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 | 3025.5 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.g.3025.20 |
$q$-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 | ||||||||
\(5\) | − 2.52623i | − 1.12976i | −0.825172 | − | 0.564882i | \(-0.808922\pi\) | ||||
0.825172 | − | 0.564882i | \(-0.191078\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.70432i | − 1.71992i | −0.510364 | − | 0.859958i | \(-0.670489\pi\) | ||||
0.510364 | − | 0.859958i | \(-0.329511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.06046i | − 0.848818i | −0.905471 | − | 0.424409i | \(-0.860482\pi\) | ||||
0.905471 | − | 0.424409i | \(-0.139518\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.49926 | −1.33377 | −0.666883 | − | 0.745163i | \(-0.732372\pi\) | ||||
−0.666883 | + | 0.745163i | \(0.732372\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.28486i | − 1.67126i | −0.549291 | − | 0.835631i | \(-0.685102\pi\) | ||||
0.549291 | − | 0.835631i | \(-0.314898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.539732 | −0.112542 | −0.0562710 | − | 0.998416i | \(-0.517921\pi\) | ||||
−0.0562710 | + | 0.998416i | \(0.517921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.38184 | −0.276367 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.35116i | 1.55077i | 0.631488 | + | 0.775386i | \(0.282445\pi\) | ||||
−0.631488 | + | 0.775386i | \(0.717555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.74848 | −1.21206 | −0.606032 | − | 0.795441i | \(-0.707239\pi\) | ||||
−0.606032 | + | 0.795441i | \(0.707239\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.52623i | 0.427011i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 10.2711i | − 1.68855i | −0.535908 | − | 0.844277i | \(-0.680031\pi\) | ||||
0.535908 | − | 0.844277i | \(-0.319969\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.58370 | 0.872028 | 0.436014 | − | 0.899940i | \(-0.356390\pi\) | ||||
0.436014 | + | 0.899940i | \(0.356390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.98332i | − 0.607451i | −0.952760 | − | 0.303725i | \(-0.901770\pi\) | ||||
0.952760 | − | 0.303725i | \(-0.0982305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.83840 | −0.705754 | −0.352877 | − | 0.935670i | \(-0.614797\pi\) | ||||
−0.352877 | + | 0.935670i | \(0.614797\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.1320i | 1.52910i | 0.644562 | + | 0.764552i | \(0.277040\pi\) | ||||
−0.644562 | + | 0.764552i | \(0.722960\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.4104 | −1.94310 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 10.1647i | − 1.32333i | −0.749798 | − | 0.661666i | \(-0.769850\pi\) | ||||
0.749798 | − | 0.661666i | \(-0.230150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4.14075i | − 0.530169i | −0.964225 | − | 0.265084i | \(-0.914600\pi\) | ||||
0.964225 | − | 0.265084i | \(-0.0853998\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.73142 | −0.958964 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.96348i | 0.728555i | 0.931290 | + | 0.364278i | \(0.118684\pi\) | ||||
−0.931290 | + | 0.364278i | \(0.881316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.93014 | 0.585100 | 0.292550 | − | 0.956250i | \(-0.405496\pi\) | ||||
0.292550 | + | 0.956250i | \(0.405496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.66798 | 1.01451 | 0.507255 | − | 0.861796i | \(-0.330660\pi\) | ||||
0.507255 | + | 0.861796i | \(0.330660\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.70432i | 0.650067i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0532 | −1.35609 | −0.678044 | − | 0.735021i | \(-0.737172\pi\) | ||||
−0.678044 | + | 0.735021i | \(0.737172\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.83393i | 0.640357i | 0.947357 | + | 0.320178i | \(0.103743\pi\) | ||||
−0.947357 | + | 0.320178i | \(0.896257\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8924i | 1.50684i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.28810 | 0.984537 | 0.492268 | − | 0.870444i | \(-0.336168\pi\) | ||||
0.492268 | + | 0.870444i | \(0.336168\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.06046i | 0.320823i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.4032 | −1.88813 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3500 | 1.25395 | 0.626974 | − | 0.779040i | \(-0.284293\pi\) | ||||
0.626974 | + | 0.779040i | \(0.284293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.33719i | 0.929085i | 0.885551 | + | 0.464542i | \(0.153781\pi\) | ||||
−0.885551 | + | 0.464542i | \(0.846219\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.28802 | 0.718110 | 0.359055 | − | 0.933316i | \(-0.383099\pi\) | ||||
0.359055 | + | 0.933316i | \(0.383099\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.31179i | 0.706858i | 0.935461 | + | 0.353429i | \(0.114984\pi\) | ||||
−0.935461 | + | 0.353429i | \(0.885016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9330i | 1.52611i | 0.646336 | + | 0.763053i | \(0.276300\pi\) | ||||
