Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,3,Mod(31,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.h (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.97549476762\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 31.5 | ||
Character | \(\chi\) | \(=\) | 256.31 |
Dual form | 256.3.h.a.223.5 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 1.58190 | − | 0.655246i | 0.527302 | − | 0.218415i | −0.103119 | − | 0.994669i | \(-0.532882\pi\) |
0.630421 | + | 0.776254i | \(0.282882\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.18866 | − | 1.73500i | −0.837732 | − | 0.347000i | −0.0777729 | − | 0.996971i | \(-0.524781\pi\) |
−0.759959 | + | 0.649971i | \(0.774781\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.93197 | + | 3.93197i | −0.561710 | + | 0.561710i | −0.929793 | − | 0.368083i | \(-0.880014\pi\) |
0.368083 | + | 0.929793i | \(0.380014\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.29089 | + | 4.29089i | −0.476765 | + | 0.476765i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.2355 | − | 5.89652i | −1.29413 | − | 0.536048i | −0.373919 | − | 0.927462i | \(-0.621986\pi\) |
−0.920215 | + | 0.391414i | \(0.871986\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.454935 | + | 0.188440i | −0.0349950 | + | 0.0144954i | −0.400112 | − | 0.916466i | \(-0.631029\pi\) |
0.365117 | + | 0.930962i | \(0.381029\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.76291 | −0.517527 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.5635i | 1.56256i | 0.624181 | + | 0.781280i | \(0.285433\pi\) | ||||
−0.624181 | + | 0.781280i | \(0.714567\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.25040 | − | 17.5040i | −0.381600 | − | 0.921264i | −0.991657 | − | 0.128906i | \(-0.958853\pi\) |
0.610057 | − | 0.792358i | \(-0.291147\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.64359 | + | 8.79641i | −0.173504 | + | 0.418877i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.775848 | − | 0.775848i | −0.0337325 | − | 0.0337325i | 0.690039 | − | 0.723772i | \(-0.257593\pi\) |
−0.723772 | + | 0.690039i | \(0.757593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.14303 | − | 3.14303i | −0.125721 | − | 0.125721i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.87340 | + | 23.8365i | −0.365682 | + | 0.882833i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.9907 | + | 43.4334i | 0.620369 | + | 1.49770i | 0.851271 | + | 0.524727i | \(0.175833\pi\) |
−0.230901 | + | 0.972977i | \(0.574167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 39.6852i | − | 1.28017i | −0.768306 | − | 0.640083i | \(-0.778900\pi\) | ||
0.768306 | − | 0.640083i | \(-0.221100\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −26.3828 | −0.799480 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 23.2916 | − | 9.64771i | 0.665475 | − | 0.275649i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −36.4715 | − | 15.1070i | −0.985717 | − | 0.408297i | −0.169177 | − | 0.985586i | \(-0.554111\pi\) |
−0.816540 | + | 0.577288i | \(0.804111\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.596189 | + | 0.596189i | −0.0152869 | + | 0.0152869i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 38.9661 | − | 38.9661i | 0.950392 | − | 0.950392i | −0.0484342 | − | 0.998826i | \(-0.515423\pi\) |
0.998826 | + | 0.0484342i | \(0.0154231\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14.2899 | − | 5.91907i | −0.332324 | − | 0.137653i | 0.210282 | − | 0.977641i | \(-0.432562\pi\) |
−0.542605 | + | 0.839988i | \(0.682562\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 25.4177 | − | 10.5284i | 0.564839 | − | 0.233964i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −62.1759 | −1.32289 | −0.661446 | − | 0.749993i | \(-0.730057\pi\) | ||||
−0.661446 | + | 0.749993i | \(0.730057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.0792i | 0.368964i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.4057 | + | 42.0210i | 0.341287 | + | 0.823940i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4986 | + | 27.7600i | −0.216954 | + | 0.523773i | −0.994462 | − | 0.105100i | \(-0.966484\pi\) |
0.777508 | + | 0.628874i | \(0.216484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 49.3970 | + | 49.3970i | 0.898128 | + | 0.898128i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22.9389 | − | 22.9389i | −0.402437 | − | 0.402437i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.30584 | + | 12.8094i | −0.0899295 | + | 0.217109i | −0.962445 | − | 0.271478i | \(-0.912488\pi\) |
0.872515 | + | 0.488587i | \(0.162488\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.1407 | − | 34.1386i | −0.231814 | − | 0.559650i | 0.764576 | − | 0.644533i | \(-0.222948\pi\) |
−0.996391 | + | 0.0848835i | \(0.972948\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 33.7433i | − | 0.535607i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.23251 | 0.0343463 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26.1257 | − | 10.8216i | 0.389937 | − | 0.161517i | −0.179097 | − | 0.983831i | \(-0.557318\pi\) |
0.569033 | + | 0.822314i | \(0.307318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.73569 | − | 0.718946i | −0.0251549 | − | 0.0104195i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −17.7859 | + | 17.7859i | −0.250505 | + | 0.250505i | −0.821178 | − | 0.570672i | \(-0.806683\pi\) |
0.570672 | + | 0.821178i | \(0.306683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.8313 | − | 12.8313i | 0.175771 | − | 0.175771i | −0.613738 | − | 0.789510i | \(-0.710335\pi\) |
0.789510 | + | 0.613738i | \(0.210335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.03144 | − | 2.91252i | −0.0937525 | − | 0.0388336i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 79.1584 | − | 32.7885i | 1.02803 | − | 0.425824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 144.157 | 1.82477 | 0.912383 | − | 0.409337i | \(-0.134240\pi\) | ||||
0.912383 | + | 0.409337i | \(0.134240\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 10.4375i | − | 0.128858i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.9897 | − | 26.5314i | −0.132406 | − | 0.319655i | 0.843747 | − | 0.536741i | \(-0.180345\pi\) |
−0.976153 | + | 0.217086i | \(0.930345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 46.0877 | − | 111.266i | 0.542208 | − | 1.30901i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 56.9192 | + | 56.9192i | 0.654244 | + | 0.654244i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.92267 | − | 5.92267i | −0.0665469 | − | 0.0665469i | 0.673050 | − | 0.739597i | \(-0.264984\pi\) |
−0.739597 | + | 0.673050i | \(0.764984\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.04785 | − | 2.52973i | 0.0115148 | − | 0.0277993i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.0036 | − | 62.7782i | −0.279608 | − | 0.675034i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 85.8978i | 0.904187i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66.9192 | 0.689889 | 0.344944 | − | 0.938623i | \(-0.387898\pi\) | ||||
0.344944 | + | 0.938623i | \(0.387898\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 86.3841 | − | 35.7815i | 0.872566 | − | 0.361429i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −23.3697 | − | 9.68007i | −0.231384 | − | 0.0958422i | 0.263979 | − | 0.964528i | \(-0.414965\pi\) |
−0.495363 | + | 0.868686i | \(0.664965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5454 | − | 15.5454i | 0.150927 | − | 0.150927i | −0.627605 | − | 0.778532i | \(-0.715965\pi\) |
0.778532 | + | 0.627605i | \(0.215965\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.5235 | − | 30.5235i | 0.290700 | − | 0.290700i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 107.060 | + | 44.3456i | 1.00056 | + | 0.414444i | 0.822001 | − | 0.569485i | \(-0.192857\pi\) |
0.178556 | + | 0.983930i | \(0.442857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −82.3132 | + | 34.0952i | −0.755167 | + | 0.312800i | −0.726848 | − | 0.686799i | \(-0.759015\pi\) |
