Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(2015,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.2015");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2015.24 | ||
Character | \(\chi\) | \(=\) | 2736.2015 |
Dual form | 2736.2.d.b.2015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 2.95877i | 1.32320i | 0.749857 | + | 0.661600i | \(0.230122\pi\) | ||||
−0.749857 | + | 0.661600i | \(0.769878\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.569970i | 0.215428i | 0.994182 | + | 0.107714i | \(0.0343531\pi\) | ||||
−0.994182 | + | 0.107714i | \(0.965647\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.70925 | 0.515359 | 0.257679 | − | 0.966230i | \(-0.417042\pi\) | ||||
0.257679 | + | 0.966230i | \(0.417042\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.55382 | 0.985651 | 0.492826 | − | 0.870128i | \(-0.335964\pi\) | ||||
0.492826 | + | 0.870128i | \(0.335964\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.91049i | 1.19097i | 0.803366 | + | 0.595485i | \(0.203040\pi\) | ||||
−0.803366 | + | 0.595485i | \(0.796960\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.27966 | 1.72643 | 0.863214 | − | 0.504838i | \(-0.168448\pi\) | ||||
0.863214 | + | 0.504838i | \(0.168448\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.75430 | −0.750859 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.39518i | 0.444775i | 0.974958 | + | 0.222387i | \(0.0713849\pi\) | ||||
−0.974958 | + | 0.222387i | \(0.928615\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 4.25776i | − 0.764716i | −0.924014 | − | 0.382358i | \(-0.875112\pi\) | ||||
0.924014 | − | 0.382358i | \(-0.124888\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.68641 | −0.285055 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.95478 | −0.978959 | −0.489480 | − | 0.872015i | \(-0.662813\pi\) | ||||
−0.489480 | + | 0.872015i | \(0.662813\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 3.11214i | − 0.486034i | −0.970022 | − | 0.243017i | \(-0.921863\pi\) | ||||
0.970022 | − | 0.243017i | \(-0.0781371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.81744i | − 0.582154i | −0.956700 | − | 0.291077i | \(-0.905986\pi\) | ||||
0.956700 | − | 0.291077i | \(-0.0940135\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.85841 | −0.854537 | −0.427268 | − | 0.904125i | \(-0.640524\pi\) | ||||
−0.427268 | + | 0.904125i | \(0.640524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.67513 | 0.953591 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.30890i | 0.591873i | 0.955208 | + | 0.295937i | \(0.0956317\pi\) | ||||
−0.955208 | + | 0.295937i | \(0.904368\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.05728i | 0.681923i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.13451 | 0.277889 | 0.138945 | − | 0.990300i | \(-0.455629\pi\) | ||||
0.138945 | + | 0.990300i | \(0.455629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.19721 | 0.537398 | 0.268699 | − | 0.963224i | \(-0.413406\pi\) | ||||
0.268699 | + | 0.963224i | \(0.413406\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.5149i | 1.30421i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3687i | 1.51107i | 0.655107 | + | 0.755536i | \(0.272623\pi\) | ||||
−0.655107 | + | 0.755536i | \(0.727377\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7533 | 1.51353 | 0.756767 | − | 0.653685i | \(-0.226778\pi\) | ||||
0.756767 | + | 0.653685i | \(0.226778\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.8387 | −1.26858 | −0.634288 | − | 0.773097i | \(-0.718707\pi\) | ||||
−0.634288 | + | 0.773097i | \(0.718707\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.974222i | 0.111023i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 2.29006i | − 0.257652i | −0.991667 | − | 0.128826i | \(-0.958879\pi\) | ||||
0.991667 | − | 0.128826i | \(-0.0411209\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.73885 | 0.190863 | 0.0954316 | − | 0.995436i | \(-0.469577\pi\) | ||||
0.0954316 | + | 0.995436i | \(0.469577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.5290 | −1.57589 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6261i | 1.55036i | 0.631741 | + | 0.775179i | \(0.282341\pi\) | ||||
−0.631741 | + | 0.775179i | \(0.717659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.02557i | 0.212337i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.95877 | −0.303563 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.53416 | −0.561909 | −0.280954 | − | 0.959721i | \(-0.590651\pi\) | ||||
−0.280954 | + | 0.959721i | \(0.590651\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 2.79060i | − 0.277675i | −0.990315 | − | 0.138838i | \(-0.955663\pi\) | ||||
0.990315 | − | 0.138838i | \(-0.0443366\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 7.21853i | − 0.711263i | −0.934626 | − | 0.355631i | \(-0.884266\pi\) | ||||
0.934626 | − | 0.355631i | \(-0.115734\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.58913 | 0.830342 | 0.415171 | − | 0.909743i | \(-0.363722\pi\) | ||||