−0.646336 | + | 0.763053i | \(0.723700\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.91459 | −0.650470 | −0.325235 | − | 0.945633i | \(-0.605443\pi\) | ||||
−0.325235 | + | 0.945633i | \(0.605443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.36349i | 0.127146i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.49926 | 0.504116 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.5393 | −1.95811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9.14031i | − 0.817534i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6103 | 1.56267 | 0.781333 | − | 0.624115i | \(-0.214540\pi\) | ||||
0.781333 | + | 0.624115i | \(0.214540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7551i | 0.939675i | 0.882753 | + | 0.469838i | \(0.155688\pi\) | ||||
−0.882753 | + | 0.469838i | \(0.844312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.28486i | 0.631678i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.56413 | −0.133633 | −0.0668164 | − | 0.997765i | \(-0.521284\pi\) | ||||
−0.0668164 | + | 0.997765i | \(0.521284\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 11.2728i | − 0.956149i | −0.878319 | − | 0.478074i | \(-0.841335\pi\) | ||||
0.878319 | − | 0.478074i | \(-0.158665\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.4578 | −1.45990 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.0970 | 1.75201 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 6.48749i | − 0.531476i | −0.964045 | − | 0.265738i | \(-0.914384\pi\) | ||||
0.964045 | − | 0.265738i | \(-0.0856156\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.383325 | 0.0311945 | 0.0155973 | − | 0.999878i | \(-0.495035\pi\) | ||||
0.0155973 | + | 0.999878i | \(0.495035\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.0482i | 1.36935i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.66658i | 0.691669i | 0.938296 | + | 0.345834i | \(0.112404\pi\) | ||||
−0.938296 | + | 0.345834i | \(0.887596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.539732 | 0.0425369 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 25.0771i | − 1.96419i | −0.188382 | − | 0.982096i | \(-0.560324\pi\) | ||||
0.188382 | − | 0.982096i | \(-0.439676\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.75411 | −0.677414 | −0.338707 | − | 0.940892i | \(-0.609989\pi\) | ||||
−0.338707 | + | 0.940892i | \(0.609989\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.63361 | 0.279508 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 9.29760i | − 0.706883i | −0.935457 | − | 0.353442i | \(-0.885011\pi\) | ||||
0.935457 | − | 0.353442i | \(-0.114989\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.38184 | 0.104457 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.65495i | 0.572158i | 0.958206 | + | 0.286079i | \(0.0923520\pi\) | ||||
−0.958206 | + | 0.286079i | \(0.907648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2.50424i | − 0.186138i | −0.995660 | − | 0.0930692i | \(-0.970332\pi\) | ||||
0.995660 | − | 0.0930692i | \(-0.0296678\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.9471 | −1.90767 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.3695i | 2.29397i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.20627 | −0.231997 | −0.115999 | − | 0.993249i | \(-0.537007\pi\) | ||||
−0.115999 | + | 0.993249i | \(0.537007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9544 | 0.788518 | 0.394259 | − | 0.918999i | \(-0.371001\pi\) | ||||
0.394259 | + | 0.918999i | \(0.371001\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.87749i | 0.561248i | 0.959818 | + | 0.280624i | \(0.0905414\pi\) | ||||
−0.959818 | + | 0.280624i | \(0.909459\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00753 | −0.0714217 | −0.0357109 | − | 0.999362i | \(-0.511370\pi\) | ||||
−0.0357109 | + | 0.999362i | \(0.511370\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.35116i | − 0.586137i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 14.1057i | − 0.985186i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.5552 | −2.87443 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 16.2709i | − 1.12014i | −0.828446 | − | 0.560069i | \(-0.810775\pi\) | ||||
0.828446 | − | 0.560069i | \(-0.189225\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.0628 | −0.686276 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.74848 | 0.458117 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.8302i | 1.13212i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.78339 | −0.186390 | −0.0931949 | − | 0.995648i | \(-0.529708\pi\) | ||||
−0.0931949 | + | 0.995648i | \(0.529708\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 11.4440i | − 0.759565i | −0.925076 | − | 0.379782i | \(-0.875999\pi\) | ||||
0.925076 | − | 0.379782i | \(-0.124001\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.54391i | 0.300270i | 0.988666 | + | 0.150135i | \(0.0479708\pi\) | ||||
−0.988666 | + | 0.150135i | \(0.952029\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0188 | 1.04943 | 0.524715 | − | 0.851278i | \(-0.324172\pi\) | ||||
