Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(641,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.h (of order \(2\), degree \(1\), 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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.5 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.641 |
Dual form | 768.3.h.f.641.7 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.44949 | − | 1.73205i | 0.816497 | − | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.82843 | −0.565685 | −0.282843 | − | 0.959166i | \(-0.591277\pi\) | ||||
−0.282843 | + | 0.959166i | \(0.591277\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.3923 | 1.48461 | 0.742307 | − | 0.670059i | \(-0.233731\pi\) | ||||
0.742307 | + | 0.670059i | \(0.233731\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | − | 8.48528i | 0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.6969 | −1.33609 | −0.668043 | − | 0.744123i | \(-0.732868\pi\) | ||||
−0.668043 | + | 0.744123i | \(0.732868\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.00000i | − | 0.461538i | −0.973009 | − | 0.230769i | \(-0.925876\pi\) | ||
0.973009 | − | 0.230769i | \(-0.0741242\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.92820 | + | 4.89898i | −0.461880 | + | 0.326599i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 22.6274i | − | 1.33102i | −0.746387 | − | 0.665512i | \(-0.768213\pi\) | ||
0.746387 | − | 0.665512i | \(-0.231787\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.3923i | 0.546963i | 0.961877 | + | 0.273482i | \(0.0881753\pi\) | ||||
−0.961877 | + | 0.273482i | \(0.911825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 25.4558 | − | 18.0000i | 1.21218 | − | 0.857143i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 29.3939i | − | 1.27799i | −0.769209 | − | 0.638997i | \(-0.779349\pi\) | ||
0.769209 | − | 0.638997i | \(-0.220651\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −17.0000 | −0.680000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.34847 | − | 25.9808i | −0.272166 | − | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 31.1127 | 1.07285 | 0.536426 | − | 0.843947i | \(-0.319774\pi\) | ||||
0.536426 | + | 0.843947i | \(0.319774\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.1769 | 1.00571 | 0.502853 | − | 0.864372i | \(-0.332284\pi\) | ||||
0.502853 | + | 0.864372i | \(0.332284\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −36.0000 | + | 25.4558i | −1.09091 | + | 0.771389i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −29.3939 | −0.839825 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.0000i | 1.02703i | 0.858082 | + | 0.513514i | \(0.171656\pi\) | ||||
−0.858082 | + | 0.513514i | \(0.828344\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.3923 | − | 14.6969i | −0.266469 | − | 0.376845i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.65685i | − | 0.137972i | −0.997618 | − | 0.0689860i | \(-0.978024\pi\) | ||
0.997618 | − | 0.0689860i | \(-0.0219764\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.3923i | − | 0.241682i | −0.992672 | − | 0.120841i | \(-0.961441\pi\) | ||
0.992672 | − | 0.120841i | \(-0.0385590\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.48528 | + | 24.0000i | −0.188562 | + | 0.533333i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 58.7878i | − | 1.25080i | −0.780303 | − | 0.625402i | \(-0.784935\pi\) | ||
0.780303 | − | 0.625402i | \(-0.215065\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 59.0000 | 1.20408 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −39.1918 | − | 55.4256i | −0.768467 | − | 1.08678i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.1421 | −0.266833 | −0.133416 | − | 0.991060i | \(-0.542595\pi\) | ||||
−0.133416 | + | 0.991060i | \(0.542595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 41.5692 | 0.755804 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.0000 | + | 25.4558i | 0.315789 | + | 0.446594i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.6969 | −0.249101 | −0.124550 | − | 0.992213i | \(-0.539749\pi\) | ||||
−0.124550 | + | 0.992213i | \(0.539749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 22.0000i | − | 0.360656i | −0.983607 | − | 0.180328i | \(-0.942284\pi\) | ||
0.983607 | − | 0.180328i | \(-0.0577159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 31.1769 | − | 88.1816i | 0.494872 | − | 1.39971i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.9706i | 0.261086i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 114.315i | − | 1.70620i | −0.521748 | − | 0.853100i | \(-0.674720\pi\) | ||
0.521748 | − | 0.853100i | \(-0.325280\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −50.9117 | − | 72.0000i | −0.737851 | − | 1.04348i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.3939i | 0.413998i | 0.978341 | + | 0.206999i | \(0.0663697\pi\) | ||||
−0.978341 | + | 0.206999i | \(0.933630\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30.0000 | 0.410959 | 0.205479 | − | 0.978661i | \(-0.434125\pi\) | ||||
0.205479 | + | 0.978661i | \(0.434125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −41.6413 | + | 29.4449i | −0.555218 | + | 0.392598i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −152.735 | −1.98357 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31.1769 | 0.394644 | 0.197322 | − | 0.980339i | \(-0.436775\pi\) | ||||
0.197322 | + | 0.980339i | \(0.436775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −63.0000 | − | 50.9117i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −73.4847 | −0.885358 | −0.442679 | − | 0.896680i | \(-0.645972\pi\) | ||||
−0.442679 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 64.0000i | 0.752941i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 76.2102 | − | 53.8888i | 0.875980 | − | 0.619411i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.65685i | − | 0.0635602i | −0.999495 | − | 0.0317801i | \(-0.989882\pi\) | ||
0.999495 | − | 0.0317801i | \(-0.0101176\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 62.3538i | − | 0.685207i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 76.3675 | − | 54.0000i | 0.821156 | − | 0.580645i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 29.3939i | − | 0.309409i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 90.0000 | 0.927835 | 0.463918 | − | 0.885878i | \(-0.346443\pi\) | ||||
0.463918 | + | 0.885878i | \(0.346443\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −44.0908 | + | 124.708i | −0.445362 | + | 1.25967i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.82843 | −0.0280042 | −0.0140021 | − | 0.999902i | \(-0.504457\pi\) | ||||
−0.0140021 | + | 0.999902i | \(0.504457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −72.7461 | −0.706273 | −0.353137 | − | 0.935572i | \(-0.614885\pi\) | ||||
−0.353137 | + | 0.935572i | \(0.614885\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −72.0000 | + | 50.9117i | −0.685714 | + | 0.484873i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −73.4847 | −0.686773 | −0.343386 | − | 0.939194i | \(-0.611574\pi\) | ||||
−0.343386 | + | 0.939194i | \(0.611574\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 138.000i | 1.26606i | 0.774129 | + | 0.633028i | \(0.218188\pi\) | ||||
−0.774129 | + | 0.633028i | \(0.781812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 65.8179 | + | 93.0806i | 0.592954 | + | 0.838564i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 192.333i | 1.70206i | 0.525115 | + | 0.851031i | \(0.324022\pi\) | ||||
