Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(296,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.296");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 296.65 | ||
Character | \(\chi\) | \(=\) | 531.296 |
Dual form | 531.5.b.a.296.12 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.05329i | 1.51332i | 0.653807 | + | 0.756661i | \(0.273171\pi\) | ||||
−0.653807 | + | 0.756661i | \(0.726829\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −20.6423 | −1.29014 | ||||||||
\(5\) | 34.3242i | 1.37297i | 0.727145 | + | 0.686484i | \(0.240847\pi\) | ||||
−0.727145 | + | 0.686484i | \(0.759153\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.09902 | −0.104062 | −0.0520308 | − | 0.998645i | \(-0.516569\pi\) | ||||
−0.0520308 | + | 0.998645i | \(0.516569\pi\) | |||||||
\(8\) | − 28.1013i | − 0.439082i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −207.774 | −2.07774 | ||||||||
\(11\) | − 148.668i | − 1.22866i | −0.789049 | − | 0.614330i | \(-0.789426\pi\) | ||||
0.789049 | − | 0.614330i | \(-0.210574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 69.3021 | 0.410071 | 0.205036 | − | 0.978754i | \(-0.434269\pi\) | ||||
0.205036 | + | 0.978754i | \(0.434269\pi\) | |||||||
\(14\) | − 30.8658i | − 0.157479i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −160.172 | −0.625671 | ||||||||
\(17\) | − 321.266i | − 1.11165i | −0.831300 | − | 0.555824i | \(-0.812403\pi\) | ||||
0.831300 | − | 0.555824i | \(-0.187597\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76.0665 | 0.210710 | 0.105355 | − | 0.994435i | \(-0.466402\pi\) | ||||
0.105355 | + | 0.994435i | \(0.466402\pi\) | |||||||
\(20\) | − 708.530i | − 1.77133i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 899.929 | 1.85936 | ||||||||
\(23\) | − 232.292i | − 0.439115i | −0.975600 | − | 0.219558i | \(-0.929539\pi\) | ||||
0.975600 | − | 0.219558i | \(-0.0704614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −553.149 | −0.885039 | ||||||||
\(26\) | 419.506i | 0.620570i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 105.256 | 0.134254 | ||||||||
\(29\) | − 806.320i | − 0.958763i | −0.877607 | − | 0.479382i | \(-0.840861\pi\) | ||||
0.877607 | − | 0.479382i | \(-0.159139\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 882.027 | 0.917823 | 0.458911 | − | 0.888482i | \(-0.348240\pi\) | ||||
0.458911 | + | 0.888482i | \(0.348240\pi\) | |||||||
\(32\) | − 1419.19i | − 1.38592i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1944.72 | 1.68228 | ||||||||
\(35\) | − 175.020i | − 0.142873i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1272.10 | −0.929221 | −0.464610 | − | 0.885515i | \(-0.653806\pi\) | ||||
−0.464610 | + | 0.885515i | \(0.653806\pi\) | |||||||
\(38\) | 460.452i | 0.318873i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 964.553 | 0.602846 | ||||||||
\(41\) | − 2407.30i | − 1.43206i | −0.698069 | − | 0.716031i | \(-0.745957\pi\) | ||||
0.698069 | − | 0.716031i | \(-0.254043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 358.183 | 0.193717 | 0.0968584 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968584 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(44\) | 3068.85i | 1.58515i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1406.13 | 0.664523 | ||||||||
\(47\) | − 1990.82i | − 0.901233i | −0.892718 | − | 0.450616i | \(-0.851204\pi\) | ||||
0.892718 | − | 0.450616i | \(-0.148796\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2375.00 | −0.989171 | ||||||||
\(50\) | − 3348.37i | − 1.33935i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1430.56 | −0.529051 | ||||||||
\(53\) | − 1991.68i | − 0.709036i | −0.935049 | − | 0.354518i | \(-0.884645\pi\) | ||||
0.935049 | − | 0.354518i | \(-0.115355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5102.90 | 1.68691 | ||||||||
\(56\) | 143.289i | 0.0456916i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4880.89 | 1.45092 | ||||||||
\(59\) | − 453.188i | − 0.130189i | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6446.83 | −1.73255 | −0.866276 | − | 0.499565i | \(-0.833493\pi\) | ||||
−0.866276 | + | 0.499565i | \(0.833493\pi\) | |||||||
\(62\) | 5339.17i | 1.38896i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6028.00 | 1.47168 | ||||||||
\(65\) | 2378.74i | 0.563015i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2781.90 | −0.619715 | −0.309858 | − | 0.950783i | \(-0.600281\pi\) | ||||
−0.309858 | + | 0.950783i | \(0.600281\pi\) | |||||||
\(68\) | 6631.68i | 1.43419i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1059.44 | 0.216213 | ||||||||
\(71\) | 6198.13i | 1.22954i | 0.788705 | + | 0.614771i | \(0.210752\pi\) | ||||
−0.788705 | + | 0.614771i | \(0.789248\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5122.02 | 0.961159 | 0.480579 | − | 0.876951i | \(-0.340426\pi\) | ||||
0.480579 | + | 0.876951i | \(0.340426\pi\) | |||||||
\(74\) | − 7700.41i | − 1.40621i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1570.19 | −0.271847 | ||||||||
\(77\) | 758.060i | 0.127856i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4187.53 | 0.670972 | 0.335486 | − | 0.942045i | \(-0.391100\pi\) | ||||
0.335486 | + | 0.942045i | \(0.391100\pi\) | |||||||
\(80\) | − 5497.77i | − 0.859026i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14572.1 | 2.16717 | ||||||||
\(83\) | − 3309.98i | − 0.480474i | −0.970714 | − | 0.240237i | \(-0.922775\pi\) | ||||
0.970714 | − | 0.240237i | \(-0.0772251\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11027.2 | 1.52626 | ||||||||
\(86\) | 2168.18i | 0.293156i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4177.75 | −0.539483 | ||||||||
\(89\) | 4942.81i | 0.624013i | 0.950080 | + | 0.312007i | \(0.101001\pi\) | ||||
−0.950080 | + | 0.312007i | \(0.898999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −353.372 | −0.0426727 | ||||||||
\(92\) | 4795.04i | 0.566522i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12051.0 | 1.36386 | ||||||||
\(95\) | 2610.92i | 0.289299i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16251.7 | 1.72725 | 0.863624 | − | 0.504137i | \(-0.168189\pi\) | ||||
0.863624 | + | 0.504137i | \(0.168189\pi\) | |||||||
\(98\) | − 14376.6i | − 1.49693i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11418.3 | 1.14183 | ||||||||
\(101\) | 2394.47i | 0.234729i | 0.993089 | + | 0.117365i | \(0.0374446\pi\) | ||||
−0.993089 | + | 0.117365i | \(0.962555\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6511.44 | −0.613766 | −0.306883 | − | 0.951747i | \(-0.599286\pi\) | ||||
−0.306883 | + | 0.951747i | \(0.599286\pi\) | |||||||
\(104\) | − 1947.48i | − 0.180055i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12056.2 | 1.07300 | ||||||||
\(107\) | 5817.11i | 0.508089i | 0.967193 | + | 0.254044i | \(0.0817609\pi\) | ||||
−0.967193 | + | 0.254044i | \(0.918239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −659.114 | −0.0554763 | −0.0277382 | − | 0.999615i | \(-0.508830\pi\) | ||||
