Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
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([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (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: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.14 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.f.3025.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0.940450i | 0.420582i | 0.977639 | + | 0.210291i | \(0.0674411\pi\) | ||||
−0.977639 | + | 0.210291i | \(0.932559\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.98632i | − 1.80494i | −0.430749 | − | 0.902472i | \(-0.641751\pi\) | ||||
0.430749 | − | 0.902472i | \(-0.358249\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.59017i | 1.82778i | 0.405957 | + | 0.913892i | \(0.366938\pi\) | ||||
−0.405957 | + | 0.913892i | \(0.633062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.64225 | −0.640840 | −0.320420 | − | 0.947276i | \(-0.603824\pi\) | ||||
−0.320420 | + | 0.947276i | \(0.603824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.83430i | − 1.33848i | −0.743047 | − | 0.669240i | \(-0.766620\pi\) | ||||
0.743047 | − | 0.669240i | \(-0.233380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.88452 | −0.601464 | −0.300732 | − | 0.953709i | \(-0.597231\pi\) | ||||
−0.300732 | + | 0.953709i | \(0.597231\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.11555 | 0.823111 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.09794i | − 0.575274i | −0.957740 | − | 0.287637i | \(-0.907130\pi\) | ||||
0.957740 | − | 0.287637i | \(-0.0928696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.52412 | −0.632950 | −0.316475 | − | 0.948601i | \(-0.602499\pi\) | ||||
−0.316475 | + | 0.948601i | \(0.602499\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 0.940450i | − 0.158965i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.213560i | 0.0351090i | 0.999846 | + | 0.0175545i | \(0.00558806\pi\) | ||||
−0.999846 | + | 0.0175545i | \(0.994412\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.63291 | −0.255017 | −0.127509 | − | 0.991837i | \(-0.540698\pi\) | ||||
−0.127509 | + | 0.991837i | \(0.540698\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.16716i | 1.09298i | 0.837465 | + | 0.546491i | \(0.184037\pi\) | ||||
−0.837465 | + | 0.546491i | \(0.815963\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.32639 | 1.36039 | 0.680197 | − | 0.733030i | \(-0.261894\pi\) | ||||
0.680197 | + | 0.733030i | \(0.261894\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.51044i | 1.03164i | 0.856698 | + | 0.515819i | \(0.172512\pi\) | ||||
−0.856698 | + | 0.515819i | \(0.827488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.62983 | 0.759126 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.9280i | 1.55289i | 0.630186 | + | 0.776444i | \(0.282979\pi\) | ||||
−0.630186 | + | 0.776444i | \(0.717021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.48304i | − 0.189884i | −0.995483 | − | 0.0949419i | \(-0.969733\pi\) | ||||
0.995483 | − | 0.0949419i | \(-0.0302665\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.19772 | −0.768733 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0555i | 1.59498i | 0.603329 | + | 0.797492i | \(0.293840\pi\) | ||||
−0.603329 | + | 0.797492i | \(0.706160\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.54642 | 0.183526 | 0.0917632 | − | 0.995781i | \(-0.470750\pi\) | ||||
0.0917632 | + | 0.995781i | \(0.470750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.96871 | −0.347461 | −0.173731 | − | 0.984793i | \(-0.555582\pi\) | ||||
−0.173731 | + | 0.984793i | \(0.555582\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.98632i | 0.682204i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9515 | −1.79468 | −0.897341 | − | 0.441338i | \(-0.854504\pi\) | ||||
−0.897341 | + | 0.441338i | \(0.854504\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.74782i | − 0.960198i | −0.877214 | − | 0.480099i | \(-0.840601\pi\) | ||||
0.877214 | − | 0.480099i | \(-0.159399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.48490i | − 0.269526i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.50339 | 0.795358 | 0.397679 | − | 0.917525i | \(-0.369816\pi\) | ||||
0.397679 | + | 0.917525i | \(0.369816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 6.59017i | − 0.690837i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.48686 | 0.562940 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7529 | 1.09179 | 0.545894 | − | 0.837854i | \(-0.316190\pi\) | ||||
0.545894 | + | 0.837854i | \(0.316190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.54920i | 0.353159i | 0.984286 | + | 0.176579i | \(0.0565033\pi\) | ||||
−0.984286 | + | 0.176579i | \(0.943497\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.3303 | −1.51054 | −0.755271 | − | 0.655413i | \(-0.772495\pi\) | ||||
−0.755271 | + | 0.655413i | \(0.772495\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.41633i | − 0.233596i | −0.993156 | − | 0.116798i | \(-0.962737\pi\) | ||||
