Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(671,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.h (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.12 | ||
Character | \(\chi\) | \(=\) | 2240.671 |
Dual form | 2240.2.h.f.671.11 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.421861i | 0.243561i | 0.992557 | + | 0.121781i | \(0.0388604\pi\) | ||||
−0.992557 | + | 0.121781i | \(0.961140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.02538 | + | 2.43897i | −0.387558 | + | 0.921845i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82203 | 0.940678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.89956 | −0.572739 | −0.286370 | − | 0.958119i | \(-0.592449\pi\) | ||||
−0.286370 | + | 0.958119i | \(0.592449\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.65608 | 1.29137 | 0.645683 | − | 0.763606i | \(-0.276573\pi\) | ||||
0.645683 | + | 0.763606i | \(0.276573\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.421861i | 0.108924i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.19944i | 1.74612i | 0.487613 | + | 0.873060i | \(0.337868\pi\) | ||||
−0.487613 | + | 0.873060i | \(0.662132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.834050i | − | 0.191344i | −0.995413 | − | 0.0956721i | \(-0.969500\pi\) | ||
0.995413 | − | 0.0956721i | \(-0.0305000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.02891 | − | 0.432568i | −0.224526 | − | 0.0943941i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.76981i | − | 1.20309i | −0.798839 | − | 0.601544i | \(-0.794552\pi\) | ||
0.798839 | − | 0.601544i | \(-0.205448\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.45609i | 0.472674i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.84493i | 0.899681i | 0.893109 | + | 0.449841i | \(0.148519\pi\) | ||||
−0.893109 | + | 0.449841i | \(0.851481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.04358 | −0.726249 | −0.363124 | − | 0.931741i | \(-0.618290\pi\) | ||||
−0.363124 | + | 0.931741i | \(0.618290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.801350i | − | 0.139497i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.02538 | + | 2.43897i | −0.173321 | + | 0.412262i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.68101i | − | 0.769553i | −0.923010 | − | 0.384777i | \(-0.874278\pi\) | ||
0.923010 | − | 0.384777i | \(-0.125722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.96422i | 0.314527i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.81861i | 0.908714i | 0.890820 | + | 0.454357i | \(0.150131\pi\) | ||||
−0.890820 | + | 0.454357i | \(0.849869\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.6338 | 1.92663 | 0.963316 | − | 0.268371i | \(-0.0864854\pi\) | ||||
0.963316 | + | 0.268371i | \(0.0864854\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82203 | 0.420684 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.30483 | −0.919654 | −0.459827 | − | 0.888008i | \(-0.652089\pi\) | ||||
−0.459827 | + | 0.888008i | \(0.652089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89718 | − | 5.00176i | −0.699597 | − | 0.714537i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.03716 | −0.425287 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.637428i | − | 0.0875574i | −0.999041 | − | 0.0437787i | \(-0.986060\pi\) | ||
0.999041 | − | 0.0437787i | \(-0.0139397\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.89956 | −0.256137 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.351853 | 0.0466040 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.32592i | 0.693376i | 0.937981 | + | 0.346688i | \(0.112694\pi\) | ||||
−0.937981 | + | 0.346688i | \(0.887306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.80404 | −0.999204 | −0.499602 | − | 0.866255i | \(-0.666520\pi\) | ||||
−0.499602 | + | 0.866255i | \(0.666520\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.89366 | + | 6.88287i | −0.364567 | + | 0.867159i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.65608 | 0.577516 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.64973 | 0.568055 | 0.284027 | − | 0.958816i | \(-0.408329\pi\) | ||||
0.284027 | + | 0.958816i | \(0.408329\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.43406 | 0.293026 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.42998i | 0.763098i | 0.924349 | + | 0.381549i | \(0.124609\pi\) | ||||
−0.924349 | + | 0.381549i | \(0.875391\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.227709i | − | 0.0266513i | −0.999911 | − | 0.0133257i | \(-0.995758\pi\) | ||
0.999911 | − | 0.0133257i | \(-0.00424182\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.421861i | 0.0487123i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.94778 | − | 4.63298i | 0.221970 | − | 0.527977i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.17831i | 0.807623i | 0.914842 | + | 0.403811i | \(0.132315\pi\) | ||||
−0.914842 | + | 0.403811i | \(0.867685\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.42998 | 0.825553 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.76612i | − | 0.523150i | −0.965183 | − | 0.261575i | \(-0.915758\pi\) | ||
0.965183 | − | 0.261575i | \(-0.0842418\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.19944i | 0.780889i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.04389 | −0.219128 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9442i | 1.26609i | 0.774117 | + | 0.633043i | \(0.218194\pi\) | ||||
−0.774117 | + | 0.633043i | \(0.781806\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.77427 | + | 11.3561i | −0.500479 | + | 1.19044i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.70583i | − | 0.176886i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.834050i | − | 0.0855717i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3285i | 1.04870i | 0.851502 | + | 0.524351i | \(0.175692\pi\) | ||||
−0.851502 | + | 0.524351i | \(0.824308\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.36063 | −0.538763 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.0777 | 1.50029 | 0.750145 | − | 0.661273i | \(-0.229984\pi\) | ||||
0.750145 | + | 0.661273i | \(0.229984\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5333 | −1.43201 | −0.716006 | − | 0.698095i | \(-0.754032\pi\) | ||||
−0.716006 | + | 0.698095i | \(0.754032\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.02891 | − | 0.432568i | −0.100411 | − | 0.0422143i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.91022 | 0.958057 | 0.479029 | − | 0.877799i | \(-0.340989\pi\) | ||||
0.479029 | + | 0.877799i | \(0.340989\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.77892i | − | 0.745085i | −0.928015 | − | 0.372543i | \(-0.878486\pi\) | ||
0.928015 | − | 0.372543i | \(-0.121514\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.97473 | 0.187433 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.75220 | 0.447050 | 0.223525 | − | 0.974698i | \(-0.428244\pi\) | ||||
