Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,3,Mod(2161,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.2161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.d (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: | \(112.806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 1380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2161.4 | ||
Character | \(\chi\) | \(=\) | 4140.2161 |
Dual form | 4140.3.d.c.2161.29 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.23458i | − | 0.604940i | −0.953159 | − | 0.302470i | \(-0.902189\pi\) | ||
0.953159 | − | 0.302470i | \(-0.0978112\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.42048i | − | 0.310953i | −0.987840 | − | 0.155476i | \(-0.950309\pi\) | ||
0.987840 | − | 0.155476i | \(-0.0496913\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.7692 | −1.05917 | −0.529583 | − | 0.848258i | \(-0.677652\pi\) | ||||
−0.529583 | + | 0.848258i | \(0.677652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.48070i | 0.322394i | 0.986922 | + | 0.161197i | \(0.0515355\pi\) | ||||
−0.986922 | + | 0.161197i | \(0.948465\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.66120i | 0.245326i | 0.992448 | + | 0.122663i | \(0.0391435\pi\) | ||||
−0.992448 | + | 0.122663i | \(0.960857\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.0674 | − | 17.3774i | −0.655104 | − | 0.755539i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −51.3592 | −1.77101 | −0.885504 | − | 0.464633i | \(-0.846186\pi\) | ||||
−0.885504 | + | 0.464633i | \(0.846186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.0494 | 1.16288 | 0.581442 | − | 0.813588i | \(-0.302489\pi\) | ||||
0.581442 | + | 0.813588i | \(0.302489\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.46881 | −0.270537 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 70.1247i | 1.89526i | 0.319369 | + | 0.947631i | \(0.396529\pi\) | ||||
−0.319369 | + | 0.947631i | \(0.603471\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 29.1052 | 0.709883 | 0.354942 | − | 0.934888i | \(-0.384501\pi\) | ||||
0.354942 | + | 0.934888i | \(0.384501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.5556i | 0.571062i | 0.958370 | + | 0.285531i | \(0.0921699\pi\) | ||||
−0.958370 | + | 0.285531i | \(0.907830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −58.9027 | −1.25325 | −0.626624 | − | 0.779322i | \(-0.715564\pi\) | ||||
−0.626624 | + | 0.779322i | \(0.715564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 31.0683 | 0.634048 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26.4800i | 0.499622i | 0.968295 | + | 0.249811i | \(0.0803685\pi\) | ||||
−0.968295 | + | 0.249811i | \(0.919632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.64843 | −0.139062 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.79966 | 0.149147 | 0.0745734 | − | 0.997216i | \(-0.476241\pi\) | ||||
0.0745734 | + | 0.997216i | \(0.476241\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 30.1183i | − | 0.493743i | −0.969048 | − | 0.246872i | \(-0.920597\pi\) | ||
0.969048 | − | 0.246872i | \(-0.0794026\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 30.7888i | 0.473674i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.12183i | − | 0.0764452i | −0.999269 | − | 0.0382226i | \(-0.987830\pi\) | ||
0.999269 | − | 0.0382226i | \(-0.0121696\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45.7745 | 0.644711 | 0.322355 | − | 0.946619i | \(-0.395525\pi\) | ||||
0.322355 | + | 0.946619i | \(0.395525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 75.2188 | 1.03039 | 0.515197 | − | 0.857072i | \(-0.327719\pi\) | ||||
0.515197 | + | 0.857072i | \(0.327719\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.4843 | −0.188108 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 62.2814i | 0.788372i | 0.919031 | + | 0.394186i | \(0.128973\pi\) | ||||
−0.919031 | + | 0.394186i | \(0.871027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 137.687i | − | 1.65888i | −0.558596 | − | 0.829440i | \(-0.688660\pi\) | ||
0.558596 | − | 0.829440i | \(-0.311340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.2552 | 0.144179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 64.5505i | 0.725286i | 0.931928 | + | 0.362643i | \(0.118126\pi\) | ||||
−0.931928 | + | 0.362643i | \(0.881874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 58.3066i | 0.640732i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.4228 | 0.109713 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 171.496i | 1.76800i | 0.467486 | + | 0.884000i | \(0.345160\pi\) | ||||
−0.467486 | + | 0.884000i | \(0.654840\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −52.1005 | −0.515847 | −0.257923 | − | 0.966165i | \(-0.583038\pi\) | ||||
−0.257923 | + | 0.966165i | \(0.583038\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 32.9011i | − | 0.319429i | −0.987163 | − | 0.159714i | \(-0.948943\pi\) | ||
0.987163 | − | 0.159714i | \(-0.0510573\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 35.3025i | 0.329930i | 0.986299 | + | 0.164965i | \(0.0527511\pi\) | ||||
