Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(2.13746 - 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.37 |
Dual form | 252.4.k.d.109.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.91238 | − | 8.50848i | 0.439376 | − | 0.761022i | −0.558265 | − | 0.829663i | \(-0.688533\pi\) |
0.997641 | + | 0.0686406i | \(0.0218662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.3248 | + | 8.74657i | −0.881454 | + | 0.472270i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.08762 | − | 12.2761i | −0.194273 | − | 0.336490i | 0.752389 | − | 0.658719i | \(-0.228901\pi\) |
−0.946662 | + | 0.322229i | \(0.895568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26.1238 | −0.557341 | −0.278670 | − | 0.960387i | \(-0.589894\pi\) | ||||
−0.278670 | + | 0.960387i | \(0.589894\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −39.2990 | − | 68.0679i | −0.560671 | − | 0.971111i | −0.997438 | − | 0.0715361i | \(-0.977210\pi\) |
0.436767 | − | 0.899575i | \(-0.356123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −36.5876 | + | 63.3716i | −0.441778 | + | 0.765181i | −0.997822 | − | 0.0659715i | \(-0.978985\pi\) |
0.556044 | + | 0.831153i | \(0.312319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −48.0000 | + | 83.1384i | −0.435161 | + | 0.753720i | −0.997309 | − | 0.0733164i | \(-0.976642\pi\) |
0.562148 | + | 0.827037i | \(0.309975\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.2371 | + | 24.6594i | 0.113897 | + | 0.197275i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −173.021 | −1.10790 | −0.553951 | − | 0.832549i | \(-0.686880\pi\) | ||||
−0.553951 | + | 0.832549i | \(0.686880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.6238 | − | 58.2381i | −0.194807 | − | 0.337415i | 0.752030 | − | 0.659128i | \(-0.229075\pi\) |
−0.946837 | + | 0.321713i | \(0.895741\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.77326 | + | 181.865i | −0.0278817 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 150.835 | − | 261.254i | 0.670193 | − | 1.16081i | −0.307656 | − | 0.951498i | \(-0.599545\pi\) |
0.977849 | − | 0.209311i | \(-0.0671221\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −472.042 | −1.79806 | −0.899031 | − | 0.437886i | \(-0.855727\pi\) | ||||
−0.899031 | + | 0.437886i | \(0.855727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −463.670 | −1.64440 | −0.822198 | − | 0.569201i | \(-0.807253\pi\) | ||||
−0.822198 | + | 0.569201i | \(0.807253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −45.5980 | + | 78.9781i | −0.141514 | + | 0.245109i | −0.928067 | − | 0.372413i | \(-0.878530\pi\) |
0.786553 | + | 0.617523i | \(0.211864\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 189.995 | − | 285.571i | 0.553921 | − | 0.832569i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −81.6341 | − | 141.394i | −0.211572 | − | 0.366453i | 0.740635 | − | 0.671908i | \(-0.234525\pi\) |
−0.952207 | + | 0.305455i | \(0.901192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −139.268 | −0.341435 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −300.263 | − | 520.071i | −0.662558 | − | 1.14758i | −0.979941 | − | 0.199286i | \(-0.936138\pi\) |
0.317384 | − | 0.948297i | \(-0.397196\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −285.846 | + | 495.099i | −0.599980 | + | 1.03920i | 0.392844 | + | 0.919605i | \(0.371491\pi\) |
−0.992823 | + | 0.119590i | \(0.961842\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −128.330 | + | 222.274i | −0.244882 | + | 0.424148i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 269.711 | + | 467.154i | 0.491798 | + | 0.851820i | 0.999955 | − | 0.00944469i | \(-0.00300638\pi\) |
−0.508157 | + | 0.861264i | \(0.669673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1064.39 | 1.77916 | 0.889578 | − | 0.456783i | \(-0.150998\pi\) | ||||
0.889578 | + | 0.456783i | \(0.150998\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 221.340 | + | 383.372i | 0.354875 | + | 0.614662i | 0.987097 | − | 0.160126i | \(-0.0511900\pi\) |
−0.632221 | + | 0.774788i | \(0.717857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 223.078 | + | 138.412i | 0.330157 | + | 0.204851i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 22.8505 | − | 39.5782i | 0.0325428 | − | 0.0563658i | −0.849295 | − | 0.527918i | \(-0.822973\pi\) |
0.881838 | + | 0.471552i | \(0.156306\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 686.464 | 0.907822 | 0.453911 | − | 0.891047i | \(-0.350028\pi\) | ||||
0.453911 | + | 0.891047i | \(0.350028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −772.206 | −0.985382 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 330.072 | − | 571.702i | 0.393119 | − | 0.680902i | −0.599740 | − | 0.800195i | \(-0.704729\pi\) |
0.992859 | + | 0.119293i | \(0.0380627\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 426.464 | − | 228.493i | 0.491270 | − | 0.263215i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 359.464 | + | 622.610i | 0.388213 | + | 0.672405i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 658.320 | 0.689095 | 0.344548 | − | 0.938769i | \(-0.388032\pi\) | ||||
0.344548 | + | 0.938769i | \(0.388032\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −901.949 | − | 1562.22i | −0.888586 | − | 1.53908i | −0.841547 | − | 0.540184i | \(-0.818355\pi\) |
−0.0470394 | − | 0.998893i | \(-0.514979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 537.454 | − | 930.898i | 0.514145 | − | 0.890525i | −0.485721 | − | 0.874114i | \(-0.661443\pi\) |
0.999865 | − | 0.0164107i | \(-0.00522392\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −829.676 | + | 1437.04i | −0.749605 | + | 1.29835i | 0.198407 | + | 0.980120i | \(0.436423\pi\) |
−0.948012 | + | 0.318235i | \(0.896910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −299.464 | − | 518.687i | −0.263151 | − | 0.455791i | 0.703927 | − | 0.710273i | \(-0.251428\pi\) |
−0.967077 | + | 0.254482i | \(0.918095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 781.650 | 0.650720 | 0.325360 | − | 0.945590i | \(-0.394514\pi\) | ||||
