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 | 724.2 | ||
Root | \(1.28932 + 0.418926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.724 |
Dual form | 825.2.bx.h.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10527 | − | 0.359123i | −0.781542 | − | 0.253938i | −0.109044 | − | 0.994037i | \(-0.534779\pi\) |
−0.672499 | + | 0.740098i | \(0.734779\pi\) | |||||||
\(3\) | −0.587785 | − | 0.809017i | −0.339358 | − | 0.467086i | ||||
\(4\) | −0.525387 | − | 0.381716i | −0.262693 | − | 0.190858i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.359123 | + | 1.10527i | 0.146611 | + | 0.451224i | ||||
\(7\) | 2.51974 | − | 3.46813i | 0.952373 | − | 1.31083i | 0.00190785 | − | 0.999998i | \(-0.499393\pi\) |
0.950465 | − | 0.310831i | \(-0.100607\pi\) | |||||||
\(8\) | 1.80980 | + | 2.49097i | 0.639860 | + | 0.880691i | ||||
\(9\) | −0.309017 | + | 0.951057i | −0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.15911 | − | 1.00996i | −0.952508 | − | 0.304514i | ||||
\(12\) | 0.649414i | 0.187470i | ||||||||
\(13\) | 4.91433 | + | 1.59676i | 1.36299 | + | 0.442863i | 0.897040 | − | 0.441948i | \(-0.145713\pi\) |
0.465950 | + | 0.884811i | \(0.345713\pi\) | |||||||
\(14\) | −4.03048 | + | 2.92831i | −1.07719 | + | 0.782624i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.704384 | − | 2.16787i | −0.176096 | − | 0.541968i | ||||
\(17\) | 4.75528 | − | 1.54508i | 1.15333 | − | 0.374738i | 0.330930 | − | 0.943655i | \(-0.392637\pi\) |
0.822395 | + | 0.568917i | \(0.192637\pi\) | |||||||
\(18\) | 0.683093 | − | 0.940197i | 0.161007 | − | 0.221607i | ||||
\(19\) | 4.53048 | − | 3.29158i | 1.03936 | − | 0.755141i | 0.0692013 | − | 0.997603i | \(-0.477955\pi\) |
0.970161 | + | 0.242462i | \(0.0779549\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.28684 | −0.935466 | ||||||||
\(22\) | 3.12896 | + | 2.25079i | 0.667097 | + | 0.479869i | ||||
\(23\) | − | 0.219819i | − | 0.0458354i | −0.999737 | − | 0.0229177i | \(-0.992704\pi\) | ||
0.999737 | − | 0.0229177i | \(-0.00729557\pi\) | |||||||
\(24\) | 0.951466 | − | 2.92831i | 0.194217 | − | 0.597739i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.85822 | − | 3.52970i | −0.952775 | − | 0.692232i | ||||
\(27\) | 0.951057 | − | 0.309017i | 0.183031 | − | 0.0594703i | ||||
\(28\) | −2.64768 | + | 0.860283i | −0.500364 | + | 0.162578i | ||||
\(29\) | 5.19262 | + | 3.77266i | 0.964246 | + | 0.700566i | 0.954133 | − | 0.299383i | \(-0.0967809\pi\) |
0.0101128 | + | 0.999949i | \(0.496781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.874813 | + | 2.69240i | −0.157121 | + | 0.483569i | −0.998370 | − | 0.0570796i | \(-0.981821\pi\) |
0.841249 | + | 0.540649i | \(0.181821\pi\) | |||||||
\(32\) | − | 3.50898i | − | 0.620306i | ||||||
\(33\) | 1.03980 | + | 3.14941i | 0.181007 | + | 0.548243i | ||||
\(34\) | −5.81074 | −0.996533 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.525387 | − | 0.381716i | 0.0875645 | − | 0.0636193i | ||||
\(37\) | −2.30883 | + | 3.17784i | −0.379570 | + | 0.522433i | −0.955471 | − | 0.295087i | \(-0.904652\pi\) |
0.575901 | + | 0.817520i | \(0.304652\pi\) | |||||||
\(38\) | −6.18947 | + | 2.01108i | −1.00406 | + | 0.326240i | ||||
\(39\) | −1.59676 | − | 4.91433i | −0.255687 | − | 0.786923i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.74165 | + | 3.44501i | −0.740521 | + | 0.538020i | −0.892874 | − | 0.450306i | \(-0.851315\pi\) |
0.152353 | + | 0.988326i | \(0.451315\pi\) | |||||||
\(42\) | 4.73811 | + | 1.53950i | 0.731106 | + | 0.237551i | ||||
\(43\) | − | 8.90173i | − | 1.35750i | −0.734369 | − | 0.678751i | \(-0.762522\pi\) | ||
0.734369 | − | 0.678751i | \(-0.237478\pi\) | |||||||
\(44\) | 1.27424 | + | 1.73650i | 0.192099 | + | 0.261788i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0789420 | + | 0.242959i | −0.0116394 | + | 0.0358223i | ||||
\(47\) | −0.139821 | − | 0.192447i | −0.0203950 | − | 0.0280713i | 0.798698 | − | 0.601732i | \(-0.205523\pi\) |
−0.819093 | + | 0.573661i | \(0.805523\pi\) | |||||||
\(48\) | −1.33982 | + | 1.84410i | −0.193386 | + | 0.266173i | ||||
\(49\) | −3.51569 | − | 10.8202i | −0.502241 | − | 1.54574i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.04508 | − | 2.93893i | −0.566425 | − | 0.411532i | ||||
\(52\) | −1.97242 | − | 2.71480i | −0.273525 | − | 0.376475i | ||||
\(53\) | 2.41255 | + | 0.783885i | 0.331389 | + | 0.107675i | 0.469986 | − | 0.882674i | \(-0.344259\pi\) |
−0.138596 | + | 0.990349i | \(0.544259\pi\) | |||||||
\(54\) | −1.16215 | −0.158148 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.1992 | 1.76382 | ||||||||
\(57\) | −5.32589 | − | 1.73049i | −0.705432 | − | 0.229209i | ||||
\(58\) | −4.38439 | − | 6.03459i | −0.575698 | − | 0.792381i | ||||
\(59\) | −6.36725 | − | 4.62608i | −0.828945 | − | 0.602264i | 0.0903156 | − | 0.995913i | \(-0.471212\pi\) |
−0.919261 | + | 0.393649i | \(0.871212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50123 | − | 4.62030i | −0.192212 | − | 0.591569i | −0.999998 | − | 0.00209225i | \(-0.999334\pi\) |
0.807785 | − | 0.589477i | \(-0.200666\pi\) | |||||||
\(62\) | 1.93381 | − | 2.66165i | 0.245594 | − | 0.338031i | ||||
\(63\) | 2.51974 | + | 3.46813i | 0.317458 | + | 0.436943i | ||||
\(64\) | −2.66892 | + | 8.21410i | −0.333615 | + | 1.02676i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0182340 | − | 3.85436i | −0.00224445 | − | 0.474439i | ||||
\(67\) | − | 12.1280i | − | 1.48167i | −0.671688 | − | 0.740834i | \(-0.734431\pi\) | ||
0.671688 | − | 0.740834i | \(-0.265569\pi\) | |||||||
\(68\) | −3.08815 | − | 1.00340i | −0.374493 | − | 0.121680i | ||||
\(69\) | −0.177837 | + | 0.129206i | −0.0214091 | + | 0.0155546i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.08459 | − | 9.49339i | −0.366073 | − | 1.12666i | −0.949306 | − | 0.314353i | \(-0.898212\pi\) |
0.583233 | − | 0.812305i | \(-0.301788\pi\) | |||||||
\(72\) | −2.92831 | + | 0.951466i | −0.345105 | + | 0.112131i | ||||
\(73\) | 8.55964 | − | 11.7813i | 1.00183 | − | 1.37890i | 0.0776335 | − | 0.996982i | \(-0.475264\pi\) |
0.924196 | − | 0.381918i | \(-0.124736\pi\) | |||||||
\(74\) | 3.69311 | − | 2.68320i | 0.429316 | − | 0.311916i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.63670 | −0.417158 | ||||||||
\(77\) | −11.4628 | + | 8.41136i | −1.30631 | + | 0.958564i | ||||
\(78\) | 6.00509i | 0.679942i | ||||||||
\(79\) | −2.47274 | + | 7.61030i | −0.278205 | + | 0.856226i | 0.710149 | + | 0.704051i | \(0.248628\pi\) |
−0.988354 | + | 0.152174i | \(0.951372\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 6.47797 | − | 2.10482i | 0.715373 | − | 0.232439i | ||||
\(83\) | −11.9386 | + | 3.87908i | −1.31043 | + | 0.425784i | −0.879197 | − | 0.476458i | \(-0.841921\pi\) |
−0.431231 | + | 0.902242i | \(0.641921\pi\) | |||||||
\(84\) | 2.25225 | + | 1.63636i | 0.245741 | + | 0.178541i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.19682 | + | 9.83880i | −0.344722 | + | 1.06094i | ||||
\(87\) | − | 6.41843i | − | 0.688128i | ||||||
\(88\) | −3.20157 | − | 9.69707i | −0.341288 | − | 1.03371i | ||||
\(89\) | 2.56545 | 0.271937 | 0.135969 | − | 0.990713i | \(-0.456585\pi\) | ||||
0.135969 | + | 0.990713i | \(0.456585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.9206 | − | 13.0201i | 1.87859 | − | 1.36488i | ||||
\(92\) | −0.0839083 | + | 0.115490i | −0.00874805 | + | 0.0120407i | ||||
\(93\) | 2.69240 | − | 0.874813i | 0.279189 | − | 0.0907139i | ||||
\(94\) | 0.0854274 | + | 0.262919i | 0.00881116 | + | 0.0271180i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.83882 | + | 2.06253i | −0.289736 | + | 0.210506i | ||||
\(97\) | −1.91351 | − | 0.621738i | −0.194288 | − | 0.0631279i | 0.210257 | − | 0.977646i | \(-0.432570\pi\) |
−0.404545 | + | 0.914518i | \(0.632570\pi\) | |||||||
\(98\) | 13.2218i | 1.33560i | ||||||||
\(99\) | 1.93675 | − | 2.69240i | 0.194650 | − | 0.270596i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.34385 | + | 7.21362i | −0.233221 | + | 0.717782i | 0.764131 | + | 0.645061i | \(0.223168\pi\) |
−0.997352 | + | 0.0727205i | \(0.976832\pi\) | |||||||
\(102\) | 3.41546 | + | 4.70098i | 0.338181 | + | 0.465467i | ||||
\(103\) | −9.91508 | + | 13.6469i | −0.976962 | + | 1.34467i | −0.0385116 | + | 0.999258i | \(0.512262\pi\) |
−0.938450 | + | 0.345414i | \(0.887738\pi\) | |||||||
\(104\) | 4.91645 | + | 15.1313i | 0.482098 | + | 1.48374i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.38500 | − | 1.73281i | −0.231652 | − | 0.168305i | ||||
\(107\) | 4.56216 | + | 6.27928i | 0.441041 | + | 0.607041i | 0.970443 | − | 0.241330i | \(-0.0775837\pi\) |
−0.529402 | + | 0.848371i | \(0.677584\pi\) | |||||||
\(108\) | −0.617629 | − | 0.200680i | −0.0594314 | − | 0.0193104i | ||||
\(109\) | −4.45671 | −0.426876 | −0.213438 | − | 0.976957i | \(-0.568466\pi\) | ||||
−0.213438 | + | 0.976957i | \(0.568466\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.92802 | 0.372831 | ||||||||
\(112\) | −9.29332 | − | 3.01958i | −0.878136 | − | 0.285324i | ||||
\(113\) | 4.53327 | + | 6.23952i | 0.426455 | + | 0.586964i | 0.967135 | − | 0.254264i | \(-0.0818331\pi\) |
−0.540680 | + | 0.841228i | \(0.681833\pi\) | |||||||
\(114\) | 5.26508 | + | 3.82530i | 0.493120 | + | 0.358273i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.28805 | − | 3.96421i | −0.119593 | − | 0.368068i | ||||
\(117\) | −3.03722 | + | 4.18038i | −0.280792 | + | 0.386476i | ||||