0.993156 | − | 0.116798i | \(-0.0372629\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.86711i | 0.657750i | 0.944373 | + | 0.328875i | \(0.106669\pi\) | ||||
−0.944373 | + | 0.328875i | \(0.893331\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.4539 | −1.45378 | −0.726891 | − | 0.686752i | \(-0.759036\pi\) | ||||
−0.726891 | + | 0.686752i | \(0.759036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.71274i | − 0.252965i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.64225 | 0.242215 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.8360 | −2.25782 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.57272i | 0.766767i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.96760 | −0.707010 | −0.353505 | − | 0.935433i | \(-0.615010\pi\) | ||||
−0.353505 | + | 0.935433i | \(0.615010\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.53780i | 0.134358i | 0.997741 | + | 0.0671790i | \(0.0213999\pi\) | ||||
−0.997741 | + | 0.0671790i | \(0.978600\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.83430i | 0.505898i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.34042 | 0.541699 | 0.270849 | − | 0.962622i | \(-0.412695\pi\) | ||||
0.270849 | + | 0.962622i | \(0.412695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.13659i | 0.690137i | 0.938578 | + | 0.345068i | \(0.112144\pi\) | ||||
−0.938578 | + | 0.345068i | \(0.887856\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 39.4509 | 3.29905 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.91346 | 0.241950 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 15.2594i | − 1.25010i | −0.780586 | − | 0.625048i | \(-0.785079\pi\) | ||||
0.780586 | − | 0.625048i | \(-0.214921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.728441 | 0.0592797 | 0.0296398 | − | 0.999561i | \(-0.490564\pi\) | ||||
0.0296398 | + | 0.999561i | \(0.490564\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3.31425i | − 0.266207i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1207i | 0.967337i | 0.875251 | + | 0.483669i | \(0.160696\pi\) | ||||
−0.875251 | + | 0.483669i | \(0.839304\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.88452 | 0.227332 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 5.45067i | − 0.426929i | −0.976951 | − | 0.213465i | \(-0.931525\pi\) | ||||
0.976951 | − | 0.213465i | \(-0.0684748\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.96762 | 0.152259 | 0.0761297 | − | 0.997098i | \(-0.475744\pi\) | ||||
0.0761297 | + | 0.997098i | \(0.475744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −30.4303 | −2.34079 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.48602i | 0.341066i | 0.985352 | + | 0.170533i | \(0.0545489\pi\) | ||||
−0.985352 | + | 0.170533i | \(0.945451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.11555 | −0.311107 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.8086i | 1.85428i | 0.374716 | + | 0.927140i | \(0.377740\pi\) | ||||
−0.374716 | + | 0.927140i | \(0.622260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6114i | 1.68070i | 0.542048 | + | 0.840348i | \(0.317649\pi\) | ||||
−0.542048 | + | 0.840348i | \(0.682351\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.200842 | −0.0147662 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8174i | 1.15668i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.3035 | −1.17968 | −0.589838 | − | 0.807521i | \(-0.700809\pi\) | ||||
−0.589838 | + | 0.807521i | \(0.700809\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.98388 | 0.502711 | 0.251355 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251355 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 13.5891i | − 0.968182i | −0.875018 | − | 0.484091i | \(-0.839150\pi\) | ||||
0.875018 | − | 0.484091i | \(-0.160850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.2305 | −1.43410 | −0.717052 | − | 0.697020i | \(-0.754509\pi\) | ||||
−0.717052 | + | 0.697020i | \(0.754509\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.09794i | 0.217433i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.53567i | − 0.107256i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −34.9260 | −2.41588 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.1090i | 1.31552i | 0.753230 | + | 0.657758i | \(0.228495\pi\) | ||||
−0.753230 | + | 0.657758i | \(0.771505\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.74035 | −0.459688 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.52412 | 0.239233 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 17.4129i | − 1.17132i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9241 | 1.40118 | 0.700592 | − | 0.713562i | \(-0.252920\pi\) | ||||
0.700592 | + | 0.713562i | \(0.252920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.48329i | 0.164821i | 0.996598 | + | 0.0824107i | \(0.0262619\pi\) | ||||
−0.996598 | + | 0.0824107i | \(0.973738\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 10.3155i | − 0.681669i | −0.940123 | − | 0.340835i | \(-0.889290\pi\) | ||||
0.940123 | − | 0.340835i | \(-0.110710\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.5208 | −1.27885 | −0.639424 | − | 0.768855i | \(-0.720827\pi\) | ||||