−0.0277382 | + | 0.999615i | \(0.508830\pi\) | |||||||
\(110\) | 30889.3i | 2.55284i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 816.719 | 0.0651084 | ||||||||
\(113\) | 4935.39i | 0.386513i | 0.981148 | + | 0.193257i | \(0.0619050\pi\) | ||||
−0.981148 | + | 0.193257i | \(0.938095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7973.23 | 0.602890 | ||||||||
\(116\) | 16644.3i | 1.23694i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2743.28 | 0.197018 | ||||||||
\(119\) | 1638.14i | 0.115680i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7461.11 | −0.509604 | ||||||||
\(122\) | − 39024.5i | − 2.62191i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −18207.1 | −1.18412 | ||||||||
\(125\) | 2466.22i | 0.157838i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10916.6 | −0.676828 | −0.338414 | − | 0.940997i | \(-0.609890\pi\) | ||||
−0.338414 | + | 0.940997i | \(0.609890\pi\) | |||||||
\(128\) | 13782.2i | 0.841201i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14399.2 | −0.852023 | ||||||||
\(131\) | − 4652.94i | − 0.271135i | −0.990768 | − | 0.135567i | \(-0.956714\pi\) | ||||
0.990768 | − | 0.135567i | \(-0.0432857\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −387.864 | −0.0219269 | ||||||||
\(134\) | − 16839.7i | − 0.937829i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9027.99 | −0.488105 | ||||||||
\(137\) | − 8997.95i | − 0.479405i | −0.970846 | − | 0.239702i | \(-0.922950\pi\) | ||||
0.970846 | − | 0.239702i | \(-0.0770499\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −32517.1 | −1.68299 | −0.841496 | − | 0.540263i | \(-0.818325\pi\) | ||||
−0.841496 | + | 0.540263i | \(0.818325\pi\) | |||||||
\(140\) | 3612.81i | 0.184327i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −37519.0 | −1.86069 | ||||||||
\(143\) | − 10303.0i | − 0.503838i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27676.3 | 1.31635 | ||||||||
\(146\) | 31005.0i | 1.45454i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 26259.2 | 1.19883 | ||||||||
\(149\) | − 18444.7i | − 0.830805i | −0.909638 | − | 0.415402i | \(-0.863641\pi\) | ||||
0.909638 | − | 0.415402i | \(-0.136359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10564.8 | 0.463348 | 0.231674 | − | 0.972793i | \(-0.425580\pi\) | ||||
0.231674 | + | 0.972793i | \(0.425580\pi\) | |||||||
\(152\) | − 2137.56i | − 0.0925193i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4588.75 | −0.193488 | ||||||||
\(155\) | 30274.9i | 1.26014i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15812.9 | −0.641523 | −0.320761 | − | 0.947160i | \(-0.603939\pi\) | ||||
−0.320761 | + | 0.947160i | \(0.603939\pi\) | |||||||
\(158\) | 25348.4i | 1.01540i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 48712.4 | 1.90283 | ||||||||
\(161\) | 1184.46i | 0.0456950i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7471.75 | −0.281221 | −0.140610 | − | 0.990065i | \(-0.544906\pi\) | ||||
−0.140610 | + | 0.990065i | \(0.544906\pi\) | |||||||
\(164\) | 49692.1i | 1.84757i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 20036.3 | 0.727111 | ||||||||
\(167\) | 38695.1i | 1.38747i | 0.720232 | + | 0.693733i | \(0.244035\pi\) | ||||
−0.720232 | + | 0.693733i | \(0.755965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23758.2 | −0.831841 | ||||||||
\(170\) | 66750.9i | 2.30972i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7393.72 | −0.249923 | ||||||||
\(173\) | 7440.75i | 0.248613i | 0.992244 | + | 0.124307i | \(0.0396706\pi\) | ||||
−0.992244 | + | 0.124307i | \(0.960329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2820.52 | 0.0920985 | ||||||||
\(176\) | 23812.4i | 0.768737i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −29920.2 | −0.944333 | ||||||||
\(179\) | − 32354.8i | − 1.00979i | −0.863180 | − | 0.504897i | \(-0.831531\pi\) | ||||
0.863180 | − | 0.504897i | \(-0.168469\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18355.0 | 0.560270 | 0.280135 | − | 0.959961i | \(-0.409621\pi\) | ||||
0.280135 | + | 0.959961i | \(0.409621\pi\) | |||||||
\(182\) | − 2139.07i | − 0.0645775i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6527.70 | −0.192808 | ||||||||
\(185\) | − 43663.9i | − 1.27579i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −47762.0 | −1.36584 | ||||||||
\(188\) | 41095.2i | 1.16272i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15804.7 | −0.437802 | ||||||||
\(191\) | − 9333.68i | − 0.255850i | −0.991784 | − | 0.127925i | \(-0.959168\pi\) | ||||
0.991784 | − | 0.127925i | \(-0.0408317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −28456.8 | −0.763961 | −0.381981 | − | 0.924170i | \(-0.624758\pi\) | ||||
−0.381981 | + | 0.924170i | \(0.624758\pi\) | |||||||
\(194\) | 98376.0i | 2.61388i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 49025.5 | 1.27617 | ||||||||
\(197\) | − 36243.1i | − 0.933885i | −0.884288 | − | 0.466942i | \(-0.845356\pi\) | ||||
0.884288 | − | 0.466942i | \(-0.154644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 51882.7 | 1.31014 | 0.655068 | − | 0.755570i | \(-0.272640\pi\) | ||||
0.655068 | + | 0.755570i | \(0.272640\pi\) | |||||||
\(200\) | 15544.2i | 0.388605i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14494.4 | −0.355221 | ||||||||
\(203\) | 4111.44i | 0.0997704i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 82628.4 | 1.96617 | ||||||||
\(206\) | − 39415.6i | − 0.928825i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11100.2 | −0.256570 | ||||||||
\(209\) | − 11308.6i | − 0.258891i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −33215.6 | −0.746066 | −0.373033 | − | 0.927818i | \(-0.621682\pi\) | ||||
−0.373033 | + | 0.927818i | \(0.621682\pi\) | |||||||
\(212\) | 41112.9i | 0.914759i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −35212.6 | −0.768902 | ||||||||
\(215\) | 12294.3i | 0.265967i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4497.47 | −0.0955101 | ||||||||
\(218\) | − 3989.81i | − 0.0839536i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −105336. | −2.17636 | ||||||||
\(221\) | − 22264.4i | − 0.455855i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −38862.5 | −0.781486 | −0.390743 | − | 0.920500i | \(-0.627782\pi\) | ||||
−0.390743 | + | 0.920500i | \(0.627782\pi\) | |||||||
\(224\) | 7236.46i | 0.144222i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −29875.3 | −0.584919 | ||||||||
\(227\) | − 75821.4i | − 1.47143i | −0.677290 | − | 0.735716i | \(-0.736846\pi\) | ||||
0.677290 | − | 0.735716i | \(-0.263154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 93042.1 | 1.77422 | 0.887112 | − | 0.461555i | \(-0.152708\pi\) | ||||
0.887112 | + | 0.461555i | \(0.152708\pi\) | |||||||
\(230\) | 48264.2i | 0.912368i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −22658.6 | −0.420976 | ||||||||