−0.0283190 | + | 0.999599i | \(0.509015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −67.5933 | −0.608949 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.91566i | − | 0.0877492i | −0.999037 | − | 0.0438746i | \(-0.986030\pi\) | ||
0.999037 | − | 0.0438746i | \(-0.0139702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.90367 | + | 4.59586i | 0.0165536 | + | 0.0399640i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.14350 | − | 2.76065i | 0.00977350 | − | 0.0235953i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −104.447 | − | 104.447i | −0.877705 | − | 0.877705i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 82.3196 | + | 82.3196i | 0.680327 | + | 0.680327i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 36.1082 | − | 87.1730i | 0.293563 | − | 0.708724i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 51.0869 | + | 123.335i | 0.408695 | + | 0.986678i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 59.4093i | 0.467790i | 0.972262 | + | 0.233895i | \(0.0751471\pi\) | ||||
−0.972262 | + | 0.233895i | \(0.924853\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −26.4837 | −0.205300 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −176.426 | + | 73.0781i | −1.34676 | + | 0.557848i | −0.935390 | − | 0.353618i | \(-0.884951\pi\) |
−0.411375 | + | 0.911466i | \(0.634951\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 97.3336 | + | 40.3169i | 0.731832 | + | 0.303135i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 82.7126 | − | 82.7126i | 0.612686 | − | 0.612686i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −138.710 | + | 138.710i | −1.01248 | + | 1.01248i | −0.0125608 | + | 0.999921i | \(0.503998\pi\) |
−0.999921 | + | 0.0125608i | \(0.996002\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −63.7662 | − | 26.4128i | −0.458750 | − | 0.190020i | 0.141327 | − | 0.989963i | \(-0.454863\pi\) |
−0.600077 | + | 0.799943i | \(0.704863\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −98.3563 | + | 40.7405i | −0.697563 | + | 0.288940i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.58736 | 0.0530584 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 213.142i | − | 1.46994i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.8464 | + | 28.5996i | 0.0805874 | + | 0.194555i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −41.3888 | + | 99.9214i | −0.277777 | + | 0.670613i | −0.999773 | − | 0.0212835i | \(-0.993225\pi\) |
0.721996 | + | 0.691897i | \(0.243225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −159.036 | − | 159.036i | −1.05322 | − | 1.05322i | −0.998502 | − | 0.0547164i | \(-0.982575\pi\) |
−0.0547164 | − | 0.998502i | \(-0.517425\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −113.981 | − | 113.981i | −0.744974 | − | 0.744974i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −68.8537 | + | 166.228i | −0.444218 | + | 1.07244i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31.5775 | − | 76.2349i | −0.201131 | − | 0.485573i | 0.790843 | − | 0.612020i | \(-0.209643\pi\) |
−0.991973 | + | 0.126447i | \(0.959643\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 51.4480i | 0.323573i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.10122 | 0.0378958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −192.658 | + | 79.8016i | −1.18195 | + | 0.489581i | −0.885126 | − | 0.465351i | \(-0.845928\pi\) |
−0.296826 | + | 0.954932i | \(0.595928\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 110.509 | + | 45.7742i | 0.669749 | + | 0.277419i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −76.7432 | + | 76.7432i | −0.459540 | + | 0.459540i | −0.898504 | − | 0.438964i | \(-0.855345\pi\) |
0.438964 | + | 0.898504i | \(0.355345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −119.330 | + | 119.330i | −0.706092 | + | 0.706092i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 106.218 | + | 43.9971i | 0.621160 | + | 0.257293i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −46.0052 | + | 19.0560i | −0.265926 | + | 0.110150i | −0.511663 | − | 0.859187i | \(-0.670970\pi\) |
0.245737 | + | 0.969337i | \(0.420970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.7166 | 0.141238 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.7399i | 0.134124i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −29.4799 | − | 71.1707i | −0.164692 | − | 0.397602i | 0.819891 | − | 0.572520i | \(-0.194034\pi\) |
−0.984583 | + | 0.174918i | \(0.944034\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −46.7381 | + | 112.836i | −0.258222 | + | 0.623402i | −0.998821 | − | 0.0485445i | \(-0.984542\pi\) |
0.740599 | + | 0.671947i | \(0.234542\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −44.7384 | − | 44.7384i | −0.244472 | − | 0.244472i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 126.556 | + | 126.556i | 0.684087 | + | 0.684087i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 156.632 | − | 378.144i | 0.837606 | − | 2.02216i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −54.9025 | − | 132.546i | −0.290489 | − | 0.701303i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 227.376i | − | 1.19045i | −0.803559 | − | 0.595226i | \(-0.797063\pi\) | ||
0.803559 | − | 0.595226i | \(-0.202937\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −46.4565 | −0.240707 | −0.120354 | − | 0.992731i | \(-0.538403\pi\) | ||||
−0.120354 | + | 0.992731i | \(0.538403\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.53162 | − | 1.46285i | 0.0181109 | − | 0.00750177i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 186.490 | + | 77.2467i | 0.946650 | + | 0.392115i | 0.801971 | − | 0.597363i | \(-0.203785\pi\) |
0.144680 | + | 0.989479i | \(0.453785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −54.5057 | + | 54.5057i | −0.273898 | + | 0.273898i | −0.830667 | − | 0.556769i | \(-0.812041\pi\) |
0.556769 | + | 0.830667i | \(0.312041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34.2376 | − | 34.2376i | 0.170336 | − | 0.170336i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −241.518 | − | 100.040i | −1.18974 | − | 0.492808i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −230.822 | + | 95.6095i | −1.12596 | + | 0.466388i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.65815 | 0.0321650 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 291.930i | 1.39679i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 35.0586 | + | 84.6390i | 0.166155 | + | 0.401133i | 0.984923 | − | 0.172991i | \(-0.0553430\pi\) |
−0.818769 | + | 0.574123i | \(0.805343\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.4814 | + | 39.7897i | −0.0773776 | + | 0.186806i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 49.5860 | + | 49.5860i | 0.230632 | + | 0.230632i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 156.041 | + | 156.041i | 0.719082 | + | 0.719082i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.8902 | − | 28.7056i | 0.0542933 | − | 0.131076i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00564 | − | 12.0847i | −0.0226499 | − | 0.0546818i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 428.136i | 1.91989i | 0.280181 | + | 0.959947i | \(0.409606\pi\) | ||||
−0.280181 | + | 0.959947i | \(0.590394\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26.9728 | 0.119879 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −112.195 | + | 46.4728i | −0.494252 | + | 0.204726i | −0.615865 | − | 0.787852i | \(-0.711193\pi\) |
0.121613 | + | 0.992578i | \(0.461193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −128.033 | − | 53.0331i | −0.559097 | − | 0.231586i | 0.0851960 | − | 0.996364i | \(-0.472848\pi\) |
−0.644293 | + | 0.764779i | \(0.722848\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 103.736 | − | 103.736i | 0.449076 | − | 0.449076i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −90.6042 | + | 90.6042i | −0.388859 | + | 0.388859i | −0.874280 | − | 0.485421i | \(-0.838666\pi\) |