−0.639424 | + | 0.768855i | \(0.720827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.77100i | 0.572157i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.8520 | 1.15475 | 0.577376 | − | 0.816478i | \(-0.304077\pi\) | ||||
0.577376 | + | 0.816478i | \(0.304077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.72097 | 0.432935 | 0.216468 | − | 0.976290i | \(-0.430546\pi\) | ||||
0.216468 | + | 0.976290i | \(0.430546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.940450i | 0.0600831i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.4490 | 2.44645 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 28.1618i | − 1.77756i | −0.458336 | − | 0.888779i | \(-0.651555\pi\) | ||||
0.458336 | − | 0.888779i | \(-0.348445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.2677i | 1.08561i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.9286 | 1.55500 | 0.777502 | − | 0.628880i | \(-0.216486\pi\) | ||||
0.777502 | + | 0.628880i | \(0.216486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 0.213560i | − 0.0132700i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.0635 | −1.17550 | −0.587751 | − | 0.809042i | \(-0.699987\pi\) | ||||
−0.587751 | + | 0.809042i | \(0.699987\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.06319 | −0.433888 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.2410i | 0.624406i | 0.950015 | + | 0.312203i | \(0.101067\pi\) | ||||
−0.950015 | + | 0.312203i | \(0.898933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.45674 | 0.270728 | 0.135364 | − | 0.990796i | \(-0.456780\pi\) | ||||
0.135364 | + | 0.990796i | \(0.456780\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 24.6370i | − 1.48567i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0596i | 0.964929i | 0.875915 | + | 0.482465i | \(0.160258\pi\) | ||||
−0.875915 | + | 0.482465i | \(0.839742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.3739 | −1.87161 | −0.935806 | − | 0.352516i | \(-0.885326\pi\) | ||||
−0.935806 | + | 0.352516i | \(0.885326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.4627i | 0.978605i | 0.872114 | + | 0.489302i | \(0.162749\pi\) | ||||
−0.872114 | + | 0.489302i | \(0.837251\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.63291 | 0.0963874 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0185 | −0.589324 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.78733i | − 0.338100i | −0.985608 | − | 0.169050i | \(-0.945930\pi\) | ||||
0.985608 | − | 0.169050i | \(-0.0540699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2177 | −0.653117 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 19.0095i | − 1.09935i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.16716i | − 0.413108i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.39472 | 0.0798617 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0312i | 1.31446i | 0.753691 | + | 0.657229i | \(0.228272\pi\) | ||||
−0.753691 | + | 0.657229i | \(0.771728\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7123 | −0.890964 | −0.445482 | − | 0.895291i | \(-0.646968\pi\) | ||||
−0.445482 | + | 0.895291i | \(0.646968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.53462 | −0.369358 | −0.184679 | − | 0.982799i | \(-0.559125\pi\) | ||||
−0.184679 | + | 0.982799i | \(0.559125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.9169i | 1.11865i | 0.828949 | + | 0.559324i | \(0.188939\pi\) | ||||
−0.828949 | + | 0.559324i | \(0.811061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.5453 | −1.03834 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.4157i | 0.857751i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.1222i | 1.50447i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.32639 | −0.514180 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.3692i | 1.17456i | 0.809384 | + | 0.587280i | \(0.199801\pi\) | ||||
−0.809384 | + | 0.587280i | \(0.800199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.2780 | −0.670821 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.56768 | −0.521185 | −0.260592 | − | 0.965449i | \(-0.583918\pi\) | ||||
−0.260592 | + | 0.965449i | \(0.583918\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.0965i | 1.14244i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.63471i | 0.302487i | 0.988497 | + | 0.151243i | \(0.0483278\pi\) | ||||
−0.988497 | + | 0.151243i | \(0.951672\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 33.2219i | − 1.77833i | −0.457591 | − | 0.889163i | \(-0.651287\pi\) | ||||
0.457591 | − | 0.889163i | \(-0.348713\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.20112 | 0.330052 | 0.165026 | − | 0.986289i | \(-0.447229\pi\) | ||||
0.165026 | + | 0.986289i | \(0.447229\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.45433i | 0.0771879i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.76894 | −0.0933609 | −0.0466805 | − | 0.998910i | \(-0.514864\pi\) | ||||
