Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(343,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.343");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.g (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.2 | ||
Character | \(\chi\) | \(=\) | 684.343 |
Dual form | 684.3.g.d.343.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98942 | + | 0.205433i | −0.994711 | + | 0.102716i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.91559 | − | 0.817384i | 0.978899 | − | 0.204346i | ||||
\(5\) | −0.0956487 | −0.0191297 | −0.00956487 | − | 0.999954i | \(-0.503045\pi\) | ||||
−0.00956487 | + | 0.999954i | \(0.503045\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 9.56723i | − | 1.36675i | −0.730069 | − | 0.683373i | \(-0.760512\pi\) | ||
0.730069 | − | 0.683373i | \(-0.239488\pi\) | |||||||
\(8\) | −7.62185 | + | 2.43051i | −0.952731 | + | 0.303814i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.190286 | − | 0.0196494i | 0.0190286 | − | 0.00196494i | ||||
\(11\) | 7.63102i | 0.693729i | 0.937915 | + | 0.346865i | \(0.112754\pi\) | ||||
−0.937915 | + | 0.346865i | \(0.887246\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.83922 | 0.603017 | 0.301509 | − | 0.953463i | \(-0.402510\pi\) | ||||
0.301509 | + | 0.953463i | \(0.402510\pi\) | |||||||
\(14\) | 1.96542 | + | 19.0332i | 0.140387 | + | 1.35952i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.6638 | − | 6.40109i | 0.916485 | − | 0.400068i | ||||
\(17\) | 16.6975 | 0.982206 | 0.491103 | − | 0.871102i | \(-0.336594\pi\) | ||||
0.491103 | + | 0.871102i | \(0.336594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890i | 0.229416i | ||||||||
\(20\) | −0.374522 | + | 0.0781817i | −0.0187261 | + | 0.00390909i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.56766 | − | 15.1813i | −0.0712573 | − | 0.690060i | ||||
\(23\) | − | 6.37991i | − | 0.277387i | −0.990335 | − | 0.138694i | \(-0.955710\pi\) | ||
0.990335 | − | 0.138694i | \(-0.0442903\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.9909 | −0.999634 | ||||||||
\(26\) | −15.5955 | + | 1.61043i | −0.599828 | + | 0.0619397i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.82010 | − | 37.4614i | −0.279289 | − | 1.33791i | ||||
\(29\) | 19.5690 | 0.674792 | 0.337396 | − | 0.941363i | \(-0.390454\pi\) | ||||
0.337396 | + | 0.941363i | \(0.390454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 57.7824i | − | 1.86395i | −0.362526 | − | 0.931973i | \(-0.618086\pi\) | ||
0.362526 | − | 0.931973i | \(-0.381914\pi\) | |||||||
\(32\) | −27.8574 | + | 15.7469i | −0.870544 | + | 0.492090i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −33.2184 | + | 3.43021i | −0.977011 | + | 0.100889i | ||||
\(35\) | 0.915093i | 0.0261455i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 50.5873 | 1.36722 | 0.683612 | − | 0.729846i | \(-0.260408\pi\) | ||||
0.683612 | + | 0.729846i | \(0.260408\pi\) | |||||||
\(38\) | −0.895460 | − | 8.67169i | −0.0235647 | − | 0.228202i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.729020 | − | 0.232475i | 0.0182255 | − | 0.00581189i | ||||
\(41\) | −57.9622 | −1.41371 | −0.706857 | − | 0.707357i | \(-0.749887\pi\) | ||||
−0.706857 | + | 0.707357i | \(0.749887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.2206i | 0.307457i | 0.988113 | + | 0.153728i | \(0.0491280\pi\) | ||||
−0.988113 | + | 0.153728i | \(0.950872\pi\) | |||||||
\(44\) | 6.23748 | + | 29.8800i | 0.141761 | + | 0.679091i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.31064 | + | 12.6923i | 0.0284922 | + | 0.275920i | ||||
\(47\) | 42.0176i | 0.893992i | 0.894536 | + | 0.446996i | \(0.147506\pi\) | ||||
−0.894536 | + | 0.446996i | \(0.852494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −42.5319 | −0.867997 | ||||||||
\(50\) | 49.7173 | − | 5.13394i | 0.994347 | − | 0.102679i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 30.6952 | − | 6.40766i | 0.590293 | − | 0.123224i | ||||
\(53\) | −40.5786 | −0.765634 | −0.382817 | − | 0.923824i | \(-0.625046\pi\) | ||||
−0.382817 | + | 0.923824i | \(0.625046\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.729898i | − | 0.0132709i | ||||||
\(56\) | 23.2533 | + | 72.9200i | 0.415237 | + | 1.30214i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −38.9309 | + | 4.02010i | −0.671222 | + | 0.0693121i | ||||
\(59\) | − | 89.4572i | − | 1.51622i | −0.652124 | − | 0.758112i | \(-0.726122\pi\) | ||
0.652124 | − | 0.758112i | \(-0.273878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 30.2988 | 0.496701 | 0.248350 | − | 0.968670i | \(-0.420112\pi\) | ||||
0.248350 | + | 0.968670i | \(0.420112\pi\) | |||||||
\(62\) | 11.8704 | + | 114.953i | 0.191458 | + | 1.85409i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 52.1852 | − | 37.0500i | 0.815394 | − | 0.578906i | ||||
\(65\) | −0.749812 | −0.0115356 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 61.0526i | − | 0.911233i | −0.890176 | − | 0.455616i | \(-0.849419\pi\) | ||
0.890176 | − | 0.455616i | \(-0.150581\pi\) | |||||||
\(68\) | 65.3807 | − | 13.6483i | 0.961480 | − | 0.200710i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.187990 | − | 1.82051i | −0.00268557 | − | 0.0260072i | ||||
\(71\) | − | 134.657i | − | 1.89658i | −0.317411 | − | 0.948288i | \(-0.602813\pi\) | ||
0.317411 | − | 0.948288i | \(-0.397187\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 50.8095 | 0.696021 | 0.348010 | − | 0.937491i | \(-0.386857\pi\) | ||||
0.348010 | + | 0.937491i | \(0.386857\pi\) | |||||||
\(74\) | −100.639 | + | 10.3923i | −1.35999 | + | 0.140436i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.56289 | + | 17.0677i | 0.0468802 | + | 0.224575i | ||||
\(77\) | 73.0077 | 0.948152 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.4587i | − | 0.132388i | −0.997807 | − | 0.0661941i | \(-0.978914\pi\) | ||
0.997807 | − | 0.0661941i | \(-0.0210857\pi\) | |||||||
\(80\) | −1.40257 | + | 0.612256i | −0.0175321 | + | 0.00765320i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 115.311 | − | 11.9073i | 1.40624 | − | 0.145211i | ||||
\(83\) | − | 80.3969i | − | 0.968638i | −0.874892 | − | 0.484319i | \(-0.839068\pi\) | ||
0.874892 | − | 0.484319i | \(-0.160932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.59709 | −0.0187894 | ||||||||
\(86\) | −2.71595 | − | 26.3014i | −0.0315808 | − | 0.305830i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −18.5473 | − | 58.1625i | −0.210765 | − | 0.660938i | ||||
\(89\) | −73.9080 | −0.830427 | −0.415214 | − | 0.909724i | \(-0.636293\pi\) | ||||
−0.415214 | + | 0.909724i | \(0.636293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 74.9996i | − | 0.824172i | ||||||
\(92\) | −5.21483 | − | 24.9811i | −0.0566830 | − | 0.271534i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.63179 | − | 83.5908i | −0.0918276 | − | 0.889263i | ||||
\(95\) | − | 0.416923i | − | 0.00438866i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −101.252 | −1.04383 | −0.521916 | − | 0.852997i | \(-0.674783\pi\) | ||||
−0.521916 | + | 0.852997i | \(0.674783\pi\) | |||||||
\(98\) | 84.6138 | − | 8.73743i | 0.863406 | − | 0.0891575i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −97.8540 | + | 20.4271i | −0.978540 | + | 0.204271i | ||||
\(101\) | 73.2306 | 0.725056 | 0.362528 | − | 0.931973i | \(-0.381914\pi\) | ||||
0.362528 | + | 0.931973i | \(0.381914\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.6014i | − | 0.161179i | −0.996747 | − | 0.0805895i | \(-0.974320\pi\) | ||
0.996747 | − | 0.0805895i | \(-0.0256803\pi\) | |||||||
\(104\) | −59.7494 | + | 19.0533i | −0.574513 | + | 0.183205i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 80.7280 | − | 8.33617i | 0.761584 | − | 0.0786431i | ||||
\(107\) | − | 135.797i | − | 1.26913i | −0.772871 | − | 0.634563i | \(-0.781180\pi\) | ||
0.772871 | − | 0.634563i | \(-0.218820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21.3010 | −0.195422 | −0.0977109 | − | 0.995215i | \(-0.531152\pi\) | ||||
−0.0977109 | + | 0.995215i | \(0.531152\pi\) | |||||||
