Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (of order \(3\), degree \(2\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.11 | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.l.1873.11 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | 3.52959 | 1.57848 | 0.789239 | − | 0.614086i | \(-0.210475\pi\) | ||||
0.789239 | + | 0.614086i | \(0.210475\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.16715 | − | 2.37440i | −0.441141 | − | 0.897438i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.32073 | −0.699726 | −0.349863 | − | 0.936801i | \(-0.613772\pi\) | ||||
−0.349863 | + | 0.936801i | \(0.613772\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.35884 | − | 4.08563i | −0.654224 | − | 1.13315i | −0.982088 | − | 0.188424i | \(-0.939662\pi\) |
0.327864 | − | 0.944725i | \(-0.393671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.636946 | + | 1.10322i | 0.154482 | + | 0.267571i | 0.932870 | − | 0.360212i | \(-0.117296\pi\) |
−0.778388 | + | 0.627783i | \(0.783962\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.78386 | + | 4.82178i | −0.638661 | + | 1.10619i | 0.347066 | + | 0.937841i | \(0.387178\pi\) |
−0.985727 | + | 0.168352i | \(0.946155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.29710 | −0.687492 | −0.343746 | − | 0.939063i | \(-0.611696\pi\) | ||||
−0.343746 | + | 0.939063i | \(0.611696\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.45798 | 1.49160 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.32116 | − | 7.48447i | 0.802419 | − | 1.38983i | −0.115601 | − | 0.993296i | \(-0.536879\pi\) |
0.918020 | − | 0.396535i | \(-0.129787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.25821 | − | 7.37543i | 0.764797 | − | 1.32467i | −0.175557 | − | 0.984469i | \(-0.556173\pi\) |
0.940354 | − | 0.340197i | \(-0.110494\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.11956 | − | 8.38064i | −0.696332 | − | 1.41659i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.84024 | + | 4.91943i | −0.466932 | + | 0.808750i | −0.999286 | − | 0.0377716i | \(-0.987974\pi\) |
0.532354 | + | 0.846522i | \(0.321307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.66553 | − | 2.88478i | −0.260112 | − | 0.450528i | 0.706159 | − | 0.708053i | \(-0.250426\pi\) |
−0.966272 | + | 0.257525i | \(0.917093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0444165 | + | 0.0769317i | −0.00677346 | + | 0.0117320i | −0.869392 | − | 0.494123i | \(-0.835489\pi\) |
0.862619 | + | 0.505855i | \(0.168823\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.52607 | − | 6.10733i | −0.514330 | − | 0.890845i | −0.999862 | − | 0.0166264i | \(-0.994707\pi\) |
0.485532 | − | 0.874219i | \(-0.338626\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.27552 | + | 5.54256i | −0.610789 | + | 0.791794i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.41816 | − | 5.92042i | −0.469520 | − | 0.813233i | 0.529873 | − | 0.848077i | \(-0.322240\pi\) |
−0.999393 | + | 0.0348444i | \(0.988906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.19121 | −1.10450 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.99745 | − | 6.92378i | 0.520423 | − | 0.901400i | −0.479295 | − | 0.877654i | \(-0.659107\pi\) |
0.999718 | − | 0.0237457i | \(-0.00755920\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.67764 | − | 11.5660i | −0.854985 | − | 1.48088i | −0.876659 | − | 0.481112i | \(-0.840233\pi\) |
0.0216747 | − | 0.999765i | \(-0.493100\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.32572 | − | 14.4206i | −1.03268 | − | 1.78865i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.06402 | − | 5.30704i | 0.374330 | − | 0.648358i | −0.615897 | − | 0.787827i | \(-0.711206\pi\) |
0.990226 | + | 0.139469i | \(0.0445394\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.30202 | 0.154522 | 0.0772609 | − | 0.997011i | \(-0.475383\pi\) | ||||
0.0772609 | + | 0.997011i | \(0.475383\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.64529 | + | 11.5100i | 0.777772 | + | 1.34714i | 0.933223 | + | 0.359297i | \(0.116984\pi\) |
−0.155451 | + | 0.987844i | \(0.549683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.70864 | + | 5.51033i | 0.308678 | + | 0.627961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.01403 | − | 8.68455i | −0.564122 | − | 0.977088i | −0.997131 | − | 0.0756985i | \(-0.975881\pi\) |
0.433009 | − | 0.901390i | \(-0.357452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.90243 | + | 10.2233i | −0.647876 | + | 1.12215i | 0.335753 | + | 0.941950i | \(0.391009\pi\) |
−0.983629 | + | 0.180204i | \(0.942324\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.24815 | + | 3.89392i | 0.243847 | + | 0.422355i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.561496 | + | 0.972540i | −0.0595185 | + | 0.103089i | −0.894249 | − | 0.447569i | \(-0.852290\pi\) |
0.834731 | + | 0.550658i | \(0.185623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.94778 | + | 10.3694i | −0.728325 | + | 1.08700i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.82586 | + | 17.0189i | −1.00811 | + | 1.74610i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50818 | + | 6.07635i | −0.356202 | + | 0.616960i | −0.987323 | − | 0.158724i | \(-0.949262\pi\) |
0.631121 | + | 0.775685i | \(0.282595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.74111 | 0.969277 | 0.484638 | − | 0.874715i | \(-0.338951\pi\) | ||||
0.484638 | + | 0.874715i | \(0.338951\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2856 | −1.01347 | −0.506734 | − | 0.862103i | \(-0.669147\pi\) | ||||
−0.506734 | + | 0.862103i | \(0.669147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.72201 | − | 4.71465i | 0.263146 | − | 0.455783i | −0.703930 | − | 0.710269i | \(-0.748573\pi\) |
0.967076 | + | 0.254487i | \(0.0819065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.417404 | + | 0.722965i | 0.0399800 | + | 0.0692475i | 0.885323 | − | 0.464977i | \(-0.153937\pi\) |
