Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.47 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.d.5615.48 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 4.18263 | 1.87053 | 0.935264 | − | 0.353951i | \(-0.115162\pi\) | ||||
0.935264 | + | 0.353951i | \(0.115162\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.86730i | 0.563011i | 0.959560 | + | 0.281506i | \(0.0908338\pi\) | ||||
−0.959560 | + | 0.281506i | \(0.909166\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.07604i | 0.853139i | 0.904455 | + | 0.426569i | \(0.140278\pi\) | ||||
−0.904455 | + | 0.426569i | \(0.859722\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.504885i | 0.122453i | 0.998124 | + | 0.0612263i | \(0.0195011\pi\) | ||||
−0.998124 | + | 0.0612263i | \(0.980499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.05596 | −0.701085 | −0.350543 | − | 0.936547i | \(-0.614003\pi\) | ||||
−0.350543 | + | 0.936547i | \(0.614003\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.97229 | 1.24531 | 0.622654 | − | 0.782497i | \(-0.286054\pi\) | ||||
0.622654 | + | 0.782497i | \(0.286054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.4944 | 2.49887 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.52884 | 0.655289 | 0.327644 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327644 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 10.8980i | − 1.95734i | −0.205435 | − | 0.978671i | \(-0.565861\pi\) | ||||
0.205435 | − | 0.978671i | \(-0.434139\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 4.18263i | − 0.706993i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.3660i | 1.86856i | 0.356542 | + | 0.934279i | \(0.383956\pi\) | ||||
−0.356542 | + | 0.934279i | \(0.616044\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 7.26960i | − 1.13532i | −0.823263 | − | 0.567660i | \(-0.807849\pi\) | ||||
0.823263 | − | 0.567660i | \(-0.192151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.02120 | −1.37572 | −0.687860 | − | 0.725844i | \(-0.741450\pi\) | ||||
−0.687860 | + | 0.725844i | \(0.741450\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.327367 | −0.0477513 | −0.0238757 | − | 0.999715i | \(-0.507601\pi\) | ||||
−0.0238757 | + | 0.999715i | \(0.507601\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.32940 | 1.14413 | 0.572066 | − | 0.820208i | \(-0.306142\pi\) | ||||
0.572066 | + | 0.820208i | \(0.306142\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.81021i | 1.05313i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.98008i | 0.778540i | 0.921124 | + | 0.389270i | \(0.127273\pi\) | ||||
−0.921124 | + | 0.389270i | \(0.872727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 13.2783i | − 1.70011i | −0.526691 | − | 0.850057i | \(-0.676568\pi\) | ||||
0.526691 | − | 0.850057i | \(-0.323432\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.8659i | 1.59582i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.21499 | 1.12579 | 0.562895 | − | 0.826528i | \(-0.309688\pi\) | ||||
0.562895 | + | 0.826528i | \(0.309688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.02460 | 1.07102 | 0.535512 | − | 0.844528i | \(-0.320119\pi\) | ||||
0.535512 | + | 0.844528i | \(0.320119\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.416491 | 0.0487466 | 0.0243733 | − | 0.999703i | \(-0.492241\pi\) | ||||
0.0243733 | + | 0.999703i | \(0.492241\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.86730 | 0.212798 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00459i | 0.675569i | 0.941224 | + | 0.337784i | \(0.109677\pi\) | ||||
−0.941224 | + | 0.337784i | \(0.890323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.62368i | − 0.287987i | −0.989579 | − | 0.143993i | \(-0.954006\pi\) | ||||
0.989579 | − | 0.143993i | \(-0.0459944\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.11175i | 0.229051i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.69486i | 0.603654i | 0.953363 | + | 0.301827i | \(0.0975966\pi\) | ||||
−0.953363 | + | 0.301827i | \(0.902403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.07604 | 0.322456 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.7819 | −1.31140 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.21289 | 0.630824 | 0.315412 | − | 0.948955i | \(-0.397857\pi\) | ||||
0.315412 | + | 0.948955i | \(0.397857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.85216 | −0.184296 | −0.0921482 | − | 0.995745i | \(-0.529373\pi\) | ||||
−0.0921482 | + | 0.995745i | \(0.529373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.74001i | 0.269982i | 0.990847 | + | 0.134991i | \(0.0431005\pi\) | ||||
−0.990847 | + | 0.134991i | \(0.956900\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.22506i | 0.408452i | 0.978924 | + | 0.204226i | \(0.0654677\pi\) | ||||
−0.978924 | + | 0.204226i | \(0.934532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9420i | 1.33540i | 0.744432 | + | 0.667698i | \(0.232720\pi\) | ||||
−0.744432 | + | 0.667698i | \(0.767280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.49447i | 0.705020i | 0.935808 | + | 0.352510i | \(0.114672\pi\) | ||||