\(110\) | 0.149945 | + | 1.45207i | 0.00136313 | + | 0.0132007i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −61.2407 | − | 140.292i | −0.546792 | − | 1.25260i | ||||
\(113\) | 46.7834 | 0.414013 | 0.207006 | − | 0.978340i | \(-0.433628\pi\) | ||||
0.207006 | + | 0.978340i | \(0.433628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.610230i | 0.00530635i | ||||||||
\(116\) | 76.6241 | − | 15.9954i | 0.660553 | − | 0.137891i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.3774 | + | 177.968i | 0.155741 | + | 1.50820i | ||||
\(119\) | − | 159.749i | − | 1.34243i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 62.7675 | 0.518740 | ||||||||
\(122\) | −60.2770 | + | 6.22435i | −0.494074 | + | 0.0510193i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −47.2304 | − | 226.252i | −0.380890 | − | 1.82462i | ||||
\(125\) | 4.78156 | 0.0382525 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 81.0214i | 0.637964i | 0.947761 | + | 0.318982i | \(0.103341\pi\) | ||||
−0.947761 | + | 0.318982i | \(0.896659\pi\) | |||||||
\(128\) | −96.2071 | + | 84.4286i | −0.751618 | + | 0.659599i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.49169 | − | 0.154036i | 0.0114745 | − | 0.00118489i | ||||
\(131\) | − | 189.253i | − | 1.44468i | −0.691540 | − | 0.722339i | \(-0.743067\pi\) | ||
0.691540 | − | 0.722339i | \(-0.256933\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41.7026 | 0.313553 | ||||||||
\(134\) | 12.5422 | + | 121.459i | 0.0935985 | + | 0.906413i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −127.266 | + | 40.5835i | −0.935778 | + | 0.298408i | ||||
\(137\) | 237.261 | 1.73183 | 0.865916 | − | 0.500189i | \(-0.166736\pi\) | ||||
0.865916 | + | 0.500189i | \(0.166736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 189.051i | − | 1.36008i | −0.733176 | − | 0.680039i | \(-0.761963\pi\) | ||
0.733176 | − | 0.680039i | \(-0.238037\pi\) | |||||||
\(140\) | 0.747983 | + | 3.58313i | 0.00534273 | + | 0.0255938i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 27.6629 | + | 267.889i | 0.194809 | + | 1.88654i | ||||
\(143\) | 59.8213i | 0.418331i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.87175 | −0.0129086 | ||||||||
\(146\) | −101.082 | + | 10.4379i | −0.692339 | + | 0.0714927i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 198.079 | − | 41.3492i | 1.33837 | − | 0.279387i | ||||
\(149\) | 85.9682 | 0.576968 | 0.288484 | − | 0.957485i | \(-0.406849\pi\) | ||||
0.288484 | + | 0.957485i | \(0.406849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 69.8538i | − | 0.462608i | −0.972882 | − | 0.231304i | \(-0.925701\pi\) | ||
0.972882 | − | 0.231304i | \(-0.0742991\pi\) | |||||||
\(152\) | −10.5944 | − | 33.2229i | −0.0696997 | − | 0.218572i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −145.243 | + | 14.9982i | −0.943137 | + | 0.0973907i | ||||
\(155\) | 5.52681i | 0.0356568i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 66.1082 | 0.421071 | 0.210536 | − | 0.977586i | \(-0.432479\pi\) | ||||
0.210536 | + | 0.977586i | \(0.432479\pi\) | |||||||
\(158\) | 2.14855 | + | 20.8067i | 0.0135984 | + | 0.131688i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.66453 | − | 1.50617i | 0.0166533 | − | 0.00941356i | ||||
\(161\) | −61.0380 | −0.379118 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 209.537i | 1.28550i | 0.766075 | + | 0.642752i | \(0.222207\pi\) | ||||
−0.766075 | + | 0.642752i | \(0.777793\pi\) | |||||||
\(164\) | −226.957 | + | 47.3774i | −1.38388 | + | 0.288887i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.5161 | + | 159.943i | 0.0994949 | + | 0.963514i | ||||
\(167\) | − | 94.6876i | − | 0.566992i | −0.958973 | − | 0.283496i | \(-0.908506\pi\) | ||
0.958973 | − | 0.283496i | \(-0.0914942\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −107.547 | −0.636370 | ||||||||
\(170\) | 3.17729 | − | 0.328095i | 0.0186900 | − | 0.00192997i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.8063 | + | 51.7666i | 0.0628275 | + | 0.300969i | ||||
\(173\) | −107.114 | −0.619156 | −0.309578 | − | 0.950874i | \(-0.600188\pi\) | ||||
−0.309578 | + | 0.950874i | \(0.600188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 239.093i | 1.36625i | ||||||||
\(176\) | 48.8469 | + | 111.900i | 0.277539 | + | 0.635793i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 147.034 | − | 15.1831i | 0.826035 | − | 0.0852984i | ||||
\(179\) | 202.586i | 1.13176i | 0.824486 | + | 0.565882i | \(0.191464\pi\) | ||||
−0.824486 | + | 0.565882i | \(0.808536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 189.134 | 1.04494 | 0.522471 | − | 0.852657i | \(-0.325010\pi\) | ||||
0.522471 | + | 0.852657i | \(0.325010\pi\) | |||||||
\(182\) | 15.4074 | + | 149.206i | 0.0846559 | + | 0.819812i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.5064 | + | 48.6267i | 0.0842741 | + | 0.264275i | ||||
\(185\) | −4.83861 | −0.0261546 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 127.419i | 0.681385i | ||||||||
\(188\) | 34.3445 | + | 164.524i | 0.182684 | + | 0.875128i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0856496 | + | 0.829436i | 0.000450787 | + | 0.00436545i | ||||
\(191\) | − | 236.358i | − | 1.23748i | −0.785597 | − | 0.618739i | \(-0.787644\pi\) | ||
0.785597 | − | 0.618739i | \(-0.212356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.36645 | −0.0381681 | −0.0190841 | − | 0.999818i | \(-0.506075\pi\) | ||||
−0.0190841 | + | 0.999818i | \(0.506075\pi\) | |||||||
\(194\) | 201.432 | − | 20.8004i | 1.03831 | − | 0.107219i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −166.538 | + | 34.7649i | −0.849681 | + | 0.177372i | ||||
\(197\) | −247.192 | −1.25478 | −0.627391 | − | 0.778705i | \(-0.715877\pi\) | ||||
−0.627391 | + | 0.778705i | \(0.715877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 174.589i | 0.877330i | 0.898651 | + | 0.438665i | \(0.144548\pi\) | ||||
−0.898651 | + | 0.438665i | \(0.855452\pi\) | |||||||
\(200\) | 190.477 | − | 60.7406i | 0.952383 | − | 0.303703i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −145.687 | + | 15.0440i | −0.721221 | + | 0.0744751i | ||||
\(203\) | − | 187.221i | − | 0.922269i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.54401 | 0.0270440 | ||||||||
\(206\) | 3.41048 | + | 33.0272i | 0.0165557 | + | 0.160326i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 114.953 | − | 50.1796i | 0.552656 | − | 0.241248i | ||||
\(209\) | −33.2629 | −0.159152 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 234.077i | 1.10937i | 0.832061 | + | 0.554684i | \(0.187161\pi\) | ||||
−0.832061 | + | 0.554684i | \(0.812839\pi\) | |||||||
\(212\) | −158.889 | + | 33.1683i | −0.749478 | + | 0.156454i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.8970 | + | 270.157i | 0.130360 | + | 1.26241i | ||||
\(215\) | − | 1.26454i | − | 0.00588156i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −552.817 | −2.54754 | ||||||||
\(218\) | 42.3766 | − | 4.37592i | 0.194388 | − | 0.0200730i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.596607 | − | 2.85798i | −0.00271185 | − | 0.0129908i | ||||
\(221\) | 130.895 | 0.592287 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 142.738i | 0.640082i | 0.947404 | + | 0.320041i | \(0.103697\pi\) | ||||
−0.947404 | + | 0.320041i | \(0.896303\pi\) | |||||||
\(224\) | 150.654 | + | 266.518i | 0.672563 | + | 1.18981i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −93.0719 | + | 9.61084i | −0.411823 | + | 0.0425258i | ||||
\(227\) | 338.494i | 1.49116i | 0.666414 | + | 0.745582i | \(0.267828\pi\) | ||||
−0.666414 | + | 0.745582i | \(0.732172\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −104.649 | −0.456981 | −0.228491 | − | 0.973546i | \(-0.573379\pi\) | ||||
−0.228491 | + | 0.973546i | \(0.573379\pi\) | |||||||
\(230\) | −0.125361 | − | 1.21400i | −0.000545048 | − | 0.00527828i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −149.152 | + | 47.5626i | −0.642895 | + | 0.205011i | ||||
\(233\) | −106.731 | −0.458075 | −0.229037 | − | 0.973418i | \(-0.573558\pi\) | ||||
−0.229037 | + | 0.973418i | \(0.573558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4.01893i | − | 0.0171018i | ||||||
