Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,5,Mod(21,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, 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("22.21");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.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: | \(2.27413918784\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{553})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 271x^{2} + 272x + 19602 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.3 | ||
Root | \(-11.2580 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.21 |
Dual form | 22.5.b.a.21.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(-1\) |
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 | ||||||||
\(3\) | −11.2580 | −1.25089 | −0.625443 | − | 0.780270i | \(-0.715082\pi\) | ||||
−0.625443 | + | 0.780270i | \(0.715082\pi\) | |||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | −19.2580 | −0.770319 | −0.385160 | − | 0.922850i | \(-0.625854\pi\) | ||||
−0.385160 | + | 0.922850i | \(0.625854\pi\) | |||||||
\(6\) | − | 31.8424i | − | 0.884510i | ||||||
\(7\) | 33.9411i | 0.692676i | 0.938110 | + | 0.346338i | \(0.112575\pi\) | ||||
−0.938110 | + | 0.346338i | \(0.887425\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | 45.7420 | 0.564716 | ||||||||
\(10\) | − | 54.4698i | − | 0.544698i | ||||||
\(11\) | 2.03190 | + | 120.983i | 0.0167926 | + | 0.999859i | ||||
\(12\) | 90.0638 | 0.625443 | ||||||||
\(13\) | 72.2602i | 0.427575i | 0.976880 | + | 0.213788i | \(0.0685801\pi\) | ||||
−0.976880 | + | 0.213788i | \(0.931420\pi\) | |||||||
\(14\) | −96.0000 | −0.489796 | ||||||||
\(15\) | 216.806 | 0.963581 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − | 517.873i | − | 1.79195i | −0.444107 | − | 0.895974i | \(-0.646479\pi\) | ||
0.444107 | − | 0.895974i | \(-0.353521\pi\) | |||||||
\(18\) | 129.378i | 0.399315i | ||||||||
\(19\) | 411.672i | 1.14036i | 0.821518 | + | 0.570182i | \(0.193127\pi\) | ||||
−0.821518 | + | 0.570182i | \(0.806873\pi\) | |||||||
\(20\) | 154.064 | 0.385160 | ||||||||
\(21\) | − | 382.108i | − | 0.866459i | ||||||
\(22\) | −342.191 | + | 5.74709i | −0.707007 | + | 0.0118742i | ||||
\(23\) | −967.641 | −1.82919 | −0.914594 | − | 0.404373i | \(-0.867490\pi\) | ||||
−0.914594 | + | 0.404373i | \(0.867490\pi\) | |||||||
\(24\) | 254.739i | 0.442255i | ||||||||
\(25\) | −254.130 | −0.406609 | ||||||||
\(26\) | −204.383 | −0.302341 | ||||||||
\(27\) | 396.933 | 0.544490 | ||||||||
\(28\) | − | 271.529i | − | 0.346338i | ||||||
\(29\) | 640.503i | 0.761597i | 0.924658 | + | 0.380799i | \(0.124351\pi\) | ||||
−0.924658 | + | 0.380799i | \(0.875649\pi\) | |||||||
\(30\) | 613.219i | 0.681355i | ||||||||
\(31\) | 716.487 | 0.745564 | 0.372782 | − | 0.927919i | \(-0.378404\pi\) | ||||
0.372782 | + | 0.927919i | \(0.378404\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | −22.8751 | − | 1362.02i | −0.0210056 | − | 1.25071i | ||||
\(34\) | 1464.77 | 1.26710 | ||||||||
\(35\) | − | 653.637i | − | 0.533582i | ||||||
\(36\) | −365.936 | −0.282358 | ||||||||
\(37\) | 1209.64 | 0.883590 | 0.441795 | − | 0.897116i | \(-0.354342\pi\) | ||||
0.441795 | + | 0.897116i | \(0.354342\pi\) | |||||||
\(38\) | −1164.38 | −0.806359 | ||||||||
\(39\) | − | 813.504i | − | 0.534848i | ||||||
\(40\) | 435.758i | 0.272349i | ||||||||
\(41\) | 966.781i | 0.575122i | 0.957762 | + | 0.287561i | \(0.0928445\pi\) | ||||
−0.957762 | + | 0.287561i | \(0.907156\pi\) | |||||||
\(42\) | 1080.77 | 0.612679 | ||||||||
\(43\) | 2720.75i | 1.47147i | 0.677269 | + | 0.735736i | \(0.263163\pi\) | ||||
−0.677269 | + | 0.735736i | \(0.736837\pi\) | |||||||
\(44\) | −16.2552 | − | 967.864i | −0.00839630 | − | 0.499929i | ||||
\(45\) | −880.899 | −0.435012 | ||||||||
\(46\) | − | 2736.90i | − | 1.29343i | ||||||
\(47\) | −177.085 | −0.0801651 | −0.0400826 | − | 0.999196i | \(-0.512762\pi\) | ||||
−0.0400826 | + | 0.999196i | \(0.512762\pi\) | |||||||
\(48\) | −720.510 | −0.312722 | ||||||||
\(49\) | 1249.00 | 0.520200 | ||||||||
\(50\) | − | 718.789i | − | 0.287516i | ||||||
\(51\) | 5830.20i | 2.24152i | ||||||||
\(52\) | − | 578.082i | − | 0.213788i | ||||||
\(53\) | −4023.28 | −1.43228 | −0.716140 | − | 0.697956i | \(-0.754093\pi\) | ||||
−0.716140 | + | 0.697956i | \(0.754093\pi\) | |||||||
\(54\) | 1122.70i | 0.385013i | ||||||||
\(55\) | −39.1304 | − | 2329.89i | −0.0129357 | − | 0.770210i | ||||
\(56\) | 768.000 | 0.244898 | ||||||||
\(57\) | − | 4634.59i | − | 1.42647i | ||||||
\(58\) | −1811.62 | −0.538531 | ||||||||
\(59\) | −1988.02 | −0.571107 | −0.285554 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285554 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(60\) | −1734.45 | −0.481791 | ||||||||
\(61\) | − | 2396.69i | − | 0.644097i | −0.946723 | − | 0.322049i | \(-0.895629\pi\) | ||
0.946723 | − | 0.322049i | \(-0.104371\pi\) | |||||||
\(62\) | 2026.53i | 0.527193i | ||||||||
\(63\) | 1552.54i | 0.391165i | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − | 1391.59i | − | 0.329370i | ||||||
\(66\) | 3852.38 | − | 64.7006i | 0.884385 | − | 0.0148532i | ||||
\(67\) | −2007.13 | −0.447122 | −0.223561 | − | 0.974690i | \(-0.571768\pi\) | ||||
−0.223561 | + | 0.974690i | \(0.571768\pi\) | |||||||
\(68\) | 4142.98i | 0.895974i | ||||||||
\(69\) | 10893.7 | 2.28811 | ||||||||
\(70\) | 1848.77 | 0.377299 | ||||||||
\(71\) | 4255.04 | 0.844086 | 0.422043 | − | 0.906576i | \(-0.361313\pi\) | ||||
0.422043 | + | 0.906576i | \(0.361313\pi\) | |||||||
\(72\) | − | 1035.02i | − | 0.199657i | ||||||
\(73\) | 1288.68i | 0.241824i | 0.992663 | + | 0.120912i | \(0.0385819\pi\) | ||||
−0.992663 | + | 0.120912i | \(0.961418\pi\) | |||||||
\(74\) | 3421.37i | 0.624793i | ||||||||
\(75\) | 2860.99 | 0.508621 | ||||||||
\(76\) | − | 3293.37i | − | 0.570182i | ||||||
\(77\) | −4106.30 | + | 68.9651i | −0.692578 | + | 0.0116318i | ||||
\(78\) | 2300.94 | 0.378195 | ||||||||
\(79\) | 1480.23i | 0.237178i | 0.992943 | + | 0.118589i | \(0.0378371\pi\) | ||||
−0.992943 | + | 0.118589i | \(0.962163\pi\) | |||||||
\(80\) | −1232.51 | −0.192580 | ||||||||
\(81\) | −8173.77 | −1.24581 | ||||||||
\(82\) | −2734.47 | −0.406673 | ||||||||
\(83\) | − | 10124.2i | − | 1.46963i | −0.678270 | − | 0.734813i | \(-0.737270\pi\) | ||
0.678270 | − | 0.734813i | \(-0.262730\pi\) | |||||||
\(84\) | 3056.87i | 0.433229i | ||||||||
\(85\) | 9973.18i | 1.38037i | ||||||||
\(86\) | −7695.45 | −1.04049 | ||||||||
\(87\) | − | 7210.77i | − | 0.952672i | ||||||
\(88\) | 2737.53 | − | 45.9767i | 0.353504 | − | 0.00593708i | ||||
\(89\) | 5133.72 | 0.648115 | 0.324058 | − | 0.946037i | \(-0.394953\pi\) | ||||
0.324058 | + | 0.946037i | \(0.394953\pi\) | |||||||
\(90\) | − | 2491.56i | − | 0.307600i | ||||||
\(91\) | −2452.59 | −0.296171 | ||||||||
\(92\) | 7741.13 | 0.914594 | ||||||||
\(93\) | −8066.19 | −0.932615 | ||||||||
\(94\) | − | 500.871i | − | 0.0566853i | ||||||
\(95\) | − | 7927.96i | − | 0.878444i | ||||||
\(96\) | − | 2037.91i | − | 0.221128i | ||||||
\(97\) | 2239.34 | 0.238000 | 0.119000 | − | 0.992894i | \(-0.462031\pi\) | ||||
0.119000 | + | 0.992894i | \(0.462031\pi\) | |||||||
\(98\) | 3532.71i | 0.367837i | ||||||||
\(99\) | 92.9434 | + | 5534.00i | 0.00948305 | + | 0.564637i | ||||
\(100\) | 2033.04 | 0.203304 | ||||||||
\(101\) | 15580.0i | 1.52730i | 0.645629 | + | 0.763651i | \(0.276595\pi\) | ||||
−0.645629 | + | 0.763651i | \(0.723405\pi\) | |||||||
\(102\) | −16490.3 | −1.58500 | ||||||||
\(103\) | −9119.47 | −0.859597 | −0.429799 | − | 0.902925i | \(-0.641415\pi\) | ||||
−0.429799 | + | 0.902925i | \(0.641415\pi\) | |||||||
\(104\) | 1635.06 | 0.151171 | ||||||||
\(105\) | 7358.63i | 0.667450i | ||||||||
\(106\) | − | 11379.5i | − | 1.01278i | ||||||
\(107\) | − | 11204.9i | − | 0.978684i | −0.872092 | − | 0.489342i | \(-0.837237\pi\) | ||
0.872092 | − | 0.489342i | \(-0.162763\pi\) | |||||||
\(108\) | −3175.47 | −0.272245 | ||||||||