\(118\) | 5.37618 | + | 7.39968i | 0.494918 | + | 0.681196i | ||||
\(119\) | 6.62353 | − | 20.3851i | 0.607178 | − | 1.86870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.95996 | + | 6.38115i | 0.814542 | + | 0.580105i | ||||
\(122\) | 5.64579i | 0.511146i | ||||||||
\(123\) | 5.57414 | + | 1.81115i | 0.502603 | + | 0.163306i | ||||
\(124\) | 1.48735 | − | 1.08062i | 0.133568 | − | 0.0970426i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.53950 | − | 4.73811i | −0.137150 | − | 0.422104i | ||||
\(127\) | 1.45620 | − | 0.473149i | 0.129217 | − | 0.0419852i | −0.243695 | − | 0.969852i | \(-0.578359\pi\) |
0.372912 | + | 0.927867i | \(0.378359\pi\) | |||||||
\(128\) | 1.77470 | − | 2.44266i | 0.156863 | − | 0.215903i | ||||
\(129\) | −7.20165 | + | 5.23231i | −0.634070 | + | 0.460679i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.66108 | 0.232500 | 0.116250 | − | 0.993220i | \(-0.462913\pi\) | ||||
0.116250 | + | 0.993220i | \(0.462913\pi\) | |||||||
\(132\) | 0.655882 | − | 2.05157i | 0.0570872 | − | 0.178566i | ||||
\(133\) | − | 24.0062i | − | 2.08160i | ||||||
\(134\) | −4.35544 | + | 13.4047i | −0.376252 | + | 1.15799i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.4549 | + | 9.04898i | 1.06799 | + | 0.775944i | ||||
\(137\) | 9.75352 | − | 3.16911i | 0.833300 | − | 0.270756i | 0.138865 | − | 0.990311i | \(-0.455655\pi\) |
0.694435 | + | 0.719556i | \(0.255655\pi\) | |||||||
\(138\) | 0.242959 | − | 0.0789420i | 0.0206820 | − | 0.00671999i | ||||
\(139\) | −4.28381 | − | 3.11237i | −0.363348 | − | 0.263987i | 0.391099 | − | 0.920348i | \(-0.372095\pi\) |
−0.754447 | + | 0.656361i | \(0.772095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0735083 | + | 0.226235i | −0.00619051 | + | 0.0190524i | ||||
\(142\) | 11.6005i | 0.973491i | ||||||||
\(143\) | −13.9123 | − | 10.0076i | −1.16340 | − | 0.836880i | ||||
\(144\) | 2.27943 | 0.189953 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.6916 | + | 9.94756i | −1.13313 | + | 0.823266i | ||||
\(147\) | −6.68724 | + | 9.20420i | −0.551554 | + | 0.759149i | ||||
\(148\) | 2.42606 | − | 0.788275i | 0.199421 | − | 0.0647958i | ||||
\(149\) | −1.17068 | − | 3.60300i | −0.0959062 | − | 0.295169i | 0.891583 | − | 0.452858i | \(-0.149596\pi\) |
−0.987489 | + | 0.157689i | \(0.949596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.78939 | − | 3.47969i | 0.389755 | − | 0.283173i | −0.375600 | − | 0.926782i | \(-0.622563\pi\) |
0.765355 | + | 0.643608i | \(0.222563\pi\) | |||||||
\(152\) | 16.3985 | + | 5.32819i | 1.33009 | + | 0.432173i | ||||
\(153\) | 5.00000i | 0.404226i | ||||||||
\(154\) | 15.6902 | − | 5.18024i | 1.26435 | − | 0.417436i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.03696 | + | 3.19144i | −0.0830233 | + | 0.255519i | ||||
\(157\) | −4.36671 | − | 6.01026i | −0.348501 | − | 0.479671i | 0.598399 | − | 0.801198i | \(-0.295804\pi\) |
−0.946900 | + | 0.321528i | \(0.895804\pi\) | |||||||
\(158\) | 5.46607 | − | 7.52340i | 0.434857 | − | 0.598530i | ||||
\(159\) | −0.783885 | − | 2.41255i | −0.0621661 | − | 0.191328i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.762360 | − | 0.553887i | −0.0600824 | − | 0.0436524i | ||||
\(162\) | 0.683093 | + | 0.940197i | 0.0536689 | + | 0.0738688i | ||||
\(163\) | 5.06044 | + | 1.64424i | 0.396364 | + | 0.128786i | 0.500415 | − | 0.865785i | \(-0.333181\pi\) |
−0.104051 | + | 0.994572i | \(0.533181\pi\) | |||||||
\(164\) | 3.80621 | 0.297215 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5884 | 1.13228 | ||||||||
\(167\) | 1.87490 | + | 0.609193i | 0.145084 | + | 0.0471407i | 0.380659 | − | 0.924716i | \(-0.375697\pi\) |
−0.235575 | + | 0.971856i | \(0.575697\pi\) | |||||||
\(168\) | −7.75831 | − | 10.6784i | −0.598567 | − | 0.823856i | ||||
\(169\) | 11.0838 | + | 8.05285i | 0.852599 | + | 0.619450i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.73049 | + | 5.32589i | 0.132334 | + | 0.407281i | ||||
\(172\) | −3.39793 | + | 4.67685i | −0.259090 | + | 0.356607i | ||||
\(173\) | 1.16090 | + | 1.59784i | 0.0882617 | + | 0.121482i | 0.850864 | − | 0.525385i | \(-0.176079\pi\) |
−0.762603 | + | 0.646867i | \(0.776079\pi\) | |||||||
\(174\) | −2.30501 | + | 7.09409i | −0.174742 | + | 0.537801i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0357642 | + | 7.55994i | 0.00269583 | + | 0.569852i | ||||
\(177\) | 7.87035i | 0.591572i | ||||||||
\(178\) | −2.83551 | − | 0.921313i | −0.212530 | − | 0.0690553i | ||||
\(179\) | −1.63676 | + | 1.18918i | −0.122337 | + | 0.0888832i | −0.647271 | − | 0.762260i | \(-0.724090\pi\) |
0.524934 | + | 0.851143i | \(0.324090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.22299 | + | 19.1524i | 0.462551 | + | 1.42359i | 0.862036 | + | 0.506846i | \(0.169189\pi\) |
−0.399485 | + | 0.916740i | \(0.630811\pi\) | |||||||
\(182\) | −24.4829 | + | 7.95498i | −1.81479 | + | 0.589662i | ||||
\(183\) | −2.85550 | + | 3.93026i | −0.211085 | + | 0.290533i | ||||
\(184\) | 0.547562 | − | 0.397827i | 0.0403668 | − | 0.0293282i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.28999 | −0.241234 | ||||||||
\(187\) | −16.5829 | + | 0.0784497i | −1.21266 | + | 0.00573681i | ||||
\(188\) | 0.154481i | 0.0112667i | ||||||||
\(189\) | 1.32471 | − | 4.07703i | 0.0963583 | − | 0.296560i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2463 | − | 7.44439i | −0.741398 | − | 0.538657i | 0.151751 | − | 0.988419i | \(-0.451509\pi\) |
−0.893149 | + | 0.449762i | \(0.851509\pi\) | |||||||
\(192\) | 8.21410 | − | 2.66892i | 0.592802 | − | 0.192613i | ||||
\(193\) | 13.2502 | − | 4.30526i | 0.953773 | − | 0.309900i | 0.209525 | − | 0.977803i | \(-0.432808\pi\) |
0.744248 | + | 0.667904i | \(0.232808\pi\) | |||||||
\(194\) | 1.89166 | + | 1.37437i | 0.135813 | + | 0.0986743i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.28314 | + | 7.02678i | −0.163081 | + | 0.501913i | ||||
\(197\) | − | 14.6060i | − | 1.04064i | −0.853972 | − | 0.520319i | \(-0.825813\pi\) | ||
0.853972 | − | 0.520319i | \(-0.174187\pi\) | |||||||
\(198\) | −3.10753 | + | 2.28029i | −0.220842 | + | 0.162053i | ||||
\(199\) | 11.8748 | 0.841784 | 0.420892 | − | 0.907111i | \(-0.361717\pi\) | ||||
0.420892 | + | 0.907111i | \(0.361717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.81174 | + | 7.12864i | −0.692067 | + | 0.502816i | ||||
\(202\) | 5.18115 | − | 7.13125i | 0.364545 | − | 0.501753i | ||||
\(203\) | 26.1681 | − | 8.50254i | 1.83664 | − | 0.596762i | ||||
\(204\) | 1.00340 | + | 3.08815i | 0.0702520 | + | 0.216213i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.8597 | − | 11.5228i | 1.10500 | − | 0.802830i | ||||
\(207\) | 0.209060 | + | 0.0679277i | 0.0145307 | + | 0.00472130i | ||||
\(208\) | − | 11.7784i | − | 0.816683i | ||||||
\(209\) | −17.6366 | + | 5.82288i | −1.21995 | + | 0.402777i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.90710 | + | 21.2579i | −0.475504 | + | 1.46345i | 0.369772 | + | 0.929122i | \(0.379436\pi\) |
−0.845277 | + | 0.534329i | \(0.820564\pi\) | |||||||
\(212\) | −0.968301 | − | 1.33275i | −0.0665032 | − | 0.0915338i | ||||
\(213\) | −5.86724 | + | 8.07556i | −0.402017 | + | 0.553328i | ||||
\(214\) | −2.78738 | − | 8.57866i | −0.190541 | − | 0.586425i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.49097 | + | 1.80980i | 0.169489 | + | 0.123141i | ||||
\(217\) | 7.13328 | + | 9.81811i | 0.484238 | + | 0.666497i | ||||
\(218\) | 4.92586 | + | 1.60051i | 0.333621 | + | 0.108400i | ||||
\(219\) | −14.5625 | −0.984044 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.8362 | 1.73793 | ||||||||
\(222\) | −4.34152 | − | 1.41064i | −0.291384 | − | 0.0946762i | ||||
\(223\) | 11.2610 | + | 15.4994i | 0.754091 | + | 1.03792i | 0.997683 | + | 0.0680388i | \(0.0216742\pi\) |
−0.243592 | + | 0.969878i | \(0.578326\pi\) | |||||||
\(224\) | −12.1696 | − | 8.84173i | −0.813115 | − | 0.590763i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.76973 | − | 8.52434i | −0.184239 | − | 0.567031i | ||||
\(227\) | −9.03772 | + | 12.4394i | −0.599855 | + | 0.825629i | −0.995695 | − | 0.0926901i | \(-0.970453\pi\) |
0.395840 | + | 0.918319i | \(0.370453\pi\) | |||||||
\(228\) | 2.13760 | + | 2.94215i | 0.141566 | + | 0.194849i | ||||
\(229\) | −2.75064 | + | 8.46560i | −0.181767 | + | 0.559422i | −0.999878 | − | 0.0156388i | \(-0.995022\pi\) |
0.818110 | + | 0.575061i | \(0.195022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.5426 | + | 4.32954i | 0.891038 | + | 0.284863i | ||||
\(232\) | 19.7624i | 1.29747i | ||||||||
\(233\) | 21.7185 | + | 7.05677i | 1.42283 | + | 0.462304i | 0.916499 | − | 0.400037i | \(-0.131003\pi\) |
0.506327 | + | 0.862342i | \(0.331003\pi\) | |||||||
\(234\) | 4.85822 | − | 3.52970i | 0.317592 | − | 0.230744i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.57942 | + | 4.86096i | 0.102812 | + | 0.316422i | ||||
\(237\) | 7.61030 | − | 2.47274i | 0.494342 | − | 0.160621i | ||||
\(238\) | −14.6416 | + | 20.1524i | −0.949071 | + | 1.30628i | ||||
\(239\) | 13.6405 | − | 9.91037i | 0.882327 | − | 0.641048i | −0.0515388 | − | 0.998671i | \(-0.516413\pi\) |
0.933866 | + | 0.357623i | \(0.116413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9607 | −0.770459 | −0.385229 | − | 0.922821i | \(-0.625878\pi\) | ||||
−0.385229 | + | 0.922821i | \(0.625878\pi\) | |||||||