0.415171 | + | 0.909743i | \(0.363722\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.2842 | −1.65553 | −0.827763 | − | 0.561077i | \(-0.810387\pi\) | ||||
−0.827763 | + | 0.561077i | \(0.810387\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.52206i | − 0.237255i | −0.992939 | − | 0.118628i | \(-0.962150\pi\) | ||||
0.992939 | − | 0.118628i | \(-0.0378495\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.4976i | 2.28441i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.79883 | −0.256569 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.07846 | −0.734405 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.68574i | 0.329663i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 9.49347i | − 0.842410i | −0.906966 | − | 0.421205i | \(-0.861607\pi\) | ||||
0.906966 | − | 0.421205i | \(-0.138393\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.47277 | −0.478159 | −0.239079 | − | 0.971000i | \(-0.576846\pi\) | ||||
−0.239079 | + | 0.971000i | \(0.576846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.569970 | −0.0494226 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.6155i | 0.906946i | 0.891270 | + | 0.453473i | \(0.149815\pi\) | ||||
−0.891270 | + | 0.453473i | \(0.850185\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.6801i | 1.75407i | 0.480430 | + | 0.877033i | \(0.340481\pi\) | ||||
−0.480430 | + | 0.877033i | \(0.659519\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.07437 | 0.507964 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.08679 | −0.588526 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.11655i | 0.173395i | 0.996235 | + | 0.0866973i | \(0.0276313\pi\) | ||||
−0.996235 | + | 0.0866973i | \(0.972369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 11.8036i | − 0.960567i | −0.877113 | − | 0.480284i | \(-0.840534\pi\) | ||||
0.877113 | − | 0.480284i | \(-0.159466\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.5977 | 1.01187 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4017 | −1.22919 | −0.614594 | − | 0.788843i | \(-0.710680\pi\) | ||||
−0.614594 | + | 0.788843i | \(0.710680\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.71915i | 0.371921i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.2526i | 1.35133i | 0.737209 | + | 0.675665i | \(0.236143\pi\) | ||||
−0.737209 | + | 0.675665i | \(0.763857\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.0656 | −1.78487 | −0.892437 | − | 0.451173i | \(-0.851006\pi\) | ||||
−0.892437 | + | 0.451173i | \(0.851006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.370392 | −0.0284917 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3.81082i | − 0.289731i | −0.989451 | − | 0.144866i | \(-0.953725\pi\) | ||||
0.989451 | − | 0.144866i | \(-0.0462750\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.13984i | − 0.161756i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.85047 | 0.287798 | 0.143899 | − | 0.989592i | \(-0.454036\pi\) | ||||
0.143899 | + | 0.989592i | \(0.454036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3304 | 1.21383 | 0.606916 | − | 0.794766i | \(-0.292406\pi\) | ||||
0.606916 | + | 0.794766i | \(0.292406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 17.6188i | − 1.29536i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.39327i | 0.613777i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.711877 | −0.0515096 | −0.0257548 | − | 0.999668i | \(-0.508199\pi\) | ||||
−0.0257548 | + | 0.999668i | \(0.508199\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.08186 | −0.365800 | −0.182900 | − | 0.983132i | \(-0.558548\pi\) | ||||
−0.182900 | + | 0.983132i | \(0.558548\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.3093i | 0.805757i | 0.915254 | + | 0.402878i | \(0.131990\pi\) | ||||
−0.915254 | + | 0.402878i | \(0.868010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5428i | 1.17269i | 0.810062 | + | 0.586345i | \(0.199434\pi\) | ||||
−0.810062 | + | 0.586345i | \(0.800566\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.36518 | −0.0958170 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.20808 | 0.643120 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.70925i | 0.118231i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 13.6026i | − 0.936439i | −0.883612 | − | 0.468220i | \(-0.844896\pi\) | ||||
0.883612 | − | 0.468220i | \(-0.155104\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.2949 | 0.770306 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.42679 | 0.164741 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.4510i | 1.17388i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 24.3517i | − 1.63071i | −0.578960 | − | 0.815356i | \(-0.696541\pi\) | ||||
0.578960 | − | 0.815356i | \(-0.303459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.7382 | 1.64193 | 0.820967 | − | 0.570976i | \(-0.193435\pi\) | ||||
0.820967 | + | 0.570976i | \(0.193435\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.04362 | 0.531537 | 0.265769 | − | 0.964037i | \(-0.414374\pi\) | ||||