\(109\) | 10286.3i | 0.865776i | 0.901448 | + | 0.432888i | \(0.142505\pi\) | ||||
−0.901448 | + | 0.432888i | \(0.857495\pi\) | |||||||
\(110\) | 6589.91 | − | 110.677i | 0.544621 | − | 0.00914689i | ||||
\(111\) | −13618.0 | −1.10527 | ||||||||
\(112\) | 2172.23i | 0.173169i | ||||||||
\(113\) | 17026.9 | 1.33345 | 0.666727 | − | 0.745302i | \(-0.267695\pi\) | ||||
0.666727 | + | 0.745302i | \(0.267695\pi\) | |||||||
\(114\) | 13108.6 | 1.00866 | ||||||||
\(115\) | 18634.8 | 1.40906 | ||||||||
\(116\) | − | 5124.03i | − | 0.380799i | ||||||
\(117\) | 3305.33i | 0.241459i | ||||||||
\(118\) | − | 5622.98i | − | 0.403834i | ||||||
\(119\) | 17577.2 | 1.24124 | ||||||||
\(120\) | − | 4905.76i | − | 0.340677i | ||||||
\(121\) | −14632.7 | + | 491.651i | −0.999436 | + | 0.0335805i | ||||
\(122\) | 6778.85 | 0.455446 | ||||||||
\(123\) | − | 10884.0i | − | 0.719413i | ||||||
\(124\) | −5731.89 | −0.372782 | ||||||||
\(125\) | 16930.3 | 1.08354 | ||||||||
\(126\) | −4391.23 | −0.276596 | ||||||||
\(127\) | 27813.0i | 1.72441i | 0.506558 | + | 0.862206i | \(0.330918\pi\) | ||||
−0.506558 | + | 0.862206i | \(0.669082\pi\) | |||||||
\(128\) | − | 1448.15i | − | 0.0883883i | ||||||
\(129\) | − | 30630.1i | − | 1.84064i | ||||||
\(130\) | 3936.00 | 0.232899 | ||||||||
\(131\) | 6310.74i | 0.367738i | 0.982951 | + | 0.183869i | \(0.0588621\pi\) | ||||
−0.982951 | + | 0.183869i | \(0.941138\pi\) | |||||||
\(132\) | 183.001 | + | 10896.2i | 0.0105028 | + | 0.625355i | ||||
\(133\) | −13972.6 | −0.789903 | ||||||||
\(134\) | − | 5677.02i | − | 0.316163i | ||||||
\(135\) | −7644.13 | −0.419431 | ||||||||
\(136\) | −11718.1 | −0.633549 | ||||||||
\(137\) | −14207.1 | −0.756944 | −0.378472 | − | 0.925613i | \(-0.623550\pi\) | ||||
−0.378472 | + | 0.925613i | \(0.623550\pi\) | |||||||
\(138\) | 30812.0i | 1.61794i | ||||||||
\(139\) | − | 27772.6i | − | 1.43743i | −0.695306 | − | 0.718714i | \(-0.744731\pi\) | ||
0.695306 | − | 0.718714i | \(-0.255269\pi\) | |||||||
\(140\) | 5229.10i | 0.266791i | ||||||||
\(141\) | 1993.62 | 0.100277 | ||||||||
\(142\) | 12035.1i | 0.596859i | ||||||||
\(143\) | −8742.26 | + | 146.826i | −0.427515 | + | 0.00718010i | ||||
\(144\) | 2927.49 | 0.141179 | ||||||||
\(145\) | − | 12334.8i | − | 0.586673i | ||||||
\(146\) | −3644.94 | −0.170995 | ||||||||
\(147\) | −14061.2 | −0.650711 | ||||||||
\(148\) | −9677.08 | −0.441795 | ||||||||
\(149\) | 23436.8i | 1.05567i | 0.849348 | + | 0.527833i | \(0.176995\pi\) | ||||
−0.849348 | + | 0.527833i | \(0.823005\pi\) | |||||||
\(150\) | 8092.11i | 0.359649i | ||||||||
\(151\) | 6556.14i | 0.287538i | 0.989611 | + | 0.143769i | \(0.0459222\pi\) | ||||
−0.989611 | + | 0.143769i | \(0.954078\pi\) | |||||||
\(152\) | 9315.06 | 0.403180 | ||||||||
\(153\) | − | 23688.6i | − | 1.01194i | ||||||
\(154\) | −195.063 | − | 11614.4i | −0.00822494 | − | 0.489727i | ||||
\(155\) | −13798.1 | −0.574322 | ||||||||
\(156\) | 6508.03i | 0.267424i | ||||||||
\(157\) | 2315.17 | 0.0939254 | 0.0469627 | − | 0.998897i | \(-0.485046\pi\) | ||||
0.0469627 | + | 0.998897i | \(0.485046\pi\) | |||||||
\(158\) | −4186.72 | −0.167710 | ||||||||
\(159\) | 45293.9 | 1.79162 | ||||||||
\(160\) | − | 3486.07i | − | 0.136174i | ||||||
\(161\) | − | 32842.8i | − | 1.26704i | ||||||
\(162\) | − | 23118.9i | − | 0.880922i | ||||||
\(163\) | −21728.0 | −0.817796 | −0.408898 | − | 0.912580i | \(-0.634087\pi\) | ||||
−0.408898 | + | 0.912580i | \(0.634087\pi\) | |||||||
\(164\) | − | 7734.25i | − | 0.287561i | ||||||
\(165\) | 440.529 | + | 26229.8i | 0.0161810 | + | 0.963446i | ||||
\(166\) | 28635.7 | 1.03918 | ||||||||
\(167\) | 26470.6i | 0.949143i | 0.880217 | + | 0.474571i | \(0.157397\pi\) | ||||
−0.880217 | + | 0.474571i | \(0.842603\pi\) | |||||||
\(168\) | −8646.13 | −0.306339 | ||||||||
\(169\) | 23339.5 | 0.817179 | ||||||||
\(170\) | −28208.4 | −0.976070 | ||||||||
\(171\) | 18830.7i | 0.643982i | ||||||||
\(172\) | − | 21766.0i | − | 0.735736i | ||||||
\(173\) | − | 6136.89i | − | 0.205048i | −0.994731 | − | 0.102524i | \(-0.967308\pi\) | ||
0.994731 | − | 0.102524i | \(-0.0326919\pi\) | |||||||
\(174\) | 20395.1 | 0.673641 | ||||||||
\(175\) | − | 8625.47i | − | 0.281648i | ||||||
\(176\) | 130.042 | + | 7742.91i | 0.00419815 | + | 0.249965i | ||||
\(177\) | 22381.1 | 0.714390 | ||||||||
\(178\) | 14520.4i | 0.458287i | ||||||||
\(179\) | −8164.31 | −0.254808 | −0.127404 | − | 0.991851i | \(-0.540665\pi\) | ||||
−0.127404 | + | 0.991851i | \(0.540665\pi\) | |||||||
\(180\) | 7047.19 | 0.217506 | ||||||||
\(181\) | −10130.6 | −0.309228 | −0.154614 | − | 0.987975i | \(-0.549413\pi\) | ||||
−0.154614 | + | 0.987975i | \(0.549413\pi\) | |||||||
\(182\) | − | 6936.98i | − | 0.209425i | ||||||
\(183\) | 26981.8i | 0.805692i | ||||||||
\(184\) | 21895.2i | 0.646716i | ||||||||
\(185\) | −23295.1 | −0.680647 | ||||||||
\(186\) | − | 22814.6i | − | 0.659459i | ||||||
\(187\) | 62653.8 | − | 1052.27i | 1.79170 | − | 0.0300915i | ||||
\(188\) | 1416.68 | 0.0400826 | ||||||||
\(189\) | 13472.4i | 0.377155i | ||||||||
\(190\) | 22423.7 | 0.621154 | ||||||||
\(191\) | 13853.6 | 0.379749 | 0.189875 | − | 0.981808i | \(-0.439192\pi\) | ||||
0.189875 | + | 0.981808i | \(0.439192\pi\) | |||||||
\(192\) | 5764.08 | 0.156361 | ||||||||
\(193\) | − | 55752.8i | − | 1.49676i | −0.663270 | − | 0.748380i | \(-0.730832\pi\) | ||
0.663270 | − | 0.748380i | \(-0.269168\pi\) | |||||||
\(194\) | 6333.81i | 0.168291i | ||||||||
\(195\) | 15666.4i | 0.412004i | ||||||||
\(196\) | −9992.00 | −0.260100 | ||||||||
\(197\) | 38577.9i | 0.994046i | 0.867737 | + | 0.497023i | \(0.165574\pi\) | ||||
−0.867737 | + | 0.497023i | \(0.834426\pi\) | |||||||
\(198\) | −15652.5 | + | 262.884i | −0.399258 | + | 0.00670553i | ||||
\(199\) | −43741.2 | −1.10455 | −0.552275 | − | 0.833662i | \(-0.686240\pi\) | ||||
−0.552275 | + | 0.833662i | \(0.686240\pi\) | |||||||
\(200\) | 5750.31i | 0.143758i | ||||||||
\(201\) | 22596.2 | 0.559299 | ||||||||
\(202\) | −44066.9 | −1.07997 | ||||||||
\(203\) | −21739.4 | −0.527540 | ||||||||
\(204\) | − | 46641.6i | − | 1.12076i | ||||||
\(205\) | − | 18618.2i | − | 0.443028i | ||||||
\(206\) | − | 25793.7i | − | 0.607827i | ||||||
\(207\) | −44261.8 | −1.03297 | ||||||||
\(208\) | 4624.66i | 0.106894i | ||||||||
\(209\) | −49805.2 | + | 836.477i | −1.14020 | + | 0.0191497i | ||||
\(210\) | −20813.4 | −0.471958 | ||||||||
\(211\) | 40460.8i | 0.908803i | 0.890797 | + | 0.454402i | \(0.150147\pi\) | ||||
−0.890797 | + | 0.454402i | \(0.849853\pi\) | |||||||
\(212\) | 32186.2 | 0.716140 | ||||||||
\(213\) | −47903.1 | −1.05586 | ||||||||
\(214\) | 31692.4 | 0.692034 | ||||||||
\(215\) | − | 52396.2i | − | 1.13350i | ||||||
\(216\) | − | 8981.58i | − | 0.192506i | ||||||
\(217\) | 24318.4i | 0.516434i | ||||||||
\(218\) | −29094.0 | −0.612196 | ||||||||
\(219\) | − | 14507.9i | − | 0.302494i | ||||||
\(220\) | 313.043 | + | 18639.1i | 0.00646783 | + | 0.385105i | ||||
\(221\) | 37421.6 | 0.766193 | ||||||||
\(222\) | − | 38517.6i | − | 0.781545i | ||||||
\(223\) | 12067.6 | 0.242667 | 0.121334 | − | 0.992612i | \(-0.461283\pi\) | ||||
0.121334 | + | 0.992612i | \(0.461283\pi\) | |||||||
\(224\) | −6144.00 | −0.122449 | ||||||||
\(225\) | −11624.4 | −0.229619 | ||||||||
\(226\) | 48159.3i | 0.942894i | ||||||||
\(227\) | 38616.4i | 0.749411i | 0.927144 | + | 0.374705i | \(0.122256\pi\) | ||||
−0.927144 | + | 0.374705i | \(0.877744\pi\) | |||||||
\(228\) | 37076.7i | 0.713233i | ||||||||
\(229\) | 74080.9 | 1.41265 | 0.706326 | − | 0.707887i | \(-0.250351\pi\) | ||||
0.706326 | + | 0.707887i | \(0.250351\pi\) | |||||||
\(230\) | 52707.2i | 0.996355i | ||||||||
\(231\) | 46228.6 | − | 776.408i | 0.866337 | − | 0.0145501i | ||||
\(232\) | 14492.9 | 0.269265 | ||||||||
\(233\) | − | 51719.5i | − | 0.952670i | −0.879264 | − | 0.476335i | \(-0.841965\pi\) | ||
0.879264 | − | 0.476335i | \(-0.158035\pi\) | |||||||
\(234\) | −9348.89 | −0.170737 | ||||||||
