Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,5,Mod(37,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, 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("38.37");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(3.92805859719\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 450x^{6} + 68229x^{4} + 4001228x^{2} + 77475204 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(-6.38941i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.37 |
Dual form | 38.5.b.a.37.7 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(-1\) |
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 | ||||||
\(3\) | − | 7.80363i | − | 0.867070i | −0.901137 | − | 0.433535i | \(-0.857266\pi\) | ||
0.901137 | − | 0.433535i | \(-0.142734\pi\) | |||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | −33.0971 | −1.32388 | −0.661941 | − | 0.749556i | \(-0.730267\pi\) | ||||
−0.661941 | + | 0.749556i | \(0.730267\pi\) | |||||||
\(6\) | −22.0720 | −0.613111 | ||||||||
\(7\) | 16.0783 | 0.328129 | 0.164064 | − | 0.986450i | \(-0.447539\pi\) | ||||
0.164064 | + | 0.986450i | \(0.447539\pi\) | |||||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | 20.1034 | 0.248190 | ||||||||
\(10\) | 93.6127i | 0.936127i | ||||||||
\(11\) | −215.592 | −1.78175 | −0.890875 | − | 0.454248i | \(-0.849908\pi\) | ||||
−0.890875 | + | 0.454248i | \(0.849908\pi\) | |||||||
\(12\) | 62.4290i | 0.433535i | ||||||||
\(13\) | − | 281.497i | − | 1.66567i | −0.553525 | − | 0.832833i | \(-0.686718\pi\) | ||
0.553525 | − | 0.832833i | \(-0.313282\pi\) | |||||||
\(14\) | − | 45.4764i | − | 0.232022i | ||||||
\(15\) | 258.277i | 1.14790i | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 226.582 | 0.784022 | 0.392011 | − | 0.919961i | \(-0.371780\pi\) | ||||
0.392011 | + | 0.919961i | \(0.371780\pi\) | |||||||
\(18\) | − | 56.8610i | − | 0.175497i | ||||||
\(19\) | 13.9969 | − | 360.729i | 0.0387726 | − | 0.999248i | ||||
\(20\) | 264.777 | 0.661941 | ||||||||
\(21\) | − | 125.469i | − | 0.284511i | ||||||
\(22\) | 609.786i | 1.25989i | ||||||||
\(23\) | 414.609 | 0.783760 | 0.391880 | − | 0.920016i | \(-0.371825\pi\) | ||||
0.391880 | + | 0.920016i | \(0.371825\pi\) | |||||||
\(24\) | 176.576 | 0.306555 | ||||||||
\(25\) | 470.416 | 0.752666 | ||||||||
\(26\) | −796.195 | −1.17780 | ||||||||
\(27\) | − | 788.973i | − | 1.08227i | ||||||
\(28\) | −128.627 | −0.164064 | ||||||||
\(29\) | 606.612i | 0.721298i | 0.932702 | + | 0.360649i | \(0.117445\pi\) | ||||
−0.932702 | + | 0.360649i | \(0.882555\pi\) | |||||||
\(30\) | 730.518 | 0.811687 | ||||||||
\(31\) | − | 478.655i | − | 0.498080i | −0.968493 | − | 0.249040i | \(-0.919885\pi\) | ||
0.968493 | − | 0.249040i | \(-0.0801151\pi\) | |||||||
\(32\) | − | 181.019i | − | 0.176777i | ||||||
\(33\) | 1682.40i | 1.54490i | ||||||||
\(34\) | − | 640.871i | − | 0.554387i | ||||||
\(35\) | −532.145 | −0.434404 | ||||||||
\(36\) | −160.827 | −0.124095 | ||||||||
\(37\) | − | 104.604i | − | 0.0764094i | −0.999270 | − | 0.0382047i | \(-0.987836\pi\) | ||
0.999270 | − | 0.0382047i | \(-0.0121639\pi\) | |||||||
\(38\) | −1020.29 | − | 39.5893i | −0.706575 | − | 0.0274164i | ||||
\(39\) | −2196.70 | −1.44425 | ||||||||
\(40\) | − | 748.901i | − | 0.468063i | ||||||
\(41\) | 1891.12i | 1.12500i | 0.826799 | + | 0.562498i | \(0.190159\pi\) | ||||
−0.826799 | + | 0.562498i | \(0.809841\pi\) | |||||||
\(42\) | −354.881 | −0.201179 | ||||||||
\(43\) | 315.912 | 0.170855 | 0.0854277 | − | 0.996344i | \(-0.472774\pi\) | ||||
0.0854277 | + | 0.996344i | \(0.472774\pi\) | |||||||
\(44\) | 1724.73 | 0.890875 | ||||||||
\(45\) | −665.364 | −0.328575 | ||||||||
\(46\) | − | 1172.69i | − | 0.554202i | ||||||
\(47\) | −474.327 | −0.214725 | −0.107362 | − | 0.994220i | \(-0.534241\pi\) | ||||
−0.107362 | + | 0.994220i | \(0.534241\pi\) | |||||||
\(48\) | − | 499.432i | − | 0.216767i | ||||||
\(49\) | −2142.49 | −0.892331 | ||||||||
\(50\) | − | 1330.54i | − | 0.532215i | ||||||
\(51\) | − | 1768.16i | − | 0.679801i | ||||||
\(52\) | 2251.98i | 0.832833i | ||||||||
\(53\) | − | 774.381i | − | 0.275679i | −0.990455 | − | 0.137839i | \(-0.955984\pi\) | ||
0.990455 | − | 0.137839i | \(-0.0440158\pi\) | |||||||
\(54\) | −2231.55 | −0.765279 | ||||||||
\(55\) | 7135.46 | 2.35883 | ||||||||
\(56\) | 363.811i | 0.116011i | ||||||||
\(57\) | −2814.99 | − | 109.227i | −0.866418 | − | 0.0336186i | ||||
\(58\) | 1715.76 | 0.510035 | ||||||||
\(59\) | 567.212i | 0.162945i | 0.996676 | + | 0.0814725i | \(0.0259623\pi\) | ||||
−0.996676 | + | 0.0814725i | \(0.974038\pi\) | |||||||
\(60\) | − | 2066.22i | − | 0.573949i | ||||||
\(61\) | 4799.51 | 1.28984 | 0.644922 | − | 0.764248i | \(-0.276890\pi\) | ||||
0.644922 | + | 0.764248i | \(0.276890\pi\) | |||||||
\(62\) | −1353.84 | −0.352196 | ||||||||
\(63\) | 323.229 | 0.0814384 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 9316.74i | 2.20515i | ||||||||
\(66\) | 4758.54 | 1.09241 | ||||||||
\(67\) | 4464.01i | 0.994433i | 0.867627 | + | 0.497216i | \(0.165644\pi\) | ||||
−0.867627 | + | 0.497216i | \(0.834356\pi\) | |||||||
\(68\) | −1812.66 | −0.392011 | ||||||||
\(69\) | − | 3235.45i | − | 0.679575i | ||||||
\(70\) | 1505.13i | 0.307170i | ||||||||
\(71\) | − | 7636.34i | − | 1.51485i | −0.652924 | − | 0.757423i | \(-0.726458\pi\) | ||
0.652924 | − | 0.757423i | \(-0.273542\pi\) | |||||||
\(72\) | 454.888i | 0.0877484i | ||||||||
\(73\) | 8396.65 | 1.57565 | 0.787826 | − | 0.615898i | \(-0.211207\pi\) | ||||
0.787826 | + | 0.615898i | \(0.211207\pi\) | |||||||
\(74\) | −295.866 | −0.0540296 | ||||||||
\(75\) | − | 3670.95i | − | 0.652614i | ||||||
\(76\) | −111.975 | + | 2885.83i | −0.0193863 | + | 0.499624i | ||||
\(77\) | −3466.35 | −0.584644 | ||||||||
\(78\) | 6213.21i | 1.02124i | ||||||||
\(79\) | − | 9706.71i | − | 1.55531i | −0.628689 | − | 0.777657i | \(-0.716408\pi\) | ||
0.628689 | − | 0.777657i | \(-0.283592\pi\) | |||||||
\(80\) | −2118.21 | −0.330971 | ||||||||
\(81\) | −4528.48 | −0.690212 | ||||||||
\(82\) | 5348.89 | 0.795492 | ||||||||
\(83\) | −10589.4 | −1.53715 | −0.768575 | − | 0.639760i | \(-0.779034\pi\) | ||||
−0.768575 | + | 0.639760i | \(0.779034\pi\) | |||||||
\(84\) | 1003.75i | 0.142255i | ||||||||
\(85\) | −7499.21 | −1.03795 | ||||||||
\(86\) | − | 893.533i | − | 0.120813i | ||||||
\(87\) | 4733.77 | 0.625416 | ||||||||
\(88\) | − | 4878.29i | − | 0.629944i | ||||||
\(89\) | − | 10281.7i | − | 1.29804i | −0.760773 | − | 0.649018i | \(-0.775180\pi\) | ||
0.760773 | − | 0.649018i | \(-0.224820\pi\) | |||||||
\(90\) | 1881.93i | 0.232337i | ||||||||
\(91\) | − | 4526.01i | − | 0.546553i | ||||||
\(92\) | −3316.87 | −0.391880 | ||||||||
\(93\) | −3735.24 | −0.431870 | ||||||||
\(94\) | 1341.60i | 0.151833i | ||||||||
\(95\) | −463.257 | + | 11939.1i | −0.0513304 | + | 1.32289i | ||||
\(96\) | −1412.61 | −0.153278 | ||||||||
\(97\) | 15477.3i | 1.64494i | 0.568806 | + | 0.822472i | \(0.307406\pi\) | ||||
−0.568806 | + | 0.822472i | \(0.692594\pi\) | |||||||
\(98\) | 6059.87i | 0.630974i | ||||||||
\(99\) | −4334.13 | −0.442213 | ||||||||
\(100\) | −3763.33 | −0.376333 | ||||||||
\(101\) | 10464.5 | 1.02583 | 0.512914 | − | 0.858440i | \(-0.328566\pi\) | ||||
0.512914 | + | 0.858440i | \(0.328566\pi\) | |||||||
\(102\) | −5001.12 | −0.480692 | ||||||||
\(103\) | − | 3224.53i | − | 0.303943i | −0.988385 | − | 0.151972i | \(-0.951438\pi\) | ||
0.988385 | − | 0.151972i | \(-0.0485622\pi\) | |||||||
\(104\) | 6369.56 | 0.588902 | ||||||||
\(105\) | 4152.66i | 0.376659i | ||||||||
\(106\) | −2190.28 | −0.194934 | ||||||||
\(107\) | − | 7740.93i | − | 0.676123i | −0.941124 | − | 0.338061i | \(-0.890229\pi\) | ||
0.941124 | − | 0.338061i | \(-0.109771\pi\) | |||||||