0.325360 | + | 0.945590i | \(0.394514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 471.588 | + | 816.815i | 0.382398 | + | 0.662333i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1236.91 | + | 767.460i | 0.952833 | + | 0.591201i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 565.031 | − | 978.663i | 0.424516 | − | 0.735284i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1507.85 | 1.07893 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 25.3722 | 0.0177277 | 0.00886385 | − | 0.999961i | \(-0.497179\pi\) | ||||
0.00886385 | + | 0.999961i | \(0.497179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −237.789 | + | 411.862i | −0.158593 | + | 0.274691i | −0.934362 | − | 0.356326i | \(-0.884029\pi\) |
0.775768 | + | 0.631018i | \(0.217362\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 42.9995 | − | 1354.54i | 0.0280341 | − | 0.883111i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 529.268 | + | 916.720i | 0.330062 | + | 0.571683i | 0.982524 | − | 0.186138i | \(-0.0595971\pi\) |
−0.652462 | + | 0.757821i | \(0.726264\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2580.99 | 1.57494 | 0.787470 | − | 0.616352i | \(-0.211390\pi\) | ||||
0.787470 | + | 0.616352i | \(0.211390\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 185.155 | + | 320.699i | 0.108276 | + | 0.187540i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −849.943 | + | 1472.14i | −0.486786 | + | 0.843138i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −50.9377 | + | 88.2266i | −0.0280066 | + | 0.0485088i | −0.879689 | − | 0.475549i | \(-0.842249\pi\) |
0.851682 | + | 0.524058i | \(0.175583\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 889.211 | + | 1540.16i | 0.479225 | + | 0.830042i | 0.999716 | − | 0.0238249i | \(-0.00758441\pi\) |
−0.520491 | + | 0.853867i | \(0.674251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −660.690 | −0.342374 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −699.629 | − | 1211.79i | −0.355646 | − | 0.615997i | 0.631582 | − | 0.775309i | \(-0.282406\pi\) |
−0.987228 | + | 0.159312i | \(0.949073\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 56.4119 | − | 1777.05i | 0.0276142 | − | 0.869883i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1807.71 | + | 3131.05i | −0.868656 | + | 1.50456i | −0.00528615 | + | 0.999986i | \(0.501683\pi\) |
−0.863370 | + | 0.504571i | \(0.831651\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1076.72 | 0.498917 | 0.249459 | − | 0.968385i | \(-0.419747\pi\) | ||||
0.249459 | + | 0.968385i | \(0.419747\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1514.55 | −0.689372 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 936.815 | − | 1622.61i | 0.411704 | − | 0.713091i | −0.583373 | − | 0.812205i | \(-0.698267\pi\) |
0.995076 | + | 0.0991132i | \(0.0316006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −448.103 | − | 278.033i | −0.193562 | − | 0.120099i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1346.15 | − | 2331.59i | −0.562099 | − | 0.973583i | −0.997313 | − | 0.0732565i | \(-0.976661\pi\) |
0.435215 | − | 0.900327i | \(-0.356672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 461.670 | 0.189589 | 0.0947947 | − | 0.995497i | \(-0.469781\pi\) | ||||
0.0947947 | + | 0.995497i | \(0.469781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1481.92 | − | 2566.76i | −0.588934 | − | 1.02006i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −557.073 | + | 964.879i | −0.217846 | + | 0.377321i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1882.41 | + | 3260.43i | −0.713124 | + | 1.23517i | 0.250555 | + | 0.968102i | \(0.419387\pi\) |
−0.963679 | + | 0.267064i | \(0.913946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1463.10 | − | 2534.16i | −0.545680 | − | 0.945145i | −0.998564 | − | 0.0535755i | \(-0.982938\pi\) |
0.452884 | − | 0.891569i | \(-0.350395\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5045.55 | −1.82477 | −0.912387 | − | 0.409330i | \(-0.865763\pi\) | ||||
−0.912387 | + | 0.409330i | \(0.865763\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2146.12 | − | 3717.20i | −0.764496 | − | 1.32415i | −0.940513 | − | 0.339759i | \(-0.889654\pi\) |
0.176016 | − | 0.984387i | \(-0.443679\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2824.52 | − | 1513.34i | 0.976564 | − | 0.523229i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2318.85 | + | 4016.36i | −0.790025 | + | 1.36836i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1037.28 | 0.343301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3625.76 | 1.18297 | 0.591487 | − | 0.806315i | \(-0.298541\pi\) | ||||
0.591487 | + | 0.806315i | \(0.298541\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2277.72 | + | 3945.13i | −0.722509 | + | 1.25142i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1058.28 | + | 656.629i | 0.331064 | + | 0.205414i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1026.64 | + | 1778.19i | 0.312485 | + | 0.541239i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3145.00 | −0.944417 | −0.472208 | − | 0.881487i | \(-0.656543\pi\) | ||||
−0.472208 | + | 0.881487i | \(0.656543\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −772.873 | − | 1338.65i | −0.225980 | − | 0.391408i | 0.730633 | − | 0.682770i | \(-0.239225\pi\) |
−0.956613 | + | 0.291362i | \(0.905892\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2036.07 | − | 3526.58i | 0.587544 | − | 1.01766i | −0.407009 | − | 0.913424i | \(-0.633428\pi\) |
0.994553 | − | 0.104232i | \(-0.0332383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1507.86 | + | 2611.68i | −0.423961 | + | 0.734322i | −0.996323 | − | 0.0856790i | \(-0.972694\pi\) |
0.572362 | + | 0.820001i | \(0.306027\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 447.989 | + | 775.940i | 0.124356 | + | 0.215390i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4647.38 | −1.25780 | −0.628900 | − | 0.777486i | \(-0.716495\pi\) | ||||