\(233\) | − 68111.6i | − 1.25461i | −0.778773 | − | 0.627306i | \(-0.784158\pi\) | ||||
0.778773 | − | 0.627306i | \(-0.215842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 68333.4 | 1.23736 | ||||||||
\(236\) | 9354.84i | 0.167963i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9916.15 | −0.175061 | ||||||||
\(239\) | 22873.1i | 0.400433i | 0.979752 | + | 0.200216i | \(0.0641645\pi\) | ||||
−0.979752 | + | 0.200216i | \(0.935836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 54776.3 | 0.943102 | 0.471551 | − | 0.881839i | \(-0.343694\pi\) | ||||
0.471551 | + | 0.881839i | \(0.343694\pi\) | |||||||
\(242\) | − 45164.3i | − 0.771195i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 133077. | 2.23524 | ||||||||
\(245\) | − 81519.9i | − 1.35810i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5271.56 | 0.0864063 | ||||||||
\(248\) | − 24786.1i | − 0.403000i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14928.8 | −0.238860 | ||||||||
\(251\) | − 109451.i | − 1.73729i | −0.495438 | − | 0.868644i | \(-0.664992\pi\) | ||||
0.495438 | − | 0.868644i | \(-0.335008\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34534.3 | −0.539523 | ||||||||
\(254\) | − 66081.1i | − 1.02426i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13020.1 | 0.198671 | ||||||||
\(257\) | 42118.9i | 0.637691i | 0.947807 | + | 0.318846i | \(0.103295\pi\) | ||||
−0.947807 | + | 0.318846i | \(0.896705\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6486.48 | 0.0966962 | ||||||||
\(260\) | − 49102.6i | − 0.726370i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 28165.6 | 0.410314 | ||||||||
\(263\) | − 81685.9i | − 1.18096i | −0.807052 | − | 0.590481i | \(-0.798938\pi\) | ||||
0.807052 | − | 0.590481i | \(-0.201062\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 68362.9 | 0.973483 | ||||||||
\(266\) | − 2347.85i | − 0.0331824i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 57424.9 | 0.799522 | ||||||||
\(269\) | − 26304.9i | − 0.363523i | −0.983343 | − | 0.181762i | \(-0.941820\pi\) | ||||
0.983343 | − | 0.181762i | \(-0.0581799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −131117. | −1.78534 | −0.892671 | − | 0.450709i | \(-0.851171\pi\) | ||||
−0.892671 | + | 0.450709i | \(0.851171\pi\) | |||||||
\(272\) | 51457.8i | 0.695527i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 54467.2 | 0.725494 | ||||||||
\(275\) | 82235.4i | 1.08741i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20798.7 | 0.271067 | 0.135534 | − | 0.990773i | \(-0.456725\pi\) | ||||
0.135534 | + | 0.990773i | \(0.456725\pi\) | |||||||
\(278\) | − 196835.i | − 2.54691i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4918.27 | −0.0627331 | ||||||||
\(281\) | 30019.1i | 0.380176i | 0.981767 | + | 0.190088i | \(0.0608774\pi\) | ||||
−0.981767 | + | 0.190088i | \(0.939123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −72440.4 | −0.904499 | −0.452249 | − | 0.891891i | \(-0.649378\pi\) | ||||
−0.452249 | + | 0.891891i | \(0.649378\pi\) | |||||||
\(284\) | − 127944.i | − 1.58629i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 62367.0 | 0.762470 | ||||||||
\(287\) | 12274.8i | 0.149023i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19691.1 | −0.235762 | ||||||||
\(290\) | 167532.i | 1.99206i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −105730. | −1.24003 | ||||||||
\(293\) | − 142815.i | − 1.66357i | −0.555101 | − | 0.831783i | \(-0.687320\pi\) | ||||
0.555101 | − | 0.831783i | \(-0.312680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15555.3 | 0.178745 | ||||||||
\(296\) | 35747.7i | 0.408004i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 111651. | 1.25728 | ||||||||
\(299\) | − 16098.3i | − 0.180069i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1826.38 | −0.0201585 | ||||||||
\(302\) | 63951.8i | 0.701196i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12183.7 | −0.131836 | ||||||||
\(305\) | − 221282.i | − 2.37874i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 129232. | 1.37117 | 0.685586 | − | 0.727992i | \(-0.259546\pi\) | ||||
0.685586 | + | 0.727992i | \(0.259546\pi\) | |||||||
\(308\) | − 15648.1i | − 0.164953i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −183263. | −1.90700 | ||||||||
\(311\) | − 46811.4i | − 0.483984i | −0.970278 | − | 0.241992i | \(-0.922199\pi\) | ||||
0.970278 | − | 0.241992i | \(-0.0778008\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22268.0 | −0.227297 | −0.113648 | − | 0.993521i | \(-0.536254\pi\) | ||||
−0.113648 | + | 0.993521i | \(0.536254\pi\) | |||||||
\(314\) | − 95720.0i | − 0.970831i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −86440.4 | −0.865650 | ||||||||
\(317\) | − 33901.4i | − 0.337365i | −0.985670 | − | 0.168682i | \(-0.946049\pi\) | ||||
0.985670 | − | 0.168682i | \(-0.0539512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −119874. | −1.17799 | ||||||||
\(320\) | 206906.i | 2.02057i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7169.88 | −0.0691513 | ||||||||
\(323\) | − 24437.6i | − 0.234236i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −38334.4 | −0.362929 | ||||||||
\(326\) | − 45228.7i | − 0.425577i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −67648.1 | −0.628793 | ||||||||
\(329\) | 10151.2i | 0.0937837i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 151611. | 1.38381 | 0.691904 | − | 0.721989i | \(-0.256772\pi\) | ||||
0.691904 | + | 0.721989i | \(0.256772\pi\) | |||||||
\(332\) | 68325.7i | 0.619880i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −234232. | −2.09968 | ||||||||
\(335\) | − 95486.5i | − 0.850848i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −123967. | −1.09156 | −0.545780 | − | 0.837928i | \(-0.683767\pi\) | ||||
−0.545780 | + | 0.837928i | \(0.683767\pi\) | |||||||
\(338\) | − 143815.i | − 1.25884i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −227627. | −1.96909 | ||||||||
\(341\) | − 131129.i | − 1.12769i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24352.9 | 0.206996 | ||||||||
\(344\) | − 10065.4i | − 0.0850577i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −45041.0 | −0.376232 | ||||||||
\(347\) | 188629.i | 1.56657i | 0.621662 | + | 0.783286i | \(0.286458\pi\) | ||||
−0.621662 | + | 0.783286i | \(0.713542\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28962.2 | 0.237783 | 0.118892 | − | 0.992907i | \(-0.462066\pi\) | ||||
0.118892 | + | 0.992907i | \(0.462066\pi\) | |||||||
\(350\) | 17073.4i | 0.139375i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −210987. | −1.70283 | ||||||||
\(353\) | − 217090.i | − 1.74217i | −0.491135 | − | 0.871083i | \(-0.663418\pi\) | ||||
0.491135 | − | 0.871083i | \(-0.336582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −212746. | −1.68812 | ||||||||
\(356\) | − 102031.i | − 0.805067i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 195853. | 1.52814 | ||||||||
