Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,5,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.b (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: | \(0.620219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.5.b.a.5.2 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.82843i | − | 0.707107i | ||||||
\(3\) | −3.00000 | + | 8.48528i | −0.333333 | + | 0.942809i | ||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | − | 16.9706i | − | 0.678823i | −0.940638 | − | 0.339411i | \(-0.889772\pi\) | ||
0.940638 | − | 0.339411i | \(-0.110228\pi\) | |||||||
\(6\) | 24.0000 | + | 8.48528i | 0.666667 | + | 0.235702i | ||||
\(7\) | 26.0000 | 0.530612 | 0.265306 | − | 0.964164i | \(-0.414527\pi\) | ||||
0.265306 | + | 0.964164i | \(0.414527\pi\) | |||||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | −63.0000 | − | 50.9117i | −0.777778 | − | 0.628539i | ||||
\(10\) | −48.0000 | −0.480000 | ||||||||
\(11\) | 118.794i | 0.981768i | 0.871225 | + | 0.490884i | \(0.163326\pi\) | ||||
−0.871225 | + | 0.490884i | \(0.836674\pi\) | |||||||
\(12\) | 24.0000 | − | 67.8823i | 0.166667 | − | 0.471405i | ||||
\(13\) | 50.0000 | 0.295858 | 0.147929 | − | 0.988998i | \(-0.452739\pi\) | ||||
0.147929 | + | 0.988998i | \(0.452739\pi\) | |||||||
\(14\) | − | 73.5391i | − | 0.375200i | ||||||
\(15\) | 144.000 | + | 50.9117i | 0.640000 | + | 0.226274i | ||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − | 203.647i | − | 0.704660i | −0.935876 | − | 0.352330i | \(-0.885389\pi\) | ||
0.935876 | − | 0.352330i | \(-0.114611\pi\) | |||||||
\(18\) | −144.000 | + | 178.191i | −0.444444 | + | 0.549972i | ||||
\(19\) | −358.000 | −0.991690 | −0.495845 | − | 0.868411i | \(-0.665142\pi\) | ||||
−0.495845 | + | 0.868411i | \(0.665142\pi\) | |||||||
\(20\) | 135.765i | 0.339411i | ||||||||
\(21\) | −78.0000 | + | 220.617i | −0.176871 | + | 0.500266i | ||||
\(22\) | 336.000 | 0.694215 | ||||||||
\(23\) | − | 373.352i | − | 0.705770i | −0.935667 | − | 0.352885i | \(-0.885201\pi\) | ||
0.935667 | − | 0.352885i | \(-0.114799\pi\) | |||||||
\(24\) | −192.000 | − | 67.8823i | −0.333333 | − | 0.117851i | ||||
\(25\) | 337.000 | 0.539200 | ||||||||
\(26\) | − | 141.421i | − | 0.209203i | ||||||
\(27\) | 621.000 | − | 381.838i | 0.851852 | − | 0.523783i | ||||
\(28\) | −208.000 | −0.265306 | ||||||||
\(29\) | 1442.50i | 1.71522i | 0.514303 | + | 0.857609i | \(0.328051\pi\) | ||||
−0.514303 | + | 0.857609i | \(0.671949\pi\) | |||||||
\(30\) | 144.000 | − | 407.294i | 0.160000 | − | 0.452548i | ||||
\(31\) | −742.000 | −0.772112 | −0.386056 | − | 0.922475i | \(-0.626163\pi\) | ||||
−0.386056 | + | 0.922475i | \(0.626163\pi\) | |||||||
\(32\) | − | 181.019i | − | 0.176777i | ||||||
\(33\) | −1008.00 | − | 356.382i | −0.925620 | − | 0.327256i | ||||
\(34\) | −576.000 | −0.498270 | ||||||||
\(35\) | − | 441.235i | − | 0.360192i | ||||||
\(36\) | 504.000 | + | 407.294i | 0.388889 | + | 0.314270i | ||||
\(37\) | 1874.00 | 1.36888 | 0.684441 | − | 0.729068i | \(-0.260046\pi\) | ||||
0.684441 | + | 0.729068i | \(0.260046\pi\) | |||||||
\(38\) | 1012.58i | 0.701231i | ||||||||
\(39\) | −150.000 | + | 424.264i | −0.0986193 | + | 0.278938i | ||||
\(40\) | 384.000 | 0.240000 | ||||||||
\(41\) | − | 2409.82i | − | 1.43356i | −0.697298 | − | 0.716782i | \(-0.745614\pi\) | ||
0.697298 | − | 0.716782i | \(-0.254386\pi\) | |||||||
\(42\) | 624.000 | + | 220.617i | 0.353741 | + | 0.125067i | ||||
\(43\) | −262.000 | −0.141698 | −0.0708491 | − | 0.997487i | \(-0.522571\pi\) | ||||
−0.0708491 | + | 0.997487i | \(0.522571\pi\) | |||||||
\(44\) | − | 950.352i | − | 0.490884i | ||||||
\(45\) | −864.000 | + | 1069.15i | −0.426667 | + | 0.527973i | ||||
\(46\) | −1056.00 | −0.499055 | ||||||||
\(47\) | 1697.06i | 0.768246i | 0.923282 | + | 0.384123i | \(0.125496\pi\) | ||||
−0.923282 | + | 0.384123i | \(0.874504\pi\) | |||||||
\(48\) | −192.000 | + | 543.058i | −0.0833333 | + | 0.235702i | ||||
\(49\) | −1725.00 | −0.718451 | ||||||||
\(50\) | − | 953.180i | − | 0.381272i | ||||||
\(51\) | 1728.00 | + | 610.940i | 0.664360 | + | 0.234887i | ||||
\(52\) | −400.000 | −0.147929 | ||||||||
\(53\) | 458.205i | 0.163120i | 0.996668 | + | 0.0815602i | \(0.0259903\pi\) | ||||
−0.996668 | + | 0.0815602i | \(0.974010\pi\) | |||||||
\(54\) | −1080.00 | − | 1756.45i | −0.370370 | − | 0.602350i | ||||
\(55\) | 2016.00 | 0.666446 | ||||||||
\(56\) | 588.313i | 0.187600i | ||||||||
\(57\) | 1074.00 | − | 3037.73i | 0.330563 | − | 0.934974i | ||||
\(58\) | 4080.00 | 1.21284 | ||||||||
\(59\) | 1815.85i | 0.521646i | 0.965387 | + | 0.260823i | \(0.0839939\pi\) | ||||
−0.965387 | + | 0.260823i | \(0.916006\pi\) | |||||||
\(60\) | −1152.00 | − | 407.294i | −0.320000 | − | 0.113137i | ||||
\(61\) | −1486.00 | −0.399355 | −0.199678 | − | 0.979862i | \(-0.563989\pi\) | ||||
−0.199678 | + | 0.979862i | \(0.563989\pi\) | |||||||
\(62\) | 2098.69i | 0.545966i | ||||||||
\(63\) | −1638.00 | − | 1323.70i | −0.412698 | − | 0.333511i | ||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − | 848.528i | − | 0.200835i | ||||||
\(66\) | −1008.00 | + | 2851.05i | −0.231405 | + | 0.654512i | ||||
\(67\) | −4486.00 | −0.999332 | −0.499666 | − | 0.866218i | \(-0.666544\pi\) | ||||
−0.499666 | + | 0.866218i | \(0.666544\pi\) | |||||||
\(68\) | 1629.17i | 0.352330i | ||||||||
\(69\) | 3168.00 | + | 1120.06i | 0.665406 | + | 0.235257i | ||||
\(70\) | −1248.00 | −0.254694 | ||||||||
\(71\) | − | 3563.82i | − | 0.706967i | −0.935441 | − | 0.353483i | \(-0.884997\pi\) | ||
0.935441 | − | 0.353483i | \(-0.115003\pi\) | |||||||
\(72\) | 1152.00 | − | 1425.53i | 0.222222 | − | 0.274986i | ||||
\(73\) | 290.000 | 0.0544192 | 0.0272096 | − | 0.999630i | \(-0.491338\pi\) | ||||
0.0272096 | + | 0.999630i | \(0.491338\pi\) | |||||||
\(74\) | − | 5300.47i | − | 0.967946i | ||||||
\(75\) | −1011.00 | + | 2859.54i | −0.179733 | + | 0.508363i | ||||
\(76\) | 2864.00 | 0.495845 | ||||||||
\(77\) | 3088.64i | 0.520938i | ||||||||
\(78\) | 1200.00 | + | 424.264i | 0.197239 | + | 0.0697344i | ||||
\(79\) | 9818.00 | 1.57315 | 0.786573 | − | 0.617498i | \(-0.211854\pi\) | ||||
0.786573 | + | 0.617498i | \(0.211854\pi\) | |||||||
\(80\) | − | 1086.12i | − | 0.169706i | ||||||
\(81\) | 1377.00 | + | 6414.87i | 0.209877 | + | 0.977728i | ||||
\(82\) | −6816.00 | −1.01368 | ||||||||
\(83\) | − | 7110.67i | − | 1.03218i | −0.856535 | − | 0.516088i | \(-0.827388\pi\) | ||
0.856535 | − | 0.516088i | \(-0.172612\pi\) | |||||||
\(84\) | 624.000 | − | 1764.94i | 0.0884354 | − | 0.250133i | ||||
\(85\) | −3456.00 | −0.478339 | ||||||||
\(86\) | 741.048i | 0.100196i | ||||||||
\(87\) | −12240.0 | − | 4327.49i | −1.61712 | − | 0.571739i | ||||
\(88\) | −2688.00 | −0.347107 | ||||||||
\(89\) | 7840.40i | 0.989825i | 0.868943 | + | 0.494912i | \(0.164800\pi\) | ||||
−0.868943 | + | 0.494912i | \(0.835200\pi\) | |||||||
\(90\) | 3024.00 | + | 2443.76i | 0.373333 | + | 0.301699i | ||||
\(91\) | 1300.00 | 0.156986 | ||||||||
\(92\) | 2986.82i | 0.352885i | ||||||||
\(93\) | 2226.00 | − | 6296.08i | 0.257371 | − | 0.727955i | ||||
\(94\) | 4800.00 | 0.543232 | ||||||||
\(95\) | 6075.46i | 0.673181i | ||||||||
\(96\) | 1536.00 | + | 543.058i | 0.166667 | + | 0.0589256i | ||||
\(97\) | −478.000 | −0.0508024 | −0.0254012 | − | 0.999677i | \(-0.508086\pi\) | ||||
−0.0254012 | + | 0.999677i | \(0.508086\pi\) | |||||||
\(98\) | 4879.04i | 0.508021i | ||||||||
\(99\) | 6048.00 | − | 7484.02i | 0.617080 | − | 0.763597i | ||||
\(100\) | −2696.00 | −0.269600 | ||||||||
\(101\) | − | 13729.2i | − | 1.34587i | −0.739703 | − | 0.672933i | \(-0.765034\pi\) | ||
0.739703 | − | 0.672933i | \(-0.234966\pi\) | |||||||
\(102\) | 1728.00 | − | 4887.52i | 0.166090 | − | 0.469773i | ||||
\(103\) | 2138.00 | 0.201527 | 0.100764 | − | 0.994910i | \(-0.467871\pi\) | ||||
0.100764 | + | 0.994910i | \(0.467871\pi\) | |||||||
\(104\) | 1131.37i | 0.104602i | ||||||||
\(105\) | 3744.00 | + | 1323.70i | 0.339592 | + | 0.120064i | ||||
\(106\) | 1296.00 | 0.115344 | ||||||||
\(107\) | 10844.2i | 0.947174i | 0.880747 | + | 0.473587i | \(0.157041\pi\) | ||||
−0.880747 | + | 0.473587i | \(0.842959\pi\) | |||||||
\(108\) | −4968.00 | + | 3054.70i | −0.425926 | + | 0.261891i | ||||
\(109\) | −4750.00 | −0.399798 | −0.199899 | − | 0.979817i | \(-0.564061\pi\) | ||||
−0.199899 | + | 0.979817i | \(0.564061\pi\) | |||||||
\(110\) | − | 5702.11i | − | 0.471249i | ||||||
\(111\) | −5622.00 | + | 15901.4i | −0.456294 | + | 1.29059i | ||||
\(112\) | 1664.00 | 0.132653 | ||||||||
\(113\) | 3190.47i | 0.249860i | 0.992166 | + | 0.124930i | \(0.0398707\pi\) | ||||
−0.992166 | + | 0.124930i | \(0.960129\pi\) | |||||||
\(114\) | −8592.00 | − | 3037.73i | −0.661127 | − | 0.233744i | ||||
