Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,3,Mod(1149,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.1149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.c (of order \(2\), degree \(1\), not 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: | \(31.3352304014\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1149.8 | ||
Character | \(\chi\) | \(=\) | 1150.1149 |
Dual form | 1150.3.c.c.1149.7 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | − | 0.278523i | − | 0.0928408i | −0.998922 | − | 0.0464204i | \(-0.985219\pi\) | ||
0.998922 | − | 0.0464204i | \(-0.0147814\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.393890 | 0.0656484 | ||||||||
\(7\) | 8.51262 | 1.21609 | 0.608044 | − | 0.793903i | \(-0.291954\pi\) | ||||
0.608044 | + | 0.793903i | \(0.291954\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 8.92243 | 0.991381 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 7.57553i | − | 0.688684i | −0.938844 | − | 0.344342i | \(-0.888102\pi\) | ||
0.938844 | − | 0.344342i | \(-0.111898\pi\) | |||||||
\(12\) | 0.557045i | 0.0464204i | ||||||||
\(13\) | − | 2.64076i | − | 0.203135i | −0.994829 | − | 0.101568i | \(-0.967614\pi\) | ||
0.994829 | − | 0.101568i | \(-0.0323858\pi\) | |||||||
\(14\) | 12.0387i | 0.859904i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 7.56057 | 0.444739 | 0.222370 | − | 0.974962i | \(-0.428621\pi\) | ||||
0.222370 | + | 0.974962i | \(0.428621\pi\) | |||||||
\(18\) | 12.6182i | 0.701012i | ||||||||
\(19\) | − | 24.2676i | − | 1.27724i | −0.769522 | − | 0.638620i | \(-0.779505\pi\) | ||
0.769522 | − | 0.638620i | \(-0.220495\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.37096i | − | 0.112903i | ||||||
\(22\) | 10.7134 | 0.486973 | ||||||||
\(23\) | −16.7738 | − | 15.7366i | −0.729295 | − | 0.684199i | ||||
\(24\) | −0.787781 | −0.0328242 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.73460 | 0.143638 | ||||||||
\(27\) | − | 4.99180i | − | 0.184881i | ||||||
\(28\) | −17.0252 | −0.608044 | ||||||||
\(29\) | 31.8513 | 1.09832 | 0.549161 | − | 0.835717i | \(-0.314947\pi\) | ||||
0.549161 | + | 0.835717i | \(0.314947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −56.5071 | −1.82281 | −0.911405 | − | 0.411511i | \(-0.865001\pi\) | ||||
−0.911405 | + | 0.411511i | \(0.865001\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −2.10995 | −0.0639380 | ||||||||
\(34\) | 10.6923i | 0.314478i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17.8449 | −0.495690 | ||||||||
\(37\) | 39.9378 | 1.07940 | 0.539700 | − | 0.841858i | \(-0.318538\pi\) | ||||
0.539700 | + | 0.841858i | \(0.318538\pi\) | |||||||
\(38\) | 34.3195 | 0.903146 | ||||||||
\(39\) | −0.735511 | −0.0188593 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.5710 | −1.03832 | −0.519159 | − | 0.854678i | \(-0.673755\pi\) | ||||
−0.519159 | + | 0.854678i | \(0.673755\pi\) | |||||||
\(42\) | 3.35304 | 0.0798342 | ||||||||
\(43\) | −20.5721 | −0.478420 | −0.239210 | − | 0.970968i | \(-0.576888\pi\) | ||||
−0.239210 | + | 0.970968i | \(0.576888\pi\) | |||||||
\(44\) | 15.1511i | 0.344342i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 22.2549 | − | 23.7217i | 0.483802 | − | 0.515690i | ||||
\(47\) | − | 84.3049i | − | 1.79372i | −0.442314 | − | 0.896860i | \(-0.645842\pi\) | ||
0.442314 | − | 0.896860i | \(-0.354158\pi\) | |||||||
\(48\) | − | 1.11409i | − | 0.0232102i | ||||||
\(49\) | 23.4647 | 0.478871 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2.10579i | − | 0.0412900i | ||||||
\(52\) | 5.28152i | 0.101568i | ||||||||
\(53\) | −11.9189 | −0.224885 | −0.112443 | − | 0.993658i | \(-0.535867\pi\) | ||||
−0.112443 | + | 0.993658i | \(0.535867\pi\) | |||||||
\(54\) | 7.05947 | 0.130731 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 24.0773i | − | 0.429952i | ||||||
\(57\) | −6.75907 | −0.118580 | ||||||||
\(58\) | 45.0446i | 0.776631i | ||||||||
\(59\) | −67.6561 | −1.14671 | −0.573357 | − | 0.819306i | \(-0.694359\pi\) | ||||
−0.573357 | + | 0.819306i | \(0.694359\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 35.1621i | − | 0.576428i | −0.957566 | − | 0.288214i | \(-0.906939\pi\) | ||
0.957566 | − | 0.288214i | \(-0.0930614\pi\) | |||||||
\(62\) | − | 79.9131i | − | 1.28892i | ||||||
\(63\) | 75.9532 | 1.20561 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 2.98393i | − | 0.0452110i | ||||||
\(67\) | 44.0660 | 0.657701 | 0.328850 | − | 0.944382i | \(-0.393339\pi\) | ||||
0.328850 | + | 0.944382i | \(0.393339\pi\) | |||||||
\(68\) | −15.1211 | −0.222370 | ||||||||
\(69\) | −4.38299 | + | 4.67188i | −0.0635216 | + | 0.0677084i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.86597 | 0.124873 | 0.0624364 | − | 0.998049i | \(-0.480113\pi\) | ||||
0.0624364 | + | 0.998049i | \(0.480113\pi\) | |||||||
\(72\) | − | 25.2364i | − | 0.350506i | ||||||
\(73\) | − | 87.4150i | − | 1.19747i | −0.800949 | − | 0.598733i | \(-0.795671\pi\) | ||
0.800949 | − | 0.598733i | \(-0.204329\pi\) | |||||||
\(74\) | 56.4805i | 0.763250i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 48.5352i | 0.638620i | ||||||||
\(77\) | − | 64.4876i | − | 0.837501i | ||||||
\(78\) | − | 1.04017i | − | 0.0133355i | ||||||
\(79\) | 154.217i | 1.95211i | 0.217517 | + | 0.976057i | \(0.430204\pi\) | ||||
−0.217517 | + | 0.976057i | \(0.569796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 78.9115 | 0.974216 | ||||||||
\(82\) | − | 60.2046i | − | 0.734202i | ||||||
\(83\) | 141.642 | 1.70653 | 0.853266 | − | 0.521476i | \(-0.174618\pi\) | ||||
0.853266 | + | 0.521476i | \(0.174618\pi\) | |||||||
\(84\) | 4.74191i | 0.0564513i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 29.0933i | − | 0.338294i | ||||||
\(87\) | − | 8.87131i | − | 0.101969i | ||||||
\(88\) | −21.4268 | −0.243487 | ||||||||
\(89\) | 63.7252i | 0.716013i | 0.933719 | + | 0.358007i | \(0.116543\pi\) | ||||
−0.933719 | + | 0.358007i | \(0.883457\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 22.4798i | − | 0.247030i | ||||||
\(92\) | 33.5476 | + | 31.4732i | 0.364648 | + | 0.342100i | ||||
\(93\) | 15.7385i | 0.169231i | ||||||||
\(94\) | 119.225 | 1.26835 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.57556 | 0.0164121 | ||||||||
\(97\) | 143.322 | 1.47755 | 0.738775 | − | 0.673952i | \(-0.235404\pi\) | ||||
0.738775 | + | 0.673952i | \(0.235404\pi\) | |||||||
\(98\) | 33.1841i | 0.338613i | ||||||||
\(99\) | − | 67.5921i | − | 0.682748i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 27.7102 | 0.274359 | 0.137179 | − | 0.990546i | \(-0.456196\pi\) | ||||
0.137179 | + | 0.990546i | \(0.456196\pi\) | |||||||
\(102\) | 2.97803 | 0.0291964 | ||||||||
\(103\) | 133.542 | 1.29652 | 0.648261 | − | 0.761418i | \(-0.275497\pi\) | ||||
0.648261 | + | 0.761418i | \(0.275497\pi\) | |||||||
\(104\) | −7.46919 | −0.0718192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 16.8559i | − | 0.159018i | ||||||
\(107\) | 50.3091 | 0.470179 | 0.235089 | − | 0.971974i | \(-0.424462\pi\) | ||||
0.235089 | + | 0.971974i | \(0.424462\pi\) | |||||||
\(108\) | 9.98360i | 0.0924407i | ||||||||
\(109\) | − | 128.819i | − | 1.18182i | −0.806737 | − | 0.590911i | \(-0.798768\pi\) | ||
0.806737 | − | 0.590911i | \(-0.201232\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 11.1236i | − | 0.100212i | ||||||
\(112\) | 34.0505 | 0.304022 | ||||||||