−0.986299 | + | 0.164965i | \(0.947249\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 56.0630i | − | 0.514339i | −0.966366 | − | 0.257170i | \(-0.917210\pi\) | ||
0.966366 | − | 0.257170i | \(-0.0827899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 79.6420i | 0.704796i | 0.935850 | + | 0.352398i | \(0.114634\pi\) | ||||
−0.935850 | + | 0.352398i | \(0.885366\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −38.8570 | + | 33.6917i | −0.337887 | + | 0.292971i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.2085 | 0.195029 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 109.300 | 0.903308 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −48.5699 | −0.382440 | −0.191220 | − | 0.981547i | \(-0.561244\pi\) | ||||
−0.191220 | + | 0.981547i | \(0.561244\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.25291 | −0.0248314 | −0.0124157 | − | 0.999923i | \(-0.503952\pi\) | ||||
−0.0124157 | + | 0.999923i | \(0.503952\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.7382 | 0.148408 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.210618i | 0.00153735i | 1.00000 | 0.000768677i | \(0.000244678\pi\) | |||||
−1.00000 | 0.000768677i | \(0.999755\pi\) | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 34.9353 | 0.251333 | 0.125666 | − | 0.992073i | \(-0.459893\pi\) | ||||
0.125666 | + | 0.992073i | \(0.459893\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 47.0972i | 0.329351i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 114.843i | 0.792018i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 294.015i | − | 1.97326i | −0.162983 | − | 0.986629i | \(-0.552111\pi\) | ||
0.162983 | − | 0.986629i | \(-0.447889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −76.5200 | −0.506755 | −0.253377 | − | 0.967368i | \(-0.581541\pi\) | ||||
−0.253377 | + | 0.967368i | \(0.581541\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 80.6090i | − | 0.520058i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 118.942i | 0.757592i | 0.925480 | + | 0.378796i | \(0.123662\pi\) | ||||
−0.925480 | + | 0.378796i | \(0.876338\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −73.5859 | + | 63.8041i | −0.457055 | + | 0.396299i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 285.654 | 1.75248 | 0.876240 | − | 0.481874i | \(-0.160044\pi\) | ||||
0.876240 | + | 0.481874i | \(0.160044\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 144.508 | 0.865316 | 0.432658 | − | 0.901558i | \(-0.357576\pi\) | ||||
0.432658 | + | 0.901558i | \(0.357576\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.5900 | 0.121834 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 118.670 | 0.685954 | 0.342977 | − | 0.939344i | \(-0.388565\pi\) | ||||
0.342977 | + | 0.939344i | \(0.388565\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.1729i | 0.120988i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2624 | 0.0685053 | 0.0342526 | − | 0.999413i | \(-0.489095\pi\) | ||||
0.0342526 | + | 0.999413i | \(0.489095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 228.077i | − | 1.26009i | −0.776557 | − | 0.630047i | \(-0.783035\pi\) | ||
0.776557 | − | 0.630047i | \(-0.216965\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 156.804 | 0.847587 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.7466 | 0.100249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 266.736i | 1.39652i | 0.715843 | + | 0.698261i | \(0.246042\pi\) | ||||
−0.715843 | + | 0.698261i | \(0.753958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 133.378 | 0.691077 | 0.345538 | − | 0.938405i | \(-0.387696\pi\) | ||||
0.345538 | + | 0.938405i | \(0.387696\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 119.937 | 0.608819 | 0.304409 | − | 0.952541i | \(-0.401541\pi\) | ||||
0.304409 | + | 0.952541i | \(0.401541\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 37.3932i | − | 0.187905i | −0.995577 | − | 0.0939526i | \(-0.970050\pi\) | ||
0.995577 | − | 0.0939526i | \(-0.0299502\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 217.485i | 1.07135i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 65.0812i | − | 0.317469i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.9435 | 0.0762849 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 145.771 | 0.690858 | 0.345429 | − | 0.938445i | \(-0.387733\pi\) | ||||
0.345429 | + | 0.938445i | \(0.387733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 54.9081 | 0.255387 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 152.654i | − | 0.703476i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 75.4647i | − | 0.341469i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 202.014 | 0.905894 | 0.452947 | − | 0.891538i | \(-0.350373\pi\) | ||||
0.452947 | + | 0.891538i | \(0.350373\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 222.735i | − | 0.981213i | −0.871381 | − | 0.490607i | \(-0.836775\pi\) | ||
0.871381 | − | 0.490607i | \(-0.163225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.7736i | − | 0.0470461i | −0.999723 | − | 0.0235231i | \(-0.992512\pi\) | ||
0.999723 | − | 0.0235231i | \(-0.00748832\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −306.711 | −1.31636 | −0.658179 | − | 0.752862i | \(-0.728673\pi\) | ||||
