Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,5,Mod(17,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.17");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.s (of order \(6\), 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: | \(11.5774358654\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 33.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.33 |
Dual form | 112.5.s.b.17.2 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 12.9853 | − | 7.49706i | 1.44281 | − | 0.833006i | 0.444773 | − | 0.895643i | \(-0.353284\pi\) |
0.998036 | + | 0.0626373i | \(0.0199511\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 21.9853 | + | 12.6932i | 0.879411 | + | 0.507728i | 0.870464 | − | 0.492232i | \(-0.163819\pi\) |
0.00894701 | + | 0.999960i | \(0.497152\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | − | 48.4974i | 0.142857 | − | 0.989743i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 71.9117 | − | 124.555i | 0.887799 | − | 1.53771i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.9853 | + | 38.0796i | 0.181697 | + | 0.314708i | 0.942458 | − | 0.334324i | \(-0.108508\pi\) |
−0.760762 | + | 0.649031i | \(0.775174\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 162.507i | 0.961579i | 0.876836 | + | 0.480790i | \(0.159650\pi\) | ||||
−0.876836 | + | 0.480790i | \(0.840350\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 380.647 | 1.69176 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 93.7355 | − | 54.1182i | 0.324344 | − | 0.187260i | −0.328983 | − | 0.944336i | \(-0.606706\pi\) |
0.653327 | + | 0.757076i | \(0.273373\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −389.338 | − | 224.784i | −1.07850 | − | 0.622671i | −0.148007 | − | 0.988986i | \(-0.547286\pi\) |
−0.930491 | + | 0.366315i | \(0.880619\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −272.691 | − | 682.232i | −0.618347 | − | 1.54701i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −217.911 | + | 377.433i | −0.411931 | + | 0.713485i | −0.995101 | − | 0.0988653i | \(-0.968479\pi\) |
0.583170 | + | 0.812350i | \(0.301812\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.73506 | + | 16.8616i | 0.0155761 | + | 0.0269786i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 941.981i | − | 1.29215i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 742.118 | 0.882423 | 0.441212 | − | 0.897403i | \(-0.354549\pi\) | ||||
0.441212 | + | 0.897403i | \(0.354549\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 900.175 | − | 519.716i | 0.936707 | − | 0.540808i | 0.0477804 | − | 0.998858i | \(-0.484785\pi\) |
0.888926 | + | 0.458050i | \(0.151452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 570.970 | + | 329.650i | 0.524307 | + | 0.302709i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 769.485 | − | 977.377i | 0.628151 | − | 0.797859i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −493.338 | + | 854.486i | −0.360364 | + | 0.624168i | −0.988021 | − | 0.154322i | \(-0.950681\pi\) |
0.627657 | + | 0.778490i | \(0.284014\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1218.32 | + | 2110.20i | 0.801001 | + | 1.38737i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1143.70i | − | 0.680366i | −0.940359 | − | 0.340183i | \(-0.889511\pi\) | ||
0.940359 | − | 0.340183i | \(-0.110489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2418.82 | −1.30818 | −0.654089 | − | 0.756418i | \(-0.726948\pi\) | ||||
−0.654089 | + | 0.756418i | \(0.726948\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3162.00 | − | 1825.58i | 1.56148 | − | 0.901521i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1165.17 | + | 672.714i | 0.527467 | + | 0.304533i | 0.739984 | − | 0.672624i | \(-0.234833\pi\) |
−0.212517 | + | 0.977157i | \(0.568166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2303.00 | − | 678.964i | −0.959184 | − | 0.282784i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 811.455 | − | 1405.48i | 0.311978 | − | 0.540362i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1783.10 | + | 3088.42i | 0.634782 | + | 1.09947i | 0.986561 | + | 0.163391i | \(0.0522432\pi\) |
−0.351780 | + | 0.936083i | \(0.614423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1116.26i | 0.369010i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6740.88 | −2.07475 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3710.93 | + | 2142.50i | −1.06605 | + | 0.615485i | −0.927100 | − | 0.374814i | \(-0.877707\pi\) |
−0.138952 | + | 0.990299i | \(0.544373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1209.57 | − | 698.345i | −0.325066 | − | 0.187677i | 0.328583 | − | 0.944475i | \(-0.393429\pi\) |
−0.653648 | + | 0.756799i | \(0.726762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5537.20 | − | 4359.41i | −1.39511 | − | 1.09837i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2062.73 | + | 3572.76i | −0.488221 | + | 0.845623i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3632.89 | + | 6292.36i | 0.809288 | + | 1.40173i | 0.913358 | + | 0.407158i | \(0.133480\pi\) |
−0.104070 | + | 0.994570i | \(0.533187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6534.77i | 1.37256i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5987.76 | −1.18781 | −0.593906 | − | 0.804534i | \(-0.702415\pi\) | ||||
−0.593906 | + | 0.804534i | \(0.702415\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −500.123 | + | 288.746i | −0.0938494 | + | 0.0541840i | −0.546190 | − | 0.837661i | \(-0.683922\pi\) |
0.452341 | + | 0.891845i | \(0.350589\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 252.825 | + | 145.969i | 0.0449467 | + | 0.0259500i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2000.66 | − | 799.672i | 0.337436 | − | 0.134875i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1573.12 | + | 2724.72i | −0.252061 | + | 0.436583i | −0.964093 | − | 0.265564i | \(-0.914442\pi\) |
0.712032 | + | 0.702147i | \(0.247775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1237.24 | − | 2142.95i | −0.188574 | − | 0.326620i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4729.96i | 0.686596i | 0.939227 | + | 0.343298i | \(0.111544\pi\) | ||||
−0.939227 | + | 0.343298i | \(0.888456\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2747.74 | 0.380309 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9636.61 | − | 5563.70i | 1.27317 | − | 0.735064i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −725.651 | − | 418.955i | −0.0916110 | − | 0.0528916i | 0.453495 | − | 0.891259i | \(-0.350177\pi\) |
−0.545106 | + | 0.838367i | \(0.683510\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7881.16 | + | 1137.55i | 0.951716 | + | 0.137368i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7792.69 | − | 13497.3i | 0.900993 | − | 1.56057i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5706.47 | − | 9883.89i | −0.632295 | − | 1.09517i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5622.23i | 0.597537i | 0.954326 | + | 0.298769i | \(0.0965759\pi\) | ||||
−0.954326 | + | 0.298769i | \(0.903424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6323.99 | 0.645240 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5703.21 | + | 3292.75i | −0.559083 | + | 0.322787i | −0.752778 | − | 0.658275i | \(-0.771286\pi\) |
0.193694 | + | 0.981062i | \(0.437953\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1320.25 | − | 762.249i | −0.124447 | − | 0.0718492i | 0.436484 | − | 0.899712i | \(-0.356223\pi\) |
−0.560931 | + | 0.827863i | \(0.689557\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2664.53 | − | 18460.4i | 0.241680 | − | 1.67441i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5303.31 | − | 9185.61i | 0.463212 | − | 0.802306i | −0.535907 | − | 0.844277i | \(-0.680030\pi\) |
0.999119 | + | 0.0419706i | \(0.0133636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6976.13 | + | 12083.0i | 0.587167 | + | 1.01700i | 0.994601 | + | 0.103769i | \(0.0330902\pi\) |
−0.407434 | + | 0.913235i | \(0.633576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14794.3i | 1.20074i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8811.30 | −0.690054 | −0.345027 | − | 0.938593i | \(-0.612130\pi\) | ||||
