Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [96,3,Mod(65,96)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(96, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("96.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 96 = 2^{5} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 96.e (of order \(2\), degree \(1\), 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: | \(2.61581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.3 | ||
Root | \(-0.517638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 96.65 |
Dual form | 96.3.e.a.65.4 |
$q$-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 \(\left(\mathbb{Z}/96\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(65\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.73205 | − | 2.44949i | 0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.82843i | 0.565685i | 0.959166 | + | 0.282843i | \(0.0912774\pi\) | ||||
−0.959166 | + | 0.282843i | \(0.908723\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | − | 14.6969i | − | 1.33609i | −0.744123 | − | 0.668043i | \(-0.767132\pi\) | ||
0.744123 | − | 0.668043i | \(-0.232868\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.00000 | −0.461538 | −0.230769 | − | 0.973009i | \(-0.574124\pi\) | ||||
−0.230769 | + | 0.973009i | \(0.574124\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.92820 | + | 4.89898i | 0.461880 | + | 0.326599i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.6274i | 1.33102i | 0.746387 | + | 0.665512i | \(0.231787\pi\) | ||||
−0.746387 | + | 0.665512i | \(0.768213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.3923 | −0.546963 | −0.273482 | − | 0.961877i | \(-0.588175\pi\) | ||||
−0.273482 | + | 0.961877i | \(0.588175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.0000 | − | 25.4558i | 0.857143 | − | 1.21218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.3939i | 1.27799i | 0.769209 | + | 0.638997i | \(0.220651\pi\) | ||||
−0.769209 | + | 0.638997i | \(0.779349\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.0000 | 0.680000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −25.9808 | − | 7.34847i | −0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 31.1127i | 1.07285i | 0.843947 | + | 0.536426i | \(0.180226\pi\) | ||||
−0.843947 | + | 0.536426i | \(0.819774\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.1769 | −1.00571 | −0.502853 | − | 0.864372i | \(-0.667716\pi\) | ||||
−0.502853 | + | 0.864372i | \(0.667716\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −36.0000 | − | 25.4558i | −1.09091 | − | 0.771389i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 29.3939i | 0.839825i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −38.0000 | −1.02703 | −0.513514 | − | 0.858082i | \(-0.671656\pi\) | ||||
−0.513514 | + | 0.858082i | \(0.671656\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −10.3923 | −0.241682 | −0.120841 | − | 0.992672i | \(-0.538559\pi\) | ||||
−0.120841 | + | 0.992672i | \(0.538559\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24.0000 | − | 8.48528i | 0.533333 | − | 0.188562i | ||||
\(46\) | 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 | ||||||||
\(51\) | 55.4256 | + | 39.1918i | 1.08678 | + | 0.768467i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.1421i | 0.266833i | 0.991060 | + | 0.133416i | \(0.0425948\pi\) | ||||
−0.991060 | + | 0.133416i | \(0.957405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 41.5692 | 0.755804 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.0000 | + | 25.4558i | −0.315789 | + | 0.446594i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 14.6969i | − | 0.249101i | −0.992213 | − | 0.124550i | \(-0.960251\pi\) | ||
0.992213 | − | 0.124550i | \(-0.0397488\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22.0000 | −0.360656 | −0.180328 | − | 0.983607i | \(-0.557716\pi\) | ||||
−0.180328 | + | 0.983607i | \(0.557716\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −31.1769 | − | 88.1816i | −0.494872 | − | 1.39971i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 16.9706i | − | 0.261086i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 114.315 | 1.70620 | 0.853100 | − | 0.521748i | \(-0.174720\pi\) | ||||
0.853100 | + | 0.521748i | \(0.174720\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 72.0000 | + | 50.9117i | 1.04348 | + | 0.737851i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 29.3939i | − | 0.413998i | −0.978341 | − | 0.206999i | \(-0.933630\pi\) | ||
0.978341 | − | 0.206999i | \(-0.0663697\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −30.0000 | −0.410959 | −0.205479 | − | 0.978661i | \(-0.565875\pi\) | ||||
−0.205479 | + | 0.978661i | \(0.565875\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 29.4449 | − | 41.6413i | 0.392598 | − | 0.555218i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 152.735i | − | 1.98357i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31.1769 | −0.394644 | −0.197322 | − | 0.980339i | \(-0.563225\pi\) | ||||
−0.197322 | + | 0.980339i | \(0.563225\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −63.0000 | + | 50.9117i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 73.4847i | 0.885358i | 0.896680 | + | 0.442679i | \(0.145972\pi\) | ||||
−0.896680 | + | 0.442679i | \(0.854028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −64.0000 | −0.752941 | ||||||||
\(86\) | 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 | ||||||||
\(91\) | −62.3538 | −0.685207 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −54.0000 | + | 76.3675i | −0.580645 | + | 0.821156i | ||||
\(94\) | 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 | ||||||||
\(99\) | −124.708 | + | 44.0908i | −1.25967 | + | 0.445362i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.82843i | 0.0280042i | 0.999902 | + | 0.0140021i | \(0.00445716\pi\) | ||||
−0.999902 | + | 0.0140021i | \(0.995543\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | − | 73.4847i | − | 0.686773i | −0.939194 | − | 0.343386i | \(-0.888426\pi\) | ||
0.939194 | − | 0.343386i | \(-0.111574\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 138.000 | 1.26606 | 0.633028 | − | 0.774129i | \(-0.281812\pi\) | ||||
0.633028 | + | 0.774129i | \(0.281812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −65.8179 | + | 93.0806i | −0.592954 | + | 0.838564i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 192.333i | − | 1.70206i | −0.525115 | − | 0.851031i | \(-0.675978\pi\) | ||
