Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,2,Mod(139,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("414.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.30580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 4x^{10} - 3x^{9} + 22x^{8} - 9x^{7} + 69x^{6} - 27x^{5} + 198x^{4} - 81x^{3} + 324x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.2 | ||
Root | \(1.20109 + 1.24795i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 414.277 |
Dual form | 414.2.e.e.139.2 |
$q$-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 \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(235\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −1.20109 | − | 1.24795i | −0.693452 | − | 0.720503i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.39132 | + | 2.40983i | 0.622216 | + | 1.07771i | 0.989072 | + | 0.147432i | \(0.0471007\pi\) |
−0.366856 | + | 0.930278i | \(0.619566\pi\) | |||||||
\(6\) | −1.68130 | + | 0.416203i | −0.686388 | + | 0.169914i | ||||
\(7\) | −1.77657 | + | 3.07710i | −0.671479 | + | 1.16304i | 0.306006 | + | 0.952030i | \(0.401007\pi\) |
−0.977485 | + | 0.211006i | \(0.932326\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.114750 | + | 2.99780i | −0.0382500 | + | 0.999268i | ||||
\(10\) | 2.78263 | 0.879946 | ||||||||
\(11\) | −2.05222 | + | 3.55455i | −0.618767 | + | 1.07174i | 0.370944 | + | 0.928655i | \(0.379034\pi\) |
−0.989711 | + | 0.143081i | \(0.954299\pi\) | |||||||
\(12\) | −0.480208 | + | 1.66415i | −0.138624 | + | 0.480399i | ||||
\(13\) | 0.851125 | + | 1.47419i | 0.236059 | + | 0.408867i | 0.959580 | − | 0.281436i | \(-0.0908106\pi\) |
−0.723521 | + | 0.690303i | \(0.757477\pi\) | |||||||
\(14\) | 1.77657 | + | 3.07710i | 0.474807 | + | 0.822391i | ||||
\(15\) | 1.33624 | − | 4.63072i | 0.345017 | − | 1.19565i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.77050 | −0.429409 | −0.214705 | − | 0.976679i | \(-0.568879\pi\) | ||||
−0.214705 | + | 0.976679i | \(0.568879\pi\) | |||||||
\(18\) | 2.53880 | + | 1.59828i | 0.598401 | + | 0.376718i | ||||
\(19\) | −3.17269 | −0.727864 | −0.363932 | − | 0.931425i | \(-0.618566\pi\) | ||||
−0.363932 | + | 0.931425i | \(0.618566\pi\) | |||||||
\(20\) | 1.39132 | − | 2.40983i | 0.311108 | − | 0.538855i | ||||
\(21\) | 5.97389 | − | 1.47883i | 1.30361 | − | 0.322706i | ||||
\(22\) | 2.05222 | + | 3.55455i | 0.437534 | + | 0.757832i | ||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | ||||
\(24\) | 1.20109 | + | 1.24795i | 0.245172 | + | 0.254736i | ||||
\(25\) | −1.37153 | + | 2.37555i | −0.274305 | + | 0.475110i | ||||
\(26\) | 1.70225 | 0.333839 | ||||||||
\(27\) | 3.87893 | − | 3.45744i | 0.746501 | − | 0.665385i | ||||
\(28\) | 3.55313 | 0.671479 | ||||||||
\(29\) | 3.55222 | − | 6.15262i | 0.659630 | − | 1.14251i | −0.321081 | − | 0.947052i | \(-0.604046\pi\) |
0.980711 | − | 0.195461i | \(-0.0626205\pi\) | |||||||
\(30\) | −3.34220 | − | 3.47258i | −0.610200 | − | 0.634004i | ||||
\(31\) | −0.890708 | − | 1.54275i | −0.159976 | − | 0.277086i | 0.774884 | − | 0.632104i | \(-0.217808\pi\) |
−0.934860 | + | 0.355017i | \(0.884475\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 6.90079 | − | 1.70828i | 1.20127 | − | 0.297373i | ||||
\(34\) | −0.885250 | + | 1.53330i | −0.151819 | + | 0.262958i | ||||
\(35\) | −9.88707 | −1.67122 | ||||||||
\(36\) | 2.65355 | − | 1.39953i | 0.442258 | − | 0.233254i | ||||
\(37\) | −1.29204 | −0.212410 | −0.106205 | − | 0.994344i | \(-0.533870\pi\) | ||||
−0.106205 | + | 0.994344i | \(0.533870\pi\) | |||||||
\(38\) | −1.58634 | + | 2.74763i | −0.257339 | + | 0.445724i | ||||
\(39\) | 0.817434 | − | 2.83280i | 0.130894 | − | 0.453611i | ||||
\(40\) | −1.39132 | − | 2.40983i | −0.219987 | − | 0.381028i | ||||
\(41\) | 4.67784 | + | 8.10225i | 0.730555 | + | 1.26536i | 0.956646 | + | 0.291253i | \(0.0940721\pi\) |
−0.226091 | + | 0.974106i | \(0.572595\pi\) | |||||||
\(42\) | 1.70624 | − | 5.91295i | 0.263279 | − | 0.912388i | ||||
\(43\) | −3.80661 | + | 6.59325i | −0.580503 | + | 1.00546i | 0.414916 | + | 0.909860i | \(0.363811\pi\) |
−0.995420 | + | 0.0956016i | \(0.969523\pi\) | |||||||
\(44\) | 4.10444 | 0.618767 | ||||||||
\(45\) | −7.38386 | + | 3.89437i | −1.10072 | + | 0.580538i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 5.11270 | − | 8.85546i | 0.745764 | − | 1.29170i | −0.204073 | − | 0.978956i | \(-0.565418\pi\) |
0.949837 | − | 0.312746i | \(-0.101249\pi\) | |||||||
\(48\) | 1.68130 | − | 0.416203i | 0.242675 | − | 0.0600737i | ||||
\(49\) | −2.81238 | − | 4.87118i | −0.401768 | − | 0.695883i | ||||
\(50\) | 1.37153 | + | 2.37555i | 0.193963 | + | 0.335954i | ||||
\(51\) | 2.12654 | + | 2.20949i | 0.297775 | + | 0.309391i | ||||
\(52\) | 0.851125 | − | 1.47419i | 0.118030 | − | 0.204434i | ||||
\(53\) | 10.8814 | 1.49467 | 0.747335 | − | 0.664448i | \(-0.231333\pi\) | ||||
0.747335 | + | 0.664448i | \(0.231333\pi\) | |||||||
\(54\) | −1.05477 | − | 5.08797i | −0.143535 | − | 0.692385i | ||||
\(55\) | −11.4211 | −1.54003 | ||||||||
\(56\) | 1.77657 | − | 3.07710i | 0.237404 | − | 0.411195i | ||||
\(57\) | 3.81069 | + | 3.95935i | 0.504739 | + | 0.524429i | ||||
\(58\) | −3.55222 | − | 6.15262i | −0.466429 | − | 0.807879i | ||||
\(59\) | 2.17463 | + | 3.76656i | 0.283112 | + | 0.490365i | 0.972150 | − | 0.234361i | \(-0.0752998\pi\) |
−0.689037 | + | 0.724726i | \(0.741966\pi\) | |||||||
\(60\) | −4.67845 | + | 1.15814i | −0.603985 | + | 0.149515i | ||||
\(61\) | −4.83454 | + | 8.37368i | −0.619000 | + | 1.07214i | 0.370669 | + | 0.928765i | \(0.379129\pi\) |
−0.989669 | + | 0.143374i | \(0.954205\pi\) | |||||||
\(62\) | −1.78142 | −0.226240 | ||||||||
\(63\) | −9.02070 | − | 5.67890i | −1.13650 | − | 0.715474i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.36837 | + | 4.10213i | −0.293760 | + | 0.508807i | ||||
\(66\) | 1.97098 | − | 6.83040i | 0.242611 | − | 0.840764i | ||||
\(67\) | −0.446697 | − | 0.773701i | −0.0545727 | − | 0.0945227i | 0.837449 | − | 0.546516i | \(-0.184046\pi\) |
−0.892021 | + | 0.451994i | \(0.850713\pi\) | |||||||
\(68\) | 0.885250 | + | 1.53330i | 0.107352 | + | 0.185940i | ||||
\(69\) | 0.480208 | − | 1.66415i | 0.0578103 | − | 0.200340i | ||||
\(70\) | −4.94353 | + | 8.56245i | −0.590865 | + | 1.02341i | ||||
\(71\) | −9.82973 | −1.16657 | −0.583287 | − | 0.812266i | \(-0.698234\pi\) | ||||
−0.583287 | + | 0.812266i | \(0.698234\pi\) | |||||||
\(72\) | 0.114750 | − | 2.99780i | 0.0135234 | − | 0.353295i | ||||
\(73\) | −10.1956 | −1.19331 | −0.596655 | − | 0.802498i | \(-0.703504\pi\) | ||||
−0.596655 | + | 0.802498i | \(0.703504\pi\) | |||||||
\(74\) | −0.646020 | + | 1.11894i | −0.0750983 | + | 0.130074i | ||||
\(75\) | 4.61189 | − | 1.14167i | 0.532536 | − | 0.131828i | ||||
\(76\) | 1.58634 | + | 2.74763i | 0.181966 | + | 0.315174i | ||||
\(77\) | −7.29180 | − | 12.6298i | −0.830978 | − | 1.43930i | ||||
\(78\) | −2.04456 | − | 2.12432i | −0.231501 | − | 0.240532i | ||||
\(79\) | −5.37347 | + | 9.30713i | −0.604563 | + | 1.04713i | 0.387557 | + | 0.921846i | \(0.373319\pi\) |
−0.992120 | + | 0.125288i | \(0.960014\pi\) | |||||||
\(80\) | −2.78263 | −0.311108 | ||||||||
\(81\) | −8.97366 | − | 0.687996i | −0.997074 | − | 0.0764441i | ||||
\(82\) | 9.35568 | 1.03316 | ||||||||
\(83\) | 6.68659 | − | 11.5815i | 0.733948 | − | 1.27124i | −0.221235 | − | 0.975220i | \(-0.571009\pi\) |
0.955183 | − | 0.296015i | \(-0.0956578\pi\) | |||||||
\(84\) | −4.26764 | − | 4.43413i | −0.465638 | − | 0.483803i | ||||
\(85\) | −2.46333 | − | 4.26661i | −0.267185 | − | 0.462778i | ||||
\(86\) | 3.80661 | + | 6.59325i | 0.410478 | + | 0.710968i | ||||
\(87\) | −11.9447 | + | 2.95689i | −1.28061 | + | 0.317012i | ||||
\(88\) | 2.05222 | − | 3.55455i | 0.218767 | − | 0.378916i | ||||
\(89\) | 15.2267 | 1.61403 | 0.807015 | − | 0.590531i | \(-0.201082\pi\) | ||||
0.807015 | + | 0.590531i | \(0.201082\pi\) | |||||||
\(90\) | −0.319307 | + | 8.34179i | −0.0336580 | + | 0.879302i | ||||
\(91\) | −6.04832 | −0.634036 | ||||||||
\(92\) | 0.500000 | − | 0.866025i | 0.0521286 | − | 0.0902894i | ||||
\(93\) | −0.855451 | + | 2.96455i | −0.0887061 | + | 0.307409i | ||||
\(94\) | −5.11270 | − | 8.85546i | −0.527335 | − | 0.913371i | ||||
\(95\) | −4.41421 | − | 7.64564i | −0.452889 | − | 0.784426i | ||||
\(96\) | 0.480208 | − | 1.66415i | 0.0490111 | − | 0.169847i | ||||
\(97\) | 6.33599 | − | 10.9743i | 0.643322 | − | 1.11427i | −0.341364 | − | 0.939931i | \(-0.610889\pi\) |
0.984686 | − | 0.174336i | \(-0.0557779\pi\) | |||||||
\(98\) | −5.62476 | −0.568186 | ||||||||
\(99\) | −10.4203 | − | 6.56003i | −1.04728 | − | 0.659308i | ||||
\(100\) | 2.74305 | 0.274305 | ||||||||
\(101\) | −3.51196 | + | 6.08290i | −0.349453 | + | 0.605271i | −0.986152 | − | 0.165841i | \(-0.946966\pi\) |
0.636699 | + | 0.771112i | \(0.280299\pi\) | |||||||
\(102\) | 2.97674 | − | 0.736888i | 0.294742 | − | 0.0729627i | ||||
\(103\) | 7.56516 | + | 13.1032i | 0.745417 | + | 1.29110i | 0.950000 | + | 0.312251i | \(0.101083\pi\) |
−0.204582 | + | 0.978849i | \(0.565584\pi\) | |||||||
\(104\) | −0.851125 | − | 1.47419i | −0.0834596 | − | 0.144556i | ||||
\(105\) | 11.8753 | + | 12.3386i | 1.15891 | + | 1.20412i | ||||
\(106\) | 5.44068 | − | 9.42353i | 0.528446 | − | 0.915294i | ||||
\(107\) | 7.83535 | 0.757472 | 0.378736 | − | 0.925505i | \(-0.376359\pi\) | ||||
0.378736 | + | 0.925505i | \(0.376359\pi\) | |||||||
\(108\) | −4.93370 | − | 1.63053i | −0.474745 | − | 0.156898i | ||||
\(109\) | 1.06132 | 0.101656 | 0.0508281 | − | 0.998707i | \(-0.483814\pi\) | ||||
0.0508281 | + | 0.998707i | \(0.483814\pi\) | |||||||
\(110\) | −5.71057 | + | 9.89100i | −0.544482 | + | 0.943070i | ||||
\(111\) | 1.55186 | + | 1.61240i | 0.147296 | + | 0.153042i | ||||
\(112\) | −1.77657 | − | 3.07710i | −0.167870 | − | 0.290759i | ||||
\(113\) | −4.66618 | − | 8.08207i | −0.438958 | − | 0.760297i | 0.558652 | − | 0.829402i | \(-0.311319\pi\) |