\(236\) | −73.1209 | − | 350.278i | −0.309834 | − | 1.48423i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 32.8176 | + | 317.808i | 0.137889 | + | 1.33533i | ||||
\(239\) | − | 246.219i | − | 1.03020i | −0.857129 | − | 0.515102i | \(-0.827754\pi\) | ||
0.857129 | − | 0.515102i | \(-0.172246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 95.2425 | 0.395197 | 0.197599 | − | 0.980283i | \(-0.436686\pi\) | ||||
0.197599 | + | 0.980283i | \(0.436686\pi\) | |||||||
\(242\) | −124.871 | + | 12.8945i | −0.515996 | + | 0.0532830i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 118.638 | − | 24.7657i | 0.486220 | − | 0.101499i | ||||
\(245\) | 4.06812 | 0.0166046 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.1704i | 0.138342i | ||||||||
\(248\) | 140.441 | + | 440.408i | 0.566293 | + | 1.77584i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.51254 | + | 0.982289i | −0.0380502 | + | 0.00392915i | ||||
\(251\) | 478.257i | 1.90541i | 0.303903 | + | 0.952703i | \(0.401710\pi\) | ||||
−0.303903 | + | 0.952703i | \(0.598290\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48.6852 | 0.192432 | ||||||||
\(254\) | −16.6444 | − | 161.186i | −0.0655293 | − | 0.634589i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 174.052 | − | 187.728i | 0.679891 | − | 0.733313i | ||||
\(257\) | −395.469 | −1.53879 | −0.769395 | − | 0.638773i | \(-0.779442\pi\) | ||||
−0.769395 | + | 0.638773i | \(0.779442\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 483.980i | − | 1.86865i | ||||||
\(260\) | −2.93596 | + | 0.612884i | −0.0112921 | + | 0.00235725i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 38.8787 | + | 376.503i | 0.148392 | + | 1.43704i | ||||
\(263\) | 105.268i | 0.400260i | 0.979769 | + | 0.200130i | \(0.0641365\pi\) | ||||
−0.979769 | + | 0.200130i | \(0.935863\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.88129 | 0.0146464 | ||||||||
\(266\) | −82.9640 | + | 8.56707i | −0.311895 | + | 0.0322070i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −49.9034 | − | 239.057i | −0.186207 | − | 0.892005i | ||||
\(269\) | 27.1446 | 0.100909 | 0.0504546 | − | 0.998726i | \(-0.483933\pi\) | ||||
0.0504546 | + | 0.998726i | \(0.483933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 228.783i | 0.844218i | 0.906545 | + | 0.422109i | \(0.138710\pi\) | ||||
−0.906545 | + | 0.422109i | \(0.861290\pi\) | |||||||
\(272\) | 244.848 | − | 106.882i | 0.900177 | − | 0.392949i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −472.012 | + | 48.7412i | −1.72267 | + | 0.177887i | ||||
\(275\) | − | 190.706i | − | 0.693475i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.16335 | −0.0114200 | −0.00571002 | − | 0.999984i | \(-0.501818\pi\) | ||||
−0.00571002 | + | 0.999984i | \(0.501818\pi\) | |||||||
\(278\) | 38.8372 | + | 376.102i | 0.139702 | + | 1.35288i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.22415 | − | 6.97470i | −0.00794338 | − | 0.0249097i | ||||
\(281\) | 228.667 | 0.813763 | 0.406881 | − | 0.913481i | \(-0.366616\pi\) | ||||
0.406881 | + | 0.913481i | \(0.366616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 86.7931i | 0.306690i | 0.988173 | + | 0.153345i | \(0.0490045\pi\) | ||||
−0.988173 | + | 0.153345i | \(0.950995\pi\) | |||||||
\(284\) | −110.066 | − | 527.262i | −0.387558 | − | 1.85656i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.2892 | − | 119.010i | −0.0429694 | − | 0.416118i | ||||
\(287\) | 554.538i | 1.93219i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.1934 | −0.0352714 | ||||||||
\(290\) | 3.72369 | − | 0.384518i | 0.0128403 | − | 0.00132592i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 198.949 | − | 41.5309i | 0.681334 | − | 0.142229i | ||||
\(293\) | −423.581 | −1.44567 | −0.722835 | − | 0.691021i | \(-0.757161\pi\) | ||||
−0.722835 | + | 0.691021i | \(0.757161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.55647i | 0.0290050i | ||||||||
\(296\) | −385.569 | + | 122.953i | −1.30260 | + | 0.415382i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −171.027 | + | 17.6607i | −0.573916 | + | 0.0592640i | ||||
\(299\) | − | 50.0135i | − | 0.167269i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 126.485 | 0.420215 | ||||||||
\(302\) | 14.3502 | + | 138.969i | 0.0475174 | + | 0.460161i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 27.9017 | + | 63.9179i | 0.0917819 | + | 0.210256i | ||||
\(305\) | −2.89804 | −0.00950176 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 130.373i | − | 0.424669i | −0.977197 | − | 0.212335i | \(-0.931893\pi\) | ||
0.977197 | − | 0.212335i | \(-0.0681067\pi\) | |||||||
\(308\) | 285.869 | − | 59.6754i | 0.928145 | − | 0.193751i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.13539 | − | 10.9952i | −0.00366254 | − | 0.0354682i | ||||
\(311\) | 355.493i | 1.14306i | 0.820580 | + | 0.571532i | \(0.193651\pi\) | ||||
−0.820580 | + | 0.571532i | \(0.806349\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 190.194 | 0.607648 | 0.303824 | − | 0.952728i | \(-0.401736\pi\) | ||||
0.303824 | + | 0.952728i | \(0.401736\pi\) | |||||||
\(314\) | −131.517 | + | 13.5808i | −0.418844 | + | 0.0432509i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.54875 | − | 40.9519i | −0.0270530 | − | 0.129595i | ||||
\(317\) | 268.849 | 0.848105 | 0.424053 | − | 0.905638i | \(-0.360607\pi\) | ||||
0.424053 | + | 0.905638i | \(0.360607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 149.331i | 0.468123i | ||||||||
\(320\) | −4.99145 | + | 3.54379i | −0.0155983 | + | 0.0110743i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 121.430 | − | 12.5392i | 0.377113 | − | 0.0389416i | ||||
\(323\) | 72.7827i | 0.225334i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −195.909 | −0.602796 | ||||||||
\(326\) | −43.0457 | − | 416.857i | −0.132042 | − | 1.27870i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 441.780 | − | 140.878i | 1.34689 | − | 0.429506i | ||||
\(329\) | 401.992 | 1.22186 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 372.121i | − | 1.12423i | −0.827059 | − | 0.562116i | \(-0.809988\pi\) | ||
0.827059 | − | 0.562116i | \(-0.190012\pi\) | |||||||
\(332\) | −65.7152 | − | 314.802i | −0.197937 | − | 0.948198i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.4519 | + | 188.374i | 0.0582393 | + | 0.563993i | ||||
\(335\) | 5.83960i | 0.0174317i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 589.875 | 1.75037 | 0.875186 | − | 0.483787i | \(-0.160739\pi\) | ||||
0.875186 | + | 0.483787i | \(0.160739\pi\) | |||||||
\(338\) | 213.955 | − | 22.0936i | 0.633004 | − | 0.0653656i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.25358 | + | 1.30544i | −0.0183929 | + | 0.00383953i | ||||
\(341\) | 440.938 | 1.29307 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 61.8822i | − | 0.180415i | ||||||
\(344\) | −32.1329 | − | 100.766i | −0.0934096 | − | 0.292923i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 213.095 | − | 22.0047i | 0.615881 | − | 0.0635974i | ||||
\(347\) | − | 496.275i | − | 1.43019i | −0.699028 | − | 0.715094i | \(-0.746384\pi\) | ||
0.699028 | − | 0.715094i | \(-0.253616\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 483.924 | 1.38660 | 0.693302 | − | 0.720648i | \(-0.256155\pi\) | ||||
0.693302 | + | 0.720648i | \(0.256155\pi\) | |||||||
\(350\) | −49.1175 | − | 475.657i | −0.140336 | − | 1.35902i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −120.165 | − | 212.581i | −0.341377 | − | 0.603922i | ||||
\(353\) | 29.0531 | 0.0823034 | 0.0411517 | − | 0.999153i | \(-0.486897\pi\) | ||||
0.0411517 | + | 0.999153i | \(0.486897\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.8798i | 0.0362810i | ||||||||
\(356\) | −289.394 | + | 60.4113i | −0.812904 | + | 0.169695i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.6177 | − | 403.028i | −0.116251 | − | 1.12578i | ||||
\(359\) | − | 332.143i | − | 0.925191i | −0.886570 | − | 0.462595i | \(-0.846918\pi\) | ||