\(115\) | −6336.00 | −0.479093 | ||||||||
\(116\) | − | 11540.0i | − | 0.857609i | ||||||
\(117\) | −3150.00 | − | 2545.58i | −0.230112 | − | 0.185958i | ||||
\(118\) | 5136.00 | 0.368860 | ||||||||
\(119\) | − | 5294.82i | − | 0.373901i | ||||||
\(120\) | −1152.00 | + | 3258.35i | −0.0800000 | + | 0.226274i | ||||
\(121\) | 529.000 | 0.0361314 | ||||||||
\(122\) | 4203.04i | 0.282387i | ||||||||
\(123\) | 20448.0 | + | 7229.46i | 1.35158 | + | 0.477854i | ||||
\(124\) | 5936.00 | 0.386056 | ||||||||
\(125\) | − | 16325.7i | − | 1.04484i | ||||||
\(126\) | −3744.00 | + | 4632.96i | −0.235828 | + | 0.291822i | ||||
\(127\) | 8282.00 | 0.513485 | 0.256743 | − | 0.966480i | \(-0.417351\pi\) | ||||
0.256743 | + | 0.966480i | \(0.417351\pi\) | |||||||
\(128\) | 1448.15i | 0.0883883i | ||||||||
\(129\) | 786.000 | − | 2223.14i | 0.0472327 | − | 0.133594i | ||||
\(130\) | −2400.00 | −0.142012 | ||||||||
\(131\) | − | 5413.61i | − | 0.315460i | −0.987482 | − | 0.157730i | \(-0.949582\pi\) | ||
0.987482 | − | 0.157730i | \(-0.0504176\pi\) | |||||||
\(132\) | 8064.00 | + | 2851.05i | 0.462810 | + | 0.163628i | ||||
\(133\) | −9308.00 | −0.526203 | ||||||||
\(134\) | 12688.3i | 0.706634i | ||||||||
\(135\) | −6480.00 | − | 10538.7i | −0.355556 | − | 0.578256i | ||||
\(136\) | 4608.00 | 0.249135 | ||||||||
\(137\) | 18090.6i | 0.963856i | 0.876211 | + | 0.481928i | \(0.160063\pi\) | ||||
−0.876211 | + | 0.481928i | \(0.839937\pi\) | |||||||
\(138\) | 3168.00 | − | 8960.46i | 0.166352 | − | 0.470513i | ||||
\(139\) | −23206.0 | −1.20108 | −0.600538 | − | 0.799596i | \(-0.705047\pi\) | ||||
−0.600538 | + | 0.799596i | \(0.705047\pi\) | |||||||
\(140\) | 3529.88i | 0.180096i | ||||||||
\(141\) | −14400.0 | − | 5091.17i | −0.724310 | − | 0.256082i | ||||
\(142\) | −10080.0 | −0.499901 | ||||||||
\(143\) | 5939.70i | 0.290464i | ||||||||
\(144\) | −4032.00 | − | 3258.35i | −0.194444 | − | 0.157135i | ||||
\(145\) | 24480.0 | 1.16433 | ||||||||
\(146\) | − | 820.244i | − | 0.0384802i | ||||||
\(147\) | 5175.00 | − | 14637.1i | 0.239484 | − | 0.677362i | ||||
\(148\) | −14992.0 | −0.684441 | ||||||||
\(149\) | 11183.6i | 0.503743i | 0.967761 | + | 0.251872i | \(0.0810460\pi\) | ||||
−0.967761 | + | 0.251872i | \(0.918954\pi\) | |||||||
\(150\) | 8088.00 | + | 2859.54i | 0.359467 | + | 0.127091i | ||||
\(151\) | 14426.0 | 0.632692 | 0.316346 | − | 0.948644i | \(-0.397544\pi\) | ||||
0.316346 | + | 0.948644i | \(0.397544\pi\) | |||||||
\(152\) | − | 8100.62i | − | 0.350615i | ||||||
\(153\) | −10368.0 | + | 12829.7i | −0.442907 | + | 0.548069i | ||||
\(154\) | 8736.00 | 0.368359 | ||||||||
\(155\) | 12592.2i | 0.524127i | ||||||||
\(156\) | 1200.00 | − | 3394.11i | 0.0493097 | − | 0.139469i | ||||
\(157\) | 49010.0 | 1.98832 | 0.994158 | − | 0.107935i | \(-0.0344238\pi\) | ||||
0.994158 | + | 0.107935i | \(0.0344238\pi\) | |||||||
\(158\) | − | 27769.5i | − | 1.11238i | ||||||
\(159\) | −3888.00 | − | 1374.62i | −0.153791 | − | 0.0543735i | ||||
\(160\) | −3072.00 | −0.120000 | ||||||||
\(161\) | − | 9707.16i | − | 0.374490i | ||||||
\(162\) | 18144.0 | − | 3894.74i | 0.691358 | − | 0.148405i | ||||
\(163\) | −42982.0 | −1.61775 | −0.808875 | − | 0.587981i | \(-0.799923\pi\) | ||||
−0.808875 | + | 0.587981i | \(0.799923\pi\) | |||||||
\(164\) | 19278.6i | 0.716782i | ||||||||
\(165\) | −6048.00 | + | 17106.3i | −0.222149 | + | 0.628332i | ||||
\(166\) | −20112.0 | −0.729859 | ||||||||
\(167\) | − | 44157.4i | − | 1.58333i | −0.610957 | − | 0.791663i | \(-0.709215\pi\) | ||
0.610957 | − | 0.791663i | \(-0.290785\pi\) | |||||||
\(168\) | −4992.00 | − | 1764.94i | −0.176871 | − | 0.0625333i | ||||
\(169\) | −26061.0 | −0.912468 | ||||||||
\(170\) | 9775.04i | 0.338237i | ||||||||
\(171\) | 22554.0 | + | 18226.4i | 0.771314 | + | 0.623316i | ||||
\(172\) | 2096.00 | 0.0708491 | ||||||||
\(173\) | 22418.1i | 0.749043i | 0.927218 | + | 0.374522i | \(0.122193\pi\) | ||||
−0.927218 | + | 0.374522i | \(0.877807\pi\) | |||||||
\(174\) | −12240.0 | + | 34619.9i | −0.404281 | + | 1.14348i | ||||
\(175\) | 8762.00 | 0.286106 | ||||||||
\(176\) | 7602.81i | 0.245442i | ||||||||
\(177\) | −15408.0 | − | 5447.55i | −0.491813 | − | 0.173882i | ||||
\(178\) | 22176.0 | 0.699912 | ||||||||
\(179\) | − | 30597.9i | − | 0.954962i | −0.878642 | − | 0.477481i | \(-0.841550\pi\) | ||
0.878642 | − | 0.477481i | \(-0.158450\pi\) | |||||||
\(180\) | 6912.00 | − | 8553.16i | 0.213333 | − | 0.263987i | ||||
\(181\) | −13102.0 | −0.399927 | −0.199963 | − | 0.979803i | \(-0.564082\pi\) | ||||
−0.199963 | + | 0.979803i | \(0.564082\pi\) | |||||||
\(182\) | − | 3676.96i | − | 0.111006i | ||||||
\(183\) | 4458.00 | − | 12609.1i | 0.133118 | − | 0.376516i | ||||
\(184\) | 8448.00 | 0.249527 | ||||||||
\(185\) | − | 31802.8i | − | 0.929228i | ||||||
\(186\) | −17808.0 | − | 6296.08i | −0.514742 | − | 0.181989i | ||||
\(187\) | 24192.0 | 0.691813 | ||||||||
\(188\) | − | 13576.5i | − | 0.384123i | ||||||
\(189\) | 16146.0 | − | 9927.78i | 0.452003 | − | 0.277926i | ||||
\(190\) | 17184.0 | 0.476011 | ||||||||
\(191\) | 70326.0i | 1.92774i | 0.266367 | + | 0.963872i | \(0.414177\pi\) | ||||
−0.266367 | + | 0.963872i | \(0.585823\pi\) | |||||||
\(192\) | 1536.00 | − | 4344.46i | 0.0416667 | − | 0.117851i | ||||
\(193\) | 18050.0 | 0.484577 | 0.242288 | − | 0.970204i | \(-0.422102\pi\) | ||||
0.242288 | + | 0.970204i | \(0.422102\pi\) | |||||||
\(194\) | 1351.99i | 0.0359227i | ||||||||
\(195\) | 7200.00 | + | 2545.58i | 0.189349 | + | 0.0669450i | ||||
\(196\) | 13800.0 | 0.359225 | ||||||||
\(197\) | 26321.3i | 0.678228i | 0.940745 | + | 0.339114i | \(0.110127\pi\) | ||||
−0.940745 | + | 0.339114i | \(0.889873\pi\) | |||||||
\(198\) | −21168.0 | − | 17106.3i | −0.539945 | − | 0.436341i | ||||
\(199\) | −37222.0 | −0.939926 | −0.469963 | − | 0.882686i | \(-0.655733\pi\) | ||||
−0.469963 | + | 0.882686i | \(0.655733\pi\) | |||||||
\(200\) | 7625.44i | 0.190636i | ||||||||
\(201\) | 13458.0 | − | 38065.0i | 0.333111 | − | 0.942179i | ||||
\(202\) | −38832.0 | −0.951671 | ||||||||
\(203\) | 37504.9i | 0.910115i | ||||||||
\(204\) | −13824.0 | − | 4887.52i | −0.332180 | − | 0.117443i | ||||
\(205\) | −40896.0 | −0.973135 | ||||||||
\(206\) | − | 6047.18i | − | 0.142501i | ||||||
\(207\) | −19008.0 | + | 23521.2i | −0.443604 | + | 0.548932i | ||||
\(208\) | 3200.00 | 0.0739645 | ||||||||
\(209\) | − | 42528.2i | − | 0.973609i | ||||||
\(210\) | 3744.00 | − | 10589.6i | 0.0848980 | − | 0.240128i | ||||
\(211\) | 15098.0 | 0.339121 | 0.169560 | − | 0.985520i | \(-0.445765\pi\) | ||||
0.169560 | + | 0.985520i | \(0.445765\pi\) | |||||||
\(212\) | − | 3665.64i | − | 0.0815602i | ||||||
\(213\) | 30240.0 | + | 10691.5i | 0.666534 | + | 0.235656i | ||||
\(214\) | 30672.0 | 0.669753 | ||||||||
\(215\) | 4446.29i | 0.0961879i | ||||||||
\(216\) | 8640.00 | + | 14051.6i | 0.185185 | + | 0.301175i | ||||
\(217\) | −19292.0 | −0.409692 | ||||||||
\(218\) | 13435.0i | 0.282700i | ||||||||
\(219\) | −870.000 | + | 2460.73i | −0.0181397 | + | 0.0513069i | ||||
\(220\) | −16128.0 | −0.333223 | ||||||||
\(221\) | − | 10182.3i | − | 0.208479i | ||||||
\(222\) | 44976.0 | + | 15901.4i | 0.912588 | + | 0.322649i | ||||
\(223\) | 58778.0 | 1.18197 | 0.590983 | − | 0.806684i | \(-0.298740\pi\) | ||||
0.590983 | + | 0.806684i | \(0.298740\pi\) | |||||||
\(224\) | − | 4706.50i | − | 0.0937999i | ||||||
\(225\) | −21231.0 | − | 17157.2i | −0.419378 | − | 0.338908i | ||||
\(226\) | 9024.00 | 0.176678 | ||||||||
\(227\) | − | 68001.0i | − | 1.31967i | −0.751412 | − | 0.659833i | \(-0.770627\pi\) | ||
0.751412 | − | 0.659833i | \(-0.229373\pi\) | |||||||
\(228\) | −8592.00 | + | 24301.8i | −0.165282 | + | 0.467487i | ||||
\(229\) | 28562.0 | 0.544650 | 0.272325 | − | 0.962205i | \(-0.412207\pi\) | ||||
0.272325 | + | 0.962205i | \(0.412207\pi\) | |||||||
\(230\) | 17920.9i | 0.338770i | ||||||||
\(231\) | −26208.0 | − | 9265.93i | −0.491145 | − | 0.173646i | ||||
\(232\) | −32640.0 | −0.606421 | ||||||||
\(233\) | − | 22503.0i | − | 0.414503i | −0.978288 | − | 0.207252i | \(-0.933548\pi\) | ||
0.978288 | − | 0.207252i | \(-0.0664519\pi\) | |||||||
\(234\) | −7200.00 | + | 8909.55i | −0.131492 | + | 0.162714i | ||||
\(235\) | 28800.0 | 0.521503 | ||||||||
\(236\) | − | 14526.8i | − | 0.260823i | ||||||
\(237\) | −29454.0 | + | 83308.5i | −0.524382 | + | 1.48318i | ||||
\(238\) | −14976.0 | −0.264388 | ||||||||
\(239\) | − | 1289.76i | − | 0.0225795i | −0.999936 | − | 0.0112897i | \(-0.996406\pi\) | ||
0.999936 | − | 0.0112897i | \(-0.00359371\pi\) | |||||||
\(240\) | 9216.00 | + | 3258.35i | 0.160000 | + | 0.0565685i | ||||
\(241\) | −61246.0 | −1.05449 | −0.527246 | − | 0.849712i | \(-0.676776\pi\) | ||||
