Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(451,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + \cdots + 101626561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 451.8 | ||
Root | \(1.92573 - 3.33546i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.451 |
Dual form | 1050.3.p.i.901.8 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 1.22474i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | + | 0.866025i | 0.500000 | + | 0.288675i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 2.67372 | − | 6.46925i | 0.381960 | − | 0.924179i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.578394 | + | 1.00181i | −0.0525813 | + | 0.0910735i | −0.891118 | − | 0.453772i | \(-0.850078\pi\) |
0.838537 | + | 0.544845i | \(0.183412\pi\) | |||||||
\(12\) | −3.00000 | + | 1.73205i | −0.250000 | + | 0.144338i | ||||
\(13\) | − | 14.8176i | − | 1.13981i | −0.821710 | − | 0.569906i | \(-0.806979\pi\) | ||
0.821710 | − | 0.569906i | \(-0.193021\pi\) | |||||||
\(14\) | 9.81379 | − | 1.29982i | 0.700985 | − | 0.0928446i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −10.9271 | − | 6.30878i | −0.642772 | − | 0.371105i | 0.142909 | − | 0.989736i | \(-0.454354\pi\) |
−0.785682 | + | 0.618631i | \(0.787688\pi\) | |||||||
\(18\) | −2.12132 | + | 3.67423i | −0.117851 | + | 0.204124i | ||||
\(19\) | 16.7162 | − | 9.65108i | 0.879798 | − | 0.507951i | 0.00920603 | − | 0.999958i | \(-0.497070\pi\) |
0.870592 | + | 0.492006i | \(0.163736\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.61312 | − | 7.38837i | 0.457768 | − | 0.351827i | ||||
\(22\) | −1.63595 | −0.0743612 | ||||||||
\(23\) | −12.1504 | − | 21.0450i | −0.528277 | − | 0.915002i | −0.999457 | − | 0.0329648i | \(-0.989505\pi\) |
0.471180 | − | 0.882037i | \(-0.343828\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 18.1477 | − | 10.4776i | 0.697990 | − | 0.402985i | ||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 8.53135 | + | 11.1003i | 0.304691 | + | 0.396438i | ||||
\(29\) | 49.0382 | 1.69097 | 0.845486 | − | 0.533998i | \(-0.179311\pi\) | ||||
0.845486 | + | 0.533998i | \(0.179311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −24.9581 | − | 14.4096i | −0.805100 | − | 0.464825i | 0.0401515 | − | 0.999194i | \(-0.487216\pi\) |
−0.845251 | + | 0.534369i | \(0.820549\pi\) | |||||||
\(32\) | 2.82843 | − | 4.89898i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.73518 | + | 1.00181i | −0.0525813 | + | 0.0303578i | ||||
\(34\) | − | 17.8439i | − | 0.524822i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −26.6579 | − | 46.1728i | −0.720484 | − | 1.24791i | −0.960806 | − | 0.277221i | \(-0.910586\pi\) |
0.240322 | − | 0.970693i | \(-0.422747\pi\) | |||||||
\(38\) | 23.6402 | + | 13.6487i | 0.622111 | + | 0.359176i | ||||
\(39\) | 12.8324 | − | 22.2264i | 0.329036 | − | 0.569906i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 38.0398i | 0.927800i | 0.885888 | + | 0.463900i | \(0.153550\pi\) | ||||
−0.885888 | + | 0.463900i | \(0.846450\pi\) | |||||||
\(42\) | 15.8464 | + | 6.54925i | 0.377294 | + | 0.155935i | ||||
\(43\) | 63.5774 | 1.47854 | 0.739272 | − | 0.673407i | \(-0.235170\pi\) | ||||
0.739272 | + | 0.673407i | \(0.235170\pi\) | |||||||
\(44\) | −1.15679 | − | 2.00362i | −0.0262906 | − | 0.0455367i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.1832 | − | 29.7622i | 0.373548 | − | 0.647004i | ||||
\(47\) | −21.8175 | + | 12.5964i | −0.464203 | + | 0.268008i | −0.713810 | − | 0.700340i | \(-0.753032\pi\) |
0.249607 | + | 0.968347i | \(0.419699\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | −34.7024 | − | 34.5940i | −0.708213 | − | 0.705999i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.9271 | − | 18.9263i | −0.214257 | − | 0.371105i | ||||
\(52\) | 25.6648 | + | 14.8176i | 0.493553 | + | 0.284953i | ||||
\(53\) | 10.4160 | − | 18.0411i | 0.196529 | − | 0.340397i | −0.750872 | − | 0.660448i | \(-0.770366\pi\) |
0.947401 | + | 0.320050i | \(0.103700\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.56243 | + | 18.2978i | −0.135043 | + | 0.326747i | ||||
\(57\) | 33.4323 | 0.586532 | ||||||||
\(58\) | 34.6752 | + | 60.0593i | 0.597849 | + | 1.03550i | ||||
\(59\) | 21.1419 | + | 12.2063i | 0.358337 | + | 0.206886i | 0.668351 | − | 0.743846i | \(-0.267000\pi\) |
−0.310014 | + | 0.950732i | \(0.600334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.53376 | − | 3.19492i | 0.0907174 | − | 0.0523757i | −0.453955 | − | 0.891025i | \(-0.649987\pi\) |
0.544672 | + | 0.838649i | \(0.316654\pi\) | |||||||
\(62\) | − | 40.7564i | − | 0.657361i | ||||||
\(63\) | 20.8182 | − | 2.75734i | 0.330447 | − | 0.0437674i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.45392 | − | 1.41677i | −0.0371806 | − | 0.0214662i | ||||
\(67\) | 62.2451 | − | 107.812i | 0.929031 | − | 1.60913i | 0.144085 | − | 0.989565i | \(-0.453976\pi\) |
0.784946 | − | 0.619564i | \(-0.212690\pi\) | |||||||
\(68\) | 21.8543 | − | 12.6176i | 0.321386 | − | 0.185552i | ||||
\(69\) | − | 42.0901i | − | 0.610001i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −118.973 | −1.67567 | −0.837835 | − | 0.545924i | \(-0.816179\pi\) | ||||
−0.837835 | + | 0.545924i | \(0.816179\pi\) | |||||||
\(72\) | −4.24264 | − | 7.34847i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 34.2336 | + | 19.7648i | 0.468953 | + | 0.270750i | 0.715801 | − | 0.698304i | \(-0.246062\pi\) |
−0.246848 | + | 0.969054i | \(0.579395\pi\) | |||||||
\(74\) | 37.7000 | − | 65.2983i | 0.509459 | − | 0.882409i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 38.6043i | 0.507951i | ||||||||
\(77\) | 4.93448 | + | 6.42033i | 0.0640842 | + | 0.0833809i | ||||
\(78\) | 36.2955 | 0.465327 | ||||||||
\(79\) | 46.4356 | + | 80.4288i | 0.587792 | + | 1.01809i | 0.994521 | + | 0.104537i | \(0.0333360\pi\) |
−0.406729 | + | 0.913549i | \(0.633331\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −46.5891 | + | 26.8982i | −0.568159 | + | 0.328027i | ||||
\(83\) | − | 5.79665i | − | 0.0698392i | −0.999390 | − | 0.0349196i | \(-0.988882\pi\) | ||
0.999390 | − | 0.0349196i | \(-0.0111175\pi\) | |||||||
\(84\) | 3.18391 | + | 24.0388i | 0.0379037 | + | 0.286176i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 44.9560 | + | 77.8661i | 0.522744 | + | 0.905420i | ||||
\(87\) | 73.5573 | + | 42.4683i | 0.845486 | + | 0.488142i | ||||
\(88\) | 1.63595 | − | 2.83354i | 0.0185903 | − | 0.0321993i | ||||
\(89\) | 131.622 | − | 75.9919i | 1.47890 | − | 0.853842i | 0.479182 | − | 0.877715i | \(-0.340933\pi\) |
0.999715 | + | 0.0238738i | \(0.00759998\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −95.8586 | − | 39.6181i | −1.05339 | − | 0.435363i | ||||
\(92\) | 48.6014 | 0.528277 | ||||||||
\(93\) | −24.9581 | − | 43.2287i | −0.268367 | − | 0.464825i | ||||
\(94\) | −30.8546 | − | 17.8139i | −0.328241 | − | 0.189510i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | − | 4.89898i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | 144.310i | 1.48773i | 0.668331 | + | 0.743864i | \(0.267009\pi\) | ||||
−0.668331 | + | 0.743864i | \(0.732991\pi\) | |||||||
\(98\) | 17.8305 | − | 66.9632i | 0.181943 | − | 0.683298i | ||||
\(99\) | −3.47036 | −0.0350542 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −33.8480 | − | 19.5422i | −0.335129 | − | 0.193487i | 0.322987 | − | 0.946403i | \(-0.395313\pi\) |
−0.658116 | + | 0.752917i | \(0.728646\pi\) | |||||||
\(102\) | 15.4533 | − | 26.7659i | 0.151503 | − | 0.262411i | ||||
\(103\) | −32.7730 | + | 18.9215i | −0.318185 | + | 0.183704i | −0.650583 | − | 0.759435i | \(-0.725475\pi\) |
0.332398 | + | 0.943139i | \(0.392142\pi\) | |||||||
\(104\) | 41.9104i | 0.402985i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 29.4609 | 0.277933 | ||||||||
\(107\) | 41.5160 | + | 71.9079i | 0.388000 | + | 0.672036i | 0.992180 | − | 0.124811i | \(-0.0398326\pi\) |
−0.604180 | + | 0.796848i | \(0.706499\pi\) | |||||||
\(108\) | −9.00000 | − | 5.19615i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 23.8962 | − | 41.3894i | 0.219231 | − | 0.379719i | −0.735342 | − | 0.677696i | \(-0.762978\pi\) |
0.954573 | + | 0.297977i | \(0.0963118\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 92.3457i | − | 0.831943i | ||||||
\(112\) | −27.7576 | + | 3.67646i | −0.247836 | + | 0.0328255i | ||||
\(113\) | 16.2283 | 0.143613 | 0.0718064 | − | 0.997419i | \(-0.477124\pi\) | ||||
0.0718064 | + | 0.997419i | \(0.477124\pi\) | |||||||
\(114\) | 23.6402 | + | 40.9461i | 0.207370 | + | 0.359176i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −49.0382 | + | 84.9366i | −0.422743 | + | 0.732212i | ||||
\(117\) | 38.4972 | − | 22.2264i | 0.329036 | − | 0.189969i | ||||
\(118\) | 34.5246i | 0.292581i | ||||||||
\(119\) | −70.0292 | + | 53.8224i | −0.588481 | + | 0.452289i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 59.8309 | + | 103.630i | 0.494470 | + | 0.856448i | ||||
\(122\) | 7.82592 | + | 4.51830i | 0.0641469 | + | 0.0370352i | ||||