\(242\) | −7.61154 | − | 10.2706i | −0.489288 | − | 0.660220i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.974917 | + | 3.00049i | −0.0624127 | + | 0.192087i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.51049 | − | 4.00361i | −0.351336 | − | 0.255261i | ||||
\(247\) | 27.5201 | − | 8.94184i | 1.75106 | − | 0.568955i | ||||
\(248\) | −8.28992 | + | 2.69356i | −0.526410 | + | 0.171041i | ||||
\(249\) | 10.1556 | + | 7.37844i | 0.643582 | + | 0.467590i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.94533 | − | 15.2201i | 0.312146 | − | 0.960687i | −0.664767 | − | 0.747051i | \(-0.731469\pi\) |
0.976913 | − | 0.213637i | \(-0.0685308\pi\) | |||||||
\(252\) | − | 2.78393i | − | 0.175371i | ||||||
\(253\) | −0.222008 | + | 0.694432i | −0.0139575 | + | 0.0436586i | ||||
\(254\) | −1.77941 | −0.111650 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.1359 | − | 8.09073i | 0.695996 | − | 0.505671i | ||||
\(257\) | −3.21780 | + | 4.42893i | −0.200721 | + | 0.276269i | −0.897498 | − | 0.441019i | \(-0.854617\pi\) |
0.696776 | + | 0.717288i | \(0.254617\pi\) | |||||||
\(258\) | 9.83880 | − | 3.19682i | 0.612537 | − | 0.199025i | ||||
\(259\) | 5.20348 | + | 16.0147i | 0.323328 | + | 0.995103i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.19262 | + | 3.77266i | −0.321415 | + | 0.233522i | ||||
\(262\) | −2.94121 | − | 0.955657i | −0.181709 | − | 0.0590407i | ||||
\(263\) | 11.9841i | 0.738971i | 0.929236 | + | 0.369486i | \(0.120466\pi\) | ||||
−0.929236 | + | 0.369486i | \(0.879534\pi\) | |||||||
\(264\) | −5.96326 | + | 8.28992i | −0.367014 | + | 0.510209i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.62119 | + | 26.5333i | −0.528599 | + | 1.62686i | ||||
\(267\) | −1.50793 | − | 2.07549i | −0.0922841 | − | 0.127018i | ||||
\(268\) | −4.62944 | + | 6.37188i | −0.282788 | + | 0.389224i | ||||
\(269\) | −4.21700 | − | 12.9786i | −0.257115 | − | 0.791318i | −0.993406 | − | 0.114653i | \(-0.963424\pi\) |
0.736291 | − | 0.676665i | \(-0.236576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.57702 | − | 6.95812i | −0.581763 | − | 0.422675i | 0.257596 | − | 0.966253i | \(-0.417070\pi\) |
−0.839359 | + | 0.543577i | \(0.817070\pi\) | |||||||
\(272\) | −6.69909 | − | 9.22050i | −0.406192 | − | 0.559075i | ||||
\(273\) | −21.0670 | − | 6.84507i | −1.27503 | − | 0.414283i | ||||
\(274\) | −11.9184 | −0.720014 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.142753 | 0.00859274 | ||||||||
\(277\) | −9.76148 | − | 3.17170i | −0.586511 | − | 0.190569i | 0.000704561 | − | 1.00000i | \(-0.499776\pi\) |
−0.587215 | + | 0.809431i | \(0.699776\pi\) | |||||||
\(278\) | 3.61703 | + | 4.97841i | 0.216935 | + | 0.298585i | ||||
\(279\) | −2.29029 | − | 1.66399i | −0.137116 | − | 0.0996207i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.908167 | − | 2.79505i | −0.0541767 | − | 0.166739i | 0.920307 | − | 0.391197i | \(-0.127939\pi\) |
−0.974484 | + | 0.224458i | \(0.927939\pi\) | |||||||
\(282\) | 0.162493 | − | 0.223652i | 0.00967629 | − | 0.0133183i | ||||
\(283\) | −12.8301 | − | 17.6592i | −0.762673 | − | 1.04973i | −0.996987 | − | 0.0775682i | \(-0.975284\pi\) |
0.234314 | − | 0.972161i | \(-0.424716\pi\) | |||||||
\(284\) | −2.00318 | + | 6.16514i | −0.118867 | + | 0.365834i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7828 | + | 16.0573i | 0.696731 | + | 0.949490i | ||||
\(287\) | 25.1252i | 1.48309i | ||||||||
\(288\) | 3.33724 | + | 1.08433i | 0.196649 | + | 0.0638950i | ||||
\(289\) | 6.47214 | − | 4.70228i | 0.380714 | − | 0.276605i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.621738 | + | 1.91351i | 0.0364469 | + | 0.112172i | ||||
\(292\) | −8.99424 | + | 2.92241i | −0.526348 | + | 0.171021i | ||||
\(293\) | −14.5574 | + | 20.0365i | −0.850452 | + | 1.17055i | 0.133311 | + | 0.991074i | \(0.457439\pi\) |
−0.983763 | + | 0.179473i | \(0.942561\pi\) | |||||||
\(294\) | 10.6966 | − | 7.77156i | 0.623840 | − | 0.453246i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.0944 | −0.702974 | ||||||||
\(297\) | −3.31659 | + | 0.0156899i | −0.192448 | + | 0.000910423i | ||||
\(298\) | 4.40269i | 0.255041i | ||||||||
\(299\) | 0.350999 | − | 1.08026i | 0.0202988 | − | 0.0624732i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.8723 | − | 22.4301i | −1.77945 | − | 1.29285i | ||||
\(302\) | −6.54319 | + | 2.12601i | −0.376518 | + | 0.122338i | ||||
\(303\) | 7.21362 | − | 2.34385i | 0.414411 | − | 0.134650i | ||||
\(304\) | −10.3269 | − | 7.50295i | −0.592289 | − | 0.430323i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.79562 | − | 5.52634i | 0.102649 | − | 0.315920i | ||||
\(307\) | 4.94023i | 0.281954i | 0.990013 | + | 0.140977i | \(0.0450243\pi\) | ||||
−0.990013 | + | 0.140977i | \(0.954976\pi\) | |||||||
\(308\) | 9.23316 | − | 0.0436798i | 0.526108 | − | 0.00248889i | ||||
\(309\) | 16.8685 | 0.959618 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1722 | − | 8.11707i | 0.633517 | − | 0.460277i | −0.224100 | − | 0.974566i | \(-0.571944\pi\) |
0.857617 | + | 0.514289i | \(0.171944\pi\) | |||||||
\(312\) | 9.35164 | − | 12.8714i | 0.529432 | − | 0.728701i | ||||
\(313\) | 3.87017 | − | 1.25750i | 0.218755 | − | 0.0710779i | −0.197589 | − | 0.980285i | \(-0.563311\pi\) |
0.416344 | + | 0.909207i | \(0.363311\pi\) | |||||||
\(314\) | 2.66796 | + | 8.21113i | 0.150562 | + | 0.463381i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.20412 | − | 3.05447i | 0.236500 | − | 0.171827i | ||||
\(317\) | −24.5562 | − | 7.97880i | −1.37921 | − | 0.448134i | −0.476803 | − | 0.879010i | \(-0.658205\pi\) |
−0.902411 | + | 0.430876i | \(0.858205\pi\) | |||||||
\(318\) | 2.94803i | 0.165317i | ||||||||
\(319\) | −12.5938 | − | 17.1626i | −0.705119 | − | 0.960921i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.39847 | − | 7.38173i | 0.133870 | − | 0.412008i | ||||
\(322\) | 0.643698 | + | 0.885974i | 0.0358719 | + | 0.0493734i | ||||
\(323\) | 16.4579 | − | 22.6524i | 0.915743 | − | 1.26041i | ||||
\(324\) | 0.200680 | + | 0.617629i | 0.0111489 | + | 0.0343127i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.00265 | − | 3.63464i | −0.277071 | − | 0.201304i | ||||
\(327\) | 2.61959 | + | 3.60556i | 0.144864 | + | 0.199388i | ||||
\(328\) | −17.1628 | − | 5.57654i | −0.947659 | − | 0.307913i | ||||
\(329\) | −1.01974 | −0.0562203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.35008 | −0.184137 | −0.0920684 | − | 0.995753i | \(-0.529348\pi\) | ||||
−0.0920684 | + | 0.995753i | \(0.529348\pi\) | |||||||
\(332\) | 7.75307 | + | 2.51913i | 0.425505 | + | 0.138255i | ||||
\(333\) | −2.30883 | − | 3.17784i | −0.126523 | − | 0.174144i | ||||
\(334\) | −1.85349 | − | 1.34664i | −0.101419 | − | 0.0736850i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.01958 | + | 9.29332i | 0.164732 | + | 0.506992i | ||||
\(337\) | 16.1052 | − | 22.1669i | 0.877307 | − | 1.20751i | −0.0998530 | − | 0.995002i | \(-0.531837\pi\) |
0.977160 | − | 0.212507i | \(-0.0681628\pi\) | |||||||
\(338\) | −9.35859 | − | 12.8810i | −0.509040 | − | 0.700634i | ||||
\(339\) | 2.38328 | − | 7.33499i | 0.129442 | − | 0.398382i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.48285 | − | 7.62206i | 0.296913 | − | 0.412758i | ||||
\(342\) | − | 6.50800i | − | 0.351912i | ||||||
\(343\) | −17.8452 | − | 5.79826i | −0.963550 | − | 0.313076i | ||||
\(344\) | 22.1739 | − | 16.1103i | 1.19554 | − | 0.868610i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.709284 | − | 2.18295i | −0.0381313 | − | 0.117356i | ||||
\(347\) | 15.0519 | − | 4.89065i | 0.808027 | − | 0.262544i | 0.124265 | − | 0.992249i | \(-0.460343\pi\) |
0.683762 | + | 0.729705i | \(0.260343\pi\) | |||||||
\(348\) | −2.45002 | + | 3.37216i | −0.131335 | + | 0.180767i | ||||
\(349\) | −2.96043 | + | 2.15088i | −0.158468 | + | 0.115134i | −0.664194 | − | 0.747561i | \(-0.731225\pi\) |
0.505725 | + | 0.862695i | \(0.331225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.16724 | 0.275807 | ||||||||
\(352\) | −3.54393 | + | 11.0853i | −0.188892 | + | 0.590846i | ||||
\(353\) | − | 27.4937i | − | 1.46334i | −0.681658 | − | 0.731671i | \(-0.738741\pi\) | ||
0.681658 | − | 0.731671i | \(-0.261259\pi\) | |||||||
\(354\) | 2.82643 | − | 8.69884i | 0.150223 | − | 0.462338i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.34785 | − | 0.979273i | −0.0714361 | − | 0.0519014i | ||||
\(357\) | −20.3851 | + | 6.62353i | −1.07890 | + | 0.350555i | ||||
\(358\) | 2.23612 | − | 0.726559i | 0.118183 | − | 0.0383998i | ||||
\(359\) | 0.387309 | + | 0.281397i | 0.0204414 | + | 0.0148515i | 0.597959 | − | 0.801527i | \(-0.295979\pi\) |
−0.577518 | + | 0.816378i | \(0.695979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.81936 | − | 11.7548i | 0.201019 | − | 0.618673i | ||||
\(362\) | − | 23.4033i | − | 1.23005i | ||||||
\(363\) | −0.104074 | − | 10.9995i | −0.00546247 | − | 0.577324i | ||||
\(364\) | −14.3852 | −0.753992 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.56754 | − | 3.31851i | 0.238749 | − | 0.173462i | ||||
\(367\) | 14.9639 | − | 20.5961i | 0.781111 | − | 1.07511i | −0.214047 | − | 0.976823i | \(-0.568665\pi\) |
0.995158 | − | 0.0982843i | \(-0.0313355\pi\) | |||||||
\(368\) | −0.476539 | + | 0.154837i | −0.0248413 | + | 0.00807143i | ||||
\(369\) | −1.81115 | − | 5.57414i | −0.0942846 | − | 0.290178i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.79762 | − | 6.39184i | 0.456750 | − | 0.331848i | ||||