0.223525 | + | 0.974698i | \(0.428244\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.76981i | − | 0.538038i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.1396 | 1.21476 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.5592 | − | 7.38218i | −1.60965 | − | 0.676723i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.39167 | −0.671970 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.45464 | −0.221327 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.70233i | − | 0.506000i | −0.967466 | − | 0.253000i | \(-0.918583\pi\) | ||
0.967466 | − | 0.253000i | \(-0.0814172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.32969i | 0.469253i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9659i | 1.48232i | 0.671329 | + | 0.741159i | \(0.265724\pi\) | ||||
−0.671329 | + | 0.741159i | \(0.734276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.03423 | + | 0.855220i | 0.176390 | + | 0.0741570i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.45609i | 0.211386i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.75958 | −0.577510 | −0.288755 | − | 0.957403i | \(-0.593241\pi\) | ||||
−0.288755 | + | 0.957403i | \(0.593241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.36998i | 0.455476i | 0.973722 | + | 0.227738i | \(0.0731329\pi\) | ||||
−0.973722 | + | 0.227738i | \(0.926867\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 2.65976i | − | 0.223992i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.84452 | −0.739616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.84493i | 0.402350i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.11005 | − | 2.06593i | 0.174034 | − | 0.170395i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.6260i | − | 0.952436i | −0.879327 | − | 0.476218i | \(-0.842007\pi\) | ||
0.879327 | − | 0.476218i | \(-0.157993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.29014i | 0.430505i | 0.976558 | + | 0.215253i | \(0.0690575\pi\) | ||||
−0.976558 | + | 0.215253i | \(0.930943\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.3171i | 1.64254i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.04358 | −0.324788 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.9118 | −1.74875 | −0.874375 | − | 0.485250i | \(-0.838728\pi\) | ||||
−0.874375 | + | 0.485250i | \(0.838728\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.268906 | 0.0213256 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.0724 | + | 5.91626i | 1.10906 | + | 0.466267i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.817106 | −0.0640007 | −0.0320003 | − | 0.999488i | \(-0.510188\pi\) | ||||
−0.0320003 | + | 0.999488i | \(0.510188\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 0.801350i | − | 0.0623850i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.5609 | 1.04937 | 0.524686 | − | 0.851296i | \(-0.324183\pi\) | ||||
0.524686 | + | 0.851296i | \(0.324183\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.67912 | 0.667624 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 2.35372i | − | 0.179993i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.49980 | −0.418142 | −0.209071 | − | 0.977900i | \(-0.567044\pi\) | ||||
−0.209071 | + | 0.977900i | \(0.567044\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.02538 | + | 2.43897i | −0.0775116 | + | 0.184369i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.24679 | −0.168879 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.9886 | 1.79299 | 0.896496 | − | 0.443052i | \(-0.146104\pi\) | ||||
0.896496 | + | 0.443052i | \(0.146104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.9178 | 1.55481 | 0.777403 | − | 0.629003i | \(-0.216537\pi\) | ||||
0.777403 | + | 0.629003i | \(0.216537\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.29221i | − | 0.243368i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.68101i | − | 0.344155i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 13.6758i | − | 1.00007i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.99033 | − | 2.51843i | −0.435732 | − | 0.183189i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9342i | 1.22532i | 0.790348 | + | 0.612658i | \(0.209900\pi\) | ||||
−0.790348 | + | 0.612658i | \(0.790100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00369 | 0.360173 | 0.180087 | − | 0.983651i | \(-0.442362\pi\) | ||||
0.180087 | + | 0.983651i | \(0.442362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.96422i | 0.140661i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 27.1869i | − | 1.93699i | −0.249043 | − | 0.968493i | \(-0.580116\pi\) | ||
0.249043 | − | 0.968493i | \(-0.419884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.206346 | −0.0146275 | −0.00731373 | − | 0.999973i | \(-0.502328\pi\) | ||||
−0.00731373 | + | 0.999973i | \(0.502328\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.96154i | 0.138356i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.8167 | − | 4.96791i | −0.829367 | − | 0.348679i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.81861i | 0.406389i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 16.2826i | − | 1.13172i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.58433i | 0.109590i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.7712 | −1.56764 | −0.783818 | − | 0.620991i | \(-0.786730\pi\) | ||||
−0.783818 | + | 0.620991i | \(0.786730\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.71255 | −0.185861 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.6338 | 0.861616 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.14622 | − | 9.86219i | 0.281464 | − | 0.669489i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0960615 | 0.00649123 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.5212i | 2.25488i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9007 | 0.997828 | 0.498914 | − | 0.866652i | \(-0.333732\pi\) | ||||
0.498914 | + | 0.866652i | \(0.333732\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82203 | 0.188136 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.0299i | 1.06394i | 0.846762 | + | 0.531972i | \(0.178549\pi\) | ||||
−0.846762 | + | 0.531972i | \(0.821451\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7458 | 1.10660 | 0.553298 | − | 0.832983i | \(-0.313369\pi\) | ||||
0.553298 | + | 0.832983i | \(0.313369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.95447 | + | 0.821690i | 0.128595 | + | 0.0540632i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.11183 | −0.269375 | −0.134687 | − | 0.990888i | \(-0.543003\pi\) | ||||
−0.134687 | + | 0.990888i | \(0.543003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.30483 | −0.411282 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.02825 | −0.196706 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.53385i | 0.163901i | 0.996636 | + | 0.0819506i | \(0.0261150\pi\) | ||||