−0.628900 | + | 0.777486i | \(0.716495\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −559.138 | − | 968.456i | −0.149449 | − | 0.258854i | 0.781575 | − | 0.623812i | \(-0.214417\pi\) |
−0.931024 | + | 0.364958i | \(0.881083\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1496.45 | − | 3019.40i | −0.390223 | − | 0.787357i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 955.806 | − | 1655.50i | 0.246221 | − | 0.426467i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −883.518 | −0.222180 | −0.111090 | − | 0.993810i | \(-0.535434\pi\) | ||||
−0.111090 | + | 0.993810i | \(0.535434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1360.82 | 0.338159 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2934.44 | + | 5082.61i | −0.712240 | + | 1.23364i | 0.251775 | + | 0.967786i | \(0.418986\pi\) |
−0.964015 | + | 0.265849i | \(0.914348\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −177.269 | + | 5584.20i | −0.0425287 | + | 1.33971i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2437.81 | + | 4222.41i | 0.571565 | + | 0.989980i | 0.996406 | + | 0.0847114i | \(0.0269968\pi\) |
−0.424841 | + | 0.905268i | \(0.639670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1604.07 | −0.371839 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2763.55 | − | 4786.61i | −0.626382 | − | 1.08493i | −0.988272 | − | 0.152704i | \(-0.951202\pi\) |
0.361890 | − | 0.932221i | \(-0.382132\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1612.37 | − | 2792.70i | 0.361418 | − | 0.625994i | −0.626777 | − | 0.779199i | \(-0.715626\pi\) |
0.988194 | + | 0.153205i | \(0.0489594\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 201.815 | − | 349.554i | 0.0442542 | − | 0.0766504i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 979.022 | + | 1695.72i | 0.212360 | + | 0.367818i | 0.952453 | − | 0.304687i | \(-0.0985517\pi\) |
−0.740093 | + | 0.672505i | \(0.765218\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8531.16 | −1.81113 | −0.905563 | − | 0.424212i | \(-0.860551\pi\) | ||||
−0.905563 | + | 0.424212i | \(0.860551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3954.93 | − | 6850.14i | −0.830728 | − | 1.43886i | −0.897461 | − | 0.441093i | \(-0.854591\pi\) |
0.0667331 | − | 0.997771i | \(-0.478742\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7705.96 | − | 4128.74i | 1.58491 | − | 0.849171i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −632.324 | + | 1095.22i | −0.128704 | + | 0.222922i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8321.41 | 1.65919 | 0.829594 | − | 0.558367i | \(-0.188572\pi\) | ||||
0.829594 | + | 0.558367i | \(0.188572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5900.02 | −1.16445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1253.94 | − | 2171.89i | 0.242533 | − | 0.420079i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7569.30 | − | 4055.52i | 1.44946 | − | 0.776600i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2808.36 | + | 4864.22i | 0.527234 | + | 0.913196i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2541.79 | 0.472533 | 0.236267 | − | 0.971688i | \(-0.424076\pi\) | ||||
0.236267 | + | 0.971688i | \(0.424076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −303.855 | − | 526.292i | −0.0554020 | − | 0.0959590i | 0.836994 | − | 0.547212i | \(-0.184311\pi\) |
−0.892396 | + | 0.451253i | \(0.850977\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5513.64 | + | 9549.90i | −0.995684 | + | 1.72458i | −0.417471 | + | 0.908690i | \(0.637084\pi\) |
−0.578213 | + | 0.815886i | \(0.696250\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3630.80 | − | 6288.73i | 0.643300 | − | 1.11423i | −0.341391 | − | 0.939921i | \(-0.610898\pi\) |
0.984691 | − | 0.174307i | \(-0.0557685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1226.31 | + | 2124.02i | 0.215235 | + | 0.372798i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5751.43 | 0.990768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −371.927 | − | 644.197i | −0.0634794 | − | 0.109950i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 53.5890 | − | 1688.12i | 0.00898011 | − | 0.282885i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3316.36 | + | 5744.11i | −0.550706 | + | 0.953851i | 0.447517 | + | 0.894275i | \(0.352308\pi\) |
−0.998224 | + | 0.0595761i | \(0.981025\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5299.69 | 0.864338 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8104.59 | 1.31005 | 0.655023 | − | 0.755609i | \(-0.272659\pi\) | ||||
0.655023 | + | 0.755609i | \(0.272659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −476.625 | + | 825.539i | −0.0756912 | + | 0.131101i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −603.854 | + | 6323.68i | −0.0950584 | + | 0.995472i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2968.64 | − | 5141.83i | −0.459265 | − | 0.795470i | 0.539657 | − | 0.841885i | \(-0.318554\pi\) |
−0.998922 | + | 0.0464146i | \(0.985220\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 268.472 | 0.0411775 | 0.0205888 | − | 0.999788i | \(-0.493446\pi\) | ||||
0.0205888 | + | 0.999788i | \(0.493446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1331.40 | + | 2306.06i | 0.200747 | + | 0.347703i | 0.948769 | − | 0.315970i | \(-0.102330\pi\) |
−0.748023 | + | 0.663673i | \(0.768997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5228.69 | − | 9056.36i | 0.781719 | − | 1.35398i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −781.637 | + | 1353.83i | −0.114911 | + | 0.199032i | −0.917744 | − | 0.397172i | \(-0.869992\pi\) |
0.802833 | + | 0.596204i | \(0.203325\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 752.192 | + | 1302.83i | 0.109665 | + | 0.189945i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4349.22 | 0.623695 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −605.408 | − | 1048.60i | −0.0861091 | − | 0.149145i | 0.819754 | − | 0.572716i | \(-0.194110\pi\) |