0.886570 | − | 0.462595i | \(-0.153082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | −376.268 | + | 38.8544i | −1.03941 | + | 0.107333i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −61.3035 | − | 293.668i | −0.168416 | − | 0.806781i | ||||
\(365\) | −4.85986 | −0.0133147 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 250.955i | 0.683801i | 0.939736 | + | 0.341900i | \(0.111071\pi\) | ||||
−0.939736 | + | 0.341900i | \(0.888929\pi\) | |||||||
\(368\) | −40.8383 | − | 93.5534i | −0.110974 | − | 0.254221i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.62603 | − | 0.994008i | 0.0260163 | − | 0.00268651i | ||||
\(371\) | 388.225i | 1.04643i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −451.339 | −1.21002 | −0.605012 | − | 0.796217i | \(-0.706832\pi\) | ||||
−0.605012 | + | 0.796217i | \(0.706832\pi\) | |||||||
\(374\) | −26.1760 | − | 253.490i | −0.0699894 | − | 0.677781i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −102.124 | − | 320.252i | −0.271607 | − | 0.851734i | ||||
\(377\) | 153.405 | 0.406911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 244.546i | 0.645241i | 0.946528 | + | 0.322620i | \(0.104564\pi\) | ||||
−0.946528 | + | 0.322620i | \(0.895436\pi\) | |||||||
\(380\) | −0.340786 | − | 1.63250i | −0.000896806 | − | 0.00429606i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 48.5557 | + | 470.216i | 0.127109 | + | 1.23093i | ||||
\(383\) | 176.792i | 0.461599i | 0.973001 | + | 0.230799i | \(0.0741341\pi\) | ||||
−0.973001 | + | 0.230799i | \(0.925866\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.98310 | −0.0181379 | ||||||||
\(386\) | 14.6550 | − | 1.51331i | 0.0379662 | − | 0.00392049i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −396.461 | + | 82.7616i | −1.02181 | + | 0.213303i | ||||
\(389\) | −209.991 | −0.539822 | −0.269911 | − | 0.962885i | \(-0.586994\pi\) | ||||
−0.269911 | + | 0.962885i | \(0.586994\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 106.528i | − | 0.272451i | ||||||
\(392\) | 324.171 | − | 103.374i | 0.826968 | − | 0.263710i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 491.769 | − | 50.7813i | 1.24814 | − | 0.128887i | ||||
\(395\) | 1.00036i | 0.00253255i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −435.374 | −1.09666 | −0.548329 | − | 0.836262i | \(-0.684736\pi\) | ||||
−0.548329 | + | 0.836262i | \(0.684736\pi\) | |||||||
\(398\) | −35.8662 | − | 347.330i | −0.0901161 | − | 0.872689i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −366.460 | + | 159.969i | −0.916150 | + | 0.399922i | ||||
\(401\) | 694.395 | 1.73166 | 0.865830 | − | 0.500339i | \(-0.166791\pi\) | ||||
0.865830 | + | 0.500339i | \(0.166791\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 452.969i | − | 1.12399i | ||||||
\(404\) | 286.742 | − | 59.8576i | 0.709756 | − | 0.148162i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 38.4612 | + | 372.461i | 0.0947321 | + | 0.917391i | ||||
\(407\) | 386.033i | 0.948483i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −587.460 | −1.43633 | −0.718166 | − | 0.695871i | \(-0.755018\pi\) | ||||
−0.718166 | + | 0.695871i | \(0.755018\pi\) | |||||||
\(410\) | −11.0294 | + | 1.13892i | −0.0269009 | + | 0.00277786i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.5697 | − | 65.0045i | −0.0329363 | − | 0.157778i | ||||
\(413\) | −855.858 | −2.07229 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.68986i | 0.0185298i | ||||||||
\(416\) | −218.380 | + | 123.443i | −0.524953 | + | 0.296739i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 66.1738 | − | 6.83328i | 0.158311 | − | 0.0163475i | ||||
\(419\) | − | 485.542i | − | 1.15881i | −0.815040 | − | 0.579405i | \(-0.803285\pi\) | ||
0.815040 | − | 0.579405i | \(-0.196715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −450.385 | −1.06980 | −0.534900 | − | 0.844916i | \(-0.679651\pi\) | ||||
−0.534900 | + | 0.844916i | \(0.679651\pi\) | |||||||
\(422\) | −48.0870 | − | 465.677i | −0.113950 | − | 1.10350i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 309.284 | − | 98.6268i | 0.729444 | − | 0.232610i | ||||
\(425\) | −417.285 | −0.981847 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 289.875i | − | 0.678864i | ||||||
\(428\) | −110.998 | − | 531.724i | −0.259341 | − | 1.24235i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.259777 | + | 2.51570i | 0.000604133 | + | 0.00585046i | ||||
\(431\) | 241.465i | 0.560244i | 0.959964 | + | 0.280122i | \(0.0903750\pi\) | ||||
−0.959964 | + | 0.280122i | \(0.909625\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 650.587 | 1.50251 | 0.751255 | − | 0.660012i | \(-0.229449\pi\) | ||||
0.751255 | + | 0.660012i | \(0.229449\pi\) | |||||||
\(434\) | 1099.79 | − | 113.567i | 2.53407 | − | 0.261674i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −83.4060 | + | 17.4111i | −0.191298 | + | 0.0399337i | ||||
\(437\) | 27.8094 | 0.0636370 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 624.375i | − | 1.42227i | −0.703057 | − | 0.711134i | \(-0.748182\pi\) | ||
0.703057 | − | 0.711134i | \(-0.251818\pi\) | |||||||
\(440\) | 1.77402 | + | 5.56317i | 0.00403187 | + | 0.0126436i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −260.406 | + | 26.8902i | −0.589154 | + | 0.0608375i | ||||
\(443\) | 502.356i | 1.13399i | 0.823722 | + | 0.566994i | \(0.191894\pi\) | ||||
−0.823722 | + | 0.566994i | \(0.808106\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.06921 | 0.0158859 | ||||||||
\(446\) | −29.3231 | − | 283.967i | −0.0657469 | − | 0.636697i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −354.466 | − | 499.268i | −0.791218 | − | 1.11444i | ||||
\(449\) | 134.312 | 0.299136 | 0.149568 | − | 0.988751i | \(-0.452212\pi\) | ||||
0.149568 | + | 0.988751i | \(0.452212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 442.311i | − | 0.980734i | ||||||
\(452\) | 183.185 | − | 38.2400i | 0.405276 | − | 0.0846018i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −69.5377 | − | 673.407i | −0.153167 | − | 1.48328i | ||||
\(455\) | 7.17362i | 0.0157662i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 330.353 | 0.722873 | 0.361437 | − | 0.932397i | \(-0.382286\pi\) | ||||
0.361437 | + | 0.932397i | \(0.382286\pi\) | |||||||
\(458\) | 208.190 | − | 21.4983i | 0.454564 | − | 0.0469394i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.498792 | + | 2.38941i | 0.00108433 | + | 0.00519438i | ||||
\(461\) | 285.670 | 0.619674 | 0.309837 | − | 0.950790i | \(-0.399725\pi\) | ||||
0.309837 | + | 0.950790i | \(0.399725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 455.529i | 0.983864i | 0.870634 | + | 0.491932i | \(0.163709\pi\) | ||||
−0.870634 | + | 0.491932i | \(0.836291\pi\) | |||||||
\(464\) | 286.955 | − | 125.263i | 0.618437 | − | 0.269963i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 212.334 | − | 21.9261i | 0.455652 | − | 0.0470517i | ||||
\(467\) | 236.094i | 0.505556i | 0.967524 | + | 0.252778i | \(0.0813442\pi\) | ||||
−0.967524 | + | 0.252778i | \(0.918656\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −584.104 | −1.24542 | ||||||||
\(470\) | 0.825620 | + | 7.99535i | 0.00175664 | + | 0.0170114i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 217.427 | + | 681.830i | 0.460650 | + | 1.44455i | ||||
\(473\) | −100.887 | −0.213292 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 108.933i | − | 0.229332i | ||||||
\(476\) | −130.576 | − | 625.512i | −0.274320 | − | 1.31410i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 50.5813 | + | 489.833i | 0.105819 | + | 1.02475i | ||||
\(479\) | 426.197i | 0.889765i | 0.895589 | + | 0.444882i | \(0.146755\pi\) | ||||
−0.895589 | + | 0.444882i | \(0.853245\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 396.565 | 0.824459 | ||||||||
\(482\) | −189.478 | + | 19.5659i | −0.393107 | + | 0.0405932i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 245.772 | − | 51.3052i | 0.507794 | − | 0.106002i | ||||
\(485\) | 9.68460 | 0.0199683 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 929.716i | 1.90907i | 0.298103 | + | 0.954534i | \(0.403646\pi\) | ||||
−0.298103 | + | 0.954534i | \(0.596354\pi\) | |||||||