0.265769 | + | 0.964037i | \(0.414374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 13.8280i | − 0.905901i | −0.891536 | − | 0.452951i | \(-0.850371\pi\) | ||||
0.891536 | − | 0.452951i | \(-0.149629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 17.3337i | − 1.13072i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.99484 | 0.129036 | 0.0645178 | − | 0.997917i | \(-0.479449\pi\) | ||||
0.0645178 | + | 0.997917i | \(0.479449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.12602 | 0.394611 | 0.197306 | − | 0.980342i | \(-0.436781\pi\) | ||||
0.197306 | + | 0.980342i | \(0.436781\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.7502i | 1.26179i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.55382i | 0.226124i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.97473 | 0.566480 | 0.283240 | − | 0.959049i | \(-0.408591\pi\) | ||||
0.283240 | + | 0.959049i | \(0.408591\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.1520 | 0.889730 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 9.65103i | − 0.602015i | −0.953622 | − | 0.301007i | \(-0.902677\pi\) | ||||
0.953622 | − | 0.301007i | \(-0.0973229\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 3.39404i | − 0.210896i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.74147 | 0.169046 | 0.0845231 | − | 0.996422i | \(-0.473063\pi\) | ||||
0.0845231 | + | 0.996422i | \(0.473063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.7490 | −0.783167 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8606i | 0.967040i | 0.875333 | + | 0.483520i | \(0.160642\pi\) | ||||
−0.875333 | + | 0.483520i | \(0.839358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 10.0169i | − 0.608484i | −0.952595 | − | 0.304242i | \(-0.901597\pi\) | ||||
0.952595 | − | 0.304242i | \(-0.0984031\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.41704 | −0.386962 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.21067 | 0.0727419 | 0.0363709 | − | 0.999338i | \(-0.488420\pi\) | ||||
0.0363709 | + | 0.999338i | \(0.488420\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.4526i | 1.75699i | 0.477748 | + | 0.878497i | \(0.341453\pi\) | ||||
−0.477748 | + | 0.878497i | \(0.658547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 17.8603i | − 1.06168i | −0.847471 | − | 0.530841i | \(-0.821876\pi\) | ||||
0.847471 | − | 0.530841i | \(-0.178124\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.77382 | 0.104705 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.11296 | −0.418409 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.61432i | − 0.503254i | −0.967824 | − | 0.251627i | \(-0.919034\pi\) | ||||
0.967824 | − | 0.251627i | \(-0.0809656\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.31551i | 0.367703i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.4244 | 1.70166 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.17582 | 0.125412 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.4186i | 0.711086i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.66899i | − 0.0952541i | −0.998865 | − | 0.0476271i | \(-0.984834\pi\) | ||||
0.998865 | − | 0.0476271i | \(-0.0151659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7976 | −0.895802 | −0.447901 | − | 0.894083i | \(-0.647828\pi\) | ||||
−0.447901 | + | 0.894083i | \(0.647828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.4916 | 1.83653 | 0.918267 | − | 0.395961i | \(-0.129589\pi\) | ||||
0.918267 | + | 0.395961i | \(0.129589\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 9.48080i | − 0.532495i | −0.963905 | − | 0.266247i | \(-0.914216\pi\) | ||||
0.963905 | − | 0.266247i | \(-0.0857838\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.09397i | 0.229218i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.91049 | −0.273227 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.3421 | −0.740085 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3.33911i | − 0.184091i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.2220i | 0.561852i | 0.959729 | + | 0.280926i | \(0.0906416\pi\) | ||||
−0.959729 | + | 0.280926i | \(0.909358\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −36.5960 | −1.99945 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6998 | 0.637326 | 0.318663 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318663 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7.27758i | − 0.394103i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.79441i | 0.420859i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.7600 | 1.06078 | 0.530388 | − | 0.847755i | \(-0.322046\pi\) | ||||
0.530388 | + | 0.847755i | \(0.322046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.61480 | 0.139967 | 0.0699836 | − | 0.997548i | \(-0.477705\pi\) | ||||
0.0699836 | + | 0.997548i | \(0.477705\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.48062i | − 0.0788056i | −0.999223 | − | 0.0394028i | \(-0.987454\pi\) | ||||