−0.527246 | + | 0.849712i | \(0.676776\pi\) | |||||||
\(242\) | − | 1496.24i | − | 0.0255488i | ||||||
\(243\) | −58563.0 | − | 7560.39i | −0.991770 | − | 0.128036i | ||||
\(244\) | 11888.0 | 0.199678 | ||||||||
\(245\) | 29274.2i | 0.487700i | ||||||||
\(246\) | 20448.0 | − | 57835.7i | 0.337894 | − | 0.955709i | ||||
\(247\) | −17900.0 | −0.293399 | ||||||||
\(248\) | − | 16789.5i | − | 0.272983i | ||||||
\(249\) | 60336.0 | + | 21332.0i | 0.973146 | + | 0.344059i | ||||
\(250\) | −46176.0 | −0.738816 | ||||||||
\(251\) | 45260.5i | 0.718409i | 0.933259 | + | 0.359205i | \(0.116952\pi\) | ||||
−0.933259 | + | 0.359205i | \(0.883048\pi\) | |||||||
\(252\) | 13104.0 | + | 10589.6i | 0.206349 | + | 0.166755i | ||||
\(253\) | 44352.0 | 0.692903 | ||||||||
\(254\) | − | 23425.0i | − | 0.363089i | ||||||
\(255\) | 10368.0 | − | 29325.1i | 0.159446 | − | 0.450982i | ||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 85260.1i | 1.29086i | 0.763819 | + | 0.645431i | \(0.223322\pi\) | ||||
−0.763819 | + | 0.645431i | \(0.776678\pi\) | |||||||
\(258\) | −6288.00 | − | 2223.14i | −0.0944655 | − | 0.0333986i | ||||
\(259\) | 48724.0 | 0.726346 | ||||||||
\(260\) | 6788.23i | 0.100418i | ||||||||
\(261\) | 73440.0 | − | 90877.4i | 1.07808 | − | 1.33406i | ||||
\(262\) | −15312.0 | −0.223064 | ||||||||
\(263\) | − | 84751.0i | − | 1.22527i | −0.790364 | − | 0.612637i | \(-0.790109\pi\) | ||
0.790364 | − | 0.612637i | \(-0.209891\pi\) | |||||||
\(264\) | 8064.00 | − | 22808.4i | 0.115702 | − | 0.327256i | ||||
\(265\) | 7776.00 | 0.110730 | ||||||||
\(266\) | 26327.0i | 0.372082i | ||||||||
\(267\) | −66528.0 | − | 23521.2i | −0.933216 | − | 0.329942i | ||||
\(268\) | 35888.0 | 0.499666 | ||||||||
\(269\) | 42918.6i | 0.593117i | 0.955015 | + | 0.296559i | \(0.0958390\pi\) | ||||
−0.955015 | + | 0.296559i | \(0.904161\pi\) | |||||||
\(270\) | −29808.0 | + | 18328.2i | −0.408889 | + | 0.251416i | ||||
\(271\) | −27430.0 | −0.373497 | −0.186749 | − | 0.982408i | \(-0.559795\pi\) | ||||
−0.186749 | + | 0.982408i | \(0.559795\pi\) | |||||||
\(272\) | − | 13033.4i | − | 0.176165i | ||||||
\(273\) | −3900.00 | + | 11030.9i | −0.0523286 | + | 0.148008i | ||||
\(274\) | 51168.0 | 0.681549 | ||||||||
\(275\) | 40033.6i | 0.529369i | ||||||||
\(276\) | −25344.0 | − | 8960.46i | −0.332703 | − | 0.117628i | ||||
\(277\) | −93934.0 | −1.22423 | −0.612115 | − | 0.790768i | \(-0.709681\pi\) | ||||
−0.612115 | + | 0.790768i | \(0.709681\pi\) | |||||||
\(278\) | 65636.5i | 0.849289i | ||||||||
\(279\) | 46746.0 | + | 37776.5i | 0.600532 | + | 0.485303i | ||||
\(280\) | 9984.00 | 0.127347 | ||||||||
\(281\) | − | 24471.6i | − | 0.309919i | −0.987921 | − | 0.154960i | \(-0.950475\pi\) | ||
0.987921 | − | 0.154960i | \(-0.0495248\pi\) | |||||||
\(282\) | −14400.0 | + | 40729.4i | −0.181077 | + | 0.512164i | ||||
\(283\) | −65830.0 | −0.821961 | −0.410980 | − | 0.911644i | \(-0.634813\pi\) | ||||
−0.410980 | + | 0.911644i | \(0.634813\pi\) | |||||||
\(284\) | 28510.5i | 0.353483i | ||||||||
\(285\) | −51552.0 | − | 18226.4i | −0.634681 | − | 0.224394i | ||||
\(286\) | 16800.0 | 0.205389 | ||||||||
\(287\) | − | 62655.3i | − | 0.760666i | ||||||
\(288\) | −9216.00 | + | 11404.2i | −0.111111 | + | 0.137493i | ||||
\(289\) | 42049.0 | 0.503454 | ||||||||
\(290\) | − | 69239.9i | − | 0.823304i | ||||||
\(291\) | 1434.00 | − | 4055.96i | 0.0169341 | − | 0.0478970i | ||||
\(292\) | −2320.00 | −0.0272096 | ||||||||
\(293\) | − | 90028.8i | − | 1.04869i | −0.851506 | − | 0.524344i | \(-0.824311\pi\) | ||
0.851506 | − | 0.524344i | \(-0.175689\pi\) | |||||||
\(294\) | −41400.0 | − | 14637.1i | −0.478967 | − | 0.169340i | ||||
\(295\) | 30816.0 | 0.354105 | ||||||||
\(296\) | 42403.8i | 0.483973i | ||||||||
\(297\) | 45360.0 | + | 73771.0i | 0.514233 | + | 0.836321i | ||||
\(298\) | 31632.0 | 0.356200 | ||||||||
\(299\) | − | 18667.6i | − | 0.208808i | ||||||
\(300\) | 8088.00 | − | 22876.3i | 0.0898667 | − | 0.254181i | ||||
\(301\) | −6812.00 | −0.0751868 | ||||||||
\(302\) | − | 40802.9i | − | 0.447380i | ||||||
\(303\) | 116496. | + | 41187.6i | 1.26890 | + | 0.448622i | ||||
\(304\) | −22912.0 | −0.247922 | ||||||||
\(305\) | 25218.3i | 0.271091i | ||||||||
\(306\) | 36288.0 | + | 29325.1i | 0.387543 | + | 0.313182i | ||||
\(307\) | 67322.0 | 0.714299 | 0.357150 | − | 0.934047i | \(-0.383749\pi\) | ||||
0.357150 | + | 0.934047i | \(0.383749\pi\) | |||||||
\(308\) | − | 24709.1i | − | 0.260469i | ||||||
\(309\) | −6414.00 | + | 18141.5i | −0.0671757 | + | 0.190001i | ||||
\(310\) | 35616.0 | 0.370614 | ||||||||
\(311\) | 131997.i | 1.36472i | 0.731017 | + | 0.682360i | \(0.239046\pi\) | ||||
−0.731017 | + | 0.682360i | \(0.760954\pi\) | |||||||
\(312\) | −9600.00 | − | 3394.11i | −0.0986193 | − | 0.0348672i | ||||
\(313\) | −22078.0 | −0.225357 | −0.112679 | − | 0.993631i | \(-0.535943\pi\) | ||||
−0.112679 | + | 0.993631i | \(0.535943\pi\) | |||||||
\(314\) | − | 138621.i | − | 1.40595i | ||||||
\(315\) | −22464.0 | + | 27797.8i | −0.226395 | + | 0.280149i | ||||
\(316\) | −78544.0 | −0.786573 | ||||||||
\(317\) | − | 117894.i | − | 1.17321i | −0.809874 | − | 0.586604i | \(-0.800465\pi\) | ||
0.809874 | − | 0.586604i | \(-0.199535\pi\) | |||||||
\(318\) | −3888.00 | + | 10996.9i | −0.0384478 | + | 0.108747i | ||||
\(319\) | −171360. | −1.68395 | ||||||||
\(320\) | 8688.93i | 0.0848528i | ||||||||
\(321\) | −92016.0 | − | 32532.6i | −0.893004 | − | 0.315725i | ||||
\(322\) | −27456.0 | −0.264805 | ||||||||
\(323\) | 72905.5i | 0.698804i | ||||||||
\(324\) | −11016.0 | − | 51319.0i | −0.104938 | − | 0.488864i | ||||
\(325\) | 16850.0 | 0.159527 | ||||||||
\(326\) | 121571.i | 1.14392i | ||||||||
\(327\) | 14250.0 | − | 40305.1i | 0.133266 | − | 0.376933i | ||||
\(328\) | 54528.0 | 0.506841 | ||||||||
\(329\) | 44123.5i | 0.407641i | ||||||||
\(330\) | 48384.0 | + | 17106.3i | 0.444298 | + | 0.157083i | ||||
\(331\) | 167642. | 1.53012 | 0.765062 | − | 0.643956i | \(-0.222708\pi\) | ||||
0.765062 | + | 0.643956i | \(0.222708\pi\) | |||||||
\(332\) | 56885.3i | 0.516088i | ||||||||
\(333\) | −118062. | − | 95408.5i | −1.06469 | − | 0.860396i | ||||
\(334\) | −124896. | −1.11958 | ||||||||
\(335\) | 76129.9i | 0.678369i | ||||||||
\(336\) | −4992.00 | + | 14119.5i | −0.0442177 | + | 0.125067i | ||||
\(337\) | 162914. | 1.43449 | 0.717247 | − | 0.696819i | \(-0.245402\pi\) | ||||
0.717247 | + | 0.696819i | \(0.245402\pi\) | |||||||
\(338\) | 73711.6i | 0.645212i | ||||||||
\(339\) | −27072.0 | − | 9571.40i | −0.235571 | − | 0.0832868i | ||||
\(340\) | 27648.0 | 0.239170 | ||||||||
\(341\) | − | 88145.1i | − | 0.758035i | ||||||
\(342\) | 51552.0 | − | 63792.3i | 0.440751 | − | 0.545402i | ||||
\(343\) | −107276. | −0.911831 | ||||||||
\(344\) | − | 5928.38i | − | 0.0500979i | ||||||
\(345\) | 19008.0 | − | 53762.7i | 0.159698 | − | 0.451693i | ||||
\(346\) | 63408.0 | 0.529654 | ||||||||
\(347\) | − | 132184.i | − | 1.09779i | −0.835892 | − | 0.548895i | \(-0.815049\pi\) | ||
0.835892 | − | 0.548895i | \(-0.184951\pi\) | |||||||
\(348\) | 97920.0 | + | 34619.9i | 0.808561 | + | 0.285870i | ||||
\(349\) | 53234.0 | 0.437057 | 0.218529 | − | 0.975831i | \(-0.429874\pi\) | ||||
0.218529 | + | 0.975831i | \(0.429874\pi\) | |||||||
\(350\) | − | 24782.7i | − | 0.202308i | ||||||
\(351\) | 31050.0 | − | 19091.9i | 0.252027 | − | 0.154965i | ||||
\(352\) | 21504.0 | 0.173554 | ||||||||
\(353\) | 144861.i | 1.16252i | 0.813717 | + | 0.581261i | \(0.197440\pi\) | ||||
−0.813717 | + | 0.581261i | \(0.802560\pi\) | |||||||
\(354\) | −15408.0 | + | 43580.4i | −0.122953 | + | 0.347764i | ||||
\(355\) | −60480.0 | −0.479905 | ||||||||
\(356\) | − | 62723.2i | − | 0.494912i | ||||||
\(357\) | 44928.0 | + | 15884.4i | 0.352517 | + | 0.124634i | ||||
\(358\) | −86544.0 | −0.675260 | ||||||||
\(359\) | − | 12931.6i | − | 0.100337i | −0.998741 | − | 0.0501686i | \(-0.984024\pi\) | ||
0.998741 | − | 0.0501686i | \(-0.0159759\pi\) | |||||||
\(360\) | −24192.0 | − | 19550.1i | −0.186667 | − | 0.150849i | ||||
\(361\) | −2157.00 | −0.0165514 | ||||||||
\(362\) | 37058.1i | 0.282791i | ||||||||
\(363\) | −1587.00 | + | 4488.71i | −0.0120438 | + | 0.0340650i | ||||
\(364\) | −10400.0 | −0.0784929 | ||||||||
\(365\) | − | 4921.46i | − | 0.0369410i | ||||||
\(366\) | −35664.0 | − | 12609.1i | −0.266237 | − | 0.0941289i | ||||
\(367\) | −44326.0 | −0.329099 | −0.164549 | − | 0.986369i | \(-0.552617\pi\) | ||||
−0.164549 | + | 0.986369i | \(0.552617\pi\) | |||||||
\(368\) | − | 23894.6i | − | 0.176443i | ||||||
\(369\) | −122688. | + | 151819.i | −0.901051 | + | 1.11499i | ||||
\(370\) | −89952.0 | −0.657064 | ||||||||
