Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.5 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.c.5615.6 |
$q$-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 | ||||||||
\(5\) | −2.21305 | −0.989704 | −0.494852 | − | 0.868977i | \(-0.664778\pi\) | ||||
−0.494852 | + | 0.868977i | \(0.664778\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.42373i | − 0.730781i | −0.930854 | − | 0.365390i | \(-0.880935\pi\) | ||||
0.930854 | − | 0.365390i | \(-0.119065\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.11593i | − 0.309504i | −0.987953 | − | 0.154752i | \(-0.950542\pi\) | ||||
0.987953 | − | 0.154752i | \(-0.0494579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.701326i | 0.170097i | 0.996377 | + | 0.0850483i | \(0.0271044\pi\) | ||||
−0.996377 | + | 0.0850483i | \(0.972896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.938340 | −0.215270 | −0.107635 | − | 0.994190i | \(-0.534328\pi\) | ||||
−0.107635 | + | 0.994190i | \(0.534328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.30502 | 0.897658 | 0.448829 | − | 0.893618i | \(-0.351841\pi\) | ||||
0.448829 | + | 0.893618i | \(0.351841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.102426 | −0.0204852 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.26130 | 0.791303 | 0.395652 | − | 0.918401i | \(-0.370519\pi\) | ||||
0.395652 | + | 0.918401i | \(0.370519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.02221i | 1.26123i | 0.776098 | + | 0.630613i | \(0.217196\pi\) | ||||
−0.776098 | + | 0.630613i | \(0.782804\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.21305i | − 0.374073i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.12583i | 0.513883i | 0.966427 | + | 0.256941i | \(0.0827148\pi\) | ||||
−0.966427 | + | 0.256941i | \(0.917285\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.157922i | 0.0246632i | 0.999924 | + | 0.0123316i | \(0.00392537\pi\) | ||||
−0.999924 | + | 0.0123316i | \(0.996075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.08975 | −1.08118 | −0.540588 | − | 0.841287i | \(-0.681798\pi\) | ||||
−0.540588 | + | 0.841287i | \(0.681798\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.867970 | −0.126607 | −0.0633033 | − | 0.997994i | \(-0.520164\pi\) | ||||
−0.0633033 | + | 0.997994i | \(0.520164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.91444 | 0.537689 | 0.268845 | − | 0.963184i | \(-0.413358\pi\) | ||||
0.268845 | + | 0.963184i | \(0.413358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.36382i | 0.723257i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 7.28820i | − 0.948843i | −0.880298 | − | 0.474421i | \(-0.842657\pi\) | ||||
0.880298 | − | 0.474421i | \(-0.157343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.57877i | 0.586251i | 0.956074 | + | 0.293126i | \(0.0946955\pi\) | ||||
−0.956074 | + | 0.293126i | \(0.905305\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.46961i | 0.306318i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.1677 | −1.85303 | −0.926513 | − | 0.376264i | \(-0.877209\pi\) | ||||
−0.926513 | + | 0.376264i | \(0.877209\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.93451 | −0.822975 | −0.411487 | − | 0.911416i | \(-0.634991\pi\) | ||||
−0.411487 | + | 0.911416i | \(0.634991\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.02133 | 0.821785 | 0.410893 | − | 0.911684i | \(-0.365217\pi\) | ||||
0.410893 | + | 0.911684i | \(0.365217\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.42373 | 0.276209 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6.65903i | − 0.749200i | −0.927187 | − | 0.374600i | \(-0.877780\pi\) | ||||
0.927187 | − | 0.374600i | \(-0.122220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.41084i | − 0.923210i | −0.887086 | − | 0.461605i | \(-0.847274\pi\) | ||||
0.887086 | − | 0.461605i | \(-0.152726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1.55207i | − 0.168345i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 7.34335i | − 0.778393i | −0.921155 | − | 0.389197i | \(-0.872753\pi\) | ||||
0.921155 | − | 0.389197i | \(-0.127247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.11593 | 0.116982 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.07659 | 0.213054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.99425 | 0.811693 | 0.405846 | − | 0.913941i | \(-0.366977\pi\) | ||||
0.405846 | + | 0.913941i | \(0.366977\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6519 | 1.55742 | 0.778709 | − | 0.627385i | \(-0.215875\pi\) | ||||
0.778709 | + | 0.627385i | \(0.215875\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.90314i | 0.483121i | 0.970386 | + | 0.241560i | \(0.0776592\pi\) | ||||
−0.970386 | + | 0.241560i | \(0.922341\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 15.1434i | − 1.46397i | −0.681320 | − | 0.731986i | \(-0.738594\pi\) | ||||
0.681320 | − | 0.731986i | \(-0.261406\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.72939i | − 0.261428i | −0.991420 | − | 0.130714i | \(-0.958273\pi\) | ||||
