Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.8246417619\) |
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 | 193.1 | ||
Root | \(-1.63746 - 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.193 |
Dual form | 336.4.q.h.289.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.91238 | − | 8.50848i | −0.439376 | − | 0.761022i | 0.558265 | − | 0.829663i | \(-0.311467\pi\) |
−0.997641 | + | 0.0686406i | \(0.978134\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.3248 | + | 8.74657i | 0.881454 | + | 0.472270i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.08762 | + | 12.2761i | −0.194273 | + | 0.336490i | −0.946662 | − | 0.322229i | \(-0.895568\pi\) |
0.752389 | + | 0.658719i | \(0.228901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26.1238 | −0.557341 | −0.278670 | − | 0.960387i | \(-0.589894\pi\) | ||||
−0.278670 | + | 0.960387i | \(0.589894\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 29.4743 | 0.507348 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 39.2990 | − | 68.0679i | 0.560671 | − | 0.971111i | −0.436767 | − | 0.899575i | \(-0.643877\pi\) |
0.997438 | − | 0.0715361i | \(-0.0227901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.5876 | + | 63.3716i | 0.441778 | + | 0.765181i | 0.997822 | − | 0.0659715i | \(-0.0210147\pi\) |
−0.556044 | + | 0.831153i | \(0.687681\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −47.2114 | + | 29.2931i | −0.490589 | + | 0.304394i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −48.0000 | − | 83.1384i | −0.435161 | − | 0.753720i | 0.562148 | − | 0.827037i | \(-0.309975\pi\) |
−0.997309 | + | 0.0733164i | \(0.976642\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.2371 | − | 24.6594i | 0.113897 | − | 0.197275i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 173.021 | 1.10790 | 0.553951 | − | 0.832549i | \(-0.313120\pi\) | ||||
0.553951 | + | 0.832549i | \(0.313120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 33.6238 | − | 58.2381i | 0.194807 | − | 0.337415i | −0.752030 | − | 0.659128i | \(-0.770925\pi\) |
0.946837 | + | 0.321713i | \(0.104259\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −21.2629 | − | 36.8284i | −0.112163 | − | 0.194273i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.77326 | − | 181.865i | −0.0278817 | − | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 150.835 | + | 261.254i | 0.670193 | + | 1.16081i | 0.977849 | + | 0.209311i | \(0.0671221\pi\) |
−0.307656 | + | 0.951498i | \(0.599545\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.1856 | − | 67.8715i | 0.160890 | − | 0.278670i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 472.042 | 1.79806 | 0.899031 | − | 0.437886i | \(-0.144273\pi\) | ||||
0.899031 | + | 0.437886i | \(0.144273\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 463.670 | 1.64440 | 0.822198 | − | 0.569201i | \(-0.192747\pi\) | ||||
0.822198 | + | 0.569201i | \(0.192747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −44.2114 | + | 76.5764i | −0.146459 | + | 0.253674i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −45.5980 | − | 78.9781i | −0.141514 | − | 0.245109i | 0.786553 | − | 0.617523i | \(-0.211864\pi\) |
−0.928067 | + | 0.372413i | \(0.878530\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 189.995 | + | 285.571i | 0.553921 | + | 0.832569i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 117.897 | + | 204.204i | 0.323704 | + | 0.560671i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 81.6341 | − | 141.394i | 0.211572 | − | 0.366453i | −0.740635 | − | 0.671908i | \(-0.765475\pi\) |
0.952207 | + | 0.305455i | \(0.0988084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 139.268 | 0.341435 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −219.526 | −0.510121 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −300.263 | + | 520.071i | −0.662558 | + | 1.14758i | 0.317384 | + | 0.948297i | \(0.397196\pi\) |
−0.979941 | + | 0.199286i | \(0.936138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −285.846 | − | 495.099i | −0.599980 | − | 1.03920i | −0.992823 | − | 0.119590i | \(-0.961842\pi\) |
0.392844 | − | 0.919605i | \(-0.371491\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.28862 | − | 166.598i | −0.0105762 | − | 0.333166i | ||||
\(64\) | 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 | \(-0.996994\pi\) |
0.508157 | + | 0.861264i | \(0.330327\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 288.000 | 0.502480 | ||||||||
\(70\) | 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 | −0.632221 | − | 0.774788i | \(-0.717857\pi\) |
0.987097 | + | 0.160126i | \(0.0511900\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 42.7114 | + | 73.9783i | 0.0657585 | + | 0.113897i | ||||
\(76\) | 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 | \(-0.177027\pi\) |
−0.881838 | + | 0.471552i | \(0.843694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 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 | ||||||||
\(87\) | −259.531 | + | 449.521i | −0.319824 | + | 0.553951i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −330.072 | − | 571.702i | −0.393119 | − | 0.680902i | 0.599740 | − | 0.800195i | \(-0.295271\pi\) |
−0.992859 | + | 0.119293i | \(0.961937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −426.464 | − | 228.493i | −0.491270 | − | 0.263215i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 100.871 | + | 174.714i | 0.112472 | + | 0.194807i | ||||
\(94\) | 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 | ||||||||
\(99\) | 127.577 | 0.129515 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 901.949 | − | 1562.22i | 0.888586 | − | 1.53908i | 0.0470394 | − | 0.998893i | \(-0.485021\pi\) |
0.841547 | − | 0.540184i | \(-0.181645\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −537.454 | − | 930.898i | −0.514145 | − | 0.890525i | −0.999865 | − | 0.0164107i | \(-0.994776\pi\) |
0.485721 | − | 0.874114i | \(-0.338557\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 481.160 | + | 257.799i | 0.447204 | + | 0.239605i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −829.676 | − | 1437.04i | −0.749605 | − | 1.29835i | −0.948012 | − | 0.318235i | \(-0.896910\pi\) |
0.198407 | − | 0.980120i | \(-0.436423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −299.464 | + | 518.687i | −0.263151 | + | 0.455791i | −0.967077 | − | 0.254482i | \(-0.918095\pi\) |
0.703927 | + | 0.710273i | \(0.251428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −905.011 | −0.773872 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −781.650 | −0.650720 | −0.325360 | − | 0.945590i | \(-0.605486\pi\) | ||||