−0.525115 | + | 0.851031i | \(0.675978\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83.1384i | 0.722943i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −50.9117 | − | 18.0000i | −0.435143 | − | 0.153846i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 235.151i | − | 1.97606i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 95.0000 | 0.785124 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.79796 | − | 13.8564i | −0.0796582 | − | 0.112654i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 118.794 | 0.950352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −51.9615 | −0.409146 | −0.204573 | − | 0.978851i | \(-0.565581\pi\) | ||||
−0.204573 | + | 0.978851i | \(0.565581\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.0000 | − | 25.4558i | −0.139535 | − | 0.197332i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 44.0908 | 0.336571 | 0.168286 | − | 0.985738i | \(-0.446177\pi\) | ||||
0.168286 | + | 0.985738i | \(0.446177\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 108.000i | 0.812030i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.7846 | + | 73.4847i | 0.153960 | + | 0.544331i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 39.5980i | 0.289036i | 0.989502 | + | 0.144518i | \(0.0461632\pi\) | ||||
−0.989502 | + | 0.144518i | \(0.953837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 135.100i | − | 0.971942i | −0.873975 | − | 0.485971i | \(-0.838466\pi\) | ||
0.873975 | − | 0.485971i | \(-0.161534\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −101.823 | − | 144.000i | −0.722152 | − | 1.02128i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 88.1816i | 0.616655i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −88.0000 | −0.606897 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 144.520 | − | 102.191i | 0.983129 | − | 0.695177i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 189.505 | 1.27184 | 0.635922 | − | 0.771754i | \(-0.280620\pi\) | ||||
0.635922 | + | 0.771754i | \(0.280620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 176.669 | 1.16999 | 0.584997 | − | 0.811035i | \(-0.301096\pi\) | ||||
0.584997 | + | 0.811035i | \(0.301096\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −192.000 | − | 67.8823i | −1.25490 | − | 0.443675i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −88.1816 | −0.568914 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 154.000i | 0.980892i | 0.871472 | + | 0.490446i | \(0.163166\pi\) | ||||
−0.871472 | + | 0.490446i | \(0.836834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −34.6410 | + | 24.4949i | −0.217868 | + | 0.154056i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 305.470i | − | 1.89733i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 72.7461i | − | 0.446295i | −0.974785 | − | 0.223148i | \(-0.928367\pi\) | ||
0.974785 | − | 0.223148i | \(-0.0716332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 101.823 | − | 72.0000i | 0.617111 | − | 0.436364i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 264.545i | 1.58410i | 0.610455 | + | 0.792051i | \(0.290986\pi\) | ||||
−0.610455 | + | 0.792051i | \(0.709014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 133.000 | 0.786982 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 88.1816 | + | 31.1769i | 0.515682 | + | 0.182321i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 223.446 | 1.29159 | 0.645797 | − | 0.763509i | \(-0.276525\pi\) | ||||
0.645797 | + | 0.763509i | \(0.276525\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −176.669 | −1.00954 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −36.0000 | + | 25.4558i | −0.203390 | + | 0.143818i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 102.879 | 0.574741 | 0.287370 | − | 0.957820i | \(-0.407219\pi\) | ||||
0.287370 | + | 0.957820i | \(0.407219\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 234.000i | − | 1.29282i | −0.762991 | − | 0.646409i | \(-0.776270\pi\) | ||
0.762991 | − | 0.646409i | \(-0.223730\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −38.1051 | − | 53.8888i | −0.208225 | − | 0.294474i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 107.480i | − | 0.580974i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 332.554i | 1.77836i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −76.3675 | − | 270.000i | −0.404061 | − | 1.42857i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 117.576i | − | 0.615579i | −0.951455 | − | 0.307789i | \(-0.900411\pi\) | ||
0.951455 | − | 0.307789i | \(-0.0995892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 82.0000 | 0.424870 | 0.212435 | − | 0.977175i | \(-0.431861\pi\) | ||||
0.212435 | + | 0.977175i | \(0.431861\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 29.3939 | + | 41.5692i | 0.150738 | + | 0.213175i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −206.475 | −1.04810 | −0.524049 | − | 0.851688i | \(-0.675579\pi\) | ||||
−0.524049 | + | 0.851688i | \(0.675579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −322.161 | −1.61890 | −0.809451 | − | 0.587188i | \(-0.800235\pi\) | ||||
−0.809451 | + | 0.587188i | \(0.800235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −198.000 | − | 280.014i | −0.985075 | − | 1.39311i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 323.333 | 1.59277 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0000i | 0.0780488i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −249.415 | − | 88.1816i | −1.20490 | − | 0.425998i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 152.735i | − | 0.730790i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 135.100i | 0.640284i | 0.947370 | + | 0.320142i | \(0.103731\pi\) | ||||
−0.947370 | + | 0.320142i | \(0.896269\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 50.9117 | + | 72.0000i | 0.239022 | + | 0.338028i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.3939i | 0.136716i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 324.000 | 1.49309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 73.4847 | − | 51.9615i | 0.335547 | − | 0.237267i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −135.765 | −0.614319 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 363.731 | 1.63108 | 0.815540 | − | 0.578701i | \(-0.196440\pi\) | ||||
0.815540 | + | 0.578701i | \(0.196440\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −51.0000 | + | 144.250i | −0.226667 | + | 0.641110i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.6969 | −0.0647442 | −0.0323721 | − | 0.999476i | \(-0.510306\pi\) | ||||
−0.0323721 | + | 0.999476i | \(0.510306\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 246.000i | 1.07424i | 0.843507 | + | 0.537118i | \(0.180487\pi\) | ||||
−0.843507 | + | 0.537118i | \(0.819513\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −374.123 | + | 264.545i | −1.61958 | + | 1.14522i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 209.304i | 0.898299i | 0.893457 | + | 0.449149i | \(0.148273\pi\) | ||||
−0.893457 | + | 0.449149i | \(0.851727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 166.277i | 0.707561i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 76.3675 | − | 54.0000i | 0.322226 | − | 0.227848i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 411.514i | 1.72182i | 0.508760 | + | 0.860909i | \(0.330104\pi\) | ||||