0.485421 | + | 0.874280i | \(0.338666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 260.434 | + | 107.875i | 1.10823 | + | 0.459043i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 228.042 | − | 94.4581i | 0.962202 | − | 0.398557i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −283.775 | −1.18734 | −0.593672 | − | 0.804707i | \(-0.702323\pi\) | ||||
−0.593672 | + | 0.804707i | \(0.702323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 309.483i | − | 1.28416i | −0.766636 | − | 0.642082i | \(-0.778071\pi\) | ||
0.766636 | − | 0.642082i | \(-0.221929\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −95.6997 | − | 231.040i | −0.393826 | − | 0.950780i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 31.3674 | − | 75.7277i | 0.128030 | − | 0.309093i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.59693 | + | 6.59693i | 0.0267082 | + | 0.0267082i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −34.7692 | − | 34.7692i | −0.139635 | − | 0.139635i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −33.9351 | + | 81.9265i | −0.135199 | + | 0.326400i | −0.976951 | − | 0.213465i | \(-0.931525\pi\) |
0.841751 | + | 0.539866i | \(0.181525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.46975 | + | 15.6194i | 0.0255721 | + | 0.0617366i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 206.210i | − | 0.808668i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 193.069 | 0.751241 | 0.375621 | − | 0.926774i | \(-0.377430\pi\) | ||||
0.375621 | + | 0.926774i | \(0.377430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 202.805 | − | 84.0047i | 0.783032 | − | 0.324342i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −263.564 | − | 109.172i | −1.00982 | − | 0.418283i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.4799 | − | 14.4799i | 0.0550568 | − | 0.0550568i | −0.679042 | − | 0.734099i | \(-0.737605\pi\) |
0.734099 | + | 0.679042i | \(0.237605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 96.3271 | − | 96.3271i | 0.363498 | − | 0.363498i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.2499 | − | 5.48830i | −0.0496252 | − | 0.0205554i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 125.951 | − | 52.1707i | 0.468220 | − | 0.193943i | −0.136083 | − | 0.990697i | \(-0.543451\pi\) |
0.604303 | + | 0.796754i | \(0.293451\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 490.650 | 1.81052 | 0.905258 | − | 0.424863i | \(-0.139678\pi\) | ||||
0.905258 | + | 0.424863i | \(0.139678\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 4.68840i | − | 0.0171736i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.2096 | + | 63.2755i | 0.0953076 | + | 0.230093i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 183.667 | − | 443.412i | 0.663059 | − | 1.60076i | −0.129926 | − | 0.991524i | \(-0.541474\pi\) |
0.792985 | − | 0.609241i | \(-0.208526\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 170.285 | + | 170.285i | 0.610339 | + | 0.610339i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −164.474 | − | 164.474i | −0.585316 | − | 0.585316i | 0.351043 | − | 0.936359i | \(-0.385827\pi\) |
−0.936359 | + | 0.351043i | \(0.885827\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −98.6436 | + | 238.147i | −0.348564 | + | 0.841508i | 0.648226 | + | 0.761448i | \(0.275511\pi\) |
−0.996790 | + | 0.0800601i | \(0.974489\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 56.2842 | + | 135.882i | 0.197488 | + | 0.476779i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 306.427i | 1.06769i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −416.621 | −1.44159 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 105.860 | − | 43.8486i | 0.363779 | − | 0.150682i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 60.5536 | + | 25.0821i | 0.206668 | + | 0.0856045i | 0.483616 | − | 0.875280i | \(-0.339323\pi\) |
−0.276948 | + | 0.960885i | \(0.589323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 44.4487 | − | 44.4487i | 0.150674 | − | 0.150674i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 281.105 | − | 281.105i | 0.946481 | − | 0.946481i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.499162 | + | 0.206759i | 0.00166944 | + | 0.000691503i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 79.4611 | − | 32.9139i | 0.263990 | − | 0.109348i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.3115 | −0.142942 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 167.529i | 0.549276i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 166.166 | + | 401.160i | 0.541257 | + | 1.30671i | 0.923836 | + | 0.382787i | \(0.125036\pi\) |
−0.382580 | + | 0.923923i | \(0.624964\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.4053 | − | 34.7775i | 0.0466191 | − | 0.112548i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 261.640 | + | 261.640i | 0.841288 | + | 0.841288i | 0.989026 | − | 0.147739i | \(-0.0471995\pi\) |
−0.147739 | + | 0.989026i | \(0.547199\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −301.723 | − | 301.723i | −0.963972 | − | 0.963972i | 0.0354015 | − | 0.999373i | \(-0.488729\pi\) |
−0.999373 | + | 0.0354015i | \(0.988729\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −58.5445 | + | 141.339i | −0.185856 | + | 0.448695i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.4511 | − | 27.6454i | −0.0361233 | − | 0.0872094i | 0.904788 | − | 0.425862i | \(-0.140029\pi\) |
−0.940912 | + | 0.338652i | \(0.890029\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 724.378i | − | 2.27078i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 198.415 | 0.618117 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 464.968 | − | 192.596i | 1.43953 | − | 0.596273i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.02215 | + | 0.837602i | 0.00622200 | + | 0.00257724i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −107.871 | + | 107.871i | −0.329880 | + | 0.329880i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 244.474 | − | 244.474i | 0.743081 | − | 0.743081i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −117.333 | − | 48.6009i | −0.354480 | − | 0.146830i | 0.198335 | − | 0.980134i | \(-0.436447\pi\) |
−0.552815 | + | 0.833304i | \(0.686447\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 221.318 | − | 91.6728i | 0.664617 | − | 0.275294i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −128.207 | −0.382709 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 148.325i | − | 0.440134i | −0.975485 | − | 0.220067i | \(-0.929372\pi\) | ||
0.975485 | − | 0.220067i | \(-0.0706276\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.49720 | − | 15.6856i | −0.0191658 | − | 0.0462703i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −234.004 | + | 564.937i | −0.686230 | + | 1.65671i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −263.753 | − | 263.753i | −0.768961 | − | 0.768961i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.02284 | + | 6.02284i | 0.0174575 | + | 0.0174575i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −215.625 | + | 520.565i | −0.621398 | + | 1.50019i | 0.228664 | + | 0.973505i | \(0.426564\pi\) |
−0.850062 | + | 0.526682i | \(0.823436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 92.9006 | + | 224.282i | 0.266191 | + | 0.642641i | 0.999298 | − | 0.0374720i | \(-0.0119305\pi\) |
−0.733107 | + | 0.680113i | \(0.761930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 12.7046i | − | 0.0361955i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 453.234 | 1.28395 | 0.641975 | − | 0.766726i | \(-0.278115\pi\) | ||||
0.641975 | + | 0.766726i | \(0.278115\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 105.357 | − | 43.6405i | 0.296782 | − | 0.122931i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −233.664 | − | 96.7866i | −0.654520 | − | 0.271111i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −175.857 | + | 175.857i | −0.489852 | + | 0.489852i | −0.908259 | − | 0.418407i | \(-0.862588\pi\) |
0.418407 | + | 0.908259i | \(0.362588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44333 | − | 1.44333i | 0.00399816 | − | 0.00399816i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 184.161 | + | 76.2821i | 0.507332 | + | 0.210144i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −76.0082 | + | 31.4836i | −0.208242 | + | 0.0862566i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −115.194 | −0.313879 | −0.156939 | − | 0.987608i | \(-0.550163\pi\) | ||||