−0.845343 | + | 0.534224i | \(0.820604\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.44881 | − | 9.43761i | −0.512581 | − | 0.887815i | −0.999894 | − | 0.0145882i | \(-0.995356\pi\) |
0.487313 | − | 0.873227i | \(-0.337977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.6374 | −1.08519 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.87608 | − | 2.79999i | 0.171980 | − | 0.256674i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.61421 | −0.510383 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.67565 | 0.775974 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.90354 | 0.878797 | 0.439399 | − | 0.898292i | \(-0.355192\pi\) | ||||
0.439399 | + | 0.898292i | \(0.355192\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.1844 | 1.50141 | 0.750704 | − | 0.660639i | \(-0.229715\pi\) | ||||
0.750704 | + | 0.660639i | \(0.229715\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.6980 | + | 0.982238i | 1.27448 | + | 0.0851708i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.0939 | 1.37500 | 0.687498 | − | 0.726186i | \(-0.258709\pi\) | ||||
0.687498 | + | 0.726186i | \(0.258709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.11151 | − | 1.92519i | −0.0942768 | − | 0.163292i | 0.815030 | − | 0.579419i | \(-0.196721\pi\) |
−0.909307 | + | 0.416127i | \(0.863387\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.47422 | + | 9.48163i | 0.457778 | + | 0.792894i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2519 | − | 26.4171i | 1.26660 | − | 2.19382i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.93692 | −0.568295 | −0.284147 | − | 0.958781i | \(-0.591710\pi\) | ||||
−0.284147 | + | 0.958781i | \(0.591710\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5167 | −1.26273 | −0.631365 | − | 0.775486i | \(-0.717505\pi\) | ||||
−0.631365 | + | 0.775486i | \(0.717505\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.0297 | − | 26.0322i | 1.20722 | − | 2.09096i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.401055 | + | 0.694648i | −0.0320077 | + | 0.0554389i | −0.881586 | − | 0.472024i | \(-0.843523\pi\) |
0.849578 | + | 0.527463i | \(0.176857\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.84821 | + | 7.82862i | 0.303281 | + | 0.616982i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.77500 | + | 3.07438i | −0.139028 | + | 0.240804i | −0.927129 | − | 0.374742i | \(-0.877731\pi\) |
0.788101 | + | 0.615546i | \(0.211065\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.865131 | + | 1.49845i | 0.0669459 | + | 0.115954i | 0.897556 | − | 0.440901i | \(-0.145341\pi\) |
−0.830610 | + | 0.556855i | \(0.812008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.62823 | + | 8.01633i | −0.356018 | + | 0.616641i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.11729 | + | 1.93521i | 0.0849462 | + | 0.147131i | 0.905368 | − | 0.424627i | \(-0.139595\pi\) |
−0.820422 | + | 0.571758i | \(0.806262\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.70458 | − | 17.7082i | −0.658005 | − | 1.33861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.350412 | − | 0.606931i | −0.0261910 | − | 0.0453641i | 0.852633 | − | 0.522511i | \(-0.175004\pi\) |
−0.878824 | + | 0.477146i | \(0.841671\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6339 | −1.45938 | −0.729688 | − | 0.683780i | \(-0.760335\pi\) | ||||
−0.729688 | + | 0.683780i | \(0.760335\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.0249 | + | 17.3636i | −0.737042 | + | 1.27659i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.47818 | − | 2.56028i | −0.108095 | − | 0.187226i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.04289 | − | 13.9307i | −0.581963 | − | 1.00799i | −0.995247 | − | 0.0973872i | \(-0.968951\pi\) |
0.413284 | − | 0.910602i | \(-0.364382\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.292732 | − | 0.507026i | 0.0210713 | − | 0.0364965i | −0.855297 | − | 0.518137i | \(-0.826626\pi\) |
0.876369 | + | 0.481641i | \(0.159959\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.2923 | 1.23203 | 0.616014 | − | 0.787735i | \(-0.288746\pi\) | ||||
0.616014 | + | 0.787735i | \(0.288746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2119 | + | 21.1517i | 0.865681 | + | 1.49940i | 0.866369 | + | 0.499404i | \(0.166448\pi\) |
−0.000687656 | 1.00000i | \(0.500219\pi\) | ||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.8145 | − | 1.52465i | −1.60127 | − | 0.107009i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.87864 | − | 10.1821i | −0.410582 | − | 0.711149i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.46058 | − | 11.1900i | 0.446888 | − | 0.774032i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.58733 | + | 9.67754i | 0.384648 | + | 0.666230i | 0.991720 | − | 0.128417i | \(-0.0409895\pi\) |
−0.607072 | + | 0.794647i | \(0.707656\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.156772 | + | 0.271537i | −0.0106918 | + | 0.0185187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.4822 | − | 1.50244i | −1.52619 | − | 0.101992i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00490 | − | 5.20464i | 0.202132 | − | 0.350102i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.32951 | − | 2.30277i | 0.0890303 | − | 0.154205i | −0.818071 | − | 0.575117i | \(-0.804957\pi\) |
0.907101 | + | 0.420912i | \(0.138290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9157 | 0.790874 | 0.395437 | − | 0.918493i | \(-0.370593\pi\) | ||||
0.395437 | + | 0.918493i | \(0.370593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.6128 | −1.95687 | −0.978434 | − | 0.206561i | \(-0.933773\pi\) | ||||
−0.978434 | + | 0.206561i | \(0.933773\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.84417 | + | 3.19420i | −0.120816 | + | 0.209259i | −0.920090 | − | 0.391708i | \(-0.871884\pi\) |
0.799274 | + | 0.600967i | \(0.205218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.4456 | − | 21.5563i | −0.811859 | − | 1.40618i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.03590 | + | 13.9186i | 0.519799 | + | 0.900319i | 0.999735 | + | 0.0230153i | \(0.00732663\pi\) |
