Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,3,Mod(7,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.l (of order \(12\), degree \(4\), 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: | \(1.06267303101\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 178 x^{8} - 620 x^{7} + 1088 x^{6} + 640 x^{5} + 7921 x^{4} - 22128 x^{3} + 28800 x^{2} - 17280 x + 5184 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 19.3 | ||
Root | \(2.74087 - 2.74087i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.19 |
Dual form | 39.3.l.b.37.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00323 | + | 3.74409i | 0.501613 | + | 1.87205i | 0.489288 | + | 0.872122i | \(0.337257\pi\) |
0.0123254 | + | 0.999924i | \(0.496077\pi\) | |||||||
\(3\) | 0.866025 | − | 1.50000i | 0.288675 | − | 0.500000i | ||||
\(4\) | −9.54767 | + | 5.51235i | −2.38692 | + | 1.37809i | ||||
\(5\) | 3.30327 | − | 3.30327i | 0.660653 | − | 0.660653i | −0.294881 | − | 0.955534i | \(-0.595280\pi\) |
0.955534 | + | 0.294881i | \(0.0952799\pi\) | |||||||
\(6\) | 6.48496 | + | 1.73764i | 1.08083 | + | 0.289607i | ||||
\(7\) | 0.235277 | − | 0.878067i | 0.0336111 | − | 0.125438i | −0.947082 | − | 0.320992i | \(-0.895984\pi\) |
0.980693 | + | 0.195554i | \(0.0626504\pi\) | |||||||
\(8\) | −19.2537 | − | 19.2537i | −2.40672 | − | 2.40672i | ||||
\(9\) | −1.50000 | − | 2.59808i | −0.166667 | − | 0.288675i | ||||
\(10\) | 15.6817 | + | 9.05381i | 1.56817 | + | 0.905381i | ||||
\(11\) | 5.60803 | − | 1.50267i | 0.509821 | − | 0.136606i | 0.00526673 | − | 0.999986i | \(-0.498324\pi\) |
0.504554 | + | 0.863380i | \(0.331657\pi\) | |||||||
\(12\) | 19.0953i | 1.59128i | ||||||||
\(13\) | −3.44589 | + | 12.5350i | −0.265068 | + | 0.964230i | ||||
\(14\) | 3.52360 | 0.251686 | ||||||||
\(15\) | −2.09419 | − | 7.81561i | −0.139613 | − | 0.521041i | ||||
\(16\) | 30.7226 | − | 53.2130i | 1.92016 | − | 3.32581i | ||||
\(17\) | 6.85933 | − | 3.96024i | 0.403490 | − | 0.232955i | −0.284499 | − | 0.958676i | \(-0.591827\pi\) |
0.687989 | + | 0.725721i | \(0.258494\pi\) | |||||||
\(18\) | 8.22260 | − | 8.22260i | 0.456811 | − | 0.456811i | ||||
\(19\) | −27.7306 | − | 7.43040i | −1.45951 | − | 0.391074i | −0.560188 | − | 0.828366i | \(-0.689271\pi\) |
−0.899320 | + | 0.437292i | \(0.855938\pi\) | |||||||
\(20\) | −13.3297 | + | 49.7472i | −0.666487 | + | 2.48736i | ||||
\(21\) | −1.11334 | − | 1.11334i | −0.0530164 | − | 0.0530164i | ||||
\(22\) | 11.2522 | + | 19.4895i | 0.511466 | + | 0.885885i | ||||
\(23\) | −9.29823 | − | 5.36834i | −0.404271 | − | 0.233406i | 0.284054 | − | 0.958808i | \(-0.408320\pi\) |
−0.688325 | + | 0.725402i | \(0.741654\pi\) | |||||||
\(24\) | −45.5549 | + | 12.2064i | −1.89812 | + | 0.508599i | ||||
\(25\) | 3.17685i | 0.127074i | ||||||||
\(26\) | −50.3892 | − | 0.326284i | −1.93804 | − | 0.0125494i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 2.59386 | + | 9.68042i | 0.0926379 | + | 0.345729i | ||||
\(29\) | 7.56721 | − | 13.1068i | 0.260938 | − | 0.451958i | −0.705553 | − | 0.708657i | \(-0.749301\pi\) |
0.966491 | + | 0.256699i | \(0.0826348\pi\) | |||||||
\(30\) | 27.1614 | − | 15.6817i | 0.905381 | − | 0.522722i | ||||
\(31\) | −13.6593 | + | 13.6593i | −0.440624 | + | 0.440624i | −0.892222 | − | 0.451598i | \(-0.850854\pi\) |
0.451598 | + | 0.892222i | \(0.350854\pi\) | |||||||
\(32\) | 124.852 | + | 33.4539i | 3.90162 | + | 1.04544i | ||||
\(33\) | 2.60270 | − | 9.71339i | 0.0788696 | − | 0.294345i | ||||
\(34\) | 21.7090 | + | 21.7090i | 0.638499 | + | 0.638499i | ||||
\(35\) | −2.12331 | − | 3.67768i | −0.0606659 | − | 0.105076i | ||||
\(36\) | 28.6430 | + | 16.5370i | 0.795639 | + | 0.459362i | ||||
\(37\) | −2.46101 | + | 0.659427i | −0.0665139 | + | 0.0178223i | −0.291923 | − | 0.956442i | \(-0.594295\pi\) |
0.225409 | + | 0.974264i | \(0.427628\pi\) | |||||||
\(38\) | − | 111.280i | − | 2.92843i | ||||||
\(39\) | 15.8183 | + | 16.0244i | 0.405596 | + | 0.410883i | ||||
\(40\) | −127.201 | −3.18001 | ||||||||
\(41\) | 11.4567 | + | 42.7572i | 0.279433 | + | 1.04286i | 0.952812 | + | 0.303560i | \(0.0981754\pi\) |
−0.673379 | + | 0.739297i | \(0.735158\pi\) | |||||||
\(42\) | 3.05153 | − | 5.28540i | 0.0726554 | − | 0.125843i | ||||
\(43\) | −3.74071 | + | 2.15970i | −0.0869932 | + | 0.0502255i | −0.542866 | − | 0.839820i | \(-0.682661\pi\) |
0.455872 | + | 0.890045i | \(0.349327\pi\) | |||||||
\(44\) | −45.2604 | + | 45.2604i | −1.02864 | + | 1.02864i | ||||
\(45\) | −13.5370 | − | 3.62724i | −0.300823 | − | 0.0806053i | ||||
\(46\) | 10.7713 | − | 40.1991i | 0.234159 | − | 0.873893i | ||||
\(47\) | 18.4764 | + | 18.4764i | 0.393115 | + | 0.393115i | 0.875796 | − | 0.482681i | \(-0.160337\pi\) |
−0.482681 | + | 0.875796i | \(0.660337\pi\) | |||||||
\(48\) | −53.2130 | − | 92.1677i | −1.10860 | − | 1.92016i | ||||
\(49\) | 41.7196 | + | 24.0868i | 0.851420 | + | 0.491568i | ||||
\(50\) | −11.8944 | + | 3.18710i | −0.237888 | + | 0.0637420i | ||||
\(51\) | − | 13.7187i | − | 0.268993i | ||||||
\(52\) | −36.1970 | − | 138.675i | −0.696097 | − | 2.66682i | ||||
\(53\) | 81.0078 | 1.52845 | 0.764224 | − | 0.644951i | \(-0.223122\pi\) | ||||
0.764224 | + | 0.644951i | \(0.223122\pi\) | |||||||
\(54\) | −5.21292 | − | 19.4549i | −0.0965355 | − | 0.360275i | ||||
\(55\) | 13.5611 | − | 23.4885i | 0.246566 | − | 0.427064i | ||||
\(56\) | −21.4361 | + | 12.3761i | −0.382787 | + | 0.221002i | ||||
\(57\) | −35.1610 | + | 35.1610i | −0.616861 | + | 0.616861i | ||||
\(58\) | 56.6647 | + | 15.1832i | 0.976977 | + | 0.261780i | ||||
\(59\) | 3.85460 | − | 14.3856i | 0.0653322 | − | 0.243823i | −0.925536 | − | 0.378661i | \(-0.876385\pi\) |
0.990868 | + | 0.134838i | \(0.0430514\pi\) | |||||||
\(60\) | 63.0770 | + | 63.0770i | 1.05128 | + | 1.05128i | ||||
\(61\) | 17.7204 | + | 30.6926i | 0.290498 | + | 0.503158i | 0.973928 | − | 0.226859i | \(-0.0728456\pi\) |
−0.683429 | + | 0.730017i | \(0.739512\pi\) | |||||||
\(62\) | −64.8452 | − | 37.4384i | −1.04589 | − | 0.603845i | ||||
\(63\) | −2.63420 | + | 0.705832i | −0.0418127 | + | 0.0112037i | ||||
\(64\) | 255.238i | 3.98809i | ||||||||
\(65\) | 30.0237 | + | 52.7891i | 0.461903 | + | 0.812140i | ||||
\(66\) | 38.9789 | 0.590590 | ||||||||
\(67\) | −24.9466 | − | 93.1019i | −0.372337 | − | 1.38958i | −0.857197 | − | 0.514989i | \(-0.827796\pi\) |
0.484860 | − | 0.874592i | \(-0.338871\pi\) | |||||||
\(68\) | −43.6604 | + | 75.6220i | −0.642065 | + | 1.11209i | ||||
\(69\) | −16.1050 | + | 9.29823i | −0.233406 | + | 0.134757i | ||||
\(70\) | 11.6394 | − | 11.6394i | 0.166277 | − | 0.166277i | ||||
\(71\) | −94.0489 | − | 25.2003i | −1.32463 | − | 0.354934i | −0.473921 | − | 0.880567i | \(-0.657162\pi\) |
−0.850711 | + | 0.525633i | \(0.823828\pi\) | |||||||
\(72\) | −21.1421 | + | 78.9033i | −0.293640 | + | 1.09588i | ||||
\(73\) | 3.74695 | + | 3.74695i | 0.0513281 | + | 0.0513281i | 0.732305 | − | 0.680977i | \(-0.238445\pi\) |
−0.680977 | + | 0.732305i | \(0.738445\pi\) | |||||||
\(74\) | −4.93791 | − | 8.55271i | −0.0667285 | − | 0.115577i | ||||
\(75\) | 4.76528 | + | 2.75123i | 0.0635370 | + | 0.0366831i | ||||
\(76\) | 305.722 | − | 81.9179i | 4.02266 | − | 1.07787i | ||||
\(77\) | − | 5.27777i | − | 0.0685425i | ||||||
\(78\) | −44.1277 | + | 75.3012i | −0.565740 | + | 0.965399i | ||||
\(79\) | 43.6772 | 0.552876 | 0.276438 | − | 0.961032i | \(-0.410846\pi\) | ||||
0.276438 | + | 0.961032i | \(0.410846\pi\) | |||||||
\(80\) | −74.2920 | − | 277.262i | −0.928650 | − | 3.46577i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −148.593 | + | 85.7902i | −1.81211 | + | 1.04622i | ||||
\(83\) | −29.7042 | + | 29.7042i | −0.357882 | + | 0.357882i | −0.863032 | − | 0.505150i | \(-0.831437\pi\) |
0.505150 | + | 0.863032i | \(0.331437\pi\) | |||||||
\(84\) | 16.7670 | + | 4.49270i | 0.199607 | + | 0.0534845i | ||||
\(85\) | 9.57649 | − | 35.7399i | 0.112665 | − | 0.420470i | ||||
\(86\) | −11.8389 | − | 11.8389i | −0.137661 | − | 0.137661i | ||||
\(87\) | −13.1068 | − | 22.7016i | −0.150653 | − | 0.260938i | ||||
\(88\) | −136.908 | − | 79.0436i | −1.55577 | − | 0.898223i | ||||
\(89\) | −27.1548 | + | 7.27610i | −0.305110 | + | 0.0817540i | −0.408126 | − | 0.912926i | \(-0.633817\pi\) |
0.103016 | + | 0.994680i | \(0.467151\pi\) | |||||||
\(90\) | − | 54.3229i | − | 0.603588i | ||||||
\(91\) | 10.1958 | + | 5.97492i | 0.112042 | + | 0.0656584i | ||||
\(92\) | 118.369 | 1.28661 | ||||||||
\(93\) | 8.65967 | + | 32.3183i | 0.0931148 | + | 0.347509i | ||||
\(94\) | −50.6414 | + | 87.7135i | −0.538738 | + | 0.933122i | ||||
\(95\) | −116.146 | + | 67.0571i | −1.22259 | + | 0.705864i | ||||
\(96\) | 158.306 | − | 158.306i | 1.64902 | − | 1.64902i | ||||
\(97\) | −129.936 | − | 34.8163i | −1.33955 | − | 0.358930i | −0.483281 | − | 0.875465i | \(-0.660555\pi\) |
−0.856266 | + | 0.516535i | \(0.827222\pi\) | |||||||
\(98\) | −48.3291 | + | 180.367i | −0.493154 | + | 1.84048i | ||||
\(99\) | −12.3161 | − | 12.3161i | −0.124405 | − | 0.124405i | ||||
\(100\) | −17.5119 | − | 30.3315i | −0.175119 | − | 0.303315i | ||||
\(101\) | 85.7700 | + | 49.5193i | 0.849208 | + | 0.490290i | 0.860383 | − | 0.509647i | \(-0.170224\pi\) |
−0.0111758 | + | 0.999938i | \(0.503557\pi\) | |||||||
\(102\) | 51.3640 | − | 13.7629i | 0.503568 | − | 0.134931i | ||||
\(103\) | − | 132.264i | − | 1.28412i | −0.766655 | − | 0.642059i | \(-0.778080\pi\) | ||
0.766655 | − | 0.642059i | \(-0.221920\pi\) | |||||||
\(104\) | 307.692 | − | 174.999i | 2.95857 | − | 1.68268i | ||||
\(105\) | −7.35535 | −0.0700510 | ||||||||
\(106\) | 81.2692 | + | 303.301i | 0.766690 | + | 2.86133i | ||||
\(107\) | 69.0289 | − | 119.561i | 0.645130 | − | 1.11740i | −0.339142 | − | 0.940735i | \(-0.610137\pi\) |
0.984272 | − | 0.176662i | \(-0.0565299\pi\) | |||||||
\(108\) | 49.6111 | − | 28.6430i | 0.459362 | − | 0.265213i | ||||
\(109\) | 26.2463 | − | 26.2463i | 0.240792 | − | 0.240792i | −0.576386 | − | 0.817178i | \(-0.695538\pi\) |
0.817178 | + | 0.576386i | \(0.195538\pi\) | |||||||
\(110\) | 101.548 | + | 27.2097i | 0.923165 | + | 0.247361i | ||||
\(111\) | −1.14216 | + | 4.26260i | −0.0102897 | + | 0.0384018i | ||||