0.524715 | + | 0.851278i | \(0.324172\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.2229i | 0.797335i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.2968 | −1.24821 | −0.624104 | − | 0.781341i | \(-0.714536\pi\) | ||||
−0.624104 | + | 0.781341i | \(0.714536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.1358 | −1.42589 | −0.712947 | − | 0.701218i | \(-0.752640\pi\) | ||||
−0.712947 | + | 0.701218i | \(0.752640\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.52623i | − 0.161395i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.2950 | −1.41860 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.94172i | 0.501277i | 0.968081 | + | 0.250638i | \(0.0806405\pi\) | ||||
−0.968081 | + | 0.250638i | \(0.919360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.07881i | 0.193563i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.02501 | −0.438208 | −0.219104 | − | 0.975701i | \(-0.570313\pi\) | ||||
−0.219104 | + | 0.975701i | \(0.570313\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.2711i | 0.638213i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.4695 | 1.20054 | 0.600270 | − | 0.799798i | \(-0.295060\pi\) | ||||
0.600270 | + | 0.799798i | \(0.295060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.1221 | 1.72753 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.4258i | 0.940526i | 0.882526 | + | 0.470263i | \(0.155841\pi\) | ||||
−0.882526 | + | 0.470263i | \(0.844159\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.28198 | −0.442349 | −0.221174 | − | 0.975234i | \(-0.570989\pi\) | ||||
−0.221174 | + | 0.975234i | \(0.570989\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.88244i | 0.475329i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.43449i | 0.146275i | 0.997322 | + | 0.0731373i | \(0.0233011\pi\) | ||||
−0.997322 | + | 0.0731373i | \(0.976699\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.1555 | −1.08307 | −0.541534 | − | 0.840679i | \(-0.682156\pi\) | ||||
−0.541534 | + | 0.840679i | \(0.682156\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 31.2909i | − 1.86005i | −0.367496 | − | 0.930025i | \(-0.619785\pi\) | ||||
0.367496 | − | 0.930025i | \(-0.380215\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.58370 | −0.329596 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.2418 | 0.778931 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 18.3419i | − 1.07155i | −0.844362 | − | 0.535773i | \(-0.820020\pi\) | ||||
0.844362 | − | 0.535773i | \(-0.179980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.6784 | −1.49505 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.65183i | 0.0955276i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.98332i | 0.229595i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.4605 | −0.598966 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.5811i | 1.40292i | 0.712709 | + | 0.701460i | \(0.247468\pi\) | ||||
−0.712709 | + | 0.701460i | \(0.752532\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.95251 | 0.394240 | 0.197120 | − | 0.980379i | \(-0.436841\pi\) | ||||
0.197120 | + | 0.980379i | \(0.436841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.81498 | −0.554775 | −0.277388 | − | 0.960758i | \(-0.589469\pi\) | ||||
−0.277388 | + | 0.960758i | \(0.589469\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.69289i | 0.375910i | 0.982178 | + | 0.187955i | \(0.0601860\pi\) | ||||
−0.982178 | + | 0.187955i | \(0.939814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 47.6377 | 2.66720 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.0613i | 2.22907i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.22905i | 0.234586i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.83840 | 0.266750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.10916i | 0.115930i | 0.998319 | + | 0.0579651i | \(0.0184612\pi\) | ||||
−0.998319 | + | 0.0579651i | \(0.981539\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.0651 | 0.823096 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.53954 | −0.301758 | −0.150879 | − | 0.988552i | \(-0.548210\pi\) | ||||
−0.150879 | + | 0.988552i | \(0.548210\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38.4955i | 2.08465i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 9.63790i | − 0.517389i | −0.965959 | − | 0.258695i | \(-0.916708\pi\) | ||||
0.965959 | − | 0.258695i | \(-0.0832924\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.04565i | 0.430674i | 0.976540 | + | 0.215337i | \(0.0690850\pi\) | ||||
−0.976540 | + | 0.215337i | \(0.930915\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.2775 | 1.45184 | 0.725918 | − | 0.687782i | \(-0.241415\pi\) | ||||
0.725918 | + | 0.687782i | \(0.241415\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 12.4547i | − 0.661025i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.36413 | 0.388664 | 0.194332 | − | 0.980936i | \(-0.437746\pi\) | ||||
0.194332 | + | 0.980936i | \(0.437746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −34.0692 | −1.79312 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 21.8973i | − 1.14616i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.8746 | −1.14185 | −0.570923 | − | 0.821003i | \(-0.693415\pi\) | ||||