−0.325360 | + | 0.945590i | \(0.605486\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −471.588 | + | 816.815i | −0.382398 | + | 0.662333i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.557 | + | 203.615i | 0.0928901 | + | 0.160890i | ||||
\(118\) | 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 | ||||||||
\(123\) | −708.062 | + | 1226.40i | −0.519056 | + | 0.899031i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1507.85 | −1.07893 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −25.3722 | −0.0177277 | −0.00886385 | − | 0.999961i | \(-0.502821\pi\) | ||||
−0.00886385 | + | 0.999961i | \(0.502821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −695.505 | + | 1204.65i | −0.474696 | + | 0.822198i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −237.789 | − | 411.862i | −0.158593 | − | 0.274691i | 0.775768 | − | 0.631018i | \(-0.217362\pi\) |
−0.934362 | + | 0.356326i | \(0.884029\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 42.9995 | + | 1354.54i | 0.0280341 | + | 0.883111i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −132.634 | − | 229.729i | −0.0845580 | − | 0.146459i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −529.268 | + | 916.720i | −0.330062 | + | 0.571683i | −0.982524 | − | 0.186138i | \(-0.940403\pi\) |
0.652462 | + | 0.757821i | \(0.273736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2580.99 | −1.57494 | −0.787470 | − | 0.616352i | \(-0.788610\pi\) | ||||
−0.787470 | + | 0.616352i | \(0.788610\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 273.588 | 0.163406 | ||||||||
\(142\) | 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 | ||||||||
\(147\) | −1026.93 | + | 65.2648i | −0.576188 | + | 0.0366187i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 50.9377 | + | 88.2266i | 0.0280066 | + | 0.0485088i | 0.879689 | − | 0.475549i | \(-0.157751\pi\) |
−0.851682 | + | 0.524058i | \(0.824417\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −889.211 | + | 1540.16i | −0.479225 | + | 0.830042i | −0.999716 | − | 0.0238249i | \(-0.992416\pi\) |
0.520491 | + | 0.853867i | \(0.325749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −707.382 | −0.373781 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −660.690 | −0.342374 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −699.629 | + | 1211.79i | −0.355646 | + | 0.615997i | −0.987228 | − | 0.159312i | \(-0.949073\pi\) |
0.631582 | + | 0.775309i | \(0.282406\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 244.902 | + | 424.183i | 0.122151 | + | 0.211572i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −56.4119 | − | 1777.05i | −0.0276142 | − | 0.869883i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1807.71 | + | 3131.05i | 0.868656 | + | 1.50456i | 0.863370 | + | 0.504571i | \(0.168349\pi\) |
0.00528615 | + | 0.999986i | \(0.498317\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −208.902 | + | 361.830i | −0.0985638 | + | 0.170718i | ||||
\(166\) | 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 | ||||||||
\(171\) | 329.289 | − | 570.345i | 0.147259 | − | 0.255060i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −936.815 | − | 1622.61i | −0.411704 | − | 0.713091i | 0.583373 | − | 0.812205i | \(-0.301733\pi\) |
−0.995076 | + | 0.0991132i | \(0.968399\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 448.103 | − | 278.033i | 0.193562 | − | 0.120099i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −900.789 | − | 1560.21i | −0.382528 | − | 0.662558i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1346.15 | + | 2331.59i | −0.562099 | + | 0.973583i | 0.435215 | + | 0.900327i | \(0.356672\pi\) |
−0.997313 | + | 0.0732565i | \(0.976661\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 461.670 | 0.189589 | 0.0947947 | − | 0.995497i | \(-0.469781\pi\) | ||||
0.0947947 | + | 0.995497i | \(0.469781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1715.07 | 0.692797 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 440.768 | + | 236.157i | 0.169636 | + | 0.0908885i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1882.41 | − | 3260.43i | −0.713124 | − | 1.23517i | −0.963679 | − | 0.267064i | \(-0.913946\pi\) |
0.250555 | − | 0.968102i | \(-0.419387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1463.10 | + | 2534.16i | −0.545680 | + | 0.945145i | 0.452884 | + | 0.891569i | \(0.350395\pi\) |
−0.998564 | + | 0.0535755i | \(0.982938\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −769.978 | −0.282766 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5045.55 | 1.82477 | 0.912387 | − | 0.409330i | \(-0.134237\pi\) | ||||
0.912387 | + | 0.409330i | \(0.134237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2146.12 | − | 3717.20i | 0.764496 | − | 1.32415i | −0.176016 | − | 0.984387i | \(-0.556321\pi\) |
0.940513 | − | 0.339759i | \(-0.110346\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −809.134 | − | 1401.46i | −0.283940 | − | 0.491798i | ||||
\(202\) | 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 | ||||||||
\(207\) | −432.000 | + | 748.246i | −0.145054 | + | 0.251240i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1037.28 | −0.343301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3625.76 | −1.18297 | −0.591487 | − | 0.806315i | \(-0.701459\pi\) | ||||
−0.591487 | + | 0.806315i | \(0.701459\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1596.59 | + | 2765.37i | −0.513598 | + | 0.889578i | ||||
\(214\) | 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 | ||||||||
\(219\) | 664.020 | + | 1150.12i | 0.204887 | + | 0.354875i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1026.64 | + | 1778.19i | −0.312485 | + | 0.541239i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3145.00 | 0.944417 | 0.472208 | − | 0.881487i | \(-0.343457\pi\) | ||||
0.472208 | + | 0.881487i | \(0.343457\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −256.268 | −0.0759313 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −772.873 | + | 1338.65i | −0.225980 | + | 0.391408i | −0.956613 | − | 0.291362i | \(-0.905892\pi\) |
0.730633 | + | 0.682770i | \(0.239225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2036.07 | + | 3526.58i | 0.587544 | + | 1.01766i | 0.994553 | + | 0.104232i | \(0.0332383\pi\) |
−0.407009 | + | 0.913424i | \(0.633428\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.9892 | − | 787.191i | −0.00711760 | − | 0.224214i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1507.86 | + | 2611.68i | 0.423961 | + | 0.734322i | 0.996323 | − | 0.0856790i | \(-0.0273060\pi\) |