0.525115 | − | 0.851031i | \(-0.324022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −83.1384 | −0.722943 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.0000 | + | 50.9117i | 0.153846 | + | 0.435143i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 235.151i | 1.97606i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −95.0000 | −0.785124 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.8564 | − | 9.79796i | −0.112654 | − | 0.0796582i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 118.794i | 0.950352i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 51.9615 | 0.409146 | 0.204573 | − | 0.978851i | \(-0.434419\pi\) | ||||
0.204573 | + | 0.978851i | \(0.434419\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.0000 | + | 25.4558i | −0.139535 | + | 0.197332i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 44.0908i | − | 0.336571i | −0.985738 | − | 0.168286i | \(-0.946177\pi\) | ||
0.985738 | − | 0.168286i | \(-0.0538231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −108.000 | −0.812030 | ||||||||
\(134\) | 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 | ||||||||
\(139\) | −135.100 | −0.971942 | −0.485971 | − | 0.873975i | \(-0.661534\pi\) | ||||
−0.485971 | + | 0.873975i | \(0.661534\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −144.000 | − | 101.823i | −1.02128 | − | 0.722152i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 88.1816i | 0.616655i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −88.0000 | −0.606897 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 102.191 | − | 144.520i | 0.695177 | − | 0.983129i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 189.505i | − | 1.27184i | −0.771754 | − | 0.635922i | \(-0.780620\pi\) | ||
0.771754 | − | 0.635922i | \(-0.219380\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | − | 88.1816i | − | 0.568914i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 154.000 | 0.980892 | 0.490446 | − | 0.871472i | \(-0.336834\pi\) | ||||
0.490446 | + | 0.871472i | \(0.336834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34.6410 | + | 24.4949i | 0.217868 | + | 0.154056i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 305.470i | 1.89733i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 72.7461 | 0.446295 | 0.223148 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223148 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 72.0000 | − | 101.823i | 0.436364 | − | 0.617111i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 264.545i | − | 1.58410i | −0.610455 | − | 0.792051i | \(-0.709014\pi\) | ||
0.610455 | − | 0.792051i | \(-0.290986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −133.000 | −0.786982 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.1769 | + | 88.1816i | 0.182321 | + | 0.515682i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 223.446i | 1.29159i | 0.763509 | + | 0.645797i | \(0.223475\pi\) | ||||
−0.763509 | + | 0.645797i | \(0.776525\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 176.669 | 1.00954 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −36.0000 | − | 25.4558i | −0.203390 | − | 0.143818i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 102.879i | − | 0.574741i | −0.957820 | − | 0.287370i | \(-0.907219\pi\) | ||
0.957820 | − | 0.287370i | \(-0.0927810\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 234.000 | 1.29282 | 0.646409 | − | 0.762991i | \(-0.276270\pi\) | ||||
0.646409 | + | 0.762991i | \(0.276270\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −38.1051 | + | 53.8888i | −0.208225 | + | 0.294474i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 107.480i | − | 0.580974i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 332.554 | 1.77836 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −270.000 | − | 76.3675i | −1.42857 | − | 0.404061i | ||||
\(190\) | 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 | ||||||||
\(195\) | −41.5692 | − | 29.3939i | −0.213175 | − | 0.150738i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 206.475i | 1.04810i | 0.851688 | + | 0.524049i | \(0.175579\pi\) | ||||
−0.851688 | + | 0.524049i | \(0.824421\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 323.333i | 1.59277i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0000 | 0.0780488 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 249.415 | − | 88.1816i | 1.20490 | − | 0.425998i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 152.735i | 0.730790i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −135.100 | −0.640284 | −0.320142 | − | 0.947370i | \(-0.603731\pi\) | ||||
−0.320142 | + | 0.947370i | \(0.603731\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −72.0000 | − | 50.9117i | −0.338028 | − | 0.239022i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 29.3939i | − | 0.136716i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −324.000 | −1.49309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −51.9615 | + | 73.4847i | −0.237267 | + | 0.335547i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 135.765i | − | 0.614319i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −363.731 | −1.63108 | −0.815540 | − | 0.578701i | \(-0.803560\pi\) | ||||
−0.815540 | + | 0.578701i | \(0.803560\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −51.0000 | − | 144.250i | −0.226667 | − | 0.641110i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.6969i | 0.0647442i | 0.999476 | + | 0.0323721i | \(0.0103062\pi\) | ||||
−0.999476 | + | 0.0323721i | \(0.989694\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −246.000 | −1.07424 | −0.537118 | − | 0.843507i | \(-0.680487\pi\) | ||||
−0.537118 | + | 0.843507i | \(0.680487\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | 166.277 | 0.707561 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −54.0000 | + | 76.3675i | −0.227848 | + | 0.322226i | ||||
\(238\) | 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 | ||||||||
\(243\) | 15.5885 | + | 242.499i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 166.877i | 0.681131i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 62.3538 | 0.252445 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 180.000 | + | 127.279i | 0.722892 | + | 0.511162i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 396.817i | 1.58095i | 0.612497 | + | 0.790473i | \(0.290165\pi\) | ||||