\(123\) | −32.9434 | + | 57.0597i | −0.267833 | + | 0.463900i | ||||
\(124\) | 49.9162 | − | 28.8191i | 0.402550 | − | 0.232412i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.0977 | + | 23.5472i | 0.143633 | + | 0.186883i | ||||
\(127\) | −80.5643 | −0.634365 | −0.317182 | − | 0.948365i | \(-0.602737\pi\) | ||||
−0.317182 | + | 0.948365i | \(0.602737\pi\) | |||||||
\(128\) | 5.65685 | + | 9.79796i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 95.3661 | + | 55.0597i | 0.739272 | + | 0.426819i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 107.981 | − | 62.3429i | 0.824283 | − | 0.475900i | −0.0276082 | − | 0.999619i | \(-0.508789\pi\) |
0.851891 | + | 0.523719i | \(0.175456\pi\) | |||||||
\(132\) | − | 4.00723i | − | 0.0303578i | ||||||
\(133\) | −17.7409 | − | 133.945i | −0.133390 | − | 1.00711i | ||||
\(134\) | 176.056 | 1.31385 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 30.9066 | + | 17.8439i | 0.227254 | + | 0.131205i | ||||
\(137\) | −38.0330 | + | 65.8750i | −0.277613 | + | 0.480840i | −0.970791 | − | 0.239927i | \(-0.922877\pi\) |
0.693178 | + | 0.720766i | \(0.256210\pi\) | |||||||
\(138\) | 51.5496 | − | 29.7622i | 0.373548 | − | 0.215668i | ||||
\(139\) | − | 91.7680i | − | 0.660201i | −0.943946 | − | 0.330101i | \(-0.892917\pi\) | ||
0.943946 | − | 0.330101i | \(-0.107083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −43.6350 | −0.309468 | ||||||||
\(142\) | −84.1263 | − | 145.711i | −0.592439 | − | 1.02613i | ||||
\(143\) | 14.8444 | + | 8.57039i | 0.103807 | + | 0.0599328i | ||||
\(144\) | 6.00000 | − | 10.3923i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 55.9032i | 0.382898i | ||||||||
\(147\) | −22.0944 | − | 81.9441i | −0.150302 | − | 0.557443i | ||||
\(148\) | 106.632 | 0.720484 | ||||||||
\(149\) | 49.4579 | + | 85.6637i | 0.331933 | + | 0.574924i | 0.982891 | − | 0.184190i | \(-0.0589660\pi\) |
−0.650958 | + | 0.759114i | \(0.725633\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −48.8950 | + | 84.6886i | −0.323808 | + | 0.560852i | −0.981270 | − | 0.192635i | \(-0.938297\pi\) |
0.657462 | + | 0.753487i | \(0.271630\pi\) | |||||||
\(152\) | −47.2804 | + | 27.2974i | −0.311055 | + | 0.179588i | ||||
\(153\) | − | 37.8527i | − | 0.247403i | ||||||
\(154\) | −4.37406 | + | 10.5833i | −0.0284030 | + | 0.0687230i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 25.6648 | + | 44.4527i | 0.164518 | + | 0.284953i | ||||
\(157\) | −115.530 | − | 66.7013i | −0.735860 | − | 0.424849i | 0.0847022 | − | 0.996406i | \(-0.473006\pi\) |
−0.820562 | + | 0.571557i | \(0.806339\pi\) | |||||||
\(158\) | −65.6698 | + | 113.743i | −0.415632 | + | 0.719895i | ||||
\(159\) | 31.2480 | − | 18.0411i | 0.196529 | − | 0.113466i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −168.632 | + | 22.3352i | −1.04741 | + | 0.138728i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | −16.3746 | − | 28.3616i | −0.100458 | − | 0.173998i | 0.811416 | − | 0.584469i | \(-0.198697\pi\) |
−0.911873 | + | 0.410472i | \(0.865364\pi\) | |||||||
\(164\) | −65.8869 | − | 38.0398i | −0.401749 | − | 0.231950i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.09942 | − | 4.09885i | 0.0427676 | − | 0.0246919i | ||||
\(167\) | 171.659i | 1.02790i | 0.857821 | + | 0.513948i | \(0.171818\pi\) | ||||
−0.857821 | + | 0.513948i | \(0.828182\pi\) | |||||||
\(168\) | −27.1900 | + | 20.8975i | −0.161845 | + | 0.124390i | ||||
\(169\) | −50.5603 | −0.299173 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 50.1485 | + | 28.9532i | 0.293266 | + | 0.169317i | ||||
\(172\) | −63.5774 | + | 110.119i | −0.369636 | + | 0.640229i | ||||
\(173\) | −175.336 | + | 101.230i | −1.01350 | + | 0.585145i | −0.912215 | − | 0.409712i | \(-0.865629\pi\) |
−0.101287 | + | 0.994857i | \(0.532296\pi\) | |||||||
\(174\) | 120.119i | 0.690336i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.62715 | 0.0262906 | ||||||||
\(177\) | 21.1419 | + | 36.6188i | 0.119446 | + | 0.206886i | ||||
\(178\) | 186.141 | + | 107.469i | 1.04574 | + | 0.603757i | ||||
\(179\) | 39.3459 | − | 68.1491i | 0.219810 | − | 0.380721i | −0.734940 | − | 0.678132i | \(-0.762790\pi\) |
0.954750 | + | 0.297411i | \(0.0961230\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 58.1509i | − | 0.321276i | −0.987013 | − | 0.160638i | \(-0.948645\pi\) | ||
0.987013 | − | 0.160638i | \(-0.0513551\pi\) | |||||||
\(182\) | −19.2602 | − | 145.416i | −0.105825 | − | 0.798992i | ||||
\(183\) | 11.0675 | 0.0604783 | ||||||||
\(184\) | 34.3664 | + | 59.5244i | 0.186774 | + | 0.323502i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 35.2961 | − | 61.1346i | 0.189764 | − | 0.328681i | ||||
\(187\) | 12.6404 | − | 7.29793i | 0.0675956 | − | 0.0390263i | ||||
\(188\) | − | 50.3854i | − | 0.268008i | ||||||
\(189\) | 33.6152 | + | 13.8931i | 0.177858 | + | 0.0735083i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −184.204 | − | 319.051i | −0.964419 | − | 1.67042i | −0.711168 | − | 0.703022i | \(-0.751834\pi\) |
−0.253251 | − | 0.967401i | \(-0.581500\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 140.409 | − | 243.196i | 0.727510 | − | 1.26008i | −0.230422 | − | 0.973091i | \(-0.574011\pi\) |
0.957932 | − | 0.286994i | \(-0.0926559\pi\) | |||||||
\(194\) | −176.742 | + | 102.042i | −0.911044 | + | 0.525991i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 94.6209 | − | 25.5124i | 0.482760 | − | 0.130165i | ||||
\(197\) | −7.61779 | −0.0386690 | −0.0193345 | − | 0.999813i | \(-0.506155\pi\) | ||||
−0.0193345 | + | 0.999813i | \(0.506155\pi\) | |||||||
\(198\) | −2.45392 | − | 4.25031i | −0.0123935 | − | 0.0214662i | ||||
\(199\) | −174.795 | − | 100.918i | −0.878366 | − | 0.507125i | −0.00824641 | − | 0.999966i | \(-0.502625\pi\) |
−0.870119 | + | 0.492841i | \(0.835958\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 186.735 | − | 107.812i | 0.929031 | − | 0.536376i | ||||
\(202\) | − | 55.2736i | − | 0.273632i | ||||||
\(203\) | 131.114 | − | 317.240i | 0.645884 | − | 1.56276i | ||||
\(204\) | 43.7085 | 0.214257 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −46.3481 | − | 26.7591i | −0.224991 | − | 0.129898i | ||||
\(207\) | 36.4511 | − | 63.1351i | 0.176092 | − | 0.305001i | ||||
\(208\) | −51.3296 | + | 29.6351i | −0.246777 | + | 0.142477i | ||||
\(209\) | 22.3285i | 0.106835i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 30.3818 | 0.143989 | 0.0719947 | − | 0.997405i | \(-0.477064\pi\) | ||||
0.0719947 | + | 0.997405i | \(0.477064\pi\) | |||||||
\(212\) | 20.8320 | + | 36.0821i | 0.0982643 | + | 0.170199i | ||||
\(213\) | −178.459 | − | 103.033i | −0.837835 | − | 0.483724i | ||||
\(214\) | −58.7126 | + | 101.693i | −0.274358 | + | 0.475202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −159.950 | + | 122.933i | −0.737097 | + | 0.566512i | ||||
\(218\) | 67.5886 | 0.310039 | ||||||||
\(219\) | 34.2336 | + | 59.2943i | 0.156318 | + | 0.270750i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −93.4808 | + | 161.914i | −0.422990 | + | 0.732640i | ||||
\(222\) | 113.100 | − | 65.2983i | 0.509459 | − | 0.294136i | ||||
\(223\) | − | 16.7377i | − | 0.0750569i | −0.999296 | − | 0.0375284i | \(-0.988052\pi\) | ||
0.999296 | − | 0.0375284i | \(-0.0119485\pi\) | |||||||
\(224\) | −24.1303 | − | 31.3963i | −0.107725 | − | 0.140162i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.4751 | + | 19.8755i | 0.0507748 | + | 0.0879446i | ||||
\(227\) | 366.738 | + | 211.736i | 1.61558 | + | 0.932758i | 0.988044 | + | 0.154175i | \(0.0492719\pi\) |
0.627541 | + | 0.778583i | \(0.284061\pi\) | |||||||
\(228\) | −33.4323 | + | 57.9065i | −0.146633 | + | 0.253976i | ||||
\(229\) | −350.596 | + | 202.417i | −1.53099 | + | 0.883916i | −0.531672 | + | 0.846951i | \(0.678436\pi\) |
−0.999317 | + | 0.0369660i | \(0.988231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.84155 | + | 13.9039i | 0.00797209 | + | 0.0601900i | ||||
\(232\) | −138.701 | −0.597849 | ||||||||
\(233\) | 138.649 | + | 240.147i | 0.595061 | + | 1.03068i | 0.993538 | + | 0.113497i | \(0.0362053\pi\) |
−0.398478 | + | 0.917178i | \(0.630461\pi\) | |||||||
\(234\) | 54.4432 | + | 31.4328i | 0.232663 | + | 0.134328i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −42.2838 | + | 24.4125i | −0.179169 | + | 0.103443i | ||||
\(237\) | 160.858i | 0.678724i | ||||||||
\(238\) | −115.437 | − | 47.7097i | −0.485029 | − | 0.200461i | ||||
\(239\) | 290.247 | 1.21442 | 0.607211 | − | 0.794541i | \(-0.292288\pi\) | ||||
0.607211 | + | 0.794541i | \(0.292288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −350.574 | − | 202.404i | −1.45466 | − | 0.839850i | −0.455922 | − | 0.890020i | \(-0.650690\pi\) |
−0.998741 | + | 0.0501703i | \(0.984024\pi\) | |||||||
\(242\) | −84.6137 | + | 146.555i | −0.349643 | + | 0.605600i | ||||
\(243\) | −13.5000 | + | 7.79423i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 12.7797i | 0.0523757i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −93.1781 | −0.378773 | ||||||||