−0.996636 | + | 0.0819506i | \(0.973885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 25.9867i | − | 1.67395i | −0.547240 | − | 0.836976i | \(-0.684321\pi\) | ||
0.547240 | − | 0.836976i | \(-0.315679\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.5027i | 0.673747i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.89718 | − | 5.00176i | −0.312869 | − | 0.319551i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.88341i | − | 0.247095i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.01064 | 0.127419 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.9340i | − | 0.753269i | −0.926362 | − | 0.376634i | \(-0.877081\pi\) | ||
0.926362 | − | 0.376634i | \(-0.122919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.9601i | 0.689056i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.03716 | −0.190194 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.44000i | 0.0898250i | 0.998991 | + | 0.0449125i | \(0.0143009\pi\) | ||||
−0.998991 | + | 0.0449125i | \(0.985699\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4169 | + | 4.79982i | 0.709409 | + | 0.298247i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.6726i | 0.846310i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9905i | 0.801026i | 0.916291 | + | 0.400513i | \(0.131168\pi\) | ||||
−0.916291 | + | 0.400513i | \(0.868832\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.637428i | − | 0.0391569i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.03880 | −0.308370 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.3509 | −0.935958 | −0.467979 | − | 0.883740i | \(-0.655018\pi\) | ||||
−0.467979 | + | 0.883740i | \(0.655018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.3155 | 0.869604 | 0.434802 | − | 0.900526i | \(-0.356818\pi\) | ||||
0.434802 | + | 0.900526i | \(0.356818\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.79068 | − | 2.01407i | −0.289945 | − | 0.121897i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.89956 | −0.114548 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.30303i | 0.198460i | 0.995065 | + | 0.0992298i | \(0.0316379\pi\) | ||||
−0.995065 | + | 0.0992298i | \(0.968362\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.4111 | −0.683166 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.82096 | 0.168284 | 0.0841421 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841421 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.2934i | 1.32520i | 0.748972 | + | 0.662602i | \(0.230548\pi\) | ||||
−0.748972 | + | 0.662602i | \(0.769452\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.351853 | 0.0208420 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.1914 | − | 5.96630i | −0.837693 | − | 0.352179i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −34.8319 | −2.04893 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.35719 | −0.255423 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.85574 | 0.575778 | 0.287889 | − | 0.957664i | \(-0.407047\pi\) | ||||
0.287889 | + | 0.957664i | \(0.407047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.32592i | 0.310087i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.66549i | − | 0.270719i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 26.8647i | − | 1.55363i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9544 | + | 30.8134i | −0.746681 | + | 1.77606i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.36070i | 0.365413i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.80404 | −0.446858 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 32.9065i | − | 1.87808i | −0.343814 | − | 0.939038i | \(-0.611719\pi\) | ||
0.343814 | − | 0.939038i | \(-0.388281\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.13104i | − | 0.348782i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.9734 | −1.52952 | −0.764759 | − | 0.644316i | \(-0.777142\pi\) | ||||
−0.764759 | + | 0.644316i | \(0.777142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.5471i | − | 1.16139i | −0.814121 | − | 0.580695i | \(-0.802781\pi\) | ||
0.814121 | − | 0.580695i | \(-0.197219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.89366 | + | 6.88287i | −0.163039 | + | 0.387806i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7.66436i | − | 0.430473i | −0.976562 | − | 0.215237i | \(-0.930948\pi\) | ||
0.976562 | − | 0.215237i | \(-0.0690523\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.20324i | − | 0.515283i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.18073i | 0.233346i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00469 | 0.334110 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.65608 | 0.258273 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.28162 | 0.181474 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.46486 | − | 15.3773i | 0.356419 | − | 0.847779i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0404 | −1.15649 | −0.578243 | − | 0.815864i | \(-0.696262\pi\) | ||||
−0.578243 | + | 0.815864i | \(0.696262\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 13.2100i | − | 0.723902i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.64973 | 0.254042 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.8596 | −1.40866 | −0.704330 | − | 0.709873i | \(-0.748752\pi\) | ||||
−0.704330 | + | 0.709873i | \(0.748752\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.00477i | 0.108884i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.68103 | 0.415951 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2206 | − | 6.81538i | 0.929827 | − | 0.367996i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.43406 | 0.131045 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.3946 | 1.25589 | 0.627944 | − | 0.778259i | \(-0.283897\pi\) | ||||
0.627944 | + | 0.778259i | \(0.283897\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.9021 | −1.33298 | −0.666489 | − | 0.745515i | \(-0.732204\pi\) | ||||
−0.666489 | + | 0.745515i | \(0.732204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.4357i | 0.610395i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 17.9466i | − | 0.955201i | −0.878577 | − | 0.477600i | \(-0.841507\pi\) | ||
0.878577 | − | 0.477600i | \(-0.158493\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.42998i | 0.341268i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.11425 | − | 7.40755i | 0.164823 | − | 0.392049i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 32.1939i | − | 1.69913i | −0.527483 | − | 0.849565i | \(-0.676864\pi\) | ||
0.527483 | − | 0.849565i | \(-0.323136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3044 | 0.963387 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.11825i | − | 0.163666i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.227709i | − | 0.0119188i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.96776 | −0.468113 | −0.234057 | − | 0.972223i | \(-0.575200\pi\) | ||||