−0.612497 | + | 0.790473i | \(0.709835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 432.000 | 1.70751 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −110.851 | + | 156.767i | −0.434711 | + | 0.614774i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 384.666i | − | 1.49676i | −0.663273 | − | 0.748378i | \(-0.730833\pi\) | ||
0.663273 | − | 0.748378i | \(-0.269167\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −394.908 | −1.52474 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 264.000 | − | 93.3381i | 1.01149 | − | 0.357617i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 499.696i | − | 1.89998i | −0.312274 | − | 0.949992i | \(-0.601091\pi\) | ||
0.312274 | − | 0.949992i | \(-0.398909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −40.0000 | −0.150943 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.8564 | − | 9.79796i | −0.0518967 | − | 0.0366965i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.7990i | 0.0736022i | 0.999323 | + | 0.0368011i | \(0.0117168\pi\) | ||||
−0.999323 | + | 0.0368011i | \(0.988283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 135.100 | 0.498524 | 0.249262 | − | 0.968436i | \(-0.419812\pi\) | ||||
0.249262 | + | 0.968436i | \(0.419812\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −108.000 | + | 152.735i | −0.395604 | + | 0.559469i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 249.848i | − | 0.908538i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −198.000 | −0.714801 | −0.357401 | − | 0.933951i | \(-0.616337\pi\) | ||||
−0.357401 | + | 0.933951i | \(0.616337\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −51.9615 | −0.183610 | −0.0918048 | − | 0.995777i | \(-0.529264\pi\) | ||||
−0.0918048 | + | 0.995777i | \(0.529264\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −72.0000 | − | 50.9117i | −0.252632 | − | 0.178638i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 58.7878i | − | 0.204835i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −223.000 | −0.771626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 155.885 | − | 220.454i | 0.535686 | − | 0.757574i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 359.210i | − | 1.22597i | −0.790093 | − | 0.612987i | \(-0.789968\pi\) | ||
0.790093 | − | 0.612987i | \(-0.210032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.5692 | 0.140913 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −108.000 | + | 381.838i | −0.363636 | + | 1.28565i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 176.363i | − | 0.589844i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −108.000 | −0.358804 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.92820 | + | 4.89898i | 0.0228654 | + | 0.0161682i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 62.2254i | − | 0.204018i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 197.454 | 0.643172 | 0.321586 | − | 0.946880i | \(-0.395784\pi\) | ||||
0.321586 | + | 0.946880i | \(0.395784\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −126.000 | + | 178.191i | −0.407767 | + | 0.576670i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 264.545i | 0.850627i | 0.905046 | + | 0.425313i | \(0.139836\pi\) | ||||
−0.905046 | + | 0.425313i | \(0.860164\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 266.000 | 0.849840 | 0.424920 | − | 0.905231i | \(-0.360302\pi\) | ||||
0.424920 | + | 0.905231i | \(0.360302\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 249.415 | − | 88.1816i | 0.791795 | − | 0.279942i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 421.436i | − | 1.32945i | −0.747088 | − | 0.664725i | \(-0.768549\pi\) | ||
0.747088 | − | 0.664725i | \(-0.231451\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 457.261 | 1.43342 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −180.000 | − | 127.279i | −0.560748 | − | 0.396508i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 235.151i | − | 0.728022i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −102.000 | −0.313846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 239.023 | − | 338.030i | 0.730957 | − | 1.03373i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 610.940i | − | 1.85696i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 197.454 | 0.596537 | 0.298269 | − | 0.954482i | \(-0.403591\pi\) | ||||
0.298269 | + | 0.954482i | \(0.403591\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 114.000 | + | 322.441i | 0.342342 | + | 0.968290i | ||||
\(334\) | 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 | ||||||||
\(339\) | −471.118 | − | 333.131i | −1.38973 | − | 0.982686i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 458.205i | 1.34371i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 103.923 | 0.302983 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −144.000 | + | 203.647i | −0.417391 | + | 0.590280i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 426.211i | − | 1.22827i | −0.789199 | − | 0.614137i | \(-0.789504\pi\) | ||
0.789199 | − | 0.614137i | \(-0.210496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −166.000 | −0.475645 | −0.237822 | − | 0.971309i | \(-0.576434\pi\) | ||||
−0.237822 | + | 0.971309i | \(0.576434\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 155.885 | + | 44.0908i | 0.444116 | + | 0.125615i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 22.6274i | − | 0.0641003i | −0.999486 | − | 0.0320502i | \(-0.989796\pi\) | ||
0.999486 | − | 0.0320502i | \(-0.0102036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 83.1384 | 0.234193 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 576.000 | + | 407.294i | 1.61345 | + | 1.14088i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 88.1816i | 0.245631i | 0.992430 | + | 0.122816i | \(0.0391924\pi\) | ||||
−0.992430 | + | 0.122816i | \(0.960808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −253.000 | −0.700831 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −164.545 | + | 232.702i | −0.453292 | + | 0.641051i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 84.8528i | − | 0.232473i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 135.100 | 0.368120 | 0.184060 | − | 0.982915i | \(-0.441076\pi\) | ||||