\(371\) | 11913.3i | 0.0865537i | ||||||||
\(372\) | −17808.0 | + | 50368.6i | −0.128685 | + | 0.363977i | ||||
\(373\) | −60718.0 | −0.436415 | −0.218208 | − | 0.975902i | \(-0.570021\pi\) | ||||
−0.218208 | + | 0.975902i | \(0.570021\pi\) | |||||||
\(374\) | − | 68425.3i | − | 0.489185i | ||||||
\(375\) | 138528. | + | 48977.0i | 0.985088 | + | 0.348281i | ||||
\(376\) | −38400.0 | −0.271616 | ||||||||
\(377\) | 72124.9i | 0.507461i | ||||||||
\(378\) | −28080.0 | − | 45667.8i | −0.196523 | − | 0.319614i | ||||
\(379\) | 30458.0 | 0.212043 | 0.106021 | − | 0.994364i | \(-0.466189\pi\) | ||||
0.106021 | + | 0.994364i | \(0.466189\pi\) | |||||||
\(380\) | − | 48603.7i | − | 0.336591i | ||||||
\(381\) | −24846.0 | + | 70275.1i | −0.171162 | + | 0.484118i | ||||
\(382\) | 198912. | 1.36312 | ||||||||
\(383\) | − | 235687.i | − | 1.60671i | −0.595498 | − | 0.803357i | \(-0.703045\pi\) | ||
0.595498 | − | 0.803357i | \(-0.296955\pi\) | |||||||
\(384\) | −12288.0 | − | 4344.46i | −0.0833333 | − | 0.0294628i | ||||
\(385\) | 52416.0 | 0.353625 | ||||||||
\(386\) | − | 51053.1i | − | 0.342648i | ||||||
\(387\) | 16506.0 | + | 13338.9i | 0.110210 | + | 0.0890629i | ||||
\(388\) | 3824.00 | 0.0254012 | ||||||||
\(389\) | 150410.i | 0.993980i | 0.867756 | + | 0.496990i | \(0.165561\pi\) | ||||
−0.867756 | + | 0.496990i | \(0.834439\pi\) | |||||||
\(390\) | 7200.00 | − | 20364.7i | 0.0473373 | − | 0.133890i | ||||
\(391\) | −76032.0 | −0.497328 | ||||||||
\(392\) | − | 39032.3i | − | 0.254011i | ||||||
\(393\) | 45936.0 | + | 16240.8i | 0.297419 | + | 0.105153i | ||||
\(394\) | 74448.0 | 0.479579 | ||||||||
\(395\) | − | 166617.i | − | 1.06789i | ||||||
\(396\) | −48384.0 | + | 59872.1i | −0.308540 | + | 0.381799i | ||||
\(397\) | 172658. | 1.09548 | 0.547742 | − | 0.836648i | \(-0.315488\pi\) | ||||
0.547742 | + | 0.836648i | \(0.315488\pi\) | |||||||
\(398\) | 105280.i | 0.664628i | ||||||||
\(399\) | 27924.0 | − | 78981.0i | 0.175401 | − | 0.496109i | ||||
\(400\) | 21568.0 | 0.134800 | ||||||||
\(401\) | − | 167466.i | − | 1.04145i | −0.853726 | − | 0.520723i | \(-0.825662\pi\) | ||
0.853726 | − | 0.520723i | \(-0.174338\pi\) | |||||||
\(402\) | −107664. | − | 38065.0i | −0.666221 | − | 0.235545i | ||||
\(403\) | −37100.0 | −0.228436 | ||||||||
\(404\) | 109833.i | 0.672933i | ||||||||
\(405\) | 108864. | − | 23368.5i | 0.663704 | − | 0.142469i | ||||
\(406\) | 106080. | 0.643549 | ||||||||
\(407\) | 222620.i | 1.34393i | ||||||||
\(408\) | −13824.0 | + | 39100.2i | −0.0830450 | + | 0.234887i | ||||
\(409\) | −150430. | −0.899265 | −0.449633 | − | 0.893214i | \(-0.648445\pi\) | ||||
−0.449633 | + | 0.893214i | \(0.648445\pi\) | |||||||
\(410\) | 115671.i | 0.688110i | ||||||||
\(411\) | −153504. | − | 54271.9i | −0.908732 | − | 0.321285i | ||||
\(412\) | −17104.0 | −0.100764 | ||||||||
\(413\) | 47212.1i | 0.276792i | ||||||||
\(414\) | 66528.0 | + | 53762.7i | 0.388154 | + | 0.313676i | ||||
\(415\) | −120672. | −0.700665 | ||||||||
\(416\) | − | 9050.97i | − | 0.0523008i | ||||||
\(417\) | 69618.0 | − | 196909.i | 0.400359 | − | 1.13239i | ||||
\(418\) | −120288. | −0.688446 | ||||||||
\(419\) | 178276.i | 1.01546i | 0.861515 | + | 0.507732i | \(0.169516\pi\) | ||||
−0.861515 | + | 0.507732i | \(0.830484\pi\) | |||||||
\(420\) | −29952.0 | − | 10589.6i | −0.169796 | − | 0.0600319i | ||||
\(421\) | −216046. | −1.21894 | −0.609470 | − | 0.792809i | \(-0.708618\pi\) | ||||
−0.609470 | + | 0.792809i | \(0.708618\pi\) | |||||||
\(422\) | − | 42703.6i | − | 0.239795i | ||||||
\(423\) | 86400.0 | − | 106915.i | 0.482873 | − | 0.597525i | ||||
\(424\) | −10368.0 | −0.0576718 | ||||||||
\(425\) | − | 68629.0i | − | 0.379953i | ||||||
\(426\) | 30240.0 | − | 85531.6i | 0.166634 | − | 0.471311i | ||||
\(427\) | −38636.0 | −0.211903 | ||||||||
\(428\) | − | 86753.5i | − | 0.473587i | ||||||
\(429\) | −50400.0 | − | 17819.1i | −0.273852 | − | 0.0968213i | ||||
\(430\) | 12576.0 | 0.0680151 | ||||||||
\(431\) | 5498.46i | 0.0295997i | 0.999890 | + | 0.0147998i | \(0.00471110\pi\) | ||||
−0.999890 | + | 0.0147998i | \(0.995289\pi\) | |||||||
\(432\) | 39744.0 | − | 24437.6i | 0.212963 | − | 0.130946i | ||||
\(433\) | 108002. | 0.576044 | 0.288022 | − | 0.957624i | \(-0.407002\pi\) | ||||
0.288022 | + | 0.957624i | \(0.407002\pi\) | |||||||
\(434\) | 54566.0i | 0.289696i | ||||||||
\(435\) | −73440.0 | + | 207720.i | −0.388109 | + | 1.09774i | ||||
\(436\) | 38000.0 | 0.199899 | ||||||||
\(437\) | 133660.i | 0.699905i | ||||||||
\(438\) | 6960.00 | + | 2460.73i | 0.0362795 | + | 0.0128267i | ||||
\(439\) | 357722. | 1.85617 | 0.928083 | − | 0.372374i | \(-0.121456\pi\) | ||||
0.928083 | + | 0.372374i | \(0.121456\pi\) | |||||||
\(440\) | 45616.9i | 0.235624i | ||||||||
\(441\) | 108675. | + | 87822.7i | 0.558795 | + | 0.451575i | ||||
\(442\) | −28800.0 | −0.147417 | ||||||||
\(443\) | 86261.4i | 0.439551i | 0.975551 | + | 0.219775i | \(0.0705324\pi\) | ||||
−0.975551 | + | 0.219775i | \(0.929468\pi\) | |||||||
\(444\) | 44976.0 | − | 127211.i | 0.228147 | − | 0.645297i | ||||
\(445\) | 133056. | 0.671915 | ||||||||
\(446\) | − | 166249.i | − | 0.835776i | ||||||
\(447\) | −94896.0 | − | 33550.8i | −0.474934 | − | 0.167914i | ||||
\(448\) | −13312.0 | −0.0663265 | ||||||||
\(449\) | − | 301397.i | − | 1.49502i | −0.664251 | − | 0.747509i | \(-0.731250\pi\) | ||
0.664251 | − | 0.747509i | \(-0.268750\pi\) | |||||||
\(450\) | −48528.0 | + | 60050.3i | −0.239644 | + | 0.296545i | ||||
\(451\) | 286272. | 1.40743 | ||||||||
\(452\) | − | 25523.7i | − | 0.124930i | ||||||
\(453\) | −43278.0 | + | 122409.i | −0.210897 | + | 0.596507i | ||||
\(454\) | −192336. | −0.933144 | ||||||||
\(455\) | − | 22061.7i | − | 0.106566i | ||||||
\(456\) | 68736.0 | + | 24301.8i | 0.330563 | + | 0.116872i | ||||
\(457\) | −399070. | −1.91081 | −0.955403 | − | 0.295305i | \(-0.904579\pi\) | ||||
−0.955403 | + | 0.295305i | \(0.904579\pi\) | |||||||
\(458\) | − | 80785.5i | − | 0.385126i | ||||||
\(459\) | −77760.0 | − | 126465.i | −0.369089 | − | 0.600266i | ||||
\(460\) | 50688.0 | 0.239546 | ||||||||
\(461\) | − | 38268.6i | − | 0.180070i | −0.995939 | − | 0.0900349i | \(-0.971302\pi\) | ||
0.995939 | − | 0.0900349i | \(-0.0286979\pi\) | |||||||
\(462\) | −26208.0 | + | 74127.4i | −0.122786 | + | 0.347292i | ||||
\(463\) | 144410. | 0.673652 | 0.336826 | − | 0.941567i | \(-0.390647\pi\) | ||||
0.336826 | + | 0.941567i | \(0.390647\pi\) | |||||||
\(464\) | 92319.9i | 0.428804i | ||||||||
\(465\) | −106848. | − | 37776.5i | −0.494152 | − | 0.174709i | ||||
\(466\) | −63648.0 | −0.293098 | ||||||||
\(467\) | 148204.i | 0.679557i | 0.940505 | + | 0.339779i | \(0.110352\pi\) | ||||
−0.940505 | + | 0.339779i | \(0.889648\pi\) | |||||||
\(468\) | 25200.0 | + | 20364.7i | 0.115056 | + | 0.0929792i | ||||
\(469\) | −116636. | −0.530258 | ||||||||
\(470\) | − | 81458.7i | − | 0.368758i | ||||||
\(471\) | −147030. | + | 415864.i | −0.662772 | + | 1.87460i | ||||
\(472\) | −41088.0 | −0.184430 | ||||||||
\(473\) | − | 31124.0i | − | 0.139115i | ||||||
\(474\) | 235632. | + | 83308.5i | 1.04876 | + | 0.370794i | ||||
\(475\) | −120646. | −0.534719 | ||||||||
\(476\) | 42358.5i | 0.186951i | ||||||||
\(477\) | 23328.0 | − | 28866.9i | 0.102528 | − | 0.126871i | ||||
\(478\) | −3648.00 | −0.0159661 | ||||||||
\(479\) | − | 305606.i | − | 1.33196i | −0.745970 | − | 0.665979i | \(-0.768014\pi\) | ||
0.745970 | − | 0.665979i | \(-0.231986\pi\) | |||||||
\(480\) | 9216.00 | − | 26066.8i | 0.0400000 | − | 0.113137i | ||||
\(481\) | 93700.0 | 0.404995 | ||||||||
\(482\) | 173230.i | 0.745639i | ||||||||
\(483\) | 82368.0 | + | 29121.5i | 0.353073 | + | 0.124830i | ||||
\(484\) | −4232.00 | −0.0180657 | ||||||||
\(485\) | 8111.93i | 0.0344858i | ||||||||
\(486\) | −21384.0 | + | 165641.i | −0.0905350 | + | 0.701287i | ||||
\(487\) | −196774. | −0.829678 | −0.414839 | − | 0.909895i | \(-0.636162\pi\) | ||||
−0.414839 | + | 0.909895i | \(0.636162\pi\) | |||||||
\(488\) | − | 33624.3i | − | 0.141193i | ||||||
\(489\) | 128946. | − | 364714.i | 0.539250 | − | 1.52523i | ||||
\(490\) | 82800.0 | 0.344856 | ||||||||
\(491\) | − | 166193.i | − | 0.689365i | −0.938719 | − | 0.344682i | \(-0.887987\pi\) | ||
0.938719 | − | 0.344682i | \(-0.112013\pi\) | |||||||
\(492\) | −163584. | − | 57835.7i | −0.675788 | − | 0.238927i | ||||
\(493\) | 293760. | 1.20865 | ||||||||
\(494\) | 50628.8i | 0.207465i | ||||||||
\(495\) | −127008. | − | 102638.i | −0.518347 | − | 0.418888i | ||||
\(496\) | −47488.0 | −0.193028 | ||||||||
\(497\) | − | 92659.3i | − | 0.375125i | ||||||
\(498\) | 60336.0 | − | 170656.i | 0.243286 | − | 0.688118i | ||||
\(499\) | 189050. | 0.759234 | 0.379617 | − | 0.925144i | \(-0.376056\pi\) | ||||