−0.572362 | + | 0.820001i | \(0.693973\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −447.989 | + | 775.940i | −0.124356 | + | 0.215390i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 137.103 | 0.0375772 | ||||||||
\(238\) | 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 | −0.931024 | − | 0.364958i | \(-0.881083\pi\) |
0.781575 | + | 0.623812i | \(0.214417\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 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 | ||||||||
\(249\) | −1029.70 | + | 1783.49i | −0.262066 | + | 0.453911i | ||||
\(250\) | 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 | ||||||||
\(255\) | 1158.31 | − | 2006.25i | 0.284455 | − | 0.492691i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2934.44 | + | 5082.61i | 0.712240 | + | 1.23364i | 0.964015 | + | 0.265849i | \(0.0856523\pi\) |
−0.251775 | + | 0.967786i | \(0.581014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 177.269 | + | 5584.20i | 0.0425287 | + | 1.33971i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −778.594 | − | 1348.56i | −0.184650 | − | 0.319824i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2437.81 | − | 4222.41i | 0.571565 | − | 0.989980i | −0.424841 | − | 0.905268i | \(-0.639670\pi\) |
0.996406 | − | 0.0847114i | \(-0.0269968\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1604.07 | −0.371839 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1980.43 | 0.453935 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2763.55 | − | 4786.61i | 0.626382 | − | 1.08493i | −0.361890 | − | 0.932221i | \(-0.617868\pi\) |
0.988272 | − | 0.152704i | \(-0.0487983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1612.37 | − | 2792.70i | −0.361418 | − | 0.625994i | 0.626777 | − | 0.779199i | \(-0.284374\pi\) |
−0.988194 | + | 0.153205i | \(0.951041\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1233.34 | − | 765.246i | 0.273425 | − | 0.169651i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 201.815 | + | 349.554i | 0.0442542 | + | 0.0766504i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 979.022 | − | 1695.72i | 0.212360 | − | 0.367818i | −0.740093 | − | 0.672505i | \(-0.765218\pi\) |
0.952453 | + | 0.304687i | \(0.0985517\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −605.228 | −0.129871 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8531.16 | 1.81113 | 0.905563 | − | 0.424212i | \(-0.139449\pi\) | ||||
0.905563 | + | 0.424212i | \(0.139449\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3954.93 | − | 6850.14i | 0.830728 | − | 1.43886i | −0.0667331 | − | 0.997771i | \(-0.521258\pi\) |
0.897461 | − | 0.441093i | \(-0.145409\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1078.39 | + | 1867.83i | 0.224135 | + | 0.388213i | ||||
\(286\) | 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 | ||||||||
\(291\) | −987.480 | + | 1710.36i | −0.198925 | + | 0.344548i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8321.41 | −1.65919 | −0.829594 | − | 0.558367i | \(-0.811428\pi\) | ||||
−0.829594 | + | 0.558367i | \(0.811428\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5900.02 | 1.16445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −191.366 | + | 331.455i | −0.0373878 | + | 0.0647575i | ||||
\(298\) | 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 | ||||||||
\(303\) | 2705.85 | + | 4686.66i | 0.513026 | + | 0.888586i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2808.36 | + | 4864.22i | −0.527234 | + | 0.913196i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2541.79 | −0.472533 | −0.236267 | − | 0.971688i | \(-0.575924\pi\) | ||||
−0.236267 | + | 0.971688i | \(0.575924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3224.72 | 0.593683 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −303.855 | + | 526.292i | −0.0554020 | + | 0.0959590i | −0.892396 | − | 0.451253i | \(-0.850977\pi\) |
0.836994 | + | 0.547212i | \(0.184311\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5513.64 | − | 9549.90i | −0.995684 | − | 1.72458i | −0.578213 | − | 0.815886i | \(-0.696250\pi\) |
−0.417471 | − | 0.908690i | \(-0.637084\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1391.52 | + | 863.392i | −0.248899 | + | 0.154434i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3630.80 | − | 6288.73i | −0.643300 | − | 1.11423i | −0.984691 | − | 0.174307i | \(-0.944231\pi\) |
0.341391 | − | 0.939921i | \(-0.389102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1226.31 | + | 2124.02i | −0.215235 | + | 0.372798i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4978.05 | 0.865570 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5751.43 | 0.990768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −371.927 | + | 644.197i | −0.0634794 | + | 0.109950i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −898.392 | − | 1556.06i | −0.151930 | − | 0.263151i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −53.5890 | − | 1688.12i | −0.00898011 | − | 0.282885i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3316.36 | + | 5744.11i | 0.550706 | + | 0.953851i | 0.998224 | + | 0.0595761i | \(0.0189749\pi\) |
−0.447517 | + | 0.894275i | \(0.647692\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1357.52 | − | 2351.29i | 0.223398 | − | 0.386936i | ||||
\(334\) | 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 | ||||||||
\(339\) | 1172.47 | − | 2030.78i | 0.187847 | − | 0.325360i | ||||
\(340\) | 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 | ||||||||
\(345\) | −1414.76 | − | 2450.44i | −0.220778 | − | 0.382398i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2968.64 | + | 5141.83i | −0.459265 | + | 0.795470i | −0.998922 | − | 0.0464146i | \(-0.985220\pi\) |
0.539657 | + | 0.841885i | \(0.318554\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 268.472 | 0.0411775 | 0.0205888 | − | 0.999788i | \(-0.493446\pi\) | ||||
0.0205888 | + | 0.999788i | \(0.493446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −705.341 | −0.107260 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1331.40 | + | 2306.06i | −0.200747 | + | 0.347703i | −0.948769 | − | 0.315970i | \(-0.897670\pi\) |
0.748023 | + | 0.663673i | \(0.231003\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5228.69 | − | 9056.36i | −0.781719 | − | 1.35398i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 138.558 | + | 4364.77i | 0.0205414 | + | 0.647081i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −781.637 | − | 1353.83i | −0.114911 | − | 0.199032i | 0.802833 | − | 0.596204i | \(-0.203325\pi\) |