−0.345027 | + | 0.938593i | \(0.612130\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9581.68 | + | 5531.99i | −0.724513 | + | 0.418298i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20241.0 | + | 11686.1i | 1.47863 | + | 0.853689i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1968.45 | − | 4924.76i | −0.139005 | − | 0.347769i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6353.79 | − | 11005.1i | 0.433973 | − | 0.751663i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8574.35 | − | 14851.2i | −0.566749 | − | 0.981638i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 15372.2i | − | 0.983823i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3992.70 | −0.247548 | −0.123774 | − | 0.992310i | \(-0.539500\pi\) | ||||
−0.123774 | + | 0.992310i | \(0.539500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −31409.1 | + | 18134.0i | −1.88745 | + | 1.08972i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17515.4 | + | 10112.5i | 1.02065 | + | 0.589272i | 0.914292 | − | 0.405056i | \(-0.132748\pi\) |
0.106357 | + | 0.994328i | \(0.466081\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13626.8 | + | 17308.4i | −0.770355 | + | 0.978483i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11956.8 | − | 20709.7i | 0.656063 | − | 1.13634i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12528.9 | − | 21700.6i | −0.667530 | − | 1.15620i | −0.978593 | − | 0.205807i | \(-0.934018\pi\) |
0.311062 | − | 0.950389i | \(-0.399315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20070.1i | − | 1.03877i | −0.854541 | − | 0.519385i | \(-0.826161\pi\) | ||
0.854541 | − | 0.519385i | \(-0.173839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20173.5 | 1.01471 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6188.20 | + | 3572.76i | −0.302616 | + | 0.174716i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16315.7 | + | 9419.86i | 0.776013 | + | 0.448031i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −34995.3 | + | 8449.18i | −1.61948 | + | 0.391003i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21353.9 | − | 36986.1i | 0.961846 | − | 1.66597i | 0.243986 | − | 0.969779i | \(-0.421545\pi\) |
0.717860 | − | 0.696188i | \(-0.245122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14803.7 | + | 25640.8i | 0.649258 | + | 1.12455i | 0.983301 | + | 0.181989i | \(0.0582536\pi\) |
−0.334043 | + | 0.942558i | \(0.608413\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 15566.9i | − | 0.664998i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26387.5 | 1.09833 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10597.6 | − | 6118.53i | 0.429940 | − | 0.248226i | −0.269381 | − | 0.963034i | \(-0.586819\pi\) |
0.699321 | + | 0.714808i | \(0.253486\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 46308.1 | + | 26736.0i | 1.83174 | + | 1.05755i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16779.2 | + | 13210.2i | 0.647319 | + | 0.509632i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10765.6 | − | 18646.5i | 0.405193 | − | 0.701814i | −0.589151 | − | 0.808023i | \(-0.700538\pi\) |
0.994344 | + | 0.106209i | \(0.0338711\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8368.63 | + | 14494.9i | 0.307388 | + | 0.532411i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16578.9i | − | 0.594461i | −0.954806 | − | 0.297230i | \(-0.903937\pi\) | ||
0.954806 | − | 0.297230i | \(-0.0960629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2152.52 | 0.0753658 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −55995.9 | + | 32329.2i | −1.91498 | + | 1.10561i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −34972.8 | − | 20191.5i | −1.16852 | − | 0.674648i | −0.215192 | − | 0.976572i | \(-0.569038\pi\) |
−0.953332 | + | 0.301924i | \(0.902371\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 885.891 | − | 354.094i | 0.0289270 | − | 0.0115623i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −32124.9 | + | 55642.0i | −1.02541 | + | 1.77606i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −26747.2 | − | 46327.5i | −0.834780 | − | 1.44588i | −0.894209 | − | 0.447649i | \(-0.852261\pi\) |
0.0594290 | − | 0.998233i | \(-0.481072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 54202.1i | 1.65447i | 0.561857 | + | 0.827235i | \(0.310087\pi\) | ||||
−0.561857 | + | 0.827235i | \(0.689913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20942.1 | −0.625343 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21692.3 | + | 12524.1i | −0.633815 | + | 0.365934i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4121.60 | + | 2379.61i | 0.117864 | + | 0.0680491i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −45683.6 | − | 6593.86i | −1.27890 | − | 0.184594i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −601.936 | + | 1042.58i | −0.0165000 | + | 0.0285788i | −0.874158 | − | 0.485643i | \(-0.838586\pi\) |
0.857658 | + | 0.514221i | \(0.171919\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25656.5 | − | 44438.3i | −0.688783 | − | 1.19301i | −0.972232 | − | 0.234019i | \(-0.924812\pi\) |
0.283449 | − | 0.958987i | \(-0.408521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 61857.7i | 1.62676i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1456.28 | −0.0375242 | −0.0187621 | − | 0.999824i | \(-0.505973\pi\) | ||||
−0.0187621 | + | 0.999824i | \(0.505973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −59546.3 | + | 34379.1i | −1.50366 | + | 0.868137i | −0.503667 | + | 0.863898i | \(0.668016\pi\) |
−0.999991 | + | 0.00423890i | \(0.998651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 94348.3 | + | 54472.0i | 2.33530 | + | 1.34828i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5194.82 | − | 35990.8i | 0.126060 | − | 0.873372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14517.2 | − | 25144.5i | 0.345441 | − | 0.598322i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 31340.7 | + | 54283.7i | 0.731423 | + | 1.26686i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 19767.8i | − | 0.452549i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 622.821 | 0.0139894 | 0.00699469 | − | 0.999976i | \(-0.497774\pi\) | ||||
0.00699469 | + | 0.999976i | \(0.497774\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −77752.8 | + | 44890.6i | −1.71379 | + | 0.989455i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −53178.5 | − | 30702.6i | −1.15043 | − | 0.664199i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18903.7 | − | 47294.2i | −0.401446 | − | 1.00436i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4329.50 | + | 7498.91i | −0.0902712 | + | 0.156354i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8794.58 | + | 15232.7i | 0.180066 | + | 0.311883i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11509.7i | − | 0.231449i | −0.993281 | − | 0.115725i | \(-0.963081\pi\) | ||
0.993281 | − | 0.115725i | \(-0.0369190\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2800.26 | 0.0553138 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 48815.4 | − | 28183.6i | 0.947339 | − | 0.546946i | 0.0550855 | − | 0.998482i | \(-0.482457\pi\) |
0.892253 | + | 0.451535i | \(0.149124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −36484.4 | − | 21064.3i | −0.695722 | − | 0.401675i | 0.110030 | − | 0.993928i | \(-0.464905\pi\) |
−0.805752 | + | 0.592253i | \(0.798239\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19984.0 | − | 25383.0i | 0.374505 | − | 0.475685i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27550.9 | − | 47719.6i | 0.507486 | − | 0.878992i | −0.492476 | − | 0.870326i | \(-0.663908\pi\) |
0.999962 | − | 0.00866633i | \(-0.00275861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17077.8 | + | 29579.6i | 0.309240 | + | 0.535620i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 47174.9i | 0.839875i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23082.5 | −0.404098 | −0.202049 | − | 0.979375i | \(-0.564760\pi\) | ||||