−0.0466805 | + | 0.998910i | \(0.514864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0390 | −0.791526 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.79192i | − 0.146136i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.62872 | −0.502615 | −0.251308 | − | 0.967907i | \(-0.580861\pi\) | ||||
−0.251308 | + | 0.967907i | \(0.580861\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 7.51044i | − 0.389922i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 19.6983i | − 1.01994i | −0.860192 | − | 0.509970i | \(-0.829657\pi\) | ||||
0.860192 | − | 0.509970i | \(-0.170343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.4160 | 1.05148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 16.3324i | − 0.838941i | −0.907769 | − | 0.419470i | \(-0.862216\pi\) | ||||
0.907769 | − | 0.419470i | \(-0.137784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.7037 | −0.904618 | −0.452309 | − | 0.891861i | \(-0.649400\pi\) | ||||
−0.452309 | + | 0.891861i | \(0.649400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.62983 | −0.286923 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 24.4174i | − 1.23801i | −0.785387 | − | 0.619005i | \(-0.787536\pi\) | ||||
0.785387 | − | 0.619005i | \(-0.212464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.62162 | 0.385442 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 15.0016i | − 0.754811i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.4996i | 1.07903i | 0.841975 | + | 0.539517i | \(0.181393\pi\) | ||||
−0.841975 | + | 0.539517i | \(0.818607\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.0629 | 1.45133 | 0.725667 | − | 0.688046i | \(-0.241531\pi\) | ||||
0.725667 | + | 0.688046i | \(0.241531\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 23.2245i | − 1.15690i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.27844 | 0.0633698 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.96315 | −0.294859 | −0.147429 | − | 0.989073i | \(-0.547100\pi\) | ||||
−0.147429 | + | 0.989073i | \(0.547100\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11.9280i | − 0.586937i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.22689 | 0.403842 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.8317i | 1.40852i | 0.709941 | + | 0.704261i | \(0.248721\pi\) | ||||
−0.709941 | + | 0.704261i | \(0.751279\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.3324i | 1.47831i | 0.673534 | + | 0.739156i | \(0.264776\pi\) | ||||
−0.673534 | + | 0.739156i | \(0.735224\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.8743 | −0.527482 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.48304i | 0.0717693i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.3775 | −1.55957 | −0.779785 | − | 0.626048i | \(-0.784671\pi\) | ||||
−0.779785 | + | 0.626048i | \(0.784671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.9777 | −1.48869 | −0.744346 | − | 0.667794i | \(-0.767239\pi\) | ||||
−0.744346 | + | 0.667794i | \(0.767239\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.8291i | 0.805047i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.76381 | −0.418274 | −0.209137 | − | 0.977886i | \(-0.567065\pi\) | ||||
−0.209137 | + | 0.977886i | \(0.567065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 7.53477i | − 0.357988i | −0.983850 | − | 0.178994i | \(-0.942716\pi\) | ||||
0.983850 | − | 0.178994i | \(-0.0572842\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.05656i | 0.334513i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.5584 | 1.53653 | 0.768263 | − | 0.640134i | \(-0.221121\pi\) | ||||
0.768263 | + | 0.640134i | \(0.221121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.77510i | 0.460292i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.19772 | 0.290554 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.81122 | −0.178281 | −0.0891407 | − | 0.996019i | \(-0.528412\pi\) | ||||
−0.0891407 | + | 0.996019i | \(0.528412\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 6.29754i | − 0.293306i | −0.989188 | − | 0.146653i | \(-0.953150\pi\) | ||||
0.989188 | − | 0.146653i | \(-0.0468500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8418 | −0.596811 | −0.298405 | − | 0.954439i | \(-0.596455\pi\) | ||||
−0.298405 | + | 0.954439i | \(0.596455\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.5588i | 1.59919i | 0.600538 | + | 0.799596i | \(0.294953\pi\) | ||||
−0.600538 | + | 0.799596i | \(0.705047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 13.0555i | − 0.602847i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 42.9049 | 1.97277 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 24.0114i | − 1.10172i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5950 | 0.758244 | 0.379122 | − | 0.925347i | \(-0.376226\pi\) | ||||
0.379122 | + | 0.925347i | \(0.376226\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.40739 | −0.0641717 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.1125i | 0.459186i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.4209 | −1.19724 | −0.598622 | − | 0.801032i | \(-0.704285\pi\) | ||||
−0.598622 | + | 0.801032i | \(0.704285\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.70049i | 0.167001i | 0.996508 | + | 0.0835003i | \(0.0266100\pi\) | ||||