−0.997609 | + | 0.0691053i | \(0.977986\pi\) | |||||||
\(114\) | 5.33424 | − | 1.32048i | 0.499598 | − | 0.123674i | ||||
\(115\) | −1.39132 | + | 2.40983i | −0.129741 | + | 0.224718i | ||||
\(116\) | −7.10444 | −0.659630 | ||||||||
\(117\) | −4.51700 | + | 2.38234i | −0.417597 | + | 0.220248i | ||||
\(118\) | 4.34925 | 0.400381 | ||||||||
\(119\) | 3.14541 | − | 5.44801i | 0.288339 | − | 0.499418i | ||||
\(120\) | −1.33624 | + | 4.63072i | −0.121982 | + | 0.422725i | ||||
\(121\) | −2.92320 | − | 5.06312i | −0.265745 | − | 0.460284i | ||||
\(122\) | 4.83454 | + | 8.37368i | 0.437699 | + | 0.758117i | ||||
\(123\) | 4.49267 | − | 15.5693i | 0.405091 | − | 1.40383i | ||||
\(124\) | −0.890708 | + | 1.54275i | −0.0799879 | + | 0.138543i | ||||
\(125\) | 6.28026 | 0.561724 | ||||||||
\(126\) | −9.42842 | + | 4.97270i | −0.839950 | + | 0.443004i | ||||
\(127\) | 8.84373 | 0.784754 | 0.392377 | − | 0.919804i | \(-0.371653\pi\) | ||||
0.392377 | + | 0.919804i | \(0.371653\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 12.8001 | − | 3.16865i | 1.12699 | − | 0.278984i | ||||
\(130\) | 2.36837 | + | 4.10213i | 0.207720 | + | 0.359781i | ||||
\(131\) | 5.84578 | + | 10.1252i | 0.510748 | + | 0.884642i | 0.999922 | + | 0.0124560i | \(0.00396496\pi\) |
−0.489174 | + | 0.872186i | \(0.662702\pi\) | |||||||
\(132\) | −4.92981 | − | 5.12212i | −0.429085 | − | 0.445824i | ||||
\(133\) | 5.63649 | − | 9.76269i | 0.488746 | − | 0.846532i | ||||
\(134\) | −0.893393 | −0.0771774 | ||||||||
\(135\) | 13.7287 | + | 4.53717i | 1.18158 | + | 0.390498i | ||||
\(136\) | 1.77050 | 0.151819 | ||||||||
\(137\) | −7.19047 | + | 12.4543i | −0.614323 | + | 1.06404i | 0.376179 | + | 0.926547i | \(0.377238\pi\) |
−0.990503 | + | 0.137493i | \(0.956096\pi\) | |||||||
\(138\) | −1.20109 | − | 1.24795i | −0.102244 | − | 0.106232i | ||||
\(139\) | 3.60352 | + | 6.24148i | 0.305647 | + | 0.529395i | 0.977405 | − | 0.211375i | \(-0.0677941\pi\) |
−0.671759 | + | 0.740770i | \(0.734461\pi\) | |||||||
\(140\) | 4.94353 | + | 8.56245i | 0.417805 | + | 0.723659i | ||||
\(141\) | −17.1920 | + | 4.25585i | −1.44783 | + | 0.358407i | ||||
\(142\) | −4.91487 | + | 8.51280i | −0.412447 | + | 0.714378i | ||||
\(143\) | −6.98677 | −0.584263 | ||||||||
\(144\) | −2.53880 | − | 1.59828i | −0.211567 | − | 0.133190i | ||||
\(145\) | 19.7690 | 1.64173 | ||||||||
\(146\) | −5.09782 | + | 8.82969i | −0.421899 | + | 0.730750i | ||||
\(147\) | −2.70106 | + | 9.36045i | −0.222779 | + | 0.772037i | ||||
\(148\) | 0.646020 | + | 1.11894i | 0.0531025 | + | 0.0919763i | ||||
\(149\) | 10.5105 | + | 18.2047i | 0.861053 | + | 1.49139i | 0.870914 | + | 0.491436i | \(0.163528\pi\) |
−0.00986095 | + | 0.999951i | \(0.503139\pi\) | |||||||
\(150\) | 1.31724 | − | 4.56485i | 0.107552 | − | 0.372719i | ||||
\(151\) | 11.1760 | − | 19.3575i | 0.909492 | − | 1.57529i | 0.0947218 | − | 0.995504i | \(-0.469804\pi\) |
0.814771 | − | 0.579783i | \(-0.196863\pi\) | |||||||
\(152\) | 3.17269 | 0.257339 | ||||||||
\(153\) | 0.203165 | − | 5.30761i | 0.0164249 | − | 0.429095i | ||||
\(154\) | −14.5836 | −1.17518 | ||||||||
\(155\) | 2.47851 | − | 4.29291i | 0.199079 | − | 0.344815i | ||||
\(156\) | −2.86199 | + | 0.708481i | −0.229143 | + | 0.0567239i | ||||
\(157\) | −2.11914 | − | 3.67045i | −0.169126 | − | 0.292934i | 0.768987 | − | 0.639264i | \(-0.220761\pi\) |
−0.938113 | + | 0.346330i | \(0.887428\pi\) | |||||||
\(158\) | 5.37347 | + | 9.30713i | 0.427491 | + | 0.740435i | ||||
\(159\) | −13.0695 | − | 13.5794i | −1.03648 | − | 1.07691i | ||||
\(160\) | −1.39132 | + | 2.40983i | −0.109993 | + | 0.190514i | ||||
\(161\) | −3.55313 | −0.280026 | ||||||||
\(162\) | −5.08265 | + | 7.42742i | −0.399331 | + | 0.583554i | ||||
\(163\) | −7.55605 | −0.591835 | −0.295918 | − | 0.955213i | \(-0.595625\pi\) | ||||
−0.295918 | + | 0.955213i | \(0.595625\pi\) | |||||||
\(164\) | 4.67784 | − | 8.10225i | 0.365278 | − | 0.632680i | ||||
\(165\) | 13.7179 | + | 14.2530i | 1.06793 | + | 1.10959i | ||||
\(166\) | −6.68659 | − | 11.5815i | −0.518980 | − | 0.898899i | ||||
\(167\) | −4.79999 | − | 8.31383i | −0.371435 | − | 0.643344i | 0.618352 | − | 0.785901i | \(-0.287801\pi\) |
−0.989786 | + | 0.142558i | \(0.954467\pi\) | |||||||
\(168\) | −5.97389 | + | 1.47883i | −0.460896 | + | 0.114094i | ||||
\(169\) | 5.05117 | − | 8.74889i | 0.388552 | − | 0.672992i | ||||
\(170\) | −4.92665 | −0.377857 | ||||||||
\(171\) | 0.364066 | − | 9.51109i | 0.0278408 | − | 0.727332i | ||||
\(172\) | 7.61323 | 0.580503 | ||||||||
\(173\) | 5.23267 | − | 9.06325i | 0.397833 | − | 0.689066i | −0.595626 | − | 0.803262i | \(-0.703096\pi\) |
0.993458 | + | 0.114196i | \(0.0364292\pi\) | |||||||
\(174\) | −3.41161 | + | 11.8229i | −0.258633 | + | 0.896288i | ||||
\(175\) | −4.87321 | − | 8.44065i | −0.368380 | − | 0.638053i | ||||
\(176\) | −2.05222 | − | 3.55455i | −0.154692 | − | 0.267934i | ||||
\(177\) | 2.08855 | − | 7.23781i | 0.156985 | − | 0.544027i | ||||
\(178\) | 7.61337 | − | 13.1867i | 0.570646 | − | 0.988388i | ||||
\(179\) | 9.07927 | 0.678616 | 0.339308 | − | 0.940675i | \(-0.389807\pi\) | ||||
0.339308 | + | 0.940675i | \(0.389807\pi\) | |||||||
\(180\) | 7.06455 | + | 4.44742i | 0.526560 | + | 0.331491i | ||||
\(181\) | −26.3796 | −1.96078 | −0.980391 | − | 0.197060i | \(-0.936861\pi\) | ||||
−0.980391 | + | 0.197060i | \(0.936861\pi\) | |||||||
\(182\) | −3.02416 | + | 5.23800i | −0.224166 | + | 0.388266i | ||||
\(183\) | 16.2567 | − | 4.02430i | 1.20173 | − | 0.297485i | ||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | −1.79764 | − | 3.11360i | −0.132165 | − | 0.228916i | ||||
\(186\) | 2.13965 | + | 2.22311i | 0.156886 | + | 0.163007i | ||||
\(187\) | 3.63345 | − | 6.29332i | 0.265704 | − | 0.460213i | ||||
\(188\) | −10.2254 | −0.745764 | ||||||||
\(189\) | 3.74772 | + | 18.0782i | 0.272607 | + | 1.31500i | ||||
\(190\) | −8.82842 | −0.640481 | ||||||||
\(191\) | −1.03116 | + | 1.78602i | −0.0746123 | + | 0.129232i | −0.900918 | − | 0.433990i | \(-0.857105\pi\) |
0.826305 | + | 0.563222i | \(0.190439\pi\) | |||||||
\(192\) | −1.20109 | − | 1.24795i | −0.0866814 | − | 0.0900629i | ||||
\(193\) | 2.79416 | + | 4.83962i | 0.201128 | + | 0.348364i | 0.948892 | − | 0.315601i | \(-0.102206\pi\) |
−0.747764 | + | 0.663964i | \(0.768873\pi\) | |||||||
\(194\) | −6.33599 | − | 10.9743i | −0.454898 | − | 0.787906i | ||||
\(195\) | 7.96388 | − | 1.97144i | 0.570305 | − | 0.141178i | ||||
\(196\) | −2.81238 | + | 4.87118i | −0.200884 | + | 0.347942i | ||||
\(197\) | −23.6455 | −1.68467 | −0.842337 | − | 0.538951i | \(-0.818821\pi\) | ||||
−0.842337 | + | 0.538951i | \(0.818821\pi\) | |||||||
\(198\) | −10.8913 | + | 5.74426i | −0.774013 | + | 0.408227i | ||||
\(199\) | 3.42356 | 0.242690 | 0.121345 | − | 0.992610i | \(-0.461279\pi\) | ||||
0.121345 | + | 0.992610i | \(0.461279\pi\) | |||||||
\(200\) | 1.37153 | − | 2.37555i | 0.0969815 | − | 0.167977i | ||||
\(201\) | −0.429015 | + | 1.48674i | −0.0302604 | + | 0.104867i | ||||
\(202\) | 3.51196 | + | 6.08290i | 0.247101 | + | 0.427991i | ||||
\(203\) | 12.6215 | + | 21.8611i | 0.885856 | + | 1.53435i | ||||
\(204\) | 0.850209 | − | 2.94638i | 0.0595265 | − | 0.206288i | ||||
\(205\) | −13.0167 | + | 22.5456i | −0.909126 | + | 1.57465i | ||||
\(206\) | 15.1303 | 1.05418 | ||||||||
\(207\) | −2.65355 | + | 1.39953i | −0.184434 | + | 0.0972738i | ||||
\(208\) | −1.70225 | −0.118030 | ||||||||
\(209\) | 6.51104 | − | 11.2775i | 0.450378 | − | 0.780078i | ||||
\(210\) | 16.6231 | − | 4.11503i | 1.14711 | − | 0.283964i | ||||
\(211\) | 8.52713 | + | 14.7694i | 0.587032 | + | 1.01677i | 0.994619 | + | 0.103603i | \(0.0330370\pi\) |
−0.407587 | + | 0.913166i | \(0.633630\pi\) | |||||||
\(212\) | −5.44068 | − | 9.42353i | −0.373667 | − | 0.647211i | ||||
\(213\) | 11.8064 | + | 12.2670i | 0.808963 | + | 0.840521i | ||||
\(214\) | 3.91768 | − | 6.78561i | 0.267807 | − | 0.463855i | ||||
\(215\) | −21.1848 | −1.44479 | ||||||||
\(216\) | −3.87893 | + | 3.45744i | −0.263928 | + | 0.235249i | ||||
\(217\) | 6.32961 | 0.429682 | ||||||||
\(218\) | 0.530661 | − | 0.919132i | 0.0359409 | − | 0.0622515i | ||||
\(219\) | 12.2459 | + | 12.7236i | 0.827502 | + | 0.859784i | ||||
\(220\) | 5.71057 | + | 9.89100i | 0.385007 | + | 0.666851i | ||||
\(221\) | −1.50692 | − | 2.61006i | −0.101366 | − | 0.175571i | ||||
\(222\) | 2.17231 | − | 0.537751i | 0.145796 | − | 0.0360915i | ||||
\(223\) | 11.7173 | − | 20.2950i | 0.784650 | − | 1.35905i | −0.144559 | − | 0.989496i | \(-0.546176\pi\) |
0.929208 | − | 0.369557i | \(-0.120490\pi\) | |||||||
\(224\) | −3.55313 | −0.237404 | ||||||||
\(225\) | −6.96406 | − | 4.38416i | −0.464270 | − | 0.292277i | ||||
\(226\) | −9.33237 | −0.620780 | ||||||||
\(227\) | 7.87710 | − | 13.6435i | 0.522821 | − | 0.905553i | −0.476826 | − | 0.878998i | \(-0.658213\pi\) |
0.999647 | − | 0.0265556i | \(-0.00845389\pi\) | |||||||
\(228\) | 1.52355 | − | 5.27983i | 0.100900 | − | 0.349665i | ||||
\(229\) | 5.92574 | + | 10.2637i | 0.391584 | + | 0.678243i | 0.992659 | − | 0.120950i | \(-0.0385940\pi\) |
−0.601075 | + | 0.799193i | \(0.705261\pi\) | |||||||
\(230\) | 1.39132 | + | 2.40983i | 0.0917407 | + | 0.158900i | ||||
\(231\) | −7.00317 | + | 24.2693i | −0.460775 | + | 1.59680i | ||||
\(232\) | −3.55222 | + | 6.15262i | −0.233215 | + | 0.403939i | ||||
\(233\) | 1.98591 | 0.130101 | 0.0650507 | − | 0.997882i | \(-0.479279\pi\) | ||||
0.0650507 | + | 0.997882i | \(0.479279\pi\) | |||||||
\(234\) | −0.195333 | + | 5.10301i | −0.0127693 | + | 0.333594i | ||||
\(235\) | 28.4536 | 1.85611 | ||||||||
\(236\) | 2.17463 | − | 3.76656i | 0.141556 | − | 0.245182i | ||||
\(237\) | 18.0689 | − | 4.47291i | 1.17370 | − | 0.290547i | ||||
\(238\) | −3.14541 | − | 5.44801i | −0.203887 | − | 0.353142i | ||||