−0.905863 | + | 0.423570i | \(0.860777\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2569.37 | + | 1594.21i | 0.359556 | + | 0.223093i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2385.93 | − | 4132.55i | 0.331203 | − | 0.573661i | −0.651545 | − | 0.758610i | \(-0.725879\pi\) |
0.982748 | + | 0.184949i | \(0.0592121\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4519.95 | 0.617479 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4118.66 | −0.558209 | −0.279104 | − | 0.960261i | \(-0.590038\pi\) | ||||
−0.279104 | + | 0.960261i | \(0.590038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1767.99 | − | 3062.25i | 0.235875 | − | 0.408547i | −0.723652 | − | 0.690165i | \(-0.757538\pi\) |
0.959527 | + | 0.281618i | \(0.0908712\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2273.52 | − | 1218.12i | 0.300959 | − | 0.161250i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4803.23 | + | 8319.44i | 0.626050 | + | 1.08435i | 0.988337 | + | 0.152284i | \(0.0486627\pi\) |
−0.362287 | + | 0.932067i | \(0.618004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7545.41 | 0.975928 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −224.500 | − | 388.846i | −0.0285971 | − | 0.0495316i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2683.54 | + | 4648.02i | −0.339252 | + | 0.587601i | −0.984292 | − | 0.176547i | \(-0.943507\pi\) |
0.645041 | + | 0.764148i | \(0.276840\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7032.91 | + | 12181.4i | −0.875828 | + | 1.51698i | −0.0199492 | + | 0.999801i | \(0.506350\pi\) |
−0.855878 | + | 0.517177i | \(0.826983\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 878.379 | + | 1521.40i | 0.108574 | + | 0.188055i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4276.25 | −0.520801 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1636.22 | − | 2834.02i | −0.197814 | − | 0.342624i | 0.750005 | − | 0.661432i | \(-0.230051\pi\) |
−0.947819 | + | 0.318808i | \(0.896718\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9450.55 | + | 5863.75i | 1.12598 | + | 0.698635i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3372.17 | − | 5840.77i | 0.398876 | − | 0.690873i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8077.07 | −0.941744 | −0.470872 | − | 0.882202i | \(-0.656061\pi\) | ||||
−0.470872 | + | 0.882202i | \(0.656061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8051.68 | 0.932101 | 0.466051 | − | 0.884758i | \(-0.345676\pi\) | ||||
0.466051 | + | 0.884758i | \(0.345676\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1119.01 | − | 1938.18i | 0.127718 | − | 0.221213i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 335.939 | − | 10582.5i | 0.0380732 | − | 1.19936i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4950.11 | − | 8573.84i | −0.553221 | − | 0.958207i | −0.998040 | − | 0.0625863i | \(-0.980065\pi\) |
0.444818 | − | 0.895621i | \(-0.353268\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −511.795 | −0.0568021 | −0.0284010 | − | 0.999597i | \(-0.509042\pi\) | ||||
−0.0284010 | + | 0.999597i | \(0.509042\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3512.41 | − | 6083.68i | −0.384488 | − | 0.665954i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 651.130 | − | 1127.79i | 0.0707898 | − | 0.122612i | −0.828458 | − | 0.560051i | \(-0.810781\pi\) |
0.899248 | + | 0.437440i | \(0.144115\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4100.16 | + | 7101.69i | −0.439739 | + | 0.761651i | −0.997669 | − | 0.0682372i | \(-0.978263\pi\) |
0.557930 | + | 0.829888i | \(0.311596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3242.88 | − | 5616.83i | −0.345454 | − | 0.598344i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5788.12 | 0.608370 | 0.304185 | − | 0.952613i | \(-0.401616\pi\) | ||||
0.304185 | + | 0.952613i | \(0.401616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3345.65 | + | 5794.84i | 0.349314 | + | 0.605030i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 150.819 | − | 4751.01i | 0.0155396 | − | 0.489518i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3629.59 | + | 6286.63i | −0.371521 | + | 0.643493i | −0.989800 | − | 0.142466i | \(-0.954497\pi\) |
0.618279 | + | 0.785959i | \(0.287830\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5966.92 | 0.602835 | 0.301418 | − | 0.953492i | \(-0.402540\pi\) | ||||
0.301418 | + | 0.953492i | \(0.402540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8884.02 | −0.891740 | −0.445870 | − | 0.895098i | \(-0.647106\pi\) | ||||
−0.445870 | + | 0.895098i | \(0.647106\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2014.68 | + | 3489.53i | −0.199632 | + | 0.345774i | −0.948409 | − | 0.317049i | \(-0.897308\pi\) |
0.748777 | + | 0.662822i | \(0.230641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8488.96 | − | 5267.12i | −0.835787 | − | 0.518578i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3286.32 | + | 5692.07i | 0.319461 | + | 0.553323i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2083.61 | −0.201269 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8720.33 | − | 15104.0i | −0.831820 | − | 1.44075i | −0.896593 | − | 0.442855i | \(-0.853966\pi\) |
0.0647733 | − | 0.997900i | \(-0.479368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3940.38 | + | 6824.94i | −0.373526 | + | 0.646966i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3233.91 | − | 5601.30i | 0.302772 | − | 0.524417i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2136.14 | + | 3699.90i | 0.198763 | + | 0.344268i | 0.948128 | − | 0.317890i | \(-0.102974\pi\) |
−0.749364 | + | 0.662158i | \(0.769641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2013.29 | −0.185048 | −0.0925240 | − | 0.995710i | \(-0.529493\pi\) | ||||