\(247\) | −143.005 | − | 247.693i | −0.578970 | − | 1.00280i | ||||
\(248\) | 70.5922 | + | 40.7564i | 0.284646 | + | 0.164340i | ||||
\(249\) | 5.02005 | − | 8.69498i | 0.0201608 | − | 0.0349196i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 155.805i | 0.620739i | 0.950616 | + | 0.310369i | \(0.100453\pi\) | ||||
−0.950616 | + | 0.310369i | \(0.899547\pi\) | |||||||
\(252\) | −16.0423 | + | 38.8155i | −0.0636600 | + | 0.154030i | ||||
\(253\) | 28.1108 | 0.111110 | ||||||||
\(254\) | −56.9676 | − | 98.6707i | −0.224282 | − | 0.388467i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 22.4315 | − | 12.9508i | 0.0872821 | − | 0.0503923i | −0.455724 | − | 0.890121i | \(-0.650619\pi\) |
0.543006 | + | 0.839729i | \(0.317286\pi\) | |||||||
\(258\) | 155.732i | 0.603613i | ||||||||
\(259\) | −369.980 | + | 49.0033i | −1.42849 | + | 0.189202i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 73.5573 | + | 127.405i | 0.281829 | + | 0.488142i | ||||
\(262\) | 152.708 | + | 88.1662i | 0.582856 | + | 0.336512i | ||||
\(263\) | −157.902 | + | 273.495i | −0.600389 | + | 1.03990i | 0.392373 | + | 0.919806i | \(0.371654\pi\) |
−0.992762 | + | 0.120098i | \(0.961679\pi\) | |||||||
\(264\) | 4.90784 | − | 2.83354i | 0.0185903 | − | 0.0107331i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 151.504 | − | 116.442i | 0.569564 | − | 0.437751i | ||||
\(267\) | 263.244 | 0.985931 | ||||||||
\(268\) | 124.490 | + | 215.623i | 0.464516 | + | 0.804565i | ||||
\(269\) | −41.4157 | − | 23.9114i | −0.153962 | − | 0.0888899i | 0.421040 | − | 0.907042i | \(-0.361665\pi\) |
−0.575002 | + | 0.818152i | \(0.694999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 294.580 | − | 170.076i | 1.08701 | − | 0.627587i | 0.154233 | − | 0.988035i | \(-0.450709\pi\) |
0.932779 | + | 0.360448i | \(0.117376\pi\) | |||||||
\(272\) | 50.4703i | 0.185552i | ||||||||
\(273\) | −109.478 | − | 142.443i | −0.401017 | − | 0.521769i | ||||
\(274\) | −107.573 | −0.392604 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 72.9022 | + | 42.0901i | 0.264138 | + | 0.152500i | ||||
\(277\) | 105.293 | − | 182.374i | 0.380121 | − | 0.658388i | −0.610959 | − | 0.791663i | \(-0.709216\pi\) |
0.991079 | + | 0.133274i | \(0.0425491\pi\) | |||||||
\(278\) | 112.392 | − | 64.8898i | 0.404289 | − | 0.233416i | ||||
\(279\) | − | 86.4574i | − | 0.309883i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 471.785 | 1.67895 | 0.839476 | − | 0.543397i | \(-0.182862\pi\) | ||||
0.839476 | + | 0.543397i | \(0.182862\pi\) | |||||||
\(282\) | −30.8546 | − | 53.4418i | −0.109414 | − | 0.189510i | ||||
\(283\) | −405.534 | − | 234.135i | −1.43298 | − | 0.827333i | −0.435636 | − | 0.900123i | \(-0.643476\pi\) |
−0.997347 | + | 0.0727901i | \(0.976810\pi\) | |||||||
\(284\) | 118.973 | − | 206.067i | 0.418917 | − | 0.725586i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.2407i | 0.0847578i | ||||||||
\(287\) | 246.089 | + | 101.708i | 0.857453 | + | 0.354383i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −64.8985 | − | 112.408i | −0.224562 | − | 0.388953i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −124.976 | + | 216.464i | −0.429470 | + | 0.743864i | ||||
\(292\) | −68.4671 | + | 39.5295i | −0.234476 | + | 0.135375i | ||||
\(293\) | 63.5067i | 0.216746i | 0.994110 | + | 0.108373i | \(0.0345642\pi\) | ||||
−0.994110 | + | 0.108373i | \(0.965436\pi\) | |||||||
\(294\) | 84.7375 | − | 85.0032i | 0.288223 | − | 0.289127i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 75.3999 | + | 130.597i | 0.254730 | + | 0.441204i | ||||
\(297\) | −5.20555 | − | 3.00542i | −0.0175271 | − | 0.0101193i | ||||
\(298\) | −69.9441 | + | 121.147i | −0.234712 | + | 0.406533i | ||||
\(299\) | −311.836 | + | 180.039i | −1.04293 | + | 0.602136i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 169.988 | − | 411.298i | 0.564745 | − | 1.36644i | ||||
\(302\) | −138.296 | −0.457934 | ||||||||
\(303\) | −33.8480 | − | 58.6265i | −0.111710 | − | 0.193487i | ||||
\(304\) | −66.8646 | − | 38.6043i | −0.219949 | − | 0.126988i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 46.3599 | − | 26.7659i | 0.151503 | − | 0.0874703i | ||||
\(307\) | 211.610i | 0.689283i | 0.938734 | + | 0.344642i | \(0.112000\pi\) | ||||
−0.938734 | + | 0.344642i | \(0.888000\pi\) | |||||||
\(308\) | −16.0548 | + | 2.12644i | −0.0521261 | + | 0.00690403i | ||||
\(309\) | −65.5460 | −0.212123 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 58.3090 | + | 33.6647i | 0.187489 | + | 0.108247i | 0.590806 | − | 0.806813i | \(-0.298810\pi\) |
−0.403318 | + | 0.915060i | \(0.632143\pi\) | |||||||
\(312\) | −36.2955 | + | 62.8656i | −0.116332 | + | 0.201492i | ||||
\(313\) | 119.714 | − | 69.1168i | 0.382472 | − | 0.220821i | −0.296421 | − | 0.955057i | \(-0.595793\pi\) |
0.678893 | + | 0.734237i | \(0.262460\pi\) | |||||||
\(314\) | − | 188.660i | − | 0.600827i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −185.742 | −0.587792 | ||||||||
\(317\) | 9.91216 | + | 17.1684i | 0.0312686 | + | 0.0541589i | 0.881236 | − | 0.472676i | \(-0.156712\pi\) |
−0.849968 | + | 0.526835i | \(0.823379\pi\) | |||||||
\(318\) | 44.1914 | + | 25.5139i | 0.138967 | + | 0.0802325i | ||||
\(319\) | −28.3634 | + | 49.1268i | −0.0889135 | + | 0.154003i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 143.816i | 0.448024i | ||||||||
\(322\) | −146.596 | − | 190.738i | −0.455267 | − | 0.592355i | ||||
\(323\) | −243.546 | −0.754013 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.1572 | − | 40.1094i | 0.0710342 | − | 0.123035i | ||||
\(327\) | 71.6885 | − | 41.3894i | 0.219231 | − | 0.126573i | ||||
\(328\) | − | 107.593i | − | 0.328027i | ||||||
\(329\) | 23.1550 | + | 174.822i | 0.0703799 | + | 0.531374i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 131.139 | + | 227.139i | 0.396189 | + | 0.686220i | 0.993252 | − | 0.115974i | \(-0.0369991\pi\) |
−0.597063 | + | 0.802194i | \(0.703666\pi\) | |||||||
\(332\) | 10.0401 | + | 5.79665i | 0.0302412 | + | 0.0174598i | ||||
\(333\) | 79.9737 | − | 138.519i | 0.240161 | − | 0.415972i | ||||
\(334\) | −210.238 | + | 121.381i | −0.629455 | + | 0.363416i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −44.8203 | − | 18.5241i | −0.133394 | − | 0.0551312i | ||||
\(337\) | −578.125 | −1.71550 | −0.857752 | − | 0.514063i | \(-0.828140\pi\) | ||||
−0.857752 | + | 0.514063i | \(0.828140\pi\) | |||||||
\(338\) | −35.7515 | − | 61.9235i | −0.105774 | − | 0.183206i | ||||
\(339\) | 24.3424 | + | 14.0541i | 0.0718064 | + | 0.0414575i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.8712 | − | 16.6688i | 0.0846664 | − | 0.0488822i | ||||
\(342\) | 81.8921i | 0.239451i | ||||||||
\(343\) | −316.582 | + | 132.004i | −0.922978 | + | 0.384852i | ||||
\(344\) | −179.824 | −0.522744 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −247.962 | − | 143.161i | −0.716654 | − | 0.413760i | ||||
\(347\) | 229.861 | − | 398.131i | 0.662423 | − | 1.14735i | −0.317554 | − | 0.948240i | \(-0.602861\pi\) |
0.979977 | − | 0.199110i | \(-0.0638052\pi\) | |||||||
\(348\) | −147.115 | + | 84.9366i | −0.422743 | + | 0.244071i | ||||
\(349\) | − | 389.147i | − | 1.11504i | −0.830165 | − | 0.557518i | \(-0.811754\pi\) | ||
0.830165 | − | 0.557518i | \(-0.188246\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 76.9943 | 0.219357 | ||||||||
\(352\) | 3.27189 | + | 5.66708i | 0.00929515 | + | 0.0160997i | ||||
\(353\) | −559.415 | − | 322.978i | −1.58475 | − | 0.914953i | −0.994153 | − | 0.107983i | \(-0.965561\pi\) |
−0.590593 | − | 0.806970i | \(-0.701106\pi\) | |||||||
\(354\) | −29.8991 | + | 51.7868i | −0.0844608 | + | 0.146290i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 303.968i | 0.853842i | ||||||||
\(357\) | −151.655 | + | 20.0866i | −0.424805 | + | 0.0562649i | ||||
\(358\) | 111.287 | 0.310858 | ||||||||
\(359\) | 33.0206 | + | 57.1934i | 0.0919794 | + | 0.159313i | 0.908344 | − | 0.418224i | \(-0.137347\pi\) |
−0.816365 | + | 0.577537i | \(0.804014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.78661 | − | 10.0227i | 0.0160294 | − | 0.0277637i | ||||
\(362\) | 71.2200 | − | 41.1189i | 0.196740 | − | 0.113588i | ||||
\(363\) | 207.260i | 0.570965i | ||||||||
\(364\) | 164.479 | − | 126.414i | 0.451866 | − | 0.347291i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.82592 | + | 13.5549i | 0.0213823 | + | 0.0370352i | ||||
\(367\) | −519.556 | − | 299.966i | −1.41568 | − | 0.817346i | −0.419768 | − | 0.907631i | \(-0.637889\pi\) |
−0.995916 | + | 0.0902858i | \(0.971222\pi\) | |||||||
\(368\) | −48.6014 | + | 84.1802i | −0.132069 | + | 0.228750i | ||||
\(369\) | −98.8303 | + | 57.0597i | −0.267833 | + | 0.154633i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −88.8627 | − | 115.621i | −0.239522 | − | 0.311646i | ||||
\(372\) | 99.8324 | 0.268367 | ||||||||
\(373\) | 202.376 | + | 350.526i | 0.542564 | + | 0.939748i | 0.998756 | + | 0.0498667i | \(0.0158796\pi\) |
−0.456192 | + | 0.889881i | \(0.650787\pi\) | |||||||