\(112\) | −39.4963 | − | 39.4963i | −0.352645 | − | 0.352645i | ||||
\(113\) | −90.5319 | − | 156.806i | −0.801167 | − | 1.38766i | −0.918848 | − | 0.394611i | \(-0.870879\pi\) |
0.117681 | − | 0.993051i | \(-0.462454\pi\) | |||||||
\(114\) | −166.921 | − | 96.3717i | −1.46422 | − | 0.845366i | ||||
\(115\) | −48.4476 | + | 12.9815i | −0.421283 | + | 0.112883i | ||||
\(116\) | 166.852i | 1.43838i | ||||||||
\(117\) | 37.7357 | − | 9.84980i | 0.322527 | − | 0.0841864i | ||||
\(118\) | 57.7279 | 0.489219 | ||||||||
\(119\) | −1.86351 | − | 6.95471i | −0.0156597 | − | 0.0584429i | ||||
\(120\) | −110.159 | + | 190.801i | −0.917991 | + | 1.59001i | ||||
\(121\) | −75.5971 | + | 43.6460i | −0.624769 | + | 0.360711i | ||||
\(122\) | −97.1385 | + | 97.1385i | −0.796217 | + | 0.796217i | ||||
\(123\) | 74.0576 | + | 19.8437i | 0.602094 | + | 0.161331i | ||||
\(124\) | 55.1198 | − | 205.710i | 0.444514 | − | 1.65895i | ||||
\(125\) | 93.0757 | + | 93.0757i | 0.744605 | + | 0.744605i | ||||
\(126\) | −5.28540 | − | 9.15459i | −0.0419476 | − | 0.0726554i | ||||
\(127\) | 188.451 | + | 108.802i | 1.48387 | + | 0.856710i | 0.999832 | − | 0.0183386i | \(-0.00583769\pi\) |
0.484034 | + | 0.875049i | \(0.339171\pi\) | |||||||
\(128\) | −456.228 | + | 122.246i | −3.56428 | + | 0.955045i | ||||
\(129\) | 7.48141i | 0.0579954i | ||||||||
\(130\) | −167.527 | + | 165.371i | −1.28867 | + | 1.27208i | ||||
\(131\) | −158.787 | −1.21212 | −0.606058 | − | 0.795421i | \(-0.707250\pi\) | ||||
−0.606058 | + | 0.795421i | \(0.707250\pi\) | |||||||
\(132\) | 28.6939 | + | 107.087i | 0.217378 | + | 0.811267i | ||||
\(133\) | −13.0488 | + | 22.6012i | −0.0981112 | + | 0.169934i | ||||
\(134\) | 323.555 | − | 186.805i | 2.41459 | − | 1.39406i | ||||
\(135\) | −17.1643 | + | 17.1643i | −0.127143 | + | 0.127143i | ||||
\(136\) | −208.317 | − | 55.8184i | −1.53174 | − | 0.410430i | ||||
\(137\) | 62.8465 | − | 234.546i | 0.458733 | − | 1.71202i | −0.218141 | − | 0.975917i | \(-0.569999\pi\) |
0.676874 | − | 0.736098i | \(-0.263334\pi\) | |||||||
\(138\) | −50.9704 | − | 50.9704i | −0.369351 | − | 0.369351i | ||||
\(139\) | 39.8702 | + | 69.0573i | 0.286836 | + | 0.496815i | 0.973053 | − | 0.230582i | \(-0.0740631\pi\) |
−0.686217 | + | 0.727397i | \(0.740730\pi\) | |||||||
\(140\) | 40.5452 | + | 23.4088i | 0.289609 | + | 0.167206i | ||||
\(141\) | 43.7157 | − | 11.7136i | 0.310040 | − | 0.0830751i | ||||
\(142\) | − | 377.409i | − | 2.65781i | ||||||
\(143\) | −0.488720 | + | 75.4746i | −0.00341762 | + | 0.527794i | ||||
\(144\) | −184.335 | −1.28011 | ||||||||
\(145\) | −18.2987 | − | 68.2917i | −0.126198 | − | 0.470978i | ||||
\(146\) | −10.2699 | + | 17.7880i | −0.0703418 | + | 0.121836i | ||||
\(147\) | 72.2605 | − | 41.7196i | 0.491568 | − | 0.283807i | ||||
\(148\) | 19.8619 | − | 19.8619i | 0.134202 | − | 0.134202i | ||||
\(149\) | −46.6353 | − | 12.4959i | −0.312988 | − | 0.0838650i | 0.0989054 | − | 0.995097i | \(-0.468466\pi\) |
−0.411894 | + | 0.911232i | \(0.635133\pi\) | |||||||
\(150\) | −5.52022 | + | 20.6017i | −0.0368015 | + | 0.137345i | ||||
\(151\) | 181.386 | + | 181.386i | 1.20123 | + | 1.20123i | 0.973793 | + | 0.227437i | \(0.0730346\pi\) |
0.227437 | + | 0.973793i | \(0.426965\pi\) | |||||||
\(152\) | 390.856 | + | 676.982i | 2.57142 | + | 4.45383i | ||||
\(153\) | −20.5780 | − | 11.8807i | −0.134497 | − | 0.0776517i | ||||
\(154\) | 19.7605 | − | 5.29480i | 0.128315 | − | 0.0343818i | ||||
\(155\) | 90.2409i | 0.582199i | ||||||||
\(156\) | −239.360 | − | 65.8003i | −1.53436 | − | 0.421797i | ||||
\(157\) | 80.3793 | 0.511970 | 0.255985 | − | 0.966681i | \(-0.417600\pi\) | ||||
0.255985 | + | 0.966681i | \(0.417600\pi\) | |||||||
\(158\) | 43.8181 | + | 163.531i | 0.277330 | + | 1.03501i | ||||
\(159\) | 70.1548 | − | 121.512i | 0.441225 | − | 0.764224i | ||||
\(160\) | 522.926 | − | 301.911i | 3.26829 | − | 1.88695i | ||||
\(161\) | −6.90142 | + | 6.90142i | −0.0428660 | + | 0.0428660i | ||||
\(162\) | −33.6968 | − | 9.02904i | −0.208005 | − | 0.0557348i | ||||
\(163\) | −45.5771 | + | 170.096i | −0.279614 | + | 1.04353i | 0.673072 | + | 0.739577i | \(0.264974\pi\) |
−0.952686 | + | 0.303956i | \(0.901692\pi\) | |||||||
\(164\) | −345.077 | − | 345.077i | −2.10413 | − | 2.10413i | ||||
\(165\) | −23.4885 | − | 40.6833i | −0.142355 | − | 0.246566i | ||||
\(166\) | −141.015 | − | 81.4153i | −0.849490 | − | 0.490453i | ||||
\(167\) | −140.594 | + | 37.6720i | −0.841880 | + | 0.225581i | −0.653890 | − | 0.756590i | \(-0.726864\pi\) |
−0.187990 | + | 0.982171i | \(0.560197\pi\) | |||||||
\(168\) | 42.8721i | 0.255191i | ||||||||
\(169\) | −145.252 | − | 86.3883i | −0.859478 | − | 0.511173i | ||||
\(170\) | 143.421 | 0.843653 | ||||||||
\(171\) | 22.2912 | + | 83.1919i | 0.130358 | + | 0.486503i | ||||
\(172\) | 23.8100 | − | 41.2401i | 0.138430 | − | 0.239768i | ||||
\(173\) | 136.733 | − | 78.9429i | 0.790364 | − | 0.456317i | −0.0497264 | − | 0.998763i | \(-0.515835\pi\) |
0.840091 | + | 0.542446i | \(0.182502\pi\) | |||||||
\(174\) | 71.8479 | − | 71.8479i | 0.412919 | − | 0.412919i | ||||
\(175\) | 2.78949 | + | 0.747441i | 0.0159399 | + | 0.00427109i | ||||
\(176\) | 92.3315 | − | 344.586i | 0.524611 | − | 1.95787i | ||||
\(177\) | −18.2402 | − | 18.2402i | −0.103052 | − | 0.103052i | ||||
\(178\) | −54.4848 | − | 94.3705i | −0.306094 | − | 0.530171i | ||||
\(179\) | −82.5165 | − | 47.6409i | −0.460986 | − | 0.266150i | 0.251473 | − | 0.967864i | \(-0.419085\pi\) |
−0.712459 | + | 0.701714i | \(0.752418\pi\) | |||||||
\(180\) | 149.242 | − | 39.9892i | 0.829121 | − | 0.222162i | ||||
\(181\) | 169.256i | 0.935116i | 0.883962 | + | 0.467558i | \(0.154866\pi\) | ||||
−0.883962 | + | 0.467558i | \(0.845134\pi\) | |||||||
\(182\) | −12.1419 | + | 44.1683i | −0.0667139 | + | 0.242683i | ||||
\(183\) | 61.3853 | 0.335439 | ||||||||
\(184\) | 75.6652 | + | 282.386i | 0.411224 | + | 1.53471i | ||||
\(185\) | −5.95112 | + | 10.3076i | −0.0321682 | + | 0.0557170i | ||||
\(186\) | −112.315 | + | 64.8452i | −0.603845 | + | 0.348630i | ||||
\(187\) | 32.5164 | − | 32.5164i | 0.173885 | − | 0.173885i | ||||
\(188\) | −278.255 | − | 74.5582i | −1.48008 | − | 0.396586i | ||||
\(189\) | −1.22254 | + | 4.56257i | −0.00646845 | + | 0.0241406i | ||||
\(190\) | −367.589 | − | 367.589i | −1.93468 | − | 1.93468i | ||||
\(191\) | 46.3432 | + | 80.2688i | 0.242635 | + | 0.420256i | 0.961464 | − | 0.274931i | \(-0.0886550\pi\) |
−0.718829 | + | 0.695187i | \(0.755322\pi\) | |||||||
\(192\) | 382.857 | + | 221.043i | 1.99405 | + | 1.15126i | ||||
\(193\) | −310.573 | + | 83.2179i | −1.60919 | + | 0.431181i | −0.947801 | − | 0.318863i | \(-0.896699\pi\) |
−0.661388 | + | 0.750044i | \(0.730032\pi\) | |||||||
\(194\) | − | 521.421i | − | 2.68774i | ||||||
\(195\) | 105.185 | + | 0.681103i | 0.539410 | + | 0.00349283i | ||||
\(196\) | −531.100 | −2.70969 | ||||||||
\(197\) | −29.0041 | − | 108.245i | −0.147229 | − | 0.549466i | −0.999646 | − | 0.0266038i | \(-0.991531\pi\) |
0.852417 | − | 0.522863i | \(-0.175136\pi\) | |||||||
\(198\) | 33.7567 | − | 58.4684i | 0.170489 | − | 0.295295i | ||||
\(199\) | −59.4497 | + | 34.3233i | −0.298742 | + | 0.172479i | −0.641878 | − | 0.766807i | \(-0.721844\pi\) |
0.343136 | + | 0.939286i | \(0.388511\pi\) | |||||||
\(200\) | 61.1663 | − | 61.1663i | 0.305831 | − | 0.305831i | ||||
\(201\) | −161.257 | − | 43.2087i | −0.802275 | − | 0.214969i | ||||
\(202\) | −99.3582 | + | 370.810i | −0.491872 | + | 1.83569i | ||||
\(203\) | −9.72825 | − | 9.72825i | −0.0479224 | − | 0.0479224i | ||||
\(204\) | 75.6220 | + | 130.981i | 0.370696 | + | 0.642065i | ||||
\(205\) | 179.083 | + | 103.394i | 0.873576 | + | 0.504359i | ||||
\(206\) | 495.209 | − | 132.691i | 2.40393 | − | 0.644131i | ||||
\(207\) | 32.2100i | 0.155604i | ||||||||
\(208\) | 561.158 | + | 568.473i | 2.69788 | + | 2.73304i | ||||
\(209\) | −166.680 | −0.797511 | ||||||||
\(210\) | −7.37908 | − | 27.5391i | −0.0351385 | − | 0.131139i | ||||
\(211\) | −22.2146 | + | 38.4768i | −0.105282 | + | 0.182355i | −0.913854 | − | 0.406044i | \(-0.866908\pi\) |
0.808571 | + | 0.588398i | \(0.200241\pi\) | |||||||
\(212\) | −773.435 | + | 446.543i | −3.64828 | + | 2.10633i | ||||
\(213\) | −119.249 | + | 119.249i | −0.559856 | + | 0.559856i | ||||
\(214\) | 516.901 | + | 138.503i | 2.41542 | + | 0.647211i | ||||
\(215\) | −5.22249 | + | 19.4906i | −0.0242907 | + | 0.0906540i | ||||
\(216\) | 100.045 | + | 100.045i | 0.463173 | + | 0.463173i | ||||
\(217\) | 8.78009 | + | 15.2076i | 0.0404612 | + | 0.0700809i | ||||
\(218\) | 124.599 | + | 71.9375i | 0.571557 | + | 0.329989i | ||||
\(219\) | 8.86539 | − | 2.37547i | 0.0404812 | − | 0.0108469i | ||||
\(220\) | 299.014i | 1.35916i | ||||||||
\(221\) | 26.0050 | + | 99.6282i | 0.117670 | + | 0.450806i | ||||
\(222\) | −17.1054 | −0.0770514 | ||||||||
\(223\) | −78.3280 | − | 292.324i | −0.351247 | − | 1.31087i | −0.885142 | − | 0.465320i | \(-0.845939\pi\) |
0.533896 | − | 0.845550i | \(-0.320727\pi\) | |||||||
\(224\) | 58.7496 | − | 101.757i | 0.262275 | − | 0.454274i | ||||
\(225\) | 8.25370 | − | 4.76528i | 0.0366831 | − | 0.0211790i | ||||
\(226\) | 496.272 | − | 496.272i | 2.19589 | − | 2.19589i | ||||
\(227\) | 302.517 | + | 81.0591i | 1.33267 | + | 0.357088i | 0.853711 | − | 0.520747i | \(-0.174347\pi\) |
0.478962 | + | 0.877836i | \(0.341013\pi\) | |||||||
\(228\) | 141.886 | − | 529.526i | 0.622307 | − | 2.32248i | ||||
\(229\) | −113.873 | − | 113.873i | −0.497260 | − | 0.497260i | 0.413324 | − | 0.910584i | \(-0.364368\pi\) |
−0.910584 | + | 0.413324i | \(0.864368\pi\) | |||||||
\(230\) | −97.2078 | − | 168.369i | −0.422643 | − | 0.732039i | ||||
\(231\) | −7.91666 | − | 4.57068i | −0.0342712 | − | 0.0197865i | ||||
\(232\) | −398.052 | + | 106.658i | −1.71574 | + | 0.459731i | ||||
\(233\) | 191.488i | 0.821838i | 0.911672 | + | 0.410919i | \(0.134792\pi\) | ||||
−0.911672 | + | 0.410919i | \(0.865208\pi\) | |||||||
\(234\) | 74.7360 | + | 131.404i | 0.319385 | + | 0.561557i | ||||
\(235\) | 122.065 | 0.519426 | ||||||||
\(236\) | 42.4958 | + | 158.596i | 0.180067 | + | 0.672018i | ||||