−0.917744 | + | 0.397172i | \(0.869992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 752.192 | − | 1302.83i | 0.109665 | − | 0.189945i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3390.19 | −0.490189 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4349.22 | −0.623695 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 605.408 | − | 1048.60i | 0.0861091 | − | 0.149145i | −0.819754 | − | 0.572716i | \(-0.805890\pi\) |
0.905863 | + | 0.423570i | \(0.139223\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2124.19 | − | 3679.20i | −0.299677 | − | 0.519056i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2569.37 | − | 1594.21i | 0.359556 | − | 0.223093i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2385.93 | + | 4132.55i | 0.331203 | + | 0.573661i | 0.982748 | − | 0.184949i | \(-0.0592121\pi\) |
−0.651545 | + | 0.758610i | \(0.725879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2261.77 | − | 3917.50i | 0.311459 | − | 0.539464i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4519.95 | −0.617479 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4118.66 | 0.558209 | 0.279104 | − | 0.960261i | \(-0.409962\pi\) | ||||
0.279104 | + | 0.960261i | \(0.409962\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.0583 | − | 65.9189i | 0.00511754 | − | 0.00886385i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1767.99 | + | 3062.25i | 0.235875 | + | 0.408547i | 0.959527 | − | 0.281618i | \(-0.0908712\pi\) |
−0.723652 | + | 0.690165i | \(0.757538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2273.52 | + | 1218.12i | 0.300959 | + | 0.161250i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2086.52 | − | 3613.95i | −0.274066 | − | 0.474696i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4803.23 | + | 8319.44i | −0.626050 | + | 1.08435i | 0.362287 | + | 0.932067i | \(0.381996\pi\) |
−0.988337 | + | 0.152284i | \(0.951337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7545.41 | −0.975928 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1426.73 | 0.183127 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −224.500 | + | 388.846i | −0.0285971 | + | 0.0495316i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2683.54 | − | 4648.02i | −0.339252 | − | 0.587601i | 0.645041 | − | 0.764148i | \(-0.276840\pi\) |
−0.984292 | + | 0.176547i | \(0.943507\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3583.70 | − | 1920.10i | −0.449648 | − | 0.240915i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7032.91 | + | 12181.4i | 0.875828 | + | 1.51698i | 0.855878 | + | 0.517177i | \(0.173017\pi\) |
0.0199492 | + | 0.999801i | \(0.493650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −878.379 | + | 1521.40i | −0.108574 | + | 0.188055i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 795.805 | 0.0976392 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4276.25 | −0.520801 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1636.22 | + | 2834.02i | −0.197814 | + | 0.342624i | −0.947819 | − | 0.318808i | \(-0.896718\pi\) |
0.750005 | + | 0.661432i | \(0.230051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1587.80 | − | 2750.16i | −0.190561 | − | 0.330062i | ||||
\(412\) | 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 | ||||||||
\(417\) | 3871.49 | − | 6705.61i | 0.454646 | − | 0.787470i | ||||
\(418\) | 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 | ||||||||
\(423\) | −410.382 | + | 710.803i | −0.0471713 | + | 0.0817031i | ||||
\(424\) | 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 | ||||||||
\(429\) | 555.466 | + | 962.096i | 0.0625132 | + | 0.108276i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4950.11 | + | 8573.84i | −0.553221 | + | 0.958207i | 0.444818 | + | 0.895621i | \(0.353268\pi\) |
−0.998040 | + | 0.0625863i | \(0.980065\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −511.795 | −0.0568021 | −0.0284010 | − | 0.999597i | \(-0.509042\pi\) | ||||
−0.0284010 | + | 0.999597i | \(0.509042\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5099.66 | 0.562092 | ||||||||
\(436\) | 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 | \(-0.189219\pi\) |
−0.899248 | + | 0.437440i | \(0.855885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1370.83 | − | 2765.93i | 0.148022 | − | 0.298665i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4100.16 | − | 7101.69i | −0.439739 | − | 0.761651i | 0.557930 | − | 0.829888i | \(-0.311596\pi\) |
−0.997669 | + | 0.0682372i | \(0.978263\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3242.88 | + | 5616.83i | −0.345454 | + | 0.598344i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −305.626 | −0.0323392 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5788.12 | −0.608370 | −0.304185 | − | 0.952613i | \(-0.598384\pi\) | ||||
−0.304185 | + | 0.952613i | \(0.598384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3345.65 | + | 5794.84i | −0.349314 | + | 0.605030i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2667.63 | − | 4620.48i | −0.276681 | − | 0.479225i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 150.819 | + | 4751.01i | 0.0155396 | + | 0.489518i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3629.59 | − | 6286.63i | −0.371521 | − | 0.643493i | 0.618279 | − | 0.785959i | \(-0.287830\pi\) |
−0.989800 | + | 0.142466i | \(0.954497\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1061.07 | − | 1837.83i | 0.107901 | − | 0.186890i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5966.92 | −0.602835 | −0.301418 | − | 0.953492i | \(-0.597460\pi\) | ||||
−0.301418 | + | 0.953492i | \(0.597460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8884.02 | 0.891740 | 0.445870 | − | 0.895098i | \(-0.352894\pi\) | ||||
0.445870 | + | 0.895098i | \(0.352894\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 991.035 | − | 1716.52i | 0.0988347 | − | 0.171187i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2014.68 | − | 3489.53i | −0.199632 | − | 0.345774i | 0.748777 | − | 0.662822i | \(-0.230641\pi\) |
−0.948409 | + | 0.317049i | \(0.897308\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8488.96 | + | 5267.12i | −0.835787 | + | 0.518578i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2098.89 | − | 3635.38i | −0.205332 | − | 0.355646i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3286.32 | + | 5692.07i | −0.319461 | + | 0.553323i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2083.61 | 0.201269 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1469.41 | −0.141048 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8720.33 | + | 15104.0i | −0.831820 | + | 1.44075i | 0.0647733 | + | 0.997900i | \(0.479368\pi\) |