\(374\) | 17.8762 | + | 10.3208i | 0.0477973 | + | 0.0275958i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 61.7093 | − | 35.6279i | 0.164120 | − | 0.0947550i | ||||
\(377\) | − | 726.627i | − | 1.92739i | ||||||
\(378\) | 6.75409 | + | 50.9939i | 0.0178680 | + | 0.134905i | ||||
\(379\) | −239.675 | −0.632388 | −0.316194 | − | 0.948695i | \(-0.602405\pi\) | ||||
−0.316194 | + | 0.948695i | \(0.602405\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −120.846 | − | 69.7707i | −0.317182 | − | 0.183125i | ||||
\(382\) | 260.504 | − | 451.206i | 0.681947 | − | 1.18117i | ||||
\(383\) | −553.486 | + | 319.555i | −1.44513 | + | 0.834347i | −0.998186 | − | 0.0602133i | \(-0.980822\pi\) |
−0.446947 | + | 0.894561i | \(0.647489\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 397.138 | 1.02885 | ||||||||
\(387\) | 95.3661 | + | 165.179i | 0.246424 | + | 0.426819i | ||||
\(388\) | −249.952 | − | 144.310i | −0.644205 | − | 0.371932i | ||||
\(389\) | −260.797 | + | 451.714i | −0.670429 | + | 1.16122i | 0.307353 | + | 0.951596i | \(0.400557\pi\) |
−0.977782 | + | 0.209622i | \(0.932777\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 306.616i | 0.784184i | ||||||||
\(392\) | 98.1533 | + | 97.8465i | 0.250391 | + | 0.249608i | ||||
\(393\) | 215.962 | 0.549522 | ||||||||
\(394\) | −5.38659 | − | 9.32985i | −0.0136716 | − | 0.0236798i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.47036 | − | 6.01085i | 0.00876355 | − | 0.0151789i | ||||
\(397\) | −125.712 | + | 72.5800i | −0.316656 | + | 0.182821i | −0.649901 | − | 0.760019i | \(-0.725190\pi\) |
0.333245 | + | 0.942840i | \(0.391856\pi\) | |||||||
\(398\) | − | 285.439i | − | 0.717182i | ||||||
\(399\) | 89.3887 | − | 216.282i | 0.224032 | − | 0.542060i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −107.021 | − | 185.366i | −0.266886 | − | 0.462260i | 0.701170 | − | 0.712994i | \(-0.252661\pi\) |
−0.968056 | + | 0.250734i | \(0.919328\pi\) | |||||||
\(402\) | 264.084 | + | 152.469i | 0.656924 | + | 0.379275i | ||||
\(403\) | −213.515 | + | 369.818i | −0.529813 | + | 0.917663i | ||||
\(404\) | 67.6960 | − | 39.0843i | 0.167564 | − | 0.0967434i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 481.250 | − | 63.7410i | 1.18535 | − | 0.156998i | ||||
\(407\) | 61.6751 | 0.151536 | ||||||||
\(408\) | 30.9066 | + | 53.5318i | 0.0757515 | + | 0.131205i | ||||
\(409\) | −479.754 | − | 276.986i | −1.17299 | − | 0.677228i | −0.218610 | − | 0.975812i | \(-0.570152\pi\) |
−0.954383 | + | 0.298585i | \(0.903486\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −114.099 | + | 65.8750i | −0.277613 | + | 0.160280i | ||||
\(412\) | − | 75.6861i | − | 0.183704i | ||||||
\(413\) | 135.493 | − | 104.136i | 0.328070 | − | 0.252145i | ||||
\(414\) | 103.099 | 0.249032 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −72.5910 | − | 41.9104i | −0.174497 | − | 0.100746i | ||||
\(417\) | 79.4734 | − | 137.652i | 0.190584 | − | 0.330101i | ||||
\(418\) | −27.3467 | + | 15.7886i | −0.0654228 | + | 0.0377719i | ||||
\(419\) | 268.003i | 0.639626i | 0.947481 | + | 0.319813i | \(0.103620\pi\) | ||||
−0.947481 | + | 0.319813i | \(0.896380\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.12915 | −0.0216844 | −0.0108422 | − | 0.999941i | \(-0.503451\pi\) | ||||
−0.0108422 | + | 0.999941i | \(0.503451\pi\) | |||||||
\(422\) | 21.4831 | + | 37.2099i | 0.0509079 | + | 0.0881751i | ||||
\(423\) | −65.4526 | − | 37.7891i | −0.154734 | − | 0.0893358i | ||||
\(424\) | −29.4609 | + | 51.0278i | −0.0694833 | + | 0.120349i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 291.422i | − | 0.684089i | ||||||
\(427\) | −5.87299 | − | 44.3416i | −0.0137541 | − | 0.103845i | ||||
\(428\) | −166.064 | −0.388000 | ||||||||
\(429\) | 14.8444 | + | 25.7112i | 0.0346022 | + | 0.0599328i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 134.221 | − | 232.478i | 0.311419 | − | 0.539393i | −0.667251 | − | 0.744833i | \(-0.732529\pi\) |
0.978670 | + | 0.205440i | \(0.0658626\pi\) | |||||||
\(432\) | 18.0000 | − | 10.3923i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 472.254i | 1.09066i | 0.838223 | + | 0.545328i | \(0.183595\pi\) | ||||
−0.838223 | + | 0.545328i | \(0.816405\pi\) | |||||||
\(434\) | −263.663 | − | 108.971i | −0.607519 | − | 0.251086i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 47.7924 | + | 82.7788i | 0.109616 | + | 0.189860i | ||||
\(437\) | −406.215 | − | 234.528i | −0.929553 | − | 0.536678i | ||||
\(438\) | −48.4136 | + | 83.8548i | −0.110533 | + | 0.191449i | ||||
\(439\) | 475.788 | − | 274.696i | 1.08380 | − | 0.625731i | 0.151880 | − | 0.988399i | \(-0.451467\pi\) |
0.931919 | + | 0.362667i | \(0.118134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 37.8241 | − | 142.050i | 0.0857689 | − | 0.322110i | ||||
\(442\) | −264.404 | −0.598198 | ||||||||
\(443\) | 235.405 | + | 407.734i | 0.531388 | + | 0.920392i | 0.999329 | + | 0.0366317i | \(0.0116628\pi\) |
−0.467940 | + | 0.883760i | \(0.655004\pi\) | |||||||
\(444\) | 159.947 | + | 92.3457i | 0.360242 | + | 0.207986i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.4994 | − | 11.8353i | 0.0459628 | − | 0.0265366i | ||||
\(447\) | 171.327i | 0.383283i | ||||||||
\(448\) | 21.3898 | − | 51.7540i | 0.0477450 | − | 0.115522i | ||||
\(449\) | 559.525 | 1.24616 | 0.623079 | − | 0.782159i | \(-0.285882\pi\) | ||||
0.623079 | + | 0.782159i | \(0.285882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.1086 | − | 22.0020i | −0.0844980 | − | 0.0487849i | ||||
\(452\) | −16.2283 | + | 28.1082i | −0.0359032 | + | 0.0621862i | ||||
\(453\) | −146.685 | + | 84.6886i | −0.323808 | + | 0.186951i | ||||
\(454\) | 598.880i | 1.31912i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −94.5609 | −0.207370 | ||||||||
\(457\) | 313.689 | + | 543.325i | 0.686409 | + | 1.18890i | 0.972992 | + | 0.230840i | \(0.0741473\pi\) |
−0.286583 | + | 0.958055i | \(0.592519\pi\) | |||||||
\(458\) | −495.818 | − | 286.261i | −1.08257 | − | 0.625023i | ||||
\(459\) | 32.7814 | − | 56.7790i | 0.0714192 | − | 0.123702i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 223.659i | 0.485160i | 0.970131 | + | 0.242580i | \(0.0779936\pi\) | ||||
−0.970131 | + | 0.242580i | \(0.922006\pi\) | |||||||
\(462\) | −15.7265 | + | 12.0870i | −0.0340401 | + | 0.0261623i | ||||
\(463\) | 397.204 | 0.857893 | 0.428946 | − | 0.903330i | \(-0.358885\pi\) | ||||
0.428946 | + | 0.903330i | \(0.358885\pi\) | |||||||
\(464\) | −98.0764 | − | 169.873i | −0.211371 | − | 0.366106i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −196.079 | + | 339.620i | −0.420771 | + | 0.728797i | ||||
\(467\) | 289.014 | − | 166.862i | 0.618874 | − | 0.357307i | −0.157557 | − | 0.987510i | \(-0.550362\pi\) |
0.776430 | + | 0.630203i | \(0.217028\pi\) | |||||||
\(468\) | 88.9054i | 0.189969i | ||||||||
\(469\) | −531.035 | − | 690.937i | −1.13227 | − | 1.47321i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −115.530 | − | 200.104i | −0.245287 | − | 0.424849i | ||||
\(472\) | −59.7983 | − | 34.5246i | −0.126691 | − | 0.0731452i | ||||
\(473\) | −36.7728 | + | 63.6924i | −0.0777438 | + | 0.134656i | ||||
\(474\) | −197.009 | + | 113.743i | −0.415632 | + | 0.239965i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −23.1940 | − | 175.117i | −0.0487268 | − | 0.367892i | ||||
\(477\) | 62.4961 | 0.131019 | ||||||||
\(478\) | 205.235 | + | 355.478i | 0.429363 | + | 0.743678i | ||||
\(479\) | 527.265 | + | 304.417i | 1.10076 | + | 0.635526i | 0.936421 | − | 0.350878i | \(-0.114117\pi\) |
0.164341 | + | 0.986404i | \(0.447450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −684.169 | + | 395.005i | −1.42239 | + | 0.821217i | ||||
\(482\) | − | 572.484i | − | 1.18773i | ||||||
\(483\) | −272.291 | − | 112.537i | −0.563750 | − | 0.232996i | ||||
\(484\) | −239.324 | −0.494470 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | − | 11.0227i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | −159.238 | + | 275.809i | −0.326978 | + | 0.566343i | −0.981911 | − | 0.189344i | \(-0.939364\pi\) |
0.654932 | + | 0.755687i | \(0.272697\pi\) | |||||||
\(488\) | −15.6518 | + | 9.03659i | −0.0320734 | + | 0.0185176i | ||||
\(489\) | − | 56.7232i | − | 0.115998i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 523.303 | 1.06579 | 0.532895 | − | 0.846181i | \(-0.321104\pi\) | ||||
0.532895 | + | 0.846181i | \(0.321104\pi\) | |||||||
\(492\) | −65.8869 | − | 114.119i | −0.133916 | − | 0.231950i | ||||
\(493\) | −535.847 | − | 309.371i | −1.08691 | − | 0.627528i | ||||
\(494\) | 202.240 | − | 350.290i | 0.409393 | − | 0.709090i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 115.277i | 0.232412i | ||||||||
\(497\) | −318.100 | + | 769.663i | −0.640039 | + | 1.54862i | ||||
\(498\) | 14.1988 | 0.0285117 | ||||||||
\(499\) | 391.909 | + | 678.806i | 0.785388 | + | 1.36033i | 0.928767 | + | 0.370664i | \(0.120870\pi\) |
−0.143379 | + | 0.989668i | \(0.545797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −148.661 | + | 257.488i | −0.296728 | + | 0.513948i | ||||