−0.479936 | + | 0.877304i | \(0.659340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.49867 | 0.289785 | 0.144892 | − | 0.989447i | \(-0.453716\pi\) | ||||
0.144892 | + | 0.989447i | \(0.453716\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.0908 | + | 19.5629i | −0.964117 | + | 1.24983i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.2667 | 1.67131 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2696 | −1.09005 | −0.545023 | − | 0.838421i | \(-0.683479\pi\) | ||||
−0.545023 | + | 0.838421i | \(0.683479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.65167 | 0.481057 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.82173 | −0.300771 | −0.150386 | − | 0.988627i | \(-0.548052\pi\) | ||||
−0.150386 | + | 0.988627i | \(0.548052\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.9957 | + | 1.00213i | 0.931786 | + | 0.0622693i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.0903 | 1.73212 | 0.866062 | − | 0.499936i | \(-0.166643\pi\) | ||||
0.866062 | + | 0.499936i | \(0.166643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0647 | − | 20.8966i | −0.741128 | − | 1.28367i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4126 | − | 21.4993i | −0.756810 | − | 1.31083i | −0.944469 | − | 0.328599i | \(-0.893423\pi\) |
0.187659 | − | 0.982234i | \(-0.439910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.79671 | − | 8.30815i | 0.291379 | − | 0.504684i | −0.682757 | − | 0.730646i | \(-0.739219\pi\) |
0.974136 | + | 0.225962i | \(0.0725524\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.3080 | −1.04371 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.9383 | 1.01772 | 0.508862 | − | 0.860848i | \(-0.330067\pi\) | ||||
0.508862 | + | 0.860848i | \(0.330067\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.4291 | + | 19.7958i | −0.681805 | + | 1.18092i | 0.292625 | + | 0.956227i | \(0.405471\pi\) |
−0.974430 | + | 0.224693i | \(0.927862\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.17811 | − | 7.23669i | 0.248363 | − | 0.430177i | −0.714709 | − | 0.699422i | \(-0.753441\pi\) |
0.963072 | + | 0.269245i | \(0.0867742\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.90570 | + | 7.32161i | −0.289574 | + | 0.432181i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.68860 | − | 13.3170i | 0.452271 | − | 0.783356i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.16141 | + | 3.74368i | 0.126271 | + | 0.218708i | 0.922229 | − | 0.386644i | \(-0.126366\pi\) |
−0.795958 | + | 0.605352i | \(0.793032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1093 | − | 24.4381i | 0.821477 | − | 1.42284i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.77732 | + | 13.4707i | 0.449774 | + | 0.779031i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.234507 | + | 0.0156716i | 0.0135168 | + | 0.000903298i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.5693 | − | 40.8233i | −1.34958 | − | 2.33753i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.22888 | 0.526720 | 0.263360 | − | 0.964698i | \(-0.415169\pi\) | ||||
0.263360 | + | 0.964698i | \(0.415169\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.55365 | − | 16.5474i | 0.541738 | − | 0.938317i | −0.457067 | − | 0.889432i | \(-0.651100\pi\) |
0.998804 | − | 0.0488847i | \(-0.0155667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.83951 | − | 4.91818i | −0.160499 | − | 0.277992i | 0.774549 | − | 0.632514i | \(-0.217977\pi\) |
−0.935048 | + | 0.354522i | \(0.884644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.1341 | − | 24.4809i | −0.793848 | − | 1.37499i | −0.923568 | − | 0.383434i | \(-0.874741\pi\) |
0.129720 | − | 0.991551i | \(-0.458592\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0282 | + | 17.3694i | −0.561474 | + | 0.972501i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.09266 | −0.394646 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.5922 | − | 30.4705i | −0.975838 | − | 1.69020i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.3858 | + | 15.5005i | −0.572586 | + | 0.854568i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.34045 | − | 5.78584i | −0.183608 | − | 0.318018i | 0.759499 | − | 0.650509i | \(-0.225444\pi\) |
−0.943107 | + | 0.332491i | \(0.892111\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.8147 | − | 18.7317i | 0.590872 | − | 1.02342i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.49421 | − | 6.05215i | −0.190342 | − | 0.329681i | 0.755022 | − | 0.655700i | \(-0.227626\pi\) |
−0.945363 | + | 0.326018i | \(0.894293\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.88215 | + | 17.1164i | −0.535148 | + | 0.926904i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1504 | + | 3.68279i | 0.980030 | + | 0.198852i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.14410 | + | 7.17780i | −0.222467 | + | 0.385324i | −0.955557 | − | 0.294808i | \(-0.904744\pi\) |
0.733089 | + | 0.680132i | \(0.238078\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.05373 | − | 5.28921i | 0.163462 | − | 0.283125i | −0.772646 | − | 0.634837i | \(-0.781067\pi\) |
0.936108 | + | 0.351712i | \(0.114400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.7208 | 1.42221 | 0.711104 | − | 0.703087i | \(-0.248196\pi\) | ||||
0.711104 | + | 0.703087i | \(0.248196\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.59561 | 0.243909 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.45603 | − | 4.25397i | 0.129624 | − | 0.224516i | −0.793907 | − | 0.608040i | \(-0.791956\pi\) |
0.923531 | + | 0.383523i | \(0.125289\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.99972 | − | 10.3918i | −0.315775 | − | 0.546938i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.4551 | + | 40.6255i | 1.22770 | + | 2.12643i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.7064 | 1.60286 | 0.801430 | − | 0.598089i | \(-0.204073\pi\) | ||||