−0.896593 | + | 0.442855i | \(0.853966\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3940.38 | − | 6824.94i | −0.373526 | − | 0.646966i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4701.53 | + | 2519.01i | 0.442913 | + | 0.237306i | ||||
\(484\) | 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 | \(-0.897026\pi\) |
0.749364 | + | 0.662158i | \(0.230359\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10846.3 | −1.00304 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | −626.707 | − | 1085.49i | −0.0569059 | − | 0.0985638i | ||||
\(496\) | 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 | \(-0.236919\pi\) |
−0.954477 | + | 0.298284i | \(0.903586\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1615.08 | + | 2797.40i | −0.144025 | + | 0.249459i | ||||
\(502\) | 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 | ||||||||
\(507\) | 2271.82 | − | 3934.91i | 0.199004 | − | 0.344686i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4077.69 | − | 7062.77i | −0.355089 | − | 0.615033i | 0.632044 | − | 0.774932i | \(-0.282216\pi\) |
−0.987133 | + | 0.159900i | \(0.948883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6966.51 | − | 4322.49i | 0.603093 | − | 0.374199i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 987.866 | + | 1711.03i | 0.0850202 | + | 0.147259i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5280.35 | + | 9145.84i | −0.451806 | + | 0.782551i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1292.73 | 0.109969 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5620.89 | 0.475394 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 166.009 | − | 287.536i | 0.0139597 | − | 0.0241789i | −0.858961 | − | 0.512041i | \(-0.828890\pi\) |
0.872921 | + | 0.487862i | \(0.162223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3627.42 | + | 6282.87i | 0.303281 | + | 0.525298i | 0.976877 | − | 0.213802i | \(-0.0685847\pi\) |
−0.673596 | + | 0.739099i | \(0.735251\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 50.1965 | + | 1581.26i | 0.00417286 | + | 0.131451i | ||||
\(526\) | 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 | ||||||||
\(531\) | 5404.73 | 0.441705 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12331.5 | −1.00213 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8151.36 | + | 14118.6i | −0.658718 | + | 1.14093i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4038.44 | − | 6994.78i | −0.324528 | − | 0.562099i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4852.32 | + | 308.382i | −0.387763 | + | 0.0246437i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2705.10 | − | 4685.36i | −0.214974 | − | 0.372347i | 0.738290 | − | 0.674483i | \(-0.235633\pi\) |
−0.953265 | + | 0.302137i | \(0.902300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −692.505 | + | 1199.45i | −0.0547297 | + | 0.0947947i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5884.32 | 0.462489 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18673.9 | 1.45967 | 0.729834 | − | 0.683625i | \(-0.239597\pi\) | ||||
0.729834 | + | 0.683625i | \(0.239597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2572.61 | + | 4455.89i | −0.199993 | + | 0.346399i | ||||
\(550\) | 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 | ||||||||
\(555\) | 4445.75 | + | 7700.27i | 0.340021 | + | 0.588934i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4104.74 | − | 7109.62i | 0.312250 | − | 0.540833i | −0.666599 | − | 0.745417i | \(-0.732251\pi\) |
0.978849 | + | 0.204583i | \(0.0655839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12112.8 | −0.916489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3342.44 | −0.251547 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8761.10 | − | 15174.7i | 0.655837 | − | 1.13594i | −0.325846 | − | 0.945423i | \(-0.605649\pi\) |
0.981683 | − | 0.190521i | \(-0.0610176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3839.76 | + | 6650.65i | 0.285911 | + | 0.495212i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1274.71 | + | 790.914i | −0.0944139 | + | 0.0585807i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4528.41 | + | 7843.44i | 0.333640 | + | 0.577881i | 0.983223 | − | 0.182410i | \(-0.0583898\pi\) |
−0.649583 | + | 0.760291i | \(0.725056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5358.27 | − | 9280.80i | 0.392709 | − | 0.680191i | −0.600097 | − | 0.799927i | \(-0.704871\pi\) |
0.992806 | + | 0.119736i | \(0.0382047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11294.5 | 0.823444 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2733.53 | −0.198254 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1608.62 | + | 2786.21i | −0.116062 | + | 0.201025i | −0.918204 | − | 0.396109i | \(-0.870360\pi\) |
0.802142 | + | 0.597133i | \(0.203694\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4389.30 | − | 7602.49i | −0.315048 | − | 0.545680i | ||||
\(580\) | 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 | ||||||||
\(585\) | 1154.97 | − | 2000.46i | 0.0816274 | − | 0.141383i | ||||
\(586\) | 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 | ||||||||
\(591\) | −7568.32 | + | 13108.7i | −0.526767 | + | 0.912387i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10555.2 | + | 18282.1i | 0.730945 | + | 1.26603i | 0.956480 | + | 0.291799i | \(0.0942537\pi\) |
−0.225535 | + | 0.974235i | \(0.572413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12606.1 | − | 6754.15i | −0.868569 | − | 0.465367i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6438.37 | + | 11151.6i | 0.441382 | + | 0.764496i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7868.98 | + | 13629.5i | −0.536758 | + | 0.929692i | 0.462318 | + | 0.886714i | \(0.347018\pi\) |
−0.999076 | + | 0.0429777i | \(0.986316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4856.96 | −0.329650 | −0.164825 | − | 0.986323i | \(-0.552706\pi\) | ||||
−0.164825 | + | 0.986323i | \(0.552706\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4854.80 | 0.327866 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5551.29 | − | 9615.12i | 0.373045 | − | 0.646132i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8629.29 | − | 14946.4i | −0.577022 | − | 0.999431i | −0.995819 | − | 0.0913513i | \(-0.970881\pi\) |
0.418797 | − | 0.908080i | \(-0.362452\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8168.55 | + | 5068.31i | −0.543524 | + | 0.337239i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1191.19 | + | 2063.20i | 0.0788714 | + | 0.136609i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8058.53 | + | 13957.8i | −0.530964 | + | 0.919657i | 0.468383 | + | 0.883526i | \(0.344837\pi\) |
