 23.0152i | −0.241480 | − | 0.743199i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4558 | − | 11.2293i | 0.498576 | − | 0.362236i | ||||
\(962\) | −1.92667 | − | 0.626012i | −0.0621182 | − | 0.0201834i | ||||
\(963\) | −1.99008 | − | 0.646615i | −0.0641293 | − | 0.0208369i | ||||
\(964\) | 32.4865 | − | 23.6028i | 1.04632 | − | 0.760196i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.67881 | + | 8.24453i | 0.0861893 | + | 0.265263i | ||||
\(967\) | 16.6600i | 0.535750i | 0.963454 | + | 0.267875i | \(0.0863214\pi\) | ||||
−0.963454 | + | 0.267875i | \(0.913679\pi\) | |||||||
\(968\) | −54.8689 | + | 0.955240i | −1.76355 | + | 0.0307026i | ||||
\(969\) | 37.2704 | 1.19730 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.98271 | − | 6.52632i | −0.288269 | − | 0.209440i | 0.434247 | − | 0.900794i | \(-0.357014\pi\) |
−0.722516 | + | 0.691354i | \(0.757014\pi\) | |||||||
\(972\) | −2.36959 | − | 3.26145i | −0.0760045 | − | 0.104611i | ||||
\(973\) | −41.3858 | − | 13.4471i | −1.32677 | − | 0.431093i | ||||
\(974\) | 7.54021 | − | 23.2064i | 0.241604 | − | 0.743580i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.1273 | − | 22.6153i | −0.996362 | − | 0.723899i | ||||
\(977\) | −17.8936 | + | 5.81397i | −0.572466 | + | 0.186005i | −0.580923 | − | 0.813959i | \(-0.697308\pi\) |
0.00845665 | + | 0.999964i | \(0.497308\pi\) | |||||||
\(978\) | 12.3508i | 0.394935i | ||||||||
\(979\) | −4.81187 | − | 2.39924i | −0.153788 | − | 0.0766802i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.06818 | − | 6.36521i | −0.0660320 | − | 0.203226i | ||||
\(982\) | 7.17940 | − | 9.88160i | 0.229104 | − | 0.315335i | ||||
\(983\) | −0.810250 | − | 1.11521i | −0.0258430 | − | 0.0355698i | 0.795900 | − | 0.605428i | \(-0.206998\pi\) |
−0.821743 | + | 0.569858i | \(0.806998\pi\) | |||||||
\(984\) | −16.7224 | + | 51.4664i | −0.533092 | + | 1.64069i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 50.0336 | − | 36.3516i | 1.59340 | − | 1.15767i | ||||
\(987\) | −23.1800 | + | 31.9045i | −0.737827 | + | 1.01553i | ||||
\(988\) | 8.94918 | − | 2.90777i | 0.284711 | − | 0.0925083i | ||||
\(989\) | 5.92233 | 0.188319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.3186 | −1.47136 | −0.735680 | − | 0.677329i | \(-0.763137\pi\) | ||||
−0.735680 | + | 0.677329i | \(0.763137\pi\) | |||||||
\(992\) | −1.01909 | + | 0.331122i | −0.0323561 | + | 0.0105131i | ||||
\(993\) | 8.30074 | − | 11.4250i | 0.263416 | − | 0.362561i | ||||
\(994\) | 20.0623 | − | 14.5761i | 0.636339 | − | 0.462327i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 20.2380 | − | 62.2861i | 0.641265 | − | 1.97361i | ||||
\(997\) | −8.55054 | − | 11.7688i | −0.270798 | − | 0.372722i | 0.651861 | − | 0.758339i | \(-0.273989\pi\) |
−0.922659 | + | 0.385617i | \(0.873989\pi\) | |||||||
\(998\) | −63.1917 | + | 86.9759i | −2.00030 | + | 2.75317i | ||||
\(999\) | −0.814038 | − | 2.50535i | −0.0257550 | − | 0.0792658i |
(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 | 825.2.bx.h.49.1 | 16 | ||
5.2 | odd | 4 | 825.2.n.k.676.1 | 8 | |||
5.3 | odd | 4 | 165.2.m.a.16.2 | ✓ | 8 | ||
5.4 | even | 2 | inner | 825.2.bx.h.49.4 | 16 | ||
11.9 | even | 5 | inner | 825.2.bx.h.724.4 | 16 | ||
15.8 | even | 4 | 495.2.n.d.181.1 | 8 | |||
55.3 | odd | 20 | 1815.2.a.x.1.3 | 4 | |||
55.8 | even | 20 | 1815.2.a.o.1.2 | 4 | |||
55.9 | even | 10 | inner | 825.2.bx.h.724.1 | 16 | ||
55.42 | odd | 20 | 825.2.n.k.526.1 | 8 | |||
55.47 | odd | 20 | 9075.2.a.cl.1.2 | 4 | |||
55.52 | even | 20 | 9075.2.a.dj.1.3 | 4 | |||
55.53 | odd | 20 | 165.2.m.a.31.2 | yes | 8 | ||
165.8 | odd | 20 | 5445.2.a.bv.1.3 | 4 | |||
165.53 | even | 20 | 495.2.n.d.361.1 | 8 | |||
165.113 | even | 20 | 5445.2.a.be.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.16.2 | ✓ | 8 | 5.3 | odd | 4 | ||
165.2.m.a.31.2 | yes | 8 | 55.53 | odd | 20 | ||
495.2.n.d.181.1 | 8 | 15.8 | even | 4 | |||
495.2.n.d.361.1 | 8 | 165.53 | even | 20 | |||
825.2.n.k.526.1 | 8 | 55.42 | odd | 20 | |||
825.2.n.k.676.1 | 8 | 5.2 | odd | 4 | |||
825.2.bx.h.49.1 | 16 | 1.1 | even | 1 | trivial | ||
825.2.bx.h.49.4 | 16 | 5.4 | even | 2 | inner | ||
825.2.bx.h.724.1 | 16 | 55.9 | even | 10 | inner | ||
825.2.bx.h.724.4 | 16 | 11.9 | even | 5 | inner | ||
1815.2.a.o.1.2 | 4 | 55.8 | even | 20 | |||
1815.2.a.x.1.3 | 4 | 55.3 | odd | 20 | |||
5445.2.a.be.1.2 | 4 | 165.113 | even | 20 | |||
5445.2.a.bv.1.3 | 4 | 165.8 | odd | 20 | |||
9075.2.a.cl.1.2 | 4 | 55.47 | odd | 20 | |||
9075.2.a.dj.1.3 | 4 | 55.52 | even | 20 |