\(113\) | −86.3028 | −0.763742 | −0.381871 | − | 0.924216i | \(-0.624720\pi\) | ||||
−0.381871 | + | 0.924216i | \(0.624720\pi\) | |||||||
\(114\) | − | 9.55876i | − | 0.0838488i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −63.7027 | −0.549161 | ||||||||
\(117\) | − | 23.5620i | − | 0.201384i | ||||||
\(118\) | − | 95.6802i | − | 0.810849i | ||||||
\(119\) | 64.3602 | 0.540842 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 63.6114 | 0.525714 | ||||||||
\(122\) | 49.7267 | 0.407596 | ||||||||
\(123\) | 11.8570i | 0.0963983i | ||||||||
\(124\) | 113.014 | 0.911405 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 107.414i | 0.852492i | ||||||||
\(127\) | 11.0135i | 0.0867206i | 0.999059 | + | 0.0433603i | \(0.0138063\pi\) | ||||
−0.999059 | + | 0.0433603i | \(0.986194\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 5.72978i | 0.0444169i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.63941 | 0.0277818 | 0.0138909 | − | 0.999904i | \(-0.495578\pi\) | ||||
0.0138909 | + | 0.999904i | \(0.495578\pi\) | |||||||
\(132\) | 4.21991 | 0.0319690 | ||||||||
\(133\) | − | 206.581i | − | 1.55324i | ||||||
\(134\) | 62.3187i | 0.465065i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 21.3845i | − | 0.157239i | ||||||
\(137\) | −9.69785 | −0.0707873 | −0.0353936 | − | 0.999373i | \(-0.511268\pi\) | ||||
−0.0353936 | + | 0.999373i | \(0.511268\pi\) | |||||||
\(138\) | −6.60703 | − | 6.19849i | −0.0478771 | − | 0.0449166i | ||||
\(139\) | −8.05485 | −0.0579486 | −0.0289743 | − | 0.999580i | \(-0.509224\pi\) | ||||
−0.0289743 | + | 0.999580i | \(0.509224\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.4808 | −0.166531 | ||||||||
\(142\) | 12.5384i | 0.0882984i | ||||||||
\(143\) | −20.0051 | −0.139896 | ||||||||
\(144\) | 35.6897 | 0.247845 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 123.624 | 0.846737 | ||||||||
\(147\) | − | 6.53544i | − | 0.0444588i | ||||||
\(148\) | −79.8755 | −0.539700 | ||||||||
\(149\) | 144.062i | 0.966859i | 0.875383 | + | 0.483430i | \(0.160609\pi\) | ||||
−0.875383 | + | 0.483430i | \(0.839391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −109.956 | −0.728188 | −0.364094 | − | 0.931362i | \(-0.618621\pi\) | ||||
−0.364094 | + | 0.931362i | \(0.618621\pi\) | |||||||
\(152\) | −68.6391 | −0.451573 | ||||||||
\(153\) | 67.4586 | 0.440906 | ||||||||
\(154\) | 91.1992 | 0.592202 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.47102 | 0.00942963 | ||||||||
\(157\) | 24.8208 | 0.158094 | 0.0790471 | − | 0.996871i | \(-0.474812\pi\) | ||||
0.0790471 | + | 0.996871i | \(0.474812\pi\) | |||||||
\(158\) | −218.096 | −1.38035 | ||||||||
\(159\) | 3.31969i | 0.0208785i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −142.789 | − | 133.960i | −0.886887 | − | 0.832047i | ||||
\(162\) | 111.598i | 0.688875i | ||||||||
\(163\) | 108.964i | 0.668489i | 0.942486 | + | 0.334244i | \(0.108481\pi\) | ||||
−0.942486 | + | 0.334244i | \(0.891519\pi\) | |||||||
\(164\) | 85.1421 | 0.519159 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 200.312i | 1.20670i | ||||||||
\(167\) | − | 72.1383i | − | 0.431966i | −0.976397 | − | 0.215983i | \(-0.930704\pi\) | ||
0.976397 | − | 0.215983i | \(-0.0692955\pi\) | |||||||
\(168\) | −6.70608 | −0.0399171 | ||||||||
\(169\) | 162.026 | 0.958736 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 216.526i | − | 1.26623i | ||||||
\(172\) | 41.1441 | 0.239210 | ||||||||
\(173\) | − | 150.077i | − | 0.867497i | −0.901034 | − | 0.433748i | \(-0.857191\pi\) | ||
0.901034 | − | 0.433748i | \(-0.142809\pi\) | |||||||
\(174\) | 12.5459 | 0.0721031 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 30.3021i | − | 0.172171i | ||||||
\(177\) | 18.8437i | 0.106462i | ||||||||
\(178\) | −90.1210 | −0.506298 | ||||||||
\(179\) | −207.058 | −1.15675 | −0.578375 | − | 0.815771i | \(-0.696313\pi\) | ||||
−0.578375 | + | 0.815771i | \(0.696313\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 331.138i | 1.82949i | 0.404031 | + | 0.914746i | \(0.367609\pi\) | ||||
−0.404031 | + | 0.914746i | \(0.632391\pi\) | |||||||
\(182\) | 31.7912 | 0.174677 | ||||||||
\(183\) | −9.79343 | −0.0535160 | ||||||||
\(184\) | −44.5098 | + | 47.4434i | −0.241901 | + | 0.257845i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −22.2576 | −0.119665 | ||||||||
\(187\) | − | 57.2753i | − | 0.306285i | ||||||
\(188\) | 168.610i | 0.896860i | ||||||||
\(189\) | − | 42.4933i | − | 0.224832i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 172.749i | 0.904447i | 0.891905 | + | 0.452223i | \(0.149369\pi\) | ||||
−0.891905 | + | 0.452223i | \(0.850631\pi\) | |||||||
\(192\) | 2.22818i | 0.0116051i | ||||||||
\(193\) | 136.450i | 0.706996i | 0.935435 | + | 0.353498i | \(0.115008\pi\) | ||||
−0.935435 | + | 0.353498i | \(0.884992\pi\) | |||||||
\(194\) | 202.689i | 1.04479i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −46.9293 | −0.239435 | ||||||||
\(197\) | 271.090i | 1.37609i | 0.725667 | + | 0.688046i | \(0.241531\pi\) | ||||
−0.725667 | + | 0.688046i | \(0.758469\pi\) | |||||||
\(198\) | 95.5896 | 0.482776 | ||||||||
\(199\) | − | 257.292i | − | 1.29292i | −0.762946 | − | 0.646462i | \(-0.776248\pi\) | ||
0.762946 | − | 0.646462i | \(-0.223752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 12.2734i | − | 0.0610615i | ||||||
\(202\) | 39.1882i | 0.194001i | ||||||||
\(203\) | 271.138 | 1.33566 | ||||||||
\(204\) | 4.21158i | 0.0206450i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 188.857i | 0.916780i | ||||||||
\(207\) | −149.663 | − | 140.408i | −0.723009 | − | 0.678302i | ||||
\(208\) | − | 10.5630i | − | 0.0507838i | ||||||
\(209\) | −183.840 | −0.879615 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 54.1944 | 0.256846 | 0.128423 | − | 0.991720i | \(-0.459009\pi\) | ||||
0.128423 | + | 0.991720i | \(0.459009\pi\) | |||||||
\(212\) | 23.8378 | 0.112443 | ||||||||
\(213\) | − | 2.46937i | − | 0.0115933i | ||||||
\(214\) | 71.1478i | 0.332467i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.1189 | −0.0653655 | ||||||||
\(217\) | −481.023 | −2.21670 | ||||||||
\(218\) | 182.177 | 0.835674 | ||||||||
\(219\) | −24.3471 | −0.111174 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 19.9656i | − | 0.0903423i | ||||||
\(222\) | 15.7311 | 0.0708608 | ||||||||
\(223\) | 104.611i | 0.469105i | 0.972103 | + | 0.234553i | \(0.0753625\pi\) | ||||
−0.972103 | + | 0.234553i | \(0.924637\pi\) | |||||||
\(224\) | 48.1546i | 0.214976i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 122.051i | − | 0.540047i | ||||||
\(227\) | 200.484 | 0.883190 | 0.441595 | − | 0.897215i | \(-0.354413\pi\) | ||||
0.441595 | + | 0.897215i | \(0.354413\pi\) | |||||||
\(228\) | 13.5181 | 0.0592901 | ||||||||
\(229\) | − | 22.0718i | − | 0.0963834i | −0.998838 | − | 0.0481917i | \(-0.984654\pi\) | ||
0.998838 | − | 0.0481917i | \(-0.0153458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.9612 | −0.0777543 | ||||||||
\(232\) | − | 90.0892i | − | 0.388315i | ||||||
\(233\) | − | 338.632i | − | 1.45335i | −0.686979 | − | 0.726677i | \(-0.741064\pi\) | ||
0.686979 | − | 0.726677i | \(-0.258936\pi\) | |||||||
\(234\) | 33.3217 | 0.142400 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 135.312 | 0.573357 | ||||||||
\(237\) | 42.9529 | 0.181236 | ||||||||
\(238\) | 91.0191i | 0.382433i | ||||||||
\(239\) | −149.374 | −0.624997 | −0.312499 | − | 0.949918i | \(-0.601166\pi\) | ||||