\(488\) | −230.933 | + | 73.6415i | −0.473222 | + | 0.150905i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.09320 | + | 0.835724i | −0.0165167 | + | 0.00170556i | ||||
\(491\) | 770.529i | 1.56931i | 0.619935 | + | 0.784653i | \(0.287159\pi\) | ||||
−0.619935 | + | 0.784653i | \(0.712841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 326.753 | 0.662784 | ||||||||
\(494\) | −7.01971 | − | 67.9793i | −0.0142099 | − | 0.137610i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −369.870 | − | 847.307i | −0.745706 | − | 1.70828i | ||||
\(497\) | −1288.29 | −2.59214 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 701.981i | − | 1.40677i | −0.710807 | − | 0.703387i | \(-0.751670\pi\) | ||
0.710807 | − | 0.703387i | \(-0.248330\pi\) | |||||||
\(500\) | 18.7227 | − | 3.90837i | 0.0374453 | − | 0.00781674i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −98.2496 | − | 951.455i | −0.195716 | − | 1.89533i | ||||
\(503\) | 766.313i | 1.52348i | 0.647880 | + | 0.761742i | \(0.275656\pi\) | ||||
−0.647880 | + | 0.761742i | \(0.724344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.00442 | −0.0138701 | ||||||||
\(506\) | −96.8554 | + | 10.0015i | −0.191414 | + | 0.0197659i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 66.2256 | + | 317.247i | 0.130365 | + | 0.624502i | ||||
\(509\) | 576.596 | 1.13280 | 0.566401 | − | 0.824130i | \(-0.308335\pi\) | ||||
0.566401 | + | 0.824130i | \(0.308335\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 486.106i | − | 0.951284i | ||||||
\(512\) | −307.697 | + | 409.226i | −0.600972 | + | 0.799270i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 786.755 | − | 81.2423i | 1.53065 | − | 0.158059i | ||||
\(515\) | 1.58791i | 0.00308331i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −320.637 | −0.620188 | ||||||||
\(518\) | 99.4253 | + | 962.840i | 0.191941 | + | 1.85876i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.71495 | − | 1.82243i | 0.0109903 | − | 0.00350467i | ||||
\(521\) | −278.971 | −0.535453 | −0.267727 | − | 0.963495i | \(-0.586272\pi\) | ||||
−0.267727 | + | 0.963495i | \(0.586272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 15.9961i | − | 0.0305854i | −0.999883 | − | 0.0152927i | \(-0.995132\pi\) | ||
0.999883 | − | 0.0152927i | \(-0.00486800\pi\) | |||||||
\(524\) | −154.692 | − | 741.037i | −0.295214 | − | 1.41419i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.6256 | − | 209.423i | −0.0411133 | − | 0.398143i | ||||
\(527\) | − | 964.821i | − | 1.83078i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 488.297 | 0.923056 | ||||||||
\(530\) | −7.72153 | + | 0.797344i | −0.0145689 | + | 0.00150442i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 163.290 | − | 34.0870i | 0.306937 | − | 0.0640734i | ||||
\(533\) | −454.379 | −0.852493 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.9888i | 0.0242781i | ||||||||
\(536\) | 148.389 | + | 465.334i | 0.276845 | + | 0.868160i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −54.0020 | + | 5.57638i | −0.100375 | + | 0.0103650i | ||||
\(539\) | − | 324.562i | − | 0.602155i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 973.220 | 1.79893 | 0.899464 | − | 0.436995i | \(-0.143957\pi\) | ||||
0.899464 | + | 0.436995i | \(0.143957\pi\) | |||||||
\(542\) | −46.9995 | − | 455.146i | −0.0867149 | − | 0.839752i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −465.149 | + | 262.934i | −0.855054 | + | 0.483334i | ||||
\(545\) | 2.03741 | 0.00373837 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 266.112i | − | 0.486494i | −0.969964 | − | 0.243247i | \(-0.921787\pi\) | ||
0.969964 | − | 0.243247i | \(-0.0782126\pi\) | |||||||
\(548\) | 929.018 | − | 193.933i | 1.69529 | − | 0.353893i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 39.1772 | + | 379.394i | 0.0712312 | + | 0.689807i | ||||
\(551\) | 85.2991i | 0.154808i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −100.061 | −0.180941 | ||||||||
\(554\) | 6.29323 | − | 0.649855i | 0.0113596 | − | 0.00117302i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −154.527 | − | 740.247i | −0.277927 | − | 1.33138i | ||||
\(557\) | 470.329 | 0.844398 | 0.422199 | − | 0.906503i | \(-0.361258\pi\) | ||||
0.422199 | + | 0.906503i | \(0.361258\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 103.639i | 0.185402i | ||||||||
\(560\) | 5.85759 | + | 13.4187i | 0.0104600 | + | 0.0239620i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −454.916 | + | 46.9757i | −0.809459 | + | 0.0835867i | ||||
\(563\) | 146.073i | 0.259455i | 0.991550 | + | 0.129728i | \(0.0414103\pi\) | ||||
−0.991550 | + | 0.129728i | \(0.958590\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.47477 | −0.00791995 | ||||||||
\(566\) | −17.8301 | − | 172.668i | −0.0315020 | − | 0.305067i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 327.285 | + | 1026.33i | 0.576206 | + | 1.80693i | ||||
\(569\) | −485.326 | −0.852945 | −0.426472 | − | 0.904501i | \(-0.640244\pi\) | ||||
−0.426472 | + | 0.904501i | \(0.640244\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 162.231i | − | 0.284118i | −0.989858 | − | 0.142059i | \(-0.954628\pi\) | ||
0.989858 | − | 0.142059i | \(-0.0453722\pi\) | |||||||
\(572\) | 48.8970 | + | 234.236i | 0.0854842 | + | 0.409503i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −113.920 | − | 1103.21i | −0.198467 | − | 1.92197i | ||||
\(575\) | 159.439i | 0.277286i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 126.190 | 0.218700 | 0.109350 | − | 0.994003i | \(-0.465123\pi\) | ||||
0.109350 | + | 0.994003i | \(0.465123\pi\) | |||||||
\(578\) | 20.2790 | − | 2.09406i | 0.0350848 | − | 0.00362295i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.32900 | + | 1.52994i | −0.0126362 | + | 0.00263782i | ||||
\(581\) | −769.176 | −1.32388 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 309.656i | − | 0.531143i | ||||||
\(584\) | −387.262 | + | 123.493i | −0.663121 | + | 0.211461i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 842.682 | − | 87.0174i | 1.43802 | − | 0.148494i | ||||
\(587\) | 358.563i | 0.610839i | 0.952218 | + | 0.305420i | \(0.0987967\pi\) | ||||
−0.952218 | + | 0.305420i | \(0.901203\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 251.867 | 0.427619 | ||||||||
\(590\) | −1.75778 | − | 17.0224i | −0.00297928 | − | 0.0288516i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 741.800 | − | 323.814i | 1.25304 | − | 0.546982i | ||||
\(593\) | 684.571 | 1.15442 | 0.577210 | − | 0.816596i | \(-0.304141\pi\) | ||||
0.577210 | + | 0.816596i | \(0.304141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.2798i | 0.0256803i | ||||||||
\(596\) | 336.617 | − | 70.2690i | 0.564793 | − | 0.117901i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.2744 | + | 99.4979i | 0.0171813 | + | 0.166384i | ||||
\(599\) | 126.965i | 0.211961i | 0.994368 | + | 0.105981i | \(0.0337981\pi\) | ||||
−0.994368 | + | 0.105981i | \(0.966202\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −613.265 | −1.02041 | −0.510204 | − | 0.860054i | \(-0.670430\pi\) | ||||
−0.510204 | + | 0.860054i | \(0.670430\pi\) | |||||||
\(602\) | −251.632 | + | 25.9841i | −0.417993 | + | 0.0431630i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −57.0974 | − | 273.519i | −0.0945320 | − | 0.452846i | ||||
\(605\) | −6.00363 | −0.00992336 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 177.313i | 0.292114i | 0.989276 | + | 0.146057i | \(0.0466583\pi\) | ||||
−0.989276 | + | 0.146057i | \(0.953342\pi\) | |||||||
\(608\) | −68.6391 | − | 121.428i | −0.112893 | − | 0.199717i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.76542 | − | 0.595351i | 0.00945150 | − | 0.000975986i | ||||
\(611\) | 329.385i | 0.539092i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −529.686 | −0.864087 | −0.432044 | − | 0.901853i | \(-0.642207\pi\) | ||||
−0.432044 | + | 0.901853i | \(0.642207\pi\) | |||||||
\(614\) | 26.7830 | + | 259.368i | 0.0436205 | + | 0.422423i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −556.454 | + | 177.446i | −0.903334 | + | 0.288062i | ||||
\(617\) | 1003.40 | 1.62625 | 0.813125 | − | 0.582090i | \(-0.197765\pi\) | ||||