\(237\) | 37.8255 | − | 65.5158i | 0.159601 | − | 0.276438i | ||||
\(238\) | 24.1696 | − | 13.9543i | 0.101553 | − | 0.0586315i | ||||
\(239\) | −173.094 | + | 173.094i | −0.724244 | + | 0.724244i | −0.969467 | − | 0.245223i | \(-0.921139\pi\) |
0.245223 | + | 0.969467i | \(0.421139\pi\) | |||||||
\(240\) | −480.231 | − | 128.678i | −2.00096 | − | 0.536157i | ||||
\(241\) | 15.1870 | − | 56.6788i | 0.0630167 | − | 0.235182i | −0.927233 | − | 0.374485i | \(-0.877820\pi\) |
0.990250 | + | 0.139303i | \(0.0444863\pi\) | |||||||
\(242\) | −239.256 | − | 239.256i | −0.988660 | − | 0.988660i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −338.377 | − | 195.362i | −1.38679 | − | 0.800664i | ||||
\(245\) | 217.376 | − | 58.2458i | 0.887250 | − | 0.237738i | ||||
\(246\) | 297.186i | 1.20807i | ||||||||
\(247\) | 188.697 | − | 321.999i | 0.763954 | − | 1.30364i | ||||
\(248\) | 525.987 | 2.12091 | ||||||||
\(249\) | 18.8317 | + | 70.2809i | 0.0756294 | + | 0.282253i | ||||
\(250\) | −255.108 | + | 441.860i | −1.02043 | + | 1.76744i | ||||
\(251\) | 98.6857 | − | 56.9762i | 0.393170 | − | 0.226997i | −0.290363 | − | 0.956917i | \(-0.593776\pi\) |
0.683533 | + | 0.729920i | \(0.260443\pi\) | |||||||
\(252\) | 21.2597 | − | 21.2597i | 0.0843638 | − | 0.0843638i | ||||
\(253\) | −60.2116 | − | 16.1336i | −0.237990 | − | 0.0637693i | ||||
\(254\) | −218.307 | + | 814.731i | −0.859475 | + | 3.20760i | ||||
\(255\) | −45.3164 | − | 45.3164i | −0.177711 | − | 0.177711i | ||||
\(256\) | −404.923 | − | 701.348i | −1.58173 | − | 2.73964i | ||||
\(257\) | −324.407 | − | 187.297i | −1.26229 | − | 0.728781i | −0.288769 | − | 0.957399i | \(-0.593246\pi\) |
−0.973516 | + | 0.228618i | \(0.926579\pi\) | |||||||
\(258\) | −28.0111 | + | 7.50555i | −0.108570 | + | 0.0290913i | ||||
\(259\) | 2.31608i | 0.00894241i | ||||||||
\(260\) | −577.648 | − | 338.511i | −2.22172 | − | 1.30197i | ||||
\(261\) | −45.4033 | −0.173959 | ||||||||
\(262\) | −159.300 | − | 594.514i | −0.608013 | − | 2.26914i | ||||
\(263\) | 57.8742 | − | 100.241i | 0.220054 | − | 0.381145i | −0.734770 | − | 0.678316i | \(-0.762710\pi\) |
0.954824 | + | 0.297171i | \(0.0960433\pi\) | |||||||
\(264\) | −237.131 | + | 136.908i | −0.898223 | + | 0.518589i | ||||
\(265\) | 267.590 | − | 267.590i | 1.00977 | − | 1.00977i | ||||
\(266\) | −97.7118 | − | 26.1818i | −0.367337 | − | 0.0984278i | ||||
\(267\) | −12.6026 | + | 47.0335i | −0.0472007 | + | 0.176155i | ||||
\(268\) | 751.392 | + | 751.392i | 2.80370 | + | 2.80370i | ||||
\(269\) | 51.2997 | + | 88.8537i | 0.190705 | + | 0.330311i | 0.945484 | − | 0.325668i | \(-0.105589\pi\) |
−0.754779 | + | 0.655979i | \(0.772256\pi\) | |||||||
\(270\) | −81.4843 | − | 47.0450i | −0.301794 | − | 0.174241i | ||||
\(271\) | −89.8030 | + | 24.0626i | −0.331376 | + | 0.0887920i | −0.420671 | − | 0.907213i | \(-0.638205\pi\) |
0.0892948 | + | 0.996005i | \(0.471539\pi\) | |||||||
\(272\) | − | 486.674i | − | 1.78924i | ||||||
\(273\) | 17.7922 | − | 10.1193i | 0.0651730 | − | 0.0370670i | ||||
\(274\) | 941.212 | 3.43508 | ||||||||
\(275\) | 4.77375 | + | 17.8159i | 0.0173591 | + | 0.0647850i | ||||
\(276\) | 102.510 | − | 177.553i | 0.371414 | − | 0.643307i | ||||
\(277\) | 366.341 | − | 211.507i | 1.32253 | − | 0.763563i | 0.338398 | − | 0.941003i | \(-0.390115\pi\) |
0.984132 | + | 0.177441i | \(0.0567818\pi\) | |||||||
\(278\) | −218.558 | + | 218.558i | −0.786179 | + | 0.786179i | ||||
\(279\) | 55.9770 | + | 14.9990i | 0.200634 | + | 0.0537598i | ||||
\(280\) | −29.9274 | + | 111.691i | −0.106884 | + | 0.398895i | ||||
\(281\) | 6.57627 | + | 6.57627i | 0.0234031 | + | 0.0234031i | 0.718712 | − | 0.695308i | \(-0.244732\pi\) |
−0.695308 | + | 0.718712i | \(0.744732\pi\) | |||||||
\(282\) | 87.7135 | + | 151.924i | 0.311041 | + | 0.538738i | ||||
\(283\) | 48.9456 | + | 28.2588i | 0.172953 | + | 0.0998543i | 0.583977 | − | 0.811770i | \(-0.301496\pi\) |
−0.411025 | + | 0.911624i | \(0.634829\pi\) | |||||||
\(284\) | 1036.86 | − | 277.826i | 3.65092 | − | 0.978260i | ||||
\(285\) | 232.293i | 0.815062i | ||||||||
\(286\) | −283.074 | + | 73.8883i | −0.989770 | + | 0.258351i | ||||
\(287\) | 40.2392 | 0.140206 | ||||||||
\(288\) | −100.362 | − | 374.555i | −0.348478 | − | 1.30054i | ||||
\(289\) | −113.133 | + | 195.952i | −0.391464 | + | 0.678035i | ||||
\(290\) | 237.333 | − | 137.024i | 0.818389 | − | 0.472497i | ||||
\(291\) | −164.752 | + | 164.752i | −0.566159 | + | 0.566159i | ||||
\(292\) | −56.4292 | − | 15.1202i | −0.193251 | − | 0.0517813i | ||||
\(293\) | 53.0538 | − | 197.999i | 0.181071 | − | 0.675766i | −0.814367 | − | 0.580351i | \(-0.802916\pi\) |
0.995438 | − | 0.0954150i | \(-0.0304178\pi\) | |||||||
\(294\) | 228.696 | + | 228.696i | 0.777876 | + | 0.777876i | ||||
\(295\) | −34.7866 | − | 60.2521i | −0.117921 | − | 0.204244i | ||||
\(296\) | 60.0802 | + | 34.6873i | 0.202973 | + | 0.117187i | ||||
\(297\) | −29.1402 | + | 7.80809i | −0.0981151 | + | 0.0262899i | ||||
\(298\) | − | 187.143i | − | 0.627997i | ||||||
\(299\) | 99.3326 | − | 98.0545i | 0.332216 | − | 0.327942i | ||||
\(300\) | −60.6630 | −0.202210 | ||||||||
\(301\) | 1.01626 | + | 3.79272i | 0.00337627 | + | 0.0126004i | ||||
\(302\) | −497.154 | + | 861.096i | −1.64621 | + | 2.85131i | ||||
\(303\) | 148.558 | − | 85.7700i | 0.490290 | − | 0.283069i | ||||
\(304\) | −1247.35 | + | 1247.35i | −4.10313 | + | 4.10313i | ||||
\(305\) | 159.921 | + | 42.8507i | 0.524332 | + | 0.140494i | ||||
\(306\) | 23.8381 | − | 88.9650i | 0.0779023 | − | 0.290735i | ||||
\(307\) | −21.2456 | − | 21.2456i | −0.0692039 | − | 0.0692039i | 0.671658 | − | 0.740862i | \(-0.265583\pi\) |
−0.740862 | + | 0.671658i | \(0.765583\pi\) | |||||||
\(308\) | 29.0929 | + | 50.3904i | 0.0944575 | + | 0.163605i | ||||
\(309\) | −198.396 | − | 114.544i | −0.642059 | − | 0.370693i | ||||
\(310\) | −337.870 | + | 90.5321i | −1.08990 | + | 0.292039i | ||||
\(311\) | 328.015i | 1.05471i | 0.849645 | + | 0.527355i | \(0.176816\pi\) | ||||
−0.849645 | + | 0.527355i | \(0.823184\pi\) | |||||||
\(312\) | 3.96994 | − | 613.091i | 0.0127242 | − | 1.96504i | ||||
\(313\) | −572.183 | −1.82806 | −0.914030 | − | 0.405647i | \(-0.867046\pi\) | ||||
−0.914030 | + | 0.405647i | \(0.867046\pi\) | |||||||
\(314\) | 80.6387 | + | 300.948i | 0.256811 | + | 0.958432i | ||||
\(315\) | −6.36992 | + | 11.0330i | −0.0202220 | + | 0.0350255i | ||||
\(316\) | −417.015 | + | 240.764i | −1.31967 | + | 0.761911i | ||||
\(317\) | 263.833 | − | 263.833i | 0.832280 | − | 0.832280i | −0.155548 | − | 0.987828i | \(-0.549714\pi\) |
0.987828 | + | 0.155548i | \(0.0497143\pi\) | |||||||
\(318\) | 525.332 | + | 140.762i | 1.65199 | + | 0.442649i | ||||
\(319\) | 22.7420 | − | 84.8743i | 0.0712915 | − | 0.266064i | ||||
\(320\) | 843.119 | + | 843.119i | 2.63475 | + | 2.63475i | ||||
\(321\) | −119.561 | − | 207.087i | −0.372466 | − | 0.645130i | ||||
\(322\) | −32.7633 | − | 18.9159i | −0.101749 | − | 0.0587450i | ||||
\(323\) | −219.640 | + | 58.8523i | −0.680000 | + | 0.182205i | ||||
\(324\) | − | 99.2222i | − | 0.306241i | ||||||
\(325\) | −39.8218 | − | 10.9471i | −0.122529 | − | 0.0336833i | ||||
\(326\) | −682.579 | −2.09380 | ||||||||
\(327\) | −16.6395 | − | 62.0994i | −0.0508852 | − | 0.189906i | ||||
\(328\) | 602.650 | − | 1043.82i | 1.83735 | − | 3.18238i | ||||
\(329\) | 20.5706 | − | 11.8765i | 0.0625247 | − | 0.0360987i | ||||
\(330\) | 128.758 | − | 128.758i | 0.390175 | − | 0.390175i | ||||
\(331\) | 82.4800 | + | 22.1005i | 0.249184 | + | 0.0667688i | 0.381249 | − | 0.924472i | \(-0.375494\pi\) |
−0.132065 | + | 0.991241i | \(0.542161\pi\) | |||||||
\(332\) | 119.866 | − | 447.346i | 0.361042 | − | 1.34743i | ||||
\(333\) | 5.40476 | + | 5.40476i | 0.0162305 | + | 0.0162305i | ||||
\(334\) | −282.095 | − | 488.603i | −0.844596 | − | 1.46288i | ||||
\(335\) | −389.946 | − | 225.135i | −1.16402 | − | 0.672046i | ||||
\(336\) | −93.4492 | + | 25.0396i | −0.278123 | + | 0.0745228i | ||||
\(337\) | − | 151.474i | − | 0.449476i | −0.974419 | − | 0.224738i | \(-0.927847\pi\) | ||
0.974419 | − | 0.224738i | \(-0.0721527\pi\) | |||||||
\(338\) | 177.725 | − | 630.503i | 0.525814 | − | 1.86539i | ||||
\(339\) | −313.612 | −0.925108 | ||||||||
\(340\) | 105.578 | + | 394.022i | 0.310523 | + | 1.15889i | ||||
\(341\) | −56.0765 | + | 97.1274i | −0.164447 | + | 0.284831i | ||||
\(342\) | −289.115 | + | 166.921i | −0.845366 | + | 0.488072i | ||||
\(343\) | 62.4622 | − | 62.4622i | 0.182106 | − | 0.182106i | ||||
\(344\) | 113.605 | + | 30.4403i | 0.330247 | + | 0.0884893i | ||||
\(345\) | −22.4846 | + | 83.9137i | −0.0651728 | + | 0.243228i | ||||
\(346\) | 432.744 | + | 432.744i | 1.25070 | + | 1.25070i | ||||
\(347\) | 68.0738 | + | 117.907i | 0.196178 | + | 0.339790i | 0.947286 | − | 0.320389i | \(-0.103814\pi\) |
−0.751108 | + | 0.660179i | \(0.770480\pi\) | |||||||
\(348\) | 250.278 | + | 144.498i | 0.719191 | + | 0.415225i | ||||
\(349\) | −162.066 | + | 43.4254i | −0.464371 | + | 0.124428i | −0.483416 | − | 0.875391i | \(-0.660604\pi\) |
0.0190447 | + | 0.999819i | \(0.493938\pi\) | |||||||
\(350\) | 11.1940i | 0.0319827i | ||||||||
\(351\) | 17.9053 | − | 65.1337i | 0.0510124 | − | 0.185566i | ||||
\(352\) | 750.442 | 2.13194 | ||||||||
\(353\) | 82.1005 | + | 306.403i | 0.232579 | + | 0.867998i | 0.979225 | + | 0.202776i | \(0.0649963\pi\) |
−0.746646 | + | 0.665222i | \(0.768337\pi\) | |||||||
\(354\) | 49.9938 | − | 86.5918i | 0.141225 | − | 0.244610i | ||||
\(355\) | −393.912 | + | 227.425i | −1.10961 | + | 0.640634i | ||||
\(356\) | 219.156 | − | 219.156i | 0.615608 | − | 0.615608i | ||||
\(357\) | −12.0459 | − | 3.22769i | −0.0337421 | − | 0.00904116i | ||||
\(358\) | 95.5892 | − | 356.744i | 0.267009 | − | 0.996491i | ||||
\(359\) | −61.9541 | − | 61.9541i | −0.172574 | − | 0.172574i | 0.615535 | − | 0.788109i | \(-0.288940\pi\) |
−0.788109 | + | 0.615535i | \(0.788940\pi\) | |||||||
\(360\) | 190.801 | + | 330.477i | 0.530002 | + | 0.917991i | ||||
\(361\) | 401.143 | + | 231.600i | 1.11120 | + | 0.641551i | ||||
\(362\) | −633.710 | + | 169.802i | −1.75058 | + | 0.469067i | ||||