−0.312499 | + | 0.949918i | \(0.601166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 133.030i | 0.551991i | 0.961159 | + | 0.275995i | \(0.0890074\pi\) | ||||
−0.961159 | + | 0.275995i | \(0.910993\pi\) | |||||||
\(242\) | 89.9601i | 0.371736i | ||||||||
\(243\) | − | 66.9048i | − | 0.275328i | ||||||
\(244\) | 70.3242i | 0.288214i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.7683 | −0.0681639 | ||||||||
\(247\) | −64.0848 | −0.259453 | ||||||||
\(248\) | 159.826i | 0.644461i | ||||||||
\(249\) | − | 39.4505i | − | 0.158436i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 376.920i | − | 1.50167i | −0.660489 | − | 0.750836i | \(-0.729651\pi\) | ||
0.660489 | − | 0.750836i | \(-0.270349\pi\) | |||||||
\(252\) | −151.906 | −0.602803 | ||||||||
\(253\) | −119.213 | + | 127.070i | −0.471197 | + | 0.502254i | ||||
\(254\) | −15.5755 | −0.0613208 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 226.085i | − | 0.879708i | −0.898069 | − | 0.439854i | \(-0.855030\pi\) | ||
0.898069 | − | 0.439854i | \(-0.144970\pi\) | |||||||
\(258\) | −8.10314 | −0.0314075 | ||||||||
\(259\) | 339.975 | 1.31264 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 284.191 | 1.08885 | ||||||||
\(262\) | 5.14690i | 0.0196447i | ||||||||
\(263\) | 2.43654 | 0.00926441 | 0.00463221 | − | 0.999989i | \(-0.498526\pi\) | ||||
0.00463221 | + | 0.999989i | \(0.498526\pi\) | |||||||
\(264\) | 5.96785i | 0.0226055i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 292.149 | 1.09830 | ||||||||
\(267\) | 17.7489 | 0.0664753 | ||||||||
\(268\) | −88.1319 | −0.328850 | ||||||||
\(269\) | 311.337 | 1.15739 | 0.578694 | − | 0.815545i | \(-0.303563\pi\) | ||||
0.578694 | + | 0.815545i | \(0.303563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 260.751 | 0.962182 | 0.481091 | − | 0.876671i | \(-0.340241\pi\) | ||||
0.481091 | + | 0.876671i | \(0.340241\pi\) | |||||||
\(272\) | 30.2423 | 0.111185 | ||||||||
\(273\) | −6.26112 | −0.0229345 | ||||||||
\(274\) | − | 13.7148i | − | 0.0500541i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.76599 | − | 9.34376i | 0.0317608 | − | 0.0338542i | ||||
\(277\) | 182.267i | 0.658004i | 0.944329 | + | 0.329002i | \(0.106712\pi\) | ||||
−0.944329 | + | 0.329002i | \(0.893288\pi\) | |||||||
\(278\) | − | 11.3913i | − | 0.0409758i | ||||||
\(279\) | −504.180 | −1.80710 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.60502i | 0.0163880i | 0.999966 | + | 0.00819398i | \(0.00260825\pi\) | ||||
−0.999966 | + | 0.00819398i | \(0.997392\pi\) | |||||||
\(282\) | − | 33.2069i | − | 0.117755i | ||||||
\(283\) | −332.897 | −1.17631 | −0.588157 | − | 0.808747i | \(-0.700146\pi\) | ||||
−0.588157 | + | 0.808747i | \(0.700146\pi\) | |||||||
\(284\) | −17.7319 | −0.0624364 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 28.2915i | − | 0.0989215i | ||||||
\(287\) | −362.391 | −1.26269 | ||||||||
\(288\) | 50.4729i | 0.175253i | ||||||||
\(289\) | −231.838 | −0.802207 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 39.9185i | − | 0.137177i | ||||||
\(292\) | 174.830i | 0.598733i | ||||||||
\(293\) | −336.114 | −1.14715 | −0.573574 | − | 0.819154i | \(-0.694443\pi\) | ||||
−0.573574 | + | 0.819154i | \(0.694443\pi\) | |||||||
\(294\) | 9.24251 | 0.0314371 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 112.961i | − | 0.381625i | ||||||
\(297\) | −37.8155 | −0.127325 | ||||||||
\(298\) | −203.734 | −0.683673 | ||||||||
\(299\) | −41.5565 | + | 44.2955i | −0.138985 | + | 0.148146i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −175.122 | −0.581801 | ||||||||
\(302\) | − | 155.502i | − | 0.514907i | ||||||
\(303\) | − | 7.71792i | − | 0.0254717i | ||||||
\(304\) | − | 97.0703i | − | 0.319310i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 95.4009i | 0.311768i | ||||||||
\(307\) | 457.934i | 1.49164i | 0.666147 | + | 0.745821i | \(0.267943\pi\) | ||||
−0.666147 | + | 0.745821i | \(0.732057\pi\) | |||||||
\(308\) | 128.975i | 0.418750i | ||||||||
\(309\) | − | 37.1944i | − | 0.120370i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −455.620 | −1.46502 | −0.732508 | − | 0.680758i | \(-0.761650\pi\) | ||||
−0.732508 | + | 0.680758i | \(0.761650\pi\) | |||||||
\(312\) | 2.08034i | 0.00666775i | ||||||||
\(313\) | 589.353 | 1.88292 | 0.941458 | − | 0.337130i | \(-0.109456\pi\) | ||||
0.941458 | + | 0.337130i | \(0.109456\pi\) | |||||||
\(314\) | 35.1019i | 0.111789i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 308.434i | − | 0.976057i | ||||||
\(317\) | 386.251i | 1.21846i | 0.792994 | + | 0.609229i | \(0.208521\pi\) | ||||
−0.792994 | + | 0.609229i | \(0.791479\pi\) | |||||||
\(318\) | −4.69475 | −0.0147634 | ||||||||
\(319\) | − | 241.291i | − | 0.756397i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 14.0122i | − | 0.0436518i | ||||||
\(322\) | 189.447 | − | 201.934i | 0.588346 | − | 0.627124i | ||||
\(323\) | − | 183.477i | − | 0.568039i | ||||||
\(324\) | −157.823 | −0.487108 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −154.098 | −0.472693 | ||||||||
\(327\) | −35.8789 | −0.109721 | ||||||||
\(328\) | 120.409i | 0.367101i | ||||||||
\(329\) | − | 717.655i | − | 2.18132i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 220.712 | 0.666803 | 0.333402 | − | 0.942785i | \(-0.391804\pi\) | ||||
0.333402 | + | 0.942785i | \(0.391804\pi\) | |||||||
\(332\) | −283.284 | −0.853266 | ||||||||
\(333\) | 356.342 | 1.07010 | ||||||||
\(334\) | 102.019 | 0.305446 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 9.48382i | − | 0.0282257i | ||||||
\(337\) | 193.563 | 0.574371 | 0.287185 | − | 0.957875i | \(-0.407280\pi\) | ||||
0.287185 | + | 0.957875i | \(0.407280\pi\) | |||||||
\(338\) | 229.140i | 0.677929i | ||||||||
\(339\) | 24.0373i | 0.0709064i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 428.071i | 1.25534i | ||||||||
\(342\) | 306.213 | 0.895361 | ||||||||
\(343\) | −217.373 | −0.633739 | ||||||||
\(344\) | 58.1866i | 0.169147i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 212.241 | 0.613413 | ||||||||
\(347\) | 262.429i | 0.756278i | 0.925749 | + | 0.378139i | \(0.123436\pi\) | ||||
−0.925749 | + | 0.378139i | \(0.876564\pi\) | |||||||
\(348\) | 17.7426i | 0.0509846i | ||||||||
\(349\) | −229.831 | −0.658543 | −0.329271 | − | 0.944235i | \(-0.606803\pi\) | ||||
−0.329271 | + | 0.944235i | \(0.606803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.1821 | −0.0375560 | ||||||||
\(352\) | 42.8536 | 0.121743 | ||||||||
\(353\) | 367.482i | 1.04103i | 0.853854 | + | 0.520513i | \(0.174259\pi\) | ||||
−0.853854 | + | 0.520513i | \(0.825741\pi\) | |||||||
\(354\) | −26.6491 | −0.0752799 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 127.450i | − | 0.358007i | ||||||
\(357\) | − | 17.9258i | − | 0.0502123i | ||||||
\(358\) | − | 292.824i | − | 0.817945i | ||||||
\(359\) | − | 239.971i | − | 0.668442i | −0.942495 | − | 0.334221i | \(-0.891527\pi\) | ||
0.942495 | − | 0.334221i | \(-0.108473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −227.915 | −0.631344 | ||||||||
\(362\) | −468.300 | −1.29365 | ||||||||
\(363\) | − | 17.7172i | − | 0.0488077i | ||||||
\(364\) | 44.9595i | 0.123515i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 13.8500i | − | 0.0378416i | ||||||
\(367\) | 389.113 | 1.06025 | 0.530127 | − | 0.847918i | \(-0.322144\pi\) | ||||
0.530127 | + | 0.847918i | \(0.322144\pi\) | |||||||