0.999223 | − | 0.0394028i | \(-0.0125456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.7339i | 2.00271i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.0406 | −1.53271 | −0.766353 | − | 0.642420i | \(-0.777931\pi\) | ||||
−0.766353 | + | 0.642420i | \(0.777931\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 32.0693i | − 1.67858i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 17.9185i | − 0.935337i | −0.883904 | − | 0.467668i | \(-0.845094\pi\) | ||||
0.883904 | − | 0.467668i | \(-0.154906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.45594 | −0.127506 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.65432 | 0.292770 | 0.146385 | − | 0.989228i | \(-0.453236\pi\) | ||||
0.146385 | + | 0.989228i | \(0.453236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.51204i | 0.438393i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 31.7595i | − 1.63138i | −0.578493 | − | 0.815688i | \(-0.696359\pi\) | ||||
0.578493 | − | 0.815688i | \(-0.303641\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.2692 | −1.34229 | −0.671146 | − | 0.741325i | \(-0.734198\pi\) | ||||
−0.671146 | + | 0.741325i | \(0.734198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.88249 | −0.146905 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 8.02764i | − 0.407017i | −0.979073 | − | 0.203509i | \(-0.934765\pi\) | ||||
0.979073 | − | 0.203509i | \(-0.0652345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.6572i | 2.05612i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.77576 | 0.340926 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.24160 | 0.162691 | 0.0813457 | − | 0.996686i | \(-0.474078\pi\) | ||||
0.0813457 | + | 0.996686i | \(0.474078\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 7.12034i | − 0.355573i | −0.984069 | − | 0.177786i | \(-0.943106\pi\) | ||||
0.984069 | − | 0.177786i | \(-0.0568936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 15.1313i | − 0.753743i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1782 | −0.504515 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.49493 | −0.420047 | −0.210024 | − | 0.977696i | \(-0.567354\pi\) | ||||
−0.210024 | + | 0.977696i | \(0.567354\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.21660i | 0.0598652i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.14484i | 0.252550i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.98442 | 0.194652 | 0.0973258 | − | 0.995253i | \(-0.468971\pi\) | ||||
0.0973258 | + | 0.995253i | \(0.468971\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.1475 | 1.46930 | 0.734650 | − | 0.678446i | \(-0.237346\pi\) | ||||
0.734650 | + | 0.678446i | \(0.237346\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 18.4355i | − 0.894251i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.39229i | 0.115771i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.6558 | 1.38030 | 0.690152 | − | 0.723665i | \(-0.257544\pi\) | ||||
0.690152 | + | 0.723665i | \(0.257544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7254 | 0.563487 | 0.281743 | − | 0.959490i | \(-0.409087\pi\) | ||||
0.281743 | + | 0.959490i | \(0.409087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.27966i | 0.396070i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 39.5668i | − 1.88842i | −0.329343 | − | 0.944211i | \(-0.606827\pi\) | ||||
0.329343 | − | 0.944211i | \(-0.393173\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.5909 | 0.978303 | 0.489151 | − | 0.872199i | \(-0.337307\pi\) | ||||
0.489151 | + | 0.872199i | \(0.337307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −43.2751 | −2.05144 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 30.6253i | − 1.44530i | −0.691217 | − | 0.722648i | \(-0.742925\pi\) | ||||
0.691217 | − | 0.722648i | \(-0.257075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 5.31942i | − 0.250482i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.99318 | −0.280965 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.4736 | 1.51905 | 0.759525 | − | 0.650478i | \(-0.225431\pi\) | ||||
0.759525 | + | 0.650478i | \(0.225431\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 7.17109i | − 0.333991i | −0.985958 | − | 0.166995i | \(-0.946594\pi\) | ||||
0.985958 | − | 0.166995i | \(-0.0534065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 24.9553i | − 1.15977i | −0.814699 | − | 0.579884i | \(-0.803098\pi\) | ||||
0.814699 | − | 0.579884i | \(-0.196902\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.4340 | −1.68596 | −0.842981 | − | 0.537943i | \(-0.819202\pi\) | ||||
−0.842981 | + | 0.537943i | \(0.819202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.04976 | −0.325528 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 6.52496i | − 0.300018i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3.75430i | − 0.172259i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.0402 | −1.64672 | −0.823360 | − | 0.567520i | \(-0.807903\pi\) | ||||
−0.823360 | + | 0.567520i | \(0.807903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.1622 | −0.964913 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 16.3743i | − 0.743518i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.8944i | 1.08276i | 0.840778 | + | 0.541380i | \(0.182098\pi\) | ||||