−0.202049 | + | 0.979375i | \(0.564760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 70643.9 | − | 40786.3i | 1.21630 | − | 0.702231i | 0.252175 | − | 0.967682i | \(-0.418854\pi\) |
0.964124 | + | 0.265451i | \(0.0855209\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 33946.4 | + | 19599.0i | 0.574886 | + | 0.331910i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −42013.9 | − | 44159.7i | −0.699940 | − | 0.735688i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36529.0 | − | 63270.0i | 0.598747 | − | 1.03706i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35460.8 | + | 61419.8i | 0.571939 | + | 0.990627i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27207.6i | 0.431859i | 0.976409 | + | 0.215930i | \(0.0692782\pi\) | ||||
−0.976409 | + | 0.215930i | \(0.930722\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19163.4 | −0.299385 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 35680.1 | − | 20599.9i | 0.548714 | − | 0.316800i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 93469.3 | + | 53964.5i | 1.41515 | + | 0.817038i | 0.995868 | − | 0.0908179i | \(-0.0289481\pi\) |
0.419283 | + | 0.907856i | \(0.362281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37987.0 | + | 29907.0i | 0.566286 | + | 0.445834i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 53366.9 | − | 92434.3i | 0.783414 | − | 1.35691i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20072.0 | − | 34765.8i | −0.290188 | − | 0.502621i | 0.683666 | − | 0.729795i | \(-0.260385\pi\) |
−0.973854 | + | 0.227174i | \(0.927051\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 90533.1i | 1.28919i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12563.7 | −0.176236 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 91239.0 | − | 52676.9i | 1.26089 | − | 0.727973i | 0.287641 | − | 0.957738i | \(-0.407129\pi\) |
0.973246 | + | 0.229765i | \(0.0737958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13189.3 | + | 7614.84i | 0.179590 | + | 0.103687i | 0.587100 | − | 0.809514i | \(-0.300269\pi\) |
−0.407510 | + | 0.913201i | \(0.633603\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 110867. | − | 44314.1i | 1.48757 | − | 0.594589i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −428.056 | + | 741.415i | −0.00566025 | + | 0.00980384i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4935.81 | + | 8549.07i | 0.0643278 | + | 0.111419i | 0.896396 | − | 0.443255i | \(-0.146176\pi\) |
−0.832068 | + | 0.554674i | \(0.812843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 149495.i | − | 1.92051i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −155117. | −1.96448 | −0.982240 | − | 0.187631i | \(-0.939919\pi\) | ||||
−0.982240 | + | 0.187631i | \(0.939919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 94970.0 | − | 54831.0i | 1.18581 | − | 0.684626i | 0.228456 | − | 0.973554i | \(-0.426632\pi\) |
0.957351 | + | 0.288929i | \(0.0932990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −148200. | − | 85563.4i | −1.82456 | − | 1.05341i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −55466.3 | − | 8005.87i | −0.673388 | − | 0.0971952i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −35902.9 | + | 62185.7i | −0.429867 | + | 0.744552i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 42150.2 | + | 73006.2i | 0.497752 | + | 0.862132i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 89912.4i | − | 1.04733i | −0.851924 | − | 0.523666i | \(-0.824564\pi\) | ||
0.851924 | − | 0.523666i | \(-0.175436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −108781. | −1.25000 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35870.3 | − | 20709.7i | 0.406651 | − | 0.234780i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −61335.5 | − | 35412.1i | −0.686072 | − | 0.396104i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16931.7 | + | 117307.i | −0.186883 | + | 1.29476i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −49371.9 | + | 85514.6i | −0.537767 | + | 0.931440i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17728.5 | − | 30706.6i | −0.190578 | − | 0.330090i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 141681.i | 1.50327i | 0.659582 | + | 0.751633i | \(0.270733\pi\) | ||||
−0.659582 | + | 0.751633i | \(0.729267\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22858.5 | −0.239403 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 74171.3 | − | 42822.8i | 0.766858 | − | 0.442746i | −0.0648948 | − | 0.997892i | \(-0.520671\pi\) |
0.831753 | + | 0.555147i | \(0.187338\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15442.6 | + | 8915.78i | 0.157627 | + | 0.0910061i | 0.576739 | − | 0.816929i | \(-0.304325\pi\) |
−0.419112 | + | 0.907935i | \(0.637658\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −66401.9 | − | 166128.i | −0.669206 | − | 1.67425i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −40402.6 | + | 69979.4i | −0.402060 | + | 0.696388i | −0.993974 | − | 0.109613i | \(-0.965039\pi\) |
0.591914 | + | 0.806001i | \(0.298372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16315.7 | + | 28259.6i | 0.160333 | + | 0.277705i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 159037.i | − | 1.54343i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −48659.7 | −0.466406 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2740.13 | + | 1582.01i | −0.0259421 | + | 0.0149777i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 181174. | + | 104601.i | 1.69434 | + | 0.978228i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 40781.1 | − | 51799.0i | 0.376762 | − | 0.478552i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 36402.1 | − | 63050.3i | 0.332254 | − | 0.575482i | −0.650699 | − | 0.759336i | \(-0.725524\pi\) |
0.982954 | + | 0.183854i | \(0.0588574\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 70953.5 | + | 122895.i | 0.639860 | + | 1.10827i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 184452.i | 1.64359i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 126538. | 1.11419 | 0.557095 | − | 0.830449i | \(-0.311916\pi\) | ||||
0.557095 | + | 0.830449i | \(0.311916\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −114417. | + | 66058.8i | −0.995616 | + | 0.574819i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39581.2 | + | 22852.2i | 0.340393 | + | 0.196526i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −49049.0 | + | 106937.i | −0.416910 | + | 0.908948i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −82947.2 | + | 143669.i | −0.696889 | + | 1.20705i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33474.6 | − | 57979.8i | −0.278008 | − | 0.481524i | 0.692882 | − | 0.721051i | \(-0.256341\pi\) |
−0.970890 | + | 0.239528i | \(0.923007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25527.5i | 0.209583i | 0.994494 | + | 0.104792i | \(0.0334176\pi\) | ||||
−0.994494 | + | 0.104792i | \(0.966582\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 153078. | 1.24251 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −48995.9 | + | 28287.8i | −0.393197 | + | 0.227013i | −0.683545 | − | 0.729909i | \(-0.739563\pi\) |
0.290347 | + | 0.956921i | \(0.406229\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −131643. | − | 76003.9i | −1.04458 | − | 0.603086i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −62482.0 | − | 49191.8i | −0.490251 | − | 0.385973i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18902.4 | − | 32739.9i | 0.146665 | − | 0.254032i | −0.783328 | − | 0.621609i | \(-0.786479\pi\) |
0.929993 | + | 0.367577i | \(0.119813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35895.4 | + | 62172.6i | 0.275438 | + | 0.477073i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 190539.i | − | 1.44601i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14660.5 | −0.110043 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9367.27 | + | 5408.20i | −0.0695474 | + | 0.0401532i | −0.534370 | − | 0.845250i | \(-0.679451\pi\) |