\(363\) | 151.194i | 0.416513i | ||||||||
\(364\) | −130.282 | − | 0.843614i | −0.357918 | − | 0.00231762i | ||||
\(365\) | 24.7544 | 0.0678202 | ||||||||
\(366\) | 61.5833 | + | 229.832i | 0.168260 | + | 0.627956i | ||||
\(367\) | −232.100 | + | 402.010i | −0.632426 | + | 1.09539i | 0.354628 | + | 0.935007i | \(0.384607\pi\) |
−0.987054 | + | 0.160387i | \(0.948726\pi\) | |||||||
\(368\) | −571.331 | + | 329.858i | −1.55253 | + | 0.896353i | ||||
\(369\) | 93.9012 | − | 93.9012i | 0.254475 | − | 0.254475i | ||||
\(370\) | −44.5631 | − | 11.9406i | −0.120441 | − | 0.0322720i | ||||
\(371\) | 19.0593 | − | 71.1303i | 0.0513728 | − | 0.191726i | ||||
\(372\) | −260.830 | − | 260.830i | −0.701155 | − | 0.701155i | ||||
\(373\) | 28.9854 | + | 50.2042i | 0.0777088 | + | 0.134596i | 0.902261 | − | 0.431190i | \(-0.141906\pi\) |
−0.824552 | + | 0.565786i | \(0.808573\pi\) | |||||||
\(374\) | 154.366 | + | 89.1232i | 0.412743 | + | 0.238297i | ||||
\(375\) | 220.219 | − | 59.0076i | 0.587252 | − | 0.157354i | ||||
\(376\) | − | 711.481i | − | 1.89224i | ||||||
\(377\) | 138.218 | + | 140.019i | 0.366625 | + | 0.371404i | ||||
\(378\) | −18.3092 | −0.0484370 | ||||||||
\(379\) | −18.1969 | − | 67.9119i | −0.0480130 | − | 0.179187i | 0.937755 | − | 0.347297i | \(-0.112900\pi\) |
−0.985768 | + | 0.168110i | \(0.946234\pi\) | |||||||
\(380\) | 739.284 | − | 1280.48i | 1.94548 | − | 3.36968i | ||||
\(381\) | 326.407 | − | 188.451i | 0.856710 | − | 0.494622i | ||||
\(382\) | −254.041 | + | 254.041i | −0.665029 | + | 0.665029i | ||||
\(383\) | 201.339 | + | 53.9485i | 0.525688 | + | 0.140858i | 0.511896 | − | 0.859047i | \(-0.328943\pi\) |
0.0137918 | + | 0.999905i | \(0.495610\pi\) | |||||||
\(384\) | −211.736 | + | 790.209i | −0.551396 | + | 2.05784i | ||||
\(385\) | −17.4339 | − | 17.4339i | −0.0452828 | − | 0.0452828i | ||||
\(386\) | −623.151 | − | 1079.33i | −1.61438 | − | 2.79619i | ||||
\(387\) | 11.2221 | + | 6.47909i | 0.0289977 | + | 0.0167418i | ||||
\(388\) | 1432.51 | − | 383.839i | 3.69202 | − | 0.989275i | ||||
\(389\) | 459.988i | 1.18249i | 0.806492 | + | 0.591245i | \(0.201363\pi\) | ||||
−0.806492 | + | 0.591245i | \(0.798637\pi\) | |||||||
\(390\) | 102.974 | + | 394.505i | 0.264036 | + | 1.01155i | ||||
\(391\) | −85.0395 | −0.217492 | ||||||||
\(392\) | −339.497 | − | 1267.02i | −0.866064 | − | 3.23219i | ||||
\(393\) | −137.514 | + | 238.181i | −0.349908 | + | 0.606058i | ||||
\(394\) | 376.181 | − | 217.188i | 0.954775 | − | 0.551239i | ||||
\(395\) | 144.277 | − | 144.277i | 0.365259 | − | 0.365259i | ||||
\(396\) | 185.480 | + | 49.6993i | 0.468385 | + | 0.125503i | ||||
\(397\) | −149.364 | + | 557.434i | −0.376232 | + | 1.40412i | 0.475305 | + | 0.879821i | \(0.342338\pi\) |
−0.851537 | + | 0.524295i | \(0.824329\pi\) | |||||||
\(398\) | −188.151 | − | 188.151i | −0.472741 | − | 0.472741i | ||||
\(399\) | 22.6012 | + | 39.1464i | 0.0566445 | + | 0.0981112i | ||||
\(400\) | 169.050 | + | 97.6010i | 0.422625 | + | 0.244002i | ||||
\(401\) | 141.512 | − | 37.9181i | 0.352898 | − | 0.0945588i | −0.0780149 | − | 0.996952i | \(-0.524858\pi\) |
0.430913 | + | 0.902393i | \(0.358192\pi\) | |||||||
\(402\) | − | 647.110i | − | 1.60973i | ||||||
\(403\) | −124.151 | − | 218.288i | −0.308067 | − | 0.541658i | ||||
\(404\) | −1091.87 | −2.70265 | ||||||||
\(405\) | 10.8817 | + | 40.6111i | 0.0268684 | + | 0.100274i | ||||
\(406\) | 26.6638 | − | 46.1831i | 0.0656745 | − | 0.113752i | ||||
\(407\) | −12.8105 | + | 7.39617i | −0.0314755 | + | 0.0181724i | ||||
\(408\) | −264.136 | + | 264.136i | −0.647391 | + | 0.647391i | ||||
\(409\) | 220.136 | + | 58.9852i | 0.538230 | + | 0.144218i | 0.517686 | − | 0.855571i | \(-0.326794\pi\) |
0.0205438 | + | 0.999789i | \(0.493460\pi\) | |||||||
\(410\) | −207.454 | + | 774.231i | −0.505986 | + | 1.88837i | ||||
\(411\) | −297.393 | − | 297.393i | −0.723583 | − | 0.723583i | ||||
\(412\) | 729.086 | + | 1262.81i | 1.76963 | + | 3.06508i | ||||
\(413\) | −11.7246 | − | 6.76919i | −0.0283888 | − | 0.0163903i | ||||
\(414\) | −120.597 | + | 32.3139i | −0.291298 | + | 0.0780530i | ||||
\(415\) | 196.242i | 0.472872i | ||||||||
\(416\) | −849.569 | + | 1449.74i | −2.04223 | + | 3.48494i | ||||
\(417\) | 138.115 | 0.331210 | ||||||||
\(418\) | −167.218 | − | 624.064i | −0.400042 | − | 1.49298i | ||||
\(419\) | 206.102 | − | 356.979i | 0.491889 | − | 0.851977i | −0.508067 | − | 0.861318i | \(-0.669640\pi\) |
0.999956 | + | 0.00934013i | \(0.00297310\pi\) | |||||||
\(420\) | 70.2264 | − | 40.5452i | 0.167206 | − | 0.0965363i | ||||
\(421\) | 516.646 | − | 516.646i | 1.22719 | − | 1.22719i | 0.262163 | − | 0.965024i | \(-0.415564\pi\) |
0.965024 | − | 0.262163i | \(-0.0844358\pi\) | |||||||
\(422\) | −166.347 | − | 44.5725i | −0.394187 | − | 0.105622i | ||||
\(423\) | 20.2885 | − | 75.7178i | 0.0479634 | − | 0.179002i | ||||
\(424\) | −1559.70 | − | 1559.70i | −3.67855 | − | 3.67855i | ||||
\(425\) | 12.5811 | + | 21.7911i | 0.0296026 | + | 0.0512731i | ||||
\(426\) | −566.114 | − | 326.846i | −1.32891 | − | 0.767245i | ||||
\(427\) | 31.1194 | − | 8.33842i | 0.0728792 | − | 0.0195279i | ||||
\(428\) | 1522.04i | 3.55618i | ||||||||
\(429\) | 112.789 | + | 66.0960i | 0.262911 | + | 0.154070i | ||||
\(430\) | −78.2140 | −0.181893 | ||||||||
\(431\) | −22.6165 | − | 84.4059i | −0.0524745 | − | 0.195837i | 0.934713 | − | 0.355404i | \(-0.115657\pi\) |
−0.987187 | + | 0.159567i | \(0.948990\pi\) | |||||||
\(432\) | −159.639 | + | 276.503i | −0.369535 | + | 0.640053i | ||||
\(433\) | −270.622 | + | 156.244i | −0.624994 | + | 0.360840i | −0.778811 | − | 0.627259i | \(-0.784177\pi\) |
0.153817 | + | 0.988099i | \(0.450843\pi\) | |||||||
\(434\) | −48.1301 | + | 48.1301i | −0.110899 | + | 0.110899i | ||||
\(435\) | −118.285 | − | 31.6943i | −0.271919 | − | 0.0728605i | ||||
\(436\) | −105.912 | + | 395.269i | −0.242918 | + | 0.906581i | ||||
\(437\) | 217.957 | + | 217.957i | 0.498757 | + | 0.498757i | ||||
\(438\) | 17.7880 | + | 30.8097i | 0.0406118 | + | 0.0703418i | ||||
\(439\) | 114.773 | + | 66.2644i | 0.261443 | + | 0.150944i | 0.624992 | − | 0.780631i | \(-0.285102\pi\) |
−0.363550 | + | 0.931575i | \(0.618435\pi\) | |||||||
\(440\) | −713.344 | + | 191.140i | −1.62124 | + | 0.434409i | ||||
\(441\) | − | 144.521i | − | 0.327712i | ||||||
\(442\) | −346.928 | + | 197.315i | −0.784905 | + | 0.446414i | ||||
\(443\) | 762.677 | 1.72162 | 0.860809 | − | 0.508928i | \(-0.169958\pi\) | ||||
0.860809 | + | 0.508928i | \(0.169958\pi\) | |||||||
\(444\) | −12.5920 | − | 46.9939i | −0.0283603 | − | 0.105842i | ||||
\(445\) | −65.6646 | + | 113.734i | −0.147561 | + | 0.255583i | ||||
\(446\) | 1015.91 | − | 586.535i | 2.27782 | − | 1.31510i | ||||
\(447\) | −59.1312 | + | 59.1312i | −0.132284 | + | 0.132284i | ||||
\(448\) | 224.116 | + | 60.0517i | 0.500259 | + | 0.134044i | ||||
\(449\) | 71.2323 | − | 265.843i | 0.158647 | − | 0.592077i | −0.840119 | − | 0.542402i | \(-0.817515\pi\) |
0.998765 | − | 0.0496748i | \(-0.0158185\pi\) | |||||||
\(450\) | 26.1220 | + | 26.1220i | 0.0580488 | + | 0.0580488i | ||||
\(451\) | 128.500 | + | 222.568i | 0.284921 | + | 0.493498i | ||||
\(452\) | 1728.74 | + | 998.086i | 3.82464 | + | 2.20816i | ||||
\(453\) | 429.163 | − | 114.994i | 0.947380 | − | 0.253850i | ||||
\(454\) | 1213.97i | 2.67394i | ||||||||
\(455\) | 53.4163 | − | 13.9428i | 0.117398 | − | 0.0306435i | ||||
\(456\) | 1353.96 | 2.96922 | ||||||||
\(457\) | 147.457 | + | 550.316i | 0.322662 | + | 1.20419i | 0.916641 | + | 0.399711i | \(0.130890\pi\) |
−0.593979 | + | 0.804481i | \(0.702444\pi\) | |||||||
\(458\) | 312.110 | − | 540.590i | 0.681462 | − | 1.18033i | ||||
\(459\) | −35.6421 | + | 20.5780i | −0.0776517 | + | 0.0448322i | ||||
\(460\) | 391.003 | − | 391.003i | 0.850006 | − | 0.850006i | ||||
\(461\) | −131.737 | − | 35.2989i | −0.285764 | − | 0.0765704i | 0.113090 | − | 0.993585i | \(-0.463925\pi\) |
−0.398854 | + | 0.917014i | \(0.630592\pi\) | |||||||
\(462\) | 9.17086 | − | 34.2261i | 0.0198504 | − | 0.0740825i | ||||
\(463\) | −555.943 | − | 555.943i | −1.20074 | − | 1.20074i | −0.973942 | − | 0.226798i | \(-0.927174\pi\) |
−0.226798 | − | 0.973942i | \(-0.572826\pi\) | |||||||
\(464\) | −464.968 | − | 805.348i | −1.00209 | − | 1.73566i | ||||
\(465\) | 135.361 | + | 78.1509i | 0.291100 | + | 0.168066i | ||||
\(466\) | −716.950 | + | 192.106i | −1.53852 | + | 0.412245i | ||||
\(467\) | − | 684.656i | − | 1.46607i | −0.680189 | − | 0.733037i | \(-0.738102\pi\) | ||
0.680189 | − | 0.733037i | \(-0.261898\pi\) | |||||||
\(468\) | −305.992 | + | 302.055i | −0.653829 | + | 0.645416i | ||||
\(469\) | −87.6191 | −0.186821 | ||||||||
\(470\) | 122.459 | + | 457.023i | 0.260551 | + | 0.972390i | ||||
\(471\) | 69.6105 | − | 120.569i | 0.147793 | − | 0.255985i | ||||
\(472\) | −351.191 | + | 202.760i | −0.744049 | + | 0.429577i | ||||
\(473\) | −17.7327 | + | 17.7327i | −0.0374898 | + | 0.0374898i | ||||
\(474\) | 283.245 | + | 75.8952i | 0.597563 | + | 0.160116i | ||||
\(475\) | 23.6053 | − | 88.0961i | 0.0496953 | − | 0.185466i | ||||
\(476\) | 56.1289 | + | 56.1289i | 0.117918 | + | 0.117918i | ||||
\(477\) | −121.512 | − | 210.464i | −0.254741 | − | 0.441225i | ||||
\(478\) | −821.733 | − | 474.428i | −1.71911 | − | 0.992527i | ||||
\(479\) | −808.391 | + | 216.608i | −1.68766 | + | 0.452208i | −0.969785 | − | 0.243960i | \(-0.921554\pi\) |
−0.717879 | + | 0.696168i | \(0.754887\pi\) | |||||||
\(480\) | − | 1045.85i | − | 2.17886i | ||||||
\(481\) | 0.214468 | − | 33.1211i | 0.000445880 | − | 0.0688588i | ||||
\(482\) | 227.447 | 0.471881 | ||||||||
\(483\) | 4.37533 | + | 16.3289i | 0.00905865 | + | 0.0338073i | ||||
\(484\) | 481.184 | − | 833.435i | 0.994181 | − | 1.72197i | ||||
\(485\) | −544.221 | + | 314.206i | −1.12210 | + | 0.647848i | ||||
\(486\) | −42.7259 | + | 42.7259i | −0.0879133 | + | 0.0879133i | ||||
\(487\) | 421.775 | + | 113.014i | 0.866068 | + | 0.232062i | 0.664387 | − | 0.747389i | \(-0.268693\pi\) |
0.201681 | + | 0.979451i | \(0.435359\pi\) | |||||||
\(488\) | 249.764 | − | 932.132i | 0.511812 | − | 1.91011i | ||||
\(489\) | 215.673 | + | 215.673i | 0.441049 | + | 0.441049i | ||||