−0.658179 | + | 0.752862i | \(0.728673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 131.710i | 0.560470i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 133.517 | 0.558647 | 0.279323 | − | 0.960197i | \(-0.409890\pi\) | ||||
0.279323 | + | 0.960197i | \(0.409890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 164.609i | 0.683023i | 0.939878 | + | 0.341511i | \(0.110939\pi\) | ||||
−0.939878 | + | 0.341511i | \(0.889061\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 69.4709i | − | 0.283555i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 64.1808i | − | 0.259841i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 214.404i | − | 0.854200i | −0.904205 | − | 0.427100i | \(-0.859535\pi\) | ||
0.904205 | − | 0.427100i | \(-0.140465\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −59.4390 | + | 51.5378i | −0.234937 | + | 0.203707i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −155.697 | −0.605827 | −0.302913 | − | 0.953018i | \(-0.597959\pi\) | ||||
−0.302913 | + | 0.953018i | \(0.597959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 296.948 | 1.14652 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 508.041i | 1.93171i | 0.259077 | + | 0.965857i | \(0.416582\pi\) | ||||
−0.259077 | + | 0.965857i | \(0.583418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 59.2110 | 0.223438 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 137.722 | 0.511977 | 0.255988 | − | 0.966680i | \(-0.417599\pi\) | ||||
0.255988 | + | 0.966680i | \(0.417599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −449.193 | −1.65754 | −0.828769 | − | 0.559590i | \(-0.810958\pi\) | ||||
−0.828769 | + | 0.559590i | \(0.810958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.1024i | 0.0621906i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −265.137 | −0.957173 | −0.478586 | − | 0.878041i | \(-0.658851\pi\) | ||||
−0.478586 | + | 0.878041i | \(0.658851\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 81.2479i | 0.289138i | 0.989495 | + | 0.144569i | \(0.0461796\pi\) | ||||
−0.989495 | + | 0.144569i | \(0.953820\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 279.323i | 0.987009i | 0.869743 | + | 0.493504i | \(0.164284\pi\) | ||||
−0.869743 | + | 0.493504i | \(0.835716\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 123.248i | − | 0.429437i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 258.962 | 0.896062 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 144.258i | 0.492348i | 0.969226 | + | 0.246174i | \(0.0791734\pi\) | ||||
−0.969226 | + | 0.246174i | \(0.920827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 19.6766i | − | 0.0667005i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 207.466 | + | 239.272i | 0.693865 | + | 0.800241i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 103.983 | 0.345458 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −67.3466 | −0.220809 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −463.385 | −1.50940 | −0.754698 | − | 0.656072i | \(-0.772217\pi\) | ||||
−0.754698 | + | 0.656072i | \(0.772217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 365.413 | 1.17496 | 0.587480 | − | 0.809238i | \(-0.300120\pi\) | ||||
0.587480 | + | 0.809238i | \(0.300120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 224.561i | − | 0.717449i | −0.933444 | − | 0.358724i | \(-0.883212\pi\) | ||
0.933444 | − | 0.358724i | \(-0.116788\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −112.230 | −0.354037 | −0.177018 | − | 0.984208i | \(-0.556645\pi\) | ||||
−0.177018 | + | 0.984208i | \(0.556645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 175.673i | 0.550700i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.5466 | −0.0790918 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 68.8458 | 0.211833 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 249.428i | 0.758140i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 446.817 | 1.34990 | 0.674950 | − | 0.737863i | \(-0.264165\pi\) | ||||
0.674950 | + | 0.737863i | \(0.264165\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.4528 | −0.0341873 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 615.666i | 1.82690i | 0.406949 | + | 0.913451i | \(0.366593\pi\) | ||||
−0.406949 | + | 0.913451i | \(0.633407\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 123.306i | − | 0.361602i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 339.056i | − | 0.988501i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 499.046 | 1.43817 | 0.719087 | − | 0.694920i | \(-0.244560\pi\) | ||||
0.719087 | + | 0.694920i | \(0.244560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −380.579 | −1.09048 | −0.545242 | − | 0.838279i | \(-0.683562\pi\) | ||||
−0.545242 | + | 0.838279i | \(0.683562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 419.035 | 1.18707 | 0.593535 | − | 0.804809i | \(-0.297732\pi\) | ||||
0.593535 | + | 0.804809i | \(0.297732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 102.355i | − | 0.288323i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 319.353i | 0.889561i | 0.895640 | + | 0.444781i | \(0.146718\pi\) | ||||