\(359\) | 20152.3i | 0.156364i | 0.996939 | + | 0.0781818i | \(0.0249115\pi\) | ||||
−0.996939 | + | 0.0781818i | \(0.975089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −124535. | −0.955601 | ||||||||
\(362\) | 111108.i | 0.847870i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7294.42 | 0.0550539 | ||||||||
\(365\) | 175809.i | 1.31964i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32590.5 | 0.241969 | 0.120984 | − | 0.992654i | \(-0.461395\pi\) | ||||
0.120984 | + | 0.992654i | \(0.461395\pi\) | |||||||
\(368\) | 37206.6i | 0.274742i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 264310. | 1.93068 | ||||||||
\(371\) | 10155.6i | 0.0737834i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25683.9 | −0.184605 | −0.0923024 | − | 0.995731i | \(-0.529423\pi\) | ||||
−0.0923024 | + | 0.995731i | \(0.529423\pi\) | |||||||
\(374\) | − 289117.i | − 2.06695i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −55944.7 | −0.395715 | ||||||||
\(377\) | − 55879.6i | − 0.393161i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −103918. | −0.723459 | −0.361730 | − | 0.932283i | \(-0.617814\pi\) | ||||
−0.361730 | + | 0.932283i | \(0.617814\pi\) | |||||||
\(380\) | − 53895.4i | − 0.373237i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 56499.4 | 0.387184 | ||||||||
\(383\) | − 143133.i | − 0.975759i | −0.872911 | − | 0.487879i | \(-0.837771\pi\) | ||||
0.872911 | − | 0.487879i | \(-0.162229\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26019.8 | −0.175542 | ||||||||
\(386\) | − 172257.i | − 1.15612i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −335472. | −2.22840 | ||||||||
\(389\) | 37268.5i | 0.246288i | 0.992389 | + | 0.123144i | \(0.0392977\pi\) | ||||
−0.992389 | + | 0.123144i | \(0.960702\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −74627.6 | −0.488142 | ||||||||
\(392\) | 66740.5i | 0.434328i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 219390. | 1.41327 | ||||||||
\(395\) | 143734.i | 0.921222i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 228939. | 1.45257 | 0.726287 | − | 0.687391i | \(-0.241244\pi\) | ||||
0.726287 | + | 0.687391i | \(0.241244\pi\) | |||||||
\(398\) | 314061.i | 1.98266i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 88598.9 | 0.553743 | ||||||||
\(401\) | 290022.i | 1.80361i | 0.432142 | + | 0.901805i | \(0.357758\pi\) | ||||
−0.432142 | + | 0.901805i | \(0.642242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 61126.3 | 0.376373 | ||||||||
\(404\) | − 49427.4i | − 0.302834i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24887.7 | −0.150985 | ||||||||
\(407\) | 189121.i | 1.14170i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 62204.2 | 0.371854 | 0.185927 | − | 0.982564i | \(-0.440471\pi\) | ||||
0.185927 | + | 0.982564i | \(0.440471\pi\) | |||||||
\(410\) | 500174.i | 2.97545i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 134411. | 0.791846 | ||||||||
\(413\) | 2310.81i | 0.0135477i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 113612. | 0.659674 | ||||||||
\(416\) | − 98352.6i | − 0.568328i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 68454.4 | 0.391786 | ||||||||
\(419\) | 227802.i | 1.29756i | 0.760974 | + | 0.648782i | \(0.224721\pi\) | ||||
−0.760974 | + | 0.648782i | \(0.775279\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 296676. | 1.67385 | 0.836927 | − | 0.547314i | \(-0.184350\pi\) | ||||
0.836927 | + | 0.547314i | \(0.184350\pi\) | |||||||
\(422\) | − 201064.i | − 1.12904i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −55968.8 | −0.311325 | ||||||||
\(425\) | 177708.i | 0.983852i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32872.5 | 0.180292 | ||||||||
\(428\) | − 120079.i | − 0.655508i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −74421.1 | −0.402494 | ||||||||
\(431\) | 149726.i | 0.806014i | 0.915197 | + | 0.403007i | \(0.132035\pi\) | ||||
−0.915197 | + | 0.403007i | \(0.867965\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −125543. | −0.669602 | −0.334801 | − | 0.942289i | \(-0.608669\pi\) | ||||
−0.334801 | + | 0.942289i | \(0.608669\pi\) | |||||||
\(434\) | − 27224.5i | − 0.144537i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13605.6 | 0.0715725 | ||||||||
\(437\) | − 17669.6i | − 0.0925261i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −204301. | −1.06009 | −0.530044 | − | 0.847970i | \(-0.677825\pi\) | ||||
−0.530044 | + | 0.847970i | \(0.677825\pi\) | |||||||
\(440\) | − 143398.i | − 0.740692i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 134773. | 0.689856 | ||||||||
\(443\) | 132125.i | 0.673251i | 0.941639 | + | 0.336625i | \(0.109286\pi\) | ||||
−0.941639 | + | 0.336625i | \(0.890714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −169658. | −0.856749 | ||||||||
\(446\) | − 235246.i | − 1.18264i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −30736.9 | −0.153145 | ||||||||
\(449\) | − 57959.1i | − 0.287494i | −0.989614 | − | 0.143747i | \(-0.954085\pi\) | ||||
0.989614 | − | 0.143747i | \(-0.0459152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −357887. | −1.75952 | ||||||||
\(452\) | − 101878.i | − 0.498658i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 458969. | 2.22675 | ||||||||
\(455\) | − 12129.2i | − 0.0585882i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −297632. | −1.42511 | −0.712553 | − | 0.701618i | \(-0.752461\pi\) | ||||
−0.712553 | + | 0.701618i | \(0.752461\pi\) | |||||||
\(458\) | 563211.i | 2.68497i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −164586. | −0.777816 | ||||||||
\(461\) | − 236589.i | − 1.11325i | −0.830764 | − | 0.556625i | \(-0.812096\pi\) | ||||
0.830764 | − | 0.556625i | \(-0.187904\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −43406.7 | −0.202486 | −0.101243 | − | 0.994862i | \(-0.532282\pi\) | ||||
−0.101243 | + | 0.994862i | \(0.532282\pi\) | |||||||
\(464\) | 129150.i | 0.599871i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 412299. | 1.89863 | ||||||||
\(467\) | − 34421.1i | − 0.157831i | −0.996881 | − | 0.0789153i | \(-0.974854\pi\) | ||||
0.996881 | − | 0.0789153i | \(-0.0251457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14185.0 | 0.0644885 | ||||||||
\(470\) | 413642.i | 1.87253i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12735.1 | −0.0571637 | ||||||||
\(473\) | − 53250.2i | − 0.238012i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −42076.1 | −0.186487 | ||||||||
\(476\) | − 33815.1i | − 0.149244i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −138458. | −0.605984 | ||||||||
\(479\) | − 63497.4i | − 0.276748i | −0.990380 | − | 0.138374i | \(-0.955812\pi\) | ||||
0.990380 | − | 0.138374i | \(-0.0441877\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −88159.4 | −0.381047 | ||||||||
\(482\) | 331577.i | 1.42722i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 154015. | 0.657463 | ||||||||
