Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(229,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.18 | ||
Character | \(\chi\) | \(=\) | 690.229 |
Dual form | 690.3.f.a.229.20 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 1.15789 | − | 4.86408i | 0.231579 | − | 0.972816i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −1.79343 | −0.256204 | −0.128102 | − | 0.991761i | \(-0.540888\pi\) | ||||
−0.128102 | + | 0.991761i | \(0.540888\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −6.87885 | − | 1.63751i | −0.687885 | − | 0.163751i | ||||
\(11\) | 0.382184i | 0.0347440i | 0.999849 | + | 0.0173720i | \(0.00552995\pi\) | ||||
−0.999849 | + | 0.0173720i | \(0.994470\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | 24.0468i | 1.84976i | 0.380264 | + | 0.924878i | \(0.375833\pi\) | ||||
−0.380264 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(14\) | 2.53629i | 0.181164i | ||||||||
\(15\) | 8.42483 | + | 2.00553i | 0.561656 | + | 0.133702i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 22.1605 | 1.30356 | 0.651779 | − | 0.758409i | \(-0.274023\pi\) | ||||
0.651779 | + | 0.758409i | \(0.274023\pi\) | |||||||
\(18\) | 4.24264i | 0.235702i | ||||||||
\(19\) | 17.6049i | 0.926573i | 0.886209 | + | 0.463286i | \(0.153330\pi\) | ||||
−0.886209 | + | 0.463286i | \(0.846670\pi\) | |||||||
\(20\) | −2.31579 | + | 9.72816i | −0.115789 | + | 0.486408i | ||||
\(21\) | − | 3.10631i | − | 0.147919i | ||||||
\(22\) | 0.540489 | 0.0245677 | ||||||||
\(23\) | −1.50786 | − | 22.9505i | −0.0655591 | − | 0.997849i | ||||
\(24\) | −4.89898 | −0.204124 | ||||||||
\(25\) | −22.3186 | − | 11.2642i | −0.892742 | − | 0.450567i | ||||
\(26\) | 34.0074 | 1.30798 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 3.58685 | 0.128102 | ||||||||
\(29\) | −1.79697 | −0.0619646 | −0.0309823 | − | 0.999520i | \(-0.509864\pi\) | ||||
−0.0309823 | + | 0.999520i | \(0.509864\pi\) | |||||||
\(30\) | 2.83625 | − | 11.9145i | 0.0945417 | − | 0.397151i | ||||
\(31\) | 40.3465 | 1.30150 | 0.650750 | − | 0.759292i | \(-0.274455\pi\) | ||||
0.650750 | + | 0.759292i | \(0.274455\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | −0.661961 | −0.0200594 | ||||||||
\(34\) | − | 31.3397i | − | 0.921755i | ||||||
\(35\) | −2.07660 | + | 8.72337i | −0.0593314 | + | 0.249239i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 42.7110 | 1.15435 | 0.577175 | − | 0.816620i | \(-0.304155\pi\) | ||||
0.577175 | + | 0.816620i | \(0.304155\pi\) | |||||||
\(38\) | 24.8971 | 0.655186 | ||||||||
\(39\) | −41.6503 | −1.06796 | ||||||||
\(40\) | 13.7577 | + | 3.27502i | 0.343942 | + | 0.0818755i | ||||
\(41\) | 1.26689 | 0.0308998 | 0.0154499 | − | 0.999881i | \(-0.495082\pi\) | ||||
0.0154499 | + | 0.999881i | \(0.495082\pi\) | |||||||
\(42\) | −4.39298 | −0.104595 | ||||||||
\(43\) | 16.5675 | 0.385291 | 0.192646 | − | 0.981268i | \(-0.438293\pi\) | ||||
0.192646 | + | 0.981268i | \(0.438293\pi\) | |||||||
\(44\) | − | 0.764367i | − | 0.0173720i | ||||||
\(45\) | −3.47368 | + | 14.5922i | −0.0771930 | + | 0.324272i | ||||
\(46\) | −32.4569 | + | 2.13244i | −0.705586 | + | 0.0463573i | ||||
\(47\) | 5.75045i | 0.122350i | 0.998127 | + | 0.0611750i | \(0.0194848\pi\) | ||||
−0.998127 | + | 0.0611750i | \(0.980515\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −45.7836 | −0.934360 | ||||||||
\(50\) | −15.9300 | + | 31.5632i | −0.318599 | + | 0.631264i | ||||
\(51\) | 38.3831i | 0.752610i | ||||||||
\(52\) | − | 48.0937i | − | 0.924878i | ||||||
\(53\) | 81.4797 | 1.53735 | 0.768677 | − | 0.639637i | \(-0.220915\pi\) | ||||
0.768677 | + | 0.639637i | \(0.220915\pi\) | |||||||
\(54\) | −7.34847 | −0.136083 | ||||||||
\(55\) | 1.85897 | + | 0.442528i | 0.0337995 | + | 0.00804597i | ||||
\(56\) | − | 5.07258i | − | 0.0905818i | ||||||
\(57\) | −30.4925 | −0.534957 | ||||||||
\(58\) | 2.54131i | 0.0438156i | ||||||||
\(59\) | 18.0948 | 0.306691 | 0.153346 | − | 0.988173i | \(-0.450995\pi\) | ||||
0.153346 | + | 0.988173i | \(0.450995\pi\) | |||||||
\(60\) | −16.8497 | − | 4.01106i | −0.280828 | − | 0.0668511i | ||||
\(61\) | 33.1411i | 0.543296i | 0.962397 | + | 0.271648i | \(0.0875687\pi\) | ||||
−0.962397 | + | 0.271648i | \(0.912431\pi\) | |||||||
\(62\) | − | 57.0586i | − | 0.920300i | ||||||
\(63\) | 5.38028 | 0.0854013 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 116.966 | + | 27.8437i | 1.79947 | + | 0.428365i | ||||
\(66\) | 0.936155i | 0.0141842i | ||||||||
\(67\) | 116.835 | 1.74381 | 0.871904 | − | 0.489677i | \(-0.162885\pi\) | ||||
0.871904 | + | 0.489677i | \(0.162885\pi\) | |||||||
\(68\) | −44.3210 | −0.651779 | ||||||||
\(69\) | 39.7515 | − | 2.61169i | 0.576108 | − | 0.0378506i | ||||
\(70\) | 12.3367 | + | 2.93676i | 0.176239 | + | 0.0419537i | ||||
\(71\) | 28.3516 | 0.399318 | 0.199659 | − | 0.979865i | \(-0.436017\pi\) | ||||
0.199659 | + | 0.979865i | \(0.436017\pi\) | |||||||
\(72\) | − | 8.48528i | − | 0.117851i | ||||||
\(73\) | 112.311i | 1.53850i | 0.638948 | + | 0.769250i | \(0.279370\pi\) | ||||
−0.638948 | + | 0.769250i | \(0.720630\pi\) | |||||||
\(74\) | − | 60.4025i | − | 0.816249i | ||||||
\(75\) | 19.5101 | − | 38.6569i | 0.260135 | − | 0.515425i | ||||
\(76\) | − | 35.2098i | − | 0.463286i | ||||||
\(77\) | − | 0.685419i | − | 0.00890154i | ||||||
\(78\) | 58.9025i | 0.755160i | ||||||||
\(79\) | − | 62.0766i | − | 0.785780i | −0.919585 | − | 0.392890i | \(-0.871475\pi\) | ||
0.919585 | − | 0.392890i | \(-0.128525\pi\) | |||||||
\(80\) | 4.63158 | − | 19.4563i | 0.0578947 | − | 0.243204i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 1.79165i | − | 0.0218494i | ||||||
\(83\) | 148.140 | 1.78481 | 0.892407 | − | 0.451231i | \(-0.149015\pi\) | ||||
0.892407 | + | 0.451231i | \(0.149015\pi\) | |||||||
\(84\) | 6.21261i | 0.0739597i | ||||||||
\(85\) | 25.6595 | − | 107.790i | 0.301877 | − | 1.26812i | ||||
\(86\) | − | 23.4300i | − | 0.272442i | ||||||
\(87\) | − | 3.11245i | − | 0.0357753i | ||||||
\(88\) | −1.08098 | −0.0122838 | ||||||||
\(89\) | 102.736i | 1.15434i | 0.816623 | + | 0.577171i | \(0.195843\pi\) | ||||
−0.816623 | + | 0.577171i | \(0.804157\pi\) | |||||||
\(90\) | 20.6365 | + | 4.91253i | 0.229295 | + | 0.0545837i | ||||
\(91\) | − | 43.1262i | − | 0.473915i | ||||||
\(92\) | 3.01572 | + | 45.9010i | 0.0327796 | + | 0.498924i | ||||
\(93\) | 69.8822i | 0.751422i | ||||||||
\(94\) | 8.13236 | 0.0865145 | ||||||||
\(95\) | 85.6316 | + | 20.3846i | 0.901385 | + | 0.214575i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −150.611 | −1.55269 | −0.776343 | − | 0.630310i | \(-0.782928\pi\) | ||||
−0.776343 | + | 0.630310i | \(0.782928\pi\) | |||||||
\(98\) | 64.7478i | 0.660692i | ||||||||
\(99\) | − | 1.14655i | − | 0.0115813i | ||||||
\(100\) | 44.6371 | + | 22.5284i | 0.446371 | + | 0.225284i | ||||
\(101\) | −105.835 | −1.04787 | −0.523937 | − | 0.851757i | \(-0.675537\pi\) | ||||
−0.523937 | + | 0.851757i | \(0.675537\pi\) | |||||||
\(102\) | 54.2819 | 0.532175 | ||||||||
\(103\) | −110.093 | −1.06886 | −0.534432 | − | 0.845211i | \(-0.679474\pi\) | ||||
−0.534432 | + | 0.845211i | \(0.679474\pi\) | |||||||
\(104\) | −68.0147 | −0.653988 | ||||||||
\(105\) | −15.1093 | − | 3.59678i | −0.143898 | − | 0.0342550i | ||||
\(106\) | − | 115.230i | − | 1.08707i | ||||||
\(107\) | 145.434 | 1.35920 | 0.679599 | − | 0.733584i | \(-0.262154\pi\) | ||||
0.679599 | + | 0.733584i | \(0.262154\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | − | 108.845i | − | 0.998578i | −0.866435 | − | 0.499289i | \(-0.833595\pi\) | ||
0.866435 | − | 0.499289i | \(-0.166405\pi\) | |||||||
\(110\) | 0.625830 | − | 2.62898i | 0.00568936 | − | 0.0238998i | ||||
\(111\) | 73.9776i | 0.666465i | ||||||||
\(112\) | −7.17371 | −0.0640510 | ||||||||
\(113\) | −56.0495 | −0.496013 | −0.248007 | − | 0.968758i | \(-0.579775\pi\) | ||||
−0.248007 | + | 0.968758i | \(0.579775\pi\) | |||||||
\(114\) | 43.1230i | 0.378272i | ||||||||
\(115\) | −113.379 | − | 19.2399i | −0.985905 | − | 0.167304i | ||||
\(116\) | 3.59395 | 0.0309823 | ||||||||
\(117\) | − | 72.1405i | − | 0.616585i | ||||||
\(118\) | − | 25.5899i | − | 0.216863i | ||||||
\(119\) | −39.7432 | −0.333977 | ||||||||
