Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(3005,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.3005");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3005.2 | ||
Character | \(\chi\) | \(=\) | 6012.3005 |
Dual form | 6012.2.h.a.3005.1 |
$q$-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 \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).
\(n\) | \(3007\) | \(3341\) | \(4681\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.09297 | −1.83043 | −0.915216 | − | 0.402963i | \(-0.867980\pi\) | ||||
−0.915216 | + | 0.402963i | \(0.867980\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.29241 | 0.866449 | 0.433224 | − | 0.901286i | \(-0.357376\pi\) | ||||
0.433224 | + | 0.901286i | \(0.357376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.40323i | − | 0.423089i | −0.977368 | − | 0.211545i | \(-0.932151\pi\) | ||
0.977368 | − | 0.211545i | \(-0.0678494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.26451i | − | 1.46011i | −0.683387 | − | 0.730057i | \(-0.739494\pi\) | ||
0.683387 | − | 0.730057i | \(-0.260506\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.313267 | −0.0759783 | −0.0379891 | − | 0.999278i | \(-0.512095\pi\) | ||||
−0.0379891 | + | 0.999278i | \(0.512095\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.473923 | −0.108725 | −0.0543627 | − | 0.998521i | \(-0.517313\pi\) | ||||
−0.0543627 | + | 0.998521i | \(0.517313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.04034 | 1.67653 | 0.838263 | − | 0.545265i | \(-0.183571\pi\) | ||||
0.838263 | + | 0.545265i | \(0.183571\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.7524 | 2.35048 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.26656i | 0.420889i | 0.977606 | + | 0.210445i | \(0.0674912\pi\) | ||||
−0.977606 | + | 0.210445i | \(0.932509\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.40647 | 0.252609 | 0.126304 | − | 0.991992i | \(-0.459688\pi\) | ||||
0.126304 | + | 0.991992i | \(0.459688\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.38276 | −1.58598 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.51582i | 0.577997i | 0.957330 | + | 0.288998i | \(0.0933222\pi\) | ||||
−0.957330 | + | 0.288998i | \(0.906678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.02537 | −0.316310 | −0.158155 | − | 0.987414i | \(-0.550554\pi\) | ||||
−0.158155 | + | 0.987414i | \(0.550554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.09211i | − | 1.08154i | −0.841171 | − | 0.540769i | \(-0.818133\pi\) | ||
0.841171 | − | 0.540769i | \(-0.181867\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.55435i | 1.24778i | 0.781512 | + | 0.623890i | \(0.214449\pi\) | ||||
−0.781512 | + | 0.623890i | \(0.785551\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74486 | −0.249266 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.65647 | −1.18906 | −0.594529 | − | 0.804074i | \(-0.702661\pi\) | ||||
−0.594529 | + | 0.804074i | \(0.702661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.74337i | 0.774436i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.04140 | 0.265767 | 0.132884 | − | 0.991132i | \(-0.457576\pi\) | ||||
0.132884 | + | 0.991132i | \(0.457576\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9929 | 1.53554 | 0.767770 | − | 0.640726i | \(-0.221366\pi\) | ||||
0.767770 | + | 0.640726i | \(0.221366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.5475i | 2.67264i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.40852i | − | 0.294247i | −0.989118 | − | 0.147124i | \(-0.952998\pi\) | ||
0.989118 | − | 0.147124i | \(-0.0470016\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6701 | −1.26631 | −0.633153 | − | 0.774027i | \(-0.718240\pi\) | ||||
−0.633153 | + | 0.774027i | \(0.718240\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.44685i | 0.637505i | 0.947838 | + | 0.318753i | \(0.103264\pi\) | ||||
−0.947838 | + | 0.318753i | \(0.896736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.21677i | − | 0.366585i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.13005i | 0.352158i | 0.984376 | + | 0.176079i | \(0.0563415\pi\) | ||||
−0.984376 | + | 0.176079i | \(0.943659\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.01486 | −0.550452 | −0.275226 | − | 0.961380i | \(-0.588753\pi\) | ||||
−0.275226 | + | 0.961380i | \(0.588753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.28219 | 0.139073 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.62776i | 0.384542i | 0.981342 | + | 0.192271i | \(0.0615853\pi\) | ||||
−0.981342 | + | 0.192271i | \(0.938415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 12.0684i | − | 1.26511i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.93975 | 0.199014 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.7994 | 1.40111 | 0.700557 | − | 0.713596i | \(-0.252935\pi\) | ||||
0.700557 | + | 0.713596i | \(0.252935\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.20749 | 0.418661 | 0.209330 | − | 0.977845i | \(-0.432872\pi\) | ||||