0.379617 | + | 0.925144i | \(0.376056\pi\) | |||||||
\(500\) | 130605.i | 0.522422i | ||||||||
\(501\) | 374688. | + | 132472.i | 1.49277 | + | 0.527776i | ||||
\(502\) | 128016. | 0.507992 | ||||||||
\(503\) | 344061.i | 1.35988i | 0.733269 | + | 0.679939i | \(0.237994\pi\) | ||||
−0.733269 | + | 0.679939i | \(0.762006\pi\) | |||||||
\(504\) | 29952.0 | − | 37063.7i | 0.117914 | − | 0.145911i | ||||
\(505\) | −232992. | −0.913605 | ||||||||
\(506\) | − | 125446.i | − | 0.489956i | ||||||
\(507\) | 78183.0 | − | 221135.i | 0.304156 | − | 0.860283i | ||||
\(508\) | −66256.0 | −0.256743 | ||||||||
\(509\) | 353208.i | 1.36331i | 0.731673 | + | 0.681656i | \(0.238740\pi\) | ||||
−0.731673 | + | 0.681656i | \(0.761260\pi\) | |||||||
\(510\) | −82944.0 | − | 29325.1i | −0.318893 | − | 0.112746i | ||||
\(511\) | 7540.00 | 0.0288755 | ||||||||
\(512\) | − | 11585.2i | − | 0.0441942i | ||||||
\(513\) | −222318. | + | 136698.i | −0.844773 | + | 0.519430i | ||||
\(514\) | 241152. | 0.912777 | ||||||||
\(515\) | − | 36283.1i | − | 0.136801i | ||||||
\(516\) | −6288.00 | + | 17785.1i | −0.0236164 | + | 0.0667972i | ||||
\(517\) | −201600. | −0.754240 | ||||||||
\(518\) | − | 137812.i | − | 0.513604i | ||||||
\(519\) | −190224. | − | 67254.3i | −0.706205 | − | 0.249681i | ||||
\(520\) | 19200.0 | 0.0710059 | ||||||||
\(521\) | 276043.i | 1.01695i | 0.861075 | + | 0.508477i | \(0.169791\pi\) | ||||
−0.861075 | + | 0.508477i | \(0.830209\pi\) | |||||||
\(522\) | −257040. | − | 207720.i | −0.943321 | − | 0.762319i | ||||
\(523\) | −146950. | −0.537237 | −0.268619 | − | 0.963247i | \(-0.586567\pi\) | ||||
−0.268619 | + | 0.963247i | \(0.586567\pi\) | |||||||
\(524\) | 43308.9i | 0.157730i | ||||||||
\(525\) | −26286.0 | + | 74348.0i | −0.0953687 | + | 0.269743i | ||||
\(526\) | −239712. | −0.866400 | ||||||||
\(527\) | 151106.i | 0.544077i | ||||||||
\(528\) | −64512.0 | − | 22808.4i | −0.231405 | − | 0.0818140i | ||||
\(529\) | 140449. | 0.501889 | ||||||||
\(530\) | − | 21993.8i | − | 0.0782978i | ||||||
\(531\) | 92448.0 | − | 114399.i | 0.327875 | − | 0.405725i | ||||
\(532\) | 74464.0 | 0.263101 | ||||||||
\(533\) | − | 120491.i | − | 0.424131i | ||||||
\(534\) | −66528.0 | + | 188170.i | −0.233304 | + | 0.659883i | ||||
\(535\) | 184032. | 0.642963 | ||||||||
\(536\) | − | 101507.i | − | 0.353317i | ||||||
\(537\) | 259632. | + | 91793.8i | 0.900346 | + | 0.318321i | ||||
\(538\) | 121392. | 0.419397 | ||||||||
\(539\) | − | 204920.i | − | 0.705352i | ||||||
\(540\) | 51840.0 | + | 84309.8i | 0.177778 | + | 0.289128i | ||||
\(541\) | −244942. | −0.836891 | −0.418445 | − | 0.908242i | \(-0.637425\pi\) | ||||
−0.418445 | + | 0.908242i | \(0.637425\pi\) | |||||||
\(542\) | 77583.8i | 0.264102i | ||||||||
\(543\) | 39306.0 | − | 111174.i | 0.133309 | − | 0.377055i | ||||
\(544\) | −36864.0 | −0.124567 | ||||||||
\(545\) | 80610.2i | 0.271392i | ||||||||
\(546\) | 31200.0 | + | 11030.9i | 0.104657 | + | 0.0370019i | ||||
\(547\) | −283366. | −0.947050 | −0.473525 | − | 0.880780i | \(-0.657019\pi\) | ||||
−0.473525 | + | 0.880780i | \(0.657019\pi\) | |||||||
\(548\) | − | 144725.i | − | 0.481928i | ||||||
\(549\) | 93618.0 | + | 75654.8i | 0.310609 | + | 0.251010i | ||||
\(550\) | 113232. | 0.374321 | ||||||||
\(551\) | − | 516414.i | − | 1.70096i | ||||||
\(552\) | −25344.0 | + | 71683.7i | −0.0831758 | + | 0.235257i | ||||
\(553\) | 255268. | 0.834730 | ||||||||
\(554\) | 265685.i | 0.865662i | ||||||||
\(555\) | 269856. | + | 95408.5i | 0.876085 | + | 0.309743i | ||||
\(556\) | 185648. | 0.600538 | ||||||||
\(557\) | − | 47093.3i | − | 0.151792i | −0.997116 | − | 0.0758960i | \(-0.975818\pi\) | ||
0.997116 | − | 0.0758960i | \(-0.0241817\pi\) | |||||||
\(558\) | 106848. | − | 132218.i | 0.343161 | − | 0.424640i | ||||
\(559\) | −13100.0 | −0.0419225 | ||||||||
\(560\) | − | 28239.0i | − | 0.0900479i | ||||||
\(561\) | −72576.0 | + | 205276.i | −0.230604 | + | 0.652247i | ||||
\(562\) | −69216.0 | −0.219146 | ||||||||
\(563\) | 84.8528i | 0.000267701i | 1.00000 | 0.000133850i | \(4.26059e-5\pi\) | |||||
−1.00000 | 0.000133850i | \(0.999957\pi\) | ||||||||
\(564\) | 115200. | + | 40729.4i | 0.362155 | + | 0.128041i | ||||
\(565\) | 54144.0 | 0.169611 | ||||||||
\(566\) | 186195.i | 0.581214i | ||||||||
\(567\) | 35802.0 | + | 166787.i | 0.111363 | + | 0.518794i | ||||
\(568\) | 80640.0 | 0.249950 | ||||||||
\(569\) | − | 239115.i | − | 0.738555i | −0.929319 | − | 0.369277i | \(-0.879605\pi\) | ||
0.929319 | − | 0.369277i | \(-0.120395\pi\) | |||||||
\(570\) | −51552.0 | + | 145811.i | −0.158670 | + | 0.448788i | ||||
\(571\) | −140710. | −0.431571 | −0.215786 | − | 0.976441i | \(-0.569231\pi\) | ||||
−0.215786 | + | 0.976441i | \(0.569231\pi\) | |||||||
\(572\) | − | 47517.6i | − | 0.145232i | ||||||
\(573\) | −596736. | − | 210978.i | −1.81749 | − | 0.642581i | ||||
\(574\) | −177216. | −0.537872 | ||||||||
\(575\) | − | 125820.i | − | 0.380551i | ||||||
\(576\) | 32256.0 | + | 26066.8i | 0.0972222 | + | 0.0785674i | ||||
\(577\) | 36002.0 | 0.108137 | 0.0540686 | − | 0.998537i | \(-0.482781\pi\) | ||||
0.0540686 | + | 0.998537i | \(0.482781\pi\) | |||||||
\(578\) | − | 118933.i | − | 0.355996i | ||||||
\(579\) | −54150.0 | + | 153159.i | −0.161526 | + | 0.456863i | ||||
\(580\) | −195840. | −0.582164 | ||||||||
\(581\) | − | 184877.i | − | 0.547686i | ||||||
\(582\) | −11472.0 | − | 4055.96i | −0.0338683 | − | 0.0119742i | ||||
\(583\) | −54432.0 | −0.160146 | ||||||||
\(584\) | 6561.95i | 0.0192401i | ||||||||
\(585\) | −43200.0 | + | 53457.3i | −0.126233 | + | 0.156205i | ||||
\(586\) | −254640. | −0.741535 | ||||||||
\(587\) | 316179.i | 0.917606i | 0.888538 | + | 0.458803i | \(0.151722\pi\) | ||||
−0.888538 | + | 0.458803i | \(0.848278\pi\) | |||||||
\(588\) | −41400.0 | + | 117097.i | −0.119742 | + | 0.338681i | ||||
\(589\) | 265636. | 0.765696 | ||||||||
\(590\) | − | 87160.8i | − | 0.250390i | ||||||
\(591\) | −223344. | − | 78964.0i | −0.639439 | − | 0.226076i | ||||
\(592\) | 119936. | 0.342221 | ||||||||
\(593\) | 262093.i | 0.745327i | 0.927967 | + | 0.372663i | \(0.121555\pi\) | ||||
−0.927967 | + | 0.372663i | \(0.878445\pi\) | |||||||
\(594\) | 208656. | − | 128297.i | 0.591368 | − | 0.363618i | ||||
\(595\) | −89856.0 | −0.253813 | ||||||||
\(596\) | − | 89468.8i | − | 0.251872i | ||||||
\(597\) | 111666. | − | 315839.i | 0.313309 | − | 0.886171i | ||||
\(598\) | −52800.0 | −0.147649 | ||||||||
\(599\) | 606494.i | 1.69034i | 0.534501 | + | 0.845168i | \(0.320499\pi\) | ||||
−0.534501 | + | 0.845168i | \(0.679501\pi\) | |||||||
\(600\) | −64704.0 | − | 22876.3i | −0.179733 | − | 0.0635453i | ||||
\(601\) | 306530. | 0.848641 | 0.424321 | − | 0.905512i | \(-0.360513\pi\) | ||||
0.424321 | + | 0.905512i | \(0.360513\pi\) | |||||||
\(602\) | 19267.2i | 0.0531651i | ||||||||
\(603\) | 282618. | + | 228390.i | 0.777258 | + | 0.628119i | ||||
\(604\) | −115408. | −0.316346 | ||||||||
\(605\) | − | 8977.43i | − | 0.0245268i | ||||||
\(606\) | 116496. | − | 329500.i | 0.317224 | − | 0.897244i | ||||
\(607\) | 563162. | 1.52847 | 0.764233 | − | 0.644940i | \(-0.223118\pi\) | ||||
0.764233 | + | 0.644940i | \(0.223118\pi\) | |||||||
\(608\) | 64804.9i | 0.175308i | ||||||||
\(609\) | −318240. | − | 112515.i | −0.858065 | − | 0.303372i | ||||
\(610\) | 71328.0 | 0.191690 | ||||||||
\(611\) | 84852.8i | 0.227292i | ||||||||
\(612\) | 82944.0 | − | 102638.i | 0.221453 | − | 0.274034i | ||||
\(613\) | 111314. | 0.296230 | 0.148115 | − | 0.988970i | \(-0.452679\pi\) | ||||
0.148115 | + | 0.988970i | \(0.452679\pi\) | |||||||
\(614\) | − | 190415.i | − | 0.505086i | ||||||
\(615\) | 122688. | − | 347014.i | 0.324378 | − | 0.917481i | ||||
\(616\) | −69888.0 | −0.184179 | ||||||||
\(617\) | − | 121340.i | − | 0.318737i | −0.987219 | − | 0.159368i | \(-0.949054\pi\) | ||
0.987219 | − | 0.159368i | \(-0.0509457\pi\) | |||||||
\(618\) | 51312.0 | + | 18141.5i | 0.134351 | + | 0.0475004i | ||||
\(619\) | −581158. | −1.51675 | −0.758373 | − | 0.651821i | \(-0.774005\pi\) | ||||
−0.758373 | + | 0.651821i | \(0.774005\pi\) | |||||||
\(620\) | − | 100737.i | − | 0.262064i | ||||||
\(621\) | −142560. | − | 231852.i | −0.369670 | − | 0.601212i | ||||
\(622\) | 373344. | 0.965002 | ||||||||
\(623\) | 203850.i | 0.525213i | ||||||||
\(624\) | −9600.00 | + | 27152.9i | −0.0246548 | + | 0.0697344i | ||||
\(625\) | −66431.0 | −0.170063 | ||||||||
\(626\) | 62446.0i | 0.159351i | ||||||||
\(627\) | 360864. | + | 127585.i | 0.917928 | + | 0.324536i | ||||
\(628\) | −392080. | −0.994158 | ||||||||
\(629\) | − | 381634.i | − | 0.964597i | ||||||
\(630\) | 78624.0 | + | 63537.8i | 0.198095 | + | 0.160085i | ||||