\(368\) | −67.0952 | − | 62.9463i | −0.182324 | − | 0.171050i | ||||
\(369\) | −379.837 | −1.02937 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −101.461 | −0.273480 | ||||||||
\(372\) | − | 31.4770i | − | 0.0846156i | ||||||
\(373\) | 546.309 | 1.46463 | 0.732317 | − | 0.680964i | \(-0.238439\pi\) | ||||
0.732317 | + | 0.680964i | \(0.238439\pi\) | |||||||
\(374\) | 80.9995 | 0.216576 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −238.450 | −0.634176 | ||||||||
\(377\) | − | 84.1117i | − | 0.223108i | ||||||
\(378\) | 60.0946 | 0.158980 | ||||||||
\(379\) | 295.837i | 0.780573i | 0.920693 | + | 0.390287i | \(0.127624\pi\) | ||||
−0.920693 | + | 0.390287i | \(0.872376\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.06751 | 0.00805122 | ||||||||
\(382\) | −244.304 | −0.639541 | ||||||||
\(383\) | −566.033 | −1.47789 | −0.738946 | − | 0.673765i | \(-0.764676\pi\) | ||||
−0.738946 | + | 0.673765i | \(0.764676\pi\) | |||||||
\(384\) | −3.15112 | −0.00820605 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −192.970 | −0.499921 | ||||||||
\(387\) | −183.553 | −0.474296 | ||||||||
\(388\) | −286.645 | −0.738775 | ||||||||
\(389\) | − | 196.043i | − | 0.503966i | −0.967732 | − | 0.251983i | \(-0.918917\pi\) | ||
0.967732 | − | 0.251983i | \(-0.0810826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −126.819 | − | 118.978i | −0.324346 | − | 0.304290i | ||||
\(392\) | − | 66.3681i | − | 0.169306i | ||||||
\(393\) | − | 1.01366i | − | 0.00257928i | ||||||
\(394\) | −383.380 | −0.973045 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 135.184i | 0.341374i | ||||||||
\(397\) | 298.788i | 0.752616i | 0.926495 | + | 0.376308i | \(0.122806\pi\) | ||||
−0.926495 | + | 0.376308i | \(0.877194\pi\) | |||||||
\(398\) | 363.866 | 0.914236 | ||||||||
\(399\) | −57.5374 | −0.144204 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 785.114i | − | 1.95789i | −0.204121 | − | 0.978946i | \(-0.565433\pi\) | ||
0.204121 | − | 0.978946i | \(-0.434567\pi\) | |||||||
\(402\) | 17.3572 | 0.0431770 | ||||||||
\(403\) | 149.222i | 0.370277i | ||||||||
\(404\) | −55.4204 | −0.137179 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 383.447i | 0.944452i | ||||||||
\(407\) | − | 302.550i | − | 0.743365i | ||||||
\(408\) | −5.95607 | −0.0145982 | ||||||||
\(409\) | −358.186 | −0.875761 | −0.437881 | − | 0.899033i | \(-0.644271\pi\) | ||||
−0.437881 | + | 0.899033i | \(0.644271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.70107i | 0.00657195i | ||||||||
\(412\) | −267.084 | −0.648261 | ||||||||
\(413\) | −575.930 | −1.39450 | ||||||||
\(414\) | 198.568 | − | 211.655i | 0.479632 | − | 0.511245i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.9384 | 0.0359096 | ||||||||
\(417\) | 2.24346i | 0.00537999i | ||||||||
\(418\) | − | 259.988i | − | 0.621982i | ||||||
\(419\) | − | 195.271i | − | 0.466042i | −0.972472 | − | 0.233021i | \(-0.925139\pi\) | ||
0.972472 | − | 0.233021i | \(-0.0748610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 768.042i | 1.82433i | 0.409826 | + | 0.912164i | \(0.365590\pi\) | ||||
−0.409826 | + | 0.912164i | \(0.634410\pi\) | |||||||
\(422\) | 76.6425i | 0.181617i | ||||||||
\(423\) | − | 752.204i | − | 1.77826i | ||||||
\(424\) | 33.7118i | 0.0795089i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.49222 | 0.00819770 | ||||||||
\(427\) | − | 299.321i | − | 0.700987i | ||||||
\(428\) | −100.618 | −0.235089 | ||||||||
\(429\) | 5.57188i | 0.0129881i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 333.122i | − | 0.772905i | −0.922309 | − | 0.386453i | \(-0.873700\pi\) | ||
0.922309 | − | 0.386453i | \(-0.126300\pi\) | |||||||
\(432\) | − | 19.9672i | − | 0.0462204i | ||||||
\(433\) | −7.49741 | −0.0173150 | −0.00865752 | − | 0.999963i | \(-0.502756\pi\) | ||||
−0.00865752 | + | 0.999963i | \(0.502756\pi\) | |||||||
\(434\) | − | 680.270i | − | 1.56744i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 257.637i | 0.590911i | ||||||||
\(437\) | −381.889 | + | 407.059i | −0.873887 | + | 0.931485i | ||||
\(438\) | − | 34.4319i | − | 0.0786117i | ||||||
\(439\) | 303.939 | 0.692344 | 0.346172 | − | 0.938171i | \(-0.387481\pi\) | ||||
0.346172 | + | 0.938171i | \(0.387481\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 209.362 | 0.474743 | ||||||||
\(442\) | 28.2357 | 0.0638816 | ||||||||
\(443\) | 637.145i | 1.43825i | 0.694881 | + | 0.719125i | \(0.255457\pi\) | ||||
−0.694881 | + | 0.719125i | \(0.744543\pi\) | |||||||
\(444\) | 22.2471i | 0.0501062i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −147.942 | −0.331708 | ||||||||
\(447\) | 40.1245 | 0.0897640 | ||||||||
\(448\) | −68.1009 | −0.152011 | ||||||||
\(449\) | −88.9331 | −0.198069 | −0.0990346 | − | 0.995084i | \(-0.531575\pi\) | ||||
−0.0990346 | + | 0.995084i | \(0.531575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 322.498i | 0.715073i | ||||||||
\(452\) | 172.606 | 0.381871 | ||||||||
\(453\) | 30.6253i | 0.0676056i | ||||||||
\(454\) | 283.527i | 0.624509i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.1175i | 0.0419244i | ||||||||
\(457\) | −377.669 | −0.826410 | −0.413205 | − | 0.910638i | \(-0.635591\pi\) | ||||
−0.413205 | + | 0.910638i | \(0.635591\pi\) | |||||||
\(458\) | 31.2142 | 0.0681534 | ||||||||
\(459\) | − | 37.7408i | − | 0.0822240i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −585.070 | −1.26913 | −0.634566 | − | 0.772869i | \(-0.718821\pi\) | ||||
−0.634566 | + | 0.772869i | \(0.718821\pi\) | |||||||
\(462\) | − | 25.4010i | − | 0.0549806i | ||||||
\(463\) | − | 225.877i | − | 0.487854i | −0.969794 | − | 0.243927i | \(-0.921564\pi\) | ||
0.969794 | − | 0.243927i | \(-0.0784358\pi\) | |||||||
\(464\) | 127.405 | 0.274580 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 478.897 | 1.02768 | ||||||||
\(467\) | 702.984 | 1.50532 | 0.752659 | − | 0.658410i | \(-0.228771\pi\) | ||||
0.752659 | + | 0.658410i | \(0.228771\pi\) | |||||||
\(468\) | 47.1240i | 0.100692i | ||||||||
\(469\) | 375.117 | 0.799822 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 6.91315i | − | 0.0146776i | ||||||
\(472\) | 191.360i | 0.405424i | ||||||||
\(473\) | 155.844i | 0.329480i | ||||||||
\(474\) | 60.7446i | 0.128153i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −128.720 | −0.270421 | ||||||||
\(477\) | −106.346 | −0.222947 | ||||||||
\(478\) | − | 211.247i | − | 0.441940i | ||||||
\(479\) | − | 291.706i | − | 0.608989i | −0.952514 | − | 0.304494i | \(-0.901512\pi\) | ||
0.952514 | − | 0.304494i | \(-0.0984875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 105.466i | − | 0.219264i | ||||||
\(482\) | −188.132 | −0.390316 | ||||||||
\(483\) | −37.3107 | + | 39.7699i | −0.0772479 | + | 0.0823394i | ||||
\(484\) | −127.223 | −0.262857 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 94.6177 | 0.194687 | ||||||||
\(487\) | − | 205.957i | − | 0.422909i | −0.977388 | − | 0.211454i | \(-0.932180\pi\) | ||
0.977388 | − | 0.211454i | \(-0.0678200\pi\) | |||||||
\(488\) | −99.4534 | −0.203798 | ||||||||
\(489\) | 30.3488 | 0.0620630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −192.478 | −0.392012 | −0.196006 | − | 0.980603i | \(-0.562797\pi\) | ||||
−0.196006 | + | 0.980603i | \(0.562797\pi\) | |||||||
\(492\) | − | 23.7140i | − | 0.0481992i | ||||||
\(493\) | 240.814 | 0.488467 | ||||||||