−0.999347 | + | 0.0361315i | \(0.988496\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13913.1 | 0.912243 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17507.3 | −1.14233 | −0.571164 | − | 0.820836i | \(-0.693508\pi\) | ||||
−0.571164 | + | 0.820836i | \(0.693508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4859.24 | − | 8416.46i | 0.315524 | − | 0.546504i | −0.664025 | − | 0.747711i | \(-0.731153\pi\) |
0.979549 | + | 0.201207i | \(0.0644863\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1296.00 | − | 2244.74i | −0.0837467 | − | 0.145054i | ||||
\(622\) | 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 | ||||||||
\(627\) | 1555.92 | − | 2694.93i | 0.0991025 | − | 0.171651i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23710.7 | 1.50303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5144.78 | −0.324580 | −0.162290 | − | 0.986743i | \(-0.551888\pi\) | ||||
−0.162290 | + | 0.986743i | \(0.551888\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5438.63 | − | 9419.99i | 0.341495 | − | 0.591487i | ||||
\(634\) | 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 | ||||||||
\(639\) | −4789.76 | − | 8296.12i | −0.296526 | − | 0.513598i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10843.0 | + | 18780.7i | −0.668135 | + | 1.15724i | 0.310290 | + | 0.950642i | \(0.399574\pi\) |
−0.978425 | + | 0.206602i | \(0.933760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14171.1 | 0.869132 | 0.434566 | − | 0.900640i | \(-0.356902\pi\) | ||||
0.434566 | + | 0.900640i | \(0.356902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13666.3 | 0.834281 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10026.6 | − | 17366.6i | 0.609254 | − | 1.05526i | −0.382109 | − | 0.924117i | \(-0.624802\pi\) |
0.991364 | − | 0.131142i | \(-0.0418645\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4256.30 | − | 7372.13i | −0.257434 | − | 0.445888i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 118.549 | + | 3734.44i | 0.00713716 | + | 0.224830i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11820.6 | − | 20473.8i | −0.708385 | − | 1.22696i | −0.965456 | − | 0.260566i | \(-0.916091\pi\) |
0.257072 | − | 0.966392i | \(-0.417242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2336.21 | + | 4046.44i | −0.139364 | + | 0.241386i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3984.12 | −0.236584 | ||||||||
\(658\) | 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 | −0.860231 | − | 0.509904i | \(-0.829681\pi\) |
0.871705 | + | 0.490030i | \(0.163014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3079.91 | − | 5334.57i | −0.180413 | − | 0.312485i | ||||
\(664\) | 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 | ||||||||
\(669\) | −4717.50 | + | 8170.96i | −0.272630 | + | 0.472208i | ||||
\(670\) | 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 | ||||||||
\(675\) | 384.402 | − | 665.805i | 0.0219195 | − | 0.0379657i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 881.061 | + | 1526.04i | 0.0500176 | + | 0.0866331i | 0.889950 | − | 0.456058i | \(-0.150739\pi\) |
−0.839933 | + | 0.542691i | \(0.817406\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10746.9 | + | 5758.04i | 0.607406 | + | 0.325439i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2318.62 | − | 4015.96i | −0.130469 | − | 0.225980i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1114.44 | + | 1930.26i | −0.0624344 | + | 0.108140i | −0.895553 | − | 0.444955i | \(-0.853220\pi\) |
0.833119 | + | 0.553094i | \(0.186553\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10399.9 | 0.580085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12216.4 | −0.678437 | ||||||||
\(688\) | 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 | \(-0.00823527\pi\) |
−0.522236 | + | 0.852801i | \(0.674902\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2082.67 | + | 1115.86i | 0.114162 | + | 0.0611661i | ||||
\(694\) | 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 | ||||||||
\(699\) | −9047.14 | −0.489548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23697.7 | −1.27682 | −0.638409 | − | 0.769697i | \(-0.720407\pi\) | ||||
−0.638409 | + | 0.769697i | \(0.720407\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11037.4 | + | 19117.3i | −0.592153 | + | 1.02564i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1343.97 | − | 2327.82i | −0.0717968 | − | 0.124356i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28388.2 | − | 17613.9i | 1.51011 | − | 0.936972i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11395.5 | + | 19737.6i | 0.603620 | + | 1.04550i | 0.992268 | + | 0.124114i | \(0.0396088\pi\) |
−0.388648 | + | 0.921386i | \(0.627058\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −205.654 | + | 356.204i | −0.0108476 | + | 0.0187886i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6455.76 | −0.339089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3638.21 | −0.190296 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6971.08 | − | 12074.3i | 0.363096 | − | 0.628900i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15922.4 | + | 27578.4i | 0.825876 | + | 1.43046i | 0.901248 | + | 0.433304i | \(0.142652\pi\) |
−0.0753721 | + | 0.997155i | \(0.524014\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −631.642 | − | 19897.5i | −0.0326263 | − | 1.02777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1677.41 | − | 2905.37i | −0.0862845 | − | 0.149449i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2463.32 | − | 4266.59i | 0.126187 | − | 0.218562i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22500.0 | 1.14784 | 0.573920 | − | 0.818912i | \(-0.305422\pi\) | ||||
0.573920 | + | 0.818912i | \(0.305422\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18221.8 | − | 31561.1i | 0.921966 | − | 1.59689i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1611.38 | + | 2790.99i | 0.0811972 | + | 0.140638i | 0.903764 | − | 0.428030i | \(-0.140792\pi\) |
−0.822567 | + | 0.568668i | \(0.807459\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5599.96 | + | 8417.00i | 0.281031 | + | 0.422402i | ||||
\(736\) | 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 | \(-0.682276\pi\) |
0.998798 | + | 0.0490199i | \(0.0156098\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5734.84 | 0.284311 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | −3089.09 | − | 5350.46i | −0.151304 | − | 0.262066i | ||||