\(108\) | 6311.79i | 0.541134i | ||||||||
\(109\) | 12613.1i | 1.06162i | 0.847492 | + | 0.530809i | \(0.178112\pi\) | ||||
−0.847492 | + | 0.530809i | \(0.821888\pi\) | |||||||
\(110\) | − | 20182.1i | − | 1.66794i | ||||||
\(111\) | −816.294 | −0.0662523 | ||||||||
\(112\) | 1029.01 | 0.0820322 | ||||||||
\(113\) | − | 900.876i | − | 0.0705518i | −0.999378 | − | 0.0352759i | \(-0.988769\pi\) | ||
0.999378 | − | 0.0352759i | \(-0.0112310\pi\) | |||||||
\(114\) | −308.940 | + | 7962.00i | −0.0237719 | + | 0.612650i | ||||
\(115\) | −13722.3 | −1.03761 | ||||||||
\(116\) | − | 4852.89i | − | 0.360649i | ||||||
\(117\) | − | 5659.06i | − | 0.413402i | ||||||
\(118\) | 1604.32 | 0.115220 | ||||||||
\(119\) | 3643.06 | 0.257260 | ||||||||
\(120\) | −5844.15 | −0.405843 | ||||||||
\(121\) | 31838.8 | 2.17464 | ||||||||
\(122\) | − | 13575.1i | − | 0.912058i | ||||||
\(123\) | 14757.6 | 0.975449 | ||||||||
\(124\) | 3829.24i | 0.249040i | ||||||||
\(125\) | 5116.28 | 0.327442 | ||||||||
\(126\) | − | 914.229i | − | 0.0575856i | ||||||
\(127\) | − | 16688.1i | − | 1.03467i | −0.855784 | − | 0.517334i | \(-0.826925\pi\) | ||
0.855784 | − | 0.517334i | \(-0.173075\pi\) | |||||||
\(128\) | 1448.15i | 0.0883883i | ||||||||
\(129\) | − | 2465.26i | − | 0.148144i | ||||||
\(130\) | 26351.7 | 1.55927 | ||||||||
\(131\) | 9365.24 | 0.545728 | 0.272864 | − | 0.962053i | \(-0.412029\pi\) | ||||
0.272864 | + | 0.962053i | \(0.412029\pi\) | |||||||
\(132\) | − | 13459.2i | − | 0.772451i | ||||||
\(133\) | 225.047 | − | 5799.91i | 0.0127224 | − | 0.327882i | ||||
\(134\) | 12626.1 | 0.703170 | ||||||||
\(135\) | 26112.7i | 1.43280i | ||||||||
\(136\) | 5126.97i | 0.277194i | ||||||||
\(137\) | −36021.1 | −1.91918 | −0.959591 | − | 0.281399i | \(-0.909201\pi\) | ||||
−0.959591 | + | 0.281399i | \(0.909201\pi\) | |||||||
\(138\) | −9151.25 | −0.480532 | ||||||||
\(139\) | −10371.8 | −0.536813 | −0.268406 | − | 0.963306i | \(-0.586497\pi\) | ||||
−0.268406 | + | 0.963306i | \(0.586497\pi\) | |||||||
\(140\) | 4257.16 | 0.217202 | ||||||||
\(141\) | 3701.47i | 0.186181i | ||||||||
\(142\) | −21598.8 | −1.07116 | ||||||||
\(143\) | 60688.6i | 2.96780i | ||||||||
\(144\) | 1286.62 | 0.0620475 | ||||||||
\(145\) | − | 20077.1i | − | 0.954914i | ||||||
\(146\) | − | 23749.3i | − | 1.11415i | ||||||
\(147\) | 16719.2i | 0.773714i | ||||||||
\(148\) | 836.835i | 0.0382047i | ||||||||
\(149\) | 1353.29 | 0.0609562 | 0.0304781 | − | 0.999535i | \(-0.490297\pi\) | ||||
0.0304781 | + | 0.999535i | \(0.490297\pi\) | |||||||
\(150\) | −10383.0 | −0.461468 | ||||||||
\(151\) | − | 29132.7i | − | 1.27769i | −0.769334 | − | 0.638847i | \(-0.779412\pi\) | ||
0.769334 | − | 0.638847i | \(-0.220588\pi\) | |||||||
\(152\) | 8162.36 | + | 316.714i | 0.353288 | + | 0.0137082i | ||||
\(153\) | 4555.07 | 0.194586 | ||||||||
\(154\) | 9804.33i | 0.413406i | ||||||||
\(155\) | 15842.1i | 0.659399i | ||||||||
\(156\) | 17573.6 | 0.722124 | ||||||||
\(157\) | −11934.0 | −0.484156 | −0.242078 | − | 0.970257i | \(-0.577829\pi\) | ||||
−0.242078 | + | 0.970257i | \(0.577829\pi\) | |||||||
\(158\) | −27454.7 | −1.09977 | ||||||||
\(159\) | −6042.98 | −0.239033 | ||||||||
\(160\) | 5991.21i | 0.234032i | ||||||||
\(161\) | 6666.22 | 0.257174 | ||||||||
\(162\) | 12808.5i | 0.488053i | ||||||||
\(163\) | 13818.7 | 0.520108 | 0.260054 | − | 0.965594i | \(-0.416260\pi\) | ||||
0.260054 | + | 0.965594i | \(0.416260\pi\) | |||||||
\(164\) | − | 15128.9i | − | 0.562498i | ||||||
\(165\) | − | 55682.5i | − | 2.04527i | ||||||
\(166\) | 29951.4i | 1.08693i | ||||||||
\(167\) | − | 10267.5i | − | 0.368157i | −0.982912 | − | 0.184079i | \(-0.941070\pi\) | ||
0.982912 | − | 0.184079i | \(-0.0589301\pi\) | |||||||
\(168\) | 2839.04 | 0.100590 | ||||||||
\(169\) | −50679.8 | −1.77444 | ||||||||
\(170\) | 21211.0i | 0.733943i | ||||||||
\(171\) | 281.386 | − | 7251.87i | 0.00962298 | − | 0.248003i | ||||
\(172\) | −2527.29 | −0.0854277 | ||||||||
\(173\) | − | 29001.7i | − | 0.969015i | −0.874787 | − | 0.484508i | \(-0.838999\pi\) | ||
0.874787 | − | 0.484508i | \(-0.161001\pi\) | |||||||
\(174\) | − | 13389.1i | − | 0.442236i | ||||||
\(175\) | 7563.50 | 0.246971 | ||||||||
\(176\) | −13797.9 | −0.445438 | ||||||||
\(177\) | 4426.31 | 0.141285 | ||||||||
\(178\) | −29081.2 | −0.917850 | ||||||||
\(179\) | 25479.5i | 0.795217i | 0.917555 | + | 0.397608i | \(0.130160\pi\) | ||||
−0.917555 | + | 0.397608i | \(0.869840\pi\) | |||||||
\(180\) | 5322.91 | 0.164287 | ||||||||
\(181\) | 31158.1i | 0.951073i | 0.879696 | + | 0.475536i | \(0.157746\pi\) | ||||
−0.879696 | + | 0.475536i | \(0.842254\pi\) | |||||||
\(182\) | −12801.5 | −0.386471 | ||||||||
\(183\) | − | 37453.6i | − | 1.11839i | ||||||
\(184\) | 9381.53i | 0.277101i | ||||||||
\(185\) | 3462.10i | 0.101157i | ||||||||
\(186\) | 10564.9i | 0.305378i | ||||||||
\(187\) | −48849.3 | −1.39693 | ||||||||
\(188\) | 3794.62 | 0.107362 | ||||||||
\(189\) | − | 12685.4i | − | 0.355123i | ||||||
\(190\) | 33768.8 | + | 1310.29i | 0.935423 | + | 0.0362961i | ||||
\(191\) | 17888.8 | 0.490359 | 0.245179 | − | 0.969478i | \(-0.421153\pi\) | ||||
0.245179 | + | 0.969478i | \(0.421153\pi\) | |||||||
\(192\) | 3995.46i | 0.108384i | ||||||||
\(193\) | 784.195i | 0.0210528i | 0.999945 | + | 0.0105264i | \(0.00335071\pi\) | ||||
−0.999945 | + | 0.0105264i | \(0.996649\pi\) | |||||||
\(194\) | 43776.4 | 1.16315 | ||||||||
\(195\) | 72704.4 | 1.91202 | ||||||||
\(196\) | 17139.9 | 0.446166 | ||||||||
\(197\) | 42272.4 | 1.08924 | 0.544621 | − | 0.838682i | \(-0.316673\pi\) | ||||
0.544621 | + | 0.838682i | \(0.316673\pi\) | |||||||
\(198\) | 12258.8i | 0.312692i | ||||||||
\(199\) | −15361.7 | −0.387911 | −0.193955 | − | 0.981010i | \(-0.562132\pi\) | ||||
−0.193955 | + | 0.981010i | \(0.562132\pi\) | |||||||
\(200\) | 10644.3i | 0.266108i | ||||||||
\(201\) | 34835.5 | 0.862243 | ||||||||
\(202\) | − | 29598.0i | − | 0.725369i | ||||||
\(203\) | 9753.30i | 0.236679i | ||||||||
\(204\) | 14145.3i | 0.339901i | ||||||||
\(205\) | − | 62590.4i | − | 1.48936i | ||||||
\(206\) | −9120.36 | −0.214920 | ||||||||
\(207\) | 8335.05 | 0.194521 | ||||||||
\(208\) | − | 18015.8i | − | 0.416416i | ||||||
\(209\) | −3017.62 | + | 77770.1i | −0.0690831 | + | 1.78041i | ||||
\(210\) | 11745.5 | 0.266338 | ||||||||
\(211\) | 36036.6i | 0.809429i | 0.914443 | + | 0.404714i | \(0.132629\pi\) | ||||
−0.914443 | + | 0.404714i | \(0.867371\pi\) | |||||||
\(212\) | 6195.05i | 0.137839i | ||||||||
\(213\) | −59591.2 | −1.31348 | ||||||||
\(214\) | −21894.7 | −0.478091 | ||||||||
\(215\) | −10455.8 | −0.226193 | ||||||||
\(216\) | 17852.4 | 0.382639 | ||||||||
\(217\) | − | 7695.96i | − | 0.163434i | ||||||
\(218\) | 35675.2 | 0.750677 | ||||||||
\(219\) | − | 65524.3i | − | 1.36620i | ||||||
\(220\) | −57083.7 | −1.17941 | ||||||||
\(221\) | − | 63782.3i | − | 1.30592i | ||||||
\(222\) | 2308.83i | 0.0468474i | ||||||||
\(223\) | 44099.4i | 0.886795i | 0.896325 | + | 0.443398i | \(0.146227\pi\) | ||||
−0.896325 | + | 0.443398i | \(0.853773\pi\) | |||||||
\(224\) | − | 2910.49i | − | 0.0580056i | ||||||
\(225\) | 9456.96 | 0.186804 | ||||||||
\(226\) | −2548.06 | −0.0498876 | ||||||||
\(227\) | 34866.5i | 0.676638i | 0.941032 | + | 0.338319i | \(0.109858\pi\) | ||||
−0.941032 | + | 0.338319i | \(0.890142\pi\) | |||||||
\(228\) | 22519.9 | + | 873.814i | 0.433209 | + | 0.0168093i | ||||
\(229\) | 26085.5 | 0.497425 | 0.248712 | − | 0.968577i | \(-0.419993\pi\) | ||||
0.248712 | + | 0.968577i | \(0.419993\pi\) | |||||||
\(230\) | 38812.7i | 0.733699i | ||||||||
\(231\) | 27050.1i | 0.506927i | ||||||||
\(232\) | −13726.1 | −0.255017 | ||||||||