−0.234057 | + | 0.972223i | \(0.575200\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.4203i | 0.854807i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.55467 | + | 0.653607i | 0.0807144 | + | 0.0339336i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 19.2075i | − | 0.994524i | −0.867600 | − | 0.497262i | \(-0.834339\pi\) | ||
0.867600 | − | 0.497262i | \(-0.165661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.421861i | 0.0217848i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.5584i | 1.16182i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.5548 | 1.10719 | 0.553597 | − | 0.832784i | \(-0.313255\pi\) | ||||
0.553597 | + | 0.832784i | \(0.313255\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.40559 | 0.123242 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.1089 | 1.18081 | 0.590406 | − | 0.807107i | \(-0.298968\pi\) | ||||
0.590406 | + | 0.807107i | \(0.298968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.94778 | − | 4.63298i | 0.0992679 | − | 0.236118i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 35.6529 | 1.81234 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 14.3793i | − | 0.729058i | −0.931192 | − | 0.364529i | \(-0.881230\pi\) | ||
0.931192 | − | 0.364529i | \(-0.118770\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5394 | 2.10074 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.15725 | −0.361035 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.17831i | 0.361180i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.4913 | −0.877864 | −0.438932 | − | 0.898520i | \(-0.644643\pi\) | ||||
−0.438932 | + | 0.898520i | \(0.644643\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.360784 | + | 0.858160i | −0.0180618 | + | 0.0429617i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.9119 | 1.74342 | 0.871709 | − | 0.490024i | \(-0.163012\pi\) | ||||
0.871709 | + | 0.490024i | \(0.163012\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.8273 | −0.937852 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.42998 | 0.369198 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.89186i | 0.440753i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 34.0866i | − | 1.68547i | −0.538327 | − | 0.842736i | \(-0.680943\pi\) | ||
0.538327 | − | 0.842736i | \(-0.319057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.85160i | − | 0.140659i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.9898 | − | 5.46110i | −0.639185 | − | 0.268723i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.76612i | − | 0.233960i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.26538 | −0.110936 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 25.3178i | − | 1.23685i | −0.785842 | − | 0.618427i | \(-0.787770\pi\) | ||
0.785842 | − | 0.618427i | \(-0.212230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.7943i | 1.11093i | 0.831541 | + | 0.555463i | \(0.187459\pi\) | ||||
−0.831541 | + | 0.555463i | \(0.812541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.7924 | −0.865098 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.19944i | 0.349224i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.00212 | − | 19.0338i | 0.387250 | − | 0.921112i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 3.73115i | − | 0.180142i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.06648i | − | 0.0513707i | −0.999670 | − | 0.0256854i | \(-0.991823\pi\) | ||
0.999670 | − | 0.0256854i | \(-0.00817680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8877i | 0.571286i | 0.958336 | + | 0.285643i | \(0.0922072\pi\) | ||||
−0.958336 | + | 0.285643i | \(0.907793\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.04389 | −0.0979968 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.81231 | −0.230204 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.4015 | 1.92826 | 0.964128 | − | 0.265437i | \(-0.0855162\pi\) | ||||
0.964128 | + | 0.265437i | \(0.0855162\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.8200 | − | 14.1151i | −0.658096 | − | 0.672149i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.09808 | 0.242217 | 0.121109 | − | 0.992639i | \(-0.461355\pi\) | ||||
0.121109 | + | 0.992639i | \(0.461355\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.9442i | 0.566211i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.90454 | 0.231977 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.3965 | −0.726608 | −0.363304 | − | 0.931671i | \(-0.618351\pi\) | ||||
−0.363304 | + | 0.931671i | \(0.618351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 11.0528i | − | 0.520456i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.23170 | −0.104854 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.77427 | + | 11.3561i | −0.223821 | + | 0.532380i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3274 | 0.716987 | 0.358493 | − | 0.933532i | \(-0.383291\pi\) | ||||
0.358493 | + | 0.933532i | \(0.383291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.6824 | −0.825346 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.2470 | 0.523824 | 0.261912 | − | 0.965092i | \(-0.415647\pi\) | ||||
0.261912 | + | 0.965092i | \(0.415647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.4061i | − | 1.41309i | −0.707667 | − | 0.706546i | \(-0.750252\pi\) | ||
0.707667 | − | 0.706546i | \(-0.249748\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1.70583i | − | 0.0791059i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 7.30584i | − | 0.338074i | −0.985610 | − | 0.169037i | \(-0.945934\pi\) | ||
0.985610 | − | 0.169037i | \(-0.0540658\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.76775 | + | 11.3406i | −0.220154 | + | 0.523659i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 9.24372i | − | 0.425928i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.9986 | −1.10346 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.834050i | − | 0.0382688i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.79884i | − | 0.0823633i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.42872 | −0.248045 | −0.124022 | − | 0.992279i | \(-0.539579\pi\) | ||||
−0.124022 | + | 0.992279i | \(0.539579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 21.7952i | − | 0.993774i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.49584 | + | 5.93660i | −0.113565 | + | 0.270124i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3285i | 0.468994i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 34.7819i | − | 1.57612i | −0.615599 | − | 0.788060i | \(-0.711086\pi\) | ||
0.615599 | − | 0.788060i | \(-0.288914\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 0.344705i | − | 0.0155881i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.1387 | −1.63092 | −0.815458 | − | 0.578816i | \(-0.803515\pi\) | ||||