−0.935808 | + | 0.352510i | \(0.885328\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.9799 | 2.32938 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.504885 | 0.0462827 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.51320 | 0.683018 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.3462 | 2.80369 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0939i | 1.60557i | 0.596267 | + | 0.802787i | \(0.296650\pi\) | ||||
−0.596267 | + | 0.802787i | \(0.703350\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.32625i | 0.814839i | 0.913241 | + | 0.407419i | \(0.133571\pi\) | ||||
−0.913241 | + | 0.407419i | \(0.866429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.05596i | 0.264985i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 6.53069i | − 0.557955i | −0.960298 | − | 0.278977i | \(-0.910005\pi\) | ||||
0.960298 | − | 0.278977i | \(-0.0899954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1589 | 0.861664 | 0.430832 | − | 0.902432i | \(-0.358220\pi\) | ||||
0.430832 | + | 0.902432i | \(0.358220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.74387 | −0.480327 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.7598 | 1.22574 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.72516 | 0.796716 | 0.398358 | − | 0.917230i | \(-0.369580\pi\) | ||||
0.398358 | + | 0.917230i | \(0.369580\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 12.4664i | − 1.01450i | −0.861800 | − | 0.507249i | \(-0.830662\pi\) | ||||
0.861800 | − | 0.507249i | \(-0.169338\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 45.5823i | − 3.66126i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3627i | 0.906838i | 0.891297 | + | 0.453419i | \(0.149796\pi\) | ||||
−0.891297 | + | 0.453419i | \(0.850204\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 5.97229i | − 0.470682i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.59449 | 0.281542 | 0.140771 | − | 0.990042i | \(-0.455042\pi\) | ||||
0.140771 | + | 0.990042i | \(0.455042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.3801 | −1.57706 | −0.788531 | − | 0.614995i | \(-0.789158\pi\) | ||||
−0.788531 | + | 0.614995i | \(0.789158\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.53800 | 0.272154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.49761 | −0.341947 | −0.170974 | − | 0.985276i | \(-0.554691\pi\) | ||||
−0.170974 | + | 0.985276i | \(0.554691\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 12.4944i | − 0.944486i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2.63430i | − 0.196897i | −0.995142 | − | 0.0984485i | \(-0.968612\pi\) | ||||
0.995142 | − | 0.0984485i | \(-0.0313880\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 10.3748i | − 0.771151i | −0.922676 | − | 0.385576i | \(-0.874003\pi\) | ||||
0.922676 | − | 0.385576i | \(-0.125997\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 47.5397i | 3.49519i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.942770 | −0.0689422 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.1707 | −1.31479 | −0.657395 | − | 0.753547i | \(-0.728341\pi\) | ||||
−0.657395 | + | 0.753547i | \(0.728341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.7704 | −1.20716 | −0.603578 | − | 0.797304i | \(-0.706259\pi\) | ||||
−0.603578 | + | 0.797304i | \(0.706259\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.2240 | −1.36965 | −0.684826 | − | 0.728706i | \(-0.740122\pi\) | ||||
−0.684826 | + | 0.728706i | \(0.740122\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.68931i | − 0.119752i | −0.998206 | − | 0.0598761i | \(-0.980929\pi\) | ||||
0.998206 | − | 0.0598761i | \(-0.0190706\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3.52884i | − 0.247676i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 30.4060i | − 2.12365i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 5.70638i | − 0.394719i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1544 | 0.974427 | 0.487213 | − | 0.873283i | \(-0.338013\pi\) | ||||
0.487213 | + | 0.873283i | \(0.338013\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −37.7323 | −2.57332 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.8980 | −0.739806 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.55304 | −0.104469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.33032i | − 0.0890851i | −0.999007 | − | 0.0445425i | \(-0.985817\pi\) | ||||
0.999007 | − | 0.0445425i | \(-0.0141830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.34646i | 0.421229i | 0.977569 | + | 0.210615i | \(0.0675465\pi\) | ||||
−0.977569 | + | 0.210615i | \(0.932453\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 13.9920i | − 0.924619i | −0.886719 | − | 0.462309i | \(-0.847021\pi\) | ||||
0.886719 | − | 0.462309i | \(-0.152979\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.0797i | − 0.922392i | −0.887298 | − | 0.461196i | \(-0.847420\pi\) | ||||