0.801430 | + | 0.598089i | \(0.204073\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0679 | + | 15.0261i | −0.522701 | + | 0.780116i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5838 | 0.858676 | 0.429338 | − | 0.903144i | \(-0.358747\pi\) | ||||
0.429338 | + | 0.903144i | \(0.358747\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.7716 | −2.09985 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.08857 | −0.210016 | −0.105008 | − | 0.994471i | \(-0.533487\pi\) | ||||
−0.105008 | + | 0.994471i | \(0.533487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.3538 | 1.55101 | 0.775503 | − | 0.631344i | \(-0.217496\pi\) | ||||
0.775503 | + | 0.631344i | \(0.217496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.56038 | + | 19.4492i | 0.487242 | + | 0.991223i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.46764 | 0.175816 | 0.0879082 | − | 0.996129i | \(-0.471982\pi\) | ||||
0.0879082 | + | 0.996129i | \(0.471982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.10007 | − | 3.63743i | −0.106205 | − | 0.183953i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.6974 | − | 30.6529i | −0.890455 | − | 1.54231i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.04243 | + | 12.1979i | −0.353450 | + | 0.612193i | −0.986851 | − | 0.161630i | \(-0.948325\pi\) |
0.633402 | + | 0.773823i | \(0.281658\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.9319 | 0.545911 | 0.272955 | − | 0.962027i | \(-0.411999\pi\) | ||||
0.272955 | + | 0.962027i | \(0.411999\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.1777 | −2.00139 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.59142 | − | 11.4167i | 0.326725 | − | 0.565904i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.99397 | + | 13.8460i | −0.395276 | + | 0.684639i | −0.993136 | − | 0.116962i | \(-0.962685\pi\) |
0.597860 | + | 0.801600i | \(0.296018\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.1054 | − | 1.41043i | −1.03853 | − | 0.0694029i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.8331 | + | 36.0841i | −1.02266 | + | 1.77130i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.56197 | − | 6.16951i | −0.174014 | − | 0.301400i | 0.765806 | − | 0.643072i | \(-0.222340\pi\) |
−0.939819 | + | 0.341671i | \(0.889007\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6326 | + | 28.8086i | −0.810625 | + | 1.40404i | 0.101802 | + | 0.994805i | \(0.467539\pi\) |
−0.912427 | + | 0.409239i | \(0.865794\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.75033 | + | 8.22781i | 0.230425 | + | 0.399107i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.6685 | + | 29.3547i | −0.951826 | + | 1.42057i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.62382 | − | 4.54459i | −0.126385 | − | 0.218905i | 0.795889 | − | 0.605443i | \(-0.207004\pi\) |
−0.922273 | + | 0.386538i | \(0.873671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.1053 | 1.06231 | 0.531156 | − | 0.847274i | \(-0.321758\pi\) | ||||
0.531156 | + | 0.847274i | \(0.321758\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.17865 | − | 15.8979i | 0.439074 | − | 0.760499i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3083 | + | 29.9788i | 0.826079 | + | 1.43081i | 0.901092 | + | 0.433628i | \(0.142767\pi\) |
−0.0750132 | + | 0.997183i | \(0.523900\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.20461 | + | 3.81850i | 0.104744 | + | 0.181423i | 0.913634 | − | 0.406538i | \(-0.133264\pi\) |
−0.808889 | + | 0.587961i | \(0.799931\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.98185 | + | 3.43266i | −0.0939486 | + | 0.162724i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6336 | 0.926568 | 0.463284 | − | 0.886210i | \(-0.346671\pi\) | ||||
0.463284 | + | 0.886210i | \(0.346671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.86525 | + | 6.69481i | 0.182007 | + | 0.315246i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.5228 | + | 36.5995i | −1.14965 | + | 1.71581i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.4196 | + | 26.7075i | 0.721297 | + | 1.24932i | 0.960480 | + | 0.278349i | \(0.0897872\pi\) |
−0.239183 | + | 0.970975i | \(0.576879\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.6297 | − | 23.6074i | 0.634800 | − | 1.09951i | −0.351757 | − | 0.936091i | \(-0.614416\pi\) |
0.986557 | − | 0.163415i | \(-0.0522510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.959750 | + | 1.66234i | 0.0446034 | + | 0.0772553i | 0.887465 | − | 0.460875i | \(-0.152464\pi\) |
−0.842862 | + | 0.538130i | \(0.819131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.88655 | − | 8.46376i | 0.226123 | − | 0.391656i | −0.730533 | − | 0.682877i | \(-0.760728\pi\) |
0.956656 | + | 0.291221i | \(0.0940616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.1772 | − | 1.08109i | −0.746994 | − | 0.0499201i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.103079 | − | 0.178538i | 0.00473957 | − | 0.00820917i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7619 | + | 35.9607i | −0.952623 | + | 1.64999i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.3762 | 0.702556 | 0.351278 | − | 0.936271i | \(-0.385747\pi\) | ||||
0.351278 | + | 0.936271i | \(0.385747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.7986 | 1.22191 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.3824 | + | 21.4470i | −0.562258 | + | 0.973859i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.18342 | − | 8.97794i | −0.234883 | − | 0.406829i | 0.724356 | − | 0.689427i | \(-0.242137\pi\) |
−0.959239 | + | 0.282597i | \(0.908804\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.94718 | − | 12.0329i | −0.313522 | − | 0.543035i | 0.665600 | − | 0.746308i | \(-0.268175\pi\) |
−0.979122 | + | 0.203273i | \(0.934842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0094 | 0.495837 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.51966 | − | 3.09152i | −0.0681660 | − | 0.138674i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.40977 | 0.152642 | 0.0763210 | − | 0.997083i | \(-0.475683\pi\) | ||||