0.464823 | + | 0.885404i | \(0.346118\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −142453. | − | 82245.1i | −1.04621 | − | 0.604028i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 162262. | − | 64856.9i | 1.17888 | − | 0.471203i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15511.7 | − | 26867.0i | 0.111491 | − | 0.193109i | −0.804880 | − | 0.593437i | \(-0.797771\pi\) |
0.916372 | + | 0.400328i | \(0.131104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −115246. | − | 199613.i | −0.819531 | − | 1.41947i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 120599.i | 0.848519i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 98527.5 | 0.685929 | 0.342964 | − | 0.939348i | \(-0.388569\pi\) | ||||
0.342964 | + | 0.939348i | \(0.388569\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −51846.3 | + | 29933.5i | −0.357164 | + | 0.206209i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4454.26 | + | 2571.67i | 0.0303653 | + | 0.0175314i | 0.515106 | − | 0.857127i | \(-0.327753\pi\) |
−0.484741 | + | 0.874658i | \(0.661086\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 54135.5 | + | 7813.79i | 0.365225 | + | 0.0527157i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −173941. | + | 301275.i | −1.16140 | + | 2.01160i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −43141.0 | − | 74722.4i | −0.285096 | − | 0.493801i | 0.687537 | − | 0.726150i | \(-0.258692\pi\) |
−0.972632 | + | 0.232349i | \(0.925359\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 47171.9i | 0.308553i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 303256. | 1.96347 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −69170.8 | + | 39935.8i | −0.443331 | + | 0.255957i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −135036. | − | 77963.1i | −0.856778 | − | 0.494661i | 0.00615368 | − | 0.999981i | \(-0.498041\pi\) |
−0.862932 | + | 0.505320i | \(0.831375\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −47186.2 | + | 326915.i | −0.296394 | + | 2.05347i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17307.2 | + | 29977.0i | −0.107631 | + | 0.186423i | −0.914810 | − | 0.403884i | \(-0.867660\pi\) |
0.807179 | + | 0.590307i | \(0.200993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 84457.5 | + | 146285.i | 0.520030 | + | 0.900718i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 62817.9i | − | 0.382978i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −43384.7 | −0.261907 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −271749. | + | 156894.i | −1.62450 | + | 0.937907i | −0.638809 | + | 0.769366i | \(0.720572\pi\) |
−0.985695 | + | 0.168542i | \(0.946094\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −325382. | − | 187859.i | −1.92624 | − | 1.11211i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 77929.4 | + | 194968.i | 0.456879 | + | 1.14304i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −60038.3 | + | 103989.i | −0.348604 | + | 0.603800i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −150466. | − | 260615.i | −0.865301 | − | 1.49875i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7324.74i | 0.0417219i | 0.999782 | + | 0.0208609i | \(0.00664073\pi\) | ||||
−0.999782 | + | 0.0208609i | \(0.993359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25178.3 | −0.142057 | −0.0710285 | − | 0.997474i | \(-0.522628\pi\) | ||||
−0.0710285 | + | 0.997474i | \(0.522628\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 167579. | − | 96752.0i | 0.936569 | − | 0.540728i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1825.04 | + | 1053.69i | 0.0101040 | + | 0.00583357i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42334.9 | + | 53772.6i | −0.232190 | + | 0.294920i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −53570.3 | + | 92786.6i | −0.291078 | + | 0.504162i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6913.59 | + | 11974.7i | 0.0372176 | + | 0.0644629i | 0.884034 | − | 0.467422i | \(-0.154817\pi\) |
−0.846817 | + | 0.531885i | \(0.821484\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 47438.8i | − | 0.253022i | −0.991965 | − | 0.126511i | \(-0.959622\pi\) | ||
0.991965 | − | 0.126511i | \(-0.0403779\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 282485. | 1.49285 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 169682. | − | 97966.0i | 0.888532 | − | 0.512994i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −95101.7 | − | 54907.0i | −0.493469 | − | 0.284904i | 0.232544 | − | 0.972586i | \(-0.425295\pi\) |
−0.726012 | + | 0.687682i | \(0.758628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −250181. | + | 238024.i | −1.28640 | + | 1.22389i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −41280.4 | + | 71499.7i | −0.210347 | + | 0.364331i | −0.951823 | − | 0.306648i | \(-0.900793\pi\) |
0.741476 | + | 0.670979i | \(0.234126\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10635.8 | − | 18421.7i | −0.0537092 | − | 0.0930270i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 640367.i | − | 3.20490i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −330438. | −1.63907 | −0.819534 | − | 0.573030i | \(-0.805768\pi\) | ||||
−0.819534 | + | 0.573030i | \(0.805768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 43551.5 | − | 25144.5i | 0.214116 | − | 0.123620i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 384461. | + | 221969.i | 1.87351 | + | 1.08167i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 158830. | + | 125047.i | 0.767204 | + | 0.604017i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 186644. | − | 323276.i | 0.893677 | − | 1.54789i | 0.0582431 | − | 0.998302i | \(-0.481450\pi\) |
0.835434 | − | 0.549591i | \(-0.185217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −50978.3 | − | 88297.0i | −0.241969 | − | 0.419103i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 20355.2i | − | 0.0957798i | −0.998853 | − | 0.0478899i | \(-0.984750\pi\) | ||
0.998853 | − | 0.0478899i | \(-0.0152497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31552.7 | 0.147189 | 0.0735944 | − | 0.997288i | \(-0.476553\pi\) | ||||
0.0735944 | + | 0.997288i | \(0.476553\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 342649. | − | 197828.i | 1.58469 | − | 0.914919i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 209452. | + | 120927.i | 0.960397 | + | 0.554486i | 0.896295 | − | 0.443458i | \(-0.146248\pi\) |
0.0641019 | + | 0.997943i | \(0.479582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 330593. | − | 132139.i | 1.50296 | − | 0.600740i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 91741.9 | − | 158902.i | 0.413548 | − | 0.716286i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −53178.5 | − | 92107.8i | −0.237691 | − | 0.411694i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8753.16i | − | 0.0387951i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 512903. | 2.25423 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −235631. | + | 136042.i | −1.02698 | + | 0.592926i | −0.916117 | − | 0.400910i | \(-0.868694\pi\) |
−0.110861 | + | 0.993836i | \(0.535361\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −138860. | − | 80170.8i | −0.600187 | − | 0.346518i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 316920. | + | 45743.4i | 1.35848 | + | 0.196080i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −71364.1 | + | 123606.i | −0.303387 | + | 0.525481i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −203873. | − | 353119.i | −0.859611 | − | 1.48889i | −0.872300 | − | 0.488971i | \(-0.837372\pi\) |
0.0126891 | − | 0.999919i | \(-0.495961\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 322840.i | − | 1.35011i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 286772. | 1.18953 | 0.594763 | − | 0.803901i | \(-0.297246\pi\) | ||||
0.594763 | + | 0.803901i | \(0.297246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 69562.8 | − | 40162.1i | 0.286209 | − | 0.165243i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 139035. | + | 80271.8i | 0.567431 | + | 0.327606i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −41914.3 | + | 290391.i | −0.169687 | + | 1.17563i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 175718. | − | 304352.i | 0.705690 | − | 1.22229i | −0.260751 | − | 0.965406i | \(-0.583970\pi\) |