−0.156939 | + | 0.987608i | \(0.550163\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 334.398i | 0.906228i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −63.9394 | − | 154.363i | −0.172343 | − | 0.416074i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 95.1961 | − | 229.824i | 0.255217 | − | 0.616149i | −0.743393 | − | 0.668855i | \(-0.766785\pi\) |
0.998610 | + | 0.0527059i | \(0.0167846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 161.629 | + | 161.629i | 0.431011 | + | 0.431011i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.3692 | − | 16.3692i | −0.0434197 | − | 0.0434197i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 264.738 | − | 639.134i | 0.698517 | − | 1.68637i | −0.0283560 | − | 0.999598i | \(-0.509027\pi\) |
0.726873 | − | 0.686772i | \(-0.240973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.9277 | + | 93.9798i | 0.102172 | + | 0.246666i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 217.725i | − | 0.568473i | −0.958754 | − | 0.284236i | \(-0.908260\pi\) | ||
0.958754 | − | 0.284236i | \(-0.0917401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −388.455 | −1.00897 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 86.7145 | − | 35.9183i | 0.224068 | − | 0.0928122i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −452.405 | − | 187.392i | −1.16299 | − | 0.481728i | −0.284123 | − | 0.958788i | \(-0.591703\pi\) |
−0.878871 | + | 0.477060i | \(0.841703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.6092 | − | 20.6092i | 0.0527091 | − | 0.0527091i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −231.205 | + | 231.205i | −0.588308 | + | 0.588308i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −603.823 | − | 250.112i | −1.52866 | − | 0.633194i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 281.846 | − | 116.745i | 0.709940 | − | 0.294067i | 0.00166042 | − | 0.999999i | \(-0.499471\pi\) |
0.708280 | + | 0.705932i | \(0.249471\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 180.390 | 0.452105 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 173.814i | 0.433452i | 0.976232 | + | 0.216726i | \(0.0695378\pi\) | ||||
−0.976232 | + | 0.216726i | \(0.930462\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.47829 | + | 18.0542i | 0.0185565 | + | 0.0447995i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.1090 | + | 43.7190i | −0.0447136 | + | 0.107948i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 430.110 | + | 430.110i | 1.05678 | + | 1.05678i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 322.065 | + | 322.065i | 0.787446 | + | 0.787446i | 0.981075 | − | 0.193629i | \(-0.0620258\pi\) |
−0.193629 | + | 0.981075i | \(0.562026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −128.537 | + | 310.315i | −0.312742 | + | 0.755025i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −29.5039 | − | 71.2287i | −0.0714380 | − | 0.172467i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 130.198i | 0.313730i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −118.179 | −0.283403 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.9903 | − | 5.79496i | 0.0333896 | − | 0.0138304i | −0.365926 | − | 0.930644i | \(-0.619248\pi\) |
0.399316 | + | 0.916813i | \(0.369248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 507.883 | + | 210.372i | 1.20637 | + | 0.499696i | 0.893053 | − | 0.449952i | \(-0.148559\pi\) |
0.313320 | + | 0.949648i | \(0.398559\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 266.790 | − | 266.790i | 0.630708 | − | 0.630708i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 83.4900 | − | 83.4900i | 0.196447 | − | 0.196447i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 189.833 | + | 78.6313i | 0.444573 | + | 0.184148i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.0025 | − | 4.97159i | 0.0279778 | − | 0.0115888i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −654.734 | −1.51910 | −0.759552 | − | 0.650447i | \(-0.774582\pi\) | ||||
−0.759552 | + | 0.650447i | \(0.774582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 366.488i | 0.846392i | 0.906038 | + | 0.423196i | \(0.139092\pi\) | ||||
−0.906038 | + | 0.423196i | \(0.860908\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −139.660 | − | 337.170i | −0.321058 | − | 0.775103i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.95524 | + | 19.2057i | −0.0182042 | + | 0.0439489i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −124.489 | − | 124.489i | −0.283573 | − | 0.283573i | 0.550959 | − | 0.834532i | \(-0.314262\pi\) |
−0.834532 | + | 0.550959i | \(0.814262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −77.5759 | − | 77.5759i | −0.175909 | − | 0.175909i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 147.480 | − | 356.047i | 0.332911 | − | 0.803718i | −0.665448 | − | 0.746445i | \(-0.731759\pi\) |
0.998359 | − | 0.0572735i | \(-0.0182407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.5322 | + | 35.0839i | 0.0326567 | + | 0.0788402i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 185.186i | 0.414286i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −689.326 | −1.53525 | −0.767623 | − | 0.640901i | \(-0.778561\pi\) | ||||
−0.767623 | + | 0.640901i | \(0.778561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −784.465 | + | 324.936i | −1.73939 | + | 0.720479i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −355.788 | − | 147.372i | −0.785403 | − | 0.325325i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.77817 | + | 8.77817i | −0.0192927 | + | 0.0192927i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 86.4503 | − | 86.4503i | 0.189169 | − | 0.189169i | −0.606168 | − | 0.795337i | \(-0.707294\pi\) |
0.795337 | + | 0.606168i | \(0.207294\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −633.181 | − | 262.272i | −1.37948 | − | 0.571399i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.31579 | − | 1.37344i | 0.00719259 | − | 0.00297927i | −0.379084 | − | 0.925362i | \(-0.623761\pi\) |
0.386277 | + | 0.922383i | \(0.373761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −113.007 | −0.244075 | −0.122038 | − | 0.992525i | \(-0.538943\pi\) | ||||
−0.122038 | + | 0.992525i | \(0.538943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 308.072i | 0.662521i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −150.402 | − | 363.102i | −0.322059 | − | 0.777520i | −0.999134 | − | 0.0416055i | \(-0.986753\pi\) |
0.677075 | − | 0.735914i | \(-0.263247\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −60.1753 | + | 145.276i | −0.128306 | + | 0.309757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −99.9053 | − | 99.9053i | −0.212113 | − | 0.212113i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 168.522 | + | 168.522i | 0.356282 | + | 0.356282i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.2275 | + | 77.8040i | −0.0678473 | + | 0.163798i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −69.7759 | − | 168.454i | −0.146281 | − | 0.353153i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 205.624i | − | 0.429278i | −0.976693 | − | 0.214639i | \(-0.931142\pi\) | ||
0.976693 | − | 0.214639i | \(-0.0688575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.4390 | 0.0404136 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.65155 | − | 3.99780i | 0.0199825 | − | 0.00827702i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −280.302 | − | 116.105i | −0.577942 | − | 0.239391i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −573.249 | + | 573.249i | −1.17710 | + | 1.17710i | −0.196623 | + | 0.980479i | \(0.562998\pi\) |
−0.980479 | + | 0.196623i | \(0.937002\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −252.477 | + | 252.477i | −0.516313 | + | 0.516313i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 421.115 | + | 174.432i | 0.857669 | + | 0.355258i | 0.767795 | − | 0.640695i | \(-0.221354\pi\) |