0.209330 | + | 0.977845i | \(0.432872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.4177i | − | 1.71621i | −0.513470 | − | 0.858107i | \(-0.671640\pi\) | ||
0.513470 | − | 0.858107i | \(-0.328360\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.21671i | − | 0.891013i | −0.895279 | − | 0.445507i | \(-0.853024\pi\) | ||
0.895279 | − | 0.445507i | \(-0.146976\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.7151i | − | 1.31367i | −0.754036 | − | 0.656833i | \(-0.771895\pi\) | ||
0.754036 | − | 0.656833i | \(-0.228105\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9552 | −1.12465 | −0.562326 | − | 0.826916i | \(-0.690093\pi\) | ||||
−0.562326 | + | 0.826916i | \(0.690093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −32.9089 | −3.06877 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.718135 | −0.0658313 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.03095 | 0.820996 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −27.6375 | −2.47197 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.269256 | 0.0238926 | 0.0119463 | − | 0.999929i | \(-0.496197\pi\) | ||||
0.0119463 | + | 0.999929i | \(0.496197\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7781 | 0.941688 | 0.470844 | − | 0.882217i | \(-0.343949\pi\) | ||||
0.470844 | + | 0.882217i | \(0.343949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.08642 | −0.0942049 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 13.6657i | − | 1.16754i | −0.811920 | − | 0.583768i | \(-0.801578\pi\) | ||
0.811920 | − | 0.583768i | \(-0.198422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.54589i | 0.724853i | 0.932012 | + | 0.362426i | \(0.118052\pi\) | ||||
−0.932012 | + | 0.362426i | \(0.881948\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.38731 | −0.617758 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.27696i | − | 0.770409i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.13771 | −0.338974 | −0.169487 | − | 0.985532i | \(-0.554211\pi\) | ||||
−0.169487 | + | 0.985532i | \(0.554211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.7983i | − | 1.12289i | −0.827515 | − | 0.561443i | \(-0.810246\pi\) | ||
0.827515 | − | 0.561443i | \(-0.189754\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.75662 | −0.462383 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.9049 | −1.26935 | −0.634675 | − | 0.772779i | \(-0.718866\pi\) | ||||
−0.634675 | + | 0.772779i | \(0.718866\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.4317 | 1.45263 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.80969i | − | 0.768354i | −0.923259 | − | 0.384177i | \(-0.874485\pi\) | ||
0.923259 | − | 0.384177i | \(-0.125515\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.8941 | − | 5.05270i | 0.920395 | − | 0.390990i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.7151 | −1.13193 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.08630i | − | 0.310675i | −0.987861 | − | 0.155338i | \(-0.950353\pi\) | ||
0.987861 | − | 0.155338i | \(-0.0496466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26.9413 | 2.03657 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 25.8548i | − | 1.93248i | −0.257650 | − | 0.966238i | \(-0.582948\pi\) | ||
0.257650 | − | 0.966238i | \(-0.417052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.62380 | 0.343685 | 0.171842 | − | 0.985124i | \(-0.445028\pi\) | ||||
0.171842 | + | 0.985124i | \(0.445028\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 14.3901i | − | 1.05798i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.439584i | 0.0321456i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20.0201i | − | 1.44861i | −0.689482 | − | 0.724303i | \(-0.742162\pi\) | ||
0.689482 | − | 0.724303i | \(-0.257838\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.5047i | 1.83586i | 0.396737 | + | 0.917932i | \(0.370143\pi\) | ||||
−0.396737 | + | 0.917932i | \(0.629857\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.7184 | 1.33363 | 0.666817 | − | 0.745222i | \(-0.267656\pi\) | ||||
0.666817 | + | 0.745222i | \(0.267656\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.99785 | 0.141624 | 0.0708120 | − | 0.997490i | \(-0.477441\pi\) | ||||
0.0708120 | + | 0.997490i | \(0.477441\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.19588i | 0.364679i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.28978 | 0.578983 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.665022i | 0.0460005i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.85976 | −0.541088 | −0.270544 | − | 0.962708i | \(-0.587204\pi\) | ||||
−0.270544 | + | 0.962708i | \(0.587204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.0278i | 1.97968i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.22419 | 0.218873 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.64920i | 0.110937i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.96950 | −0.667607 | −0.333803 | − | 0.942643i | \(-0.608332\pi\) | ||||
−0.333803 | + | 0.942643i | \(0.608332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.58319 | −0.171452 | −0.0857262 | − | 0.996319i | \(-0.527321\pi\) | ||||