\(120\) | −5.67250 | + | 23.8290i | −0.0472709 | + | 0.198575i | ||||
\(121\) | 120.854 | 0.998793 | ||||||||
\(122\) | 46.8686 | 0.384169 | ||||||||
\(123\) | 2.19432i | 0.0178400i | ||||||||
\(124\) | −80.6930 | −0.650750 | ||||||||
\(125\) | −80.6325 | + | 95.5165i | −0.645060 | + | 0.764132i | ||||
\(126\) | − | 7.60887i | − | 0.0603878i | ||||||
\(127\) | 67.2083i | 0.529199i | 0.964358 | + | 0.264599i | \(0.0852397\pi\) | ||||
−0.964358 | + | 0.264599i | \(0.914760\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 28.6958i | 0.222448i | ||||||||
\(130\) | 39.3769 | − | 165.415i | 0.302899 | − | 1.27242i | ||||
\(131\) | −144.689 | −1.10450 | −0.552249 | − | 0.833679i | \(-0.686230\pi\) | ||||
−0.552249 | + | 0.833679i | \(0.686230\pi\) | |||||||
\(132\) | 1.32392 | 0.0100297 | ||||||||
\(133\) | − | 31.5731i | − | 0.237392i | ||||||
\(134\) | − | 165.230i | − | 1.23306i | ||||||
\(135\) | −25.2745 | − | 6.01660i | −0.187219 | − | 0.0445674i | ||||
\(136\) | 62.6793i | 0.460877i | ||||||||
\(137\) | −66.2233 | −0.483381 | −0.241691 | − | 0.970353i | \(-0.577702\pi\) | ||||
−0.241691 | + | 0.970353i | \(0.577702\pi\) | |||||||
\(138\) | −3.69349 | − | 56.2171i | −0.0267644 | − | 0.407370i | ||||
\(139\) | 58.2706 | 0.419213 | 0.209606 | − | 0.977786i | \(-0.432782\pi\) | ||||
0.209606 | + | 0.977786i | \(0.432782\pi\) | |||||||
\(140\) | 4.15320 | − | 17.4467i | 0.0296657 | − | 0.124620i | ||||
\(141\) | −9.96007 | −0.0706388 | ||||||||
\(142\) | − | 40.0952i | − | 0.282360i | ||||||
\(143\) | −9.19030 | −0.0642679 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | −2.08071 | + | 8.74063i | −0.0143497 | + | 0.0602802i | ||||
\(146\) | 158.831 | 1.08788 | ||||||||
\(147\) | − | 79.2996i | − | 0.539453i | ||||||
\(148\) | −85.4220 | −0.577175 | ||||||||
\(149\) | 178.281i | 1.19652i | 0.801303 | + | 0.598259i | \(0.204140\pi\) | ||||
−0.801303 | + | 0.598259i | \(0.795860\pi\) | |||||||
\(150\) | −54.6691 | − | 27.5915i | −0.364461 | − | 0.183943i | ||||
\(151\) | 216.913 | 1.43651 | 0.718257 | − | 0.695778i | \(-0.244940\pi\) | ||||
0.718257 | + | 0.695778i | \(0.244940\pi\) | |||||||
\(152\) | −49.7941 | −0.327593 | ||||||||
\(153\) | −66.4815 | −0.434519 | ||||||||
\(154\) | −0.969328 | −0.00629434 | ||||||||
\(155\) | 46.7170 | − | 196.249i | 0.301400 | − | 1.26612i | ||||
\(156\) | 83.3007 | 0.533979 | ||||||||
\(157\) | −132.164 | −0.841810 | −0.420905 | − | 0.907105i | \(-0.638287\pi\) | ||||
−0.420905 | + | 0.907105i | \(0.638287\pi\) | |||||||
\(158\) | −87.7896 | −0.555631 | ||||||||
\(159\) | 141.127i | 0.887592i | ||||||||
\(160\) | −27.5154 | − | 6.55004i | −0.171971 | − | 0.0409378i | ||||
\(161\) | 2.70424 | + | 41.1601i | 0.0167965 | + | 0.255653i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | − | 98.3005i | − | 0.603070i | −0.953455 | − | 0.301535i | \(-0.902501\pi\) | ||
0.953455 | − | 0.301535i | \(-0.0974991\pi\) | |||||||
\(164\) | −2.53378 | −0.0154499 | ||||||||
\(165\) | −0.766482 | + | 3.21983i | −0.00464534 | + | 0.0195141i | ||||
\(166\) | − | 209.501i | − | 1.26205i | ||||||
\(167\) | − | 69.3323i | − | 0.415164i | −0.978218 | − | 0.207582i | \(-0.933441\pi\) | ||
0.978218 | − | 0.207582i | \(-0.0665593\pi\) | |||||||
\(168\) | 8.78596 | 0.0522974 | ||||||||
\(169\) | −409.250 | −2.42160 | ||||||||
\(170\) | −152.439 | − | 36.2880i | −0.896698 | − | 0.213459i | ||||
\(171\) | − | 52.8146i | − | 0.308858i | ||||||
\(172\) | −33.1350 | −0.192646 | ||||||||
\(173\) | 337.945i | 1.95344i | 0.214522 | + | 0.976719i | \(0.431181\pi\) | ||||
−0.214522 | + | 0.976719i | \(0.568819\pi\) | |||||||
\(174\) | −4.40167 | −0.0252970 | ||||||||
\(175\) | 40.0267 | + | 20.2015i | 0.228724 | + | 0.115437i | ||||
\(176\) | 1.52873i | 0.00868599i | ||||||||
\(177\) | 31.3411i | 0.177068i | ||||||||
\(178\) | 145.291 | 0.816243 | ||||||||
\(179\) | −135.350 | −0.756146 | −0.378073 | − | 0.925776i | \(-0.623413\pi\) | ||||
−0.378073 | + | 0.925776i | \(0.623413\pi\) | |||||||
\(180\) | 6.94737 | − | 29.1845i | 0.0385965 | − | 0.162136i | ||||
\(181\) | − | 275.222i | − | 1.52057i | −0.649592 | − | 0.760283i | \(-0.725060\pi\) | ||
0.649592 | − | 0.760283i | \(-0.274940\pi\) | |||||||
\(182\) | −60.9897 | −0.335108 | ||||||||
\(183\) | −57.4020 | −0.313672 | ||||||||
\(184\) | 64.9139 | − | 4.26487i | 0.352793 | − | 0.0231787i | ||||
\(185\) | 49.4548 | − | 207.750i | 0.267323 | − | 1.12297i | ||||
\(186\) | 98.8284 | 0.531335 | ||||||||
\(187\) | 8.46938i | 0.0452908i | ||||||||
\(188\) | − | 11.5009i | − | 0.0611750i | ||||||
\(189\) | 9.31892i | 0.0493065i | ||||||||
\(190\) | 28.8282 | − | 121.101i | 0.151727 | − | 0.637375i | ||||
\(191\) | 43.3590i | 0.227010i | 0.993537 | + | 0.113505i | \(0.0362079\pi\) | ||||
−0.993537 | + | 0.113505i | \(0.963792\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | − | 41.4539i | − | 0.214787i | −0.994217 | − | 0.107394i | \(-0.965749\pi\) | ||
0.994217 | − | 0.107394i | \(-0.0342505\pi\) | |||||||
\(194\) | 212.996i | 1.09792i | ||||||||
\(195\) | −48.2267 | + | 202.591i | −0.247316 | + | 1.03893i | ||||
\(196\) | 91.5672 | 0.467180 | ||||||||
\(197\) | − | 208.208i | − | 1.05689i | −0.848966 | − | 0.528447i | \(-0.822774\pi\) | ||
0.848966 | − | 0.528447i | \(-0.177226\pi\) | |||||||
\(198\) | −1.62147 | −0.00818923 | ||||||||
\(199\) | − | 270.493i | − | 1.35926i | −0.733554 | − | 0.679631i | \(-0.762140\pi\) | ||
0.733554 | − | 0.679631i | \(-0.237860\pi\) | |||||||
\(200\) | 31.8599 | − | 63.1264i | 0.159300 | − | 0.315632i | ||||
\(201\) | 202.364i | 1.00679i | ||||||||
\(202\) | 149.674i | 0.740959i | ||||||||
\(203\) | 3.22274 | 0.0158756 | ||||||||
\(204\) | − | 76.7662i | − | 0.376305i | ||||||
\(205\) | 1.46693 | − | 6.16226i | 0.00715574 | − | 0.0300598i | ||||
\(206\) | 155.695i | 0.755801i | ||||||||
\(207\) | 4.52358 | + | 68.8516i | 0.0218530 | + | 0.332616i | ||||
\(208\) | 96.1873i | 0.462439i | ||||||||
\(209\) | −6.72830 | −0.0321928 | ||||||||
\(210\) | −5.08661 | + | 21.3678i | −0.0242220 | + | 0.101752i | ||||
\(211\) | 20.2818 | 0.0961222 | 0.0480611 | − | 0.998844i | \(-0.484696\pi\) | ||||
0.0480611 | + | 0.998844i | \(0.484696\pi\) | |||||||
\(212\) | −162.959 | −0.768677 | ||||||||
\(213\) | 49.1063i | 0.230546i | ||||||||
\(214\) | − | 205.675i | − | 0.961098i | ||||||
\(215\) | 19.1834 | − | 80.5857i | 0.0892253 | − | 0.374817i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −72.3585 | −0.333449 | ||||||||
\(218\) | −153.930 | −0.706102 | ||||||||
\(219\) | −194.528 | −0.888254 | ||||||||
\(220\) | −3.71794 | − | 0.885057i | −0.0168997 | − | 0.00402299i | ||||
\(221\) | 532.890i | 2.41126i | ||||||||
\(222\) | 104.620 | 0.471262 | ||||||||
\(223\) | 195.211i | 0.875386i | 0.899124 | + | 0.437693i | \(0.144204\pi\) | ||||
−0.899124 | + | 0.437693i | \(0.855796\pi\) | |||||||
\(224\) | 10.1452i | 0.0452909i | ||||||||
\(225\) | 66.9557 | + | 33.7926i | 0.297581 | + | 0.150189i | ||||
\(226\) | 79.2660i | 0.350734i | ||||||||
\(227\) | 89.0856 | 0.392448 | 0.196224 | − | 0.980559i | \(-0.437132\pi\) | ||||
0.196224 | + | 0.980559i | \(0.437132\pi\) | |||||||
\(228\) | 60.9851 | 0.267479 | ||||||||
\(229\) | 240.109i | 1.04851i | 0.851561 | + | 0.524255i | \(0.175656\pi\) | ||||
−0.851561 | + | 0.524255i | \(0.824344\pi\) | |||||||
\(230\) | −27.2094 | + | 160.342i | −0.118302 | + | 0.697140i | ||||
\(231\) | 1.18718 | 0.00513931 | ||||||||
\(232\) | − | 5.08261i | − | 0.0219078i | ||||||
\(233\) | 366.956i | 1.57492i | 0.616367 | + | 0.787459i | \(0.288604\pi\) | ||||
−0.616367 | + | 0.787459i | \(0.711396\pi\) | |||||||
\(234\) | −102.022 | −0.435992 | ||||||||
\(235\) | 27.9706 | + | 6.65841i | 0.119024 | + | 0.0283337i | ||||
\(236\) | −36.1895 | −0.153346 | ||||||||
\(237\) | 107.520 | 0.453670 | ||||||||
\(238\) | 56.2054i | 0.236157i | ||||||||
\(239\) | 312.460 | 1.30737 | 0.653683 | − | 0.756769i | \(-0.273223\pi\) | ||||
0.653683 | + | 0.756769i | \(0.273223\pi\) | |||||||
\(240\) | 33.6993 | + | 8.02213i | 0.140414 | + | 0.0334255i | ||||
\(241\) | 187.089i | 0.776302i | 0.921596 | + | 0.388151i | \(0.126886\pi\) | ||||
−0.921596 | + | 0.388151i | \(0.873114\pi\) | |||||||