0.991420 | − | 0.130714i | \(-0.0417270\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.84331i | − 0.267476i | −0.991017 | − | 0.133738i | \(-0.957302\pi\) | ||||
0.991017 | − | 0.133738i | \(-0.0426980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.52720 | −0.888416 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.701326 | −0.0642905 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.12555 | 0.465959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2919 | 1.00998 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 10.4243i | − 0.925006i | −0.886618 | − | 0.462503i | \(-0.846951\pi\) | ||||
0.886618 | − | 0.462503i | \(-0.153049\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.3573i | 1.86600i | 0.359881 | + | 0.932998i | \(0.382817\pi\) | ||||
−0.359881 | + | 0.932998i | \(0.617183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.938340i | − 0.0813644i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11.2577i | − 0.961812i | −0.876772 | − | 0.480906i | \(-0.840308\pi\) | ||||
0.876772 | − | 0.480906i | \(-0.159692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.11586 | −0.688379 | −0.344189 | − | 0.938900i | \(-0.611846\pi\) | ||||
−0.344189 | + | 0.938900i | \(0.611846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.70472 | −0.226180 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.43045 | −0.783156 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.90580 | −0.401899 | −0.200949 | − | 0.979602i | \(-0.564403\pi\) | ||||
−0.200949 | + | 0.979602i | \(0.564403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 18.9521i | − 1.54230i | −0.636654 | − | 0.771150i | \(-0.719682\pi\) | ||||
0.636654 | − | 0.771150i | \(-0.280318\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 15.5405i | − 1.24824i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0907i | 0.805326i | 0.915348 | + | 0.402663i | \(0.131915\pi\) | ||||
−0.915348 | + | 0.402663i | \(0.868085\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.30502i | 0.339283i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.9762 | 1.56466 | 0.782330 | − | 0.622864i | \(-0.214031\pi\) | ||||
0.782330 | + | 0.622864i | \(0.214031\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8623 | 1.07270 | 0.536348 | − | 0.843997i | \(-0.319803\pi\) | ||||
0.536348 | + | 0.843997i | \(0.319803\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7547 | 0.904207 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.4796 | 1.63306 | 0.816531 | − | 0.577301i | \(-0.195894\pi\) | ||||
0.816531 | + | 0.577301i | \(0.195894\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 0.102426i | − 0.00774268i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.94291i | − 0.294707i | −0.989084 | − | 0.147354i | \(-0.952925\pi\) | ||||
0.989084 | − | 0.147354i | \(-0.0470755\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 11.7849i | − 0.875962i | −0.898984 | − | 0.437981i | \(-0.855694\pi\) | ||||
0.898984 | − | 0.437981i | \(-0.144306\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 6.91760i | − 0.508592i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.69982 | 0.124303 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.6064 | 1.20160 | 0.600798 | − | 0.799401i | \(-0.294850\pi\) | ||||
0.600798 | + | 0.799401i | \(0.294850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.90416 | 0.496972 | 0.248486 | − | 0.968635i | \(-0.420067\pi\) | ||||
0.248486 | + | 0.968635i | \(0.420067\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.98273 | −0.639993 | −0.319997 | − | 0.947419i | \(-0.603682\pi\) | ||||
−0.319997 | + | 0.947419i | \(0.603682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4427i | 0.811153i | 0.914061 | + | 0.405577i | \(0.132929\pi\) | ||||
−0.914061 | + | 0.405577i | \(0.867071\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.26130i | 0.299085i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 0.349488i | − 0.0244093i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.27428i | 0.157315i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8035 | −1.63870 | −0.819351 | − | 0.573292i | \(-0.805666\pi\) | ||||
−0.819351 | + | 0.573292i | \(0.805666\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.6899 | 1.07004 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.02221 | −0.476698 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.782633 | 0.0526456 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4.42841i | − 0.296549i | −0.988946 | − | 0.148274i | \(-0.952628\pi\) | ||||
0.988946 | − | 0.148274i | \(-0.0473718\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 6.46751i | − 0.429264i | −0.976695 | − | 0.214632i | \(-0.931145\pi\) | ||||
0.976695 | − | 0.214632i | \(-0.0688552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4715i | 0.758056i | 0.925385 | + | 0.379028i | \(0.123742\pi\) | ||||
−0.925385 | + | 0.379028i | \(0.876258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8678i | 1.30158i | 0.759256 | + | 0.650792i | \(0.225563\pi\) | ||||