−0.0857262 | + | 0.996319i | \(0.527321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0922633 | −0.00609693 | −0.00304846 | − | 0.999995i | \(-0.500970\pi\) | ||||
−0.00304846 | + | 0.999995i | \(0.500970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.0534i | 1.44477i | 0.691492 | + | 0.722384i | \(0.256954\pi\) | ||||
−0.691492 | + | 0.722384i | \(0.743046\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 35.0127i | − | 2.28398i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 21.9512i | − | 1.41991i | −0.704249 | − | 0.709953i | \(-0.748716\pi\) | ||
0.704249 | − | 0.709953i | \(-0.251284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.8816i | 1.34510i | 0.740052 | + | 0.672550i | \(0.234801\pi\) | ||||
−0.740052 | + | 0.672550i | \(0.765199\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.14168 | 0.456265 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.49497i | 0.158751i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.8849i | − | 0.939526i | −0.882793 | − | 0.469763i | \(-0.844339\pi\) | ||
0.882793 | − | 0.469763i | \(-0.155661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 11.2824i | − | 0.709320i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.502162 | 0.0313240 | 0.0156620 | − | 0.999877i | \(-0.495014\pi\) | ||||
0.0156620 | + | 0.999877i | \(0.495014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.05969i | 0.500804i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.6073i | 1.08571i | 0.839826 | + | 0.542855i | \(0.182657\pi\) | ||||
−0.839826 | + | 0.542855i | \(0.817343\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.4307 | 2.17649 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.56273 | 0.217223 | 0.108612 | − | 0.994084i | \(-0.465359\pi\) | ||||
0.108612 | + | 0.994084i | \(0.465359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.9568i | 1.03005i | 0.857174 | + | 0.515027i | \(0.172218\pi\) | ||||
−0.857174 | + | 0.515027i | \(0.827782\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 16.4913i | − | 0.994464i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 16.7583i | − | 1.00691i | −0.864022 | − | 0.503454i | \(-0.832062\pi\) | ||
0.864022 | − | 0.503454i | \(-0.167938\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.5849i | − | 0.750752i | −0.926873 | − | 0.375376i | \(-0.877514\pi\) | ||
0.926873 | − | 0.375376i | \(-0.122486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.95647 | 0.354075 | 0.177038 | − | 0.984204i | \(-0.443349\pi\) | ||||
0.177038 | + | 0.984204i | \(0.443349\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.64297 | −0.274066 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9019 | −0.994227 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1176i | 0.649494i | 0.945801 | + | 0.324747i | \(0.105279\pi\) | ||||
−0.945801 | + | 0.324747i | \(0.894721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.35539 | −0.486469 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 42.3285i | − | 2.44792i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 16.2580i | − | 0.937097i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −49.0868 | −2.81070 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.18955i | 0.124964i | 0.998046 | + | 0.0624821i | \(0.0199016\pi\) | ||||
−0.998046 | + | 0.0624821i | \(0.980098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 23.8065i | − | 1.34994i | −0.737844 | − | 0.674971i | \(-0.764156\pi\) | ||
0.737844 | − | 0.674971i | \(-0.235844\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.6598i | − | 1.22428i | −0.790748 | − | 0.612142i | \(-0.790308\pi\) | ||
0.790748 | − | 0.612142i | \(-0.209692\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 28.9496i | − | 1.62597i | −0.582282 | − | 0.812987i | \(-0.697840\pi\) | ||
0.582282 | − | 0.812987i | \(-0.302160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.18050 | 0.178074 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.148464 | 0.00826076 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 61.8708i | − | 3.43197i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.6101i | 1.08114i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 30.2737i | − | 1.66400i | −0.554779 | − | 0.831998i | \(-0.687197\pi\) | ||
0.554779 | − | 0.831998i | \(-0.312803\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.85800i | 0.538600i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.69185 | 0.0921611 | 0.0460805 | − | 0.998938i | \(-0.485327\pi\) | ||||
0.0460805 | + | 0.998938i | \(0.485327\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.97359i | − | 0.106876i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0468 | −1.08243 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.9707 | 1.01840 | 0.509201 | − | 0.860648i | \(-0.329941\pi\) | ||||
0.509201 | + | 0.860648i | \(0.329941\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.5336i | − | 0.563849i | −0.959437 | − | 0.281925i | \(-0.909027\pi\) | ||
0.959437 | − | 0.281925i | \(-0.0909728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.52080i | 0.506741i | 0.967369 | + | 0.253370i | \(0.0815392\pi\) | ||||