\(239\) | −7.79942 | − | 13.5090i | −0.504502 | − | 0.873824i | −0.999986 | − | 0.00520659i | \(-0.998343\pi\) |
0.495484 | − | 0.868617i | \(-0.334991\pi\) | |||||||
\(240\) | 3.34220 | + | 3.47258i | 0.215738 | + | 0.224154i | ||||
\(241\) | −0.449125 | + | 0.777907i | −0.0289307 | + | 0.0501094i | −0.880128 | − | 0.474736i | \(-0.842544\pi\) |
0.851198 | + | 0.524845i | \(0.175877\pi\) | |||||||
\(242\) | −5.84639 | −0.375820 | ||||||||
\(243\) | 9.91962 | + | 12.0250i | 0.636344 | + | 0.771405i | ||||
\(244\) | 9.66909 | 0.619000 | ||||||||
\(245\) | 7.82582 | − | 13.5547i | 0.499973 | − | 0.865979i | ||||
\(246\) | −11.2370 | − | 11.6754i | −0.716447 | − | 0.744396i | ||||
\(247\) | −2.70035 | − | 4.67715i | −0.171819 | − | 0.297600i | ||||
\(248\) | 0.890708 | + | 1.54275i | 0.0565600 | + | 0.0979648i | ||||
\(249\) | −22.4843 | + | 5.56595i | −1.42489 | + | 0.352728i | ||||
\(250\) | 3.14013 | − | 5.43887i | 0.198599 | − | 0.343984i | ||||
\(251\) | −14.4019 | −0.909042 | −0.454521 | − | 0.890736i | \(-0.650190\pi\) | ||||
−0.454521 | + | 0.890736i | \(0.650190\pi\) | |||||||
\(252\) | −0.407722 | + | 10.6516i | −0.0256841 | + | 0.670988i | ||||
\(253\) | −4.10444 | −0.258044 | ||||||||
\(254\) | 4.42187 | − | 7.65890i | 0.277452 | − | 0.480562i | ||||
\(255\) | −2.36582 | + | 8.19870i | −0.148153 | + | 0.513422i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.51981 | + | 2.63238i | 0.0948030 | + | 0.164204i | 0.909526 | − | 0.415646i | \(-0.136445\pi\) |
−0.814723 | + | 0.579850i | \(0.803111\pi\) | |||||||
\(258\) | 3.65594 | − | 12.6696i | 0.227609 | − | 0.788773i | ||||
\(259\) | 2.29540 | − | 3.97574i | 0.142629 | − | 0.247041i | ||||
\(260\) | 4.73674 | 0.293760 | ||||||||
\(261\) | 18.0367 | + | 11.3549i | 1.11645 | + | 0.702849i | ||||
\(262\) | 11.6916 | 0.722307 | ||||||||
\(263\) | −3.26043 | + | 5.64724i | −0.201047 | + | 0.348223i | −0.948866 | − | 0.315679i | \(-0.897768\pi\) |
0.747819 | + | 0.663903i | \(0.231101\pi\) | |||||||
\(264\) | −6.90079 | + | 1.70828i | −0.424715 | + | 0.105137i | ||||
\(265\) | 15.1394 | + | 26.2222i | 0.930007 | + | 1.61082i | ||||
\(266\) | −5.63649 | − | 9.76269i | −0.345595 | − | 0.598589i | ||||
\(267\) | −18.2887 | − | 19.0022i | −1.11925 | − | 1.16291i | ||||
\(268\) | −0.446697 | + | 0.773701i | −0.0272863 | + | 0.0472613i | ||||
\(269\) | 22.6509 | 1.38105 | 0.690524 | − | 0.723309i | \(-0.257380\pi\) | ||||
0.690524 | + | 0.723309i | \(0.257380\pi\) | |||||||
\(270\) | 10.7936 | − | 9.62079i | 0.656880 | − | 0.585503i | ||||
\(271\) | −6.25005 | −0.379664 | −0.189832 | − | 0.981817i | \(-0.560794\pi\) | ||||
−0.189832 | + | 0.981817i | \(0.560794\pi\) | |||||||
\(272\) | 0.885250 | − | 1.53330i | 0.0536762 | − | 0.0929698i | ||||
\(273\) | 7.26459 | + | 7.54799i | 0.439673 | + | 0.456825i | ||||
\(274\) | 7.19047 | + | 12.4543i | 0.434392 | + | 0.752390i | ||||
\(275\) | −5.62934 | − | 9.75030i | −0.339462 | − | 0.587965i | ||||
\(276\) | −1.68130 | + | 0.416203i | −0.101202 | + | 0.0250525i | ||||
\(277\) | −9.91276 | + | 17.1694i | −0.595600 | + | 1.03161i | 0.397862 | + | 0.917445i | \(0.369752\pi\) |
−0.993462 | + | 0.114164i | \(0.963581\pi\) | |||||||
\(278\) | 7.20704 | 0.432250 | ||||||||
\(279\) | 4.72708 | − | 2.49314i | 0.283003 | − | 0.149260i | ||||
\(280\) | 9.88707 | 0.590865 | ||||||||
\(281\) | 2.35490 | − | 4.07880i | 0.140481 | − | 0.243321i | −0.787197 | − | 0.616702i | \(-0.788468\pi\) |
0.927678 | + | 0.373381i | \(0.121802\pi\) | |||||||
\(282\) | −4.91032 | + | 17.0166i | −0.292406 | + | 1.01333i | ||||
\(283\) | 0.767952 | + | 1.33013i | 0.0456500 | + | 0.0790681i | 0.887948 | − | 0.459945i | \(-0.152131\pi\) |
−0.842298 | + | 0.539013i | \(0.818797\pi\) | |||||||
\(284\) | 4.91487 | + | 8.51280i | 0.291644 | + | 0.505142i | ||||
\(285\) | −4.23948 | + | 14.6918i | −0.251125 | + | 0.870269i | ||||
\(286\) | −3.49339 | + | 6.05072i | −0.206568 | + | 0.357787i | ||||
\(287\) | −33.2420 | −1.96221 | ||||||||
\(288\) | −2.65355 | + | 1.39953i | −0.156362 | + | 0.0824679i | ||||
\(289\) | −13.8653 | −0.815608 | ||||||||
\(290\) | 9.88452 | − | 17.1205i | 0.580439 | − | 1.00535i | ||||
\(291\) | −21.3054 | + | 5.27412i | −1.24895 | + | 0.309174i | ||||
\(292\) | 5.09782 | + | 8.82969i | 0.298327 | + | 0.516718i | ||||
\(293\) | −5.80357 | − | 10.0521i | −0.339048 | − | 0.587248i | 0.645206 | − | 0.764009i | \(-0.276772\pi\) |
−0.984254 | + | 0.176760i | \(0.943438\pi\) | |||||||
\(294\) | 6.75586 | + | 7.01941i | 0.394010 | + | 0.409380i | ||||
\(295\) | −6.05119 | + | 10.4810i | −0.352314 | + | 0.610225i | ||||
\(296\) | 1.29204 | 0.0750983 | ||||||||
\(297\) | 4.32922 | + | 20.8833i | 0.251207 | + | 1.21177i | ||||
\(298\) | 21.0210 | 1.21771 | ||||||||
\(299\) | −0.851125 | + | 1.47419i | −0.0492218 | + | 0.0852547i | ||||
\(300\) | −3.29466 | − | 3.42319i | −0.190217 | − | 0.197638i | ||||
\(301\) | −13.5254 | − | 23.4267i | −0.779592 | − | 1.35029i | ||||
\(302\) | −11.1760 | − | 19.3575i | −0.643108 | − | 1.11390i | ||||
\(303\) | 11.8093 | − | 2.92338i | 0.678429 | − | 0.167944i | ||||
\(304\) | 1.58634 | − | 2.74763i | 0.0909830 | − | 0.157587i | ||||
\(305\) | −26.9055 | −1.54061 | ||||||||
\(306\) | −4.49494 | − | 2.82975i | −0.256959 | − | 0.161766i | ||||
\(307\) | 33.8011 | 1.92913 | 0.964567 | − | 0.263839i | \(-0.0849888\pi\) | ||||
0.964567 | + | 0.263839i | \(0.0849888\pi\) | |||||||
\(308\) | −7.29180 | + | 12.6298i | −0.415489 | + | 0.719648i | ||||
\(309\) | 7.26570 | − | 25.1791i | 0.413332 | − | 1.43239i | ||||
\(310\) | −2.47851 | − | 4.29291i | −0.140770 | − | 0.243821i | ||||
\(311\) | −2.38088 | − | 4.12380i | −0.135007 | − | 0.233839i | 0.790593 | − | 0.612342i | \(-0.209772\pi\) |
−0.925600 | + | 0.378503i | \(0.876439\pi\) | |||||||
\(312\) | −0.817434 | + | 2.83280i | −0.0462781 | + | 0.160376i | ||||
\(313\) | 11.9525 | − | 20.7023i | 0.675594 | − | 1.17016i | −0.300701 | − | 0.953718i | \(-0.597221\pi\) |
0.976295 | − | 0.216444i | \(-0.0694460\pi\) | |||||||
\(314\) | −4.23828 | −0.239180 | ||||||||
\(315\) | 1.13454 | − | 29.6395i | 0.0639242 | − | 1.67000i | ||||
\(316\) | 10.7469 | 0.604563 | ||||||||
\(317\) | −12.1759 | + | 21.0894i | −0.683869 | + | 1.18450i | 0.289921 | + | 0.957050i | \(0.406371\pi\) |
−0.973791 | + | 0.227446i | \(0.926962\pi\) | |||||||
\(318\) | −18.2948 | + | 4.52886i | −1.02592 | + | 0.253966i | ||||
\(319\) | 14.5798 | + | 25.2530i | 0.816315 | + | 1.41390i | ||||
\(320\) | 1.39132 | + | 2.40983i | 0.0777770 | + | 0.134714i | ||||
\(321\) | −9.41099 | − | 9.77811i | −0.525270 | − | 0.545761i | ||||
\(322\) | −1.77657 | + | 3.07710i | −0.0990042 | + | 0.171480i | ||||
\(323\) | 5.61724 | 0.312552 | ||||||||
\(324\) | 3.89101 | + | 8.11542i | 0.216167 | + | 0.450857i | ||||
\(325\) | −4.66936 | −0.259009 | ||||||||
\(326\) | −3.77802 | + | 6.54373i | −0.209245 | + | 0.362424i | ||||
\(327\) | −1.27475 | − | 1.32448i | −0.0704937 | − | 0.0732437i | ||||
\(328\) | −4.67784 | − | 8.10225i | −0.258290 | − | 0.447372i | ||||
\(329\) | 18.1661 | + | 31.4646i | 1.00153 | + | 1.73470i | ||||
\(330\) | 19.2024 | − | 4.75351i | 1.05706 | − | 0.261672i | ||||
\(331\) | −9.52877 | + | 16.5043i | −0.523749 | + | 0.907159i | 0.475869 | + | 0.879516i | \(0.342134\pi\) |
−0.999618 | + | 0.0276433i | \(0.991200\pi\) | |||||||
\(332\) | −13.3732 | −0.733948 | ||||||||
\(333\) | 0.148262 | − | 3.87329i | 0.00812469 | − | 0.212255i | ||||
\(334\) | −9.59999 | −0.525288 | ||||||||
\(335\) | 1.24299 | − | 2.15293i | 0.0679120 | − | 0.117627i | ||||
\(336\) | −1.70624 | + | 5.91295i | −0.0930833 | + | 0.322578i | ||||
\(337\) | −12.7081 | − | 22.0110i | −0.692253 | − | 1.19902i | −0.971098 | − | 0.238681i | \(-0.923285\pi\) |
0.278845 | − | 0.960336i | \(-0.410048\pi\) | |||||||
\(338\) | −5.05117 | − | 8.74889i | −0.274748 | − | 0.475877i | ||||
\(339\) | −4.48148 | + | 15.5305i | −0.243401 | + | 0.843500i | ||||
\(340\) | −2.46333 | + | 4.26661i | −0.133593 | + | 0.231389i | ||||
\(341\) | 7.31171 | 0.395951 | ||||||||
\(342\) | −8.05482 | − | 5.07084i | −0.435555 | − | 0.274199i | ||||
\(343\) | −4.88642 | −0.263842 | ||||||||
\(344\) | 3.80661 | − | 6.59325i | 0.205239 | − | 0.355484i | ||||
\(345\) | 4.67845 | − | 1.15814i | 0.251879 | − | 0.0623522i | ||||
\(346\) | −5.23267 | − | 9.06325i | −0.281310 | − | 0.487243i | ||||
\(347\) | 11.3339 | + | 19.6310i | 0.608438 | + | 1.05385i | 0.991498 | + | 0.130122i | \(0.0415368\pi\) |
−0.383060 | + | 0.923723i | \(0.625130\pi\) | |||||||
\(348\) | 8.53309 | + | 8.86597i | 0.457422 | + | 0.475266i | ||||
\(349\) | −6.76024 | + | 11.7091i | −0.361867 | + | 0.626772i | −0.988268 | − | 0.152729i | \(-0.951194\pi\) |
0.626401 | + | 0.779501i | \(0.284527\pi\) | |||||||
\(350\) | −9.74642 | −0.520968 | ||||||||
\(351\) | 8.39838 | + | 2.77557i | 0.448272 | + | 0.148149i | ||||
\(352\) | −4.10444 | −0.218767 | ||||||||
\(353\) | 17.4879 | − | 30.2899i | 0.930785 | − | 1.61217i | 0.148801 | − | 0.988867i | \(-0.452459\pi\) |
0.781984 | − | 0.623299i | \(-0.214208\pi\) | |||||||
\(354\) | −5.22386 | − | 5.42764i | −0.277645 | − | 0.288476i | ||||
\(355\) | −13.6763 | − | 23.6880i | −0.725861 | − | 1.25723i | ||||
\(356\) | −7.61337 | − | 13.1867i | −0.403508 | − | 0.698896i | ||||
\(357\) | −10.5768 | + | 2.61826i | −0.559782 | + | 0.138573i | ||||
\(358\) | 4.53963 | − | 7.86288i | 0.239927 | − | 0.415566i | ||||
\(359\) | 3.12656 | 0.165014 | 0.0825068 | − | 0.996590i | \(-0.473707\pi\) | ||||
0.0825068 | + | 0.996590i | \(0.473707\pi\) | |||||||
\(360\) | 7.38386 | − | 3.89437i | 0.389163 | − | 0.205251i | ||||
\(361\) | −8.93406 | −0.470214 | ||||||||
\(362\) | −13.1898 | + | 22.8454i | −0.693241 | + | 1.20073i | ||||
\(363\) | −2.80749 | + | 9.72928i | −0.147355 | + | 0.510655i | ||||
\(364\) | 3.02416 | + | 5.23800i | 0.158509 | + | 0.274546i | ||||
\(365\) | −14.1854 | − | 24.5698i | −0.742496 | − | 1.28604i | ||||