\(485\) | 557825.i | 2.37145i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 245908. | 1.03685 | 0.518423 | − | 0.855125i | \(-0.326519\pi\) | ||||
0.518423 | + | 0.855125i | \(0.326519\pi\) | |||||||
\(488\) | 181164.i | 0.760733i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 493464. | 2.05524 | ||||||||
\(491\) | − 233648.i | − 0.969170i | −0.874744 | − | 0.484585i | \(-0.838971\pi\) | ||||
0.874744 | − | 0.484585i | \(-0.161029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −259043. | −1.06581 | ||||||||
\(494\) | 31910.3i | 0.130761i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −141276. | −0.574255 | ||||||||
\(497\) | − 31604.3i | − 0.127948i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −372352. | −1.49539 | −0.747693 | − | 0.664045i | \(-0.768838\pi\) | ||||
−0.747693 | + | 0.664045i | \(0.768838\pi\) | |||||||
\(500\) | − 50908.6i | − 0.203634i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 662537. | 2.62908 | ||||||||
\(503\) | − 401246.i | − 1.58589i | −0.609290 | − | 0.792947i | \(-0.708546\pi\) | ||||
0.609290 | − | 0.792947i | \(-0.291454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −82188.3 | −0.322275 | ||||||||
\(506\) | − 209046.i | − 0.816472i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 225343. | 0.873207 | ||||||||
\(509\) | − 302843.i | − 1.16891i | −0.811425 | − | 0.584456i | \(-0.801308\pi\) | ||||
0.811425 | − | 0.584456i | \(-0.198692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26117.2 | −0.100020 | ||||||||
\(512\) | 299330.i | 1.14186i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −254958. | −0.965033 | ||||||||
\(515\) | − 223500.i | − 0.842680i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −295971. | −1.10731 | ||||||||
\(518\) | 39264.5i | 0.146332i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 66845.5 | 0.247210 | ||||||||
\(521\) | 113627.i | 0.418608i | 0.977851 | + | 0.209304i | \(0.0671197\pi\) | ||||
−0.977851 | + | 0.209304i | \(0.932880\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −333102. | −1.21779 | −0.608896 | − | 0.793250i | \(-0.708388\pi\) | ||||
−0.608896 | + | 0.793250i | \(0.708388\pi\) | |||||||
\(524\) | 96047.5i | 0.349803i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 494469. | 1.78718 | ||||||||
\(527\) | − 283366.i | − 1.02030i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 225881. | 0.807178 | ||||||||
\(530\) | 413820.i | 1.47319i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8006.42 | 0.0282888 | ||||||||
\(533\) | − 166831.i | − 0.587247i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −199667. | −0.697589 | ||||||||
\(536\) | 78175.0i | 0.272106i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 159231. | 0.550128 | ||||||||
\(539\) | 353086.i | 1.21535i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20526.2 | 0.0701317 | 0.0350658 | − | 0.999385i | \(-0.488836\pi\) | ||||
0.0350658 | + | 0.999385i | \(0.488836\pi\) | |||||||
\(542\) | − 793691.i | − 2.70180i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −455937. | −1.54066 | ||||||||
\(545\) | − 22623.6i | − 0.0761672i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23527.0 | −0.0786305 | −0.0393153 | − | 0.999227i | \(-0.512518\pi\) | ||||
−0.0393153 | + | 0.999227i | \(0.512518\pi\) | |||||||
\(548\) | 185739.i | 0.618502i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −497795. | −1.64560 | ||||||||
\(551\) | − 61333.9i | − 0.202021i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21352.3 | −0.0698224 | ||||||||
\(554\) | 125901.i | 0.410212i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 671228. | 2.17130 | ||||||||
\(557\) | 273042.i | 0.880075i | 0.897980 | + | 0.440037i | \(0.145035\pi\) | ||||
−0.897980 | + | 0.440037i | \(0.854965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24822.8 | 0.0794378 | ||||||||
\(560\) | 28033.2i | 0.0893916i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −181714. | −0.575329 | ||||||||
\(563\) | − 136595.i | − 0.430942i | −0.976510 | − | 0.215471i | \(-0.930871\pi\) | ||||
0.976510 | − | 0.215471i | \(-0.0691287\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −169403. | −0.530670 | ||||||||
\(566\) | − 438503.i | − 1.36880i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 174175. | 0.539871 | ||||||||
\(569\) | 536600.i | 1.65740i | 0.559695 | + | 0.828698i | \(0.310918\pi\) | ||||
−0.559695 | + | 0.828698i | \(0.689082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 254762. | 0.781380 | 0.390690 | − | 0.920522i | \(-0.372236\pi\) | ||||
0.390690 | + | 0.920522i | \(0.372236\pi\) | |||||||
\(572\) | 212677.i | 0.650024i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −74303.1 | −0.225519 | ||||||||
\(575\) | 128492.i | 0.388634i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 117827. | 0.353909 | 0.176954 | − | 0.984219i | \(-0.443375\pi\) | ||||
0.176954 | + | 0.984219i | \(0.443375\pi\) | |||||||
\(578\) | − 119196.i | − 0.356784i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −571302. | −1.69828 | ||||||||
\(581\) | 16877.7i | 0.0499988i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −296099. | −0.871164 | ||||||||
\(584\) | − 143935.i | − 0.422028i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 864503. | 2.51751 | ||||||||
\(587\) | 342790.i | 0.994837i | 0.867511 | + | 0.497419i | \(0.165719\pi\) | ||||
−0.867511 | + | 0.497419i | \(0.834281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 67092.7 | 0.193395 | ||||||||
\(590\) | 94160.7i | 0.270499i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 203755. | 0.581387 | ||||||||
\(593\) | 37979.0i | 0.108003i | 0.998541 | + | 0.0540013i | \(0.0171975\pi\) | ||||
−0.998541 | + | 0.0540013i | \(0.982802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −56227.9 | −0.158825 | ||||||||
\(596\) | 380741.i | 1.07186i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 97447.7 | 0.272502 | ||||||||
\(599\) | − 68518.6i | − 0.190965i | −0.995431 | − | 0.0954827i | \(-0.969561\pi\) | ||||
0.995431 | − | 0.0954827i | \(-0.0304395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 322023. | 0.891533 | 0.445767 | − | 0.895149i | \(-0.352931\pi\) | ||||
0.445767 | + | 0.895149i | \(0.352931\pi\) | |||||||
\(602\) | − 11055.6i | − 0.0305063i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −218082. | −0.597786 | ||||||||
\(605\) | − 256096.i | − 0.699669i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 66326.6 | 0.180016 | 0.0900079 | − | 0.995941i | \(-0.471311\pi\) | ||||
0.0900079 | + | 0.995941i | \(0.471311\pi\) | |||||||
\(608\) | − 107953.i | − 0.292029i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.33948e6 | 3.59980 | ||||||||
\(611\) | − 137968.i | − 0.369570i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 153314. | 0.408001 | 0.204000 | − | 0.978971i | \(-0.434606\pi\) | ||||
0.204000 | + | 0.978971i | \(0.434606\pi\) | |||||||