\(748\) | 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 | \(-0.0446873\pi\) |
−0.616263 | + | 0.787541i | \(0.711354\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1325.28 | − | 2295.45i | 0.0641378 | − | 0.111090i | ||||
\(754\) | 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 | ||||||||
\(759\) | −2041.24 | + | 3535.52i | −0.0976181 | + | 0.169080i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1687.57 | + | 2922.96i | 0.0803868 | + | 0.139234i | 0.903416 | − | 0.428765i | \(-0.141051\pi\) |
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9425.40 | + | 5848.15i | −0.447212 | + | 0.277480i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3474.93 | + | 6018.75i | 0.164230 | + | 0.284455i | ||||
\(766\) | 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 | ||||||||
\(771\) | −17606.7 | −0.822423 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11581.8 | + | 20060.2i | −0.538897 | + | 0.933396i | 0.460067 | + | 0.887884i | \(0.347825\pi\) |
−0.998964 | + | 0.0455122i | \(0.985508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −957.411 | − | 1658.29i | −0.0443758 | − | 0.0768611i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14774.1 | − | 7915.74i | −0.682133 | − | 0.365477i | ||||
\(778\) | 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 | ||||||||
\(783\) | 4671.56 | 0.213216 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13747.4 | 0.625050 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4951.47 | + | 8576.20i | −0.224271 | + | 0.388448i | −0.956100 | − | 0.293039i | \(-0.905333\pi\) |
0.731830 | + | 0.681488i | \(0.238667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7313.42 | + | 12667.2i | 0.329993 | + | 0.571565i | ||||
\(790\) | 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 | ||||||||
\(795\) | 2406.11 | − | 4167.50i | 0.107341 | − | 0.185919i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16844.5 | 0.748638 | 0.374319 | − | 0.927300i | \(-0.377877\pi\) | ||||
0.374319 | + | 0.927300i | \(0.377877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7167.83 | −0.317371 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2970.65 | + | 5145.32i | −0.131040 | + | 0.226967i | ||||
\(802\) | 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 | ||||||||
\(807\) | 8290.66 | + | 14359.8i | 0.361642 | + | 0.626382i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17215.3 | − | 29817.8i | 0.748157 | − | 1.29585i | −0.200549 | − | 0.979684i | \(-0.564272\pi\) |
0.948705 | − | 0.316162i | \(-0.102394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 62.4498 | 0.00270396 | 0.00135198 | − | 0.999999i | \(-0.499570\pi\) | ||||
0.00135198 | + | 0.999999i | \(0.499570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9674.20 | 0.417329 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 138.159 | + | 4352.18i | 0.00589457 | + | 0.185687i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19475.8 | − | 33733.1i | −0.827906 | − | 1.43398i | −0.899678 | − | 0.436555i | \(-0.856198\pi\) |
0.0717711 | − | 0.997421i | \(-0.477135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17741.2 | + | 30728.6i | −0.751420 | + | 1.30150i | 0.195715 | + | 0.980661i | \(0.437297\pi\) |
−0.947135 | + | 0.320836i | \(0.896036\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1210.89 | −0.0511003 | ||||||||
\(826\) | 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 | 0.0288439 | + | 0.999584i | \(0.490817\pi\) |
−0.880087 | + | 0.474812i | \(0.842516\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2937.07 | + | 5087.15i | 0.122606 | + | 0.212360i | ||||
\(832\) | 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 | ||||||||
\(837\) | 907.841 | − | 1572.43i | 0.0374906 | − | 0.0649355i | ||||
\(838\) | 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 | ||||||||
\(843\) | −12796.7 | + | 22164.6i | −0.522827 | + | 0.905563i | ||||
\(844\) | 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 | ||||||||
\(849\) | 11864.8 | + | 20550.4i | 0.479621 | + | 0.830728i | ||||
\(850\) | 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 | ||||||||
\(855\) | −6470.36 | −0.258809 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12805.0 | + | 22178.9i | −0.510397 | + | 0.884034i | 0.489530 | + | 0.871986i | \(0.337168\pi\) |
−0.999927 | + | 0.0120476i | \(0.996165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1989.70 | − | 3446.26i | −0.0790309 | − | 0.136886i | 0.823801 | − | 0.566879i | \(-0.191849\pi\) |
−0.902832 | + | 0.429993i | \(0.858516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22285.7 | + | 13827.6i | −0.882109 | + | 0.547319i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12410.2 | − | 21495.0i | −0.489510 | − | 0.847856i | 0.510417 | − | 0.859927i | \(-0.329491\pi\) |
−0.999927 | + | 0.0120708i | \(0.996158\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9203.97 | + | 15941.7i | −0.361786 | + | 0.626631i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3793.94 | 0.148615 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 647.823 | 0.0252887 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7045.87 | − | 12203.8i | 0.274099 | − | 0.474754i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2962.44 | − | 5131.09i | −0.114849 | − | 0.198925i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24615.2 | − | 13188.5i | −0.951024 | − | 0.509545i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25009.7 | − | 43318.1i | −0.962963 | − | 1.66790i | −0.714992 | − | 0.699133i | \(-0.753570\pi\) |
−0.247971 | − | 0.968767i | \(-0.579764\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12482.1 | − | 21619.7i | 0.478966 | − | 0.829594i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10386.4 | −0.397193 | −0.198596 | − | 0.980081i | \(-0.563638\pi\) | ||||
−0.198596 | + | 0.980081i | \(0.563638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36366.4 | −1.38599 | −0.692994 | − | 0.720944i | \(-0.743709\pi\) | ||||
−0.692994 | + | 0.720944i | \(0.743709\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8850.02 | + | 15328.7i | −0.336147 | + | 0.582224i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3803.65 | − | 6588.12i | −0.143984 | − | 0.249388i | 0.785009 | − | 0.619484i | \(-0.212658\pi\) |
−0.928994 | + | 0.370096i | \(0.879325\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −414.195 | − | 221.920i | −0.0156261 | − | 0.00837227i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −574.098 | − | 994.366i | −0.0215858 | − | 0.0373878i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3336.65 | − | 5779.24i | 0.125035 | − | 0.216568i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26451.1 | 0.987891 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7523.64 | −0.280053 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | −21890.5 | + | 13582.3i | −0.806723 | + | 0.500545i | ||||