0.0898735 | + | 0.995953i | \(0.471354\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1153.74 | + | 477.897i | −2.34025 | + | 0.969364i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −423.914 | −0.856392 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 139.867i | − | 0.281423i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 115.301 | + | 278.361i | 0.231064 | + | 0.557837i | 0.996303 | − | 0.0859086i | \(-0.0273793\pi\) |
−0.765239 | + | 0.643746i | \(0.777379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −71.1147 | + | 171.686i | −0.141946 | + | 0.342687i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −526.474 | − | 526.474i | −1.04667 | − | 1.04667i | −0.998856 | − | 0.0478110i | \(-0.984775\pi\) |
−0.0478110 | − | 0.998856i | \(-0.515225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 81.0930 | + | 81.0930i | 0.160580 | + | 0.160580i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −110.578 | + | 266.958i | −0.218102 | + | 0.526545i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 98.1719 | + | 237.008i | 0.192872 | + | 0.465634i | 0.990500 | − | 0.137516i | \(-0.0439119\pi\) |
−0.797628 | + | 0.603150i | \(0.793912\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 100.905i | 0.197465i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 488.821 | 0.952867 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −92.0858 | + | 38.1432i | −0.178807 | + | 0.0740644i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 885.103 | + | 366.622i | 1.71200 | + | 0.709133i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −60.2895 | + | 60.2895i | −0.116165 | + | 0.116165i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.3980 | + | 42.3980i | −0.0813781 | + | 0.0813781i | −0.746624 | − | 0.665246i | \(-0.768327\pi\) |
0.665246 | + | 0.746624i | \(0.268327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 160.929 | + | 66.6589i | 0.307703 | + | 0.127455i | 0.531192 | − | 0.847252i | \(-0.321744\pi\) |
−0.223488 | + | 0.974707i | \(0.571744\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 39.0993 | − | 16.1955i | 0.0744749 | − | 0.0308485i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1054.18 | 2.00034 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 527.796i | − | 0.997724i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.1971 | − | 77.7306i | −0.0606348 | − | 0.146385i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.3843 | + | 25.0698i | −0.0194827 | + | 0.0470353i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −371.497 | − | 371.497i | −0.694386 | − | 0.694386i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −93.2687 | − | 93.2687i | −0.173685 | − | 0.173685i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 106.605 | − | 257.366i | 0.197782 | − | 0.477488i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.6178 | + | 71.5038i | 0.0547465 | + | 0.132170i | 0.948886 | − | 0.315618i | \(-0.102212\pi\) |
−0.894140 | + | 0.447788i | \(0.852212\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 209.121i | 0.385121i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 403.937 | 0.741169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 157.659 | − | 65.3046i | 0.288225 | − | 0.119387i | −0.233886 | − | 0.972264i | \(-0.575144\pi\) |
0.522112 | + | 0.852877i | \(0.325144\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 207.161 | + | 85.8089i | 0.377342 | + | 0.156300i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 629.819 | − | 629.819i | 1.14305 | − | 1.14305i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −566.819 | + | 566.819i | −1.02499 | + | 1.02499i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 283.125 | + | 117.274i | 0.510136 | + | 0.211305i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 890.709 | − | 368.944i | 1.59912 | − | 0.662376i | 0.607827 | − | 0.794069i | \(-0.292041\pi\) |
0.991291 | + | 0.131693i | \(0.0420413\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.61638 | 0.0136250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 700.821i | − | 1.24923i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 106.191 | + | 256.369i | 0.188617 | + | 0.455362i | 0.989694 | − | 0.143200i | \(-0.0457392\pi\) |
−0.801077 | + | 0.598562i | \(0.795739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.2037 | + | 41.5333i | −0.0304490 | + | 0.0735103i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 41.0398 | + | 41.0398i | 0.0723806 | + | 0.0723806i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −351.714 | − | 351.714i | −0.618126 | − | 0.618126i | 0.326925 | − | 0.945050i | \(-0.393988\pi\) |
−0.945050 | + | 0.326925i | \(0.893988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 179.708 | − | 433.854i | 0.314725 | − | 0.759814i | −0.684792 | − | 0.728739i | \(-0.740107\pi\) |
0.999517 | − | 0.0310755i | \(-0.00989322\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −148.987 | − | 359.688i | −0.260013 | − | 0.627727i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.87703i | 0.00848179i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 662.602 | 1.14836 | 0.574179 | − | 0.818730i | \(-0.305321\pi\) | ||||
0.574179 | + | 0.818730i | \(0.305321\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −73.4898 | + | 30.4405i | −0.126925 | + | 0.0525742i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 147.532 | + | 61.1096i | 0.253927 | + | 0.105180i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 327.375 | − | 327.375i | 0.561535 | − | 0.561535i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.57946 | + | 9.57946i | −0.0163751 | + | 0.0163751i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 650.448 | + | 269.424i | 1.10809 | + | 0.458985i | 0.860279 | − | 0.509824i | \(-0.170289\pi\) |
0.247809 | + | 0.968809i | \(0.420289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −694.650 | + | 287.733i | −1.17937 | + | 0.488512i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 345.625 | 0.584814 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 430.692i | − | 0.726293i | −0.931732 | − | 0.363147i | \(-0.881702\pi\) | ||
0.931732 | − | 0.363147i | \(-0.118298\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 256.277 | + | 618.708i | 0.430718 | + | 1.03985i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −50.5082 | + | 121.938i | −0.0846033 | + | 0.204250i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0528 | + | 16.0528i | 0.0267993 | + | 0.0267993i | 0.720379 | − | 0.693580i | \(-0.243968\pi\) |
−0.693580 | + | 0.720379i | \(0.743968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 201.233 | + | 201.233i | 0.334831 | + | 0.334831i | 0.854418 | − | 0.519587i | \(-0.173914\pi\) |
−0.519587 | + | 0.854418i | \(0.673914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −65.6682 | + | 158.537i | −0.108902 | + | 0.262914i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −201.984 | − | 487.633i | −0.333858 | − | 0.806005i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 713.329i | 1.17517i | 0.809162 | + | 0.587586i | \(0.199921\pi\) | ||||
−0.809162 | + | 0.587586i | \(0.800079\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −447.609 | −0.734990 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.2860 | − | 11.7164i | 0.0462946 | − | 0.0191759i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 349.658 | + | 144.833i | 0.570404 | + | 0.236269i | 0.649195 | − | 0.760622i | \(-0.275106\pi\) |
−0.0787907 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −302.490 | + | 302.490i | −0.491854 | + | 0.491854i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 185.331 | − | 185.331i | 0.300374 | − | 0.300374i | −0.540786 | − | 0.841160i | \(-0.681873\pi\) |
0.841160 | + | 0.540786i | \(0.181873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −740.280 | − | 306.634i | −1.19593 | − | 0.495370i | −0.306248 | − | 0.951952i | \(-0.599074\pi\) |