−0.996508 | + | 0.0835003i | \(0.973390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.18554i | 0.368658i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.54642 | −0.0693664 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.12488i | 0.0951229i | 0.998868 | + | 0.0475614i | \(0.0151450\pi\) | ||||
−0.998868 | + | 0.0475614i | \(0.984855\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.3846 | 1.93443 | 0.967213 | − | 0.253968i | \(-0.0817359\pi\) | ||||
0.967213 | + | 0.253968i | \(0.0817359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.33785 | −0.148532 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.34482i | 0.103932i | 0.998649 | + | 0.0519662i | \(0.0165488\pi\) | ||||
−0.998649 | + | 0.0519662i | \(0.983451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.96871 | 0.131328 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 14.4174i | − 0.635306i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 55.8307i | − 2.45543i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.53436 | 0.373897 | 0.186949 | − | 0.982370i | \(-0.440140\pi\) | ||||
0.186949 | + | 0.982370i | \(0.440140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 30.8607i | − 1.34944i | −0.738072 | − | 0.674722i | \(-0.764264\pi\) | ||||
0.738072 | − | 0.674722i | \(-0.235736\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.31160 | 0.405620 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.6796 | −0.638241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 10.7611i | − 0.466116i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.27244 | 0.0982461 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.98632i | − 0.257849i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 15.2568i | − 0.655940i | −0.944688 | − | 0.327970i | \(-0.893636\pi\) | ||||
0.944688 | − | 0.327970i | \(-0.106364\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.45817 | −0.276638 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.6416i | 1.52393i | 0.647621 | + | 0.761963i | \(0.275764\pi\) | ||||
−0.647621 | + | 0.761963i | \(0.724236\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.0743 | −0.769992 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.9515 | 0.678326 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.3871i | 1.20280i | 0.798949 | + | 0.601399i | \(0.205390\pi\) | ||||
−0.798949 | + | 0.601399i | \(0.794610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.2328 | −1.99773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0963i | 0.551942i | 0.961166 | + | 0.275971i | \(0.0889993\pi\) | ||||
−0.961166 | + | 0.275971i | \(0.911001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 14.5336i | − 0.611435i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0434 | 0.840263 | 0.420132 | − | 0.907463i | \(-0.361984\pi\) | ||||
0.420132 | + | 0.907463i | \(0.361984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.91621i | 0.289434i | 0.989473 | + | 0.144717i | \(0.0462272\pi\) | ||||
−0.989473 | + | 0.144717i | \(0.953773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.8714 | −0.495071 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2279 | 0.966992 | 0.483496 | − | 0.875347i | \(-0.339367\pi\) | ||||
0.483496 | + | 0.875347i | \(0.339367\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.74782i | 0.362921i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.9599 | 1.86205 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.76774i | 0.0729624i | 0.999334 | + | 0.0364812i | \(0.0116149\pi\) | ||||
−0.999334 | + | 0.0364812i | \(0.988385\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.5607i | 0.847191i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.8807 | 0.611079 | 0.305540 | − | 0.952179i | \(-0.401163\pi\) | ||||
0.305540 | + | 0.952179i | \(0.401163\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.48490i | 0.101871i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.47561 | −0.0602916 | −0.0301458 | − | 0.999546i | \(-0.509597\pi\) | ||||
−0.0301458 | + | 0.999546i | \(0.509597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.1957 | −0.456684 | −0.228342 | − | 0.973581i | \(-0.573330\pi\) | ||||
−0.228342 | + | 0.973581i | \(0.573330\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 23.3570i | − 0.949598i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.4554 | 1.27674 | 0.638368 | − | 0.769731i | \(-0.279610\pi\) | ||||
0.638368 | + | 0.769731i | \(0.279610\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 61.4625i | 2.48651i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9222i | 0.764262i | 0.924108 | + | 0.382131i | \(0.124810\pi\) | ||||
−0.924108 | + | 0.382131i | \(0.875190\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.1549 | −0.489339 | −0.244669 | − | 0.969607i | \(-0.578679\pi\) | ||||
−0.244669 | + | 0.969607i | \(0.578679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.9619i | 0.601371i | 0.953723 | + | 0.300686i | \(0.0972155\pi\) | ||||