\(494\) | − | 90.6296i | − | 0.183461i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −226.028 | −0.455703 | ||||||||
\(497\) | 75.4726 | 0.151856 | ||||||||
\(498\) | 55.7915 | 0.112031 | ||||||||
\(499\) | −887.386 | −1.77833 | −0.889164 | − | 0.457589i | \(-0.848713\pi\) | ||||
−0.889164 | + | 0.457589i | \(0.848713\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0921 | −0.0401041 | ||||||||
\(502\) | 533.045 | 1.06184 | ||||||||
\(503\) | −330.810 | −0.657673 | −0.328837 | − | 0.944387i | \(-0.606657\pi\) | ||||
−0.328837 | + | 0.944387i | \(0.606657\pi\) | |||||||
\(504\) | − | 214.828i | − | 0.426246i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −179.704 | − | 168.592i | −0.355147 | − | 0.333187i | ||||
\(507\) | − | 45.1280i | − | 0.0890099i | ||||||
\(508\) | − | 22.0270i | − | 0.0433603i | ||||||
\(509\) | 407.928 | 0.801430 | 0.400715 | − | 0.916203i | \(-0.368762\pi\) | ||||
0.400715 | + | 0.916203i | \(0.368762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 744.131i | − | 1.45622i | ||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −121.139 | −0.236138 | ||||||||
\(514\) | 319.733 | 0.622048 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 11.4596i | − | 0.0222085i | ||||||
\(517\) | −638.654 | −1.23531 | ||||||||
\(518\) | 480.797i | 0.928180i | ||||||||
\(519\) | −41.7998 | −0.0805391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 458.780i | 0.880576i | 0.897857 | + | 0.440288i | \(0.145124\pi\) | ||||
−0.897857 | + | 0.440288i | \(0.854876\pi\) | |||||||
\(522\) | 401.907i | 0.769937i | ||||||||
\(523\) | −404.987 | −0.774354 | −0.387177 | − | 0.922005i | \(-0.626550\pi\) | ||||
−0.387177 | + | 0.922005i | \(0.626550\pi\) | |||||||
\(524\) | −7.27882 | −0.0138909 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.44579i | 0.00655093i | ||||||||
\(527\) | −427.226 | −0.810675 | ||||||||
\(528\) | −8.43982 | −0.0159845 | ||||||||
\(529\) | 33.7199 | + | 527.924i | 0.0637427 | + | 0.997966i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −603.656 | −1.13683 | ||||||||
\(532\) | 413.161i | 0.776619i | ||||||||
\(533\) | 112.420i | 0.210919i | ||||||||
\(534\) | 25.1007i | 0.0470051i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 124.637i | − | 0.232532i | ||||||
\(537\) | 57.6703i | 0.107394i | ||||||||
\(538\) | 440.298i | 0.818397i | ||||||||
\(539\) | − | 177.757i | − | 0.329791i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1047.51 | 1.93625 | 0.968123 | − | 0.250477i | \(-0.0805875\pi\) | ||||
0.968123 | + | 0.250477i | \(0.0805875\pi\) | |||||||
\(542\) | 368.758i | 0.680366i | ||||||||
\(543\) | 92.2294 | 0.169851 | ||||||||
\(544\) | 42.7690i | 0.0786195i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 8.85457i | − | 0.0162172i | ||||||
\(547\) | − | 123.784i | − | 0.226296i | −0.993578 | − | 0.113148i | \(-0.963907\pi\) | ||
0.993578 | − | 0.113148i | \(-0.0360934\pi\) | |||||||
\(548\) | 19.3957 | 0.0353936 | ||||||||
\(549\) | − | 313.731i | − | 0.571459i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 772.955i | − | 1.40282i | ||||||
\(552\) | 13.2141 | + | 12.3970i | 0.0239385 | + | 0.0224583i | ||||
\(553\) | 1312.79i | 2.37394i | ||||||||
\(554\) | −257.765 | −0.465279 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.1097 | 0.0289743 | ||||||||
\(557\) | −246.292 | −0.442176 | −0.221088 | − | 0.975254i | \(-0.570961\pi\) | ||||
−0.221088 | + | 0.975254i | \(0.570961\pi\) | |||||||
\(558\) | − | 713.019i | − | 1.27781i | ||||||
\(559\) | 54.3259i | 0.0971840i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.9525 | −0.0284357 | ||||||||
\(562\) | −6.51248 | −0.0115880 | ||||||||
\(563\) | 574.776 | 1.02092 | 0.510458 | − | 0.859902i | \(-0.329476\pi\) | ||||
0.510458 | + | 0.859902i | \(0.329476\pi\) | |||||||
\(564\) | 46.9616 | 0.0832653 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 470.787i | − | 0.831780i | ||||||
\(567\) | 671.743 | 1.18473 | ||||||||
\(568\) | − | 25.0768i | − | 0.0441492i | ||||||
\(569\) | 794.332i | 1.39601i | 0.716091 | + | 0.698007i | \(0.245930\pi\) | ||||
−0.716091 | + | 0.698007i | \(0.754070\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 416.688i | 0.729751i | 0.931056 | + | 0.364876i | \(0.118889\pi\) | ||||
−0.931056 | + | 0.364876i | \(0.881111\pi\) | |||||||
\(572\) | 40.0103 | 0.0699480 | ||||||||
\(573\) | 48.1146 | 0.0839696 | ||||||||
\(574\) | − | 512.498i | − | 0.892854i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −71.3794 | −0.123923 | ||||||||
\(577\) | 282.647i | 0.489856i | 0.969541 | + | 0.244928i | \(0.0787643\pi\) | ||||
−0.969541 | + | 0.244928i | \(0.921236\pi\) | |||||||
\(578\) | − | 327.868i | − | 0.567246i | ||||||
\(579\) | 38.0044 | 0.0656381 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1205.75 | 2.07529 | ||||||||
\(582\) | 56.4533 | 0.0969988 | ||||||||
\(583\) | 90.2920i | 0.154875i | ||||||||
\(584\) | −247.247 | −0.423368 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 475.337i | − | 0.811156i | ||||||
\(587\) | 168.123i | 0.286410i | 0.989693 | + | 0.143205i | \(0.0457408\pi\) | ||||
−0.989693 | + | 0.143205i | \(0.954259\pi\) | |||||||
\(588\) | 13.0709i | 0.0222294i | ||||||||
\(589\) | 1371.29i | 2.32817i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 75.5048 | 0.127758 | ||||||||
\(592\) | 159.751 | 0.269850 | ||||||||
\(593\) | − | 419.364i | − | 0.707191i | −0.935398 | − | 0.353595i | \(-0.884959\pi\) | ||
0.935398 | − | 0.353595i | \(-0.115041\pi\) | |||||||
\(594\) | − | 53.4792i | − | 0.0900323i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 288.124i | − | 0.483430i | ||||||
\(597\) | −71.6616 | −0.120036 | ||||||||
\(598\) | −62.6433 | − | 58.7698i | −0.104755 | − | 0.0982773i | ||||
\(599\) | 519.774 | 0.867736 | 0.433868 | − | 0.900977i | \(-0.357148\pi\) | ||||
0.433868 | + | 0.900977i | \(0.357148\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1089.19 | 1.81230 | 0.906151 | − | 0.422955i | \(-0.139007\pi\) | ||||
0.906151 | + | 0.422955i | \(0.139007\pi\) | |||||||
\(602\) | − | 247.660i | − | 0.411395i | ||||||
\(603\) | 393.175 | 0.652032 | ||||||||
\(604\) | 219.913 | 0.364094 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.9148 | 0.0180112 | ||||||||
\(607\) | − | 890.673i | − | 1.46734i | −0.679508 | − | 0.733668i | \(-0.737807\pi\) | ||
0.679508 | − | 0.733668i | \(-0.262193\pi\) | |||||||
\(608\) | 137.278 | 0.225786 | ||||||||
\(609\) | − | 75.5181i | − | 0.124003i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −222.629 | −0.364368 | ||||||||
\(612\) | −134.917 | −0.220453 | ||||||||
\(613\) | −629.354 | −1.02668 | −0.513339 | − | 0.858186i | \(-0.671592\pi\) | ||||
−0.513339 | + | 0.858186i | \(0.671592\pi\) | |||||||
\(614\) | −647.616 | −1.05475 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −182.398 | −0.296101 | ||||||||
\(617\) | −157.187 | −0.254760 | −0.127380 | − | 0.991854i | \(-0.540657\pi\) | ||||
−0.127380 | + | 0.991854i | \(0.540657\pi\) | |||||||
\(618\) | 52.6008 | 0.0851146 | ||||||||
\(619\) | 462.293i | 0.746838i | 0.927663 | + | 0.373419i | \(0.121815\pi\) | ||||
−0.927663 | + | 0.373419i | \(0.878185\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −78.5539 | + | 83.7314i | −0.126496 | + | 0.134833i | ||||
\(622\) | − | 644.344i | − | 1.03592i | ||||||
\(623\) | 542.468i | 0.870735i | ||||||||