\(235\) | 3410.29 | 0.0617527 | ||||||||
\(236\) | 15904.2 | 0.285554 | ||||||||
\(237\) | − | 16664.4i | − | 0.296683i | ||||||
\(238\) | 49715.8i | 0.877689i | ||||||||
\(239\) | − | 16911.3i | − | 0.296062i | −0.988983 | − | 0.148031i | \(-0.952706\pi\) | ||
0.988983 | − | 0.148031i | \(-0.0472935\pi\) | |||||||
\(240\) | 13875.6 | 0.240895 | ||||||||
\(241\) | − | 59892.0i | − | 1.03118i | −0.856835 | − | 0.515590i | \(-0.827573\pi\) | ||
0.856835 | − | 0.515590i | \(-0.172427\pi\) | |||||||
\(242\) | −1390.60 | − | 41387.6i | −0.0237450 | − | 0.706708i | ||||
\(243\) | 59868.5 | 1.01388 | ||||||||
\(244\) | 19173.5i | 0.322049i | ||||||||
\(245\) | −24053.2 | −0.400720 | ||||||||
\(246\) | 30784.6 | 0.508702 | ||||||||
\(247\) | −29747.5 | −0.487592 | ||||||||
\(248\) | − | 16212.2i | − | 0.263597i | ||||||
\(249\) | 113979.i | 1.83833i | ||||||||
\(250\) | 47886.0i | 0.766177i | ||||||||
\(251\) | −19186.2 | −0.304538 | −0.152269 | − | 0.988339i | \(-0.548658\pi\) | ||||
−0.152269 | + | 0.988339i | \(0.548658\pi\) | |||||||
\(252\) | − | 12420.3i | − | 0.195583i | ||||||
\(253\) | −1966.15 | − | 117068.i | −0.0307168 | − | 1.82893i | ||||
\(254\) | −78667.1 | −1.21934 | ||||||||
\(255\) | − | 112278.i | − | 1.72669i | ||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 30625.1 | 0.463672 | 0.231836 | − | 0.972755i | \(-0.425527\pi\) | ||||
0.231836 | + | 0.972755i | \(0.425527\pi\) | |||||||
\(258\) | 86635.1 | 1.30153 | ||||||||
\(259\) | 41056.4i | 0.612042i | ||||||||
\(260\) | 11132.7i | 0.164685i | ||||||||
\(261\) | 29297.9i | 0.430086i | ||||||||
\(262\) | −17849.5 | −0.260030 | ||||||||
\(263\) | 73815.1i | 1.06717i | 0.845746 | + | 0.533585i | \(0.179156\pi\) | ||||
−0.845746 | + | 0.533585i | \(0.820844\pi\) | |||||||
\(264\) | −30819.1 | + | 517.605i | −0.442193 | + | 0.00742661i | ||||
\(265\) | 77480.2 | 1.10331 | ||||||||
\(266\) | − | 39520.5i | − | 0.558546i | ||||||
\(267\) | −57795.3 | −0.810718 | ||||||||
\(268\) | 16057.0 | 0.223561 | ||||||||
\(269\) | −87292.0 | −1.20634 | −0.603170 | − | 0.797612i | \(-0.706096\pi\) | ||||
−0.603170 | + | 0.797612i | \(0.706096\pi\) | |||||||
\(270\) | − | 21620.9i | − | 0.296583i | ||||||
\(271\) | 4518.78i | 0.0615294i | 0.999527 | + | 0.0307647i | \(0.00979425\pi\) | ||||
−0.999527 | + | 0.0307647i | \(0.990206\pi\) | |||||||
\(272\) | − | 33143.9i | − | 0.447987i | ||||||
\(273\) | 27611.2 | 0.370477 | ||||||||
\(274\) | − | 40183.7i | − | 0.535240i | ||||||
\(275\) | −516.369 | − | 30745.4i | −0.00682801 | − | 0.406551i | ||||
\(276\) | −87149.4 | −1.14405 | ||||||||
\(277\) | − | 4641.04i | − | 0.0604861i | −0.999543 | − | 0.0302431i | \(-0.990372\pi\) | ||
0.999543 | − | 0.0302431i | \(-0.00962813\pi\) | |||||||
\(278\) | 78552.6 | 1.01642 | ||||||||
\(279\) | 32773.6 | 0.421032 | ||||||||
\(280\) | −14790.1 | −0.188650 | ||||||||
\(281\) | 58621.1i | 0.742406i | 0.928552 | + | 0.371203i | \(0.121055\pi\) | ||||
−0.928552 | + | 0.371203i | \(0.878945\pi\) | |||||||
\(282\) | 5638.80i | 0.0709069i | ||||||||
\(283\) | 90326.0i | 1.12782i | 0.825836 | + | 0.563910i | \(0.190704\pi\) | ||||
−0.825836 | + | 0.563910i | \(0.809296\pi\) | |||||||
\(284\) | −34040.3 | −0.422043 | ||||||||
\(285\) | 89252.8i | 1.09883i | ||||||||
\(286\) | −415.286 | − | 24726.8i | −0.00507710 | − | 0.302299i | ||||
\(287\) | −32813.6 | −0.398373 | ||||||||
\(288\) | 8280.19i | 0.0998287i | ||||||||
\(289\) | −184671. | −2.21108 | ||||||||
\(290\) | 34888.1 | 0.414840 | ||||||||
\(291\) | −25210.4 | −0.297710 | ||||||||
\(292\) | − | 10309.4i | − | 0.120912i | ||||||
\(293\) | 77687.4i | 0.904931i | 0.891782 | + | 0.452465i | \(0.149455\pi\) | ||||
−0.891782 | + | 0.452465i | \(0.850545\pi\) | |||||||
\(294\) | − | 39771.1i | − | 0.460122i | ||||||
\(295\) | 38285.3 | 0.439935 | ||||||||
\(296\) | − | 27370.9i | − | 0.312396i | ||||||
\(297\) | 806.531 | + | 48022.2i | 0.00914341 | + | 0.544414i | ||||
\(298\) | −66289.4 | −0.746469 | ||||||||
\(299\) | − | 69922.0i | − | 0.782116i | ||||||
\(300\) | −22887.9 | −0.254311 | ||||||||
\(301\) | −92345.3 | −1.01925 | ||||||||
\(302\) | −18543.6 | −0.203320 | ||||||||
\(303\) | − | 175399.i | − | 1.91048i | ||||||
\(304\) | 26347.0i | 0.285091i | ||||||||
\(305\) | 46155.3i | 0.496160i | ||||||||
\(306\) | 67001.3 | 0.715551 | ||||||||
\(307\) | − | 60487.2i | − | 0.641781i | −0.947116 | − | 0.320890i | \(-0.896018\pi\) | ||
0.947116 | − | 0.320890i | \(-0.103982\pi\) | |||||||
\(308\) | 32850.4 | − | 551.721i | 0.346289 | − | 0.00581591i | ||||
\(309\) | 102667. | 1.07526 | ||||||||
\(310\) | − | 39026.9i | − | 0.406107i | ||||||
\(311\) | 32106.2 | 0.331947 | 0.165973 | − | 0.986130i | \(-0.446923\pi\) | ||||
0.165973 | + | 0.986130i | \(0.446923\pi\) | |||||||
\(312\) | −18407.5 | −0.189097 | ||||||||
\(313\) | 111475. | 1.13786 | 0.568932 | − | 0.822384i | \(-0.307357\pi\) | ||||
0.568932 | + | 0.822384i | \(0.307357\pi\) | |||||||
\(314\) | 6548.28i | 0.0664153i | ||||||||
\(315\) | − | 29898.7i | − | 0.301322i | ||||||
\(316\) | − | 11841.8i | − | 0.118589i | ||||||
\(317\) | 139267. | 1.38589 | 0.692945 | − | 0.720990i | \(-0.256313\pi\) | ||||
0.692945 | + | 0.720990i | \(0.256313\pi\) | |||||||
\(318\) | 128111.i | 1.26687i | ||||||||
\(319\) | −77490.0 | + | 1301.44i | −0.761490 | + | 0.0127892i | ||||
\(320\) | 9860.08 | 0.0962899 | ||||||||
\(321\) | 126145.i | 1.22422i | ||||||||
\(322\) | 92893.5 | 0.895929 | ||||||||
\(323\) | 213194. | 2.04347 | ||||||||
\(324\) | 65390.2 | 0.622906 | ||||||||
\(325\) | − | 18363.5i | − | 0.173856i | ||||||
\(326\) | − | 61456.1i | − | 0.578269i | ||||||
\(327\) | − | 115803.i | − | 1.08299i | ||||||
\(328\) | 21875.7 | 0.203336 | ||||||||
\(329\) | − | 6010.46i | − | 0.0555285i | ||||||
\(330\) | −74189.1 | + | 1246.00i | −0.681259 | + | 0.0114417i | ||||
\(331\) | −60223.2 | −0.549677 | −0.274839 | − | 0.961490i | \(-0.588624\pi\) | ||||
−0.274839 | + | 0.961490i | \(0.588624\pi\) | |||||||
\(332\) | 80994.0i | 0.734813i | ||||||||
\(333\) | 55331.2 | 0.498978 | ||||||||
\(334\) | −74870.3 | −0.671145 | ||||||||
\(335\) | 38653.3 | 0.344427 | ||||||||
\(336\) | − | 24454.9i | − | 0.216615i | ||||||
\(337\) | − | 85639.9i | − | 0.754078i | −0.926197 | − | 0.377039i | \(-0.876942\pi\) | ||
0.926197 | − | 0.377039i | \(-0.123058\pi\) | |||||||
\(338\) | 66014.0i | 0.577833i | ||||||||
\(339\) | −191688. | −1.66800 | ||||||||
\(340\) | − | 79785.5i | − | 0.690186i | ||||||
\(341\) | 1455.83 | + | 86682.7i | 0.0125200 | + | 0.745459i | ||||
\(342\) | −53261.2 | −0.455364 | ||||||||
\(343\) | 123885.i | 1.05301i | ||||||||
\(344\) | 61563.6 | 0.520244 | ||||||||
\(345\) | −209790. | −1.76257 | ||||||||
\(346\) | 17357.8 | 0.144991 | ||||||||
\(347\) | − | 99499.7i | − | 0.826348i | −0.910652 | − | 0.413174i | \(-0.864420\pi\) | ||
0.910652 | − | 0.413174i | \(-0.135580\pi\) | |||||||
\(348\) | 57686.2i | 0.476336i | ||||||||
\(349\) | 47515.3i | 0.390106i | 0.980793 | + | 0.195053i | \(0.0624878\pi\) | ||||
−0.980793 | + | 0.195053i | \(0.937512\pi\) | |||||||
\(350\) | 24396.5 | 0.199155 | ||||||||
\(351\) | 28682.5i | 0.232811i | ||||||||
\(352\) | −21900.3 | + | 367.814i | −0.176752 | + | 0.00296854i | ||||
\(353\) | 167482. | 1.34406 | 0.672030 | − | 0.740524i | \(-0.265423\pi\) | ||||
0.672030 | + | 0.740524i | \(0.265423\pi\) | |||||||
\(354\) | 63303.4i | 0.505150i | ||||||||
\(355\) | −81943.4 | −0.650216 | ||||||||
\(356\) | −41069.8 | −0.324058 | ||||||||
\(357\) | −197884. | −1.55265 | ||||||||
\(358\) | − | 23092.2i | − | 0.180177i | ||||||
\(359\) | 5063.91i | 0.0392914i | 0.999807 | + | 0.0196457i | \(0.00625382\pi\) | ||||
−0.999807 | + | 0.0196457i | \(0.993746\pi\) | |||||||
\(360\) | 19932.5i | 0.153800i | ||||||||
\(361\) | −39152.4 | −0.300431 | ||||||||
\(362\) | − | 28653.7i | − | 0.218657i | ||||||
\(363\) | 164735. | − | 5535.00i | 1.25018 | − | 0.0420053i | ||||
\(364\) | 19620.8 | 0.148086 | ||||||||