\(490\) | 436.155 | + | 755.443i | 0.890113 | + | 1.54172i | ||||
\(491\) | −384.073 | − | 221.744i | −0.782226 | − | 0.451618i | 0.0549929 | − | 0.998487i | \(-0.482486\pi\) |
−0.837218 | + | 0.546869i | \(0.815820\pi\) | |||||||
\(492\) | −816.462 | + | 218.770i | −1.65948 | + | 0.444655i | ||||
\(493\) | − | 119.872i | − | 0.243148i | ||||||
\(494\) | 1394.90 | + | 383.460i | 2.82368 | + | 0.776234i | ||||
\(495\) | −81.3667 | −0.164377 | ||||||||
\(496\) | 307.205 | + | 1146.50i | 0.619365 | + | 2.31150i | ||||
\(497\) | −44.2552 | + | 76.6522i | −0.0890446 | + | 0.154230i | ||||
\(498\) | −244.246 | + | 141.015i | −0.490453 | + | 0.283163i | ||||
\(499\) | −453.730 | + | 453.730i | −0.909279 | + | 0.909279i | −0.996214 | − | 0.0869354i | \(-0.972293\pi\) |
0.0869354 | + | 0.996214i | \(0.472293\pi\) | |||||||
\(500\) | −1401.72 | − | 375.590i | −2.80344 | − | 0.751180i | ||||
\(501\) | −65.2499 | + | 243.516i | −0.130239 | + | 0.486059i | ||||
\(502\) | 312.328 | + | 312.328i | 0.622168 | + | 0.622168i | ||||
\(503\) | 163.827 | + | 283.757i | 0.325700 | + | 0.564129i | 0.981654 | − | 0.190672i | \(-0.0610666\pi\) |
−0.655954 | + | 0.754801i | \(0.727733\pi\) | |||||||
\(504\) | 64.3082 | + | 37.1283i | 0.127596 | + | 0.0736673i | ||||
\(505\) | 446.897 | − | 119.746i | 0.884944 | − | 0.237120i | ||||
\(506\) | − | 241.623i | − | 0.477517i | ||||||
\(507\) | −255.374 | + | 143.063i | −0.503696 | + | 0.282176i | ||||
\(508\) | −2399.02 | −4.72249 | ||||||||
\(509\) | −97.4223 | − | 363.585i | −0.191399 | − | 0.714312i | −0.993170 | − | 0.116680i | \(-0.962775\pi\) |
0.801770 | − | 0.597632i | \(-0.203892\pi\) | |||||||
\(510\) | 124.206 | − | 215.132i | 0.243542 | − | 0.421827i | ||||
\(511\) | 4.17165 | − | 2.40850i | 0.00816370 | − | 0.00471332i | ||||
\(512\) | 883.754 | − | 883.754i | 1.72608 | − | 1.72608i | ||||
\(513\) | 144.093 | + | 38.6095i | 0.280882 | + | 0.0752622i | ||||
\(514\) | 375.802 | − | 1402.51i | 0.731132 | − | 2.72862i | ||||
\(515\) | −436.904 | − | 436.904i | −0.848357 | − | 0.848357i | ||||
\(516\) | −41.2401 | − | 71.4300i | −0.0799228 | − | 0.138430i | ||||
\(517\) | 131.380 | + | 75.8524i | 0.254120 | + | 0.146716i | ||||
\(518\) | −8.67163 | + | 2.32356i | −0.0167406 | + | 0.00448563i | ||||
\(519\) | − | 273.466i | − | 0.526910i | ||||||
\(520\) | 438.319 | − | 1594.46i | 0.842920 | − | 3.06626i | ||||
\(521\) | −615.884 | −1.18212 | −0.591060 | − | 0.806628i | \(-0.701290\pi\) | ||||
−0.591060 | + | 0.806628i | \(0.701290\pi\) | |||||||
\(522\) | −45.5497 | − | 169.994i | −0.0872601 | − | 0.325659i | ||||
\(523\) | −122.231 | + | 211.711i | −0.233712 | + | 0.404801i | −0.958898 | − | 0.283752i | \(-0.908421\pi\) |
0.725185 | + | 0.688554i | \(0.241754\pi\) | |||||||
\(524\) | 1516.05 | − | 875.290i | 2.89322 | − | 1.67040i | ||||
\(525\) | 3.53693 | − | 3.53693i | 0.00673701 | − | 0.00673701i | ||||
\(526\) | 433.373 | + | 116.122i | 0.823903 | + | 0.220764i | ||||
\(527\) | −39.5997 | + | 147.788i | −0.0751418 | + | 0.280433i | ||||
\(528\) | −436.918 | − | 436.918i | −0.827495 | − | 0.827495i | ||||
\(529\) | −206.862 | − | 358.295i | −0.391043 | − | 0.677307i | ||||
\(530\) | 1270.34 | + | 733.429i | 2.39686 | + | 1.38383i | ||||
\(531\) | −43.1567 | + | 11.5638i | −0.0812743 | + | 0.0217774i | ||||
\(532\) | − | 287.718i | − | 0.540823i | ||||||
\(533\) | −575.439 | − | 3.72613i | −1.07962 | − | 0.00699087i | ||||
\(534\) | −188.741 | −0.353447 | ||||||||
\(535\) | −166.923 | − | 622.964i | −0.312005 | − | 1.16442i | ||||
\(536\) | −1312.25 | + | 2272.88i | −2.44822 | + | 4.24044i | ||||
\(537\) | −142.923 | + | 82.5165i | −0.266150 | + | 0.153662i | ||||
\(538\) | −281.211 | + | 281.211i | −0.522698 | + | 0.522698i | ||||
\(539\) | 270.159 | + | 72.3889i | 0.501223 | + | 0.134302i | ||||
\(540\) | 69.2633 | − | 258.494i | 0.128265 | − | 0.478693i | ||||
\(541\) | 264.659 | + | 264.659i | 0.489204 | + | 0.489204i | 0.908055 | − | 0.418851i | \(-0.137567\pi\) |
−0.418851 | + | 0.908055i | \(0.637567\pi\) | |||||||
\(542\) | −180.185 | − | 312.090i | −0.332446 | − | 0.575813i | ||||
\(543\) | 253.884 | + | 146.580i | 0.467558 | + | 0.269945i | ||||
\(544\) | 988.885 | − | 264.971i | 1.81780 | − | 0.487079i | ||||
\(545\) | − | 173.397i | − | 0.318160i | ||||||
\(546\) | 55.7372 | + | 56.4638i | 0.102083 | + | 0.103413i | ||||
\(547\) | 439.360 | 0.803218 | 0.401609 | − | 0.915811i | \(-0.368451\pi\) | ||||
0.401609 | + | 0.915811i | \(0.368451\pi\) | |||||||
\(548\) | 692.863 | + | 2585.80i | 1.26435 | + | 4.71861i | ||||
\(549\) | 53.1612 | − | 92.0779i | 0.0968328 | − | 0.167719i | ||||
\(550\) | −61.9151 | + | 35.7467i | −0.112573 | + | 0.0649940i | ||||
\(551\) | −307.232 | + | 307.232i | −0.557590 | + | 0.557590i | ||||
\(552\) | 489.107 | + | 131.056i | 0.886064 | + | 0.237420i | ||||
\(553\) | 10.2763 | − | 38.3515i | 0.0185827 | − | 0.0693517i | ||||
\(554\) | 1159.42 | + | 1159.42i | 2.09282 | + | 2.09282i | ||||
\(555\) | 10.3076 | + | 17.8534i | 0.0185723 | + | 0.0321682i | ||||
\(556\) | −761.335 | − | 439.557i | −1.36931 | − | 0.790570i | ||||
\(557\) | 81.7290 | − | 21.8992i | 0.146731 | − | 0.0393164i | −0.184706 | − | 0.982794i | \(-0.559133\pi\) |
0.331437 | + | 0.943477i | \(0.392467\pi\) | |||||||
\(558\) | 224.631i | 0.402564i | ||||||||
\(559\) | −14.1817 | − | 54.3318i | −0.0253698 | − | 0.0971946i | ||||
\(560\) | −260.934 | −0.465953 | ||||||||
\(561\) | −20.6146 | − | 76.9347i | −0.0367461 | − | 0.137138i | ||||
\(562\) | −18.0247 | + | 31.2197i | −0.0320724 | + | 0.0555510i | ||||
\(563\) | 131.716 | − | 76.0461i | 0.233953 | − | 0.135073i | −0.378441 | − | 0.925625i | \(-0.623540\pi\) |
0.612394 | + | 0.790552i | \(0.290206\pi\) | |||||||
\(564\) | −352.813 | + | 352.813i | −0.625556 | + | 0.625556i | ||||
\(565\) | −817.023 | − | 218.921i | −1.44606 | − | 0.387470i | ||||
\(566\) | −56.6999 | + | 211.607i | −0.100176 | + | 0.373864i | ||||
\(567\) | 5.78511 | + | 5.78511i | 0.0102030 | + | 0.0102030i | ||||
\(568\) | 1325.59 | + | 2295.99i | 2.33379 | + | 4.04224i | ||||
\(569\) | −634.451 | − | 366.300i | −1.11503 | − | 0.643761i | −0.174901 | − | 0.984586i | \(-0.555960\pi\) |
−0.940127 | + | 0.340825i | \(0.889294\pi\) | |||||||
\(570\) | −869.725 | + | 233.042i | −1.52583 | + | 0.408846i | ||||
\(571\) | − | 965.471i | − | 1.69084i | −0.534100 | − | 0.845421i | \(-0.679349\pi\) | ||
0.534100 | − | 0.845421i | \(-0.320651\pi\) | |||||||
\(572\) | −411.376 | − | 723.300i | −0.719189 | − | 1.26451i | ||||
\(573\) | 160.538 | 0.280170 | ||||||||
\(574\) | 40.3690 | + | 150.659i | 0.0703293 | + | 0.262472i | ||||
\(575\) | 17.0544 | − | 29.5391i | 0.0296598 | − | 0.0513723i | ||||
\(576\) | 663.128 | − | 382.857i | 1.15126 | − | 0.664682i | ||||
\(577\) | 232.745 | − | 232.745i | 0.403371 | − | 0.403371i | −0.476048 | − | 0.879419i | \(-0.657931\pi\) |
0.879419 | + | 0.476048i | \(0.157931\pi\) | |||||||
\(578\) | −847.161 | − | 226.996i | −1.46568 | − | 0.392727i | ||||
\(579\) | −144.138 | + | 537.929i | −0.248942 | + | 0.929065i | ||||
\(580\) | 551.158 | + | 551.158i | 0.950272 | + | 0.950272i | ||||
\(581\) | 19.0936 | + | 33.0710i | 0.0328633 | + | 0.0569209i | ||||
\(582\) | −782.132 | − | 451.564i | −1.34387 | − | 0.775883i | ||||
\(583\) | 454.294 | − | 121.728i | 0.779235 | − | 0.208795i | ||||
\(584\) | − | 144.286i | − | 0.247065i | ||||||
\(585\) | 92.1145 | − | 157.188i | 0.157461 | − | 0.268697i | ||||
\(586\) | 794.553 | 1.35589 | ||||||||
\(587\) | −34.0511 | − | 127.081i | −0.0580087 | − | 0.216492i | 0.930837 | − | 0.365435i | \(-0.119080\pi\) |
−0.988846 | + | 0.148943i | \(0.952413\pi\) | |||||||
\(588\) | −459.946 | + | 796.649i | −0.782221 | + | 1.35485i | ||||
\(589\) | 480.277 | − | 277.288i | 0.815410 | − | 0.470777i | ||||
\(590\) | 190.691 | − | 190.691i | 0.323204 | − | 0.323204i | ||||
\(591\) | −187.486 | − | 50.2366i | −0.317235 | − | 0.0850028i | ||||
\(592\) | −40.5185 | + | 151.217i | −0.0684435 | + | 0.255434i | ||||
\(593\) | 310.017 | + | 310.017i | 0.522794 | + | 0.522794i | 0.918414 | − | 0.395620i | \(-0.129470\pi\) |
−0.395620 | + | 0.918414i | \(0.629470\pi\) | |||||||
\(594\) | −58.4684 | − | 101.270i | −0.0984317 | − | 0.170489i | ||||
\(595\) | −29.1289 | − | 16.8176i | −0.0489562 | − | 0.0282649i | ||||
\(596\) | 514.140 | − | 137.763i | 0.862650 | − | 0.231146i | ||||
\(597\) | 118.899i | 0.199161i | ||||||||
\(598\) | 466.778 | + | 273.540i | 0.780566 | + | 0.457424i | ||||
\(599\) | 934.777 | 1.56056 | 0.780281 | − | 0.625429i | \(-0.215076\pi\) | ||||
0.780281 | + | 0.625429i | \(0.215076\pi\) | |||||||
\(600\) | −38.7779 | − | 144.721i | −0.0646298 | − | 0.241202i | ||||
\(601\) | 479.955 | − | 831.307i | 0.798595 | − | 1.38321i | −0.121937 | − | 0.992538i | \(-0.538910\pi\) |
0.920531 | − | 0.390669i | \(-0.127756\pi\) | |||||||
\(602\) | −13.1808 | + | 7.60992i | −0.0218950 | + | 0.0126411i | ||||
\(603\) | −204.466 | + | 204.466i | −0.339081 | + | 0.339081i | ||||
\(604\) | −2731.67 | − | 731.949i | −4.52263 | − | 1.21184i | ||||
\(605\) | −105.543 | + | 393.892i | −0.174451 | + | 0.651061i | ||||
\(606\) | 470.168 | + | 470.168i | 0.775855 | + | 0.775855i | ||||
\(607\) | 137.053 | + | 237.384i | 0.225788 | + | 0.391077i | 0.956556 | − | 0.291550i | \(-0.0941709\pi\) |
−0.730767 | + | 0.682627i | \(0.760838\pi\) | |||||||
\(608\) | −3213.64 | − | 1855.40i | −5.28560 | − | 3.05164i | ||||
\(609\) | −23.0173 | + | 6.16746i | −0.0377952 | + | 0.0101272i | ||||
\(610\) | 641.749i | 1.05205i | ||||||||
\(611\) | −295.269 | + | 167.934i | −0.483256 | + | 0.274851i | ||||
\(612\) | 261.962 | 0.428043 | ||||||||
\(613\) | 97.1779 | + | 362.673i | 0.158528 | + | 0.591636i | 0.998777 | + | 0.0494352i | \(0.0157421\pi\) |
−0.840249 | + | 0.542201i | \(0.817591\pi\) | |||||||
\(614\) | 58.2314 | − | 100.860i | 0.0948394 | − | 0.164267i | ||||
\(615\) | 310.181 | − | 179.083i | 0.504359 | − | 0.291192i | ||||
\(616\) | −101.617 | + | 101.617i | −0.164962 | + | 0.164962i | ||||
\(617\) | 236.820 | + | 63.4556i | 0.383824 | + | 0.102845i | 0.445571 | − | 0.895246i | \(-0.353001\pi\) |