0.0763210 | + | 0.997083i | \(0.475683\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.8911 | 1.95701 | 0.978504 | − | 0.206227i | \(-0.0661185\pi\) | ||||
0.978504 | + | 0.206227i | \(0.0661185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.3821 | 1.52998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.3348 | −1.74348 | −0.871742 | − | 0.489966i | \(-0.837009\pi\) | ||||
−0.871742 | + | 0.489966i | \(0.837009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.5732 | − | 29.2124i | 0.865868 | − | 1.29228i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.3038 | −1.59974 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.18305 | + | 14.1735i | 0.359890 | + | 0.623348i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.4779 | − | 21.6124i | −0.546669 | − | 0.946858i | −0.998500 | − | 0.0547547i | \(-0.982562\pi\) |
0.451831 | − | 0.892104i | \(-0.350771\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.1575 | − | 26.2536i | 0.662792 | − | 1.14799i | −0.317086 | − | 0.948397i | \(-0.602704\pi\) |
0.979879 | − | 0.199594i | \(-0.0639622\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.8490 | 0.472589 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.1291 | −0.527354 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.85744 | + | 13.6095i | −0.340343 | + | 0.589492i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.60755 | − | 16.6408i | 0.415371 | − | 0.719443i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.92233 | − | 12.8628i | 0.427385 | − | 0.554039i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2812 | + | 24.7357i | −0.613996 | + | 1.06347i | 0.376563 | + | 0.926391i | \(0.377106\pi\) |
−0.990560 | + | 0.137082i | \(0.956228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.47326 | + | 2.55177i | 0.0631077 | + | 0.109306i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.89233 | + | 6.74171i | −0.166424 | + | 0.288255i | −0.937160 | − | 0.348900i | \(-0.886555\pi\) |
0.770736 | + | 0.637154i | \(0.219889\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0590 | + | 41.6714i | 1.02495 | + | 1.77526i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.7684 | + | 22.0415i | −0.628018 | + | 0.937299i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.2470 | + | 40.2650i | 0.985008 | + | 1.70608i | 0.641900 | + | 0.766788i | \(0.278146\pi\) |
0.343108 | + | 0.939296i | \(0.388520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.419086 | 0.0177254 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.9913 | + | 24.2336i | −0.589663 | + | 1.02133i | 0.404614 | + | 0.914488i | \(0.367406\pi\) |
−0.994276 | + | 0.106838i | \(0.965927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.2320 | − | 33.3109i | −0.809098 | − | 1.40140i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.44979 | + | 7.70726i | 0.186545 | + | 0.323105i | 0.944096 | − | 0.329671i | \(-0.106938\pi\) |
−0.757551 | + | 0.652776i | \(0.773604\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.1652 | + | 27.9989i | −0.676492 | + | 1.17172i | 0.299539 | + | 0.954084i | \(0.403167\pi\) |
−0.976031 | + | 0.217634i | \(0.930166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.5897 | −1.02546 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.8414 | − | 29.1701i | −0.701115 | − | 1.21437i | −0.968075 | − | 0.250659i | \(-0.919353\pi\) |
0.266960 | − | 0.963707i | \(-0.413981\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.1632 | + | 2.08257i | 1.29287 | + | 0.0863997i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.93262 | + | 13.7397i | 0.328536 | + | 0.569040i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.24076 | + | 2.14907i | −0.0512118 | + | 0.0887015i | −0.890495 | − | 0.454993i | \(-0.849642\pi\) |
0.839283 | + | 0.543695i | \(0.182975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.7085 | + | 41.0643i | 0.976891 | + | 1.69202i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.0903 | − | 26.1371i | 0.619684 | − | 1.07332i | −0.369859 | − | 0.929088i | \(-0.620594\pi\) |
0.989543 | − | 0.144236i | \(-0.0460725\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.62177 | − | 9.88280i | 0.271466 | − | 0.405155i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.20414 | − | 14.2100i | 0.335212 | − | 0.580604i | −0.648314 | − | 0.761373i | \(-0.724525\pi\) |
0.983526 | + | 0.180769i | \(0.0578588\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.96998 | + | 5.14416i | −0.121148 | + | 0.209835i | −0.920221 | − | 0.391400i | \(-0.871991\pi\) |
0.799073 | + | 0.601235i | \(0.205324\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.8159 | −0.805629 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.95146 | 0.241563 | 0.120781 | − | 0.992679i | \(-0.461460\pi\) | ||||
0.120781 | + | 0.992679i | \(0.461460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.6348 | + | 28.8124i | −0.672974 | + | 1.16562i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5920 | + | 27.0062i | 0.629756 | + | 1.09077i | 0.987601 | + | 0.156988i | \(0.0501783\pi\) |
−0.357845 | + | 0.933781i | \(0.616488\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1437 | + | 19.3014i | 0.448627 | + | 0.777045i | 0.998297 | − | 0.0583367i | \(-0.0185797\pi\) |
−0.549670 | + | 0.835382i | \(0.685246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.5887 | −1.39024 | −0.695118 | − | 0.718895i | \(-0.744648\pi\) | ||||
−0.695118 | + | 0.718895i | \(0.744648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.96454 | + | 0.198115i | 0.118772 | + | 0.00793729i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.66844 | −0.266738 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.23631 | −0.288530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.2933 | 1.04672 | 0.523360 | − | 0.852112i | \(-0.324678\pi\) | ||||