\(365\) | − | 24817.4i | − | 0.186282i | ||||||
\(366\) | −76316.1 | −0.569711 | ||||||||
\(367\) | 264021. | 1.96023 | 0.980115 | − | 0.198429i | \(-0.0635841\pi\) | ||||
0.980115 | + | 0.198429i | \(0.0635841\pi\) | |||||||
\(368\) | −61929.0 | −0.457297 | ||||||||
\(369\) | 44222.5i | 0.324781i | ||||||||
\(370\) | − | 65888.6i | − | 0.481290i | ||||||
\(371\) | − | 136555.i | − | 0.992106i | ||||||
\(372\) | 64529.5 | 0.466308 | ||||||||
\(373\) | − | 270510.i | − | 1.94431i | −0.234339 | − | 0.972155i | \(-0.575293\pi\) | ||
0.234339 | − | 0.972155i | \(-0.424707\pi\) | |||||||
\(374\) | 2976.26 | + | 177212.i | 0.0212779 | + | 1.26692i | ||||
\(375\) | −190601. | −1.35538 | ||||||||
\(376\) | 4006.97i | 0.0283426i | ||||||||
\(377\) | −46282.9 | −0.325640 | ||||||||
\(378\) | −38105.6 | −0.266689 | ||||||||
\(379\) | −38850.0 | −0.270466 | −0.135233 | − | 0.990814i | \(-0.543178\pi\) | ||||
−0.135233 | + | 0.990814i | \(0.543178\pi\) | |||||||
\(380\) | 63423.7i | 0.439222i | ||||||||
\(381\) | − | 313118.i | − | 2.15704i | ||||||
\(382\) | 39184.0i | 0.268523i | ||||||||
\(383\) | −243070. | −1.65704 | −0.828522 | − | 0.559956i | \(-0.810818\pi\) | ||||
−0.828522 | + | 0.559956i | \(0.810818\pi\) | |||||||
\(384\) | 16303.3i | 0.110564i | ||||||||
\(385\) | 79079.0 | − | 1328.13i | 0.533506 | − | 0.00896022i | ||||
\(386\) | 157693. | 1.05837 | ||||||||
\(387\) | 124453.i | 0.830964i | ||||||||
\(388\) | −17914.7 | −0.119000 | ||||||||
\(389\) | −142544. | −0.941995 | −0.470998 | − | 0.882135i | \(-0.656106\pi\) | ||||
−0.470998 | + | 0.882135i | \(0.656106\pi\) | |||||||
\(390\) | −44311.4 | −0.291331 | ||||||||
\(391\) | 501115.i | 3.27781i | ||||||||
\(392\) | − | 28261.6i | − | 0.183918i | ||||||
\(393\) | − | 71046.2i | − | 0.459998i | ||||||
\(394\) | −109115. | −0.702897 | ||||||||
\(395\) | − | 28506.2i | − | 0.182703i | ||||||
\(396\) | −743.547 | − | 44272.0i | −0.00474153 | − | 0.282318i | ||||
\(397\) | −73860.0 | −0.468628 | −0.234314 | − | 0.972161i | \(-0.575284\pi\) | ||||
−0.234314 | + | 0.972161i | \(0.575284\pi\) | |||||||
\(398\) | − | 123719.i | − | 0.781034i | ||||||
\(399\) | 157303. | 0.988079 | ||||||||
\(400\) | −16264.3 | −0.101652 | ||||||||
\(401\) | 225776. | 1.40407 | 0.702034 | − | 0.712143i | \(-0.252275\pi\) | ||||
0.702034 | + | 0.712143i | \(0.252275\pi\) | |||||||
\(402\) | 63911.8i | 0.395484i | ||||||||
\(403\) | 51773.5i | 0.318785i | ||||||||
\(404\) | − | 124640.i | − | 0.763651i | ||||||
\(405\) | 157410. | 0.959673 | ||||||||
\(406\) | − | 61488.3i | − | 0.373027i | ||||||
\(407\) | 2457.86 | + | 146345.i | 0.0148378 | + | 0.883466i | ||||
\(408\) | 131922. | 0.792498 | ||||||||
\(409\) | − | 97972.9i | − | 0.585679i | −0.956162 | − | 0.292839i | \(-0.905400\pi\) | ||
0.956162 | − | 0.292839i | \(-0.0946001\pi\) | |||||||
\(410\) | 52660.3 | 0.313268 | ||||||||
\(411\) | 159943. | 0.946851 | ||||||||
\(412\) | 72955.7 | 0.429799 | ||||||||
\(413\) | − | 67475.8i | − | 0.395592i | ||||||
\(414\) | − | 125191.i | − | 0.730422i | ||||||
\(415\) | 194973.i | 1.13208i | ||||||||
\(416\) | −13080.5 | −0.0755854 | ||||||||
\(417\) | 312663.i | 1.79806i | ||||||||
\(418\) | −2365.91 | − | 140870.i | −0.0135409 | − | 0.806246i | ||||
\(419\) | −64572.5 | −0.367807 | −0.183903 | − | 0.982944i | \(-0.558873\pi\) | ||||
−0.183903 | + | 0.982944i | \(0.558873\pi\) | |||||||
\(420\) | − | 58869.1i | − | 0.333725i | ||||||
\(421\) | 203272. | 1.14687 | 0.573434 | − | 0.819252i | \(-0.305611\pi\) | ||||
0.573434 | + | 0.819252i | \(0.305611\pi\) | |||||||
\(422\) | −114441. | −0.642621 | ||||||||
\(423\) | −8100.21 | −0.0452706 | ||||||||
\(424\) | 91036.3i | 0.506388i | ||||||||
\(425\) | 131607.i | 0.728621i | ||||||||
\(426\) | − | 135491.i | − | 0.746603i | ||||||
\(427\) | 81346.2 | 0.446151 | ||||||||
\(428\) | 89639.6i | 0.489342i | ||||||||
\(429\) | 98420.1 | − | 1652.96i | 0.534773 | − | 0.00898149i | ||||
\(430\) | 148199. | 0.801507 | ||||||||
\(431\) | − | 11113.4i | − | 0.0598266i | −0.999552 | − | 0.0299133i | \(-0.990477\pi\) | ||
0.999552 | − | 0.0299133i | \(-0.00952311\pi\) | |||||||
\(432\) | 25403.7 | 0.136123 | ||||||||
\(433\) | −288512. | −1.53882 | −0.769409 | − | 0.638756i | \(-0.779449\pi\) | ||||
−0.769409 | + | 0.638756i | \(0.779449\pi\) | |||||||
\(434\) | −68782.7 | −0.365174 | ||||||||
\(435\) | 138865.i | 0.733861i | ||||||||
\(436\) | − | 82290.2i | − | 0.432888i | ||||||
\(437\) | − | 398350.i | − | 2.08594i | ||||||
\(438\) | 41034.6 | 0.213896 | ||||||||
\(439\) | − | 107467.i | − | 0.557630i | −0.960345 | − | 0.278815i | \(-0.910058\pi\) | ||
0.960345 | − | 0.278815i | \(-0.0899417\pi\) | |||||||
\(440\) | −52719.3 | + | 885.419i | −0.272311 | + | 0.00457345i | ||||
\(441\) | 57131.8 | 0.293765 | ||||||||
\(442\) | 105844.i | 0.541780i | ||||||||
\(443\) | −130812. | −0.666563 | −0.333281 | − | 0.942827i | \(-0.608156\pi\) | ||||
−0.333281 | + | 0.942827i | \(0.608156\pi\) | |||||||
\(444\) | 108944. | 0.552636 | ||||||||
\(445\) | −98865.0 | −0.499255 | ||||||||
\(446\) | 34132.3i | 0.171592i | ||||||||
\(447\) | − | 263851.i | − | 1.32052i | ||||||
\(448\) | − | 17377.9i | − | 0.0865845i | ||||||
\(449\) | −158898. | −0.788181 | −0.394090 | − | 0.919072i | \(-0.628940\pi\) | ||||
−0.394090 | + | 0.919072i | \(0.628940\pi\) | |||||||
\(450\) | − | 32878.9i | − | 0.162365i | ||||||
\(451\) | −116964. | + | 1964.41i | −0.575041 | + | 0.00965780i | ||||
\(452\) | −136215. | −0.666727 | ||||||||
\(453\) | − | 73808.9i | − | 0.359677i | ||||||
\(454\) | −109224. | −0.529913 | ||||||||
\(455\) | 47232.0 | 0.228146 | ||||||||
\(456\) | −104869. | −0.504332 | ||||||||
\(457\) | 291561.i | 1.39604i | 0.716079 | + | 0.698019i | \(0.245935\pi\) | ||||
−0.716079 | + | 0.698019i | \(0.754065\pi\) | |||||||
\(458\) | 209532.i | 0.998896i | ||||||||
\(459\) | − | 205561.i | − | 0.975698i | ||||||
\(460\) | −149078. | −0.704529 | ||||||||
\(461\) | 62731.9i | 0.295180i | 0.989049 | + | 0.147590i | \(0.0471515\pi\) | ||||
−0.989049 | + | 0.147590i | \(0.952848\pi\) | |||||||
\(462\) | 2196.01 | + | 130754.i | 0.0102885 | + | 0.612593i | ||||
\(463\) | −170883. | −0.797146 | −0.398573 | − | 0.917137i | \(-0.630494\pi\) | ||||
−0.398573 | + | 0.917137i | \(0.630494\pi\) | |||||||
\(464\) | 40992.2i | 0.190399i | ||||||||
\(465\) | 155339. | 0.718411 | ||||||||
\(466\) | 146285. | 0.673639 | ||||||||
\(467\) | 94559.0 | 0.433580 | 0.216790 | − | 0.976218i | \(-0.430441\pi\) | ||||
0.216790 | + | 0.976218i | \(0.430441\pi\) | |||||||
\(468\) | − | 26442.6i | − | 0.120729i | ||||||
\(469\) | − | 68124.3i | − | 0.309711i | ||||||
\(470\) | 9645.77i | 0.0436658i | ||||||||
\(471\) | −26064.1 | −0.117490 | ||||||||
\(472\) | 44983.8i | 0.201917i | ||||||||
\(473\) | −329164. | + | 5528.30i | −1.47126 | + | 0.0247098i | ||||
\(474\) | 47134.0 | 0.209786 | ||||||||
\(475\) | − | 104618.i | − | 0.463682i | ||||||
\(476\) | −140618. | −0.620620 | ||||||||
\(477\) | −184033. | −0.808832 | ||||||||
\(478\) | 47832.5 | 0.209347 | ||||||||
\(479\) | − | 154781.i | − | 0.674600i | −0.941397 | − | 0.337300i | \(-0.890486\pi\) | ||
0.941397 | − | 0.337300i | \(-0.109514\pi\) | |||||||
\(480\) | 39246.0i | 0.170339i | ||||||||
\(481\) | 87408.6i | 0.377802i | ||||||||
\(482\) | 169400. | 0.729155 | ||||||||
\(483\) | 369744.i | 1.58492i | ||||||||
\(484\) | 117062. | − | 3933.21i | 0.499718 | − | 0.0167902i | ||||
\(485\) | −43125.1 | −0.183336 | ||||||||
\(486\) | 169334.i | 0.716920i | ||||||||
\(487\) | 205330. | 0.865754 | 0.432877 | − | 0.901453i | \(-0.357498\pi\) | ||||
0.432877 | + | 0.901453i | \(0.357498\pi\) | |||||||
\(488\) | −54230.8 | −0.227723 | ||||||||
\(489\) | 244614. | 1.02297 | ||||||||
\(490\) | − | 68032.8i | − | 0.283352i | ||||||
\(491\) | − | 180799.i | − | 0.749950i | −0.927035 | − | 0.374975i | \(-0.877651\pi\) | ||
0.927035 | − | 0.374975i | \(-0.122349\pi\) | |||||||
\(492\) | 87071.9i | 0.359706i | ||||||||