\(366\) | 4.64318 | − | 16.0908i | 0.242703 | − | 0.841081i | ||||
\(367\) | 9.60731 | − | 16.6403i | 0.501498 | − | 0.868619i | −0.498501 | − | 0.866889i | \(-0.666116\pi\) |
0.999999 | − | 0.00173004i | \(-0.000550688\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −24.8258 | + | 13.0935i | −1.29238 | + | 0.681621i | ||||
\(370\) | −3.59528 | −0.186909 | ||||||||
\(371\) | −19.3315 | + | 33.4831i | −1.00364 | + | 1.73835i | ||||
\(372\) | 2.99510 | − | 0.741431i | 0.155289 | − | 0.0384414i | ||||
\(373\) | −5.36638 | − | 9.29484i | −0.277860 | − | 0.481268i | 0.692992 | − | 0.720945i | \(-0.256292\pi\) |
−0.970853 | + | 0.239676i | \(0.922959\pi\) | |||||||
\(374\) | −3.63345 | − | 6.29332i | −0.187881 | − | 0.325420i | ||||
\(375\) | −7.54318 | − | 7.83745i | −0.389528 | − | 0.404724i | ||||
\(376\) | −5.11270 | + | 8.85546i | −0.263667 | + | 0.456685i | ||||
\(377\) | 12.0935 | 0.622848 | ||||||||
\(378\) | 17.5301 | + | 5.79350i | 0.901650 | + | 0.297985i | ||||
\(379\) | −26.2176 | −1.34671 | −0.673353 | − | 0.739321i | \(-0.735147\pi\) | ||||
−0.673353 | + | 0.739321i | \(0.735147\pi\) | |||||||
\(380\) | −4.41421 | + | 7.64564i | −0.226444 | + | 0.392213i | ||||
\(381\) | −10.6221 | − | 11.0365i | −0.544189 | − | 0.565418i | ||||
\(382\) | 1.03116 | + | 1.78602i | 0.0527588 | + | 0.0913810i | ||||
\(383\) | −2.06077 | − | 3.56936i | −0.105301 | − | 0.182386i | 0.808560 | − | 0.588413i | \(-0.200247\pi\) |
−0.913861 | + | 0.406027i | \(0.866914\pi\) | |||||||
\(384\) | −1.68130 | + | 0.416203i | −0.0857986 | + | 0.0212393i | ||||
\(385\) | 20.2904 | − | 35.1440i | 1.03410 | − | 1.79111i | ||||
\(386\) | 5.58832 | 0.284438 | ||||||||
\(387\) | −19.3285 | − | 12.1681i | −0.982521 | − | 0.618537i | ||||
\(388\) | −12.6720 | −0.643322 | ||||||||
\(389\) | 7.81113 | − | 13.5293i | 0.396040 | − | 0.685961i | −0.597193 | − | 0.802097i | \(-0.703718\pi\) |
0.993233 | + | 0.116136i | \(0.0370509\pi\) | |||||||
\(390\) | 2.27462 | − | 7.88265i | 0.115180 | − | 0.399153i | ||||
\(391\) | −0.885250 | − | 1.53330i | −0.0447690 | − | 0.0775422i | ||||
\(392\) | 2.81238 | + | 4.87118i | 0.142047 | + | 0.246032i | ||||
\(393\) | 5.61439 | − | 19.4565i | 0.283208 | − | 0.981452i | ||||
\(394\) | −11.8228 | + | 20.4776i | −0.595622 | + | 1.03165i | ||||
\(395\) | −29.9048 | −1.50467 | ||||||||
\(396\) | −0.470984 | + | 12.3043i | −0.0236678 | + | 0.618314i | ||||
\(397\) | 15.8394 | 0.794955 | 0.397477 | − | 0.917612i | \(-0.369886\pi\) | ||||
0.397477 | + | 0.917612i | \(0.369886\pi\) | |||||||
\(398\) | 1.71178 | − | 2.96489i | 0.0858038 | − | 0.148617i | ||||
\(399\) | −18.9533 | + | 4.69185i | −0.948851 | + | 0.234886i | ||||
\(400\) | −1.37153 | − | 2.37555i | −0.0685763 | − | 0.118778i | ||||
\(401\) | −1.42817 | − | 2.47367i | −0.0713196 | − | 0.123529i | 0.828160 | − | 0.560491i | \(-0.189388\pi\) |
−0.899480 | + | 0.436962i | \(0.856054\pi\) | |||||||
\(402\) | 1.07305 | + | 1.11491i | 0.0535188 | + | 0.0556066i | ||||
\(403\) | 1.51621 | − | 2.62615i | 0.0755276 | − | 0.130818i | ||||
\(404\) | 7.02393 | 0.349453 | ||||||||
\(405\) | −10.8273 | − | 22.5822i | −0.538011 | − | 1.12212i | ||||
\(406\) | 25.2430 | 1.25279 | ||||||||
\(407\) | 2.65155 | − | 4.59262i | 0.131432 | − | 0.227648i | ||||
\(408\) | −2.12654 | − | 2.20949i | −0.105279 | − | 0.109386i | ||||
\(409\) | 9.73340 | + | 16.8587i | 0.481286 | + | 0.833611i | 0.999769 | − | 0.0214761i | \(-0.00683658\pi\) |
−0.518484 | + | 0.855088i | \(0.673503\pi\) | |||||||
\(410\) | 13.0167 | + | 22.5456i | 0.642849 | + | 1.11345i | ||||
\(411\) | 24.1787 | − | 5.98539i | 1.19265 | − | 0.295238i | ||||
\(412\) | 7.56516 | − | 13.1032i | 0.372709 | − | 0.645550i | ||||
\(413\) | −15.4535 | −0.760416 | ||||||||
\(414\) | −0.114750 | + | 2.99780i | −0.00563966 | + | 0.147334i | ||||
\(415\) | 37.2126 | 1.82670 | ||||||||
\(416\) | −0.851125 | + | 1.47419i | −0.0417298 | + | 0.0722782i | ||||
\(417\) | 3.46088 | − | 11.9936i | 0.169480 | − | 0.587329i | ||||
\(418\) | −6.51104 | − | 11.2775i | −0.318466 | − | 0.551599i | ||||
\(419\) | 17.8208 | + | 30.8665i | 0.870602 | + | 1.50793i | 0.861375 | + | 0.507970i | \(0.169604\pi\) |
0.00922773 | + | 0.999957i | \(0.497063\pi\) | |||||||
\(420\) | 4.74785 | − | 16.4536i | 0.231672 | − | 0.802853i | ||||
\(421\) | −6.80073 | + | 11.7792i | −0.331447 | + | 0.574083i | −0.982796 | − | 0.184695i | \(-0.940870\pi\) |
0.651349 | + | 0.758779i | \(0.274204\pi\) | |||||||
\(422\) | 17.0543 | 0.830188 | ||||||||
\(423\) | 25.9603 | + | 16.3430i | 1.26223 | + | 0.794626i | ||||
\(424\) | −10.8814 | −0.528446 | ||||||||
\(425\) | 2.42829 | − | 4.20591i | 0.117789 | − | 0.204017i | ||||
\(426\) | 16.5267 | − | 4.09117i | 0.800724 | − | 0.198218i | ||||
\(427\) | −17.1778 | − | 29.7528i | −0.831291 | − | 1.43984i | ||||
\(428\) | −3.91768 | − | 6.78561i | −0.189368 | − | 0.327995i | ||||
\(429\) | 8.39176 | + | 8.71913i | 0.405158 | + | 0.420964i | ||||
\(430\) | −10.5924 | + | 18.3466i | −0.510812 | + | 0.884752i | ||||
\(431\) | −17.0437 | −0.820966 | −0.410483 | − | 0.911868i | \(-0.634640\pi\) | ||||
−0.410483 | + | 0.911868i | \(0.634640\pi\) | |||||||
\(432\) | 1.05477 | + | 5.08797i | 0.0507475 | + | 0.244795i | ||||
\(433\) | −10.7139 | −0.514878 | −0.257439 | − | 0.966295i | \(-0.582879\pi\) | ||||
−0.257439 | + | 0.966295i | \(0.582879\pi\) | |||||||
\(434\) | 3.16480 | − | 5.48160i | 0.151915 | − | 0.263125i | ||||
\(435\) | −23.7445 | − | 24.6707i | −1.13846 | − | 1.18287i | ||||
\(436\) | −0.530661 | − | 0.919132i | −0.0254141 | − | 0.0440185i | ||||
\(437\) | −1.58634 | − | 2.74763i | −0.0758851 | − | 0.131437i | ||||
\(438\) | 17.1420 | − | 4.24346i | 0.819074 | − | 0.202760i | ||||
\(439\) | 15.9496 | − | 27.6255i | 0.761234 | − | 1.31850i | −0.180981 | − | 0.983487i | \(-0.557927\pi\) |
0.942215 | − | 0.335009i | \(-0.108739\pi\) | |||||||
\(440\) | 11.4211 | 0.544482 | ||||||||
\(441\) | 14.9256 | − | 7.87199i | 0.710742 | − | 0.374857i | ||||
\(442\) | −3.01383 | −0.143353 | ||||||||
\(443\) | −1.90330 | + | 3.29661i | −0.0904283 | + | 0.156626i | −0.907691 | − | 0.419638i | \(-0.862157\pi\) |
0.817263 | + | 0.576265i | \(0.195490\pi\) | |||||||
\(444\) | 0.620449 | − | 2.15015i | 0.0294452 | − | 0.102042i | ||||
\(445\) | 21.1852 | + | 36.6939i | 1.00428 | + | 1.73946i | ||||
\(446\) | −11.7173 | − | 20.2950i | −0.554831 | − | 0.960996i | ||||
\(447\) | 10.0944 | − | 34.9821i | 0.477451 | − | 1.65460i | ||||
\(448\) | −1.77657 | + | 3.07710i | −0.0839349 | + | 0.145379i | ||||
\(449\) | −11.0761 | −0.522715 | −0.261358 | − | 0.965242i | \(-0.584170\pi\) | ||||
−0.261358 | + | 0.965242i | \(0.584170\pi\) | |||||||
\(450\) | −7.27882 | + | 3.83897i | −0.343127 | + | 0.180971i | ||||
\(451\) | −38.3998 | −1.80817 | ||||||||
\(452\) | −4.66618 | + | 8.08207i | −0.219479 | + | 0.380149i | ||||
\(453\) | −37.5806 | + | 9.30300i | −1.76569 | + | 0.437093i | ||||
\(454\) | −7.87710 | − | 13.6435i | −0.369691 | − | 0.640323i | ||||
\(455\) | −8.41513 | − | 14.5754i | −0.394507 | − | 0.683307i | ||||
\(456\) | −3.81069 | − | 3.95935i | −0.178452 | − | 0.185413i | ||||
\(457\) | 8.43995 | − | 14.6184i | 0.394804 | − | 0.683821i | −0.598272 | − | 0.801293i | \(-0.704146\pi\) |
0.993076 | + | 0.117472i | \(0.0374790\pi\) | |||||||
\(458\) | 11.8515 | 0.553783 | ||||||||
\(459\) | −6.86765 | + | 6.12140i | −0.320554 | + | 0.285722i | ||||
\(460\) | 2.78263 | 0.129741 | ||||||||
\(461\) | −8.64366 | + | 14.9713i | −0.402575 | + | 0.697281i | −0.994036 | − | 0.109053i | \(-0.965218\pi\) |
0.591461 | + | 0.806334i | \(0.298551\pi\) | |||||||
\(462\) | 17.5163 | + | 18.1996i | 0.814931 | + | 0.846722i | ||||
\(463\) | 15.7710 | + | 27.3162i | 0.732940 | + | 1.26949i | 0.955621 | + | 0.294599i | \(0.0951859\pi\) |
−0.222681 | + | 0.974891i | \(0.571481\pi\) | |||||||
\(464\) | 3.55222 | + | 6.15262i | 0.164908 | + | 0.285628i | ||||
\(465\) | −8.33426 | + | 2.06313i | −0.386492 | + | 0.0956754i | ||||
\(466\) | 0.992956 | − | 1.71985i | 0.0459978 | − | 0.0796705i | ||||
\(467\) | −19.7008 | −0.911642 | −0.455821 | − | 0.890071i | \(-0.650654\pi\) | ||||
−0.455821 | + | 0.890071i | \(0.650654\pi\) | |||||||
\(468\) | 4.32167 | + | 2.72067i | 0.199769 | + | 0.125763i | ||||
\(469\) | 3.17435 | 0.146578 | ||||||||
\(470\) | 14.2268 | − | 24.6415i | 0.656232 | − | 1.13663i | ||||
\(471\) | −2.03526 | + | 7.05313i | −0.0937796 | + | 0.324991i | ||||
\(472\) | −2.17463 | − | 3.76656i | −0.100095 | − | 0.173370i | ||||
\(473\) | −15.6240 | − | 27.0616i | −0.718392 | − | 1.24429i | ||||
\(474\) | 5.16077 | − | 17.8845i | 0.237042 | − | 0.821464i | ||||
\(475\) | 4.35142 | − | 7.53688i | 0.199657 | − | 0.345816i | ||||
\(476\) | −6.29082 | −0.288339 | ||||||||
\(477\) | −1.24864 | + | 32.6202i | −0.0571711 | + | 1.49358i | ||||
\(478\) | −15.5988 | −0.713474 | ||||||||
\(479\) | −8.22003 | + | 14.2375i | −0.375583 | + | 0.650529i | −0.990414 | − | 0.138130i | \(-0.955891\pi\) |
0.614831 | + | 0.788659i | \(0.289224\pi\) | |||||||
\(480\) | 4.67845 | − | 1.15814i | 0.213541 | − | 0.0528617i | ||||
\(481\) | −1.09969 | − | 1.90471i | −0.0501414 | − | 0.0868475i | ||||
\(482\) | 0.449125 | + | 0.777907i | 0.0204571 | + | 0.0354327i | ||||
\(483\) | 4.26764 | + | 4.43413i | 0.194185 | + | 0.201760i | ||||
\(484\) | −2.92320 | + | 5.06312i | −0.132873 | + | 0.230142i | ||||
\(485\) | 35.2615 | 1.60114 | ||||||||
\(486\) | 15.3738 | − | 2.57814i | 0.697369 | − | 0.116947i | ||||
\(487\) | −23.5907 | −1.06899 | −0.534497 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534497 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(488\) | 4.83454 | − | 8.37368i | 0.218850 | − | 0.379059i | ||||
\(489\) | 9.07552 | + | 9.42956i | 0.410409 | + | 0.426419i | ||||
\(490\) | −7.82582 | − | 13.5547i | −0.353535 | − | 0.612340i | ||||
\(491\) | −1.60947 | − | 2.78769i | −0.0726346 | − | 0.125807i | 0.827421 | − | 0.561583i | \(-0.189807\pi\) |