\(631\) | 232346. | 0.583548 | 0.291774 | − | 0.956487i | \(-0.405755\pi\) | ||||
0.291774 | + | 0.956487i | \(0.405755\pi\) | |||||||
\(632\) | 222156.i | 0.556191i | ||||||||
\(633\) | −45294.0 | + | 128111.i | −0.113040 | + | 0.319726i | ||||
\(634\) | −333456. | −0.829583 | ||||||||
\(635\) | − | 140550.i | − | 0.348565i | ||||||
\(636\) | 31104.0 | + | 10996.9i | 0.0768957 | + | 0.0271867i | ||||
\(637\) | −86250.0 | −0.212559 | ||||||||
\(638\) | 484679.i | 1.19073i | ||||||||
\(639\) | −181440. | + | 224521.i | −0.444356 | + | 0.549863i | ||||
\(640\) | 24576.0 | 0.0600000 | ||||||||
\(641\) | 653570.i | 1.59066i | 0.606179 | + | 0.795328i | \(0.292701\pi\) | ||||
−0.606179 | + | 0.795328i | \(0.707299\pi\) | |||||||
\(642\) | −92016.0 | + | 260261.i | −0.223251 | + | 0.631449i | ||||
\(643\) | −424678. | −1.02716 | −0.513580 | − | 0.858042i | \(-0.671681\pi\) | ||||
−0.513580 | + | 0.858042i | \(0.671681\pi\) | |||||||
\(644\) | 77657.3i | 0.187245i | ||||||||
\(645\) | −37728.0 | − | 13338.9i | −0.0906869 | − | 0.0320626i | ||||
\(646\) | 206208. | 0.494129 | ||||||||
\(647\) | − | 427964.i | − | 1.02235i | −0.859478 | − | 0.511173i | \(-0.829211\pi\) | ||
0.859478 | − | 0.511173i | \(-0.170789\pi\) | |||||||
\(648\) | −145152. | + | 31158.0i | −0.345679 | + | 0.0742026i | ||||
\(649\) | −215712. | −0.512136 | ||||||||
\(650\) | − | 47659.0i | − | 0.112802i | ||||||
\(651\) | 57876.0 | − | 163698.i | 0.136564 | − | 0.386262i | ||||
\(652\) | 343856. | 0.808875 | ||||||||
\(653\) | − | 720621.i | − | 1.68998i | −0.534785 | − | 0.844988i | \(-0.679607\pi\) | ||
0.534785 | − | 0.844988i | \(-0.320393\pi\) | |||||||
\(654\) | −114000. | − | 40305.1i | −0.266532 | − | 0.0942333i | ||||
\(655\) | −91872.0 | −0.214141 | ||||||||
\(656\) | − | 154228.i | − | 0.358391i | ||||||
\(657\) | −18270.0 | − | 14764.4i | −0.0423261 | − | 0.0342046i | ||||
\(658\) | 124800. | 0.288246 | ||||||||
\(659\) | 40135.4i | 0.0924180i | 0.998932 | + | 0.0462090i | \(0.0147140\pi\) | ||||
−0.998932 | + | 0.0462090i | \(0.985286\pi\) | |||||||
\(660\) | 48384.0 | − | 136851.i | 0.111074 | − | 0.314166i | ||||
\(661\) | −358510. | −0.820537 | −0.410269 | − | 0.911965i | \(-0.634565\pi\) | ||||
−0.410269 | + | 0.911965i | \(0.634565\pi\) | |||||||
\(662\) | − | 474163.i | − | 1.08196i | ||||||
\(663\) | 86400.0 | + | 30547.0i | 0.196556 | + | 0.0694931i | ||||
\(664\) | 160896. | 0.364930 | ||||||||
\(665\) | 157962.i | 0.357198i | ||||||||
\(666\) | −269856. | + | 333930.i | −0.608392 | + | 0.752847i | ||||
\(667\) | 538560. | 1.21055 | ||||||||
\(668\) | 353259.i | 0.791663i | ||||||||
\(669\) | −176334. | + | 498748.i | −0.393989 | + | 1.11437i | ||||
\(670\) | 215328. | 0.479679 | ||||||||
\(671\) | − | 176528.i | − | 0.392074i | ||||||
\(672\) | 39936.0 | + | 14119.5i | 0.0884354 | + | 0.0312666i | ||||
\(673\) | 582434. | 1.28593 | 0.642964 | − | 0.765896i | \(-0.277705\pi\) | ||||
0.642964 | + | 0.765896i | \(0.277705\pi\) | |||||||
\(674\) | − | 460790.i | − | 1.01434i | ||||||
\(675\) | 209277. | − | 128679.i | 0.459319 | − | 0.282424i | ||||
\(676\) | 208488. | 0.456234 | ||||||||
\(677\) | − | 37352.2i | − | 0.0814965i | −0.999169 | − | 0.0407482i | \(-0.987026\pi\) | ||
0.999169 | − | 0.0407482i | \(-0.0129742\pi\) | |||||||
\(678\) | −27072.0 | + | 76571.2i | −0.0588926 | + | 0.166574i | ||||
\(679\) | −12428.0 | −0.0269564 | ||||||||
\(680\) | − | 78200.4i | − | 0.169118i | ||||||
\(681\) | 577008. | + | 204003.i | 1.24419 | + | 0.439889i | ||||
\(682\) | −249312. | −0.536012 | ||||||||
\(683\) | − | 161848.i | − | 0.346950i | −0.984838 | − | 0.173475i | \(-0.944500\pi\) | ||
0.984838 | − | 0.173475i | \(-0.0554995\pi\) | |||||||
\(684\) | −180432. | − | 145811.i | −0.385657 | − | 0.311658i | ||||
\(685\) | 307008. | 0.654287 | ||||||||
\(686\) | 303422.i | 0.644762i | ||||||||
\(687\) | −85686.0 | + | 242357.i | −0.181550 | + | 0.513501i | ||||
\(688\) | −16768.0 | −0.0354246 | ||||||||
\(689\) | 22910.3i | 0.0482605i | ||||||||
\(690\) | −152064. | − | 53762.7i | −0.319395 | − | 0.112923i | ||||
\(691\) | −630118. | −1.31967 | −0.659836 | − | 0.751410i | \(-0.729374\pi\) | ||||
−0.659836 | + | 0.751410i | \(0.729374\pi\) | |||||||
\(692\) | − | 179345.i | − | 0.374522i | ||||||
\(693\) | 157248. | − | 194584.i | 0.327430 | − | 0.405174i | ||||
\(694\) | −373872. | −0.776254 | ||||||||
\(695\) | 393819.i | 0.815318i | ||||||||
\(696\) | 97920.0 | − | 276960.i | 0.202140 | − | 0.571739i | ||||
\(697\) | −490752. | −1.01017 | ||||||||
\(698\) | − | 150568.i | − | 0.309046i | ||||||
\(699\) | 190944. | + | 67508.9i | 0.390797 | + | 0.138168i | ||||
\(700\) | −70096.0 | −0.143053 | ||||||||
\(701\) | 457747.i | 0.931514i | 0.884913 | + | 0.465757i | \(0.154218\pi\) | ||||
−0.884913 | + | 0.465757i | \(0.845782\pi\) | |||||||
\(702\) | −54000.0 | − | 87822.7i | −0.109577 | − | 0.178210i | ||||
\(703\) | −670892. | −1.35751 | ||||||||
\(704\) | − | 60822.5i | − | 0.122721i | ||||||
\(705\) | −86400.0 | + | 244376.i | −0.173834 | + | 0.491678i | ||||
\(706\) | 409728. | 0.822027 | ||||||||
\(707\) | − | 356959.i | − | 0.714133i | ||||||
\(708\) | 123264. | + | 43580.4i | 0.245906 | + | 0.0869410i | ||||
\(709\) | 274130. | 0.545336 | 0.272668 | − | 0.962108i | \(-0.412094\pi\) | ||||
0.272668 | + | 0.962108i | \(0.412094\pi\) | |||||||
\(710\) | 171063.i | 0.339344i | ||||||||
\(711\) | −618534. | − | 499851.i | −1.22356 | − | 0.988784i | ||||
\(712\) | −177408. | −0.349956 | ||||||||
\(713\) | 277027.i | 0.544934i | ||||||||
\(714\) | 44928.0 | − | 127076.i | 0.0881294 | − | 0.249267i | ||||
\(715\) | 100800. | 0.197173 | ||||||||
\(716\) | 244783.i | 0.477481i | ||||||||
\(717\) | 10944.0 | + | 3869.29i | 0.0212881 | + | 0.00752650i | ||||
\(718\) | −36576.0 | −0.0709492 | ||||||||
\(719\) | 304045.i | 0.588138i | 0.955784 | + | 0.294069i | \(0.0950096\pi\) | ||||
−0.955784 | + | 0.294069i | \(0.904990\pi\) | |||||||
\(720\) | −55296.0 | + | 68425.3i | −0.106667 | + | 0.131993i | ||||
\(721\) | 55588.0 | 0.106933 | ||||||||
\(722\) | 6100.92i | 0.0117036i | ||||||||
\(723\) | 183738. | − | 519690.i | 0.351498 | − | 0.994185i | ||||
\(724\) | 104816. | 0.199963 | ||||||||
\(725\) | 486122.i | 0.924845i | ||||||||
\(726\) | 12696.0 | + | 4488.71i | 0.0240876 | + | 0.00851626i | ||||
\(727\) | 364058. | 0.688814 | 0.344407 | − | 0.938821i | \(-0.388080\pi\) | ||||
0.344407 | + | 0.938821i | \(0.388080\pi\) | |||||||
\(728\) | 29415.6i | 0.0555029i | ||||||||
\(729\) | 239841. | − | 474242.i | 0.451303 | − | 0.892371i | ||||
\(730\) | −13920.0 | −0.0261212 | ||||||||
\(731\) | 53355.4i | 0.0998491i | ||||||||
\(732\) | −35664.0 | + | 100873.i | −0.0665592 | + | 0.188258i | ||||
\(733\) | −301198. | −0.560588 | −0.280294 | − | 0.959914i | \(-0.590432\pi\) | ||||
−0.280294 | + | 0.959914i | \(0.590432\pi\) | |||||||
\(734\) | 125373.i | 0.232708i | ||||||||
\(735\) | −248400. | − | 87822.7i | −0.459808 | − | 0.162567i | ||||
\(736\) | −67584.0 | −0.124764 | ||||||||
\(737\) | − | 532910.i | − | 0.981112i | ||||||
\(738\) | 429408. | + | 347014.i | 0.788420 | + | 0.637139i | ||||
\(739\) | 872570. | 1.59776 | 0.798880 | − | 0.601491i | \(-0.205426\pi\) | ||||
0.798880 | + | 0.601491i | \(0.205426\pi\) | |||||||
\(740\) | 254423.i | 0.464614i | ||||||||
\(741\) | 53700.0 | − | 151887.i | 0.0977998 | − | 0.276620i | ||||
\(742\) | 33696.0 | 0.0612027 | ||||||||
\(743\) | − | 874222.i | − | 1.58359i | −0.610784 | − | 0.791797i | \(-0.709146\pi\) | ||
0.610784 | − | 0.791797i | \(-0.290854\pi\) | |||||||
\(744\) | 142464. | + | 50368.6i | 0.257371 | + | 0.0909943i | ||||
\(745\) | 189792. | 0.341952 | ||||||||
\(746\) | 171736.i | 0.308592i | ||||||||
\(747\) | −362016. | + | 447972.i | −0.648764 | + | 0.802804i | ||||
\(748\) | −193536. | −0.345906 | ||||||||
\(749\) | 281949.i | 0.502582i | ||||||||
\(750\) | 138528. | − | 391816.i | 0.246272 | − | 0.696562i | ||||
\(751\) | 916250. | 1.62455 | 0.812277 | − | 0.583272i | \(-0.198228\pi\) | ||||
0.812277 | + | 0.583272i | \(0.198228\pi\) | |||||||
\(752\) | 108612.i | 0.192062i | ||||||||
\(753\) | −384048. | − | 135781.i | −0.677323 | − | 0.239470i | ||||
\(754\) | 204000. | 0.358829 | ||||||||
\(755\) | − | 244817.i | − | 0.429485i | ||||||
\(756\) | −129168. | + | 79422.2i | −0.226002 | + | 0.138963i | ||||
\(757\) | −691630. | −1.20693 | −0.603465 | − | 0.797390i | \(-0.706214\pi\) | ||||
−0.603465 | + | 0.797390i | \(0.706214\pi\) | |||||||
\(758\) | − | 86148.2i | − | 0.149937i | ||||||
\(759\) | −133056. | + | 376339.i | −0.230968 | + | 0.653275i | ||||
\(760\) | −137472. | −0.238006 | ||||||||
\(761\) | 90249.5i | 0.155839i | 0.996960 | + | 0.0779193i | \(0.0248277\pi\) | ||||