\(493\) | 331699. | 1.36474 | ||||||||
\(494\) | − | 84138.6i | − | 0.344779i | ||||||
\(495\) | −1789.90 | − | 106574.i | −0.00730498 | − | 0.434950i | ||||
\(496\) | 45855.2 | 0.186391 | ||||||||
\(497\) | 144421.i | 0.584678i | ||||||||
\(498\) | −322380. | −1.29990 | ||||||||
\(499\) | 198403. | 0.796797 | 0.398399 | − | 0.917212i | \(-0.369566\pi\) | ||||
0.398399 | + | 0.917212i | \(0.369566\pi\) | |||||||
\(500\) | −135442. | −0.541769 | ||||||||
\(501\) | − | 298006.i | − | 1.18727i | ||||||
\(502\) | − | 54266.8i | − | 0.215341i | ||||||
\(503\) | 278604.i | 1.10116i | 0.834781 | + | 0.550582i | \(0.185594\pi\) | ||||
−0.834781 | + | 0.550582i | \(0.814406\pi\) | |||||||
\(504\) | 35129.9 | 0.138298 | ||||||||
\(505\) | − | 300040.i | − | 1.17651i | ||||||
\(506\) | 331118. | − | 5561.12i | 1.29325 | − | 0.0217201i | ||||
\(507\) | −262755. | −1.02220 | ||||||||
\(508\) | − | 222504.i | − | 0.862206i | ||||||
\(509\) | −195175. | −0.753336 | −0.376668 | − | 0.926348i | \(-0.622930\pi\) | ||||
−0.376668 | + | 0.926348i | \(0.622930\pi\) | |||||||
\(510\) | 317570. | 1.22095 | ||||||||
\(511\) | −43739.2 | −0.167506 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 163406.i | 0.620917i | ||||||||
\(514\) | 86620.8i | 0.327866i | ||||||||
\(515\) | 175622. | 0.662164 | ||||||||
\(516\) | 245041.i | 0.920322i | ||||||||
\(517\) | −359.819 | − | 21424.2i | −0.00134618 | − | 0.0801538i | ||||
\(518\) | −116125. | −0.432779 | ||||||||
\(519\) | 69089.0i | 0.256492i | ||||||||
\(520\) | −31488.0 | −0.116450 | ||||||||
\(521\) | −2617.52 | −0.00964304 | −0.00482152 | − | 0.999988i | \(-0.501535\pi\) | ||||
−0.00482152 | + | 0.999988i | \(0.501535\pi\) | |||||||
\(522\) | −82867.0 | −0.304117 | ||||||||
\(523\) | − | 309803.i | − | 1.13261i | −0.824194 | − | 0.566307i | \(-0.808372\pi\) | ||
0.824194 | − | 0.566307i | \(-0.191628\pi\) | |||||||
\(524\) | − | 50486.0i | − | 0.183869i | ||||||
\(525\) | 97105.3i | 0.352310i | ||||||||
\(526\) | −208781. | −0.754603 | ||||||||
\(527\) | − | 371049.i | − | 1.33601i | ||||||
\(528\) | −1464.01 | − | 87169.5i | −0.00525141 | − | 0.312677i | ||||
\(529\) | 656488. | 2.34593 | ||||||||
\(530\) | 219147.i | 0.780160i | ||||||||
\(531\) | −90936.2 | −0.322513 | ||||||||
\(532\) | 111781. | 0.394952 | ||||||||
\(533\) | −69859.8 | −0.245908 | ||||||||
\(534\) | − | 163470.i | − | 0.573264i | ||||||
\(535\) | 215785.i | 0.753899i | ||||||||
\(536\) | 45416.2i | 0.158081i | ||||||||
\(537\) | 91913.7 | 0.318736 | ||||||||
\(538\) | − | 246899.i | − | 0.853012i | ||||||
\(539\) | 2537.85 | + | 151108.i | 0.00873551 | + | 0.520127i | ||||
\(540\) | 61153.1 | 0.209716 | ||||||||
\(541\) | 197545.i | 0.674948i | 0.941335 | + | 0.337474i | \(0.109573\pi\) | ||||
−0.941335 | + | 0.337474i | \(0.890427\pi\) | |||||||
\(542\) | −12781.0 | −0.0435079 | ||||||||
\(543\) | 114050. | 0.386809 | ||||||||
\(544\) | 93745.0 | 0.316775 | ||||||||
\(545\) | − | 198093.i | − | 0.666923i | ||||||
\(546\) | 78096.4i | 0.261966i | ||||||||
\(547\) | 440541.i | 1.47235i | 0.676790 | + | 0.736176i | \(0.263370\pi\) | ||||
−0.676790 | + | 0.736176i | \(0.736630\pi\) | |||||||
\(548\) | 113657. | 0.378472 | ||||||||
\(549\) | − | 109629.i | − | 0.363732i | ||||||
\(550\) | 86961.2 | − | 1460.51i | 0.287475 | − | 0.00482813i | ||||
\(551\) | −263677. | −0.868498 | ||||||||
\(552\) | − | 246496.i | − | 0.808968i | ||||||
\(553\) | −50240.6 | −0.164288 | ||||||||
\(554\) | 13126.8 | 0.0427701 | ||||||||
\(555\) | 262256. | 0.851411 | ||||||||
\(556\) | 222180.i | 0.718714i | ||||||||
\(557\) | 422793.i | 1.36275i | 0.731933 | + | 0.681376i | \(0.238618\pi\) | ||||
−0.731933 | + | 0.681376i | \(0.761382\pi\) | |||||||
\(558\) | 92697.6i | 0.297715i | ||||||||
\(559\) | −196602. | −0.629165 | ||||||||
\(560\) | − | 41832.8i | − | 0.133395i | ||||||
\(561\) | −705355. | + | 11846.4i | −2.24121 | + | 0.0376410i | ||||
\(562\) | −165805. | −0.524960 | ||||||||
\(563\) | 52520.6i | 0.165696i | 0.996562 | + | 0.0828482i | \(0.0264017\pi\) | ||||
−0.996562 | + | 0.0828482i | \(0.973598\pi\) | |||||||
\(564\) | −15948.9 | −0.0501387 | ||||||||
\(565\) | −327903. | −1.02718 | ||||||||
\(566\) | −255481. | −0.797490 | ||||||||
\(567\) | − | 277427.i | − | 0.862944i | ||||||
\(568\) | − | 96280.5i | − | 0.298430i | ||||||
\(569\) | 140197.i | 0.433025i | 0.976280 | + | 0.216513i | \(0.0694683\pi\) | ||||
−0.976280 | + | 0.216513i | \(0.930532\pi\) | |||||||
\(570\) | −252445. | −0.776993 | ||||||||
\(571\) | − | 207548.i | − | 0.636569i | −0.947995 | − | 0.318284i | \(-0.896893\pi\) | ||
0.947995 | − | 0.318284i | \(-0.103107\pi\) | |||||||
\(572\) | 69938.1 | − | 1174.61i | 0.213758 | − | 0.00359005i | ||||
\(573\) | −155964. | −0.475023 | ||||||||
\(574\) | − | 92810.9i | − | 0.281693i | ||||||
\(575\) | 245907. | 0.743764 | ||||||||
\(576\) | −23419.9 | −0.0705895 | ||||||||
\(577\) | −273572. | −0.821712 | −0.410856 | − | 0.911700i | \(-0.634770\pi\) | ||||
−0.410856 | + | 0.911700i | \(0.634770\pi\) | |||||||
\(578\) | − | 522329.i | − | 1.56347i | ||||||
\(579\) | 627664.i | 1.87228i | ||||||||
\(580\) | 98678.4i | 0.293336i | ||||||||
\(581\) | 343628. | 1.01797 | ||||||||
\(582\) | − | 71305.8i | − | 0.210513i | ||||||
\(583\) | −8174.91 | − | 486748.i | −0.0240517 | − | 1.43208i | ||||
\(584\) | 29159.5 | 0.0854977 | ||||||||
\(585\) | − | 63654.0i | − | 0.186000i | ||||||
\(586\) | −219733. | −0.639883 | ||||||||
\(587\) | −576701. | −1.67369 | −0.836843 | − | 0.547442i | \(-0.815602\pi\) | ||||
−0.836843 | + | 0.547442i | \(0.815602\pi\) | |||||||
\(588\) | 112490. | 0.325355 | ||||||||
\(589\) | 294957.i | 0.850214i | ||||||||
\(590\) | 108287.i | 0.311081i | ||||||||
\(591\) | − | 434309.i | − | 1.24344i | ||||||
\(592\) | 77416.7 | 0.220898 | ||||||||
\(593\) | 671956.i | 1.91087i | 0.295202 | + | 0.955435i | \(0.404613\pi\) | ||||
−0.295202 | + | 0.955435i | \(0.595387\pi\) | |||||||
\(594\) | −135827. | + | 2281.21i | −0.384959 | + | 0.00646536i | ||||
\(595\) | −338501. | −0.956150 | ||||||||
\(596\) | − | 187495.i | − | 0.527833i | ||||||
\(597\) | 492438. | 1.38167 | ||||||||
\(598\) | 197769. | 0.553040 | ||||||||
\(599\) | 582984. | 1.62481 | 0.812406 | − | 0.583092i | \(-0.198157\pi\) | ||||
0.812406 | + | 0.583092i | \(0.198157\pi\) | |||||||
\(600\) | − | 64736.9i | − | 0.179825i | ||||||
\(601\) | − | 377092.i | − | 1.04399i | −0.852947 | − | 0.521997i | \(-0.825187\pi\) | ||
0.852947 | − | 0.521997i | \(-0.174813\pi\) | |||||||
\(602\) | − | 261192.i | − | 0.720721i | ||||||
\(603\) | −91810.2 | −0.252497 | ||||||||
\(604\) | − | 52449.2i | − | 0.143769i | ||||||
\(605\) | 281797. | − | 9468.21i | 0.769885 | − | 0.0258677i | ||||
\(606\) | 496104. | 1.35091 | ||||||||
\(607\) | − | 465535.i | − | 1.26350i | −0.775173 | − | 0.631750i | \(-0.782337\pi\) | ||
0.775173 | − | 0.631750i | \(-0.217663\pi\) | |||||||
\(608\) | −74520.5 | −0.201590 | ||||||||
\(609\) | 244742. | 0.659893 | ||||||||
\(610\) | −130547. | −0.350838 | ||||||||
\(611\) | − | 12796.2i | − | 0.0342766i | ||||||
\(612\) | 189508.i | 0.505971i | ||||||||
\(613\) | 623300.i | 1.65873i | 0.558705 | + | 0.829366i | \(0.311298\pi\) | ||||
−0.558705 | + | 0.829366i | \(0.688702\pi\) | |||||||
\(614\) | 171084. | 0.453807 | ||||||||
\(615\) | 209604.i | 0.554177i | ||||||||
\(616\) | 1560.50 | + | 92914.9i | 0.00411247 | + | 0.244863i | ||||
\(617\) | 197189. | 0.517980 | 0.258990 | − | 0.965880i | \(-0.416610\pi\) | ||||
0.258990 | + | 0.965880i | \(0.416610\pi\) | |||||||
\(618\) | 290385.i | 0.760322i | ||||||||
\(619\) | 214900. | 0.560861 | 0.280431 | − | 0.959874i | \(-0.409523\pi\) | ||||
0.280431 | + | 0.959874i | \(0.409523\pi\) | |||||||
\(620\) | 110385. | 0.287161 | ||||||||
\(621\) | −384089. | −0.995976 | ||||||||
\(622\) | 90810.1i | 0.234722i | ||||||||
\(623\) | 174244.i | 0.448934i | ||||||||
\(624\) | − | 52064.3i | − | 0.133712i | ||||||