−0.759256 | + | 0.650792i | \(0.774437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.92086 | 0.125303 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2210 | 0.661138 | 0.330569 | − | 0.943782i | \(-0.392759\pi\) | ||||
0.330569 | + | 0.943782i | \(0.392759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.1808 | 1.81529 | 0.907643 | − | 0.419744i | \(-0.137880\pi\) | ||||
0.907643 | + | 0.419744i | \(0.137880\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.21305 | 0.141386 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.04712i | 0.0666269i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4.62338i | − 0.291825i | −0.989297 | − | 0.145913i | \(-0.953388\pi\) | ||||
0.989297 | − | 0.145913i | \(-0.0466118\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 10.4342i | − 0.655991i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 29.6682i | − 1.85065i | −0.379174 | − | 0.925326i | \(-0.623792\pi\) | ||||
0.379174 | − | 0.925326i | \(-0.376208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.12583 | −0.194230 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8635 | 0.978185 | 0.489093 | − | 0.872232i | \(-0.337328\pi\) | ||||
0.489093 | + | 0.872232i | \(0.337328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.66283 | −0.532153 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.13803 | −0.191329 | −0.0956644 | − | 0.995414i | \(-0.530498\pi\) | ||||
−0.0956644 | + | 0.995414i | \(0.530498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 22.7174i | − 1.37998i | −0.723817 | − | 0.689992i | \(-0.757614\pi\) | ||||
0.723817 | − | 0.689992i | \(-0.242386\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.248252i | 0.0149702i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.8267i | 1.49169i | 0.666119 | + | 0.745845i | \(0.267954\pi\) | ||||
−0.666119 | + | 0.745845i | \(0.732046\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 30.2207i | − 1.80282i | −0.432970 | − | 0.901408i | \(-0.642535\pi\) | ||||
0.432970 | − | 0.901408i | \(-0.357465\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9803 | 0.890488 | 0.445244 | − | 0.895409i | \(-0.353117\pi\) | ||||
0.445244 | + | 0.895409i | \(0.353117\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.157922 | −0.00932182 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5081 | 0.971067 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.58993 | −0.443408 | −0.221704 | − | 0.975114i | \(-0.571162\pi\) | ||||
−0.221704 | + | 0.975114i | \(0.571162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.1291i | 0.939074i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.80411i | − 0.277829i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.08975i | − 0.408646i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 10.1330i | − 0.580216i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1246 | 1.03443 | 0.517214 | − | 0.855856i | \(-0.326969\pi\) | ||||
0.517214 | + | 0.855856i | \(0.326969\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.0291 | −0.965631 | −0.482816 | − | 0.875722i | \(-0.660386\pi\) | ||||
−0.482816 | + | 0.875722i | \(0.660386\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.44270 | 0.420686 | 0.210343 | − | 0.977628i | \(-0.432542\pi\) | ||||
0.210343 | + | 0.977628i | \(0.432542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.40549 | 0.135106 | 0.0675528 | − | 0.997716i | \(-0.478481\pi\) | ||||
0.0675528 | + | 0.997716i | \(0.478481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 10.3282i | − 0.578269i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 0.658082i | − 0.0366167i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.114301i | 0.00634025i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 0.867970i | − 0.0478528i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3776 | −0.790265 | −0.395133 | − | 0.918624i | \(-0.629301\pi\) | ||||
−0.395133 | + | 0.918624i | \(0.629301\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.5667 | 1.83395 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4430 | 1.11360 | 0.556800 | − | 0.830646i | \(-0.312029\pi\) | ||||
0.556800 | + | 0.830646i | \(0.312029\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.0199 | 0.921679 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6.62453i | − 0.355623i | −0.984065 | − | 0.177812i | \(-0.943098\pi\) | ||||
0.984065 | − | 0.177812i | \(-0.0569018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 33.7876i | − 1.80861i | −0.426889 | − | 0.904304i | \(-0.640391\pi\) | ||||
0.426889 | − | 0.904304i | \(-0.359609\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 26.5976i | − 1.41565i | −0.706390 | − | 0.707823i | \(-0.749677\pi\) | ||||
0.706390 | − | 0.707823i | \(-0.250323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3464 | 0.814501 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.7098 | 1.56802 | 0.784012 | − | 0.620746i | \(-0.213170\pi\) | ||||