0.523360 | + | 0.852112i | \(0.324678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.9554 | 1.38716 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.7301 | + | 4.39419i | 1.29681 | + | 0.174104i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.5346 | 1.28504 | 0.642519 | − | 0.766269i | \(-0.277889\pi\) | ||||
0.642519 | + | 0.766269i | \(0.277889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.21987 | − | 9.04107i | −0.205851 | − | 0.356545i | 0.744552 | − | 0.667564i | \(-0.232663\pi\) |
−0.950404 | + | 0.311019i | \(0.899330\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.685824 | + | 1.18788i | 0.0269625 | + | 0.0467005i | 0.879192 | − | 0.476468i | \(-0.158083\pi\) |
−0.852229 | + | 0.523168i | \(0.824750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.27699 | + | 16.0682i | −0.364154 | + | 0.630733i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.25134 | 0.283767 | 0.141883 | − | 0.989883i | \(-0.454684\pi\) | ||||
0.141883 | + | 0.989883i | \(0.454684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 60.6538 | 2.36994 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3187 | + | 23.0686i | −0.518822 | + | 0.898626i | 0.480939 | + | 0.876754i | \(0.340296\pi\) |
−0.999761 | + | 0.0218722i | \(0.993037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.4099 | − | 30.1549i | 0.677168 | − | 1.17289i | −0.298662 | − | 0.954359i | \(-0.596540\pi\) |
0.975830 | − | 0.218531i | \(-0.0701265\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 51.8779 | + | 3.46689i | 2.01174 | + | 0.134440i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2473 | + | 24.6770i | −0.551657 | + | 0.955498i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.4970 | + | 26.8416i | 0.598255 | + | 1.03621i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.23841 | − | 14.2693i | 0.317567 | − | 0.550043i | −0.662412 | − | 0.749139i | \(-0.730467\pi\) |
0.979980 | + | 0.199096i | \(0.0638007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.5827 | − | 18.3297i | −0.406725 | − | 0.704469i | 0.587795 | − | 0.809010i | \(-0.299996\pi\) |
−0.994521 | + | 0.104541i | \(0.966663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.5223 | + | 1.23780i | 0.710819 | + | 0.0475026i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.0756 | + | 24.3796i | 0.538587 | + | 0.932859i | 0.998980 | + | 0.0451447i | \(0.0143749\pi\) |
−0.460394 | + | 0.887715i | \(0.652292\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 56.8049 | 2.17040 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.1258 | + | 27.9306i | −0.614343 | + | 1.06407i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.53980 | + | 16.5234i | 0.362911 | + | 0.628580i | 0.988439 | − | 0.151622i | \(-0.0484496\pi\) |
−0.625528 | + | 0.780202i | \(0.715116\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.92316 | − | 6.79511i | −0.148814 | − | 0.257753i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.12171 | − | 3.67490i | 0.0803653 | − | 0.139197i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.8508 | −0.900834 | −0.450417 | − | 0.892818i | \(-0.648725\pi\) | ||||
−0.450417 | + | 0.892818i | \(0.648725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.8136 | − | 27.3900i | −0.596422 | − | 1.03303i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.3693 | − | 23.1293i | −0.427588 | − | 0.869865i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0493 | − | 17.4059i | −0.377409 | − | 0.653691i | 0.613276 | − | 0.789869i | \(-0.289851\pi\) |
−0.990684 | + | 0.136178i | \(0.956518\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.0397 | + | 24.3175i | −0.525792 | + | 0.910698i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.3217 | + | 33.4662i | 0.722592 | + | 1.25157i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.29246 | + | 5.70270i | −0.122788 | + | 0.212675i | −0.920866 | − | 0.389879i | \(-0.872517\pi\) |
0.798078 | + | 0.602554i | \(0.205850\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0048 | + | 24.4220i | 0.447082 | + | 0.909524i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.2271 | − | 55.8190i | 1.19688 | − | 2.07307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2342 | + | 31.5826i | −0.676269 | + | 1.17133i | 0.299827 | + | 0.953994i | \(0.403071\pi\) |
−0.976096 | + | 0.217339i | \(0.930262\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.113164 | −0.00418551 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.3647 | 0.862997 | 0.431498 | − | 0.902114i | \(-0.357985\pi\) | ||||
0.431498 | + | 0.902114i | \(0.357985\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.11077 | + | 12.3162i | −0.261928 | + | 0.453673i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.4596 | − | 25.0448i | −0.531906 | − | 0.921288i | −0.999306 | − | 0.0372422i | \(-0.988143\pi\) |
0.467400 | − | 0.884046i | \(-0.345191\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.6794 | + | 20.2292i | 0.428474 | + | 0.742139i | 0.996738 | − | 0.0807074i | \(-0.0257179\pi\) |
−0.568264 | + | 0.822847i | \(0.692385\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.4845 | −0.897041 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.3714 | − | 0.960415i | −0.525121 | − | 0.0350928i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.71323 | 0.0625167 | 0.0312584 | − | 0.999511i | \(-0.490049\pi\) | ||||
0.0312584 | + | 0.999511i | \(0.490049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −54.7675 | −1.99319 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4587 | 1.03435 | 0.517175 | − | 0.855880i | \(-0.326984\pi\) | ||||
0.517175 | + | 0.855880i | \(0.326984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.1051 | 1.23631 | 0.618154 | − | 0.786057i | \(-0.287881\pi\) | ||||
0.618154 | + | 0.786057i | \(0.287881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.22943 | − | 1.83489i | 0.0445084 | − | 0.0664275i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.7173 | −1.36189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.48467 | + | 4.30357i | 0.0895995 | + | 0.155191i | 0.907342 | − | 0.420394i | \(-0.138108\pi\) |