−0.967369 | + | 0.253370i | \(0.918461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 43.6724 | 2.31789 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.5816i | 0.822366i | 0.911553 | + | 0.411183i | \(0.134884\pi\) | ||||
−0.911553 | + | 0.411183i | \(0.865116\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7754 | −0.988179 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 22.2938i | − | 1.16691i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.7003 | −1.65474 | −0.827371 | − | 0.561655i | \(-0.810165\pi\) | ||||
−0.827371 | + | 0.561655i | \(0.810165\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.8442 | −1.03026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.7719i | − | 0.971973i | −0.873966 | − | 0.485986i | \(-0.838460\pi\) | ||
0.873966 | − | 0.485986i | \(-0.161540\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.9323 | 0.614546 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.3145i | 1.24895i | 0.781045 | + | 0.624475i | \(0.214687\pi\) | ||||
−0.781045 | + | 0.624475i | \(0.785313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 26.0531i | − | 1.33125i | −0.746285 | − | 0.665627i | \(-0.768164\pi\) | ||
0.746285 | − | 0.665627i | \(-0.231836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.1662i | 0.671009i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.3750 | −1.54007 | −0.770036 | − | 0.638001i | \(-0.779762\pi\) | ||||
−0.770036 | + | 0.638001i | \(0.779762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.51877 | −0.127380 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 12.8112i | − | 0.644602i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.8263 | −0.995053 | −0.497527 | − | 0.867449i | \(-0.665758\pi\) | ||||
−0.497527 | + | 0.867449i | \(0.665758\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.0482552 | −0.00240975 | −0.00120487 | − | 0.999999i | \(-0.500384\pi\) | ||||
−0.00120487 | + | 0.999999i | \(0.500384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.40436i | − | 0.368837i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.93349 | 0.244544 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5257 | 0.668804 | 0.334402 | − | 0.942431i | \(-0.391466\pi\) | ||||
0.334402 | + | 0.942431i | \(0.391466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.67972 | 0.230274 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.5257 | 1.00757 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.3643i | 0.604036i | 0.953302 | + | 0.302018i | \(0.0976603\pi\) | ||||
−0.953302 | + | 0.302018i | \(0.902340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.8891 | −1.65166 | −0.825828 | − | 0.563923i | \(-0.809292\pi\) | ||||
−0.825828 | + | 0.563923i | \(0.809292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.68164 | −0.178586 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.4927 | 1.33047 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.6335i | − | 0.608534i | −0.952587 | − | 0.304267i | \(-0.901589\pi\) | ||
0.952587 | − | 0.304267i | \(-0.0984115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.31009 | 0.399357 | 0.199679 | − | 0.979861i | \(-0.436010\pi\) | ||||
0.199679 | + | 0.979861i | \(0.436010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.81050 | −0.182281 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 32.4531i | − | 1.54890i | −0.632634 | − | 0.774451i | \(-0.718026\pi\) | ||
0.632634 | − | 0.774451i | \(-0.281974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.84588 | −0.325258 | −0.162629 | − | 0.986687i | \(-0.551997\pi\) | ||||
−0.162629 | + | 0.986687i | \(0.551997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 14.8483i | − | 0.703879i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.2495i | − | 0.814056i | −0.913416 | − | 0.407028i | \(-0.866565\pi\) | ||
0.913416 | − | 0.407028i | \(-0.133435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.84205i | 0.133827i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 49.3957i | 2.31571i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 23.2886i | − | 1.08939i | −0.838633 | − | 0.544697i | \(-0.816645\pi\) | ||
0.838633 | − | 0.544697i | \(-0.183355\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.93021i | − | 0.0898990i | −0.998989 | − | 0.0449495i | \(-0.985687\pi\) | ||
0.998989 | − | 0.0449495i | \(-0.0143127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.27902i | 0.338285i | 0.985592 | + | 0.169142i | \(0.0540998\pi\) | ||||
−0.985592 | + | 0.169142i | \(0.945900\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.77061i | 0.220757i | 0.993890 | + | 0.110379i | \(0.0352064\pi\) | ||||
−0.993890 | + | 0.110379i | \(0.964794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.52131i | − | 0.254950i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.95185 | −0.457587 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.56974 | −0.255557 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.73270 | −0.0791691 | −0.0395846 | − | 0.999216i | \(-0.512603\pi\) | ||||