−0.508760 | + | 0.860909i | \(0.669896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 210.000 | 0.871369 | 0.435685 | − | 0.900099i | \(-0.356506\pi\) | ||||
0.435685 | + | 0.900099i | \(0.356506\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −242.499 | − | 15.5885i | −0.997940 | − | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −166.877 | −0.681131 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 62.3538 | 0.252445 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −180.000 | + | 127.279i | −0.722892 | + | 0.511162i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 396.817 | 1.58095 | 0.790473 | − | 0.612497i | \(-0.209835\pi\) | ||||
0.790473 | + | 0.612497i | \(0.209835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 432.000i | 1.70751i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 110.851 | + | 156.767i | 0.434711 | + | 0.614774i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 384.666i | 1.49676i | 0.663273 | + | 0.748378i | \(0.269167\pi\) | ||||
−0.663273 | + | 0.748378i | \(0.730833\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 394.908i | 1.52474i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 93.3381 | − | 264.000i | 0.357617 | − | 1.01149i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 499.696i | 1.89998i | 0.312274 | + | 0.949992i | \(0.398909\pi\) | ||||
−0.312274 | + | 0.949992i | \(0.601091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.0000 | 0.150943 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.79796 | − | 13.8564i | −0.0366965 | − | 0.0518967i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.7990 | 0.0736022 | 0.0368011 | − | 0.999323i | \(-0.488283\pi\) | ||||
0.0368011 | + | 0.999323i | \(0.488283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −135.100 | −0.498524 | −0.249262 | − | 0.968436i | \(-0.580188\pi\) | ||||
−0.249262 | + | 0.968436i | \(0.580188\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −108.000 | − | 152.735i | −0.395604 | − | 0.559469i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 249.848 | 0.908538 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 198.000i | 0.714801i | 0.933951 | + | 0.357401i | \(0.116337\pi\) | ||||
−0.933951 | + | 0.357401i | \(0.883663\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 93.5307 | − | 264.545i | 0.335236 | − | 0.948190i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 197.990i | 0.704590i | 0.935889 | + | 0.352295i | \(0.114599\pi\) | ||||
−0.935889 | + | 0.352295i | \(0.885401\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 51.9615i | − | 0.183610i | −0.995777 | − | 0.0918048i | \(-0.970736\pi\) | ||
0.995777 | − | 0.0918048i | \(-0.0292636\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −50.9117 | − | 72.0000i | −0.178638 | − | 0.252632i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 58.7878i | − | 0.204835i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −223.000 | −0.771626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 220.454 | − | 155.885i | 0.757574 | − | 0.535686i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 359.210 | 1.22597 | 0.612987 | − | 0.790093i | \(-0.289968\pi\) | ||||
0.612987 | + | 0.790093i | \(0.289968\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.5692 | 0.140913 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 108.000 | + | 381.838i | 0.363636 | + | 1.28565i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −176.363 | −0.589844 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 108.000i | − | 0.358804i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.92820 | + | 4.89898i | −0.0228654 | + | 0.0161682i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 62.2254i | 0.204018i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 197.454i | − | 0.643172i | −0.946880 | − | 0.321586i | \(-0.895784\pi\) | ||
0.946880 | − | 0.321586i | \(-0.104216\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −178.191 | + | 126.000i | −0.576670 | + | 0.407767i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 264.545i | − | 0.850627i | −0.905046 | − | 0.425313i | \(-0.860164\pi\) | ||
0.905046 | − | 0.425313i | \(-0.139836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −266.000 | −0.849840 | −0.424920 | − | 0.905231i | \(-0.639698\pi\) | ||||
−0.424920 | + | 0.905231i | \(0.639698\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −88.1816 | + | 249.415i | −0.279942 | + | 0.791795i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −421.436 | −1.32945 | −0.664725 | − | 0.747088i | \(-0.731451\pi\) | ||||
−0.664725 | + | 0.747088i | \(0.731451\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −457.261 | −1.43342 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −180.000 | + | 127.279i | −0.560748 | + | 0.396508i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 235.151 | 0.728022 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 102.000i | 0.313846i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 239.023 | + | 338.030i | 0.730957 | + | 1.03373i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 610.940i | − | 1.85696i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 197.454i | 0.596537i | 0.954482 | + | 0.298269i | \(0.0964091\pi\) | ||||
−0.954482 | + | 0.298269i | \(0.903591\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 322.441 | + | 114.000i | 0.968290 | + | 0.342342i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 323.333i | 0.965172i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 522.000 | 1.54896 | 0.774481 | − | 0.632598i | \(-0.218011\pi\) | ||||
0.774481 | + | 0.632598i | \(0.218011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 333.131 | + | 471.118i | 0.982686 | + | 1.38973i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −458.205 | −1.34371 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 103.923 | 0.302983 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 144.000 | + | 203.647i | 0.417391 | + | 0.590280i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −426.211 | −1.22827 | −0.614137 | − | 0.789199i | \(-0.710496\pi\) | ||||
−0.614137 | + | 0.789199i | \(0.710496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 166.000i | − | 0.475645i | −0.971309 | − | 0.237822i | \(-0.923566\pi\) | ||
0.971309 | − | 0.237822i | \(-0.0764336\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −155.885 | + | 44.0908i | −0.444116 | + | 0.125615i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.6274i | 0.0641003i | 0.999486 | + | 0.0320502i | \(0.0102036\pi\) | ||||
−0.999486 | + | 0.0320502i | \(0.989796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 83.1384i | − | 0.234193i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −407.294 | − | 576.000i | −1.14088 | − | 1.61345i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 88.1816i | − | 0.245631i | −0.992430 | − | 0.122816i | \(-0.960808\pi\) | ||
0.992430 | − | 0.122816i | \(-0.0391924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 253.000 | 0.700831 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 232.702 | − | 164.545i | 0.641051 | − | 0.453292i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −84.8528 | −0.232473 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −135.100 | −0.368120 | −0.184060 | − | 0.982915i | \(-0.558924\pi\) | ||||