−0.817742 | + | 0.575584i | \(0.804775\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.74814 | + | 9.95607i | 0.206746 | + | 0.358095i | 0.950688 | − | 0.310150i | \(-0.100379\pi\) |
−0.743941 | + | 0.668245i | \(0.767046\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.7576 | − | 55.0058i | 1.14077 | − | 1.97587i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.5464 | 0.664494 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.02165 | −0.108123 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.41556 | + | 2.45182i | −0.0505235 | + | 0.0875092i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.3005 | − | 42.0898i | 0.866221 | − | 1.50034i | 0.000391003 | − | 1.00000i | \(-0.499876\pi\) |
0.865830 | − | 0.500339i | \(-0.166791\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.0491 | + | 23.9527i | −0.570639 | + | 0.851661i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.5030 | + | 54.5647i | −1.11870 | + | 1.93765i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.8556 | − | 29.1947i | −0.597056 | − | 1.03413i | −0.993253 | − | 0.115965i | \(-0.963004\pi\) |
0.396198 | − | 0.918165i | \(-0.370330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.49183 | − | 7.78007i | 0.158909 | − | 0.275239i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.4219 | − | 26.7115i | −0.544228 | − | 0.942630i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.5826 | + | 27.6318i | 0.478723 | + | 0.973892i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.93617 | + | 13.7459i | 0.279021 | + | 0.483278i | 0.971142 | − | 0.238503i | \(-0.0766568\pi\) |
−0.692121 | + | 0.721782i | \(0.743323\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.2524 | −0.956963 | −0.478481 | − | 0.878098i | \(-0.658813\pi\) | ||||
−0.478481 | + | 0.878098i | \(0.658813\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.26500 | + | 10.8513i | −0.219454 | + | 0.380105i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.247299 | − | 0.428334i | −0.00865188 | − | 0.0149855i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.1694 | + | 21.0781i | 0.424717 | + | 0.735631i | 0.996394 | − | 0.0848477i | \(-0.0270404\pi\) |
−0.571677 | + | 0.820479i | \(0.693707\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.76898 | + | 9.99217i | −0.201094 | + | 0.348305i | −0.948881 | − | 0.315633i | \(-0.897783\pi\) |
0.747787 | + | 0.663939i | \(0.231116\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.8582 | −1.21214 | −0.606069 | − | 0.795412i | \(-0.707255\pi\) | ||||
−0.606069 | + | 0.795412i | \(0.707255\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.64018 | − | 13.2332i | −0.265354 | − | 0.459607i | 0.702302 | − | 0.711879i | \(-0.252156\pi\) |
−0.967656 | + | 0.252272i | \(0.918822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.83795 | − | 1.18654i | −0.306217 | − | 0.0411113i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.05356 | + | 5.28891i | 0.105673 | + | 0.183030i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.39990 | + | 14.5490i | −0.289997 | + | 0.502289i | −0.973809 | − | 0.227369i | \(-0.926988\pi\) |
0.683812 | + | 0.729658i | \(0.260321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8448 | − | 39.5684i | −0.787753 | − | 1.36443i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.3357 | + | 28.2943i | −0.561967 | + | 0.973355i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.55263 | + | 13.3304i | 0.225151 | + | 0.458037i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.36454 | − | 16.2199i | 0.321012 | − | 0.556009i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4270 | + | 19.7921i | −0.391253 | + | 0.677670i | −0.992615 | − | 0.121306i | \(-0.961292\pi\) |
0.601362 | + | 0.798977i | \(0.294625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.1743 | 1.20153 | 0.600765 | − | 0.799426i | \(-0.294863\pi\) | ||||
0.600765 | + | 0.799426i | \(0.294863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.5704 | −0.360658 | −0.180329 | − | 0.983606i | \(-0.557716\pi\) | ||||
−0.180329 | + | 0.983606i | \(0.557716\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.29326 | + | 12.6323i | −0.248265 | + | 0.430008i | −0.963045 | − | 0.269342i | \(-0.913194\pi\) |
0.714779 | + | 0.699350i | \(0.246527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.94358 | + | 6.83048i | 0.134086 | + | 0.232243i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.6362 | + | 20.1545i | 0.394731 | + | 0.683694i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.9101 | −0.979582 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1258 | − | 20.5994i | −0.342314 | − | 0.696388i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3183 | 0.382191 | 0.191096 | − | 0.981571i | \(-0.438796\pi\) | ||||
0.191096 | + | 0.981571i | \(0.438796\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.733220 | 0.0247028 | 0.0123514 | − | 0.999924i | \(-0.496068\pi\) | ||||
0.0123514 | + | 0.999924i | \(0.496068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1726 | 0.476944 | 0.238472 | − | 0.971149i | \(-0.423353\pi\) | ||||
0.238472 | + | 0.971149i | \(0.423353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.6325 | −1.12927 | −0.564634 | − | 0.825341i | \(-0.690983\pi\) | ||||
−0.564634 | + | 0.825341i | \(0.690983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.5589 | − | 23.5149i | −0.387674 | − | 0.788666i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.2643 | 1.31393 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.23681 | − | 2.14221i | −0.0413419 | − | 0.0716063i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.8008 | − | 63.7408i | −1.22737 | − | 2.12588i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.35436 | − | 7.54198i | 0.145065 | − | 0.251260i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −69.2996 | −2.30360 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.58510 | −0.318268 | −0.159134 | − | 0.987257i | \(-0.550870\pi\) | ||||