0.887298 | − | 0.461196i | \(-0.152580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.36925 | −0.0893202 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1737 | 0.852134 | 0.426067 | − | 0.904691i | \(-0.359899\pi\) | ||||
0.426067 | + | 0.904691i | \(0.359899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.46846 | 0.481086 | 0.240543 | − | 0.970639i | \(-0.422675\pi\) | ||||
0.240543 | + | 0.970639i | \(0.422675\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.18263 | −0.267218 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 9.40024i | − 0.598123i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 16.3203i | − 1.03013i | −0.857151 | − | 0.515065i | \(-0.827768\pi\) | ||||
0.857151 | − | 0.515065i | \(-0.172232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1520i | 0.701123i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 13.6939i | − 0.854205i | −0.904203 | − | 0.427102i | \(-0.859534\pi\) | ||||
0.904203 | − | 0.427102i | \(-0.140466\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3660 | 0.706249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.63480 | 0.285794 | 0.142897 | − | 0.989738i | \(-0.454358\pi\) | ||||
0.142897 | + | 0.989738i | \(0.454358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.8388 | 2.14013 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.6544 | −1.74709 | −0.873545 | − | 0.486743i | \(-0.838185\pi\) | ||||
−0.873545 | + | 0.486743i | \(0.838185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.27458i | 0.502645i | 0.967903 | + | 0.251322i | \(0.0808654\pi\) | ||||
−0.967903 | + | 0.251322i | \(0.919135\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.3307i | 1.40689i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5278i | 0.752724i | 0.926473 | + | 0.376362i | \(0.122825\pi\) | ||||
−0.926473 | + | 0.376362i | \(0.877175\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 8.63112i | − 0.514889i | −0.966293 | − | 0.257445i | \(-0.917119\pi\) | ||||
0.966293 | − | 0.257445i | \(-0.0828805\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.73498 | −0.519241 | −0.259620 | − | 0.965711i | \(-0.583597\pi\) | ||||
−0.259620 | + | 0.965711i | \(0.583597\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.26960 | −0.429111 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7451 | 0.985005 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.3572 | −1.77348 | −0.886742 | − | 0.462265i | \(-0.847037\pi\) | ||||
−0.886742 | + | 0.462265i | \(0.847037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.0124i | 1.45628i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.3710i | 1.06242i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.02120i | 0.519973i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 55.5382i | − 3.18011i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.1705 | 1.66485 | 0.832425 | − | 0.554138i | \(-0.186952\pi\) | ||||
0.832425 | + | 0.554138i | \(0.186952\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4778 | −0.764253 | −0.382127 | − | 0.924110i | \(-0.624808\pi\) | ||||
−0.382127 | + | 0.924110i | \(0.624808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.7291 | 1.17168 | 0.585838 | − | 0.810428i | \(-0.300765\pi\) | ||||
0.585838 | + | 0.810428i | \(0.300765\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.453146 | −0.0254512 | −0.0127256 | − | 0.999919i | \(-0.504051\pi\) | ||||
−0.0127256 | + | 0.999919i | \(0.504051\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.58939i | 0.368935i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.54291i | − 0.0858497i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.4331i | 2.13189i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.327367i | 0.0180483i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.8798 | −1.36752 | −0.683759 | − | 0.729708i | \(-0.739656\pi\) | ||||
−0.683759 | + | 0.729708i | \(0.739656\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.5429 | 2.10582 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.8036 | 1.18772 | 0.593860 | − | 0.804568i | \(-0.297603\pi\) | ||||
0.593860 | + | 0.804568i | \(0.297603\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.3498 | 1.10201 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 20.7794i | − 1.11550i | −0.830010 | − | 0.557748i | \(-0.811665\pi\) | ||||
0.830010 | − | 0.557748i | \(-0.188335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 30.5928i | − 1.63760i | −0.574081 | − | 0.818799i | \(-0.694640\pi\) | ||||
0.574081 | − | 0.818799i | \(-0.305360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.5174i | 1.03881i | 0.854529 | + | 0.519403i | \(0.173846\pi\) | ||||
−0.854529 | + | 0.519403i | \(0.826154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.7466 | 2.00338 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.3969 | −1.07651 | −0.538254 | − | 0.842783i | \(-0.680916\pi\) | ||||
−0.538254 | + | 0.842783i | \(0.680916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.66111 | −0.508479 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.74203 | 0.0911818 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.6785i | 1.34041i | 0.742177 | + | 0.670203i | \(0.233793\pi\) | ||||