−0.895640 | + | 0.444781i | \(0.853282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 339.273 | 0.939815 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 168.194i | − | 0.460807i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 109.262i | 0.297716i | 0.988859 | + | 0.148858i | \(0.0475597\pi\) | ||||
−0.988859 | + | 0.148858i | \(0.952440\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 112.131 | 0.302241 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 597.530i | 1.60196i | 0.598694 | + | 0.800978i | \(0.295687\pi\) | ||||
−0.598694 | + | 0.800978i | \(0.704313\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 707.174 | 1.87579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 518.720i | − | 1.36865i | −0.729175 | − | 0.684327i | \(-0.760096\pi\) | ||
0.729175 | − | 0.684327i | \(-0.239904\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 130.657i | 0.341142i | 0.985345 | + | 0.170571i | \(0.0545612\pi\) | ||||
−0.985345 | + | 0.170571i | \(0.945439\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.3879i | 0.0841244i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 641.056i | 1.64796i | 0.566619 | + | 0.823980i | \(0.308251\pi\) | ||||
−0.566619 | + | 0.823980i | \(0.691749\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 95.2403 | − | 82.5799i | 0.243581 | − | 0.211202i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 139.265 | 0.352571 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 66.6553 | 0.167897 | 0.0839487 | − | 0.996470i | \(-0.473247\pi\) | ||||
0.0839487 | + | 0.996470i | \(0.473247\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 121.218i | − | 0.302290i | −0.988512 | − | 0.151145i | \(-0.951704\pi\) | ||
0.988512 | − | 0.151145i | \(-0.0482960\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −496.371 | −1.23169 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 239.860 | 0.589337 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 534.724 | 1.30739 | 0.653697 | − | 0.756756i | \(-0.273217\pi\) | ||||
0.653697 | + | 0.756756i | \(0.273217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 37.2628i | − | 0.0902248i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −307.877 | −0.741873 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 431.194i | 1.02910i | 0.857460 | + | 0.514551i | \(0.172041\pi\) | ||||
−0.857460 | + | 0.514551i | \(0.827959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 111.757i | 0.265456i | 0.991153 | + | 0.132728i | \(0.0423737\pi\) | ||||
−0.991153 | + | 0.132728i | \(0.957626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 27.4035i | − | 0.0644788i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −127.538 | −0.298685 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 811.648i | 1.88317i | 0.336769 | + | 0.941587i | \(0.390666\pi\) | ||||
−0.336769 | + | 0.941587i | \(0.609334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 583.128i | − | 1.34672i | −0.739317 | − | 0.673358i | \(-0.764851\pi\) | ||
0.739317 | − | 0.673358i | \(-0.235149\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 80.9994 | − | 70.2321i | 0.185353 | − | 0.160714i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −107.124 | −0.244017 | −0.122009 | − | 0.992529i | \(-0.538934\pi\) | ||||
−0.122009 | + | 0.992529i | \(0.538934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 704.580 | 1.59047 | 0.795237 | − | 0.606298i | \(-0.207346\pi\) | ||||
0.795237 | + | 0.606298i | \(0.207346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 144.339 | 0.324358 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −744.078 | −1.65719 | −0.828595 | − | 0.559849i | \(-0.810859\pi\) | ||||
−0.828595 | + | 0.559849i | \(0.810859\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 99.5539i | − | 0.220740i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 130.378 | 0.286544 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 315.363i | 0.690073i | 0.938589 | + | 0.345037i | \(0.112133\pi\) | ||||
−0.938589 | + | 0.345037i | \(0.887867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 135.783 | 0.294541 | 0.147270 | − | 0.989096i | \(-0.452951\pi\) | ||||
0.147270 | + | 0.989096i | \(0.452951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 182.888 | 0.395006 | 0.197503 | − | 0.980302i | \(-0.436717\pi\) | ||||
0.197503 | + | 0.980302i | \(0.436717\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 590.693i | 1.26487i | 0.774614 | + | 0.632434i | \(0.217944\pi\) | ||||
−0.774614 | + | 0.632434i | \(0.782056\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.6888 | −0.0462447 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 83.9922 | 0.177573 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 23.3060i | − | 0.0490652i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 690.631i | 1.44182i | 0.693030 | + | 0.720909i | \(0.256275\pi\) | ||||
−0.693030 | + | 0.720909i | \(0.743725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 965.558i | − | 2.00740i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 383.477 | 0.790674 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 415.787 | 0.853772 | 0.426886 | − | 0.904305i | \(-0.359611\pi\) | ||||