−0.0925240 | + | 0.995710i | \(0.529493\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6799.54 | + | 11777.2i | 0.621169 | + | 1.07590i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17375.9 | + | 9309.78i | −1.56824 | + | 0.840243i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2440.23 | − | 4226.60i | 0.218917 | − | 0.379176i | −0.735560 | − | 0.677460i | \(-0.763081\pi\) |
0.954477 | + | 0.298284i | \(0.0964142\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12961.9 | −1.14899 | −0.574496 | − | 0.818508i | \(-0.694802\pi\) | ||||
−0.574496 | + | 0.818508i | \(0.694802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17722.8 | −1.56170 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4077.69 | − | 7062.77i | 0.355089 | − | 0.615033i | −0.632044 | − | 0.774932i | \(-0.717784\pi\) |
0.987133 | + | 0.159900i | \(0.0511172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6966.51 | − | 4322.49i | −0.603093 | − | 0.374199i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5280.35 | − | 9145.84i | −0.451806 | − | 0.782551i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1292.73 | 0.109969 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −166.009 | − | 287.536i | −0.0139597 | − | 0.0241789i | 0.858961 | − | 0.512041i | \(-0.171110\pi\) |
−0.872921 | + | 0.487862i | \(0.837777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3627.42 | + | 6282.87i | −0.303281 | + | 0.525298i | −0.976877 | − | 0.213802i | \(-0.931415\pi\) |
0.673596 | + | 0.739099i | \(0.264749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2642.76 | + | 4577.40i | −0.218445 | + | 0.378358i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1475.50 | + | 2555.64i | 0.121271 | + | 0.210047i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12331.5 | 1.00213 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8151.36 | + | 14118.6i | 0.658718 | + | 1.14093i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4852.32 | − | 308.382i | −0.387763 | − | 0.0246437i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2705.10 | + | 4685.36i | −0.214974 | + | 0.372347i | −0.953265 | − | 0.302137i | \(-0.902300\pi\) |
0.738290 | + | 0.674483i | \(0.235633\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5884.32 | −0.462489 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18673.9 | −1.45967 | −0.729834 | − | 0.683625i | \(-0.760403\pi\) | ||||
−0.729834 | + | 0.683625i | \(0.760403\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6330.42 | − | 10964.6i | 0.489446 | − | 0.847746i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.8550 | + | 845.968i | −0.00206508 | + | 0.0650528i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4104.74 | − | 7109.62i | −0.312250 | − | 0.540833i | 0.666599 | − | 0.745417i | \(-0.267749\pi\) |
−0.978849 | + | 0.204583i | \(0.934416\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12112.8 | 0.916489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8761.10 | + | 15174.7i | 0.655837 | + | 1.13594i | 0.981683 | + | 0.190521i | \(0.0610176\pi\) |
−0.325846 | + | 0.945423i | \(0.605649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3839.76 | − | 6650.65i | 0.285911 | − | 0.495212i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4528.41 | + | 7843.44i | −0.333640 | + | 0.577881i | −0.983223 | − | 0.182410i | \(-0.941610\pi\) |
0.649583 | + | 0.760291i | \(0.274944\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5358.27 | − | 9280.80i | −0.392709 | − | 0.680191i | 0.600097 | − | 0.799927i | \(-0.295129\pi\) |
−0.992806 | + | 0.119736i | \(0.961795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2733.53 | −0.198254 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1608.62 | − | 2786.21i | −0.116062 | − | 0.201025i | 0.802142 | − | 0.597133i | \(-0.203694\pi\) |
−0.918204 | + | 0.396109i | \(0.870360\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11206.4 | + | 6004.21i | −0.800203 | + | 0.428738i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1157.18 | + | 2004.30i | −0.0822053 | + | 0.142384i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3248.45 | −0.228412 | −0.114206 | − | 0.993457i | \(-0.536432\pi\) | ||||
−0.114206 | + | 0.993457i | \(0.536432\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4920.85 | 0.344245 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10555.2 | + | 18282.1i | −0.730945 | + | 1.26603i | 0.225535 | + | 0.974235i | \(0.427587\pi\) |
−0.956480 | + | 0.291799i | \(0.905746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12606.1 | − | 6754.15i | 0.868569 | − | 0.465367i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7868.98 | − | 13629.5i | −0.536758 | − | 0.929692i | −0.999076 | − | 0.0429777i | \(-0.986316\pi\) |
0.462318 | − | 0.886714i | \(-0.347018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4856.96 | −0.329650 | −0.164825 | − | 0.986323i | \(-0.552706\pi\) | ||||
−0.164825 | + | 0.986323i | \(0.552706\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5551.29 | − | 9615.12i | −0.373045 | − | 0.646132i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8629.29 | − | 14946.4i | 0.577022 | − | 0.999431i | −0.418797 | − | 0.908080i | \(-0.637548\pi\) |
0.995819 | − | 0.0913513i | \(-0.0291186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1191.19 | − | 2063.20i | 0.0788714 | − | 0.136609i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8058.53 | − | 13957.8i | −0.530964 | − | 0.919657i | −0.999347 | − | 0.0361315i | \(-0.988496\pi\) |
0.468383 | − | 0.883526i | \(-0.344837\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17507.3 | 1.14233 | 0.571164 | − | 0.820836i | \(-0.306492\pi\) | ||||
0.571164 | + | 0.820836i | \(0.306492\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4859.24 | − | 8416.46i | −0.315524 | − | 0.546504i | 0.664025 | − | 0.747711i | \(-0.268847\pi\) |
−0.979549 | + | 0.201207i | \(0.935514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −387.917 | + | 12219.9i | −0.0249463 | + | 0.785842i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5627.47 | − | 9747.06i | 0.360158 | − | 0.623812i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23710.7 | −1.50303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5144.78 | 0.324580 | 0.162290 | − | 0.986743i | \(-0.448112\pi\) | ||||