0.966442 | − | 0.256886i | \(-0.0826964\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −124293. | − | 215282.i | −0.495189 | − | 0.857693i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 116045.i | 0.458660i | 0.973349 | + | 0.229330i | \(0.0736535\pi\) | ||||
−0.973349 | + | 0.229330i | \(0.926347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −167182. | −0.655552 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27951.1 | − | 16137.6i | 0.108738 | − | 0.0627802i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 72030.7 | + | 41586.9i | 0.278024 | + | 0.160517i | 0.632528 | − | 0.774537i | \(-0.282017\pi\) |
−0.354505 | + | 0.935054i | \(0.615351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10502.6 | + | 26275.9i | 0.0402212 | + | 0.100627i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −211742. | + | 366749.i | −0.804587 | + | 1.39359i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19350.8 | − | 33516.5i | −0.0729598 | − | 0.126370i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 59159.2i | 0.221330i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −605508. | −2.24794 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 174948. | − | 101006.i | 0.644517 | − | 0.372112i | −0.141835 | − | 0.989890i | \(-0.545300\pi\) |
0.786352 | + | 0.617778i | \(0.211967\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24134.0 | + | 13933.8i | 0.0882321 | + | 0.0509408i | 0.543467 | − | 0.839431i | \(-0.317111\pi\) |
−0.455235 | + | 0.890371i | \(0.650445\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8848.88 | − | 11239.6i | 0.0321048 | − | 0.0407785i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56252.3 | − | 97431.8i | 0.202544 | − | 0.350816i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44949.9 | + | 77855.5i | 0.160626 | + | 0.278213i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 616284.i | 2.18571i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 185858. | 0.654226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 233190. | − | 134632.i | 0.814707 | − | 0.470372i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −694640. | − | 401050.i | −2.40886 | − | 1.39075i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24777.4 | − | 102625.i | −0.0852861 | − | 0.353243i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18996.8 | − | 32903.4i | 0.0649062 | − | 0.112421i | −0.831746 | − | 0.555156i | \(-0.812659\pi\) |
0.896652 | + | 0.442735i | \(0.145992\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 406356. | + | 703829.i | 1.37818 | + | 2.38708i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 354198.i | 1.19249i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −360160. | −1.20371 | −0.601854 | − | 0.798606i | \(-0.705571\pi\) | ||||
−0.601854 | + | 0.798606i | \(0.705571\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −173964. | + | 100438.i | −0.577185 | + | 0.333238i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −288934. | − | 166816.i | −0.951691 | − | 0.549459i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 121130. | + | 95365.1i | 0.396097 | + | 0.311845i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −187787. | + | 325257.i | −0.609650 | + | 1.05594i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −155272. | − | 268938.i | −0.500474 | − | 0.866847i | −1.00000 | 0.000547960i | \(-0.999826\pi\) | |
0.499525 | − | 0.866299i | \(-0.333508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 393075.i | − | 1.25792i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 71360.2 | 0.226741 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14453.4 | + | 8344.68i | −0.0455988 | + | 0.0263265i | −0.522626 | − | 0.852562i | \(-0.675048\pi\) |
0.477027 | + | 0.878888i | \(0.341714\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −193719. | − | 111844.i | −0.606841 | − | 0.350360i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −112588. | + | 45002.0i | −0.350209 | + | 0.139980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 65131.1 | − | 112810.i | 0.201170 | − | 0.348437i | −0.747736 | − | 0.663997i | \(-0.768859\pi\) |
0.948906 | + | 0.315560i | \(0.102192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −249119. | − | 431487.i | −0.764073 | − | 1.32341i | −0.940735 | − | 0.339142i | \(-0.889863\pi\) |
0.176662 | − | 0.984272i | \(-0.443470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18051.0i | 0.0549784i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8485.52 | −0.0256651 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29199.1 | + | 16858.1i | −0.0877035 | + | 0.0506357i | −0.543210 | − | 0.839597i | \(-0.682791\pi\) |
0.455507 | + | 0.890232i | \(0.349458\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −666313. | − | 384696.i | −1.98756 | − | 1.14752i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 229391. | + | 33109.7i | 0.679554 | + | 0.0980851i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −78404.0 | + | 135800.i | −0.230675 | + | 0.399541i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 296669. | + | 513846.i | 0.866884 | + | 1.50149i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 356809.i | 1.03552i | 0.855525 | + | 0.517762i | \(0.173235\pi\) | ||||
−0.855525 | + | 0.517762i | \(0.826765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −467296. | −1.34698 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18910.1 | + | 10917.8i | −0.0541402 | + | 0.0312579i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28872.6 | − | 16669.6i | −0.0821063 | − | 0.0474041i | 0.458385 | − | 0.888754i | \(-0.348428\pi\) |
−0.540491 | + | 0.841350i | \(0.681762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19234.1 | − | 133258.i | 0.0543299 | − | 0.376409i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −515484. | + | 892844.i | −1.44633 | + | 2.50511i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 162165. | + | 280878.i | 0.451963 | + | 0.782824i | 0.998508 | − | 0.0546064i | \(-0.0173904\pi\) |
−0.546545 | + | 0.837430i | \(0.684057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 66322.0i | − | 0.183615i | −0.995777 | − | 0.0918076i | \(-0.970736\pi\) | ||
0.995777 | − | 0.0918076i | \(-0.0292645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.04499e6 | 2.87394 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 279380. | − | 161300.i | 0.763281 | − | 0.440680i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 422322. | + | 243828.i | 1.14622 | + | 0.661768i | 0.947962 | − | 0.318383i | \(-0.103140\pi\) |
0.198253 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −202369. | − | 506297.i | −0.545643 | − | 1.36512i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −109321. | + | 189349.i | −0.292833 | + | 0.507201i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 170755. | + | 295757.i | 0.454415 | + | 0.787070i | 0.998654 | − | 0.0518597i | \(-0.0165149\pi\) |
−0.544239 | + | 0.838930i | \(0.683182\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 435344.i | − | 1.15102i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 240873. | 0.632728 | 0.316364 | − | 0.948638i | \(-0.397538\pi\) | ||||
0.316364 | + | 0.948638i | \(0.397538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 133658. | − | 77167.4i | 0.348830 | − | 0.201397i | −0.315340 | − | 0.948979i | \(-0.602119\pi\) |
0.664170 | + | 0.747582i | \(0.268785\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 355535. | + | 205268.i | 0.921932 | + | 0.532278i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25397.8 | + | 32259.5i | −0.0654364 | + | 0.0831154i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 201207. | − | 348501.i | 0.515091 | − | 0.892164i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −148200. | − | 256690.i | −0.376976 | − | 0.652941i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 106794.i | 0.269927i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −220248. | −0.553164 | −0.276582 | − | 0.960990i | \(-0.589202\pi\) | ||||