\(242\) | − | 170.913i | − | 0.706253i | ||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | − | 66.2822i | − | 0.271648i | ||||||
\(245\) | −53.0126 | + | 222.695i | −0.216378 | + | 0.908960i | ||||
\(246\) | 3.10324 | 0.0126148 | ||||||||
\(247\) | −423.342 | −1.71393 | ||||||||
\(248\) | 114.117i | 0.460150i | ||||||||
\(249\) | 256.585i | 1.03046i | ||||||||
\(250\) | 135.081 | + | 114.032i | 0.540323 | + | 0.456126i | ||||
\(251\) | − | 100.664i | − | 0.401051i | −0.979688 | − | 0.200525i | \(-0.935735\pi\) | ||
0.979688 | − | 0.200525i | \(-0.0642649\pi\) | |||||||
\(252\) | −10.7606 | −0.0427006 | ||||||||
\(253\) | 8.77131 | − | 0.576279i | 0.0346692 | − | 0.00227778i | ||||
\(254\) | 95.0468 | 0.374200 | ||||||||
\(255\) | 186.698 | + | 44.4436i | 0.732151 | + | 0.174289i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 43.1857i | 0.168038i | 0.996464 | + | 0.0840188i | \(0.0267756\pi\) | ||||
−0.996464 | + | 0.0840188i | \(0.973224\pi\) | |||||||
\(258\) | 40.5820 | 0.157294 | ||||||||
\(259\) | −76.5990 | −0.295749 | ||||||||
\(260\) | −233.931 | − | 55.6874i | −0.899736 | − | 0.214182i | ||||
\(261\) | 5.39092 | 0.0206549 | ||||||||
\(262\) | 204.621i | 0.780998i | ||||||||
\(263\) | −149.557 | −0.568657 | −0.284329 | − | 0.958727i | \(-0.591771\pi\) | ||||
−0.284329 | + | 0.958727i | \(0.591771\pi\) | |||||||
\(264\) | − | 1.87231i | − | 0.00709208i | ||||||
\(265\) | 94.3450 | − | 396.324i | 0.356019 | − | 1.49556i | ||||
\(266\) | −44.6511 | −0.167861 | ||||||||
\(267\) | −177.945 | −0.666459 | ||||||||
\(268\) | −233.670 | −0.871904 | ||||||||
\(269\) | 7.50830 | 0.0279119 | 0.0139560 | − | 0.999903i | \(-0.495558\pi\) | ||||
0.0139560 | + | 0.999903i | \(0.495558\pi\) | |||||||
\(270\) | −8.50875 | + | 35.7435i | −0.0315139 | + | 0.132384i | ||||
\(271\) | −333.946 | −1.23227 | −0.616136 | − | 0.787640i | \(-0.711303\pi\) | ||||
−0.616136 | + | 0.787640i | \(0.711303\pi\) | |||||||
\(272\) | 88.6420 | 0.325890 | ||||||||
\(273\) | 74.6968 | 0.273615 | ||||||||
\(274\) | 93.6538i | 0.341802i | ||||||||
\(275\) | 4.30499 | − | 8.52979i | 0.0156545 | − | 0.0310174i | ||||
\(276\) | −79.5029 | + | 5.22338i | −0.288054 | + | 0.0189253i | ||||
\(277\) | 17.8761i | 0.0645347i | 0.999479 | + | 0.0322674i | \(0.0102728\pi\) | ||||
−0.999479 | + | 0.0322674i | \(0.989727\pi\) | |||||||
\(278\) | − | 82.4070i | − | 0.296428i | ||||||
\(279\) | −121.040 | −0.433833 | ||||||||
\(280\) | −24.6734 | − | 5.87351i | −0.0881194 | − | 0.0209768i | ||||
\(281\) | − | 375.566i | − | 1.33654i | −0.743921 | − | 0.668268i | \(-0.767036\pi\) | ||
0.743921 | − | 0.668268i | \(-0.232964\pi\) | |||||||
\(282\) | 14.0857i | 0.0499492i | ||||||||
\(283\) | −401.091 | −1.41728 | −0.708642 | − | 0.705568i | \(-0.750692\pi\) | ||||
−0.708642 | + | 0.705568i | \(0.750692\pi\) | |||||||
\(284\) | −56.7031 | −0.199659 | ||||||||
\(285\) | −35.3072 | + | 148.318i | −0.123885 | + | 0.520415i | ||||
\(286\) | 12.9971i | 0.0454442i | ||||||||
\(287\) | −2.27208 | −0.00791664 | ||||||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | 202.087 | 0.699264 | ||||||||
\(290\) | 12.3611 | + | 2.94256i | 0.0426245 | + | 0.0101468i | ||||
\(291\) | − | 260.865i | − | 0.896444i | ||||||
\(292\) | − | 224.621i | − | 0.769250i | ||||||
\(293\) | −79.9606 | −0.272903 | −0.136452 | − | 0.990647i | \(-0.543570\pi\) | ||||
−0.136452 | + | 0.990647i | \(0.543570\pi\) | |||||||
\(294\) | −112.147 | −0.381451 | ||||||||
\(295\) | 20.9518 | − | 88.0144i | 0.0710232 | − | 0.298354i | ||||
\(296\) | 120.805i | 0.408125i | ||||||||
\(297\) | 1.98588 | 0.00668648 | ||||||||
\(298\) | 252.127 | 0.846065 | ||||||||
\(299\) | 551.887 | − | 36.2593i | 1.84578 | − | 0.121268i | ||||
\(300\) | −39.0203 | + | 77.3138i | −0.130068 | + | 0.257713i | ||||
\(301\) | −29.7126 | −0.0987131 | ||||||||
\(302\) | − | 306.762i | − | 1.01577i | ||||||
\(303\) | − | 183.312i | − | 0.604991i | ||||||
\(304\) | 70.4195i | 0.231643i | ||||||||
\(305\) | 161.201 | + | 38.3739i | 0.528527 | + | 0.125816i | ||||
\(306\) | 94.0190i | 0.307252i | ||||||||
\(307\) | 245.949i | 0.801137i | 0.916267 | + | 0.400568i | \(0.131187\pi\) | ||||
−0.916267 | + | 0.400568i | \(0.868813\pi\) | |||||||
\(308\) | 1.37084i | 0.00445077i | ||||||||
\(309\) | − | 190.687i | − | 0.617109i | ||||||
\(310\) | −277.538 | − | 66.0678i | −0.895282 | − | 0.213122i | ||||
\(311\) | −426.643 | −1.37184 | −0.685921 | − | 0.727676i | \(-0.740601\pi\) | ||||
−0.685921 | + | 0.727676i | \(0.740601\pi\) | |||||||
\(312\) | − | 117.805i | − | 0.377580i | ||||||
\(313\) | −330.486 | −1.05587 | −0.527933 | − | 0.849286i | \(-0.677033\pi\) | ||||
−0.527933 | + | 0.849286i | \(0.677033\pi\) | |||||||
\(314\) | 186.908i | 0.595250i | ||||||||
\(315\) | 6.22980 | − | 26.1701i | 0.0197771 | − | 0.0830798i | ||||
\(316\) | 124.153i | 0.392890i | ||||||||
\(317\) | 45.8757i | 0.144718i | 0.997379 | + | 0.0723591i | \(0.0230528\pi\) | ||||
−0.997379 | + | 0.0723591i | \(0.976947\pi\) | |||||||
\(318\) | 199.584 | 0.627622 | ||||||||
\(319\) | − | 0.686774i | − | 0.00215290i | ||||||
\(320\) | −9.26316 | + | 38.9126i | −0.0289474 | + | 0.121602i | ||||
\(321\) | 251.899i | 0.784733i | ||||||||
\(322\) | 58.2092 | − | 3.82437i | 0.180774 | − | 0.0118769i | ||||
\(323\) | 390.133i | 1.20784i | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 270.868 | − | 536.691i | 0.833440 | − | 1.65136i | ||||
\(326\) | −139.018 | −0.426435 | ||||||||
\(327\) | 188.525 | 0.576530 | ||||||||
\(328\) | 3.58331i | 0.0109247i | ||||||||
\(329\) | − | 10.3130i | − | 0.0313465i | ||||||
\(330\) | 4.55353 | + | 1.08397i | 0.0137986 | + | 0.00328475i | ||||
\(331\) | −528.078 | −1.59540 | −0.797701 | − | 0.603053i | \(-0.793951\pi\) | ||||
−0.797701 | + | 0.603053i | \(0.793951\pi\) | |||||||
\(332\) | −296.279 | −0.892407 | ||||||||
\(333\) | −128.133 | −0.384784 | ||||||||
\(334\) | −98.0507 | −0.293565 | ||||||||
\(335\) | 135.283 | − | 568.295i | 0.403829 | − | 1.69640i | ||||
\(336\) | − | 12.4252i | − | 0.0369798i | ||||||
\(337\) | 478.649 | 1.42032 | 0.710162 | − | 0.704039i | \(-0.248622\pi\) | ||||
0.710162 | + | 0.704039i | \(0.248622\pi\) | |||||||
\(338\) | 578.767i | 1.71233i | ||||||||
\(339\) | − | 97.0806i | − | 0.286373i | ||||||
\(340\) | −51.3190 | + | 215.581i | −0.150938 | + | 0.634061i | ||||
\(341\) | 15.4198i | 0.0452193i | ||||||||
\(342\) | −74.6912 | −0.218395 | ||||||||
\(343\) | 169.988 | 0.495590 | ||||||||
\(344\) | 46.8600i | 0.136221i | ||||||||
\(345\) | 33.3245 | − | 196.378i | 0.0965929 | − | 0.569213i | ||||
\(346\) | 477.926 | 1.38129 | ||||||||
\(347\) | − | 45.8278i | − | 0.132069i | −0.997817 | − | 0.0660344i | \(-0.978965\pi\) | ||
0.997817 | − | 0.0660344i | \(-0.0210347\pi\) | |||||||
\(348\) | 6.22490i | 0.0178877i | ||||||||
\(349\) | 38.0051 | 0.108897 | 0.0544486 | − | 0.998517i | \(-0.482660\pi\) | ||||
0.0544486 | + | 0.998517i | \(0.482660\pi\) | |||||||
\(350\) | 28.5692 | − | 56.6063i | 0.0816264 | − | 0.161732i | ||||
\(351\) | 124.951 | 0.355986 | ||||||||
\(352\) | 2.16196 | 0.00614192 | ||||||||
\(353\) | − | 332.010i | − | 0.940540i | −0.882523 | − | 0.470270i | \(-0.844157\pi\) | ||
0.882523 | − | 0.470270i | \(-0.155843\pi\) | |||||||
\(354\) | 44.3230 | 0.125206 | ||||||||
\(355\) | 32.8281 | − | 137.904i | 0.0924736 | − | 0.388463i | ||||
\(356\) | − | 205.473i | − | 0.577171i | ||||||
\(357\) | − | 68.8373i | − | 0.192822i | ||||||
\(358\) | 191.414i | 0.534676i | ||||||||
\(359\) | 384.549i | 1.07117i | 0.844482 | + | 0.535584i | \(0.179909\pi\) | ||||
−0.844482 | + | 0.535584i | \(0.820091\pi\) | |||||||
\(360\) | −41.2731 | − | 9.82506i | −0.114647 | − | 0.0272918i | ||||
\(361\) | 51.0681 | 0.141463 | ||||||||
\(362\) | −389.223 | −1.07520 | ||||||||
\(363\) | 209.325i | 0.576653i | ||||||||
\(364\) | 86.2525i | 0.236957i | ||||||||
\(365\) | 546.287 | + | 130.044i | 1.49668 | + | 0.356284i | ||||
\(366\) | 81.1787i | 0.221800i | ||||||||
\(367\) | 158.946 | 0.433096 | 0.216548 | − | 0.976272i | \(-0.430520\pi\) | ||||
0.216548 | + | 0.976272i | \(0.430520\pi\) | |||||||
\(368\) | −6.03144 | − | 91.8021i | −0.0163898 | − | 0.249462i | ||||