−0.184060 | + | 0.982915i | \(0.558924\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −48.0000 | − | 16.9706i | −0.130081 | − | 0.0459907i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −146.969 | −0.396144 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 118.000i | 0.316354i | 0.987411 | + | 0.158177i | \(0.0505616\pi\) | ||||
−0.987411 | + | 0.158177i | \(0.949438\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 290.985 | − | 205.757i | 0.775959 | − | 0.548686i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 186.676i | − | 0.495162i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 592.361i | − | 1.56296i | −0.623931 | − | 0.781479i | \(-0.714465\pi\) | ||
0.623931 | − | 0.781479i | \(-0.285535\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −127.279 | + | 90.0000i | −0.334066 | + | 0.236220i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 352.727i | − | 0.920957i | −0.887671 | − | 0.460478i | \(-0.847678\pi\) | ||
0.887671 | − | 0.460478i | \(-0.152322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 432.000 | 1.12208 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −88.1816 | − | 31.1769i | −0.227860 | − | 0.0805605i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 359.210 | 0.923420 | 0.461710 | − | 0.887031i | \(-0.347236\pi\) | ||||
0.461710 | + | 0.887031i | \(0.347236\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −665.108 | −1.70104 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 108.000 | − | 76.3675i | 0.274809 | − | 0.194319i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −88.1816 | −0.223245 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 214.000i | − | 0.539043i | −0.962994 | − | 0.269521i | \(-0.913135\pi\) | ||
0.962994 | − | 0.269521i | \(-0.0868655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 187.061 | + | 264.545i | 0.468826 | + | 0.663020i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 226.274i | − | 0.564275i | −0.959374 | − | 0.282137i | \(-0.908957\pi\) | ||
0.959374 | − | 0.282137i | \(-0.0910434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 187.061i | − | 0.464172i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 178.191 | + | 144.000i | 0.439978 | + | 0.355556i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 558.484i | − | 1.37220i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −114.000 | −0.278729 | −0.139364 | − | 0.990241i | \(-0.544506\pi\) | ||||
−0.139364 | + | 0.990241i | \(0.544506\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 68.5857 | + | 96.9948i | 0.166875 | + | 0.235997i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −152.735 | −0.369819 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 207.846 | 0.500834 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −234.000 | − | 330.926i | −0.561151 | − | 0.793587i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −367.423 | −0.876906 | −0.438453 | − | 0.898754i | \(-0.644473\pi\) | ||||
−0.438453 | + | 0.898754i | \(0.644473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 534.000i | 1.26841i | 0.773166 | + | 0.634204i | \(0.218672\pi\) | ||||
−0.773166 | + | 0.634204i | \(0.781328\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −498.831 | − | 176.363i | −1.17927 | − | 0.416934i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 384.666i | 0.905097i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 228.631i | − | 0.535435i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 152.735 | + | 216.000i | 0.356026 | + | 0.503497i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 293.939i | − | 0.681993i | −0.940065 | − | 0.340996i | \(-0.889236\pi\) | ||
0.940065 | − | 0.340996i | \(-0.110764\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −614.000 | −1.41801 | −0.709007 | − | 0.705202i | \(-0.750857\pi\) | ||||
−0.709007 | + | 0.705202i | \(0.750857\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −215.555 | + | 152.420i | −0.495529 | + | 0.350392i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 305.470 | 0.699016 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 342.946 | 0.781198 | 0.390599 | − | 0.920561i | \(-0.372268\pi\) | ||||
0.390599 | + | 0.920561i | \(0.372268\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 177.000 | − | 500.632i | 0.401361 | − | 1.13522i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 514.393 | 1.16116 | 0.580579 | − | 0.814204i | \(-0.302826\pi\) | ||||
0.580579 | + | 0.814204i | \(0.302826\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.0000i | 0.0359551i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 464.190 | − | 328.232i | 1.03846 | − | 0.734299i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 214.960i | − | 0.478754i | −0.970927 | − | 0.239377i | \(-0.923057\pi\) | ||
0.970927 | − | 0.239377i | \(-0.0769432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 83.1384i | 0.184342i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 432.749 | − | 306.000i | 0.955297 | − | 0.675497i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 176.363i | 0.387612i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −786.000 | −1.71991 | −0.859956 | − | 0.510368i | \(-0.829509\pi\) | ||||
−0.859956 | + | 0.510368i | \(0.829509\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −587.878 | + | 166.277i | −1.28078 | + | 0.362259i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 811.759 | 1.76086 | 0.880432 | − | 0.474172i | \(-0.157252\pi\) | ||||
0.880432 | + | 0.474172i | \(0.157252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 446.869 | 0.965160 | 0.482580 | − | 0.875852i | \(-0.339700\pi\) | ||||
0.482580 | + | 0.875852i | \(0.339700\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −216.000 | + | 152.735i | −0.464516 | + | 0.328463i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −426.211 | −0.912658 | −0.456329 | − | 0.889811i | \(-0.650836\pi\) | ||||
−0.456329 | + | 0.889811i | \(0.650836\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1188.00i | − | 2.53305i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 266.736 | + | 377.221i | 0.566318 | + | 0.800895i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 152.735i | 0.322907i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 176.669i | − | 0.371935i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −42.4264 | + | 120.000i | −0.0889442 | + | 0.251572i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 117.576i | − | 0.245460i | −0.992440 | − | 0.122730i | \(-0.960835\pi\) | ||
0.992440 | − | 0.122730i | \(-0.0391650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 228.000 | 0.474012 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −529.090 | − | 748.246i | −1.09542 | − | 1.54916i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −254.558 | −0.524863 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 426.084 | 0.874917 | 0.437458 | − | 0.899239i | \(-0.355879\pi\) | ||||
0.437458 | + | 0.899239i | \(0.355879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −126.000 | − | 178.191i | −0.257669 | − | 0.364399i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −191.060 | −0.389125 | −0.194562 | − | 0.980890i | \(-0.562329\pi\) | ||||
−0.194562 | + | 0.980890i | \(0.562329\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 704.000i | − | 1.42799i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 124.708 | − | 352.727i | 0.251935 | − | 0.712579i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 305.470i | 0.614628i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 862.561i | − | 1.72858i | −0.502994 | − | 0.864290i | \(-0.667768\pi\) | ||