0.184060 | + | 0.982915i | \(0.441076\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −48.0000 | + | 16.9706i | −0.130081 | + | 0.0459907i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 146.969i | 0.396144i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −118.000 | −0.316354 | −0.158177 | − | 0.987411i | \(-0.550562\pi\) | ||||
−0.158177 | + | 0.987411i | \(0.550562\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 290.985 | + | 205.757i | 0.775959 | + | 0.548686i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 186.676i | − | 0.495162i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −592.361 | −1.56296 | −0.781479 | − | 0.623931i | \(-0.785535\pi\) | ||||
−0.781479 | + | 0.623931i | \(0.785535\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 90.0000 | − | 127.279i | 0.236220 | − | 0.334066i | ||||
\(382\) | 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 | ||||||||
\(387\) | 31.1769 | + | 88.1816i | 0.0805605 | + | 0.227860i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 359.210i | − | 0.923420i | −0.887031 | − | 0.461710i | \(-0.847236\pi\) | ||
0.887031 | − | 0.461710i | \(-0.152764\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −665.108 | −1.70104 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −108.000 | − | 76.3675i | −0.274809 | − | 0.194319i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 88.1816i | − | 0.223245i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −214.000 | −0.539043 | −0.269521 | − | 0.962994i | \(-0.586865\pi\) | ||||
−0.269521 | + | 0.962994i | \(0.586865\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −187.061 | + | 264.545i | −0.468826 | + | 0.663020i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 226.274i | 0.564275i | 0.959374 | + | 0.282137i | \(0.0910434\pi\) | ||||
−0.959374 | + | 0.282137i | \(0.908957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 187.061 | 0.464172 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −144.000 | − | 178.191i | −0.355556 | − | 0.439978i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 558.484i | 1.37220i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 114.000 | 0.278729 | 0.139364 | − | 0.990241i | \(-0.455494\pi\) | ||||
0.139364 | + | 0.990241i | \(0.455494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 96.9948 | + | 68.5857i | 0.235997 | + | 0.166875i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 152.735i | − | 0.369819i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −207.846 | −0.500834 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −234.000 | + | 330.926i | −0.561151 | + | 0.793587i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 367.423i | 0.876906i | 0.898754 | + | 0.438453i | \(0.144473\pi\) | ||||
−0.898754 | + | 0.438453i | \(0.855527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −534.000 | −1.26841 | −0.634204 | − | 0.773166i | \(-0.718672\pi\) | ||||
−0.634204 | + | 0.773166i | \(0.718672\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −498.831 | + | 176.363i | −1.17927 | + | 0.416934i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 384.666i | 0.905097i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −228.631 | −0.535435 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 216.000 | + | 152.735i | 0.503497 | + | 0.356026i | ||||
\(430\) | 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 | ||||||||
\(435\) | −152.420 | + | 215.555i | −0.350392 | + | 0.495529i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 305.470i | − | 0.699016i | ||||||
\(438\) | 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 | ||||||||
\(443\) | 514.393i | 1.16116i | 0.814204 | + | 0.580579i | \(0.197174\pi\) | ||||
−0.814204 | + | 0.580579i | \(0.802826\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.0000 | 0.0359551 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −464.190 | − | 328.232i | −1.03846 | − | 0.734299i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 214.960i | 0.478754i | 0.970927 | + | 0.239377i | \(0.0769432\pi\) | ||||
−0.970927 | + | 0.239377i | \(0.923057\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −83.1384 | −0.184342 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 306.000 | − | 432.749i | 0.675497 | − | 0.955297i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 176.363i | − | 0.387612i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 786.000 | 1.71991 | 0.859956 | − | 0.510368i | \(-0.170491\pi\) | ||||
0.859956 | + | 0.510368i | \(0.170491\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 166.277 | − | 587.878i | 0.362259 | − | 1.28078i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 811.759i | 1.76086i | 0.474172 | + | 0.880432i | \(0.342748\pi\) | ||||
−0.474172 | + | 0.880432i | \(0.657252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −446.869 | −0.965160 | −0.482580 | − | 0.875852i | \(-0.660300\pi\) | ||||
−0.482580 | + | 0.875852i | \(0.660300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −216.000 | − | 152.735i | −0.464516 | − | 0.328463i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 426.211i | 0.912658i | 0.889811 | + | 0.456329i | \(0.150836\pi\) | ||||
−0.889811 | + | 0.456329i | \(0.849164\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1188.00 | 2.53305 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 266.736 | − | 377.221i | 0.566318 | − | 0.800895i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 152.735i | 0.322907i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −176.669 | −0.371935 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 120.000 | − | 42.4264i | 0.251572 | − | 0.0889442i | ||||
\(478\) | 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 | ||||||||
\(483\) | 748.246 | + | 529.090i | 1.54916 | + | 1.09542i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 254.558i | 0.524863i | ||||||||
\(486\) | 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 | ||||||||
\(491\) | − | 191.060i | − | 0.389125i | −0.980890 | − | 0.194562i | \(-0.937671\pi\) | ||
0.980890 | − | 0.194562i | \(-0.0623286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −704.000 | −1.42799 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −124.708 | − | 352.727i | −0.251935 | − | 0.712579i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 305.470i | − | 0.614628i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 862.561 | 1.72858 | 0.864290 | − | 0.502994i | \(-0.167768\pi\) | ||||