−0.889681 | + | 0.456582i | \(0.849074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.1538 | − | 10.8332i | 0.0421156 | − | 0.0174448i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 46.5755 | 0.0747601 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 494.120i | − | 0.790591i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 191.286 | + | 461.805i | 0.305081 | + | 0.736532i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 401.295 | − | 968.812i | 0.637989 | − | 1.54024i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.0415 | − | 25.0415i | −0.0396854 | − | 0.0396854i | 0.686986 | − | 0.726671i | \(-0.258934\pi\) |
−0.726671 | + | 0.686986i | \(0.758934\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 110.919 | + | 110.919i | 0.175227 | + | 0.175227i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 103.075 | − | 248.845i | 0.162323 | − | 0.391882i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.40686 | − | 8.22488i | −0.00534828 | − | 0.0129119i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 152.634i | − | 0.238864i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −150.813 | −0.235278 | −0.117639 | − | 0.993056i | \(-0.537533\pi\) | ||||
−0.117639 | + | 0.993056i | \(0.537533\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −635.355 | + | 263.173i | −0.988110 | + | 0.409289i | −0.817424 | − | 0.576037i | \(-0.804598\pi\) |
−0.170686 | + | 0.985325i | \(0.554598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 110.931 | + | 45.9492i | 0.171987 | + | 0.0712391i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 460.454 | − | 460.454i | 0.711675 | − | 0.711675i | −0.255211 | − | 0.966885i | \(-0.582145\pi\) |
0.966885 | + | 0.255211i | \(0.0821448\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 151.062 | − | 151.062i | 0.232762 | − | 0.232762i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 349.087 | + | 144.597i | 0.536232 | + | 0.222115i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −308.661 | + | 127.852i | −0.472682 | + | 0.195791i | −0.606291 | − | 0.795243i | \(-0.707343\pi\) |
0.133609 | + | 0.991034i | \(0.457343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 865.779 | 1.32180 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 110.115i | 0.167603i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −187.311 | − | 452.209i | −0.284235 | − | 0.686205i | 0.715690 | − | 0.698418i | \(-0.246112\pi\) |
−0.999925 | + | 0.0122131i | \(0.996112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 279.659 | − | 675.156i | 0.423084 | − | 1.02142i | −0.558348 | − | 0.829607i | \(-0.688564\pi\) |
0.981432 | − | 0.191809i | \(-0.0614355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.8369 | − | 15.8369i | −0.0238867 | − | 0.0238867i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −337.747 | − | 337.747i | −0.507891 | − | 0.507891i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.7397 | − | 47.6558i | 0.0295947 | − | 0.0714479i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 280.535 | + | 677.271i | 0.419335 | + | 1.01236i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 569.360i | 0.848525i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 74.6107 | 0.110863 | 0.0554314 | − | 0.998462i | \(-0.482347\pi\) | ||||
0.0554314 | + | 0.998462i | \(0.482347\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 105.951 | − | 43.8865i | 0.156965 | − | 0.0650170i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 250.770 | + | 103.872i | 0.370413 | + | 0.153430i | 0.560122 | − | 0.828410i | \(-0.310754\pi\) |
−0.189709 | + | 0.981840i | \(0.560754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −263.124 | + | 263.124i | −0.387517 | + | 0.387517i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −147.031 | + | 147.031i | −0.215905 | + | 0.215905i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1198.32 | + | 496.359i | 1.75449 | + | 0.726734i | 0.997291 | + | 0.0735510i | \(0.0234332\pi\) |
0.757200 | + | 0.653183i | \(0.226567\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 821.671 | − | 340.347i | 1.19952 | − | 0.496857i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −237.286 | −0.345395 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 14.7958i | − | 0.0214743i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −337.819 | − | 815.567i | −0.488884 | − | 1.18027i | −0.955282 | − | 0.295696i | \(-0.904449\pi\) |
0.466398 | − | 0.884575i | \(-0.345551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −198.968 | + | 480.351i | −0.287111 | + | 0.693147i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 221.269 | + | 221.269i | 0.318372 | + | 0.318372i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1035.08 | + | 1035.08i | 1.48504 | + | 1.48504i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −83.9591 | + | 202.695i | −0.120113 | + | 0.289979i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −487.432 | − | 1176.77i | −0.695338 | − | 1.67870i | −0.733737 | − | 0.679433i | \(-0.762226\pi\) |
0.0383989 | − | 0.999262i | \(-0.487774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 747.930i | 1.06391i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 482.666 | 0.684632 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 129.951 | − | 53.8274i | 0.183806 | − | 0.0761349i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −949.384 | − | 393.248i | −1.33905 | − | 0.554651i | −0.405824 | − | 0.913951i | \(-0.633015\pi\) |
−0.933222 | + | 0.359300i | \(0.883015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −618.559 | + | 618.559i | −0.869985 | + | 0.869985i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.7896 | + | 30.7896i | −0.0431832 | + | 0.0431832i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.7809 | − | 13.1641i | −0.0444487 | − | 0.0184113i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −448.906 | + | 185.943i | −0.626089 | + | 0.259335i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −349.072 | −0.485496 | −0.242748 | − | 0.970089i | \(-0.578049\pi\) | ||||
−0.242748 | + | 0.970089i | \(0.578049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 122.248i | 0.169554i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −202.788 | − | 489.573i | −0.280481 | − | 0.677141i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 79.9673 | − | 193.058i | 0.110300 | − | 0.266287i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 256.931 | + | 256.931i | 0.353413 | + | 0.353413i | 0.861378 | − | 0.507965i | \(-0.169602\pi\) |
−0.507965 | + | 0.861378i | \(0.669602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −236.352 | − | 236.352i | −0.324214 | − | 0.324214i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 157.231 | − | 379.590i | 0.215091 | − | 0.519275i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −473.293 | − | 1142.63i | −0.645694 | − | 1.55884i | −0.818887 | − | 0.573955i | \(-0.805409\pi\) |
0.173194 | − | 0.984888i | \(-0.444591\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 140.347i | − | 0.190949i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −435.722 | −0.591211 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −137.009 | + | 56.7511i | −0.185398 | + | 0.0767945i | −0.473451 | − | 0.880820i | \(-0.656992\pi\) |
0.288053 | + | 0.957614i | \(0.406992\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.7583 | + | 6.11310i | 0.0199168 | + | 0.00824979i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 644.593 | − | 644.593i | 0.867555 | − | 0.867555i | −0.124647 | − | 0.992201i | \(-0.539780\pi\) |
0.992201 | + | 0.124647i | \(0.0397797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 346.727 | − | 346.727i | 0.465405 | − | 0.465405i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 160.999 | + | 66.6878i | 0.215527 | + | 0.0892742i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −595.321 | + | 246.590i | −0.794821 | + | 0.329225i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.5402 | 0.0246873 | 0.0123437 | − | 0.999924i | \(-0.496071\pi\) | ||||