−0.742177 | + | 0.670203i | \(0.766207\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 8.32940i | − 0.432441i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12.4313i | − 0.643669i | −0.946796 | − | 0.321835i | \(-0.895700\pi\) | ||||
0.946796 | − | 0.321835i | \(-0.104300\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.8548i | 0.559053i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.90048 | 0.508553 | 0.254277 | − | 0.967132i | \(-0.418163\pi\) | ||||
0.254277 | + | 0.967132i | \(0.418163\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.6536 | 1.20864 | 0.604320 | − | 0.796741i | \(-0.293445\pi\) | ||||
0.604320 | + | 0.796741i | \(0.293445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.81021 | 0.398045 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.14513 | 0.159465 | 0.0797323 | − | 0.996816i | \(-0.474593\pi\) | ||||
0.0797323 | + | 0.996816i | \(0.474593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.01532i | 0.152491i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.1150i | 1.26367i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.2176i | 0.613183i | 0.951841 | + | 0.306592i | \(0.0991886\pi\) | ||||
−0.951841 | + | 0.306592i | \(0.900811\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.0797i | 1.75180i | 0.482494 | + | 0.875899i | \(0.339731\pi\) | ||||
−0.482494 | + | 0.875899i | \(0.660269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.5227 | 1.66988 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.2237 | −1.05202 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.3489 | −1.35231 | −0.676157 | − | 0.736757i | \(-0.736356\pi\) | ||||
−0.676157 | + | 0.736757i | \(0.736356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.98008 | 0.294260 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 10.9739i | − 0.538687i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 14.6442i | − 0.715417i | −0.933833 | − | 0.357709i | \(-0.883558\pi\) | ||||
0.933833 | − | 0.357709i | \(-0.116442\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 20.2168i | − 0.985305i | −0.870226 | − | 0.492653i | \(-0.836027\pi\) | ||||
0.870226 | − | 0.492653i | \(-0.163973\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.30822i | 0.305994i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.2783 | −0.642583 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.6656 | 0.947260 | 0.473630 | − | 0.880724i | \(-0.342943\pi\) | ||||
0.473630 | + | 0.880724i | \(0.342943\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.9996 | 0.576666 | 0.288333 | − | 0.957530i | \(-0.406899\pi\) | ||||
0.288333 | + | 0.957530i | \(0.406899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.2511 | −0.873068 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.82113i | 0.373282i | 0.982428 | + | 0.186641i | \(0.0597601\pi\) | ||||
−0.982428 | + | 0.186641i | \(0.940240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.9854i | 1.42465i | 0.701850 | + | 0.712325i | \(0.252358\pi\) | ||||
−0.701850 | + | 0.712325i | \(0.747642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.8195i | 1.12915i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 42.0892i | − 1.98631i | −0.116797 | − | 0.993156i | \(-0.537263\pi\) | ||||
0.116797 | − | 0.993156i | \(-0.462737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5745 | 0.639198 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.8659 | 0.603163 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.1655 | −0.569079 | −0.284540 | − | 0.958664i | \(-0.591841\pi\) | ||||
−0.284540 | + | 0.958664i | \(0.591841\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.0054 | −1.35091 | −0.675457 | − | 0.737399i | \(-0.736054\pi\) | ||||
−0.675457 | + | 0.737399i | \(0.736054\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.21317i | 0.242277i | 0.992636 | + | 0.121138i | \(0.0386545\pi\) | ||||
−0.992636 | + | 0.121138i | \(0.961346\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 12.3061i | − 0.569460i | −0.958608 | − | 0.284730i | \(-0.908096\pi\) | ||||
0.958608 | − | 0.284730i | \(-0.0919039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 9.21499i | − 0.425509i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 16.8452i | − 0.774545i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.1823 | −1.75192 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.9609 | 0.912038 | 0.456019 | − | 0.889970i | \(-0.349275\pi\) | ||||
0.456019 | + | 0.889970i | \(0.349275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.9622 | −1.59414 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.9862 | 1.17997 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.61420i | − 0.254404i | −0.991877 | − | 0.127202i | \(-0.959400\pi\) | ||||
0.991877 | − | 0.127202i | \(-0.0405996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.07131i | 0.409382i | 0.978827 | + | 0.204691i | \(0.0656190\pi\) | ||||