0.864290 | + | 0.502994i | \(0.167768\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −648.000 | − | 458.205i | −1.29341 | − | 0.914581i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 205.757i | − | 0.409060i | −0.978860 | − | 0.204530i | \(-0.934433\pi\) | ||
0.978860 | − | 0.204530i | \(-0.0655666\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.0158416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −230.363 | + | 325.782i | −0.454364 | + | 0.642568i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 845.700i | 1.66149i | 0.556651 | + | 0.830746i | \(0.312086\pi\) | ||||
−0.556651 | + | 0.830746i | \(0.687914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −311.769 | −0.610116 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 270.000 | + | 76.3675i | 0.526316 | + | 0.148865i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 205.757i | − | 0.399528i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −864.000 | −1.67118 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 654.715 | 1.25185 | 0.625923 | − | 0.779885i | \(-0.284723\pi\) | ||||
0.625923 | + | 0.779885i | \(0.284723\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 306.000 | − | 432.749i | 0.582857 | − | 0.824284i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 705.453i | − | 1.33862i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −335.000 | −0.633270 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −124.708 | + | 44.0908i | −0.234854 | + | 0.0830336i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.9411i | 0.0636794i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 207.846 | 0.388497 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −252.000 | − | 178.191i | −0.469274 | − | 0.331827i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 867.119i | − | 1.60876i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 330.000 | 0.609982 | 0.304991 | − | 0.952355i | \(-0.401347\pi\) | ||||
0.304991 | + | 0.952355i | \(0.401347\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 405.300 | − | 573.181i | 0.746409 | − | 1.05558i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 390.323i | 0.716189i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −93.5307 | −0.170989 | −0.0854943 | − | 0.996339i | \(-0.527247\pi\) | ||||
−0.0854943 | + | 0.996339i | \(0.527247\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 66.0000 | + | 186.676i | 0.120219 | + | 0.340029i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 323.333i | − | 0.586811i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −324.000 | −0.585895 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −263.272 | − | 186.161i | −0.474363 | − | 0.335426i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 613.769i | − | 1.10192i | −0.834532 | − | 0.550959i | \(-0.814262\pi\) | ||
0.834532 | − | 0.550959i | \(-0.185738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 62.3538 | 0.111545 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 576.000 | − | 814.587i | 1.02674 | − | 1.45203i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 543.787i | 0.965873i | 0.875655 | + | 0.482937i | \(0.160430\pi\) | ||||
−0.875655 | + | 0.482937i | \(0.839570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 544.000 | 0.962832 | ||||||||
\(566\) | 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 | ||||||||
\(571\) | 613.146 | 1.07381 | 0.536905 | − | 0.843642i | \(-0.319593\pi\) | ||||
0.536905 | + | 0.843642i | \(0.319593\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −288.000 | − | 203.647i | −0.502618 | − | 0.355404i | ||||
\(574\) | 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 | ||||||||
\(579\) | 142.028 | − | 200.858i | 0.245299 | − | 0.346905i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 763.675i | 1.31442i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 207.846 | 0.356511 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −144.000 | + | 50.9117i | −0.246154 | + | 0.0870285i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.0908i | 0.0751121i | 0.999295 | + | 0.0375561i | \(0.0119573\pi\) | ||||
−0.999295 | + | 0.0375561i | \(0.988043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 324.000 | 0.550085 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 505.759 | + | 357.626i | 0.855768 | + | 0.605119i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 260.215i | 0.438812i | 0.975634 | + | 0.219406i | \(0.0704119\pi\) | ||||
−0.975634 | + | 0.219406i | \(0.929588\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −665.108 | −1.11783 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −558.000 | + | 789.131i | −0.934673 | + | 1.32183i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 734.847i | 1.22679i | 0.789776 | + | 0.613395i | \(0.210197\pi\) | ||||
−0.789776 | + | 0.613395i | \(0.789803\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 130.000 | 0.216306 | 0.108153 | − | 0.994134i | \(-0.465506\pi\) | ||||
0.108153 | + | 0.994134i | \(0.465506\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −342.946 | − | 969.998i | −0.568733 | − | 1.60862i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 268.701i | − | 0.444133i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −613.146 | −1.01013 | −0.505063 | − | 0.863083i | \(-0.668531\pi\) | ||||
−0.505063 | + | 0.863083i | \(0.668531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 792.000 | + | 560.029i | 1.30049 | + | 0.919587i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 352.727i | 0.577294i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 794.000 | 1.29527 | 0.647635 | − | 0.761951i | \(-0.275758\pi\) | ||||
0.647635 | + | 0.761951i | \(0.275758\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | −966.484 | −1.56136 | −0.780682 | − | 0.624928i | \(-0.785128\pi\) | ||||
−0.780682 | + | 0.624928i | \(0.785128\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 216.000 | − | 763.675i | 0.347826 | − | 1.22975i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 58.7878i | − | 0.0943624i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 89.0000 | 0.142400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 374.123 | + | 264.545i | 0.596687 | + | 0.421922i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 859.842i | − | 1.36700i | ||||||