\(614\) | 782276.i | 2.07503i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21302.4 | 0.0561394 | ||||||||
\(617\) | 17700.3i | 0.0464956i | 0.999730 | + | 0.0232478i | \(0.00740066\pi\) | ||||
−0.999730 | + | 0.0232478i | \(0.992599\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28034.0 | −0.0731651 | −0.0365826 | − | 0.999331i | \(-0.511647\pi\) | ||||
−0.0365826 | + | 0.999331i | \(0.511647\pi\) | |||||||
\(620\) | − 624943.i | − 1.62576i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 283363. | 0.732424 | ||||||||
\(623\) | − 25203.5i | − 0.0649358i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −430369. | −1.10175 | ||||||||
\(626\) | − 134795.i | − 0.343973i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 326415. | 0.827657 | ||||||||
\(629\) | 408684.i | 1.03297i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 325646. | 0.817875 | 0.408937 | − | 0.912562i | \(-0.365899\pi\) | ||||
0.408937 | + | 0.912562i | \(0.365899\pi\) | |||||||
\(632\) | − 117675.i | − 0.294612i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 205215. | 0.510542 | ||||||||
\(635\) | − 374702.i | − 0.929263i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −164592. | −0.405631 | ||||||||
\(638\) | − 725631.i | − 1.78268i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −473064. | −1.15494 | ||||||||
\(641\) | 314713.i | 0.765947i | 0.923759 | + | 0.382974i | \(0.125100\pi\) | ||||
−0.923759 | + | 0.382974i | \(0.874900\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −464152. | −1.12263 | −0.561317 | − | 0.827601i | \(-0.689705\pi\) | ||||
−0.561317 | + | 0.827601i | \(0.689705\pi\) | |||||||
\(644\) | − 24450.0i | − 0.0589532i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 147928. | 0.354475 | ||||||||
\(647\) | 27753.6i | 0.0662996i | 0.999450 | + | 0.0331498i | \(0.0105538\pi\) | ||||
−0.999450 | + | 0.0331498i | \(0.989446\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −67374.4 | −0.159958 | ||||||||
\(650\) | − 232049.i | − 0.549229i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 154234. | 0.362815 | ||||||||
\(653\) | − 594080.i | − 1.39322i | −0.717451 | − | 0.696609i | \(-0.754691\pi\) | ||||
0.717451 | − | 0.696609i | \(-0.245309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 159708. | 0.372259 | ||||||||
\(656\) | 385581.i | 0.896000i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −61448.4 | −0.141925 | ||||||||
\(659\) | 373514.i | 0.860075i | 0.902811 | + | 0.430037i | \(0.141500\pi\) | ||||
−0.902811 | + | 0.430037i | \(0.858500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 179178. | 0.410092 | 0.205046 | − | 0.978752i | \(-0.434266\pi\) | ||||
0.205046 | + | 0.978752i | \(0.434266\pi\) | |||||||
\(662\) | 917748.i | 2.09415i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −93014.7 | −0.210967 | ||||||||
\(665\) | − 13313.1i | − 0.0301049i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −187302. | −0.421007 | ||||||||
\(668\) | − 798755.i | − 1.79003i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 578007. | 1.28761 | ||||||||
\(671\) | 958436.i | 2.12872i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −293020. | −0.646945 | −0.323472 | − | 0.946238i | \(-0.604850\pi\) | ||||
−0.323472 | + | 0.946238i | \(0.604850\pi\) | |||||||
\(674\) | − 750411.i | − 1.65188i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 490425. | 1.07320 | ||||||||
\(677\) | − 631124.i | − 1.37701i | −0.725232 | − | 0.688505i | \(-0.758267\pi\) | ||||
0.725232 | − | 0.688505i | \(-0.241733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −82867.5 | −0.179740 | ||||||||
\(680\) | − 309878.i | − 0.670152i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 793762. | 1.70656 | ||||||||
\(683\) | 476419.i | 1.02129i | 0.859793 | + | 0.510643i | \(0.170593\pi\) | ||||
−0.859793 | + | 0.510643i | \(0.829407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 308847. | 0.658207 | ||||||||
\(686\) | 147415.i | 0.313252i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −57370.8 | −0.121203 | ||||||||
\(689\) | − 138028.i | − 0.290755i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 311263. | 0.651886 | 0.325943 | − | 0.945389i | \(-0.394318\pi\) | ||||
0.325943 | + | 0.945389i | \(0.394318\pi\) | |||||||
\(692\) | − 153594.i | − 0.320747i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.14183e6 | −2.37073 | ||||||||
\(695\) | − 1.11612e6i | − 2.31069i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −773383. | −1.59195 | ||||||||
\(698\) | 175317.i | 0.359843i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −58222.0 | −0.118820 | ||||||||
\(701\) | 14396.4i | 0.0292967i | 0.999893 | + | 0.0146484i | \(0.00466289\pi\) | ||||
−0.999893 | + | 0.0146484i | \(0.995337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −96764.4 | −0.195797 | ||||||||
\(704\) | − 896170.i | − 1.80819i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.31411e6 | 2.63646 | ||||||||
\(707\) | − 12209.5i | − 0.0244263i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 868112. | 1.72696 | 0.863482 | − | 0.504379i | \(-0.168279\pi\) | ||||
0.863482 | + | 0.504379i | \(0.168279\pi\) | |||||||
\(710\) | − 1.28781e6i | − 2.55467i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 138899. | 0.273993 | ||||||||
\(713\) | − 204888.i | − 0.403030i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 353642. | 0.691753 | ||||||||
\(716\) | 667878.i | 1.30278i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −121988. | −0.236629 | ||||||||
\(719\) | − 398354.i | − 0.770570i | −0.922798 | − | 0.385285i | \(-0.874103\pi\) | ||||
0.922798 | − | 0.385285i | \(-0.125897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33201.9 | 0.0638694 | ||||||||
\(722\) | − 753846.i | − 1.44613i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −378890. | −0.722830 | ||||||||
\(725\) | 446015.i | 0.848542i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 836262. | 1.58224 | 0.791122 | − | 0.611659i | \(-0.209497\pi\) | ||||
0.791122 | + | 0.611659i | \(0.209497\pi\) | |||||||
\(728\) | 9930.21i | 0.0187368i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.06422e6 | −1.99704 | ||||||||
\(731\) | − 115072.i | − 0.215345i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −411743. | −0.766334 | −0.383167 | − | 0.923679i | \(-0.625167\pi\) | ||||
−0.383167 | + | 0.923679i | \(0.625167\pi\) | |||||||
\(734\) | 197280.i | 0.366176i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −329666. | −0.608581 | ||||||||
\(737\) | 413579.i | 0.761419i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 759107. | 1.39000 | 0.694999 | − | 0.719011i | \(-0.255405\pi\) | ||||
0.694999 | + | 0.719011i | \(0.255405\pi\) | |||||||
\(740\) | 901324.i | 1.64595i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −61474.9 | −0.111658 | ||||||||
\(743\) | 127989.i | 0.231844i | 0.993258 | + | 0.115922i | \(0.0369823\pi\) | ||||