−0.0395846 | + | 0.999216i | \(0.512603\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.5091 | 0.843940 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −56.4805 | −2.56465 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9288i | 0.540544i | 0.962784 | + | 0.270272i | \(0.0871136\pi\) | ||||
−0.962784 | + | 0.270272i | \(0.912886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.7052i | − | 0.753895i | −0.926235 | − | 0.376948i | \(-0.876974\pi\) | ||
0.926235 | − | 0.376948i | \(-0.123026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.710037i | − | 0.0319784i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.4602 | −1.09719 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7439i | 0.615263i | 0.951506 | + | 0.307631i | \(0.0995364\pi\) | ||||
−0.951506 | + | 0.307631i | \(0.900464\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.44347i | − | 0.331888i | −0.986135 | − | 0.165944i | \(-0.946933\pi\) | ||
0.986135 | − | 0.165944i | \(-0.0530671\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.2211 | −0.766330 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.1790i | 0.894418i | 0.894429 | + | 0.447209i | \(0.147582\pi\) | ||||
−0.894429 | + | 0.447209i | \(0.852418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4864i | 0.552366i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 71.2901i | 3.14142i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0037 | 0.527922 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.8880 | 1.17798 | 0.588991 | − | 0.808139i | \(-0.299525\pi\) | ||||
0.588991 | + | 0.808139i | \(0.299525\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0539 | −0.876895 | −0.438448 | − | 0.898757i | \(-0.644472\pi\) | ||||
−0.438448 | + | 0.898757i | \(0.644472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.440599 | −0.0191928 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.6471 | 1.81074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.6626i | 0.461848i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.7238i | 1.63094i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.44844i | 0.105462i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 21.8696i | − | 0.940248i | −0.882600 | − | 0.470124i | \(-0.844209\pi\) | ||
0.882600 | − | 0.470124i | \(-0.155791\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 56.1355i | 2.40458i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.8845i | 1.27777i | 0.769303 | + | 0.638884i | \(0.220604\pi\) | ||||
−0.769303 | + | 0.638884i | \(0.779396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.07417i | − | 0.0457613i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.17536i | 0.305127i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.7789i | 1.30414i | 0.758158 | + | 0.652071i | \(0.226100\pi\) | ||||
−0.758158 | + | 0.652071i | \(0.773900\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.3365 | −1.57917 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.0579i | 1.05607i | 0.849224 | + | 0.528033i | \(0.177070\pi\) | ||||
−0.849224 | + | 0.528033i | \(0.822930\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 48.9323 | 2.05860 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.04649 | −0.211560 | −0.105780 | − | 0.994390i | \(-0.533734\pi\) | ||||
−0.105780 | + | 0.994390i | \(0.533734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5.72341i | − | 0.239517i | −0.992803 | − | 0.119759i | \(-0.961788\pi\) | ||
0.992803 | − | 0.119759i | \(-0.0382120\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 94.4935 | 3.94065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9725 | 0.789835 | 0.394917 | − | 0.918717i | \(-0.370773\pi\) | ||||
0.394917 | + | 0.918717i | \(0.370773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.4961 | −0.476939 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.1470i | 0.503077i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.7081 | −1.26746 | −0.633730 | − | 0.773554i | \(-0.718477\pi\) | ||||
−0.633730 | + | 0.773554i | \(0.718477\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.666556 | −0.0274650 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.8134 | −1.75814 | −0.879068 | − | 0.476696i | \(-0.841834\pi\) | ||||
−0.879068 | + | 0.476696i | \(0.841834\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.93931 | 0.120500 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.22309i | 0.213410i | 0.994291 | + | 0.106705i | \(0.0340300\pi\) | ||||
−0.994291 | + | 0.106705i | \(0.965970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.4071 | 1.48508 | 0.742538 | − | 0.669804i | \(-0.233622\pi\) | ||||
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.9634 | −1.50278 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.7018i | 0.677904i | 0.940804 | + | 0.338952i | \(0.110072\pi\) | ||||
−0.940804 | + | 0.338952i | \(0.889928\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 45.0345 | 1.82190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.1592 | −0.693055 | −0.346527 | − | 0.938040i | \(-0.612639\pi\) | ||||