0.784012 | + | 0.620746i | \(0.213170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1195 | −0.953659 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.5385 | −0.813324 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6932i | 0.819176i | 0.912271 | + | 0.409588i | \(0.134328\pi\) | ||||
−0.912271 | + | 0.409588i | \(0.865672\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.91444i | 0.203227i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 11.0269i | − 0.570951i | −0.958386 | − | 0.285475i | \(-0.907849\pi\) | ||||
0.958386 | − | 0.285475i | \(-0.0921515\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 4.75533i | − 0.244912i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.84736 | 0.403092 | 0.201546 | − | 0.979479i | \(-0.435403\pi\) | ||||
0.201546 | + | 0.979479i | \(0.435403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.26238 | −0.166700 | −0.0833500 | − | 0.996520i | \(-0.526562\pi\) | ||||
−0.0833500 | + | 0.996520i | \(0.526562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.36382 | −0.273365 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.15697 | 0.0586609 | 0.0293304 | − | 0.999570i | \(-0.490662\pi\) | ||||
0.0293304 | + | 0.999570i | \(0.490662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.01922i | 0.152688i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.7367i | 0.741486i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.41295i | 0.121103i | 0.998165 | + | 0.0605513i | \(0.0192859\pi\) | ||||
−0.998165 | + | 0.0605513i | \(0.980714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.48047i | 0.373557i | 0.982402 | + | 0.186778i | \(0.0598047\pi\) | ||||
−0.982402 | + | 0.186778i | \(0.940195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.83631 | 0.390355 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.57615 | 0.375536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.49823 | −0.370764 | −0.185382 | − | 0.982667i | \(-0.559352\pi\) | ||||
−0.185382 | + | 0.982667i | \(0.559352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.28820 | 0.358629 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.6136i | 0.913705i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.7682i | 1.30771i | 0.756619 | + | 0.653856i | \(0.226850\pi\) | ||||
−0.756619 | + | 0.653856i | \(0.773150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 28.1616i | − 1.37251i | −0.727359 | − | 0.686257i | \(-0.759253\pi\) | ||||
0.727359 | − | 0.686257i | \(-0.240747\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 0.0718340i | − 0.00348446i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.57877 | −0.221582 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.9359 | −1.44196 | −0.720980 | − | 0.692955i | \(-0.756308\pi\) | ||||
−0.720980 | + | 0.692955i | \(0.756308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.1106 | −1.87954 | −0.939768 | − | 0.341814i | \(-0.888959\pi\) | ||||
−0.939768 | + | 0.341814i | \(0.888959\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.03957 | −0.193239 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.4351i | 1.50031i | 0.661260 | + | 0.750157i | \(0.270022\pi\) | ||||
−0.661260 | + | 0.750157i | \(0.729978\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 24.2344i | − 1.15141i | −0.817656 | − | 0.575707i | \(-0.804727\pi\) | ||||
0.817656 | − | 0.575707i | \(-0.195273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.2512i | 0.770379i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 22.6066i | − 1.06687i | −0.845841 | − | 0.533435i | \(-0.820901\pi\) | ||||
0.845841 | − | 0.533435i | \(-0.179099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.382759 | 0.0180234 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.46961 | −0.115777 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.35271 | −0.437502 | −0.218751 | − | 0.975781i | \(-0.570198\pi\) | ||||
−0.218751 | + | 0.975781i | \(0.570198\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.5898 | 0.539789 | 0.269895 | − | 0.962890i | \(-0.413011\pi\) | ||||
0.269895 | + | 0.962890i | \(0.413011\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 17.8299i | − 0.828625i | −0.910135 | − | 0.414312i | \(-0.864022\pi\) | ||||
0.910135 | − | 0.414312i | \(-0.135978\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.50180i | 0.162044i | 0.996712 | + | 0.0810221i | \(0.0258184\pi\) | ||||
−0.996712 | + | 0.0810221i | \(0.974182\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 15.1677i | − 0.700378i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.1836i | 0.790103i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0961103 | 0.00440985 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.2987 | 0.836087 | 0.418043 | − | 0.908427i | \(-0.362716\pi\) | ||||
0.418043 | + | 0.908427i | \(0.362716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.48822 | 0.159049 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.6916 | −0.803336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 24.3559i | − 1.10367i | −0.833953 | − | 0.551836i | \(-0.813928\pi\) | ||||