−0.840778 | + | 0.541380i | \(0.817902\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.453416 | 0.0204624 | 0.0102312 | − | 0.999948i | \(-0.496743\pi\) | ||||
0.0102312 | + | 0.999948i | \(0.496743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.7615 | −0.529713 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.26897i | 0.326058i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 37.4719i | − 1.67747i | −0.544539 | − | 0.838735i | \(-0.683295\pi\) | ||||
0.544539 | − | 0.838735i | \(-0.316705\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.9757 | −1.69325 | −0.846626 | − | 0.532188i | \(-0.821370\pi\) | ||||
−0.846626 | + | 0.532188i | \(0.821370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.25674 | 0.367420 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 41.8041i | − 1.85294i | −0.376374 | − | 0.926468i | \(-0.622829\pi\) | ||||
0.376374 | − | 0.926468i | \(-0.377171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 6.17774i | − 0.273287i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.3579 | 0.941143 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0135 | −0.440393 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 30.4902i | − 1.33580i | −0.744252 | − | 0.667899i | \(-0.767194\pi\) | ||||
0.744252 | − | 0.667899i | \(-0.232806\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.9130i | 1.26428i | 0.774856 | + | 0.632138i | \(0.217822\pi\) | ||||
−0.774856 | + | 0.632138i | \(0.782178\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.9077 | 0.910753 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 45.5528 | 1.98055 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 11.0600i | − 0.479060i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.4132i | 1.09871i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.4095 | 0.491441 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.3339 | 1.39014 | 0.695072 | − | 0.718940i | \(-0.255372\pi\) | ||||
0.695072 | + | 0.718940i | \(0.255372\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 51.1399i | − 2.19059i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.92847i | 0.381754i | 0.981614 | + | 0.190877i | \(0.0611331\pi\) | ||||
−0.981614 | + | 0.190877i | \(0.938867\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.39518 | −0.102038 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.30527 | 0.0555056 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 0.828782i | − 0.0351166i | −0.999846 | − | 0.0175583i | \(-0.994411\pi\) | ||||
0.999846 | − | 0.0175583i | \(-0.00558927\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 13.5665i | − 0.573800i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.3635 | −0.689638 | −0.344819 | − | 0.938669i | \(-0.612060\pi\) | ||||
−0.344819 | + | 0.938669i | \(0.612060\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.46218 | 0.313936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 0.104329i | − 0.00437368i | −0.999998 | − | 0.00218684i | \(-0.999304\pi\) | ||||
0.999998 | − | 0.00218684i | \(-0.000696093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.44526i | 0.186028i | 0.995665 | + | 0.0930142i | \(0.0296502\pi\) | ||||
−0.995665 | + | 0.0930142i | \(0.970350\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.0843 | −1.29630 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.9811 | −0.998346 | −0.499173 | − | 0.866502i | \(-0.666363\pi\) | ||||
−0.499173 | + | 0.866502i | \(0.666363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.991089i | 0.0411173i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.36500i | 0.305027i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.8155 | −0.446401 | −0.223201 | − | 0.974773i | \(-0.571651\pi\) | ||||
−0.223201 | + | 0.974773i | \(0.571651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.25776 | 0.175438 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.0703i | 1.19377i | 0.802325 | + | 0.596887i | \(0.203596\pi\) | ||||
−0.802325 | + | 0.596887i | \(0.796404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 8.28109i | − 0.339492i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.11836 | 0.209131 | 0.104565 | − | 0.994518i | \(-0.466655\pi\) | ||||
0.104565 | + | 0.994518i | \(0.466655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.3642 | −0.912254 | −0.456127 | − | 0.889915i | \(-0.650764\pi\) | ||||
−0.456127 | + | 0.889915i | \(0.650764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 23.9023i | − 0.971765i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 6.11562i | − 0.248226i | −0.992268 | − | 0.124113i | \(-0.960392\pi\) | ||||
0.992268 | − | 0.124113i | \(-0.0396085\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.8197 | −0.842275 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.7179 | −1.52341 | −0.761707 | − | 0.647922i | \(-0.775638\pi\) | ||||