0.813125 | + | 0.582090i | \(0.197765\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 563.776i | − | 0.910784i | −0.890291 | − | 0.455392i | \(-0.849499\pi\) | ||
0.890291 | − | 0.455392i | \(-0.150501\pi\) | |||||||
\(620\) | 4.51753 | + | 21.6407i | 0.00728633 | + | 0.0349044i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −73.0298 | − | 707.225i | −0.117411 | − | 1.13702i | ||||
\(623\) | 707.095i | 1.13498i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 624.314 | 0.998902 | ||||||||
\(626\) | −378.376 | + | 39.0720i | −0.604434 | + | 0.0624154i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 258.853 | − | 54.0358i | 0.412186 | − | 0.0860442i | ||||
\(629\) | 844.681 | 1.34289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1937i | 0.0494354i | 0.999694 | + | 0.0247177i | \(0.00786868\pi\) | ||||
−0.999694 | + | 0.0247177i | \(0.992131\pi\) | |||||||
\(632\) | 25.4199 | + | 79.7144i | 0.0402214 | + | 0.126130i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −534.855 | + | 55.2304i | −0.843620 | + | 0.0871143i | ||||
\(635\) | − | 7.74959i | − | 0.0122041i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −333.417 | −0.523417 | ||||||||
\(638\) | −30.6775 | − | 297.083i | −0.0480838 | − | 0.465647i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.20209 | − | 8.07549i | 0.0143783 | − | 0.0126180i | ||||
\(641\) | 122.049 | 0.190403 | 0.0952017 | − | 0.995458i | \(-0.469650\pi\) | ||||
0.0952017 | + | 0.995458i | \(0.469650\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 167.907i | 0.261130i | 0.991440 | + | 0.130565i | \(0.0416792\pi\) | ||||
−0.991440 | + | 0.130565i | \(0.958321\pi\) | |||||||
\(644\) | −239.000 | + | 49.8915i | −0.371118 | + | 0.0774713i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.9519 | − | 144.796i | −0.0231454 | − | 0.224142i | ||||
\(647\) | 185.483i | 0.286682i | 0.989673 | + | 0.143341i | \(0.0457846\pi\) | ||||
−0.989673 | + | 0.143341i | \(0.954215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 682.650 | 1.05185 | ||||||||
\(650\) | 389.745 | − | 40.2461i | 0.599608 | − | 0.0619170i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 171.272 | + | 820.462i | 0.262687 | + | 1.25838i | ||||
\(653\) | −759.904 | −1.16371 | −0.581856 | − | 0.813292i | \(-0.697673\pi\) | ||||
−0.581856 | + | 0.813292i | \(0.697673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1018i | 0.0276363i | ||||||||
\(656\) | −849.945 | + | 371.021i | −1.29565 | + | 0.565582i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −799.732 | + | 82.5823i | −1.21540 | + | 0.125505i | ||||
\(659\) | 443.323i | 0.672721i | 0.941733 | + | 0.336360i | \(0.109196\pi\) | ||||
−0.941733 | + | 0.336360i | \(0.890804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −826.457 | −1.25031 | −0.625157 | − | 0.780499i | \(-0.714965\pi\) | ||||
−0.625157 | + | 0.780499i | \(0.714965\pi\) | |||||||
\(662\) | 76.4457 | + | 740.305i | 0.115477 | + | 1.11829i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 195.406 | + | 612.773i | 0.294286 | + | 0.922851i | ||||
\(665\) | −3.98880 | −0.00599819 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 124.848i | − | 0.187179i | ||||||
\(668\) | −77.3962 | − | 370.758i | −0.115863 | − | 0.555028i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.19964 | − | 11.6174i | −0.00179051 | − | 0.0173394i | ||||
\(671\) | 231.210i | 0.344576i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −853.769 | −1.26860 | −0.634301 | − | 0.773086i | \(-0.718712\pi\) | ||||
−0.634301 | + | 0.773086i | \(0.718712\pi\) | |||||||
\(674\) | −1173.51 | + | 121.180i | −1.74111 | + | 0.179792i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −421.109 | + | 87.9069i | −0.622942 | + | 0.130040i | ||||
\(677\) | 1219.09 | 1.80072 | 0.900360 | − | 0.435146i | \(-0.143303\pi\) | ||||
0.900360 | + | 0.435146i | \(0.143303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 968.699i | 1.42665i | ||||||||
\(680\) | 12.1728 | − | 3.88176i | 0.0179012 | − | 0.00570847i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −877.212 | + | 90.5831i | −1.28624 | + | 0.132820i | ||||
\(683\) | − | 218.976i | − | 0.320610i | −0.987068 | − | 0.160305i | \(-0.948752\pi\) | ||
0.987068 | − | 0.160305i | \(-0.0512477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.6937 | −0.0331295 | ||||||||
\(686\) | 12.7126 | + | 123.110i | 0.0185315 | + | 0.179460i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 84.6264 | + | 193.864i | 0.123004 | + | 0.281779i | ||||
\(689\) | −318.105 | −0.461690 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 211.157i | − | 0.305582i | −0.988259 | − | 0.152791i | \(-0.951174\pi\) | ||
0.988259 | − | 0.152791i | \(-0.0488261\pi\) | |||||||
\(692\) | −419.415 | + | 87.5532i | −0.606091 | + | 0.126522i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 101.951 | + | 987.301i | 0.146904 | + | 1.42262i | ||||
\(695\) | 18.0825i | 0.0260180i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −967.825 | −1.38856 | ||||||||
\(698\) | −962.730 | + | 99.4139i | −1.37927 | + | 0.142427i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 195.431 | + | 936.192i | 0.279187 | + | 1.33742i | ||||
\(701\) | 119.133 | 0.169947 | 0.0849737 | − | 0.996383i | \(-0.472919\pi\) | ||||
0.0849737 | + | 0.996383i | \(0.472919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 220.505i | 0.313663i | ||||||||
\(704\) | 282.729 | + | 398.227i | 0.401604 | + | 0.565663i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −57.7989 | + | 5.96845i | −0.0818681 | + | 0.00845390i | ||||
\(707\) | − | 700.614i | − | 0.990968i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 678.269 | 0.956656 | 0.478328 | − | 0.878181i | \(-0.341243\pi\) | ||||
0.478328 | + | 0.878181i | \(0.341243\pi\) | |||||||
\(710\) | −2.64592 | − | 25.6233i | −0.00372665 | − | 0.0360891i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 563.316 | − | 179.634i | 0.791174 | − | 0.252296i | ||||
\(713\) | −368.646 | −0.517035 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.72183i | − | 0.00800256i | ||||||
\(716\) | 165.590 | + | 793.243i | 0.231271 | + | 1.10788i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 68.2331 | + | 660.773i | 0.0950322 | + | 0.920297i | ||||
\(719\) | − | 553.637i | − | 0.770010i | −0.922914 | − | 0.385005i | \(-0.874200\pi\) | ||
0.922914 | − | 0.385005i | \(-0.125800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −158.830 | −0.220291 | ||||||||
\(722\) | 37.7990 | − | 3.90322i | 0.0523532 | − | 0.00540612i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 740.574 | − | 154.596i | 1.02289 | − | 0.213530i | ||||
\(725\) | −489.045 | −0.674545 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 179.368i | 0.246724i | 0.992362 | + | 0.123362i | \(0.0393676\pi\) | ||||
−0.992362 | + | 0.123362i | \(0.960632\pi\) | |||||||
\(728\) | 182.288 | + | 571.636i | 0.250395 | + | 0.785214i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.66832 | − | 0.998375i | 0.0132443 | − | 0.00136764i | ||||
\(731\) | 220.751i | 0.301986i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −681.854 | −0.930224 | −0.465112 | − | 0.885252i | \(-0.653986\pi\) | ||||
−0.465112 | + | 0.885252i | \(0.653986\pi\) | |||||||
\(734\) | −51.5543 | − | 499.255i | −0.0702375 | − | 0.680184i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 100.464 | + | 177.728i | 0.136499 | + | 0.241478i | ||||
\(737\) | 465.894 | 0.632149 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 900.871i | 1.21904i | 0.792770 | + | 0.609520i | \(0.208638\pi\) | ||||
−0.792770 | + | 0.609520i | \(0.791362\pi\) | |||||||
\(740\) | −18.9460 | + | 3.95500i | −0.0256027 | + | 0.00534460i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −79.7540 | − | 772.343i | −0.107485 | − | 1.04089i | ||||
\(743\) | − | 832.140i | − | 1.11997i | −0.828502 | − | 0.559987i | \(-0.810806\pi\) | ||
0.828502 | − | 0.559987i | \(-0.189194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.22275 | −0.0110372 | ||||||||