0.426886 | + | 0.904305i | \(0.359611\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 395.472 | 0.805443 | 0.402721 | − | 0.915323i | \(-0.368064\pi\) | ||||
0.402721 | + | 0.915323i | \(0.368064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 281.485i | − | 0.570963i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 193.836i | − | 0.390011i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −901.606 | −1.80683 | −0.903413 | − | 0.428772i | \(-0.858946\pi\) | ||||
−0.903413 | + | 0.428772i | \(0.858946\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 76.8603i | − | 0.152804i | −0.997077 | − | 0.0764019i | \(-0.975657\pi\) | ||
0.997077 | − | 0.0764019i | \(-0.0243432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 116.500i | 0.230694i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −530.564 | −1.04237 | −0.521183 | − | 0.853445i | \(-0.674509\pi\) | ||||
−0.521183 | + | 0.853445i | \(0.674509\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 318.520i | − | 0.623327i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −73.5692 | −0.142853 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 201.475i | 0.389701i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 194.897i | − | 0.374083i | −0.982352 | − | 0.187042i | \(-0.940110\pi\) | ||
0.982352 | − | 0.187042i | \(-0.0598899\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 418.691i | 0.800557i | 0.916394 | + | 0.400279i | \(0.131087\pi\) | ||||
−0.916394 | + | 0.400279i | \(0.868913\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 197.576i | 0.374907i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −74.9472 | + | 523.664i | −0.141677 | + | 0.989913i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −400.755 | −0.751885 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 78.9387 | 0.147549 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 106.269i | − | 0.197159i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −221.165 | −0.408808 | −0.204404 | − | 0.978887i | \(-0.565526\pi\) | ||||
−0.204404 | + | 0.978887i | \(0.565526\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −125.361 | −0.230020 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −606.362 | −1.10852 | −0.554262 | − | 0.832342i | \(-0.686999\pi\) | ||||
−0.554262 | + | 0.832342i | \(0.686999\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 239.395i | − | 0.434474i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 263.736 | 0.476918 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 474.639i | 0.852135i | 0.904691 | + | 0.426068i | \(0.140101\pi\) | ||||
−0.904691 | + | 0.426068i | \(0.859899\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 338.111i | − | 0.604849i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 831.865i | 1.47756i | 0.673948 | + | 0.738779i | \(0.264597\pi\) | ||||
−0.673948 | + | 0.738779i | \(0.735403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 178.085 | 0.315194 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 58.3947i | 0.102627i | 0.998683 | + | 0.0513135i | \(0.0163408\pi\) | ||||
−0.998683 | + | 0.0513135i | \(0.983659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 423.510i | − | 0.741698i | −0.928693 | − | 0.370849i | \(-0.879067\pi\) | ||
0.928693 | − | 0.370849i | \(-0.120933\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 75.3370 | + | 86.8869i | 0.131021 | + | 0.151108i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −434.749 | −0.753465 | −0.376733 | − | 0.926322i | \(-0.622952\pi\) | ||||
−0.376733 | + | 0.926322i | \(0.622952\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −583.046 | −1.00352 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 90.5742 | 0.155359 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 196.392 | 0.334568 | 0.167284 | − | 0.985909i | \(-0.446500\pi\) | ||||
0.167284 | + | 0.985909i | \(0.446500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 168.034i | 0.285286i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 779.875 | 1.31514 | 0.657568 | − | 0.753395i | \(-0.271585\pi\) | ||||
0.657568 | + | 0.753395i | \(0.271585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 51.8957i | − | 0.0872197i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 729.208 | 1.21738 | 0.608688 | − | 0.793410i | \(-0.291696\pi\) | ||||
0.608688 | + | 0.793410i | \(0.291696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −98.3505 | −0.163645 | −0.0818224 | − | 0.996647i | \(-0.526074\pi\) | ||||
−0.0818224 | + | 0.996647i | \(0.526074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 244.403i | − | 0.403972i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −949.398 | −1.56408 | −0.782042 | − | 0.623226i | \(-0.785822\pi\) | ||||
−0.782042 | + | 0.623226i | \(0.785822\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 811.041 | 1.32740 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 354.757i | − | 0.578722i | −0.957220 | − | 0.289361i | \(-0.906557\pi\) | ||