−0.570923 | + | 0.821003i | \(0.693415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 11.1320i | − 0.577947i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.99106i | 0.465539i | 0.972532 | + | 0.232770i | \(0.0747788\pi\) | ||||
−0.972532 | + | 0.232770i | \(0.925221\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.5584 | 1.31632 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.9165i | 1.48534i | 0.669656 | + | 0.742671i | \(0.266442\pi\) | ||||
−0.669656 | + | 0.742671i | \(0.733558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.5404 | −0.640786 | −0.320393 | − | 0.947285i | \(-0.603815\pi\) | ||||
−0.320393 | + | 0.947285i | \(0.603815\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4104 | 0.734423 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 7.50374i | − 0.380455i | −0.981740 | − | 0.190227i | \(-0.939077\pi\) | ||||
0.981740 | − | 0.190227i | \(-0.0609225\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.96813 | 0.150105 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.4491i | 1.53206i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 27.6639i | − 1.38841i | −0.719778 | − | 0.694205i | \(-0.755756\pi\) | ||||
0.719778 | − | 0.694205i | \(-0.244244\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.8414 | −1.78983 | −0.894916 | − | 0.446234i | \(-0.852765\pi\) | ||||
−0.894916 | + | 0.446234i | \(0.852765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.6534i | 1.02882i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −58.5894 | −2.90417 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4056 | 0.910097 | 0.455048 | − | 0.890467i | \(-0.349622\pi\) | ||||
0.455048 | + | 0.890467i | \(0.349622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.1647i | 0.500173i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.7378 | 0.723452 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.0173724i | 0 0.000848699i | 1.00000 | 0.000424349i | \(0.000135075\pi\) | |||||
−1.00000 | 0.000424349i | \(0.999865\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.03437i | 0.0504121i | 0.999682 | + | 0.0252060i | \(0.00802418\pi\) | ||||
−0.999682 | + | 0.0252060i | \(0.991976\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.59908 | 0.368609 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.14075i | 0.200385i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.1392 | −0.488390 | −0.244195 | − | 0.969726i | \(-0.578524\pi\) | ||||
−0.244195 | + | 0.969726i | \(0.578524\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.5806 | −1.61378 | −0.806890 | − | 0.590701i | \(-0.798851\pi\) | ||||
−0.806890 | + | 0.590701i | \(0.798851\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.93188i | 0.188087i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.92098 | 0.187138 | 0.0935692 | − | 0.995613i | \(-0.470172\pi\) | ||||
0.0935692 | + | 0.995613i | \(0.470172\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.6306i | 1.64535i | 0.568514 | + | 0.822674i | \(0.307519\pi\) | ||||
−0.568514 | + | 0.822674i | \(0.692481\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 23.4639i | − 1.11229i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.7862 | −0.839383 | −0.419691 | − | 0.907667i | \(-0.637862\pi\) | ||||
−0.419691 | + | 0.907667i | \(0.637862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 31.8512i | − 1.49982i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.73142 | 0.362454 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5852 | 0.541933 | 0.270966 | − | 0.962589i | \(-0.412657\pi\) | ||||
0.270966 | + | 0.962589i | \(0.412657\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 12.5948i | − 0.586596i | −0.956021 | − | 0.293298i | \(-0.905247\pi\) | ||||
0.956021 | − | 0.293298i | \(-0.0947529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.16107 | 0.146907 | 0.0734537 | − | 0.997299i | \(-0.476598\pi\) | ||||
0.0734537 | + | 0.997299i | \(0.476598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 20.8974i | − 0.967015i | −0.875340 | − | 0.483507i | \(-0.839363\pi\) | ||||
0.875340 | − | 0.483507i | \(-0.160637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 5.96348i | − 0.275368i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.7221 | −1.04476 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0665i | 0.461882i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.2766 | −1.29199 | −0.645996 | − | 0.763341i | \(-0.723558\pi\) | ||||
−0.645996 | + | 0.763341i | \(0.723558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.4341 | −1.43327 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 31.1988i | − 1.41667i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.8879 | 1.21841 | 0.609203 | − | 0.793014i | \(-0.291489\pi\) | ||||
0.609203 | + | 0.793014i | \(0.291489\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00142i | 0.270840i | 0.990788 | + | 0.135420i | \(0.0432384\pi\) | ||||