\(233\) | 75466.8 | 1.39009 | 0.695047 | − | 0.718964i | \(-0.255383\pi\) | ||||
0.695047 | + | 0.718964i | \(0.255383\pi\) | |||||||
\(234\) | −16006.2 | −0.292319 | ||||||||
\(235\) | 15698.8 | 0.284271 | ||||||||
\(236\) | − | 4537.69i | − | 0.0814725i | ||||||
\(237\) | −75747.5 | −1.34856 | ||||||||
\(238\) | − | 10304.1i | − | 0.181910i | ||||||
\(239\) | −42891.8 | −0.750895 | −0.375447 | − | 0.926844i | \(-0.622511\pi\) | ||||
−0.375447 | + | 0.926844i | \(0.622511\pi\) | |||||||
\(240\) | 16529.7i | 0.286975i | ||||||||
\(241\) | 15629.3i | 0.269095i | 0.990907 | + | 0.134547i | \(0.0429580\pi\) | ||||
−0.990907 | + | 0.134547i | \(0.957042\pi\) | |||||||
\(242\) | − | 90053.8i | − | 1.53770i | ||||||
\(243\) | − | 28568.3i | − | 0.483806i | ||||||
\(244\) | −38396.1 | −0.644922 | ||||||||
\(245\) | 70910.1 | 1.18134 | ||||||||
\(246\) | − | 41740.7i | − | 0.689747i | ||||||
\(247\) | −101544. | − | 3940.10i | −1.66441 | − | 0.0645822i | ||||
\(248\) | 10830.7 | 0.176098 | ||||||||
\(249\) | 82635.9i | 1.33282i | ||||||||
\(250\) | − | 14471.0i | − | 0.231536i | ||||||
\(251\) | 76998.8 | 1.22218 | 0.611092 | − | 0.791560i | \(-0.290731\pi\) | ||||
0.611092 | + | 0.791560i | \(0.290731\pi\) | |||||||
\(252\) | −2585.83 | −0.0407192 | ||||||||
\(253\) | −89386.3 | −1.39646 | ||||||||
\(254\) | −47201.2 | −0.731620 | ||||||||
\(255\) | 58521.0i | 0.899977i | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 8903.45i | 0.134801i | 0.997726 | + | 0.0674003i | \(0.0214705\pi\) | ||||
−0.997726 | + | 0.0674003i | \(0.978530\pi\) | |||||||
\(258\) | −6972.80 | −0.104753 | ||||||||
\(259\) | − | 1681.86i | − | 0.0250721i | ||||||
\(260\) | − | 74533.9i | − | 1.10257i | ||||||
\(261\) | 12195.0i | 0.179019i | ||||||||
\(262\) | − | 26488.9i | − | 0.385888i | ||||||
\(263\) | −79232.7 | −1.14549 | −0.572747 | − | 0.819732i | \(-0.694122\pi\) | ||||
−0.572747 | + | 0.819732i | \(0.694122\pi\) | |||||||
\(264\) | −38068.3 | −0.546205 | ||||||||
\(265\) | 25629.8i | 0.364966i | ||||||||
\(266\) | −16404.6 | − | 636.529i | −0.231848 | − | 0.00899611i | ||||
\(267\) | −80234.9 | −1.12549 | ||||||||
\(268\) | − | 35712.1i | − | 0.497216i | ||||||
\(269\) | − | 132817.i | − | 1.83548i | −0.397177 | − | 0.917742i | \(-0.630010\pi\) | ||
0.397177 | − | 0.917742i | \(-0.369990\pi\) | |||||||
\(270\) | 73857.9 | 1.01314 | ||||||||
\(271\) | 73016.0 | 0.994213 | 0.497106 | − | 0.867690i | \(-0.334396\pi\) | ||||
0.497106 | + | 0.867690i | \(0.334396\pi\) | |||||||
\(272\) | 14501.3 | 0.196005 | ||||||||
\(273\) | −35319.3 | −0.473900 | ||||||||
\(274\) | 101883.i | 1.35707i | ||||||||
\(275\) | −101418. | −1.34106 | ||||||||
\(276\) | 25883.6i | 0.339787i | ||||||||
\(277\) | 66280.9 | 0.863831 | 0.431916 | − | 0.901914i | \(-0.357838\pi\) | ||||
0.431916 | + | 0.901914i | \(0.357838\pi\) | |||||||
\(278\) | 29335.8i | 0.379584i | ||||||||
\(279\) | − | 9622.59i | − | 0.123619i | ||||||
\(280\) | − | 12041.1i | − | 0.153585i | ||||||
\(281\) | 112860.i | 1.42932i | 0.699473 | + | 0.714659i | \(0.253418\pi\) | ||||
−0.699473 | + | 0.714659i | \(0.746582\pi\) | |||||||
\(282\) | 10469.3 | 0.131650 | ||||||||
\(283\) | 80766.6 | 1.00846 | 0.504230 | − | 0.863569i | \(-0.331776\pi\) | ||||
0.504230 | + | 0.863569i | \(0.331776\pi\) | |||||||
\(284\) | 61090.7i | 0.757423i | ||||||||
\(285\) | 93168.0 | + | 3615.08i | 1.14704 | + | 0.0445070i | ||||
\(286\) | 171653. | 2.09855 | ||||||||
\(287\) | 30406.0i | 0.369144i | ||||||||
\(288\) | − | 3639.10i | − | 0.0438742i | ||||||
\(289\) | −32181.5 | −0.385310 | ||||||||
\(290\) | −56786.5 | −0.675226 | ||||||||
\(291\) | 120779. | 1.42628 | ||||||||
\(292\) | −67173.2 | −0.787826 | ||||||||
\(293\) | − | 133666.i | − | 1.55699i | −0.627653 | − | 0.778493i | \(-0.715984\pi\) | ||
0.627653 | − | 0.778493i | \(-0.284016\pi\) | |||||||
\(294\) | 47289.0 | 0.547098 | ||||||||
\(295\) | − | 18773.0i | − | 0.215720i | ||||||
\(296\) | 2366.93 | 0.0270148 | ||||||||
\(297\) | 170096.i | 1.92833i | ||||||||
\(298\) | − | 3827.68i | − | 0.0431025i | ||||||
\(299\) | − | 116711.i | − | 1.30548i | ||||||
\(300\) | 29367.6i | 0.326307i | ||||||||
\(301\) | 5079.33 | 0.0560626 | ||||||||
\(302\) | −82399.8 | −0.903467 | ||||||||
\(303\) | − | 81660.8i | − | 0.889464i | ||||||
\(304\) | 895.803 | − | 23086.6i | 0.00969316 | − | 0.249812i | ||||
\(305\) | −158850. | −1.70760 | ||||||||
\(306\) | − | 12883.7i | − | 0.137593i | ||||||
\(307\) | 100857.i | 1.07011i | 0.844816 | + | 0.535057i | \(0.179710\pi\) | ||||
−0.844816 | + | 0.535057i | \(0.820290\pi\) | |||||||
\(308\) | 27730.8 | 0.292322 | ||||||||
\(309\) | −25163.1 | −0.263540 | ||||||||
\(310\) | 44808.1 | 0.466266 | ||||||||
\(311\) | 121531. | 1.25651 | 0.628254 | − | 0.778009i | \(-0.283770\pi\) | ||||
0.628254 | + | 0.778009i | \(0.283770\pi\) | |||||||
\(312\) | − | 49705.7i | − | 0.510619i | ||||||
\(313\) | 189932. | 1.93869 | 0.969346 | − | 0.245700i | \(-0.0790180\pi\) | ||||
0.969346 | + | 0.245700i | \(0.0790180\pi\) | |||||||
\(314\) | 33754.3i | 0.342350i | ||||||||
\(315\) | −10697.9 | −0.107815 | ||||||||
\(316\) | 77653.7i | 0.777657i | ||||||||
\(317\) | 67336.1i | 0.670085i | 0.942203 | + | 0.335042i | \(0.108751\pi\) | ||||
−0.942203 | + | 0.335042i | \(0.891249\pi\) | |||||||
\(318\) | 17092.1i | 0.169022i | ||||||||
\(319\) | − | 130781.i | − | 1.28517i | ||||||
\(320\) | 16945.7 | 0.165485 | ||||||||
\(321\) | −60407.3 | −0.586246 | ||||||||
\(322\) | − | 18854.9i | − | 0.181850i | ||||||
\(323\) | 3171.45 | − | 81734.7i | 0.0303986 | − | 0.783432i | ||||
\(324\) | 36227.8 | 0.345106 | ||||||||
\(325\) | − | 132421.i | − | 1.25369i | ||||||
\(326\) | − | 39085.3i | − | 0.367772i | ||||||
\(327\) | 98427.7 | 0.920496 | ||||||||
\(328\) | −42791.1 | −0.397746 | ||||||||
\(329\) | −7626.38 | −0.0704574 | ||||||||
\(330\) | −157494. | −1.44622 | ||||||||
\(331\) | − | 154310.i | − | 1.40844i | −0.709984 | − | 0.704218i | \(-0.751298\pi\) | ||
0.709984 | − | 0.704218i | \(-0.248702\pi\) | |||||||
\(332\) | 84715.4 | 0.768575 | ||||||||
\(333\) | − | 2102.90i | − | 0.0189640i | ||||||
\(334\) | −29041.0 | −0.260327 | ||||||||
\(335\) | − | 147746.i | − | 1.31651i | ||||||
\(336\) | − | 8030.03i | − | 0.0711277i | ||||||
\(337\) | 127543.i | 1.12304i | 0.827463 | + | 0.561521i | \(0.189783\pi\) | ||||
−0.827463 | + | 0.561521i | \(0.810217\pi\) | |||||||
\(338\) | 143344.i | 1.25472i | ||||||||
\(339\) | −7030.10 | −0.0611733 | ||||||||
\(340\) | 59993.7 | 0.518976 | ||||||||
\(341\) | 103194.i | 0.887454i | ||||||||
\(342\) | −20511.4 | − | 795.879i | −0.175365 | − | 0.00680447i | ||||
\(343\) | −73051.6 | −0.620929 | ||||||||
\(344\) | 7148.26i | 0.0604065i | ||||||||
\(345\) | 107084.i | 0.899677i | ||||||||
\(346\) | −82029.1 | −0.685197 | ||||||||
\(347\) | −71084.5 | −0.590359 | −0.295179 | − | 0.955442i | \(-0.595379\pi\) | ||||
−0.295179 | + | 0.955442i | \(0.595379\pi\) | |||||||
\(348\) | −37870.2 | −0.312708 | ||||||||
\(349\) | 83601.6 | 0.686378 | 0.343189 | − | 0.939266i | \(-0.388493\pi\) | ||||
0.343189 | + | 0.939266i | \(0.388493\pi\) | |||||||
\(350\) | − | 21392.8i | − | 0.174635i | ||||||
\(351\) | −222094. | −1.80270 | ||||||||
\(352\) | 39026.3i | 0.314972i | ||||||||
\(353\) | −40368.7 | −0.323963 | −0.161981 | − | 0.986794i | \(-0.551788\pi\) | ||||
−0.161981 | + | 0.986794i | \(0.551788\pi\) | |||||||
\(354\) | − | 12519.5i | − | 0.0999034i | ||||||
\(355\) | 252740.i | 2.00548i | ||||||||
\(356\) | 82254.0i | 0.649018i | ||||||||
\(357\) | − | 28429.1i | − | 0.223063i | ||||||
\(358\) | 72067.0 | 0.562303 | ||||||||
\(359\) | 143079. | 1.11016 | 0.555081 | − | 0.831796i | \(-0.312687\pi\) | ||||
0.555081 | + | 0.831796i | \(0.312687\pi\) | |||||||