\(372\) | −1.74848 | − | 0.568116i | −0.0906545 | − | 0.0294554i | ||||
\(373\) | − | 2.75967i | − | 0.142890i | −0.997445 | − | 0.0714451i | \(-0.977239\pi\) | ||
0.997445 | − | 0.0714451i | \(-0.0227611\pi\) | |||||||
\(374\) | 18.3568 | + | 5.86861i | 0.949205 | + | 0.303459i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.226333 | − | 0.696580i | 0.0116722 | − | 0.0359234i | ||||
\(377\) | 19.4942 | + | 26.8315i | 1.00400 | + | 1.38189i | ||||
\(378\) | −2.92831 | + | 4.03048i | −0.150616 | + | 0.207305i | ||||
\(379\) | 6.69130 | + | 20.5937i | 0.343709 | + | 1.05783i | 0.962271 | + | 0.272092i | \(0.0877156\pi\) |
−0.618562 | + | 0.785736i | \(0.712284\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.23872 | − | 0.899983i | −0.0634616 | − | 0.0461075i | ||||
\(382\) | 8.65148 | + | 11.9077i | 0.442648 | + | 0.609253i | ||||
\(383\) | 15.4351 | + | 5.01518i | 0.788699 | + | 0.256264i | 0.675550 | − | 0.737314i | \(-0.263906\pi\) |
0.113149 | + | 0.993578i | \(0.463906\pi\) | |||||||
\(384\) | −3.01930 | −0.154078 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.1912 | −0.824109 | ||||||||
\(387\) | 8.46605 | + | 2.75079i | 0.430353 | + | 0.139830i | ||||
\(388\) | 0.768007 | + | 1.05707i | 0.0389897 | + | 0.0536647i | ||||
\(389\) | −13.1802 | − | 9.57598i | −0.668263 | − | 0.485522i | 0.201180 | − | 0.979554i | \(-0.435522\pi\) |
−0.869443 | + | 0.494033i | \(0.835522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.339639 | − | 1.04530i | −0.0171763 | − | 0.0528631i | ||||
\(392\) | 20.5901 | − | 28.3398i | 1.03996 | − | 1.43138i | ||||
\(393\) | −1.56415 | − | 2.15286i | −0.0789007 | − | 0.108598i | ||||
\(394\) | −5.24537 | + | 16.1436i | −0.264258 | + | 0.813302i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.04527 | + | 0.675263i | −0.102779 | + | 0.0339332i | ||||
\(397\) | 19.9673i | 1.00213i | 0.865410 | + | 0.501064i | \(0.167058\pi\) | ||||
−0.865410 | + | 0.501064i | \(0.832942\pi\) | |||||||
\(398\) | −13.1249 | − | 4.26453i | −0.657890 | − | 0.213761i | ||||
\(399\) | −19.4214 | + | 14.1105i | −0.972288 | + | 0.706408i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.44448 | − | 25.9894i | −0.421697 | − | 1.29785i | −0.906122 | − | 0.423017i | \(-0.860971\pi\) |
0.484425 | − | 0.874833i | \(-0.339029\pi\) | |||||||
\(402\) | 13.4047 | − | 4.35544i | 0.668563 | − | 0.217229i | ||||
\(403\) | −8.59825 | + | 11.8345i | −0.428309 | + | 0.589517i | ||||
\(404\) | 3.98498 | − | 2.89526i | 0.198260 | − | 0.144044i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −31.9763 | −1.58696 | ||||||||
\(407\) | 10.5034 | − | 7.70731i | 0.520632 | − | 0.382037i | ||||
\(408\) | − | 15.3950i | − | 0.762168i | ||||||
\(409\) | −7.70626 | + | 23.7174i | −0.381050 | + | 1.17275i | 0.558255 | + | 0.829669i | \(0.311471\pi\) |
−0.939305 | + | 0.343082i | \(0.888529\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.29684 | − | 6.02801i | −0.409253 | − | 0.297340i | ||||
\(412\) | 10.4185 | − | 3.38518i | 0.513283 | − | 0.166776i | ||||
\(413\) | −32.0876 | + | 10.4259i | −1.57893 | + | 0.513025i | ||||
\(414\) | −0.206673 | − | 0.150157i | −0.0101574 | − | 0.00737980i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.60301 | − | 17.2443i | 0.274710 | − | 0.845471i | ||||
\(417\) | 5.29507i | 0.259301i | ||||||||
\(418\) | 21.5843 | − | 0.102110i | 1.05572 | − | 0.00499437i | ||||
\(419\) | −16.8256 | −0.821986 | −0.410993 | − | 0.911639i | \(-0.634818\pi\) | ||||
−0.410993 | + | 0.911639i | \(0.634818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0933 | + | 13.8721i | −0.930551 | + | 0.676085i | −0.946128 | − | 0.323793i | \(-0.895042\pi\) |
0.0155763 | + | 0.999879i | \(0.495042\pi\) | |||||||
\(422\) | 15.2684 | − | 21.0151i | 0.743253 | − | 1.02300i | ||||
\(423\) | 0.226235 | − | 0.0735083i | 0.0109999 | − | 0.00357409i | ||||
\(424\) | 2.41359 | + | 7.42826i | 0.117214 | + | 0.360748i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.38499 | − | 6.81859i | 0.454704 | − | 0.330362i | ||||
\(427\) | −19.8065 | − | 6.43552i | −0.958504 | − | 0.311437i | ||||
\(428\) | − | 5.04050i | − | 0.243642i | ||||||
\(429\) | 0.0810736 | + | 17.1376i | 0.00391427 | + | 0.827411i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6362 | + | 35.8126i | −0.560497 | + | 1.72503i | 0.120469 | + | 0.992717i | \(0.461560\pi\) |
−0.680966 | + | 0.732315i | \(0.738440\pi\) | |||||||
\(432\) | −1.33982 | − | 1.84410i | −0.0644620 | − | 0.0887243i | ||||
\(433\) | −18.2068 | + | 25.0594i | −0.874961 | + | 1.20428i | 0.102831 | + | 0.994699i | \(0.467210\pi\) |
−0.977791 | + | 0.209581i | \(0.932790\pi\) | |||||||
\(434\) | −4.35827 | − | 13.4134i | −0.209204 | − | 0.643862i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.34150 | + | 1.70120i | 0.112137 | + | 0.0814726i | ||||
\(437\) | −0.723552 | − | 0.995884i | −0.0346122 | − | 0.0476396i | ||||
\(438\) | 16.0955 | + | 5.22974i | 0.769072 | + | 0.249887i | ||||
\(439\) | 28.2131 | 1.34654 | 0.673268 | − | 0.739399i | \(-0.264890\pi\) | ||||
0.673268 | + | 0.739399i | \(0.264890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.3770 | 0.541762 | ||||||||
\(442\) | −28.5559 | − | 9.27837i | −1.35827 | − | 0.441327i | ||||
\(443\) | −8.60636 | − | 11.8456i | −0.408900 | − | 0.562803i | 0.554050 | − | 0.832484i | \(-0.313082\pi\) |
−0.962950 | + | 0.269681i | \(0.913082\pi\) | |||||||
\(444\) | −2.06373 | − | 1.49939i | −0.0979404 | − | 0.0711578i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.88019 | − | 21.1751i | −0.325787 | − | 1.00267i | ||||
\(447\) | −2.22677 | + | 3.06489i | −0.105323 | + | 0.144964i | ||||
\(448\) | 21.7626 | + | 29.9536i | 1.02818 | + | 1.41517i | ||||
\(449\) | −3.70749 | + | 11.4105i | −0.174967 | + | 0.538493i | −0.999632 | − | 0.0271282i | \(-0.991364\pi\) |
0.824665 | + | 0.565622i | \(0.191364\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.4587 | − | 6.09429i | 0.869187 | − | 0.286969i | ||||
\(452\) | − | 5.00858i | − | 0.235584i | ||||||
\(453\) | −5.63026 | − | 1.82938i | −0.264533 | − | 0.0859519i | ||||
\(454\) | 14.4564 | − | 10.5032i | 0.678471 | − | 0.492938i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.32819 | − | 16.3985i | −0.249515 | − | 0.767929i | ||||
\(457\) | 9.55211 | − | 3.10367i | 0.446829 | − | 0.145183i | −0.0769553 | − | 0.997035i | \(-0.524520\pi\) |
0.523784 | + | 0.851851i | \(0.324520\pi\) | |||||||
\(458\) | 6.08039 | − | 8.36893i | 0.284118 | − | 0.391055i | ||||
\(459\) | 4.04508 | − | 2.93893i | 0.188808 | − | 0.137177i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.4491 | −0.626386 | −0.313193 | − | 0.949689i | \(-0.601399\pi\) | ||||
−0.313193 | + | 0.949689i | \(0.601399\pi\) | |||||||
\(462\) | −13.4134 | − | 9.64876i | −0.624046 | − | 0.448901i | ||||
\(463\) | 18.7836i | 0.872946i | 0.899717 | + | 0.436473i | \(0.143773\pi\) | ||||
−0.899717 | + | 0.436473i | \(0.856227\pi\) | |||||||
\(464\) | 4.52104 | − | 13.9143i | 0.209884 | − | 0.645957i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.4705 | − | 15.5992i | −0.994602 | − | 0.722620i | ||||
\(467\) | 25.2515 | − | 8.20470i | 1.16850 | − | 0.379668i | 0.340416 | − | 0.940275i | \(-0.389432\pi\) |
0.828082 | + | 0.560607i | \(0.189432\pi\) | |||||||
\(468\) | 3.19144 | − | 1.03696i | 0.147524 | − | 0.0479335i | ||||
\(469\) | −42.0614 | − | 30.5594i | −1.94221 | − | 1.41110i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.29571 | + | 7.06548i | −0.105781 | + | 0.325560i | ||||
\(472\) | − | 24.2329i | − | 1.11541i | ||||||
\(473\) | −8.99039 | + | 28.1216i | −0.413379 | + | 1.29303i | ||||
\(474\) | −9.29944 | −0.427137 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −11.2613 | + | 8.18178i | −0.516159 | + | 0.375011i | ||||
\(477\) | −1.49104 | + | 2.05224i | −0.0682699 | + | 0.0939655i | ||||
\(478\) | −18.6354 | + | 6.05501i | −0.852363 | + | 0.276950i | ||||
\(479\) | −3.33214 | − | 10.2553i | −0.152249 | − | 0.468575i | 0.845623 | − | 0.533781i | \(-0.179229\pi\) |
−0.997872 | + | 0.0652062i | \(0.979229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4206 | + | 11.9303i | −0.748716 | + | 0.543974i | ||||
\(482\) | 13.2198 | + | 4.29538i | 0.602146 | + | 0.195649i | ||||
\(483\) | 0.942328i | 0.0428774i | ||||||||
\(484\) | −2.27166 | − | 6.77273i | −0.103257 | − | 0.307851i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.359123 | − | 1.10527i | 0.0162902 | − | 0.0501360i | ||||
\(487\) | 4.00338 | + | 5.51018i | 0.181410 | + | 0.249690i | 0.890031 | − | 0.455899i | \(-0.150682\pi\) |
−0.708621 | + | 0.705589i | \(0.750682\pi\) | |||||||
\(488\) | 8.79212 | − | 12.1013i | 0.398001 | − | 0.547801i | ||||
\(489\) | −1.64424 | − | 5.06044i | −0.0743549 | − | 0.228841i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.1116 | − | 15.3385i | −0.952754 | − | 0.692216i | −0.00129727 | − | 0.999999i | \(-0.500413\pi\) |
−0.951457 | + | 0.307783i | \(0.900413\pi\) | |||||||
\(492\) | −2.23724 | − | 3.07929i | −0.100862 | − | 0.138825i | ||||
\(493\) | 30.5215 | + | 9.91703i | 1.37462 | + | 0.446640i | ||||
\(494\) | −33.6283 | −1.51301 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.45297 | 0.289747 | ||||||||
\(497\) | −40.6967 | − | 13.2231i | −1.82549 | − | 0.593139i | ||||
\(498\) | −8.57484 | − | 11.8022i | −0.384248 | − | 0.528871i | ||||