−0.990788 | + | 0.135420i | \(0.956762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 45.9252i | − 2.06837i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.93014 | −0.221147 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.3124i | 0.819777i | 0.912136 | + | 0.409888i | \(0.134432\pi\) | ||||
−0.912136 | + | 0.409888i | \(0.865568\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.95874 | 0.310275 | 0.155137 | − | 0.987893i | \(-0.450418\pi\) | ||||
0.155137 | + | 0.987893i | \(0.450418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.5879 | 1.04965 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 15.2426i | − 0.675618i | −0.941215 | − | 0.337809i | \(-0.890314\pi\) | ||||
0.941215 | − | 0.337809i | \(-0.109686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.66798 | −0.383449 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 18.4112i | − 0.811295i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.5998i | 1.21384i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0764 | −0.572887 | −0.286444 | − | 0.958097i | \(-0.592473\pi\) | ||||
−0.286444 | + | 0.958097i | \(0.592473\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.9123i | 1.04561i | 0.852452 | + | 0.522806i | \(0.175115\pi\) | ||||
−0.852452 | + | 0.522806i | \(0.824885\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.1116 | 1.61661 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7087 | −0.987334 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 17.0887i | − 0.740193i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.4713 | 0.798583 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.70432i | − 0.245702i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 13.9717i | − 0.600689i | −0.953831 | − | 0.300345i | \(-0.902898\pi\) | ||||
0.953831 | − | 0.300345i | \(-0.0971017\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.2504 | 1.72414 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 21.5760i | − 0.922522i | −0.887264 | − | 0.461261i | \(-0.847397\pi\) | ||||
0.887264 | − | 0.461261i | \(-0.152603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 60.8371 | 2.59175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0532 | 0.512553 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 0.679074i | − 0.0287733i | −0.999897 | − | 0.0143866i | \(-0.995420\pi\) | ||||
0.999897 | − | 0.0143866i | \(-0.00457957\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.1908 | −0.515615 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.8429i | 0.667698i | 0.942626 | + | 0.333849i | \(0.108348\pi\) | ||||
−0.942626 | + | 0.333849i | \(0.891652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.4678i | 0.734877i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.24267 | −0.135940 | −0.0679698 | − | 0.997687i | \(-0.521652\pi\) | ||||
−0.0679698 | + | 0.997687i | \(0.521652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.38251i | − 0.0578563i | −0.999581 | − | 0.0289281i | \(-0.990791\pi\) | ||||
0.999581 | − | 0.0289281i | \(-0.00920939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.745822 | 0.0311029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.57598 | −0.315392 | −0.157696 | − | 0.987488i | \(-0.550407\pi\) | ||||
−0.157696 | + | 0.987488i | \(0.550407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.83393i | − 0.242032i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 63.5007 | 2.62993 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 5.03970i | − 0.208011i | −0.994577 | − | 0.104005i | \(-0.966834\pi\) | ||||
0.994577 | − | 0.104005i | \(-0.0331659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.1618i | 2.02568i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.94121 | 0.326106 | 0.163053 | − | 0.986617i | \(-0.447866\pi\) | ||||
0.163053 | + | 0.986617i | \(0.447866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 13.8924i | − 0.569532i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.0131 | −1.34888 | −0.674439 | − | 0.738331i | \(-0.735614\pi\) | ||||
−0.674439 | + | 0.738331i | \(0.735614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4038 | 1.64810 | 0.824052 | − | 0.566513i | \(-0.191708\pi\) | ||||
0.824052 | + | 0.566513i | \(0.191708\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 54.4131i | 2.21221i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.544975 | −0.0221199 | −0.0110599 | − | 0.999939i | \(-0.503521\pi\) | ||||
−0.0110599 | + | 0.999939i | \(0.503521\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.8077i | 0.599056i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.75425i | 0.111243i | 0.998452 | + | 0.0556215i | \(0.0177140\pi\) | ||||
−0.998452 | + | 0.0556215i | \(0.982286\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.6720 | −1.31533 | −0.657664 | − | 0.753312i | \(-0.728455\pi\) | ||||
−0.657664 | + | 0.753312i | \(0.728455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4789i | 0.421183i | 0.977574 | + | 0.210591i | \(0.0675389\pi\) | ||||