\(624\) | −2.94204 | −0.00471481 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 833.471i | 1.33142i | ||||||||
\(627\) | 51.2035i | 0.0816642i | ||||||||
\(628\) | −49.6416 | −0.0790471 | ||||||||
\(629\) | 301.952 | 0.480051 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 411.630i | − | 0.652345i | −0.945310 | − | 0.326173i | \(-0.894241\pi\) | ||
0.945310 | − | 0.326173i | \(-0.105759\pi\) | |||||||
\(632\) | 436.191 | 0.690176 | ||||||||
\(633\) | − | 15.0944i | − | 0.0238458i | ||||||
\(634\) | −546.242 | −0.861581 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 6.63937i | − | 0.0104393i | ||||||
\(637\) | − | 61.9645i | − | 0.0972756i | ||||||
\(638\) | 341.236 | 0.534853 | ||||||||
\(639\) | 79.1060 | 0.123797 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 251.089i | 0.391715i | 0.980632 | + | 0.195857i | \(0.0627490\pi\) | ||||
−0.980632 | + | 0.195857i | \(0.937251\pi\) | |||||||
\(642\) | 19.8163 | 0.0308665 | ||||||||
\(643\) | 102.907 | 0.160042 | 0.0800211 | − | 0.996793i | \(-0.474501\pi\) | ||||
0.0800211 | + | 0.996793i | \(0.474501\pi\) | |||||||
\(644\) | 285.578 | + | 267.919i | 0.443444 | + | 0.416023i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 259.475 | 0.401664 | ||||||||
\(647\) | 437.368i | 0.675993i | 0.941147 | + | 0.337997i | \(0.109749\pi\) | ||||
−0.941147 | + | 0.337997i | \(0.890251\pi\) | |||||||
\(648\) | − | 223.195i | − | 0.344437i | ||||||
\(649\) | 512.530i | 0.789723i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 133.976i | 0.205800i | ||||||||
\(652\) | − | 217.927i | − | 0.334244i | ||||||
\(653\) | − | 94.4001i | − | 0.144564i | −0.997384 | − | 0.0722819i | \(-0.976972\pi\) | ||
0.997384 | − | 0.0722819i | \(-0.0230281\pi\) | |||||||
\(654\) | − | 50.7404i | − | 0.0775847i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −170.284 | −0.259580 | ||||||||
\(657\) | − | 779.954i | − | 1.18714i | ||||||
\(658\) | 1014.92 | 1.54243 | ||||||||
\(659\) | − | 759.727i | − | 1.15285i | −0.817151 | − | 0.576424i | \(-0.804448\pi\) | ||
0.817151 | − | 0.576424i | \(-0.195552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 581.754i | 0.880112i | 0.897970 | + | 0.440056i | \(0.145041\pi\) | ||||
−0.897970 | + | 0.440056i | \(0.854959\pi\) | |||||||
\(662\) | 312.134i | 0.471501i | ||||||||
\(663\) | −5.56088 | −0.00838745 | ||||||||
\(664\) | − | 400.625i | − | 0.603350i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 503.943i | 0.756672i | ||||||||
\(667\) | −534.267 | − | 501.231i | −0.801001 | − | 0.751471i | ||||
\(668\) | 144.277i | 0.215983i | ||||||||
\(669\) | 29.1364 | 0.0435521 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −266.371 | −0.396977 | ||||||||
\(672\) | 13.4122 | 0.0199586 | ||||||||
\(673\) | − | 831.173i | − | 1.23503i | −0.786560 | − | 0.617513i | \(-0.788140\pi\) | ||
0.786560 | − | 0.617513i | \(-0.211860\pi\) | |||||||
\(674\) | 273.739i | 0.406142i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −324.053 | −0.479368 | ||||||||
\(677\) | 106.706 | 0.157616 | 0.0788079 | − | 0.996890i | \(-0.474889\pi\) | ||||
0.0788079 | + | 0.996890i | \(0.474889\pi\) | |||||||
\(678\) | −33.9938 | −0.0501384 | ||||||||
\(679\) | 1220.05 | 1.79683 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 55.8393i | − | 0.0819961i | ||||||
\(682\) | −605.384 | −0.887660 | ||||||||
\(683\) | 380.675i | 0.557357i | 0.960385 | + | 0.278678i | \(0.0898963\pi\) | ||||
−0.960385 | + | 0.278678i | \(0.910104\pi\) | |||||||
\(684\) | 433.051i | 0.633116i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 307.411i | − | 0.448121i | ||||||
\(687\) | −6.14749 | −0.00894832 | ||||||||
\(688\) | −82.2883 | −0.119605 | ||||||||
\(689\) | 31.4750i | 0.0456821i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −318.845 | −0.461425 | −0.230713 | − | 0.973022i | \(-0.574106\pi\) | ||||
−0.230713 | + | 0.973022i | \(0.574106\pi\) | |||||||
\(692\) | 300.154i | 0.433748i | ||||||||
\(693\) | − | 575.385i | − | 0.830282i | ||||||
\(694\) | −371.130 | −0.534769 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −25.0919 | −0.0360515 | ||||||||
\(697\) | −321.861 | −0.461781 | ||||||||
\(698\) | − | 325.031i | − | 0.465660i | ||||||
\(699\) | −94.3165 | −0.134931 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 112.754i | 0.160848i | 0.996761 | + | 0.0804239i | \(0.0256274\pi\) | ||||
−0.996761 | + | 0.0804239i | \(0.974373\pi\) | |||||||
\(702\) | − | 18.6424i | − | 0.0265561i | ||||||
\(703\) | − | 969.193i | − | 1.37865i | ||||||
\(704\) | 60.6042i | 0.0860855i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −519.698 | −0.736116 | ||||||||
\(707\) | 235.887 | 0.333644 | ||||||||
\(708\) | − | 37.6875i | − | 0.0532309i | ||||||
\(709\) | 465.481i | 0.656531i | 0.944585 | + | 0.328266i | \(0.106464\pi\) | ||||
−0.944585 | + | 0.328266i | \(0.893536\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1375.99i | 1.93529i | ||||||||
\(712\) | 180.242 | 0.253149 | ||||||||
\(713\) | 947.838 | + | 889.229i | 1.32937 | + | 1.24717i | ||||
\(714\) | 25.3509 | 0.0355054 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 414.116 | 0.578375 | ||||||||
\(717\) | 41.6041i | 0.0580253i | ||||||||
\(718\) | 339.370 | 0.472660 | ||||||||
\(719\) | 347.913 | 0.483885 | 0.241943 | − | 0.970291i | \(-0.422215\pi\) | ||||
0.241943 | + | 0.970291i | \(0.422215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1136.79 | 1.57669 | ||||||||
\(722\) | − | 322.321i | − | 0.446428i | ||||||
\(723\) | 37.0518 | 0.0512473 | ||||||||
\(724\) | − | 662.276i | − | 0.914746i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.0559 | 0.0345123 | ||||||||
\(727\) | 88.3077 | 0.121469 | 0.0607343 | − | 0.998154i | \(-0.480656\pi\) | ||||
0.0607343 | + | 0.998154i | \(0.480656\pi\) | |||||||
\(728\) | −63.5824 | −0.0873385 | ||||||||
\(729\) | 691.569 | 0.948654 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −155.536 | −0.212772 | ||||||||
\(732\) | 19.5869 | 0.0267580 | ||||||||
\(733\) | 510.848 | 0.696928 | 0.348464 | − | 0.937322i | \(-0.386703\pi\) | ||||
0.348464 | + | 0.937322i | \(0.386703\pi\) | |||||||
\(734\) | 550.289i | 0.749712i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 89.0196 | − | 94.8869i | 0.120950 | − | 0.128922i | ||||
\(737\) | − | 333.823i | − | 0.452948i | ||||||
\(738\) | − | 537.171i | − | 0.727873i | ||||||
\(739\) | 416.763 | 0.563955 | 0.281978 | − | 0.959421i | \(-0.409010\pi\) | ||||
0.281978 | + | 0.959421i | \(0.409010\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.8491i | 0.0240878i | ||||||||
\(742\) | − | 143.488i | − | 0.193380i | ||||||
\(743\) | −633.469 | −0.852583 | −0.426291 | − | 0.904586i | \(-0.640180\pi\) | ||||
−0.426291 | + | 0.904586i | \(0.640180\pi\) | |||||||
\(744\) | 44.5152 | 0.0598323 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 772.597i | 1.03565i | ||||||||
\(747\) | 1263.79 | 1.69182 | ||||||||
\(748\) | 114.551i | 0.153142i | ||||||||
\(749\) | 428.262 | 0.571779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1282.52i | 1.70775i | 0.520475 | + | 0.853877i | \(0.325755\pi\) | ||||
−0.520475 | + | 0.853877i | \(0.674245\pi\) | |||||||
\(752\) | − | 337.219i | − | 0.448430i | ||||||
\(753\) | −104.981 | −0.139416 | ||||||||
\(754\) | 118.952 | 0.157761 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 84.9866i | 0.112416i | ||||||||
\(757\) | 1233.64 | 1.62964 | 0.814819 | − | 0.579716i | \(-0.196836\pi\) | ||||