\(360\) | − | 15055.5i | − | 0.116169i | ||||||
\(361\) | −129929. | − | 10098.2i | −0.996993 | − | 0.0774869i | ||||
\(362\) | 88128.4 | 0.672510 | ||||||||
\(363\) | − | 248458.i | − | 1.88556i | ||||||
\(364\) | 36208.0i | 0.273277i | ||||||||
\(365\) | −277904. | −2.08598 | ||||||||
\(366\) | −105935. | −0.790818 | ||||||||
\(367\) | −30831.7 | −0.228910 | −0.114455 | − | 0.993428i | \(-0.536512\pi\) | ||||
−0.114455 | + | 0.993428i | \(0.536512\pi\) | |||||||
\(368\) | 26535.0 | 0.195940 | ||||||||
\(369\) | 38017.9i | 0.279213i | ||||||||
\(370\) | 9792.30 | 0.0715288 | ||||||||
\(371\) | − | 12450.8i | − | 0.0904582i | ||||||
\(372\) | 29882.0 | 0.215935 | ||||||||
\(373\) | 199882.i | 1.43666i | 0.695701 | + | 0.718332i | \(0.255094\pi\) | ||||
−0.695701 | + | 0.718332i | \(0.744906\pi\) | |||||||
\(374\) | 138167.i | 0.987779i | ||||||||
\(375\) | − | 39925.5i | − | 0.283915i | ||||||
\(376\) | − | 10732.8i | − | 0.0759167i | ||||||
\(377\) | 170760. | 1.20144 | ||||||||
\(378\) | −35879.6 | −0.251110 | ||||||||
\(379\) | − | 49499.6i | − | 0.344606i | −0.985044 | − | 0.172303i | \(-0.944879\pi\) | ||
0.985044 | − | 0.172303i | \(-0.0551209\pi\) | |||||||
\(380\) | 3706.06 | − | 95512.5i | 0.0256652 | − | 0.661444i | ||||
\(381\) | −130228. | −0.897129 | ||||||||
\(382\) | − | 50597.1i | − | 0.346736i | ||||||
\(383\) | 49593.2i | 0.338084i | 0.985609 | + | 0.169042i | \(0.0540674\pi\) | ||||
−0.985609 | + | 0.169042i | \(0.945933\pi\) | |||||||
\(384\) | 11300.9 | 0.0766389 | ||||||||
\(385\) | 114726. | 0.774000 | ||||||||
\(386\) | 2218.04 | 0.0148866 | ||||||||
\(387\) | 6350.90 | 0.0424046 | ||||||||
\(388\) | − | 123818.i | − | 0.822472i | ||||||
\(389\) | −15826.9 | −0.104592 | −0.0522958 | − | 0.998632i | \(-0.516654\pi\) | ||||
−0.0522958 | + | 0.998632i | \(0.516654\pi\) | |||||||
\(390\) | − | 205639.i | − | 1.35200i | ||||||
\(391\) | 93943.1 | 0.614485 | ||||||||
\(392\) | − | 48479.0i | − | 0.315487i | ||||||
\(393\) | − | 73082.8i | − | 0.473184i | ||||||
\(394\) | − | 119564.i | − | 0.770211i | ||||||
\(395\) | 321264.i | 2.05905i | ||||||||
\(396\) | 34673.0 | 0.221106 | ||||||||
\(397\) | −2861.99 | −0.0181588 | −0.00907939 | − | 0.999959i | \(-0.502890\pi\) | ||||
−0.00907939 | + | 0.999959i | \(0.502890\pi\) | |||||||
\(398\) | 43449.3i | 0.274294i | ||||||||
\(399\) | −45260.3 | − | 1756.18i | −0.284297 | − | 0.0110312i | ||||
\(400\) | 30106.6 | 0.188166 | ||||||||
\(401\) | − | 226034.i | − | 1.40567i | −0.711351 | − | 0.702837i | \(-0.751916\pi\) | ||
0.711351 | − | 0.702837i | \(-0.248084\pi\) | |||||||
\(402\) | − | 98529.6i | − | 0.609698i | ||||||
\(403\) | −134740. | −0.829634 | ||||||||
\(404\) | −83715.7 | −0.512914 | ||||||||
\(405\) | 149879. | 0.913759 | ||||||||
\(406\) | 27586.5 | 0.167357 | ||||||||
\(407\) | 22551.9i | 0.136142i | ||||||||
\(408\) | 40009.0 | 0.240346 | ||||||||
\(409\) | − | 300321.i | − | 1.79531i | −0.440700 | − | 0.897655i | \(-0.645270\pi\) | ||
0.440700 | − | 0.897655i | \(-0.354730\pi\) | |||||||
\(410\) | −177032. | −1.05314 | ||||||||
\(411\) | 281095.i | 1.66406i | ||||||||
\(412\) | 25796.3i | 0.151972i | ||||||||
\(413\) | 9119.81i | 0.0534670i | ||||||||
\(414\) | − | 23575.1i | − | 0.137547i | ||||||
\(415\) | 350479. | 2.03501 | ||||||||
\(416\) | −50956.5 | −0.294451 | ||||||||
\(417\) | 80937.4i | 0.465454i | ||||||||
\(418\) | 219967. | + | 8535.12i | 1.25894 | + | 0.0488492i | ||||
\(419\) | −88915.8 | −0.506467 | −0.253233 | − | 0.967405i | \(-0.581494\pi\) | ||||
−0.253233 | + | 0.967405i | \(0.581494\pi\) | |||||||
\(420\) | − | 33221.3i | − | 0.188329i | ||||||
\(421\) | − | 52919.8i | − | 0.298575i | −0.988794 | − | 0.149288i | \(-0.952302\pi\) | ||
0.988794 | − | 0.149288i | \(-0.0476980\pi\) | |||||||
\(422\) | 101927. | 0.572353 | ||||||||
\(423\) | −9535.59 | −0.0532926 | ||||||||
\(424\) | 17522.3 | 0.0974671 | ||||||||
\(425\) | 106588. | 0.590106 | ||||||||
\(426\) | 168549.i | 0.928769i | ||||||||
\(427\) | 77168.1 | 0.423235 | ||||||||
\(428\) | 61927.4i | 0.338061i | ||||||||
\(429\) | 473591. | 2.57329 | ||||||||
\(430\) | 29573.3i | 0.159942i | ||||||||
\(431\) | 18064.2i | 0.0972442i | 0.998817 | + | 0.0486221i | \(0.0154830\pi\) | ||||
−0.998817 | + | 0.0486221i | \(0.984517\pi\) | |||||||
\(432\) | − | 50494.3i | − | 0.270567i | ||||||
\(433\) | 188974.i | 1.00792i | 0.863726 | + | 0.503961i | \(0.168125\pi\) | ||||
−0.863726 | + | 0.503961i | \(0.831875\pi\) | |||||||
\(434\) | −21767.5 | −0.115566 | ||||||||
\(435\) | −156674. | −0.827977 | ||||||||
\(436\) | − | 100905.i | − | 0.530809i | ||||||
\(437\) | 5803.25 | − | 149561.i | 0.0303884 | − | 0.783171i | ||||
\(438\) | −185331. | −0.966049 | ||||||||
\(439\) | 249410.i | 1.29415i | 0.762427 | + | 0.647074i | \(0.224008\pi\) | ||||
−0.762427 | + | 0.647074i | \(0.775992\pi\) | |||||||
\(440\) | 161457.i | 0.833972i | ||||||||
\(441\) | −43071.3 | −0.221468 | ||||||||
\(442\) | −180404. | −0.923423 | ||||||||
\(443\) | 43050.1 | 0.219365 | 0.109682 | − | 0.993967i | \(-0.465017\pi\) | ||||
0.109682 | + | 0.993967i | \(0.465017\pi\) | |||||||
\(444\) | 6530.35 | 0.0331261 | ||||||||
\(445\) | 340296.i | 1.71845i | ||||||||
\(446\) | 124732. | 0.627059 | ||||||||
\(447\) | − | 10560.6i | − | 0.0528533i | ||||||
\(448\) | −8232.10 | −0.0410161 | ||||||||
\(449\) | 19223.8i | 0.0953556i | 0.998863 | + | 0.0476778i | \(0.0151821\pi\) | ||||
−0.998863 | + | 0.0476778i | \(0.984818\pi\) | |||||||
\(450\) | − | 26748.3i | − | 0.132090i | ||||||
\(451\) | − | 407709.i | − | 2.00446i | ||||||
\(452\) | 7207.01i | 0.0352759i | ||||||||
\(453\) | −227341. | −1.10785 | ||||||||
\(454\) | 98617.2 | 0.478455 | ||||||||
\(455\) | 149798.i | 0.723572i | ||||||||
\(456\) | 2471.52 | − | 63696.0i | 0.0118860 | − | 0.306325i | ||||
\(457\) | 38484.7 | 0.184271 | 0.0921353 | − | 0.995747i | \(-0.470631\pi\) | ||||
0.0921353 | + | 0.995747i | \(0.470631\pi\) | |||||||
\(458\) | − | 73780.8i | − | 0.351732i | ||||||
\(459\) | − | 178767.i | − | 0.848521i | ||||||
\(460\) | 109779. | 0.518803 | ||||||||
\(461\) | −203940. | −0.959623 | −0.479812 | − | 0.877371i | \(-0.659295\pi\) | ||||
−0.479812 | + | 0.877371i | \(0.659295\pi\) | |||||||
\(462\) | 76509.3 | 0.358452 | ||||||||
\(463\) | −203200. | −0.947900 | −0.473950 | − | 0.880552i | \(-0.657172\pi\) | ||||
−0.473950 | + | 0.880552i | \(0.657172\pi\) | |||||||
\(464\) | 38823.2i | 0.180325i | ||||||||
\(465\) | 123626. | 0.571745 | ||||||||
\(466\) | − | 213452.i | − | 0.982945i | ||||||
\(467\) | −121674. | −0.557912 | −0.278956 | − | 0.960304i | \(-0.589988\pi\) | ||||
−0.278956 | + | 0.960304i | \(0.589988\pi\) | |||||||
\(468\) | 45272.4i | 0.206701i | ||||||||
\(469\) | 71773.8i | 0.326302i | ||||||||
\(470\) | − | 44403.0i | − | 0.201010i | ||||||
\(471\) | 93128.2i | 0.419797i | ||||||||
\(472\) | −12834.5 | −0.0576098 | ||||||||
\(473\) | −68108.0 | −0.304422 | ||||||||
\(474\) | 214246.i | 0.953579i | ||||||||
\(475\) | 6584.37 | − | 169693.i | 0.0291828 | − | 0.752100i | ||||
\(476\) | −29144.5 | −0.128630 | ||||||||
\(477\) | − | 15567.7i | − | 0.0684207i | ||||||
\(478\) | 121316.i | 0.530963i | ||||||||
\(479\) | −208037. | −0.906711 | −0.453355 | − | 0.891330i | \(-0.649773\pi\) | ||||
−0.453355 | + | 0.891330i | \(0.649773\pi\) | |||||||
\(480\) | 46753.2 | 0.202922 | ||||||||
\(481\) | −29445.9 | −0.127272 | ||||||||
\(482\) | 44206.3 | 0.190279 | ||||||||
\(483\) | − | 52020.7i | − | 0.222988i | ||||||
\(484\) | −254711. | −1.08732 | ||||||||
\(485\) | − | 512253.i | − | 2.17771i | ||||||
\(486\) | −80803.3 | −0.342103 | ||||||||
\(487\) | − | 47417.7i | − | 0.199932i | −0.994991 | − | 0.0999660i | \(-0.968127\pi\) | ||