−0.815458 | + | 0.578816i | \(0.803515\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.8808 | −1.57095 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.36063 | −0.240942 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.6825 | − | 6.59318i | −0.703458 | − | 0.295745i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.2593 | −1.13076 | −0.565381 | − | 0.824830i | \(-0.691271\pi\) | ||||
−0.565381 | + | 0.824830i | \(0.691271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.72080i | 0.255586i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.0796 | 1.69789 | 0.848943 | − | 0.528485i | \(-0.177240\pi\) | ||||
0.848943 | + | 0.528485i | \(0.177240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.0777 | 0.670950 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.66138i | 0.162607i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.52937 | 0.200761 | 0.100380 | − | 0.994949i | \(-0.467994\pi\) | ||||
0.100380 | + | 0.994949i | \(0.467994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.555376 | + | 0.233489i | 0.0245684 | + | 0.0103289i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.04850 | 0.0904434 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.5333 | −0.640415 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.9764 | 0.526722 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.32015i | − | 0.101843i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 24.4806i | − | 1.07251i | −0.844055 | − | 0.536257i | \(-0.819838\pi\) | ||
0.844055 | − | 0.536257i | \(-0.180162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.1816i | − | 1.05739i | −0.848812 | − | 0.528694i | \(-0.822682\pi\) | ||
0.848812 | − | 0.528694i | \(-0.177318\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.02891 | − | 0.432568i | −0.0449052 | − | 0.0188788i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 29.1115i | − | 1.26812i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2907 | −0.447422 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.0299i | 0.652243i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.0919i | 1.17348i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.91022 | 0.428456 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.1198i | 0.436704i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.30250 | + | 9.50115i | 0.400687 | + | 0.409243i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.51920i | 0.151302i | 0.997134 | + | 0.0756512i | \(0.0241035\pi\) | ||||
−0.997134 | + | 0.0756512i | \(0.975896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.82438i | 0.378690i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7.77892i | − | 0.333212i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3167 | 0.654893 | 0.327446 | − | 0.944870i | \(-0.393812\pi\) | ||||
0.327446 | + | 0.944870i | \(0.393812\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.0233 | −0.939929 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.04092 | 0.172149 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.5077 | − | 7.36051i | −0.744503 | − | 0.313001i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.97473 | 0.0838228 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 19.0219i | − | 0.805985i | −0.915203 | − | 0.402993i | \(-0.867970\pi\) | ||
0.915203 | − | 0.402993i | \(-0.132030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 58.8239 | 2.48798 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.76927 | 0.243579 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 17.8461i | − | 0.752125i | −0.926594 | − | 0.376063i | \(-0.877278\pi\) | ||
0.926594 | − | 0.376063i | \(-0.122722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.75220 | 0.199927 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.61857 | + | 18.1215i | −0.319950 | + | 0.761032i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.78552 | 0.158697 | 0.0793486 | − | 0.996847i | \(-0.474716\pi\) | ||||
0.0793486 | + | 0.996847i | \(0.474716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.65474 | −0.404038 | −0.202019 | − | 0.979382i | \(-0.564750\pi\) | ||||
−0.202019 | + | 0.979382i | \(0.564750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.14387 | −0.298440 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.76981i | − | 0.240618i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 38.2814i | − | 1.59368i | −0.604194 | − | 0.796838i | \(-0.706505\pi\) | ||
0.604194 | − | 0.796838i | \(-0.293495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.11086i | 0.0877243i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.6244 | + | 4.88710i | 0.482263 | + | 0.202751i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.21083i | 0.0501476i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.1396 | 0.543257 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.95450i | 0.245768i | 0.992421 | + | 0.122884i | \(0.0392144\pi\) | ||||
−0.992421 | + | 0.122884i | \(0.960786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.37255i | 0.138963i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4691 | 0.471775 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.82852i | 0.239349i | 0.992813 | + | 0.119674i | \(0.0381850\pi\) | ||||
−0.992813 | + | 0.119674i | \(0.961815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.5592 | − | 7.38218i | −0.719858 | − | 0.302640i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 0.0870491i | − | 0.00356268i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.5376i | 0.716568i | 0.933613 | + | 0.358284i | \(0.116638\pi\) | ||||
−0.933613 | + | 0.358284i | \(0.883362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.75204i | 0.193840i | 0.995292 | + | 0.0969199i | \(0.0308991\pi\) | ||||
−0.995292 | + | 0.0969199i | \(0.969101\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.1217 | 0.534357 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.39167 | −0.300514 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2743 | 0.660555 | 0.330277 | − | 0.943884i | \(-0.392858\pi\) | ||||
0.330277 | + | 0.943884i | \(0.392858\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.09576 | − | 4.98498i | 0.0849246 | − | 0.202002i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.3558 | −1.18761 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 31.6544i | − | 1.27851i | −0.768996 | − | 0.639254i | \(-0.779243\pi\) | ||
0.768996 | − | 0.639254i | \(-0.220757\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.45464 | −0.0989807 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.6932 | −1.19540 | −0.597701 | − | 0.801719i | \(-0.703919\pi\) | ||||
−0.597701 | + | 0.801719i | \(0.703919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16.1041i | − | 0.647277i | −0.946181 | − | 0.323638i | \(-0.895094\pi\) | ||