−0.900055 | + | 0.435776i | \(0.856474\pi\) | |||||||
\(492\) | −15.7297 | + | 3.89386i | −0.709150 | + | 0.175549i | ||||
\(493\) | −6.28920 | + | 10.8932i | −0.283251 | + | 0.490606i | ||||
\(494\) | −5.40070 | −0.242989 | ||||||||
\(495\) | 1.31058 | − | 34.2383i | 0.0589060 | − | 1.53890i | ||||
\(496\) | 1.78142 | 0.0799879 | ||||||||
\(497\) | 17.4632 | − | 30.2471i | 0.783331 | − | 1.35677i | ||||
\(498\) | −6.42191 | + | 22.2550i | −0.287773 | + | 0.997270i | ||||
\(499\) | −4.47955 | − | 7.75881i | −0.200532 | − | 0.347332i | 0.748168 | − | 0.663510i | \(-0.230934\pi\) |
−0.948700 | + | 0.316177i | \(0.897601\pi\) | |||||||
\(500\) | −3.14013 | − | 5.43887i | −0.140431 | − | 0.243234i | ||||
\(501\) | −4.60999 | + | 15.9758i | −0.205959 | + | 0.713747i | ||||
\(502\) | −7.20097 | + | 12.4724i | −0.321395 | + | 0.556672i | ||||
\(503\) | 26.9673 | 1.20241 | 0.601205 | − | 0.799095i | \(-0.294687\pi\) | ||||
0.601205 | + | 0.799095i | \(0.294687\pi\) | |||||||
\(504\) | 9.02070 | + | 5.67890i | 0.401814 | + | 0.252958i | ||||
\(505\) | −19.5450 | −0.869742 | ||||||||
\(506\) | −2.05222 | + | 3.55455i | −0.0912322 | + | 0.158019i | ||||
\(507\) | −16.9851 | + | 4.20463i | −0.754334 | + | 0.186734i | ||||
\(508\) | −4.42187 | − | 7.65890i | −0.196189 | − | 0.339809i | ||||
\(509\) | −15.7229 | − | 27.2328i | −0.696904 | − | 1.20707i | −0.969535 | − | 0.244955i | \(-0.921227\pi\) |
0.272630 | − | 0.962119i | \(-0.412106\pi\) | |||||||
\(510\) | 5.91737 | + | 6.14821i | 0.262026 | + | 0.272247i | ||||
\(511\) | 18.1132 | − | 31.3731i | 0.801283 | − | 1.38786i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −12.3066 | + | 10.9694i | −0.543351 | + | 0.484310i | ||||
\(514\) | 3.03962 | 0.134072 | ||||||||
\(515\) | −21.0511 | + | 36.4615i | −0.927621 | + | 1.60669i | ||||
\(516\) | −9.14420 | − | 9.50092i | −0.402551 | − | 0.418255i | ||||
\(517\) | 20.9848 | + | 36.3467i | 0.922909 | + | 1.59852i | ||||
\(518\) | −2.29540 | − | 3.97574i | −0.100854 | − | 0.174684i | ||||
\(519\) | −17.5954 | + | 4.35571i | −0.772352 | + | 0.191194i | ||||
\(520\) | 2.36837 | − | 4.10213i | 0.103860 | − | 0.179890i | ||||
\(521\) | 13.6965 | 0.600053 | 0.300026 | − | 0.953931i | \(-0.403004\pi\) | ||||
0.300026 | + | 0.953931i | \(0.403004\pi\) | |||||||
\(522\) | 18.8520 | − | 9.94284i | 0.825129 | − | 0.435186i | ||||
\(523\) | 25.9587 | 1.13509 | 0.567547 | − | 0.823341i | \(-0.307893\pi\) | ||||
0.567547 | + | 0.823341i | \(0.307893\pi\) | |||||||
\(524\) | 5.84578 | − | 10.1252i | 0.255374 | − | 0.442321i | ||||
\(525\) | −4.68031 | + | 16.2195i | −0.204266 | + | 0.707878i | ||||
\(526\) | 3.26043 | + | 5.64724i | 0.142162 | + | 0.246231i | ||||
\(527\) | 1.57700 | + | 2.73144i | 0.0686951 | + | 0.118983i | ||||
\(528\) | −1.97098 | + | 6.83040i | −0.0857761 | + | 0.297255i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | 30.2788 | 1.31523 | ||||||||
\(531\) | −11.5410 | + | 6.08689i | −0.500835 | + | 0.264149i | ||||
\(532\) | −11.2730 | −0.488746 | ||||||||
\(533\) | −7.96285 | + | 13.7921i | −0.344909 | + | 0.597400i | ||||
\(534\) | −25.6007 | + | 6.33741i | −1.10785 | + | 0.274247i | ||||
\(535\) | 10.9015 | + | 18.8819i | 0.471311 | + | 0.816335i | ||||
\(536\) | 0.446697 | + | 0.773701i | 0.0192944 | + | 0.0334188i | ||||
\(537\) | −10.9050 | − | 11.3305i | −0.470587 | − | 0.488945i | ||||
\(538\) | 11.3254 | − | 19.6162i | 0.488274 | − | 0.845716i | ||||
\(539\) | 23.0865 | 0.994404 | ||||||||
\(540\) | −2.93503 | − | 14.1580i | −0.126303 | − | 0.609262i | ||||
\(541\) | −7.70265 | −0.331163 | −0.165581 | − | 0.986196i | \(-0.552950\pi\) | ||||
−0.165581 | + | 0.986196i | \(0.552950\pi\) | |||||||
\(542\) | −3.12503 | + | 5.41271i | −0.134231 | + | 0.232496i | ||||
\(543\) | 31.6844 | + | 32.9204i | 1.35971 | + | 1.41275i | ||||
\(544\) | −0.885250 | − | 1.53330i | −0.0379548 | − | 0.0657396i | ||||
\(545\) | 1.47664 | + | 2.55761i | 0.0632521 | + | 0.109556i | ||||
\(546\) | 10.1690 | − | 2.51733i | 0.435195 | − | 0.107732i | ||||
\(547\) | −17.5774 | + | 30.4449i | −0.751553 | + | 1.30173i | 0.195516 | + | 0.980700i | \(0.437362\pi\) |
−0.947070 | + | 0.321028i | \(0.895972\pi\) | |||||||
\(548\) | 14.3809 | 0.614323 | ||||||||
\(549\) | −24.5479 | − | 15.4539i | −1.04768 | − | 0.659556i | ||||
\(550\) | −11.2587 | −0.480071 | ||||||||
\(551\) | −11.2701 | + | 19.5203i | −0.480121 | + | 0.831594i | ||||
\(552\) | −0.480208 | + | 1.66415i | −0.0204390 | + | 0.0708310i | ||||
\(553\) | −19.0927 | − | 33.0695i | −0.811903 | − | 1.40626i | ||||
\(554\) | 9.91276 | + | 17.1694i | 0.421153 | + | 0.729458i | ||||
\(555\) | −1.72648 | + | 5.98308i | −0.0732851 | + | 0.253968i | ||||
\(556\) | 3.60352 | − | 6.24148i | 0.152823 | − | 0.264698i | ||||
\(557\) | 34.3347 | 1.45481 | 0.727404 | − | 0.686210i | \(-0.240727\pi\) | ||||
0.727404 | + | 0.686210i | \(0.240727\pi\) | |||||||
\(558\) | 0.204418 | − | 5.34034i | 0.00865369 | − | 0.226074i | ||||
\(559\) | −12.9596 | −0.548133 | ||||||||
\(560\) | 4.94353 | − | 8.56245i | 0.208902 | − | 0.361830i | ||||
\(561\) | −12.2179 | + | 3.02451i | −0.515838 | + | 0.127695i | ||||
\(562\) | −2.35490 | − | 4.07880i | −0.0993353 | − | 0.172054i | ||||
\(563\) | 3.42054 | + | 5.92455i | 0.144159 | + | 0.249690i | 0.929059 | − | 0.369932i | \(-0.120619\pi\) |
−0.784900 | + | 0.619622i | \(0.787286\pi\) | |||||||
\(564\) | 12.2817 | + | 12.7608i | 0.517151 | + | 0.537326i | ||||
\(565\) | 12.9843 | − | 22.4894i | 0.546253 | − | 0.946138i | ||||
\(566\) | 1.53590 | 0.0645588 | ||||||||
\(567\) | 18.0594 | − | 26.3906i | 0.758421 | − | 1.10830i | ||||
\(568\) | 9.82973 | 0.412447 | ||||||||
\(569\) | −1.79047 | + | 3.10118i | −0.0750602 | + | 0.130008i | −0.901112 | − | 0.433585i | \(-0.857248\pi\) |
0.826052 | + | 0.563594i | \(0.190582\pi\) | |||||||
\(570\) | 10.6038 | + | 11.0174i | 0.444143 | + | 0.461469i | ||||
\(571\) | 23.3591 | + | 40.4592i | 0.977549 | + | 1.69316i | 0.671253 | + | 0.741228i | \(0.265756\pi\) |
0.306296 | + | 0.951936i | \(0.400910\pi\) | |||||||
\(572\) | 3.49339 | + | 6.05072i | 0.146066 | + | 0.252993i | ||||
\(573\) | 3.46739 | − | 0.858346i | 0.144852 | − | 0.0358579i | ||||
\(574\) | −16.6210 | + | 28.7884i | −0.693746 | + | 1.20160i | ||||
\(575\) | −2.74305 | −0.114393 | ||||||||
\(576\) | −0.114750 | + | 2.99780i | −0.00478125 | + | 0.124909i | ||||
\(577\) | −2.93068 | −0.122006 | −0.0610029 | − | 0.998138i | \(-0.519430\pi\) | ||||
−0.0610029 | + | 0.998138i | \(0.519430\pi\) | |||||||
\(578\) | −6.93267 | + | 12.0077i | −0.288361 | + | 0.499456i | ||||
\(579\) | 2.68356 | − | 9.29981i | 0.111525 | − | 0.386487i | ||||
\(580\) | −9.88452 | − | 17.1205i | −0.410432 | − | 0.710890i | ||||
\(581\) | 23.7583 | + | 41.1506i | 0.985662 | + | 1.70722i | ||||
\(582\) | −6.08519 | + | 21.0881i | −0.252239 | + | 0.874130i | ||||
\(583\) | −22.3309 | + | 38.6783i | −0.924852 | + | 1.60189i | ||||
\(584\) | 10.1956 | 0.421899 | ||||||||
\(585\) | −12.0256 | − | 7.57062i | −0.497198 | − | 0.313007i | ||||
\(586\) | −11.6071 | −0.479486 | ||||||||
\(587\) | 9.58395 | − | 16.5999i | 0.395572 | − | 0.685151i | −0.597602 | − | 0.801793i | \(-0.703880\pi\) |
0.993174 | + | 0.116642i | \(0.0372130\pi\) | |||||||
\(588\) | 9.45692 | − | 2.34104i | 0.389997 | − | 0.0965429i | ||||
\(589\) | 2.82594 | + | 4.89467i | 0.116441 | + | 0.201681i | ||||
\(590\) | 6.05119 | + | 10.4810i | 0.249123 | + | 0.431494i | ||||
\(591\) | 28.4005 | + | 29.5084i | 1.16824 | + | 1.21381i | ||||
\(592\) | 0.646020 | − | 1.11894i | 0.0265513 | − | 0.0459881i | ||||
\(593\) | 19.8234 | 0.814048 | 0.407024 | − | 0.913417i | \(-0.366566\pi\) | ||||
0.407024 | + | 0.913417i | \(0.366566\pi\) | |||||||
\(594\) | 20.2500 | + | 6.69241i | 0.830869 | + | 0.274593i | ||||
\(595\) | 17.5051 | 0.717637 | ||||||||
\(596\) | 10.5105 | − | 18.2047i | 0.430526 | − | 0.745694i | ||||
\(597\) | −4.11202 | − | 4.27243i | −0.168294 | − | 0.174859i | ||||
\(598\) | 0.851125 | + | 1.47419i | 0.0348051 | + | 0.0602842i | ||||
\(599\) | 17.6338 | + | 30.5426i | 0.720496 | + | 1.24794i | 0.960801 | + | 0.277239i | \(0.0894192\pi\) |
−0.240305 | + | 0.970697i | \(0.577247\pi\) | |||||||
\(600\) | −4.61189 | + | 1.14167i | −0.188280 | + | 0.0466083i | ||||
\(601\) | 0.969650 | − | 1.67948i | 0.0395529 | − | 0.0685076i | −0.845571 | − | 0.533863i | \(-0.820740\pi\) |
0.885124 | + | 0.465355i | \(0.154073\pi\) | |||||||
\(602\) | −27.0508 | −1.10251 | ||||||||
\(603\) | 2.37066 | − | 1.25033i | 0.0965409 | − | 0.0509173i | ||||
\(604\) | −22.3521 | −0.909492 | ||||||||
\(605\) | 8.13418 | − | 14.0888i | 0.330702 | − | 0.572792i | ||||
\(606\) | 3.37295 | − | 11.6889i | 0.137017 | − | 0.474828i | ||||
\(607\) | −2.24299 | − | 3.88498i | −0.0910402 | − | 0.157686i | 0.816909 | − | 0.576767i | \(-0.195686\pi\) |
−0.907949 | + | 0.419080i | \(0.862353\pi\) | |||||||
\(608\) | −1.58634 | − | 2.74763i | −0.0643347 | − | 0.111431i | ||||
\(609\) | 12.1219 | − | 42.0082i | 0.491204 | − | 1.70226i | ||||
\(610\) | −13.4528 | + | 23.3009i | −0.544687 | + | 0.943425i | ||||
\(611\) | 17.4062 | 0.704179 | ||||||||
\(612\) | −4.69811 | + | 2.47786i | −0.189910 | + | 0.100162i | ||||
\(613\) | −23.1365 | −0.934474 | −0.467237 | − | 0.884132i | \(-0.654750\pi\) | ||||
−0.467237 | + | 0.884132i | \(0.654750\pi\) | |||||||
\(614\) | 16.9006 | − | 29.2727i | 0.682052 | − | 1.18135i | ||||
\(615\) | 43.7700 | − | 10.8352i | 1.76498 | − | 0.436917i | ||||
\(616\) | 7.29180 | + | 12.6298i | 0.293795 | + | 0.508868i | ||||
\(617\) | 9.34249 | + | 16.1817i | 0.376114 | + | 0.651449i | 0.990493 | − | 0.137562i | \(-0.0439266\pi\) |
−0.614379 | + | 0.789011i | \(0.710593\pi\) | |||||||
\(618\) | −18.1729 | − | 18.8819i | −0.731022 | − | 0.759540i | ||||
\(619\) | 6.23823 | − | 10.8049i | 0.250736 | − | 0.434287i | −0.712993 | − | 0.701171i | \(-0.752661\pi\) |