0.814819 | + | 0.579716i | \(0.196836\pi\) | |||||||
\(758\) | −418.377 | −0.551949 | ||||||||
\(759\) | 35.3919 | + | 33.2035i | 0.0466297 | + | 0.0437463i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −262.559 | −0.345018 | −0.172509 | − | 0.985008i | \(-0.555187\pi\) | ||||
−0.172509 | + | 0.985008i | \(0.555187\pi\) | |||||||
\(762\) | 4.33812i | 0.00569307i | ||||||||
\(763\) | − | 1096.58i | − | 1.43720i | ||||||
\(764\) | − | 345.499i | − | 0.452223i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 800.491i | − | 1.04503i | ||||||
\(767\) | 178.663i | 0.232938i | ||||||||
\(768\) | − | 4.45636i | − | 0.00580255i | ||||||
\(769\) | 801.510i | 1.04228i | 0.853473 | + | 0.521138i | \(0.174492\pi\) | ||||
−0.853473 | + | 0.521138i | \(0.825508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −62.9698 | −0.0816729 | ||||||||
\(772\) | − | 272.900i | − | 0.353498i | ||||||
\(773\) | −1143.79 | −1.47967 | −0.739837 | − | 0.672786i | \(-0.765097\pi\) | ||||
−0.739837 | + | 0.672786i | \(0.765097\pi\) | |||||||
\(774\) | − | 259.583i | − | 0.335378i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 405.377i | − | 0.522393i | ||||||
\(777\) | − | 94.6907i | − | 0.121867i | ||||||
\(778\) | 277.246 | 0.356357 | ||||||||
\(779\) | 1033.10i | 1.32618i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 67.1644i | − | 0.0859979i | ||||||
\(782\) | 168.260 | − | 179.350i | 0.215166 | − | 0.229347i | ||||
\(783\) | − | 158.995i | − | 0.203059i | ||||||
\(784\) | 93.8587 | 0.119718 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.43353 | 0.00182383 | ||||||||
\(787\) | 111.467 | 0.141635 | 0.0708175 | − | 0.997489i | \(-0.477439\pi\) | ||||
0.0708175 | + | 0.997489i | \(0.477439\pi\) | |||||||
\(788\) | − | 542.181i | − | 0.688046i | ||||||
\(789\) | − | 0.678632i | − | 0.000860116i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −734.663 | −0.928777 | ||||||||
\(792\) | −191.179 | −0.241388 | ||||||||
\(793\) | −92.8546 | −0.117093 | ||||||||
\(794\) | −422.551 | −0.532180 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 514.584i | 0.646462i | ||||||||
\(797\) | 231.014 | 0.289855 | 0.144927 | − | 0.989442i | \(-0.453705\pi\) | ||||
0.144927 | + | 0.989442i | \(0.453705\pi\) | |||||||
\(798\) | − | 81.3701i | − | 0.101968i | ||||||
\(799\) | − | 637.393i | − | 0.797738i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 568.583i | 0.709842i | ||||||||
\(802\) | 1110.32 | 1.38444 | ||||||||
\(803\) | −662.215 | −0.824676 | ||||||||
\(804\) | 24.5467i | 0.0305307i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −211.031 | −0.261825 | ||||||||
\(807\) | − | 86.7145i | − | 0.107453i | ||||||
\(808\) | − | 78.3763i | − | 0.0970004i | ||||||
\(809\) | 165.201 | 0.204204 | 0.102102 | − | 0.994774i | \(-0.467443\pi\) | ||||
0.102102 | + | 0.994774i | \(0.467443\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 317.322 | 0.391273 | 0.195636 | − | 0.980677i | \(-0.437323\pi\) | ||||
0.195636 | + | 0.980677i | \(0.437323\pi\) | |||||||
\(812\) | −542.276 | −0.667828 | ||||||||
\(813\) | − | 72.6251i | − | 0.0893298i | ||||||
\(814\) | 427.870 | 0.525638 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 8.42315i | − | 0.0103225i | ||||||
\(817\) | 499.234i | 0.611058i | ||||||||
\(818\) | − | 506.552i | − | 0.619257i | ||||||
\(819\) | − | 200.574i | − | 0.244901i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1389.82 | −1.69284 | −0.846421 | − | 0.532514i | \(-0.821247\pi\) | ||||
−0.846421 | + | 0.532514i | \(0.821247\pi\) | |||||||
\(822\) | −3.81989 | −0.00464707 | ||||||||
\(823\) | 948.001i | 1.15188i | 0.817490 | + | 0.575942i | \(0.195365\pi\) | ||||
−0.817490 | + | 0.575942i | \(0.804635\pi\) | |||||||
\(824\) | − | 377.713i | − | 0.458390i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 814.489i | − | 0.986064i | ||||||
\(827\) | 1177.54 | 1.42387 | 0.711935 | − | 0.702245i | \(-0.247819\pi\) | ||||
0.711935 | + | 0.702245i | \(0.247819\pi\) | |||||||
\(828\) | 299.326 | + | 280.817i | 0.361505 | + | 0.339151i | ||||
\(829\) | 1278.78 | 1.54256 | 0.771279 | − | 0.636497i | \(-0.219617\pi\) | ||||
0.771279 | + | 0.636497i | \(0.219617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.7655 | 0.0610897 | ||||||||
\(832\) | 21.1261i | 0.0253919i | ||||||||
\(833\) | 177.406 | 0.212973 | ||||||||
\(834\) | −3.17273 | −0.00380423 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 367.679 | 0.439808 | ||||||||
\(837\) | 282.072i | 0.337004i | ||||||||
\(838\) | 276.156 | 0.329541 | ||||||||
\(839\) | 1435.77i | 1.71128i | 0.517570 | + | 0.855641i | \(0.326837\pi\) | ||||
−0.517570 | + | 0.855641i | \(0.673163\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 173.507 | 0.206311 | ||||||||
\(842\) | −1086.18 | −1.28999 | ||||||||
\(843\) | 1.28260 | 0.00152147 | ||||||||
\(844\) | −108.389 | −0.128423 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1063.78 | 1.25742 | ||||||||
\(847\) | 541.500 | 0.639315 | ||||||||
\(848\) | −47.6757 | −0.0562213 | ||||||||
\(849\) | 92.7193i | 0.109210i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −669.908 | − | 628.484i | −0.787201 | − | 0.738524i | ||||
\(852\) | 4.93875i | 0.00579665i | ||||||||
\(853\) | 812.996i | 0.953102i | 0.879147 | + | 0.476551i | \(0.158113\pi\) | ||||
−0.879147 | + | 0.476551i | \(0.841887\pi\) | |||||||
\(854\) | 423.304 | 0.495673 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 142.296i | − | 0.166233i | ||||||
\(857\) | 958.841i | 1.11883i | 0.828886 | + | 0.559417i | \(0.188975\pi\) | ||||
−0.828886 | + | 0.559417i | \(0.811025\pi\) | |||||||
\(858\) | −7.87983 | −0.00918395 | ||||||||
\(859\) | 383.654 | 0.446628 | 0.223314 | − | 0.974747i | \(-0.428312\pi\) | ||||
0.223314 | + | 0.974747i | \(0.428312\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 100.934i | 0.117229i | ||||||||
\(862\) | 471.106 | 0.546526 | ||||||||
\(863\) | 1017.48i | 1.17900i | 0.807767 | + | 0.589502i | \(0.200676\pi\) | ||||
−0.807767 | + | 0.589502i | \(0.799324\pi\) | |||||||
\(864\) | 28.2379 | 0.0326827 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 10.6029i | − | 0.0122436i | ||||||
\(867\) | 64.5721i | 0.0744776i | ||||||||
\(868\) | 962.047 | 1.10835 | ||||||||
\(869\) | 1168.27 | 1.34439 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 116.368i | − | 0.133602i | ||||||
\(872\) | −364.354 | −0.417837 | ||||||||
\(873\) | 1278.78 | 1.46482 | ||||||||
\(874\) | −575.669 | − | 540.072i | −0.658660 | − | 0.617932i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 48.6941 | 0.0555869 | ||||||||
\(877\) | − | 1443.83i | − | 1.64633i | −0.567806 | − | 0.823163i | \(-0.692207\pi\) | ||
0.567806 | − | 0.823163i | \(-0.307793\pi\) | |||||||
\(878\) | 429.835i | 0.489561i | ||||||||
\(879\) | 93.6154i | 0.106502i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 894.988i | − | 1.01588i | −0.861393 | − | 0.507939i | \(-0.830408\pi\) | ||
0.861393 | − | 0.507939i | \(-0.169592\pi\) | |||||||
\(882\) | 296.082i | 0.335694i | ||||||||
\(883\) | − | 870.115i | − | 0.985407i | −0.870197 | − | 0.492704i | \(-0.836009\pi\) | ||
0.870197 | − | 0.492704i | \(-0.163991\pi\) | |||||||
\(884\) | 39.9313i | 0.0451711i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −901.058 | −1.01700 | ||||||||
\(887\) | 529.330i | 0.596764i | 0.954446 | + | 0.298382i | \(0.0964470\pi\) | ||||