−0.978827 | + | 0.204691i | \(0.934381\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.78166i | 0.0802418i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 9.02460i | − 0.404809i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.4346 | 1.63103 | 0.815517 | − | 0.578732i | \(-0.196452\pi\) | ||||
0.815517 | + | 0.578732i | \(0.196452\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.10995 | 0.183253 | 0.0916267 | − | 0.995793i | \(-0.470793\pi\) | ||||
0.0916267 | + | 0.995793i | \(0.470793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.74688 | −0.344732 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5175 | −0.776450 | −0.388225 | − | 0.921565i | \(-0.626912\pi\) | ||||
−0.388225 | + | 0.921565i | \(0.626912\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 0.416491i | − 0.0184245i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.4605i | 0.505008i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 0.611291i | − 0.0268845i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.7567i | 1.78558i | 0.450472 | + | 0.892791i | \(0.351256\pi\) | ||||
−0.450472 | + | 0.892791i | \(0.648744\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.03412 | −0.307581 | −0.153790 | − | 0.988103i | \(-0.549148\pi\) | ||||
−0.153790 | + | 0.988103i | \(0.549148\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.50225 | 0.239682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.6683 | 0.550794 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.3615 | 0.968586 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.6718i | 0.764020i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.86730i | − 0.0804302i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 19.6764i | − 0.845953i | −0.906141 | − | 0.422976i | \(-0.860985\pi\) | ||||
0.906141 | − | 0.422976i | \(-0.139015\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 58.3140i | 2.49790i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8078 | −0.761408 | −0.380704 | − | 0.924697i | \(-0.624318\pi\) | ||||
−0.380704 | + | 0.924697i | \(0.624318\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.7840 | −0.459413 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00459 | 0.255341 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.99646 | 0.254078 | 0.127039 | − | 0.991898i | \(-0.459453\pi\) | ||||
0.127039 | + | 0.991898i | \(0.459453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 27.7495i | − 1.17368i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.4848i | 0.863333i | 0.902033 | + | 0.431667i | \(0.142074\pi\) | ||||
−0.902033 | + | 0.431667i | \(0.857926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.3466i | 1.31876i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 38.1889i | − 1.60096i | −0.599359 | − | 0.800480i | \(-0.704578\pi\) | ||||
0.599359 | − | 0.800480i | \(-0.295422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3551 | −0.475198 | −0.237599 | − | 0.971363i | \(-0.576360\pi\) | ||||
−0.237599 | + | 0.971363i | \(0.576360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 74.6200 | 3.11187 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.7869 | −0.865371 | −0.432685 | − | 0.901545i | \(-0.642434\pi\) | ||||
−0.432685 | + | 0.901545i | \(0.642434\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.62368 | −0.108849 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.5535i | 0.644159i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 24.3849i | − 1.00647i | −0.864148 | − | 0.503237i | \(-0.832142\pi\) | ||||
0.864148 | − | 0.503237i | \(-0.167858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.3039i | 1.37226i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 32.5053i | − 1.33483i | −0.744684 | − | 0.667417i | \(-0.767400\pi\) | ||||
0.744684 | − | 0.667417i | \(-0.232600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.11175 | 0.0865731 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.4800 | −0.428200 | −0.214100 | − | 0.976812i | \(-0.568682\pi\) | ||||
−0.214100 | + | 0.976812i | \(0.568682\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4946 | −0.917575 | −0.458787 | − | 0.888546i | \(-0.651716\pi\) | ||||
−0.458787 | + | 0.888546i | \(0.651716\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.4249 | 1.27761 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 32.3672i | − 1.31374i | −0.754002 | − | 0.656872i | \(-0.771879\pi\) | ||||
0.754002 | − | 0.656872i | \(-0.228121\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.00699i | − 0.0407385i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 34.8714i | − 1.40844i | −0.709981 | − | 0.704220i | \(-0.751297\pi\) | ||||
0.709981 | − | 0.704220i | \(-0.248703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.47324i | 0.0995688i | 0.998760 | + | 0.0497844i | \(0.0158534\pi\) | ||||
−0.998760 | + | 0.0497844i | \(0.984147\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2375 | 0.612447 | 0.306223 | − | 0.951960i | \(-0.400935\pi\) | ||||