0.833953 | − | 0.551836i | \(-0.186072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 25.8479i | − 1.16650i | −0.812292 | − | 0.583250i | \(-0.801781\pi\) | ||||
0.812292 | − | 0.583250i | \(-0.198219\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.98856i | 0.134598i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6.93451i | − 0.311055i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.5430 | 0.606270 | 0.303135 | − | 0.952948i | \(-0.401967\pi\) | ||||
0.303135 | + | 0.952948i | \(0.401967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.6930 | −0.788890 | −0.394445 | − | 0.918920i | \(-0.629063\pi\) | ||||
−0.394445 | + | 0.918920i | \(0.629063\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.6383 | −1.54138 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.0147 | 0.532544 | 0.266272 | − | 0.963898i | \(-0.414208\pi\) | ||||
0.266272 | + | 0.963898i | \(0.414208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.02133i | 0.310606i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 10.8509i | − 0.478147i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.10372i | 0.0925216i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 17.5217i | − 0.767638i | −0.923408 | − | 0.383819i | \(-0.874609\pi\) | ||||
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.61428 | 0.245495 | 0.122748 | − | 0.992438i | \(-0.460829\pi\) | ||||
0.122748 | + | 0.992438i | \(0.460829\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.92486 | −0.214530 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.46684 | −0.194210 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.176230 | 0.00763337 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.5131i | 1.44890i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.42373i | 0.104397i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.1532i | 1.46836i | 0.678954 | + | 0.734181i | \(0.262433\pi\) | ||||
−0.678954 | + | 0.734181i | \(0.737567\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.04027i | 0.258737i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6399 | −0.925255 | −0.462627 | − | 0.886553i | \(-0.653093\pi\) | ||||
−0.462627 | + | 0.886553i | \(0.653093\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.99855 | −0.170344 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.65903 | 0.283171 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.9554 | 1.09976 | 0.549882 | − | 0.835242i | \(-0.314673\pi\) | ||||
0.549882 | + | 0.835242i | \(0.314673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.91168i | 0.334629i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 13.9262i | − 0.586921i | −0.955971 | − | 0.293460i | \(-0.905193\pi\) | ||||
0.955971 | − | 0.293460i | \(-0.0948069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.29237i | 0.264722i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 18.6130i | − 0.780296i | −0.920752 | − | 0.390148i | \(-0.872424\pi\) | ||||
0.920752 | − | 0.390148i | \(-0.127576\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.69112 | −0.196317 | −0.0981586 | − | 0.995171i | \(-0.531295\pi\) | ||||
−0.0981586 | + | 0.995171i | \(0.531295\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.440945 | −0.0183887 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.27967 | −0.386318 | −0.193159 | − | 0.981167i | \(-0.561873\pi\) | ||||
−0.193159 | + | 0.981167i | \(0.561873\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.41084 | 0.348940 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9.48752i | − 0.392933i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 34.3528i | − 1.41789i | −0.705264 | − | 0.708945i | \(-0.749171\pi\) | ||||
0.705264 | − | 0.708945i | \(-0.250829\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 6.58922i | − 0.271504i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.4288i | 1.82447i | 0.409666 | + | 0.912236i | \(0.365645\pi\) | ||||
−0.409666 | + | 0.912236i | \(0.634355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.55207 | 0.0636285 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8604 | −0.566322 | −0.283161 | − | 0.959072i | \(-0.591383\pi\) | ||||
−0.283161 | + | 0.959072i | \(0.591383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.51128 | −0.265601 | −0.132800 | − | 0.991143i | \(-0.542397\pi\) | ||||
−0.132800 | + | 0.991143i | \(0.542397\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.3431 | −0.461162 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 43.5994i | − 1.76964i | −0.465929 | − | 0.884822i | \(-0.654280\pi\) | ||||
0.465929 | − | 0.884822i | \(-0.345720\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.968597i | 0.0391852i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.4072i | 0.905017i | 0.891760 | + | 0.452508i | \(0.149471\pi\) | ||||
−0.891760 | + | 0.452508i | \(0.850529\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.5128i | 1.22840i | 0.789151 | + | 0.614199i | \(0.210521\pi\) | ||||
−0.789151 | + | 0.614199i | \(0.789479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.5504 | 0.544637 | 0.272319 | − | 0.962207i | \(-0.412210\pi\) | ||||