\(502\) | −190.822 | + | 110.171i | −0.380123 | + | 0.219464i | ||||
\(503\) | 58.0772i | 0.115462i | 0.998332 | + | 0.0577308i | \(0.0183865\pi\) | ||||
−0.998332 | + | 0.0577308i | \(0.981613\pi\) | |||||||
\(504\) | −58.8827 | + | 7.79895i | −0.116831 | + | 0.0154741i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 19.8773 | + | 34.4286i | 0.0392833 | + | 0.0680406i | ||||
\(507\) | −75.8404 | − | 43.7865i | −0.149587 | − | 0.0863639i | ||||
\(508\) | 80.5643 | − | 139.541i | 0.158591 | − | 0.274688i | ||||
\(509\) | −811.110 | + | 468.295i | −1.59354 | + | 0.920029i | −0.600843 | + | 0.799367i | \(0.705168\pi\) |
−0.992694 | + | 0.120662i | \(0.961498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 219.394 | − | 168.620i | 0.429343 | − | 0.329981i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 50.1485 | + | 86.8597i | 0.0977553 | + | 0.169317i | ||||
\(514\) | 31.7229 | + | 18.3152i | 0.0617178 | + | 0.0356328i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −190.732 | + | 110.119i | −0.369636 | + | 0.213410i | ||||
\(517\) | − | 29.1426i | − | 0.0563687i | ||||||
\(518\) | −321.632 | − | 418.480i | −0.620910 | − | 0.807876i | ||||
\(519\) | −350.672 | −0.675668 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −607.133 | − | 350.528i | −1.16532 | − | 0.672799i | −0.212749 | − | 0.977107i | \(-0.568242\pi\) |
−0.952574 | + | 0.304308i | \(0.901575\pi\) | |||||||
\(522\) | −104.026 | + | 180.178i | −0.199283 | + | 0.345168i | ||||
\(523\) | 594.464 | − | 343.214i | 1.13664 | − | 0.656241i | 0.191046 | − | 0.981581i | \(-0.438812\pi\) |
0.945597 | + | 0.325340i | \(0.105479\pi\) | |||||||
\(524\) | 249.372i | 0.475900i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −446.615 | −0.849078 | ||||||||
\(527\) | 181.814 | + | 314.910i | 0.344997 | + | 0.597553i | ||||
\(528\) | 6.94073 | + | 4.00723i | 0.0131453 | + | 0.00758945i | ||||
\(529\) | −30.7626 | + | 53.2824i | −0.0581524 | + | 0.100723i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 73.2376i | 0.137924i | ||||||||
\(532\) | 249.741 | + | 103.217i | 0.469438 | + | 0.194017i | ||||
\(533\) | 563.657 | 1.05752 | ||||||||
\(534\) | 186.141 | + | 322.406i | 0.348579 | + | 0.603757i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −176.056 | + | 304.937i | −0.328462 | + | 0.568913i | ||||
\(537\) | 118.038 | − | 68.1491i | 0.219810 | − | 0.126907i | ||||
\(538\) | − | 67.6316i | − | 0.125709i | ||||||
\(539\) | 54.7282 | − | 14.7562i | 0.101537 | − | 0.0273770i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −398.250 | − | 689.789i | −0.736136 | − | 1.27503i | −0.954223 | − | 0.299096i | \(-0.903315\pi\) |
0.218087 | − | 0.975929i | \(-0.430018\pi\) | |||||||
\(542\) | 416.599 | + | 240.524i | 0.768634 | + | 0.443771i | ||||
\(543\) | 50.3602 | − | 87.2263i | 0.0927443 | − | 0.160638i | ||||
\(544\) | −61.8132 | + | 35.6879i | −0.113627 | + | 0.0656027i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 97.0440 | − | 234.805i | 0.177736 | − | 0.430045i | ||||
\(547\) | 395.055 | 0.722221 | 0.361111 | − | 0.932523i | \(-0.382398\pi\) | ||||
0.361111 | + | 0.932523i | \(0.382398\pi\) | |||||||
\(548\) | −76.0659 | − | 131.750i | −0.138806 | − | 0.240420i | ||||
\(549\) | 16.6013 | + | 9.58476i | 0.0302391 | + | 0.0174586i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 819.730 | − | 473.271i | 1.48771 | − | 0.858932i | ||||
\(552\) | 119.049i | 0.215668i | ||||||||
\(553\) | 644.470 | − | 85.3592i | 1.16541 | − | 0.154357i | ||||
\(554\) | 297.815 | 0.537572 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 158.947 | + | 91.7680i | 0.285876 | + | 0.165050i | ||||
\(557\) | −20.8443 | + | 36.1034i | −0.0374224 | + | 0.0648175i | −0.884130 | − | 0.467241i | \(-0.845248\pi\) |
0.846708 | + | 0.532059i | \(0.178581\pi\) | |||||||
\(558\) | 105.888 | − | 61.1346i | 0.189764 | − | 0.109560i | ||||
\(559\) | − | 942.063i | − | 1.68526i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.2808 | 0.0450637 | ||||||||
\(562\) | 333.603 | + | 577.817i | 0.593599 | + | 1.02814i | ||||
\(563\) | 640.642 | + | 369.875i | 1.13791 | + | 0.656972i | 0.945912 | − | 0.324424i | \(-0.105170\pi\) |
0.191996 | + | 0.981396i | \(0.438504\pi\) | |||||||
\(564\) | 43.6350 | − | 75.5781i | 0.0773671 | − | 0.134004i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 662.234i | − | 1.17003i | ||||||
\(567\) | 38.3911 | + | 49.9512i | 0.0677091 | + | 0.0880974i | ||||
\(568\) | 336.505 | 0.592439 | ||||||||
\(569\) | −2.38030 | − | 4.12281i | −0.00418331 | − | 0.00724570i | 0.863926 | − | 0.503618i | \(-0.167998\pi\) |
−0.868109 | + | 0.496373i | \(0.834665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −399.848 | + | 692.557i | −0.700260 | + | 1.21289i | 0.268116 | + | 0.963387i | \(0.413599\pi\) |
−0.968375 | + | 0.249498i | \(0.919734\pi\) | |||||||
\(572\) | −29.6887 | + | 17.1408i | −0.0519033 | + | 0.0299664i | ||||
\(573\) | − | 638.101i | − | 1.11362i | ||||||
\(574\) | 49.4451 | + | 373.315i | 0.0861412 | + | 0.650374i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 148.871 | + | 85.9510i | 0.258009 | + | 0.148962i | 0.623426 | − | 0.781882i | \(-0.285740\pi\) |
−0.365417 | + | 0.930844i | \(0.619074\pi\) | |||||||
\(578\) | 91.7804 | − | 158.968i | 0.158790 | − | 0.275032i | ||||
\(579\) | 421.228 | − | 243.196i | 0.727510 | − | 0.420028i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.5000 | − | 15.4986i | −0.0645439 | − | 0.0266758i | ||||
\(582\) | −353.485 | −0.607362 | ||||||||
\(583\) | 12.0491 | + | 20.8697i | 0.0206675 | + | 0.0357971i | ||||
\(584\) | −96.8271 | − | 55.9032i | −0.165800 | − | 0.0957246i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −77.7795 | + | 44.9060i | −0.132730 | + | 0.0766314i | ||||
\(587\) | − | 724.352i | − | 1.23399i | −0.786967 | − | 0.616994i | \(-0.788350\pi\) | ||
0.786967 | − | 0.616994i | \(-0.211650\pi\) | |||||||
\(588\) | 164.026 | + | 43.6755i | 0.278955 | + | 0.0742781i | ||||
\(589\) | −556.271 | −0.944433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.4267 | − | 6.59720i | −0.0193345 | − | 0.0111628i | ||||
\(592\) | −106.632 | + | 184.691i | −0.180121 | + | 0.311979i | ||||
\(593\) | 894.293 | − | 516.320i | 1.50808 | − | 0.870692i | 0.508127 | − | 0.861282i | \(-0.330338\pi\) |
0.999956 | − | 0.00940925i | \(-0.00299510\pi\) | |||||||
\(594\) | − | 8.50062i | − | 0.0143108i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −197.832 | −0.331933 | ||||||||
\(597\) | −174.795 | − | 302.753i | −0.292789 | − | 0.507125i | ||||
\(598\) | −441.003 | − | 254.613i | −0.737464 | − | 0.425775i | ||||
\(599\) | 212.436 | − | 367.949i | 0.354650 | − | 0.614272i | −0.632408 | − | 0.774636i | \(-0.717933\pi\) |
0.987058 | + | 0.160363i | \(0.0512666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 749.418i | 1.24695i | 0.781843 | + | 0.623476i | \(0.214280\pi\) | ||||
−0.781843 | + | 0.623476i | \(0.785720\pi\) | |||||||
\(602\) | 623.935 | − | 82.6395i | 1.03644 | − | 0.137275i | ||||
\(603\) | 373.471 | 0.619354 | ||||||||
\(604\) | −97.7900 | − | 169.377i | −0.161904 | − | 0.280426i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 47.8683 | − | 82.9104i | 0.0789906 | − | 0.136816i | ||||
\(607\) | 205.133 | − | 118.434i | 0.337945 | − | 0.195113i | −0.321418 | − | 0.946938i | \(-0.604159\pi\) |
0.659363 | + | 0.751825i | \(0.270826\pi\) | |||||||
\(608\) | − | 109.189i | − | 0.179588i | ||||||
\(609\) | 471.410 | − | 362.312i | 0.774072 | − | 0.594929i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 186.647 | + | 323.283i | 0.305478 | + | 0.529104i | ||||
\(612\) | 65.5628 | + | 37.8527i | 0.107129 | + | 0.0618508i | ||||
\(613\) | −469.189 | + | 812.659i | −0.765398 | + | 1.32571i | 0.174638 | + | 0.984633i | \(0.444124\pi\) |
−0.940036 | + | 0.341075i | \(0.889209\pi\) | |||||||
\(614\) | −259.168 | + | 149.631i | −0.422098 | + | 0.243698i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.9568 | − | 18.1594i | −0.0226572 | − | 0.0294796i | ||||
\(617\) | −225.176 | −0.364952 | −0.182476 | − | 0.983210i | \(-0.558411\pi\) | ||||
−0.182476 | + | 0.983210i | \(0.558411\pi\) | |||||||
\(618\) | −46.3481 | − | 80.2772i | −0.0749969 | − | 0.129898i | ||||
\(619\) | 916.115 | + | 528.919i | 1.47999 | + | 0.854473i | 0.999743 | − | 0.0226591i | \(-0.00721323\pi\) |
0.480248 | + | 0.877133i | \(0.340547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 109.353 | − | 63.1351i | 0.176092 | − | 0.101667i | ||||
\(622\) | 95.2182i | 0.153084i | ||||||||
\(623\) | −139.691 | − | 1054.68i | −0.224222 | − | 1.69290i | ||||
\(624\) | −102.659 | −0.164518 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 169.301 | + | 97.7460i | 0.270449 | + | 0.156144i | ||||
\(627\) | −19.3371 | + | 33.4928i | −0.0308406 | + | 0.0534175i | ||||
\(628\) | 231.060 | − | 133.403i | 0.367930 | − | 0.212424i | ||||