−0.953723 | + | 0.300686i | \(0.902784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.50339 | −0.300617 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5156 | 0.500623 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 0.564278i | − 0.0224992i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.71232 | 0.346832 | 0.173416 | − | 0.984849i | \(-0.444519\pi\) | ||||
0.173416 | + | 0.984849i | \(0.444519\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 7.49313i | − 0.297356i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.59017i | 0.261112i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.31021 | 0.288736 | 0.144368 | − | 0.989524i | \(-0.453885\pi\) | ||||
0.144368 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 11.1766i | − 0.440763i | −0.975414 | − | 0.220381i | \(-0.929270\pi\) | ||||
0.975414 | − | 0.220381i | \(-0.0707302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.13625 | 0.280555 | 0.140277 | − | 0.990112i | \(-0.455201\pi\) | ||||
0.140277 | + | 0.990112i | \(0.455201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 71.4046 | 2.80288 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.6385i | 0.611982i | 0.952034 | + | 0.305991i | \(0.0989878\pi\) | ||||
−0.952034 | + | 0.305991i | \(0.901012\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.44622 | −0.0565086 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.73739i | − 0.0676791i | −0.999427 | − | 0.0338395i | \(-0.989226\pi\) | ||||
0.999427 | − | 0.0338395i | \(-0.0107735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.7968i | 0.886691i | 0.896351 | + | 0.443345i | \(0.146208\pi\) | ||||
−0.896351 | + | 0.443345i | \(0.853792\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.48686 | −0.212771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.93608i | 0.346006i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.87795 | −0.342729 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.1667 | −0.507538 | −0.253769 | − | 0.967265i | \(-0.581670\pi\) | ||||
−0.253769 | + | 0.967265i | \(0.581670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 37.3183i | − 1.43426i | −0.696941 | − | 0.717129i | \(-0.745456\pi\) | ||||
0.696941 | − | 0.717129i | \(-0.254544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7529 | −0.412657 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 6.72259i | − 0.257233i | −0.991694 | − | 0.128616i | \(-0.958946\pi\) | ||||
0.991694 | − | 0.128616i | \(-0.0410536\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.96285i | 0.227829i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −49.4951 | −1.88561 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.18845i | 0.311503i | 0.987796 | + | 0.155752i | \(0.0497800\pi\) | ||||
−0.987796 | + | 0.155752i | \(0.950220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.65205 | −0.290259 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.31455 | 0.163425 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 5.85226i | − 0.221037i | −0.993874 | − | 0.110518i | \(-0.964749\pi\) | ||||
0.993874 | − | 0.110518i | \(-0.0352511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.24597 | 0.0469927 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 3.54920i | − 0.133482i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.3444i | 1.70294i | 0.524399 | + | 0.851472i | \(0.324290\pi\) | ||||
−0.524399 | + | 0.851472i | \(0.675710\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1654 | 0.380697 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.1015i | 1.38752i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.1182 | −1.08592 | −0.542962 | − | 0.839757i | \(-0.682697\pi\) | ||||
−0.542962 | + | 0.839757i | \(0.682697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3303 | 0.570931 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 12.7498i | − 0.473514i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.5099 | 1.57661 | 0.788303 | − | 0.615287i | \(-0.210960\pi\) | ||||
0.788303 | + | 0.615287i | \(0.210960\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 18.9374i | − 0.700426i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.79234i | 0.103137i | 0.998669 | + | 0.0515687i | \(0.0164221\pi\) | ||||
−0.998669 | + | 0.0515687i | \(0.983578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 78.1544 | 2.87886 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 15.4715i | − 0.569129i | −0.958657 | − | 0.284565i | \(-0.908151\pi\) | ||||
0.958657 | − | 0.284565i | \(-0.0918490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.2897 | 0.670984 | 0.335492 | − | 0.942043i | \(-0.391097\pi\) | ||||
0.335492 | + | 0.942043i | \(0.391097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.3507 | 0.525768 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.41633i | 0.0882908i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1167 | −0.405655 | −0.202828 | − | 0.979214i | \(-0.565013\pi\) | ||||
−0.202828 | + | 0.979214i | \(0.565013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.685062i | 0.0249320i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.8173i | 0.429507i | 0.976668 | + | 0.214753i | \(0.0688948\pi\) | ||||