0.963729 | + | 0.266884i | \(0.0859942\pi\) | |||||||
\(620\) | −4.95703 | −0.199079 | ||||||||
\(621\) | 4.93370 | + | 1.63053i | 0.197982 | + | 0.0654310i | ||||
\(622\) | −4.76176 | −0.190929 | ||||||||
\(623\) | −27.0513 | + | 46.8542i | −1.08379 | + | 1.87718i | ||||
\(624\) | 2.04456 | + | 2.12432i | 0.0818479 | + | 0.0850408i | ||||
\(625\) | 15.5955 | + | 27.0121i | 0.623819 | + | 1.08049i | ||||
\(626\) | −11.9525 | − | 20.7023i | −0.477717 | − | 0.827430i | ||||
\(627\) | −21.8941 | + | 5.41983i | −0.874364 | + | 0.216447i | ||||
\(628\) | −2.11914 | + | 3.67045i | −0.0845628 | + | 0.146467i | ||||
\(629\) | 2.28756 | 0.0912109 | ||||||||
\(630\) | −25.1013 | − | 15.8023i | −1.00006 | − | 0.629578i | ||||
\(631\) | 34.2107 | 1.36191 | 0.680953 | − | 0.732327i | \(-0.261566\pi\) | ||||
0.680953 | + | 0.732327i | \(0.261566\pi\) | |||||||
\(632\) | 5.37347 | − | 9.30713i | 0.213745 | − | 0.370218i | ||||
\(633\) | 8.18960 | − | 28.3809i | 0.325507 | − | 1.12804i | ||||
\(634\) | 12.1759 | + | 21.0894i | 0.483569 | + | 0.837566i | ||||
\(635\) | 12.3044 | + | 21.3119i | 0.488286 | + | 0.845737i | ||||
\(636\) | −5.22532 | + | 18.1082i | −0.207197 | + | 0.718038i | ||||
\(637\) | 4.78737 | − | 8.29197i | 0.189683 | − | 0.328540i | ||||
\(638\) | 29.1597 | 1.15444 | ||||||||
\(639\) | 1.12796 | − | 29.4676i | 0.0446215 | − | 1.16572i | ||||
\(640\) | 2.78263 | 0.109993 | ||||||||
\(641\) | −1.05824 | + | 1.83292i | −0.0417978 | + | 0.0723959i | −0.886167 | − | 0.463365i | \(-0.846642\pi\) |
0.844370 | + | 0.535761i | \(0.179975\pi\) | |||||||
\(642\) | −13.1736 | + | 3.26110i | −0.519920 | + | 0.128705i | ||||
\(643\) | −20.2717 | − | 35.1116i | −0.799438 | − | 1.38467i | −0.919983 | − | 0.391959i | \(-0.871797\pi\) |
0.120545 | − | 0.992708i | \(-0.461536\pi\) | |||||||
\(644\) | 1.77657 | + | 3.07710i | 0.0700065 | + | 0.121255i | ||||
\(645\) | 25.4450 | + | 26.4376i | 1.00189 | + | 1.04098i | ||||
\(646\) | 2.80862 | − | 4.86467i | 0.110504 | − | 0.191398i | ||||
\(647\) | 27.1978 | 1.06925 | 0.534627 | − | 0.845088i | \(-0.320452\pi\) | ||||
0.534627 | + | 0.845088i | \(0.320452\pi\) | |||||||
\(648\) | 8.97366 | + | 0.687996i | 0.352519 | + | 0.0270271i | ||||
\(649\) | −17.8512 | −0.700722 | ||||||||
\(650\) | −2.33468 | + | 4.04378i | −0.0915736 | + | 0.158610i | ||||
\(651\) | −7.60245 | − | 7.89902i | −0.297964 | − | 0.309587i | ||||
\(652\) | 3.77802 | + | 6.54373i | 0.147959 | + | 0.256272i | ||||
\(653\) | 22.0042 | + | 38.1124i | 0.861092 | + | 1.49145i | 0.870876 | + | 0.491502i | \(0.163552\pi\) |
−0.00978470 | + | 0.999952i | \(0.503115\pi\) | |||||||
\(654\) | −1.78440 | + | 0.441726i | −0.0697757 | + | 0.0172728i | ||||
\(655\) | −16.2667 | + | 28.1747i | −0.635591 | + | 1.10088i | ||||
\(656\) | −9.35568 | −0.365278 | ||||||||
\(657\) | 1.16995 | − | 30.5645i | 0.0456441 | − | 1.19244i | ||||
\(658\) | 36.3322 | 1.41638 | ||||||||
\(659\) | −0.174968 | + | 0.303053i | −0.00681578 | + | 0.0118053i | −0.869413 | − | 0.494086i | \(-0.835503\pi\) |
0.862597 | + | 0.505891i | \(0.168836\pi\) | |||||||
\(660\) | 5.48453 | − | 19.0065i | 0.213485 | − | 0.739827i | ||||
\(661\) | −16.1774 | − | 28.0201i | −0.629228 | − | 1.08985i | −0.987707 | − | 0.156317i | \(-0.950038\pi\) |
0.358479 | − | 0.933538i | \(-0.383295\pi\) | |||||||
\(662\) | 9.52877 | + | 16.5043i | 0.370346 | + | 0.641459i | ||||
\(663\) | −1.44727 | + | 5.01547i | −0.0562072 | + | 0.194785i | ||||
\(664\) | −6.68659 | + | 11.5815i | −0.259490 | + | 0.449450i | ||||
\(665\) | 31.3686 | 1.21642 | ||||||||
\(666\) | −3.28023 | − | 2.06504i | −0.127106 | − | 0.0800187i | ||||
\(667\) | 7.10444 | 0.275085 | ||||||||
\(668\) | −4.79999 | + | 8.31383i | −0.185717 | + | 0.321672i | ||||
\(669\) | −39.4007 | + | 9.75357i | −1.52332 | + | 0.377095i | ||||
\(670\) | −1.24299 | − | 2.15293i | −0.0480210 | − | 0.0831748i | ||||
\(671\) | −19.8431 | − | 34.3692i | −0.766034 | − | 1.32681i | ||||
\(672\) | 4.26764 | + | 4.43413i | 0.164628 | + | 0.171050i | ||||
\(673\) | 22.9616 | − | 39.7706i | 0.885103 | − | 1.53304i | 0.0395084 | − | 0.999219i | \(-0.487421\pi\) |
0.845595 | − | 0.533825i | \(-0.179246\pi\) | |||||||
\(674\) | −25.4161 | −0.978993 | ||||||||
\(675\) | 2.89328 | + | 13.9566i | 0.111362 | + | 0.537188i | ||||
\(676\) | −10.1023 | −0.388552 | ||||||||
\(677\) | −23.5854 | + | 40.8511i | −0.906460 | + | 1.57003i | −0.0875139 | + | 0.996163i | \(0.527892\pi\) |
−0.818946 | + | 0.573871i | \(0.805441\pi\) | |||||||
\(678\) | 11.2090 | + | 11.6463i | 0.430481 | + | 0.447274i | ||||
\(679\) | 22.5126 | + | 38.9930i | 0.863955 | + | 1.49641i | ||||
\(680\) | 2.46333 | + | 4.26661i | 0.0944643 | + | 0.163617i | ||||
\(681\) | −26.4876 | + | 6.55695i | −1.01501 | + | 0.251263i | ||||
\(682\) | 3.65585 | − | 6.33212i | 0.139990 | − | 0.242470i | ||||
\(683\) | 3.71123 | 0.142006 | 0.0710032 | − | 0.997476i | \(-0.477380\pi\) | ||||
0.0710032 | + | 0.997476i | \(0.477380\pi\) | |||||||
\(684\) | −8.41888 | + | 4.44026i | −0.321904 | + | 0.169777i | ||||
\(685\) | −40.0169 | −1.52897 | ||||||||
\(686\) | −2.44321 | + | 4.23176i | −0.0932821 | + | 0.161569i | ||||
\(687\) | 5.69118 | − | 19.7226i | 0.217132 | − | 0.752466i | ||||
\(688\) | −3.80661 | − | 6.59325i | −0.145126 | − | 0.251365i | ||||
\(689\) | 9.26139 | + | 16.0412i | 0.352831 | + | 0.611121i | ||||
\(690\) | 1.33624 | − | 4.63072i | 0.0508699 | − | 0.176289i | ||||
\(691\) | −7.48520 | + | 12.9647i | −0.284750 | + | 0.493202i | −0.972549 | − | 0.232700i | \(-0.925244\pi\) |
0.687798 | + | 0.725902i | \(0.258577\pi\) | |||||||
\(692\) | −10.4653 | −0.397833 | ||||||||
\(693\) | 38.6983 | − | 20.4101i | 1.47003 | − | 0.775317i | ||||
\(694\) | 22.6679 | 0.860461 | ||||||||
\(695\) | −10.0273 | + | 17.3678i | −0.380356 | + | 0.658796i | ||||
\(696\) | 11.9447 | − | 2.95689i | 0.452763 | − | 0.112081i | ||||
\(697\) | −8.28211 | − | 14.3450i | −0.313707 | − | 0.543357i | ||||
\(698\) | 6.76024 | + | 11.7091i | 0.255879 | + | 0.443195i | ||||
\(699\) | −2.38527 | − | 2.47832i | −0.0902190 | − | 0.0937385i | ||||
\(700\) | −4.87321 | + | 8.44065i | −0.184190 | + | 0.319027i | ||||
\(701\) | −28.3822 | −1.07198 | −0.535990 | − | 0.844224i | \(-0.680062\pi\) | ||||
−0.535990 | + | 0.844224i | \(0.680062\pi\) | |||||||
\(702\) | 6.60291 | − | 5.88543i | 0.249211 | − | 0.222131i | ||||
\(703\) | 4.09924 | 0.154606 | ||||||||
\(704\) | −2.05222 | + | 3.55455i | −0.0773459 | + | 0.133967i | ||||
\(705\) | −34.1754 | − | 35.5086i | −1.28712 | − | 1.33733i | ||||
\(706\) | −17.4879 | − | 30.2899i | −0.658164 | − | 1.13997i | ||||
\(707\) | −12.4785 | − | 21.6134i | −0.469301 | − | 0.812854i | ||||
\(708\) | −7.31240 | + | 1.81017i | −0.274817 | + | 0.0680304i | ||||
\(709\) | 17.7168 | − | 30.6864i | 0.665369 | − | 1.15245i | −0.313816 | − | 0.949484i | \(-0.601607\pi\) |
0.979185 | − | 0.202970i | \(-0.0650593\pi\) | |||||||
\(710\) | −27.3526 | −1.02652 | ||||||||
\(711\) | −27.2843 | − | 17.1766i | −1.02324 | − | 0.644173i | ||||
\(712\) | −15.2267 | −0.570646 | ||||||||
\(713\) | 0.890708 | − | 1.54275i | 0.0333573 | − | 0.0577765i | ||||
\(714\) | −3.02091 | + | 10.4689i | −0.113055 | + | 0.391788i | ||||
\(715\) | −9.72081 | − | 16.8369i | −0.363538 | − | 0.629666i | ||||
\(716\) | −4.53963 | − | 7.86288i | −0.169654 | − | 0.293849i | ||||
\(717\) | −7.49069 | + | 25.9588i | −0.279745 | + | 0.969450i | ||||
\(718\) | 1.56328 | − | 2.70768i | 0.0583411 | − | 0.101050i | ||||
\(719\) | −12.4519 | −0.464377 | −0.232189 | − | 0.972671i | \(-0.574589\pi\) | ||||
−0.232189 | + | 0.972671i | \(0.574589\pi\) | |||||||
\(720\) | 0.319307 | − | 8.34179i | 0.0118999 | − | 0.310880i | ||||
\(721\) | −53.7600 | −2.00213 | ||||||||
\(722\) | −4.46703 | + | 7.73712i | −0.166246 | + | 0.287946i | ||||
\(723\) | 1.51023 | − | 0.373854i | 0.0561660 | − | 0.0139038i | ||||
\(724\) | 13.1898 | + | 22.8454i | 0.490196 | + | 0.849044i | ||||
\(725\) | 9.74391 | + | 16.8770i | 0.361880 | + | 0.626794i | ||||
\(726\) | 7.02206 | + | 7.29600i | 0.260613 | + | 0.270780i | ||||
\(727\) | −19.0540 | + | 33.0026i | −0.706675 | + | 1.22400i | 0.259408 | + | 0.965768i | \(0.416472\pi\) |
−0.966084 | + | 0.258230i | \(0.916861\pi\) | |||||||
\(728\) | 6.04832 | 0.224166 | ||||||||
\(729\) | 3.09221 | − | 26.8223i | 0.114526 | − | 0.993420i | ||||
\(730\) | −28.3707 | −1.05005 | ||||||||
\(731\) | 6.73961 | − | 11.6733i | 0.249273 | − | 0.431754i | ||||
\(732\) | −11.6135 | − | 12.0665i | −0.429246 | − | 0.445992i | ||||
\(733\) | 2.14422 | + | 3.71389i | 0.0791985 | + | 0.137176i | 0.902904 | − | 0.429842i | \(-0.141431\pi\) |
−0.823706 | + | 0.567017i | \(0.808097\pi\) | |||||||
\(734\) | −9.60731 | − | 16.6403i | −0.354612 | − | 0.614206i | ||||
\(735\) | −26.3151 | + | 6.51426i | −0.970648 | + | 0.240282i | ||||
\(736\) | −0.500000 | + | 0.866025i | −0.0184302 | + | 0.0319221i | ||||
\(737\) | 3.66688 | 0.135071 | ||||||||
\(738\) | −1.07356 | + | 28.0465i | −0.0395184 | + | 1.03241i | ||||
\(739\) | 24.8250 | 0.913204 | 0.456602 | − | 0.889671i | \(-0.349066\pi\) | ||||
0.456602 | + | 0.889671i | \(0.349066\pi\) | |||||||
\(740\) | −1.79764 | + | 3.11360i | −0.0660825 | + | 0.114458i | ||||
\(741\) | −2.59346 | + | 8.98759i | −0.0952732 | + | 0.330167i | ||||
\(742\) | 19.3315 | + | 33.4831i | 0.709680 | + | 1.22920i | ||||
\(743\) | 6.42145 | + | 11.1223i | 0.235580 | + | 0.408037i | 0.959441 | − | 0.281909i | \(-0.0909677\pi\) |
−0.723861 | + | 0.689946i | \(0.757634\pi\) | |||||||
\(744\) | 0.855451 | − | 2.96455i | 0.0313623 | − | 0.108686i | ||||
\(745\) | −29.2468 | + | 50.6570i | −1.07152 | + | 1.85593i | ||||
\(746\) | −10.7328 | −0.392954 | ||||||||
\(747\) | 33.9518 | + | 21.3741i | 1.24223 | + | 0.782036i | ||||
\(748\) | −7.26690 | −0.265704 | ||||||||