\(629\) | 672.716i | 1.06950i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 877.283 | 1.39031 | 0.695153 | − | 0.718862i | \(-0.255336\pi\) | ||||
0.695153 | + | 0.718862i | \(0.255336\pi\) | |||||||
\(632\) | −131.340 | − | 227.487i | −0.207816 | − | 0.359948i | ||||
\(633\) | 45.5726 | + | 26.3114i | 0.0719947 | + | 0.0415662i | ||||
\(634\) | −14.0179 | + | 24.2797i | −0.0221103 | + | 0.0382961i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 72.1643i | 0.113466i | ||||||||
\(637\) | −512.598 | + | 514.205i | −0.804707 | + | 0.807230i | ||||
\(638\) | −80.2238 | −0.125743 | ||||||||
\(639\) | −178.459 | − | 309.100i | −0.279278 | − | 0.483724i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.8684 | + | 46.5374i | −0.0419163 | + | 0.0726012i | −0.886222 | − | 0.463260i | \(-0.846680\pi\) |
0.844306 | + | 0.535861i | \(0.180013\pi\) | |||||||
\(642\) | −176.138 | + | 101.693i | −0.274358 | + | 0.158401i | ||||
\(643\) | − | 99.7799i | − | 0.155179i | −0.996985 | − | 0.0775893i | \(-0.975278\pi\) | ||
0.996985 | − | 0.0775893i | \(-0.0247223\pi\) | |||||||
\(644\) | 129.947 | − | 314.415i | 0.201781 | − | 0.488222i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −172.213 | − | 298.282i | −0.266584 | − | 0.461737i | ||||
\(647\) | 657.905 | + | 379.842i | 1.01685 | + | 0.587081i | 0.913191 | − | 0.407531i | \(-0.133610\pi\) |
0.103663 | + | 0.994612i | \(0.466944\pi\) | |||||||
\(648\) | 12.7279 | − | 22.0454i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −24.4567 | + | 14.1201i | −0.0376836 | + | 0.0217567i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −346.388 | + | 45.8787i | −0.532086 | + | 0.0704742i | ||||
\(652\) | 65.4983 | 0.100458 | ||||||||
\(653\) | 574.896 | + | 995.749i | 0.880392 | + | 1.52488i | 0.850906 | + | 0.525318i | \(0.176054\pi\) |
0.0294854 | + | 0.999565i | \(0.490613\pi\) | |||||||
\(654\) | 101.383 | + | 58.5334i | 0.155020 | + | 0.0895007i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 131.774 | − | 76.0796i | 0.200875 | − | 0.115975i | ||||
\(657\) | 118.589i | 0.180500i | ||||||||
\(658\) | −197.740 | + | 151.977i | −0.300516 | + | 0.230968i | ||||
\(659\) | 213.700 | 0.324280 | 0.162140 | − | 0.986768i | \(-0.448160\pi\) | ||||
0.162140 | + | 0.986768i | \(0.448160\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 665.936 | + | 384.479i | 1.00747 | + | 0.581662i | 0.910449 | − | 0.413621i | \(-0.135736\pi\) |
0.0970187 | + | 0.995283i | \(0.469069\pi\) | |||||||
\(662\) | −185.458 | + | 321.223i | −0.280148 | + | 0.485231i | ||||
\(663\) | −280.442 | + | 161.914i | −0.422990 | + | 0.244213i | ||||
\(664\) | 16.3954i | 0.0246919i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 226.200 | 0.339639 | ||||||||
\(667\) | −595.832 | − | 1032.01i | −0.893301 | − | 1.54724i | ||||
\(668\) | −297.322 | − | 171.659i | −0.445092 | − | 0.256974i | ||||
\(669\) | 14.4953 | − | 25.1065i | 0.0216671 | − | 0.0375284i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.39169i | 0.0110159i | ||||||||
\(672\) | −9.00545 | − | 67.9919i | −0.0134010 | − | 0.101178i | ||||
\(673\) | 1299.78 | 1.93133 | 0.965664 | − | 0.259796i | \(-0.0836553\pi\) | ||||
0.965664 | + | 0.259796i | \(0.0836553\pi\) | |||||||
\(674\) | −408.796 | − | 708.056i | −0.606523 | − | 1.05053i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 50.5603 | − | 87.5730i | 0.0747933 | − | 0.129546i | ||||
\(677\) | −1073.60 | + | 619.840i | −1.58581 | + | 0.915569i | −0.591826 | + | 0.806066i | \(0.701593\pi\) |
−0.993986 | + | 0.109504i | \(0.965074\pi\) | |||||||
\(678\) | 39.7509i | 0.0586297i | ||||||||
\(679\) | 933.575 | + | 385.844i | 1.37493 | + | 0.568253i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 366.738 | + | 635.208i | 0.538528 | + | 0.932758i | ||||
\(682\) | 40.8301 | + | 23.5733i | 0.0598682 | + | 0.0345649i | ||||
\(683\) | −233.043 | + | 403.643i | −0.341205 | + | 0.590985i | −0.984657 | − | 0.174502i | \(-0.944168\pi\) |
0.643452 | + | 0.765487i | \(0.277502\pi\) | |||||||
\(684\) | −100.297 | + | 57.9065i | −0.146633 | + | 0.0846586i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −385.528 | − | 294.391i | −0.561995 | − | 0.429141i | ||||
\(687\) | −701.193 | −1.02066 | ||||||||
\(688\) | −127.155 | − | 220.239i | −0.184818 | − | 0.320114i | ||||
\(689\) | −267.325 | − | 154.340i | −0.387989 | − | 0.224006i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −93.9272 | + | 54.2289i | −0.135929 | + | 0.0784788i | −0.566423 | − | 0.824115i | \(-0.691673\pi\) |
0.430493 | + | 0.902594i | \(0.358340\pi\) | |||||||
\(692\) | − | 404.921i | − | 0.585145i | ||||||
\(693\) | −9.27879 | + | 22.4507i | −0.0133893 | + | 0.0323963i | ||||
\(694\) | 650.145 | 0.936808 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −208.051 | − | 120.119i | −0.298924 | − | 0.172584i | ||||
\(697\) | 239.985 | − | 415.666i | 0.344311 | − | 0.596364i | ||||
\(698\) | 476.606 | − | 275.169i | 0.682817 | − | 0.394224i | ||||
\(699\) | 480.295i | 0.687117i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 528.400 | 0.753780 | 0.376890 | − | 0.926258i | \(-0.376993\pi\) | ||||
0.376890 | + | 0.926258i | \(0.376993\pi\) | |||||||
\(702\) | 54.4432 | + | 94.2984i | 0.0775544 | + | 0.134328i | ||||
\(703\) | −891.235 | − | 514.555i | −1.26776 | − | 0.731942i | ||||
\(704\) | −4.62715 | + | 8.01446i | −0.00657266 | + | 0.0113842i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 913.521i | − | 1.29394i | ||||||
\(707\) | −216.923 | + | 166.721i | −0.306822 | + | 0.235815i | ||||
\(708\) | −84.5675 | −0.119446 | ||||||||
\(709\) | 466.779 | + | 808.484i | 0.658362 | + | 1.14032i | 0.981040 | + | 0.193808i | \(0.0620837\pi\) |
−0.322678 | + | 0.946509i | \(0.604583\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −139.307 | + | 241.286i | −0.195931 | + | 0.339362i | ||||
\(712\) | −372.283 | + | 214.938i | −0.522869 | + | 0.301879i | ||||
\(713\) | 700.326i | 0.982224i | ||||||||
\(714\) | −131.837 | − | 171.536i | −0.184646 | − | 0.240246i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 78.6918 | + | 136.298i | 0.109905 | + | 0.190361i | ||||
\(717\) | 435.370 | + | 251.361i | 0.607211 | + | 0.350573i | ||||
\(718\) | −46.6982 | + | 80.8836i | −0.0650392 | + | 0.112651i | ||||
\(719\) | 557.452 | − | 321.845i | 0.775316 | − | 0.447629i | −0.0594517 | − | 0.998231i | \(-0.518935\pi\) |
0.834768 | + | 0.550602i | \(0.185602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.7821 | + | 262.608i | 0.0482414 | + | 0.364227i | ||||
\(722\) | 16.3670 | 0.0226690 | ||||||||
\(723\) | −350.574 | − | 607.211i | −0.484887 | − | 0.839850i | ||||
\(724\) | 100.720 | + | 58.1509i | 0.139116 | + | 0.0803189i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −253.841 | + | 146.555i | −0.349643 | + | 0.201867i | ||||
\(727\) | 317.353i | 0.436524i | 0.975890 | + | 0.218262i | \(0.0700388\pi\) | ||||
−0.975890 | + | 0.218262i | \(0.929961\pi\) | |||||||
\(728\) | 271.129 | + | 112.057i | 0.372430 | + | 0.153924i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −694.719 | − | 401.096i | −0.950368 | − | 0.548695i | ||||
\(732\) | −11.0675 | + | 19.1695i | −0.0151196 | + | 0.0261879i | ||||
\(733\) | 727.023 | − | 419.747i | 0.991846 | − | 0.572643i | 0.0860205 | − | 0.996293i | \(-0.472585\pi\) |
0.905826 | + | 0.423651i | \(0.139252\pi\) | |||||||
\(734\) | − | 848.431i | − | 1.15590i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −137.466 | −0.186774 | ||||||||
\(737\) | 72.0044 | + | 124.715i | 0.0976993 | + | 0.169220i | ||||
\(738\) | −139.767 | − | 80.6946i | −0.189386 | − | 0.109342i | ||||
\(739\) | 459.403 | − | 795.709i | 0.621654 | − | 1.07674i | −0.367523 | − | 0.930014i | \(-0.619794\pi\) |
0.989178 | − | 0.146723i | \(-0.0468725\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 495.386i | − | 0.668537i | ||||||
\(742\) | 78.7703 | − | 190.590i | 0.106160 | − | 0.256860i | ||||
\(743\) | 1034.18 | 1.39190 | 0.695952 | − | 0.718088i | \(-0.254983\pi\) | ||||
0.695952 | + | 0.718088i | \(0.254983\pi\) | |||||||
\(744\) | 70.5922 | + | 122.269i | 0.0948819 | + | 0.164340i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −286.203 | + | 495.719i | −0.383651 | + | 0.664502i | ||||
\(747\) | 15.0601 | − | 8.69498i | 0.0201608 | − | 0.0116399i | ||||
\(748\) | 29.1917i | 0.0390263i | ||||||||
\(749\) | 576.193 | − | 76.3160i | 0.769283 | − | 0.101891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 340.948 | + | 590.540i | 0.453992 | + | 0.786338i | 0.998630 | − | 0.0523339i | \(-0.0166660\pi\) |
−0.544637 | + | 0.838672i | \(0.683333\pi\) | |||||||
\(752\) | 87.2701 | + | 50.3854i | 0.116051 | + | 0.0670019i | ||||
\(753\) | −134.931 | + | 233.708i | −0.179192 | + | 0.310369i | ||||
\(754\) | 889.932 | − | 513.803i | 1.18028 | − | 0.681436i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −57.6787 | + | 44.3302i | −0.0762946 | + | 0.0586378i | ||||
\(757\) | −183.172 | −0.241971 | −0.120985 | − | 0.992654i | \(-0.538605\pi\) | ||||