−0.993258 | + | 0.115922i | \(0.963018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 633099. | 1.14067 | ||||||||
\(746\) | − 155472.i | − 0.279367i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 985917. | 1.76213 | ||||||||
\(749\) | − 29661.5i | − 0.0528725i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −556352. | −0.986439 | −0.493219 | − | 0.869905i | \(-0.664180\pi\) | ||||
−0.493219 | + | 0.869905i | \(0.664180\pi\) | |||||||
\(752\) | 318874.i | 0.563876i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 338256. | 0.594980 | ||||||||
\(755\) | 362628.i | 0.636162i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 571874. | 0.997950 | 0.498975 | − | 0.866616i | \(-0.333710\pi\) | ||||
0.498975 | + | 0.866616i | \(0.333710\pi\) | |||||||
\(758\) | − 629048.i | − 1.09483i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 73370.2 | 0.127026 | ||||||||
\(761\) | 625719.i | 1.08046i | 0.841516 | + | 0.540232i | \(0.181663\pi\) | ||||
−0.841516 | + | 0.540232i | \(0.818337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3360.83 | 0.00577295 | ||||||||
\(764\) | 192669.i | 0.330084i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 866426. | 1.47664 | ||||||||
\(767\) | − 31406.8i | − 0.0533868i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 511008. | 0.864122 | 0.432061 | − | 0.901844i | \(-0.357786\pi\) | ||||
0.432061 | + | 0.901844i | \(0.357786\pi\) | |||||||
\(770\) | − 157505.i | − 0.265652i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 587414. | 0.985620 | ||||||||
\(773\) | − 102844.i | − 0.172116i | −0.996290 | − | 0.0860578i | \(-0.972573\pi\) | ||||
0.996290 | − | 0.0860578i | \(-0.0274270\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −487893. | −0.812308 | ||||||||
\(776\) | − 456693.i | − 0.758404i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −225597. | −0.372713 | ||||||||
\(779\) | − 183114.i | − 0.301750i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 921462. | 1.51069 | ||||||||
\(782\) | − 451742.i | − 0.738716i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 380408. | 0.618896 | ||||||||
\(785\) | − 542764.i | − 0.880789i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −184960. | −0.298626 | −0.149313 | − | 0.988790i | \(-0.547706\pi\) | ||||
−0.149313 | + | 0.988790i | \(0.547706\pi\) | |||||||
\(788\) | 748142.i | 1.20485i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −870061. | −1.39411 | ||||||||
\(791\) | − 25165.6i | − 0.0402212i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −446779. | −0.710470 | ||||||||
\(794\) | 1.38583e6i | 2.19821i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.07098e6 | −1.69027 | ||||||||
\(797\) | 1.14811e6i | 1.80745i | 0.428108 | + | 0.903727i | \(0.359180\pi\) | ||||
−0.428108 | + | 0.903727i | \(0.640820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −639585. | −1.00185 | ||||||||
\(800\) | 785022.i | 1.22660i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.75559e6 | −2.72944 | ||||||||
\(803\) | − 761479.i | − 1.18094i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −40655.6 | −0.0627377 | ||||||||
\(806\) | 370015.i | 0.569573i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 67287.7 | 0.103065 | ||||||||
\(809\) | 355139.i | 0.542627i | 0.962491 | + | 0.271313i | \(0.0874580\pi\) | ||||
−0.962491 | + | 0.271313i | \(0.912542\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −524603. | −0.797608 | −0.398804 | − | 0.917036i | \(-0.630575\pi\) | ||||
−0.398804 | + | 0.917036i | \(0.630575\pi\) | |||||||
\(812\) | − 84869.6i | − 0.128718i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.14480e6 | −1.72775 | ||||||||
\(815\) | − 256462.i | − 0.386106i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27245.7 | 0.0408182 | ||||||||
\(818\) | 376540.i | 0.562736i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.70564e6 | −2.53665 | ||||||||
\(821\) | − 808509.i | − 1.19950i | −0.800189 | − | 0.599748i | \(-0.795268\pi\) | ||||
0.800189 | − | 0.599748i | \(-0.204732\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.00364e6 | −1.48176 | −0.740880 | − | 0.671638i | \(-0.765591\pi\) | ||||
−0.740880 | + | 0.671638i | \(0.765591\pi\) | |||||||
\(824\) | 182980.i | 0.269494i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13988.0 | −0.0205020 | ||||||||
\(827\) | 298747.i | 0.436811i | 0.975858 | + | 0.218405i | \(0.0700855\pi\) | ||||
−0.975858 | + | 0.218405i | \(0.929915\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 168772. | 0.245579 | 0.122789 | − | 0.992433i | \(-0.460816\pi\) | ||||
0.122789 | + | 0.992433i | \(0.460816\pi\) | |||||||
\(830\) | 687729.i | 0.998300i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 417753. | 0.603494 | ||||||||
\(833\) | 763008.i | 1.09961i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.32818e6 | −1.90495 | ||||||||
\(836\) | 233436.i | 0.334007i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.37895e6 | −1.96363 | ||||||||
\(839\) | − 546526.i | − 0.776402i | −0.921575 | − | 0.388201i | \(-0.873097\pi\) | ||||
0.921575 | − | 0.388201i | \(-0.126903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57129.4 | 0.0807733 | ||||||||
\(842\) | 1.79586e6i | 2.53308i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 685647. | 0.962533 | ||||||||
\(845\) | − 815481.i | − 1.14209i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38044.3 | 0.0530302 | ||||||||
\(848\) | 319012.i | 0.443624i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.07572e6 | −1.48888 | ||||||||
\(851\) | 295499.i | 0.408035i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −67958.4 | −0.0933997 | −0.0466998 | − | 0.998909i | \(-0.514870\pi\) | ||||
−0.0466998 | + | 0.998909i | \(0.514870\pi\) | |||||||
\(854\) | 198987.i | 0.272840i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 163468. | 0.223093 | ||||||||
\(857\) | 789404.i | 1.07483i | 0.843319 | + | 0.537413i | \(0.180598\pi\) | ||||
−0.843319 | + | 0.537413i | \(0.819402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −885103. | −1.19952 | −0.599760 | − | 0.800180i | \(-0.704737\pi\) | ||||
−0.599760 | + | 0.800180i | \(0.704737\pi\) | |||||||
\(860\) | − 253783.i | − 0.343136i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −906335. | −1.21976 | ||||||||
\(863\) | 1.06409e6i | 1.42876i | 0.699760 | + | 0.714378i | \(0.253290\pi\) | ||||
−0.699760 | + | 0.714378i | \(0.746710\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −255397. | −0.341338 | ||||||||
\(866\) | − 759948.i | − 1.01332i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 92838.2 | 0.123222 | ||||||||
\(869\) | − 622551.i | − 0.824396i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −192792. | −0.254127 | ||||||||
\(872\) | 18521.9i | 0.0243587i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 106959. | 0.140022 | ||||||||