0.272319 | + | 0.962207i | \(0.412210\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.34335 | 0.294205 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.4774 | −0.979095 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.19222 | −0.0874097 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.5393i | 1.05651i | 0.849085 | + | 0.528257i | \(0.177154\pi\) | ||||
−0.849085 | + | 0.528257i | \(0.822846\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.0694i | 0.915482i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.11593i | 0.0442149i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 10.3318i | − 0.408083i | −0.978962 | − | 0.204041i | \(-0.934592\pi\) | ||||
0.978962 | − | 0.204041i | \(-0.0654077\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.5130 | −0.532901 | −0.266450 | − | 0.963849i | \(-0.585851\pi\) | ||||
−0.266450 | + | 0.963849i | \(0.585851\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.31247 | −0.326797 | −0.163399 | − | 0.986560i | \(-0.552246\pi\) | ||||
−0.163399 | + | 0.986560i | \(0.552246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6646 | −0.693396 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.56899 | −0.100533 | −0.0502663 | − | 0.998736i | \(-0.516007\pi\) | ||||
−0.0502663 | + | 0.998736i | \(0.516007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 47.2647i | − 1.84678i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 12.7747i | − 0.497632i | −0.968551 | − | 0.248816i | \(-0.919959\pi\) | ||||
0.968551 | − | 0.248816i | \(-0.0800414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 25.8624i | − 1.00593i | −0.864307 | − | 0.502965i | \(-0.832242\pi\) | ||||
0.864307 | − | 0.502965i | \(-0.167758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.07659i | 0.0805267i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.3450 | 0.710320 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.0977 | 0.428421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.9446 | −1.30847 | −0.654235 | − | 0.756292i | \(-0.727009\pi\) | ||||
−0.654235 | + | 0.756292i | \(0.727009\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.1280 | 1.31165 | 0.655823 | − | 0.754915i | \(-0.272322\pi\) | ||||
0.655823 | + | 0.754915i | \(0.272322\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.99425i | 0.306791i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.80951i | 0.260559i | 0.991477 | + | 0.130279i | \(0.0415874\pi\) | ||||
−0.991477 | + | 0.130279i | \(0.958413\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.9139i | 0.951910i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 4.36825i | − 0.166417i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.06521 | 0.192690 | 0.0963448 | − | 0.995348i | \(-0.469285\pi\) | ||||
0.0963448 | + | 0.995348i | \(0.469285\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.9608 | 0.681291 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.110755 | −0.00419513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.7933 | −1.69182 | −0.845910 | − | 0.533326i | \(-0.820942\pi\) | ||||
−0.845910 | + | 0.533326i | \(0.820942\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.93309i | − 0.110624i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.6519i | 0.588649i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.5597i | 1.52325i | 0.648018 | + | 0.761625i | \(0.275598\pi\) | ||||
−0.648018 | + | 0.761625i | \(0.724402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.2307i | 1.13215i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.98566 | 0.223851 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.2926 | −0.495729 | −0.247864 | − | 0.968795i | \(-0.579729\pi\) | ||||
−0.247864 | + | 0.968795i | \(0.579729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.90314 | −0.182603 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.436468 | −0.0162100 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.6102i | 1.06109i | 0.847656 | + | 0.530546i | \(0.178013\pi\) | ||||
−0.847656 | + | 0.530546i | \(0.821987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 4.97222i | − 0.183904i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.9007i | 1.25215i | 0.779763 | + | 0.626075i | \(0.215340\pi\) | ||||
−0.779763 | + | 0.626075i | \(0.784660\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.7623i | 1.35416i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.1200 | 0.409055 | 0.204528 | − | 0.978861i | \(-0.434434\pi\) | ||||
0.204528 | + | 0.978861i | \(0.434434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.7857 | −1.67971 | −0.839857 | − | 0.542808i | \(-0.817361\pi\) | ||||
−0.839857 | + | 0.542808i | \(0.817361\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.8568 | 0.397761 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1434 | 0.553329 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 13.8013i | − 0.503616i | −0.967777 | − | 0.251808i | \(-0.918975\pi\) | ||||