0.0123437 | + | 0.999924i | \(0.496071\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 151.836i | 0.201641i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 390.220 | + | 942.075i | 0.516848 | + | 1.24778i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −100.854 | + | 243.482i | −0.133228 | + | 0.321641i | −0.976389 | − | 0.216021i | \(-0.930692\pi\) |
0.843161 | + | 0.537661i | \(0.180692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.4691 | + | 20.4691i | 0.0269685 | + | 0.0269685i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −272.267 | − | 272.267i | −0.357775 | − | 0.357775i | 0.505217 | − | 0.862992i | \(-0.331412\pi\) |
−0.862992 | + | 0.505217i | \(0.831412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 189.591 | − | 457.714i | 0.248482 | − | 0.599888i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 279.671 | + | 675.185i | 0.365583 | + | 0.882594i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.82730i | − | 0.00890130i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −341.927 | −0.444638 | −0.222319 | − | 0.974974i | \(-0.571363\pi\) | ||||
−0.222319 | + | 0.974974i | \(0.571363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 305.417 | − | 126.508i | 0.396131 | − | 0.164083i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 366.728 | + | 151.904i | 0.474421 | + | 0.196512i | 0.607065 | − | 0.794652i | \(-0.292347\pi\) |
−0.132644 | + | 0.991164i | \(0.542347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −124.732 | + | 124.732i | −0.160944 | + | 0.160944i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 265.775 | − | 265.775i | 0.342053 | − | 0.342053i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −964.582 | − | 399.543i | −1.23823 | − | 0.512892i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 358.065 | − | 148.315i | 0.458470 | − | 0.189904i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1212.93 | −1.54908 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 374.109i | 0.476572i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 167.684 | + | 404.824i | 0.213067 | + | 0.514389i | 0.993892 | − | 0.110361i | \(-0.0352008\pi\) |
−0.780825 | + | 0.624750i | \(0.785201\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.4179 | − | 32.3938i | 0.0170063 | − | 0.0410568i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.9881 | + | 38.9881i | 0.0492896 | + | 0.0492896i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8662 | + | 12.8662i | 0.0162247 | + | 0.0162247i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 89.2623 | − | 215.498i | 0.112280 | − | 0.271067i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 230.548 | + | 556.591i | 0.289269 | + | 0.698358i | 0.999987 | − | 0.00511971i | \(-0.00162966\pi\) |
−0.710718 | + | 0.703477i | \(0.751630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1651.61i | − | 2.06710i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 50.8270 | 0.0634545 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −258.320 | + | 106.999i | −0.321693 | + | 0.133250i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.5559 | − | 10.5856i | −0.0317465 | − | 0.0131498i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 165.058 | − | 165.058i | 0.204533 | − | 0.204533i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 195.031 | − | 195.031i | 0.241077 | − | 0.241077i | −0.576219 | − | 0.817296i | \(-0.695472\pi\) |
0.817296 | + | 0.576219i | \(0.195472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −889.956 | − | 368.632i | −1.09736 | − | 0.454540i | −0.240791 | − | 0.970577i | \(-0.577407\pi\) |
−0.856566 | + | 0.516037i | \(0.827407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 776.161 | − | 321.496i | 0.954688 | − | 0.395445i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 945.435 | 1.16004 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 293.046i | 0.358686i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.35859 | + | 15.3510i | 0.00776385 | + | 0.0187436i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −328.443 | + | 792.932i | −0.400052 | + | 0.965812i | 0.587600 | + | 0.809151i | \(0.300073\pi\) |
−0.987653 | + | 0.156660i | \(0.949927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 319.915 | + | 319.915i | 0.388718 | + | 0.388718i | 0.874230 | − | 0.485512i | \(-0.161367\pi\) |
−0.485512 | + | 0.874230i | \(0.661367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 82.9221 | + | 82.9221i | 0.100512 | + | 0.100512i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −352.335 | + | 850.612i | −0.426040 | + | 1.02855i | 0.554492 | + | 0.832189i | \(0.312913\pi\) |
−0.980532 | + | 0.196362i | \(0.937087\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 459.660 | + | 1109.72i | 0.554475 | + | 1.33862i | 0.914086 | + | 0.405519i | \(0.132909\pi\) |
−0.359611 | + | 0.933102i | \(0.617091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 821.783i | − | 0.988908i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −480.248 | −0.576528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 454.600 | − | 188.302i | 0.544432 | − | 0.225511i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 945.956 | + | 391.828i | 1.13017 | + | 0.468133i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −439.790 | + | 439.790i | −0.524184 | + | 0.524184i | −0.918832 | − | 0.394648i | \(-0.870866\pi\) |
0.394648 | + | 0.918832i | \(0.370866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −968.120 | + | 968.120i | −1.15115 | + | 1.15115i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −367.953 | − | 152.411i | −0.436480 | − | 0.180796i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 706.868 | − | 292.794i | 0.836530 | − | 0.346502i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −647.356 | −0.764293 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 441.361i | 0.519860i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.5756 | + | 40.0171i | 0.0194778 | + | 0.0470236i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −639.942 | + | 1544.96i | −0.750225 | + | 1.81120i | −0.192248 | + | 0.981346i | \(0.561578\pi\) |
−0.557977 | + | 0.829857i | \(0.688422\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −368.578 | − | 368.578i | −0.431085 | − | 0.431085i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −628.373 | − | 628.373i | −0.733224 | − | 0.733224i | 0.238033 | − | 0.971257i | \(-0.423497\pi\) |
−0.971257 | + | 0.238033i | \(0.923497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −467.557 | + | 1128.78i | −0.544304 | + | 1.31407i | 0.377357 | + | 0.926068i | \(0.376833\pi\) |
−0.921660 | + | 0.387998i | \(0.873167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 200.785 | + | 484.738i | 0.233200 | + | 0.562994i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 709.297i | − | 0.821896i | −0.911659 | − | 0.410948i | \(-0.865198\pi\) | ||
0.911659 | − | 0.410948i | \(-0.134802\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 225.762 | 0.260997 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −659.054 | + | 272.989i | −0.760155 | + | 0.314866i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2052.14 | − | 850.023i | −2.36149 | − | 0.978162i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.84629 | + | 9.84629i | −0.0113046 | + | 0.0113046i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −287.143 | + | 287.143i | −0.328915 | + | 0.328915i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −685.820 | − | 284.076i | −0.783795 | − | 0.324658i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −927.972 | + | 384.378i | −1.05812 | + | 0.438288i | −0.842784 | − | 0.538252i | \(-0.819085\pi\) |
−0.215337 | + | 0.976540i | \(0.569085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 112.225 | 0.127673 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 660.780i | 0.750034i | 0.927018 | + | 0.375017i | \(0.122363\pi\) | ||||
−0.927018 | + | 0.375017i | \(0.877637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −476.753 | − | 1150.98i | −0.539924 | − | 1.30349i | −0.924775 | − | 0.380514i | \(-0.875747\pi\) |