0.162290 | + | 0.986743i | \(0.448112\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 124.638 | − | 215.879i | 0.00778913 | − | 0.0134912i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4963.38 | + | 7460.19i | −0.308723 | + | 0.464024i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10843.0 | + | 18780.7i | 0.668135 | + | 1.15724i | 0.978425 | + | 0.206602i | \(0.0662405\pi\) |
−0.310290 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14171.1 | −0.869132 | −0.434566 | − | 0.900640i | \(-0.643098\pi\) | ||||
−0.434566 | + | 0.900640i | \(0.643098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10026.6 | + | 17366.6i | 0.609254 | + | 1.05526i | 0.991364 | + | 0.131142i | \(0.0418645\pi\) |
−0.382109 | + | 0.924117i | \(0.624802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4256.30 | + | 7372.13i | −0.257434 | + | 0.445888i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11820.6 | − | 20473.8i | 0.708385 | − | 1.22696i | −0.257072 | − | 0.966392i | \(-0.582758\pi\) |
0.965456 | − | 0.260566i | \(-0.0839091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2336.21 | + | 4046.44i | 0.139364 | + | 0.241386i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2367.34 | −0.139937 | −0.0699685 | − | 0.997549i | \(-0.522290\pi\) | ||||
−0.0699685 | + | 0.997549i | \(0.522290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 194.991 | + | 337.733i | 0.0114739 | + | 0.0198734i | 0.871705 | − | 0.490030i | \(-0.163014\pi\) |
−0.860231 | + | 0.509904i | \(0.829681\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11313.9 | − | 7019.88i | −0.659749 | − | 0.409352i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8305.00 | − | 14384.7i | 0.482115 | − | 0.835048i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8103.86 | 0.466239 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28764.5 | 1.64753 | 0.823766 | − | 0.566930i | \(-0.191869\pi\) | ||||
0.823766 | + | 0.566930i | \(0.191869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −881.061 | + | 1526.04i | −0.0500176 | + | 0.0866331i | −0.889950 | − | 0.456058i | \(-0.849261\pi\) |
0.839933 | + | 0.542691i | \(0.182594\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10746.9 | + | 5758.04i | −0.607406 | + | 0.325439i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1114.44 | − | 1930.26i | −0.0624344 | − | 0.108140i | 0.833119 | − | 0.553094i | \(-0.186553\pi\) |
−0.895553 | + | 0.444955i | \(0.853220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10399.9 | 0.580085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2132.59 | + | 3693.76i | 0.117918 | + | 0.204239i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8672.14 | + | 15020.6i | −0.477429 | + | 0.826932i | −0.999665 | − | 0.0258690i | \(-0.991765\pi\) |
0.522236 | + | 0.852801i | \(0.325098\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12678.8 | − | 21960.3i | 0.691992 | − | 1.19856i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18550.8 | + | 32130.9i | 1.00812 | + | 1.74612i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23697.7 | 1.27682 | 0.638409 | − | 0.769697i | \(-0.279593\pi\) | ||||
0.638409 | + | 0.769697i | \(0.279593\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11037.4 | + | 19117.3i | 0.592153 | + | 1.02564i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28388.2 | + | 17613.9i | 1.51011 | + | 0.936972i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11395.5 | − | 19737.6i | 0.603620 | − | 1.04550i | −0.388648 | − | 0.921386i | \(-0.627058\pi\) |
0.992268 | − | 0.124114i | \(-0.0396088\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6455.76 | 0.339089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3638.21 | 0.190296 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15922.4 | − | 27578.4i | 0.825876 | − | 1.43046i | −0.0753721 | − | 0.997155i | \(-0.524014\pi\) |
0.901248 | − | 0.433304i | \(-0.142652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −631.642 | + | 19897.5i | −0.0326263 | + | 1.02777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2463.32 | − | 4266.59i | −0.126187 | − | 0.218562i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22500.0 | −1.14784 | −0.573920 | − | 0.818912i | \(-0.694578\pi\) | ||||
−0.573920 | + | 0.818912i | \(0.694578\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18221.8 | + | 31561.1i | 0.921966 | + | 1.59689i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1611.38 | − | 2790.99i | 0.0811972 | − | 0.140638i | −0.822567 | − | 0.568668i | \(-0.807459\pi\) |
0.903764 | + | 0.428030i | \(0.140792\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3823.23 | − | 6622.02i | 0.191086 | − | 0.330971i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9179.77 | − | 15899.8i | −0.456946 | − | 0.791454i | 0.541851 | − | 0.840474i | \(-0.317724\pi\) |
−0.998798 | + | 0.0490199i | \(0.984390\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12890.4 | −0.636478 | −0.318239 | − | 0.948010i | \(-0.603091\pi\) | ||||
−0.318239 | + | 0.948010i | \(0.603091\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 500.450 | + | 866.805i | 0.0246108 | + | 0.0426272i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 975.075 | − | 30716.1i | 0.0475680 | − | 1.49846i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7695.10 | + | 13328.3i | −0.373899 | + | 0.647612i | −0.990162 | − | 0.139929i | \(-0.955313\pi\) |
0.616263 | + | 0.787541i | \(0.288646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17472.6 | 0.842241 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13974.6 | 0.670957 | 0.335479 | − | 0.942048i | \(-0.391102\pi\) | ||||
0.335479 | + | 0.942048i | \(0.391102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1687.57 | + | 2922.96i | −0.0803868 | + | 0.139234i | −0.903416 | − | 0.428765i | \(-0.858949\pi\) |