−0.977574 | + | 0.210591i | \(0.932461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.28810 | −0.372120 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9997 | −1.19999 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 56.4832i | 2.25213i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.94128 | 0.316138 | 0.158069 | − | 0.987428i | \(-0.449473\pi\) | ||||
0.158069 | + | 0.987428i | \(0.449473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 44.4878i | − 1.76544i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.06046i | − 0.121260i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.5222 | −0.692084 | −0.346042 | − | 0.938219i | \(-0.612475\pi\) | ||||
−0.346042 | + | 0.938219i | \(0.612475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 34.7998i | − 1.37237i | −0.727426 | − | 0.686186i | \(-0.759284\pi\) | ||||
0.727426 | − | 0.686186i | \(-0.240716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.4054 | 0.959474 | 0.479737 | − | 0.877412i | \(-0.340732\pi\) | ||||
0.479737 | + | 0.877412i | \(0.340732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −57.9827 | −2.27602 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 20.9374i | − 0.819345i | −0.912233 | − | 0.409673i | \(-0.865643\pi\) | ||||
0.912233 | − | 0.409673i | \(-0.134357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.1698 | 1.06161 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 27.6061i | − 1.07538i | −0.843143 | − | 0.537690i | \(-0.819297\pi\) | ||||
0.843143 | − | 0.537690i | \(-0.180703\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 31.2679i | − 1.21618i | −0.793868 | − | 0.608090i | \(-0.791936\pi\) | ||||
0.793868 | − | 0.608090i | \(-0.208064\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.4032 | 0.713647 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.50739i | − 0.174527i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.6201 | −0.911846 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.7023 | 0.720923 | 0.360461 | − | 0.932774i | \(-0.382619\pi\) | ||||
0.360461 | + | 0.932774i | \(0.382619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.58757i | 0.0610152i | 0.999535 | + | 0.0305076i | \(0.00971238\pi\) | ||||
−0.999535 | + | 0.0305076i | \(0.990288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.3500 | −0.473948 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.1798i | 1.30785i | 0.756557 | + | 0.653927i | \(0.226880\pi\) | ||||
−0.756557 | + | 0.653927i | \(0.773120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.95135i | 0.150974i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.0691 | 1.29793 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 39.5718i | − 1.50538i | −0.658373 | − | 0.752692i | \(-0.728755\pi\) | ||||
0.658373 | − | 0.752692i | \(-0.271245\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.4778 | −1.08022 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.7062 | −1.16308 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.2500i | 1.14253i | 0.820767 | + | 0.571263i | \(0.193546\pi\) | ||||
−0.820767 | + | 0.571263i | \(0.806454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −74.8233 | −2.82202 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 9.33719i | − 0.351161i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 51.5735i | − 1.93688i | −0.249244 | − | 0.968441i | \(-0.580182\pi\) | ||||
0.249244 | − | 0.968441i | \(-0.419818\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.64237 | 0.136408 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44.1025i | 1.64934i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2028 | 0.417795 | 0.208898 | − | 0.977938i | \(-0.433012\pi\) | ||||
0.208898 | + | 0.977938i | \(0.433012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.28802 | −0.271420 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 11.5399i | − 0.428583i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.814724 | 0.0302164 | 0.0151082 | − | 0.999886i | \(-0.495191\pi\) | ||||
0.0151082 | + | 0.999886i | \(0.495191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.9053i | 0.810197i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7283i | 0.470131i | 0.971980 | + | 0.235066i | \(0.0755305\pi\) | ||||
−0.971980 | + | 0.235066i | \(0.924470\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.0176 | 1.25305 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 9.13395i | − 0.335998i | −0.985787 | − | 0.167999i | \(-0.946269\pi\) | ||||
0.985787 | − | 0.167999i | \(-0.0537305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.4112 | 0.565383 | 0.282692 | − | 0.959211i | \(-0.408773\pi\) | ||||
0.282692 | + | 0.959211i | \(0.408773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.3889 | −0.600442 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 7.31179i | − 0.267167i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.7526 | −1.48708 | −0.743542 | − | 0.668690i | \(-0.766856\pi\) | ||||
−0.743542 | + | 0.668690i | \(0.766856\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 0.968366i | − 0.0352424i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 26.0085i | − 0.945296i | −0.881251 | − | 0.472648i | \(-0.843298\pi\) | ||||