\(749\) | −13.9200 | + | 24.1102i | −0.508627 | + | 0.880967i | ||||
\(750\) | −10.5590 | + | 2.61387i | −0.385561 | + | 0.0954449i | ||||
\(751\) | 1.17145 | + | 2.02901i | 0.0427468 | + | 0.0740397i | 0.886607 | − | 0.462523i | \(-0.153056\pi\) |
−0.843860 | + | 0.536563i | \(0.819722\pi\) | |||||||
\(752\) | 5.11270 | + | 8.85546i | 0.186441 | + | 0.322925i | ||||
\(753\) | 17.2981 | + | 17.9729i | 0.630376 | + | 0.654968i | ||||
\(754\) | 6.04676 | − | 10.4733i | 0.220210 | − | 0.381415i | ||||
\(755\) | 62.1976 | 2.26360 | ||||||||
\(756\) | 13.7824 | − | 12.2847i | 0.501260 | − | 0.446792i | ||||
\(757\) | 22.3582 | 0.812622 | 0.406311 | − | 0.913735i | \(-0.366815\pi\) | ||||
0.406311 | + | 0.913735i | \(0.366815\pi\) | |||||||
\(758\) | −13.1088 | + | 22.7051i | −0.476133 | + | 0.824686i | ||||
\(759\) | 4.92981 | + | 5.12212i | 0.178941 | + | 0.185921i | ||||
\(760\) | 4.41421 | + | 7.64564i | 0.160120 | + | 0.277336i | ||||
\(761\) | −3.62069 | − | 6.27122i | −0.131250 | − | 0.227332i | 0.792909 | − | 0.609341i | \(-0.208566\pi\) |
−0.924159 | + | 0.382009i | \(0.875232\pi\) | |||||||
\(762\) | −14.8690 | + | 3.68079i | −0.538646 | + | 0.133341i | ||||
\(763\) | −1.88551 | + | 3.26580i | −0.0682601 | + | 0.118230i | ||||
\(764\) | 2.06232 | 0.0746123 | ||||||||
\(765\) | 13.0731 | − | 6.89498i | 0.472660 | − | 0.249288i | ||||
\(766\) | −4.12154 | −0.148917 | ||||||||
\(767\) | −3.70175 | + | 6.41163i | −0.133663 | + | 0.231510i | ||||
\(768\) | −0.480208 | + | 1.66415i | −0.0173280 | + | 0.0600499i | ||||
\(769\) | −12.4106 | − | 21.4959i | −0.447539 | − | 0.775161i | 0.550686 | − | 0.834712i | \(-0.314366\pi\) |
−0.998225 | + | 0.0595518i | \(0.981033\pi\) | |||||||
\(770\) | −20.2904 | − | 35.1440i | −0.731216 | − | 1.26650i | ||||
\(771\) | 1.45965 | − | 5.05838i | 0.0525680 | − | 0.182173i | ||||
\(772\) | 2.79416 | − | 4.83962i | 0.100564 | − | 0.174182i | ||||
\(773\) | 30.3720 | 1.09241 | 0.546203 | − | 0.837653i | \(-0.316073\pi\) | ||||
0.546203 | + | 0.837653i | \(0.316073\pi\) | |||||||
\(774\) | −20.2021 | + | 10.6549i | −0.726149 | + | 0.382983i | ||||
\(775\) | 4.88651 | 0.175529 | ||||||||
\(776\) | −6.33599 | + | 10.9743i | −0.227449 | + | 0.393953i | ||||
\(777\) | −7.71851 | + | 1.91070i | −0.276900 | + | 0.0685461i | ||||
\(778\) | −7.81113 | − | 13.5293i | −0.280042 | − | 0.485048i | ||||
\(779\) | −14.8413 | − | 25.7059i | −0.531745 | − | 0.921010i | ||||
\(780\) | −5.68926 | − | 5.91120i | −0.203708 | − | 0.211655i | ||||
\(781\) | 20.1728 | − | 34.9402i | 0.721838 | − | 1.25026i | ||||
\(782\) | −1.77050 | −0.0633129 | ||||||||
\(783\) | −7.49352 | − | 36.1472i | −0.267796 | − | 1.29179i | ||||
\(784\) | 5.62476 | 0.200884 | ||||||||
\(785\) | 5.89678 | − | 10.2135i | 0.210465 | − | 0.364536i | ||||
\(786\) | −14.0427 | − | 14.5905i | −0.500885 | − | 0.520425i | ||||
\(787\) | −15.1620 | − | 26.2613i | −0.540466 | − | 0.936114i | −0.998877 | − | 0.0473743i | \(-0.984915\pi\) |
0.458411 | − | 0.888740i | \(-0.348419\pi\) | |||||||
\(788\) | 11.8228 | + | 20.4776i | 0.421169 | + | 0.729486i | ||||
\(789\) | 10.9635 | − | 2.71400i | 0.390312 | − | 0.0966211i | ||||
\(790\) | −14.9524 | + | 25.8983i | −0.531983 | + | 0.921421i | ||||
\(791\) | 33.1592 | 1.17900 | ||||||||
\(792\) | 10.4203 | + | 6.56003i | 0.370271 | + | 0.233101i | ||||
\(793\) | −16.4592 | −0.584483 | ||||||||
\(794\) | 7.91968 | − | 13.7173i | 0.281059 | − | 0.486808i | ||||
\(795\) | 14.5401 | − | 50.3886i | 0.515686 | − | 1.78710i | ||||
\(796\) | −1.71178 | − | 2.96489i | −0.0606724 | − | 0.105088i | ||||
\(797\) | −10.4010 | − | 18.0151i | −0.368423 | − | 0.638128i | 0.620896 | − | 0.783893i | \(-0.286769\pi\) |
−0.989319 | + | 0.145765i | \(0.953436\pi\) | |||||||
\(798\) | −5.41338 | + | 18.7599i | −0.191632 | + | 0.664095i | ||||
\(799\) | −9.05204 | + | 15.6786i | −0.320238 | + | 0.554669i | ||||
\(800\) | −2.74305 | −0.0969815 | ||||||||
\(801\) | −1.74727 | + | 45.6468i | −0.0617367 | + | 1.61285i | ||||
\(802\) | −2.85635 | −0.100861 | ||||||||
\(803\) | 20.9237 | − | 36.2409i | 0.738381 | − | 1.27891i | ||||
\(804\) | 1.50206 | − | 0.371833i | 0.0529737 | − | 0.0131135i | ||||
\(805\) | −4.94353 | − | 8.56245i | −0.174237 | − | 0.301787i | ||||
\(806\) | −1.51621 | − | 2.62615i | −0.0534061 | − | 0.0925021i | ||||
\(807\) | −27.2058 | − | 28.2671i | −0.957690 | − | 0.995050i | ||||
\(808\) | 3.51196 | − | 6.08290i | 0.123550 | − | 0.213996i | ||||
\(809\) | −8.08187 | −0.284143 | −0.142072 | − | 0.989856i | \(-0.545376\pi\) | ||||
−0.142072 | + | 0.989856i | \(0.545376\pi\) | |||||||
\(810\) | −24.9704 | − | 1.91444i | −0.877371 | − | 0.0672666i | ||||
\(811\) | 34.9201 | 1.22621 | 0.613106 | − | 0.790001i | \(-0.289920\pi\) | ||||
0.613106 | + | 0.790001i | \(0.289920\pi\) | |||||||
\(812\) | 12.6215 | − | 21.8611i | 0.442928 | − | 0.767174i | ||||
\(813\) | 7.50690 | + | 7.79974i | 0.263278 | + | 0.273549i | ||||
\(814\) | −2.65155 | − | 4.59262i | −0.0929367 | − | 0.160971i | ||||
\(815\) | −10.5129 | − | 18.2088i | −0.368249 | − | 0.637827i | ||||
\(816\) | −2.97674 | + | 0.736888i | −0.104207 | + | 0.0257962i | ||||
\(817\) | 12.0772 | − | 20.9183i | 0.422528 | − | 0.731839i | ||||
\(818\) | 19.4668 | 0.680641 | ||||||||
\(819\) | 0.694045 | − | 18.1317i | 0.0242519 | − | 0.633572i | ||||
\(820\) | 26.0334 | 0.909126 | ||||||||
\(821\) | −6.07469 | + | 10.5217i | −0.212008 | + | 0.367209i | −0.952343 | − | 0.305029i | \(-0.901334\pi\) |
0.740335 | + | 0.672238i | \(0.234667\pi\) | |||||||
\(822\) | 6.90585 | − | 23.9321i | 0.240869 | − | 0.834727i | ||||
\(823\) | 1.64369 | + | 2.84696i | 0.0572955 | + | 0.0992387i | 0.893250 | − | 0.449559i | \(-0.148419\pi\) |
−0.835955 | + | 0.548798i | \(0.815086\pi\) | |||||||
\(824\) | −7.56516 | − | 13.1032i | −0.263545 | − | 0.456473i | ||||
\(825\) | −5.40651 | + | 18.7361i | −0.188230 | + | 0.652309i | ||||
\(826\) | −7.72674 | + | 13.3831i | −0.268848 | + | 0.465658i | ||||
\(827\) | 6.07229 | 0.211154 | 0.105577 | − | 0.994411i | \(-0.466331\pi\) | ||||
0.105577 | + | 0.994411i | \(0.466331\pi\) | |||||||
\(828\) | 2.53880 | + | 1.59828i | 0.0882294 | + | 0.0555440i | ||||
\(829\) | −12.2327 | −0.424858 | −0.212429 | − | 0.977177i | \(-0.568137\pi\) | ||||
−0.212429 | + | 0.977177i | \(0.568137\pi\) | |||||||
\(830\) | 18.6063 | − | 32.2271i | 0.645835 | − | 1.11862i | ||||
\(831\) | 33.3327 | − | 8.25144i | 1.15630 | − | 0.286239i | ||||
\(832\) | 0.851125 | + | 1.47419i | 0.0295074 | + | 0.0511084i | ||||
\(833\) | 4.97932 | + | 8.62443i | 0.172523 | + | 0.298819i | ||||
\(834\) | −8.65633 | − | 8.99401i | −0.299744 | − | 0.311437i | ||||
\(835\) | 13.3566 | − | 23.1343i | 0.462225 | − | 0.800597i | ||||
\(836\) | −13.0221 | −0.450378 | ||||||||
\(837\) | −8.78897 | − | 2.90466i | −0.303791 | − | 0.100400i | ||||
\(838\) | 35.6416 | 1.23122 | ||||||||
\(839\) | 12.9001 | − | 22.3436i | 0.445360 | − | 0.771386i | −0.552717 | − | 0.833369i | \(-0.686409\pi\) |
0.998077 | + | 0.0619829i | \(0.0197424\pi\) | |||||||
\(840\) | −11.8753 | − | 12.3386i | −0.409737 | − | 0.425720i | ||||
\(841\) | −10.7365 | − | 18.5962i | −0.370224 | − | 0.641247i | ||||
\(842\) | 6.80073 | + | 11.7792i | 0.234369 | + | 0.405938i | ||||
\(843\) | −7.91858 | + | 1.96023i | −0.272730 | + | 0.0675139i | ||||
\(844\) | 8.52713 | − | 14.7694i | 0.293516 | − | 0.508385i | ||||
\(845\) | 28.1111 | 0.967052 | ||||||||
\(846\) | 27.1336 | − | 14.3107i | 0.932873 | − | 0.492013i | ||||
\(847\) | 20.7730 | 0.713769 | ||||||||
\(848\) | −5.44068 | + | 9.42353i | −0.186834 | + | 0.323605i | ||||
\(849\) | 0.737554 | − | 2.55598i | 0.0253128 | − | 0.0877209i | ||||
\(850\) | −2.42829 | − | 4.20591i | −0.0832895 | − | 0.144262i | ||||
\(851\) | −0.646020 | − | 1.11894i | −0.0221453 | − | 0.0383568i | ||||
\(852\) | 4.72032 | − | 16.3582i | 0.161716 | − | 0.560422i | ||||
\(853\) | 23.2329 | − | 40.2406i | 0.795479 | − | 1.37781i | −0.127055 | − | 0.991896i | \(-0.540552\pi\) |
0.922534 | − | 0.385915i | \(-0.126114\pi\) | |||||||
\(854\) | −34.3556 | −1.17562 | ||||||||
\(855\) | 23.4267 | − | 12.3556i | 0.801175 | − | 0.422553i | ||||
\(856\) | −7.83535 | −0.267807 | ||||||||
\(857\) | 0.779842 | − | 1.35073i | 0.0266389 | − | 0.0461399i | −0.852399 | − | 0.522893i | \(-0.824853\pi\) |
0.879038 | + | 0.476753i | \(0.158186\pi\) | |||||||
\(858\) | 11.7469 | − | 2.90792i | 0.401032 | − | 0.0992746i | ||||
\(859\) | −20.2819 | − | 35.1293i | −0.692009 | − | 1.19859i | −0.971179 | − | 0.238353i | \(-0.923393\pi\) |
0.279170 | − | 0.960242i | \(-0.409941\pi\) | |||||||
\(860\) | 10.5924 | + | 18.3466i | 0.361198 | + | 0.625614i | ||||
\(861\) | 39.9267 | + | 41.4843i | 1.36070 | + | 1.41378i | ||||
\(862\) | −8.52184 | + | 14.7603i | −0.290255 | + | 0.502737i | ||||
\(863\) | −47.9157 | −1.63107 | −0.815534 | − | 0.578709i | \(-0.803557\pi\) | ||||
−0.815534 | + | 0.578709i | \(0.803557\pi\) | |||||||
\(864\) | 4.93370 | + | 1.63053i | 0.167848 | + | 0.0554718i | ||||
\(865\) | 29.1212 | 0.990151 | ||||||||
\(866\) | −5.35696 | + | 9.27853i | −0.182037 | + | 0.315297i | ||||
\(867\) | 16.6536 | + | 17.3032i | 0.565584 | + | 0.587648i | ||||
\(868\) | −3.16480 | − | 5.48160i | −0.107420 | − | 0.186058i | ||||
\(869\) | −22.0551 | − | 38.2005i | −0.748167 | − | 1.29586i | ||||
\(870\) | −33.2377 | + | 8.22794i | −1.12686 | + | 0.278953i | ||||
\(871\) | 0.760389 | − | 1.31703i | 0.0257648 | − | 0.0446259i | ||||
\(872\) | −1.06132 | −0.0359409 | ||||||||
\(873\) | 32.1716 | + | 20.2534i | 1.08884 | + | 0.685472i | ||||
\(874\) | −3.17269 | −0.107318 | ||||||||
\(875\) | −11.1573 | + | 19.3250i | −0.377186 | + | 0.653305i | ||||
\(876\) | 4.89603 | − | 16.9671i | 0.165422 | − | 0.573265i | ||||
\(877\) | 7.84509 | + | 13.5881i | 0.264910 | + | 0.458837i | 0.967540 | − | 0.252718i | \(-0.0813245\pi\) |
−0.702630 | + | 0.711555i | \(0.747991\pi\) | |||||||