0.502994 | − | 0.864290i | \(-0.332232\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 458.205 | + | 648.000i | 0.914581 | + | 1.29341i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 205.757i | 0.409060i | 0.978860 | + | 0.204530i | \(0.0655666\pi\) | ||||
−0.978860 | + | 0.204530i | \(0.934433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | 0.0158416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 325.782 | − | 230.363i | 0.642568 | − | 0.454364i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 845.700 | 1.66149 | 0.830746 | − | 0.556651i | \(-0.187914\pi\) | ||||
0.830746 | + | 0.556651i | \(0.187914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 311.769 | 0.610116 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 270.000 | − | 76.3675i | 0.526316 | − | 0.148865i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 205.757 | 0.399528 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 864.000i | 1.67118i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 547.328 | − | 387.019i | 1.05458 | − | 0.745702i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.5980i | 0.0760038i | 0.999278 | + | 0.0380019i | \(0.0120993\pi\) | ||||
−0.999278 | + | 0.0380019i | \(0.987901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 654.715i | 1.25185i | 0.779885 | + | 0.625923i | \(0.215277\pi\) | ||||
−0.779885 | + | 0.625923i | \(0.784723\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −432.749 | + | 306.000i | −0.824284 | + | 0.582857i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 705.453i | − | 1.33862i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −335.000 | −0.633270 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −44.0908 | + | 124.708i | −0.0830336 | + | 0.234854i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.9411 | −0.0636794 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 207.846 | 0.388497 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 252.000 | − | 178.191i | 0.469274 | − | 0.331827i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −867.119 | −1.60876 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 330.000i | 0.609982i | 0.952355 | + | 0.304991i | \(0.0986534\pi\) | ||||
−0.952355 | + | 0.304991i | \(0.901347\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −405.300 | − | 573.181i | −0.746409 | − | 1.05558i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 390.323i | − | 0.716189i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 93.5307i | 0.170989i | 0.996339 | + | 0.0854943i | \(0.0272469\pi\) | ||||
−0.996339 | + | 0.0854943i | \(0.972753\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −186.676 | − | 66.0000i | −0.340029 | − | 0.120219i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 323.333i | 0.586811i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 324.000 | 0.585895 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −186.161 | − | 263.272i | −0.335426 | − | 0.474363i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −613.769 | −1.10192 | −0.550959 | − | 0.834532i | \(-0.685738\pi\) | ||||
−0.550959 | + | 0.834532i | \(0.685738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −62.3538 | −0.111545 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 576.000 | + | 814.587i | 1.02674 | + | 1.45203i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −543.787 | −0.965873 | −0.482937 | − | 0.875655i | \(-0.660430\pi\) | ||||
−0.482937 | + | 0.875655i | \(0.660430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 544.000i | − | 0.962832i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −654.715 | − | 529.090i | −1.15470 | − | 0.933139i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.65685i | 0.00994175i | 0.999988 | + | 0.00497087i | \(0.00158228\pi\) | ||||
−0.999988 | + | 0.00497087i | \(0.998418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 613.146i | 1.07381i | 0.843642 | + | 0.536905i | \(0.180407\pi\) | ||||
−0.843642 | + | 0.536905i | \(0.819593\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −203.647 | − | 288.000i | −0.355404 | − | 0.502618i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 499.696i | 0.869036i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −502.000 | −0.870017 | −0.435009 | − | 0.900426i | \(-0.643255\pi\) | ||||
−0.435009 | + | 0.900426i | \(0.643255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 200.858 | − | 142.028i | 0.346905 | − | 0.245299i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −763.675 | −1.31442 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 207.846 | 0.356511 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 144.000 | + | 50.9117i | 0.246154 | + | 0.0870285i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.0908 | 0.0751121 | 0.0375561 | − | 0.999295i | \(-0.488043\pi\) | ||||
0.0375561 | + | 0.999295i | \(0.488043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 324.000i | 0.550085i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −505.759 | + | 357.626i | −0.855768 | + | 0.605119i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 260.215i | − | 0.438812i | −0.975634 | − | 0.219406i | \(-0.929588\pi\) | ||
0.975634 | − | 0.219406i | \(-0.0704119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 665.108i | 1.11783i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −789.131 | + | 558.000i | −1.32183 | + | 0.934673i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 734.847i | − | 1.22679i | −0.789776 | − | 0.613395i | \(-0.789803\pi\) | ||
0.789776 | − | 0.613395i | \(-0.210197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −130.000 | −0.216306 | −0.108153 | − | 0.994134i | \(-0.534494\pi\) | ||||
−0.108153 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −969.998 | − | 342.946i | −1.60862 | − | 0.568733i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −268.701 | −0.444133 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 613.146 | 1.01013 | 0.505063 | − | 0.863083i | \(-0.331469\pi\) | ||||
0.505063 | + | 0.863083i | \(0.331469\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 792.000 | − | 560.029i | 1.30049 | − | 0.919587i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −352.727 | −0.577294 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 794.000i | − | 1.29527i | −0.761951 | − | 0.647635i | \(-0.775758\pi\) | ||
0.761951 | − | 0.647635i | \(-0.224242\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.7128 | + | 39.1918i | 0.0450615 | + | 0.0637266i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 639.225i | 1.03602i | 0.855374 | + | 0.518010i | \(0.173327\pi\) | ||||
−0.855374 | + | 0.518010i | \(0.826673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 966.484i | − | 1.56136i | −0.624928 | − | 0.780682i | \(-0.714872\pi\) | ||
0.624928 | − | 0.780682i | \(-0.285128\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −763.675 | + | 216.000i | −1.22975 | + | 0.347826i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 58.7878i | − | 0.0943624i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 89.0000 | 0.142400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −264.545 | − | 374.123i | −0.421922 | − | 0.596687i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 859.842 | 1.36700 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 93.5307 | 0.148226 | 0.0741131 | − | 0.997250i | \(-0.476387\pi\) | ||||