−0.996960 | + | 0.0779193i | \(0.975172\pi\) | |||||||
\(762\) | 198768. | + | 70275.1i | 0.342323 | + | 0.121030i | ||||
\(763\) | −123500. | −0.212138 | ||||||||
\(764\) | − | 562608.i | − | 0.963872i | ||||||
\(765\) | 217728. | + | 175951.i | 0.372042 | + | 0.300655i | ||||
\(766\) | −666624. | −1.13612 | ||||||||
\(767\) | 90792.5i | 0.154333i | ||||||||
\(768\) | −12288.0 | + | 34755.7i | −0.0208333 | + | 0.0589256i | ||||
\(769\) | −515326. | −0.871424 | −0.435712 | − | 0.900086i | \(-0.643503\pi\) | ||||
−0.435712 | + | 0.900086i | \(0.643503\pi\) | |||||||
\(770\) | − | 148255.i | − | 0.250050i | ||||||
\(771\) | −723456. | − | 255780.i | −1.21704 | − | 0.430287i | ||||
\(772\) | −144400. | −0.242288 | ||||||||
\(773\) | 100449.i | 0.168107i | 0.996461 | + | 0.0840535i | \(0.0267867\pi\) | ||||
−0.996461 | + | 0.0840535i | \(0.973213\pi\) | |||||||
\(774\) | 37728.0 | − | 46686.0i | 0.0629770 | − | 0.0779300i | ||||
\(775\) | −250054. | −0.416323 | ||||||||
\(776\) | − | 10815.9i | − | 0.0179614i | ||||||
\(777\) | −146172. | + | 413437.i | −0.242115 | + | 0.684805i | ||||
\(778\) | 425424. | 0.702850 | ||||||||
\(779\) | 862716.i | 1.42165i | ||||||||
\(780\) | −57600.0 | − | 20364.7i | −0.0946746 | − | 0.0334725i | ||||
\(781\) | 423360. | 0.694077 | ||||||||
\(782\) | 215051.i | 0.351664i | ||||||||
\(783\) | 550800. | + | 895791.i | 0.898401 | + | 1.46111i | ||||
\(784\) | −110400. | −0.179613 | ||||||||
\(785\) | − | 831727.i | − | 1.34971i | ||||||
\(786\) | 45936.0 | − | 129927.i | 0.0743546 | − | 0.210307i | ||||
\(787\) | −107878. | −0.174174 | −0.0870870 | − | 0.996201i | \(-0.527756\pi\) | ||||
−0.0870870 | + | 0.996201i | \(0.527756\pi\) | |||||||
\(788\) | − | 210571.i | − | 0.339114i | ||||||
\(789\) | 719136. | + | 254253.i | 1.15520 | + | 0.408425i | ||||
\(790\) | −471264. | −0.755110 | ||||||||
\(791\) | 82952.1i | 0.132579i | ||||||||
\(792\) | 169344. | + | 136851.i | 0.269972 | + | 0.218171i | ||||
\(793\) | −74300.0 | −0.118152 | ||||||||
\(794\) | − | 488351.i | − | 0.774624i | ||||||
\(795\) | −23328.0 | + | 65981.5i | −0.0369099 | + | 0.104397i | ||||
\(796\) | 297776. | 0.469963 | ||||||||
\(797\) | − | 489482.i | − | 0.770584i | −0.922795 | − | 0.385292i | \(-0.874101\pi\) | ||
0.922795 | − | 0.385292i | \(-0.125899\pi\) | |||||||
\(798\) | −223392. | − | 78981.0i | −0.350802 | − | 0.124027i | ||||
\(799\) | 345600. | 0.541353 | ||||||||
\(800\) | − | 61003.5i | − | 0.0953180i | ||||||
\(801\) | 399168. | − | 493945.i | 0.622144 | − | 0.769864i | ||||
\(802\) | −473664. | −0.736413 | ||||||||
\(803\) | 34450.2i | 0.0534270i | ||||||||
\(804\) | −107664. | + | 304520.i | −0.166555 | + | 0.471089i | ||||
\(805\) | −164736. | −0.254212 | ||||||||
\(806\) | 104935.i | 0.161528i | ||||||||
\(807\) | −364176. | − | 128756.i | −0.559196 | − | 0.197706i | ||||
\(808\) | 310656. | 0.475836 | ||||||||
\(809\) | − | 1.04074e6i | − | 1.59017i | −0.606497 | − | 0.795086i | \(-0.707426\pi\) | ||
0.606497 | − | 0.795086i | \(-0.292574\pi\) | |||||||
\(810\) | −66096.0 | − | 307914.i | −0.100741 | − | 0.469309i | ||||
\(811\) | 611066. | 0.929066 | 0.464533 | − | 0.885556i | \(-0.346222\pi\) | ||||
0.464533 | + | 0.885556i | \(0.346222\pi\) | |||||||
\(812\) | − | 300040.i | − | 0.455058i | ||||||
\(813\) | 82290.0 | − | 232751.i | 0.124499 | − | 0.352136i | ||||
\(814\) | 629664. | 0.950299 | ||||||||
\(815\) | 729429.i | 1.09817i | ||||||||
\(816\) | 110592. | + | 39100.2i | 0.166090 | + | 0.0587217i | ||||
\(817\) | 93796.0 | 0.140521 | ||||||||
\(818\) | 425480.i | 0.635877i | ||||||||
\(819\) | −81900.0 | − | 66185.2i | −0.122100 | − | 0.0986718i | ||||
\(820\) | 327168. | 0.486568 | ||||||||
\(821\) | 345300.i | 0.512283i | 0.966639 | + | 0.256142i | \(0.0824514\pi\) | ||||
−0.966639 | + | 0.256142i | \(0.917549\pi\) | |||||||
\(822\) | −153504. | + | 434175.i | −0.227183 | + | 0.642571i | ||||
\(823\) | −178150. | −0.263018 | −0.131509 | − | 0.991315i | \(-0.541982\pi\) | ||||
−0.131509 | + | 0.991315i | \(0.541982\pi\) | |||||||
\(824\) | 48377.4i | 0.0712506i | ||||||||
\(825\) | −339696. | − | 120101.i | −0.499094 | − | 0.176456i | ||||
\(826\) | 133536. | 0.195721 | ||||||||
\(827\) | 1.13844e6i | 1.66455i | 0.554361 | + | 0.832277i | \(0.312963\pi\) | ||||
−0.554361 | + | 0.832277i | \(0.687037\pi\) | |||||||
\(828\) | 152064. | − | 188170.i | 0.221802 | − | 0.274466i | ||||
\(829\) | 100082. | 0.145629 | 0.0728143 | − | 0.997346i | \(-0.476802\pi\) | ||||
0.0728143 | + | 0.997346i | \(0.476802\pi\) | |||||||
\(830\) | 341312.i | 0.495445i | ||||||||
\(831\) | 281802. | − | 797056.i | 0.408077 | − | 1.15422i | ||||
\(832\) | −25600.0 | −0.0369822 | ||||||||
\(833\) | 351291.i | 0.506263i | ||||||||
\(834\) | −556944. | − | 196909.i | −0.800718 | − | 0.283096i | ||||
\(835\) | −749376. | −1.07480 | ||||||||
\(836\) | 340226.i | 0.486805i | ||||||||
\(837\) | −460782. | + | 283324.i | −0.657725 | + | 0.404419i | ||||
\(838\) | 504240. | 0.718041 | ||||||||
\(839\) | − | 1.13964e6i | − | 1.61899i | −0.587127 | − | 0.809495i | \(-0.699741\pi\) | ||
0.587127 | − | 0.809495i | \(-0.300259\pi\) | |||||||
\(840\) | −29952.0 | + | 84717.0i | −0.0424490 | + | 0.120064i | ||||
\(841\) | −1.37352e6 | −1.94197 | ||||||||
\(842\) | 611070.i | 0.861920i | ||||||||
\(843\) | 207648. | + | 73414.7i | 0.292195 | + | 0.103306i | ||||
\(844\) | −120784. | −0.169560 | ||||||||
\(845\) | 442270.i | 0.619404i | ||||||||
\(846\) | −302400. | − | 244376.i | −0.422514 | − | 0.341443i | ||||
\(847\) | 13754.0 | 0.0191718 | ||||||||
\(848\) | 29325.1i | 0.0407801i | ||||||||
\(849\) | 197490. | − | 558586.i | 0.273987 | − | 0.774952i | ||||
\(850\) | −194112. | −0.268667 | ||||||||
\(851\) | − | 699662.i | − | 0.966116i | ||||||
\(852\) | −241920. | − | 85531.6i | −0.333267 | − | 0.117828i | ||||
\(853\) | 172754. | 0.237427 | 0.118713 | − | 0.992929i | \(-0.462123\pi\) | ||||
0.118713 | + | 0.992929i | \(0.462123\pi\) | |||||||
\(854\) | 109279.i | 0.149838i | ||||||||
\(855\) | 309312. | − | 382754.i | 0.423121 | − | 0.523585i | ||||
\(856\) | −245376. | −0.334876 | ||||||||
\(857\) | − | 299802.i | − | 0.408200i | −0.978950 | − | 0.204100i | \(-0.934573\pi\) | ||
0.978950 | − | 0.204100i | \(-0.0654267\pi\) | |||||||
\(858\) | −50400.0 | + | 142553.i | −0.0684630 | + | 0.193643i | ||||
\(859\) | 8186.00 | 0.0110939 | 0.00554696 | − | 0.999985i | \(-0.498234\pi\) | ||||
0.00554696 | + | 0.999985i | \(0.498234\pi\) | |||||||
\(860\) | − | 35570.3i | − | 0.0480940i | ||||||
\(861\) | 531648. | + | 187966.i | 0.717163 | + | 0.253555i | ||||
\(862\) | 15552.0 | 0.0209301 | ||||||||
\(863\) | 387336.i | 0.520076i | 0.965598 | + | 0.260038i | \(0.0837350\pi\) | ||||
−0.965598 | + | 0.260038i | \(0.916265\pi\) | |||||||
\(864\) | −69120.0 | − | 112413.i | −0.0925926 | − | 0.150588i | ||||
\(865\) | 380448. | 0.508467 | ||||||||
\(866\) | − | 305476.i | − | 0.407325i | ||||||
\(867\) | −126147. | + | 356798.i | −0.167818 | + | 0.474661i | ||||
\(868\) | 154336. | 0.204846 | ||||||||
\(869\) | 1.16632e6i | 1.54446i | ||||||||
\(870\) | 587520. | + | 207720.i | 0.776219 | + | 0.274435i | ||||
\(871\) | −224300. | −0.295660 | ||||||||
\(872\) | − | 107480.i | − | 0.141350i | ||||||
\(873\) | 30114.0 | + | 24335.8i | 0.0395130 | + | 0.0319313i | ||||
\(874\) | 378048. | 0.494908 | ||||||||
\(875\) | − | 424468.i | − | 0.554407i | ||||||
\(876\) | 6960.00 | − | 19685.9i | 0.00906987 | − | 0.0256535i | ||||
\(877\) | 245426. | 0.319096 | 0.159548 | − | 0.987190i | \(-0.448996\pi\) | ||||
0.159548 | + | 0.987190i | \(0.448996\pi\) | |||||||
\(878\) | − | 1.01179e6i | − | 1.31251i | ||||||
\(879\) | 763920. | + | 270087.i | 0.988713 | + | 0.349563i | ||||
\(880\) | 129024. | 0.166612 | ||||||||
\(881\) | 607071.i | 0.782146i | 0.920360 | + | 0.391073i | \(0.127896\pi\) | ||||
−0.920360 | + | 0.391073i | \(0.872104\pi\) | |||||||
\(882\) | 248400. | − | 307379.i | 0.319311 | − | 0.395128i | ||||
\(883\) | 759962. | 0.974699 | 0.487349 | − | 0.873207i | \(-0.337964\pi\) | ||||
0.487349 | + | 0.873207i | \(0.337964\pi\) | |||||||
\(884\) | 81458.7i | 0.104240i | ||||||||
\(885\) | −92448.0 | + | 261482.i | −0.118035 | + | 0.333854i | ||||
\(886\) | 243984. | 0.310809 | ||||||||
\(887\) | 5736.05i | 0.00729064i | 0.999993 | + | 0.00364532i | \(0.00116034\pi\) | ||||
−0.999993 | + | 0.00364532i | \(0.998840\pi\) | |||||||
\(888\) | −359808. | − | 127211.i | −0.456294 | − | 0.161324i | ||||
\(889\) | 215332. | 0.272461 | ||||||||
\(890\) | − | 376339.i | − | 0.475116i | ||||||
\(891\) | −762048. | + | 163579.i | −0.959902 | + | 0.206050i | ||||
\(892\) | −470224. | −0.590983 | ||||||||