−0.276582 | + | 0.960990i | \(0.589202\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8087.50 | − | 4669.32i | 0.0201840 | − | 0.0116532i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −87780.7 | − | 50680.2i | −0.217696 | − | 0.125687i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 110336. | − | 374253.i | 0.271919 | − | 0.922331i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −430590. | + | 745804.i | −1.05454 | + | 1.82651i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 340604. | + | 589943.i | 0.828960 | + | 1.43580i | 0.898855 | + | 0.438247i | \(0.144400\pi\) |
−0.0698947 | + | 0.997554i | \(0.522266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 572102.i | 1.38373i | 0.722027 | + | 0.691865i | \(0.243211\pi\) | ||||
−0.722027 | + | 0.691865i | \(0.756789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −920716. | −2.21313 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 525915. | − | 303637.i | 1.25634 | − | 0.725348i | 0.283979 | − | 0.958830i | \(-0.408345\pi\) |
0.972361 | + | 0.233482i | \(0.0750120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −163171. | − | 94207.1i | −0.387396 | − | 0.223663i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −600037. | − | 472407.i | −1.41585 | − | 1.11469i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 242335. | − | 419737.i | 0.568316 | − | 0.984353i | −0.428416 | − | 0.903581i | \(-0.640928\pi\) |
0.996733 | − | 0.0807713i | \(-0.0257383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 256720. | + | 444652.i | 0.598380 | + | 1.03642i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 83057.0i | 0.192418i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −329627. | −0.759017 | −0.379509 | − | 0.925188i | \(-0.623907\pi\) | ||||
−0.379509 | + | 0.925188i | \(0.623907\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −182392. | + | 105304.i | −0.417449 | + | 0.241014i | −0.693985 | − | 0.719989i | \(-0.744147\pi\) |
0.276536 | + | 0.961003i | \(0.410813\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 228400. | + | 131867.i | 0.519600 | + | 0.299991i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −519288. | + | 207562.i | −1.17426 | + | 0.469358i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −161716. | + | 280100.i | −0.363497 | + | 0.629595i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −86289.2 | − | 149457.i | −0.192799 | − | 0.333937i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 61413.2i | − | 0.136401i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 94709.8 | 0.209105 | 0.104553 | − | 0.994519i | \(-0.466659\pi\) | ||||
0.104553 | + | 0.994519i | \(0.466659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15883.3 | − | 9170.24i | 0.0348605 | − | 0.0201267i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 466400. | + | 269276.i | 1.01761 | + | 0.587517i | 0.913411 | − | 0.407039i | \(-0.133439\pi\) |
0.104199 | + | 0.994556i | \(0.466772\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 272664. | + | 39355.6i | 0.591408 | + | 0.0853625i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 422588. | − | 731944.i | 0.911219 | − | 1.57828i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −64535.9 | − | 111779.i | −0.138344 | − | 0.239618i | 0.788526 | − | 0.615001i | \(-0.210845\pi\) |
−0.926870 | + | 0.375383i | \(0.877511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 636126.i | − | 1.35570i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −631680. | −1.33839 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −501890. | + | 289766.i | −1.05723 | + | 0.610393i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −113201. | − | 65356.6i | −0.237079 | − | 0.136878i | 0.376754 | − | 0.926313i | \(-0.377040\pi\) |
−0.613834 | + | 0.789435i | \(0.710373\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44268.0 | − | 306697.i | 0.0921771 | − | 0.638622i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 254753. | − | 441246.i | 0.527413 | − | 0.913505i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −61894.8 | − | 107205.i | −0.127406 | − | 0.220673i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 826204.i | − | 1.69096i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −182501. | −0.371389 | −0.185694 | − | 0.982608i | \(-0.559453\pi\) | ||||
−0.185694 | + | 0.982608i | \(0.559453\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 384150. | − | 221789.i | 0.777302 | − | 0.448776i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 443520. | + | 256066.i | 0.892349 | + | 0.515198i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 119767. | + | 299640.i | 0.239607 | + | 0.599462i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −406899. | + | 704770.i | −0.809458 | + | 1.40202i | 0.103783 | + | 0.994600i | \(0.466905\pi\) |
−0.913240 | + | 0.407422i | \(0.866428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 226251. | + | 391878.i | 0.447560 | + | 0.775196i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 453008.i | 0.891101i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −181399. | −0.354832 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −299732. | + | 173051.i | −0.583036 | + | 0.336616i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 364222. | + | 210283.i | 0.704544 | + | 0.406769i | 0.809038 | − | 0.587757i | \(-0.199989\pi\) |
−0.104494 | + | 0.994526i | \(0.533322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46208.9 | + | 58693.1i | −0.0888904 | + | 0.112906i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 611554. | − | 1.05924e6i | 1.16992 | − | 2.02637i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7224.56 | + | 12513.3i | 0.0137447 | + | 0.0238065i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 172948.i | 0.327225i | 0.986525 | + | 0.163613i | \(0.0523147\pi\) | ||||
−0.986525 | + | 0.163613i | \(0.947685\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 788171. | 1.48308 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −226729. | + | 130902.i | −0.424300 | + | 0.244970i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 113936. | + | 65780.9i | 0.212057 | + | 0.122431i | 0.602267 | − | 0.798295i | \(-0.294264\pi\) |
−0.390210 | + | 0.920726i | \(0.627598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −876629. | − | 258445.i | −1.62271 | − | 0.478403i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −159740. | + | 276678.i | −0.294090 | + | 0.509378i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −244884. | − | 424151.i | −0.448406 | − | 0.776662i | 0.549877 | − | 0.835246i | \(-0.314675\pi\) |
−0.998282 | + | 0.0585842i | \(0.981341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.09544e6i | − | 1.99504i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −580258. | −1.05110 | −0.525549 | − | 0.850763i | \(-0.676140\pi\) | ||||
−0.525549 | + | 0.850763i | \(0.676140\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 938945. | − | 542100.i | 1.69172 | − | 0.976713i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 589139. | + | 340139.i | 1.05579 | + | 0.609559i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −408355. | − | 321496.i | −0.727904 | − | 0.573076i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 218698. | − | 378797.i | 0.387763 | − | 0.671624i | −0.604386 | − | 0.796692i | \(-0.706581\pi\) |
0.992148 | + | 0.125067i | \(0.0399147\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 203977. | + | 353298.i | 0.359742 | + | 0.623091i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 751627.i | 1.31859i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24171.7 | −0.0421809 | −0.0210905 | − | 0.999778i | \(-0.506714\pi\) | ||||
−0.0210905 | + | 0.999778i | \(0.506714\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −248842. | + | 143669.i | −0.431956 | + | 0.249390i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −561376. | − | 324111.i | −0.969359 | − | 0.559659i | −0.0703180 | − | 0.997525i | \(-0.522401\pi\) |