0.0741131 | + | 0.997250i | \(0.476387\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 234.000 | + | 330.926i | 0.369668 | + | 0.522790i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 146.969 | 0.231448 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 354.000i | − | 0.555730i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 249.415 | + | 88.1816i | 0.390321 | + | 0.137999i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 622.254i | 0.970755i | 0.874305 | + | 0.485378i | \(0.161318\pi\) | ||||
−0.874305 | + | 0.485378i | \(0.838682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 592.361i | 0.921246i | 0.887596 | + | 0.460623i | \(0.152374\pi\) | ||||
−0.887596 | + | 0.460623i | \(0.847626\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 50.9117 | + | 72.0000i | 0.0789328 | + | 0.111628i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1263.94i | − | 1.95353i | −0.214303 | − | 0.976767i | \(-0.568748\pi\) | ||
0.214303 | − | 0.976767i | \(-0.431252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 216.000 | 0.332820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 793.635 | − | 561.184i | 1.21910 | − | 0.862035i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −591.141 | −0.905270 | −0.452635 | − | 0.891696i | \(-0.649516\pi\) | ||||
−0.452635 | + | 0.891696i | \(0.649516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −124.708 | −0.190393 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 90.0000 | − | 254.558i | 0.136986 | − | 0.387456i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1161.06 | 1.76185 | 0.880924 | − | 0.473257i | \(-0.156922\pi\) | ||||
0.880924 | + | 0.473257i | \(0.156922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 442.000i | − | 0.668684i | −0.942452 | − | 0.334342i | \(-0.891486\pi\) | ||
0.942452 | − | 0.334342i | \(-0.108514\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −332.554 | + | 235.151i | −0.501589 | + | 0.354677i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 305.470i | − | 0.459354i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 914.523i | − | 1.37110i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 890.955 | − | 630.000i | 1.33177 | − | 0.941704i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 323.333i | 0.481867i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −742.000 | −1.10253 | −0.551263 | − | 0.834332i | \(-0.685854\pi\) | ||||
−0.551263 | + | 0.834332i | \(0.685854\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 124.924 | + | 441.673i | 0.185073 | + | 0.654330i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.82843 | −0.00417788 | −0.00208894 | − | 0.999998i | \(-0.500665\pi\) | ||||
−0.00208894 | + | 0.999998i | \(0.500665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 935.307 | 1.37748 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.0000 | + | 25.4558i | −0.0528634 | + | 0.0373801i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −249.848 | −0.365810 | −0.182905 | − | 0.983131i | \(-0.558550\pi\) | ||||
−0.182905 | + | 0.983131i | \(0.558550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 112.000i | − | 0.163504i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 426.084 | + | 602.574i | 0.620210 | + | 0.877110i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 84.8528i | 0.123154i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 322.161i | − | 0.466225i | −0.972450 | − | 0.233112i | \(-0.925109\pi\) | ||
0.972450 | − | 0.233112i | \(-0.0748910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −458.205 | + | 1296.00i | −0.661191 | + | 1.87013i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 382.120i | 0.549814i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −128.000 | −0.183644 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 362.524 | + | 512.687i | 0.518633 | + | 0.733458i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 234.759 | 0.334892 | 0.167446 | − | 0.985881i | \(-0.446448\pi\) | ||||
0.167446 | + | 0.985881i | \(0.446448\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −394.908 | −0.561746 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 288.000 | + | 407.294i | 0.408511 | + | 0.577721i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.3939 | −0.0415755 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 102.000i | 0.143865i | 0.997410 | + | 0.0719323i | \(0.0229166\pi\) | ||||
−0.997410 | + | 0.0719323i | \(0.977083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 93.5307 | − | 264.545i | 0.131548 | − | 0.372074i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 916.410i | − | 1.28529i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 249.415i | − | 0.348833i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 712.764 | + | 1008.00i | 0.994092 | + | 1.40586i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 529.090i | − | 0.735869i | −0.929852 | − | 0.367934i | \(-0.880065\pi\) | ||
0.929852 | − | 0.367934i | \(-0.119935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −756.000 | −1.04854 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 514.393 | − | 363.731i | 0.711470 | − | 0.503085i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −528.916 | −0.729539 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1070.41 | −1.47236 | −0.736181 | − | 0.676785i | \(-0.763373\pi\) | ||||
−0.736181 | + | 0.676785i | \(0.763373\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −621.000 | + | 381.838i | −0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −235.151 | −0.321684 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 378.000i | 0.515689i | 0.966186 | + | 0.257844i | \(0.0830122\pi\) | ||||
−0.966186 | + | 0.257844i | \(0.916988\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −408.764 | + | 289.040i | −0.556141 | + | 0.393251i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1680.09i | 2.27963i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1111.98i | − | 1.50470i | −0.658761 | − | 0.752352i | \(-0.728919\pi\) | ||
0.658761 | − | 0.752352i | \(-0.271081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 152.735 | − | 108.000i | 0.206120 | − | 0.145749i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 205.757i | − | 0.276928i | −0.990368 | − | 0.138464i | \(-0.955784\pi\) | ||
0.990368 | − | 0.138464i | \(-0.0442164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −536.000 | −0.719463 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −220.454 | + | 623.538i | −0.295119 | + | 0.834723i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −763.675 | −1.01959 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −218.238 | −0.290597 | −0.145299 | − | 0.989388i | \(-0.546414\pi\) | ||||
−0.145299 | + | 0.989388i | \(0.546414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 972.000 | − | 687.308i | 1.29084 | − | 0.912759i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −499.696 | −0.661849 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1098.00i | − | 1.45046i | −0.688505 | − | 0.725231i | \(-0.741733\pi\) | ||
0.688505 | − | 0.725231i | \(-0.258267\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 748.246 | + | 1058.18i | 0.985831 | + | 1.39418i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1250.16i | 1.64279i | 0.570358 | + | 0.821396i | \(0.306804\pi\) | ||||