−0.346527 | + | 0.938040i | \(0.612639\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 34.0578i | − | 1.37112i | −0.728017 | − | 0.685559i | \(-0.759558\pi\) | ||
0.728017 | − | 0.685559i | \(-0.240442\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 21.0690i | − | 0.846833i | −0.905935 | − | 0.423416i | \(-0.860831\pi\) | ||
0.905935 | − | 0.423416i | \(-0.139169\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.31632i | 0.333186i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 54.3573 | 2.17429 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.10139i | − | 0.0439152i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.2976 | 0.648797 | 0.324398 | − | 0.945921i | \(-0.394838\pi\) | ||||
0.324398 | + | 0.945921i | \(0.394838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.10206 | −0.0437337 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.18586i | 0.363957i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.8706 | −0.547858 | −0.273929 | − | 0.961750i | \(-0.588323\pi\) | ||||
−0.273929 | + | 0.961750i | \(0.588323\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.1271i | 0.714865i | 0.933939 | + | 0.357432i | \(0.116348\pi\) | ||||
−0.933939 | + | 0.357432i | \(0.883652\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.0926 | −1.34032 | −0.670159 | − | 0.742218i | \(-0.733774\pi\) | ||||
−0.670159 | + | 0.742218i | \(0.733774\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.86455i | − | 0.112443i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 28.3491i | − | 1.10939i | −0.832055 | − | 0.554693i | \(-0.812836\pi\) | ||
0.832055 | − | 0.554693i | \(-0.187164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −44.1145 | −1.72370 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.2879 | −0.829260 | −0.414630 | − | 0.909990i | \(-0.636089\pi\) | ||||
−0.414630 | + | 0.909990i | \(0.636089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15.5357i | − | 0.604267i | −0.953266 | − | 0.302134i | \(-0.902301\pi\) | ||
0.953266 | − | 0.302134i | \(-0.0976989\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.44671 | 0.172436 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.2239i | 0.705632i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 16.8288i | − | 0.649670i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.1672i | − | 1.08577i | −0.839808 | − | 0.542883i | \(-0.817333\pi\) | ||
0.839808 | − | 0.542883i | \(-0.182667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 44.4868i | − | 1.70977i | −0.518820 | − | 0.854883i | \(-0.673629\pi\) | ||
0.518820 | − | 0.854883i | \(-0.326371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.6338 | 1.21399 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.976098 | −0.0373493 | −0.0186747 | − | 0.999826i | \(-0.505945\pi\) | ||||
−0.0186747 | + | 0.999826i | \(0.505945\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.9332i | 2.13710i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45.5721i | 1.73616i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.3214i | 1.83823i | 0.393985 | + | 0.919117i | \(0.371096\pi\) | ||||
−0.393985 | + | 0.919117i | \(0.628904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 34.9781i | − | 1.32679i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.634480 | 0.0240327 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.1624i | − | 1.02591i | −0.858416 | − | 0.512955i | \(-0.828551\pi\) | ||
0.858416 | − | 0.512955i | \(-0.171449\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.66623i | − | 0.0628429i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.64528 | 0.362748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 0.178679i | − | 0.00671042i | −0.999994 | − | 0.00335521i | \(-0.998932\pi\) | ||
0.999994 | − | 0.00335521i | \(-0.00106800\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.3085 | 0.423505 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.2361 | 1.13076 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.2941 | 0.794137 | 0.397068 | − | 0.917789i | \(-0.370028\pi\) | ||||
0.397068 | + | 0.917789i | \(0.370028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 39.9284i | − | 1.48701i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.6375i | 0.989293i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.3771i | 0.681570i | 0.940141 | + | 0.340785i | \(0.110693\pi\) | ||||
−0.940141 | + | 0.340785i | \(0.889307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.22172i | 0.0821733i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.1446 | 1.18729 | 0.593644 | − | 0.804727i | \(-0.297689\pi\) | ||||
0.593644 | + | 0.804727i | \(0.297689\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.37970 | −0.124493 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16.9885i | − | 0.624931i | −0.949929 | − | 0.312465i | \(-0.898845\pi\) | ||
0.949929 | − | 0.312465i | \(-0.101155\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18.7879i | − | 0.689262i | −0.938738 | − | 0.344631i | \(-0.888004\pi\) | ||