−0.159134 | + | 0.987257i | \(0.550870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.37499 | + | 16.2380i | −0.310607 | + | 0.537988i | −0.978494 | − | 0.206275i | \(-0.933866\pi\) |
0.667887 | + | 0.744263i | \(0.267199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.6979 | − | 23.7255i | 0.453336 | − | 0.785201i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.0568 | − | 40.8026i | −0.662333 | − | 1.34742i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.2895 | + | 36.8745i | −0.702276 | + | 1.21638i | 0.265390 | + | 0.964141i | \(0.414499\pi\) |
−0.967666 | + | 0.252236i | \(0.918834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.07126 | − | 5.31958i | −0.101092 | − | 0.175096i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.1824 | + | 36.6890i | −0.696474 | + | 1.20633i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.0762 | + | 33.0409i | 0.625869 | + | 1.08404i | 0.988372 | + | 0.152054i | \(0.0485889\pi\) |
−0.362503 | + | 0.931983i | \(0.618078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.8226 | − | 36.0453i | −0.485790 | − | 1.18134i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.21736 | − | 9.03673i | −0.170626 | − | 0.295533i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.48960 | 0.212006 | 0.106003 | − | 0.994366i | \(-0.466195\pi\) | ||||
0.106003 | + | 0.994366i | \(0.466195\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.233235 | + | 0.403976i | −0.00760326 | + | 0.0131692i | −0.869802 | − | 0.493401i | \(-0.835754\pi\) |
0.862199 | + | 0.506570i | \(0.169087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.49142 | + | 9.51142i | 0.178825 | + | 0.309734i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.55575 | + | 13.0869i | 0.245529 | + | 0.425268i | 0.962280 | − | 0.272060i | \(-0.0877051\pi\) |
−0.716751 | + | 0.697329i | \(0.754372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.3503 | − | 54.3003i | 1.01767 | − | 1.76266i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.6802 | −0.637503 | −0.318751 | − | 0.947838i | \(-0.603264\pi\) | ||||
−0.318751 | + | 0.947838i | \(0.603264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.3881 | − | 49.1696i | −0.918616 | − | 1.59109i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.7840 | − | 38.2133i | −0.606568 | − | 1.23397i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7647 | − | 35.9655i | −0.669828 | − | 1.16018i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.03322 | − | 1.78959i | 0.0332606 | − | 0.0576090i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.83228 | − | 15.2980i | −0.284027 | − | 0.491949i | 0.688346 | − | 0.725383i | \(-0.258337\pi\) |
−0.972373 | + | 0.233433i | \(0.925004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.7523 | + | 20.3555i | −0.377148 | + | 0.653240i | −0.990646 | − | 0.136456i | \(-0.956429\pi\) |
0.613498 | + | 0.789697i | \(0.289762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.27386 | + | 4.88614i | −0.104955 | + | 0.156642i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.71689 | + | 4.70580i | −0.0869211 | + | 0.150552i | −0.906208 | − | 0.422832i | \(-0.861036\pi\) |
0.819287 | + | 0.573384i | \(0.194369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.30308 | − | 2.25700i | 0.0416466 | − | 0.0721341i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.10690 | −0.0671997 | −0.0335998 | − | 0.999435i | \(-0.510697\pi\) | ||||
−0.0335998 | + | 0.999435i | \(0.510697\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 61.0348 | 1.94473 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.146446 | − | 0.253651i | 0.00465670 | − | 0.00806564i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.91172 | − | 15.4356i | −0.283090 | − | 0.490327i | 0.689054 | − | 0.724710i | \(-0.258026\pi\) |
−0.972144 | + | 0.234383i | \(0.924693\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.1031 | + | 74.6567i | 1.36646 | + | 2.36678i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.4954 | −1.15582 | −0.577911 | − | 0.816100i | \(-0.696132\pi\) | ||||
−0.577911 | + | 0.816100i | \(0.696132\pi\) | |||||||
\(998\) | 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 | 3024.2.t.l.289.11 | 22 | ||
3.2 | odd | 2 | 1008.2.t.k.961.5 | 22 | |||
4.3 | odd | 2 | 1512.2.t.d.289.11 | 22 | |||
7.4 | even | 3 | 3024.2.q.k.2881.1 | 22 | |||
9.4 | even | 3 | 3024.2.q.k.2305.1 | 22 | |||
9.5 | odd | 6 | 1008.2.q.k.625.4 | 22 | |||
12.11 | even | 2 | 504.2.t.d.457.7 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.q.k.529.4 | 22 | |||
28.11 | odd | 6 | 1512.2.q.c.1369.1 | 22 | |||
36.23 | even | 6 | 504.2.q.d.121.8 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.q.c.793.1 | 22 | |||
63.4 | even | 3 | inner | 3024.2.t.l.1873.11 | 22 | ||
63.32 | odd | 6 | 1008.2.t.k.193.5 | 22 | |||
84.11 | even | 6 | 504.2.q.d.25.8 | ✓ | 22 | ||
252.67 | odd | 6 | 1512.2.t.d.361.11 | 22 | |||
252.95 | even | 6 | 504.2.t.d.193.7 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.8 | ✓ | 22 | 84.11 | even | 6 | ||
504.2.q.d.121.8 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.d.193.7 | yes | 22 | 252.95 | even | 6 | ||
504.2.t.d.457.7 | yes | 22 | 12.11 | even | 2 | ||
1008.2.q.k.529.4 | 22 | 21.11 | odd | 6 | |||
1008.2.q.k.625.4 | 22 | 9.5 | odd | 6 | |||
1008.2.t.k.193.5 | 22 | 63.32 | odd | 6 | |||
1008.2.t.k.961.5 | 22 | 3.2 | odd | 2 | |||
1512.2.q.c.793.1 | 22 | 36.31 | odd | 6 | |||
1512.2.q.c.1369.1 | 22 | 28.11 | odd | 6 | |||
1512.2.t.d.289.11 | 22 | 4.3 | odd | 2 | |||
1512.2.t.d.361.11 | 22 | 252.67 | odd | 6 | |||
3024.2.q.k.2305.1 | 22 | 9.4 | even | 3 | |||
3024.2.q.k.2881.1 | 22 | 7.4 | even | 3 | |||
3024.2.t.l.289.11 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.l.1873.11 | 22 | 63.4 | even | 3 | inner |