\(499\) | 15.6815 | + | 11.3933i | 0.702000 | + | 0.510033i | 0.880583 | − | 0.473892i | \(-0.157151\pi\) |
−0.178583 | + | 0.983925i | \(0.557151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.609193 | − | 1.87490i | −0.0272167 | − | 0.0837644i | ||||
\(502\) | −10.9318 | + | 15.0464i | −0.487911 | + | 0.671552i | ||||
\(503\) | −11.0752 | − | 15.2437i | −0.493819 | − | 0.679683i | 0.487268 | − | 0.873253i | \(-0.337993\pi\) |
−0.981087 | + | 0.193570i | \(0.937993\pi\) | |||||||
\(504\) | −4.07878 | + | 12.5532i | −0.181684 | + | 0.559164i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.494765 | − | 0.687805i | 0.0219950 | − | 0.0305767i | ||||
\(507\) | − | 13.7003i | − | 0.608453i | ||||||
\(508\) | −0.945678 | − | 0.307270i | −0.0419577 | − | 0.0136329i | ||||
\(509\) | −4.16741 | + | 3.02780i | −0.184717 | + | 0.134205i | −0.676301 | − | 0.736625i | \(-0.736418\pi\) |
0.491584 | + | 0.870830i | \(0.336418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.2911 | − | 59.3718i | −0.853387 | − | 2.62645i | ||||
\(512\) | −20.9568 | + | 6.80928i | −0.926168 | + | 0.300930i | ||||
\(513\) | 3.29158 | − | 4.53048i | 0.145327 | − | 0.200025i | ||||
\(514\) | 5.14707 | − | 3.73956i | 0.227027 | − | 0.164945i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.78091 | 0.254490 | ||||||||
\(517\) | 0.247346 | + | 0.749175i | 0.0108783 | + | 0.0329487i | ||||
\(518\) | − | 19.5692i | − | 0.859820i | ||||||
\(519\) | 0.610322 | − | 1.87838i | 0.0267902 | − | 0.0824516i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.5759 | + | 24.3944i | 1.47099 | + | 1.06874i | 0.980326 | + | 0.197387i | \(0.0632455\pi\) |
0.490663 | + | 0.871349i | \(0.336754\pi\) | |||||||
\(522\) | 7.09409 | − | 2.30501i | 0.310500 | − | 0.100887i | ||||
\(523\) | 6.58397 | − | 2.13926i | 0.287897 | − | 0.0935434i | −0.161508 | − | 0.986871i | \(-0.551636\pi\) |
0.449405 | + | 0.893328i | \(0.351636\pi\) | |||||||
\(524\) | −1.39810 | − | 1.01578i | −0.0610762 | − | 0.0443745i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.30377 | − | 13.2456i | 0.187653 | − | 0.577537i | ||||
\(527\) | 14.1548i | 0.616592i | ||||||||
\(528\) | 6.09510 | − | 4.47256i | 0.265255 | − | 0.194643i | ||||
\(529\) | 22.9517 | 0.997899 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.36725 | − | 4.62608i | 0.276315 | − | 0.200755i | ||||
\(532\) | −9.16355 | + | 12.6125i | −0.397290 | + | 0.546823i | ||||
\(533\) | −28.8029 | + | 9.35863i | −1.24759 | + | 0.405367i | ||||
\(534\) | 0.921313 | + | 2.83551i | 0.0398691 | + | 0.122704i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 30.2104 | − | 21.9492i | 1.30489 | − | 0.948059i | ||||
\(537\) | 1.92413 | + | 0.625187i | 0.0830322 | + | 0.0269788i | ||||
\(538\) | 15.8592i | 0.683740i | ||||||||
\(539\) | 0.178505 | + | 37.7329i | 0.00768874 | + | 1.62527i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.78173 | + | 27.0274i | −0.377556 | + | 1.16200i | 0.564182 | + | 0.825651i | \(0.309192\pi\) |
−0.941738 | + | 0.336348i | \(0.890808\pi\) | |||||||
\(542\) | 8.08635 | + | 11.1299i | 0.347339 | + | 0.478071i | ||||
\(543\) | 11.8368 | − | 16.2920i | 0.507967 | − | 0.699156i | ||||
\(544\) | −5.42167 | − | 16.6862i | −0.232452 | − | 0.715415i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 20.8264 | + | 15.1313i | 0.891288 | + | 0.647559i | ||||
\(547\) | 15.1996 | + | 20.9205i | 0.649889 | + | 0.894496i | 0.999094 | − | 0.0425503i | \(-0.0135483\pi\) |
−0.349205 | + | 0.937046i | \(0.613548\pi\) | |||||||
\(548\) | −6.33407 | − | 2.05807i | −0.270578 | − | 0.0879162i | ||||
\(549\) | 4.85807 | 0.207337 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.9431 | 1.53123 | ||||||||
\(552\) | −0.643698 | − | 0.209150i | −0.0273976 | − | 0.00890202i | ||||
\(553\) | 20.1628 | + | 27.7518i | 0.857411 | + | 1.18012i | ||||
\(554\) | 9.65002 | + | 7.01115i | 0.409990 | + | 0.297875i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.06262 | + | 3.27039i | 0.0450649 | + | 0.138696i | ||||
\(557\) | 4.73996 | − | 6.52399i | 0.200838 | − | 0.276430i | −0.696704 | − | 0.717359i | \(-0.745351\pi\) |
0.897542 | + | 0.440929i | \(0.145351\pi\) | |||||||
\(558\) | 1.93381 | + | 2.66165i | 0.0818645 | + | 0.112677i | ||||
\(559\) | 14.2140 | − | 43.7461i | 0.601186 | − | 1.85026i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.81067 | + | 13.3698i | 0.414207 | + | 0.564472i | ||||
\(562\) | 3.41542i | 0.144071i | ||||||||
\(563\) | 28.2003 | + | 9.16284i | 1.18850 | + | 0.386168i | 0.835519 | − | 0.549462i | \(-0.185167\pi\) |
0.352983 | + | 0.935630i | \(0.385167\pi\) | |||||||
\(564\) | 0.124978 | − | 0.0908017i | 0.00526252 | − | 0.00382344i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.83892 | + | 24.1257i | 0.329494 | + | 1.01408i | ||||
\(567\) | −4.07703 | + | 1.32471i | −0.171219 | + | 0.0556325i | ||||
\(568\) | 18.0653 | − | 24.8647i | 0.758002 | − | 1.04330i | ||||
\(569\) | −34.0618 | + | 24.7473i | −1.42794 | + | 1.03746i | −0.437548 | + | 0.899195i | \(0.644153\pi\) |
−0.990395 | + | 0.138266i | \(0.955847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.6823 | −1.11662 | −0.558311 | − | 0.829632i | \(-0.688550\pi\) | ||||
−0.558311 | + | 0.829632i | \(0.688550\pi\) | |||||||
\(572\) | 3.48924 | + | 10.5684i | 0.145893 | + | 0.441887i | ||||
\(573\) | 12.6652i | 0.529094i | ||||||||
\(574\) | 9.02304 | − | 27.7700i | 0.376614 | − | 1.15910i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.98733 | − | 5.07659i | −0.291139 | − | 0.211525i | ||||
\(577\) | −3.14627 | + | 1.02228i | −0.130981 | + | 0.0425582i | −0.373774 | − | 0.927520i | \(-0.621936\pi\) |
0.242793 | + | 0.970078i | \(0.421936\pi\) | |||||||
\(578\) | −8.84214 | + | 2.87299i | −0.367785 | + | 0.119500i | ||||
\(579\) | −11.2713 | − | 8.18910i | −0.468420 | − | 0.340327i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.6290 | + | 51.1788i | −0.689887 | + | 2.12325i | ||||
\(582\) | − | 2.33822i | − | 0.0969225i | ||||||
\(583\) | −6.82982 | − | 4.91296i | −0.282862 | − | 0.203474i | ||||
\(584\) | 44.8381 | 1.85542 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.2854 | − | 16.9178i | 0.961911 | − | 0.698869i | ||||
\(587\) | 5.01246 | − | 6.89906i | 0.206886 | − | 0.284755i | −0.692947 | − | 0.720989i | \(-0.743688\pi\) |
0.899833 | + | 0.436234i | \(0.143688\pi\) | |||||||
\(588\) | 7.02678 | − | 2.28314i | 0.289779 | − | 0.0941550i | ||||
\(589\) | 4.89893 | + | 15.0774i | 0.201857 | + | 0.621252i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.8165 | + | 8.58522i | −0.486068 | + | 0.353149i | ||||
\(592\) | 8.51544 | + | 2.76684i | 0.349983 | + | 0.113716i | ||||
\(593\) | − | 23.4343i | − | 0.962333i | −0.876629 | − | 0.481167i | \(-0.840213\pi\) | ||
0.876629 | − | 0.481167i | \(-0.159787\pi\) | |||||||
\(594\) | 3.67135 | + | 1.17372i | 0.150637 | + | 0.0481584i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.760259 | + | 2.33984i | −0.0311414 | + | 0.0958434i | ||||
\(597\) | −6.97985 | − | 9.60694i | −0.285666 | − | 0.393186i | ||||
\(598\) | −0.775895 | + | 1.06793i | −0.0317287 | + | 0.0436708i | ||||
\(599\) | −5.82017 | − | 17.9126i | −0.237805 | − | 0.731890i | −0.996737 | − | 0.0807194i | \(-0.974278\pi\) |
0.758931 | − | 0.651171i | \(-0.225722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.4664 | + | 22.1351i | 1.24275 | + | 0.902911i | 0.997778 | − | 0.0666198i | \(-0.0212214\pi\) |
0.244971 | + | 0.969530i | \(0.421221\pi\) | |||||||
\(602\) | 26.0670 | + | 35.8782i | 1.06241 | + | 1.46229i | ||||
\(603\) | 11.5344 | + | 3.74775i | 0.469717 | + | 0.152620i | ||||
\(604\) | −3.84453 | −0.156432 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.81471 | −0.358073 | ||||||||
\(607\) | 27.9306 | + | 9.07520i | 1.13367 | + | 0.368351i | 0.814969 | − | 0.579505i | \(-0.196754\pi\) |
0.318699 | + | 0.947856i | \(0.396754\pi\) | |||||||
\(608\) | −11.5501 | − | 15.8973i | −0.468418 | − | 0.644723i | ||||
\(609\) | −22.2599 | − | 16.1728i | −0.902019 | − | 0.655355i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.379834 | − | 1.16901i | −0.0153665 | − | 0.0472931i | ||||
\(612\) | 1.90858 | − | 2.62693i | 0.0771498 | − | 0.106188i | ||||
\(613\) | 7.58894 | + | 10.4453i | 0.306515 | + | 0.421881i | 0.934290 | − | 0.356513i | \(-0.116035\pi\) |
−0.627776 | + | 0.778394i | \(0.716035\pi\) | |||||||
\(614\) | 1.77415 | − | 5.46027i | 0.0715989 | − | 0.220359i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −41.6978 | − | 13.3307i | −1.68005 | − | 0.537109i | ||||
\(617\) | − | 41.6041i | − | 1.67492i | −0.546500 | − | 0.837459i | \(-0.684040\pi\) | ||
0.546500 | − | 0.837459i | \(-0.315960\pi\) | |||||||
\(618\) | −18.6443 | − | 6.05789i | −0.749982 | − | 0.243684i | ||||
\(619\) | 3.45545 | − | 2.51053i | 0.138886 | − | 0.100907i | −0.516173 | − | 0.856484i | \(-0.672644\pi\) |
0.655059 | + | 0.755578i | \(0.272644\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0679277 | − | 0.209060i | −0.00272585 | − | 0.00838929i | ||||
\(622\) | −15.2633 | + | 4.95935i | −0.612002 | + | 0.198852i | ||||
\(623\) | 6.46427 | − | 8.89731i | 0.258986 | − | 0.356463i | ||||
\(624\) | −9.52890 | + | 6.92315i | −0.381461 | + | 0.277148i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.72918 | −0.189016 | ||||||||
\(627\) | 15.0774 | + | 10.8457i | 0.602132 | + | 0.433137i | ||||
\(628\) | 4.82455i | 0.192521i | ||||||||