0.938738 | − | 0.344631i | \(-0.111996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.9355 | 0.620469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 21.1285i | − | 0.772018i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.66376i | − | 0.133692i | −0.997763 | − | 0.0668462i | \(-0.978706\pi\) | ||
0.997763 | − | 0.0668462i | \(-0.0212937\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 56.4759i | 2.05537i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −54.8790 | −1.99461 | −0.997306 | − | 0.0733524i | \(-0.976630\pi\) | ||||
−0.997306 | + | 0.0733524i | \(0.976630\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.2256i | 0.805678i | 0.915271 | + | 0.402839i | \(0.131976\pi\) | ||||
−0.915271 | + | 0.402839i | \(0.868024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 31.4406i | − | 1.13823i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 10.7470i | − | 0.388050i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.6337i | 0.455583i | 0.973710 | + | 0.227792i | \(0.0731505\pi\) | ||||
−0.973710 | + | 0.227792i | \(0.926849\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.6153 | 1.02922 | 0.514611 | − | 0.857424i | \(-0.327936\pi\) | ||||
0.514611 | + | 0.857424i | \(0.327936\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.5294 | 0.593753 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.959869 | 0.0343909 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9726i | 0.535760i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 65.0984 | 2.32346 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4638i | 0.765103i | 0.923934 | + | 0.382552i | \(0.124955\pi\) | ||||
−0.923934 | + | 0.382552i | \(0.875045\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.4062 | −0.974453 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 63.1370i | − | 2.24206i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.7969 | 1.05546 | 0.527730 | − | 0.849412i | \(-0.323043\pi\) | ||||
0.527730 | + | 0.849412i | \(0.323043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.67979i | − | 0.0948042i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.64317 | 0.269722 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −75.4406 | −2.65893 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 36.4507i | − | 1.28154i | −0.767733 | − | 0.640770i | \(-0.778615\pi\) | ||
0.767733 | − | 0.640770i | \(-0.221385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.3990i | 0.821649i | 0.911714 | + | 0.410825i | \(0.134759\pi\) | ||||
−0.911714 | + | 0.410825i | \(0.865241\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.1508i | 1.40642i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.36111i | 0.117590i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.804310 | 0.0280706 | 0.0140353 | − | 0.999902i | \(-0.495532\pi\) | ||||
0.0140353 | + | 0.999902i | \(0.495532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 14.0945i | − | 0.491304i | −0.969358 | − | 0.245652i | \(-0.920998\pi\) | ||
0.969358 | − | 0.245652i | \(-0.0790020\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.5615 | 0.958409 | 0.479204 | − | 0.877703i | \(-0.340925\pi\) | ||||
0.479204 | + | 0.877703i | \(0.340925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.36108i | 0.0472721i | 0.999721 | + | 0.0236361i | \(0.00752430\pi\) | ||||
−0.999721 | + | 0.0236361i | \(0.992476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.546607 | 0.0189388 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.6823 | + | 20.6806i | −1.68472 | + | 0.715680i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.3893i | 1.04916i | 0.851362 | + | 0.524578i | \(0.175777\pi\) | ||||
−0.851362 | + | 0.524578i | \(0.824223\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.8627 | 0.822852 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 60.2285 | 2.07192 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.7026 | 0.711351 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.2684i | 0.969027i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.51966 | 0.223229 | 0.111614 | − | 0.993752i | \(-0.464398\pi\) | ||||
0.111614 | + | 0.993752i | \(0.464398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.2333i | 1.20355i | 0.798667 | + | 0.601773i | \(0.205539\pi\) | ||||
−0.798667 | + | 0.601773i | \(0.794461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.2774 | 0.521259 | 0.260629 | − | 0.965439i | \(-0.416070\pi\) | ||||
0.260629 | + | 0.965439i | \(0.416070\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.76077i | 0.298220i | 0.988821 | + | 0.149110i | \(0.0476409\pi\) | ||||
−0.988821 | + | 0.149110i | \(0.952359\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.7251i | 0.568670i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.39218 | 0.148994 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.6797 | −0.429635 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −63.3564 | −2.14184 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.8404 | −1.75053 | −0.875263 | − | 0.483647i | \(-0.839312\pi\) | ||||