−0.899041 | + | 0.437865i | \(0.855735\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 634828. | − | 253743.i | 1.09045 | − | 0.435859i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 197594. | − | 342243.i | 0.337638 | − | 0.584806i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −348172. | − | 603051.i | −0.591838 | − | 1.02509i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 179564.i | 0.303646i | 0.988408 | + | 0.151823i | \(0.0485143\pi\) | ||||
−0.988408 | + | 0.151823i | \(0.951486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.61830e6 | 2.72239 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 529068. | − | 305457.i | 0.885426 | − | 0.511201i | 0.0129823 | − | 0.999916i | \(-0.495867\pi\) |
0.872444 | + | 0.488715i | \(0.162534\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17526.5 | + | 10118.9i | 0.0291805 | + | 0.0168474i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 717486. | + | 103560.i | 1.18842 | + | 0.171534i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −257085. | + | 445284.i | −0.423644 | + | 0.733773i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −131643. | − | 228012.i | −0.215821 | − | 0.373814i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 699061.i | − | 1.14023i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 310655. | 0.504126 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.03191e6 | + | 595774.i | −1.66607 | + | 0.961905i | −0.696342 | + | 0.717710i | \(0.745190\pi\) |
−0.969726 | + | 0.244195i | \(0.921476\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −521282. | − | 300963.i | −0.837373 | − | 0.483458i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −61679.1 | + | 427325.i | −0.0985791 | + | 0.682976i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 113486. | − | 196563.i | 0.180466 | − | 0.312576i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 678732. | + | 1.17560e6i | 1.07390 | + | 1.86005i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 900495.i | 1.41764i | 0.705392 | + | 0.708818i | \(0.250771\pi\) | ||||
−0.705392 | + | 0.708818i | \(0.749229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 145624. | 0.228108 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −104366. | + | 60255.5i | −0.162664 | + | 0.0939142i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21990.7 | − | 12696.3i | −0.0341042 | − | 0.0196901i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 201215. | + | 503411.i | 0.310505 | + | 0.776838i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 789843. | − | 1.36805e6i | 1.21281 | − | 2.10065i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −277882. | − | 481306.i | −0.424584 | − | 0.735401i | 0.571798 | − | 0.820395i | \(-0.306246\pi\) |
−0.996381 | + | 0.0849939i | \(0.972913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 70954.2i | 0.107879i | 0.998544 | + | 0.0539395i | \(0.0171778\pi\) | ||||
−0.998544 | + | 0.0539395i | \(0.982822\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 228356. | 0.345486 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 473368. | − | 273299.i | 0.712662 | − | 0.411455i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 941738. | + | 543713.i | 1.41087 | + | 0.814564i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 708435. | − | 899833.i | 1.05617 | − | 1.34151i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 312356. | − | 541016.i | 0.463408 | − | 0.802646i | −0.535720 | − | 0.844396i | \(-0.679960\pi\) |
0.999128 | + | 0.0417495i | \(0.0132931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −105029. | − | 181916.i | −0.155064 | − | 0.268579i | 0.778018 | − | 0.628242i | \(-0.216225\pi\) |
−0.933082 | + | 0.359663i | \(0.882892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12836.6i | 0.0188601i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 880910. | 1.28801 | 0.644007 | − | 0.765020i | \(-0.277271\pi\) | ||||
0.644007 | + | 0.765020i | \(0.277271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.11951e6 | + | 646349.i | −1.62899 | + | 0.940498i | −0.644595 | + | 0.764524i | \(0.722974\pi\) |
−0.984395 | + | 0.175974i | \(0.943692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 128186. | + | 74008.1i | 0.185625 | + | 0.107171i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −252617. | + | 60991.2i | −0.364060 | + | 0.0878977i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 210440. | − | 364492.i | 0.301825 | − | 0.522775i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −489563. | − | 847948.i | −0.698808 | − | 1.21037i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.11586e6i | 1.58520i | 0.609741 | + | 0.792601i | \(0.291274\pi\) | ||||
−0.609741 | + | 0.792601i | \(0.708726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −156542. | −0.221330 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.01424e6 | + | 1.16292e6i | −2.83437 | + | 1.63642i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47323.8 | + | 27322.4i | 0.0662775 | + | 0.0382653i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −489242. | − | 385178.i | −0.681957 | − | 0.536902i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 822142. | − | 1.42399e6i | 1.14059 | − | 1.97557i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −215008. | − | 372404.i | −0.296889 | − | 0.514228i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.28959e6i | 1.77236i | 0.463341 | + | 0.886180i | \(0.346650\pi\) | ||||
−0.463341 | + | 0.886180i | \(0.653350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.64145e6 | −2.24540 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −566854. | + | 327273.i | −0.771809 | + | 0.445604i | −0.833519 | − | 0.552490i | \(-0.813678\pi\) |
0.0617109 | + | 0.998094i | \(0.480344\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −211796. | − | 122281.i | −0.287033 | − | 0.165718i | 0.349570 | − | 0.936910i | \(-0.386328\pi\) |
−0.636603 | + | 0.771192i | \(0.719661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −780266. | + | 311875.i | −1.05253 | + | 0.420702i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −232638. | + | 402942.i | −0.312363 | + | 0.541029i | −0.978873 | − | 0.204467i | \(-0.934454\pi\) |
0.666510 | + | 0.745496i | \(0.267787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −512591. | − | 887833.i | −0.685075 | − | 1.18659i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.07667e6i | 1.43233i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −138342. | −0.183195 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.02255e6 | + | 590370.i | −1.34787 | + | 0.778194i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 700275. | + | 404304.i | 0.918840 | + | 0.530493i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −745514. | − | 107606.i | −0.973732 | − | 0.140546i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −152086. | + | 263420.i | −0.197738 | + | 0.342492i | −0.947795 | − | 0.318882i | \(-0.896693\pi\) |
0.750057 | + | 0.661373i | \(0.230026\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −674078. | − | 1.16754e6i | −0.872434 | − | 1.51110i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 697876.i | 0.899138i | 0.893246 | + | 0.449569i | \(0.148422\pi\) | ||||
−0.893246 | + | 0.449569i | \(0.851578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −891773. | −1.14375 | −0.571877 | − | 0.820339i | \(-0.693785\pi\) | ||||
−0.571877 | + | 0.820339i | \(0.693785\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.41255e6 | + | 815537.i | −1.80351 | + | 1.04126i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.09340e6 | + | 631278.i | 1.38974 | + | 0.802367i | 0.993286 | − | 0.115687i | \(-0.0369070\pi\) |