0.306223 | + | 0.951960i | \(0.400935\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.69486 | 0.228160 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 68.6375 | 2.74550 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.73852 | −0.228810 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2064i | 0.923832i | 0.886924 | + | 0.461916i | \(0.152838\pi\) | ||||
−0.886924 | + | 0.461916i | \(0.847162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 75.6800i | 3.00327i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.07604i | − 0.121877i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 29.5988i | − 1.16908i | −0.811364 | − | 0.584541i | \(-0.801275\pi\) | ||||
0.811364 | − | 0.584541i | \(-0.198725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.8060 | −1.13600 | −0.567999 | − | 0.823029i | \(-0.692282\pi\) | ||||
−0.567999 | + | 0.823029i | \(0.692282\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.3622 | 1.07572 | 0.537860 | − | 0.843034i | \(-0.319233\pi\) | ||||
0.537860 | + | 0.843034i | \(0.319233\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.1666 | −0.438327 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.9292 | −1.56255 | −0.781275 | − | 0.624187i | \(-0.785430\pi\) | ||||
−0.781275 | + | 0.624187i | \(0.785430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.0082i | 1.52418i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 14.9809i | − 0.583572i | −0.956484 | − | 0.291786i | \(-0.905751\pi\) | ||||
0.956484 | − | 0.291786i | \(-0.0942495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0963i | 1.28730i | 0.765322 | + | 0.643648i | \(0.222580\pi\) | ||||
−0.765322 | + | 0.643648i | \(0.777420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.7819i | 0.495662i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0753 | 0.816037 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.7945 | 0.957183 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.1189 | −0.467150 | −0.233575 | − | 0.972339i | \(-0.575043\pi\) | ||||
−0.233575 | + | 0.972339i | \(0.575043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.7231 | 1.06549 | 0.532743 | − | 0.846277i | \(-0.321161\pi\) | ||||
0.532743 | + | 0.846277i | \(0.321161\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 6.21289i | − 0.238429i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.79813i | 0.374915i | 0.982273 | + | 0.187457i | \(0.0600247\pi\) | ||||
−0.982273 | + | 0.187457i | \(0.939975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 27.3155i | − 1.04367i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.6215i | 0.976103i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.4765 | 1.42567 | 0.712837 | − | 0.701330i | \(-0.247410\pi\) | ||||
0.712837 | + | 0.701330i | \(0.247410\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 42.4908 | 1.61177 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.67031 | 0.139023 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.6525 | −0.855575 | −0.427787 | − | 0.903879i | \(-0.640707\pi\) | ||||
−0.427787 | + | 0.903879i | \(0.640707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 34.7340i | − 1.31002i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.85216i | 0.0696575i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.58535i | − 0.0595393i | −0.999557 | − | 0.0297696i | \(-0.990523\pi\) | ||||
0.999557 | − | 0.0297696i | \(-0.00947737\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 65.0861i | − 2.43749i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0245 | −0.898465 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.7228 | 0.660948 | 0.330474 | − | 0.943815i | \(-0.392791\pi\) | ||||
0.330474 | + | 0.943815i | \(0.392791\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.74001 | 0.102043 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44.0906 | 1.63749 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 3.31812i | − 0.123062i | −0.998105 | − | 0.0615312i | \(-0.980402\pi\) | ||||
0.998105 | − | 0.0615312i | \(-0.0195984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 4.55467i | − 0.168460i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 18.8547i | − 0.696414i | −0.937418 | − | 0.348207i | \(-0.886791\pi\) | ||||
0.937418 | − | 0.348207i | \(-0.113209\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.2071i | 0.633832i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.3560 | 1.22702 | 0.613510 | − | 0.789687i | \(-0.289757\pi\) | ||||
0.613510 | + | 0.789687i | \(0.289757\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.0826 | −0.993565 | −0.496783 | − | 0.867875i | \(-0.665485\pi\) | ||||
−0.496783 | + | 0.867875i | \(0.665485\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.6767 | 1.49028 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.22506 | 0.154380 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.3284i | 1.61757i | 0.588107 | + | 0.808783i | \(0.299874\pi\) | ||||
−0.588107 | + | 0.808783i | \(0.700126\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 52.1421i | − 1.89765i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.3093i | 0.447391i | 0.974659 | + | 0.223695i | \(0.0718121\pi\) | ||||