0.994991 | − | 0.0999660i | \(-0.0318734\pi\) | |||||||
\(488\) | 108601.i | 0.456029i | ||||||||
\(489\) | − | 107836.i | − | 0.450970i | ||||||
\(490\) | − | 200564.i | − | 0.835335i | ||||||
\(491\) | −218823. | −0.907676 | −0.453838 | − | 0.891084i | \(-0.649946\pi\) | ||||
−0.453838 | + | 0.891084i | \(0.649946\pi\) | |||||||
\(492\) | −118061. | −0.487725 | ||||||||
\(493\) | 137447.i | 0.565513i | ||||||||
\(494\) | −11144.3 | + | 287210.i | −0.0456665 | + | 1.17692i | ||||
\(495\) | 143447. | 0.585438 | ||||||||
\(496\) | − | 30633.9i | − | 0.124520i | ||||||
\(497\) | − | 122780.i | − | 0.497065i | ||||||
\(498\) | 233730. | 0.942443 | ||||||||
\(499\) | 147213. | 0.591214 | 0.295607 | − | 0.955310i | \(-0.404478\pi\) | ||||
0.295607 | + | 0.955310i | \(0.404478\pi\) | |||||||
\(500\) | −40930.2 | −0.163721 | ||||||||
\(501\) | −80124.1 | −0.319218 | ||||||||
\(502\) | − | 217786.i | − | 0.864215i | ||||||
\(503\) | 189477. | 0.748895 | 0.374448 | − | 0.927248i | \(-0.377832\pi\) | ||||
0.374448 | + | 0.927248i | \(0.377832\pi\) | |||||||
\(504\) | 7313.83i | 0.0287928i | ||||||||
\(505\) | −346343. | −1.35807 | ||||||||
\(506\) | 252823.i | 0.987450i | ||||||||
\(507\) | 395486.i | 1.53856i | ||||||||
\(508\) | 133505.i | 0.517334i | ||||||||
\(509\) | − | 117829.i | − | 0.454797i | −0.973802 | − | 0.227398i | \(-0.926978\pi\) | ||
0.973802 | − | 0.227398i | \(-0.0730220\pi\) | |||||||
\(510\) | 165522. | 0.636380 | ||||||||
\(511\) | 135004. | 0.517017 | ||||||||
\(512\) | − | 11585.2i | − | 0.0441942i | ||||||
\(513\) | −284605. | − | 11043.2i | −1.08145 | − | 0.0419624i | ||||
\(514\) | 25182.8 | 0.0953185 | ||||||||
\(515\) | 106723.i | 0.402385i | ||||||||
\(516\) | 19722.1i | 0.0740718i | ||||||||
\(517\) | 102261. | 0.382586 | ||||||||
\(518\) | −4757.03 | −0.0177287 | ||||||||
\(519\) | −226318. | −0.840204 | ||||||||
\(520\) | −210814. | −0.779637 | ||||||||
\(521\) | − | 254449.i | − | 0.937402i | −0.883357 | − | 0.468701i | \(-0.844722\pi\) | ||
0.883357 | − | 0.468701i | \(-0.155278\pi\) | |||||||
\(522\) | 34492.6 | 0.126586 | ||||||||
\(523\) | − | 33047.5i | − | 0.120819i | −0.998174 | − | 0.0604094i | \(-0.980759\pi\) | ||
0.998174 | − | 0.0604094i | \(-0.0192406\pi\) | |||||||
\(524\) | −74921.9 | −0.272864 | ||||||||
\(525\) | − | 59022.7i | − | 0.214141i | ||||||
\(526\) | 224104.i | 0.809987i | ||||||||
\(527\) | − | 108455.i | − | 0.390505i | ||||||
\(528\) | 107673.i | 0.386226i | ||||||||
\(529\) | −107940. | −0.385720 | ||||||||
\(530\) | 72491.9 | 0.258070 | ||||||||
\(531\) | 11402.9i | 0.0404414i | ||||||||
\(532\) | −1800.38 | + | 46399.3i | −0.00636121 | + | 0.163941i | ||||
\(533\) | 532345. | 1.87387 | ||||||||
\(534\) | 226939.i | 0.795840i | ||||||||
\(535\) | 256202.i | 0.895107i | ||||||||
\(536\) | −101009. | −0.351585 | ||||||||
\(537\) | 198833. | 0.689508 | ||||||||
\(538\) | −375665. | −1.29788 | ||||||||
\(539\) | 461903. | 1.58991 | ||||||||
\(540\) | − | 208902.i | − | 0.716398i | ||||||
\(541\) | −363239. | −1.24108 | −0.620538 | − | 0.784176i | \(-0.713086\pi\) | ||||
−0.620538 | + | 0.784176i | \(0.713086\pi\) | |||||||
\(542\) | − | 206520.i | − | 0.703014i | ||||||
\(543\) | 243146. | 0.824647 | ||||||||
\(544\) | − | 41015.8i | − | 0.138597i | ||||||
\(545\) | − | 417456.i | − | 1.40546i | ||||||
\(546\) | 99898.0i | 0.335098i | ||||||||
\(547\) | 899.921i | 0.00300767i | 0.999999 | + | 0.00150383i | \(0.000478685\pi\) | ||||
−0.999999 | + | 0.00150383i | \(0.999521\pi\) | |||||||
\(548\) | 288169. | 0.959591 | ||||||||
\(549\) | 96486.5 | 0.320127 | ||||||||
\(550\) | 286853.i | 0.948274i | ||||||||
\(551\) | 218822. | + | 8490.69i | 0.720756 | + | 0.0279666i | ||||
\(552\) | 73210.0 | 0.240266 | ||||||||
\(553\) | − | 156068.i | − | 0.510343i | ||||||
\(554\) | − | 187471.i | − | 0.610821i | ||||||
\(555\) | 27016.9 | 0.0877102 | ||||||||
\(556\) | 82974.1 | 0.268406 | ||||||||
\(557\) | 340311. | 1.09690 | 0.548448 | − | 0.836184i | \(-0.315219\pi\) | ||||
0.548448 | + | 0.836184i | \(0.315219\pi\) | |||||||
\(558\) | −27216.8 | −0.0874115 | ||||||||
\(559\) | − | 88928.3i | − | 0.284588i | ||||||
\(560\) | −34057.3 | −0.108601 | ||||||||
\(561\) | 381202.i | 1.21124i | ||||||||
\(562\) | 319217. | 1.01068 | ||||||||
\(563\) | 631686.i | 1.99289i | 0.0842180 | + | 0.996447i | \(0.473161\pi\) | ||||
−0.0842180 | + | 0.996447i | \(0.526839\pi\) | |||||||
\(564\) | − | 29611.8i | − | 0.0930907i | ||||||
\(565\) | 29816.3i | 0.0934023i | ||||||||
\(566\) | − | 228442.i | − | 0.713089i | ||||||
\(567\) | −72810.3 | −0.226478 | ||||||||
\(568\) | 172791. | 0.535579 | ||||||||
\(569\) | 5519.19i | 0.0170471i | 0.999964 | + | 0.00852356i | \(0.00271317\pi\) | ||||
−0.999964 | + | 0.00852356i | \(0.997287\pi\) | |||||||
\(570\) | 10225.0 | − | 263519.i | 0.0314712 | − | 0.811077i | ||||
\(571\) | −478673. | −1.46814 | −0.734068 | − | 0.679076i | \(-0.762381\pi\) | ||||
−0.734068 | + | 0.679076i | \(0.762381\pi\) | |||||||
\(572\) | − | 485508.i | − | 1.48390i | ||||||
\(573\) | − | 139597.i | − | 0.425175i | ||||||
\(574\) | 86001.1 | 0.261024 | ||||||||
\(575\) | 195039. | 0.589909 | ||||||||
\(576\) | −10292.9 | −0.0310238 | ||||||||
\(577\) | 65914.9 | 0.197985 | 0.0989925 | − | 0.995088i | \(-0.468438\pi\) | ||||
0.0989925 | + | 0.995088i | \(0.468438\pi\) | |||||||
\(578\) | 91023.0i | 0.272455i | ||||||||
\(579\) | 6119.56 | 0.0182542 | ||||||||
\(580\) | 160617.i | 0.477457i | ||||||||
\(581\) | −170260. | −0.504383 | ||||||||
\(582\) | − | 341614.i | − | 1.00853i | ||||||
\(583\) | 166950.i | 0.491191i | ||||||||
\(584\) | 189994.i | 0.557077i | ||||||||
\(585\) | 187298.i | 0.547295i | ||||||||
\(586\) | −378064. | −1.10096 | ||||||||
\(587\) | 289436. | 0.839994 | 0.419997 | − | 0.907526i | \(-0.362031\pi\) | ||||
0.419997 | + | 0.907526i | \(0.362031\pi\) | |||||||
\(588\) | − | 133753.i | − | 0.386857i | ||||||
\(589\) | −172664. | − | 6699.69i | −0.497705 | − | 0.0193119i | ||||
\(590\) | −53098.2 | −0.152537 | ||||||||
\(591\) | − | 329878.i | − | 0.944449i | ||||||
\(592\) | − | 6694.68i | − | 0.0191023i | ||||||
\(593\) | 388285. | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(594\) | 481105. | 1.36354 | ||||||||
\(595\) | −120575. | −0.340582 | ||||||||
\(596\) | −10826.3 | −0.0304781 | ||||||||
\(597\) | 119877.i | 0.336346i | ||||||||
\(598\) | −330110. | −0.923115 | ||||||||
\(599\) | 601872.i | 1.67745i | 0.544553 | + | 0.838727i | \(0.316699\pi\) | ||||
−0.544553 | + | 0.838727i | \(0.683301\pi\) | |||||||
\(600\) | 83064.2 | 0.230734 | ||||||||
\(601\) | − | 176095.i | − | 0.487527i | −0.969835 | − | 0.243764i | \(-0.921618\pi\) | ||
0.969835 | − | 0.243764i | \(-0.0783821\pi\) | |||||||
\(602\) | − | 14366.5i | − | 0.0396423i | ||||||
\(603\) | 89741.7i | 0.246808i | ||||||||
\(604\) | 233062.i | 0.638847i | ||||||||
\(605\) | −1.05377e6 | −2.87896 | ||||||||
\(606\) | −230972. | −0.628946 | ||||||||
\(607\) | − | 607939.i | − | 1.64999i | −0.565137 | − | 0.824997i | \(-0.691177\pi\) | ||
0.565137 | − | 0.824997i | \(-0.308823\pi\) | |||||||
\(608\) | −65298.8 | − | 2533.71i | −0.176644 | − | 0.00685410i | ||||
\(609\) | 76111.1 | 0.205217 | ||||||||
\(610\) | 449295.i | 1.20746i | ||||||||
\(611\) | 133522.i | 0.357660i | ||||||||
\(612\) | −36440.6 | −0.0972932 | ||||||||
\(613\) | 194933. | 0.518757 | 0.259379 | − | 0.965776i | \(-0.416482\pi\) | ||||
0.259379 | + | 0.965776i | \(0.416482\pi\) | |||||||
\(614\) | 285267. | 0.756685 | ||||||||
\(615\) | −488432. | −1.29138 | ||||||||
\(616\) | − | 78434.6i | − | 0.206703i | ||||||
\(617\) | 148271. | 0.389480 | 0.194740 | − | 0.980855i | \(-0.437614\pi\) | ||||