\(904\) | 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 | \(-0.676752\pi\) |
0.999498 | + | 0.0316794i | \(0.0100856\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16235.1 | −0.592391 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | −8425.08 | − | 14592.7i | −0.304399 | − | 0.527234i | ||||
\(916\) | 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 | \(-0.163275\pi\) |
−0.860649 | + | 0.509198i | \(0.829942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3812.69 | − | 6603.77i | 0.136409 | − | 0.236267i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27805.9 | −0.991596 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8589.84 | 0.305332 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4837.09 | + | 8378.08i | −0.171382 | + | 0.296842i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16573.7 | + | 28706.5i | 0.585323 | + | 1.01381i | 0.994835 | + | 0.101504i | \(0.0323655\pi\) |
−0.409512 | + | 0.912305i | \(0.634301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11145.6 | + | 22488.7i | −0.392356 | + | 0.791661i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −911.564 | − | 1578.87i | −0.0319863 | − | 0.0554020i | ||||
\(934\) | 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 | ||||||||
\(939\) | 33081.8 | 1.14972 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13065.1 | − | 22629.5i | 0.452616 | − | 0.783954i | −0.545932 | − | 0.837830i | \(-0.683824\pi\) |
0.998548 | + | 0.0538758i | \(0.0171575\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22658.0 | − | 39244.8i | −0.782445 | − | 1.35523i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −155.878 | − | 4910.36i | −0.00536583 | − | 0.169031i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3984.35 | + | 6901.09i | 0.136720 | + | 0.236806i | 0.926253 | − | 0.376902i | \(-0.123011\pi\) |
−0.789533 | + | 0.613708i | \(0.789677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5782.24 | + | 10015.1i | −0.197786 | + | 0.342576i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21784.8 | 0.742819 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6742.36 | −0.229178 | −0.114589 | − | 0.993413i | \(-0.536555\pi\) | ||||
−0.114589 | + | 0.993413i | \(0.536555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18494.2 | + | 32033.0i | −0.626659 | + | 1.08541i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3678.92 | − | 6372.07i | −0.124266 | − | 0.215235i | ||||
\(958\) | 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 | ||||||||
\(963\) | −7467.08 | + | 12933.4i | −0.249868 | + | 0.432785i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28749.2 | 0.959035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7202.50 | 0.239521 | 0.119760 | − | 0.992803i | \(-0.461787\pi\) | ||||
0.119760 | + | 0.992803i | \(0.461787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8627.14 | + | 14942.7i | −0.286010 | + | 0.495384i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6852.86 | + | 11869.5i | 0.226487 | + | 0.392286i | 0.956764 | − | 0.290864i | \(-0.0939427\pi\) |
−0.730278 | + | 0.683150i | \(0.760609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42134.0 | − | 22574.8i | −1.38824 | − | 0.743798i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1115.78 | − | 1932.59i | −0.0366499 | − | 0.0634794i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28274.0 | − | 48972.0i | 0.925860 | − | 1.60364i | 0.135687 | − | 0.990752i | \(-0.456676\pi\) |
0.790173 | − | 0.612884i | \(-0.209991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9357.71 | 0.305489 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5390.35 | 0.175434 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8681.87 | − | 15037.4i | 0.281698 | − | 0.487914i | −0.690105 | − | 0.723709i | \(-0.742436\pi\) |
0.971803 | + | 0.235794i | \(0.0757692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24785.6 | − | 42930.0i | −0.801762 | − | 1.38869i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4466.26 | + | 2392.96i | 0.144035 | + | 0.0771719i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22256.2 | − | 38548.8i | −0.715576 | − | 1.23941i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24519.7 | − | 42469.4i | 0.785968 | − | 1.36134i | −0.142451 | − | 0.989802i | \(-0.545498\pi\) |
0.928419 | − | 0.371535i | \(-0.121168\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19898.2 | −0.635901 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42170.3 | −1.34361 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4558.30 | − | 7895.21i | 0.144797 | − | 0.250796i | −0.784500 | − | 0.620129i | \(-0.787080\pi\) |
0.929297 | + | 0.369333i | \(0.120414\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4072.55 | + | 7053.86i | 0.128979 | + | 0.223398i |
(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 | 336.4.q.h.193.1 | 4 | ||
4.3 | odd | 2 | 84.4.i.b.25.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 336.4.q.h.289.1 | 4 | ||
7.3 | odd | 6 | 2352.4.a.bp.1.1 | 2 | |||
7.4 | even | 3 | 2352.4.a.cb.1.2 | 2 | |||
12.11 | even | 2 | 252.4.k.d.109.2 | 4 | |||
28.3 | even | 6 | 588.4.a.h.1.1 | 2 | |||
28.11 | odd | 6 | 588.4.a.g.1.2 | 2 | |||
28.19 | even | 6 | 588.4.i.i.373.2 | 4 | |||
28.23 | odd | 6 | 84.4.i.b.37.1 | yes | 4 | ||
28.27 | even | 2 | 588.4.i.i.361.2 | 4 | |||
84.11 | even | 6 | 1764.4.a.x.1.1 | 2 | |||
84.23 | even | 6 | 252.4.k.d.37.2 | 4 | |||
84.47 | odd | 6 | 1764.4.k.z.1549.1 | 4 | |||
84.59 | odd | 6 | 1764.4.a.p.1.2 | 2 | |||
84.83 | odd | 2 | 1764.4.k.z.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.b.25.1 | ✓ | 4 | 4.3 | odd | 2 | ||
84.4.i.b.37.1 | yes | 4 | 28.23 | odd | 6 | ||
252.4.k.d.37.2 | 4 | 84.23 | even | 6 | |||
252.4.k.d.109.2 | 4 | 12.11 | even | 2 | |||
336.4.q.h.193.1 | 4 | 1.1 | even | 1 | trivial | ||
336.4.q.h.289.1 | 4 | 7.2 | even | 3 | inner | ||
588.4.a.g.1.2 | 2 | 28.11 | odd | 6 | |||
588.4.a.h.1.1 | 2 | 28.3 | even | 6 | |||
588.4.i.i.361.2 | 4 | 28.27 | even | 2 | |||
588.4.i.i.373.2 | 4 | 28.19 | even | 6 | |||
1764.4.a.p.1.2 | 2 | 84.59 | odd | 6 | |||
1764.4.a.x.1.1 | 2 | 84.11 | even | 6 | |||
1764.4.k.z.361.1 | 4 | 84.83 | odd | 2 | |||
1764.4.k.z.1549.1 | 4 | 84.47 | odd | 6 | |||
2352.4.a.bp.1.1 | 2 | 7.3 | odd | 6 | |||
2352.4.a.cb.1.2 | 2 | 7.4 | even | 3 |