−0.120985 | + | 0.992654i | \(0.538605\pi\) | |||||||
\(758\) | −169.476 | − | 293.541i | −0.223583 | − | 0.387257i | ||||
\(759\) | 42.1662 | + | 24.3447i | 0.0555549 | + | 0.0320747i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −673.743 | + | 388.985i | −0.885338 | + | 0.511150i | −0.872415 | − | 0.488766i | \(-0.837447\pi\) |
−0.0129235 | + | 0.999916i | \(0.504114\pi\) | |||||||
\(762\) | − | 197.341i | − | 0.258978i | ||||||
\(763\) | −203.867 | − | 265.254i | −0.267191 | − | 0.347646i | ||||
\(764\) | 736.816 | 0.964419 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −782.747 | − | 451.919i | −1.02186 | − | 0.589973i | ||||
\(767\) | 180.867 | − | 313.271i | 0.235811 | − | 0.408437i | ||||
\(768\) | −24.0000 | + | 13.8564i | −0.0312500 | + | 0.0180422i | ||||
\(769\) | 302.546i | 0.393428i | 0.980461 | + | 0.196714i | \(0.0630271\pi\) | ||||
−0.980461 | + | 0.196714i | \(0.936973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.8630 | 0.0581881 | ||||||||
\(772\) | 280.819 | + | 486.393i | 0.363755 | + | 0.630042i | ||||
\(773\) | 110.995 | + | 64.0833i | 0.143591 | + | 0.0829020i | 0.570074 | − | 0.821593i | \(-0.306914\pi\) |
−0.426484 | + | 0.904495i | \(0.640248\pi\) | |||||||
\(774\) | −134.868 | + | 233.598i | −0.174248 | + | 0.301807i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 408.169i | − | 0.525991i | ||||||
\(777\) | −597.407 | − | 246.907i | −0.768864 | − | 0.317769i | ||||
\(778\) | −737.645 | −0.948130 | ||||||||
\(779\) | 367.125 | + | 635.879i | 0.471277 | + | 0.816277i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 68.8130 | − | 119.188i | 0.0881089 | − | 0.152609i | ||||
\(782\) | −375.526 | + | 216.810i | −0.480213 | + | 0.277251i | ||||
\(783\) | 254.810i | 0.325428i | ||||||||
\(784\) | −50.4321 | + | 189.401i | −0.0643267 | + | 0.241582i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 152.708 | + | 264.499i | 0.194285 | + | 0.336512i | ||||
\(787\) | 466.311 | + | 269.225i | 0.592518 | + | 0.342090i | 0.766092 | − | 0.642731i | \(-0.222199\pi\) |
−0.173575 | + | 0.984821i | \(0.555532\pi\) | |||||||
\(788\) | 7.61779 | − | 13.1944i | 0.00966725 | − | 0.0167442i | ||||
\(789\) | −473.707 | + | 273.495i | −0.600389 | + | 0.346635i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.3898 | − | 104.985i | 0.0548544 | − | 0.132724i | ||||
\(792\) | 9.81567 | 0.0123935 | ||||||||
\(793\) | −47.3409 | − | 81.9969i | −0.0596985 | − | 0.103401i | ||||
\(794\) | −177.784 | − | 102.644i | −0.223909 | − | 0.129274i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 349.589 | − | 201.836i | 0.439183 | − | 0.253562i | ||||
\(797\) | 207.481i | 0.260328i | 0.991492 | + | 0.130164i | \(0.0415504\pi\) | ||||
−0.991492 | + | 0.130164i | \(0.958450\pi\) | |||||||
\(798\) | 328.098 | − | 43.4561i | 0.411150 | − | 0.0544563i | ||||
\(799\) | 317.871 | 0.397836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 394.866 | + | 227.976i | 0.492966 | + | 0.284614i | ||||
\(802\) | 151.351 | − | 262.148i | 0.188717 | − | 0.326867i | ||||
\(803\) | −39.6010 | + | 22.8636i | −0.0493163 | + | 0.0284728i | ||||
\(804\) | 431.247i | 0.536376i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −603.911 | −0.749269 | ||||||||
\(807\) | −41.4157 | − | 71.7341i | −0.0513206 | − | 0.0888899i | ||||
\(808\) | 95.7366 | + | 55.2736i | 0.118486 | + | 0.0684079i | ||||
\(809\) | −722.858 | + | 1252.03i | −0.893520 | + | 1.54762i | −0.0578954 | + | 0.998323i | \(0.518439\pi\) |
−0.835625 | + | 0.549300i | \(0.814894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 207.868i | 0.256310i | 0.991754 | + | 0.128155i | \(0.0409055\pi\) | ||||
−0.991754 | + | 0.128155i | \(0.959094\pi\) | |||||||
\(812\) | 418.362 | + | 544.337i | 0.515224 | + | 0.670366i | ||||
\(813\) | 589.161 | 0.724675 | ||||||||
\(814\) | 43.6109 | + | 75.5363i | 0.0535760 | + | 0.0927964i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −43.7085 | + | 75.7054i | −0.0535644 | + | 0.0927762i | ||||
\(817\) | 1062.77 | − | 613.591i | 1.30082 | − | 0.751029i | ||||
\(818\) | − | 783.435i | − | 0.957745i | ||||||
\(819\) | −40.8571 | − | 308.475i | −0.0498866 | − | 0.376648i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −307.642 | − | 532.851i | −0.374716 | − | 0.649027i | 0.615568 | − | 0.788083i | \(-0.288926\pi\) |
−0.990285 | + | 0.139056i | \(0.955593\pi\) | |||||||
\(822\) | −161.360 | − | 93.1613i | −0.196302 | − | 0.113335i | ||||
\(823\) | −167.804 | + | 290.645i | −0.203893 | + | 0.353153i | −0.949779 | − | 0.312920i | \(-0.898693\pi\) |
0.745886 | + | 0.666073i | \(0.232026\pi\) | |||||||
\(824\) | 92.6961 | − | 53.5181i | 0.112495 | − | 0.0649492i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 223.348 | + | 92.3091i | 0.270397 | + | 0.111754i | ||||
\(827\) | 1453.38 | 1.75741 | 0.878707 | − | 0.477362i | \(-0.158407\pi\) | ||||
0.878707 | + | 0.477362i | \(0.158407\pi\) | |||||||
\(828\) | 72.9022 | + | 126.270i | 0.0880461 | + | 0.152500i | ||||
\(829\) | −11.2468 | − | 6.49333i | −0.0135667 | − | 0.00783273i | 0.493201 | − | 0.869915i | \(-0.335827\pi\) |
−0.506768 | + | 0.862082i | \(0.669160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 315.880 | − | 182.374i | 0.380121 | − | 0.219463i | ||||
\(832\) | − | 118.541i | − | 0.142477i | ||||||
\(833\) | 160.952 | + | 596.943i | 0.193220 | + | 0.716618i | ||||
\(834\) | 224.785 | 0.269526 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −38.6741 | − | 22.3285i | −0.0462609 | − | 0.0267087i | ||||
\(837\) | 74.8743 | − | 129.686i | 0.0894555 | − | 0.154942i | ||||
\(838\) | −328.236 | + | 189.507i | −0.391689 | + | 0.226142i | ||||
\(839\) | − | 940.714i | − | 1.12123i | −0.828076 | − | 0.560616i | \(-0.810564\pi\) | ||
0.828076 | − | 0.560616i | \(-0.189436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1563.74 | 1.85939 | ||||||||
\(842\) | −6.45529 | − | 11.1809i | −0.00766661 | − | 0.0132790i | ||||
\(843\) | 707.678 | + | 408.578i | 0.839476 | + | 0.484671i | ||||
\(844\) | −30.3818 | + | 52.6228i | −0.0359973 | + | 0.0623492i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 106.884i | − | 0.126340i | ||||||
\(847\) | 830.381 | − | 109.983i | 0.980379 | − | 0.129850i | ||||
\(848\) | −83.3281 | −0.0982643 | ||||||||
\(849\) | −405.534 | − | 702.406i | −0.477661 | − | 0.827333i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −647.806 | + | 1122.03i | −0.761230 | + | 1.31849i | ||||
\(852\) | 356.918 | − | 206.067i | 0.418917 | − | 0.241862i | ||||
\(853\) | − | 1176.97i | − | 1.37980i | −0.723903 | − | 0.689902i | \(-0.757654\pi\) | ||
0.723903 | − | 0.689902i | \(-0.242346\pi\) | |||||||
\(854\) | 50.1543 | − | 38.5472i | 0.0587287 | − | 0.0451372i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −117.425 | − | 203.386i | −0.137179 | − | 0.237601i | ||||
\(857\) | −415.523 | − | 239.902i | −0.484858 | − | 0.279933i | 0.237581 | − | 0.971368i | \(-0.423645\pi\) |
−0.722439 | + | 0.691435i | \(0.756979\pi\) | |||||||
\(858\) | −20.9931 | + | 36.3611i | −0.0244675 | + | 0.0423789i | ||||
\(859\) | 1185.54 | − | 684.470i | 1.38014 | − | 0.796821i | 0.387960 | − | 0.921676i | \(-0.373180\pi\) |
0.992175 | + | 0.124855i | \(0.0398465\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 281.052 | + | 365.681i | 0.326425 | + | 0.424717i | ||||
\(862\) | 379.635 | 0.440412 | ||||||||
\(863\) | 42.7677 | + | 74.0758i | 0.0495570 | + | 0.0858352i | 0.889740 | − | 0.456468i | \(-0.150886\pi\) |
−0.840183 | + | 0.542303i | \(0.817552\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −578.391 | + | 333.934i | −0.667888 | + | 0.385605i | ||||
\(867\) | − | 224.815i | − | 0.259302i | ||||||
\(868\) | −52.9762 | − | 399.975i | −0.0610324 | − | 0.460800i | ||||
\(869\) | −107.432 | −0.123627 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1597.51 | − | 922.321i | −1.83411 | − | 1.05892i | ||||
\(872\) | −67.5886 | + | 117.067i | −0.0775099 | + | 0.134251i | ||||
\(873\) | −374.927 | + | 216.464i | −0.429470 | + | 0.247955i | ||||
\(874\) | − | 663.346i | − | 0.758977i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −136.934 | −0.156318 | ||||||||
\(877\) | −236.635 | − | 409.863i | −0.269823 | − | 0.467347i | 0.698993 | − | 0.715128i | \(-0.253632\pi\) |
−0.968816 | + | 0.247781i | \(0.920299\pi\) | |||||||
\(878\) | 672.865 | + | 388.479i | 0.766361 | + | 0.442459i | ||||
\(879\) | −54.9984 | + | 95.2601i | −0.0625693 | + | 0.108373i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 442.658i | 0.502449i | 0.967929 | + | 0.251225i | \(0.0808333\pi\) | ||||
−0.967929 | + | 0.251225i | \(0.919167\pi\) | |||||||
\(882\) | 200.721 | − | 54.1200i | 0.227575 | − | 0.0613605i | ||||
\(883\) | −432.227 | −0.489498 | −0.244749 | − | 0.969586i | \(-0.578706\pi\) | ||||
−0.244749 | + | 0.969586i | \(0.578706\pi\) | |||||||
\(884\) | −186.962 | − | 323.827i | −0.211495 | − | 0.366320i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −332.913 | + | 576.622i | −0.375748 | + | 0.650815i | ||||