0.946181 | − | 0.323638i | \(-0.104906\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.1712 | 0.568669 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.1317 | − | 12.2474i | −1.16714 | − | 0.490682i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.668366 | −0.0266920 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.7006 | 1.34373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.78949i | 0.270285i | 0.990826 | + | 0.135143i | \(0.0431493\pi\) | ||||
−0.990826 | + | 0.135143i | \(0.956851\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 9.60628i | − | 0.381815i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 5.70233i | − | 0.226290i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.8017 | − | 23.2886i | −0.903436 | − | 0.922728i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.1456i | 0.717829i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2906 | −0.406456 | −0.203228 | − | 0.979131i | \(-0.565143\pi\) | ||||
−0.203228 | + | 0.979131i | \(0.565143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.1456i | − | 1.74093i | −0.492230 | − | 0.870465i | \(-0.663818\pi\) | ||
0.492230 | − | 0.870465i | \(-0.336182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.32969i | 0.209856i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.57865 | −0.258634 | −0.129317 | − | 0.991603i | \(-0.541278\pi\) | ||||
−0.129317 | + | 0.991603i | \(0.541278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10.1169i | − | 0.397123i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.16047 | + | 1.74913i | 0.163062 | + | 0.0685536i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.9386i | 1.24985i | 0.780683 | + | 0.624927i | \(0.214871\pi\) | ||||
−0.780683 | + | 0.624927i | \(0.785129\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.9659i | 0.662913i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.642603i | − | 0.0250703i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.4842 | 1.46018 | 0.730088 | − | 0.683353i | \(-0.239479\pi\) | ||||
0.730088 | + | 0.683353i | \(0.239479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.7477 | −0.768098 | −0.384049 | − | 0.923313i | \(-0.625471\pi\) | ||||
−0.384049 | + | 0.923313i | \(0.625471\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.1413 | −0.549201 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.03423 | + | 0.855220i | 0.0788839 | + | 0.0331640i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.9543 | 1.08240 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.28604i | 0.243032i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.8242 | 0.572284 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.1738 | 1.47149 | 0.735745 | − | 0.677258i | \(-0.236832\pi\) | ||||
0.735745 | + | 0.677258i | \(0.236832\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.45609i | 0.0945348i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.5570 | −1.13597 | −0.567984 | − | 0.823040i | \(-0.692276\pi\) | ||||
−0.567984 | + | 0.823040i | \(0.692276\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.1910 | − | 10.5907i | −0.966741 | − | 0.406433i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.76240 | −0.259136 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.95463 | 0.227848 | 0.113924 | − | 0.993489i | \(-0.463658\pi\) | ||||
0.113924 | + | 0.993489i | \(0.463658\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.75958 | −0.258270 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.06441i | 0.269524i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.96792i | − | 0.113069i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.60671i | 0.365456i | 0.983163 | + | 0.182728i | \(0.0584928\pi\) | ||||
−0.983163 | + | 0.182728i | \(0.941507\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.49669 | − | 13.0744i | 0.208802 | − | 0.496656i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.36998i | 0.203695i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.8907 | −1.58672 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.73462i | − | 0.0656092i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6155i | 0.476481i | 0.971206 | + | 0.238240i | \(0.0765706\pi\) | ||||
−0.971206 | + | 0.238240i | \(0.923429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.90420 | −0.147250 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2.65976i | − | 0.100172i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.4604 | + | 36.7742i | −0.581450 | + | 1.38304i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 18.4188i | − | 0.691731i | −0.938284 | − | 0.345866i | \(-0.887585\pi\) | ||
0.938284 | − | 0.345866i | \(-0.112415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.2574i | 0.759713i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.3307i | 0.873742i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.84452 | −0.330766 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.06893 | −0.0399200 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.9006 | −1.52534 | −0.762668 | − | 0.646791i | \(-0.776111\pi\) | ||||
−0.762668 | + | 0.646791i | \(0.776111\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9022 | − | 35.4464i | 0.554988 | − | 1.32009i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.9628 | 0.407710 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.84493i | 0.179936i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0462 | 0.780559 | 0.390279 | − | 0.920696i | \(-0.372378\pi\) | ||||
0.390279 | + | 0.920696i | \(0.372378\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.8593 | 0.661454 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 90.9560i | 3.36413i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.67124 | −0.357215 | −0.178608 | − | 0.983920i | \(-0.557159\pi\) | ||||
−0.178608 | + | 0.983920i | \(0.557159\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.11005 | − | 2.06593i | 0.0778302 | − | 0.0762029i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.83245 | −0.325347 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.0213 | −1.06757 | −0.533783 | − | 0.845621i | \(-0.679230\pi\) | ||||
−0.533783 | + | 0.845621i | \(0.679230\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.63826 | 0.0601828 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.59397i | 0.351969i | 0.984393 | + | 0.175984i | \(0.0563108\pi\) | ||||
−0.984393 | + | 0.175984i | \(0.943689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 11.6260i | − | 0.425942i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 13.4502i | − | 0.492115i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1618 | + | 24.1708i | −0.371303 | + | 0.883180i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 0.422026i | − | 0.0153999i | −0.999970 | − | 0.00769997i | \(-0.997549\pi\) | ||