−0.570358 | + | 0.821396i | \(0.693196\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1434.14i | 1.87960i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 543.058 | + | 192.000i | 0.709880 | + | 0.250980i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 88.1816i | 0.114970i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −334.000 | −0.434330 | −0.217165 | − | 0.976135i | \(-0.569681\pi\) | ||||
−0.217165 | + | 0.976135i | \(0.569681\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 666.261 | + | 942.236i | 0.864152 | + | 1.22210i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 562.857 | 0.728146 | 0.364073 | − | 0.931370i | \(-0.381386\pi\) | ||||
0.364073 | + | 0.931370i | \(0.381386\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −530.008 | −0.683881 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 684.000 | + | 967.322i | 0.880309 | + | 1.24494i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.7878 | 0.0754657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 432.000i | − | 0.553137i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −228.631 | − | 808.332i | −0.291993 | − | 1.03235i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 435.578i | − | 0.554876i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 841.777i | 1.06960i | 0.844978 | + | 0.534801i | \(0.179613\pi\) | ||||
−0.844978 | + | 0.534801i | \(0.820387\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 865.499 | + | 1224.00i | 1.09696 | + | 1.55133i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1998.78i | 2.52691i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −132.000 | −0.166456 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 97.9796 | − | 69.2820i | 0.123245 | − | 0.0871472i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 393.151 | 0.493289 | 0.246645 | − | 0.969106i | \(-0.420672\pi\) | ||||
0.246645 | + | 0.969106i | \(0.420672\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1330.22 | −1.66485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.0000 | − | 16.9706i | −0.0599251 | − | 0.0211867i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −440.908 | −0.549076 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 864.000i | 1.07329i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.4974 | − | 34.2929i | 0.0600959 | − | 0.0424942i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1227.54i | − | 1.51735i | −0.651468 | − | 0.758676i | \(-0.725847\pi\) | ||
0.651468 | − | 0.758676i | \(-0.274153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1153.55i | 1.42237i | 0.703003 | + | 0.711187i | \(0.251842\pi\) | ||||
−0.703003 | + | 0.711187i | \(0.748158\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −330.926 | + | 234.000i | −0.407043 | + | 0.287823i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 205.757i | 0.252463i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 108.000 | 0.132191 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −529.090 | − | 187.061i | −0.646019 | − | 0.228402i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 370.524 | 0.451308 | 0.225654 | − | 0.974207i | \(-0.427548\pi\) | ||||
0.225654 | + | 0.974207i | \(0.427548\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −405.300 | −0.492466 | −0.246233 | − | 0.969211i | \(-0.579193\pi\) | ||||
−0.246233 | + | 0.969211i | \(0.579193\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 612.000 | − | 432.749i | 0.741818 | − | 0.524545i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1043.48 | 1.26177 | 0.630884 | − | 0.775877i | \(-0.282692\pi\) | ||||
0.630884 | + | 0.775877i | \(0.282692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 486.000i | − | 0.586248i | −0.956074 | − | 0.293124i | \(-0.905305\pi\) | ||
0.956074 | − | 0.293124i | \(-0.0946950\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 342.946 | + | 484.999i | 0.412691 | + | 0.583633i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1335.02i | − | 1.60266i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 748.246i | − | 0.896103i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −229.103 | − | 810.000i | −0.273719 | − | 0.967742i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 264.545i | 0.315310i | 0.987494 | + | 0.157655i | \(0.0503934\pi\) | ||||
−0.987494 | + | 0.157655i | \(0.949607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 127.000 | 0.151011 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 342.929 | + | 484.974i | 0.406795 | + | 0.575296i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −376.181 | −0.445184 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 987.269 | 1.16561 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −90.0000 | − | 127.279i | −0.106007 | − | 0.149917i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1116.97 | 1.31254 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1642.00i | − | 1.92497i | −0.271334 | − | 0.962485i | \(-0.587465\pi\) | ||
0.271334 | − | 0.962485i | \(-0.412535\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −249.415 | − | 88.1816i | −0.291714 | − | 0.103136i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1057.83i | − | 1.23434i | −0.786829 | − | 0.617171i | \(-0.788279\pi\) | ||
0.786829 | − | 0.617171i | \(-0.211721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 93.5307i | − | 0.108883i | −0.998517 | − | 0.0544416i | \(-0.982662\pi\) | ||
0.998517 | − | 0.0544416i | \(-0.0173379\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −101.823 | − | 144.000i | −0.118262 | − | 0.167247i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 235.151i | 0.272481i | 0.990676 | + | 0.136240i | \(0.0435020\pi\) | ||||
−0.990676 | + | 0.136240i | \(0.956498\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −632.000 | −0.730636 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −546.236 | + | 386.247i | −0.630030 | + | 0.445499i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −458.205 | −0.527279 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −685.892 | −0.787477 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 270.000 | − | 763.675i | 0.309278 | − | 0.874771i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1234.54 | 1.41091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 550.000i | − | 0.627138i | −0.949565 | − | 0.313569i | \(-0.898475\pi\) | ||
0.949565 | − | 0.313569i | \(-0.101525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 879.882 | − | 622.170i | 1.00100 | − | 0.707816i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1210.57i | − | 1.37408i | −0.726618 | − | 0.687041i | \(-0.758909\pi\) | ||
0.726618 | − | 0.687041i | \(-0.241091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 841.777i | 0.953314i | 0.879089 | + | 0.476657i | \(0.158152\pi\) | ||||
−0.879089 | + | 0.476657i | \(0.841848\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 101.823 | − | 72.0000i | 0.115055 | − | 0.0813559i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1146.36i | 1.29240i | 0.763167 | + | 0.646201i | \(0.223643\pi\) | ||||