\(746\) | 897.903 | − | 92.7197i | 1.20362 | − | 0.124289i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 104.150 | + | 498.921i | 0.139238 | + | 0.667007i | ||||
\(749\) | −1299.20 | −1.73457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 947.298i | 1.26138i | 0.776034 | + | 0.630691i | \(0.217228\pi\) | ||||
−0.776034 | + | 0.630691i | \(0.782772\pi\) | |||||||
\(752\) | 268.959 | + | 616.137i | 0.357658 | + | 0.819331i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −305.188 | + | 31.5145i | −0.404759 | + | 0.0417964i | ||||
\(755\) | 6.68142i | 0.00884957i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 494.147 | 0.652770 | 0.326385 | − | 0.945237i | \(-0.394169\pi\) | ||||
0.326385 | + | 0.945237i | \(0.394169\pi\) | |||||||
\(758\) | −50.2378 | − | 486.506i | −0.0662768 | − | 0.641828i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.01334 | + | 3.17773i | 0.00133334 | + | 0.00418122i | ||||
\(761\) | −768.733 | −1.01016 | −0.505081 | − | 0.863072i | \(-0.668537\pi\) | ||||
−0.505081 | + | 0.863072i | \(0.668537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 203.791i | 0.267092i | ||||||||
\(764\) | −193.195 | − | 925.483i | −0.252874 | − | 1.21137i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.3189 | − | 351.715i | −0.0474137 | − | 0.459157i | ||||
\(767\) | − | 701.275i | − | 0.914309i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 412.161 | 0.535970 | 0.267985 | − | 0.963423i | \(-0.413642\pi\) | ||||
0.267985 | + | 0.963423i | \(0.413642\pi\) | |||||||
\(770\) | 13.8923 | − | 1.43456i | 0.0180420 | − | 0.00186306i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −28.8440 | + | 6.02122i | −0.0373627 | + | 0.00779951i | ||||
\(773\) | 267.935 | 0.346617 | 0.173309 | − | 0.984868i | \(-0.444554\pi\) | ||||
0.173309 | + | 0.984868i | \(0.444554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1444.03i | 1.86326i | ||||||||
\(776\) | 771.726 | − | 246.094i | 0.994492 | − | 0.317131i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 417.760 | − | 43.1390i | 0.536967 | − | 0.0554485i | ||||
\(779\) | − | 252.652i | − | 0.324328i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1027.57 | 1.31571 | ||||||||
\(782\) | 21.8844 | + | 211.930i | 0.0279852 | + | 0.271010i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −623.677 | + | 272.250i | −0.795507 | + | 0.347258i | ||||
\(785\) | −6.32316 | −0.00805498 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 110.453i | 0.140346i | 0.997535 | + | 0.0701731i | \(0.0223552\pi\) | ||||
−0.997535 | + | 0.0701731i | \(0.977645\pi\) | |||||||
\(788\) | −967.904 | + | 202.051i | −1.22830 | + | 0.256410i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.205506 | − | 1.99014i | −0.000260135 | − | 0.00251916i | ||||
\(791\) | − | 447.588i | − | 0.565850i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 237.519 | 0.299519 | ||||||||
\(794\) | 866.141 | − | 89.4399i | 1.09086 | − | 0.112645i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 142.706 | + | 683.618i | 0.179279 | + | 0.858817i | ||||
\(797\) | 1548.70 | 1.94317 | 0.971583 | − | 0.236701i | \(-0.0760660\pi\) | ||||
0.971583 | + | 0.236701i | \(0.0760660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 701.589i | 0.878084i | ||||||||
\(800\) | 696.181 | − | 393.528i | 0.870226 | − | 0.491910i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1381.44 | + | 142.651i | −1.72250 | + | 0.177870i | ||||
\(803\) | 387.728i | 0.482850i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.83821 | 0.00725243 | ||||||||
\(806\) | 93.0546 | + | 901.146i | 0.115452 | + | 1.11805i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −558.153 | + | 177.988i | −0.690784 | + | 0.220282i | ||||
\(809\) | 728.020 | 0.899901 | 0.449950 | − | 0.893054i | \(-0.351442\pi\) | ||||
0.449950 | + | 0.893054i | \(0.351442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 954.297i | − | 1.17669i | −0.808609 | − | 0.588346i | \(-0.799779\pi\) | ||
0.808609 | − | 0.588346i | \(-0.200221\pi\) | |||||||
\(812\) | −153.031 | − | 733.080i | −0.188462 | − | 0.902808i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −79.3037 | − | 767.981i | −0.0974247 | − | 0.943466i | ||||
\(815\) | − | 20.0420i | − | 0.0245914i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −57.6274 | −0.0705354 | ||||||||
\(818\) | 1168.71 | − | 120.683i | 1.42874 | − | 0.147535i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.7081 | − | 4.53159i | 0.0264733 | − | 0.00552633i | ||||
\(821\) | 721.057 | 0.878267 | 0.439133 | − | 0.898422i | \(-0.355286\pi\) | ||||
0.439133 | + | 0.898422i | \(0.355286\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1434.21i | 1.74266i | 0.490699 | + | 0.871329i | \(0.336741\pi\) | ||||
−0.490699 | + | 0.871329i | \(0.663259\pi\) | |||||||
\(824\) | 40.3500 | + | 126.534i | 0.0489684 | + | 0.153560i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1702.66 | − | 175.821i | 2.06133 | − | 0.212858i | ||||
\(827\) | − | 1384.86i | − | 1.67456i | −0.546774 | − | 0.837280i | \(-0.684144\pi\) | ||
0.546774 | − | 0.837280i | \(-0.315856\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −671.349 | −0.809829 | −0.404915 | − | 0.914354i | \(-0.632699\pi\) | ||||
−0.404915 | + | 0.914354i | \(0.632699\pi\) | |||||||
\(830\) | −1.57975 | − | 15.2984i | −0.00190331 | − | 0.0184318i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 409.092 | − | 290.443i | 0.491697 | − | 0.349090i | ||||
\(833\) | −710.176 | −0.852552 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.05675i | 0.0108464i | ||||||||
\(836\) | −130.244 | + | 27.1885i | −0.155794 | + | 0.0325222i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 99.7461 | + | 965.947i | 0.119029 | + | 1.15268i | ||||
\(839\) | − | 1429.20i | − | 1.70346i | −0.523983 | − | 0.851729i | \(-0.675554\pi\) | ||
0.523983 | − | 0.851729i | \(-0.324446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −458.056 | −0.544656 | ||||||||
\(842\) | 896.006 | − | 92.5239i | 1.06414 | − | 0.109886i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 191.330 | + | 916.549i | 0.226695 | + | 1.08596i | ||||
\(845\) | 10.2867 | 0.0121736 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 600.511i | − | 0.708986i | ||||||
\(848\) | −595.035 | + | 259.747i | −0.701693 | + | 0.306306i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 830.155 | − | 85.7239i | 0.976653 | − | 0.100852i | ||||
\(851\) | − | 322.742i | − | 0.379250i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −399.859 | −0.468768 | −0.234384 | − | 0.972144i | \(-0.575307\pi\) | ||||
−0.234384 | + | 0.972144i | \(0.575307\pi\) | |||||||
\(854\) | 59.5498 | + | 576.684i | 0.0697304 | + | 0.675274i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 330.055 | + | 1035.02i | 0.385578 | + | 1.20914i | ||||
\(857\) | 86.5773 | 0.101024 | 0.0505118 | − | 0.998723i | \(-0.483915\pi\) | ||||
0.0505118 | + | 0.998723i | \(0.483915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1144.17i | − | 1.33198i | −0.745960 | − | 0.665991i | \(-0.768009\pi\) | ||
0.745960 | − | 0.665991i | \(-0.231991\pi\) | |||||||
\(860\) | −1.03361 | − | 4.95141i | −0.00120187 | − | 0.00575746i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −49.6048 | − | 480.376i | −0.0575462 | − | 0.557281i | ||||
\(863\) | − | 1121.50i | − | 1.29954i | −0.760130 | − | 0.649771i | \(-0.774865\pi\) | ||
0.760130 | − | 0.649771i | \(-0.225135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.2453 | 0.0118443 | ||||||||
\(866\) | −1294.29 | + | 133.652i | −1.49456 | + | 0.154332i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2164.61 | + | 451.864i | −2.49379 | + | 0.520580i | ||||
\(869\) | 79.8104 | 0.0918416 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 478.605i | − | 0.549489i | ||||||
\(872\) | 162.353 | − | 51.7723i | 0.186185 | − | 0.0593719i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −55.3245 | + | 5.71295i | −0.0633004 | + | 0.00653656i | ||||
\(875\) | − | 45.7463i | − | 0.0522815i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1460.55 | 1.66540 | 0.832698 | − | 0.553727i | \(-0.186795\pi\) | ||||