0.384851 | − | 0.922979i | \(-0.374253\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 41.1888 | − | 99.4385i | 0.0465410 | − | 0.112360i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −248.725 | − | 248.725i | −0.280411 | − | 0.280411i | 0.552862 | − | 0.833273i | \(-0.313536\pi\) |
−0.833273 | + | 0.552862i | \(0.813536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −233.595 | − | 233.595i | −0.262762 | − | 0.262762i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −61.5448 | + | 148.582i | −0.0690738 | + | 0.166759i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 450.800 | + | 1088.33i | 0.504815 | + | 1.21873i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 349.257i | 0.390232i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.925104 | 0.00103133 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1723.66 | − | 713.964i | 1.91731 | − | 0.794176i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −737.403 | − | 305.442i | −0.818427 | − | 0.339004i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 104.133 | − | 104.133i | 0.115319 | − | 0.115319i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 391.540 | − | 391.540i | 0.432641 | − | 0.432641i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 301.032 | + | 124.692i | 0.331899 | + | 0.137477i | 0.542409 | − | 0.840115i | \(-0.317512\pi\) |
−0.210510 | + | 0.977592i | \(0.567512\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 141.813 | − | 58.7409i | 0.156010 | − | 0.0646214i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1283.61 | −1.40901 | −0.704507 | − | 0.709697i | \(-0.748832\pi\) | ||||
−0.704507 | + | 0.709697i | \(0.748832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 442.488i | 0.484652i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 109.773 | + | 265.015i | 0.119970 | + | 0.289634i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 406.361 | − | 981.043i | 0.443142 | − | 1.06984i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −299.609 | − | 299.609i | −0.326017 | − | 0.326017i | 0.525053 | − | 0.851070i | \(-0.324046\pi\) |
−0.851070 | + | 0.525053i | \(0.824046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 525.717 | + | 525.717i | 0.570811 | + | 0.570811i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.73985 | − | 11.4430i | 0.00513526 | − | 0.0123976i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 67.1494 | + | 162.113i | 0.0725940 | + | 0.175257i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 133.407i | 0.143913i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 166.333 | 0.179045 | 0.0895225 | − | 0.995985i | \(-0.471466\pi\) | ||||
0.0895225 | + | 0.995985i | \(0.471466\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 316.459 | − | 131.082i | 0.339913 | − | 0.140797i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 585.329 | + | 242.451i | 0.627363 | + | 0.259862i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1312.16 | + | 1312.16i | −1.40338 | + | 1.40338i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 919.394 | − | 919.394i | 0.981211 | − | 0.981211i | −0.0186162 | − | 0.999827i | \(-0.505926\pi\) |
0.999827 | + | 0.0186162i | \(0.00592605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −675.000 | − | 279.594i | −0.718850 | − | 0.297757i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −540.855 | + | 224.029i | −0.574766 | + | 0.238076i | −0.651082 | − | 0.759008i | \(-0.725684\pi\) |
0.0763153 | + | 0.997084i | \(0.475684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −60.4635 | −0.0641182 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 650.447i | 0.688304i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −149.824 | − | 361.708i | −0.158209 | − | 0.381951i | 0.824821 | − | 0.565394i | \(-0.191276\pi\) |
−0.983030 | + | 0.183443i | \(0.941276\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.41948 | + | 8.25535i | −0.00360324 | + | 0.00869900i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.2291 | − | 36.2291i | −0.0380958 | − | 0.0380958i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −400.363 | − | 400.363i | −0.420108 | − | 0.420108i | 0.465133 | − | 0.885241i | \(-0.346006\pi\) |
−0.885241 | + | 0.465133i | \(0.846006\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −394.498 | + | 952.401i | −0.413086 | + | 0.997279i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −474.646 | − | 1145.90i | −0.495973 | − | 1.19738i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1090.81i | − | 1.13744i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −613.912 | −0.638827 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −649.662 | + | 269.099i | −0.674623 | + | 0.279438i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 194.590 | + | 80.6020i | 0.201648 | + | 0.0835254i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 450.402 | − | 450.402i | 0.465772 | − | 0.465772i | −0.434770 | − | 0.900542i | \(-0.643170\pi\) |
0.900542 | + | 0.434770i | \(0.143170\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 609.338 | − | 609.338i | 0.628831 | − | 0.628831i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1287.15 | + | 533.155i | 1.32559 | + | 0.549079i | 0.929395 | − | 0.369086i | \(-0.120329\pi\) |
0.396198 | + | 0.918165i | \(0.370329\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 354.581 | − | 146.872i | 0.364421 | − | 0.150948i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.74769 | 0.00384378 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1408.92i | − | 1.44208i | −0.692891 | − | 0.721042i | \(-0.743664\pi\) | ||
0.692891 | − | 0.721042i | \(-0.256336\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.3888 | + | 119.235i | 0.0504482 | + | 0.121793i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 206.898 | − | 499.495i | 0.210905 | − | 0.509169i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 748.725 | + | 748.725i | 0.761674 | + | 0.761674i | 0.976625 | − | 0.214951i | \(-0.0689592\pi\) |
−0.214951 | + | 0.976625i | \(0.568959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −647.120 | − | 647.120i | −0.656975 | − | 0.656975i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 226.544 | − | 546.925i | 0.229527 | − | 0.554128i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.49449 | + | 15.6791i | 0.00656673 | + | 0.0158535i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1179.74i | 1.19045i | 0.803559 | + | 0.595225i | \(0.202937\pi\) | ||||
−0.803559 | + | 0.595225i | \(0.797063\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −217.455 | −0.218988 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 322.873 | − | 133.738i | 0.324496 | − | 0.134411i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1523.14 | − | 630.907i | −1.52773 | − | 0.632805i | −0.548606 | − | 0.836081i | \(-0.684841\pi\) |
−0.979121 | + | 0.203276i | \(0.934841\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 720.196 | − | 720.196i | 0.720917 | − | 0.720917i |
(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 | 256.3.h.a.31.5 | 28 | ||
4.3 | odd | 2 | 256.3.h.b.31.3 | 28 | |||
8.3 | odd | 2 | 32.3.h.a.27.1 | yes | 28 | ||
8.5 | even | 2 | 128.3.h.a.15.3 | 28 | |||
24.11 | even | 2 | 288.3.u.a.91.7 | 28 | |||
32.3 | odd | 8 | 128.3.h.a.111.3 | 28 | |||
32.13 | even | 8 | 256.3.h.b.223.3 | 28 | |||
32.19 | odd | 8 | inner | 256.3.h.a.223.5 | 28 | ||
32.29 | even | 8 | 32.3.h.a.19.1 | ✓ | 28 | ||
96.29 | odd | 8 | 288.3.u.a.19.7 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.1 | ✓ | 28 | 32.29 | even | 8 | ||
32.3.h.a.27.1 | yes | 28 | 8.3 | odd | 2 | ||
128.3.h.a.15.3 | 28 | 8.5 | even | 2 | |||
128.3.h.a.111.3 | 28 | 32.3 | odd | 8 | |||
256.3.h.a.31.5 | 28 | 1.1 | even | 1 | trivial | ||
256.3.h.a.223.5 | 28 | 32.19 | odd | 8 | inner | ||
256.3.h.b.31.3 | 28 | 4.3 | odd | 2 | |||
256.3.h.b.223.3 | 28 | 32.13 | even | 8 | |||
288.3.u.a.19.7 | 28 | 96.29 | odd | 8 | |||
288.3.u.a.91.7 | 28 | 24.11 | even | 2 |