0.194740 | + | 0.980855i | \(0.437614\pi\) | |||||||
\(618\) | 71171.9i | 0.186351i | ||||||||
\(619\) | −572353. | −1.49377 | −0.746884 | − | 0.664955i | \(-0.768451\pi\) | ||||
−0.746884 | + | 0.664955i | \(0.768451\pi\) | |||||||
\(620\) | − | 126737.i | − | 0.329700i | ||||||
\(621\) | − | 327115.i | − | 0.848238i | ||||||
\(622\) | − | 343741.i | − | 0.888485i | ||||||
\(623\) | − | 165313.i | − | 0.425923i | ||||||
\(624\) | −140589. | −0.361062 | ||||||||
\(625\) | −463344. | −1.18616 | ||||||||
\(626\) | − | 537208.i | − | 1.37086i | ||||||
\(627\) | 606889. | + | 23548.4i | 1.54374 | + | 0.0598999i | ||||
\(628\) | 95471.7 | 0.242078 | ||||||||
\(629\) | − | 23701.5i | − | 0.0599066i | ||||||
\(630\) | 30258.3i | 0.0762366i | ||||||||
\(631\) | 236439. | 0.593829 | 0.296914 | − | 0.954904i | \(-0.404042\pi\) | ||||
0.296914 | + | 0.954904i | \(0.404042\pi\) | |||||||
\(632\) | 219638. | 0.549886 | ||||||||
\(633\) | 281216. | 0.701831 | ||||||||
\(634\) | 190455. | 0.473821 | ||||||||
\(635\) | 552329.i | 1.36978i | ||||||||
\(636\) | 48343.9 | 0.119516 | ||||||||
\(637\) | 603105.i | 1.48633i | ||||||||
\(638\) | −369903. | −0.908755 | ||||||||
\(639\) | − | 153516.i | − | 0.375970i | ||||||
\(640\) | − | 47929.7i | − | 0.117016i | ||||||
\(641\) | 247053.i | 0.601275i | 0.953738 | + | 0.300638i | \(0.0971995\pi\) | ||||
−0.953738 | + | 0.300638i | \(0.902801\pi\) | |||||||
\(642\) | 170858.i | 0.414538i | ||||||||
\(643\) | 543389. | 1.31428 | 0.657142 | − | 0.753767i | \(-0.271765\pi\) | ||||
0.657142 | + | 0.753767i | \(0.271765\pi\) | |||||||
\(644\) | −53329.7 | −0.128587 | ||||||||
\(645\) | 81592.8i | 0.196125i | ||||||||
\(646\) | −231181. | − | 8970.22i | −0.553970 | − | 0.0214950i | ||||
\(647\) | −263444. | −0.629332 | −0.314666 | − | 0.949202i | \(-0.601893\pi\) | ||||
−0.314666 | + | 0.949202i | \(0.601893\pi\) | |||||||
\(648\) | − | 102468.i | − | 0.244027i | ||||||
\(649\) | − | 122286.i | − | 0.290327i | ||||||
\(650\) | −374543. | −0.886492 | ||||||||
\(651\) | −60056.4 | −0.141709 | ||||||||
\(652\) | −110550. | −0.260054 | ||||||||
\(653\) | −261207. | −0.612574 | −0.306287 | − | 0.951939i | \(-0.599087\pi\) | ||||
−0.306287 | + | 0.951939i | \(0.599087\pi\) | |||||||
\(654\) | − | 278396.i | − | 0.650889i | ||||||
\(655\) | −309962. | −0.722480 | ||||||||
\(656\) | 121031.i | 0.281249i | ||||||||
\(657\) | 168801. | 0.391061 | ||||||||
\(658\) | 21570.7i | 0.0498209i | ||||||||
\(659\) | − | 532996.i | − | 1.22731i | −0.789576 | − | 0.613653i | \(-0.789699\pi\) | ||
0.789576 | − | 0.613653i | \(-0.210301\pi\) | |||||||
\(660\) | 445460.i | 1.02263i | ||||||||
\(661\) | 495346.i | 1.13372i | 0.823814 | + | 0.566860i | \(0.191842\pi\) | ||||
−0.823814 | + | 0.566860i | \(0.808158\pi\) | |||||||
\(662\) | −436454. | −0.995915 | ||||||||
\(663\) | −497734. | −1.13232 | ||||||||
\(664\) | − | 239611.i | − | 0.543465i | ||||||
\(665\) | −7448.39 | + | 191960.i | −0.0168430 | + | 0.434078i | ||||
\(666\) | −5947.91 | −0.0134096 | ||||||||
\(667\) | 251507.i | 0.565325i | ||||||||
\(668\) | 82140.3i | 0.184079i | ||||||||
\(669\) | 344136. | 0.768913 | ||||||||
\(670\) | −417888. | −0.930915 | ||||||||
\(671\) | −1.03474e6 | −2.29818 | ||||||||
\(672\) | −22712.4 | −0.0502949 | ||||||||
\(673\) | − | 425648.i | − | 0.939768i | −0.882728 | − | 0.469884i | \(-0.844296\pi\) | ||
0.882728 | − | 0.469884i | \(-0.155704\pi\) | |||||||
\(674\) | 360745. | 0.794110 | ||||||||
\(675\) | − | 371146.i | − | 0.814586i | ||||||
\(676\) | 405439. | 0.887221 | ||||||||
\(677\) | 423249.i | 0.923461i | 0.887020 | + | 0.461730i | \(0.152771\pi\) | ||||
−0.887020 | + | 0.461730i | \(0.847229\pi\) | |||||||
\(678\) | 19884.1i | 0.0432561i | ||||||||
\(679\) | 248849.i | 0.539754i | ||||||||
\(680\) | − | 169688.i | − | 0.366972i | ||||||
\(681\) | 272085. | 0.586692 | ||||||||
\(682\) | 291877. | 0.627525 | ||||||||
\(683\) | − | 310900.i | − | 0.666467i | −0.942844 | − | 0.333233i | \(-0.891860\pi\) | ||
0.942844 | − | 0.333233i | \(-0.108140\pi\) | |||||||
\(684\) | −2251.08 | + | 58015.0i | −0.00481149 | + | 0.124002i | ||||
\(685\) | 1.19219e6 | 2.54077 | ||||||||
\(686\) | 206621.i | 0.439063i | ||||||||
\(687\) | − | 203561.i | − | 0.431302i | ||||||
\(688\) | 20218.3 | 0.0427139 | ||||||||
\(689\) | −217986. | −0.459188 | ||||||||
\(690\) | 302879. | 0.636168 | ||||||||
\(691\) | 314072. | 0.657769 | 0.328885 | − | 0.944370i | \(-0.393327\pi\) | ||||
0.328885 | + | 0.944370i | \(0.393327\pi\) | |||||||
\(692\) | 232013.i | 0.484508i | ||||||||
\(693\) | −69685.5 | −0.145103 | ||||||||
\(694\) | 201057.i | 0.417447i | ||||||||
\(695\) | 343275. | 0.710677 | ||||||||
\(696\) | 107113.i | 0.221118i | ||||||||
\(697\) | 428494.i | 0.882021i | ||||||||
\(698\) | − | 236461.i | − | 0.485343i | ||||||
\(699\) | − | 588915.i | − | 1.20531i | ||||||
\(700\) | −60508.0 | −0.123486 | ||||||||
\(701\) | 607472. | 1.23620 | 0.618102 | − | 0.786098i | \(-0.287902\pi\) | ||||
0.618102 | + | 0.786098i | \(0.287902\pi\) | |||||||
\(702\) | 628177.i | 1.27470i | ||||||||
\(703\) | −37733.8 | − | 1464.14i | −0.0763519 | − | 0.00296259i | ||||
\(704\) | 110383. | 0.222719 | ||||||||
\(705\) | − | 122508.i | − | 0.246482i | ||||||
\(706\) | 114180.i | 0.229076i | ||||||||
\(707\) | 168251. | 0.336604 | ||||||||
\(708\) | −35410.5 | −0.0706424 | ||||||||
\(709\) | −293984. | −0.584833 | −0.292416 | − | 0.956291i | \(-0.594459\pi\) | ||||
−0.292416 | + | 0.956291i | \(0.594459\pi\) | |||||||
\(710\) | 714858. | 1.41809 | ||||||||
\(711\) | − | 195138.i | − | 0.386013i | ||||||
\(712\) | 232649. | 0.458925 | ||||||||
\(713\) | − | 198455.i | − | 0.390375i | ||||||
\(714\) | −80409.6 | −0.157729 | ||||||||
\(715\) | − | 2.00861e6i | − | 3.92902i | ||||||
\(716\) | − | 203836.i | − | 0.397608i | ||||||
\(717\) | 334712.i | 0.651078i | ||||||||
\(718\) | − | 404688.i | − | 0.785003i | ||||||
\(719\) | 911462. | 1.76312 | 0.881558 | − | 0.472075i | \(-0.156495\pi\) | ||||
0.881558 | + | 0.472075i | \(0.156495\pi\) | |||||||
\(720\) | −42583.3 | −0.0821436 | ||||||||
\(721\) | − | 51845.1i | − | 0.0997326i | ||||||
\(722\) | −28562.0 | + | 367495.i | −0.0547915 | + | 0.704981i | ||||
\(723\) | 121965. | 0.233324 | ||||||||
\(724\) | − | 249265.i | − | 0.475536i | ||||||
\(725\) | 285360.i | 0.542896i | ||||||||
\(726\) | −702747. | −1.33329 | ||||||||
\(727\) | −174790. | −0.330710 | −0.165355 | − | 0.986234i | \(-0.552877\pi\) | ||||
−0.165355 | + | 0.986234i | \(0.552877\pi\) | |||||||
\(728\) | 102412. | 0.193236 | ||||||||
\(729\) | −589743. | −1.10971 | ||||||||
\(730\) | 786032.i | 1.47501i | ||||||||
\(731\) | 71580.0 | 0.133954 | ||||||||
\(732\) | 299629.i | 0.559193i | ||||||||
\(733\) | −401715. | −0.747671 | −0.373835 | − | 0.927495i | \(-0.621958\pi\) | ||||
−0.373835 | + | 0.927495i | \(0.621958\pi\) | |||||||
\(734\) | 87205.3i | 0.161864i | ||||||||
\(735\) | − | 553356.i | − | 1.02431i | ||||||
\(736\) | − | 75052.3i | − | 0.138551i | ||||||
\(737\) | − | 962404.i | − | 1.77183i | ||||||
\(738\) | 107531. | 0.197433 | ||||||||
\(739\) | −302531. | −0.553963 | −0.276982 | − | 0.960875i | \(-0.589334\pi\) | ||||
−0.276982 | + | 0.960875i | \(0.589334\pi\) | |||||||
\(740\) | − | 27696.8i | − | 0.0505785i | ||||||
\(741\) | −30747.0 | + | 792413.i | −0.0559973 | + | 1.44316i | ||||
\(742\) | −35216.0 | −0.0639636 | ||||||||
\(743\) | 909052.i | 1.64669i | 0.567543 | + | 0.823344i | \(0.307894\pi\) | ||||
−0.567543 | + | 0.823344i | \(0.692106\pi\) | |||||||
\(744\) | − | 84518.9i | − | 0.152689i | ||||||
\(745\) | −44789.9 | −0.0806989 | ||||||||
\(746\) | 565350. | 1.01587 | ||||||||
\(747\) | −212883. | −0.381505 | ||||||||
\(748\) | 390794. | 0.698466 | ||||||||