0.957220 | − | 0.289361i | \(-0.0934428\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1080.07i | − | 1.75052i | −0.483654 | − | 0.875259i | \(-0.660691\pi\) | ||
0.483654 | − | 0.875259i | \(-0.339309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 207.082i | 0.334542i | 0.985911 | + | 0.167271i | \(0.0534955\pi\) | ||||
−0.985911 | + | 0.167271i | \(0.946504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 273.344 | 0.438755 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −384.332 | −0.611021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 899.817i | 1.42602i | 0.701155 | + | 0.713009i | \(0.252668\pi\) | ||||
−0.701155 | + | 0.713009i | \(0.747332\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 108.606i | 0.171032i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −427.785 | −0.671562 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 102.776i | 0.160337i | 0.996781 | + | 0.0801683i | \(0.0255458\pi\) | ||||
−0.996781 | + | 0.0801683i | \(0.974454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 120.818i | − | 0.187897i | −0.995577 | − | 0.0939484i | \(-0.970051\pi\) | ||
0.995577 | − | 0.0939484i | \(-0.0299489\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1042.16 | 1.61076 | 0.805379 | − | 0.592760i | \(-0.201962\pi\) | ||||
0.805379 | + | 0.592760i | \(0.201962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.0991i | − | 0.0463776i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −694.904 | −1.06417 | −0.532085 | − | 0.846691i | \(-0.678591\pi\) | ||||
−0.532085 | + | 0.846691i | \(0.678591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.27372i | 0.0111049i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 541.740i | 0.822063i | 0.911621 | + | 0.411032i | \(0.134831\pi\) | ||||
−0.911621 | + | 0.411032i | \(0.865169\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 243.406i | − | 0.368239i | −0.982904 | − | 0.184120i | \(-0.941057\pi\) | ||
0.982904 | − | 0.184120i | \(-0.0589434\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 44.1360i | − | 0.0663699i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 773.850 | + | 892.489i | 1.16019 | + | 1.33806i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −103.019 | −0.153531 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 335.090 | 0.497905 | 0.248952 | − | 0.968516i | \(-0.419914\pi\) | ||||
0.248952 | + | 0.968516i | \(0.419914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 639.438i | − | 0.944517i | −0.881460 | − | 0.472258i | \(-0.843439\pi\) | ||
0.881460 | − | 0.472258i | \(-0.156561\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 726.214 | 1.06953 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −366.380 | −0.536428 | −0.268214 | − | 0.963359i | \(-0.586433\pi\) | ||||
−0.268214 | + | 0.963359i | \(0.586433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.470955 | 0.000687526 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 364.607i | − | 0.529183i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 243.486 | 0.352367 | 0.176184 | − | 0.984357i | \(-0.443625\pi\) | ||||
0.176184 | + | 0.984357i | \(0.443625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 78.1176i | − | 0.112399i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 159.517i | 0.228862i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 213.429i | 0.304463i | 0.988345 | + | 0.152232i | \(0.0486460\pi\) | ||||
−0.988345 | + | 0.152232i | \(0.951354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −326.865 | −0.464957 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 220.624i | 0.312056i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 804.957i | − | 1.13534i | −0.823256 | − | 0.567671i | \(-0.807845\pi\) | ||
0.823256 | − | 0.567671i | \(-0.192155\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −543.171 | − | 626.445i | −0.761811 | − | 0.878604i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 105.313 | 0.147290 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −550.092 | −0.765079 | −0.382540 | − | 0.923939i | \(-0.624950\pi\) | ||||
−0.382540 | + | 0.923939i | \(0.624950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −139.323 | −0.193235 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 256.796 | 0.354201 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 719.138i | 0.989185i | 0.869125 | + | 0.494593i | \(0.164683\pi\) | ||||
−0.869125 | + | 0.494593i | \(0.835317\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −134.582 | −0.184107 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1139.86i | 1.55506i | 0.628844 | + | 0.777532i | \(0.283529\pi\) | ||||
−0.628844 | + | 0.777532i | \(0.716471\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.5191 | −0.0237708 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 805.483 | 1.08996 | 0.544982 | − | 0.838448i | \(-0.316537\pi\) | ||||
0.544982 | + | 0.838448i | \(0.316537\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 75.8211i | 0.102047i | 0.998697 | + | 0.0510236i | \(0.0162484\pi\) | ||||