0.396455 | + | 0.918054i | \(0.370240\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27948.9 | + | 193636.i | −0.0353640 | + | 0.245009i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 54401.9 | − | 94226.9i | 0.0685265 | − | 0.118691i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −302431. | − | 523826.i | −0.379248 | − | 0.656877i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.35803e6i | − | 1.69537i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.06195e6 | −1.31983 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 668036. | − | 385691.i | 0.826572 | − | 0.477221i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 334280. | + | 192997.i | 0.411776 | + | 0.237739i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 659590. | + | 1.65020e6i | 0.808907 | + | 2.02377i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −687998. | + | 1.19165e6i | −0.840021 | + | 1.45496i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 475990. | + | 824439.i | 0.578607 | + | 1.00218i | 0.995639 | + | 0.0932848i | \(0.0297367\pi\) |
−0.417033 | + | 0.908891i | \(0.636930\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 947149.i | 1.14628i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 743243. | 0.895559 | 0.447779 | − | 0.894144i | \(-0.352215\pi\) | ||||
0.447779 | + | 0.894144i | \(0.352215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −180115. | + | 103989.i | −0.216077 | + | 0.124752i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −460418. | − | 265823.i | −0.549934 | − | 0.317505i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 613038. | − | 778662.i | 0.729035 | − | 0.925999i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −262150. | + | 454057.i | −0.310398 | + | 0.537625i | −0.978449 | − | 0.206491i | \(-0.933796\pi\) |
0.668050 | + | 0.744116i | \(0.267129\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.06219e6 | + | 1.83977e6i | 1.25223 | + | 2.16892i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 973052.i | − | 1.14218i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19210.7 | −0.0224522 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −189883. | + | 109629.i | −0.220967 | + | 0.127575i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 848178. | + | 489696.i | 0.982779 | + | 0.567408i | 0.903108 | − | 0.429414i | \(-0.141280\pi\) |
0.0796709 | + | 0.996821i | \(0.474613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 744024. | + | 782024.i | 0.858396 | + | 0.902237i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 642090. | − | 1.11213e6i | 0.737620 | − | 1.27759i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 60409.7 | + | 104633.i | 0.0691009 | + | 0.119686i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.13988e6i | − | 1.29831i | −0.760656 | − | 0.649155i | \(-0.775123\pi\) | ||
0.760656 | − | 0.649155i | \(-0.224877\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 267368. | 0.303235 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 693791. | − | 400561.i | 0.783519 | − | 0.452365i | −0.0541569 | − | 0.998532i | \(-0.517247\pi\) |
0.837676 | + | 0.546167i | \(0.183914\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 431669. | + | 249224.i | 0.485431 | + | 0.280264i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −920670. | − | 724840.i | −1.03096 | − | 0.811668i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 340143. | − | 589145.i | 0.379282 | − | 0.656935i | −0.611676 | − | 0.791108i | \(-0.709504\pi\) |
0.990958 | + | 0.134173i | \(0.0428378\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −46923.3 | − | 81273.5i | −0.0521022 | − | 0.0902436i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.21160e6i | 1.33967i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −394774. | −0.434673 | −0.217337 | − | 0.976097i | \(-0.569737\pi\) | ||||
−0.217337 | + | 0.976097i | \(0.569737\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26467.5 | + | 15281.0i | −0.0290206 | + | 0.0167550i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 423727. | + | 244639.i | 0.462660 | + | 0.267117i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.14013e6 | + | 455714.i | −1.23970 | + | 0.495513i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78449.9 | − | 135879.i | 0.0849465 | − | 0.147132i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −762740. | − | 1.32110e6i | −0.822478 | − | 1.42457i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.30265e6i | − | 1.39886i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 604328. | 0.646279 | 0.323140 | − | 0.946351i | \(-0.395262\pi\) | ||||
0.323140 | + | 0.946351i | \(0.395262\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −631860. | + | 364804.i | −0.672935 | + | 0.388519i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −657301. | − | 379493.i | −0.697149 | − | 0.402499i | 0.109136 | − | 0.994027i | \(-0.465192\pi\) |
−0.806285 | + | 0.591528i | \(0.798525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −973346. | − | 140490.i | −1.02811 | − | 0.148396i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23720.9 | + | 41085.8i | −0.0249530 | + | 0.0432198i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −612591. | − | 1.06104e6i | −0.641773 | − | 1.11158i | −0.985037 | − | 0.172345i | \(-0.944866\pi\) |
0.343263 | − | 0.939239i | \(-0.388468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 36843.3i | − | 0.0384409i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00666e6 | 2.08514 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.03964e6 | − | 600236.i | 1.07591 | − | 0.621177i | 0.146120 | − | 0.989267i | \(-0.453322\pi\) |
0.929790 | + | 0.368090i | \(0.119988\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32016.6 | − | 18484.8i | −0.0329992 | − | 0.0190521i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 141214. | − | 978362.i | 0.144959 | − | 1.00430i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 527088. | − | 912944.i | 0.538878 | − | 0.933365i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 904963. | + | 1.56744e6i | 0.921475 | + | 1.59604i | 0.797134 | + | 0.603802i | \(0.206348\pi\) |
0.124340 | + | 0.992240i | \(0.460318\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1.09164e6i | − | 1.10708i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.74552e6 | −1.76311 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 648903. | − | 374644.i | 0.652814 | − | 0.376902i | −0.136719 | − | 0.990610i | \(-0.543656\pi\) |
0.789534 | + | 0.613707i | \(0.210323\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 804909. | + | 464715.i | 0.806521 | + | 0.465645i |
(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 | 112.5.s.b.33.2 | 4 | ||
4.3 | odd | 2 | 14.5.d.a.5.1 | yes | 4 | ||
7.2 | even | 3 | 784.5.c.b.97.4 | 4 | |||
7.3 | odd | 6 | inner | 112.5.s.b.17.2 | 4 | ||
7.5 | odd | 6 | 784.5.c.b.97.1 | 4 | |||
12.11 | even | 2 | 126.5.n.a.19.2 | 4 | |||
20.3 | even | 4 | 350.5.i.a.299.3 | 8 | |||
20.7 | even | 4 | 350.5.i.a.299.2 | 8 | |||
20.19 | odd | 2 | 350.5.k.a.201.2 | 4 | |||
28.3 | even | 6 | 14.5.d.a.3.1 | ✓ | 4 | ||
28.11 | odd | 6 | 98.5.d.a.31.1 | 4 | |||
28.19 | even | 6 | 98.5.b.b.97.4 | 4 | |||
28.23 | odd | 6 | 98.5.b.b.97.3 | 4 | |||
28.27 | even | 2 | 98.5.d.a.19.1 | 4 | |||
84.23 | even | 6 | 882.5.c.b.685.2 | 4 | |||
84.47 | odd | 6 | 882.5.c.b.685.1 | 4 | |||
84.59 | odd | 6 | 126.5.n.a.73.2 | 4 | |||
140.3 | odd | 12 | 350.5.i.a.199.2 | 8 | |||
140.59 | even | 6 | 350.5.k.a.101.2 | 4 | |||
140.87 | odd | 12 | 350.5.i.a.199.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.5.d.a.3.1 | ✓ | 4 | 28.3 | even | 6 | ||
14.5.d.a.5.1 | yes | 4 | 4.3 | odd | 2 | ||
98.5.b.b.97.3 | 4 | 28.23 | odd | 6 | |||
98.5.b.b.97.4 | 4 | 28.19 | even | 6 | |||
98.5.d.a.19.1 | 4 | 28.27 | even | 2 | |||
98.5.d.a.31.1 | 4 | 28.11 | odd | 6 | |||
112.5.s.b.17.2 | 4 | 7.3 | odd | 6 | inner | ||
112.5.s.b.33.2 | 4 | 1.1 | even | 1 | trivial | ||
126.5.n.a.19.2 | 4 | 12.11 | even | 2 | |||
126.5.n.a.73.2 | 4 | 84.59 | odd | 6 | |||
350.5.i.a.199.2 | 8 | 140.3 | odd | 12 | |||
350.5.i.a.199.3 | 8 | 140.87 | odd | 12 | |||
350.5.i.a.299.2 | 8 | 20.7 | even | 4 | |||
350.5.i.a.299.3 | 8 | 20.3 | even | 4 | |||
350.5.k.a.101.2 | 4 | 140.59 | even | 6 | |||
350.5.k.a.201.2 | 4 | 20.19 | odd | 2 | |||
784.5.c.b.97.1 | 4 | 7.5 | odd | 6 | |||
784.5.c.b.97.4 | 4 | 7.2 | even | 3 | |||
882.5.c.b.685.1 | 4 | 84.47 | odd | 6 | |||
882.5.c.b.685.2 | 4 | 84.23 | even | 6 |