−0.761707 | + | 0.647922i | \(0.775638\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.3799i | 1.54512i | 0.634943 | + | 0.772559i | \(0.281024\pi\) | ||||
−0.634943 | + | 0.772559i | \(0.718976\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.86517i | 0.235741i | 0.993029 | + | 0.117871i | \(0.0376068\pi\) | ||||
−0.993029 | + | 0.117871i | \(0.962393\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.33641 | −0.333991 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6767 | −1.18707 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 29.2409i | − 1.16591i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 11.1860i | − 0.445307i | −0.974898 | − | 0.222654i | \(-0.928528\pi\) | ||||
0.974898 | − | 0.222654i | \(-0.0714719\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.0890 | 1.11468 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.7222 | 0.939908 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 39.4688i | − 1.55892i | −0.626450 | − | 0.779462i | \(-0.715493\pi\) | ||||
0.626450 | − | 0.779462i | \(-0.284507\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.3994i | 1.47489i | 0.675409 | + | 0.737443i | \(0.263967\pi\) | ||||
−0.675409 | + | 0.737443i | \(0.736033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.71980 | −0.0676122 | −0.0338061 | − | 0.999428i | \(-0.510763\pi\) | ||||
−0.0338061 | + | 0.999428i | \(0.510763\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.64841 | 0.143213 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.8547i | 0.737840i | 0.929461 | + | 0.368920i | \(0.120272\pi\) | ||||
−0.929461 | + | 0.368920i | \(0.879728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 16.1927i | − 0.632700i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.6461 | 0.414714 | 0.207357 | − | 0.978265i | \(-0.433514\pi\) | ||||
0.207357 | + | 0.978265i | \(0.433514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.9227 | 0.541532 | 0.270766 | − | 0.962645i | \(-0.412723\pi\) | ||||
0.270766 | + | 0.962645i | \(0.412723\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1.68641i | − 0.0653961i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.8313i | 0.767871i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.17410 | 0.276953 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.2932 | 1.39900 | 0.699500 | − | 0.714633i | \(-0.253406\pi\) | ||||
0.699500 | + | 0.714633i | \(0.253406\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.72096i | 0.296741i | 0.988932 | + | 0.148370i | \(0.0474028\pi\) | ||||
−0.988932 | + | 0.148370i | \(0.952597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 3.15430i | − 0.121051i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.9531 | −0.725220 | −0.362610 | − | 0.931941i | \(-0.618114\pi\) | ||||
−0.362610 | + | 0.931941i | \(0.618114\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.4089 | −1.20007 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.3131i | 0.583381i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 32.5480i | − 1.23818i | −0.785319 | − | 0.619091i | \(-0.787501\pi\) | ||||
0.785319 | − | 0.619091i | \(-0.212499\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −61.1877 | −2.32098 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.2821 | 0.578852 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.55361i | 0.171987i | 0.996296 | + | 0.0859937i | \(0.0274065\pi\) | ||||
−0.996296 | + | 0.0859937i | \(0.972593\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.95478i | − 0.224589i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.59056 | 0.0598191 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.6482 | 1.86458 | 0.932289 | − | 0.361715i | \(-0.117809\pi\) | ||||
0.932289 | + | 0.361715i | \(0.117809\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 35.2528i | − 1.32023i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.9726i | 0.672138i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.55893 | 0.0581381 | 0.0290691 | − | 0.999577i | \(-0.490746\pi\) | ||||
0.0290691 | + | 0.999577i | \(0.490746\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.11434 | 0.153226 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 8.99223i | − 0.333963i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 39.8464i | − 1.47782i | −0.673803 | − | 0.738911i | \(-0.735340\pi\) | ||||
0.673803 | − | 0.738911i | \(-0.264660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.7455 | 0.693328 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.6913 | 1.24442 | 0.622209 | − | 0.782851i | \(-0.286235\pi\) | ||||
0.622209 | + | 0.782851i | \(0.286235\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.1411i | 0.778744i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 6.29537i | − 0.231579i | −0.993274 | − | 0.115789i | \(-0.963060\pi\) | ||||
0.993274 | − | 0.115789i | \(-0.0369398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.2166 | 1.69552 | 0.847760 | − | 0.530379i | \(-0.177950\pi\) | ||||