\(749\) | − | 124461.i | − | 0.221855i | ||||||
\(750\) | −112926. | −0.200758 | ||||||||
\(751\) | − | 370317.i | − | 0.656589i | −0.944575 | − | 0.328295i | \(-0.893526\pi\) | ||
0.944575 | − | 0.328295i | \(-0.106474\pi\) | |||||||
\(752\) | −30356.9 | −0.0536812 | ||||||||
\(753\) | − | 600870.i | − | 1.05972i | ||||||
\(754\) | − | 482981.i | − | 0.849547i | ||||||
\(755\) | 964208.i | 1.69152i | ||||||||
\(756\) | 101483.i | 0.177562i | ||||||||
\(757\) | 154581. | 0.269751 | 0.134876 | − | 0.990863i | \(-0.456937\pi\) | ||||
0.134876 | + | 0.990863i | \(0.456937\pi\) | |||||||
\(758\) | −140006. | −0.243674 | ||||||||
\(759\) | 697538.i | 1.21083i | ||||||||
\(760\) | −270150. | − | 10482.3i | −0.467711 | − | 0.0181480i | ||||
\(761\) | −722058. | −1.24682 | −0.623409 | − | 0.781896i | \(-0.714253\pi\) | ||||
−0.623409 | + | 0.781896i | \(0.714253\pi\) | |||||||
\(762\) | 368341.i | 0.634366i | ||||||||
\(763\) | 202797.i | 0.348347i | ||||||||
\(764\) | −143110. | −0.245179 | ||||||||
\(765\) | −150760. | −0.257610 | ||||||||
\(766\) | 140271. | 0.239062 | ||||||||
\(767\) | 159669. | 0.271412 | ||||||||
\(768\) | − | 31963.7i | − | 0.0541919i | ||||||
\(769\) | 496131. | 0.838965 | 0.419482 | − | 0.907763i | \(-0.362212\pi\) | ||||
0.419482 | + | 0.907763i | \(0.362212\pi\) | |||||||
\(770\) | − | 324495.i | − | 0.547301i | ||||||
\(771\) | 69479.2 | 0.116882 | ||||||||
\(772\) | − | 6273.56i | − | 0.0105264i | ||||||
\(773\) | 317854.i | 0.531948i | 0.963980 | + | 0.265974i | \(0.0856935\pi\) | ||||
−0.963980 | + | 0.265974i | \(0.914306\pi\) | |||||||
\(774\) | − | 17963.1i | − | 0.0299846i | ||||||
\(775\) | − | 225167.i | − | 0.374888i | ||||||
\(776\) | −350211. | −0.581575 | ||||||||
\(777\) | −13124.6 | −0.0217393 | ||||||||
\(778\) | 44765.2i | 0.0739574i | ||||||||
\(779\) | 682180. | + | 26469.8i | 1.12415 | + | 0.0436190i | ||||
\(780\) | −581635. | −0.956008 | ||||||||
\(781\) | 1.64633e6i | 2.69908i | ||||||||
\(782\) | − | 265711.i | − | 0.434506i | ||||||
\(783\) | 478601. | 0.780638 | ||||||||
\(784\) | −137119. | −0.223083 | ||||||||
\(785\) | 394979. | 0.640966 | ||||||||
\(786\) | −206709. | −0.334592 | ||||||||
\(787\) | 206097.i | 0.332752i | 0.986062 | + | 0.166376i | \(0.0532066\pi\) | ||||
−0.986062 | + | 0.166376i | \(0.946793\pi\) | |||||||
\(788\) | −338179. | −0.544621 | ||||||||
\(789\) | 618302.i | 0.993223i | ||||||||
\(790\) | 908671. | 1.45597 | ||||||||
\(791\) | − | 14484.6i | − | 0.0231501i | ||||||
\(792\) | − | 98070.1i | − | 0.156346i | ||||||
\(793\) | − | 1.35105e6i | − | 2.14845i | ||||||
\(794\) | 8094.92i | 0.0128402i | ||||||||
\(795\) | 200005. | 0.316451 | ||||||||
\(796\) | 122893. | 0.193955 | ||||||||
\(797\) | − | 406943.i | − | 0.640644i | −0.947309 | − | 0.320322i | \(-0.896209\pi\) | ||
0.947309 | − | 0.320322i | \(-0.103791\pi\) | |||||||
\(798\) | −4967.23 | + | 128016.i | −0.00780025 | + | 0.201028i | ||||
\(799\) | −107474. | −0.168349 | ||||||||
\(800\) | − | 85154.4i | − | 0.133054i | ||||||
\(801\) | − | 206698.i | − | 0.322160i | ||||||
\(802\) | −639320. | −0.993961 | ||||||||
\(803\) | −1.81025e6 | −2.80742 | ||||||||
\(804\) | −278684. | −0.431121 | ||||||||
\(805\) | −220632. | −0.340469 | ||||||||
\(806\) | 381103.i | 0.586640i | ||||||||
\(807\) | −1.03646e6 | −1.59149 | ||||||||
\(808\) | 236784.i | 0.362685i | ||||||||
\(809\) | −301170. | −0.460166 | −0.230083 | − | 0.973171i | \(-0.573900\pi\) | ||||
−0.230083 | + | 0.973171i | \(0.573900\pi\) | |||||||
\(810\) | − | 423923.i | − | 0.646125i | ||||||
\(811\) | − | 454953.i | − | 0.691711i | −0.938288 | − | 0.345855i | \(-0.887589\pi\) | ||
0.938288 | − | 0.345855i | \(-0.112411\pi\) | |||||||
\(812\) | − | 78026.4i | − | 0.118339i | ||||||
\(813\) | − | 569789.i | − | 0.862052i | ||||||
\(814\) | 63786.3 | 0.0962672 | ||||||||
\(815\) | −457360. | −0.688562 | ||||||||
\(816\) | − | 113162.i | − | 0.169950i | ||||||
\(817\) | 4421.79 | − | 113958.i | 0.00662451 | − | 0.170727i | ||||
\(818\) | −849436. | −1.26948 | ||||||||
\(819\) | − | 90988.1i | − | 0.135649i | ||||||
\(820\) | 500723.i | 0.744681i | ||||||||
\(821\) | −833823. | −1.23705 | −0.618526 | − | 0.785764i | \(-0.712270\pi\) | ||||
−0.618526 | + | 0.785764i | \(0.712270\pi\) | |||||||
\(822\) | 795058. | 1.17667 | ||||||||
\(823\) | 903550. | 1.33399 | 0.666995 | − | 0.745063i | \(-0.267580\pi\) | ||||
0.666995 | + | 0.745063i | \(0.267580\pi\) | |||||||
\(824\) | 72962.9 | 0.107460 | ||||||||
\(825\) | 791427.i | 1.16279i | ||||||||
\(826\) | 25794.7 | 0.0378069 | ||||||||
\(827\) | 273012.i | 0.399182i | 0.979879 | + | 0.199591i | \(0.0639613\pi\) | ||||
−0.979879 | + | 0.199591i | \(0.936039\pi\) | |||||||
\(828\) | −66680.4 | −0.0972607 | ||||||||
\(829\) | 29206.8i | 0.0424986i | 0.999774 | + | 0.0212493i | \(0.00676438\pi\) | ||||
−0.999774 | + | 0.0212493i | \(0.993236\pi\) | |||||||
\(830\) | − | 991304.i | − | 1.43897i | ||||||
\(831\) | − | 517232.i | − | 0.749002i | ||||||
\(832\) | 144127.i | 0.208208i | ||||||||
\(833\) | −485450. | −0.699607 | ||||||||
\(834\) | 228925. | 0.329126 | ||||||||
\(835\) | 339826.i | 0.487397i | ||||||||
\(836\) | 24141.0 | − | 622161.i | 0.0345416 | − | 0.890205i | ||||
\(837\) | −377646. | −0.539056 | ||||||||
\(838\) | 251492.i | 0.358126i | ||||||||
\(839\) | − | 563481.i | − | 0.800488i | −0.916409 | − | 0.400244i | \(-0.868925\pi\) | ||
0.916409 | − | 0.400244i | \(-0.131075\pi\) | |||||||
\(840\) | −93964.0 | −0.133169 | ||||||||
\(841\) | 339303. | 0.479729 | ||||||||
\(842\) | −149680. | −0.211125 | ||||||||
\(843\) | 880720. | 1.23932 | ||||||||
\(844\) | − | 288293.i | − | 0.404714i | ||||||
\(845\) | 1.67735e6 | 2.34915 | ||||||||
\(846\) | 26970.7i | 0.0376835i | ||||||||
\(847\) | 511915. | 0.713561 | ||||||||
\(848\) | − | 49560.4i | − | 0.0689197i | ||||||
\(849\) | − | 630272.i | − | 0.874405i | ||||||
\(850\) | − | 301476.i | − | 0.417268i | ||||||
\(851\) | − | 43369.9i | − | 0.0598866i | ||||||
\(852\) | 476729. | 0.656739 | ||||||||
\(853\) | −852435. | −1.17156 | −0.585778 | − | 0.810472i | \(-0.699211\pi\) | ||||
−0.585778 | + | 0.810472i | \(0.699211\pi\) | |||||||
\(854\) | − | 218264.i | − | 0.299273i | ||||||
\(855\) | −9313.04 | + | 240016.i | −0.0127397 | + | 0.328328i | ||||
\(856\) | 175157. | 0.239045 | ||||||||
\(857\) | 103865.i | 0.141419i | 0.997497 | + | 0.0707097i | \(0.0225264\pi\) | ||||
−0.997497 | + | 0.0707097i | \(0.977474\pi\) | |||||||
\(858\) | − | 1.33952e6i | − | 1.81959i | ||||||
\(859\) | −74101.6 | −0.100425 | −0.0502125 | − | 0.998739i | \(-0.515990\pi\) | ||||
−0.0502125 | + | 0.998739i | \(0.515990\pi\) | |||||||
\(860\) | 83646.0 | 0.113096 | ||||||||
\(861\) | 237277. | 0.320073 | ||||||||
\(862\) | 51093.2 | 0.0687621 | ||||||||
\(863\) | 434232.i | 0.583042i | 0.956564 | + | 0.291521i | \(0.0941613\pi\) | ||||
−0.956564 | + | 0.291521i | \(0.905839\pi\) | |||||||
\(864\) | −142819. | −0.191320 | ||||||||
\(865\) | 959870.i | 1.28286i | ||||||||
\(866\) | 534500. | 0.712709 | ||||||||
\(867\) | 251132.i | 0.334091i | ||||||||
\(868\) | 61567.7i | 0.0817172i | ||||||||
\(869\) | 2.09269e6i | 2.77118i | ||||||||
\(870\) | 443141.i | 0.585468i | ||||||||
\(871\) | 1.25661e6 | 1.65639 | ||||||||
\(872\) | −285401. | −0.375338 | ||||||||
\(873\) | 311146.i | 0.408259i | ||||||||
\(874\) | −423023. | − | 16414.1i | −0.553785 | − | 0.0214879i | ||||
\(875\) | 82261.1 | 0.107443 | ||||||||
\(876\) | 524194.i | 0.683100i | ||||||||
\(877\) | 493156.i | 0.641188i | 0.947217 | + | 0.320594i | \(0.103883\pi\) | ||||
−0.947217 | + | 0.320594i | \(0.896117\pi\) | |||||||
\(878\) | 705437. | 0.915101 | ||||||||