−0.0617470 | + | 0.998092i | \(0.519667\pi\) | |||||||
\(618\) | 229.828 | − | 857.728i | 0.371889 | − | 1.38791i | ||||
\(619\) | 334.351 | + | 334.351i | 0.540147 | + | 0.540147i | 0.923572 | − | 0.383425i | \(-0.125256\pi\) |
−0.383425 | + | 0.923572i | \(0.625256\pi\) | |||||||
\(620\) | −497.439 | − | 861.590i | −0.802321 | − | 1.38966i | ||||
\(621\) | 48.3150 | + | 27.8947i | 0.0778020 | + | 0.0449190i | ||||
\(622\) | −1228.12 | + | 329.073i | −1.97446 | + | 0.529056i | ||||
\(623\) | 25.5556i | 0.0410203i | ||||||||
\(624\) | 1338.69 | − | 349.425i | 2.14533 | − | 0.559976i | ||||
\(625\) | 535.486 | 0.856778 | ||||||||
\(626\) | −574.029 | − | 2142.30i | −0.916979 | − | 3.42221i | ||||
\(627\) | −144.349 | + | 250.020i | −0.230221 | + | 0.398755i | ||||
\(628\) | −767.435 | + | 443.079i | −1.22203 | + | 0.705539i | ||||
\(629\) | −14.2694 | + | 14.2694i | −0.0226859 | + | 0.0226859i | ||||
\(630\) | −47.6991 | − | 12.7809i | −0.0757129 | − | 0.0202872i | ||||
\(631\) | −16.9296 | + | 63.1822i | −0.0268298 | + | 0.100130i | −0.978042 | − | 0.208406i | \(-0.933172\pi\) |
0.951213 | + | 0.308536i | \(0.0998391\pi\) | |||||||
\(632\) | −840.949 | − | 840.949i | −1.33062 | − | 1.33062i | ||||
\(633\) | 38.4768 | + | 66.6438i | 0.0607848 | + | 0.105282i | ||||
\(634\) | 1252.50 | + | 723.131i | 1.97555 | + | 1.14058i | ||||
\(635\) | 981.907 | − | 263.101i | 1.54631 | − | 0.414332i | ||||
\(636\) | 1546.87i | 2.43219i | ||||||||
\(637\) | −445.689 | + | 439.954i | −0.699669 | + | 0.690666i | ||||
\(638\) | 340.592 | 0.533844 | ||||||||
\(639\) | 75.6010 | + | 282.147i | 0.118311 | + | 0.441544i | ||||
\(640\) | −1103.23 | + | 1910.85i | −1.72380 | + | 2.98571i | ||||
\(641\) | −404.577 | + | 233.583i | −0.631166 | + | 0.364404i | −0.781204 | − | 0.624276i | \(-0.785394\pi\) |
0.150037 | + | 0.988680i | \(0.452061\pi\) | |||||||
\(642\) | 655.404 | − | 655.404i | 1.02088 | − | 1.02088i | ||||
\(643\) | −535.165 | − | 143.397i | −0.832294 | − | 0.223012i | −0.182580 | − | 0.983191i | \(-0.558445\pi\) |
−0.649714 | + | 0.760179i | \(0.725111\pi\) | |||||||
\(644\) | 27.8494 | − | 103.936i | 0.0432445 | − | 0.161391i | ||||
\(645\) | 24.7131 | + | 24.7131i | 0.0383149 | + | 0.0383149i | ||||
\(646\) | −440.697 | − | 763.310i | −0.682194 | − | 1.18159i | ||||
\(647\) | 365.279 | + | 210.894i | 0.564573 | + | 0.325956i | 0.754979 | − | 0.655749i | \(-0.227647\pi\) |
−0.190406 | + | 0.981705i | \(0.560980\pi\) | |||||||
\(648\) | 236.710 | − | 63.4262i | 0.365293 | − | 0.0978800i | ||||
\(649\) | − | 86.4668i | − | 0.133231i | ||||||
\(650\) | 1.03656 | − | 160.079i | 0.00159470 | − | 0.246275i | ||||
\(651\) | 30.4151 | 0.0467206 | ||||||||
\(652\) | −502.473 | − | 1875.26i | −0.770665 | − | 2.87616i | ||||
\(653\) | −182.251 | + | 315.668i | −0.279098 | + | 0.483412i | −0.971161 | − | 0.238425i | \(-0.923369\pi\) |
0.692063 | + | 0.721837i | \(0.256702\pi\) | |||||||
\(654\) | 215.813 | − | 124.599i | 0.329989 | − | 0.190519i | ||||
\(655\) | −524.516 | + | 524.516i | −0.800788 | + | 0.800788i | ||||
\(656\) | 2627.22 | + | 703.961i | 4.00490 | + | 1.07311i | ||||
\(657\) | 4.11444 | − | 15.3553i | 0.00626247 | − | 0.0233718i | ||||
\(658\) | 65.1036 | + | 65.1036i | 0.0989416 | + | 0.0989416i | ||||
\(659\) | 286.379 | + | 496.022i | 0.434565 | + | 0.752689i | 0.997260 | − | 0.0739756i | \(-0.0235687\pi\) |
−0.562695 | + | 0.826665i | \(0.690235\pi\) | |||||||
\(660\) | 448.521 | + | 258.954i | 0.679578 | + | 0.392354i | ||||
\(661\) | 849.859 | − | 227.719i | 1.28572 | − | 0.344507i | 0.449685 | − | 0.893187i | \(-0.351536\pi\) |
0.836032 | + | 0.548681i | \(0.184870\pi\) | |||||||
\(662\) | 330.985i | 0.499977i | ||||||||
\(663\) | 171.963 | + | 47.2730i | 0.259371 | + | 0.0713016i | ||||
\(664\) | 1143.83 | 1.72264 | ||||||||
\(665\) | 31.5541 | + | 117.761i | 0.0474497 | + | 0.177085i | ||||
\(666\) | −14.8137 | + | 25.6581i | −0.0222428 | + | 0.0385257i | ||||
\(667\) | −140.723 | + | 81.2466i | −0.210979 | + | 0.121809i | ||||
\(668\) | 1134.68 | − | 1134.68i | 1.69863 | − | 1.69863i | ||||
\(669\) | −506.320 | − | 135.668i | −0.756831 | − | 0.202792i | ||||
\(670\) | 451.723 | − | 1685.85i | 0.674214 | − | 2.51620i | ||||
\(671\) | 145.497 | + | 145.497i | 0.216837 | + | 0.216837i | ||||
\(672\) | −101.757 | − | 176.249i | −0.151425 | − | 0.262275i | ||||
\(673\) | 44.2409 | + | 25.5425i | 0.0657369 | + | 0.0379532i | 0.532508 | − | 0.846425i | \(-0.321250\pi\) |
−0.466771 | + | 0.884378i | \(0.654583\pi\) | |||||||
\(674\) | 567.131 | − | 151.962i | 0.841441 | − | 0.225463i | ||||
\(675\) | − | 16.5074i | − | 0.0244554i | ||||||
\(676\) | 1863.02 | + | 24.1282i | 2.75594 | + | 0.0356925i | ||||
\(677\) | −1045.92 | −1.54494 | −0.772469 | − | 0.635053i | \(-0.780978\pi\) | ||||
−0.772469 | + | 0.635053i | \(0.780978\pi\) | |||||||
\(678\) | −314.624 | − | 1174.19i | −0.464047 | − | 1.73185i | ||||
\(679\) | −61.1420 | + | 105.901i | −0.0900472 | + | 0.155966i | ||||
\(680\) | −872.511 | + | 503.744i | −1.28310 | + | 0.740801i | ||||
\(681\) | 383.576 | − | 383.576i | 0.563254 | − | 0.563254i | ||||
\(682\) | −419.912 | − | 112.515i | −0.615706 | − | 0.164978i | ||||
\(683\) | 161.532 | − | 602.846i | 0.236504 | − | 0.882644i | −0.740962 | − | 0.671547i | \(-0.765630\pi\) |
0.977465 | − | 0.211096i | \(-0.0677034\pi\) | |||||||
\(684\) | −671.412 | − | 671.412i | −0.981596 | − | 0.981596i | ||||
\(685\) | −567.170 | − | 982.367i | −0.827985 | − | 1.43411i | ||||
\(686\) | 296.528 | + | 171.201i | 0.432257 | + | 0.249564i | ||||
\(687\) | −269.426 | + | 72.1923i | −0.392177 | + | 0.105083i | ||||
\(688\) | 265.406i | 0.385764i | ||||||||
\(689\) | −279.144 | + | 1015.43i | −0.405143 | + | 1.47378i | ||||
\(690\) | −336.738 | −0.488026 | ||||||||
\(691\) | 138.390 | + | 516.478i | 0.200275 | + | 0.747436i | 0.990838 | + | 0.135055i | \(0.0431213\pi\) |
−0.790563 | + | 0.612380i | \(0.790212\pi\) | |||||||
\(692\) | −870.321 | + | 1507.44i | −1.25769 | + | 2.17838i | ||||
\(693\) | −13.7121 | + | 7.91666i | −0.0197865 | + | 0.0114237i | ||||
\(694\) | −373.162 | + | 373.162i | −0.537698 | + | 0.537698i | ||||
\(695\) | 359.817 | + | 96.4126i | 0.517722 | + | 0.138723i | ||||
\(696\) | −184.737 | + | 689.446i | −0.265426 | + | 0.990583i | ||||
\(697\) | 247.914 | + | 247.914i | 0.355687 | + | 0.355687i | ||||
\(698\) | −325.177 | − | 563.223i | −0.465870 | − | 0.806910i | ||||
\(699\) | 287.232 | + | 165.834i | 0.410919 | + | 0.237244i | ||||
\(700\) | −30.7533 | + | 8.24031i | −0.0439332 | + | 0.0117719i | ||||
\(701\) | − | 1086.67i | − | 1.55017i | −0.631854 | − | 0.775087i | \(-0.717706\pi\) | ||
0.631854 | − | 0.775087i | \(-0.282294\pi\) | |||||||
\(702\) | 261.830 | + | 1.69542i | 0.372977 | + | 0.00241513i | ||||
\(703\) | 73.1453 | 0.104047 | ||||||||
\(704\) | 383.538 | + | 1431.38i | 0.544798 | + | 2.03321i | ||||
\(705\) | 105.712 | − | 183.098i | 0.149945 | − | 0.259713i | ||||
\(706\) | −1064.84 | + | 614.784i | −1.50827 | + | 0.870798i | ||||
\(707\) | 63.6610 | − | 63.6610i | 0.0900439 | − | 0.0900439i | ||||
\(708\) | 274.697 | + | 73.6048i | 0.387990 | + | 0.103962i | ||||
\(709\) | −115.524 | + | 431.140i | −0.162939 | + | 0.608096i | 0.835355 | + | 0.549710i | \(0.185262\pi\) |
−0.998294 | + | 0.0583855i | \(0.981405\pi\) | |||||||
\(710\) | −1246.68 | − | 1246.68i | −1.75589 | − | 1.75589i | ||||
\(711\) | −65.5158 | − | 113.477i | −0.0921460 | − | 0.159601i | ||||
\(712\) | 662.924 | + | 382.739i | 0.931073 | + | 0.537555i | ||||
\(713\) | 200.336 | − | 53.6798i | 0.280976 | − | 0.0752872i | ||||
\(714\) | − | 48.3391i | − | 0.0677018i | ||||||
\(715\) | 247.698 | + | 250.927i | 0.346431 | + | 0.350947i | ||||
\(716\) | 1050.45 | 1.46711 | ||||||||
\(717\) | 109.737 | + | 409.545i | 0.153051 | + | 0.571193i | ||||
\(718\) | 169.808 | − | 294.116i | 0.236501 | − | 0.409632i | ||||
\(719\) | −905.624 | + | 522.862i | −1.25956 | + | 0.727207i | −0.972989 | − | 0.230851i | \(-0.925849\pi\) |
−0.286571 | + | 0.958059i | \(0.592516\pi\) | |||||||
\(720\) | −608.909 | + | 608.909i | −0.845707 | + | 0.845707i | ||||
\(721\) | −116.137 | − | 31.1188i | −0.161077 | − | 0.0431606i | ||||
\(722\) | −464.694 | + | 1734.26i | −0.643621 | + | 2.40203i | ||||
\(723\) | −71.8658 | − | 71.8658i | −0.0993994 | − | 0.0993994i | ||||
\(724\) | −932.998 | − | 1616.00i | −1.28867 | − | 2.23204i | ||||
\(725\) | 41.6383 | + | 24.0399i | 0.0574322 | + | 0.0331585i | ||||
\(726\) | −566.085 | + | 151.682i | −0.779731 | + | 0.208928i | ||||
\(727\) | 346.434i | 0.476525i | 0.971201 | + | 0.238263i | \(0.0765779\pi\) | ||||
−0.971201 | + | 0.238263i | \(0.923422\pi\) | |||||||
\(728\) | −81.2682 | − | 311.347i | −0.111632 | − | 0.427675i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 24.8343 | + | 92.6827i | 0.0340195 | + | 0.126963i | ||||
\(731\) | −17.1058 | + | 29.6282i | −0.0234006 | + | 0.0405310i | ||||
\(732\) | −586.086 | + | 338.377i | −0.800664 | + | 0.462263i | ||||
\(733\) | −632.247 | + | 632.247i | −0.862547 | + | 0.862547i | −0.991633 | − | 0.129087i | \(-0.958796\pi\) |
0.129087 | + | 0.991633i | \(0.458796\pi\) | |||||||
\(734\) | −1738.01 | − | 465.698i | −2.36786 | − | 0.634467i | ||||
\(735\) | 100.885 | − | 376.507i | 0.137258 | − | 0.512254i | ||||
\(736\) | −981.308 | − | 981.308i | −1.33330 | − | 1.33330i | ||||
\(737\) | −279.802 | − | 484.632i | −0.379650 | − | 0.657574i | ||||
\(738\) | 445.779 | + | 257.371i | 0.604037 | + | 0.348741i | ||||
\(739\) | 31.2351 | − | 8.36942i | 0.0422667 | − | 0.0113253i | −0.237624 | − | 0.971357i | \(-0.576369\pi\) |
0.279890 | + | 0.960032i | \(0.409702\pi\) | |||||||
\(740\) | − | 131.219i | − | 0.177322i | ||||||
\(741\) | −319.582 | − | 561.904i | −0.431285 | − | 0.758305i | ||||
\(742\) | 285.439 | 0.384689 | ||||||||
\(743\) | 192.884 | + | 719.854i | 0.259602 | + | 0.968847i | 0.965472 | + | 0.260506i | \(0.0838895\pi\) |
−0.705870 | + | 0.708341i | \(0.749444\pi\) | |||||||
\(744\) | 455.518 | − | 788.980i | 0.612255 | − | 1.06046i | ||||
\(745\) | −195.326 | + | 112.772i | −0.262183 | + | 0.151371i | ||||