−0.875263 | + | 0.483647i | \(0.839312\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6955 | −0.461414 | −0.230707 | − | 0.973023i | \(-0.574104\pi\) | ||||
−0.230707 | + | 0.973023i | \(0.574104\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.19585 | −0.309465 | −0.154732 | − | 0.987956i | \(-0.549452\pi\) | ||||
−0.154732 | + | 0.987956i | \(0.549452\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.3766 | 0.784908 | 0.392454 | − | 0.919772i | \(-0.371626\pi\) | ||||
0.392454 | + | 0.919772i | \(0.371626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.617244 | 0.0207017 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 4.05410i | − | 0.135665i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 105.823i | 3.53727i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.18784i | 0.106320i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.71178 | 0.0903425 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.9251 | −0.629092 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.41355 | 0.279367 | 0.139684 | − | 0.990196i | \(-0.455391\pi\) | ||||
0.139684 | + | 0.990196i | \(0.455391\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.20618i | − | 0.139357i | −0.997570 | − | 0.0696784i | \(-0.977803\pi\) | ||
0.997570 | − | 0.0696784i | \(-0.0221973\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.03699i | 0.232890i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.7078 | 0.815924 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.5330 | −1.56797 | −0.783985 | − | 0.620780i | \(-0.786816\pi\) | ||||
−0.783985 | + | 0.620780i | \(0.786816\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 56.1728i | 1.84895i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.3193i | 1.35857i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.94411i | 0.162211i | 0.996706 | + | 0.0811055i | \(0.0258451\pi\) | ||||
−0.996706 | + | 0.0811055i | \(0.974155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.826931 | 0.0271016 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.79921i | − | 0.0588403i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.97855i | 0.325985i | 0.986627 | + | 0.162993i | \(0.0521147\pi\) | ||||
−0.986627 | + | 0.162993i | \(0.947885\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.5662 | 1.38762 | 0.693810 | − | 0.720158i | \(-0.255931\pi\) | ||||
0.693810 | + | 0.720158i | \(0.255931\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.2847 | −0.530301 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.5239i | 1.25186i | 0.779879 | + | 0.625930i | \(0.215280\pi\) | ||||
−0.779879 | + | 0.625930i | \(0.784720\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.6750 | 0.930830 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.3136 | −0.593235 | −0.296618 | − | 0.954996i | \(-0.595859\pi\) | ||||
−0.296618 | + | 0.954996i | \(0.595859\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81.9418i | 2.65157i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 31.3273i | − | 1.01161i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0219 | −0.936189 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 104.390i | − | 3.36043i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.66245 | 0.278566 | 0.139283 | − | 0.990253i | \(-0.455520\pi\) | ||||
0.139283 | + | 0.990253i | \(0.455520\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.4415 | −0.559726 | −0.279863 | − | 0.960040i | \(-0.590289\pi\) | ||||
−0.279863 | + | 0.960040i | \(0.590289\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.5907i | 0.628048i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.5726 | 1.04209 | 0.521045 | − | 0.853530i | \(-0.325543\pi\) | ||||
0.521045 | + | 0.853530i | \(0.325543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.09058 | 0.162696 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.4885 | 1.57844 | 0.789219 | − | 0.614112i | \(-0.210486\pi\) | ||||
0.789219 | + | 0.614112i | \(0.210486\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −76.6140 | −2.44113 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 57.0230i | − | 1.81323i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 30.9501i | − | 0.983161i | −0.870832 | − | 0.491580i | \(-0.836419\pi\) | ||
0.870832 | − | 0.491580i | \(-0.163581\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.17716 | −0.259233 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.5747 | −1.47504 | −0.737518 | − | 0.675328i | \(-0.764002\pi\) | ||||
−0.737518 | + | 0.675328i | \(0.764002\pi\) | |||||||
\(998\) | 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 | 6012.2.h.a.3005.2 | yes | 56 | |
3.2 | odd | 2 | inner | 6012.2.h.a.3005.56 | yes | 56 | |
167.166 | odd | 2 | inner | 6012.2.h.a.3005.55 | yes | 56 | |
501.500 | even | 2 | inner | 6012.2.h.a.3005.1 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.h.a.3005.1 | ✓ | 56 | 501.500 | even | 2 | inner | |
6012.2.h.a.3005.2 | yes | 56 | 1.1 | even | 1 | trivial | |
6012.2.h.a.3005.55 | yes | 56 | 167.166 | odd | 2 | inner | |
6012.2.h.a.3005.56 | yes | 56 | 3.2 | odd | 2 | inner |