\(630\) | 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 | ||||||||
\(635\) | 146.969i | 0.231448i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −354.000 | −0.555730 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −249.415 | + | 88.1816i | −0.390321 | + | 0.137999i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 622.254i | − | 0.970755i | −0.874305 | − | 0.485378i | \(-0.838682\pi\) | ||
0.874305 | − | 0.485378i | \(-0.161318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −592.361 | −0.921246 | −0.460623 | − | 0.887596i | \(-0.652374\pi\) | ||||
−0.460623 | + | 0.887596i | \(0.652374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −72.0000 | − | 50.9117i | −0.111628 | − | 0.0789328i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1263.94i | 1.95353i | 0.214303 | + | 0.976767i | \(0.431252\pi\) | ||||
−0.214303 | + | 0.976767i | \(0.568748\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −216.000 | −0.332820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −561.184 | + | 793.635i | −0.862035 | + | 1.21910i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 591.141i | − | 0.905270i | −0.891696 | − | 0.452635i | \(-0.850484\pi\) | ||
0.891696 | − | 0.452635i | \(-0.149516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 124.708 | 0.190393 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 90.0000 | + | 254.558i | 0.136986 | + | 0.387456i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1161.06i | − | 1.76185i | −0.473257 | − | 0.880924i | \(-0.656922\pi\) | ||
0.473257 | − | 0.880924i | \(-0.343078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 442.000 | 0.668684 | 0.334342 | − | 0.942452i | \(-0.391486\pi\) | ||||
0.334342 | + | 0.942452i | \(0.391486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −332.554 | − | 235.151i | −0.501589 | − | 0.354677i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 305.470i | − | 0.459354i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −914.523 | −1.37110 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −630.000 | + | 890.955i | −0.941704 | + | 1.33177i | ||||
\(670\) | 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 | ||||||||
\(675\) | −441.673 | − | 124.924i | −0.654330 | − | 0.185073i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.82843i | 0.00417788i | 0.999998 | + | 0.00208894i | \(0.000664931\pi\) | ||||
−0.999998 | + | 0.00208894i | \(0.999335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 935.307 | 1.37748 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.0000 | + | 25.4558i | 0.0528634 | + | 0.0373801i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 249.848i | − | 0.365810i | −0.983131 | − | 0.182905i | \(-0.941450\pi\) | ||
0.983131 | − | 0.182905i | \(-0.0585500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −112.000 | −0.163504 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −426.084 | + | 602.574i | −0.620210 | + | 0.877110i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 84.8528i | − | 0.123154i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 322.161 | 0.466225 | 0.233112 | − | 0.972450i | \(-0.425109\pi\) | ||||
0.233112 | + | 0.972450i | \(0.425109\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1296.00 | + | 458.205i | −1.87013 | + | 0.661191i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 382.120i | − | 0.549814i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 128.000 | 0.183644 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 512.687 | + | 362.524i | 0.733458 | + | 0.518633i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 234.759i | 0.334892i | 0.985881 | + | 0.167446i | \(0.0535520\pi\) | ||||
−0.985881 | + | 0.167446i | \(0.946448\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 394.908 | 0.561746 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 288.000 | − | 407.294i | 0.408511 | − | 0.577721i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.3939i | 0.0415755i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −102.000 | −0.143865 | −0.0719323 | − | 0.997410i | \(-0.522917\pi\) | ||||
−0.0719323 | + | 0.997410i | \(0.522917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 93.5307 | + | 264.545i | 0.131548 | + | 0.372074i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 916.410i | − | 1.28529i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −249.415 | −0.348833 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1008.00 | + | 712.764i | 1.40586 | + | 0.994092i | ||||
\(718\) | 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 | ||||||||
\(723\) | 363.731 | − | 514.393i | 0.503085 | − | 0.711470i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 528.916i | 0.729539i | ||||||||
\(726\) | 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 | ||||||||
\(731\) | − | 235.151i | − | 0.321684i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 378.000 | 0.515689 | 0.257844 | − | 0.966186i | \(-0.416988\pi\) | ||||
0.257844 | + | 0.966186i | \(0.416988\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 408.764 | + | 289.040i | 0.556141 | + | 0.393251i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1680.09i | − | 2.27963i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1111.98 | 1.50470 | 0.752352 | − | 0.658761i | \(-0.228919\pi\) | ||||
0.752352 | + | 0.658761i | \(0.228919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 108.000 | − | 152.735i | 0.145749 | − | 0.206120i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 205.757i | 0.276928i | 0.990368 | + | 0.138464i | \(0.0442164\pi\) | ||||
−0.990368 | + | 0.138464i | \(0.955784\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 536.000 | 0.719463 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 623.538 | − | 220.454i | 0.834723 | − | 0.295119i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 763.675i | − | 1.01959i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 218.238 | 0.290597 | 0.145299 | − | 0.989388i | \(-0.453586\pi\) | ||||
0.145299 | + | 0.989388i | \(0.453586\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 972.000 | + | 687.308i | 1.29084 | + | 0.912759i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 499.696i | 0.661849i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1098.00 | 1.45046 | 0.725231 | − | 0.688505i | \(-0.241733\pi\) | ||||