\(369\) | −3.80067 | −0.0102999 | ||||||||
\(370\) | −293.802 | − | 69.9397i | −0.794061 | − | 0.189026i | ||||
\(371\) | −146.128 | −0.393876 | ||||||||
\(372\) | − | 139.764i | − | 0.375711i | ||||||
\(373\) | 353.352 | 0.947324 | 0.473662 | − | 0.880707i | \(-0.342932\pi\) | ||||
0.473662 | + | 0.880707i | \(0.342932\pi\) | |||||||
\(374\) | 11.9775 | 0.0320254 | ||||||||
\(375\) | −165.439 | − | 139.660i | −0.441172 | − | 0.372425i | ||||
\(376\) | −16.2647 | −0.0432573 | ||||||||
\(377\) | − | 43.2115i | − | 0.114619i | ||||||
\(378\) | 13.1789 | 0.0348649 | ||||||||
\(379\) | − | 494.663i | − | 1.30518i | −0.757712 | − | 0.652589i | \(-0.773683\pi\) | ||
0.757712 | − | 0.652589i | \(-0.226317\pi\) | |||||||
\(380\) | −171.263 | − | 40.7692i | −0.450692 | − | 0.107287i | ||||
\(381\) | −116.408 | −0.305533 | ||||||||
\(382\) | 61.3189 | 0.160521 | ||||||||
\(383\) | 329.711 | 0.860864 | 0.430432 | − | 0.902623i | \(-0.358361\pi\) | ||||
0.430432 | + | 0.902623i | \(0.358361\pi\) | |||||||
\(384\) | −19.5959 | −0.0510310 | ||||||||
\(385\) | −3.33393 | − | 0.793642i | −0.00865956 | − | 0.00206141i | ||||
\(386\) | −58.6247 | −0.151878 | ||||||||
\(387\) | −49.7025 | −0.128430 | ||||||||
\(388\) | 301.221 | 0.776343 | ||||||||
\(389\) | − | 318.459i | − | 0.818660i | −0.912386 | − | 0.409330i | \(-0.865762\pi\) | ||
0.912386 | − | 0.409330i | \(-0.134238\pi\) | |||||||
\(390\) | 286.506 | + | 68.2028i | 0.734632 | + | 0.174879i | ||||
\(391\) | −33.4149 | − | 508.595i | −0.0854601 | − | 1.30075i | ||||
\(392\) | − | 129.496i | − | 0.330346i | ||||||
\(393\) | − | 250.609i | − | 0.637682i | ||||||
\(394\) | −294.451 | −0.747337 | ||||||||
\(395\) | −301.946 | − | 71.8782i | −0.764420 | − | 0.181970i | ||||
\(396\) | 2.29310i | 0.00579066i | ||||||||
\(397\) | 68.2935i | 0.172024i | 0.996294 | + | 0.0860119i | \(0.0274123\pi\) | ||||
−0.996294 | + | 0.0860119i | \(0.972588\pi\) | |||||||
\(398\) | −382.535 | −0.961143 | ||||||||
\(399\) | 54.6862 | 0.137058 | ||||||||
\(400\) | −89.2742 | − | 45.0567i | −0.223186 | − | 0.112642i | ||||
\(401\) | − | 486.040i | − | 1.21207i | −0.795438 | − | 0.606035i | \(-0.792759\pi\) | ||
0.795438 | − | 0.606035i | \(-0.207241\pi\) | |||||||
\(402\) | 286.186 | 0.711906 | ||||||||
\(403\) | 970.206i | 2.40746i | ||||||||
\(404\) | 211.671 | 0.523937 | ||||||||
\(405\) | 10.4211 | − | 43.7767i | 0.0257310 | − | 0.108091i | ||||
\(406\) | − | 4.55765i | − | 0.0112257i | ||||||
\(407\) | 16.3234i | 0.0401067i | ||||||||
\(408\) | −108.564 | −0.266088 | ||||||||
\(409\) | −124.021 | −0.303230 | −0.151615 | − | 0.988440i | \(-0.548447\pi\) | ||||
−0.151615 | + | 0.988440i | \(0.548447\pi\) | |||||||
\(410\) | −8.71475 | − | 2.07455i | −0.0212555 | − | 0.00505987i | ||||
\(411\) | − | 114.702i | − | 0.279080i | ||||||
\(412\) | 220.186 | 0.534432 | ||||||||
\(413\) | −32.4517 | −0.0785754 | ||||||||
\(414\) | 97.3708 | − | 6.39731i | 0.235195 | − | 0.0154524i | ||||
\(415\) | 171.530 | − | 720.563i | 0.413325 | − | 1.73630i | ||||
\(416\) | 136.029 | 0.326994 | ||||||||
\(417\) | 100.928i | 0.242033i | ||||||||
\(418\) | 9.51525i | 0.0227638i | ||||||||
\(419\) | − | 628.400i | − | 1.49976i | −0.661573 | − | 0.749881i | \(-0.730111\pi\) | ||
0.661573 | − | 0.749881i | \(-0.269889\pi\) | |||||||
\(420\) | 30.2187 | + | 7.19355i | 0.0719492 | + | 0.0171275i | ||||
\(421\) | − | 258.480i | − | 0.613966i | −0.951715 | − | 0.306983i | \(-0.900681\pi\) | ||
0.951715 | − | 0.306983i | \(-0.0993195\pi\) | |||||||
\(422\) | − | 28.6828i | − | 0.0679687i | ||||||
\(423\) | − | 17.2513i | − | 0.0407833i | ||||||
\(424\) | 230.460i | 0.543537i | ||||||||
\(425\) | −494.590 | − | 249.620i | −1.16374 | − | 0.587341i | ||||
\(426\) | 69.4468 | 0.163021 | ||||||||
\(427\) | − | 59.4361i | − | 0.139195i | ||||||
\(428\) | −290.868 | −0.679599 | ||||||||
\(429\) | − | 15.9181i | − | 0.0371051i | ||||||
\(430\) | −113.965 | − | 27.1295i | −0.265036 | − | 0.0630918i | ||||
\(431\) | − | 360.875i | − | 0.837298i | −0.908148 | − | 0.418649i | \(-0.862504\pi\) | ||
0.908148 | − | 0.418649i | \(-0.137496\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | 527.704 | 1.21872 | 0.609358 | − | 0.792896i | \(-0.291427\pi\) | ||||
0.609358 | + | 0.792896i | \(0.291427\pi\) | |||||||
\(434\) | 102.330i | 0.235784i | ||||||||
\(435\) | −15.1392 | − | 3.60389i | −0.0348028 | − | 0.00828481i | ||||
\(436\) | 217.690i | 0.499289i | ||||||||
\(437\) | 404.041 | − | 26.5457i | 0.924579 | − | 0.0607453i | ||||
\(438\) | 275.103i | 0.628090i | ||||||||
\(439\) | 678.504 | 1.54557 | 0.772784 | − | 0.634669i | \(-0.218864\pi\) | ||||
0.772784 | + | 0.634669i | \(0.218864\pi\) | |||||||
\(440\) | −1.25166 | + | 5.25797i | −0.00284468 | + | 0.0119499i | ||||
\(441\) | 137.351 | 0.311453 | ||||||||
\(442\) | 753.620 | 1.70502 | ||||||||
\(443\) | 296.200i | 0.668624i | 0.942462 | + | 0.334312i | \(0.108504\pi\) | ||||
−0.942462 | + | 0.334312i | \(0.891496\pi\) | |||||||
\(444\) | − | 147.955i | − | 0.333232i | ||||||
\(445\) | 499.718 | + | 118.958i | 1.12296 | + | 0.267321i | ||||
\(446\) | 276.070 | 0.618991 | ||||||||
\(447\) | −308.792 | −0.690810 | ||||||||
\(448\) | 14.3474 | 0.0320255 | ||||||||
\(449\) | 535.630 | 1.19294 | 0.596470 | − | 0.802635i | \(-0.296569\pi\) | ||||
0.596470 | + | 0.802635i | \(0.296569\pi\) | |||||||
\(450\) | 47.7899 | − | 94.6896i | 0.106200 | − | 0.210421i | ||||
\(451\) | 0.484185i | 0.00107358i | ||||||||
\(452\) | 112.099 | 0.248007 | ||||||||
\(453\) | 375.705i | 0.829371i | ||||||||
\(454\) | − | 125.986i | − | 0.277502i | ||||||
\(455\) | −209.770 | − | 49.9356i | −0.461032 | − | 0.109749i | ||||
\(456\) | − | 86.2460i | − | 0.189136i | ||||||
\(457\) | −198.709 | −0.434813 | −0.217406 | − | 0.976081i | \(-0.569760\pi\) | ||||
−0.217406 | + | 0.976081i | \(0.569760\pi\) | |||||||
\(458\) | 339.565 | 0.741409 | ||||||||
\(459\) | − | 115.149i | − | 0.250870i | ||||||
\(460\) | 226.758 | + | 38.4799i | 0.492953 | + | 0.0836519i | ||||
\(461\) | −677.481 | −1.46959 | −0.734795 | − | 0.678290i | \(-0.762722\pi\) | ||||
−0.734795 | + | 0.678290i | \(0.762722\pi\) | |||||||
\(462\) | − | 1.67893i | − | 0.00363404i | ||||||
\(463\) | 317.422i | 0.685576i | 0.939413 | + | 0.342788i | \(0.111371\pi\) | ||||
−0.939413 | + | 0.342788i | \(0.888629\pi\) | |||||||
\(464\) | −7.18790 | −0.0154912 | ||||||||
\(465\) | 339.913 | + | 80.9162i | 0.730995 | + | 0.174013i | ||||
\(466\) | 518.954 | 1.11364 | ||||||||
\(467\) | −231.177 | −0.495025 | −0.247512 | − | 0.968885i | \(-0.579613\pi\) | ||||
−0.247512 | + | 0.968885i | \(0.579613\pi\) | |||||||
\(468\) | 144.281i | 0.308293i | ||||||||
\(469\) | −209.535 | −0.446770 | ||||||||
\(470\) | 9.41642 | − | 39.5565i | 0.0200349 | − | 0.0841627i | ||||
\(471\) | − | 228.915i | − | 0.486019i | ||||||
\(472\) | 51.1797i | 0.108432i | ||||||||
\(473\) | 6.33183i | 0.0133865i | ||||||||
\(474\) | − | 152.056i | − | 0.320793i | ||||||
\(475\) | 198.305 | − | 392.916i | 0.417484 | − | 0.827191i | ||||
\(476\) | 79.4865 | 0.166988 | ||||||||
\(477\) | −244.439 | −0.512451 | ||||||||
\(478\) | − | 441.886i | − | 0.924447i | ||||||
\(479\) | − | 603.191i | − | 1.25927i | −0.776891 | − | 0.629636i | \(-0.783204\pi\) | ||
0.776891 | − | 0.629636i | \(-0.216796\pi\) | |||||||
\(480\) | 11.3450 | − | 47.6581i | 0.0236354 | − | 0.0992876i | ||||
\(481\) | 1027.06i | 2.13527i | ||||||||
\(482\) | 264.583 | 0.548928 | ||||||||
\(483\) | −71.2914 | + | 4.68388i | −0.147601 | + | 0.00969747i | ||||
\(484\) | −241.708 | −0.499396 | ||||||||
\(485\) | −174.391 | + | 732.582i | −0.359570 | + | 1.51048i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 432.259i | 0.887596i | 0.896127 | + | 0.443798i | \(0.146369\pi\) | ||||
−0.896127 | + | 0.443798i | \(0.853631\pi\) | |||||||
\(488\) | −93.7371 | −0.192084 | ||||||||
\(489\) | 170.261 | 0.348183 | ||||||||
\(490\) | 314.939 | + | 74.9712i | 0.642732 | + | 0.153002i | ||||
\(491\) | −457.843 | −0.932471 | −0.466235 | − | 0.884661i | \(-0.654390\pi\) | ||||
−0.466235 | + | 0.884661i | \(0.654390\pi\) | |||||||
\(492\) | − | 4.38864i | − | 0.00892000i | ||||||