\(875\) | − 12575.3i | − 0.0164249i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.18410e6 | −1.53954 | −0.769770 | − | 0.638321i | \(-0.779629\pi\) | ||||
−0.769770 | + | 0.638321i | \(0.779629\pi\) | |||||||
\(878\) | − 1.23669e6i | − 1.60425i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −817341. | −1.05545 | ||||||||
\(881\) | − 1.43432e6i | − 1.84796i | −0.382438 | − | 0.923981i | \(-0.624916\pi\) | ||||
0.382438 | − | 0.923981i | \(-0.375084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.47737e6 | 1.89481 | 0.947407 | − | 0.320032i | \(-0.103694\pi\) | ||||
0.947407 | + | 0.320032i | \(0.103694\pi\) | |||||||
\(884\) | 459589.i | 0.588119i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −799790. | −1.01885 | ||||||||
\(887\) | − 109487.i | − 0.139161i | −0.997576 | − | 0.0695804i | \(-0.977834\pi\) | ||||
0.997576 | − | 0.0695804i | \(-0.0221660\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55663.8 | 0.0704318 | ||||||||
\(890\) | − 1.02699e6i | − 1.29654i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 802212. | 1.00823 | ||||||||
\(893\) | − 151435.i | − 0.189899i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.11055e6 | 1.38641 | ||||||||
\(896\) | − 70275.9i | − 0.0875367i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 350843. | 0.435071 | ||||||||
\(899\) | − 711196.i | − 0.879974i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −639861. | −0.788199 | ||||||||
\(902\) | − 2.16640e6i | − 2.66271i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 138691. | 0.169711 | ||||||||
\(905\) | 630021.i | 0.769233i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.22088e6 | −1.48409 | −0.742043 | − | 0.670352i | \(-0.766143\pi\) | ||||
−0.742043 | + | 0.670352i | \(0.766143\pi\) | |||||||
\(908\) | 1.56513e6i | 1.89836i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 73421.7 | 0.0886628 | ||||||||
\(911\) | − 439298.i | − 0.529326i | −0.964341 | − | 0.264663i | \(-0.914739\pi\) | ||||
0.964341 | − | 0.264663i | \(-0.0852607\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −492088. | −0.590338 | ||||||||
\(914\) | − 1.80165e6i | − 2.15664i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.92060e6 | −2.28901 | ||||||||
\(917\) | 23725.4i | 0.0282147i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4513.39 | 0.00534406 | 0.00267203 | − | 0.999996i | \(-0.499149\pi\) | ||||
0.00267203 | + | 0.999996i | \(0.499149\pi\) | |||||||
\(920\) | − 224058.i | − 0.264719i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.43214e6 | 1.68471 | ||||||||
\(923\) | 429543.i | 0.504200i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 703663. | 0.822396 | ||||||||
\(926\) | − 262753.i | − 0.306426i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.14432e6 | −1.32877 | ||||||||
\(929\) | 1.54617e6i | 1.79154i | 0.444519 | + | 0.895769i | \(0.353375\pi\) | ||||
−0.444519 | + | 0.895769i | \(0.646625\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −180658. | −0.208429 | ||||||||
\(932\) | 1.40598e6i | 1.61863i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 208361. | 0.238849 | ||||||||
\(935\) | − 1.63939e6i | − 1.87525i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.09079e6 | −1.24240 | −0.621201 | − | 0.783652i | \(-0.713355\pi\) | ||||
−0.621201 | + | 0.783652i | \(0.713355\pi\) | |||||||
\(938\) | 85865.7i | 0.0975919i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.41056e6 | −1.59638 | ||||||||
\(941\) | − 129887.i | − 0.146685i | −0.997307 | − | 0.0733425i | \(-0.976633\pi\) | ||||
0.997307 | − | 0.0733425i | \(-0.0233666\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −559195. | −0.628840 | ||||||||
\(944\) | 72587.9i | 0.0814555i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 322339. | 0.360189 | ||||||||
\(947\) | 1.00321e6i | 1.11864i | 0.828952 | + | 0.559320i | \(0.188938\pi\) | ||||
−0.828952 | + | 0.559320i | \(0.811062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 354966. | 0.394144 | ||||||||
\(950\) | − 254699.i | − 0.282215i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 46033.9 | 0.0507930 | ||||||||
\(953\) | − 529351.i | − 0.582851i | −0.956594 | − | 0.291426i | \(-0.905870\pi\) | ||||
0.956594 | − | 0.291426i | \(-0.0941296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 320371. | 0.351274 | ||||||||
\(956\) | − 472154.i | − 0.516616i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 384368. | 0.418810 | ||||||||
\(959\) | 45880.7i | 0.0498876i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −145549. | −0.157602 | ||||||||
\(962\) | − 533654.i | − 0.576647i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.13071e6 | −1.21674 | ||||||||
\(965\) | − 976756.i | − 1.04889i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −455368. | −0.486979 | −0.243489 | − | 0.969904i | \(-0.578292\pi\) | ||||
−0.243489 | + | 0.969904i | \(0.578292\pi\) | |||||||
\(968\) | 209667.i | 0.223758i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.37668e6 | −3.58877 | ||||||||
\(971\) | 100791.i | 0.106901i | 0.998570 | + | 0.0534506i | \(0.0170220\pi\) | ||||
−0.998570 | + | 0.0534506i | \(0.982978\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 165805. | 0.175135 | ||||||||
\(974\) | 1.48855e6i | 1.56908i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.03260e6 | 1.08401 | ||||||||
\(977\) | 429967.i | 0.450449i | 0.974307 | + | 0.225224i | \(0.0723116\pi\) | ||||
−0.974307 | + | 0.225224i | \(0.927688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 734836. | 0.766700 | ||||||||
\(980\) | 1.68276e6i | 1.75214i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.41434e6 | 1.46667 | ||||||||
\(983\) | 1.10232e6i | 1.14077i | 0.821377 | + | 0.570386i | \(0.193206\pi\) | ||||
−0.821377 | + | 0.570386i | \(0.806794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.24402e6 | 1.28219 | ||||||||
\(986\) | − 1.56807e6i | − 1.61291i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −108817. | −0.111477 | ||||||||
\(989\) | − 83202.9i | − 0.0850640i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −223311. | −0.227385 | −0.113693 | − | 0.993516i | \(-0.536268\pi\) | ||||
−0.113693 | + | 0.993516i | \(0.536268\pi\) | |||||||
\(992\) | − 1.25176e6i | − 1.27203i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 191310. | 0.193627 | ||||||||
\(995\) | 1.78083e6i | 1.79877i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −222839. | −0.224182 | −0.112091 | − | 0.993698i | \(-0.535755\pi\) | ||||
−0.112091 | + | 0.993698i | \(0.535755\pi\) | |||||||
\(998\) | − 2.25396e6i | − 2.26300i | ||||||||
\(999\) | 0 | 0 |
(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 | 531.5.b.a.296.65 | yes | 76 | |
3.2 | odd | 2 | inner | 531.5.b.a.296.12 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
531.5.b.a.296.12 | ✓ | 76 | 3.2 | odd | 2 | inner | |
531.5.b.a.296.65 | yes | 76 | 1.1 | even | 1 | trivial |