−0.976668 | + | 0.214753i | \(0.931105\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2039 | −0.442390 | −0.221195 | − | 0.975230i | \(-0.570996\pi\) | ||||
−0.221195 | + | 0.975230i | \(0.570996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 6.86711i | − 0.248606i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −78.6073 | −2.83835 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.32578 | −0.264175 | −0.132087 | − | 0.991238i | \(-0.542168\pi\) | ||||
−0.132087 | + | 0.991238i | \(0.542168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 7.26470i | − 0.261293i | −0.991429 | − | 0.130647i | \(-0.958295\pi\) | ||||
0.991429 | − | 0.130647i | \(-0.0417053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.5037 | −0.520988 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.52686i | 0.341335i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 9.25737i | − 0.331255i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.3989 | −0.406844 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.02431i | − 0.107805i | −0.998546 | − | 0.0539025i | \(-0.982834\pi\) | ||||
0.998546 | − | 0.0539025i | \(-0.0171660\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4539 | 0.549478 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.77348 | 0.347067 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.6317i | 0.730813i | 0.930848 | + | 0.365406i | \(0.119070\pi\) | ||||
−0.930848 | + | 0.365406i | \(0.880930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.6426 | −0.871794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.7716i | 0.627148i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.71274i | 0.0956117i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.5889 | 1.04029 | 0.520145 | − | 0.854078i | \(-0.325878\pi\) | ||||
0.520145 | + | 0.854078i | \(0.325878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 42.6230i | − 1.49670i | −0.663307 | − | 0.748348i | \(-0.730847\pi\) | ||||
0.663307 | − | 0.748348i | \(-0.269153\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.12608 | 0.179559 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.8153 | 1.46293 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 48.6214i | − 1.69690i | −0.529276 | − | 0.848450i | \(-0.677536\pi\) | ||||
0.529276 | − | 0.848450i | \(-0.322464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.7228 | −0.826924 | −0.413462 | − | 0.910521i | \(-0.635680\pi\) | ||||
−0.413462 | + | 0.910521i | \(0.635680\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 29.3889i | − 1.02195i | −0.859595 | − | 0.510976i | \(-0.829284\pi\) | ||||
0.859595 | − | 0.510976i | \(-0.170716\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 26.4785i | − 0.919635i | −0.888013 | − | 0.459818i | \(-0.847915\pi\) | ||||
0.888013 | − | 0.459818i | \(-0.152085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.64225 | −0.0915485 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.85045i | 0.0640375i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.51211 | 0.121252 | 0.0606258 | − | 0.998161i | \(-0.480690\pi\) | ||||
0.0606258 | + | 0.998161i | \(0.480690\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.4027 | 0.669060 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 28.6182i | − 0.984496i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.8360 | 0.853376 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 0.616017i | − 0.0211168i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 28.2378i | − 0.966843i | −0.875388 | − | 0.483422i | \(-0.839394\pi\) | ||||
0.875388 | − | 0.483422i | \(-0.160606\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.8126 | −0.437669 | −0.218834 | − | 0.975762i | \(-0.570225\pi\) | ||||
−0.218834 | + | 0.975762i | \(0.570225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 35.4496i | − 1.20952i | −0.796406 | − | 0.604762i | \(-0.793268\pi\) | ||||
0.796406 | − | 0.604762i | \(-0.206732\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.3418 | 1.10093 | 0.550465 | − | 0.834858i | \(-0.314451\pi\) | ||||
0.550465 | + | 0.834858i | \(0.314451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.21887 | −0.143446 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 95.4907i | 3.23930i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −86.0380 | −2.91529 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 8.57272i | − 0.289811i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 6.53592i | − 0.220702i | −0.993893 | − | 0.110351i | \(-0.964802\pi\) | ||||
0.993893 | − | 0.110351i | \(-0.0351976\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.0057 | −1.78581 | −0.892904 | − | 0.450248i | \(-0.851336\pi\) | ||||
−0.892904 | + | 0.450248i | \(0.851336\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0481i | 0.943894i | 0.881627 | + | 0.471947i | \(0.156449\pi\) | ||||
−0.881627 | + | 0.471947i | \(0.843551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.58627 | −0.153992 | −0.0769959 | − | 0.997031i | \(-0.524533\pi\) | ||||