0.881251 | − | 0.472648i | \(-0.156702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3686 | −0.375861 | −0.187931 | − | 0.982182i | \(-0.560178\pi\) | ||||
−0.187931 | + | 0.982182i | \(0.560178\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 15.9330i | − 0.576814i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.1086 | −1.12327 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.7525 | −1.14502 | −0.572512 | − | 0.819896i | \(-0.694031\pi\) | ||||
−0.572512 | + | 0.819896i | \(0.694031\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.3614i | 0.588478i | 0.955732 | + | 0.294239i | \(0.0950662\pi\) | ||||
−0.955732 | + | 0.294239i | \(0.904934\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.32530 | 0.334975 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 40.6765i | − 1.45739i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 28.1231i | − 1.00632i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.8938 | 0.781422 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 25.4664i | − 0.907781i | −0.891058 | − | 0.453890i | \(-0.850036\pi\) | ||||
0.891058 | − | 0.453890i | \(-0.149964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.91459 | 0.245854 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.6726 | −0.450016 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 27.4312i | − 0.971664i | −0.874052 | − | 0.485832i | \(-0.838517\pi\) | ||||
0.874052 | − | 0.485832i | \(-0.161483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.6076 | 0.941310 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 49.4449i | − 1.74487i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.36349i | − 0.0480566i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.8507 | 0.838546 | 0.419273 | − | 0.907860i | \(-0.362285\pi\) | ||||
0.419273 | + | 0.907860i | \(0.362285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.8123i | 0.976622i | 0.872670 | + | 0.488311i | \(0.162387\pi\) | ||||
−0.872670 | + | 0.488311i | \(0.837613\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −63.3506 | −2.21907 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.0179 | −1.01521 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 53.9215i | − 1.88187i | −0.338583 | − | 0.940936i | \(-0.609948\pi\) | ||||
0.338583 | − | 0.940936i | \(-0.390052\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4932 | 0.400628 | 0.200314 | − | 0.979732i | \(-0.435804\pi\) | ||||
0.200314 | + | 0.979732i | \(0.435804\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.946387i | 0.0329091i | 0.999865 | + | 0.0164546i | \(0.00523788\pi\) | ||||
−0.999865 | + | 0.0164546i | \(0.994762\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.9151i | 1.49050i | 0.666783 | + | 0.745252i | \(0.267671\pi\) | ||||
−0.666783 | + | 0.745252i | \(0.732329\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.49926 | −0.190538 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.1149i | 0.765318i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.2098 | 1.07748 | 0.538741 | − | 0.842471i | \(-0.318900\pi\) | ||||
0.538741 | + | 0.842471i | \(0.318900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −40.7419 | −1.40489 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 9.17933i | − 0.315779i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.5393 | 0.740097 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.54363i | 0.190033i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 8.84389i | − 0.302809i | −0.988472 | − | 0.151404i | \(-0.951620\pi\) | ||||
0.988472 | − | 0.151404i | \(-0.0483796\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −49.1414 | −1.67864 | −0.839319 | − | 0.543640i | \(-0.817046\pi\) | ||||
−0.839319 | + | 0.543640i | \(0.817046\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 43.8201i | − 1.49512i | −0.664193 | − | 0.747561i | \(-0.731225\pi\) | ||||
0.664193 | − | 0.747561i | \(-0.268775\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.5811 | 1.07503 | 0.537516 | − | 0.843253i | \(-0.319363\pi\) | ||||
0.537516 | + | 0.843253i | \(0.319363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.4879 | −0.798612 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 68.7552i | 2.33236i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.2510 | 0.618411 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.14031i | 0.308999i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.7451i | 1.13949i | 0.821821 | + | 0.569746i | \(0.192959\pi\) | ||||
−0.821821 | + | 0.569746i | \(0.807041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.58523 | 0.289244 | 0.144622 | − | 0.989487i | \(-0.453803\pi\) | ||||
0.144622 | + | 0.989487i | \(0.453803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.07348i | 0.271694i | 0.990730 | + | 0.135847i | \(0.0433756\pi\) | ||||
−0.990730 | + | 0.135847i | \(0.956624\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.4397 | 1.05564 | 0.527821 | − | 0.849356i | \(-0.323009\pi\) | ||||