\(746\) | −158.890 | + | 158.890i | −0.212989 | + | 0.212989i | ||||
\(747\) | 121.730 | + | 32.6175i | 0.162959 | + | 0.0436646i | ||||
\(748\) | −131.214 | + | 489.698i | −0.175420 | + | 0.654676i | ||||
\(749\) | −88.7421 | − | 88.7421i | −0.118481 | − | 0.118481i | ||||
\(750\) | 441.860 | + | 765.324i | 0.589147 | + | 1.02043i | ||||
\(751\) | −894.943 | − | 516.695i | −1.19167 | − | 0.688010i | −0.232983 | − | 0.972481i | \(-0.574849\pi\) |
−0.958685 | + | 0.284471i | \(0.908182\pi\) | |||||||
\(752\) | 1550.83 | − | 415.543i | 2.06227 | − | 0.552584i | ||||
\(753\) | − | 197.371i | − | 0.262114i | ||||||
\(754\) | −385.582 | + | 657.971i | −0.511382 | + | 0.872641i | ||||
\(755\) | 1198.33 | 1.58719 | ||||||||
\(756\) | −13.4781 | − | 50.3010i | −0.0178282 | − | 0.0665357i | ||||
\(757\) | 378.681 | − | 655.895i | 0.500240 | − | 0.866440i | −0.499760 | − | 0.866164i | \(-0.666579\pi\) |
1.00000 | 0.000276678i | \(-8.80693e-5\pi\) | ||||||||
\(758\) | 236.013 | − | 136.262i | 0.311362 | − | 0.179765i | ||||
\(759\) | −76.3452 | + | 76.3452i | −0.100587 | + | 0.100587i | ||||
\(760\) | 3527.35 | + | 945.151i | 4.64125 | + | 1.24362i | ||||
\(761\) | 215.400 | − | 803.884i | 0.283049 | − | 1.05635i | −0.667205 | − | 0.744874i | \(-0.732509\pi\) |
0.950253 | − | 0.311478i | \(-0.100824\pi\) | |||||||
\(762\) | 1033.04 | + | 1033.04i | 1.35569 | + | 1.35569i | ||||
\(763\) | −16.8708 | − | 29.2212i | −0.0221112 | − | 0.0382977i | ||||
\(764\) | −884.939 | − | 510.920i | −1.15830 | − | 0.668743i | ||||
\(765\) | −107.220 | + | 28.7295i | −0.140157 | + | 0.0375548i | ||||
\(766\) | 807.953i | 1.05477i | ||||||||
\(767\) | 167.040 | + | 97.8883i | 0.217784 | + | 0.127625i | ||||
\(768\) | −1402.70 | −1.82643 | ||||||||
\(769\) | 251.358 | + | 938.081i | 0.326864 | + | 1.21987i | 0.912425 | + | 0.409243i | \(0.134207\pi\) |
−0.585562 | + | 0.810628i | \(0.699126\pi\) | |||||||
\(770\) | 47.7840 | − | 82.7642i | 0.0620571 | − | 0.107486i | ||||
\(771\) | −561.890 | + | 324.407i | −0.728781 | + | 0.420762i | ||||
\(772\) | 2506.52 | − | 2506.52i | 3.24679 | − | 3.24679i | ||||
\(773\) | −657.402 | − | 176.150i | −0.850456 | − | 0.227879i | −0.192838 | − | 0.981231i | \(-0.561769\pi\) |
−0.657618 | + | 0.753352i | \(0.728436\pi\) | |||||||
\(774\) | −13.0000 | + | 48.5167i | −0.0167959 | + | 0.0626830i | ||||
\(775\) | −43.3937 | − | 43.3937i | −0.0559919 | − | 0.0559919i | ||||
\(776\) | 1831.41 | + | 3172.10i | 2.36007 | + | 4.08776i | ||||
\(777\) | 3.47413 | + | 2.00579i | 0.00447120 | + | 0.00258145i | ||||
\(778\) | −1722.24 | + | 461.473i | −2.21367 | + | 0.593152i | ||||
\(779\) | − | 1270.81i | − | 1.63134i | ||||||
\(780\) | −1008.03 | + | 573.313i | −1.29234 | + | 0.735017i | ||||
\(781\) | −565.297 | −0.723811 | ||||||||
\(782\) | −85.3139 | − | 318.396i | −0.109097 | − | 0.407156i | ||||
\(783\) | −39.3204 | + | 68.1049i | −0.0502176 | + | 0.0869794i | ||||
\(784\) | 2563.46 | − | 1480.02i | 3.26973 | − | 1.88778i | ||||
\(785\) | 265.514 | − | 265.514i | 0.338235 | − | 0.338235i | ||||
\(786\) | −1029.73 | − | 275.915i | −1.31009 | − | 0.351037i | ||||
\(787\) | −193.341 | + | 721.557i | −0.245668 | + | 0.916845i | 0.727379 | + | 0.686236i | \(0.240738\pi\) |
−0.973047 | + | 0.230609i | \(0.925928\pi\) | |||||||
\(788\) | 873.605 | + | 873.605i | 1.10864 | + | 1.10864i | ||||
\(789\) | −100.241 | − | 173.623i | −0.127048 | − | 0.220054i | ||||
\(790\) | 684.931 | + | 395.445i | 0.867001 | + | 0.500563i | ||||
\(791\) | −158.986 | + | 42.6002i | −0.200994 | + | 0.0538562i | ||||
\(792\) | 474.262i | 0.598815i | ||||||||
\(793\) | −445.794 | + | 116.362i | −0.562162 | + | 0.146736i | ||||
\(794\) | −2236.93 | −2.81729 | ||||||||
\(795\) | −169.645 | − | 633.126i | −0.213391 | − | 0.796384i | ||||
\(796\) | 378.404 | − | 655.415i | 0.475382 | − | 0.823385i | ||||
\(797\) | 431.093 | − | 248.892i | 0.540895 | − | 0.312286i | −0.204547 | − | 0.978857i | \(-0.565572\pi\) |
0.745442 | + | 0.666571i | \(0.232239\pi\) | |||||||
\(798\) | −123.894 | + | 123.894i | −0.155255 | + | 0.155255i | ||||
\(799\) | 199.907 | + | 53.5649i | 0.250196 | + | 0.0670399i | ||||
\(800\) | −106.278 | + | 396.635i | −0.132848 | + | 0.495794i | ||||
\(801\) | 59.6361 | + | 59.6361i | 0.0744520 | + | 0.0744520i | ||||
\(802\) | 283.938 | + | 491.794i | 0.354037 | + | 0.613210i | ||||
\(803\) | 26.6435 | + | 15.3826i | 0.0331799 | + | 0.0191564i | ||||
\(804\) | 1777.81 | − | 476.363i | 2.21121 | − | 0.592492i | ||||
\(805\) | 45.5945i | 0.0566391i | ||||||||
\(806\) | 692.739 | − | 683.826i | 0.859478 | − | 0.848419i | ||||
\(807\) | 177.707 | 0.220208 | ||||||||
\(808\) | −697.961 | − | 2604.83i | −0.863813 | − | 3.22379i | ||||
\(809\) | 26.3804 | − | 45.6922i | 0.0326087 | − | 0.0564799i | −0.849261 | − | 0.527974i | \(-0.822952\pi\) |
0.881869 | + | 0.471494i | \(0.156285\pi\) | |||||||
\(810\) | −141.135 | + | 81.4843i | −0.174241 | + | 0.100598i | ||||
\(811\) | −883.046 | + | 883.046i | −1.08884 | + | 1.08884i | −0.0931873 | + | 0.995649i | \(0.529706\pi\) |
−0.995649 | + | 0.0931873i | \(0.970294\pi\) | |||||||
\(812\) | 146.508 | + | 39.2566i | 0.180428 | + | 0.0483455i | ||||
\(813\) | −41.6777 | + | 155.543i | −0.0512641 | + | 0.191320i | ||||
\(814\) | −40.5438 | − | 40.5438i | −0.0498081 | − | 0.0498081i | ||||
\(815\) | 411.319 | + | 712.426i | 0.504686 | + | 0.874142i | ||||
\(816\) | −730.012 | − | 421.472i | −0.894622 | − | 0.516510i | ||||
\(817\) | 119.780 | − | 32.0949i | 0.146609 | − | 0.0392838i | ||||
\(818\) | 883.385i | 1.07993i | ||||||||
\(819\) | 0.229561 | − | 35.4519i | 0.000280295 | − | 0.0432868i | ||||
\(820\) | −2279.77 | −2.78020 | ||||||||
\(821\) | −150.881 | − | 563.097i | −0.183778 | − | 0.685867i | −0.994889 | − | 0.100976i | \(-0.967804\pi\) |
0.811111 | − | 0.584892i | \(-0.198863\pi\) | |||||||
\(822\) | 815.113 | − | 1411.82i | 0.991622 | − | 1.71754i | ||||
\(823\) | 1096.00 | − | 632.773i | 1.33171 | − | 0.768862i | 0.346147 | − | 0.938180i | \(-0.387490\pi\) |
0.985561 | + | 0.169319i | \(0.0541567\pi\) | |||||||
\(824\) | −2546.58 | + | 2546.58i | −3.09051 | + | 3.09051i | ||||
\(825\) | 30.8580 | + | 8.26838i | 0.0374036 | + | 0.0100223i | ||||
\(826\) | 13.5821 | − | 50.6890i | 0.0164432 | − | 0.0613668i | ||||
\(827\) | 513.651 | + | 513.651i | 0.621102 | + | 0.621102i | 0.945813 | − | 0.324712i | \(-0.105267\pi\) |
−0.324712 | + | 0.945813i | \(0.605267\pi\) | |||||||
\(828\) | −177.553 | − | 307.530i | −0.214436 | − | 0.371414i | ||||
\(829\) | −759.340 | − | 438.405i | −0.915972 | − | 0.528836i | −0.0336239 | − | 0.999435i | \(-0.510705\pi\) |
−0.882348 | + | 0.470598i | \(0.844038\pi\) | |||||||
\(830\) | −734.748 | + | 196.875i | −0.885238 | + | 0.237199i | ||||
\(831\) | − | 732.681i | − | 0.881686i | ||||||
\(832\) | −3199.40 | − | 879.521i | −3.84544 | − | 1.05712i | ||||
\(833\) | 381.558 | 0.458053 | ||||||||
\(834\) | 138.560 | + | 517.114i | 0.166139 | + | 0.620040i | ||||
\(835\) | −339.978 | + | 588.860i | −0.407160 | + | 0.705222i | ||||
\(836\) | 1591.40 | − | 918.796i | 1.90359 | − | 1.09904i | ||||
\(837\) | 70.9760 | − | 70.9760i | 0.0847981 | − | 0.0847981i | ||||
\(838\) | 1543.33 | + | 413.533i | 1.84168 | + | 0.493477i | ||||
\(839\) | 122.684 | − | 457.864i | 0.146227 | − | 0.545726i | −0.853471 | − | 0.521140i | \(-0.825507\pi\) |
0.999698 | − | 0.0245853i | \(-0.00782652\pi\) | |||||||
\(840\) | 141.618 | + | 141.618i | 0.168593 | + | 0.168593i | ||||
\(841\) | 305.975 | + | 529.964i | 0.363822 | + | 0.630159i | ||||
\(842\) | 2452.68 | + | 1416.06i | 2.91292 | + | 1.68178i | ||||
\(843\) | 15.5596 | − | 4.16919i | 0.0184574 | − | 0.00494566i | ||||
\(844\) | − | 489.818i | − | 0.580353i | ||||||
\(845\) | −765.169 | + | 194.442i | −0.905525 | + | 0.230109i | ||||
\(846\) | 303.848 | 0.359159 | ||||||||
\(847\) | 20.5378 | + | 76.6482i | 0.0242477 | + | 0.0904938i | ||||
\(848\) | 2488.77 | − | 4310.67i | 2.93486 | − | 5.08334i | ||||
\(849\) | 84.7763 | − | 48.9456i | 0.0998543 | − | 0.0576509i | ||||
\(850\) | −68.9661 | + | 68.9661i | −0.0811366 | + | 0.0811366i | ||||
\(851\) | 26.4231 | + | 7.08005i | 0.0310495 | + | 0.00831968i | ||||
\(852\) | 481.209 | − | 1795.89i | 0.564799 | − | 2.10786i | ||||
\(853\) | −703.767 | − | 703.767i | −0.825049 | − | 0.825049i | 0.161778 | − | 0.986827i | \(-0.448277\pi\) |
−0.986827 | + | 0.161778i | \(0.948277\pi\) | |||||||
\(854\) | 62.4396 | + | 108.149i | 0.0731143 | + | 0.126638i | ||||
\(855\) | 348.439 | + | 201.171i | 0.407531 | + | 0.235288i | ||||
\(856\) | −3631.07 | + | 972.942i | −4.24190 | + | 1.13661i | ||||
\(857\) | 12.6753i | 0.0147903i | 0.999973 | + | 0.00739514i | \(0.00235397\pi\) | ||||
−0.999973 | + | 0.00739514i | \(0.997646\pi\) | |||||||
\(858\) | −134.317 | + | 488.600i | −0.156547 | + | 0.569464i | ||||
\(859\) | 317.200 | 0.369266 | 0.184633 | − | 0.982808i | \(-0.440890\pi\) | ||||
0.184633 | + | 0.982808i | \(0.440890\pi\) | |||||||
\(860\) | −57.5764 | − | 214.878i | −0.0669493 | − | 0.249858i | ||||
\(861\) | 34.8481 | − | 60.3588i | 0.0404740 | − | 0.0701031i | ||||
\(862\) | 293.334 | − | 169.357i | 0.340295 | − | 0.196469i | ||||
\(863\) | −26.7486 | + | 26.7486i | −0.0309949 | + | 0.0309949i | −0.722434 | − | 0.691439i | \(-0.756977\pi\) |
0.691439 | + | 0.722434i | \(0.256977\pi\) | |||||||
\(864\) | −648.749 | − | 173.832i | −0.750866 | − | 0.201194i | ||||
\(865\) | 190.896 | − | 712.435i | 0.220690 | − | 0.823625i | ||||
\(866\) | −856.487 | − | 856.487i | −0.989015 | − | 0.989015i | ||||
\(867\) | 195.952 | + | 339.399i | 0.226012 | + | 0.391464i | ||||
\(868\) | −167.659 | − | 96.7978i | −0.193155 | − | 0.111518i | ||||
\(869\) | 244.943 | − | 65.6323i | 0.281868 | − | 0.0755262i | ||||
\(870\) | − | 474.666i | − | 0.545593i | ||||||
\(871\) | 1252.99 | + | 8.11350i | 1.43857 | + | 0.00931515i | ||||
\(872\) | −1010.68 | −1.15903 | ||||||||
\(873\) | 104.449 | + | 389.808i | 0.119643 | + | 0.446516i | ||||
\(874\) | −597.391 | + | 1034.71i | −0.683514 | + | 1.18388i | ||||
\(875\) | 103.625 | − | 59.8281i | 0.118429 | − | 0.0683750i | ||||
\(876\) | −71.5493 | + | 71.5493i | −0.0816773 | + | 0.0816773i | ||||