0.847760 | + | 0.530379i | \(0.177950\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.26238 | −0.229436 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.89554i | 0.178879i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 33.6850i | − 1.22918i | −0.788846 | − | 0.614591i | \(-0.789321\pi\) | ||||
0.788846 | − | 0.614591i | \(-0.210679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.9242 | 1.27102 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.5063 | 1.29050 | 0.645249 | − | 0.763973i | \(-0.276754\pi\) | ||||
0.645249 | + | 0.763973i | \(0.276754\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 2.95585i | − 0.107150i | −0.998564 | − | 0.0535748i | \(-0.982938\pi\) | ||||
0.998564 | − | 0.0535748i | \(-0.0170616\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9.85147i | − 0.356647i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.58564 | 0.273902 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.239047 | −0.00862026 | −0.00431013 | − | 0.999991i | \(-0.501372\pi\) | ||||
−0.00431013 | + | 0.999991i | \(0.501372\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 13.2405i | − 0.476229i | −0.971237 | − | 0.238114i | \(-0.923471\pi\) | ||||
0.971237 | − | 0.238114i | \(-0.0765293\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.9849i | 0.574194i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.11214 | 0.111504 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.7985 | 0.780013 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 45.5700i | − 1.62646i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 12.9966i | − 0.463279i | −0.972802 | − | 0.231640i | \(-0.925591\pi\) | ||||
0.972802 | − | 0.231640i | \(-0.0744090\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.43750 | 0.0511115 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9161 | 0.529687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.1127i | 0.854114i | 0.904225 | + | 0.427057i | \(0.140450\pi\) | ||||
−0.904225 | + | 0.427057i | \(0.859550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 28.7677i | − 1.01773i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.5261 | −0.653772 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.9629 | −0.492127 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.5178i | 0.369788i | 0.982758 | + | 0.184894i | \(0.0591942\pi\) | ||||
−0.982758 | + | 0.184894i | \(0.940806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.3137i | 0.888883i | 0.895808 | + | 0.444441i | \(0.146598\pi\) | ||||
−0.895808 | + | 0.444441i | \(0.853402\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51.0465 | −1.78808 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.81744 | 0.133555 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.8811i | 0.658956i | 0.944163 | + | 0.329478i | \(0.106873\pi\) | ||||
−0.944163 | + | 0.329478i | \(0.893127\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3.76306i | − 0.131172i | −0.997847 | − | 0.0655860i | \(-0.979108\pi\) | ||||
0.997847 | − | 0.0655860i | \(-0.0208917\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.5208 | 1.06131 | 0.530656 | − | 0.847587i | \(-0.321946\pi\) | ||||
0.530656 | + | 0.847587i | \(0.321946\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.1222 | 1.60189 | 0.800945 | − | 0.598738i | \(-0.204331\pi\) | ||||
0.800945 | + | 0.598738i | \(0.204331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.7782i | 1.13570i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 68.2459i | − 2.36175i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.1716 | −1.04164 | −0.520819 | − | 0.853667i | \(-0.674374\pi\) | ||||
−0.520819 | + | 0.853667i | \(0.674374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2631 | 0.802176 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.09590i | − 0.0377002i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 4.60448i | − 0.158212i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −49.3035 | −1.69010 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.4674 | 0.632313 | 0.316156 | − | 0.948707i | \(-0.397608\pi\) | ||||
0.316156 | + | 0.948707i | \(0.397608\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 23.9843i | − 0.819290i | −0.912245 | − | 0.409645i | \(-0.865653\pi\) | ||||
0.912245 | − | 0.409645i | \(-0.134347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 17.4158i | − 0.594219i | −0.954843 | − | 0.297110i | \(-0.903977\pi\) | ||||
0.954843 | − | 0.297110i | \(-0.0960227\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.4424 | −0.593746 | −0.296873 | − | 0.954917i | \(-0.595944\pi\) | ||||
−0.296873 | + | 0.954917i | \(0.595944\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.2753 | 0.383373 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 3.91429i | − 0.132783i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.9559i | 1.48939i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.10076 | −0.0710187 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.46831 | −0.252187 | −0.126093 | − | 0.992018i | \(-0.540244\pi\) | ||||