0.725231 | + | 0.688505i | \(0.241733\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 1434.14 | 1.87960 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 192.000 | + | 543.058i | 0.250980 | + | 0.709880i | ||||
\(766\) | 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 | ||||||||
\(771\) | −942.236 | − | 666.261i | −1.22210 | − | 0.864152i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 562.857i | − | 0.728146i | −0.931370 | − | 0.364073i | \(-0.881386\pi\) | ||
0.931370 | − | 0.364073i | \(-0.118614\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −530.008 | −0.683881 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −684.000 | + | 967.322i | −0.880309 | + | 1.24494i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.7878i | 0.0754657i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −432.000 | −0.553137 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 228.631 | − | 808.332i | 0.291993 | − | 1.03235i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 435.578i | 0.554876i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −841.777 | −1.06960 | −0.534801 | − | 0.844978i | \(-0.679613\pi\) | ||||
−0.534801 | + | 0.844978i | \(0.679613\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1224.00 | − | 865.499i | −1.55133 | − | 1.09696i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1998.78i | − | 2.52691i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 132.000 | 0.166456 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −69.2820 | + | 97.9796i | −0.0871472 | + | 0.123245i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 393.151i | 0.493289i | 0.969106 | + | 0.246645i | \(0.0793280\pi\) | ||||
−0.969106 | + | 0.246645i | \(0.920672\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1330.22 | 1.66485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.0000 | + | 16.9706i | −0.0599251 | + | 0.0211867i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 440.908i | 0.549076i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −864.000 | −1.07329 | ||||||||
\(806\) | 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 | ||||||||
\(811\) | 1153.55 | 1.42237 | 0.711187 | − | 0.703003i | \(-0.248158\pi\) | ||||
0.711187 | + | 0.703003i | \(0.248158\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 234.000 | − | 330.926i | 0.287823 | − | 0.407043i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 205.757i | 0.252463i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 108.000 | 0.132191 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 187.061 | + | 529.090i | 0.228402 | + | 0.646019i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 370.524i | − | 0.451308i | −0.974207 | − | 0.225654i | \(-0.927548\pi\) | ||
0.974207 | − | 0.225654i | \(-0.0724519\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | 1043.48i | 1.26177i | 0.775877 | + | 0.630884i | \(0.217308\pi\) | ||||
−0.775877 | + | 0.630884i | \(0.782692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −486.000 | −0.586248 | −0.293124 | − | 0.956074i | \(-0.594695\pi\) | ||||
−0.293124 | + | 0.956074i | \(0.594695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −342.946 | + | 484.999i | −0.412691 | + | 0.583633i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1335.02i | 1.60266i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 748.246 | 0.896103 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 810.000 | + | 229.103i | 0.967742 | + | 0.273719i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 264.545i | − | 0.315310i | −0.987494 | − | 0.157655i | \(-0.949607\pi\) | ||
0.987494 | − | 0.157655i | \(-0.0503934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −127.000 | −0.151011 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 484.974 | + | 342.929i | 0.575296 | + | 0.406795i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 376.181i | − | 0.445184i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −987.269 | −1.16561 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −90.0000 | + | 127.279i | −0.106007 | + | 0.149917i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1116.97i | − | 1.31254i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1642.00 | 1.92497 | 0.962485 | − | 0.271334i | \(-0.0874647\pi\) | ||||
0.962485 | + | 0.271334i | \(0.0874647\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −93.5307 | −0.108883 | −0.0544416 | − | 0.998517i | \(-0.517338\pi\) | ||||
−0.0544416 | + | 0.998517i | \(0.517338\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −144.000 | − | 101.823i | −0.167247 | − | 0.118262i | ||||
\(862\) | 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 | ||||||||
\(867\) | −386.247 | + | 546.236i | −0.445499 | + | 0.630030i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 458.205i | 0.527279i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −685.892 | −0.787477 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −270.000 | − | 763.675i | −0.309278 | − | 0.874771i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1234.54i | 1.41091i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −550.000 | −0.627138 | −0.313569 | − | 0.949565i | \(-0.601525\pi\) | ||||
−0.313569 | + | 0.949565i | \(0.601525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −879.882 | − | 622.170i | −1.00100 | − | 0.707816i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1210.57i | 1.37408i | 0.726618 | + | 0.687041i | \(0.241091\pi\) | ||||
−0.726618 | + | 0.687041i | \(0.758909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −841.777 | −0.953314 | −0.476657 | − | 0.879089i | \(-0.658152\pi\) | ||||
−0.476657 | + | 0.879089i | \(0.658152\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 72.0000 | − | 101.823i | 0.0813559 | − | 0.115055i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1146.36i | − | 1.29240i | −0.763167 | − | 0.646201i | \(-0.776357\pi\) | ||