\(877\) | −445.096 | − | 119.263i | −0.507521 | − | 0.135990i | −0.00403275 | − | 0.999992i | \(-0.501284\pi\) |
−0.503488 | + | 0.864002i | \(0.667950\pi\) | |||||||
\(878\) | −132.956 | + | 496.200i | −0.151431 | + | 0.565148i | ||||
\(879\) | −251.053 | − | 251.053i | −0.285612 | − | 0.285612i | ||||
\(880\) | −833.264 | − | 1443.26i | −0.946891 | − | 1.64006i | ||||
\(881\) | 1118.08 | + | 645.522i | 1.26910 | + | 0.732715i | 0.974818 | − | 0.223003i | \(-0.0715860\pi\) |
0.294283 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(882\) | 541.100 | − | 144.987i | 0.613492 | − | 0.164385i | ||||
\(883\) | − | 721.384i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(884\) | −797.473 | − | 807.868i | −0.902118 | − | 0.913877i | ||||
\(885\) | −120.504 | −0.136163 | ||||||||
\(886\) | 765.138 | + | 2855.53i | 0.863587 | + | 3.22295i | ||||
\(887\) | 300.489 | − | 520.463i | 0.338770 | − | 0.586767i | −0.645431 | − | 0.763818i | \(-0.723322\pi\) |
0.984202 | + | 0.177051i | \(0.0566557\pi\) | |||||||
\(888\) | 104.062 | − | 60.0802i | 0.117187 | − | 0.0676578i | ||||
\(889\) | 139.874 | − | 139.874i | 0.157339 | − | 0.157339i | ||||
\(890\) | −491.709 | − | 131.753i | −0.552482 | − | 0.148037i | ||||
\(891\) | −13.5240 | + | 50.4723i | −0.0151785 | + | 0.0566468i | ||||
\(892\) | 2359.24 | + | 2359.24i | 2.64489 | + | 2.64489i | ||||
\(893\) | −375.076 | − | 649.650i | −0.420018 | − | 0.727492i | ||||
\(894\) | −280.715 | − | 162.071i | −0.313998 | − | 0.181287i | ||||
\(895\) | −429.945 | + | 115.203i | −0.480385 | + | 0.128719i | ||||
\(896\) | 429.360i | 0.479197i | ||||||||
\(897\) | −61.0572 | − | 233.917i | −0.0680682 | − | 0.260777i | ||||
\(898\) | 1066.80 | 1.18798 | ||||||||
\(899\) | 75.6670 | + | 282.393i | 0.0841680 | + | 0.314119i | ||||
\(900\) | −52.5357 | + | 90.9945i | −0.0583730 | + | 0.101105i | ||||
\(901\) | 555.659 | − | 320.810i | 0.616714 | − | 0.356060i | ||||
\(902\) | −704.400 | + | 704.400i | −0.780931 | + | 0.780931i | ||||
\(903\) | 6.56918 | + | 1.76021i | 0.00727484 | + | 0.00194929i | ||||
\(904\) | −1276.02 | + | 4762.18i | −1.41153 | + | 5.26790i | ||||
\(905\) | 559.098 | + | 559.098i | 0.617788 | + | 0.617788i | ||||
\(906\) | 861.096 | + | 1491.46i | 0.950437 | + | 1.64621i | ||||
\(907\) | −281.007 | − | 162.240i | −0.309820 | − | 0.178875i | 0.337026 | − | 0.941495i | \(-0.390579\pi\) |
−0.646846 | + | 0.762621i | \(0.723912\pi\) | |||||||
\(908\) | −3335.15 | + | 893.652i | −3.67308 | + | 0.984198i | ||||
\(909\) | − | 297.116i | − | 0.326860i | ||||||
\(910\) | 105.792 | + | 186.008i | 0.116255 | + | 0.204404i | ||||
\(911\) | −894.435 | −0.981817 | −0.490908 | − | 0.871211i | \(-0.663335\pi\) | ||||
−0.490908 | + | 0.871211i | \(0.663335\pi\) | |||||||
\(912\) | 790.788 | + | 2951.26i | 0.867093 | + | 3.23603i | ||||
\(913\) | −121.947 | + | 211.218i | −0.133567 | + | 0.231345i | ||||
\(914\) | −1912.50 | + | 1104.18i | −2.09245 | + | 1.20808i | ||||
\(915\) | 202.772 | − | 202.772i | 0.221609 | − | 0.221609i | ||||
\(916\) | 1714.92 | + | 459.512i | 1.87219 | + | 0.501651i | ||||
\(917\) | −37.3590 | + | 139.426i | −0.0407405 | + | 0.152046i | ||||
\(918\) | −112.803 | − | 112.803i | −0.122879 | − | 0.122879i | ||||
\(919\) | 160.850 | + | 278.600i | 0.175027 | + | 0.303155i | 0.940171 | − | 0.340704i | \(-0.110665\pi\) |
−0.765144 | + | 0.643860i | \(0.777332\pi\) | |||||||
\(920\) | 1182.74 | + | 682.855i | 1.28559 | + | 0.742234i | ||||
\(921\) | −50.2676 | + | 13.4692i | −0.0545794 | + | 0.0146245i | ||||
\(922\) | − | 528.650i | − | 0.573373i | ||||||
\(923\) | 639.968 | − | 1092.06i | 0.693356 | − | 1.18317i | ||||
\(924\) | 100.781 | 0.109070 | ||||||||
\(925\) | −2.09490 | − | 7.81827i | −0.00226476 | − | 0.00845219i | ||||
\(926\) | 1523.76 | − | 2639.24i | 1.64553 | − | 2.85015i | ||||
\(927\) | −343.632 | + | 198.396i | −0.370693 | + | 0.214020i | ||||
\(928\) | 1383.25 | − | 1383.25i | 1.49057 | − | 1.49057i | ||||
\(929\) | 1606.59 | + | 430.484i | 1.72937 | + | 0.463384i | 0.980039 | − | 0.198806i | \(-0.0637064\pi\) |
0.749336 | + | 0.662190i | \(0.230373\pi\) | |||||||
\(930\) | −156.806 | + | 585.209i | −0.168609 | + | 0.629256i | ||||
\(931\) | −977.937 | − | 977.937i | −1.05042 | − | 1.05042i | ||||
\(932\) | −1055.55 | − | 1828.27i | −1.13256 | − | 1.96166i | ||||
\(933\) | 492.022 | + | 284.069i | 0.527355 | + | 0.304468i | ||||
\(934\) | 2563.42 | − | 686.865i | 2.74456 | − | 0.735402i | ||||
\(935\) | − | 214.821i | − | 0.229755i | ||||||
\(936\) | −916.199 | − | 536.907i | −0.978845 | − | 0.573619i | ||||
\(937\) | 34.1401 | 0.0364355 | 0.0182178 | − | 0.999834i | \(-0.494201\pi\) | ||||
0.0182178 | + | 0.999834i | \(0.494201\pi\) | |||||||
\(938\) | −87.9018 | − | 328.054i | −0.0937120 | − | 0.349738i | ||||
\(939\) | −495.525 | + | 858.274i | −0.527715 | + | 0.914030i | ||||
\(940\) | −1165.44 | + | 672.865i | −1.23983 | + | 0.715814i | ||||
\(941\) | 135.813 | − | 135.813i | 0.144328 | − | 0.144328i | −0.631251 | − | 0.775579i | \(-0.717458\pi\) |
0.775579 | + | 0.631251i | \(0.217458\pi\) | |||||||
\(942\) | 521.257 | + | 139.670i | 0.553351 | + | 0.148270i | ||||
\(943\) | 123.007 | − | 459.069i | 0.130443 | − | 0.486818i | ||||
\(944\) | −647.076 | − | 647.076i | −0.685462 | − | 0.685462i | ||||
\(945\) | 11.0330 | + | 19.1098i | 0.0116752 | + | 0.0202220i | ||||
\(946\) | −84.1827 | − | 48.6029i | −0.0889881 | − | 0.0513773i | ||||
\(947\) | −1083.44 | + | 290.306i | −1.14407 | + | 0.306554i | −0.780588 | − | 0.625046i | \(-0.785080\pi\) |
−0.363486 | + | 0.931600i | \(0.618414\pi\) | |||||||
\(948\) | 834.030i | 0.879779i | ||||||||
\(949\) | −59.8796 | + | 34.0564i | −0.0630976 | + | 0.0358867i | ||||
\(950\) | 353.522 | 0.372128 | ||||||||
\(951\) | −167.263 | − | 624.235i | −0.175882 | − | 0.656399i | ||||
\(952\) | −98.0247 | + | 169.784i | −0.102967 | + | 0.178344i | ||||
\(953\) | −310.812 | + | 179.447i | −0.326140 | + | 0.188297i | −0.654126 | − | 0.756385i | \(-0.726963\pi\) |
0.327986 | + | 0.944683i | \(0.393630\pi\) | |||||||
\(954\) | 666.094 | − | 666.094i | 0.698212 | − | 0.698212i | ||||
\(955\) | 418.233 | + | 112.065i | 0.437941 | + | 0.117346i | ||||
\(956\) | 698.490 | − | 2606.80i | 0.730638 | − | 2.72678i | ||||
\(957\) | −107.616 | − | 107.616i | −0.112452 | − | 0.112452i | ||||
\(958\) | −1622.00 | − | 2809.38i | −1.69311 | − | 2.93255i | ||||
\(959\) | −191.161 | − | 110.367i | −0.199334 | − | 0.115085i | ||||
\(960\) | 1994.84 | − | 534.516i | 2.07796 | − | 0.556788i | ||||
\(961\) | 587.845i | 0.611701i | ||||||||
\(962\) | 124.224 | − | 32.4250i | 0.129130 | − | 0.0337058i | ||||
\(963\) | −414.173 | −0.430086 | ||||||||
\(964\) | 167.432 | + | 624.866i | 0.173685 | + | 0.648201i | ||||
\(965\) | −751.016 | + | 1300.80i | −0.778255 | + | 1.34798i | ||||
\(966\) | −56.7476 | + | 32.7633i | −0.0587450 | + | 0.0339164i | ||||
\(967\) | 139.945 | − | 139.945i | 0.144721 | − | 0.144721i | −0.631034 | − | 0.775755i | \(-0.717369\pi\) |
0.775755 | + | 0.631034i | \(0.217369\pi\) | |||||||
\(968\) | 2295.88 | + | 615.178i | 2.37177 | + | 0.635515i | ||||
\(969\) | −101.935 | + | 380.427i | −0.105196 | + | 0.392598i | ||||
\(970\) | −1722.39 | − | 1722.39i | −1.77566 | − | 1.77566i | ||||
\(971\) | 711.780 | + | 1232.84i | 0.733038 | + | 1.26966i | 0.955579 | + | 0.294736i | \(0.0952316\pi\) |
−0.222541 | + | 0.974923i | \(0.571435\pi\) | |||||||
\(972\) | −148.833 | − | 85.9290i | −0.153121 | − | 0.0884043i | ||||
\(973\) | 70.0175 | − | 18.7611i | 0.0719604 | − | 0.0192817i | ||||
\(974\) | 1692.54i | 1.73773i | ||||||||
\(975\) | −50.9073 | + | 50.2522i | −0.0522126 | + | 0.0515408i | ||||
\(976\) | 2177.66 | 2.23121 | ||||||||
\(977\) | −8.38753 | − | 31.3027i | −0.00858499 | − | 0.0320396i | 0.961500 | − | 0.274803i | \(-0.0886127\pi\) |
−0.970085 | + | 0.242764i | \(0.921946\pi\) | |||||||
\(978\) | −591.131 | + | 1023.87i | −0.604428 | + | 1.04690i | ||||
\(979\) | −141.351 | + | 81.6092i | −0.144383 | + | 0.0833598i | ||||
\(980\) | −1754.36 | + | 1754.36i | −1.79017 | + | 1.79017i | ||||
\(981\) | −107.559 | − | 28.8204i | −0.109642 | − | 0.0293786i | ||||
\(982\) | 444.920 | − | 1660.46i | 0.453075 | − | 1.69090i | ||||
\(983\) | −370.965 | − | 370.965i | −0.377381 | − | 0.377381i | 0.492776 | − | 0.870156i | \(-0.335982\pi\) |
−0.870156 | + | 0.492776i | \(0.835982\pi\) | |||||||
\(984\) | −1043.82 | − | 1807.95i | −1.06079 | − | 1.83735i | ||||
\(985\) | −453.370 | − | 261.753i | −0.460274 | − | 0.265739i | ||||
\(986\) | 448.811 | − | 120.259i | 0.455184 | − | 0.121966i | ||||
\(987\) | − | 41.1413i | − | 0.0416831i | ||||||
\(988\) | −26.6426 | + | 4114.50i | −0.0269662 | + | 4.16447i | ||||
\(989\) | 46.3759 | 0.0468917 | ||||||||
\(990\) | −81.6292 | − | 304.644i | −0.0824537 | − | 0.307722i | ||||
\(991\) | 600.773 | − | 1040.57i | 0.606229 | − | 1.05002i | −0.385627 | − | 0.922655i | \(-0.626015\pi\) |
0.991856 | − | 0.127365i | \(-0.0406518\pi\) | |||||||
\(992\) | −2162.35 | + | 1248.43i | −2.17979 | + | 1.25850i | ||||
\(993\) | 104.580 | − | 104.580i | 0.105318 | − | 0.105318i | ||||
\(994\) | −331.391 | − | 88.7959i | −0.333391 | − | 0.0893319i | ||||
\(995\) | −82.9992 | + | 309.757i | −0.0834163 | + | 0.311314i | ||||
\(996\) | −567.212 | − | 567.212i | −0.569490 | − | 0.569490i | ||||
\(997\) | −523.573 | − | 906.855i | −0.525148 | − | 0.909584i | −0.999571 | − | 0.0292865i | \(-0.990676\pi\) |
0.474423 | − | 0.880297i | \(-0.342657\pi\) | |||||||
\(998\) | −2154.00 | − | 1243.61i | −2.15832 | − | 1.24611i | ||||
\(999\) | 12.7878 | − | 3.42648i | 0.0128006 | − | 0.00342991i |
(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 | 39.3.l.b.19.3 | ✓ | 12 | |
3.2 | odd | 2 | 117.3.bd.d.19.1 | 12 | |||
13.11 | odd | 12 | inner | 39.3.l.b.37.3 | yes | 12 | |
39.11 | even | 12 | 117.3.bd.d.37.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.3.l.b.19.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
39.3.l.b.37.3 | yes | 12 | 13.11 | odd | 12 | inner | |
117.3.bd.d.19.1 | 12 | 3.2 | odd | 2 | |||
117.3.bd.d.37.1 | 12 | 39.11 | even | 12 |