0.967777 | − | 0.251808i | \(-0.0810252\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.9418i | 1.52642i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.94985i | 0.216251i | 0.994137 | + | 0.108126i | \(0.0344848\pi\) | ||||
−0.994137 | + | 0.108126i | \(0.965515\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1237i | 1.38198i | 0.722864 | + | 0.690991i | \(0.242825\pi\) | ||||
−0.722864 | + | 0.690991i | \(0.757175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.72939 | 0.0988106 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.13314 | −0.293671 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5207 | 0.559689 | 0.279845 | − | 0.960045i | \(-0.409717\pi\) | ||||
0.279845 | + | 0.960045i | \(0.409717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.6525 | 1.42620 | 0.713101 | − | 0.701061i | \(-0.247290\pi\) | ||||
0.713101 | + | 0.701061i | \(0.247290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 0.719256i | − 0.0258365i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 0.148184i | − 0.00530925i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.8073i | 0.601414i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 22.3312i | − 0.797035i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.2403 | 1.79087 | 0.895436 | − | 0.445189i | \(-0.146864\pi\) | ||||
0.895436 | + | 0.445189i | \(0.146864\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.84331 | 0.101096 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.10960 | 0.181447 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.78519 | 0.0632345 | 0.0316173 | − | 0.999500i | \(-0.489934\pi\) | ||||
0.0316173 | + | 0.999500i | \(0.489934\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 0.608730i | − 0.0215353i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 17.0178i | − 0.600545i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 9.52720i | − 0.335790i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 31.9043i | − 1.12169i | −0.827919 | − | 0.560847i | \(-0.810476\pi\) | ||||
0.827919 | − | 0.560847i | \(-0.189524\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.5528 | 0.440789 | 0.220394 | − | 0.975411i | \(-0.429266\pi\) | ||||
0.220394 | + | 0.975411i | \(0.429266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −44.2084 | −1.54855 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.65259 | 0.232745 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.1349 | 1.47052 | 0.735260 | − | 0.677786i | \(-0.237060\pi\) | ||||
0.735260 | + | 0.677786i | \(0.237060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.50592i | − 0.0524931i | −0.999656 | − | 0.0262465i | \(-0.991645\pi\) | ||||
0.999656 | − | 0.0262465i | \(-0.00835549\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 40.6098i | − 1.41214i | −0.708141 | − | 0.706071i | \(-0.750466\pi\) | ||||
0.708141 | − | 0.706071i | \(-0.249534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 35.4547i | − 1.23139i | −0.787984 | − | 0.615696i | \(-0.788875\pi\) | ||||
0.787984 | − | 0.615696i | \(-0.211125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.701326i | − 0.0242995i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.6779 | −1.06165 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.8372 | 1.09914 | 0.549571 | − | 0.835447i | \(-0.314791\pi\) | ||||
0.549571 | + | 0.835447i | \(0.314791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8413 | −0.373839 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.0137 | −0.894898 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.12555i | 0.176116i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.4567i | 0.461291i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 30.0499i | − 1.02889i | −0.857523 | − | 0.514445i | \(-0.827998\pi\) | ||||
0.857523 | − | 0.514445i | \(-0.172002\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 26.7594i | − 0.914085i | −0.889445 | − | 0.457043i | \(-0.848909\pi\) | ||||
0.889445 | − | 0.457043i | \(-0.151091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.98544 | 0.135981 | 0.0679907 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679907 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.1318 | 1.12782 | 0.563910 | − | 0.825836i | \(-0.309296\pi\) | ||||
0.563910 | + | 0.825836i | \(0.309296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.5353 | −1.61625 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.1397 | −0.547501 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9261i | 0.573519i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.2919i | 0.381736i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 4.35210i | − 0.146960i | −0.997297 | − | 0.0734800i | \(-0.976589\pi\) | ||||
0.997297 | − | 0.0734800i | \(-0.0234105\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.2945i | 1.25648i | 0.778018 | + | 0.628242i | \(0.216225\pi\) | ||||
−0.778018 | + | 0.628242i | \(0.783775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.7359 | 1.50548 | 0.752742 | − | 0.658315i | \(-0.228731\pi\) | ||||