−0.974659 | + | 0.223695i | \(0.928188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.85054i | 0.0670820i | 0.999437 | + | 0.0335410i | \(0.0106784\pi\) | ||||
−0.999437 | + | 0.0335410i | \(0.989322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.9420 | 0.504733 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.3949 | −0.664203 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.2463 | −1.12677 | −0.563386 | − | 0.826194i | \(-0.690502\pi\) | ||||
−0.563386 | + | 0.826194i | \(0.690502\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.4521 | −1.59883 | −0.799415 | − | 0.600779i | \(-0.794857\pi\) | ||||
−0.799415 | + | 0.600779i | \(0.794857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 136.164i | − 4.89115i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.2156i | 0.795956i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.8516i | 0.602998i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.5257i | 1.69627i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0995 | −1.00164 | −0.500820 | − | 0.865551i | \(-0.666968\pi\) | ||||
−0.500820 | + | 0.865551i | \(0.666968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.49447 | 0.266473 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.8446 | 1.45043 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.9492 | 1.52134 | 0.760670 | − | 0.649139i | \(-0.224871\pi\) | ||||
0.760670 | + | 0.649139i | \(0.224871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 0.165282i | − 0.00584727i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.777712i | 0.0274449i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 24.9799i | − 0.880425i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.54301i | 0.300356i | 0.988659 | + | 0.150178i | \(0.0479847\pi\) | ||||
−0.988659 | + | 0.150178i | \(0.952015\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6880 | −1.21806 | −0.609030 | − | 0.793147i | \(-0.708441\pi\) | ||||
−0.609030 | + | 0.793147i | \(0.708441\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.0344 | 0.526632 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.5684 | 0.964497 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.46951 | −0.295588 | −0.147794 | − | 0.989018i | \(-0.547217\pi\) | ||||
−0.147794 | + | 0.989018i | \(0.547217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 44.5109i | − 1.55155i | −0.631008 | − | 0.775777i | \(-0.717358\pi\) | ||||
0.631008 | − | 0.775777i | \(-0.282642\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 36.3895i | − 1.26539i | −0.774403 | − | 0.632693i | \(-0.781949\pi\) | ||||
0.774403 | − | 0.632693i | \(-0.218051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 39.2607i | − 1.36358i | −0.731548 | − | 0.681790i | \(-0.761202\pi\) | ||||
0.731548 | − | 0.681790i | \(-0.238798\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.504885i | − 0.0174932i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −85.2425 | −2.94994 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.1101 | 0.521659 | 0.260830 | − | 0.965385i | \(-0.416004\pi\) | ||||
0.260830 | + | 0.965385i | \(0.416004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5473 | −0.570596 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.7981 | 0.509072 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 7.51320i | − 0.258157i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 67.8810i | 2.32693i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 23.4153i | − 0.801724i | −0.916138 | − | 0.400862i | \(-0.868711\pi\) | ||||
0.916138 | − | 0.400862i | \(-0.131289\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.7800i | 0.709833i | 0.934898 | + | 0.354916i | \(0.115491\pi\) | ||||
−0.934898 | + | 0.354916i | \(0.884509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0088 | −0.409735 | −0.204868 | − | 0.978790i | \(-0.565676\pi\) | ||||
−0.204868 | + | 0.978790i | \(0.565676\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.5254 | 0.392328 | 0.196164 | − | 0.980571i | \(-0.437151\pi\) | ||||
0.196164 | + | 0.980571i | \(0.437151\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.8118 | −0.639622 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.2123 | −0.380353 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.3456i | 0.960455i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 31.3462i | − 1.05969i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 7.25986i | − 0.245148i | −0.992459 | − | 0.122574i | \(-0.960885\pi\) | ||||
0.992459 | − | 0.122574i | \(-0.0391149\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.7411i | 0.361876i | 0.983495 | + | 0.180938i | \(0.0579133\pi\) | ||||
−0.983495 | + | 0.180938i | \(0.942087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.09009 | −0.305906 | −0.152953 | − | 0.988233i | \(-0.548878\pi\) | ||||
−0.152953 | + | 0.988233i | \(0.548878\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.0988 | −0.977041 | −0.488521 | − | 0.872552i | \(-0.662463\pi\) | ||||