\(493\) | −39.8218 | −0.0807745 | ||||||||
\(494\) | 598.695i | 1.21193i | ||||||||
\(495\) | −5.57692 | − | 1.32759i | −0.0112665 | − | 0.00268199i | ||||
\(496\) | 161.386 | 0.325375 | ||||||||
\(497\) | −50.8465 | −0.102307 | ||||||||
\(498\) | 362.866 | 0.728647 | ||||||||
\(499\) | 232.828 | 0.466589 | 0.233294 | − | 0.972406i | \(-0.425049\pi\) | ||||
0.233294 | + | 0.972406i | \(0.425049\pi\) | |||||||
\(500\) | 161.265 | − | 191.033i | 0.322530 | − | 0.382066i | ||||
\(501\) | 120.087 | 0.239695 | ||||||||
\(502\) | −142.360 | −0.283586 | ||||||||
\(503\) | 874.235 | 1.73804 | 0.869021 | − | 0.494775i | \(-0.164750\pi\) | ||||
0.869021 | + | 0.494775i | \(0.164750\pi\) | |||||||
\(504\) | 15.2177i | 0.0301939i | ||||||||
\(505\) | −122.546 | + | 514.792i | −0.242666 | + | 1.01939i | ||||
\(506\) | −0.814982 | − | 12.4045i | −0.00161064 | − | 0.0245148i | ||||
\(507\) | − | 708.842i | − | 1.39811i | ||||||
\(508\) | − | 134.417i | − | 0.264599i | ||||||
\(509\) | 670.805 | 1.31789 | 0.658944 | − | 0.752192i | \(-0.271003\pi\) | ||||
0.658944 | + | 0.752192i | \(0.271003\pi\) | |||||||
\(510\) | 62.8527 | − | 264.032i | 0.123241 | − | 0.517709i | ||||
\(511\) | − | 201.421i | − | 0.394170i | ||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 91.4776 | 0.178319 | ||||||||
\(514\) | 61.0738 | 0.118821 | ||||||||
\(515\) | −127.476 | + | 535.501i | −0.247526 | + | 1.03981i | ||||
\(516\) | − | 57.3916i | − | 0.111224i | ||||||
\(517\) | −2.19773 | −0.00425092 | ||||||||
\(518\) | 108.327i | 0.209126i | ||||||||
\(519\) | −585.338 | −1.12782 | ||||||||
\(520\) | −78.7539 | + | 330.829i | −0.151450 | + | 0.636210i | ||||
\(521\) | 251.816i | 0.483332i | 0.970359 | + | 0.241666i | \(0.0776939\pi\) | ||||
−0.970359 | + | 0.241666i | \(0.922306\pi\) | |||||||
\(522\) | − | 7.62392i | − | 0.0146052i | ||||||
\(523\) | −755.642 | −1.44482 | −0.722411 | − | 0.691464i | \(-0.756966\pi\) | ||||
−0.722411 | + | 0.691464i | \(0.756966\pi\) | |||||||
\(524\) | 289.378 | 0.552249 | ||||||||
\(525\) | −34.9900 | + | 69.3283i | −0.0666477 | + | 0.132054i | ||||
\(526\) | 211.505i | 0.402102i | ||||||||
\(527\) | 894.098 | 1.69658 | ||||||||
\(528\) | −2.64785 | −0.00501486 | ||||||||
\(529\) | −524.453 | + | 69.2123i | −0.991404 | + | 0.130836i | ||||
\(530\) | −560.487 | − | 133.424i | −1.05752 | − | 0.251743i | ||||
\(531\) | −54.2843 | −0.102230 | ||||||||
\(532\) | 63.1461i | 0.118696i | ||||||||
\(533\) | 30.4647i | 0.0571571i | ||||||||
\(534\) | 251.652i | 0.471258i | ||||||||
\(535\) | 168.398 | − | 707.404i | 0.314762 | − | 1.32225i | ||||
\(536\) | 330.460i | 0.616529i | ||||||||
\(537\) | − | 234.433i | − | 0.436561i | ||||||
\(538\) | − | 10.6183i | − | 0.0197367i | ||||||
\(539\) | − | 17.4977i | − | 0.0324634i | ||||||
\(540\) | 50.5490 | + | 12.0332i | 0.0936093 | + | 0.0222837i | ||||
\(541\) | −422.567 | −0.781085 | −0.390543 | − | 0.920585i | \(-0.627713\pi\) | ||||
−0.390543 | + | 0.920585i | \(0.627713\pi\) | |||||||
\(542\) | 472.270i | 0.871348i | ||||||||
\(543\) | 476.699 | 0.877899 | ||||||||
\(544\) | − | 125.359i | − | 0.230439i | ||||||
\(545\) | −529.431 | − | 126.031i | −0.971433 | − | 0.231250i | ||||
\(546\) | − | 105.637i | − | 0.193475i | ||||||
\(547\) | − | 962.341i | − | 1.75931i | −0.475615 | − | 0.879653i | \(-0.657774\pi\) | ||
0.475615 | − | 0.879653i | \(-0.342226\pi\) | |||||||
\(548\) | 132.447 | 0.241691 | ||||||||
\(549\) | − | 99.4232i | − | 0.181099i | ||||||
\(550\) | −12.0629 | − | 6.08817i | −0.0219326 | − | 0.0110694i | ||||
\(551\) | − | 31.6355i | − | 0.0574147i | ||||||
\(552\) | 7.38697 | + | 112.434i | 0.0133822 | + | 0.203685i | ||||
\(553\) | 111.330i | 0.201320i | ||||||||
\(554\) | 25.2807 | 0.0456329 | ||||||||
\(555\) | 359.833 | + | 85.6583i | 0.648348 | + | 0.154339i | ||||
\(556\) | −116.541 | −0.209606 | ||||||||
\(557\) | 157.867 | 0.283424 | 0.141712 | − | 0.989908i | \(-0.454739\pi\) | ||||
0.141712 | + | 0.989908i | \(0.454739\pi\) | |||||||
\(558\) | 171.176i | 0.306767i | ||||||||
\(559\) | 398.396i | 0.712695i | ||||||||
\(560\) | −8.30640 | + | 34.8935i | −0.0148329 | + | 0.0623098i | ||||
\(561\) | −14.6694 | −0.0261486 | ||||||||
\(562\) | −531.131 | −0.945073 | ||||||||
\(563\) | −417.217 | −0.741060 | −0.370530 | − | 0.928820i | \(-0.620824\pi\) | ||||
−0.370530 | + | 0.928820i | \(0.620824\pi\) | |||||||
\(564\) | 19.9201 | 0.0353194 | ||||||||
\(565\) | −64.8994 | + | 272.629i | −0.114866 | + | 0.482530i | ||||
\(566\) | 567.229i | 1.00217i | ||||||||
\(567\) | −16.1408 | −0.0284671 | ||||||||
\(568\) | 80.1903i | 0.141180i | ||||||||
\(569\) | 93.8235i | 0.164892i | 0.996596 | + | 0.0824460i | \(0.0262732\pi\) | ||||
−0.996596 | + | 0.0824460i | \(0.973727\pi\) | |||||||
\(570\) | 209.754 | + | 49.9319i | 0.367989 | + | 0.0875998i | ||||
\(571\) | − | 781.206i | − | 1.36814i | −0.729418 | − | 0.684068i | \(-0.760209\pi\) | ||
0.729418 | − | 0.684068i | \(-0.239791\pi\) | |||||||
\(572\) | 18.3806 | 0.0321339 | ||||||||
\(573\) | −75.1000 | −0.131065 | ||||||||
\(574\) | 3.21320i | 0.00559791i | ||||||||
\(575\) | −224.866 | + | 529.207i | −0.391071 | + | 0.920361i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 877.034i | 1.51999i | 0.649929 | + | 0.759995i | \(0.274799\pi\) | ||||
−0.649929 | + | 0.759995i | \(0.725201\pi\) | |||||||
\(578\) | − | 285.795i | − | 0.494454i | ||||||
\(579\) | 71.8003 | 0.124007 | ||||||||
\(580\) | 4.16141 | − | 17.4813i | 0.00717485 | − | 0.0301401i | ||||
\(581\) | −265.678 | −0.457276 | ||||||||
\(582\) | −368.919 | −0.633882 | ||||||||
\(583\) | 31.1402i | 0.0534138i | ||||||||
\(584\) | −317.662 | −0.543942 | ||||||||
\(585\) | −350.897 | − | 83.5311i | −0.599824 | − | 0.142788i | ||||
\(586\) | 113.081i | 0.192972i | ||||||||
\(587\) | − | 820.156i | − | 1.39720i | −0.715513 | − | 0.698600i | \(-0.753807\pi\) | ||
0.715513 | − | 0.698600i | \(-0.246193\pi\) | |||||||
\(588\) | 158.599i | 0.269726i | ||||||||
\(589\) | 710.296i | 1.20593i | ||||||||
\(590\) | −124.471 | − | 29.6304i | −0.210968 | − | 0.0502210i | ||||
\(591\) | 360.627 | 0.610198 | ||||||||
\(592\) | 170.844 | 0.288588 | ||||||||
\(593\) | − | 423.705i | − | 0.714510i | −0.934007 | − | 0.357255i | \(-0.883713\pi\) | ||
0.934007 | − | 0.357255i | \(-0.116287\pi\) | |||||||
\(594\) | − | 2.80846i | − | 0.00472805i | ||||||
\(595\) | −46.0185 | + | 193.314i | −0.0773420 | + | 0.324898i | ||||
\(596\) | − | 356.562i | − | 0.598259i | ||||||
\(597\) | 468.508 | 0.784770 | ||||||||
\(598\) | −51.2783 | − | 780.486i | −0.0857497 | − | 1.30516i | ||||
\(599\) | 874.974 | 1.46073 | 0.730363 | − | 0.683060i | \(-0.239351\pi\) | ||||
0.730363 | + | 0.683060i | \(0.239351\pi\) | |||||||
\(600\) | 109.338 | + | 55.1830i | 0.182230 | + | 0.0919717i | ||||
\(601\) | −644.991 | −1.07320 | −0.536598 | − | 0.843838i | \(-0.680291\pi\) | ||||
−0.536598 | + | 0.843838i | \(0.680291\pi\) | |||||||
\(602\) | 42.0200i | 0.0698007i | ||||||||
\(603\) | −350.505 | −0.581269 | ||||||||
\(604\) | −433.827 | −0.718257 | ||||||||
\(605\) | 139.936 | − | 587.843i | 0.231299 | − | 0.971642i | ||||
\(606\) | −259.243 | −0.427793 | ||||||||
\(607\) | 251.491i | 0.414318i | 0.978307 | + | 0.207159i | \(0.0664217\pi\) | ||||
−0.978307 | + | 0.207159i | \(0.933578\pi\) | |||||||
\(608\) | 99.5883 | 0.163796 | ||||||||
\(609\) | 5.58195i | 0.00916577i | ||||||||
\(610\) | 54.2689 | − | 227.972i | 0.0889653 | − | 0.373725i | ||||
\(611\) | −138.280 | −0.226318 | ||||||||
\(612\) | 132.963 | 0.217260 | ||||||||
\(613\) | 986.481 | 1.60927 | 0.804634 | − | 0.593771i | \(-0.202361\pi\) | ||||
0.804634 | + | 0.593771i | \(0.202361\pi\) | |||||||
\(614\) | 347.824 | 0.566489 | ||||||||
\(615\) | 10.6733 | + | 2.54079i | 0.0173550 | + | 0.00413137i | ||||
\(616\) | 1.93866 | 0.00314717 | ||||||||
\(617\) | −192.369 | −0.311782 | −0.155891 | − | 0.987774i | \(-0.549825\pi\) | ||||
−0.155891 | + | 0.987774i | \(0.549825\pi\) | |||||||
\(618\) | −269.672 | −0.436362 | ||||||||
\(619\) | 864.558i | 1.39670i | 0.715756 | + | 0.698351i | \(0.246082\pi\) | ||||
−0.715756 | + | 0.698351i | \(0.753918\pi\) | |||||||
\(620\) | −93.4340 | + | 392.497i | −0.150700 | + | 0.633060i | ||||