0.752742 | + | 0.658315i | \(0.228731\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.69357 | −0.124018 | −0.0620090 | − | 0.998076i | \(-0.519751\pi\) | ||||
−0.0620090 | + | 0.998076i | \(0.519751\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4243 | 0.349619 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.814451 | 0.0272546 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.72584i | 0.291673i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.9237i | 0.998012i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.74530i | 0.0914591i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.0804i | 0.866943i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.61629 | 0.319304 | 0.159652 | − | 0.987173i | \(-0.448963\pi\) | ||||
0.159652 | + | 0.987173i | \(0.448963\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.1598 | −1.76126 | −0.880632 | − | 0.473802i | \(-0.842881\pi\) | ||||
−0.880632 | + | 0.473802i | \(0.842881\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.3856 | −0.674664 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.3573 | −0.705280 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.3183i | 1.09907i | 0.835471 | + | 0.549534i | \(0.185195\pi\) | ||||
−0.835471 | + | 0.549534i | \(0.814805\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.73845i | 0.254714i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 0.320166i | − 0.0105270i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.5434i | 0.444343i | 0.975008 | + | 0.222172i | \(0.0713146\pi\) | ||||
−0.975008 | + | 0.222172i | \(0.928685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.938340 | 0.0307528 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.76178 | −0.123024 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.3432 | 1.38329 | 0.691647 | − | 0.722236i | \(-0.256886\pi\) | ||||
0.691647 | + | 0.722236i | \(0.256886\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.9773 | −1.98780 | −0.993902 | − | 0.110267i | \(-0.964829\pi\) | ||||
−0.993902 | + | 0.110267i | \(0.964829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.679855i | 0.0221391i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.4879i | 1.28318i | 0.767047 | + | 0.641591i | \(0.221725\pi\) | ||||
−0.767047 | + | 0.641591i | \(0.778275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 7.83534i | − 0.254346i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 25.8210i | − 0.836425i | −0.908349 | − | 0.418213i | \(-0.862657\pi\) | ||||
0.908349 | − | 0.418213i | \(-0.137343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.7507 | −1.18922 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2577 | 0.363531 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.3114 | −0.590690 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.2792 | −0.491856 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.92813i | 0.158478i | 0.996856 | + | 0.0792390i | \(0.0252490\pi\) | ||||
−0.996856 | + | 0.0792390i | \(0.974751\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.9043i | 0.670850i | 0.942067 | + | 0.335425i | \(0.108880\pi\) | ||||
−0.942067 | + | 0.335425i | \(0.891120\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8.11586i | − 0.260183i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.6995i | 0.534266i | 0.963660 | + | 0.267133i | \(0.0860763\pi\) | ||||
−0.963660 | + | 0.267133i | \(0.913924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.7983 | −0.568835 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.7932 | −0.886465 | −0.443232 | − | 0.896407i | \(-0.646168\pi\) | ||||
−0.443232 | + | 0.896407i | \(0.646168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.8792 | 0.633404 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.5215 | −0.970526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 38.3482i | − 1.21817i | −0.793104 | − | 0.609086i | \(-0.791536\pi\) | ||||
0.793104 | − | 0.609086i | \(-0.208464\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 25.3233i | − 0.802802i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.7418i | 0.878590i | 0.898343 | + | 0.439295i | \(0.144772\pi\) | ||||
−0.898343 | + | 0.439295i | \(0.855228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.j.c.5615.5 | 32 | ||
3.2 | odd | 2 | inner | 6048.2.j.c.5615.28 | 32 | ||
4.3 | odd | 2 | 1512.2.j.c.323.12 | yes | 32 | ||
8.3 | odd | 2 | inner | 6048.2.j.c.5615.27 | 32 | ||
8.5 | even | 2 | 1512.2.j.c.323.22 | yes | 32 | ||
12.11 | even | 2 | 1512.2.j.c.323.21 | yes | 32 | ||
24.5 | odd | 2 | 1512.2.j.c.323.11 | ✓ | 32 | ||
24.11 | even | 2 | inner | 6048.2.j.c.5615.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.11 | ✓ | 32 | 24.5 | odd | 2 | ||
1512.2.j.c.323.12 | yes | 32 | 4.3 | odd | 2 | ||
1512.2.j.c.323.21 | yes | 32 | 12.11 | even | 2 | ||
1512.2.j.c.323.22 | yes | 32 | 8.5 | even | 2 | ||
6048.2.j.c.5615.5 | 32 | 1.1 | even | 1 | trivial | ||
6048.2.j.c.5615.6 | 32 | 24.11 | even | 2 | inner | ||
6048.2.j.c.5615.27 | 32 | 8.3 | odd | 2 | inner | ||
6048.2.j.c.5615.28 | 32 | 3.2 | odd | 2 | inner |