−0.126093 | + | 0.992018i | \(0.540244\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 23.2123i | − 0.782042i | −0.920382 | − | 0.391021i | \(-0.872122\pi\) | ||||
0.920382 | − | 0.391021i | \(-0.127878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.7029i | 1.23515i | 0.786512 | + | 0.617575i | \(0.211885\pi\) | ||||
−0.786512 | + | 0.617575i | \(0.788115\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.1244 | 1.68301 | 0.841507 | − | 0.540246i | \(-0.181669\pi\) | ||||
0.841507 | + | 0.540246i | \(0.181669\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.41099 | 0.181479 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.85841i | − 0.196044i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3926i | 0.380814i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.1981 | 0.340126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.1588 | −0.704903 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48.3179i | 1.60614i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.8688i | 1.19101i | 0.803353 | + | 0.595503i | \(0.203047\pi\) | ||||
−0.803353 | + | 0.595503i | \(0.796953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.0961 | −1.42784 | −0.713919 | − | 0.700229i | \(-0.753081\pi\) | ||||
−0.713919 | + | 0.700229i | \(0.753081\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.97212 | 0.0983630 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 3.11932i | − 0.103009i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 21.5024i | − 0.709300i | −0.934999 | − | 0.354650i | \(-0.884600\pi\) | ||||
0.934999 | − | 0.354650i | \(-0.115400\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.3227 | 1.49182 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.3560 | 0.735061 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.3969i | 0.636391i | 0.948025 | + | 0.318196i | \(0.103077\pi\) | ||||
−0.948025 | + | 0.318196i | \(0.896923\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.67513i | 0.218769i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.8337 | −0.812150 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.4396 | −1.25577 | −0.627884 | − | 0.778307i | \(-0.716079\pi\) | ||||
−0.627884 | + | 0.778307i | \(0.716079\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.5127i | 1.51627i | 0.652098 | + | 0.758135i | \(0.273889\pi\) | ||||
−0.652098 | + | 0.758135i | \(0.726111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 25.7674i | − 0.839103i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.8937 | 1.42635 | 0.713177 | − | 0.700984i | \(-0.247256\pi\) | ||||
0.713177 | + | 0.700984i | \(0.247256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.5188 | −1.25037 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 4.72133i | − 0.152939i | −0.997072 | − | 0.0764694i | \(-0.975635\pi\) | ||||
0.997072 | − | 0.0764694i | \(-0.0243648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2.10628i | − 0.0681576i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.05053 | −0.195382 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.8715 | 0.415210 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 15.0360i | − 0.484027i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 33.2550i | − 1.06941i | −0.845039 | − | 0.534704i | \(-0.820423\pi\) | ||||
0.845039 | − | 0.534704i | \(-0.179577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3041 | 0.362766 | 0.181383 | − | 0.983413i | \(-0.441943\pi\) | ||||
0.181383 | + | 0.983413i | \(0.441943\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.7871 | −0.377875 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.7282i | 0.919095i | 0.888153 | + | 0.459548i | \(0.151988\pi\) | ||||
−0.888153 | + | 0.459548i | \(0.848012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.9996i | 0.798991i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.4309 | 0.906806 | 0.453403 | − | 0.891306i | \(-0.350210\pi\) | ||||
0.453403 | + | 0.891306i | \(0.350210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.4617 | −1.06618 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 31.6071i | − 1.00505i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 6.74590i | − 0.214290i | −0.994243 | − | 0.107145i | \(-0.965829\pi\) | ||||
0.994243 | − | 0.107145i | \(-0.0341710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.9463 | −1.55170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −56.9248 | −1.80283 | −0.901414 | − | 0.432959i | \(-0.857469\pi\) | ||||
−0.901414 | + | 0.432959i | \(0.857469\pi\) | |||||||
\(998\) | 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 | 2736.2.d.b.2015.24 | yes | 24 | |
3.2 | odd | 2 | inner | 2736.2.d.b.2015.2 | yes | 24 | |
4.3 | odd | 2 | inner | 2736.2.d.b.2015.23 | yes | 24 | |
12.11 | even | 2 | inner | 2736.2.d.b.2015.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.d.b.2015.1 | ✓ | 24 | 12.11 | even | 2 | inner | |
2736.2.d.b.2015.2 | yes | 24 | 3.2 | odd | 2 | inner | |
2736.2.d.b.2015.23 | yes | 24 | 4.3 | odd | 2 | inner | |
2736.2.d.b.2015.24 | yes | 24 | 1.1 | even | 1 | trivial |