0.823029 | + | 0.567999i | \(0.192282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9425.40 | + | 5848.15i | 0.447212 | + | 0.277480i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7843.99 | + | 13586.2i | 0.369270 | + | 0.639595i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31253.9 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11581.8 | + | 20060.2i | 0.538897 | + | 0.933396i | 0.998964 | + | 0.0455122i | \(0.0144920\pi\) |
−0.460067 | + | 0.887884i | \(0.652175\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 957.411 | − | 1658.29i | 0.0443758 | − | 0.0768611i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17270.9 | − | 29914.0i | 0.794343 | − | 1.37584i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7544.01 | − | 13066.6i | −0.345641 | − | 0.598668i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13747.4 | −0.625050 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4951.47 | + | 8576.20i | 0.224271 | + | 0.388448i | 0.956100 | − | 0.293039i | \(-0.0946667\pi\) |
−0.731830 | + | 0.681488i | \(0.761333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12760.2 | + | 6836.75i | −0.573580 | + | 0.307316i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7467.36 | − | 12933.8i | 0.334393 | − | 0.579186i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16844.5 | −0.748638 | −0.374319 | − | 0.927300i | \(-0.622123\pi\) | ||||
−0.374319 | + | 0.927300i | \(0.622123\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7167.83 | 0.317371 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3137.55 | − | 5434.40i | 0.137885 | − | 0.238824i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14842.9 | − | 9209.52i | −0.649867 | − | 0.403221i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17215.3 | − | 29817.8i | −0.748157 | − | 1.29585i | −0.948705 | − | 0.316162i | \(-0.897606\pi\) |
0.200549 | − | 0.979684i | \(-0.435728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −62.4498 | −0.00270396 | −0.00135198 | − | 0.999999i | \(-0.500430\pi\) | ||||
−0.00135198 | + | 0.999999i | \(0.500430\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17760.3 | + | 30761.8i | 0.763334 | + | 1.32213i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16964.6 | − | 29383.5i | 0.726458 | − | 1.25826i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19475.8 | − | 33733.1i | 0.827906 | − | 1.43398i | −0.0717711 | − | 0.997421i | \(-0.522865\pi\) |
0.899678 | − | 0.436555i | \(-0.143802\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17741.2 | + | 30728.6i | 0.751420 | + | 1.30150i | 0.947135 | + | 0.320836i | \(0.103964\pi\) |
−0.195715 | + | 0.980661i | \(0.562703\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7945.87 | −0.334105 | −0.167053 | − | 0.985948i | \(-0.553425\pi\) | ||||
−0.167053 | + | 0.985948i | \(0.553425\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20318.2 | − | 35192.2i | −0.851243 | − | 1.47440i | −0.880087 | − | 0.474812i | \(-0.842516\pi\) |
0.0288439 | − | 0.999584i | \(-0.490817\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26904.8 | − | 1709.90i | −1.11908 | − | 0.0711217i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5289.26 | − | 9161.26i | 0.219212 | − | 0.379687i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27723.5 | −1.14079 | −0.570394 | − | 0.821371i | \(-0.693209\pi\) | ||||
−0.570394 | + | 0.821371i | \(0.693209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5547.19 | 0.227446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7440.04 | + | 12886.5i | −0.302893 | + | 0.524627i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −664.052 | + | 20918.5i | −0.0269387 | + | 0.848605i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14480.2 | + | 25080.4i | 0.583283 | + | 1.01028i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37599.1 | 1.50922 | 0.754612 | − | 0.656171i | \(-0.227825\pi\) | ||||
0.754612 | + | 0.656171i | \(0.227825\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12805.0 | + | 22178.9i | 0.510397 | + | 0.884034i | 0.999927 | + | 0.0120476i | \(0.00383496\pi\) |
−0.489530 | + | 0.871986i | \(0.662832\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1989.70 | − | 3446.26i | 0.0790309 | − | 0.136886i | −0.823801 | − | 0.566879i | \(-0.808151\pi\) |
0.902832 | + | 0.429993i | \(0.141484\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12410.2 | + | 21495.0i | −0.489510 | + | 0.847856i | −0.999927 | − | 0.0120708i | \(-0.996158\pi\) |
0.510417 | + | 0.859927i | \(0.329491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9203.97 | − | 15941.7i | −0.361786 | − | 0.626631i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −647.823 | −0.0252887 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7045.87 | − | 12203.8i | −0.274099 | − | 0.474754i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24615.2 | + | 13188.5i | −0.951024 | + | 0.509545i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25009.7 | + | 43318.1i | −0.962963 | + | 1.66790i | −0.247971 | + | 0.968767i | \(0.579764\pi\) |
−0.714992 | + | 0.699133i | \(0.753570\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10386.4 | 0.397193 | 0.198596 | − | 0.980081i | \(-0.436362\pi\) | ||||
0.198596 | + | 0.980081i | \(0.436362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36366.4 | 1.38599 | 0.692994 | − | 0.720944i | \(-0.256291\pi\) | ||||
0.692994 | + | 0.720944i | \(0.256291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3803.65 | + | 6588.12i | −0.143984 | + | 0.249388i | −0.928994 | − | 0.370096i | \(-0.879325\pi\) |