\(887\) | −451.613 | + | 260.739i | −0.509146 | + | 0.293956i | −0.732483 | − | 0.680786i | \(-0.761638\pi\) |
0.223337 | + | 0.974741i | \(0.428305\pi\) | |||||||
\(888\) | 261.193i | 0.294136i | ||||||||
\(889\) | −215.407 | + | 521.191i | −0.242302 | + | 0.586266i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.20555 | − | 9.01627i | −0.00584237 | − | 0.0101193i | ||||
\(892\) | 28.9905 | + | 16.7377i | 0.0325006 | + | 0.0187642i | ||||
\(893\) | −243.137 | + | 421.125i | −0.272270 | + | 0.471585i | ||||
\(894\) | −209.832 | + | 121.147i | −0.234712 | + | 0.135511i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 78.5103 | − | 10.3986i | 0.0876231 | − | 0.0116056i | ||||
\(897\) | −623.673 | −0.695287 | ||||||||
\(898\) | 395.644 | + | 685.275i | 0.440583 | + | 0.763113i | ||||
\(899\) | −1223.90 | − | 706.619i | −1.36140 | − | 0.786005i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −227.634 | + | 131.425i | −0.252646 | + | 0.145865i | ||||
\(902\) | − | 62.2311i | − | 0.0689923i | ||||||
\(903\) | 611.177 | − | 469.733i | 0.676830 | − | 0.520192i | ||||
\(904\) | −45.9004 | −0.0507748 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −207.444 | − | 119.768i | −0.228967 | − | 0.132194i | ||||
\(907\) | 633.871 | − | 1097.90i | 0.698865 | − | 1.21047i | −0.269995 | − | 0.962862i | \(-0.587022\pi\) |
0.968860 | − | 0.247608i | \(-0.0796446\pi\) | |||||||
\(908\) | −733.475 | + | 423.472i | −0.807792 | + | 0.466379i | ||||
\(909\) | − | 117.253i | − | 0.128991i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 789.834 | 0.866997 | 0.433498 | − | 0.901154i | \(-0.357279\pi\) | ||||
0.433498 | + | 0.901154i | \(0.357279\pi\) | |||||||
\(912\) | −66.8646 | − | 115.813i | −0.0733165 | − | 0.126988i | ||||
\(913\) | 5.80713 | + | 3.35275i | 0.00636049 | + | 0.00367223i | ||||
\(914\) | −443.623 | + | 768.378i | −0.485364 | + | 0.840676i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 809.668i | − | 0.883916i | ||||||
\(917\) | −114.601 | − | 865.244i | −0.124973 | − | 0.943560i | ||||
\(918\) | 92.7198 | 0.101002 | ||||||||
\(919\) | 506.816 | + | 877.831i | 0.551486 | + | 0.955202i | 0.998168 | + | 0.0605090i | \(0.0192724\pi\) |
−0.446681 | + | 0.894693i | \(0.647394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −183.260 | + | 317.415i | −0.198979 | + | 0.344642i | ||||
\(922\) | −273.925 | + | 158.151i | −0.297098 | + | 0.171530i | ||||
\(923\) | 1762.88i | 1.90995i | ||||||||
\(924\) | −25.9238 | − | 10.7142i | −0.0280561 | − | 0.0115955i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 280.866 | + | 486.474i | 0.303311 | + | 0.525350i | ||||
\(927\) | −98.3191 | − | 56.7645i | −0.106062 | − | 0.0612347i | ||||
\(928\) | 138.701 | − | 240.237i | 0.149462 | − | 0.258876i | ||||
\(929\) | 546.568 | − | 315.561i | 0.588340 | − | 0.339678i | −0.176101 | − | 0.984372i | \(-0.556348\pi\) |
0.764441 | + | 0.644694i | \(0.223015\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −913.960 | − | 243.362i | −0.981697 | − | 0.261399i | ||||
\(932\) | −554.596 | −0.595061 | ||||||||
\(933\) | 58.3090 | + | 100.994i | 0.0624963 | + | 0.108247i | ||||
\(934\) | 408.727 | + | 235.979i | 0.437610 | + | 0.252654i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −108.886 | + | 62.8656i | −0.116332 | + | 0.0671641i | ||||
\(937\) | 867.113i | 0.925414i | 0.886511 | + | 0.462707i | \(0.153122\pi\) | ||||
−0.886511 | + | 0.462707i | \(0.846878\pi\) | |||||||
\(938\) | 470.724 | − | 1138.95i | 0.501838 | − | 1.21423i | ||||
\(939\) | 239.428 | 0.254982 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1151.28 | − | 664.692i | −1.22346 | − | 0.706367i | −0.257809 | − | 0.966196i | \(-0.583001\pi\) |
−0.965655 | + | 0.259829i | \(0.916334\pi\) | |||||||
\(942\) | 163.384 | − | 282.990i | 0.173444 | − | 0.300414i | ||||
\(943\) | 800.550 | − | 462.197i | 0.848939 | − | 0.490135i | ||||
\(944\) | − | 97.6502i | − | 0.103443i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −104.009 | −0.109946 | ||||||||
\(947\) | −770.741 | − | 1334.96i | −0.813877 | − | 1.40968i | −0.910132 | − | 0.414319i | \(-0.864020\pi\) |
0.0962547 | − | 0.995357i | \(-0.469314\pi\) | |||||||
\(948\) | −278.613 | − | 160.858i | −0.293896 | − | 0.169681i | ||||
\(949\) | 292.866 | − | 507.258i | 0.308604 | − | 0.534519i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.3367i | 0.0361059i | ||||||||
\(952\) | 198.073 | − | 152.233i | 0.208059 | − | 0.159908i | ||||
\(953\) | 114.779 | 0.120439 | 0.0602196 | − | 0.998185i | \(-0.480820\pi\) | ||||
0.0602196 | + | 0.998185i | \(0.480820\pi\) | |||||||
\(954\) | 44.1914 | + | 76.5418i | 0.0463222 | + | 0.0802325i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −290.247 | + | 502.722i | −0.303605 | + | 0.525860i | ||||
\(957\) | −85.0902 | + | 49.1268i | −0.0889135 | + | 0.0513342i | ||||
\(958\) | 861.020i | 0.898769i | ||||||||
\(959\) | 324.472 | + | 422.176i | 0.338345 | + | 0.440225i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −65.2290 | − | 112.980i | −0.0678761 | − | 0.117565i | ||||
\(962\) | −967.561 | − | 558.622i | −1.00578 | − | 0.580688i | ||||
\(963\) | −124.548 | + | 215.724i | −0.129333 | + | 0.224012i | ||||
\(964\) | 701.147 | − | 404.808i | 0.727331 | − | 0.419925i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −54.7097 | − | 413.063i | −0.0566353 | − | 0.427602i | ||||
\(967\) | 881.904 | 0.912000 | 0.456000 | − | 0.889980i | \(-0.349282\pi\) | ||||
0.456000 | + | 0.889980i | \(0.349282\pi\) | |||||||
\(968\) | −169.227 | − | 293.110i | −0.174822 | − | 0.302800i | ||||
\(969\) | −365.319 | − | 210.917i | −0.377007 | − | 0.217665i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 407.102 | − | 235.041i | 0.419261 | − | 0.242060i | −0.275500 | − | 0.961301i | \(-0.588843\pi\) |
0.694761 | + | 0.719241i | \(0.255510\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −593.670 | − | 245.362i | −0.610144 | − | 0.252171i | ||||
\(974\) | −450.394 | −0.462417 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.1350 | − | 12.7797i | −0.0226794 | − | 0.0130939i | ||||
\(977\) | −527.971 | + | 914.472i | −0.540400 | + | 0.936000i | 0.458481 | + | 0.888704i | \(0.348394\pi\) |
−0.998881 | + | 0.0472957i | \(0.984940\pi\) | |||||||
\(978\) | 69.4715 | − | 40.1094i | 0.0710342 | − | 0.0410116i | ||||
\(979\) | 175.813i | 0.179584i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 143.377 | 0.146154 | ||||||||
\(982\) | 370.031 | + | 640.913i | 0.376814 | + | 0.652661i | ||||
\(983\) | 128.137 | + | 73.9799i | 0.130353 | + | 0.0752593i | 0.563758 | − | 0.825940i | \(-0.309355\pi\) |
−0.433406 | + | 0.901199i | \(0.642688\pi\) | |||||||
\(984\) | 93.1781 | − | 161.389i | 0.0946932 | − | 0.164013i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 875.034i | − | 0.887458i | ||||||
\(987\) | −116.668 | + | 282.286i | −0.118205 | + | 0.286004i | ||||
\(988\) | 572.022 | 0.578970 | ||||||||
\(989\) | −772.489 | − | 1337.99i | −0.781081 | − | 1.35287i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 653.220 | − | 1131.41i | 0.659153 | − | 1.14169i | −0.321682 | − | 0.946848i | \(-0.604248\pi\) |
0.980835 | − | 0.194839i | \(-0.0624183\pi\) | |||||||
\(992\) | −141.184 | + | 81.5128i | −0.142323 | + | 0.0821702i | ||||
\(993\) | 454.278i | 0.457480i | ||||||||
\(994\) | −1167.57 | + | 154.643i | −1.17462 | + | 0.155577i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.0401 | + | 17.3900i | 0.0100804 | + | 0.0174598i | ||||
\(997\) | 306.223 | + | 176.798i | 0.307145 | + | 0.177330i | 0.645648 | − | 0.763635i | \(-0.276587\pi\) |
−0.338503 | + | 0.940965i | \(0.609921\pi\) | |||||||
\(998\) | −554.242 | + | 959.976i | −0.555353 | + | 0.961900i | ||||
\(999\) | 239.921 | − | 138.519i | 0.240161 | − | 0.138657i |
(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 | 1050.3.p.i.451.8 | 16 | ||
5.2 | odd | 4 | 1050.3.q.e.199.6 | 32 | |||
5.3 | odd | 4 | 1050.3.q.e.199.13 | 32 | |||
5.4 | even | 2 | 210.3.o.b.31.3 | ✓ | 16 | ||
7.5 | odd | 6 | inner | 1050.3.p.i.901.8 | 16 | ||
15.14 | odd | 2 | 630.3.v.c.451.5 | 16 | |||
35.4 | even | 6 | 1470.3.f.d.391.16 | 16 | |||
35.12 | even | 12 | 1050.3.q.e.649.14 | 32 | |||
35.19 | odd | 6 | 210.3.o.b.61.3 | yes | 16 | ||
35.24 | odd | 6 | 1470.3.f.d.391.10 | 16 | |||
35.33 | even | 12 | 1050.3.q.e.649.6 | 32 | |||
105.89 | even | 6 | 630.3.v.c.271.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.3 | ✓ | 16 | 5.4 | even | 2 | ||
210.3.o.b.61.3 | yes | 16 | 35.19 | odd | 6 | ||
630.3.v.c.271.5 | 16 | 105.89 | even | 6 | |||
630.3.v.c.451.5 | 16 | 15.14 | odd | 2 | |||
1050.3.p.i.451.8 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.p.i.901.8 | 16 | 7.5 | odd | 6 | inner | ||
1050.3.q.e.199.6 | 32 | 5.2 | odd | 4 | |||
1050.3.q.e.199.13 | 32 | 5.3 | odd | 4 | |||
1050.3.q.e.649.6 | 32 | 35.33 | even | 12 | |||
1050.3.q.e.649.14 | 32 | 35.12 | even | 12 | |||
1470.3.f.d.391.10 | 16 | 35.24 | odd | 6 | |||
1470.3.f.d.391.16 | 16 | 35.4 | even | 6 |