\(878\) | −15.9496 | − | 27.6255i | −0.538274 | − | 0.932317i | ||||
\(879\) | −5.57384 | + | 19.3160i | −0.188001 | + | 0.651513i | ||||
\(880\) | 5.71057 | − | 9.89100i | 0.192503 | − | 0.333425i | ||||
\(881\) | 15.9802 | 0.538385 | 0.269193 | − | 0.963086i | \(-0.413243\pi\) | ||||
0.269193 | + | 0.963086i | \(0.413243\pi\) | |||||||
\(882\) | 0.645441 | − | 16.8619i | 0.0217331 | − | 0.567771i | ||||
\(883\) | 50.2366 | 1.69060 | 0.845298 | − | 0.534296i | \(-0.179423\pi\) | ||||
0.845298 | + | 0.534296i | \(0.179423\pi\) | |||||||
\(884\) | −1.50692 | + | 2.61006i | −0.0506831 | + | 0.0877857i | ||||
\(885\) | 20.3477 | − | 5.03705i | 0.683982 | − | 0.169318i | ||||
\(886\) | 1.90330 | + | 3.29661i | 0.0639425 | + | 0.110752i | ||||
\(887\) | −1.49885 | − | 2.59609i | −0.0503266 | − | 0.0871682i | 0.839765 | − | 0.542951i | \(-0.182693\pi\) |
−0.890091 | + | 0.455782i | \(0.849360\pi\) | |||||||
\(888\) | −1.55186 | − | 1.61240i | −0.0520771 | − | 0.0541086i | ||||
\(889\) | −15.7115 | + | 27.2131i | −0.526946 | + | 0.912697i | ||||
\(890\) | 42.3704 | 1.42026 | ||||||||
\(891\) | 20.8614 | − | 30.4854i | 0.698884 | − | 1.02130i | ||||
\(892\) | −23.4346 | −0.784650 | ||||||||
\(893\) | −16.2210 | + | 28.0956i | −0.542815 | + | 0.940183i | ||||
\(894\) | −25.2482 | − | 26.2331i | −0.844425 | − | 0.877366i | ||||
\(895\) | 12.6321 | + | 21.8795i | 0.422246 | + | 0.731351i | ||||
\(896\) | 1.77657 | + | 3.07710i | 0.0593509 | + | 0.102799i | ||||
\(897\) | 2.86199 | − | 0.708481i | 0.0955592 | − | 0.0236555i | ||||
\(898\) | −5.53807 | + | 9.59222i | −0.184808 | + | 0.320096i | ||||
\(899\) | −12.6560 | −0.422100 | ||||||||
\(900\) | −0.314765 | + | 8.22313i | −0.0104922 | + | 0.274104i | ||||
\(901\) | −19.2654 | −0.641825 | ||||||||
\(902\) | −19.1999 | + | 33.2552i | −0.639286 | + | 1.10728i | ||||
\(903\) | −12.9900 | + | 45.0167i | −0.432281 | + | 1.49806i | ||||
\(904\) | 4.66618 | + | 8.08207i | 0.155195 | + | 0.268806i | ||||
\(905\) | −36.7024 | − | 63.5705i | −1.22003 | − | 2.11315i | ||||
\(906\) | −10.7336 | + | 37.1972i | −0.356602 | + | 1.23579i | ||||
\(907\) | −20.7754 | + | 35.9841i | −0.689837 | + | 1.19483i | 0.282053 | + | 0.959399i | \(0.408984\pi\) |
−0.971890 | + | 0.235434i | \(0.924349\pi\) | |||||||
\(908\) | −15.7542 | −0.522821 | ||||||||
\(909\) | −17.8323 | − | 11.2262i | −0.591462 | − | 0.372349i | ||||
\(910\) | −16.8303 | −0.557918 | ||||||||
\(911\) | −0.685864 | + | 1.18795i | −0.0227237 | + | 0.0393586i | −0.877164 | − | 0.480192i | \(-0.840567\pi\) |
0.854440 | + | 0.519550i | \(0.173900\pi\) | |||||||
\(912\) | −5.33424 | + | 1.32048i | −0.176634 | + | 0.0437255i | ||||
\(913\) | 27.4447 | + | 47.5355i | 0.908286 | + | 1.57320i | ||||
\(914\) | −8.43995 | − | 14.6184i | −0.279169 | − | 0.483535i | ||||
\(915\) | 32.3161 | + | 33.5767i | 1.06834 | + | 1.11001i | ||||
\(916\) | 5.92574 | − | 10.2637i | 0.195792 | − | 0.339121i | ||||
\(917\) | −41.5417 | −1.37183 | ||||||||
\(918\) | 1.86746 | + | 9.00826i | 0.0616355 | + | 0.297317i | ||||
\(919\) | 15.6120 | 0.514991 | 0.257496 | − | 0.966279i | \(-0.417103\pi\) | ||||
0.257496 | + | 0.966279i | \(0.417103\pi\) | |||||||
\(920\) | 1.39132 | − | 2.40983i | 0.0458704 | − | 0.0794498i | ||||
\(921\) | −40.5983 | − | 42.1821i | −1.33776 | − | 1.38995i | ||||
\(922\) | 8.64366 | + | 14.9713i | 0.284664 | + | 0.493052i | ||||
\(923\) | −8.36633 | − | 14.4909i | −0.275381 | − | 0.476974i | ||||
\(924\) | 24.5194 | − | 6.06974i | 0.806630 | − | 0.199680i | ||||
\(925\) | 1.77207 | − | 3.06931i | 0.0582652 | − | 0.100918i | ||||
\(926\) | 31.5420 | 1.03653 | ||||||||
\(927\) | −40.1491 | + | 21.1753i | −1.31867 | + | 0.695487i | ||||
\(928\) | 7.10444 | 0.233215 | ||||||||
\(929\) | 23.1938 | − | 40.1728i | 0.760963 | − | 1.31803i | −0.181392 | − | 0.983411i | \(-0.558060\pi\) |
0.942355 | − | 0.334615i | \(-0.108606\pi\) | |||||||
\(930\) | −2.38041 | + | 8.24924i | −0.0780566 | + | 0.270503i | ||||
\(931\) | 8.92280 | + | 15.4547i | 0.292433 | + | 0.506509i | ||||
\(932\) | −0.992956 | − | 1.71985i | −0.0325254 | − | 0.0563356i | ||||
\(933\) | −2.28664 | + | 7.92428i | −0.0748611 | + | 0.259429i | ||||
\(934\) | −9.85038 | + | 17.0614i | −0.322314 | + | 0.558265i | ||||
\(935\) | 20.2211 | 0.661302 | ||||||||
\(936\) | 4.51700 | − | 2.38234i | 0.147643 | − | 0.0778693i | ||||
\(937\) | −26.9503 | −0.880429 | −0.440215 | − | 0.897893i | \(-0.645098\pi\) | ||||
−0.440215 | + | 0.897893i | \(0.645098\pi\) | |||||||
\(938\) | 1.58717 | − | 2.74906i | 0.0518230 | − | 0.0897601i | ||||
\(939\) | −40.1914 | + | 9.94931i | −1.31160 | + | 0.324684i | ||||
\(940\) | −14.2268 | − | 24.6415i | −0.464026 | − | 0.803717i | ||||
\(941\) | 5.27501 | + | 9.13659i | 0.171961 | + | 0.297844i | 0.939105 | − | 0.343630i | \(-0.111656\pi\) |
−0.767145 | + | 0.641474i | \(0.778323\pi\) | |||||||
\(942\) | 5.09056 | + | 5.28915i | 0.165860 | + | 0.172330i | ||||
\(943\) | −4.67784 | + | 8.10225i | −0.152331 | + | 0.263846i | ||||
\(944\) | −4.34925 | −0.141556 | ||||||||
\(945\) | −38.3513 | + | 34.1840i | −1.24757 | + | 1.11200i | ||||
\(946\) | −31.2480 | −1.01596 | ||||||||
\(947\) | −23.7353 | + | 41.1108i | −0.771294 | + | 1.33592i | 0.165560 | + | 0.986200i | \(0.447057\pi\) |
−0.936854 | + | 0.349721i | \(0.886277\pi\) | |||||||
\(948\) | −12.9081 | − | 13.4116i | −0.419235 | − | 0.435590i | ||||
\(949\) | −8.67776 | − | 15.0303i | −0.281692 | − | 0.487905i | ||||
\(950\) | −4.35142 | − | 7.53688i | −0.141179 | − | 0.244529i | ||||
\(951\) | 40.9429 | − | 10.1353i | 1.32766 | − | 0.328661i | ||||
\(952\) | −3.14541 | + | 5.44801i | −0.101943 | + | 0.176571i | ||||
\(953\) | −35.8534 | −1.16140 | −0.580702 | − | 0.814116i | \(-0.697222\pi\) | ||||
−0.580702 | + | 0.814116i | \(0.697222\pi\) | |||||||
\(954\) | 27.6256 | + | 17.3914i | 0.894412 | + | 0.563069i | ||||
\(955\) | −5.73869 | −0.185700 | ||||||||
\(956\) | −7.79942 | + | 13.5090i | −0.252251 | + | 0.436912i | ||||
\(957\) | 14.0027 | − | 48.5262i | 0.452644 | − | 1.56863i | ||||
\(958\) | 8.22003 | + | 14.2375i | 0.265577 | + | 0.459993i | ||||
\(959\) | −25.5487 | − | 44.2517i | −0.825011 | − | 1.42896i | ||||
\(960\) | 1.33624 | − | 4.63072i | 0.0431271 | − | 0.149456i | ||||
\(961\) | 13.9133 | − | 24.0985i | 0.448815 | − | 0.777371i | ||||
\(962\) | −2.19937 | −0.0709107 | ||||||||
\(963\) | −0.899107 | + | 23.4889i | −0.0289733 | + | 0.756918i | ||||
\(964\) | 0.898250 | 0.0289307 | ||||||||
\(965\) | −7.77512 | + | 13.4669i | −0.250290 | + | 0.433515i | ||||
\(966\) | 5.97389 | − | 1.47883i | 0.192207 | − | 0.0475804i | ||||
\(967\) | 4.23819 | + | 7.34075i | 0.136291 | + | 0.236063i | 0.926090 | − | 0.377303i | \(-0.123148\pi\) |
−0.789799 | + | 0.613366i | \(0.789815\pi\) | |||||||
\(968\) | 2.92320 | + | 5.06312i | 0.0939551 | + | 0.162735i | ||||
\(969\) | −6.74683 | − | 7.01003i | −0.216739 | − | 0.225194i | ||||
\(970\) | 17.6307 | − | 30.5373i | 0.566089 | − | 0.980495i | ||||
\(971\) | 34.5376 | 1.10836 | 0.554182 | − | 0.832395i | \(-0.313031\pi\) | ||||
0.554182 | + | 0.832395i | \(0.313031\pi\) | |||||||
\(972\) | 5.45416 | − | 14.6032i | 0.174942 | − | 0.468396i | ||||
\(973\) | −25.6076 | −0.820941 | ||||||||
\(974\) | −11.7953 | + | 20.4301i | −0.377947 | + | 0.654623i | ||||
\(975\) | 5.60833 | + | 5.82711i | 0.179610 | + | 0.186617i | ||||
\(976\) | −4.83454 | − | 8.37368i | −0.154750 | − | 0.268035i | ||||
\(977\) | −21.9704 | − | 38.0538i | −0.702895 | − | 1.21745i | −0.967446 | − | 0.253078i | \(-0.918557\pi\) |
0.264551 | − | 0.964372i | \(-0.414776\pi\) | |||||||
\(978\) | 12.7040 | − | 3.14485i | 0.406229 | − | 0.100561i | ||||
\(979\) | −31.2486 | + | 54.1241i | −0.998709 | + | 1.72981i | ||||
\(980\) | −15.6516 | −0.499973 | ||||||||
\(981\) | −0.121787 | + | 3.18164i | −0.00388835 | + | 0.101582i | ||||
\(982\) | −3.21895 | −0.102721 | ||||||||
\(983\) | 8.73641 | − | 15.1319i | 0.278648 | − | 0.482633i | −0.692401 | − | 0.721513i | \(-0.743447\pi\) |
0.971049 | + | 0.238880i | \(0.0767804\pi\) | |||||||
\(984\) | −4.49267 | + | 15.5693i | −0.143221 | + | 0.496330i | ||||
\(985\) | −32.8984 | − | 56.9818i | −1.04823 | − | 1.81559i | ||||
\(986\) | 6.28920 | + | 10.8932i | 0.200289 | + | 0.346911i | ||||
\(987\) | 17.4470 | − | 60.4623i | 0.555345 | − | 1.92454i | ||||
\(988\) | −2.70035 | + | 4.67715i | −0.0859096 | + | 0.148800i | ||||
\(989\) | −7.61323 | −0.242087 | ||||||||
\(990\) | −28.9960 | − | 18.2542i | −0.921553 | − | 0.580156i | ||||
\(991\) | 17.0866 | 0.542773 | 0.271386 | − | 0.962470i | \(-0.412518\pi\) | ||||
0.271386 | + | 0.962470i | \(0.412518\pi\) | |||||||
\(992\) | 0.890708 | − | 1.54275i | 0.0282800 | − | 0.0489824i | ||||
\(993\) | 32.0415 | − | 7.93181i | 1.01681 | − | 0.251708i | ||||
\(994\) | −17.4632 | − | 30.2471i | −0.553898 | − | 0.959380i | ||||
\(995\) | 4.76326 | + | 8.25020i | 0.151005 | + | 0.261549i | ||||
\(996\) | 16.0624 | + | 16.6890i | 0.508957 | + | 0.528812i | ||||
\(997\) | −17.1355 | + | 29.6796i | −0.542688 | + | 0.939964i | 0.456060 | + | 0.889949i | \(0.349260\pi\) |
−0.998748 | + | 0.0500146i | \(0.984073\pi\) | |||||||
\(998\) | −8.95911 | −0.283596 | ||||||||
\(999\) | −5.01174 | + | 4.46715i | −0.158564 | + | 0.141334i |
(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 | 414.2.e.e.277.2 | yes | 12 | |
3.2 | odd | 2 | 1242.2.e.e.829.2 | 12 | |||
9.2 | odd | 6 | 3726.2.a.x.1.5 | 6 | |||
9.4 | even | 3 | inner | 414.2.e.e.139.2 | ✓ | 12 | |
9.5 | odd | 6 | 1242.2.e.e.415.2 | 12 | |||
9.7 | even | 3 | 3726.2.a.w.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.2.e.e.139.2 | ✓ | 12 | 9.4 | even | 3 | inner | |
414.2.e.e.277.2 | yes | 12 | 1.1 | even | 1 | trivial | |
1242.2.e.e.415.2 | 12 | 9.5 | odd | 6 | |||
1242.2.e.e.829.2 | 12 | 3.2 | odd | 2 | |||
3726.2.a.w.1.2 | 6 | 9.7 | even | 3 | |||
3726.2.a.x.1.5 | 6 | 9.2 | odd | 6 |