0.999970 | − | 0.00769997i | \(-0.00245100\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.03449 | 0.183467 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.29014i | 0.192528i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 39.3511i | − | 1.43024i | −0.699001 | − | 0.715121i | \(-0.746372\pi\) | ||
0.699001 | − | 0.715121i | \(-0.253628\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.62364 | −0.167827 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.8389i | 0.682911i | 0.939898 | + | 0.341455i | \(0.110920\pi\) | ||||
−0.939898 | + | 0.341455i | \(0.889080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.9726 | + | 7.97636i | 0.686853 | + | 0.288764i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.3171i | 0.734565i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.7979i | 0.895401i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.7564i | 1.86638i | 0.359380 | + | 0.933191i | \(0.382988\pi\) | ||||
−0.359380 | + | 0.933191i | \(0.617012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.607481 | −0.0218779 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.1875 | 1.19367 | 0.596836 | − | 0.802363i | \(-0.296424\pi\) | ||||
0.596836 | + | 0.802363i | \(0.296424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.04358 | −0.145250 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.02486 | + | 4.81632i | −0.0726413 | + | 0.172785i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.85301 | 0.173877 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 12.2141i | − | 0.437056i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.8996 | −0.425256 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.9118 | −0.782065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 30.7062i | − | 1.09456i | −0.836951 | − | 0.547278i | \(-0.815664\pi\) | ||
0.836951 | − | 0.547278i | \(-0.184336\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.48016 | −0.195099 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.87283 | + | 11.5905i | −0.173258 | + | 0.412111i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.3362 | −1.29034 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.268906 | 0.00953710 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.18345 | 0.0419198 | 0.0209599 | − | 0.999780i | \(-0.493328\pi\) | ||||
0.0209599 | + | 0.999780i | \(0.493328\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 45.3912i | − | 1.60583i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.7070i | 1.19098i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.432547i | 0.0152643i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.0724 | + | 5.91626i | 0.495987 | + | 0.208521i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.47592i | − | 0.227963i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.5452 | 0.511383 | 0.255691 | − | 0.966758i | \(-0.417697\pi\) | ||||
0.255691 | + | 0.966758i | \(0.417697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.4140i | − | 1.34890i | −0.738321 | − | 0.674449i | \(-0.764381\pi\) | ||
0.738321 | − | 0.674449i | \(-0.235619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.03914i | 0.211802i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.817106 | −0.0286220 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 10.5372i | − | 0.368650i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.4731 | + | 32.0472i | −0.470790 | + | 1.11982i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.0218i | 0.873265i | 0.899640 | + | 0.436633i | \(0.143829\pi\) | ||||
−0.899640 | + | 0.436633i | \(0.856171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29.1029i | − | 1.01446i | −0.861810 | − | 0.507232i | \(-0.830669\pi\) | ||
0.861810 | − | 0.507232i | \(-0.169331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.801350i | − | 0.0278994i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.9359 | −1.28439 | −0.642194 | − | 0.766542i | \(-0.721976\pi\) | ||||
−0.642194 | + | 0.766542i | \(0.721976\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.85695 | 0.203420 | 0.101710 | − | 0.994814i | \(-0.467569\pi\) | ||||
0.101710 | + | 0.994814i | \(0.467569\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.39342 | −0.0483371 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.0099 | − | 35.2570i | 1.24767 | − | 1.22158i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.5609 | 0.469294 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.93139i | − | 0.343279i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.99477 | −0.276010 | −0.138005 | − | 0.990432i | \(-0.544069\pi\) | ||||
−0.138005 | + | 0.990432i | \(0.544069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.52664 | 0.190574 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.19005i | 0.0409875i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.67912 | 0.298571 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.57929 | − | 18.0281i | 0.260427 | − | 0.619452i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.40470 | −0.322768 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.0085 | −0.925841 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.4916 | 1.00977 | 0.504886 | − | 0.863186i | \(-0.331535\pi\) | ||||
0.504886 | + | 0.863186i | \(0.331535\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.35372i | − | 0.0804954i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.42236i | 0.151065i | 0.997143 | + | 0.0755325i | \(0.0240657\pi\) | ||||
−0.997143 | + | 0.0755325i | \(0.975934\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.7417i | 1.01477i | 0.861718 | + | 0.507387i | \(0.169389\pi\) | ||||
−0.861718 | + | 0.507387i | \(0.830611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.51694 | − | 5.98680i | 0.0857773 | − | 0.204030i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.3281i | 0.385613i | 0.981237 | + | 0.192806i | \(0.0617589\pi\) | ||||
−0.981237 | + | 0.192806i | \(0.938241\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.49980 | −0.186999 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 14.6942i | − | 0.499041i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.6356i | − | 0.462557i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.6495 | 0.733566 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.1474i | 0.986491i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.02538 | + | 2.43897i | −0.0346642 | + | 0.0824523i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.1172i | 1.42220i | 0.703093 | + | 0.711098i | \(0.251802\pi\) | ||||
−0.703093 | + | 0.711098i | \(0.748198\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.15775i | 0.140237i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.9740i | 1.31307i | 0.754296 | + | 0.656534i | \(0.227978\pi\) | ||||
−0.754296 | + | 0.656534i | \(0.772022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.2610 | 0.446268 | 0.223134 | − | 0.974788i | \(-0.428371\pi\) | ||||