\(625\) | −167211. | −0.428061 | ||||||||
\(626\) | 315300.i | 0.804592i | ||||||||
\(627\) | 560706. | − | 9417.04i | 1.42626 | − | 0.0239541i | ||||
\(628\) | −18521.3 | −0.0469627 | ||||||||
\(629\) | − | 626437.i | − | 1.58335i | ||||||
\(630\) | 84566.3 | 0.213067 | ||||||||
\(631\) | −40334.6 | −0.101302 | −0.0506511 | − | 0.998716i | \(-0.516130\pi\) | ||||
−0.0506511 | + | 0.998716i | \(0.516130\pi\) | |||||||
\(632\) | 33493.8 | 0.0838551 | ||||||||
\(633\) | − | 455507.i | − | 1.13681i | ||||||
\(634\) | 393906.i | 0.979973i | ||||||||
\(635\) | − | 535623.i | − | 1.32835i | ||||||
\(636\) | −362352. | −0.895810 | ||||||||
\(637\) | 90253.1i | 0.222425i | ||||||||
\(638\) | −3681.03 | − | 219175.i | −0.00904333 | − | 0.538455i | ||||
\(639\) | 194634. | 0.476669 | ||||||||
\(640\) | 27888.5i | 0.0680872i | ||||||||
\(641\) | −19965.1 | −0.0485909 | −0.0242954 | − | 0.999705i | \(-0.507734\pi\) | ||||
−0.0242954 | + | 0.999705i | \(0.507734\pi\) | |||||||
\(642\) | −356792. | −0.865656 | ||||||||
\(643\) | 21885.5 | 0.0529340 | 0.0264670 | − | 0.999650i | \(-0.491574\pi\) | ||||
0.0264670 | + | 0.999650i | \(0.491574\pi\) | |||||||
\(644\) | 262743.i | 0.633518i | ||||||||
\(645\) | 589875.i | 1.41788i | ||||||||
\(646\) | 603002.i | 1.44495i | ||||||||
\(647\) | −345969. | −0.826472 | −0.413236 | − | 0.910624i | \(-0.635602\pi\) | ||||
−0.413236 | + | 0.910624i | \(0.635602\pi\) | |||||||
\(648\) | 184951.i | 0.440461i | ||||||||
\(649\) | −4039.47 | − | 240517.i | −0.00959037 | − | 0.571027i | ||||
\(650\) | 51939.9 | 0.122935 | ||||||||
\(651\) | − | 273776.i | − | 0.646000i | ||||||
\(652\) | 173824. | 0.408898 | ||||||||
\(653\) | 380939. | 0.893366 | 0.446683 | − | 0.894692i | \(-0.352605\pi\) | ||||
0.446683 | + | 0.894692i | \(0.352605\pi\) | |||||||
\(654\) | 327539. | 0.765787 | ||||||||
\(655\) | − | 121532.i | − | 0.283275i | ||||||
\(656\) | 61874.0i | 0.143781i | ||||||||
\(657\) | 58946.8i | 0.136562i | ||||||||
\(658\) | 17000.1 | 0.0392645 | ||||||||
\(659\) | 149577.i | 0.344424i | 0.985060 | + | 0.172212i | \(0.0550914\pi\) | ||||
−0.985060 | + | 0.172212i | \(0.944909\pi\) | |||||||
\(660\) | −3524.23 | − | 209838.i | −0.00809052 | − | 0.481723i | ||||
\(661\) | −637662. | −1.45945 | −0.729723 | − | 0.683743i | \(-0.760351\pi\) | ||||
−0.729723 | + | 0.683743i | \(0.760351\pi\) | |||||||
\(662\) | − | 170337.i | − | 0.388681i | ||||||
\(663\) | −421292. | −0.958420 | ||||||||
\(664\) | −229086. | −0.519591 | ||||||||
\(665\) | 269084. | 0.608477 | ||||||||
\(666\) | 156500.i | 0.352831i | ||||||||
\(667\) | − | 619777.i | − | 1.39311i | ||||||
\(668\) | − | 211765.i | − | 0.474571i | ||||||
\(669\) | −135857. | −0.303549 | ||||||||
\(670\) | 109328.i | 0.243546i | ||||||||
\(671\) | 289958. | − | 4869.84i | 0.644006 | − | 0.0108161i | ||||
\(672\) | 69169.0 | 0.153170 | ||||||||
\(673\) | 165463.i | 0.365318i | 0.983176 | + | 0.182659i | \(0.0584704\pi\) | ||||
−0.983176 | + | 0.182659i | \(0.941530\pi\) | |||||||
\(674\) | 242226. | 0.533214 | ||||||||
\(675\) | −100873. | −0.221394 | ||||||||
\(676\) | −186716. | −0.408590 | ||||||||
\(677\) | 420292.i | 0.917009i | 0.888692 | + | 0.458504i | \(0.151615\pi\) | ||||
−0.888692 | + | 0.458504i | \(0.848385\pi\) | |||||||
\(678\) | − | 542176.i | − | 1.17945i | ||||||
\(679\) | 76005.7i | 0.164857i | ||||||||
\(680\) | 225667. | 0.488035 | ||||||||
\(681\) | − | 434742.i | − | 0.937428i | ||||||
\(682\) | −245176. | + | 4117.72i | −0.527119 | + | 0.00885294i | ||||
\(683\) | 265281. | 0.568677 | 0.284338 | − | 0.958724i | \(-0.408226\pi\) | ||||
0.284338 | + | 0.958724i | \(0.408226\pi\) | |||||||
\(684\) | − | 150646.i | − | 0.321991i | ||||||
\(685\) | 273600. | 0.583089 | ||||||||
\(686\) | −350400. | −0.744588 | ||||||||
\(687\) | −834001. | −1.76707 | ||||||||
\(688\) | 174128.i | 0.367868i | ||||||||
\(689\) | − | 290723.i | − | 0.612408i | ||||||
\(690\) | − | 593376.i | − | 1.24633i | ||||||
\(691\) | −72314.2 | −0.151449 | −0.0757247 | − | 0.997129i | \(-0.524127\pi\) | ||||
−0.0757247 | + | 0.997129i | \(0.524127\pi\) | |||||||
\(692\) | 49095.1i | 0.102524i | ||||||||
\(693\) | −187830. | + | 3154.60i | −0.391110 | + | 0.00656868i | ||||
\(694\) | 281428. | 0.584316 | ||||||||
\(695\) | 534843.i | 1.10728i | ||||||||
\(696\) | −163161. | −0.336820 | ||||||||
\(697\) | 500669. | 1.03059 | ||||||||
\(698\) | −134393. | −0.275846 | ||||||||
\(699\) | 582257.i | 1.19168i | ||||||||
\(700\) | 69003.8i | 0.140824i | ||||||||
\(701\) | − | 142549.i | − | 0.290088i | −0.989425 | − | 0.145044i | \(-0.953668\pi\) | ||
0.989425 | − | 0.145044i | \(-0.0463324\pi\) | |||||||
\(702\) | −81126.4 | −0.164622 | ||||||||
\(703\) | 497972.i | 1.00761i | ||||||||
\(704\) | −1040.33 | − | 61943.3i | −0.00209907 | − | 0.124982i | ||||
\(705\) | −38393.0 | −0.0772456 | ||||||||
\(706\) | 473711.i | 0.950394i | ||||||||
\(707\) | −528803. | −1.05793 | ||||||||
\(708\) | −179049. | −0.357195 | ||||||||
\(709\) | −588664. | −1.17105 | −0.585525 | − | 0.810654i | \(-0.699112\pi\) | ||||
−0.585525 | + | 0.810654i | \(0.699112\pi\) | |||||||
\(710\) | − | 231771.i | − | 0.459772i | ||||||
\(711\) | 67708.7i | 0.133938i | ||||||||
\(712\) | − | 116163.i | − | 0.229143i | ||||||
\(713\) | −693302. | −1.36378 | ||||||||
\(714\) | − | 559699.i | − | 1.09789i | ||||||
\(715\) | 168358. | − | 2827.57i | 0.329323 | − | 0.00553097i | ||||
\(716\) | 65314.5 | 0.127404 | ||||||||
\(717\) | 190387.i | 0.370340i | ||||||||
\(718\) | −14322.9 | −0.0277832 | ||||||||
\(719\) | −133520. | −0.258280 | −0.129140 | − | 0.991626i | \(-0.541222\pi\) | ||||
−0.129140 | + | 0.991626i | \(0.541222\pi\) | |||||||
\(720\) | −56377.5 | −0.108753 | ||||||||
\(721\) | − | 309525.i | − | 0.595422i | ||||||
\(722\) | − | 110740.i | − | 0.212437i | ||||||
\(723\) | 674263.i | 1.28989i | ||||||||
\(724\) | 81044.9 | 0.154614 | ||||||||
\(725\) | − | 162771.i | − | 0.309672i | ||||||
\(726\) | 15655.3 | + | 465941.i | 0.0297023 | + | 0.884011i | ||||
\(727\) | 224313. | 0.424410 | 0.212205 | − | 0.977225i | \(-0.431936\pi\) | ||||
0.212205 | + | 0.977225i | \(0.431936\pi\) | |||||||
\(728\) | 55495.9i | 0.104712i | ||||||||
\(729\) | −11922.8 | −0.0224348 | ||||||||
\(730\) | 70194.1 | 0.131721 | ||||||||
\(731\) | 1.40900e6 | 2.63680 | ||||||||
\(732\) | − | 215855.i | − | 0.402846i | ||||||
\(733\) | − | 297252.i | − | 0.553243i | −0.960979 | − | 0.276622i | \(-0.910785\pi\) | ||
0.960979 | − | 0.276622i | \(-0.0892149\pi\) | |||||||
\(734\) | 746765.i | 1.38609i | ||||||||
\(735\) | 270790. | 0.501255 | ||||||||
\(736\) | − | 175162.i | − | 0.323358i | ||||||
\(737\) | −4078.30 | − | 242829.i | −0.00750834 | − | 0.447059i | ||||
\(738\) | −125080. | −0.229655 | ||||||||
\(739\) | 268988.i | 0.492543i | 0.969201 | + | 0.246272i | \(0.0792056\pi\) | ||||
−0.969201 | + | 0.246272i | \(0.920794\pi\) | |||||||
\(740\) | 186361. | 0.340323 | ||||||||
\(741\) | 334896. | 0.609922 | ||||||||
\(742\) | 386235. | 0.701525 | ||||||||
\(743\) | 133653.i | 0.242104i | 0.992646 | + | 0.121052i | \(0.0386267\pi\) | ||||
−0.992646 | + | 0.121052i | \(0.961373\pi\) | |||||||
\(744\) | 182517.i | 0.329729i | ||||||||
\(745\) | − | 451346.i | − | 0.813200i | ||||||
\(746\) | 765117. | 1.37483 | ||||||||
\(747\) | − | 463104.i | − | 0.829921i | ||||||
\(748\) | −501230. | + | 8418.14i | −0.895848 | + | 0.0150457i | ||||
\(749\) | 380309. | 0.677911 | ||||||||
\(750\) | − | 539100.i | − | 0.958400i | ||||||
\(751\) | 201267. | 0.356856 | 0.178428 | − | 0.983953i | \(-0.442899\pi\) | ||||
0.178428 | + | 0.983953i | \(0.442899\pi\) | |||||||
\(752\) | −11333.4 | −0.0200413 | ||||||||
\(753\) | 215998. | 0.380942 | ||||||||
\(754\) | − | 130908.i | − | 0.230262i | ||||||
\(755\) | − | 126258.i | − | 0.221496i | ||||||
\(756\) | − | 107779.i | − | 0.188578i | ||||||
\(757\) | 835429. | 1.45787 | 0.728934 | − | 0.684584i | \(-0.240016\pi\) | ||||