−0.998697 | + | 0.0510236i | \(0.983752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −657.438 | −0.882468 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 149.491 | 0.199588 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 543.632i | − | 0.723878i | −0.932202 | − | 0.361939i | \(-0.882115\pi\) | ||
0.932202 | − | 0.361939i | \(-0.117885\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 171.104i | 0.226628i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 650.293i | 0.859039i | 0.903058 | + | 0.429520i | \(0.141317\pi\) | ||||
−0.903058 | + | 0.429520i | \(0.858683\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 59.2182 | 0.0778162 | 0.0389081 | − | 0.999243i | \(-0.487612\pi\) | ||||
0.0389081 | + | 0.999243i | \(0.487612\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −237.403 | −0.311144 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −121.164 | −0.157971 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 822.423i | − | 1.06947i | −0.845019 | − | 0.534736i | \(-0.820411\pi\) | ||
0.845019 | − | 0.534736i | \(-0.179589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 62.2749i | 0.0805626i | 0.999188 | + | 0.0402813i | \(0.0128254\pi\) | ||||
−0.999188 | + | 0.0402813i | \(0.987175\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −180.247 | −0.232577 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 135.665i | 0.174153i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 156.571i | − | 0.200475i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 265.962 | 0.338805 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 404.988i | 0.514597i | 0.966332 | + | 0.257299i | \(0.0828324\pi\) | ||||
−0.966332 | + | 0.257299i | \(0.917168\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 337.250 | 0.426359 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 414.704i | 0.522956i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 232.050i | − | 0.291154i | −0.989347 | − | 0.145577i | \(-0.953496\pi\) | ||
0.989347 | − | 0.145577i | \(-0.0465039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 322.828i | − | 0.404040i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 257.285i | − | 0.320404i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 142.670 | + | 164.543i | 0.177230 | + | 0.204401i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −276.617 | −0.341925 | −0.170962 | − | 0.985278i | \(-0.554688\pi\) | ||||
−0.170962 | + | 0.985278i | \(0.554688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.1869 | −0.0655819 | −0.0327909 | − | 0.999462i | \(-0.510440\pi\) | ||||
−0.0327909 | + | 0.999462i | \(0.510440\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 638.743i | − | 0.783733i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −114.459 | −0.140096 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −831.053 | −1.01224 | −0.506122 | − | 0.862462i | \(-0.668922\pi\) | ||||
−0.506122 | + | 0.862462i | \(0.668922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 225.779 | 0.274336 | 0.137168 | − | 0.990548i | \(-0.456200\pi\) | ||||
0.137168 | + | 0.990548i | \(0.456200\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 454.191i | − | 0.549203i | −0.961558 | − | 0.274602i | \(-0.911454\pi\) | ||
0.961558 | − | 0.274602i | \(-0.0885460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1391.70 | 1.67877 | 0.839386 | − | 0.543536i | \(-0.182915\pi\) | ||||
0.839386 | + | 0.543536i | \(0.182915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 170.276i | 0.204413i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 323.129i | − | 0.386981i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 132.957i | − | 0.158471i | −0.996856 | − | 0.0792355i | \(-0.974752\pi\) | ||
0.996856 | − | 0.0792355i | \(-0.0252479\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1796.77 | 2.13647 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 46.0406i | − | 0.0544860i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 462.841i | − | 0.546447i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1218.58 | − | 1056.60i | 1.43194 | − | 1.24159i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 104.622 | 0.122651 | 0.0613256 | − | 0.998118i | \(-0.480467\pi\) | ||||
0.0613256 | + | 0.998118i | \(0.480467\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.9854 | −0.0373226 | −0.0186613 | − | 0.999826i | \(-0.505940\pi\) | ||||
−0.0186613 | + | 0.999826i | \(0.505940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 984.302 | 1.14587 | 0.572935 | − | 0.819601i | \(-0.305805\pi\) | ||||
0.572935 | + | 0.819601i | \(0.305805\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −668.524 | −0.774651 | −0.387326 | − | 0.921943i | \(-0.626601\pi\) | ||||
−0.387326 | + | 0.921943i | \(0.626601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 265.354i | − | 0.306768i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 213.032 | 0.245147 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.5233i | 0.0809682i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 47.3440 | 0.0541075 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1103.98 | 1.25881 | 0.629405 | − | 0.777077i | \(-0.283299\pi\) | ||||