\(879\) | −1.04308e6 | −1.35002 | ||||||||
\(880\) | 456669. | 0.589707 | ||||||||
\(881\) | −699253. | −0.900913 | −0.450456 | − | 0.892798i | \(-0.648739\pi\) | ||||
−0.450456 | + | 0.892798i | \(0.648739\pi\) | |||||||
\(882\) | 121824.i | 0.156601i | ||||||||
\(883\) | 657183. | 0.842878 | 0.421439 | − | 0.906857i | \(-0.361525\pi\) | ||||
0.421439 | + | 0.906857i | \(0.361525\pi\) | |||||||
\(884\) | 510259.i | 0.652959i | ||||||||
\(885\) | −146498. | −0.187044 | ||||||||
\(886\) | − | 121764.i | − | 0.155114i | ||||||
\(887\) | − | 123664.i | − | 0.157179i | −0.996907 | − | 0.0785895i | \(-0.974958\pi\) | ||
0.996907 | − | 0.0785895i | \(-0.0250416\pi\) | |||||||
\(888\) | − | 18470.6i | − | 0.0234237i | ||||||
\(889\) | − | 268317.i | − | 0.339504i | ||||||
\(890\) | 962502. | 1.21513 | ||||||||
\(891\) | 976303. | 1.22978 | ||||||||
\(892\) | − | 352796.i | − | 0.443398i | ||||||
\(893\) | −6639.12 | + | 171103.i | −0.00832545 | + | 0.214563i | ||||
\(894\) | −29869.8 | −0.0373729 | ||||||||
\(895\) | − | 843298.i | − | 1.05277i | ||||||
\(896\) | 23283.9i | 0.0290028i | ||||||||
\(897\) | −910772. | −1.13194 | ||||||||
\(898\) | 54373.1 | 0.0674266 | ||||||||
\(899\) | 290358. | 0.359264 | ||||||||
\(900\) | −75655.7 | −0.0934021 | ||||||||
\(901\) | − | 175461.i | − | 0.216138i | ||||||
\(902\) | −1.15318e6 | −1.41737 | ||||||||
\(903\) | − | 39637.2i | − | 0.0486102i | ||||||
\(904\) | 20384.5 | 0.0249438 | ||||||||
\(905\) | − | 1.03124e6i | − | 1.25911i | ||||||
\(906\) | 643017.i | 0.783368i | ||||||||
\(907\) | 30174.9i | 0.0366801i | 0.999832 | + | 0.0183401i | \(0.00583815\pi\) | ||||
−0.999832 | + | 0.0183401i | \(0.994162\pi\) | |||||||
\(908\) | − | 278932.i | − | 0.338319i | ||||||
\(909\) | 210371. | 0.254600 | ||||||||
\(910\) | 423691. | 0.511643 | ||||||||
\(911\) | − | 198609.i | − | 0.239311i | −0.992815 | − | 0.119655i | \(-0.961821\pi\) | ||
0.992815 | − | 0.119655i | \(-0.0381790\pi\) | |||||||
\(912\) | −180159. | − | 6990.51i | −0.216604 | − | 0.00840464i | ||||
\(913\) | 2.28299e6 | 2.73882 | ||||||||
\(914\) | − | 108851.i | − | 0.130299i | ||||||
\(915\) | 1.23960e6i | 1.48061i | ||||||||
\(916\) | −208684. | −0.248712 | ||||||||
\(917\) | 150577. | 0.179069 | ||||||||
\(918\) | −505630. | −0.599995 | ||||||||
\(919\) | −1.20577e6 | −1.42769 | −0.713845 | − | 0.700304i | \(-0.753048\pi\) | ||||
−0.713845 | + | 0.700304i | \(0.753048\pi\) | |||||||
\(920\) | − | 310501.i | − | 0.366849i | ||||||
\(921\) | 787052. | 0.927863 | ||||||||
\(922\) | 576830.i | 0.678556i | ||||||||
\(923\) | −2.14961e6 | −2.52323 | ||||||||
\(924\) | − | 216401.i | − | 0.253464i | ||||||
\(925\) | − | 49207.6i | − | 0.0575107i | ||||||
\(926\) | 574737.i | 0.670267i | ||||||||
\(927\) | − | 64824.1i | − | 0.0754357i | ||||||
\(928\) | 109808. | 0.127509 | ||||||||
\(929\) | 1.04643e6 | 1.21249 | 0.606246 | − | 0.795277i | \(-0.292675\pi\) | ||||
0.606246 | + | 0.795277i | \(0.292675\pi\) | |||||||
\(930\) | − | 349666.i | − | 0.404285i | ||||||
\(931\) | −29988.2 | + | 772856.i | −0.0345980 | + | 0.891660i | ||||
\(932\) | −603735. | −0.695047 | ||||||||
\(933\) | − | 948380.i | − | 1.08948i | ||||||
\(934\) | 344147.i | 0.394503i | ||||||||
\(935\) | 1.61677e6 | 1.84937 | ||||||||
\(936\) | 128050. | 0.146160 | ||||||||
\(937\) | 251416. | 0.286361 | 0.143181 | − | 0.989697i | \(-0.454267\pi\) | ||||
0.143181 | + | 0.989697i | \(0.454267\pi\) | |||||||
\(938\) | 203007. | 0.230731 | ||||||||
\(939\) | − | 1.48216e6i | − | 1.68098i | ||||||
\(940\) | −125591. | −0.142135 | ||||||||
\(941\) | − | 1.26323e6i | − | 1.42660i | −0.700858 | − | 0.713301i | \(-0.747199\pi\) | ||
0.700858 | − | 0.713301i | \(-0.252801\pi\) | |||||||
\(942\) | 263406. | 0.296841 | ||||||||
\(943\) | 784074.i | 0.881726i | ||||||||
\(944\) | 36301.6i | 0.0407363i | ||||||||
\(945\) | 419848.i | 0.470142i | ||||||||
\(946\) | 192638.i | 0.215259i | ||||||||
\(947\) | −1.04458e6 | −1.16477 | −0.582386 | − | 0.812913i | \(-0.697881\pi\) | ||||
−0.582386 | + | 0.812913i | \(0.697881\pi\) | |||||||
\(948\) | 605980. | 0.674282 | ||||||||
\(949\) | − | 2.36363e6i | − | 2.62451i | ||||||
\(950\) | −479963. | − | 18623.4i | −0.531815 | − | 0.0206354i | ||||
\(951\) | 525466. | 0.581010 | ||||||||
\(952\) | 82433.1i | 0.0909552i | ||||||||
\(953\) | − | 928965.i | − | 1.02285i | −0.859327 | − | 0.511427i | \(-0.829117\pi\) | ||
0.859327 | − | 0.511427i | \(-0.170883\pi\) | |||||||
\(954\) | −44032.1 | −0.0483808 | ||||||||
\(955\) | −592066. | −0.649178 | ||||||||
\(956\) | 343135. | 0.375447 | ||||||||
\(957\) | −1.02056e6 | −1.11434 | ||||||||
\(958\) | 588417.i | 0.641141i | ||||||||
\(959\) | −579159. | −0.629739 | ||||||||
\(960\) | − | 132238.i | − | 0.143487i | ||||||
\(961\) | 694411. | 0.751916 | ||||||||
\(962\) | 83285.5i | 0.0899952i | ||||||||
\(963\) | − | 155619.i | − | 0.167807i | ||||||
\(964\) | − | 125034.i | − | 0.134547i | ||||||
\(965\) | − | 25954.5i | − | 0.0278714i | ||||||
\(966\) | −147137. | −0.157676 | ||||||||
\(967\) | −72252.5 | −0.0772680 | −0.0386340 | − | 0.999253i | \(-0.512301\pi\) | ||||
−0.0386340 | + | 0.999253i | \(0.512301\pi\) | |||||||
\(968\) | 720431.i | 0.768850i | ||||||||
\(969\) | −637827. | − | 24748.8i | −0.679290 | − | 0.0263577i | ||||
\(970\) | −1.44887e6 | −1.53988 | ||||||||
\(971\) | − | 217697.i | − | 0.230895i | −0.993314 | − | 0.115447i | \(-0.963170\pi\) | ||
0.993314 | − | 0.115447i | \(-0.0368302\pi\) | |||||||
\(972\) | 228546.i | 0.241903i | ||||||||
\(973\) | −166761. | −0.176144 | ||||||||
\(974\) | −134117. | −0.141373 | ||||||||
\(975\) | −1.03336e6 | −1.08704 | ||||||||
\(976\) | 307169. | 0.322461 | ||||||||
\(977\) | − | 1.19511e6i | − | 1.25204i | −0.779805 | − | 0.626022i | \(-0.784682\pi\) | ||
0.779805 | − | 0.626022i | \(-0.215318\pi\) | |||||||
\(978\) | −305007. | −0.318884 | ||||||||
\(979\) | 2.21666e6i | 2.31278i | ||||||||
\(980\) | −567281. | −0.590671 | ||||||||
\(981\) | 253566.i | 0.263483i | ||||||||
\(982\) | 618926.i | 0.641824i | ||||||||
\(983\) | 743610.i | 0.769552i | 0.923010 | + | 0.384776i | \(0.125721\pi\) | ||||
−0.923010 | + | 0.384776i | \(0.874279\pi\) | |||||||
\(984\) | 333926.i | 0.344873i | ||||||||
\(985\) | −1.39909e6 | −1.44203 | ||||||||
\(986\) | 388760. | 0.399878 | ||||||||
\(987\) | 59513.5i | 0.0610915i | ||||||||
\(988\) | 812353. | + | 31520.8i | 0.832206 | + | 0.0322911i | ||||
\(989\) | 130980. | 0.133910 | ||||||||
\(990\) | − | 405729.i | − | 0.413967i | ||||||
\(991\) | 213907.i | 0.217810i | 0.994052 | + | 0.108905i | \(0.0347345\pi\) | ||||
−0.994052 | + | 0.108905i | \(0.965266\pi\) | |||||||
\(992\) | −86645.8 | −0.0880489 | ||||||||
\(993\) | −1.20418e6 | −1.22121 | ||||||||
\(994\) | −347273. | −0.351478 | ||||||||
\(995\) | 508426. | 0.513549 | ||||||||
\(996\) | − | 661088.i | − | 0.666408i | ||||||
\(997\) | 563076. | 0.566470 | 0.283235 | − | 0.959051i | \(-0.408592\pi\) | ||||
0.283235 | + | 0.959051i | \(0.408592\pi\) | |||||||
\(998\) | − | 416381.i | − | 0.418052i | ||||||
\(999\) | −82530.1 | −0.0826954 |
(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 | 38.5.b.a.37.2 | ✓ | 8 | |
3.2 | odd | 2 | 342.5.d.a.37.8 | 8 | |||
4.3 | odd | 2 | 304.5.e.e.113.6 | 8 | |||
19.18 | odd | 2 | inner | 38.5.b.a.37.7 | yes | 8 | |
57.56 | even | 2 | 342.5.d.a.37.4 | 8 | |||
76.75 | even | 2 | 304.5.e.e.113.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.5.b.a.37.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
38.5.b.a.37.7 | yes | 8 | 19.18 | odd | 2 | inner | |
304.5.e.e.113.3 | 8 | 76.75 | even | 2 | |||
304.5.e.e.113.6 | 8 | 4.3 | odd | 2 | |||
342.5.d.a.37.4 | 8 | 57.56 | even | 2 | |||
342.5.d.a.37.8 | 8 | 3.2 | odd | 2 |