0.763167 | − | 0.646201i | \(-0.223643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 540.000 | 0.607424 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 748.246 | + | 925.907i | 0.839782 | + | 1.03918i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 610.940i | 0.684144i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 290.985 | 0.325122 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −432.000 | − | 305.470i | −0.481605 | − | 0.340546i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 969.998i | − | 1.07897i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −320.000 | −0.355161 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −187.061 | + | 264.545i | −0.207156 | + | 0.292962i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 661.852i | 0.731328i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1506.88 | −1.66139 | −0.830697 | − | 0.556725i | \(-0.812058\pi\) | ||||
−0.830697 | + | 0.556725i | \(0.812058\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.0000 | − | 8.48528i | 0.0264026 | − | 0.00933474i | ||||
\(910\) | 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 | ||||||||
\(915\) | −152.420 | − | 107.778i | −0.166580 | − | 0.117790i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 458.205i | − | 0.499679i | ||||||
\(918\) | 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 | ||||||||
\(923\) | 176.363i | 0.191076i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −646.000 | −0.698378 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 218.238 | + | 617.271i | 0.235424 | + | 0.665881i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 667.509i | 0.718524i | 0.933237 | + | 0.359262i | \(0.116972\pi\) | ||||
−0.933237 | + | 0.359262i | \(0.883028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −613.146 | −0.658589 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 648.000 | + | 458.205i | 0.694534 | + | 0.491110i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 940.604i | 1.00599i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1402.00 | 1.49626 | 0.748132 | − | 0.663550i | \(-0.230951\pi\) | ||||
0.748132 | + | 0.663550i | \(0.230951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 460.726 | − | 651.564i | 0.490656 | − | 0.693892i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1694.23i | 1.80045i | 0.435420 | + | 0.900227i | \(0.356600\pi\) | ||||
−0.435420 | + | 0.900227i | \(0.643400\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 166.277 | 0.176328 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 216.000 | − | 763.675i | 0.228571 | − | 0.808122i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1190.45i | 1.25708i | 0.777778 | + | 0.628539i | \(0.216347\pi\) | ||||
−0.777778 | + | 0.628539i | \(0.783653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 180.000 | 0.189673 | ||||||||
\(950\) | 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 | ||||||||
\(955\) | 332.554 | 0.348224 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 792.000 | − | 1120.06i | 0.827586 | − | 1.17038i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 411.514i | 0.429108i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | 0.0114464 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −623.538 | + | 220.454i | −0.647496 | + | 0.228924i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 231.931i | 0.240343i | ||||||||
\(966\) | 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 | ||||||||
\(971\) | 808.332i | 0.832473i | 0.909256 | + | 0.416237i | \(0.136651\pi\) | ||||
−0.909256 | + | 0.416237i | \(0.863349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1404.00 | −1.44296 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −176.669 | + | 249.848i | −0.181199 | + | 0.256254i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 565.685i | − | 0.579002i | −0.957178 | − | 0.289501i | \(-0.906511\pi\) | ||
0.957178 | − | 0.289501i | \(-0.0934894\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −83.1384 | −0.0849218 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −414.000 | − | 1170.97i | −0.422018 | − | 1.19365i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 558.484i | − | 0.568142i | −0.958803 | − | 0.284071i | \(-0.908315\pi\) | ||
0.958803 | − | 0.284071i | \(-0.0916852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −584.000 | −0.592893 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1496.49 | − | 1058.18i | −1.51620 | − | 1.07212i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 305.470i | − | 0.308868i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 550.792 | 0.555794 | 0.277897 | − | 0.960611i | \(-0.410363\pi\) | ||||
0.277897 | + | 0.960611i | \(0.410363\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 342.000 | − | 483.661i | 0.344411 | − | 0.487071i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 911.210i | − | 0.915789i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1606.00 | −1.61083 | −0.805416 | − | 0.592710i | \(-0.798058\pi\) | ||||
−0.805416 | + | 0.592710i | \(0.798058\pi\) | |||||||
\(998\) | 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 | 96.3.e.a.65.3 | yes | 4 | |
3.2 | odd | 2 | inner | 96.3.e.a.65.4 | yes | 4 | |
4.3 | odd | 2 | inner | 96.3.e.a.65.2 | yes | 4 | |
8.3 | odd | 2 | 192.3.e.e.65.3 | 4 | |||
8.5 | even | 2 | 192.3.e.e.65.2 | 4 | |||
12.11 | even | 2 | inner | 96.3.e.a.65.1 | ✓ | 4 | |
16.3 | odd | 4 | 768.3.h.f.641.2 | 8 | |||
16.5 | even | 4 | 768.3.h.f.641.1 | 8 | |||
16.11 | odd | 4 | 768.3.h.f.641.7 | 8 | |||
16.13 | even | 4 | 768.3.h.f.641.8 | 8 | |||
24.5 | odd | 2 | 192.3.e.e.65.1 | 4 | |||
24.11 | even | 2 | 192.3.e.e.65.4 | 4 | |||
48.5 | odd | 4 | 768.3.h.f.641.6 | 8 | |||
48.11 | even | 4 | 768.3.h.f.641.4 | 8 | |||
48.29 | odd | 4 | 768.3.h.f.641.3 | 8 | |||
48.35 | even | 4 | 768.3.h.f.641.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.3.e.a.65.1 | ✓ | 4 | 12.11 | even | 2 | inner | |
96.3.e.a.65.2 | yes | 4 | 4.3 | odd | 2 | inner | |
96.3.e.a.65.3 | yes | 4 | 1.1 | even | 1 | trivial | |
96.3.e.a.65.4 | yes | 4 | 3.2 | odd | 2 | inner | |
192.3.e.e.65.1 | 4 | 24.5 | odd | 2 | |||
192.3.e.e.65.2 | 4 | 8.5 | even | 2 | |||
192.3.e.e.65.3 | 4 | 8.3 | odd | 2 | |||
192.3.e.e.65.4 | 4 | 24.11 | even | 2 | |||
768.3.h.f.641.1 | 8 | 16.5 | even | 4 | |||
768.3.h.f.641.2 | 8 | 16.3 | odd | 4 | |||
768.3.h.f.641.3 | 8 | 48.29 | odd | 4 | |||
768.3.h.f.641.4 | 8 | 48.11 | even | 4 | |||
768.3.h.f.641.5 | 8 | 48.35 | even | 4 | |||
768.3.h.f.641.6 | 8 | 48.5 | odd | 4 | |||
768.3.h.f.641.7 | 8 | 16.11 | odd | 4 | |||
768.3.h.f.641.8 | 8 | 16.13 | even | 4 |