0.629405 | + | 0.777077i | \(0.283299\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 607.647i | 0.689724i | 0.938653 | + | 0.344862i | \(0.112074\pi\) | ||||
−0.938653 | + | 0.344862i | \(0.887926\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 85.7974 | 0.0971659 | 0.0485829 | − | 0.998819i | \(-0.484529\pi\) | ||||
0.0485829 | + | 0.998819i | \(0.484529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −689.893 | −0.777782 | −0.388891 | − | 0.921284i | \(-0.627142\pi\) | ||||
−0.388891 | + | 0.921284i | \(0.627142\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 205.673i | 0.231353i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 274.557i | − | 0.307455i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 27.4197i | − | 0.0306365i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1851.47 | −2.05948 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −145.129 | −0.161075 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −509.996 | −0.563531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1182.25i | 1.30348i | 0.758444 | + | 0.651738i | \(0.225960\pi\) | ||||
−0.758444 | + | 0.651738i | \(0.774040\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 611.652i | − | 0.671407i | −0.941968 | − | 0.335704i | \(-0.891026\pi\) | ||
0.941968 | − | 0.335704i | \(-0.108974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −470.956 | −0.515833 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.7747i | 0.0150215i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1037.12i | − | 1.12854i | −0.825592 | − | 0.564268i | \(-0.809159\pi\) | ||
0.825592 | − | 0.564268i | \(-0.190841\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −630.276 | −0.682856 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 350.623i | − | 0.379052i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −944.065 | −1.01622 | −0.508108 | − | 0.861293i | \(-0.669655\pi\) | ||||
−0.508108 | + | 0.861293i | \(0.669655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 144.816i | 0.155549i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 41.9188i | − | 0.0448329i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1307.12i | 1.39500i | 0.716583 | + | 0.697502i | \(0.245705\pi\) | ||||
−0.716583 | + | 0.697502i | \(0.754295\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 710.928i | − | 0.755502i | −0.925907 | − | 0.377751i | \(-0.876697\pi\) | ||
0.925907 | − | 0.377751i | \(-0.123303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −438.540 | − | 505.773i | −0.465048 | − | 0.536344i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −674.787 | −0.712552 | −0.356276 | − | 0.934381i | \(-0.615954\pi\) | ||||
−0.356276 | + | 0.934381i | \(0.615954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1035.70 | −1.09136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 671.206i | − | 0.704309i | −0.935942 | − | 0.352154i | \(-0.885449\pi\) | ||
0.935942 | − | 0.352154i | \(-0.114551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 596.439 | 0.624543 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.891877 | 0.000930007 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 338.562 | 0.352301 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 298.242i | − | 0.309059i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1886.45 | −1.95083 | −0.975413 | − | 0.220385i | \(-0.929269\pi\) | ||||
−0.975413 | + | 0.220385i | \(0.929269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1134.32i | − | 1.16819i | −0.811684 | − | 0.584096i | \(-0.801449\pi\) | ||
0.811684 | − | 0.584096i | \(-0.198551\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 147.936i | − | 0.152041i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 37.6770i | − | 0.0385640i | −0.999814 | − | 0.0192820i | \(-0.993862\pi\) | ||
0.999814 | − | 0.0192820i | \(-0.00613803\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 220.794 | 0.225530 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1653.42i | 1.68201i | 0.541027 | + | 0.841005i | \(0.318036\pi\) | ||||
−0.541027 | + | 0.841005i | \(0.681964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 268.188i | − | 0.272272i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 426.713 | − | 369.990i | 0.431459 | − | 0.374105i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1681.88 | 1.69715 | 0.848576 | − | 0.529073i | \(-0.177460\pi\) | ||||
0.848576 | + | 0.529073i | \(0.177460\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −83.6136 | −0.0840338 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1474.49 | −1.47893 | −0.739463 | − | 0.673198i | \(-0.764920\pi\) | ||||
−0.739463 | + | 0.673198i | \(0.764920\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4140.3.d.c.2161.4 | 32 | ||
3.2 | odd | 2 | 1380.3.d.a.781.26 | yes | 32 | ||
23.22 | odd | 2 | inner | 4140.3.d.c.2161.29 | 32 | ||
69.68 | even | 2 | 1380.3.d.a.781.23 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.3.d.a.781.23 | ✓ | 32 | 69.68 | even | 2 | ||
1380.3.d.a.781.26 | yes | 32 | 3.2 | odd | 2 | ||
4140.3.d.c.2161.4 | 32 | 1.1 | even | 1 | trivial | ||
4140.3.d.c.2161.29 | 32 | 23.22 | odd | 2 | inner |