\(893\) | − | 607546.i | − | 0.761862i | ||||||
\(894\) | −94896.0 | + | 268406.i | −0.118733 | + | 0.335829i | ||||
\(895\) | −519264. | −0.648249 | ||||||||
\(896\) | 37652.0i | 0.0468999i | ||||||||
\(897\) | 158400. | + | 56002.9i | 0.196866 | + | 0.0696026i | ||||
\(898\) | −852480. | −1.05714 | ||||||||
\(899\) | − | 1.07033e6i | − | 1.32434i | ||||||
\(900\) | 169848. | + | 137258.i | 0.209689 | + | 0.169454i | ||||
\(901\) | 93312.0 | 0.114944 | ||||||||
\(902\) | − | 809699.i | − | 0.995201i | ||||||
\(903\) | 20436.0 | − | 57801.7i | 0.0250623 | − | 0.0708868i | ||||
\(904\) | −72192.0 | −0.0883389 | ||||||||
\(905\) | 222348.i | 0.271479i | ||||||||
\(906\) | 346224. | + | 122409.i | 0.421794 | + | 0.149127i | ||||
\(907\) | −138502. | −0.168361 | −0.0841805 | − | 0.996451i | \(-0.526827\pi\) | ||||
−0.0841805 | + | 0.996451i | \(0.526827\pi\) | |||||||
\(908\) | 544008.i | 0.659833i | ||||||||
\(909\) | −698976. | + | 864939.i | −0.845930 | + | 1.04679i | ||||
\(910\) | −62400.0 | −0.0753532 | ||||||||
\(911\) | 266845.i | 0.321531i | 0.986993 | + | 0.160765i | \(0.0513962\pi\) | ||||
−0.986993 | + | 0.160765i | \(0.948604\pi\) | |||||||
\(912\) | 68736.0 | − | 194415.i | 0.0826408 | − | 0.233744i | ||||
\(913\) | 844704. | 1.01336 | ||||||||
\(914\) | 1.12874e6i | 1.35114i | ||||||||
\(915\) | −213984. | − | 75654.8i | −0.255587 | − | 0.0903637i | ||||
\(916\) | −228496. | −0.272325 | ||||||||
\(917\) | − | 140754.i | − | 0.167387i | ||||||
\(918\) | −357696. | + | 219938.i | −0.424452 | + | 0.260985i | ||||
\(919\) | −1.44266e6 | −1.70818 | −0.854090 | − | 0.520125i | \(-0.825885\pi\) | ||||
−0.854090 | + | 0.520125i | \(0.825885\pi\) | |||||||
\(920\) | − | 143367.i | − | 0.169385i | ||||||
\(921\) | −201966. | + | 571246.i | −0.238100 | + | 0.673448i | ||||
\(922\) | −108240. | −0.127329 | ||||||||
\(923\) | − | 178191.i | − | 0.209162i | ||||||
\(924\) | 209664. | + | 74127.4i | 0.245573 | + | 0.0868230i | ||||
\(925\) | 631538. | 0.738101 | ||||||||
\(926\) | − | 408453.i | − | 0.476344i | ||||||
\(927\) | −134694. | − | 108849.i | −0.156743 | − | 0.126668i | ||||
\(928\) | 261120. | 0.303210 | ||||||||
\(929\) | − | 511696.i | − | 0.592899i | −0.955048 | − | 0.296450i | \(-0.904197\pi\) | ||
0.955048 | − | 0.296450i | \(-0.0958027\pi\) | |||||||
\(930\) | −106848. | + | 302212.i | −0.123538 | + | 0.349418i | ||||
\(931\) | 617550. | 0.712480 | ||||||||
\(932\) | 180024.i | 0.207252i | ||||||||
\(933\) | −1.12003e6 | − | 395991.i | −1.28667 | − | 0.454907i | ||||
\(934\) | 419184. | 0.480519 | ||||||||
\(935\) | − | 410552.i | − | 0.469618i | ||||||
\(936\) | 57600.0 | − | 71276.4i | 0.0657462 | − | 0.0813568i | ||||
\(937\) | 868610. | 0.989340 | 0.494670 | − | 0.869081i | \(-0.335289\pi\) | ||||
0.494670 | + | 0.869081i | \(0.335289\pi\) | |||||||
\(938\) | 329896.i | 0.374949i | ||||||||
\(939\) | 66234.0 | − | 187338.i | 0.0751190 | − | 0.212469i | ||||
\(940\) | −230400. | −0.260751 | ||||||||
\(941\) | − | 101942.i | − | 0.115126i | −0.998342 | − | 0.0575632i | \(-0.981667\pi\) | ||
0.998342 | − | 0.0575632i | \(-0.0183331\pi\) | |||||||
\(942\) | 1.17624e6 | + | 415864.i | 1.32554 | + | 0.468651i | ||||
\(943\) | −899712. | −1.01177 | ||||||||
\(944\) | 116214.i | 0.130412i | ||||||||
\(945\) | −168480. | − | 274007.i | −0.188662 | − | 0.306830i | ||||
\(946\) | −88032.0 | −0.0983690 | ||||||||
\(947\) | − | 233159.i | − | 0.259987i | −0.991515 | − | 0.129993i | \(-0.958504\pi\) | ||
0.991515 | − | 0.129993i | \(-0.0414956\pi\) | |||||||
\(948\) | 235632. | − | 666468.i | 0.262191 | − | 0.741588i | ||||
\(949\) | 14500.0 | 0.0161004 | ||||||||
\(950\) | 341238.i | 0.378104i | ||||||||
\(951\) | 1.00037e6 | + | 353683.i | 1.10611 | + | 0.391069i | ||||
\(952\) | 119808. | 0.132194 | ||||||||
\(953\) | 927916.i | 1.02170i | 0.859670 | + | 0.510850i | \(0.170669\pi\) | ||||
−0.859670 | + | 0.510850i | \(0.829331\pi\) | |||||||
\(954\) | −81648.0 | − | 65981.5i | −0.0897116 | − | 0.0724980i | ||||
\(955\) | 1.19347e6 | 1.30860 | ||||||||
\(956\) | 10318.1i | 0.0112897i | ||||||||
\(957\) | 514080. | − | 1.45404e6i | 0.561315 | − | 1.58764i | ||||
\(958\) | −864384. | −0.941837 | ||||||||
\(959\) | 470356.i | 0.511434i | ||||||||
\(960\) | −73728.0 | − | 26066.8i | −0.0800000 | − | 0.0282843i | ||||
\(961\) | −372957. | −0.403842 | ||||||||
\(962\) | − | 265024.i | − | 0.286375i | ||||||
\(963\) | 552096. | − | 683184.i | 0.595336 | − | 0.736691i | ||||
\(964\) | 489968. | 0.527246 | ||||||||
\(965\) | − | 306319.i | − | 0.328942i | ||||||
\(966\) | 82368.0 | − | 232972.i | 0.0882682 | − | 0.249660i | ||||
\(967\) | 150746. | 0.161210 | 0.0806052 | − | 0.996746i | \(-0.474315\pi\) | ||||
0.0806052 | + | 0.996746i | \(0.474315\pi\) | |||||||
\(968\) | 11969.9i | 0.0127744i | ||||||||
\(969\) | −618624. | − | 218717.i | −0.658839 | − | 0.232935i | ||||
\(970\) | 22944.0 | 0.0243852 | ||||||||
\(971\) | 508150.i | 0.538956i | 0.963007 | + | 0.269478i | \(0.0868511\pi\) | ||||
−0.963007 | + | 0.269478i | \(0.913149\pi\) | |||||||
\(972\) | 468504. | + | 60483.1i | 0.495885 | + | 0.0640179i | ||||
\(973\) | −603356. | −0.637306 | ||||||||
\(974\) | 556561.i | 0.586671i | ||||||||
\(975\) | −50550.0 | + | 142977.i | −0.0531755 | + | 0.150403i | ||||
\(976\) | −95104.0 | −0.0998388 | ||||||||
\(977\) | 214576.i | 0.224798i | 0.993663 | + | 0.112399i | \(0.0358534\pi\) | ||||
−0.993663 | + | 0.112399i | \(0.964147\pi\) | |||||||
\(978\) | −1.03157e6 | − | 364714.i | −1.07850 | − | 0.381307i | ||||
\(979\) | −931392. | −0.971778 | ||||||||
\(980\) | − | 234194.i | − | 0.243850i | ||||||
\(981\) | 299250. | + | 241831.i | 0.310954 | + | 0.251289i | ||||
\(982\) | −470064. | −0.487454 | ||||||||
\(983\) | 1.34831e6i | 1.39535i | 0.716414 | + | 0.697675i | \(0.245782\pi\) | ||||
−0.716414 | + | 0.697675i | \(0.754218\pi\) | |||||||
\(984\) | −163584. | + | 462685.i | −0.168947 | + | 0.477854i | ||||
\(985\) | 446688. | 0.460396 | ||||||||
\(986\) | − | 830879.i | − | 0.854641i | ||||||
\(987\) | −374400. | − | 132370.i | −0.384328 | − | 0.135880i | ||||
\(988\) | 143200. | 0.146700 | ||||||||
\(989\) | 97818.3i | 0.100006i | ||||||||
\(990\) | −290304. | + | 359233.i | −0.296198 | + | 0.366527i | ||||
\(991\) | −879910. | −0.895965 | −0.447982 | − | 0.894042i | \(-0.647857\pi\) | ||||
−0.447982 | + | 0.894042i | \(0.647857\pi\) | |||||||
\(992\) | 134316.i | 0.136491i | ||||||||
\(993\) | −502926. | + | 1.42249e6i | −0.510042 | + | 1.44262i | ||||
\(994\) | −262080. | −0.265253 | ||||||||
\(995\) | 631678.i | 0.638043i | ||||||||
\(996\) | −482688. | − | 170656.i | −0.486573 | − | 0.172029i | ||||
\(997\) | 935378. | 0.941016 | 0.470508 | − | 0.882396i | \(-0.344071\pi\) | ||||
0.470508 | + | 0.882396i | \(0.344071\pi\) | |||||||
\(998\) | − | 534714.i | − | 0.536859i | ||||||
\(999\) | 1.16375e6 | − | 715564.i | 1.16609 | − | 0.716997i |
(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 | 6.5.b.a.5.1 | ✓ | 2 | |
3.2 | odd | 2 | inner | 6.5.b.a.5.2 | yes | 2 | |
4.3 | odd | 2 | 48.5.e.b.17.1 | 2 | |||
5.2 | odd | 4 | 150.5.b.a.149.4 | 4 | |||
5.3 | odd | 4 | 150.5.b.a.149.1 | 4 | |||
5.4 | even | 2 | 150.5.d.a.101.2 | 2 | |||
7.6 | odd | 2 | 294.5.b.a.197.1 | 2 | |||
8.3 | odd | 2 | 192.5.e.c.65.2 | 2 | |||
8.5 | even | 2 | 192.5.e.d.65.1 | 2 | |||
9.2 | odd | 6 | 162.5.d.a.53.2 | 4 | |||
9.4 | even | 3 | 162.5.d.a.107.2 | 4 | |||
9.5 | odd | 6 | 162.5.d.a.107.1 | 4 | |||
9.7 | even | 3 | 162.5.d.a.53.1 | 4 | |||
12.11 | even | 2 | 48.5.e.b.17.2 | 2 | |||
15.2 | even | 4 | 150.5.b.a.149.2 | 4 | |||
15.8 | even | 4 | 150.5.b.a.149.3 | 4 | |||
15.14 | odd | 2 | 150.5.d.a.101.1 | 2 | |||
21.20 | even | 2 | 294.5.b.a.197.2 | 2 | |||
24.5 | odd | 2 | 192.5.e.d.65.2 | 2 | |||
24.11 | even | 2 | 192.5.e.c.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.5.b.a.5.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6.5.b.a.5.2 | yes | 2 | 3.2 | odd | 2 | inner | |
48.5.e.b.17.1 | 2 | 4.3 | odd | 2 | |||
48.5.e.b.17.2 | 2 | 12.11 | even | 2 | |||
150.5.b.a.149.1 | 4 | 5.3 | odd | 4 | |||
150.5.b.a.149.2 | 4 | 15.2 | even | 4 | |||
150.5.b.a.149.3 | 4 | 15.8 | even | 4 | |||
150.5.b.a.149.4 | 4 | 5.2 | odd | 4 | |||
150.5.d.a.101.1 | 2 | 15.14 | odd | 2 | |||
150.5.d.a.101.2 | 2 | 5.4 | even | 2 | |||
162.5.d.a.53.1 | 4 | 9.7 | even | 3 | |||
162.5.d.a.53.2 | 4 | 9.2 | odd | 6 | |||
162.5.d.a.107.1 | 4 | 9.5 | odd | 6 | |||
162.5.d.a.107.2 | 4 | 9.4 | even | 3 | |||
192.5.e.c.65.1 | 2 | 24.11 | even | 2 | |||
192.5.e.c.65.2 | 2 | 8.3 | odd | 2 | |||
192.5.e.d.65.1 | 2 | 8.5 | even | 2 | |||
192.5.e.d.65.2 | 2 | 24.5 | odd | 2 | |||
294.5.b.a.197.1 | 2 | 7.6 | odd | 2 | |||
294.5.b.a.197.2 | 2 | 21.20 | even | 2 |