0.728934 | + | 0.684584i | \(0.240016\pi\) | |||||||
\(758\) | − | 109884.i | − | 0.191248i | ||||||
\(759\) | 22134.9 | + | 1.31795e6i | 0.0384233 | + | 2.28778i | ||||
\(760\) | −179389. | −0.310577 | ||||||||
\(761\) | 345963.i | 0.597393i | 0.954348 | + | 0.298696i | \(0.0965518\pi\) | ||||
−0.954348 | + | 0.298696i | \(0.903448\pi\) | |||||||
\(762\) | 885633. | 1.52526 | ||||||||
\(763\) | −349128. | −0.599702 | ||||||||
\(764\) | −110829. | −0.189875 | ||||||||
\(765\) | 456194.i | 0.779518i | ||||||||
\(766\) | − | 687506.i | − | 1.17171i | ||||||
\(767\) | − | 143655.i | − | 0.244191i | ||||||
\(768\) | −46112.7 | −0.0781804 | ||||||||
\(769\) | − | 1.05669e6i | − | 1.78688i | −0.449183 | − | 0.893440i | \(-0.648285\pi\) | ||
0.449183 | − | 0.893440i | \(-0.351715\pi\) | |||||||
\(770\) | 3756.51 | + | 223669.i | 0.00633583 | + | 0.377246i | ||||
\(771\) | −344776. | −0.580001 | ||||||||
\(772\) | 446022.i | 0.748380i | ||||||||
\(773\) | −224559. | −0.375813 | −0.187907 | − | 0.982187i | \(-0.560170\pi\) | ||||
−0.187907 | + | 0.982187i | \(0.560170\pi\) | |||||||
\(774\) | −352005. | −0.587580 | ||||||||
\(775\) | −182081. | −0.303153 | ||||||||
\(776\) | − | 50670.4i | − | 0.0841456i | ||||||
\(777\) | − | 462212.i | − | 0.765595i | ||||||
\(778\) | − | 403174.i | − | 0.666091i | ||||||
\(779\) | −397996. | −0.655849 | ||||||||
\(780\) | − | 125332.i | − | 0.206002i | ||||||
\(781\) | 8645.83 | + | 514787.i | 0.0141744 | + | 0.843967i | ||||
\(782\) | −1.41737e6 | −2.31776 | ||||||||
\(783\) | 254237.i | 0.414682i | ||||||||
\(784\) | 79936.0 | 0.130050 | ||||||||
\(785\) | −44585.4 | −0.0723525 | ||||||||
\(786\) | 200949. | 0.325268 | ||||||||
\(787\) | − | 227376.i | − | 0.367109i | −0.983010 | − | 0.183554i | \(-0.941240\pi\) | ||
0.983010 | − | 0.183554i | \(-0.0587603\pi\) | |||||||
\(788\) | − | 308623.i | − | 0.497023i | ||||||
\(789\) | − | 831008.i | − | 1.33491i | ||||||
\(790\) | 80627.7 | 0.129190 | ||||||||
\(791\) | 577911.i | 0.923651i | ||||||||
\(792\) | 125220. | − | 2103.07i | 0.199629 | − | 0.00335277i | ||||
\(793\) | 173185. | 0.275400 | ||||||||
\(794\) | − | 208908.i | − | 0.331370i | ||||||
\(795\) | −872270. | −1.38012 | ||||||||
\(796\) | 349930. | 0.552275 | ||||||||
\(797\) | −972019. | −1.53023 | −0.765117 | − | 0.643891i | \(-0.777319\pi\) | ||||
−0.765117 | + | 0.643891i | \(0.777319\pi\) | |||||||
\(798\) | 444920.i | 0.698677i | ||||||||
\(799\) | 91707.4i | 0.143652i | ||||||||
\(800\) | − | 46002.5i | − | 0.0718789i | ||||||
\(801\) | 234827. | 0.366001 | ||||||||
\(802\) | 638590.i | 0.992826i | ||||||||
\(803\) | −155908. | + | 2618.47i | −0.241790 | + | 0.00406085i | ||||
\(804\) | −180770. | −0.279649 | ||||||||
\(805\) | 632486.i | 0.976021i | ||||||||
\(806\) | −146438. | −0.225415 | ||||||||
\(807\) | 982732. | 1.50900 | ||||||||
\(808\) | 352535. | 0.539983 | ||||||||
\(809\) | − | 56475.6i | − | 0.0862906i | −0.999069 | − | 0.0431453i | \(-0.986262\pi\) | ||
0.999069 | − | 0.0431453i | \(-0.0137378\pi\) | |||||||
\(810\) | 445224.i | 0.678591i | ||||||||
\(811\) | − | 224590.i | − | 0.341467i | −0.985317 | − | 0.170733i | \(-0.945386\pi\) | ||
0.985317 | − | 0.170733i | \(-0.0546137\pi\) | |||||||
\(812\) | 173915. | 0.263770 | ||||||||
\(813\) | − | 50872.3i | − | 0.0769663i | ||||||
\(814\) | −413927. | + | 6951.89i | −0.624705 | + | 0.0104919i | ||||
\(815\) | 418438. | 0.629964 | ||||||||
\(816\) | 373133.i | 0.560381i | ||||||||
\(817\) | −1.12006e6 | −1.67801 | ||||||||
\(818\) | 277109. | 0.414137 | ||||||||
\(819\) | −112187. | −0.167253 | ||||||||
\(820\) | 148946.i | 0.221514i | ||||||||
\(821\) | − | 719097.i | − | 1.06684i | −0.845849 | − | 0.533422i | \(-0.820906\pi\) | ||
0.845849 | − | 0.533422i | \(-0.179094\pi\) | |||||||
\(822\) | 452387.i | 0.669525i | ||||||||
\(823\) | 52447.6 | 0.0774330 | 0.0387165 | − | 0.999250i | \(-0.487673\pi\) | ||||
0.0387165 | + | 0.999250i | \(0.487673\pi\) | |||||||
\(824\) | 206350.i | 0.303913i | ||||||||
\(825\) | 5813.26 | + | 346131.i | 0.00854107 | + | 0.508549i | ||||
\(826\) | 190850. | 0.279726 | ||||||||
\(827\) | 121409.i | 0.177517i | 0.996053 | + | 0.0887586i | \(0.0282900\pi\) | ||||
−0.996053 | + | 0.0887586i | \(0.971710\pi\) | |||||||
\(828\) | 354095. | 0.516486 | ||||||||
\(829\) | 555136. | 0.807774 | 0.403887 | − | 0.914809i | \(-0.367659\pi\) | ||||
0.403887 | + | 0.914809i | \(0.367659\pi\) | |||||||
\(830\) | −551466. | −0.800502 | ||||||||
\(831\) | 52248.7i | 0.0756612i | ||||||||
\(832\) | − | 36997.2i | − | 0.0534469i | ||||||
\(833\) | − | 646823.i | − | 0.932171i | ||||||
\(834\) | −884344. | −1.27142 | ||||||||
\(835\) | − | 509771.i | − | 0.731143i | ||||||
\(836\) | 398442. | − | 6691.82i | 0.570102 | − | 0.00957484i | ||||
\(837\) | 284398. | 0.405952 | ||||||||
\(838\) | − | 182639.i | − | 0.260079i | ||||||
\(839\) | −728123. | −1.03438 | −0.517191 | − | 0.855870i | \(-0.673022\pi\) | ||||
−0.517191 | + | 0.855870i | \(0.673022\pi\) | |||||||
\(840\) | 166507. | 0.235979 | ||||||||
\(841\) | 297036. | 0.419969 | ||||||||
\(842\) | 574940.i | 0.810958i | ||||||||
\(843\) | − | 659955.i | − | 0.928665i | ||||||
\(844\) | − | 323687.i | − | 0.454402i | ||||||
\(845\) | −449471. | −0.629489 | ||||||||
\(846\) | − | 22910.9i | − | 0.0320111i | ||||||
\(847\) | −16687.2 | − | 496652.i | −0.0232604 | − | 0.692285i | ||||
\(848\) | −257490. | −0.358070 | ||||||||
\(849\) | − | 1.01689e6i | − | 1.41078i | ||||||
\(850\) | −372241. | −0.515213 | ||||||||
\(851\) | −1.17049e6 | −1.61625 | ||||||||
\(852\) | 383225. | 0.527928 | ||||||||
\(853\) | 560810.i | 0.770757i | 0.922759 | + | 0.385379i | \(0.125929\pi\) | ||||
−0.922759 | + | 0.385379i | \(0.874071\pi\) | |||||||
\(854\) | 230082.i | 0.315476i | ||||||||
\(855\) | − | 362641.i | − | 0.496072i | ||||||
\(856\) | −253539. | −0.346017 | ||||||||
\(857\) | 1.02077e6i | 1.38984i | 0.719086 | + | 0.694921i | \(0.244561\pi\) | ||||
−0.719086 | + | 0.694921i | \(0.755439\pi\) | |||||||
\(858\) | 4675.28 | + | 278374.i | 0.00635087 | + | 0.378141i | ||||
\(859\) | 350246. | 0.474665 | 0.237332 | − | 0.971428i | \(-0.423727\pi\) | ||||
0.237332 | + | 0.971428i | \(0.423727\pi\) | |||||||
\(860\) | 419169.i | 0.566751i | ||||||||
\(861\) | 369415. | 0.498320 | ||||||||
\(862\) | 31433.6 | 0.0423038 | ||||||||
\(863\) | −516997. | −0.694170 | −0.347085 | − | 0.937834i | \(-0.612829\pi\) | ||||
−0.347085 | + | 0.937834i | \(0.612829\pi\) | |||||||
\(864\) | 71852.6i | 0.0962532i | ||||||||
\(865\) | 118184.i | 0.157953i | ||||||||
\(866\) | − | 816034.i | − | 1.08811i | ||||||
\(867\) | 2.07903e6 | 2.76581 | ||||||||
\(868\) | − | 194547.i | − | 0.258217i | ||||||
\(869\) | −179082. | + | 3007.68i | −0.237145 | + | 0.00398284i | ||||
\(870\) | −392769. | −0.518918 | ||||||||
\(871\) | − | 145036.i | − | 0.191178i | ||||||
\(872\) | 232752. | 0.306098 | ||||||||
\(873\) | 102432. | 0.134402 | ||||||||
\(874\) | 1.12670e6 | 1.47498 | ||||||||
\(875\) | 574632.i | 0.750540i | ||||||||
\(876\) | 116063.i | 0.151247i | ||||||||
\(877\) | 657406.i | 0.854741i | 0.904077 | + | 0.427371i | \(0.140560\pi\) | ||||
−0.904077 | + | 0.427371i | \(0.859440\pi\) | |||||||
\(878\) | 303963. | 0.394304 | ||||||||
\(879\) | − | 874603.i | − | 1.13197i | ||||||
\(880\) | −2504.34 | − | 149113.i | −0.00323391 | − | 0.192553i | ||||
\(881\) | 869395. | 1.12012 | 0.560061 | − | 0.828452i | \(-0.310778\pi\) | ||||
0.560061 | + | 0.828452i | \(0.310778\pi\) | |||||||
\(882\) | 161593.i | 0.207724i | ||||||||
\(883\) | 955758. | 1.22582 | 0.612910 | − | 0.790153i | \(-0.289999\pi\) | ||||
0.612910 | + | 0.790153i | \(0.289999\pi\) | |||||||
\(884\) | −299373. | −0.383096 | ||||||||
\(885\) | −431015. | −0.550308 | ||||||||
\(886\) | − | 369993.i | − | 0.471331i | ||||||
\(887\) | − | 436265.i | − | 0.554503i | −0.960797 | − | 0.277251i | \(-0.910577\pi\) | ||
0.960797 | − | 0.277251i | \(-0.0894235\pi\) | |||||||