−0.763167 | + | 0.646201i | \(0.776357\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −540.000 | −0.607424 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 925.907 | + | 748.246i | 1.03918 | + | 0.839782i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 610.940 | 0.684144 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −290.985 | −0.325122 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −432.000 | + | 305.470i | −0.481605 | + | 0.340546i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 969.998 | 1.07897 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 320.000i | 0.355161i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −187.061 | − | 264.545i | −0.207156 | − | 0.292962i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 661.852i | 0.731328i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1506.88i | − | 1.66139i | −0.556725 | − | 0.830697i | \(-0.687942\pi\) | ||
0.556725 | − | 0.830697i | \(-0.312058\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.48528 | + | 24.0000i | −0.00933474 | + | 0.0264026i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1469.69i | 1.61328i | 0.591046 | + | 0.806638i | \(0.298715\pi\) | ||||
−0.591046 | + | 0.806638i | \(0.701285\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1080.00 | 1.18291 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 107.778 | + | 152.420i | 0.117790 | + | 0.166580i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 458.205 | 0.499679 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1070.41 | −1.16475 | −0.582376 | − | 0.812919i | \(-0.697877\pi\) | ||||
−0.582376 | + | 0.812919i | \(0.697877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −342.000 | − | 483.661i | −0.371336 | − | 0.525148i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 176.363 | 0.191076 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 646.000i | − | 0.698378i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −218.238 | + | 617.271i | −0.235424 | + | 0.665881i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 667.509i | − | 0.718524i | −0.933237 | − | 0.359262i | \(-0.883028\pi\) | ||
0.933237 | − | 0.359262i | \(-0.116972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 613.146i | 0.658589i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −458.205 | − | 648.000i | −0.491110 | − | 0.694534i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 940.604i | − | 1.00599i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1402.00 | −1.49626 | −0.748132 | − | 0.663550i | \(-0.769049\pi\) | ||||
−0.748132 | + | 0.663550i | \(0.769049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −651.564 | + | 460.726i | −0.693892 | + | 0.490656i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1694.23 | 1.80045 | 0.900227 | − | 0.435420i | \(-0.143400\pi\) | ||||
0.900227 | + | 0.435420i | \(0.143400\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −166.277 | −0.176328 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 216.000 | + | 763.675i | 0.228571 | + | 0.808122i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1190.45 | −1.25708 | −0.628539 | − | 0.777778i | \(-0.716347\pi\) | ||||
−0.628539 | + | 0.777778i | \(0.716347\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 180.000i | − | 0.189673i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1032.30 | + | 729.948i | −1.08549 | + | 0.767558i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 401.637i | − | 0.421445i | −0.977546 | − | 0.210722i | \(-0.932418\pi\) | ||
0.977546 | − | 0.210722i | \(-0.0675816\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 332.554i | 0.348224i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1120.06 | + | 792.000i | −1.17038 | + | 0.827586i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 411.514i | 0.429108i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | 0.0114464 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −220.454 | + | 623.538i | −0.228924 | + | 0.647496i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −231.931 | −0.240343 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1423.75 | 1.47233 | 0.736166 | − | 0.676801i | \(-0.236634\pi\) | ||||
0.736166 | + | 0.676801i | \(0.236634\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 576.000 | − | 407.294i | 0.594427 | − | 0.420324i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 808.332 | 0.832473 | 0.416237 | − | 0.909256i | \(-0.363349\pi\) | ||||
0.416237 | + | 0.909256i | \(0.363349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1404.00i | − | 1.44296i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 176.669 | + | 249.848i | 0.181199 | + | 0.256254i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 565.685i | 0.579002i | 0.957178 | + | 0.289501i | \(0.0934894\pi\) | ||||
−0.957178 | + | 0.289501i | \(0.906511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 83.1384i | 0.0849218i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1170.97 | + | 414.000i | 1.19365 | + | 0.422018i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 558.484i | 0.568142i | 0.958803 | + | 0.284071i | \(0.0916852\pi\) | ||||
−0.958803 | + | 0.284071i | \(0.908315\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 584.000 | 0.592893 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1058.18 | − | 1496.49i | −1.07212 | − | 1.51620i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −305.470 | −0.308868 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −550.792 | −0.555794 | −0.277897 | − | 0.960611i | \(-0.589637\pi\) | ||||
−0.277897 | + | 0.960611i | \(0.589637\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 342.000 | + | 483.661i | 0.344411 | + | 0.487071i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 911.210 | 0.915789 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1606.00i | 1.61083i | 0.592710 | + | 0.805416i | \(0.298058\pi\) | ||||
−0.592710 | + | 0.805416i | \(0.701942\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 987.269 | − | 279.242i | 0.988257 | − | 0.279521i |
(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 | 768.3.h.f.641.5 | 8 | ||
3.2 | odd | 2 | inner | 768.3.h.f.641.2 | 8 | ||
4.3 | odd | 2 | inner | 768.3.h.f.641.3 | 8 | ||
8.3 | odd | 2 | inner | 768.3.h.f.641.6 | 8 | ||
8.5 | even | 2 | inner | 768.3.h.f.641.4 | 8 | ||
12.11 | even | 2 | inner | 768.3.h.f.641.8 | 8 | ||
16.3 | odd | 4 | 192.3.e.e.65.1 | 4 | |||
16.5 | even | 4 | 96.3.e.a.65.1 | ✓ | 4 | ||
16.11 | odd | 4 | 96.3.e.a.65.4 | yes | 4 | ||
16.13 | even | 4 | 192.3.e.e.65.4 | 4 | |||
24.5 | odd | 2 | inner | 768.3.h.f.641.7 | 8 | ||
24.11 | even | 2 | inner | 768.3.h.f.641.1 | 8 | ||
48.5 | odd | 4 | 96.3.e.a.65.2 | yes | 4 | ||
48.11 | even | 4 | 96.3.e.a.65.3 | yes | 4 | ||
48.29 | odd | 4 | 192.3.e.e.65.3 | 4 | |||
48.35 | even | 4 | 192.3.e.e.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.3.e.a.65.1 | ✓ | 4 | 16.5 | even | 4 | ||
96.3.e.a.65.2 | yes | 4 | 48.5 | odd | 4 | ||
96.3.e.a.65.3 | yes | 4 | 48.11 | even | 4 | ||
96.3.e.a.65.4 | yes | 4 | 16.11 | odd | 4 | ||
192.3.e.e.65.1 | 4 | 16.3 | odd | 4 | |||
192.3.e.e.65.2 | 4 | 48.35 | even | 4 | |||
192.3.e.e.65.3 | 4 | 48.29 | odd | 4 | |||
192.3.e.e.65.4 | 4 | 16.13 | even | 4 | |||
768.3.h.f.641.1 | 8 | 24.11 | even | 2 | inner | ||
768.3.h.f.641.2 | 8 | 3.2 | odd | 2 | inner | ||
768.3.h.f.641.3 | 8 | 4.3 | odd | 2 | inner | ||
768.3.h.f.641.4 | 8 | 8.5 | even | 2 | inner | ||
768.3.h.f.641.5 | 8 | 1.1 | even | 1 | trivial | ||
768.3.h.f.641.6 | 8 | 8.3 | odd | 2 | inner | ||
768.3.h.f.641.7 | 8 | 24.5 | odd | 2 | inner | ||
768.3.h.f.641.8 | 8 | 12.11 | even | 2 | inner |