0.223134 | + | 0.974788i | \(0.428371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.24679 | −0.0755252 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.0616 | −0.371411 | −0.185706 | − | 0.982605i | \(-0.559457\pi\) | ||||
−0.185706 | + | 0.982605i | \(0.559457\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.9078 | + | 5.84706i | 0.466453 | + | 0.196104i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.1137 | −0.472826 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.25854i | 0.175970i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.9886 | 0.801851 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.3332 | 0.378403 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 19.5909i | − | 0.653392i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.58912 | 0.152886 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.9990 | − | 5.46497i | −0.432578 | − | 0.181863i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.9178 | 0.695330 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.0808 | 0.600362 | 0.300181 | − | 0.953882i | \(-0.402953\pi\) | ||||
0.300181 | + | 0.953882i | \(0.402953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.5499 | 1.41129 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.9387i | 1.09131i | 0.838011 | + | 0.545654i | \(0.183719\pi\) | ||||
−0.838011 | + | 0.545654i | \(0.816281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.05354i | 0.299628i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 3.29221i | − | 0.108837i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −41.3794 | − | 17.3965i | −1.36647 | − | 0.574484i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.4808i | 1.63222i | 0.577896 | + | 0.816111i | \(0.303874\pi\) | ||||
−0.577896 | + | 0.816111i | \(0.696126\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8820 | 0.457426 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.9385i | 0.985438i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.68101i | − | 0.153911i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.0135 | −1.34706 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.0077i | 0.689241i | 0.938742 | + | 0.344621i | \(0.111992\pi\) | ||||
−0.938742 | + | 0.344621i | \(0.888008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.17172 | + | 4.08449i | −0.136723 | + | 0.133864i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 11.3790i | − | 0.372532i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 13.6758i | − | 0.447245i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.45821i | 0.308986i | 0.987994 | + | 0.154493i | \(0.0493744\pi\) | ||||
−0.987994 | + | 0.154493i | \(0.950626\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.66801 | 0.282870 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.2269 | −0.952771 | −0.476385 | − | 0.879237i | \(-0.658053\pi\) | ||||
−0.476385 | + | 0.879237i | \(0.658053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.5723 | 1.09326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.99033 | − | 2.51843i | −0.194865 | − | 0.0819244i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.7292 | 0.933573 | 0.466787 | − | 0.884370i | \(-0.345412\pi\) | ||||
0.466787 | + | 0.884370i | \(0.345412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.06023i | − | 0.0344166i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.23329 | 0.104847 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.8837 | 0.741276 | 0.370638 | − | 0.928777i | \(-0.379139\pi\) | ||||
0.370638 | + | 0.928777i | \(0.379139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.9342i | 0.547978i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.88249 | 0.125503 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.93116 | − | 16.4864i | 0.223819 | − | 0.532375i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6494 | −0.472563 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.9670 | 0.901223 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.00369 | 0.161074 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.1050i | − | 0.743006i | −0.928432 | − | 0.371503i | \(-0.878843\pi\) | ||
0.928432 | − | 0.371503i | \(-0.121157\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.53314i | 0.0813762i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 55.3373i | − | 1.77586i | −0.459981 | − | 0.887929i | \(-0.652144\pi\) | ||
0.459981 | − | 0.887929i | \(-0.347856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.0972 | − | 5.50628i | −0.419878 | − | 0.176523i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.96422i | 0.0629053i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.5869 | 1.81038 | 0.905188 | − | 0.425011i | \(-0.139730\pi\) | ||||
0.905188 | + | 0.425011i | \(0.139730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 22.6888i | − | 0.725137i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 21.9524i | − | 0.700885i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.1612 | −1.05768 | −0.528839 | − | 0.848722i | \(-0.677373\pi\) | ||||
−0.528839 | + | 0.848722i | \(0.677373\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 27.1869i | − | 0.866246i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.48708 | + | 2.72727i | 0.206486 | + | 0.0868100i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 72.8944i | − | 2.31791i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 0.564256i | − | 0.0179242i | −0.999960 | − | 0.00896210i | \(-0.997147\pi\) | ||
0.999960 | − | 0.00896210i | \(-0.00285276\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.87613i | − | 0.281675i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.206346 | −0.00654160 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.2119 | 0.513437 | 0.256719 | − | 0.966486i | \(-0.417359\pi\) | ||||
0.256719 | + | 0.966486i | \(0.417359\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.4970 | 0.363748 |
(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 | 2240.2.h.f.671.12 | yes | 24 | |
4.3 | odd | 2 | inner | 2240.2.h.f.671.13 | yes | 24 | |
7.6 | odd | 2 | 2240.2.h.e.671.13 | yes | 24 | ||
8.3 | odd | 2 | 2240.2.h.e.671.14 | yes | 24 | ||
8.5 | even | 2 | 2240.2.h.e.671.11 | ✓ | 24 | ||
28.27 | even | 2 | 2240.2.h.e.671.12 | yes | 24 | ||
56.13 | odd | 2 | inner | 2240.2.h.f.671.14 | yes | 24 | |
56.27 | even | 2 | inner | 2240.2.h.f.671.11 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.h.e.671.11 | ✓ | 24 | 8.5 | even | 2 | ||
2240.2.h.e.671.12 | yes | 24 | 28.27 | even | 2 | ||
2240.2.h.e.671.13 | yes | 24 | 7.6 | odd | 2 | ||
2240.2.h.e.671.14 | yes | 24 | 8.3 | odd | 2 | ||
2240.2.h.f.671.11 | yes | 24 | 56.27 | even | 2 | inner | |
2240.2.h.f.671.12 | yes | 24 | 1.1 | even | 1 | trivial | |
2240.2.h.f.671.13 | yes | 24 | 4.3 | odd | 2 | inner | |
2240.2.h.f.671.14 | yes | 24 | 56.13 | odd | 2 | inner |