0.785009 | + | 0.619484i | \(0.212658\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −414.195 | + | 221.920i | −0.0156261 | + | 0.00837227i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3336.65 | − | 5779.24i | −0.125035 | − | 0.216568i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26451.1 | −0.987891 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5817.61 | + | 10076.4i | 0.215827 | + | 0.373823i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6416.28 | + | 11113.3i | −0.237245 | + | 0.410920i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2267.90 | − | 3928.11i | 0.0833011 | − | 0.144282i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12901.5 | − | 22346.1i | −0.472314 | − | 0.818072i | 0.527184 | − | 0.849751i | \(-0.323248\pi\) |
−0.999498 | + | 0.0316794i | \(0.989914\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8165.21 | −0.296954 | −0.148477 | − | 0.988916i | \(-0.547437\pi\) | ||||
−0.148477 | + | 0.988916i | \(0.547437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4865.40 | − | 8427.12i | −0.176365 | − | 0.305473i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 279.461 | − | 8803.38i | 0.0100639 | − | 0.317026i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −296.804 | + | 514.079i | −0.0106536 | + | 0.0184526i | −0.871303 | − | 0.490745i | \(-0.836725\pi\) |
0.860649 | + | 0.509198i | \(0.170058\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27805.9 | −0.991596 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8589.84 | 0.305332 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16573.7 | + | 28706.5i | −0.585323 | + | 1.01381i | 0.409512 | + | 0.912305i | \(0.365699\pi\) |
−0.994835 | + | 0.101504i | \(0.967635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11145.6 | + | 22488.7i | 0.392356 | + | 0.791661i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5473.11 | + | 9479.70i | 0.191433 | + | 0.331571i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24883.8 | −0.867575 | −0.433788 | − | 0.901015i | \(-0.642823\pi\) | ||||
−0.433788 | + | 0.901015i | \(0.642823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13065.1 | − | 22629.5i | −0.452616 | − | 0.783954i | 0.545932 | − | 0.837830i | \(-0.316176\pi\) |
−0.998548 | + | 0.0538758i | \(0.982842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22658.0 | − | 39244.8i | 0.782445 | − | 1.35523i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3984.35 | − | 6901.09i | 0.136720 | − | 0.236806i | −0.789533 | − | 0.613708i | \(-0.789677\pi\) |
0.926253 | + | 0.376902i | \(0.123011\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5782.24 | − | 10015.1i | −0.197786 | − | 0.342576i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6742.36 | 0.229178 | 0.114589 | − | 0.993413i | \(-0.463445\pi\) | ||||
0.114589 | + | 0.993413i | \(0.463445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18494.2 | + | 32033.0i | 0.626659 | + | 1.08541i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16658.3 | − | 10335.9i | −0.560923 | − | 0.348034i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12634.4 | − | 21883.4i | 0.424101 | − | 0.734564i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28749.2 | −0.959035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7202.50 | −0.239521 | −0.119760 | − | 0.992803i | \(-0.538213\pi\) | ||||
−0.119760 | + | 0.992803i | \(0.538213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6852.86 | − | 11869.5i | 0.226487 | − | 0.392286i | −0.730278 | − | 0.683150i | \(-0.760609\pi\) |
0.956764 | + | 0.290864i | \(0.0939427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42134.0 | + | 22574.8i | −1.38824 | + | 0.743798i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28274.0 | − | 48972.0i | −0.925860 | − | 1.60364i | −0.790173 | − | 0.612884i | \(-0.790009\pi\) |
−0.135687 | − | 0.990752i | \(-0.543324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9357.71 | −0.305489 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8681.87 | + | 15037.4i | 0.281698 | + | 0.487914i | 0.971803 | − | 0.235794i | \(-0.0757692\pi\) |
−0.690105 | + | 0.723709i | \(0.742436\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24785.6 | + | 42930.0i | −0.801762 | + | 1.38869i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22256.2 | − | 38548.8i | 0.715576 | − | 1.23941i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24519.7 | − | 42469.4i | −0.785968 | − | 1.36134i | −0.928419 | − | 0.371535i | \(-0.878832\pi\) |
0.142451 | − | 0.989802i | \(-0.454502\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42170.3 | −1.34361 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4558.30 | + | 7895.21i | 0.144797 | + | 0.250796i | 0.929297 | − | 0.369333i | \(-0.120414\pi\) |
−0.784500 | + | 0.620129i | \(0.787080\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.4.k.d.37.2 | 4 | ||
3.2 | odd | 2 | 84.4.i.b.37.1 | yes | 4 | ||
7.2 | even | 3 | 1764.4.a.x.1.1 | 2 | |||
7.3 | odd | 6 | 1764.4.k.z.361.1 | 4 | |||
7.4 | even | 3 | inner | 252.4.k.d.109.2 | 4 | ||
7.5 | odd | 6 | 1764.4.a.p.1.2 | 2 | |||
7.6 | odd | 2 | 1764.4.k.z.1549.1 | 4 | |||
12.11 | even | 2 | 336.4.q.h.289.1 | 4 | |||
21.2 | odd | 6 | 588.4.a.g.1.2 | 2 | |||
21.5 | even | 6 | 588.4.a.h.1.1 | 2 | |||
21.11 | odd | 6 | 84.4.i.b.25.1 | ✓ | 4 | ||
21.17 | even | 6 | 588.4.i.i.361.2 | 4 | |||
21.20 | even | 2 | 588.4.i.i.373.2 | 4 | |||
84.11 | even | 6 | 336.4.q.h.193.1 | 4 | |||
84.23 | even | 6 | 2352.4.a.cb.1.2 | 2 | |||
84.47 | odd | 6 | 2352.4.a.bp.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.b.25.1 | ✓ | 4 | 21.11 | odd | 6 | ||
84.4.i.b.37.1 | yes | 4 | 3.2 | odd | 2 | ||
252.4.k.d.37.2 | 4 | 1.1 | even | 1 | trivial | ||
252.4.k.d.109.2 | 4 | 7.4 | even | 3 | inner | ||
336.4.q.h.193.1 | 4 | 84.11 | even | 6 | |||
336.4.q.h.289.1 | 4 | 12.11 | even | 2 | |||
588.4.a.g.1.2 | 2 | 21.2 | odd | 6 | |||
588.4.a.h.1.1 | 2 | 21.5 | even | 6 | |||
588.4.i.i.361.2 | 4 | 21.17 | even | 6 | |||
588.4.i.i.373.2 | 4 | 21.20 | even | 2 | |||
1764.4.a.p.1.2 | 2 | 7.5 | odd | 6 | |||
1764.4.a.x.1.1 | 2 | 7.2 | even | 3 | |||
1764.4.k.z.361.1 | 4 | 7.3 | odd | 6 | |||
1764.4.k.z.1549.1 | 4 | 7.6 | odd | 2 | |||
2352.4.a.bp.1.1 | 2 | 84.47 | odd | 6 | |||
2352.4.a.cb.1.2 | 2 | 84.23 | even | 6 |