\(888\) | 308141.i | 0.390772i | ||||||||
\(889\) | −944006. | −1.19446 | ||||||||
\(890\) | − | 279633.i | − | 0.353027i | ||||||
\(891\) | −16608.3 | − | 988887.i | −0.0209204 | − | 1.24564i | ||||
\(892\) | −96540.7 | −0.121334 | ||||||||
\(893\) | − | 72900.7i | − | 0.0914174i | ||||||
\(894\) | 746284. | 0.933747 | ||||||||
\(895\) | 157228. | 0.196284 | ||||||||
\(896\) | 49152.0 | 0.0612245 | ||||||||
\(897\) | 787180.i | 0.978338i | ||||||||
\(898\) | − | 449432.i | − | 0.557328i | ||||||
\(899\) | 458912.i | 0.567819i | ||||||||
\(900\) | 92995.5 | 0.114809 | ||||||||
\(901\) | 2.08355e6i | 2.56657i | ||||||||
\(902\) | −5556.18 | − | 330824.i | −0.00682909 | − | 0.406616i | ||||
\(903\) | 1.03962e6 | 1.27497 | ||||||||
\(904\) | − | 385274.i | − | 0.471447i | ||||||
\(905\) | 195095. | 0.238204 | ||||||||
\(906\) | 208763. | 0.254330 | ||||||||
\(907\) | −707203. | −0.859666 | −0.429833 | − | 0.902909i | \(-0.641427\pi\) | ||||
−0.429833 | + | 0.902909i | \(0.641427\pi\) | |||||||
\(908\) | − | 308931.i | − | 0.374705i | ||||||
\(909\) | 712661.i | 0.862493i | ||||||||
\(910\) | 133592.i | 0.161324i | ||||||||
\(911\) | 132785. | 0.159998 | 0.0799989 | − | 0.996795i | \(-0.474508\pi\) | ||||
0.0799989 | + | 0.996795i | \(0.474508\pi\) | |||||||
\(912\) | − | 296614.i | − | 0.356616i | ||||||
\(913\) | 1.22486e6 | − | 20571.5i | 1.46942 | − | 0.0246788i | ||||
\(914\) | −824660. | −0.987149 | ||||||||
\(915\) | − | 519615.i | − | 0.620640i | ||||||
\(916\) | −592647. | −0.706326 | ||||||||
\(917\) | −214194. | −0.254723 | ||||||||
\(918\) | 581414. | 0.689923 | ||||||||
\(919\) | 964589.i | 1.14212i | 0.820909 | + | 0.571059i | \(0.193467\pi\) | ||||
−0.820909 | + | 0.571059i | \(0.806533\pi\) | |||||||
\(920\) | − | 421657.i | − | 0.498178i | ||||||
\(921\) | 680963.i | 0.802795i | ||||||||
\(922\) | −177432. | −0.208723 | ||||||||
\(923\) | 307470.i | 0.360911i | ||||||||
\(924\) | −369829. | + | 6211.26i | −0.433168 | + | 0.00727505i | ||||
\(925\) | −307405. | −0.359275 | ||||||||
\(926\) | − | 483331.i | − | 0.563667i | ||||||
\(927\) | −417143. | −0.485429 | ||||||||
\(928\) | −115943. | −0.134633 | ||||||||
\(929\) | 634849. | 0.735596 | 0.367798 | − | 0.929906i | \(-0.380112\pi\) | ||||
0.367798 | + | 0.929906i | \(0.380112\pi\) | |||||||
\(930\) | 439364.i | 0.507994i | ||||||||
\(931\) | 514178.i | 0.593217i | ||||||||
\(932\) | 413756.i | 0.476335i | ||||||||
\(933\) | −361451. | −0.415228 | ||||||||
\(934\) | 267453.i | 0.306587i | ||||||||
\(935\) | −1.20659e6 | + | 20264.6i | −1.38018 | + | 0.0231800i | ||||
\(936\) | 74791.1 | 0.0853686 | ||||||||
\(937\) | − | 3331.90i | − | 0.00379501i | −0.999998 | − | 0.00189750i | \(-0.999396\pi\) | ||
0.999998 | − | 0.00189750i | \(-0.000603995\pi\) | |||||||
\(938\) | 192685. | 0.218998 | ||||||||
\(939\) | −1.25499e6 | −1.42334 | ||||||||
\(940\) | −27282.3 | −0.0308764 | ||||||||
\(941\) | − | 1.13619e6i | − | 1.28313i | −0.767069 | − | 0.641564i | \(-0.778286\pi\) | ||
0.767069 | − | 0.641564i | \(-0.221714\pi\) | |||||||
\(942\) | − | 73720.4i | − | 0.0830780i | ||||||
\(943\) | − | 935496.i | − | 1.05201i | ||||||
\(944\) | −127234. | −0.142777 | ||||||||
\(945\) | − | 259451.i | − | 0.290530i | ||||||
\(946\) | −15636.4 | − | 931018.i | −0.0174725 | − | 1.04034i | ||||
\(947\) | 156679. | 0.174707 | 0.0873536 | − | 0.996177i | \(-0.472159\pi\) | ||||
0.0873536 | + | 0.996177i | \(0.472159\pi\) | |||||||
\(948\) | 133315.i | 0.148341i | ||||||||
\(949\) | −93120.3 | −0.103398 | ||||||||
\(950\) | 295905. | 0.327873 | ||||||||
\(951\) | −1.56786e6 | −1.73359 | ||||||||
\(952\) | − | 397726.i | − | 0.438844i | ||||||
\(953\) | − | 343607.i | − | 0.378334i | −0.981945 | − | 0.189167i | \(-0.939421\pi\) | ||
0.981945 | − | 0.189167i | \(-0.0605788\pi\) | |||||||
\(954\) | − | 520523.i | − | 0.571931i | ||||||
\(955\) | −266793. | −0.292528 | ||||||||
\(956\) | 135291.i | 0.148031i | ||||||||
\(957\) | 872380. | − | 14651.6i | 0.952537 | − | 0.0159978i | ||||
\(958\) | 437786. | 0.477014 | ||||||||
\(959\) | − | 482205.i | − | 0.524317i | ||||||
\(960\) | −111005. | −0.120448 | ||||||||
\(961\) | −410168. | −0.444135 | ||||||||
\(962\) | −247229. | −0.267146 | ||||||||
\(963\) | − | 512537.i | − | 0.552679i | ||||||
\(964\) | 479136.i | 0.515590i | ||||||||
\(965\) | 1.07369e6i | 1.15298i | ||||||||
\(966\) | −1.04579e6 | −1.12071 | ||||||||
\(967\) | − | 395609.i | − | 0.423071i | −0.977370 | − | 0.211536i | \(-0.932154\pi\) | ||
0.977370 | − | 0.211536i | \(-0.0678464\pi\) | |||||||
\(968\) | 11124.8 | + | 331101.i | 0.0118725 | + | 0.353354i | ||||
\(969\) | −2.40013e6 | −2.55615 | ||||||||
\(970\) | − | 121976.i | − | 0.129638i | ||||||
\(971\) | 1.28188e6 | 1.35960 | 0.679799 | − | 0.733398i | \(-0.262067\pi\) | ||||
0.679799 | + | 0.733398i | \(0.262067\pi\) | |||||||
\(972\) | −478948. | −0.506939 | ||||||||
\(973\) | 942632. | 0.995672 | ||||||||
\(974\) | 580761.i | 0.612181i | ||||||||
\(975\) | 206736.i | 0.217474i | ||||||||
\(976\) | − | 153388.i | − | 0.161024i | ||||||
\(977\) | −1.02959e6 | −1.07863 | −0.539316 | − | 0.842103i | \(-0.681317\pi\) | ||||
−0.539316 | + | 0.842103i | \(0.681317\pi\) | |||||||
\(978\) | 691872.i | 0.723349i | ||||||||
\(979\) | 10431.2 | + | 621092.i | 0.0108835 | + | 0.648024i | ||||
\(980\) | 192426. | 0.200360 | ||||||||
\(981\) | 470515.i | 0.488918i | ||||||||
\(982\) | 511376. | 0.530295 | ||||||||
\(983\) | 1.35529e6 | 1.40257 | 0.701284 | − | 0.712882i | \(-0.252610\pi\) | ||||
0.701284 | + | 0.712882i | \(0.252610\pi\) | |||||||
\(984\) | −246277. | −0.254351 | ||||||||
\(985\) | − | 742933.i | − | 0.765732i | ||||||
\(986\) | 938187.i | 0.965019i | ||||||||
\(987\) | 67665.6i | 0.0694598i | ||||||||
\(988\) | 237980. | 0.243796 | ||||||||
\(989\) | − | 2.63271e6i | − | 2.69160i | ||||||
\(990\) | 301436. | − | 5062.61i | 0.307556 | − | 0.00516540i | ||||
\(991\) | −47967.0 | −0.0488422 | −0.0244211 | − | 0.999702i | \(-0.507774\pi\) | ||||
−0.0244211 | + | 0.999702i | \(0.507774\pi\) | |||||||
\(992\) | 129698.i | 0.131798i | ||||||||
\(993\) | 677991. | 0.687584 | ||||||||
\(994\) | −408484. | −0.413430 | ||||||||
\(995\) | 842368. | 0.850855 | ||||||||
\(996\) | − | 911828.i | − | 0.919167i | ||||||
\(997\) | 1.71845e6i | 1.72881i | 0.502798 | + | 0.864404i | \(0.332304\pi\) | ||||
−0.502798 | + | 0.864404i | \(0.667696\pi\) | |||||||
\(998\) | 561169.i | 0.563421i | ||||||||
\(999\) | 480145. | 0.481106 |
(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 | 22.5.b.a.21.3 | yes | 4 | |
3.2 | odd | 2 | 198.5.d.a.109.2 | 4 | |||
4.3 | odd | 2 | 176.5.h.e.65.3 | 4 | |||
5.2 | odd | 4 | 550.5.c.a.549.3 | 8 | |||
5.3 | odd | 4 | 550.5.c.a.549.6 | 8 | |||
5.4 | even | 2 | 550.5.d.a.351.2 | 4 | |||
8.3 | odd | 2 | 704.5.h.j.65.1 | 4 | |||
8.5 | even | 2 | 704.5.h.i.65.4 | 4 | |||
11.10 | odd | 2 | inner | 22.5.b.a.21.1 | ✓ | 4 | |
33.32 | even | 2 | 198.5.d.a.109.4 | 4 | |||
44.43 | even | 2 | 176.5.h.e.65.4 | 4 | |||
55.32 | even | 4 | 550.5.c.a.549.7 | 8 | |||
55.43 | even | 4 | 550.5.c.a.549.2 | 8 | |||
55.54 | odd | 2 | 550.5.d.a.351.4 | 4 | |||
88.21 | odd | 2 | 704.5.h.i.65.3 | 4 | |||
88.43 | even | 2 | 704.5.h.j.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.5.b.a.21.1 | ✓ | 4 | 11.10 | odd | 2 | inner | |
22.5.b.a.21.3 | yes | 4 | 1.1 | even | 1 | trivial | |
176.5.h.e.65.3 | 4 | 4.3 | odd | 2 | |||
176.5.h.e.65.4 | 4 | 44.43 | even | 2 | |||
198.5.d.a.109.2 | 4 | 3.2 | odd | 2 | |||
198.5.d.a.109.4 | 4 | 33.32 | even | 2 | |||
550.5.c.a.549.2 | 8 | 55.43 | even | 4 | |||
550.5.c.a.549.3 | 8 | 5.2 | odd | 4 | |||
550.5.c.a.549.6 | 8 | 5.3 | odd | 4 | |||
550.5.c.a.549.7 | 8 | 55.32 | even | 4 | |||
550.5.d.a.351.2 | 4 | 5.4 | even | 2 | |||
550.5.d.a.351.4 | 4 | 55.54 | odd | 2 | |||
704.5.h.i.65.3 | 4 | 88.21 | odd | 2 | |||
704.5.h.i.65.4 | 4 | 8.5 | even | 2 | |||
704.5.h.j.65.1 | 4 | 8.3 | odd | 2 | |||
704.5.h.j.65.2 | 4 | 88.43 | even | 2 |