\(629\) | −6.06913 | + | 18.6789i | −0.241992 | + | 0.744775i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2892 | + | 16.1941i | 0.887319 | + | 0.644675i | 0.935178 | − | 0.354179i | \(-0.115240\pi\) |
−0.0478586 | + | 0.998854i | \(0.515240\pi\) | |||||||
\(632\) | −23.4322 | + | 7.61358i | −0.932082 | + | 0.302852i | ||||
\(633\) | 21.2579 | − | 6.90710i | 0.844924 | − | 0.274532i | ||||
\(634\) | 24.2758 | + | 17.6374i | 0.964116 | + | 0.700471i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.509066 | + | 1.56674i | −0.0201858 | + | 0.0621254i | ||||
\(637\) | − | 58.7877i | − | 2.32925i | ||||||
\(638\) | 7.75607 | + | 23.4920i | 0.307066 | + | 0.930057i | ||||
\(639\) | 9.98194 | 0.394879 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.41712 | + | 5.38885i | −0.292958 | + | 0.212847i | −0.724550 | − | 0.689222i | \(-0.757952\pi\) |
0.431591 | + | 0.902069i | \(0.357952\pi\) | |||||||
\(642\) | −5.30190 | + | 7.29744i | −0.209249 | + | 0.288007i | ||||
\(643\) | 3.24223 | − | 1.05346i | 0.127861 | − | 0.0415446i | −0.244387 | − | 0.969678i | \(-0.578587\pi\) |
0.372249 | + | 0.928133i | \(0.378587\pi\) | |||||||
\(644\) | 0.189106 | + | 0.582010i | 0.00745184 | + | 0.0229344i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.3254 | + | 19.1265i | −1.03576 | + | 0.752523i | ||||
\(647\) | −21.2663 | − | 6.90986i | −0.836066 | − | 0.271654i | −0.140468 | − | 0.990085i | \(-0.544861\pi\) |
−0.695598 | + | 0.718431i | \(0.744861\pi\) | |||||||
\(648\) | − | 3.07901i | − | 0.120955i | ||||||
\(649\) | 15.4427 | + | 21.0450i | 0.606179 | + | 0.826087i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.75019 | − | 11.5419i | 0.146981 | − | 0.452362i | ||||
\(652\) | −2.03106 | − | 2.79551i | −0.0795423 | − | 0.109481i | ||||
\(653\) | −8.69667 | + | 11.9699i | −0.340327 | + | 0.468420i | −0.944537 | − | 0.328405i | \(-0.893489\pi\) |
0.604210 | + | 0.796825i | \(0.293489\pi\) | |||||||
\(654\) | −1.60051 | − | 4.92586i | −0.0625848 | − | 0.192616i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.8083 | + | 7.85267i | 0.421992 | + | 0.306595i | ||||
\(657\) | 8.55964 | + | 11.7813i | 0.333943 | + | 0.459633i | ||||
\(658\) | 1.12709 | + | 0.366214i | 0.0439385 | + | 0.0142765i | ||||
\(659\) | 47.4724 | 1.84926 | 0.924631 | − | 0.380864i | \(-0.124373\pi\) | ||||
0.924631 | + | 0.380864i | \(0.124373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6525 | −0.842184 | −0.421092 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421092 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(662\) | 3.70273 | + | 1.20309i | 0.143911 | + | 0.0467594i | ||||
\(663\) | −15.1861 | − | 20.9019i | −0.589780 | − | 0.811763i | ||||
\(664\) | −31.2690 | − | 22.7183i | −1.21347 | − | 0.881641i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.41064 | + | 4.34152i | 0.0546614 | + | 0.168230i | ||||
\(667\) | 0.829302 | − | 1.14144i | 0.0321107 | − | 0.0441966i | ||||
\(668\) | −0.752510 | − | 1.03574i | −0.0291155 | − | 0.0400740i | ||||
\(669\) | 5.92024 | − | 18.2206i | 0.228890 | − | 0.704451i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0762228 | + | 16.1122i | 0.00294255 | + | 0.622005i | ||||
\(672\) | 15.0424i | 0.580275i | ||||||||
\(673\) | −36.5133 | − | 11.8639i | −1.40748 | − | 0.457319i | −0.495880 | − | 0.868391i | \(-0.665154\pi\) |
−0.911603 | + | 0.411072i | \(0.865154\pi\) | |||||||
\(674\) | −25.7612 | + | 18.7166i | −0.992285 | + | 0.720937i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.74938 | − | 8.46172i | −0.105745 | − | 0.325451i | ||||
\(677\) | −21.8108 | + | 7.08677i | −0.838259 | + | 0.272367i | −0.696520 | − | 0.717537i | \(-0.745269\pi\) |
−0.141739 | + | 0.989904i | \(0.545269\pi\) | |||||||
\(678\) | −5.26833 | + | 7.25124i | −0.202329 | + | 0.278482i | ||||
\(679\) | −6.97782 | + | 5.06969i | −0.267784 | + | 0.194557i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.3759 | 0.589206 | ||||||||
\(682\) | −8.79727 | + | 6.45540i | −0.336865 | + | 0.247190i | ||||
\(683\) | 25.9084i | 0.991359i | 0.868505 | + | 0.495680i | \(0.165081\pi\) | ||||
−0.868505 | + | 0.495680i | \(0.834919\pi\) | |||||||
\(684\) | 1.12380 | − | 3.45871i | 0.0429697 | − | 0.132247i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.6414 | + | 12.8173i | 0.673553 | + | 0.489365i | ||||
\(687\) | 8.46560 | − | 2.75064i | 0.322983 | − | 0.104943i | ||||
\(688\) | −19.2978 | + | 6.27024i | −0.735722 | + | 0.239050i | ||||
\(689\) | 10.6044 | + | 7.70454i | 0.403995 | + | 0.293520i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.57824 | − | 14.0904i | 0.174165 | − | 0.536023i | −0.825430 | − | 0.564505i | \(-0.809067\pi\) |
0.999594 | + | 0.0284814i | \(0.00906715\pi\) | |||||||
\(692\) | − | 1.28262i | − | 0.0487579i | ||||||
\(693\) | −4.45748 | − | 13.5010i | −0.169325 | − | 0.512862i | ||||
\(694\) | −18.3927 | −0.698177 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15.9881 | − | 11.6161i | 0.606029 | − | 0.440305i | ||||
\(697\) | −17.2250 | + | 23.7082i | −0.652445 | + | 0.898014i | ||||
\(698\) | 4.04450 | − | 1.31414i | 0.153087 | − | 0.0497409i | ||||
\(699\) | −7.05677 | − | 21.7185i | −0.266911 | − | 0.821469i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.45471 | + | 3.23653i | −0.168252 | + | 0.122242i | −0.668725 | − | 0.743510i | \(-0.733160\pi\) |
0.500473 | + | 0.865752i | \(0.333160\pi\) | |||||||
\(702\) | −5.71118 | − | 1.85567i | −0.215555 | − | 0.0700379i | ||||
\(703\) | 21.9968i | 0.829626i | ||||||||
\(704\) | 16.7273 | − | 23.2538i | 0.630435 | − | 0.876409i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.87362 | + | 30.3879i | −0.371599 | + | 1.14366i | ||||
\(707\) | 19.1119 | + | 26.3052i | 0.718775 | + | 0.989309i | ||||
\(708\) | 3.00424 | − | 4.13498i | 0.112906 | − | 0.155402i | ||||
\(709\) | 5.53161 | + | 17.0245i | 0.207744 | + | 0.639370i | 0.999590 | + | 0.0286488i | \(0.00912044\pi\) |
−0.791846 | + | 0.610721i | \(0.790880\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.47371 | − | 4.70342i | −0.242783 | − | 0.176392i | ||||
\(712\) | 4.64294 | + | 6.39046i | 0.174002 | + | 0.239493i | ||||
\(713\) | 0.591840 | + | 0.192300i | 0.0221646 | + | 0.00720171i | ||||
\(714\) | 24.9097 | 0.932222 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.31386 | 0.0491012 | ||||||||
\(717\) | −16.0353 | − | 5.21019i | −0.598850 | − | 0.194578i | ||||
\(718\) | −0.327024 | − | 0.450110i | −0.0122044 | − | 0.0167980i | ||||
\(719\) | 26.3673 | + | 19.1570i | 0.983334 | + | 0.714434i | 0.958451 | − | 0.285256i | \(-0.0920786\pi\) |
0.0248831 | + | 0.999690i | \(0.492079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.3459 | + | 68.7735i | 0.832204 | + | 2.56126i | ||||
\(722\) | −8.44284 | + | 11.6206i | −0.314210 | + | 0.432473i | ||||
\(723\) | 7.03035 | + | 9.67644i | 0.261461 | + | 0.359871i | ||||
\(724\) | 4.04130 | − | 12.4378i | 0.150194 | − | 0.462248i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.83515 | + | 12.1948i | −0.142336 | + | 0.452591i | ||||
\(727\) | 43.0199i | 1.59552i | 0.602976 | + | 0.797759i | \(0.293982\pi\) | ||||
−0.602976 | + | 0.797759i | \(0.706018\pi\) | |||||||
\(728\) | 64.8654 | + | 21.0760i | 2.40407 | + | 0.781130i | ||||
\(729\) | 0.809017 | − | 0.587785i | 0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.7539 | − | 42.3302i | −0.508708 | − | 1.56564i | ||||
\(732\) | 3.00049 | − | 0.974917i | 0.110901 | − | 0.0360340i | ||||
\(733\) | 23.9267 | − | 32.9323i | 0.883755 | − | 1.21638i | −0.0916123 | − | 0.995795i | \(-0.529202\pi\) |
0.975367 | − | 0.220589i | \(-0.0707979\pi\) | |||||||
\(734\) | −23.9357 | + | 17.3903i | −0.883483 | + | 0.641888i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.771340 | −0.0284320 | ||||||||
\(737\) | −12.2488 | + | 38.3136i | −0.451189 | + | 1.41130i | ||||
\(738\) | 6.81134i | 0.250729i | ||||||||
\(739\) | −11.7810 | + | 36.2581i | −0.433370 | + | 1.33377i | 0.461379 | + | 0.887203i | \(0.347355\pi\) |
−0.894748 | + | 0.446571i | \(0.852645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.4100 | − | 17.0084i | −0.859989 | − | 0.624819i | ||||
\(742\) | −12.0192 | + | 3.90527i | −0.441238 | + | 0.143367i | ||||
\(743\) | 17.1553 | − | 5.57409i | 0.629366 | − | 0.204493i | 0.0230717 | − | 0.999734i | \(-0.492655\pi\) |
0.606294 | + | 0.795240i | \(0.292655\pi\) | |||||||
\(744\) | 7.05183 | + | 5.12345i | 0.258532 | + | 0.187835i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.991061 | + | 3.05017i | −0.0362853 | + | 0.111675i | ||||
\(747\) | − | 12.5530i | − | 0.459289i | ||||||
\(748\) | 8.74240 | + | 6.28875i | 0.319654 | + | 0.229940i | ||||
\(749\) | 33.2728 | 1.21576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1861 | − | 10.3068i | 0.517657 | − | 0.376100i | −0.298064 | − | 0.954546i | \(-0.596341\pi\) |
0.815720 | + | 0.578446i | \(0.196341\pi\) | |||||||
\(752\) | −0.318713 | + | 0.438670i | −0.0116223 | + | 0.0159967i | ||||
\(753\) | −15.2201 | + | 4.94533i | −0.554653 | + | 0.180218i | ||||
\(754\) | −11.9105 | − | 36.6568i | −0.433756 | − | 1.33496i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.25225 | + | 1.63636i | −0.0819136 | + | 0.0595137i | ||||
\(757\) | 24.6903 | + | 8.02236i | 0.897383 | + | 0.291578i | 0.721157 | − | 0.692772i | \(-0.243611\pi\) |
0.176227 | + | 0.984350i | \(0.443611\pi\) | |||||||
\(758\) | − | 25.1646i | − | 0.914019i | ||||||