−0.488521 | + | 0.872552i | \(0.662463\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0939 | 0.606850 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.00042 | 0.0334778 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 11.0183i | − 0.368301i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 38.4574i | − 1.28262i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.20539i | 0.140102i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 43.3938i | − 1.44246i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.9962 | −0.996008 | −0.498004 | − | 0.867175i | \(-0.665933\pi\) | ||||
−0.498004 | + | 0.867175i | \(0.665933\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.3253 | −1.43543 | −0.717716 | − | 0.696336i | \(-0.754812\pi\) | ||||
−0.717716 | + | 0.696336i | \(0.754812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.89919 | 0.162140 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.32625 | 0.307980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.6079i | 1.47148i | 0.677264 | + | 0.735740i | \(0.263165\pi\) | ||||
−0.677264 | + | 0.735740i | \(0.736835\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.7600i | 0.913732i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 142.011i | 4.66929i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 7.73251i | − 0.253695i | −0.991922 | − | 0.126848i | \(-0.959514\pi\) | ||||
0.991922 | − | 0.126848i | \(-0.0404860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.05596 | 0.100155 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.94326 | −0.128958 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.6210 | 0.837002 | 0.418501 | − | 0.908216i | \(-0.362556\pi\) | ||||
0.418501 | + | 0.908216i | \(0.362556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.8529 | 1.00578 | 0.502888 | − | 0.864352i | \(-0.332271\pi\) | ||||
0.502888 | + | 0.864352i | \(0.332271\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 43.4161i | − 1.41382i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 39.5682i | − 1.28579i | −0.765953 | − | 0.642897i | \(-0.777732\pi\) | ||||
0.765953 | − | 0.642897i | \(-0.222268\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.28114i | 0.0415876i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.36408i | 0.141366i | 0.997499 | + | 0.0706832i | \(0.0225179\pi\) | ||||
−0.997499 | + | 0.0706832i | \(0.977482\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −76.0015 | −2.45935 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.53069 | −0.210887 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −87.7668 | −2.83119 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −70.1442 | −2.25802 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.1938i | 1.64628i | 0.567837 | + | 0.823141i | \(0.307780\pi\) | ||||
−0.567837 | + | 0.823141i | \(0.692220\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 47.6773i | − 1.53004i | −0.644008 | − | 0.765019i | \(-0.722730\pi\) | ||||
0.644008 | − | 0.765019i | \(-0.277270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 10.1589i | − 0.325678i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 10.1656i | − 0.325225i | −0.986690 | − | 0.162613i | \(-0.948008\pi\) | ||||
0.986690 | − | 0.162613i | \(-0.0519921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6340 | −0.339864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.35716 | −0.234657 | −0.117328 | − | 0.993093i | \(-0.537433\pi\) | ||||
−0.117328 | + | 0.993093i | \(0.537433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −80.4068 | −2.56197 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.8772 | −1.71320 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.5907i | 0.590552i | 0.955412 | + | 0.295276i | \(0.0954116\pi\) | ||||
−0.955412 | + | 0.295276i | \(0.904588\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 7.06577i | − 0.224000i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.19288i | 0.132790i | 0.997793 | + | 0.0663950i | \(0.0211497\pi\) | ||||
−0.997793 | + | 0.0663950i | \(0.978850\pi\) | |||||||
\(998\) | 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 | 6048.2.j.d.5615.47 | 48 | ||
3.2 | odd | 2 | inner | 6048.2.j.d.5615.2 | 48 | ||
4.3 | odd | 2 | 1512.2.j.d.323.4 | yes | 48 | ||
8.3 | odd | 2 | inner | 6048.2.j.d.5615.1 | 48 | ||
8.5 | even | 2 | 1512.2.j.d.323.46 | yes | 48 | ||
12.11 | even | 2 | 1512.2.j.d.323.45 | yes | 48 | ||
24.5 | odd | 2 | 1512.2.j.d.323.3 | ✓ | 48 | ||
24.11 | even | 2 | inner | 6048.2.j.d.5615.48 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.3 | ✓ | 48 | 24.5 | odd | 2 | ||
1512.2.j.d.323.4 | yes | 48 | 4.3 | odd | 2 | ||
1512.2.j.d.323.45 | yes | 48 | 12.11 | even | 2 | ||
1512.2.j.d.323.46 | yes | 48 | 8.5 | even | 2 | ||
6048.2.j.d.5615.1 | 48 | 8.3 | odd | 2 | inner | ||
6048.2.j.d.5615.2 | 48 | 3.2 | odd | 2 | inner | ||
6048.2.j.d.5615.47 | 48 | 1.1 | even | 1 | trivial | ||
6048.2.j.d.5615.48 | 48 | 24.11 | even | 2 | inner |