\(621\) | −119.254 | + | 7.83507i | −0.192036 | + | 0.0126169i | ||||
\(622\) | 603.364i | 0.970039i | ||||||||
\(623\) | − | 184.250i | − | 0.295747i | ||||||
\(624\) | −166.601 | −0.266989 | ||||||||
\(625\) | 371.236 | + | 502.801i | 0.593978 | + | 0.804481i | ||||
\(626\) | 467.377i | 0.746609i | ||||||||
\(627\) | − | 11.6538i | − | 0.0185865i | ||||||
\(628\) | 264.328 | 0.420905 | ||||||||
\(629\) | 946.496 | 1.50476 | ||||||||
\(630\) | −37.0101 | − | 8.81027i | −0.0587463 | − | 0.0139846i | ||||
\(631\) | 643.458i | 1.01974i | 0.860251 | + | 0.509871i | \(0.170307\pi\) | ||||
−0.860251 | + | 0.509871i | \(0.829693\pi\) | |||||||
\(632\) | 175.579 | 0.277815 | ||||||||
\(633\) | 35.1291i | 0.0554962i | ||||||||
\(634\) | 64.8780 | 0.102331 | ||||||||
\(635\) | 326.906 | + | 77.8201i | 0.514813 | + | 0.122551i | ||||
\(636\) | − | 282.254i | − | 0.443796i | ||||||
\(637\) | − | 1100.95i | − | 1.72834i | ||||||
\(638\) | −0.971245 | −0.00152233 | ||||||||
\(639\) | −85.0547 | −0.133106 | ||||||||
\(640\) | 55.0308 | + | 13.1001i | 0.0859856 | + | 0.0204689i | ||||
\(641\) | − | 716.907i | − | 1.11842i | −0.829026 | − | 0.559210i | \(-0.811105\pi\) | ||
0.829026 | − | 0.559210i | \(-0.188895\pi\) | |||||||
\(642\) | 356.240 | 0.554890 | ||||||||
\(643\) | −275.422 | −0.428339 | −0.214170 | − | 0.976796i | \(-0.568705\pi\) | ||||
−0.214170 | + | 0.976796i | \(0.568705\pi\) | |||||||
\(644\) | −5.40847 | − | 82.3202i | −0.00839825 | − | 0.127826i | ||||
\(645\) | 139.579 | + | 33.2267i | 0.216401 | + | 0.0515142i | ||||
\(646\) | 551.731 | 0.854073 | ||||||||
\(647\) | − | 593.326i | − | 0.917041i | −0.888684 | − | 0.458521i | \(-0.848380\pi\) | ||
0.888684 | − | 0.458521i | \(-0.151620\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | 6.91553i | 0.0106557i | ||||||||
\(650\) | −758.995 | − | 383.065i | −1.16768 | − | 0.589331i | ||||
\(651\) | − | 125.329i | − | 0.192517i | ||||||
\(652\) | 196.601i | 0.301535i | ||||||||
\(653\) | − | 376.904i | − | 0.577188i | −0.957452 | − | 0.288594i | \(-0.906812\pi\) | ||
0.957452 | − | 0.288594i | \(-0.0931877\pi\) | |||||||
\(654\) | − | 266.615i | − | 0.407668i | ||||||
\(655\) | −167.535 | + | 703.780i | −0.255778 | + | 1.07447i | ||||
\(656\) | 5.06756 | 0.00772494 | ||||||||
\(657\) | − | 336.932i | − | 0.512833i | ||||||
\(658\) | −14.5848 | −0.0221654 | ||||||||
\(659\) | − | 821.196i | − | 1.24612i | −0.782172 | − | 0.623062i | \(-0.785888\pi\) | ||
0.782172 | − | 0.623062i | \(-0.214112\pi\) | |||||||
\(660\) | 1.53296 | − | 6.43967i | 0.00232267 | − | 0.00975707i | ||||
\(661\) | 1108.77i | 1.67741i | 0.544587 | + | 0.838705i | \(0.316687\pi\) | ||||
−0.544587 | + | 0.838705i | \(0.683313\pi\) | |||||||
\(662\) | 746.816i | 1.12812i | ||||||||
\(663\) | −922.992 | −1.39214 | ||||||||
\(664\) | 419.002i | 0.631027i | ||||||||
\(665\) | −153.574 | − | 36.5583i | −0.230938 | − | 0.0549749i | ||||
\(666\) | 181.207i | 0.272083i | ||||||||
\(667\) | 2.70959 | + | 41.2415i | 0.00406235 | + | 0.0618313i | ||||
\(668\) | 138.665i | 0.207582i | ||||||||
\(669\) | −338.115 | −0.505404 | ||||||||
\(670\) | −803.691 | − | 191.319i | −1.19954 | − | 0.285550i | ||||
\(671\) | −12.6660 | −0.0188763 | ||||||||
\(672\) | −17.5719 | −0.0261487 | ||||||||
\(673\) | 45.4888i | 0.0675911i | 0.999429 | + | 0.0337955i | \(0.0107595\pi\) | ||||
−0.999429 | + | 0.0337955i | \(0.989240\pi\) | |||||||
\(674\) | − | 676.912i | − | 1.00432i | ||||||
\(675\) | −58.5304 | + | 115.971i | −0.0867117 | + | 0.171808i | ||||
\(676\) | 818.500 | 1.21080 | ||||||||
\(677\) | −206.922 | −0.305645 | −0.152822 | − | 0.988254i | \(-0.548836\pi\) | ||||
−0.152822 | + | 0.988254i | \(0.548836\pi\) | |||||||
\(678\) | −137.293 | −0.202497 | ||||||||
\(679\) | 270.109 | 0.397804 | ||||||||
\(680\) | 304.877 | + | 72.5761i | 0.448349 | + | 0.106730i | ||||
\(681\) | 154.301i | 0.226580i | ||||||||
\(682\) | 21.8069 | 0.0319749 | ||||||||
\(683\) | 437.345i | 0.640330i | 0.947362 | + | 0.320165i | \(0.103738\pi\) | ||||
−0.947362 | + | 0.320165i | \(0.896262\pi\) | |||||||
\(684\) | 105.629i | 0.154429i | ||||||||
\(685\) | −76.6796 | + | 322.115i | −0.111941 | + | 0.470241i | ||||
\(686\) | − | 240.399i | − | 0.350435i | ||||||
\(687\) | −415.881 | −0.605358 | ||||||||
\(688\) | 66.2701 | 0.0963228 | ||||||||
\(689\) | 1959.33i | 2.84373i | ||||||||
\(690\) | −277.721 | − | 47.1280i | −0.402494 | − | 0.0683015i | ||||
\(691\) | −552.016 | −0.798866 | −0.399433 | − | 0.916762i | \(-0.630793\pi\) | ||||
−0.399433 | + | 0.916762i | \(0.630793\pi\) | |||||||
\(692\) | − | 675.890i | − | 0.976719i | ||||||
\(693\) | 2.05626i | 0.00296718i | ||||||||
\(694\) | −64.8104 | −0.0933867 | ||||||||
\(695\) | 67.4712 | − | 283.433i | 0.0970809 | − | 0.407817i | ||||
\(696\) | 8.80334 | 0.0126485 | ||||||||
\(697\) | 28.0749 | 0.0402797 | ||||||||
\(698\) | − | 53.7474i | − | 0.0770020i | ||||||
\(699\) | −635.587 | −0.909280 | ||||||||
\(700\) | −80.0534 | − | 40.4030i | −0.114362 | − | 0.0577186i | ||||
\(701\) | 645.651i | 0.921042i | 0.887649 | + | 0.460521i | \(0.152337\pi\) | ||||
−0.887649 | + | 0.460521i | \(0.847663\pi\) | |||||||
\(702\) | − | 176.707i | − | 0.251720i | ||||||
\(703\) | 751.922i | 1.06959i | ||||||||
\(704\) | − | 3.05747i | − | 0.00434300i | ||||||
\(705\) | −11.5327 | + | 48.4466i | −0.0163585 | + | 0.0687186i | ||||
\(706\) | −469.534 | −0.665062 | ||||||||
\(707\) | 189.808 | 0.268470 | ||||||||
\(708\) | − | 62.6821i | − | 0.0885341i | ||||||
\(709\) | − | 552.330i | − | 0.779027i | −0.921021 | − | 0.389513i | \(-0.872643\pi\) | ||
0.921021 | − | 0.389513i | \(-0.127357\pi\) | |||||||
\(710\) | −195.026 | − | 46.4260i | −0.274685 | − | 0.0653887i | ||||
\(711\) | 186.230i | 0.261927i | ||||||||
\(712\) | −290.582 | −0.408121 | ||||||||
\(713\) | −60.8369 | − | 925.973i | −0.0853252 | − | 1.29870i | ||||
\(714\) | −97.3506 | −0.136345 | ||||||||
\(715\) | −10.6414 | + | 44.7024i | −0.0148831 | + | 0.0625208i | ||||
\(716\) | 270.700 | 0.378073 | ||||||||
\(717\) | 541.197i | 0.754808i | ||||||||
\(718\) | 543.835 | 0.757430 | ||||||||
\(719\) | 882.221 | 1.22701 | 0.613505 | − | 0.789691i | \(-0.289759\pi\) | ||||
0.613505 | + | 0.789691i | \(0.289759\pi\) | |||||||
\(720\) | −13.8947 | + | 58.3690i | −0.0192982 | + | 0.0810680i | ||||
\(721\) | 197.444 | 0.273847 | ||||||||
\(722\) | − | 72.2213i | − | 0.100029i | ||||||
\(723\) | −324.047 | −0.448198 | ||||||||
\(724\) | 550.445i | 0.760283i | ||||||||
\(725\) | 40.1059 | + | 20.2415i | 0.0553185 | + | 0.0279192i | ||||
\(726\) | 296.030 | 0.407755 | ||||||||
\(727\) | −574.892 | −0.790773 | −0.395387 | − | 0.918515i | \(-0.629389\pi\) | ||||
−0.395387 | + | 0.918515i | \(0.629389\pi\) | |||||||
\(728\) | 121.979 | 0.167554 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 183.910 | − | 772.567i | 0.251931 | − | 1.05831i | ||||
\(731\) | 367.144 | 0.502249 | ||||||||
\(732\) | 114.804 | 0.156836 | ||||||||
\(733\) | −563.848 | −0.769233 | −0.384617 | − | 0.923076i | \(-0.625666\pi\) | ||||
−0.384617 | + | 0.923076i | \(0.625666\pi\) | |||||||
\(734\) | − | 224.784i | − | 0.306245i | ||||||
\(735\) | −385.719 | − | 91.8205i | −0.524788 | − | 0.124926i | ||||
\(736\) | −129.828 | + | 8.52974i | −0.176396 | + | 0.0115893i | ||||
\(737\) | 44.6525i | 0.0605868i | ||||||||
\(738\) | 5.37496i | 0.00728315i | ||||||||
\(739\) | 1029.01 | 1.39244 | 0.696218 | − | 0.717831i | \(-0.254865\pi\) | ||||
0.696218 | + | 0.717831i | \(0.254865\pi\) | |||||||
\(740\) | −98.9096 | + | 415.499i | −0.133662 | + | 0.561486i | ||||
\(741\) | − | 733.249i | − | 0.989540i | ||||||
\(742\) | 206.656i | 0.278512i | ||||||||
\(743\) | 71.4526 | 0.0961678 | 0.0480839 | − | 0.998843i | \(-0.484689\pi\) | ||||
0.0480839 | + | 0.998843i | \(0.484689\pi\) | |||||||
\(744\) | −197.657 | −0.265668 | ||||||||
\(745\) | 867.173 | + | 206.431i | 1.16399 | + | 0.277088i | ||||
\(746\) | − | 499.715i | − | 0.669860i | ||||||
\(747\) | −444.419 | −0.594938 | ||||||||
\(748\) | − | 16.9388i | − | 0.0226454i | ||||||
\(749\) | −260.826 | −0.348232 | ||||||||
\(750\) | −197.508 | + | 233.967i | −0.263344 | + | 0.311956i | ||||