−0.0769959 | + | 0.997031i | \(0.524533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.96760 | 0.267225 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 54.4129i | − 1.82086i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.3312 | −0.779876 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.9175i | 0.364120i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 19.8445i | − 0.661115i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.2649 | −0.706870 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 31.8338i | − 1.05703i | −0.848925 | − | 0.528513i | \(-0.822750\pi\) | ||||
0.848925 | − | 0.528513i | \(-0.177250\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.9123 | −1.85246 | −0.926228 | − | 0.376964i | \(-0.876968\pi\) | ||||
−0.926228 | + | 0.376964i | \(0.876968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.3673 | −1.73310 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.53780i | − 0.0507826i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.6749 | 1.70460 | 0.852299 | − | 0.523055i | \(-0.175208\pi\) | ||||
0.852299 | + | 0.523055i | \(0.175208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.1912i | 0.335447i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.878917i | 0.0288986i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.6988 | 0.351016 | 0.175508 | − | 0.984478i | \(-0.443843\pi\) | ||||
0.175508 | + | 0.984478i | \(0.443843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 5.83430i | − 0.191211i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.8754 | −0.486478 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3422 | 0.958568 | 0.479284 | − | 0.877660i | \(-0.340896\pi\) | ||||
0.479284 | + | 0.877660i | \(0.340896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 37.2035i | − 1.21280i | −0.795160 | − | 0.606399i | \(-0.792613\pi\) | ||||
0.795160 | − | 0.606399i | \(-0.207387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.71015 | 0.153384 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.7353i | 0.836283i | 0.908382 | + | 0.418142i | \(0.137318\pi\) | ||||
−0.908382 | + | 0.418142i | \(0.862682\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 19.5643i | − 0.635084i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.6526 | −0.571824 | −0.285912 | − | 0.958256i | \(-0.592297\pi\) | ||||
−0.285912 | + | 0.958256i | \(0.592297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 15.3326i | − 0.496150i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.34042 | −0.204743 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.5806 | −0.599374 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.56799i | 0.211431i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.22421 | −0.296631 | −0.148315 | − | 0.988940i | \(-0.547385\pi\) | ||||
−0.148315 | + | 0.988940i | \(0.547385\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.945630i | 0.0303467i | 0.999885 | + | 0.0151734i | \(0.00483002\pi\) | ||||
−0.999885 | + | 0.0151734i | \(0.995170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8.13659i | − 0.260847i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.7944 | 1.11317 | 0.556585 | − | 0.830791i | \(-0.312111\pi\) | ||||
0.556585 | + | 0.830791i | \(0.312111\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 44.9177i | − 1.43558i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.7133 | −0.756336 | −0.378168 | − | 0.925737i | \(-0.623446\pi\) | ||||
−0.378168 | + | 0.925737i | \(0.623446\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.7799 | 0.407200 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 20.6738i | − 0.657389i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.1109 | 0.765908 | 0.382954 | − | 0.923767i | \(-0.374907\pi\) | ||||
0.382954 | + | 0.923767i | \(0.374907\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 19.0258i | − 0.603158i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 30.0398i | − 0.951371i | −0.879615 | − | 0.475685i | \(-0.842200\pi\) | ||||
0.879615 | − | 0.475685i | \(-0.157800\pi\) | |||||||
\(998\) | 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.c.f.3025.14 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.f.3025.12 | 24 | ||
4.3 | odd | 2 | 1512.2.c.g.757.19 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.g.757.20 | yes | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.f.3025.11 | 24 | ||
12.11 | even | 2 | 1512.2.c.g.757.6 | yes | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.f.3025.13 | 24 | ||
24.11 | even | 2 | 1512.2.c.g.757.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.5 | ✓ | 24 | 24.11 | even | 2 | ||
1512.2.c.g.757.6 | yes | 24 | 12.11 | even | 2 | ||
1512.2.c.g.757.19 | yes | 24 | 4.3 | odd | 2 | ||
1512.2.c.g.757.20 | yes | 24 | 8.3 | odd | 2 | ||
6048.2.c.f.3025.11 | 24 | 8.5 | even | 2 | inner | ||
6048.2.c.f.3025.12 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.f.3025.13 | 24 | 24.5 | odd | 2 | inner | ||
6048.2.c.f.3025.14 | 24 | 1.1 | even | 1 | trivial |