0.832698 | + | 0.553727i | \(0.186795\pi\) | |||||||
\(878\) | 128.267 | + | 1242.15i | 0.146090 | + | 1.41474i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.67214 | − | 10.7030i | −0.00530925 | − | 0.0121626i | ||||
\(881\) | −1514.46 | −1.71902 | −0.859512 | − | 0.511116i | \(-0.829232\pi\) | ||||
−0.859512 | + | 0.511116i | \(0.829232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 715.217i | 0.809986i | 0.914320 | + | 0.404993i | \(0.132726\pi\) | ||||
−0.914320 | + | 0.404993i | \(0.867274\pi\) | |||||||
\(884\) | 512.533 | − | 106.992i | 0.579789 | − | 0.121031i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −103.200 | − | 999.399i | −0.116479 | − | 1.12799i | ||||
\(887\) | − | 922.246i | − | 1.03974i | −0.854247 | − | 0.519868i | \(-0.825981\pi\) | ||
0.854247 | − | 0.519868i | \(-0.174019\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 775.150 | 0.871935 | ||||||||
\(890\) | −14.0636 | + | 1.45225i | −0.0158018 | + | 0.00163174i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 116.672 | + | 558.906i | 0.130798 | + | 0.626576i | ||||
\(893\) | −183.151 | −0.205096 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 19.3771i | − | 0.0216503i | ||||||
\(896\) | 807.748 | + | 920.435i | 0.901504 | + | 1.02727i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −267.204 | + | 27.5921i | −0.297554 | + | 0.0307262i | ||||
\(899\) | − | 1130.74i | − | 1.25778i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −677.561 | −0.752010 | ||||||||
\(902\) | 90.8651 | + | 879.943i | 0.100737 | + | 0.975547i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −356.576 | + | 113.708i | −0.394443 | + | 0.125783i | ||||
\(905\) | −18.0905 | −0.0199895 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 467.193i | − | 0.515098i | −0.966265 | − | 0.257549i | \(-0.917085\pi\) | ||
0.966265 | − | 0.257549i | \(-0.0829148\pi\) | |||||||
\(908\) | 276.680 | + | 1325.41i | 0.304713 | + | 1.45970i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.47370 | − | 14.2714i | −0.00161945 | − | 0.0156828i | ||||
\(911\) | 686.124i | 0.753155i | 0.926385 | + | 0.376577i | \(0.122899\pi\) | ||||
−0.926385 | + | 0.376577i | \(0.877101\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 613.511 | 0.671972 | ||||||||
\(914\) | −657.212 | + | 67.8653i | −0.719050 | + | 0.0742509i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −409.762 | + | 85.5382i | −0.447338 | + | 0.0933823i | ||||
\(917\) | −1810.62 | −1.97451 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 810.952i | 0.882429i | 0.897402 | + | 0.441215i | \(0.145452\pi\) | ||||
−0.897402 | + | 0.441215i | \(0.854548\pi\) | |||||||
\(920\) | −1.48317 | − | 4.65108i | −0.00161214 | − | 0.00505552i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −568.318 | + | 58.6859i | −0.616397 | + | 0.0636507i | ||||
\(923\) | − | 1055.61i | − | 1.14367i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1264.22 | −1.36672 | ||||||||
\(926\) | −93.5806 | − | 906.240i | −0.101059 | − | 0.978660i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −545.141 | + | 308.150i | −0.587436 | + | 0.332058i | ||||
\(929\) | 714.900 | 0.769538 | 0.384769 | − | 0.923013i | \(-0.374281\pi\) | ||||
0.384769 | + | 0.923013i | \(0.374281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 185.392i | − | 0.199132i | ||||||
\(932\) | −417.917 | + | 87.2406i | −0.448409 | + | 0.0936057i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −48.5015 | − | 469.691i | −0.0519288 | − | 0.502882i | ||||
\(935\) | − | 12.1875i | − | 0.0130347i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 295.227 | 0.315077 | 0.157539 | − | 0.987513i | \(-0.449644\pi\) | ||||
0.157539 | + | 0.987513i | \(0.449644\pi\) | |||||||
\(938\) | 1162.03 | − | 119.994i | 1.23884 | − | 0.127925i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.28501 | − | 15.7365i | −0.00349469 | − | 0.0167410i | ||||
\(941\) | 150.067 | 0.159476 | 0.0797382 | − | 0.996816i | \(-0.474592\pi\) | ||||
0.0797382 | + | 0.996816i | \(0.474592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 369.794i | 0.392146i | ||||||||
\(944\) | −572.624 | − | 1311.78i | −0.606593 | − | 1.38960i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 200.707 | − | 20.7255i | 0.212163 | − | 0.0219085i | ||||
\(947\) | − | 475.749i | − | 0.502374i | −0.967939 | − | 0.251187i | \(-0.919179\pi\) | ||
0.967939 | − | 0.251187i | \(-0.0808210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 398.307 | 0.419712 | ||||||||
\(950\) | 22.3783 | + | 216.713i | 0.0235561 | + | 0.228119i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 388.271 | + | 1217.58i | 0.407848 | + | 1.27897i | ||||
\(953\) | 150.444 | 0.157863 | 0.0789317 | − | 0.996880i | \(-0.474849\pi\) | ||||
0.0789317 | + | 0.996880i | \(0.474849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.6074i | 0.0236726i | ||||||||
\(956\) | −201.255 | − | 964.092i | −0.210518 | − | 1.00846i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −87.5548 | − | 847.886i | −0.0913933 | − | 0.885058i | ||||
\(959\) | − | 2269.93i | − | 2.36698i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2377.80 | −2.47430 | ||||||||
\(962\) | −788.935 | + | 81.4674i | −0.820098 | + | 0.0846854i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 372.931 | − | 77.8497i | 0.386858 | − | 0.0807570i | ||||
\(965\) | 0.704591 | 0.000730147 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1359.56i | − | 1.40595i | −0.711214 | − | 0.702976i | \(-0.751854\pi\) | ||
0.711214 | − | 0.702976i | \(-0.248146\pi\) | |||||||
\(968\) | −478.405 | + | 152.557i | −0.494220 | + | 0.157600i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.2668 | + | 1.98953i | −0.0198626 | + | 0.00205107i | ||||
\(971\) | 1070.02i | 1.10198i | 0.834513 | + | 0.550989i | \(0.185749\pi\) | ||||
−0.834513 | + | 0.550989i | \(0.814251\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1808.69 | −1.85888 | ||||||||
\(974\) | −190.994 | − | 1849.60i | −0.196092 | − | 1.89897i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 444.294 | − | 193.945i | 0.455219 | − | 0.198714i | ||||
\(977\) | −512.923 | −0.524998 | −0.262499 | − | 0.964932i | \(-0.584547\pi\) | ||||
−0.262499 | + | 0.964932i | \(0.584547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 563.994i | − | 0.576092i | ||||||
\(980\) | 15.9291 | − | 3.32521i | 0.0162542 | − | 0.00339308i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −158.292 | − | 1532.91i | −0.161193 | − | 1.56101i | ||||
\(983\) | 1799.31i | 1.83042i | 0.402974 | + | 0.915212i | \(0.367977\pi\) | ||||
−0.402974 | + | 0.915212i | \(0.632023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.6436 | 0.0240037 | ||||||||
\(986\) | −650.049 | + | 67.1257i | −0.659279 | + | 0.0680788i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 27.9303 | + | 133.797i | 0.0282696 | + | 0.135422i | ||||
\(989\) | 84.3464 | 0.0852845 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 921.947i | 0.930320i | 0.885227 | + | 0.465160i | \(0.154003\pi\) | ||||
−0.885227 | + | 0.465160i | \(0.845997\pi\) | |||||||
\(992\) | 909.892 | + | 1609.67i | 0.917230 | + | 1.62265i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2562.96 | − | 264.657i | 2.57843 | − | 0.266255i | ||||
\(995\) | − | 16.6992i | − | 0.0167831i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1642.31 | 1.64725 | 0.823625 | − | 0.567134i | \(-0.191948\pi\) | ||||
0.823625 | + | 0.567134i | \(0.191948\pi\) | |||||||
\(998\) | 144.210 | + | 1396.54i | 0.144499 | + | 1.39933i | ||||
\(999\) | 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 | 684.3.g.d.343.2 | yes | 36 | |
3.2 | odd | 2 | inner | 684.3.g.d.343.35 | yes | 36 | |
4.3 | odd | 2 | inner | 684.3.g.d.343.1 | ✓ | 36 | |
12.11 | even | 2 | inner | 684.3.g.d.343.36 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.g.d.343.1 | ✓ | 36 | 4.3 | odd | 2 | inner | |
684.3.g.d.343.2 | yes | 36 | 1.1 | even | 1 | trivial | |
684.3.g.d.343.35 | yes | 36 | 3.2 | odd | 2 | inner | |
684.3.g.d.343.36 | yes | 36 | 12.11 | even | 2 | inner |