\(751\) | − | 579.354i | − | 0.771444i | −0.922615 | − | 0.385722i | \(-0.873952\pi\) | ||
0.922615 | − | 0.385722i | \(-0.126048\pi\) | |||||||
\(752\) | 23.0018i | 0.0305875i | ||||||||
\(753\) | 174.355 | 0.231547 | ||||||||
\(754\) | −61.1103 | −0.0810482 | ||||||||
\(755\) | 251.163 | − | 1055.08i | 0.332666 | − | 1.39746i | ||||
\(756\) | − | 18.6378i | − | 0.0246532i | ||||||
\(757\) | 1033.03 | 1.36464 | 0.682321 | − | 0.731052i | \(-0.260970\pi\) | ||||
0.682321 | + | 0.731052i | \(0.260970\pi\) | |||||||
\(758\) | −699.559 | −0.922900 | ||||||||
\(759\) | 0.998145 | + | 15.1924i | 0.00131508 | + | 0.0200163i | ||||
\(760\) | −57.6564 | + | 242.203i | −0.0758636 | + | 0.318688i | ||||
\(761\) | −714.171 | −0.938463 | −0.469232 | − | 0.883075i | \(-0.655469\pi\) | ||||
−0.469232 | + | 0.883075i | \(0.655469\pi\) | |||||||
\(762\) | 164.626i | 0.216045i | ||||||||
\(763\) | 195.206i | 0.255840i | ||||||||
\(764\) | − | 86.7180i | − | 0.113505i | ||||||
\(765\) | −76.9785 | + | 323.371i | −0.100626 | + | 0.422708i | ||||
\(766\) | − | 466.282i | − | 0.608723i | ||||||
\(767\) | 435.122i | 0.567304i | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | − | 129.899i | − | 0.168919i | −0.996427 | − | 0.0844595i | \(-0.973084\pi\) | ||
0.996427 | − | 0.0844595i | \(-0.0269164\pi\) | |||||||
\(770\) | −1.12238 | + | 4.71489i | −0.00145764 | + | 0.00612323i | ||||
\(771\) | −74.7998 | −0.0970166 | ||||||||
\(772\) | 82.9079i | 0.107394i | ||||||||
\(773\) | 946.778 | 1.22481 | 0.612405 | − | 0.790544i | \(-0.290202\pi\) | ||||
0.612405 | + | 0.790544i | \(0.290202\pi\) | |||||||
\(774\) | 70.2900i | 0.0908140i | ||||||||
\(775\) | −900.476 | − | 454.471i | −1.16190 | − | 0.586414i | ||||
\(776\) | − | 425.991i | − | 0.548958i | ||||||
\(777\) | − | 132.673i | − | 0.170751i | ||||||
\(778\) | −450.369 | −0.578880 | ||||||||
\(779\) | 22.3035i | 0.0286309i | ||||||||
\(780\) | 96.4534 | − | 405.181i | 0.123658 | − | 0.519463i | ||||
\(781\) | 10.8355i | 0.0138739i | ||||||||
\(782\) | −719.262 | + | 47.2558i | −0.919772 | + | 0.0604294i | ||||
\(783\) | 9.33735i | 0.0119251i | ||||||||
\(784\) | −183.134 | −0.233590 | ||||||||
\(785\) | −153.032 | + | 642.857i | −0.194945 | + | 0.818926i | ||||
\(786\) | −354.415 | −0.450909 | ||||||||
\(787\) | −1533.79 | −1.94890 | −0.974450 | − | 0.224603i | \(-0.927892\pi\) | ||||
−0.974450 | + | 0.224603i | \(0.927892\pi\) | |||||||
\(788\) | 416.417i | 0.528447i | ||||||||
\(789\) | − | 259.040i | − | 0.328315i | ||||||
\(790\) | −101.651 | + | 427.016i | −0.128672 | + | 0.540526i | ||||
\(791\) | 100.521 | 0.127081 | ||||||||
\(792\) | 3.24294 | 0.00409462 | ||||||||
\(793\) | −796.938 | −1.00497 | ||||||||
\(794\) | 96.5815 | 0.121639 | ||||||||
\(795\) | 686.453 | + | 163.410i | 0.863463 | + | 0.205548i | ||||
\(796\) | 540.986i | 0.679631i | ||||||||
\(797\) | 197.370 | 0.247641 | 0.123820 | − | 0.992305i | \(-0.460485\pi\) | ||||
0.123820 | + | 0.992305i | \(0.460485\pi\) | |||||||
\(798\) | − | 77.3379i | − | 0.0969147i | ||||||
\(799\) | 127.433i | 0.159490i | ||||||||
\(800\) | −63.7199 | + | 126.253i | −0.0796498 | + | 0.157816i | ||||
\(801\) | − | 308.209i | − | 0.384781i | ||||||
\(802\) | −687.364 | −0.857062 | ||||||||
\(803\) | −42.9232 | −0.0534536 | ||||||||
\(804\) | − | 404.729i | − | 0.503394i | ||||||
\(805\) | 203.337 | + | 34.5054i | 0.252593 | + | 0.0428639i | ||||
\(806\) | 1372.08 | 1.70233 | ||||||||
\(807\) | 13.0048i | 0.0161149i | ||||||||
\(808\) | − | 299.347i | − | 0.370480i | ||||||
\(809\) | −86.0327 | −0.106345 | −0.0531723 | − | 0.998585i | \(-0.516933\pi\) | ||||
−0.0531723 | + | 0.998585i | \(0.516933\pi\) | |||||||
\(810\) | −61.9096 | − | 14.7376i | −0.0764317 | − | 0.0181946i | ||||
\(811\) | 104.317 | 0.128628 | 0.0643138 | − | 0.997930i | \(-0.479514\pi\) | ||||
0.0643138 | + | 0.997930i | \(0.479514\pi\) | |||||||
\(812\) | −6.44549 | −0.00793779 | ||||||||
\(813\) | − | 578.411i | − | 0.711452i | ||||||
\(814\) | 23.0848 | 0.0283597 | ||||||||
\(815\) | −478.141 | − | 113.822i | −0.586677 | − | 0.139658i | ||||
\(816\) | 153.532i | 0.188152i | ||||||||
\(817\) | 291.669i | 0.357000i | ||||||||
\(818\) | 175.392i | 0.214416i | ||||||||
\(819\) | 129.379i | 0.157972i | ||||||||
\(820\) | −2.93385 | + | 12.3245i | −0.00357787 | + | 0.0150299i | ||||
\(821\) | 971.740 | 1.18361 | 0.591803 | − | 0.806083i | \(-0.298416\pi\) | ||||
0.591803 | + | 0.806083i | \(0.298416\pi\) | |||||||
\(822\) | −162.213 | −0.197340 | ||||||||
\(823\) | − | 867.841i | − | 1.05448i | −0.849715 | − | 0.527242i | \(-0.823226\pi\) | ||
0.849715 | − | 0.527242i | \(-0.176774\pi\) | |||||||
\(824\) | − | 311.390i | − | 0.377900i | ||||||
\(825\) | 14.7740 | + | 7.45646i | 0.0179079 | + | 0.00903813i | ||||
\(826\) | 45.8936i | 0.0555612i | ||||||||
\(827\) | −778.152 | −0.940933 | −0.470467 | − | 0.882418i | \(-0.655914\pi\) | ||||
−0.470467 | + | 0.882418i | \(0.655914\pi\) | |||||||
\(828\) | −9.04716 | − | 137.703i | −0.0109265 | − | 0.166308i | ||||
\(829\) | −1589.70 | −1.91761 | −0.958805 | − | 0.284067i | \(-0.908316\pi\) | ||||
−0.958805 | + | 0.284067i | \(0.908316\pi\) | |||||||
\(830\) | −1019.03 | − | 242.580i | −1.22775 | − | 0.292265i | ||||
\(831\) | −30.9624 | −0.0372591 | ||||||||
\(832\) | − | 192.375i | − | 0.231220i | ||||||
\(833\) | −1014.59 | −1.21799 | ||||||||
\(834\) | 142.733 | 0.171143 | ||||||||
\(835\) | −337.238 | − | 80.2795i | −0.403878 | − | 0.0961431i | ||||
\(836\) | 13.4566 | 0.0160964 | ||||||||
\(837\) | − | 209.647i | − | 0.250474i | ||||||
\(838\) | −888.692 | −1.06049 | ||||||||
\(839\) | − | 678.335i | − | 0.808504i | −0.914648 | − | 0.404252i | \(-0.867532\pi\) | ||
0.914648 | − | 0.404252i | \(-0.132468\pi\) | |||||||
\(840\) | 10.1732 | − | 42.7356i | 0.0121110 | − | 0.0508758i | ||||
\(841\) | −837.771 | −0.996160 | ||||||||
\(842\) | −365.545 | −0.434139 | ||||||||
\(843\) | 650.500 | 0.771649 | ||||||||
\(844\) | −40.5636 | −0.0480611 | ||||||||
\(845\) | −473.868 | + | 1990.63i | −0.560791 | + | 2.35577i | ||||
\(846\) | −24.3971 | −0.0288382 | ||||||||
\(847\) | −216.743 | −0.255895 | ||||||||
\(848\) | 325.919 | 0.384338 | ||||||||
\(849\) | − | 694.711i | − | 0.818269i | ||||||
\(850\) | −353.016 | + | 699.456i | −0.415313 | + | 0.822890i | ||||
\(851\) | −64.4022 | − | 980.239i | −0.0756782 | − | 1.15187i | ||||
\(852\) | − | 98.2127i | − | 0.115273i | ||||||
\(853\) | − | 882.085i | − | 1.03410i | −0.855956 | − | 0.517049i | \(-0.827031\pi\) | ||
0.855956 | − | 0.517049i | \(-0.172969\pi\) | |||||||
\(854\) | −84.0554 | −0.0984255 | ||||||||
\(855\) | −256.895 | − | 61.1538i | −0.300462 | − | 0.0715249i | ||||
\(856\) | 411.350i | 0.480549i | ||||||||
\(857\) | 551.436i | 0.643450i | 0.946833 | + | 0.321725i | \(0.104263\pi\) | ||||
−0.946833 | + | 0.321725i | \(0.895737\pi\) | |||||||
\(858\) | −22.5116 | −0.0262372 | ||||||||
\(859\) | 282.824 | 0.329248 | 0.164624 | − | 0.986356i | \(-0.447359\pi\) | ||||
0.164624 | + | 0.986356i | \(0.447359\pi\) | |||||||
\(860\) | −38.3669 | + | 161.171i | −0.0446126 | + | 0.187409i | ||||
\(861\) | − | 3.93535i | − | 0.00457068i | ||||||
\(862\) | −510.355 | −0.592059 | ||||||||
\(863\) | 127.380i | 0.147602i | 0.997273 | + | 0.0738009i | \(0.0235129\pi\) | ||||
−0.997273 | + | 0.0738009i | \(0.976487\pi\) | |||||||
\(864\) | −29.3939 | −0.0340207 | ||||||||
\(865\) | 1643.79 | + | 391.305i | 1.90034 | + | 0.452375i | ||||
\(866\) | − | 746.286i | − | 0.861762i | ||||||
\(867\) | 350.026i | 0.403720i | ||||||||
\(868\) | 144.717 | 0.166725 | ||||||||
\(869\) | 23.7247 | 0.0273011 | ||||||||
\(870\) | −5.09667 | + | 21.4101i | −0.00585824 | + | 0.0246093i | ||||
\(871\) | 2809.51i | 3.22562i | ||||||||
\(872\) | 307.860 | 0.353051 | ||||||||
\(873\) | 451.832 | 0.517562 | ||||||||
\(874\) | −37.5413 | − | 571.401i | −0.0429534 | − | 0.653776i | ||||
\(875\) | 144.608 | − | 171.302i | 0.165267 | − | 0.195774i | ||||
\(876\) | 389.055 | 0.444127 | ||||||||
\(877\) | 795.079i | 0.906589i | 0.891361 | + | 0.453295i | \(0.149751\pi\) | ||||
−0.891361 | + | 0.453295i | \(0.850249\pi\) | |||||||