\(759\) | 0.692300 | − | 0.228568i | 0.0251289 | − | 0.00829651i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.65430 | − | 26.6352i | 0.313718 | − | 0.965525i | −0.662561 | − | 0.749008i | \(-0.730530\pi\) |
0.976279 | − | 0.216517i | \(-0.0694697\pi\) | |||||||
\(762\) | 1.04591 | + | 1.43958i | 0.0378894 | + | 0.0521503i | ||||
\(763\) | −11.2298 | + | 15.4564i | −0.406545 | + | 0.559561i | ||||
\(764\) | 2.54164 | + | 7.82237i | 0.0919534 | + | 0.283003i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.2589 | − | 11.0862i | −0.551326 | − | 0.400562i | ||||
\(767\) | −23.9040 | − | 32.9011i | −0.863124 | − | 1.18799i | ||||
\(768\) | −13.0911 | − | 4.25355i | −0.472384 | − | 0.153487i | ||||
\(769\) | −22.9537 | −0.827732 | −0.413866 | − | 0.910338i | \(-0.635822\pi\) | ||||
−0.413866 | + | 0.910338i | \(0.635822\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.47446 | 0.197158 | ||||||||
\(772\) | −8.60489 | − | 2.79590i | −0.309697 | − | 0.100627i | ||||
\(773\) | 13.8295 | + | 19.0347i | 0.497414 | + | 0.684631i | 0.981734 | − | 0.190259i | \(-0.0609329\pi\) |
−0.484320 | + | 0.874891i | \(0.660933\pi\) | |||||||
\(774\) | −8.36938 | − | 6.08071i | −0.300831 | − | 0.218567i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.91434 | − | 5.89172i | −0.0687207 | − | 0.211500i | ||||
\(777\) | 9.89761 | − | 13.6229i | 0.355075 | − | 0.488718i | ||||
\(778\) | 11.1287 | + | 15.3173i | 0.398983 | + | 0.549153i | ||||
\(779\) | −10.1424 | + | 31.2151i | −0.363389 | + | 1.11840i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.156616 | + | 33.1060i | 0.00560416 | + | 1.18463i | ||||
\(782\) | 1.27731i | 0.0456765i | ||||||||
\(783\) | 6.10429 | + | 1.98341i | 0.218150 | + | 0.0708811i | ||||
\(784\) | −20.9804 | + | 15.2431i | −0.749298 | + | 0.544397i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.955657 | + | 2.94121i | 0.0340872 | + | 0.104910i | ||||
\(787\) | −24.0356 | + | 7.80964i | −0.856777 | + | 0.278384i | −0.704282 | − | 0.709921i | \(-0.748731\pi\) |
−0.152495 | + | 0.988304i | \(0.548731\pi\) | |||||||
\(788\) | −5.57536 | + | 7.67383i | −0.198614 | + | 0.273369i | ||||
\(789\) | 9.69534 | − | 7.04408i | 0.345163 | − | 0.250776i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.0621 | 1.17555 | ||||||||
\(792\) | 10.2118 | − | 0.0483095i | 0.362861 | − | 0.00171660i | ||||
\(793\) | − | 25.1028i | − | 0.891427i | ||||||
\(794\) | 7.17071 | − | 22.0692i | 0.254479 | − | 0.783205i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.23888 | − | 4.53281i | −0.221131 | − | 0.160661i | ||||
\(797\) | 8.23277 | − | 2.67499i | 0.291620 | − | 0.0947530i | −0.159554 | − | 0.987189i | \(-0.551006\pi\) |
0.451173 | + | 0.892436i | \(0.351006\pi\) | |||||||
\(798\) | 26.5333 | − | 8.62119i | 0.939268 | − | 0.305187i | ||||
\(799\) | −0.962236 | − | 0.699105i | −0.0340414 | − | 0.0247326i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.792768 | + | 2.43989i | −0.0280111 | + | 0.0862092i | ||||
\(802\) | 31.7579i | 1.12141i | ||||||||
\(803\) | −38.9395 | + | 28.5736i | −1.37415 | + | 1.00834i | ||||
\(804\) | 7.87607 | 0.277768 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.7534 | − | 9.99243i | 0.484443 | − | 0.351968i | ||||
\(807\) | −8.02120 | + | 11.0402i | −0.282360 | + | 0.388635i | ||||
\(808\) | −22.2108 | + | 7.21672i | −0.781373 | + | 0.253883i | ||||
\(809\) | 3.15582 | + | 9.71261i | 0.110953 | + | 0.341477i | 0.991081 | − | 0.133258i | \(-0.0425438\pi\) |
−0.880129 | + | 0.474735i | \(0.842544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.5273 | − | 27.9917i | 1.35288 | − | 0.982923i | 0.354015 | − | 0.935240i | \(-0.384816\pi\) |
0.998862 | − | 0.0476835i | \(-0.0151839\pi\) | |||||||
\(812\) | −16.9940 | − | 5.52167i | −0.596371 | − | 0.193773i | ||||
\(813\) | 11.8379i | 0.415172i | ||||||||
\(814\) | −14.3769 | + | 4.74664i | −0.503910 | + | 0.166370i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.52192 | + | 10.8394i | −0.123292 | + | 0.379453i | ||||
\(817\) | −29.3008 | − | 40.3291i | −1.02510 | − | 1.41094i | ||||
\(818\) | 17.0350 | − | 23.4466i | 0.595613 | − | 0.819792i | ||||
\(819\) | 6.84507 | + | 21.0670i | 0.239186 | + | 0.736139i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4767 | + | 27.9550i | 1.34285 | + | 0.975635i | 0.999334 | + | 0.0364868i | \(0.0116167\pi\) |
0.343512 | + | 0.939148i | \(0.388383\pi\) | |||||||
\(822\) | 7.00543 | + | 9.64215i | 0.244343 | + | 0.336309i | ||||
\(823\) | −23.5253 | − | 7.64384i | −0.820041 | − | 0.266448i | −0.131196 | − | 0.991356i | \(-0.541882\pi\) |
−0.688845 | + | 0.724909i | \(0.741882\pi\) | |||||||
\(824\) | −51.9384 | −1.80936 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 39.2096 | 1.36428 | ||||||||
\(827\) | 1.48523 | + | 0.482580i | 0.0516465 | + | 0.0167810i | 0.334726 | − | 0.942315i | \(-0.391356\pi\) |
−0.283080 | + | 0.959096i | \(0.591356\pi\) | |||||||
\(828\) | −0.0839083 | − | 0.115490i | −0.00291602 | − | 0.00401355i | ||||
\(829\) | 34.1365 | + | 24.8016i | 1.18561 | + | 0.861396i | 0.992793 | − | 0.119839i | \(-0.0382377\pi\) |
0.192817 | + | 0.981235i | \(0.438238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.17170 | + | 9.76148i | 0.110025 | + | 0.338622i | ||||
\(832\) | −26.2320 | + | 36.1052i | −0.909430 | + | 1.25172i | ||||
\(833\) | −33.4362 | − | 46.0210i | −1.15850 | − | 1.59453i | ||||
\(834\) | 1.90158 | − | 5.85247i | 0.0658465 | − | 0.202655i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.4887 | + | 3.67292i | 0.397346 | + | 0.127031i | ||||
\(837\) | 2.83095i | 0.0978521i | ||||||||
\(838\) | 18.5968 | + | 6.04247i | 0.642416 | + | 0.208734i | ||||
\(839\) | −5.09236 | + | 3.69982i | −0.175808 | + | 0.127732i | −0.672209 | − | 0.740361i | \(-0.734654\pi\) |
0.496401 | + | 0.868093i | \(0.334654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.76886 | + | 11.5994i | 0.129961 | + | 0.399978i | ||||
\(842\) | 26.0850 | − | 8.47554i | 0.898949 | − | 0.292086i | ||||
\(843\) | −1.72744 | + | 2.37761i | −0.0594961 | + | 0.0818893i | ||||
\(844\) | 11.7434 | − | 8.53205i | 0.404223 | − | 0.293685i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.276449 | −0.00950451 | ||||||||
\(847\) | 44.7074 | − | 14.9954i | 1.53617 | − | 0.515249i | ||||
\(848\) | − | 5.78225i | − | 0.198563i | ||||||
\(849\) | −6.74521 | + | 20.7596i | −0.231495 | + | 0.712468i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.698548 | + | 0.507525i | 0.0239459 | + | 0.0173977i | ||||
\(852\) | 6.16514 | − | 2.00318i | 0.211214 | − | 0.0686276i | ||||
\(853\) | 6.91532 | − | 2.24692i | 0.236776 | − | 0.0769332i | −0.188225 | − | 0.982126i | \(-0.560274\pi\) |
0.425002 | + | 0.905193i | \(0.360274\pi\) | |||||||
\(854\) | 19.5803 | + | 14.2259i | 0.670025 | + | 0.486802i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.38491 | + | 22.7284i | −0.252411 | + | 0.776841i | ||||
\(857\) | − | 39.8590i | − | 1.36156i | −0.732489 | − | 0.680779i | \(-0.761641\pi\) | ||
0.732489 | − | 0.680779i | \(-0.238359\pi\) | |||||||
\(858\) | 6.06490 | − | 18.9707i | 0.207052 | − | 0.647650i | ||||
\(859\) | −13.5278 | −0.461564 | −0.230782 | − | 0.973006i | \(-0.574128\pi\) | ||||
−0.230782 | + | 0.973006i | \(0.574128\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.3267 | − | 14.7682i | 0.692732 | − | 0.503299i | ||||
\(862\) | 25.7223 | − | 35.4037i | 0.876104 | − | 1.20585i | ||||
\(863\) | −47.8493 | + | 15.5472i | −1.62881 | + | 0.529232i | −0.973997 | − | 0.226560i | \(-0.927252\pi\) |
−0.654812 | + | 0.755792i | \(0.727252\pi\) | |||||||
\(864\) | −1.08433 | − | 3.33724i | −0.0368898 | − | 0.113535i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.1228 | − | 21.1589i | 0.989632 | − | 0.719010i | ||||
\(867\) | −7.60845 | − | 2.47214i | −0.258397 | − | 0.0839581i | ||||
\(868\) | − | 7.88119i | − | 0.267505i | ||||||
\(869\) | 15.4977 | − | 21.5444i | 0.525725 | − | 0.730844i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.3655 | − | 59.6009i | 0.656175 | − | 2.01950i | ||||
\(872\) | −8.06574 | − | 11.1015i | −0.273140 | − | 0.375946i | ||||
\(873\) | 1.18262 | − | 1.62773i | 0.0400255 | − | 0.0550903i | ||||
\(874\) | 0.442073 | + | 1.36056i | 0.0149534 | + | 0.0460217i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.65096 | + | 5.55875i | 0.258502 | + | 0.187813i | ||||
\(877\) | −0.709667 | − | 0.976773i | −0.0239638 | − | 0.0329833i | 0.796867 | − | 0.604155i | \(-0.206489\pi\) |
−0.820831 | + | 0.571171i | \(0.806489\pi\) | |||||||
\(878\) | −31.1830 | − | 10.1320i | −1.05237 | − | 0.341937i | ||||
\(879\) | 24.7665 | 0.835354 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.91816 | 0.0646245 | 0.0323123 | − | 0.999478i | \(-0.489713\pi\) | ||||
0.0323123 | + | 0.999478i | \(0.489713\pi\) | |||||||
\(882\) | −12.5746 | − | 4.08575i | −0.423410 | − | 0.137574i | ||||
\(883\) | −34.1439 | − | 46.9950i | −1.14903 | − | 1.58151i | −0.745446 | − | 0.666566i | \(-0.767763\pi\) |
−0.403587 | − | 0.914941i | \(-0.632237\pi\) | |||||||
\(884\) | −13.5740 | − | 9.86208i | −0.456543 | − | 0.331698i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.25828 | + | 16.1833i | 0.176656 | + | 0.543690i | ||||
\(887\) | −17.7762 | + | 24.4668i | −0.596866 | + | 0.821516i | −0.995417 | − | 0.0956306i | \(-0.969513\pi\) |
0.398551 | + | 0.917146i | \(0.369513\pi\) | |||||||