0.527821 | + | 0.849356i | \(0.323009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.6103 | −0.590632 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.2471i | 1.17950i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.3382 | 0.646404 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 56.3577i | − 1.87963i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 61.2180i | − 2.03947i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.32628 | −0.210293 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.4183i | 0.345932i | 0.984928 | + | 0.172966i | \(0.0553352\pi\) | ||||
−0.984928 | + | 0.172966i | \(0.944665\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.9123 | −1.58741 | −0.793703 | − | 0.608305i | \(-0.791850\pi\) | ||||
−0.793703 | + | 0.608305i | \(0.791850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.2786 | 1.10136 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 10.7551i | − 0.355164i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.6472 | 1.24187 | 0.620933 | − | 0.783863i | \(-0.286754\pi\) | ||||
0.620933 | + | 0.783863i | \(0.286754\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 15.0885i | − 0.496644i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1929i | 0.466661i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.8135 | 1.47028 | 0.735141 | − | 0.677914i | \(-0.237116\pi\) | ||||
0.735141 | + | 0.677914i | \(0.237116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 7.28486i | − 0.238752i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 79.2466 | 2.59164 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.2431 | 0.955330 | 0.477665 | − | 0.878542i | \(-0.341483\pi\) | ||||
0.477665 | + | 0.878542i | \(0.341483\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 11.7936i | − 0.384460i | −0.981350 | − | 0.192230i | \(-0.938428\pi\) | ||||
0.981350 | − | 0.192230i | \(-0.0615719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.01371 | −0.0981398 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.5710i | 0.473493i | 0.971572 | + | 0.236746i | \(0.0760810\pi\) | ||||
−0.971572 | + | 0.236746i | \(0.923919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 26.5280i | − 0.861134i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.0151 | −1.74972 | −0.874860 | − | 0.484375i | \(-0.839047\pi\) | ||||
−0.874860 | + | 0.484375i | \(0.839047\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.09977i | 0.262102i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.56413 | 0.0505084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5420 | 0.469097 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 27.6735i | − 0.890840i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.1750 | −1.25978 | −0.629892 | − | 0.776683i | \(-0.716901\pi\) | ||||
−0.629892 | + | 0.776683i | \(0.716901\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.39896i | − 0.0769864i | −0.999259 | − | 0.0384932i | \(-0.987744\pi\) | ||||
0.999259 | − | 0.0384932i | \(-0.0122558\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.2728i | 0.361390i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.7447 | 0.503717 | 0.251858 | − | 0.967764i | \(-0.418958\pi\) | ||||
0.251858 | + | 0.967764i | \(0.418958\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 52.9823i | − 1.69332i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.5566 | 0.464285 | 0.232142 | − | 0.972682i | \(-0.425426\pi\) | ||||
0.232142 | + | 0.972682i | \(0.425426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.9004 | 0.634078 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.14993i | 0.0683637i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.2853 | 0.739681 | 0.369841 | − | 0.929095i | \(-0.379412\pi\) | ||||
0.369841 | + | 0.929095i | \(0.379412\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.54525i | 0.0806897i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.38107i | − 0.0437390i | −0.999761 | − | 0.0218695i | \(-0.993038\pi\) | ||||
0.999761 | − | 0.0218695i | \(-0.00696184\pi\) | |||||||
\(998\) | 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.g.3025.5 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.g.3025.19 | 24 | ||
4.3 | odd | 2 | 1512.2.c.f.757.8 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.f.757.7 | ✓ | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.g.3025.20 | 24 | ||
12.11 | even | 2 | 1512.2.c.f.757.17 | yes | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.g.3025.6 | 24 | ||
24.11 | even | 2 | 1512.2.c.f.757.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.7 | ✓ | 24 | 8.3 | odd | 2 | ||
1512.2.c.f.757.8 | yes | 24 | 4.3 | odd | 2 | ||
1512.2.c.f.757.17 | yes | 24 | 12.11 | even | 2 | ||
1512.2.c.f.757.18 | yes | 24 | 24.11 | even | 2 | ||
6048.2.c.g.3025.5 | 24 | 1.1 | even | 1 | trivial | ||
6048.2.c.g.3025.6 | 24 | 24.5 | odd | 2 | inner | ||
6048.2.c.g.3025.19 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.g.3025.20 | 24 | 8.5 | even | 2 | inner |