\(878\) | − | 959.550i | − | 1.09288i | ||||||
\(879\) | − | 138.496i | − | 0.157561i | ||||||
\(880\) | 7.43589 | + | 1.77011i | 0.00844987 | + | 0.00201149i | ||||
\(881\) | − | 291.283i | − | 0.330628i | −0.986241 | − | 0.165314i | \(-0.947136\pi\) | ||
0.986241 | − | 0.165314i | \(-0.0528638\pi\) | |||||||
\(882\) | − | 194.243i | − | 0.220231i | ||||||
\(883\) | − | 1565.87i | − | 1.77335i | −0.462396 | − | 0.886674i | \(-0.653010\pi\) | ||
0.462396 | − | 0.886674i | \(-0.346990\pi\) | |||||||
\(884\) | − | 1065.78i | − | 1.20563i | ||||||
\(885\) | 152.445 | + | 36.2897i | 0.172255 | + | 0.0410053i | ||||
\(886\) | 418.891 | 0.472788 | ||||||||
\(887\) | 452.662i | 0.510329i | 0.966898 | + | 0.255165i | \(0.0821297\pi\) | ||||
−0.966898 | + | 0.255165i | \(0.917870\pi\) | |||||||
\(888\) | −209.240 | −0.235631 | ||||||||
\(889\) | − | 120.533i | − | 0.135583i | ||||||
\(890\) | 168.232 | − | 706.708i | 0.189025 | − | 0.794054i | ||||
\(891\) | 3.43965i | 0.00386044i | ||||||||
\(892\) | − | 390.422i | − | 0.437693i | ||||||
\(893\) | −101.236 | −0.113366 | ||||||||
\(894\) | 436.698i | 0.488476i | ||||||||
\(895\) | −156.721 | + | 658.354i | −0.175107 | + | 0.735591i | ||||
\(896\) | − | 20.2903i | − | 0.0226454i | ||||||
\(897\) | 62.8029 | + | 955.897i | 0.0700143 | + | 1.06566i | ||||
\(898\) | − | 757.495i | − | 0.843536i | ||||||
\(899\) | −72.5017 | −0.0806470 | ||||||||
\(900\) | −133.911 | − | 67.5851i | −0.148790 | − | 0.0750946i | ||||
\(901\) | 1805.63 | 2.00403 | ||||||||
\(902\) | 0.684741 | 0.000759136 | ||||||||
\(903\) | − | 51.4638i | − | 0.0569920i | ||||||
\(904\) | − | 158.532i | − | 0.175367i | ||||||
\(905\) | −1338.70 | − | 318.679i | −1.47923 | − | 0.352131i | ||||
\(906\) | 531.327 | 0.586454 | ||||||||
\(907\) | 656.602 | 0.723927 | 0.361964 | − | 0.932192i | \(-0.382106\pi\) | ||||
0.361964 | + | 0.932192i | \(0.382106\pi\) | |||||||
\(908\) | −178.171 | −0.196224 | ||||||||
\(909\) | 317.506 | 0.349291 | ||||||||
\(910\) | −70.6197 | + | 296.659i | −0.0776040 | + | 0.325999i | ||||
\(911\) | 176.046i | 0.193245i | 0.995321 | + | 0.0966224i | \(0.0308039\pi\) | ||||
−0.995321 | + | 0.0966224i | \(0.969196\pi\) | |||||||
\(912\) | −121.970 | −0.133739 | ||||||||
\(913\) | 56.6165i | 0.0620115i | ||||||||
\(914\) | 281.017i | 0.307459i | ||||||||
\(915\) | −66.4655 | + | 279.208i | −0.0726399 | + | 0.305145i | ||||
\(916\) | − | 480.218i | − | 0.524255i | ||||||
\(917\) | 259.490 | 0.282977 | ||||||||
\(918\) | −162.846 | −0.177392 | ||||||||
\(919\) | 481.329i | 0.523753i | 0.965101 | + | 0.261877i | \(0.0843414\pi\) | ||||
−0.965101 | + | 0.261877i | \(0.915659\pi\) | |||||||
\(920\) | 54.4187 | − | 320.685i | 0.0591508 | − | 0.348570i | ||||
\(921\) | −425.996 | −0.462536 | ||||||||
\(922\) | 958.102i | 1.03916i | ||||||||
\(923\) | 681.765i | 0.738640i | ||||||||
\(924\) | −2.37436 | −0.00256965 | ||||||||
\(925\) | −953.248 | − | 481.104i | −1.03054 | − | 0.520113i | ||||
\(926\) | 448.902 | 0.484775 | ||||||||
\(927\) | 330.279 | 0.356288 | ||||||||
\(928\) | 10.1652i | 0.0109539i | ||||||||
\(929\) | 409.397 | 0.440686 | 0.220343 | − | 0.975422i | \(-0.429282\pi\) | ||||
0.220343 | + | 0.975422i | \(0.429282\pi\) | |||||||
\(930\) | 114.433 | − | 480.709i | 0.123046 | − | 0.516892i | ||||
\(931\) | − | 806.015i | − | 0.865752i | ||||||
\(932\) | − | 733.912i | − | 0.787459i | ||||||
\(933\) | − | 738.967i | − | 0.792034i | ||||||
\(934\) | 326.933i | 0.350035i | ||||||||
\(935\) | 41.1957 | + | 9.80665i | 0.0440596 | + | 0.0104884i | ||||
\(936\) | 204.044 | 0.217996 | ||||||||
\(937\) | 89.4309 | 0.0954439 | 0.0477219 | − | 0.998861i | \(-0.484804\pi\) | ||||
0.0477219 | + | 0.998861i | \(0.484804\pi\) | |||||||
\(938\) | 296.328i | 0.315914i | ||||||||
\(939\) | − | 572.418i | − | 0.609604i | ||||||
\(940\) | −55.9413 | − | 13.3168i | −0.0595120 | − | 0.0141668i | ||||
\(941\) | 667.808i | 0.709679i | 0.934927 | + | 0.354840i | \(0.115465\pi\) | ||||
−0.934927 | + | 0.354840i | \(0.884535\pi\) | |||||||
\(942\) | −323.735 | −0.343668 | ||||||||
\(943\) | −1.91029 | − | 29.0758i | −0.00202576 | − | 0.0308333i | ||||
\(944\) | 72.3791 | 0.0766728 | ||||||||
\(945\) | 45.3280 | + | 10.7903i | 0.0479661 | + | 0.0114183i | ||||
\(946\) | 8.95456 | 0.00946571 | ||||||||
\(947\) | − | 1474.86i | − | 1.55740i | −0.627396 | − | 0.778701i | \(-0.715879\pi\) | ||
0.627396 | − | 0.778701i | \(-0.284121\pi\) | |||||||
\(948\) | −215.040 | −0.226835 | ||||||||
\(949\) | −2700.71 | −2.84585 | ||||||||
\(950\) | −555.667 | − | 280.445i | −0.584912 | − | 0.295205i | ||||
\(951\) | −79.4590 | −0.0835531 | ||||||||
\(952\) | − | 112.411i | − | 0.118079i | ||||||
\(953\) | −1738.41 | −1.82415 | −0.912073 | − | 0.410029i | \(-0.865519\pi\) | ||||
−0.912073 | + | 0.410029i | \(0.865519\pi\) | |||||||
\(954\) | 345.689i | 0.362358i | ||||||||
\(955\) | 210.902 | + | 50.2052i | 0.220839 | + | 0.0525708i | ||||
\(956\) | −624.921 | −0.653683 | ||||||||
\(957\) | 1.18953 | 0.00124298 | ||||||||
\(958\) | −853.041 | −0.890439 | ||||||||
\(959\) | 118.767 | 0.123844 | ||||||||
\(960\) | −67.3987 | − | 16.0443i | −0.0702070 | − | 0.0167128i | ||||
\(961\) | 666.841 | 0.693903 | ||||||||
\(962\) | 1452.49 | 1.50986 | ||||||||
\(963\) | −436.303 | −0.453066 | ||||||||
\(964\) | − | 374.177i | − | 0.388151i | ||||||
\(965\) | −201.635 | − | 47.9993i | −0.208949 | − | 0.0497402i | ||||
\(966\) | 6.62400 | + | 100.821i | 0.00685714 | + | 0.104370i | ||||
\(967\) | 745.833i | 0.771285i | 0.922648 | + | 0.385643i | \(0.126020\pi\) | ||||
−0.922648 | + | 0.385643i | \(0.873980\pi\) | |||||||
\(968\) | 341.827i | 0.353127i | ||||||||
\(969\) | −675.730 | −0.697348 | ||||||||
\(970\) | 1036.03 | + | 246.626i | 1.06807 | + | 0.254254i | ||||
\(971\) | 715.785i | 0.737162i | 0.929596 | + | 0.368581i | \(0.120156\pi\) | ||||
−0.929596 | + | 0.368581i | \(0.879844\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −104.504 | −0.107404 | ||||||||
\(974\) | 611.307 | 0.627625 | ||||||||
\(975\) | 929.575 | + | 469.157i | 0.953411 | + | 0.481187i | ||||
\(976\) | 132.564i | 0.135824i | ||||||||
\(977\) | −1471.89 | −1.50654 | −0.753268 | − | 0.657713i | \(-0.771524\pi\) | ||||
−0.753268 | + | 0.657713i | \(0.771524\pi\) | |||||||
\(978\) | − | 240.786i | − | 0.246202i | ||||||
\(979\) | −39.2642 | −0.0401064 | ||||||||
\(980\) | 106.025 | − | 445.390i | 0.108189 | − | 0.454480i | ||||
\(981\) | 326.535i | 0.332859i | ||||||||
\(982\) | 647.488i | 0.659356i | ||||||||
\(983\) | 1276.85 | 1.29894 | 0.649468 | − | 0.760389i | \(-0.274992\pi\) | ||||
0.649468 | + | 0.760389i | \(0.274992\pi\) | |||||||
\(984\) | −6.20647 | −0.00630739 | ||||||||
\(985\) | −1012.74 | − | 241.083i | −1.02816 | − | 0.244755i | ||||
\(986\) | 56.3166i | 0.0571162i | ||||||||
\(987\) | 17.8627 | 0.0180979 | ||||||||
\(988\) | 846.683 | 0.856967 | ||||||||
\(989\) | −24.9815 | − | 380.233i | −0.0252593 | − | 0.384462i | ||||
\(990\) | −1.87749 | + | 7.88695i | −0.00189645 | + | 0.00796662i | ||||
\(991\) | −157.977 | −0.159411 | −0.0797057 | − | 0.996818i | \(-0.525398\pi\) | ||||
−0.0797057 | + | 0.996818i | \(0.525398\pi\) | |||||||
\(992\) | − | 228.234i | − | 0.230075i | ||||||
\(993\) | − | 914.659i | − | 0.921106i | ||||||
\(994\) | 71.9077i | 0.0723418i | ||||||||
\(995\) | −1315.70 | − | 313.203i | −1.32231 | − | 0.314776i | ||||
\(996\) | − | 513.170i | − | 0.515231i | ||||||
\(997\) | − | 710.953i | − | 0.713092i | −0.934278 | − | 0.356546i | \(-0.883954\pi\) | ||
0.934278 | − | 0.356546i | \(-0.116046\pi\) | |||||||
\(998\) | − | 329.268i | − | 0.329928i | ||||||
\(999\) | − | 221.933i | − | 0.222155i |
(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 | 690.3.f.a.229.18 | yes | 48 | |
5.4 | even | 2 | inner | 690.3.f.a.229.19 | yes | 48 | |
23.22 | odd | 2 | inner | 690.3.f.a.229.17 | ✓ | 48 | |
115.114 | odd | 2 | inner | 690.3.f.a.229.20 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.f.a.229.17 | ✓ | 48 | 23.22 | odd | 2 | inner | |
690.3.f.a.229.18 | yes | 48 | 1.1 | even | 1 | trivial | |
690.3.f.a.229.19 | yes | 48 | 5.4 | even | 2 | inner | |
690.3.f.a.229.20 | yes | 48 | 115.114 | odd | 2 | inner |