−0.954446 | + | 0.298382i | \(0.903553\pi\) | |||||||
\(888\) | −31.4622 | −0.0354304 | ||||||||
\(889\) | 93.7539i | 0.105460i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 597.796i | − | 0.670927i | ||||||
\(892\) | − | 209.221i | − | 0.234553i | ||||||
\(893\) | −2045.87 | −2.29101 | ||||||||
\(894\) | 56.7446i | 0.0634728i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 96.3093i | − | 0.107488i | ||||||
\(897\) | 12.3373 | + | 11.5744i | 0.0137540 | + | 0.0129035i | ||||
\(898\) | − | 125.770i | − | 0.140056i | ||||||
\(899\) | −1799.83 | −2.00203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −90.1138 | −0.100015 | ||||||||
\(902\) | −456.081 | −0.505633 | ||||||||
\(903\) | 48.7755i | 0.0540149i | ||||||||
\(904\) | 244.101i | 0.270023i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −43.3107 | −0.0478044 | ||||||||
\(907\) | 691.482 | 0.762384 | 0.381192 | − | 0.924496i | \(-0.375514\pi\) | ||||
0.381192 | + | 0.924496i | \(0.375514\pi\) | |||||||
\(908\) | −400.968 | −0.441595 | ||||||||
\(909\) | 247.242 | 0.271994 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1794.49i | − | 1.96980i | −0.173115 | − | 0.984902i | \(-0.555383\pi\) | ||
0.173115 | − | 0.984902i | \(-0.444617\pi\) | |||||||
\(912\) | −27.0363 | −0.0296450 | ||||||||
\(913\) | − | 1073.01i | − | 1.17526i | ||||||
\(914\) | − | 534.105i | − | 0.584360i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.1436i | 0.0481917i | ||||||||
\(917\) | 30.9809 | 0.0337851 | ||||||||
\(918\) | 53.3736 | 0.0581412 | ||||||||
\(919\) | − | 428.705i | − | 0.466491i | −0.972418 | − | 0.233245i | \(-0.925065\pi\) | ||
0.972418 | − | 0.233245i | \(-0.0749345\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 127.545 | 0.138485 | ||||||||
\(922\) | − | 827.413i | − | 0.897411i | ||||||
\(923\) | − | 23.4129i | − | 0.0253661i | ||||||
\(924\) | 35.9225 | 0.0388771 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 319.438 | 0.344965 | ||||||||
\(927\) | 1191.52 | 1.28535 | ||||||||
\(928\) | 180.178i | 0.194158i | ||||||||
\(929\) | −1577.01 | −1.69754 | −0.848768 | − | 0.528766i | \(-0.822655\pi\) | ||||
−0.848768 | + | 0.528766i | \(0.822655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 569.431i | − | 0.611633i | ||||||
\(932\) | 677.263i | 0.726677i | ||||||||
\(933\) | 126.900i | 0.136013i | ||||||||
\(934\) | 994.169i | 1.06442i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −66.6433 | −0.0712001 | ||||||||
\(937\) | 141.317 | 0.150818 | 0.0754091 | − | 0.997153i | \(-0.475974\pi\) | ||||
0.0754091 | + | 0.997153i | \(0.475974\pi\) | |||||||
\(938\) | 530.495i | 0.565560i | ||||||||
\(939\) | − | 164.148i | − | 0.174812i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1506.21i | 1.60065i | 0.599566 | + | 0.800325i | \(0.295340\pi\) | ||||
−0.599566 | + | 0.800325i | \(0.704660\pi\) | |||||||
\(942\) | 9.77667 | 0.0103786 | ||||||||
\(943\) | 714.078 | + | 669.923i | 0.757240 | + | 0.710417i | ||||
\(944\) | −270.624 | −0.286678 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −220.397 | −0.232978 | ||||||||
\(947\) | − | 1689.84i | − | 1.78441i | −0.451632 | − | 0.892205i | \(-0.649158\pi\) | ||
0.451632 | − | 0.892205i | \(-0.350842\pi\) | |||||||
\(948\) | −85.9058 | −0.0906179 | ||||||||
\(949\) | −230.842 | −0.243248 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 107.580 | 0.113123 | ||||||||
\(952\) | − | 182.038i | − | 0.191217i | ||||||
\(953\) | −990.482 | −1.03933 | −0.519665 | − | 0.854370i | \(-0.673943\pi\) | ||||
−0.519665 | + | 0.854370i | \(0.673943\pi\) | |||||||
\(954\) | − | 150.395i | − | 0.157647i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 298.749 | 0.312499 | ||||||||
\(957\) | −67.2049 | −0.0702245 | ||||||||
\(958\) | 412.534 | 0.430620 | ||||||||
\(959\) | −82.5541 | −0.0860836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2232.05 | 2.32264 | ||||||||
\(962\) | 149.151 | 0.155043 | ||||||||
\(963\) | 448.879 | 0.466126 | ||||||||
\(964\) | − | 266.059i | − | 0.275995i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −56.2432 | − | 52.7654i | −0.0582227 | − | 0.0546225i | ||||
\(967\) | − | 1528.09i | − | 1.58024i | −0.612954 | − | 0.790118i | \(-0.710019\pi\) | ||
0.612954 | − | 0.790118i | \(-0.289981\pi\) | |||||||
\(968\) | − | 179.920i | − | 0.185868i | ||||||
\(969\) | −51.1024 | −0.0527372 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 616.239i | − | 0.634643i | −0.948318 | − | 0.317322i | \(-0.897217\pi\) | ||
0.948318 | − | 0.317322i | \(-0.102783\pi\) | |||||||
\(972\) | 133.810i | 0.137664i | ||||||||
\(973\) | −68.5679 | −0.0704706 | ||||||||
\(974\) | 291.267 | 0.299042 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 140.648i | − | 0.144107i | ||||||
\(977\) | −1393.79 | −1.42660 | −0.713299 | − | 0.700859i | \(-0.752800\pi\) | ||||
−0.713299 | + | 0.700859i | \(0.752800\pi\) | |||||||
\(978\) | 42.9197i | 0.0438852i | ||||||||
\(979\) | 482.752 | 0.493107 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1149.37i | − | 1.17164i | ||||||
\(982\) | − | 272.205i | − | 0.277195i | ||||||
\(983\) | 1033.22 | 1.05109 | 0.525543 | − | 0.850767i | \(-0.323862\pi\) | ||||
0.525543 | + | 0.850767i | \(0.323862\pi\) | |||||||
\(984\) | 33.5367 | 0.0340820 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 340.563i | 0.345398i | ||||||||
\(987\) | −199.883 | −0.202516 | ||||||||
\(988\) | 128.170 | 0.129726 | ||||||||
\(989\) | 345.071 | + | 323.734i | 0.348909 | + | 0.327335i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1122.80 | −1.13300 | −0.566501 | − | 0.824061i | \(-0.691703\pi\) | ||||
−0.566501 | + | 0.824061i | \(0.691703\pi\) | |||||||
\(992\) | − | 319.652i | − | 0.322230i | ||||||
\(993\) | − | 61.4732i | − | 0.0619066i | ||||||
\(994\) | 106.734i | 0.107379i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 78.9011i | 0.0792179i | ||||||||
\(997\) | 718.650i | 0.720812i | 0.932795 | + | 0.360406i | \(0.117362\pi\) | ||||
−0.932795 | + | 0.360406i | \(0.882638\pi\) | |||||||
\(998\) | − | 1254.95i | − | 1.25747i | ||||||
\(999\) | − | 199.361i | − | 0.199561i |
(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 | 1150.3.c.c.1149.8 | 32 | ||
5.2 | odd | 4 | 230.3.d.a.91.3 | ✓ | 16 | ||
5.3 | odd | 4 | 1150.3.d.b.551.13 | 16 | |||
5.4 | even | 2 | inner | 1150.3.c.c.1149.25 | 32 | ||
15.2 | even | 4 | 2070.3.c.a.91.16 | 16 | |||
20.7 | even | 4 | 1840.3.k.d.321.9 | 16 | |||
23.22 | odd | 2 | inner | 1150.3.c.c.1149.26 | 32 | ||
115.22 | even | 4 | 230.3.d.a.91.4 | yes | 16 | ||
115.68 | even | 4 | 1150.3.d.b.551.14 | 16 | |||
115.114 | odd | 2 | inner | 1150.3.c.c.1149.7 | 32 | ||
345.137 | odd | 4 | 2070.3.c.a.91.9 | 16 | |||
460.367 | odd | 4 | 1840.3.k.d.321.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.3 | ✓ | 16 | 5.2 | odd | 4 | ||
230.3.d.a.91.4 | yes | 16 | 115.22 | even | 4 | ||
1150.3.c.c.1149.7 | 32 | 115.114 | odd | 2 | inner | ||
1150.3.c.c.1149.8 | 32 | 1.1 | even | 1 | trivial | ||
1150.3.c.c.1149.25 | 32 | 5.4 | even | 2 | inner | ||
1150.3.c.c.1149.26 | 32 | 23.22 | odd | 2 | inner | ||
1150.3.d.b.551.13 | 16 | 5.3 | odd | 4 | |||
1150.3.d.b.551.14 | 16 | 115.68 | even | 4 | |||
1840.3.k.d.321.9 | 16 | 20.7 | even | 4 | |||
1840.3.k.d.321.10 | 16 | 460.367 | odd | 4 | |||
2070.3.c.a.91.9 | 16 | 345.137 | odd | 4 | |||
2070.3.c.a.91.16 | 16 | 15.2 | even | 4 |