\(888\) | 7.10892 | + | 9.78459i | 0.238560 | + | 0.328349i | ||||
\(889\) | 2.02832 | − | 6.24251i | 0.0680275 | − | 0.209367i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.96213 | + | 2.67395i | 0.0657340 | + | 0.0895808i | ||||
\(892\) | − | 12.4417i | − | 0.416578i | ||||||
\(893\) | −1.26691 | − | 0.411644i | −0.0423956 | − | 0.0137752i | ||||
\(894\) | 3.56185 | − | 2.58784i | 0.119126 | − | 0.0865503i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.99968 | − | 12.3098i | −0.133620 | − | 0.411240i | ||||
\(897\) | −1.08026 | + | 0.350999i | −0.0360689 | + | 0.0117195i | ||||
\(898\) | 8.19553 | − | 11.2802i | 0.273488 | − | 0.376425i | ||||
\(899\) | −14.7001 | + | 10.6802i | −0.490275 | + | 0.356206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6835 | 0.422550 | ||||||||
\(902\) | −22.5904 | + | 0.106870i | −0.752179 | + | 0.00355837i | ||||
\(903\) | 38.1603i | 1.26990i | ||||||||
\(904\) | −7.33815 | + | 22.5845i | −0.244063 | + | 0.751149i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.56597 | + | 4.04391i | 0.184917 | + | 0.134350i | ||||
\(907\) | −30.4023 | + | 9.87830i | −1.00949 | + | 0.328004i | −0.766652 | − | 0.642063i | \(-0.778079\pi\) |
−0.242839 | + | 0.970066i | \(0.578079\pi\) | |||||||
\(908\) | 9.49660 | − | 3.08563i | 0.315156 | − | 0.102400i | ||||
\(909\) | −6.13627 | − | 4.45826i | −0.203527 | − | 0.147871i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0211 | + | 49.3079i | −0.530803 | + | 1.63364i | 0.221745 | + | 0.975105i | \(0.428825\pi\) |
−0.752547 | + | 0.658538i | \(0.771175\pi\) | |||||||
\(912\) | 12.7648i | 0.422684i | ||||||||
\(913\) | 41.6330 | − | 0.196955i | 1.37785 | − | 0.00651826i | ||||
\(914\) | −11.6722 | −0.386083 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.67660 | − | 3.39775i | 0.154519 | − | 0.112265i | ||||
\(917\) | 6.70525 | − | 9.22898i | 0.221427 | − | 0.304768i | ||||
\(918\) | −5.52634 | + | 1.79562i | −0.182396 | + | 0.0592642i | ||||
\(919\) | 10.5710 | + | 32.5341i | 0.348704 | + | 1.07320i | 0.959571 | + | 0.281468i | \(0.0908212\pi\) |
−0.610866 | + | 0.791734i | \(0.709179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.99673 | − | 2.90379i | 0.131697 | − | 0.0956832i | ||||
\(922\) | 14.8648 | + | 4.82988i | 0.489547 | + | 0.159064i | ||||
\(923\) | − | 51.5790i | − | 1.69774i | ||||||
\(924\) | −5.46245 | − | 7.44411i | −0.179702 | − | 0.244893i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.74561 | − | 20.7609i | 0.221675 | − | 0.682244i | ||||
\(927\) | −9.91508 | − | 13.6469i | −0.325654 | − | 0.448224i | ||||
\(928\) | 13.2382 | − | 18.2208i | 0.434565 | − | 0.598127i | ||||
\(929\) | −5.66990 | − | 17.4502i | −0.186023 | − | 0.572521i | 0.813941 | − | 0.580947i | \(-0.197318\pi\) |
−0.999964 | + | 0.00842624i | \(0.997318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51.5433 | − | 37.4484i | −1.68926 | − | 1.22732i | ||||
\(932\) | −8.71693 | − | 11.9978i | −0.285533 | − | 0.393002i | ||||
\(933\) | −13.1337 | − | 4.26740i | −0.429978 | − | 0.139708i | ||||
\(934\) | −30.8561 | −1.00964 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.9100 | −0.520033 | ||||||||
\(937\) | −3.21852 | − | 1.04576i | −0.105144 | − | 0.0341635i | 0.255972 | − | 0.966684i | \(-0.417604\pi\) |
−0.361117 | + | 0.932521i | \(0.617604\pi\) | |||||||
\(938\) | 35.5145 | + | 48.8815i | 1.15959 | + | 1.59604i | ||||
\(939\) | −3.29217 | − | 2.39190i | −0.107436 | − | 0.0780567i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.8465 | − | 33.3822i | −0.353587 | − | 1.08823i | −0.956824 | − | 0.290668i | \(-0.906123\pi\) |
0.603237 | − | 0.797562i | \(-0.293877\pi\) | |||||||
\(942\) | 5.07476 | − | 6.98480i | 0.165344 | − | 0.227577i | ||||
\(943\) | 0.757278 | + | 1.04230i | 0.0246604 | + | 0.0339421i | ||||
\(944\) | −5.54375 | + | 17.0619i | −0.180434 | + | 0.555318i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.0359 | − | 27.8532i | 0.651423 | − | 0.905585i | ||||
\(947\) | 39.0512i | 1.26899i | 0.772925 | + | 0.634497i | \(0.218793\pi\) | ||||
−0.772925 | + | 0.634497i | \(0.781207\pi\) | |||||||
\(948\) | −4.94223 | − | 1.60583i | −0.160516 | − | 0.0521549i | ||||
\(949\) | 60.8769 | − | 44.2297i | 1.97615 | − | 1.43576i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.97880 | + | 24.5562i | 0.258730 | + | 0.796290i | ||||
\(952\) | 62.7660 | − | 20.3939i | 2.03426 | − | 0.660971i | ||||
\(953\) | 14.5055 | − | 19.9652i | 0.469881 | − | 0.646735i | −0.506640 | − | 0.862158i | \(-0.669113\pi\) |
0.976521 | + | 0.215422i | \(0.0691127\pi\) | |||||||
\(954\) | 2.38500 | − | 1.73281i | 0.0772173 | − | 0.0561017i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.9495 | −0.354131 | ||||||||
\(957\) | −6.48236 | + | 20.2765i | −0.209545 | + | 0.655448i | ||||
\(958\) | 12.5315i | 0.404873i | ||||||||
\(959\) | 13.5855 | − | 41.8118i | 0.438698 | − | 1.35017i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.5958 | + | 13.5107i | 0.599865 | + | 0.435827i | ||||
\(962\) | 22.4336 | − | 7.28913i | 0.723290 | − | 0.235011i | ||||
\(963\) | −7.38173 | + | 2.39847i | −0.237873 | + | 0.0772896i | ||||
\(964\) | 6.28401 | + | 4.56560i | 0.202394 | + | 0.147048i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.338412 | − | 1.04153i | 0.0108882 | − | 0.0335105i | ||||
\(967\) | − | 1.20724i | − | 0.0388222i | −0.999812 | − | 0.0194111i | \(-0.993821\pi\) | ||
0.999812 | − | 0.0194111i | \(-0.00617914\pi\) | |||||||
\(968\) | 0.320445 | + | 33.8676i | 0.0102995 | + | 1.08855i | ||||
\(969\) | −27.9999 | −0.899486 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.7599 | + | 29.6138i | −1.30805 | + | 0.950353i | −0.999999 | − | 0.00101751i | \(-0.999676\pi\) |
−0.308049 | + | 0.951370i | \(0.599676\pi\) | |||||||
\(972\) | 0.381716 | − | 0.525387i | 0.0122435 | − | 0.0168518i | ||||
\(973\) | −21.5882 | + | 7.01442i | −0.692085 | + | 0.224872i | ||||
\(974\) | −2.44597 | − | 7.52793i | −0.0783740 | − | 0.241210i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.95877 | + | 6.50893i | −0.286763 | + | 0.208346i | ||||
\(977\) | 5.59535 | + | 1.81804i | 0.179011 | + | 0.0581642i | 0.397151 | − | 0.917753i | \(-0.369999\pi\) |
−0.218140 | + | 0.975917i | \(0.569999\pi\) | |||||||
\(978\) | 6.18362i | 0.197730i | ||||||||
\(979\) | −8.10454 | − | 2.59100i | −0.259022 | − | 0.0828088i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.37720 | − | 4.23858i | 0.0439706 | − | 0.135328i | ||||
\(982\) | 17.8256 | + | 24.5348i | 0.568837 | + | 0.782937i | ||||
\(983\) | 21.4482 | − | 29.5210i | 0.684093 | − | 0.941573i | −0.315881 | − | 0.948799i | \(-0.602300\pi\) |
0.999974 | + | 0.00722580i | \(0.00230006\pi\) | |||||||
\(984\) | 5.57654 | + | 17.1628i | 0.177774 | + | 0.547131i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −30.1730 | − | 21.9219i | −0.960903 | − | 0.698137i | ||||
\(987\) | 0.599391 | + | 0.824990i | 0.0190788 | + | 0.0262597i | ||||
\(988\) | −17.8720 | − | 5.80695i | −0.568583 | − | 0.184744i | ||||
\(989\) | −1.95677 | −0.0622216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.8404 | −1.17027 | −0.585137 | − | 0.810934i | \(-0.698959\pi\) | ||||
−0.585137 | + | 0.810934i | \(0.698959\pi\) | |||||||
\(992\) | 9.44757 | + | 3.06970i | 0.299961 | + | 0.0974631i | ||||
\(993\) | 1.96913 | + | 2.71027i | 0.0624883 | + | 0.0860078i | ||||
\(994\) | 40.2320 | + | 29.2302i | 1.27608 | + | 0.927127i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.51913 | − | 7.75307i | −0.0798216 | − | 0.245666i | ||||
\(997\) | −20.4957 | + | 28.2099i | −0.649105 | + | 0.893417i | −0.999060 | − | 0.0433498i | \(-0.986197\pi\) |
0.349955 | + | 0.936767i | \(0.386197\pi\) | |||||||
\(998\) | −13.2406 | − | 18.2242i | −0.419125 | − | 0.576877i | ||||
\(999\) | −1.21383 | + | 3.73577i | −0.0384037 | + | 0.118195i |
(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.724.2 | 16 | ||
5.2 | odd | 4 | 165.2.m.a.31.1 | yes | 8 | ||
5.3 | odd | 4 | 825.2.n.k.526.2 | 8 | |||
5.4 | even | 2 | inner | 825.2.bx.h.724.3 | 16 | ||
11.5 | even | 5 | inner | 825.2.bx.h.49.3 | 16 | ||
15.2 | even | 4 | 495.2.n.d.361.2 | 8 | |||
55.7 | even | 20 | 1815.2.a.o.1.3 | 4 | |||
55.18 | even | 20 | 9075.2.a.dj.1.2 | 4 | |||
55.27 | odd | 20 | 165.2.m.a.16.1 | ✓ | 8 | ||
55.37 | odd | 20 | 1815.2.a.x.1.2 | 4 | |||
55.38 | odd | 20 | 825.2.n.k.676.2 | 8 | |||
55.48 | odd | 20 | 9075.2.a.cl.1.3 | 4 | |||
55.49 | even | 10 | inner | 825.2.bx.h.49.2 | 16 | ||
165.62 | odd | 20 | 5445.2.a.bv.1.2 | 4 | |||
165.92 | even | 20 | 5445.2.a.be.1.3 | 4 | |||
165.137 | even | 20 | 495.2.n.d.181.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.16.1 | ✓ | 8 | 55.27 | odd | 20 | ||
165.2.m.a.31.1 | yes | 8 | 5.2 | odd | 4 | ||
495.2.n.d.181.2 | 8 | 165.137 | even | 20 | |||
495.2.n.d.361.2 | 8 | 15.2 | even | 4 | |||
825.2.n.k.526.2 | 8 | 5.3 | odd | 4 | |||
825.2.n.k.676.2 | 8 | 55.38 | odd | 20 | |||
825.2.bx.h.49.2 | 16 | 55.49 | even | 10 | inner | ||
825.2.bx.h.49.3 | 16 | 11.5 | even | 5 | inner | ||
825.2.bx.h.724.2 | 16 | 1.1 | even | 1 | trivial | ||
825.2.bx.h.724.3 | 16 | 5.4 | even | 2 | inner | ||
1815.2.a.o.1.3 | 4 | 55.7 | even | 20 | |||
1815.2.a.x.1.2 | 4 | 55.37 | odd | 20 | |||
5445.2.a.be.1.3 | 4 | 165.92 | even | 20 | |||
5445.2.a.bv.1.2 | 4 | 165.62 | odd | 20 | |||
9075.2.a.cl.1.3 | 4 | 55.48 | odd | 20 | |||
9075.2.a.dj.1.2 | 4 | 55.18 | even | 20 |